LMFDB - Embedded newform 5586.2.a.bw.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.29268.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 5x + 16 $ x^4 - x^3 - 9x^2 + 5x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.43292$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.11806 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.11806 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -2.11806 q^{10} +3.35203 q^{11} -1.00000 q^{12} -4.23612 q^{13} -2.11806 q^{15} +1.00000 q^{16} +6.95628 q^{17} -1.00000 q^{18} +1.00000 q^{19} +2.11806 q^{20} -3.35203 q^{22} -7.18070 q^{23} +1.00000 q^{24} -0.513812 q^{25} +4.23612 q^{26} -1.00000 q^{27} +7.29877 q^{29} +2.11806 q^{30} +4.54883 q^{31} -1.00000 q^{32} -3.35203 q^{33} -6.95628 q^{34} +1.00000 q^{36} -0.252218 q^{37} -1.00000 q^{38} +4.23612 q^{39} -2.11806 q^{40} -10.3359 q^{41} +3.17133 q^{43} +3.35203 q^{44} +2.11806 q^{45} +7.18070 q^{46} +7.15524 q^{47} -1.00000 q^{48} +0.513812 q^{50} -6.95628 q^{51} -4.23612 q^{52} +1.75733 q^{53} +1.00000 q^{54} +7.09982 q^{55} -1.00000 q^{57} -7.29877 q^{58} +13.0465 q^{59} -2.11806 q^{60} +6.91911 q^{61} -4.54883 q^{62} +1.00000 q^{64} -8.97238 q^{65} +3.35203 q^{66} -4.30616 q^{67} +6.95628 q^{68} +7.18070 q^{69} -10.4518 q^{71} -1.00000 q^{72} -12.7667 q^{73} +0.252218 q^{74} +0.513812 q^{75} +1.00000 q^{76} -4.23612 q^{78} +2.27114 q^{79} +2.11806 q^{80} +1.00000 q^{81} +10.3359 q^{82} +16.5699 q^{83} +14.7338 q^{85} -3.17133 q^{86} -7.29877 q^{87} -3.35203 q^{88} +3.79365 q^{89} -2.11806 q^{90} -7.18070 q^{92} -4.54883 q^{93} -7.15524 q^{94} +2.11806 q^{95} +1.00000 q^{96} -6.18070 q^{97} +3.35203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{12} + 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{22} - 5 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{27} - 3 q^{29} + 9 q^{31} - 4 q^{32} + 2 q^{33} - 10 q^{34} + 4 q^{36} - 14 q^{37} - 4 q^{38} + 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} + 7 q^{47} - 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} + 4 q^{54} - 4 q^{57} + 3 q^{58} + 7 q^{59} + 23 q^{61} - 9 q^{62} + 4 q^{64} - 48 q^{65} - 2 q^{66} + 6 q^{67} + 10 q^{68} + 5 q^{69} + 2 q^{71} - 4 q^{72} - 5 q^{73} + 14 q^{74} - 4 q^{75} + 4 q^{76} - 11 q^{79} + 4 q^{81} - 4 q^{82} + 14 q^{83} + 6 q^{85} - 21 q^{86} + 3 q^{87} + 2 q^{88} + 10 q^{89} - 5 q^{92} - 9 q^{93} - 7 q^{94} + 4 q^{96} - q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^12 + 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^22 - 5 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^27 - 3 * q^29 + 9 * q^31 - 4 * q^32 + 2 * q^33 - 10 * q^34 + 4 * q^36 - 14 * q^37 - 4 * q^38 + 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 + 7 * q^47 - 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 + 4 * q^54 - 4 * q^57 + 3 * q^58 + 7 * q^59 + 23 * q^61 - 9 * q^62 + 4 * q^64 - 48 * q^65 - 2 * q^66 + 6 * q^67 + 10 * q^68 + 5 * q^69 + 2 * q^71 - 4 * q^72 - 5 * q^73 + 14 * q^74 - 4 * q^75 + 4 * q^76 - 11 * q^79 + 4 * q^81 - 4 * q^82 + 14 * q^83 + 6 * q^85 - 21 * q^86 + 3 * q^87 + 2 * q^88 + 10 * q^89 - 5 * q^92 - 9 * q^93 - 7 * q^94 + 4 * q^96 - q^97 - 2 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.11806	0.947226	0.473613	−	0.880733i	$-0.342949\pi$
$5$	2.11806	0.947226	0.473613	+	0.880733i	$0.342949\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.11806	−0.669790
$11$	3.35203	1.01068	0.505338	−	0.862922i	$-0.331368\pi$
$11$	3.35203	1.01068	0.505338	+	0.862922i	$0.331368\pi$
$12$	−1.00000	−0.288675
$13$	−4.23612	−1.17489	−0.587445	−	0.809264i	$-0.699866\pi$
$13$	−4.23612	−1.17489	−0.587445	+	0.809264i	$0.699866\pi$
$14$	0	0
$15$	−2.11806	−0.546881
$16$	1.00000	0.250000
$17$	6.95628	1.68715	0.843573	−	0.537014i	$-0.180448\pi$
$17$	6.95628	1.68715	0.843573	+	0.537014i	$0.180448\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.11806	0.473613
$21$	0	0
$22$	−3.35203	−0.714656
$23$	−7.18070	−1.49728	−0.748640	−	0.662977i	$-0.769293\pi$
$23$	−7.18070	−1.49728	−0.748640	+	0.662977i	$0.769293\pi$
$24$	1.00000	0.204124
$25$	−0.513812	−0.102762
$26$	4.23612	0.830772
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.29877	1.35535	0.677673	−	0.735363i	$-0.262988\pi$
$29$	7.29877	1.35535	0.677673	+	0.735363i	$0.262988\pi$
$30$	2.11806	0.386704
$31$	4.54883	0.816994	0.408497	−	0.912760i	$-0.366053\pi$
$31$	4.54883	0.816994	0.408497	+	0.912760i	$0.366053\pi$
$32$	−1.00000	−0.176777
$33$	−3.35203	−0.583514
$34$	−6.95628	−1.19299
$35$	0	0
$36$	1.00000	0.166667
$37$	−0.252218	−0.0414644	−0.0207322	−	0.999785i	$-0.506600\pi$
$37$	−0.252218	−0.0414644	−0.0207322	+	0.999785i	$0.506600\pi$
$38$	−1.00000	−0.162221
$39$	4.23612	0.678323
$40$	−2.11806	−0.334895
$41$	−10.3359	−1.61420	−0.807101	−	0.590413i	$-0.798965\pi$
$41$	−10.3359	−1.61420	−0.807101	+	0.590413i	$0.798965\pi$
$42$	0	0
$43$	3.17133	0.483623	0.241812	−	0.970323i	$-0.422258\pi$
$43$	3.17133	0.483623	0.241812	+	0.970323i	$0.422258\pi$
$44$	3.35203	0.505338
$45$	2.11806	0.315742
$46$	7.18070	1.05874
$47$	7.15524	1.04370	0.521849	−	0.853038i	$-0.325242\pi$
$47$	7.15524	1.04370	0.521849	+	0.853038i	$0.325242\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	0.513812	0.0726639
$51$	−6.95628	−0.974075
$52$	−4.23612	−0.587445
$53$	1.75733	0.241388	0.120694	−	0.992690i	$-0.461488\pi$
$53$	1.75733	0.241388	0.120694	+	0.992690i	$0.461488\pi$
$54$	1.00000	0.136083
$55$	7.09982	0.957339
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−7.29877	−0.958375
$59$	13.0465	1.69852	0.849258	−	0.527978i	$-0.177050\pi$
$59$	13.0465	1.69852	0.849258	+	0.527978i	$0.177050\pi$
$60$	−2.11806	−0.273441
$61$	6.91911	0.885901	0.442951	−	0.896546i	$-0.353932\pi$
$61$	6.91911	0.885901	0.442951	+	0.896546i	$0.353932\pi$
$62$	−4.54883	−0.577702
$63$	0	0
$64$	1.00000	0.125000
$65$	−8.97238	−1.11289
$66$	3.35203	0.412607
$67$	−4.30616	−0.526081	−0.263041	−	0.964785i	$-0.584725\pi$
$67$	−4.30616	−0.526081	−0.263041	+	0.964785i	$0.584725\pi$
$68$	6.95628	0.843573
$69$	7.18070	0.864455
$70$	0	0
$71$	−10.4518	−1.24041	−0.620203	−	0.784441i	$-0.712950\pi$
$71$	−10.4518	−1.24041	−0.620203	+	0.784441i	$0.712950\pi$
$72$	−1.00000	−0.117851
$73$	−12.7667	−1.49423	−0.747115	−	0.664695i	$-0.768562\pi$
$73$	−12.7667	−1.49423	−0.747115	+	0.664695i	$0.768562\pi$
$74$	0.252218	0.0293197
$75$	0.513812	0.0593298
$76$	1.00000	0.114708
$77$	0	0
$78$	−4.23612	−0.479647
$79$	2.27114	0.255524	0.127762	−	0.991805i	$-0.459221\pi$
$79$	2.27114	0.255524	0.127762	+	0.991805i	$0.459221\pi$
$80$	2.11806	0.236807
$81$	1.00000	0.111111
$82$	10.3359	1.14141
$83$	16.5699	1.81878	0.909392	−	0.415940i	$-0.136547\pi$
$83$	16.5699	1.81878	0.909392	+	0.415940i	$0.136547\pi$
$84$	0	0
$85$	14.7338	1.59811
$86$	−3.17133	−0.341973
$87$	−7.29877	−0.782510
$88$	−3.35203	−0.357328
$89$	3.79365	0.402126	0.201063	−	0.979578i	$-0.435560\pi$
$89$	3.79365	0.402126	0.201063	+	0.979578i	$0.435560\pi$
$90$	−2.11806	−0.223263
$91$	0	0
$92$	−7.18070	−0.748640
$93$	−4.54883	−0.471692
$94$	−7.15524	−0.738006
$95$	2.11806	0.217309
$96$	1.00000	0.102062
$97$	−6.18070	−0.627555	−0.313778	−	0.949496i	$-0.601595\pi$
$97$	−6.18070	−0.627555	−0.313778	+	0.949496i	$0.601595\pi$
$98$	0	0
$99$	3.35203	0.336892
$100$	−0.513812	−0.0513812
$101$	13.2296	1.31639	0.658196	−	0.752846i	$-0.271320\pi$
$101$	13.2296	1.31639	0.658196	+	0.752846i	$0.271320\pi$
$102$	6.95628	0.688775
$103$	−7.45400	−0.734465	−0.367232	−	0.930129i	$-0.619695\pi$
$103$	−7.45400	−0.734465	−0.367232	+	0.930129i	$0.619695\pi$
$104$	4.23612	0.415386
$105$	0	0
$106$	−1.75733	−0.170687
$107$	8.60708	0.832078	0.416039	−	0.909347i	$-0.363418\pi$
$107$	8.60708	0.832078	0.416039	+	0.909347i	$0.363418\pi$
$108$	−1.00000	−0.0962250
$109$	6.30746	0.604145	0.302073	−	0.953285i	$-0.402321\pi$
$109$	6.30746	0.604145	0.302073	+	0.953285i	$0.402321\pi$
$110$	−7.09982	−0.676941
$111$	0.252218	0.0239395
$112$	0	0
$113$	1.97453	0.185748	0.0928741	−	0.995678i	$-0.470395\pi$
$113$	1.97453	0.185748	0.0928741	+	0.995678i	$0.470395\pi$
$114$	1.00000	0.0936586
$115$	−15.2092	−1.41826
$116$	7.29877	0.677673
$117$	−4.23612	−0.391630
$118$	−13.0465	−1.20103
$119$	0	0
$120$	2.11806	0.193352
$121$	0.236125	0.0214659
$122$	−6.91911	−0.626427
$123$	10.3359	0.931960
$124$	4.54883	0.408497
$125$	−11.6786	−1.04457
$126$	0	0
$127$	12.2296	1.08520	0.542600	−	0.839991i	$-0.317440\pi$
$127$	12.2296	1.08520	0.542600	+	0.839991i	$0.317440\pi$
$128$	−1.00000	−0.0883883
$129$	−3.17133	−0.279220
$130$	8.97238	0.786930
$131$	−1.02108	−0.0892122	−0.0446061	−	0.999005i	$-0.514203\pi$
$131$	−1.02108	−0.0892122	−0.0446061	+	0.999005i	$0.514203\pi$
$132$	−3.35203	−0.291757
$133$	0	0
$134$	4.30616	0.371996
$135$	−2.11806	−0.182294
$136$	−6.95628	−0.596496
$137$	−6.12761	−0.523517	−0.261759	−	0.965133i	$-0.584302\pi$
$137$	−6.12761	−0.523517	−0.261759	+	0.965133i	$0.584302\pi$
$138$	−7.18070	−0.611262
$139$	18.3476	1.55623	0.778113	−	0.628124i	$-0.216177\pi$
$139$	18.3476	1.55623	0.778113	+	0.628124i	$0.216177\pi$
$140$	0	0
$141$	−7.15524	−0.602580
$142$	10.4518	0.877100
$143$	−14.1996	−1.18743
$144$	1.00000	0.0833333
$145$	15.4592	1.28382
$146$	12.7667	1.05658
$147$	0	0
$148$	−0.252218	−0.0207322
$149$	−21.9102	−1.79496	−0.897478	−	0.441058i	$-0.854603\pi$
$149$	−21.9102	−1.79496	−0.897478	+	0.441058i	$0.854603\pi$
$150$	−0.513812	−0.0419525
$151$	0.349200	0.0284175	0.0142088	−	0.999899i	$-0.495477\pi$
$151$	0.349200	0.0284175	0.0142088	+	0.999899i	$0.495477\pi$
$152$	−1.00000	−0.0811107
$153$	6.95628	0.562382
$154$	0	0
$155$	9.63471	0.773878
$156$	4.23612	0.339161
$157$	13.0487	1.04140	0.520700	−	0.853740i	$-0.325671\pi$
$157$	13.0487	1.04140	0.520700	+	0.853740i	$0.325671\pi$
$158$	−2.27114	−0.180682
$159$	−1.75733	−0.139365
$160$	−2.11806	−0.167448
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	15.4614	1.21103	0.605515	−	0.795834i	$-0.292967\pi$
$163$	15.4614	1.21103	0.605515	+	0.795834i	$0.292967\pi$
$164$	−10.3359	−0.807101
$165$	−7.09982	−0.552720
$166$	−16.5699	−1.28607
$167$	−4.68797	−0.362766	−0.181383	−	0.983413i	$-0.558057\pi$
$167$	−4.68797	−0.362766	−0.181383	+	0.983413i	$0.558057\pi$
$168$	0	0
$169$	4.94475	0.380366
$170$	−14.7338	−1.13003
$171$	1.00000	0.0764719
$172$	3.17133	0.241812
$173$	−21.5283	−1.63677	−0.818385	−	0.574670i	$-0.805130\pi$
$173$	−21.5283	−1.63677	−0.818385	+	0.574670i	$0.805130\pi$
$174$	7.29877	0.553318
$175$	0	0
$176$	3.35203	0.252669
$177$	−13.0465	−0.980639
$178$	−3.79365	−0.284346
$179$	1.83822	0.137395	0.0686976	−	0.997638i	$-0.478116\pi$
$179$	1.83822	0.137395	0.0686976	+	0.997638i	$0.478116\pi$
$180$	2.11806	0.157871
$181$	20.3848	1.51519	0.757596	−	0.652724i	$-0.226374\pi$
$181$	20.3848	1.51519	0.757596	+	0.652724i	$0.226374\pi$
$182$	0	0
$183$	−6.91911	−0.511475
$184$	7.18070	0.529369
$185$	−0.534213	−0.0392761
$186$	4.54883	0.333536
$187$	23.3177	1.70516
$188$	7.15524	0.521849
$189$	0	0
$190$	−2.11806	−0.153660
$191$	−5.49789	−0.397814	−0.198907	−	0.980018i	$-0.563739\pi$
$191$	−5.49789	−0.397814	−0.198907	+	0.980018i	$0.563739\pi$
$192$	−1.00000	−0.0721688
$193$	7.89871	0.568562	0.284281	−	0.958741i	$-0.408245\pi$
$193$	7.89871	0.568562	0.284281	+	0.958741i	$0.408245\pi$
$194$	6.18070	0.443749
$195$	8.97238	0.642525
$196$	0	0
$197$	−1.93736	−0.138031	−0.0690155	−	0.997616i	$-0.521986\pi$
$197$	−1.93736	−0.138031	−0.0690155	+	0.997616i	$0.521986\pi$
$198$	−3.35203	−0.238219
$199$	8.73823	0.619437	0.309718	−	0.950828i	$-0.399765\pi$
$199$	8.73823	0.619437	0.309718	+	0.950828i	$0.399765\pi$
$200$	0.513812	0.0363320
$201$	4.30616	0.303733
$202$	−13.2296	−0.930830
$203$	0	0
$204$	−6.95628	−0.487037
$205$	−21.8922	−1.52902
$206$	7.45400	0.519345
$207$	−7.18070	−0.499093
$208$	−4.23612	−0.293722
$209$	3.35203	0.231865
$210$	0	0
$211$	−23.3870	−1.61003	−0.805013	−	0.593257i	$-0.797842\pi$
$211$	−23.3870	−1.61003	−0.805013	+	0.593257i	$0.797842\pi$
$212$	1.75733	0.120694
$213$	10.4518	0.716149
$214$	−8.60708	−0.588368
$215$	6.71707	0.458101
$216$	1.00000	0.0680414
$217$	0	0
$218$	−6.30746	−0.427195
$219$	12.7667	0.862694
$220$	7.09982	0.478669
$221$	−29.4677	−1.98221
$222$	−0.252218	−0.0169278
$223$	9.80320	0.656471	0.328236	−	0.944596i	$-0.393546\pi$
$223$	9.80320	0.656471	0.328236	+	0.944596i	$0.393546\pi$
$224$	0	0
$225$	−0.513812	−0.0342541
$226$	−1.97453	−0.131344
$227$	−18.2835	−1.21352	−0.606760	−	0.794885i	$-0.707531\pi$
$227$	−18.2835	−1.21352	−0.606760	+	0.794885i	$0.707531\pi$
$228$	−1.00000	−0.0662266
$229$	−1.44463	−0.0954636	−0.0477318	−	0.998860i	$-0.515199\pi$
$229$	−1.44463	−0.0954636	−0.0477318	+	0.998860i	$0.515199\pi$
$230$	15.2092	1.00286
$231$	0	0
$232$	−7.29877	−0.479188
$233$	−15.6808	−1.02728	−0.513640	−	0.858006i	$-0.671703\pi$
$233$	−15.6808	−1.02728	−0.513640	+	0.858006i	$0.671703\pi$
$234$	4.23612	0.276924
$235$	15.1552	0.988619
$236$	13.0465	0.849258
$237$	−2.27114	−0.147527
$238$	0	0
$239$	3.76818	0.243744	0.121872	−	0.992546i	$-0.461110\pi$
$239$	3.76818	0.243744	0.121872	+	0.992546i	$0.461110\pi$
$240$	−2.11806	−0.136720
$241$	2.99561	0.192964	0.0964821	−	0.995335i	$-0.469241\pi$
$241$	2.99561	0.192964	0.0964821	+	0.995335i	$0.469241\pi$
$242$	−0.236125	−0.0151787
$243$	−1.00000	−0.0641500
$244$	6.91911	0.442951
$245$	0	0
$246$	−10.3359	−0.658995
$247$	−4.23612	−0.269538
$248$	−4.54883	−0.288851
$249$	−16.5699	−1.05008
$250$	11.6786	0.738619
$251$	26.2922	1.65955	0.829775	−	0.558098i	$-0.188469\pi$
$251$	26.2922	1.65955	0.829775	+	0.558098i	$0.188469\pi$
$252$	0	0
$253$	−24.0700	−1.51327
$254$	−12.2296	−0.767352
$255$	−14.7338	−0.922669
$256$	1.00000	0.0625000
$257$	−19.7317	−1.23083	−0.615414	−	0.788204i	$-0.711011\pi$
$257$	−19.7317	−1.23083	−0.615414	+	0.788204i	$0.711011\pi$
$258$	3.17133	0.197438
$259$	0	0
$260$	−8.97238	−0.556443
$261$	7.29877	0.451782
$262$	1.02108	0.0630825
$263$	−4.44247	−0.273935	−0.136967	−	0.990576i	$-0.543736\pi$
$263$	−4.44247	−0.273935	−0.136967	+	0.990576i	$0.543736\pi$
$264$	3.35203	0.206303
$265$	3.72214	0.228649
$266$	0	0
$267$	−3.79365	−0.232168
$268$	−4.30616	−0.263041
$269$	19.4796	1.18769	0.593847	−	0.804578i	$-0.297608\pi$
$269$	19.4796	1.18769	0.593847	+	0.804578i	$0.297608\pi$
$270$	2.11806	0.128901
$271$	1.57578	0.0957215	0.0478608	−	0.998854i	$-0.484760\pi$
$271$	1.57578	0.0957215	0.0478608	+	0.998854i	$0.484760\pi$
$272$	6.95628	0.421787
$273$	0	0
$274$	6.12761	0.370183
$275$	−1.72231	−0.103859
$276$	7.18070	0.432228
$277$	9.80612	0.589192	0.294596	−	0.955622i	$-0.404815\pi$
$277$	9.80612	0.589192	0.294596	+	0.955622i	$0.404815\pi$
$278$	−18.3476	−1.10042
$279$	4.54883	0.272331
$280$	0	0
$281$	−3.60641	−0.215140	−0.107570	−	0.994198i	$-0.534307\pi$
$281$	−3.60641	−0.215140	−0.107570	+	0.994198i	$0.534307\pi$
$282$	7.15524	0.426088
$283$	−21.5327	−1.27999	−0.639994	−	0.768380i	$-0.721063\pi$
$283$	−21.5327	−1.27999	−0.639994	+	0.768380i	$0.721063\pi$
$284$	−10.4518	−0.620203
$285$	−2.11806	−0.125463
$286$	14.1996	0.839642
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	31.3899	1.84646
$290$	−15.4592	−0.907798
$291$	6.18070	0.362319
$292$	−12.7667	−0.747115
$293$	−24.2946	−1.41930	−0.709651	−	0.704553i	$-0.751148\pi$
$293$	−24.2946	−1.41930	−0.709651	+	0.704553i	$0.751148\pi$
$294$	0	0
$295$	27.6334	1.60888
$296$	0.252218	0.0146599
$297$	−3.35203	−0.194505
$298$	21.9102	1.26923
$299$	30.4184	1.75914
$300$	0.513812	0.0296649
$301$	0	0
$302$	−0.349200	−0.0200942
$303$	−13.2296	−0.760020
$304$	1.00000	0.0573539
$305$	14.6551	0.839149
$306$	−6.95628	−0.397664
$307$	5.79365	0.330661	0.165331	−	0.986238i	$-0.447131\pi$
$307$	5.79365	0.330661	0.165331	+	0.986238i	$0.447131\pi$
$308$	0	0
$309$	7.45400	0.424043
$310$	−9.63471	−0.547215
$311$	18.6786	1.05917	0.529583	−	0.848258i	$-0.322348\pi$
$311$	18.6786	1.05917	0.529583	+	0.848258i	$0.322348\pi$
$312$	−4.23612	−0.239823
$313$	25.7369	1.45473	0.727366	−	0.686249i	$-0.240744\pi$
$313$	25.7369	1.45473	0.727366	+	0.686249i	$0.240744\pi$
$314$	−13.0487	−0.736381
$315$	0	0
$316$	2.27114	0.127762
$317$	−20.7528	−1.16559	−0.582796	−	0.812619i	$-0.698041\pi$
$317$	−20.7528	−1.16559	−0.582796	+	0.812619i	$0.698041\pi$
$318$	1.75733	0.0985463
$319$	24.4657	1.36982
$320$	2.11806	0.118403
$321$	−8.60708	−0.480401
$322$	0	0
$323$	6.95628	0.387058
$324$	1.00000	0.0555556
$325$	2.17657	0.120734
$326$	−15.4614	−0.856328
$327$	−6.30746	−0.348804
$328$	10.3359	0.570707
$329$	0	0
$330$	7.09982	0.390832
$331$	−35.0035	−1.92397	−0.961983	−	0.273108i	$-0.911948\pi$
$331$	−35.0035	−1.92397	−0.961983	+	0.273108i	$0.911948\pi$
$332$	16.5699	0.909392
$333$	−0.252218	−0.0138215
$334$	4.68797	0.256514
$335$	−9.12072	−0.498318
$336$	0	0
$337$	−9.06565	−0.493837	−0.246919	−	0.969036i	$-0.579418\pi$
$337$	−9.06565	−0.493837	−0.246919	+	0.969036i	$0.579418\pi$
$338$	−4.94475	−0.268959
$339$	−1.97453	−0.107242
$340$	14.7338	0.799055
$341$	15.2478	0.825716
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−3.17133	−0.170987
$345$	15.2092	0.818835
$346$	21.5283	1.15737
$347$	−17.6560	−0.947822	−0.473911	−	0.880573i	$-0.657158\pi$
$347$	−17.6560	−0.947822	−0.473911	+	0.880573i	$0.657158\pi$
$348$	−7.29877	−0.391255
$349$	19.9745	1.06921	0.534606	−	0.845101i	$-0.320460\pi$
$349$	19.9745	1.06921	0.534606	+	0.845101i	$0.320460\pi$
$350$	0	0
$351$	4.23612	0.226108
$352$	−3.35203	−0.178664
$353$	22.5028	1.19770	0.598851	−	0.800860i	$-0.295624\pi$
$353$	22.5028	1.19770	0.598851	+	0.800860i	$0.295624\pi$
$354$	13.0465	0.693416
$355$	−22.1377	−1.17495
$356$	3.79365	0.201063
$357$	0	0
$358$	−1.83822	−0.0971530
$359$	−9.83589	−0.519119	−0.259559	−	0.965727i	$-0.583577\pi$
$359$	−9.83589	−0.519119	−0.259559	+	0.965727i	$0.583577\pi$
$360$	−2.11806	−0.111632
$361$	1.00000	0.0526316
$362$	−20.3848	−1.07140
$363$	−0.236125	−0.0123933
$364$	0	0
$365$	−27.0407	−1.41537
$366$	6.91911	0.361668
$367$	35.3346	1.84445	0.922224	−	0.386655i	$-0.126370\pi$
$367$	35.3346	1.84445	0.922224	+	0.386655i	$0.126370\pi$
$368$	−7.18070	−0.374320
$369$	−10.3359	−0.538068
$370$	0.534213	0.0277724
$371$	0	0
$372$	−4.54883	−0.235846
$373$	33.8294	1.75162	0.875811	−	0.482654i	$-0.160327\pi$
$373$	33.8294	1.75162	0.875811	+	0.482654i	$0.160327\pi$
$374$	−23.3177	−1.20573
$375$	11.6786	0.603080
$376$	−7.15524	−0.369003
$377$	−30.9185	−1.59238
$378$	0	0
$379$	25.4999	1.30984	0.654920	−	0.755698i	$-0.272702\pi$
$379$	25.4999	1.30984	0.654920	+	0.755698i	$0.272702\pi$
$380$	2.11806	0.108654
$381$	−12.2296	−0.626540
$382$	5.49789	0.281297
$383$	35.7186	1.82514	0.912568	−	0.408926i	$-0.134096\pi$
$383$	35.7186	1.82514	0.912568	+	0.408926i	$0.134096\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−7.89871	−0.402034
$387$	3.17133	0.161208
$388$	−6.18070	−0.313778
$389$	22.0248	1.11670	0.558350	−	0.829606i	$-0.311435\pi$
$389$	22.0248	1.11670	0.558350	+	0.829606i	$0.311435\pi$
$390$	−8.97238	−0.454334
$391$	−49.9510	−2.52613
$392$	0	0
$393$	1.02108	0.0515067
$394$	1.93736	0.0976027
$395$	4.81042	0.242039
$396$	3.35203	0.168446
$397$	19.7317	0.990305	0.495153	−	0.868806i	$-0.335112\pi$
$397$	19.7317	0.990305	0.495153	+	0.868806i	$0.335112\pi$
$398$	−8.73823	−0.438008
$399$	0	0
$400$	−0.513812	−0.0256906
$401$	14.8528	0.741711	0.370856	−	0.928691i	$-0.379064\pi$
$401$	14.8528	0.741711	0.370856	+	0.928691i	$0.379064\pi$
$402$	−4.30616	−0.214772
$403$	−19.2694	−0.959878
$404$	13.2296	0.658196
$405$	2.11806	0.105247
$406$	0	0
$407$	−0.845443	−0.0419070
$408$	6.95628	0.344387
$409$	6.03632	0.298477	0.149238	−	0.988801i	$-0.452318\pi$
$409$	6.03632	0.298477	0.149238	+	0.988801i	$0.452318\pi$
$410$	21.8922	1.08118
$411$	6.12761	0.302253
$412$	−7.45400	−0.367232
$413$	0	0
$414$	7.18070	0.352912
$415$	35.0961	1.72280
$416$	4.23612	0.207693
$417$	−18.3476	−0.898488
$418$	−3.35203	−0.163953
$419$	14.1370	0.690637	0.345319	−	0.938486i	$-0.387771\pi$
$419$	14.1370	0.690637	0.345319	+	0.938486i	$0.387771\pi$
$420$	0	0
$421$	−35.7565	−1.74266	−0.871331	−	0.490695i	$-0.836743\pi$
$421$	−35.7565	−1.74266	−0.871331	+	0.490695i	$0.836743\pi$
$422$	23.3870	1.13846
$423$	7.15524	0.347899
$424$	−1.75733	−0.0853436
$425$	−3.57422	−0.173375
$426$	−10.4518	−0.506394
$427$	0	0
$428$	8.60708	0.416039
$429$	14.1996	0.685565
$430$	−6.71707	−0.323926
$431$	17.4242	0.839295	0.419648	−	0.907687i	$-0.362154\pi$
$431$	17.4242	0.839295	0.419648	+	0.907687i	$0.362154\pi$
$432$	−1.00000	−0.0481125
$433$	−0.745628	−0.0358326	−0.0179163	−	0.999839i	$-0.505703\pi$
$433$	−0.745628	−0.0358326	−0.0179163	+	0.999839i	$0.505703\pi$
$434$	0	0
$435$	−15.4592	−0.741214
$436$	6.30746	0.302073
$437$	−7.18070	−0.343500
$438$	−12.7667	−0.610017
$439$	11.7289	0.559788	0.279894	−	0.960031i	$-0.409701\pi$
$439$	11.7289	0.559788	0.279894	+	0.960031i	$0.409701\pi$
$440$	−7.09982	−0.338470
$441$	0	0
$442$	29.4677	1.40163
$443$	6.95611	0.330495	0.165247	−	0.986252i	$-0.447158\pi$
$443$	6.95611	0.330495	0.165247	+	0.986252i	$0.447158\pi$
$444$	0.252218	0.0119697
$445$	8.03519	0.380905
$446$	−9.80320	−0.464195
$447$	21.9102	1.03632
$448$	0	0
$449$	−27.5823	−1.30169	−0.650844	−	0.759211i	$-0.725585\pi$
$449$	−27.5823	−1.30169	−0.650844	+	0.759211i	$0.725585\pi$
$450$	0.513812	0.0242213
$451$	−34.6464	−1.63144
$452$	1.97453	0.0928741
$453$	−0.349200	−0.0164069
$454$	18.2835	0.858088
$455$	0	0
$456$	1.00000	0.0468293
$457$	20.7733	0.971732	0.485866	−	0.874033i	$-0.338504\pi$
$457$	20.7733	0.971732	0.485866	+	0.874033i	$0.338504\pi$
$458$	1.44463	0.0675030
$459$	−6.95628	−0.324692
$460$	−15.2092	−0.709132
$461$	33.6610	1.56775	0.783875	−	0.620918i	$-0.213240\pi$
$461$	33.6610	1.56775	0.783875	+	0.620918i	$0.213240\pi$
$462$	0	0
$463$	−18.4933	−0.859458	−0.429729	−	0.902958i	$-0.641391\pi$
$463$	−18.4933	−0.859458	−0.429729	+	0.902958i	$0.641391\pi$
$464$	7.29877	0.338837
$465$	−9.63471	−0.446799
$466$	15.6808	0.726397
$467$	−13.4329	−0.621602	−0.310801	−	0.950475i	$-0.600597\pi$
$467$	−13.4329	−0.621602	−0.310801	+	0.950475i	$0.600597\pi$
$468$	−4.23612	−0.195815
$469$	0	0
$470$	−15.1552	−0.699059
$471$	−13.0487	−0.601253
$472$	−13.0465	−0.600516
$473$	10.6304	0.488786
$474$	2.27114	0.104317
$475$	−0.513812	−0.0235753
$476$	0	0
$477$	1.75733	0.0804627
$478$	−3.76818	−0.172353
$479$	−4.05893	−0.185457	−0.0927287	−	0.995691i	$-0.529559\pi$
$479$	−4.05893	−0.185457	−0.0927287	+	0.995691i	$0.529559\pi$
$480$	2.11806	0.0966759
$481$	1.06843	0.0487161
$482$	−2.99561	−0.136446
$483$	0	0
$484$	0.236125	0.0107329
$485$	−13.0911	−0.594437
$486$	1.00000	0.0453609
$487$	37.5078	1.69964	0.849820	−	0.527073i	$-0.176711\pi$
$487$	37.5078	1.69964	0.849820	+	0.527073i	$0.176711\pi$
$488$	−6.91911	−0.313213
$489$	−15.4614	−0.699189
$490$	0	0
$491$	−27.2230	−1.22856	−0.614279	−	0.789089i	$-0.710553\pi$
$491$	−27.2230	−1.22856	−0.614279	+	0.789089i	$0.710553\pi$
$492$	10.3359	0.465980
$493$	50.7723	2.28667
$494$	4.23612	0.190592
$495$	7.09982	0.319113
$496$	4.54883	0.204249
$497$	0	0
$498$	16.5699	0.742515
$499$	6.93651	0.310521	0.155260	−	0.987874i	$-0.450378\pi$
$499$	6.93651	0.310521	0.155260	+	0.987874i	$0.450378\pi$
$500$	−11.6786	−0.522283
$501$	4.68797	0.209443
$502$	−26.2922	−1.17348
$503$	24.0509	1.07237	0.536187	−	0.844099i	$-0.319864\pi$
$503$	24.0509	1.07237	0.536187	+	0.844099i	$0.319864\pi$
$504$	0	0
$505$	28.0211	1.24692
$506$	24.0700	1.07004
$507$	−4.94475	−0.219604
$508$	12.2296	0.542600
$509$	32.3685	1.43471	0.717355	−	0.696707i	$-0.245352\pi$
$509$	32.3685	1.43471	0.717355	+	0.696707i	$0.245352\pi$
$510$	14.7338	0.652426
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	19.7317	0.870327
$515$	−15.7880	−0.695704
$516$	−3.17133	−0.139610
$517$	23.9846	1.05484
$518$	0	0
$519$	21.5283	0.944990
$520$	8.97238	0.393465
$521$	12.5146	0.548273	0.274137	−	0.961691i	$-0.411608\pi$
$521$	12.5146	0.548273	0.274137	+	0.961691i	$0.411608\pi$
$522$	−7.29877	−0.319458
$523$	−15.9658	−0.698134	−0.349067	−	0.937098i	$-0.613501\pi$
$523$	−15.9658	−0.698134	−0.349067	+	0.937098i	$0.613501\pi$
$524$	−1.02108	−0.0446061
$525$	0	0
$526$	4.44247	0.193701
$527$	31.6430	1.37839
$528$	−3.35203	−0.145879
$529$	28.5625	1.24185
$530$	−3.72214	−0.161679
$531$	13.0465	0.566172
$532$	0	0
$533$	43.7843	1.89651
$534$	3.79365	0.164167
$535$	18.2303	0.788166
$536$	4.30616	0.185998
$537$	−1.83822	−0.0793251
$538$	−19.4796	−0.839827
$539$	0	0
$540$	−2.11806	−0.0911469
$541$	−40.2696	−1.73132	−0.865662	−	0.500628i	$-0.833102\pi$
$541$	−40.2696	−1.73132	−0.865662	+	0.500628i	$0.833102\pi$
$542$	−1.57578	−0.0676853
$543$	−20.3848	−0.874796
$544$	−6.95628	−0.298248
$545$	13.3596	0.572263
$546$	0	0
$547$	7.22088	0.308743	0.154371	−	0.988013i	$-0.450665\pi$
$547$	7.22088	0.308743	0.154371	+	0.988013i	$0.450665\pi$
$548$	−6.12761	−0.261759
$549$	6.91911	0.295300
$550$	1.72231	0.0734397
$551$	7.29877	0.310938
$552$	−7.18070	−0.305631
$553$	0	0
$554$	−9.80612	−0.416622
$555$	0.534213	0.0226761
$556$	18.3476	0.778113
$557$	2.72532	0.115476	0.0577378	−	0.998332i	$-0.481611\pi$
$557$	2.72532	0.115476	0.0577378	+	0.998332i	$0.481611\pi$
$558$	−4.54883	−0.192567
$559$	−13.4341	−0.568204
$560$	0	0
$561$	−23.3177	−0.984474
$562$	3.60641	0.152127
$563$	18.3468	0.773225	0.386613	−	0.922242i	$-0.373645\pi$
$563$	18.3468	0.773225	0.386613	+	0.922242i	$0.373645\pi$
$564$	−7.15524	−0.301290
$565$	4.18218	0.175946
$566$	21.5327	0.905088
$567$	0	0
$568$	10.4518	0.438550
$569$	36.2931	1.52148	0.760742	−	0.649054i	$-0.224835\pi$
$569$	36.2931	1.52148	0.760742	+	0.649054i	$0.224835\pi$
$570$	2.11806	0.0887159
$571$	45.8110	1.91713	0.958566	−	0.284871i	$-0.0919508\pi$
$571$	45.8110	1.91713	0.958566	+	0.284871i	$0.0919508\pi$
$572$	−14.1996	−0.593716
$573$	5.49789	0.229678
$574$	0	0
$575$	3.68953	0.153864
$576$	1.00000	0.0416667
$577$	−15.8893	−0.661478	−0.330739	−	0.943722i	$-0.607298\pi$
$577$	−15.8893	−0.661478	−0.330739	+	0.943722i	$0.607298\pi$
$578$	−31.3899	−1.30565
$579$	−7.89871	−0.328259
$580$	15.4592	0.641910
$581$	0	0
$582$	−6.18070	−0.256198
$583$	5.89063	0.243965
$584$	12.7667	0.528290
$585$	−8.97238	−0.370962
$586$	24.2946	1.00360
$587$	−4.19680	−0.173220	−0.0866102	−	0.996242i	$-0.527603\pi$
$587$	−4.19680	−0.173220	−0.0866102	+	0.996242i	$0.527603\pi$
$588$	0	0
$589$	4.54883	0.187431
$590$	−27.6334	−1.13765
$591$	1.93736	0.0796923
$592$	−0.252218	−0.0103661
$593$	−24.7295	−1.01552	−0.507758	−	0.861499i	$-0.669526\pi$
$593$	−24.7295	−1.01552	−0.507758	+	0.861499i	$0.669526\pi$
$594$	3.35203	0.137536
$595$	0	0
$596$	−21.9102	−0.897478
$597$	−8.73823	−0.357632
$598$	−30.4184	−1.24390
$599$	−4.53928	−0.185470	−0.0927350	−	0.995691i	$-0.529561\pi$
$599$	−4.53928	−0.185470	−0.0927350	+	0.995691i	$0.529561\pi$
$600$	−0.513812	−0.0209763
$601$	9.37441	0.382390	0.191195	−	0.981552i	$-0.438764\pi$
$601$	9.37441	0.382390	0.191195	+	0.981552i	$0.438764\pi$
$602$	0	0
$603$	−4.30616	−0.175360
$604$	0.349200	0.0142088
$605$	0.500127	0.0203331
$606$	13.2296	0.537415
$607$	20.7608	0.842654	0.421327	−	0.906909i	$-0.361564\pi$
$607$	20.7608	0.842654	0.421327	+	0.906909i	$0.361564\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−14.6551	−0.593368
$611$	−30.3105	−1.22623
$612$	6.95628	0.281191
$613$	3.25738	0.131564	0.0657822	−	0.997834i	$-0.479046\pi$
$613$	3.25738	0.131564	0.0657822	+	0.997834i	$0.479046\pi$
$614$	−5.79365	−0.233813
$615$	21.8922	0.882777
$616$	0	0
$617$	−9.82446	−0.395518	−0.197759	−	0.980251i	$-0.563366\pi$
$617$	−9.82446	−0.395518	−0.197759	+	0.980251i	$0.563366\pi$
$618$	−7.45400	−0.299844
$619$	−13.7702	−0.553470	−0.276735	−	0.960946i	$-0.589252\pi$
$619$	−13.7702	−0.553470	−0.276735	+	0.960946i	$0.589252\pi$
$620$	9.63471	0.386939
$621$	7.18070	0.288152
$622$	−18.6786	−0.748944
$623$	0	0
$624$	4.23612	0.169581
$625$	−22.1669	−0.886678
$626$	−25.7369	−1.02865
$627$	−3.35203	−0.133867
$628$	13.0487	0.520700
$629$	−1.75450	−0.0699565
$630$	0	0
$631$	45.3832	1.80668	0.903338	−	0.428930i	$-0.141109\pi$
$631$	45.3832	1.80668	0.903338	+	0.428930i	$0.141109\pi$
$632$	−2.27114	−0.0903412
$633$	23.3870	0.929549
$634$	20.7528	0.824198
$635$	25.9030	1.02793
$636$	−1.75733	−0.0696827
$637$	0	0
$638$	−24.4657	−0.968607
$639$	−10.4518	−0.413469
$640$	−2.11806	−0.0837238
$641$	−21.0779	−0.832525	−0.416263	−	0.909244i	$-0.636660\pi$
$641$	−21.0779	−0.832525	−0.416263	+	0.909244i	$0.636660\pi$
$642$	8.60708	0.339694
$643$	28.6923	1.13151	0.565757	−	0.824572i	$-0.308584\pi$
$643$	28.6923	1.13151	0.565757	+	0.824572i	$0.308584\pi$
$644$	0	0
$645$	−6.71707	−0.264484
$646$	−6.95628	−0.273691
$647$	0.851482	0.0334752	0.0167376	−	0.999860i	$-0.494672\pi$
$647$	0.851482	0.0334752	0.0167376	+	0.999860i	$0.494672\pi$
$648$	−1.00000	−0.0392837
$649$	43.7325	1.71665
$650$	−2.17657	−0.0853721
$651$	0	0
$652$	15.4614	0.605515
$653$	−1.01471	−0.0397087	−0.0198544	−	0.999803i	$-0.506320\pi$
$653$	−1.01471	−0.0397087	−0.0198544	+	0.999803i	$0.506320\pi$
$654$	6.30746	0.246641
$655$	−2.16271	−0.0845041
$656$	−10.3359	−0.403551
$657$	−12.7667	−0.498077
$658$	0	0
$659$	10.9687	0.427279	0.213639	−	0.976913i	$-0.431468\pi$
$659$	10.9687	0.427279	0.213639	+	0.976913i	$0.431468\pi$
$660$	−7.09982	−0.276360
$661$	−20.2667	−0.788282	−0.394141	−	0.919050i	$-0.628958\pi$
$661$	−20.2667	−0.788282	−0.394141	+	0.919050i	$0.628958\pi$
$662$	35.0035	1.36045
$663$	29.4677	1.14443
$664$	−16.5699	−0.643037
$665$	0	0
$666$	0.252218	0.00977325
$667$	−52.4103	−2.02933
$668$	−4.68797	−0.181383
$669$	−9.80320	−0.379014
$670$	9.12072	0.352364
$671$	23.1931	0.895359
$672$	0	0
$673$	40.5792	1.56421	0.782107	−	0.623145i	$-0.214145\pi$
$673$	40.5792	1.56421	0.782107	+	0.623145i	$0.214145\pi$
$674$	9.06565	0.349196
$675$	0.513812	0.0197766
$676$	4.94475	0.190183
$677$	−9.11282	−0.350234	−0.175117	−	0.984548i	$-0.556030\pi$
$677$	−9.11282	−0.350234	−0.175117	+	0.984548i	$0.556030\pi$
$678$	1.97453	0.0758314
$679$	0	0
$680$	−14.7338	−0.565017
$681$	18.2835	0.700626
$682$	−15.2478	−0.583870
$683$	−4.07959	−0.156101	−0.0780505	−	0.996949i	$-0.524870\pi$
$683$	−4.07959	−0.156101	−0.0780505	+	0.996949i	$0.524870\pi$
$684$	1.00000	0.0382360
$685$	−12.9787	−0.495889
$686$	0	0
$687$	1.44463	0.0551159
$688$	3.17133	0.120906
$689$	−7.44428	−0.283604
$690$	−15.2092	−0.579004
$691$	−1.46638	−0.0557839	−0.0278920	−	0.999611i	$-0.508879\pi$
$691$	−1.46638	−0.0557839	−0.0278920	+	0.999611i	$0.508879\pi$
$692$	−21.5283	−0.818385
$693$	0	0
$694$	17.6560	0.670211
$695$	38.8615	1.47410
$696$	7.29877	0.276659
$697$	−71.8997	−2.72340
$698$	−19.9745	−0.756047
$699$	15.6808	0.593100
$700$	0	0
$701$	18.9890	0.717204	0.358602	−	0.933491i	$-0.383254\pi$
$701$	18.9890	0.717204	0.358602	+	0.933491i	$0.383254\pi$
$702$	−4.23612	−0.159882
$703$	−0.252218	−0.00951258
$704$	3.35203	0.126334
$705$	−15.1552	−0.570779
$706$	−22.5028	−0.846904
$707$	0	0
$708$	−13.0465	−0.490319
$709$	−20.6079	−0.773947	−0.386974	−	0.922091i	$-0.626480\pi$
$709$	−20.6079	−0.773947	−0.386974	+	0.922091i	$0.626480\pi$
$710$	22.1377	0.830812
$711$	2.27114	0.0851745
$712$	−3.79365	−0.142173
$713$	−32.6638	−1.22327
$714$	0	0
$715$	−30.0757	−1.12477
$716$	1.83822	0.0686976
$717$	−3.76818	−0.140725
$718$	9.83589	0.367072
$719$	5.02797	0.187512	0.0937559	−	0.995595i	$-0.470113\pi$
$719$	5.02797	0.187512	0.0937559	+	0.995595i	$0.470113\pi$
$720$	2.11806	0.0789355
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−2.99561	−0.111408
$724$	20.3848	0.757596
$725$	−3.75019	−0.139279
$726$	0.236125	0.00876342
$727$	−12.6690	−0.469866	−0.234933	−	0.972012i	$-0.575487\pi$
$727$	−12.6690	−0.469866	−0.234933	+	0.972012i	$0.575487\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	27.0407	1.00082
$731$	22.0607	0.815943
$732$	−6.91911	−0.255738
$733$	3.30832	0.122195	0.0610977	−	0.998132i	$-0.480540\pi$
$733$	3.30832	0.122195	0.0610977	+	0.998132i	$0.480540\pi$
$734$	−35.3346	−1.30422
$735$	0	0
$736$	7.18070	0.264684
$737$	−14.4344	−0.531698
$738$	10.3359	0.380471
$739$	−20.4897	−0.753726	−0.376863	−	0.926269i	$-0.622997\pi$
$739$	−20.4897	−0.753726	−0.376863	+	0.926269i	$0.622997\pi$
$740$	−0.534213	−0.0196381
$741$	4.23612	0.155618
$742$	0	0
$743$	13.7973	0.506172	0.253086	−	0.967444i	$-0.418554\pi$
$743$	13.7973	0.506172	0.253086	+	0.967444i	$0.418554\pi$
$744$	4.54883	0.166768
$745$	−46.4073	−1.70023
$746$	−33.8294	−1.23858
$747$	16.5699	0.606261
$748$	23.3177	0.852579
$749$	0	0
$750$	−11.6786	−0.426442
$751$	−8.81343	−0.321607	−0.160803	−	0.986986i	$-0.551408\pi$
$751$	−8.81343	−0.321607	−0.160803	+	0.986986i	$0.551408\pi$
$752$	7.15524	0.260925
$753$	−26.2922	−0.958142
$754$	30.9185	1.12598
$755$	0.739628	0.0269178
$756$	0	0
$757$	−16.4445	−0.597684	−0.298842	−	0.954303i	$-0.596600\pi$
$757$	−16.4445	−0.597684	−0.298842	+	0.954303i	$0.596600\pi$
$758$	−25.4999	−0.926197
$759$	24.0700	0.873684
$760$	−2.11806	−0.0768302
$761$	−27.6653	−1.00287	−0.501434	−	0.865196i	$-0.667194\pi$
$761$	−27.6653	−1.00287	−0.501434	+	0.865196i	$0.667194\pi$
$762$	12.2296	0.443031
$763$	0	0
$764$	−5.49789	−0.198907
$765$	14.7338	0.532703
$766$	−35.7186	−1.29057
$767$	−55.2668	−1.99557
$768$	−1.00000	−0.0360844
$769$	−6.46278	−0.233054	−0.116527	−	0.993188i	$-0.537176\pi$
$769$	−6.46278	−0.233054	−0.116527	+	0.993188i	$0.537176\pi$
$770$	0	0
$771$	19.7317	0.710619
$772$	7.89871	0.284281
$773$	−24.5329	−0.882387	−0.441194	−	0.897412i	$-0.645445\pi$
$773$	−24.5329	−0.882387	−0.441194	+	0.897412i	$0.645445\pi$
$774$	−3.17133	−0.113991
$775$	−2.33724	−0.0839562
$776$	6.18070	0.221874
$777$	0	0
$778$	−22.0248	−0.789626
$779$	−10.3359	−0.370323
$780$	8.97238	0.321263
$781$	−35.0349	−1.25365
$782$	49.9510	1.78624
$783$	−7.29877	−0.260837
$784$	0	0
$785$	27.6380	0.986441
$786$	−1.02108	−0.0364207
$787$	1.21281	0.0432320	0.0216160	−	0.999766i	$-0.493119\pi$
$787$	1.21281	0.0432320	0.0216160	+	0.999766i	$0.493119\pi$
$788$	−1.93736	−0.0690155
$789$	4.44247	0.158156
$790$	−4.81042	−0.171147
$791$	0	0
$792$	−3.35203	−0.119109
$793$	−29.3102	−1.04084
$794$	−19.7317	−0.700251
$795$	−3.72214	−0.132011
$796$	8.73823	0.309718
$797$	3.35867	0.118970	0.0594851	−	0.998229i	$-0.481054\pi$
$797$	3.35867	0.118970	0.0594851	+	0.998229i	$0.481054\pi$
$798$	0	0
$799$	49.7738	1.76087
$800$	0.513812	0.0181660
$801$	3.79365	0.134042
$802$	−14.8528	−0.524469
$803$	−42.7944	−1.51018
$804$	4.30616	0.151867
$805$	0	0
$806$	19.2694	0.678736
$807$	−19.4796	−0.685716
$808$	−13.2296	−0.465415
$809$	−11.8885	−0.417977	−0.208988	−	0.977918i	$-0.567017\pi$
$809$	−11.8885	−0.417977	−0.208988	+	0.977918i	$0.567017\pi$
$810$	−2.11806	−0.0744211
$811$	−27.5357	−0.966908	−0.483454	−	0.875370i	$-0.660618\pi$
$811$	−27.5357	−0.966908	−0.483454	+	0.875370i	$0.660618\pi$
$812$	0	0
$813$	−1.57578	−0.0552648
$814$	0.845443	0.0296328
$815$	32.7482	1.14712
$816$	−6.95628	−0.243519
$817$	3.17133	0.110951
$818$	−6.03632	−0.211055
$819$	0	0
$820$	−21.8922	−0.764508
$821$	38.6740	1.34973	0.674867	−	0.737940i	$-0.264201\pi$
$821$	38.6740	1.34973	0.674867	+	0.737940i	$0.264201\pi$
$822$	−6.12761	−0.213725
$823$	35.1566	1.22548	0.612741	−	0.790284i	$-0.290067\pi$
$823$	35.1566	1.22548	0.612741	+	0.790284i	$0.290067\pi$
$824$	7.45400	0.259672
$825$	1.72231	0.0599633
$826$	0	0
$827$	0.861710	0.0299646	0.0149823	−	0.999888i	$-0.495231\pi$
$827$	0.861710	0.0299646	0.0149823	+	0.999888i	$0.495231\pi$
$828$	−7.18070	−0.249547
$829$	3.85131	0.133761	0.0668807	−	0.997761i	$-0.478695\pi$
$829$	3.85131	0.133761	0.0668807	+	0.997761i	$0.478695\pi$
$830$	−35.0961	−1.21820
$831$	−9.80612	−0.340170
$832$	−4.23612	−0.146861
$833$	0	0
$834$	18.3476	0.635327
$835$	−9.92942	−0.343622
$836$	3.35203	0.115932
$837$	−4.54883	−0.157231
$838$	−14.1370	−0.488354
$839$	−14.4709	−0.499593	−0.249796	−	0.968298i	$-0.580364\pi$
$839$	−14.4709	−0.499593	−0.249796	+	0.968298i	$0.580364\pi$
$840$	0	0
$841$	24.2720	0.836965
$842$	35.7565	1.23225
$843$	3.60641	0.124211
$844$	−23.3870	−0.805013
$845$	10.4733	0.360292
$846$	−7.15524	−0.246002
$847$	0	0
$848$	1.75733	0.0603470
$849$	21.5327	0.739002
$850$	3.57422	0.122595
$851$	1.81110	0.0620838
$852$	10.4518	0.358074
$853$	−22.3323	−0.764642	−0.382321	−	0.924030i	$-0.624875\pi$
$853$	−22.3323	−0.764642	−0.382321	+	0.924030i	$0.624875\pi$
$854$	0	0
$855$	2.11806	0.0724362
$856$	−8.60708	−0.294184
$857$	−31.6095	−1.07976	−0.539879	−	0.841742i	$-0.681530\pi$
$857$	−31.6095	−1.07976	−0.539879	+	0.841742i	$0.681530\pi$
$858$	−14.1996	−0.484767
$859$	23.7120	0.809042	0.404521	−	0.914529i	$-0.367438\pi$
$859$	23.7120	0.809042	0.404521	+	0.914529i	$0.367438\pi$
$860$	6.71707	0.229050
$861$	0	0
$862$	−17.4242	−0.593471
$863$	−27.9287	−0.950703	−0.475351	−	0.879796i	$-0.657679\pi$
$863$	−27.9287	−0.950703	−0.475351	+	0.879796i	$0.657679\pi$
$864$	1.00000	0.0340207
$865$	−45.5984	−1.55039
$866$	0.745628	0.0253375
$867$	−31.3899	−1.06606
$868$	0	0
$869$	7.61295	0.258252
$870$	15.4592	0.524117
$871$	18.2414	0.618088
$872$	−6.30746	−0.213598
$873$	−6.18070	−0.209185
$874$	7.18070	0.242891
$875$	0	0
$876$	12.7667	0.431347
$877$	−12.2884	−0.414949	−0.207474	−	0.978240i	$-0.566524\pi$
$877$	−12.2884	−0.414949	−0.207474	+	0.978240i	$0.566524\pi$
$878$	−11.7289	−0.395830
$879$	24.2946	0.819435
$880$	7.09982	0.239335
$881$	−20.8380	−0.702049	−0.351024	−	0.936366i	$-0.614167\pi$
$881$	−20.8380	−0.702049	−0.351024	+	0.936366i	$0.614167\pi$
$882$	0	0
$883$	−43.9662	−1.47958	−0.739790	−	0.672838i	$-0.765075\pi$
$883$	−43.9662	−1.47958	−0.739790	+	0.672838i	$0.765075\pi$
$884$	−29.4677	−0.991106
$885$	−27.6334	−0.928887
$886$	−6.95611	−0.233695
$887$	0.211414	0.00709860	0.00354930	−	0.999994i	$-0.498870\pi$
$887$	0.211414	0.00709860	0.00354930	+	0.999994i	$0.498870\pi$
$888$	−0.252218	−0.00846388
$889$	0	0
$890$	−8.03519	−0.269340
$891$	3.35203	0.112297
$892$	9.80320	0.328236
$893$	7.15524	0.239441
$894$	−21.9102	−0.732788
$895$	3.89347	0.130144
$896$	0	0
$897$	−30.4184	−1.01564
$898$	27.5823	0.920433
$899$	33.2009	1.10731
$900$	−0.513812	−0.0171271
$901$	12.2245	0.407257
$902$	34.6464	1.15360
$903$	0	0
$904$	−1.97453	−0.0656719
$905$	43.1763	1.43523
$906$	0.349200	0.0116014
$907$	29.9876	0.995722	0.497861	−	0.867257i	$-0.334119\pi$
$907$	29.9876	0.995722	0.497861	+	0.867257i	$0.334119\pi$
$908$	−18.2835	−0.606760
$909$	13.2296	0.438798
$910$	0	0
$911$	36.8337	1.22035	0.610177	−	0.792265i	$-0.291098\pi$
$911$	36.8337	1.22035	0.610177	+	0.792265i	$0.291098\pi$
$912$	−1.00000	−0.0331133
$913$	55.5429	1.83820
$914$	−20.7733	−0.687118
$915$	−14.6551	−0.484483
$916$	−1.44463	−0.0477318
$917$	0	0
$918$	6.95628	0.229592
$919$	20.6736	0.681959	0.340980	−	0.940071i	$-0.389241\pi$
$919$	20.6736	0.681959	0.340980	+	0.940071i	$0.389241\pi$
$920$	15.2092	0.501432
$921$	−5.79365	−0.190907
$922$	−33.6610	−1.10857
$923$	44.2753	1.45734
$924$	0	0
$925$	0.129592	0.00426097
$926$	18.4933	0.607729
$927$	−7.45400	−0.244822
$928$	−7.29877	−0.239594
$929$	−52.4833	−1.72192	−0.860960	−	0.508673i	$-0.830136\pi$
$929$	−52.4833	−1.72192	−0.860960	+	0.508673i	$0.830136\pi$
$930$	9.63471	0.315934
$931$	0	0
$932$	−15.6808	−0.513640
$933$	−18.6786	−0.611510
$934$	13.4329	0.439539
$935$	49.3883	1.61517
$936$	4.23612	0.138462
$937$	8.21848	0.268486	0.134243	−	0.990948i	$-0.457140\pi$
$937$	8.21848	0.268486	0.134243	+	0.990948i	$0.457140\pi$
$938$	0	0
$939$	−25.7369	−0.839890
$940$	15.1552	0.494309
$941$	21.0823	0.687265	0.343632	−	0.939104i	$-0.388343\pi$
$941$	21.0823	0.687265	0.343632	+	0.939104i	$0.388343\pi$
$942$	13.0487	0.425150
$943$	74.2193	2.41691
$944$	13.0465	0.424629
$945$	0	0
$946$	−10.6304	−0.345624
$947$	54.1725	1.76037	0.880185	−	0.474631i	$-0.157418\pi$
$947$	54.1725	1.76037	0.880185	+	0.474631i	$0.157418\pi$
$948$	−2.27114	−0.0737633
$949$	54.0814	1.75556
$950$	0.513812	0.0166702
$951$	20.7528	0.672955
$952$	0	0
$953$	21.4081	0.693477	0.346739	−	0.937962i	$-0.387289\pi$
$953$	21.4081	0.693477	0.346739	+	0.937962i	$0.387289\pi$
$954$	−1.75733	−0.0568957
$955$	−11.6449	−0.376819
$956$	3.76818	0.121872
$957$	−24.4657	−0.790864
$958$	4.05893	0.131138
$959$	0	0
$960$	−2.11806	−0.0683602
$961$	−10.3081	−0.332521
$962$	−1.06843	−0.0344475
$963$	8.60708	0.277359
$964$	2.99561	0.0964821
$965$	16.7300	0.538556
$966$	0	0
$967$	41.4314	1.33234	0.666171	−	0.745799i	$-0.267932\pi$
$967$	41.4314	1.33234	0.666171	+	0.745799i	$0.267932\pi$
$968$	−0.236125	−0.00758934
$969$	−6.95628	−0.223468
$970$	13.0911	0.420330
$971$	17.7463	0.569506	0.284753	−	0.958601i	$-0.408088\pi$
$971$	17.7463	0.569506	0.284753	+	0.958601i	$0.408088\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−37.5078	−1.20183
$975$	−2.17657	−0.0697060
$976$	6.91911	0.221475
$977$	−32.7975	−1.04929	−0.524643	−	0.851323i	$-0.675801\pi$
$977$	−32.7975	−1.04929	−0.524643	+	0.851323i	$0.675801\pi$
$978$	15.4614	0.494401
$979$	12.7164	0.406419
$980$	0	0
$981$	6.30746	0.201382
$982$	27.2230	0.868722
$983$	−20.0570	−0.639717	−0.319859	−	0.947465i	$-0.603635\pi$
$983$	−20.0570	−0.639717	−0.319859	+	0.947465i	$0.603635\pi$
$984$	−10.3359	−0.329498
$985$	−4.10345	−0.130747
$986$	−50.7723	−1.61692
$987$	0	0
$988$	−4.23612	−0.134769
$989$	−22.7724	−0.724119
$990$	−7.09982	−0.225647
$991$	20.3566	0.646648	0.323324	−	0.946288i	$-0.395200\pi$
$991$	20.3566	0.646648	0.323324	+	0.946288i	$0.395200\pi$
$992$	−4.54883	−0.144426
$993$	35.0035	1.11080
$994$	0	0
$995$	18.5081	0.586747
$996$	−16.5699	−0.525038
$997$	0.263842	0.00835596	0.00417798	−	0.999991i	$-0.498670\pi$
$997$	0.263842	0.00835596	0.00417798	+	0.999991i	$0.498670\pi$
$998$	−6.93651	−0.219571
$999$	0.252218	0.00797982

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bw.1.3		4
7.2	even	3		798.2.j.l.571.2	yes	8
7.4	even	3		798.2.j.l.457.2	✓	8
7.6	odd	2		5586.2.a.bz.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.2	✓	8	7.4	even	3
798.2.j.l.571.2	yes	8	7.2	even	3
5586.2.a.bw.1.3		4	1.1	even	1	trivial
5586.2.a.bz.1.2		4	7.6	odd	2

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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.11806 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.11806 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -2.11806 q^{10} +3.35203 q^{11} -1.00000 q^{12} -4.23612 q^{13} -2.11806 q^{15} +1.00000 q^{16} +6.95628 q^{17} -1.00000 q^{18} +1.00000 q^{19} +2.11806 q^{20} -3.35203 q^{22} -7.18070 q^{23} +1.00000 q^{24} -0.513812 q^{25} +4.23612 q^{26} -1.00000 q^{27} +7.29877 q^{29} +2.11806 q^{30} +4.54883 q^{31} -1.00000 q^{32} -3.35203 q^{33} -6.95628 q^{34} +1.00000 q^{36} -0.252218 q^{37} -1.00000 q^{38} +4.23612 q^{39} -2.11806 q^{40} -10.3359 q^{41} +3.17133 q^{43} +3.35203 q^{44} +2.11806 q^{45} +7.18070 q^{46} +7.15524 q^{47} -1.00000 q^{48} +0.513812 q^{50} -6.95628 q^{51} -4.23612 q^{52} +1.75733 q^{53} +1.00000 q^{54} +7.09982 q^{55} -1.00000 q^{57} -7.29877 q^{58} +13.0465 q^{59} -2.11806 q^{60} +6.91911 q^{61} -4.54883 q^{62} +1.00000 q^{64} -8.97238 q^{65} +3.35203 q^{66} -4.30616 q^{67} +6.95628 q^{68} +7.18070 q^{69} -10.4518 q^{71} -1.00000 q^{72} -12.7667 q^{73} +0.252218 q^{74} +0.513812 q^{75} +1.00000 q^{76} -4.23612 q^{78} +2.27114 q^{79} +2.11806 q^{80} +1.00000 q^{81} +10.3359 q^{82} +16.5699 q^{83} +14.7338 q^{85} -3.17133 q^{86} -7.29877 q^{87} -3.35203 q^{88} +3.79365 q^{89} -2.11806 q^{90} -7.18070 q^{92} -4.54883 q^{93} -7.15524 q^{94} +2.11806 q^{95} +1.00000 q^{96} -6.18070 q^{97} +3.35203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} - 4 q^{12} + 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} + 2 q^{22} - 5 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{27} - 3 q^{29} + 9 q^{31} - 4 q^{32} + 2 q^{33} - 10 q^{34} + 4 q^{36} - 14 q^{37} - 4 q^{38} + 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} + 7 q^{47} - 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} + 4 q^{54} - 4 q^{57} + 3 q^{58} + 7 q^{59} + 23 q^{61} - 9 q^{62} + 4 q^{64} - 48 q^{65} - 2 q^{66} + 6 q^{67} + 10 q^{68} + 5 q^{69} + 2 q^{71} - 4 q^{72} - 5 q^{73} + 14 q^{74} - 4 q^{75} + 4 q^{76} - 11 q^{79} + 4 q^{81} - 4 q^{82} + 14 q^{83} + 6 q^{85} - 21 q^{86} + 3 q^{87} + 2 q^{88} + 10 q^{89} - 5 q^{92} - 9 q^{93} - 7 q^{94} + 4 q^{96} - q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 - 4 * q^12 + 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 + 2 * q^22 - 5 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^27 - 3 * q^29 + 9 * q^31 - 4 * q^32 + 2 * q^33 - 10 * q^34 + 4 * q^36 - 14 * q^37 - 4 * q^38 + 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 + 7 * q^47 - 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 + 4 * q^54 - 4 * q^57 + 3 * q^58 + 7 * q^59 + 23 * q^61 - 9 * q^62 + 4 * q^64 - 48 * q^65 - 2 * q^66 + 6 * q^67 + 10 * q^68 + 5 * q^69 + 2 * q^71 - 4 * q^72 - 5 * q^73 + 14 * q^74 - 4 * q^75 + 4 * q^76 - 11 * q^79 + 4 * q^81 - 4 * q^82 + 14 * q^83 + 6 * q^85 - 21 * q^86 + 3 * q^87 + 2 * q^88 + 10 * q^89 - 5 * q^92 - 9 * q^93 - 7 * q^94 + 4 * q^96 - q^97 - 2 * q^99

Introduction

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