LMFDB - Embedded newform 6026.2.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.27206 q^{3} +1.00000 q^{4} +0.0411842 q^{5} -2.27206 q^{6} +3.26699 q^{7} +1.00000 q^{8} +2.16224 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.27206 q^{3} +1.00000 q^{4} +0.0411842 q^{5} -2.27206 q^{6} +3.26699 q^{7} +1.00000 q^{8} +2.16224 q^{9} +0.0411842 q^{10} +5.60760 q^{11} -2.27206 q^{12} +4.95582 q^{13} +3.26699 q^{14} -0.0935730 q^{15} +1.00000 q^{16} -0.692963 q^{17} +2.16224 q^{18} +4.88774 q^{19} +0.0411842 q^{20} -7.42279 q^{21} +5.60760 q^{22} +1.00000 q^{23} -2.27206 q^{24} -4.99830 q^{25} +4.95582 q^{26} +1.90343 q^{27} +3.26699 q^{28} +5.50390 q^{29} -0.0935730 q^{30} +7.75676 q^{31} +1.00000 q^{32} -12.7408 q^{33} -0.692963 q^{34} +0.134549 q^{35} +2.16224 q^{36} +6.90837 q^{37} +4.88774 q^{38} -11.2599 q^{39} +0.0411842 q^{40} +6.69078 q^{41} -7.42279 q^{42} -12.3910 q^{43} +5.60760 q^{44} +0.0890504 q^{45} +1.00000 q^{46} -1.37213 q^{47} -2.27206 q^{48} +3.67323 q^{49} -4.99830 q^{50} +1.57445 q^{51} +4.95582 q^{52} -1.24615 q^{53} +1.90343 q^{54} +0.230945 q^{55} +3.26699 q^{56} -11.1052 q^{57} +5.50390 q^{58} +12.6008 q^{59} -0.0935730 q^{60} -7.76087 q^{61} +7.75676 q^{62} +7.06404 q^{63} +1.00000 q^{64} +0.204102 q^{65} -12.7408 q^{66} -7.78670 q^{67} -0.692963 q^{68} -2.27206 q^{69} +0.134549 q^{70} +10.8692 q^{71} +2.16224 q^{72} -16.0873 q^{73} +6.90837 q^{74} +11.3564 q^{75} +4.88774 q^{76} +18.3200 q^{77} -11.2599 q^{78} -7.18504 q^{79} +0.0411842 q^{80} -10.8114 q^{81} +6.69078 q^{82} -5.02632 q^{83} -7.42279 q^{84} -0.0285392 q^{85} -12.3910 q^{86} -12.5052 q^{87} +5.60760 q^{88} -13.1696 q^{89} +0.0890504 q^{90} +16.1906 q^{91} +1.00000 q^{92} -17.6238 q^{93} -1.37213 q^{94} +0.201298 q^{95} -2.27206 q^{96} -0.428640 q^{97} +3.67323 q^{98} +12.1250 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−2.27206	−1.31177	−0.655886	−	0.754860i	$-0.727705\pi$
$3$	−2.27206	−1.31177	−0.655886	+	0.754860i	$0.727705\pi$
$4$	1.00000	0.500000
$5$	0.0411842	0.0184182	0.00920908	−	0.999958i	$-0.497069\pi$
$5$	0.0411842	0.0184182	0.00920908	+	0.999958i	$0.497069\pi$
$6$	−2.27206	−0.927564
$7$	3.26699	1.23481	0.617403	−	0.786647i	$-0.288185\pi$
$7$	3.26699	1.23481	0.617403	+	0.786647i	$0.288185\pi$
$8$	1.00000	0.353553
$9$	2.16224	0.720748
$10$	0.0411842	0.0130236
$11$	5.60760	1.69075	0.845377	−	0.534170i	$-0.179376\pi$
$11$	5.60760	1.69075	0.845377	+	0.534170i	$0.179376\pi$
$12$	−2.27206	−0.655886
$13$	4.95582	1.37450	0.687249	−	0.726422i	$-0.258818\pi$
$13$	4.95582	1.37450	0.687249	+	0.726422i	$0.258818\pi$
$14$	3.26699	0.873140
$15$	−0.0935730	−0.0241604
$16$	1.00000	0.250000
$17$	−0.692963	−0.168068	−0.0840342	−	0.996463i	$-0.526780\pi$
$17$	−0.692963	−0.168068	−0.0840342	+	0.996463i	$0.526780\pi$
$18$	2.16224	0.509646
$19$	4.88774	1.12132	0.560662	−	0.828045i	$-0.310547\pi$
$19$	4.88774	1.12132	0.560662	+	0.828045i	$0.310547\pi$
$20$	0.0411842	0.00920908
$21$	−7.42279	−1.61979
$22$	5.60760	1.19554
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.27206	−0.463782
$25$	−4.99830	−0.999661
$26$	4.95582	0.971916
$27$	1.90343	0.366315
$28$	3.26699	0.617403
$29$	5.50390	1.02205	0.511024	−	0.859567i	$-0.329266\pi$
$29$	5.50390	1.02205	0.511024	+	0.859567i	$0.329266\pi$
$30$	−0.0935730	−0.0170840
$31$	7.75676	1.39315	0.696577	−	0.717482i	$-0.254705\pi$
$31$	7.75676	1.39315	0.696577	+	0.717482i	$0.254705\pi$
$32$	1.00000	0.176777
$33$	−12.7408	−2.21789
$34$	−0.692963	−0.118842
$35$	0.134549	0.0227429
$36$	2.16224	0.360374
$37$	6.90837	1.13573	0.567865	−	0.823122i	$-0.307770\pi$
$37$	6.90837	1.13573	0.567865	+	0.823122i	$0.307770\pi$
$38$	4.88774	0.792896
$39$	−11.2599	−1.80303
$40$	0.0411842	0.00651180
$41$	6.69078	1.04492	0.522462	−	0.852662i	$-0.325014\pi$
$41$	6.69078	1.04492	0.522462	+	0.852662i	$0.325014\pi$
$42$	−7.42279	−1.14536
$43$	−12.3910	−1.88961	−0.944803	−	0.327640i	$-0.893747\pi$
$43$	−12.3910	−1.88961	−0.944803	+	0.327640i	$0.893747\pi$
$44$	5.60760	0.845377
$45$	0.0890504	0.0132749
$46$	1.00000	0.147442
$47$	−1.37213	−0.200146	−0.100073	−	0.994980i	$-0.531908\pi$
$47$	−1.37213	−0.200146	−0.100073	+	0.994980i	$0.531908\pi$
$48$	−2.27206	−0.327943
$49$	3.67323	0.524748
$50$	−4.99830	−0.706867
$51$	1.57445	0.220467
$52$	4.95582	0.687249
$53$	−1.24615	−0.171172	−0.0855861	−	0.996331i	$-0.527276\pi$
$53$	−1.24615	−0.171172	−0.0855861	+	0.996331i	$0.527276\pi$
$54$	1.90343	0.259024
$55$	0.230945	0.0311406
$56$	3.26699	0.436570
$57$	−11.1052	−1.47092
$58$	5.50390	0.722697
$59$	12.6008	1.64049	0.820245	−	0.572012i	$-0.193837\pi$
$59$	12.6008	1.64049	0.820245	+	0.572012i	$0.193837\pi$
$60$	−0.0935730	−0.0120802
$61$	−7.76087	−0.993677	−0.496839	−	0.867843i	$-0.665506\pi$
$61$	−7.76087	−0.993677	−0.496839	+	0.867843i	$0.665506\pi$
$62$	7.75676	0.985109
$63$	7.06404	0.889985
$64$	1.00000	0.125000
$65$	0.204102	0.0253157
$66$	−12.7408	−1.56828
$67$	−7.78670	−0.951297	−0.475649	−	0.879635i	$-0.657787\pi$
$67$	−7.78670	−0.951297	−0.475649	+	0.879635i	$0.657787\pi$
$68$	−0.692963	−0.0840342
$69$	−2.27206	−0.273524
$70$	0.134549	0.0160816
$71$	10.8692	1.28994	0.644969	−	0.764209i	$-0.276870\pi$
$71$	10.8692	1.28994	0.644969	+	0.764209i	$0.276870\pi$
$72$	2.16224	0.254823
$73$	−16.0873	−1.88288	−0.941439	−	0.337183i	$-0.890526\pi$
$73$	−16.0873	−1.88288	−0.941439	+	0.337183i	$0.890526\pi$
$74$	6.90837	0.803082
$75$	11.3564	1.31133
$76$	4.88774	0.560662
$77$	18.3200	2.08775
$78$	−11.2599	−1.27493
$79$	−7.18504	−0.808380	−0.404190	−	0.914675i	$-0.632446\pi$
$79$	−7.18504	−0.808380	−0.404190	+	0.914675i	$0.632446\pi$
$80$	0.0411842	0.00460454
$81$	−10.8114	−1.20127
$82$	6.69078	0.738873
$83$	−5.02632	−0.551711	−0.275855	−	0.961199i	$-0.588961\pi$
$83$	−5.02632	−0.551711	−0.275855	+	0.961199i	$0.588961\pi$
$84$	−7.42279	−0.809893
$85$	−0.0285392	−0.00309551
$86$	−12.3910	−1.33615
$87$	−12.5052	−1.34069
$88$	5.60760	0.597772
$89$	−13.1696	−1.39598	−0.697988	−	0.716109i	$-0.745921\pi$
$89$	−13.1696	−1.39598	−0.697988	+	0.716109i	$0.745921\pi$
$90$	0.0890504	0.00938674
$91$	16.1906	1.69724
$92$	1.00000	0.104257
$93$	−17.6238	−1.82750
$94$	−1.37213	−0.141525
$95$	0.201298	0.0206527
$96$	−2.27206	−0.231891
$97$	−0.428640	−0.0435218	−0.0217609	−	0.999763i	$-0.506927\pi$
$97$	−0.428640	−0.0435218	−0.0217609	+	0.999763i	$0.506927\pi$
$98$	3.67323	0.371053
$99$	12.1250	1.21861
$100$	−4.99830	−0.499830
$101$	−0.0932263	−0.00927636	−0.00463818	−	0.999989i	$-0.501476\pi$
$101$	−0.0932263	−0.00927636	−0.00463818	+	0.999989i	$0.501476\pi$
$102$	1.57445	0.155894
$103$	−10.2171	−1.00672	−0.503359	−	0.864077i	$-0.667903\pi$
$103$	−10.2171	−1.00672	−0.503359	+	0.864077i	$0.667903\pi$
$104$	4.95582	0.485958
$105$	−0.305702	−0.0298335
$106$	−1.24615	−0.121037
$107$	−7.41644	−0.716974	−0.358487	−	0.933535i	$-0.616707\pi$
$107$	−7.41644	−0.716974	−0.358487	+	0.933535i	$0.616707\pi$
$108$	1.90343	0.183157
$109$	−12.9382	−1.23926	−0.619628	−	0.784896i	$-0.712717\pi$
$109$	−12.9382	−1.23926	−0.619628	+	0.784896i	$0.712717\pi$
$110$	0.230945	0.0220197
$111$	−15.6962	−1.48982
$112$	3.26699	0.308702
$113$	−4.10724	−0.386377	−0.193189	−	0.981162i	$-0.561883\pi$
$113$	−4.10724	−0.386377	−0.193189	+	0.981162i	$0.561883\pi$
$114$	−11.1052	−1.04010
$115$	0.0411842	0.00384045
$116$	5.50390	0.511024
$117$	10.7157	0.990666
$118$	12.6008	1.16000
$119$	−2.26391	−0.207532
$120$	−0.0935730	−0.00854200
$121$	20.4451	1.85865
$122$	−7.76087	−0.702636
$123$	−15.2018	−1.37070
$124$	7.75676	0.696577
$125$	−0.411773	−0.0368301
$126$	7.06404	0.629314
$127$	1.94807	0.172863	0.0864316	−	0.996258i	$-0.472454\pi$
$127$	1.94807	0.172863	0.0864316	+	0.996258i	$0.472454\pi$
$128$	1.00000	0.0883883
$129$	28.1530	2.47873
$130$	0.204102	0.0179009
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−12.7408	−1.10894
$133$	15.9682	1.38462
$134$	−7.78670	−0.672669
$135$	0.0783912	0.00674684
$136$	−0.692963	−0.0594211
$137$	−6.33271	−0.541040	−0.270520	−	0.962714i	$-0.587196\pi$
$137$	−6.33271	−0.541040	−0.270520	+	0.962714i	$0.587196\pi$
$138$	−2.27206	−0.193410
$139$	−3.42341	−0.290370	−0.145185	−	0.989405i	$-0.546378\pi$
$139$	−3.42341	−0.290370	−0.145185	+	0.989405i	$0.546378\pi$
$140$	0.134549	0.0113714
$141$	3.11756	0.262546
$142$	10.8692	0.912124
$143$	27.7902	2.32394
$144$	2.16224	0.180187
$145$	0.226674	0.0188242
$146$	−16.0873	−1.33140
$147$	−8.34580	−0.688350
$148$	6.90837	0.567865
$149$	4.66957	0.382546	0.191273	−	0.981537i	$-0.438738\pi$
$149$	4.66957	0.382546	0.191273	+	0.981537i	$0.438738\pi$
$150$	11.3564	0.927249
$151$	−4.09387	−0.333154	−0.166577	−	0.986028i	$-0.553271\pi$
$151$	−4.09387	−0.333154	−0.166577	+	0.986028i	$0.553271\pi$
$152$	4.88774	0.396448
$153$	−1.49836	−0.121135
$154$	18.3200	1.47627
$155$	0.319456	0.0256593
$156$	−11.2599	−0.901514
$157$	5.18726	0.413989	0.206994	−	0.978342i	$-0.433632\pi$
$157$	5.18726	0.413989	0.206994	+	0.978342i	$0.433632\pi$
$158$	−7.18504	−0.571611
$159$	2.83133	0.224539
$160$	0.0411842	0.00325590
$161$	3.26699	0.257475
$162$	−10.8114	−0.849426
$163$	22.8242	1.78773	0.893866	−	0.448334i	$-0.147982\pi$
$163$	22.8242	1.78773	0.893866	+	0.448334i	$0.147982\pi$
$164$	6.69078	0.522462
$165$	−0.524719	−0.0408493
$166$	−5.02632	−0.390118
$167$	−22.8737	−1.77002	−0.885009	−	0.465573i	$-0.845848\pi$
$167$	−22.8737	−1.77002	−0.885009	+	0.465573i	$0.845848\pi$
$168$	−7.42279	−0.572681
$169$	11.5601	0.889242
$170$	−0.0285392	−0.00218885
$171$	10.5685	0.808193
$172$	−12.3910	−0.944803
$173$	−12.4924	−0.949780	−0.474890	−	0.880045i	$-0.657512\pi$
$173$	−12.4924	−0.949780	−0.474890	+	0.880045i	$0.657512\pi$
$174$	−12.5052	−0.948014
$175$	−16.3294	−1.23439
$176$	5.60760	0.422688
$177$	−28.6299	−2.15195
$178$	−13.1696	−0.987105
$179$	3.04827	0.227839	0.113919	−	0.993490i	$-0.463659\pi$
$179$	3.04827	0.227839	0.113919	+	0.993490i	$0.463659\pi$
$180$	0.0890504	0.00663743
$181$	−9.23172	−0.686188	−0.343094	−	0.939301i	$-0.611475\pi$
$181$	−9.23172	−0.686188	−0.343094	+	0.939301i	$0.611475\pi$
$182$	16.1906	1.20013
$183$	17.6331	1.30348
$184$	1.00000	0.0737210
$185$	0.284516	0.0209180
$186$	−17.6238	−1.29224
$187$	−3.88586	−0.284162
$188$	−1.37213	−0.100073
$189$	6.21848	0.452328
$190$	0.201298	0.0146037
$191$	−25.1166	−1.81738	−0.908688	−	0.417476i	$-0.862915\pi$
$191$	−25.1166	−1.81738	−0.908688	+	0.417476i	$0.862915\pi$
$192$	−2.27206	−0.163972
$193$	19.6289	1.41292	0.706460	−	0.707753i	$-0.250291\pi$
$193$	19.6289	1.41292	0.706460	+	0.707753i	$0.250291\pi$
$194$	−0.428640	−0.0307746
$195$	−0.463731	−0.0332084
$196$	3.67323	0.262374
$197$	11.5286	0.821380	0.410690	−	0.911775i	$-0.365288\pi$
$197$	11.5286	0.821380	0.410690	+	0.911775i	$0.365288\pi$
$198$	12.1250	0.861686
$199$	18.8782	1.33824	0.669120	−	0.743154i	$-0.266671\pi$
$199$	18.8782	1.33824	0.669120	+	0.743154i	$0.266671\pi$
$200$	−4.99830	−0.353433
$201$	17.6918	1.24789
$202$	−0.0932263	−0.00655938
$203$	17.9812	1.26203
$204$	1.57445	0.110234
$205$	0.275555	0.0192456
$206$	−10.2171	−0.711858
$207$	2.16224	0.150286
$208$	4.95582	0.343624
$209$	27.4085	1.89588
$210$	−0.305702	−0.0210954
$211$	13.4870	0.928483	0.464242	−	0.885709i	$-0.346327\pi$
$211$	13.4870	0.928483	0.464242	+	0.885709i	$0.346327\pi$
$212$	−1.24615	−0.0855861
$213$	−24.6955	−1.69211
$214$	−7.41644	−0.506977
$215$	−0.510313	−0.0348030
$216$	1.90343	0.129512
$217$	25.3413	1.72028
$218$	−12.9382	−0.876286
$219$	36.5513	2.46991
$220$	0.230945	0.0155703
$221$	−3.43420	−0.231009
$222$	−15.6962	−1.05346
$223$	2.90322	0.194414	0.0972071	−	0.995264i	$-0.469009\pi$
$223$	2.90322	0.194414	0.0972071	+	0.995264i	$0.469009\pi$
$224$	3.26699	0.218285
$225$	−10.8076	−0.720504
$226$	−4.10724	−0.273210
$227$	−16.1030	−1.06879	−0.534396	−	0.845234i	$-0.679461\pi$
$227$	−16.1030	−1.06879	−0.534396	+	0.845234i	$0.679461\pi$
$228$	−11.1052	−0.735462
$229$	12.4693	0.823995	0.411997	−	0.911185i	$-0.364831\pi$
$229$	12.4693	0.823995	0.411997	+	0.911185i	$0.364831\pi$
$230$	0.0411842	0.00271561
$231$	−41.6240	−2.73866
$232$	5.50390	0.361348
$233$	−16.2733	−1.06610	−0.533051	−	0.846083i	$-0.678955\pi$
$233$	−16.2733	−1.06610	−0.533051	+	0.846083i	$0.678955\pi$
$234$	10.7157	0.700507
$235$	−0.0565102	−0.00368632
$236$	12.6008	0.820245
$237$	16.3248	1.06041
$238$	−2.26391	−0.146747
$239$	−20.7688	−1.34342	−0.671712	−	0.740812i	$-0.734441\pi$
$239$	−20.7688	−1.34342	−0.671712	+	0.740812i	$0.734441\pi$
$240$	−0.0935730	−0.00604011
$241$	25.9457	1.67131	0.835655	−	0.549255i	$-0.185089\pi$
$241$	25.9457	1.67131	0.835655	+	0.549255i	$0.185089\pi$
$242$	20.4451	1.31426
$243$	18.8539	1.20948
$244$	−7.76087	−0.496839
$245$	0.151279	0.00966488
$246$	−15.2018	−0.969234
$247$	24.2228	1.54126
$248$	7.75676	0.492555
$249$	11.4201	0.723719
$250$	−0.411773	−0.0260428
$251$	−11.6556	−0.735693	−0.367846	−	0.929887i	$-0.619905\pi$
$251$	−11.6556	−0.735693	−0.367846	+	0.929887i	$0.619905\pi$
$252$	7.06404	0.444992
$253$	5.60760	0.352547
$254$	1.94807	0.122233
$255$	0.0648426	0.00406060
$256$	1.00000	0.0625000
$257$	−21.6195	−1.34859	−0.674295	−	0.738462i	$-0.735552\pi$
$257$	−21.6195	−1.34859	−0.674295	+	0.738462i	$0.735552\pi$
$258$	28.1530	1.75273
$259$	22.5696	1.40241
$260$	0.204102	0.0126578
$261$	11.9008	0.736639
$262$	1.00000	0.0617802
$263$	19.9579	1.23066	0.615329	−	0.788271i	$-0.289023\pi$
$263$	19.9579	1.23066	0.615329	+	0.788271i	$0.289023\pi$
$264$	−12.7408	−0.784141
$265$	−0.0513218	−0.00315267
$266$	15.9682	0.979074
$267$	29.9221	1.83120
$268$	−7.78670	−0.475649
$269$	9.81517	0.598441	0.299221	−	0.954184i	$-0.403273\pi$
$269$	9.81517	0.598441	0.299221	+	0.954184i	$0.403273\pi$
$270$	0.0783912	0.00477074
$271$	−13.3579	−0.811436	−0.405718	−	0.913998i	$-0.632979\pi$
$271$	−13.3579	−0.811436	−0.405718	+	0.913998i	$0.632979\pi$
$272$	−0.692963	−0.0420171
$273$	−36.7860	−2.22639
$274$	−6.33271	−0.382573
$275$	−28.0285	−1.69018
$276$	−2.27206	−0.136762
$277$	9.31197	0.559502	0.279751	−	0.960073i	$-0.409748\pi$
$277$	9.31197	0.559502	0.279751	+	0.960073i	$0.409748\pi$
$278$	−3.42341	−0.205322
$279$	16.7720	1.00411
$280$	0.134549	0.00804081
$281$	18.7421	1.11806	0.559030	−	0.829147i	$-0.311174\pi$
$281$	18.7421	1.11806	0.559030	+	0.829147i	$0.311174\pi$
$282$	3.11756	0.185648
$283$	−18.0600	−1.07356	−0.536779	−	0.843723i	$-0.680359\pi$
$283$	−18.0600	−1.07356	−0.536779	+	0.843723i	$0.680359\pi$
$284$	10.8692	0.644969
$285$	−0.457360	−0.0270917
$286$	27.7902	1.64327
$287$	21.8587	1.29028
$288$	2.16224	0.127412
$289$	−16.5198	−0.971753
$290$	0.226674	0.0133107
$291$	0.973895	0.0570907
$292$	−16.0873	−0.941439
$293$	−10.8752	−0.635335	−0.317668	−	0.948202i	$-0.602900\pi$
$293$	−10.8752	−0.635335	−0.317668	+	0.948202i	$0.602900\pi$
$294$	−8.34580	−0.486737
$295$	0.518956	0.0302148
$296$	6.90837	0.401541
$297$	10.6737	0.619348
$298$	4.66957	0.270501
$299$	4.95582	0.286602
$300$	11.3564	0.655664
$301$	−40.4812	−2.33330
$302$	−4.09387	−0.235576
$303$	0.211815	0.0121685
$304$	4.88774	0.280331
$305$	−0.319625	−0.0183017
$306$	−1.49836	−0.0856554
$307$	30.8191	1.75894	0.879469	−	0.475955i	$-0.157898\pi$
$307$	30.8191	1.75894	0.879469	+	0.475955i	$0.157898\pi$
$308$	18.3200	1.04388
$309$	23.2138	1.32059
$310$	0.319456	0.0181439
$311$	14.1611	0.803000	0.401500	−	0.915859i	$-0.368489\pi$
$311$	14.1611	0.803000	0.401500	+	0.915859i	$0.368489\pi$
$312$	−11.2599	−0.637467
$313$	14.9731	0.846332	0.423166	−	0.906052i	$-0.360919\pi$
$313$	14.9731	0.846332	0.423166	+	0.906052i	$0.360919\pi$
$314$	5.18726	0.292734
$315$	0.290927	0.0163919
$316$	−7.18504	−0.404190
$317$	21.8806	1.22894	0.614469	−	0.788941i	$-0.289370\pi$
$317$	21.8806	1.22894	0.614469	+	0.788941i	$0.289370\pi$
$318$	2.83133	0.158773
$319$	30.8636	1.72803
$320$	0.0411842	0.00230227
$321$	16.8506	0.940507
$322$	3.26699	0.182062
$323$	−3.38703	−0.188459
$324$	−10.8114	−0.600635
$325$	−24.7707	−1.37403
$326$	22.8242	1.26412
$327$	29.3964	1.62562
$328$	6.69078	0.369437
$329$	−4.48274	−0.247142
$330$	−0.524719	−0.0288848
$331$	32.1522	1.76724	0.883622	−	0.468201i	$-0.155098\pi$
$331$	32.1522	1.76724	0.883622	+	0.468201i	$0.155098\pi$
$332$	−5.02632	−0.275855
$333$	14.9376	0.818575
$334$	−22.8737	−1.25159
$335$	−0.320689	−0.0175211
$336$	−7.42279	−0.404947
$337$	26.1456	1.42424	0.712120	−	0.702057i	$-0.247735\pi$
$337$	26.1456	1.42424	0.712120	+	0.702057i	$0.247735\pi$
$338$	11.5601	0.628789
$339$	9.33189	0.506839
$340$	−0.0285392	−0.00154775
$341$	43.4968	2.35548
$342$	10.5685	0.571479
$343$	−10.8685	−0.586845
$344$	−12.3910	−0.668076
$345$	−0.0935730	−0.00503780
$346$	−12.4924	−0.671596
$347$	−18.3954	−0.987516	−0.493758	−	0.869599i	$-0.664377\pi$
$347$	−18.3954	−0.987516	−0.493758	+	0.869599i	$0.664377\pi$
$348$	−12.5052	−0.670347
$349$	−10.2983	−0.551257	−0.275629	−	0.961264i	$-0.588886\pi$
$349$	−10.2983	−0.551257	−0.275629	+	0.961264i	$0.588886\pi$
$350$	−16.3294	−0.872844
$351$	9.43304	0.503499
$352$	5.60760	0.298886
$353$	−21.4410	−1.14119	−0.570594	−	0.821232i	$-0.693287\pi$
$353$	−21.4410	−1.14119	−0.570594	+	0.821232i	$0.693287\pi$
$354$	−28.6299	−1.52166
$355$	0.447640	0.0237583
$356$	−13.1696	−0.697988
$357$	5.14372	0.272235
$358$	3.04827	0.161106
$359$	−4.29892	−0.226888	−0.113444	−	0.993544i	$-0.536188\pi$
$359$	−4.29892	−0.226888	−0.113444	+	0.993544i	$0.536188\pi$
$360$	0.0890504	0.00469337
$361$	4.89001	0.257369
$362$	−9.23172	−0.485208
$363$	−46.4525	−2.43812
$364$	16.1906	0.848619
$365$	−0.662544	−0.0346791
$366$	17.6331	0.921699
$367$	−27.8006	−1.45118	−0.725591	−	0.688126i	$-0.758433\pi$
$367$	−27.8006	−1.45118	−0.725591	+	0.688126i	$0.758433\pi$
$368$	1.00000	0.0521286
$369$	14.4671	0.753127
$370$	0.284516	0.0147913
$371$	−4.07117	−0.211364
$372$	−17.6238	−0.913751
$373$	−21.6354	−1.12024	−0.560120	−	0.828412i	$-0.689245\pi$
$373$	−21.6354	−1.12024	−0.560120	+	0.828412i	$0.689245\pi$
$374$	−3.88586	−0.200933
$375$	0.935571	0.0483127
$376$	−1.37213	−0.0707623
$377$	27.2763	1.40480
$378$	6.21848	0.319844
$379$	35.7258	1.83511	0.917555	−	0.397609i	$-0.130160\pi$
$379$	35.7258	1.83511	0.917555	+	0.397609i	$0.130160\pi$
$380$	0.201298	0.0103264
$381$	−4.42613	−0.226757
$382$	−25.1166	−1.28508
$383$	−28.2499	−1.44350	−0.721751	−	0.692153i	$-0.756662\pi$
$383$	−28.2499	−1.44350	−0.721751	+	0.692153i	$0.756662\pi$
$384$	−2.27206	−0.115945
$385$	0.754494	0.0384526
$386$	19.6289	0.999086
$387$	−26.7923	−1.36193
$388$	−0.428640	−0.0217609
$389$	−32.9944	−1.67288	−0.836441	−	0.548057i	$-0.815368\pi$
$389$	−32.9944	−1.67288	−0.836441	+	0.548057i	$0.815368\pi$
$390$	−0.463731	−0.0234819
$391$	−0.692963	−0.0350447
$392$	3.67323	0.185526
$393$	−2.27206	−0.114610
$394$	11.5286	0.580803
$395$	−0.295910	−0.0148889
$396$	12.1250	0.609304
$397$	27.2865	1.36947	0.684736	−	0.728791i	$-0.259918\pi$
$397$	27.2865	1.36947	0.684736	+	0.728791i	$0.259918\pi$
$398$	18.8782	0.946279
$399$	−36.2807	−1.81631
$400$	−4.99830	−0.249915
$401$	1.59442	0.0796213	0.0398107	−	0.999207i	$-0.487325\pi$
$401$	1.59442	0.0796213	0.0398107	+	0.999207i	$0.487325\pi$
$402$	17.6918	0.882388
$403$	38.4411	1.91489
$404$	−0.0932263	−0.00463818
$405$	−0.445261	−0.0221252
$406$	17.9812	0.892391
$407$	38.7394	1.92024
$408$	1.57445	0.0779470
$409$	−26.2169	−1.29634	−0.648171	−	0.761495i	$-0.724466\pi$
$409$	−26.2169	−1.29634	−0.648171	+	0.761495i	$0.724466\pi$
$410$	0.275555	0.0136087
$411$	14.3883	0.709721
$412$	−10.2171	−0.503359
$413$	41.1669	2.02569
$414$	2.16224	0.106269
$415$	−0.207005	−0.0101615
$416$	4.95582	0.242979
$417$	7.77818	0.380899
$418$	27.4085	1.34059
$419$	−14.1205	−0.689833	−0.344916	−	0.938633i	$-0.612093\pi$
$419$	−14.1205	−0.689833	−0.344916	+	0.938633i	$0.612093\pi$
$420$	−0.305702	−0.0149167
$421$	14.1993	0.692030	0.346015	−	0.938229i	$-0.387535\pi$
$421$	14.1993	0.692030	0.346015	+	0.938229i	$0.387535\pi$
$422$	13.4870	0.656537
$423$	−2.96688	−0.144255
$424$	−1.24615	−0.0605185
$425$	3.46364	0.168011
$426$	−24.6955	−1.19650
$427$	−25.3547	−1.22700
$428$	−7.41644	−0.358487
$429$	−63.1410	−3.04848
$430$	−0.510313	−0.0246095
$431$	17.5767	0.846640	0.423320	−	0.905980i	$-0.360865\pi$
$431$	17.5767	0.846640	0.423320	+	0.905980i	$0.360865\pi$
$432$	1.90343	0.0915787
$433$	−18.6081	−0.894248	−0.447124	−	0.894472i	$-0.647552\pi$
$433$	−18.6081	−0.894248	−0.447124	+	0.894472i	$0.647552\pi$
$434$	25.3413	1.21642
$435$	−0.515016	−0.0246931
$436$	−12.9382	−0.619628
$437$	4.88774	0.233812
$438$	36.5513	1.74649
$439$	−28.0542	−1.33895	−0.669477	−	0.742832i	$-0.733482\pi$
$439$	−28.0542	−1.33895	−0.669477	+	0.742832i	$0.733482\pi$
$440$	0.230945	0.0110099
$441$	7.94243	0.378211
$442$	−3.43420	−0.163348
$443$	−29.4578	−1.39958	−0.699792	−	0.714346i	$-0.746724\pi$
$443$	−29.4578	−1.39958	−0.699792	+	0.714346i	$0.746724\pi$
$444$	−15.6962	−0.744910
$445$	−0.542381	−0.0257113
$446$	2.90322	0.137472
$447$	−10.6095	−0.501814
$448$	3.26699	0.154351
$449$	32.5868	1.53786	0.768932	−	0.639330i	$-0.220788\pi$
$449$	32.5868	1.53786	0.768932	+	0.639330i	$0.220788\pi$
$450$	−10.8076	−0.509473
$451$	37.5192	1.76671
$452$	−4.10724	−0.193189
$453$	9.30150	0.437023
$454$	−16.1030	−0.755750
$455$	0.666798	0.0312600
$456$	−11.1052	−0.520050
$457$	31.2988	1.46410	0.732048	−	0.681253i	$-0.238564\pi$
$457$	31.2988	1.46410	0.732048	+	0.681253i	$0.238564\pi$
$458$	12.4693	0.582652
$459$	−1.31901	−0.0615659
$460$	0.0411842	0.00192022
$461$	−26.4961	−1.23405	−0.617024	−	0.786944i	$-0.711662\pi$
$461$	−26.4961	−1.23405	−0.617024	+	0.786944i	$0.711662\pi$
$462$	−41.6240	−1.93652
$463$	−9.68480	−0.450091	−0.225045	−	0.974348i	$-0.572253\pi$
$463$	−9.68480	−0.450091	−0.225045	+	0.974348i	$0.572253\pi$
$464$	5.50390	0.255512
$465$	−0.725823	−0.0336592
$466$	−16.2733	−0.753848
$467$	−30.3936	−1.40645	−0.703225	−	0.710967i	$-0.748257\pi$
$467$	−30.3936	−1.40645	−0.703225	+	0.710967i	$0.748257\pi$
$468$	10.7157	0.495333
$469$	−25.4391	−1.17467
$470$	−0.0565102	−0.00260662
$471$	−11.7858	−0.543059
$472$	12.6008	0.580001
$473$	−69.4836	−3.19486
$474$	16.3248	0.749824
$475$	−24.4304	−1.12094
$476$	−2.26391	−0.103766
$477$	−2.69449	−0.123372
$478$	−20.7688	−0.949944
$479$	−9.02771	−0.412487	−0.206243	−	0.978501i	$-0.566124\pi$
$479$	−9.02771	−0.412487	−0.206243	+	0.978501i	$0.566124\pi$
$480$	−0.0935730	−0.00427100
$481$	34.2366	1.56106
$482$	25.9457	1.18179
$483$	−7.42279	−0.337749
$484$	20.4451	0.929324
$485$	−0.0176532	−0.000801591 0
$486$	18.8539	0.855231
$487$	−0.0174484	−0.000790664 0	−0.000395332	−	1.00000i	$-0.500126\pi$
$487$	−0.0174484	−0.000790664 0	−0.000395332		1.00000i	$0.500126\pi$
$488$	−7.76087	−0.351318
$489$	−51.8580	−2.34510
$490$	0.151279	0.00683410
$491$	−24.3487	−1.09884	−0.549421	−	0.835546i	$-0.685152\pi$
$491$	−24.3487	−1.09884	−0.549421	+	0.835546i	$0.685152\pi$
$492$	−15.2018	−0.685352
$493$	−3.81400	−0.171774
$494$	24.2228	1.08983
$495$	0.499359	0.0224445
$496$	7.75676	0.348289
$497$	35.5096	1.59282
$498$	11.4201	0.511747
$499$	10.8199	0.484364	0.242182	−	0.970231i	$-0.422137\pi$
$499$	10.8199	0.484364	0.242182	+	0.970231i	$0.422137\pi$
$500$	−0.411773	−0.0184150
$501$	51.9703	2.32186
$502$	−11.6556	−0.520213
$503$	16.3496	0.728994	0.364497	−	0.931205i	$-0.381241\pi$
$503$	16.3496	0.728994	0.364497	+	0.931205i	$0.381241\pi$
$504$	7.06404	0.314657
$505$	−0.00383945	−0.000170853 0
$506$	5.60760	0.249288
$507$	−26.2653	−1.16648
$508$	1.94807	0.0864316
$509$	−1.83763	−0.0814514	−0.0407257	−	0.999170i	$-0.512967\pi$
$509$	−1.83763	−0.0814514	−0.0407257	+	0.999170i	$0.512967\pi$
$510$	0.0648426	0.00287128
$511$	−52.5571	−2.32499
$512$	1.00000	0.0441942
$513$	9.30346	0.410758
$514$	−21.6195	−0.953597
$515$	−0.420783	−0.0185419
$516$	28.1530	1.23937
$517$	−7.69436	−0.338398
$518$	22.5696	0.991651
$519$	28.3835	1.24590
$520$	0.204102	0.00895045
$521$	−5.05755	−0.221576	−0.110788	−	0.993844i	$-0.535337\pi$
$521$	−5.05755	−0.221576	−0.110788	+	0.993844i	$0.535337\pi$
$522$	11.9008	0.520883
$523$	−33.5105	−1.46531	−0.732656	−	0.680599i	$-0.761720\pi$
$523$	−33.5105	−1.46531	−0.732656	+	0.680599i	$0.761720\pi$
$524$	1.00000	0.0436852
$525$	37.1014	1.61924
$526$	19.9579	0.870206
$527$	−5.37515	−0.234145
$528$	−12.7408	−0.554471
$529$	1.00000	0.0434783
$530$	−0.0513218	−0.00222928
$531$	27.2461	1.18238
$532$	15.9682	0.692310
$533$	33.1583	1.43625
$534$	29.9221	1.29486
$535$	−0.305440	−0.0132053
$536$	−7.78670	−0.336334
$537$	−6.92585	−0.298872
$538$	9.81517	0.423162
$539$	20.5980	0.887219
$540$	0.0783912	0.00337342
$541$	24.1964	1.04028	0.520142	−	0.854080i	$-0.325879\pi$
$541$	24.1964	1.04028	0.520142	+	0.854080i	$0.325879\pi$
$542$	−13.3579	−0.573772
$543$	20.9750	0.900123
$544$	−0.692963	−0.0297106
$545$	−0.532850	−0.0228248
$546$	−36.7860	−1.57430
$547$	−30.8785	−1.32027	−0.660134	−	0.751148i	$-0.729500\pi$
$547$	−30.8785	−1.32027	−0.660134	+	0.751148i	$0.729500\pi$
$548$	−6.33271	−0.270520
$549$	−16.7809	−0.716191
$550$	−28.0285	−1.19514
$551$	26.9016	1.14605
$552$	−2.27206	−0.0967052
$553$	−23.4735	−0.998193
$554$	9.31197	0.395628
$555$	−0.646437	−0.0274397
$556$	−3.42341	−0.145185
$557$	−6.08711	−0.257919	−0.128960	−	0.991650i	$-0.541164\pi$
$557$	−6.08711	−0.257919	−0.128960	+	0.991650i	$0.541164\pi$
$558$	16.7720	0.710016
$559$	−61.4074	−2.59726
$560$	0.134549	0.00568571
$561$	8.82890	0.372756
$562$	18.7421	0.790588
$563$	−3.22590	−0.135955	−0.0679777	−	0.997687i	$-0.521655\pi$
$563$	−3.22590	−0.135955	−0.0679777	+	0.997687i	$0.521655\pi$
$564$	3.11756	0.131273
$565$	−0.169154	−0.00711635
$566$	−18.0600	−0.759119
$567$	−35.3209	−1.48334
$568$	10.8692	0.456062
$569$	26.3676	1.10539	0.552694	−	0.833384i	$-0.313600\pi$
$569$	26.3676	1.10539	0.552694	+	0.833384i	$0.313600\pi$
$570$	−0.457360	−0.0191567
$571$	−23.1586	−0.969156	−0.484578	−	0.874748i	$-0.661027\pi$
$571$	−23.1586	−0.969156	−0.484578	+	0.874748i	$0.661027\pi$
$572$	27.7902	1.16197
$573$	57.0664	2.38398
$574$	21.8587	0.912365
$575$	−4.99830	−0.208444
$576$	2.16224	0.0900935
$577$	12.7006	0.528732	0.264366	−	0.964422i	$-0.414837\pi$
$577$	12.7006	0.528732	0.264366	+	0.964422i	$0.414837\pi$
$578$	−16.5198	−0.687133
$579$	−44.5980	−1.85343
$580$	0.226674	0.00941211
$581$	−16.4210	−0.681256
$582$	0.973895	0.0403692
$583$	−6.98792	−0.289410
$584$	−16.0873	−0.665698
$585$	0.441318	0.0182462
$586$	−10.8752	−0.449250
$587$	6.45479	0.266418	0.133209	−	0.991088i	$-0.457472\pi$
$587$	6.45479	0.266418	0.133209	+	0.991088i	$0.457472\pi$
$588$	−8.34580	−0.344175
$589$	37.9130	1.56218
$590$	0.518956	0.0213651
$591$	−26.1937	−1.07746
$592$	6.90837	0.283932
$593$	19.3627	0.795131	0.397565	−	0.917574i	$-0.369855\pi$
$593$	19.3627	0.795131	0.397565	+	0.917574i	$0.369855\pi$
$594$	10.6737	0.437945
$595$	−0.0932372	−0.00382235
$596$	4.66957	0.191273
$597$	−42.8924	−1.75547
$598$	4.95582	0.202659
$599$	−17.7223	−0.724112	−0.362056	−	0.932156i	$-0.617925\pi$
$599$	−17.7223	−0.724112	−0.362056	+	0.932156i	$0.617925\pi$
$600$	11.3564	0.463624
$601$	11.8665	0.484043	0.242021	−	0.970271i	$-0.422190\pi$
$601$	11.8665	0.484043	0.242021	+	0.970271i	$0.422190\pi$
$602$	−40.4812	−1.64989
$603$	−16.8368	−0.685646
$604$	−4.09387	−0.166577
$605$	0.842017	0.0342329
$606$	0.211815	0.00860441
$607$	28.9949	1.17687	0.588434	−	0.808545i	$-0.299745\pi$
$607$	28.9949	1.17687	0.588434	+	0.808545i	$0.299745\pi$
$608$	4.88774	0.198224
$609$	−40.8543	−1.65550
$610$	−0.319625	−0.0129413
$611$	−6.80004	−0.275100
$612$	−1.49836	−0.0605675
$613$	33.7932	1.36489	0.682446	−	0.730936i	$-0.260916\pi$
$613$	33.7932	1.36489	0.682446	+	0.730936i	$0.260916\pi$
$614$	30.8191	1.24376
$615$	−0.626076	−0.0252458
$616$	18.3200	0.738133
$617$	23.1033	0.930105	0.465053	−	0.885283i	$-0.346035\pi$
$617$	23.1033	0.930105	0.465053	+	0.885283i	$0.346035\pi$
$618$	23.2138	0.933796
$619$	−35.8363	−1.44038	−0.720191	−	0.693776i	$-0.755946\pi$
$619$	−35.8363	−1.44038	−0.720191	+	0.693776i	$0.755946\pi$
$620$	0.319456	0.0128297
$621$	1.90343	0.0763819
$622$	14.1611	0.567807
$623$	−43.0250	−1.72376
$624$	−11.2599	−0.450757
$625$	24.9746	0.998982
$626$	14.9731	0.598447
$627$	−62.2736	−2.48697
$628$	5.18726	0.206994
$629$	−4.78725	−0.190880
$630$	0.290927	0.0115908
$631$	−3.99677	−0.159109	−0.0795545	−	0.996831i	$-0.525350\pi$
$631$	−3.99677	−0.159109	−0.0795545	+	0.996831i	$0.525350\pi$
$632$	−7.18504	−0.285805
$633$	−30.6432	−1.21796
$634$	21.8806	0.868991
$635$	0.0802298	0.00318382
$636$	2.83133	0.112269
$637$	18.2039	0.721264
$638$	30.8636	1.22190
$639$	23.5019	0.929720
$640$	0.0411842	0.00162795
$641$	6.14552	0.242733	0.121367	−	0.992608i	$-0.461272\pi$
$641$	6.14552	0.242733	0.121367	+	0.992608i	$0.461272\pi$
$642$	16.8506	0.665039
$643$	−4.19193	−0.165314	−0.0826569	−	0.996578i	$-0.526341\pi$
$643$	−4.19193	−0.165314	−0.0826569	+	0.996578i	$0.526341\pi$
$644$	3.26699	0.128738
$645$	1.15946	0.0456537
$646$	−3.38703	−0.133261
$647$	16.6343	0.653961	0.326980	−	0.945031i	$-0.393969\pi$
$647$	16.6343	0.653961	0.326980	+	0.945031i	$0.393969\pi$
$648$	−10.8114	−0.424713
$649$	70.6605	2.77367
$650$	−24.7707	−0.971586
$651$	−57.5768	−2.25661
$652$	22.8242	0.893866
$653$	−39.2258	−1.53502	−0.767512	−	0.641035i	$-0.778505\pi$
$653$	−39.2258	−1.53502	−0.767512	+	0.641035i	$0.778505\pi$
$654$	29.3964	1.14949
$655$	0.0411842	0.00160920
$656$	6.69078	0.261231
$657$	−34.7847	−1.35708
$658$	−4.48274	−0.174755
$659$	−44.8903	−1.74868	−0.874338	−	0.485317i	$-0.838704\pi$
$659$	−44.8903	−1.74868	−0.874338	+	0.485317i	$0.838704\pi$
$660$	−0.524719	−0.0204247
$661$	21.5496	0.838180	0.419090	−	0.907945i	$-0.362349\pi$
$661$	21.5496	0.838180	0.419090	+	0.907945i	$0.362349\pi$
$662$	32.1522	1.24963
$663$	7.80270	0.303032
$664$	−5.02632	−0.195059
$665$	0.657638	0.0255021
$666$	14.9376	0.578820
$667$	5.50390	0.213112
$668$	−22.8737	−0.885009
$669$	−6.59629	−0.255027
$670$	−0.320689	−0.0123893
$671$	−43.5198	−1.68006
$672$	−7.42279	−0.286340
$673$	40.7811	1.57200	0.785998	−	0.618229i	$-0.212149\pi$
$673$	40.7811	1.57200	0.785998	+	0.618229i	$0.212149\pi$
$674$	26.1456	1.00709
$675$	−9.51391	−0.366191
$676$	11.5601	0.444621
$677$	−32.0247	−1.23081	−0.615405	−	0.788211i	$-0.711008\pi$
$677$	−32.0247	−1.23081	−0.615405	+	0.788211i	$0.711008\pi$
$678$	9.33189	0.358389
$679$	−1.40036	−0.0537410
$680$	−0.0285392	−0.00109443
$681$	36.5869	1.40201
$682$	43.4968	1.66558
$683$	31.1082	1.19032	0.595161	−	0.803606i	$-0.297088\pi$
$683$	31.1082	1.19032	0.595161	+	0.803606i	$0.297088\pi$
$684$	10.5685	0.404096
$685$	−0.260808	−0.00996495
$686$	−10.8685	−0.414962
$687$	−28.3310	−1.08089
$688$	−12.3910	−0.472401
$689$	−6.17570	−0.235276
$690$	−0.0935730	−0.00356226
$691$	−20.0751	−0.763693	−0.381846	−	0.924226i	$-0.624712\pi$
$691$	−20.0751	−0.763693	−0.381846	+	0.924226i	$0.624712\pi$
$692$	−12.4924	−0.474890
$693$	39.6123	1.50475
$694$	−18.3954	−0.698279
$695$	−0.140990	−0.00534807
$696$	−12.5052	−0.474007
$697$	−4.63647	−0.175619
$698$	−10.2983	−0.389798
$699$	36.9740	1.39848
$700$	−16.3294	−0.617194
$701$	−17.0535	−0.644101	−0.322051	−	0.946722i	$-0.604372\pi$
$701$	−17.0535	−0.644101	−0.322051	+	0.946722i	$0.604372\pi$
$702$	9.43304	0.356027
$703$	33.7663	1.27352
$704$	5.60760	0.211344
$705$	0.128394	0.00483561
$706$	−21.4410	−0.806942
$707$	−0.304569	−0.0114545
$708$	−28.6299	−1.07598
$709$	−24.6888	−0.927206	−0.463603	−	0.886043i	$-0.653444\pi$
$709$	−24.6888	−0.927206	−0.463603	+	0.886043i	$0.653444\pi$
$710$	0.447640	0.0167996
$711$	−15.5358	−0.582638
$712$	−13.1696	−0.493552
$713$	7.75676	0.290493
$714$	5.14372	0.192499
$715$	1.14452	0.0428026
$716$	3.04827	0.113919
$717$	47.1880	1.76227
$718$	−4.29892	−0.160434
$719$	−14.4262	−0.538005	−0.269002	−	0.963140i	$-0.586694\pi$
$719$	−14.4262	−0.538005	−0.269002	+	0.963140i	$0.586694\pi$
$720$	0.0890504	0.00331871
$721$	−33.3791	−1.24310
$722$	4.89001	0.181987
$723$	−58.9501	−2.19238
$724$	−9.23172	−0.343094
$725$	−27.5101	−1.02170
$726$	−46.4525	−1.72401
$727$	−0.0675327	−0.00250465	−0.00125232	−	0.999999i	$-0.500399\pi$
$727$	−0.0675327	−0.00250465	−0.00125232	+	0.999999i	$0.500399\pi$
$728$	16.1906	0.600064
$729$	−10.4029	−0.385292
$730$	−0.662544	−0.0245219
$731$	8.58649	0.317583
$732$	17.6331	0.651740
$733$	18.3348	0.677212	0.338606	−	0.940928i	$-0.390045\pi$
$733$	18.3348	0.677212	0.338606	+	0.940928i	$0.390045\pi$
$734$	−27.8006	−1.02614
$735$	−0.343715	−0.0126781
$736$	1.00000	0.0368605
$737$	−43.6647	−1.60841
$738$	14.4671	0.532541
$739$	−33.0695	−1.21648	−0.608240	−	0.793753i	$-0.708124\pi$
$739$	−33.0695	−1.21648	−0.608240	+	0.793753i	$0.708124\pi$
$740$	0.284516	0.0104590
$741$	−55.0355	−2.02178
$742$	−4.07117	−0.149457
$743$	12.1804	0.446856	0.223428	−	0.974720i	$-0.428275\pi$
$743$	12.1804	0.446856	0.223428	+	0.974720i	$0.428275\pi$
$744$	−17.6238	−0.646120
$745$	0.192313	0.00704579
$746$	−21.6354	−0.792129
$747$	−10.8681	−0.397645
$748$	−3.88586	−0.142081
$749$	−24.2294	−0.885325
$750$	0.935571	0.0341622
$751$	16.2578	0.593254	0.296627	−	0.954993i	$-0.404138\pi$
$751$	16.2578	0.593254	0.296627	+	0.954993i	$0.404138\pi$
$752$	−1.37213	−0.0500365
$753$	26.4821	0.965062
$754$	27.2763	0.993345
$755$	−0.168603	−0.00613608
$756$	6.21848	0.226164
$757$	−30.1787	−1.09686	−0.548431	−	0.836196i	$-0.684775\pi$
$757$	−30.1787	−1.09686	−0.548431	+	0.836196i	$0.684775\pi$
$758$	35.7258	1.29762
$759$	−12.7408	−0.462461
$760$	0.201298	0.00730184
$761$	3.68500	0.133581	0.0667905	−	0.997767i	$-0.478724\pi$
$761$	3.68500	0.133581	0.0667905	+	0.997767i	$0.478724\pi$
$762$	−4.42613	−0.160342
$763$	−42.2690	−1.53024
$764$	−25.1166	−0.908688
$765$	−0.0617087	−0.00223108
$766$	−28.2499	−1.02071
$767$	62.4475	2.25485
$768$	−2.27206	−0.0819858
$769$	0.139946	0.00504658	0.00252329	−	0.999997i	$-0.499197\pi$
$769$	0.139946	0.00504658	0.00252329	+	0.999997i	$0.499197\pi$
$770$	0.754494	0.0271901
$771$	49.1208	1.76904
$772$	19.6289	0.706460
$773$	8.15088	0.293167	0.146583	−	0.989198i	$-0.453172\pi$
$773$	8.15088	0.293167	0.146583	+	0.989198i	$0.453172\pi$
$774$	−26.7923	−0.963030
$775$	−38.7706	−1.39268
$776$	−0.428640	−0.0153873
$777$	−51.2794	−1.83964
$778$	−32.9944	−1.18291
$779$	32.7028	1.17170
$780$	−0.463731	−0.0166042
$781$	60.9501	2.18097
$782$	−0.692963	−0.0247803
$783$	10.4763	0.374391
$784$	3.67323	0.131187
$785$	0.213633	0.00762490
$786$	−2.27206	−0.0810416
$787$	38.1366	1.35942	0.679712	−	0.733479i	$-0.262105\pi$
$787$	38.1366	1.35942	0.679712	+	0.733479i	$0.262105\pi$
$788$	11.5286	0.410690
$789$	−45.3455	−1.61434
$790$	−0.295910	−0.0105280
$791$	−13.4183	−0.477101
$792$	12.1250	0.430843
$793$	−38.4615	−1.36581
$794$	27.2865	0.968363
$795$	0.116606	0.00413559
$796$	18.8782	0.669120
$797$	−17.1325	−0.606863	−0.303432	−	0.952853i	$-0.598132\pi$
$797$	−17.1325	−0.606863	−0.303432	+	0.952853i	$0.598132\pi$
$798$	−36.2807	−1.28432
$799$	0.950837	0.0336382
$800$	−4.99830	−0.176717
$801$	−28.4759	−1.00615
$802$	1.59442	0.0563008
$803$	−90.2112	−3.18348
$804$	17.6918	0.623943
$805$	0.134549	0.00474221
$806$	38.4411	1.35403
$807$	−22.3006	−0.785019
$808$	−0.0932263	−0.00327969
$809$	43.9457	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$809$	43.9457	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$810$	−0.445261	−0.0156449
$811$	17.3319	0.608604	0.304302	−	0.952576i	$-0.401577\pi$
$811$	17.3319	0.608604	0.304302	+	0.952576i	$0.401577\pi$
$812$	17.9812	0.631016
$813$	30.3500	1.06442
$814$	38.7394	1.35781
$815$	0.939999	0.0329267
$816$	1.57445	0.0551169
$817$	−60.5639	−2.11886
$818$	−26.2169	−0.916653
$819$	35.0081	1.22328
$820$	0.275555	0.00962279
$821$	−34.1395	−1.19148	−0.595738	−	0.803179i	$-0.703140\pi$
$821$	−34.1395	−1.19148	−0.595738	+	0.803179i	$0.703140\pi$
$822$	14.3883	0.501849
$823$	−11.8846	−0.414270	−0.207135	−	0.978312i	$-0.566414\pi$
$823$	−11.8846	−0.414270	−0.207135	+	0.978312i	$0.566414\pi$
$824$	−10.2171	−0.355929
$825$	63.6823	2.21713
$826$	41.1669	1.43238
$827$	13.4943	0.469242	0.234621	−	0.972087i	$-0.424615\pi$
$827$	13.4943	0.469242	0.234621	+	0.972087i	$0.424615\pi$
$828$	2.16224	0.0751432
$829$	−14.0620	−0.488395	−0.244197	−	0.969726i	$-0.578524\pi$
$829$	−14.0620	−0.488395	−0.244197	+	0.969726i	$0.578524\pi$
$830$	−0.207005	−0.00718526
$831$	−21.1573	−0.733940
$832$	4.95582	0.171812
$833$	−2.54542	−0.0881935
$834$	7.77818	0.269336
$835$	−0.942035	−0.0326005
$836$	27.4085	0.947942
$837$	14.7644	0.510333
$838$	−14.1205	−0.487785
$839$	44.9159	1.55067	0.775334	−	0.631551i	$-0.217581\pi$
$839$	44.9159	1.55067	0.775334	+	0.631551i	$0.217581\pi$
$840$	−0.305702	−0.0105477
$841$	1.29286	0.0445814
$842$	14.1993	0.489339
$843$	−42.5831	−1.46664
$844$	13.4870	0.464242
$845$	0.476096	0.0163782
$846$	−2.96688	−0.102004
$847$	66.7941	2.29507
$848$	−1.24615	−0.0427930
$849$	41.0334	1.40826
$850$	3.46364	0.118802
$851$	6.90837	0.236816
$852$	−24.6955	−0.846053
$853$	11.8263	0.404923	0.202462	−	0.979290i	$-0.435106\pi$
$853$	11.8263	0.404923	0.202462	+	0.979290i	$0.435106\pi$
$854$	−25.3547	−0.867620
$855$	0.435255	0.0148854
$856$	−7.41644	−0.253489
$857$	−20.7847	−0.709992	−0.354996	−	0.934868i	$-0.615518\pi$
$857$	−20.7847	−0.709992	−0.354996	+	0.934868i	$0.615518\pi$
$858$	−63.1410	−2.15560
$859$	−17.9836	−0.613594	−0.306797	−	0.951775i	$-0.599257\pi$
$859$	−17.9836	−0.613594	−0.306797	+	0.951775i	$0.599257\pi$
$860$	−0.510313	−0.0174015
$861$	−49.6643	−1.69255
$862$	17.5767	0.598665
$863$	−9.80835	−0.333880	−0.166940	−	0.985967i	$-0.553389\pi$
$863$	−9.80835	−0.333880	−0.166940	+	0.985967i	$0.553389\pi$
$864$	1.90343	0.0647559
$865$	−0.514490	−0.0174932
$866$	−18.6081	−0.632329
$867$	37.5339	1.27472
$868$	25.3413	0.860139
$869$	−40.2908	−1.36677
$870$	−0.515016	−0.0174607
$871$	−38.5895	−1.30755
$872$	−12.9382	−0.438143
$873$	−0.926825	−0.0313683
$874$	4.88774	0.165330
$875$	−1.34526	−0.0454780
$876$	36.5513	1.23495
$877$	58.0570	1.96045	0.980223	−	0.197897i	$-0.0634111\pi$
$877$	58.0570	1.96045	0.980223	+	0.197897i	$0.0634111\pi$
$878$	−28.0542	−0.946784
$879$	24.7091	0.833416
$880$	0.230945	0.00778514
$881$	−19.6229	−0.661113	−0.330557	−	0.943786i	$-0.607236\pi$
$881$	−19.6229	−0.661113	−0.330557	+	0.943786i	$0.607236\pi$
$882$	7.94243	0.267436
$883$	−9.19524	−0.309444	−0.154722	−	0.987958i	$-0.549448\pi$
$883$	−9.19524	−0.309444	−0.154722	+	0.987958i	$0.549448\pi$
$884$	−3.43420	−0.115505
$885$	−1.17910	−0.0396350
$886$	−29.4578	−0.989656
$887$	−49.2022	−1.65205	−0.826024	−	0.563634i	$-0.809403\pi$
$887$	−49.2022	−1.65205	−0.826024	+	0.563634i	$0.809403\pi$
$888$	−15.6962	−0.526731
$889$	6.36433	0.213453
$890$	−0.542381	−0.0181806
$891$	−60.6261	−2.03105
$892$	2.90322	0.0972071
$893$	−6.70662	−0.224429
$894$	−10.6095	−0.354836
$895$	0.125541	0.00419637
$896$	3.26699	0.109143
$897$	−11.2599	−0.375957
$898$	32.5868	1.08743
$899$	42.6924	1.42387
$900$	−10.8076	−0.360252
$901$	0.863538	0.0287686
$902$	37.5192	1.24925
$903$	91.9756	3.06076
$904$	−4.10724	−0.136605
$905$	−0.380201	−0.0126383
$906$	9.30150	0.309022
$907$	41.7166	1.38518	0.692588	−	0.721333i	$-0.256470\pi$
$907$	41.7166	1.38518	0.692588	+	0.721333i	$0.256470\pi$
$908$	−16.1030	−0.534396
$909$	−0.201578	−0.00668592
$910$	0.666798	0.0221041
$911$	−35.1141	−1.16338	−0.581691	−	0.813410i	$-0.697609\pi$
$911$	−35.1141	−1.16338	−0.581691	+	0.813410i	$0.697609\pi$
$912$	−11.1052	−0.367731
$913$	−28.1856	−0.932807
$914$	31.2988	1.03527
$915$	0.726207	0.0240077
$916$	12.4693	0.411997
$917$	3.26699	0.107886
$918$	−1.31901	−0.0435337
$919$	55.4259	1.82833	0.914166	−	0.405340i	$-0.132847\pi$
$919$	55.4259	1.82833	0.914166	+	0.405340i	$0.132847\pi$
$920$	0.0411842	0.00135780
$921$	−70.0228	−2.30733
$922$	−26.4961	−0.872604
$923$	53.8658	1.77302
$924$	−41.6240	−1.36933
$925$	−34.5301	−1.13534
$926$	−9.68480	−0.318262
$927$	−22.0918	−0.725591
$928$	5.50390	0.180674
$929$	51.1113	1.67691	0.838454	−	0.544972i	$-0.183460\pi$
$929$	51.1113	1.67691	0.838454	+	0.544972i	$0.183460\pi$
$930$	−0.725823	−0.0238007
$931$	17.9538	0.588413
$932$	−16.2733	−0.533051
$933$	−32.1747	−1.05335
$934$	−30.3936	−0.994510
$935$	−0.160036	−0.00523374
$936$	10.7157	0.350253
$937$	−27.3705	−0.894155	−0.447077	−	0.894495i	$-0.647535\pi$
$937$	−27.3705	−0.894155	−0.447077	+	0.894495i	$0.647535\pi$
$938$	−25.4391	−0.830616
$939$	−34.0198	−1.11020
$940$	−0.0565102	−0.00184316
$941$	27.5792	0.899056	0.449528	−	0.893266i	$-0.351592\pi$
$941$	27.5792	0.899056	0.449528	+	0.893266i	$0.351592\pi$
$942$	−11.7858	−0.384001
$943$	6.69078	0.217882
$944$	12.6008	0.410123
$945$	0.256103	0.00833105
$946$	−69.4836	−2.25911
$947$	18.8324	0.611970	0.305985	−	0.952036i	$-0.401014\pi$
$947$	18.8324	0.611970	0.305985	+	0.952036i	$0.401014\pi$
$948$	16.3248	0.530205
$949$	−79.7258	−2.58801
$950$	−24.4304	−0.792627
$951$	−49.7141	−1.61209
$952$	−2.26391	−0.0733736
$953$	44.1835	1.43124	0.715621	−	0.698488i	$-0.246144\pi$
$953$	44.1835	1.43124	0.715621	+	0.698488i	$0.246144\pi$
$954$	−2.69449	−0.0872372
$955$	−1.03441	−0.0334727
$956$	−20.7688	−0.671712
$957$	−70.1239	−2.26678
$958$	−9.02771	−0.291672
$959$	−20.6889	−0.668080
$960$	−0.0935730	−0.00302005
$961$	29.1673	0.940881
$962$	34.2366	1.10383
$963$	−16.0362	−0.516758
$964$	25.9457	0.835655
$965$	0.808402	0.0260234
$966$	−7.42279	−0.238824
$967$	−13.4952	−0.433977	−0.216988	−	0.976174i	$-0.569623\pi$
$967$	−13.4952	−0.433977	−0.216988	+	0.976174i	$0.569623\pi$
$968$	20.4451	0.657132
$969$	7.69552	0.247216
$970$	−0.0176532	−0.000566811 0
$971$	−14.4143	−0.462578	−0.231289	−	0.972885i	$-0.574294\pi$
$971$	−14.4143	−0.462578	−0.231289	+	0.972885i	$0.574294\pi$
$972$	18.8539	0.604739
$973$	−11.1842	−0.358550
$974$	−0.0174484	−0.000559084 0
$975$	56.2804	1.80242
$976$	−7.76087	−0.248419
$977$	43.1111	1.37924	0.689622	−	0.724169i	$-0.257776\pi$
$977$	43.1111	1.37924	0.689622	+	0.724169i	$0.257776\pi$
$978$	−51.8580	−1.65824
$979$	−73.8499	−2.36025
$980$	0.151279	0.00483244
$981$	−27.9756	−0.893192
$982$	−24.3487	−0.776998
$983$	21.5634	0.687764	0.343882	−	0.939013i	$-0.388258\pi$
$983$	21.5634	0.687764	0.343882	+	0.939013i	$0.388258\pi$
$984$	−15.2018	−0.484617
$985$	0.474797	0.0151283
$986$	−3.81400	−0.121462
$987$	10.1850	0.324194
$988$	24.2228	0.770629
$989$	−12.3910	−0.394010
$990$	0.499359	0.0158707
$991$	19.9907	0.635025	0.317512	−	0.948254i	$-0.397153\pi$
$991$	19.9907	0.635025	0.317512	+	0.948254i	$0.397153\pi$
$992$	7.75676	0.246277
$993$	−73.0516	−2.31822
$994$	35.5096	1.12630
$995$	0.777485	0.0246479
$996$	11.4201	0.361860
$997$	41.5956	1.31735	0.658673	−	0.752429i	$-0.271118\pi$
$997$	41.5956	1.31735	0.658673	+	0.752429i	$0.271118\pi$
$998$	10.8199	0.342497
$999$	13.1496	0.416035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.8	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.8	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.27206 q^{3} +1.00000 q^{4} +0.0411842 q^{5} -2.27206 q^{6} +3.26699 q^{7} +1.00000 q^{8} +2.16224 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.27206 q^{3} +1.00000 q^{4} +0.0411842 q^{5} -2.27206 q^{6} +3.26699 q^{7} +1.00000 q^{8} +2.16224 q^{9} +0.0411842 q^{10} +5.60760 q^{11} -2.27206 q^{12} +4.95582 q^{13} +3.26699 q^{14} -0.0935730 q^{15} +1.00000 q^{16} -0.692963 q^{17} +2.16224 q^{18} +4.88774 q^{19} +0.0411842 q^{20} -7.42279 q^{21} +5.60760 q^{22} +1.00000 q^{23} -2.27206 q^{24} -4.99830 q^{25} +4.95582 q^{26} +1.90343 q^{27} +3.26699 q^{28} +5.50390 q^{29} -0.0935730 q^{30} +7.75676 q^{31} +1.00000 q^{32} -12.7408 q^{33} -0.692963 q^{34} +0.134549 q^{35} +2.16224 q^{36} +6.90837 q^{37} +4.88774 q^{38} -11.2599 q^{39} +0.0411842 q^{40} +6.69078 q^{41} -7.42279 q^{42} -12.3910 q^{43} +5.60760 q^{44} +0.0890504 q^{45} +1.00000 q^{46} -1.37213 q^{47} -2.27206 q^{48} +3.67323 q^{49} -4.99830 q^{50} +1.57445 q^{51} +4.95582 q^{52} -1.24615 q^{53} +1.90343 q^{54} +0.230945 q^{55} +3.26699 q^{56} -11.1052 q^{57} +5.50390 q^{58} +12.6008 q^{59} -0.0935730 q^{60} -7.76087 q^{61} +7.75676 q^{62} +7.06404 q^{63} +1.00000 q^{64} +0.204102 q^{65} -12.7408 q^{66} -7.78670 q^{67} -0.692963 q^{68} -2.27206 q^{69} +0.134549 q^{70} +10.8692 q^{71} +2.16224 q^{72} -16.0873 q^{73} +6.90837 q^{74} +11.3564 q^{75} +4.88774 q^{76} +18.3200 q^{77} -11.2599 q^{78} -7.18504 q^{79} +0.0411842 q^{80} -10.8114 q^{81} +6.69078 q^{82} -5.02632 q^{83} -7.42279 q^{84} -0.0285392 q^{85} -12.3910 q^{86} -12.5052 q^{87} +5.60760 q^{88} -13.1696 q^{89} +0.0890504 q^{90} +16.1906 q^{91} +1.00000 q^{92} -17.6238 q^{93} -1.37213 q^{94} +0.201298 q^{95} -2.27206 q^{96} -0.428640 q^{97} +3.67323 q^{98} +12.1250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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