LMFDB - Embedded newform 5586.2.a.bz.1.1

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:	$1$
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			1.1
Root			$1.83719$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.49248 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.49248 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.49248 q^{10} -3.46193 q^{11} +1.00000 q^{12} +4.98496 q^{13} -2.49248 q^{15} +1.00000 q^{16} -2.24299 q^{17} -1.00000 q^{18} -1.00000 q^{19} -2.49248 q^{20} +3.46193 q^{22} +6.00404 q^{23} -1.00000 q^{24} +1.21245 q^{25} -4.98496 q^{26} +1.00000 q^{27} -5.51156 q^{29} +2.49248 q^{30} +7.28407 q^{31} -1.00000 q^{32} -3.46193 q^{33} +2.24299 q^{34} +1.00000 q^{36} -9.16685 q^{37} +1.00000 q^{38} +4.98496 q^{39} +2.49248 q^{40} -4.64383 q^{41} +9.54211 q^{43} -3.46193 q^{44} -2.49248 q^{45} -6.00404 q^{46} -5.36021 q^{47} +1.00000 q^{48} -1.21245 q^{50} -2.24299 q^{51} +4.98496 q^{52} -5.87423 q^{53} -1.00000 q^{54} +8.62878 q^{55} -1.00000 q^{57} +5.51156 q^{58} +8.67842 q^{59} -2.49248 q^{60} -4.37526 q^{61} -7.28407 q^{62} +1.00000 q^{64} -12.4249 q^{65} +3.46193 q^{66} +15.1583 q^{67} -2.24299 q^{68} +6.00404 q^{69} +12.0907 q^{71} -1.00000 q^{72} -14.4204 q^{73} +9.16685 q^{74} +1.21245 q^{75} -1.00000 q^{76} -4.98496 q^{78} -7.08667 q^{79} -2.49248 q^{80} +1.00000 q^{81} +4.64383 q^{82} +5.59823 q^{83} +5.59061 q^{85} -9.54211 q^{86} -5.51156 q^{87} +3.46193 q^{88} -7.52952 q^{89} +2.49248 q^{90} +6.00404 q^{92} +7.28407 q^{93} +5.36021 q^{94} +2.49248 q^{95} -1.00000 q^{96} -7.00404 q^{97} -3.46193 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.49248	−1.11467	−0.557335	−	0.830288i	$-0.688176\pi$
$5$	−2.49248	−1.11467	−0.557335	+	0.830288i	$0.688176\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.49248	0.788191
$11$	−3.46193	−1.04381	−0.521906	−	0.853003i	$-0.674779\pi$
$11$	−3.46193	−1.04381	−0.521906	+	0.853003i	$0.674779\pi$
$12$	1.00000	0.288675
$13$	4.98496	1.38258	0.691289	−	0.722578i	$-0.257043\pi$
$13$	4.98496	1.38258	0.691289	+	0.722578i	$0.257043\pi$
$14$	0	0
$15$	−2.49248	−0.643555
$16$	1.00000	0.250000
$17$	−2.24299	−0.544006	−0.272003	−	0.962296i	$-0.587686\pi$
$17$	−2.24299	−0.544006	−0.272003	+	0.962296i	$0.587686\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.49248	−0.557335
$21$	0	0
$22$	3.46193	0.738086
$23$	6.00404	1.25193	0.625964	−	0.779852i	$-0.284705\pi$
$23$	6.00404	1.25193	0.625964	+	0.779852i	$0.284705\pi$
$24$	−1.00000	−0.204124
$25$	1.21245	0.242489
$26$	−4.98496	−0.977630
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.51156	−1.02347	−0.511736	−	0.859143i	$-0.670997\pi$
$29$	−5.51156	−1.02347	−0.511736	+	0.859143i	$0.670997\pi$
$30$	2.49248	0.455062
$31$	7.28407	1.30826	0.654129	−	0.756383i	$-0.273035\pi$
$31$	7.28407	1.30826	0.654129	+	0.756383i	$0.273035\pi$
$32$	−1.00000	−0.176777
$33$	−3.46193	−0.602645
$34$	2.24299	0.384670
$35$	0	0
$36$	1.00000	0.166667
$37$	−9.16685	−1.50702	−0.753511	−	0.657436i	$-0.771641\pi$
$37$	−9.16685	−1.50702	−0.753511	+	0.657436i	$0.771641\pi$
$38$	1.00000	0.162221
$39$	4.98496	0.798232
$40$	2.49248	0.394095
$41$	−4.64383	−0.725244	−0.362622	−	0.931936i	$-0.618118\pi$
$41$	−4.64383	−0.725244	−0.362622	+	0.931936i	$0.618118\pi$
$42$	0	0
$43$	9.54211	1.45516	0.727579	−	0.686024i	$-0.240645\pi$
$43$	9.54211	1.45516	0.727579	+	0.686024i	$0.240645\pi$
$44$	−3.46193	−0.521906
$45$	−2.49248	−0.371557
$46$	−6.00404	−0.885247
$47$	−5.36021	−0.781868	−0.390934	−	0.920419i	$-0.627848\pi$
$47$	−5.36021	−0.781868	−0.390934	+	0.920419i	$0.627848\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−1.21245	−0.171466
$51$	−2.24299	−0.314082
$52$	4.98496	0.691289
$53$	−5.87423	−0.806887	−0.403443	−	0.915005i	$-0.632187\pi$
$53$	−5.87423	−0.806887	−0.403443	+	0.915005i	$0.632187\pi$
$54$	−1.00000	−0.136083
$55$	8.62878	1.16350
$56$	0	0
$57$	−1.00000	−0.132453
$58$	5.51156	0.723704
$59$	8.67842	1.12983	0.564917	−	0.825148i	$-0.308908\pi$
$59$	8.67842	1.12983	0.564917	+	0.825148i	$0.308908\pi$
$60$	−2.49248	−0.321778
$61$	−4.37526	−0.560194	−0.280097	−	0.959972i	$-0.590367\pi$
$61$	−4.37526	−0.560194	−0.280097	+	0.959972i	$0.590367\pi$
$62$	−7.28407	−0.925078
$63$	0	0
$64$	1.00000	0.125000
$65$	−12.4249	−1.54112
$66$	3.46193	0.426134
$67$	15.1583	1.85188	0.925940	−	0.377670i	$-0.123274\pi$
$67$	15.1583	1.85188	0.925940	+	0.377670i	$0.123274\pi$
$68$	−2.24299	−0.272003
$69$	6.00404	0.722802
$70$	0	0
$71$	12.0907	1.43490	0.717452	−	0.696608i	$-0.245308\pi$
$71$	12.0907	1.43490	0.717452	+	0.696608i	$0.245308\pi$
$72$	−1.00000	−0.117851
$73$	−14.4204	−1.68778	−0.843889	−	0.536518i	$-0.819739\pi$
$73$	−14.4204	−1.68778	−0.843889	+	0.536518i	$0.819739\pi$
$74$	9.16685	1.06563
$75$	1.21245	0.140001
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−4.98496	−0.564435
$79$	−7.08667	−0.797313	−0.398656	−	0.917100i	$-0.630523\pi$
$79$	−7.08667	−0.797313	−0.398656	+	0.917100i	$0.630523\pi$
$80$	−2.49248	−0.278667
$81$	1.00000	0.111111
$82$	4.64383	0.512825
$83$	5.59823	0.614486	0.307243	−	0.951631i	$-0.400594\pi$
$83$	5.59823	0.614486	0.307243	+	0.951631i	$0.400594\pi$
$84$	0	0
$85$	5.59061	0.606387
$86$	−9.54211	−1.02895
$87$	−5.51156	−0.590902
$88$	3.46193	0.369043
$89$	−7.52952	−0.798127	−0.399064	−	0.916923i	$-0.630665\pi$
$89$	−7.52952	−0.798127	−0.399064	+	0.916923i	$0.630665\pi$
$90$	2.49248	0.262730
$91$	0	0
$92$	6.00404	0.625964
$93$	7.28407	0.755323
$94$	5.36021	0.552864
$95$	2.49248	0.255723
$96$	−1.00000	−0.102062
$97$	−7.00404	−0.711153	−0.355576	−	0.934647i	$-0.615715\pi$
$97$	−7.00404	−0.711153	−0.355576	+	0.934647i	$0.615715\pi$
$98$	0	0
$99$	−3.46193	−0.347937
$100$	1.21245	0.121245
$101$	−7.09569	−0.706047	−0.353024	−	0.935614i	$-0.614846\pi$
$101$	−7.09569	−0.706047	−0.353024	+	0.935614i	$0.614846\pi$
$102$	2.24299	0.222089
$103$	−7.15135	−0.704643	−0.352322	−	0.935879i	$-0.614608\pi$
$103$	−7.15135	−0.704643	−0.352322	+	0.935879i	$0.614608\pi$
$104$	−4.98496	−0.488815
$105$	0	0
$106$	5.87423	0.570555
$107$	−15.7305	−1.52072	−0.760362	−	0.649499i	$-0.774979\pi$
$107$	−15.7305	−1.52072	−0.760362	+	0.649499i	$0.774979\pi$
$108$	1.00000	0.0962250
$109$	8.31707	0.796631	0.398315	−	0.917249i	$-0.369595\pi$
$109$	8.31707	0.796631	0.398315	+	0.917249i	$0.369595\pi$
$110$	−8.62878	−0.822722
$111$	−9.16685	−0.870079
$112$	0	0
$113$	13.3643	1.25720	0.628602	−	0.777727i	$-0.283628\pi$
$113$	13.3643	1.25720	0.628602	+	0.777727i	$0.283628\pi$
$114$	1.00000	0.0936586
$115$	−14.9649	−1.39549
$116$	−5.51156	−0.511736
$117$	4.98496	0.460859
$118$	−8.67842	−0.798913
$119$	0	0
$120$	2.49248	0.227531
$121$	0.984956	0.0895414
$122$	4.37526	0.396117
$123$	−4.64383	−0.418720
$124$	7.28407	0.654129
$125$	9.44040	0.844375
$126$	0	0
$127$	6.09569	0.540905	0.270452	−	0.962733i	$-0.412827\pi$
$127$	6.09569	0.540905	0.270452	+	0.962733i	$0.412827\pi$
$128$	−1.00000	−0.0883883
$129$	9.54211	0.840136
$130$	12.4249	1.08974
$131$	−9.31416	−0.813782	−0.406891	−	0.913477i	$-0.633387\pi$
$131$	−9.31416	−0.813782	−0.406891	+	0.913477i	$0.633387\pi$
$132$	−3.46193	−0.301322
$133$	0	0
$134$	−15.1583	−1.30948
$135$	−2.49248	−0.214518
$136$	2.24299	0.192335
$137$	−7.78510	−0.665126	−0.332563	−	0.943081i	$-0.607913\pi$
$137$	−7.78510	−0.665126	−0.332563	+	0.943081i	$0.607913\pi$
$138$	−6.00404	−0.511098
$139$	−12.5882	−1.06771	−0.533857	−	0.845575i	$-0.679258\pi$
$139$	−12.5882	−1.06771	−0.533857	+	0.845575i	$0.679258\pi$
$140$	0	0
$141$	−5.36021	−0.451411
$142$	−12.0907	−1.01463
$143$	−17.2576	−1.44315
$144$	1.00000	0.0833333
$145$	13.7374	1.14083
$146$	14.4204	1.19344
$147$	0	0
$148$	−9.16685	−0.753511
$149$	16.2922	1.33471	0.667353	−	0.744742i	$-0.267427\pi$
$149$	16.2922	1.33471	0.667353	+	0.744742i	$0.267427\pi$
$150$	−1.21245	−0.0989958
$151$	19.9735	1.62542	0.812710	−	0.582669i	$-0.197991\pi$
$151$	19.9735	1.62542	0.812710	+	0.582669i	$0.197991\pi$
$152$	1.00000	0.0811107
$153$	−2.24299	−0.181335
$154$	0	0
$155$	−18.1554	−1.45828
$156$	4.98496	0.399116
$157$	0.739053	0.0589828	0.0294914	−	0.999565i	$-0.490611\pi$
$157$	0.739053	0.0589828	0.0294914	+	0.999565i	$0.490611\pi$
$158$	7.08667	0.563785
$159$	−5.87423	−0.465856
$160$	2.49248	0.197048
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−5.79808	−0.454141	−0.227071	−	0.973878i	$-0.572915\pi$
$163$	−5.79808	−0.454141	−0.227071	+	0.973878i	$0.572915\pi$
$164$	−4.64383	−0.362622
$165$	8.62878	0.671750
$166$	−5.59823	−0.434507
$167$	−17.1058	−1.32368	−0.661842	−	0.749644i	$-0.730225\pi$
$167$	−17.1058	−1.32368	−0.661842	+	0.749644i	$0.730225\pi$
$168$	0	0
$169$	11.8498	0.911522
$170$	−5.59061	−0.428780
$171$	−1.00000	−0.0764719
$172$	9.54211	0.727579
$173$	2.58412	0.196467	0.0982336	−	0.995163i	$-0.468681\pi$
$173$	2.58412	0.196467	0.0982336	+	0.995163i	$0.468681\pi$
$174$	5.51156	0.417830
$175$	0	0
$176$	−3.46193	−0.260953
$177$	8.67842	0.652310
$178$	7.52952	0.564361
$179$	−3.24948	−0.242878	−0.121439	−	0.992599i	$-0.538751\pi$
$179$	−3.24948	−0.242878	−0.121439	+	0.992599i	$0.538751\pi$
$180$	−2.49248	−0.185778
$181$	−12.4559	−0.925840	−0.462920	−	0.886400i	$-0.653198\pi$
$181$	−12.4559	−0.925840	−0.462920	+	0.886400i	$0.653198\pi$
$182$	0	0
$183$	−4.37526	−0.323428
$184$	−6.00404	−0.442624
$185$	22.8482	1.67983
$186$	−7.28407	−0.534094
$187$	7.76509	0.567839
$188$	−5.36021	−0.390934
$189$	0	0
$190$	−2.49248	−0.180823
$191$	−16.4444	−1.18988	−0.594939	−	0.803771i	$-0.702824\pi$
$191$	−16.4444	−1.18988	−0.594939	+	0.803771i	$0.702824\pi$
$192$	1.00000	0.0721688
$193$	−18.6854	−1.34500	−0.672501	−	0.740096i	$-0.734780\pi$
$193$	−18.6854	−1.34500	−0.672501	+	0.740096i	$0.734780\pi$
$194$	7.00404	0.502861
$195$	−12.4249	−0.889765
$196$	0	0
$197$	−15.4965	−1.10408	−0.552041	−	0.833817i	$-0.686151\pi$
$197$	−15.4965	−1.10408	−0.552041	+	0.833817i	$0.686151\pi$
$198$	3.46193	0.246029
$199$	1.45948	0.103460	0.0517299	−	0.998661i	$-0.483527\pi$
$199$	1.45948	0.103460	0.0517299	+	0.998661i	$0.483527\pi$
$200$	−1.21245	−0.0857329
$201$	15.1583	1.06918
$202$	7.09569	0.499251
$203$	0	0
$204$	−2.24299	−0.157041
$205$	11.5746	0.808408
$206$	7.15135	0.498258
$207$	6.00404	0.417310
$208$	4.98496	0.345644
$209$	3.46193	0.239467
$210$	0	0
$211$	−23.3953	−1.61060	−0.805298	−	0.592870i	$-0.797995\pi$
$211$	−23.3953	−1.61060	−0.805298	+	0.592870i	$0.797995\pi$
$212$	−5.87423	−0.403443
$213$	12.0907	0.828442
$214$	15.7305	1.07531
$215$	−23.7835	−1.62202
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−8.31707	−0.563303
$219$	−14.4204	−0.974439
$220$	8.62878	0.581752
$221$	−11.1812	−0.752131
$222$	9.16685	0.615239
$223$	−14.8221	−0.992564	−0.496282	−	0.868161i	$-0.665302\pi$
$223$	−14.8221	−0.992564	−0.496282	+	0.868161i	$0.665302\pi$
$224$	0	0
$225$	1.21245	0.0808297
$226$	−13.3643	−0.888977
$227$	−16.2295	−1.07719	−0.538594	−	0.842566i	$-0.681044\pi$
$227$	−16.2295	−1.07719	−0.538594	+	0.842566i	$0.681044\pi$
$228$	−1.00000	−0.0662266
$229$	6.39480	0.422580	0.211290	−	0.977423i	$-0.432233\pi$
$229$	6.39480	0.422580	0.211290	+	0.977423i	$0.432233\pi$
$230$	14.9649	0.986759
$231$	0	0
$232$	5.51156	0.361852
$233$	−21.3798	−1.40063	−0.700317	−	0.713832i	$-0.746958\pi$
$233$	−21.3798	−1.40063	−0.700317	+	0.713832i	$0.746958\pi$
$234$	−4.98496	−0.325877
$235$	13.3602	0.871524
$236$	8.67842	0.564917
$237$	−7.08667	−0.460329
$238$	0	0
$239$	18.8938	1.22214	0.611068	−	0.791578i	$-0.290740\pi$
$239$	18.8938	1.22214	0.611068	+	0.791578i	$0.290740\pi$
$240$	−2.49248	−0.160889
$241$	−4.05009	−0.260889	−0.130445	−	0.991456i	$-0.541641\pi$
$241$	−4.05009	−0.260889	−0.130445	+	0.991456i	$0.541641\pi$
$242$	−0.984956	−0.0633153
$243$	1.00000	0.0641500
$244$	−4.37526	−0.280097
$245$	0	0
$246$	4.64383	0.296080
$247$	−4.98496	−0.317185
$248$	−7.28407	−0.462539
$249$	5.59823	0.354774
$250$	−9.44040	−0.597063
$251$	−6.59917	−0.416536	−0.208268	−	0.978072i	$-0.566783\pi$
$251$	−6.59917	−0.416536	−0.208268	+	0.978072i	$0.566783\pi$
$252$	0	0
$253$	−20.7856	−1.30678
$254$	−6.09569	−0.382477
$255$	5.59061	0.350098
$256$	1.00000	0.0625000
$257$	2.65125	0.165380	0.0826902	−	0.996575i	$-0.473649\pi$
$257$	2.65125	0.165380	0.0826902	+	0.996575i	$0.473649\pi$
$258$	−9.54211	−0.594066
$259$	0	0
$260$	−12.4249	−0.770559
$261$	−5.51156	−0.341157
$262$	9.31416	0.575431
$263$	−1.45544	−0.0897463	−0.0448731	−	0.998993i	$-0.514288\pi$
$263$	−1.45544	−0.0897463	−0.0448731	+	0.998993i	$0.514288\pi$
$264$	3.46193	0.213067
$265$	14.6414	0.899413
$266$	0	0
$267$	−7.52952	−0.460799
$268$	15.1583	0.925940
$269$	−14.3232	−0.873299	−0.436650	−	0.899632i	$-0.643835\pi$
$269$	−14.3232	−0.873299	−0.436650	+	0.899632i	$0.643835\pi$
$270$	2.49248	0.151687
$271$	−20.6658	−1.25536	−0.627680	−	0.778472i	$-0.715995\pi$
$271$	−20.6658	−1.25536	−0.627680	+	0.778472i	$0.715995\pi$
$272$	−2.24299	−0.136001
$273$	0	0
$274$	7.78510	0.470315
$275$	−4.19740	−0.253113
$276$	6.00404	0.361401
$277$	−28.5421	−1.71493	−0.857464	−	0.514544i	$-0.827961\pi$
$277$	−28.5421	−1.71493	−0.857464	+	0.514544i	$0.827961\pi$
$278$	12.5882	0.754988
$279$	7.28407	0.436086
$280$	0	0
$281$	−13.6443	−0.813950	−0.406975	−	0.913439i	$-0.633416\pi$
$281$	−13.6443	−0.813950	−0.406975	+	0.913439i	$0.633416\pi$
$282$	5.36021	0.319196
$283$	1.53403	0.0911886	0.0455943	−	0.998960i	$-0.485482\pi$
$283$	1.53403	0.0911886	0.0455943	+	0.998960i	$0.485482\pi$
$284$	12.0907	0.717452
$285$	2.49248	0.147642
$286$	17.2576	1.02046
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−11.9690	−0.704058
$290$	−13.7374	−0.806691
$291$	−7.00404	−0.410584
$292$	−14.4204	−0.843889
$293$	33.3773	1.94992	0.974962	−	0.222373i	$-0.0713804\pi$
$293$	33.3773	1.94992	0.974962	+	0.222373i	$0.0713804\pi$
$294$	0	0
$295$	−21.6308	−1.25939
$296$	9.16685	0.532813
$297$	−3.46193	−0.200882
$298$	−16.2922	−0.943779
$299$	29.9299	1.73089
$300$	1.21245	0.0700006
$301$	0	0
$302$	−19.9735	−1.14935
$303$	−7.09569	−0.407636
$304$	−1.00000	−0.0573539
$305$	10.9052	0.624432
$306$	2.24299	0.128223
$307$	−9.52952	−0.543878	−0.271939	−	0.962314i	$-0.587665\pi$
$307$	−9.52952	−0.543878	−0.271939	+	0.962314i	$0.587665\pi$
$308$	0	0
$309$	−7.15135	−0.406826
$310$	18.1554	1.03116
$311$	−16.4404	−0.932249	−0.466125	−	0.884719i	$-0.654350\pi$
$311$	−16.4404	−0.932249	−0.466125	+	0.884719i	$0.654350\pi$
$312$	−4.98496	−0.282218
$313$	−10.9940	−0.621416	−0.310708	−	0.950505i	$-0.600566\pi$
$313$	−10.9940	−0.621416	−0.310708	+	0.950505i	$0.600566\pi$
$314$	−0.739053	−0.0417072
$315$	0	0
$316$	−7.08667	−0.398656
$317$	6.66291	0.374226	0.187113	−	0.982338i	$-0.440087\pi$
$317$	6.66291	0.374226	0.187113	+	0.982338i	$0.440087\pi$
$318$	5.87423	0.329410
$319$	19.0806	1.06831
$320$	−2.49248	−0.139334
$321$	−15.7305	−0.877991
$322$	0	0
$323$	2.24299	0.124804
$324$	1.00000	0.0555556
$325$	6.04399	0.335260
$326$	5.79808	0.321126
$327$	8.31707	0.459935
$328$	4.64383	0.256412
$329$	0	0
$330$	−8.62878	−0.474999
$331$	25.8102	1.41866	0.709329	−	0.704878i	$-0.248998\pi$
$331$	25.8102	1.41866	0.709329	+	0.704878i	$0.248998\pi$
$332$	5.59823	0.307243
$333$	−9.16685	−0.502340
$334$	17.1058	0.935985
$335$	−37.7817	−2.06424
$336$	0	0
$337$	10.0932	0.549810	0.274905	−	0.961471i	$-0.411354\pi$
$337$	10.0932	0.549810	0.274905	+	0.961471i	$0.411354\pi$
$338$	−11.8498	−0.644543
$339$	13.3643	0.725847
$340$	5.59061	0.303194
$341$	−25.2169	−1.36557
$342$	1.00000	0.0540738
$343$	0	0
$344$	−9.54211	−0.514476
$345$	−14.9649	−0.805685
$346$	−2.58412	−0.138923
$347$	−0.369228	−0.0198212	−0.00991059	−	0.999951i	$-0.503155\pi$
$347$	−0.369228	−0.0198212	−0.00991059	+	0.999951i	$0.503155\pi$
$348$	−5.51156	−0.295451
$349$	−31.3643	−1.67889	−0.839445	−	0.543445i	$-0.817120\pi$
$349$	−31.3643	−1.67889	−0.839445	+	0.543445i	$0.817120\pi$
$350$	0	0
$351$	4.98496	0.266077
$352$	3.46193	0.184521
$353$	22.8192	1.21454	0.607272	−	0.794494i	$-0.292264\pi$
$353$	22.8192	1.21454	0.607272	+	0.794494i	$0.292264\pi$
$354$	−8.67842	−0.461253
$355$	−30.1358	−1.59944
$356$	−7.52952	−0.399064
$357$	0	0
$358$	3.24948	0.171741
$359$	24.0276	1.26813	0.634065	−	0.773280i	$-0.281385\pi$
$359$	24.0276	1.26813	0.634065	+	0.773280i	$0.281385\pi$
$360$	2.49248	0.131365
$361$	1.00000	0.0526316
$362$	12.4559	0.654668
$363$	0.984956	0.0516968
$364$	0	0
$365$	35.9425	1.88131
$366$	4.37526	0.228698
$367$	−15.8096	−0.825256	−0.412628	−	0.910900i	$-0.635389\pi$
$367$	−15.8096	−0.825256	−0.412628	+	0.910900i	$0.635389\pi$
$368$	6.00404	0.312982
$369$	−4.64383	−0.241748
$370$	−22.8482	−1.18782
$371$	0	0
$372$	7.28407	0.377662
$373$	30.8507	1.59739	0.798694	−	0.601737i	$-0.205524\pi$
$373$	30.8507	1.59739	0.798694	+	0.601737i	$0.205524\pi$
$374$	−7.76509	−0.401523
$375$	9.44040	0.487500
$376$	5.36021	0.276432
$377$	−27.4749	−1.41503
$378$	0	0
$379$	23.5450	1.20943	0.604713	−	0.796443i	$-0.293288\pi$
$379$	23.5450	1.20943	0.604713	+	0.796443i	$0.293288\pi$
$380$	2.49248	0.127861
$381$	6.09569	0.312291
$382$	16.4444	0.841371
$383$	−4.87271	−0.248984	−0.124492	−	0.992221i	$-0.539730\pi$
$383$	−4.87271	−0.248984	−0.124492	+	0.992221i	$0.539730\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	18.6854	0.951060
$387$	9.54211	0.485053
$388$	−7.00404	−0.355576
$389$	−28.2856	−1.43414	−0.717068	−	0.697003i	$-0.754516\pi$
$389$	−28.2856	−1.43414	−0.717068	+	0.697003i	$0.754516\pi$
$390$	12.4249	0.629159
$391$	−13.4670	−0.681057
$392$	0	0
$393$	−9.31416	−0.469837
$394$	15.4965	0.780703
$395$	17.6634	0.888741
$396$	−3.46193	−0.173969
$397$	−2.65125	−0.133062	−0.0665312	−	0.997784i	$-0.521193\pi$
$397$	−2.65125	−0.133062	−0.0665312	+	0.997784i	$0.521193\pi$
$398$	−1.45948	−0.0731571
$399$	0	0
$400$	1.21245	0.0606223
$401$	−7.45292	−0.372181	−0.186090	−	0.982533i	$-0.559582\pi$
$401$	−7.45292	−0.372181	−0.186090	+	0.982533i	$0.559582\pi$
$402$	−15.1583	−0.756027
$403$	36.3108	1.80877
$404$	−7.09569	−0.353024
$405$	−2.49248	−0.123852
$406$	0	0
$407$	31.7350	1.57305
$408$	2.24299	0.111045
$409$	−17.4037	−0.860560	−0.430280	−	0.902696i	$-0.641585\pi$
$409$	−17.4037	−0.860560	−0.430280	+	0.902696i	$0.641585\pi$
$410$	−11.5746	−0.571630
$411$	−7.78510	−0.384011
$412$	−7.15135	−0.352322
$413$	0	0
$414$	−6.00404	−0.295082
$415$	−13.9535	−0.684949
$416$	−4.98496	−0.244408
$417$	−12.5882	−0.616445
$418$	−3.46193	−0.169329
$419$	3.76105	0.183739	0.0918696	−	0.995771i	$-0.470716\pi$
$419$	3.76105	0.183739	0.0918696	+	0.995771i	$0.470716\pi$
$420$	0	0
$421$	31.6343	1.54176	0.770882	−	0.636978i	$-0.219816\pi$
$421$	31.6343	1.54176	0.770882	+	0.636978i	$0.219816\pi$
$422$	23.3953	1.13886
$423$	−5.36021	−0.260623
$424$	5.87423	0.285278
$425$	−2.71951	−0.131916
$426$	−12.0907	−0.585797
$427$	0	0
$428$	−15.7305	−0.760362
$429$	−17.2576	−0.833203
$430$	23.7835	1.14694
$431$	−1.66582	−0.0802398	−0.0401199	−	0.999195i	$-0.512774\pi$
$431$	−1.66582	−0.0802398	−0.0401199	+	0.999195i	$0.512774\pi$
$432$	1.00000	0.0481125
$433$	−16.1062	−0.774015	−0.387008	−	0.922076i	$-0.626491\pi$
$433$	−16.1062	−0.774015	−0.387008	+	0.922076i	$0.626491\pi$
$434$	0	0
$435$	13.7374	0.658660
$436$	8.31707	0.398315
$437$	−6.00404	−0.287212
$438$	14.4204	0.689032
$439$	−21.0867	−1.00641	−0.503206	−	0.864167i	$-0.667846\pi$
$439$	−21.0867	−1.00641	−0.503206	+	0.864167i	$0.667846\pi$
$440$	−8.62878	−0.411361
$441$	0	0
$442$	11.1812	0.531837
$443$	−18.5958	−0.883512	−0.441756	−	0.897135i	$-0.645644\pi$
$443$	−18.5958	−0.883512	−0.441756	+	0.897135i	$0.645644\pi$
$444$	−9.16685	−0.435040
$445$	18.7672	0.889648
$446$	14.8221	0.701849
$447$	16.2922	0.770592
$448$	0	0
$449$	19.7410	0.931637	0.465818	−	0.884880i	$-0.345760\pi$
$449$	19.7410	0.931637	0.465818	+	0.884880i	$0.345760\pi$
$450$	−1.21245	−0.0571552
$451$	16.0766	0.757018
$452$	13.3643	0.628602
$453$	19.9735	0.938437
$454$	16.2295	0.761687
$455$	0	0
$456$	1.00000	0.0468293
$457$	0.468893	0.0219339	0.0109669	−	0.999940i	$-0.496509\pi$
$457$	0.468893	0.0219339	0.0109669	+	0.999940i	$0.496509\pi$
$458$	−6.39480	−0.298809
$459$	−2.24299	−0.104694
$460$	−14.9649	−0.697744
$461$	19.0556	0.887510	0.443755	−	0.896148i	$-0.353646\pi$
$461$	19.0556	0.887510	0.443755	+	0.896148i	$0.353646\pi$
$462$	0	0
$463$	−9.65575	−0.448741	−0.224370	−	0.974504i	$-0.572033\pi$
$463$	−9.65575	−0.448741	−0.224370	+	0.974504i	$0.572033\pi$
$464$	−5.51156	−0.255868
$465$	−18.1554	−0.841936
$466$	21.3798	0.990398
$467$	9.16281	0.424004	0.212002	−	0.977269i	$-0.432002\pi$
$467$	9.16281	0.424004	0.212002	+	0.977269i	$0.432002\pi$
$468$	4.98496	0.230430
$469$	0	0
$470$	−13.3602	−0.616261
$471$	0.739053	0.0340537
$472$	−8.67842	−0.399456
$473$	−33.0341	−1.51891
$474$	7.08667	0.325502
$475$	−1.21245	−0.0556308
$476$	0	0
$477$	−5.87423	−0.268962
$478$	−18.8938	−0.864181
$479$	−42.8212	−1.95655	−0.978276	−	0.207309i	$-0.933529\pi$
$479$	−42.8212	−1.95655	−0.978276	+	0.207309i	$0.933529\pi$
$480$	2.49248	0.113766
$481$	−45.6964	−2.08357
$482$	4.05009	0.184477
$483$	0	0
$484$	0.984956	0.0447707
$485$	17.4574	0.792700
$486$	−1.00000	−0.0453609
$487$	−26.3153	−1.19246	−0.596230	−	0.802814i	$-0.703335\pi$
$487$	−26.3153	−1.19246	−0.596230	+	0.802814i	$0.703335\pi$
$488$	4.37526	0.198059
$489$	−5.79808	−0.262198
$490$	0	0
$491$	−14.2064	−0.641127	−0.320563	−	0.947227i	$-0.603872\pi$
$491$	−14.2064	−0.641127	−0.320563	+	0.947227i	$0.603872\pi$
$492$	−4.64383	−0.209360
$493$	12.3624	0.556775
$494$	4.98496	0.224284
$495$	8.62878	0.387835
$496$	7.28407	0.327065
$497$	0	0
$498$	−5.59823	−0.250863
$499$	34.0325	1.52351	0.761753	−	0.647868i	$-0.224339\pi$
$499$	34.0325	1.52351	0.761753	+	0.647868i	$0.224339\pi$
$500$	9.44040	0.422187
$501$	−17.1058	−0.764229
$502$	6.59917	0.294535
$503$	−18.2003	−0.811512	−0.405756	−	0.913981i	$-0.632992\pi$
$503$	−18.2003	−0.811512	−0.405756	+	0.913981i	$0.632992\pi$
$504$	0	0
$505$	17.6858	0.787009
$506$	20.7856	0.924031
$507$	11.8498	0.526267
$508$	6.09569	0.270452
$509$	4.56478	0.202330	0.101165	−	0.994870i	$-0.467743\pi$
$509$	4.56478	0.202330	0.101165	+	0.994870i	$0.467743\pi$
$510$	−5.59061	−0.247556
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−2.65125	−0.116942
$515$	17.8246	0.785445
$516$	9.54211	0.420068
$517$	18.5567	0.816122
$518$	0	0
$519$	2.58412	0.113430
$520$	12.4249	0.544868
$521$	40.5160	1.77504	0.887520	−	0.460769i	$-0.152426\pi$
$521$	40.5160	1.77504	0.887520	+	0.460769i	$0.152426\pi$
$522$	5.51156	0.241235
$523$	29.4644	1.28839	0.644195	−	0.764861i	$-0.277193\pi$
$523$	29.4644	1.28839	0.644195	+	0.764861i	$0.277193\pi$
$524$	−9.31416	−0.406891
$525$	0	0
$526$	1.45544	0.0634602
$527$	−16.3381	−0.711700
$528$	−3.46193	−0.150661
$529$	13.0485	0.567326
$530$	−14.6414	−0.635981
$531$	8.67842	0.376611
$532$	0	0
$533$	−23.1493	−1.00271
$534$	7.52952	0.325834
$535$	39.2079	1.69511
$536$	−15.1583	−0.654739
$537$	−3.24948	−0.140226
$538$	14.3232	0.617516
$539$	0	0
$540$	−2.49248	−0.107259
$541$	−5.52800	−0.237667	−0.118834	−	0.992914i	$-0.537916\pi$
$541$	−5.52800	−0.237667	−0.118834	+	0.992914i	$0.537916\pi$
$542$	20.6658	0.887673
$543$	−12.4559	−0.534534
$544$	2.24299	0.0961676
$545$	−20.7301	−0.887980
$546$	0	0
$547$	−13.7329	−0.587178	−0.293589	−	0.955932i	$-0.594850\pi$
$547$	−13.7329	−0.587178	−0.293589	+	0.955932i	$0.594850\pi$
$548$	−7.78510	−0.332563
$549$	−4.37526	−0.186731
$550$	4.19740	0.178978
$551$	5.51156	0.234800
$552$	−6.00404	−0.255549
$553$	0	0
$554$	28.5421	1.21264
$555$	22.8482	0.969851
$556$	−12.5882	−0.533857
$557$	−0.399242	−0.0169164	−0.00845821	−	0.999964i	$-0.502692\pi$
$557$	−0.399242	−0.0169164	−0.00845821	+	0.999964i	$0.502692\pi$
$558$	−7.28407	−0.308359
$559$	47.5670	2.01187
$560$	0	0
$561$	7.76509	0.327842
$562$	13.6443	0.575549
$563$	−26.1242	−1.10100	−0.550501	−	0.834834i	$-0.685563\pi$
$563$	−26.1242	−1.10100	−0.550501	+	0.834834i	$0.685563\pi$
$564$	−5.36021	−0.225706
$565$	−33.3101	−1.40137
$566$	−1.53403	−0.0644801
$567$	0	0
$568$	−12.0907	−0.507315
$569$	3.06316	0.128414	0.0642072	−	0.997937i	$-0.479548\pi$
$569$	3.06316	0.128414	0.0642072	+	0.997937i	$0.479548\pi$
$570$	−2.49248	−0.104398
$571$	5.89066	0.246517	0.123258	−	0.992375i	$-0.460666\pi$
$571$	5.89066	0.246517	0.123258	+	0.992375i	$0.460666\pi$
$572$	−17.2576	−0.721575
$573$	−16.4444	−0.686976
$574$	0	0
$575$	7.27957	0.303579
$576$	1.00000	0.0416667
$577$	25.7896	1.07364	0.536818	−	0.843698i	$-0.319626\pi$
$577$	25.7896	1.07364	0.536818	+	0.843698i	$0.319626\pi$
$578$	11.9690	0.497844
$579$	−18.6854	−0.776537
$580$	13.7374	0.570416
$581$	0	0
$582$	7.00404	0.290327
$583$	20.3362	0.842237
$584$	14.4204	0.596719
$585$	−12.4249	−0.513706
$586$	−33.3773	−1.37880
$587$	−0.822143	−0.0339335	−0.0169667	−	0.999856i	$-0.505401\pi$
$587$	−0.822143	−0.0339335	−0.0169667	+	0.999856i	$0.505401\pi$
$588$	0	0
$589$	−7.28407	−0.300135
$590$	21.6308	0.890524
$591$	−15.4965	−0.637442
$592$	−9.16685	−0.376755
$593$	16.6407	0.683352	0.341676	−	0.939818i	$-0.389005\pi$
$593$	16.6407	0.683352	0.341676	+	0.939818i	$0.389005\pi$
$594$	3.46193	0.142045
$595$	0	0
$596$	16.2922	0.667353
$597$	1.45948	0.0597325
$598$	−29.9299	−1.22392
$599$	8.57670	0.350434	0.175217	−	0.984530i	$-0.443937\pi$
$599$	8.57670	0.350434	0.175217	+	0.984530i	$0.443937\pi$
$600$	−1.21245	−0.0494979
$601$	−13.6993	−0.558805	−0.279403	−	0.960174i	$-0.590136\pi$
$601$	−13.6993	−0.558805	−0.279403	+	0.960174i	$0.590136\pi$
$602$	0	0
$603$	15.1583	0.617294
$604$	19.9735	0.812710
$605$	−2.45498	−0.0998091
$606$	7.09569	0.288243
$607$	−42.5405	−1.72667	−0.863333	−	0.504635i	$-0.831627\pi$
$607$	−42.5405	−1.72667	−0.863333	+	0.504635i	$0.831627\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−10.9052	−0.441540
$611$	−26.7204	−1.08099
$612$	−2.24299	−0.0906677
$613$	14.5096	0.586036	0.293018	−	0.956107i	$-0.405340\pi$
$613$	14.5096	0.586036	0.293018	+	0.956107i	$0.405340\pi$
$614$	9.52952	0.384580
$615$	11.5746	0.466734
$616$	0	0
$617$	−25.3468	−1.02042	−0.510211	−	0.860049i	$-0.670433\pi$
$617$	−25.3468	−1.02042	−0.510211	+	0.860049i	$0.670433\pi$
$618$	7.15135	0.287669
$619$	15.9944	0.642867	0.321434	−	0.946932i	$-0.395835\pi$
$619$	15.9944	0.642867	0.321434	+	0.946932i	$0.395835\pi$
$620$	−18.1554	−0.729138
$621$	6.00404	0.240934
$622$	16.4404	0.659200
$623$	0	0
$624$	4.98496	0.199558
$625$	−29.5922	−1.18369
$626$	10.9940	0.439407
$627$	3.46193	0.138256
$628$	0.739053	0.0294914
$629$	20.5612	0.819829
$630$	0	0
$631$	−25.6970	−1.02298	−0.511491	−	0.859288i	$-0.670907\pi$
$631$	−25.6970	−1.02298	−0.511491	+	0.859288i	$0.670907\pi$
$632$	7.08667	0.281893
$633$	−23.3953	−0.929878
$634$	−6.66291	−0.264618
$635$	−15.1934	−0.602930
$636$	−5.87423	−0.232928
$637$	0	0
$638$	−19.0806	−0.755410
$639$	12.0907	0.478301
$640$	2.49248	0.0985238
$641$	44.0747	1.74085	0.870424	−	0.492303i	$-0.163845\pi$
$641$	44.0747	1.74085	0.870424	+	0.492303i	$0.163845\pi$
$642$	15.7305	0.620833
$643$	−22.7730	−0.898078	−0.449039	−	0.893512i	$-0.648234\pi$
$643$	−22.7730	−0.898078	−0.449039	+	0.893512i	$0.648234\pi$
$644$	0	0
$645$	−23.7835	−0.936474
$646$	−2.24299	−0.0882494
$647$	−30.3678	−1.19388	−0.596941	−	0.802285i	$-0.703618\pi$
$647$	−30.3678	−1.19388	−0.596941	+	0.802285i	$0.703618\pi$
$648$	−1.00000	−0.0392837
$649$	−30.0441	−1.17933
$650$	−6.04399	−0.237065
$651$	0	0
$652$	−5.79808	−0.227071
$653$	−4.63535	−0.181395	−0.0906976	−	0.995878i	$-0.528910\pi$
$653$	−4.63535	−0.181395	−0.0906976	+	0.995878i	$0.528910\pi$
$654$	−8.31707	−0.325223
$655$	23.2153	0.907098
$656$	−4.64383	−0.181311
$657$	−14.4204	−0.562592
$658$	0	0
$659$	−18.8998	−0.736232	−0.368116	−	0.929780i	$-0.619997\pi$
$659$	−18.8998	−0.736232	−0.368116	+	0.929780i	$0.619997\pi$
$660$	8.62878	0.335875
$661$	−25.8042	−1.00367	−0.501833	−	0.864964i	$-0.667341\pi$
$661$	−25.8042	−1.00367	−0.501833	+	0.864964i	$0.667341\pi$
$662$	−25.8102	−1.00314
$663$	−11.1812	−0.434243
$664$	−5.59823	−0.217254
$665$	0	0
$666$	9.16685	0.355208
$667$	−33.0916	−1.28131
$668$	−17.1058	−0.661842
$669$	−14.8221	−0.573057
$670$	37.7817	1.45964
$671$	15.1468	0.584737
$672$	0	0
$673$	15.7844	0.608445	0.304223	−	0.952601i	$-0.401603\pi$
$673$	15.7844	0.608445	0.304223	+	0.952601i	$0.401603\pi$
$674$	−10.0932	−0.388774
$675$	1.21245	0.0466671
$676$	11.8498	0.455761
$677$	24.0786	0.925415	0.462707	−	0.886511i	$-0.346878\pi$
$677$	24.0786	0.925415	0.462707	+	0.886511i	$0.346878\pi$
$678$	−13.3643	−0.513251
$679$	0	0
$680$	−5.59061	−0.214390
$681$	−16.2295	−0.621914
$682$	25.2169	0.965607
$683$	14.8506	0.568243	0.284122	−	0.958788i	$-0.408298\pi$
$683$	14.8506	0.568243	0.284122	+	0.958788i	$0.408298\pi$
$684$	−1.00000	−0.0382360
$685$	19.4042	0.741396
$686$	0	0
$687$	6.39480	0.243977
$688$	9.54211	0.363790
$689$	−29.2828	−1.11558
$690$	14.9649	0.569705
$691$	−38.2941	−1.45678	−0.728389	−	0.685164i	$-0.759731\pi$
$691$	−38.2941	−1.45678	−0.728389	+	0.685164i	$0.759731\pi$
$692$	2.58412	0.0982336
$693$	0	0
$694$	0.369228	0.0140157
$695$	31.3757	1.19015
$696$	5.51156	0.208915
$697$	10.4161	0.394537
$698$	31.3643	1.18715
$699$	−21.3798	−0.808657
$700$	0	0
$701$	−24.6068	−0.929385	−0.464693	−	0.885472i	$-0.653835\pi$
$701$	−24.6068	−0.929385	−0.464693	+	0.885472i	$0.653835\pi$
$702$	−4.98496	−0.188145
$703$	9.16685	0.345734
$704$	−3.46193	−0.130476
$705$	13.3602	0.503175
$706$	−22.8192	−0.858813
$707$	0	0
$708$	8.67842	0.326155
$709$	17.2665	0.648457	0.324229	−	0.945979i	$-0.394895\pi$
$709$	17.2665	0.648457	0.324229	+	0.945979i	$0.394895\pi$
$710$	30.1358	1.13098
$711$	−7.08667	−0.265771
$712$	7.52952	0.282181
$713$	43.7339	1.63785
$714$	0	0
$715$	43.0141	1.60864
$716$	−3.24948	−0.121439
$717$	18.8938	0.705601
$718$	−24.0276	−0.896703
$719$	−43.2527	−1.61305	−0.806526	−	0.591198i	$-0.798655\pi$
$719$	−43.2527	−1.61305	−0.806526	+	0.591198i	$0.798655\pi$
$720$	−2.49248	−0.0928892
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−4.05009	−0.150625
$724$	−12.4559	−0.462920
$725$	−6.68247	−0.248181
$726$	−0.984956	−0.0365551
$727$	26.0766	0.967127	0.483564	−	0.875309i	$-0.339342\pi$
$727$	26.0766	0.967127	0.483564	+	0.875309i	$0.339342\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−35.9425	−1.33029
$731$	−21.4029	−0.791615
$732$	−4.37526	−0.161714
$733$	8.21894	0.303573	0.151787	−	0.988413i	$-0.451497\pi$
$733$	8.21894	0.303573	0.151787	+	0.988413i	$0.451497\pi$
$734$	15.8096	0.583544
$735$	0	0
$736$	−6.00404	−0.221312
$737$	−52.4770	−1.93301
$738$	4.64383	0.170942
$739$	38.5978	1.41984	0.709921	−	0.704282i	$-0.248731\pi$
$739$	38.5978	1.41984	0.709921	+	0.704282i	$0.248731\pi$
$740$	22.8482	0.839916
$741$	−4.98496	−0.183127
$742$	0	0
$743$	−5.51309	−0.202256	−0.101128	−	0.994873i	$-0.532245\pi$
$743$	−5.51309	−0.202256	−0.101128	+	0.994873i	$0.532245\pi$
$744$	−7.28407	−0.267047
$745$	−40.6078	−1.48776
$746$	−30.8507	−1.12952
$747$	5.59823	0.204829
$748$	7.76509	0.283920
$749$	0	0
$750$	−9.44040	−0.344714
$751$	19.2600	0.702808	0.351404	−	0.936224i	$-0.385704\pi$
$751$	19.2600	0.702808	0.351404	+	0.936224i	$0.385704\pi$
$752$	−5.36021	−0.195467
$753$	−6.59917	−0.240487
$754$	27.4749	1.00058
$755$	−49.7835	−1.81181
$756$	0	0
$757$	−0.556024	−0.0202090	−0.0101045	−	0.999949i	$-0.503216\pi$
$757$	−0.556024	−0.0202090	−0.0101045	+	0.999949i	$0.503216\pi$
$758$	−23.5450	−0.855194
$759$	−20.7856	−0.754468
$760$	−2.49248	−0.0904117
$761$	−9.17692	−0.332663	−0.166332	−	0.986070i	$-0.553192\pi$
$761$	−9.17692	−0.332663	−0.166332	+	0.986070i	$0.553192\pi$
$762$	−6.09569	−0.220823
$763$	0	0
$764$	−16.4444	−0.594939
$765$	5.59061	0.202129
$766$	4.87271	0.176058
$767$	43.2615	1.56208
$768$	1.00000	0.0360844
$769$	−10.2515	−0.369680	−0.184840	−	0.982769i	$-0.559177\pi$
$769$	−10.2515	−0.369680	−0.184840	+	0.982769i	$0.559177\pi$
$770$	0	0
$771$	2.65125	0.0954824
$772$	−18.6854	−0.672501
$773$	25.3728	0.912596	0.456298	−	0.889827i	$-0.349175\pi$
$773$	25.3728	0.912596	0.456298	+	0.889827i	$0.349175\pi$
$774$	−9.54211	−0.342984
$775$	8.83154	0.317238
$776$	7.00404	0.251430
$777$	0	0
$778$	28.2856	1.01409
$779$	4.64383	0.166382
$780$	−12.4249	−0.444882
$781$	−41.8572	−1.49777
$782$	13.4670	0.481580
$783$	−5.51156	−0.196967
$784$	0	0
$785$	−1.84207	−0.0657464
$786$	9.31416	0.332225
$787$	−21.2886	−0.758856	−0.379428	−	0.925221i	$-0.623879\pi$
$787$	−21.2886	−0.758856	−0.379428	+	0.925221i	$0.623879\pi$
$788$	−15.4965	−0.552041
$789$	−1.45544	−0.0518150
$790$	−17.6634	−0.628435
$791$	0	0
$792$	3.46193	0.123014
$793$	−21.8105	−0.774512
$794$	2.65125	0.0940893
$795$	14.6414	0.519276
$796$	1.45948	0.0517299
$797$	−41.1949	−1.45920	−0.729600	−	0.683874i	$-0.760294\pi$
$797$	−41.1949	−1.45920	−0.729600	+	0.683874i	$0.760294\pi$
$798$	0	0
$799$	12.0229	0.425341
$800$	−1.21245	−0.0428664
$801$	−7.52952	−0.266042
$802$	7.45292	0.263172
$803$	49.9223	1.76172
$804$	15.1583	0.534592
$805$	0	0
$806$	−36.3108	−1.27899
$807$	−14.3232	−0.504200
$808$	7.09569	0.249625
$809$	−18.3968	−0.646797	−0.323398	−	0.946263i	$-0.604825\pi$
$809$	−18.3968	−0.646797	−0.323398	+	0.946263i	$0.604825\pi$
$810$	2.49248	0.0875767
$811$	18.8662	0.662482	0.331241	−	0.943546i	$-0.392533\pi$
$811$	18.8662	0.662482	0.331241	+	0.943546i	$0.392533\pi$
$812$	0	0
$813$	−20.6658	−0.724782
$814$	−31.7350	−1.11231
$815$	14.4516	0.506217
$816$	−2.24299	−0.0785205
$817$	−9.54211	−0.333836
$818$	17.4037	0.608508
$819$	0	0
$820$	11.5746	0.404204
$821$	16.6517	0.581149	0.290574	−	0.956852i	$-0.406154\pi$
$821$	16.6517	0.581149	0.290574	+	0.956852i	$0.406154\pi$
$822$	7.78510	0.271537
$823$	−35.3894	−1.23360	−0.616798	−	0.787122i	$-0.711570\pi$
$823$	−35.3894	−1.23360	−0.616798	+	0.787122i	$0.711570\pi$
$824$	7.15135	0.249129
$825$	−4.19740	−0.146135
$826$	0	0
$827$	−2.71432	−0.0943862	−0.0471931	−	0.998886i	$-0.515028\pi$
$827$	−2.71432	−0.0943862	−0.0471931	+	0.998886i	$0.515028\pi$
$828$	6.00404	0.208655
$829$	−12.5291	−0.435152	−0.217576	−	0.976043i	$-0.569815\pi$
$829$	−12.5291	−0.435152	−0.217576	+	0.976043i	$0.569815\pi$
$830$	13.9535	0.484332
$831$	−28.5421	−0.990114
$832$	4.98496	0.172822
$833$	0	0
$834$	12.5882	0.435892
$835$	42.6357	1.47547
$836$	3.46193	0.119733
$837$	7.28407	0.251774
$838$	−3.76105	−0.129923
$839$	−5.50546	−0.190070	−0.0950348	−	0.995474i	$-0.530296\pi$
$839$	−5.50546	−0.190070	−0.0950348	+	0.995474i	$0.530296\pi$
$840$	0	0
$841$	1.37732	0.0474939
$842$	−31.6343	−1.09019
$843$	−13.6443	−0.469934
$844$	−23.3953	−0.805298
$845$	−29.5353	−1.01605
$846$	5.36021	0.184288
$847$	0	0
$848$	−5.87423	−0.201722
$849$	1.53403	0.0526478
$850$	2.71951	0.0932784
$851$	−55.0382	−1.88668
$852$	12.0907	0.414221
$853$	47.3276	1.62047	0.810233	−	0.586108i	$-0.199340\pi$
$853$	47.3276	1.62047	0.810233	+	0.586108i	$0.199340\pi$
$854$	0	0
$855$	2.49248	0.0852409
$856$	15.7305	0.537657
$857$	−54.1773	−1.85066	−0.925331	−	0.379161i	$-0.876213\pi$
$857$	−54.1773	−1.85066	−0.925331	+	0.379161i	$0.876213\pi$
$858$	17.2576	0.589164
$859$	51.7842	1.76685	0.883426	−	0.468570i	$-0.155231\pi$
$859$	51.7842	1.76685	0.883426	+	0.468570i	$0.155231\pi$
$860$	−23.7835	−0.811011
$861$	0	0
$862$	1.66582	0.0567381
$863$	−26.6679	−0.907785	−0.453893	−	0.891056i	$-0.649965\pi$
$863$	−26.6679	−0.907785	−0.453893	+	0.891056i	$0.649965\pi$
$864$	−1.00000	−0.0340207
$865$	−6.44087	−0.218996
$866$	16.1062	0.547311
$867$	−11.9690	−0.406488
$868$	0	0
$869$	24.5336	0.832244
$870$	−13.7374	−0.465743
$871$	75.5634	2.56037
$872$	−8.31707	−0.281652
$873$	−7.00404	−0.237051
$874$	6.00404	0.203090
$875$	0	0
$876$	−14.4204	−0.487219
$877$	−11.7318	−0.396155	−0.198078	−	0.980186i	$-0.563470\pi$
$877$	−11.7318	−0.396155	−0.198078	+	0.980186i	$0.563470\pi$
$878$	21.0867	0.711641
$879$	33.3773	1.12579
$880$	8.62878	0.290876
$881$	11.8406	0.398918	0.199459	−	0.979906i	$-0.436081\pi$
$881$	11.8406	0.398918	0.199459	+	0.979906i	$0.436081\pi$
$882$	0	0
$883$	35.5167	1.19523	0.597616	−	0.801782i	$-0.296115\pi$
$883$	35.5167	1.19523	0.597616	+	0.801782i	$0.296115\pi$
$884$	−11.1812	−0.376065
$885$	−21.6308	−0.727110
$886$	18.5958	0.624738
$887$	38.9544	1.30796	0.653980	−	0.756512i	$-0.273098\pi$
$887$	38.9544	1.30796	0.653980	+	0.756512i	$0.273098\pi$
$888$	9.16685	0.307619
$889$	0	0
$890$	−18.7672	−0.629076
$891$	−3.46193	−0.115979
$892$	−14.8221	−0.496282
$893$	5.36021	0.179373
$894$	−16.2922	−0.544891
$895$	8.09927	0.270729
$896$	0	0
$897$	29.9299	0.999329
$898$	−19.7410	−0.658767
$899$	−40.1466	−1.33896
$900$	1.21245	0.0404149
$901$	13.1759	0.438951
$902$	−16.0766	−0.535292
$903$	0	0
$904$	−13.3643	−0.444488
$905$	31.0461	1.03201
$906$	−19.9735	−0.663575
$907$	55.1428	1.83099	0.915493	−	0.402333i	$-0.131801\pi$
$907$	55.1428	1.83099	0.915493	+	0.402333i	$0.131801\pi$
$908$	−16.2295	−0.538594
$909$	−7.09569	−0.235349
$910$	0	0
$911$	11.9618	0.396313	0.198157	−	0.980170i	$-0.436505\pi$
$911$	11.9618	0.396313	0.198157	+	0.980170i	$0.436505\pi$
$912$	−1.00000	−0.0331133
$913$	−19.3807	−0.641407
$914$	−0.468893	−0.0155096
$915$	10.9052	0.360516
$916$	6.39480	0.211290
$917$	0	0
$918$	2.24299	0.0740298
$919$	36.9365	1.21842	0.609211	−	0.793008i	$-0.291486\pi$
$919$	36.9365	1.21842	0.609211	+	0.793008i	$0.291486\pi$
$920$	14.9649	0.493379
$921$	−9.52952	−0.314008
$922$	−19.0556	−0.627564
$923$	60.2717	1.98387
$924$	0	0
$925$	−11.1143	−0.365436
$926$	9.65575	0.317308
$927$	−7.15135	−0.234881
$928$	5.51156	0.180926
$929$	24.2806	0.796620	0.398310	−	0.917251i	$-0.369597\pi$
$929$	24.2806	0.796620	0.398310	+	0.917251i	$0.369597\pi$
$930$	18.1554	0.595339
$931$	0	0
$932$	−21.3798	−0.700317
$933$	−16.4404	−0.538234
$934$	−9.16281	−0.299816
$935$	−19.3543	−0.632954
$936$	−4.98496	−0.162938
$937$	24.5823	0.803068	0.401534	−	0.915844i	$-0.368477\pi$
$937$	24.5823	0.803068	0.401534	+	0.915844i	$0.368477\pi$
$938$	0	0
$939$	−10.9940	−0.358775
$940$	13.3602	0.435762
$941$	7.35723	0.239839	0.119919	−	0.992784i	$-0.461736\pi$
$941$	7.35723	0.239839	0.119919	+	0.992784i	$0.461736\pi$
$942$	−0.739053	−0.0240796
$943$	−27.8817	−0.907954
$944$	8.67842	0.282458
$945$	0	0
$946$	33.0341	1.07403
$947$	−29.0462	−0.943876	−0.471938	−	0.881632i	$-0.656445\pi$
$947$	−29.0462	−0.943876	−0.471938	+	0.881632i	$0.656445\pi$
$948$	−7.08667	−0.230164
$949$	−71.8849	−2.33348
$950$	1.21245	0.0393369
$951$	6.66291	0.216060
$952$	0	0
$953$	−5.84772	−0.189426	−0.0947131	−	0.995505i	$-0.530193\pi$
$953$	−5.84772	−0.189426	−0.0947131	+	0.995505i	$0.530193\pi$
$954$	5.87423	0.190185
$955$	40.9874	1.32632
$956$	18.8938	0.611068
$957$	19.0806	0.616790
$958$	42.8212	1.38349
$959$	0	0
$960$	−2.49248	−0.0804444
$961$	22.0577	0.711539
$962$	45.6964	1.47331
$963$	−15.7305	−0.506908
$964$	−4.05009	−0.130445
$965$	46.5729	1.49923
$966$	0	0
$967$	11.7775	0.378738	0.189369	−	0.981906i	$-0.439356\pi$
$967$	11.7775	0.378738	0.189369	+	0.981906i	$0.439356\pi$
$968$	−0.984956	−0.0316577
$969$	2.24299	0.0720553
$970$	−17.4574	−0.560524
$971$	33.4810	1.07446	0.537228	−	0.843437i	$-0.319471\pi$
$971$	33.4810	1.07446	0.537228	+	0.843437i	$0.319471\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	26.3153	0.843196
$975$	6.04399	0.193563
$976$	−4.37526	−0.140049
$977$	−17.3969	−0.556575	−0.278288	−	0.960498i	$-0.589767\pi$
$977$	−17.3969	−0.556575	−0.278288	+	0.960498i	$0.589767\pi$
$978$	5.79808	0.185402
$979$	26.0667	0.833094
$980$	0	0
$981$	8.31707	0.265544
$982$	14.2064	0.453345
$983$	−13.9218	−0.444036	−0.222018	−	0.975043i	$-0.571264\pi$
$983$	−13.9218	−0.444036	−0.222018	+	0.975043i	$0.571264\pi$
$984$	4.64383	0.148040
$985$	38.6247	1.23069
$986$	−12.3624	−0.393699
$987$	0	0
$988$	−4.98496	−0.158593
$989$	57.2912	1.82175
$990$	−8.62878	−0.274241
$991$	−39.9694	−1.26967	−0.634834	−	0.772648i	$-0.718932\pi$
$991$	−39.9694	−1.26967	−0.634834	+	0.772648i	$0.718932\pi$
$992$	−7.28407	−0.231270
$993$	25.8102	0.819062
$994$	0	0
$995$	−3.63772	−0.115324
$996$	5.59823	0.177387
$997$	−35.3277	−1.11884	−0.559419	−	0.828885i	$-0.688976\pi$
$997$	−35.3277	−1.11884	−0.559419	+	0.828885i	$0.688976\pi$
$998$	−34.0325	−1.07728
$999$	−9.16685	−0.290026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bz.1.1		4
7.3	odd	6		798.2.j.l.457.1	✓	8
7.5	odd	6		798.2.j.l.571.1	yes	8
7.6	odd	2		5586.2.a.bw.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.1	✓	8	7.3	odd	6
798.2.j.l.571.1	yes	8	7.5	odd	6
5586.2.a.bw.1.4		4	7.6	odd	2
5586.2.a.bz.1.1		4	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.49248 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.49248 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.49248 q^{10} -3.46193 q^{11} +1.00000 q^{12} +4.98496 q^{13} -2.49248 q^{15} +1.00000 q^{16} -2.24299 q^{17} -1.00000 q^{18} -1.00000 q^{19} -2.49248 q^{20} +3.46193 q^{22} +6.00404 q^{23} -1.00000 q^{24} +1.21245 q^{25} -4.98496 q^{26} +1.00000 q^{27} -5.51156 q^{29} +2.49248 q^{30} +7.28407 q^{31} -1.00000 q^{32} -3.46193 q^{33} +2.24299 q^{34} +1.00000 q^{36} -9.16685 q^{37} +1.00000 q^{38} +4.98496 q^{39} +2.49248 q^{40} -4.64383 q^{41} +9.54211 q^{43} -3.46193 q^{44} -2.49248 q^{45} -6.00404 q^{46} -5.36021 q^{47} +1.00000 q^{48} -1.21245 q^{50} -2.24299 q^{51} +4.98496 q^{52} -5.87423 q^{53} -1.00000 q^{54} +8.62878 q^{55} -1.00000 q^{57} +5.51156 q^{58} +8.67842 q^{59} -2.49248 q^{60} -4.37526 q^{61} -7.28407 q^{62} +1.00000 q^{64} -12.4249 q^{65} +3.46193 q^{66} +15.1583 q^{67} -2.24299 q^{68} +6.00404 q^{69} +12.0907 q^{71} -1.00000 q^{72} -14.4204 q^{73} +9.16685 q^{74} +1.21245 q^{75} -1.00000 q^{76} -4.98496 q^{78} -7.08667 q^{79} -2.49248 q^{80} +1.00000 q^{81} +4.64383 q^{82} +5.59823 q^{83} +5.59061 q^{85} -9.54211 q^{86} -5.51156 q^{87} +3.46193 q^{88} -7.52952 q^{89} +2.49248 q^{90} +6.00404 q^{92} +7.28407 q^{93} +5.36021 q^{94} +2.49248 q^{95} -1.00000 q^{96} -7.00404 q^{97} -3.46193 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

L-functions

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