LMFDB - Embedded newform 531.8.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [531,8,Mod(1,531)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(531, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("531.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	531.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$165.876448532$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 $ x^16 - 6x^15 - 1493x^14 + 8791x^13 + 890490x^12 - 5107725x^11 - 269092298x^10 + 1488374176x^9 + 42885295136x^8 - 226132003872x^7 - 3353576629440x^6 + 16796366777600x^5 + 99470801612800x^4 - 494039551757568x^3 - 493048066650624x^2 + 3193975642099712*x - 2385018853548032
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$4.55626$ 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)

$f(q)$	$=$	$q+4.55626 q^{2} -107.241 q^{4} +540.445 q^{5} -1238.10 q^{7} -1071.82 q^{8} +O(q^{10})$	\(q+4.55626 q^{2} -107.241 q^{4} +540.445 q^{5} -1238.10 q^{7} -1071.82 q^{8} +2462.40 q^{10} -3521.59 q^{11} -4832.75 q^{13} -5641.10 q^{14} +8843.32 q^{16} -2243.59 q^{17} +53136.6 q^{19} -57957.6 q^{20} -16045.3 q^{22} +56390.0 q^{23} +213955. q^{25} -22019.3 q^{26} +132774. q^{28} +137347. q^{29} -121430. q^{31} +177485. q^{32} -10222.4 q^{34} -669124. q^{35} -476697. q^{37} +242104. q^{38} -579257. q^{40} -140564. q^{41} +696919. q^{43} +377657. q^{44} +256927. q^{46} -783363. q^{47} +709348. q^{49} +974835. q^{50} +518267. q^{52} -1.05434e6 q^{53} -1.90322e6 q^{55} +1.32702e6 q^{56} +625790. q^{58} -205379. q^{59} +378219. q^{61} -553265. q^{62} -323278. q^{64} -2.61184e6 q^{65} -1.12190e6 q^{67} +240604. q^{68} -3.04870e6 q^{70} -3.82821e6 q^{71} -1.68355e6 q^{73} -2.17195e6 q^{74} -5.69840e6 q^{76} +4.36008e6 q^{77} +5.56662e6 q^{79} +4.77932e6 q^{80} -640447. q^{82} +1.80553e6 q^{83} -1.21254e6 q^{85} +3.17534e6 q^{86} +3.77449e6 q^{88} -8.26085e6 q^{89} +5.98343e6 q^{91} -6.04729e6 q^{92} -3.56920e6 q^{94} +2.87174e7 q^{95} -9.36799e6 q^{97} +3.23197e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) $ 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * 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 $

$2$	4.55626	0.402720	0.201360	−	0.979517i	$-0.435464\pi$
$2$	4.55626	0.402720	0.201360	+	0.979517i	$0.435464\pi$
$3$	0	0
$3$	0	0
$4$	−107.241	−0.837817
$5$	540.445	1.93355	0.966777	−	0.255623i	$-0.0822806\pi$
$5$	540.445	1.93355	0.966777	+	0.255623i	$0.0822806\pi$
$6$	0	0
$7$	−1238.10	−1.36431	−0.682154	−	0.731208i	$-0.738957\pi$
$7$	−1238.10	−1.36431	−0.682154	+	0.731208i	$0.738957\pi$
$8$	−1071.82	−0.740125
$9$	0	0
$10$	2462.40	0.778680
$11$	−3521.59	−0.797745	−0.398872	−	0.917006i	$-0.630598\pi$
$11$	−3521.59	−0.797745	−0.398872	+	0.917006i	$0.630598\pi$
$12$	0	0
$13$	−4832.75	−0.610089	−0.305044	−	0.952338i	$-0.598671\pi$
$13$	−4832.75	−0.610089	−0.305044	+	0.952338i	$0.598671\pi$
$14$	−5641.10	−0.549434
$15$	0	0
$16$	8843.32	0.539753
$17$	−2243.59	−0.110757	−0.0553787	−	0.998465i	$-0.517637\pi$
$17$	−2243.59	−0.110757	−0.0553787	+	0.998465i	$0.517637\pi$
$18$	0	0
$19$	53136.6	1.77728	0.888641	−	0.458603i	$-0.151650\pi$
$19$	53136.6	1.77728	0.888641	+	0.458603i	$0.151650\pi$
$20$	−57957.6	−1.61996
$21$	0	0
$22$	−16045.3	−0.321268
$23$	56390.0	0.966394	0.483197	−	0.875512i	$-0.339475\pi$
$23$	56390.0	0.966394	0.483197	+	0.875512i	$0.339475\pi$
$24$	0	0
$25$	213955.	2.73863
$26$	−22019.3	−0.245695
$27$	0	0
$28$	132774.	1.14304
$29$	137347.	1.04575	0.522874	−	0.852410i	$-0.324860\pi$
$29$	137347.	1.04575	0.522874	+	0.852410i	$0.324860\pi$
$30$	0	0
$31$	−121430.	−0.732081	−0.366041	−	0.930599i	$-0.619287\pi$
$31$	−121430.	−0.732081	−0.366041	+	0.930599i	$0.619287\pi$
$32$	177485.	0.957495
$33$	0	0
$34$	−10222.4	−0.0446042
$35$	−669124.	−2.63796
$36$	0	0
$37$	−476697.	−1.54716	−0.773581	−	0.633697i	$-0.781537\pi$
$37$	−476697.	−1.54716	−0.773581	+	0.633697i	$0.781537\pi$
$38$	242104.	0.715747
$39$	0	0
$40$	−579257.	−1.43107
$41$	−140564.	−0.318516	−0.159258	−	0.987237i	$-0.550910\pi$
$41$	−140564.	−0.318516	−0.159258	+	0.987237i	$0.550910\pi$
$42$	0	0
$43$	696919.	1.33673	0.668363	−	0.743835i	$-0.266995\pi$
$43$	696919.	1.33673	0.668363	+	0.743835i	$0.266995\pi$
$44$	377657.	0.668364
$45$	0	0
$46$	256927.	0.389186
$47$	−783363.	−1.10058	−0.550289	−	0.834974i	$-0.685482\pi$
$47$	−783363.	−1.10058	−0.550289	+	0.834974i	$0.685482\pi$
$48$	0	0
$49$	709348.	0.861337
$50$	974835.	1.10290
$51$	0	0
$52$	518267.	0.511142
$53$	−1.05434e6	−0.972781	−0.486390	−	0.873742i	$-0.661687\pi$
$53$	−1.05434e6	−0.972781	−0.486390	+	0.873742i	$0.661687\pi$
$54$	0	0
$55$	−1.90322e6	−1.54248
$56$	1.32702e6	1.00976
$57$	0	0
$58$	625790.	0.421144
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	0	0
$61$	378219.	0.213348	0.106674	−	0.994294i	$-0.465980\pi$
$61$	378219.	0.213348	0.106674	+	0.994294i	$0.465980\pi$
$62$	−553265.	−0.294824
$63$	0	0
$64$	−323278.	−0.154151
$65$	−2.61184e6	−1.17964
$66$	0	0
$67$	−1.12190e6	−0.455714	−0.227857	−	0.973695i	$-0.573172\pi$
$67$	−1.12190e6	−0.455714	−0.227857	+	0.973695i	$0.573172\pi$
$68$	240604.	0.0927943
$69$	0	0
$70$	−3.04870e6	−1.06236
$71$	−3.82821e6	−1.26938	−0.634689	−	0.772767i	$-0.718872\pi$
$71$	−3.82821e6	−1.26938	−0.634689	+	0.772767i	$0.718872\pi$
$72$	0	0
$73$	−1.68355e6	−0.506518	−0.253259	−	0.967398i	$-0.581503\pi$
$73$	−1.68355e6	−0.506518	−0.253259	+	0.967398i	$0.581503\pi$
$74$	−2.17195e6	−0.623073
$75$	0	0
$76$	−5.69840e6	−1.48904
$77$	4.36008e6	1.08837
$78$	0	0
$79$	5.56662e6	1.27027	0.635136	−	0.772401i	$-0.280944\pi$
$79$	5.56662e6	1.27027	0.635136	+	0.772401i	$0.280944\pi$
$80$	4.77932e6	1.04364
$81$	0	0
$82$	−640447.	−0.128273
$83$	1.80553e6	0.346602	0.173301	−	0.984869i	$-0.444557\pi$
$83$	1.80553e6	0.346602	0.173301	+	0.984869i	$0.444557\pi$
$84$	0	0
$85$	−1.21254e6	−0.214155
$86$	3.17534e6	0.538327
$87$	0	0
$88$	3.77449e6	0.590431
$89$	−8.26085e6	−1.24211	−0.621055	−	0.783767i	$-0.713296\pi$
$89$	−8.26085e6	−1.24211	−0.621055	+	0.783767i	$0.713296\pi$
$90$	0	0
$91$	5.98343e6	0.832349
$92$	−6.04729e6	−0.809661
$93$	0	0
$94$	−3.56920e6	−0.443225
$95$	2.87174e7	3.43647
$96$	0	0
$97$	−9.36799e6	−1.04219	−0.521093	−	0.853500i	$-0.674476\pi$
$97$	−9.36799e6	−1.04219	−0.521093	+	0.853500i	$0.674476\pi$
$98$	3.23197e6	0.346878
$99$	0	0
$100$	−2.29447e7	−2.29447
$101$	−5.17821e6	−0.500097	−0.250049	−	0.968233i	$-0.580447\pi$
$101$	−5.17821e6	−0.500097	−0.250049	+	0.968233i	$0.580447\pi$
$102$	0	0
$103$	−1.63595e7	−1.47516	−0.737579	−	0.675261i	$-0.764031\pi$
$103$	−1.63595e7	−1.47516	−0.737579	+	0.675261i	$0.764031\pi$
$104$	5.17982e6	0.451542
$105$	0	0
$106$	−4.80384e6	−0.391758
$107$	1.15281e7	0.909734	0.454867	−	0.890559i	$-0.349687\pi$
$107$	1.15281e7	0.909734	0.454867	+	0.890559i	$0.349687\pi$
$108$	0	0
$109$	−1.66988e6	−0.123507	−0.0617535	−	0.998091i	$-0.519669\pi$
$109$	−1.66988e6	−0.123507	−0.0617535	+	0.998091i	$0.519669\pi$
$110$	−8.67157e6	−0.621188
$111$	0	0
$112$	−1.09489e7	−0.736390
$113$	2.82765e6	0.184353	0.0921767	−	0.995743i	$-0.470618\pi$
$113$	2.82765e6	0.184353	0.0921767	+	0.995743i	$0.470618\pi$
$114$	0	0
$115$	3.04756e7	1.86857
$116$	−1.47292e7	−0.876145
$117$	0	0
$118$	−935759.	−0.0524297
$119$	2.77779e6	0.151107
$120$	0	0
$121$	−7.08560e6	−0.363603
$122$	1.72326e6	0.0859195
$123$	0	0
$124$	1.30222e7	0.613350
$125$	7.34087e7	3.36173
$126$	0	0
$127$	4.15154e7	1.79844	0.899221	−	0.437496i	$-0.144134\pi$
$127$	4.15154e7	1.79844	0.899221	+	0.437496i	$0.144134\pi$
$128$	−2.41910e7	−1.01957
$129$	0	0
$130$	−1.19002e7	−0.475064
$131$	−4.63759e7	−1.80237	−0.901183	−	0.433438i	$-0.857300\pi$
$131$	−4.63759e7	−1.80237	−0.901183	+	0.433438i	$0.857300\pi$
$132$	0	0
$133$	−6.57885e7	−2.42476
$134$	−5.11167e6	−0.183525
$135$	0	0
$136$	2.40472e6	0.0819743
$137$	3.20418e6	0.106462	0.0532310	−	0.998582i	$-0.483048\pi$
$137$	3.20418e6	0.106462	0.0532310	+	0.998582i	$0.483048\pi$
$138$	0	0
$139$	3.74591e7	1.18306	0.591529	−	0.806284i	$-0.298525\pi$
$139$	3.74591e7	1.18306	0.591529	+	0.806284i	$0.298525\pi$
$140$	7.17572e7	2.21013
$141$	0	0
$142$	−1.74423e7	−0.511204
$143$	1.70190e7	0.486695
$144$	0	0
$145$	7.42286e7	2.02201
$146$	−7.67067e6	−0.203985
$147$	0	0
$148$	5.11212e7	1.29624
$149$	−2.39531e7	−0.593212	−0.296606	−	0.955000i	$-0.595855\pi$
$149$	−2.39531e7	−0.593212	−0.296606	+	0.955000i	$0.595855\pi$
$150$	0	0
$151$	−6.59208e7	−1.55813	−0.779064	−	0.626945i	$-0.784305\pi$
$151$	−6.59208e7	−1.55813	−0.779064	+	0.626945i	$0.784305\pi$
$152$	−5.69527e7	−1.31541
$153$	0	0
$154$	1.98656e7	0.438308
$155$	−6.56261e7	−1.41552
$156$	0	0
$157$	−6.45045e7	−1.33027	−0.665137	−	0.746721i	$-0.731627\pi$
$157$	−6.45045e7	−1.33027	−0.665137	+	0.746721i	$0.731627\pi$
$158$	2.53629e7	0.511564
$159$	0	0
$160$	9.59207e7	1.85137
$161$	−6.98164e7	−1.31846
$162$	0	0
$163$	−3.88407e7	−0.702474	−0.351237	−	0.936287i	$-0.614239\pi$
$163$	−3.88407e7	−0.702474	−0.351237	+	0.936287i	$0.614239\pi$
$164$	1.50742e7	0.266858
$165$	0	0
$166$	8.22644e6	0.139583
$167$	−2.62525e7	−0.436178	−0.218089	−	0.975929i	$-0.569982\pi$
$167$	−2.62525e7	−0.436178	−0.218089	+	0.975929i	$0.569982\pi$
$168$	0	0
$169$	−3.93930e7	−0.627792
$170$	−5.52463e6	−0.0862446
$171$	0	0
$172$	−7.47380e7	−1.11993
$173$	9.81294e6	0.144091	0.0720457	−	0.997401i	$-0.477047\pi$
$173$	9.81294e6	0.144091	0.0720457	+	0.997401i	$0.477047\pi$
$174$	0	0
$175$	−2.64898e8	−3.73633
$176$	−3.11425e7	−0.430585
$177$	0	0
$178$	−3.76386e7	−0.500222
$179$	3.88790e7	0.506675	0.253337	−	0.967378i	$-0.418472\pi$
$179$	3.88790e7	0.506675	0.253337	+	0.967378i	$0.418472\pi$
$180$	0	0
$181$	−5.75554e7	−0.721458	−0.360729	−	0.932671i	$-0.617472\pi$
$181$	−5.75554e7	−0.721458	−0.360729	+	0.932671i	$0.617472\pi$
$182$	2.72621e7	0.335204
$183$	0	0
$184$	−6.04397e7	−0.715253
$185$	−2.57628e8	−2.99152
$186$	0	0
$187$	7.90100e6	0.0883561
$188$	8.40083e7	0.922082
$189$	0	0
$190$	1.30844e8	1.38394
$191$	−1.56708e8	−1.62733	−0.813663	−	0.581337i	$-0.802530\pi$
$191$	−1.56708e8	−1.62733	−0.813663	+	0.581337i	$0.802530\pi$
$192$	0	0
$193$	5.44941e7	0.545631	0.272816	−	0.962066i	$-0.412045\pi$
$193$	5.44941e7	0.545631	0.272816	+	0.962066i	$0.412045\pi$
$194$	−4.26830e7	−0.419709
$195$	0	0
$196$	−7.60709e7	−0.721642
$197$	−1.46168e8	−1.36213	−0.681066	−	0.732222i	$-0.738483\pi$
$197$	−1.46168e8	−1.36213	−0.681066	+	0.732222i	$0.738483\pi$
$198$	0	0
$199$	5.06585e7	0.455687	0.227843	−	0.973698i	$-0.426833\pi$
$199$	5.06585e7	0.455687	0.227843	+	0.973698i	$0.426833\pi$
$200$	−2.29321e8	−2.02693
$201$	0	0
$202$	−2.35932e7	−0.201399
$203$	−1.70050e8	−1.42672
$204$	0	0
$205$	−7.59672e7	−0.615868
$206$	−7.45379e7	−0.594076
$207$	0	0
$208$	−4.27376e7	−0.329297
$209$	−1.87125e8	−1.41782
$210$	0	0
$211$	3.36247e7	0.246416	0.123208	−	0.992381i	$-0.460682\pi$
$211$	3.36247e7	0.246416	0.123208	+	0.992381i	$0.460682\pi$
$212$	1.13068e8	0.815012
$213$	0	0
$214$	5.25250e7	0.366368
$215$	3.76646e8	2.58463
$216$	0	0
$217$	1.50342e8	0.998784
$218$	−7.60839e6	−0.0497388
$219$	0	0
$220$	2.04103e8	1.29232
$221$	1.08427e7	0.0675718
$222$	0	0
$223$	8.68957e7	0.524725	0.262362	−	0.964969i	$-0.415498\pi$
$223$	8.68957e7	0.524725	0.262362	+	0.964969i	$0.415498\pi$
$224$	−2.19744e8	−1.30632
$225$	0	0
$226$	1.28835e7	0.0742428
$227$	−3.64696e7	−0.206938	−0.103469	−	0.994633i	$-0.532994\pi$
$227$	−3.64696e7	−0.206938	−0.103469	+	0.994633i	$0.532994\pi$
$228$	0	0
$229$	2.19546e8	1.20809	0.604047	−	0.796949i	$-0.293554\pi$
$229$	2.19546e8	1.20809	0.604047	+	0.796949i	$0.293554\pi$
$230$	1.38855e8	0.752512
$231$	0	0
$232$	−1.47211e8	−0.773985
$233$	−1.19989e8	−0.621435	−0.310718	−	0.950502i	$-0.600569\pi$
$233$	−1.19989e8	−0.621435	−0.310718	+	0.950502i	$0.600569\pi$
$234$	0	0
$235$	−4.23364e8	−2.12803
$236$	2.20250e7	0.109074
$237$	0	0
$238$	1.26563e7	0.0608539
$239$	2.23797e8	1.06038	0.530189	−	0.847879i	$-0.322121\pi$
$239$	2.23797e8	1.06038	0.530189	+	0.847879i	$0.322121\pi$
$240$	0	0
$241$	−1.78627e8	−0.822030	−0.411015	−	0.911629i	$-0.634826\pi$
$241$	−1.78627e8	−0.822030	−0.411015	+	0.911629i	$0.634826\pi$
$242$	−3.22838e7	−0.146430
$243$	0	0
$244$	−4.05604e7	−0.178746
$245$	3.83363e8	1.66544
$246$	0	0
$247$	−2.56796e8	−1.08430
$248$	1.30150e8	0.541832
$249$	0	0
$250$	3.34469e8	1.35384
$251$	3.44628e8	1.37560	0.687800	−	0.725900i	$-0.258577\pi$
$251$	3.44628e8	1.37560	0.687800	+	0.725900i	$0.258577\pi$
$252$	0	0
$253$	−1.98582e8	−0.770936
$254$	1.89155e8	0.724268
$255$	0	0
$256$	−6.88409e7	−0.256452
$257$	1.65611e7	0.0608588	0.0304294	−	0.999537i	$-0.490313\pi$
$257$	1.65611e7	0.0608588	0.0304294	+	0.999537i	$0.490313\pi$
$258$	0	0
$259$	5.90198e8	2.11081
$260$	2.80095e8	0.988321
$261$	0	0
$262$	−2.11301e8	−0.725849
$263$	−3.89298e8	−1.31958	−0.659792	−	0.751448i	$-0.729356\pi$
$263$	−3.89298e8	−1.31958	−0.659792	+	0.751448i	$0.729356\pi$
$264$	0	0
$265$	−5.69812e8	−1.88092
$266$	−2.99749e8	−0.976500
$267$	0	0
$268$	1.20313e8	0.381805
$269$	2.69260e8	0.843410	0.421705	−	0.906733i	$-0.361432\pi$
$269$	2.69260e8	0.843410	0.421705	+	0.906733i	$0.361432\pi$
$270$	0	0
$271$	−4.95264e8	−1.51163	−0.755813	−	0.654787i	$-0.772758\pi$
$271$	−4.95264e8	−1.51163	−0.755813	+	0.654787i	$0.772758\pi$
$272$	−1.98408e7	−0.0597816
$273$	0	0
$274$	1.45990e7	0.0428743
$275$	−7.53462e8	−2.18473
$276$	0	0
$277$	3.16965e8	0.896051	0.448025	−	0.894021i	$-0.352127\pi$
$277$	3.16965e8	0.896051	0.448025	+	0.894021i	$0.352127\pi$
$278$	1.70673e8	0.476441
$279$	0	0
$280$	7.17178e8	1.95242
$281$	4.50536e8	1.21132	0.605658	−	0.795725i	$-0.292910\pi$
$281$	4.50536e8	1.21132	0.605658	+	0.795725i	$0.292910\pi$
$282$	0	0
$283$	4.67571e8	1.22629	0.613147	−	0.789969i	$-0.289903\pi$
$283$	4.67571e8	1.22629	0.613147	+	0.789969i	$0.289903\pi$
$284$	4.10539e8	1.06351
$285$	0	0
$286$	7.75428e7	0.196002
$287$	1.74033e8	0.434554
$288$	0	0
$289$	−4.05305e8	−0.987733
$290$	3.38205e8	0.814304
$291$	0	0
$292$	1.80544e8	0.424369
$293$	1.60508e7	0.0372786	0.0186393	−	0.999826i	$-0.494067\pi$
$293$	1.60508e7	0.0372786	0.0186393	+	0.999826i	$0.494067\pi$
$294$	0	0
$295$	−1.10996e8	−0.251727
$296$	5.10931e8	1.14509
$297$	0	0
$298$	−1.09136e8	−0.238898
$299$	−2.72519e8	−0.589586
$300$	0	0
$301$	−8.62855e8	−1.82371
$302$	−3.00352e8	−0.627489
$303$	0	0
$304$	4.69904e8	0.959294
$305$	2.04406e8	0.412520
$306$	0	0
$307$	−6.56164e7	−0.129428	−0.0647140	−	0.997904i	$-0.520614\pi$
$307$	−6.56164e7	−0.129428	−0.0647140	+	0.997904i	$0.520614\pi$
$308$	−4.67577e8	−0.911854
$309$	0	0
$310$	−2.99009e8	−0.570057
$311$	−4.44680e8	−0.838275	−0.419138	−	0.907923i	$-0.637668\pi$
$311$	−4.44680e8	−0.838275	−0.419138	+	0.907923i	$0.637668\pi$
$312$	0	0
$313$	2.94757e8	0.543324	0.271662	−	0.962393i	$-0.412427\pi$
$313$	2.94757e8	0.543324	0.271662	+	0.962393i	$0.412427\pi$
$314$	−2.93899e8	−0.535728
$315$	0	0
$316$	−5.96967e8	−1.06425
$317$	3.97400e8	0.700682	0.350341	−	0.936622i	$-0.386066\pi$
$317$	3.97400e8	0.700682	0.350341	+	0.936622i	$0.386066\pi$
$318$	0	0
$319$	−4.83680e8	−0.834240
$320$	−1.74714e8	−0.298059
$321$	0	0
$322$	−3.18101e8	−0.530970
$323$	−1.19217e8	−0.196847
$324$	0	0
$325$	−1.03399e9	−1.67081
$326$	−1.76968e8	−0.282900
$327$	0	0
$328$	1.50659e8	0.235742
$329$	9.69882e8	1.50153
$330$	0	0
$331$	−1.15349e9	−1.74830	−0.874150	−	0.485656i	$-0.838581\pi$
$331$	−1.15349e9	−1.74830	−0.874150	+	0.485656i	$0.838581\pi$
$332$	−1.93626e8	−0.290389
$333$	0	0
$334$	−1.19613e8	−0.175658
$335$	−6.06325e8	−0.881148
$336$	0	0
$337$	−1.00153e9	−1.42547	−0.712735	−	0.701434i	$-0.752544\pi$
$337$	−1.00153e9	−1.42547	−0.712735	+	0.701434i	$0.752544\pi$
$338$	−1.79485e8	−0.252824
$339$	0	0
$340$	1.30033e8	0.179423
$341$	4.27625e8	0.584014
$342$	0	0
$343$	1.41385e8	0.189179
$344$	−7.46969e8	−0.989346
$345$	0	0
$346$	4.47103e7	0.0580285
$347$	2.60064e8	0.334139	0.167069	−	0.985945i	$-0.446570\pi$
$347$	2.60064e8	0.334139	0.167069	+	0.985945i	$0.446570\pi$
$348$	0	0
$349$	−2.45544e8	−0.309201	−0.154600	−	0.987977i	$-0.549409\pi$
$349$	−2.45544e8	−0.309201	−0.154600	+	0.987977i	$0.549409\pi$
$350$	−1.20694e9	−1.50470
$351$	0	0
$352$	−6.25028e8	−0.763836
$353$	8.28455e8	1.00244	0.501219	−	0.865320i	$-0.332885\pi$
$353$	8.28455e8	1.00244	0.501219	+	0.865320i	$0.332885\pi$
$354$	0	0
$355$	−2.06893e9	−2.45441
$356$	8.85898e8	1.04066
$357$	0	0
$358$	1.77143e8	0.204048
$359$	−8.66890e8	−0.988857	−0.494428	−	0.869218i	$-0.664623\pi$
$359$	−8.66890e8	−0.988857	−0.494428	+	0.869218i	$0.664623\pi$
$360$	0	0
$361$	1.92963e9	2.15873
$362$	−2.62237e8	−0.290546
$363$	0	0
$364$	−6.41666e8	−0.697356
$365$	−9.09863e8	−0.979380
$366$	0	0
$367$	−1.45949e9	−1.54124	−0.770620	−	0.637295i	$-0.780053\pi$
$367$	−1.45949e9	−1.54124	−0.770620	+	0.637295i	$0.780053\pi$
$368$	4.98674e8	0.521615
$369$	0	0
$370$	−1.17382e9	−1.20475
$371$	1.30538e9	1.32717
$372$	0	0
$373$	−1.35964e9	−1.35657	−0.678287	−	0.734798i	$-0.737277\pi$
$373$	−1.35964e9	−1.35657	−0.678287	+	0.734798i	$0.737277\pi$
$374$	3.59990e7	0.0355828
$375$	0	0
$376$	8.39622e8	0.814566
$377$	−6.63766e8	−0.637999
$378$	0	0
$379$	1.81549e9	1.71300	0.856500	−	0.516147i	$-0.172634\pi$
$379$	1.81549e9	1.71300	0.856500	+	0.516147i	$0.172634\pi$
$380$	−3.07967e9	−2.87913
$381$	0	0
$382$	−7.14002e8	−0.655357
$383$	5.43039e8	0.493896	0.246948	−	0.969029i	$-0.420572\pi$
$383$	5.43039e8	0.493896	0.246948	+	0.969029i	$0.420572\pi$
$384$	0	0
$385$	2.35638e9	2.10442
$386$	2.48289e8	0.219737
$387$	0	0
$388$	1.00463e9	0.873161
$389$	−1.90428e9	−1.64024	−0.820121	−	0.572190i	$-0.806094\pi$
$389$	−1.90428e9	−1.64024	−0.820121	+	0.572190i	$0.806094\pi$
$390$	0	0
$391$	−1.26516e8	−0.107035
$392$	−7.60291e8	−0.637498
$393$	0	0
$394$	−6.65977e8	−0.548558
$395$	3.00845e9	2.45614
$396$	0	0
$397$	−2.75416e8	−0.220913	−0.110457	−	0.993881i	$-0.535231\pi$
$397$	−2.75416e8	−0.220913	−0.110457	+	0.993881i	$0.535231\pi$
$398$	2.30813e8	0.183514
$399$	0	0
$400$	1.89207e9	1.47818
$401$	−1.17696e9	−0.911501	−0.455751	−	0.890108i	$-0.650629\pi$
$401$	−1.17696e9	−0.911501	−0.455751	+	0.890108i	$0.650629\pi$
$402$	0	0
$403$	5.86840e8	0.446635
$404$	5.55314e8	0.418990
$405$	0	0
$406$	−7.74790e8	−0.574570
$407$	1.67873e9	1.23424
$408$	0	0
$409$	−1.75837e9	−1.27080	−0.635402	−	0.772181i	$-0.719166\pi$
$409$	−1.75837e9	−1.27080	−0.635402	+	0.772181i	$0.719166\pi$
$410$	−3.46126e8	−0.248022
$411$	0	0
$412$	1.75440e9	1.23591
$413$	2.54280e8	0.177618
$414$	0	0
$415$	9.75787e8	0.670173
$416$	−8.57741e8	−0.584157
$417$	0	0
$418$	−8.52591e8	−0.570984
$419$	−2.47153e9	−1.64141	−0.820705	−	0.571353i	$-0.806419\pi$
$419$	−2.47153e9	−1.64141	−0.820705	+	0.571353i	$0.806419\pi$
$420$	0	0
$421$	−1.28349e9	−0.838313	−0.419157	−	0.907914i	$-0.637674\pi$
$421$	−1.28349e9	−0.838313	−0.419157	+	0.907914i	$0.637674\pi$
$422$	1.53203e8	0.0992367
$423$	0	0
$424$	1.13006e9	0.719980
$425$	−4.80028e8	−0.303323
$426$	0	0
$427$	−4.68272e8	−0.291072
$428$	−1.23628e9	−0.762191
$429$	0	0
$430$	1.71610e9	1.04088
$431$	−1.78192e9	−1.07206	−0.536030	−	0.844199i	$-0.680077\pi$
$431$	−1.78192e9	−1.07206	−0.536030	+	0.844199i	$0.680077\pi$
$432$	0	0
$433$	8.17222e8	0.483763	0.241881	−	0.970306i	$-0.422236\pi$
$433$	8.17222e8	0.483763	0.241881	+	0.970306i	$0.422236\pi$
$434$	6.84998e8	0.402230
$435$	0	0
$436$	1.79079e8	0.103476
$437$	2.99637e9	1.71756
$438$	0	0
$439$	−2.53136e9	−1.42800	−0.714001	−	0.700145i	$-0.753119\pi$
$439$	−2.53136e9	−1.42800	−0.714001	+	0.700145i	$0.753119\pi$
$440$	2.03990e9	1.14163
$441$	0	0
$442$	4.94022e7	0.0272125
$443$	7.10880e8	0.388493	0.194247	−	0.980953i	$-0.437774\pi$
$443$	7.10880e8	0.388493	0.194247	+	0.980953i	$0.437774\pi$
$444$	0	0
$445$	−4.46453e9	−2.40169
$446$	3.95919e8	0.211317
$447$	0	0
$448$	4.00250e8	0.210309
$449$	−1.22783e9	−0.640139	−0.320070	−	0.947394i	$-0.603706\pi$
$449$	−1.22783e9	−0.640139	−0.320070	+	0.947394i	$0.603706\pi$
$450$	0	0
$451$	4.95009e8	0.254095
$452$	−3.03239e8	−0.154454
$453$	0	0
$454$	−1.66165e8	−0.0833382
$455$	3.23371e9	1.60939
$456$	0	0
$457$	3.07883e9	1.50897	0.754483	−	0.656319i	$-0.227888\pi$
$457$	3.07883e9	1.50897	0.754483	+	0.656319i	$0.227888\pi$
$458$	1.00031e9	0.486524
$459$	0	0
$460$	−3.26822e9	−1.56552
$461$	−1.77409e9	−0.843379	−0.421689	−	0.906740i	$-0.638563\pi$
$461$	−1.77409e9	−0.843379	−0.421689	+	0.906740i	$0.638563\pi$
$462$	0	0
$463$	3.91361e9	1.83250	0.916249	−	0.400608i	$-0.131201\pi$
$463$	3.91361e9	1.83250	0.916249	+	0.400608i	$0.131201\pi$
$464$	1.21461e9	0.564446
$465$	0	0
$466$	−5.46701e8	−0.250264
$467$	3.15577e9	1.43383	0.716914	−	0.697162i	$-0.245554\pi$
$467$	3.15577e9	1.43383	0.716914	+	0.697162i	$0.245554\pi$
$468$	0	0
$469$	1.38902e9	0.621735
$470$	−1.92896e9	−0.856998
$471$	0	0
$472$	2.20129e8	0.0963561
$473$	−2.45426e9	−1.06637
$474$	0	0
$475$	1.13689e10	4.86732
$476$	−2.97892e8	−0.126600
$477$	0	0
$478$	1.01967e9	0.427036
$479$	3.08907e9	1.28426	0.642130	−	0.766596i	$-0.278051\pi$
$479$	3.08907e9	1.28426	0.642130	+	0.766596i	$0.278051\pi$
$480$	0	0
$481$	2.30376e9	0.943907
$482$	−8.13870e8	−0.331048
$483$	0	0
$484$	7.59864e8	0.304633
$485$	−5.06288e9	−2.01512
$486$	0	0
$487$	−8.99853e8	−0.353037	−0.176518	−	0.984297i	$-0.556484\pi$
$487$	−8.99853e8	−0.353037	−0.176518	+	0.984297i	$0.556484\pi$
$488$	−4.05381e8	−0.157904
$489$	0	0
$490$	1.74670e9	0.670706
$491$	8.98595e8	0.342593	0.171297	−	0.985220i	$-0.445204\pi$
$491$	8.98595e8	0.342593	0.171297	+	0.985220i	$0.445204\pi$
$492$	0	0
$493$	−3.08151e8	−0.115824
$494$	−1.17003e9	−0.436669
$495$	0	0
$496$	−1.07384e9	−0.395143
$497$	4.73970e9	1.73182
$498$	0	0
$499$	−2.94063e8	−0.105947	−0.0529734	−	0.998596i	$-0.516870\pi$
$499$	−2.94063e8	−0.105947	−0.0529734	+	0.998596i	$0.516870\pi$
$500$	−7.87239e9	−2.81651
$501$	0	0
$502$	1.57021e9	0.553982
$503$	3.01250e9	1.05545	0.527727	−	0.849414i	$-0.323044\pi$
$503$	3.01250e9	1.05545	0.527727	+	0.849414i	$0.323044\pi$
$504$	0	0
$505$	−2.79853e9	−0.966965
$506$	−9.04791e8	−0.310471
$507$	0	0
$508$	−4.45213e9	−1.50676
$509$	−7.20984e8	−0.242333	−0.121167	−	0.992632i	$-0.538664\pi$
$509$	−7.20984e8	−0.242333	−0.121167	+	0.992632i	$0.538664\pi$
$510$	0	0
$511$	2.08440e9	0.691047
$512$	2.78279e9	0.916296
$513$	0	0
$514$	7.54567e7	0.0245091
$515$	−8.84138e9	−2.85230
$516$	0	0
$517$	2.75868e9	0.877980
$518$	2.68909e9	0.850064
$519$	0	0
$520$	2.79941e9	0.873081
$521$	3.99688e9	1.23820	0.619098	−	0.785314i	$-0.287498\pi$
$521$	3.99688e9	1.23820	0.619098	+	0.785314i	$0.287498\pi$
$522$	0	0
$523$	2.17294e9	0.664190	0.332095	−	0.943246i	$-0.392245\pi$
$523$	2.17294e9	0.664190	0.332095	+	0.943246i	$0.392245\pi$
$524$	4.97338e9	1.51005
$525$	0	0
$526$	−1.77374e9	−0.531423
$527$	2.72439e8	0.0810834
$528$	0	0
$529$	−2.24997e8	−0.0660819
$530$	−2.59621e9	−0.757485
$531$	0	0
$532$	7.05519e9	2.03151
$533$	6.79313e8	0.194323
$534$	0	0
$535$	6.23030e9	1.75902
$536$	1.20247e9	0.337286
$537$	0	0
$538$	1.22682e9	0.339658
$539$	−2.49803e9	−0.687127
$540$	0	0
$541$	−4.30836e9	−1.16983	−0.584914	−	0.811096i	$-0.698872\pi$
$541$	−4.30836e9	−1.16983	−0.584914	+	0.811096i	$0.698872\pi$
$542$	−2.25655e9	−0.608762
$543$	0	0
$544$	−3.98204e8	−0.106050
$545$	−9.02476e8	−0.238808
$546$	0	0
$547$	7.88729e8	0.206050	0.103025	−	0.994679i	$-0.467148\pi$
$547$	7.88729e8	0.206050	0.103025	+	0.994679i	$0.467148\pi$
$548$	−3.43617e8	−0.0891956
$549$	0	0
$550$	−3.43297e9	−0.879833
$551$	7.29818e9	1.85859
$552$	0	0
$553$	−6.89203e9	−1.73304
$554$	1.44418e9	0.360858
$555$	0	0
$556$	−4.01714e9	−0.991186
$557$	−5.29917e9	−1.29932	−0.649658	−	0.760226i	$-0.725088\pi$
$557$	−5.29917e9	−1.29932	−0.649658	+	0.760226i	$0.725088\pi$
$558$	0	0
$559$	−3.36804e9	−0.815522
$560$	−5.91728e9	−1.42385
$561$	0	0
$562$	2.05276e9	0.487821
$563$	5.56156e9	1.31346	0.656731	−	0.754125i	$-0.271939\pi$
$563$	5.56156e9	1.31346	0.656731	+	0.754125i	$0.271939\pi$
$564$	0	0
$565$	1.52819e9	0.356457
$566$	2.13037e9	0.493853
$567$	0	0
$568$	4.10314e9	0.939500
$569$	−3.31033e9	−0.753319	−0.376659	−	0.926352i	$-0.622927\pi$
$569$	−3.31033e9	−0.753319	−0.376659	+	0.926352i	$0.622927\pi$
$570$	0	0
$571$	−3.86639e8	−0.0869118	−0.0434559	−	0.999055i	$-0.513837\pi$
$571$	−3.86639e8	−0.0869118	−0.0434559	+	0.999055i	$0.513837\pi$
$572$	−1.82512e9	−0.407761
$573$	0	0
$574$	7.92938e8	0.175004
$575$	1.20649e10	2.64659
$576$	0	0
$577$	3.94872e9	0.855739	0.427870	−	0.903840i	$-0.359264\pi$
$577$	3.94872e9	0.855739	0.427870	+	0.903840i	$0.359264\pi$
$578$	−1.84667e9	−0.397780
$579$	0	0
$580$	−7.96031e9	−1.69407
$581$	−2.23542e9	−0.472871
$582$	0	0
$583$	3.71295e9	0.776031
$584$	1.80445e9	0.374887
$585$	0	0
$586$	7.31315e7	0.0150128
$587$	1.13309e9	0.231223	0.115612	−	0.993294i	$-0.463117\pi$
$587$	1.13309e9	0.231223	0.115612	+	0.993294i	$0.463117\pi$
$588$	0	0
$589$	−6.45237e9	−1.30112
$590$	−5.05726e8	−0.101376
$591$	0	0
$592$	−4.21558e9	−0.835086
$593$	−6.61359e9	−1.30240	−0.651202	−	0.758904i	$-0.725735\pi$
$593$	−6.61359e9	−1.30240	−0.651202	+	0.758904i	$0.725735\pi$
$594$	0	0
$595$	1.50124e9	0.292174
$596$	2.56874e9	0.497003
$597$	0	0
$598$	−1.24167e9	−0.237438
$599$	2.36330e9	0.449289	0.224644	−	0.974441i	$-0.427878\pi$
$599$	2.36330e9	0.449289	0.224644	+	0.974441i	$0.427878\pi$
$600$	0	0
$601$	−4.40437e9	−0.827605	−0.413803	−	0.910367i	$-0.635800\pi$
$601$	−4.40437e9	−0.827605	−0.413803	+	0.910367i	$0.635800\pi$
$602$	−3.93139e9	−0.734443
$603$	0	0
$604$	7.06938e9	1.30543
$605$	−3.82937e9	−0.703047
$606$	0	0
$607$	−2.71725e9	−0.493138	−0.246569	−	0.969125i	$-0.579303\pi$
$607$	−2.71725e9	−0.493138	−0.246569	+	0.969125i	$0.579303\pi$
$608$	9.43095e9	1.70174
$609$	0	0
$610$	9.31327e8	0.166130
$611$	3.78580e9	0.671450
$612$	0	0
$613$	−1.02118e10	−1.79056	−0.895282	−	0.445500i	$-0.853026\pi$
$613$	−1.02118e10	−1.79056	−0.895282	+	0.445500i	$0.853026\pi$
$614$	−2.98965e8	−0.0521233
$615$	0	0
$616$	−4.67320e9	−0.805530
$617$	−3.23817e9	−0.555011	−0.277506	−	0.960724i	$-0.589508\pi$
$617$	−3.23817e9	−0.555011	−0.277506	+	0.960724i	$0.589508\pi$
$618$	0	0
$619$	−1.72870e9	−0.292956	−0.146478	−	0.989214i	$-0.546794\pi$
$619$	−1.72870e9	−0.292956	−0.146478	+	0.989214i	$0.546794\pi$
$620$	7.03777e9	1.18594
$621$	0	0
$622$	−2.02608e9	−0.337590
$623$	1.02278e10	1.69462
$624$	0	0
$625$	2.29581e10	3.76145
$626$	1.34299e9	0.218807
$627$	0	0
$628$	6.91750e9	1.11453
$629$	1.06951e9	0.171360
$630$	0	0
$631$	7.57564e9	1.20037	0.600187	−	0.799859i	$-0.295093\pi$
$631$	7.57564e9	1.20037	0.600187	+	0.799859i	$0.295093\pi$
$632$	−5.96639e9	−0.940160
$633$	0	0
$634$	1.81066e9	0.282179
$635$	2.24368e10	3.47738
$636$	0	0
$637$	−3.42811e9	−0.525492
$638$	−2.20377e9	−0.335965
$639$	0	0
$640$	−1.30739e10	−1.97140
$641$	5.56603e9	0.834723	0.417362	−	0.908740i	$-0.362955\pi$
$641$	5.56603e9	0.834723	0.417362	+	0.908740i	$0.362955\pi$
$642$	0	0
$643$	−7.76877e9	−1.15243	−0.576214	−	0.817299i	$-0.695471\pi$
$643$	−7.76877e9	−1.15243	−0.576214	+	0.817299i	$0.695471\pi$
$644$	7.48715e9	1.10463
$645$	0	0
$646$	−5.43183e8	−0.0792743
$647$	−6.50327e9	−0.943989	−0.471994	−	0.881602i	$-0.656466\pi$
$647$	−6.50327e9	−0.943989	−0.471994	+	0.881602i	$0.656466\pi$
$648$	0	0
$649$	7.23260e8	0.103858
$650$	−4.71114e9	−0.672867
$651$	0	0
$652$	4.16530e9	0.588545
$653$	9.96747e9	1.40084	0.700420	−	0.713731i	$-0.252996\pi$
$653$	9.96747e9	1.40084	0.700420	+	0.713731i	$0.252996\pi$
$654$	0	0
$655$	−2.50636e10	−3.48497
$656$	−1.24306e9	−0.171920
$657$	0	0
$658$	4.41903e9	0.604695
$659$	−1.28708e10	−1.75189	−0.875946	−	0.482410i	$-0.839762\pi$
$659$	−1.28708e10	−1.75189	−0.875946	+	0.482410i	$0.839762\pi$
$660$	0	0
$661$	−4.36910e9	−0.588420	−0.294210	−	0.955741i	$-0.595056\pi$
$661$	−4.36910e9	−0.588420	−0.294210	+	0.955741i	$0.595056\pi$
$662$	−5.25560e9	−0.704075
$663$	0	0
$664$	−1.93519e9	−0.256529
$665$	−3.55550e10	−4.68841
$666$	0	0
$667$	7.74501e9	1.01061
$668$	2.81534e9	0.365437
$669$	0	0
$670$	−2.76257e9	−0.354856
$671$	−1.33193e9	−0.170197
$672$	0	0
$673$	−2.50718e9	−0.317053	−0.158527	−	0.987355i	$-0.550674\pi$
$673$	−2.50718e9	−0.317053	−0.158527	+	0.987355i	$0.550674\pi$
$674$	−4.56321e9	−0.574065
$675$	0	0
$676$	4.22453e9	0.525974
$677$	−4.46850e9	−0.553479	−0.276739	−	0.960945i	$-0.589254\pi$
$677$	−4.46850e9	−0.553479	−0.276739	+	0.960945i	$0.589254\pi$
$678$	0	0
$679$	1.15985e10	1.42186
$680$	1.29962e9	0.158502
$681$	0	0
$682$	1.94837e9	0.235194
$683$	3.36244e9	0.403815	0.201908	−	0.979405i	$-0.435286\pi$
$683$	3.36244e9	0.403815	0.201908	+	0.979405i	$0.435286\pi$
$684$	0	0
$685$	1.73168e9	0.205850
$686$	6.44185e8	0.0761862
$687$	0	0
$688$	6.16308e9	0.721503
$689$	5.09536e9	0.593483
$690$	0	0
$691$	1.73704e9	0.200279	0.100140	−	0.994973i	$-0.468071\pi$
$691$	1.73704e9	0.200279	0.100140	+	0.994973i	$0.468071\pi$
$692$	−1.05235e9	−0.120722
$693$	0	0
$694$	1.18492e9	0.134564
$695$	2.02446e10	2.28751
$696$	0	0
$697$	3.15369e8	0.0352780
$698$	−1.11876e9	−0.124521
$699$	0	0
$700$	2.84078e10	3.13036
$701$	−7.43794e9	−0.815529	−0.407764	−	0.913087i	$-0.633692\pi$
$701$	−7.43794e9	−0.815529	−0.407764	+	0.913087i	$0.633692\pi$
$702$	0	0
$703$	−2.53301e10	−2.74975
$704$	1.13845e9	0.122973
$705$	0	0
$706$	3.77465e9	0.403702
$707$	6.41114e9	0.682287
$708$	0	0
$709$	−3.13976e9	−0.330853	−0.165426	−	0.986222i	$-0.552900\pi$
$709$	−3.13976e9	−0.330853	−0.165426	+	0.986222i	$0.552900\pi$
$710$	−9.42659e9	−0.988441
$711$	0	0
$712$	8.85412e9	0.919317
$713$	−6.84742e9	−0.707479
$714$	0	0
$715$	9.19780e9	0.941051
$716$	−4.16940e9	−0.424501
$717$	0	0
$718$	−3.94977e9	−0.398232
$719$	1.62139e10	1.62680	0.813402	−	0.581701i	$-0.197613\pi$
$719$	1.62139e10	1.62680	0.813402	+	0.581701i	$0.197613\pi$
$720$	0	0
$721$	2.02546e10	2.01257
$722$	8.79190e9	0.869365
$723$	0	0
$724$	6.17227e9	0.604449
$725$	2.93862e10	2.86392
$726$	0	0
$727$	1.44572e10	1.39545	0.697725	−	0.716366i	$-0.254196\pi$
$727$	1.44572e10	1.39545	0.697725	+	0.716366i	$0.254196\pi$
$728$	−6.41314e9	−0.616043
$729$	0	0
$730$	−4.14557e9	−0.394416
$731$	−1.56360e9	−0.148052
$732$	0	0
$733$	8.79960e9	0.825275	0.412638	−	0.910895i	$-0.364608\pi$
$733$	8.79960e9	0.825275	0.412638	+	0.910895i	$0.364608\pi$
$734$	−6.64982e9	−0.620688
$735$	0	0
$736$	1.00084e10	0.925318
$737$	3.95087e9	0.363544
$738$	0	0
$739$	1.06478e10	0.970523	0.485262	−	0.874369i	$-0.338724\pi$
$739$	1.06478e10	0.970523	0.485262	+	0.874369i	$0.338724\pi$
$740$	2.76282e10	2.50635
$741$	0	0
$742$	5.94764e9	0.534479
$743$	6.58260e9	0.588758	0.294379	−	0.955689i	$-0.404887\pi$
$743$	6.58260e9	0.588758	0.294379	+	0.955689i	$0.404887\pi$
$744$	0	0
$745$	−1.29453e10	−1.14701
$746$	−6.19487e9	−0.546319
$747$	0	0
$748$	−8.47307e8	−0.0740262
$749$	−1.42729e10	−1.24116
$750$	0	0
$751$	−8.17849e9	−0.704585	−0.352293	−	0.935890i	$-0.614598\pi$
$751$	−8.17849e9	−0.704585	−0.352293	+	0.935890i	$0.614598\pi$
$752$	−6.92753e9	−0.594040
$753$	0	0
$754$	−3.02429e9	−0.256935
$755$	−3.56265e10	−3.01272
$756$	0	0
$757$	1.76129e10	1.47569	0.737844	−	0.674972i	$-0.235844\pi$
$757$	1.76129e10	1.47569	0.737844	+	0.674972i	$0.235844\pi$
$758$	8.27185e9	0.689860
$759$	0	0
$760$	−3.07798e10	−2.54342
$761$	1.93708e10	1.59331	0.796657	−	0.604431i	$-0.206600\pi$
$761$	1.93708e10	1.59331	0.796657	+	0.604431i	$0.206600\pi$
$762$	0	0
$763$	2.06748e9	0.168502
$764$	1.68055e10	1.36340
$765$	0	0
$766$	2.47423e9	0.198902
$767$	9.92546e8	0.0794268
$768$	0	0
$769$	9.07869e9	0.719915	0.359957	−	0.932969i	$-0.382791\pi$
$769$	9.07869e9	0.719915	0.359957	+	0.932969i	$0.382791\pi$
$770$	1.07363e10	0.847492
$771$	0	0
$772$	−5.84398e9	−0.457139
$773$	1.79639e10	1.39886	0.699428	−	0.714703i	$-0.253438\pi$
$773$	1.79639e10	1.39886	0.699428	+	0.714703i	$0.253438\pi$
$774$	0	0
$775$	−2.59805e10	−2.00490
$776$	1.00408e10	0.771348
$777$	0	0
$778$	−8.67641e9	−0.660558
$779$	−7.46912e9	−0.566093
$780$	0	0
$781$	1.34814e10	1.01264
$782$	−5.76440e8	−0.0431052
$783$	0	0
$784$	6.27299e9	0.464909
$785$	−3.48611e10	−2.57216
$786$	0	0
$787$	−9.95896e9	−0.728287	−0.364143	−	0.931343i	$-0.618638\pi$
$787$	−9.95896e9	−0.728287	−0.364143	+	0.931343i	$0.618638\pi$
$788$	1.56751e10	1.14122
$789$	0	0
$790$	1.37073e10	0.989135
$791$	−3.50092e9	−0.251515
$792$	0	0
$793$	−1.82784e9	−0.130161
$794$	−1.25486e9	−0.0889662
$795$	0	0
$796$	−5.43264e9	−0.381782
$797$	−2.78445e10	−1.94821	−0.974105	−	0.226095i	$-0.927404\pi$
$797$	−2.78445e10	−1.94821	−0.974105	+	0.226095i	$0.927404\pi$
$798$	0	0
$799$	1.75755e9	0.121897
$800$	3.79738e10	2.62222
$801$	0	0
$802$	−5.36254e9	−0.367080
$803$	5.92875e9	0.404072
$804$	0	0
$805$	−3.77319e10	−2.54931
$806$	2.67380e9	0.179869
$807$	0	0
$808$	5.55009e9	0.370135
$809$	−6.81852e9	−0.452762	−0.226381	−	0.974039i	$-0.572689\pi$
$809$	−6.81852e9	−0.452762	−0.226381	+	0.974039i	$0.572689\pi$
$810$	0	0
$811$	3.94141e9	0.259465	0.129732	−	0.991549i	$-0.458588\pi$
$811$	3.94141e9	0.259465	0.129732	+	0.991549i	$0.458588\pi$
$812$	1.82362e10	1.19533
$813$	0	0
$814$	7.64872e9	0.497053
$815$	−2.09912e10	−1.35827
$816$	0	0
$817$	3.70319e10	2.37574
$818$	−8.01159e9	−0.511778
$819$	0	0
$820$	8.14676e9	0.515985
$821$	−2.49119e10	−1.57111	−0.785553	−	0.618795i	$-0.787621\pi$
$821$	−2.49119e10	−1.57111	−0.785553	+	0.618795i	$0.787621\pi$
$822$	0	0
$823$	−2.21681e9	−0.138621	−0.0693105	−	0.997595i	$-0.522080\pi$
$823$	−2.21681e9	−0.138621	−0.0693105	+	0.997595i	$0.522080\pi$
$824$	1.75343e10	1.09180
$825$	0	0
$826$	1.15856e9	0.0715302
$827$	1.70597e10	1.04882	0.524410	−	0.851466i	$-0.324286\pi$
$827$	1.70597e10	1.04882	0.524410	+	0.851466i	$0.324286\pi$
$828$	0	0
$829$	−5.39778e9	−0.329060	−0.164530	−	0.986372i	$-0.552611\pi$
$829$	−5.39778e9	−0.329060	−0.164530	+	0.986372i	$0.552611\pi$
$830$	4.44594e9	0.269892
$831$	0	0
$832$	1.56232e9	0.0940457
$833$	−1.59149e9	−0.0953994
$834$	0	0
$835$	−1.41880e10	−0.843373
$836$	2.00674e10	1.18787
$837$	0	0
$838$	−1.12609e10	−0.661028
$839$	−1.48286e10	−0.866830	−0.433415	−	0.901194i	$-0.642692\pi$
$839$	−1.48286e10	−0.866830	−0.433415	+	0.901194i	$0.642692\pi$
$840$	0	0
$841$	1.61441e9	0.0935895
$842$	−5.84793e9	−0.337606
$843$	0	0
$844$	−3.60593e9	−0.206452
$845$	−2.12897e10	−1.21387
$846$	0	0
$847$	8.77268e9	0.496067
$848$	−9.32386e9	−0.525062
$849$	0	0
$850$	−2.18713e9	−0.122154
$851$	−2.68809e10	−1.49517
$852$	0	0
$853$	1.65358e10	0.912227	0.456114	−	0.889922i	$-0.349241\pi$
$853$	1.65358e10	0.912227	0.456114	+	0.889922i	$0.349241\pi$
$854$	−2.13357e9	−0.117221
$855$	0	0
$856$	−1.23560e10	−0.673318
$857$	−1.32332e10	−0.718176	−0.359088	−	0.933304i	$-0.616912\pi$
$857$	−1.32332e10	−0.718176	−0.359088	+	0.933304i	$0.616912\pi$
$858$	0	0
$859$	−4.23318e9	−0.227872	−0.113936	−	0.993488i	$-0.536346\pi$
$859$	−4.23318e9	−0.227872	−0.113936	+	0.993488i	$0.536346\pi$
$860$	−4.03917e10	−2.16545
$861$	0	0
$862$	−8.11891e9	−0.431740
$863$	−3.99379e8	−0.0211518	−0.0105759	−	0.999944i	$-0.503366\pi$
$863$	−3.99379e8	−0.0211518	−0.0105759	+	0.999944i	$0.503366\pi$
$864$	0	0
$865$	5.30335e9	0.278608
$866$	3.72347e9	0.194821
$867$	0	0
$868$	−1.61228e10	−0.836798
$869$	−1.96033e10	−1.01335
$870$	0	0
$871$	5.42187e9	0.278026
$872$	1.78980e9	0.0914108
$873$	0	0
$874$	1.36522e10	0.691694
$875$	−9.08873e10	−4.58643
$876$	0	0
$877$	9.41245e9	0.471199	0.235599	−	0.971850i	$-0.424295\pi$
$877$	9.41245e9	0.471199	0.235599	+	0.971850i	$0.424295\pi$
$878$	−1.15335e10	−0.575085
$879$	0	0
$880$	−1.68308e10	−0.832560
$881$	6.45929e8	0.0318250	0.0159125	−	0.999873i	$-0.494935\pi$
$881$	6.45929e8	0.0318250	0.0159125	+	0.999873i	$0.494935\pi$
$882$	0	0
$883$	3.76342e10	1.83959	0.919793	−	0.392403i	$-0.128356\pi$
$883$	3.76342e10	1.83959	0.919793	+	0.392403i	$0.128356\pi$
$884$	−1.16278e9	−0.0566128
$885$	0	0
$886$	3.23895e9	0.156454
$887$	1.95731e10	0.941732	0.470866	−	0.882205i	$-0.343941\pi$
$887$	1.95731e10	0.941732	0.470866	+	0.882205i	$0.343941\pi$
$888$	0	0
$889$	−5.14002e10	−2.45363
$890$	−2.03416e10	−0.967207
$891$	0	0
$892$	−9.31874e9	−0.439623
$893$	−4.16253e10	−1.95604
$894$	0	0
$895$	2.10119e10	0.979683
$896$	2.99509e10	1.39101
$897$	0	0
$898$	−5.59429e9	−0.257797
$899$	−1.66781e10	−0.765573
$900$	0	0
$901$	2.36551e9	0.107743
$902$	2.25539e9	0.102329
$903$	0	0
$904$	−3.03072e9	−0.136445
$905$	−3.11055e10	−1.39498
$906$	0	0
$907$	−2.68155e10	−1.19333	−0.596665	−	0.802491i	$-0.703508\pi$
$907$	−2.68155e10	−1.19333	−0.596665	+	0.802491i	$0.703508\pi$
$908$	3.91102e9	0.173376
$909$	0	0
$910$	1.47336e10	0.648134
$911$	3.43001e10	1.50307	0.751537	−	0.659690i	$-0.229313\pi$
$911$	3.43001e10	1.50307	0.751537	+	0.659690i	$0.229313\pi$
$912$	0	0
$913$	−6.35832e9	−0.276500
$914$	1.40280e10	0.607691
$915$	0	0
$916$	−2.35442e10	−1.01216
$917$	5.74180e10	2.45898
$918$	0	0
$919$	1.59456e10	0.677698	0.338849	−	0.940841i	$-0.389962\pi$
$919$	1.59456e10	0.677698	0.338849	+	0.940841i	$0.389962\pi$
$920$	−3.26643e10	−1.38298
$921$	0	0
$922$	−8.08321e9	−0.339645
$923$	1.85008e10	0.774434
$924$	0	0
$925$	−1.01992e11	−4.23710
$926$	1.78314e10	0.737984
$927$	0	0
$928$	2.43771e10	1.00130
$929$	−1.42285e9	−0.0582242	−0.0291121	−	0.999576i	$-0.509268\pi$
$929$	−1.42285e9	−0.0582242	−0.0291121	+	0.999576i	$0.509268\pi$
$930$	0	0
$931$	3.76924e10	1.53084
$932$	1.28677e10	0.520649
$933$	0	0
$934$	1.43785e10	0.577431
$935$	4.27005e9	0.170841
$936$	0	0
$937$	−2.31807e10	−0.920532	−0.460266	−	0.887781i	$-0.652246\pi$
$937$	−2.31807e10	−0.920532	−0.460266	+	0.887781i	$0.652246\pi$
$938$	6.32875e9	0.250385
$939$	0	0
$940$	4.54018e10	1.78290
$941$	−3.37421e10	−1.32010	−0.660052	−	0.751220i	$-0.729466\pi$
$941$	−3.37421e10	−1.32010	−0.660052	+	0.751220i	$0.729466\pi$
$942$	0	0
$943$	−7.92642e9	−0.307812
$944$	−1.81623e9	−0.0702699
$945$	0	0
$946$	−1.11822e10	−0.429447
$947$	−2.26076e10	−0.865029	−0.432514	−	0.901627i	$-0.642374\pi$
$947$	−2.26076e10	−0.865029	−0.432514	+	0.901627i	$0.642374\pi$
$948$	0	0
$949$	8.13617e9	0.309021
$950$	5.17995e10	1.96017
$951$	0	0
$952$	−2.97728e9	−0.111838
$953$	−1.78597e10	−0.668420	−0.334210	−	0.942499i	$-0.608469\pi$
$953$	−1.78597e10	−0.668420	−0.334210	+	0.942499i	$0.608469\pi$
$954$	0	0
$955$	−8.46920e10	−3.14652
$956$	−2.40001e10	−0.888403
$957$	0	0
$958$	1.40746e10	0.517197
$959$	−3.96709e9	−0.145247
$960$	0	0
$961$	−1.27674e10	−0.464057
$962$	1.04965e10	0.380130
$963$	0	0
$964$	1.91561e10	0.688710
$965$	2.94511e10	1.05501
$966$	0	0
$967$	−1.61338e8	−0.00573778	−0.00286889	−	0.999996i	$-0.500913\pi$
$967$	−1.61338e8	−0.00573778	−0.00286889	+	0.999996i	$0.500913\pi$
$968$	7.59446e9	0.269112
$969$	0	0
$970$	−2.30678e10	−0.811530
$971$	4.94599e10	1.73375	0.866874	−	0.498527i	$-0.166125\pi$
$971$	4.94599e10	1.73375	0.866874	+	0.498527i	$0.166125\pi$
$972$	0	0
$973$	−4.63782e10	−1.61406
$974$	−4.09996e9	−0.142175
$975$	0	0
$976$	3.34471e9	0.115155
$977$	1.43208e10	0.491290	0.245645	−	0.969360i	$-0.421000\pi$
$977$	1.43208e10	0.491290	0.245645	+	0.969360i	$0.421000\pi$
$978$	0	0
$979$	2.90913e10	0.990886
$980$	−4.11121e10	−1.39533
$981$	0	0
$982$	4.09423e9	0.137969
$983$	5.16305e10	1.73368	0.866840	−	0.498587i	$-0.166148\pi$
$983$	5.16305e10	1.73368	0.866840	+	0.498587i	$0.166148\pi$
$984$	0	0
$985$	−7.89955e10	−2.63375
$986$	−1.40402e9	−0.0466448
$987$	0	0
$988$	2.75390e10	0.908445
$989$	3.92992e10	1.29181
$990$	0	0
$991$	−4.70999e10	−1.53731	−0.768656	−	0.639662i	$-0.779074\pi$
$991$	−4.70999e10	−1.53731	−0.768656	+	0.639662i	$0.779074\pi$
$992$	−2.15520e10	−0.700964
$993$	0	0
$994$	2.15953e10	0.697440
$995$	2.73781e10	0.881094
$996$	0	0
$997$	−5.20068e10	−1.66198	−0.830992	−	0.556284i	$-0.812227\pi$
$997$	−5.20068e10	−1.66198	−0.830992	+	0.556284i	$0.812227\pi$
$998$	−1.33982e9	−0.0426669
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.8.a.b.1.10		16
3.2	odd	2		177.8.a.a.1.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.a.1.7	✓	16	3.2	odd	2
531.8.a.b.1.10		16	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)

\(f(q)\)	\(=\)	\(q+4.55626 q^{2} -107.241 q^{4} +540.445 q^{5} -1238.10 q^{7} -1071.82 q^{8} +O(q^{10})\)	\(q+4.55626 q^{2} -107.241 q^{4} +540.445 q^{5} -1238.10 q^{7} -1071.82 q^{8} +2462.40 q^{10} -3521.59 q^{11} -4832.75 q^{13} -5641.10 q^{14} +8843.32 q^{16} -2243.59 q^{17} +53136.6 q^{19} -57957.6 q^{20} -16045.3 q^{22} +56390.0 q^{23} +213955. q^{25} -22019.3 q^{26} +132774. q^{28} +137347. q^{29} -121430. q^{31} +177485. q^{32} -10222.4 q^{34} -669124. q^{35} -476697. q^{37} +242104. q^{38} -579257. q^{40} -140564. q^{41} +696919. q^{43} +377657. q^{44} +256927. q^{46} -783363. q^{47} +709348. q^{49} +974835. q^{50} +518267. q^{52} -1.05434e6 q^{53} -1.90322e6 q^{55} +1.32702e6 q^{56} +625790. q^{58} -205379. q^{59} +378219. q^{61} -553265. q^{62} -323278. q^{64} -2.61184e6 q^{65} -1.12190e6 q^{67} +240604. q^{68} -3.04870e6 q^{70} -3.82821e6 q^{71} -1.68355e6 q^{73} -2.17195e6 q^{74} -5.69840e6 q^{76} +4.36008e6 q^{77} +5.56662e6 q^{79} +4.77932e6 q^{80} -640447. q^{82} +1.80553e6 q^{83} -1.21254e6 q^{85} +3.17534e6 q^{86} +3.77449e6 q^{88} -8.26085e6 q^{89} +5.98343e6 q^{91} -6.04729e6 q^{92} -3.56920e6 q^{94} +2.87174e7 q^{95} -9.36799e6 q^{97} +3.23197e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8}+O(q^{10}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8	\( 16 q + 6 q^{2} + 974 q^{4} + 68 q^{5} - 2343 q^{7} - 819 q^{8} - 3479 q^{10} - 898 q^{11} - 8172 q^{13} + 13315 q^{14} + 3138 q^{16} + 44985 q^{17} - 40137 q^{19} - 130657 q^{20} + 109394 q^{22} + 2833 q^{23} + 285746 q^{25} + 129420 q^{26} + 112890 q^{28} - 144375 q^{29} - 141759 q^{31} + 36224 q^{32} - 341332 q^{34} + 78859 q^{35} - 297971 q^{37} - 329075 q^{38} - 203048 q^{40} - 659077 q^{41} - 1431608 q^{43} - 254916 q^{44} + 873113 q^{46} + 1574073 q^{47} + 1893545 q^{49} - 302533 q^{50} - 4972548 q^{52} - 587736 q^{53} - 4624036 q^{55} + 5798506 q^{56} - 6991380 q^{58} - 3286064 q^{59} - 6117131 q^{61} + 11570258 q^{62} - 19063011 q^{64} + 5335514 q^{65} - 16518710 q^{67} + 17284669 q^{68} - 39189486 q^{70} + 10882582 q^{71} - 21097441 q^{73} + 16717030 q^{74} - 40864952 q^{76} + 3404601 q^{77} - 3784458 q^{79} + 27466195 q^{80} - 24990117 q^{82} + 1951425 q^{83} - 23238675 q^{85} + 35910572 q^{86} - 27843055 q^{88} - 10499443 q^{89} + 699217 q^{91} + 20062766 q^{92} - 59358988 q^{94} + 29236333 q^{95} - 25158976 q^{97} - 2120460 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 + 974 * q^4 + 68 * q^5 - 2343 * q^7 - 819 * q^8 - 3479 * q^10 - 898 * q^11 - 8172 * q^13 + 13315 * q^14 + 3138 * q^16 + 44985 * q^17 - 40137 * q^19 - 130657 * q^20 + 109394 * q^22 + 2833 * q^23 + 285746 * q^25 + 129420 * q^26 + 112890 * q^28 - 144375 * q^29 - 141759 * q^31 + 36224 * q^32 - 341332 * q^34 + 78859 * q^35 - 297971 * q^37 - 329075 * q^38 - 203048 * q^40 - 659077 * q^41 - 1431608 * q^43 - 254916 * q^44 + 873113 * q^46 + 1574073 * q^47 + 1893545 * q^49 - 302533 * q^50 - 4972548 * q^52 - 587736 * q^53 - 4624036 * q^55 + 5798506 * q^56 - 6991380 * q^58 - 3286064 * q^59 - 6117131 * q^61 + 11570258 * q^62 - 19063011 * q^64 + 5335514 * q^65 - 16518710 * q^67 + 17284669 * q^68 - 39189486 * q^70 + 10882582 * q^71 - 21097441 * q^73 + 16717030 * q^74 - 40864952 * q^76 + 3404601 * q^77 - 3784458 * q^79 + 27466195 * q^80 - 24990117 * q^82 + 1951425 * q^83 - 23238675 * q^85 + 35910572 * q^86 - 27843055 * q^88 - 10499443 * q^89 + 699217 * q^91 + 20062766 * q^92 - 59358988 * q^94 + 29236333 * q^95 - 25158976 * q^97 - 2120460 * q^98

Introduction

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