LMFDB - Embedded newform 6038.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.79976 q^{3} +1.00000 q^{4} -2.91282 q^{5} -2.79976 q^{6} -0.947335 q^{7} +1.00000 q^{8} +4.83868 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.79976 q^{3} +1.00000 q^{4} -2.91282 q^{5} -2.79976 q^{6} -0.947335 q^{7} +1.00000 q^{8} +4.83868 q^{9} -2.91282 q^{10} +0.813334 q^{11} -2.79976 q^{12} +4.37274 q^{13} -0.947335 q^{14} +8.15521 q^{15} +1.00000 q^{16} -3.08451 q^{17} +4.83868 q^{18} +1.10604 q^{19} -2.91282 q^{20} +2.65232 q^{21} +0.813334 q^{22} -0.454313 q^{23} -2.79976 q^{24} +3.48453 q^{25} +4.37274 q^{26} -5.14786 q^{27} -0.947335 q^{28} -5.84889 q^{29} +8.15521 q^{30} +7.93897 q^{31} +1.00000 q^{32} -2.27714 q^{33} -3.08451 q^{34} +2.75942 q^{35} +4.83868 q^{36} +4.37451 q^{37} +1.10604 q^{38} -12.2426 q^{39} -2.91282 q^{40} -8.69577 q^{41} +2.65232 q^{42} -11.1663 q^{43} +0.813334 q^{44} -14.0942 q^{45} -0.454313 q^{46} -3.48913 q^{47} -2.79976 q^{48} -6.10256 q^{49} +3.48453 q^{50} +8.63590 q^{51} +4.37274 q^{52} -4.18987 q^{53} -5.14786 q^{54} -2.36910 q^{55} -0.947335 q^{56} -3.09665 q^{57} -5.84889 q^{58} -3.20587 q^{59} +8.15521 q^{60} +15.3151 q^{61} +7.93897 q^{62} -4.58385 q^{63} +1.00000 q^{64} -12.7370 q^{65} -2.27714 q^{66} -1.14745 q^{67} -3.08451 q^{68} +1.27197 q^{69} +2.75942 q^{70} +1.65385 q^{71} +4.83868 q^{72} +6.65252 q^{73} +4.37451 q^{74} -9.75585 q^{75} +1.10604 q^{76} -0.770500 q^{77} -12.2426 q^{78} -13.0537 q^{79} -2.91282 q^{80} -0.103238 q^{81} -8.69577 q^{82} +2.55888 q^{83} +2.65232 q^{84} +8.98463 q^{85} -11.1663 q^{86} +16.3755 q^{87} +0.813334 q^{88} +7.88994 q^{89} -14.0942 q^{90} -4.14245 q^{91} -0.454313 q^{92} -22.2272 q^{93} -3.48913 q^{94} -3.22170 q^{95} -2.79976 q^{96} +8.29553 q^{97} -6.10256 q^{98} +3.93546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.79976	−1.61644	−0.808222	−	0.588878i	$-0.799570\pi$
$3$	−2.79976	−1.61644	−0.808222	+	0.588878i	$0.799570\pi$
$4$	1.00000	0.500000
$5$	−2.91282	−1.30265	−0.651327	−	0.758797i	$-0.725787\pi$
$5$	−2.91282	−1.30265	−0.651327	+	0.758797i	$0.725787\pi$
$6$	−2.79976	−1.14300
$7$	−0.947335	−0.358059	−0.179030	−	0.983844i	$-0.557296\pi$
$7$	−0.947335	−0.358059	−0.179030	+	0.983844i	$0.557296\pi$
$8$	1.00000	0.353553
$9$	4.83868	1.61289
$10$	−2.91282	−0.921115
$11$	0.813334	0.245229	0.122615	−	0.992454i	$-0.460872\pi$
$11$	0.813334	0.245229	0.122615	+	0.992454i	$0.460872\pi$
$12$	−2.79976	−0.808222
$13$	4.37274	1.21278	0.606389	−	0.795168i	$-0.292617\pi$
$13$	4.37274	1.21278	0.606389	+	0.795168i	$0.292617\pi$
$14$	−0.947335	−0.253186
$15$	8.15521	2.10567
$16$	1.00000	0.250000
$17$	−3.08451	−0.748104	−0.374052	−	0.927408i	$-0.622032\pi$
$17$	−3.08451	−0.748104	−0.374052	+	0.927408i	$0.622032\pi$
$18$	4.83868	1.14049
$19$	1.10604	0.253743	0.126872	−	0.991919i	$-0.459506\pi$
$19$	1.10604	0.253743	0.126872	+	0.991919i	$0.459506\pi$
$20$	−2.91282	−0.651327
$21$	2.65232	0.578783
$22$	0.813334	0.173403
$23$	−0.454313	−0.0947308	−0.0473654	−	0.998878i	$-0.515083\pi$
$23$	−0.454313	−0.0947308	−0.0473654	+	0.998878i	$0.515083\pi$
$24$	−2.79976	−0.571499
$25$	3.48453	0.696905
$26$	4.37274	0.857564
$27$	−5.14786	−0.990706
$28$	−0.947335	−0.179030
$29$	−5.84889	−1.08611	−0.543055	−	0.839697i	$-0.682733\pi$
$29$	−5.84889	−1.08611	−0.543055	+	0.839697i	$0.682733\pi$
$30$	8.15521	1.48893
$31$	7.93897	1.42588	0.712941	−	0.701224i	$-0.247363\pi$
$31$	7.93897	1.42588	0.712941	+	0.701224i	$0.247363\pi$
$32$	1.00000	0.176777
$33$	−2.27714	−0.396400
$34$	−3.08451	−0.528989
$35$	2.75942	0.466427
$36$	4.83868	0.806446
$37$	4.37451	0.719166	0.359583	−	0.933113i	$-0.382919\pi$
$37$	4.37451	0.719166	0.359583	+	0.933113i	$0.382919\pi$
$38$	1.10604	0.179424
$39$	−12.2426	−1.96039
$40$	−2.91282	−0.460557
$41$	−8.69577	−1.35805	−0.679025	−	0.734115i	$-0.737597\pi$
$41$	−8.69577	−1.35805	−0.679025	+	0.734115i	$0.737597\pi$
$42$	2.65232	0.409261
$43$	−11.1663	−1.70284	−0.851421	−	0.524483i	$-0.824259\pi$
$43$	−11.1663	−1.70284	−0.851421	+	0.524483i	$0.824259\pi$
$44$	0.813334	0.122615
$45$	−14.0942	−2.10104
$46$	−0.454313	−0.0669848
$47$	−3.48913	−0.508942	−0.254471	−	0.967080i	$-0.581901\pi$
$47$	−3.48913	−0.508942	−0.254471	+	0.967080i	$0.581901\pi$
$48$	−2.79976	−0.404111
$49$	−6.10256	−0.871794
$50$	3.48453	0.492787
$51$	8.63590	1.20927
$52$	4.37274	0.606389
$53$	−4.18987	−0.575523	−0.287761	−	0.957702i	$-0.592911\pi$
$53$	−4.18987	−0.575523	−0.287761	+	0.957702i	$0.592911\pi$
$54$	−5.14786	−0.700535
$55$	−2.36910	−0.319449
$56$	−0.947335	−0.126593
$57$	−3.09665	−0.410162
$58$	−5.84889	−0.767996
$59$	−3.20587	−0.417368	−0.208684	−	0.977983i	$-0.566918\pi$
$59$	−3.20587	−0.417368	−0.208684	+	0.977983i	$0.566918\pi$
$60$	8.15521	1.05283
$61$	15.3151	1.96089	0.980447	−	0.196785i	$-0.0630502\pi$
$61$	15.3151	1.96089	0.980447	+	0.196785i	$0.0630502\pi$
$62$	7.93897	1.00825
$63$	−4.58385	−0.577511
$64$	1.00000	0.125000
$65$	−12.7370	−1.57983
$66$	−2.27714	−0.280297
$67$	−1.14745	−0.140183	−0.0700916	−	0.997541i	$-0.522329\pi$
$67$	−1.14745	−0.140183	−0.0700916	+	0.997541i	$0.522329\pi$
$68$	−3.08451	−0.374052
$69$	1.27197	0.153127
$70$	2.75942	0.329814
$71$	1.65385	0.196276	0.0981379	−	0.995173i	$-0.468711\pi$
$71$	1.65385	0.196276	0.0981379	+	0.995173i	$0.468711\pi$
$72$	4.83868	0.570244
$73$	6.65252	0.778618	0.389309	−	0.921107i	$-0.372714\pi$
$73$	6.65252	0.778618	0.389309	+	0.921107i	$0.372714\pi$
$74$	4.37451	0.508527
$75$	−9.75585	−1.12651
$76$	1.10604	0.126872
$77$	−0.770500	−0.0878066
$78$	−12.2426	−1.38620
$79$	−13.0537	−1.46865	−0.734326	−	0.678797i	$-0.762502\pi$
$79$	−13.0537	−1.46865	−0.734326	+	0.678797i	$0.762502\pi$
$80$	−2.91282	−0.325663
$81$	−0.103238	−0.0114709
$82$	−8.69577	−0.960287
$83$	2.55888	0.280873	0.140437	−	0.990090i	$-0.455149\pi$
$83$	2.55888	0.280873	0.140437	+	0.990090i	$0.455149\pi$
$84$	2.65232	0.289391
$85$	8.98463	0.974520
$86$	−11.1663	−1.20409
$87$	16.3755	1.75564
$88$	0.813334	0.0867016
$89$	7.88994	0.836332	0.418166	−	0.908371i	$-0.362673\pi$
$89$	7.88994	0.836332	0.418166	+	0.908371i	$0.362673\pi$
$90$	−14.0942	−1.48566
$91$	−4.14245	−0.434247
$92$	−0.454313	−0.0473654
$93$	−22.2272	−2.30486
$94$	−3.48913	−0.359877
$95$	−3.22170	−0.330539
$96$	−2.79976	−0.285750
$97$	8.29553	0.842283	0.421142	−	0.906995i	$-0.361630\pi$
$97$	8.29553	0.842283	0.421142	+	0.906995i	$0.361630\pi$
$98$	−6.10256	−0.616451
$99$	3.93546	0.395528
$100$	3.48453	0.348453
$101$	−15.7774	−1.56991	−0.784953	−	0.619555i	$-0.787313\pi$
$101$	−15.7774	−1.56991	−0.784953	+	0.619555i	$0.787313\pi$
$102$	8.63590	0.855082
$103$	−2.71280	−0.267300	−0.133650	−	0.991029i	$-0.542670\pi$
$103$	−2.71280	−0.267300	−0.133650	+	0.991029i	$0.542670\pi$
$104$	4.37274	0.428782
$105$	−7.72572	−0.753953
$106$	−4.18987	−0.406956
$107$	4.85668	0.469513	0.234756	−	0.972054i	$-0.424571\pi$
$107$	4.85668	0.469513	0.234756	+	0.972054i	$0.424571\pi$
$108$	−5.14786	−0.495353
$109$	−0.0943351	−0.00903566	−0.00451783	−	0.999990i	$-0.501438\pi$
$109$	−0.0943351	−0.00903566	−0.00451783	+	0.999990i	$0.501438\pi$
$110$	−2.36910	−0.225884
$111$	−12.2476	−1.16249
$112$	−0.947335	−0.0895148
$113$	4.56013	0.428981	0.214491	−	0.976726i	$-0.431191\pi$
$113$	4.56013	0.428981	0.214491	+	0.976726i	$0.431191\pi$
$114$	−3.09665	−0.290028
$115$	1.32333	0.123401
$116$	−5.84889	−0.543055
$117$	21.1583	1.95608
$118$	−3.20587	−0.295124
$119$	2.92207	0.267865
$120$	8.15521	0.744465
$121$	−10.3385	−0.939863
$122$	15.3151	1.38656
$123$	24.3461	2.19521
$124$	7.93897	0.712941
$125$	4.41430	0.394827
$126$	−4.58385	−0.408362
$127$	19.9789	1.77284	0.886420	−	0.462882i	$-0.153185\pi$
$127$	19.9789	1.77284	0.886420	+	0.462882i	$0.153185\pi$
$128$	1.00000	0.0883883
$129$	31.2629	2.75255
$130$	−12.7370	−1.11711
$131$	−3.10228	−0.271047	−0.135524	−	0.990774i	$-0.543272\pi$
$131$	−3.10228	−0.271047	−0.135524	+	0.990774i	$0.543272\pi$
$132$	−2.27714	−0.198200
$133$	−1.04779	−0.0908551
$134$	−1.14745	−0.0991245
$135$	14.9948	1.29055
$136$	−3.08451	−0.264495
$137$	7.21421	0.616352	0.308176	−	0.951329i	$-0.400281\pi$
$137$	7.21421	0.616352	0.308176	+	0.951329i	$0.400281\pi$
$138$	1.27197	0.108277
$139$	9.55097	0.810102	0.405051	−	0.914294i	$-0.367254\pi$
$139$	9.55097	0.810102	0.405051	+	0.914294i	$0.367254\pi$
$140$	2.75942	0.233213
$141$	9.76875	0.822677
$142$	1.65385	0.138788
$143$	3.55649	0.297409
$144$	4.83868	0.403223
$145$	17.0368	1.41483
$146$	6.65252	0.550566
$147$	17.0857	1.40921
$148$	4.37451	0.359583
$149$	−16.2312	−1.32971	−0.664857	−	0.746971i	$-0.731507\pi$
$149$	−16.2312	−1.32971	−0.664857	+	0.746971i	$0.731507\pi$
$150$	−9.75585	−0.796562
$151$	7.96931	0.648533	0.324267	−	0.945966i	$-0.394882\pi$
$151$	7.96931	0.648533	0.324267	+	0.945966i	$0.394882\pi$
$152$	1.10604	0.0897118
$153$	−14.9250	−1.20661
$154$	−0.770500	−0.0620886
$155$	−23.1248	−1.85743
$156$	−12.2426	−0.980195
$157$	−1.05869	−0.0844927	−0.0422464	−	0.999107i	$-0.513451\pi$
$157$	−1.05869	−0.0844927	−0.0422464	+	0.999107i	$0.513451\pi$
$158$	−13.0537	−1.03849
$159$	11.7306	0.930300
$160$	−2.91282	−0.230279
$161$	0.430387	0.0339192
$162$	−0.103238	−0.00811113
$163$	4.19651	0.328696	0.164348	−	0.986402i	$-0.447448\pi$
$163$	4.19651	0.328696	0.164348	+	0.986402i	$0.447448\pi$
$164$	−8.69577	−0.679025
$165$	6.63291	0.516371
$166$	2.55888	0.198607
$167$	10.9872	0.850214	0.425107	−	0.905143i	$-0.360237\pi$
$167$	10.9872	0.850214	0.425107	+	0.905143i	$0.360237\pi$
$168$	2.65232	0.204631
$169$	6.12082	0.470832
$170$	8.98463	0.689090
$171$	5.35178	0.409260
$172$	−11.1663	−0.851421
$173$	9.45729	0.719025	0.359512	−	0.933140i	$-0.382943\pi$
$173$	9.45729	0.719025	0.359512	+	0.933140i	$0.382943\pi$
$174$	16.3755	1.24142
$175$	−3.30102	−0.249533
$176$	0.813334	0.0613073
$177$	8.97566	0.674652
$178$	7.88994	0.591376
$179$	13.8094	1.03216	0.516082	−	0.856539i	$-0.327390\pi$
$179$	13.8094	1.03216	0.516082	+	0.856539i	$0.327390\pi$
$180$	−14.0942	−1.05052
$181$	23.9979	1.78375	0.891873	−	0.452285i	$-0.149391\pi$
$181$	23.9979	1.78375	0.891873	+	0.452285i	$0.149391\pi$
$182$	−4.14245	−0.307059
$183$	−42.8786	−3.16967
$184$	−0.454313	−0.0334924
$185$	−12.7422	−0.936824
$186$	−22.2272	−1.62978
$187$	−2.50874	−0.183457
$188$	−3.48913	−0.254471
$189$	4.87675	0.354731
$190$	−3.22170	−0.233727
$191$	−1.65485	−0.119741	−0.0598704	−	0.998206i	$-0.519069\pi$
$191$	−1.65485	−0.119741	−0.0598704	+	0.998206i	$0.519069\pi$
$192$	−2.79976	−0.202056
$193$	4.37744	0.315095	0.157547	−	0.987511i	$-0.449641\pi$
$193$	4.37744	0.315095	0.157547	+	0.987511i	$0.449641\pi$
$194$	8.29553	0.595584
$195$	35.6606	2.55371
$196$	−6.10256	−0.435897
$197$	−24.7330	−1.76216	−0.881078	−	0.472972i	$-0.843181\pi$
$197$	−24.7330	−1.76216	−0.881078	+	0.472972i	$0.843181\pi$
$198$	3.93546	0.279681
$199$	2.04494	0.144962	0.0724810	−	0.997370i	$-0.476908\pi$
$199$	2.04494	0.144962	0.0724810	+	0.997370i	$0.476908\pi$
$200$	3.48453	0.246393
$201$	3.21259	0.226598
$202$	−15.7774	−1.11009
$203$	5.54086	0.388892
$204$	8.63590	0.604634
$205$	25.3292	1.76907
$206$	−2.71280	−0.189010
$207$	−2.19827	−0.152791
$208$	4.37274	0.303195
$209$	0.899580	0.0622253
$210$	−7.72572	−0.533125
$211$	−12.0338	−0.828442	−0.414221	−	0.910176i	$-0.635946\pi$
$211$	−12.0338	−0.828442	−0.414221	+	0.910176i	$0.635946\pi$
$212$	−4.18987	−0.287761
$213$	−4.63039	−0.317269
$214$	4.85668	0.331996
$215$	32.5254	2.21821
$216$	−5.14786	−0.350268
$217$	−7.52087	−0.510550
$218$	−0.0943351	−0.00638918
$219$	−18.6255	−1.25859
$220$	−2.36910	−0.159724
$221$	−13.4878	−0.907285
$222$	−12.2476	−0.822006
$223$	17.1164	1.14620	0.573101	−	0.819485i	$-0.305740\pi$
$223$	17.1164	1.14620	0.573101	+	0.819485i	$0.305740\pi$
$224$	−0.947335	−0.0632965
$225$	16.8605	1.12403
$226$	4.56013	0.303336
$227$	3.18864	0.211638	0.105819	−	0.994385i	$-0.466254\pi$
$227$	3.18864	0.211638	0.105819	+	0.994385i	$0.466254\pi$
$228$	−3.09665	−0.205081
$229$	−11.2700	−0.744739	−0.372370	−	0.928084i	$-0.621455\pi$
$229$	−11.2700	−0.744739	−0.372370	+	0.928084i	$0.621455\pi$
$230$	1.32333	0.0872580
$231$	2.15722	0.141934
$232$	−5.84889	−0.383998
$233$	−1.83112	−0.119961	−0.0599804	−	0.998200i	$-0.519104\pi$
$233$	−1.83112	−0.119961	−0.0599804	+	0.998200i	$0.519104\pi$
$234$	21.1583	1.38316
$235$	10.1632	0.662976
$236$	−3.20587	−0.208684
$237$	36.5472	2.37399
$238$	2.92207	0.189409
$239$	28.2705	1.82867	0.914334	−	0.404961i	$-0.132715\pi$
$239$	28.2705	1.82867	0.914334	+	0.404961i	$0.132715\pi$
$240$	8.15521	0.526417
$241$	6.14914	0.396101	0.198050	−	0.980192i	$-0.436539\pi$
$241$	6.14914	0.396101	0.198050	+	0.980192i	$0.436539\pi$
$242$	−10.3385	−0.664583
$243$	15.7326	1.00925
$244$	15.3151	0.980447
$245$	17.7757	1.13564
$246$	24.3461	1.55225
$247$	4.83643	0.307734
$248$	7.93897	0.504125
$249$	−7.16425	−0.454016
$250$	4.41430	0.279185
$251$	−1.98202	−0.125104	−0.0625520	−	0.998042i	$-0.519924\pi$
$251$	−1.98202	−0.125104	−0.0625520	+	0.998042i	$0.519924\pi$
$252$	−4.58385	−0.288755
$253$	−0.369508	−0.0232308
$254$	19.9789	1.25359
$255$	−25.1548	−1.57526
$256$	1.00000	0.0625000
$257$	−4.04950	−0.252601	−0.126300	−	0.991992i	$-0.540310\pi$
$257$	−4.04950	−0.252601	−0.126300	+	0.991992i	$0.540310\pi$
$258$	31.2629	1.94635
$259$	−4.14413	−0.257504
$260$	−12.7370	−0.789915
$261$	−28.3009	−1.75178
$262$	−3.10228	−0.191659
$263$	21.9536	1.35371	0.676857	−	0.736114i	$-0.263342\pi$
$263$	21.9536	1.35371	0.676857	+	0.736114i	$0.263342\pi$
$264$	−2.27714	−0.140148
$265$	12.2043	0.749706
$266$	−1.04779	−0.0642442
$267$	−22.0900	−1.35188
$268$	−1.14745	−0.0700916
$269$	13.8618	0.845170	0.422585	−	0.906323i	$-0.361123\pi$
$269$	13.8618	0.845170	0.422585	+	0.906323i	$0.361123\pi$
$270$	14.9948	0.912554
$271$	6.14379	0.373209	0.186604	−	0.982435i	$-0.440252\pi$
$271$	6.14379	0.373209	0.186604	+	0.982435i	$0.440252\pi$
$272$	−3.08451	−0.187026
$273$	11.5979	0.701935
$274$	7.21421	0.435826
$275$	2.83408	0.170902
$276$	1.27197	0.0765635
$277$	−16.8528	−1.01258	−0.506292	−	0.862362i	$-0.668984\pi$
$277$	−16.8528	−1.01258	−0.506292	+	0.862362i	$0.668984\pi$
$278$	9.55097	0.572829
$279$	38.4141	2.29979
$280$	2.75942	0.164907
$281$	−18.9591	−1.13100	−0.565501	−	0.824747i	$-0.691317\pi$
$281$	−18.9591	−1.13100	−0.565501	+	0.824747i	$0.691317\pi$
$282$	9.76875	0.581721
$283$	3.62074	0.215231	0.107615	−	0.994193i	$-0.465679\pi$
$283$	3.62074	0.215231	0.107615	+	0.994193i	$0.465679\pi$
$284$	1.65385	0.0981379
$285$	9.02000	0.534299
$286$	3.55649	0.210300
$287$	8.23781	0.486263
$288$	4.83868	0.285122
$289$	−7.48579	−0.440340
$290$	17.0368	1.00043
$291$	−23.2255	−1.36150
$292$	6.65252	0.389309
$293$	−24.8277	−1.45045	−0.725226	−	0.688511i	$-0.758265\pi$
$293$	−24.8277	−1.45045	−0.725226	+	0.688511i	$0.758265\pi$
$294$	17.0857	0.996459
$295$	9.33811	0.543686
$296$	4.37451	0.254264
$297$	−4.18693	−0.242950
$298$	−16.2312	−0.940250
$299$	−1.98659	−0.114888
$300$	−9.75585	−0.563254
$301$	10.5782	0.609718
$302$	7.96931	0.458582
$303$	44.1729	2.53767
$304$	1.10604	0.0634358
$305$	−44.6100	−2.55436
$306$	−14.9250	−0.853203
$307$	−4.08352	−0.233059	−0.116529	−	0.993187i	$-0.537177\pi$
$307$	−4.08352	−0.233059	−0.116529	+	0.993187i	$0.537177\pi$
$308$	−0.770500	−0.0439033
$309$	7.59520	0.432076
$310$	−23.1248	−1.31340
$311$	−11.3817	−0.645397	−0.322699	−	0.946502i	$-0.604590\pi$
$311$	−11.3817	−0.645397	−0.322699	+	0.946502i	$0.604590\pi$
$312$	−12.2426	−0.693102
$313$	33.8148	1.91132	0.955661	−	0.294468i	$-0.0951424\pi$
$313$	33.8148	1.91132	0.955661	+	0.294468i	$0.0951424\pi$
$314$	−1.05869	−0.0597454
$315$	13.3519	0.752296
$316$	−13.0537	−0.734326
$317$	25.5804	1.43674	0.718369	−	0.695663i	$-0.244889\pi$
$317$	25.5804	1.43674	0.718369	+	0.695663i	$0.244889\pi$
$318$	11.7306	0.657821
$319$	−4.75709	−0.266346
$320$	−2.91282	−0.162832
$321$	−13.5975	−0.758941
$322$	0.430387	0.0239845
$323$	−3.41160	−0.189826
$324$	−0.103238	−0.00573543
$325$	15.2369	0.845192
$326$	4.19651	0.232423
$327$	0.264116	0.0146056
$328$	−8.69577	−0.480144
$329$	3.30538	0.182232
$330$	6.63291	0.365129
$331$	31.6995	1.74236	0.871182	−	0.490961i	$-0.163354\pi$
$331$	31.6995	1.74236	0.871182	+	0.490961i	$0.163354\pi$
$332$	2.55888	0.140437
$333$	21.1669	1.15994
$334$	10.9872	0.601192
$335$	3.34232	0.182610
$336$	2.65232	0.144696
$337$	30.7963	1.67758	0.838792	−	0.544452i	$-0.183262\pi$
$337$	30.7963	1.67758	0.838792	+	0.544452i	$0.183262\pi$
$338$	6.12082	0.332929
$339$	−12.7673	−0.693424
$340$	8.98463	0.487260
$341$	6.45703	0.349668
$342$	5.35178	0.289391
$343$	12.4125	0.670213
$344$	−11.1663	−0.602046
$345$	−3.70502	−0.199471
$346$	9.45729	0.508427
$347$	6.66375	0.357729	0.178864	−	0.983874i	$-0.442758\pi$
$347$	6.66375	0.357729	0.178864	+	0.983874i	$0.442758\pi$
$348$	16.3755	0.877819
$349$	−12.3352	−0.660289	−0.330145	−	0.943930i	$-0.607097\pi$
$349$	−12.3352	−0.660289	−0.330145	+	0.943930i	$0.607097\pi$
$350$	−3.30102	−0.176447
$351$	−22.5102	−1.20151
$352$	0.813334	0.0433508
$353$	34.4718	1.83475	0.917373	−	0.398028i	$-0.130305\pi$
$353$	34.4718	1.83475	0.917373	+	0.398028i	$0.130305\pi$
$354$	8.97566	0.477051
$355$	−4.81737	−0.255679
$356$	7.88994	0.418166
$357$	−8.18110	−0.432990
$358$	13.8094	0.729850
$359$	21.6280	1.14148	0.570742	−	0.821129i	$-0.306656\pi$
$359$	21.6280	1.14148	0.570742	+	0.821129i	$0.306656\pi$
$360$	−14.0942	−0.742830
$361$	−17.7767	−0.935614
$362$	23.9979	1.26130
$363$	28.9453	1.51924
$364$	−4.14245	−0.217123
$365$	−19.3776	−1.01427
$366$	−42.8786	−2.24130
$367$	24.4447	1.27600	0.638001	−	0.770036i	$-0.279762\pi$
$367$	24.4447	1.27600	0.638001	+	0.770036i	$0.279762\pi$
$368$	−0.454313	−0.0236827
$369$	−42.0760	−2.19039
$370$	−12.7422	−0.662434
$371$	3.96921	0.206071
$372$	−22.2272	−1.15243
$373$	−11.9694	−0.619751	−0.309876	−	0.950777i	$-0.600287\pi$
$373$	−11.9694	−0.619751	−0.309876	+	0.950777i	$0.600287\pi$
$374$	−2.50874	−0.129724
$375$	−12.3590	−0.638216
$376$	−3.48913	−0.179938
$377$	−25.5756	−1.31721
$378$	4.87675	0.250833
$379$	−30.7232	−1.57815	−0.789073	−	0.614300i	$-0.789439\pi$
$379$	−30.7232	−1.57815	−0.789073	+	0.614300i	$0.789439\pi$
$380$	−3.22170	−0.165270
$381$	−55.9362	−2.86570
$382$	−1.65485	−0.0846695
$383$	−7.13403	−0.364532	−0.182266	−	0.983249i	$-0.558343\pi$
$383$	−7.13403	−0.364532	−0.182266	+	0.983249i	$0.558343\pi$
$384$	−2.79976	−0.142875
$385$	2.24433	0.114382
$386$	4.37744	0.222806
$387$	−54.0300	−2.74650
$388$	8.29553	0.421142
$389$	9.13020	0.462919	0.231460	−	0.972844i	$-0.425650\pi$
$389$	9.13020	0.462919	0.231460	+	0.972844i	$0.425650\pi$
$390$	35.6606	1.80574
$391$	1.40133	0.0708685
$392$	−6.10256	−0.308226
$393$	8.68564	0.438133
$394$	−24.7330	−1.24603
$395$	38.0230	1.91314
$396$	3.93546	0.197764
$397$	25.7509	1.29240	0.646200	−	0.763168i	$-0.276357\pi$
$397$	25.7509	1.29240	0.646200	+	0.763168i	$0.276357\pi$
$398$	2.04494	0.102504
$399$	2.93357	0.146862
$400$	3.48453	0.174226
$401$	26.5672	1.32670	0.663351	−	0.748308i	$-0.269133\pi$
$401$	26.5672	1.32670	0.663351	+	0.748308i	$0.269133\pi$
$402$	3.21259	0.160229
$403$	34.7150	1.72928
$404$	−15.7774	−0.784953
$405$	0.300713	0.0149426
$406$	5.54086	0.274988
$407$	3.55794	0.176361
$408$	8.63590	0.427541
$409$	−19.5253	−0.965463	−0.482731	−	0.875769i	$-0.660355\pi$
$409$	−19.5253	−0.965463	−0.482731	+	0.875769i	$0.660355\pi$
$410$	25.3292	1.25092
$411$	−20.1981	−0.996298
$412$	−2.71280	−0.133650
$413$	3.03703	0.149442
$414$	−2.19827	−0.108039
$415$	−7.45355	−0.365880
$416$	4.37274	0.214391
$417$	−26.7404	−1.30949
$418$	0.899580	0.0439999
$419$	11.7075	0.571951	0.285975	−	0.958237i	$-0.407682\pi$
$419$	11.7075	0.571951	0.285975	+	0.958237i	$0.407682\pi$
$420$	−7.72572	−0.376977
$421$	−16.5941	−0.808745	−0.404373	−	0.914594i	$-0.632510\pi$
$421$	−16.5941	−0.808745	−0.404373	+	0.914594i	$0.632510\pi$
$422$	−12.0338	−0.585797
$423$	−16.8828	−0.820869
$424$	−4.18987	−0.203478
$425$	−10.7481	−0.521358
$426$	−4.63039	−0.224343
$427$	−14.5085	−0.702116
$428$	4.85668	0.234756
$429$	−9.95734	−0.480745
$430$	32.5254	1.56851
$431$	−6.49371	−0.312791	−0.156396	−	0.987694i	$-0.549987\pi$
$431$	−6.49371	−0.312791	−0.156396	+	0.987694i	$0.549987\pi$
$432$	−5.14786	−0.247677
$433$	−33.6668	−1.61792	−0.808961	−	0.587862i	$-0.799970\pi$
$433$	−33.6668	−1.61792	−0.808961	+	0.587862i	$0.799970\pi$
$434$	−7.52087	−0.361013
$435$	−47.6989	−2.28699
$436$	−0.0943351	−0.00451783
$437$	−0.502489	−0.0240373
$438$	−18.6255	−0.889960
$439$	30.6130	1.46108	0.730541	−	0.682869i	$-0.239268\pi$
$439$	30.6130	1.46108	0.730541	+	0.682869i	$0.239268\pi$
$440$	−2.36910	−0.112942
$441$	−29.5283	−1.40611
$442$	−13.4878	−0.641547
$443$	−34.8387	−1.65524	−0.827618	−	0.561292i	$-0.810304\pi$
$443$	−34.8387	−1.65524	−0.827618	+	0.561292i	$0.810304\pi$
$444$	−12.2476	−0.581246
$445$	−22.9820	−1.08945
$446$	17.1164	0.810487
$447$	45.4436	2.14941
$448$	−0.947335	−0.0447574
$449$	−23.4563	−1.10697	−0.553485	−	0.832859i	$-0.686702\pi$
$449$	−23.4563	−1.10697	−0.553485	+	0.832859i	$0.686702\pi$
$450$	16.8605	0.794812
$451$	−7.07256	−0.333034
$452$	4.56013	0.214491
$453$	−22.3122	−1.04832
$454$	3.18864	0.149651
$455$	12.0662	0.565673
$456$	−3.09665	−0.145014
$457$	26.3692	1.23350	0.616750	−	0.787159i	$-0.288449\pi$
$457$	26.3692	1.23350	0.616750	+	0.787159i	$0.288449\pi$
$458$	−11.2700	−0.526610
$459$	15.8786	0.741151
$460$	1.32333	0.0617007
$461$	−6.16345	−0.287060	−0.143530	−	0.989646i	$-0.545845\pi$
$461$	−6.16345	−0.287060	−0.143530	+	0.989646i	$0.545845\pi$
$462$	2.15722	0.100363
$463$	−7.59250	−0.352853	−0.176427	−	0.984314i	$-0.556454\pi$
$463$	−7.59250	−0.352853	−0.176427	+	0.984314i	$0.556454\pi$
$464$	−5.84889	−0.271528
$465$	64.7440	3.00243
$466$	−1.83112	−0.0848251
$467$	−4.30473	−0.199199	−0.0995995	−	0.995028i	$-0.531756\pi$
$467$	−4.30473	−0.199199	−0.0995995	+	0.995028i	$0.531756\pi$
$468$	21.1583	0.978041
$469$	1.08702	0.0501939
$470$	10.1632	0.468795
$471$	2.96408	0.136578
$472$	−3.20587	−0.147562
$473$	−9.08191	−0.417587
$474$	36.5472	1.67867
$475$	3.85403	0.176835
$476$	2.92207	0.133933
$477$	−20.2734	−0.928256
$478$	28.2705	1.29306
$479$	7.11127	0.324922	0.162461	−	0.986715i	$-0.448057\pi$
$479$	7.11127	0.324922	0.162461	+	0.986715i	$0.448057\pi$
$480$	8.15521	0.372233
$481$	19.1286	0.872189
$482$	6.14914	0.280086
$483$	−1.20498	−0.0548286
$484$	−10.3385	−0.469931
$485$	−24.1634	−1.09720
$486$	15.7326	0.713646
$487$	33.0674	1.49843	0.749214	−	0.662328i	$-0.230432\pi$
$487$	33.0674	1.49843	0.749214	+	0.662328i	$0.230432\pi$
$488$	15.3151	0.693280
$489$	−11.7492	−0.531319
$490$	17.7757	0.803022
$491$	34.0189	1.53525	0.767626	−	0.640899i	$-0.221438\pi$
$491$	34.0189	1.53525	0.767626	+	0.640899i	$0.221438\pi$
$492$	24.3461	1.09761
$493$	18.0410	0.812524
$494$	4.83643	0.217601
$495$	−11.4633	−0.515236
$496$	7.93897	0.356470
$497$	−1.56675	−0.0702783
$498$	−7.16425	−0.321038
$499$	−24.8790	−1.11374	−0.556869	−	0.830600i	$-0.687997\pi$
$499$	−24.8790	−1.11374	−0.556869	+	0.830600i	$0.687997\pi$
$500$	4.41430	0.197414
$501$	−30.7615	−1.37432
$502$	−1.98202	−0.0884618
$503$	15.3531	0.684560	0.342280	−	0.939598i	$-0.388801\pi$
$503$	15.3531	0.684560	0.342280	+	0.939598i	$0.388801\pi$
$504$	−4.58385	−0.204181
$505$	45.9566	2.04504
$506$	−0.369508	−0.0164266
$507$	−17.1368	−0.761074
$508$	19.9789	0.886420
$509$	7.50982	0.332867	0.166434	−	0.986053i	$-0.446775\pi$
$509$	7.50982	0.332867	0.166434	+	0.986053i	$0.446775\pi$
$510$	−25.1548	−1.11388
$511$	−6.30216	−0.278791
$512$	1.00000	0.0441942
$513$	−5.69375	−0.251385
$514$	−4.04950	−0.178616
$515$	7.90190	0.348199
$516$	31.2629	1.37627
$517$	−2.83783	−0.124808
$518$	−4.14413	−0.182083
$519$	−26.4782	−1.16226
$520$	−12.7370	−0.558554
$521$	−4.42846	−0.194014	−0.0970072	−	0.995284i	$-0.530927\pi$
$521$	−4.42846	−0.194014	−0.0970072	+	0.995284i	$0.530927\pi$
$522$	−28.3009	−1.23870
$523$	29.8006	1.30309	0.651544	−	0.758610i	$-0.274121\pi$
$523$	29.8006	1.30309	0.651544	+	0.758610i	$0.274121\pi$
$524$	−3.10228	−0.135524
$525$	9.24207	0.403357
$526$	21.9536	0.957220
$527$	−24.4879	−1.06671
$528$	−2.27714	−0.0990999
$529$	−22.7936	−0.991026
$530$	12.2043	0.530122
$531$	−15.5121	−0.673170
$532$	−1.04779	−0.0454275
$533$	−38.0243	−1.64702
$534$	−22.0900	−0.955927
$535$	−14.1466	−0.611612
$536$	−1.14745	−0.0495623
$537$	−38.6631	−1.66843
$538$	13.8618	0.597626
$539$	−4.96341	−0.213789
$540$	14.9948	0.645273
$541$	12.6073	0.542030	0.271015	−	0.962575i	$-0.412641\pi$
$541$	12.6073	0.542030	0.271015	+	0.962575i	$0.412641\pi$
$542$	6.14379	0.263898
$543$	−67.1883	−2.88333
$544$	−3.08451	−0.132247
$545$	0.274781	0.0117703
$546$	11.5979	0.496343
$547$	−10.4506	−0.446835	−0.223417	−	0.974723i	$-0.571721\pi$
$547$	−10.4506	−0.446835	−0.223417	+	0.974723i	$0.571721\pi$
$548$	7.21421	0.308176
$549$	74.1047	3.16271
$550$	2.83408	0.120846
$551$	−6.46911	−0.275593
$552$	1.27197	0.0541386
$553$	12.3662	0.525864
$554$	−16.8528	−0.716006
$555$	35.6751	1.51432
$556$	9.55097	0.405051
$557$	14.2898	0.605480	0.302740	−	0.953073i	$-0.402099\pi$
$557$	14.2898	0.605480	0.302740	+	0.953073i	$0.402099\pi$
$558$	38.4141	1.62620
$559$	−48.8272	−2.06517
$560$	2.75942	0.116607
$561$	7.02387	0.296548
$562$	−18.9591	−0.799739
$563$	33.5963	1.41591	0.707957	−	0.706256i	$-0.249617\pi$
$563$	33.5963	1.41591	0.707957	+	0.706256i	$0.249617\pi$
$564$	9.76875	0.411339
$565$	−13.2829	−0.558814
$566$	3.62074	0.152191
$567$	0.0978009	0.00410725
$568$	1.65385	0.0693940
$569$	10.2331	0.428994	0.214497	−	0.976725i	$-0.431189\pi$
$569$	10.2331	0.428994	0.214497	+	0.976725i	$0.431189\pi$
$570$	9.02000	0.377806
$571$	14.6632	0.613637	0.306819	−	0.951768i	$-0.400735\pi$
$571$	14.6632	0.613637	0.306819	+	0.951768i	$0.400735\pi$
$572$	3.55649	0.148704
$573$	4.63319	0.193554
$574$	8.23781	0.343840
$575$	−1.58307	−0.0660184
$576$	4.83868	0.201612
$577$	23.3998	0.974147	0.487073	−	0.873361i	$-0.338064\pi$
$577$	23.3998	0.974147	0.487073	+	0.873361i	$0.338064\pi$
$578$	−7.48579	−0.311368
$579$	−12.2558	−0.509333
$580$	17.0368	0.707413
$581$	−2.42412	−0.100569
$582$	−23.2255	−0.962729
$583$	−3.40776	−0.141135
$584$	6.65252	0.275283
$585$	−61.6302	−2.54810
$586$	−24.8277	−1.02562
$587$	−28.1897	−1.16352	−0.581758	−	0.813362i	$-0.697635\pi$
$587$	−28.1897	−1.16352	−0.581758	+	0.813362i	$0.697635\pi$
$588$	17.0857	0.704603
$589$	8.78083	0.361808
$590$	9.33811	0.384444
$591$	69.2466	2.84843
$592$	4.37451	0.179791
$593$	−20.7894	−0.853717	−0.426859	−	0.904318i	$-0.640380\pi$
$593$	−20.7894	−0.853717	−0.426859	+	0.904318i	$0.640380\pi$
$594$	−4.18693	−0.171792
$595$	−8.51146	−0.348936
$596$	−16.2312	−0.664857
$597$	−5.72535	−0.234323
$598$	−1.98659	−0.0812377
$599$	37.8469	1.54638	0.773190	−	0.634174i	$-0.218660\pi$
$599$	37.8469	1.54638	0.773190	+	0.634174i	$0.218660\pi$
$600$	−9.75585	−0.398281
$601$	36.1652	1.47521	0.737604	−	0.675234i	$-0.235957\pi$
$601$	36.1652	1.47521	0.737604	+	0.675234i	$0.235957\pi$
$602$	10.5782	0.431136
$603$	−5.55214	−0.226100
$604$	7.96931	0.324267
$605$	30.1142	1.22432
$606$	44.1729	1.79440
$607$	−1.34996	−0.0547932	−0.0273966	−	0.999625i	$-0.508722\pi$
$607$	−1.34996	−0.0547932	−0.0273966	+	0.999625i	$0.508722\pi$
$608$	1.10604	0.0448559
$609$	−15.5131	−0.628622
$610$	−44.6100	−1.80621
$611$	−15.2571	−0.617235
$612$	−14.9250	−0.603306
$613$	−18.2172	−0.735786	−0.367893	−	0.929868i	$-0.619921\pi$
$613$	−18.2172	−0.735786	−0.367893	+	0.929868i	$0.619921\pi$
$614$	−4.08352	−0.164797
$615$	−70.9158	−2.85960
$616$	−0.770500	−0.0310443
$617$	−15.9507	−0.642153	−0.321076	−	0.947053i	$-0.604045\pi$
$617$	−15.9507	−0.642153	−0.321076	+	0.947053i	$0.604045\pi$
$618$	7.59520	0.305524
$619$	−0.668569	−0.0268720	−0.0134360	−	0.999910i	$-0.504277\pi$
$619$	−0.668569	−0.0268720	−0.0134360	+	0.999910i	$0.504277\pi$
$620$	−23.1248	−0.928715
$621$	2.33874	0.0938504
$622$	−11.3817	−0.456365
$623$	−7.47442	−0.299456
$624$	−12.2426	−0.490097
$625$	−30.2807	−1.21123
$626$	33.8148	1.35151
$627$	−2.51861	−0.100584
$628$	−1.05869	−0.0422464
$629$	−13.4932	−0.538011
$630$	13.3519	0.531954
$631$	−18.7787	−0.747570	−0.373785	−	0.927515i	$-0.621940\pi$
$631$	−18.7787	−0.747570	−0.373785	+	0.927515i	$0.621940\pi$
$632$	−13.0537	−0.519247
$633$	33.6918	1.33913
$634$	25.5804	1.01593
$635$	−58.1949	−2.30940
$636$	11.7306	0.465150
$637$	−26.6849	−1.05729
$638$	−4.75709	−0.188335
$639$	8.00244	0.316572
$640$	−2.91282	−0.115139
$641$	6.15117	0.242957	0.121478	−	0.992594i	$-0.461237\pi$
$641$	6.15117	0.242957	0.121478	+	0.992594i	$0.461237\pi$
$642$	−13.5975	−0.536652
$643$	−47.3221	−1.86620	−0.933101	−	0.359613i	$-0.882909\pi$
$643$	−47.3221	−1.86620	−0.933101	+	0.359613i	$0.882909\pi$
$644$	0.430387	0.0169596
$645$	−91.0634	−3.58562
$646$	−3.41160	−0.134227
$647$	34.1503	1.34259	0.671294	−	0.741192i	$-0.265739\pi$
$647$	34.1503	1.34259	0.671294	+	0.741192i	$0.265739\pi$
$648$	−0.103238	−0.00405556
$649$	−2.60744	−0.102351
$650$	15.2369	0.597641
$651$	21.0567	0.825276
$652$	4.19651	0.164348
$653$	6.10609	0.238950	0.119475	−	0.992837i	$-0.461879\pi$
$653$	6.10609	0.238950	0.119475	+	0.992837i	$0.461879\pi$
$654$	0.264116	0.0103278
$655$	9.03637	0.353080
$656$	−8.69577	−0.339513
$657$	32.1894	1.25583
$658$	3.30538	0.128857
$659$	18.0301	0.702355	0.351177	−	0.936309i	$-0.385781\pi$
$659$	18.0301	0.702355	0.351177	+	0.936309i	$0.385781\pi$
$660$	6.63291	0.258186
$661$	−14.4931	−0.563716	−0.281858	−	0.959456i	$-0.590951\pi$
$661$	−14.4931	−0.563716	−0.281858	+	0.959456i	$0.590951\pi$
$662$	31.6995	1.23204
$663$	37.7625	1.46657
$664$	2.55888	0.0993037
$665$	3.05203	0.118353
$666$	21.1669	0.820199
$667$	2.65722	0.102888
$668$	10.9872	0.425107
$669$	−47.9220	−1.85277
$670$	3.34232	0.129125
$671$	12.4563	0.480868
$672$	2.65232	0.102315
$673$	−20.7232	−0.798821	−0.399410	−	0.916772i	$-0.630785\pi$
$673$	−20.7232	−0.798821	−0.399410	+	0.916772i	$0.630785\pi$
$674$	30.7963	1.18623
$675$	−17.9379	−0.690429
$676$	6.12082	0.235416
$677$	−27.6022	−1.06084	−0.530420	−	0.847735i	$-0.677966\pi$
$677$	−27.6022	−1.06084	−0.530420	+	0.847735i	$0.677966\pi$
$678$	−12.7673	−0.490325
$679$	−7.85865	−0.301587
$680$	8.98463	0.344545
$681$	−8.92745	−0.342101
$682$	6.45703	0.247253
$683$	−2.53424	−0.0969699	−0.0484849	−	0.998824i	$-0.515439\pi$
$683$	−2.53424	−0.0969699	−0.0484849	+	0.998824i	$0.515439\pi$
$684$	5.35178	0.204630
$685$	−21.0137	−0.802893
$686$	12.4125	0.473912
$687$	31.5532	1.20383
$688$	−11.1663	−0.425710
$689$	−18.3212	−0.697981
$690$	−3.70502	−0.141048
$691$	−22.7288	−0.864644	−0.432322	−	0.901719i	$-0.642306\pi$
$691$	−22.7288	−0.864644	−0.432322	+	0.901719i	$0.642306\pi$
$692$	9.45729	0.359512
$693$	−3.72820	−0.141623
$694$	6.66375	0.252952
$695$	−27.8203	−1.05528
$696$	16.3755	0.620712
$697$	26.8222	1.01596
$698$	−12.3352	−0.466895
$699$	5.12671	0.193910
$700$	−3.30102	−0.124767
$701$	35.0403	1.32345	0.661727	−	0.749745i	$-0.269824\pi$
$701$	35.0403	1.32345	0.661727	+	0.749745i	$0.269824\pi$
$702$	−22.5102	−0.849594
$703$	4.83839	0.182483
$704$	0.813334	0.0306537
$705$	−28.4546	−1.07166
$706$	34.4718	1.29736
$707$	14.9465	0.562119
$708$	8.97566	0.337326
$709$	−40.1474	−1.50777	−0.753884	−	0.657007i	$-0.771822\pi$
$709$	−40.1474	−1.50777	−0.753884	+	0.657007i	$0.771822\pi$
$710$	−4.81737	−0.180793
$711$	−63.1624	−2.36878
$712$	7.88994	0.295688
$713$	−3.60678	−0.135075
$714$	−8.18110	−0.306170
$715$	−10.3594	−0.387421
$716$	13.8094	0.516082
$717$	−79.1508	−2.95594
$718$	21.6280	0.807151
$719$	6.59848	0.246082	0.123041	−	0.992402i	$-0.460735\pi$
$719$	6.59848	0.246082	0.123041	+	0.992402i	$0.460735\pi$
$720$	−14.0942	−0.525260
$721$	2.56993	0.0957092
$722$	−17.7767	−0.661579
$723$	−17.2161	−0.640275
$724$	23.9979	0.891873
$725$	−20.3806	−0.756916
$726$	28.9453	1.07426
$727$	−35.5217	−1.31743	−0.658714	−	0.752394i	$-0.728899\pi$
$727$	−35.5217	−1.31743	−0.658714	+	0.752394i	$0.728899\pi$
$728$	−4.14245	−0.153529
$729$	−43.7379	−1.61992
$730$	−19.3776	−0.717197
$731$	34.4425	1.27390
$732$	−42.8786	−1.58484
$733$	−25.0322	−0.924586	−0.462293	−	0.886727i	$-0.652973\pi$
$733$	−25.0322	−0.924586	−0.462293	+	0.886727i	$0.652973\pi$
$734$	24.4447	0.902270
$735$	−49.7676	−1.83571
$736$	−0.454313	−0.0167462
$737$	−0.933259	−0.0343770
$738$	−42.0760	−1.54884
$739$	−37.5680	−1.38196	−0.690981	−	0.722873i	$-0.742821\pi$
$739$	−37.5680	−1.38196	−0.690981	+	0.722873i	$0.742821\pi$
$740$	−12.7422	−0.468412
$741$	−13.5408	−0.497435
$742$	3.96921	0.145714
$743$	33.1336	1.21556	0.607778	−	0.794107i	$-0.292061\pi$
$743$	33.1336	1.21556	0.607778	+	0.794107i	$0.292061\pi$
$744$	−22.2272	−0.814890
$745$	47.2787	1.73216
$746$	−11.9694	−0.438230
$747$	12.3816	0.453018
$748$	−2.50874	−0.0917285
$749$	−4.60090	−0.168113
$750$	−12.3590	−0.451287
$751$	15.0297	0.548441	0.274220	−	0.961667i	$-0.411580\pi$
$751$	15.0297	0.548441	0.274220	+	0.961667i	$0.411580\pi$
$752$	−3.48913	−0.127236
$753$	5.54918	0.202224
$754$	−25.5756	−0.931409
$755$	−23.2132	−0.844814
$756$	4.87675	0.177366
$757$	24.7554	0.899752	0.449876	−	0.893091i	$-0.351468\pi$
$757$	24.7554	0.899752	0.449876	+	0.893091i	$0.351468\pi$
$758$	−30.7232	−1.11592
$759$	1.03454	0.0375512
$760$	−3.22170	−0.116863
$761$	11.8805	0.430669	0.215335	−	0.976540i	$-0.430916\pi$
$761$	11.8805	0.430669	0.215335	+	0.976540i	$0.430916\pi$
$762$	−55.9362	−2.02635
$763$	0.0893670	0.00323530
$764$	−1.65485	−0.0598704
$765$	43.4737	1.57180
$766$	−7.13403	−0.257763
$767$	−14.0184	−0.506175
$768$	−2.79976	−0.101028
$769$	−11.4073	−0.411359	−0.205679	−	0.978619i	$-0.565940\pi$
$769$	−11.4073	−0.411359	−0.205679	+	0.978619i	$0.565940\pi$
$770$	2.24433	0.0808800
$771$	11.3376	0.408315
$772$	4.37744	0.157547
$773$	30.7836	1.10721	0.553605	−	0.832780i	$-0.313252\pi$
$773$	30.7836	1.10721	0.553605	+	0.832780i	$0.313252\pi$
$774$	−54.0300	−1.94207
$775$	27.6636	0.993705
$776$	8.29553	0.297792
$777$	11.6026	0.416241
$778$	9.13020	0.327333
$779$	−9.61788	−0.344596
$780$	35.6606	1.27685
$781$	1.34513	0.0481326
$782$	1.40133	0.0501116
$783$	30.1092	1.07602
$784$	−6.10256	−0.217948
$785$	3.08378	0.110065
$786$	8.68564	0.309806
$787$	−28.0603	−1.00024	−0.500120	−	0.865956i	$-0.666711\pi$
$787$	−28.0603	−1.00024	−0.500120	+	0.865956i	$0.666711\pi$
$788$	−24.7330	−0.881078
$789$	−61.4648	−2.18820
$790$	38.0230	1.35280
$791$	−4.31998	−0.153601
$792$	3.93546	0.139840
$793$	66.9687	2.37813
$794$	25.7509	0.913865
$795$	−34.1692	−1.21186
$796$	2.04494	0.0724810
$797$	19.0218	0.673785	0.336893	−	0.941543i	$-0.390624\pi$
$797$	19.0218	0.673785	0.336893	+	0.941543i	$0.390624\pi$
$798$	2.93357	0.103847
$799$	10.7623	0.380742
$800$	3.48453	0.123197
$801$	38.1769	1.34891
$802$	26.5672	0.938121
$803$	5.41071	0.190940
$804$	3.21259	0.113299
$805$	−1.25364	−0.0441850
$806$	34.7150	1.22278
$807$	−38.8098	−1.36617
$808$	−15.7774	−0.555046
$809$	−34.8603	−1.22562	−0.612812	−	0.790229i	$-0.709962\pi$
$809$	−34.8603	−1.22562	−0.612812	+	0.790229i	$0.709962\pi$
$810$	0.300713	0.0105660
$811$	44.0835	1.54798	0.773991	−	0.633196i	$-0.218257\pi$
$811$	44.0835	1.54798	0.773991	+	0.633196i	$0.218257\pi$
$812$	5.54086	0.194446
$813$	−17.2012	−0.603271
$814$	3.55794	0.124706
$815$	−12.2237	−0.428177
$816$	8.63590	0.302317
$817$	−12.3504	−0.432085
$818$	−19.5253	−0.682685
$819$	−20.0440	−0.700393
$820$	25.3292	0.884535
$821$	31.2403	1.09029	0.545146	−	0.838341i	$-0.316474\pi$
$821$	31.2403	1.09029	0.545146	+	0.838341i	$0.316474\pi$
$822$	−20.1981	−0.704489
$823$	27.1077	0.944917	0.472458	−	0.881353i	$-0.343367\pi$
$823$	27.1077	0.944917	0.472458	+	0.881353i	$0.343367\pi$
$824$	−2.71280	−0.0945048
$825$	−7.93476	−0.276253
$826$	3.03703	0.105672
$827$	−15.7594	−0.548007	−0.274004	−	0.961729i	$-0.588348\pi$
$827$	−15.7594	−0.548007	−0.274004	+	0.961729i	$0.588348\pi$
$828$	−2.19827	−0.0763953
$829$	−7.41669	−0.257592	−0.128796	−	0.991671i	$-0.541111\pi$
$829$	−7.41669	−0.257592	−0.128796	+	0.991671i	$0.541111\pi$
$830$	−7.45355	−0.258717
$831$	47.1838	1.63679
$832$	4.37274	0.151597
$833$	18.8234	0.652192
$834$	−26.7404	−0.925946
$835$	−32.0037	−1.10753
$836$	0.899580	0.0311126
$837$	−40.8687	−1.41263
$838$	11.7075	0.404430
$839$	6.20359	0.214172	0.107086	−	0.994250i	$-0.465848\pi$
$839$	6.20359	0.214172	0.107086	+	0.994250i	$0.465848\pi$
$840$	−7.72572	−0.266563
$841$	5.20946	0.179636
$842$	−16.5941	−0.571869
$843$	53.0809	1.82820
$844$	−12.0338	−0.414221
$845$	−17.8288	−0.613331
$846$	−16.8828	−0.580442
$847$	9.79402	0.336526
$848$	−4.18987	−0.143881
$849$	−10.1372	−0.347908
$850$	−10.7481	−0.368656
$851$	−1.98740	−0.0681272
$852$	−4.63039	−0.158634
$853$	1.92854	0.0660321	0.0330161	−	0.999455i	$-0.489489\pi$
$853$	1.92854	0.0660321	0.0330161	+	0.999455i	$0.489489\pi$
$854$	−14.5085	−0.496471
$855$	−15.5888	−0.533124
$856$	4.85668	0.165998
$857$	13.8501	0.473111	0.236556	−	0.971618i	$-0.423981\pi$
$857$	13.8501	0.473111	0.236556	+	0.971618i	$0.423981\pi$
$858$	−9.95734	−0.339938
$859$	6.39435	0.218172	0.109086	−	0.994032i	$-0.465208\pi$
$859$	6.39435	0.218172	0.109086	+	0.994032i	$0.465208\pi$
$860$	32.5254	1.10911
$861$	−23.0639	−0.786016
$862$	−6.49371	−0.221177
$863$	48.3447	1.64567	0.822837	−	0.568278i	$-0.192390\pi$
$863$	48.3447	1.64567	0.822837	+	0.568278i	$0.192390\pi$
$864$	−5.14786	−0.175134
$865$	−27.5474	−0.936640
$866$	−33.6668	−1.14404
$867$	20.9584	0.711786
$868$	−7.52087	−0.255275
$869$	−10.6170	−0.360156
$870$	−47.6989	−1.61714
$871$	−5.01749	−0.170011
$872$	−0.0943351	−0.00319459
$873$	40.1394	1.35851
$874$	−0.502489	−0.0169969
$875$	−4.18182	−0.141371
$876$	−18.6255	−0.629296
$877$	3.62923	0.122550	0.0612752	−	0.998121i	$-0.480483\pi$
$877$	3.62923	0.122550	0.0612752	+	0.998121i	$0.480483\pi$
$878$	30.6130	1.03314
$879$	69.5118	2.34457
$880$	−2.36910	−0.0798622
$881$	−7.70473	−0.259579	−0.129790	−	0.991542i	$-0.541430\pi$
$881$	−7.70473	−0.259579	−0.129790	+	0.991542i	$0.541430\pi$
$882$	−29.5283	−0.994269
$883$	16.5902	0.558305	0.279152	−	0.960247i	$-0.409947\pi$
$883$	16.5902	0.558305	0.279152	+	0.960247i	$0.409947\pi$
$884$	−13.4878	−0.453642
$885$	−26.1445	−0.878838
$886$	−34.8387	−1.17043
$887$	36.9433	1.24043	0.620217	−	0.784431i	$-0.287045\pi$
$887$	36.9433	1.24043	0.620217	+	0.784431i	$0.287045\pi$
$888$	−12.2476	−0.411003
$889$	−18.9267	−0.634781
$890$	−22.9820	−0.770358
$891$	−0.0839668	−0.00281299
$892$	17.1164	0.573101
$893$	−3.85913	−0.129141
$894$	45.4436	1.51986
$895$	−40.2243	−1.34455
$896$	−0.947335	−0.0316483
$897$	5.56198	0.185709
$898$	−23.4563	−0.782746
$899$	−46.4341	−1.54867
$900$	16.8605	0.562017
$901$	12.9237	0.430551
$902$	−7.07256	−0.235491
$903$	−29.6165	−0.985575
$904$	4.56013	0.151668
$905$	−69.9015	−2.32360
$906$	−22.3122	−0.741273
$907$	50.8105	1.68714	0.843568	−	0.537022i	$-0.180451\pi$
$907$	50.8105	1.68714	0.843568	+	0.537022i	$0.180451\pi$
$908$	3.18864	0.105819
$909$	−76.3416	−2.53209
$910$	12.0662	0.399991
$911$	27.0546	0.896360	0.448180	−	0.893943i	$-0.352072\pi$
$911$	27.0546	0.896360	0.448180	+	0.893943i	$0.352072\pi$
$912$	−3.09665	−0.102540
$913$	2.08122	0.0688784
$914$	26.3692	0.872217
$915$	124.898	4.12899
$916$	−11.2700	−0.372370
$917$	2.93890	0.0970509
$918$	15.8786	0.524073
$919$	42.5764	1.40447	0.702234	−	0.711947i	$-0.252186\pi$
$919$	42.5764	1.40447	0.702234	+	0.711947i	$0.252186\pi$
$920$	1.32333	0.0436290
$921$	11.4329	0.376726
$922$	−6.16345	−0.202982
$923$	7.23184	0.238039
$924$	2.15722	0.0709672
$925$	15.2431	0.501191
$926$	−7.59250	−0.249505
$927$	−13.1264	−0.431126
$928$	−5.84889	−0.191999
$929$	30.4343	0.998517	0.499259	−	0.866453i	$-0.333606\pi$
$929$	30.4343	0.998517	0.499259	+	0.866453i	$0.333606\pi$
$930$	64.7440	2.12304
$931$	−6.74968	−0.221212
$932$	−1.83112	−0.0599804
$933$	31.8661	1.04325
$934$	−4.30473	−0.140855
$935$	7.30750	0.238981
$936$	21.1583	0.691579
$937$	−9.98085	−0.326060	−0.163030	−	0.986621i	$-0.552127\pi$
$937$	−9.98085	−0.326060	−0.163030	+	0.986621i	$0.552127\pi$
$938$	1.08702	0.0354924
$939$	−94.6733	−3.08955
$940$	10.1632	0.331488
$941$	−28.4324	−0.926869	−0.463434	−	0.886131i	$-0.653383\pi$
$941$	−28.4324	−0.926869	−0.463434	+	0.886131i	$0.653383\pi$
$942$	2.96408	0.0965751
$943$	3.95060	0.128649
$944$	−3.20587	−0.104342
$945$	−14.2051	−0.462092
$946$	−9.08191	−0.295278
$947$	−52.0705	−1.69206	−0.846032	−	0.533133i	$-0.821015\pi$
$947$	−52.0705	−1.69206	−0.846032	+	0.533133i	$0.821015\pi$
$948$	36.5472	1.18700
$949$	29.0897	0.944291
$950$	3.85403	0.125041
$951$	−71.6190	−2.32241
$952$	2.92207	0.0947047
$953$	−42.1047	−1.36391	−0.681953	−	0.731396i	$-0.738869\pi$
$953$	−42.1047	−1.36391	−0.681953	+	0.731396i	$0.738869\pi$
$954$	−20.2734	−0.656376
$955$	4.82028	0.155981
$956$	28.2705	0.914334
$957$	13.3187	0.430534
$958$	7.11127	0.229755
$959$	−6.83428	−0.220690
$960$	8.15521	0.263208
$961$	32.0273	1.03314
$962$	19.1286	0.616731
$963$	23.4999	0.757273
$964$	6.14914	0.198050
$965$	−12.7507	−0.410459
$966$	−1.20498	−0.0387696
$967$	25.3030	0.813690	0.406845	−	0.913497i	$-0.366629\pi$
$967$	25.3030	0.813690	0.406845	+	0.913497i	$0.366629\pi$
$968$	−10.3385	−0.332292
$969$	9.55166	0.306844
$970$	−24.1634	−0.775840
$971$	3.84901	0.123521	0.0617603	−	0.998091i	$-0.480329\pi$
$971$	3.84901	0.123521	0.0617603	+	0.998091i	$0.480329\pi$
$972$	15.7326	0.504624
$973$	−9.04797	−0.290065
$974$	33.0674	1.05955
$975$	−42.6598	−1.36621
$976$	15.3151	0.490223
$977$	41.9265	1.34135	0.670674	−	0.741752i	$-0.266005\pi$
$977$	41.9265	1.34135	0.670674	+	0.741752i	$0.266005\pi$
$978$	−11.7492	−0.375699
$979$	6.41715	0.205093
$980$	17.7757	0.567822
$981$	−0.456457	−0.0145736
$982$	34.0189	1.08559
$983$	−2.71802	−0.0866913	−0.0433457	−	0.999060i	$-0.513802\pi$
$983$	−2.71802	−0.0866913	−0.0433457	+	0.999060i	$0.513802\pi$
$984$	24.3461	0.776125
$985$	72.0429	2.29548
$986$	18.0410	0.574541
$987$	−9.25428	−0.294567
$988$	4.83643	0.153867
$989$	5.07299	0.161312
$990$	−11.4633	−0.364327
$991$	33.3593	1.05969	0.529847	−	0.848093i	$-0.322249\pi$
$991$	33.3593	1.05969	0.529847	+	0.848093i	$0.322249\pi$
$992$	7.93897	0.252063
$993$	−88.7512	−2.81643
$994$	−1.56675	−0.0496943
$995$	−5.95654	−0.188835
$996$	−7.16425	−0.227008
$997$	34.4972	1.09254	0.546269	−	0.837610i	$-0.316048\pi$
$997$	34.4972	1.09254	0.546269	+	0.837610i	$0.316048\pi$
$998$	−24.8790	−0.787532
$999$	−22.5194	−0.712482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.7	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.7	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.79976 q^{3} +1.00000 q^{4} -2.91282 q^{5} -2.79976 q^{6} -0.947335 q^{7} +1.00000 q^{8} +4.83868 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.79976 q^{3} +1.00000 q^{4} -2.91282 q^{5} -2.79976 q^{6} -0.947335 q^{7} +1.00000 q^{8} +4.83868 q^{9} -2.91282 q^{10} +0.813334 q^{11} -2.79976 q^{12} +4.37274 q^{13} -0.947335 q^{14} +8.15521 q^{15} +1.00000 q^{16} -3.08451 q^{17} +4.83868 q^{18} +1.10604 q^{19} -2.91282 q^{20} +2.65232 q^{21} +0.813334 q^{22} -0.454313 q^{23} -2.79976 q^{24} +3.48453 q^{25} +4.37274 q^{26} -5.14786 q^{27} -0.947335 q^{28} -5.84889 q^{29} +8.15521 q^{30} +7.93897 q^{31} +1.00000 q^{32} -2.27714 q^{33} -3.08451 q^{34} +2.75942 q^{35} +4.83868 q^{36} +4.37451 q^{37} +1.10604 q^{38} -12.2426 q^{39} -2.91282 q^{40} -8.69577 q^{41} +2.65232 q^{42} -11.1663 q^{43} +0.813334 q^{44} -14.0942 q^{45} -0.454313 q^{46} -3.48913 q^{47} -2.79976 q^{48} -6.10256 q^{49} +3.48453 q^{50} +8.63590 q^{51} +4.37274 q^{52} -4.18987 q^{53} -5.14786 q^{54} -2.36910 q^{55} -0.947335 q^{56} -3.09665 q^{57} -5.84889 q^{58} -3.20587 q^{59} +8.15521 q^{60} +15.3151 q^{61} +7.93897 q^{62} -4.58385 q^{63} +1.00000 q^{64} -12.7370 q^{65} -2.27714 q^{66} -1.14745 q^{67} -3.08451 q^{68} +1.27197 q^{69} +2.75942 q^{70} +1.65385 q^{71} +4.83868 q^{72} +6.65252 q^{73} +4.37451 q^{74} -9.75585 q^{75} +1.10604 q^{76} -0.770500 q^{77} -12.2426 q^{78} -13.0537 q^{79} -2.91282 q^{80} -0.103238 q^{81} -8.69577 q^{82} +2.55888 q^{83} +2.65232 q^{84} +8.98463 q^{85} -11.1663 q^{86} +16.3755 q^{87} +0.813334 q^{88} +7.88994 q^{89} -14.0942 q^{90} -4.14245 q^{91} -0.454313 q^{92} -22.2272 q^{93} -3.48913 q^{94} -3.22170 q^{95} -2.79976 q^{96} +8.29553 q^{97} -6.10256 q^{98} +3.93546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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