LMFDB - Embedded newform 531.8.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, 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("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.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:	$165.876448532$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 $ x^17 - 2x^16 - 1669x^15 + 2385x^14 + 1108684x^13 - 848131x^12 - 377920980x^11 + 12724944x^10 + 71331230512x^9 + 50741131904x^8 - 7480805165760x^7 - 10751966150272x^6 + 413177144536320x^5 + 886760582981376x^4 - 10454479722123264x^3 - 29180140031461376x^2 + 79787300207378432x + 248723246810300416
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$11.5967$ of defining polynomial
Character	$\chi$	$=$	531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.5967 q^{2} +6.48306 q^{4} +401.104 q^{5} +213.573 q^{7} +1409.19 q^{8} +O(q^{10})$	\(q-11.5967 q^{2} +6.48306 q^{4} +401.104 q^{5} +213.573 q^{7} +1409.19 q^{8} -4651.48 q^{10} +4974.14 q^{11} -12649.9 q^{13} -2476.74 q^{14} -17171.8 q^{16} -36937.0 q^{17} -31065.7 q^{19} +2600.38 q^{20} -57683.5 q^{22} -52594.0 q^{23} +82759.6 q^{25} +146697. q^{26} +1384.61 q^{28} +209912. q^{29} -11865.2 q^{31} +18759.2 q^{32} +428347. q^{34} +85665.0 q^{35} +16919.7 q^{37} +360259. q^{38} +565233. q^{40} -801040. q^{41} +720238. q^{43} +32247.7 q^{44} +609916. q^{46} +54403.0 q^{47} -777930. q^{49} -959737. q^{50} -82010.4 q^{52} +295498. q^{53} +1.99515e6 q^{55} +300965. q^{56} -2.43428e6 q^{58} +205379. q^{59} +1.37027e6 q^{61} +137597. q^{62} +1.98045e6 q^{64} -5.07395e6 q^{65} +3.05207e6 q^{67} -239465. q^{68} -993430. q^{70} +4.70310e6 q^{71} -3.65576e6 q^{73} -196212. q^{74} -201401. q^{76} +1.06234e6 q^{77} +6.37313e6 q^{79} -6.88768e6 q^{80} +9.28941e6 q^{82} +2.08701e6 q^{83} -1.48156e7 q^{85} -8.35238e6 q^{86} +7.00953e6 q^{88} -1.43644e6 q^{89} -2.70169e6 q^{91} -340970. q^{92} -630894. q^{94} -1.24606e7 q^{95} -6.42693e6 q^{97} +9.02140e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) $ 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * 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 $

$2$	−11.5967	−1.02501	−0.512506	−	0.858684i	$-0.671283\pi$
$2$	−11.5967	−1.02501	−0.512506	+	0.858684i	$0.671283\pi$
$3$	0	0
$3$	0	0
$4$	6.48306	0.0506489
$5$	401.104	1.43503	0.717517	−	0.696541i	$-0.245279\pi$
$5$	401.104	1.43503	0.717517	+	0.696541i	$0.245279\pi$
$6$	0	0
$7$	213.573	0.235344	0.117672	−	0.993053i	$-0.462457\pi$
$7$	213.573	0.235344	0.117672	+	0.993053i	$0.462457\pi$
$8$	1409.19	0.973096
$9$	0	0
$10$	−4651.48	−1.47093
$11$	4974.14	1.12679	0.563396	−	0.826187i	$-0.309495\pi$
$11$	4974.14	1.12679	0.563396	+	0.826187i	$0.309495\pi$
$12$	0	0
$13$	−12649.9	−1.59693	−0.798467	−	0.602038i	$-0.794355\pi$
$13$	−12649.9	−1.59693	−0.798467	+	0.602038i	$0.794355\pi$
$14$	−2476.74	−0.241230
$15$	0	0
$16$	−17171.8	−1.04808
$17$	−36937.0	−1.82344	−0.911718	−	0.410816i	$-0.865244\pi$
$17$	−36937.0	−1.82344	−0.911718	+	0.410816i	$0.865244\pi$
$18$	0	0
$19$	−31065.7	−1.03907	−0.519533	−	0.854451i	$-0.673894\pi$
$19$	−31065.7	−1.03907	−0.519533	+	0.854451i	$0.673894\pi$
$20$	2600.38	0.0726829
$21$	0	0
$22$	−57683.5	−1.15497
$23$	−52594.0	−0.901341	−0.450670	−	0.892690i	$-0.648815\pi$
$23$	−52594.0	−0.901341	−0.450670	+	0.892690i	$0.648815\pi$
$24$	0	0
$25$	82759.6	1.05932
$26$	146697.	1.63688
$27$	0	0
$28$	1384.61	0.0119199
$29$	209912.	1.59825	0.799123	−	0.601167i	$-0.205298\pi$
$29$	209912.	1.59825	0.799123	+	0.601167i	$0.205298\pi$
$30$	0	0
$31$	−11865.2	−0.0715333	−0.0357667	−	0.999360i	$-0.511387\pi$
$31$	−11865.2	−0.0715333	−0.0357667	+	0.999360i	$0.511387\pi$
$32$	18759.2	0.101202
$33$	0	0
$34$	428347.	1.86904
$35$	85665.0	0.337727
$36$	0	0
$37$	16919.7	0.0549143	0.0274572	−	0.999623i	$-0.491259\pi$
$37$	16919.7	0.0549143	0.0274572	+	0.999623i	$0.491259\pi$
$38$	360259.	1.06505
$39$	0	0
$40$	565233.	1.39643
$41$	−801040.	−1.81514	−0.907571	−	0.419898i	$-0.862066\pi$
$41$	−801040.	−1.81514	−0.907571	+	0.419898i	$0.862066\pi$
$42$	0	0
$43$	720238.	1.38145	0.690727	−	0.723115i	$-0.257290\pi$
$43$	720238.	1.38145	0.690727	+	0.723115i	$0.257290\pi$
$44$	32247.7	0.0570708
$45$	0	0
$46$	609916.	0.923885
$47$	54403.0	0.0764329	0.0382164	−	0.999269i	$-0.487832\pi$
$47$	54403.0	0.0764329	0.0382164	+	0.999269i	$0.487832\pi$
$48$	0	0
$49$	−777930.	−0.944613
$50$	−959737.	−1.08582
$51$	0	0
$52$	−82010.4	−0.0808830
$53$	295498.	0.272639	0.136320	−	0.990665i	$-0.456473\pi$
$53$	295498.	0.272639	0.136320	+	0.990665i	$0.456473\pi$
$54$	0	0
$55$	1.99515e6	1.61698
$56$	300965.	0.229012
$57$	0	0
$58$	−2.43428e6	−1.63822
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	1.37027e6	0.772952	0.386476	−	0.922300i	$-0.373692\pi$
$61$	1.37027e6	0.772952	0.386476	+	0.922300i	$0.373692\pi$
$62$	137597.	0.0733225
$63$	0	0
$64$	1.98045e6	0.944350
$65$	−5.07395e6	−2.29166
$66$	0	0
$67$	3.05207e6	1.23975	0.619873	−	0.784702i	$-0.287184\pi$
$67$	3.05207e6	1.23975	0.619873	+	0.784702i	$0.287184\pi$
$68$	−239465.	−0.0923551
$69$	0	0
$70$	−993430.	−0.346174
$71$	4.70310e6	1.55948	0.779740	−	0.626104i	$-0.215351\pi$
$71$	4.70310e6	1.55948	0.779740	+	0.626104i	$0.215351\pi$
$72$	0	0
$73$	−3.65576e6	−1.09989	−0.549943	−	0.835202i	$-0.685351\pi$
$73$	−3.65576e6	−1.09989	−0.549943	+	0.835202i	$0.685351\pi$
$74$	−196212.	−0.0562878
$75$	0	0
$76$	−201401.	−0.0526275
$77$	1.06234e6	0.265184
$78$	0	0
$79$	6.37313e6	1.45431	0.727157	−	0.686471i	$-0.240841\pi$
$79$	6.37313e6	1.45431	0.727157	+	0.686471i	$0.240841\pi$
$80$	−6.88768e6	−1.50404
$81$	0	0
$82$	9.28941e6	1.86054
$83$	2.08701e6	0.400636	0.200318	−	0.979731i	$-0.435802\pi$
$83$	2.08701e6	0.400636	0.200318	+	0.979731i	$0.435802\pi$
$84$	0	0
$85$	−1.48156e7	−2.61669
$86$	−8.35238e6	−1.41601
$87$	0	0
$88$	7.00953e6	1.09648
$89$	−1.43644e6	−0.215984	−0.107992	−	0.994152i	$-0.534442\pi$
$89$	−1.43644e6	−0.215984	−0.107992	+	0.994152i	$0.534442\pi$
$90$	0	0
$91$	−2.70169e6	−0.375829
$92$	−340970.	−0.0456519
$93$	0	0
$94$	−630894.	−0.0783446
$95$	−1.24606e7	−1.49109
$96$	0	0
$97$	−6.42693e6	−0.714994	−0.357497	−	0.933914i	$-0.616370\pi$
$97$	−6.42693e6	−0.714994	−0.357497	+	0.933914i	$0.616370\pi$
$98$	9.02140e6	0.968240
$99$	0	0
$100$	536536.	0.0536536
$101$	−1.06724e6	−0.103071	−0.0515356	−	0.998671i	$-0.516412\pi$
$101$	−1.06724e6	−0.103071	−0.0515356	+	0.998671i	$0.516412\pi$
$102$	0	0
$103$	−9.80605e6	−0.884227	−0.442113	−	0.896959i	$-0.645771\pi$
$103$	−9.80605e6	−0.884227	−0.442113	+	0.896959i	$0.645771\pi$
$104$	−1.78262e7	−1.55397
$105$	0	0
$106$	−3.42679e6	−0.279459
$107$	1.96135e7	1.54779	0.773895	−	0.633314i	$-0.218306\pi$
$107$	1.96135e7	1.54779	0.773895	+	0.633314i	$0.218306\pi$
$108$	0	0
$109$	2.55432e7	1.88922	0.944610	−	0.328194i	$-0.106440\pi$
$109$	2.55432e7	1.88922	0.944610	+	0.328194i	$0.106440\pi$
$110$	−2.31371e7	−1.65743
$111$	0	0
$112$	−3.66743e6	−0.246660
$113$	1.24785e7	0.813559	0.406780	−	0.913526i	$-0.366652\pi$
$113$	1.24785e7	0.813559	0.406780	+	0.913526i	$0.366652\pi$
$114$	0	0
$115$	−2.10957e7	−1.29345
$116$	1.36087e6	0.0809494
$117$	0	0
$118$	−2.38172e6	−0.133445
$119$	−7.88875e6	−0.429135
$120$	0	0
$121$	5.25490e6	0.269659
$122$	−1.58906e7	−0.792284
$123$	0	0
$124$	−76922.7	−0.00362308
$125$	1.85896e6	0.0851305
$126$	0	0
$127$	−1.73455e7	−0.751403	−0.375701	−	0.926741i	$-0.622598\pi$
$127$	−1.73455e7	−0.751403	−0.375701	+	0.926741i	$0.622598\pi$
$128$	−2.53678e7	−1.06917
$129$	0	0
$130$	5.88410e7	2.34897
$131$	1.36249e7	0.529520	0.264760	−	0.964314i	$-0.414707\pi$
$131$	1.36249e7	0.529520	0.264760	+	0.964314i	$0.414707\pi$
$132$	0	0
$133$	−6.63478e6	−0.244538
$134$	−3.53939e7	−1.27075
$135$	0	0
$136$	−5.20514e7	−1.77438
$137$	1.67308e7	0.555898	0.277949	−	0.960596i	$-0.410345\pi$
$137$	1.67308e7	0.555898	0.277949	+	0.960596i	$0.410345\pi$
$138$	0	0
$139$	1.17094e7	0.369813	0.184907	−	0.982756i	$-0.440802\pi$
$139$	1.17094e7	0.369813	0.184907	+	0.982756i	$0.440802\pi$
$140$	555371.	0.0171055
$141$	0	0
$142$	−5.45403e7	−1.59848
$143$	−6.29226e7	−1.79941
$144$	0	0
$145$	8.41965e7	2.29354
$146$	4.23947e7	1.12740
$147$	0	0
$148$	109691.	0.00278135
$149$	−153329.	−0.00379728	−0.00189864	−	0.999998i	$-0.500604\pi$
$149$	−153329.	−0.00379728	−0.00189864	+	0.999998i	$0.500604\pi$
$150$	0	0
$151$	7.64791e7	1.80769	0.903843	−	0.427863i	$-0.140734\pi$
$151$	7.64791e7	1.80769	0.903843	+	0.427863i	$0.140734\pi$
$152$	−4.37775e7	−1.01111
$153$	0	0
$154$	−1.23196e7	−0.271816
$155$	−4.75917e6	−0.102653
$156$	0	0
$157$	−6.86729e6	−0.141624	−0.0708119	−	0.997490i	$-0.522559\pi$
$157$	−6.86729e6	−0.141624	−0.0708119	+	0.997490i	$0.522559\pi$
$158$	−7.39072e7	−1.49069
$159$	0	0
$160$	7.52439e6	0.145228
$161$	−1.12327e7	−0.212125
$162$	0	0
$163$	−1.89828e7	−0.343323	−0.171662	−	0.985156i	$-0.554914\pi$
$163$	−1.89828e7	−0.343323	−0.171662	+	0.985156i	$0.554914\pi$
$164$	−5.19319e6	−0.0919350
$165$	0	0
$166$	−2.42024e7	−0.410657
$167$	1.70383e7	0.283085	0.141543	−	0.989932i	$-0.454794\pi$
$167$	1.70383e7	0.283085	0.141543	+	0.989932i	$0.454794\pi$
$168$	0	0
$169$	9.72727e7	1.55020
$170$	1.71812e8	2.68214
$171$	0	0
$172$	4.66935e6	0.0699692
$173$	8.07641e6	0.118592	0.0592962	−	0.998240i	$-0.481114\pi$
$173$	8.07641e6	0.118592	0.0592962	+	0.998240i	$0.481114\pi$
$174$	0	0
$175$	1.76752e7	0.249305
$176$	−8.54149e7	−1.18097
$177$	0	0
$178$	1.66579e7	0.221386
$179$	−4.99947e7	−0.651536	−0.325768	−	0.945450i	$-0.605623\pi$
$179$	−4.99947e7	−0.651536	−0.325768	+	0.945450i	$0.605623\pi$
$180$	0	0
$181$	7.07416e7	0.886747	0.443373	−	0.896337i	$-0.353782\pi$
$181$	7.07416e7	0.886747	0.443373	+	0.896337i	$0.353782\pi$
$182$	3.13306e7	0.385229
$183$	0	0
$184$	−7.41151e7	−0.877091
$185$	6.78655e6	0.0788039
$186$	0	0
$187$	−1.83730e8	−2.05463
$188$	352698.	0.00387124
$189$	0	0
$190$	1.44501e8	1.52839
$191$	1.40226e8	1.45617	0.728086	−	0.685486i	$-0.240410\pi$
$191$	1.40226e8	1.45617	0.728086	+	0.685486i	$0.240410\pi$
$192$	0	0
$193$	−5.81729e7	−0.582465	−0.291233	−	0.956652i	$-0.594065\pi$
$193$	−5.81729e7	−0.582465	−0.291233	+	0.956652i	$0.594065\pi$
$194$	7.45311e7	0.732878
$195$	0	0
$196$	−5.04337e6	−0.0478436
$197$	−6.06171e7	−0.564889	−0.282445	−	0.959284i	$-0.591145\pi$
$197$	−6.06171e7	−0.564889	−0.282445	+	0.959284i	$0.591145\pi$
$198$	0	0
$199$	234342.	0.00210797	0.00105398	−	0.999999i	$-0.499665\pi$
$199$	234342.	0.00210797	0.00105398	+	0.999999i	$0.499665\pi$
$200$	1.16624e8	1.03082
$201$	0	0
$202$	1.23765e7	0.105649
$203$	4.48314e7	0.376137
$204$	0	0
$205$	−3.21300e8	−2.60479
$206$	1.13718e8	0.906343
$207$	0	0
$208$	2.17222e8	1.67372
$209$	−1.54525e8	−1.17081
$210$	0	0
$211$	−2.04520e8	−1.49881	−0.749406	−	0.662111i	$-0.769661\pi$
$211$	−2.04520e8	−1.49881	−0.749406	+	0.662111i	$0.769661\pi$
$212$	1.91573e6	0.0138089
$213$	0	0
$214$	−2.27452e8	−1.58650
$215$	2.88891e8	1.98243
$216$	0	0
$217$	−2.53408e6	−0.0168349
$218$	−2.96216e8	−1.93647
$219$	0	0
$220$	1.29347e7	0.0818985
$221$	4.67251e8	2.91191
$222$	0	0
$223$	2.44062e8	1.47378	0.736892	−	0.676011i	$-0.236293\pi$
$223$	2.44062e8	1.47378	0.736892	+	0.676011i	$0.236293\pi$
$224$	4.00645e6	0.0238173
$225$	0	0
$226$	−1.44710e8	−0.833908
$227$	1.77415e8	1.00670	0.503350	−	0.864083i	$-0.332101\pi$
$227$	1.77415e8	1.00670	0.503350	+	0.864083i	$0.332101\pi$
$228$	0	0
$229$	2.17580e8	1.19728	0.598638	−	0.801020i	$-0.295709\pi$
$229$	2.17580e8	1.19728	0.598638	+	0.801020i	$0.295709\pi$
$230$	2.44640e8	1.32581
$231$	0	0
$232$	2.95806e8	1.55525
$233$	3.27814e8	1.69778	0.848890	−	0.528570i	$-0.177272\pi$
$233$	3.27814e8	1.69778	0.848890	+	0.528570i	$0.177272\pi$
$234$	0	0
$235$	2.18213e7	0.109684
$236$	1.33148e6	0.00659393
$237$	0	0
$238$	9.14833e7	0.439868
$239$	−2.79462e8	−1.32413	−0.662064	−	0.749448i	$-0.730319\pi$
$239$	−2.79462e8	−1.32413	−0.662064	+	0.749448i	$0.730319\pi$
$240$	0	0
$241$	3.83280e8	1.76383	0.881915	−	0.471409i	$-0.156254\pi$
$241$	3.83280e8	1.76383	0.881915	+	0.471409i	$0.156254\pi$
$242$	−6.09394e7	−0.276404
$243$	0	0
$244$	8.88356e6	0.0391492
$245$	−3.12031e8	−1.35555
$246$	0	0
$247$	3.92979e8	1.65932
$248$	−1.67203e7	−0.0696088
$249$	0	0
$250$	−2.15578e7	−0.0872598
$251$	4.23948e8	1.69221	0.846106	−	0.533014i	$-0.178941\pi$
$251$	4.23948e8	1.69221	0.846106	+	0.533014i	$0.178941\pi$
$252$	0	0
$253$	−2.61610e8	−1.01562
$254$	2.01150e8	0.770196
$255$	0	0
$256$	4.06850e7	0.151564
$257$	−1.80864e8	−0.664638	−0.332319	−	0.943167i	$-0.607831\pi$
$257$	−1.80864e8	−0.664638	−0.332319	+	0.943167i	$0.607831\pi$
$258$	0	0
$259$	3.61358e6	0.0129237
$260$	−3.28947e7	−0.116070
$261$	0	0
$262$	−1.58003e8	−0.542764
$263$	−4.23691e8	−1.43616	−0.718082	−	0.695958i	$-0.754980\pi$
$263$	−4.23691e8	−1.43616	−0.718082	+	0.695958i	$0.754980\pi$
$264$	0	0
$265$	1.18525e8	0.391247
$266$	7.69415e7	0.250654
$267$	0	0
$268$	1.97868e7	0.0627918
$269$	−3.48418e8	−1.09136	−0.545679	−	0.837994i	$-0.683728\pi$
$269$	−3.48418e8	−1.09136	−0.545679	+	0.837994i	$0.683728\pi$
$270$	0	0
$271$	−1.26441e8	−0.385918	−0.192959	−	0.981207i	$-0.561809\pi$
$271$	−1.26441e8	−0.385918	−0.192959	+	0.981207i	$0.561809\pi$
$272$	6.34275e8	1.91111
$273$	0	0
$274$	−1.94022e8	−0.569802
$275$	4.11658e8	1.19364
$276$	0	0
$277$	−2.22094e8	−0.627852	−0.313926	−	0.949447i	$-0.601644\pi$
$277$	−2.22094e8	−0.627852	−0.313926	+	0.949447i	$0.601644\pi$
$278$	−1.35790e8	−0.379063
$279$	0	0
$280$	1.20719e8	0.328640
$281$	3.20287e8	0.861128	0.430564	−	0.902560i	$-0.358315\pi$
$281$	3.20287e8	0.861128	0.430564	+	0.902560i	$0.358315\pi$
$282$	0	0
$283$	2.46262e8	0.645870	0.322935	−	0.946421i	$-0.395331\pi$
$283$	2.46262e8	0.645870	0.322935	+	0.946421i	$0.395331\pi$
$284$	3.04905e7	0.0789860
$285$	0	0
$286$	7.29694e8	1.84442
$287$	−1.71080e8	−0.427183
$288$	0	0
$289$	9.54005e8	2.32492
$290$	−9.76400e8	−2.35090
$291$	0	0
$292$	−2.37005e7	−0.0557080
$293$	−2.26005e8	−0.524905	−0.262453	−	0.964945i	$-0.584531\pi$
$293$	−2.26005e8	−0.524905	−0.262453	+	0.964945i	$0.584531\pi$
$294$	0	0
$295$	8.23784e7	0.186826
$296$	2.38431e7	0.0534369
$297$	0	0
$298$	1.77811e6	0.00389226
$299$	6.65312e8	1.43938
$300$	0	0
$301$	1.53823e8	0.325117
$302$	−8.86903e8	−1.85290
$303$	0	0
$304$	5.33453e8	1.08903
$305$	5.49622e8	1.10921
$306$	0	0
$307$	5.53693e8	1.09216	0.546078	−	0.837734i	$-0.316120\pi$
$307$	5.53693e8	1.09216	0.546078	+	0.837734i	$0.316120\pi$
$308$	6.88722e6	0.0134313
$309$	0	0
$310$	5.51906e7	0.105220
$311$	−8.72060e8	−1.64394	−0.821968	−	0.569534i	$-0.807124\pi$
$311$	−8.72060e8	−1.64394	−0.821968	+	0.569534i	$0.807124\pi$
$312$	0	0
$313$	3.27729e8	0.604102	0.302051	−	0.953292i	$-0.402329\pi$
$313$	3.27729e8	0.604102	0.302051	+	0.953292i	$0.402329\pi$
$314$	7.96378e7	0.145166
$315$	0	0
$316$	4.13174e7	0.0736594
$317$	−1.07872e9	−1.90196	−0.950982	−	0.309246i	$-0.899923\pi$
$317$	−1.07872e9	−1.90196	−0.950982	+	0.309246i	$0.899923\pi$
$318$	0	0
$319$	1.04413e9	1.80089
$320$	7.94365e8	1.35518
$321$	0	0
$322$	1.30262e8	0.217431
$323$	1.14747e9	1.89467
$324$	0	0
$325$	−1.04690e9	−1.69167
$326$	2.20137e8	0.351910
$327$	0	0
$328$	−1.12882e9	−1.76631
$329$	1.16190e7	0.0179880
$330$	0	0
$331$	1.91834e8	0.290755	0.145378	−	0.989376i	$-0.453560\pi$
$331$	1.91834e8	0.290755	0.145378	+	0.989376i	$0.453560\pi$
$332$	1.35302e7	0.0202918
$333$	0	0
$334$	−1.97587e8	−0.290166
$335$	1.22420e9	1.77908
$336$	0	0
$337$	4.73052e8	0.673294	0.336647	−	0.941631i	$-0.390707\pi$
$337$	4.73052e8	0.673294	0.336647	+	0.941631i	$0.390707\pi$
$338$	−1.12804e9	−1.58897
$339$	0	0
$340$	−9.60504e7	−0.132533
$341$	−5.90190e7	−0.0806031
$342$	0	0
$343$	−3.42031e8	−0.457653
$344$	1.01496e9	1.34429
$345$	0	0
$346$	−9.36596e7	−0.121559
$347$	2.39433e8	0.307631	0.153815	−	0.988100i	$-0.450844\pi$
$347$	2.39433e8	0.307631	0.153815	+	0.988100i	$0.450844\pi$
$348$	0	0
$349$	2.55293e8	0.321477	0.160738	−	0.986997i	$-0.448612\pi$
$349$	2.55293e8	0.321477	0.160738	+	0.986997i	$0.448612\pi$
$350$	−2.04974e8	−0.255541
$351$	0	0
$352$	9.33108e7	0.114034
$353$	−9.16807e8	−1.10934	−0.554672	−	0.832069i	$-0.687156\pi$
$353$	−9.16807e8	−1.10934	−0.554672	+	0.832069i	$0.687156\pi$
$354$	0	0
$355$	1.88643e9	2.23791
$356$	−9.31252e6	−0.0109394
$357$	0	0
$358$	5.79773e8	0.667832
$359$	1.06121e8	0.121051	0.0605256	−	0.998167i	$-0.480722\pi$
$359$	1.06121e8	0.121051	0.0605256	+	0.998167i	$0.480722\pi$
$360$	0	0
$361$	7.12032e7	0.0796570
$362$	−8.20368e8	−0.908926
$363$	0	0
$364$	−1.75152e7	−0.0190353
$365$	−1.46634e9	−1.57837
$366$	0	0
$367$	1.13340e9	1.19689	0.598444	−	0.801164i	$-0.295786\pi$
$367$	1.13340e9	1.19689	0.598444	+	0.801164i	$0.295786\pi$
$368$	9.03134e8	0.944680
$369$	0	0
$370$	−7.87014e7	−0.0807749
$371$	6.31103e7	0.0641640
$372$	0	0
$373$	3.48649e8	0.347863	0.173931	−	0.984758i	$-0.444353\pi$
$373$	3.48649e8	0.347863	0.173931	+	0.984758i	$0.444353\pi$
$374$	2.13066e9	2.10602
$375$	0	0
$376$	7.66643e7	0.0743765
$377$	−2.65537e9	−2.55229
$378$	0	0
$379$	−1.97757e8	−0.186592	−0.0932962	−	0.995638i	$-0.529740\pi$
$379$	−1.97757e8	−0.186592	−0.0932962	+	0.995638i	$0.529740\pi$
$380$	−8.07826e7	−0.0755223
$381$	0	0
$382$	−1.62616e9	−1.49259
$383$	1.60320e9	1.45811	0.729056	−	0.684454i	$-0.239959\pi$
$383$	1.60320e9	1.45811	0.729056	+	0.684454i	$0.239959\pi$
$384$	0	0
$385$	4.26110e8	0.380547
$386$	6.74613e8	0.597034
$387$	0	0
$388$	−4.16662e7	−0.0362137
$389$	7.74392e8	0.667018	0.333509	−	0.942747i	$-0.391767\pi$
$389$	7.74392e8	0.667018	0.333509	+	0.942747i	$0.391767\pi$
$390$	0	0
$391$	1.94267e9	1.64354
$392$	−1.09625e9	−0.919199
$393$	0	0
$394$	7.02957e8	0.579018
$395$	2.55629e9	2.08699
$396$	0	0
$397$	−1.24932e9	−1.00209	−0.501044	−	0.865422i	$-0.667050\pi$
$397$	−1.24932e9	−1.00209	−0.501044	+	0.865422i	$0.667050\pi$
$398$	−2.71759e6	−0.00216069
$399$	0	0
$400$	−1.42113e9	−1.11026
$401$	2.10043e9	1.62668	0.813341	−	0.581788i	$-0.197647\pi$
$401$	2.10043e9	1.62668	0.813341	+	0.581788i	$0.197647\pi$
$402$	0	0
$403$	1.50094e8	0.114234
$404$	−6.91899e6	−0.00522045
$405$	0	0
$406$	−5.19896e8	−0.385545
$407$	8.41607e7	0.0618770
$408$	0	0
$409$	2.09675e9	1.51535	0.757677	−	0.652629i	$-0.226334\pi$
$409$	2.09675e9	1.51535	0.757677	+	0.652629i	$0.226334\pi$
$410$	3.72602e9	2.66994
$411$	0	0
$412$	−6.35732e7	−0.0447851
$413$	4.38634e7	0.0306392
$414$	0	0
$415$	8.37107e8	0.574927
$416$	−2.37303e8	−0.161613
$417$	0	0
$418$	1.79198e9	1.20009
$419$	7.54525e8	0.501100	0.250550	−	0.968104i	$-0.419388\pi$
$419$	7.54525e8	0.501100	0.250550	+	0.968104i	$0.419388\pi$
$420$	0	0
$421$	−1.83091e8	−0.119586	−0.0597931	−	0.998211i	$-0.519044\pi$
$421$	−1.83091e8	−0.119586	−0.0597931	+	0.998211i	$0.519044\pi$
$422$	2.37175e9	1.53630
$423$	0	0
$424$	4.16413e8	0.265304
$425$	−3.05689e9	−1.93161
$426$	0	0
$427$	2.92653e8	0.181909
$428$	1.27155e8	0.0783938
$429$	0	0
$430$	−3.35017e9	−2.03202
$431$	−2.72495e8	−0.163941	−0.0819706	−	0.996635i	$-0.526121\pi$
$431$	−2.72495e8	−0.163941	−0.0819706	+	0.996635i	$0.526121\pi$
$432$	0	0
$433$	−9.06889e8	−0.536842	−0.268421	−	0.963302i	$-0.586502\pi$
$433$	−9.06889e8	−0.536842	−0.268421	+	0.963302i	$0.586502\pi$
$434$	2.93869e7	0.0172560
$435$	0	0
$436$	1.65598e8	0.0956870
$437$	1.63387e9	0.936552
$438$	0	0
$439$	−6.54375e7	−0.0369148	−0.0184574	−	0.999830i	$-0.505876\pi$
$439$	−6.54375e7	−0.0369148	−0.0184574	+	0.999830i	$0.505876\pi$
$440$	2.81155e9	1.57348
$441$	0	0
$442$	−5.41857e9	−2.98474
$443$	−2.60048e9	−1.42115	−0.710575	−	0.703621i	$-0.751565\pi$
$443$	−2.60048e9	−1.42115	−0.710575	+	0.703621i	$0.751565\pi$
$444$	0	0
$445$	−5.76162e8	−0.309945
$446$	−2.83031e9	−1.51065
$447$	0	0
$448$	4.22970e8	0.222247
$449$	−2.52865e9	−1.31834	−0.659168	−	0.751996i	$-0.729091\pi$
$449$	−2.52865e9	−1.31834	−0.659168	+	0.751996i	$0.729091\pi$
$450$	0	0
$451$	−3.98448e9	−2.04529
$452$	8.08992e7	0.0412059
$453$	0	0
$454$	−2.05742e9	−1.03188
$455$	−1.08366e9	−0.539327
$456$	0	0
$457$	−1.26888e9	−0.621888	−0.310944	−	0.950428i	$-0.600645\pi$
$457$	−1.26888e9	−0.621888	−0.310944	+	0.950428i	$0.600645\pi$
$458$	−2.52320e9	−1.22722
$459$	0	0
$460$	−1.36765e8	−0.0655121
$461$	−6.17722e8	−0.293656	−0.146828	−	0.989162i	$-0.546906\pi$
$461$	−6.17722e8	−0.293656	−0.146828	+	0.989162i	$0.546906\pi$
$462$	0	0
$463$	1.76885e9	0.828241	0.414120	−	0.910222i	$-0.364089\pi$
$463$	1.76885e9	0.828241	0.414120	+	0.910222i	$0.364089\pi$
$464$	−3.60456e9	−1.67510
$465$	0	0
$466$	−3.80155e9	−1.74024
$467$	−2.09197e9	−0.950489	−0.475244	−	0.879854i	$-0.657640\pi$
$467$	−2.09197e9	−0.950489	−0.475244	+	0.879854i	$0.657640\pi$
$468$	0	0
$469$	6.51839e8	0.291767
$470$	−2.53054e8	−0.112427
$471$	0	0
$472$	2.89419e8	0.126686
$473$	3.58257e9	1.55661
$474$	0	0
$475$	−2.57098e9	−1.10071
$476$	−5.11432e7	−0.0217352
$477$	0	0
$478$	3.24083e9	1.35725
$479$	7.21973e8	0.300156	0.150078	−	0.988674i	$-0.452048\pi$
$479$	7.21973e8	0.300156	0.150078	+	0.988674i	$0.452048\pi$
$480$	0	0
$481$	−2.14033e8	−0.0876945
$482$	−4.44478e9	−1.80795
$483$	0	0
$484$	3.40678e7	0.0136580
$485$	−2.57787e9	−1.02604
$486$	0	0
$487$	2.53074e9	0.992878	0.496439	−	0.868072i	$-0.334641\pi$
$487$	2.53074e9	0.992878	0.496439	+	0.868072i	$0.334641\pi$
$488$	1.93098e9	0.752156
$489$	0	0
$490$	3.61852e9	1.38946
$491$	−4.02112e9	−1.53307	−0.766535	−	0.642203i	$-0.778021\pi$
$491$	−4.02112e9	−1.53307	−0.766535	+	0.642203i	$0.778021\pi$
$492$	0	0
$493$	−7.75351e9	−2.91430
$494$	−4.55725e9	−1.70082
$495$	0	0
$496$	2.03746e8	0.0749729
$497$	1.00445e9	0.367014
$498$	0	0
$499$	−1.21528e9	−0.437849	−0.218924	−	0.975742i	$-0.570255\pi$
$499$	−1.21528e9	−0.437849	−0.218924	+	0.975742i	$0.570255\pi$
$500$	1.20518e7	0.00431177
$501$	0	0
$502$	−4.91640e9	−1.73454
$503$	−4.23068e9	−1.48225	−0.741126	−	0.671366i	$-0.765708\pi$
$503$	−4.23068e9	−1.48225	−0.741126	+	0.671366i	$0.765708\pi$
$504$	0	0
$505$	−4.28075e8	−0.147911
$506$	3.03381e9	1.04103
$507$	0	0
$508$	−1.12452e8	−0.0380577
$509$	−5.89664e9	−1.98195	−0.990974	−	0.134052i	$-0.957201\pi$
$509$	−5.89664e9	−1.98195	−0.990974	+	0.134052i	$0.957201\pi$
$510$	0	0
$511$	−7.80771e8	−0.258851
$512$	2.77526e9	0.913818
$513$	0	0
$514$	2.09742e9	0.681262
$515$	−3.93325e9	−1.26890
$516$	0	0
$517$	2.70608e8	0.0861239
$518$	−4.19055e7	−0.0132470
$519$	0	0
$520$	−7.15017e9	−2.23000
$521$	3.53847e8	0.109618	0.0548092	−	0.998497i	$-0.482545\pi$
$521$	3.53847e8	0.109618	0.0548092	+	0.998497i	$0.482545\pi$
$522$	0	0
$523$	1.49203e9	0.456059	0.228029	−	0.973654i	$-0.426772\pi$
$523$	1.49203e9	0.456059	0.228029	+	0.973654i	$0.426772\pi$
$524$	8.83307e7	0.0268196
$525$	0	0
$526$	4.91341e9	1.47209
$527$	4.38264e8	0.130436
$528$	0	0
$529$	−6.38695e8	−0.187585
$530$	−1.37450e9	−0.401033
$531$	0	0
$532$	−4.30137e7	−0.0123856
$533$	1.01331e10	2.89866
$534$	0	0
$535$	7.86706e9	2.22113
$536$	4.30096e9	1.20639
$537$	0	0
$538$	4.04049e9	1.11866
$539$	−3.86953e9	−1.06438
$540$	0	0
$541$	−2.13831e9	−0.580603	−0.290302	−	0.956935i	$-0.593756\pi$
$541$	−2.13831e9	−0.580603	−0.290302	+	0.956935i	$0.593756\pi$
$542$	1.46630e9	0.395571
$543$	0	0
$544$	−6.92908e8	−0.184535
$545$	1.02455e10	2.71110
$546$	0	0
$547$	−2.11049e9	−0.551351	−0.275676	−	0.961251i	$-0.588902\pi$
$547$	−2.11049e9	−0.551351	−0.275676	+	0.961251i	$0.588902\pi$
$548$	1.08467e8	0.0281556
$549$	0	0
$550$	−4.77387e9	−1.22349
$551$	−6.52104e9	−1.66068
$552$	0	0
$553$	1.36113e9	0.342264
$554$	2.57555e9	0.643556
$555$	0	0
$556$	7.59126e7	0.0187306
$557$	5.51882e9	1.35317	0.676586	−	0.736364i	$-0.263459\pi$
$557$	5.51882e9	1.35317	0.676586	+	0.736364i	$0.263459\pi$
$558$	0	0
$559$	−9.11098e9	−2.20609
$560$	−1.47102e9	−0.353966
$561$	0	0
$562$	−3.71427e9	−0.882666
$563$	3.94126e8	0.0930798	0.0465399	−	0.998916i	$-0.485181\pi$
$563$	3.94126e8	0.0930798	0.0465399	+	0.998916i	$0.485181\pi$
$564$	0	0
$565$	5.00520e9	1.16749
$566$	−2.85582e9	−0.662024
$567$	0	0
$568$	6.62757e9	1.51752
$569$	5.23096e9	1.19039	0.595194	−	0.803582i	$-0.297075\pi$
$569$	5.23096e9	1.19039	0.595194	+	0.803582i	$0.297075\pi$
$570$	0	0
$571$	3.54290e9	0.796401	0.398201	−	0.917298i	$-0.369635\pi$
$571$	3.54290e9	0.796401	0.398201	+	0.917298i	$0.369635\pi$
$572$	−4.07931e8	−0.0911383
$573$	0	0
$574$	1.98397e9	0.437867
$575$	−4.35266e9	−0.954811
$576$	0	0
$577$	−5.36264e8	−0.116215	−0.0581077	−	0.998310i	$-0.518507\pi$
$577$	−5.36264e8	−0.116215	−0.0581077	+	0.998310i	$0.518507\pi$
$578$	−1.10633e10	−2.38307
$579$	0	0
$580$	5.45851e8	0.116165
$581$	4.45728e8	0.0942873
$582$	0	0
$583$	1.46985e9	0.307208
$584$	−5.15167e9	−1.07029
$585$	0	0
$586$	2.62090e9	0.538034
$587$	1.65503e9	0.337733	0.168867	−	0.985639i	$-0.445989\pi$
$587$	1.65503e9	0.337733	0.168867	+	0.985639i	$0.445989\pi$
$588$	0	0
$589$	3.68599e8	0.0743278
$590$	−9.55316e8	−0.191498
$591$	0	0
$592$	−2.90541e8	−0.0575548
$593$	8.05027e9	1.58533	0.792664	−	0.609659i	$-0.208693\pi$
$593$	8.05027e9	1.58533	0.792664	+	0.609659i	$0.208693\pi$
$594$	0	0
$595$	−3.16421e9	−0.615823
$596$	−994042.	−0.000192328 0
$597$	0	0
$598$	−7.71541e9	−1.47538
$599$	2.91923e7	0.00554976	0.00277488	−	0.999996i	$-0.499117\pi$
$599$	2.91923e7	0.00554976	0.00277488	+	0.999996i	$0.499117\pi$
$600$	0	0
$601$	−5.20322e9	−0.977713	−0.488856	−	0.872364i	$-0.662586\pi$
$601$	−5.20322e9	−0.977713	−0.488856	+	0.872364i	$0.662586\pi$
$602$	−1.78384e9	−0.333249
$603$	0	0
$604$	4.95818e8	0.0915574
$605$	2.10776e9	0.386970
$606$	0	0
$607$	7.88385e9	1.43080	0.715398	−	0.698717i	$-0.246245\pi$
$607$	7.88385e9	1.43080	0.715398	+	0.698717i	$0.246245\pi$
$608$	−5.82766e8	−0.105155
$609$	0	0
$610$	−6.37379e9	−1.13696
$611$	−6.88195e8	−0.122058
$612$	0	0
$613$	−3.27886e9	−0.574926	−0.287463	−	0.957792i	$-0.592812\pi$
$613$	−3.27886e9	−0.574926	−0.287463	+	0.957792i	$0.592812\pi$
$614$	−6.42100e9	−1.11947
$615$	0	0
$616$	1.49704e9	0.258049
$617$	−1.20684e9	−0.206848	−0.103424	−	0.994637i	$-0.532980\pi$
$617$	−1.20684e9	−0.206848	−0.103424	+	0.994637i	$0.532980\pi$
$618$	0	0
$619$	−4.26264e9	−0.722372	−0.361186	−	0.932494i	$-0.617628\pi$
$619$	−4.26264e9	−0.722372	−0.361186	+	0.932494i	$0.617628\pi$
$620$	−3.08540e7	−0.00519925
$621$	0	0
$622$	1.01130e10	1.68505
$623$	−3.06784e8	−0.0508306
$624$	0	0
$625$	−5.71996e9	−0.937158
$626$	−3.80057e9	−0.619211
$627$	0	0
$628$	−4.45210e7	−0.00717310
$629$	−6.24962e8	−0.100133
$630$	0	0
$631$	−3.40983e9	−0.540294	−0.270147	−	0.962819i	$-0.587072\pi$
$631$	−3.40983e9	−0.540294	−0.270147	+	0.962819i	$0.587072\pi$
$632$	8.98098e9	1.41519
$633$	0	0
$634$	1.25096e10	1.94954
$635$	−6.95733e9	−1.07829
$636$	0	0
$637$	9.84077e9	1.50849
$638$	−1.21084e10	−1.84593
$639$	0	0
$640$	−1.01751e10	−1.53430
$641$	7.05809e9	1.05848	0.529242	−	0.848471i	$-0.322476\pi$
$641$	7.05809e9	1.05848	0.529242	+	0.848471i	$0.322476\pi$
$642$	0	0
$643$	9.53642e9	1.41464	0.707322	−	0.706892i	$-0.249903\pi$
$643$	9.53642e9	1.41464	0.707322	+	0.706892i	$0.249903\pi$
$644$	−7.28220e7	−0.0107439
$645$	0	0
$646$	−1.33069e10	−1.94206
$647$	−1.17077e10	−1.69945	−0.849723	−	0.527230i	$-0.823231\pi$
$647$	−1.17077e10	−1.69945	−0.849723	+	0.527230i	$0.823231\pi$
$648$	0	0
$649$	1.02158e9	0.146696
$650$	1.21406e10	1.73398
$651$	0	0
$652$	−1.23066e8	−0.0173889
$653$	1.32050e9	0.185584	0.0927921	−	0.995686i	$-0.470421\pi$
$653$	1.32050e9	0.185584	0.0927921	+	0.995686i	$0.470421\pi$
$654$	0	0
$655$	5.46499e9	0.759879
$656$	1.37553e10	1.90242
$657$	0	0
$658$	−1.34742e8	−0.0184379
$659$	2.98482e9	0.406275	0.203137	−	0.979150i	$-0.434886\pi$
$659$	2.98482e9	0.406275	0.203137	+	0.979150i	$0.434886\pi$
$660$	0	0
$661$	−1.22973e10	−1.65617	−0.828087	−	0.560600i	$-0.810571\pi$
$661$	−1.22973e10	−1.65617	−0.828087	+	0.560600i	$0.810571\pi$
$662$	−2.22464e9	−0.298027
$663$	0	0
$664$	2.94100e9	0.389858
$665$	−2.66124e9	−0.350920
$666$	0	0
$667$	−1.10401e10	−1.44056
$668$	1.10460e8	0.0143380
$669$	0	0
$670$	−1.41966e10	−1.82358
$671$	6.81592e9	0.870955
$672$	0	0
$673$	−7.89633e9	−0.998557	−0.499278	−	0.866442i	$-0.666401\pi$
$673$	−7.89633e9	−0.998557	−0.499278	+	0.866442i	$0.666401\pi$
$674$	−5.48584e9	−0.690134
$675$	0	0
$676$	6.30625e8	0.0785159
$677$	1.34037e9	0.166021	0.0830106	−	0.996549i	$-0.473546\pi$
$677$	1.34037e9	0.166021	0.0830106	+	0.996549i	$0.473546\pi$
$678$	0	0
$679$	−1.37262e9	−0.168270
$680$	−2.08780e10	−2.54629
$681$	0	0
$682$	6.84425e8	0.0826191
$683$	6.85009e9	0.822667	0.411333	−	0.911485i	$-0.365063\pi$
$683$	6.85009e9	0.822667	0.411333	+	0.911485i	$0.365063\pi$
$684$	0	0
$685$	6.71080e9	0.797732
$686$	3.96643e9	0.469100
$687$	0	0
$688$	−1.23678e10	−1.44788
$689$	−3.73803e9	−0.435387
$690$	0	0
$691$	1.48604e10	1.71340	0.856698	−	0.515818i	$-0.172512\pi$
$691$	1.48604e10	1.71340	0.856698	+	0.515818i	$0.172512\pi$
$692$	5.23599e7	0.00600658
$693$	0	0
$694$	−2.77662e9	−0.315325
$695$	4.69668e9	0.530694
$696$	0	0
$697$	2.95880e10	3.30980
$698$	−2.96055e9	−0.329518
$699$	0	0
$700$	1.14589e8	0.0126270
$701$	1.54673e10	1.69590	0.847952	−	0.530073i	$-0.177836\pi$
$701$	1.54673e10	1.69590	0.847952	+	0.530073i	$0.177836\pi$
$702$	0	0
$703$	−5.25620e8	−0.0570596
$704$	9.85102e9	1.06409
$705$	0	0
$706$	1.06319e10	1.13709
$707$	−2.27934e8	−0.0242572
$708$	0	0
$709$	2.09686e9	0.220957	0.110478	−	0.993879i	$-0.464762\pi$
$709$	2.09686e9	0.220957	0.110478	+	0.993879i	$0.464762\pi$
$710$	−2.18764e10	−2.29388
$711$	0	0
$712$	−2.02422e9	−0.210173
$713$	6.24037e8	0.0644759
$714$	0	0
$715$	−2.52385e10	−2.58222
$716$	−3.24119e8	−0.0329996
$717$	0	0
$718$	−1.23065e9	−0.124079
$719$	1.96050e10	1.96705	0.983527	−	0.180761i	$-0.0578561\pi$
$719$	1.96050e10	1.96705	0.983527	+	0.180761i	$0.0578561\pi$
$720$	0	0
$721$	−2.09431e9	−0.208097
$722$	−8.25721e8	−0.0816494
$723$	0	0
$724$	4.58622e8	0.0449128
$725$	1.73722e10	1.69306
$726$	0	0
$727$	−1.11617e10	−1.07735	−0.538677	−	0.842513i	$-0.681075\pi$
$727$	−1.11617e10	−1.07735	−0.538677	+	0.842513i	$0.681075\pi$
$728$	−3.80720e9	−0.365717
$729$	0	0
$730$	1.70047e10	1.61785
$731$	−2.66035e10	−2.51899
$732$	0	0
$733$	1.37783e10	1.29221	0.646103	−	0.763250i	$-0.276397\pi$
$733$	1.37783e10	1.29221	0.646103	+	0.763250i	$0.276397\pi$
$734$	−1.31437e10	−1.22683
$735$	0	0
$736$	−9.86621e8	−0.0912175
$737$	1.51814e10	1.39694
$738$	0	0
$739$	3.03220e9	0.276377	0.138189	−	0.990406i	$-0.455872\pi$
$739$	3.03220e9	0.276377	0.138189	+	0.990406i	$0.455872\pi$
$740$	4.39976e7	0.00399133
$741$	0	0
$742$	−7.31870e8	−0.0657689
$743$	1.93427e9	0.173004	0.0865020	−	0.996252i	$-0.472431\pi$
$743$	1.93427e9	0.173004	0.0865020	+	0.996252i	$0.472431\pi$
$744$	0	0
$745$	−6.15009e7	−0.00544923
$746$	−4.04318e9	−0.356563
$747$	0	0
$748$	−1.19113e9	−0.104065
$749$	4.18891e9	0.364263
$750$	0	0
$751$	5.54431e9	0.477647	0.238824	−	0.971063i	$-0.423238\pi$
$751$	5.54431e9	0.477647	0.238824	+	0.971063i	$0.423238\pi$
$752$	−9.34197e8	−0.0801081
$753$	0	0
$754$	3.07935e10	2.61613
$755$	3.06761e10	2.59409
$756$	0	0
$757$	1.76557e10	1.47927	0.739637	−	0.673006i	$-0.234997\pi$
$757$	1.76557e10	1.47927	0.739637	+	0.673006i	$0.234997\pi$
$758$	2.29332e9	0.191259
$759$	0	0
$760$	−1.75593e10	−1.45098
$761$	−2.32983e9	−0.191636	−0.0958180	−	0.995399i	$-0.530547\pi$
$761$	−2.32983e9	−0.191636	−0.0958180	+	0.995399i	$0.530547\pi$
$762$	0	0
$763$	5.45534e9	0.444617
$764$	9.09095e8	0.0737535
$765$	0	0
$766$	−1.85918e10	−1.49458
$767$	−2.59803e9	−0.207903
$768$	0	0
$769$	8.88822e9	0.704811	0.352405	−	0.935847i	$-0.385364\pi$
$769$	8.88822e9	0.704811	0.352405	+	0.935847i	$0.385364\pi$
$770$	−4.94146e9	−0.390066
$771$	0	0
$772$	−3.77138e8	−0.0295012
$773$	1.51855e9	0.118250	0.0591251	−	0.998251i	$-0.481169\pi$
$773$	1.51855e9	0.118250	0.0591251	+	0.998251i	$0.481169\pi$
$774$	0	0
$775$	−9.81957e8	−0.0757769
$776$	−9.05679e9	−0.695758
$777$	0	0
$778$	−8.98038e9	−0.683701
$779$	2.48848e10	1.88605
$780$	0	0
$781$	2.33939e10	1.75721
$782$	−2.25285e10	−1.68464
$783$	0	0
$784$	1.33585e10	0.990034
$785$	−2.75450e9	−0.203235
$786$	0	0
$787$	5.14294e9	0.376097	0.188048	−	0.982160i	$-0.439784\pi$
$787$	5.14294e9	0.376097	0.188048	+	0.982160i	$0.439784\pi$
$788$	−3.92984e8	−0.0286110
$789$	0	0
$790$	−2.96445e10	−2.13919
$791$	2.66508e9	0.191466
$792$	0	0
$793$	−1.73339e10	−1.23435
$794$	1.44879e10	1.02715
$795$	0	0
$796$	1.51925e6	0.000106766 0
$797$	−2.31164e10	−1.61739	−0.808697	−	0.588225i	$-0.799827\pi$
$797$	−2.31164e10	−1.61739	−0.808697	+	0.588225i	$0.799827\pi$
$798$	0	0
$799$	−2.00948e9	−0.139371
$800$	1.55250e9	0.107206
$801$	0	0
$802$	−2.43580e10	−1.66737
$803$	−1.81843e10	−1.23934
$804$	0	0
$805$	−4.50547e9	−0.304407
$806$	−1.74059e9	−0.117091
$807$	0	0
$808$	−1.50395e9	−0.100298
$809$	−2.29952e10	−1.52692	−0.763462	−	0.645853i	$-0.776502\pi$
$809$	−2.29952e10	−1.52692	−0.763462	+	0.645853i	$0.776502\pi$
$810$	0	0
$811$	−2.76002e9	−0.181694	−0.0908468	−	0.995865i	$-0.528957\pi$
$811$	−2.76002e9	−0.181694	−0.0908468	+	0.995865i	$0.528957\pi$
$812$	2.90645e8	0.0190510
$813$	0	0
$814$	−9.75985e8	−0.0634246
$815$	−7.61407e9	−0.492680
$816$	0	0
$817$	−2.23747e10	−1.43542
$818$	−2.43153e10	−1.55326
$819$	0	0
$820$	−2.08301e9	−0.131930
$821$	−5.67826e9	−0.358108	−0.179054	−	0.983839i	$-0.557304\pi$
$821$	−5.67826e9	−0.358108	−0.179054	+	0.983839i	$0.557304\pi$
$822$	0	0
$823$	−2.56662e7	−0.00160495	−0.000802475	−	1.00000i	$-0.500255\pi$
$823$	−2.56662e7	−0.00160495	−0.000802475		1.00000i	$0.500255\pi$
$824$	−1.38186e10	−0.860437
$825$	0	0
$826$	−5.08670e8	−0.0314055
$827$	2.08817e10	1.28380	0.641899	−	0.766789i	$-0.278147\pi$
$827$	2.08817e10	1.28380	0.641899	+	0.766789i	$0.278147\pi$
$828$	0	0
$829$	−2.54198e10	−1.54964	−0.774821	−	0.632180i	$-0.782160\pi$
$829$	−2.54198e10	−1.54964	−0.774821	+	0.632180i	$0.782160\pi$
$830$	−9.70767e9	−0.589307
$831$	0	0
$832$	−2.50525e10	−1.50807
$833$	2.87344e10	1.72244
$834$	0	0
$835$	6.83412e9	0.406237
$836$	−1.00179e9	−0.0593003
$837$	0	0
$838$	−8.74999e9	−0.513634
$839$	3.56300e9	0.208281	0.104140	−	0.994563i	$-0.466791\pi$
$839$	3.56300e9	0.208281	0.104140	+	0.994563i	$0.466791\pi$
$840$	0	0
$841$	2.68130e10	1.55439
$842$	2.12325e9	0.122577
$843$	0	0
$844$	−1.32592e9	−0.0759132
$845$	3.90165e10	2.22459
$846$	0	0
$847$	1.12230e9	0.0634627
$848$	−5.07423e9	−0.285749
$849$	0	0
$850$	3.54498e10	1.97992
$851$	−8.89873e8	−0.0494965
$852$	0	0
$853$	2.29229e10	1.26458	0.632291	−	0.774731i	$-0.282115\pi$
$853$	2.29229e10	1.26458	0.632291	+	0.774731i	$0.282115\pi$
$854$	−3.39380e9	−0.186459
$855$	0	0
$856$	2.76392e10	1.50615
$857$	1.48684e10	0.806924	0.403462	−	0.914996i	$-0.367807\pi$
$857$	1.48684e10	0.806924	0.403462	+	0.914996i	$0.367807\pi$
$858$	0	0
$859$	−2.17432e10	−1.17043	−0.585217	−	0.810877i	$-0.698991\pi$
$859$	−2.17432e10	−1.17043	−0.585217	+	0.810877i	$0.698991\pi$
$860$	1.87290e9	0.100408
$861$	0	0
$862$	3.16004e9	0.168042
$863$	1.50753e10	0.798414	0.399207	−	0.916861i	$-0.369285\pi$
$863$	1.50753e10	0.798414	0.399207	+	0.916861i	$0.369285\pi$
$864$	0	0
$865$	3.23948e9	0.170184
$866$	1.05169e10	0.550269
$867$	0	0
$868$	−1.64286e7	−0.000852671 0
$869$	3.17009e10	1.63871
$870$	0	0
$871$	−3.86085e10	−1.97979
$872$	3.59953e10	1.83839
$873$	0	0
$874$	−1.89474e10	−0.959977
$875$	3.97024e8	0.0200350
$876$	0	0
$877$	−1.29162e10	−0.646598	−0.323299	−	0.946297i	$-0.604792\pi$
$877$	−1.29162e10	−0.646598	−0.323299	+	0.946297i	$0.604792\pi$
$878$	7.58858e8	0.0378381
$879$	0	0
$880$	−3.42603e10	−1.69473
$881$	2.47400e10	1.21895	0.609473	−	0.792807i	$-0.291381\pi$
$881$	2.47400e10	1.21895	0.609473	+	0.792807i	$0.291381\pi$
$882$	0	0
$883$	2.21032e10	1.08042	0.540211	−	0.841530i	$-0.318345\pi$
$883$	2.21032e10	1.08042	0.540211	+	0.841530i	$0.318345\pi$
$884$	3.02922e9	0.147485
$885$	0	0
$886$	3.01569e10	1.45670
$887$	8.79294e9	0.423060	0.211530	−	0.977372i	$-0.432155\pi$
$887$	8.79294e9	0.423060	0.211530	+	0.977372i	$0.432155\pi$
$888$	0	0
$889$	−3.70452e9	−0.176838
$890$	6.68156e9	0.317697
$891$	0	0
$892$	1.58227e9	0.0746455
$893$	−1.69006e9	−0.0794188
$894$	0	0
$895$	−2.00531e10	−0.934976
$896$	−5.41787e9	−0.251623
$897$	0	0
$898$	2.93239e10	1.35131
$899$	−2.49064e9	−0.114328
$900$	0	0
$901$	−1.09148e10	−0.497141
$902$	4.62068e10	2.09644
$903$	0	0
$904$	1.75847e10	0.791671
$905$	2.83747e10	1.27251
$906$	0	0
$907$	−6.78075e8	−0.0301753	−0.0150877	−	0.999886i	$-0.504803\pi$
$907$	−6.78075e8	−0.0301753	−0.0150877	+	0.999886i	$0.504803\pi$
$908$	1.15019e9	0.0509882
$909$	0	0
$910$	1.25668e10	0.552817
$911$	−1.87905e10	−0.823424	−0.411712	−	0.911314i	$-0.635069\pi$
$911$	−1.87905e10	−0.823424	−0.411712	+	0.911314i	$0.635069\pi$
$912$	0	0
$913$	1.03811e10	0.451434
$914$	1.47148e10	0.637443
$915$	0	0
$916$	1.41058e9	0.0606407
$917$	2.90990e9	0.124619
$918$	0	0
$919$	3.67497e10	1.56189	0.780943	−	0.624603i	$-0.214739\pi$
$919$	3.67497e10	1.56189	0.780943	+	0.624603i	$0.214739\pi$
$920$	−2.97279e10	−1.25866
$921$	0	0
$922$	7.16352e9	0.301001
$923$	−5.94939e10	−2.49039
$924$	0	0
$925$	1.40026e9	0.0581720
$926$	−2.05128e10	−0.848957
$927$	0	0
$928$	3.93777e9	0.161746
$929$	−5.36643e9	−0.219599	−0.109800	−	0.993954i	$-0.535021\pi$
$929$	−5.36643e9	−0.219599	−0.109800	+	0.993954i	$0.535021\pi$
$930$	0	0
$931$	2.41669e10	0.981515
$932$	2.12524e9	0.0859907
$933$	0	0
$934$	2.42599e10	0.974262
$935$	−7.36948e10	−2.94847
$936$	0	0
$937$	−2.19515e10	−0.871717	−0.435859	−	0.900015i	$-0.643555\pi$
$937$	−2.19515e10	−0.871717	−0.435859	+	0.900015i	$0.643555\pi$
$938$	−7.55918e9	−0.299064
$939$	0	0
$940$	1.41469e8	0.00555537
$941$	−2.82488e10	−1.10519	−0.552595	−	0.833450i	$-0.686362\pi$
$941$	−2.82488e10	−1.10519	−0.552595	+	0.833450i	$0.686362\pi$
$942$	0	0
$943$	4.21299e10	1.63606
$944$	−3.52673e9	−0.136449
$945$	0	0
$946$	−4.15459e10	−1.59554
$947$	−2.51489e10	−0.962264	−0.481132	−	0.876648i	$-0.659774\pi$
$947$	−2.51489e10	−0.962264	−0.481132	+	0.876648i	$0.659774\pi$
$948$	0	0
$949$	4.62452e10	1.75645
$950$	2.98149e10	1.12824
$951$	0	0
$952$	−1.11168e10	−0.417589
$953$	4.09484e10	1.53254	0.766269	−	0.642519i	$-0.222111\pi$
$953$	4.09484e10	1.53254	0.766269	+	0.642519i	$0.222111\pi$
$954$	0	0
$955$	5.62453e10	2.08966
$956$	−1.81177e9	−0.0670656
$957$	0	0
$958$	−8.37249e9	−0.307663
$959$	3.57325e9	0.130827
$960$	0	0
$961$	−2.73718e10	−0.994883
$962$	2.48207e9	0.0898879
$963$	0	0
$964$	2.48483e9	0.0893360
$965$	−2.33334e10	−0.835858
$966$	0	0
$967$	−5.25463e10	−1.86874	−0.934372	−	0.356299i	$-0.884038\pi$
$967$	−5.25463e10	−1.86874	−0.934372	+	0.356299i	$0.884038\pi$
$968$	7.40517e9	0.262404
$969$	0	0
$970$	2.98947e10	1.05170
$971$	2.49973e9	0.0876246	0.0438123	−	0.999040i	$-0.486050\pi$
$971$	2.49973e9	0.0876246	0.0438123	+	0.999040i	$0.486050\pi$
$972$	0	0
$973$	2.50081e9	0.0870332
$974$	−2.93482e10	−1.01771
$975$	0	0
$976$	−2.35300e10	−0.810118
$977$	2.71796e10	0.932420	0.466210	−	0.884674i	$-0.345619\pi$
$977$	2.71796e10	0.932420	0.466210	+	0.884674i	$0.345619\pi$
$978$	0	0
$979$	−7.14505e9	−0.243369
$980$	−2.02292e9	−0.0686573
$981$	0	0
$982$	4.66316e10	1.57141
$983$	−3.97905e9	−0.133611	−0.0668055	−	0.997766i	$-0.521281\pi$
$983$	−3.97905e9	−0.133611	−0.0668055	+	0.997766i	$0.521281\pi$
$984$	0	0
$985$	−2.43138e10	−0.810635
$986$	8.99150e10	2.98719
$987$	0	0
$988$	2.54771e9	0.0840427
$989$	−3.78802e10	−1.24516
$990$	0	0
$991$	−2.12813e9	−0.0694610	−0.0347305	−	0.999397i	$-0.511057\pi$
$991$	−2.12813e9	−0.0694610	−0.0347305	+	0.999397i	$0.511057\pi$
$992$	−2.22581e8	−0.00723931
$993$	0	0
$994$	−1.16483e10	−0.376194
$995$	9.39956e7	0.00302501
$996$	0	0
$997$	−1.59834e8	−0.00510784	−0.00255392	−	0.999997i	$-0.500813\pi$
$997$	−1.59834e8	−0.00510784	−0.00255392	+	0.999997i	$0.500813\pi$
$998$	1.40932e10	0.448800
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.5		17
3.2	odd	2		177.8.a.c.1.13	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.13	✓	17	3.2	odd	2
531.8.a.c.1.5		17	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	531.a (trivial)

\(f(q)\)	\(=\)	\(q-11.5967 q^{2} +6.48306 q^{4} +401.104 q^{5} +213.573 q^{7} +1409.19 q^{8} +O(q^{10})\)	\(q-11.5967 q^{2} +6.48306 q^{4} +401.104 q^{5} +213.573 q^{7} +1409.19 q^{8} -4651.48 q^{10} +4974.14 q^{11} -12649.9 q^{13} -2476.74 q^{14} -17171.8 q^{16} -36937.0 q^{17} -31065.7 q^{19} +2600.38 q^{20} -57683.5 q^{22} -52594.0 q^{23} +82759.6 q^{25} +146697. q^{26} +1384.61 q^{28} +209912. q^{29} -11865.2 q^{31} +18759.2 q^{32} +428347. q^{34} +85665.0 q^{35} +16919.7 q^{37} +360259. q^{38} +565233. q^{40} -801040. q^{41} +720238. q^{43} +32247.7 q^{44} +609916. q^{46} +54403.0 q^{47} -777930. q^{49} -959737. q^{50} -82010.4 q^{52} +295498. q^{53} +1.99515e6 q^{55} +300965. q^{56} -2.43428e6 q^{58} +205379. q^{59} +1.37027e6 q^{61} +137597. q^{62} +1.98045e6 q^{64} -5.07395e6 q^{65} +3.05207e6 q^{67} -239465. q^{68} -993430. q^{70} +4.70310e6 q^{71} -3.65576e6 q^{73} -196212. q^{74} -201401. q^{76} +1.06234e6 q^{77} +6.37313e6 q^{79} -6.88768e6 q^{80} +9.28941e6 q^{82} +2.08701e6 q^{83} -1.48156e7 q^{85} -8.35238e6 q^{86} +7.00953e6 q^{88} -1.43644e6 q^{89} -2.70169e6 q^{91} -340970. q^{92} -630894. q^{94} -1.24606e7 q^{95} -6.42693e6 q^{97} +9.02140e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8} + 6521 q^{10} + 1764 q^{11} + 18192 q^{13} + 7827 q^{14} + 139226 q^{16} + 15507 q^{17} + 52083 q^{19} - 721 q^{20} - 234434 q^{22} - 63823 q^{23} + 202153 q^{25} + 367956 q^{26} + 182306 q^{28} + 502955 q^{29} + 347531 q^{31} + 243908 q^{32} - 330872 q^{34} - 92641 q^{35} + 447615 q^{37} - 775669 q^{38} + 2203270 q^{40} - 940335 q^{41} + 478562 q^{43} + 596924 q^{44} - 3078663 q^{46} - 703121 q^{47} + 1895082 q^{49} + 876967 q^{50} + 6278296 q^{52} + 1005974 q^{53} + 5212846 q^{55} - 3425294 q^{56} + 6710166 q^{58} + 3491443 q^{59} + 11510749 q^{61} - 5996234 q^{62} + 29496941 q^{64} - 11094180 q^{65} + 14007144 q^{67} - 19688159 q^{68} + 30909708 q^{70} - 5229074 q^{71} + 5452211 q^{73} - 12819662 q^{74} + 41929340 q^{76} - 9930777 q^{77} + 15275654 q^{79} - 36576105 q^{80} + 32025935 q^{82} - 7826609 q^{83} + 11836945 q^{85} - 51649136 q^{86} + 30223741 q^{88} + 6436185 q^{89} + 11633535 q^{91} - 43357972 q^{92} - 4494252 q^{94} - 23741055 q^{95} + 26377540 q^{97} - 26517816 q^{98}+O(q^{100}) \) 17 * q - 2 * q^2 + 1166 * q^4 + 318 * q^5 + 3145 * q^7 - 2355 * q^8 + 6521 * q^10 + 1764 * q^11 + 18192 * q^13 + 7827 * q^14 + 139226 * q^16 + 15507 * q^17 + 52083 * q^19 - 721 * q^20 - 234434 * q^22 - 63823 * q^23 + 202153 * q^25 + 367956 * q^26 + 182306 * q^28 + 502955 * q^29 + 347531 * q^31 + 243908 * q^32 - 330872 * q^34 - 92641 * q^35 + 447615 * q^37 - 775669 * q^38 + 2203270 * q^40 - 940335 * q^41 + 478562 * q^43 + 596924 * q^44 - 3078663 * q^46 - 703121 * q^47 + 1895082 * q^49 + 876967 * q^50 + 6278296 * q^52 + 1005974 * q^53 + 5212846 * q^55 - 3425294 * q^56 + 6710166 * q^58 + 3491443 * q^59 + 11510749 * q^61 - 5996234 * q^62 + 29496941 * q^64 - 11094180 * q^65 + 14007144 * q^67 - 19688159 * q^68 + 30909708 * q^70 - 5229074 * q^71 + 5452211 * q^73 - 12819662 * q^74 + 41929340 * q^76 - 9930777 * q^77 + 15275654 * q^79 - 36576105 * q^80 + 32025935 * q^82 - 7826609 * q^83 + 11836945 * q^85 - 51649136 * q^86 + 30223741 * q^88 + 6436185 * q^89 + 11633535 * q^91 - 43357972 * q^92 - 4494252 * q^94 - 23741055 * q^95 + 26377540 * q^97 - 26517816 * q^98

Introduction

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