LMFDB - Embedded newform 531.8.a.c.1.6

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			1.6
Root			$9.14085$ 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)

$f(q)$	$=$	$q-9.14085 q^{2} -44.4448 q^{4} +27.9722 q^{5} -1415.76 q^{7} +1576.29 q^{8} +O(q^{10})$	\(q-9.14085 q^{2} -44.4448 q^{4} +27.9722 q^{5} -1415.76 q^{7} +1576.29 q^{8} -255.690 q^{10} +4887.09 q^{11} -5210.02 q^{13} +12941.3 q^{14} -8719.72 q^{16} -5796.28 q^{17} +24940.5 q^{19} -1243.22 q^{20} -44672.2 q^{22} +63003.2 q^{23} -77342.6 q^{25} +47624.1 q^{26} +62923.2 q^{28} -86556.7 q^{29} +268352. q^{31} -122060. q^{32} +52983.0 q^{34} -39601.9 q^{35} -235277. q^{37} -227977. q^{38} +44092.3 q^{40} +585710. q^{41} -806765. q^{43} -217206. q^{44} -575903. q^{46} -557072. q^{47} +1.18083e6 q^{49} +706977. q^{50} +231559. q^{52} -2.07376e6 q^{53} +136703. q^{55} -2.23165e6 q^{56} +791202. q^{58} +205379. q^{59} -1.17120e6 q^{61} -2.45297e6 q^{62} +2.23185e6 q^{64} -145736. q^{65} +4.57510e6 q^{67} +257615. q^{68} +361995. q^{70} -798821. q^{71} -2.35826e6 q^{73} +2.15063e6 q^{74} -1.10847e6 q^{76} -6.91895e6 q^{77} +117864. q^{79} -243910. q^{80} -5.35389e6 q^{82} -2.44537e6 q^{83} -162135. q^{85} +7.37452e6 q^{86} +7.70349e6 q^{88} +5.83686e6 q^{89} +7.37614e6 q^{91} -2.80017e6 q^{92} +5.09211e6 q^{94} +697640. q^{95} -6.38002e6 q^{97} -1.07938e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.14085	−0.807945	−0.403972	−	0.914771i	$-0.632371\pi$
$2$	−9.14085	−0.807945	−0.403972	+	0.914771i	$0.632371\pi$
$3$	0	0
$3$	0	0
$4$	−44.4448	−0.347225
$5$	27.9722	0.100076	0.0500382	−	0.998747i	$-0.484066\pi$
$5$	27.9722	0.100076	0.0500382	+	0.998747i	$0.484066\pi$
$6$	0	0
$7$	−1415.76	−1.56008	−0.780040	−	0.625730i	$-0.784801\pi$
$7$	−1415.76	−1.56008	−0.780040	+	0.625730i	$0.784801\pi$
$8$	1576.29	1.08848
$9$	0	0
$10$	−255.690	−0.0808562
$11$	4887.09	1.10707	0.553536	−	0.832825i	$-0.313278\pi$
$11$	4887.09	1.10707	0.553536	+	0.832825i	$0.313278\pi$
$12$	0	0
$13$	−5210.02	−0.657715	−0.328858	−	0.944380i	$-0.606664\pi$
$13$	−5210.02	−0.657715	−0.328858	+	0.944380i	$0.606664\pi$
$14$	12941.3	1.26046
$15$	0	0
$16$	−8719.72	−0.532210
$17$	−5796.28	−0.286140	−0.143070	−	0.989713i	$-0.545697\pi$
$17$	−5796.28	−0.286140	−0.143070	+	0.989713i	$0.545697\pi$
$18$	0	0
$19$	24940.5	0.834194	0.417097	−	0.908862i	$-0.363048\pi$
$19$	24940.5	0.834194	0.417097	+	0.908862i	$0.363048\pi$
$20$	−1243.22	−0.0347490
$21$	0	0
$22$	−44672.2	−0.894454
$23$	63003.2	1.07973	0.539865	−	0.841751i	$-0.318475\pi$
$23$	63003.2	1.07973	0.539865	+	0.841751i	$0.318475\pi$
$24$	0	0
$25$	−77342.6	−0.989985
$26$	47624.1	0.531398
$27$	0	0
$28$	62923.2	0.541699
$29$	−86556.7	−0.659034	−0.329517	−	0.944150i	$-0.606886\pi$
$29$	−86556.7	−0.659034	−0.329517	+	0.944150i	$0.606886\pi$
$30$	0	0
$31$	268352.	1.61785	0.808927	−	0.587909i	$-0.200049\pi$
$31$	268352.	1.61785	0.808927	+	0.587909i	$0.200049\pi$
$32$	−122060.	−0.658488
$33$	0	0
$34$	52983.0	0.231185
$35$	−39601.9	−0.156127
$36$	0	0
$37$	−235277.	−0.763614	−0.381807	−	0.924242i	$-0.624698\pi$
$37$	−235277.	−0.763614	−0.381807	+	0.924242i	$0.624698\pi$
$38$	−227977.	−0.673983
$39$	0	0
$40$	44092.3	0.108931
$41$	585710.	1.32721	0.663605	−	0.748083i	$-0.269026\pi$
$41$	585710.	1.32721	0.663605	+	0.748083i	$0.269026\pi$
$42$	0	0
$43$	−806765.	−1.54742	−0.773709	−	0.633541i	$-0.781601\pi$
$43$	−806765.	−1.54742	−0.773709	+	0.633541i	$0.781601\pi$
$44$	−217206.	−0.384403
$45$	0	0
$46$	−575903.	−0.872363
$47$	−557072.	−0.782652	−0.391326	−	0.920252i	$-0.627984\pi$
$47$	−557072.	−0.782652	−0.391326	+	0.920252i	$0.627984\pi$
$48$	0	0
$49$	1.18083e6	1.43385
$50$	706977.	0.799853
$51$	0	0
$52$	231559.	0.228375
$53$	−2.07376e6	−1.91334	−0.956671	−	0.291170i	$-0.905955\pi$
$53$	−2.07376e6	−1.91334	−0.956671	+	0.291170i	$0.905955\pi$
$54$	0	0
$55$	136703.	0.110792
$56$	−2.23165e6	−1.69812
$57$	0	0
$58$	791202.	0.532463
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−1.17120e6	−0.660656	−0.330328	−	0.943866i	$-0.607159\pi$
$61$	−1.17120e6	−0.660656	−0.330328	+	0.943866i	$0.607159\pi$
$62$	−2.45297e6	−1.30714
$63$	0	0
$64$	2.23185e6	1.06423
$65$	−145736.	−0.0658217
$66$	0	0
$67$	4.57510e6	1.85840	0.929199	−	0.369579i	$-0.120498\pi$
$67$	4.57510e6	1.85840	0.929199	+	0.369579i	$0.120498\pi$
$68$	257615.	0.0993549
$69$	0	0
$70$	361995.	0.126142
$71$	−798821.	−0.264878	−0.132439	−	0.991191i	$-0.542281\pi$
$71$	−798821.	−0.264878	−0.132439	+	0.991191i	$0.542281\pi$
$72$	0	0
$73$	−2.35826e6	−0.709516	−0.354758	−	0.934958i	$-0.615437\pi$
$73$	−2.35826e6	−0.709516	−0.354758	+	0.934958i	$0.615437\pi$
$74$	2.15063e6	0.616958
$75$	0	0
$76$	−1.10847e6	−0.289653
$77$	−6.91895e6	−1.72712
$78$	0	0
$79$	117864.	0.0268958	0.0134479	−	0.999910i	$-0.495719\pi$
$79$	117864.	0.0268958	0.0134479	+	0.999910i	$0.495719\pi$
$80$	−243910.	−0.0532616
$81$	0	0
$82$	−5.35389e6	−1.07231
$83$	−2.44537e6	−0.469431	−0.234715	−	0.972064i	$-0.575416\pi$
$83$	−2.44537e6	−0.469431	−0.234715	+	0.972064i	$0.575416\pi$
$84$	0	0
$85$	−162135.	−0.0286358
$86$	7.37452e6	1.25023
$87$	0	0
$88$	7.70349e6	1.20503
$89$	5.83686e6	0.877636	0.438818	−	0.898576i	$-0.355397\pi$
$89$	5.83686e6	0.877636	0.438818	+	0.898576i	$0.355397\pi$
$90$	0	0
$91$	7.37614e6	1.02609
$92$	−2.80017e6	−0.374910
$93$	0	0
$94$	5.09211e6	0.632340
$95$	697640.	0.0834831
$96$	0	0
$97$	−6.38002e6	−0.709776	−0.354888	−	0.934909i	$-0.615481\pi$
$97$	−6.38002e6	−0.709776	−0.354888	+	0.934909i	$0.615481\pi$
$98$	−1.07938e7	−1.15847
$99$	0	0
$100$	3.43748e6	0.343748
$101$	1.63929e7	1.58319	0.791593	−	0.611048i	$-0.209252\pi$
$101$	1.63929e7	1.58319	0.791593	+	0.611048i	$0.209252\pi$
$102$	0	0
$103$	−1.41494e7	−1.27587	−0.637935	−	0.770090i	$-0.720211\pi$
$103$	−1.41494e7	−1.27587	−0.637935	+	0.770090i	$0.720211\pi$
$104$	−8.21252e6	−0.715912
$105$	0	0
$106$	1.89559e7	1.54588
$107$	−1.58657e7	−1.25204	−0.626019	−	0.779808i	$-0.715317\pi$
$107$	−1.58657e7	−1.25204	−0.626019	+	0.779808i	$0.715317\pi$
$108$	0	0
$109$	−8.25579e6	−0.610613	−0.305307	−	0.952254i	$-0.598759\pi$
$109$	−8.25579e6	−0.610613	−0.305307	+	0.952254i	$0.598759\pi$
$110$	−1.24958e6	−0.0895136
$111$	0	0
$112$	1.23450e7	0.830289
$113$	−2.60775e7	−1.70016	−0.850082	−	0.526651i	$-0.823448\pi$
$113$	−2.60775e7	−1.70016	−0.850082	+	0.526651i	$0.823448\pi$
$114$	0	0
$115$	1.76234e6	0.108055
$116$	3.84700e6	0.228833
$117$	0	0
$118$	−1.87734e6	−0.105185
$119$	8.20615e6	0.446401
$120$	0	0
$121$	4.39649e6	0.225610
$122$	1.07057e7	0.533774
$123$	0	0
$124$	−1.19269e7	−0.561760
$125$	−4.34877e6	−0.199150
$126$	0	0
$127$	1.28036e7	0.554649	0.277325	−	0.960776i	$-0.410552\pi$
$127$	1.28036e7	0.554649	0.277325	+	0.960776i	$0.410552\pi$
$128$	−4.77741e6	−0.201353
$129$	0	0
$130$	1.33215e6	0.0531803
$131$	−2.45517e6	−0.0954184	−0.0477092	−	0.998861i	$-0.515192\pi$
$131$	−2.45517e6	−0.0954184	−0.0477092	+	0.998861i	$0.515192\pi$
$132$	0	0
$133$	−3.53097e7	−1.30141
$134$	−4.18203e7	−1.50148
$135$	0	0
$136$	−9.13664e6	−0.311459
$137$	1.15632e7	0.384198	0.192099	−	0.981376i	$-0.438471\pi$
$137$	1.15632e7	0.384198	0.192099	+	0.981376i	$0.438471\pi$
$138$	0	0
$139$	−1.38898e7	−0.438678	−0.219339	−	0.975649i	$-0.570390\pi$
$139$	−1.38898e7	−0.438678	−0.219339	+	0.975649i	$0.570390\pi$
$140$	1.76010e6	0.0542112
$141$	0	0
$142$	7.30191e6	0.214007
$143$	−2.54619e7	−0.728139
$144$	0	0
$145$	−2.42118e6	−0.0659537
$146$	2.15565e7	0.573250
$147$	0	0
$148$	1.04569e7	0.265146
$149$	−6.33739e6	−0.156949	−0.0784745	−	0.996916i	$-0.525005\pi$
$149$	−6.33739e6	−0.156949	−0.0784745	+	0.996916i	$0.525005\pi$
$150$	0	0
$151$	−6.02966e6	−0.142519	−0.0712596	−	0.997458i	$-0.522702\pi$
$151$	−6.02966e6	−0.142519	−0.0712596	+	0.997458i	$0.522702\pi$
$152$	3.93135e7	0.908007
$153$	0	0
$154$	6.32451e7	1.39542
$155$	7.50640e6	0.161909
$156$	0	0
$157$	3.30649e6	0.0681896	0.0340948	−	0.999419i	$-0.489145\pi$
$157$	3.30649e6	0.0681896	0.0340948	+	0.999419i	$0.489145\pi$
$158$	−1.07737e6	−0.0217303
$159$	0	0
$160$	−3.41428e6	−0.0658990
$161$	−8.91975e7	−1.68447
$162$	0	0
$163$	3.35536e7	0.606851	0.303425	−	0.952855i	$-0.401870\pi$
$163$	3.35536e7	0.606851	0.303425	+	0.952855i	$0.401870\pi$
$164$	−2.60318e7	−0.460840
$165$	0	0
$166$	2.23528e7	0.379274
$167$	−4.17102e7	−0.693002	−0.346501	−	0.938050i	$-0.612630\pi$
$167$	−4.17102e7	−0.693002	−0.346501	+	0.938050i	$0.612630\pi$
$168$	0	0
$169$	−3.56042e7	−0.567411
$170$	1.48205e6	0.0231362
$171$	0	0
$172$	3.58565e7	0.537302
$173$	9.03552e7	1.32676	0.663379	−	0.748284i	$-0.269122\pi$
$173$	9.03552e7	1.32676	0.663379	+	0.748284i	$0.269122\pi$
$174$	0	0
$175$	1.09499e8	1.54445
$176$	−4.26141e7	−0.589195
$177$	0	0
$178$	−5.33539e7	−0.709081
$179$	2.78323e6	0.0362713	0.0181357	−	0.999836i	$-0.494227\pi$
$179$	2.78323e6	0.0362713	0.0181357	+	0.999836i	$0.494227\pi$
$180$	0	0
$181$	−1.28005e8	−1.60455	−0.802274	−	0.596955i	$-0.796377\pi$
$181$	−1.28005e8	−1.60455	−0.802274	+	0.596955i	$0.796377\pi$
$182$	−6.74243e7	−0.829022
$183$	0	0
$184$	9.93115e7	1.17527
$185$	−6.58122e6	−0.0764197
$186$	0	0
$187$	−2.83270e7	−0.316778
$188$	2.47590e7	0.271757
$189$	0	0
$190$	−6.37702e6	−0.0674497
$191$	1.75929e8	1.82693	0.913464	−	0.406920i	$-0.133397\pi$
$191$	1.75929e8	1.82693	0.913464	+	0.406920i	$0.133397\pi$
$192$	0	0
$193$	−9.04189e7	−0.905333	−0.452667	−	0.891680i	$-0.649527\pi$
$193$	−9.04189e7	−0.905333	−0.452667	+	0.891680i	$0.649527\pi$
$194$	5.83188e7	0.573460
$195$	0	0
$196$	−5.24820e7	−0.497868
$197$	7.90918e7	0.737055	0.368527	−	0.929617i	$-0.379862\pi$
$197$	7.90918e7	0.737055	0.368527	+	0.929617i	$0.379862\pi$
$198$	0	0
$199$	1.80077e8	1.61985	0.809923	−	0.586537i	$-0.199509\pi$
$199$	1.80077e8	1.61985	0.809923	+	0.586537i	$0.199509\pi$
$200$	−1.21915e8	−1.07758
$201$	0	0
$202$	−1.49845e8	−1.27913
$203$	1.22544e8	1.02814
$204$	0	0
$205$	1.63836e7	0.132822
$206$	1.29337e8	1.03083
$207$	0	0
$208$	4.54300e7	0.350042
$209$	1.21886e8	0.923513
$210$	0	0
$211$	2.21867e8	1.62594	0.812968	−	0.582308i	$-0.197850\pi$
$211$	2.21867e8	1.62594	0.812968	+	0.582308i	$0.197850\pi$
$212$	9.21678e7	0.664361
$213$	0	0
$214$	1.45026e8	1.01158
$215$	−2.25670e7	−0.154860
$216$	0	0
$217$	−3.79923e8	−2.52398
$218$	7.54650e7	0.493342
$219$	0	0
$220$	−6.07572e6	−0.0384697
$221$	3.01988e7	0.188199
$222$	0	0
$223$	2.20216e8	1.32978	0.664892	−	0.746940i	$-0.268478\pi$
$223$	2.20216e8	1.32978	0.664892	+	0.746940i	$0.268478\pi$
$224$	1.72807e8	1.02729
$225$	0	0
$226$	2.38370e8	1.37364
$227$	−1.55341e8	−0.881444	−0.440722	−	0.897644i	$-0.645277\pi$
$227$	−1.55341e8	−0.881444	−0.440722	+	0.897644i	$0.645277\pi$
$228$	0	0
$229$	−2.23695e8	−1.23093	−0.615464	−	0.788165i	$-0.711031\pi$
$229$	−2.23695e8	−1.23093	−0.615464	+	0.788165i	$0.711031\pi$
$230$	−1.61093e7	−0.0873029
$231$	0	0
$232$	−1.36439e8	−0.717347
$233$	−1.96538e8	−1.01789	−0.508946	−	0.860798i	$-0.669965\pi$
$233$	−1.96538e8	−1.01789	−0.508946	+	0.860798i	$0.669965\pi$
$234$	0	0
$235$	−1.55825e7	−0.0783250
$236$	−9.12803e6	−0.0452049
$237$	0	0
$238$	−7.50112e7	−0.360667
$239$	3.22046e8	1.52589	0.762947	−	0.646461i	$-0.223752\pi$
$239$	3.22046e8	1.52589	0.762947	+	0.646461i	$0.223752\pi$
$240$	0	0
$241$	1.17931e8	0.542711	0.271355	−	0.962479i	$-0.412528\pi$
$241$	1.17931e8	0.542711	0.271355	+	0.962479i	$0.412528\pi$
$242$	−4.01877e7	−0.182280
$243$	0	0
$244$	5.20536e7	0.229396
$245$	3.30305e7	0.143494
$246$	0	0
$247$	−1.29940e8	−0.548662
$248$	4.23002e8	1.76101
$249$	0	0
$250$	3.97514e7	0.160903
$251$	4.16401e8	1.66209	0.831043	−	0.556208i	$-0.187744\pi$
$251$	4.16401e8	1.66209	0.831043	+	0.556208i	$0.187744\pi$
$252$	0	0
$253$	3.07903e8	1.19534
$254$	−1.17036e8	−0.448126
$255$	0	0
$256$	−2.42008e8	−0.901549
$257$	−3.87165e8	−1.42276	−0.711378	−	0.702810i	$-0.751928\pi$
$257$	−3.87165e8	−1.42276	−0.711378	+	0.702810i	$0.751928\pi$
$258$	0	0
$259$	3.33096e8	1.19130
$260$	6.47720e6	0.0228550
$261$	0	0
$262$	2.24424e7	0.0770928
$263$	1.55540e8	0.527227	0.263613	−	0.964628i	$-0.415086\pi$
$263$	1.55540e8	0.527227	0.263613	+	0.964628i	$0.415086\pi$
$264$	0	0
$265$	−5.80076e7	−0.191480
$266$	3.22761e8	1.05147
$267$	0	0
$268$	−2.03339e8	−0.645283
$269$	−2.06155e8	−0.645743	−0.322872	−	0.946443i	$-0.604648\pi$
$269$	−2.06155e8	−0.645743	−0.322872	+	0.946443i	$0.604648\pi$
$270$	0	0
$271$	2.53618e8	0.774082	0.387041	−	0.922062i	$-0.373497\pi$
$271$	2.53618e8	0.774082	0.387041	+	0.922062i	$0.373497\pi$
$272$	5.05420e7	0.152286
$273$	0	0
$274$	−1.05697e8	−0.310410
$275$	−3.77980e8	−1.09598
$276$	0	0
$277$	5.09014e8	1.43896	0.719482	−	0.694511i	$-0.244379\pi$
$277$	5.09014e8	1.43896	0.719482	+	0.694511i	$0.244379\pi$
$278$	1.26965e8	0.354427
$279$	0	0
$280$	−6.24242e7	−0.169942
$281$	1.26418e8	0.339888	0.169944	−	0.985454i	$-0.445641\pi$
$281$	1.26418e8	0.339888	0.169944	+	0.985454i	$0.445641\pi$
$282$	0	0
$283$	2.56537e8	0.672819	0.336409	−	0.941716i	$-0.390787\pi$
$283$	2.56537e8	0.672819	0.336409	+	0.941716i	$0.390787\pi$
$284$	3.55035e7	0.0919722
$285$	0	0
$286$	2.32743e8	0.588296
$287$	−8.29226e8	−2.07055
$288$	0	0
$289$	−3.76742e8	−0.918124
$290$	2.21316e7	0.0532869
$291$	0	0
$292$	1.04813e8	0.246362
$293$	−9.81288e7	−0.227908	−0.113954	−	0.993486i	$-0.536352\pi$
$293$	−9.81288e7	−0.227908	−0.113954	+	0.993486i	$0.536352\pi$
$294$	0	0
$295$	5.74490e6	0.0130288
$296$	−3.70866e8	−0.831181
$297$	0	0
$298$	5.79292e7	0.126806
$299$	−3.28248e8	−0.710155
$300$	0	0
$301$	1.14219e9	2.41409
$302$	5.51162e7	0.115148
$303$	0	0
$304$	−2.17474e8	−0.443966
$305$	−3.27609e7	−0.0661160
$306$	0	0
$307$	4.01381e8	0.791722	0.395861	−	0.918311i	$-0.370446\pi$
$307$	4.01381e8	0.791722	0.395861	+	0.918311i	$0.370446\pi$
$308$	3.07512e8	0.599700
$309$	0	0
$310$	−6.86149e7	−0.130813
$311$	9.27378e8	1.74822	0.874109	−	0.485730i	$-0.161446\pi$
$311$	9.27378e8	1.74822	0.874109	+	0.485730i	$0.161446\pi$
$312$	0	0
$313$	8.01269e8	1.47697	0.738487	−	0.674268i	$-0.235541\pi$
$313$	8.01269e8	1.47697	0.738487	+	0.674268i	$0.235541\pi$
$314$	−3.02241e7	−0.0550934
$315$	0	0
$316$	−5.23842e6	−0.00933890
$317$	2.96984e8	0.523632	0.261816	−	0.965118i	$-0.415679\pi$
$317$	2.96984e8	0.523632	0.261816	+	0.965118i	$0.415679\pi$
$318$	0	0
$319$	−4.23011e8	−0.729598
$320$	6.24299e7	0.106504
$321$	0	0
$322$	8.15341e8	1.36095
$323$	−1.44562e8	−0.238696
$324$	0	0
$325$	4.02957e8	0.651128
$326$	−3.06708e8	−0.490302
$327$	0	0
$328$	9.23251e8	1.44465
$329$	7.88681e8	1.22100
$330$	0	0
$331$	4.65841e8	0.706057	0.353029	−	0.935612i	$-0.385152\pi$
$331$	4.65841e8	0.706057	0.353029	+	0.935612i	$0.385152\pi$
$332$	1.08684e8	0.162998
$333$	0	0
$334$	3.81267e8	0.559908
$335$	1.27976e8	0.185982
$336$	0	0
$337$	9.05809e8	1.28924	0.644618	−	0.764505i	$-0.277017\pi$
$337$	9.05809e8	1.28924	0.644618	+	0.764505i	$0.277017\pi$
$338$	3.25453e8	0.458436
$339$	0	0
$340$	7.20605e6	0.00994308
$341$	1.31146e9	1.79108
$342$	0	0
$343$	−5.05839e8	−0.676836
$344$	−1.27170e9	−1.68434
$345$	0	0
$346$	−8.25923e8	−1.07195
$347$	−8.14436e8	−1.04642	−0.523208	−	0.852205i	$-0.675265\pi$
$347$	−8.14436e8	−1.04642	−0.523208	+	0.852205i	$0.675265\pi$
$348$	0	0
$349$	1.34997e9	1.69994	0.849972	−	0.526827i	$-0.176619\pi$
$349$	1.34997e9	1.69994	0.849972	+	0.526827i	$0.176619\pi$
$350$	−1.00091e9	−1.24783
$351$	0	0
$352$	−5.96517e8	−0.728994
$353$	−6.77178e8	−0.819391	−0.409695	−	0.912222i	$-0.634365\pi$
$353$	−6.77178e8	−0.819391	−0.409695	+	0.912222i	$0.634365\pi$
$354$	0	0
$355$	−2.23448e7	−0.0265080
$356$	−2.59418e8	−0.304737
$357$	0	0
$358$	−2.54411e7	−0.0293052
$359$	−7.72908e8	−0.881652	−0.440826	−	0.897592i	$-0.645315\pi$
$359$	−7.72908e8	−0.881652	−0.440826	+	0.897592i	$0.645315\pi$
$360$	0	0
$361$	−2.71844e8	−0.304120
$362$	1.17008e9	1.29639
$363$	0	0
$364$	−3.27831e8	−0.356283
$365$	−6.59658e7	−0.0710058
$366$	0	0
$367$	1.86496e9	1.96942	0.984712	−	0.174192i	$-0.0557312\pi$
$367$	1.86496e9	1.96942	0.984712	+	0.174192i	$0.0557312\pi$
$368$	−5.49371e8	−0.574643
$369$	0	0
$370$	6.01580e7	0.0617429
$371$	2.93595e9	2.98497
$372$	0	0
$373$	1.15094e9	1.14834	0.574171	−	0.818735i	$-0.305324\pi$
$373$	1.15094e9	1.14834	0.574171	+	0.818735i	$0.305324\pi$
$374$	2.58933e8	0.255939
$375$	0	0
$376$	−8.78109e8	−0.851904
$377$	4.50962e8	0.433457
$378$	0	0
$379$	8.25715e7	0.0779100	0.0389550	−	0.999241i	$-0.487597\pi$
$379$	8.25715e7	0.0779100	0.0389550	+	0.999241i	$0.487597\pi$
$380$	−3.10065e7	−0.0289874
$381$	0	0
$382$	−1.60814e9	−1.47606
$383$	6.72581e8	0.611714	0.305857	−	0.952077i	$-0.401057\pi$
$383$	6.72581e8	0.611714	0.305857	+	0.952077i	$0.401057\pi$
$384$	0	0
$385$	−1.93538e8	−0.172844
$386$	8.26505e8	0.731459
$387$	0	0
$388$	2.83559e8	0.246452
$389$	9.07409e8	0.781591	0.390795	−	0.920478i	$-0.372200\pi$
$389$	9.07409e8	0.781591	0.390795	+	0.920478i	$0.372200\pi$
$390$	0	0
$391$	−3.65185e8	−0.308954
$392$	1.86134e9	1.56072
$393$	0	0
$394$	−7.22967e8	−0.595500
$395$	3.29690e6	0.00269163
$396$	0	0
$397$	2.34468e9	1.88069	0.940345	−	0.340223i	$-0.110503\pi$
$397$	2.34468e9	1.88069	0.940345	+	0.340223i	$0.110503\pi$
$398$	−1.64606e9	−1.30875
$399$	0	0
$400$	6.74406e8	0.526879
$401$	−1.03275e9	−0.799819	−0.399910	−	0.916555i	$-0.630958\pi$
$401$	−1.03275e9	−0.799819	−0.399910	+	0.916555i	$0.630958\pi$
$402$	0	0
$403$	−1.39812e9	−1.06409
$404$	−7.28581e8	−0.549722
$405$	0	0
$406$	−1.12015e9	−0.830684
$407$	−1.14982e9	−0.845376
$408$	0	0
$409$	−4.25915e8	−0.307816	−0.153908	−	0.988085i	$-0.549186\pi$
$409$	−4.25915e8	−0.307816	−0.153908	+	0.988085i	$0.549186\pi$
$410$	−1.49760e8	−0.107313
$411$	0	0
$412$	6.28865e8	0.443014
$413$	−2.90767e8	−0.203105
$414$	0	0
$415$	−6.84024e7	−0.0469789
$416$	6.35934e8	0.433097
$417$	0	0
$418$	−1.11415e9	−0.746148
$419$	9.70564e8	0.644577	0.322289	−	0.946641i	$-0.395548\pi$
$419$	9.70564e8	0.644577	0.322289	+	0.946641i	$0.395548\pi$
$420$	0	0
$421$	3.26959e6	0.00213553	0.00106777	−	0.999999i	$-0.499660\pi$
$421$	3.26959e6	0.00213553	0.00106777	+	0.999999i	$0.499660\pi$
$422$	−2.02805e9	−1.31367
$423$	0	0
$424$	−3.26885e9	−2.08264
$425$	4.48299e8	0.283274
$426$	0	0
$427$	1.65813e9	1.03068
$428$	7.05150e8	0.434739
$429$	0	0
$430$	2.06281e8	0.125118
$431$	−9.95591e8	−0.598978	−0.299489	−	0.954100i	$-0.596816\pi$
$431$	−9.95591e8	−0.598978	−0.299489	+	0.954100i	$0.596816\pi$
$432$	0	0
$433$	−1.28699e9	−0.761847	−0.380924	−	0.924606i	$-0.624394\pi$
$433$	−1.28699e9	−0.761847	−0.380924	+	0.924606i	$0.624394\pi$
$434$	3.47282e9	2.03924
$435$	0	0
$436$	3.66927e8	0.212020
$437$	1.57133e9	0.900705
$438$	0	0
$439$	5.89758e8	0.332697	0.166348	−	0.986067i	$-0.446802\pi$
$439$	5.89758e8	0.332697	0.166348	+	0.986067i	$0.446802\pi$
$440$	2.15483e8	0.120595
$441$	0	0
$442$	−2.76042e8	−0.152054
$443$	−3.59302e8	−0.196357	−0.0981786	−	0.995169i	$-0.531302\pi$
$443$	−3.59302e8	−0.196357	−0.0981786	+	0.995169i	$0.531302\pi$
$444$	0	0
$445$	1.63270e8	0.0878306
$446$	−2.01296e9	−1.07439
$447$	0	0
$448$	−3.15977e9	−1.66028
$449$	−2.56647e9	−1.33806	−0.669028	−	0.743237i	$-0.733290\pi$
$449$	−2.56647e9	−1.33806	−0.669028	+	0.743237i	$0.733290\pi$
$450$	0	0
$451$	2.86242e9	1.46932
$452$	1.15901e9	0.590340
$453$	0	0
$454$	1.41995e9	0.712158
$455$	2.06327e8	0.102687
$456$	0	0
$457$	−1.46001e9	−0.715565	−0.357782	−	0.933805i	$-0.616467\pi$
$457$	−1.46001e9	−0.715565	−0.357782	+	0.933805i	$0.616467\pi$
$458$	2.04477e9	0.994522
$459$	0	0
$460$	−7.83268e7	−0.0375196
$461$	4.94351e7	0.0235008	0.0117504	−	0.999931i	$-0.496260\pi$
$461$	4.94351e7	0.0235008	0.0117504	+	0.999931i	$0.496260\pi$
$462$	0	0
$463$	−2.80354e9	−1.31272	−0.656361	−	0.754447i	$-0.727905\pi$
$463$	−2.80354e9	−1.31272	−0.656361	+	0.754447i	$0.727905\pi$
$464$	7.54750e8	0.350744
$465$	0	0
$466$	1.79653e9	0.822401
$467$	−2.95995e9	−1.34485	−0.672426	−	0.740164i	$-0.734748\pi$
$467$	−2.95995e9	−1.34485	−0.672426	+	0.740164i	$0.734748\pi$
$468$	0	0
$469$	−6.47725e9	−2.89925
$470$	1.42438e8	0.0632823
$471$	0	0
$472$	3.23737e8	0.141708
$473$	−3.94274e9	−1.71310
$474$	0	0
$475$	−1.92896e9	−0.825839
$476$	−3.64721e8	−0.155002
$477$	0	0
$478$	−2.94377e9	−1.23284
$479$	−2.16259e9	−0.899084	−0.449542	−	0.893259i	$-0.648413\pi$
$479$	−2.16259e9	−0.899084	−0.449542	+	0.893259i	$0.648413\pi$
$480$	0	0
$481$	1.22580e9	0.502241
$482$	−1.07799e9	−0.438480
$483$	0	0
$484$	−1.95401e8	−0.0783374
$485$	−1.78463e8	−0.0710317
$486$	0	0
$487$	−2.92186e9	−1.14633	−0.573163	−	0.819441i	$-0.694284\pi$
$487$	−2.92186e9	−1.14633	−0.573163	+	0.819441i	$0.694284\pi$
$488$	−1.84615e9	−0.719113
$489$	0	0
$490$	−3.01927e8	−0.115935
$491$	−1.26732e9	−0.483171	−0.241585	−	0.970380i	$-0.577667\pi$
$491$	−1.26732e9	−0.483171	−0.241585	+	0.970380i	$0.577667\pi$
$492$	0	0
$493$	5.01707e8	0.188576
$494$	1.18777e9	0.443289
$495$	0	0
$496$	−2.33996e9	−0.861038
$497$	1.13094e9	0.413230
$498$	0	0
$499$	−2.05947e9	−0.742000	−0.371000	−	0.928633i	$-0.620985\pi$
$499$	−2.05947e9	−0.742000	−0.371000	+	0.928633i	$0.620985\pi$
$500$	1.93280e8	0.0691500
$501$	0	0
$502$	−3.80626e9	−1.34287
$503$	−1.28852e9	−0.451443	−0.225721	−	0.974192i	$-0.572474\pi$
$503$	−1.28852e9	−0.451443	−0.225721	+	0.974192i	$0.572474\pi$
$504$	0	0
$505$	4.58546e8	0.158440
$506$	−2.81449e9	−0.965769
$507$	0	0
$508$	−5.69053e8	−0.192588
$509$	−7.14570e7	−0.0240177	−0.0120089	−	0.999928i	$-0.503823\pi$
$509$	−7.14570e7	−0.0240177	−0.0120089	+	0.999928i	$0.503823\pi$
$510$	0	0
$511$	3.33874e9	1.10690
$512$	2.82367e9	0.929755
$513$	0	0
$514$	3.53902e9	1.14951
$515$	−3.95788e8	−0.127684
$516$	0	0
$517$	−2.72246e9	−0.866453
$518$	−3.04478e9	−0.962503
$519$	0	0
$520$	−2.29722e8	−0.0716459
$521$	1.07670e8	0.0333551	0.0166776	−	0.999861i	$-0.494691\pi$
$521$	1.07670e8	0.0333551	0.0166776	+	0.999861i	$0.494691\pi$
$522$	0	0
$523$	1.67231e9	0.511165	0.255582	−	0.966787i	$-0.417733\pi$
$523$	1.67231e9	0.511165	0.255582	+	0.966787i	$0.417733\pi$
$524$	1.09120e8	0.0331317
$525$	0	0
$526$	−1.42177e9	−0.425970
$527$	−1.55545e9	−0.462933
$528$	0	0
$529$	5.64582e8	0.165818
$530$	5.30239e8	0.154706
$531$	0	0
$532$	1.56933e9	0.451882
$533$	−3.05156e9	−0.872926
$534$	0	0
$535$	−4.43800e8	−0.125299
$536$	7.21170e9	2.02284
$537$	0	0
$538$	1.88443e9	0.521725
$539$	5.77085e9	1.58737
$540$	0	0
$541$	1.37337e9	0.372903	0.186452	−	0.982464i	$-0.440301\pi$
$541$	1.37337e9	0.372903	0.186452	+	0.982464i	$0.440301\pi$
$542$	−2.31828e9	−0.625416
$543$	0	0
$544$	7.07493e8	0.188420
$545$	−2.30933e8	−0.0611079
$546$	0	0
$547$	−3.99898e9	−1.04470	−0.522352	−	0.852730i	$-0.674945\pi$
$547$	−3.99898e9	−1.04470	−0.522352	+	0.852730i	$0.674945\pi$
$548$	−5.13923e8	−0.133403
$549$	0	0
$550$	3.45506e9	0.885495
$551$	−2.15877e9	−0.549762
$552$	0	0
$553$	−1.66867e8	−0.0419596
$554$	−4.65282e9	−1.16260
$555$	0	0
$556$	6.17331e8	0.152320
$557$	2.15460e9	0.528291	0.264146	−	0.964483i	$-0.414910\pi$
$557$	2.15460e9	0.528291	0.264146	+	0.964483i	$0.414910\pi$
$558$	0	0
$559$	4.20327e9	1.01776
$560$	3.45318e8	0.0830923
$561$	0	0
$562$	−1.15557e9	−0.274611
$563$	5.78892e9	1.36716	0.683578	−	0.729878i	$-0.260423\pi$
$563$	5.78892e9	1.36716	0.683578	+	0.729878i	$0.260423\pi$
$564$	0	0
$565$	−7.29444e8	−0.170146
$566$	−2.34497e9	−0.543600
$567$	0	0
$568$	−1.25918e9	−0.288315
$569$	2.74050e9	0.623643	0.311822	−	0.950141i	$-0.399061\pi$
$569$	2.74050e9	0.623643	0.311822	+	0.950141i	$0.399061\pi$
$570$	0	0
$571$	8.65695e9	1.94598	0.972991	−	0.230844i	$-0.0741488\pi$
$571$	8.65695e9	1.94598	0.972991	+	0.230844i	$0.0741488\pi$
$572$	1.13165e9	0.252828
$573$	0	0
$574$	7.57983e9	1.67289
$575$	−4.87283e9	−1.06892
$576$	0	0
$577$	−5.33758e9	−1.15672	−0.578361	−	0.815781i	$-0.696308\pi$
$577$	−5.33758e9	−1.15672	−0.578361	+	0.815781i	$0.696308\pi$
$578$	3.44374e9	0.741794
$579$	0	0
$580$	1.07609e8	0.0229008
$581$	3.46206e9	0.732349
$582$	0	0
$583$	−1.01347e10	−2.11821
$584$	−3.71731e9	−0.772297
$585$	0	0
$586$	8.96981e8	0.184137
$587$	7.46525e9	1.52339	0.761695	−	0.647936i	$-0.224367\pi$
$587$	7.46525e9	1.52339	0.761695	+	0.647936i	$0.224367\pi$
$588$	0	0
$589$	6.69283e9	1.34960
$590$	−5.25133e7	−0.0105266
$591$	0	0
$592$	2.05155e9	0.406403
$593$	−3.09092e9	−0.608690	−0.304345	−	0.952562i	$-0.598438\pi$
$593$	−3.09092e9	−0.608690	−0.304345	+	0.952562i	$0.598438\pi$
$594$	0	0
$595$	2.29544e8	0.0446742
$596$	2.81664e8	0.0544966
$597$	0	0
$598$	3.00047e9	0.573766
$599$	−2.66060e9	−0.505809	−0.252904	−	0.967491i	$-0.581386\pi$
$599$	−2.66060e9	−0.505809	−0.252904	+	0.967491i	$0.581386\pi$
$600$	0	0
$601$	4.24214e8	0.0797122	0.0398561	−	0.999205i	$-0.487310\pi$
$601$	4.24214e8	0.0797122	0.0398561	+	0.999205i	$0.487310\pi$
$602$	−1.04406e10	−1.95045
$603$	0	0
$604$	2.67987e8	0.0494862
$605$	1.22980e8	0.0225782
$606$	0	0
$607$	1.13859e9	0.206637	0.103318	−	0.994648i	$-0.467054\pi$
$607$	1.13859e9	0.206637	0.103318	+	0.994648i	$0.467054\pi$
$608$	−3.04423e9	−0.549306
$609$	0	0
$610$	2.99463e8	0.0534181
$611$	2.90236e9	0.514762
$612$	0	0
$613$	−1.59219e9	−0.279179	−0.139590	−	0.990209i	$-0.544578\pi$
$613$	−1.59219e9	−0.279179	−0.139590	+	0.990209i	$0.544578\pi$
$614$	−3.66896e9	−0.639667
$615$	0	0
$616$	−1.09063e10	−1.87994
$617$	5.01588e9	0.859705	0.429853	−	0.902899i	$-0.358566\pi$
$617$	5.01588e9	0.859705	0.429853	+	0.902899i	$0.358566\pi$
$618$	0	0
$619$	−1.05539e10	−1.78854	−0.894268	−	0.447532i	$-0.852303\pi$
$619$	−1.05539e10	−1.78854	−0.894268	+	0.447532i	$0.852303\pi$
$620$	−3.33621e8	−0.0562188
$621$	0	0
$622$	−8.47703e9	−1.41246
$623$	−8.26360e9	−1.36918
$624$	0	0
$625$	5.92074e9	0.970054
$626$	−7.32428e9	−1.19331
$627$	0	0
$628$	−1.46956e8	−0.0236771
$629$	1.36373e9	0.218500
$630$	0	0
$631$	−5.24953e9	−0.831797	−0.415899	−	0.909411i	$-0.636533\pi$
$631$	−5.24953e9	−0.831797	−0.415899	+	0.909411i	$0.636533\pi$
$632$	1.85787e8	0.0292756
$633$	0	0
$634$	−2.71469e9	−0.423066
$635$	3.58144e8	0.0555073
$636$	0	0
$637$	−6.15218e9	−0.943063
$638$	3.86668e9	0.589475
$639$	0	0
$640$	−1.33634e8	−0.0201506
$641$	4.54601e9	0.681753	0.340876	−	0.940108i	$-0.389276\pi$
$641$	4.54601e9	0.681753	0.340876	+	0.940108i	$0.389276\pi$
$642$	0	0
$643$	3.12857e9	0.464095	0.232048	−	0.972704i	$-0.425458\pi$
$643$	3.12857e9	0.464095	0.232048	+	0.972704i	$0.425458\pi$
$644$	3.96437e9	0.584889
$645$	0	0
$646$	1.32142e9	0.192853
$647$	5.99209e9	0.869788	0.434894	−	0.900482i	$-0.356786\pi$
$647$	5.99209e9	0.869788	0.434894	+	0.900482i	$0.356786\pi$
$648$	0	0
$649$	1.00371e9	0.144129
$650$	−3.68337e9	−0.526076
$651$	0	0
$652$	−1.49128e9	−0.210714
$653$	−1.00926e10	−1.41842	−0.709210	−	0.704997i	$-0.750948\pi$
$653$	−1.00926e10	−1.41842	−0.709210	+	0.704997i	$0.750948\pi$
$654$	0	0
$655$	−6.86765e7	−0.00954913
$656$	−5.10723e9	−0.706353
$657$	0	0
$658$	−7.20921e9	−0.986500
$659$	−1.22466e10	−1.66693	−0.833465	−	0.552573i	$-0.813646\pi$
$659$	−1.22466e10	−1.66693	−0.833465	+	0.552573i	$0.813646\pi$
$660$	0	0
$661$	−6.31287e8	−0.0850201	−0.0425101	−	0.999096i	$-0.513535\pi$
$661$	−6.31287e8	−0.0850201	−0.0425101	+	0.999096i	$0.513535\pi$
$662$	−4.25819e9	−0.570455
$663$	0	0
$664$	−3.85462e9	−0.510968
$665$	−9.87690e8	−0.130240
$666$	0	0
$667$	−5.45335e9	−0.711579
$668$	1.85380e9	0.240628
$669$	0	0
$670$	−1.16981e9	−0.150263
$671$	−5.72375e9	−0.731394
$672$	0	0
$673$	1.33894e10	1.69320	0.846599	−	0.532232i	$-0.178647\pi$
$673$	1.33894e10	1.69320	0.846599	+	0.532232i	$0.178647\pi$
$674$	−8.27987e9	−1.04163
$675$	0	0
$676$	1.58242e9	0.197019
$677$	1.86123e9	0.230536	0.115268	−	0.993334i	$-0.463227\pi$
$677$	1.86123e9	0.230536	0.115268	+	0.993334i	$0.463227\pi$
$678$	0	0
$679$	9.03258e9	1.10731
$680$	−2.55572e8	−0.0311696
$681$	0	0
$682$	−1.19879e10	−1.44710
$683$	1.29941e10	1.56054	0.780268	−	0.625445i	$-0.215082\pi$
$683$	1.29941e10	1.56054	0.780268	+	0.625445i	$0.215082\pi$
$684$	0	0
$685$	3.23447e8	0.0384491
$686$	4.62380e9	0.546846
$687$	0	0
$688$	7.03477e9	0.823550
$689$	1.08043e10	1.25843
$690$	0	0
$691$	−9.85622e9	−1.13642	−0.568208	−	0.822885i	$-0.692363\pi$
$691$	−9.85622e9	−1.13642	−0.568208	+	0.822885i	$0.692363\pi$
$692$	−4.01582e9	−0.460684
$693$	0	0
$694$	7.44464e9	0.845446
$695$	−3.88529e8	−0.0439012
$696$	0	0
$697$	−3.39494e9	−0.379767
$698$	−1.23399e10	−1.37346
$699$	0	0
$700$	−4.86664e9	−0.536273
$701$	9.35979e9	1.02625	0.513125	−	0.858314i	$-0.328488\pi$
$701$	9.35979e9	1.02625	0.513125	+	0.858314i	$0.328488\pi$
$702$	0	0
$703$	−5.86793e9	−0.637002
$704$	1.09073e10	1.17818
$705$	0	0
$706$	6.18998e9	0.662023
$707$	−2.32085e10	−2.46990
$708$	0	0
$709$	−9.52210e9	−1.00339	−0.501696	−	0.865044i	$-0.667290\pi$
$709$	−9.52210e9	−1.00339	−0.501696	+	0.865044i	$0.667290\pi$
$710$	2.04250e8	0.0214170
$711$	0	0
$712$	9.20060e9	0.955292
$713$	1.69071e10	1.74685
$714$	0	0
$715$	−7.12224e8	−0.0728694
$716$	−1.23700e8	−0.0125943
$717$	0	0
$718$	7.06504e9	0.712327
$719$	6.22106e9	0.624185	0.312092	−	0.950052i	$-0.398970\pi$
$719$	6.22106e9	0.624185	0.312092	+	0.950052i	$0.398970\pi$
$720$	0	0
$721$	2.00321e10	1.99046
$722$	2.48489e9	0.245712
$723$	0	0
$724$	5.68917e9	0.557140
$725$	6.69452e9	0.652433
$726$	0	0
$727$	4.54280e9	0.438483	0.219242	−	0.975671i	$-0.429642\pi$
$727$	4.54280e9	0.438483	0.219242	+	0.975671i	$0.429642\pi$
$728$	1.16270e10	1.11688
$729$	0	0
$730$	6.02984e8	0.0573688
$731$	4.67624e9	0.442778
$732$	0	0
$733$	9.84479e9	0.923299	0.461649	−	0.887062i	$-0.347258\pi$
$733$	9.84479e9	0.923299	0.461649	+	0.887062i	$0.347258\pi$
$734$	−1.70474e10	−1.59119
$735$	0	0
$736$	−7.69016e9	−0.710989
$737$	2.23589e10	2.05738
$738$	0	0
$739$	8.69557e9	0.792579	0.396289	−	0.918126i	$-0.370298\pi$
$739$	8.69557e9	0.792579	0.396289	+	0.918126i	$0.370298\pi$
$740$	2.92501e8	0.0265348
$741$	0	0
$742$	−2.68370e10	−2.41169
$743$	−1.41962e10	−1.26973	−0.634864	−	0.772624i	$-0.718944\pi$
$743$	−1.41962e10	−1.26973	−0.634864	+	0.772624i	$0.718944\pi$
$744$	0	0
$745$	−1.77271e8	−0.0157069
$746$	−1.05206e10	−0.927797
$747$	0	0
$748$	1.25899e9	0.109993
$749$	2.24621e10	1.95328
$750$	0	0
$751$	1.57390e10	1.35593	0.677967	−	0.735092i	$-0.262861\pi$
$751$	1.57390e10	1.35593	0.677967	+	0.735092i	$0.262861\pi$
$752$	4.85751e9	0.416535
$753$	0	0
$754$	−4.12218e9	−0.350209
$755$	−1.68663e8	−0.0142628
$756$	0	0
$757$	2.58251e9	0.216374	0.108187	−	0.994131i	$-0.465495\pi$
$757$	2.58251e9	0.216374	0.108187	+	0.994131i	$0.465495\pi$
$758$	−7.54774e8	−0.0629470
$759$	0	0
$760$	1.09968e9	0.0908700
$761$	1.11863e9	0.0920114	0.0460057	−	0.998941i	$-0.485351\pi$
$761$	1.11863e9	0.0920114	0.0460057	+	0.998941i	$0.485351\pi$
$762$	0	0
$763$	1.16882e10	0.952605
$764$	−7.81914e9	−0.634355
$765$	0	0
$766$	−6.14796e9	−0.494231
$767$	−1.07003e9	−0.0856272
$768$	0	0
$769$	4.81105e9	0.381503	0.190751	−	0.981638i	$-0.438908\pi$
$769$	4.81105e9	0.381503	0.190751	+	0.981638i	$0.438908\pi$
$770$	1.76910e9	0.139648
$771$	0	0
$772$	4.01865e9	0.314354
$773$	9.07363e9	0.706566	0.353283	−	0.935516i	$-0.385065\pi$
$773$	9.07363e9	0.706566	0.353283	+	0.935516i	$0.385065\pi$
$774$	0	0
$775$	−2.07551e10	−1.60165
$776$	−1.00568e10	−0.772579
$777$	0	0
$778$	−8.29449e9	−0.631482
$779$	1.46079e10	1.10715
$780$	0	0
$781$	−3.90391e9	−0.293239
$782$	3.33810e9	0.249618
$783$	0	0
$784$	−1.02965e10	−0.763107
$785$	9.24897e7	0.00682417
$786$	0	0
$787$	−9.67486e9	−0.707511	−0.353755	−	0.935338i	$-0.615095\pi$
$787$	−9.67486e9	−0.707511	−0.353755	+	0.935338i	$0.615095\pi$
$788$	−3.51522e9	−0.255924
$789$	0	0
$790$	−3.01365e7	−0.00217469
$791$	3.69194e10	2.65239
$792$	0	0
$793$	6.10196e9	0.434524
$794$	−2.14324e10	−1.51949
$795$	0	0
$796$	−8.00351e9	−0.562451
$797$	−5.79578e9	−0.405516	−0.202758	−	0.979229i	$-0.564990\pi$
$797$	−5.79578e9	−0.405516	−0.202758	+	0.979229i	$0.564990\pi$
$798$	0	0
$799$	3.22895e9	0.223948
$800$	9.44041e9	0.651893
$801$	0	0
$802$	9.44026e9	0.646210
$803$	−1.15251e10	−0.785486
$804$	0	0
$805$	−2.49505e9	−0.168575
$806$	1.27800e10	0.859724
$807$	0	0
$808$	2.58401e10	1.72327
$809$	5.99978e9	0.398396	0.199198	−	0.979959i	$-0.436166\pi$
$809$	5.99978e9	0.398396	0.199198	+	0.979959i	$0.436166\pi$
$810$	0	0
$811$	2.58658e10	1.70275	0.851377	−	0.524553i	$-0.175768\pi$
$811$	2.58658e10	1.70275	0.851377	+	0.524553i	$0.175768\pi$
$812$	−5.44643e9	−0.356998
$813$	0	0
$814$	1.05103e10	0.683017
$815$	9.38566e8	0.0607314
$816$	0	0
$817$	−2.01211e10	−1.29085
$818$	3.89323e9	0.248699
$819$	0	0
$820$	−7.28166e8	−0.0461192
$821$	−6.65337e9	−0.419605	−0.209802	−	0.977744i	$-0.567282\pi$
$821$	−6.65337e9	−0.419605	−0.209802	+	0.977744i	$0.567282\pi$
$822$	0	0
$823$	2.32319e10	1.45273	0.726366	−	0.687308i	$-0.241208\pi$
$823$	2.32319e10	1.45273	0.726366	+	0.687308i	$0.241208\pi$
$824$	−2.23035e10	−1.38876
$825$	0	0
$826$	2.65786e9	0.164098
$827$	−4.17843e9	−0.256888	−0.128444	−	0.991717i	$-0.540998\pi$
$827$	−4.17843e9	−0.256888	−0.128444	+	0.991717i	$0.540998\pi$
$828$	0	0
$829$	1.91468e10	1.16722	0.583612	−	0.812033i	$-0.301639\pi$
$829$	1.91468e10	1.16722	0.583612	+	0.812033i	$0.301639\pi$
$830$	6.25256e8	0.0379564
$831$	0	0
$832$	−1.16280e10	−0.699961
$833$	−6.84445e9	−0.410281
$834$	0	0
$835$	−1.16673e9	−0.0693531
$836$	−5.41722e9	−0.320667
$837$	0	0
$838$	−8.87178e9	−0.520783
$839$	−8.57931e9	−0.501517	−0.250758	−	0.968050i	$-0.580680\pi$
$839$	−8.57931e9	−0.501517	−0.250758	+	0.968050i	$0.580680\pi$
$840$	0	0
$841$	−9.75781e9	−0.565674
$842$	−2.98869e7	−0.00172539
$843$	0	0
$844$	−9.86082e9	−0.564566
$845$	−9.95927e8	−0.0567844
$846$	0	0
$847$	−6.22438e9	−0.351969
$848$	1.80826e10	1.01830
$849$	0	0
$850$	−4.09784e9	−0.228870
$851$	−1.48232e10	−0.824497
$852$	0	0
$853$	1.55006e10	0.855118	0.427559	−	0.903987i	$-0.359374\pi$
$853$	1.55006e10	0.855118	0.427559	+	0.903987i	$0.359374\pi$
$854$	−1.51568e10	−0.832729
$855$	0	0
$856$	−2.50091e10	−1.36282
$857$	2.35700e10	1.27916	0.639582	−	0.768723i	$-0.279107\pi$
$857$	2.35700e10	1.27916	0.639582	+	0.768723i	$0.279107\pi$
$858$	0	0
$859$	−1.55175e10	−0.835307	−0.417654	−	0.908606i	$-0.637147\pi$
$859$	−1.55175e10	−0.835307	−0.417654	+	0.908606i	$0.637147\pi$
$860$	1.00299e9	0.0537712
$861$	0	0
$862$	9.10055e9	0.483941
$863$	1.31058e10	0.694104	0.347052	−	0.937846i	$-0.387183\pi$
$863$	1.31058e10	0.694104	0.347052	+	0.937846i	$0.387183\pi$
$864$	0	0
$865$	2.52743e9	0.132777
$866$	1.17642e10	0.615531
$867$	0	0
$868$	1.68856e10	0.876390
$869$	5.76010e8	0.0297756
$870$	0	0
$871$	−2.38364e10	−1.22230
$872$	−1.30135e10	−0.664642
$873$	0	0
$874$	−1.43633e10	−0.727720
$875$	6.15681e9	0.310690
$876$	0	0
$877$	−3.93591e10	−1.97037	−0.985183	−	0.171509i	$-0.945136\pi$
$877$	−3.93591e10	−1.97037	−0.985183	+	0.171509i	$0.945136\pi$
$878$	−5.39089e9	−0.268800
$879$	0	0
$880$	−1.19201e9	−0.0589644
$881$	2.83704e10	1.39781	0.698907	−	0.715213i	$-0.253670\pi$
$881$	2.83704e10	1.39781	0.698907	+	0.715213i	$0.253670\pi$
$882$	0	0
$883$	−2.71601e10	−1.32760	−0.663802	−	0.747908i	$-0.731058\pi$
$883$	−2.71601e10	−1.32760	−0.663802	+	0.747908i	$0.731058\pi$
$884$	−1.34218e9	−0.0653473
$885$	0	0
$886$	3.28433e9	0.158646
$887$	2.72456e10	1.31088	0.655441	−	0.755246i	$-0.272483\pi$
$887$	2.72456e10	1.31088	0.655441	+	0.755246i	$0.272483\pi$
$888$	0	0
$889$	−1.81268e10	−0.865297
$890$	−1.49242e9	−0.0709622
$891$	0	0
$892$	−9.78744e9	−0.461734
$893$	−1.38936e10	−0.652884
$894$	0	0
$895$	7.78530e7	0.00362990
$896$	6.76366e9	0.314126
$897$	0	0
$898$	2.34597e10	1.08108
$899$	−2.32277e10	−1.06622
$900$	0	0
$901$	1.20201e10	0.547484
$902$	−2.61650e10	−1.18713
$903$	0	0
$904$	−4.11057e10	−1.85060
$905$	−3.58059e9	−0.160577
$906$	0	0
$907$	−2.89542e10	−1.28850	−0.644251	−	0.764814i	$-0.722831\pi$
$907$	−2.89542e10	−1.28850	−0.644251	+	0.764814i	$0.722831\pi$
$908$	6.90409e9	0.306059
$909$	0	0
$910$	−1.88600e9	−0.0829655
$911$	−4.90888e9	−0.215114	−0.107557	−	0.994199i	$-0.534303\pi$
$911$	−4.90888e9	−0.215114	−0.107557	+	0.994199i	$0.534303\pi$
$912$	0	0
$913$	−1.19508e10	−0.519694
$914$	1.33457e10	0.578137
$915$	0	0
$916$	9.94210e9	0.427409
$917$	3.47593e9	0.148860
$918$	0	0
$919$	−8.65519e8	−0.0367851	−0.0183926	−	0.999831i	$-0.505855\pi$
$919$	−8.65519e8	−0.0367851	−0.0183926	+	0.999831i	$0.505855\pi$
$920$	2.77796e9	0.117617
$921$	0	0
$922$	−4.51879e8	−0.0189873
$923$	4.16188e9	0.174214
$924$	0	0
$925$	1.81969e10	0.755966
$926$	2.56267e10	1.06061
$927$	0	0
$928$	1.05651e10	0.433966
$929$	−1.75729e10	−0.719100	−0.359550	−	0.933126i	$-0.617070\pi$
$929$	−1.75729e10	−0.719100	−0.359550	+	0.933126i	$0.617070\pi$
$930$	0	0
$931$	2.94506e10	1.19611
$932$	8.73512e9	0.353438
$933$	0	0
$934$	2.70564e10	1.08657
$935$	−7.92367e8	−0.0317019
$936$	0	0
$937$	−1.98729e9	−0.0789174	−0.0394587	−	0.999221i	$-0.512563\pi$
$937$	−1.98729e9	−0.0789174	−0.0394587	+	0.999221i	$0.512563\pi$
$938$	5.92076e10	2.34243
$939$	0	0
$940$	6.92562e8	0.0271964
$941$	−9.16263e9	−0.358473	−0.179237	−	0.983806i	$-0.557363\pi$
$941$	−9.16263e9	−0.358473	−0.179237	+	0.983806i	$0.557363\pi$
$942$	0	0
$943$	3.69016e10	1.43303
$944$	−1.79085e9	−0.0692878
$945$	0	0
$946$	3.60400e10	1.38409
$947$	8.66497e9	0.331545	0.165772	−	0.986164i	$-0.446988\pi$
$947$	8.66497e9	0.331545	0.165772	+	0.986164i	$0.446988\pi$
$948$	0	0
$949$	1.22866e10	0.466660
$950$	1.76323e10	0.667233
$951$	0	0
$952$	1.29353e10	0.485900
$953$	−4.09329e10	−1.53196	−0.765979	−	0.642866i	$-0.777745\pi$
$953$	−4.09329e10	−1.53196	−0.765979	+	0.642866i	$0.777745\pi$
$954$	0	0
$955$	4.92113e9	0.182832
$956$	−1.43133e10	−0.529829
$957$	0	0
$958$	1.97679e10	0.726411
$959$	−1.63707e10	−0.599379
$960$	0	0
$961$	4.45004e10	1.61745
$962$	−1.12049e10	−0.405783
$963$	0	0
$964$	−5.24142e9	−0.188443
$965$	−2.52921e9	−0.0906024
$966$	0	0
$967$	4.75373e10	1.69060	0.845302	−	0.534289i	$-0.179421\pi$
$967$	4.75373e10	1.69060	0.845302	+	0.534289i	$0.179421\pi$
$968$	6.93016e9	0.245572
$969$	0	0
$970$	1.63131e9	0.0573897
$971$	−4.18209e10	−1.46597	−0.732986	−	0.680244i	$-0.761874\pi$
$971$	−4.18209e10	−1.46597	−0.732986	+	0.680244i	$0.761874\pi$
$972$	0	0
$973$	1.96647e10	0.684372
$974$	2.67083e10	0.926168
$975$	0	0
$976$	1.02125e10	0.351608
$977$	3.63532e10	1.24713	0.623565	−	0.781771i	$-0.285684\pi$
$977$	3.63532e10	1.24713	0.623565	+	0.781771i	$0.285684\pi$
$978$	0	0
$979$	2.85253e10	0.971606
$980$	−1.46804e9	−0.0498248
$981$	0	0
$982$	1.15844e10	0.390375
$983$	−1.22719e10	−0.412072	−0.206036	−	0.978544i	$-0.566056\pi$
$983$	−1.22719e10	−0.412072	−0.206036	+	0.978544i	$0.566056\pi$
$984$	0	0
$985$	2.21237e9	0.0737617
$986$	−4.58603e9	−0.152359
$987$	0	0
$988$	5.77518e9	0.190509
$989$	−5.08288e10	−1.67079
$990$	0	0
$991$	−3.42031e10	−1.11637	−0.558185	−	0.829717i	$-0.688502\pi$
$991$	−3.42031e10	−1.11637	−0.558185	+	0.829717i	$0.688502\pi$
$992$	−3.27550e10	−1.06534
$993$	0	0
$994$	−1.03378e10	−0.333867
$995$	5.03716e9	0.162108
$996$	0	0
$997$	6.42072e9	0.205187	0.102594	−	0.994723i	$-0.467286\pi$
$997$	6.42072e9	0.205187	0.102594	+	0.994723i	$0.467286\pi$
$998$	1.88253e10	0.599495
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.6		17
3.2	odd	2		177.8.a.c.1.12	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.12	✓	17	3.2	odd	2
531.8.a.c.1.6		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)

\(f(q)\)	\(=\)	\(q-9.14085 q^{2} -44.4448 q^{4} +27.9722 q^{5} -1415.76 q^{7} +1576.29 q^{8} +O(q^{10})\)	\(q-9.14085 q^{2} -44.4448 q^{4} +27.9722 q^{5} -1415.76 q^{7} +1576.29 q^{8} -255.690 q^{10} +4887.09 q^{11} -5210.02 q^{13} +12941.3 q^{14} -8719.72 q^{16} -5796.28 q^{17} +24940.5 q^{19} -1243.22 q^{20} -44672.2 q^{22} +63003.2 q^{23} -77342.6 q^{25} +47624.1 q^{26} +62923.2 q^{28} -86556.7 q^{29} +268352. q^{31} -122060. q^{32} +52983.0 q^{34} -39601.9 q^{35} -235277. q^{37} -227977. q^{38} +44092.3 q^{40} +585710. q^{41} -806765. q^{43} -217206. q^{44} -575903. q^{46} -557072. q^{47} +1.18083e6 q^{49} +706977. q^{50} +231559. q^{52} -2.07376e6 q^{53} +136703. q^{55} -2.23165e6 q^{56} +791202. q^{58} +205379. q^{59} -1.17120e6 q^{61} -2.45297e6 q^{62} +2.23185e6 q^{64} -145736. q^{65} +4.57510e6 q^{67} +257615. q^{68} +361995. q^{70} -798821. q^{71} -2.35826e6 q^{73} +2.15063e6 q^{74} -1.10847e6 q^{76} -6.91895e6 q^{77} +117864. q^{79} -243910. q^{80} -5.35389e6 q^{82} -2.44537e6 q^{83} -162135. q^{85} +7.37452e6 q^{86} +7.70349e6 q^{88} +5.83686e6 q^{89} +7.37614e6 q^{91} -2.80017e6 q^{92} +5.09211e6 q^{94} +697640. q^{95} -6.38002e6 q^{97} -1.07938e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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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