LMFDB - Embedded newform 387.8.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,8,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, 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("387.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	387.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:	$120.893004862$
Analytic rank:	$1$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$21.1822$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.1822 q^{2} +364.050 q^{4} -122.553 q^{5} -90.8173 q^{7} -5236.10 q^{8} +O(q^{10})$	\(q-22.1822 q^{2} +364.050 q^{4} -122.553 q^{5} -90.8173 q^{7} -5236.10 q^{8} +2718.48 q^{10} -3410.31 q^{11} -11275.0 q^{13} +2014.53 q^{14} +69549.8 q^{16} -9720.37 q^{17} +25351.7 q^{19} -44615.2 q^{20} +75648.2 q^{22} +52795.4 q^{23} -63105.9 q^{25} +250104. q^{26} -33062.0 q^{28} +216763. q^{29} +142113. q^{31} -872545. q^{32} +215619. q^{34} +11129.9 q^{35} -74290.8 q^{37} -562357. q^{38} +641697. q^{40} +273026. q^{41} -79507.0 q^{43} -1.24152e6 q^{44} -1.17112e6 q^{46} +112553. q^{47} -815295. q^{49} +1.39983e6 q^{50} -4.10466e6 q^{52} -1.41102e6 q^{53} +417942. q^{55} +475528. q^{56} -4.80827e6 q^{58} +1.44713e6 q^{59} +3.19474e6 q^{61} -3.15239e6 q^{62} +1.04526e7 q^{64} +1.38178e6 q^{65} -3.52359e6 q^{67} -3.53870e6 q^{68} -246885. q^{70} +327344. q^{71} +2.80064e6 q^{73} +1.64793e6 q^{74} +9.22928e6 q^{76} +309715. q^{77} +3.35723e6 q^{79} -8.52350e6 q^{80} -6.05633e6 q^{82} -7.10311e6 q^{83} +1.19126e6 q^{85} +1.76364e6 q^{86} +1.78567e7 q^{88} +1.32585e6 q^{89} +1.02396e6 q^{91} +1.92201e7 q^{92} -2.49668e6 q^{94} -3.10692e6 q^{95} +1.29568e7 q^{97} +1.80850e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8}+O(q^{10}) $ 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8} + 4667 q^{10} - 1620 q^{11} + 13550 q^{13} - 44160 q^{14} + 114026 q^{16} - 110880 q^{17} + 105058 q^{19} - 167251 q^{20} + 201504 q^{22} - 160184 q^{23} + 270149 q^{25} - 272104 q^{26} + 208172 q^{28} - 285546 q^{29} - 99616 q^{31} - 200126 q^{32} - 80941 q^{34} + 187104 q^{35} + 176038 q^{37} - 652165 q^{38} - 895387 q^{40} + 410260 q^{41} - 1033591 q^{43} + 2177076 q^{44} - 3975765 q^{46} + 424556 q^{47} - 1561359 q^{49} + 4063801 q^{50} - 4172312 q^{52} - 3992458 q^{53} + 406960 q^{55} - 1559556 q^{56} - 4052005 q^{58} - 2248836 q^{59} + 6210394 q^{61} - 885317 q^{62} - 3096318 q^{64} - 5600420 q^{65} - 1993648 q^{67} - 9327135 q^{68} - 1105098 q^{70} - 4978064 q^{71} + 8224814 q^{73} + 3613563 q^{74} + 10687121 q^{76} - 17261892 q^{77} + 6945708 q^{79} - 15822799 q^{80} - 508449 q^{82} - 22937328 q^{83} - 575532 q^{85} + 1272112 q^{86} + 11202656 q^{88} - 9291302 q^{89} + 25581108 q^{91} + 14388137 q^{92} - 24645805 q^{94} - 30750464 q^{95} + 10001852 q^{97} + 32304856 q^{98}+O(q^{100}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8 + 4667 * q^10 - 1620 * q^11 + 13550 * q^13 - 44160 * q^14 + 114026 * q^16 - 110880 * q^17 + 105058 * q^19 - 167251 * q^20 + 201504 * q^22 - 160184 * q^23 + 270149 * q^25 - 272104 * q^26 + 208172 * q^28 - 285546 * q^29 - 99616 * q^31 - 200126 * q^32 - 80941 * q^34 + 187104 * q^35 + 176038 * q^37 - 652165 * q^38 - 895387 * q^40 + 410260 * q^41 - 1033591 * q^43 + 2177076 * q^44 - 3975765 * q^46 + 424556 * q^47 - 1561359 * q^49 + 4063801 * q^50 - 4172312 * q^52 - 3992458 * q^53 + 406960 * q^55 - 1559556 * q^56 - 4052005 * q^58 - 2248836 * q^59 + 6210394 * q^61 - 885317 * q^62 - 3096318 * q^64 - 5600420 * q^65 - 1993648 * q^67 - 9327135 * q^68 - 1105098 * q^70 - 4978064 * q^71 + 8224814 * q^73 + 3613563 * q^74 + 10687121 * q^76 - 17261892 * q^77 + 6945708 * q^79 - 15822799 * q^80 - 508449 * q^82 - 22937328 * q^83 - 575532 * q^85 + 1272112 * q^86 + 11202656 * q^88 - 9291302 * q^89 + 25581108 * q^91 + 14388137 * q^92 - 24645805 * q^94 - 30750464 * q^95 + 10001852 * q^97 + 32304856 * 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 $

$2$	−22.1822	−1.96065	−0.980324	−	0.197397i	$-0.936751\pi$
$2$	−22.1822	−1.96065	−0.980324	+	0.197397i	$0.936751\pi$
$3$	0	0
$3$	0	0
$4$	364.050	2.84414
$5$	−122.553	−0.438457	−0.219229	−	0.975674i	$-0.570354\pi$
$5$	−122.553	−0.438457	−0.219229	+	0.975674i	$0.570354\pi$
$6$	0	0
$7$	−90.8173	−0.100075	−0.0500375	−	0.998747i	$-0.515934\pi$
$7$	−90.8173	−0.100075	−0.0500375	+	0.998747i	$0.515934\pi$
$8$	−5236.10	−3.61570
$9$	0	0
$10$	2718.48	0.859660
$11$	−3410.31	−0.772538	−0.386269	−	0.922386i	$-0.626236\pi$
$11$	−3410.31	−0.772538	−0.386269	+	0.922386i	$0.626236\pi$
$12$	0	0
$13$	−11275.0	−1.42336	−0.711680	−	0.702504i	$-0.752065\pi$
$13$	−11275.0	−1.42336	−0.711680	+	0.702504i	$0.752065\pi$
$14$	2014.53	0.196212
$15$	0	0
$16$	69549.8	4.24498
$17$	−9720.37	−0.479857	−0.239928	−	0.970791i	$-0.577124\pi$
$17$	−9720.37	−0.479857	−0.239928	+	0.970791i	$0.577124\pi$
$18$	0	0
$19$	25351.7	0.847949	0.423975	−	0.905674i	$-0.360635\pi$
$19$	25351.7	0.847949	0.423975	+	0.905674i	$0.360635\pi$
$20$	−44615.2	−1.24703
$21$	0	0
$22$	75648.2	1.51467
$23$	52795.4	0.904792	0.452396	−	0.891817i	$-0.350569\pi$
$23$	52795.4	0.904792	0.452396	+	0.891817i	$0.350569\pi$
$24$	0	0
$25$	−63105.9	−0.807755
$26$	250104.	2.79071
$27$	0	0
$28$	−33062.0	−0.284627
$29$	216763.	1.65041	0.825204	−	0.564835i	$-0.191060\pi$
$29$	216763.	1.65041	0.825204	+	0.564835i	$0.191060\pi$
$30$	0	0
$31$	142113.	0.856780	0.428390	−	0.903594i	$-0.359081\pi$
$31$	142113.	0.856780	0.428390	+	0.903594i	$0.359081\pi$
$32$	−872545.	−4.70721
$33$	0	0
$34$	215619.	0.940830
$35$	11129.9	0.0438786
$36$	0	0
$37$	−74290.8	−0.241118	−0.120559	−	0.992706i	$-0.538469\pi$
$37$	−74290.8	−0.241118	−0.120559	+	0.992706i	$0.538469\pi$
$38$	−562357.	−1.66253
$39$	0	0
$40$	641697.	1.58533
$41$	273026.	0.618673	0.309337	−	0.950953i	$-0.399893\pi$
$41$	273026.	0.618673	0.309337	+	0.950953i	$0.399893\pi$
$42$	0	0
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−1.24152e6	−2.19720
$45$	0	0
$46$	−1.17112e6	−1.77398
$47$	112553.	0.158130	0.0790652	−	0.996869i	$-0.474806\pi$
$47$	112553.	0.158130	0.0790652	+	0.996869i	$0.474806\pi$
$48$	0	0
$49$	−815295.	−0.989985
$50$	1.39983e6	1.58372
$51$	0	0
$52$	−4.10466e6	−4.04823
$53$	−1.41102e6	−1.30187	−0.650936	−	0.759132i	$-0.725624\pi$
$53$	−1.41102e6	−1.30187	−0.650936	+	0.759132i	$0.725624\pi$
$54$	0	0
$55$	417942.	0.338725
$56$	475528.	0.361841
$57$	0	0
$58$	−4.80827e6	−3.23587
$59$	1.44713e6	0.917329	0.458665	−	0.888609i	$-0.348328\pi$
$59$	1.44713e6	0.917329	0.458665	+	0.888609i	$0.348328\pi$
$60$	0	0
$61$	3.19474e6	1.80211	0.901054	−	0.433708i	$-0.142795\pi$
$61$	3.19474e6	1.80211	0.901054	+	0.433708i	$0.142795\pi$
$62$	−3.15239e6	−1.67984
$63$	0	0
$64$	1.04526e7	4.98419
$65$	1.38178e6	0.624083
$66$	0	0
$67$	−3.52359e6	−1.43128	−0.715638	−	0.698472i	$-0.753864\pi$
$67$	−3.52359e6	−1.43128	−0.715638	+	0.698472i	$0.753864\pi$
$68$	−3.53870e6	−1.36478
$69$	0	0
$70$	−246885.	−0.0860304
$71$	327344.	0.108542	0.0542712	−	0.998526i	$-0.482716\pi$
$71$	327344.	0.108542	0.0542712	+	0.998526i	$0.482716\pi$
$72$	0	0
$73$	2.80064e6	0.842613	0.421306	−	0.906918i	$-0.361572\pi$
$73$	2.80064e6	0.842613	0.421306	+	0.906918i	$0.361572\pi$
$74$	1.64793e6	0.472746
$75$	0	0
$76$	9.22928e6	2.41168
$77$	309715.	0.0773117
$78$	0	0
$79$	3.35723e6	0.766101	0.383051	−	0.923727i	$-0.374874\pi$
$79$	3.35723e6	0.766101	0.383051	+	0.923727i	$0.374874\pi$
$80$	−8.52350e6	−1.86124
$81$	0	0
$82$	−6.05633e6	−1.21300
$83$	−7.10311e6	−1.36356	−0.681781	−	0.731556i	$-0.738794\pi$
$83$	−7.10311e6	−1.36356	−0.681781	+	0.731556i	$0.738794\pi$
$84$	0	0
$85$	1.19126e6	0.210397
$86$	1.76364e6	0.298996
$87$	0	0
$88$	1.78567e7	2.79327
$89$	1.32585e6	0.199356	0.0996778	−	0.995020i	$-0.468219\pi$
$89$	1.32585e6	0.199356	0.0996778	+	0.995020i	$0.468219\pi$
$90$	0	0
$91$	1.02396e6	0.142443
$92$	1.92201e7	2.57335
$93$	0	0
$94$	−2.49668e6	−0.310038
$95$	−3.10692e6	−0.371789
$96$	0	0
$97$	1.29568e7	1.44144	0.720718	−	0.693228i	$-0.243812\pi$
$97$	1.29568e7	1.44144	0.720718	+	0.693228i	$0.243812\pi$
$98$	1.80850e7	1.94101
$99$	0	0
$100$	−2.29737e7	−2.29737
$101$	−309915.	−0.0299308	−0.0149654	−	0.999888i	$-0.504764\pi$
$101$	−309915.	−0.0299308	−0.0149654	+	0.999888i	$0.504764\pi$
$102$	0	0
$103$	1.99810e7	1.80172	0.900858	−	0.434113i	$-0.142938\pi$
$103$	1.99810e7	1.80172	0.900858	+	0.434113i	$0.142938\pi$
$104$	5.90370e7	5.14645
$105$	0	0
$106$	3.12996e7	2.55251
$107$	−1.77323e6	−0.139934	−0.0699669	−	0.997549i	$-0.522289\pi$
$107$	−1.77323e6	−0.139934	−0.0699669	+	0.997549i	$0.522289\pi$
$108$	0	0
$109$	7.12031e6	0.526631	0.263315	−	0.964710i	$-0.415184\pi$
$109$	7.12031e6	0.526631	0.263315	+	0.964710i	$0.415184\pi$
$110$	−9.27088e6	−0.664120
$111$	0	0
$112$	−6.31632e6	−0.424816
$113$	9.47406e6	0.617677	0.308839	−	0.951114i	$-0.400060\pi$
$113$	9.47406e6	0.617677	0.308839	+	0.951114i	$0.400060\pi$
$114$	0	0
$115$	−6.47021e6	−0.396713
$116$	7.89123e7	4.69399
$117$	0	0
$118$	−3.21005e7	−1.79856
$119$	882778.	0.0480216
$120$	0	0
$121$	−7.85694e6	−0.403185
$122$	−7.08663e7	−3.53330
$123$	0	0
$124$	5.17363e7	2.43680
$125$	1.73082e7	0.792623
$126$	0	0
$127$	2.94089e7	1.27399	0.636994	−	0.770868i	$-0.280177\pi$
$127$	2.94089e7	1.27399	0.636994	+	0.770868i	$0.280177\pi$
$128$	−1.20176e8	−5.06503
$129$	0	0
$130$	−3.06509e7	−1.22361
$131$	−4.80770e7	−1.86848	−0.934238	−	0.356650i	$-0.883919\pi$
$131$	−4.80770e7	−1.86848	−0.934238	+	0.356650i	$0.883919\pi$
$132$	0	0
$133$	−2.30237e6	−0.0848585
$134$	7.81609e7	2.80623
$135$	0	0
$136$	5.08968e7	1.73502
$137$	−5.87744e6	−0.195284	−0.0976419	−	0.995222i	$-0.531130\pi$
$137$	−5.87744e6	−0.195284	−0.0976419	+	0.995222i	$0.531130\pi$
$138$	0	0
$139$	−5.12513e7	−1.61865	−0.809326	−	0.587360i	$-0.800167\pi$
$139$	−5.12513e7	−1.61865	−0.809326	+	0.587360i	$0.800167\pi$
$140$	4.05183e6	0.124797
$141$	0	0
$142$	−7.26120e6	−0.212813
$143$	3.84513e7	1.09960
$144$	0	0
$145$	−2.65648e7	−0.723633
$146$	−6.21244e7	−1.65207
$147$	0	0
$148$	−2.70455e7	−0.685771
$149$	6.91179e6	0.171174	0.0855871	−	0.996331i	$-0.472723\pi$
$149$	6.91179e6	0.171174	0.0855871	+	0.996331i	$0.472723\pi$
$150$	0	0
$151$	−6.97335e7	−1.64825	−0.824124	−	0.566410i	$-0.808332\pi$
$151$	−6.97335e7	−1.64825	−0.824124	+	0.566410i	$0.808332\pi$
$152$	−1.32744e8	−3.06593
$153$	0	0
$154$	−6.87016e6	−0.151581
$155$	−1.74164e7	−0.375661
$156$	0	0
$157$	−6.10206e7	−1.25843	−0.629213	−	0.777233i	$-0.716623\pi$
$157$	−6.10206e7	−1.25843	−0.629213	+	0.777233i	$0.716623\pi$
$158$	−7.44707e7	−1.50205
$159$	0	0
$160$	1.06933e8	2.06391
$161$	−4.79474e6	−0.0905470
$162$	0	0
$163$	−1.28985e6	−0.0233282	−0.0116641	−	0.999932i	$-0.503713\pi$
$163$	−1.28985e6	−0.0233282	−0.0116641	+	0.999932i	$0.503713\pi$
$164$	9.93952e7	1.75959
$165$	0	0
$166$	1.57563e8	2.67347
$167$	8.25906e7	1.37222	0.686109	−	0.727499i	$-0.259317\pi$
$167$	8.25906e7	1.37222	0.686109	+	0.727499i	$0.259317\pi$
$168$	0	0
$169$	6.43771e7	1.02595
$170$	−2.64247e7	−0.412514
$171$	0	0
$172$	−2.89445e7	−0.433727
$173$	6.06382e6	0.0890400	0.0445200	−	0.999008i	$-0.485824\pi$
$173$	6.06382e6	0.0890400	0.0445200	+	0.999008i	$0.485824\pi$
$174$	0	0
$175$	5.73110e6	0.0808361
$176$	−2.37186e8	−3.27941
$177$	0	0
$178$	−2.94102e7	−0.390866
$179$	5.06661e7	0.660286	0.330143	−	0.943931i	$-0.392903\pi$
$179$	5.06661e7	0.660286	0.330143	+	0.943931i	$0.392903\pi$
$180$	0	0
$181$	−2.08989e6	−0.0261968	−0.0130984	−	0.999914i	$-0.504169\pi$
$181$	−2.08989e6	−0.0261968	−0.0130984	+	0.999914i	$0.504169\pi$
$182$	−2.27138e7	−0.279280
$183$	0	0
$184$	−2.76442e8	−3.27146
$185$	9.10452e6	0.105720
$186$	0	0
$187$	3.31495e7	0.370707
$188$	4.09749e7	0.449744
$189$	0	0
$190$	6.89182e7	0.728948
$191$	−1.78113e8	−1.84960	−0.924800	−	0.380454i	$-0.875768\pi$
$191$	−1.78113e8	−1.84960	−0.924800	+	0.380454i	$0.875768\pi$
$192$	0	0
$193$	1.26757e8	1.26917	0.634586	−	0.772852i	$-0.281170\pi$
$193$	1.26757e8	1.26917	0.634586	+	0.772852i	$0.281170\pi$
$194$	−2.87410e8	−2.82615
$195$	0	0
$196$	−2.96808e8	−2.81565
$197$	1.27815e8	1.19110	0.595550	−	0.803318i	$-0.296934\pi$
$197$	1.27815e8	1.19110	0.595550	+	0.803318i	$0.296934\pi$
$198$	0	0
$199$	−1.29981e8	−1.16921	−0.584606	−	0.811318i	$-0.698751\pi$
$199$	−1.29981e8	−1.16921	−0.584606	+	0.811318i	$0.698751\pi$
$200$	3.30429e8	2.92060
$201$	0	0
$202$	6.87459e6	0.0586837
$203$	−1.96858e7	−0.165164
$204$	0	0
$205$	−3.34601e7	−0.271262
$206$	−4.43222e8	−3.53253
$207$	0	0
$208$	−7.84173e8	−6.04214
$209$	−8.64573e7	−0.655073
$210$	0	0
$211$	−1.85689e8	−1.36081	−0.680406	−	0.732836i	$-0.738196\pi$
$211$	−1.85689e8	−1.36081	−0.680406	+	0.732836i	$0.738196\pi$
$212$	−5.13682e8	−3.70270
$213$	0	0
$214$	3.93342e7	0.274361
$215$	9.74378e6	0.0668641
$216$	0	0
$217$	−1.29064e7	−0.0857422
$218$	−1.57944e8	−1.03254
$219$	0	0
$220$	1.52152e8	0.963380
$221$	1.09597e8	0.683009
$222$	0	0
$223$	1.57910e7	0.0953545	0.0476773	−	0.998863i	$-0.484818\pi$
$223$	1.57910e7	0.0953545	0.0476773	+	0.998863i	$0.484818\pi$
$224$	7.92422e7	0.471073
$225$	0	0
$226$	−2.10155e8	−1.21105
$227$	−3.37705e7	−0.191623	−0.0958113	−	0.995400i	$-0.530545\pi$
$227$	−3.37705e7	−0.191623	−0.0958113	+	0.995400i	$0.530545\pi$
$228$	0	0
$229$	2.60087e8	1.43118	0.715590	−	0.698520i	$-0.246158\pi$
$229$	2.60087e8	1.43118	0.715590	+	0.698520i	$0.246158\pi$
$230$	1.43523e8	0.777813
$231$	0	0
$232$	−1.13499e9	−5.96738
$233$	−1.45083e8	−0.751398	−0.375699	−	0.926742i	$-0.622597\pi$
$233$	−1.45083e8	−0.751398	−0.375699	+	0.926742i	$0.622597\pi$
$234$	0	0
$235$	−1.37937e7	−0.0693334
$236$	5.26827e8	2.60901
$237$	0	0
$238$	−1.95819e7	−0.0941535
$239$	1.55295e8	0.735808	0.367904	−	0.929864i	$-0.380076\pi$
$239$	1.55295e8	0.735808	0.367904	+	0.929864i	$0.380076\pi$
$240$	0	0
$241$	3.22999e8	1.48642	0.743211	−	0.669057i	$-0.233302\pi$
$241$	3.22999e8	1.48642	0.743211	+	0.669057i	$0.233302\pi$
$242$	1.74284e8	0.790504
$243$	0	0
$244$	1.16304e9	5.12544
$245$	9.99165e7	0.434066
$246$	0	0
$247$	−2.85841e8	−1.20694
$248$	−7.44119e8	−3.09786
$249$	0	0
$250$	−3.83934e8	−1.55405
$251$	2.35414e8	0.939668	0.469834	−	0.882755i	$-0.344314\pi$
$251$	2.35414e8	0.939668	0.469834	+	0.882755i	$0.344314\pi$
$252$	0	0
$253$	−1.80049e8	−0.698986
$254$	−6.52354e8	−2.49784
$255$	0	0
$256$	1.32783e9	4.94655
$257$	4.25190e7	0.156249	0.0781245	−	0.996944i	$-0.475107\pi$
$257$	4.25190e7	0.156249	0.0781245	+	0.996944i	$0.475107\pi$
$258$	0	0
$259$	6.74689e6	0.0241298
$260$	5.03036e8	1.77498
$261$	0	0
$262$	1.06645e9	3.66342
$263$	−1.04522e8	−0.354292	−0.177146	−	0.984185i	$-0.556686\pi$
$263$	−1.04522e8	−0.354292	−0.177146	+	0.984185i	$0.556686\pi$
$264$	0	0
$265$	1.72924e8	0.570815
$266$	5.10717e7	0.166378
$267$	0	0
$268$	−1.28276e9	−4.07074
$269$	1.86374e8	0.583784	0.291892	−	0.956451i	$-0.405715\pi$
$269$	1.86374e8	0.583784	0.291892	+	0.956451i	$0.405715\pi$
$270$	0	0
$271$	3.37243e8	1.02932	0.514660	−	0.857394i	$-0.327918\pi$
$271$	3.37243e8	1.02932	0.514660	+	0.857394i	$0.327918\pi$
$272$	−6.76049e8	−2.03698
$273$	0	0
$274$	1.30375e8	0.382883
$275$	2.15211e8	0.624022
$276$	0	0
$277$	−4.22893e8	−1.19550	−0.597752	−	0.801681i	$-0.703939\pi$
$277$	−4.22893e8	−1.19550	−0.597752	+	0.801681i	$0.703939\pi$
$278$	1.13687e9	3.17360
$279$	0	0
$280$	−5.82772e7	−0.158652
$281$	−3.41588e8	−0.918396	−0.459198	−	0.888334i	$-0.651863\pi$
$281$	−3.41588e8	−0.918396	−0.459198	+	0.888334i	$0.651863\pi$
$282$	0	0
$283$	−1.93785e8	−0.508238	−0.254119	−	0.967173i	$-0.581785\pi$
$283$	−1.93785e8	−0.508238	−0.254119	+	0.967173i	$0.581785\pi$
$284$	1.19169e8	0.308710
$285$	0	0
$286$	−8.52934e8	−2.15593
$287$	−2.47955e7	−0.0619137
$288$	0	0
$289$	−3.15853e8	−0.769738
$290$	5.89265e8	1.41879
$291$	0	0
$292$	1.01957e9	2.39651
$293$	−4.63942e8	−1.07752	−0.538762	−	0.842458i	$-0.681108\pi$
$293$	−4.63942e8	−1.07752	−0.538762	+	0.842458i	$0.681108\pi$
$294$	0	0
$295$	−1.77349e8	−0.402210
$296$	3.88994e8	0.871809
$297$	0	0
$298$	−1.53319e8	−0.335612
$299$	−5.95268e8	−1.28785
$300$	0	0
$301$	7.22061e6	0.0152613
$302$	1.54684e9	3.23163
$303$	0	0
$304$	1.76321e9	3.59953
$305$	−3.91523e8	−0.790147
$306$	0	0
$307$	1.10340e8	0.217644	0.108822	−	0.994061i	$-0.465292\pi$
$307$	1.10340e8	0.217644	0.108822	+	0.994061i	$0.465292\pi$
$308$	1.12752e8	0.219885
$309$	0	0
$310$	3.86333e8	0.736539
$311$	1.65769e8	0.312494	0.156247	−	0.987718i	$-0.450060\pi$
$311$	1.65769e8	0.312494	0.156247	+	0.987718i	$0.450060\pi$
$312$	0	0
$313$	−1.02978e9	−1.89818	−0.949091	−	0.315003i	$-0.897994\pi$
$313$	−1.02978e9	−1.89818	−0.949091	+	0.315003i	$0.897994\pi$
$314$	1.35357e9	2.46733
$315$	0	0
$316$	1.22220e9	2.17890
$317$	−6.40081e8	−1.12857	−0.564284	−	0.825581i	$-0.690848\pi$
$317$	−6.40081e8	−1.12857	−0.564284	+	0.825581i	$0.690848\pi$
$318$	0	0
$319$	−7.39228e8	−1.27500
$320$	−1.28099e9	−2.18535
$321$	0	0
$322$	1.06358e8	0.177531
$323$	−2.46428e8	−0.406894
$324$	0	0
$325$	7.11519e8	1.14973
$326$	2.86116e7	0.0457383
$327$	0	0
$328$	−1.42959e9	−2.23694
$329$	−1.02218e7	−0.0158249
$330$	0	0
$331$	−4.29838e8	−0.651489	−0.325744	−	0.945458i	$-0.605615\pi$
$331$	−4.29838e8	−0.651489	−0.325744	+	0.945458i	$0.605615\pi$
$332$	−2.58588e9	−3.87816
$333$	0	0
$334$	−1.83204e9	−2.69044
$335$	4.31824e8	0.627553
$336$	0	0
$337$	−3.78144e8	−0.538211	−0.269105	−	0.963111i	$-0.586728\pi$
$337$	−3.78144e8	−0.538211	−0.269105	+	0.963111i	$0.586728\pi$
$338$	−1.42803e9	−2.01153
$339$	0	0
$340$	4.33676e8	0.598397
$341$	−4.84651e8	−0.661895
$342$	0	0
$343$	1.48835e8	0.199148
$344$	4.16306e8	0.551389
$345$	0	0
$346$	−1.34509e8	−0.174576
$347$	3.18524e8	0.409250	0.204625	−	0.978840i	$-0.434403\pi$
$347$	3.18524e8	0.409250	0.204625	+	0.978840i	$0.434403\pi$
$348$	0	0
$349$	9.98844e8	1.25779	0.628896	−	0.777489i	$-0.283507\pi$
$349$	9.98844e8	1.25779	0.628896	+	0.777489i	$0.283507\pi$
$350$	−1.27128e8	−0.158491
$351$	0	0
$352$	2.97565e9	3.63649
$353$	−1.22295e8	−0.147978	−0.0739890	−	0.997259i	$-0.523573\pi$
$353$	−1.22295e8	−0.147978	−0.0739890	+	0.997259i	$0.523573\pi$
$354$	0	0
$355$	−4.01168e7	−0.0475912
$356$	4.82674e8	0.566994
$357$	0	0
$358$	−1.12389e9	−1.29459
$359$	1.04011e9	1.18645	0.593225	−	0.805037i	$-0.297854\pi$
$359$	1.04011e9	1.18645	0.593225	+	0.805037i	$0.297854\pi$
$360$	0	0
$361$	−2.51162e8	−0.280982
$362$	4.63583e7	0.0513627
$363$	0	0
$364$	3.72774e8	0.405127
$365$	−3.43226e8	−0.369450
$366$	0	0
$367$	3.08148e8	0.325408	0.162704	−	0.986675i	$-0.447978\pi$
$367$	3.08148e8	0.325408	0.162704	+	0.986675i	$0.447978\pi$
$368$	3.67191e9	3.84082
$369$	0	0
$370$	−2.01958e8	−0.207279
$371$	1.28145e8	0.130285
$372$	0	0
$373$	−1.52740e9	−1.52395	−0.761977	−	0.647604i	$-0.775771\pi$
$373$	−1.52740e9	−1.52395	−0.761977	+	0.647604i	$0.775771\pi$
$374$	−7.35329e8	−0.726827
$375$	0	0
$376$	−5.89339e8	−0.571752
$377$	−2.44400e9	−2.34912
$378$	0	0
$379$	−6.94059e8	−0.654876	−0.327438	−	0.944873i	$-0.606185\pi$
$379$	−6.94059e8	−0.654876	−0.327438	+	0.944873i	$0.606185\pi$
$380$	−1.13107e9	−1.05742
$381$	0	0
$382$	3.95093e9	3.62641
$383$	−4.76633e8	−0.433500	−0.216750	−	0.976227i	$-0.569546\pi$
$383$	−4.76633e8	−0.433500	−0.216750	+	0.976227i	$0.569546\pi$
$384$	0	0
$385$	−3.79564e7	−0.0338979
$386$	−2.81174e9	−2.48840
$387$	0	0
$388$	4.71691e9	4.09964
$389$	−7.93506e8	−0.683482	−0.341741	−	0.939794i	$-0.611016\pi$
$389$	−7.93506e8	−0.683482	−0.341741	+	0.939794i	$0.611016\pi$
$390$	0	0
$391$	−5.13191e8	−0.434171
$392$	4.26896e9	3.57949
$393$	0	0
$394$	−2.83521e9	−2.33533
$395$	−4.11437e8	−0.335903
$396$	0	0
$397$	1.68006e9	1.34759	0.673795	−	0.738918i	$-0.264663\pi$
$397$	1.68006e9	1.34759	0.673795	+	0.738918i	$0.264663\pi$
$398$	2.88326e9	2.29241
$399$	0	0
$400$	−4.38900e9	−3.42891
$401$	7.52355e8	0.582663	0.291331	−	0.956622i	$-0.405902\pi$
$401$	7.52355e8	0.582663	0.291331	+	0.956622i	$0.405902\pi$
$402$	0	0
$403$	−1.60233e9	−1.21951
$404$	−1.12824e8	−0.0851272
$405$	0	0
$406$	4.36674e8	0.323829
$407$	2.53355e8	0.186272
$408$	0	0
$409$	−4.62613e8	−0.334338	−0.167169	−	0.985928i	$-0.553463\pi$
$409$	−4.62613e8	−0.334338	−0.167169	+	0.985928i	$0.553463\pi$
$410$	7.42218e8	0.531848
$411$	0	0
$412$	7.27407e9	5.12433
$413$	−1.31424e8	−0.0918017
$414$	0	0
$415$	8.70504e8	0.597864
$416$	9.83795e9	6.70005
$417$	0	0
$418$	1.91781e9	1.28437
$419$	−1.30611e9	−0.867420	−0.433710	−	0.901053i	$-0.642796\pi$
$419$	−1.30611e9	−0.867420	−0.433710	+	0.901053i	$0.642796\pi$
$420$	0	0
$421$	−2.16516e8	−0.141417	−0.0707087	−	0.997497i	$-0.522526\pi$
$421$	−2.16516e8	−0.141417	−0.0707087	+	0.997497i	$0.522526\pi$
$422$	4.11899e9	2.66807
$423$	0	0
$424$	7.38825e9	4.70718
$425$	6.13413e8	0.387607
$426$	0	0
$427$	−2.90137e8	−0.180346
$428$	−6.45545e8	−0.397991
$429$	0	0
$430$	−2.16138e8	−0.131097
$431$	−2.46067e9	−1.48041	−0.740207	−	0.672379i	$-0.765273\pi$
$431$	−2.46067e9	−1.48041	−0.740207	+	0.672379i	$0.765273\pi$
$432$	0	0
$433$	−1.42408e9	−0.843001	−0.421500	−	0.906828i	$-0.638496\pi$
$433$	−1.42408e9	−0.843001	−0.421500	+	0.906828i	$0.638496\pi$
$434$	2.86291e8	0.168110
$435$	0	0
$436$	2.59215e9	1.49781
$437$	1.33845e9	0.767218
$438$	0	0
$439$	−1.86431e9	−1.05170	−0.525851	−	0.850577i	$-0.676253\pi$
$439$	−1.86431e9	−1.05170	−0.525851	+	0.850577i	$0.676253\pi$
$440$	−2.18839e9	−1.22473
$441$	0	0
$442$	−2.43111e9	−1.33914
$443$	4.59781e8	0.251269	0.125634	−	0.992077i	$-0.459903\pi$
$443$	4.59781e8	0.251269	0.125634	+	0.992077i	$0.459903\pi$
$444$	0	0
$445$	−1.62486e8	−0.0874089
$446$	−3.50278e8	−0.186957
$447$	0	0
$448$	−9.49277e8	−0.498792
$449$	−1.81677e9	−0.947192	−0.473596	−	0.880742i	$-0.657044\pi$
$449$	−1.81677e9	−0.947192	−0.473596	+	0.880742i	$0.657044\pi$
$450$	0	0
$451$	−9.31106e8	−0.477948
$452$	3.44903e9	1.75676
$453$	0	0
$454$	7.49103e8	0.375704
$455$	−1.25489e8	−0.0624550
$456$	0	0
$457$	−1.28773e9	−0.631131	−0.315566	−	0.948904i	$-0.602194\pi$
$457$	−1.28773e9	−0.631131	−0.315566	+	0.948904i	$0.602194\pi$
$458$	−5.76930e9	−2.80604
$459$	0	0
$460$	−2.35548e9	−1.12831
$461$	1.09265e8	0.0519430	0.0259715	−	0.999663i	$-0.491732\pi$
$461$	1.09265e8	0.0519430	0.0259715	+	0.999663i	$0.491732\pi$
$462$	0	0
$463$	−1.73669e9	−0.813185	−0.406592	−	0.913610i	$-0.633283\pi$
$463$	−1.73669e9	−0.813185	−0.406592	+	0.913610i	$0.633283\pi$
$464$	1.50758e10	7.00595
$465$	0	0
$466$	3.21825e9	1.47323
$467$	2.48860e9	1.13070	0.565349	−	0.824852i	$-0.308741\pi$
$467$	2.48860e9	1.13070	0.565349	+	0.824852i	$0.308741\pi$
$468$	0	0
$469$	3.20003e8	0.143235
$470$	3.05974e8	0.135938
$471$	0	0
$472$	−7.57731e9	−3.31679
$473$	2.71144e8	0.117811
$474$	0	0
$475$	−1.59984e9	−0.684935
$476$	3.21375e8	0.136580
$477$	0	0
$478$	−3.44478e9	−1.44266
$479$	−8.40928e8	−0.349611	−0.174805	−	0.984603i	$-0.555930\pi$
$479$	−8.40928e8	−0.349611	−0.174805	+	0.984603i	$0.555930\pi$
$480$	0	0
$481$	8.37628e8	0.343197
$482$	−7.16483e9	−2.91435
$483$	0	0
$484$	−2.86032e9	−1.14671
$485$	−1.58788e9	−0.632008
$486$	0	0
$487$	−1.41392e9	−0.554718	−0.277359	−	0.960766i	$-0.589459\pi$
$487$	−1.41392e9	−0.554718	−0.277359	+	0.960766i	$0.589459\pi$
$488$	−1.67279e10	−6.51588
$489$	0	0
$490$	−2.21637e9	−0.851050
$491$	2.99438e9	1.14162	0.570810	−	0.821082i	$-0.306629\pi$
$491$	2.99438e9	1.14162	0.570810	+	0.821082i	$0.306629\pi$
$492$	0	0
$493$	−2.10701e9	−0.791959
$494$	6.34057e9	2.36638
$495$	0	0
$496$	9.88395e9	3.63701
$497$	−2.97285e7	−0.0108624
$498$	0	0
$499$	−3.88719e9	−1.40050	−0.700251	−	0.713897i	$-0.746929\pi$
$499$	−3.88719e9	−1.40050	−0.700251	+	0.713897i	$0.746929\pi$
$500$	6.30104e9	2.25433
$501$	0	0
$502$	−5.22200e9	−1.84236
$503$	2.25318e9	0.789420	0.394710	−	0.918806i	$-0.370845\pi$
$503$	2.25318e9	0.789420	0.394710	+	0.918806i	$0.370845\pi$
$504$	0	0
$505$	3.79809e7	0.0131234
$506$	3.99388e9	1.37047
$507$	0	0
$508$	1.07063e10	3.62340
$509$	−2.23850e9	−0.752393	−0.376196	−	0.926540i	$-0.622768\pi$
$509$	−2.23850e9	−0.752393	−0.376196	+	0.926540i	$0.622768\pi$
$510$	0	0
$511$	−2.54347e8	−0.0843244
$512$	−1.40717e10	−4.63341
$513$	0	0
$514$	−9.43165e8	−0.306349
$515$	−2.44872e9	−0.789976
$516$	0	0
$517$	−3.83841e8	−0.122162
$518$	−1.49661e8	−0.0473101
$519$	0	0
$520$	−7.23513e9	−2.25650
$521$	−3.53193e7	−0.0109416	−0.00547079	−	0.999985i	$-0.501741\pi$
$521$	−3.53193e7	−0.0109416	−0.00547079	+	0.999985i	$0.501741\pi$
$522$	0	0
$523$	1.93242e9	0.590671	0.295335	−	0.955394i	$-0.404569\pi$
$523$	1.93242e9	0.590671	0.295335	+	0.955394i	$0.404569\pi$
$524$	−1.75024e10	−5.31420
$525$	0	0
$526$	2.31852e9	0.694642
$527$	−1.38139e9	−0.411131
$528$	0	0
$529$	−6.17469e8	−0.181351
$530$	−3.83584e9	−1.11917
$531$	0	0
$532$	−8.38178e8	−0.241349
$533$	−3.07837e9	−0.880595
$534$	0	0
$535$	2.17314e8	0.0613550
$536$	1.84498e10	5.17507
$537$	0	0
$538$	−4.13419e9	−1.14460
$539$	2.78041e9	0.764801
$540$	0	0
$541$	4.16649e9	1.13130	0.565652	−	0.824644i	$-0.308625\pi$
$541$	4.16649e9	1.13130	0.565652	+	0.824644i	$0.308625\pi$
$542$	−7.48079e9	−2.01813
$543$	0	0
$544$	8.48147e9	2.25878
$545$	−8.72612e8	−0.230905
$546$	0	0
$547$	−2.80094e9	−0.731725	−0.365862	−	0.930669i	$-0.619226\pi$
$547$	−2.80094e9	−0.731725	−0.365862	+	0.930669i	$0.619226\pi$
$548$	−2.13968e9	−0.555414
$549$	0	0
$550$	−4.77385e9	−1.22349
$551$	5.49530e9	1.39946
$552$	0	0
$553$	−3.04894e8	−0.0766675
$554$	9.38068e9	2.34396
$555$	0	0
$556$	−1.86580e10	−4.60367
$557$	−4.87182e9	−1.19453	−0.597266	−	0.802043i	$-0.703746\pi$
$557$	−4.87182e9	−1.19453	−0.597266	+	0.802043i	$0.703746\pi$
$558$	0	0
$559$	8.96441e8	0.217060
$560$	7.74081e8	0.186264
$561$	0	0
$562$	7.57716e9	1.80065
$563$	−6.20948e9	−1.46648	−0.733240	−	0.679970i	$-0.761993\pi$
$563$	−6.20948e9	−1.46648	−0.733240	+	0.679970i	$0.761993\pi$
$564$	0	0
$565$	−1.16107e9	−0.270825
$566$	4.29857e9	0.996475
$567$	0	0
$568$	−1.71400e9	−0.392457
$569$	5.71470e9	1.30047	0.650235	−	0.759733i	$-0.274670\pi$
$569$	5.71470e9	1.30047	0.650235	+	0.759733i	$0.274670\pi$
$570$	0	0
$571$	2.96607e9	0.666737	0.333368	−	0.942797i	$-0.391815\pi$
$571$	2.96607e9	0.666737	0.333368	+	0.942797i	$0.391815\pi$
$572$	1.39982e10	3.12741
$573$	0	0
$574$	5.50019e8	0.121391
$575$	−3.33170e9	−0.730851
$576$	0	0
$577$	5.24837e9	1.13739	0.568694	−	0.822549i	$-0.307449\pi$
$577$	5.24837e9	1.13739	0.568694	+	0.822549i	$0.307449\pi$
$578$	7.00631e9	1.50918
$579$	0	0
$580$	−9.67090e9	−2.05811
$581$	6.45085e8	0.136458
$582$	0	0
$583$	4.81203e9	1.00575
$584$	−1.46644e10	−3.04664
$585$	0	0
$586$	1.02912e10	2.11264
$587$	−1.22772e9	−0.250534	−0.125267	−	0.992123i	$-0.539979\pi$
$587$	−1.22772e9	−0.250534	−0.125267	+	0.992123i	$0.539979\pi$
$588$	0	0
$589$	3.60282e9	0.726505
$590$	3.93400e9	0.788591
$591$	0	0
$592$	−5.16690e9	−1.02354
$593$	−6.05113e9	−1.19164	−0.595820	−	0.803118i	$-0.703173\pi$
$593$	−6.05113e9	−1.19164	−0.595820	+	0.803118i	$0.703173\pi$
$594$	0	0
$595$	−1.08187e8	−0.0210554
$596$	2.51623e9	0.486843
$597$	0	0
$598$	1.32044e10	2.52501
$599$	−5.84902e9	−1.11196	−0.555980	−	0.831196i	$-0.687657\pi$
$599$	−5.84902e9	−1.11196	−0.555980	+	0.831196i	$0.687657\pi$
$600$	0	0
$601$	−8.45352e9	−1.58846	−0.794231	−	0.607616i	$-0.792126\pi$
$601$	−8.45352e9	−1.58846	−0.794231	+	0.607616i	$0.792126\pi$
$602$	−1.60169e8	−0.0299220
$603$	0	0
$604$	−2.53865e10	−4.68784
$605$	9.62888e8	0.176779
$606$	0	0
$607$	−9.03739e8	−0.164015	−0.0820074	−	0.996632i	$-0.526133\pi$
$607$	−9.03739e8	−0.164015	−0.0820074	+	0.996632i	$0.526133\pi$
$608$	−2.21205e10	−3.99147
$609$	0	0
$610$	8.68484e9	1.54920
$611$	−1.26904e9	−0.225076
$612$	0	0
$613$	−3.64313e9	−0.638797	−0.319399	−	0.947620i	$-0.603481\pi$
$613$	−3.64313e9	−0.638797	−0.319399	+	0.947620i	$0.603481\pi$
$614$	−2.44757e9	−0.426723
$615$	0	0
$616$	−1.62170e9	−0.279536
$617$	−8.10529e9	−1.38922	−0.694609	−	0.719387i	$-0.744423\pi$
$617$	−8.10529e9	−1.38922	−0.694609	+	0.719387i	$0.744423\pi$
$618$	0	0
$619$	−7.22020e9	−1.22358	−0.611789	−	0.791021i	$-0.709550\pi$
$619$	−7.22020e9	−1.22358	−0.611789	+	0.791021i	$0.709550\pi$
$620$	−6.34042e9	−1.06843
$621$	0	0
$622$	−3.67712e9	−0.612691
$623$	−1.20410e8	−0.0199505
$624$	0	0
$625$	2.80898e9	0.460224
$626$	2.28427e10	3.72166
$627$	0	0
$628$	−2.22145e10	−3.57914
$629$	7.22134e8	0.115702
$630$	0	0
$631$	4.23517e8	0.0671070	0.0335535	−	0.999437i	$-0.489318\pi$
$631$	4.23517e8	0.0671070	0.0335535	+	0.999437i	$0.489318\pi$
$632$	−1.75788e10	−2.76999
$633$	0	0
$634$	1.41984e10	2.21272
$635$	−3.60413e9	−0.558590
$636$	0	0
$637$	9.19245e9	1.40911
$638$	1.63977e10	2.49983
$639$	0	0
$640$	1.47278e10	2.22080
$641$	−3.03264e9	−0.454797	−0.227398	−	0.973802i	$-0.573022\pi$
$641$	−3.03264e9	−0.454797	−0.227398	+	0.973802i	$0.573022\pi$
$642$	0	0
$643$	−2.78734e9	−0.413478	−0.206739	−	0.978396i	$-0.566285\pi$
$643$	−2.78734e9	−0.413478	−0.206739	+	0.978396i	$0.566285\pi$
$644$	−1.74552e9	−0.257528
$645$	0	0
$646$	5.46631e9	0.797776
$647$	1.73353e9	0.251632	0.125816	−	0.992054i	$-0.459845\pi$
$647$	1.73353e9	0.251632	0.125816	+	0.992054i	$0.459845\pi$
$648$	0	0
$649$	−4.93516e9	−0.708672
$650$	−1.57830e10	−2.25421
$651$	0	0
$652$	−4.69568e8	−0.0663486
$653$	9.51546e9	1.33731	0.668657	−	0.743571i	$-0.266869\pi$
$653$	9.51546e9	1.33731	0.668657	+	0.743571i	$0.266869\pi$
$654$	0	0
$655$	5.89195e9	0.819247
$656$	1.89889e10	2.62626
$657$	0	0
$658$	2.26741e8	0.0310270
$659$	−7.55803e9	−1.02875	−0.514375	−	0.857565i	$-0.671976\pi$
$659$	−7.55803e9	−1.02875	−0.514375	+	0.857565i	$0.671976\pi$
$660$	0	0
$661$	−1.39999e9	−0.188547	−0.0942733	−	0.995546i	$-0.530053\pi$
$661$	−1.39999e9	−0.188547	−0.0942733	+	0.995546i	$0.530053\pi$
$662$	9.53475e9	1.27734
$663$	0	0
$664$	3.71926e10	4.93024
$665$	2.82162e8	0.0372068
$666$	0	0
$667$	1.14441e10	1.49328
$668$	3.00671e10	3.90278
$669$	0	0
$670$	−9.57881e9	−1.23041
$671$	−1.08950e10	−1.39220
$672$	0	0
$673$	−5.04985e8	−0.0638595	−0.0319298	−	0.999490i	$-0.510165\pi$
$673$	−5.04985e8	−0.0638595	−0.0319298	+	0.999490i	$0.510165\pi$
$674$	8.38806e9	1.05524
$675$	0	0
$676$	2.34365e10	2.91796
$677$	8.77580e9	1.08699	0.543496	−	0.839412i	$-0.317100\pi$
$677$	8.77580e9	1.08699	0.543496	+	0.839412i	$0.317100\pi$
$678$	0	0
$679$	−1.17670e9	−0.144252
$680$	−6.23753e9	−0.760732
$681$	0	0
$682$	1.07506e10	1.29774
$683$	−5.66666e9	−0.680541	−0.340271	−	0.940328i	$-0.610519\pi$
$683$	−5.66666e9	−0.680541	−0.340271	+	0.940328i	$0.610519\pi$
$684$	0	0
$685$	7.20295e8	0.0856236
$686$	−3.30148e9	−0.390458
$687$	0	0
$688$	−5.52969e9	−0.647353
$689$	1.59093e10	1.85303
$690$	0	0
$691$	−7.72356e9	−0.890522	−0.445261	−	0.895401i	$-0.646889\pi$
$691$	−7.72356e9	−0.890522	−0.445261	+	0.895401i	$0.646889\pi$
$692$	2.20753e9	0.253242
$693$	0	0
$694$	−7.06555e9	−0.802394
$695$	6.28098e9	0.709709
$696$	0	0
$697$	−2.65392e9	−0.296874
$698$	−2.21566e10	−2.46609
$699$	0	0
$700$	2.08641e9	0.229909
$701$	9.02472e9	0.989511	0.494755	−	0.869032i	$-0.335258\pi$
$701$	9.02472e9	0.989511	0.494755	+	0.869032i	$0.335258\pi$
$702$	0	0
$703$	−1.88340e9	−0.204455
$704$	−3.56466e10	−3.85047
$705$	0	0
$706$	2.71277e9	0.290133
$707$	2.81456e7	0.00299532
$708$	0	0
$709$	1.01828e10	1.07301	0.536505	−	0.843897i	$-0.319744\pi$
$709$	1.01828e10	1.07301	0.536505	+	0.843897i	$0.319744\pi$
$710$	8.89878e8	0.0933096
$711$	0	0
$712$	−6.94226e9	−0.720810
$713$	7.50294e9	0.775207
$714$	0	0
$715$	−4.71230e9	−0.482127
$716$	1.84450e10	1.87794
$717$	0	0
$718$	−2.30720e10	−2.32621
$719$	3.88344e9	0.389642	0.194821	−	0.980839i	$-0.437587\pi$
$719$	3.88344e9	0.389642	0.194821	+	0.980839i	$0.437587\pi$
$720$	0	0
$721$	−1.81462e9	−0.180307
$722$	5.57133e9	0.550907
$723$	0	0
$724$	−7.60823e8	−0.0745073
$725$	−1.36790e10	−1.33313
$726$	0	0
$727$	3.21178e9	0.310009	0.155005	−	0.987914i	$-0.450461\pi$
$727$	3.21178e9	0.310009	0.155005	+	0.987914i	$0.450461\pi$
$728$	−5.36158e9	−0.515030
$729$	0	0
$730$	7.61351e9	0.724360
$731$	7.72837e8	0.0731775
$732$	0	0
$733$	2.53300e9	0.237559	0.118779	−	0.992921i	$-0.462102\pi$
$733$	2.53300e9	0.237559	0.118779	+	0.992921i	$0.462102\pi$
$734$	−6.83540e9	−0.638010
$735$	0	0
$736$	−4.60664e10	−4.25904
$737$	1.20165e10	1.10571
$738$	0	0
$739$	8.64031e9	0.787542	0.393771	−	0.919209i	$-0.371170\pi$
$739$	8.64031e9	0.787542	0.393771	+	0.919209i	$0.371170\pi$
$740$	3.31450e9	0.300681
$741$	0	0
$742$	−2.84254e9	−0.255443
$743$	7.96383e9	0.712297	0.356148	−	0.934429i	$-0.384090\pi$
$743$	7.96383e9	0.712297	0.356148	+	0.934429i	$0.384090\pi$
$744$	0	0
$745$	−8.47057e8	−0.0750526
$746$	3.38811e10	2.98794
$747$	0	0
$748$	1.20681e10	1.05434
$749$	1.61040e8	0.0140039
$750$	0	0
$751$	3.65497e9	0.314879	0.157439	−	0.987529i	$-0.449676\pi$
$751$	3.65497e9	0.314879	0.157439	+	0.987529i	$0.449676\pi$
$752$	7.82804e9	0.671260
$753$	0	0
$754$	5.42132e10	4.60580
$755$	8.54602e9	0.722686
$756$	0	0
$757$	1.20006e9	0.100546	0.0502732	−	0.998736i	$-0.483991\pi$
$757$	1.20006e9	0.100546	0.0502732	+	0.998736i	$0.483991\pi$
$758$	1.53958e10	1.28398
$759$	0	0
$760$	1.62681e10	1.34428
$761$	−2.32910e9	−0.191576	−0.0957880	−	0.995402i	$-0.530537\pi$
$761$	−2.32910e9	−0.191576	−0.0957880	+	0.995402i	$0.530537\pi$
$762$	0	0
$763$	−6.46647e8	−0.0527025
$764$	−6.48418e10	−5.26052
$765$	0	0
$766$	1.05728e10	0.849940
$767$	−1.63164e10	−1.30569
$768$	0	0
$769$	−4.56990e9	−0.362381	−0.181190	−	0.983448i	$-0.557995\pi$
$769$	−4.56990e9	−0.362381	−0.181190	+	0.983448i	$0.557995\pi$
$770$	8.41956e8	0.0664618
$771$	0	0
$772$	4.61458e10	3.60970
$773$	−1.34361e10	−1.04627	−0.523135	−	0.852250i	$-0.675238\pi$
$773$	−1.34361e10	−1.04627	−0.523135	+	0.852250i	$0.675238\pi$
$774$	0	0
$775$	−8.96819e9	−0.692068
$776$	−6.78429e10	−5.21181
$777$	0	0
$778$	1.76017e10	1.34007
$779$	6.92169e9	0.524603
$780$	0	0
$781$	−1.11634e9	−0.0838532
$782$	1.13837e10	0.851255
$783$	0	0
$784$	−5.67036e10	−4.20247
$785$	7.47823e9	0.551766
$786$	0	0
$787$	2.05668e10	1.50403	0.752014	−	0.659147i	$-0.229082\pi$
$787$	2.05668e10	1.50403	0.752014	+	0.659147i	$0.229082\pi$
$788$	4.65308e10	3.38765
$789$	0	0
$790$	9.12657e9	0.658586
$791$	−8.60408e8	−0.0618140
$792$	0	0
$793$	−3.60207e10	−2.56505
$794$	−3.72674e10	−2.64215
$795$	0	0
$796$	−4.73194e10	−3.32540
$797$	−1.49135e10	−1.04346	−0.521729	−	0.853111i	$-0.674713\pi$
$797$	−1.49135e10	−1.04346	−0.521729	+	0.853111i	$0.674713\pi$
$798$	0	0
$799$	−1.09406e9	−0.0758799
$800$	5.50628e10	3.80227
$801$	0	0
$802$	−1.66889e10	−1.14240
$803$	−9.55107e9	−0.650950
$804$	0	0
$805$	5.87607e8	0.0397010
$806$	3.55432e10	2.39102
$807$	0	0
$808$	1.62275e9	0.108221
$809$	2.29446e10	1.52356	0.761781	−	0.647835i	$-0.224325\pi$
$809$	2.29446e10	1.52356	0.761781	+	0.647835i	$0.224325\pi$
$810$	0	0
$811$	4.15707e9	0.273662	0.136831	−	0.990594i	$-0.456308\pi$
$811$	4.15707e9	0.273662	0.136831	+	0.990594i	$0.456308\pi$
$812$	−7.16660e9	−0.469750
$813$	0	0
$814$	−5.61996e9	−0.365215
$815$	1.58074e8	0.0102284
$816$	0	0
$817$	−2.01564e9	−0.129311
$818$	1.02618e10	0.655520
$819$	0	0
$820$	−1.21811e10	−0.771506
$821$	−1.06838e10	−0.673790	−0.336895	−	0.941542i	$-0.609377\pi$
$821$	−1.06838e10	−0.673790	−0.336895	+	0.941542i	$0.609377\pi$
$822$	0	0
$823$	−1.14304e10	−0.714766	−0.357383	−	0.933958i	$-0.616331\pi$
$823$	−1.14304e10	−0.714766	−0.357383	+	0.933958i	$0.616331\pi$
$824$	−1.04622e11	−6.51447
$825$	0	0
$826$	2.91528e9	0.179991
$827$	1.17022e10	0.719448	0.359724	−	0.933059i	$-0.382871\pi$
$827$	1.17022e10	0.719448	0.359724	+	0.933059i	$0.382871\pi$
$828$	0	0
$829$	−1.53161e10	−0.933699	−0.466850	−	0.884337i	$-0.654611\pi$
$829$	−1.53161e10	−0.933699	−0.466850	+	0.884337i	$0.654611\pi$
$830$	−1.93097e10	−1.17220
$831$	0	0
$832$	−1.17853e11	−7.09430
$833$	7.92497e9	0.475051
$834$	0	0
$835$	−1.01217e10	−0.601659
$836$	−3.14747e10	−1.86312
$837$	0	0
$838$	2.89723e10	1.70070
$839$	−1.05214e10	−0.615043	−0.307521	−	0.951541i	$-0.599500\pi$
$839$	−1.05214e10	−0.615043	−0.307521	+	0.951541i	$0.599500\pi$
$840$	0	0
$841$	2.97361e10	1.72385
$842$	4.80280e9	0.277270
$843$	0	0
$844$	−6.76001e10	−3.87034
$845$	−7.88958e9	−0.449837
$846$	0	0
$847$	7.13546e8	0.0403487
$848$	−9.81363e10	−5.52642
$849$	0	0
$850$	−1.36068e10	−0.759960
$851$	−3.92221e9	−0.218161
$852$	0	0
$853$	−2.95826e10	−1.63198	−0.815989	−	0.578068i	$-0.803807\pi$
$853$	−2.95826e10	−1.63198	−0.815989	+	0.578068i	$0.803807\pi$
$854$	6.43588e9	0.353594
$855$	0	0
$856$	9.28482e9	0.505959
$857$	−6.19614e9	−0.336270	−0.168135	−	0.985764i	$-0.553775\pi$
$857$	−6.19614e9	−0.336270	−0.168135	+	0.985764i	$0.553775\pi$
$858$	0	0
$859$	2.78077e10	1.49689	0.748443	−	0.663199i	$-0.230802\pi$
$859$	2.78077e10	1.49689	0.748443	+	0.663199i	$0.230802\pi$
$860$	3.54722e9	0.190171
$861$	0	0
$862$	5.45831e10	2.90257
$863$	−3.15999e10	−1.67359	−0.836793	−	0.547519i	$-0.815572\pi$
$863$	−3.15999e10	−1.67359	−0.836793	+	0.547519i	$0.815572\pi$
$864$	0	0
$865$	−7.43137e8	−0.0390402
$866$	3.15893e10	1.65283
$867$	0	0
$868$	−4.69855e9	−0.243863
$869$	−1.14492e10	−0.591842
$870$	0	0
$871$	3.97284e10	2.03722
$872$	−3.72826e10	−1.90414
$873$	0	0
$874$	−2.96899e10	−1.50424
$875$	−1.57188e9	−0.0793217
$876$	0	0
$877$	2.48099e10	1.24201	0.621006	−	0.783806i	$-0.286724\pi$
$877$	2.48099e10	1.24201	0.621006	+	0.783806i	$0.286724\pi$
$878$	4.13545e10	2.06201
$879$	0	0
$880$	2.90678e10	1.43788
$881$	−2.37579e9	−0.117056	−0.0585279	−	0.998286i	$-0.518641\pi$
$881$	−2.37579e9	−0.117056	−0.0585279	+	0.998286i	$0.518641\pi$
$882$	0	0
$883$	−1.16100e10	−0.567505	−0.283752	−	0.958898i	$-0.591579\pi$
$883$	−1.16100e10	−0.567505	−0.283752	+	0.958898i	$0.591579\pi$
$884$	3.98988e10	1.94257
$885$	0	0
$886$	−1.01990e10	−0.492649
$887$	−1.53556e10	−0.738813	−0.369407	−	0.929268i	$-0.620439\pi$
$887$	−1.53556e10	−0.738813	−0.369407	+	0.929268i	$0.620439\pi$
$888$	0	0
$889$	−2.67084e9	−0.127494
$890$	3.60429e9	0.171378
$891$	0	0
$892$	5.74869e9	0.271201
$893$	2.85342e9	0.134086
$894$	0	0
$895$	−6.20926e9	−0.289507
$896$	1.09140e10	0.506883
$897$	0	0
$898$	4.03000e10	1.85711
$899$	3.08049e10	1.41404
$900$	0	0
$901$	1.37157e10	0.624712
$902$	2.06540e10	0.937088
$903$	0	0
$904$	−4.96071e10	−2.23334
$905$	2.56121e8	0.0114862
$906$	0	0
$907$	3.31807e9	0.147659	0.0738295	−	0.997271i	$-0.476478\pi$
$907$	3.31807e9	0.147659	0.0738295	+	0.997271i	$0.476478\pi$
$908$	−1.22941e10	−0.545001
$909$	0	0
$910$	2.78363e9	0.122452
$911$	3.21961e9	0.141087	0.0705437	−	0.997509i	$-0.477527\pi$
$911$	3.21961e9	0.141087	0.0705437	+	0.997509i	$0.477527\pi$
$912$	0	0
$913$	2.42238e10	1.05340
$914$	2.85648e10	1.23743
$915$	0	0
$916$	9.46846e10	4.07047
$917$	4.36622e9	0.186988
$918$	0	0
$919$	7.57125e9	0.321783	0.160892	−	0.986972i	$-0.448563\pi$
$919$	7.57125e9	0.321783	0.160892	+	0.986972i	$0.448563\pi$
$920$	3.38787e10	1.43439
$921$	0	0
$922$	−2.42373e9	−0.101842
$923$	−3.69080e9	−0.154495
$924$	0	0
$925$	4.68818e9	0.194764
$926$	3.85236e10	1.59437
$927$	0	0
$928$	−1.89135e11	−7.76881
$929$	2.89017e10	1.18268	0.591342	−	0.806421i	$-0.298598\pi$
$929$	2.89017e10	1.18268	0.591342	+	0.806421i	$0.298598\pi$
$930$	0	0
$931$	−2.06691e10	−0.839457
$932$	−5.28173e10	−2.13708
$933$	0	0
$934$	−5.52027e10	−2.21690
$935$	−4.06255e9	−0.162539
$936$	0	0
$937$	3.91577e10	1.55499	0.777496	−	0.628888i	$-0.216489\pi$
$937$	3.91577e10	1.55499	0.777496	+	0.628888i	$0.216489\pi$
$938$	−7.09836e9	−0.280833
$939$	0	0
$940$	−5.02158e9	−0.197194
$941$	2.41576e10	0.945127	0.472564	−	0.881297i	$-0.343329\pi$
$941$	2.41576e10	0.945127	0.472564	+	0.881297i	$0.343329\pi$
$942$	0	0
$943$	1.44145e10	0.559771
$944$	1.00647e11	3.89404
$945$	0	0
$946$	−6.01456e9	−0.230986
$947$	−3.20511e10	−1.22636	−0.613179	−	0.789944i	$-0.710110\pi$
$947$	−3.20511e10	−1.22636	−0.613179	+	0.789944i	$0.710110\pi$
$948$	0	0
$949$	−3.15773e10	−1.19934
$950$	3.54880e10	1.34292
$951$	0	0
$952$	−4.62231e9	−0.173632
$953$	−4.93663e9	−0.184759	−0.0923794	−	0.995724i	$-0.529447\pi$
$953$	−4.93663e9	−0.184759	−0.0923794	+	0.995724i	$0.529447\pi$
$954$	0	0
$955$	2.18281e10	0.810970
$956$	5.65350e10	2.09274
$957$	0	0
$958$	1.86536e10	0.685463
$959$	5.33773e8	0.0195430
$960$	0	0
$961$	−7.31640e9	−0.265929
$962$	−1.85804e10	−0.672888
$963$	0	0
$964$	1.17588e11	4.22759
$965$	−1.55344e10	−0.556478
$966$	0	0
$967$	3.10919e10	1.10574	0.552872	−	0.833266i	$-0.313532\pi$
$967$	3.10919e10	1.10574	0.552872	+	0.833266i	$0.313532\pi$
$968$	4.11397e10	1.45780
$969$	0	0
$970$	3.52228e10	1.23915
$971$	−3.37297e10	−1.18235	−0.591174	−	0.806544i	$-0.701335\pi$
$971$	−3.37297e10	−1.18235	−0.591174	+	0.806544i	$0.701335\pi$
$972$	0	0
$973$	4.65451e9	0.161986
$974$	3.13637e10	1.08761
$975$	0	0
$976$	2.22193e11	7.64991
$977$	2.60034e10	0.892072	0.446036	−	0.895015i	$-0.352835\pi$
$977$	2.60034e10	0.892072	0.446036	+	0.895015i	$0.352835\pi$
$978$	0	0
$979$	−4.52155e9	−0.154010
$980$	3.63746e10	1.23454
$981$	0	0
$982$	−6.64219e10	−2.23831
$983$	4.35623e9	0.146276	0.0731381	−	0.997322i	$-0.476699\pi$
$983$	4.35623e9	0.146276	0.0731381	+	0.997322i	$0.476699\pi$
$984$	0	0
$985$	−1.56640e10	−0.522247
$986$	4.67381e10	1.55275
$987$	0	0
$988$	−1.04060e11	−3.43269
$989$	−4.19761e9	−0.137980
$990$	0	0
$991$	−3.99586e10	−1.30423	−0.652113	−	0.758122i	$-0.726117\pi$
$991$	−3.99586e10	−1.30423	−0.652113	+	0.758122i	$0.726117\pi$
$992$	−1.24000e11	−4.03304
$993$	0	0
$994$	6.59442e8	0.0212973
$995$	1.59295e10	0.512649
$996$	0	0
$997$	1.79270e10	0.572894	0.286447	−	0.958096i	$-0.407526\pi$
$997$	1.79270e10	0.572894	0.286447	+	0.958096i	$0.407526\pi$
$998$	8.62264e10	2.74589
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.d.1.1		13
3.2	odd	2		43.8.a.b.1.13	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.13	✓	13	3.2	odd	2
387.8.a.d.1.1		13	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-22.1822 q^{2} +364.050 q^{4} -122.553 q^{5} -90.8173 q^{7} -5236.10 q^{8} +O(q^{10})\)	\(q-22.1822 q^{2} +364.050 q^{4} -122.553 q^{5} -90.8173 q^{7} -5236.10 q^{8} +2718.48 q^{10} -3410.31 q^{11} -11275.0 q^{13} +2014.53 q^{14} +69549.8 q^{16} -9720.37 q^{17} +25351.7 q^{19} -44615.2 q^{20} +75648.2 q^{22} +52795.4 q^{23} -63105.9 q^{25} +250104. q^{26} -33062.0 q^{28} +216763. q^{29} +142113. q^{31} -872545. q^{32} +215619. q^{34} +11129.9 q^{35} -74290.8 q^{37} -562357. q^{38} +641697. q^{40} +273026. q^{41} -79507.0 q^{43} -1.24152e6 q^{44} -1.17112e6 q^{46} +112553. q^{47} -815295. q^{49} +1.39983e6 q^{50} -4.10466e6 q^{52} -1.41102e6 q^{53} +417942. q^{55} +475528. q^{56} -4.80827e6 q^{58} +1.44713e6 q^{59} +3.19474e6 q^{61} -3.15239e6 q^{62} +1.04526e7 q^{64} +1.38178e6 q^{65} -3.52359e6 q^{67} -3.53870e6 q^{68} -246885. q^{70} +327344. q^{71} +2.80064e6 q^{73} +1.64793e6 q^{74} +9.22928e6 q^{76} +309715. q^{77} +3.35723e6 q^{79} -8.52350e6 q^{80} -6.05633e6 q^{82} -7.10311e6 q^{83} +1.19126e6 q^{85} +1.76364e6 q^{86} +1.78567e7 q^{88} +1.32585e6 q^{89} +1.02396e6 q^{91} +1.92201e7 q^{92} -2.49668e6 q^{94} -3.10692e6 q^{95} +1.29568e7 q^{97} +1.80850e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8}+O(q^{10}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8} + 4667 q^{10} - 1620 q^{11} + 13550 q^{13} - 44160 q^{14} + 114026 q^{16} - 110880 q^{17} + 105058 q^{19} - 167251 q^{20} + 201504 q^{22} - 160184 q^{23} + 270149 q^{25} - 272104 q^{26} + 208172 q^{28} - 285546 q^{29} - 99616 q^{31} - 200126 q^{32} - 80941 q^{34} + 187104 q^{35} + 176038 q^{37} - 652165 q^{38} - 895387 q^{40} + 410260 q^{41} - 1033591 q^{43} + 2177076 q^{44} - 3975765 q^{46} + 424556 q^{47} - 1561359 q^{49} + 4063801 q^{50} - 4172312 q^{52} - 3992458 q^{53} + 406960 q^{55} - 1559556 q^{56} - 4052005 q^{58} - 2248836 q^{59} + 6210394 q^{61} - 885317 q^{62} - 3096318 q^{64} - 5600420 q^{65} - 1993648 q^{67} - 9327135 q^{68} - 1105098 q^{70} - 4978064 q^{71} + 8224814 q^{73} + 3613563 q^{74} + 10687121 q^{76} - 17261892 q^{77} + 6945708 q^{79} - 15822799 q^{80} - 508449 q^{82} - 22937328 q^{83} - 575532 q^{85} + 1272112 q^{86} + 11202656 q^{88} - 9291302 q^{89} + 25581108 q^{91} + 14388137 q^{92} - 24645805 q^{94} - 30750464 q^{95} + 10001852 q^{97} + 32304856 q^{98}+O(q^{100}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8 + 4667 * q^10 - 1620 * q^11 + 13550 * q^13 - 44160 * q^14 + 114026 * q^16 - 110880 * q^17 + 105058 * q^19 - 167251 * q^20 + 201504 * q^22 - 160184 * q^23 + 270149 * q^25 - 272104 * q^26 + 208172 * q^28 - 285546 * q^29 - 99616 * q^31 - 200126 * q^32 - 80941 * q^34 + 187104 * q^35 + 176038 * q^37 - 652165 * q^38 - 895387 * q^40 + 410260 * q^41 - 1033591 * q^43 + 2177076 * q^44 - 3975765 * q^46 + 424556 * q^47 - 1561359 * q^49 + 4063801 * q^50 - 4172312 * q^52 - 3992458 * q^53 + 406960 * q^55 - 1559556 * q^56 - 4052005 * q^58 - 2248836 * q^59 + 6210394 * q^61 - 885317 * q^62 - 3096318 * q^64 - 5600420 * q^65 - 1993648 * q^67 - 9327135 * q^68 - 1105098 * q^70 - 4978064 * q^71 + 8224814 * q^73 + 3613563 * q^74 + 10687121 * q^76 - 17261892 * q^77 + 6945708 * q^79 - 15822799 * q^80 - 508449 * q^82 - 22937328 * q^83 - 575532 * q^85 + 1272112 * q^86 + 11202656 * q^88 - 9291302 * q^89 + 25581108 * q^91 + 14388137 * q^92 - 24645805 * q^94 - 30750464 * q^95 + 10001852 * q^97 + 32304856 * q^98

Introduction

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