LMFDB - Embedded newform 531.8.a.c.1.12

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			1.12
Root			$-8.14464$ 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)

$f(q)$	$=$	$q+8.14464 q^{2} -61.6648 q^{4} +54.3103 q^{5} -413.400 q^{7} -1544.75 q^{8} +O(q^{10})$	\(q+8.14464 q^{2} -61.6648 q^{4} +54.3103 q^{5} -413.400 q^{7} -1544.75 q^{8} +442.338 q^{10} -5302.90 q^{11} -13494.1 q^{13} -3367.00 q^{14} -4688.37 q^{16} -13725.3 q^{17} -57847.2 q^{19} -3349.03 q^{20} -43190.2 q^{22} +11834.5 q^{23} -75175.4 q^{25} -109904. q^{26} +25492.2 q^{28} +137312. q^{29} +110476. q^{31} +159543. q^{32} -111788. q^{34} -22451.9 q^{35} +154147. q^{37} -471145. q^{38} -83896.0 q^{40} -58042.4 q^{41} -607469. q^{43} +327002. q^{44} +96387.4 q^{46} +765556. q^{47} -652643. q^{49} -612277. q^{50} +832107. q^{52} -779953. q^{53} -288002. q^{55} +638601. q^{56} +1.11836e6 q^{58} +205379. q^{59} +745383. q^{61} +899790. q^{62} +1.89953e6 q^{64} -732866. q^{65} -343978. q^{67} +846369. q^{68} -182863. q^{70} -4.41562e6 q^{71} +1.38449e6 q^{73} +1.25547e6 q^{74} +3.56714e6 q^{76} +2.19222e6 q^{77} -6.92496e6 q^{79} -254627. q^{80} -472735. q^{82} -4.41025e6 q^{83} -745427. q^{85} -4.94762e6 q^{86} +8.19166e6 q^{88} +2.65103e6 q^{89} +5.57844e6 q^{91} -729769. q^{92} +6.23518e6 q^{94} -3.14170e6 q^{95} +531245. q^{97} -5.31555e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.14464	0.719892	0.359946	−	0.932973i	$-0.382795\pi$
$2$	8.14464	0.719892	0.359946	+	0.932973i	$0.382795\pi$
$3$	0	0
$3$	0	0
$4$	−61.6648	−0.481756
$5$	54.3103	0.194307	0.0971533	−	0.995269i	$-0.469026\pi$
$5$	54.3103	0.194307	0.0971533	+	0.995269i	$0.469026\pi$
$6$	0	0
$7$	−413.400	−0.455541	−0.227770	−	0.973715i	$-0.573144\pi$
$7$	−413.400	−0.455541	−0.227770	+	0.973715i	$0.573144\pi$
$8$	−1544.75	−1.06670
$9$	0	0
$10$	442.338	0.139880
$11$	−5302.90	−1.20126	−0.600632	−	0.799525i	$-0.705084\pi$
$11$	−5302.90	−1.20126	−0.600632	+	0.799525i	$0.705084\pi$
$12$	0	0
$13$	−13494.1	−1.70349	−0.851747	−	0.523953i	$-0.824457\pi$
$13$	−13494.1	−1.70349	−0.851747	+	0.523953i	$0.824457\pi$
$14$	−3367.00	−0.327940
$15$	0	0
$16$	−4688.37	−0.286155
$17$	−13725.3	−0.677566	−0.338783	−	0.940865i	$-0.610015\pi$
$17$	−13725.3	−0.677566	−0.338783	+	0.940865i	$0.610015\pi$
$18$	0	0
$19$	−57847.2	−1.93484	−0.967420	−	0.253177i	$-0.918525\pi$
$19$	−57847.2	−1.93484	−0.967420	+	0.253177i	$0.918525\pi$
$20$	−3349.03	−0.0936083
$21$	0	0
$22$	−43190.2	−0.864780
$23$	11834.5	0.202815	0.101408	−	0.994845i	$-0.467665\pi$
$23$	11834.5	0.202815	0.101408	+	0.994845i	$0.467665\pi$
$24$	0	0
$25$	−75175.4	−0.962245
$26$	−109904.	−1.22633
$27$	0	0
$28$	25492.2	0.219460
$29$	137312.	1.04548	0.522739	−	0.852493i	$-0.324910\pi$
$29$	137312.	1.04548	0.522739	+	0.852493i	$0.324910\pi$
$30$	0	0
$31$	110476.	0.666044	0.333022	−	0.942919i	$-0.391932\pi$
$31$	110476.	0.666044	0.333022	+	0.942919i	$0.391932\pi$
$32$	159543.	0.860703
$33$	0	0
$34$	−111788.	−0.487774
$35$	−22451.9	−0.0885146
$36$	0	0
$37$	154147.	0.500297	0.250149	−	0.968207i	$-0.419520\pi$
$37$	154147.	0.500297	0.250149	+	0.968207i	$0.419520\pi$
$38$	−471145.	−1.39288
$39$	0	0
$40$	−83896.0	−0.207268
$41$	−58042.4	−0.131523	−0.0657615	−	0.997835i	$-0.520948\pi$
$41$	−58042.4	−0.131523	−0.0657615	+	0.997835i	$0.520948\pi$
$42$	0	0
$43$	−607469.	−1.16516	−0.582578	−	0.812775i	$-0.697956\pi$
$43$	−607469.	−1.16516	−0.582578	+	0.812775i	$0.697956\pi$
$44$	327002.	0.578716
$45$	0	0
$46$	96387.4	0.146005
$47$	765556.	1.07556	0.537780	−	0.843085i	$-0.319263\pi$
$47$	765556.	1.07556	0.537780	+	0.843085i	$0.319263\pi$
$48$	0	0
$49$	−652643.	−0.792483
$50$	−612277.	−0.692712
$51$	0	0
$52$	832107.	0.820668
$53$	−779953.	−0.719619	−0.359810	−	0.933026i	$-0.617158\pi$
$53$	−779953.	−0.719619	−0.359810	+	0.933026i	$0.617158\pi$
$54$	0	0
$55$	−288002.	−0.233414
$56$	638601.	0.485927
$57$	0	0
$58$	1.11836e6	0.752630
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	745383.	0.420460	0.210230	−	0.977652i	$-0.432579\pi$
$61$	745383.	0.420460	0.210230	+	0.977652i	$0.432579\pi$
$62$	899790.	0.479480
$63$	0	0
$64$	1.89953e6	0.905768
$65$	−732866.	−0.331000
$66$	0	0
$67$	−343978.	−0.139723	−0.0698616	−	0.997557i	$-0.522256\pi$
$67$	−343978.	−0.139723	−0.0698616	+	0.997557i	$0.522256\pi$
$68$	846369.	0.326421
$69$	0	0
$70$	−182863.	−0.0637209
$71$	−4.41562e6	−1.46416	−0.732078	−	0.681221i	$-0.761449\pi$
$71$	−4.41562e6	−1.46416	−0.732078	+	0.681221i	$0.761449\pi$
$72$	0	0
$73$	1.38449e6	0.416544	0.208272	−	0.978071i	$-0.433216\pi$
$73$	1.38449e6	0.416544	0.208272	+	0.978071i	$0.433216\pi$
$74$	1.25547e6	0.360160
$75$	0	0
$76$	3.56714e6	0.932121
$77$	2.19222e6	0.547225
$78$	0	0
$79$	−6.92496e6	−1.58024	−0.790119	−	0.612953i	$-0.789981\pi$
$79$	−6.92496e6	−1.58024	−0.790119	+	0.612953i	$0.789981\pi$
$80$	−254627.	−0.0556019
$81$	0	0
$82$	−472735.	−0.0946824
$83$	−4.41025e6	−0.846623	−0.423312	−	0.905984i	$-0.639132\pi$
$83$	−4.41025e6	−0.846623	−0.423312	+	0.905984i	$0.639132\pi$
$84$	0	0
$85$	−745427.	−0.131655
$86$	−4.94762e6	−0.838787
$87$	0	0
$88$	8.19166e6	1.28139
$89$	2.65103e6	0.398612	0.199306	−	0.979937i	$-0.436131\pi$
$89$	2.65103e6	0.398612	0.199306	+	0.979937i	$0.436131\pi$
$90$	0	0
$91$	5.57844e6	0.776011
$92$	−729769.	−0.0977075
$93$	0	0
$94$	6.23518e6	0.774287
$95$	−3.14170e6	−0.375952
$96$	0	0
$97$	531245.	0.0591009	0.0295504	−	0.999563i	$-0.490592\pi$
$97$	531245.	0.0591009	0.0295504	+	0.999563i	$0.490592\pi$
$98$	−5.31555e6	−0.570502
$99$	0	0
$100$	4.63567e6	0.463567
$101$	−2.90692e6	−0.280742	−0.140371	−	0.990099i	$-0.544830\pi$
$101$	−2.90692e6	−0.280742	−0.140371	+	0.990099i	$0.544830\pi$
$102$	0	0
$103$	1.71445e7	1.54595	0.772974	−	0.634438i	$-0.218768\pi$
$103$	1.71445e7	1.54595	0.772974	+	0.634438i	$0.218768\pi$
$104$	2.08450e7	1.81712
$105$	0	0
$106$	−6.35244e6	−0.518048
$107$	7.73354e6	0.610289	0.305144	−	0.952306i	$-0.401295\pi$
$107$	7.73354e6	0.610289	0.305144	+	0.952306i	$0.401295\pi$
$108$	0	0
$109$	5.26465e6	0.389383	0.194691	−	0.980865i	$-0.437629\pi$
$109$	5.26465e6	0.389383	0.194691	+	0.980865i	$0.437629\pi$
$110$	−2.34567e6	−0.168033
$111$	0	0
$112$	1.93817e6	0.130355
$113$	−2.92949e7	−1.90993	−0.954966	−	0.296716i	$-0.904108\pi$
$113$	−2.92949e7	−1.90993	−0.954966	+	0.296716i	$0.904108\pi$
$114$	0	0
$115$	642733.	0.0394083
$116$	−8.46729e6	−0.503665
$117$	0	0
$118$	1.67274e6	0.0937219
$119$	5.67405e6	0.308659
$120$	0	0
$121$	8.63353e6	0.443037
$122$	6.07088e6	0.302686
$123$	0	0
$124$	−6.81249e6	−0.320871
$125$	−8.32580e6	−0.381277
$126$	0	0
$127$	1.91366e7	0.828995	0.414497	−	0.910051i	$-0.363957\pi$
$127$	1.91366e7	0.828995	0.414497	+	0.910051i	$0.363957\pi$
$128$	−4.95050e6	−0.208648
$129$	0	0
$130$	−5.96894e6	−0.238284
$131$	−2.05015e6	−0.0796775	−0.0398387	−	0.999206i	$-0.512684\pi$
$131$	−2.05015e6	−0.0796775	−0.0398387	+	0.999206i	$0.512684\pi$
$132$	0	0
$133$	2.39141e7	0.881399
$134$	−2.80157e6	−0.100586
$135$	0	0
$136$	2.12022e7	0.722762
$137$	1.22263e7	0.406232	0.203116	−	0.979155i	$-0.434893\pi$
$137$	1.22263e7	0.406232	0.203116	+	0.979155i	$0.434893\pi$
$138$	0	0
$139$	2.28834e7	0.722719	0.361359	−	0.932427i	$-0.382313\pi$
$139$	2.28834e7	0.722719	0.361359	+	0.932427i	$0.382313\pi$
$140$	1.38449e6	0.0426424
$141$	0	0
$142$	−3.59636e7	−1.05403
$143$	7.15575e7	2.04635
$144$	0	0
$145$	7.45744e6	0.203143
$146$	1.12762e7	0.299866
$147$	0	0
$148$	−9.50542e6	−0.241021
$149$	1.01691e7	0.251843	0.125921	−	0.992040i	$-0.459811\pi$
$149$	1.01691e7	0.251843	0.125921	+	0.992040i	$0.459811\pi$
$150$	0	0
$151$	−5.75910e7	−1.36124	−0.680620	−	0.732636i	$-0.738290\pi$
$151$	−5.75910e7	−1.36124	−0.680620	+	0.732636i	$0.738290\pi$
$152$	8.93597e7	2.06390
$153$	0	0
$154$	1.78548e7	0.393943
$155$	6.00000e6	0.129417
$156$	0	0
$157$	−1.36932e7	−0.282395	−0.141197	−	0.989981i	$-0.545095\pi$
$157$	−1.36932e7	−0.282395	−0.141197	+	0.989981i	$0.545095\pi$
$158$	−5.64014e7	−1.13760
$159$	0	0
$160$	8.66484e6	0.167240
$161$	−4.89236e6	−0.0923907
$162$	0	0
$163$	−5.01230e7	−0.906527	−0.453263	−	0.891377i	$-0.649740\pi$
$163$	−5.01230e7	−0.906527	−0.453263	+	0.891377i	$0.649740\pi$
$164$	3.57917e6	0.0633620
$165$	0	0
$166$	−3.59199e7	−0.609477
$167$	−3.87403e6	−0.0643659	−0.0321829	−	0.999482i	$-0.510246\pi$
$167$	−3.87403e6	−0.0643659	−0.0321829	+	0.999482i	$0.510246\pi$
$168$	0	0
$169$	1.19341e8	1.90189
$170$	−6.07124e6	−0.0947777
$171$	0	0
$172$	3.74594e7	0.561321
$173$	5.96811e7	0.876346	0.438173	−	0.898891i	$-0.355626\pi$
$173$	5.96811e7	0.876346	0.438173	+	0.898891i	$0.355626\pi$
$174$	0	0
$175$	3.10775e7	0.438342
$176$	2.48619e7	0.343748
$177$	0	0
$178$	2.15917e7	0.286957
$179$	1.10240e8	1.43666	0.718330	−	0.695703i	$-0.244907\pi$
$179$	1.10240e8	1.43666	0.718330	+	0.695703i	$0.244907\pi$
$180$	0	0
$181$	−5.56564e7	−0.697654	−0.348827	−	0.937187i	$-0.613420\pi$
$181$	−5.56564e7	−0.697654	−0.348827	+	0.937187i	$0.613420\pi$
$182$	4.54344e7	0.558644
$183$	0	0
$184$	−1.82813e7	−0.216344
$185$	8.37176e6	0.0972111
$186$	0	0
$187$	7.27840e7	0.813936
$188$	−4.72079e7	−0.518157
$189$	0	0
$190$	−2.55881e7	−0.270645
$191$	−1.30425e7	−0.135439	−0.0677194	−	0.997704i	$-0.521572\pi$
$191$	−1.30425e7	−0.135439	−0.0677194	+	0.997704i	$0.521572\pi$
$192$	0	0
$193$	1.67962e8	1.68175	0.840873	−	0.541232i	$-0.182042\pi$
$193$	1.67962e8	1.68175	0.840873	+	0.541232i	$0.182042\pi$
$194$	4.32680e6	0.0425462
$195$	0	0
$196$	4.02451e7	0.381783
$197$	3.14534e7	0.293114	0.146557	−	0.989202i	$-0.453181\pi$
$197$	3.14534e7	0.293114	0.146557	+	0.989202i	$0.453181\pi$
$198$	0	0
$199$	−5.07710e6	−0.0456699	−0.0228350	−	0.999739i	$-0.507269\pi$
$199$	−5.07710e6	−0.0456699	−0.0228350	+	0.999739i	$0.507269\pi$
$200$	1.16127e8	1.02643
$201$	0	0
$202$	−2.36758e7	−0.202104
$203$	−5.67647e7	−0.476258
$204$	0	0
$205$	−3.15230e6	−0.0255558
$206$	1.39636e8	1.11291
$207$	0	0
$208$	6.32651e7	0.487464
$209$	3.06758e8	2.32426
$210$	0	0
$211$	2.48172e7	0.181871	0.0909357	−	0.995857i	$-0.471014\pi$
$211$	2.48172e7	0.181871	0.0909357	+	0.995857i	$0.471014\pi$
$212$	4.80956e7	0.346681
$213$	0	0
$214$	6.29870e7	0.439342
$215$	−3.29918e7	−0.226398
$216$	0	0
$217$	−4.56709e7	−0.303410
$218$	4.28787e7	0.280313
$219$	0	0
$220$	1.77596e7	0.112448
$221$	1.85210e8	1.15423
$222$	0	0
$223$	−1.11098e8	−0.670868	−0.335434	−	0.942064i	$-0.608883\pi$
$223$	−1.11098e8	−0.670868	−0.335434	+	0.942064i	$0.608883\pi$
$224$	−6.59552e7	−0.392085
$225$	0	0
$226$	−2.38597e8	−1.37494
$227$	−1.42670e8	−0.809549	−0.404774	−	0.914417i	$-0.632650\pi$
$227$	−1.42670e8	−0.809549	−0.404774	+	0.914417i	$0.632650\pi$
$228$	0	0
$229$	−8.79526e7	−0.483977	−0.241989	−	0.970279i	$-0.577800\pi$
$229$	−8.79526e7	−0.483977	−0.241989	+	0.970279i	$0.577800\pi$
$230$	5.23483e6	0.0283697
$231$	0	0
$232$	−2.12113e8	−1.11521
$233$	−2.33751e8	−1.21062	−0.605311	−	0.795989i	$-0.706951\pi$
$233$	−2.33751e8	−1.21062	−0.605311	+	0.795989i	$0.706951\pi$
$234$	0	0
$235$	4.15776e7	0.208988
$236$	−1.26646e7	−0.0627193
$237$	0	0
$238$	4.62131e7	0.222201
$239$	−2.35581e8	−1.11621	−0.558107	−	0.829769i	$-0.688472\pi$
$239$	−2.35581e8	−1.11621	−0.558107	+	0.829769i	$0.688472\pi$
$240$	0	0
$241$	1.34696e8	0.619862	0.309931	−	0.950759i	$-0.399694\pi$
$241$	1.34696e8	0.619862	0.309931	+	0.950759i	$0.399694\pi$
$242$	7.03171e7	0.318938
$243$	0	0
$244$	−4.59639e7	−0.202559
$245$	−3.54453e7	−0.153985
$246$	0	0
$247$	7.80594e8	3.29599
$248$	−1.70658e8	−0.710472
$249$	0	0
$250$	−6.78106e7	−0.274478
$251$	−4.35229e8	−1.73724	−0.868621	−	0.495478i	$-0.834993\pi$
$251$	−4.35229e8	−1.73724	−0.868621	+	0.495478i	$0.834993\pi$
$252$	0	0
$253$	−6.27569e7	−0.243635
$254$	1.55861e8	0.596786
$255$	0	0
$256$	−2.83460e8	−1.05597
$257$	−2.77869e8	−1.02112	−0.510558	−	0.859844i	$-0.670561\pi$
$257$	−2.77869e8	−1.02112	−0.510558	+	0.859844i	$0.670561\pi$
$258$	0	0
$259$	−6.37243e7	−0.227906
$260$	4.51920e7	0.159461
$261$	0	0
$262$	−1.66977e7	−0.0573592
$263$	−1.34074e8	−0.454463	−0.227231	−	0.973841i	$-0.572967\pi$
$263$	−1.34074e8	−0.454463	−0.227231	+	0.973841i	$0.572967\pi$
$264$	0	0
$265$	−4.23595e7	−0.139827
$266$	1.94771e8	0.634512
$267$	0	0
$268$	2.12113e7	0.0673124
$269$	−4.06253e8	−1.27252	−0.636258	−	0.771476i	$-0.719519\pi$
$269$	−4.06253e8	−1.27252	−0.636258	+	0.771476i	$0.719519\pi$
$270$	0	0
$271$	4.61228e8	1.40774	0.703871	−	0.710328i	$-0.251453\pi$
$271$	4.61228e8	1.40774	0.703871	+	0.710328i	$0.251453\pi$
$272$	6.43494e7	0.193889
$273$	0	0
$274$	9.95791e7	0.292443
$275$	3.98647e8	1.15591
$276$	0	0
$277$	−2.60294e8	−0.735843	−0.367922	−	0.929857i	$-0.619931\pi$
$277$	−2.60294e8	−0.735843	−0.367922	+	0.929857i	$0.619931\pi$
$278$	1.86377e8	0.520279
$279$	0	0
$280$	3.46826e7	0.0944188
$281$	3.88226e8	1.04379	0.521894	−	0.853010i	$-0.325226\pi$
$281$	3.88226e8	1.04379	0.521894	+	0.853010i	$0.325226\pi$
$282$	0	0
$283$	6.85015e8	1.79658	0.898292	−	0.439398i	$-0.144808\pi$
$283$	6.85015e8	1.79658	0.898292	+	0.439398i	$0.144808\pi$
$284$	2.72288e8	0.705365
$285$	0	0
$286$	5.82811e8	1.47315
$287$	2.39947e7	0.0599141
$288$	0	0
$289$	−2.21954e8	−0.540905
$290$	6.07382e7	0.146241
$291$	0	0
$292$	−8.53744e7	−0.200672
$293$	7.03513e7	0.163394	0.0816969	−	0.996657i	$-0.473966\pi$
$293$	7.03513e7	0.163394	0.0816969	+	0.996657i	$0.473966\pi$
$294$	0	0
$295$	1.11542e7	0.0252966
$296$	−2.38118e8	−0.533669
$297$	0	0
$298$	8.28235e7	0.181299
$299$	−1.59695e8	−0.345495
$300$	0	0
$301$	2.51128e8	0.530776
$302$	−4.69058e8	−0.979946
$303$	0	0
$304$	2.71209e8	0.553665
$305$	4.04820e7	0.0816982
$306$	0	0
$307$	6.19217e8	1.22140	0.610701	−	0.791861i	$-0.290888\pi$
$307$	6.19217e8	1.22140	0.610701	+	0.791861i	$0.290888\pi$
$308$	−1.35183e8	−0.263629
$309$	0	0
$310$	4.88679e7	0.0931661
$311$	−6.09567e8	−1.14911	−0.574553	−	0.818468i	$-0.694824\pi$
$311$	−6.09567e8	−1.14911	−0.574553	+	0.818468i	$0.694824\pi$
$312$	0	0
$313$	−5.97609e8	−1.10157	−0.550785	−	0.834647i	$-0.685672\pi$
$313$	−5.97609e8	−1.10157	−0.550785	+	0.834647i	$0.685672\pi$
$314$	−1.11526e8	−0.203294
$315$	0	0
$316$	4.27026e8	0.761289
$317$	2.89237e8	0.509972	0.254986	−	0.966945i	$-0.417929\pi$
$317$	2.89237e8	0.509972	0.254986	+	0.966945i	$0.417929\pi$
$318$	0	0
$319$	−7.28150e8	−1.25589
$320$	1.03164e8	0.175997
$321$	0	0
$322$	−3.98466e7	−0.0665113
$323$	7.93972e8	1.31098
$324$	0	0
$325$	1.01442e9	1.63918
$326$	−4.08234e8	−0.652601
$327$	0	0
$328$	8.96611e7	0.140296
$329$	−3.16481e8	−0.489962
$330$	0	0
$331$	−6.01918e8	−0.912304	−0.456152	−	0.889902i	$-0.650773\pi$
$331$	−6.01918e8	−0.912304	−0.456152	+	0.889902i	$0.650773\pi$
$332$	2.71957e8	0.407866
$333$	0	0
$334$	−3.15526e7	−0.0463365
$335$	−1.86815e7	−0.0271491
$336$	0	0
$337$	4.06076e8	0.577966	0.288983	−	0.957334i	$-0.406683\pi$
$337$	4.06076e8	0.577966	0.288983	+	0.957334i	$0.406683\pi$
$338$	9.71989e8	1.36916
$339$	0	0
$340$	4.59666e7	0.0634258
$341$	−5.85844e8	−0.800095
$342$	0	0
$343$	6.10255e8	0.816549
$344$	9.38388e8	1.24288
$345$	0	0
$346$	4.86082e8	0.630874
$347$	−1.23529e8	−0.158714	−0.0793568	−	0.996846i	$-0.525287\pi$
$347$	−1.23529e8	−0.158714	−0.0793568	+	0.996846i	$0.525287\pi$
$348$	0	0
$349$	−3.88573e8	−0.489309	−0.244655	−	0.969610i	$-0.578675\pi$
$349$	−3.88573e8	−0.489309	−0.244655	+	0.969610i	$0.578675\pi$
$350$	2.53115e8	0.315559
$351$	0	0
$352$	−8.46041e8	−1.03393
$353$	−1.30943e8	−0.158443	−0.0792213	−	0.996857i	$-0.525243\pi$
$353$	−1.30943e8	−0.158443	−0.0792213	+	0.996857i	$0.525243\pi$
$354$	0	0
$355$	−2.39814e8	−0.284495
$356$	−1.63475e8	−0.192034
$357$	0	0
$358$	8.97866e8	1.03424
$359$	−1.28579e9	−1.46669	−0.733346	−	0.679856i	$-0.762042\pi$
$359$	−1.28579e9	−1.46669	−0.733346	+	0.679856i	$0.762042\pi$
$360$	0	0
$361$	2.45243e9	2.74361
$362$	−4.53301e8	−0.502235
$363$	0	0
$364$	−3.43993e8	−0.373848
$365$	7.51922e7	0.0809372
$366$	0	0
$367$	1.23889e9	1.30828	0.654139	−	0.756374i	$-0.273031\pi$
$367$	1.23889e9	1.30828	0.654139	+	0.756374i	$0.273031\pi$
$368$	−5.54843e7	−0.0580367
$369$	0	0
$370$	6.81850e7	0.0699814
$371$	3.22433e8	0.327816
$372$	0	0
$373$	−1.91108e8	−0.190676	−0.0953382	−	0.995445i	$-0.530393\pi$
$373$	−1.91108e8	−0.190676	−0.0953382	+	0.995445i	$0.530393\pi$
$374$	5.92800e8	0.585946
$375$	0	0
$376$	−1.18259e9	−1.14730
$377$	−1.85289e9	−1.78096
$378$	0	0
$379$	−4.82547e8	−0.455305	−0.227653	−	0.973742i	$-0.573105\pi$
$379$	−4.82547e8	−0.455305	−0.227653	+	0.973742i	$0.573105\pi$
$380$	1.93732e8	0.181117
$381$	0	0
$382$	−1.06226e8	−0.0975012
$383$	4.67810e8	0.425475	0.212738	−	0.977109i	$-0.431762\pi$
$383$	4.67810e8	0.425475	0.212738	+	0.977109i	$0.431762\pi$
$384$	0	0
$385$	1.19060e8	0.106329
$386$	1.36799e9	1.21068
$387$	0	0
$388$	−3.27591e7	−0.0284722
$389$	−2.37119e8	−0.204241	−0.102120	−	0.994772i	$-0.532563\pi$
$389$	−2.37119e8	−0.204241	−0.102120	+	0.994772i	$0.532563\pi$
$390$	0	0
$391$	−1.62432e8	−0.137421
$392$	1.00817e9	0.845344
$393$	0	0
$394$	2.56177e8	0.211010
$395$	−3.76097e8	−0.307051
$396$	0	0
$397$	−3.19338e8	−0.256144	−0.128072	−	0.991765i	$-0.540879\pi$
$397$	−3.19338e8	−0.256144	−0.128072	+	0.991765i	$0.540879\pi$
$398$	−4.13512e7	−0.0328774
$399$	0	0
$400$	3.52450e8	0.275351
$401$	1.08909e9	0.843451	0.421725	−	0.906724i	$-0.361425\pi$
$401$	1.08909e9	0.843451	0.421725	+	0.906724i	$0.361425\pi$
$402$	0	0
$403$	−1.49077e9	−1.13460
$404$	1.79254e8	0.135249
$405$	0	0
$406$	−4.62328e8	−0.342854
$407$	−8.17424e8	−0.600990
$408$	0	0
$409$	1.68562e9	1.21822	0.609112	−	0.793084i	$-0.291526\pi$
$409$	1.68562e9	1.21822	0.609112	+	0.793084i	$0.291526\pi$
$410$	−2.56744e7	−0.0183974
$411$	0	0
$412$	−1.05721e9	−0.744769
$413$	−8.49037e7	−0.0593064
$414$	0	0
$415$	−2.39522e8	−0.164504
$416$	−2.15288e9	−1.46620
$417$	0	0
$418$	2.49843e9	1.67321
$419$	−1.13922e9	−0.756588	−0.378294	−	0.925686i	$-0.623489\pi$
$419$	−1.13922e9	−0.756588	−0.378294	+	0.925686i	$0.623489\pi$
$420$	0	0
$421$	9.61423e8	0.627953	0.313977	−	0.949431i	$-0.398339\pi$
$421$	9.61423e8	0.627953	0.313977	+	0.949431i	$0.398339\pi$
$422$	2.02127e8	0.130928
$423$	0	0
$424$	1.20483e9	0.767621
$425$	1.03181e9	0.651984
$426$	0	0
$427$	−3.08141e8	−0.191537
$428$	−4.76887e8	−0.294010
$429$	0	0
$430$	−2.68707e8	−0.162982
$431$	−2.62811e8	−0.158115	−0.0790575	−	0.996870i	$-0.525191\pi$
$431$	−2.62811e8	−0.158115	−0.0790575	+	0.996870i	$0.525191\pi$
$432$	0	0
$433$	−2.86742e9	−1.69740	−0.848698	−	0.528877i	$-0.822613\pi$
$433$	−2.86742e9	−1.69740	−0.848698	+	0.528877i	$0.822613\pi$
$434$	−3.71973e8	−0.218423
$435$	0	0
$436$	−3.24643e8	−0.187587
$437$	−6.84590e8	−0.392415
$438$	0	0
$439$	−2.91897e8	−0.164666	−0.0823330	−	0.996605i	$-0.526237\pi$
$439$	−2.91897e8	−0.164666	−0.0823330	+	0.996605i	$0.526237\pi$
$440$	4.44892e8	0.248983
$441$	0	0
$442$	1.50847e9	0.830920
$443$	2.33184e9	1.27434	0.637169	−	0.770724i	$-0.280105\pi$
$443$	2.33184e9	1.27434	0.637169	+	0.770724i	$0.280105\pi$
$444$	0	0
$445$	1.43979e8	0.0774529
$446$	−9.04850e8	−0.482953
$447$	0	0
$448$	−7.85267e8	−0.412614
$449$	2.29986e9	1.19905	0.599527	−	0.800355i	$-0.295355\pi$
$449$	2.29986e9	1.19905	0.599527	+	0.800355i	$0.295355\pi$
$450$	0	0
$451$	3.07793e8	0.157994
$452$	1.80646e9	0.920121
$453$	0	0
$454$	−1.16200e9	−0.582788
$455$	3.02967e8	0.150784
$456$	0	0
$457$	1.34778e9	0.660560	0.330280	−	0.943883i	$-0.392857\pi$
$457$	1.34778e9	0.660560	0.330280	+	0.943883i	$0.392857\pi$
$458$	−7.16343e8	−0.348411
$459$	0	0
$460$	−3.96340e7	−0.0189852
$461$	−1.79615e9	−0.853865	−0.426932	−	0.904284i	$-0.640406\pi$
$461$	−1.79615e9	−0.853865	−0.426932	+	0.904284i	$0.640406\pi$
$462$	0	0
$463$	−3.73066e9	−1.74684	−0.873418	−	0.486971i	$-0.838102\pi$
$463$	−3.73066e9	−1.74684	−0.873418	+	0.486971i	$0.838102\pi$
$464$	−6.43768e8	−0.299169
$465$	0	0
$466$	−1.90382e9	−0.871517
$467$	4.18677e9	1.90226	0.951129	−	0.308793i	$-0.0999249\pi$
$467$	4.18677e9	1.90226	0.951129	+	0.308793i	$0.0999249\pi$
$468$	0	0
$469$	1.42200e8	0.0636496
$470$	3.38635e8	0.150449
$471$	0	0
$472$	−3.17260e8	−0.138873
$473$	3.22134e9	1.39966
$474$	0	0
$475$	4.34869e9	1.86179
$476$	−3.49889e8	−0.148698
$477$	0	0
$478$	−1.91872e9	−0.803553
$479$	−4.05633e9	−1.68639	−0.843197	−	0.537605i	$-0.819329\pi$
$479$	−4.05633e9	−1.68639	−0.843197	+	0.537605i	$0.819329\pi$
$480$	0	0
$481$	−2.08006e9	−0.852254
$482$	1.09705e9	0.446233
$483$	0	0
$484$	−5.32385e8	−0.213436
$485$	2.88521e7	0.0114837
$486$	0	0
$487$	−3.44990e9	−1.35349	−0.676745	−	0.736218i	$-0.736610\pi$
$487$	−3.44990e9	−1.35349	−0.676745	+	0.736218i	$0.736610\pi$
$488$	−1.15143e9	−0.448507
$489$	0	0
$490$	−2.88689e8	−0.110852
$491$	3.70056e9	1.41086	0.705428	−	0.708782i	$-0.250755\pi$
$491$	3.70056e9	1.41086	0.705428	+	0.708782i	$0.250755\pi$
$492$	0	0
$493$	−1.88465e9	−0.708380
$494$	6.35766e9	2.37276
$495$	0	0
$496$	−5.17953e8	−0.190592
$497$	1.82542e9	0.666982
$498$	0	0
$499$	3.49353e9	1.25867	0.629336	−	0.777133i	$-0.283327\pi$
$499$	3.49353e9	1.25867	0.629336	+	0.777133i	$0.283327\pi$
$500$	5.13408e8	0.183682
$501$	0	0
$502$	−3.54479e9	−1.25063
$503$	−3.77577e9	−1.32287	−0.661436	−	0.750002i	$-0.730053\pi$
$503$	−3.77577e9	−1.32287	−0.661436	+	0.750002i	$0.730053\pi$
$504$	0	0
$505$	−1.57876e8	−0.0545501
$506$	−5.11132e8	−0.175391
$507$	0	0
$508$	−1.18005e9	−0.399373
$509$	2.35210e9	0.790575	0.395288	−	0.918557i	$-0.370645\pi$
$509$	2.35210e9	0.790575	0.395288	+	0.918557i	$0.370645\pi$
$510$	0	0
$511$	−5.72349e8	−0.189753
$512$	−1.67502e9	−0.551538
$513$	0	0
$514$	−2.26315e9	−0.735092
$515$	9.31124e8	0.300388
$516$	0	0
$517$	−4.05967e9	−1.29203
$518$	−5.19011e8	−0.164068
$519$	0	0
$520$	1.13210e9	0.353079
$521$	1.51952e9	0.470734	0.235367	−	0.971907i	$-0.424371\pi$
$521$	1.51952e9	0.470734	0.235367	+	0.971907i	$0.424371\pi$
$522$	0	0
$523$	5.57185e9	1.70311	0.851556	−	0.524264i	$-0.175659\pi$
$523$	5.57185e9	1.70311	0.851556	+	0.524264i	$0.175659\pi$
$524$	1.26422e8	0.0383851
$525$	0	0
$526$	−1.09198e9	−0.327164
$527$	−1.51632e9	−0.451289
$528$	0	0
$529$	−3.26477e9	−0.958866
$530$	−3.45003e8	−0.100660
$531$	0	0
$532$	−1.47465e9	−0.424619
$533$	7.83227e8	0.224049
$534$	0	0
$535$	4.20011e8	0.118583
$536$	5.31360e8	0.149043
$537$	0	0
$538$	−3.30878e9	−0.916074
$539$	3.46090e9	0.951981
$540$	0	0
$541$	−1.01713e9	−0.276177	−0.138088	−	0.990420i	$-0.544096\pi$
$541$	−1.01713e9	−0.276177	−0.138088	+	0.990420i	$0.544096\pi$
$542$	3.75654e9	1.01342
$543$	0	0
$544$	−2.18978e9	−0.583183
$545$	2.85925e8	0.0756596
$546$	0	0
$547$	−3.76396e8	−0.0983308	−0.0491654	−	0.998791i	$-0.515656\pi$
$547$	−3.76396e8	−0.0983308	−0.0491654	+	0.998791i	$0.515656\pi$
$548$	−7.53934e8	−0.195705
$549$	0	0
$550$	3.24684e9	0.832131
$551$	−7.94310e9	−2.02283
$552$	0	0
$553$	2.86278e9	0.719863
$554$	−2.12000e9	−0.529727
$555$	0	0
$556$	−1.41110e9	−0.348174
$557$	−7.16500e9	−1.75680	−0.878401	−	0.477924i	$-0.841389\pi$
$557$	−7.16500e9	−1.75680	−0.878401	+	0.477924i	$0.841389\pi$
$558$	0	0
$559$	8.19721e9	1.98484
$560$	1.05263e8	0.0253289
$561$	0	0
$562$	3.16196e9	0.751414
$563$	−4.65876e9	−1.10025	−0.550125	−	0.835082i	$-0.685420\pi$
$563$	−4.65876e9	−1.10025	−0.550125	+	0.835082i	$0.685420\pi$
$564$	0	0
$565$	−1.59102e9	−0.371112
$566$	5.57921e9	1.29335
$567$	0	0
$568$	6.82103e9	1.56182
$569$	4.71634e9	1.07328	0.536639	−	0.843812i	$-0.319694\pi$
$569$	4.71634e9	1.07328	0.536639	+	0.843812i	$0.319694\pi$
$570$	0	0
$571$	−8.11800e9	−1.82483	−0.912416	−	0.409265i	$-0.865785\pi$
$571$	−8.11800e9	−1.82483	−0.912416	+	0.409265i	$0.865785\pi$
$572$	−4.41258e9	−0.985840
$573$	0	0
$574$	1.95429e8	0.0431317
$575$	−8.89660e8	−0.195158
$576$	0	0
$577$	−2.96457e9	−0.642460	−0.321230	−	0.947001i	$-0.604096\pi$
$577$	−2.96457e9	−0.642460	−0.321230	+	0.947001i	$0.604096\pi$
$578$	−1.80774e9	−0.389393
$579$	0	0
$580$	−4.59862e8	−0.0978654
$581$	1.82320e9	0.385671
$582$	0	0
$583$	4.13601e9	0.864453
$584$	−2.13870e9	−0.444329
$585$	0	0
$586$	5.72986e8	0.117626
$587$	−4.79349e9	−0.978180	−0.489090	−	0.872233i	$-0.662671\pi$
$587$	−4.79349e9	−0.978180	−0.489090	+	0.872233i	$0.662671\pi$
$588$	0	0
$589$	−6.39075e9	−1.28869
$590$	9.08470e7	0.0182108
$591$	0	0
$592$	−7.22697e8	−0.143163
$593$	−6.55987e9	−1.29183	−0.645913	−	0.763411i	$-0.723523\pi$
$593$	−6.55987e9	−1.29183	−0.645913	+	0.763411i	$0.723523\pi$
$594$	0	0
$595$	3.08160e8	0.0599745
$596$	−6.27073e8	−0.121327
$597$	0	0
$598$	−1.30066e9	−0.248719
$599$	−8.15165e9	−1.54971	−0.774857	−	0.632137i	$-0.782178\pi$
$599$	−8.15165e9	−1.54971	−0.774857	+	0.632137i	$0.782178\pi$
$600$	0	0
$601$	−3.63784e9	−0.683570	−0.341785	−	0.939778i	$-0.611031\pi$
$601$	−3.63784e9	−0.683570	−0.341785	+	0.939778i	$0.611031\pi$
$602$	2.04534e9	0.382102
$603$	0	0
$604$	3.55133e9	0.655786
$605$	4.68890e8	0.0860849
$606$	0	0
$607$	4.53989e9	0.823920	0.411960	−	0.911202i	$-0.364844\pi$
$607$	4.53989e9	0.823920	0.411960	+	0.911202i	$0.364844\pi$
$608$	−9.22913e9	−1.66532
$609$	0	0
$610$	3.29712e8	0.0588139
$611$	−1.03305e10	−1.83221
$612$	0	0
$613$	5.71720e9	1.00247	0.501235	−	0.865311i	$-0.332879\pi$
$613$	5.71720e9	1.00247	0.501235	+	0.865311i	$0.332879\pi$
$614$	5.04330e9	0.879277
$615$	0	0
$616$	−3.38643e9	−0.583727
$617$	2.37562e9	0.407172	0.203586	−	0.979057i	$-0.434740\pi$
$617$	2.37562e9	0.407172	0.203586	+	0.979057i	$0.434740\pi$
$618$	0	0
$619$	5.60279e9	0.949483	0.474742	−	0.880125i	$-0.342542\pi$
$619$	5.60279e9	0.949483	0.474742	+	0.880125i	$0.342542\pi$
$620$	−3.69989e8	−0.0623473
$621$	0	0
$622$	−4.96470e9	−0.827231
$623$	−1.09594e9	−0.181584
$624$	0	0
$625$	5.42090e9	0.888160
$626$	−4.86732e9	−0.793011
$627$	0	0
$628$	8.44389e8	0.136045
$629$	−2.11571e9	−0.338984
$630$	0	0
$631$	−1.14283e10	−1.81083	−0.905415	−	0.424527i	$-0.860440\pi$
$631$	−1.14283e10	−1.81083	−0.905415	+	0.424527i	$0.860440\pi$
$632$	1.06974e10	1.68565
$633$	0	0
$634$	2.35573e9	0.367124
$635$	1.03932e9	0.161079
$636$	0	0
$637$	8.80680e9	1.34999
$638$	−5.93052e9	−0.904108
$639$	0	0
$640$	−2.68863e8	−0.0405417
$641$	8.14000e8	0.122073	0.0610367	−	0.998136i	$-0.480559\pi$
$641$	8.14000e8	0.122073	0.0610367	+	0.998136i	$0.480559\pi$
$642$	0	0
$643$	−1.34257e10	−1.99158	−0.995792	−	0.0916394i	$-0.970789\pi$
$643$	−1.34257e10	−1.99158	−0.995792	+	0.0916394i	$0.970789\pi$
$644$	3.01686e8	0.0445098
$645$	0	0
$646$	6.46662e9	0.943765
$647$	2.58413e9	0.375102	0.187551	−	0.982255i	$-0.439945\pi$
$647$	2.58413e9	0.375102	0.187551	+	0.982255i	$0.439945\pi$
$648$	0	0
$649$	−1.08910e9	−0.156391
$650$	8.26210e9	1.18003
$651$	0	0
$652$	3.09082e9	0.436725
$653$	−9.14859e9	−1.28575	−0.642877	−	0.765969i	$-0.722259\pi$
$653$	−9.14859e9	−1.28575	−0.642877	+	0.765969i	$0.722259\pi$
$654$	0	0
$655$	−1.11344e8	−0.0154819
$656$	2.72124e8	0.0376360
$657$	0	0
$658$	−2.57763e9	−0.352719
$659$	3.05757e9	0.416176	0.208088	−	0.978110i	$-0.433276\pi$
$659$	3.05757e9	0.416176	0.208088	+	0.978110i	$0.433276\pi$
$660$	0	0
$661$	−5.81198e9	−0.782743	−0.391371	−	0.920233i	$-0.627999\pi$
$661$	−5.81198e9	−0.782743	−0.391371	+	0.920233i	$0.627999\pi$
$662$	−4.90241e9	−0.656760
$663$	0	0
$664$	6.81275e9	0.903096
$665$	1.29878e9	0.171262
$666$	0	0
$667$	1.62501e9	0.212039
$668$	2.38891e8	0.0310086
$669$	0	0
$670$	−1.52154e8	−0.0195444
$671$	−3.95269e9	−0.505084
$672$	0	0
$673$	−7.68542e9	−0.971885	−0.485943	−	0.873991i	$-0.661524\pi$
$673$	−7.68542e9	−0.971885	−0.485943	+	0.873991i	$0.661524\pi$
$674$	3.30734e9	0.416073
$675$	0	0
$676$	−7.35913e9	−0.916248
$677$	−5.12888e9	−0.635276	−0.317638	−	0.948212i	$-0.602890\pi$
$677$	−5.12888e9	−0.635276	−0.317638	+	0.948212i	$0.602890\pi$
$678$	0	0
$679$	−2.19617e8	−0.0269229
$680$	1.15150e9	0.140437
$681$	0	0
$682$	−4.77149e9	−0.575982
$683$	−9.14761e9	−1.09859	−0.549294	−	0.835629i	$-0.685103\pi$
$683$	−9.14761e9	−1.09859	−0.549294	+	0.835629i	$0.685103\pi$
$684$	0	0
$685$	6.64016e8	0.0789335
$686$	4.97031e9	0.587827
$687$	0	0
$688$	2.84804e9	0.333416
$689$	1.05247e10	1.22587
$690$	0	0
$691$	1.46307e10	1.68691	0.843455	−	0.537200i	$-0.180518\pi$
$691$	1.46307e10	1.68691	0.843455	+	0.537200i	$0.180518\pi$
$692$	−3.68022e9	−0.422185
$693$	0	0
$694$	−1.00610e9	−0.114257
$695$	1.24281e9	0.140429
$696$	0	0
$697$	7.96651e8	0.0891155
$698$	−3.16479e9	−0.352250
$699$	0	0
$700$	−1.91639e9	−0.211174
$701$	5.51419e9	0.604601	0.302300	−	0.953213i	$-0.402245\pi$
$701$	5.51419e9	0.604601	0.302300	+	0.953213i	$0.402245\pi$
$702$	0	0
$703$	−8.91696e9	−0.967996
$704$	−1.00730e10	−1.08807
$705$	0	0
$706$	−1.06649e9	−0.114061
$707$	1.20172e9	0.127890
$708$	0	0
$709$	4.43575e9	0.467417	0.233709	−	0.972307i	$-0.424914\pi$
$709$	4.43575e9	0.467417	0.233709	+	0.972307i	$0.424914\pi$
$710$	−1.95320e9	−0.204806
$711$	0	0
$712$	−4.09519e9	−0.425201
$713$	1.30743e9	0.135084
$714$	0	0
$715$	3.88631e9	0.397619
$716$	−6.79793e9	−0.692119
$717$	0	0
$718$	−1.04723e10	−1.05586
$719$	5.67887e9	0.569785	0.284893	−	0.958559i	$-0.408042\pi$
$719$	5.67887e9	0.569785	0.284893	+	0.958559i	$0.408042\pi$
$720$	0	0
$721$	−7.08754e9	−0.704242
$722$	1.99742e10	1.97510
$723$	0	0
$724$	3.43204e9	0.336099
$725$	−1.03225e10	−1.00601
$726$	0	0
$727$	−1.26294e10	−1.21903	−0.609514	−	0.792775i	$-0.708636\pi$
$727$	−1.26294e10	−1.21903	−0.609514	+	0.792775i	$0.708636\pi$
$728$	−8.61731e9	−0.827774
$729$	0	0
$730$	6.12414e8	0.0582660
$731$	8.33771e9	0.789470
$732$	0	0
$733$	8.87757e9	0.832588	0.416294	−	0.909230i	$-0.363329\pi$
$733$	8.87757e9	0.832588	0.416294	+	0.909230i	$0.363329\pi$
$734$	1.00903e10	0.941819
$735$	0	0
$736$	1.88811e9	0.174564
$737$	1.82408e9	0.167844
$738$	0	0
$739$	−1.67534e10	−1.52703	−0.763515	−	0.645791i	$-0.776528\pi$
$739$	−1.67534e10	−1.52703	−0.763515	+	0.645791i	$0.776528\pi$
$740$	−5.16243e8	−0.0468320
$741$	0	0
$742$	2.62610e9	0.235992
$743$	−1.87784e10	−1.67957	−0.839784	−	0.542921i	$-0.817318\pi$
$743$	−1.87784e10	−1.67957	−0.839784	+	0.542921i	$0.817318\pi$
$744$	0	0
$745$	5.52286e8	0.0489347
$746$	−1.55650e9	−0.137266
$747$	0	0
$748$	−4.48821e9	−0.392118
$749$	−3.19705e9	−0.278011
$750$	0	0
$751$	2.58308e9	0.222535	0.111268	−	0.993790i	$-0.464509\pi$
$751$	2.58308e9	0.222535	0.111268	+	0.993790i	$0.464509\pi$
$752$	−3.58921e9	−0.307777
$753$	0	0
$754$	−1.50911e10	−1.28210
$755$	−3.12778e9	−0.264498
$756$	0	0
$757$	5.60643e9	0.469733	0.234867	−	0.972028i	$-0.424535\pi$
$757$	5.60643e9	0.469733	0.234867	+	0.972028i	$0.424535\pi$
$758$	−3.93018e9	−0.327770
$759$	0	0
$760$	4.85315e9	0.401030
$761$	−1.71960e8	−0.0141443	−0.00707216	−	0.999975i	$-0.502251\pi$
$761$	−1.71960e8	−0.0141443	−0.00707216	+	0.999975i	$0.502251\pi$
$762$	0	0
$763$	−2.17641e9	−0.177380
$764$	8.04260e8	0.0652484
$765$	0	0
$766$	3.81015e9	0.306296
$767$	−2.77139e9	−0.221776
$768$	0	0
$769$	−1.69708e10	−1.34574	−0.672869	−	0.739762i	$-0.734938\pi$
$769$	−1.69708e10	−1.34574	−0.672869	+	0.739762i	$0.734938\pi$
$770$	9.69702e8	0.0765457
$771$	0	0
$772$	−1.03573e10	−0.810191
$773$	5.87486e9	0.457477	0.228739	−	0.973488i	$-0.426540\pi$
$773$	5.87486e9	0.457477	0.228739	+	0.973488i	$0.426540\pi$
$774$	0	0
$775$	−8.30510e9	−0.640898
$776$	−8.20642e8	−0.0630431
$777$	0	0
$778$	−1.93125e9	−0.147031
$779$	3.35759e9	0.254476
$780$	0	0
$781$	2.34156e10	1.75884
$782$	−1.32295e9	−0.0989280
$783$	0	0
$784$	3.05983e9	0.226773
$785$	−7.43684e8	−0.0548712
$786$	0	0
$787$	1.81450e9	0.132692	0.0663461	−	0.997797i	$-0.478866\pi$
$787$	1.81450e9	0.132692	0.0663461	+	0.997797i	$0.478866\pi$
$788$	−1.93957e9	−0.141209
$789$	0	0
$790$	−3.06318e9	−0.221043
$791$	1.21105e10	0.870052
$792$	0	0
$793$	−1.00582e10	−0.716252
$794$	−2.60089e9	−0.184396
$795$	0	0
$796$	3.13078e8	0.0220017
$797$	−7.68250e9	−0.537525	−0.268762	−	0.963207i	$-0.586615\pi$
$797$	−7.68250e9	−0.537525	−0.268762	+	0.963207i	$0.586615\pi$
$798$	0	0
$799$	−1.05075e10	−0.728763
$800$	−1.19937e10	−0.828207
$801$	0	0
$802$	8.87028e9	0.607193
$803$	−7.34182e9	−0.500379
$804$	0	0
$805$	−2.65706e8	−0.0179521
$806$	−1.21418e10	−0.816791
$807$	0	0
$808$	4.49047e9	0.299469
$809$	2.53283e10	1.68185	0.840924	−	0.541154i	$-0.182012\pi$
$809$	2.53283e10	1.68185	0.840924	+	0.541154i	$0.182012\pi$
$810$	0	0
$811$	−1.04893e9	−0.0690513	−0.0345256	−	0.999404i	$-0.510992\pi$
$811$	−1.04893e9	−0.0690513	−0.0345256	+	0.999404i	$0.510992\pi$
$812$	3.50038e9	0.229440
$813$	0	0
$814$	−6.65763e9	−0.432647
$815$	−2.72220e9	−0.176144
$816$	0	0
$817$	3.51404e10	2.25439
$818$	1.37287e10	0.876989
$819$	0	0
$820$	1.94386e8	0.0123117
$821$	1.22269e10	0.771110	0.385555	−	0.922685i	$-0.374010\pi$
$821$	1.22269e10	0.771110	0.385555	+	0.922685i	$0.374010\pi$
$822$	0	0
$823$	6.96726e8	0.0435675	0.0217837	−	0.999763i	$-0.493065\pi$
$823$	6.96726e8	0.0435675	0.0217837	+	0.999763i	$0.493065\pi$
$824$	−2.64840e10	−1.64907
$825$	0	0
$826$	−6.91510e8	−0.0426942
$827$	2.23328e10	1.37301	0.686505	−	0.727125i	$-0.259144\pi$
$827$	2.23328e10	1.37301	0.686505	+	0.727125i	$0.259144\pi$
$828$	0	0
$829$	1.33734e10	0.815267	0.407633	−	0.913146i	$-0.366354\pi$
$829$	1.33734e10	0.815267	0.407633	+	0.913146i	$0.366354\pi$
$830$	−1.95082e9	−0.118425
$831$	0	0
$832$	−2.56324e10	−1.54297
$833$	8.95774e9	0.536959
$834$	0	0
$835$	−2.10400e8	−0.0125067
$836$	−1.89162e10	−1.11972
$837$	0	0
$838$	−9.27856e9	−0.544661
$839$	1.68025e10	0.982217	0.491108	−	0.871098i	$-0.336592\pi$
$839$	1.68025e10	0.982217	0.491108	+	0.871098i	$0.336592\pi$
$840$	0	0
$841$	1.60463e9	0.0930226
$842$	7.83045e9	0.452058
$843$	0	0
$844$	−1.53035e9	−0.0876176
$845$	6.48145e9	0.369550
$846$	0	0
$847$	−3.56910e9	−0.201821
$848$	3.65671e9	0.205923
$849$	0	0
$850$	8.40370e9	0.469358
$851$	1.82424e9	0.101468
$852$	0	0
$853$	−6.95279e9	−0.383563	−0.191782	−	0.981438i	$-0.561427\pi$
$853$	−6.95279e9	−0.383563	−0.191782	+	0.981438i	$0.561427\pi$
$854$	−2.50970e9	−0.137886
$855$	0	0
$856$	−1.19464e10	−0.650997
$857$	3.47269e10	1.88466	0.942330	−	0.334687i	$-0.108630\pi$
$857$	3.47269e10	1.88466	0.942330	+	0.334687i	$0.108630\pi$
$858$	0	0
$859$	−1.72796e10	−0.930161	−0.465081	−	0.885268i	$-0.653975\pi$
$859$	−1.72796e10	−0.930161	−0.465081	+	0.885268i	$0.653975\pi$
$860$	2.03443e9	0.109068
$861$	0	0
$862$	−2.14050e9	−0.113826
$863$	3.64236e10	1.92906	0.964529	−	0.263977i	$-0.0850343\pi$
$863$	3.64236e10	1.92906	0.964529	+	0.263977i	$0.0850343\pi$
$864$	0	0
$865$	3.24130e9	0.170280
$866$	−2.33541e10	−1.22194
$867$	0	0
$868$	2.81628e9	0.146170
$869$	3.67224e10	1.89828
$870$	0	0
$871$	4.64165e9	0.238018
$872$	−8.13258e9	−0.415356
$873$	0	0
$874$	−5.57575e9	−0.282496
$875$	3.44188e9	0.173687
$876$	0	0
$877$	−2.21634e9	−0.110953	−0.0554763	−	0.998460i	$-0.517668\pi$
$877$	−2.21634e9	−0.110953	−0.0554763	+	0.998460i	$0.517668\pi$
$878$	−2.37740e9	−0.118542
$879$	0	0
$880$	1.35026e9	0.0667925
$881$	2.32029e10	1.14321	0.571607	−	0.820528i	$-0.306320\pi$
$881$	2.32029e10	1.14321	0.571607	+	0.820528i	$0.306320\pi$
$882$	0	0
$883$	1.94888e10	0.952624	0.476312	−	0.879276i	$-0.341973\pi$
$883$	1.94888e10	0.952624	0.476312	+	0.879276i	$0.341973\pi$
$884$	−1.14209e10	−0.556057
$885$	0	0
$886$	1.89920e10	0.917386
$887$	−9.83405e9	−0.473151	−0.236575	−	0.971613i	$-0.576025\pi$
$887$	−9.83405e9	−0.473151	−0.236575	+	0.971613i	$0.576025\pi$
$888$	0	0
$889$	−7.91107e9	−0.377641
$890$	1.17265e9	0.0557577
$891$	0	0
$892$	6.85080e9	0.323195
$893$	−4.42853e10	−2.08104
$894$	0	0
$895$	5.98717e9	0.279152
$896$	2.04654e9	0.0950477
$897$	0	0
$898$	1.87315e10	0.863189
$899$	1.51697e10	0.696334
$900$	0	0
$901$	1.07051e10	0.487590
$902$	2.50686e9	0.113739
$903$	0	0
$904$	4.52534e10	2.03733
$905$	−3.02272e9	−0.135559
$906$	0	0
$907$	2.35757e10	1.04915	0.524577	−	0.851363i	$-0.324224\pi$
$907$	2.35757e10	1.04915	0.524577	+	0.851363i	$0.324224\pi$
$908$	8.79773e9	0.390005
$909$	0	0
$910$	2.46756e9	0.108548
$911$	2.65692e10	1.16430	0.582149	−	0.813082i	$-0.302212\pi$
$911$	2.65692e10	1.16430	0.582149	+	0.813082i	$0.302212\pi$
$912$	0	0
$913$	2.33871e10	1.01702
$914$	1.09772e10	0.475532
$915$	0	0
$916$	5.42358e9	0.233159
$917$	8.47531e8	0.0362964
$918$	0	0
$919$	2.32295e10	0.987271	0.493636	−	0.869669i	$-0.335668\pi$
$919$	2.32295e10	0.987271	0.493636	+	0.869669i	$0.335668\pi$
$920$	−9.92863e8	−0.0420370
$921$	0	0
$922$	−1.46290e10	−0.614690
$923$	5.95846e10	2.49418
$924$	0	0
$925$	−1.15880e10	−0.481409
$926$	−3.03849e10	−1.25753
$927$	0	0
$928$	2.19071e10	0.899845
$929$	−8.90068e9	−0.364224	−0.182112	−	0.983278i	$-0.558293\pi$
$929$	−8.90068e9	−0.364224	−0.182112	+	0.983278i	$0.558293\pi$
$930$	0	0
$931$	3.77536e10	1.53333
$932$	1.44142e10	0.583224
$933$	0	0
$934$	3.40997e10	1.36942
$935$	3.95292e9	0.158153
$936$	0	0
$937$	2.70936e10	1.07592	0.537959	−	0.842971i	$-0.319196\pi$
$937$	2.70936e10	1.07592	0.537959	+	0.842971i	$0.319196\pi$
$938$	1.15817e9	0.0458208
$939$	0	0
$940$	−2.56387e9	−0.100681
$941$	4.63143e10	1.81197	0.905987	−	0.423306i	$-0.139131\pi$
$941$	4.63143e10	1.81197	0.905987	+	0.423306i	$0.139131\pi$
$942$	0	0
$943$	−6.86900e8	−0.0266749
$944$	−9.62892e8	−0.0372542
$945$	0	0
$946$	2.62367e10	1.00760
$947$	−4.89914e10	−1.87454	−0.937271	−	0.348601i	$-0.886657\pi$
$947$	−4.89914e10	−1.87454	−0.937271	+	0.348601i	$0.886657\pi$
$948$	0	0
$949$	−1.86824e10	−0.709580
$950$	3.54185e10	1.34029
$951$	0	0
$952$	−8.76500e9	−0.329248
$953$	−3.63170e10	−1.35921	−0.679603	−	0.733580i	$-0.737848\pi$
$953$	−3.63170e10	−1.35921	−0.679603	+	0.733580i	$0.737848\pi$
$954$	0	0
$955$	−7.08341e8	−0.0263166
$956$	1.45270e10	0.537743
$957$	0	0
$958$	−3.30374e10	−1.21402
$959$	−5.05436e9	−0.185055
$960$	0	0
$961$	−1.53076e10	−0.556385
$962$	−1.69414e10	−0.613530
$963$	0	0
$964$	−8.30599e9	−0.298622
$965$	9.12207e9	0.326774
$966$	0	0
$967$	−3.38245e10	−1.20293	−0.601463	−	0.798901i	$-0.705415\pi$
$967$	−3.38245e10	−1.20293	−0.601463	+	0.798901i	$0.705415\pi$
$968$	−1.33367e10	−0.472589
$969$	0	0
$970$	2.34990e8	0.00826701
$971$	−4.01598e10	−1.40775	−0.703873	−	0.710326i	$-0.748548\pi$
$971$	−4.01598e10	−1.40775	−0.703873	+	0.710326i	$0.748548\pi$
$972$	0	0
$973$	−9.46001e9	−0.329228
$974$	−2.80982e10	−0.974366
$975$	0	0
$976$	−3.49463e9	−0.120317
$977$	−1.49500e10	−0.512872	−0.256436	−	0.966561i	$-0.582548\pi$
$977$	−1.49500e10	−0.512872	−0.256436	+	0.966561i	$0.582548\pi$
$978$	0	0
$979$	−1.40582e10	−0.478838
$980$	2.18572e9	0.0741830
$981$	0	0
$982$	3.01398e10	1.01566
$983$	−2.98689e10	−1.00295	−0.501477	−	0.865171i	$-0.667210\pi$
$983$	−2.98689e10	−1.00295	−0.501477	+	0.865171i	$0.667210\pi$
$984$	0	0
$985$	1.70825e9	0.0569539
$986$	−1.53498e10	−0.509957
$987$	0	0
$988$	−4.81351e10	−1.58786
$989$	−7.18906e9	−0.236312
$990$	0	0
$991$	1.42111e10	0.463842	0.231921	−	0.972735i	$-0.425499\pi$
$991$	1.42111e10	0.463842	0.231921	+	0.972735i	$0.425499\pi$
$992$	1.76257e10	0.573266
$993$	0	0
$994$	1.48674e10	0.480155
$995$	−2.75739e8	−0.00887396
$996$	0	0
$997$	2.29718e10	0.734112	0.367056	−	0.930199i	$-0.380366\pi$
$997$	2.29718e10	0.734112	0.367056	+	0.930199i	$0.380366\pi$
$998$	2.84536e10	0.906108
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+8.14464 q^{2} -61.6648 q^{4} +54.3103 q^{5} -413.400 q^{7} -1544.75 q^{8} +O(q^{10})\)	\(q+8.14464 q^{2} -61.6648 q^{4} +54.3103 q^{5} -413.400 q^{7} -1544.75 q^{8} +442.338 q^{10} -5302.90 q^{11} -13494.1 q^{13} -3367.00 q^{14} -4688.37 q^{16} -13725.3 q^{17} -57847.2 q^{19} -3349.03 q^{20} -43190.2 q^{22} +11834.5 q^{23} -75175.4 q^{25} -109904. q^{26} +25492.2 q^{28} +137312. q^{29} +110476. q^{31} +159543. q^{32} -111788. q^{34} -22451.9 q^{35} +154147. q^{37} -471145. q^{38} -83896.0 q^{40} -58042.4 q^{41} -607469. q^{43} +327002. q^{44} +96387.4 q^{46} +765556. q^{47} -652643. q^{49} -612277. q^{50} +832107. q^{52} -779953. q^{53} -288002. q^{55} +638601. q^{56} +1.11836e6 q^{58} +205379. q^{59} +745383. q^{61} +899790. q^{62} +1.89953e6 q^{64} -732866. q^{65} -343978. q^{67} +846369. q^{68} -182863. q^{70} -4.41562e6 q^{71} +1.38449e6 q^{73} +1.25547e6 q^{74} +3.56714e6 q^{76} +2.19222e6 q^{77} -6.92496e6 q^{79} -254627. q^{80} -472735. q^{82} -4.41025e6 q^{83} -745427. q^{85} -4.94762e6 q^{86} +8.19166e6 q^{88} +2.65103e6 q^{89} +5.57844e6 q^{91} -729769. q^{92} +6.23518e6 q^{94} -3.14170e6 q^{95} +531245. q^{97} -5.31555e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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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