LMFDB - Embedded newform 405.8.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,8,Mod(1,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("405.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	405.a (trivial)

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:	yes
Analytic conductor:	$126.515935321$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 1479 x^{13} + 9623 x^{12} + 858424 x^{11} - 5043114 x^{10} - 248945154 x^{9} + \cdots + 784812676793472 $ x^15 - 7x^14 - 1479x^13 + 9623x^12 + 858424x^11 - 5043114x^10 - 248945154x^9 + 1250661006x^8 + 38068075521x^7 - 145949082795x^6 - 2962070172819x^5 + 6595509983499x^4 + 100284834644406x^3 - 44138883317076x^2 - 768967569531540x + 784812676793472
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{33} $
Twist minimal:	no (minimal twist has level 45)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$15.1697$ of defining polynomial
Character	$\chi$	$=$	405.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-14.1697 q^{2} +72.7792 q^{4} +125.000 q^{5} -1587.51 q^{7} +782.460 q^{8} +O(q^{10})$	\(q-14.1697 q^{2} +72.7792 q^{4} +125.000 q^{5} -1587.51 q^{7} +782.460 q^{8} -1771.21 q^{10} +5446.11 q^{11} +8848.89 q^{13} +22494.4 q^{14} -20402.9 q^{16} +28524.0 q^{17} +17605.5 q^{19} +9097.40 q^{20} -77169.5 q^{22} +31995.5 q^{23} +15625.0 q^{25} -125386. q^{26} -115538. q^{28} -61571.2 q^{29} +254866. q^{31} +188948. q^{32} -404175. q^{34} -198438. q^{35} -544384. q^{37} -249464. q^{38} +97807.5 q^{40} -103050. q^{41} +578298. q^{43} +396363. q^{44} -453365. q^{46} +700969. q^{47} +1.69664e6 q^{49} -221401. q^{50} +644015. q^{52} +373781. q^{53} +680763. q^{55} -1.24216e6 q^{56} +872443. q^{58} -122387. q^{59} +260717. q^{61} -3.61136e6 q^{62} -65748.1 q^{64} +1.10611e6 q^{65} +456611. q^{67} +2.07595e6 q^{68} +2.81180e6 q^{70} -4.98797e6 q^{71} +3.69501e6 q^{73} +7.71373e6 q^{74} +1.28131e6 q^{76} -8.64573e6 q^{77} -6.34040e6 q^{79} -2.55037e6 q^{80} +1.46018e6 q^{82} -4.13316e6 q^{83} +3.56550e6 q^{85} -8.19428e6 q^{86} +4.26136e6 q^{88} -671500. q^{89} -1.40477e7 q^{91} +2.32860e6 q^{92} -9.93249e6 q^{94} +2.20069e6 q^{95} -2.66280e6 q^{97} -2.40408e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 8 q^{2} + 1088 q^{4} + 1875 q^{5} + 1289 q^{7} + 4434 q^{8}+O(q^{10}) $ 15 * q + 8 * q^2 + 1088 * q^4 + 1875 * q^5 + 1289 * q^7 + 4434 * q^8	\( 15 q + 8 q^{2} + 1088 q^{4} + 1875 q^{5} + 1289 q^{7} + 4434 q^{8} + 1000 q^{10} + 1658 q^{11} + 9874 q^{13} + 7695 q^{14} + 62612 q^{16} - 3598 q^{17} + 21376 q^{19} + 136000 q^{20} - 52519 q^{22} + 96441 q^{23} + 234375 q^{25} + 126146 q^{26} + 174449 q^{28} + 259297 q^{29} + 373568 q^{31} + 1134550 q^{32} + 423851 q^{34} + 161125 q^{35} + 517872 q^{37} + 690059 q^{38} + 554250 q^{40} + 520501 q^{41} + 1898836 q^{43} + 1277707 q^{44} + 3154677 q^{46} + 2259041 q^{47} + 4316308 q^{49} + 125000 q^{50} + 5398554 q^{52} - 102274 q^{53} + 207250 q^{55} - 504621 q^{56} + 3190987 q^{58} - 1680874 q^{59} - 1066457 q^{61} - 274110 q^{62} + 6541980 q^{64} + 1234250 q^{65} + 6522389 q^{67} + 1420717 q^{68} + 961875 q^{70} - 32786 q^{71} + 5359102 q^{73} - 4045556 q^{74} + 4649241 q^{76} + 2586078 q^{77} + 9319346 q^{79} + 7826500 q^{80} + 7460620 q^{82} - 12758277 q^{83} - 449750 q^{85} - 20044675 q^{86} + 6691143 q^{88} - 18776241 q^{89} + 9244102 q^{91} - 13862829 q^{92} + 25905119 q^{94} + 2672000 q^{95} + 2788224 q^{97} - 1679531 q^{98}+O(q^{100}) \) 15 * q + 8 * q^2 + 1088 * q^4 + 1875 * q^5 + 1289 * q^7 + 4434 * q^8 + 1000 * q^10 + 1658 * q^11 + 9874 * q^13 + 7695 * q^14 + 62612 * q^16 - 3598 * q^17 + 21376 * q^19 + 136000 * q^20 - 52519 * q^22 + 96441 * q^23 + 234375 * q^25 + 126146 * q^26 + 174449 * q^28 + 259297 * q^29 + 373568 * q^31 + 1134550 * q^32 + 423851 * q^34 + 161125 * q^35 + 517872 * q^37 + 690059 * q^38 + 554250 * q^40 + 520501 * q^41 + 1898836 * q^43 + 1277707 * q^44 + 3154677 * q^46 + 2259041 * q^47 + 4316308 * q^49 + 125000 * q^50 + 5398554 * q^52 - 102274 * q^53 + 207250 * q^55 - 504621 * q^56 + 3190987 * q^58 - 1680874 * q^59 - 1066457 * q^61 - 274110 * q^62 + 6541980 * q^64 + 1234250 * q^65 + 6522389 * q^67 + 1420717 * q^68 + 961875 * q^70 - 32786 * q^71 + 5359102 * q^73 - 4045556 * q^74 + 4649241 * q^76 + 2586078 * q^77 + 9319346 * q^79 + 7826500 * q^80 + 7460620 * q^82 - 12758277 * q^83 - 449750 * q^85 - 20044675 * q^86 + 6691143 * q^88 - 18776241 * q^89 + 9244102 * q^91 - 13862829 * q^92 + 25905119 * q^94 + 2672000 * q^95 + 2788224 * q^97 - 1679531 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−14.1697	−1.25243	−0.626216	−	0.779649i	$-0.715397\pi$
$2$	−14.1697	−1.25243	−0.626216	+	0.779649i	$0.715397\pi$
$3$	0	0
$3$	0	0
$4$	72.7792	0.568587
$5$	125.000	0.447214
$5$	125.000	0.447214
$6$	0	0
$7$	−1587.51	−1.74933	−0.874667	−	0.484725i	$-0.838920\pi$
$7$	−1587.51	−1.74933	−0.874667	+	0.484725i	$0.838920\pi$
$8$	782.460	0.540315
$9$	0	0
$10$	−1771.21	−0.560105
$11$	5446.11	1.23371	0.616853	−	0.787078i	$-0.288407\pi$
$11$	5446.11	1.23371	0.616853	+	0.787078i	$0.288407\pi$
$12$	0	0
$13$	8848.89	1.11709	0.558543	−	0.829475i	$-0.311360\pi$
$13$	8848.89	1.11709	0.558543	+	0.829475i	$0.311360\pi$
$14$	22494.4	2.19092
$15$	0	0
$16$	−20402.9	−1.24530
$17$	28524.0	1.40812	0.704059	−	0.710141i	$-0.251369\pi$
$17$	28524.0	1.40812	0.704059	+	0.710141i	$0.251369\pi$
$18$	0	0
$19$	17605.5	0.588858	0.294429	−	0.955673i	$-0.404871\pi$
$19$	17605.5	0.588858	0.294429	+	0.955673i	$0.404871\pi$
$20$	9097.40	0.254280
$21$	0	0
$22$	−77169.5	−1.54513
$23$	31995.5	0.548329	0.274164	−	0.961683i	$-0.411599\pi$
$23$	31995.5	0.548329	0.274164	+	0.961683i	$0.411599\pi$
$24$	0	0
$25$	15625.0	0.200000
$26$	−125386.	−1.39908
$27$	0	0
$28$	−115538.	−0.994649
$29$	−61571.2	−0.468797	−0.234399	−	0.972141i	$-0.575312\pi$
$29$	−61571.2	−0.468797	−0.234399	+	0.972141i	$0.575312\pi$
$30$	0	0
$31$	254866.	1.53654	0.768272	−	0.640123i	$-0.221117\pi$
$31$	254866.	1.53654	0.768272	+	0.640123i	$0.221117\pi$
$32$	188948.	1.01933
$33$	0	0
$34$	−404175.	−1.76357
$35$	−198438.	−0.782326
$36$	0	0
$37$	−544384.	−1.76685	−0.883424	−	0.468575i	$-0.844768\pi$
$37$	−544384.	−1.76685	−0.883424	+	0.468575i	$0.844768\pi$
$38$	−249464.	−0.737505
$39$	0	0
$40$	97807.5	0.241636
$41$	−103050.	−0.233510	−0.116755	−	0.993161i	$-0.537249\pi$
$41$	−103050.	−0.233510	−0.116755	+	0.993161i	$0.537249\pi$
$42$	0	0
$43$	578298.	1.10921	0.554603	−	0.832115i	$-0.312870\pi$
$43$	578298.	1.10921	0.554603	+	0.832115i	$0.312870\pi$
$44$	396363.	0.701470
$45$	0	0
$46$	−453365.	−0.686745
$47$	700969.	0.984818	0.492409	−	0.870364i	$-0.336116\pi$
$47$	700969.	0.984818	0.492409	+	0.870364i	$0.336116\pi$
$48$	0	0
$49$	1.69664e6	2.06017
$50$	−221401.	−0.250487
$51$	0	0
$52$	644015.	0.635162
$53$	373781.	0.344867	0.172434	−	0.985021i	$-0.444837\pi$
$53$	373781.	0.344867	0.172434	+	0.985021i	$0.444837\pi$
$54$	0	0
$55$	680763.	0.551730
$56$	−1.24216e6	−0.945192
$57$	0	0
$58$	872443.	0.587137
$59$	−122387.	−0.0775805	−0.0387903	−	0.999247i	$-0.512350\pi$
$59$	−122387.	−0.0775805	−0.0387903	+	0.999247i	$0.512350\pi$
$60$	0	0
$61$	260717.	0.147067	0.0735336	−	0.997293i	$-0.476572\pi$
$61$	260717.	0.147067	0.0735336	+	0.997293i	$0.476572\pi$
$62$	−3.61136e6	−1.92442
$63$	0	0
$64$	−65748.1	−0.0313511
$65$	1.10611e6	0.499576
$66$	0	0
$67$	456611.	0.185475	0.0927374	−	0.995691i	$-0.470438\pi$
$67$	456611.	0.185475	0.0927374	+	0.995691i	$0.470438\pi$
$68$	2.07595e6	0.800639
$69$	0	0
$70$	2.81180e6	0.979810
$71$	−4.98797e6	−1.65394	−0.826970	−	0.562246i	$-0.809938\pi$
$71$	−4.98797e6	−1.65394	−0.826970	+	0.562246i	$0.809938\pi$
$72$	0	0
$73$	3.69501e6	1.11169	0.555847	−	0.831285i	$-0.312394\pi$
$73$	3.69501e6	1.11169	0.555847	+	0.831285i	$0.312394\pi$
$74$	7.71373e6	2.21286
$75$	0	0
$76$	1.28131e6	0.334817
$77$	−8.64573e6	−2.15816
$78$	0	0
$79$	−6.34040e6	−1.44684	−0.723422	−	0.690406i	$-0.757432\pi$
$79$	−6.34040e6	−1.44684	−0.723422	+	0.690406i	$0.757432\pi$
$80$	−2.55037e6	−0.556913
$81$	0	0
$82$	1.46018e6	0.292455
$83$	−4.13316e6	−0.793430	−0.396715	−	0.917942i	$-0.629850\pi$
$83$	−4.13316e6	−0.793430	−0.396715	+	0.917942i	$0.629850\pi$
$84$	0	0
$85$	3.56550e6	0.629730
$86$	−8.19428e6	−1.38921
$87$	0	0
$88$	4.26136e6	0.666590
$89$	−671500.	−0.100967	−0.0504837	−	0.998725i	$-0.516076\pi$
$89$	−671500.	−0.100967	−0.0504837	+	0.998725i	$0.516076\pi$
$90$	0	0
$91$	−1.40477e7	−1.95416
$92$	2.32860e6	0.311773
$93$	0	0
$94$	−9.93249e6	−1.23342
$95$	2.20069e6	0.263345
$96$	0	0
$97$	−2.66280e6	−0.296236	−0.148118	−	0.988970i	$-0.547322\pi$
$97$	−2.66280e6	−0.296236	−0.148118	+	0.988970i	$0.547322\pi$
$98$	−2.40408e7	−2.58022
$99$	0	0
$100$	1.13717e6	0.113717
$101$	−4.48325e6	−0.432980	−0.216490	−	0.976285i	$-0.569461\pi$
$101$	−4.48325e6	−0.432980	−0.216490	+	0.976285i	$0.569461\pi$
$102$	0	0
$103$	−6.60142e6	−0.595261	−0.297630	−	0.954681i	$-0.596196\pi$
$103$	−6.60142e6	−0.595261	−0.297630	+	0.954681i	$0.596196\pi$
$104$	6.92390e6	0.603579
$105$	0	0
$106$	−5.29635e6	−0.431923
$107$	2.06756e7	1.63161	0.815804	−	0.578329i	$-0.196295\pi$
$107$	2.06756e7	1.63161	0.815804	+	0.578329i	$0.196295\pi$
$108$	0	0
$109$	3.20823e6	0.237286	0.118643	−	0.992937i	$-0.462146\pi$
$109$	3.20823e6	0.237286	0.118643	+	0.992937i	$0.462146\pi$
$110$	−9.64618e6	−0.691005
$111$	0	0
$112$	3.23898e7	2.17844
$113$	1.69033e6	0.110204	0.0551018	−	0.998481i	$-0.482452\pi$
$113$	1.69033e6	0.110204	0.0551018	+	0.998481i	$0.482452\pi$
$114$	0	0
$115$	3.99943e6	0.245220
$116$	−4.48110e6	−0.266552
$117$	0	0
$118$	1.73418e6	0.0971644
$119$	−4.52821e7	−2.46327
$120$	0	0
$121$	1.01729e7	0.522031
$122$	−3.69428e6	−0.184192
$123$	0	0
$124$	1.85489e7	0.873660
$125$	1.95312e6	0.0894427
$126$	0	0
$127$	−2.13533e7	−0.925023	−0.462511	−	0.886613i	$-0.653052\pi$
$127$	−2.13533e7	−0.925023	−0.462511	+	0.886613i	$0.653052\pi$
$128$	−2.32537e7	−0.980069
$129$	0	0
$130$	−1.56732e7	−0.625686
$131$	−2.83548e7	−1.10199	−0.550994	−	0.834509i	$-0.685751\pi$
$131$	−2.83548e7	−1.10199	−0.550994	+	0.834509i	$0.685751\pi$
$132$	0	0
$133$	−2.79488e7	−1.03011
$134$	−6.47003e6	−0.232295
$135$	0	0
$136$	2.23189e7	0.760828
$137$	3.59741e7	1.19527	0.597637	−	0.801767i	$-0.296106\pi$
$137$	3.59741e7	1.19527	0.597637	+	0.801767i	$0.296106\pi$
$138$	0	0
$139$	1.43690e7	0.453812	0.226906	−	0.973917i	$-0.427139\pi$
$139$	1.43690e7	0.453812	0.226906	+	0.973917i	$0.427139\pi$
$140$	−1.44422e7	−0.444821
$141$	0	0
$142$	7.06779e7	2.07145
$143$	4.81920e7	1.37816
$144$	0	0
$145$	−7.69640e6	−0.209652
$146$	−5.23570e7	−1.39232
$147$	0	0
$148$	−3.96198e7	−1.00461
$149$	2.57862e6	0.0638610	0.0319305	−	0.999490i	$-0.489834\pi$
$149$	2.57862e6	0.0638610	0.0319305	+	0.999490i	$0.489834\pi$
$150$	0	0
$151$	−2.25337e7	−0.532614	−0.266307	−	0.963888i	$-0.585804\pi$
$151$	−2.25337e7	−0.532614	−0.266307	+	0.963888i	$0.585804\pi$
$152$	1.37756e7	0.318169
$153$	0	0
$154$	1.22507e8	2.70295
$155$	3.18582e7	0.687164
$156$	0	0
$157$	−2.87711e7	−0.593345	−0.296673	−	0.954979i	$-0.595877\pi$
$157$	−2.87711e7	−0.593345	−0.296673	+	0.954979i	$0.595877\pi$
$158$	8.98413e7	1.81207
$159$	0	0
$160$	2.36184e7	0.455860
$161$	−5.07930e7	−0.959210
$162$	0	0
$163$	7.75003e7	1.40167	0.700837	−	0.713322i	$-0.252810\pi$
$163$	7.75003e7	1.40167	0.700837	+	0.713322i	$0.252810\pi$
$164$	−7.49990e6	−0.132771
$165$	0	0
$166$	5.85654e7	0.993717
$167$	−1.37770e7	−0.228901	−0.114451	−	0.993429i	$-0.536511\pi$
$167$	−1.37770e7	−0.228901	−0.114451	+	0.993429i	$0.536511\pi$
$168$	0	0
$169$	1.55543e7	0.247883
$170$	−5.05219e7	−0.788694
$171$	0	0
$172$	4.20881e7	0.630680
$173$	−1.98619e7	−0.291649	−0.145824	−	0.989311i	$-0.546583\pi$
$173$	−1.98619e7	−0.291649	−0.145824	+	0.989311i	$0.546583\pi$
$174$	0	0
$175$	−2.48048e7	−0.349867
$176$	−1.11117e8	−1.53633
$177$	0	0
$178$	9.51493e6	0.126455
$179$	1.24838e8	1.62690	0.813448	−	0.581638i	$-0.197588\pi$
$179$	1.24838e8	1.62690	0.813448	+	0.581638i	$0.197588\pi$
$180$	0	0
$181$	8.67803e7	1.08779	0.543896	−	0.839152i	$-0.316948\pi$
$181$	8.67803e7	1.08779	0.543896	+	0.839152i	$0.316948\pi$
$182$	1.99051e8	2.44745
$183$	0	0
$184$	2.50352e7	0.296270
$185$	−6.80480e7	−0.790158
$186$	0	0
$187$	1.55345e8	1.73720
$188$	5.10159e7	0.559955
$189$	0	0
$190$	−3.11830e7	−0.329822
$191$	−1.07588e8	−1.11724	−0.558622	−	0.829422i	$-0.688670\pi$
$191$	−1.07588e8	−1.11724	−0.558622	+	0.829422i	$0.688670\pi$
$192$	0	0
$193$	6.11202e7	0.611976	0.305988	−	0.952035i	$-0.401013\pi$
$193$	6.11202e7	0.611976	0.305988	+	0.952035i	$0.401013\pi$
$194$	3.77310e7	0.371016
$195$	0	0
$196$	1.23480e8	1.17139
$197$	−1.34089e7	−0.124957	−0.0624786	−	0.998046i	$-0.519901\pi$
$197$	−1.34089e7	−0.124957	−0.0624786	+	0.998046i	$0.519901\pi$
$198$	0	0
$199$	2.02539e8	1.82190	0.910949	−	0.412520i	$-0.135351\pi$
$199$	2.02539e8	1.82190	0.910949	+	0.412520i	$0.135351\pi$
$200$	1.22259e7	0.108063
$201$	0	0
$202$	6.35261e7	0.542278
$203$	9.77448e7	0.820082
$204$	0	0
$205$	−1.28813e7	−0.104429
$206$	9.35399e7	0.745524
$207$	0	0
$208$	−1.80543e8	−1.39110
$209$	9.58813e7	0.726477
$210$	0	0
$211$	−7.98458e7	−0.585145	−0.292573	−	0.956243i	$-0.594511\pi$
$211$	−7.98458e7	−0.585145	−0.292573	+	0.956243i	$0.594511\pi$
$212$	2.72035e7	0.196087
$213$	0	0
$214$	−2.92967e8	−2.04348
$215$	7.22872e7	0.496052
$216$	0	0
$217$	−4.04601e8	−2.68793
$218$	−4.54595e7	−0.297185
$219$	0	0
$220$	4.95454e7	0.313707
$221$	2.52406e8	1.57299
$222$	0	0
$223$	8.28221e7	0.500126	0.250063	−	0.968230i	$-0.419549\pi$
$223$	8.28221e7	0.500126	0.250063	+	0.968230i	$0.419549\pi$
$224$	−2.99956e8	−1.78315
$225$	0	0
$226$	−2.39513e7	−0.138023
$227$	−2.51035e7	−0.142444	−0.0712218	−	0.997461i	$-0.522690\pi$
$227$	−2.51035e7	−0.142444	−0.0712218	+	0.997461i	$0.522690\pi$
$228$	0	0
$229$	7.72730e6	0.0425210	0.0212605	−	0.999774i	$-0.493232\pi$
$229$	7.72730e6	0.0425210	0.0212605	+	0.999774i	$0.493232\pi$
$230$	−5.66706e7	−0.307122
$231$	0	0
$232$	−4.81770e7	−0.253298
$233$	1.81671e8	0.940890	0.470445	−	0.882429i	$-0.344093\pi$
$233$	1.81671e8	0.940890	0.470445	+	0.882429i	$0.344093\pi$
$234$	0	0
$235$	8.76211e7	0.440424
$236$	−8.90721e6	−0.0441113
$237$	0	0
$238$	6.41632e8	3.08508
$239$	6.91830e7	0.327798	0.163899	−	0.986477i	$-0.447593\pi$
$239$	6.91830e7	0.327798	0.163899	+	0.986477i	$0.447593\pi$
$240$	0	0
$241$	5.46590e7	0.251537	0.125769	−	0.992060i	$-0.459860\pi$
$241$	5.46590e7	0.251537	0.125769	+	0.992060i	$0.459860\pi$
$242$	−1.44147e8	−0.653808
$243$	0	0
$244$	1.89748e7	0.0836205
$245$	2.12080e8	0.921335
$246$	0	0
$247$	1.55789e8	0.657805
$248$	1.99422e8	0.830218
$249$	0	0
$250$	−2.76751e7	−0.112021
$251$	−1.67326e8	−0.667892	−0.333946	−	0.942592i	$-0.608380\pi$
$251$	−1.67326e8	−0.667892	−0.333946	+	0.942592i	$0.608380\pi$
$252$	0	0
$253$	1.74251e8	0.676476
$254$	3.02569e8	1.15853
$255$	0	0
$256$	3.37912e8	1.25882
$257$	−1.92976e8	−0.709147	−0.354574	−	0.935028i	$-0.615374\pi$
$257$	−1.92976e8	−0.709147	−0.354574	+	0.935028i	$0.615374\pi$
$258$	0	0
$259$	8.64213e8	3.09081
$260$	8.05019e7	0.284053
$261$	0	0
$262$	4.01778e8	1.38017
$263$	2.64898e8	0.897912	0.448956	−	0.893554i	$-0.351796\pi$
$263$	2.64898e8	0.897912	0.448956	+	0.893554i	$0.351796\pi$
$264$	0	0
$265$	4.67227e7	0.154229
$266$	3.96025e8	1.29014
$267$	0	0
$268$	3.32318e7	0.105459
$269$	1.43614e8	0.449846	0.224923	−	0.974376i	$-0.427787\pi$
$269$	1.43614e8	0.449846	0.224923	+	0.974376i	$0.427787\pi$
$270$	0	0
$271$	−3.01559e8	−0.920405	−0.460203	−	0.887814i	$-0.652223\pi$
$271$	−3.01559e8	−0.920405	−0.460203	+	0.887814i	$0.652223\pi$
$272$	−5.81973e8	−1.75352
$273$	0	0
$274$	−5.09740e8	−1.49700
$275$	8.50954e7	0.246741
$276$	0	0
$277$	−8.55477e7	−0.241841	−0.120920	−	0.992662i	$-0.538585\pi$
$277$	−8.55477e7	−0.241841	−0.120920	+	0.992662i	$0.538585\pi$
$278$	−2.03604e8	−0.568369
$279$	0	0
$280$	−1.55270e8	−0.422702
$281$	4.59839e8	1.23633	0.618163	−	0.786050i	$-0.287877\pi$
$281$	4.59839e8	1.23633	0.618163	+	0.786050i	$0.287877\pi$
$282$	0	0
$283$	5.28600e8	1.38636	0.693178	−	0.720767i	$-0.256210\pi$
$283$	5.28600e8	1.38636	0.693178	+	0.720767i	$0.256210\pi$
$284$	−3.63021e8	−0.940410
$285$	0	0
$286$	−6.82864e8	−1.72605
$287$	1.63593e8	0.408486
$288$	0	0
$289$	4.03280e8	0.982799
$290$	1.09055e8	0.262576
$291$	0	0
$292$	2.68920e8	0.632095
$293$	−2.28126e8	−0.529832	−0.264916	−	0.964271i	$-0.585344\pi$
$293$	−2.28126e8	−0.529832	−0.264916	+	0.964271i	$0.585344\pi$
$294$	0	0
$295$	−1.52984e7	−0.0346951
$296$	−4.25959e8	−0.954655
$297$	0	0
$298$	−3.65382e7	−0.0799816
$299$	2.83124e8	0.612531
$300$	0	0
$301$	−9.18052e8	−1.94037
$302$	3.19294e8	0.667063
$303$	0	0
$304$	−3.59203e8	−0.733302
$305$	3.25897e7	0.0657704
$306$	0	0
$307$	7.37110e8	1.45394	0.726972	−	0.686667i	$-0.240927\pi$
$307$	7.37110e8	1.45394	0.726972	+	0.686667i	$0.240927\pi$
$308$	−6.29230e8	−1.22710
$309$	0	0
$310$	−4.51420e8	−0.860626
$311$	−6.23750e7	−0.117584	−0.0587921	−	0.998270i	$-0.518725\pi$
$311$	−6.23750e7	−0.117584	−0.0587921	+	0.998270i	$0.518725\pi$
$312$	0	0
$313$	4.06042e8	0.748455	0.374228	−	0.927337i	$-0.377908\pi$
$313$	4.06042e8	0.748455	0.374228	+	0.927337i	$0.377908\pi$
$314$	4.07676e8	0.743125
$315$	0	0
$316$	−4.61449e8	−0.822657
$317$	4.58904e8	0.809123	0.404562	−	0.914511i	$-0.367424\pi$
$317$	4.58904e8	0.809123	0.404562	+	0.914511i	$0.367424\pi$
$318$	0	0
$319$	−3.35323e8	−0.578358
$320$	−8.21851e6	−0.0140207
$321$	0	0
$322$	7.19720e8	1.20135
$323$	5.02179e8	0.829182
$324$	0	0
$325$	1.38264e8	0.223417
$326$	−1.09815e9	−1.75550
$327$	0	0
$328$	−8.06326e7	−0.126169
$329$	−1.11279e9	−1.72278
$330$	0	0
$331$	2.07571e8	0.314607	0.157304	−	0.987550i	$-0.449720\pi$
$331$	2.07571e8	0.314607	0.157304	+	0.987550i	$0.449720\pi$
$332$	−3.00808e8	−0.451134
$333$	0	0
$334$	1.95216e8	0.286684
$335$	5.70764e7	0.0829469
$336$	0	0
$337$	−2.16938e8	−0.308767	−0.154383	−	0.988011i	$-0.549339\pi$
$337$	−2.16938e8	−0.308767	−0.154383	+	0.988011i	$0.549339\pi$
$338$	−2.20399e8	−0.310457
$339$	0	0
$340$	2.59494e8	0.358057
$341$	1.38802e9	1.89564
$342$	0	0
$343$	−1.38604e9	−1.85459
$344$	4.52495e8	0.599321
$345$	0	0
$346$	2.81437e8	0.365270
$347$	−4.86302e8	−0.624817	−0.312409	−	0.949948i	$-0.601136\pi$
$347$	−4.86302e8	−0.624817	−0.312409	+	0.949948i	$0.601136\pi$
$348$	0	0
$349$	−2.29156e7	−0.0288565	−0.0144282	−	0.999896i	$-0.504593\pi$
$349$	−2.29156e7	−0.0288565	−0.0144282	+	0.999896i	$0.504593\pi$
$350$	3.51476e8	0.438184
$351$	0	0
$352$	1.02903e9	1.25756
$353$	−4.34061e8	−0.525217	−0.262609	−	0.964902i	$-0.584583\pi$
$353$	−4.34061e8	−0.525217	−0.262609	+	0.964902i	$0.584583\pi$
$354$	0	0
$355$	−6.23497e8	−0.739665
$356$	−4.88713e7	−0.0574088
$357$	0	0
$358$	−1.76891e9	−2.03758
$359$	−1.52370e9	−1.73808	−0.869038	−	0.494746i	$-0.835261\pi$
$359$	−1.52370e9	−1.73808	−0.869038	+	0.494746i	$0.835261\pi$
$360$	0	0
$361$	−5.83919e8	−0.653247
$362$	−1.22965e9	−1.36239
$363$	0	0
$364$	−1.02238e9	−1.11111
$365$	4.61876e8	0.497165
$366$	0	0
$367$	−2.04186e8	−0.215622	−0.107811	−	0.994171i	$-0.534384\pi$
$367$	−2.04186e8	−0.215622	−0.107811	+	0.994171i	$0.534384\pi$
$368$	−6.52801e8	−0.682831
$369$	0	0
$370$	9.64216e8	0.989620
$371$	−5.93381e8	−0.603288
$372$	0	0
$373$	−4.11491e8	−0.410562	−0.205281	−	0.978703i	$-0.565811\pi$
$373$	−4.11491e8	−0.410562	−0.205281	+	0.978703i	$0.565811\pi$
$374$	−2.20118e9	−2.17573
$375$	0	0
$376$	5.48480e8	0.532112
$377$	−5.44837e8	−0.523687
$378$	0	0
$379$	2.16590e8	0.204363	0.102181	−	0.994766i	$-0.467418\pi$
$379$	2.16590e8	0.204363	0.102181	+	0.994766i	$0.467418\pi$
$380$	1.60164e8	0.149735
$381$	0	0
$382$	1.52449e9	1.39927
$383$	1.86980e9	1.70059	0.850296	−	0.526305i	$-0.176423\pi$
$383$	1.86980e9	1.70059	0.850296	+	0.526305i	$0.176423\pi$
$384$	0	0
$385$	−1.08072e9	−0.965160
$386$	−8.66053e8	−0.766459
$387$	0	0
$388$	−1.93797e8	−0.168436
$389$	−8.80182e8	−0.758139	−0.379070	−	0.925368i	$-0.623756\pi$
$389$	−8.80182e8	−0.758139	−0.379070	+	0.925368i	$0.623756\pi$
$390$	0	0
$391$	9.12639e8	0.772112
$392$	1.32755e9	1.11314
$393$	0	0
$394$	1.89999e8	0.156500
$395$	−7.92550e8	−0.647048
$396$	0	0
$397$	1.80894e9	1.45097	0.725484	−	0.688239i	$-0.241616\pi$
$397$	1.80894e9	1.45097	0.725484	+	0.688239i	$0.241616\pi$
$398$	−2.86991e9	−2.28180
$399$	0	0
$400$	−3.18796e8	−0.249059
$401$	1.18998e8	0.0921585	0.0460792	−	0.998938i	$-0.485327\pi$
$401$	1.18998e8	0.0921585	0.0460792	+	0.998938i	$0.485327\pi$
$402$	0	0
$403$	2.25528e9	1.71645
$404$	−3.26287e8	−0.246187
$405$	0	0
$406$	−1.38501e9	−1.02710
$407$	−2.96477e9	−2.17977
$408$	0	0
$409$	1.93782e8	0.140050	0.0700248	−	0.997545i	$-0.477692\pi$
$409$	1.93782e8	0.140050	0.0700248	+	0.997545i	$0.477692\pi$
$410$	1.82523e8	0.130790
$411$	0	0
$412$	−4.80446e8	−0.338458
$413$	1.94290e8	0.135714
$414$	0	0
$415$	−5.16645e8	−0.354833
$416$	1.67198e9	1.13868
$417$	0	0
$418$	−1.35861e9	−0.909864
$419$	−2.59371e9	−1.72255	−0.861274	−	0.508140i	$-0.830333\pi$
$419$	−2.59371e9	−1.72255	−0.861274	+	0.508140i	$0.830333\pi$
$420$	0	0
$421$	−2.58032e9	−1.68533	−0.842666	−	0.538437i	$-0.819015\pi$
$421$	−2.58032e9	−1.68533	−0.842666	+	0.538437i	$0.819015\pi$
$422$	1.13139e9	0.732855
$423$	0	0
$424$	2.92469e8	0.186337
$425$	4.45688e8	0.281624
$426$	0	0
$427$	−4.13891e8	−0.257269
$428$	1.50476e9	0.927711
$429$	0	0
$430$	−1.02429e9	−0.621272
$431$	2.38743e9	1.43635	0.718175	−	0.695863i	$-0.244978\pi$
$431$	2.38743e9	1.43635	0.718175	+	0.695863i	$0.244978\pi$
$432$	0	0
$433$	−2.28952e9	−1.35530	−0.677651	−	0.735384i	$-0.737002\pi$
$433$	−2.28952e9	−1.35530	−0.677651	+	0.735384i	$0.737002\pi$
$434$	5.73306e9	3.36645
$435$	0	0
$436$	2.33492e8	0.134918
$437$	5.63296e8	0.322888
$438$	0	0
$439$	3.06968e9	1.73168	0.865838	−	0.500325i	$-0.166786\pi$
$439$	3.06968e9	1.73168	0.865838	+	0.500325i	$0.166786\pi$
$440$	5.32670e8	0.298108
$441$	0	0
$442$	−3.57650e9	−1.97007
$443$	2.69061e9	1.47041	0.735205	−	0.677845i	$-0.237086\pi$
$443$	2.69061e9	1.47041	0.735205	+	0.677845i	$0.237086\pi$
$444$	0	0
$445$	−8.39376e7	−0.0451540
$446$	−1.17356e9	−0.626374
$447$	0	0
$448$	1.04376e8	0.0548436
$449$	−7.49434e8	−0.390725	−0.195363	−	0.980731i	$-0.562588\pi$
$449$	−7.49434e8	−0.390725	−0.195363	+	0.980731i	$0.562588\pi$
$450$	0	0
$451$	−5.61222e8	−0.288082
$452$	1.23021e8	0.0626604
$453$	0	0
$454$	3.55708e8	0.178401
$455$	−1.75596e9	−0.873926
$456$	0	0
$457$	−3.10016e9	−1.51942	−0.759709	−	0.650264i	$-0.774658\pi$
$457$	−3.10016e9	−1.51942	−0.759709	+	0.650264i	$0.774658\pi$
$458$	−1.09493e8	−0.0532547
$459$	0	0
$460$	2.91075e8	0.139429
$461$	4.00381e8	0.190336	0.0951679	−	0.995461i	$-0.469661\pi$
$461$	4.00381e8	0.190336	0.0951679	+	0.995461i	$0.469661\pi$
$462$	0	0
$463$	2.61953e9	1.22656	0.613282	−	0.789864i	$-0.289849\pi$
$463$	2.61953e9	1.22656	0.613282	+	0.789864i	$0.289849\pi$
$464$	1.25623e9	0.583791
$465$	0	0
$466$	−2.57421e9	−1.17840
$467$	2.13796e9	0.971381	0.485690	−	0.874131i	$-0.338568\pi$
$467$	2.13796e9	0.971381	0.485690	+	0.874131i	$0.338568\pi$
$468$	0	0
$469$	−7.24874e8	−0.324457
$470$	−1.24156e9	−0.551602
$471$	0	0
$472$	−9.57628e7	−0.0419179
$473$	3.14947e9	1.36843
$474$	0	0
$475$	2.75086e8	0.117772
$476$	−3.29559e9	−1.40058
$477$	0	0
$478$	−9.80299e8	−0.410545
$479$	7.25094e8	0.301453	0.150727	−	0.988575i	$-0.451839\pi$
$479$	7.25094e8	0.301453	0.150727	+	0.988575i	$0.451839\pi$
$480$	0	0
$481$	−4.81719e9	−1.97372
$482$	−7.74500e8	−0.315034
$483$	0	0
$484$	7.40376e8	0.296820
$485$	−3.32850e8	−0.132481
$486$	0	0
$487$	4.04706e8	0.158777	0.0793886	−	0.996844i	$-0.474703\pi$
$487$	4.04706e8	0.158777	0.0793886	+	0.996844i	$0.474703\pi$
$488$	2.04001e8	0.0794626
$489$	0	0
$490$	−3.00510e9	−1.15391
$491$	−4.69323e8	−0.178931	−0.0894657	−	0.995990i	$-0.528516\pi$
$491$	−4.69323e8	−0.178931	−0.0894657	+	0.995990i	$0.528516\pi$
$492$	0	0
$493$	−1.75626e9	−0.660122
$494$	−2.20748e9	−0.823857
$495$	0	0
$496$	−5.20000e9	−1.91345
$497$	7.91844e9	2.89329
$498$	0	0
$499$	−3.63323e9	−1.30901	−0.654503	−	0.756060i	$-0.727122\pi$
$499$	−3.63323e9	−1.30901	−0.654503	+	0.756060i	$0.727122\pi$
$500$	1.42147e8	0.0508560
$501$	0	0
$502$	2.37096e9	0.836490
$503$	−3.55566e9	−1.24575	−0.622877	−	0.782320i	$-0.714036\pi$
$503$	−3.55566e9	−1.24575	−0.622877	+	0.782320i	$0.714036\pi$
$504$	0	0
$505$	−5.60406e8	−0.193635
$506$	−2.46907e9	−0.847241
$507$	0	0
$508$	−1.55408e9	−0.525956
$509$	4.65150e9	1.56344	0.781719	−	0.623631i	$-0.214343\pi$
$509$	4.65150e9	1.56344	0.781719	+	0.623631i	$0.214343\pi$
$510$	0	0
$511$	−5.86585e9	−1.94472
$512$	−1.81163e9	−0.596520
$513$	0	0
$514$	2.73440e9	0.888159
$515$	−8.25178e8	−0.266209
$516$	0	0
$517$	3.81755e9	1.21498
$518$	−1.22456e10	−3.87103
$519$	0	0
$520$	8.65488e8	0.269929
$521$	1.25080e9	0.387485	0.193743	−	0.981052i	$-0.437937\pi$
$521$	1.25080e9	0.387485	0.193743	+	0.981052i	$0.437937\pi$
$522$	0	0
$523$	5.71916e9	1.74814	0.874071	−	0.485799i	$-0.161471\pi$
$523$	5.71916e9	1.74814	0.874071	+	0.485799i	$0.161471\pi$
$524$	−2.06364e9	−0.626577
$525$	0	0
$526$	−3.75351e9	−1.12457
$527$	7.26979e9	2.16364
$528$	0	0
$529$	−2.38112e9	−0.699336
$530$	−6.62044e8	−0.193162
$531$	0	0
$532$	−2.03409e9	−0.585707
$533$	−9.11879e8	−0.260851
$534$	0	0
$535$	2.58445e9	0.729677
$536$	3.57280e8	0.100215
$537$	0	0
$538$	−2.03496e9	−0.563402
$539$	9.24007e9	2.54164
$540$	0	0
$541$	−5.92476e9	−1.60872	−0.804360	−	0.594143i	$-0.797491\pi$
$541$	−5.92476e9	−1.60872	−0.804360	+	0.594143i	$0.797491\pi$
$542$	4.27298e9	1.15275
$543$	0	0
$544$	5.38954e9	1.43534
$545$	4.01029e8	0.106118
$546$	0	0
$547$	3.15966e9	0.825439	0.412719	−	0.910858i	$-0.364579\pi$
$547$	3.15966e9	0.825439	0.412719	+	0.910858i	$0.364579\pi$
$548$	2.61816e9	0.679618
$549$	0	0
$550$	−1.20577e9	−0.309027
$551$	−1.08399e9	−0.276055
$552$	0	0
$553$	1.00654e10	2.53101
$554$	1.21218e9	0.302889
$555$	0	0
$556$	1.04577e9	0.258032
$557$	2.67265e9	0.655313	0.327656	−	0.944797i	$-0.393741\pi$
$557$	2.67265e9	0.655313	0.327656	+	0.944797i	$0.393741\pi$
$558$	0	0
$559$	5.11729e9	1.23908
$560$	4.04872e9	0.974227
$561$	0	0
$562$	−6.51576e9	−1.54842
$563$	4.84830e9	1.14501	0.572506	−	0.819900i	$-0.305971\pi$
$563$	4.84830e9	1.14501	0.572506	+	0.819900i	$0.305971\pi$
$564$	0	0
$565$	2.11291e8	0.0492846
$566$	−7.49008e9	−1.73632
$567$	0	0
$568$	−3.90289e9	−0.893649
$569$	−6.81940e9	−1.55186	−0.775931	−	0.630818i	$-0.782719\pi$
$569$	−6.81940e9	−1.55186	−0.775931	+	0.630818i	$0.782719\pi$
$570$	0	0
$571$	−6.16570e8	−0.138598	−0.0692989	−	0.997596i	$-0.522076\pi$
$571$	−6.16570e8	−0.138598	−0.0692989	+	0.997596i	$0.522076\pi$
$572$	3.50737e9	0.783603
$573$	0	0
$574$	−2.31805e9	−0.511602
$575$	4.99929e8	0.109666
$576$	0	0
$577$	9.00936e9	1.95244	0.976222	−	0.216771i	$-0.0695525\pi$
$577$	9.00936e9	1.95244	0.976222	+	0.216771i	$0.0695525\pi$
$578$	−5.71435e9	−1.23089
$579$	0	0
$580$	−5.60138e8	−0.119206
$581$	6.56142e9	1.38797
$582$	0	0
$583$	2.03565e9	0.425465
$584$	2.89120e9	0.600665
$585$	0	0
$586$	3.23247e9	0.663579
$587$	8.80343e9	1.79646	0.898232	−	0.439522i	$-0.144852\pi$
$587$	8.80343e9	1.79646	0.898232	+	0.439522i	$0.144852\pi$
$588$	0	0
$589$	4.48703e9	0.904806
$590$	2.16772e8	0.0434532
$591$	0	0
$592$	1.11070e10	2.20025
$593$	1.43818e9	0.283220	0.141610	−	0.989923i	$-0.454772\pi$
$593$	1.43818e9	0.283220	0.141610	+	0.989923i	$0.454772\pi$
$594$	0	0
$595$	−5.66026e9	−1.10161
$596$	1.87670e8	0.0363106
$597$	0	0
$598$	−4.01177e9	−0.767153
$599$	6.89028e8	0.130991	0.0654957	−	0.997853i	$-0.479137\pi$
$599$	6.89028e8	0.130991	0.0654957	+	0.997853i	$0.479137\pi$
$600$	0	0
$601$	4.06928e9	0.764639	0.382320	−	0.924030i	$-0.375125\pi$
$601$	4.06928e9	0.764639	0.382320	+	0.924030i	$0.375125\pi$
$602$	1.30085e10	2.43018
$603$	0	0
$604$	−1.63998e9	−0.302838
$605$	1.27161e9	0.233459
$606$	0	0
$607$	9.28000e9	1.68418	0.842088	−	0.539340i	$-0.181326\pi$
$607$	9.28000e9	1.68418	0.842088	+	0.539340i	$0.181326\pi$
$608$	3.32651e9	0.600243
$609$	0	0
$610$	−4.61784e8	−0.0823730
$611$	6.20279e9	1.10013
$612$	0	0
$613$	9.72207e8	0.170470	0.0852348	−	0.996361i	$-0.472836\pi$
$613$	9.72207e8	0.170470	0.0852348	+	0.996361i	$0.472836\pi$
$614$	−1.04446e10	−1.82097
$615$	0	0
$616$	−6.76494e9	−1.16609
$617$	−1.11807e10	−1.91633	−0.958164	−	0.286221i	$-0.907601\pi$
$617$	−1.11807e10	−1.91633	−0.958164	+	0.286221i	$0.907601\pi$
$618$	0	0
$619$	−1.09554e9	−0.185656	−0.0928281	−	0.995682i	$-0.529591\pi$
$619$	−1.09554e9	−0.185656	−0.0928281	+	0.995682i	$0.529591\pi$
$620$	2.31861e9	0.390713
$621$	0	0
$622$	8.83832e8	0.147266
$623$	1.06601e9	0.176626
$624$	0	0
$625$	2.44141e8	0.0400000
$626$	−5.75348e9	−0.937390
$627$	0	0
$628$	−2.09394e9	−0.337369
$629$	−1.55280e10	−2.48793
$630$	0	0
$631$	8.06380e9	1.27772	0.638862	−	0.769321i	$-0.279405\pi$
$631$	8.06380e9	1.27772	0.638862	+	0.769321i	$0.279405\pi$
$632$	−4.96111e9	−0.781752
$633$	0	0
$634$	−6.50251e9	−1.01337
$635$	−2.66917e9	−0.413683
$636$	0	0
$637$	1.50133e10	2.30139
$638$	4.75142e9	0.724354
$639$	0	0
$640$	−2.90671e9	−0.438300
$641$	−1.20472e10	−1.80669	−0.903343	−	0.428919i	$-0.858895\pi$
$641$	−1.20472e10	−1.80669	−0.903343	+	0.428919i	$0.858895\pi$
$642$	0	0
$643$	−6.78073e9	−1.00586	−0.502931	−	0.864327i	$-0.667745\pi$
$643$	−6.78073e9	−1.00586	−0.502931	+	0.864327i	$0.667745\pi$
$644$	−3.69668e9	−0.545395
$645$	0	0
$646$	−7.11570e9	−1.03849
$647$	−7.37841e9	−1.07102	−0.535510	−	0.844529i	$-0.679881\pi$
$647$	−7.37841e9	−1.07102	−0.535510	+	0.844529i	$0.679881\pi$
$648$	0	0
$649$	−6.66532e8	−0.0957116
$650$	−1.95915e9	−0.279815
$651$	0	0
$652$	5.64041e9	0.796974
$653$	−1.24944e10	−1.75597	−0.877987	−	0.478685i	$-0.841114\pi$
$653$	−1.24944e10	−1.75597	−0.877987	+	0.478685i	$0.841114\pi$
$654$	0	0
$655$	−3.54435e9	−0.492824
$656$	2.10252e9	0.290789
$657$	0	0
$658$	1.57679e10	2.15766
$659$	1.36321e9	0.185551	0.0927754	−	0.995687i	$-0.470426\pi$
$659$	1.36321e9	0.185551	0.0927754	+	0.995687i	$0.470426\pi$
$660$	0	0
$661$	−5.86014e9	−0.789228	−0.394614	−	0.918847i	$-0.629122\pi$
$661$	−5.86014e9	−0.789228	−0.394614	+	0.918847i	$0.629122\pi$
$662$	−2.94121e9	−0.394024
$663$	0	0
$664$	−3.23403e9	−0.428702
$665$	−3.49360e9	−0.460679
$666$	0	0
$667$	−1.97000e9	−0.257055
$668$	−1.00268e9	−0.130150
$669$	0	0
$670$	−8.08754e8	−0.103885
$671$	1.41989e9	0.181438
$672$	0	0
$673$	−5.63137e9	−0.712133	−0.356066	−	0.934461i	$-0.615882\pi$
$673$	−5.63137e9	−0.712133	−0.356066	+	0.934461i	$0.615882\pi$
$674$	3.07394e9	0.386710
$675$	0	0
$676$	1.13203e9	0.140943
$677$	−4.29962e9	−0.532562	−0.266281	−	0.963895i	$-0.585795\pi$
$677$	−4.29962e9	−0.532562	−0.266281	+	0.963895i	$0.585795\pi$
$678$	0	0
$679$	4.22722e9	0.518216
$680$	2.78986e9	0.340253
$681$	0	0
$682$	−1.96678e10	−2.37417
$683$	−8.18926e9	−0.983495	−0.491748	−	0.870738i	$-0.663642\pi$
$683$	−8.18926e9	−0.983495	−0.491748	+	0.870738i	$0.663642\pi$
$684$	0	0
$685$	4.49676e9	0.534543
$686$	1.96398e10	2.32275
$687$	0	0
$688$	−1.17990e10	−1.38129
$689$	3.30755e9	0.385247
$690$	0	0
$691$	1.15361e10	1.33011	0.665053	−	0.746796i	$-0.268409\pi$
$691$	1.15361e10	1.33011	0.665053	+	0.746796i	$0.268409\pi$
$692$	−1.44553e9	−0.165828
$693$	0	0
$694$	6.89073e9	0.782541
$695$	1.79613e9	0.202951
$696$	0	0
$697$	−2.93940e9	−0.328810
$698$	3.24707e8	0.0361408
$699$	0	0
$700$	−1.80527e9	−0.198930
$701$	−1.50937e9	−0.165494	−0.0827470	−	0.996571i	$-0.526369\pi$
$701$	−1.50937e9	−0.165494	−0.0827470	+	0.996571i	$0.526369\pi$
$702$	0	0
$703$	−9.58414e9	−1.04042
$704$	−3.58071e8	−0.0386781
$705$	0	0
$706$	6.15049e9	0.657799
$707$	7.11719e9	0.757427
$708$	0	0
$709$	−2.71527e9	−0.286122	−0.143061	−	0.989714i	$-0.545695\pi$
$709$	−2.71527e9	−0.286122	−0.143061	+	0.989714i	$0.545695\pi$
$710$	8.83473e9	0.926380
$711$	0	0
$712$	−5.25422e8	−0.0545542
$713$	8.15454e9	0.842531
$714$	0	0
$715$	6.02400e9	0.616331
$716$	9.08558e9	0.925032
$717$	0	0
$718$	2.15903e10	2.17682
$719$	−1.01787e10	−1.02127	−0.510634	−	0.859798i	$-0.670589\pi$
$719$	−1.01787e10	−1.02127	−0.510634	+	0.859798i	$0.670589\pi$
$720$	0	0
$721$	1.04798e10	1.04131
$722$	8.27393e9	0.818147
$723$	0	0
$724$	6.31580e9	0.618505
$725$	−9.62051e8	−0.0937594
$726$	0	0
$727$	9.99017e9	0.964278	0.482139	−	0.876095i	$-0.339860\pi$
$727$	9.99017e9	0.964278	0.482139	+	0.876095i	$0.339860\pi$
$728$	−1.09917e10	−1.05586
$729$	0	0
$730$	−6.54462e9	−0.622665
$731$	1.64954e10	1.56189
$732$	0	0
$733$	−8.15662e9	−0.764973	−0.382487	−	0.923961i	$-0.624932\pi$
$733$	−8.15662e9	−0.764973	−0.382487	+	0.923961i	$0.624932\pi$
$734$	2.89324e9	0.270052
$735$	0	0
$736$	6.04546e9	0.558930
$737$	2.48675e9	0.228821
$738$	0	0
$739$	−5.79589e9	−0.528280	−0.264140	−	0.964484i	$-0.585088\pi$
$739$	−5.79589e9	−0.528280	−0.264140	+	0.964484i	$0.585088\pi$
$740$	−4.95248e9	−0.449274
$741$	0	0
$742$	8.40800e9	0.755578
$743$	−2.00709e10	−1.79517	−0.897587	−	0.440836i	$-0.854682\pi$
$743$	−2.00709e10	−1.79517	−0.897587	+	0.440836i	$0.854682\pi$
$744$	0	0
$745$	3.22328e8	0.0285595
$746$	5.83068e9	0.514201
$747$	0	0
$748$	1.13059e10	0.987753
$749$	−3.28227e10	−2.85423
$750$	0	0
$751$	7.64646e9	0.658750	0.329375	−	0.944199i	$-0.393162\pi$
$751$	7.64646e9	0.658750	0.329375	+	0.944199i	$0.393162\pi$
$752$	−1.43018e10	−1.22639
$753$	0	0
$754$	7.72015e9	0.655883
$755$	−2.81671e9	−0.238192
$756$	0	0
$757$	1.50730e10	1.26289	0.631443	−	0.775422i	$-0.282463\pi$
$757$	1.50730e10	1.26289	0.631443	+	0.775422i	$0.282463\pi$
$758$	−3.06901e9	−0.255951
$759$	0	0
$760$	1.72195e9	0.142289
$761$	−6.16862e9	−0.507390	−0.253695	−	0.967284i	$-0.581646\pi$
$761$	−6.16862e9	−0.507390	−0.253695	+	0.967284i	$0.581646\pi$
$762$	0	0
$763$	−5.09309e9	−0.415093
$764$	−7.83018e9	−0.635251
$765$	0	0
$766$	−2.64945e10	−2.12988
$767$	−1.08299e9	−0.0866642
$768$	0	0
$769$	2.02154e10	1.60302	0.801510	−	0.597981i	$-0.204030\pi$
$769$	2.02154e10	1.60302	0.801510	+	0.597981i	$0.204030\pi$
$770$	1.53134e10	1.20880
$771$	0	0
$772$	4.44828e9	0.347962
$773$	−8.79891e9	−0.685174	−0.342587	−	0.939486i	$-0.611303\pi$
$773$	−8.79891e9	−0.685174	−0.342587	+	0.939486i	$0.611303\pi$
$774$	0	0
$775$	3.98227e9	0.307309
$776$	−2.08354e9	−0.160061
$777$	0	0
$778$	1.24719e10	0.949518
$779$	−1.81425e9	−0.137504
$780$	0	0
$781$	−2.71650e10	−2.04048
$782$	−1.29318e10	−0.967018
$783$	0	0
$784$	−3.46164e10	−2.56552
$785$	−3.59639e9	−0.265352
$786$	0	0
$787$	1.14191e10	0.835062	0.417531	−	0.908663i	$-0.362895\pi$
$787$	1.14191e10	0.835062	0.417531	+	0.908663i	$0.362895\pi$
$788$	−9.75888e8	−0.0710491
$789$	0	0
$790$	1.12302e10	0.810385
$791$	−2.68341e9	−0.192783
$792$	0	0
$793$	2.30706e9	0.164287
$794$	−2.56321e10	−1.81724
$795$	0	0
$796$	1.47407e10	1.03591
$797$	1.31340e10	0.918949	0.459474	−	0.888191i	$-0.348038\pi$
$797$	1.31340e10	0.918949	0.459474	+	0.888191i	$0.348038\pi$
$798$	0	0
$799$	1.99944e10	1.38674
$800$	2.95231e9	0.203867
$801$	0	0
$802$	−1.68616e9	−0.115422
$803$	2.01234e10	1.37150
$804$	0	0
$805$	−6.34913e9	−0.428972
$806$	−3.19565e10	−2.14974
$807$	0	0
$808$	−3.50796e9	−0.233946
$809$	−2.49937e9	−0.165963	−0.0829814	−	0.996551i	$-0.526444\pi$
$809$	−2.49937e9	−0.165963	−0.0829814	+	0.996551i	$0.526444\pi$
$810$	0	0
$811$	4.41362e9	0.290551	0.145275	−	0.989391i	$-0.453593\pi$
$811$	4.41362e9	0.290551	0.145275	+	0.989391i	$0.453593\pi$
$812$	7.11379e9	0.466289
$813$	0	0
$814$	4.20098e10	2.73002
$815$	9.68754e9	0.626847
$816$	0	0
$817$	1.01812e10	0.653164
$818$	−2.74582e9	−0.175403
$819$	0	0
$820$	−9.37488e8	−0.0593769
$821$	−2.41435e10	−1.52265	−0.761323	−	0.648373i	$-0.775450\pi$
$821$	−2.41435e10	−1.52265	−0.761323	+	0.648373i	$0.775450\pi$
$822$	0	0
$823$	2.50506e10	1.56646	0.783229	−	0.621734i	$-0.213571\pi$
$823$	2.50506e10	1.56646	0.783229	+	0.621734i	$0.213571\pi$
$824$	−5.16535e9	−0.321628
$825$	0	0
$826$	−2.75302e9	−0.169973
$827$	6.73891e9	0.414305	0.207153	−	0.978309i	$-0.433580\pi$
$827$	6.73891e9	0.414305	0.207153	+	0.978309i	$0.433580\pi$
$828$	0	0
$829$	8.81728e8	0.0537519	0.0268759	−	0.999639i	$-0.491444\pi$
$829$	8.81728e8	0.0537519	0.0268759	+	0.999639i	$0.491444\pi$
$830$	7.32068e9	0.444404
$831$	0	0
$832$	−5.81798e8	−0.0350219
$833$	4.83949e10	2.90096
$834$	0	0
$835$	−1.72213e9	−0.102368
$836$	6.97817e9	0.413066
$837$	0	0
$838$	3.67519e10	2.15738
$839$	1.53663e10	0.898259	0.449129	−	0.893467i	$-0.351734\pi$
$839$	1.53663e10	0.898259	0.449129	+	0.893467i	$0.351734\pi$
$840$	0	0
$841$	−1.34589e10	−0.780229
$842$	3.65622e10	2.11076
$843$	0	0
$844$	−5.81112e9	−0.332706
$845$	1.94429e9	0.110857
$846$	0	0
$847$	−1.61496e10	−0.913206
$848$	−7.62623e9	−0.429462
$849$	0	0
$850$	−6.31524e9	−0.352715
$851$	−1.74178e10	−0.968813
$852$	0	0
$853$	1.78907e10	0.986972	0.493486	−	0.869754i	$-0.335722\pi$
$853$	1.78907e10	0.986972	0.493486	+	0.869754i	$0.335722\pi$
$854$	5.86469e9	0.322213
$855$	0	0
$856$	1.61779e10	0.881582
$857$	4.80615e9	0.260834	0.130417	−	0.991459i	$-0.458368\pi$
$857$	4.80615e9	0.260834	0.130417	+	0.991459i	$0.458368\pi$
$858$	0	0
$859$	−2.57254e10	−1.38480	−0.692398	−	0.721516i	$-0.743446\pi$
$859$	−2.57254e10	−1.38480	−0.692398	+	0.721516i	$0.743446\pi$
$860$	5.26101e9	0.282049
$861$	0	0
$862$	−3.38291e10	−1.79893
$863$	3.46286e9	0.183399	0.0916997	−	0.995787i	$-0.470770\pi$
$863$	3.46286e9	0.183399	0.0916997	+	0.995787i	$0.470770\pi$
$864$	0	0
$865$	−2.48274e9	−0.130429
$866$	3.24417e10	1.69742
$867$	0	0
$868$	−2.94465e10	−1.52832
$869$	−3.45305e10	−1.78498
$870$	0	0
$871$	4.04050e9	0.207192
$872$	2.51031e9	0.128209
$873$	0	0
$874$	−7.98170e9	−0.404395
$875$	−3.10060e9	−0.156465
$876$	0	0
$877$	−3.63610e10	−1.82028	−0.910139	−	0.414303i	$-0.864025\pi$
$877$	−3.63610e10	−1.82028	−0.910139	+	0.414303i	$0.864025\pi$
$878$	−4.34962e10	−2.16881
$879$	0	0
$880$	−1.38896e10	−0.687067
$881$	8.18644e9	0.403348	0.201674	−	0.979453i	$-0.435362\pi$
$881$	8.18644e9	0.403348	0.201674	+	0.979453i	$0.435362\pi$
$882$	0	0
$883$	−6.82519e9	−0.333620	−0.166810	−	0.985989i	$-0.553347\pi$
$883$	−6.82519e9	−0.333620	−0.166810	+	0.985989i	$0.553347\pi$
$884$	1.83699e10	0.894383
$885$	0	0
$886$	−3.81251e10	−1.84159
$887$	5.33390e9	0.256633	0.128316	−	0.991733i	$-0.459043\pi$
$887$	5.33390e9	0.256633	0.128316	+	0.991733i	$0.459043\pi$
$888$	0	0
$889$	3.38986e10	1.61817
$890$	1.18937e9	0.0565524
$891$	0	0
$892$	6.02773e9	0.284365
$893$	1.23409e10	0.579918
$894$	0	0
$895$	1.56047e10	0.727570
$896$	3.69154e10	1.71447
$897$	0	0
$898$	1.06192e10	0.489357
$899$	−1.56924e10	−0.720328
$900$	0	0
$901$	1.06617e10	0.485614
$902$	7.95232e9	0.360804
$903$	0	0
$904$	1.32261e9	0.0595447
$905$	1.08475e10	0.486476
$906$	0	0
$907$	−1.26859e10	−0.564542	−0.282271	−	0.959335i	$-0.591088\pi$
$907$	−1.26859e10	−0.564542	−0.282271	+	0.959335i	$0.591088\pi$
$908$	−1.82701e9	−0.0809917
$909$	0	0
$910$	2.48813e10	1.09453
$911$	8.19088e9	0.358935	0.179468	−	0.983764i	$-0.442562\pi$
$911$	8.19088e9	0.358935	0.179468	+	0.983764i	$0.442562\pi$
$912$	0	0
$913$	−2.25096e10	−0.978859
$914$	4.39282e10	1.90297
$915$	0	0
$916$	5.62387e8	0.0241769
$917$	4.50134e10	1.92775
$918$	0	0
$919$	1.28182e10	0.544783	0.272391	−	0.962187i	$-0.412185\pi$
$919$	1.28182e10	0.544783	0.272391	+	0.962187i	$0.412185\pi$
$920$	3.12940e9	0.132496
$921$	0	0
$922$	−5.67327e9	−0.238383
$923$	−4.41380e10	−1.84760
$924$	0	0
$925$	−8.50600e9	−0.353370
$926$	−3.71179e10	−1.53619
$927$	0	0
$928$	−1.16337e10	−0.477861
$929$	−8.69604e9	−0.355849	−0.177925	−	0.984044i	$-0.556938\pi$
$929$	−8.69604e9	−0.355849	−0.177925	+	0.984044i	$0.556938\pi$
$930$	0	0
$931$	2.98701e10	1.21315
$932$	1.32218e10	0.534978
$933$	0	0
$934$	−3.02941e10	−1.21659
$935$	1.94181e10	0.776902
$936$	0	0
$937$	4.21585e10	1.67416	0.837080	−	0.547081i	$-0.184261\pi$
$937$	4.21585e10	1.67416	0.837080	+	0.547081i	$0.184261\pi$
$938$	1.02712e10	0.406361
$939$	0	0
$940$	6.37699e9	0.250420
$941$	−1.44517e10	−0.565399	−0.282700	−	0.959209i	$-0.591230\pi$
$941$	−1.44517e10	−0.565399	−0.282700	+	0.959209i	$0.591230\pi$
$942$	0	0
$943$	−3.29714e9	−0.128040
$944$	2.49705e9	0.0966107
$945$	0	0
$946$	−4.46269e10	−1.71387
$947$	−4.14350e10	−1.58541	−0.792706	−	0.609604i	$-0.791329\pi$
$947$	−4.14350e10	−1.58541	−0.792706	+	0.609604i	$0.791329\pi$
$948$	0	0
$949$	3.26967e10	1.24186
$950$	−3.89787e9	−0.147501
$951$	0	0
$952$	−3.54314e10	−1.33094
$953$	−1.85697e9	−0.0694992	−0.0347496	−	0.999396i	$-0.511063\pi$
$953$	−1.85697e9	−0.0694992	−0.0347496	+	0.999396i	$0.511063\pi$
$954$	0	0
$955$	−1.34485e10	−0.499647
$956$	5.03508e9	0.186382
$957$	0	0
$958$	−1.02743e10	−0.377550
$959$	−5.71091e10	−2.09093
$960$	0	0
$961$	3.74438e10	1.36097
$962$	6.82579e10	2.47195
$963$	0	0
$964$	3.97804e9	0.143021
$965$	7.64003e9	0.273684
$966$	0	0
$967$	−4.20681e10	−1.49610	−0.748050	−	0.663643i	$-0.769010\pi$
$967$	−4.20681e10	−1.49610	−0.748050	+	0.663643i	$0.769010\pi$
$968$	7.95989e9	0.282061
$969$	0	0
$970$	4.71637e9	0.165923
$971$	4.48349e9	0.157163	0.0785813	−	0.996908i	$-0.474961\pi$
$971$	4.48349e9	0.157163	0.0785813	+	0.996908i	$0.474961\pi$
$972$	0	0
$973$	−2.28109e10	−0.793868
$974$	−5.73455e9	−0.198858
$975$	0	0
$976$	−5.31940e9	−0.183142
$977$	1.37025e10	0.470077	0.235039	−	0.971986i	$-0.424478\pi$
$977$	1.37025e10	0.470077	0.235039	+	0.971986i	$0.424478\pi$
$978$	0	0
$979$	−3.65706e9	−0.124564
$980$	1.54350e10	0.523860
$981$	0	0
$982$	6.65014e9	0.224100
$983$	−2.20524e10	−0.740488	−0.370244	−	0.928935i	$-0.620726\pi$
$983$	−2.20524e10	−0.740488	−0.370244	+	0.928935i	$0.620726\pi$
$984$	0	0
$985$	−1.67611e9	−0.0558825
$986$	2.48856e10	0.826758
$987$	0	0
$988$	1.13382e10	0.374020
$989$	1.85029e10	0.608209
$990$	0	0
$991$	3.97974e10	1.29896	0.649481	−	0.760378i	$-0.274986\pi$
$991$	3.97974e10	1.29896	0.649481	+	0.760378i	$0.274986\pi$
$992$	4.81562e10	1.56625
$993$	0	0
$994$	−1.12202e11	−3.62366
$995$	2.53174e10	0.814777
$996$	0	0
$997$	−2.28904e10	−0.731510	−0.365755	−	0.930711i	$-0.619189\pi$
$997$	−2.28904e10	−0.731510	−0.365755	+	0.930711i	$0.619189\pi$
$998$	5.14817e10	1.63944
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.8.a.j.1.3		15
3.2	odd	2		405.8.a.i.1.13		15
9.2	odd	6		45.8.e.b.31.3	yes	30
9.4	even	3		135.8.e.b.46.13		30
9.5	odd	6		45.8.e.b.16.3	✓	30
9.7	even	3		135.8.e.b.91.13		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.8.e.b.16.3	✓	30	9.5	odd	6
45.8.e.b.31.3	yes	30	9.2	odd	6
135.8.e.b.46.13		30	9.4	even	3
135.8.e.b.91.13		30	9.7	even	3
405.8.a.i.1.13		15	3.2	odd	2
405.8.a.j.1.3		15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	405.a (trivial)

\(f(q)\)	\(=\)	\(q-14.1697 q^{2} +72.7792 q^{4} +125.000 q^{5} -1587.51 q^{7} +782.460 q^{8} +O(q^{10})\)	\(q-14.1697 q^{2} +72.7792 q^{4} +125.000 q^{5} -1587.51 q^{7} +782.460 q^{8} -1771.21 q^{10} +5446.11 q^{11} +8848.89 q^{13} +22494.4 q^{14} -20402.9 q^{16} +28524.0 q^{17} +17605.5 q^{19} +9097.40 q^{20} -77169.5 q^{22} +31995.5 q^{23} +15625.0 q^{25} -125386. q^{26} -115538. q^{28} -61571.2 q^{29} +254866. q^{31} +188948. q^{32} -404175. q^{34} -198438. q^{35} -544384. q^{37} -249464. q^{38} +97807.5 q^{40} -103050. q^{41} +578298. q^{43} +396363. q^{44} -453365. q^{46} +700969. q^{47} +1.69664e6 q^{49} -221401. q^{50} +644015. q^{52} +373781. q^{53} +680763. q^{55} -1.24216e6 q^{56} +872443. q^{58} -122387. q^{59} +260717. q^{61} -3.61136e6 q^{62} -65748.1 q^{64} +1.10611e6 q^{65} +456611. q^{67} +2.07595e6 q^{68} +2.81180e6 q^{70} -4.98797e6 q^{71} +3.69501e6 q^{73} +7.71373e6 q^{74} +1.28131e6 q^{76} -8.64573e6 q^{77} -6.34040e6 q^{79} -2.55037e6 q^{80} +1.46018e6 q^{82} -4.13316e6 q^{83} +3.56550e6 q^{85} -8.19428e6 q^{86} +4.26136e6 q^{88} -671500. q^{89} -1.40477e7 q^{91} +2.32860e6 q^{92} -9.93249e6 q^{94} +2.20069e6 q^{95} -2.66280e6 q^{97} -2.40408e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 8 q^{2} + 1088 q^{4} + 1875 q^{5} + 1289 q^{7} + 4434 q^{8}+O(q^{10}) \) 15 * q + 8 * q^2 + 1088 * q^4 + 1875 * q^5 + 1289 * q^7 + 4434 * q^8	\( 15 q + 8 q^{2} + 1088 q^{4} + 1875 q^{5} + 1289 q^{7} + 4434 q^{8} + 1000 q^{10} + 1658 q^{11} + 9874 q^{13} + 7695 q^{14} + 62612 q^{16} - 3598 q^{17} + 21376 q^{19} + 136000 q^{20} - 52519 q^{22} + 96441 q^{23} + 234375 q^{25} + 126146 q^{26} + 174449 q^{28} + 259297 q^{29} + 373568 q^{31} + 1134550 q^{32} + 423851 q^{34} + 161125 q^{35} + 517872 q^{37} + 690059 q^{38} + 554250 q^{40} + 520501 q^{41} + 1898836 q^{43} + 1277707 q^{44} + 3154677 q^{46} + 2259041 q^{47} + 4316308 q^{49} + 125000 q^{50} + 5398554 q^{52} - 102274 q^{53} + 207250 q^{55} - 504621 q^{56} + 3190987 q^{58} - 1680874 q^{59} - 1066457 q^{61} - 274110 q^{62} + 6541980 q^{64} + 1234250 q^{65} + 6522389 q^{67} + 1420717 q^{68} + 961875 q^{70} - 32786 q^{71} + 5359102 q^{73} - 4045556 q^{74} + 4649241 q^{76} + 2586078 q^{77} + 9319346 q^{79} + 7826500 q^{80} + 7460620 q^{82} - 12758277 q^{83} - 449750 q^{85} - 20044675 q^{86} + 6691143 q^{88} - 18776241 q^{89} + 9244102 q^{91} - 13862829 q^{92} + 25905119 q^{94} + 2672000 q^{95} + 2788224 q^{97} - 1679531 q^{98}+O(q^{100}) \) 15 * q + 8 * q^2 + 1088 * q^4 + 1875 * q^5 + 1289 * q^7 + 4434 * q^8 + 1000 * q^10 + 1658 * q^11 + 9874 * q^13 + 7695 * q^14 + 62612 * q^16 - 3598 * q^17 + 21376 * q^19 + 136000 * q^20 - 52519 * q^22 + 96441 * q^23 + 234375 * q^25 + 126146 * q^26 + 174449 * q^28 + 259297 * q^29 + 373568 * q^31 + 1134550 * q^32 + 423851 * q^34 + 161125 * q^35 + 517872 * q^37 + 690059 * q^38 + 554250 * q^40 + 520501 * q^41 + 1898836 * q^43 + 1277707 * q^44 + 3154677 * q^46 + 2259041 * q^47 + 4316308 * q^49 + 125000 * q^50 + 5398554 * q^52 - 102274 * q^53 + 207250 * q^55 - 504621 * q^56 + 3190987 * q^58 - 1680874 * q^59 - 1066457 * q^61 - 274110 * q^62 + 6541980 * q^64 + 1234250 * q^65 + 6522389 * q^67 + 1420717 * q^68 + 961875 * q^70 - 32786 * q^71 + 5359102 * q^73 - 4045556 * q^74 + 4649241 * q^76 + 2586078 * q^77 + 9319346 * q^79 + 7826500 * q^80 + 7460620 * q^82 - 12758277 * q^83 - 449750 * q^85 - 20044675 * q^86 + 6691143 * q^88 - 18776241 * q^89 + 9244102 * q^91 - 13862829 * q^92 + 25905119 * q^94 + 2672000 * q^95 + 2788224 * q^97 - 1679531 * q^98

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