LMFDB - Embedded newform 8018.2.a.j.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.833135 q^{3} +1.00000 q^{4} -3.18557 q^{5} -0.833135 q^{6} +0.455061 q^{7} +1.00000 q^{8} -2.30589 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.833135 q^{3} +1.00000 q^{4} -3.18557 q^{5} -0.833135 q^{6} +0.455061 q^{7} +1.00000 q^{8} -2.30589 q^{9} -3.18557 q^{10} -1.37320 q^{11} -0.833135 q^{12} +5.32549 q^{13} +0.455061 q^{14} +2.65401 q^{15} +1.00000 q^{16} -7.33327 q^{17} -2.30589 q^{18} -1.00000 q^{19} -3.18557 q^{20} -0.379127 q^{21} -1.37320 q^{22} -4.82410 q^{23} -0.833135 q^{24} +5.14783 q^{25} +5.32549 q^{26} +4.42052 q^{27} +0.455061 q^{28} +1.65207 q^{29} +2.65401 q^{30} +5.97363 q^{31} +1.00000 q^{32} +1.14406 q^{33} -7.33327 q^{34} -1.44963 q^{35} -2.30589 q^{36} -8.53380 q^{37} -1.00000 q^{38} -4.43685 q^{39} -3.18557 q^{40} -2.32519 q^{41} -0.379127 q^{42} -5.06700 q^{43} -1.37320 q^{44} +7.34555 q^{45} -4.82410 q^{46} +3.59352 q^{47} -0.833135 q^{48} -6.79292 q^{49} +5.14783 q^{50} +6.10961 q^{51} +5.32549 q^{52} +0.902921 q^{53} +4.42052 q^{54} +4.37442 q^{55} +0.455061 q^{56} +0.833135 q^{57} +1.65207 q^{58} -0.573811 q^{59} +2.65401 q^{60} -0.904971 q^{61} +5.97363 q^{62} -1.04932 q^{63} +1.00000 q^{64} -16.9647 q^{65} +1.14406 q^{66} +7.39328 q^{67} -7.33327 q^{68} +4.01912 q^{69} -1.44963 q^{70} +11.9031 q^{71} -2.30589 q^{72} +1.44472 q^{73} -8.53380 q^{74} -4.28884 q^{75} -1.00000 q^{76} -0.624890 q^{77} -4.43685 q^{78} -1.09630 q^{79} -3.18557 q^{80} +3.23477 q^{81} -2.32519 q^{82} -16.3459 q^{83} -0.379127 q^{84} +23.3606 q^{85} -5.06700 q^{86} -1.37640 q^{87} -1.37320 q^{88} -7.72987 q^{89} +7.34555 q^{90} +2.42342 q^{91} -4.82410 q^{92} -4.97684 q^{93} +3.59352 q^{94} +3.18557 q^{95} -0.833135 q^{96} +11.9548 q^{97} -6.79292 q^{98} +3.16644 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.833135	−0.481011	−0.240505	−	0.970648i	$-0.577313\pi$
$3$	−0.833135	−0.481011	−0.240505	+	0.970648i	$0.577313\pi$
$4$	1.00000	0.500000
$5$	−3.18557	−1.42463	−0.712314	−	0.701861i	$-0.752353\pi$
$5$	−3.18557	−1.42463	−0.712314	+	0.701861i	$0.752353\pi$
$6$	−0.833135	−0.340126
$7$	0.455061	0.171997	0.0859985	−	0.996295i	$-0.472592\pi$
$7$	0.455061	0.171997	0.0859985	+	0.996295i	$0.472592\pi$
$8$	1.00000	0.353553
$9$	−2.30589	−0.768629
$10$	−3.18557	−1.00736
$11$	−1.37320	−0.414035	−0.207018	−	0.978337i	$-0.566376\pi$
$11$	−1.37320	−0.414035	−0.207018	+	0.978337i	$0.566376\pi$
$12$	−0.833135	−0.240505
$13$	5.32549	1.47702	0.738512	−	0.674240i	$-0.235529\pi$
$13$	5.32549	1.47702	0.738512	+	0.674240i	$0.235529\pi$
$14$	0.455061	0.121620
$15$	2.65401	0.685261
$16$	1.00000	0.250000
$17$	−7.33327	−1.77858	−0.889290	−	0.457344i	$-0.848801\pi$
$17$	−7.33327	−1.77858	−0.889290	+	0.457344i	$0.848801\pi$
$18$	−2.30589	−0.543503
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.18557	−0.712314
$21$	−0.379127	−0.0827324
$22$	−1.37320	−0.292767
$23$	−4.82410	−1.00589	−0.502947	−	0.864317i	$-0.667751\pi$
$23$	−4.82410	−1.00589	−0.502947	+	0.864317i	$0.667751\pi$
$24$	−0.833135	−0.170063
$25$	5.14783	1.02957
$26$	5.32549	1.04441
$27$	4.42052	0.850729
$28$	0.455061	0.0859985
$29$	1.65207	0.306782	0.153391	−	0.988166i	$-0.450981\pi$
$29$	1.65207	0.306782	0.153391	+	0.988166i	$0.450981\pi$
$30$	2.65401	0.484553
$31$	5.97363	1.07290	0.536448	−	0.843934i	$-0.319766\pi$
$31$	5.97363	1.07290	0.536448	+	0.843934i	$0.319766\pi$
$32$	1.00000	0.176777
$33$	1.14406	0.199155
$34$	−7.33327	−1.25765
$35$	−1.44963	−0.245032
$36$	−2.30589	−0.384314
$37$	−8.53380	−1.40295	−0.701474	−	0.712695i	$-0.747474\pi$
$37$	−8.53380	−1.40295	−0.701474	+	0.712695i	$0.747474\pi$
$38$	−1.00000	−0.162221
$39$	−4.43685	−0.710464
$40$	−3.18557	−0.503682
$41$	−2.32519	−0.363134	−0.181567	−	0.983379i	$-0.558117\pi$
$41$	−2.32519	−0.363134	−0.181567	+	0.983379i	$0.558117\pi$
$42$	−0.379127	−0.0585006
$43$	−5.06700	−0.772710	−0.386355	−	0.922350i	$-0.626266\pi$
$43$	−5.06700	−0.772710	−0.386355	+	0.922350i	$0.626266\pi$
$44$	−1.37320	−0.207018
$45$	7.34555	1.09501
$46$	−4.82410	−0.711275
$47$	3.59352	0.524169	0.262085	−	0.965045i	$-0.415590\pi$
$47$	3.59352	0.524169	0.262085	+	0.965045i	$0.415590\pi$
$48$	−0.833135	−0.120253
$49$	−6.79292	−0.970417
$50$	5.14783	0.728013
$51$	6.10961	0.855516
$52$	5.32549	0.738512
$53$	0.902921	0.124026	0.0620129	−	0.998075i	$-0.480248\pi$
$53$	0.902921	0.124026	0.0620129	+	0.998075i	$0.480248\pi$
$54$	4.42052	0.601556
$55$	4.37442	0.589846
$56$	0.455061	0.0608101
$57$	0.833135	0.110351
$58$	1.65207	0.216928
$59$	−0.573811	−0.0747038	−0.0373519	−	0.999302i	$-0.511892\pi$
$59$	−0.573811	−0.0747038	−0.0373519	+	0.999302i	$0.511892\pi$
$60$	2.65401	0.342631
$61$	−0.904971	−0.115870	−0.0579348	−	0.998320i	$-0.518452\pi$
$61$	−0.904971	−0.115870	−0.0579348	+	0.998320i	$0.518452\pi$
$62$	5.97363	0.758651
$63$	−1.04932	−0.132202
$64$	1.00000	0.125000
$65$	−16.9647	−2.10421
$66$	1.14406	0.140824
$67$	7.39328	0.903232	0.451616	−	0.892212i	$-0.350848\pi$
$67$	7.39328	0.903232	0.451616	+	0.892212i	$0.350848\pi$
$68$	−7.33327	−0.889290
$69$	4.01912	0.483846
$70$	−1.44963	−0.173264
$71$	11.9031	1.41264	0.706321	−	0.707892i	$-0.250353\pi$
$71$	11.9031	1.41264	0.706321	+	0.707892i	$0.250353\pi$
$72$	−2.30589	−0.271751
$73$	1.44472	0.169092	0.0845461	−	0.996420i	$-0.473056\pi$
$73$	1.44472	0.169092	0.0845461	+	0.996420i	$0.473056\pi$
$74$	−8.53380	−0.992035
$75$	−4.28884	−0.495232
$76$	−1.00000	−0.114708
$77$	−0.624890	−0.0712128
$78$	−4.43685	−0.502374
$79$	−1.09630	−0.123344	−0.0616718	−	0.998096i	$-0.519643\pi$
$79$	−1.09630	−0.123344	−0.0616718	+	0.998096i	$0.519643\pi$
$80$	−3.18557	−0.356157
$81$	3.23477	0.359419
$82$	−2.32519	−0.256774
$83$	−16.3459	−1.79420	−0.897098	−	0.441831i	$-0.854329\pi$
$83$	−16.3459	−1.79420	−0.897098	+	0.441831i	$0.854329\pi$
$84$	−0.379127	−0.0413662
$85$	23.3606	2.53382
$86$	−5.06700	−0.546388
$87$	−1.37640	−0.147565
$88$	−1.37320	−0.146384
$89$	−7.72987	−0.819364	−0.409682	−	0.912228i	$-0.634360\pi$
$89$	−7.72987	−0.819364	−0.409682	+	0.912228i	$0.634360\pi$
$90$	7.34555	0.774289
$91$	2.42342	0.254044
$92$	−4.82410	−0.502947
$93$	−4.97684	−0.516074
$94$	3.59352	0.370644
$95$	3.18557	0.326832
$96$	−0.833135	−0.0850315
$97$	11.9548	1.21382	0.606911	−	0.794770i	$-0.292408\pi$
$97$	11.9548	1.21382	0.606911	+	0.794770i	$0.292408\pi$
$98$	−6.79292	−0.686188
$99$	3.16644	0.318239
$100$	5.14783	0.514783
$101$	2.91069	0.289625	0.144812	−	0.989459i	$-0.453742\pi$
$101$	2.91069	0.289625	0.144812	+	0.989459i	$0.453742\pi$
$102$	6.10961	0.604941
$103$	−4.95450	−0.488181	−0.244091	−	0.969752i	$-0.578489\pi$
$103$	−4.95450	−0.488181	−0.244091	+	0.969752i	$0.578489\pi$
$104$	5.32549	0.522207
$105$	1.20774	0.117863
$106$	0.902921	0.0876995
$107$	9.71232	0.938926	0.469463	−	0.882952i	$-0.344448\pi$
$107$	9.71232	0.938926	0.469463	+	0.882952i	$0.344448\pi$
$108$	4.42052	0.425365
$109$	1.66637	0.159609	0.0798045	−	0.996811i	$-0.474570\pi$
$109$	1.66637	0.159609	0.0798045	+	0.996811i	$0.474570\pi$
$110$	4.37442	0.417084
$111$	7.10981	0.674833
$112$	0.455061	0.0429993
$113$	−12.1584	−1.14377	−0.571885	−	0.820334i	$-0.693788\pi$
$113$	−12.1584	−1.14377	−0.571885	+	0.820334i	$0.693788\pi$
$114$	0.833135	0.0780302
$115$	15.3675	1.43303
$116$	1.65207	0.153391
$117$	−12.2800	−1.13528
$118$	−0.573811	−0.0528236
$119$	−3.33709	−0.305910
$120$	2.65401	0.242276
$121$	−9.11432	−0.828575
$122$	−0.904971	−0.0819322
$123$	1.93720	0.174671
$124$	5.97363	0.536448
$125$	−0.470923	−0.0421206
$126$	−1.04932	−0.0934808
$127$	15.9802	1.41801	0.709006	−	0.705203i	$-0.249144\pi$
$127$	15.9802	1.41801	0.709006	+	0.705203i	$0.249144\pi$
$128$	1.00000	0.0883883
$129$	4.22149	0.371682
$130$	−16.9647	−1.48790
$131$	6.63129	0.579378	0.289689	−	0.957121i	$-0.406448\pi$
$131$	6.63129	0.579378	0.289689	+	0.957121i	$0.406448\pi$
$132$	1.14406	0.0995777
$133$	−0.455061	−0.0394588
$134$	7.39328	0.638682
$135$	−14.0819	−1.21197
$136$	−7.33327	−0.628823
$137$	16.9545	1.44852	0.724261	−	0.689526i	$-0.242181\pi$
$137$	16.9545	1.44852	0.724261	+	0.689526i	$0.242181\pi$
$138$	4.01912	0.342131
$139$	4.46835	0.379000	0.189500	−	0.981881i	$-0.439313\pi$
$139$	4.46835	0.379000	0.189500	+	0.981881i	$0.439313\pi$
$140$	−1.44963	−0.122516
$141$	−2.99389	−0.252131
$142$	11.9031	0.998889
$143$	−7.31296	−0.611540
$144$	−2.30589	−0.192157
$145$	−5.26279	−0.437051
$146$	1.44472	0.119566
$147$	5.65942	0.466781
$148$	−8.53380	−0.701474
$149$	3.87568	0.317508	0.158754	−	0.987318i	$-0.449252\pi$
$149$	3.87568	0.317508	0.158754	+	0.987318i	$0.449252\pi$
$150$	−4.28884	−0.350182
$151$	7.69964	0.626587	0.313294	−	0.949656i	$-0.398568\pi$
$151$	7.69964	0.626587	0.313294	+	0.949656i	$0.398568\pi$
$152$	−1.00000	−0.0811107
$153$	16.9097	1.36707
$154$	−0.624890	−0.0503551
$155$	−19.0294	−1.52848
$156$	−4.43685	−0.355232
$157$	2.51487	0.200709	0.100354	−	0.994952i	$-0.468002\pi$
$157$	2.51487	0.200709	0.100354	+	0.994952i	$0.468002\pi$
$158$	−1.09630	−0.0872171
$159$	−0.752255	−0.0596577
$160$	−3.18557	−0.251841
$161$	−2.19526	−0.173011
$162$	3.23477	0.254148
$163$	−17.0284	−1.33377	−0.666885	−	0.745161i	$-0.732373\pi$
$163$	−17.0284	−1.33377	−0.666885	+	0.745161i	$0.732373\pi$
$164$	−2.32519	−0.181567
$165$	−3.64448	−0.283722
$166$	−16.3459	−1.26869
$167$	3.30469	0.255725	0.127862	−	0.991792i	$-0.459188\pi$
$167$	3.30469	0.255725	0.127862	+	0.991792i	$0.459188\pi$
$168$	−0.379127	−0.0292503
$169$	15.3608	1.18160
$170$	23.3606	1.79168
$171$	2.30589	0.176336
$172$	−5.06700	−0.386355
$173$	23.1168	1.75753	0.878767	−	0.477251i	$-0.158367\pi$
$173$	23.1168	1.75753	0.878767	+	0.477251i	$0.158367\pi$
$174$	−1.37640	−0.104345
$175$	2.34258	0.177082
$176$	−1.37320	−0.103509
$177$	0.478062	0.0359333
$178$	−7.72987	−0.579378
$179$	−8.85098	−0.661553	−0.330777	−	0.943709i	$-0.607311\pi$
$179$	−8.85098	−0.661553	−0.330777	+	0.943709i	$0.607311\pi$
$180$	7.34555	0.547505
$181$	−20.1368	−1.49675	−0.748377	−	0.663273i	$-0.769167\pi$
$181$	−20.1368	−1.49675	−0.748377	+	0.663273i	$0.769167\pi$
$182$	2.42342	0.179636
$183$	0.753963	0.0557345
$184$	−4.82410	−0.355637
$185$	27.1850	1.99868
$186$	−4.97684	−0.364919
$187$	10.0700	0.736395
$188$	3.59352	0.262085
$189$	2.01161	0.146323
$190$	3.18557	0.231105
$191$	−0.896810	−0.0648909	−0.0324454	−	0.999474i	$-0.510330\pi$
$191$	−0.896810	−0.0648909	−0.0324454	+	0.999474i	$0.510330\pi$
$192$	−0.833135	−0.0601263
$193$	15.7414	1.13309	0.566544	−	0.824031i	$-0.308280\pi$
$193$	15.7414	1.13309	0.566544	+	0.824031i	$0.308280\pi$
$194$	11.9548	0.858302
$195$	14.1339	1.01215
$196$	−6.79292	−0.485209
$197$	18.1808	1.29533	0.647664	−	0.761926i	$-0.275746\pi$
$197$	18.1808	1.29533	0.647664	+	0.761926i	$0.275746\pi$
$198$	3.16644	0.225029
$199$	21.6872	1.53736	0.768681	−	0.639633i	$-0.220914\pi$
$199$	21.6872	1.53736	0.768681	+	0.639633i	$0.220914\pi$
$200$	5.14783	0.364007
$201$	−6.15960	−0.434464
$202$	2.91069	0.204796
$203$	0.751794	0.0527656
$204$	6.10961	0.427758
$205$	7.40704	0.517330
$206$	−4.95450	−0.345196
$207$	11.1238	0.773159
$208$	5.32549	0.369256
$209$	1.37320	0.0949862
$210$	1.20774	0.0833417
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	0.902921	0.0620129
$213$	−9.91692	−0.679496
$214$	9.71232	0.663921
$215$	16.1413	1.10082
$216$	4.42052	0.300778
$217$	2.71837	0.184535
$218$	1.66637	0.112861
$219$	−1.20365	−0.0813351
$220$	4.37442	0.294923
$221$	−39.0533	−2.62701
$222$	7.10981	0.477179
$223$	22.8355	1.52918	0.764588	−	0.644520i	$-0.222943\pi$
$223$	22.8355	1.52918	0.764588	+	0.644520i	$0.222943\pi$
$224$	0.455061	0.0304051
$225$	−11.8703	−0.791354
$226$	−12.1584	−0.808767
$227$	14.3922	0.955247	0.477623	−	0.878565i	$-0.341498\pi$
$227$	14.3922	0.955247	0.477623	+	0.878565i	$0.341498\pi$
$228$	0.833135	0.0551757
$229$	−3.06103	−0.202279	−0.101139	−	0.994872i	$-0.532249\pi$
$229$	−3.06103	−0.202279	−0.101139	+	0.994872i	$0.532249\pi$
$230$	15.3675	1.01330
$231$	0.520618	0.0342541
$232$	1.65207	0.108464
$233$	8.74764	0.573077	0.286539	−	0.958069i	$-0.407495\pi$
$233$	8.74764	0.573077	0.286539	+	0.958069i	$0.407495\pi$
$234$	−12.2800	−0.802767
$235$	−11.4474	−0.746746
$236$	−0.573811	−0.0373519
$237$	0.913367	0.0593296
$238$	−3.33709	−0.216311
$239$	16.8769	1.09168	0.545838	−	0.837891i	$-0.316211\pi$
$239$	16.8769	1.09168	0.545838	+	0.837891i	$0.316211\pi$
$240$	2.65401	0.171315
$241$	8.38468	0.540105	0.270052	−	0.962846i	$-0.412959\pi$
$241$	8.38468	0.540105	0.270052	+	0.962846i	$0.412959\pi$
$242$	−9.11432	−0.585891
$243$	−15.9566	−1.02361
$244$	−0.904971	−0.0579348
$245$	21.6393	1.38248
$246$	1.93720	0.123511
$247$	−5.32549	−0.338853
$248$	5.97363	0.379326
$249$	13.6183	0.863027
$250$	−0.470923	−0.0297838
$251$	−19.9311	−1.25804	−0.629020	−	0.777389i	$-0.716544\pi$
$251$	−19.9311	−1.25804	−0.629020	+	0.777389i	$0.716544\pi$
$252$	−1.04932	−0.0661009
$253$	6.62445	0.416476
$254$	15.9802	1.00269
$255$	−19.4625	−1.21879
$256$	1.00000	0.0625000
$257$	−10.1018	−0.630133	−0.315066	−	0.949070i	$-0.602027\pi$
$257$	−10.1018	−0.630133	−0.315066	+	0.949070i	$0.602027\pi$
$258$	4.22149	0.262819
$259$	−3.88340	−0.241303
$260$	−16.9647	−1.05211
$261$	−3.80949	−0.235802
$262$	6.63129	0.409682
$263$	−9.27824	−0.572121	−0.286060	−	0.958212i	$-0.592346\pi$
$263$	−9.27824	−0.572121	−0.286060	+	0.958212i	$0.592346\pi$
$264$	1.14406	0.0704120
$265$	−2.87631	−0.176691
$266$	−0.455061	−0.0279016
$267$	6.44002	0.394123
$268$	7.39328	0.451616
$269$	−18.6878	−1.13941	−0.569707	−	0.821848i	$-0.692943\pi$
$269$	−18.6878	−1.13941	−0.569707	+	0.821848i	$0.692943\pi$
$270$	−14.0819	−0.856994
$271$	22.5817	1.37174	0.685869	−	0.727725i	$-0.259422\pi$
$271$	22.5817	1.37174	0.685869	+	0.727725i	$0.259422\pi$
$272$	−7.33327	−0.444645
$273$	−2.01904	−0.122198
$274$	16.9545	1.02426
$275$	−7.06900	−0.426277
$276$	4.01912	0.241923
$277$	−5.78007	−0.347291	−0.173645	−	0.984808i	$-0.555555\pi$
$277$	−5.78007	−0.347291	−0.173645	+	0.984808i	$0.555555\pi$
$278$	4.46835	0.267994
$279$	−13.7745	−0.824658
$280$	−1.44963	−0.0866318
$281$	−27.1568	−1.62004	−0.810020	−	0.586402i	$-0.800544\pi$
$281$	−27.1568	−1.62004	−0.810020	+	0.586402i	$0.800544\pi$
$282$	−2.99389	−0.178283
$283$	18.8095	1.11811	0.559054	−	0.829132i	$-0.311165\pi$
$283$	18.8095	1.11811	0.559054	+	0.829132i	$0.311165\pi$
$284$	11.9031	0.706321
$285$	−2.65401	−0.157210
$286$	−7.31296	−0.432424
$287$	−1.05810	−0.0624579
$288$	−2.30589	−0.135876
$289$	36.7769	2.16335
$290$	−5.26279	−0.309041
$291$	−9.95993	−0.583862
$292$	1.44472	0.0845461
$293$	33.1965	1.93936	0.969680	−	0.244377i	$-0.0785835\pi$
$293$	33.1965	1.93936	0.969680	+	0.244377i	$0.0785835\pi$
$294$	5.65942	0.330064
$295$	1.82791	0.106425
$296$	−8.53380	−0.496017
$297$	−6.07025	−0.352232
$298$	3.87568	0.224512
$299$	−25.6907	−1.48573
$300$	−4.28884	−0.247616
$301$	−2.30579	−0.132904
$302$	7.69964	0.443064
$303$	−2.42500	−0.139313
$304$	−1.00000	−0.0573539
$305$	2.88284	0.165071
$306$	16.9097	0.966663
$307$	−2.16914	−0.123799	−0.0618996	−	0.998082i	$-0.519716\pi$
$307$	−2.16914	−0.123799	−0.0618996	+	0.998082i	$0.519716\pi$
$308$	−0.624890	−0.0356064
$309$	4.12776	0.234820
$310$	−19.0294	−1.08080
$311$	30.4081	1.72429	0.862143	−	0.506666i	$-0.169122\pi$
$311$	30.4081	1.72429	0.862143	+	0.506666i	$0.169122\pi$
$312$	−4.43685	−0.251187
$313$	−33.7663	−1.90859	−0.954293	−	0.298873i	$-0.903389\pi$
$313$	−33.7663	−1.90859	−0.954293	+	0.298873i	$0.903389\pi$
$314$	2.51487	0.141922
$315$	3.34268	0.188339
$316$	−1.09630	−0.0616718
$317$	−28.5722	−1.60477	−0.802386	−	0.596805i	$-0.796437\pi$
$317$	−28.5722	−1.60477	−0.802386	+	0.596805i	$0.796437\pi$
$318$	−0.752255	−0.0421844
$319$	−2.26863	−0.127019
$320$	−3.18557	−0.178079
$321$	−8.09167	−0.451633
$322$	−2.19526	−0.122337
$323$	7.33327	0.408034
$324$	3.23477	0.179710
$325$	27.4147	1.52069
$326$	−17.0284	−0.943118
$327$	−1.38831	−0.0767736
$328$	−2.32519	−0.128387
$329$	1.63527	0.0901555
$330$	−3.64448	−0.200622
$331$	−4.88317	−0.268403	−0.134202	−	0.990954i	$-0.542847\pi$
$331$	−4.88317	−0.268403	−0.134202	+	0.990954i	$0.542847\pi$
$332$	−16.3459	−0.897098
$333$	19.6780	1.07835
$334$	3.30469	0.180825
$335$	−23.5518	−1.28677
$336$	−0.379127	−0.0206831
$337$	36.3051	1.97766	0.988832	−	0.149033i	$-0.0476162\pi$
$337$	36.3051	1.97766	0.988832	+	0.149033i	$0.0476162\pi$
$338$	15.3608	0.835519
$339$	10.1296	0.550165
$340$	23.3606	1.26691
$341$	−8.20298	−0.444216
$342$	2.30589	0.124688
$343$	−6.27662	−0.338906
$344$	−5.06700	−0.273194
$345$	−12.8032	−0.689300
$346$	23.1168	1.24276
$347$	−9.37740	−0.503405	−0.251703	−	0.967805i	$-0.580991\pi$
$347$	−9.37740	−0.503405	−0.251703	+	0.967805i	$0.580991\pi$
$348$	−1.37640	−0.0737827
$349$	19.9950	1.07031	0.535153	−	0.844755i	$-0.320254\pi$
$349$	19.9950	1.07031	0.535153	+	0.844755i	$0.320254\pi$
$350$	2.34258	0.125216
$351$	23.5414	1.25655
$352$	−1.37320	−0.0731918
$353$	−19.6389	−1.04527	−0.522637	−	0.852555i	$-0.675052\pi$
$353$	−19.6389	−1.04527	−0.522637	+	0.852555i	$0.675052\pi$
$354$	0.478062	0.0254087
$355$	−37.9182	−2.01249
$356$	−7.72987	−0.409682
$357$	2.78024	0.147146
$358$	−8.85098	−0.467789
$359$	−12.3866	−0.653740	−0.326870	−	0.945069i	$-0.605994\pi$
$359$	−12.3866	−0.653740	−0.326870	+	0.945069i	$0.605994\pi$
$360$	7.34555	0.387145
$361$	1.00000	0.0526316
$362$	−20.1368	−1.05837
$363$	7.59346	0.398553
$364$	2.42342	0.127022
$365$	−4.60227	−0.240894
$366$	0.753963	0.0394103
$367$	14.2061	0.741551	0.370776	−	0.928723i	$-0.379092\pi$
$367$	14.2061	0.741551	0.370776	+	0.928723i	$0.379092\pi$
$368$	−4.82410	−0.251474
$369$	5.36162	0.279115
$370$	27.1850	1.41328
$371$	0.410884	0.0213321
$372$	−4.97684	−0.258037
$373$	30.1257	1.55985	0.779925	−	0.625872i	$-0.215257\pi$
$373$	30.1257	1.55985	0.779925	+	0.625872i	$0.215257\pi$
$374$	10.0700	0.520710
$375$	0.392342	0.0202605
$376$	3.59352	0.185322
$377$	8.79809	0.453125
$378$	2.01161	0.103466
$379$	0.617767	0.0317326	0.0158663	−	0.999874i	$-0.494949\pi$
$379$	0.617767	0.0317326	0.0158663	+	0.999874i	$0.494949\pi$
$380$	3.18557	0.163416
$381$	−13.3136	−0.682079
$382$	−0.896810	−0.0458848
$383$	12.4877	0.638093	0.319046	−	0.947739i	$-0.396637\pi$
$383$	12.4877	0.638093	0.319046	+	0.947739i	$0.396637\pi$
$384$	−0.833135	−0.0425157
$385$	1.99063	0.101452
$386$	15.7414	0.801215
$387$	11.6839	0.593927
$388$	11.9548	0.606911
$389$	22.5256	1.14209	0.571047	−	0.820918i	$-0.306538\pi$
$389$	22.5256	1.14209	0.571047	+	0.820918i	$0.306538\pi$
$390$	14.1339	0.715697
$391$	35.3764	1.78906
$392$	−6.79292	−0.343094
$393$	−5.52476	−0.278687
$394$	18.1808	0.915935
$395$	3.49234	0.175719
$396$	3.16644	0.159120
$397$	2.21743	0.111290	0.0556449	−	0.998451i	$-0.482279\pi$
$397$	2.21743	0.111290	0.0556449	+	0.998451i	$0.482279\pi$
$398$	21.6872	1.08708
$399$	0.379127	0.0189801
$400$	5.14783	0.257392
$401$	−21.1119	−1.05428	−0.527138	−	0.849780i	$-0.676735\pi$
$401$	−21.1119	−1.05428	−0.527138	+	0.849780i	$0.676735\pi$
$402$	−6.15960	−0.307213
$403$	31.8125	1.58469
$404$	2.91069	0.144812
$405$	−10.3046	−0.512039
$406$	0.751794	0.0373109
$407$	11.7186	0.580870
$408$	6.10961	0.302471
$409$	−27.5064	−1.36010	−0.680052	−	0.733164i	$-0.738043\pi$
$409$	−27.5064	−1.36010	−0.680052	+	0.733164i	$0.738043\pi$
$410$	7.40704	0.365808
$411$	−14.1254	−0.696755
$412$	−4.95450	−0.244091
$413$	−0.261119	−0.0128488
$414$	11.1238	0.546706
$415$	52.0710	2.55606
$416$	5.32549	0.261104
$417$	−3.72274	−0.182303
$418$	1.37320	0.0671654
$419$	−8.97773	−0.438591	−0.219296	−	0.975658i	$-0.570376\pi$
$419$	−8.97773	−0.438591	−0.219296	+	0.975658i	$0.570376\pi$
$420$	1.20774	0.0589314
$421$	29.8005	1.45239	0.726194	−	0.687489i	$-0.241287\pi$
$421$	29.8005	1.45239	0.726194	+	0.687489i	$0.241287\pi$
$422$	−1.00000	−0.0486792
$423$	−8.28625	−0.402892
$424$	0.902921	0.0438497
$425$	−37.7504	−1.83117
$426$	−9.91692	−0.480476
$427$	−0.411817	−0.0199292
$428$	9.71232	0.469463
$429$	6.09268	0.294157
$430$	16.1413	0.778400
$431$	27.8167	1.33988	0.669941	−	0.742414i	$-0.266319\pi$
$431$	27.8167	1.33988	0.669941	+	0.742414i	$0.266319\pi$
$432$	4.42052	0.212682
$433$	1.22663	0.0589483	0.0294741	−	0.999566i	$-0.490617\pi$
$433$	1.22663	0.0589483	0.0294741	+	0.999566i	$0.490617\pi$
$434$	2.71837	0.130486
$435$	4.38461	0.210226
$436$	1.66637	0.0798045
$437$	4.82410	0.230768
$438$	−1.20365	−0.0575126
$439$	35.1401	1.67714	0.838572	−	0.544790i	$-0.183391\pi$
$439$	35.1401	1.67714	0.838572	+	0.544790i	$0.183391\pi$
$440$	4.37442	0.208542
$441$	15.6637	0.745890
$442$	−39.0533	−1.85757
$443$	−0.756700	−0.0359519	−0.0179759	−	0.999838i	$-0.505722\pi$
$443$	−0.756700	−0.0359519	−0.0179759	+	0.999838i	$0.505722\pi$
$444$	7.10981	0.337417
$445$	24.6240	1.16729
$446$	22.8355	1.08129
$447$	−3.22896	−0.152725
$448$	0.455061	0.0214996
$449$	13.1481	0.620497	0.310249	−	0.950655i	$-0.399588\pi$
$449$	13.1481	0.620497	0.310249	+	0.950655i	$0.399588\pi$
$450$	−11.8703	−0.559572
$451$	3.19295	0.150350
$452$	−12.1584	−0.571885
$453$	−6.41483	−0.301395
$454$	14.3922	0.675461
$455$	−7.71998	−0.361918
$456$	0.833135	0.0390151
$457$	30.8512	1.44316	0.721580	−	0.692331i	$-0.243416\pi$
$457$	30.8512	1.44316	0.721580	+	0.692331i	$0.243416\pi$
$458$	−3.06103	−0.143033
$459$	−32.4169	−1.51309
$460$	15.3675	0.716513
$461$	11.9807	0.557997	0.278998	−	0.960292i	$-0.409998\pi$
$461$	11.9807	0.557997	0.278998	+	0.960292i	$0.409998\pi$
$462$	0.520618	0.0242213
$463$	24.1856	1.12400	0.562000	−	0.827137i	$-0.310032\pi$
$463$	24.1856	1.12400	0.562000	+	0.827137i	$0.310032\pi$
$464$	1.65207	0.0766955
$465$	15.8540	0.735214
$466$	8.74764	0.405227
$467$	−10.4573	−0.483904	−0.241952	−	0.970288i	$-0.577788\pi$
$467$	−10.4573	−0.483904	−0.241952	+	0.970288i	$0.577788\pi$
$468$	−12.2800	−0.567642
$469$	3.36439	0.155353
$470$	−11.4474	−0.528029
$471$	−2.09523	−0.0965430
$472$	−0.573811	−0.0264118
$473$	6.95800	0.319929
$474$	0.913367	0.0419523
$475$	−5.14783	−0.236199
$476$	−3.33709	−0.152955
$477$	−2.08203	−0.0953298
$478$	16.8769	0.771931
$479$	0.600314	0.0274290	0.0137145	−	0.999906i	$-0.495634\pi$
$479$	0.600314	0.0274290	0.0137145	+	0.999906i	$0.495634\pi$
$480$	2.65401	0.121138
$481$	−45.4467	−2.07219
$482$	8.38468	0.381912
$483$	1.82895	0.0832200
$484$	−9.11432	−0.414287
$485$	−38.0827	−1.72925
$486$	−15.9566	−0.723804
$487$	−10.6381	−0.482060	−0.241030	−	0.970518i	$-0.577485\pi$
$487$	−10.6381	−0.482060	−0.241030	+	0.970518i	$0.577485\pi$
$488$	−0.904971	−0.0409661
$489$	14.1870	0.641557
$490$	21.6393	0.977564
$491$	26.5876	1.19988	0.599940	−	0.800045i	$-0.295191\pi$
$491$	26.5876	1.19988	0.599940	+	0.800045i	$0.295191\pi$
$492$	1.93720	0.0873355
$493$	−12.1151	−0.545637
$494$	−5.32549	−0.239605
$495$	−10.0869	−0.453373
$496$	5.97363	0.268224
$497$	5.41666	0.242970
$498$	13.6183	0.610253
$499$	29.1220	1.30368	0.651840	−	0.758356i	$-0.273997\pi$
$499$	29.1220	1.30368	0.651840	+	0.758356i	$0.273997\pi$
$500$	−0.470923	−0.0210603
$501$	−2.75325	−0.123006
$502$	−19.9311	−0.889569
$503$	−39.3717	−1.75550	−0.877748	−	0.479123i	$-0.840955\pi$
$503$	−39.3717	−1.75550	−0.877748	+	0.479123i	$0.840955\pi$
$504$	−1.04932	−0.0467404
$505$	−9.27220	−0.412608
$506$	6.62445	0.294493
$507$	−12.7976	−0.568363
$508$	15.9802	0.709006
$509$	−7.79577	−0.345542	−0.172771	−	0.984962i	$-0.555272\pi$
$509$	−7.79577	−0.345542	−0.172771	+	0.984962i	$0.555272\pi$
$510$	−19.4625	−0.861816
$511$	0.657438	0.0290834
$512$	1.00000	0.0441942
$513$	−4.42052	−0.195171
$514$	−10.1018	−0.445571
$515$	15.7829	0.695477
$516$	4.22149	0.185841
$517$	−4.93462	−0.217024
$518$	−3.88340	−0.170627
$519$	−19.2594	−0.845393
$520$	−16.9647	−0.743951
$521$	−7.38055	−0.323348	−0.161674	−	0.986844i	$-0.551689\pi$
$521$	−7.38055	−0.323348	−0.161674	+	0.986844i	$0.551689\pi$
$522$	−3.80949	−0.166737
$523$	21.5036	0.940285	0.470142	−	0.882591i	$-0.344203\pi$
$523$	21.5036	0.940285	0.470142	+	0.882591i	$0.344203\pi$
$524$	6.63129	0.289689
$525$	−1.95168	−0.0851784
$526$	−9.27824	−0.404550
$527$	−43.8062	−1.90823
$528$	1.14406	0.0497888
$529$	0.271927	0.0118229
$530$	−2.87631	−0.124939
$531$	1.32314	0.0574195
$532$	−0.455061	−0.0197294
$533$	−12.3828	−0.536357
$534$	6.44002	0.278687
$535$	−30.9392	−1.33762
$536$	7.39328	0.319341
$537$	7.37406	0.318214
$538$	−18.6878	−0.805688
$539$	9.32803	0.401787
$540$	−14.0819	−0.605986
$541$	21.0641	0.905615	0.452808	−	0.891608i	$-0.350422\pi$
$541$	21.0641	0.905615	0.452808	+	0.891608i	$0.350422\pi$
$542$	22.5817	0.969966
$543$	16.7766	0.719955
$544$	−7.33327	−0.314412
$545$	−5.30832	−0.227383
$546$	−2.01904	−0.0864069
$547$	3.74167	0.159982	0.0799911	−	0.996796i	$-0.474511\pi$
$547$	3.74167	0.159982	0.0799911	+	0.996796i	$0.474511\pi$
$548$	16.9545	0.724261
$549$	2.08676	0.0890607
$550$	−7.06900	−0.301423
$551$	−1.65207	−0.0703807
$552$	4.01912	0.171065
$553$	−0.498884	−0.0212147
$554$	−5.78007	−0.245572
$555$	−22.6488	−0.961386
$556$	4.46835	0.189500
$557$	−28.4889	−1.20712	−0.603558	−	0.797319i	$-0.706251\pi$
$557$	−28.4889	−1.20712	−0.603558	+	0.797319i	$0.706251\pi$
$558$	−13.7745	−0.583121
$559$	−26.9842	−1.14131
$560$	−1.44963	−0.0612580
$561$	−8.38971	−0.354214
$562$	−27.1568	−1.14554
$563$	−23.7436	−1.00067	−0.500337	−	0.865830i	$-0.666791\pi$
$563$	−23.7436	−1.00067	−0.500337	+	0.865830i	$0.666791\pi$
$564$	−2.99389	−0.126065
$565$	38.7315	1.62945
$566$	18.8095	0.790621
$567$	1.47202	0.0618190
$568$	11.9031	0.499444
$569$	−13.2276	−0.554530	−0.277265	−	0.960793i	$-0.589428\pi$
$569$	−13.2276	−0.554530	−0.277265	+	0.960793i	$0.589428\pi$
$570$	−2.65401	−0.111164
$571$	−2.60624	−0.109068	−0.0545338	−	0.998512i	$-0.517367\pi$
$571$	−2.60624	−0.109068	−0.0545338	+	0.998512i	$0.517367\pi$
$572$	−7.31296	−0.305770
$573$	0.747163	0.0312132
$574$	−1.05810	−0.0441644
$575$	−24.8336	−1.03563
$576$	−2.30589	−0.0960786
$577$	−23.7294	−0.987869	−0.493935	−	0.869499i	$-0.664442\pi$
$577$	−23.7294	−0.987869	−0.493935	+	0.869499i	$0.664442\pi$
$578$	36.7769	1.52972
$579$	−13.1147	−0.545028
$580$	−5.26279	−0.218525
$581$	−7.43839	−0.308596
$582$	−9.95993	−0.412852
$583$	−1.23989	−0.0513510
$584$	1.44472	0.0597831
$585$	39.1187	1.61736
$586$	33.1965	1.37133
$587$	15.7660	0.650731	0.325365	−	0.945588i	$-0.394513\pi$
$587$	15.7660	0.650731	0.325365	+	0.945588i	$0.394513\pi$
$588$	5.65942	0.233390
$589$	−5.97363	−0.246139
$590$	1.82791	0.0752539
$591$	−15.1470	−0.623066
$592$	−8.53380	−0.350737
$593$	−11.9745	−0.491734	−0.245867	−	0.969304i	$-0.579073\pi$
$593$	−11.9745	−0.491734	−0.245867	+	0.969304i	$0.579073\pi$
$594$	−6.07025	−0.249066
$595$	10.6305	0.435809
$596$	3.87568	0.158754
$597$	−18.0683	−0.739487
$598$	−25.6907	−1.05057
$599$	−44.9879	−1.83816	−0.919079	−	0.394074i	$-0.871065\pi$
$599$	−44.9879	−1.83816	−0.919079	+	0.394074i	$0.871065\pi$
$600$	−4.28884	−0.175091
$601$	−28.1297	−1.14743	−0.573717	−	0.819054i	$-0.694499\pi$
$601$	−28.1297	−1.14743	−0.573717	+	0.819054i	$0.694499\pi$
$602$	−2.30579	−0.0939772
$603$	−17.0481	−0.694250
$604$	7.69964	0.313294
$605$	29.0343	1.18041
$606$	−2.42500	−0.0985088
$607$	−38.4071	−1.55890	−0.779448	−	0.626466i	$-0.784501\pi$
$607$	−38.4071	−1.55890	−0.779448	+	0.626466i	$0.784501\pi$
$608$	−1.00000	−0.0405554
$609$	−0.626346	−0.0253808
$610$	2.88284	0.116723
$611$	19.1373	0.774211
$612$	16.9097	0.683534
$613$	−33.3788	−1.34816	−0.674078	−	0.738660i	$-0.735459\pi$
$613$	−33.3788	−1.34816	−0.674078	+	0.738660i	$0.735459\pi$
$614$	−2.16914	−0.0875393
$615$	−6.17107	−0.248841
$616$	−0.624890	−0.0251775
$617$	47.2890	1.90378	0.951892	−	0.306434i	$-0.0991358\pi$
$617$	47.2890	1.90378	0.951892	+	0.306434i	$0.0991358\pi$
$618$	4.12776	0.166043
$619$	21.1255	0.849104	0.424552	−	0.905404i	$-0.360432\pi$
$619$	21.1255	0.849104	0.424552	+	0.905404i	$0.360432\pi$
$620$	−19.0294	−0.764238
$621$	−21.3250	−0.855743
$622$	30.4081	1.21925
$623$	−3.51756	−0.140928
$624$	−4.43685	−0.177616
$625$	−24.2390	−0.969560
$626$	−33.7663	−1.34957
$627$	−1.14406	−0.0456894
$628$	2.51487	0.100354
$629$	62.5807	2.49526
$630$	3.34268	0.133175
$631$	20.5307	0.817313	0.408656	−	0.912688i	$-0.365997\pi$
$631$	20.5307	0.817313	0.408656	+	0.912688i	$0.365997\pi$
$632$	−1.09630	−0.0436085
$633$	0.833135	0.0331141
$634$	−28.5722	−1.13475
$635$	−50.9059	−2.02014
$636$	−0.752255	−0.0298289
$637$	−36.1756	−1.43333
$638$	−2.26863	−0.0898157
$639$	−27.4473	−1.08580
$640$	−3.18557	−0.125921
$641$	−30.8519	−1.21858	−0.609288	−	0.792949i	$-0.708545\pi$
$641$	−30.8519	−1.21858	−0.609288	+	0.792949i	$0.708545\pi$
$642$	−8.09167	−0.319353
$643$	−34.4269	−1.35766	−0.678832	−	0.734293i	$-0.737514\pi$
$643$	−34.4269	−1.35766	−0.678832	+	0.734293i	$0.737514\pi$
$644$	−2.19526	−0.0865054
$645$	−13.4478	−0.529508
$646$	7.33327	0.288524
$647$	−38.7395	−1.52301	−0.761504	−	0.648160i	$-0.775539\pi$
$647$	−38.7395	−1.52301	−0.761504	+	0.648160i	$0.775539\pi$
$648$	3.23477	0.127074
$649$	0.787957	0.0309300
$650$	27.4147	1.07529
$651$	−2.26477	−0.0887632
$652$	−17.0284	−0.666885
$653$	11.4101	0.446513	0.223257	−	0.974760i	$-0.428331\pi$
$653$	11.4101	0.446513	0.223257	+	0.974760i	$0.428331\pi$
$654$	−1.38831	−0.0542871
$655$	−21.1244	−0.825399
$656$	−2.32519	−0.0907834
$657$	−3.33137	−0.129969
$658$	1.63527	0.0637496
$659$	17.7793	0.692582	0.346291	−	0.938127i	$-0.387441\pi$
$659$	17.7793	0.692582	0.346291	+	0.938127i	$0.387441\pi$
$660$	−3.64448	−0.141861
$661$	2.10288	0.0817927	0.0408963	−	0.999163i	$-0.486979\pi$
$661$	2.10288	0.0817927	0.0408963	+	0.999163i	$0.486979\pi$
$662$	−4.88317	−0.189790
$663$	32.5366	1.26362
$664$	−16.3459	−0.634344
$665$	1.44963	0.0562142
$666$	19.6780	0.762506
$667$	−7.96976	−0.308590
$668$	3.30469	0.127862
$669$	−19.0250	−0.735549
$670$	−23.5518	−0.909884
$671$	1.24271	0.0479741
$672$	−0.379127	−0.0146252
$673$	−11.5112	−0.443725	−0.221862	−	0.975078i	$-0.571214\pi$
$673$	−11.5112	−0.443725	−0.221862	+	0.975078i	$0.571214\pi$
$674$	36.3051	1.39842
$675$	22.7561	0.875882
$676$	15.3608	0.590801
$677$	−7.77062	−0.298649	−0.149325	−	0.988788i	$-0.547710\pi$
$677$	−7.77062	−0.298649	−0.149325	+	0.988788i	$0.547710\pi$
$678$	10.1296	0.389026
$679$	5.44015	0.208774
$680$	23.3606	0.895839
$681$	−11.9907	−0.459484
$682$	−8.20298	−0.314108
$683$	−5.31652	−0.203431	−0.101716	−	0.994814i	$-0.532433\pi$
$683$	−5.31652	−0.203431	−0.101716	+	0.994814i	$0.532433\pi$
$684$	2.30589	0.0881678
$685$	−54.0097	−2.06361
$686$	−6.27662	−0.239643
$687$	2.55025	0.0972982
$688$	−5.06700	−0.193177
$689$	4.80850	0.183189
$690$	−12.8032	−0.487409
$691$	12.6891	0.482717	0.241359	−	0.970436i	$-0.422407\pi$
$691$	12.6891	0.482717	0.241359	+	0.970436i	$0.422407\pi$
$692$	23.1168	0.878767
$693$	1.44093	0.0547362
$694$	−9.37740	−0.355961
$695$	−14.2342	−0.539935
$696$	−1.37640	−0.0521723
$697$	17.0512	0.645862
$698$	19.9950	0.756820
$699$	−7.28797	−0.275656
$700$	2.34258	0.0885411
$701$	−39.1862	−1.48004	−0.740021	−	0.672583i	$-0.765185\pi$
$701$	−39.1862	−1.48004	−0.740021	+	0.672583i	$0.765185\pi$
$702$	23.5414	0.888514
$703$	8.53380	0.321858
$704$	−1.37320	−0.0517544
$705$	9.53723	0.359193
$706$	−19.6389	−0.739120
$707$	1.32454	0.0498146
$708$	0.478062	0.0179667
$709$	8.99691	0.337886	0.168943	−	0.985626i	$-0.445965\pi$
$709$	8.99691	0.337886	0.168943	+	0.985626i	$0.445965\pi$
$710$	−37.9182	−1.42305
$711$	2.52795	0.0948054
$712$	−7.72987	−0.289689
$713$	−28.8174	−1.07922
$714$	2.78024	0.104048
$715$	23.2959	0.871218
$716$	−8.85098	−0.330777
$717$	−14.0607	−0.525108
$718$	−12.3866	−0.462264
$719$	8.60958	0.321083	0.160541	−	0.987029i	$-0.448676\pi$
$719$	8.60958	0.321083	0.160541	+	0.987029i	$0.448676\pi$
$720$	7.34555	0.273753
$721$	−2.25460	−0.0839657
$722$	1.00000	0.0372161
$723$	−6.98557	−0.259796
$724$	−20.1368	−0.748377
$725$	8.50459	0.315853
$726$	7.59346	0.281820
$727$	12.0735	0.447783	0.223891	−	0.974614i	$-0.428124\pi$
$727$	12.0735	0.447783	0.223891	+	0.974614i	$0.428124\pi$
$728$	2.42342	0.0898181
$729$	3.58965	0.132950
$730$	−4.60227	−0.170337
$731$	37.1577	1.37433
$732$	0.753963	0.0278673
$733$	7.15842	0.264402	0.132201	−	0.991223i	$-0.457796\pi$
$733$	7.15842	0.264402	0.132201	+	0.991223i	$0.457796\pi$
$734$	14.2061	0.524356
$735$	−18.0284	−0.664989
$736$	−4.82410	−0.177819
$737$	−10.1524	−0.373970
$738$	5.36162	0.197364
$739$	34.5839	1.27219	0.636095	−	0.771611i	$-0.280549\pi$
$739$	34.5839	1.27219	0.636095	+	0.771611i	$0.280549\pi$
$740$	27.1850	0.999340
$741$	4.43685	0.162992
$742$	0.410884	0.0150840
$743$	20.8265	0.764049	0.382024	−	0.924152i	$-0.375227\pi$
$743$	20.8265	0.764049	0.382024	+	0.924152i	$0.375227\pi$
$744$	−4.97684	−0.182460
$745$	−12.3462	−0.452331
$746$	30.1257	1.10298
$747$	37.6918	1.37907
$748$	10.0700	0.368197
$749$	4.41970	0.161492
$750$	0.392342	0.0143263
$751$	−19.9945	−0.729608	−0.364804	−	0.931084i	$-0.618864\pi$
$751$	−19.9945	−0.729608	−0.364804	+	0.931084i	$0.618864\pi$
$752$	3.59352	0.131042
$753$	16.6053	0.605131
$754$	8.79809	0.320408
$755$	−24.5277	−0.892654
$756$	2.01161	0.0731614
$757$	11.5252	0.418889	0.209445	−	0.977821i	$-0.432834\pi$
$757$	11.5252	0.418889	0.209445	+	0.977821i	$0.432834\pi$
$758$	0.617767	0.0224383
$759$	−5.51906	−0.200329
$760$	3.18557	0.115553
$761$	−21.0011	−0.761289	−0.380644	−	0.924722i	$-0.624298\pi$
$761$	−21.0011	−0.761289	−0.380644	+	0.924722i	$0.624298\pi$
$762$	−13.3136	−0.482302
$763$	0.758299	0.0274523
$764$	−0.896810	−0.0324454
$765$	−53.8669	−1.94756
$766$	12.4877	0.451200
$767$	−3.05582	−0.110339
$768$	−0.833135	−0.0300632
$769$	0.0863922	0.00311538	0.00155769	−	0.999999i	$-0.499504\pi$
$769$	0.0863922	0.00311538	0.00155769	+	0.999999i	$0.499504\pi$
$770$	1.99063	0.0717373
$771$	8.41616	0.303100
$772$	15.7414	0.566544
$773$	24.6308	0.885910	0.442955	−	0.896544i	$-0.353930\pi$
$773$	24.6308	0.885910	0.442955	+	0.896544i	$0.353930\pi$
$774$	11.6839	0.419970
$775$	30.7512	1.10462
$776$	11.9548	0.429151
$777$	3.23540	0.116069
$778$	22.5256	0.807582
$779$	2.32519	0.0833085
$780$	14.1339	0.506074
$781$	−16.3454	−0.584884
$782$	35.3764	1.26506
$783$	7.30302	0.260989
$784$	−6.79292	−0.242604
$785$	−8.01129	−0.285935
$786$	−5.52476	−0.197062
$787$	20.9715	0.747553	0.373777	−	0.927519i	$-0.378063\pi$
$787$	20.9715	0.747553	0.373777	+	0.927519i	$0.378063\pi$
$788$	18.1808	0.647664
$789$	7.73002	0.275196
$790$	3.49234	0.124252
$791$	−5.53284	−0.196725
$792$	3.16644	0.112515
$793$	−4.81941	−0.171142
$794$	2.21743	0.0786938
$795$	2.39636	0.0849901
$796$	21.6872	0.768681
$797$	24.2083	0.857503	0.428751	−	0.903423i	$-0.358954\pi$
$797$	24.2083	0.857503	0.428751	+	0.903423i	$0.358954\pi$
$798$	0.379127	0.0134210
$799$	−26.3523	−0.932277
$800$	5.14783	0.182003
$801$	17.8242	0.629787
$802$	−21.1119	−0.745486
$803$	−1.98390	−0.0700101
$804$	−6.15960	−0.217232
$805$	6.99315	0.246476
$806$	31.8125	1.12055
$807$	15.5695	0.548071
$808$	2.91069	0.102398
$809$	9.72882	0.342047	0.171023	−	0.985267i	$-0.445293\pi$
$809$	9.72882	0.342047	0.171023	+	0.985267i	$0.445293\pi$
$810$	−10.3046	−0.362066
$811$	−48.0361	−1.68677	−0.843387	−	0.537306i	$-0.819442\pi$
$811$	−48.0361	−1.68677	−0.843387	+	0.537306i	$0.819442\pi$
$812$	0.751794	0.0263828
$813$	−18.8136	−0.659821
$814$	11.7186	0.410737
$815$	54.2452	1.90013
$816$	6.10961	0.213879
$817$	5.06700	0.177272
$818$	−27.5064	−0.961738
$819$	−5.58814	−0.195265
$820$	7.40704	0.258665
$821$	28.2737	0.986759	0.493379	−	0.869814i	$-0.335761\pi$
$821$	28.2737	0.986759	0.493379	+	0.869814i	$0.335761\pi$
$822$	−14.1254	−0.492680
$823$	8.82928	0.307770	0.153885	−	0.988089i	$-0.450822\pi$
$823$	8.82928	0.307770	0.153885	+	0.988089i	$0.450822\pi$
$824$	−4.95450	−0.172598
$825$	5.88943	0.205044
$826$	−0.261119	−0.00908549
$827$	−21.3964	−0.744024	−0.372012	−	0.928228i	$-0.621332\pi$
$827$	−21.3964	−0.744024	−0.372012	+	0.928228i	$0.621332\pi$
$828$	11.1238	0.386580
$829$	39.6866	1.37837	0.689186	−	0.724585i	$-0.257968\pi$
$829$	39.6866	1.37837	0.689186	+	0.724585i	$0.257968\pi$
$830$	52.0710	1.80741
$831$	4.81557	0.167050
$832$	5.32549	0.184628
$833$	49.8143	1.72596
$834$	−3.72274	−0.128908
$835$	−10.5273	−0.364312
$836$	1.37320	0.0474931
$837$	26.4065	0.912743
$838$	−8.97773	−0.310131
$839$	−25.0347	−0.864295	−0.432148	−	0.901803i	$-0.642244\pi$
$839$	−25.0347	−0.864295	−0.432148	+	0.901803i	$0.642244\pi$
$840$	1.20774	0.0416708
$841$	−26.2707	−0.905885
$842$	29.8005	1.02699
$843$	22.6253	0.779257
$844$	−1.00000	−0.0344214
$845$	−48.9329	−1.68334
$846$	−8.28625	−0.284887
$847$	−4.14758	−0.142512
$848$	0.902921	0.0310064
$849$	−15.6708	−0.537821
$850$	−37.7504	−1.29483
$851$	41.1679	1.41122
$852$	−9.91692	−0.339748
$853$	−26.5940	−0.910562	−0.455281	−	0.890348i	$-0.650461\pi$
$853$	−26.5940	−0.910562	−0.455281	+	0.890348i	$0.650461\pi$
$854$	−0.411817	−0.0140921
$855$	−7.34555	−0.251213
$856$	9.71232	0.331960
$857$	11.6047	0.396410	0.198205	−	0.980161i	$-0.436489\pi$
$857$	11.6047	0.396410	0.198205	+	0.980161i	$0.436489\pi$
$858$	6.09268	0.208001
$859$	18.1323	0.618666	0.309333	−	0.950954i	$-0.399894\pi$
$859$	18.1323	0.618666	0.309333	+	0.950954i	$0.399894\pi$
$860$	16.1413	0.550412
$861$	0.881543	0.0300429
$862$	27.8167	0.947440
$863$	−28.6228	−0.974332	−0.487166	−	0.873309i	$-0.661969\pi$
$863$	−28.6228	−0.974332	−0.487166	+	0.873309i	$0.661969\pi$
$864$	4.42052	0.150389
$865$	−73.6400	−2.50383
$866$	1.22663	0.0416827
$867$	−30.6401	−1.04059
$868$	2.71837	0.0922674
$869$	1.50544	0.0510686
$870$	4.38461	0.148652
$871$	39.3728	1.33410
$872$	1.66637	0.0564303
$873$	−27.5663	−0.932979
$874$	4.82410	0.163178
$875$	−0.214299	−0.00724462
$876$	−1.20365	−0.0406676
$877$	27.2418	0.919891	0.459945	−	0.887947i	$-0.347869\pi$
$877$	27.2418	0.919891	0.459945	+	0.887947i	$0.347869\pi$
$878$	35.1401	1.18592
$879$	−27.6572	−0.932853
$880$	4.37442	0.147462
$881$	6.22330	0.209668	0.104834	−	0.994490i	$-0.466569\pi$
$881$	6.22330	0.209668	0.104834	+	0.994490i	$0.466569\pi$
$882$	15.6637	0.527424
$883$	−29.6032	−0.996227	−0.498114	−	0.867112i	$-0.665974\pi$
$883$	−29.6032	−0.996227	−0.498114	+	0.867112i	$0.665974\pi$
$884$	−39.0533	−1.31350
$885$	−1.52290	−0.0511916
$886$	−0.756700	−0.0254218
$887$	−42.9830	−1.44323	−0.721614	−	0.692296i	$-0.756599\pi$
$887$	−42.9830	−1.44323	−0.721614	+	0.692296i	$0.756599\pi$
$888$	7.10981	0.238590
$889$	7.27196	0.243894
$890$	24.6240	0.825398
$891$	−4.44199	−0.148812
$892$	22.8355	0.764588
$893$	−3.59352	−0.120253
$894$	−3.22896	−0.107993
$895$	28.1954	0.942467
$896$	0.455061	0.0152025
$897$	21.4038	0.714652
$898$	13.1481	0.438758
$899$	9.86887	0.329145
$900$	−11.8703	−0.395677
$901$	−6.62137	−0.220590
$902$	3.19295	0.106314
$903$	1.92104	0.0639281
$904$	−12.1584	−0.404384
$905$	64.1470	2.13232
$906$	−6.41483	−0.213119
$907$	17.1721	0.570189	0.285095	−	0.958499i	$-0.407975\pi$
$907$	17.1721	0.570189	0.285095	+	0.958499i	$0.407975\pi$
$908$	14.3922	0.477623
$909$	−6.71173	−0.222614
$910$	−7.71998	−0.255915
$911$	−32.8096	−1.08703	−0.543515	−	0.839399i	$-0.682907\pi$
$911$	−32.8096	−1.08703	−0.543515	+	0.839399i	$0.682907\pi$
$912$	0.833135	0.0275878
$913$	22.4462	0.742860
$914$	30.8512	1.02047
$915$	−2.40180	−0.0794010
$916$	−3.06103	−0.101139
$917$	3.01764	0.0996513
$918$	−32.4169	−1.06992
$919$	41.4579	1.36757	0.683785	−	0.729683i	$-0.260333\pi$
$919$	41.4579	1.36757	0.683785	+	0.729683i	$0.260333\pi$
$920$	15.3675	0.506651
$921$	1.80718	0.0595487
$922$	11.9807	0.394563
$923$	63.3900	2.08651
$924$	0.520618	0.0171271
$925$	−43.9306	−1.44443
$926$	24.1856	0.794788
$927$	11.4245	0.375230
$928$	1.65207	0.0542319
$929$	−36.4127	−1.19466	−0.597331	−	0.801995i	$-0.703772\pi$
$929$	−36.4127	−1.19466	−0.597331	+	0.801995i	$0.703772\pi$
$930$	15.8540	0.519874
$931$	6.79292	0.222629
$932$	8.74764	0.286539
$933$	−25.3340	−0.829399
$934$	−10.4573	−0.342172
$935$	−32.0788	−1.04909
$936$	−12.2800	−0.401383
$937$	−40.8069	−1.33310	−0.666552	−	0.745458i	$-0.732231\pi$
$937$	−40.8069	−1.33310	−0.666552	+	0.745458i	$0.732231\pi$
$938$	3.36439	0.109851
$939$	28.1319	0.918050
$940$	−11.4474	−0.373373
$941$	−2.98675	−0.0973654	−0.0486827	−	0.998814i	$-0.515502\pi$
$941$	−2.98675	−0.0973654	−0.0486827	+	0.998814i	$0.515502\pi$
$942$	−2.09523	−0.0682662
$943$	11.2169	0.365274
$944$	−0.573811	−0.0186759
$945$	−6.40811	−0.208456
$946$	6.95800	0.226224
$947$	2.22578	0.0723280	0.0361640	−	0.999346i	$-0.488486\pi$
$947$	2.22578	0.0723280	0.0361640	+	0.999346i	$0.488486\pi$
$948$	0.913367	0.0296648
$949$	7.69386	0.249753
$950$	−5.14783	−0.167018
$951$	23.8045	0.771913
$952$	−3.33709	−0.108156
$953$	−17.9022	−0.579910	−0.289955	−	0.957040i	$-0.593640\pi$
$953$	−17.9022	−0.579910	−0.289955	+	0.957040i	$0.593640\pi$
$954$	−2.08203	−0.0674083
$955$	2.85685	0.0924454
$956$	16.8769	0.545838
$957$	1.89007	0.0610973
$958$	0.600314	0.0193953
$959$	7.71535	0.249142
$960$	2.65401	0.0856577
$961$	4.68422	0.151104
$962$	−45.4467	−1.46526
$963$	−22.3955	−0.721685
$964$	8.38468	0.270052
$965$	−50.1452	−1.61423
$966$	1.82895	0.0588454
$967$	−52.3832	−1.68453	−0.842265	−	0.539064i	$-0.818778\pi$
$967$	−52.3832	−1.68453	−0.842265	+	0.539064i	$0.818778\pi$
$968$	−9.11432	−0.292945
$969$	−6.10961	−0.196269
$970$	−38.0827	−1.22276
$971$	−31.0804	−0.997418	−0.498709	−	0.866770i	$-0.666192\pi$
$971$	−31.0804	−0.997418	−0.498709	+	0.866770i	$0.666192\pi$
$972$	−15.9566	−0.511807
$973$	2.03337	0.0651869
$974$	−10.6381	−0.340868
$975$	−22.8401	−0.731470
$976$	−0.904971	−0.0289674
$977$	−23.4741	−0.751003	−0.375501	−	0.926822i	$-0.622529\pi$
$977$	−23.4741	−0.751003	−0.375501	+	0.926822i	$0.622529\pi$
$978$	14.1870	0.453650
$979$	10.6146	0.339246
$980$	21.6393	0.691242
$981$	−3.84245	−0.122680
$982$	26.5876	0.848444
$983$	18.3699	0.585910	0.292955	−	0.956126i	$-0.405361\pi$
$983$	18.3699	0.585910	0.292955	+	0.956126i	$0.405361\pi$
$984$	1.93720	0.0617555
$985$	−57.9161	−1.84536
$986$	−12.1151	−0.385823
$987$	−1.36240	−0.0433658
$988$	−5.32549	−0.169426
$989$	24.4437	0.777264
$990$	−10.0869	−0.320583
$991$	−21.6237	−0.686900	−0.343450	−	0.939171i	$-0.611596\pi$
$991$	−21.6237	−0.686900	−0.343450	+	0.939171i	$0.611596\pi$
$992$	5.97363	0.189663
$993$	4.06833	0.129105
$994$	5.41666	0.171806
$995$	−69.0858	−2.19017
$996$	13.6183	0.431514
$997$	55.0599	1.74376	0.871882	−	0.489716i	$-0.162899\pi$
$997$	55.0599	1.74376	0.871882	+	0.489716i	$0.162899\pi$
$998$	29.1220	0.921841
$999$	−37.7238	−1.19353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.18	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.833135 q^{3} +1.00000 q^{4} -3.18557 q^{5} -0.833135 q^{6} +0.455061 q^{7} +1.00000 q^{8} -2.30589 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.833135 q^{3} +1.00000 q^{4} -3.18557 q^{5} -0.833135 q^{6} +0.455061 q^{7} +1.00000 q^{8} -2.30589 q^{9} -3.18557 q^{10} -1.37320 q^{11} -0.833135 q^{12} +5.32549 q^{13} +0.455061 q^{14} +2.65401 q^{15} +1.00000 q^{16} -7.33327 q^{17} -2.30589 q^{18} -1.00000 q^{19} -3.18557 q^{20} -0.379127 q^{21} -1.37320 q^{22} -4.82410 q^{23} -0.833135 q^{24} +5.14783 q^{25} +5.32549 q^{26} +4.42052 q^{27} +0.455061 q^{28} +1.65207 q^{29} +2.65401 q^{30} +5.97363 q^{31} +1.00000 q^{32} +1.14406 q^{33} -7.33327 q^{34} -1.44963 q^{35} -2.30589 q^{36} -8.53380 q^{37} -1.00000 q^{38} -4.43685 q^{39} -3.18557 q^{40} -2.32519 q^{41} -0.379127 q^{42} -5.06700 q^{43} -1.37320 q^{44} +7.34555 q^{45} -4.82410 q^{46} +3.59352 q^{47} -0.833135 q^{48} -6.79292 q^{49} +5.14783 q^{50} +6.10961 q^{51} +5.32549 q^{52} +0.902921 q^{53} +4.42052 q^{54} +4.37442 q^{55} +0.455061 q^{56} +0.833135 q^{57} +1.65207 q^{58} -0.573811 q^{59} +2.65401 q^{60} -0.904971 q^{61} +5.97363 q^{62} -1.04932 q^{63} +1.00000 q^{64} -16.9647 q^{65} +1.14406 q^{66} +7.39328 q^{67} -7.33327 q^{68} +4.01912 q^{69} -1.44963 q^{70} +11.9031 q^{71} -2.30589 q^{72} +1.44472 q^{73} -8.53380 q^{74} -4.28884 q^{75} -1.00000 q^{76} -0.624890 q^{77} -4.43685 q^{78} -1.09630 q^{79} -3.18557 q^{80} +3.23477 q^{81} -2.32519 q^{82} -16.3459 q^{83} -0.379127 q^{84} +23.3606 q^{85} -5.06700 q^{86} -1.37640 q^{87} -1.37320 q^{88} -7.72987 q^{89} +7.34555 q^{90} +2.42342 q^{91} -4.82410 q^{92} -4.97684 q^{93} +3.59352 q^{94} +3.18557 q^{95} -0.833135 q^{96} +11.9548 q^{97} -6.79292 q^{98} +3.16644 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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