LMFDB - Embedded newform 6017.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$107$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23665 q^{2} +0.286457 q^{3} +3.00262 q^{4} -1.07868 q^{5} -0.640706 q^{6} -2.04238 q^{7} -2.24251 q^{8} -2.91794 q^{9} +O(q^{10})$	\(q-2.23665 q^{2} +0.286457 q^{3} +3.00262 q^{4} -1.07868 q^{5} -0.640706 q^{6} -2.04238 q^{7} -2.24251 q^{8} -2.91794 q^{9} +2.41263 q^{10} -1.00000 q^{11} +0.860122 q^{12} -1.09681 q^{13} +4.56809 q^{14} -0.308996 q^{15} -0.989517 q^{16} -5.85143 q^{17} +6.52643 q^{18} +2.80704 q^{19} -3.23886 q^{20} -0.585054 q^{21} +2.23665 q^{22} -2.16428 q^{23} -0.642384 q^{24} -3.83645 q^{25} +2.45319 q^{26} -1.69524 q^{27} -6.13248 q^{28} +7.81589 q^{29} +0.691116 q^{30} +7.09782 q^{31} +6.69823 q^{32} -0.286457 q^{33} +13.0876 q^{34} +2.20307 q^{35} -8.76147 q^{36} +5.88541 q^{37} -6.27837 q^{38} -0.314190 q^{39} +2.41895 q^{40} +10.0541 q^{41} +1.30856 q^{42} -0.200525 q^{43} -3.00262 q^{44} +3.14753 q^{45} +4.84075 q^{46} +2.96818 q^{47} -0.283454 q^{48} -2.82870 q^{49} +8.58081 q^{50} -1.67619 q^{51} -3.29331 q^{52} +9.18183 q^{53} +3.79166 q^{54} +1.07868 q^{55} +4.58005 q^{56} +0.804097 q^{57} -17.4814 q^{58} +5.33169 q^{59} -0.927796 q^{60} -10.2416 q^{61} -15.8754 q^{62} +5.95954 q^{63} -13.0026 q^{64} +1.18311 q^{65} +0.640706 q^{66} +15.4828 q^{67} -17.5696 q^{68} -0.619975 q^{69} -4.92750 q^{70} +3.08927 q^{71} +6.54352 q^{72} -7.81129 q^{73} -13.1636 q^{74} -1.09898 q^{75} +8.42847 q^{76} +2.04238 q^{77} +0.702735 q^{78} +10.5970 q^{79} +1.06737 q^{80} +8.26821 q^{81} -22.4875 q^{82} -8.06637 q^{83} -1.75669 q^{84} +6.31182 q^{85} +0.448504 q^{86} +2.23892 q^{87} +2.24251 q^{88} -0.476018 q^{89} -7.03992 q^{90} +2.24011 q^{91} -6.49852 q^{92} +2.03322 q^{93} -6.63879 q^{94} -3.02790 q^{95} +1.91876 q^{96} -15.0203 q^{97} +6.32682 q^{98} +2.91794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) $ 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * 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 $

$2$	−2.23665	−1.58155	−0.790776	−	0.612105i	$-0.790323\pi$
$2$	−2.23665	−1.58155	−0.790776	+	0.612105i	$0.790323\pi$
$3$	0.286457	0.165386	0.0826931	−	0.996575i	$-0.473648\pi$
$3$	0.286457	0.165386	0.0826931	+	0.996575i	$0.473648\pi$
$4$	3.00262	1.50131
$5$	−1.07868	−0.482400	−0.241200	−	0.970475i	$-0.577541\pi$
$5$	−1.07868	−0.482400	−0.241200	+	0.970475i	$0.577541\pi$
$6$	−0.640706	−0.261567
$7$	−2.04238	−0.771946	−0.385973	−	0.922510i	$-0.626134\pi$
$7$	−2.04238	−0.771946	−0.385973	+	0.922510i	$0.626134\pi$
$8$	−2.24251	−0.792847
$9$	−2.91794	−0.972647
$10$	2.41263	0.762941
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.860122	0.248296
$13$	−1.09681	−0.304201	−0.152101	−	0.988365i	$-0.548604\pi$
$13$	−1.09681	−0.304201	−0.152101	+	0.988365i	$0.548604\pi$
$14$	4.56809	1.22087
$15$	−0.308996	−0.0797823
$16$	−0.989517	−0.247379
$17$	−5.85143	−1.41918	−0.709591	−	0.704614i	$-0.751120\pi$
$17$	−5.85143	−1.41918	−0.709591	+	0.704614i	$0.751120\pi$
$18$	6.52643	1.53829
$19$	2.80704	0.643979	0.321989	−	0.946743i	$-0.395648\pi$
$19$	2.80704	0.643979	0.321989	+	0.946743i	$0.395648\pi$
$20$	−3.23886	−0.724232
$21$	−0.585054	−0.127669
$22$	2.23665	0.476856
$23$	−2.16428	−0.451284	−0.225642	−	0.974210i	$-0.572448\pi$
$23$	−2.16428	−0.451284	−0.225642	+	0.974210i	$0.572448\pi$
$24$	−0.642384	−0.131126
$25$	−3.83645	−0.767290
$26$	2.45319	0.481110
$27$	−1.69524	−0.326249
$28$	−6.13248	−1.15893
$29$	7.81589	1.45137	0.725687	−	0.688025i	$-0.241522\pi$
$29$	7.81589	1.45137	0.725687	+	0.688025i	$0.241522\pi$
$30$	0.691116	0.126180
$31$	7.09782	1.27481	0.637403	−	0.770531i	$-0.280009\pi$
$31$	7.09782	1.27481	0.637403	+	0.770531i	$0.280009\pi$
$32$	6.69823	1.18409
$33$	−0.286457	−0.0498658
$34$	13.0876	2.24451
$35$	2.20307	0.372387
$36$	−8.76147	−1.46024
$37$	5.88541	0.967556	0.483778	−	0.875191i	$-0.339264\pi$
$37$	5.88541	0.967556	0.483778	+	0.875191i	$0.339264\pi$
$38$	−6.27837	−1.01849
$39$	−0.314190	−0.0503107
$40$	2.41895	0.382470
$41$	10.0541	1.57018	0.785091	−	0.619380i	$-0.212616\pi$
$41$	10.0541	1.57018	0.785091	+	0.619380i	$0.212616\pi$
$42$	1.30856	0.201916
$43$	−0.200525	−0.0305797	−0.0152899	−	0.999883i	$-0.504867\pi$
$43$	−0.200525	−0.0305797	−0.0152899	+	0.999883i	$0.504867\pi$
$44$	−3.00262	−0.452662
$45$	3.14753	0.469205
$46$	4.84075	0.713730
$47$	2.96818	0.432954	0.216477	−	0.976288i	$-0.430543\pi$
$47$	2.96818	0.432954	0.216477	+	0.976288i	$0.430543\pi$
$48$	−0.283454	−0.0409131
$49$	−2.82870	−0.404100
$50$	8.58081	1.21351
$51$	−1.67619	−0.234713
$52$	−3.29331	−0.456700
$53$	9.18183	1.26122	0.630611	−	0.776099i	$-0.282805\pi$
$53$	9.18183	1.26122	0.630611	+	0.776099i	$0.282805\pi$
$54$	3.79166	0.515979
$55$	1.07868	0.145449
$56$	4.58005	0.612035
$57$	0.804097	0.106505
$58$	−17.4814	−2.29542
$59$	5.33169	0.694127	0.347063	−	0.937842i	$-0.387179\pi$
$59$	5.33169	0.694127	0.347063	+	0.937842i	$0.387179\pi$
$60$	−0.927796	−0.119778
$61$	−10.2416	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$61$	−10.2416	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$62$	−15.8754	−2.01617
$63$	5.95954	0.750831
$64$	−13.0026	−1.62532
$65$	1.18311	0.146747
$66$	0.640706	0.0788654
$67$	15.4828	1.89153	0.945764	−	0.324855i	$-0.105316\pi$
$67$	15.4828	1.89153	0.945764	+	0.324855i	$0.105316\pi$
$68$	−17.5696	−2.13063
$69$	−0.619975	−0.0746362
$70$	−4.92750	−0.588949
$71$	3.08927	0.366628	0.183314	−	0.983054i	$-0.441317\pi$
$71$	3.08927	0.366628	0.183314	+	0.983054i	$0.441317\pi$
$72$	6.54352	0.771161
$73$	−7.81129	−0.914243	−0.457121	−	0.889404i	$-0.651119\pi$
$73$	−7.81129	−0.914243	−0.457121	+	0.889404i	$0.651119\pi$
$74$	−13.1636	−1.53024
$75$	−1.09898	−0.126899
$76$	8.42847	0.966812
$77$	2.04238	0.232750
$78$	0.702735	0.0795690
$79$	10.5970	1.19226	0.596128	−	0.802889i	$-0.296705\pi$
$79$	10.5970	1.19226	0.596128	+	0.802889i	$0.296705\pi$
$80$	1.06737	0.119336
$81$	8.26821	0.918690
$82$	−22.4875	−2.48333
$83$	−8.06637	−0.885399	−0.442700	−	0.896670i	$-0.645979\pi$
$83$	−8.06637	−0.885399	−0.442700	+	0.896670i	$0.645979\pi$
$84$	−1.75669	−0.191671
$85$	6.31182	0.684613
$86$	0.448504	0.0483635
$87$	2.23892	0.240037
$88$	2.24251	0.239052
$89$	−0.476018	−0.0504578	−0.0252289	−	0.999682i	$-0.508031\pi$
$89$	−0.476018	−0.0504578	−0.0252289	+	0.999682i	$0.508031\pi$
$90$	−7.03992	−0.742073
$91$	2.24011	0.234827
$92$	−6.49852	−0.677517
$93$	2.03322	0.210835
$94$	−6.63879	−0.684739
$95$	−3.02790	−0.310656
$96$	1.91876	0.195832
$97$	−15.0203	−1.52508	−0.762542	−	0.646939i	$-0.776049\pi$
$97$	−15.0203	−1.52508	−0.762542	+	0.646939i	$0.776049\pi$
$98$	6.32682	0.639105
$99$	2.91794	0.293264
$100$	−11.5194	−1.15194
$101$	15.4029	1.53265	0.766323	−	0.642456i	$-0.222084\pi$
$101$	15.4029	1.53265	0.766323	+	0.642456i	$0.222084\pi$
$102$	3.74905	0.371211
$103$	−10.6098	−1.04541	−0.522707	−	0.852512i	$-0.675078\pi$
$103$	−10.6098	−1.04541	−0.522707	+	0.852512i	$0.675078\pi$
$104$	2.45962	0.241185
$105$	0.631085	0.0615876
$106$	−20.5366	−1.99469
$107$	3.12147	0.301764	0.150882	−	0.988552i	$-0.451789\pi$
$107$	3.12147	0.301764	0.150882	+	0.988552i	$0.451789\pi$
$108$	−5.09015	−0.489800
$109$	8.67362	0.830782	0.415391	−	0.909643i	$-0.363645\pi$
$109$	8.67362	0.830782	0.415391	+	0.909643i	$0.363645\pi$
$110$	−2.41263	−0.230036
$111$	1.68592	0.160020
$112$	2.02097	0.190963
$113$	−9.91347	−0.932581	−0.466291	−	0.884632i	$-0.654410\pi$
$113$	−9.91347	−0.932581	−0.466291	+	0.884632i	$0.654410\pi$
$114$	−1.79849	−0.168444
$115$	2.33457	0.217700
$116$	23.4681	2.17896
$117$	3.20044	0.295881
$118$	−11.9251	−1.09780
$119$	11.9508	1.09553
$120$	0.692926	0.0632552
$121$	1.00000	0.0909091
$122$	22.9069	2.07389
$123$	2.88006	0.259687
$124$	21.3120	1.91388
$125$	9.53170	0.852541
$126$	−13.3294	−1.18748
$127$	1.82090	0.161579	0.0807893	−	0.996731i	$-0.474256\pi$
$127$	1.82090	0.161579	0.0807893	+	0.996731i	$0.474256\pi$
$128$	15.6858	1.38644
$129$	−0.0574417	−0.00505746
$130$	−2.64621	−0.232088
$131$	−18.1934	−1.58956	−0.794782	−	0.606895i	$-0.792415\pi$
$131$	−18.1934	−1.58956	−0.794782	+	0.606895i	$0.792415\pi$
$132$	−0.860122	−0.0748640
$133$	−5.73303	−0.497117
$134$	−34.6297	−2.99155
$135$	1.82862	0.157382
$136$	13.1219	1.12519
$137$	−8.43803	−0.720910	−0.360455	−	0.932777i	$-0.617379\pi$
$137$	−8.43803	−0.720910	−0.360455	+	0.932777i	$0.617379\pi$
$138$	1.38667	0.118041
$139$	−12.2650	−1.04030	−0.520152	−	0.854074i	$-0.674125\pi$
$139$	−12.2650	−1.04030	−0.520152	+	0.854074i	$0.674125\pi$
$140$	6.61498	0.559068
$141$	0.850257	0.0716046
$142$	−6.90962	−0.579842
$143$	1.09681	0.0917201
$144$	2.88735	0.240613
$145$	−8.43084	−0.700143
$146$	17.4712	1.44592
$147$	−0.810301	−0.0668325
$148$	17.6717	1.45260
$149$	−3.03550	−0.248678	−0.124339	−	0.992240i	$-0.539681\pi$
$149$	−3.03550	−0.248678	−0.124339	+	0.992240i	$0.539681\pi$
$150$	2.45804	0.200698
$151$	9.64024	0.784512	0.392256	−	0.919856i	$-0.371695\pi$
$151$	9.64024	0.784512	0.392256	+	0.919856i	$0.371695\pi$
$152$	−6.29482	−0.510577
$153$	17.0741	1.38036
$154$	−4.56809	−0.368107
$155$	−7.65627	−0.614967
$156$	−0.943393	−0.0755319
$157$	−15.5123	−1.23802	−0.619008	−	0.785385i	$-0.712465\pi$
$157$	−15.5123	−1.23802	−0.619008	+	0.785385i	$0.712465\pi$
$158$	−23.7018	−1.88562
$159$	2.63020	0.208589
$160$	−7.22524	−0.571206
$161$	4.42028	0.348367
$162$	−18.4931	−1.45296
$163$	−0.971307	−0.0760787	−0.0380393	−	0.999276i	$-0.512111\pi$
$163$	−0.971307	−0.0760787	−0.0380393	+	0.999276i	$0.512111\pi$
$164$	30.1886	2.35733
$165$	0.308996	0.0240553
$166$	18.0417	1.40031
$167$	17.6044	1.36227	0.681137	−	0.732156i	$-0.261486\pi$
$167$	17.6044	1.36227	0.681137	+	0.732156i	$0.261486\pi$
$168$	1.31199	0.101222
$169$	−11.7970	−0.907462
$170$	−14.1174	−1.08275
$171$	−8.19078	−0.626364
$172$	−0.602099	−0.0459096
$173$	−25.1800	−1.91440	−0.957202	−	0.289422i	$-0.906537\pi$
$173$	−25.1800	−1.91440	−0.957202	+	0.289422i	$0.906537\pi$
$174$	−5.00768	−0.379631
$175$	7.83547	0.592306
$176$	0.989517	0.0745877
$177$	1.52730	0.114799
$178$	1.06469	0.0798017
$179$	−7.46800	−0.558185	−0.279092	−	0.960264i	$-0.590034\pi$
$179$	−7.46800	−0.558185	−0.279092	+	0.960264i	$0.590034\pi$
$180$	9.45082	0.704422
$181$	7.65278	0.568827	0.284413	−	0.958702i	$-0.408201\pi$
$181$	7.65278	0.568827	0.284413	+	0.958702i	$0.408201\pi$
$182$	−5.01034	−0.371391
$183$	−2.93378	−0.216871
$184$	4.85343	0.357799
$185$	−6.34848	−0.466749
$186$	−4.54761	−0.333447
$187$	5.85143	0.427899
$188$	8.91232	0.649998
$189$	3.46231	0.251846
$190$	6.77236	0.491318
$191$	−10.3368	−0.747945	−0.373972	−	0.927440i	$-0.622005\pi$
$191$	−10.3368	−0.747945	−0.373972	+	0.927440i	$0.622005\pi$
$192$	−3.72468	−0.268806
$193$	−0.0726682	−0.00523077	−0.00261539	−	0.999997i	$-0.500833\pi$
$193$	−0.0726682	−0.00523077	−0.00261539	+	0.999997i	$0.500833\pi$
$194$	33.5953	2.41200
$195$	0.338911	0.0242699
$196$	−8.49351	−0.606679
$197$	9.65485	0.687880	0.343940	−	0.938992i	$-0.388238\pi$
$197$	9.65485	0.687880	0.343940	+	0.938992i	$0.388238\pi$
$198$	−6.52643	−0.463813
$199$	−13.1709	−0.933662	−0.466831	−	0.884347i	$-0.654604\pi$
$199$	−13.1709	−0.933662	−0.466831	+	0.884347i	$0.654604\pi$
$200$	8.60328	0.608344
$201$	4.43517	0.312833
$202$	−34.4510	−2.42396
$203$	−15.9630	−1.12038
$204$	−5.03295	−0.352377
$205$	−10.8451	−0.757457
$206$	23.7305	1.65338
$207$	6.31525	0.438940
$208$	1.08532	0.0752531
$209$	−2.80704	−0.194167
$210$	−1.41152	−0.0974041
$211$	−20.5882	−1.41735	−0.708674	−	0.705536i	$-0.750706\pi$
$211$	−20.5882	−1.41735	−0.708674	+	0.705536i	$0.750706\pi$
$212$	27.5695	1.89348
$213$	0.884943	0.0606353
$214$	−6.98166	−0.477256
$215$	0.216302	0.0147517
$216$	3.80159	0.258665
$217$	−14.4964	−0.984081
$218$	−19.3999	−1.31393
$219$	−2.23760	−0.151203
$220$	3.23886	0.218364
$221$	6.41793	0.431717
$222$	−3.77082	−0.253081
$223$	−2.87369	−0.192436	−0.0962182	−	0.995360i	$-0.530675\pi$
$223$	−2.87369	−0.192436	−0.0962182	+	0.995360i	$0.530675\pi$
$224$	−13.6803	−0.914054
$225$	11.1945	0.746303
$226$	22.1730	1.47493
$227$	−9.09657	−0.603760	−0.301880	−	0.953346i	$-0.597614\pi$
$227$	−9.09657	−0.603760	−0.301880	+	0.953346i	$0.597614\pi$
$228$	2.41440	0.159897
$229$	−24.6620	−1.62971	−0.814855	−	0.579665i	$-0.803183\pi$
$229$	−24.6620	−1.62971	−0.814855	+	0.579665i	$0.803183\pi$
$230$	−5.22162	−0.344303
$231$	0.585054	0.0384937
$232$	−17.5272	−1.15072
$233$	12.8902	0.844464	0.422232	−	0.906488i	$-0.361247\pi$
$233$	12.8902	0.844464	0.422232	+	0.906488i	$0.361247\pi$
$234$	−7.15827	−0.467951
$235$	−3.20172	−0.208857
$236$	16.0090	1.04210
$237$	3.03559	0.197183
$238$	−26.7299	−1.73264
$239$	21.4355	1.38655	0.693275	−	0.720673i	$-0.256167\pi$
$239$	21.4355	1.38655	0.693275	+	0.720673i	$0.256167\pi$
$240$	0.305757	0.0197365
$241$	−15.4237	−0.993525	−0.496763	−	0.867886i	$-0.665478\pi$
$241$	−15.4237	−0.993525	−0.496763	+	0.867886i	$0.665478\pi$
$242$	−2.23665	−0.143778
$243$	7.45420	0.478187
$244$	−30.7516	−1.96867
$245$	3.05126	0.194938
$246$	−6.44170	−0.410708
$247$	−3.07880	−0.195899
$248$	−15.9169	−1.01073
$249$	−2.31067	−0.146433
$250$	−21.3191	−1.34834
$251$	−16.8243	−1.06194	−0.530971	−	0.847390i	$-0.678173\pi$
$251$	−16.8243	−1.06194	−0.530971	+	0.847390i	$0.678173\pi$
$252$	17.8942	1.12723
$253$	2.16428	0.136067
$254$	−4.07272	−0.255545
$255$	1.80807	0.113226
$256$	−9.07857	−0.567411
$257$	−13.8446	−0.863601	−0.431800	−	0.901969i	$-0.642122\pi$
$257$	−13.8446	−0.863601	−0.431800	+	0.901969i	$0.642122\pi$
$258$	0.128477	0.00799865
$259$	−12.0202	−0.746901
$260$	3.55243	0.220312
$261$	−22.8063	−1.41167
$262$	40.6923	2.51398
$263$	15.5109	0.956440	0.478220	−	0.878240i	$-0.341282\pi$
$263$	15.5109	0.956440	0.478220	+	0.878240i	$0.341282\pi$
$264$	0.642384	0.0395360
$265$	−9.90425	−0.608413
$266$	12.8228	0.786216
$267$	−0.136359	−0.00834502
$268$	46.4890	2.83977
$269$	10.0613	0.613447	0.306723	−	0.951799i	$-0.400767\pi$
$269$	10.0613	0.613447	0.306723	+	0.951799i	$0.400767\pi$
$270$	−4.08999	−0.248909
$271$	23.5933	1.43319	0.716595	−	0.697489i	$-0.245700\pi$
$271$	23.5933	1.43319	0.716595	+	0.697489i	$0.245700\pi$
$272$	5.79010	0.351076
$273$	0.641695	0.0388371
$274$	18.8730	1.14016
$275$	3.83645	0.231347
$276$	−1.86155	−0.112052
$277$	−10.7744	−0.647369	−0.323684	−	0.946165i	$-0.604922\pi$
$277$	−10.7744	−0.647369	−0.323684	+	0.946165i	$0.604922\pi$
$278$	27.4325	1.64529
$279$	−20.7110	−1.23994
$280$	−4.94041	−0.295246
$281$	−0.201869	−0.0120425	−0.00602124	−	0.999982i	$-0.501917\pi$
$281$	−0.201869	−0.0120425	−0.00602124	+	0.999982i	$0.501917\pi$
$282$	−1.90173	−0.113246
$283$	25.4355	1.51198	0.755992	−	0.654581i	$-0.227155\pi$
$283$	25.4355	1.51198	0.755992	+	0.654581i	$0.227155\pi$
$284$	9.27589	0.550423
$285$	−0.867363	−0.0513781
$286$	−2.45319	−0.145060
$287$	−20.5342	−1.21210
$288$	−19.5450	−1.15170
$289$	17.2393	1.01408
$290$	18.8569	1.10731
$291$	−4.30268	−0.252228
$292$	−23.4543	−1.37256
$293$	14.0631	0.821577	0.410788	−	0.911731i	$-0.365253\pi$
$293$	14.0631	0.821577	0.410788	+	0.911731i	$0.365253\pi$
$294$	1.81236	0.105699
$295$	−5.75118	−0.334847
$296$	−13.1981	−0.767124
$297$	1.69524	0.0983677
$298$	6.78936	0.393297
$299$	2.37381	0.137281
$300$	−3.29982	−0.190515
$301$	0.409547	0.0236059
$302$	−21.5619	−1.24075
$303$	4.41227	0.253478
$304$	−2.77761	−0.159307
$305$	11.0474	0.632572
$306$	−38.1890	−2.18312
$307$	−16.5151	−0.942567	−0.471284	−	0.881982i	$-0.656209\pi$
$307$	−16.5151	−0.942567	−0.471284	+	0.881982i	$0.656209\pi$
$308$	6.13248	0.349430
$309$	−3.03926	−0.172897
$310$	17.1244	0.972603
$311$	19.8203	1.12390	0.561952	−	0.827170i	$-0.310051\pi$
$311$	19.8203	1.12390	0.561952	+	0.827170i	$0.310051\pi$
$312$	0.704575	0.0398887
$313$	−0.981162	−0.0554586	−0.0277293	−	0.999615i	$-0.508828\pi$
$313$	−0.981162	−0.0554586	−0.0277293	+	0.999615i	$0.508828\pi$
$314$	34.6956	1.95799
$315$	−6.42843	−0.362201
$316$	31.8188	1.78995
$317$	5.10609	0.286786	0.143393	−	0.989666i	$-0.454199\pi$
$317$	5.10609	0.286786	0.143393	+	0.989666i	$0.454199\pi$
$318$	−5.88285	−0.329894
$319$	−7.81589	−0.437606
$320$	14.0256	0.784056
$321$	0.894169	0.0499076
$322$	−9.88663	−0.550961
$323$	−16.4252	−0.913923
$324$	24.8263	1.37924
$325$	4.20787	0.233411
$326$	2.17248	0.120322
$327$	2.48462	0.137400
$328$	−22.5464	−1.24492
$329$	−6.06214	−0.334217
$330$	−0.691116	−0.0380447
$331$	6.30452	0.346528	0.173264	−	0.984875i	$-0.444569\pi$
$331$	6.30452	0.346528	0.173264	+	0.984875i	$0.444569\pi$
$332$	−24.2202	−1.32926
$333$	−17.1733	−0.941091
$334$	−39.3751	−2.15451
$335$	−16.7010	−0.912473
$336$	0.578921	0.0315827
$337$	28.3965	1.54686	0.773428	−	0.633884i	$-0.218540\pi$
$337$	28.3965	1.54686	0.773428	+	0.633884i	$0.218540\pi$
$338$	26.3858	1.43520
$339$	−2.83979	−0.154236
$340$	18.9520	1.02782
$341$	−7.09782	−0.384369
$342$	18.3199	0.990629
$343$	20.0739	1.08389
$344$	0.449679	0.0242451
$345$	0.668754	0.0360045
$346$	56.3190	3.02773
$347$	−9.75908	−0.523895	−0.261948	−	0.965082i	$-0.584365\pi$
$347$	−9.75908	−0.523895	−0.261948	+	0.965082i	$0.584365\pi$
$348$	6.72262	0.360370
$349$	6.49976	0.347924	0.173962	−	0.984752i	$-0.444343\pi$
$349$	6.49976	0.347924	0.173962	+	0.984752i	$0.444343\pi$
$350$	−17.5252	−0.936764
$351$	1.85936	0.0992453
$352$	−6.69823	−0.357017
$353$	0.725165	0.0385967	0.0192983	−	0.999814i	$-0.493857\pi$
$353$	0.725165	0.0385967	0.0192983	+	0.999814i	$0.493857\pi$
$354$	−3.41604	−0.181561
$355$	−3.33233	−0.176862
$356$	−1.42930	−0.0757528
$357$	3.42340	0.181186
$358$	16.7033	0.882799
$359$	32.8056	1.73141	0.865705	−	0.500554i	$-0.166870\pi$
$359$	32.8056	1.73141	0.865705	+	0.500554i	$0.166870\pi$
$360$	−7.05836	−0.372008
$361$	−11.1205	−0.585291
$362$	−17.1166	−0.899630
$363$	0.286457	0.0150351
$364$	6.72618	0.352548
$365$	8.42588	0.441031
$366$	6.56185	0.342993
$367$	−11.8580	−0.618981	−0.309490	−	0.950903i	$-0.600158\pi$
$367$	−11.8580	−0.618981	−0.309490	+	0.950903i	$0.600158\pi$
$368$	2.14160	0.111638
$369$	−29.3372	−1.52723
$370$	14.1993	0.738189
$371$	−18.7528	−0.973594
$372$	6.10499	0.316529
$373$	−10.3554	−0.536182	−0.268091	−	0.963394i	$-0.586393\pi$
$373$	−10.3554	−0.536182	−0.268091	+	0.963394i	$0.586393\pi$
$374$	−13.0876	−0.676745
$375$	2.73042	0.140999
$376$	−6.65618	−0.343266
$377$	−8.57257	−0.441510
$378$	−7.74399	−0.398308
$379$	9.76440	0.501563	0.250782	−	0.968044i	$-0.419312\pi$
$379$	9.76440	0.501563	0.250782	+	0.968044i	$0.419312\pi$
$380$	−9.09162	−0.466390
$381$	0.521609	0.0267229
$382$	23.1199	1.18291
$383$	−18.9057	−0.966035	−0.483018	−	0.875611i	$-0.660459\pi$
$383$	−18.9057	−0.966035	−0.483018	+	0.875611i	$0.660459\pi$
$384$	4.49332	0.229299
$385$	−2.20307	−0.112279
$386$	0.162534	0.00827275
$387$	0.585119	0.0297433
$388$	−45.1003	−2.28962
$389$	−24.9398	−1.26450	−0.632249	−	0.774765i	$-0.717868\pi$
$389$	−24.9398	−1.26450	−0.632249	+	0.774765i	$0.717868\pi$
$390$	−0.758026	−0.0383841
$391$	12.6642	0.640454
$392$	6.34339	0.320390
$393$	−5.21163	−0.262892
$394$	−21.5946	−1.08792
$395$	−11.4308	−0.575145
$396$	8.76147	0.440280
$397$	−12.9910	−0.651998	−0.325999	−	0.945370i	$-0.605701\pi$
$397$	−12.9910	−0.651998	−0.325999	+	0.945370i	$0.605701\pi$
$398$	29.4588	1.47664
$399$	−1.64227	−0.0822162
$400$	3.79623	0.189812
$401$	17.0852	0.853194	0.426597	−	0.904442i	$-0.359712\pi$
$401$	17.0852	0.853194	0.426597	+	0.904442i	$0.359712\pi$
$402$	−9.91993	−0.494761
$403$	−7.78498	−0.387798
$404$	46.2490	2.30098
$405$	−8.91875	−0.443176
$406$	35.7037	1.77194
$407$	−5.88541	−0.291729
$408$	3.75887	0.186092
$409$	−16.8625	−0.833796	−0.416898	−	0.908953i	$-0.636883\pi$
$409$	−16.8625	−0.833796	−0.416898	+	0.908953i	$0.636883\pi$
$410$	24.2568	1.19796
$411$	−2.41714	−0.119229
$412$	−31.8572	−1.56949
$413$	−10.8893	−0.535828
$414$	−14.1250	−0.694207
$415$	8.70103	0.427117
$416$	−7.34671	−0.360202
$417$	−3.51340	−0.172052
$418$	6.27837	0.307085
$419$	5.62016	0.274563	0.137281	−	0.990532i	$-0.456164\pi$
$419$	5.62016	0.274563	0.137281	+	0.990532i	$0.456164\pi$
$420$	1.89491	0.0924621
$421$	−28.2217	−1.37544	−0.687721	−	0.725975i	$-0.741389\pi$
$421$	−28.2217	−1.37544	−0.687721	+	0.725975i	$0.741389\pi$
$422$	46.0486	2.24161
$423$	−8.66098	−0.421111
$424$	−20.5904	−0.999956
$425$	22.4487	1.08892
$426$	−1.97931	−0.0958979
$427$	20.9172	1.01225
$428$	9.37260	0.453042
$429$	0.314190	0.0151692
$430$	−0.483792	−0.0233305
$431$	40.6753	1.95926	0.979631	−	0.200805i	$-0.0643556\pi$
$431$	40.6753	1.95926	0.979631	+	0.200805i	$0.0643556\pi$
$432$	1.67747	0.0807072
$433$	30.8902	1.48449	0.742245	−	0.670129i	$-0.233761\pi$
$433$	30.8902	1.48449	0.742245	+	0.670129i	$0.233761\pi$
$434$	32.4235	1.55638
$435$	−2.41508	−0.115794
$436$	26.0436	1.24726
$437$	−6.07523	−0.290618
$438$	5.00474	0.239136
$439$	−8.75794	−0.417994	−0.208997	−	0.977916i	$-0.567020\pi$
$439$	−8.75794	−0.417994	−0.208997	+	0.977916i	$0.567020\pi$
$440$	−2.41895	−0.115319
$441$	8.25398	0.393047
$442$	−14.3547	−0.682783
$443$	11.1331	0.528949	0.264475	−	0.964393i	$-0.414801\pi$
$443$	11.1331	0.528949	0.264475	+	0.964393i	$0.414801\pi$
$444$	5.06217	0.240240
$445$	0.513471	0.0243409
$446$	6.42745	0.304348
$447$	−0.869541	−0.0411279
$448$	26.5562	1.25466
$449$	27.0789	1.27793	0.638966	−	0.769235i	$-0.279363\pi$
$449$	27.0789	1.27793	0.638966	+	0.769235i	$0.279363\pi$
$450$	−25.0383	−1.18032
$451$	−10.0541	−0.473428
$452$	−29.7664	−1.40009
$453$	2.76152	0.129747
$454$	20.3459	0.954879
$455$	−2.41636	−0.113281
$456$	−1.80320	−0.0844424
$457$	37.3561	1.74745	0.873723	−	0.486424i	$-0.161699\pi$
$457$	37.3561	1.74745	0.873723	+	0.486424i	$0.161699\pi$
$458$	55.1603	2.57747
$459$	9.91957	0.463006
$460$	7.00982	0.326834
$461$	7.13881	0.332487	0.166244	−	0.986085i	$-0.446836\pi$
$461$	7.13881	0.332487	0.166244	+	0.986085i	$0.446836\pi$
$462$	−1.30856	−0.0608798
$463$	−6.36185	−0.295660	−0.147830	−	0.989013i	$-0.547229\pi$
$463$	−6.36185	−0.295660	−0.147830	+	0.989013i	$0.547229\pi$
$464$	−7.73396	−0.359040
$465$	−2.19320	−0.101707
$466$	−28.8309	−1.33556
$467$	−36.3724	−1.68311	−0.841557	−	0.540168i	$-0.818361\pi$
$467$	−36.3724	−1.68311	−0.841557	+	0.540168i	$0.818361\pi$
$468$	9.60970	0.444208
$469$	−31.6217	−1.46016
$470$	7.16113	0.330318
$471$	−4.44361	−0.204751
$472$	−11.9564	−0.550336
$473$	0.200525	0.00922013
$474$	−6.78956	−0.311855
$475$	−10.7691	−0.494119
$476$	35.8838	1.64473
$477$	−26.7920	−1.22672
$478$	−47.9439	−2.19290
$479$	−36.3799	−1.66224	−0.831121	−	0.556092i	$-0.812300\pi$
$479$	−36.3799	−1.66224	−0.831121	+	0.556092i	$0.812300\pi$
$480$	−2.06972	−0.0944695
$481$	−6.45520	−0.294332
$482$	34.4974	1.57131
$483$	1.26622	0.0576151
$484$	3.00262	0.136483
$485$	16.2021	0.735701
$486$	−16.6725	−0.756279
$487$	−15.7829	−0.715191	−0.357596	−	0.933877i	$-0.616403\pi$
$487$	−15.7829	−0.715191	−0.357596	+	0.933877i	$0.616403\pi$
$488$	22.9669	1.03966
$489$	−0.278238	−0.0125824
$490$	−6.82461	−0.308305
$491$	26.1743	1.18123	0.590616	−	0.806953i	$-0.298885\pi$
$491$	26.1743	1.18123	0.590616	+	0.806953i	$0.298885\pi$
$492$	8.64773	0.389870
$493$	−45.7342	−2.05976
$494$	6.88620	0.309825
$495$	−3.14753	−0.141471
$496$	−7.02342	−0.315361
$497$	−6.30944	−0.283017
$498$	5.16817	0.231591
$499$	21.7594	0.974084	0.487042	−	0.873378i	$-0.338076\pi$
$499$	21.7594	0.974084	0.487042	+	0.873378i	$0.338076\pi$
$500$	28.6201	1.27993
$501$	5.04292	0.225301
$502$	37.6302	1.67952
$503$	−13.3793	−0.596552	−0.298276	−	0.954480i	$-0.596412\pi$
$503$	−13.3793	−0.596552	−0.298276	+	0.954480i	$0.596412\pi$
$504$	−13.3643	−0.595294
$505$	−16.6148	−0.739349
$506$	−4.84075	−0.215198
$507$	−3.37934	−0.150082
$508$	5.46746	0.242579
$509$	2.61429	0.115877	0.0579383	−	0.998320i	$-0.481547\pi$
$509$	2.61429	0.115877	0.0579383	+	0.998320i	$0.481547\pi$
$510$	−4.04402	−0.179072
$511$	15.9536	0.705746
$512$	−11.0660	−0.489054
$513$	−4.75860	−0.210097
$514$	30.9655	1.36583
$515$	11.4446	0.504308
$516$	−0.172476	−0.00759282
$517$	−2.96818	−0.130540
$518$	26.8851	1.18126
$519$	−7.21301	−0.316616
$520$	−2.65314	−0.116348
$521$	3.07754	0.134830	0.0674148	−	0.997725i	$-0.478525\pi$
$521$	3.07754	0.134830	0.0674148	+	0.997725i	$0.478525\pi$
$522$	51.0098	2.23264
$523$	−30.8791	−1.35025	−0.675124	−	0.737704i	$-0.735910\pi$
$523$	−30.8791	−1.35025	−0.675124	+	0.737704i	$0.735910\pi$
$524$	−54.6278	−2.38643
$525$	2.24453	0.0979593
$526$	−34.6924	−1.51266
$527$	−41.5324	−1.80918
$528$	0.283454	0.0123358
$529$	−18.3159	−0.796343
$530$	22.1524	0.962238
$531$	−15.5576	−0.675140
$532$	−17.2141	−0.746326
$533$	−11.0274	−0.477652
$534$	0.304987	0.0131981
$535$	−3.36707	−0.145571
$536$	−34.7204	−1.49969
$537$	−2.13926	−0.0923160
$538$	−22.5036	−0.970198
$539$	2.82870	0.121841
$540$	5.49064	0.236280
$541$	−31.7461	−1.36487	−0.682436	−	0.730945i	$-0.739080\pi$
$541$	−31.7461	−1.36487	−0.682436	+	0.730945i	$0.739080\pi$
$542$	−52.7700	−2.26667
$543$	2.19219	0.0940761
$544$	−39.1943	−1.68044
$545$	−9.35606	−0.400769
$546$	−1.43525	−0.0614230
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−25.3362	−1.08231
$549$	29.8844	1.27543
$550$	−8.58081	−0.365887
$551$	21.9395	0.934654
$552$	1.39030	0.0591751
$553$	−21.6431	−0.920357
$554$	24.0985	1.02385
$555$	−1.81857	−0.0771939
$556$	−36.8271	−1.56182
$557$	−26.0038	−1.10182	−0.550908	−	0.834566i	$-0.685719\pi$
$557$	−26.0038	−1.10182	−0.550908	+	0.834566i	$0.685719\pi$
$558$	46.3234	1.96103
$559$	0.219938	0.00930239
$560$	−2.17998	−0.0921208
$561$	1.67619	0.0707686
$562$	0.451511	0.0190458
$563$	35.6210	1.50125	0.750623	−	0.660731i	$-0.229753\pi$
$563$	35.6210	1.50125	0.750623	+	0.660731i	$0.229753\pi$
$564$	2.55300	0.107501
$565$	10.6935	0.449877
$566$	−56.8904	−2.39128
$567$	−16.8868	−0.709179
$568$	−6.92772	−0.290680
$569$	−5.17178	−0.216812	−0.108406	−	0.994107i	$-0.534575\pi$
$569$	−5.17178	−0.216812	−0.108406	+	0.994107i	$0.534575\pi$
$570$	1.93999	0.0812573
$571$	12.2839	0.514065	0.257032	−	0.966403i	$-0.417255\pi$
$571$	12.2839	0.514065	0.257032	+	0.966403i	$0.417255\pi$
$572$	3.29331	0.137700
$573$	−2.96105	−0.123700
$574$	45.9279	1.91699
$575$	8.30316	0.346266
$576$	37.9408	1.58087
$577$	−26.0272	−1.08353	−0.541764	−	0.840531i	$-0.682243\pi$
$577$	−26.0272	−1.08353	−0.541764	+	0.840531i	$0.682243\pi$
$578$	−38.5583	−1.60381
$579$	−0.0208163	−0.000865098 0
$580$	−25.3146	−1.05113
$581$	16.4746	0.683480
$582$	9.62361	0.398912
$583$	−9.18183	−0.380273
$584$	17.5169	0.724855
$585$	−3.45225	−0.142733
$586$	−31.4544	−1.29937
$587$	−31.2422	−1.28951	−0.644753	−	0.764391i	$-0.723040\pi$
$587$	−31.2422	−1.28951	−0.644753	+	0.764391i	$0.723040\pi$
$588$	−2.43303	−0.100336
$589$	19.9239	0.820948
$590$	12.8634	0.529578
$591$	2.76570	0.113766
$592$	−5.82372	−0.239353
$593$	−3.30947	−0.135904	−0.0679519	−	0.997689i	$-0.521646\pi$
$593$	−3.30947	−0.135904	−0.0679519	+	0.997689i	$0.521646\pi$
$594$	−3.79166	−0.155574
$595$	−12.8911	−0.528484
$596$	−9.11445	−0.373342
$597$	−3.77291	−0.154415
$598$	−5.30940	−0.217118
$599$	−42.8139	−1.74933	−0.874664	−	0.484729i	$-0.838918\pi$
$599$	−42.8139	−1.74933	−0.874664	+	0.484729i	$0.838918\pi$
$600$	2.46447	0.100612
$601$	2.42423	0.0988864	0.0494432	−	0.998777i	$-0.484255\pi$
$601$	2.42423	0.0988864	0.0494432	+	0.998777i	$0.484255\pi$
$602$	−0.916014	−0.0373340
$603$	−45.1780	−1.83979
$604$	28.9460	1.17780
$605$	−1.07868	−0.0438546
$606$	−9.86873	−0.400890
$607$	−21.7711	−0.883660	−0.441830	−	0.897099i	$-0.645671\pi$
$607$	−21.7711	−0.883660	−0.441830	+	0.897099i	$0.645671\pi$
$608$	18.8022	0.762530
$609$	−4.57271	−0.185296
$610$	−24.7092	−1.00045
$611$	−3.25554	−0.131705
$612$	51.2672	2.07235
$613$	17.3871	0.702257	0.351129	−	0.936327i	$-0.385798\pi$
$613$	17.3871	0.702257	0.351129	+	0.936327i	$0.385798\pi$
$614$	36.9386	1.49072
$615$	−3.10667	−0.125273
$616$	−4.58005	−0.184536
$617$	−46.7142	−1.88064	−0.940321	−	0.340290i	$-0.889475\pi$
$617$	−46.7142	−1.88064	−0.940321	+	0.340290i	$0.889475\pi$
$618$	6.79776	0.273446
$619$	−5.99021	−0.240767	−0.120383	−	0.992727i	$-0.538412\pi$
$619$	−5.99021	−0.240767	−0.120383	+	0.992727i	$0.538412\pi$
$620$	−22.9889	−0.923255
$621$	3.66897	0.147231
$622$	−44.3311	−1.77751
$623$	0.972208	0.0389507
$624$	0.310897	0.0124458
$625$	8.90060	0.356024
$626$	2.19452	0.0877106
$627$	−0.804097	−0.0321125
$628$	−46.5775	−1.85864
$629$	−34.4381	−1.37314
$630$	14.3782	0.572840
$631$	−0.609663	−0.0242703	−0.0121351	−	0.999926i	$-0.503863\pi$
$631$	−0.609663	−0.0242703	−0.0121351	+	0.999926i	$0.503863\pi$
$632$	−23.7639	−0.945278
$633$	−5.89763	−0.234410
$634$	−11.4205	−0.453568
$635$	−1.96417	−0.0779455
$636$	7.89749	0.313156
$637$	3.10256	0.122928
$638$	17.4814	0.692096
$639$	−9.01430	−0.356600
$640$	−16.9200	−0.668821
$641$	19.3756	0.765290	0.382645	−	0.923895i	$-0.375013\pi$
$641$	19.3756	0.765290	0.382645	+	0.923895i	$0.375013\pi$
$642$	−1.99995	−0.0789316
$643$	24.2869	0.957780	0.478890	−	0.877875i	$-0.341039\pi$
$643$	24.2869	0.957780	0.478890	+	0.877875i	$0.341039\pi$
$644$	13.2724	0.523006
$645$	0.0619613	0.00243972
$646$	36.7375	1.44542
$647$	22.8027	0.896466	0.448233	−	0.893917i	$-0.352054\pi$
$647$	22.8027	0.896466	0.448233	+	0.893917i	$0.352054\pi$
$648$	−18.5416	−0.728381
$649$	−5.33169	−0.209287
$650$	−9.41155	−0.369151
$651$	−4.15260	−0.162753
$652$	−2.91647	−0.114218
$653$	0.846375	0.0331212	0.0165606	−	0.999863i	$-0.494728\pi$
$653$	0.846375	0.0331212	0.0165606	+	0.999863i	$0.494728\pi$
$654$	−5.55724	−0.217305
$655$	19.6248	0.766806
$656$	−9.94868	−0.388431
$657$	22.7929	0.889236
$658$	13.5589	0.528582
$659$	26.1255	1.01770	0.508852	−	0.860854i	$-0.330070\pi$
$659$	26.1255	1.01770	0.508852	+	0.860854i	$0.330070\pi$
$660$	0.927796	0.0361144
$661$	−2.50707	−0.0975136	−0.0487568	−	0.998811i	$-0.515526\pi$
$661$	−2.50707	−0.0975136	−0.0487568	+	0.998811i	$0.515526\pi$
$662$	−14.1010	−0.548052
$663$	1.83846	0.0714000
$664$	18.0889	0.701986
$665$	6.18410	0.239809
$666$	38.4107	1.48838
$667$	−16.9158	−0.654982
$668$	52.8595	2.04519
$669$	−0.823189	−0.0318263
$670$	37.3544	1.44312
$671$	10.2416	0.395372
$672$	−3.91882	−0.151172
$673$	−8.33152	−0.321157	−0.160578	−	0.987023i	$-0.551336\pi$
$673$	−8.33152	−0.321157	−0.160578	+	0.987023i	$0.551336\pi$
$674$	−63.5131	−2.44643
$675$	6.50369	0.250327
$676$	−35.4219	−1.36238
$677$	4.85999	0.186785	0.0933923	−	0.995629i	$-0.470229\pi$
$677$	4.85999	0.186785	0.0933923	+	0.995629i	$0.470229\pi$
$678$	6.35162	0.243932
$679$	30.6772	1.17728
$680$	−14.1543	−0.542794
$681$	−2.60578	−0.0998536
$682$	15.8754	0.607899
$683$	24.0446	0.920039	0.460020	−	0.887909i	$-0.347842\pi$
$683$	24.0446	0.920039	0.460020	+	0.887909i	$0.347842\pi$
$684$	−24.5938	−0.940367
$685$	9.10193	0.347767
$686$	−44.8984	−1.71423
$687$	−7.06460	−0.269531
$688$	0.198423	0.00756479
$689$	−10.0708	−0.383665
$690$	−1.49577	−0.0569430
$691$	−12.7380	−0.484578	−0.242289	−	0.970204i	$-0.577898\pi$
$691$	−12.7380	−0.484578	−0.242289	+	0.970204i	$0.577898\pi$
$692$	−75.6061	−2.87411
$693$	−5.95954	−0.226384
$694$	21.8277	0.828568
$695$	13.2300	0.501843
$696$	−5.02080	−0.190313
$697$	−58.8308	−2.22837
$698$	−14.5377	−0.550261
$699$	3.69249	0.139663
$700$	23.5269	0.889235
$701$	35.2531	1.33149	0.665745	−	0.746179i	$-0.268114\pi$
$701$	35.2531	1.33149	0.665745	+	0.746179i	$0.268114\pi$
$702$	−4.15874	−0.156962
$703$	16.5206	0.623086
$704$	13.0026	0.490053
$705$	−0.917155	−0.0345421
$706$	−1.62194	−0.0610427
$707$	−31.4585	−1.18312
$708$	4.58590	0.172349
$709$	−29.4970	−1.10778	−0.553892	−	0.832588i	$-0.686858\pi$
$709$	−29.4970	−1.10778	−0.553892	+	0.832588i	$0.686858\pi$
$710$	7.45327	0.279716
$711$	−30.9215	−1.15965
$712$	1.06748	0.0400053
$713$	−15.3617	−0.575300
$714$	−7.65697	−0.286555
$715$	−1.18311	−0.0442458
$716$	−22.4236	−0.838008
$717$	6.14037	0.229316
$718$	−73.3747	−2.73832
$719$	−13.4745	−0.502515	−0.251258	−	0.967920i	$-0.580844\pi$
$719$	−13.4745	−0.502515	−0.251258	+	0.967920i	$0.580844\pi$
$720$	−3.11453	−0.116072
$721$	21.6692	0.807004
$722$	24.8728	0.925669
$723$	−4.41822	−0.164315
$724$	22.9784	0.853985
$725$	−29.9853	−1.11362
$726$	−0.640706	−0.0237788
$727$	25.8733	0.959587	0.479794	−	0.877381i	$-0.340712\pi$
$727$	25.8733	0.959587	0.479794	+	0.877381i	$0.340712\pi$
$728$	−5.02346	−0.186182
$729$	−22.6693	−0.839605
$730$	−18.8458	−0.697514
$731$	1.17336	0.0433982
$732$	−8.80902	−0.325591
$733$	−33.9239	−1.25301	−0.626505	−	0.779418i	$-0.715515\pi$
$733$	−33.9239	−1.25301	−0.626505	+	0.779418i	$0.715515\pi$
$734$	26.5221	0.978950
$735$	0.874056	0.0322400
$736$	−14.4969	−0.534361
$737$	−15.4828	−0.570317
$738$	65.6172	2.41540
$739$	10.3831	0.381948	0.190974	−	0.981595i	$-0.438835\pi$
$739$	10.3831	0.381948	0.190974	+	0.981595i	$0.438835\pi$
$740$	−19.0621	−0.700735
$741$	−0.881944	−0.0323990
$742$	41.9434	1.53979
$743$	46.0794	1.69049	0.845244	−	0.534380i	$-0.179455\pi$
$743$	46.0794	1.69049	0.845244	+	0.534380i	$0.179455\pi$
$744$	−4.55952	−0.167160
$745$	3.27433	0.119962
$746$	23.1614	0.848000
$747$	23.5372	0.861181
$748$	17.5696	0.642409
$749$	−6.37522	−0.232946
$750$	−6.10701	−0.222997
$751$	−22.8593	−0.834149	−0.417075	−	0.908872i	$-0.636945\pi$
$751$	−22.8593	−0.834149	−0.417075	+	0.908872i	$0.636945\pi$
$752$	−2.93707	−0.107104
$753$	−4.81945	−0.175631
$754$	19.1739	0.698271
$755$	−10.3987	−0.378449
$756$	10.3960	0.378099
$757$	−3.91310	−0.142224	−0.0711120	−	0.997468i	$-0.522655\pi$
$757$	−3.91310	−0.142224	−0.0711120	+	0.997468i	$0.522655\pi$
$758$	−21.8396	−0.793249
$759$	0.619975	0.0225037
$760$	6.79009	0.246303
$761$	−8.79207	−0.318712	−0.159356	−	0.987221i	$-0.550942\pi$
$761$	−8.79207	−0.318712	−0.159356	+	0.987221i	$0.550942\pi$
$762$	−1.16666	−0.0422636
$763$	−17.7148	−0.641318
$764$	−31.0375	−1.12290
$765$	−18.4175	−0.665887
$766$	42.2855	1.52784
$767$	−5.84787	−0.211154
$768$	−2.60062	−0.0938419
$769$	−10.8218	−0.390245	−0.195122	−	0.980779i	$-0.562510\pi$
$769$	−10.8218	−0.390245	−0.195122	+	0.980779i	$0.562510\pi$
$770$	4.92750	0.177575
$771$	−3.96588	−0.142828
$772$	−0.218195	−0.00785301
$773$	19.0148	0.683913	0.341957	−	0.939716i	$-0.388910\pi$
$773$	19.0148	0.683913	0.341957	+	0.939716i	$0.388910\pi$
$774$	−1.30871	−0.0470406
$775$	−27.2304	−0.978146
$776$	33.6833	1.20916
$777$	−3.44328	−0.123527
$778$	55.7817	1.99987
$779$	28.2222	1.01116
$780$	1.01762	0.0364366
$781$	−3.08927	−0.110543
$782$	−28.3253	−1.01291
$783$	−13.2498	−0.473509
$784$	2.79905	0.0999660
$785$	16.7328	0.597219
$786$	11.6566	0.415777
$787$	−29.6363	−1.05642	−0.528210	−	0.849114i	$-0.677136\pi$
$787$	−29.6363	−1.05642	−0.528210	+	0.849114i	$0.677136\pi$
$788$	28.9898	1.03272
$789$	4.44320	0.158182
$790$	25.5667	0.909622
$791$	20.2470	0.719902
$792$	−6.54352	−0.232514
$793$	11.2331	0.398900
$794$	29.0563	1.03117
$795$	−2.83715	−0.100623
$796$	−39.5473	−1.40172
$797$	29.7463	1.05367	0.526833	−	0.849969i	$-0.323379\pi$
$797$	29.7463	1.05367	0.526833	+	0.849969i	$0.323379\pi$
$798$	3.67319	0.130029
$799$	−17.3681	−0.614440
$800$	−25.6974	−0.908541
$801$	1.38899	0.0490777
$802$	−38.2137	−1.34937
$803$	7.81129	0.275655
$804$	13.3171	0.469658
$805$	−4.76807	−0.168052
$806$	17.4123	0.613323
$807$	2.88212	0.101456
$808$	−34.5412	−1.21515
$809$	−39.7300	−1.39683	−0.698416	−	0.715692i	$-0.746112\pi$
$809$	−39.7300	−1.39683	−0.698416	+	0.715692i	$0.746112\pi$
$810$	19.9482	0.700907
$811$	22.5334	0.791254	0.395627	−	0.918411i	$-0.370527\pi$
$811$	22.5334	0.791254	0.395627	+	0.918411i	$0.370527\pi$
$812$	−47.9308	−1.68204
$813$	6.75847	0.237030
$814$	13.1636	0.461385
$815$	1.04773	0.0367004
$816$	1.65862	0.0580631
$817$	−0.562881	−0.0196927
$818$	37.7155	1.31869
$819$	−6.53650	−0.228404
$820$	−32.5638	−1.13718
$821$	10.8393	0.378296	0.189148	−	0.981949i	$-0.439427\pi$
$821$	10.8393	0.378296	0.189148	+	0.981949i	$0.439427\pi$
$822$	5.40630	0.188566
$823$	−2.30836	−0.0804643	−0.0402322	−	0.999190i	$-0.512810\pi$
$823$	−2.30836	−0.0804643	−0.0402322	+	0.999190i	$0.512810\pi$
$824$	23.7926	0.828855
$825$	1.09898	0.0382615
$826$	24.3556	0.847440
$827$	−41.0394	−1.42708	−0.713540	−	0.700615i	$-0.752909\pi$
$827$	−41.0394	−1.42708	−0.713540	+	0.700615i	$0.752909\pi$
$828$	18.9623	0.658985
$829$	−28.9237	−1.00456	−0.502282	−	0.864704i	$-0.667506\pi$
$829$	−28.9237	−1.00456	−0.502282	+	0.864704i	$0.667506\pi$
$830$	−19.4612	−0.675508
$831$	−3.08640	−0.107066
$832$	14.2614	0.494425
$833$	16.5519	0.573491
$834$	7.85825	0.272109
$835$	−18.9896	−0.657161
$836$	−8.42847	−0.291505
$837$	−12.0325	−0.415904
$838$	−12.5704	−0.434236
$839$	3.49403	0.120627	0.0603137	−	0.998179i	$-0.480790\pi$
$839$	3.49403	0.120627	0.0603137	+	0.998179i	$0.480790\pi$
$840$	−1.41522	−0.0488296
$841$	32.0881	1.10649
$842$	63.1222	2.17533
$843$	−0.0578268	−0.00199166
$844$	−61.8184	−2.12788
$845$	12.7252	0.437760
$846$	19.3716	0.666010
$847$	−2.04238	−0.0701769
$848$	−9.08558	−0.312000
$849$	7.28619	0.250061
$850$	−50.2100	−1.72219
$851$	−12.7377	−0.436643
$852$	2.65715	0.0910323
$853$	−2.37078	−0.0811741	−0.0405870	−	0.999176i	$-0.512923\pi$
$853$	−2.37078	−0.0811741	−0.0405870	+	0.999176i	$0.512923\pi$
$854$	−46.7845	−1.60093
$855$	8.83523	0.302158
$856$	−6.99994	−0.239253
$857$	20.8212	0.711239	0.355619	−	0.934631i	$-0.384270\pi$
$857$	20.8212	0.711239	0.355619	+	0.934631i	$0.384270\pi$
$858$	−0.702735	−0.0239910
$859$	−18.9960	−0.648134	−0.324067	−	0.946034i	$-0.605050\pi$
$859$	−18.9960	−0.648134	−0.324067	+	0.946034i	$0.605050\pi$
$860$	0.649472	0.0221468
$861$	−5.88217	−0.200464
$862$	−90.9767	−3.09868
$863$	−51.6353	−1.75769	−0.878843	−	0.477111i	$-0.841684\pi$
$863$	−51.6353	−1.75769	−0.878843	+	0.477111i	$0.841684\pi$
$864$	−11.3551	−0.386308
$865$	27.1612	0.923509
$866$	−69.0907	−2.34780
$867$	4.93832	0.167714
$868$	−43.5272	−1.47741
$869$	−10.5970	−0.359479
$870$	5.40169	0.183134
$871$	−16.9818	−0.575405
$872$	−19.4507	−0.658683
$873$	43.8285	1.48337
$874$	13.5882	0.459627
$875$	−19.4673	−0.658115
$876$	−6.71867	−0.227003
$877$	44.3707	1.49829	0.749145	−	0.662406i	$-0.230464\pi$
$877$	44.3707	1.49829	0.749145	+	0.662406i	$0.230464\pi$
$878$	19.5885	0.661079
$879$	4.02849	0.135877
$880$	−1.06737	−0.0359811
$881$	−21.9179	−0.738433	−0.369216	−	0.929343i	$-0.620374\pi$
$881$	−21.9179	−0.738433	−0.369216	+	0.929343i	$0.620374\pi$
$882$	−18.4613	−0.621624
$883$	−19.5198	−0.656895	−0.328448	−	0.944522i	$-0.606525\pi$
$883$	−19.5198	−0.656895	−0.328448	+	0.944522i	$0.606525\pi$
$884$	19.2706	0.648141
$885$	−1.64747	−0.0553790
$886$	−24.9009	−0.836561
$887$	−43.2070	−1.45075	−0.725374	−	0.688355i	$-0.758333\pi$
$887$	−43.2070	−1.45075	−0.725374	+	0.688355i	$0.758333\pi$
$888$	−3.78069	−0.126872
$889$	−3.71896	−0.124730
$890$	−1.14846	−0.0384964
$891$	−8.26821	−0.276996
$892$	−8.62859	−0.288907
$893$	8.33180	0.278813
$894$	1.94486	0.0650459
$895$	8.05558	0.269268
$896$	−32.0363	−1.07026
$897$	0.679996	0.0227044
$898$	−60.5661	−2.02112
$899$	55.4758	1.85022
$900$	33.6129	1.12043
$901$	−53.7269	−1.78990
$902$	22.4875	0.748751
$903$	0.117318	0.00390409
$904$	22.2311	0.739395
$905$	−8.25490	−0.274402
$906$	−6.17656	−0.205202
$907$	−30.5831	−1.01549	−0.507747	−	0.861506i	$-0.669522\pi$
$907$	−30.5831	−1.01549	−0.507747	+	0.861506i	$0.669522\pi$
$908$	−27.3135	−0.906431
$909$	−44.9448	−1.49072
$910$	5.40455	0.179159
$911$	−17.9902	−0.596042	−0.298021	−	0.954559i	$-0.596327\pi$
$911$	−17.9902	−0.596042	−0.298021	+	0.954559i	$0.596327\pi$
$912$	−0.795668	−0.0263472
$913$	8.06637	0.266958
$914$	−83.5527	−2.76368
$915$	3.16461	0.104619
$916$	−74.0505	−2.44670
$917$	37.1577	1.22706
$918$	−22.1866	−0.732268
$919$	57.8215	1.90735	0.953677	−	0.300833i	$-0.0972647\pi$
$919$	57.8215	1.90735	0.953677	+	0.300833i	$0.0972647\pi$
$920$	−5.23530	−0.172603
$921$	−4.73087	−0.155888
$922$	−15.9670	−0.525846
$923$	−3.38835	−0.111529
$924$	1.75669	0.0577910
$925$	−22.5791	−0.742396
$926$	14.2293	0.467602
$927$	30.9588	1.01682
$928$	52.3526	1.71856
$929$	22.8997	0.751316	0.375658	−	0.926758i	$-0.377417\pi$
$929$	22.8997	0.751316	0.375658	+	0.926758i	$0.377417\pi$
$930$	4.90542	0.160855
$931$	−7.94027	−0.260232
$932$	38.7043	1.26780
$933$	5.67766	0.185878
$934$	81.3525	2.66193
$935$	−6.31182	−0.206419
$936$	−7.17702	−0.234588
$937$	−17.1097	−0.558948	−0.279474	−	0.960153i	$-0.590160\pi$
$937$	−17.1097	−0.558948	−0.279474	+	0.960153i	$0.590160\pi$
$938$	70.7269	2.30931
$939$	−0.281061	−0.00917208
$940$	−9.61354	−0.313559
$941$	−37.8060	−1.23244	−0.616220	−	0.787574i	$-0.711337\pi$
$941$	−37.8060	−1.23244	−0.616220	+	0.787574i	$0.711337\pi$
$942$	9.93881	0.323824
$943$	−21.7599	−0.708599
$944$	−5.27580	−0.171713
$945$	−3.73473	−0.121491
$946$	−0.448504	−0.0145821
$947$	−43.3537	−1.40880	−0.704402	−	0.709801i	$-0.748785\pi$
$947$	−43.3537	−1.40880	−0.704402	+	0.709801i	$0.748785\pi$
$948$	9.11472	0.296032
$949$	8.56753	0.278114
$950$	24.0867	0.781475
$951$	1.46268	0.0474305
$952$	−26.7999	−0.868589
$953$	−36.2690	−1.17487	−0.587434	−	0.809272i	$-0.699862\pi$
$953$	−36.2690	−1.17487	−0.587434	+	0.809272i	$0.699862\pi$
$954$	59.9245	1.94013
$955$	11.1501	0.360809
$956$	64.3628	2.08164
$957$	−2.23892	−0.0723739
$958$	81.3693	2.62892
$959$	17.2336	0.556503
$960$	4.01774	0.129672
$961$	19.3791	0.625131
$962$	14.4380	0.465501
$963$	−9.10828	−0.293510
$964$	−46.3114	−1.49159
$965$	0.0783857	0.00252333
$966$	−2.83210	−0.0911213
$967$	10.3108	0.331574	0.165787	−	0.986162i	$-0.446984\pi$
$967$	10.3108	0.331574	0.165787	+	0.986162i	$0.446984\pi$
$968$	−2.24251	−0.0720770
$969$	−4.70512	−0.151150
$970$	−36.2385	−1.16355
$971$	22.7777	0.730970	0.365485	−	0.930817i	$-0.380903\pi$
$971$	22.7777	0.730970	0.365485	+	0.930817i	$0.380903\pi$
$972$	22.3821	0.717907
$973$	25.0497	0.803058
$974$	35.3009	1.13111
$975$	1.20537	0.0386029
$976$	10.1342	0.324389
$977$	8.57513	0.274343	0.137171	−	0.990547i	$-0.456199\pi$
$977$	8.57513	0.274343	0.137171	+	0.990547i	$0.456199\pi$
$978$	0.622322	0.0198997
$979$	0.476018	0.0152136
$980$	9.16177	0.292662
$981$	−25.3091	−0.808058
$982$	−58.5429	−1.86818
$983$	24.1523	0.770340	0.385170	−	0.922846i	$-0.374143\pi$
$983$	24.1523	0.770340	0.385170	+	0.922846i	$0.374143\pi$
$984$	−6.45857	−0.205892
$985$	−10.4145	−0.331833
$986$	102.291	3.25762
$987$	−1.73655	−0.0552748
$988$	−9.24446	−0.294105
$989$	0.433992	0.0138001
$990$	7.03992	0.223743
$991$	−12.6228	−0.400977	−0.200488	−	0.979696i	$-0.564253\pi$
$991$	−12.6228	−0.400977	−0.200488	+	0.979696i	$0.564253\pi$
$992$	47.5428	1.50949
$993$	1.80598	0.0573109
$994$	14.1120	0.447607
$995$	14.2072	0.450399
$996$	−6.93806	−0.219841
$997$	−21.8782	−0.692891	−0.346445	−	0.938070i	$-0.612611\pi$
$997$	−21.8782	−0.692891	−0.346445	+	0.938070i	$0.612611\pi$
$998$	−48.6682	−1.54057
$999$	−9.97717	−0.315664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.d.1.15	✓	107

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.d.1.15	✓	107	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23665 q^{2} +0.286457 q^{3} +3.00262 q^{4} -1.07868 q^{5} -0.640706 q^{6} -2.04238 q^{7} -2.24251 q^{8} -2.91794 q^{9} +O(q^{10})\)	\(q-2.23665 q^{2} +0.286457 q^{3} +3.00262 q^{4} -1.07868 q^{5} -0.640706 q^{6} -2.04238 q^{7} -2.24251 q^{8} -2.91794 q^{9} +2.41263 q^{10} -1.00000 q^{11} +0.860122 q^{12} -1.09681 q^{13} +4.56809 q^{14} -0.308996 q^{15} -0.989517 q^{16} -5.85143 q^{17} +6.52643 q^{18} +2.80704 q^{19} -3.23886 q^{20} -0.585054 q^{21} +2.23665 q^{22} -2.16428 q^{23} -0.642384 q^{24} -3.83645 q^{25} +2.45319 q^{26} -1.69524 q^{27} -6.13248 q^{28} +7.81589 q^{29} +0.691116 q^{30} +7.09782 q^{31} +6.69823 q^{32} -0.286457 q^{33} +13.0876 q^{34} +2.20307 q^{35} -8.76147 q^{36} +5.88541 q^{37} -6.27837 q^{38} -0.314190 q^{39} +2.41895 q^{40} +10.0541 q^{41} +1.30856 q^{42} -0.200525 q^{43} -3.00262 q^{44} +3.14753 q^{45} +4.84075 q^{46} +2.96818 q^{47} -0.283454 q^{48} -2.82870 q^{49} +8.58081 q^{50} -1.67619 q^{51} -3.29331 q^{52} +9.18183 q^{53} +3.79166 q^{54} +1.07868 q^{55} +4.58005 q^{56} +0.804097 q^{57} -17.4814 q^{58} +5.33169 q^{59} -0.927796 q^{60} -10.2416 q^{61} -15.8754 q^{62} +5.95954 q^{63} -13.0026 q^{64} +1.18311 q^{65} +0.640706 q^{66} +15.4828 q^{67} -17.5696 q^{68} -0.619975 q^{69} -4.92750 q^{70} +3.08927 q^{71} +6.54352 q^{72} -7.81129 q^{73} -13.1636 q^{74} -1.09898 q^{75} +8.42847 q^{76} +2.04238 q^{77} +0.702735 q^{78} +10.5970 q^{79} +1.06737 q^{80} +8.26821 q^{81} -22.4875 q^{82} -8.06637 q^{83} -1.75669 q^{84} +6.31182 q^{85} +0.448504 q^{86} +2.23892 q^{87} +2.24251 q^{88} -0.476018 q^{89} -7.03992 q^{90} +2.24011 q^{91} -6.49852 q^{92} +2.03322 q^{93} -6.63879 q^{94} -3.02790 q^{95} +1.91876 q^{96} -15.0203 q^{97} +6.32682 q^{98} +2.91794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9}+O(q^{10}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9	\( 107 q - 3 q^{2} - 18 q^{3} + 91 q^{4} - 15 q^{5} - 54 q^{7} - 3 q^{8} + 95 q^{9} - 14 q^{10} - 107 q^{11} - 50 q^{12} - 24 q^{13} - 17 q^{14} - 47 q^{15} + 63 q^{16} + 25 q^{17} - 37 q^{18} - 55 q^{19} - 31 q^{20} + 15 q^{21} + 3 q^{22} - 38 q^{23} + 4 q^{24} + 62 q^{25} - 16 q^{26} - 57 q^{27} - 101 q^{28} + 27 q^{29} - 14 q^{30} - 112 q^{31} - 4 q^{32} + 18 q^{33} - 66 q^{34} + 8 q^{35} + 35 q^{36} - 60 q^{37} - 45 q^{38} - 58 q^{39} - 50 q^{40} - 14 q^{41} - 36 q^{42} - 78 q^{43} - 91 q^{44} - 68 q^{45} - 18 q^{46} - 109 q^{47} - 99 q^{48} + 61 q^{49} - 32 q^{50} - 10 q^{51} - 111 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 44 q^{56} + q^{57} - 98 q^{58} - 48 q^{59} - 119 q^{60} - 30 q^{61} + 32 q^{62} - 126 q^{63} + 3 q^{64} + 43 q^{65} - 77 q^{67} + 53 q^{68} - 51 q^{69} - 87 q^{70} - 40 q^{71} - 82 q^{72} - 83 q^{73} + 11 q^{74} - 69 q^{75} - 108 q^{76} + 54 q^{77} - 53 q^{78} - 66 q^{79} - 96 q^{80} + 51 q^{81} - 133 q^{82} - 32 q^{83} + 27 q^{84} - 66 q^{85} - 46 q^{86} - 136 q^{87} + 3 q^{88} - 56 q^{89} + 9 q^{90} - 86 q^{91} - 94 q^{92} - 33 q^{93} - 93 q^{94} - 25 q^{95} - 4 q^{96} - 109 q^{97} - 38 q^{98} - 95 q^{99}+O(q^{100}) \) 107 * q - 3 * q^2 - 18 * q^3 + 91 * q^4 - 15 * q^5 - 54 * q^7 - 3 * q^8 + 95 * q^9 - 14 * q^10 - 107 * q^11 - 50 * q^12 - 24 * q^13 - 17 * q^14 - 47 * q^15 + 63 * q^16 + 25 * q^17 - 37 * q^18 - 55 * q^19 - 31 * q^20 + 15 * q^21 + 3 * q^22 - 38 * q^23 + 4 * q^24 + 62 * q^25 - 16 * q^26 - 57 * q^27 - 101 * q^28 + 27 * q^29 - 14 * q^30 - 112 * q^31 - 4 * q^32 + 18 * q^33 - 66 * q^34 + 8 * q^35 + 35 * q^36 - 60 * q^37 - 45 * q^38 - 58 * q^39 - 50 * q^40 - 14 * q^41 - 36 * q^42 - 78 * q^43 - 91 * q^44 - 68 * q^45 - 18 * q^46 - 109 * q^47 - 99 * q^48 + 61 * q^49 - 32 * q^50 - 10 * q^51 - 111 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 44 * q^56 + q^57 - 98 * q^58 - 48 * q^59 - 119 * q^60 - 30 * q^61 + 32 * q^62 - 126 * q^63 + 3 * q^64 + 43 * q^65 - 77 * q^67 + 53 * q^68 - 51 * q^69 - 87 * q^70 - 40 * q^71 - 82 * q^72 - 83 * q^73 + 11 * q^74 - 69 * q^75 - 108 * q^76 + 54 * q^77 - 53 * q^78 - 66 * q^79 - 96 * q^80 + 51 * q^81 - 133 * q^82 - 32 * q^83 + 27 * q^84 - 66 * q^85 - 46 * q^86 - 136 * q^87 + 3 * q^88 - 56 * q^89 + 9 * q^90 - 86 * q^91 - 94 * q^92 - 33 * q^93 - 93 * q^94 - 25 * q^95 - 4 * q^96 - 109 * q^97 - 38 * q^98 - 95 * q^99

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