LMFDB - Embedded newform 6010.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.45664 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.45664 q^{6} +3.60299 q^{7} +1.00000 q^{8} +3.03507 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.45664 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.45664 q^{6} +3.60299 q^{7} +1.00000 q^{8} +3.03507 q^{9} -1.00000 q^{10} +3.51551 q^{11} -2.45664 q^{12} -0.574145 q^{13} +3.60299 q^{14} +2.45664 q^{15} +1.00000 q^{16} +0.123932 q^{17} +3.03507 q^{18} +5.64333 q^{19} -1.00000 q^{20} -8.85123 q^{21} +3.51551 q^{22} +7.23073 q^{23} -2.45664 q^{24} +1.00000 q^{25} -0.574145 q^{26} -0.0861489 q^{27} +3.60299 q^{28} -6.16713 q^{29} +2.45664 q^{30} +2.77626 q^{31} +1.00000 q^{32} -8.63634 q^{33} +0.123932 q^{34} -3.60299 q^{35} +3.03507 q^{36} -6.81195 q^{37} +5.64333 q^{38} +1.41047 q^{39} -1.00000 q^{40} +10.2661 q^{41} -8.85123 q^{42} -0.558818 q^{43} +3.51551 q^{44} -3.03507 q^{45} +7.23073 q^{46} +9.18687 q^{47} -2.45664 q^{48} +5.98152 q^{49} +1.00000 q^{50} -0.304456 q^{51} -0.574145 q^{52} -4.75772 q^{53} -0.0861489 q^{54} -3.51551 q^{55} +3.60299 q^{56} -13.8636 q^{57} -6.16713 q^{58} +6.21789 q^{59} +2.45664 q^{60} -14.4419 q^{61} +2.77626 q^{62} +10.9353 q^{63} +1.00000 q^{64} +0.574145 q^{65} -8.63634 q^{66} +13.4655 q^{67} +0.123932 q^{68} -17.7633 q^{69} -3.60299 q^{70} -13.2858 q^{71} +3.03507 q^{72} -3.93981 q^{73} -6.81195 q^{74} -2.45664 q^{75} +5.64333 q^{76} +12.6663 q^{77} +1.41047 q^{78} +5.63460 q^{79} -1.00000 q^{80} -8.89357 q^{81} +10.2661 q^{82} -5.50574 q^{83} -8.85123 q^{84} -0.123932 q^{85} -0.558818 q^{86} +15.1504 q^{87} +3.51551 q^{88} -1.35824 q^{89} -3.03507 q^{90} -2.06864 q^{91} +7.23073 q^{92} -6.82027 q^{93} +9.18687 q^{94} -5.64333 q^{95} -2.45664 q^{96} +5.56268 q^{97} +5.98152 q^{98} +10.6698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * 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
$3$	−2.45664	−1.41834	−0.709170	−	0.705037i	$-0.750930\pi$
$3$	−2.45664	−1.41834	−0.709170	+	0.705037i	$0.750930\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.45664	−1.00292
$7$	3.60299	1.36180	0.680901	−	0.732376i	$-0.261589\pi$
$7$	3.60299	1.36180	0.680901	+	0.732376i	$0.261589\pi$
$8$	1.00000	0.353553
$9$	3.03507	1.01169
$10$	−1.00000	−0.316228
$11$	3.51551	1.05997	0.529983	−	0.848008i	$-0.322198\pi$
$11$	3.51551	1.05997	0.529983	+	0.848008i	$0.322198\pi$
$12$	−2.45664	−0.709170
$13$	−0.574145	−0.159239	−0.0796196	−	0.996825i	$-0.525371\pi$
$13$	−0.574145	−0.159239	−0.0796196	+	0.996825i	$0.525371\pi$
$14$	3.60299	0.962939
$15$	2.45664	0.634301
$16$	1.00000	0.250000
$17$	0.123932	0.0300579	0.0150290	−	0.999887i	$-0.495216\pi$
$17$	0.123932	0.0300579	0.0150290	+	0.999887i	$0.495216\pi$
$18$	3.03507	0.715372
$19$	5.64333	1.29467	0.647334	−	0.762206i	$-0.275884\pi$
$19$	5.64333	1.29467	0.647334	+	0.762206i	$0.275884\pi$
$20$	−1.00000	−0.223607
$21$	−8.85123	−1.93150
$22$	3.51551	0.749509
$23$	7.23073	1.50771	0.753856	−	0.657040i	$-0.228192\pi$
$23$	7.23073	1.50771	0.753856	+	0.657040i	$0.228192\pi$
$24$	−2.45664	−0.501459
$25$	1.00000	0.200000
$26$	−0.574145	−0.112599
$27$	−0.0861489	−0.0165794
$28$	3.60299	0.680901
$29$	−6.16713	−1.14521	−0.572603	−	0.819833i	$-0.694066\pi$
$29$	−6.16713	−1.14521	−0.572603	+	0.819833i	$0.694066\pi$
$30$	2.45664	0.448519
$31$	2.77626	0.498632	0.249316	−	0.968422i	$-0.419794\pi$
$31$	2.77626	0.498632	0.249316	+	0.968422i	$0.419794\pi$
$32$	1.00000	0.176777
$33$	−8.63634	−1.50339
$34$	0.123932	0.0212542
$35$	−3.60299	−0.609016
$36$	3.03507	0.505845
$37$	−6.81195	−1.11988	−0.559939	−	0.828534i	$-0.689175\pi$
$37$	−6.81195	−1.11988	−0.559939	+	0.828534i	$0.689175\pi$
$38$	5.64333	0.915469
$39$	1.41047	0.225855
$40$	−1.00000	−0.158114
$41$	10.2661	1.60330	0.801650	−	0.597793i	$-0.203956\pi$
$41$	10.2661	1.60330	0.801650	+	0.597793i	$0.203956\pi$
$42$	−8.85123	−1.36578
$43$	−0.558818	−0.0852189	−0.0426094	−	0.999092i	$-0.513567\pi$
$43$	−0.558818	−0.0852189	−0.0426094	+	0.999092i	$0.513567\pi$
$44$	3.51551	0.529983
$45$	−3.03507	−0.452441
$46$	7.23073	1.06611
$47$	9.18687	1.34004	0.670021	−	0.742342i	$-0.266285\pi$
$47$	9.18687	1.34004	0.670021	+	0.742342i	$0.266285\pi$
$48$	−2.45664	−0.354585
$49$	5.98152	0.854503
$50$	1.00000	0.141421
$51$	−0.304456	−0.0426324
$52$	−0.574145	−0.0796196
$53$	−4.75772	−0.653523	−0.326761	−	0.945107i	$-0.605957\pi$
$53$	−4.75772	−0.653523	−0.326761	+	0.945107i	$0.605957\pi$
$54$	−0.0861489	−0.0117234
$55$	−3.51551	−0.474031
$56$	3.60299	0.481469
$57$	−13.8636	−1.83628
$58$	−6.16713	−0.809783
$59$	6.21789	0.809501	0.404750	−	0.914427i	$-0.367358\pi$
$59$	6.21789	0.809501	0.404750	+	0.914427i	$0.367358\pi$
$60$	2.45664	0.317151
$61$	−14.4419	−1.84909	−0.924545	−	0.381072i	$-0.875555\pi$
$61$	−14.4419	−1.84909	−0.924545	+	0.381072i	$0.875555\pi$
$62$	2.77626	0.352586
$63$	10.9353	1.37772
$64$	1.00000	0.125000
$65$	0.574145	0.0712139
$66$	−8.63634	−1.06306
$67$	13.4655	1.64507	0.822537	−	0.568711i	$-0.192558\pi$
$67$	13.4655	1.64507	0.822537	+	0.568711i	$0.192558\pi$
$68$	0.123932	0.0150290
$69$	−17.7633	−2.13845
$70$	−3.60299	−0.430639
$71$	−13.2858	−1.57674	−0.788369	−	0.615203i	$-0.789074\pi$
$71$	−13.2858	−1.57674	−0.788369	+	0.615203i	$0.789074\pi$
$72$	3.03507	0.357686
$73$	−3.93981	−0.461120	−0.230560	−	0.973058i	$-0.574056\pi$
$73$	−3.93981	−0.461120	−0.230560	+	0.973058i	$0.574056\pi$
$74$	−6.81195	−0.791873
$75$	−2.45664	−0.283668
$76$	5.64333	0.647334
$77$	12.6663	1.44346
$78$	1.41047	0.159704
$79$	5.63460	0.633942	0.316971	−	0.948435i	$-0.397334\pi$
$79$	5.63460	0.633942	0.316971	+	0.948435i	$0.397334\pi$
$80$	−1.00000	−0.111803
$81$	−8.89357	−0.988174
$82$	10.2661	1.13370
$83$	−5.50574	−0.604334	−0.302167	−	0.953255i	$-0.597710\pi$
$83$	−5.50574	−0.604334	−0.302167	+	0.953255i	$0.597710\pi$
$84$	−8.85123	−0.965749
$85$	−0.123932	−0.0134423
$86$	−0.558818	−0.0602588
$87$	15.1504	1.62429
$88$	3.51551	0.374755
$89$	−1.35824	−0.143974	−0.0719868	−	0.997406i	$-0.522934\pi$
$89$	−1.35824	−0.143974	−0.0719868	+	0.997406i	$0.522934\pi$
$90$	−3.03507	−0.319924
$91$	−2.06864	−0.216852
$92$	7.23073	0.753856
$93$	−6.82027	−0.707229
$94$	9.18687	0.947553
$95$	−5.64333	−0.578993
$96$	−2.45664	−0.250730
$97$	5.56268	0.564805	0.282402	−	0.959296i	$-0.408869\pi$
$97$	5.56268	0.564805	0.282402	+	0.959296i	$0.408869\pi$
$98$	5.98152	0.604225
$99$	10.6698	1.07236
$100$	1.00000	0.100000
$101$	−12.9591	−1.28948	−0.644741	−	0.764401i	$-0.723035\pi$
$101$	−12.9591	−1.28948	−0.644741	+	0.764401i	$0.723035\pi$
$102$	−0.304456	−0.0301457
$103$	2.90700	0.286435	0.143218	−	0.989691i	$-0.454255\pi$
$103$	2.90700	0.286435	0.143218	+	0.989691i	$0.454255\pi$
$104$	−0.574145	−0.0562995
$105$	8.85123	0.863792
$106$	−4.75772	−0.462110
$107$	−7.74517	−0.748754	−0.374377	−	0.927277i	$-0.622143\pi$
$107$	−7.74517	−0.748754	−0.374377	+	0.927277i	$0.622143\pi$
$108$	−0.0861489	−0.00828968
$109$	−15.3292	−1.46827	−0.734134	−	0.679004i	$-0.762412\pi$
$109$	−15.3292	−1.46827	−0.734134	+	0.679004i	$0.762412\pi$
$110$	−3.51551	−0.335191
$111$	16.7345	1.58837
$112$	3.60299	0.340450
$113$	20.3896	1.91809	0.959046	−	0.283249i	$-0.0914124\pi$
$113$	20.3896	1.91809	0.959046	+	0.283249i	$0.0914124\pi$
$114$	−13.8636	−1.29845
$115$	−7.23073	−0.674269
$116$	−6.16713	−0.572603
$117$	−1.74257	−0.161100
$118$	6.21789	0.572404
$119$	0.446526	0.0409330
$120$	2.45664	0.224259
$121$	1.35881	0.123529
$122$	−14.4419	−1.30750
$123$	−25.2202	−2.27403
$124$	2.77626	0.249316
$125$	−1.00000	−0.0894427
$126$	10.9353	0.974195
$127$	4.12329	0.365883	0.182942	−	0.983124i	$-0.441438\pi$
$127$	4.12329	0.365883	0.182942	+	0.983124i	$0.441438\pi$
$128$	1.00000	0.0883883
$129$	1.37281	0.120869
$130$	0.574145	0.0503558
$131$	−13.4979	−1.17932	−0.589658	−	0.807653i	$-0.700737\pi$
$131$	−13.4979	−1.17932	−0.589658	+	0.807653i	$0.700737\pi$
$132$	−8.63634	−0.751696
$133$	20.3328	1.76308
$134$	13.4655	1.16324
$135$	0.0861489	0.00741452
$136$	0.123932	0.0106271
$137$	−16.0437	−1.37071	−0.685354	−	0.728211i	$-0.740352\pi$
$137$	−16.0437	−1.37071	−0.685354	+	0.728211i	$0.740352\pi$
$138$	−17.7633	−1.51211
$139$	7.28873	0.618222	0.309111	−	0.951026i	$-0.399969\pi$
$139$	7.28873	0.618222	0.309111	+	0.951026i	$0.399969\pi$
$140$	−3.60299	−0.304508
$141$	−22.5688	−1.90064
$142$	−13.2858	−1.11492
$143$	−2.01841	−0.168788
$144$	3.03507	0.252922
$145$	6.16713	0.512152
$146$	−3.93981	−0.326061
$147$	−14.6944	−1.21198
$148$	−6.81195	−0.559939
$149$	20.3696	1.66874	0.834370	−	0.551205i	$-0.185832\pi$
$149$	20.3696	1.66874	0.834370	+	0.551205i	$0.185832\pi$
$150$	−2.45664	−0.200584
$151$	−1.60099	−0.130287	−0.0651433	−	0.997876i	$-0.520750\pi$
$151$	−1.60099	−0.130287	−0.0651433	+	0.997876i	$0.520750\pi$
$152$	5.64333	0.457734
$153$	0.376142	0.0304093
$154$	12.6663	1.02068
$155$	−2.77626	−0.222995
$156$	1.41047	0.112928
$157$	16.2133	1.29396	0.646981	−	0.762506i	$-0.276031\pi$
$157$	16.2133	1.29396	0.646981	+	0.762506i	$0.276031\pi$
$158$	5.63460	0.448265
$159$	11.6880	0.926918
$160$	−1.00000	−0.0790569
$161$	26.0522	2.05320
$162$	−8.89357	−0.698745
$163$	−10.9191	−0.855252	−0.427626	−	0.903956i	$-0.640650\pi$
$163$	−10.9191	−0.855252	−0.427626	+	0.903956i	$0.640650\pi$
$164$	10.2661	0.801650
$165$	8.63634	0.672338
$166$	−5.50574	−0.427329
$167$	−15.1964	−1.17593	−0.587966	−	0.808886i	$-0.700071\pi$
$167$	−15.1964	−1.17593	−0.587966	+	0.808886i	$0.700071\pi$
$168$	−8.85123	−0.682888
$169$	−12.6704	−0.974643
$170$	−0.123932	−0.00950516
$171$	17.1279	1.30980
$172$	−0.558818	−0.0426094
$173$	20.3704	1.54874	0.774368	−	0.632736i	$-0.218068\pi$
$173$	20.3704	1.54874	0.774368	+	0.632736i	$0.218068\pi$
$174$	15.1504	1.14855
$175$	3.60299	0.272360
$176$	3.51551	0.264992
$177$	−15.2751	−1.14815
$178$	−1.35824	−0.101805
$179$	17.9603	1.34242	0.671210	−	0.741268i	$-0.265775\pi$
$179$	17.9603	1.34242	0.671210	+	0.741268i	$0.265775\pi$
$180$	−3.03507	−0.226221
$181$	17.2647	1.28327	0.641636	−	0.767009i	$-0.278256\pi$
$181$	17.2647	1.28327	0.641636	+	0.767009i	$0.278256\pi$
$182$	−2.06864	−0.153338
$183$	35.4784	2.62264
$184$	7.23073	0.533057
$185$	6.81195	0.500825
$186$	−6.82027	−0.500087
$187$	0.435685	0.0318604
$188$	9.18687	0.670021
$189$	−0.310393	−0.0225778
$190$	−5.64333	−0.409410
$191$	9.93175	0.718636	0.359318	−	0.933215i	$-0.383009\pi$
$191$	9.93175	0.718636	0.359318	+	0.933215i	$0.383009\pi$
$192$	−2.45664	−0.177293
$193$	−6.50943	−0.468559	−0.234280	−	0.972169i	$-0.575273\pi$
$193$	−6.50943	−0.468559	−0.234280	+	0.972169i	$0.575273\pi$
$194$	5.56268	0.399377
$195$	−1.41047	−0.101006
$196$	5.98152	0.427251
$197$	14.3618	1.02324	0.511619	−	0.859213i	$-0.329046\pi$
$197$	14.3618	1.02324	0.511619	+	0.859213i	$0.329046\pi$
$198$	10.6698	0.758271
$199$	2.37936	0.168669	0.0843343	−	0.996438i	$-0.473124\pi$
$199$	2.37936	0.168669	0.0843343	+	0.996438i	$0.473124\pi$
$200$	1.00000	0.0707107
$201$	−33.0799	−2.33328
$202$	−12.9591	−0.911801
$203$	−22.2201	−1.55954
$204$	−0.304456	−0.0213162
$205$	−10.2661	−0.717018
$206$	2.90700	0.202540
$207$	21.9458	1.52534
$208$	−0.574145	−0.0398098
$209$	19.8392	1.37230
$210$	8.85123	0.610793
$211$	−17.7329	−1.22078	−0.610392	−	0.792100i	$-0.708988\pi$
$211$	−17.7329	−1.22078	−0.610392	+	0.792100i	$0.708988\pi$
$212$	−4.75772	−0.326761
$213$	32.6385	2.23635
$214$	−7.74517	−0.529449
$215$	0.558818	0.0381110
$216$	−0.0861489	−0.00586169
$217$	10.0028	0.679037
$218$	−15.3292	−1.03822
$219$	9.67868	0.654024
$220$	−3.51551	−0.237016
$221$	−0.0711550	−0.00478640
$222$	16.7345	1.12315
$223$	18.2411	1.22152	0.610758	−	0.791818i	$-0.290865\pi$
$223$	18.2411	1.22152	0.610758	+	0.791818i	$0.290865\pi$
$224$	3.60299	0.240735
$225$	3.03507	0.202338
$226$	20.3896	1.35630
$227$	−21.9209	−1.45494	−0.727470	−	0.686139i	$-0.759304\pi$
$227$	−21.9209	−1.45494	−0.727470	+	0.686139i	$0.759304\pi$
$228$	−13.8636	−0.918140
$229$	24.5133	1.61988	0.809941	−	0.586512i	$-0.199499\pi$
$229$	24.5133	1.61988	0.809941	+	0.586512i	$0.199499\pi$
$230$	−7.23073	−0.476780
$231$	−31.1166	−2.04732
$232$	−6.16713	−0.404892
$233$	−1.79660	−0.117699	−0.0588496	−	0.998267i	$-0.518743\pi$
$233$	−1.79660	−0.117699	−0.0588496	+	0.998267i	$0.518743\pi$
$234$	−1.74257	−0.113915
$235$	−9.18687	−0.599285
$236$	6.21789	0.404750
$237$	−13.8422	−0.899146
$238$	0.446526	0.0289440
$239$	16.0764	1.03990	0.519949	−	0.854197i	$-0.325951\pi$
$239$	16.0764	1.03990	0.519949	+	0.854197i	$0.325951\pi$
$240$	2.45664	0.158575
$241$	14.4307	0.929565	0.464782	−	0.885425i	$-0.346133\pi$
$241$	14.4307	0.929565	0.464782	+	0.885425i	$0.346133\pi$
$242$	1.35881	0.0873479
$243$	22.1067	1.41815
$244$	−14.4419	−0.924545
$245$	−5.98152	−0.382145
$246$	−25.2202	−1.60798
$247$	−3.24009	−0.206162
$248$	2.77626	0.176293
$249$	13.5256	0.857151
$250$	−1.00000	−0.0632456
$251$	11.1540	0.704034	0.352017	−	0.935994i	$-0.385496\pi$
$251$	11.1540	0.704034	0.352017	+	0.935994i	$0.385496\pi$
$252$	10.9353	0.688860
$253$	25.4197	1.59812
$254$	4.12329	0.258718
$255$	0.304456	0.0190658
$256$	1.00000	0.0625000
$257$	1.98081	0.123559	0.0617797	−	0.998090i	$-0.480322\pi$
$257$	1.98081	0.123559	0.0617797	+	0.998090i	$0.480322\pi$
$258$	1.37281	0.0854675
$259$	−24.5434	−1.52505
$260$	0.574145	0.0356069
$261$	−18.7176	−1.15859
$262$	−13.4979	−0.833902
$263$	24.7403	1.52555	0.762777	−	0.646662i	$-0.223835\pi$
$263$	24.7403	1.52555	0.762777	+	0.646662i	$0.223835\pi$
$264$	−8.63634	−0.531530
$265$	4.75772	0.292264
$266$	20.3328	1.24669
$267$	3.33671	0.204204
$268$	13.4655	0.822537
$269$	15.8953	0.969152	0.484576	−	0.874749i	$-0.338974\pi$
$269$	15.8953	0.969152	0.484576	+	0.874749i	$0.338974\pi$
$270$	0.0861489	0.00524285
$271$	−17.6967	−1.07500	−0.537500	−	0.843263i	$-0.680631\pi$
$271$	−17.6967	−1.07500	−0.537500	+	0.843263i	$0.680631\pi$
$272$	0.123932	0.00751449
$273$	5.08189	0.307570
$274$	−16.0437	−0.969236
$275$	3.51551	0.211993
$276$	−17.7633	−1.06922
$277$	−23.5695	−1.41615	−0.708076	−	0.706136i	$-0.750437\pi$
$277$	−23.5695	−1.41615	−0.708076	+	0.706136i	$0.750437\pi$
$278$	7.28873	0.437149
$279$	8.42615	0.504460
$280$	−3.60299	−0.215320
$281$	7.38948	0.440820	0.220410	−	0.975407i	$-0.429261\pi$
$281$	7.38948	0.440820	0.220410	+	0.975407i	$0.429261\pi$
$282$	−22.5688	−1.34395
$283$	27.6742	1.64506	0.822529	−	0.568723i	$-0.192563\pi$
$283$	27.6742	1.64506	0.822529	+	0.568723i	$0.192563\pi$
$284$	−13.2858	−0.788369
$285$	13.8636	0.821209
$286$	−2.01841	−0.119351
$287$	36.9888	2.18338
$288$	3.03507	0.178843
$289$	−16.9846	−0.999097
$290$	6.16713	0.362146
$291$	−13.6655	−0.801085
$292$	−3.93981	−0.230560
$293$	−25.8156	−1.50816	−0.754080	−	0.656782i	$-0.771917\pi$
$293$	−25.8156	−1.50816	−0.754080	+	0.656782i	$0.771917\pi$
$294$	−14.6944	−0.856996
$295$	−6.21789	−0.362020
$296$	−6.81195	−0.395937
$297$	−0.302857	−0.0175736
$298$	20.3696	1.17998
$299$	−4.15149	−0.240087
$300$	−2.45664	−0.141834
$301$	−2.01341	−0.116051
$302$	−1.60099	−0.0921266
$303$	31.8359	1.82892
$304$	5.64333	0.323667
$305$	14.4419	0.826938
$306$	0.376142	0.0215026
$307$	7.80225	0.445298	0.222649	−	0.974899i	$-0.428530\pi$
$307$	7.80225	0.445298	0.222649	+	0.974899i	$0.428530\pi$
$308$	12.6663	0.721732
$309$	−7.14144	−0.406262
$310$	−2.77626	−0.157681
$311$	−16.2630	−0.922190	−0.461095	−	0.887351i	$-0.652543\pi$
$311$	−16.2630	−0.922190	−0.461095	+	0.887351i	$0.652543\pi$
$312$	1.41047	0.0798519
$313$	−26.7237	−1.51051	−0.755257	−	0.655429i	$-0.772488\pi$
$313$	−26.7237	−1.51051	−0.755257	+	0.655429i	$0.772488\pi$
$314$	16.2133	0.914970
$315$	−10.9353	−0.616135
$316$	5.63460	0.316971
$317$	8.01624	0.450237	0.225118	−	0.974331i	$-0.427723\pi$
$317$	8.01624	0.450237	0.225118	+	0.974331i	$0.427723\pi$
$318$	11.6880	0.655430
$319$	−21.6806	−1.21388
$320$	−1.00000	−0.0559017
$321$	19.0271	1.06199
$322$	26.0522	1.45183
$323$	0.699389	0.0389151
$324$	−8.89357	−0.494087
$325$	−0.574145	−0.0318478
$326$	−10.9191	−0.604754
$327$	37.6582	2.08251
$328$	10.2661	0.566852
$329$	33.1002	1.82487
$330$	8.63634	0.475415
$331$	−13.1743	−0.724125	−0.362062	−	0.932154i	$-0.617927\pi$
$331$	−13.1743	−0.724125	−0.362062	+	0.932154i	$0.617927\pi$
$332$	−5.50574	−0.302167
$333$	−20.6747	−1.13297
$334$	−15.1964	−0.831509
$335$	−13.4655	−0.735700
$336$	−8.85123	−0.482874
$337$	23.7035	1.29121	0.645607	−	0.763670i	$-0.276604\pi$
$337$	23.7035	1.29121	0.645607	+	0.763670i	$0.276604\pi$
$338$	−12.6704	−0.689177
$339$	−50.0899	−2.72051
$340$	−0.123932	−0.00672116
$341$	9.75998	0.528533
$342$	17.1279	0.926170
$343$	−3.66957	−0.198138
$344$	−0.558818	−0.0301294
$345$	17.7633	0.956343
$346$	20.3704	1.09512
$347$	−5.34228	−0.286789	−0.143394	−	0.989666i	$-0.545802\pi$
$347$	−5.34228	−0.286789	−0.143394	+	0.989666i	$0.545802\pi$
$348$	15.1504	0.812146
$349$	−23.8069	−1.27436	−0.637178	−	0.770717i	$-0.719898\pi$
$349$	−23.8069	−1.27436	−0.637178	+	0.770717i	$0.719898\pi$
$350$	3.60299	0.192588
$351$	0.0494619	0.00264008
$352$	3.51551	0.187377
$353$	−5.65391	−0.300927	−0.150464	−	0.988616i	$-0.548077\pi$
$353$	−5.65391	−0.300927	−0.150464	+	0.988616i	$0.548077\pi$
$354$	−15.2751	−0.811863
$355$	13.2858	0.705138
$356$	−1.35824	−0.0719868
$357$	−1.09695	−0.0580569
$358$	17.9603	0.949234
$359$	18.1939	0.960238	0.480119	−	0.877203i	$-0.340593\pi$
$359$	18.1939	0.960238	0.480119	+	0.877203i	$0.340593\pi$
$360$	−3.03507	−0.159962
$361$	12.8472	0.676166
$362$	17.2647	0.907411
$363$	−3.33812	−0.175206
$364$	−2.06864	−0.108426
$365$	3.93981	0.206219
$366$	35.4784	1.85449
$367$	23.5331	1.22842	0.614209	−	0.789144i	$-0.289475\pi$
$367$	23.5331	1.22842	0.614209	+	0.789144i	$0.289475\pi$
$368$	7.23073	0.376928
$369$	31.1584	1.62204
$370$	6.81195	0.354137
$371$	−17.1420	−0.889968
$372$	−6.82027	−0.353615
$373$	−6.59200	−0.341321	−0.170660	−	0.985330i	$-0.554590\pi$
$373$	−6.59200	−0.341321	−0.170660	+	0.985330i	$0.554590\pi$
$374$	0.435685	0.0225287
$375$	2.45664	0.126860
$376$	9.18687	0.473777
$377$	3.54082	0.182362
$378$	−0.310393	−0.0159649
$379$	27.2074	1.39755	0.698776	−	0.715341i	$-0.253728\pi$
$379$	27.2074	1.39755	0.698776	+	0.715341i	$0.253728\pi$
$380$	−5.64333	−0.289497
$381$	−10.1294	−0.518947
$382$	9.93175	0.508153
$383$	29.8182	1.52364	0.761819	−	0.647790i	$-0.224307\pi$
$383$	29.8182	1.52364	0.761819	+	0.647790i	$0.224307\pi$
$384$	−2.45664	−0.125365
$385$	−12.6663	−0.645537
$386$	−6.50943	−0.331322
$387$	−1.69605	−0.0862150
$388$	5.56268	0.282402
$389$	−13.8765	−0.703566	−0.351783	−	0.936082i	$-0.614424\pi$
$389$	−13.8765	−0.703566	−0.351783	+	0.936082i	$0.614424\pi$
$390$	−1.41047	−0.0714217
$391$	0.896120	0.0453187
$392$	5.98152	0.302112
$393$	33.1594	1.67267
$394$	14.3618	0.723538
$395$	−5.63460	−0.283508
$396$	10.6698	0.536178
$397$	13.8490	0.695063	0.347532	−	0.937668i	$-0.387020\pi$
$397$	13.8490	0.695063	0.347532	+	0.937668i	$0.387020\pi$
$398$	2.37936	0.119267
$399$	−49.9504	−2.50065
$400$	1.00000	0.0500000
$401$	−0.826399	−0.0412684	−0.0206342	−	0.999787i	$-0.506569\pi$
$401$	−0.826399	−0.0412684	−0.0206342	+	0.999787i	$0.506569\pi$
$402$	−33.0799	−1.64987
$403$	−1.59398	−0.0794016
$404$	−12.9591	−0.644741
$405$	8.89357	0.441925
$406$	−22.2201	−1.10276
$407$	−23.9475	−1.18703
$408$	−0.304456	−0.0150728
$409$	−24.0996	−1.19165	−0.595825	−	0.803115i	$-0.703175\pi$
$409$	−24.0996	−1.19165	−0.595825	+	0.803115i	$0.703175\pi$
$410$	−10.2661	−0.507008
$411$	39.4136	1.94413
$412$	2.90700	0.143218
$413$	22.4030	1.10238
$414$	21.9458	1.07858
$415$	5.50574	0.270266
$416$	−0.574145	−0.0281498
$417$	−17.9058	−0.876849
$418$	19.8392	0.970366
$419$	−14.6965	−0.717969	−0.358985	−	0.933343i	$-0.616877\pi$
$419$	−14.6965	−0.717969	−0.358985	+	0.933343i	$0.616877\pi$
$420$	8.85123	0.431896
$421$	−31.7858	−1.54915	−0.774573	−	0.632485i	$-0.782035\pi$
$421$	−31.7858	−1.54915	−0.774573	+	0.632485i	$0.782035\pi$
$422$	−17.7329	−0.863224
$423$	27.8828	1.35571
$424$	−4.75772	−0.231055
$425$	0.123932	0.00601159
$426$	32.6385	1.58134
$427$	−52.0338	−2.51809
$428$	−7.74517	−0.374377
$429$	4.95851	0.239399
$430$	0.558818	0.0269486
$431$	22.1574	1.06729	0.533643	−	0.845710i	$-0.320822\pi$
$431$	22.1574	1.06729	0.533643	+	0.845710i	$0.320822\pi$
$432$	−0.0861489	−0.00414484
$433$	5.71152	0.274478	0.137239	−	0.990538i	$-0.456177\pi$
$433$	5.71152	0.274478	0.137239	+	0.990538i	$0.456177\pi$
$434$	10.0028	0.480152
$435$	−15.1504	−0.726406
$436$	−15.3292	−0.734134
$437$	40.8054	1.95199
$438$	9.67868	0.462465
$439$	38.5182	1.83837	0.919187	−	0.393820i	$-0.128847\pi$
$439$	38.5182	1.83837	0.919187	+	0.393820i	$0.128847\pi$
$440$	−3.51551	−0.167595
$441$	18.1543	0.864491
$442$	−0.0711550	−0.00338450
$443$	25.9997	1.23528	0.617642	−	0.786459i	$-0.288088\pi$
$443$	25.9997	1.23528	0.617642	+	0.786459i	$0.288088\pi$
$444$	16.7345	0.794184
$445$	1.35824	0.0643870
$446$	18.2411	0.863742
$447$	−50.0406	−2.36684
$448$	3.60299	0.170225
$449$	−21.7778	−1.02776	−0.513879	−	0.857863i	$-0.671792\pi$
$449$	−21.7778	−1.02776	−0.513879	+	0.857863i	$0.671792\pi$
$450$	3.03507	0.143074
$451$	36.0907	1.69944
$452$	20.3896	0.959046
$453$	3.93305	0.184791
$454$	−21.9209	−1.02880
$455$	2.06864	0.0969792
$456$	−13.8636	−0.649223
$457$	−18.7747	−0.878244	−0.439122	−	0.898427i	$-0.644710\pi$
$457$	−18.7747	−0.878244	−0.439122	+	0.898427i	$0.644710\pi$
$458$	24.5133	1.14543
$459$	−0.0106766	−0.000498342 0
$460$	−7.23073	−0.337135
$461$	−20.9313	−0.974869	−0.487435	−	0.873159i	$-0.662067\pi$
$461$	−20.9313	−0.974869	−0.487435	+	0.873159i	$0.662067\pi$
$462$	−31.1166	−1.44768
$463$	11.8805	0.552132	0.276066	−	0.961139i	$-0.410969\pi$
$463$	11.8805	0.552132	0.276066	+	0.961139i	$0.410969\pi$
$464$	−6.16713	−0.286302
$465$	6.82027	0.316283
$466$	−1.79660	−0.0832259
$467$	12.5479	0.580647	0.290323	−	0.956929i	$-0.406237\pi$
$467$	12.5479	0.580647	0.290323	+	0.956929i	$0.406237\pi$
$468$	−1.74257	−0.0805502
$469$	48.5161	2.24026
$470$	−9.18687	−0.423759
$471$	−39.8302	−1.83528
$472$	6.21789	0.286202
$473$	−1.96453	−0.0903291
$474$	−13.8422	−0.635792
$475$	5.64333	0.258934
$476$	0.446526	0.0204665
$477$	−14.4400	−0.661162
$478$	16.0764	0.735319
$479$	−19.0973	−0.872576	−0.436288	−	0.899807i	$-0.643707\pi$
$479$	−19.0973	−0.872576	−0.436288	+	0.899807i	$0.643707\pi$
$480$	2.45664	0.112130
$481$	3.91105	0.178328
$482$	14.4307	0.657301
$483$	−64.0009	−2.91214
$484$	1.35881	0.0617643
$485$	−5.56268	−0.252588
$486$	22.1067	1.00278
$487$	−12.4155	−0.562602	−0.281301	−	0.959620i	$-0.590766\pi$
$487$	−12.4155	−0.562602	−0.281301	+	0.959620i	$0.590766\pi$
$488$	−14.4419	−0.653752
$489$	26.8243	1.21304
$490$	−5.98152	−0.270218
$491$	−37.9815	−1.71408	−0.857040	−	0.515250i	$-0.827699\pi$
$491$	−37.9815	−1.71408	−0.857040	+	0.515250i	$0.827699\pi$
$492$	−25.2202	−1.13701
$493$	−0.764305	−0.0344226
$494$	−3.24009	−0.145778
$495$	−10.6698	−0.479572
$496$	2.77626	0.124658
$497$	−47.8687	−2.14720
$498$	13.5256	0.606097
$499$	−12.9591	−0.580130	−0.290065	−	0.957007i	$-0.593677\pi$
$499$	−12.9591	−0.580130	−0.290065	+	0.957007i	$0.593677\pi$
$500$	−1.00000	−0.0447214
$501$	37.3320	1.66787
$502$	11.1540	0.497827
$503$	13.8569	0.617849	0.308925	−	0.951087i	$-0.400031\pi$
$503$	13.8569	0.617849	0.308925	+	0.951087i	$0.400031\pi$
$504$	10.9353	0.487098
$505$	12.9591	0.576674
$506$	25.4197	1.13004
$507$	31.1265	1.38238
$508$	4.12329	0.182942
$509$	41.1791	1.82523	0.912616	−	0.408818i	$-0.134059\pi$
$509$	41.1791	1.82523	0.912616	+	0.408818i	$0.134059\pi$
$510$	0.304456	0.0134815
$511$	−14.1951	−0.627953
$512$	1.00000	0.0441942
$513$	−0.486166	−0.0214648
$514$	1.98081	0.0873697
$515$	−2.90700	−0.128098
$516$	1.37281	0.0604347
$517$	32.2965	1.42040
$518$	−24.5434	−1.07837
$519$	−50.0428	−2.19663
$520$	0.574145	0.0251779
$521$	15.2799	0.669427	0.334713	−	0.942320i	$-0.391361\pi$
$521$	15.2799	0.669427	0.334713	+	0.942320i	$0.391361\pi$
$522$	−18.7176	−0.819249
$523$	−1.43916	−0.0629303	−0.0314651	−	0.999505i	$-0.510017\pi$
$523$	−1.43916	−0.0629303	−0.0314651	+	0.999505i	$0.510017\pi$
$524$	−13.4979	−0.589658
$525$	−8.85123	−0.386300
$526$	24.7403	1.07873
$527$	0.344068	0.0149878
$528$	−8.63634	−0.375848
$529$	29.2835	1.27319
$530$	4.75772	0.206662
$531$	18.8717	0.818963
$532$	20.3328	0.881540
$533$	−5.89425	−0.255308
$534$	3.33671	0.144394
$535$	7.74517	0.334853
$536$	13.4655	0.581622
$537$	−44.1221	−1.90401
$538$	15.8953	0.685294
$539$	21.0281	0.905744
$540$	0.0861489	0.00370726
$541$	22.8975	0.984439	0.492220	−	0.870471i	$-0.336186\pi$
$541$	22.8975	0.984439	0.492220	+	0.870471i	$0.336186\pi$
$542$	−17.6967	−0.760140
$543$	−42.4130	−1.82012
$544$	0.123932	0.00531354
$545$	15.3292	0.656630
$546$	5.08189	0.217485
$547$	1.53614	0.0656807	0.0328403	−	0.999461i	$-0.489545\pi$
$547$	1.53614	0.0656807	0.0328403	+	0.999461i	$0.489545\pi$
$548$	−16.0437	−0.685354
$549$	−43.8320	−1.87070
$550$	3.51551	0.149902
$551$	−34.8031	−1.48266
$552$	−17.7633	−0.756056
$553$	20.3014	0.863304
$554$	−23.5695	−1.00137
$555$	−16.7345	−0.710340
$556$	7.28873	0.309111
$557$	20.0219	0.848356	0.424178	−	0.905579i	$-0.360563\pi$
$557$	20.0219	0.848356	0.424178	+	0.905579i	$0.360563\pi$
$558$	8.42615	0.356707
$559$	0.320842	0.0135702
$560$	−3.60299	−0.152254
$561$	−1.07032	−0.0451889
$562$	7.38948	0.311706
$563$	31.8778	1.34349	0.671744	−	0.740784i	$-0.265546\pi$
$563$	31.8778	1.34349	0.671744	+	0.740784i	$0.265546\pi$
$564$	−22.5688	−0.950318
$565$	−20.3896	−0.857797
$566$	27.6742	1.16323
$567$	−32.0434	−1.34570
$568$	−13.2858	−0.557461
$569$	−8.85844	−0.371365	−0.185683	−	0.982610i	$-0.559450\pi$
$569$	−8.85844	−0.371365	−0.185683	+	0.982610i	$0.559450\pi$
$570$	13.8636	0.580683
$571$	−22.2811	−0.932433	−0.466217	−	0.884671i	$-0.654383\pi$
$571$	−22.2811	−0.932433	−0.466217	+	0.884671i	$0.654383\pi$
$572$	−2.01841	−0.0843940
$573$	−24.3987	−1.01927
$574$	36.9888	1.54388
$575$	7.23073	0.301542
$576$	3.03507	0.126461
$577$	−39.2905	−1.63569	−0.817843	−	0.575442i	$-0.804830\pi$
$577$	−39.2905	−1.63569	−0.817843	+	0.575442i	$0.804830\pi$
$578$	−16.9846	−0.706468
$579$	15.9913	0.664577
$580$	6.16713	0.256076
$581$	−19.8371	−0.822983
$582$	−13.6655	−0.566453
$583$	−16.7258	−0.692712
$584$	−3.93981	−0.163030
$585$	1.74257	0.0720463
$586$	−25.8156	−1.06643
$587$	−10.2098	−0.421405	−0.210703	−	0.977550i	$-0.567575\pi$
$587$	−10.2098	−0.421405	−0.210703	+	0.977550i	$0.567575\pi$
$588$	−14.6944	−0.605988
$589$	15.6674	0.645562
$590$	−6.21789	−0.255987
$591$	−35.2818	−1.45130
$592$	−6.81195	−0.279970
$593$	45.5681	1.87126	0.935629	−	0.352986i	$-0.114834\pi$
$593$	45.5681	1.87126	0.935629	+	0.352986i	$0.114834\pi$
$594$	−0.302857	−0.0124264
$595$	−0.446526	−0.0183058
$596$	20.3696	0.834370
$597$	−5.84523	−0.239229
$598$	−4.15149	−0.169767
$599$	−21.2397	−0.867829	−0.433915	−	0.900954i	$-0.642868\pi$
$599$	−21.2397	−0.867829	−0.433915	+	0.900954i	$0.642868\pi$
$600$	−2.45664	−0.100292
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−2.01341	−0.0820606
$603$	40.8688	1.66430
$604$	−1.60099	−0.0651433
$605$	−1.35881	−0.0552437
$606$	31.8359	1.29324
$607$	17.8757	0.725550	0.362775	−	0.931877i	$-0.381829\pi$
$607$	17.8757	0.725550	0.362775	+	0.931877i	$0.381829\pi$
$608$	5.64333	0.228867
$609$	54.5867	2.21196
$610$	14.4419	0.584734
$611$	−5.27459	−0.213387
$612$	0.376142	0.0152047
$613$	−33.5717	−1.35595	−0.677974	−	0.735086i	$-0.737142\pi$
$613$	−33.5717	−1.35595	−0.677974	+	0.735086i	$0.737142\pi$
$614$	7.80225	0.314873
$615$	25.2202	1.01698
$616$	12.6663	0.510341
$617$	18.4714	0.743631	0.371815	−	0.928307i	$-0.378735\pi$
$617$	18.4714	0.743631	0.371815	+	0.928307i	$0.378735\pi$
$618$	−7.14144	−0.287271
$619$	6.19882	0.249152	0.124576	−	0.992210i	$-0.460243\pi$
$619$	6.19882	0.249152	0.124576	+	0.992210i	$0.460243\pi$
$620$	−2.77626	−0.111497
$621$	−0.622919	−0.0249969
$622$	−16.2630	−0.652087
$623$	−4.89374	−0.196064
$624$	1.41047	0.0564638
$625$	1.00000	0.0400000
$626$	−26.7237	−1.06809
$627$	−48.7377	−1.94640
$628$	16.2133	0.646981
$629$	−0.844220	−0.0336612
$630$	−10.9353	−0.435673
$631$	−33.6291	−1.33875	−0.669376	−	0.742924i	$-0.733439\pi$
$631$	−33.6291	−1.33875	−0.669376	+	0.742924i	$0.733439\pi$
$632$	5.63460	0.224133
$633$	43.5633	1.73149
$634$	8.01624	0.318366
$635$	−4.12329	−0.163628
$636$	11.6880	0.463459
$637$	−3.43426	−0.136070
$638$	−21.6806	−0.858343
$639$	−40.3234	−1.59517
$640$	−1.00000	−0.0395285
$641$	−28.9409	−1.14310	−0.571548	−	0.820568i	$-0.693657\pi$
$641$	−28.9409	−1.14310	−0.571548	+	0.820568i	$0.693657\pi$
$642$	19.0271	0.750939
$643$	10.1319	0.399564	0.199782	−	0.979840i	$-0.435977\pi$
$643$	10.1319	0.399564	0.199782	+	0.979840i	$0.435977\pi$
$644$	26.0522	1.02660
$645$	−1.37281	−0.0540544
$646$	0.699389	0.0275171
$647$	32.6766	1.28465	0.642324	−	0.766433i	$-0.277970\pi$
$647$	32.6766	1.28465	0.642324	+	0.766433i	$0.277970\pi$
$648$	−8.89357	−0.349372
$649$	21.8591	0.858044
$650$	−0.574145	−0.0225198
$651$	−24.5734	−0.963106
$652$	−10.9191	−0.427626
$653$	3.39346	0.132796	0.0663981	−	0.997793i	$-0.478849\pi$
$653$	3.39346	0.132796	0.0663981	+	0.997793i	$0.478849\pi$
$654$	37.6582	1.47255
$655$	13.4979	0.527406
$656$	10.2661	0.400825
$657$	−11.9576	−0.466510
$658$	33.1002	1.29038
$659$	37.6123	1.46517	0.732584	−	0.680677i	$-0.238314\pi$
$659$	37.6123	1.46517	0.732584	+	0.680677i	$0.238314\pi$
$660$	8.63634	0.336169
$661$	10.5057	0.408623	0.204311	−	0.978906i	$-0.434505\pi$
$661$	10.5057	0.408623	0.204311	+	0.978906i	$0.434505\pi$
$662$	−13.1743	−0.512034
$663$	0.174802	0.00678874
$664$	−5.50574	−0.213664
$665$	−20.3328	−0.788474
$666$	−20.6747	−0.801130
$667$	−44.5928	−1.72664
$668$	−15.1964	−0.587966
$669$	−44.8118	−1.73252
$670$	−13.4655	−0.520218
$671$	−50.7705	−1.95997
$672$	−8.85123	−0.341444
$673$	−28.7886	−1.10972	−0.554860	−	0.831944i	$-0.687228\pi$
$673$	−28.7886	−1.10972	−0.554860	+	0.831944i	$0.687228\pi$
$674$	23.7035	0.913027
$675$	−0.0861489	−0.00331587
$676$	−12.6704	−0.487321
$677$	15.0498	0.578410	0.289205	−	0.957267i	$-0.406609\pi$
$677$	15.0498	0.578410	0.289205	+	0.957267i	$0.406609\pi$
$678$	−50.0899	−1.92369
$679$	20.0423	0.769152
$680$	−0.123932	−0.00475258
$681$	53.8517	2.06360
$682$	9.75998	0.373729
$683$	−29.2667	−1.11986	−0.559930	−	0.828540i	$-0.689172\pi$
$683$	−29.2667	−1.11986	−0.559930	+	0.828540i	$0.689172\pi$
$684$	17.1279	0.654901
$685$	16.0437	0.612999
$686$	−3.66957	−0.140105
$687$	−60.2202	−2.29754
$688$	−0.558818	−0.0213047
$689$	2.73162	0.104066
$690$	17.7633	0.676237
$691$	−0.632493	−0.0240612	−0.0120306	−	0.999928i	$-0.503830\pi$
$691$	−0.632493	−0.0240612	−0.0120306	+	0.999928i	$0.503830\pi$
$692$	20.3704	0.774368
$693$	38.4432	1.46034
$694$	−5.34228	−0.202790
$695$	−7.28873	−0.276477
$696$	15.1504	0.574274
$697$	1.27230	0.0481919
$698$	−23.8069	−0.901105
$699$	4.41360	0.166938
$700$	3.60299	0.136180
$701$	21.1090	0.797274	0.398637	−	0.917109i	$-0.369483\pi$
$701$	21.1090	0.797274	0.398637	+	0.917109i	$0.369483\pi$
$702$	0.0494619	0.00186682
$703$	−38.4421	−1.44987
$704$	3.51551	0.132496
$705$	22.5688	0.849991
$706$	−5.65391	−0.212788
$707$	−46.6916	−1.75602
$708$	−15.2751	−0.574074
$709$	−20.7342	−0.778688	−0.389344	−	0.921093i	$-0.627298\pi$
$709$	−20.7342	−0.778688	−0.389344	+	0.921093i	$0.627298\pi$
$710$	13.2858	0.498608
$711$	17.1014	0.641353
$712$	−1.35824	−0.0509024
$713$	20.0744	0.751793
$714$	−1.09695	−0.0410524
$715$	2.01841	0.0754843
$716$	17.9603	0.671210
$717$	−39.4940	−1.47493
$718$	18.1939	0.678991
$719$	29.8113	1.11178	0.555888	−	0.831257i	$-0.312378\pi$
$719$	29.8113	1.11178	0.555888	+	0.831257i	$0.312378\pi$
$720$	−3.03507	−0.113110
$721$	10.4739	0.390068
$722$	12.8472	0.478121
$723$	−35.4511	−1.31844
$724$	17.2647	0.641636
$725$	−6.16713	−0.229041
$726$	−3.33812	−0.123889
$727$	−1.69260	−0.0627751	−0.0313876	−	0.999507i	$-0.509993\pi$
$727$	−1.69260	−0.0627751	−0.0313876	+	0.999507i	$0.509993\pi$
$728$	−2.06864	−0.0766688
$729$	−27.6275	−1.02324
$730$	3.93981	0.145819
$731$	−0.0692554	−0.00256150
$732$	35.4784	1.31132
$733$	−17.3052	−0.639181	−0.319591	−	0.947556i	$-0.603545\pi$
$733$	−17.3052	−0.639181	−0.319591	+	0.947556i	$0.603545\pi$
$734$	23.5331	0.868622
$735$	14.6944	0.542012
$736$	7.23073	0.266528
$737$	47.3382	1.74372
$738$	31.1584	1.14696
$739$	−44.9060	−1.65189	−0.825946	−	0.563749i	$-0.809359\pi$
$739$	−44.9060	−1.65189	−0.825946	+	0.563749i	$0.809359\pi$
$740$	6.81195	0.250412
$741$	7.95972	0.292408
$742$	−17.1420	−0.629302
$743$	20.6179	0.756398	0.378199	−	0.925724i	$-0.376544\pi$
$743$	20.6179	0.756398	0.378199	+	0.925724i	$0.376544\pi$
$744$	−6.82027	−0.250043
$745$	−20.3696	−0.746283
$746$	−6.59200	−0.241350
$747$	−16.7103	−0.611398
$748$	0.435685	0.0159302
$749$	−27.9058	−1.01965
$750$	2.45664	0.0897037
$751$	−27.3957	−0.999685	−0.499842	−	0.866116i	$-0.666609\pi$
$751$	−27.3957	−0.999685	−0.499842	+	0.866116i	$0.666609\pi$
$752$	9.18687	0.335011
$753$	−27.4013	−0.998559
$754$	3.54082	0.128949
$755$	1.60099	0.0582660
$756$	−0.310393	−0.0112889
$757$	37.2995	1.35567	0.677837	−	0.735212i	$-0.262917\pi$
$757$	37.2995	1.35567	0.677837	+	0.735212i	$0.262917\pi$
$758$	27.2074	0.988218
$759$	−62.4470	−2.26668
$760$	−5.64333	−0.204705
$761$	−48.7840	−1.76842	−0.884209	−	0.467092i	$-0.845302\pi$
$761$	−48.7840	−1.76842	−0.884209	+	0.467092i	$0.845302\pi$
$762$	−10.1294	−0.366951
$763$	−55.2308	−1.99949
$764$	9.93175	0.359318
$765$	−0.376142	−0.0135995
$766$	29.8182	1.07737
$767$	−3.56997	−0.128904
$768$	−2.45664	−0.0886463
$769$	−41.0557	−1.48051	−0.740253	−	0.672328i	$-0.765294\pi$
$769$	−41.0557	−1.48051	−0.740253	+	0.672328i	$0.765294\pi$
$770$	−12.6663	−0.456463
$771$	−4.86613	−0.175249
$772$	−6.50943	−0.234280
$773$	−54.4299	−1.95771	−0.978854	−	0.204561i	$-0.934423\pi$
$773$	−54.4299	−1.95771	−0.978854	+	0.204561i	$0.934423\pi$
$774$	−1.69605	−0.0609632
$775$	2.77626	0.0997263
$776$	5.56268	0.199689
$777$	60.2942	2.16304
$778$	−13.8765	−0.497496
$779$	57.9352	2.07574
$780$	−1.41047	−0.0505028
$781$	−46.7065	−1.67129
$782$	0.896120	0.0320452
$783$	0.531291	0.0189868
$784$	5.98152	0.213626
$785$	−16.2133	−0.578678
$786$	33.1594	1.18276
$787$	−4.85700	−0.173133	−0.0865667	−	0.996246i	$-0.527590\pi$
$787$	−4.85700	−0.173133	−0.0865667	+	0.996246i	$0.527590\pi$
$788$	14.3618	0.511619
$789$	−60.7780	−2.16375
$790$	−5.63460	−0.200470
$791$	73.4635	2.61206
$792$	10.6698	0.379135
$793$	8.29172	0.294448
$794$	13.8490	0.491484
$795$	−11.6880	−0.414530
$796$	2.37936	0.0843343
$797$	−33.7533	−1.19560	−0.597801	−	0.801644i	$-0.703959\pi$
$797$	−33.7533	−1.19560	−0.597801	+	0.801644i	$0.703959\pi$
$798$	−49.9504	−1.76823
$799$	1.13855	0.0402789
$800$	1.00000	0.0353553
$801$	−4.12236	−0.145657
$802$	−0.826399	−0.0291812
$803$	−13.8504	−0.488771
$804$	−33.0799	−1.16664
$805$	−26.0522	−0.918221
$806$	−1.59398	−0.0561454
$807$	−39.0489	−1.37459
$808$	−12.9591	−0.455901
$809$	19.2487	0.676749	0.338375	−	0.941012i	$-0.390123\pi$
$809$	19.2487	0.676749	0.338375	+	0.941012i	$0.390123\pi$
$810$	8.89357	0.312488
$811$	−44.3058	−1.55579	−0.777893	−	0.628397i	$-0.783711\pi$
$811$	−44.3058	−1.55579	−0.777893	+	0.628397i	$0.783711\pi$
$812$	−22.2201	−0.779772
$813$	43.4745	1.52472
$814$	−23.9475	−0.839359
$815$	10.9191	0.382480
$816$	−0.304456	−0.0106581
$817$	−3.15359	−0.110330
$818$	−24.0996	−0.842623
$819$	−6.27845	−0.219387
$820$	−10.2661	−0.358509
$821$	−47.2218	−1.64805	−0.824027	−	0.566551i	$-0.808277\pi$
$821$	−47.2218	−1.64805	−0.824027	+	0.566551i	$0.808277\pi$
$822$	39.4136	1.37471
$823$	10.6131	0.369950	0.184975	−	0.982743i	$-0.440780\pi$
$823$	10.6131	0.369950	0.184975	+	0.982743i	$0.440780\pi$
$824$	2.90700	0.101270
$825$	−8.63634	−0.300679
$826$	22.4030	0.779500
$827$	−50.6397	−1.76091	−0.880457	−	0.474125i	$-0.842764\pi$
$827$	−50.6397	−1.76091	−0.880457	+	0.474125i	$0.842764\pi$
$828$	21.9458	0.762668
$829$	−43.8081	−1.52152	−0.760759	−	0.649035i	$-0.775173\pi$
$829$	−43.8081	−1.52152	−0.760759	+	0.649035i	$0.775173\pi$
$830$	5.50574	0.191107
$831$	57.9017	2.00859
$832$	−0.574145	−0.0199049
$833$	0.741302	0.0256846
$834$	−17.9058	−0.620026
$835$	15.1964	0.525892
$836$	19.8392	0.686152
$837$	−0.239172	−0.00826699
$838$	−14.6965	−0.507681
$839$	33.0924	1.14248	0.571238	−	0.820784i	$-0.306463\pi$
$839$	33.0924	1.14248	0.571238	+	0.820784i	$0.306463\pi$
$840$	8.85123	0.305397
$841$	9.03343	0.311498
$842$	−31.7858	−1.09541
$843$	−18.1533	−0.625232
$844$	−17.7329	−0.610392
$845$	12.6704	0.435874
$846$	27.8828	0.958630
$847$	4.89579	0.168221
$848$	−4.75772	−0.163381
$849$	−67.9854	−2.33325
$850$	0.123932	0.00425084
$851$	−49.2554	−1.68845
$852$	32.6385	1.11818
$853$	7.43060	0.254419	0.127209	−	0.991876i	$-0.459398\pi$
$853$	7.43060	0.254419	0.127209	+	0.991876i	$0.459398\pi$
$854$	−52.0338	−1.78056
$855$	−17.1279	−0.585761
$856$	−7.74517	−0.264724
$857$	27.8503	0.951348	0.475674	−	0.879622i	$-0.342204\pi$
$857$	27.8503	0.951348	0.475674	+	0.879622i	$0.342204\pi$
$858$	4.95851	0.169281
$859$	−10.7427	−0.366536	−0.183268	−	0.983063i	$-0.558668\pi$
$859$	−10.7427	−0.366536	−0.183268	+	0.983063i	$0.558668\pi$
$860$	0.558818	0.0190555
$861$	−90.8680	−3.09677
$862$	22.1574	0.754686
$863$	5.41032	0.184170	0.0920848	−	0.995751i	$-0.470647\pi$
$863$	5.41032	0.184170	0.0920848	+	0.995751i	$0.470647\pi$
$864$	−0.0861489	−0.00293084
$865$	−20.3704	−0.692615
$866$	5.71152	0.194085
$867$	41.7251	1.41706
$868$	10.0028	0.339519
$869$	19.8085	0.671958
$870$	−15.1504	−0.513646
$871$	−7.73116	−0.261960
$872$	−15.3292	−0.519111
$873$	16.8831	0.571407
$874$	40.8054	1.38026
$875$	−3.60299	−0.121803
$876$	9.67868	0.327012
$877$	47.2175	1.59442	0.797210	−	0.603702i	$-0.206308\pi$
$877$	47.2175	1.59442	0.797210	+	0.603702i	$0.206308\pi$
$878$	38.5182	1.29993
$879$	63.4195	2.13909
$880$	−3.51551	−0.118508
$881$	−30.6598	−1.03295	−0.516477	−	0.856301i	$-0.672757\pi$
$881$	−30.6598	−1.03295	−0.516477	+	0.856301i	$0.672757\pi$
$882$	18.1543	0.611288
$883$	−46.8155	−1.57547	−0.787734	−	0.616015i	$-0.788746\pi$
$883$	−46.8155	−1.57547	−0.787734	+	0.616015i	$0.788746\pi$
$884$	−0.0711550	−0.00239320
$885$	15.2751	0.513467
$886$	25.9997	0.873478
$887$	11.2840	0.378880	0.189440	−	0.981892i	$-0.439333\pi$
$887$	11.2840	0.378880	0.189440	+	0.981892i	$0.439333\pi$
$888$	16.7345	0.561573
$889$	14.8562	0.498260
$890$	1.35824	0.0455285
$891$	−31.2654	−1.04743
$892$	18.2411	0.610758
$893$	51.8445	1.73491
$894$	−50.0406	−1.67361
$895$	−17.9603	−0.600348
$896$	3.60299	0.120367
$897$	10.1987	0.340525
$898$	−21.7778	−0.726734
$899$	−17.1216	−0.571036
$900$	3.03507	0.101169
$901$	−0.589634	−0.0196435
$902$	36.0907	1.20169
$903$	4.94622	0.164600
$904$	20.3896	0.678148
$905$	−17.2647	−0.573897
$906$	3.93305	0.130667
$907$	−25.8088	−0.856966	−0.428483	−	0.903550i	$-0.640952\pi$
$907$	−25.8088	−0.856966	−0.428483	+	0.903550i	$0.640952\pi$
$908$	−21.9209	−0.727470
$909$	−39.3319	−1.30456
$910$	2.06864	0.0685746
$911$	−29.9415	−0.992005	−0.496002	−	0.868321i	$-0.665199\pi$
$911$	−29.9415	−0.992005	−0.496002	+	0.868321i	$0.665199\pi$
$912$	−13.8636	−0.459070
$913$	−19.3555	−0.640574
$914$	−18.7747	−0.621012
$915$	−35.4784	−1.17288
$916$	24.5133	0.809941
$917$	−48.6327	−1.60599
$918$	−0.0106766	−0.000352381 0
$919$	−34.2404	−1.12949	−0.564744	−	0.825266i	$-0.691025\pi$
$919$	−34.2404	−1.12949	−0.564744	+	0.825266i	$0.691025\pi$
$920$	−7.23073	−0.238390
$921$	−19.1673	−0.631584
$922$	−20.9313	−0.689337
$923$	7.62799	0.251078
$924$	−31.1166	−1.02366
$925$	−6.81195	−0.223976
$926$	11.8805	0.390416
$927$	8.82294	0.289783
$928$	−6.16713	−0.202446
$929$	−21.0324	−0.690052	−0.345026	−	0.938593i	$-0.612130\pi$
$929$	−21.0324	−0.690052	−0.345026	+	0.938593i	$0.612130\pi$
$930$	6.82027	0.223646
$931$	33.7557	1.10630
$932$	−1.79660	−0.0588496
$933$	39.9523	1.30798
$934$	12.5479	0.410579
$935$	−0.435685	−0.0142484
$936$	−1.74257	−0.0569576
$937$	47.4404	1.54981	0.774905	−	0.632078i	$-0.217798\pi$
$937$	47.4404	1.54981	0.774905	+	0.632078i	$0.217798\pi$
$938$	48.5161	1.58411
$939$	65.6505	2.14242
$940$	−9.18687	−0.299643
$941$	−4.46283	−0.145484	−0.0727420	−	0.997351i	$-0.523175\pi$
$941$	−4.46283	−0.145484	−0.0727420	+	0.997351i	$0.523175\pi$
$942$	−39.8302	−1.29774
$943$	74.2317	2.41732
$944$	6.21789	0.202375
$945$	0.310393	0.0100971
$946$	−1.96453	−0.0638723
$947$	23.7868	0.772968	0.386484	−	0.922296i	$-0.373689\pi$
$947$	23.7868	0.772968	0.386484	+	0.922296i	$0.373689\pi$
$948$	−13.8422	−0.449573
$949$	2.26202	0.0734283
$950$	5.64333	0.183094
$951$	−19.6930	−0.638589
$952$	0.446526	0.0144720
$953$	33.0634	1.07103	0.535514	−	0.844527i	$-0.320118\pi$
$953$	33.0634	1.07103	0.535514	+	0.844527i	$0.320118\pi$
$954$	−14.4400	−0.467512
$955$	−9.93175	−0.321384
$956$	16.0764	0.519949
$957$	53.2614	1.72170
$958$	−19.0973	−0.617004
$959$	−57.8053	−1.86663
$960$	2.45664	0.0792876
$961$	−23.2924	−0.751367
$962$	3.91105	0.126097
$963$	−23.5071	−0.757506
$964$	14.4307	0.464782
$965$	6.50943	0.209546
$966$	−64.0009	−2.05920
$967$	1.16009	0.0373059	0.0186529	−	0.999826i	$-0.494062\pi$
$967$	1.16009	0.0373059	0.0186529	+	0.999826i	$0.494062\pi$
$968$	1.35881	0.0436740
$969$	−1.71815	−0.0551948
$970$	−5.56268	−0.178607
$971$	−24.8499	−0.797472	−0.398736	−	0.917066i	$-0.630551\pi$
$971$	−24.8499	−0.797472	−0.398736	+	0.917066i	$0.630551\pi$
$972$	22.1067	0.709073
$973$	26.2612	0.841895
$974$	−12.4155	−0.397820
$975$	1.41047	0.0451710
$976$	−14.4419	−0.462273
$977$	−16.5141	−0.528334	−0.264167	−	0.964477i	$-0.585097\pi$
$977$	−16.5141	−0.528334	−0.264167	+	0.964477i	$0.585097\pi$
$978$	26.8243	0.857748
$979$	−4.77492	−0.152607
$980$	−5.98152	−0.191073
$981$	−46.5251	−1.48543
$982$	−37.9815	−1.21204
$983$	42.1387	1.34401	0.672007	−	0.740544i	$-0.265432\pi$
$983$	42.1387	1.34401	0.672007	+	0.740544i	$0.265432\pi$
$984$	−25.2202	−0.803990
$985$	−14.3618	−0.457606
$986$	−0.764305	−0.0243404
$987$	−81.3152	−2.58829
$988$	−3.24009	−0.103081
$989$	−4.04066	−0.128485
$990$	−10.6698	−0.339109
$991$	13.0664	0.415067	0.207534	−	0.978228i	$-0.433456\pi$
$991$	13.0664	0.415067	0.207534	+	0.978228i	$0.433456\pi$
$992$	2.77626	0.0881464
$993$	32.3645	1.02706
$994$	−47.8687	−1.51830
$995$	−2.37936	−0.0754309
$996$	13.5256	0.428576
$997$	51.5247	1.63180	0.815901	−	0.578191i	$-0.196241\pi$
$997$	51.5247	1.63180	0.815901	+	0.578191i	$0.196241\pi$
$998$	−12.9591	−0.410214
$999$	0.586842	0.0185669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.5	✓	28	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.45664 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.45664 q^{6} +3.60299 q^{7} +1.00000 q^{8} +3.03507 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.45664 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.45664 q^{6} +3.60299 q^{7} +1.00000 q^{8} +3.03507 q^{9} -1.00000 q^{10} +3.51551 q^{11} -2.45664 q^{12} -0.574145 q^{13} +3.60299 q^{14} +2.45664 q^{15} +1.00000 q^{16} +0.123932 q^{17} +3.03507 q^{18} +5.64333 q^{19} -1.00000 q^{20} -8.85123 q^{21} +3.51551 q^{22} +7.23073 q^{23} -2.45664 q^{24} +1.00000 q^{25} -0.574145 q^{26} -0.0861489 q^{27} +3.60299 q^{28} -6.16713 q^{29} +2.45664 q^{30} +2.77626 q^{31} +1.00000 q^{32} -8.63634 q^{33} +0.123932 q^{34} -3.60299 q^{35} +3.03507 q^{36} -6.81195 q^{37} +5.64333 q^{38} +1.41047 q^{39} -1.00000 q^{40} +10.2661 q^{41} -8.85123 q^{42} -0.558818 q^{43} +3.51551 q^{44} -3.03507 q^{45} +7.23073 q^{46} +9.18687 q^{47} -2.45664 q^{48} +5.98152 q^{49} +1.00000 q^{50} -0.304456 q^{51} -0.574145 q^{52} -4.75772 q^{53} -0.0861489 q^{54} -3.51551 q^{55} +3.60299 q^{56} -13.8636 q^{57} -6.16713 q^{58} +6.21789 q^{59} +2.45664 q^{60} -14.4419 q^{61} +2.77626 q^{62} +10.9353 q^{63} +1.00000 q^{64} +0.574145 q^{65} -8.63634 q^{66} +13.4655 q^{67} +0.123932 q^{68} -17.7633 q^{69} -3.60299 q^{70} -13.2858 q^{71} +3.03507 q^{72} -3.93981 q^{73} -6.81195 q^{74} -2.45664 q^{75} +5.64333 q^{76} +12.6663 q^{77} +1.41047 q^{78} +5.63460 q^{79} -1.00000 q^{80} -8.89357 q^{81} +10.2661 q^{82} -5.50574 q^{83} -8.85123 q^{84} -0.123932 q^{85} -0.558818 q^{86} +15.1504 q^{87} +3.51551 q^{88} -1.35824 q^{89} -3.03507 q^{90} -2.06864 q^{91} +7.23073 q^{92} -6.82027 q^{93} +9.18687 q^{94} -5.64333 q^{95} -2.45664 q^{96} +5.56268 q^{97} +5.98152 q^{98} +10.6698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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