LMFDB - Embedded newform 531.8.a.c.1.10

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			1.10
Root			$-3.88629$ 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)

$f(q)$	$=$	$q+3.88629 q^{2} -112.897 q^{4} +26.2639 q^{5} -644.460 q^{7} -936.194 q^{8} +O(q^{10})$	\(q+3.88629 q^{2} -112.897 q^{4} +26.2639 q^{5} -644.460 q^{7} -936.194 q^{8} +102.069 q^{10} +5692.26 q^{11} -606.275 q^{13} -2504.56 q^{14} +10812.5 q^{16} +39283.3 q^{17} -34062.8 q^{19} -2965.10 q^{20} +22121.8 q^{22} +21244.4 q^{23} -77435.2 q^{25} -2356.16 q^{26} +72757.5 q^{28} -26193.7 q^{29} -310358. q^{31} +161853. q^{32} +152666. q^{34} -16926.0 q^{35} -330264. q^{37} -132378. q^{38} -24588.1 q^{40} -318533. q^{41} +16755.2 q^{43} -642638. q^{44} +82562.0 q^{46} -764733. q^{47} -408214. q^{49} -300935. q^{50} +68446.5 q^{52} +1.38308e6 q^{53} +149501. q^{55} +603340. q^{56} -101796. q^{58} +205379. q^{59} -354332. q^{61} -1.20614e6 q^{62} -754988. q^{64} -15923.1 q^{65} +4.54645e6 q^{67} -4.43496e6 q^{68} -65779.3 q^{70} +367019. q^{71} -1.13809e6 q^{73} -1.28350e6 q^{74} +3.84558e6 q^{76} -3.66843e6 q^{77} +3.04988e6 q^{79} +283977. q^{80} -1.23791e6 q^{82} +8.39695e6 q^{83} +1.03173e6 q^{85} +65115.7 q^{86} -5.32906e6 q^{88} +3.28661e6 q^{89} +390720. q^{91} -2.39843e6 q^{92} -2.97197e6 q^{94} -894620. q^{95} +8.46055e6 q^{97} -1.58644e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.88629	0.343503	0.171751	−	0.985140i	$-0.445057\pi$
$2$	3.88629	0.343503	0.171751	+	0.985140i	$0.445057\pi$
$3$	0	0
$3$	0	0
$4$	−112.897	−0.882006
$5$	26.2639	0.0939644	0.0469822	−	0.998896i	$-0.485040\pi$
$5$	26.2639	0.0939644	0.0469822	+	0.998896i	$0.485040\pi$
$6$	0	0
$7$	−644.460	−0.710155	−0.355077	−	0.934837i	$-0.615545\pi$
$7$	−644.460	−0.710155	−0.355077	+	0.934837i	$0.615545\pi$
$8$	−936.194	−0.646474
$9$	0	0
$10$	102.069	0.0322770
$11$	5692.26	1.28947	0.644734	−	0.764407i	$-0.276968\pi$
$11$	5692.26	1.28947	0.644734	+	0.764407i	$0.276968\pi$
$12$	0	0
$13$	−606.275	−0.0765364	−0.0382682	−	0.999268i	$-0.512184\pi$
$13$	−606.275	−0.0765364	−0.0382682	+	0.999268i	$0.512184\pi$
$14$	−2504.56	−0.243940
$15$	0	0
$16$	10812.5	0.659941
$17$	39283.3	1.93926	0.969632	−	0.244570i	$-0.0786467\pi$
$17$	39283.3	1.93926	0.969632	+	0.244570i	$0.0786467\pi$
$18$	0	0
$19$	−34062.8	−1.13931	−0.569656	−	0.821883i	$-0.692923\pi$
$19$	−34062.8	−1.13931	−0.569656	+	0.821883i	$0.692923\pi$
$20$	−2965.10	−0.0828772
$21$	0	0
$22$	22121.8	0.442935
$23$	21244.4	0.364081	0.182040	−	0.983291i	$-0.441730\pi$
$23$	21244.4	0.364081	0.182040	+	0.983291i	$0.441730\pi$
$24$	0	0
$25$	−77435.2	−0.991171
$26$	−2356.16	−0.0262905
$27$	0	0
$28$	72757.5	0.626361
$29$	−26193.7	−0.199436	−0.0997179	−	0.995016i	$-0.531794\pi$
$29$	−26193.7	−0.199436	−0.0997179	+	0.995016i	$0.531794\pi$
$30$	0	0
$31$	−310358.	−1.87110	−0.935551	−	0.353193i	$-0.885096\pi$
$31$	−310358.	−1.87110	−0.935551	+	0.353193i	$0.885096\pi$
$32$	161853.	0.873165
$33$	0	0
$34$	152666.	0.666142
$35$	−16926.0	−0.0667292
$36$	0	0
$37$	−330264.	−1.07190	−0.535951	−	0.844249i	$-0.680047\pi$
$37$	−330264.	−1.07190	−0.535951	+	0.844249i	$0.680047\pi$
$38$	−132378.	−0.391356
$39$	0	0
$40$	−24588.1	−0.0607455
$41$	−318533.	−0.721790	−0.360895	−	0.932607i	$-0.617529\pi$
$41$	−318533.	−0.721790	−0.360895	+	0.932607i	$0.617529\pi$
$42$	0	0
$43$	16755.2	0.0321374	0.0160687	−	0.999871i	$-0.494885\pi$
$43$	16755.2	0.0321374	0.0160687	+	0.999871i	$0.494885\pi$
$44$	−642638.	−1.13732
$45$	0	0
$46$	82562.0	0.125063
$47$	−764733.	−1.07440	−0.537202	−	0.843454i	$-0.680519\pi$
$47$	−764733.	−1.07440	−0.537202	+	0.843454i	$0.680519\pi$
$48$	0	0
$49$	−408214.	−0.495681
$50$	−300935.	−0.340470
$51$	0	0
$52$	68446.5	0.0675056
$53$	1.38308e6	1.27609	0.638046	−	0.769998i	$-0.279743\pi$
$53$	1.38308e6	1.27609	0.638046	+	0.769998i	$0.279743\pi$
$54$	0	0
$55$	149501.	0.121164
$56$	603340.	0.459096
$57$	0	0
$58$	−101796.	−0.0685067
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	−354332.	−0.199874	−0.0999371	−	0.994994i	$-0.531864\pi$
$61$	−354332.	−0.199874	−0.0999371	+	0.994994i	$0.531864\pi$
$62$	−1.20614e6	−0.642728
$63$	0	0
$64$	−754988.	−0.360006
$65$	−15923.1	−0.00719170
$66$	0	0
$67$	4.54645e6	1.84676	0.923380	−	0.383887i	$-0.125415\pi$
$67$	4.54645e6	1.84676	0.923380	+	0.383887i	$0.125415\pi$
$68$	−4.43496e6	−1.71044
$69$	0	0
$70$	−65779.3	−0.0229217
$71$	367019.	0.121698	0.0608491	−	0.998147i	$-0.480619\pi$
$71$	367019.	0.121698	0.0608491	+	0.998147i	$0.480619\pi$
$72$	0	0
$73$	−1.13809e6	−0.342411	−0.171205	−	0.985235i	$-0.554766\pi$
$73$	−1.13809e6	−0.342411	−0.171205	+	0.985235i	$0.554766\pi$
$74$	−1.28350e6	−0.368201
$75$	0	0
$76$	3.84558e6	1.00488
$77$	−3.66843e6	−0.915721
$78$	0	0
$79$	3.04988e6	0.695967	0.347983	−	0.937501i	$-0.386867\pi$
$79$	3.04988e6	0.695967	0.347983	+	0.937501i	$0.386867\pi$
$80$	283977.	0.0620109
$81$	0	0
$82$	−1.23791e6	−0.247937
$83$	8.39695e6	1.61194	0.805969	−	0.591958i	$-0.201645\pi$
$83$	8.39695e6	1.61194	0.805969	+	0.591958i	$0.201645\pi$
$84$	0	0
$85$	1.03173e6	0.182222
$86$	65115.7	0.0110393
$87$	0	0
$88$	−5.32906e6	−0.833607
$89$	3.28661e6	0.494177	0.247089	−	0.968993i	$-0.420526\pi$
$89$	3.28661e6	0.494177	0.247089	+	0.968993i	$0.420526\pi$
$90$	0	0
$91$	390720.	0.0543527
$92$	−2.39843e6	−0.321121
$93$	0	0
$94$	−2.97197e6	−0.369060
$95$	−894620.	−0.107055
$96$	0	0
$97$	8.46055e6	0.941234	0.470617	−	0.882338i	$-0.344031\pi$
$97$	8.46055e6	0.941234	0.470617	+	0.882338i	$0.344031\pi$
$98$	−1.58644e6	−0.170268
$99$	0	0
$100$	8.74219e6	0.874219
$101$	−7.61349e6	−0.735290	−0.367645	−	0.929966i	$-0.619836\pi$
$101$	−7.61349e6	−0.735290	−0.367645	+	0.929966i	$0.619836\pi$
$102$	0	0
$103$	4.15554e6	0.374712	0.187356	−	0.982292i	$-0.440008\pi$
$103$	4.15554e6	0.374712	0.187356	+	0.982292i	$0.440008\pi$
$104$	567591.	0.0494788
$105$	0	0
$106$	5.37505e6	0.438341
$107$	−1.11011e7	−0.876038	−0.438019	−	0.898966i	$-0.644320\pi$
$107$	−1.11011e7	−0.876038	−0.438019	+	0.898966i	$0.644320\pi$
$108$	0	0
$109$	8.22798e6	0.608556	0.304278	−	0.952583i	$-0.401585\pi$
$109$	8.22798e6	0.608556	0.304278	+	0.952583i	$0.401585\pi$
$110$	581002.	0.0416201
$111$	0	0
$112$	−6.96820e6	−0.468660
$113$	1.87058e7	1.21956	0.609779	−	0.792571i	$-0.291258\pi$
$113$	1.87058e7	1.21956	0.609779	+	0.792571i	$0.291258\pi$
$114$	0	0
$115$	557961.	0.0342106
$116$	2.95718e6	0.175904
$117$	0	0
$118$	798162.	0.0447202
$119$	−2.53165e7	−1.37718
$120$	0	0
$121$	1.29146e7	0.662725
$122$	−1.37704e6	−0.0686573
$123$	0	0
$124$	3.50384e7	1.65032
$125$	−4.08561e6	−0.187099
$126$	0	0
$127$	1.39760e7	0.605437	0.302718	−	0.953080i	$-0.402106\pi$
$127$	1.39760e7	0.605437	0.302718	+	0.953080i	$0.402106\pi$
$128$	−2.36513e7	−0.996828
$129$	0	0
$130$	−61881.8	−0.00247037
$131$	−1.69407e7	−0.658387	−0.329193	−	0.944263i	$-0.606777\pi$
$131$	−1.69407e7	−0.658387	−0.329193	+	0.944263i	$0.606777\pi$
$132$	0	0
$133$	2.19521e7	0.809087
$134$	1.76688e7	0.634367
$135$	0	0
$136$	−3.67768e7	−1.25368
$137$	2.48882e7	0.826935	0.413467	−	0.910519i	$-0.364318\pi$
$137$	2.48882e7	0.826935	0.413467	+	0.910519i	$0.364318\pi$
$138$	0	0
$139$	−5.91087e7	−1.86681	−0.933404	−	0.358826i	$-0.883177\pi$
$139$	−5.91087e7	−1.86681	−0.933404	+	0.358826i	$0.883177\pi$
$140$	1.91089e6	0.0588556
$141$	0	0
$142$	1.42634e6	0.0418036
$143$	−3.45108e6	−0.0986912
$144$	0	0
$145$	−687946.	−0.0187399
$146$	−4.42295e6	−0.117619
$147$	0	0
$148$	3.72857e7	0.945424
$149$	4.77206e7	1.18183	0.590914	−	0.806735i	$-0.298767\pi$
$149$	4.77206e7	1.18183	0.590914	+	0.806735i	$0.298767\pi$
$150$	0	0
$151$	1.71936e7	0.406393	0.203197	−	0.979138i	$-0.434867\pi$
$151$	1.71936e7	0.406393	0.203197	+	0.979138i	$0.434867\pi$
$152$	3.18894e7	0.736535
$153$	0	0
$154$	−1.42566e7	−0.314552
$155$	−8.15120e6	−0.175817
$156$	0	0
$157$	−2.53780e7	−0.523371	−0.261685	−	0.965153i	$-0.584278\pi$
$157$	−2.53780e7	−0.523371	−0.261685	+	0.965153i	$0.584278\pi$
$158$	1.18527e7	0.239066
$159$	0	0
$160$	4.25089e6	0.0820464
$161$	−1.36912e7	−0.258554
$162$	0	0
$163$	6.34001e7	1.14666	0.573328	−	0.819326i	$-0.305652\pi$
$163$	6.34001e7	1.14666	0.573328	+	0.819326i	$0.305652\pi$
$164$	3.59613e7	0.636623
$165$	0	0
$166$	3.26330e7	0.553705
$167$	3.68194e7	0.611743	0.305872	−	0.952073i	$-0.401052\pi$
$167$	3.68194e7	0.611743	0.305872	+	0.952073i	$0.401052\pi$
$168$	0	0
$169$	−6.23809e7	−0.994142
$170$	4.00960e6	0.0625936
$171$	0	0
$172$	−1.89161e6	−0.0283454
$173$	6.29918e7	0.924959	0.462480	−	0.886630i	$-0.346960\pi$
$173$	6.29918e7	0.924959	0.462480	+	0.886630i	$0.346960\pi$
$174$	0	0
$175$	4.99039e7	0.703884
$176$	6.15474e7	0.850972
$177$	0	0
$178$	1.27727e7	0.169751
$179$	1.68796e7	0.219977	0.109989	−	0.993933i	$-0.464919\pi$
$179$	1.68796e7	0.219977	0.109989	+	0.993933i	$0.464919\pi$
$180$	0	0
$181$	5.41326e7	0.678554	0.339277	−	0.940687i	$-0.389818\pi$
$181$	5.41326e7	0.678554	0.339277	+	0.940687i	$0.389818\pi$
$182$	1.51845e6	0.0186703
$183$	0	0
$184$	−1.98889e7	−0.235369
$185$	−8.67400e6	−0.100721
$186$	0	0
$187$	2.23611e8	2.50062
$188$	8.63359e7	0.947630
$189$	0	0
$190$	−3.47675e6	−0.0367736
$191$	8.74794e7	0.908425	0.454213	−	0.890893i	$-0.349921\pi$
$191$	8.74794e7	0.908425	0.454213	+	0.890893i	$0.349921\pi$
$192$	0	0
$193$	−8.18019e7	−0.819054	−0.409527	−	0.912298i	$-0.634306\pi$
$193$	−8.18019e7	−0.819054	−0.409527	+	0.912298i	$0.634306\pi$
$194$	3.28801e7	0.323316
$195$	0	0
$196$	4.60861e7	0.437193
$197$	1.92295e8	1.79199	0.895996	−	0.444061i	$-0.146463\pi$
$197$	1.92295e8	1.79199	0.895996	+	0.444061i	$0.146463\pi$
$198$	0	0
$199$	−1.44937e6	−0.0130375	−0.00651873	−	0.999979i	$-0.502075\pi$
$199$	−1.44937e6	−0.0130375	−0.00651873	+	0.999979i	$0.502075\pi$
$200$	7.24944e7	0.640766
$201$	0	0
$202$	−2.95882e7	−0.252574
$203$	1.68808e7	0.141630
$204$	0	0
$205$	−8.36590e6	−0.0678225
$206$	1.61496e7	0.128715
$207$	0	0
$208$	−6.55533e6	−0.0505095
$209$	−1.93894e8	−1.46910
$210$	0	0
$211$	−2.14625e8	−1.57286	−0.786432	−	0.617676i	$-0.788074\pi$
$211$	−2.14625e8	−1.57286	−0.786432	+	0.617676i	$0.788074\pi$
$212$	−1.56145e8	−1.12552
$213$	0	0
$214$	−4.31421e7	−0.300921
$215$	440057.	0.00301977
$216$	0	0
$217$	2.00013e8	1.32877
$218$	3.19763e7	0.209041
$219$	0	0
$220$	−1.68781e7	−0.106867
$221$	−2.38165e7	−0.148424
$222$	0	0
$223$	−2.05595e8	−1.24150	−0.620748	−	0.784011i	$-0.713171\pi$
$223$	−2.05595e8	−1.24150	−0.620748	+	0.784011i	$0.713171\pi$
$224$	−1.04308e8	−0.620082
$225$	0	0
$226$	7.26962e7	0.418921
$227$	−1.87007e8	−1.06113	−0.530563	−	0.847646i	$-0.678019\pi$
$227$	−1.87007e8	−1.06113	−0.530563	+	0.847646i	$0.678019\pi$
$228$	0	0
$229$	1.01441e8	0.558201	0.279100	−	0.960262i	$-0.409964\pi$
$229$	1.01441e8	0.558201	0.279100	+	0.960262i	$0.409964\pi$
$230$	2.16839e6	0.0117514
$231$	0	0
$232$	2.45223e7	0.128930
$233$	1.98406e8	1.02757	0.513783	−	0.857920i	$-0.328244\pi$
$233$	1.98406e8	1.02757	0.513783	+	0.857920i	$0.328244\pi$
$234$	0	0
$235$	−2.00848e7	−0.100956
$236$	−2.31866e7	−0.114827
$237$	0	0
$238$	−9.83873e7	−0.473064
$239$	−9.06262e7	−0.429399	−0.214700	−	0.976680i	$-0.568877\pi$
$239$	−9.06262e7	−0.429399	−0.214700	+	0.976680i	$0.568877\pi$
$240$	0	0
$241$	−2.22377e8	−1.02336	−0.511681	−	0.859175i	$-0.670977\pi$
$241$	−2.22377e8	−1.02336	−0.511681	+	0.859175i	$0.670977\pi$
$242$	5.01900e7	0.227648
$243$	0	0
$244$	4.00030e7	0.176290
$245$	−1.07213e7	−0.0465763
$246$	0	0
$247$	2.06514e7	0.0871988
$248$	2.90555e8	1.20962
$249$	0	0
$250$	−1.58779e7	−0.0642690
$251$	−4.71405e8	−1.88164	−0.940819	−	0.338909i	$-0.889942\pi$
$251$	−4.71405e8	−1.88164	−0.940819	+	0.338909i	$0.889942\pi$
$252$	0	0
$253$	1.20929e8	0.469470
$254$	5.43146e7	0.207969
$255$	0	0
$256$	4.72267e6	0.0175933
$257$	6.85596e6	0.0251943	0.0125972	−	0.999921i	$-0.495990\pi$
$257$	6.85596e6	0.0251943	0.0125972	+	0.999921i	$0.495990\pi$
$258$	0	0
$259$	2.12842e8	0.761216
$260$	1.79767e6	0.00634312
$261$	0	0
$262$	−6.58363e7	−0.226158
$263$	4.52181e8	1.53273	0.766367	−	0.642403i	$-0.222062\pi$
$263$	4.52181e8	1.53273	0.766367	+	0.642403i	$0.222062\pi$
$264$	0	0
$265$	3.63250e7	0.119907
$266$	8.53122e7	0.277924
$267$	0	0
$268$	−5.13279e8	−1.62885
$269$	−6.31747e7	−0.197884	−0.0989419	−	0.995093i	$-0.531546\pi$
$269$	−6.31747e7	−0.197884	−0.0989419	+	0.995093i	$0.531546\pi$
$270$	0	0
$271$	5.80213e8	1.77091	0.885453	−	0.464730i	$-0.153849\pi$
$271$	5.80213e8	1.77091	0.885453	+	0.464730i	$0.153849\pi$
$272$	4.24749e8	1.27980
$273$	0	0
$274$	9.67226e7	0.284054
$275$	−4.40781e8	−1.27808
$276$	0	0
$277$	2.08756e8	0.590146	0.295073	−	0.955475i	$-0.404656\pi$
$277$	2.08756e8	0.590146	0.295073	+	0.955475i	$0.404656\pi$
$278$	−2.29714e8	−0.641253
$279$	0	0
$280$	1.58460e7	0.0431387
$281$	6.75157e7	0.181523	0.0907617	−	0.995873i	$-0.471070\pi$
$281$	6.75157e7	0.181523	0.0907617	+	0.995873i	$0.471070\pi$
$282$	0	0
$283$	5.48132e8	1.43758	0.718791	−	0.695226i	$-0.244696\pi$
$283$	5.48132e8	1.43758	0.718791	+	0.695226i	$0.244696\pi$
$284$	−4.14352e7	−0.107338
$285$	0	0
$286$	−1.34119e7	−0.0339007
$287$	2.05282e8	0.512582
$288$	0	0
$289$	1.13284e9	2.76074
$290$	−2.67356e6	−0.00643719
$291$	0	0
$292$	1.28487e8	0.302008
$293$	−2.36630e8	−0.549582	−0.274791	−	0.961504i	$-0.588609\pi$
$293$	−2.36630e8	−0.549582	−0.274791	+	0.961504i	$0.588609\pi$
$294$	0	0
$295$	5.39404e6	0.0122331
$296$	3.09191e8	0.692956
$297$	0	0
$298$	1.85456e8	0.405961
$299$	−1.28800e7	−0.0278654
$300$	0	0
$301$	−1.07981e7	−0.0228225
$302$	6.68191e7	0.139597
$303$	0	0
$304$	−3.68303e8	−0.751878
$305$	−9.30614e6	−0.0187811
$306$	0	0
$307$	−2.84146e7	−0.0560477	−0.0280238	−	0.999607i	$-0.508921\pi$
$307$	−2.84146e7	−0.0560477	−0.0280238	+	0.999607i	$0.508921\pi$
$308$	4.14154e8	0.807671
$309$	0	0
$310$	−3.16779e7	−0.0603936
$311$	−3.86506e8	−0.728609	−0.364305	−	0.931280i	$-0.618693\pi$
$311$	−3.86506e8	−0.728609	−0.364305	+	0.931280i	$0.618693\pi$
$312$	0	0
$313$	7.79214e8	1.43632	0.718160	−	0.695878i	$-0.244984\pi$
$313$	7.79214e8	1.43632	0.718160	+	0.695878i	$0.244984\pi$
$314$	−9.86264e7	−0.179779
$315$	0	0
$316$	−3.44322e8	−0.613847
$317$	4.02260e8	0.709251	0.354625	−	0.935008i	$-0.384608\pi$
$317$	4.02260e8	0.709251	0.354625	+	0.935008i	$0.384608\pi$
$318$	0	0
$319$	−1.49101e8	−0.257166
$320$	−1.98289e7	−0.0338278
$321$	0	0
$322$	−5.32079e7	−0.0888138
$323$	−1.33810e9	−2.20943
$324$	0	0
$325$	4.69471e7	0.0758607
$326$	2.46391e8	0.393879
$327$	0	0
$328$	2.98209e8	0.466618
$329$	4.92840e8	0.762993
$330$	0	0
$331$	−6.06425e8	−0.919135	−0.459568	−	0.888143i	$-0.651996\pi$
$331$	−6.06425e8	−0.919135	−0.459568	+	0.888143i	$0.651996\pi$
$332$	−9.47989e8	−1.42174
$333$	0	0
$334$	1.43091e8	0.210135
$335$	1.19407e8	0.173530
$336$	0	0
$337$	7.34722e8	1.04573	0.522864	−	0.852416i	$-0.324864\pi$
$337$	7.34722e8	1.04573	0.522864	+	0.852416i	$0.324864\pi$
$338$	−2.42430e8	−0.341490
$339$	0	0
$340$	−1.16479e8	−0.160721
$341$	−1.76664e9	−2.41272
$342$	0	0
$343$	7.93818e8	1.06216
$344$	−1.56862e7	−0.0207760
$345$	0	0
$346$	2.44804e8	0.317726
$347$	1.10182e9	1.41566	0.707830	−	0.706382i	$-0.249674\pi$
$347$	1.10182e9	1.41566	0.707830	+	0.706382i	$0.249674\pi$
$348$	0	0
$349$	−1.38141e8	−0.173953	−0.0869766	−	0.996210i	$-0.527721\pi$
$349$	−1.38141e8	−0.173953	−0.0869766	+	0.996210i	$0.527721\pi$
$350$	1.93941e8	0.241786
$351$	0	0
$352$	9.21310e8	1.12592
$353$	2.28995e8	0.277086	0.138543	−	0.990356i	$-0.455758\pi$
$353$	2.28995e8	0.277086	0.138543	+	0.990356i	$0.455758\pi$
$354$	0	0
$355$	9.63932e6	0.0114353
$356$	−3.71047e8	−0.435867
$357$	0	0
$358$	6.55991e7	0.0755627
$359$	1.59391e9	1.81817	0.909083	−	0.416615i	$-0.136784\pi$
$359$	1.59391e9	1.81817	0.909083	+	0.416615i	$0.136784\pi$
$360$	0	0
$361$	2.66402e8	0.298031
$362$	2.10375e8	0.233085
$363$	0	0
$364$	−4.41111e7	−0.0479394
$365$	−2.98907e7	−0.0321744
$366$	0	0
$367$	−3.97853e8	−0.420137	−0.210069	−	0.977687i	$-0.567369\pi$
$367$	−3.97853e8	−0.420137	−0.210069	+	0.977687i	$0.567369\pi$
$368$	2.29705e8	0.240272
$369$	0	0
$370$	−3.37097e7	−0.0345978
$371$	−8.91340e8	−0.906222
$372$	0	0
$373$	1.35221e9	1.34916	0.674582	−	0.738200i	$-0.264324\pi$
$373$	1.35221e9	1.34916	0.674582	+	0.738200i	$0.264324\pi$
$374$	8.69016e8	0.858968
$375$	0	0
$376$	7.15939e8	0.694574
$377$	1.58806e7	0.0152641
$378$	0	0
$379$	1.69493e9	1.59924	0.799621	−	0.600506i	$-0.205034\pi$
$379$	1.69493e9	1.59924	0.799621	+	0.600506i	$0.205034\pi$
$380$	1.01000e8	0.0944229
$381$	0	0
$382$	3.39970e8	0.312046
$383$	1.90311e9	1.73088	0.865442	−	0.501010i	$-0.167038\pi$
$383$	1.90311e9	1.73088	0.865442	+	0.501010i	$0.167038\pi$
$384$	0	0
$385$	−9.63472e7	−0.0860452
$386$	−3.17906e8	−0.281347
$387$	0	0
$388$	−9.55169e8	−0.830174
$389$	1.65443e9	1.42503	0.712516	−	0.701655i	$-0.247555\pi$
$389$	1.65443e9	1.42503	0.712516	+	0.701655i	$0.247555\pi$
$390$	0	0
$391$	8.34551e8	0.706048
$392$	3.82168e8	0.320445
$393$	0	0
$394$	7.47314e8	0.615554
$395$	8.01017e7	0.0653961
$396$	0	0
$397$	−1.76432e9	−1.41518	−0.707590	−	0.706623i	$-0.750218\pi$
$397$	−1.76432e9	−1.41518	−0.707590	+	0.706623i	$0.750218\pi$
$398$	−5.63266e6	−0.00447840
$399$	0	0
$400$	−8.37266e8	−0.654114
$401$	−9.40134e8	−0.728089	−0.364045	−	0.931381i	$-0.618604\pi$
$401$	−9.40134e8	−0.728089	−0.364045	+	0.931381i	$0.618604\pi$
$402$	0	0
$403$	1.88163e8	0.143207
$404$	8.59538e8	0.648530
$405$	0	0
$406$	6.56035e7	0.0486503
$407$	−1.87995e9	−1.38218
$408$	0	0
$409$	−9.46509e8	−0.684059	−0.342029	−	0.939689i	$-0.611114\pi$
$409$	−9.46509e8	−0.684059	−0.342029	+	0.939689i	$0.611114\pi$
$410$	−3.25123e7	−0.0232972
$411$	0	0
$412$	−4.69148e8	−0.330498
$413$	−1.32359e8	−0.0924542
$414$	0	0
$415$	2.20536e8	0.151465
$416$	−9.81276e7	−0.0668289
$417$	0	0
$418$	−7.53528e8	−0.504641
$419$	7.99568e8	0.531014	0.265507	−	0.964109i	$-0.414461\pi$
$419$	7.99568e8	0.531014	0.265507	+	0.964109i	$0.414461\pi$
$420$	0	0
$421$	−1.69924e9	−1.10986	−0.554930	−	0.831897i	$-0.687255\pi$
$421$	−1.69924e9	−1.10986	−0.554930	+	0.831897i	$0.687255\pi$
$422$	−8.34094e8	−0.540283
$423$	0	0
$424$	−1.29483e9	−0.824960
$425$	−3.04191e9	−1.92214
$426$	0	0
$427$	2.28353e8	0.141941
$428$	1.25328e9	0.772671
$429$	0	0
$430$	1.71019e6	0.00103730
$431$	−1.67268e9	−1.00634	−0.503168	−	0.864188i	$-0.667832\pi$
$431$	−1.67268e9	−1.00634	−0.503168	+	0.864188i	$0.667832\pi$
$432$	0	0
$433$	1.83377e9	1.08552	0.542759	−	0.839889i	$-0.317380\pi$
$433$	1.83377e9	1.08552	0.542759	+	0.839889i	$0.317380\pi$
$434$	7.77310e8	0.456436
$435$	0	0
$436$	−9.28912e8	−0.536750
$437$	−7.23644e8	−0.414801
$438$	0	0
$439$	−8.26984e8	−0.466521	−0.233261	−	0.972414i	$-0.574940\pi$
$439$	−8.26984e8	−0.466521	−0.233261	+	0.972414i	$0.574940\pi$
$440$	−1.39962e8	−0.0783294
$441$	0	0
$442$	−9.25578e7	−0.0509841
$443$	−4.49548e8	−0.245676	−0.122838	−	0.992427i	$-0.539200\pi$
$443$	−4.49548e8	−0.245676	−0.122838	+	0.992427i	$0.539200\pi$
$444$	0	0
$445$	8.63190e7	0.0464351
$446$	−7.99000e8	−0.426457
$447$	0	0
$448$	4.86559e8	0.255660
$449$	1.26664e9	0.660377	0.330188	−	0.943915i	$-0.392888\pi$
$449$	1.26664e9	0.660377	0.330188	+	0.943915i	$0.392888\pi$
$450$	0	0
$451$	−1.81317e9	−0.930724
$452$	−2.11183e9	−1.07566
$453$	0	0
$454$	−7.26762e8	−0.364499
$455$	1.02618e7	0.00510722
$456$	0	0
$457$	−2.61328e8	−0.128079	−0.0640397	−	0.997947i	$-0.520398\pi$
$457$	−2.61328e8	−0.128079	−0.0640397	+	0.997947i	$0.520398\pi$
$458$	3.94230e8	0.191743
$459$	0	0
$460$	−6.29919e7	−0.0301740
$461$	2.60747e9	1.23956	0.619779	−	0.784777i	$-0.287222\pi$
$461$	2.60747e9	1.23956	0.619779	+	0.784777i	$0.287222\pi$
$462$	0	0
$463$	3.07005e9	1.43751	0.718757	−	0.695261i	$-0.244711\pi$
$463$	3.07005e9	1.43751	0.718757	+	0.695261i	$0.244711\pi$
$464$	−2.83218e8	−0.131616
$465$	0	0
$466$	7.71064e8	0.352971
$467$	2.89908e9	1.31720	0.658599	−	0.752494i	$-0.271149\pi$
$467$	2.89908e9	1.31720	0.658599	+	0.752494i	$0.271149\pi$
$468$	0	0
$469$	−2.93000e9	−1.31149
$470$	−7.80555e7	−0.0346785
$471$	0	0
$472$	−1.92275e8	−0.0841637
$473$	9.53752e7	0.0414402
$474$	0	0
$475$	2.63766e9	1.12925
$476$	2.85815e9	1.21468
$477$	0	0
$478$	−3.52199e8	−0.147500
$479$	2.72155e9	1.13147	0.565733	−	0.824588i	$-0.308593\pi$
$479$	2.72155e9	1.13147	0.565733	+	0.824588i	$0.308593\pi$
$480$	0	0
$481$	2.00231e8	0.0820395
$482$	−8.64220e8	−0.351528
$483$	0	0
$484$	−1.45802e9	−0.584528
$485$	2.22207e8	0.0884425
$486$	0	0
$487$	−4.18049e9	−1.64012	−0.820060	−	0.572278i	$-0.806060\pi$
$487$	−4.18049e9	−1.64012	−0.820060	+	0.572278i	$0.806060\pi$
$488$	3.31724e8	0.129213
$489$	0	0
$490$	−4.16660e7	−0.0159991
$491$	−1.16233e9	−0.443144	−0.221572	−	0.975144i	$-0.571119\pi$
$491$	−1.16233e9	−0.443144	−0.221572	+	0.975144i	$0.571119\pi$
$492$	0	0
$493$	−1.02897e9	−0.386758
$494$	8.02574e7	0.0299530
$495$	0	0
$496$	−3.35574e9	−1.23482
$497$	−2.36529e8	−0.0864245
$498$	0	0
$499$	−2.46041e9	−0.886453	−0.443227	−	0.896410i	$-0.646166\pi$
$499$	−2.46041e9	−0.886453	−0.443227	+	0.896410i	$0.646166\pi$
$500$	4.61252e8	0.165023
$501$	0	0
$502$	−1.83202e9	−0.646347
$503$	3.44444e9	1.20679	0.603394	−	0.797443i	$-0.293815\pi$
$503$	3.44444e9	1.20679	0.603394	+	0.797443i	$0.293815\pi$
$504$	0	0
$505$	−1.99960e8	−0.0690911
$506$	4.69964e8	0.161264
$507$	0	0
$508$	−1.57784e9	−0.533999
$509$	1.85883e9	0.624781	0.312391	−	0.949954i	$-0.398870\pi$
$509$	1.85883e9	0.624781	0.312391	+	0.949954i	$0.398870\pi$
$510$	0	0
$511$	7.33455e8	0.243164
$512$	3.04572e9	1.00287
$513$	0	0
$514$	2.66442e7	0.00865431
$515$	1.09141e8	0.0352096
$516$	0	0
$517$	−4.35306e9	−1.38541
$518$	8.27164e8	0.261480
$519$	0	0
$520$	1.49071e7	0.00464925
$521$	−1.66724e9	−0.516496	−0.258248	−	0.966079i	$-0.583145\pi$
$521$	−1.66724e9	−0.516496	−0.258248	+	0.966079i	$0.583145\pi$
$522$	0	0
$523$	−5.43856e8	−0.166237	−0.0831186	−	0.996540i	$-0.526488\pi$
$523$	−5.43856e8	−0.166237	−0.0831186	+	0.996540i	$0.526488\pi$
$524$	1.91255e9	0.580701
$525$	0	0
$526$	1.75730e9	0.526498
$527$	−1.21919e10	−3.62856
$528$	0	0
$529$	−2.95350e9	−0.867445
$530$	1.41169e8	0.0411884
$531$	0	0
$532$	−2.47832e9	−0.713620
$533$	1.93119e8	0.0552432
$534$	0	0
$535$	−2.91558e8	−0.0823164
$536$	−4.25636e9	−1.19388
$537$	0	0
$538$	−2.45515e8	−0.0679736
$539$	−2.32366e9	−0.639164
$540$	0	0
$541$	−2.30286e8	−0.0625283	−0.0312642	−	0.999511i	$-0.509953\pi$
$541$	−2.30286e8	−0.0625283	−0.0312642	+	0.999511i	$0.509953\pi$
$542$	2.25488e9	0.608310
$543$	0	0
$544$	6.35813e9	1.69330
$545$	2.16098e8	0.0571826
$546$	0	0
$547$	4.00304e9	1.04576	0.522882	−	0.852405i	$-0.324857\pi$
$547$	4.00304e9	1.04576	0.522882	+	0.852405i	$0.324857\pi$
$548$	−2.80979e9	−0.729361
$549$	0	0
$550$	−1.71300e9	−0.439024
$551$	8.92229e8	0.227219
$552$	0	0
$553$	−1.96553e9	−0.494244
$554$	8.11285e8	0.202717
$555$	0	0
$556$	6.67318e9	1.64654
$557$	3.49935e9	0.858014	0.429007	−	0.903301i	$-0.358864\pi$
$557$	3.49935e9	0.858014	0.429007	+	0.903301i	$0.358864\pi$
$558$	0	0
$559$	−1.01583e7	−0.00245968
$560$	−1.83012e8	−0.0440373
$561$	0	0
$562$	2.62385e8	0.0623538
$563$	−3.07572e9	−0.726385	−0.363193	−	0.931714i	$-0.618313\pi$
$563$	−3.07572e9	−0.726385	−0.363193	+	0.931714i	$0.618313\pi$
$564$	0	0
$565$	4.91287e8	0.114595
$566$	2.13020e9	0.493813
$567$	0	0
$568$	−3.43601e8	−0.0786747
$569$	2.50567e9	0.570206	0.285103	−	0.958497i	$-0.407972\pi$
$569$	2.50567e9	0.570206	0.285103	+	0.958497i	$0.407972\pi$
$570$	0	0
$571$	−6.38840e9	−1.43604	−0.718019	−	0.696023i	$-0.754951\pi$
$571$	−6.38840e9	−1.43604	−0.718019	+	0.696023i	$0.754951\pi$
$572$	3.89615e8	0.0870462
$573$	0	0
$574$	7.97784e8	0.176073
$575$	−1.64507e9	−0.360866
$576$	0	0
$577$	−3.86927e9	−0.838520	−0.419260	−	0.907866i	$-0.637710\pi$
$577$	−3.86927e9	−0.838520	−0.419260	+	0.907866i	$0.637710\pi$
$578$	4.40254e9	0.948322
$579$	0	0
$580$	7.76669e7	0.0165287
$581$	−5.41150e9	−1.14473
$582$	0	0
$583$	7.87285e9	1.64548
$584$	1.06547e9	0.221360
$585$	0	0
$586$	−9.19611e8	−0.188783
$587$	3.35794e9	0.685236	0.342618	−	0.939475i	$-0.388686\pi$
$587$	3.35794e9	0.685236	0.342618	+	0.939475i	$0.388686\pi$
$588$	0	0
$589$	1.05717e10	2.13177
$590$	2.09628e7	0.00420211
$591$	0	0
$592$	−3.57097e9	−0.707391
$593$	−9.52200e9	−1.87515	−0.937576	−	0.347780i	$-0.886936\pi$
$593$	−9.52200e9	−1.87515	−0.937576	+	0.347780i	$0.886936\pi$
$594$	0	0
$595$	−6.64909e8	−0.129406
$596$	−5.38750e9	−1.04238
$597$	0	0
$598$	−5.00553e7	−0.00957185
$599$	−4.99052e8	−0.0948750	−0.0474375	−	0.998874i	$-0.515105\pi$
$599$	−4.99052e8	−0.0948750	−0.0474375	+	0.998874i	$0.515105\pi$
$600$	0	0
$601$	−4.14166e9	−0.778241	−0.389120	−	0.921187i	$-0.627221\pi$
$601$	−4.14166e9	−0.778241	−0.389120	+	0.921187i	$0.627221\pi$
$602$	−4.19645e7	−0.00783960
$603$	0	0
$604$	−1.94110e9	−0.358441
$605$	3.39188e8	0.0622726
$606$	0	0
$607$	−4.83852e9	−0.878117	−0.439059	−	0.898458i	$-0.644688\pi$
$607$	−4.83852e9	−0.878117	−0.439059	+	0.898458i	$0.644688\pi$
$608$	−5.51317e9	−0.994807
$609$	0	0
$610$	−3.61663e7	−0.00645134
$611$	4.63639e8	0.0822310
$612$	0	0
$613$	2.78195e9	0.487795	0.243898	−	0.969801i	$-0.421574\pi$
$613$	2.78195e9	0.487795	0.243898	+	0.969801i	$0.421574\pi$
$614$	−1.10427e8	−0.0192525
$615$	0	0
$616$	3.43437e9	0.591990
$617$	−6.18863e9	−1.06071	−0.530354	−	0.847776i	$-0.677941\pi$
$617$	−6.18863e9	−1.06071	−0.530354	+	0.847776i	$0.677941\pi$
$618$	0	0
$619$	3.57626e9	0.606055	0.303027	−	0.952982i	$-0.402003\pi$
$619$	3.57626e9	0.606055	0.303027	+	0.952982i	$0.402003\pi$
$620$	9.20244e8	0.155072
$621$	0	0
$622$	−1.50207e9	−0.250279
$623$	−2.11809e9	−0.350942
$624$	0	0
$625$	5.94232e9	0.973590
$626$	3.02825e9	0.493380
$627$	0	0
$628$	2.86510e9	0.461616
$629$	−1.29739e10	−2.07870
$630$	0	0
$631$	1.06672e10	1.69024	0.845121	−	0.534574i	$-0.179528\pi$
$631$	1.06672e10	1.69024	0.845121	+	0.534574i	$0.179528\pi$
$632$	−2.85528e9	−0.449924
$633$	0	0
$634$	1.56330e9	0.243629
$635$	3.67063e8	0.0568895
$636$	0	0
$637$	2.47490e8	0.0379376
$638$	−5.79449e8	−0.0883371
$639$	0	0
$640$	−6.21174e8	−0.0936664
$641$	2.94407e9	0.441515	0.220757	−	0.975329i	$-0.429147\pi$
$641$	2.94407e9	0.441515	0.220757	+	0.975329i	$0.429147\pi$
$642$	0	0
$643$	−1.24967e10	−1.85378	−0.926889	−	0.375335i	$-0.877528\pi$
$643$	−1.24967e10	−1.85378	−0.926889	+	0.375335i	$0.877528\pi$
$644$	1.54569e9	0.228046
$645$	0	0
$646$	−5.20024e9	−0.758943
$647$	1.89232e9	0.274682	0.137341	−	0.990524i	$-0.456144\pi$
$647$	1.89232e9	0.274682	0.137341	+	0.990524i	$0.456144\pi$
$648$	0	0
$649$	1.16907e9	0.167874
$650$	1.82450e8	0.0260583
$651$	0	0
$652$	−7.15767e9	−1.01136
$653$	1.18782e9	0.166937	0.0834687	−	0.996510i	$-0.473400\pi$
$653$	1.18782e9	0.166937	0.0834687	+	0.996510i	$0.473400\pi$
$654$	0	0
$655$	−4.44927e8	−0.0618649
$656$	−3.44413e9	−0.476338
$657$	0	0
$658$	1.91532e9	0.262090
$659$	1.27625e10	1.73715	0.868574	−	0.495559i	$-0.165037\pi$
$659$	1.27625e10	1.73715	0.868574	+	0.495559i	$0.165037\pi$
$660$	0	0
$661$	5.94189e9	0.800239	0.400120	−	0.916463i	$-0.368969\pi$
$661$	5.94189e9	0.800239	0.400120	+	0.916463i	$0.368969\pi$
$662$	−2.35674e9	−0.315725
$663$	0	0
$664$	−7.86118e9	−1.04208
$665$	5.76547e8	0.0760254
$666$	0	0
$667$	−5.56469e8	−0.0726107
$668$	−4.15679e9	−0.539561
$669$	0	0
$670$	4.64051e8	0.0596079
$671$	−2.01695e9	−0.257731
$672$	0	0
$673$	−4.95302e9	−0.626350	−0.313175	−	0.949695i	$-0.601393\pi$
$673$	−4.95302e9	−0.626350	−0.313175	+	0.949695i	$0.601393\pi$
$674$	2.85534e9	0.359210
$675$	0	0
$676$	7.04261e9	0.876839
$677$	−1.35131e9	−0.167377	−0.0836886	−	0.996492i	$-0.526670\pi$
$677$	−1.35131e9	−0.167377	−0.0836886	+	0.996492i	$0.526670\pi$
$678$	0	0
$679$	−5.45249e9	−0.668421
$680$	−9.65900e8	−0.117802
$681$	0	0
$682$	−6.86567e9	−0.828777
$683$	−1.43057e10	−1.71806	−0.859029	−	0.511927i	$-0.828932\pi$
$683$	−1.43057e10	−1.71806	−0.859029	+	0.511927i	$0.828932\pi$
$684$	0	0
$685$	6.53659e8	0.0777024
$686$	3.08501e9	0.364856
$687$	0	0
$688$	1.81166e8	0.0212088
$689$	−8.38527e8	−0.0976675
$690$	0	0
$691$	−1.07877e10	−1.24382	−0.621909	−	0.783089i	$-0.713643\pi$
$691$	−1.07877e10	−1.24382	−0.621909	+	0.783089i	$0.713643\pi$
$692$	−7.11157e9	−0.815820
$693$	0	0
$694$	4.28201e9	0.486283
$695$	−1.55242e9	−0.175414
$696$	0	0
$697$	−1.25130e10	−1.39974
$698$	−5.36854e8	−0.0597533
$699$	0	0
$700$	−5.63399e9	−0.620830
$701$	3.29304e9	0.361064	0.180532	−	0.983569i	$-0.442218\pi$
$701$	3.29304e9	0.361064	0.180532	+	0.983569i	$0.442218\pi$
$702$	0	0
$703$	1.12497e10	1.22123
$704$	−4.29759e9	−0.464216
$705$	0	0
$706$	8.89939e8	0.0951796
$707$	4.90659e9	0.522170
$708$	0	0
$709$	4.66010e9	0.491059	0.245530	−	0.969389i	$-0.421038\pi$
$709$	4.66010e9	0.491059	0.245530	+	0.969389i	$0.421038\pi$
$710$	3.74612e7	0.00392805
$711$	0	0
$712$	−3.07690e9	−0.319473
$713$	−6.59338e9	−0.681232
$714$	0	0
$715$	−9.06386e7	−0.00927346
$716$	−1.90566e9	−0.194021
$717$	0	0
$718$	6.19440e9	0.624544
$719$	2.36164e9	0.236954	0.118477	−	0.992957i	$-0.462199\pi$
$719$	2.36164e9	0.236954	0.118477	+	0.992957i	$0.462199\pi$
$720$	0	0
$721$	−2.67808e9	−0.266103
$722$	1.03531e9	0.102374
$723$	0	0
$724$	−6.11140e9	−0.598488
$725$	2.02831e9	0.197675
$726$	0	0
$727$	2.97525e9	0.287180	0.143590	−	0.989637i	$-0.454135\pi$
$727$	2.97525e9	0.287180	0.143590	+	0.989637i	$0.454135\pi$
$728$	−3.65790e8	−0.0351376
$729$	0	0
$730$	−1.16164e8	−0.0110520
$731$	6.58201e8	0.0623229
$732$	0	0
$733$	−1.37632e10	−1.29079	−0.645397	−	0.763848i	$-0.723308\pi$
$733$	−1.37632e10	−1.29079	−0.645397	+	0.763848i	$0.723308\pi$
$734$	−1.54617e9	−0.144318
$735$	0	0
$736$	3.43848e9	0.317903
$737$	2.58796e10	2.38134
$738$	0	0
$739$	1.14115e10	1.04013	0.520064	−	0.854127i	$-0.325908\pi$
$739$	1.14115e10	1.04013	0.520064	+	0.854127i	$0.325908\pi$
$740$	9.79266e8	0.0888362
$741$	0	0
$742$	−3.46400e9	−0.311290
$743$	−5.94931e9	−0.532115	−0.266057	−	0.963957i	$-0.585721\pi$
$743$	−5.94931e9	−0.532115	−0.266057	+	0.963957i	$0.585721\pi$
$744$	0	0
$745$	1.25333e9	0.111050
$746$	5.25509e9	0.463441
$747$	0	0
$748$	−2.52449e10	−2.20556
$749$	7.15422e9	0.622123
$750$	0	0
$751$	−7.58856e9	−0.653762	−0.326881	−	0.945066i	$-0.605998\pi$
$751$	−7.58856e9	−0.653762	−0.326881	+	0.945066i	$0.605998\pi$
$752$	−8.26865e9	−0.709043
$753$	0	0
$754$	6.17164e7	0.00524326
$755$	4.51569e8	0.0381865
$756$	0	0
$757$	−1.43522e10	−1.20250	−0.601248	−	0.799063i	$-0.705329\pi$
$757$	−1.43522e10	−1.20250	−0.601248	+	0.799063i	$0.705329\pi$
$758$	6.58698e9	0.549343
$759$	0	0
$760$	8.37538e8	0.0692081
$761$	5.32785e9	0.438233	0.219117	−	0.975699i	$-0.429682\pi$
$761$	5.32785e9	0.438233	0.219117	+	0.975699i	$0.429682\pi$
$762$	0	0
$763$	−5.30260e9	−0.432169
$764$	−9.87614e9	−0.801236
$765$	0	0
$766$	7.39602e9	0.594563
$767$	−1.24516e8	−0.00996419
$768$	0	0
$769$	8.89088e9	0.705022	0.352511	−	0.935808i	$-0.385328\pi$
$769$	8.89088e9	0.705022	0.352511	+	0.935808i	$0.385328\pi$
$770$	−3.74433e8	−0.0295567
$771$	0	0
$772$	9.23517e9	0.722411
$773$	2.40093e10	1.86961	0.934807	−	0.355155i	$-0.115572\pi$
$773$	2.40093e10	1.86961	0.934807	+	0.355155i	$0.115572\pi$
$774$	0	0
$775$	2.40327e10	1.85458
$776$	−7.92071e9	−0.608483
$777$	0	0
$778$	6.42959e9	0.489502
$779$	1.08501e10	0.822343
$780$	0	0
$781$	2.08917e9	0.156926
$782$	3.24331e9	0.242529
$783$	0	0
$784$	−4.41380e9	−0.327120
$785$	−6.66525e8	−0.0491782
$786$	0	0
$787$	1.74554e10	1.27649	0.638246	−	0.769833i	$-0.279660\pi$
$787$	1.74554e10	1.27649	0.638246	+	0.769833i	$0.279660\pi$
$788$	−2.17095e10	−1.58055
$789$	0	0
$790$	3.11298e8	0.0224637
$791$	−1.20552e10	−0.866075
$792$	0	0
$793$	2.14823e8	0.0152976
$794$	−6.85667e9	−0.486118
$795$	0	0
$796$	1.63629e8	0.0114991
$797$	2.13622e10	1.49466	0.747329	−	0.664454i	$-0.231336\pi$
$797$	2.13622e10	1.49466	0.747329	+	0.664454i	$0.231336\pi$
$798$	0	0
$799$	−3.00413e10	−2.08355
$800$	−1.25331e10	−0.865456
$801$	0	0
$802$	−3.65363e9	−0.250101
$803$	−6.47831e9	−0.441527
$804$	0	0
$805$	−3.59583e8	−0.0242948
$806$	7.31254e8	0.0491921
$807$	0	0
$808$	7.12770e9	0.475346
$809$	8.12776e9	0.539698	0.269849	−	0.962903i	$-0.413026\pi$
$809$	8.12776e9	0.539698	0.269849	+	0.962903i	$0.413026\pi$
$810$	0	0
$811$	−4.71482e9	−0.310379	−0.155190	−	0.987885i	$-0.549599\pi$
$811$	−4.71482e9	−0.310379	−0.155190	+	0.987885i	$0.549599\pi$
$812$	−1.90578e9	−0.124919
$813$	0	0
$814$	−7.30601e9	−0.474783
$815$	1.66513e9	0.107745
$816$	0	0
$817$	−5.70730e8	−0.0366145
$818$	−3.67841e9	−0.234976
$819$	0	0
$820$	9.44483e8	0.0598199
$821$	1.97226e10	1.24383	0.621917	−	0.783083i	$-0.286354\pi$
$821$	1.97226e10	1.24383	0.621917	+	0.783083i	$0.286354\pi$
$822$	0	0
$823$	1.20133e9	0.0751215	0.0375608	−	0.999294i	$-0.488041\pi$
$823$	1.20133e9	0.0751215	0.0375608	+	0.999294i	$0.488041\pi$
$824$	−3.89040e9	−0.242242
$825$	0	0
$826$	−5.14383e8	−0.0317583
$827$	−8.23556e9	−0.506319	−0.253159	−	0.967425i	$-0.581470\pi$
$827$	−8.23556e9	−0.506319	−0.253159	+	0.967425i	$0.581470\pi$
$828$	0	0
$829$	3.37482e9	0.205736	0.102868	−	0.994695i	$-0.467198\pi$
$829$	3.37482e9	0.205736	0.102868	+	0.994695i	$0.467198\pi$
$830$	8.57067e8	0.0520285
$831$	0	0
$832$	4.57731e8	0.0275536
$833$	−1.60360e10	−0.961255
$834$	0	0
$835$	9.67020e8	0.0574821
$836$	2.18900e10	1.29576
$837$	0	0
$838$	3.10735e9	0.182405
$839$	−2.19151e10	−1.28108	−0.640540	−	0.767925i	$-0.721289\pi$
$839$	−2.19151e10	−1.28108	−0.640540	+	0.767925i	$0.721289\pi$
$840$	0	0
$841$	−1.65638e10	−0.960225
$842$	−6.60375e9	−0.381240
$843$	0	0
$844$	2.42305e10	1.38728
$845$	−1.63836e9	−0.0934140
$846$	0	0
$847$	−8.32297e9	−0.470637
$848$	1.49545e10	0.842145
$849$	0	0
$850$	−1.18217e10	−0.660260
$851$	−7.01627e9	−0.390259
$852$	0	0
$853$	−2.68331e10	−1.48030	−0.740148	−	0.672444i	$-0.765245\pi$
$853$	−2.68331e10	−1.48030	−0.740148	+	0.672444i	$0.765245\pi$
$854$	8.87446e8	0.0487573
$855$	0	0
$856$	1.03928e10	0.566336
$857$	3.79081e9	0.205731	0.102865	−	0.994695i	$-0.467199\pi$
$857$	3.79081e9	0.205731	0.102865	+	0.994695i	$0.467199\pi$
$858$	0	0
$859$	−1.08182e10	−0.582342	−0.291171	−	0.956671i	$-0.594045\pi$
$859$	−1.08182e10	−0.582342	−0.291171	+	0.956671i	$0.594045\pi$
$860$	−4.96810e7	−0.00266346
$861$	0	0
$862$	−6.50053e9	−0.345679
$863$	2.34587e10	1.24241	0.621206	−	0.783647i	$-0.286643\pi$
$863$	2.34587e10	1.24241	0.621206	+	0.783647i	$0.286643\pi$
$864$	0	0
$865$	1.65441e9	0.0869133
$866$	7.12655e9	0.372878
$867$	0	0
$868$	−2.25809e10	−1.17198
$869$	1.73607e10	0.897426
$870$	0	0
$871$	−2.75640e9	−0.141344
$872$	−7.70299e9	−0.393415
$873$	0	0
$874$	−2.81229e9	−0.142485
$875$	2.63301e9	0.132869
$876$	0	0
$877$	3.42071e10	1.71245	0.856224	−	0.516605i	$-0.172805\pi$
$877$	3.42071e10	1.71245	0.856224	+	0.516605i	$0.172805\pi$
$878$	−3.21390e9	−0.160251
$879$	0	0
$880$	1.61647e9	0.0799611
$881$	5.54512e9	0.273209	0.136605	−	0.990626i	$-0.456381\pi$
$881$	5.54512e9	0.273209	0.136605	+	0.990626i	$0.456381\pi$
$882$	0	0
$883$	1.95899e10	0.957568	0.478784	−	0.877933i	$-0.341078\pi$
$883$	1.95899e10	0.957568	0.478784	+	0.877933i	$0.341078\pi$
$884$	2.68881e9	0.130911
$885$	0	0
$886$	−1.74707e9	−0.0843904
$887$	−2.41962e10	−1.16416	−0.582081	−	0.813131i	$-0.697762\pi$
$887$	−2.41962e10	−1.16416	−0.582081	+	0.813131i	$0.697762\pi$
$888$	0	0
$889$	−9.00695e9	−0.429954
$890$	3.35460e8	0.0159506
$891$	0	0
$892$	2.32110e10	1.09501
$893$	2.60489e10	1.22408
$894$	0	0
$895$	4.43324e8	0.0206700
$896$	1.52423e10	0.707902
$897$	0	0
$898$	4.92254e9	0.226841
$899$	8.12941e9	0.373164
$900$	0	0
$901$	5.43320e10	2.47468
$902$	−7.04650e9	−0.319706
$903$	0	0
$904$	−1.75123e10	−0.788412
$905$	1.42173e9	0.0637599
$906$	0	0
$907$	−1.77861e10	−0.791510	−0.395755	−	0.918356i	$-0.629517\pi$
$907$	−1.77861e10	−0.791510	−0.395755	+	0.918356i	$0.629517\pi$
$908$	2.11125e10	0.935919
$909$	0	0
$910$	3.98804e7	0.00175434
$911$	3.79625e10	1.66357	0.831783	−	0.555101i	$-0.187320\pi$
$911$	3.79625e10	1.66357	0.831783	+	0.555101i	$0.187320\pi$
$912$	0	0
$913$	4.77976e10	2.07854
$914$	−1.01560e9	−0.0439956
$915$	0	0
$916$	−1.14524e10	−0.492337
$917$	1.09176e10	0.467556
$918$	0	0
$919$	−4.00064e10	−1.70030	−0.850149	−	0.526543i	$-0.823488\pi$
$919$	−4.00064e10	−1.70030	−0.850149	+	0.526543i	$0.823488\pi$
$920$	−5.22359e8	−0.0221163
$921$	0	0
$922$	1.01334e10	0.425791
$923$	−2.22514e8	−0.00931434
$924$	0	0
$925$	2.55740e10	1.06244
$926$	1.19311e10	0.493790
$927$	0	0
$928$	−4.23953e9	−0.174140
$929$	4.55114e10	1.86237	0.931183	−	0.364552i	$-0.118778\pi$
$929$	4.55114e10	1.86237	0.931183	+	0.364552i	$0.118778\pi$
$930$	0	0
$931$	1.39049e10	0.564735
$932$	−2.23994e10	−0.906319
$933$	0	0
$934$	1.12667e10	0.452461
$935$	5.87288e9	0.234969
$936$	0	0
$937$	3.78655e9	0.150368	0.0751839	−	0.997170i	$-0.476046\pi$
$937$	3.78655e9	0.150368	0.0751839	+	0.997170i	$0.476046\pi$
$938$	−1.13868e10	−0.450498
$939$	0	0
$940$	2.26751e9	0.0890435
$941$	9.78869e9	0.382966	0.191483	−	0.981496i	$-0.438670\pi$
$941$	9.78869e9	0.382966	0.191483	+	0.981496i	$0.438670\pi$
$942$	0	0
$943$	−6.76705e9	−0.262790
$944$	2.22065e9	0.0859170
$945$	0	0
$946$	3.70655e8	0.0142348
$947$	−3.55199e10	−1.35909	−0.679543	−	0.733635i	$-0.737822\pi$
$947$	−3.55199e10	−1.35909	−0.679543	+	0.733635i	$0.737822\pi$
$948$	0	0
$949$	6.89997e8	0.0262069
$950$	1.02507e10	0.387901
$951$	0	0
$952$	2.37012e10	0.890309
$953$	1.87406e9	0.0701389	0.0350695	−	0.999385i	$-0.488835\pi$
$953$	1.87406e9	0.0701389	0.0350695	+	0.999385i	$0.488835\pi$
$954$	0	0
$955$	2.29755e9	0.0853596
$956$	1.02314e10	0.378733
$957$	0	0
$958$	1.05767e10	0.388661
$959$	−1.60394e10	−0.587251
$960$	0	0
$961$	6.88096e10	2.50102
$962$	7.78154e8	0.0281808
$963$	0	0
$964$	2.51056e10	0.902612
$965$	−2.14843e9	−0.0769620
$966$	0	0
$967$	2.52830e10	0.899158	0.449579	−	0.893241i	$-0.351574\pi$
$967$	2.52830e10	0.899158	0.449579	+	0.893241i	$0.351574\pi$
$968$	−1.20906e10	−0.428434
$969$	0	0
$970$	8.63559e8	0.0303802
$971$	−2.33470e10	−0.818396	−0.409198	−	0.912446i	$-0.634192\pi$
$971$	−2.33470e10	−0.818396	−0.409198	+	0.912446i	$0.634192\pi$
$972$	0	0
$973$	3.80932e10	1.32572
$974$	−1.62466e10	−0.563385
$975$	0	0
$976$	−3.83121e9	−0.131905
$977$	3.73874e9	0.128261	0.0641304	−	0.997942i	$-0.479573\pi$
$977$	3.73874e9	0.128261	0.0641304	+	0.997942i	$0.479573\pi$
$978$	0	0
$979$	1.87082e10	0.637225
$980$	1.21040e9	0.0410806
$981$	0	0
$982$	−4.51716e9	−0.152221
$983$	4.06366e10	1.36452	0.682261	−	0.731109i	$-0.260997\pi$
$983$	4.06366e10	1.36452	0.682261	+	0.731109i	$0.260997\pi$
$984$	0	0
$985$	5.05041e9	0.168384
$986$	−3.99889e9	−0.132853
$987$	0	0
$988$	−2.33148e9	−0.0769099
$989$	3.55956e8	0.0117006
$990$	0	0
$991$	2.46369e10	0.804134	0.402067	−	0.915610i	$-0.368292\pi$
$991$	2.46369e10	0.804134	0.402067	+	0.915610i	$0.368292\pi$
$992$	−5.02325e10	−1.63378
$993$	0	0
$994$	−9.19219e8	−0.0296870
$995$	−3.80660e7	−0.00122506
$996$	0	0
$997$	−1.08445e10	−0.346558	−0.173279	−	0.984873i	$-0.555436\pi$
$997$	−1.08445e10	−0.346558	−0.173279	+	0.984873i	$0.555436\pi$
$998$	−9.56186e9	−0.304499
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.c.1.10		17
3.2	odd	2		177.8.a.c.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.8	✓	17	3.2	odd	2
531.8.a.c.1.10		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)

\(f(q)\)	\(=\)	\(q+3.88629 q^{2} -112.897 q^{4} +26.2639 q^{5} -644.460 q^{7} -936.194 q^{8} +O(q^{10})\)	\(q+3.88629 q^{2} -112.897 q^{4} +26.2639 q^{5} -644.460 q^{7} -936.194 q^{8} +102.069 q^{10} +5692.26 q^{11} -606.275 q^{13} -2504.56 q^{14} +10812.5 q^{16} +39283.3 q^{17} -34062.8 q^{19} -2965.10 q^{20} +22121.8 q^{22} +21244.4 q^{23} -77435.2 q^{25} -2356.16 q^{26} +72757.5 q^{28} -26193.7 q^{29} -310358. q^{31} +161853. q^{32} +152666. q^{34} -16926.0 q^{35} -330264. q^{37} -132378. q^{38} -24588.1 q^{40} -318533. q^{41} +16755.2 q^{43} -642638. q^{44} +82562.0 q^{46} -764733. q^{47} -408214. q^{49} -300935. q^{50} +68446.5 q^{52} +1.38308e6 q^{53} +149501. q^{55} +603340. q^{56} -101796. q^{58} +205379. q^{59} -354332. q^{61} -1.20614e6 q^{62} -754988. q^{64} -15923.1 q^{65} +4.54645e6 q^{67} -4.43496e6 q^{68} -65779.3 q^{70} +367019. q^{71} -1.13809e6 q^{73} -1.28350e6 q^{74} +3.84558e6 q^{76} -3.66843e6 q^{77} +3.04988e6 q^{79} +283977. q^{80} -1.23791e6 q^{82} +8.39695e6 q^{83} +1.03173e6 q^{85} +65115.7 q^{86} -5.32906e6 q^{88} +3.28661e6 q^{89} +390720. q^{91} -2.39843e6 q^{92} -2.97197e6 q^{94} -894620. q^{95} +8.46055e6 q^{97} -1.58644e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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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