LMFDB - Embedded newform 8018.2.a.j.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.19254 q^{3} +1.00000 q^{4} +1.33631 q^{5} -2.19254 q^{6} -4.99100 q^{7} +1.00000 q^{8} +1.80723 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.19254 q^{3} +1.00000 q^{4} +1.33631 q^{5} -2.19254 q^{6} -4.99100 q^{7} +1.00000 q^{8} +1.80723 q^{9} +1.33631 q^{10} +3.23517 q^{11} -2.19254 q^{12} +3.93273 q^{13} -4.99100 q^{14} -2.92992 q^{15} +1.00000 q^{16} +2.30236 q^{17} +1.80723 q^{18} -1.00000 q^{19} +1.33631 q^{20} +10.9430 q^{21} +3.23517 q^{22} +2.41135 q^{23} -2.19254 q^{24} -3.21427 q^{25} +3.93273 q^{26} +2.61520 q^{27} -4.99100 q^{28} +7.68845 q^{29} -2.92992 q^{30} -10.1826 q^{31} +1.00000 q^{32} -7.09323 q^{33} +2.30236 q^{34} -6.66954 q^{35} +1.80723 q^{36} +3.67800 q^{37} -1.00000 q^{38} -8.62266 q^{39} +1.33631 q^{40} -8.72443 q^{41} +10.9430 q^{42} +9.15875 q^{43} +3.23517 q^{44} +2.41502 q^{45} +2.41135 q^{46} -9.14506 q^{47} -2.19254 q^{48} +17.9101 q^{49} -3.21427 q^{50} -5.04802 q^{51} +3.93273 q^{52} +5.22097 q^{53} +2.61520 q^{54} +4.32320 q^{55} -4.99100 q^{56} +2.19254 q^{57} +7.68845 q^{58} -9.07487 q^{59} -2.92992 q^{60} -1.01640 q^{61} -10.1826 q^{62} -9.01987 q^{63} +1.00000 q^{64} +5.25536 q^{65} -7.09323 q^{66} -14.2825 q^{67} +2.30236 q^{68} -5.28697 q^{69} -6.66954 q^{70} -5.03857 q^{71} +1.80723 q^{72} +0.0673096 q^{73} +3.67800 q^{74} +7.04740 q^{75} -1.00000 q^{76} -16.1467 q^{77} -8.62266 q^{78} +17.2366 q^{79} +1.33631 q^{80} -11.1556 q^{81} -8.72443 q^{82} -7.67587 q^{83} +10.9430 q^{84} +3.07668 q^{85} +9.15875 q^{86} -16.8572 q^{87} +3.23517 q^{88} +16.3005 q^{89} +2.41502 q^{90} -19.6282 q^{91} +2.41135 q^{92} +22.3258 q^{93} -9.14506 q^{94} -1.33631 q^{95} -2.19254 q^{96} -11.3545 q^{97} +17.9101 q^{98} +5.84668 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	−2.19254	−1.26586	−0.632932	−	0.774208i	$-0.718149\pi$
$3$	−2.19254	−1.26586	−0.632932	+	0.774208i	$0.718149\pi$
$4$	1.00000	0.500000
$5$	1.33631	0.597618	0.298809	−	0.954313i	$-0.403411\pi$
$5$	1.33631	0.597618	0.298809	+	0.954313i	$0.403411\pi$
$6$	−2.19254	−0.895100
$7$	−4.99100	−1.88642	−0.943210	−	0.332198i	$-0.892210\pi$
$7$	−4.99100	−1.88642	−0.943210	+	0.332198i	$0.892210\pi$
$8$	1.00000	0.353553
$9$	1.80723	0.602410
$10$	1.33631	0.422580
$11$	3.23517	0.975439	0.487719	−	0.873000i	$-0.337829\pi$
$11$	3.23517	0.975439	0.487719	+	0.873000i	$0.337829\pi$
$12$	−2.19254	−0.632932
$13$	3.93273	1.09074	0.545371	−	0.838194i	$-0.316389\pi$
$13$	3.93273	1.09074	0.545371	+	0.838194i	$0.316389\pi$
$14$	−4.99100	−1.33390
$15$	−2.92992	−0.756502
$16$	1.00000	0.250000
$17$	2.30236	0.558405	0.279202	−	0.960232i	$-0.409930\pi$
$17$	2.30236	0.558405	0.279202	+	0.960232i	$0.409930\pi$
$18$	1.80723	0.425968
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.33631	0.298809
$21$	10.9430	2.38795
$22$	3.23517	0.689739
$23$	2.41135	0.502800	0.251400	−	0.967883i	$-0.419109\pi$
$23$	2.41135	0.502800	0.251400	+	0.967883i	$0.419109\pi$
$24$	−2.19254	−0.447550
$25$	−3.21427	−0.642853
$26$	3.93273	0.771272
$27$	2.61520	0.503295
$28$	−4.99100	−0.943210
$29$	7.68845	1.42771	0.713854	−	0.700294i	$-0.246948\pi$
$29$	7.68845	1.42771	0.713854	+	0.700294i	$0.246948\pi$
$30$	−2.92992	−0.534928
$31$	−10.1826	−1.82885	−0.914427	−	0.404751i	$-0.867358\pi$
$31$	−10.1826	−1.82885	−0.914427	+	0.404751i	$0.867358\pi$
$32$	1.00000	0.176777
$33$	−7.09323	−1.23477
$34$	2.30236	0.394852
$35$	−6.66954	−1.12736
$36$	1.80723	0.301205
$37$	3.67800	0.604659	0.302330	−	0.953203i	$-0.402236\pi$
$37$	3.67800	0.604659	0.302330	+	0.953203i	$0.402236\pi$
$38$	−1.00000	−0.162221
$39$	−8.62266	−1.38073
$40$	1.33631	0.211290
$41$	−8.72443	−1.36253	−0.681264	−	0.732038i	$-0.738569\pi$
$41$	−8.72443	−1.36253	−0.681264	+	0.732038i	$0.738569\pi$
$42$	10.9430	1.68853
$43$	9.15875	1.39670	0.698348	−	0.715758i	$-0.253919\pi$
$43$	9.15875	1.39670	0.698348	+	0.715758i	$0.253919\pi$
$44$	3.23517	0.487719
$45$	2.41502	0.360011
$46$	2.41135	0.355533
$47$	−9.14506	−1.33394	−0.666972	−	0.745083i	$-0.732410\pi$
$47$	−9.14506	−1.33394	−0.666972	+	0.745083i	$0.732410\pi$
$48$	−2.19254	−0.316466
$49$	17.9101	2.55858
$50$	−3.21427	−0.454566
$51$	−5.04802	−0.706864
$52$	3.93273	0.545371
$53$	5.22097	0.717155	0.358577	−	0.933500i	$-0.383262\pi$
$53$	5.22097	0.717155	0.358577	+	0.933500i	$0.383262\pi$
$54$	2.61520	0.355883
$55$	4.32320	0.582940
$56$	−4.99100	−0.666950
$57$	2.19254	0.290409
$58$	7.68845	1.00954
$59$	−9.07487	−1.18145	−0.590724	−	0.806874i	$-0.701158\pi$
$59$	−9.07487	−1.18145	−0.590724	+	0.806874i	$0.701158\pi$
$60$	−2.92992	−0.378251
$61$	−1.01640	−0.130137	−0.0650686	−	0.997881i	$-0.520727\pi$
$61$	−1.01640	−0.130137	−0.0650686	+	0.997881i	$0.520727\pi$
$62$	−10.1826	−1.29319
$63$	−9.01987	−1.13640
$64$	1.00000	0.125000
$65$	5.25536	0.651847
$66$	−7.09323	−0.873116
$67$	−14.2825	−1.74488	−0.872440	−	0.488721i	$-0.837464\pi$
$67$	−14.2825	−1.74488	−0.872440	+	0.488721i	$0.837464\pi$
$68$	2.30236	0.279202
$69$	−5.28697	−0.636476
$70$	−6.66954	−0.797162
$71$	−5.03857	−0.597968	−0.298984	−	0.954258i	$-0.596648\pi$
$71$	−5.03857	−0.597968	−0.298984	+	0.954258i	$0.596648\pi$
$72$	1.80723	0.212984
$73$	0.0673096	0.00787800	0.00393900	−	0.999992i	$-0.498746\pi$
$73$	0.0673096	0.00787800	0.00393900	+	0.999992i	$0.498746\pi$
$74$	3.67800	0.427559
$75$	7.04740	0.813764
$76$	−1.00000	−0.114708
$77$	−16.1467	−1.84009
$78$	−8.62266	−0.976324
$79$	17.2366	1.93927	0.969634	−	0.244562i	$-0.0786441\pi$
$79$	17.2366	1.93927	0.969634	+	0.244562i	$0.0786441\pi$
$80$	1.33631	0.149404
$81$	−11.1556	−1.23951
$82$	−8.72443	−0.963453
$83$	−7.67587	−0.842536	−0.421268	−	0.906936i	$-0.638415\pi$
$83$	−7.67587	−0.842536	−0.421268	+	0.906936i	$0.638415\pi$
$84$	10.9430	1.19397
$85$	3.07668	0.333713
$86$	9.15875	0.987613
$87$	−16.8572	−1.80728
$88$	3.23517	0.344870
$89$	16.3005	1.72785	0.863926	−	0.503618i	$-0.167998\pi$
$89$	16.3005	1.72785	0.863926	+	0.503618i	$0.167998\pi$
$90$	2.41502	0.254566
$91$	−19.6282	−2.05760
$92$	2.41135	0.251400
$93$	22.3258	2.31508
$94$	−9.14506	−0.943240
$95$	−1.33631	−0.137103
$96$	−2.19254	−0.223775
$97$	−11.3545	−1.15287	−0.576437	−	0.817142i	$-0.695557\pi$
$97$	−11.3545	−1.15287	−0.576437	+	0.817142i	$0.695557\pi$
$98$	17.9101	1.80919
$99$	5.84668	0.587614
$100$	−3.21427	−0.321427
$101$	7.04416	0.700920	0.350460	−	0.936578i	$-0.386025\pi$
$101$	7.04416	0.700920	0.350460	+	0.936578i	$0.386025\pi$
$102$	−5.04802	−0.499828
$103$	0.709413	0.0699006	0.0349503	−	0.999389i	$-0.488873\pi$
$103$	0.709413	0.0699006	0.0349503	+	0.999389i	$0.488873\pi$
$104$	3.93273	0.385636
$105$	14.6232	1.42708
$106$	5.22097	0.507105
$107$	−5.94411	−0.574639	−0.287319	−	0.957835i	$-0.592764\pi$
$107$	−5.94411	−0.574639	−0.287319	+	0.957835i	$0.592764\pi$
$108$	2.61520	0.251648
$109$	17.7690	1.70196	0.850982	−	0.525195i	$-0.176008\pi$
$109$	17.7690	1.70196	0.850982	+	0.525195i	$0.176008\pi$
$110$	4.32320	0.412201
$111$	−8.06416	−0.765416
$112$	−4.99100	−0.471605
$113$	3.00814	0.282982	0.141491	−	0.989940i	$-0.454810\pi$
$113$	3.00814	0.282982	0.141491	+	0.989940i	$0.454810\pi$
$114$	2.19254	0.205350
$115$	3.22231	0.300482
$116$	7.68845	0.713854
$117$	7.10734	0.657074
$118$	−9.07487	−0.835410
$119$	−11.4911	−1.05339
$120$	−2.92992	−0.267464
$121$	−0.533707	−0.0485188
$122$	−1.01640	−0.0920210
$123$	19.1287	1.72477
$124$	−10.1826	−0.914427
$125$	−10.9768	−0.981798
$126$	−9.01987	−0.803554
$127$	19.8593	1.76223	0.881114	−	0.472905i	$-0.156794\pi$
$127$	19.8593	1.76223	0.881114	+	0.472905i	$0.156794\pi$
$128$	1.00000	0.0883883
$129$	−20.0809	−1.76803
$130$	5.25536	0.460926
$131$	18.9722	1.65761	0.828806	−	0.559536i	$-0.189021\pi$
$131$	18.9722	1.65761	0.828806	+	0.559536i	$0.189021\pi$
$132$	−7.09323	−0.617386
$133$	4.99100	0.432774
$134$	−14.2825	−1.23382
$135$	3.49472	0.300778
$136$	2.30236	0.197426
$137$	17.6422	1.50728	0.753638	−	0.657290i	$-0.228297\pi$
$137$	17.6422	1.50728	0.753638	+	0.657290i	$0.228297\pi$
$138$	−5.28697	−0.450057
$139$	−15.5679	−1.32045	−0.660227	−	0.751066i	$-0.729540\pi$
$139$	−15.5679	−1.32045	−0.660227	+	0.751066i	$0.729540\pi$
$140$	−6.66954	−0.563679
$141$	20.0509	1.68859
$142$	−5.03857	−0.422827
$143$	12.7230	1.06395
$144$	1.80723	0.150602
$145$	10.2742	0.853224
$146$	0.0673096	0.00557058
$147$	−39.2685	−3.23881
$148$	3.67800	0.302330
$149$	−4.97748	−0.407771	−0.203886	−	0.978995i	$-0.565357\pi$
$149$	−4.97748	−0.407771	−0.203886	+	0.978995i	$0.565357\pi$
$150$	7.04740	0.575418
$151$	−3.25853	−0.265175	−0.132588	−	0.991171i	$-0.542329\pi$
$151$	−3.25853	−0.265175	−0.132588	+	0.991171i	$0.542329\pi$
$152$	−1.00000	−0.0811107
$153$	4.16090	0.336388
$154$	−16.1467	−1.30114
$155$	−13.6072	−1.09296
$156$	−8.62266	−0.690366
$157$	−8.55713	−0.682933	−0.341467	−	0.939894i	$-0.610924\pi$
$157$	−8.55713	−0.682933	−0.341467	+	0.939894i	$0.610924\pi$
$158$	17.2366	1.37127
$159$	−11.4472	−0.907820
$160$	1.33631	0.105645
$161$	−12.0350	−0.948492
$162$	−11.1556	−0.876468
$163$	2.50839	0.196473	0.0982363	−	0.995163i	$-0.468680\pi$
$163$	2.50839	0.196473	0.0982363	+	0.995163i	$0.468680\pi$
$164$	−8.72443	−0.681264
$165$	−9.47878	−0.737922
$166$	−7.67587	−0.595763
$167$	19.2405	1.48887	0.744436	−	0.667694i	$-0.232718\pi$
$167$	19.2405	1.48887	0.744436	+	0.667694i	$0.232718\pi$
$168$	10.9430	0.844267
$169$	2.46636	0.189720
$170$	3.07668	0.235970
$171$	−1.80723	−0.138202
$172$	9.15875	0.698348
$173$	−6.74408	−0.512743	−0.256371	−	0.966578i	$-0.582527\pi$
$173$	−6.74408	−0.512743	−0.256371	+	0.966578i	$0.582527\pi$
$174$	−16.8572	−1.27794
$175$	16.0424	1.21269
$176$	3.23517	0.243860
$177$	19.8970	1.49555
$178$	16.3005	1.22178
$179$	10.3164	0.771086	0.385543	−	0.922690i	$-0.374014\pi$
$179$	10.3164	0.771086	0.385543	+	0.922690i	$0.374014\pi$
$180$	2.41502	0.180005
$181$	−12.0472	−0.895460	−0.447730	−	0.894169i	$-0.647767\pi$
$181$	−12.0472	−0.895460	−0.447730	+	0.894169i	$0.647767\pi$
$182$	−19.6282	−1.45494
$183$	2.22851	0.164736
$184$	2.41135	0.177767
$185$	4.91496	0.361355
$186$	22.3258	1.63701
$187$	7.44852	0.544690
$188$	−9.14506	−0.666972
$189$	−13.0524	−0.949426
$190$	−1.33631	−0.0969464
$191$	20.9811	1.51814	0.759070	−	0.651009i	$-0.225654\pi$
$191$	20.9811	1.51814	0.759070	+	0.651009i	$0.225654\pi$
$192$	−2.19254	−0.158233
$193$	−14.1088	−1.01557	−0.507787	−	0.861482i	$-0.669536\pi$
$193$	−14.1088	−1.01557	−0.507787	+	0.861482i	$0.669536\pi$
$194$	−11.3545	−0.815205
$195$	−11.5226	−0.825149
$196$	17.9101	1.27929
$197$	16.6726	1.18788	0.593938	−	0.804511i	$-0.297572\pi$
$197$	16.6726	1.18788	0.593938	+	0.804511i	$0.297572\pi$
$198$	5.84668	0.415506
$199$	21.2816	1.50862	0.754308	−	0.656521i	$-0.227973\pi$
$199$	21.2816	1.50862	0.754308	+	0.656521i	$0.227973\pi$
$200$	−3.21427	−0.227283
$201$	31.3149	2.20878
$202$	7.04416	0.495625
$203$	−38.3730	−2.69326
$204$	−5.04802	−0.353432
$205$	−11.6586	−0.814271
$206$	0.709413	0.0494272
$207$	4.35785	0.302892
$208$	3.93273	0.272686
$209$	−3.23517	−0.223781
$210$	14.6232	1.00910
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	5.22097	0.358577
$213$	11.0473	0.756946
$214$	−5.94411	−0.406331
$215$	12.2390	0.834690
$216$	2.61520	0.177942
$217$	50.8215	3.44999
$218$	17.7690	1.20347
$219$	−0.147579	−0.00997246
$220$	4.32320	0.291470
$221$	9.05457	0.609076
$222$	−8.06416	−0.541231
$223$	−2.15682	−0.144431	−0.0722157	−	0.997389i	$-0.523007\pi$
$223$	−2.15682	−0.144431	−0.0722157	+	0.997389i	$0.523007\pi$
$224$	−4.99100	−0.333475
$225$	−5.80891	−0.387261
$226$	3.00814	0.200099
$227$	29.2424	1.94089	0.970444	−	0.241325i	$-0.0775820\pi$
$227$	29.2424	1.94089	0.970444	+	0.241325i	$0.0775820\pi$
$228$	2.19254	0.145204
$229$	−12.3363	−0.815209	−0.407604	−	0.913159i	$-0.633636\pi$
$229$	−12.3363	−0.815209	−0.407604	+	0.913159i	$0.633636\pi$
$230$	3.22231	0.212473
$231$	35.4023	2.32930
$232$	7.68845	0.504771
$233$	28.8405	1.88940	0.944701	−	0.327934i	$-0.106352\pi$
$233$	28.8405	1.88940	0.944701	+	0.327934i	$0.106352\pi$
$234$	7.10734	0.464621
$235$	−12.2207	−0.797188
$236$	−9.07487	−0.590724
$237$	−37.7919	−2.45485
$238$	−11.4911	−0.744856
$239$	6.55775	0.424186	0.212093	−	0.977250i	$-0.431972\pi$
$239$	6.55775	0.424186	0.212093	+	0.977250i	$0.431972\pi$
$240$	−2.92992	−0.189126
$241$	5.31595	0.342431	0.171215	−	0.985234i	$-0.445231\pi$
$241$	5.31595	0.342431	0.171215	+	0.985234i	$0.445231\pi$
$242$	−0.533707	−0.0343080
$243$	16.6135	1.06576
$244$	−1.01640	−0.0650686
$245$	23.9334	1.52905
$246$	19.1287	1.21960
$247$	−3.93273	−0.250234
$248$	−10.1826	−0.646597
$249$	16.8297	1.06654
$250$	−10.9768	−0.694236
$251$	−9.63221	−0.607980	−0.303990	−	0.952675i	$-0.598319\pi$
$251$	−9.63221	−0.607980	−0.303990	+	0.952675i	$0.598319\pi$
$252$	−9.01987	−0.568199
$253$	7.80110	0.490451
$254$	19.8593	1.24608
$255$	−6.74574	−0.422434
$256$	1.00000	0.0625000
$257$	15.4729	0.965173	0.482586	−	0.875848i	$-0.339697\pi$
$257$	15.4729	0.965173	0.482586	+	0.875848i	$0.339697\pi$
$258$	−20.0809	−1.25018
$259$	−18.3569	−1.14064
$260$	5.25536	0.325924
$261$	13.8948	0.860065
$262$	18.9722	1.17211
$263$	24.2296	1.49406	0.747032	−	0.664788i	$-0.231478\pi$
$263$	24.2296	1.49406	0.747032	+	0.664788i	$0.231478\pi$
$264$	−7.09323	−0.436558
$265$	6.97685	0.428585
$266$	4.99100	0.306018
$267$	−35.7395	−2.18722
$268$	−14.2825	−0.872440
$269$	9.02170	0.550063	0.275032	−	0.961435i	$-0.411312\pi$
$269$	9.02170	0.550063	0.275032	+	0.961435i	$0.411312\pi$
$270$	3.49472	0.212682
$271$	−8.19166	−0.497608	−0.248804	−	0.968554i	$-0.580038\pi$
$271$	−8.19166	−0.497608	−0.248804	+	0.968554i	$0.580038\pi$
$272$	2.30236	0.139601
$273$	43.0357	2.60464
$274$	17.6422	1.06580
$275$	−10.3987	−0.627064
$276$	−5.28697	−0.318238
$277$	−3.13487	−0.188356	−0.0941779	−	0.995555i	$-0.530022\pi$
$277$	−3.13487	−0.188356	−0.0941779	+	0.995555i	$0.530022\pi$
$278$	−15.5679	−0.933702
$279$	−18.4023	−1.10172
$280$	−6.66954	−0.398581
$281$	−9.92812	−0.592262	−0.296131	−	0.955147i	$-0.595696\pi$
$281$	−9.92812	−0.592262	−0.296131	+	0.955147i	$0.595696\pi$
$282$	20.0509	1.19401
$283$	13.7063	0.814752	0.407376	−	0.913260i	$-0.366444\pi$
$283$	13.7063	0.814752	0.407376	+	0.913260i	$0.366444\pi$
$284$	−5.03857	−0.298984
$285$	2.92992	0.173554
$286$	12.7230	0.752328
$287$	43.5436	2.57030
$288$	1.80723	0.106492
$289$	−11.6991	−0.688184
$290$	10.2742	0.603320
$291$	24.8952	1.45938
$292$	0.0673096	0.00393900
$293$	19.6345	1.14706	0.573529	−	0.819185i	$-0.305574\pi$
$293$	19.6345	1.14706	0.573529	+	0.819185i	$0.305574\pi$
$294$	−39.2685	−2.29018
$295$	−12.1269	−0.706054
$296$	3.67800	0.213779
$297$	8.46060	0.490934
$298$	−4.97748	−0.288338
$299$	9.48317	0.548426
$300$	7.04740	0.406882
$301$	−45.7113	−2.63476
$302$	−3.25853	−0.187507
$303$	−15.4446	−0.887268
$304$	−1.00000	−0.0573539
$305$	−1.35824	−0.0777724
$306$	4.16090	0.237863
$307$	6.29086	0.359039	0.179519	−	0.983754i	$-0.442546\pi$
$307$	6.29086	0.359039	0.179519	+	0.983754i	$0.442546\pi$
$308$	−16.1467	−0.920044
$309$	−1.55542	−0.0884845
$310$	−13.6072	−0.772836
$311$	28.9522	1.64173	0.820865	−	0.571122i	$-0.193492\pi$
$311$	28.9522	1.64173	0.820865	+	0.571122i	$0.193492\pi$
$312$	−8.62266	−0.488162
$313$	28.9569	1.63674	0.818370	−	0.574692i	$-0.194878\pi$
$313$	28.9569	1.63674	0.818370	+	0.574692i	$0.194878\pi$
$314$	−8.55713	−0.482907
$315$	−12.0534	−0.679131
$316$	17.2366	0.969634
$317$	−0.740200	−0.0415737	−0.0207869	−	0.999784i	$-0.506617\pi$
$317$	−0.740200	−0.0415737	−0.0207869	+	0.999784i	$0.506617\pi$
$318$	−11.4472	−0.641926
$319$	24.8734	1.39264
$320$	1.33631	0.0747022
$321$	13.0327	0.727414
$322$	−12.0350	−0.670685
$323$	−2.30236	−0.128107
$324$	−11.1556	−0.619756
$325$	−12.6408	−0.701187
$326$	2.50839	0.138927
$327$	−38.9593	−2.15445
$328$	−8.72443	−0.481726
$329$	45.6429	2.51638
$330$	−9.47878	−0.521789
$331$	−17.8704	−0.982247	−0.491123	−	0.871090i	$-0.663414\pi$
$331$	−17.8704	−0.982247	−0.491123	+	0.871090i	$0.663414\pi$
$332$	−7.67587	−0.421268
$333$	6.64699	0.364253
$334$	19.2405	1.05279
$335$	−19.0858	−1.04277
$336$	10.9430	0.596987
$337$	−28.7954	−1.56858	−0.784292	−	0.620392i	$-0.786974\pi$
$337$	−28.7954	−1.56858	−0.784292	+	0.620392i	$0.786974\pi$
$338$	2.46636	0.134152
$339$	−6.59547	−0.358217
$340$	3.07668	0.166856
$341$	−32.9425	−1.78394
$342$	−1.80723	−0.0977237
$343$	−54.4520	−2.94013
$344$	9.15875	0.493807
$345$	−7.06505	−0.380369
$346$	−6.74408	−0.362564
$347$	−14.9958	−0.805017	−0.402508	−	0.915416i	$-0.631862\pi$
$347$	−14.9958	−0.805017	−0.402508	+	0.915416i	$0.631862\pi$
$348$	−16.8572	−0.903642
$349$	−17.8998	−0.958155	−0.479077	−	0.877773i	$-0.659029\pi$
$349$	−17.8998	−0.958155	−0.479077	+	0.877773i	$0.659029\pi$
$350$	16.0424	0.857502
$351$	10.2849	0.548965
$352$	3.23517	0.172435
$353$	−2.11526	−0.112584	−0.0562920	−	0.998414i	$-0.517928\pi$
$353$	−2.11526	−0.112584	−0.0562920	+	0.998414i	$0.517928\pi$
$354$	19.8970	1.05751
$355$	−6.73311	−0.357356
$356$	16.3005	0.863926
$357$	25.1946	1.33344
$358$	10.3164	0.545240
$359$	1.71122	0.0903146	0.0451573	−	0.998980i	$-0.485621\pi$
$359$	1.71122	0.0903146	0.0451573	+	0.998980i	$0.485621\pi$
$360$	2.41502	0.127283
$361$	1.00000	0.0526316
$362$	−12.0472	−0.633186
$363$	1.17017	0.0614182
$364$	−19.6282	−1.02880
$365$	0.0899468	0.00470803
$366$	2.22851	0.116486
$367$	−11.7588	−0.613802	−0.306901	−	0.951741i	$-0.599292\pi$
$367$	−11.7588	−0.613802	−0.306901	+	0.951741i	$0.599292\pi$
$368$	2.41135	0.125700
$369$	−15.7670	−0.820800
$370$	4.91496	0.255517
$371$	−26.0578	−1.35286
$372$	22.3258	1.15754
$373$	16.5240	0.855582	0.427791	−	0.903878i	$-0.359292\pi$
$373$	16.5240	0.855582	0.427791	+	0.903878i	$0.359292\pi$
$374$	7.44852	0.385154
$375$	24.0671	1.24282
$376$	−9.14506	−0.471620
$377$	30.2366	1.55726
$378$	−13.0524	−0.671345
$379$	1.84920	0.0949869	0.0474934	−	0.998872i	$-0.484877\pi$
$379$	1.84920	0.0949869	0.0474934	+	0.998872i	$0.484877\pi$
$380$	−1.33631	−0.0685515
$381$	−43.5423	−2.23074
$382$	20.9811	1.07349
$383$	33.4345	1.70842	0.854211	−	0.519926i	$-0.174041\pi$
$383$	33.4345	1.70842	0.854211	+	0.519926i	$0.174041\pi$
$384$	−2.19254	−0.111888
$385$	−21.5771	−1.09967
$386$	−14.1088	−0.718120
$387$	16.5520	0.841383
$388$	−11.3545	−0.576437
$389$	16.6873	0.846081	0.423041	−	0.906111i	$-0.360963\pi$
$389$	16.6873	0.846081	0.423041	+	0.906111i	$0.360963\pi$
$390$	−11.5226	−0.583469
$391$	5.55179	0.280766
$392$	17.9101	0.904594
$393$	−41.5974	−2.09831
$394$	16.6726	0.839955
$395$	23.0335	1.15894
$396$	5.84668	0.293807
$397$	−3.09856	−0.155512	−0.0777562	−	0.996972i	$-0.524776\pi$
$397$	−3.09856	−0.155512	−0.0777562	+	0.996972i	$0.524776\pi$
$398$	21.2816	1.06675
$399$	−10.9430	−0.547833
$400$	−3.21427	−0.160713
$401$	−18.0100	−0.899377	−0.449688	−	0.893186i	$-0.648465\pi$
$401$	−18.0100	−0.899377	−0.449688	+	0.893186i	$0.648465\pi$
$402$	31.3149	1.56184
$403$	−40.0455	−1.99481
$404$	7.04416	0.350460
$405$	−14.9074	−0.740754
$406$	−38.3730	−1.90442
$407$	11.8989	0.589808
$408$	−5.04802	−0.249914
$409$	17.0555	0.843341	0.421671	−	0.906749i	$-0.361444\pi$
$409$	17.0555	0.843341	0.421671	+	0.906749i	$0.361444\pi$
$410$	−11.6586	−0.575776
$411$	−38.6812	−1.90800
$412$	0.709413	0.0349503
$413$	45.2927	2.22871
$414$	4.35785	0.214177
$415$	−10.2574	−0.503515
$416$	3.93273	0.192818
$417$	34.1333	1.67151
$418$	−3.23517	−0.158237
$419$	−3.00770	−0.146936	−0.0734678	−	0.997298i	$-0.523407\pi$
$419$	−3.00770	−0.146936	−0.0734678	+	0.997298i	$0.523407\pi$
$420$	14.6232	0.713540
$421$	−4.14400	−0.201966	−0.100983	−	0.994888i	$-0.532199\pi$
$421$	−4.14400	−0.201966	−0.100983	+	0.994888i	$0.532199\pi$
$422$	−1.00000	−0.0486792
$423$	−16.5272	−0.803580
$424$	5.22097	0.253553
$425$	−7.40040	−0.358972
$426$	11.0473	0.535242
$427$	5.07287	0.245494
$428$	−5.94411	−0.287319
$429$	−27.8957	−1.34682
$430$	12.2390	0.590215
$431$	2.40162	0.115682	0.0578411	−	0.998326i	$-0.481578\pi$
$431$	2.40162	0.115682	0.0578411	+	0.998326i	$0.481578\pi$
$432$	2.61520	0.125824
$433$	7.86916	0.378167	0.189084	−	0.981961i	$-0.439448\pi$
$433$	7.86916	0.378167	0.189084	+	0.981961i	$0.439448\pi$
$434$	50.8215	2.43951
$435$	−22.5265	−1.08006
$436$	17.7690	0.850982
$437$	−2.41135	−0.115350
$438$	−0.147579	−0.00705160
$439$	−11.3294	−0.540723	−0.270361	−	0.962759i	$-0.587143\pi$
$439$	−11.3294	−0.540723	−0.270361	+	0.962759i	$0.587143\pi$
$440$	4.32320	0.206100
$441$	32.3676	1.54131
$442$	9.05457	0.430682
$443$	−26.2483	−1.24709	−0.623547	−	0.781786i	$-0.714309\pi$
$443$	−26.2483	−1.24709	−0.623547	+	0.781786i	$0.714309\pi$
$444$	−8.06416	−0.382708
$445$	21.7826	1.03260
$446$	−2.15682	−0.102128
$447$	10.9133	0.516183
$448$	−4.99100	−0.235802
$449$	−29.4362	−1.38918	−0.694589	−	0.719407i	$-0.744414\pi$
$449$	−29.4362	−1.38918	−0.694589	+	0.719407i	$0.744414\pi$
$450$	−5.80891	−0.273835
$451$	−28.2250	−1.32906
$452$	3.00814	0.141491
$453$	7.14445	0.335676
$454$	29.2424	1.37242
$455$	−26.2295	−1.22966
$456$	2.19254	0.102675
$457$	23.6629	1.10690	0.553451	−	0.832882i	$-0.313310\pi$
$457$	23.6629	1.10690	0.553451	+	0.832882i	$0.313310\pi$
$458$	−12.3363	−0.576440
$459$	6.02113	0.281042
$460$	3.22231	0.150241
$461$	−5.91987	−0.275716	−0.137858	−	0.990452i	$-0.544022\pi$
$461$	−5.91987	−0.275716	−0.137858	+	0.990452i	$0.544022\pi$
$462$	35.4023	1.64706
$463$	−37.3810	−1.73724	−0.868620	−	0.495479i	$-0.834993\pi$
$463$	−37.3810	−1.73724	−0.868620	+	0.495479i	$0.834993\pi$
$464$	7.68845	0.356927
$465$	29.8343	1.38353
$466$	28.8405	1.33601
$467$	11.9819	0.554458	0.277229	−	0.960804i	$-0.410584\pi$
$467$	11.9819	0.554458	0.277229	+	0.960804i	$0.410584\pi$
$468$	7.10734	0.328537
$469$	71.2837	3.29158
$470$	−12.2207	−0.563697
$471$	18.7618	0.864500
$472$	−9.07487	−0.417705
$473$	29.6301	1.36239
$474$	−37.7919	−1.73584
$475$	3.21427	0.147481
$476$	−11.4911	−0.526693
$477$	9.43548	0.432021
$478$	6.55775	0.299945
$479$	6.69002	0.305675	0.152837	−	0.988251i	$-0.451159\pi$
$479$	6.69002	0.305675	0.152837	+	0.988251i	$0.451159\pi$
$480$	−2.92992	−0.133732
$481$	14.4646	0.659528
$482$	5.31595	0.242135
$483$	26.3872	1.20066
$484$	−0.533707	−0.0242594
$485$	−15.1732	−0.688978
$486$	16.6135	0.753605
$487$	4.59844	0.208375	0.104188	−	0.994558i	$-0.466776\pi$
$487$	4.59844	0.208375	0.104188	+	0.994558i	$0.466776\pi$
$488$	−1.01640	−0.0460105
$489$	−5.49975	−0.248707
$490$	23.9334	1.08120
$491$	28.7851	1.29905	0.649526	−	0.760339i	$-0.274967\pi$
$491$	28.7851	1.29905	0.649526	+	0.760339i	$0.274967\pi$
$492$	19.1287	0.862387
$493$	17.7016	0.797239
$494$	−3.93273	−0.176942
$495$	7.81300	0.351168
$496$	−10.1826	−0.457213
$497$	25.1475	1.12802
$498$	16.8297	0.754155
$499$	1.70779	0.0764511	0.0382256	−	0.999269i	$-0.487829\pi$
$499$	1.70779	0.0764511	0.0382256	+	0.999269i	$0.487829\pi$
$500$	−10.9768	−0.490899
$501$	−42.1855	−1.88471
$502$	−9.63221	−0.429906
$503$	−29.1985	−1.30190	−0.650949	−	0.759121i	$-0.725629\pi$
$503$	−29.1985	−1.30190	−0.650949	+	0.759121i	$0.725629\pi$
$504$	−9.01987	−0.401777
$505$	9.41320	0.418882
$506$	7.80110	0.346801
$507$	−5.40759	−0.240160
$508$	19.8593	0.881114
$509$	8.51309	0.377336	0.188668	−	0.982041i	$-0.439583\pi$
$509$	8.51309	0.377336	0.188668	+	0.982041i	$0.439583\pi$
$510$	−6.74574	−0.298706
$511$	−0.335942	−0.0148612
$512$	1.00000	0.0441942
$513$	−2.61520	−0.115464
$514$	15.4729	0.682480
$515$	0.947999	0.0417738
$516$	−20.0809	−0.884013
$517$	−29.5858	−1.30118
$518$	−18.3569	−0.806555
$519$	14.7867	0.649062
$520$	5.25536	0.230463
$521$	8.87578	0.388855	0.194428	−	0.980917i	$-0.437715\pi$
$521$	8.87578	0.388855	0.194428	+	0.980917i	$0.437715\pi$
$522$	13.8948	0.608158
$523$	35.5373	1.55394	0.776969	−	0.629539i	$-0.216756\pi$
$523$	35.5373	1.55394	0.776969	+	0.629539i	$0.216756\pi$
$524$	18.9722	0.828806
$525$	−35.1736	−1.53510
$526$	24.2296	1.05646
$527$	−23.4441	−1.02124
$528$	−7.09323	−0.308693
$529$	−17.1854	−0.747192
$530$	6.97685	0.303055
$531$	−16.4004	−0.711716
$532$	4.99100	0.216387
$533$	−34.3108	−1.48617
$534$	−35.7395	−1.54660
$535$	−7.94320	−0.343414
$536$	−14.2825	−0.616908
$537$	−22.6192	−0.976090
$538$	9.02170	0.388953
$539$	57.9420	2.49574
$540$	3.49472	0.150389
$541$	44.3652	1.90741	0.953704	−	0.300747i	$-0.0972360\pi$
$541$	44.3652	1.90741	0.953704	+	0.300747i	$0.0972360\pi$
$542$	−8.19166	−0.351862
$543$	26.4139	1.13353
$544$	2.30236	0.0987130
$545$	23.7450	1.01712
$546$	43.0357	1.84176
$547$	31.6895	1.35494	0.677472	−	0.735549i	$-0.263076\pi$
$547$	31.6895	1.35494	0.677472	+	0.735549i	$0.263076\pi$
$548$	17.6422	0.753638
$549$	−1.83688	−0.0783960
$550$	−10.3987	−0.443401
$551$	−7.68845	−0.327539
$552$	−5.28697	−0.225028
$553$	−86.0278	−3.65827
$554$	−3.13487	−0.133188
$555$	−10.7762	−0.457426
$556$	−15.5679	−0.660227
$557$	24.5966	1.04219	0.521095	−	0.853498i	$-0.325524\pi$
$557$	24.5966	1.04219	0.521095	+	0.853498i	$0.325524\pi$
$558$	−18.4023	−0.779033
$559$	36.0189	1.52344
$560$	−6.66954	−0.281839
$561$	−16.3312	−0.689503
$562$	−9.92812	−0.418792
$563$	−9.55585	−0.402731	−0.201365	−	0.979516i	$-0.564538\pi$
$563$	−9.55585	−0.402731	−0.201365	+	0.979516i	$0.564538\pi$
$564$	20.0509	0.844295
$565$	4.01982	0.169115
$566$	13.7063	0.576117
$567$	55.6776	2.33824
$568$	−5.03857	−0.211414
$569$	−35.6967	−1.49648	−0.748241	−	0.663427i	$-0.769102\pi$
$569$	−35.6967	−1.49648	−0.748241	+	0.663427i	$0.769102\pi$
$570$	2.92992	0.122721
$571$	−24.3701	−1.01986	−0.509928	−	0.860217i	$-0.670328\pi$
$571$	−24.3701	−1.01986	−0.509928	+	0.860217i	$0.670328\pi$
$572$	12.7230	0.531977
$573$	−46.0019	−1.92176
$574$	43.5436	1.81748
$575$	−7.75070	−0.323227
$576$	1.80723	0.0753012
$577$	−15.0012	−0.624510	−0.312255	−	0.949998i	$-0.601084\pi$
$577$	−15.0012	−0.624510	−0.312255	+	0.949998i	$0.601084\pi$
$578$	−11.6991	−0.486620
$579$	30.9341	1.28558
$580$	10.2742	0.426612
$581$	38.3103	1.58938
$582$	24.8952	1.03194
$583$	16.8907	0.699541
$584$	0.0673096	0.00278529
$585$	9.49764	0.392679
$586$	19.6345	0.811092
$587$	19.8294	0.818445	0.409223	−	0.912435i	$-0.365800\pi$
$587$	19.8294	0.818445	0.409223	+	0.912435i	$0.365800\pi$
$588$	−39.2685	−1.61941
$589$	10.1826	0.419568
$590$	−12.1269	−0.499256
$591$	−36.5554	−1.50369
$592$	3.67800	0.151165
$593$	−4.18410	−0.171820	−0.0859101	−	0.996303i	$-0.527380\pi$
$593$	−4.18410	−0.171820	−0.0859101	+	0.996303i	$0.527380\pi$
$594$	8.46060	0.347142
$595$	−15.3557	−0.629522
$596$	−4.97748	−0.203886
$597$	−46.6608	−1.90970
$598$	9.48317	0.387796
$599$	−2.87767	−0.117578	−0.0587891	−	0.998270i	$-0.518724\pi$
$599$	−2.87767	−0.117578	−0.0587891	+	0.998270i	$0.518724\pi$
$600$	7.04740	0.287709
$601$	−1.95912	−0.0799140	−0.0399570	−	0.999201i	$-0.512722\pi$
$601$	−1.95912	−0.0799140	−0.0399570	+	0.999201i	$0.512722\pi$
$602$	−45.7113	−1.86305
$603$	−25.8117	−1.05113
$604$	−3.25853	−0.132588
$605$	−0.713200	−0.0289957
$606$	−15.4446	−0.627393
$607$	−31.9372	−1.29629	−0.648146	−	0.761516i	$-0.724456\pi$
$607$	−31.9372	−1.29629	−0.648146	+	0.761516i	$0.724456\pi$
$608$	−1.00000	−0.0405554
$609$	84.1343	3.40930
$610$	−1.35824	−0.0549934
$611$	−35.9650	−1.45499
$612$	4.16090	0.168194
$613$	19.6450	0.793454	0.396727	−	0.917937i	$-0.370146\pi$
$613$	19.6450	0.793454	0.396727	+	0.917937i	$0.370146\pi$
$614$	6.29086	0.253879
$615$	25.5619	1.03076
$616$	−16.1467	−0.650569
$617$	3.49695	0.140782	0.0703909	−	0.997519i	$-0.477575\pi$
$617$	3.49695	0.140782	0.0703909	+	0.997519i	$0.477575\pi$
$618$	−1.55542	−0.0625680
$619$	42.6753	1.71527	0.857633	−	0.514263i	$-0.171934\pi$
$619$	42.6753	1.71527	0.857633	+	0.514263i	$0.171934\pi$
$620$	−13.6072	−0.546478
$621$	6.30614	0.253057
$622$	28.9522	1.16088
$623$	−81.3559	−3.25945
$624$	−8.62266	−0.345183
$625$	1.40283	0.0561132
$626$	28.9569	1.15735
$627$	7.09323	0.283276
$628$	−8.55713	−0.341467
$629$	8.46809	0.337645
$630$	−12.0534	−0.480218
$631$	−38.2894	−1.52428	−0.762139	−	0.647413i	$-0.775851\pi$
$631$	−38.2894	−1.52428	−0.762139	+	0.647413i	$0.775851\pi$
$632$	17.2366	0.685635
$633$	2.19254	0.0871456
$634$	−0.740200	−0.0293971
$635$	26.5382	1.05314
$636$	−11.4472	−0.453910
$637$	70.4354	2.79075
$638$	24.8734	0.984747
$639$	−9.10585	−0.360222
$640$	1.33631	0.0528224
$641$	38.0316	1.50216	0.751079	−	0.660212i	$-0.229534\pi$
$641$	38.0316	1.50216	0.751079	+	0.660212i	$0.229534\pi$
$642$	13.0327	0.514360
$643$	6.93025	0.273302	0.136651	−	0.990619i	$-0.456366\pi$
$643$	6.93025	0.273302	0.136651	+	0.990619i	$0.456366\pi$
$644$	−12.0350	−0.474246
$645$	−26.8344	−1.05660
$646$	−2.30236	−0.0905852
$647$	11.7510	0.461981	0.230990	−	0.972956i	$-0.425803\pi$
$647$	11.7510	0.461981	0.230990	+	0.972956i	$0.425803\pi$
$648$	−11.1556	−0.438234
$649$	−29.3587	−1.15243
$650$	−12.6408	−0.495814
$651$	−111.428	−4.36721
$652$	2.50839	0.0982363
$653$	4.23626	0.165778	0.0828888	−	0.996559i	$-0.473585\pi$
$653$	4.23626	0.165778	0.0828888	+	0.996559i	$0.473585\pi$
$654$	−38.9593	−1.52343
$655$	25.3529	0.990618
$656$	−8.72443	−0.340632
$657$	0.121644	0.00474578
$658$	45.6429	1.77935
$659$	13.5463	0.527690	0.263845	−	0.964565i	$-0.415009\pi$
$659$	13.5463	0.527690	0.263845	+	0.964565i	$0.415009\pi$
$660$	−9.47878	−0.368961
$661$	−24.5334	−0.954240	−0.477120	−	0.878838i	$-0.658319\pi$
$661$	−24.5334	−0.954240	−0.477120	+	0.878838i	$0.658319\pi$
$662$	−17.8704	−0.694553
$663$	−19.8525	−0.771007
$664$	−7.67587	−0.297882
$665$	6.66954	0.258634
$666$	6.64699	0.257565
$667$	18.5395	0.717852
$668$	19.2405	0.744436
$669$	4.72892	0.182830
$670$	−19.0858	−0.737351
$671$	−3.28824	−0.126941
$672$	10.9430	0.422134
$673$	35.0924	1.35271	0.676356	−	0.736575i	$-0.263558\pi$
$673$	35.0924	1.35271	0.676356	+	0.736575i	$0.263558\pi$
$674$	−28.7954	−1.10916
$675$	−8.40594	−0.323545
$676$	2.46636	0.0948601
$677$	8.87742	0.341187	0.170593	−	0.985341i	$-0.445432\pi$
$677$	8.87742	0.341187	0.170593	+	0.985341i	$0.445432\pi$
$678$	−6.59547	−0.253297
$679$	56.6702	2.17480
$680$	3.07668	0.117985
$681$	−64.1152	−2.45690
$682$	−32.9425	−1.26143
$683$	−27.3260	−1.04560	−0.522800	−	0.852455i	$-0.675113\pi$
$683$	−27.3260	−1.04560	−0.522800	+	0.852455i	$0.675113\pi$
$684$	−1.80723	−0.0691011
$685$	23.5755	0.900774
$686$	−54.4520	−2.07899
$687$	27.0479	1.03194
$688$	9.15875	0.349174
$689$	20.5327	0.782232
$690$	−7.06505	−0.268962
$691$	−30.1592	−1.14731	−0.573655	−	0.819097i	$-0.694475\pi$
$691$	−30.1592	−1.14731	−0.573655	+	0.819097i	$0.694475\pi$
$692$	−6.74408	−0.256371
$693$	−29.1808	−1.10849
$694$	−14.9958	−0.569233
$695$	−20.8036	−0.789127
$696$	−16.8572	−0.638971
$697$	−20.0868	−0.760842
$698$	−17.8998	−0.677518
$699$	−63.2338	−2.39172
$700$	16.0424	0.606345
$701$	−15.8188	−0.597469	−0.298734	−	0.954336i	$-0.596564\pi$
$701$	−15.8188	−0.597469	−0.298734	+	0.954336i	$0.596564\pi$
$702$	10.2849	0.388177
$703$	−3.67800	−0.138718
$704$	3.23517	0.121930
$705$	26.7943	1.00913
$706$	−2.11526	−0.0796089
$707$	−35.1574	−1.32223
$708$	19.8970	0.747776
$709$	36.1780	1.35870	0.679348	−	0.733817i	$-0.262263\pi$
$709$	36.1780	1.35870	0.679348	+	0.733817i	$0.262263\pi$
$710$	−6.73311	−0.252689
$711$	31.1505	1.16823
$712$	16.3005	0.610888
$713$	−24.5538	−0.919548
$714$	25.1946	0.942886
$715$	17.0020	0.635837
$716$	10.3164	0.385543
$717$	−14.3781	−0.536961
$718$	1.71122	0.0638621
$719$	−30.7886	−1.14822	−0.574111	−	0.818777i	$-0.694652\pi$
$719$	−30.7886	−1.14822	−0.574111	+	0.818777i	$0.694652\pi$
$720$	2.41502	0.0900027
$721$	−3.54068	−0.131862
$722$	1.00000	0.0372161
$723$	−11.6554	−0.433470
$724$	−12.0472	−0.447730
$725$	−24.7127	−0.917807
$726$	1.17017	0.0434292
$727$	−3.16482	−0.117377	−0.0586883	−	0.998276i	$-0.518692\pi$
$727$	−3.16482	−0.117377	−0.0586883	+	0.998276i	$0.518692\pi$
$728$	−19.6282	−0.727471
$729$	−2.95897	−0.109591
$730$	0.0899468	0.00332908
$731$	21.0868	0.779922
$732$	2.22851	0.0823680
$733$	−25.2690	−0.933333	−0.466666	−	0.884433i	$-0.654545\pi$
$733$	−25.2690	−0.933333	−0.466666	+	0.884433i	$0.654545\pi$
$734$	−11.7588	−0.434024
$735$	−52.4750	−1.93557
$736$	2.41135	0.0888834
$737$	−46.2061	−1.70202
$738$	−15.7670	−0.580393
$739$	19.2091	0.706619	0.353310	−	0.935506i	$-0.385056\pi$
$739$	19.2091	0.706619	0.353310	+	0.935506i	$0.385056\pi$
$740$	4.91496	0.180678
$741$	8.62266	0.316761
$742$	−26.0578	−0.956613
$743$	−19.1594	−0.702892	−0.351446	−	0.936208i	$-0.614310\pi$
$743$	−19.1594	−0.702892	−0.351446	+	0.936208i	$0.614310\pi$
$744$	22.3258	0.818504
$745$	−6.65148	−0.243691
$746$	16.5240	0.604988
$747$	−13.8721	−0.507552
$748$	7.44852	0.272345
$749$	29.6670	1.08401
$750$	24.0671	0.878808
$751$	28.2882	1.03225	0.516126	−	0.856513i	$-0.327374\pi$
$751$	28.2882	1.03225	0.516126	+	0.856513i	$0.327374\pi$
$752$	−9.14506	−0.333486
$753$	21.1190	0.769619
$754$	30.2366	1.10115
$755$	−4.35442	−0.158473
$756$	−13.0524	−0.474713
$757$	−8.86453	−0.322187	−0.161093	−	0.986939i	$-0.551502\pi$
$757$	−8.86453	−0.322187	−0.161093	+	0.986939i	$0.551502\pi$
$758$	1.84920	0.0671659
$759$	−17.1042	−0.620844
$760$	−1.33631	−0.0484732
$761$	37.9858	1.37698	0.688491	−	0.725245i	$-0.258273\pi$
$761$	37.9858	1.37698	0.688491	+	0.725245i	$0.258273\pi$
$762$	−43.5423	−1.57737
$763$	−88.6852	−3.21062
$764$	20.9811	0.759070
$765$	5.56026	0.201032
$766$	33.4345	1.20804
$767$	−35.6890	−1.28866
$768$	−2.19254	−0.0791164
$769$	52.1302	1.87986	0.939932	−	0.341363i	$-0.110888\pi$
$769$	52.1302	1.87986	0.939932	+	0.341363i	$0.110888\pi$
$770$	−21.5771	−0.777583
$771$	−33.9249	−1.22178
$772$	−14.1088	−0.507787
$773$	37.1755	1.33711	0.668555	−	0.743663i	$-0.266913\pi$
$773$	37.1755	1.33711	0.668555	+	0.743663i	$0.266913\pi$
$774$	16.5520	0.594948
$775$	32.7297	1.17568
$776$	−11.3545	−0.407602
$777$	40.2482	1.44390
$778$	16.6873	0.598270
$779$	8.72443	0.312585
$780$	−11.5226	−0.412575
$781$	−16.3006	−0.583281
$782$	5.55179	0.198532
$783$	20.1068	0.718559
$784$	17.9101	0.639645
$785$	−11.4350	−0.408133
$786$	−41.5974	−1.48373
$787$	33.7975	1.20475	0.602376	−	0.798213i	$-0.294221\pi$
$787$	33.7975	1.20475	0.602376	+	0.798213i	$0.294221\pi$
$788$	16.6726	0.593938
$789$	−53.1244	−1.89128
$790$	23.0335	0.819495
$791$	−15.0136	−0.533823
$792$	5.84668	0.207753
$793$	−3.99725	−0.141946
$794$	−3.09856	−0.109964
$795$	−15.2970	−0.542529
$796$	21.2816	0.754308
$797$	0.371231	0.0131497	0.00657484	−	0.999978i	$-0.497907\pi$
$797$	0.371231	0.0131497	0.00657484	+	0.999978i	$0.497907\pi$
$798$	−10.9430	−0.387376
$799$	−21.0552	−0.744880
$800$	−3.21427	−0.113641
$801$	29.4588	1.04087
$802$	−18.0100	−0.635955
$803$	0.217758	0.00768450
$804$	31.3149	1.10439
$805$	−16.0826	−0.566836
$806$	−40.0455	−1.41054
$807$	−19.7804	−0.696305
$808$	7.04416	0.247813
$809$	−13.5546	−0.476554	−0.238277	−	0.971197i	$-0.576583\pi$
$809$	−13.5546	−0.476554	−0.238277	+	0.971197i	$0.576583\pi$
$810$	−14.9074	−0.523793
$811$	8.47837	0.297716	0.148858	−	0.988859i	$-0.452440\pi$
$811$	8.47837	0.297716	0.148858	+	0.988859i	$0.452440\pi$
$812$	−38.3730	−1.34663
$813$	17.9605	0.629904
$814$	11.8989	0.417057
$815$	3.35200	0.117415
$816$	−5.04802	−0.176716
$817$	−9.15875	−0.320424
$818$	17.0555	0.596332
$819$	−35.4727	−1.23952
$820$	−11.6586	−0.407135
$821$	47.8117	1.66864	0.834321	−	0.551279i	$-0.185860\pi$
$821$	47.8117	1.66864	0.834321	+	0.551279i	$0.185860\pi$
$822$	−38.6812	−1.34916
$823$	50.9241	1.77510	0.887551	−	0.460710i	$-0.152405\pi$
$823$	50.9241	1.77510	0.887551	+	0.460710i	$0.152405\pi$
$824$	0.709413	0.0247136
$825$	22.7995	0.793777
$826$	45.2927	1.57593
$827$	9.99451	0.347543	0.173771	−	0.984786i	$-0.444405\pi$
$827$	9.99451	0.347543	0.173771	+	0.984786i	$0.444405\pi$
$828$	4.35785	0.151446
$829$	−8.74134	−0.303599	−0.151800	−	0.988411i	$-0.548507\pi$
$829$	−8.74134	−0.303599	−0.151800	+	0.988411i	$0.548507\pi$
$830$	−10.2574	−0.356039
$831$	6.87332	0.238433
$832$	3.93273	0.136343
$833$	41.2354	1.42872
$834$	34.1333	1.18194
$835$	25.7113	0.889776
$836$	−3.23517	−0.111891
$837$	−26.6296	−0.920453
$838$	−3.00770	−0.103899
$839$	−3.74913	−0.129434	−0.0647171	−	0.997904i	$-0.520615\pi$
$839$	−3.74913	−0.129434	−0.0647171	+	0.997904i	$0.520615\pi$
$840$	14.6232	0.504549
$841$	30.1122	1.03835
$842$	−4.14400	−0.142812
$843$	21.7678	0.749723
$844$	−1.00000	−0.0344214
$845$	3.29583	0.113380
$846$	−16.5272	−0.568217
$847$	2.66373	0.0915269
$848$	5.22097	0.179289
$849$	−30.0515	−1.03137
$850$	−7.40040	−0.253832
$851$	8.86893	0.304023
$852$	11.0473	0.378473
$853$	−22.9842	−0.786964	−0.393482	−	0.919332i	$-0.628730\pi$
$853$	−22.9842	−0.786964	−0.393482	+	0.919332i	$0.628730\pi$
$854$	5.07287	0.173590
$855$	−2.41502	−0.0825921
$856$	−5.94411	−0.203166
$857$	−10.9938	−0.375541	−0.187771	−	0.982213i	$-0.560126\pi$
$857$	−10.9938	−0.375541	−0.187771	+	0.982213i	$0.560126\pi$
$858$	−27.8957	−0.952345
$859$	−38.9355	−1.32846	−0.664231	−	0.747528i	$-0.731241\pi$
$859$	−38.9355	−1.32846	−0.664231	+	0.747528i	$0.731241\pi$
$860$	12.2390	0.417345
$861$	−95.4711	−3.25365
$862$	2.40162	0.0817997
$863$	−14.4753	−0.492745	−0.246372	−	0.969175i	$-0.579239\pi$
$863$	−14.4753	−0.492745	−0.246372	+	0.969175i	$0.579239\pi$
$864$	2.61520	0.0889708
$865$	−9.01220	−0.306424
$866$	7.86916	0.267405
$867$	25.6508	0.871147
$868$	50.8215	1.72499
$869$	55.7632	1.89164
$870$	−22.5265	−0.763721
$871$	−56.1690	−1.90322
$872$	17.7690	0.601735
$873$	−20.5202	−0.694502
$874$	−2.41135	−0.0815650
$875$	54.7854	1.85208
$876$	−0.147579	−0.00498623
$877$	0.776551	0.0262223	0.0131111	−	0.999914i	$-0.495826\pi$
$877$	0.776551	0.0262223	0.0131111	+	0.999914i	$0.495826\pi$
$878$	−11.3294	−0.382349
$879$	−43.0493	−1.45202
$880$	4.32320	0.145735
$881$	−1.16197	−0.0391479	−0.0195740	−	0.999808i	$-0.506231\pi$
$881$	−1.16197	−0.0391479	−0.0195740	+	0.999808i	$0.506231\pi$
$882$	32.3676	1.08987
$883$	−2.42935	−0.0817542	−0.0408771	−	0.999164i	$-0.513015\pi$
$883$	−2.42935	−0.0817542	−0.0408771	+	0.999164i	$0.513015\pi$
$884$	9.05457	0.304538
$885$	26.5887	0.893768
$886$	−26.2483	−0.881829
$887$	49.7491	1.67041	0.835206	−	0.549937i	$-0.185348\pi$
$887$	49.7491	1.67041	0.835206	+	0.549937i	$0.185348\pi$
$888$	−8.06416	−0.270615
$889$	−99.1177	−3.32430
$890$	21.7826	0.730155
$891$	−36.0902	−1.20907
$892$	−2.15682	−0.0722157
$893$	9.14506	0.306028
$894$	10.9133	0.364996
$895$	13.7860	0.460815
$896$	−4.99100	−0.166738
$897$	−20.7922	−0.694232
$898$	−29.4362	−0.982297
$899$	−78.2886	−2.61107
$900$	−5.80891	−0.193630
$901$	12.0206	0.400463
$902$	−28.2250	−0.939789
$903$	100.224	3.33524
$904$	3.00814	0.100049
$905$	−16.0988	−0.535143
$906$	7.14445	0.237359
$907$	−27.6025	−0.916524	−0.458262	−	0.888817i	$-0.651528\pi$
$907$	−27.6025	−0.916524	−0.458262	+	0.888817i	$0.651528\pi$
$908$	29.2424	0.970444
$909$	12.7304	0.422241
$910$	−26.2295	−0.869499
$911$	−36.9587	−1.22450	−0.612249	−	0.790665i	$-0.709735\pi$
$911$	−36.9587	−1.22450	−0.612249	+	0.790665i	$0.709735\pi$
$912$	2.19254	0.0726022
$913$	−24.8327	−0.821843
$914$	23.6629	0.782698
$915$	2.97799	0.0984492
$916$	−12.3363	−0.407604
$917$	−94.6903	−3.12695
$918$	6.02113	0.198727
$919$	−3.24644	−0.107090	−0.0535451	−	0.998565i	$-0.517052\pi$
$919$	−3.24644	−0.107090	−0.0535451	+	0.998565i	$0.517052\pi$
$920$	3.22231	0.106237
$921$	−13.7930	−0.454494
$922$	−5.91987	−0.194961
$923$	−19.8153	−0.652230
$924$	35.4023	1.16465
$925$	−11.8221	−0.388707
$926$	−37.3810	−1.22841
$927$	1.28207	0.0421088
$928$	7.68845	0.252386
$929$	−22.2003	−0.728367	−0.364184	−	0.931327i	$-0.618652\pi$
$929$	−22.2003	−0.728367	−0.364184	+	0.931327i	$0.618652\pi$
$930$	29.8343	0.978305
$931$	−17.9101	−0.586978
$932$	28.8405	0.944701
$933$	−63.4789	−2.07821
$934$	11.9819	0.392061
$935$	9.95356	0.325516
$936$	7.10734	0.232311
$937$	−51.1455	−1.67085	−0.835426	−	0.549603i	$-0.814779\pi$
$937$	−51.1455	−1.67085	−0.835426	+	0.549603i	$0.814779\pi$
$938$	71.2837	2.32750
$939$	−63.4891	−2.07189
$940$	−12.2207	−0.398594
$941$	48.9670	1.59628	0.798139	−	0.602473i	$-0.205818\pi$
$941$	48.9670	1.59628	0.798139	+	0.602473i	$0.205818\pi$
$942$	18.7618	0.611294
$943$	−21.0376	−0.685079
$944$	−9.07487	−0.295362
$945$	−17.4422	−0.567394
$946$	29.6301	0.963357
$947$	23.8941	0.776455	0.388228	−	0.921564i	$-0.373087\pi$
$947$	23.8941	0.776455	0.388228	+	0.921564i	$0.373087\pi$
$948$	−37.7919	−1.22742
$949$	0.264711	0.00859287
$950$	3.21427	0.104285
$951$	1.62292	0.0526267
$952$	−11.4911	−0.372428
$953$	45.1211	1.46162	0.730808	−	0.682583i	$-0.239143\pi$
$953$	45.1211	1.46162	0.730808	+	0.682583i	$0.239143\pi$
$954$	9.43548	0.305485
$955$	28.0374	0.907268
$956$	6.55775	0.212093
$957$	−54.5359	−1.76289
$958$	6.69002	0.216145
$959$	−88.0522	−2.84335
$960$	−2.92992	−0.0945628
$961$	72.6859	2.34471
$962$	14.4646	0.466357
$963$	−10.7424	−0.346168
$964$	5.31595	0.171215
$965$	−18.8538	−0.606926
$966$	26.3872	0.848996
$967$	16.5881	0.533436	0.266718	−	0.963775i	$-0.414061\pi$
$967$	16.5881	0.533436	0.266718	+	0.963775i	$0.414061\pi$
$968$	−0.533707	−0.0171540
$969$	5.04802	0.162166
$970$	−15.1732	−0.487181
$971$	−33.9360	−1.08906	−0.544530	−	0.838742i	$-0.683292\pi$
$971$	−33.9360	−1.08906	−0.544530	+	0.838742i	$0.683292\pi$
$972$	16.6135	0.532879
$973$	77.6995	2.49093
$974$	4.59844	0.147343
$975$	27.7155	0.887607
$976$	−1.01640	−0.0325343
$977$	23.7267	0.759083	0.379541	−	0.925175i	$-0.376082\pi$
$977$	23.7267	0.759083	0.379541	+	0.925175i	$0.376082\pi$
$978$	−5.49975	−0.175863
$979$	52.7349	1.68541
$980$	23.9334	0.764526
$981$	32.1127	1.02528
$982$	28.7851	0.918569
$983$	47.7146	1.52186	0.760929	−	0.648835i	$-0.224743\pi$
$983$	47.7146	1.52186	0.760929	+	0.648835i	$0.224743\pi$
$984$	19.1287	0.609800
$985$	22.2799	0.709896
$986$	17.7016	0.563733
$987$	−100.074	−3.18539
$988$	−3.93273	−0.125117
$989$	22.0849	0.702259
$990$	7.81300	0.248314
$991$	−58.4226	−1.85585	−0.927927	−	0.372762i	$-0.878411\pi$
$991$	−58.4226	−1.85585	−0.927927	+	0.372762i	$0.878411\pi$
$992$	−10.1826	−0.323299
$993$	39.1816	1.24339
$994$	25.1475	0.797630
$995$	28.4390	0.901575
$996$	16.8297	0.533268
$997$	33.1597	1.05018	0.525089	−	0.851048i	$-0.324032\pi$
$997$	33.1597	1.05018	0.525089	+	0.851048i	$0.324032\pi$
$998$	1.70779	0.0540591
$999$	9.61870	0.304322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.9	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.9	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.19254 q^{3} +1.00000 q^{4} +1.33631 q^{5} -2.19254 q^{6} -4.99100 q^{7} +1.00000 q^{8} +1.80723 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.19254 q^{3} +1.00000 q^{4} +1.33631 q^{5} -2.19254 q^{6} -4.99100 q^{7} +1.00000 q^{8} +1.80723 q^{9} +1.33631 q^{10} +3.23517 q^{11} -2.19254 q^{12} +3.93273 q^{13} -4.99100 q^{14} -2.92992 q^{15} +1.00000 q^{16} +2.30236 q^{17} +1.80723 q^{18} -1.00000 q^{19} +1.33631 q^{20} +10.9430 q^{21} +3.23517 q^{22} +2.41135 q^{23} -2.19254 q^{24} -3.21427 q^{25} +3.93273 q^{26} +2.61520 q^{27} -4.99100 q^{28} +7.68845 q^{29} -2.92992 q^{30} -10.1826 q^{31} +1.00000 q^{32} -7.09323 q^{33} +2.30236 q^{34} -6.66954 q^{35} +1.80723 q^{36} +3.67800 q^{37} -1.00000 q^{38} -8.62266 q^{39} +1.33631 q^{40} -8.72443 q^{41} +10.9430 q^{42} +9.15875 q^{43} +3.23517 q^{44} +2.41502 q^{45} +2.41135 q^{46} -9.14506 q^{47} -2.19254 q^{48} +17.9101 q^{49} -3.21427 q^{50} -5.04802 q^{51} +3.93273 q^{52} +5.22097 q^{53} +2.61520 q^{54} +4.32320 q^{55} -4.99100 q^{56} +2.19254 q^{57} +7.68845 q^{58} -9.07487 q^{59} -2.92992 q^{60} -1.01640 q^{61} -10.1826 q^{62} -9.01987 q^{63} +1.00000 q^{64} +5.25536 q^{65} -7.09323 q^{66} -14.2825 q^{67} +2.30236 q^{68} -5.28697 q^{69} -6.66954 q^{70} -5.03857 q^{71} +1.80723 q^{72} +0.0673096 q^{73} +3.67800 q^{74} +7.04740 q^{75} -1.00000 q^{76} -16.1467 q^{77} -8.62266 q^{78} +17.2366 q^{79} +1.33631 q^{80} -11.1556 q^{81} -8.72443 q^{82} -7.67587 q^{83} +10.9430 q^{84} +3.07668 q^{85} +9.15875 q^{86} -16.8572 q^{87} +3.23517 q^{88} +16.3005 q^{89} +2.41502 q^{90} -19.6282 q^{91} +2.41135 q^{92} +22.3258 q^{93} -9.14506 q^{94} -1.33631 q^{95} -2.19254 q^{96} -11.3545 q^{97} +17.9101 q^{98} +5.84668 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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