LMFDB - Embedded newform 90.19.g.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,19,Mod(37,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("90.37");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	90.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$184.847523939$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 210312251442601 x^{8} + \cdots + 16\!\cdots\!20 $ x^10 - 210312251442601x^8 - 206332806866338016604x^7 + 14943626398507987755185175607x^6 + 21957000927224490446331559162088016x^5 - 397974009257816141400467874121061067267359x^4 - 428209636714484751954396859436850040791573426156x^3 + 3748083761145961045652674190550015804292103203053587252x^2 + 504849727449693466420147883384086151724761968125685453928424x + 16879511451923918101045123331342660468869435139032966511523178420
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{12}\cdot 5^{17} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.4
Root			$9.75589e6 + 1.00000i$ of defining polynomial
Character	$\chi$	$=$	90.37
Dual form			90.19.g.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(256.000 + 256.000i) q^{2} +131072. i q^{4} +(1.41140e6 + 1.35005e6i) q^{5} +(-5.59623e7 - 5.59623e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +O(q^{10})$	\(q+(256.000 + 256.000i) q^{2} +131072. i q^{4} +(1.41140e6 + 1.35005e6i) q^{5} +(-5.59623e7 - 5.59623e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +(1.57043e7 + 7.06932e8i) q^{10} +1.86606e9 q^{11} +(-7.54400e9 + 7.54400e9i) q^{13} -2.86527e10i q^{14} -1.71799e10 q^{16} +(6.21409e10 + 6.21409e10i) q^{17} -2.58270e11i q^{19} +(-1.76954e11 + 1.84995e11i) q^{20} +(4.77712e11 + 4.77712e11i) q^{22} +(1.18327e12 - 1.18327e12i) q^{23} +(1.69402e11 + 3.81093e12i) q^{25} -3.86253e12 q^{26} +(7.33509e12 - 7.33509e12i) q^{28} -1.23756e13i q^{29} +1.56051e12 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +3.18162e13i q^{34} +(-3.43301e12 - 1.54537e14i) q^{35} +(-6.47453e13 - 6.47453e13i) q^{37} +(6.61170e13 - 6.61170e13i) q^{38} +(-9.26590e13 + 2.05840e12i) q^{40} -3.10084e13 q^{41} +(-4.19670e13 + 4.19670e13i) q^{43} +2.44588e14i q^{44} +6.05833e14 q^{46} +(1.22176e15 + 1.22176e15i) q^{47} +4.63515e15i q^{49} +(-9.32232e14 + 1.01897e15i) q^{50} +(-9.88807e14 - 9.88807e14i) q^{52} +(-1.53938e15 + 1.53938e15i) q^{53} +(2.63376e15 + 2.51929e15i) q^{55} +3.75557e15 q^{56} +(3.16816e15 - 3.16816e15i) q^{58} +7.41783e15i q^{59} +1.51034e16 q^{61} +(3.99492e14 + 3.99492e14i) q^{62} -2.25180e15i q^{64} +(-2.08324e16 + 4.62787e14i) q^{65} +(-8.12314e15 - 8.12314e15i) q^{67} +(-8.14493e15 + 8.14493e15i) q^{68} +(3.86827e16 - 4.04404e16i) q^{70} +2.90794e16 q^{71} +(-3.39740e16 + 3.39740e16i) q^{73} -3.31496e16i q^{74} +3.38519e16 q^{76} +(-1.04429e17 - 1.04429e17i) q^{77} -1.44224e17i q^{79} +(-2.42477e16 - 2.31938e16i) q^{80} +(-7.93814e15 - 7.93814e15i) q^{82} +(-1.04515e17 + 1.04515e17i) q^{83} +(3.81204e15 + 1.71599e17i) q^{85} -2.14871e16 q^{86} +(-6.26146e16 + 6.26146e16i) q^{88} +2.22760e17i q^{89} +8.44360e17 q^{91} +(1.55093e17 + 1.55093e17i) q^{92} +6.25540e17i q^{94} +(3.48678e17 - 3.64522e17i) q^{95} +(2.70611e17 + 2.70611e17i) q^{97} +(-1.18660e18 + 1.18660e18i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2560 q^{2} + 1436130 q^{5} - 71828530 q^{7} - 335544320 q^{8}+O(q^{10}) $ 10 * q + 2560 * q^2 + 1436130 * q^5 - 71828530 * q^7 - 335544320 * q^8	$ 10 q + 2560 q^{2} + 1436130 q^{5} - 71828530 q^{7} - 335544320 q^{8} + 280000000 q^{10} + 4684617380 q^{11} - 11858528670 q^{13} - 171798691840 q^{16} - 57425096770 q^{17} - 44876431360 q^{20} + 1199262049280 q^{22} + 2409849379970 q^{23} - 9628701268750 q^{25} - 6071566679040 q^{26} + 9414709084160 q^{28} + 44076891672220 q^{31} - 43980465111040 q^{32} + 92680242801650 q^{35} + 285126548071770 q^{37} + 268015571763200 q^{38} - 59676892856320 q^{40} - 223001245455820 q^{41} - 674098663802370 q^{43} + 12\!\cdots\!40 q^{46}+ \cdots - 14\!\cdots\!40 q^{98}+O(q^{100}) $ 10 * q + 2560 * q^2 + 1436130 * q^5 - 71828530 * q^7 - 335544320 * q^8 + 280000000 * q^10 + 4684617380 * q^11 - 11858528670 * q^13 - 171798691840 * q^16 - 57425096770 * q^17 - 44876431360 * q^20 + 1199262049280 * q^22 + 2409849379970 * q^23 - 9628701268750 * q^25 - 6071566679040 * q^26 + 9414709084160 * q^28 + 44076891672220 * q^31 - 43980465111040 * q^32 + 92680242801650 * q^35 + 285126548071770 * q^37 + 268015571763200 * q^38 - 59676892856320 * q^40 - 223001245455820 * q^41 - 674098663802370 * q^43 + 1233842882544640 * q^46 + 3332242844984130 * q^47 - 5679798331686400 * q^50 - 1554321069834240 * q^52 + 7587444943731670 * q^53 + 27897159618275340 * q^55 + 4820331051089920 * q^56 - 10419344591360000 * q^58 + 64704780211083420 * q^61 + 11283684268088320 * q^62 - 72228906553534170 * q^65 - 108403906097814130 * q^67 + 7526822283837440 * q^68 + 42813790750842880 * q^70 - 194380424551175420 * q^71 - 233767444023094070 * q^73 + 137223972742758400 * q^76 - 52847385951118940 * q^77 - 24672525531217920 * q^80 - 57088318836689920 * q^82 + 114013237779502770 * q^83 + 484088104672899650 * q^85 - 345138515866813440 * q^86 - 157189675323228160 * q^88 + 1337663581494821820 * q^91 + 315863777931427840 * q^92 + 930275560132279600 * q^95 + 853540105740755370 * q^97 - 1479412917644362240 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	256.000	+	256.000i	0.500000	+	0.500000i
$2$	256.000	+	256.000i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			131072.i			0.500000i
$5$	1.41140e6	+	1.35005e6i	0.722637	+	0.691228i
$5$	1.41140e6	+	1.35005e6i	0.722637	+	0.691228i
$6$		0			0
$7$	−5.59623e7	−	5.59623e7i	−1.38680	−	1.38680i	−0.831954	−	0.554844i	$-0.812778\pi$
$7$	−5.59623e7	−	5.59623e7i	−1.38680	−	1.38680i	−0.554844	−	0.831954i	$-0.687222\pi$
$8$	−3.35544e7	+	3.35544e7i	−0.250000	+	0.250000i
$9$		0			0
$10$	1.57043e7	+	7.06932e8i	0.0157043	+	0.706932i
$11$	1.86606e9			0.791392			0.395696	−	0.918382i	$-0.370503\pi$
$11$	1.86606e9			0.791392			0.395696	+	0.918382i	$0.370503\pi$
$12$		0			0
$13$	−7.54400e9	+	7.54400e9i	−0.711396	+	0.711396i	−0.966827	−	0.255431i	$-0.917783\pi$
$13$	−7.54400e9	+	7.54400e9i	−0.711396	+	0.711396i	0.255431	+	0.966827i	$0.417783\pi$
$14$		−	2.86527e10i		−	1.38680i
$15$		0			0
$16$	−1.71799e10			−0.250000
$17$	6.21409e10	+	6.21409e10i	0.524007	+	0.524007i	0.918779	−	0.394772i	$-0.129176\pi$
$17$	6.21409e10	+	6.21409e10i	0.524007	+	0.524007i	−0.394772	+	0.918779i	$0.629176\pi$
$18$		0			0
$19$		−	2.58270e11i		−	0.800370i	−0.916434	−	0.400185i	$-0.868946\pi$
$19$		−	2.58270e11i		−	0.800370i	0.916434	−	0.400185i	$-0.131054\pi$
$20$	−1.76954e11	+	1.84995e11i	−0.345614	+	0.361318i
$21$		0			0
$22$	4.77712e11	+	4.77712e11i	0.395696	+	0.395696i
$23$	1.18327e12	−	1.18327e12i	0.656950	−	0.656950i	−0.297707	−	0.954657i	$-0.596222\pi$
$23$	1.18327e12	−	1.18327e12i	0.656950	−	0.656950i	0.954657	+	0.297707i	$0.0962219\pi$
$24$		0			0
$25$	1.69402e11	+	3.81093e12i	0.0444076	+	0.999013i
$26$	−3.86253e12			−0.711396
$27$		0			0
$28$	7.33509e12	−	7.33509e12i	0.693399	−	0.693399i
$29$		−	1.23756e13i		−	0.853070i	−0.904471	−	0.426535i	$-0.859734\pi$
$29$		−	1.23756e13i		−	0.853070i	0.904471	−	0.426535i	$-0.140266\pi$
$30$		0			0
$31$	1.56051e12			0.0590218			0.0295109	−	0.999564i	$-0.490605\pi$
$31$	1.56051e12			0.0590218			0.0295109	+	0.999564i	$0.490605\pi$
$32$	−4.39805e12	−	4.39805e12i	−0.125000	−	0.125000i
$33$		0			0
$34$			3.18162e13i			0.524007i
$35$	−3.43301e12	−	1.54537e14i	−0.0435575	−	1.96075i
$36$		0			0
$37$	−6.47453e13	−	6.47453e13i	−0.498187	−	0.498187i	0.412686	−	0.910873i	$-0.364591\pi$
$37$	−6.47453e13	−	6.47453e13i	−0.498187	−	0.498187i	−0.910873	+	0.412686i	$0.864591\pi$
$38$	6.61170e13	−	6.61170e13i	0.400185	−	0.400185i
$39$		0			0
$40$	−9.26590e13	+	2.05840e12i	−0.353466	+	0.00785217i
$41$	−3.10084e13			−0.0947162			−0.0473581	−	0.998878i	$-0.515080\pi$
$41$	−3.10084e13			−0.0947162			−0.0473581	+	0.998878i	$0.515080\pi$
$42$		0			0
$43$	−4.19670e13	+	4.19670e13i	−0.0835010	+	0.0835010i	−0.747624	−	0.664123i	$-0.768805\pi$
$43$	−4.19670e13	+	4.19670e13i	−0.0835010	+	0.0835010i	0.664123	+	0.747624i	$0.268805\pi$
$44$			2.44588e14i			0.395696i
$45$		0			0
$46$	6.05833e14			0.656950
$47$	1.22176e15	+	1.22176e15i	1.09170	+	1.09170i	0.995347	+	0.0963551i	$0.0307184\pi$
$47$	1.22176e15	+	1.22176e15i	1.09170	+	1.09170i	0.0963551	+	0.995347i	$0.469282\pi$
$48$		0			0
$49$			4.63515e15i			2.84642i
$50$	−9.32232e14	+	1.01897e15i	−0.477303	+	0.521711i
$51$		0			0
$52$	−9.88807e14	−	9.88807e14i	−0.355698	−	0.355698i
$53$	−1.53938e15	+	1.53938e15i	−0.466512	+	0.466512i	−0.900783	−	0.434270i	$-0.857006\pi$
$53$	−1.53938e15	+	1.53938e15i	−0.466512	+	0.466512i	0.434270	+	0.900783i	$0.357006\pi$
$54$		0			0
$55$	2.63376e15	+	2.51929e15i	0.571889	+	0.547032i
$56$	3.75557e15			0.693399
$57$		0			0
$58$	3.16816e15	−	3.16816e15i	0.426535	−	0.426535i
$59$			7.41783e15i			0.856266i	0.903716	+	0.428133i	$0.140829\pi$
$59$			7.41783e15i			0.856266i	−0.903716	+	0.428133i	$0.859171\pi$
$60$		0			0
$61$	1.51034e16			1.29154			0.645769	−	0.763533i	$-0.276537\pi$
$61$	1.51034e16			1.29154			0.645769	+	0.763533i	$0.276537\pi$
$62$	3.99492e14	+	3.99492e14i	0.0295109	+	0.0295109i
$63$		0			0
$64$		−	2.25180e15i		−	0.125000i
$65$	−2.08324e16	+	4.62787e14i	−1.00582	+	0.0223440i
$66$		0			0
$67$	−8.12314e15	−	8.12314e15i	−0.298573	−	0.298573i	0.541882	−	0.840455i	$-0.317712\pi$
$67$	−8.12314e15	−	8.12314e15i	−0.298573	−	0.298573i	−0.840455	+	0.541882i	$0.817712\pi$
$68$	−8.14493e15	+	8.14493e15i	−0.262004	+	0.262004i
$69$		0			0
$70$	3.86827e16	−	4.04404e16i	0.958594	−	1.00215i
$71$	2.90794e16			0.634249			0.317125	−	0.948384i	$-0.397283\pi$
$71$	2.90794e16			0.634249			0.317125	+	0.948384i	$0.397283\pi$
$72$		0			0
$73$	−3.39740e16	+	3.39740e16i	−0.577087	+	0.577087i	−0.934100	−	0.357012i	$-0.883795\pi$
$73$	−3.39740e16	+	3.39740e16i	−0.577087	+	0.577087i	0.357012	+	0.934100i	$0.383795\pi$
$74$		−	3.31496e16i		−	0.498187i
$75$		0			0
$76$	3.38519e16			0.400185
$77$	−1.04429e17	−	1.04429e17i	−1.09750	−	1.09750i
$78$		0			0
$79$		−	1.44224e17i		−	1.20335i	−0.798739	−	0.601677i	$-0.794499\pi$
$79$		−	1.44224e17i		−	1.20335i	0.798739	−	0.601677i	$-0.205501\pi$
$80$	−2.42477e16	−	2.31938e16i	−0.180659	−	0.172807i
$81$		0			0
$82$	−7.93814e15	−	7.93814e15i	−0.0473581	−	0.0473581i
$83$	−1.04515e17	+	1.04515e17i	−0.559083	+	0.559083i	−0.929046	−	0.369963i	$-0.879370\pi$
$83$	−1.04515e17	+	1.04515e17i	−0.559083	+	0.559083i	0.369963	+	0.929046i	$0.379370\pi$
$84$		0			0
$85$	3.81204e15	+	1.71599e17i	0.0164584	+	0.740876i
$86$	−2.14871e16			−0.0835010
$87$		0			0
$88$	−6.26146e16	+	6.26146e16i	−0.197848	+	0.197848i
$89$			2.22760e17i			0.635810i	0.948123	+	0.317905i	$0.102979\pi$
$89$			2.22760e17i			0.635810i	−0.948123	+	0.317905i	$0.897021\pi$
$90$		0			0
$91$	8.44360e17			1.97313
$92$	1.55093e17	+	1.55093e17i	0.328475	+	0.328475i
$93$		0			0
$94$			6.25540e17i			1.09170i
$95$	3.48678e17	−	3.64522e17i	0.553238	−	0.578377i
$96$		0			0
$97$	2.70611e17	+	2.70611e17i	0.355958	+	0.355958i	0.862321	−	0.506362i	$-0.169010\pi$
$97$	2.70611e17	+	2.70611e17i	0.355958	+	0.355958i	−0.506362	+	0.862321i	$0.669010\pi$
$98$	−1.18660e18	+	1.18660e18i	−1.42321	+	1.42321i
$99$		0			0
$100$	−4.99507e17	+	2.22038e16i	−0.499507	+	0.0222038i
$101$	−7.45224e17			−0.681388			−0.340694	−	0.940174i	$-0.610662\pi$
$101$	−7.45224e17			−0.681388			−0.340694	+	0.940174i	$0.610662\pi$
$102$		0			0
$103$	−7.11206e17	+	7.11206e17i	−0.545080	+	0.545080i	−0.925014	−	0.379934i	$-0.875947\pi$
$103$	−7.11206e17	+	7.11206e17i	−0.545080	+	0.545080i	0.379934	+	0.925014i	$0.375947\pi$
$104$		−	5.06269e17i		−	0.355698i
$105$		0			0
$106$	−7.88163e17			−0.466512
$107$	1.19692e18	+	1.19692e18i	0.651044	+	0.651044i	0.953244	−	0.302201i	$-0.0977212\pi$
$107$	1.19692e18	+	1.19692e18i	0.651044	+	0.651044i	−0.302201	+	0.953244i	$0.597721\pi$
$108$		0			0
$109$		−	1.66844e17i		−	0.0768196i	−0.999262	−	0.0384098i	$-0.987771\pi$
$109$		−	1.66844e17i		−	0.0768196i	0.999262	−	0.0384098i	$-0.0122292\pi$
$110$	2.93053e16	+	1.31918e18i	0.0124283	+	0.559461i
$111$		0			0
$112$	9.61425e17	+	9.61425e17i	0.346700	+	0.346700i
$113$	1.58604e18	−	1.58604e18i	0.527970	−	0.527970i	−0.391997	−	0.919967i	$-0.628216\pi$
$113$	1.58604e18	−	1.58604e18i	0.527970	−	0.527970i	0.919967	+	0.391997i	$0.128216\pi$
$114$		0			0
$115$	3.26754e18	−	7.25876e16i	0.928838	−	0.0206339i
$116$	1.62210e18			0.426535
$117$		0			0
$118$	−1.89897e18	+	1.89897e18i	−0.428133	+	0.428133i
$119$		−	6.95510e18i		−	1.45339i
$120$		0			0
$121$	−2.07773e18			−0.373698
$122$	3.86648e18	+	3.86648e18i	0.645769	+	0.645769i
$123$		0			0
$124$			2.04540e17i			0.0295109i
$125$	−4.90588e18	+	5.60745e18i	−0.658456	+	0.752620i
$126$		0			0
$127$	2.54783e18	+	2.54783e18i	0.296440	+	0.296440i	0.839618	−	0.543177i	$-0.182779\pi$
$127$	2.54783e18	+	2.54783e18i	0.296440	+	0.296440i	−0.543177	+	0.839618i	$0.682779\pi$
$128$	5.76461e17	−	5.76461e17i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−5.45157e18	−	5.21463e18i	−0.514081	−	0.491737i
$131$	1.70814e18			0.150342			0.0751711	−	0.997171i	$-0.476050\pi$
$131$	1.70814e18			0.150342			0.0751711	+	0.997171i	$0.476050\pi$
$132$		0			0
$133$	−1.44534e19	+	1.44534e19i	−1.10995	+	1.10995i
$134$		−	4.15905e18i		−	0.298573i
$135$		0			0
$136$	−4.17021e18			−0.262004
$137$	1.64796e19	+	1.64796e19i	0.969309	+	0.969309i	0.999543	−	0.0302336i	$-0.00962512\pi$
$137$	1.64796e19	+	1.64796e19i	0.969309	+	0.969309i	−0.0302336	+	0.999543i	$0.509625\pi$
$138$		0			0
$139$			2.99711e19i			1.54728i	0.633624	+	0.773642i	$0.281567\pi$
$139$			2.99711e19i			1.54728i	−0.633624	+	0.773642i	$0.718433\pi$
$140$	2.02555e19	−	4.49972e17i	0.980373	−	0.0217788i
$141$		0			0
$142$	7.44432e18	+	7.44432e18i	0.317125	+	0.317125i
$143$	−1.40776e19	+	1.40776e19i	−0.562993	+	0.562993i
$144$		0			0
$145$	1.67078e19	−	1.74669e19i	0.589666	−	0.616460i
$146$	−1.73947e19			−0.577087
$147$		0			0
$148$	8.48629e18	−	8.48629e18i	0.249094	−	0.249094i
$149$			2.03839e19i			0.563134i	0.959542	+	0.281567i	$0.0908541\pi$
$149$			2.03839e19i			0.563134i	−0.959542	+	0.281567i	$0.909146\pi$
$150$		0			0
$151$	−2.52157e19			−0.617844			−0.308922	−	0.951087i	$-0.599968\pi$
$151$	−2.52157e19			−0.617844			−0.308922	+	0.951087i	$0.599968\pi$
$152$	8.66609e18	+	8.66609e18i	0.200093	+	0.200093i
$153$		0			0
$154$		−	5.34677e19i		−	1.09750i
$155$	2.20251e18	+	2.10678e18i	0.0426513	+	0.0407975i
$156$		0			0
$157$	6.48726e19	+	6.48726e19i	1.11935	+	1.11935i	0.991837	+	0.127510i	$0.0406984\pi$
$157$	6.48726e19	+	6.48726e19i	1.11935	+	1.11935i	0.127510	+	0.991837i	$0.459302\pi$
$158$	3.69213e19	−	3.69213e19i	0.601677	−	0.601677i
$159$		0			0
$160$	−2.69799e17	−	1.21450e19i	−0.00392609	−	0.176733i
$161$	−1.32437e20			−1.82211
$162$		0			0
$163$	−3.62438e19	+	3.62438e19i	−0.446217	+	0.446217i	−0.894095	−	0.447878i	$-0.852180\pi$
$163$	−3.62438e19	+	3.62438e19i	−0.446217	+	0.446217i	0.447878	+	0.894095i	$0.352180\pi$
$164$		−	4.06433e18i		−	0.0473581i
$165$		0			0
$166$	−5.35118e19			−0.559083
$167$	−1.09035e20	−	1.09035e20i	−1.07924	−	1.07924i	−0.996578	−	0.0826586i	$-0.973659\pi$
$167$	−1.09035e20	−	1.09035e20i	−1.07924	−	1.07924i	−0.0826586	−	0.996578i	$-0.526341\pi$
$168$		0			0
$169$		−	1.36851e18i		−	0.0121693i
$170$	−4.29535e19	+	4.49053e19i	−0.362209	+	0.378667i
$171$		0			0
$172$	−5.50069e18	−	5.50069e18i	−0.0417505	−	0.0417505i
$173$	−1.86169e20	+	1.86169e20i	−1.34120	+	1.34120i	−0.446327	+	0.894870i	$0.647268\pi$
$173$	−1.86169e20	+	1.86169e20i	−1.34120	+	1.34120i	−0.894870	+	0.446327i	$0.852732\pi$
$174$		0			0
$175$	2.03789e20	−	2.22749e20i	1.32385	−	1.44701i
$176$	−3.20587e19			−0.197848
$177$		0			0
$178$	−5.70266e19	+	5.70266e19i	−0.317905	+	0.317905i
$179$		−	4.39436e19i		−	0.232926i	−0.993195	−	0.116463i	$-0.962844\pi$
$179$		−	4.39436e19i		−	0.232926i	0.993195	−	0.116463i	$-0.0371557\pi$
$180$		0			0
$181$	−1.43021e20			−0.685950			−0.342975	−	0.939345i	$-0.611435\pi$
$181$	−1.43021e20			−0.685950			−0.342975	+	0.939345i	$0.611435\pi$
$182$	2.16156e20	+	2.16156e20i	0.986563	+	0.986563i
$183$		0			0
$184$			7.94077e19i			0.328475i
$185$	−3.97180e18	−	1.78791e20i	−0.0156474	−	0.704369i
$186$		0			0
$187$	1.15959e20	+	1.15959e20i	0.414695	+	0.414695i
$188$	−1.60138e20	+	1.60138e20i	−0.545851	+	0.545851i
$189$		0			0
$190$	1.82579e20	−	4.05596e18i	0.565808	−	0.0125693i
$191$	4.64193e20			1.37214			0.686070	−	0.727536i	$-0.259335\pi$
$191$	4.64193e20			1.37214			0.686070	+	0.727536i	$0.259335\pi$
$192$		0			0
$193$	−1.56222e19	+	1.56222e19i	−0.0420462	+	0.0420462i	−0.727817	−	0.685771i	$-0.759465\pi$
$193$	−1.56222e19	+	1.56222e19i	−0.0420462	+	0.0420462i	0.685771	+	0.727817i	$0.259465\pi$
$194$			1.38553e20i			0.355958i
$195$		0			0
$196$	−6.07538e20			−1.42321
$197$	1.80663e20	+	1.80663e20i	0.404272	+	0.404272i	0.879735	−	0.475464i	$-0.157720\pi$
$197$	1.80663e20	+	1.80663e20i	0.404272	+	0.404272i	−0.475464	+	0.879735i	$0.657720\pi$
$198$		0			0
$199$		−	3.83698e20i		−	0.783993i	−0.919967	−	0.391997i	$-0.871785\pi$
$199$		−	3.83698e20i		−	0.783993i	0.919967	−	0.391997i	$-0.128215\pi$
$200$	−1.33558e20	−	1.22190e20i	−0.260855	−	0.238651i
$201$		0			0
$202$	−1.90777e20	−	1.90777e20i	−0.340694	−	0.340694i
$203$	−6.92568e20	+	6.92568e20i	−1.18304	+	1.18304i
$204$		0			0
$205$	−4.37652e19	−	4.18630e19i	−0.0684454	−	0.0654705i
$206$	−3.64137e20			−0.545080
$207$		0			0
$208$	1.29605e20	−	1.29605e20i	0.177849	−	0.177849i
$209$		−	4.81947e20i		−	0.633407i
$210$		0			0
$211$	−4.55315e20			−0.549250			−0.274625	−	0.961551i	$-0.588554\pi$
$211$	−4.55315e20			−0.549250			−0.274625	+	0.961551i	$0.588554\pi$
$212$	−2.01770e20	−	2.01770e20i	−0.233256	−	0.233256i
$213$		0			0
$214$			6.12822e20i			0.651044i
$215$	−1.15890e20	+	2.57447e18i	−0.118059	+	0.00262266i
$216$		0			0
$217$	−8.73300e19	−	8.73300e19i	−0.0818514	−	0.0818514i
$218$	4.27120e19	−	4.27120e19i	0.0384098	−	0.0384098i
$219$		0			0
$220$	−3.30208e20	+	3.45212e20i	−0.273516	+	0.285945i
$221$	−9.37582e20			−0.745554
$222$		0			0
$223$	−1.57297e21	+	1.57297e21i	−1.15339	+	1.15339i	−0.167527	+	0.985868i	$0.553578\pi$
$223$	−1.57297e21	+	1.57297e21i	−1.15339	+	1.15339i	−0.985868	+	0.167527i	$0.946422\pi$
$224$			4.92250e20i			0.346700i
$225$		0			0
$226$	8.12055e20			0.527970
$227$	1.80291e21	+	1.80291e21i	1.12653	+	1.12653i	0.990738	+	0.135789i	$0.0433569\pi$
$227$	1.80291e21	+	1.80291e21i	1.12653	+	1.12653i	0.135789	+	0.990738i	$0.456643\pi$
$228$		0			0
$229$		−	7.30577e19i		−	0.0421839i	−0.999778	−	0.0210919i	$-0.993286\pi$
$229$		−	7.30577e19i		−	0.0421839i	0.999778	−	0.0210919i	$-0.00671427\pi$
$230$	8.55072e20	+	8.17907e20i	0.474736	+	0.454102i
$231$		0			0
$232$	4.15257e20	+	4.15257e20i	0.213268	+	0.213268i
$233$	−4.38512e20	+	4.38512e20i	−0.216660	+	0.216660i	−0.807089	−	0.590430i	$-0.798958\pi$
$233$	−4.38512e20	+	4.38512e20i	−0.216660	+	0.216660i	0.590430	+	0.807089i	$0.298958\pi$
$234$		0			0
$235$	7.49488e19	+	3.37383e21i	0.0342889	+	1.54352i
$236$	−9.72270e20			−0.428133
$237$		0			0
$238$	1.78051e21	−	1.78051e21i	0.726693	−	0.726693i
$239$			3.72340e21i			1.46339i	0.681634	+	0.731693i	$0.261270\pi$
$239$			3.72340e21i			1.46339i	−0.681634	+	0.731693i	$0.738730\pi$
$240$		0			0
$241$	−4.91713e21			−1.79291			−0.896455	−	0.443135i	$-0.853866\pi$
$241$	−4.91713e21			−1.79291			−0.896455	+	0.443135i	$0.853866\pi$
$242$	−5.31899e20	−	5.31899e20i	−0.186849	−	0.186849i
$243$		0			0
$244$			1.97964e21i			0.645769i
$245$	−6.25770e21	+	6.54205e21i	−1.96753	+	2.05693i
$246$		0			0
$247$	1.94839e21	+	1.94839e21i	0.569381	+	0.569381i
$248$	−5.23622e19	+	5.23622e19i	−0.0147555	+	0.0147555i
$249$		0			0
$250$	−2.69141e21	+	1.79604e20i	−0.705538	+	0.0470820i
$251$	2.81344e21			0.711499			0.355749	−	0.934581i	$-0.384226\pi$
$251$	2.81344e21			0.711499			0.355749	+	0.934581i	$0.384226\pi$
$252$		0			0
$253$	2.20805e21	−	2.20805e21i	0.519905	−	0.519905i
$254$			1.30449e21i			0.296440i
$255$		0			0
$256$	2.95148e20			0.0625000
$257$	−2.08334e21	−	2.08334e21i	−0.425953	−	0.425953i	0.461294	−	0.887247i	$-0.347385\pi$
$257$	−2.08334e21	−	2.08334e21i	−0.425953	−	0.425953i	−0.887247	+	0.461294i	$0.847385\pi$
$258$		0			0
$259$			7.24659e21i			1.38177i
$260$	−6.06585e19	−	2.73055e21i	−0.0111720	−	0.502909i
$261$		0			0
$262$	4.37283e20	+	4.37283e20i	0.0751711	+	0.0751711i
$263$	−2.64499e21	+	2.64499e21i	−0.439362	+	0.439362i	−0.891797	−	0.452436i	$-0.850555\pi$
$263$	−2.64499e21	+	2.64499e21i	−0.439362	+	0.439362i	0.452436	+	0.891797i	$0.350555\pi$
$264$		0			0
$265$	−4.25093e21	+	9.44334e19i	−0.659585	+	0.0146525i
$266$	−7.40013e21			−1.10995
$267$		0			0
$268$	1.06472e21	−	1.06472e21i	0.149287	−	0.149287i
$269$		−	1.64295e21i		−	0.222769i	−0.993777	−	0.111384i	$-0.964472\pi$
$269$		−	1.64295e21i		−	0.222769i	0.993777	−	0.111384i	$-0.0355284\pi$
$270$		0			0
$271$	1.31213e22			1.66438			0.832191	−	0.554489i	$-0.187086\pi$
$271$	1.31213e22			1.66438			0.832191	+	0.554489i	$0.187086\pi$
$272$	−1.06757e21	−	1.06757e21i	−0.131002	−	0.131002i
$273$		0			0
$274$			8.43757e21i			0.969309i
$275$	3.16114e20	+	7.11144e21i	0.0351439	+	0.790612i
$276$		0			0
$277$	−9.44927e21	−	9.44927e21i	−0.984194	−	0.984194i	0.0156834	−	0.999877i	$-0.495008\pi$
$277$	−9.44927e21	−	9.44927e21i	−0.984194	−	0.984194i	−0.999877	+	0.0156834i	$0.995008\pi$
$278$	−7.67261e21	+	7.67261e21i	−0.773642	+	0.773642i
$279$		0			0
$280$	5.30061e21	+	5.07022e21i	0.501076	+	0.479297i
$281$	−3.38501e21			−0.309887			−0.154943	−	0.987923i	$-0.549519\pi$
$281$	−3.38501e21			−0.309887			−0.154943	+	0.987923i	$0.549519\pi$
$282$		0			0
$283$	7.99584e21	−	7.99584e21i	0.686730	−	0.686730i	−0.274778	−	0.961508i	$-0.588604\pi$
$283$	7.99584e21	−	7.99584e21i	0.686730	−	0.686730i	0.961508	+	0.274778i	$0.0886042\pi$
$284$			3.81149e21i			0.317125i
$285$		0			0
$286$	−7.20772e21			−0.562993
$287$	1.73530e21	+	1.73530e21i	0.131352	+	0.131352i
$288$		0			0
$289$		−	6.34010e21i		−	0.450833i
$290$	8.74872e21	−	1.94351e20i	0.603063	−	0.0133969i
$291$		0			0
$292$	−4.45305e21	−	4.45305e21i	−0.288544	−	0.288544i
$293$	−5.40923e21	+	5.40923e21i	−0.339881	+	0.339881i	−0.856322	−	0.516442i	$-0.827256\pi$
$293$	−5.40923e21	+	5.40923e21i	−0.339881	+	0.339881i	0.516442	+	0.856322i	$0.327256\pi$
$294$		0			0
$295$	−1.00145e22	+	1.04695e22i	−0.591875	+	0.618770i
$296$	4.34498e21			0.249094
$297$		0			0
$298$	−5.21829e21	+	5.21829e21i	−0.281567	+	0.281567i
$299$			1.78531e22i			0.934703i
$300$		0			0
$301$	4.69714e21			0.231598
$302$	−6.45522e21	−	6.45522e21i	−0.308922	−	0.308922i
$303$		0			0
$304$			4.43704e21i			0.200093i
$305$	2.13170e22	+	2.03905e22i	0.933313	+	0.892747i
$306$		0			0
$307$	3.03168e22	+	3.03168e22i	1.25152	+	1.25152i	0.955039	+	0.296479i	$0.0958126\pi$
$307$	3.03168e22	+	3.03168e22i	1.25152	+	1.25152i	0.296479	+	0.955039i	$0.404187\pi$
$308$	1.36877e22	−	1.36877e22i	0.548751	−	0.548751i
$309$		0			0
$310$	2.45069e19	+	1.10318e21i	0.000926899	+	0.0417244i
$311$	1.31939e22			0.484762			0.242381	−	0.970181i	$-0.422072\pi$
$311$	1.31939e22			0.484762			0.242381	+	0.970181i	$0.422072\pi$
$312$		0			0
$313$	−3.26767e22	+	3.26767e22i	−1.13328	+	1.13328i	−0.143657	+	0.989628i	$0.545886\pi$
$313$	−3.26767e22	+	3.26767e22i	−1.13328	+	1.13328i	−0.989628	+	0.143657i	$0.954114\pi$
$314$			3.32148e22i			1.11935i
$315$		0			0
$316$	1.89037e22			0.601677
$317$	−3.05032e22	−	3.05032e22i	−0.943653	−	0.943653i	0.0548421	−	0.998495i	$-0.482534\pi$
$317$	−3.05032e22	−	3.05032e22i	−0.943653	−	0.943653i	−0.998495	+	0.0548421i	$0.982534\pi$
$318$		0			0
$319$		−	2.30937e22i		−	0.675113i
$320$	3.04005e21	−	3.17819e21i	0.0864035	−	0.0903296i
$321$		0			0
$322$	−3.39038e22	−	3.39038e22i	−0.911057	−	0.911057i
$323$	1.60491e22	−	1.60491e22i	0.419400	−	0.419400i
$324$		0			0
$325$	−3.00277e22	−	2.74717e22i	−0.742286	−	0.679103i
$326$	−1.85568e22			−0.446217
$327$		0			0
$328$	1.04047e21	−	1.04047e21i	0.0236790	−	0.0236790i
$329$		−	1.36745e23i		−	3.02794i
$330$		0			0
$331$	−6.90969e22			−1.44879			−0.724397	−	0.689383i	$-0.757882\pi$
$331$	−6.90969e22			−1.44879			−0.724397	+	0.689383i	$0.757882\pi$
$332$	−1.36990e22	−	1.36990e22i	−0.279542	−	0.279542i
$333$		0			0
$334$		−	5.58258e22i		−	1.07924i
$335$	−4.98315e20	−	2.24317e22i	−0.00937779	−	0.422142i
$336$		0			0
$337$	2.13535e22	+	2.13535e22i	0.380891	+	0.380891i	0.871423	−	0.490532i	$-0.163198\pi$
$337$	2.13535e22	+	2.13535e22i	0.380891	+	0.380891i	−0.490532	+	0.871423i	$0.663198\pi$
$338$	3.50338e20	−	3.50338e20i	0.00608467	−	0.00608467i
$339$		0			0
$340$	−2.24919e22	+	4.99652e20i	−0.370438	+	0.00822919i
$341$	2.91202e21			0.0467094
$342$		0			0
$343$	1.68264e23	−	1.68264e23i	2.56061	−	2.56061i
$344$		−	2.81636e21i		−	0.0417505i
$345$		0			0
$346$	−9.53185e22			−1.34120
$347$	5.08293e22	+	5.08293e22i	0.696865	+	0.696865i	0.963733	−	0.266868i	$-0.0859888\pi$
$347$	5.08293e22	+	5.08293e22i	0.696865	+	0.696865i	−0.266868	+	0.963733i	$0.585989\pi$
$348$		0			0
$349$		−	6.11035e22i		−	0.795494i	−0.917495	−	0.397747i	$-0.869792\pi$
$349$		−	6.11035e22i		−	0.795494i	0.917495	−	0.397747i	$-0.130208\pi$
$350$	1.09194e23	−	4.85382e21i	1.38543	−	0.0615844i
$351$		0			0
$352$	−8.20703e21	−	8.20703e21i	−0.0989240	−	0.0989240i
$353$	1.60644e21	−	1.60644e21i	0.0188752	−	0.0188752i	−0.697606	−	0.716481i	$-0.745751\pi$
$353$	1.60644e21	−	1.60644e21i	0.0188752	−	0.0188752i	0.716481	+	0.697606i	$0.245751\pi$
$354$		0			0
$355$	4.10426e22	+	3.92588e22i	0.458332	+	0.438411i
$356$	−2.91976e22			−0.317905
$357$		0			0
$358$	1.12496e22	−	1.12496e22i	0.116463	−	0.116463i
$359$		−	1.48424e23i		−	1.49849i	−0.662292	−	0.749246i	$-0.730416\pi$
$359$		−	1.48424e23i		−	1.49849i	0.662292	−	0.749246i	$-0.269584\pi$
$360$		0			0
$361$	3.74241e22			0.359407
$362$	−3.66133e22	−	3.66133e22i	−0.342975	−	0.342975i
$363$		0			0
$364$			1.10672e23i			0.986563i
$365$	−9.38178e22	+	2.08414e21i	−0.815923	+	0.0181255i
$366$		0			0
$367$	1.52028e23	+	1.52028e23i	1.25872	+	1.25872i	0.951703	+	0.307021i	$0.0993322\pi$
$367$	1.52028e23	+	1.52028e23i	1.25872	+	1.25872i	0.307021	+	0.951703i	$0.400668\pi$
$368$	−2.03284e22	+	2.03284e22i	−0.164237	+	0.164237i
$369$		0			0
$370$	4.47538e22	−	4.67873e22i	0.344361	−	0.360008i
$371$	1.72295e23			1.29392
$372$		0			0
$373$	1.06545e19	−	1.06545e19i	7.62347e−5	−	7.62347e-5i	−0.707069	−	0.707145i	$-0.749983\pi$
$373$	1.06545e19	−	1.06545e19i	7.62347e−5	−	7.62347e-5i	0.707145	+	0.707069i	$0.249983\pi$
$374$			5.93709e22i			0.414695i
$375$		0			0
$376$	−8.19907e22			−0.545851
$377$	9.33617e22	+	9.33617e22i	0.606871	+	0.606871i
$378$		0			0
$379$		−	3.50621e22i		−	0.217313i	−0.994079	−	0.108656i	$-0.965345\pi$
$379$		−	3.50621e22i		−	0.217313i	0.994079	−	0.108656i	$-0.0346548\pi$
$380$	4.77786e22	+	4.57019e22i	0.289189	+	0.276619i
$381$		0			0
$382$	1.18833e23	+	1.18833e23i	0.686070	+	0.686070i
$383$	−2.11577e23	+	2.11577e23i	−1.19311	+	1.19311i	−0.216916	+	0.976190i	$0.569600\pi$
$383$	−2.11577e23	+	2.11577e23i	−1.19311	+	1.19311i	−0.976190	+	0.216916i	$0.930400\pi$
$384$		0			0
$385$	−6.40621e21	−	2.88376e23i	−0.0344711	−	1.55172i
$386$	−7.99857e21			−0.0420462
$387$		0			0
$388$	−3.54695e22	+	3.54695e22i	−0.177979	+	0.177979i
$389$		−	8.89486e22i		−	0.436107i	−0.975937	−	0.218053i	$-0.930029\pi$
$389$		−	8.89486e22i		−	0.436107i	0.975937	−	0.218053i	$-0.0699707\pi$
$390$		0			0
$391$	1.47059e23			0.688493
$392$	−1.55530e23	−	1.55530e23i	−0.711605	−	0.711605i
$393$		0			0
$394$			9.24995e22i			0.404272i
$395$	1.94710e23	−	2.03558e23i	0.831793	−	0.869588i
$396$		0			0
$397$	3.21240e23	+	3.21240e23i	1.31134	+	1.31134i	0.920428	+	0.390913i	$0.127841\pi$
$397$	3.21240e23	+	3.21240e23i	1.31134	+	1.31134i	0.390913	+	0.920428i	$0.372159\pi$
$398$	9.82268e22	−	9.82268e22i	0.391997	−	0.391997i
$399$		0			0
$400$	−2.91030e21	−	6.54713e22i	−0.0111019	−	0.249753i
$401$	2.89446e23			1.07961			0.539807	−	0.841789i	$-0.318497\pi$
$401$	2.89446e23			1.07961			0.539807	+	0.841789i	$0.318497\pi$
$402$		0			0
$403$	−1.17725e22	+	1.17725e22i	−0.0419879	+	0.0419879i
$404$		−	9.76780e22i		−	0.340694i
$405$		0			0
$406$	−3.54595e23			−1.18304
$407$	−1.20819e23	−	1.20819e23i	−0.394262	−	0.394262i
$408$		0			0
$409$			1.33973e23i			0.418320i	0.977881	+	0.209160i	$0.0670730\pi$
$409$			1.33973e23i			0.418320i	−0.977881	+	0.209160i	$0.932927\pi$
$410$	−4.86966e20	−	2.19208e22i	−0.00148745	−	0.0669579i
$411$		0			0
$412$	−9.32191e22	−	9.32191e22i	−0.272540	−	0.272540i
$413$	4.15119e23	−	4.15119e23i	1.18747	−	1.18747i
$414$		0			0
$415$	−2.88614e23	+	6.41149e21i	−0.790468	+	0.0175601i
$416$	6.63577e22			0.177849
$417$		0			0
$418$	1.23378e23	−	1.23378e23i	0.316703	−	0.316703i
$419$		−	8.55517e22i		−	0.214933i	−0.994209	−	0.107466i	$-0.965726\pi$
$419$		−	8.55517e22i		−	0.214933i	0.994209	−	0.107466i	$-0.0342738\pi$
$420$		0			0
$421$	5.75150e23			1.38434			0.692169	−	0.721736i	$-0.256655\pi$
$421$	5.75150e23			1.38434			0.692169	+	0.721736i	$0.256655\pi$
$422$	−1.16561e23	−	1.16561e23i	−0.274625	−	0.274625i
$423$		0			0
$424$		−	1.03306e23i		−	0.233256i
$425$	−2.26288e23	+	2.47342e23i	−0.500220	+	0.546760i
$426$		0			0
$427$	−8.45223e23	−	8.45223e23i	−1.79110	−	1.79110i
$428$	−1.56882e23	+	1.56882e23i	−0.325522	+	0.325522i
$429$		0			0
$430$	−3.03269e22	−	2.90087e22i	−0.0603409	−	0.0577182i
$431$	6.24169e23			1.21621			0.608103	−	0.793858i	$-0.291931\pi$
$431$	6.24169e23			1.21621			0.608103	+	0.793858i	$0.291931\pi$
$432$		0			0
$433$	3.40765e23	−	3.40765e23i	0.636889	−	0.636889i	−0.312898	−	0.949787i	$-0.601300\pi$
$433$	3.40765e23	−	3.40765e23i	0.636889	−	0.636889i	0.949787	+	0.312898i	$0.101300\pi$
$434$		−	4.47130e22i		−	0.0818514i
$435$		0			0
$436$	2.18686e22			0.0384098
$437$	−3.05602e23	−	3.05602e23i	−0.525803	−	0.525803i
$438$		0			0
$439$			6.24674e23i			1.03151i	0.856737	+	0.515754i	$0.172488\pi$
$439$			6.24674e23i			1.03151i	−0.856737	+	0.515754i	$0.827512\pi$
$440$	−1.72907e23	+	3.84110e21i	−0.279730	+	0.00621415i
$441$		0			0
$442$	−2.40021e23	−	2.40021e23i	−0.372777	−	0.372777i
$443$	−2.21026e23	+	2.21026e23i	−0.336365	+	0.336365i	−0.854997	−	0.518633i	$-0.826441\pi$
$443$	−2.21026e23	+	2.21026e23i	−0.336365	+	0.336365i	0.518633	+	0.854997i	$0.326441\pi$
$444$		0			0
$445$	−3.00738e23	+	3.14404e23i	−0.439490	+	0.459460i
$446$	−8.05363e23			−1.15339
$447$		0			0
$448$	−1.26016e23	+	1.26016e23i	−0.173350	+	0.173350i
$449$		−	3.09194e23i		−	0.416883i	−0.978035	−	0.208441i	$-0.933161\pi$
$449$		−	3.09194e23i		−	0.416883i	0.978035	−	0.208441i	$-0.0668391\pi$
$450$		0			0
$451$	−5.78635e22			−0.0749576
$452$	2.07886e23	+	2.07886e23i	0.263985	+	0.263985i
$453$		0			0
$454$			9.23090e23i			1.12653i
$455$	1.19173e24	+	1.13993e24i	1.42585	+	1.36388i
$456$		0			0
$457$	−1.87490e23	−	1.87490e23i	−0.215642	−	0.215642i	0.591017	−	0.806659i	$-0.298727\pi$
$457$	−1.87490e23	−	1.87490e23i	−0.215642	−	0.215642i	−0.806659	+	0.591017i	$0.798727\pi$
$458$	1.87028e22	−	1.87028e22i	0.0210919	−	0.0210919i
$459$		0			0
$460$	9.51420e21	+	4.28283e23i	0.0103170	+	0.464419i
$461$	8.68149e23			0.923179			0.461589	−	0.887094i	$-0.347279\pi$
$461$	8.68149e23			0.923179			0.461589	+	0.887094i	$0.347279\pi$
$462$		0			0
$463$	1.18678e24	−	1.18678e24i	1.21378	−	1.21378i	0.244011	−	0.969772i	$-0.421537\pi$
$463$	1.18678e24	−	1.18678e24i	1.21378	−	1.21378i	0.969772	−	0.244011i	$-0.0784634\pi$
$464$			2.12611e23i			0.213268i
$465$		0			0
$466$	−2.24518e23			−0.216660
$467$	1.99709e23	+	1.99709e23i	0.189036	+	0.189036i	0.795279	−	0.606243i	$-0.207324\pi$
$467$	1.99709e23	+	1.99709e23i	0.189036	+	0.189036i	−0.606243	+	0.795279i	$0.707324\pi$
$468$		0			0
$469$			9.09180e23i			0.828122i
$470$	−8.44513e23	+	8.82887e23i	−0.754615	+	0.788904i
$471$		0			0
$472$	−2.48901e23	−	2.48901e23i	−0.214067	−	0.214067i
$473$	−7.83129e22	+	7.83129e22i	−0.0660820	+	0.0660820i
$474$		0			0
$475$	9.84249e23	−	4.37513e22i	0.799581	−	0.0355426i
$476$	9.11619e23			0.726693
$477$		0			0
$478$	−9.53191e23	+	9.53191e23i	−0.731693	+	0.731693i
$479$		−	9.63012e23i		−	0.725458i	−0.931895	−	0.362729i	$-0.881845\pi$
$479$		−	9.63012e23i		−	0.725458i	0.931895	−	0.362729i	$-0.118155\pi$
$480$		0			0
$481$	9.76877e23			0.708817
$482$	−1.25879e24	−	1.25879e24i	−0.896455	−	0.896455i
$483$		0			0
$484$		−	2.72332e23i		−	0.186849i
$485$	1.66006e22	+	7.47279e23i	0.0111802	+	0.503277i
$486$		0			0
$487$	−8.37637e23	−	8.37637e23i	−0.543620	−	0.543620i	0.380968	−	0.924588i	$-0.375591\pi$
$487$	−8.37637e23	−	8.37637e23i	−0.543620	−	0.543620i	−0.924588	+	0.380968i	$0.875591\pi$
$488$	−5.06787e23	+	5.06787e23i	−0.322884	+	0.322884i
$489$		0			0
$490$	−3.27674e24	+	7.27920e22i	−2.01223	+	0.0447012i
$491$	−2.05474e24			−1.23886			−0.619431	−	0.785051i	$-0.712637\pi$
$491$	−2.05474e24			−1.23886			−0.619431	+	0.785051i	$0.712637\pi$
$492$		0			0
$493$	7.69032e23	−	7.69032e23i	0.447015	−	0.447015i
$494$			9.97574e23i			0.569381i
$495$		0			0
$496$	−2.68094e22			−0.0147555
$497$	−1.62735e24	−	1.62735e24i	−0.879576	−	0.879576i
$498$		0			0
$499$		−	4.91102e22i		−	0.0256016i	−0.999918	−	0.0128008i	$-0.995925\pi$
$499$		−	4.91102e22i		−	0.0256016i	0.999918	−	0.0128008i	$-0.00407473\pi$
$500$	−7.34980e23	−	6.43023e23i	−0.376310	−	0.329228i
$501$		0			0
$502$	7.20241e23	+	7.20241e23i	0.355749	+	0.355749i
$503$	−4.34790e23	+	4.34790e23i	−0.210944	+	0.210944i	−0.804668	−	0.593724i	$-0.797657\pi$
$503$	−4.34790e23	+	4.34790e23i	−0.210944	+	0.210944i	0.593724	+	0.804668i	$0.297657\pi$
$504$		0			0
$505$	−1.05181e24	−	1.00609e24i	−0.492396	−	0.470994i
$506$	1.13052e24			0.519905
$507$		0			0
$508$	−3.33950e23	+	3.33950e23i	−0.148220	+	0.148220i
$509$			3.48906e24i			1.52142i	0.649094	+	0.760709i	$0.275148\pi$
$509$			3.48906e24i			1.52142i	−0.649094	+	0.760709i	$0.724852\pi$
$510$		0			0
$511$	3.80253e24			1.60061
$512$	7.55579e22	+	7.55579e22i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	1.06667e24i		−	0.425953i
$515$	−1.96396e24	+	4.36290e22i	−0.770669	+	0.0171202i
$516$		0			0
$517$	2.27987e24	+	2.27987e24i	0.863965	+	0.863965i
$518$	−1.85513e24	+	1.85513e24i	−0.690885	+	0.690885i
$519$		0			0
$520$	6.83491e23	−	7.14548e23i	0.245869	−	0.257041i
$521$	5.11124e23			0.180712			0.0903560	−	0.995910i	$-0.471199\pi$
$521$	5.11124e23			0.180712			0.0903560	+	0.995910i	$0.471199\pi$
$522$		0			0
$523$	6.29180e23	−	6.29180e23i	0.214911	−	0.214911i	−0.591439	−	0.806350i	$-0.701440\pi$
$523$	6.29180e23	−	6.29180e23i	0.214911	−	0.214911i	0.806350	+	0.591439i	$0.201440\pi$
$524$			2.23889e23i			0.0751711i
$525$		0			0
$526$	−1.35423e24			−0.439362
$527$	9.69718e22	+	9.69718e22i	0.0309279	+	0.0309279i
$528$		0			0
$529$			4.43909e23i			0.136834i
$530$	−1.11241e24	−	1.06406e24i	−0.337119	−	0.322466i
$531$		0			0
$532$	−1.89443e24	−	1.89443e24i	−0.554976	−	0.554976i
$533$	2.33927e23	−	2.33927e23i	0.0673807	−	0.0673807i
$534$		0			0
$535$	7.34250e22	+	3.30523e24i	0.0204484	+	0.920488i
$536$	5.45135e23			0.149287
$537$		0			0
$538$	4.20595e23	−	4.20595e23i	0.111384	−	0.111384i
$539$			8.64947e24i			2.25263i
$540$		0			0
$541$	−2.29158e24			−0.577245			−0.288622	−	0.957443i	$-0.593197\pi$
$541$	−2.29158e24			−0.577245			−0.288622	+	0.957443i	$0.593197\pi$
$542$	3.35905e24	+	3.35905e24i	0.832191	+	0.832191i
$543$		0			0
$544$		−	5.46597e23i		−	0.131002i
$545$	2.25248e23	−	2.35484e23i	0.0530999	−	0.0555127i
$546$		0			0
$547$	9.13742e23	+	9.13742e23i	0.208419	+	0.208419i	0.803595	−	0.595176i	$-0.202918\pi$
$547$	9.13742e23	+	9.13742e23i	0.208419	+	0.208419i	−0.595176	+	0.803595i	$0.702918\pi$
$548$	−2.16002e24	+	2.16002e24i	−0.484655	+	0.484655i
$549$		0			0
$550$	−1.73960e24	+	1.90145e24i	−0.377734	+	0.412878i
$551$	−3.19625e24			−0.682772
$552$		0			0
$553$	−8.07111e24	+	8.07111e24i	−1.66881	+	1.66881i
$554$		−	4.83803e24i		−	0.984194i
$555$		0			0
$556$	−3.92837e24			−0.773642
$557$	−4.19910e24	−	4.19910e24i	−0.813692	−	0.813692i	0.171494	−	0.985185i	$-0.445141\pi$
$557$	−4.19910e24	−	4.19910e24i	−0.813692	−	0.813692i	−0.985185	+	0.171494i	$0.945141\pi$
$558$		0			0
$559$		−	6.33198e23i		−	0.118805i
$560$	5.89787e22	+	2.65493e24i	0.0108894	+	0.490186i
$561$		0			0
$562$	−8.66562e23	−	8.66562e23i	−0.154943	−	0.154943i
$563$	2.49305e24	−	2.49305e24i	0.438688	−	0.438688i	−0.452883	−	0.891570i	$-0.649604\pi$
$563$	2.49305e24	−	2.49305e24i	0.438688	−	0.438688i	0.891570	+	0.452883i	$0.149604\pi$
$564$		0			0
$565$	4.37979e24	−	9.72960e22i	0.746478	−	0.0165828i
$566$	4.09387e24			0.686730
$567$		0			0
$568$	−9.75742e23	+	9.75742e23i	−0.158562	+	0.158562i
$569$			1.63724e24i			0.261880i	0.991390	+	0.130940i	$0.0417996\pi$
$569$			1.63724e24i			0.261880i	−0.991390	+	0.130940i	$0.958200\pi$
$570$		0			0
$571$	2.75979e24			0.427712			0.213856	−	0.976865i	$-0.431398\pi$
$571$	2.75979e24			0.427712			0.213856	+	0.976865i	$0.431398\pi$
$572$	−1.84518e24	−	1.84518e24i	−0.281497	−	0.281497i
$573$		0			0
$574$			8.88473e23i			0.131352i
$575$	4.70980e24	+	4.30891e24i	0.685475	+	0.627128i
$576$		0			0
$577$	3.67969e24	+	3.67969e24i	0.519073	+	0.519073i	0.917291	−	0.398218i	$-0.130371\pi$
$577$	3.67969e24	+	3.67969e24i	0.519073	+	0.519073i	−0.398218	+	0.917291i	$0.630371\pi$
$578$	1.62306e24	−	1.62306e24i	0.225416	−	0.225416i
$579$		0			0
$580$	2.28943e24	+	2.18992e24i	0.308230	+	0.294833i
$581$	1.16978e25			1.55067
$582$		0			0
$583$	−2.87258e24	+	2.87258e24i	−0.369194	+	0.369194i
$584$		−	2.27996e24i		−	0.288544i
$585$		0			0
$586$	−2.76952e24			−0.339881
$587$	−1.97212e24	−	1.97212e24i	−0.238336	−	0.238336i	0.577825	−	0.816161i	$-0.303902\pi$
$587$	−1.97212e24	−	1.97212e24i	−0.238336	−	0.238336i	−0.816161	+	0.577825i	$0.803902\pi$
$588$		0			0
$589$		−	4.03034e23i		−	0.0472393i
$590$	−5.24391e24	+	1.16492e23i	−0.605322	+	0.0134471i
$591$		0			0
$592$	1.11232e24	+	1.11232e24i	0.124547	+	0.124547i
$593$	1.15405e25	−	1.15405e25i	1.27272	−	1.27272i	0.328064	−	0.944655i	$-0.393604\pi$
$593$	1.15405e25	−	1.15405e25i	1.27272	−	1.27272i	0.944655	−	0.328064i	$-0.106396\pi$
$594$		0			0
$595$	9.38977e24	−	9.81643e24i	1.00462	−	1.05027i
$596$	−2.67176e24			−0.281567
$597$		0			0
$598$	−4.57040e24	+	4.57040e24i	−0.467352	+	0.467352i
$599$			1.35980e24i			0.136973i	0.997652	+	0.0684864i	$0.0218170\pi$
$599$			1.35980e24i			0.136973i	−0.997652	+	0.0684864i	$0.978183\pi$
$600$		0			0
$601$	−6.27719e24			−0.613614			−0.306807	−	0.951772i	$-0.599261\pi$
$601$	−6.27719e24			−0.613614			−0.306807	+	0.951772i	$0.599261\pi$
$602$	1.20247e24	+	1.20247e24i	0.115799	+	0.115799i
$603$		0			0
$604$		−	3.30507e24i		−	0.308922i
$605$	−2.93251e24	−	2.80505e24i	−0.270048	−	0.258311i
$606$		0			0
$607$	4.09427e24	+	4.09427e24i	0.365998	+	0.365998i	0.866015	−	0.500017i	$-0.166673\pi$
$607$	4.09427e24	+	4.09427e24i	0.365998	+	0.365998i	−0.500017	+	0.866015i	$0.666673\pi$
$608$	−1.13588e24	+	1.13588e24i	−0.100046	+	0.100046i
$609$		0			0
$610$	2.37189e23	+	1.06771e25i	0.0202828	+	0.913030i
$611$	−1.84339e25			−1.55327
$612$		0			0
$613$	1.62906e25	−	1.62906e25i	1.33288	−	1.33288i	0.430100	−	0.902781i	$-0.358478\pi$
$613$	1.62906e25	−	1.62906e25i	1.33288	−	1.33288i	0.902781	−	0.430100i	$-0.141522\pi$
$614$			1.55222e25i			1.25152i
$615$		0			0
$616$	7.00812e24			0.548751
$617$	1.44398e25	+	1.44398e25i	1.11428	+	1.11428i	0.992565	+	0.121714i	$0.0388390\pi$
$617$	1.44398e25	+	1.44398e25i	1.11428	+	1.11428i	0.121714	+	0.992565i	$0.461161\pi$
$618$		0			0
$619$		−	1.03800e25i		−	0.778001i	−0.921238	−	0.389000i	$-0.872820\pi$
$619$		−	1.03800e25i		−	0.778001i	0.921238	−	0.389000i	$-0.127180\pi$
$620$	−2.76140e23	+	2.88687e23i	−0.0203988	+	0.0213257i
$621$		0			0
$622$	3.37763e24	+	3.37763e24i	0.242381	+	0.242381i
$623$	1.24662e25	−	1.24662e25i	0.881740	−	0.881740i
$624$		0			0
$625$	−1.44945e25	+	1.29116e24i	−0.996056	+	0.0887276i
$626$	−1.67305e25			−1.13328
$627$		0			0
$628$	−8.50299e24	+	8.50299e24i	−0.559674	+	0.559674i
$629$		−	8.04666e24i		−	0.522108i
$630$		0			0
$631$	1.95594e25			1.23337			0.616683	−	0.787212i	$-0.288476\pi$
$631$	1.95594e25			1.23337			0.616683	+	0.787212i	$0.288476\pi$
$632$	4.83935e24	+	4.83935e24i	0.300839	+	0.300839i
$633$		0			0
$634$		−	1.56176e25i		−	0.943653i
$635$	1.56297e23	+	7.03572e24i	0.00931080	+	0.419127i
$636$		0			0
$637$	−3.49676e25	−	3.49676e25i	−2.02493	−	2.02493i
$638$	5.91198e24	−	5.91198e24i	0.337557	−	0.337557i
$639$		0			0
$640$	1.59187e24	−	3.53630e22i	0.0883665	−	0.00196304i
$641$	8.33904e24			0.456450			0.228225	−	0.973608i	$-0.426708\pi$
$641$	8.33904e24			0.456450			0.228225	+	0.973608i	$0.426708\pi$
$642$		0			0
$643$	9.55266e24	−	9.55266e24i	0.508423	−	0.508423i	−0.405619	−	0.914042i	$-0.632944\pi$
$643$	9.55266e24	−	9.55266e24i	0.508423	−	0.508423i	0.914042	+	0.405619i	$0.132944\pi$
$644$		−	1.73587e25i		−	0.911057i
$645$		0			0
$646$	8.21715e24			0.419400
$647$	−2.14613e25	−	2.14613e25i	−1.08023	−	1.08023i	−0.996487	−	0.0837436i	$-0.973312\pi$
$647$	−2.14613e25	−	2.14613e25i	−1.08023	−	1.08023i	−0.0837436	−	0.996487i	$-0.526688\pi$
$648$		0			0
$649$			1.38421e25i			0.677643i
$650$	−6.54319e23	−	1.47198e25i	−0.0315914	−	0.710694i
$651$		0			0
$652$	−4.75055e24	−	4.75055e24i	−0.223108	−	0.223108i
$653$	1.83449e25	−	1.83449e25i	0.849759	−	0.849759i	−0.140344	−	0.990103i	$-0.544821\pi$
$653$	1.83449e25	−	1.83449e25i	0.849759	−	0.849759i	0.990103	+	0.140344i	$0.0448208\pi$
$654$		0			0
$655$	2.41086e24	+	2.30608e24i	0.108643	+	0.103921i
$656$	5.32720e23			0.0236790
$657$		0			0
$658$	3.50066e25	−	3.50066e25i	1.51397	−	1.51397i
$659$		−	2.14134e25i		−	0.913517i	−0.889591	−	0.456759i	$-0.849010\pi$
$659$		−	2.14134e25i		−	0.913517i	0.889591	−	0.456759i	$-0.150990\pi$
$660$		0			0
$661$	2.82537e25			1.17290			0.586451	−	0.809985i	$-0.300525\pi$
$661$	2.82537e25			1.17290			0.586451	+	0.809985i	$0.300525\pi$
$662$	−1.76888e25	−	1.76888e25i	−0.724397	−	0.724397i
$663$		0			0
$664$		−	7.01389e24i		−	0.279542i
$665$	−3.99123e25	+	8.86643e23i	−1.56932	+	0.0348621i
$666$		0			0
$667$	−1.46437e25	−	1.46437e25i	−0.560424	−	0.560424i
$668$	1.42914e25	−	1.42914e25i	0.539618	−	0.539618i
$669$		0			0
$670$	5.61494e24	−	5.87008e24i	0.206382	−	0.215760i
$671$	2.81839e25			1.02211
$672$		0			0
$673$	−2.12398e25	+	2.12398e25i	−0.749919	+	0.749919i	−0.974464	−	0.224544i	$-0.927911\pi$
$673$	−2.12398e25	+	2.12398e25i	−0.749919	+	0.749919i	0.224544	+	0.974464i	$0.427911\pi$
$674$			1.09330e25i			0.380891i
$675$		0			0
$676$	1.79373e23			0.00608467
$677$	−2.57519e24	−	2.57519e24i	−0.0862009	−	0.0862009i	0.662692	−	0.748892i	$-0.269414\pi$
$677$	−2.57519e24	−	2.57519e24i	−0.0862009	−	0.0862009i	−0.748892	+	0.662692i	$0.769414\pi$
$678$		0			0
$679$		−	3.02880e25i		−	0.987285i
$680$	−5.88583e24	−	5.63001e24i	−0.189333	−	0.181104i
$681$		0			0
$682$	7.45476e23	+	7.45476e23i	0.0233547	+	0.0233547i
$683$	−1.52112e24	+	1.52112e24i	−0.0470304	+	0.0470304i	−0.730231	−	0.683200i	$-0.760588\pi$
$683$	−1.52112e24	+	1.52112e24i	−0.0470304	+	0.0470304i	0.683200	+	0.730231i	$0.260588\pi$
$684$		0			0
$685$	1.01094e24	+	4.55078e25i	0.0304447	+	1.37047i
$686$	8.61511e25			2.56061
$687$		0			0
$688$	7.20987e23	−	7.20987e23i	0.0208752	−	0.0208752i
$689$		−	2.32262e25i		−	0.663750i
$690$		0			0
$691$	−5.05112e25			−1.40632			−0.703162	−	0.711029i	$-0.748229\pi$
$691$	−5.05112e25			−1.40632			−0.703162	+	0.711029i	$0.748229\pi$
$692$	−2.44015e25	−	2.44015e25i	−0.670598	−	0.670598i
$693$		0			0
$694$			2.60246e25i			0.696865i
$695$	−4.04627e25	+	4.23012e25i	−1.06953	+	1.11812i
$696$		0			0
$697$	−1.92689e24	−	1.92689e24i	−0.0496320	−	0.0496320i
$698$	1.56425e25	−	1.56425e25i	0.397747	−	0.397747i
$699$		0			0
$700$	2.91961e25	+	2.67110e25i	0.723507	+	0.661923i
$701$	2.26069e25			0.553069			0.276535	−	0.961004i	$-0.410814\pi$
$701$	2.26069e25			0.553069			0.276535	+	0.961004i	$0.410814\pi$
$702$		0			0
$703$	−1.67217e25	+	1.67217e25i	−0.398734	+	0.398734i
$704$		−	4.20200e24i		−	0.0989240i
$705$		0			0
$706$	8.22498e23			0.0188752
$707$	4.17045e25	+	4.17045e25i	0.944948	+	0.944948i
$708$		0			0
$709$			3.17707e25i			0.701795i	0.936414	+	0.350897i	$0.114123\pi$
$709$			3.17707e25i			0.701795i	−0.936414	+	0.350897i	$0.885877\pi$
$710$	4.56673e23	+	2.05572e25i	0.00996047	+	0.448371i
$711$		0			0
$712$	−7.47459e24	−	7.47459e24i	−0.158953	−	0.158953i
$713$	1.84651e24	−	1.84651e24i	0.0387744	−	0.0387744i
$714$		0			0
$715$	−3.88746e25	+	8.63590e23i	−0.795997	+	0.0176829i
$716$	5.75977e24			0.116463
$717$		0			0
$718$	3.79966e25	−	3.79966e25i	0.749246	−	0.749246i
$719$			6.22579e25i			1.21237i	0.795324	+	0.606184i	$0.207301\pi$
$719$			6.22579e25i			1.21237i	−0.795324	+	0.606184i	$0.792699\pi$
$720$		0			0
$721$	7.96014e25			1.51183
$722$	9.58058e24	+	9.58058e24i	0.179704	+	0.179704i
$723$		0			0
$724$		−	1.87460e25i		−	0.342975i
$725$	4.71627e25	−	2.09645e24i	0.852229	−	0.0378828i
$726$		0			0
$727$	−3.56990e25	−	3.56990e25i	−0.629284	−	0.629284i	0.318604	−	0.947888i	$-0.396786\pi$
$727$	−3.56990e25	−	3.56990e25i	−0.629284	−	0.629284i	−0.947888	+	0.318604i	$0.896786\pi$
$728$	−2.83320e25	+	2.83320e25i	−0.493282	+	0.493282i
$729$		0			0
$730$	−2.45509e25	−	2.34838e25i	−0.417024	−	0.398899i
$731$	−5.21573e24			−0.0875102
$732$		0			0
$733$	−3.94039e25	+	3.94039e25i	−0.645066	+	0.645066i	−0.951796	−	0.306731i	$-0.900765\pi$
$733$	−3.94039e25	+	3.94039e25i	−0.645066	+	0.645066i	0.306731	+	0.951796i	$0.400765\pi$
$734$			7.78386e25i			1.25872i
$735$		0			0
$736$	−1.04081e25			−0.164237
$737$	−1.51583e25	−	1.51583e25i	−0.236289	−	0.236289i
$738$		0			0
$739$		−	6.16814e25i		−	0.938327i	−0.883111	−	0.469163i	$-0.844556\pi$
$739$		−	6.16814e25i		−	0.938327i	0.883111	−	0.469163i	$-0.155444\pi$
$740$	2.34345e25	−	5.20592e23i	0.352185	−	0.00782370i
$741$		0			0
$742$	4.41074e25	+	4.41074e25i	0.646958	+	0.646958i
$743$	4.73726e24	−	4.73726e24i	0.0686480	−	0.0686480i	−0.671949	−	0.740597i	$-0.734543\pi$
$743$	4.73726e24	−	4.73726e24i	0.0686480	−	0.0686480i	0.740597	+	0.671949i	$0.234543\pi$
$744$		0			0
$745$	−2.75194e25	+	2.87699e25i	−0.389254	+	0.406941i
$746$	5.45509e21			7.62347e−5
$747$		0			0
$748$	−1.51989e25	+	1.51989e25i	−0.207348	+	0.207348i
$749$		−	1.33965e26i		−	1.80573i
$750$		0			0
$751$	3.56063e25			0.468562			0.234281	−	0.972169i	$-0.424726\pi$
$751$	3.56063e25			0.468562			0.234281	+	0.972169i	$0.424726\pi$
$752$	−2.09896e25	−	2.09896e25i	−0.272926	−	0.272926i
$753$		0			0
$754$			4.78012e25i			0.606871i
$755$	−3.55894e25	−	3.40426e25i	−0.446477	−	0.427071i
$756$		0			0
$757$	2.44369e25	+	2.44369e25i	0.299352	+	0.299352i	0.840760	−	0.541408i	$-0.182108\pi$
$757$	2.44369e25	+	2.44369e25i	0.299352	+	0.299352i	−0.541408	+	0.840760i	$0.682108\pi$
$758$	8.97589e24	−	8.97589e24i	0.108656	−	0.108656i
$759$		0			0
$760$	5.31622e23	+	2.39310e25i	0.00628465	+	0.282904i
$761$	−1.10258e26			−1.28810			−0.644048	−	0.764985i	$-0.722746\pi$
$761$	−1.10258e26			−1.28810			−0.644048	+	0.764985i	$0.722746\pi$
$762$		0			0
$763$	−9.33697e24	+	9.33697e24i	−0.106533	+	0.106533i
$764$			6.08427e25i			0.686070i
$765$		0			0
$766$	−1.08327e26			−1.19311
$767$	−5.59601e25	−	5.59601e25i	−0.609145	−	0.609145i
$768$		0			0
$769$		−	1.31879e25i		−	0.140229i	−0.997539	−	0.0701146i	$-0.977664\pi$
$769$		−	1.31879e25i		−	0.140229i	0.997539	−	0.0701146i	$-0.0223365\pi$
$770$	7.21843e25	−	7.54643e25i	0.758624	−	0.793095i
$771$		0			0
$772$	−2.04763e24	−	2.04763e24i	−0.0210231	−	0.0210231i
$773$	−9.10781e25	+	9.10781e25i	−0.924269	+	0.924269i	−0.997328	−	0.0730586i	$-0.976724\pi$
$773$	−9.10781e25	+	9.10781e25i	−0.924269	+	0.924269i	0.0730586	+	0.997328i	$0.476724\pi$
$774$		0			0
$775$	2.64354e23	+	5.94702e24i	0.00262102	+	0.0589636i
$776$	−1.81604e25			−0.177979
$777$		0			0
$778$	2.27709e25	−	2.27709e25i	0.218053	−	0.218053i
$779$			8.00852e24i			0.0758080i
$780$		0			0
$781$	5.42639e25			0.501940
$782$	3.76470e25	+	3.76470e25i	0.344247	+	0.344247i
$783$		0			0
$784$		−	7.96312e25i		−	0.711605i
$785$	3.97962e24	+	1.79143e26i	0.0351572	+	1.58261i
$786$		0			0
$787$	1.44575e26	+	1.44575e26i	1.24831	+	1.24831i	0.956467	+	0.291839i	$0.0942673\pi$
$787$	1.44575e26	+	1.44575e26i	1.24831	+	1.24831i	0.291839	+	0.956467i	$0.405733\pi$
$788$	−2.36799e25	+	2.36799e25i	−0.202136	+	0.202136i
$789$		0			0
$790$	1.01957e26	−	2.26494e24i	0.850690	−	0.0188979i
$791$	−1.77517e26			−1.46438
$792$		0			0
$793$	−1.13940e26	+	1.13940e26i	−0.918795	+	0.918795i
$794$			1.64475e26i			1.31134i
$795$		0			0
$796$	5.02921e25			0.391997
$797$	9.34815e25	+	9.34815e25i	0.720445	+	0.720445i	0.968696	−	0.248251i	$-0.0798558\pi$
$797$	9.34815e25	+	9.34815e25i	0.720445	+	0.720445i	−0.248251	+	0.968696i	$0.579856\pi$
$798$		0			0
$799$			1.51842e26i			1.14412i
$800$	1.60156e25	−	1.75057e25i	0.119326	−	0.130428i
$801$		0			0
$802$	7.40982e25	+	7.40982e25i	0.539807	+	0.539807i
$803$	−6.33976e25	+	6.33976e25i	−0.456702	+	0.456702i
$804$		0			0
$805$	−1.86921e26	−	1.78797e26i	−1.31673	−	1.25950i
$806$	−6.02753e24			−0.0419879
$807$		0			0
$808$	2.50056e25	−	2.50056e25i	0.170347	−	0.170347i
$809$		−	5.06925e25i		−	0.341513i	−0.985313	−	0.170756i	$-0.945379\pi$
$809$		−	5.06925e25i		−	0.341513i	0.985313	−	0.170756i	$-0.0546211\pi$
$810$		0			0
$811$	−2.63052e26			−1.73322			−0.866611	−	0.498984i	$-0.833706\pi$
$811$	−2.63052e26			−1.73322			−0.866611	+	0.498984i	$0.833706\pi$
$812$	−9.07763e25	−	9.07763e25i	−0.591518	−	0.591518i
$813$		0			0
$814$		−	6.18592e25i		−	0.394262i
$815$	−1.00086e26	+	2.22338e24i	−0.630890	+	0.0140151i
$816$		0			0
$817$	1.08388e25	+	1.08388e25i	0.0668317	+	0.0668317i
$818$	−3.42972e25	+	3.42972e25i	−0.209160	+	0.209160i
$819$		0			0
$820$	5.48706e24	−	5.73639e24i	0.0327352	−	0.0342227i
$821$	9.04333e25			0.533629			0.266815	−	0.963748i	$-0.414029\pi$
$821$	9.04333e25			0.533629			0.266815	+	0.963748i	$0.414029\pi$
$822$		0			0
$823$	−1.31996e26	+	1.31996e26i	−0.762015	+	0.762015i	−0.976686	−	0.214671i	$-0.931132\pi$
$823$	−1.31996e26	+	1.31996e26i	−0.762015	+	0.762015i	0.214671	+	0.976686i	$0.431132\pi$
$824$		−	4.77282e25i		−	0.272540i
$825$		0			0
$826$	2.12541e26			1.18747
$827$	1.60765e26	+	1.60765e26i	0.888467	+	0.888467i	0.994376	−	0.105909i	$-0.0337751\pi$
$827$	1.60765e26	+	1.60765e26i	0.888467	+	0.888467i	−0.105909	+	0.994376i	$0.533775\pi$
$828$		0			0
$829$			1.35977e26i			0.735315i	0.929961	+	0.367657i	$0.119840\pi$
$829$			1.35977e26i			0.735315i	−0.929961	+	0.367657i	$0.880160\pi$
$830$	−7.55265e25	−	7.22438e25i	−0.404014	−	0.386454i
$831$		0			0
$832$	1.69876e25	+	1.69876e25i	0.0889245	+	0.0889245i
$833$	−2.88032e26	+	2.88032e26i	−1.49154	+	1.49154i
$834$		0			0
$835$	−6.68875e24	−	3.01094e26i	−0.0338974	−	1.52589i
$836$	6.31698e25			0.316703
$837$		0			0
$838$	2.19012e25	−	2.19012e25i	0.107466	−	0.107466i
$839$			1.90581e26i			0.925170i	0.886575	+	0.462585i	$0.153078\pi$
$839$			1.90581e26i			0.925170i	−0.886575	+	0.462585i	$0.846922\pi$
$840$		0			0
$841$	5.73014e25			0.272271
$842$	1.47238e26	+	1.47238e26i	0.692169	+	0.692169i
$843$		0			0
$844$		−	5.96791e25i		−	0.274625i
$845$	1.84756e24	−	1.93151e24i	0.00841179	−	0.00879401i
$846$		0			0
$847$	1.16275e26	+	1.16275e26i	0.518244	+	0.518244i
$848$	2.64463e25	−	2.64463e25i	0.116628	−	0.116628i
$849$		0			0
$850$	−1.21249e26	+	5.38971e24i	−0.523490	+	0.0232699i
$851$	−1.53222e26			−0.654568
$852$		0			0
$853$	1.58243e26	−	1.58243e26i	0.661888	−	0.661888i	−0.293937	−	0.955825i	$-0.594966\pi$
$853$	1.58243e26	−	1.58243e26i	0.661888	−	0.661888i	0.955825	+	0.293937i	$0.0949656\pi$
$854$		−	4.32754e26i		−	1.79110i
$855$		0			0
$856$	−8.03238e25			−0.325522
$857$	−1.46919e26	−	1.46919e26i	−0.589184	−	0.589184i	0.348226	−	0.937410i	$-0.386784\pi$
$857$	−1.46919e26	−	1.46919e26i	−0.589184	−	0.589184i	−0.937410	+	0.348226i	$0.886784\pi$
$858$		0			0
$859$		−	1.60726e26i		−	0.631171i	−0.948897	−	0.315586i	$-0.897799\pi$
$859$		−	1.60726e26i		−	0.631171i	0.948897	−	0.315586i	$-0.102201\pi$
$860$	−3.37441e23	−	1.51899e25i	−0.00131133	−	0.0590295i
$861$		0			0
$862$	1.59787e26	+	1.59787e26i	0.608103	+	0.608103i
$863$	1.43158e26	−	1.43158e26i	0.539160	−	0.539160i	−0.384122	−	0.923282i	$-0.625496\pi$
$863$	1.43158e26	−	1.43158e26i	0.539160	−	0.539160i	0.923282	+	0.384122i	$0.125496\pi$
$864$		0			0
$865$	−5.14097e26	+	1.14206e25i	−1.89627	+	0.0421252i
$866$	1.74472e26			0.636889
$867$		0			0
$868$	1.14465e25	−	1.14465e25i	0.0409257	−	0.0409257i
$869$		−	2.69131e26i		−	0.952326i
$870$		0			0
$871$	1.22562e26			0.424808
$872$	5.59835e24	+	5.59835e24i	0.0192049	+	0.0192049i
$873$		0			0
$874$		−	1.56468e26i		−	0.525803i
$875$	5.88350e26	−	3.92619e25i	1.95688	−	0.130587i
$876$		0			0
$877$	−1.59099e26	−	1.59099e26i	−0.518406	−	0.518406i	0.398683	−	0.917089i	$-0.369467\pi$
$877$	−1.59099e26	−	1.59099e26i	−0.518406	−	0.518406i	−0.917089	+	0.398683i	$0.869467\pi$
$878$	−1.59916e26	+	1.59916e26i	−0.515754	+	0.515754i
$879$		0			0
$880$	−4.52476e25	−	4.32810e25i	−0.142972	−	0.136758i
$881$	9.35636e25			0.292633			0.146317	−	0.989238i	$-0.453258\pi$
$881$	9.35636e25			0.292633			0.146317	+	0.989238i	$0.453258\pi$
$882$		0			0
$883$	−8.18140e25	+	8.18140e25i	−0.250716	+	0.250716i	−0.821264	−	0.570548i	$-0.806731\pi$
$883$	−8.18140e25	+	8.18140e25i	−0.250716	+	0.250716i	0.570548	+	0.821264i	$0.306731\pi$
$884$		−	1.22891e26i		−	0.372777i
$885$		0			0
$886$	−1.13165e26			−0.336365
$887$	−3.44366e25	−	3.44366e25i	−0.101323	−	0.101323i	0.654628	−	0.755951i	$-0.272825\pi$
$887$	−3.44366e25	−	3.44366e25i	−0.101323	−	0.101323i	−0.755951	+	0.654628i	$0.772825\pi$
$888$		0			0
$889$		−	2.85165e26i		−	0.822206i
$890$	−1.57476e26	+	3.49830e24i	−0.449475	+	0.00998498i
$891$		0			0
$892$	−2.06173e26	−	2.06173e26i	−0.576697	−	0.576697i
$893$	3.15543e26	−	3.15543e26i	0.873766	−	0.873766i
$894$		0			0
$895$	5.93263e25	−	6.20220e25i	0.161005	−	0.168321i
$896$	−6.45202e25			−0.173350
$897$		0			0
$898$	7.91537e25	−	7.91537e25i	0.208441	−	0.208441i
$899$		−	1.93123e25i		−	0.0503498i
$900$		0			0
$901$	−1.91317e26			−0.488912
$902$	−1.48131e25	−	1.48131e25i	−0.0374788	−	0.0374788i
$903$		0			0
$904$			1.06438e26i			0.263985i
$905$	−2.01860e26	−	1.93086e26i	−0.495692	−	0.474148i
$906$		0			0
$907$	−7.88728e25	−	7.88728e25i	−0.189872	−	0.189872i	0.605769	−	0.795641i	$-0.292866\pi$
$907$	−7.88728e25	−	7.88728e25i	−0.189872	−	0.189872i	−0.795641	+	0.605769i	$0.792866\pi$
$908$	−2.36311e26	+	2.36311e26i	−0.563263	+	0.563263i
$909$		0			0
$910$	1.32601e25	+	5.96905e26i	0.0309867	+	1.39487i
$911$	4.54580e26			1.05183			0.525915	−	0.850537i	$-0.323723\pi$
$911$	4.54580e26			1.05183			0.525915	+	0.850537i	$0.323723\pi$
$912$		0			0
$913$	−1.95032e26	+	1.95032e26i	−0.442454	+	0.442454i
$914$		−	9.59950e25i		−	0.215642i
$915$		0			0
$916$	9.57581e24			0.0210919
$917$	−9.55913e25	−	9.55913e25i	−0.208494	−	0.208494i
$918$		0			0
$919$			2.23707e26i			0.478453i	0.970964	+	0.239226i	$0.0768938\pi$
$919$			2.23707e26i			0.478453i	−0.970964	+	0.239226i	$0.923106\pi$
$920$	−1.07205e26	+	1.12076e26i	−0.227051	+	0.237368i
$921$		0			0
$922$	2.22246e26	+	2.22246e26i	0.461589	+	0.461589i
$923$	−2.19375e26	+	2.19375e26i	−0.451203	+	0.451203i
$924$		0			0
$925$	2.35772e26	−	2.57708e26i	0.475572	−	0.519819i
$926$	6.07631e26			1.21378
$927$		0			0
$928$	−5.44285e25	+	5.44285e25i	−0.106634	+	0.106634i
$929$			1.31862e26i			0.255846i	0.991784	+	0.127923i	$0.0408310\pi$
$929$			1.31862e26i			0.255846i	−0.991784	+	0.127923i	$0.959169\pi$
$930$		0			0
$931$	1.19712e27			2.27819
$932$	−5.74766e25	−	5.74766e25i	−0.108330	−	0.108330i
$933$		0			0
$934$			1.02251e26i			0.189036i
$935$	7.11350e24	+	3.20215e26i	0.0130250	+	0.586323i
$936$		0			0
$937$	5.00992e26	+	5.00992e26i	0.899859	+	0.899859i	0.995423	−	0.0955640i	$-0.0304655\pi$
$937$	5.00992e26	+	5.00992e26i	0.899859	+	0.899859i	−0.0955640	+	0.995423i	$0.530465\pi$
$938$	−2.32750e26	+	2.32750e26i	−0.414061	+	0.414061i
$939$		0			0
$940$	−4.42214e26	+	9.82369e24i	−0.771760	+	0.0171445i
$941$	−1.15880e26			−0.200310			−0.100155	−	0.994972i	$-0.531934\pi$
$941$	−1.15880e26			−0.200310			−0.100155	+	0.994972i	$0.531934\pi$
$942$		0			0
$943$	−3.66912e25	+	3.66912e25i	−0.0622238	+	0.0622238i
$944$		−	1.27437e26i		−	0.214067i
$945$		0			0
$946$	−4.00962e25			−0.0660820
$947$	6.16018e26	+	6.16018e26i	1.00564	+	1.00564i	0.999984	+	0.00565821i	$0.00180107\pi$
$947$	6.16018e26	+	6.16018e26i	1.00564	+	1.00564i	0.00565821	+	0.999984i	$0.498199\pi$
$948$		0			0
$949$		−	5.12600e26i		−	0.821075i
$950$	2.63168e26	+	2.40767e26i	0.417562	+	0.382019i
$951$		0			0
$952$	2.33374e26	+	2.33374e26i	0.363346	+	0.363346i
$953$	−1.81409e25	+	1.81409e25i	−0.0279783	+	0.0279783i	−0.720958	−	0.692979i	$-0.756298\pi$
$953$	−1.81409e25	+	1.81409e25i	−0.0279783	+	0.0279783i	0.692979	+	0.720958i	$0.256298\pi$
$954$		0			0
$955$	6.55162e26	+	6.26686e26i	0.991558	+	0.948461i
$956$	−4.88034e26			−0.731693
$957$		0			0
$958$	2.46531e26	−	2.46531e26i	0.362729	−	0.362729i
$959$		−	1.84448e27i		−	2.68847i
$960$		0			0
$961$	−6.96618e26			−0.996516
$962$	2.50081e26	+	2.50081e26i	0.354409	+	0.354409i
$963$		0			0
$964$		−	6.44498e26i		−	0.896455i
$965$	−4.31400e25	+	9.58346e23i	−0.0594476	+	0.00132062i
$966$		0			0
$967$	−2.57685e26	−	2.57685e26i	−0.348539	−	0.348539i	0.511026	−	0.859565i	$-0.329266\pi$
$967$	−2.57685e26	−	2.57685e26i	−0.348539	−	0.348539i	−0.859565	+	0.511026i	$0.829266\pi$
$968$	6.97171e25	−	6.97171e25i	0.0934246	−	0.0934246i
$969$		0			0
$970$	−1.87054e26	+	1.95553e26i	−0.246048	+	0.257229i
$971$	−1.04824e27			−1.36612			−0.683060	−	0.730363i	$-0.739351\pi$
$971$	−1.04824e27			−1.36612			−0.683060	+	0.730363i	$0.739351\pi$
$972$		0			0
$973$	1.67725e27	−	1.67725e27i	2.14577	−	2.14577i
$974$		−	4.28870e26i		−	0.543620i
$975$		0			0
$976$	−2.59475e26			−0.322884
$977$	−3.28018e26	−	3.28018e26i	−0.404433	−	0.404433i	0.475359	−	0.879792i	$-0.342318\pi$
$977$	−3.28018e26	−	3.28018e26i	−0.404433	−	0.404433i	−0.879792	+	0.475359i	$0.842318\pi$
$978$		0			0
$979$			4.15684e26i			0.503175i
$980$	−8.57479e26	−	8.20210e26i	−1.02846	−	0.983763i
$981$		0			0
$982$	−5.26013e26	−	5.26013e26i	−0.619431	−	0.619431i
$983$	9.76584e26	−	9.76584e26i	1.13954	−	1.13954i	0.151003	−	0.988533i	$-0.451750\pi$
$983$	9.76584e26	−	9.76584e26i	1.13954	−	1.13954i	0.988533	−	0.151003i	$-0.0482502\pi$
$984$		0			0
$985$	1.10828e25	+	4.98893e26i	0.0126976	+	0.571585i
$986$	3.93744e26			0.447015
$987$		0			0
$988$	−2.55379e26	+	2.55379e26i	−0.284690	+	0.284690i
$989$			9.93163e25i			0.109712i
$990$		0			0
$991$	6.65031e26			0.721405			0.360703	−	0.932681i	$-0.382537\pi$
$991$	6.65031e26			0.721405			0.360703	+	0.932681i	$0.382537\pi$
$992$	−6.86322e24	−	6.86322e24i	−0.00737773	−	0.00737773i
$993$		0			0
$994$		−	8.33203e26i		−	0.879576i
$995$	5.18014e26	−	5.41552e26i	0.541918	−	0.566542i
$996$		0			0
$997$	3.18035e26	+	3.18035e26i	0.326752	+	0.326752i	0.851350	−	0.524598i	$-0.175784\pi$
$997$	3.18035e26	+	3.18035e26i	0.326752	+	0.326752i	−0.524598	+	0.851350i	$0.675784\pi$
$998$	1.25722e25	−	1.25722e25i	0.0128008	−	0.0128008i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.19.g.b.37.4		10
3.2	odd	2		10.19.c.b.7.1	yes	10
5.3	odd	4	inner	90.19.g.b.73.4		10
15.2	even	4		50.19.c.d.43.5		10
15.8	even	4		10.19.c.b.3.1	✓	10
15.14	odd	2		50.19.c.d.7.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.19.c.b.3.1	✓	10	15.8	even	4
10.19.c.b.7.1	yes	10	3.2	odd	2
50.19.c.d.7.5		10	15.14	odd	2
50.19.c.d.43.5		10	15.2	even	4
90.19.g.b.37.4		10	1.1	even	1	trivial
90.19.g.b.73.4		10	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	90.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(256.000 + 256.000i) q^{2} +131072. i q^{4} +(1.41140e6 + 1.35005e6i) q^{5} +(-5.59623e7 - 5.59623e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +O(q^{10})\)	\(q+(256.000 + 256.000i) q^{2} +131072. i q^{4} +(1.41140e6 + 1.35005e6i) q^{5} +(-5.59623e7 - 5.59623e7i) q^{7} +(-3.35544e7 + 3.35544e7i) q^{8} +(1.57043e7 + 7.06932e8i) q^{10} +1.86606e9 q^{11} +(-7.54400e9 + 7.54400e9i) q^{13} -2.86527e10i q^{14} -1.71799e10 q^{16} +(6.21409e10 + 6.21409e10i) q^{17} -2.58270e11i q^{19} +(-1.76954e11 + 1.84995e11i) q^{20} +(4.77712e11 + 4.77712e11i) q^{22} +(1.18327e12 - 1.18327e12i) q^{23} +(1.69402e11 + 3.81093e12i) q^{25} -3.86253e12 q^{26} +(7.33509e12 - 7.33509e12i) q^{28} -1.23756e13i q^{29} +1.56051e12 q^{31} +(-4.39805e12 - 4.39805e12i) q^{32} +3.18162e13i q^{34} +(-3.43301e12 - 1.54537e14i) q^{35} +(-6.47453e13 - 6.47453e13i) q^{37} +(6.61170e13 - 6.61170e13i) q^{38} +(-9.26590e13 + 2.05840e12i) q^{40} -3.10084e13 q^{41} +(-4.19670e13 + 4.19670e13i) q^{43} +2.44588e14i q^{44} +6.05833e14 q^{46} +(1.22176e15 + 1.22176e15i) q^{47} +4.63515e15i q^{49} +(-9.32232e14 + 1.01897e15i) q^{50} +(-9.88807e14 - 9.88807e14i) q^{52} +(-1.53938e15 + 1.53938e15i) q^{53} +(2.63376e15 + 2.51929e15i) q^{55} +3.75557e15 q^{56} +(3.16816e15 - 3.16816e15i) q^{58} +7.41783e15i q^{59} +1.51034e16 q^{61} +(3.99492e14 + 3.99492e14i) q^{62} -2.25180e15i q^{64} +(-2.08324e16 + 4.62787e14i) q^{65} +(-8.12314e15 - 8.12314e15i) q^{67} +(-8.14493e15 + 8.14493e15i) q^{68} +(3.86827e16 - 4.04404e16i) q^{70} +2.90794e16 q^{71} +(-3.39740e16 + 3.39740e16i) q^{73} -3.31496e16i q^{74} +3.38519e16 q^{76} +(-1.04429e17 - 1.04429e17i) q^{77} -1.44224e17i q^{79} +(-2.42477e16 - 2.31938e16i) q^{80} +(-7.93814e15 - 7.93814e15i) q^{82} +(-1.04515e17 + 1.04515e17i) q^{83} +(3.81204e15 + 1.71599e17i) q^{85} -2.14871e16 q^{86} +(-6.26146e16 + 6.26146e16i) q^{88} +2.22760e17i q^{89} +8.44360e17 q^{91} +(1.55093e17 + 1.55093e17i) q^{92} +6.25540e17i q^{94} +(3.48678e17 - 3.64522e17i) q^{95} +(2.70611e17 + 2.70611e17i) q^{97} +(-1.18660e18 + 1.18660e18i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2560 q^{2} + 1436130 q^{5} - 71828530 q^{7} - 335544320 q^{8}+O(q^{10}) \) 10 * q + 2560 * q^2 + 1436130 * q^5 - 71828530 * q^7 - 335544320 * q^8	\( 10 q + 2560 q^{2} + 1436130 q^{5} - 71828530 q^{7} - 335544320 q^{8} + 280000000 q^{10} + 4684617380 q^{11} - 11858528670 q^{13} - 171798691840 q^{16} - 57425096770 q^{17} - 44876431360 q^{20} + 1199262049280 q^{22} + 2409849379970 q^{23} - 9628701268750 q^{25} - 6071566679040 q^{26} + 9414709084160 q^{28} + 44076891672220 q^{31} - 43980465111040 q^{32} + 92680242801650 q^{35} + 285126548071770 q^{37} + 268015571763200 q^{38} - 59676892856320 q^{40} - 223001245455820 q^{41} - 674098663802370 q^{43} + 12\!\cdots\!40 q^{46}+ \cdots - 14\!\cdots\!40 q^{98}+O(q^{100}) \) 10 * q + 2560 * q^2 + 1436130 * q^5 - 71828530 * q^7 - 335544320 * q^8 + 280000000 * q^10 + 4684617380 * q^11 - 11858528670 * q^13 - 171798691840 * q^16 - 57425096770 * q^17 - 44876431360 * q^20 + 1199262049280 * q^22 + 2409849379970 * q^23 - 9628701268750 * q^25 - 6071566679040 * q^26 + 9414709084160 * q^28 + 44076891672220 * q^31 - 43980465111040 * q^32 + 92680242801650 * q^35 + 285126548071770 * q^37 + 268015571763200 * q^38 - 59676892856320 * q^40 - 223001245455820 * q^41 - 674098663802370 * q^43 + 1233842882544640 * q^46 + 3332242844984130 * q^47 - 5679798331686400 * q^50 - 1554321069834240 * q^52 + 7587444943731670 * q^53 + 27897159618275340 * q^55 + 4820331051089920 * q^56 - 10419344591360000 * q^58 + 64704780211083420 * q^61 + 11283684268088320 * q^62 - 72228906553534170 * q^65 - 108403906097814130 * q^67 + 7526822283837440 * q^68 + 42813790750842880 * q^70 - 194380424551175420 * q^71 - 233767444023094070 * q^73 + 137223972742758400 * q^76 - 52847385951118940 * q^77 - 24672525531217920 * q^80 - 57088318836689920 * q^82 + 114013237779502770 * q^83 + 484088104672899650 * q^85 - 345138515866813440 * q^86 - 157189675323228160 * q^88 + 1337663581494821820 * q^91 + 315863777931427840 * q^92 + 930275560132279600 * q^95 + 853540105740755370 * q^97 - 1479412917644362240 * q^98

Introduction

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