LMFDB - Embedded newform 531.8.a.c.1.13

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			1.13
Root			$-12.3679$ 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)

$f(q)$	$=$	$q+12.3679 q^{2} +24.9655 q^{4} +477.980 q^{5} +1344.57 q^{7} -1274.32 q^{8} +O(q^{10})$	\(q+12.3679 q^{2} +24.9655 q^{4} +477.980 q^{5} +1344.57 q^{7} -1274.32 q^{8} +5911.62 q^{10} -6221.77 q^{11} +10930.7 q^{13} +16629.5 q^{14} -18956.3 q^{16} +31807.5 q^{17} -36490.6 q^{19} +11933.0 q^{20} -76950.3 q^{22} -38312.8 q^{23} +150340. q^{25} +135190. q^{26} +33567.7 q^{28} +138973. q^{29} +256427. q^{31} -71336.8 q^{32} +393392. q^{34} +642676. q^{35} +22109.8 q^{37} -451313. q^{38} -609101. q^{40} -316134. q^{41} +148255. q^{43} -155329. q^{44} -473850. q^{46} -748870. q^{47} +984312. q^{49} +1.85940e6 q^{50} +272890. q^{52} +1.94662e6 q^{53} -2.97388e6 q^{55} -1.71341e6 q^{56} +1.71880e6 q^{58} +205379. q^{59} +1.76648e6 q^{61} +3.17147e6 q^{62} +1.54412e6 q^{64} +5.22465e6 q^{65} -425592. q^{67} +794089. q^{68} +7.94856e6 q^{70} +3.19791e6 q^{71} -4.35846e6 q^{73} +273452. q^{74} -911006. q^{76} -8.36557e6 q^{77} -2.91855e6 q^{79} -9.06074e6 q^{80} -3.90993e6 q^{82} +1.97344e6 q^{83} +1.52033e7 q^{85} +1.83361e6 q^{86} +7.92854e6 q^{88} -7.72572e6 q^{89} +1.46970e7 q^{91} -956499. q^{92} -9.26197e6 q^{94} -1.74418e7 q^{95} +9.26843e6 q^{97} +1.21739e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	12.3679	1.09318	0.546590	−	0.837400i	$-0.315926\pi$
$2$	12.3679	1.09318	0.546590	+	0.837400i	$0.315926\pi$
$3$	0	0
$3$	0	0
$4$	24.9655	0.195043
$5$	477.980	1.71007	0.855037	−	0.518567i	$-0.173534\pi$
$5$	477.980	1.71007	0.855037	+	0.518567i	$0.173534\pi$
$6$	0	0
$7$	1344.57	1.48163	0.740813	−	0.671711i	$-0.234440\pi$
$7$	1344.57	1.48163	0.740813	+	0.671711i	$0.234440\pi$
$8$	−1274.32	−0.879963
$9$	0	0
$10$	5911.62	1.86942
$11$	−6221.77	−1.40942	−0.704708	−	0.709497i	$-0.748922\pi$
$11$	−6221.77	−1.40942	−0.704708	+	0.709497i	$0.748922\pi$
$12$	0	0
$13$	10930.7	1.37989	0.689947	−	0.723860i	$-0.257634\pi$
$13$	10930.7	1.37989	0.689947	+	0.723860i	$0.257634\pi$
$14$	16629.5	1.61968
$15$	0	0
$16$	−18956.3	−1.15700
$17$	31807.5	1.57021	0.785105	−	0.619362i	$-0.212609\pi$
$17$	31807.5	1.57021	0.785105	+	0.619362i	$0.212609\pi$
$18$	0	0
$19$	−36490.6	−1.22052	−0.610258	−	0.792203i	$-0.708934\pi$
$19$	−36490.6	−1.22052	−0.610258	+	0.792203i	$0.708934\pi$
$20$	11933.0	0.333538
$21$	0	0
$22$	−76950.3	−1.54075
$23$	−38312.8	−0.656594	−0.328297	−	0.944575i	$-0.606475\pi$
$23$	−38312.8	−0.656594	−0.328297	+	0.944575i	$0.606475\pi$
$24$	0	0
$25$	150340.	1.92435
$26$	135190.	1.50847
$27$	0	0
$28$	33567.7	0.288981
$29$	138973.	1.05812	0.529062	−	0.848583i	$-0.322544\pi$
$29$	138973.	1.05812	0.529062	+	0.848583i	$0.322544\pi$
$30$	0	0
$31$	256427.	1.54596	0.772979	−	0.634432i	$-0.218766\pi$
$31$	256427.	1.54596	0.772979	+	0.634432i	$0.218766\pi$
$32$	−71336.8	−0.384847
$33$	0	0
$34$	393392.	1.71652
$35$	642676.	2.53369
$36$	0	0
$37$	22109.8	0.0717594	0.0358797	−	0.999356i	$-0.488577\pi$
$37$	22109.8	0.0717594	0.0358797	+	0.999356i	$0.488577\pi$
$38$	−451313.	−1.33424
$39$	0	0
$40$	−609101.	−1.50480
$41$	−316134.	−0.716355	−0.358178	−	0.933653i	$-0.616602\pi$
$41$	−316134.	−0.716355	−0.358178	+	0.933653i	$0.616602\pi$
$42$	0	0
$43$	148255.	0.284361	0.142181	−	0.989841i	$-0.454589\pi$
$43$	148255.	0.284361	0.142181	+	0.989841i	$0.454589\pi$
$44$	−155329.	−0.274897
$45$	0	0
$46$	−473850.	−0.717776
$47$	−748870.	−1.05212	−0.526058	−	0.850448i	$-0.676331\pi$
$47$	−748870.	−1.05212	−0.526058	+	0.850448i	$0.676331\pi$
$48$	0	0
$49$	984312.	1.19522
$50$	1.85940e6	2.10367
$51$	0	0
$52$	272890.	0.269138
$53$	1.94662e6	1.79604	0.898021	−	0.439953i	$-0.145005\pi$
$53$	1.94662e6	1.79604	0.898021	+	0.439953i	$0.145005\pi$
$54$	0	0
$55$	−2.97388e6	−2.41021
$56$	−1.71341e6	−1.30378
$57$	0	0
$58$	1.71880e6	1.15672
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	0	0
$61$	1.76648e6	0.996445	0.498222	−	0.867049i	$-0.333986\pi$
$61$	1.76648e6	0.996445	0.498222	+	0.867049i	$0.333986\pi$
$62$	3.17147e6	1.69001
$63$	0	0
$64$	1.54412e6	0.736294
$65$	5.22465e6	2.35972
$66$	0	0
$67$	−425592.	−0.172875	−0.0864374	−	0.996257i	$-0.527548\pi$
$67$	−425592.	−0.172875	−0.0864374	+	0.996257i	$0.527548\pi$
$68$	794089.	0.306258
$69$	0	0
$70$	7.94856e6	2.76978
$71$	3.19791e6	1.06038	0.530191	−	0.847878i	$-0.322120\pi$
$71$	3.19791e6	1.06038	0.530191	+	0.847878i	$0.322120\pi$
$72$	0	0
$73$	−4.35846e6	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$73$	−4.35846e6	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$74$	273452.	0.0784459
$75$	0	0
$76$	−911006.	−0.238053
$77$	−8.36557e6	−2.08823
$78$	0	0
$79$	−2.91855e6	−0.665996	−0.332998	−	0.942928i	$-0.608060\pi$
$79$	−2.91855e6	−0.665996	−0.332998	+	0.942928i	$0.608060\pi$
$80$	−9.06074e6	−1.97856
$81$	0	0
$82$	−3.90993e6	−0.783105
$83$	1.97344e6	0.378835	0.189418	−	0.981897i	$-0.439340\pi$
$83$	1.97344e6	0.378835	0.189418	+	0.981897i	$0.439340\pi$
$84$	0	0
$85$	1.52033e7	2.68518
$86$	1.83361e6	0.310858
$87$	0	0
$88$	7.92854e6	1.24023
$89$	−7.72572e6	−1.16165	−0.580823	−	0.814030i	$-0.697269\pi$
$89$	−7.72572e6	−1.16165	−0.580823	+	0.814030i	$0.697269\pi$
$90$	0	0
$91$	1.46970e7	2.04449
$92$	−956499.	−0.128064
$93$	0	0
$94$	−9.26197e6	−1.15015
$95$	−1.74418e7	−2.08717
$96$	0	0
$97$	9.26843e6	1.03111	0.515555	−	0.856857i	$-0.327586\pi$
$97$	9.26843e6	1.03111	0.515555	+	0.856857i	$0.327586\pi$
$98$	1.21739e7	1.30659
$99$	0	0
$100$	3.75331e6	0.375331
$101$	−5.77631e6	−0.557861	−0.278930	−	0.960311i	$-0.589980\pi$
$101$	−5.77631e6	−0.557861	−0.278930	+	0.960311i	$0.589980\pi$
$102$	0	0
$103$	−1.72461e7	−1.55511	−0.777555	−	0.628815i	$-0.783540\pi$
$103$	−1.72461e7	−1.55511	−0.777555	+	0.628815i	$0.783540\pi$
$104$	−1.39292e7	−1.21426
$105$	0	0
$106$	2.40757e7	1.96340
$107$	−5.41952e6	−0.427679	−0.213839	−	0.976869i	$-0.568597\pi$
$107$	−5.41952e6	−0.427679	−0.213839	+	0.976869i	$0.568597\pi$
$108$	0	0
$109$	4.21169e6	0.311504	0.155752	−	0.987796i	$-0.450220\pi$
$109$	4.21169e6	0.311504	0.155752	+	0.987796i	$0.450220\pi$
$110$	−3.67807e7	−2.63479
$111$	0	0
$112$	−2.54880e7	−1.71424
$113$	1.72308e7	1.12339	0.561695	−	0.827345i	$-0.310150\pi$
$113$	1.72308e7	1.12339	0.561695	+	0.827345i	$0.310150\pi$
$114$	0	0
$115$	−1.83128e7	−1.12282
$116$	3.46952e6	0.206379
$117$	0	0
$118$	2.54011e6	0.142320
$119$	4.27672e7	2.32647
$120$	0	0
$121$	1.92232e7	0.986455
$122$	2.18476e7	1.08929
$123$	0	0
$124$	6.40182e6	0.301528
$125$	3.45174e7	1.58071
$126$	0	0
$127$	1.99947e7	0.866169	0.433085	−	0.901353i	$-0.357425\pi$
$127$	1.99947e7	0.866169	0.433085	+	0.901353i	$0.357425\pi$
$128$	2.82287e7	1.18975
$129$	0	0
$130$	6.46181e7	2.57960
$131$	−1.04080e6	−0.0404501	−0.0202251	−	0.999795i	$-0.506438\pi$
$131$	−1.04080e6	−0.0404501	−0.0202251	+	0.999795i	$0.506438\pi$
$132$	0	0
$133$	−4.90640e7	−1.80835
$134$	−5.26369e6	−0.188983
$135$	0	0
$136$	−4.05330e7	−1.38173
$137$	−4.65153e7	−1.54552	−0.772759	−	0.634699i	$-0.781124\pi$
$137$	−4.65153e7	−1.54552	−0.772759	+	0.634699i	$0.781124\pi$
$138$	0	0
$139$	−1.91042e7	−0.603360	−0.301680	−	0.953409i	$-0.597547\pi$
$139$	−1.91042e7	−0.603360	−0.301680	+	0.953409i	$0.597547\pi$
$140$	1.60447e7	0.494178
$141$	0	0
$142$	3.95515e7	1.15919
$143$	−6.80082e7	−1.94484
$144$	0	0
$145$	6.64262e7	1.80947
$146$	−5.39050e7	−1.43349
$147$	0	0
$148$	551982.	0.0139962
$149$	5.31787e7	1.31700	0.658500	−	0.752580i	$-0.271191\pi$
$149$	5.31787e7	1.31700	0.658500	+	0.752580i	$0.271191\pi$
$150$	0	0
$151$	4.97786e7	1.17658	0.588292	−	0.808648i	$-0.299800\pi$
$151$	4.97786e7	1.17658	0.588292	+	0.808648i	$0.299800\pi$
$152$	4.65008e7	1.07401
$153$	0	0
$154$	−1.03465e8	−2.28281
$155$	1.22567e8	2.64370
$156$	0	0
$157$	7.17256e7	1.47920	0.739598	−	0.673049i	$-0.235016\pi$
$157$	7.17256e7	1.47920	0.739598	+	0.673049i	$0.235016\pi$
$158$	−3.60963e7	−0.728054
$159$	0	0
$160$	−3.40976e7	−0.658118
$161$	−5.15141e7	−0.972827
$162$	0	0
$163$	−6.67080e7	−1.20648	−0.603241	−	0.797559i	$-0.706124\pi$
$163$	−6.67080e7	−1.20648	−0.603241	+	0.797559i	$0.706124\pi$
$164$	−7.89245e6	−0.139720
$165$	0	0
$166$	2.44073e7	0.414135
$167$	3.70110e7	0.614927	0.307463	−	0.951560i	$-0.400520\pi$
$167$	3.70110e7	0.614927	0.307463	+	0.951560i	$0.400520\pi$
$168$	0	0
$169$	5.67313e7	0.904106
$170$	1.88034e8	2.93538
$171$	0	0
$172$	3.70127e6	0.0554627
$173$	−3.73146e7	−0.547920	−0.273960	−	0.961741i	$-0.588334\pi$
$173$	−3.73146e7	−0.547920	−0.273960	+	0.961741i	$0.588334\pi$
$174$	0	0
$175$	2.02142e8	2.85117
$176$	1.17942e8	1.63070
$177$	0	0
$178$	−9.55511e7	−1.26989
$179$	−7.93461e7	−1.03405	−0.517023	−	0.855972i	$-0.672960\pi$
$179$	−7.93461e7	−1.03405	−0.517023	+	0.855972i	$0.672960\pi$
$180$	0	0
$181$	8.73656e7	1.09513	0.547565	−	0.836763i	$-0.315555\pi$
$181$	8.73656e7	1.09513	0.547565	+	0.836763i	$0.315555\pi$
$182$	1.81772e8	2.23499
$183$	0	0
$184$	4.88229e7	0.577779
$185$	1.05680e7	0.122714
$186$	0	0
$187$	−1.97899e8	−2.21308
$188$	−1.86959e7	−0.205208
$189$	0	0
$190$	−2.15719e8	−2.28166
$191$	1.36478e8	1.41725	0.708625	−	0.705586i	$-0.249316\pi$
$191$	1.36478e8	1.41725	0.708625	+	0.705586i	$0.249316\pi$
$192$	0	0
$193$	1.59359e8	1.59561	0.797804	−	0.602917i	$-0.205995\pi$
$193$	1.59359e8	1.59561	0.797804	+	0.602917i	$0.205995\pi$
$194$	1.14631e8	1.12719
$195$	0	0
$196$	2.45738e7	0.233118
$197$	2.20118e7	0.205127	0.102564	−	0.994726i	$-0.467295\pi$
$197$	2.20118e7	0.205127	0.102564	+	0.994726i	$0.467295\pi$
$198$	0	0
$199$	7.23177e7	0.650517	0.325259	−	0.945625i	$-0.394549\pi$
$199$	7.23177e7	0.650517	0.325259	+	0.945625i	$0.394549\pi$
$200$	−1.91582e8	−1.69336
$201$	0	0
$202$	−7.14410e7	−0.609842
$203$	1.86858e8	1.56774
$204$	0	0
$205$	−1.51106e8	−1.22502
$206$	−2.13299e8	−1.70001
$207$	0	0
$208$	−2.07205e8	−1.59654
$209$	2.27036e8	1.72022
$210$	0	0
$211$	1.37262e8	1.00592	0.502959	−	0.864310i	$-0.332245\pi$
$211$	1.37262e8	1.00592	0.502959	+	0.864310i	$0.332245\pi$
$212$	4.85984e7	0.350305
$213$	0	0
$214$	−6.70282e7	−0.467530
$215$	7.08631e7	0.486279
$216$	0	0
$217$	3.44782e8	2.29053
$218$	5.20899e7	0.340530
$219$	0	0
$220$	−7.42444e7	−0.470094
$221$	3.47677e8	2.16672
$222$	0	0
$223$	5.13329e7	0.309977	0.154988	−	0.987916i	$-0.450466\pi$
$223$	5.13329e7	0.309977	0.154988	+	0.987916i	$0.450466\pi$
$224$	−9.59170e7	−0.570200
$225$	0	0
$226$	2.13109e8	1.22807
$227$	−2.24268e8	−1.27256	−0.636278	−	0.771459i	$-0.719527\pi$
$227$	−2.24268e8	−1.27256	−0.636278	+	0.771459i	$0.719527\pi$
$228$	0	0
$229$	1.09514e8	0.602625	0.301313	−	0.953525i	$-0.402575\pi$
$229$	1.09514e8	0.602625	0.301313	+	0.953525i	$0.402575\pi$
$230$	−2.26491e8	−1.22745
$231$	0	0
$232$	−1.77096e8	−0.931110
$233$	−1.49211e8	−0.772779	−0.386390	−	0.922336i	$-0.626278\pi$
$233$	−1.49211e8	−0.772779	−0.386390	+	0.922336i	$0.626278\pi$
$234$	0	0
$235$	−3.57945e8	−1.79920
$236$	5.12739e6	0.0253924
$237$	0	0
$238$	5.28942e8	2.54325
$239$	1.38832e8	0.657804	0.328902	−	0.944364i	$-0.393321\pi$
$239$	1.38832e8	0.657804	0.328902	+	0.944364i	$0.393321\pi$
$240$	0	0
$241$	2.34611e8	1.07966	0.539831	−	0.841773i	$-0.318488\pi$
$241$	2.34611e8	1.07966	0.539831	+	0.841773i	$0.318488\pi$
$242$	2.37751e8	1.07837
$243$	0	0
$244$	4.41009e7	0.194349
$245$	4.70482e8	2.04391
$246$	0	0
$247$	−3.98867e8	−1.68418
$248$	−3.26770e8	−1.36039
$249$	0	0
$250$	4.26909e8	1.72800
$251$	−2.52396e8	−1.00745	−0.503725	−	0.863864i	$-0.668038\pi$
$251$	−2.52396e8	−1.00745	−0.503725	+	0.863864i	$0.668038\pi$
$252$	0	0
$253$	2.38374e8	0.925414
$254$	2.47293e8	0.946879
$255$	0	0
$256$	1.51483e8	0.564316
$257$	−4.59969e8	−1.69029	−0.845147	−	0.534534i	$-0.820487\pi$
$257$	−4.59969e8	−1.69029	−0.845147	+	0.534534i	$0.820487\pi$
$258$	0	0
$259$	2.97281e7	0.106321
$260$	1.30436e8	0.460247
$261$	0	0
$262$	−1.28726e7	−0.0442193
$263$	−3.87682e8	−1.31411	−0.657053	−	0.753844i	$-0.728197\pi$
$263$	−3.87682e8	−1.31411	−0.657053	+	0.753844i	$0.728197\pi$
$264$	0	0
$265$	9.30447e8	3.07136
$266$	−6.06820e8	−1.97685
$267$	0	0
$268$	−1.06251e7	−0.0337180
$269$	−2.41785e7	−0.0757351	−0.0378675	−	0.999283i	$-0.512056\pi$
$269$	−2.41785e7	−0.0757351	−0.0378675	+	0.999283i	$0.512056\pi$
$270$	0	0
$271$	−2.33181e7	−0.0711707	−0.0355853	−	0.999367i	$-0.511330\pi$
$271$	−2.33181e7	−0.0711707	−0.0355853	+	0.999367i	$0.511330\pi$
$272$	−6.02952e8	−1.81674
$273$	0	0
$274$	−5.75298e8	−1.68953
$275$	−9.35381e8	−2.71222
$276$	0	0
$277$	3.40111e7	0.0961482	0.0480741	−	0.998844i	$-0.484692\pi$
$277$	3.40111e7	0.0961482	0.0480741	+	0.998844i	$0.484692\pi$
$278$	−2.36279e8	−0.659581
$279$	0	0
$280$	−8.18976e8	−2.22955
$281$	9.09433e7	0.244511	0.122256	−	0.992499i	$-0.460987\pi$
$281$	9.09433e7	0.244511	0.122256	+	0.992499i	$0.460987\pi$
$282$	0	0
$283$	−1.54868e8	−0.406171	−0.203085	−	0.979161i	$-0.565097\pi$
$283$	−1.54868e8	−0.406171	−0.203085	+	0.979161i	$0.565097\pi$
$284$	7.98374e7	0.206820
$285$	0	0
$286$	−8.41120e8	−2.12607
$287$	−4.25063e8	−1.06137
$288$	0	0
$289$	6.01377e8	1.46556
$290$	8.21554e8	1.97808
$291$	0	0
$292$	−1.08811e8	−0.255760
$293$	2.68346e8	0.623245	0.311623	−	0.950206i	$-0.399128\pi$
$293$	2.68346e8	0.623245	0.311623	+	0.950206i	$0.399128\pi$
$294$	0	0
$295$	9.81671e7	0.222633
$296$	−2.81750e7	−0.0631456
$297$	0	0
$298$	6.57710e8	1.43972
$299$	−4.18786e8	−0.906030
$300$	0	0
$301$	1.99339e8	0.421317
$302$	6.15658e8	1.28622
$303$	0	0
$304$	6.91727e8	1.41214
$305$	8.44340e8	1.70399
$306$	0	0
$307$	−8.22676e8	−1.62272	−0.811362	−	0.584544i	$-0.801273\pi$
$307$	−8.22676e8	−1.62272	−0.811362	+	0.584544i	$0.801273\pi$
$308$	−2.08850e8	−0.407294
$309$	0	0
$310$	1.51590e9	2.89004
$311$	8.75600e8	1.65061	0.825305	−	0.564687i	$-0.191003\pi$
$311$	8.75600e8	1.65061	0.825305	+	0.564687i	$0.191003\pi$
$312$	0	0
$313$	−4.06490e8	−0.749280	−0.374640	−	0.927170i	$-0.622234\pi$
$313$	−4.06490e8	−0.749280	−0.374640	+	0.927170i	$0.622234\pi$
$314$	8.87097e8	1.61703
$315$	0	0
$316$	−7.28629e7	−0.129898
$317$	6.46224e8	1.13940	0.569699	−	0.821853i	$-0.307060\pi$
$317$	6.46224e8	1.13940	0.569699	+	0.821853i	$0.307060\pi$
$318$	0	0
$319$	−8.64655e8	−1.49134
$320$	7.38059e8	1.25912
$321$	0	0
$322$	−6.37122e8	−1.06348
$323$	−1.16067e9	−1.91647
$324$	0	0
$325$	1.64332e9	2.65540
$326$	−8.25039e8	−1.31890
$327$	0	0
$328$	4.02857e8	0.630366
$329$	−1.00690e9	−1.55884
$330$	0	0
$331$	−7.67395e8	−1.16311	−0.581555	−	0.813507i	$-0.697556\pi$
$331$	−7.67395e8	−1.16311	−0.581555	+	0.813507i	$0.697556\pi$
$332$	4.92678e7	0.0738891
$333$	0	0
$334$	4.57749e8	0.672226
$335$	−2.03425e8	−0.295629
$336$	0	0
$337$	6.41971e8	0.913715	0.456858	−	0.889540i	$-0.348975\pi$
$337$	6.41971e8	0.913715	0.456858	+	0.889540i	$0.348975\pi$
$338$	7.01649e8	0.988351
$339$	0	0
$340$	3.79559e8	0.523725
$341$	−1.59543e9	−2.17890
$342$	0	0
$343$	2.16165e8	0.289238
$344$	−1.88925e8	−0.250228
$345$	0	0
$346$	−4.61504e8	−0.598976
$347$	−6.85227e8	−0.880403	−0.440201	−	0.897899i	$-0.645093\pi$
$347$	−6.85227e8	−0.880403	−0.440201	+	0.897899i	$0.645093\pi$
$348$	0	0
$349$	−3.31439e8	−0.417363	−0.208682	−	0.977984i	$-0.566917\pi$
$349$	−3.31439e8	−0.417363	−0.208682	+	0.977984i	$0.566917\pi$
$350$	2.50008e9	3.11685
$351$	0	0
$352$	4.43841e8	0.542410
$353$	−1.17646e9	−1.42353	−0.711766	−	0.702416i	$-0.752104\pi$
$353$	−1.17646e9	−1.42353	−0.711766	+	0.702416i	$0.752104\pi$
$354$	0	0
$355$	1.52854e9	1.81333
$356$	−1.92876e8	−0.226571
$357$	0	0
$358$	−9.81346e8	−1.13040
$359$	5.67306e8	0.647123	0.323562	−	0.946207i	$-0.395120\pi$
$359$	5.67306e8	0.647123	0.323562	+	0.946207i	$0.395120\pi$
$360$	0	0
$361$	4.37693e8	0.489660
$362$	1.08053e9	1.19717
$363$	0	0
$364$	3.66918e8	0.398762
$365$	−2.08326e9	−2.24242
$366$	0	0
$367$	1.09692e8	0.115836	0.0579182	−	0.998321i	$-0.481554\pi$
$367$	1.09692e8	0.115836	0.0579182	+	0.998321i	$0.481554\pi$
$368$	7.26270e8	0.759680
$369$	0	0
$370$	1.30705e8	0.134148
$371$	2.61736e9	2.66106
$372$	0	0
$373$	−1.29535e9	−1.29243	−0.646214	−	0.763156i	$-0.723649\pi$
$373$	−1.29535e9	−1.29243	−0.646214	+	0.763156i	$0.723649\pi$
$374$	−2.44760e9	−2.41930
$375$	0	0
$376$	9.54302e8	0.925824
$377$	1.51907e9	1.46010
$378$	0	0
$379$	−3.39868e8	−0.320681	−0.160341	−	0.987062i	$-0.551259\pi$
$379$	−3.39868e8	−0.320681	−0.160341	+	0.987062i	$0.551259\pi$
$380$	−4.35443e8	−0.407088
$381$	0	0
$382$	1.68795e9	1.54931
$383$	−1.07778e9	−0.980246	−0.490123	−	0.871653i	$-0.663048\pi$
$383$	−1.07778e9	−0.980246	−0.490123	+	0.871653i	$0.663048\pi$
$384$	0	0
$385$	−3.99858e9	−3.57103
$386$	1.97094e9	1.74429
$387$	0	0
$388$	2.31391e8	0.201111
$389$	−7.02547e8	−0.605134	−0.302567	−	0.953128i	$-0.597844\pi$
$389$	−7.02547e8	−0.605134	−0.302567	+	0.953128i	$0.597844\pi$
$390$	0	0
$391$	−1.21863e9	−1.03099
$392$	−1.25433e9	−1.05175
$393$	0	0
$394$	2.72240e8	0.224241
$395$	−1.39501e9	−1.13890
$396$	0	0
$397$	−4.23518e7	−0.0339708	−0.0169854	−	0.999856i	$-0.505407\pi$
$397$	−4.23518e7	−0.0339708	−0.0169854	+	0.999856i	$0.505407\pi$
$398$	8.94419e8	0.711132
$399$	0	0
$400$	−2.84989e9	−2.22648
$401$	−1.82357e9	−1.41227	−0.706133	−	0.708079i	$-0.749562\pi$
$401$	−1.82357e9	−1.41227	−0.706133	+	0.708079i	$0.749562\pi$
$402$	0	0
$403$	2.80292e9	2.13326
$404$	−1.44208e8	−0.108807
$405$	0	0
$406$	2.31104e9	1.71383
$407$	−1.37562e8	−0.101139
$408$	0	0
$409$	−3.94853e8	−0.285367	−0.142684	−	0.989768i	$-0.545573\pi$
$409$	−3.94853e8	−0.285367	−0.142684	+	0.989768i	$0.545573\pi$
$410$	−1.86887e9	−1.33917
$411$	0	0
$412$	−4.30558e8	−0.303313
$413$	2.76145e8	0.192891
$414$	0	0
$415$	9.43265e8	0.647836
$416$	−7.79760e8	−0.531049
$417$	0	0
$418$	2.80796e9	1.88051
$419$	−1.27926e9	−0.849591	−0.424795	−	0.905289i	$-0.639654\pi$
$419$	−1.27926e9	−0.849591	−0.424795	+	0.905289i	$0.639654\pi$
$420$	0	0
$421$	−4.37766e8	−0.285926	−0.142963	−	0.989728i	$-0.545663\pi$
$421$	−4.37766e8	−0.285926	−0.142963	+	0.989728i	$0.545663\pi$
$422$	1.69765e9	1.09965
$423$	0	0
$424$	−2.48063e9	−1.58045
$425$	4.78194e9	3.02164
$426$	0	0
$427$	2.37514e9	1.47636
$428$	−1.35301e8	−0.0834157
$429$	0	0
$430$	8.76430e8	0.531591
$431$	−2.13470e9	−1.28430	−0.642150	−	0.766579i	$-0.721957\pi$
$431$	−2.13470e9	−1.28430	−0.642150	+	0.766579i	$0.721957\pi$
$432$	0	0
$433$	−2.81072e9	−1.66383	−0.831917	−	0.554900i	$-0.812757\pi$
$433$	−2.81072e9	−1.66383	−0.831917	+	0.554900i	$0.812757\pi$
$434$	4.26424e9	2.50396
$435$	0	0
$436$	1.05147e8	0.0607567
$437$	1.39806e9	0.801384
$438$	0	0
$439$	2.30629e9	1.30103	0.650516	−	0.759493i	$-0.274553\pi$
$439$	2.30629e9	1.30103	0.650516	+	0.759493i	$0.274553\pi$
$440$	3.78969e9	2.12089
$441$	0	0
$442$	4.30005e9	2.36862
$443$	−9.88032e8	−0.539956	−0.269978	−	0.962867i	$-0.587016\pi$
$443$	−9.88032e8	−0.539956	−0.269978	+	0.962867i	$0.587016\pi$
$444$	0	0
$445$	−3.69274e9	−1.98650
$446$	6.34882e8	0.338860
$447$	0	0
$448$	2.07617e9	1.09091
$449$	3.41363e8	0.177973	0.0889866	−	0.996033i	$-0.471637\pi$
$449$	3.41363e8	0.177973	0.0889866	+	0.996033i	$0.471637\pi$
$450$	0	0
$451$	1.96692e9	1.00964
$452$	4.30175e8	0.219109
$453$	0	0
$454$	−2.77373e9	−1.39113
$455$	7.02488e9	3.49622
$456$	0	0
$457$	−2.86701e6	−0.00140515	−0.000702575	−	1.00000i	$-0.500224\pi$
$457$	−2.86701e6	−0.00140515	−0.000702575		1.00000i	$0.500224\pi$
$458$	1.35447e9	0.658778
$459$	0	0
$460$	−4.57187e8	−0.218999
$461$	−2.81859e9	−1.33992	−0.669959	−	0.742398i	$-0.733688\pi$
$461$	−2.81859e9	−1.33992	−0.669959	+	0.742398i	$0.733688\pi$
$462$	0	0
$463$	1.30688e9	0.611932	0.305966	−	0.952042i	$-0.401021\pi$
$463$	1.30688e9	0.611932	0.305966	+	0.952042i	$0.401021\pi$
$464$	−2.63441e9	−1.22425
$465$	0	0
$466$	−1.84543e9	−0.844787
$467$	1.72823e9	0.785221	0.392611	−	0.919705i	$-0.371572\pi$
$467$	1.72823e9	0.785221	0.392611	+	0.919705i	$0.371572\pi$
$468$	0	0
$469$	−5.72236e8	−0.256136
$470$	−4.42704e9	−1.96685
$471$	0	0
$472$	−2.61719e8	−0.114561
$473$	−9.22410e8	−0.400784
$474$	0	0
$475$	−5.48600e9	−2.34870
$476$	1.06770e9	0.453760
$477$	0	0
$478$	1.71706e9	0.719099
$479$	−2.64444e9	−1.09941	−0.549705	−	0.835359i	$-0.685260\pi$
$479$	−2.64444e9	−1.09941	−0.549705	+	0.835359i	$0.685260\pi$
$480$	0	0
$481$	2.41675e8	0.0990203
$482$	2.90165e9	1.18027
$483$	0	0
$484$	4.79917e8	0.192401
$485$	4.43012e9	1.76327
$486$	0	0
$487$	2.49943e9	0.980594	0.490297	−	0.871556i	$-0.336888\pi$
$487$	2.49943e9	0.980594	0.490297	+	0.871556i	$0.336888\pi$
$488$	−2.25106e9	−0.876835
$489$	0	0
$490$	5.81888e9	2.23436
$491$	1.41128e9	0.538057	0.269029	−	0.963132i	$-0.413297\pi$
$491$	1.41128e9	0.538057	0.269029	+	0.963132i	$0.413297\pi$
$492$	0	0
$493$	4.42037e9	1.66148
$494$	−4.93316e9	−1.84111
$495$	0	0
$496$	−4.86090e9	−1.78867
$497$	4.29980e9	1.57109
$498$	0	0
$499$	2.12697e8	0.0766319	0.0383159	−	0.999266i	$-0.487801\pi$
$499$	2.12697e8	0.0766319	0.0383159	+	0.999266i	$0.487801\pi$
$500$	8.61744e8	0.308307
$501$	0	0
$502$	−3.12161e9	−1.10133
$503$	2.85799e7	0.0100132	0.00500660	−	0.999987i	$-0.498406\pi$
$503$	2.85799e7	0.0100132	0.00500660	+	0.999987i	$0.498406\pi$
$504$	0	0
$505$	−2.76096e9	−0.953984
$506$	2.94819e9	1.01164
$507$	0	0
$508$	4.99178e8	0.168940
$509$	1.91356e9	0.643178	0.321589	−	0.946879i	$-0.395783\pi$
$509$	1.91356e9	0.643178	0.321589	+	0.946879i	$0.395783\pi$
$510$	0	0
$511$	−5.86023e9	−1.94286
$512$	−1.73974e9	−0.572849
$513$	0	0
$514$	−5.68885e9	−1.84780
$515$	−8.24330e9	−2.65935
$516$	0	0
$517$	4.65929e9	1.48287
$518$	3.67674e8	0.116228
$519$	0	0
$520$	−6.65789e9	−2.07647
$521$	−1.49555e9	−0.463306	−0.231653	−	0.972798i	$-0.574413\pi$
$521$	−1.49555e9	−0.463306	−0.231653	+	0.972798i	$0.574413\pi$
$522$	0	0
$523$	2.48258e9	0.758835	0.379417	−	0.925226i	$-0.376124\pi$
$523$	2.48258e9	0.758835	0.379417	+	0.925226i	$0.376124\pi$
$524$	−2.59842e7	−0.00788951
$525$	0	0
$526$	−4.79482e9	−1.43656
$527$	8.15629e9	2.42748
$528$	0	0
$529$	−1.93695e9	−0.568884
$530$	1.15077e10	3.35755
$531$	0	0
$532$	−1.22491e9	−0.352705
$533$	−3.45557e9	−0.988494
$534$	0	0
$535$	−2.59043e9	−0.731363
$536$	5.42342e8	0.152124
$537$	0	0
$538$	−2.99038e8	−0.0827921
$539$	−6.12416e9	−1.68456
$540$	0	0
$541$	−6.44103e9	−1.74890	−0.874450	−	0.485115i	$-0.838778\pi$
$541$	−6.44103e9	−1.74890	−0.874450	+	0.485115i	$0.838778\pi$
$542$	−2.88397e8	−0.0778024
$543$	0	0
$544$	−2.26904e9	−0.604292
$545$	2.01311e9	0.532695
$546$	0	0
$547$	−5.40495e8	−0.141200	−0.0706002	−	0.997505i	$-0.522491\pi$
$547$	−5.40495e8	−0.141200	−0.0706002	+	0.997505i	$0.522491\pi$
$548$	−1.16128e9	−0.301442
$549$	0	0
$550$	−1.15687e10	−2.96494
$551$	−5.07120e9	−1.29146
$552$	0	0
$553$	−3.92417e9	−0.986757
$554$	4.20646e8	0.105107
$555$	0	0
$556$	−4.76945e8	−0.117681
$557$	−2.83692e9	−0.695591	−0.347795	−	0.937570i	$-0.613070\pi$
$557$	−2.83692e9	−0.695591	−0.347795	+	0.937570i	$0.613070\pi$
$558$	0	0
$559$	1.62053e9	0.392389
$560$	−1.21828e10	−2.93148
$561$	0	0
$562$	1.12478e9	0.267295
$563$	−7.86504e9	−1.85747	−0.928734	−	0.370747i	$-0.879102\pi$
$563$	−7.86504e9	−1.85747	−0.928734	+	0.370747i	$0.879102\pi$
$564$	0	0
$565$	8.23597e9	1.92108
$566$	−1.91539e9	−0.444018
$567$	0	0
$568$	−4.07517e9	−0.933097
$569$	−6.12820e9	−1.39457	−0.697285	−	0.716794i	$-0.745609\pi$
$569$	−6.12820e9	−1.39457	−0.697285	+	0.716794i	$0.745609\pi$
$570$	0	0
$571$	7.88550e9	1.77257	0.886284	−	0.463142i	$-0.153278\pi$
$571$	7.88550e9	1.77257	0.886284	+	0.463142i	$0.153278\pi$
$572$	−1.69786e9	−0.379328
$573$	0	0
$574$	−5.25715e9	−1.16027
$575$	−5.75996e9	−1.26352
$576$	0	0
$577$	4.87423e9	1.05631	0.528154	−	0.849149i	$-0.322884\pi$
$577$	4.87423e9	1.05631	0.528154	+	0.849149i	$0.322884\pi$
$578$	7.43778e9	1.60212
$579$	0	0
$580$	1.65836e9	0.352924
$581$	2.65342e9	0.561292
$582$	0	0
$583$	−1.21114e10	−2.53137
$584$	5.55408e9	1.15390
$585$	0	0
$586$	3.31889e9	0.681319
$587$	−1.45833e9	−0.297593	−0.148796	−	0.988868i	$-0.547540\pi$
$587$	−1.45833e9	−0.297593	−0.148796	+	0.988868i	$0.547540\pi$
$588$	0	0
$589$	−9.35717e9	−1.88687
$590$	1.21412e9	0.243378
$591$	0	0
$592$	−4.19120e8	−0.0830257
$593$	−2.71973e9	−0.535592	−0.267796	−	0.963476i	$-0.586295\pi$
$593$	−2.71973e9	−0.535592	−0.267796	+	0.963476i	$0.586295\pi$
$594$	0	0
$595$	2.04419e10	3.97843
$596$	1.32763e9	0.256872
$597$	0	0
$598$	−5.17951e9	−0.990454
$599$	8.04358e9	1.52917	0.764584	−	0.644524i	$-0.222944\pi$
$599$	8.04358e9	1.52917	0.764584	+	0.644524i	$0.222944\pi$
$600$	0	0
$601$	3.08370e9	0.579444	0.289722	−	0.957111i	$-0.406437\pi$
$601$	3.08370e9	0.579444	0.289722	+	0.957111i	$0.406437\pi$
$602$	2.46541e9	0.460576
$603$	0	0
$604$	1.24275e9	0.229484
$605$	9.18832e9	1.68691
$606$	0	0
$607$	5.53440e9	1.00441	0.502204	−	0.864749i	$-0.332523\pi$
$607$	5.53440e9	1.00441	0.502204	+	0.864749i	$0.332523\pi$
$608$	2.60312e9	0.469713
$609$	0	0
$610$	1.04427e10	1.86277
$611$	−8.18566e9	−1.45181
$612$	0	0
$613$	−1.57182e9	−0.275608	−0.137804	−	0.990460i	$-0.544004\pi$
$613$	−1.57182e9	−0.275608	−0.137804	+	0.990460i	$0.544004\pi$
$614$	−1.01748e10	−1.77393
$615$	0	0
$616$	1.06604e10	1.83756
$617$	3.83210e9	0.656809	0.328404	−	0.944537i	$-0.393489\pi$
$617$	3.83210e9	0.656809	0.328404	+	0.944537i	$0.393489\pi$
$618$	0	0
$619$	−5.03030e9	−0.852465	−0.426233	−	0.904614i	$-0.640159\pi$
$619$	−5.03030e9	−0.852465	−0.426233	+	0.904614i	$0.640159\pi$
$620$	3.05994e9	0.515635
$621$	0	0
$622$	1.08294e10	1.80441
$623$	−1.03877e10	−1.72113
$624$	0	0
$625$	4.75332e9	0.778784
$626$	−5.02743e9	−0.819098
$627$	0	0
$628$	1.79066e9	0.288506
$629$	7.03257e8	0.112677
$630$	0	0
$631$	5.76799e9	0.913949	0.456974	−	0.889480i	$-0.348933\pi$
$631$	5.76799e9	0.913949	0.456974	+	0.889480i	$0.348933\pi$
$632$	3.71917e9	0.586052
$633$	0	0
$634$	7.99244e9	1.24557
$635$	9.55709e9	1.48121
$636$	0	0
$637$	1.07592e10	1.64927
$638$	−1.06940e10	−1.63030
$639$	0	0
$640$	1.34927e10	2.03456
$641$	1.37617e9	0.206381	0.103191	−	0.994662i	$-0.467095\pi$
$641$	1.37617e9	0.206381	0.103191	+	0.994662i	$0.467095\pi$
$642$	0	0
$643$	8.74856e9	1.29777	0.648886	−	0.760886i	$-0.275235\pi$
$643$	8.74856e9	1.29777	0.648886	+	0.760886i	$0.275235\pi$
$644$	−1.28607e9	−0.189743
$645$	0	0
$646$	−1.43551e10	−2.09504
$647$	−8.82702e9	−1.28130	−0.640648	−	0.767835i	$-0.721334\pi$
$647$	−8.82702e9	−1.28130	−0.640648	+	0.767835i	$0.721334\pi$
$648$	0	0
$649$	−1.27782e9	−0.183490
$650$	2.03245e10	2.90283
$651$	0	0
$652$	−1.66540e9	−0.235316
$653$	2.39631e9	0.336780	0.168390	−	0.985720i	$-0.446143\pi$
$653$	2.39631e9	0.336780	0.168390	+	0.985720i	$0.446143\pi$
$654$	0	0
$655$	−4.97484e8	−0.0691727
$656$	5.99274e9	0.828824
$657$	0	0
$658$	−1.24533e10	−1.70410
$659$	3.92961e9	0.534873	0.267437	−	0.963575i	$-0.413823\pi$
$659$	3.92961e9	0.534873	0.267437	+	0.963575i	$0.413823\pi$
$660$	0	0
$661$	6.16515e9	0.830307	0.415153	−	0.909751i	$-0.363728\pi$
$661$	6.16515e9	0.830307	0.415153	+	0.909751i	$0.363728\pi$
$662$	−9.49108e9	−1.27149
$663$	0	0
$664$	−2.51480e9	−0.333361
$665$	−2.34516e10	−3.09241
$666$	0	0
$667$	−5.32444e9	−0.694757
$668$	9.23998e8	0.119937
$669$	0	0
$670$	−2.51594e9	−0.323176
$671$	−1.09906e10	−1.40441
$672$	0	0
$673$	−8.84954e9	−1.11910	−0.559549	−	0.828798i	$-0.689025\pi$
$673$	−8.84954e9	−1.11910	−0.559549	+	0.828798i	$0.689025\pi$
$674$	7.93985e9	0.998856
$675$	0	0
$676$	1.41633e9	0.176339
$677$	−5.42902e9	−0.672452	−0.336226	−	0.941781i	$-0.609151\pi$
$677$	−5.42902e9	−0.672452	−0.336226	+	0.941781i	$0.609151\pi$
$678$	0	0
$679$	1.24620e10	1.52772
$680$	−1.93740e10	−2.36286
$681$	0	0
$682$	−1.97321e10	−2.38193
$683$	−5.65530e9	−0.679178	−0.339589	−	0.940574i	$-0.610288\pi$
$683$	−5.65530e9	−0.679178	−0.339589	+	0.940574i	$0.610288\pi$
$684$	0	0
$685$	−2.22334e10	−2.64295
$686$	2.67351e9	0.316189
$687$	0	0
$688$	−2.81037e9	−0.329007
$689$	2.12779e10	2.47835
$690$	0	0
$691$	−6.11832e9	−0.705439	−0.352719	−	0.935729i	$-0.614743\pi$
$691$	−6.11832e9	−0.705439	−0.352719	+	0.935729i	$0.614743\pi$
$692$	−9.31577e8	−0.106868
$693$	0	0
$694$	−8.47484e9	−0.962439
$695$	−9.13142e9	−1.03179
$696$	0	0
$697$	−1.00554e10	−1.12483
$698$	−4.09921e9	−0.456253
$699$	0	0
$700$	5.04657e9	0.556101
$701$	1.75688e9	0.192632	0.0963160	−	0.995351i	$-0.469294\pi$
$701$	1.75688e9	0.192632	0.0963160	+	0.995351i	$0.469294\pi$
$702$	0	0
$703$	−8.06800e8	−0.0875835
$704$	−9.60715e9	−1.03774
$705$	0	0
$706$	−1.45504e10	−1.55618
$707$	−7.76663e9	−0.826541
$708$	0	0
$709$	−9.00661e9	−0.949072	−0.474536	−	0.880236i	$-0.657384\pi$
$709$	−9.00661e9	−0.949072	−0.474536	+	0.880236i	$0.657384\pi$
$710$	1.89049e10	1.98230
$711$	0	0
$712$	9.84506e9	1.02221
$713$	−9.82444e9	−1.01507
$714$	0	0
$715$	−3.25066e10	−3.32583
$716$	−1.98091e9	−0.201683
$717$	0	0
$718$	7.01640e9	0.707422
$719$	−3.19207e8	−0.0320274	−0.0160137	−	0.999872i	$-0.505098\pi$
$719$	−3.19207e8	−0.0320274	−0.0160137	+	0.999872i	$0.505098\pi$
$720$	0	0
$721$	−2.31885e10	−2.30409
$722$	5.41335e9	0.535286
$723$	0	0
$724$	2.18112e9	0.213597
$725$	2.08932e10	2.03620
$726$	0	0
$727$	7.47713e9	0.721713	0.360856	−	0.932621i	$-0.382484\pi$
$727$	7.47713e9	0.721713	0.360856	+	0.932621i	$0.382484\pi$
$728$	−1.87287e10	−1.79907
$729$	0	0
$730$	−2.57655e10	−2.45137
$731$	4.71563e9	0.446507
$732$	0	0
$733$	−7.27192e9	−0.682002	−0.341001	−	0.940063i	$-0.610766\pi$
$733$	−7.27192e9	−0.682002	−0.341001	+	0.940063i	$0.610766\pi$
$734$	1.35667e9	0.126630
$735$	0	0
$736$	2.73312e9	0.252689
$737$	2.64794e9	0.243653
$738$	0	0
$739$	6.36734e8	0.0580367	0.0290183	−	0.999579i	$-0.490762\pi$
$739$	6.36734e8	0.0580367	0.0290183	+	0.999579i	$0.490762\pi$
$740$	2.63836e8	0.0239345
$741$	0	0
$742$	3.23713e10	2.90902
$743$	−1.53224e10	−1.37045	−0.685227	−	0.728329i	$-0.740297\pi$
$743$	−1.53224e10	−1.37045	−0.685227	+	0.728329i	$0.740297\pi$
$744$	0	0
$745$	2.54184e10	2.25217
$746$	−1.60208e10	−1.41286
$747$	0	0
$748$	−4.94064e9	−0.431646
$749$	−7.28690e9	−0.633660
$750$	0	0
$751$	−1.47426e10	−1.27009	−0.635045	−	0.772475i	$-0.719018\pi$
$751$	−1.47426e10	−1.27009	−0.635045	+	0.772475i	$0.719018\pi$
$752$	1.41958e10	1.21730
$753$	0	0
$754$	1.87877e10	1.59615
$755$	2.37932e10	2.01205
$756$	0	0
$757$	1.03556e10	0.867643	0.433822	−	0.900999i	$-0.357165\pi$
$757$	1.03556e10	0.867643	0.433822	+	0.900999i	$0.357165\pi$
$758$	−4.20347e9	−0.350562
$759$	0	0
$760$	2.22265e10	1.83664
$761$	−4.05993e9	−0.333943	−0.166971	−	0.985962i	$-0.553399\pi$
$761$	−4.05993e9	−0.333943	−0.166971	+	0.985962i	$0.553399\pi$
$762$	0	0
$763$	5.66289e9	0.461533
$764$	3.40724e9	0.276424
$765$	0	0
$766$	−1.33299e10	−1.07159
$767$	2.24493e9	0.179647
$768$	0	0
$769$	−2.02272e10	−1.60396	−0.801981	−	0.597349i	$-0.796221\pi$
$769$	−2.02272e10	−1.60396	−0.801981	+	0.597349i	$0.796221\pi$
$770$	−4.94541e10	−3.90377
$771$	0	0
$772$	3.97847e9	0.311212
$773$	−1.26500e10	−0.985062	−0.492531	−	0.870295i	$-0.663928\pi$
$773$	−1.26500e10	−0.985062	−0.492531	+	0.870295i	$0.663928\pi$
$774$	0	0
$775$	3.85512e10	2.97497
$776$	−1.18110e10	−0.907339
$777$	0	0
$778$	−8.68905e9	−0.661521
$779$	1.15359e10	0.874323
$780$	0	0
$781$	−1.98967e10	−1.49452
$782$	−1.50720e10	−1.12706
$783$	0	0
$784$	−1.86589e10	−1.38287
$785$	3.42834e10	2.52953
$786$	0	0
$787$	−2.58438e9	−0.188992	−0.0944962	−	0.995525i	$-0.530124\pi$
$787$	−2.58438e9	−0.188992	−0.0944962	+	0.995525i	$0.530124\pi$
$788$	5.49535e8	0.0400086
$789$	0	0
$790$	−1.72533e10	−1.24503
$791$	2.31679e10	1.66444
$792$	0	0
$793$	1.93088e10	1.37499
$794$	−5.23804e8	−0.0371362
$795$	0	0
$796$	1.80545e9	0.126879
$797$	−2.54750e10	−1.78242	−0.891209	−	0.453593i	$-0.850142\pi$
$797$	−2.54750e10	−1.78242	−0.891209	+	0.453593i	$0.850142\pi$
$798$	0	0
$799$	−2.38197e10	−1.65205
$800$	−1.07248e10	−0.740583
$801$	0	0
$802$	−2.25537e10	−1.54386
$803$	2.71173e10	1.84817
$804$	0	0
$805$	−2.46227e10	−1.66361
$806$	3.46663e10	2.33203
$807$	0	0
$808$	7.36089e9	0.490897
$809$	−2.50645e10	−1.66433	−0.832163	−	0.554531i	$-0.812898\pi$
$809$	−2.50645e10	−1.66433	−0.832163	+	0.554531i	$0.812898\pi$
$810$	0	0
$811$	−9.63538e9	−0.634301	−0.317151	−	0.948375i	$-0.602726\pi$
$811$	−9.63538e9	−0.634301	−0.317151	+	0.948375i	$0.602726\pi$
$812$	4.66499e9	0.305777
$813$	0	0
$814$	−1.70136e9	−0.110563
$815$	−3.18851e10	−2.06317
$816$	0	0
$817$	−5.40993e9	−0.347068
$818$	−4.88351e9	−0.311958
$819$	0	0
$820$	−3.77244e9	−0.238931
$821$	2.27996e10	1.43789	0.718946	−	0.695066i	$-0.244625\pi$
$821$	2.27996e10	1.43789	0.718946	+	0.695066i	$0.244625\pi$
$822$	0	0
$823$	7.33439e9	0.458632	0.229316	−	0.973352i	$-0.426351\pi$
$823$	7.33439e9	0.458632	0.229316	+	0.973352i	$0.426351\pi$
$824$	2.19771e10	1.36844
$825$	0	0
$826$	3.41534e9	0.210865
$827$	−1.34883e9	−0.0829252	−0.0414626	−	0.999140i	$-0.513202\pi$
$827$	−1.34883e9	−0.0829252	−0.0414626	+	0.999140i	$0.513202\pi$
$828$	0	0
$829$	1.61073e10	0.981932	0.490966	−	0.871179i	$-0.336644\pi$
$829$	1.61073e10	0.981932	0.490966	+	0.871179i	$0.336644\pi$
$830$	1.16662e10	0.708202
$831$	0	0
$832$	1.68783e10	1.01601
$833$	3.13085e10	1.87674
$834$	0	0
$835$	1.76905e10	1.05157
$836$	5.66806e9	0.335516
$837$	0	0
$838$	−1.58218e10	−0.928756
$839$	1.49944e10	0.876523	0.438261	−	0.898848i	$-0.355594\pi$
$839$	1.49944e10	0.876523	0.438261	+	0.898848i	$0.355594\pi$
$840$	0	0
$841$	2.06352e9	0.119625
$842$	−5.41425e9	−0.312569
$843$	0	0
$844$	3.42682e9	0.196197
$845$	2.71165e10	1.54609
$846$	0	0
$847$	2.58469e10	1.46156
$848$	−3.69008e10	−2.07802
$849$	0	0
$850$	5.91427e10	3.30320
$851$	−8.47089e8	−0.0471168
$852$	0	0
$853$	−2.48117e9	−0.136879	−0.0684393	−	0.997655i	$-0.521802\pi$
$853$	−2.48117e9	−0.136879	−0.0684393	+	0.997655i	$0.521802\pi$
$854$	2.93756e10	1.61393
$855$	0	0
$856$	6.90622e9	0.376342
$857$	−1.30344e10	−0.707388	−0.353694	−	0.935361i	$-0.615075\pi$
$857$	−1.30344e10	−0.707388	−0.353694	+	0.935361i	$0.615075\pi$
$858$	0	0
$859$	−3.01941e10	−1.62535	−0.812673	−	0.582720i	$-0.801989\pi$
$859$	−3.01941e10	−1.62535	−0.812673	+	0.582720i	$0.801989\pi$
$860$	1.76913e9	0.0948453
$861$	0	0
$862$	−2.64018e10	−1.40397
$863$	−4.40460e9	−0.233275	−0.116638	−	0.993175i	$-0.537212\pi$
$863$	−4.40460e9	−0.233275	−0.116638	+	0.993175i	$0.537212\pi$
$864$	0	0
$865$	−1.78356e10	−0.936984
$866$	−3.47628e10	−1.81887
$867$	0	0
$868$	8.60766e9	0.446752
$869$	1.81585e10	0.938666
$870$	0	0
$871$	−4.65201e9	−0.238549
$872$	−5.36706e9	−0.274112
$873$	0	0
$874$	1.72911e10	0.876057
$875$	4.64109e10	2.34203
$876$	0	0
$877$	1.87680e10	0.939549	0.469775	−	0.882786i	$-0.344335\pi$
$877$	1.87680e10	0.939549	0.469775	+	0.882786i	$0.344335\pi$
$878$	2.85240e10	1.42226
$879$	0	0
$880$	5.63738e10	2.78861
$881$	−2.99234e10	−1.47433	−0.737165	−	0.675713i	$-0.763836\pi$
$881$	−2.99234e10	−1.47433	−0.737165	+	0.675713i	$0.763836\pi$
$882$	0	0
$883$	3.52933e10	1.72516	0.862582	−	0.505918i	$-0.168846\pi$
$883$	3.52933e10	1.72516	0.862582	+	0.505918i	$0.168846\pi$
$884$	8.67994e9	0.422604
$885$	0	0
$886$	−1.22199e10	−0.590269
$887$	1.25706e10	0.604818	0.302409	−	0.953178i	$-0.402209\pi$
$887$	1.25706e10	0.604818	0.302409	+	0.953178i	$0.402209\pi$
$888$	0	0
$889$	2.68842e10	1.28334
$890$	−4.56715e10	−2.17160
$891$	0	0
$892$	1.28155e9	0.0604587
$893$	2.73267e10	1.28413
$894$	0	0
$895$	−3.79258e10	−1.76829
$896$	3.79553e10	1.76276
$897$	0	0
$898$	4.22196e9	0.194557
$899$	3.56363e10	1.63581
$900$	0	0
$901$	6.19172e10	2.82016
$902$	2.43267e10	1.10372
$903$	0	0
$904$	−2.19576e10	−0.988541
$905$	4.17590e10	1.87275
$906$	0	0
$907$	−1.02215e10	−0.454874	−0.227437	−	0.973793i	$-0.573035\pi$
$907$	−1.02215e10	−0.454874	−0.227437	+	0.973793i	$0.573035\pi$
$908$	−5.59896e9	−0.248203
$909$	0	0
$910$	8.68832e10	3.82200
$911$	3.10518e9	0.136073	0.0680366	−	0.997683i	$-0.478327\pi$
$911$	3.10518e9	0.136073	0.0680366	+	0.997683i	$0.478327\pi$
$912$	0	0
$913$	−1.22783e10	−0.533936
$914$	−3.54590e7	−0.00153608
$915$	0	0
$916$	2.73408e9	0.117538
$917$	−1.39943e9	−0.0599320
$918$	0	0
$919$	2.97646e10	1.26501	0.632507	−	0.774554i	$-0.282026\pi$
$919$	2.97646e10	1.26501	0.632507	+	0.774554i	$0.282026\pi$
$920$	2.33364e10	0.988044
$921$	0	0
$922$	−3.48601e10	−1.46477
$923$	3.49554e10	1.46321
$924$	0	0
$925$	3.32399e9	0.138090
$926$	1.61634e10	0.668952
$927$	0	0
$928$	−9.91386e9	−0.407216
$929$	−3.44435e10	−1.40946	−0.704729	−	0.709477i	$-0.748931\pi$
$929$	−3.44435e10	−1.40946	−0.704729	+	0.709477i	$0.748931\pi$
$930$	0	0
$931$	−3.59182e10	−1.45878
$932$	−3.72513e9	−0.150725
$933$	0	0
$934$	2.13746e10	0.858388
$935$	−9.45917e10	−3.78453
$936$	0	0
$937$	2.41950e10	0.960807	0.480404	−	0.877048i	$-0.340490\pi$
$937$	2.41950e10	0.960807	0.480404	+	0.877048i	$0.340490\pi$
$938$	−7.07737e9	−0.280003
$939$	0	0
$940$	−8.93627e9	−0.350921
$941$	3.24324e10	1.26886	0.634432	−	0.772979i	$-0.281234\pi$
$941$	3.24324e10	1.26886	0.634432	+	0.772979i	$0.281234\pi$
$942$	0	0
$943$	1.21120e10	0.470355
$944$	−3.89323e9	−0.150629
$945$	0	0
$946$	−1.14083e10	−0.438129
$947$	4.68426e9	0.179232	0.0896162	−	0.995976i	$-0.471436\pi$
$947$	4.68426e9	0.179232	0.0896162	+	0.995976i	$0.471436\pi$
$948$	0	0
$949$	−4.76409e10	−1.80946
$950$	−6.78505e10	−2.56756
$951$	0	0
$952$	−5.44992e10	−2.04720
$953$	3.34959e10	1.25362	0.626811	−	0.779171i	$-0.284360\pi$
$953$	3.34959e10	1.25362	0.626811	+	0.779171i	$0.284360\pi$
$954$	0	0
$955$	6.52338e10	2.42360
$956$	3.46601e9	0.128300
$957$	0	0
$958$	−3.27063e10	−1.20185
$959$	−6.25429e10	−2.28988
$960$	0	0
$961$	3.82421e10	1.38998
$962$	2.98902e9	0.108247
$963$	0	0
$964$	5.85717e9	0.210580
$965$	7.61705e10	2.72861
$966$	0	0
$967$	4.48458e10	1.59489	0.797443	−	0.603395i	$-0.206186\pi$
$967$	4.48458e10	1.59489	0.797443	+	0.603395i	$0.206186\pi$
$968$	−2.44966e10	−0.868044
$969$	0	0
$970$	5.47914e10	1.92758
$971$	3.33761e10	1.16995	0.584977	−	0.811050i	$-0.301104\pi$
$971$	3.33761e10	1.16995	0.584977	+	0.811050i	$0.301104\pi$
$972$	0	0
$973$	−2.56868e10	−0.893954
$974$	3.09127e10	1.07197
$975$	0	0
$976$	−3.34858e10	−1.15289
$977$	2.05126e10	0.703705	0.351853	−	0.936055i	$-0.385552\pi$
$977$	2.05126e10	0.703705	0.351853	+	0.936055i	$0.385552\pi$
$978$	0	0
$979$	4.80676e10	1.63724
$980$	1.17458e10	0.398650
$981$	0	0
$982$	1.74546e10	0.588193
$983$	1.39469e9	0.0468317	0.0234158	−	0.999726i	$-0.492546\pi$
$983$	1.39469e9	0.0468317	0.0234158	+	0.999726i	$0.492546\pi$
$984$	0	0
$985$	1.05212e10	0.350783
$986$	5.46708e10	1.81629
$987$	0	0
$988$	−9.95792e9	−0.328488
$989$	−5.68008e9	−0.186710
$990$	0	0
$991$	−5.58431e10	−1.82268	−0.911342	−	0.411650i	$-0.864953\pi$
$991$	−5.58431e10	−1.82268	−0.911342	+	0.411650i	$0.864953\pi$
$992$	−1.82927e10	−0.594958
$993$	0	0
$994$	5.31796e10	1.71748
$995$	3.45664e10	1.11243
$996$	0	0
$997$	−3.23901e9	−0.103509	−0.0517546	−	0.998660i	$-0.516481\pi$
$997$	−3.23901e9	−0.103509	−0.0517546	+	0.998660i	$0.516481\pi$
$998$	2.63062e9	0.0837725
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.c.1.5	✓	17	3.2	odd	2
531.8.a.c.1.13		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)

\(f(q)\)	\(=\)	\(q+12.3679 q^{2} +24.9655 q^{4} +477.980 q^{5} +1344.57 q^{7} -1274.32 q^{8} +O(q^{10})\)	\(q+12.3679 q^{2} +24.9655 q^{4} +477.980 q^{5} +1344.57 q^{7} -1274.32 q^{8} +5911.62 q^{10} -6221.77 q^{11} +10930.7 q^{13} +16629.5 q^{14} -18956.3 q^{16} +31807.5 q^{17} -36490.6 q^{19} +11933.0 q^{20} -76950.3 q^{22} -38312.8 q^{23} +150340. q^{25} +135190. q^{26} +33567.7 q^{28} +138973. q^{29} +256427. q^{31} -71336.8 q^{32} +393392. q^{34} +642676. q^{35} +22109.8 q^{37} -451313. q^{38} -609101. q^{40} -316134. q^{41} +148255. q^{43} -155329. q^{44} -473850. q^{46} -748870. q^{47} +984312. q^{49} +1.85940e6 q^{50} +272890. q^{52} +1.94662e6 q^{53} -2.97388e6 q^{55} -1.71341e6 q^{56} +1.71880e6 q^{58} +205379. q^{59} +1.76648e6 q^{61} +3.17147e6 q^{62} +1.54412e6 q^{64} +5.22465e6 q^{65} -425592. q^{67} +794089. q^{68} +7.94856e6 q^{70} +3.19791e6 q^{71} -4.35846e6 q^{73} +273452. q^{74} -911006. q^{76} -8.36557e6 q^{77} -2.91855e6 q^{79} -9.06074e6 q^{80} -3.90993e6 q^{82} +1.97344e6 q^{83} +1.52033e7 q^{85} +1.83361e6 q^{86} +7.92854e6 q^{88} -7.72572e6 q^{89} +1.46970e7 q^{91} -956499. q^{92} -9.26197e6 q^{94} -1.74418e7 q^{95} +9.26843e6 q^{97} +1.21739e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 2 q^{2} + 1166 q^{4} + 318 q^{5} + 3145 q^{7} - 2355 q^{8}+O(q^{10}) \) 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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