LMFDB - Embedded newform 531.8.a.c.1.14

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			1.14
Root			$-13.8304$ 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)

$f(q)$	$=$	$q+13.8304 q^{2} +63.2803 q^{4} +149.469 q^{5} +14.2725 q^{7} -895.100 q^{8} +O(q^{10})$	\(q+13.8304 q^{2} +63.2803 q^{4} +149.469 q^{5} +14.2725 q^{7} -895.100 q^{8} +2067.22 q^{10} -531.760 q^{11} +4168.02 q^{13} +197.395 q^{14} -20479.5 q^{16} -4562.28 q^{17} +31839.8 q^{19} +9458.44 q^{20} -7354.45 q^{22} +56030.4 q^{23} -55784.0 q^{25} +57645.4 q^{26} +903.168 q^{28} -52043.8 q^{29} -44036.0 q^{31} -168667. q^{32} -63098.2 q^{34} +2133.30 q^{35} +11309.5 q^{37} +440358. q^{38} -133790. q^{40} +455543. q^{41} +177174. q^{43} -33649.9 q^{44} +774923. q^{46} +1.27260e6 q^{47} -823339. q^{49} -771516. q^{50} +263753. q^{52} -274388. q^{53} -79481.6 q^{55} -12775.3 q^{56} -719787. q^{58} +205379. q^{59} -152764. q^{61} -609036. q^{62} +288642. q^{64} +622989. q^{65} +2.06545e6 q^{67} -288702. q^{68} +29504.4 q^{70} +1.79110e6 q^{71} +3.32985e6 q^{73} +156414. q^{74} +2.01483e6 q^{76} -7589.54 q^{77} +6.43667e6 q^{79} -3.06105e6 q^{80} +6.30035e6 q^{82} +1.15501e6 q^{83} -681919. q^{85} +2.45039e6 q^{86} +475978. q^{88} -3.69123e6 q^{89} +59488.0 q^{91} +3.54562e6 q^{92} +1.76005e7 q^{94} +4.75907e6 q^{95} +6.33530e6 q^{97} -1.13871e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	13.8304	1.22245	0.611224	−	0.791458i	$-0.290678\pi$
$2$	13.8304	1.22245	0.611224	+	0.791458i	$0.290678\pi$
$3$	0	0
$3$	0	0
$4$	63.2803	0.494377
$5$	149.469	0.534757	0.267378	−	0.963592i	$-0.413843\pi$
$5$	149.469	0.534757	0.267378	+	0.963592i	$0.413843\pi$
$6$	0	0
$7$	14.2725	0.0157274	0.00786370	−	0.999969i	$-0.497497\pi$
$7$	14.2725	0.0157274	0.00786370	+	0.999969i	$0.497497\pi$
$8$	−895.100	−0.618097
$9$	0	0
$10$	2067.22	0.653712
$11$	−531.760	−0.120459	−0.0602297	−	0.998185i	$-0.519183\pi$
$11$	−531.760	−0.120459	−0.0602297	+	0.998185i	$0.519183\pi$
$12$	0	0
$13$	4168.02	0.526172	0.263086	−	0.964772i	$-0.415260\pi$
$13$	4168.02	0.526172	0.263086	+	0.964772i	$0.415260\pi$
$14$	197.395	0.0192259
$15$	0	0
$16$	−20479.5	−1.24997
$17$	−4562.28	−0.225222	−0.112611	−	0.993639i	$-0.535921\pi$
$17$	−4562.28	−0.225222	−0.112611	+	0.993639i	$0.535921\pi$
$18$	0	0
$19$	31839.8	1.06496	0.532480	−	0.846443i	$-0.321260\pi$
$19$	31839.8	1.06496	0.532480	+	0.846443i	$0.321260\pi$
$20$	9458.44	0.264372
$21$	0	0
$22$	−7354.45	−0.147255
$23$	56030.4	0.960231	0.480116	−	0.877205i	$-0.340595\pi$
$23$	56030.4	0.960231	0.480116	+	0.877205i	$0.340595\pi$
$24$	0	0
$25$	−55784.0	−0.714035
$26$	57645.4	0.643217
$27$	0	0
$28$	903.168	0.00777527
$29$	−52043.8	−0.396256	−0.198128	−	0.980176i	$-0.563486\pi$
$29$	−52043.8	−0.396256	−0.198128	+	0.980176i	$0.563486\pi$
$30$	0	0
$31$	−44036.0	−0.265486	−0.132743	−	0.991150i	$-0.542379\pi$
$31$	−44036.0	−0.265486	−0.132743	+	0.991150i	$0.542379\pi$
$32$	−168667.	−0.909923
$33$	0	0
$34$	−63098.2	−0.275322
$35$	2133.30	0.00841033
$36$	0	0
$37$	11309.5	0.0367059	0.0183529	−	0.999832i	$-0.494158\pi$
$37$	11309.5	0.0367059	0.0183529	+	0.999832i	$0.494158\pi$
$38$	440358.	1.30186
$39$	0	0
$40$	−133790.	−0.330531
$41$	455543.	1.03225	0.516126	−	0.856513i	$-0.327374\pi$
$41$	455543.	1.03225	0.516126	+	0.856513i	$0.327374\pi$
$42$	0	0
$43$	177174.	0.339829	0.169915	−	0.985459i	$-0.445651\pi$
$43$	177174.	0.339829	0.169915	+	0.985459i	$0.445651\pi$
$44$	−33649.9	−0.0595524
$45$	0	0
$46$	774923.	1.17383
$47$	1.27260e6	1.78792	0.893960	−	0.448147i	$-0.147916\pi$
$47$	1.27260e6	1.78792	0.893960	+	0.448147i	$0.147916\pi$
$48$	0	0
$49$	−823339.	−0.999753
$50$	−771516.	−0.872871
$51$	0	0
$52$	263753.	0.260127
$53$	−274388.	−0.253162	−0.126581	−	0.991956i	$-0.540400\pi$
$53$	−274388.	−0.253162	−0.126581	+	0.991956i	$0.540400\pi$
$54$	0	0
$55$	−79481.6	−0.0644165
$56$	−12775.3	−0.00972106
$57$	0	0
$58$	−719787.	−0.484402
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−152764.	−0.0861719	−0.0430860	−	0.999071i	$-0.513719\pi$
$61$	−152764.	−0.0861719	−0.0430860	+	0.999071i	$0.513719\pi$
$62$	−609036.	−0.324543
$63$	0	0
$64$	288642.	0.137635
$65$	622989.	0.281374
$66$	0	0
$67$	2.06545e6	0.838984	0.419492	−	0.907759i	$-0.362208\pi$
$67$	2.06545e6	0.838984	0.419492	+	0.907759i	$0.362208\pi$
$68$	−288702.	−0.111345
$69$	0	0
$70$	29504.4	0.0102812
$71$	1.79110e6	0.593904	0.296952	−	0.954892i	$-0.404030\pi$
$71$	1.79110e6	0.593904	0.296952	+	0.954892i	$0.404030\pi$
$72$	0	0
$73$	3.32985e6	1.00183	0.500916	−	0.865496i	$-0.332996\pi$
$73$	3.32985e6	1.00183	0.500916	+	0.865496i	$0.332996\pi$
$74$	156414.	0.0448710
$75$	0	0
$76$	2.01483e6	0.526492
$77$	−7589.54	−0.00189451
$78$	0	0
$79$	6.43667e6	1.46881	0.734406	−	0.678710i	$-0.237461\pi$
$79$	6.43667e6	1.46881	0.734406	+	0.678710i	$0.237461\pi$
$80$	−3.06105e6	−0.668429
$81$	0	0
$82$	6.30035e6	1.26187
$83$	1.15501e6	0.221724	0.110862	−	0.993836i	$-0.464639\pi$
$83$	1.15501e6	0.221724	0.110862	+	0.993836i	$0.464639\pi$
$84$	0	0
$85$	−681919.	−0.120439
$86$	2.45039e6	0.415423
$87$	0	0
$88$	475978.	0.0744556
$89$	−3.69123e6	−0.555016	−0.277508	−	0.960723i	$-0.589509\pi$
$89$	−3.69123e6	−0.555016	−0.277508	+	0.960723i	$0.589509\pi$
$90$	0	0
$91$	59488.0	0.00827532
$92$	3.54562e6	0.474717
$93$	0	0
$94$	1.76005e7	2.18564
$95$	4.75907e6	0.569494
$96$	0	0
$97$	6.33530e6	0.704800	0.352400	−	0.935849i	$-0.385366\pi$
$97$	6.33530e6	0.704800	0.352400	+	0.935849i	$0.385366\pi$
$98$	−1.13871e7	−1.22214
$99$	0	0
$100$	−3.53003e6	−0.353003
$101$	−8.28710e6	−0.800346	−0.400173	−	0.916440i	$-0.631050\pi$
$101$	−8.28710e6	−0.800346	−0.400173	+	0.916440i	$0.631050\pi$
$102$	0	0
$103$	1.33969e7	1.20802	0.604008	−	0.796979i	$-0.293570\pi$
$103$	1.33969e7	1.20802	0.604008	+	0.796979i	$0.293570\pi$
$104$	−3.73079e6	−0.325225
$105$	0	0
$106$	−3.79490e6	−0.309478
$107$	−7.64708e6	−0.603466	−0.301733	−	0.953393i	$-0.597565\pi$
$107$	−7.64708e6	−0.603466	−0.301733	+	0.953393i	$0.597565\pi$
$108$	0	0
$109$	8.75164e6	0.647287	0.323644	−	0.946179i	$-0.395092\pi$
$109$	8.75164e6	0.647287	0.323644	+	0.946179i	$0.395092\pi$
$110$	−1.09926e6	−0.0787458
$111$	0	0
$112$	−292293.	−0.0196588
$113$	1.76375e7	1.14990	0.574952	−	0.818187i	$-0.305021\pi$
$113$	1.76375e7	1.14990	0.574952	+	0.818187i	$0.305021\pi$
$114$	0	0
$115$	8.37480e6	0.513490
$116$	−3.29335e6	−0.195900
$117$	0	0
$118$	2.84048e6	0.159149
$119$	−65115.1	−0.00354215
$120$	0	0
$121$	−1.92044e7	−0.985490
$122$	−2.11278e6	−0.105341
$123$	0	0
$124$	−2.78661e6	−0.131250
$125$	−2.00152e7	−0.916592
$126$	0	0
$127$	−3.15626e7	−1.36729	−0.683643	−	0.729817i	$-0.739605\pi$
$127$	−3.15626e7	−1.36729	−0.683643	+	0.729817i	$0.739605\pi$
$128$	2.55814e7	1.07817
$129$	0	0
$130$	8.61620e6	0.343965
$131$	1.54251e7	0.599485	0.299742	−	0.954020i	$-0.403099\pi$
$131$	1.54251e7	0.599485	0.299742	+	0.954020i	$0.403099\pi$
$132$	0	0
$133$	454434.	0.0167490
$134$	2.85661e7	1.02561
$135$	0	0
$136$	4.08370e6	0.139209
$137$	−2.73563e6	−0.0908940	−0.0454470	−	0.998967i	$-0.514471\pi$
$137$	−2.73563e6	−0.0908940	−0.0454470	+	0.998967i	$0.514471\pi$
$138$	0	0
$139$	2.21140e7	0.698418	0.349209	−	0.937045i	$-0.386450\pi$
$139$	2.21140e7	0.698418	0.349209	+	0.937045i	$0.386450\pi$
$140$	134996.	0.00415788
$141$	0	0
$142$	2.47717e7	0.726016
$143$	−2.21638e6	−0.0633824
$144$	0	0
$145$	−7.77893e6	−0.211900
$146$	4.60532e7	1.22469
$147$	0	0
$148$	715666.	0.0181466
$149$	−4.34797e6	−0.107680	−0.0538399	−	0.998550i	$-0.517146\pi$
$149$	−4.34797e6	−0.107680	−0.0538399	+	0.998550i	$0.517146\pi$
$150$	0	0
$151$	642629.	0.0151894	0.00759470	−	0.999971i	$-0.497583\pi$
$151$	642629.	0.0151894	0.00759470	+	0.999971i	$0.497583\pi$
$152$	−2.84998e7	−0.658248
$153$	0	0
$154$	−104966.	−0.00231594
$155$	−6.58202e6	−0.141970
$156$	0	0
$157$	4.54519e7	0.937354	0.468677	−	0.883370i	$-0.344731\pi$
$157$	4.54519e7	0.937354	0.468677	+	0.883370i	$0.344731\pi$
$158$	8.90218e7	1.79555
$159$	0	0
$160$	−2.52105e7	−0.486587
$161$	799693.	0.0151019
$162$	0	0
$163$	9.12208e7	1.64982	0.824911	−	0.565262i	$-0.191225\pi$
$163$	9.12208e7	1.64982	0.824911	+	0.565262i	$0.191225\pi$
$164$	2.88269e7	0.510322
$165$	0	0
$166$	1.59743e7	0.271045
$167$	6.56493e7	1.09074	0.545371	−	0.838194i	$-0.316389\pi$
$167$	6.56493e7	1.09074	0.545371	+	0.838194i	$0.316389\pi$
$168$	0	0
$169$	−4.53762e7	−0.723143
$170$	−9.43122e6	−0.147230
$171$	0	0
$172$	1.12116e7	0.168004
$173$	1.20346e8	1.76714	0.883568	−	0.468303i	$-0.155134\pi$
$173$	1.20346e8	1.76714	0.883568	+	0.468303i	$0.155134\pi$
$174$	0	0
$175$	−796177.	−0.0112299
$176$	1.08902e7	0.150571
$177$	0	0
$178$	−5.10512e7	−0.678478
$179$	1.33167e7	0.173544	0.0867722	−	0.996228i	$-0.472345\pi$
$179$	1.33167e7	0.173544	0.0867722	+	0.996228i	$0.472345\pi$
$180$	0	0
$181$	1.20262e7	0.150748	0.0753741	−	0.997155i	$-0.475985\pi$
$181$	1.20262e7	0.150748	0.0753741	+	0.997155i	$0.475985\pi$
$182$	822744.	0.0101161
$183$	0	0
$184$	−5.01528e7	−0.593516
$185$	1.69041e6	0.0196287
$186$	0	0
$187$	2.42603e6	0.0271301
$188$	8.05302e7	0.883907
$189$	0	0
$190$	6.58198e7	0.696176
$191$	2.96173e6	0.0307559	0.0153780	−	0.999882i	$-0.495105\pi$
$191$	2.96173e6	0.0307559	0.0153780	+	0.999882i	$0.495105\pi$
$192$	0	0
$193$	−8.88812e6	−0.0889937	−0.0444968	−	0.999010i	$-0.514168\pi$
$193$	−8.88812e6	−0.0889937	−0.0444968	+	0.999010i	$0.514168\pi$
$194$	8.76198e7	0.861581
$195$	0	0
$196$	−5.21012e7	−0.494255
$197$	−5.08009e7	−0.473412	−0.236706	−	0.971581i	$-0.576068\pi$
$197$	−5.08009e7	−0.473412	−0.236706	+	0.971581i	$0.576068\pi$
$198$	0	0
$199$	3.98854e7	0.358780	0.179390	−	0.983778i	$-0.442588\pi$
$199$	3.98854e7	0.358780	0.179390	+	0.983778i	$0.442588\pi$
$200$	4.99323e7	0.441343
$201$	0	0
$202$	−1.14614e8	−0.978381
$203$	−742795.	−0.00623208
$204$	0	0
$205$	6.80896e7	0.552004
$206$	1.85284e8	1.47674
$207$	0	0
$208$	−8.53588e7	−0.657698
$209$	−1.69311e7	−0.128284
$210$	0	0
$211$	7.97162e7	0.584195	0.292098	−	0.956389i	$-0.405647\pi$
$211$	7.97162e7	0.584195	0.292098	+	0.956389i	$0.405647\pi$
$212$	−1.73633e7	−0.125158
$213$	0	0
$214$	−1.05762e8	−0.737705
$215$	2.64820e7	0.181726
$216$	0	0
$217$	−628504.	−0.00417541
$218$	1.21039e8	0.791274
$219$	0	0
$220$	−5.02962e6	−0.0318460
$221$	−1.90156e7	−0.118505
$222$	0	0
$223$	1.35288e8	0.816947	0.408473	−	0.912770i	$-0.366061\pi$
$223$	1.35288e8	0.816947	0.408473	+	0.912770i	$0.366061\pi$
$224$	−2.40730e6	−0.0143107
$225$	0	0
$226$	2.43934e8	1.40570
$227$	1.97246e8	1.11923	0.559613	−	0.828754i	$-0.310950\pi$
$227$	1.97246e8	1.11923	0.559613	+	0.828754i	$0.310950\pi$
$228$	0	0
$229$	1.35002e8	0.742875	0.371438	−	0.928458i	$-0.378865\pi$
$229$	1.35002e8	0.742875	0.371438	+	0.928458i	$0.378865\pi$
$230$	1.15827e8	0.627715
$231$	0	0
$232$	4.65844e7	0.244925
$233$	−1.36315e8	−0.705988	−0.352994	−	0.935626i	$-0.614836\pi$
$233$	−1.36315e8	−0.705988	−0.352994	+	0.935626i	$0.614836\pi$
$234$	0	0
$235$	1.90214e8	0.956102
$236$	1.29964e7	0.0643624
$237$	0	0
$238$	−900569.	−0.00433010
$239$	−1.31494e8	−0.623038	−0.311519	−	0.950240i	$-0.600838\pi$
$239$	−1.31494e8	−0.623038	−0.311519	+	0.950240i	$0.600838\pi$
$240$	0	0
$241$	2.49648e8	1.14887	0.574433	−	0.818552i	$-0.305223\pi$
$241$	2.49648e8	1.14887	0.574433	+	0.818552i	$0.305223\pi$
$242$	−2.65605e8	−1.20471
$243$	0	0
$244$	−9.66693e6	−0.0426014
$245$	−1.23064e8	−0.534624
$246$	0	0
$247$	1.32709e8	0.560351
$248$	3.94166e7	0.164096
$249$	0	0
$250$	−2.76819e8	−1.12048
$251$	−3.53873e7	−0.141250	−0.0706252	−	0.997503i	$-0.522499\pi$
$251$	−3.53873e7	−0.141250	−0.0706252	+	0.997503i	$0.522499\pi$
$252$	0	0
$253$	−2.97947e7	−0.115669
$254$	−4.36523e8	−1.67143
$255$	0	0
$256$	3.16855e8	1.18038
$257$	−4.79092e7	−0.176057	−0.0880285	−	0.996118i	$-0.528057\pi$
$257$	−4.79092e7	−0.176057	−0.0880285	+	0.996118i	$0.528057\pi$
$258$	0	0
$259$	161414.	0.000577288 0
$260$	3.94229e7	0.139105
$261$	0	0
$262$	2.13335e8	0.732838
$263$	−4.03661e8	−1.36827	−0.684135	−	0.729355i	$-0.739820\pi$
$263$	−4.03661e8	−1.36827	−0.684135	+	0.729355i	$0.739820\pi$
$264$	0	0
$265$	−4.10125e7	−0.135380
$266$	6.28501e6	0.0204748
$267$	0	0
$268$	1.30703e8	0.414775
$269$	−1.59050e8	−0.498196	−0.249098	−	0.968478i	$-0.580134\pi$
$269$	−1.59050e8	−0.498196	−0.249098	+	0.968478i	$0.580134\pi$
$270$	0	0
$271$	−2.63878e8	−0.805399	−0.402700	−	0.915332i	$-0.631928\pi$
$271$	−2.63878e8	−0.805399	−0.402700	+	0.915332i	$0.631928\pi$
$272$	9.34331e7	0.281520
$273$	0	0
$274$	−3.78349e7	−0.111113
$275$	2.96637e7	0.0860123
$276$	0	0
$277$	5.07781e8	1.43548	0.717740	−	0.696311i	$-0.245177\pi$
$277$	5.07781e8	1.43548	0.717740	+	0.696311i	$0.245177\pi$
$278$	3.05846e8	0.853779
$279$	0	0
$280$	−1.90951e6	−0.00519840
$281$	−4.01914e8	−1.08059	−0.540295	−	0.841476i	$-0.681687\pi$
$281$	−4.01914e8	−1.08059	−0.540295	+	0.841476i	$0.681687\pi$
$282$	0	0
$283$	−1.41538e7	−0.0371210	−0.0185605	−	0.999828i	$-0.505908\pi$
$283$	−1.41538e7	−0.0371210	−0.0185605	+	0.999828i	$0.505908\pi$
$284$	1.13341e8	0.293612
$285$	0	0
$286$	−3.06535e7	−0.0774816
$287$	6.50174e6	0.0162346
$288$	0	0
$289$	−3.89524e8	−0.949275
$290$	−1.07586e8	−0.259037
$291$	0	0
$292$	2.10714e8	0.495283
$293$	5.93471e7	0.137836	0.0689180	−	0.997622i	$-0.478045\pi$
$293$	5.93471e7	0.137836	0.0689180	+	0.997622i	$0.478045\pi$
$294$	0	0
$295$	3.06978e7	0.0696194
$296$	−1.01231e7	−0.0226878
$297$	0	0
$298$	−6.01342e7	−0.131633
$299$	2.33535e8	0.505247
$300$	0	0
$301$	2.52872e6	0.00534463
$302$	8.88782e6	0.0185682
$303$	0	0
$304$	−6.52063e8	−1.33117
$305$	−2.28334e7	−0.0460810
$306$	0	0
$307$	2.64952e8	0.522617	0.261308	−	0.965255i	$-0.415846\pi$
$307$	2.64952e8	0.522617	0.261308	+	0.965255i	$0.415846\pi$
$308$	−480268.	−0.000936605 0
$309$	0	0
$310$	−9.10320e7	−0.173551
$311$	−2.51765e8	−0.474607	−0.237304	−	0.971436i	$-0.576264\pi$
$311$	−2.51765e8	−0.474607	−0.237304	+	0.971436i	$0.576264\pi$
$312$	0	0
$313$	1.78674e8	0.329348	0.164674	−	0.986348i	$-0.447343\pi$
$313$	1.78674e8	0.329348	0.164674	+	0.986348i	$0.447343\pi$
$314$	6.28619e8	1.14587
$315$	0	0
$316$	4.07314e8	0.726147
$317$	−7.62555e8	−1.34451	−0.672254	−	0.740320i	$-0.734674\pi$
$317$	−7.62555e8	−1.34451	−0.672254	+	0.740320i	$0.734674\pi$
$318$	0	0
$319$	2.76748e7	0.0477328
$320$	4.31430e7	0.0736013
$321$	0	0
$322$	1.10601e7	0.0184613
$323$	−1.45262e8	−0.239852
$324$	0	0
$325$	−2.32509e8	−0.375705
$326$	1.26162e9	2.01682
$327$	0	0
$328$	−4.07757e8	−0.638032
$329$	1.81631e7	0.0281193
$330$	0	0
$331$	3.94113e8	0.597342	0.298671	−	0.954356i	$-0.403457\pi$
$331$	3.94113e8	0.597342	0.298671	+	0.954356i	$0.403457\pi$
$332$	7.30893e7	0.109615
$333$	0	0
$334$	9.07957e8	1.33338
$335$	3.08721e8	0.448652
$336$	0	0
$337$	1.50464e8	0.214155	0.107077	−	0.994251i	$-0.465851\pi$
$337$	1.50464e8	0.214155	0.107077	+	0.994251i	$0.465851\pi$
$338$	−6.27571e8	−0.884004
$339$	0	0
$340$	−4.31520e7	−0.0595422
$341$	2.34166e7	0.0319803
$342$	0	0
$343$	−2.35051e7	−0.0314509
$344$	−1.58589e8	−0.210047
$345$	0	0
$346$	1.66443e9	2.16023
$347$	−1.12645e9	−1.44730	−0.723651	−	0.690166i	$-0.757538\pi$
$347$	−1.12645e9	−1.44730	−0.723651	+	0.690166i	$0.757538\pi$
$348$	0	0
$349$	−2.40653e8	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$349$	−2.40653e8	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$350$	−1.10115e7	−0.0137280
$351$	0	0
$352$	8.96902e7	0.109609
$353$	2.62604e8	0.317754	0.158877	−	0.987298i	$-0.449213\pi$
$353$	2.62604e8	0.317754	0.158877	+	0.987298i	$0.449213\pi$
$354$	0	0
$355$	2.67714e8	0.317594
$356$	−2.33582e8	−0.274387
$357$	0	0
$358$	1.84175e8	0.212149
$359$	−1.31180e7	−0.0149636	−0.00748179	−	0.999972i	$-0.502382\pi$
$359$	−1.31180e7	−0.0149636	−0.00748179	+	0.999972i	$0.502382\pi$
$360$	0	0
$361$	1.19902e8	0.134138
$362$	1.66327e8	0.184282
$363$	0	0
$364$	3.76442e6	0.00409113
$365$	4.97710e8	0.535737
$366$	0	0
$367$	2.85308e8	0.301288	0.150644	−	0.988588i	$-0.451865\pi$
$367$	2.85308e8	0.301288	0.150644	+	0.988588i	$0.451865\pi$
$368$	−1.14747e9	−1.20026
$369$	0	0
$370$	2.33791e7	0.0239951
$371$	−3.91620e6	−0.00398159
$372$	0	0
$373$	−1.76282e8	−0.175884	−0.0879420	−	0.996126i	$-0.528029\pi$
$373$	−1.76282e8	−0.175884	−0.0879420	+	0.996126i	$0.528029\pi$
$374$	3.35531e7	0.0331651
$375$	0	0
$376$	−1.13910e9	−1.10511
$377$	−2.16919e8	−0.208499
$378$	0	0
$379$	−1.69178e9	−1.59627	−0.798137	−	0.602477i	$-0.794181\pi$
$379$	−1.69178e9	−1.59627	−0.798137	+	0.602477i	$0.794181\pi$
$380$	3.01155e8	0.281545
$381$	0	0
$382$	4.09620e7	0.0375975
$383$	−2.05814e9	−1.87189	−0.935944	−	0.352149i	$-0.885451\pi$
$383$	−2.05814e9	−1.87189	−0.935944	+	0.352149i	$0.885451\pi$
$384$	0	0
$385$	−1.13440e6	−0.00101310
$386$	−1.22926e8	−0.108790
$387$	0	0
$388$	4.00900e8	0.348437
$389$	−1.26822e9	−1.09237	−0.546187	−	0.837663i	$-0.683921\pi$
$389$	−1.26822e9	−1.09237	−0.546187	+	0.837663i	$0.683921\pi$
$390$	0	0
$391$	−2.55626e8	−0.216265
$392$	7.36971e8	0.617944
$393$	0	0
$394$	−7.02597e8	−0.578722
$395$	9.62082e8	0.785457
$396$	0	0
$397$	1.90127e9	1.52502	0.762512	−	0.646975i	$-0.223966\pi$
$397$	1.90127e9	1.52502	0.762512	+	0.646975i	$0.223966\pi$
$398$	5.51632e8	0.438590
$399$	0	0
$400$	1.14243e9	0.892522
$401$	1.68338e9	1.30370	0.651849	−	0.758349i	$-0.273993\pi$
$401$	1.68338e9	1.30370	0.651849	+	0.758349i	$0.273993\pi$
$402$	0	0
$403$	−1.83543e8	−0.139691
$404$	−5.24410e8	−0.395673
$405$	0	0
$406$	−1.02732e7	−0.00761838
$407$	−6.01391e6	−0.00442157
$408$	0	0
$409$	1.07416e8	0.0776317	0.0388159	−	0.999246i	$-0.487641\pi$
$409$	1.07416e8	0.0776317	0.0388159	+	0.999246i	$0.487641\pi$
$410$	9.41707e8	0.674795
$411$	0	0
$412$	8.47757e8	0.597215
$413$	2.93127e6	0.00204753
$414$	0	0
$415$	1.72638e8	0.118568
$416$	−7.03006e8	−0.478776
$417$	0	0
$418$	−2.34164e8	−0.156821
$419$	−2.36422e8	−0.157014	−0.0785071	−	0.996914i	$-0.525015\pi$
$419$	−2.36422e8	−0.157014	−0.0785071	+	0.996914i	$0.525015\pi$
$420$	0	0
$421$	−1.71085e9	−1.11744	−0.558722	−	0.829355i	$-0.688708\pi$
$421$	−1.71085e9	−1.11744	−0.558722	+	0.829355i	$0.688708\pi$
$422$	1.10251e9	0.714148
$423$	0	0
$424$	2.45605e8	0.156479
$425$	2.54502e8	0.160816
$426$	0	0
$427$	−2.18032e6	−0.00135526
$428$	−4.83910e8	−0.298340
$429$	0	0
$430$	3.66258e8	0.222150
$431$	−6.46052e8	−0.388685	−0.194342	−	0.980934i	$-0.562257\pi$
$431$	−6.46052e8	−0.388685	−0.194342	+	0.980934i	$0.562257\pi$
$432$	0	0
$433$	2.52351e9	1.49382	0.746908	−	0.664927i	$-0.231537\pi$
$433$	2.52351e9	1.49382	0.746908	+	0.664927i	$0.231537\pi$
$434$	−8.69247e6	−0.00510422
$435$	0	0
$436$	5.53807e8	0.320004
$437$	1.78400e9	1.02261
$438$	0	0
$439$	−1.77473e8	−0.100117	−0.0500584	−	0.998746i	$-0.515941\pi$
$439$	−1.77473e8	−0.100117	−0.0500584	+	0.998746i	$0.515941\pi$
$440$	7.11440e7	0.0398156
$441$	0	0
$442$	−2.62994e8	−0.144867
$443$	−1.83781e9	−1.00436	−0.502178	−	0.864764i	$-0.667468\pi$
$443$	−1.83781e9	−1.00436	−0.502178	+	0.864764i	$0.667468\pi$
$444$	0	0
$445$	−5.51724e8	−0.296798
$446$	1.87110e9	0.998674
$447$	0	0
$448$	4.11964e6	0.00216464
$449$	8.93570e8	0.465872	0.232936	−	0.972492i	$-0.425167\pi$
$449$	8.93570e8	0.465872	0.232936	+	0.972492i	$0.425167\pi$
$450$	0	0
$451$	−2.42239e8	−0.124345
$452$	1.11610e9	0.568487
$453$	0	0
$454$	2.72800e9	1.36820
$455$	8.89161e6	0.00442528
$456$	0	0
$457$	−5.88094e8	−0.288231	−0.144115	−	0.989561i	$-0.546034\pi$
$457$	−5.88094e8	−0.288231	−0.144115	+	0.989561i	$0.546034\pi$
$458$	1.86713e9	0.908126
$459$	0	0
$460$	5.29960e8	0.253858
$461$	2.65315e9	1.26127	0.630636	−	0.776079i	$-0.282794\pi$
$461$	2.65315e9	1.26127	0.630636	+	0.776079i	$0.282794\pi$
$462$	0	0
$463$	1.10539e9	0.517587	0.258793	−	0.965933i	$-0.416675\pi$
$463$	1.10539e9	0.517587	0.258793	+	0.965933i	$0.416675\pi$
$464$	1.06583e9	0.495307
$465$	0	0
$466$	−1.88529e9	−0.863033
$467$	−6.70125e8	−0.304472	−0.152236	−	0.988344i	$-0.548647\pi$
$467$	−6.70125e8	−0.304472	−0.152236	+	0.988344i	$0.548647\pi$
$468$	0	0
$469$	2.94792e7	0.0131950
$470$	2.63073e9	1.16878
$471$	0	0
$472$	−1.83835e8	−0.0804694
$473$	−9.42140e7	−0.0409356
$474$	0	0
$475$	−1.77615e9	−0.760418
$476$	−4.12050e6	−0.00175116
$477$	0	0
$478$	−1.81862e9	−0.761631
$479$	9.38891e7	0.0390338	0.0195169	−	0.999810i	$-0.493787\pi$
$479$	9.38891e7	0.0390338	0.0195169	+	0.999810i	$0.493787\pi$
$480$	0	0
$481$	4.71380e7	0.0193136
$482$	3.45274e9	1.40443
$483$	0	0
$484$	−1.21526e9	−0.487204
$485$	9.46931e8	0.376896
$486$	0	0
$487$	1.37204e9	0.538288	0.269144	−	0.963100i	$-0.413259\pi$
$487$	1.37204e9	0.538288	0.269144	+	0.963100i	$0.413259\pi$
$488$	1.36739e8	0.0532626
$489$	0	0
$490$	−1.70202e9	−0.653550
$491$	−3.03791e9	−1.15822	−0.579108	−	0.815251i	$-0.696599\pi$
$491$	−3.03791e9	−1.15822	−0.579108	+	0.815251i	$0.696599\pi$
$492$	0	0
$493$	2.37438e8	0.0892455
$494$	1.83542e9	0.685000
$495$	0	0
$496$	9.01834e8	0.331849
$497$	2.55635e7	0.00934056
$498$	0	0
$499$	−3.44240e9	−1.24025	−0.620126	−	0.784502i	$-0.712919\pi$
$499$	−3.44240e9	−1.24025	−0.620126	+	0.784502i	$0.712919\pi$
$500$	−1.26657e9	−0.453142
$501$	0	0
$502$	−4.89421e8	−0.172671
$503$	−1.03977e8	−0.0364291	−0.0182146	−	0.999834i	$-0.505798\pi$
$503$	−1.03977e8	−0.0364291	−0.0182146	+	0.999834i	$0.505798\pi$
$504$	0	0
$505$	−1.23866e9	−0.427990
$506$	−4.12073e8	−0.141399
$507$	0	0
$508$	−1.99729e9	−0.675955
$509$	9.41820e8	0.316560	0.158280	−	0.987394i	$-0.449405\pi$
$509$	9.41820e8	0.316560	0.158280	+	0.987394i	$0.449405\pi$
$510$	0	0
$511$	4.75253e7	0.0157562
$512$	1.10782e9	0.364774
$513$	0	0
$514$	−6.62604e8	−0.215220
$515$	2.00241e9	0.645994
$516$	0	0
$517$	−6.76715e8	−0.215372
$518$	2.23243e6	0.000705704 0
$519$	0	0
$520$	−5.57638e8	−0.173916
$521$	−9.49236e8	−0.294064	−0.147032	−	0.989132i	$-0.546972\pi$
$521$	−9.49236e8	−0.294064	−0.147032	+	0.989132i	$0.546972\pi$
$522$	0	0
$523$	−3.88735e9	−1.18822	−0.594111	−	0.804383i	$-0.702496\pi$
$523$	−3.88735e9	−1.18822	−0.594111	+	0.804383i	$0.702496\pi$
$524$	9.76104e8	0.296372
$525$	0	0
$526$	−5.58280e9	−1.67264
$527$	2.00904e8	0.0597933
$528$	0	0
$529$	−2.65425e8	−0.0779555
$530$	−5.67220e8	−0.165495
$531$	0	0
$532$	2.87567e7	0.00828034
$533$	1.89871e9	0.543142
$534$	0	0
$535$	−1.14300e9	−0.322707
$536$	−1.84879e9	−0.518574
$537$	0	0
$538$	−2.19972e9	−0.609018
$539$	4.37819e8	0.120430
$540$	0	0
$541$	−2.42183e9	−0.657588	−0.328794	−	0.944402i	$-0.606642\pi$
$541$	−2.42183e9	−0.657588	−0.328794	+	0.944402i	$0.606642\pi$
$542$	−3.64955e9	−0.984558
$543$	0	0
$544$	7.69505e8	0.204935
$545$	1.30810e9	0.346141
$546$	0	0
$547$	5.83350e9	1.52396	0.761980	−	0.647600i	$-0.224227\pi$
$547$	5.83350e9	1.52396	0.761980	+	0.647600i	$0.224227\pi$
$548$	−1.73111e8	−0.0449359
$549$	0	0
$550$	4.10261e8	0.105146
$551$	−1.65706e9	−0.421996
$552$	0	0
$553$	9.18674e7	0.0231006
$554$	7.02282e9	1.75480
$555$	0	0
$556$	1.39938e9	0.345282
$557$	−2.32049e9	−0.568967	−0.284484	−	0.958681i	$-0.591822\pi$
$557$	−2.32049e9	−0.568967	−0.284484	+	0.958681i	$0.591822\pi$
$558$	0	0
$559$	7.38465e8	0.178809
$560$	−4.36888e7	−0.0105126
$561$	0	0
$562$	−5.55863e9	−1.32096
$563$	4.30898e9	1.01764	0.508821	−	0.860873i	$-0.330082\pi$
$563$	4.30898e9	1.01764	0.508821	+	0.860873i	$0.330082\pi$
$564$	0	0
$565$	2.63626e9	0.614919
$566$	−1.95753e8	−0.0453785
$567$	0	0
$568$	−1.60322e9	−0.367090
$569$	−5.58255e9	−1.27040	−0.635198	−	0.772349i	$-0.719082\pi$
$569$	−5.58255e9	−1.27040	−0.635198	+	0.772349i	$0.719082\pi$
$570$	0	0
$571$	5.36498e9	1.20598	0.602992	−	0.797747i	$-0.293975\pi$
$571$	5.36498e9	1.20598	0.602992	+	0.797747i	$0.293975\pi$
$572$	−1.40253e8	−0.0313348
$573$	0	0
$574$	8.99217e7	0.0198460
$575$	−3.12560e9	−0.685639
$576$	0	0
$577$	4.50669e9	0.976658	0.488329	−	0.872660i	$-0.337607\pi$
$577$	4.50669e9	0.976658	0.488329	+	0.872660i	$0.337607\pi$
$578$	−5.38728e9	−1.16044
$579$	0	0
$580$	−4.92253e8	−0.104759
$581$	1.64849e7	0.00348714
$582$	0	0
$583$	1.45908e8	0.0304958
$584$	−2.98055e9	−0.619230
$585$	0	0
$586$	8.20794e8	0.168497
$587$	−4.94446e9	−1.00899	−0.504494	−	0.863415i	$-0.668321\pi$
$587$	−4.94446e9	−1.00899	−0.504494	+	0.863415i	$0.668321\pi$
$588$	0	0
$589$	−1.40210e9	−0.282732
$590$	4.24563e8	0.0851060
$591$	0	0
$592$	−2.31612e8	−0.0458812
$593$	−7.08369e9	−1.39498	−0.697490	−	0.716594i	$-0.745700\pi$
$593$	−7.08369e9	−1.39498	−0.697490	+	0.716594i	$0.745700\pi$
$594$	0	0
$595$	−9.73269e6	−0.00189419
$596$	−2.75141e8	−0.0532345
$597$	0	0
$598$	3.22989e9	0.617638
$599$	−6.53780e9	−1.24290	−0.621452	−	0.783452i	$-0.713457\pi$
$599$	−6.53780e9	−1.24290	−0.621452	+	0.783452i	$0.713457\pi$
$600$	0	0
$601$	−5.66921e9	−1.06528	−0.532638	−	0.846343i	$-0.678799\pi$
$601$	−5.66921e9	−1.06528	−0.532638	+	0.846343i	$0.678799\pi$
$602$	3.49732e7	0.00653353
$603$	0	0
$604$	4.06657e7	0.00750930
$605$	−2.87046e9	−0.526997
$606$	0	0
$607$	−3.43054e8	−0.0622590	−0.0311295	−	0.999515i	$-0.509910\pi$
$607$	−3.43054e8	−0.0622590	−0.0311295	+	0.999515i	$0.509910\pi$
$608$	−5.37032e9	−0.969031
$609$	0	0
$610$	−3.15796e8	−0.0563316
$611$	5.30420e9	0.940753
$612$	0	0
$613$	−1.95826e9	−0.343367	−0.171683	−	0.985152i	$-0.554921\pi$
$613$	−1.95826e9	−0.343367	−0.171683	+	0.985152i	$0.554921\pi$
$614$	3.66440e9	0.638872
$615$	0	0
$616$	6.79340e6	0.00117099
$617$	1.99932e9	0.342676	0.171338	−	0.985212i	$-0.445191\pi$
$617$	1.99932e9	0.342676	0.171338	+	0.985212i	$0.445191\pi$
$618$	0	0
$619$	1.57292e9	0.266556	0.133278	−	0.991079i	$-0.457450\pi$
$619$	1.57292e9	0.266556	0.133278	+	0.991079i	$0.457450\pi$
$620$	−4.16512e8	−0.0701870
$621$	0	0
$622$	−3.48202e9	−0.580182
$623$	−5.26830e7	−0.00872896
$624$	0	0
$625$	1.36647e9	0.223882
$626$	2.47113e9	0.402611
$627$	0	0
$628$	2.87621e9	0.463406
$629$	−5.15969e7	−0.00826697
$630$	0	0
$631$	3.48635e9	0.552419	0.276209	−	0.961097i	$-0.410922\pi$
$631$	3.48635e9	0.552419	0.276209	+	0.961097i	$0.410922\pi$
$632$	−5.76146e9	−0.907869
$633$	0	0
$634$	−1.05464e10	−1.64359
$635$	−4.71762e9	−0.731165
$636$	0	0
$637$	−3.43169e9	−0.526042
$638$	3.82753e8	0.0583508
$639$	0	0
$640$	3.82362e9	0.576561
$641$	−3.27300e9	−0.490843	−0.245422	−	0.969416i	$-0.578926\pi$
$641$	−3.27300e9	−0.490843	−0.245422	+	0.969416i	$0.578926\pi$
$642$	0	0
$643$	1.07236e10	1.59075	0.795373	−	0.606120i	$-0.207275\pi$
$643$	1.07236e10	1.59075	0.795373	+	0.606120i	$0.207275\pi$
$644$	5.06048e7	0.00746606
$645$	0	0
$646$	−2.00903e9	−0.293206
$647$	−1.13384e10	−1.64584	−0.822919	−	0.568159i	$-0.807656\pi$
$647$	−1.13384e10	−1.64584	−0.822919	+	0.568159i	$0.807656\pi$
$648$	0	0
$649$	−1.09212e8	−0.0156825
$650$	−3.21569e9	−0.459280
$651$	0	0
$652$	5.77248e9	0.815635
$653$	−2.78140e9	−0.390901	−0.195451	−	0.980714i	$-0.562617\pi$
$653$	−2.78140e9	−0.390901	−0.195451	+	0.980714i	$0.562617\pi$
$654$	0	0
$655$	2.30557e9	0.320578
$656$	−9.32928e9	−1.29028
$657$	0	0
$658$	2.51204e8	0.0343744
$659$	−8.83123e9	−1.20205	−0.601025	−	0.799230i	$-0.705241\pi$
$659$	−8.83123e9	−1.20205	−0.601025	+	0.799230i	$0.705241\pi$
$660$	0	0
$661$	−5.82485e9	−0.784476	−0.392238	−	0.919864i	$-0.628299\pi$
$661$	−5.82485e9	−0.784476	−0.392238	+	0.919864i	$0.628299\pi$
$662$	5.45075e9	0.730219
$663$	0	0
$664$	−1.03385e9	−0.137047
$665$	6.79238e7	0.00895666
$666$	0	0
$667$	−2.91603e9	−0.380497
$668$	4.15431e9	0.539239
$669$	0	0
$670$	4.26974e9	0.548454
$671$	8.12335e7	0.0103802
$672$	0	0
$673$	3.42844e9	0.433554	0.216777	−	0.976221i	$-0.430446\pi$
$673$	3.42844e9	0.433554	0.216777	+	0.976221i	$0.430446\pi$
$674$	2.08098e9	0.261793
$675$	0	0
$676$	−2.87142e9	−0.357506
$677$	−8.10222e9	−1.00356	−0.501781	−	0.864995i	$-0.667322\pi$
$677$	−8.10222e9	−1.00356	−0.501781	+	0.864995i	$0.667322\pi$
$678$	0	0
$679$	9.04206e7	0.0110847
$680$	6.10386e8	0.0744429
$681$	0	0
$682$	3.23861e8	0.0390943
$683$	−1.95901e9	−0.235269	−0.117634	−	0.993057i	$-0.537531\pi$
$683$	−1.95901e9	−0.235269	−0.117634	+	0.993057i	$0.537531\pi$
$684$	0	0
$685$	−4.08892e8	−0.0486061
$686$	−3.25086e8	−0.0384471
$687$	0	0
$688$	−3.62844e9	−0.424776
$689$	−1.14365e9	−0.133207
$690$	0	0
$691$	−7.12139e9	−0.821091	−0.410546	−	0.911840i	$-0.634662\pi$
$691$	−7.12139e9	−0.821091	−0.410546	+	0.911840i	$0.634662\pi$
$692$	7.61552e9	0.873632
$693$	0	0
$694$	−1.55793e10	−1.76925
$695$	3.30536e9	0.373484
$696$	0	0
$697$	−2.07831e9	−0.232486
$698$	−3.32833e9	−0.370453
$699$	0	0
$700$	−5.03823e7	−0.00555182
$701$	9.01916e9	0.988902	0.494451	−	0.869206i	$-0.335369\pi$
$701$	9.01916e9	0.988902	0.494451	+	0.869206i	$0.335369\pi$
$702$	0	0
$703$	3.60091e8	0.0390903
$704$	−1.53488e8	−0.0165794
$705$	0	0
$706$	3.63193e9	0.388437
$707$	−1.18278e8	−0.0125874
$708$	0	0
$709$	−1.63143e10	−1.71912	−0.859560	−	0.511034i	$-0.829263\pi$
$709$	−1.63143e10	−1.71912	−0.859560	+	0.511034i	$0.829263\pi$
$710$	3.70260e9	0.388242
$711$	0	0
$712$	3.30402e9	0.343054
$713$	−2.46735e9	−0.254928
$714$	0	0
$715$	−3.31280e8	−0.0338941
$716$	8.42684e8	0.0857964
$717$	0	0
$718$	−1.81427e8	−0.0182922
$719$	−6.12136e9	−0.614181	−0.307091	−	0.951680i	$-0.599355\pi$
$719$	−6.12136e9	−0.614181	−0.307091	+	0.951680i	$0.599355\pi$
$720$	0	0
$721$	1.91207e8	0.0189989
$722$	1.65829e9	0.163976
$723$	0	0
$724$	7.61019e8	0.0745265
$725$	2.90321e9	0.282941
$726$	0	0
$727$	1.56648e9	0.151201	0.0756003	−	0.997138i	$-0.475913\pi$
$727$	1.56648e9	0.151201	0.0756003	+	0.997138i	$0.475913\pi$
$728$	−5.32477e7	−0.00511495
$729$	0	0
$730$	6.88353e9	0.654910
$731$	−8.08318e8	−0.0765370
$732$	0	0
$733$	−4.77128e9	−0.447477	−0.223739	−	0.974649i	$-0.571826\pi$
$733$	−4.77128e9	−0.447477	−0.223739	+	0.974649i	$0.571826\pi$
$734$	3.94592e9	0.368309
$735$	0	0
$736$	−9.45046e9	−0.873737
$737$	−1.09833e9	−0.101064
$738$	0	0
$739$	8.82555e8	0.0804427	0.0402213	−	0.999191i	$-0.487194\pi$
$739$	8.82555e8	0.0804427	0.0402213	+	0.999191i	$0.487194\pi$
$740$	1.06970e8	0.00970399
$741$	0	0
$742$	−5.41627e7	−0.00486728
$743$	−1.56677e9	−0.140134	−0.0700672	−	0.997542i	$-0.522321\pi$
$743$	−1.56677e9	−0.140134	−0.0700672	+	0.997542i	$0.522321\pi$
$744$	0	0
$745$	−6.49886e8	−0.0575825
$746$	−2.43805e9	−0.215009
$747$	0	0
$748$	1.53520e8	0.0134125
$749$	−1.09143e8	−0.00949095
$750$	0	0
$751$	5.02135e9	0.432594	0.216297	−	0.976328i	$-0.430602\pi$
$751$	5.02135e9	0.432594	0.216297	+	0.976328i	$0.430602\pi$
$752$	−2.60621e10	−2.23484
$753$	0	0
$754$	−3.00008e9	−0.254879
$755$	9.60531e7	0.00812263
$756$	0	0
$757$	−2.94352e9	−0.246622	−0.123311	−	0.992368i	$-0.539351\pi$
$757$	−2.94352e9	−0.246622	−0.123311	+	0.992368i	$0.539351\pi$
$758$	−2.33980e10	−1.95136
$759$	0	0
$760$	−4.25984e9	−0.352002
$761$	1.87159e10	1.53945	0.769724	−	0.638376i	$-0.220394\pi$
$761$	1.87159e10	1.53945	0.769724	+	0.638376i	$0.220394\pi$
$762$	0	0
$763$	1.24908e8	0.0101801
$764$	1.87419e8	0.0152050
$765$	0	0
$766$	−2.84650e10	−2.28828
$767$	8.56023e8	0.0685017
$768$	0	0
$769$	−1.08476e10	−0.860187	−0.430093	−	0.902784i	$-0.641519\pi$
$769$	−1.08476e10	−0.860187	−0.430093	+	0.902784i	$0.641519\pi$
$770$	−1.56892e7	−0.00123847
$771$	0	0
$772$	−5.62443e8	−0.0439965
$773$	2.59403e9	0.201998	0.100999	−	0.994887i	$-0.467796\pi$
$773$	2.59403e9	0.201998	0.100999	+	0.994887i	$0.467796\pi$
$774$	0	0
$775$	2.45651e9	0.189567
$776$	−5.67073e9	−0.435635
$777$	0	0
$778$	−1.75400e10	−1.33537
$779$	1.45044e10	1.09931
$780$	0	0
$781$	−9.52435e8	−0.0715413
$782$	−3.53541e9	−0.264373
$783$	0	0
$784$	1.68616e10	1.24966
$785$	6.79366e9	0.501256
$786$	0	0
$787$	−2.06990e10	−1.51369	−0.756846	−	0.653593i	$-0.773261\pi$
$787$	−2.06990e10	−1.51369	−0.756846	+	0.653593i	$0.773261\pi$
$788$	−3.21470e9	−0.234044
$789$	0	0
$790$	1.33060e10	0.960180
$791$	2.51731e8	0.0180850
$792$	0	0
$793$	−6.36721e8	−0.0453412
$794$	2.62953e10	1.86426
$795$	0	0
$796$	2.52396e9	0.177373
$797$	6.06784e9	0.424551	0.212275	−	0.977210i	$-0.431913\pi$
$797$	6.06784e9	0.424551	0.212275	+	0.977210i	$0.431913\pi$
$798$	0	0
$799$	−5.80594e9	−0.402679
$800$	9.40891e9	0.649718
$801$	0	0
$802$	2.32819e10	1.59370
$803$	−1.77068e9	−0.120680
$804$	0	0
$805$	1.19529e8	0.00807586
$806$	−2.53847e9	−0.170765
$807$	0	0
$808$	7.41778e9	0.494691
$809$	2.20534e10	1.46438	0.732192	−	0.681098i	$-0.238497\pi$
$809$	2.20534e10	1.46438	0.732192	+	0.681098i	$0.238497\pi$
$810$	0	0
$811$	9.91610e9	0.652782	0.326391	−	0.945235i	$-0.394167\pi$
$811$	9.91610e9	0.652782	0.326391	+	0.945235i	$0.394167\pi$
$812$	−4.70043e7	−0.00308100
$813$	0	0
$814$	−8.31749e7	−0.00540514
$815$	1.36347e10	0.882253
$816$	0	0
$817$	5.64119e9	0.361904
$818$	1.48561e9	0.0949007
$819$	0	0
$820$	4.30873e9	0.272898
$821$	4.09876e9	0.258495	0.129247	−	0.991612i	$-0.458744\pi$
$821$	4.09876e9	0.258495	0.129247	+	0.991612i	$0.458744\pi$
$822$	0	0
$823$	−6.76087e9	−0.422769	−0.211384	−	0.977403i	$-0.567797\pi$
$823$	−6.76087e9	−0.422769	−0.211384	+	0.977403i	$0.567797\pi$
$824$	−1.19915e10	−0.746671
$825$	0	0
$826$	4.05407e7	0.00250300
$827$	−9.41705e8	−0.0578956	−0.0289478	−	0.999581i	$-0.509216\pi$
$827$	−9.41705e8	−0.0578956	−0.0289478	+	0.999581i	$0.509216\pi$
$828$	0	0
$829$	1.36525e10	0.832284	0.416142	−	0.909300i	$-0.363382\pi$
$829$	1.36525e10	0.832284	0.416142	+	0.909300i	$0.363382\pi$
$830$	2.38766e9	0.144943
$831$	0	0
$832$	1.20306e9	0.0724197
$833$	3.75630e9	0.225166
$834$	0	0
$835$	9.81253e9	0.583282
$836$	−1.07141e9	−0.0634209
$837$	0	0
$838$	−3.26981e9	−0.191942
$839$	2.04480e10	1.19532	0.597660	−	0.801750i	$-0.296097\pi$
$839$	2.04480e10	1.19532	0.597660	+	0.801750i	$0.296097\pi$
$840$	0	0
$841$	−1.45413e10	−0.842981
$842$	−2.36618e10	−1.36602
$843$	0	0
$844$	5.04446e9	0.288813
$845$	−6.78233e9	−0.386706
$846$	0	0
$847$	−2.74095e8	−0.0154992
$848$	5.61932e9	0.316445
$849$	0	0
$850$	3.51987e9	0.196590
$851$	6.33673e8	0.0352461
$852$	0	0
$853$	9.28799e9	0.512389	0.256195	−	0.966625i	$-0.417531\pi$
$853$	9.28799e9	0.512389	0.256195	+	0.966625i	$0.417531\pi$
$854$	−3.01547e7	−0.00165673
$855$	0	0
$856$	6.84490e9	0.373000
$857$	7.57637e9	0.411177	0.205588	−	0.978639i	$-0.434089\pi$
$857$	7.57637e9	0.411177	0.205588	+	0.978639i	$0.434089\pi$
$858$	0	0
$859$	5.27186e9	0.283784	0.141892	−	0.989882i	$-0.454681\pi$
$859$	5.27186e9	0.283784	0.141892	+	0.989882i	$0.454681\pi$
$860$	1.67579e9	0.0898412
$861$	0	0
$862$	−8.93517e9	−0.475146
$863$	−2.11332e10	−1.11925	−0.559625	−	0.828746i	$-0.689055\pi$
$863$	−2.11332e10	−1.11925	−0.559625	+	0.828746i	$0.689055\pi$
$864$	0	0
$865$	1.79880e10	0.944988
$866$	3.49012e10	1.82611
$867$	0	0
$868$	−3.97719e7	−0.00206423
$869$	−3.42276e9	−0.176932
$870$	0	0
$871$	8.60885e9	0.441450
$872$	−7.83360e9	−0.400086
$873$	0	0
$874$	2.46734e10	1.25008
$875$	−2.85668e8	−0.0144156
$876$	0	0
$877$	1.67780e10	0.839928	0.419964	−	0.907541i	$-0.362043\pi$
$877$	1.67780e10	0.839928	0.419964	+	0.907541i	$0.362043\pi$
$878$	−2.45453e9	−0.122387
$879$	0	0
$880$	1.62774e9	0.0805186
$881$	−4.60252e9	−0.226767	−0.113384	−	0.993551i	$-0.536169\pi$
$881$	−4.60252e9	−0.226767	−0.113384	+	0.993551i	$0.536169\pi$
$882$	0	0
$883$	−1.60291e10	−0.783515	−0.391758	−	0.920068i	$-0.628133\pi$
$883$	−1.60291e10	−0.783515	−0.391758	+	0.920068i	$0.628133\pi$
$884$	−1.20332e9	−0.0585864
$885$	0	0
$886$	−2.54177e10	−1.22777
$887$	3.53761e10	1.70207	0.851034	−	0.525111i	$-0.175976\pi$
$887$	3.53761e10	1.70207	0.851034	+	0.525111i	$0.175976\pi$
$888$	0	0
$889$	−4.50477e8	−0.0215038
$890$	−7.63057e9	−0.362820
$891$	0	0
$892$	8.56109e9	0.403880
$893$	4.05192e10	1.90406
$894$	0	0
$895$	1.99043e9	0.0928040
$896$	3.65110e8	0.0169569
$897$	0	0
$898$	1.23584e10	0.569504
$899$	2.29180e9	0.105200
$900$	0	0
$901$	1.25183e9	0.0570177
$902$	−3.35027e9	−0.152005
$903$	0	0
$904$	−1.57873e10	−0.710753
$905$	1.79754e9	0.0806136
$906$	0	0
$907$	−6.61497e9	−0.294376	−0.147188	−	0.989109i	$-0.547022\pi$
$907$	−6.61497e9	−0.294376	−0.147188	+	0.989109i	$0.547022\pi$
$908$	1.24818e10	0.553320
$909$	0	0
$910$	1.22975e8	0.00540967
$911$	−1.46424e10	−0.641651	−0.320826	−	0.947138i	$-0.603960\pi$
$911$	−1.46424e10	−0.641651	−0.320826	+	0.947138i	$0.603960\pi$
$912$	0	0
$913$	−6.14187e8	−0.0267087
$914$	−8.13359e9	−0.352347
$915$	0	0
$916$	8.54297e9	0.367261
$917$	2.20155e8	0.00942834
$918$	0	0
$919$	4.03688e10	1.71570	0.857850	−	0.513901i	$-0.171800\pi$
$919$	4.03688e10	1.71570	0.857850	+	0.513901i	$0.171800\pi$
$920$	−7.49629e9	−0.317387
$921$	0	0
$922$	3.66942e10	1.54184
$923$	7.46534e9	0.312495
$924$	0	0
$925$	−6.30887e8	−0.0262093
$926$	1.52880e10	0.632723
$927$	0	0
$928$	8.77806e9	0.360563
$929$	2.36038e10	0.965889	0.482945	−	0.875651i	$-0.339567\pi$
$929$	2.36038e10	0.965889	0.482945	+	0.875651i	$0.339567\pi$
$930$	0	0
$931$	−2.62150e10	−1.06470
$932$	−8.62604e9	−0.349024
$933$	0	0
$934$	−9.26811e9	−0.372200
$935$	3.62617e8	0.0145080
$936$	0	0
$937$	2.58838e10	1.02787	0.513937	−	0.857828i	$-0.328186\pi$
$937$	2.58838e10	1.02787	0.513937	+	0.857828i	$0.328186\pi$
$938$	4.07709e8	0.0161302
$939$	0	0
$940$	1.20368e10	0.472675
$941$	−1.53080e10	−0.598902	−0.299451	−	0.954112i	$-0.596804\pi$
$941$	−1.53080e10	−0.598902	−0.299451	+	0.954112i	$0.596804\pi$
$942$	0	0
$943$	2.55242e10	0.991201
$944$	−4.20606e9	−0.162732
$945$	0	0
$946$	−1.30302e9	−0.0500417
$947$	−9.43008e9	−0.360820	−0.180410	−	0.983592i	$-0.557742\pi$
$947$	−9.43008e9	−0.360820	−0.180410	+	0.983592i	$0.557742\pi$
$948$	0	0
$949$	1.38789e10	0.527136
$950$	−2.45649e10	−0.929571
$951$	0	0
$952$	5.82846e7	0.00218940
$953$	2.53714e10	0.949555	0.474777	−	0.880106i	$-0.342529\pi$
$953$	2.53714e10	0.949555	0.474777	+	0.880106i	$0.342529\pi$
$954$	0	0
$955$	4.42687e8	0.0164469
$956$	−8.32100e9	−0.308016
$957$	0	0
$958$	1.29853e9	0.0477168
$959$	−3.90442e7	−0.00142953
$960$	0	0
$961$	−2.55734e10	−0.929517
$962$	6.51938e8	0.0236099
$963$	0	0
$964$	1.57978e10	0.567973
$965$	−1.32850e9	−0.0475900
$966$	0	0
$967$	−2.23509e10	−0.794883	−0.397442	−	0.917627i	$-0.630102\pi$
$967$	−2.23509e10	−0.794883	−0.397442	+	0.917627i	$0.630102\pi$
$968$	1.71899e10	0.609128
$969$	0	0
$970$	1.30964e10	0.460736
$971$	2.51106e10	0.880217	0.440108	−	0.897945i	$-0.354940\pi$
$971$	2.51106e10	0.880217	0.440108	+	0.897945i	$0.354940\pi$
$972$	0	0
$973$	3.15622e8	0.0109843
$974$	1.89758e10	0.658028
$975$	0	0
$976$	3.12852e9	0.107712
$977$	1.40783e10	0.482970	0.241485	−	0.970405i	$-0.422366\pi$
$977$	1.40783e10	0.482970	0.241485	+	0.970405i	$0.422366\pi$
$978$	0	0
$979$	1.96284e9	0.0668569
$980$	−7.78751e9	−0.264306
$981$	0	0
$982$	−4.20155e10	−1.41586
$983$	4.03081e10	1.35349	0.676744	−	0.736218i	$-0.263390\pi$
$983$	4.03081e10	1.35349	0.676744	+	0.736218i	$0.263390\pi$
$984$	0	0
$985$	−7.59316e9	−0.253160
$986$	3.28387e9	0.109098
$987$	0	0
$988$	8.39785e9	0.277025
$989$	9.92713e9	0.326315
$990$	0	0
$991$	5.94799e10	1.94139	0.970694	−	0.240318i	$-0.0772517\pi$
$991$	5.94799e10	1.94139	0.970694	+	0.240318i	$0.0772517\pi$
$992$	7.42741e9	0.241572
$993$	0	0
$994$	3.53554e8	0.0114183
$995$	5.96163e9	0.191860
$996$	0	0
$997$	1.24113e10	0.396630	0.198315	−	0.980138i	$-0.436453\pi$
$997$	1.24113e10	0.396630	0.198315	+	0.980138i	$0.436453\pi$
$998$	−4.76099e10	−1.51614
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.14		17
3.2	odd	2		177.8.a.c.1.4	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.4	✓	17	3.2	odd	2
531.8.a.c.1.14		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)

\(f(q)\)	\(=\)	\(q+13.8304 q^{2} +63.2803 q^{4} +149.469 q^{5} +14.2725 q^{7} -895.100 q^{8} +O(q^{10})\)	\(q+13.8304 q^{2} +63.2803 q^{4} +149.469 q^{5} +14.2725 q^{7} -895.100 q^{8} +2067.22 q^{10} -531.760 q^{11} +4168.02 q^{13} +197.395 q^{14} -20479.5 q^{16} -4562.28 q^{17} +31839.8 q^{19} +9458.44 q^{20} -7354.45 q^{22} +56030.4 q^{23} -55784.0 q^{25} +57645.4 q^{26} +903.168 q^{28} -52043.8 q^{29} -44036.0 q^{31} -168667. q^{32} -63098.2 q^{34} +2133.30 q^{35} +11309.5 q^{37} +440358. q^{38} -133790. q^{40} +455543. q^{41} +177174. q^{43} -33649.9 q^{44} +774923. q^{46} +1.27260e6 q^{47} -823339. q^{49} -771516. q^{50} +263753. q^{52} -274388. q^{53} -79481.6 q^{55} -12775.3 q^{56} -719787. q^{58} +205379. q^{59} -152764. q^{61} -609036. q^{62} +288642. q^{64} +622989. q^{65} +2.06545e6 q^{67} -288702. q^{68} +29504.4 q^{70} +1.79110e6 q^{71} +3.32985e6 q^{73} +156414. q^{74} +2.01483e6 q^{76} -7589.54 q^{77} +6.43667e6 q^{79} -3.06105e6 q^{80} +6.30035e6 q^{82} +1.15501e6 q^{83} -681919. q^{85} +2.45039e6 q^{86} +475978. q^{88} -3.69123e6 q^{89} +59488.0 q^{91} +3.54562e6 q^{92} +1.76005e7 q^{94} +4.75907e6 q^{95} +6.33530e6 q^{97} -1.13871e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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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