LMFDB - Embedded newform 405.8.a.d.1.2

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 660x^{5} + 510x^{4} + 118692x^{3} - 171216x^{2} - 4927392x + 8926848 $ x^7 - x^6 - 660x^5 + 510x^4 + 118692x^3 - 171216x^2 - 4927392*x + 8926848
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{6} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-16.2196$ 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)

$f(q)$	$=$	$q-14.2196 q^{2} +74.1965 q^{4} -125.000 q^{5} +309.052 q^{7} +765.063 q^{8} +O(q^{10})$	\(q-14.2196 q^{2} +74.1965 q^{4} -125.000 q^{5} +309.052 q^{7} +765.063 q^{8} +1777.45 q^{10} -6167.54 q^{11} -8832.64 q^{13} -4394.59 q^{14} -20376.0 q^{16} -12096.1 q^{17} -51951.9 q^{19} -9274.56 q^{20} +87699.9 q^{22} +83064.7 q^{23} +15625.0 q^{25} +125596. q^{26} +22930.6 q^{28} -85784.7 q^{29} -277121. q^{31} +191811. q^{32} +172002. q^{34} -38631.5 q^{35} +605092. q^{37} +738735. q^{38} -95632.9 q^{40} -234508. q^{41} -305508. q^{43} -457610. q^{44} -1.18115e6 q^{46} -1.19855e6 q^{47} -728030. q^{49} -222181. q^{50} -655351. q^{52} -375548. q^{53} +770943. q^{55} +236444. q^{56} +1.21982e6 q^{58} +2.36221e6 q^{59} -1.69343e6 q^{61} +3.94055e6 q^{62} -119333. q^{64} +1.10408e6 q^{65} -2.98743e6 q^{67} -897489. q^{68} +549324. q^{70} +3.34064e6 q^{71} -3.72746e6 q^{73} -8.60415e6 q^{74} -3.85465e6 q^{76} -1.90609e6 q^{77} -3.90075e6 q^{79} +2.54700e6 q^{80} +3.33461e6 q^{82} -1.32674e6 q^{83} +1.51201e6 q^{85} +4.34420e6 q^{86} -4.71856e6 q^{88} -2.76332e6 q^{89} -2.72974e6 q^{91} +6.16311e6 q^{92} +1.70429e7 q^{94} +6.49399e6 q^{95} -612208. q^{97} +1.03523e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 15 q^{2} + 457 q^{4} - 875 q^{5} + 614 q^{7} + 4605 q^{8}+O(q^{10}) $ 7 * q + 15 * q^2 + 457 * q^4 - 875 * q^5 + 614 * q^7 + 4605 * q^8	\( 7 q + 15 q^{2} + 457 q^{4} - 875 q^{5} + 614 q^{7} + 4605 q^{8} - 1875 q^{10} + 3753 q^{11} - 6562 q^{13} + 19653 q^{14} + 27625 q^{16} - 23862 q^{17} + 33251 q^{19} - 57125 q^{20} + 108060 q^{22} + 62682 q^{23} + 109375 q^{25} - 186789 q^{26} + 149303 q^{28} + 78939 q^{29} - 703165 q^{31} + 1266165 q^{32} - 589398 q^{34} - 76750 q^{35} + 336776 q^{37} + 498855 q^{38} - 575625 q^{40} + 480801 q^{41} - 442792 q^{43} - 9372 q^{44} + 213447 q^{46} + 1122744 q^{47} - 954843 q^{49} + 234375 q^{50} - 1324819 q^{52} + 692028 q^{53} - 469125 q^{55} + 6614175 q^{56} - 3971220 q^{58} + 1274487 q^{59} - 2485258 q^{61} - 2438700 q^{62} + 10358137 q^{64} + 820250 q^{65} - 892402 q^{67} + 926646 q^{68} - 2456625 q^{70} + 8286201 q^{71} + 788666 q^{73} - 537042 q^{74} + 16155485 q^{76} - 5060322 q^{77} - 1308352 q^{79} - 3453125 q^{80} + 716235 q^{82} + 9226704 q^{83} + 2982750 q^{85} + 15948900 q^{86} + 16624320 q^{88} + 4459791 q^{89} - 5701496 q^{91} + 8926029 q^{92} + 43736397 q^{94} - 4156375 q^{95} - 11086048 q^{97} + 21087450 q^{98}+O(q^{100}) \) 7 * q + 15 * q^2 + 457 * q^4 - 875 * q^5 + 614 * q^7 + 4605 * q^8 - 1875 * q^10 + 3753 * q^11 - 6562 * q^13 + 19653 * q^14 + 27625 * q^16 - 23862 * q^17 + 33251 * q^19 - 57125 * q^20 + 108060 * q^22 + 62682 * q^23 + 109375 * q^25 - 186789 * q^26 + 149303 * q^28 + 78939 * q^29 - 703165 * q^31 + 1266165 * q^32 - 589398 * q^34 - 76750 * q^35 + 336776 * q^37 + 498855 * q^38 - 575625 * q^40 + 480801 * q^41 - 442792 * q^43 - 9372 * q^44 + 213447 * q^46 + 1122744 * q^47 - 954843 * q^49 + 234375 * q^50 - 1324819 * q^52 + 692028 * q^53 - 469125 * q^55 + 6614175 * q^56 - 3971220 * q^58 + 1274487 * q^59 - 2485258 * q^61 - 2438700 * q^62 + 10358137 * q^64 + 820250 * q^65 - 892402 * q^67 + 926646 * q^68 - 2456625 * q^70 + 8286201 * q^71 + 788666 * q^73 - 537042 * q^74 + 16155485 * q^76 - 5060322 * q^77 - 1308352 * q^79 - 3453125 * q^80 + 716235 * q^82 + 9226704 * q^83 + 2982750 * q^85 + 15948900 * q^86 + 16624320 * q^88 + 4459791 * q^89 - 5701496 * q^91 + 8926029 * q^92 + 43736397 * q^94 - 4156375 * q^95 - 11086048 * q^97 + 21087450 * 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 $

$2$	−14.2196	−1.25685	−0.628423	−	0.777872i	$-0.716299\pi$
$2$	−14.2196	−1.25685	−0.628423	+	0.777872i	$0.716299\pi$
$3$	0	0
$3$	0	0
$4$	74.1965	0.579660
$5$	−125.000	−0.447214
$5$	−125.000	−0.447214
$6$	0	0
$7$	309.052	0.340556	0.170278	−	0.985396i	$-0.445533\pi$
$7$	309.052	0.340556	0.170278	+	0.985396i	$0.445533\pi$
$8$	765.063	0.528302
$9$	0	0
$10$	1777.45	0.562078
$11$	−6167.54	−1.39713	−0.698567	−	0.715545i	$-0.746178\pi$
$11$	−6167.54	−1.39713	−0.698567	+	0.715545i	$0.746178\pi$
$12$	0	0
$13$	−8832.64	−1.11504	−0.557518	−	0.830165i	$-0.688246\pi$
$13$	−8832.64	−1.11504	−0.557518	+	0.830165i	$0.688246\pi$
$14$	−4394.59	−0.428026
$15$	0	0
$16$	−20376.0	−1.24365
$17$	−12096.1	−0.597138	−0.298569	−	0.954388i	$-0.596509\pi$
$17$	−12096.1	−0.597138	−0.298569	+	0.954388i	$0.596509\pi$
$18$	0	0
$19$	−51951.9	−1.73766	−0.868828	−	0.495113i	$-0.835127\pi$
$19$	−51951.9	−1.73766	−0.868828	+	0.495113i	$0.835127\pi$
$20$	−9274.56	−0.259232
$21$	0	0
$22$	87699.9	1.75598
$23$	83064.7	1.42354	0.711769	−	0.702414i	$-0.247894\pi$
$23$	83064.7	1.42354	0.711769	+	0.702414i	$0.247894\pi$
$24$	0	0
$25$	15625.0	0.200000
$26$	125596.	1.40143
$27$	0	0
$28$	22930.6	0.197407
$29$	−85784.7	−0.653156	−0.326578	−	0.945170i	$-0.605896\pi$
$29$	−85784.7	−0.653156	−0.326578	+	0.945170i	$0.605896\pi$
$30$	0	0
$31$	−277121.	−1.67072	−0.835360	−	0.549703i	$-0.814741\pi$
$31$	−277121.	−1.67072	−0.835360	+	0.549703i	$0.814741\pi$
$32$	191811.	1.03478
$33$	0	0
$34$	172002.	0.750510
$35$	−38631.5	−0.152301
$36$	0	0
$37$	605092.	1.96388	0.981941	−	0.189187i	$-0.0605854\pi$
$37$	605092.	1.96388	0.981941	+	0.189187i	$0.0605854\pi$
$38$	738735.	2.18397
$39$	0	0
$40$	−95632.9	−0.236264
$41$	−234508.	−0.531391	−0.265696	−	0.964057i	$-0.585602\pi$
$41$	−234508.	−0.531391	−0.265696	+	0.964057i	$0.585602\pi$
$42$	0	0
$43$	−305508.	−0.585981	−0.292990	−	0.956115i	$-0.594650\pi$
$43$	−305508.	−0.585981	−0.292990	+	0.956115i	$0.594650\pi$
$44$	−457610.	−0.809862
$45$	0	0
$46$	−1.18115e6	−1.78917
$47$	−1.19855e6	−1.68389	−0.841946	−	0.539562i	$-0.818590\pi$
$47$	−1.19855e6	−1.68389	−0.841946	+	0.539562i	$0.818590\pi$
$48$	0	0
$49$	−728030.	−0.884022
$50$	−222181.	−0.251369
$51$	0	0
$52$	−655351.	−0.646342
$53$	−375548.	−0.346498	−0.173249	−	0.984878i	$-0.555426\pi$
$53$	−375548.	−0.346498	−0.173249	+	0.984878i	$0.555426\pi$
$54$	0	0
$55$	770943.	0.624817
$56$	236444.	0.179916
$57$	0	0
$58$	1.21982e6	0.820916
$59$	2.36221e6	1.49739	0.748697	−	0.662912i	$-0.230680\pi$
$59$	2.36221e6	1.49739	0.748697	+	0.662912i	$0.230680\pi$
$60$	0	0
$61$	−1.69343e6	−0.955239	−0.477620	−	0.878567i	$-0.658500\pi$
$61$	−1.69343e6	−0.955239	−0.477620	+	0.878567i	$0.658500\pi$
$62$	3.94055e6	2.09984
$63$	0	0
$64$	−119333.	−0.0569024
$65$	1.10408e6	0.498659
$66$	0	0
$67$	−2.98743e6	−1.21349	−0.606745	−	0.794896i	$-0.707525\pi$
$67$	−2.98743e6	−1.21349	−0.606745	+	0.794896i	$0.707525\pi$
$68$	−897489.	−0.346137
$69$	0	0
$70$	549324.	0.191419
$71$	3.34064e6	1.10771	0.553855	−	0.832613i	$-0.313156\pi$
$71$	3.34064e6	1.10771	0.553855	+	0.832613i	$0.313156\pi$
$72$	0	0
$73$	−3.72746e6	−1.12146	−0.560729	−	0.827999i	$-0.689479\pi$
$73$	−3.72746e6	−1.12146	−0.560729	+	0.827999i	$0.689479\pi$
$74$	−8.60415e6	−2.46830
$75$	0	0
$76$	−3.85465e6	−1.00725
$77$	−1.90609e6	−0.475802
$78$	0	0
$79$	−3.90075e6	−0.890130	−0.445065	−	0.895498i	$-0.646819\pi$
$79$	−3.90075e6	−0.890130	−0.445065	+	0.895498i	$0.646819\pi$
$80$	2.54700e6	0.556179
$81$	0	0
$82$	3.33461e6	0.667877
$83$	−1.32674e6	−0.254690	−0.127345	−	0.991858i	$-0.540646\pi$
$83$	−1.32674e6	−0.254690	−0.127345	+	0.991858i	$0.540646\pi$
$84$	0	0
$85$	1.51201e6	0.267048
$86$	4.34420e6	0.736487
$87$	0	0
$88$	−4.71856e6	−0.738109
$89$	−2.76332e6	−0.415496	−0.207748	−	0.978182i	$-0.566613\pi$
$89$	−2.76332e6	−0.415496	−0.207748	+	0.978182i	$0.566613\pi$
$90$	0	0
$91$	−2.72974e6	−0.379732
$92$	6.16311e6	0.825168
$93$	0	0
$94$	1.70429e7	2.11639
$95$	6.49399e6	0.777104
$96$	0	0
$97$	−612208.	−0.0681080	−0.0340540	−	0.999420i	$-0.510842\pi$
$97$	−612208.	−0.0681080	−0.0340540	+	0.999420i	$0.510842\pi$
$98$	1.03523e7	1.11108
$99$	0	0
$100$	1.15932e6	0.115932
$101$	−1.60326e7	−1.54839	−0.774193	−	0.632950i	$-0.781844\pi$
$101$	−1.60326e7	−1.54839	−0.774193	+	0.632950i	$0.781844\pi$
$102$	0	0
$103$	−1.15850e7	−1.04464	−0.522321	−	0.852749i	$-0.674934\pi$
$103$	−1.15850e7	−1.04464	−0.522321	+	0.852749i	$0.674934\pi$
$104$	−6.75753e6	−0.589076
$105$	0	0
$106$	5.34014e6	0.435494
$107$	2.02092e7	1.59480	0.797399	−	0.603452i	$-0.206209\pi$
$107$	2.02092e7	1.59480	0.797399	+	0.603452i	$0.206209\pi$
$108$	0	0
$109$	−1.77374e7	−1.31189	−0.655946	−	0.754808i	$-0.727730\pi$
$109$	−1.77374e7	−1.31189	−0.655946	+	0.754808i	$0.727730\pi$
$110$	−1.09625e7	−0.785298
$111$	0	0
$112$	−6.29725e6	−0.423534
$113$	−7.27855e6	−0.474537	−0.237269	−	0.971444i	$-0.576252\pi$
$113$	−7.27855e6	−0.474537	−0.237269	+	0.971444i	$0.576252\pi$
$114$	0	0
$115$	−1.03831e7	−0.636626
$116$	−6.36493e6	−0.378609
$117$	0	0
$118$	−3.35896e7	−1.88199
$119$	−3.73833e6	−0.203359
$120$	0	0
$121$	1.85514e7	0.951982
$122$	2.40798e7	1.20059
$123$	0	0
$124$	−2.05614e7	−0.968450
$125$	−1.95312e6	−0.0894427
$126$	0	0
$127$	−8.18968e6	−0.354776	−0.177388	−	0.984141i	$-0.556765\pi$
$127$	−8.18968e6	−0.354776	−0.177388	+	0.984141i	$0.556765\pi$
$128$	−2.28549e7	−0.963261
$129$	0	0
$130$	−1.56996e7	−0.626737
$131$	8.97426e6	0.348778	0.174389	−	0.984677i	$-0.444205\pi$
$131$	8.97426e6	0.348778	0.174389	+	0.984677i	$0.444205\pi$
$132$	0	0
$133$	−1.60558e7	−0.591769
$134$	4.24801e7	1.52517
$135$	0	0
$136$	−9.25430e6	−0.315469
$137$	−2.16010e7	−0.717715	−0.358858	−	0.933392i	$-0.616834\pi$
$137$	−2.16010e7	−0.717715	−0.358858	+	0.933392i	$0.616834\pi$
$138$	0	0
$139$	−8.47195e6	−0.267567	−0.133783	−	0.991011i	$-0.542713\pi$
$139$	−8.47195e6	−0.267567	−0.133783	+	0.991011i	$0.542713\pi$
$140$	−2.86632e6	−0.0882829
$141$	0	0
$142$	−4.75025e7	−1.39222
$143$	5.44757e7	1.55785
$144$	0	0
$145$	1.07231e7	0.292100
$146$	5.30030e7	1.40950
$147$	0	0
$148$	4.48957e7	1.13838
$149$	−8.16097e6	−0.202111	−0.101055	−	0.994881i	$-0.532222\pi$
$149$	−8.16097e6	−0.202111	−0.101055	+	0.994881i	$0.532222\pi$
$150$	0	0
$151$	−6.32341e7	−1.49463	−0.747313	−	0.664473i	$-0.768656\pi$
$151$	−6.32341e7	−1.49463	−0.747313	+	0.664473i	$0.768656\pi$
$152$	−3.97465e7	−0.918008
$153$	0	0
$154$	2.71038e7	0.598009
$155$	3.46402e7	0.747169
$156$	0	0
$157$	5.06724e7	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$157$	5.06724e7	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$158$	5.54670e7	1.11876
$159$	0	0
$160$	−2.39763e7	−0.462767
$161$	2.56713e7	0.484794
$162$	0	0
$163$	1.83965e7	0.332719	0.166360	−	0.986065i	$-0.446799\pi$
$163$	1.83965e7	0.332719	0.166360	+	0.986065i	$0.446799\pi$
$164$	−1.73997e7	−0.308026
$165$	0	0
$166$	1.88657e7	0.320107
$167$	2.45107e7	0.407238	0.203619	−	0.979050i	$-0.434730\pi$
$167$	2.45107e7	0.407238	0.203619	+	0.979050i	$0.434730\pi$
$168$	0	0
$169$	1.52670e7	0.243305
$170$	−2.15002e7	−0.335638
$171$	0	0
$172$	−2.26676e7	−0.339670
$173$	1.04360e8	1.53240	0.766201	−	0.642601i	$-0.222145\pi$
$173$	1.04360e8	1.53240	0.766201	+	0.642601i	$0.222145\pi$
$174$	0	0
$175$	4.82894e6	0.0681112
$176$	1.25670e8	1.73755
$177$	0	0
$178$	3.92933e7	0.522214
$179$	−3.19502e7	−0.416379	−0.208189	−	0.978089i	$-0.566757\pi$
$179$	−3.19502e7	−0.416379	−0.208189	+	0.978089i	$0.566757\pi$
$180$	0	0
$181$	2.51150e7	0.314818	0.157409	−	0.987534i	$-0.449686\pi$
$181$	2.51150e7	0.314818	0.157409	+	0.987534i	$0.449686\pi$
$182$	3.88158e7	0.477264
$183$	0	0
$184$	6.35498e7	0.752058
$185$	−7.56365e7	−0.878275
$186$	0	0
$187$	7.46033e7	0.834282
$188$	−8.89283e7	−0.976085
$189$	0	0
$190$	−9.23418e7	−0.976699
$191$	−4.09531e7	−0.425276	−0.212638	−	0.977131i	$-0.568205\pi$
$191$	−4.09531e7	−0.425276	−0.212638	+	0.977131i	$0.568205\pi$
$192$	0	0
$193$	5.12605e7	0.513254	0.256627	−	0.966511i	$-0.417389\pi$
$193$	5.12605e7	0.513254	0.256627	+	0.966511i	$0.417389\pi$
$194$	8.70535e6	0.0856012
$195$	0	0
$196$	−5.40173e7	−0.512432
$197$	1.38456e8	1.29026	0.645132	−	0.764071i	$-0.276802\pi$
$197$	1.38456e8	1.29026	0.645132	+	0.764071i	$0.276802\pi$
$198$	0	0
$199$	9.12758e7	0.821051	0.410525	−	0.911849i	$-0.365345\pi$
$199$	9.12758e7	0.821051	0.410525	+	0.911849i	$0.365345\pi$
$200$	1.19541e7	0.105660
$201$	0	0
$202$	2.27977e8	1.94608
$203$	−2.65119e7	−0.222436
$204$	0	0
$205$	2.93135e7	0.237645
$206$	1.64734e8	1.31295
$207$	0	0
$208$	1.79974e8	1.38672
$209$	3.20416e8	2.42774
$210$	0	0
$211$	3.71618e7	0.272338	0.136169	−	0.990686i	$-0.456521\pi$
$211$	3.71618e7	0.272338	0.136169	+	0.990686i	$0.456521\pi$
$212$	−2.78644e7	−0.200851
$213$	0	0
$214$	−2.87366e8	−2.00441
$215$	3.81885e7	0.262059
$216$	0	0
$217$	−8.56449e7	−0.568974
$218$	2.52219e8	1.64885
$219$	0	0
$220$	5.72013e7	0.362182
$221$	1.06841e8	0.665830
$222$	0	0
$223$	−2.10573e8	−1.27156	−0.635779	−	0.771872i	$-0.719321\pi$
$223$	−2.10573e8	−1.27156	−0.635779	+	0.771872i	$0.719321\pi$
$224$	5.92794e7	0.352400
$225$	0	0
$226$	1.03498e8	0.596420
$227$	−7.84711e7	−0.445266	−0.222633	−	0.974902i	$-0.571465\pi$
$227$	−7.84711e7	−0.445266	−0.222633	+	0.974902i	$0.571465\pi$
$228$	0	0
$229$	1.09707e8	0.603682	0.301841	−	0.953358i	$-0.402399\pi$
$229$	1.09707e8	0.603682	0.301841	+	0.953358i	$0.402399\pi$
$230$	1.47643e8	0.800140
$231$	0	0
$232$	−6.56308e7	−0.345064
$233$	2.25593e7	0.116837	0.0584185	−	0.998292i	$-0.481394\pi$
$233$	2.25593e7	0.116837	0.0584185	+	0.998292i	$0.481394\pi$
$234$	0	0
$235$	1.49819e8	0.753059
$236$	1.75268e8	0.867979
$237$	0	0
$238$	5.31575e7	0.255591
$239$	2.20505e8	1.04478	0.522392	−	0.852705i	$-0.325040\pi$
$239$	2.20505e8	1.04478	0.522392	+	0.852705i	$0.325040\pi$
$240$	0	0
$241$	3.89042e8	1.79034	0.895172	−	0.445721i	$-0.147053\pi$
$241$	3.89042e8	1.79034	0.895172	+	0.445721i	$0.147053\pi$
$242$	−2.63794e8	−1.19649
$243$	0	0
$244$	−1.25646e8	−0.553714
$245$	9.10037e7	0.395347
$246$	0	0
$247$	4.58873e8	1.93755
$248$	−2.12015e8	−0.882646
$249$	0	0
$250$	2.77726e7	0.112416
$251$	−4.89891e8	−1.95543	−0.977714	−	0.209941i	$-0.932673\pi$
$251$	−4.89891e8	−1.95543	−0.977714	+	0.209941i	$0.932673\pi$
$252$	0	0
$253$	−5.12305e8	−1.98887
$254$	1.16454e8	0.445898
$255$	0	0
$256$	3.40261e8	1.26757
$257$	−4.03411e8	−1.48246	−0.741228	−	0.671253i	$-0.765756\pi$
$257$	−4.03411e8	−1.48246	−0.741228	+	0.671253i	$0.765756\pi$
$258$	0	0
$259$	1.87005e8	0.668812
$260$	8.19188e7	0.289053
$261$	0	0
$262$	−1.27610e8	−0.438360
$263$	1.35081e8	0.457878	0.228939	−	0.973441i	$-0.426474\pi$
$263$	1.35081e8	0.457878	0.228939	+	0.973441i	$0.426474\pi$
$264$	0	0
$265$	4.69435e7	0.154958
$266$	2.28307e8	0.743762
$267$	0	0
$268$	−2.21657e8	−0.703412
$269$	−3.43858e7	−0.107707	−0.0538537	−	0.998549i	$-0.517150\pi$
$269$	−3.43858e7	−0.107707	−0.0538537	+	0.998549i	$0.517150\pi$
$270$	0	0
$271$	6.23791e8	1.90391	0.951955	−	0.306237i	$-0.0990701\pi$
$271$	6.23791e8	1.90391	0.951955	+	0.306237i	$0.0990701\pi$
$272$	2.46471e8	0.742633
$273$	0	0
$274$	3.07157e8	0.902057
$275$	−9.63679e7	−0.279427
$276$	0	0
$277$	−6.48742e7	−0.183397	−0.0916987	−	0.995787i	$-0.529230\pi$
$277$	−6.48742e7	−0.183397	−0.0916987	+	0.995787i	$0.529230\pi$
$278$	1.20468e8	0.336290
$279$	0	0
$280$	−2.95555e7	−0.0804611
$281$	2.78995e8	0.750108	0.375054	−	0.927003i	$-0.377624\pi$
$281$	2.78995e8	0.750108	0.375054	+	0.927003i	$0.377624\pi$
$282$	0	0
$283$	7.19042e7	0.188583	0.0942913	−	0.995545i	$-0.469941\pi$
$283$	7.19042e7	0.188583	0.0942913	+	0.995545i	$0.469941\pi$
$284$	2.47864e8	0.642095
$285$	0	0
$286$	−7.74622e8	−1.95798
$287$	−7.24752e7	−0.180968
$288$	0	0
$289$	−2.64023e8	−0.643426
$290$	−1.52478e8	−0.367125
$291$	0	0
$292$	−2.76565e8	−0.650065
$293$	−1.48272e8	−0.344369	−0.172184	−	0.985065i	$-0.555082\pi$
$293$	−1.48272e8	−0.344369	−0.172184	+	0.985065i	$0.555082\pi$
$294$	0	0
$295$	−2.95276e8	−0.669655
$296$	4.62934e8	1.03752
$297$	0	0
$298$	1.16046e8	0.254022
$299$	−7.33681e8	−1.58730
$300$	0	0
$301$	−9.44179e7	−0.199559
$302$	8.99163e8	1.87851
$303$	0	0
$304$	1.05857e9	2.16104
$305$	2.11678e8	0.427196
$306$	0	0
$307$	1.45229e8	0.286463	0.143232	−	0.989689i	$-0.454251\pi$
$307$	1.45229e8	0.286463	0.143232	+	0.989689i	$0.454251\pi$
$308$	−1.41425e8	−0.275803
$309$	0	0
$310$	−4.92568e8	−0.939076
$311$	4.93819e7	0.0930908	0.0465454	−	0.998916i	$-0.485179\pi$
$311$	4.93819e7	0.0930908	0.0465454	+	0.998916i	$0.485179\pi$
$312$	0	0
$313$	−6.62943e8	−1.22200	−0.610999	−	0.791631i	$-0.709232\pi$
$313$	−6.62943e8	−1.22200	−0.610999	+	0.791631i	$0.709232\pi$
$314$	−7.20540e8	−1.31342
$315$	0	0
$316$	−2.89422e8	−0.515973
$317$	−5.29389e8	−0.933399	−0.466699	−	0.884416i	$-0.654557\pi$
$317$	−5.29389e8	−0.933399	−0.466699	+	0.884416i	$0.654557\pi$
$318$	0	0
$319$	5.29081e8	0.912546
$320$	1.49166e7	0.0254475
$321$	0	0
$322$	−3.65035e8	−0.609311
$323$	6.28416e8	1.03762
$324$	0	0
$325$	−1.38010e8	−0.223007
$326$	−2.61590e8	−0.418177
$327$	0	0
$328$	−1.79414e8	−0.280735
$329$	−3.70415e8	−0.573459
$330$	0	0
$331$	3.34764e8	0.507389	0.253695	−	0.967284i	$-0.418354\pi$
$331$	3.34764e8	0.507389	0.253695	+	0.967284i	$0.418354\pi$
$332$	−9.84395e7	−0.147634
$333$	0	0
$334$	−3.48532e8	−0.511835
$335$	3.73429e8	0.542690
$336$	0	0
$337$	−5.13446e8	−0.730786	−0.365393	−	0.930853i	$-0.619065\pi$
$337$	−5.13446e8	−0.730786	−0.365393	+	0.930853i	$0.619065\pi$
$338$	−2.17090e8	−0.305796
$339$	0	0
$340$	1.12186e8	0.154797
$341$	1.70916e9	2.33422
$342$	0	0
$343$	−4.79517e8	−0.641615
$344$	−2.33733e8	−0.309575
$345$	0	0
$346$	−1.48396e9	−1.92599
$347$	5.51791e8	0.708960	0.354480	−	0.935064i	$-0.384658\pi$
$347$	5.51791e8	0.708960	0.354480	+	0.935064i	$0.384658\pi$
$348$	0	0
$349$	−5.81475e8	−0.732220	−0.366110	−	0.930572i	$-0.619311\pi$
$349$	−5.81475e8	−0.732220	−0.366110	+	0.930572i	$0.619311\pi$
$350$	−6.86655e7	−0.0856052
$351$	0	0
$352$	−1.18300e9	−1.44572
$353$	2.20773e7	0.0267138	0.0133569	−	0.999911i	$-0.495748\pi$
$353$	2.20773e7	0.0267138	0.0133569	+	0.999911i	$0.495748\pi$
$354$	0	0
$355$	−4.17580e8	−0.495383
$356$	−2.05029e8	−0.240846
$357$	0	0
$358$	4.54319e8	0.523324
$359$	1.40123e9	1.59838	0.799188	−	0.601081i	$-0.205263\pi$
$359$	1.40123e9	1.59838	0.799188	+	0.601081i	$0.205263\pi$
$360$	0	0
$361$	1.80513e9	2.01945
$362$	−3.57125e8	−0.395677
$363$	0	0
$364$	−2.02537e8	−0.220115
$365$	4.65933e8	0.501532
$366$	0	0
$367$	8.51239e8	0.898918	0.449459	−	0.893301i	$-0.351617\pi$
$367$	8.51239e8	0.898918	0.449459	+	0.893301i	$0.351617\pi$
$368$	−1.69253e9	−1.77039
$369$	0	0
$370$	1.07552e9	1.10386
$371$	−1.16064e8	−0.118002
$372$	0	0
$373$	9.30739e8	0.928639	0.464319	−	0.885668i	$-0.346299\pi$
$373$	9.30739e8	0.928639	0.464319	+	0.885668i	$0.346299\pi$
$374$	−1.06083e9	−1.04856
$375$	0	0
$376$	−9.16968e8	−0.889604
$377$	7.57706e8	0.728292
$378$	0	0
$379$	−6.82275e8	−0.643758	−0.321879	−	0.946781i	$-0.604314\pi$
$379$	−6.82275e8	−0.643758	−0.321879	+	0.946781i	$0.604314\pi$
$380$	4.81831e8	0.450456
$381$	0	0
$382$	5.82337e8	0.534506
$383$	−1.21740e9	−1.10723	−0.553617	−	0.832772i	$-0.686753\pi$
$383$	−1.21740e9	−1.10723	−0.553617	+	0.832772i	$0.686753\pi$
$384$	0	0
$385$	2.38261e8	0.212785
$386$	−7.28902e8	−0.645080
$387$	0	0
$388$	−4.54237e7	−0.0394795
$389$	−5.05897e8	−0.435751	−0.217876	−	0.975977i	$-0.569913\pi$
$389$	−5.05897e8	−0.435751	−0.217876	+	0.975977i	$0.569913\pi$
$390$	0	0
$391$	−1.00476e9	−0.850049
$392$	−5.56989e8	−0.467031
$393$	0	0
$394$	−1.96878e9	−1.62166
$395$	4.87594e8	0.398078
$396$	0	0
$397$	−9.13462e8	−0.732696	−0.366348	−	0.930478i	$-0.619392\pi$
$397$	−9.13462e8	−0.732696	−0.366348	+	0.930478i	$0.619392\pi$
$398$	−1.29790e9	−1.03193
$399$	0	0
$400$	−3.18375e8	−0.248731
$401$	1.77099e9	1.37155	0.685773	−	0.727815i	$-0.259464\pi$
$401$	1.77099e9	1.37155	0.685773	+	0.727815i	$0.259464\pi$
$402$	0	0
$403$	2.44771e9	1.86291
$404$	−1.18956e9	−0.897537
$405$	0	0
$406$	3.76989e8	0.279568
$407$	−3.73193e9	−2.74381
$408$	0	0
$409$	−1.46532e9	−1.05901	−0.529507	−	0.848306i	$-0.677623\pi$
$409$	−1.46532e9	−1.05901	−0.529507	+	0.848306i	$0.677623\pi$
$410$	−4.16826e8	−0.298683
$411$	0	0
$412$	−8.59570e8	−0.605537
$413$	7.30045e8	0.509946
$414$	0	0
$415$	1.65843e8	0.113901
$416$	−1.69419e9	−1.15382
$417$	0	0
$418$	−4.55618e9	−3.05129
$419$	−1.56071e9	−1.03651	−0.518255	−	0.855226i	$-0.673418\pi$
$419$	−1.56071e9	−1.03651	−0.518255	+	0.855226i	$0.673418\pi$
$420$	0	0
$421$	2.74324e9	1.79174	0.895871	−	0.444313i	$-0.146552\pi$
$421$	2.74324e9	1.79174	0.895871	+	0.444313i	$0.146552\pi$
$422$	−5.28425e8	−0.342286
$423$	0	0
$424$	−2.87318e8	−0.183056
$425$	−1.89002e8	−0.119428
$426$	0	0
$427$	−5.23357e8	−0.325312
$428$	1.49945e9	0.924441
$429$	0	0
$430$	−5.43025e8	−0.329367
$431$	1.40579e9	0.845766	0.422883	−	0.906184i	$-0.361018\pi$
$431$	1.40579e9	0.845766	0.422883	+	0.906184i	$0.361018\pi$
$432$	0	0
$433$	2.11338e9	1.25104	0.625519	−	0.780209i	$-0.284887\pi$
$433$	2.11338e9	1.25104	0.625519	+	0.780209i	$0.284887\pi$
$434$	1.21783e9	0.715112
$435$	0	0
$436$	−1.31606e9	−0.760452
$437$	−4.31537e9	−2.47362
$438$	0	0
$439$	2.61981e9	1.47790	0.738949	−	0.673762i	$-0.235323\pi$
$439$	2.61981e9	1.47790	0.738949	+	0.673762i	$0.235323\pi$
$440$	5.89820e8	0.330092
$441$	0	0
$442$	−1.51923e9	−0.836846
$443$	2.71478e8	0.148362	0.0741809	−	0.997245i	$-0.476366\pi$
$443$	2.71478e8	0.148362	0.0741809	+	0.997245i	$0.476366\pi$
$444$	0	0
$445$	3.45415e8	0.185815
$446$	2.99426e9	1.59815
$447$	0	0
$448$	−3.68801e7	−0.0193785
$449$	−2.00677e9	−1.04625	−0.523124	−	0.852257i	$-0.675233\pi$
$449$	−2.00677e9	−1.04625	−0.523124	+	0.852257i	$0.675233\pi$
$450$	0	0
$451$	1.44634e9	0.742425
$452$	−5.40043e8	−0.275070
$453$	0	0
$454$	1.11583e9	0.559630
$455$	3.41218e8	0.169821
$456$	0	0
$457$	−4.26288e7	−0.0208928	−0.0104464	−	0.999945i	$-0.503325\pi$
$457$	−4.26288e7	−0.0208928	−0.0104464	+	0.999945i	$0.503325\pi$
$458$	−1.55998e9	−0.758735
$459$	0	0
$460$	−7.70389e8	−0.369026
$461$	3.25180e9	1.54586	0.772930	−	0.634491i	$-0.218790\pi$
$461$	3.25180e9	1.54586	0.772930	+	0.634491i	$0.218790\pi$
$462$	0	0
$463$	3.98641e9	1.86659	0.933293	−	0.359115i	$-0.116922\pi$
$463$	3.98641e9	1.86659	0.933293	+	0.359115i	$0.116922\pi$
$464$	1.74795e9	0.812300
$465$	0	0
$466$	−3.20784e8	−0.146846
$467$	−3.44760e9	−1.56642	−0.783209	−	0.621758i	$-0.786419\pi$
$467$	−3.44760e9	−1.56642	−0.783209	+	0.621758i	$0.786419\pi$
$468$	0	0
$469$	−9.23272e8	−0.413261
$470$	−2.13036e9	−0.946479
$471$	0	0
$472$	1.80724e9	0.791077
$473$	1.88424e9	0.818693
$474$	0	0
$475$	−8.11749e8	−0.347531
$476$	−2.77371e8	−0.117879
$477$	0	0
$478$	−3.13549e9	−1.31313
$479$	−8.30141e8	−0.345126	−0.172563	−	0.984999i	$-0.555205\pi$
$479$	−8.30141e8	−0.345126	−0.172563	+	0.984999i	$0.555205\pi$
$480$	0	0
$481$	−5.34456e9	−2.18980
$482$	−5.53201e9	−2.25019
$483$	0	0
$484$	1.37645e9	0.551826
$485$	7.65260e7	0.0304588
$486$	0	0
$487$	−4.93377e9	−1.93565	−0.967827	−	0.251615i	$-0.919038\pi$
$487$	−4.93377e9	−1.93565	−0.967827	+	0.251615i	$0.919038\pi$
$488$	−1.29558e9	−0.504655
$489$	0	0
$490$	−1.29404e9	−0.496889
$491$	−3.07921e9	−1.17396	−0.586980	−	0.809601i	$-0.699683\pi$
$491$	−3.07921e9	−1.17396	−0.586980	+	0.809601i	$0.699683\pi$
$492$	0	0
$493$	1.03766e9	0.390024
$494$	−6.52498e9	−2.43520
$495$	0	0
$496$	5.64663e9	2.07780
$497$	1.03243e9	0.377237
$498$	0	0
$499$	−7.83104e7	−0.0282142	−0.0141071	−	0.999900i	$-0.504491\pi$
$499$	−7.83104e7	−0.0282142	−0.0141071	+	0.999900i	$0.504491\pi$
$500$	−1.44915e8	−0.0518464
$501$	0	0
$502$	6.96605e9	2.45767
$503$	2.69501e8	0.0944219	0.0472109	−	0.998885i	$-0.484967\pi$
$503$	2.69501e8	0.0944219	0.0472109	+	0.998885i	$0.484967\pi$
$504$	0	0
$505$	2.00408e9	0.692459
$506$	7.28477e9	2.49971
$507$	0	0
$508$	−6.07646e8	−0.205649
$509$	−3.63364e9	−1.22132	−0.610660	−	0.791893i	$-0.709096\pi$
$509$	−3.63364e9	−1.22132	−0.610660	+	0.791893i	$0.709096\pi$
$510$	0	0
$511$	−1.15198e9	−0.381919
$512$	−1.91295e9	−0.629882
$513$	0	0
$514$	5.73634e9	1.86322
$515$	1.44813e9	0.467178
$516$	0	0
$517$	7.39212e9	2.35262
$518$	−2.65913e9	−0.840593
$519$	0	0
$520$	8.44691e8	0.263443
$521$	−1.91288e9	−0.592593	−0.296296	−	0.955096i	$-0.595752\pi$
$521$	−1.91288e9	−0.592593	−0.296296	+	0.955096i	$0.595752\pi$
$522$	0	0
$523$	7.08276e8	0.216495	0.108247	−	0.994124i	$-0.465476\pi$
$523$	7.08276e8	0.216495	0.108247	+	0.994124i	$0.465476\pi$
$524$	6.65858e8	0.202173
$525$	0	0
$526$	−1.92080e9	−0.575481
$527$	3.35209e9	0.997651
$528$	0	0
$529$	3.49492e9	1.02646
$530$	−6.67518e8	−0.194759
$531$	0	0
$532$	−1.19129e9	−0.343025
$533$	2.07133e9	0.592520
$534$	0	0
$535$	−2.52615e9	−0.713215
$536$	−2.28558e9	−0.641090
$537$	0	0
$538$	4.88951e8	0.135372
$539$	4.49016e9	1.23510
$540$	0	0
$541$	2.75885e9	0.749097	0.374549	−	0.927207i	$-0.377798\pi$
$541$	2.75885e9	0.749097	0.374549	+	0.927207i	$0.377798\pi$
$542$	−8.87004e9	−2.39292
$543$	0	0
$544$	−2.32016e9	−0.617906
$545$	2.21718e9	0.586696
$546$	0	0
$547$	1.35165e9	0.353108	0.176554	−	0.984291i	$-0.443505\pi$
$547$	1.35165e9	0.353108	0.176554	+	0.984291i	$0.443505\pi$
$548$	−1.60272e9	−0.416031
$549$	0	0
$550$	1.37031e9	0.351196
$551$	4.45668e9	1.13496
$552$	0	0
$553$	−1.20553e9	−0.303139
$554$	9.22484e8	0.230502
$555$	0	0
$556$	−6.28589e8	−0.155098
$557$	1.38403e9	0.339354	0.169677	−	0.985500i	$-0.445727\pi$
$557$	1.38403e9	0.339354	0.169677	+	0.985500i	$0.445727\pi$
$558$	0	0
$559$	2.69844e9	0.653389
$560$	7.87157e8	0.189410
$561$	0	0
$562$	−3.96719e9	−0.942770
$563$	1.98525e9	0.468852	0.234426	−	0.972134i	$-0.424679\pi$
$563$	1.98525e9	0.468852	0.234426	+	0.972134i	$0.424679\pi$
$564$	0	0
$565$	9.09819e8	0.212220
$566$	−1.02245e9	−0.237019
$567$	0	0
$568$	2.55580e9	0.585205
$569$	2.04260e9	0.464826	0.232413	−	0.972617i	$-0.425338\pi$
$569$	2.04260e9	0.464826	0.232413	+	0.972617i	$0.425338\pi$
$570$	0	0
$571$	−6.63626e9	−1.49175	−0.745877	−	0.666084i	$-0.767969\pi$
$571$	−6.63626e9	−1.49175	−0.745877	+	0.666084i	$0.767969\pi$
$572$	4.04191e9	0.903026
$573$	0	0
$574$	1.03057e9	0.227449
$575$	1.29789e9	0.284708
$576$	0	0
$577$	−7.80853e9	−1.69221	−0.846104	−	0.533018i	$-0.821058\pi$
$577$	−7.80853e9	−1.69221	−0.846104	+	0.533018i	$0.821058\pi$
$578$	3.75429e9	0.808687
$579$	0	0
$580$	7.95616e8	0.169319
$581$	−4.10032e8	−0.0867363
$582$	0	0
$583$	2.31621e9	0.484104
$584$	−2.85175e9	−0.592469
$585$	0	0
$586$	2.10837e9	0.432818
$587$	1.28668e9	0.262565	0.131283	−	0.991345i	$-0.458090\pi$
$587$	1.28668e9	0.262565	0.131283	+	0.991345i	$0.458090\pi$
$588$	0	0
$589$	1.43970e10	2.90314
$590$	4.19870e9	0.841653
$591$	0	0
$592$	−1.23294e10	−2.44239
$593$	−1.93979e9	−0.382000	−0.191000	−	0.981590i	$-0.561173\pi$
$593$	−1.93979e9	−0.382000	−0.191000	+	0.981590i	$0.561173\pi$
$594$	0	0
$595$	4.67291e8	0.0909448
$596$	−6.05515e8	−0.117156
$597$	0	0
$598$	1.04326e10	1.99499
$599$	−4.68780e9	−0.891199	−0.445600	−	0.895232i	$-0.647009\pi$
$599$	−4.68780e9	−0.891199	−0.445600	+	0.895232i	$0.647009\pi$
$600$	0	0
$601$	−1.72516e9	−0.324168	−0.162084	−	0.986777i	$-0.551821\pi$
$601$	−1.72516e9	−0.324168	−0.162084	+	0.986777i	$0.551821\pi$
$602$	1.34258e9	0.250815
$603$	0	0
$604$	−4.69175e9	−0.866375
$605$	−2.31893e9	−0.425739
$606$	0	0
$607$	−4.71808e9	−0.856258	−0.428129	−	0.903718i	$-0.640827\pi$
$607$	−4.71808e9	−0.856258	−0.428129	+	0.903718i	$0.640827\pi$
$608$	−9.96492e9	−1.79809
$609$	0	0
$610$	−3.00998e9	−0.536919
$611$	1.05864e10	1.87760
$612$	0	0
$613$	8.04753e9	1.41108	0.705539	−	0.708672i	$-0.250705\pi$
$613$	8.04753e9	1.41108	0.705539	+	0.708672i	$0.250705\pi$
$614$	−2.06509e9	−0.360040
$615$	0	0
$616$	−1.45828e9	−0.251367
$617$	−5.89898e9	−1.01106	−0.505532	−	0.862808i	$-0.668704\pi$
$617$	−5.89898e9	−1.01106	−0.505532	+	0.862808i	$0.668704\pi$
$618$	0	0
$619$	3.76054e9	0.637284	0.318642	−	0.947875i	$-0.396773\pi$
$619$	3.76054e9	0.637284	0.318642	+	0.947875i	$0.396773\pi$
$620$	2.57018e9	0.433104
$621$	0	0
$622$	−7.02191e8	−0.117001
$623$	−8.54011e8	−0.141500
$624$	0	0
$625$	2.44141e8	0.0400000
$626$	9.42677e9	1.53586
$627$	0	0
$628$	3.75971e9	0.605753
$629$	−7.31926e9	−1.17271
$630$	0	0
$631$	6.29568e9	0.997562	0.498781	−	0.866728i	$-0.333781\pi$
$631$	6.29568e9	0.997562	0.498781	+	0.866728i	$0.333781\pi$
$632$	−2.98432e9	−0.470258
$633$	0	0
$634$	7.52768e9	1.17314
$635$	1.02371e9	0.158661
$636$	0	0
$637$	6.43043e9	0.985716
$638$	−7.52331e9	−1.14693
$639$	0	0
$640$	2.85686e9	0.430783
$641$	−3.29752e9	−0.494521	−0.247260	−	0.968949i	$-0.579530\pi$
$641$	−3.29752e9	−0.494521	−0.247260	+	0.968949i	$0.579530\pi$
$642$	0	0
$643$	−4.06042e9	−0.602327	−0.301163	−	0.953573i	$-0.597375\pi$
$643$	−4.06042e9	−0.602327	−0.301163	+	0.953573i	$0.597375\pi$
$644$	1.90472e9	0.281016
$645$	0	0
$646$	−8.93582e9	−1.30413
$647$	2.92752e9	0.424947	0.212474	−	0.977167i	$-0.431848\pi$
$647$	2.92752e9	0.424947	0.212474	+	0.977167i	$0.431848\pi$
$648$	0	0
$649$	−1.45690e10	−2.09206
$650$	1.96244e9	0.280285
$651$	0	0
$652$	1.36495e9	0.192864
$653$	1.15064e10	1.61712	0.808562	−	0.588411i	$-0.200246\pi$
$653$	1.15064e10	1.61712	0.808562	+	0.588411i	$0.200246\pi$
$654$	0	0
$655$	−1.12178e9	−0.155978
$656$	4.77834e9	0.660867
$657$	0	0
$658$	5.26714e9	0.720749
$659$	1.10020e10	1.49752	0.748760	−	0.662842i	$-0.230650\pi$
$659$	1.10020e10	1.49752	0.748760	+	0.662842i	$0.230650\pi$
$660$	0	0
$661$	6.24642e8	0.0841252	0.0420626	−	0.999115i	$-0.486607\pi$
$661$	6.24642e8	0.0841252	0.0420626	+	0.999115i	$0.486607\pi$
$662$	−4.76021e9	−0.637710
$663$	0	0
$664$	−1.01504e9	−0.134554
$665$	2.00698e9	0.264647
$666$	0	0
$667$	−7.12568e9	−0.929793
$668$	1.81861e9	0.236060
$669$	0	0
$670$	−5.31001e9	−0.682077
$671$	1.04443e10	1.33460
$672$	0	0
$673$	3.38452e9	0.428000	0.214000	−	0.976834i	$-0.431351\pi$
$673$	3.38452e9	0.428000	0.214000	+	0.976834i	$0.431351\pi$
$674$	7.30099e9	0.918485
$675$	0	0
$676$	1.13276e9	0.141034
$677$	2.55366e9	0.316303	0.158151	−	0.987415i	$-0.449447\pi$
$677$	2.55366e9	0.316303	0.158151	+	0.987415i	$0.449447\pi$
$678$	0	0
$679$	−1.89204e8	−0.0231946
$680$	1.15679e9	0.141082
$681$	0	0
$682$	−2.43035e10	−2.93375
$683$	3.74273e9	0.449486	0.224743	−	0.974418i	$-0.427846\pi$
$683$	3.74273e9	0.449486	0.224743	+	0.974418i	$0.427846\pi$
$684$	0	0
$685$	2.70013e9	0.320972
$686$	6.81853e9	0.806410
$687$	0	0
$688$	6.22505e9	0.728757
$689$	3.31708e9	0.386357
$690$	0	0
$691$	−3.33509e9	−0.384534	−0.192267	−	0.981343i	$-0.561584\pi$
$691$	−3.33509e9	−0.384534	−0.192267	+	0.981343i	$0.561584\pi$
$692$	7.74314e9	0.888272
$693$	0	0
$694$	−7.84624e9	−0.891053
$695$	1.05899e9	0.119659
$696$	0	0
$697$	2.83664e9	0.317314
$698$	8.26832e9	0.920287
$699$	0	0
$700$	3.58290e8	0.0394813
$701$	1.20885e10	1.32544	0.662722	−	0.748866i	$-0.269401\pi$
$701$	1.20885e10	1.32544	0.662722	+	0.748866i	$0.269401\pi$
$702$	0	0
$703$	−3.14357e10	−3.41255
$704$	7.35992e8	0.0795003
$705$	0	0
$706$	−3.13931e8	−0.0335751
$707$	−4.95491e9	−0.527312
$708$	0	0
$709$	−4.76548e9	−0.502163	−0.251081	−	0.967966i	$-0.580786\pi$
$709$	−4.76548e9	−0.502163	−0.251081	+	0.967966i	$0.580786\pi$
$710$	5.93782e9	0.622619
$711$	0	0
$712$	−2.11412e9	−0.219507
$713$	−2.30190e10	−2.37833
$714$	0	0
$715$	−6.80946e9	−0.696693
$716$	−2.37060e9	−0.241358
$717$	0	0
$718$	−1.99249e10	−2.00891
$719$	−8.02111e9	−0.804792	−0.402396	−	0.915466i	$-0.631822\pi$
$719$	−8.02111e9	−0.804792	−0.402396	+	0.915466i	$0.631822\pi$
$720$	0	0
$721$	−3.58038e9	−0.355759
$722$	−2.56682e10	−2.53814
$723$	0	0
$724$	1.86345e9	0.182487
$725$	−1.34039e9	−0.130631
$726$	0	0
$727$	−5.41234e9	−0.522414	−0.261207	−	0.965283i	$-0.584120\pi$
$727$	−5.41234e9	−0.522414	−0.261207	+	0.965283i	$0.584120\pi$
$728$	−2.08843e9	−0.200613
$729$	0	0
$730$	−6.62537e9	−0.630348
$731$	3.69546e9	0.349911
$732$	0	0
$733$	1.08212e10	1.01487	0.507437	−	0.861689i	$-0.330593\pi$
$733$	1.08212e10	1.01487	0.507437	+	0.861689i	$0.330593\pi$
$734$	−1.21043e10	−1.12980
$735$	0	0
$736$	1.59327e10	1.47305
$737$	1.84251e10	1.69541
$738$	0	0
$739$	6.82663e9	0.622230	0.311115	−	0.950372i	$-0.399298\pi$
$739$	6.82663e9	0.622230	0.311115	+	0.950372i	$0.399298\pi$
$740$	−5.61196e9	−0.509101
$741$	0	0
$742$	1.65038e9	0.148310
$743$	−8.29272e9	−0.741714	−0.370857	−	0.928690i	$-0.620936\pi$
$743$	−8.29272e9	−0.741714	−0.370857	+	0.928690i	$0.620936\pi$
$744$	0	0
$745$	1.02012e9	0.0903868
$746$	−1.32347e10	−1.16716
$747$	0	0
$748$	5.53531e9	0.483600
$749$	6.24569e9	0.543118
$750$	0	0
$751$	1.10106e10	0.948575	0.474288	−	0.880370i	$-0.342706\pi$
$751$	1.10106e10	0.948575	0.474288	+	0.880370i	$0.342706\pi$
$752$	2.44217e10	2.09418
$753$	0	0
$754$	−1.07743e10	−0.915351
$755$	7.90427e9	0.668417
$756$	0	0
$757$	−9.49872e9	−0.795847	−0.397924	−	0.917419i	$-0.630269\pi$
$757$	−9.49872e9	−0.795847	−0.397924	+	0.917419i	$0.630269\pi$
$758$	9.70167e9	0.809104
$759$	0	0
$760$	4.96831e9	0.410546
$761$	3.67414e9	0.302210	0.151105	−	0.988518i	$-0.451717\pi$
$761$	3.67414e9	0.302210	0.151105	+	0.988518i	$0.451717\pi$
$762$	0	0
$763$	−5.48179e9	−0.446773
$764$	−3.03858e9	−0.246515
$765$	0	0
$766$	1.73110e10	1.39162
$767$	−2.08645e10	−1.66965
$768$	0	0
$769$	−1.98686e10	−1.57552	−0.787761	−	0.615980i	$-0.788760\pi$
$769$	−1.98686e10	−1.57552	−0.787761	+	0.615980i	$0.788760\pi$
$770$	−3.38798e9	−0.267438
$771$	0	0
$772$	3.80335e9	0.297513
$773$	9.86915e9	0.768514	0.384257	−	0.923226i	$-0.374458\pi$
$773$	9.86915e9	0.768514	0.384257	+	0.923226i	$0.374458\pi$
$774$	0	0
$775$	−4.33002e9	−0.334144
$776$	−4.68378e8	−0.0359816
$777$	0	0
$778$	7.19365e9	0.547672
$779$	1.21831e10	0.923376
$780$	0	0
$781$	−2.06036e10	−1.54762
$782$	1.42873e10	1.06838
$783$	0	0
$784$	1.48344e10	1.09942
$785$	−6.33405e9	−0.467345
$786$	0	0
$787$	1.43752e10	1.05124	0.525621	−	0.850719i	$-0.323833\pi$
$787$	1.43752e10	1.05124	0.525621	+	0.850719i	$0.323833\pi$
$788$	1.02729e10	0.747915
$789$	0	0
$790$	−6.93338e9	−0.500323
$791$	−2.24945e9	−0.161606
$792$	0	0
$793$	1.49574e10	1.06513
$794$	1.29890e10	0.920885
$795$	0	0
$796$	6.77235e9	0.475930
$797$	2.68257e10	1.87692	0.938462	−	0.345384i	$-0.112251\pi$
$797$	2.68257e10	1.87692	0.938462	+	0.345384i	$0.112251\pi$
$798$	0	0
$799$	1.44978e10	1.00552
$800$	2.99704e9	0.206956
$801$	0	0
$802$	−2.51827e10	−1.72382
$803$	2.29893e10	1.56683
$804$	0	0
$805$	−3.20891e9	−0.216807
$806$	−3.48054e10	−2.34139
$807$	0	0
$808$	−1.22660e10	−0.818016
$809$	−2.40552e10	−1.59731	−0.798655	−	0.601790i	$-0.794455\pi$
$809$	−2.40552e10	−1.59731	−0.798655	+	0.601790i	$0.794455\pi$
$810$	0	0
$811$	−1.73137e10	−1.13977	−0.569885	−	0.821725i	$-0.693012\pi$
$811$	−1.73137e10	−1.13977	−0.569885	+	0.821725i	$0.693012\pi$
$812$	−1.96709e9	−0.128937
$813$	0	0
$814$	5.30665e10	3.44854
$815$	−2.29956e9	−0.148797
$816$	0	0
$817$	1.58717e10	1.01823
$818$	2.08363e10	1.33102
$819$	0	0
$820$	2.17496e9	0.137754
$821$	2.75064e10	1.73473	0.867365	−	0.497672i	$-0.165812\pi$
$821$	2.75064e10	1.73473	0.867365	+	0.497672i	$0.165812\pi$
$822$	0	0
$823$	−1.38518e10	−0.866178	−0.433089	−	0.901351i	$-0.642576\pi$
$823$	−1.38518e10	−0.866178	−0.433089	+	0.901351i	$0.642576\pi$
$824$	−8.86329e9	−0.551887
$825$	0	0
$826$	−1.03809e10	−0.640924
$827$	−4.66379e9	−0.286728	−0.143364	−	0.989670i	$-0.545792\pi$
$827$	−4.66379e9	−0.286728	−0.143364	+	0.989670i	$0.545792\pi$
$828$	0	0
$829$	−5.80939e9	−0.354152	−0.177076	−	0.984197i	$-0.556664\pi$
$829$	−5.80939e9	−0.354152	−0.177076	+	0.984197i	$0.556664\pi$
$830$	−2.35821e9	−0.143156
$831$	0	0
$832$	1.05403e9	0.0634482
$833$	8.80633e9	0.527883
$834$	0	0
$835$	−3.06384e9	−0.182122
$836$	2.37737e10	1.40726
$837$	0	0
$838$	2.21927e10	1.30273
$839$	1.67619e10	0.979845	0.489923	−	0.871766i	$-0.337025\pi$
$839$	1.67619e10	0.979845	0.489923	+	0.871766i	$0.337025\pi$
$840$	0	0
$841$	−9.89086e9	−0.573387
$842$	−3.90077e10	−2.25194
$843$	0	0
$844$	2.75727e9	0.157863
$845$	−1.90838e9	−0.108809
$846$	0	0
$847$	5.73336e9	0.324203
$848$	7.65219e9	0.430923
$849$	0	0
$850$	2.68753e9	0.150102
$851$	5.02618e10	2.79566
$852$	0	0
$853$	2.81863e10	1.55495	0.777474	−	0.628915i	$-0.216500\pi$
$853$	2.81863e10	1.55495	0.777474	+	0.628915i	$0.216500\pi$
$854$	7.44192e9	0.408867
$855$	0	0
$856$	1.54613e10	0.842536
$857$	2.65858e9	0.144284	0.0721418	−	0.997394i	$-0.477017\pi$
$857$	2.65858e9	0.144284	0.0721418	+	0.997394i	$0.477017\pi$
$858$	0	0
$859$	−1.01671e10	−0.547296	−0.273648	−	0.961830i	$-0.588230\pi$
$859$	−1.01671e10	−0.547296	−0.273648	+	0.961830i	$0.588230\pi$
$860$	2.83345e9	0.151905
$861$	0	0
$862$	−1.99898e10	−1.06300
$863$	−3.00539e10	−1.59171	−0.795854	−	0.605488i	$-0.792978\pi$
$863$	−3.00539e10	−1.59171	−0.795854	+	0.605488i	$0.792978\pi$
$864$	0	0
$865$	−1.30450e10	−0.685311
$866$	−3.00514e10	−1.57236
$867$	0	0
$868$	−6.35455e9	−0.329811
$869$	2.40581e10	1.24363
$870$	0	0
$871$	2.63869e10	1.35309
$872$	−1.35703e10	−0.693076
$873$	0	0
$874$	6.13628e10	3.10896
$875$	−6.03617e8	−0.0304602
$876$	0	0
$877$	−3.26856e10	−1.63628	−0.818140	−	0.575019i	$-0.804995\pi$
$877$	−3.26856e10	−1.63628	−0.818140	+	0.575019i	$0.804995\pi$
$878$	−3.72526e10	−1.85749
$879$	0	0
$880$	−1.57088e10	−0.777056
$881$	9.61021e8	0.0473497	0.0236749	−	0.999720i	$-0.492463\pi$
$881$	9.61021e8	0.0473497	0.0236749	+	0.999720i	$0.492463\pi$
$882$	0	0
$883$	−1.21547e10	−0.594132	−0.297066	−	0.954857i	$-0.596008\pi$
$883$	−1.21547e10	−0.594132	−0.297066	+	0.954857i	$0.596008\pi$
$884$	7.92720e9	0.385955
$885$	0	0
$886$	−3.86031e9	−0.186468
$887$	5.62878e9	0.270820	0.135410	−	0.990790i	$-0.456765\pi$
$887$	5.62878e9	0.270820	0.135410	+	0.990790i	$0.456765\pi$
$888$	0	0
$889$	−2.53104e9	−0.120821
$890$	−4.91166e9	−0.233541
$891$	0	0
$892$	−1.56238e10	−0.737071
$893$	6.22670e10	2.92603
$894$	0	0
$895$	3.99378e9	0.186210
$896$	−7.06335e9	−0.328044
$897$	0	0
$898$	2.85354e10	1.31497
$899$	2.37728e10	1.09124
$900$	0	0
$901$	4.54268e9	0.206907
$902$	−2.05663e10	−0.933113
$903$	0	0
$904$	−5.56855e9	−0.250699
$905$	−3.13938e9	−0.140791
$906$	0	0
$907$	−3.76159e10	−1.67397	−0.836983	−	0.547229i	$-0.815683\pi$
$907$	−3.76159e10	−1.67397	−0.836983	+	0.547229i	$0.815683\pi$
$908$	−5.82228e9	−0.258103
$909$	0	0
$910$	−4.85198e9	−0.213439
$911$	−3.48318e10	−1.52638	−0.763188	−	0.646177i	$-0.776367\pi$
$911$	−3.48318e10	−1.52638	−0.763188	+	0.646177i	$0.776367\pi$
$912$	0	0
$913$	8.18273e9	0.355837
$914$	6.06164e8	0.0262590
$915$	0	0
$916$	8.13984e9	0.349930
$917$	2.77351e9	0.118778
$918$	0	0
$919$	1.22563e10	0.520899	0.260450	−	0.965487i	$-0.416129\pi$
$919$	1.22563e10	0.520899	0.260450	+	0.965487i	$0.416129\pi$
$920$	−7.94372e9	−0.336331
$921$	0	0
$922$	−4.62392e10	−1.94291
$923$	−2.95067e10	−1.23514
$924$	0	0
$925$	9.45456e9	0.392776
$926$	−5.66850e10	−2.34601
$927$	0	0
$928$	−1.64544e10	−0.675872
$929$	1.72121e10	0.704335	0.352167	−	0.935937i	$-0.385445\pi$
$929$	1.72121e10	0.704335	0.352167	+	0.935937i	$0.385445\pi$
$930$	0	0
$931$	3.78226e10	1.53613
$932$	1.67382e9	0.0677258
$933$	0	0
$934$	4.90234e10	1.96875
$935$	−9.32542e9	−0.373102
$936$	0	0
$937$	−1.40605e10	−0.558357	−0.279178	−	0.960239i	$-0.590062\pi$
$937$	−1.40605e10	−0.558357	−0.279178	+	0.960239i	$0.590062\pi$
$938$	1.31285e10	0.519406
$939$	0	0
$940$	1.11160e10	0.436518
$941$	−2.28537e10	−0.894113	−0.447056	−	0.894506i	$-0.647528\pi$
$941$	−2.28537e10	−0.894113	−0.447056	+	0.894506i	$0.647528\pi$
$942$	0	0
$943$	−1.94793e10	−0.756456
$944$	−4.81324e10	−1.86224
$945$	0	0
$946$	−2.67930e10	−1.02897
$947$	−7.28195e9	−0.278627	−0.139313	−	0.990248i	$-0.544490\pi$
$947$	−7.28195e9	−0.278627	−0.139313	+	0.990248i	$0.544490\pi$
$948$	0	0
$949$	3.29233e10	1.25047
$950$	1.15427e10	0.436793
$951$	0	0
$952$	−2.86006e9	−0.107435
$953$	−4.60122e10	−1.72206	−0.861029	−	0.508556i	$-0.830179\pi$
$953$	−4.60122e10	−1.72206	−0.861029	+	0.508556i	$0.830179\pi$
$954$	0	0
$955$	5.11914e9	0.190189
$956$	1.63607e10	0.605619
$957$	0	0
$958$	1.18043e10	0.433770
$959$	−6.67584e9	−0.244422
$960$	0	0
$961$	4.92836e10	1.79131
$962$	7.59974e10	2.75224
$963$	0	0
$964$	2.88655e10	1.03779
$965$	−6.40756e9	−0.229534
$966$	0	0
$967$	−2.28327e7	−0.000812014 0	−0.000406007	−	1.00000i	$-0.500129\pi$
$967$	−2.28327e7	−0.000812014 0	−0.000406007		1.00000i	$0.500129\pi$
$968$	1.41930e10	0.502934
$969$	0	0
$970$	−1.08817e9	−0.0382820
$971$	−3.21605e10	−1.12734	−0.563671	−	0.825999i	$-0.690611\pi$
$971$	−3.21605e10	−1.12734	−0.563671	+	0.825999i	$0.690611\pi$
$972$	0	0
$973$	−2.61827e9	−0.0911213
$974$	7.01562e10	2.43282
$975$	0	0
$976$	3.45053e10	1.18799
$977$	4.37075e10	1.49942	0.749712	−	0.661764i	$-0.230192\pi$
$977$	4.37075e10	1.49942	0.749712	+	0.661764i	$0.230192\pi$
$978$	0	0
$979$	1.70429e10	0.580503
$980$	6.75216e9	0.229167
$981$	0	0
$982$	4.37850e10	1.47549
$983$	2.16749e10	0.727814	0.363907	−	0.931435i	$-0.381443\pi$
$983$	2.16749e10	0.727814	0.363907	+	0.931435i	$0.381443\pi$
$984$	0	0
$985$	−1.73069e10	−0.577024
$986$	−1.47551e10	−0.490200
$987$	0	0
$988$	3.40467e10	1.12312
$989$	−2.53770e10	−0.834166
$990$	0	0
$991$	−2.66583e10	−0.870113	−0.435056	−	0.900403i	$-0.643272\pi$
$991$	−2.66583e10	−0.870113	−0.435056	+	0.900403i	$0.643272\pi$
$992$	−5.31548e10	−1.72883
$993$	0	0
$994$	−1.46808e10	−0.474128
$995$	−1.14095e10	−0.367185
$996$	0	0
$997$	−1.03185e10	−0.329750	−0.164875	−	0.986314i	$-0.552722\pi$
$997$	−1.03185e10	−0.329750	−0.164875	+	0.986314i	$0.552722\pi$
$998$	1.11354e9	0.0354609
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.8.a.d.1.2	yes	7
3.2	odd	2		405.8.a.a.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
405.8.a.a.1.6	✓	7	3.2	odd	2
405.8.a.d.1.2	yes	7	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)

\(f(q)\)	\(=\)	\(q-14.2196 q^{2} +74.1965 q^{4} -125.000 q^{5} +309.052 q^{7} +765.063 q^{8} +O(q^{10})\)	\(q-14.2196 q^{2} +74.1965 q^{4} -125.000 q^{5} +309.052 q^{7} +765.063 q^{8} +1777.45 q^{10} -6167.54 q^{11} -8832.64 q^{13} -4394.59 q^{14} -20376.0 q^{16} -12096.1 q^{17} -51951.9 q^{19} -9274.56 q^{20} +87699.9 q^{22} +83064.7 q^{23} +15625.0 q^{25} +125596. q^{26} +22930.6 q^{28} -85784.7 q^{29} -277121. q^{31} +191811. q^{32} +172002. q^{34} -38631.5 q^{35} +605092. q^{37} +738735. q^{38} -95632.9 q^{40} -234508. q^{41} -305508. q^{43} -457610. q^{44} -1.18115e6 q^{46} -1.19855e6 q^{47} -728030. q^{49} -222181. q^{50} -655351. q^{52} -375548. q^{53} +770943. q^{55} +236444. q^{56} +1.21982e6 q^{58} +2.36221e6 q^{59} -1.69343e6 q^{61} +3.94055e6 q^{62} -119333. q^{64} +1.10408e6 q^{65} -2.98743e6 q^{67} -897489. q^{68} +549324. q^{70} +3.34064e6 q^{71} -3.72746e6 q^{73} -8.60415e6 q^{74} -3.85465e6 q^{76} -1.90609e6 q^{77} -3.90075e6 q^{79} +2.54700e6 q^{80} +3.33461e6 q^{82} -1.32674e6 q^{83} +1.51201e6 q^{85} +4.34420e6 q^{86} -4.71856e6 q^{88} -2.76332e6 q^{89} -2.72974e6 q^{91} +6.16311e6 q^{92} +1.70429e7 q^{94} +6.49399e6 q^{95} -612208. q^{97} +1.03523e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 15 q^{2} + 457 q^{4} - 875 q^{5} + 614 q^{7} + 4605 q^{8}+O(q^{10}) \) 7 * q + 15 * q^2 + 457 * q^4 - 875 * q^5 + 614 * q^7 + 4605 * q^8	\( 7 q + 15 q^{2} + 457 q^{4} - 875 q^{5} + 614 q^{7} + 4605 q^{8} - 1875 q^{10} + 3753 q^{11} - 6562 q^{13} + 19653 q^{14} + 27625 q^{16} - 23862 q^{17} + 33251 q^{19} - 57125 q^{20} + 108060 q^{22} + 62682 q^{23} + 109375 q^{25} - 186789 q^{26} + 149303 q^{28} + 78939 q^{29} - 703165 q^{31} + 1266165 q^{32} - 589398 q^{34} - 76750 q^{35} + 336776 q^{37} + 498855 q^{38} - 575625 q^{40} + 480801 q^{41} - 442792 q^{43} - 9372 q^{44} + 213447 q^{46} + 1122744 q^{47} - 954843 q^{49} + 234375 q^{50} - 1324819 q^{52} + 692028 q^{53} - 469125 q^{55} + 6614175 q^{56} - 3971220 q^{58} + 1274487 q^{59} - 2485258 q^{61} - 2438700 q^{62} + 10358137 q^{64} + 820250 q^{65} - 892402 q^{67} + 926646 q^{68} - 2456625 q^{70} + 8286201 q^{71} + 788666 q^{73} - 537042 q^{74} + 16155485 q^{76} - 5060322 q^{77} - 1308352 q^{79} - 3453125 q^{80} + 716235 q^{82} + 9226704 q^{83} + 2982750 q^{85} + 15948900 q^{86} + 16624320 q^{88} + 4459791 q^{89} - 5701496 q^{91} + 8926029 q^{92} + 43736397 q^{94} - 4156375 q^{95} - 11086048 q^{97} + 21087450 q^{98}+O(q^{100}) \) 7 * q + 15 * q^2 + 457 * q^4 - 875 * q^5 + 614 * q^7 + 4605 * q^8 - 1875 * q^10 + 3753 * q^11 - 6562 * q^13 + 19653 * q^14 + 27625 * q^16 - 23862 * q^17 + 33251 * q^19 - 57125 * q^20 + 108060 * q^22 + 62682 * q^23 + 109375 * q^25 - 186789 * q^26 + 149303 * q^28 + 78939 * q^29 - 703165 * q^31 + 1266165 * q^32 - 589398 * q^34 - 76750 * q^35 + 336776 * q^37 + 498855 * q^38 - 575625 * q^40 + 480801 * q^41 - 442792 * q^43 - 9372 * q^44 + 213447 * q^46 + 1122744 * q^47 - 954843 * q^49 + 234375 * q^50 - 1324819 * q^52 + 692028 * q^53 - 469125 * q^55 + 6614175 * q^56 - 3971220 * q^58 + 1274487 * q^59 - 2485258 * q^61 - 2438700 * q^62 + 10358137 * q^64 + 820250 * q^65 - 892402 * q^67 + 926646 * q^68 - 2456625 * q^70 + 8286201 * q^71 + 788666 * q^73 - 537042 * q^74 + 16155485 * q^76 - 5060322 * q^77 - 1308352 * q^79 - 3453125 * q^80 + 716235 * q^82 + 9226704 * q^83 + 2982750 * q^85 + 15948900 * q^86 + 16624320 * q^88 + 4459791 * q^89 - 5701496 * q^91 + 8926029 * q^92 + 43736397 * q^94 - 4156375 * q^95 - 11086048 * q^97 + 21087450 * q^98

Introduction

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