LMFDB - Embedded newform 5.18.b.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,18,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.16110436723$
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} + 203459x^{6} + 12362849196x^{4} + 237701205446144x^{2} + 1320400799499206656 $ x^8 + 203459x^6 + 12362849196x^4 + 237701205446144*x^2 + 1320400799499206656
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.1
Root			$-330.281i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.18.b.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +O(q^{10})$	\(q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +(5.76808e8 + 1.39958e7i) q^{10} -3.40136e8 q^{11} +3.45238e9i q^{12} +6.20461e8i q^{13} -1.56596e10 q^{14} +(9.87532e9 + 2.39618e8i) q^{15} +3.59979e10 q^{16} -9.78165e9i q^{17} -8.19675e8i q^{18} -3.92941e10 q^{19} +(6.46800e9 - 2.66565e11i) q^{20} -2.68102e11 q^{21} +2.24681e11i q^{22} +2.44514e11i q^{23} +1.30135e12 q^{24} +(-7.62042e11 - 3.70026e10i) q^{25} +4.09853e11 q^{26} -1.47451e12i q^{27} +7.23689e12i q^{28} -3.98521e12 q^{29} +(1.58282e11 - 6.52327e12i) q^{30} +2.84863e12 q^{31} -8.69651e12i q^{32} +3.84668e12i q^{33} -6.46139e12 q^{34} +(2.07006e13 + 5.02286e11i) q^{35} -3.78802e11 q^{36} -2.87331e13i q^{37} +2.59562e13i q^{38} +7.01695e12 q^{39} +(-1.00479e14 - 2.43806e12i) q^{40} +2.58650e13 q^{41} +1.77098e14i q^{42} -7.92427e13i q^{43} +1.03833e14 q^{44} +(-2.62913e10 + 1.08354e12i) q^{45} +1.61517e14 q^{46} -3.42344e13i q^{47} -4.07109e14i q^{48} -3.29366e14 q^{49} +(-2.44425e13 + 5.03376e14i) q^{50} -1.10623e14 q^{51} -1.89408e14i q^{52} -6.28298e14i q^{53} -9.74008e14 q^{54} +(7.20671e12 - 2.97009e14i) q^{55} +2.72788e15 q^{56} +4.44388e14i q^{57} +2.63248e15i q^{58} +1.43672e15 q^{59} +(-3.01465e15 - 7.31483e13i) q^{60} -1.41408e15 q^{61} -1.88170e15i q^{62} -2.94167e13i q^{63} -1.02627e15 q^{64} +(-5.41791e14 - 1.31462e13i) q^{65} +2.54097e15 q^{66} +3.52003e14i q^{67} +2.98605e15i q^{68} +2.76527e15 q^{69} +(3.31792e14 - 1.36741e16i) q^{70} +5.76817e15 q^{71} +1.42786e14i q^{72} +1.24525e15i q^{73} -1.89800e16 q^{74} +(-4.18472e14 + 8.61812e15i) q^{75} +1.19953e16 q^{76} +8.06341e15i q^{77} -4.63513e15i q^{78} -8.16669e15 q^{79} +(-7.62714e14 + 3.14336e16i) q^{80} -1.65154e16 q^{81} -1.70854e16i q^{82} -2.09840e16i q^{83} +8.18438e16 q^{84} +(8.54140e15 + 2.07251e14i) q^{85} -5.23447e16 q^{86} +4.50697e16i q^{87} -3.91391e16i q^{88} -2.91132e16 q^{89} +(7.15746e14 + 1.73671e13i) q^{90} +1.47089e16 q^{91} -7.46430e16i q^{92} -3.22159e16i q^{93} -2.26140e16 q^{94} +(8.32554e14 - 3.43119e16i) q^{95} -9.83511e16 q^{96} +4.58585e16i q^{97} +2.17567e17i q^{98} -4.22065e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9}+O(q^{10}) $ 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9	$ 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9} + 329570200 q^{10} + 463296576 q^{11} - 29937907992 q^{14} + 30646226400 q^{15} + 30848001568 q^{16} - 20615713280 q^{19} - 47558579400 q^{20} - 75039699024 q^{21} + 1768741136160 q^{24} - 1789249435000 q^{25} - 838901194224 q^{26} - 4079017824720 q^{29} + 2416984007400 q^{30} + 11329328658496 q^{31} - 36406243632832 q^{34} + 4019663899200 q^{35} + 59729752432728 q^{36} + 40318460422272 q^{39} - 209747532172000 q^{40} + 97217252847456 q^{41} - 116357853210912 q^{44} - 366841998003600 q^{45} + 10\!\cdots\!36 q^{46}+ \cdots - 56\!\cdots\!68 q^{99}+O(q^{100}) $ 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9 + 329570200 * q^10 + 463296576 * q^11 - 29937907992 * q^14 + 30646226400 * q^15 + 30848001568 * q^16 - 20615713280 * q^19 - 47558579400 * q^20 - 75039699024 * q^21 + 1768741136160 * q^24 - 1789249435000 * q^25 - 838901194224 * q^26 - 4079017824720 * q^29 + 2416984007400 * q^30 + 11329328658496 * q^31 - 36406243632832 * q^34 + 4019663899200 * q^35 + 59729752432728 * q^36 + 40318460422272 * q^39 - 209747532172000 * q^40 + 97217252847456 * q^41 - 116357853210912 * q^44 - 366841998003600 * q^45 + 1081224261700136 * q^46 - 856574357621656 * q^49 - 1283266301910000 * q^50 + 2468309514424896 * q^51 - 3408409774777680 * q^54 - 2042713226757600 * q^55 + 8363016326678880 * q^56 - 1091409512240640 * q^59 - 11479379108104800 * q^60 + 8064731010774976 * q^61 - 3616160324265856 * q^64 - 11989509557901600 * q^65 + 27318846906958752 * q^66 - 12078989597365008 * q^69 - 13190931213697800 * q^70 + 25241492058140736 * q^71 - 29902523510328912 * q^74 + 3839235716880000 * q^75 + 20767634734678560 * q^76 + 3229852337730880 * q^79 + 1263407265391200 * q^80 - 49353541005202632 * q^81 + 101439947332382688 * q^84 + 25693702369787200 * q^85 - 165112838769552744 * q^86 + 92963987535626640 * q^89 + 206315814421823400 * q^90 - 225591670236809664 * q^91 + 162612564681867848 * q^94 + 204319715505252000 * q^95 - 654303222993538944 * q^96 - 56327331239952768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$		−	660.562i		−	1.82456i	−0.409564	−	0.912282i	$-0.634319\pi$
$2$		−	660.562i		−	1.82456i	0.409564	−	0.912282i	$-0.365681\pi$
$3$		−	11309.3i		−	0.995184i	−0.867411	−	0.497592i	$-0.834218\pi$
$3$		−	11309.3i		−	0.995184i	0.867411	−	0.497592i	$-0.165782\pi$
$4$	−305271.			−2.32903
$5$	−21187.7	+	873207.i	−0.0242571	+	0.999706i
$5$	−21187.7	+	873207.i	−0.0242571	+	0.999706i
$6$	−7.47047e6			−1.81578
$7$		−	2.37065e7i		−	1.55429i	−0.629319	−	0.777147i	$-0.716666\pi$
$7$		−	2.37065e7i		−	1.55429i	0.629319	−	0.777147i	$-0.283334\pi$
$8$			1.15069e8i			2.42490i
$9$	1.24087e6			0.00960874
$10$	5.76808e8	+	1.39958e7i	1.82403	+	0.0442587i
$11$	−3.40136e8			−0.478425			−0.239213	−	0.970967i	$-0.576889\pi$
$11$	−3.40136e8			−0.478425			−0.239213	+	0.970967i	$0.576889\pi$
$12$			3.45238e9i			2.31781i
$13$			6.20461e8i			0.210958i	0.994422	+	0.105479i	$0.0336376\pi$
$13$			6.20461e8i			0.210958i	−0.994422	+	0.105479i	$0.966362\pi$
$14$	−1.56596e10			−2.83591
$15$	9.87532e9	+	2.39618e8i	0.994891	+	0.0241403i
$16$	3.59979e10			2.09535
$17$		−	9.78165e9i		−	0.340092i	−0.985436	−	0.170046i	$-0.945608\pi$
$17$		−	9.78165e9i		−	0.340092i	0.985436	−	0.170046i	$-0.0543916\pi$
$18$		−	8.19675e8i		−	0.0175317i
$19$	−3.92941e10			−0.530789			−0.265395	−	0.964140i	$-0.585502\pi$
$19$	−3.92941e10			−0.530789			−0.265395	+	0.964140i	$0.585502\pi$
$20$	6.46800e9	−	2.66565e11i	0.0564956	−	2.32835i
$21$	−2.68102e11			−1.54681
$22$			2.24681e11i			0.872917i
$23$			2.44514e11i			0.651055i	0.945533	+	0.325527i	$0.105542\pi$
$23$			2.44514e11i			0.651055i	−0.945533	+	0.325527i	$0.894458\pi$
$24$	1.30135e12			2.41322
$25$	−7.62042e11	−	3.70026e10i	−0.998823	−	0.0485000i
$26$	4.09853e11			0.384906
$27$		−	1.47451e12i		−	1.00475i
$28$			7.23689e12i			3.62000i
$29$	−3.98521e12			−1.47934			−0.739670	−	0.672970i	$-0.765018\pi$
$29$	−3.98521e12			−1.47934			−0.739670	+	0.672970i	$0.765018\pi$
$30$	1.58282e11	−	6.52327e12i	0.0440455	−	1.81524i
$31$	2.84863e12			0.599877			0.299939	−	0.953959i	$-0.403034\pi$
$31$	2.84863e12			0.599877			0.299939	+	0.953959i	$0.403034\pi$
$32$		−	8.69651e12i		−	1.39820i
$33$			3.84668e12i			0.476121i
$34$	−6.46139e12			−0.620519
$35$	2.07006e13	+	5.02286e11i	1.55384	+	0.0377028i
$36$	−3.78802e11			−0.0223790
$37$		−	2.87331e13i		−	1.34483i	−0.740173	−	0.672417i	$-0.765256\pi$
$37$		−	2.87331e13i		−	1.34483i	0.740173	−	0.672417i	$-0.234744\pi$
$38$			2.59562e13i			0.968459i
$39$	7.01695e12			0.209942
$40$	−1.00479e14	−	2.43806e12i	−2.42419	−	0.0588212i
$41$	2.58650e13			0.505882			0.252941	−	0.967482i	$-0.418602\pi$
$41$	2.58650e13			0.505882			0.252941	+	0.967482i	$0.418602\pi$
$42$			1.77098e14i			2.82225i
$43$		−	7.92427e13i		−	1.03390i	−0.856016	−	0.516949i	$-0.827068\pi$
$43$		−	7.92427e13i		−	1.03390i	0.856016	−	0.516949i	$-0.172932\pi$
$44$	1.03833e14			1.11427
$45$	−2.62913e10	+	1.08354e12i	−0.000233081	+	0.00960591i
$46$	1.61517e14			1.18789
$47$		−	3.42344e13i		−	0.209716i	−0.994487	−	0.104858i	$-0.966561\pi$
$47$		−	3.42344e13i		−	0.209716i	0.994487	−	0.104858i	$-0.0334388\pi$
$48$		−	4.07109e14i		−	2.08526i
$49$	−3.29366e14			−1.41583
$50$	−2.44425e13	+	5.03376e14i	−0.0884913	+	1.82242i
$51$	−1.10623e14			−0.338454
$52$		−	1.89408e14i		−	0.491327i
$53$		−	6.28298e14i		−	1.38618i	−0.720850	−	0.693091i	$-0.756248\pi$
$53$		−	6.28298e14i		−	1.38618i	0.720850	−	0.693091i	$-0.243752\pi$
$54$	−9.74008e14			−1.83322
$55$	7.20671e12	−	2.97009e14i	0.0116052	−	0.478285i
$56$	2.72788e15			3.76901
$57$			4.44388e14i			0.528233i
$58$			2.63248e15i			2.69915i
$59$	1.43672e15			1.27389			0.636943	−	0.770911i	$-0.280199\pi$
$59$	1.43672e15			1.27389			0.636943	+	0.770911i	$0.280199\pi$
$60$	−3.01465e15	−	7.31483e13i	−2.31713	−	0.0562236i
$61$	−1.41408e15			−0.944428			−0.472214	−	0.881484i	$-0.656545\pi$
$61$	−1.41408e15			−0.944428			−0.472214	+	0.881484i	$0.656545\pi$
$62$		−	1.88170e15i		−	1.09451i
$63$		−	2.94167e13i		−	0.0149348i
$64$	−1.02627e15			−0.455757
$65$	−5.41791e14	−	1.31462e13i	−0.210896	−	0.00511724i
$66$	2.54097e15			0.868713
$67$			3.52003e14i			0.105904i	0.998597	+	0.0529518i	$0.0168630\pi$
$67$			3.52003e14i			0.105904i	−0.998597	+	0.0529518i	$0.983137\pi$
$68$			2.98605e15i			0.792084i
$69$	2.76527e15			0.647919
$70$	3.31792e14	−	1.36741e16i	0.0687910	−	2.83507i
$71$	5.76817e15			1.06009			0.530044	−	0.847970i	$-0.322175\pi$
$71$	5.76817e15			1.06009			0.530044	+	0.847970i	$0.322175\pi$
$72$			1.42786e14i			0.0233002i
$73$			1.24525e15i			0.180723i	0.995909	+	0.0903613i	$0.0288022\pi$
$73$			1.24525e15i			0.180723i	−0.995909	+	0.0903613i	$0.971198\pi$
$74$	−1.89800e16			−2.45373
$75$	−4.18472e14	+	8.61812e15i	−0.0482664	+	0.994013i
$76$	1.19953e16			1.23622
$77$			8.06341e15i			0.743614i
$78$		−	4.63513e15i		−	0.383052i
$79$	−8.16669e15			−0.605642			−0.302821	−	0.953048i	$-0.597928\pi$
$79$	−8.16669e15			−0.605642			−0.302821	+	0.953048i	$0.597928\pi$
$80$	−7.62714e14	+	3.14336e16i	−0.0508273	+	2.09474i
$81$	−1.65154e16			−0.990299
$82$		−	1.70854e16i		−	0.923013i
$83$		−	2.09840e16i		−	1.02264i	−0.859389	−	0.511322i	$-0.829156\pi$
$83$		−	2.09840e16i		−	1.02264i	0.859389	−	0.511322i	$-0.170844\pi$
$84$	8.18438e16			3.60257
$85$	8.54140e15	+	2.07251e14i	0.339992	+	0.00824966i
$86$	−5.23447e16			−1.88641
$87$			4.50697e16i			1.47222i
$88$		−	3.91391e16i		−	1.16013i
$89$	−2.91132e16			−0.783926			−0.391963	−	0.919981i	$-0.628204\pi$
$89$	−2.91132e16			−0.783926			−0.391963	+	0.919981i	$0.628204\pi$
$90$	7.15746e14	+	1.73671e13i	0.0175266	+	0.000425270i
$91$	1.47089e16			0.327891
$92$		−	7.46430e16i		−	1.51633i
$93$		−	3.22159e16i		−	0.596988i
$94$	−2.26140e16			−0.382640
$95$	8.32554e14	−	3.43119e16i	0.0128754	−	0.530633i
$96$	−9.83511e16			−1.39147
$97$			4.58585e16i			0.594100i	0.954862	+	0.297050i	$0.0960029\pi$
$97$			4.58585e16i			0.594100i	−0.954862	+	0.297050i	$0.903997\pi$
$98$			2.17567e17i			2.58327i
$99$	−4.22065e14			−0.00459706
$100$	2.32629e17	+	1.12958e16i	2.32629	+	0.112958i
$101$	1.53390e17			1.40950			0.704752	−	0.709454i	$-0.251058\pi$
$101$	1.53390e17			1.40950			0.704752	+	0.709454i	$0.251058\pi$
$102$			7.30735e16i			0.617531i
$103$		−	1.35527e17i		−	1.05416i	−0.849815	−	0.527082i	$-0.823286\pi$
$103$		−	1.35527e17i		−	1.05416i	0.849815	−	0.527082i	$-0.176714\pi$
$104$	−7.13958e16			−0.511552
$105$	5.68049e15	−	2.34109e17i	0.0375212	−	1.54635i
$106$	−4.15030e17			−2.52918
$107$			1.40345e17i			0.789649i	0.918757	+	0.394824i	$0.129195\pi$
$107$			1.40345e17i			0.789649i	−0.918757	+	0.394824i	$0.870805\pi$
$108$			4.50125e17i			2.34009i
$109$	2.67560e17			1.28616			0.643081	−	0.765798i	$-0.277656\pi$
$109$	2.67560e17			1.28616			0.643081	+	0.765798i	$0.277656\pi$
$110$	−1.96193e17	−	4.76048e15i	−0.872660	−	0.0211745i
$111$	−3.24950e17			−1.33836
$112$		−	8.53382e17i		−	3.25680i
$113$			9.95662e16i			0.352326i	0.984361	+	0.176163i	$0.0563687\pi$
$113$			9.95662e16i			0.352326i	−0.984361	+	0.176163i	$0.943631\pi$
$114$	2.93546e17			0.963795
$115$	−2.13512e17	−	5.18070e15i	−0.650863	−	0.0157927i
$116$	1.21657e18			3.44543
$117$			7.69913e14i			0.00202704i
$118$		−	9.49044e17i		−	2.32428i
$119$	−2.31888e17			−0.528603
$120$	−2.75726e16	+	1.13634e18i	−0.0585379	+	2.41251i
$121$	−3.89755e17			−0.771109
$122$			9.34085e17i			1.72317i
$123$		−	2.92513e17i		−	0.503445i
$124$	−8.69605e17			−1.39713
$125$	4.84569e16	−	6.64636e17i	0.0727143	−	0.997353i
$126$	−1.94316e16			−0.0272495
$127$			1.33130e18i			1.74559i	0.488084	+	0.872797i	$0.337696\pi$
$127$			1.33130e18i			1.74559i	−0.488084	+	0.872797i	$0.662304\pi$
$128$		−	4.61951e17i		−	0.566645i
$129$	−8.96176e17			−1.02892
$130$	−8.68386e15	+	3.57886e17i	−0.00933672	+	0.384793i
$131$	1.65183e18			1.66402			0.832010	−	0.554760i	$-0.187190\pi$
$131$	1.65183e18			1.66402			0.832010	+	0.554760i	$0.187190\pi$
$132$		−	1.17428e18i		−	1.10890i
$133$			9.31525e17i			0.825003i
$134$	2.32520e17			0.193228
$135$	1.28755e18	+	3.12416e16i	1.00445	+	0.0243723i
$136$	1.12557e18			0.824689
$137$			8.57280e17i			0.590198i	0.955467	+	0.295099i	$0.0953527\pi$
$137$			8.57280e17i			0.590198i	−0.955467	+	0.295099i	$0.904647\pi$
$138$		−	1.82664e18i		−	1.18217i
$139$	1.70531e18			1.03795			0.518976	−	0.854789i	$-0.326313\pi$
$139$	1.70531e18			1.03795			0.518976	+	0.854789i	$0.326313\pi$
$140$	−6.31930e18	−	1.53333e17i	−3.61893	−	0.0878109i
$141$	−3.87166e17			−0.208706
$142$		−	3.81024e18i		−	1.93420i
$143$		−	2.11041e17i		−	0.100928i
$144$	4.46688e16			0.0201337
$145$	8.44376e16	−	3.47991e18i	0.0358846	−	1.47890i
$146$	8.22566e17			0.329740
$147$			3.72488e18i			1.40901i
$148$			8.77139e18i			3.13216i
$149$	−1.88380e18			−0.635259			−0.317629	−	0.948215i	$-0.602887\pi$
$149$	−1.88380e18			−0.635259			−0.317629	+	0.948215i	$0.602887\pi$
$150$	5.69281e18	+	2.76427e17i	1.81364	+	0.0880652i
$151$	−3.21839e18			−0.969024			−0.484512	−	0.874785i	$-0.661003\pi$
$151$	−3.21839e18			−0.969024			−0.484512	+	0.874785i	$0.661003\pi$
$152$		−	4.52154e18i		−	1.28711i
$153$		−	1.21378e16i		−	0.00326785i
$154$	5.32638e18			1.35677
$155$	−6.03561e16	+	2.48745e18i	−0.0145513	+	0.599701i
$156$	−2.14207e18			−0.488961
$157$		−	5.70488e18i		−	1.23339i	−0.787204	−	0.616693i	$-0.788472\pi$
$157$		−	5.70488e18i		−	1.23339i	0.787204	−	0.616693i	$-0.211528\pi$
$158$			5.39461e18i			1.10503i
$159$	−7.10558e18			−1.37951
$160$	7.59386e18	+	1.84259e17i	1.39779	+	0.0339164i
$161$	5.79657e18			1.01193
$162$			1.09094e19i			1.80686i
$163$		−	2.76799e18i		−	0.435080i	−0.976051	−	0.217540i	$-0.930197\pi$
$163$		−	2.76799e18i		−	0.435080i	0.976051	−	0.217540i	$-0.0698033\pi$
$164$	−7.89581e18			−1.17821
$165$	−3.35895e18	−	8.15025e16i	−0.475981	−	0.0115493i
$166$	−1.38613e19			−1.86588
$167$		−	2.96598e18i		−	0.379384i	−0.981844	−	0.189692i	$-0.939251\pi$
$167$		−	2.96598e18i		−	0.379384i	0.981844	−	0.189692i	$-0.0607489\pi$
$168$		−	3.08503e19i		−	3.75086i
$169$	8.26544e18			0.955497
$170$	1.36902e17	−	5.64213e18i	0.0150520	−	0.620336i
$171$	−4.87591e16			−0.00510021
$172$			2.41905e19i			2.40798i
$173$		−	1.22679e19i		−	1.16246i	−0.813740	−	0.581228i	$-0.802572\pi$
$173$		−	1.22679e19i		−	1.16246i	0.813740	−	0.581228i	$-0.197428\pi$
$174$	2.97714e19			2.68615
$175$	−8.77200e17	+	1.80653e19i	−0.0753833	+	1.55247i
$176$	−1.22442e19			−1.00247
$177$		−	1.62482e19i		−	1.26775i
$178$			1.92311e19i			1.43032i
$179$	1.05059e19			0.745048			0.372524	−	0.928023i	$-0.378492\pi$
$179$	1.05059e19			0.745048			0.372524	+	0.928023i	$0.378492\pi$
$180$	8.02597e15	−	3.30773e17i	0.000542852	−	0.0223725i
$181$	−6.36140e18			−0.410473			−0.205236	−	0.978712i	$-0.565796\pi$
$181$	−6.36140e18			−0.410473			−0.205236	+	0.978712i	$0.565796\pi$
$182$		−	9.71616e18i		−	0.598257i
$183$			1.59921e19i			0.939880i
$184$	−2.81360e19			−1.57874
$185$	2.50900e19	+	6.08791e17i	1.34444	+	0.0326218i
$186$	−2.12806e19			−1.08924
$187$			3.32709e18i			0.162709i
$188$			1.04508e19i			0.488435i
$189$	−3.49555e19			−1.56167
$190$	−2.26652e19	−	5.49954e17i	−0.968174	−	0.0234920i
$191$	2.68237e19			1.09581			0.547905	−	0.836541i	$-0.315426\pi$
$191$	2.68237e19			1.09581			0.547905	+	0.836541i	$0.315426\pi$
$192$			1.16064e19i			0.453562i
$193$		−	1.22468e19i		−	0.457916i	−0.973436	−	0.228958i	$-0.926468\pi$
$193$		−	1.22468e19i		−	0.457916i	0.973436	−	0.228958i	$-0.0735319\pi$
$194$	3.02924e19			1.08397
$195$	−1.48673e17	+	6.12725e18i	−0.00509259	+	0.209880i
$196$	1.00546e20			3.29751
$197$		−	1.20855e19i		−	0.379580i	−0.981825	−	0.189790i	$-0.939219\pi$
$197$		−	1.20855e19i		−	0.379580i	0.981825	−	0.189790i	$-0.0607807\pi$
$198$			2.78800e17i			0.00838763i
$199$	−6.55776e19			−1.89018			−0.945092	−	0.326804i	$-0.894028\pi$
$199$	−6.55776e19			−1.89018			−0.945092	+	0.326804i	$0.894028\pi$
$200$	4.25785e18	−	8.76874e19i	0.117608	−	2.42205i
$201$	3.98090e18			0.105394
$202$		−	1.01324e20i		−	2.57173i
$203$			9.44751e19i			2.29933i
$204$	3.37700e19			0.788270
$205$	−5.48020e17	+	2.25855e19i	−0.0122712	+	0.505733i
$206$	−8.95237e19			−1.92339
$207$			3.03411e17i			0.00625581i
$208$			2.23353e19i			0.442031i
$209$	1.33653e19			0.253943
$210$	−1.54644e20	−	3.75232e18i	−2.82142	−	0.0684598i
$211$	−2.90167e19			−0.508449			−0.254224	−	0.967145i	$-0.581820\pi$
$211$	−2.90167e19			−0.508449			−0.254224	+	0.967145i	$0.581820\pi$
$212$			1.91801e20i			3.22846i
$213$		−	6.52337e19i		−	1.05498i
$214$	9.27065e19			1.44076
$215$	6.91953e19	+	1.67897e18i	1.03359	+	0.0250794i
$216$	1.69671e20			2.43641
$217$		−	6.75310e19i		−	0.932386i
$218$		−	1.76740e20i		−	2.34668i
$219$	1.40829e19			0.179852
$220$	−2.20000e18	+	9.06681e19i	−0.0270289	+	1.11394i
$221$	6.06913e18			0.0717450
$222$			2.14650e20i			2.44192i
$223$			1.00403e20i			1.09940i	0.835363	+	0.549699i	$0.185258\pi$
$223$			1.00403e20i			1.09940i	−0.835363	+	0.549699i	$0.814742\pi$
$224$	−2.06163e20			−2.17322
$225$	−9.45597e17	−	4.59155e16i	−0.00959743	−	0.000466024i
$226$	6.57697e19			0.642842
$227$		−	7.25392e19i		−	0.682894i	−0.939901	−	0.341447i	$-0.889083\pi$
$227$		−	7.25392e19i		−	0.682894i	0.939901	−	0.341447i	$-0.110917\pi$
$228$		−	1.35658e20i		−	1.23027i
$229$	−1.05419e20			−0.921124			−0.460562	−	0.887628i	$-0.652352\pi$
$229$	−1.05419e20			−0.921124			−0.460562	+	0.887628i	$0.652352\pi$
$230$	−3.42218e18	+	1.41038e20i	−0.0288148	+	1.18754i
$231$	9.11912e19			0.740033
$232$		−	4.58574e20i		−	3.58725i
$233$		−	1.19870e20i		−	0.904037i	−0.892008	−	0.452019i	$-0.850704\pi$
$233$		−	1.19870e20i		−	0.904037i	0.892008	−	0.452019i	$-0.149296\pi$
$234$	5.08576e17			0.00369846
$235$	2.98937e19	+	7.25350e17i	0.209654	+	0.00508711i
$236$	−4.38589e20			−2.96692
$237$			9.23592e19i			0.602725i
$238$			1.53177e20i			0.964469i
$239$	8.27461e19			0.502766			0.251383	−	0.967888i	$-0.419115\pi$
$239$	8.27461e19			0.502766			0.251383	+	0.967888i	$0.419115\pi$
$240$	3.55491e20	+	8.62573e18i	2.08465	+	0.0505825i
$241$	8.99963e19			0.509425			0.254712	−	0.967017i	$-0.418019\pi$
$241$	8.99963e19			0.509425			0.254712	+	0.967017i	$0.418019\pi$
$242$			2.57457e20i			1.40694i
$243$		−	3.64195e18i		−	0.0192168i
$244$	4.31676e20			2.19960
$245$	6.97851e18	−	2.87604e20i	0.0343440	−	1.41541i
$246$	−1.93223e20			−0.918568
$247$		−	2.43805e19i		−	0.111974i
$248$			3.27790e20i			1.45464i
$249$	−2.37314e20			−1.01772
$250$	−4.39034e20	−	3.20088e19i	−1.81973	−	0.132672i
$251$	−5.05233e19			−0.202425			−0.101213	−	0.994865i	$-0.532272\pi$
$251$	−5.05233e19			−0.202425			−0.101213	+	0.994865i	$0.532272\pi$
$252$			8.98006e18i			0.0347836i
$253$		−	8.31680e19i		−	0.311481i
$254$	8.79404e20			3.18495
$255$	2.34386e18	−	9.65969e19i	0.00820993	−	0.338354i
$256$	−4.39663e20			−1.48964
$257$			5.06773e20i			1.66105i	0.556984	+	0.830524i	$0.311959\pi$
$257$			5.06773e20i			1.66105i	−0.556984	+	0.830524i	$0.688041\pi$
$258$			5.91980e20i			1.87733i
$259$	−6.81161e20			−2.09027
$260$	1.65393e20	+	4.01314e18i	0.491183	+	0.0119182i
$261$	−4.94514e18			−0.0142146
$262$		−	1.09114e21i		−	3.03611i
$263$		−	5.09531e19i		−	0.137261i	−0.997642	−	0.0686305i	$-0.978137\pi$
$263$		−	5.09531e19i		−	0.137261i	0.997642	−	0.0686305i	$-0.0218629\pi$
$264$	−4.42634e20			−1.15455
$265$	5.48634e20	+	1.33122e19i	1.38577	+	0.0336248i
$266$	6.15330e20			1.50527
$267$			3.29249e20i			0.780151i
$268$		−	1.07456e20i		−	0.246653i
$269$	−9.13493e19			−0.203147			−0.101574	−	0.994828i	$-0.532388\pi$
$269$	−9.13493e19			−0.203147			−0.101574	+	0.994828i	$0.532388\pi$
$270$	2.06370e19	−	8.50510e20i	0.0444688	−	1.83268i
$271$	3.85248e19			0.0804455			0.0402227	−	0.999191i	$-0.487193\pi$
$271$	3.85248e19			0.0804455			0.0402227	+	0.999191i	$0.487193\pi$
$272$		−	3.52119e20i		−	0.712612i
$273$		−	1.66347e20i		−	0.326312i
$274$	5.66287e20			1.07685
$275$	2.59197e20	+	1.25859e19i	0.477862	+	0.0232036i
$276$	−8.44157e20			−1.50902
$277$			8.52898e20i			1.47849i	0.673435	+	0.739246i	$0.264818\pi$
$277$			8.52898e20i			1.47849i	−0.673435	+	0.739246i	$0.735182\pi$
$278$		−	1.12646e21i		−	1.89381i
$279$	3.53480e18			0.00576406
$280$	−5.77976e19	+	2.38200e21i	−0.0914254	+	3.76790i
$281$	7.66403e20			1.17612			0.588062	−	0.808816i	$-0.299891\pi$
$281$	7.66403e20			1.17612			0.588062	+	0.808816i	$0.299891\pi$
$282$			2.55747e20i			0.380797i
$283$		−	6.44868e20i		−	0.931721i	−0.884858	−	0.465860i	$-0.845745\pi$
$283$		−	6.44868e20i		−	0.931721i	0.884858	−	0.465860i	$-0.154255\pi$
$284$	−1.76085e21			−2.46898
$285$	−3.88042e20	−	9.41557e18i	−0.528078	−	0.0128134i
$286$	−1.39406e20			−0.184149
$287$		−	6.13167e20i		−	0.786289i
$288$		−	1.07913e19i		−	0.0134350i
$289$	7.31560e20			0.884338
$290$	−2.29870e21	−	5.57763e19i	−2.69835	−	0.0654737i
$291$	5.18625e20			0.591239
$292$		−	3.80139e20i		−	0.420908i
$293$			1.05852e21i			1.13847i	0.822173	+	0.569237i	$0.192761\pi$
$293$			1.05852e21i			1.13847i	−0.822173	+	0.569237i	$0.807239\pi$
$294$	2.46052e21			2.57083
$295$	−3.04409e19	+	1.25455e21i	−0.0309008	+	1.27351i
$296$	3.30630e21			3.26109
$297$			5.01534e20i			0.480696i
$298$			1.24436e21i			1.15907i
$299$	−1.51711e20			−0.137345
$300$	1.27747e20	−	2.63086e21i	0.112414	−	2.31509i
$301$	−1.87856e21			−1.60698
$302$			2.12595e21i			1.76805i
$303$		−	1.73473e21i		−	1.40272i
$304$	−1.41451e21			−1.11219
$305$	2.99611e19	−	1.23478e21i	0.0229091	−	0.944150i
$306$	−8.01777e18			−0.00596240
$307$		−	2.20525e21i		−	1.59508i	−0.603268	−	0.797538i	$-0.706135\pi$
$307$		−	2.20525e21i		−	1.59508i	0.603268	−	0.797538i	$-0.293865\pi$
$308$		−	2.46152e21i		−	1.73190i
$309$	−1.53270e21			−1.04909
$310$	1.64311e21	+	3.98690e19i	1.09419	+	0.0265498i
$311$	−1.67631e21			−1.08615			−0.543077	−	0.839683i	$-0.682741\pi$
$311$	−1.67631e21			−1.08615			−0.543077	+	0.839683i	$0.682741\pi$
$312$			8.07434e20i			0.509088i
$313$			1.91815e21i			1.17695i	0.808517	+	0.588473i	$0.200271\pi$
$313$			1.91815e21i			1.17695i	−0.808517	+	0.588473i	$0.799729\pi$
$314$	−3.76843e21			−2.25039
$315$	2.56869e19	+	6.23274e17i	0.0149304	+	0.000362276i
$316$	2.49305e21			1.41056
$317$			2.94101e20i			0.161992i	0.996714	+	0.0809959i	$0.0258101\pi$
$317$			2.94101e20i			0.161992i	−0.996714	+	0.0809959i	$0.974190\pi$
$318$			4.69368e21i			2.51700i
$319$	1.35551e21			0.707754
$320$	2.17444e19	−	8.96150e20i	0.0110554	−	0.455623i
$321$	1.58719e21			0.785846
$322$		−	3.82899e21i		−	1.84633i
$323$			3.84361e20i			0.180517i
$324$	5.04167e21			2.30644
$325$	2.29586e19	−	4.72817e20i	0.0102315	−	0.210710i
$326$	−1.82843e21			−0.793831
$327$		−	3.02590e21i		−	1.27997i
$328$			2.97626e21i			1.22671i
$329$	−8.11577e20			−0.325960
$330$	−5.38375e19	+	2.21879e21i	−0.0210725	+	0.868458i
$331$	3.51653e21			1.34145			0.670727	−	0.741704i	$-0.265982\pi$
$331$	3.51653e21			1.34145			0.670727	+	0.741704i	$0.265982\pi$
$332$			6.40581e21i			2.38177i
$333$		−	3.56542e19i		−	0.0129221i
$334$	−1.95922e21			−0.692210
$335$	−3.07372e20	−	7.45816e18i	−0.105873	−	0.00256892i
$336$	−9.65112e21			−3.24111
$337$			1.06259e21i			0.347947i	0.984750	+	0.173973i	$0.0556607\pi$
$337$			1.06259e21i			0.347947i	−0.984750	+	0.173973i	$0.944339\pi$
$338$		−	5.45984e21i		−	1.74336i
$339$	1.12602e21			0.350630
$340$	−2.60744e21	−	6.32677e19i	−0.791851	−	0.0192137i
$341$	−9.68922e20			−0.286996
$342$			3.22084e19i			0.00930566i
$343$			2.29325e21i			0.646325i
$344$	9.11838e21			2.50710
$345$	−5.85899e19	+	2.41466e21i	−0.0157167	+	0.647729i
$346$	−8.10369e21			−2.12098
$347$		−	6.26207e21i		−	1.59925i	−0.600498	−	0.799626i	$-0.705031\pi$
$347$		−	6.26207e21i		−	1.59925i	0.600498	−	0.799626i	$-0.294969\pi$
$348$		−	1.37585e22i		−	3.42883i
$349$	4.92952e21			1.19891			0.599457	−	0.800407i	$-0.295383\pi$
$349$	4.92952e21			1.19891			0.599457	+	0.800407i	$0.295383\pi$
$350$	1.19333e22	+	5.79445e20i	2.83257	+	0.137542i
$351$	9.14877e20			0.211959
$352$			2.95799e21i			0.668936i
$353$			1.65310e21i			0.364934i	0.983212	+	0.182467i	$0.0584083\pi$
$353$			1.65310e21i			0.364934i	−0.983212	+	0.182467i	$0.941592\pi$
$354$	−1.07330e22			−2.31309
$355$	−1.22215e20	+	5.03681e21i	−0.0257147	+	1.05978i
$356$	8.88742e21			1.82579
$357$			2.62248e21i			0.526057i
$358$		−	6.93983e21i		−	1.35939i
$359$	−5.64380e21			−1.07961			−0.539807	−	0.841789i	$-0.681503\pi$
$359$	−5.64380e21			−1.07961			−0.539807	+	0.841789i	$0.681503\pi$
$360$	−1.24682e20	−	3.02532e18i	−0.0232934	−	0.000565197i
$361$	−3.93636e21			−0.718263
$362$			4.20210e21i			0.748934i
$363$			4.40784e21i			0.767396i
$364$	−4.49020e21			−0.763667
$365$	−1.08736e21	−	2.63841e19i	−0.180669	−	0.00438381i
$366$	1.05638e22			1.71487
$367$			7.92023e20i			0.125625i	0.998025	+	0.0628125i	$0.0200070\pi$
$367$			7.92023e20i			0.125625i	−0.998025	+	0.0628125i	$0.979993\pi$
$368$			8.80199e21i			1.36419i
$369$	3.20952e19			0.00486088
$370$	4.02144e20	−	1.65735e22i	0.0595206	−	2.45301i
$371$	−1.48947e22			−2.15454
$372$			9.83458e21i			1.39040i
$373$		−	5.60332e21i		−	0.774320i	−0.922012	−	0.387160i	$-0.873456\pi$
$373$		−	5.60332e21i		−	0.774320i	0.922012	−	0.387160i	$-0.126544\pi$
$374$	2.19775e21			0.296872
$375$	−7.51654e21	−	5.48011e20i	−0.992550	−	0.0723642i
$376$	3.93932e21			0.508540
$377$		−	2.47266e21i		−	0.312078i
$378$			2.30903e22i			2.84937i
$379$	1.12046e22			1.35195			0.675977	−	0.736923i	$-0.263722\pi$
$379$	1.12046e22			1.35195			0.675977	+	0.736923i	$0.263722\pi$
$380$	−2.54154e20	+	1.04744e22i	−0.0299873	+	1.23586i
$381$	1.50560e22			1.73719
$382$		−	1.77187e22i		−	1.99937i
$383$			7.07404e21i			0.780689i	0.920669	+	0.390344i	$0.127644\pi$
$383$			7.07404e21i			0.780689i	−0.920669	+	0.390344i	$0.872356\pi$
$384$	−5.22432e21			−0.563916
$385$	−7.04103e21	−	1.70845e20i	−0.743395	−	0.0180380i
$386$	−8.08979e21			−0.835497
$387$		−	9.83302e19i		−	0.00993444i
$388$		−	1.39992e22i		−	1.38368i
$389$	1.85301e22			1.79187			0.895937	−	0.444182i	$-0.146506\pi$
$389$	1.85301e22			1.79187			0.895937	+	0.444182i	$0.146506\pi$
$390$	4.04743e21	+	9.82080e19i	0.382939	+	0.00929175i
$391$	2.39175e21			0.221418
$392$		−	3.78998e22i		−	3.43325i
$393$		−	1.86809e22i		−	1.65601i
$394$	−7.98326e21			−0.692568
$395$	1.73034e20	−	7.13121e21i	0.0146911	−	0.605463i
$396$	1.28844e20			0.0107067
$397$			2.32134e22i			1.88807i	0.329840	+	0.944037i	$0.393005\pi$
$397$			2.32134e22i			1.88807i	−0.329840	+	0.944037i	$0.606995\pi$
$398$			4.33181e22i			3.44876i
$399$	1.05349e22			0.821030
$400$	−2.74319e22	−	1.33201e21i	−2.09289	−	0.101625i
$401$	−1.49395e22			−1.11586			−0.557928	−	0.829890i	$-0.688403\pi$
$401$	−1.49395e22			−1.11586			−0.557928	+	0.829890i	$0.688403\pi$
$402$		−	2.62963e21i		−	0.192297i
$403$			1.76747e21i			0.126549i
$404$	−4.68256e22			−3.28278
$405$	3.49924e20	−	1.44214e22i	0.0240218	−	0.990008i
$406$	6.24067e22			4.19527
$407$			9.77316e21i			0.643402i
$408$		−	1.27293e22i		−	0.820717i
$409$	−2.14032e22			−1.35155			−0.675774	−	0.737109i	$-0.736190\pi$
$409$	−2.14032e22			−1.35155			−0.675774	+	0.737109i	$0.736190\pi$
$410$	1.49191e22	+	3.62002e20i	0.922742	+	0.0223897i
$411$	9.69520e21			0.587356
$412$			4.13723e22i			2.45518i
$413$		−	3.40596e22i		−	1.97999i
$414$	2.00422e20			0.0114141
$415$	1.83234e22	+	4.44604e20i	1.02234	+	0.0248064i
$416$	5.39584e21			0.294962
$417$		−	1.92858e22i		−	1.03295i
$418$		−	8.82864e21i		−	0.463335i
$419$	−4.94779e20			−0.0254444			−0.0127222	−	0.999919i	$-0.504050\pi$
$419$	−4.94779e20			−0.0254444			−0.0127222	+	0.999919i	$0.504050\pi$
$420$	−1.73409e21	+	7.14666e22i	−0.0873880	+	3.60151i
$421$	−2.45451e22			−1.21218			−0.606091	−	0.795395i	$-0.707263\pi$
$421$	−2.45451e22			−1.21218			−0.606091	+	0.795395i	$0.707263\pi$
$422$			1.91673e22i			0.927696i
$423$		−	4.24806e19i		−	0.00201510i
$424$	7.22976e22			3.36135
$425$	−3.61946e20	+	7.45402e21i	−0.0164945	+	0.339692i
$426$	−4.30910e22			−1.92488
$427$			3.35227e22i			1.46792i
$428$		−	4.28431e22i		−	1.83912i
$429$	−2.38671e21			−0.100442
$430$	1.10907e21	−	4.57078e22i	0.0457589	−	1.88586i
$431$	2.21018e22			0.894067			0.447033	−	0.894517i	$-0.352480\pi$
$431$	2.21018e22			0.894067			0.447033	+	0.894517i	$0.352480\pi$
$432$		−	5.30793e22i		−	2.10530i
$433$			2.47754e22i			0.963549i	0.876295	+	0.481774i	$0.160008\pi$
$433$			2.47754e22i			0.963549i	−0.876295	+	0.481774i	$0.839992\pi$
$434$	−4.46085e22			−1.70120
$435$	−3.93552e22	−	9.54926e20i	−1.47178	−	0.0357117i
$436$	−8.16781e22			−2.99551
$437$		−	9.60798e21i		−	0.345573i
$438$		−	9.30261e21i		−	0.328152i
$439$	−7.72167e21			−0.267155			−0.133577	−	0.991038i	$-0.542646\pi$
$439$	−7.72167e21			−0.267155			−0.133577	+	0.991038i	$0.542646\pi$
$440$	3.41765e22	+	8.29269e20i	1.15979	+	0.0281415i
$441$	−4.08701e20			−0.0136044
$442$		−	4.00904e21i		−	0.130903i
$443$		−	3.47364e21i		−	0.111264i	−0.998451	−	0.0556318i	$-0.982283\pi$
$443$		−	3.47364e21i		−	0.111264i	0.998451	−	0.0556318i	$-0.0177173\pi$
$444$	9.91979e22			3.11707
$445$	6.16844e20	−	2.54219e22i	0.0190158	−	0.783696i
$446$	6.63224e22			2.00592
$447$			2.13043e22i			0.632199i
$448$			2.43293e22i			0.708381i
$449$	3.35625e22			0.958871			0.479435	−	0.877577i	$-0.340841\pi$
$449$	3.35625e22			0.958871			0.479435	+	0.877577i	$0.340841\pi$
$450$	−3.03301e19	+	6.24626e20i	−0.000850290	+	0.0175111i
$451$	−8.79759e21			−0.242027
$452$		−	3.03946e22i		−	0.820579i
$453$			3.63976e22i			0.964357i
$454$	−4.79167e22			−1.24598
$455$	−3.11649e20	+	1.28439e22i	−0.00795369	+	0.327794i
$456$	−5.11353e22			−1.28091
$457$		−	3.47799e22i		−	0.855146i	−0.903981	−	0.427573i	$-0.859369\pi$
$457$		−	3.47799e22i		−	0.855146i	0.903981	−	0.427573i	$-0.140631\pi$
$458$			6.96359e22i			1.68065i
$459$	−1.44232e22			−0.341706
$460$	6.51788e22	+	1.58152e21i	1.51588	+	0.0367818i
$461$	4.25534e22			0.971574			0.485787	−	0.874077i	$-0.338533\pi$
$461$	4.25534e22			0.971574			0.485787	+	0.874077i	$0.338533\pi$
$462$		−	6.02375e22i		−	1.35024i
$463$			4.02870e22i			0.886597i	0.896374	+	0.443299i	$0.146192\pi$
$463$			4.02870e22i			0.886597i	−0.896374	+	0.443299i	$0.853808\pi$
$464$	−1.43459e23			−3.09974
$465$	2.81312e22	+	6.82583e20i	0.596813	+	0.0144812i
$466$	−7.91818e22			−1.64947
$467$			1.32049e21i			0.0270110i	0.999909	+	0.0135055i	$0.00429907\pi$
$467$			1.32049e21i			0.0270110i	−0.999909	+	0.0135055i	$0.995701\pi$
$468$		−	2.35032e20i		−	0.00472103i
$469$	8.34476e21			0.164606
$470$	4.79139e20	−	1.97467e22i	0.00928175	−	0.382527i
$471$	−6.45179e22			−1.22745
$472$			1.65322e23i			3.08904i
$473$			2.69533e22i			0.494643i
$474$	6.10090e22			1.09971
$475$	2.99438e22	+	1.45398e21i	0.530165	+	0.0257433i
$476$	7.07887e22			1.23113
$477$		−	7.79638e20i		−	0.0133195i
$478$		−	5.46590e22i		−	0.917328i
$479$	4.98795e22			0.822375			0.411188	−	0.911551i	$-0.365114\pi$
$479$	4.98795e22			0.822375			0.411188	+	0.911551i	$0.365114\pi$
$480$	2.08384e21	−	8.58809e22i	0.0337531	−	1.39106i
$481$	1.78278e22			0.283703
$482$		−	5.94482e22i		−	0.929477i
$483$		−	6.55548e22i		−	1.00706i
$484$	1.18981e23			1.79594
$485$	−4.00439e22	−	9.71638e20i	−0.593926	−	0.0144112i
$486$	−2.40574e21			−0.0350623
$487$			1.58494e22i			0.226996i	0.993538	+	0.113498i	$0.0362055\pi$
$487$			1.58494e22i			0.226996i	−0.993538	+	0.113498i	$0.963794\pi$
$488$		−	1.62716e23i		−	2.29014i
$489$	−3.13039e22			−0.432985
$490$	−1.89981e23	−	4.60974e21i	−2.58251	−	0.0626629i
$491$	6.29353e22			0.840817			0.420409	−	0.907335i	$-0.361887\pi$
$491$	6.29353e22			0.840817			0.420409	+	0.907335i	$0.361887\pi$
$492$			8.92958e22i			1.17254i
$493$			3.89819e22i			0.503111i
$494$	−1.61048e22			−0.204304
$495$	8.94261e18	−	3.68550e20i	0.000111512	−	0.00459571i
$496$	1.02545e23			1.25695
$497$		−	1.36743e23i		−	1.64769i
$498$			1.56760e23i			1.85689i
$499$	−1.06080e23			−1.23532			−0.617660	−	0.786445i	$-0.711919\pi$
$499$	−1.06080e23			−1.23532			−0.617660	+	0.786445i	$0.711919\pi$
$500$	−1.47925e22	+	2.02894e23i	−0.169354	+	2.32287i
$501$	−3.35431e22			−0.377557
$502$			3.33738e22i			0.369338i
$503$		−	9.88915e22i		−	1.07605i	−0.842930	−	0.538024i	$-0.819171\pi$
$503$		−	9.88915e22i		−	1.07605i	0.842930	−	0.538024i	$-0.180829\pi$
$504$	3.38496e21			0.0362154
$505$	−3.24999e21	+	1.33941e23i	−0.0341905	+	1.40909i
$506$	−5.49376e22			−0.568317
$507$		−	9.34760e22i		−	0.950895i
$508$		−	4.06406e23i		−	4.06554i
$509$	−1.44169e23			−1.41831			−0.709156	−	0.705051i	$-0.750924\pi$
$509$	−1.44169e23			−1.41831			−0.709156	+	0.705051i	$0.750924\pi$
$510$	−6.38083e22	−	1.54826e21i	−0.617349	−	0.0149795i
$511$	2.95205e22			0.280896
$512$			2.29876e23i			2.15129i
$513$			5.79397e22i			0.533309i
$514$	3.34755e23			3.03069
$515$	1.18343e23	+	2.87150e21i	1.05385	+	0.0255710i
$516$	2.73576e23			2.39638
$517$			1.16443e22i			0.100333i
$518$			4.49949e23i			3.81382i
$519$	−1.38740e23			−1.15686
$520$	1.51272e21	−	6.23433e22i	0.0124088	−	0.511401i
$521$	−2.14130e22			−0.172805			−0.0864025	−	0.996260i	$-0.527537\pi$
$521$	−2.14130e22			−0.172805			−0.0864025	+	0.996260i	$0.527537\pi$
$522$			3.26657e21i			0.0259354i
$523$		−	8.29652e22i		−	0.648084i	−0.946043	−	0.324042i	$-0.894958\pi$
$523$		−	8.29652e22i		−	0.648084i	0.946043	−	0.324042i	$-0.105042\pi$
$524$	−5.04255e23			−3.87556
$525$	2.04305e23	+	9.92048e21i	1.54499	+	0.0750203i
$526$	−3.36577e22			−0.250441
$527$		−	2.78643e22i		−	0.204013i
$528$			1.38472e23i			0.997642i
$529$	8.12628e22			0.576128
$530$	8.79355e21	−	3.62407e23i	0.0613506	−	2.52843i
$531$	1.78279e21			0.0122404
$532$		−	2.84367e23i		−	1.92146i
$533$			1.60482e22i			0.106720i
$534$	2.17490e23			1.42343
$535$	−1.22550e23	−	2.97359e21i	−0.789417	−	0.0191546i
$536$	−4.05047e22			−0.256806
$537$		−	1.18814e23i		−	0.741460i
$538$			6.03419e22i			0.370655i
$539$	1.12029e23			0.677370
$540$	−3.93053e23	−	9.53714e21i	−2.33940	−	0.0567638i
$541$	4.66901e22			0.273557			0.136779	−	0.990602i	$-0.456325\pi$
$541$	4.66901e22			0.273557			0.136779	+	0.990602i	$0.456325\pi$
$542$		−	2.54480e22i		−	0.146778i
$543$			7.19427e22i			0.408496i
$544$	−8.50662e22			−0.475517
$545$	−5.66899e21	+	2.33635e23i	−0.0311986	+	1.28578i
$546$	−1.09883e23			−0.595376
$547$		−	2.17735e22i		−	0.116155i	−0.998312	−	0.0580773i	$-0.981503\pi$
$547$		−	2.17735e22i		−	0.116155i	0.998312	−	0.0580773i	$-0.0184970\pi$
$548$		−	2.61702e23i		−	1.37459i
$549$	−1.75469e21			−0.00907476
$550$	8.31377e21	−	1.71216e23i	0.0423365	−	0.871890i
$551$	1.56595e23			0.785218
$552$			3.18198e23i			1.57114i
$553$			1.93603e23i			0.941345i
$554$	5.63392e23			2.69760
$555$	6.88497e21	−	2.83749e23i	0.0324647	−	1.33796i
$556$	−5.20581e23			−2.41742
$557$			3.95082e23i			1.80683i	0.428763	+	0.903417i	$0.358949\pi$
$557$			3.95082e23i			1.80683i	−0.428763	+	0.903417i	$0.641051\pi$
$558$		−	2.33495e21i		−	0.0105169i
$559$	4.91670e22			0.218109
$560$	7.45179e23	+	1.80812e22i	3.25584	+	0.0790006i
$561$	3.76269e22			0.161925
$562$		−	5.06257e23i		−	2.14591i
$563$		−	1.57683e23i		−	0.658359i	−0.944267	−	0.329180i	$-0.893228\pi$
$563$		−	1.57683e23i		−	0.658359i	0.944267	−	0.329180i	$-0.106772\pi$
$564$	1.18190e23			0.486082
$565$	−8.69419e22	−	2.10958e21i	−0.352223	−	0.00854643i
$566$	−4.25975e23			−1.69998
$567$			3.91522e23i			1.53922i
$568$			6.63738e23i			2.57061i
$569$	−2.40022e23			−0.915791			−0.457896	−	0.889006i	$-0.651397\pi$
$569$	−2.40022e23			−0.915791			−0.457896	+	0.889006i	$0.651397\pi$
$570$	−6.21957e21	+	2.56326e23i	−0.0233789	+	0.963511i
$571$	1.03536e23			0.383428			0.191714	−	0.981451i	$-0.438595\pi$
$571$	1.03536e23			0.383428			0.191714	+	0.981451i	$0.438595\pi$
$572$			6.44245e22i			0.235063i
$573$		−	3.03356e23i		−	1.09053i
$574$	−4.05035e23			−1.43463
$575$	9.04766e21	−	1.86330e23i	0.0315762	−	0.650289i
$576$	−1.27348e21			−0.00437925
$577$		−	5.37249e22i		−	0.182046i	−0.995849	−	0.0910229i	$-0.970986\pi$
$577$		−	5.37249e22i		−	0.182046i	0.995849	−	0.0910229i	$-0.0290137\pi$
$578$		−	4.83241e23i		−	1.61353i
$579$	−1.38502e23			−0.455711
$580$	−2.57763e22	+	1.06231e24i	−0.0835762	+	3.44441i
$581$	−4.97457e23			−1.58949
$582$		−	3.42584e23i		−	1.07875i
$583$			2.13706e23i			0.663185i
$584$	−1.43290e23			−0.438234
$585$	−6.72294e20	−	1.63127e19i	−0.00202644	−	4.91702e-5i
$586$	6.99217e23			2.07722
$587$		−	7.97439e22i		−	0.233493i	−0.993162	−	0.116746i	$-0.962753\pi$
$587$		−	7.97439e22i		−	0.233493i	0.993162	−	0.116746i	$-0.0372465\pi$
$588$		−	1.13710e24i		−	3.28163i
$589$	−1.11935e23			−0.318408
$590$	8.28712e23	+	2.01081e22i	2.32360	+	0.0563805i
$591$	−1.36679e23			−0.377752
$592$		−	1.03433e24i		−	2.81790i
$593$			2.92994e22i			0.0786854i	0.999226	+	0.0393427i	$0.0125264\pi$
$593$			2.92994e22i			0.0786854i	−0.999226	+	0.0393427i	$0.987474\pi$
$594$	3.31295e23			0.877061
$595$	4.91319e21	−	2.02486e23i	0.0128224	−	0.528447i
$596$	5.75068e23			1.47954
$597$			7.41634e23i			1.88108i
$598$			1.00215e23i			0.250595i
$599$	−2.14554e23			−0.528942			−0.264471	−	0.964394i	$-0.585197\pi$
$599$	−2.14554e23			−0.528942			−0.264471	+	0.964394i	$0.585197\pi$
$600$	−9.91680e23	−	4.81532e22i	−2.41038	−	0.117041i
$601$	3.54004e23			0.848351			0.424175	−	0.905580i	$-0.360564\pi$
$601$	3.54004e23			0.848351			0.424175	+	0.905580i	$0.360564\pi$
$602$			1.24091e24i			2.93204i
$603$			4.36792e20i			0.00101760i
$604$	9.82480e23			2.25689
$605$	8.25803e21	−	3.40337e23i	0.0187049	−	0.770882i
$606$	−1.14590e24			−2.55934
$607$		−	2.65810e23i		−	0.585419i	−0.956201	−	0.292710i	$-0.905443\pi$
$607$		−	2.65810e23i		−	0.585419i	0.956201	−	0.292710i	$-0.0945569\pi$
$608$			3.41722e23i			0.742151i
$609$	1.06844e24			2.28826
$610$	−8.15650e23	−	1.97912e22i	−1.72266	−	0.0417992i
$611$	2.12411e22			0.0442412
$612$			3.70531e21i			0.00761093i
$613$		−	6.38443e23i		−	1.29333i	−0.762776	−	0.646663i	$-0.776164\pi$
$613$		−	6.38443e23i		−	1.29333i	0.762776	−	0.646663i	$-0.223836\pi$
$614$	−1.45670e24			−2.91032
$615$	2.55425e23	+	6.19770e21i	0.503297	+	0.0122122i
$616$	−9.27849e23			−1.80319
$617$		−	8.39922e23i		−	1.60996i	−0.593301	−	0.804980i	$-0.702176\pi$
$617$		−	8.39922e23i		−	1.60996i	0.593301	−	0.804980i	$-0.297824\pi$
$618$			1.01245e24i			1.91412i
$619$	−1.78611e23			−0.333072			−0.166536	−	0.986035i	$-0.553258\pi$
$619$	−1.78611e23			−0.333072			−0.166536	+	0.986035i	$0.553258\pi$
$620$	1.84250e22	−	7.59345e23i	0.0338904	−	1.39672i
$621$	3.60539e23			0.654145
$622$			1.10731e24i			1.98175i
$623$			6.90172e23i			1.21845i
$624$	2.52595e23			0.439902
$625$	5.79338e23	+	5.63950e22i	0.995295	+	0.0968859i
$626$	1.26706e24			2.14741
$627$		−	1.51152e23i		−	0.252720i
$628$			1.74153e24i			2.87260i
$629$	−2.81057e23			−0.457367
$630$	4.11711e20	−	1.69678e22i	0.000660995	−	0.0272415i
$631$	4.46452e23			0.707173			0.353586	−	0.935402i	$-0.384962\pi$
$631$	4.46452e23			0.707173			0.353586	+	0.935402i	$0.384962\pi$
$632$		−	9.39733e23i		−	1.46862i
$633$			3.28157e23i			0.506000i
$634$	1.94272e23			0.295564
$635$	−1.16250e24	−	2.82072e22i	−1.74508	−	0.0423431i
$636$	2.16912e24			3.21291
$637$		−	2.04358e23i		−	0.298681i
$638$		−	8.95399e23i		−	1.29134i
$639$	7.15757e21			0.0101861
$640$	4.03379e23	+	9.78770e21i	0.566479	+	0.0137452i
$641$	−5.46949e23			−0.757973			−0.378987	−	0.925402i	$-0.623727\pi$
$641$	−5.46949e23			−0.757973			−0.378987	+	0.925402i	$0.623727\pi$
$642$		−	1.04844e24i		−	1.43383i
$643$		−	7.19921e23i		−	0.971609i	−0.874067	−	0.485805i	$-0.838527\pi$
$643$		−	7.19921e23i		−	0.971609i	0.874067	−	0.485805i	$-0.161473\pi$
$644$	−1.76952e24			−2.35682
$645$	1.89879e22	−	7.82547e23i	0.0249586	−	1.02862i
$646$	2.53895e23			0.329365
$647$			1.25975e24i			1.61287i	0.591324	+	0.806434i	$0.298605\pi$
$647$			1.25975e24i			1.61287i	−0.591324	+	0.806434i	$0.701395\pi$
$648$		−	1.90041e24i		−	2.40138i
$649$	−4.88680e23			−0.609459
$650$	−3.12325e23	−	1.51656e22i	−0.384453	−	0.0186679i
$651$	−7.63726e23			−0.927895
$652$			8.44985e23i			1.01332i
$653$			5.58543e23i			0.661142i	0.943781	+	0.330571i	$0.107241\pi$
$653$			5.58543e23i			0.661142i	−0.943781	+	0.330571i	$0.892759\pi$
$654$	−1.99880e24			−2.33538
$655$	−3.49985e22	+	1.44239e24i	−0.0403644	+	1.66353i
$656$	9.31084e23			1.06000
$657$			1.54520e21i			0.00173652i
$658$			5.36097e23i			0.594735i
$659$	1.40175e24			1.53513			0.767563	−	0.640973i	$-0.221469\pi$
$659$	1.40175e24			1.53513			0.767563	+	0.640973i	$0.221469\pi$
$660$	1.02539e24	+	2.48803e22i	1.10857	+	0.0268988i
$661$	−1.56535e24			−1.67070			−0.835349	−	0.549720i	$-0.814734\pi$
$661$	−1.56535e24			−1.67070			−0.835349	+	0.549720i	$0.814734\pi$
$662$		−	2.32288e24i		−	2.44757i
$663$		−	6.86373e22i		−	0.0713995i
$664$	2.41461e24			2.47981
$665$	−8.13414e23	−	1.97369e22i	−0.824760	−	0.0200122i
$666$	−2.35518e22			−0.0235773
$667$		−	9.74440e23i		−	0.963131i
$668$			9.05428e23i			0.883596i
$669$	1.13548e24			1.09410
$670$	−4.92658e21	+	2.03038e23i	−0.00468716	+	0.193171i
$671$	4.80977e23			0.451838
$672$			2.33156e24i			2.16275i
$673$		−	1.06512e24i		−	0.975593i	−0.872957	−	0.487797i	$-0.837801\pi$
$673$		−	1.06512e24i		−	0.975593i	0.872957	−	0.487797i	$-0.162199\pi$
$674$	7.01909e23			0.634851
$675$	−5.45608e22	+	1.12364e24i	−0.0487302	+	1.00356i
$676$	−2.52320e24			−2.22538
$677$		−	1.35343e23i		−	0.117878i	−0.998262	−	0.0589389i	$-0.981228\pi$
$677$		−	1.35343e23i		−	0.117878i	0.998262	−	0.0589389i	$-0.0187717\pi$
$678$		−	7.43806e23i		−	0.639746i
$679$	1.08714e24			0.923407
$680$	−2.38482e22	+	9.82852e23i	−0.0200046	+	0.824446i
$681$	−8.20365e23			−0.679605
$682$			6.40033e23i			0.523643i
$683$			6.70521e23i			0.541797i	0.962608	+	0.270898i	$0.0873207\pi$
$683$			6.70521e23i			0.541797i	−0.962608	+	0.270898i	$0.912679\pi$
$684$	1.48847e22			0.0118786
$685$	−7.48583e23	−	1.81638e22i	−0.590024	−	0.0143165i
$686$	1.51483e24			1.17926
$687$			1.19221e24i			0.916687i
$688$		−	2.85257e24i		−	2.16638i
$689$	3.89834e23			0.292426
$690$	1.59503e24	+	3.87023e22i	1.18182	+	0.0286761i
$691$	1.91000e24			1.39788			0.698941	−	0.715179i	$-0.253655\pi$
$691$	1.91000e24			1.39788			0.698941	+	0.715179i	$0.253655\pi$
$692$			3.74502e24i			2.70740i
$693$			1.00057e22i			0.00714519i
$694$	−4.13649e24			−2.91794
$695$	−3.61317e22	+	1.48909e24i	−0.0251778	+	1.03765i
$696$	−5.18613e24			−3.56998
$697$		−	2.53002e23i		−	0.172046i
$698$		−	3.25625e24i		−	2.18750i
$699$	−1.35564e24			−0.899684
$700$	2.67783e23	−	5.51481e24i	0.175570	−	3.61574i
$701$	2.38901e24			1.54745			0.773723	−	0.633524i	$-0.218392\pi$
$701$	2.38901e24			1.54745			0.773723	+	0.633524i	$0.218392\pi$
$702$		−	6.04333e23i		−	0.386733i
$703$			1.12904e24i			0.713823i
$704$	3.49072e23			0.218046
$705$	8.20317e21	−	3.38076e23i	0.00506261	−	0.208644i
$706$	1.09198e24			0.665845
$707$		−	3.63634e24i		−	2.19078i
$708$			4.96011e24i			2.95263i
$709$	1.18830e24			0.698926			0.349463	−	0.936950i	$-0.386364\pi$
$709$	1.18830e24			0.698926			0.349463	+	0.936950i	$0.386364\pi$
$710$	3.32713e24	+	8.07304e22i	1.93363	+	0.0469182i
$711$	−1.01338e22			−0.00581945
$712$		−	3.35003e24i		−	1.90094i
$713$			6.96532e23i			0.390553i
$714$	1.73231e24			0.959824
$715$	1.84282e23	+	4.47148e21i	0.100898	+	0.00244822i
$716$	−3.20716e24			−1.73524
$717$		−	9.35797e23i		−	0.500344i
$718$			3.72808e24i			1.96983i
$719$	−7.00134e23			−0.365583			−0.182791	−	0.983152i	$-0.558513\pi$
$719$	−7.00134e23			−0.365583			−0.182791	+	0.983152i	$0.558513\pi$
$720$	−9.46432e20	+	3.90051e22i	−0.000488386	+	0.0201278i
$721$	−3.21285e24			−1.63848
$722$			2.60021e24i			1.31052i
$723$		−	1.01779e24i		−	0.506971i
$724$	1.94195e24			0.956004
$725$	3.03689e24	+	1.47463e23i	1.47760	+	0.0717480i
$726$	2.91165e24			1.40016
$727$		−	6.64217e23i		−	0.315695i	−0.987464	−	0.157847i	$-0.949545\pi$
$727$		−	6.64217e23i		−	0.315695i	0.987464	−	0.157847i	$-0.0504554\pi$
$728$			1.69254e24i			0.795102i
$729$	−2.17399e24			−1.00942
$730$	−1.74283e22	+	7.18270e23i	−0.00799855	+	0.329643i
$731$	−7.75124e23			−0.351620
$732$		−	4.88193e24i		−	2.18901i
$733$		−	1.04024e24i		−	0.461054i	−0.973066	−	0.230527i	$-0.925955\pi$
$733$		−	1.04024e24i		−	0.461054i	0.973066	−	0.230527i	$-0.0740450\pi$
$734$	5.23181e23			0.229211
$735$	−3.25259e24	−	7.89218e22i	−1.40860	−	0.0341786i
$736$	2.12642e24			0.910307
$737$		−	1.19729e23i		−	0.0506670i
$738$		−	2.12008e22i		−	0.00886899i
$739$	−7.14037e23			−0.295286			−0.147643	−	0.989041i	$-0.547169\pi$
$739$	−7.14037e23			−0.295286			−0.147643	+	0.989041i	$0.547169\pi$
$740$	−7.65924e24	−	1.85846e23i	−3.13124	−	0.0759772i
$741$	−2.75725e23			−0.111435
$742$			9.83889e24i			3.93109i
$743$			3.15273e24i			1.24532i	0.782492	+	0.622661i	$0.213948\pi$
$743$			3.15273e24i			1.24532i	−0.782492	+	0.622661i	$0.786052\pi$
$744$	3.70706e24			1.44764
$745$	3.99134e22	−	1.64494e24i	0.0154096	−	0.635072i
$746$	−3.70134e24			−1.41280
$747$		−	2.60385e22i		−	0.00982632i
$748$		−	1.01566e24i		−	0.378953i
$749$	3.32708e24			1.22735
$750$	−3.61995e23	+	4.96514e24i	−0.132033	+	1.81097i
$751$	−9.62214e21			−0.00347002			−0.00173501	−	0.999998i	$-0.500552\pi$
$751$	−9.62214e21			−0.00347002			−0.00173501	+	0.999998i	$0.500552\pi$
$752$		−	1.23237e24i		−	0.439429i
$753$			5.71381e23i			0.201451i
$754$	−1.63335e24			−0.569407
$755$	6.81904e22	−	2.81032e24i	0.0235058	−	0.968739i
$756$	1.06709e25			3.63718
$757$			2.06888e24i			0.697302i	0.937253	+	0.348651i	$0.113360\pi$
$757$			2.06888e24i			0.697302i	−0.937253	+	0.348651i	$0.886640\pi$
$758$		−	7.40132e24i		−	2.46672i
$759$	−9.40568e23			−0.309981
$760$	3.94824e24	+	9.58013e22i	1.28673	+	0.0312216i
$761$	−1.54775e24			−0.498807			−0.249404	−	0.968400i	$-0.580235\pi$
$761$	−1.54775e24			−0.498807			−0.249404	+	0.968400i	$0.580235\pi$
$762$		−	9.94541e24i		−	3.16961i
$763$		−	6.34289e24i		−	1.99907i
$764$	−8.18849e24			−2.55218
$765$	1.05988e22	+	2.57172e20i	0.00326689	+	7.92688e-5i
$766$	4.67284e24			1.42442
$767$			8.91429e23i			0.268736i
$768$			4.97227e24i			1.48246i
$769$	1.41912e24			0.418451			0.209226	−	0.977867i	$-0.432906\pi$
$769$	1.41912e24			0.418451			0.209226	+	0.977867i	$0.432906\pi$
$770$	−1.12854e23	+	4.65104e24i	−0.0329114	+	1.35637i
$771$	5.73123e24			1.65305
$772$			3.73859e24i			1.06650i
$773$		−	7.68448e23i		−	0.216815i	−0.994107	−	0.108407i	$-0.965425\pi$
$773$		−	7.68448e23i		−	0.216815i	0.994107	−	0.108407i	$-0.0345751\pi$
$774$	−6.49532e22			−0.0181260
$775$	−2.17078e24	−	1.05407e23i	−0.599171	−	0.0290941i
$776$	−5.27689e24			−1.44063
$777$			7.70343e24i			2.08020i
$778$		−	1.22403e25i		−	3.26939i
$779$	−1.01634e24			−0.268517
$780$	4.53856e22	−	1.87047e24i	0.0118608	−	0.488817i
$781$	−1.96196e24			−0.507173
$782$		−	1.57990e24i		−	0.403992i
$783$			5.87624e24i			1.48636i
$784$	−1.18565e25			−2.96667
$785$	4.98154e24	+	1.20873e23i	1.23302	+	0.0299184i
$786$	−1.23399e25			−3.02149
$787$		−	1.67424e24i		−	0.405539i	−0.979226	−	0.202769i	$-0.935006\pi$
$787$		−	1.67424e24i		−	0.405539i	0.979226	−	0.202769i	$-0.0649942\pi$
$788$			3.68936e24i			0.884053i
$789$	−5.76242e23			−0.136600
$790$	−4.71061e24	−	1.14300e23i	−1.10471	−	0.0268049i
$791$	2.36036e24			0.547619
$792$		−	4.85667e22i		−	0.0111474i
$793$		−	8.77378e23i		−	0.199235i
$794$	1.53339e25			3.44491
$795$	1.50551e23	−	6.20464e24i	0.0334629	−	1.37910i
$796$	2.00189e25			4.40230
$797$			4.21412e24i			0.916877i	0.888726	+	0.458439i	$0.151591\pi$
$797$			4.21412e24i			0.916877i	−0.888726	+	0.458439i	$0.848409\pi$
$798$		−	6.95893e24i		−	1.49802i
$799$	−3.34869e23			−0.0713226
$800$	−3.21793e23	+	6.62710e24i	−0.0678129	+	1.39656i
$801$	−3.61258e22			−0.00753254
$802$			9.86845e24i			2.03595i
$803$		−	4.23554e23i		−	0.0864623i
$804$	−1.21525e24			−0.245465
$805$	−1.22816e23	+	5.06160e24i	−0.0245466	+	1.01163i
$806$	1.16752e24			0.230896
$807$			1.03309e24i			0.202169i
$808$			1.76505e25i			3.41791i
$809$	−6.29496e23			−0.120623			−0.0603116	−	0.998180i	$-0.519209\pi$
$809$	−6.29496e23			−0.120623			−0.0603116	+	0.998180i	$0.519209\pi$
$810$	−9.52621e24	−	2.31147e23i	−1.80633	−	0.0438293i
$811$	−1.97375e24			−0.370352			−0.185176	−	0.982705i	$-0.559286\pi$
$811$	−1.97375e24			−0.370352			−0.185176	+	0.982705i	$0.559286\pi$
$812$		−	2.88405e25i		−	5.35521i
$813$		−	4.35687e23i		−	0.0800581i
$814$	6.45578e24			1.17393
$815$	2.41703e24	+	5.86474e22i	0.434952	+	0.0105538i
$816$	−3.98220e24			−0.709180
$817$			3.11377e24i			0.548782i
$818$			1.41382e25i			2.46598i
$819$	1.82519e22			0.00315061
$820$	1.67295e23	−	6.89468e24i	0.0285801	−	1.17787i
$821$	−9.78759e24			−1.65485			−0.827426	−	0.561575i	$-0.810196\pi$
$821$	−9.78759e24			−1.65485			−0.827426	+	0.561575i	$0.810196\pi$
$822$		−	6.40428e24i		−	1.07167i
$823$		−	2.29900e23i		−	0.0380750i	−0.999819	−	0.0190375i	$-0.993940\pi$
$823$		−	2.29900e23i		−	0.0380750i	0.999819	−	0.0190375i	$-0.00606019\pi$
$824$	1.55949e25			2.55624
$825$	1.42337e23	−	2.93133e24i	0.0230919	−	0.475561i
$826$	−2.24985e25			−3.61262
$827$		−	4.00653e24i		−	0.636754i	−0.947964	−	0.318377i	$-0.896862\pi$
$827$		−	4.00653e24i		−	0.636754i	0.947964	−	0.318377i	$-0.103138\pi$
$828$		−	9.26226e22i		−	0.0145700i
$829$	−7.23311e24			−1.12619			−0.563095	−	0.826392i	$-0.690389\pi$
$829$	−7.23311e24			−1.12619			−0.563095	+	0.826392i	$0.690389\pi$
$830$	2.93689e23	−	1.21037e25i	0.0452609	−	1.86533i
$831$	9.64564e24			1.47137
$832$		−	6.36763e23i		−	0.0961456i
$833$			3.22174e24i			0.481513i
$834$	−1.27395e25			−1.88469
$835$	2.58992e24	+	6.28425e22i	0.379272	+	0.00920277i
$836$	−4.08004e24			−0.591441
$837$		−	4.20035e24i		−	0.602724i
$838$			3.26832e23i			0.0464249i
$839$	−8.73556e24			−1.22833			−0.614163	−	0.789179i	$-0.710506\pi$
$839$	−8.73556e24			−1.22833			−0.614163	+	0.789179i	$0.710506\pi$
$840$	2.69387e25	+	6.53648e23i	3.74975	+	0.0909851i
$841$	8.62473e24			1.18845
$842$			1.62136e25i			2.21170i
$843$		−	8.66745e24i		−	1.17046i
$844$	8.85794e24			1.18419
$845$	−1.75126e23	+	7.21744e24i	−0.0231776	+	0.955216i
$846$	−2.80611e22			−0.00367668
$847$			9.23971e24i			1.19853i
$848$		−	2.26174e25i		−	2.90454i
$849$	−7.29297e24			−0.927234
$850$	4.92385e24	+	2.39088e23i	0.619789	+	0.0300952i
$851$	7.02566e24			0.875560
$852$			1.99140e25i			2.45709i
$853$			2.48651e24i			0.303755i	0.988399	+	0.151878i	$0.0485320\pi$
$853$			2.48651e24i			0.303755i	−0.988399	+	0.151878i	$0.951468\pi$
$854$	2.21438e25			2.67831
$855$	1.03309e21	−	4.25768e22i	0.000123717	−	0.00509871i
$856$	−1.61493e25			−1.91482
$857$		−	7.73588e24i		−	0.908181i	−0.890955	−	0.454091i	$-0.849964\pi$
$857$		−	7.73588e24i		−	0.908181i	0.890955	−	0.454091i	$-0.150036\pi$
$858$			1.57657e24i			0.183262i
$859$	−9.34602e24			−1.07568			−0.537842	−	0.843045i	$-0.680760\pi$
$859$	−9.34602e24			−1.07568			−0.537842	+	0.843045i	$0.680760\pi$
$860$	−2.11233e25	−	5.12542e23i	−2.40727	−	0.0584107i
$861$	−6.93446e24			−0.782502
$862$		−	1.45996e25i		−	1.63128i
$863$		−	9.26216e24i		−	1.02476i	−0.858760	−	0.512378i	$-0.828765\pi$
$863$		−	9.26216e24i		−	1.02476i	0.858760	−	0.512378i	$-0.171235\pi$
$864$	−1.28231e25			−1.40484
$865$	1.07124e25	+	2.59928e23i	1.16211	+	0.0281979i
$866$	1.63657e25			1.75806
$867$		−	8.27340e24i		−	0.880079i
$868$			2.06152e25i			2.17156i
$869$	2.77778e24			0.289754
$870$	−6.30788e23	+	2.59966e25i	−0.0651583	+	2.68536i
$871$	−2.18404e23			−0.0223412
$872$			3.07879e25i			3.11881i
$873$			5.69046e22i			0.00570855i
$874$	−6.34667e24			−0.630520
$875$	−1.57562e25	−	1.14874e24i	−1.55018	−	0.113020i
$876$	−4.29908e24			−0.418881
$877$		−	1.25978e25i		−	1.21562i	−0.794082	−	0.607810i	$-0.792048\pi$
$877$		−	1.25978e25i		−	1.21562i	0.794082	−	0.607810i	$-0.207952\pi$
$878$			5.10065e24i			0.487441i
$879$	1.19710e25			1.13299
$880$	2.59426e23	−	1.06917e25i	0.0243171	−	1.00217i
$881$	−6.10480e24			−0.566730			−0.283365	−	0.959012i	$-0.591451\pi$
$881$	−6.10480e24			−0.566730			−0.283365	+	0.959012i	$0.591451\pi$
$882$			2.69973e23i			0.0248220i
$883$		−	7.68576e24i		−	0.699876i	−0.936773	−	0.349938i	$-0.886203\pi$
$883$		−	7.68576e24i		−	0.699876i	0.936773	−	0.349938i	$-0.113797\pi$
$884$	−1.85273e24			−0.167096
$885$	1.41881e25	+	3.44264e23i	1.26738	+	0.0307520i
$886$	−2.29456e24			−0.203008
$887$			1.57170e25i			1.37727i	0.725110	+	0.688633i	$0.241789\pi$
$887$			1.57170e25i			1.37727i	−0.725110	+	0.688633i	$0.758211\pi$
$888$		−	3.73918e25i		−	3.24538i
$889$	3.15603e25			2.71317
$890$	−1.67927e25	−	4.07464e23i	−1.42990	−	0.0346956i
$891$	5.61747e24			0.473784
$892$		−	3.06501e25i		−	2.56053i
$893$			1.34521e24i			0.111315i
$894$	1.40728e25			1.15349
$895$	−2.22597e23	+	9.17386e24i	−0.0180727	+	0.744829i
$896$	−1.09512e25			−0.880734
$897$			1.71574e24i			0.136684i
$898$		−	2.21701e25i		−	1.74952i
$899$	−1.13524e25			−0.887422
$900$	2.88663e23	+	1.40167e22i	0.0223527	+	0.00108538i
$901$	−6.14579e24			−0.471429
$902$			5.81136e24i			0.441593i
$903$			2.12452e25i			1.59924i
$904$	−1.14570e25			−0.854356
$905$	1.34784e23	−	5.55482e24i	0.00995690	−	0.410352i
$906$	2.40429e25			1.75953
$907$		−	2.48686e24i		−	0.180297i	−0.995928	−	0.0901486i	$-0.971266\pi$
$907$		−	2.48686e24i		−	0.180297i	0.995928	−	0.0901486i	$-0.0287342\pi$
$908$			2.21441e25i			1.59048i
$909$	1.90338e23			0.0135435
$910$	8.48422e24	+	2.05864e23i	0.598081	+	0.0145120i
$911$	1.32000e25			0.921867			0.460933	−	0.887435i	$-0.347515\pi$
$911$	1.32000e25			0.921867			0.460933	+	0.887435i	$0.347515\pi$
$912$			1.59970e25i			1.10683i
$913$			7.13741e24i			0.489259i
$914$	−2.29743e25			−1.56027
$915$	−1.39645e25	−	3.38837e23i	−0.939603	−	0.0227988i
$916$	3.21814e25			2.14532
$917$		−	3.91590e25i		−	2.58638i
$918$			9.52740e24i			0.623464i
$919$	−2.58452e25			−1.67571			−0.837853	−	0.545896i	$-0.816189\pi$
$919$	−2.58452e25			−1.67571			−0.837853	+	0.545896i	$0.816189\pi$
$920$	5.96139e23	−	2.45686e25i	0.0382958	−	1.57828i
$921$	−2.49397e25			−1.58739
$922$		−	2.81092e25i		−	1.77270i
$923$			3.57892e24i			0.223634i
$924$	−2.78380e25			−1.72356
$925$	−1.06320e24	+	2.18959e25i	−0.0652244	+	1.34325i
$926$	2.66121e25			1.61765
$927$		−	1.68171e23i		−	0.0101292i
$928$			3.46574e25i			2.06842i
$929$	−1.29245e25			−0.764331			−0.382165	−	0.924094i	$-0.624822\pi$
$929$	−1.29245e25			−0.764331			−0.382165	+	0.924094i	$0.624822\pi$
$930$	4.50889e23	−	1.85824e25i	0.0264219	−	1.08892i
$931$	1.29421e25			0.751508
$932$			3.65929e25i			2.10553i
$933$			1.89578e25i			1.08092i
$934$	8.72265e23			0.0492833
$935$	−2.90524e24	−	7.04935e22i	−0.162661	−	0.00394685i
$936$	−8.85932e22			−0.00491537
$937$			3.51601e24i			0.193314i	0.995318	+	0.0966570i	$0.0308150\pi$
$937$			3.51601e24i			0.193314i	−0.995318	+	0.0966570i	$0.969185\pi$
$938$		−	5.51223e24i		−	0.300333i
$939$	2.16929e25			1.17128
$940$	−9.12568e24	−	2.21428e23i	−0.488291	−	0.0118480i
$941$	−6.77453e24			−0.359225			−0.179613	−	0.983737i	$-0.557484\pi$
$941$	−6.77453e24			−0.359225			−0.179613	+	0.983737i	$0.557484\pi$
$942$			4.26181e25i			2.23955i
$943$			6.32435e24i			0.329357i
$944$	5.17189e25			2.66924
$945$	7.40628e23	−	3.05234e25i	0.0378817	−	1.56121i
$946$	1.78043e25			0.902507
$947$			1.57938e25i			0.793438i	0.917940	+	0.396719i	$0.129851\pi$
$947$			1.57938e25i			0.793438i	−0.917940	+	0.396719i	$0.870149\pi$
$948$		−	2.81945e25i		−	1.40376i
$949$	−7.72629e23			−0.0381249
$950$	9.60448e23	−	1.97797e25i	0.0469703	−	0.967319i
$951$	3.32606e24			0.161212
$952$		−	2.66832e25i		−	1.28181i
$953$			1.60725e25i			0.765232i	0.923908	+	0.382616i	$0.124977\pi$
$953$			1.60725e25i			0.765232i	−0.923908	+	0.382616i	$0.875023\pi$
$954$	−5.15000e23			−0.0243022
$955$	−5.68334e23	+	2.34227e25i	−0.0265812	+	1.09549i
$956$	−2.52600e25			−1.17096
$957$		−	1.53298e25i		−	0.704345i
$958$		−	3.29485e25i		−	1.50048i
$959$	2.03231e25			0.917342
$960$	−1.01348e25	−	2.45913e23i	−0.453429	−	0.0110021i
$961$	−1.44354e25			−0.640147
$962$		−	1.17764e25i		−	0.517634i
$963$			1.74150e23i			0.00758753i
$964$	−2.74732e25			−1.18647
$965$	1.06940e25	+	2.59482e23i	0.457782	+	0.0111077i
$966$	−4.33031e25			−1.83744
$967$			1.43849e25i			0.605037i	0.953143	+	0.302519i	$0.0978275\pi$
$967$			1.43849e25i			0.605037i	−0.953143	+	0.302519i	$0.902173\pi$
$968$		−	4.48487e25i		−	1.86986i
$969$	4.34684e24			0.179648
$970$	−6.41827e23	+	2.64515e25i	−0.0262941	+	1.08365i
$971$	3.71146e23			0.0150724			0.00753618	−	0.999972i	$-0.497601\pi$
$971$	3.71146e23			0.0150724			0.00753618	+	0.999972i	$0.497601\pi$
$972$			1.11178e24i			0.0447565i
$973$		−	4.04268e25i		−	1.61328i
$974$	1.04695e25			0.414168
$975$	−5.34721e24	−	2.59645e23i	−0.209695	−	0.0101822i
$976$	−5.09037e25			−1.97891
$977$		−	5.02948e24i		−	0.193829i	−0.995293	−	0.0969146i	$-0.969103\pi$
$977$		−	5.02948e24i		−	0.193829i	0.995293	−	0.0969146i	$-0.0308974\pi$
$978$			2.06782e25i			0.790008i
$979$	9.90244e24			0.375050
$980$	−2.13034e24	+	8.77972e25i	−0.0799883	+	3.29654i
$981$	3.32008e23			0.0123584
$982$		−	4.15727e25i		−	1.53412i
$983$			6.31866e23i			0.0231164i	0.999933	+	0.0115582i	$0.00367917\pi$
$983$			6.31866e23i			0.0231164i	−0.999933	+	0.0115582i	$0.996321\pi$
$984$	3.36593e25			1.22080
$985$	1.05532e25	+	2.56065e23i	0.379468	+	0.00920753i
$986$	2.57500e25			0.917958
$987$			9.17833e24i			0.324390i
$988$			7.44264e24i			0.260791i
$989$	1.93760e25			0.673124
$990$	−2.43451e23	−	5.90715e21i	−0.00838516	−	0.000203460i
$991$	4.61468e25			1.57585			0.787927	−	0.615769i	$-0.211155\pi$
$991$	4.61468e25			1.57585			0.787927	+	0.615769i	$0.211155\pi$
$992$		−	2.47732e25i		−	0.838750i
$993$		−	3.97693e25i		−	1.33499i
$994$	−9.03272e25			−3.00632
$995$	1.38944e24	−	5.72628e25i	0.0458505	−	1.88963i
$996$	7.24449e25			2.37030
$997$			4.92727e25i			1.59844i	0.601037	+	0.799222i	$0.294755\pi$
$997$			4.92727e25i			1.59844i	−0.601037	+	0.799222i	$0.705245\pi$
$998$			7.00725e25i			2.25392i
$999$	−4.23674e25			−1.35122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.18.b.a.4.1	✓	8
3.2	odd	2		45.18.b.b.19.8		8
4.3	odd	2		80.18.c.b.49.6		8
5.2	odd	4		25.18.a.f.1.8		8
5.3	odd	4		25.18.a.f.1.1		8
5.4	even	2	inner	5.18.b.a.4.8	yes	8
15.14	odd	2		45.18.b.b.19.1		8
20.19	odd	2		80.18.c.b.49.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.b.a.4.1	✓	8	1.1	even	1	trivial
5.18.b.a.4.8	yes	8	5.4	even	2	inner
25.18.a.f.1.1		8	5.3	odd	4
25.18.a.f.1.8		8	5.2	odd	4
45.18.b.b.19.1		8	15.14	odd	2
45.18.b.b.19.8		8	3.2	odd	2
80.18.c.b.49.3		8	20.19	odd	2
80.18.c.b.49.6		8	4.3	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +O(q^{10})\)	\(q-660.562i q^{2} -11309.3i q^{3} -305271. q^{4} +(-21187.7 + 873207. i) q^{5} -7.47047e6 q^{6} -2.37065e7i q^{7} +1.15069e8i q^{8} +1.24087e6 q^{9} +(5.76808e8 + 1.39958e7i) q^{10} -3.40136e8 q^{11} +3.45238e9i q^{12} +6.20461e8i q^{13} -1.56596e10 q^{14} +(9.87532e9 + 2.39618e8i) q^{15} +3.59979e10 q^{16} -9.78165e9i q^{17} -8.19675e8i q^{18} -3.92941e10 q^{19} +(6.46800e9 - 2.66565e11i) q^{20} -2.68102e11 q^{21} +2.24681e11i q^{22} +2.44514e11i q^{23} +1.30135e12 q^{24} +(-7.62042e11 - 3.70026e10i) q^{25} +4.09853e11 q^{26} -1.47451e12i q^{27} +7.23689e12i q^{28} -3.98521e12 q^{29} +(1.58282e11 - 6.52327e12i) q^{30} +2.84863e12 q^{31} -8.69651e12i q^{32} +3.84668e12i q^{33} -6.46139e12 q^{34} +(2.07006e13 + 5.02286e11i) q^{35} -3.78802e11 q^{36} -2.87331e13i q^{37} +2.59562e13i q^{38} +7.01695e12 q^{39} +(-1.00479e14 - 2.43806e12i) q^{40} +2.58650e13 q^{41} +1.77098e14i q^{42} -7.92427e13i q^{43} +1.03833e14 q^{44} +(-2.62913e10 + 1.08354e12i) q^{45} +1.61517e14 q^{46} -3.42344e13i q^{47} -4.07109e14i q^{48} -3.29366e14 q^{49} +(-2.44425e13 + 5.03376e14i) q^{50} -1.10623e14 q^{51} -1.89408e14i q^{52} -6.28298e14i q^{53} -9.74008e14 q^{54} +(7.20671e12 - 2.97009e14i) q^{55} +2.72788e15 q^{56} +4.44388e14i q^{57} +2.63248e15i q^{58} +1.43672e15 q^{59} +(-3.01465e15 - 7.31483e13i) q^{60} -1.41408e15 q^{61} -1.88170e15i q^{62} -2.94167e13i q^{63} -1.02627e15 q^{64} +(-5.41791e14 - 1.31462e13i) q^{65} +2.54097e15 q^{66} +3.52003e14i q^{67} +2.98605e15i q^{68} +2.76527e15 q^{69} +(3.31792e14 - 1.36741e16i) q^{70} +5.76817e15 q^{71} +1.42786e14i q^{72} +1.24525e15i q^{73} -1.89800e16 q^{74} +(-4.18472e14 + 8.61812e15i) q^{75} +1.19953e16 q^{76} +8.06341e15i q^{77} -4.63513e15i q^{78} -8.16669e15 q^{79} +(-7.62714e14 + 3.14336e16i) q^{80} -1.65154e16 q^{81} -1.70854e16i q^{82} -2.09840e16i q^{83} +8.18438e16 q^{84} +(8.54140e15 + 2.07251e14i) q^{85} -5.23447e16 q^{86} +4.50697e16i q^{87} -3.91391e16i q^{88} -2.91132e16 q^{89} +(7.15746e14 + 1.73671e13i) q^{90} +1.47089e16 q^{91} -7.46430e16i q^{92} -3.22159e16i q^{93} -2.26140e16 q^{94} +(8.32554e14 - 3.43119e16i) q^{95} -9.83511e16 q^{96} +4.58585e16i q^{97} +2.17567e17i q^{98} -4.22065e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9}+O(q^{10}) \) 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9	\( 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9} + 329570200 q^{10} + 463296576 q^{11} - 29937907992 q^{14} + 30646226400 q^{15} + 30848001568 q^{16} - 20615713280 q^{19} - 47558579400 q^{20} - 75039699024 q^{21} + 1768741136160 q^{24} - 1789249435000 q^{25} - 838901194224 q^{26} - 4079017824720 q^{29} + 2416984007400 q^{30} + 11329328658496 q^{31} - 36406243632832 q^{34} + 4019663899200 q^{35} + 59729752432728 q^{36} + 40318460422272 q^{39} - 209747532172000 q^{40} + 97217252847456 q^{41} - 116357853210912 q^{44} - 366841998003600 q^{45} + 10\!\cdots\!36 q^{46}+ \cdots - 56\!\cdots\!68 q^{99}+O(q^{100}) \) 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9 + 329570200 * q^10 + 463296576 * q^11 - 29937907992 * q^14 + 30646226400 * q^15 + 30848001568 * q^16 - 20615713280 * q^19 - 47558579400 * q^20 - 75039699024 * q^21 + 1768741136160 * q^24 - 1789249435000 * q^25 - 838901194224 * q^26 - 4079017824720 * q^29 + 2416984007400 * q^30 + 11329328658496 * q^31 - 36406243632832 * q^34 + 4019663899200 * q^35 + 59729752432728 * q^36 + 40318460422272 * q^39 - 209747532172000 * q^40 + 97217252847456 * q^41 - 116357853210912 * q^44 - 366841998003600 * q^45 + 1081224261700136 * q^46 - 856574357621656 * q^49 - 1283266301910000 * q^50 + 2468309514424896 * q^51 - 3408409774777680 * q^54 - 2042713226757600 * q^55 + 8363016326678880 * q^56 - 1091409512240640 * q^59 - 11479379108104800 * q^60 + 8064731010774976 * q^61 - 3616160324265856 * q^64 - 11989509557901600 * q^65 + 27318846906958752 * q^66 - 12078989597365008 * q^69 - 13190931213697800 * q^70 + 25241492058140736 * q^71 - 29902523510328912 * q^74 + 3839235716880000 * q^75 + 20767634734678560 * q^76 + 3229852337730880 * q^79 + 1263407265391200 * q^80 - 49353541005202632 * q^81 + 101439947332382688 * q^84 + 25693702369787200 * q^85 - 165112838769552744 * q^86 + 92963987535626640 * q^89 + 206315814421823400 * q^90 - 225591670236809664 * q^91 + 162612564681867848 * q^94 + 204319715505252000 * q^95 - 654303222993538944 * q^96 - 56327331239952768 * q^99

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