LMFDB - Embedded newform 6010.2.a.h.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.657748 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.657748 q^{6} +4.85947 q^{7} +1.00000 q^{8} -2.56737 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.657748 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.657748 q^{6} +4.85947 q^{7} +1.00000 q^{8} -2.56737 q^{9} -1.00000 q^{10} -2.72869 q^{11} +0.657748 q^{12} +5.32494 q^{13} +4.85947 q^{14} -0.657748 q^{15} +1.00000 q^{16} -4.78932 q^{17} -2.56737 q^{18} -5.55738 q^{19} -1.00000 q^{20} +3.19630 q^{21} -2.72869 q^{22} +6.81632 q^{23} +0.657748 q^{24} +1.00000 q^{25} +5.32494 q^{26} -3.66192 q^{27} +4.85947 q^{28} +4.89341 q^{29} -0.657748 q^{30} -7.03756 q^{31} +1.00000 q^{32} -1.79479 q^{33} -4.78932 q^{34} -4.85947 q^{35} -2.56737 q^{36} +7.39479 q^{37} -5.55738 q^{38} +3.50247 q^{39} -1.00000 q^{40} +8.54534 q^{41} +3.19630 q^{42} -6.13645 q^{43} -2.72869 q^{44} +2.56737 q^{45} +6.81632 q^{46} +12.2320 q^{47} +0.657748 q^{48} +16.6144 q^{49} +1.00000 q^{50} -3.15016 q^{51} +5.32494 q^{52} +12.2435 q^{53} -3.66192 q^{54} +2.72869 q^{55} +4.85947 q^{56} -3.65535 q^{57} +4.89341 q^{58} +7.37057 q^{59} -0.657748 q^{60} +4.32641 q^{61} -7.03756 q^{62} -12.4760 q^{63} +1.00000 q^{64} -5.32494 q^{65} -1.79479 q^{66} +9.57732 q^{67} -4.78932 q^{68} +4.48342 q^{69} -4.85947 q^{70} +5.46888 q^{71} -2.56737 q^{72} -10.1972 q^{73} +7.39479 q^{74} +0.657748 q^{75} -5.55738 q^{76} -13.2600 q^{77} +3.50247 q^{78} -7.85870 q^{79} -1.00000 q^{80} +5.29348 q^{81} +8.54534 q^{82} +7.47633 q^{83} +3.19630 q^{84} +4.78932 q^{85} -6.13645 q^{86} +3.21863 q^{87} -2.72869 q^{88} -3.80208 q^{89} +2.56737 q^{90} +25.8764 q^{91} +6.81632 q^{92} -4.62894 q^{93} +12.2320 q^{94} +5.55738 q^{95} +0.657748 q^{96} -0.524453 q^{97} +16.6144 q^{98} +7.00555 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.657748	0.379751	0.189875	−	0.981808i	$-0.439192\pi$
$3$	0.657748	0.379751	0.189875	+	0.981808i	$0.439192\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.657748	0.268524
$7$	4.85947	1.83671	0.918353	−	0.395761i	$-0.129519\pi$
$7$	4.85947	1.83671	0.918353	+	0.395761i	$0.129519\pi$
$8$	1.00000	0.353553
$9$	−2.56737	−0.855789
$10$	−1.00000	−0.316228
$11$	−2.72869	−0.822731	−0.411366	−	0.911470i	$-0.634948\pi$
$11$	−2.72869	−0.822731	−0.411366	+	0.911470i	$0.634948\pi$
$12$	0.657748	0.189875
$13$	5.32494	1.47687	0.738437	−	0.674322i	$-0.235564\pi$
$13$	5.32494	1.47687	0.738437	+	0.674322i	$0.235564\pi$
$14$	4.85947	1.29875
$15$	−0.657748	−0.169830
$16$	1.00000	0.250000
$17$	−4.78932	−1.16158	−0.580790	−	0.814054i	$-0.697256\pi$
$17$	−4.78932	−1.16158	−0.580790	+	0.814054i	$0.697256\pi$
$18$	−2.56737	−0.605134
$19$	−5.55738	−1.27495	−0.637475	−	0.770471i	$-0.720021\pi$
$19$	−5.55738	−1.27495	−0.637475	+	0.770471i	$0.720021\pi$
$20$	−1.00000	−0.223607
$21$	3.19630	0.697491
$22$	−2.72869	−0.581759
$23$	6.81632	1.42130	0.710650	−	0.703546i	$-0.248401\pi$
$23$	6.81632	1.42130	0.710650	+	0.703546i	$0.248401\pi$
$24$	0.657748	0.134262
$25$	1.00000	0.200000
$26$	5.32494	1.04431
$27$	−3.66192	−0.704737
$28$	4.85947	0.918353
$29$	4.89341	0.908683	0.454342	−	0.890828i	$-0.349875\pi$
$29$	4.89341	0.908683	0.454342	+	0.890828i	$0.349875\pi$
$30$	−0.657748	−0.120088
$31$	−7.03756	−1.26398	−0.631991	−	0.774975i	$-0.717762\pi$
$31$	−7.03756	−1.26398	−0.631991	+	0.774975i	$0.717762\pi$
$32$	1.00000	0.176777
$33$	−1.79479	−0.312433
$34$	−4.78932	−0.821361
$35$	−4.85947	−0.821400
$36$	−2.56737	−0.427895
$37$	7.39479	1.21570	0.607848	−	0.794053i	$-0.292033\pi$
$37$	7.39479	1.21570	0.607848	+	0.794053i	$0.292033\pi$
$38$	−5.55738	−0.901526
$39$	3.50247	0.560844
$40$	−1.00000	−0.158114
$41$	8.54534	1.33456	0.667279	−	0.744808i	$-0.267459\pi$
$41$	8.54534	1.33456	0.667279	+	0.744808i	$0.267459\pi$
$42$	3.19630	0.493201
$43$	−6.13645	−0.935800	−0.467900	−	0.883781i	$-0.654989\pi$
$43$	−6.13645	−0.935800	−0.467900	+	0.883781i	$0.654989\pi$
$44$	−2.72869	−0.411366
$45$	2.56737	0.382721
$46$	6.81632	1.00501
$47$	12.2320	1.78422	0.892112	−	0.451815i	$-0.149223\pi$
$47$	12.2320	1.78422	0.892112	+	0.451815i	$0.149223\pi$
$48$	0.657748	0.0949377
$49$	16.6144	2.37349
$50$	1.00000	0.141421
$51$	−3.15016	−0.441111
$52$	5.32494	0.738437
$53$	12.2435	1.68178	0.840889	−	0.541208i	$-0.182033\pi$
$53$	12.2435	1.68178	0.840889	+	0.541208i	$0.182033\pi$
$54$	−3.66192	−0.498325
$55$	2.72869	0.367937
$56$	4.85947	0.649374
$57$	−3.65535	−0.484163
$58$	4.89341	0.642536
$59$	7.37057	0.959566	0.479783	−	0.877387i	$-0.340715\pi$
$59$	7.37057	0.959566	0.479783	+	0.877387i	$0.340715\pi$
$60$	−0.657748	−0.0849149
$61$	4.32641	0.553939	0.276970	−	0.960879i	$-0.410670\pi$
$61$	4.32641	0.553939	0.276970	+	0.960879i	$0.410670\pi$
$62$	−7.03756	−0.893771
$63$	−12.4760	−1.57183
$64$	1.00000	0.125000
$65$	−5.32494	−0.660478
$66$	−1.79479	−0.220923
$67$	9.57732	1.17006	0.585028	−	0.811013i	$-0.301084\pi$
$67$	9.57732	1.17006	0.585028	+	0.811013i	$0.301084\pi$
$68$	−4.78932	−0.580790
$69$	4.48342	0.539740
$70$	−4.85947	−0.580818
$71$	5.46888	0.649037	0.324518	−	0.945879i	$-0.394798\pi$
$71$	5.46888	0.649037	0.324518	+	0.945879i	$0.394798\pi$
$72$	−2.56737	−0.302567
$73$	−10.1972	−1.19350	−0.596748	−	0.802429i	$-0.703541\pi$
$73$	−10.1972	−1.19350	−0.596748	+	0.802429i	$0.703541\pi$
$74$	7.39479	0.859627
$75$	0.657748	0.0759502
$76$	−5.55738	−0.637475
$77$	−13.2600	−1.51112
$78$	3.50247	0.396577
$79$	−7.85870	−0.884173	−0.442086	−	0.896973i	$-0.645762\pi$
$79$	−7.85870	−0.884173	−0.442086	+	0.896973i	$0.645762\pi$
$80$	−1.00000	−0.111803
$81$	5.29348	0.588165
$82$	8.54534	0.943675
$83$	7.47633	0.820634	0.410317	−	0.911943i	$-0.365418\pi$
$83$	7.47633	0.820634	0.410317	+	0.911943i	$0.365418\pi$
$84$	3.19630	0.348745
$85$	4.78932	0.519474
$86$	−6.13645	−0.661711
$87$	3.21863	0.345073
$88$	−2.72869	−0.290879
$89$	−3.80208	−0.403020	−0.201510	−	0.979486i	$-0.564585\pi$
$89$	−3.80208	−0.403020	−0.201510	+	0.979486i	$0.564585\pi$
$90$	2.56737	0.270624
$91$	25.8764	2.71258
$92$	6.81632	0.710650
$93$	−4.62894	−0.479998
$94$	12.2320	1.26164
$95$	5.55738	0.570175
$96$	0.657748	0.0671311
$97$	−0.524453	−0.0532501	−0.0266251	−	0.999645i	$-0.508476\pi$
$97$	−0.524453	−0.0532501	−0.0266251	+	0.999645i	$0.508476\pi$
$98$	16.6144	1.67831
$99$	7.00555	0.704085
$100$	1.00000	0.100000
$101$	13.8123	1.37437	0.687187	−	0.726480i	$-0.258845\pi$
$101$	13.8123	1.37437	0.687187	+	0.726480i	$0.258845\pi$
$102$	−3.15016	−0.311912
$103$	−14.5221	−1.43091	−0.715454	−	0.698659i	$-0.753780\pi$
$103$	−14.5221	−1.43091	−0.715454	+	0.698659i	$0.753780\pi$
$104$	5.32494	0.522154
$105$	−3.19630	−0.311927
$106$	12.2435	1.18920
$107$	−18.3375	−1.77275	−0.886376	−	0.462967i	$-0.846785\pi$
$107$	−18.3375	−1.77275	−0.886376	+	0.462967i	$0.846785\pi$
$108$	−3.66192	−0.352369
$109$	4.29714	0.411592	0.205796	−	0.978595i	$-0.434022\pi$
$109$	4.29714	0.411592	0.205796	+	0.978595i	$0.434022\pi$
$110$	2.72869	0.260170
$111$	4.86390	0.461661
$112$	4.85947	0.459177
$113$	4.20207	0.395297	0.197649	−	0.980273i	$-0.436670\pi$
$113$	4.20207	0.395297	0.197649	+	0.980273i	$0.436670\pi$
$114$	−3.65535	−0.342355
$115$	−6.81632	−0.635625
$116$	4.89341	0.454342
$117$	−13.6711	−1.26389
$118$	7.37057	0.678516
$119$	−23.2735	−2.13348
$120$	−0.657748	−0.0600439
$121$	−3.55425	−0.323113
$122$	4.32641	0.391694
$123$	5.62068	0.506799
$124$	−7.03756	−0.631991
$125$	−1.00000	−0.0894427
$126$	−12.4760	−1.11145
$127$	−16.4905	−1.46329	−0.731645	−	0.681685i	$-0.761247\pi$
$127$	−16.4905	−1.46329	−0.731645	+	0.681685i	$0.761247\pi$
$128$	1.00000	0.0883883
$129$	−4.03624	−0.355371
$130$	−5.32494	−0.467029
$131$	−3.67639	−0.321208	−0.160604	−	0.987019i	$-0.551344\pi$
$131$	−3.67639	−0.321208	−0.160604	+	0.987019i	$0.551344\pi$
$132$	−1.79479	−0.156216
$133$	−27.0059	−2.34171
$134$	9.57732	0.827355
$135$	3.66192	0.315168
$136$	−4.78932	−0.410680
$137$	8.45470	0.722334	0.361167	−	0.932501i	$-0.382378\pi$
$137$	8.45470	0.722334	0.361167	+	0.932501i	$0.382378\pi$
$138$	4.48342	0.381654
$139$	4.90005	0.415617	0.207808	−	0.978170i	$-0.433367\pi$
$139$	4.90005	0.415617	0.207808	+	0.978170i	$0.433367\pi$
$140$	−4.85947	−0.410700
$141$	8.04558	0.677560
$142$	5.46888	0.458938
$143$	−14.5301	−1.21507
$144$	−2.56737	−0.213947
$145$	−4.89341	−0.406375
$146$	−10.1972	−0.843929
$147$	10.9281	0.901335
$148$	7.39479	0.607848
$149$	−12.0456	−0.986818	−0.493409	−	0.869797i	$-0.664249\pi$
$149$	−12.0456	−0.986818	−0.493409	+	0.869797i	$0.664249\pi$
$150$	0.657748	0.0537049
$151$	−22.5424	−1.83448	−0.917238	−	0.398339i	$-0.869587\pi$
$151$	−22.5424	−1.83448	−0.917238	+	0.398339i	$0.869587\pi$
$152$	−5.55738	−0.450763
$153$	12.2959	0.994067
$154$	−13.2600	−1.06852
$155$	7.03756	0.565270
$156$	3.50247	0.280422
$157$	21.2692	1.69747	0.848734	−	0.528820i	$-0.177365\pi$
$157$	21.2692	1.69747	0.848734	+	0.528820i	$0.177365\pi$
$158$	−7.85870	−0.625204
$159$	8.05315	0.638656
$160$	−1.00000	−0.0790569
$161$	33.1237	2.61051
$162$	5.29348	0.415895
$163$	−2.61197	−0.204585	−0.102293	−	0.994754i	$-0.532618\pi$
$163$	−2.61197	−0.204585	−0.102293	+	0.994754i	$0.532618\pi$
$164$	8.54534	0.667279
$165$	1.79479	0.139724
$166$	7.47633	0.580276
$167$	8.38548	0.648888	0.324444	−	0.945905i	$-0.394823\pi$
$167$	8.38548	0.648888	0.324444	+	0.945905i	$0.394823\pi$
$168$	3.19630	0.246600
$169$	15.3550	1.18116
$170$	4.78932	0.367324
$171$	14.2678	1.09109
$172$	−6.13645	−0.467900
$173$	6.46330	0.491396	0.245698	−	0.969346i	$-0.420983\pi$
$173$	6.46330	0.491396	0.245698	+	0.969346i	$0.420983\pi$
$174$	3.21863	0.244004
$175$	4.85947	0.367341
$176$	−2.72869	−0.205683
$177$	4.84797	0.364396
$178$	−3.80208	−0.284978
$179$	18.2236	1.36209	0.681047	−	0.732240i	$-0.261525\pi$
$179$	18.2236	1.36209	0.681047	+	0.732240i	$0.261525\pi$
$180$	2.56737	0.191360
$181$	13.3120	0.989473	0.494736	−	0.869043i	$-0.335265\pi$
$181$	13.3120	0.989473	0.494736	+	0.869043i	$0.335265\pi$
$182$	25.8764	1.91809
$183$	2.84568	0.210359
$184$	6.81632	0.502505
$185$	−7.39479	−0.543676
$186$	−4.62894	−0.339410
$187$	13.0686	0.955668
$188$	12.2320	0.892112
$189$	−17.7950	−1.29440
$190$	5.55738	0.403175
$191$	−24.9236	−1.80341	−0.901705	−	0.432351i	$-0.857684\pi$
$191$	−24.9236	−1.80341	−0.901705	+	0.432351i	$0.857684\pi$
$192$	0.657748	0.0474688
$193$	1.42758	0.102759	0.0513796	−	0.998679i	$-0.483638\pi$
$193$	1.42758	0.102759	0.0513796	+	0.998679i	$0.483638\pi$
$194$	−0.524453	−0.0376535
$195$	−3.50247	−0.250817
$196$	16.6144	1.18675
$197$	−24.5490	−1.74905	−0.874523	−	0.484985i	$-0.838825\pi$
$197$	−24.5490	−1.74905	−0.874523	+	0.484985i	$0.838825\pi$
$198$	7.00555	0.497863
$199$	0.269032	0.0190712	0.00953559	−	0.999955i	$-0.496965\pi$
$199$	0.269032	0.0190712	0.00953559	+	0.999955i	$0.496965\pi$
$200$	1.00000	0.0707107
$201$	6.29946	0.444330
$202$	13.8123	0.971830
$203$	23.7794	1.66898
$204$	−3.15016	−0.220555
$205$	−8.54534	−0.596832
$206$	−14.5221	−1.01181
$207$	−17.5000	−1.21633
$208$	5.32494	0.369218
$209$	15.1644	1.04894
$210$	−3.19630	−0.220566
$211$	13.7218	0.944650	0.472325	−	0.881425i	$-0.343415\pi$
$211$	13.7218	0.944650	0.472325	+	0.881425i	$0.343415\pi$
$212$	12.2435	0.840889
$213$	3.59714	0.246472
$214$	−18.3375	−1.25352
$215$	6.13645	0.418503
$216$	−3.66192	−0.249162
$217$	−34.1988	−2.32157
$218$	4.29714	0.291039
$219$	−6.70720	−0.453231
$220$	2.72869	0.183968
$221$	−25.5028	−1.71551
$222$	4.86390	0.326444
$223$	−4.50229	−0.301495	−0.150748	−	0.988572i	$-0.548168\pi$
$223$	−4.50229	−0.301495	−0.150748	+	0.988572i	$0.548168\pi$
$224$	4.85947	0.324687
$225$	−2.56737	−0.171158
$226$	4.20207	0.279517
$227$	−2.70149	−0.179304	−0.0896521	−	0.995973i	$-0.528576\pi$
$227$	−2.70149	−0.179304	−0.0896521	+	0.995973i	$0.528576\pi$
$228$	−3.65535	−0.242082
$229$	−0.304049	−0.0200921	−0.0100461	−	0.999950i	$-0.503198\pi$
$229$	−0.304049	−0.0200921	−0.0100461	+	0.999950i	$0.503198\pi$
$230$	−6.81632	−0.449455
$231$	−8.72173	−0.573847
$232$	4.89341	0.321268
$233$	−2.17852	−0.142720	−0.0713598	−	0.997451i	$-0.522734\pi$
$233$	−2.17852	−0.142720	−0.0713598	+	0.997451i	$0.522734\pi$
$234$	−13.6711	−0.893707
$235$	−12.2320	−0.797929
$236$	7.37057	0.479783
$237$	−5.16904	−0.335765
$238$	−23.2735	−1.50860
$239$	23.0705	1.49231	0.746154	−	0.665773i	$-0.231898\pi$
$239$	23.0705	1.49231	0.746154	+	0.665773i	$0.231898\pi$
$240$	−0.657748	−0.0424574
$241$	24.1372	1.55481	0.777406	−	0.628999i	$-0.216535\pi$
$241$	24.1372	1.55481	0.777406	+	0.628999i	$0.216535\pi$
$242$	−3.55425	−0.228476
$243$	14.4675	0.928093
$244$	4.32641	0.276970
$245$	−16.6144	−1.06146
$246$	5.62068	0.358361
$247$	−29.5927	−1.88294
$248$	−7.03756	−0.446885
$249$	4.91754	0.311636
$250$	−1.00000	−0.0632456
$251$	−24.2163	−1.52852	−0.764260	−	0.644908i	$-0.776896\pi$
$251$	−24.2163	−1.52852	−0.764260	+	0.644908i	$0.776896\pi$
$252$	−12.4760	−0.785917
$253$	−18.5996	−1.16935
$254$	−16.4905	−1.03470
$255$	3.15016	0.197271
$256$	1.00000	0.0625000
$257$	−28.3103	−1.76595	−0.882974	−	0.469422i	$-0.844462\pi$
$257$	−28.3103	−1.76595	−0.882974	+	0.469422i	$0.844462\pi$
$258$	−4.03624	−0.251285
$259$	35.9348	2.23288
$260$	−5.32494	−0.330239
$261$	−12.5632	−0.777641
$262$	−3.67639	−0.227128
$263$	23.0401	1.42071	0.710357	−	0.703841i	$-0.248533\pi$
$263$	23.0401	1.42071	0.710357	+	0.703841i	$0.248533\pi$
$264$	−1.79479	−0.110462
$265$	−12.2435	−0.752114
$266$	−27.0059	−1.65584
$267$	−2.50081	−0.153047
$268$	9.57732	0.585028
$269$	−6.37155	−0.388480	−0.194240	−	0.980954i	$-0.562224\pi$
$269$	−6.37155	−0.388480	−0.194240	+	0.980954i	$0.562224\pi$
$270$	3.66192	0.222858
$271$	21.9663	1.33436	0.667179	−	0.744898i	$-0.267502\pi$
$271$	21.9663	1.33436	0.667179	+	0.744898i	$0.267502\pi$
$272$	−4.78932	−0.290395
$273$	17.0201	1.03011
$274$	8.45470	0.510767
$275$	−2.72869	−0.164546
$276$	4.48342	0.269870
$277$	−28.7993	−1.73038	−0.865190	−	0.501445i	$-0.832802\pi$
$277$	−28.7993	−1.73038	−0.865190	+	0.501445i	$0.832802\pi$
$278$	4.90005	0.293885
$279$	18.0680	1.08170
$280$	−4.85947	−0.290409
$281$	18.5761	1.10816	0.554080	−	0.832464i	$-0.313070\pi$
$281$	18.5761	1.10816	0.554080	+	0.832464i	$0.313070\pi$
$282$	8.04558	0.479107
$283$	6.54014	0.388771	0.194386	−	0.980925i	$-0.437729\pi$
$283$	6.54014	0.388771	0.194386	+	0.980925i	$0.437729\pi$
$284$	5.46888	0.324518
$285$	3.65535	0.216524
$286$	−14.5301	−0.859184
$287$	41.5258	2.45119
$288$	−2.56737	−0.151284
$289$	5.93754	0.349267
$290$	−4.89341	−0.287351
$291$	−0.344958	−0.0202218
$292$	−10.1972	−0.596748
$293$	1.40658	0.0821735	0.0410867	−	0.999156i	$-0.486918\pi$
$293$	1.40658	0.0821735	0.0410867	+	0.999156i	$0.486918\pi$
$294$	10.9281	0.637340
$295$	−7.37057	−0.429131
$296$	7.39479	0.429813
$297$	9.99226	0.579809
$298$	−12.0456	−0.697786
$299$	36.2965	2.09908
$300$	0.657748	0.0379751
$301$	−29.8199	−1.71879
$302$	−22.5424	−1.29717
$303$	9.08500	0.521920
$304$	−5.55738	−0.318738
$305$	−4.32641	−0.247729
$306$	12.2959	0.702912
$307$	−8.38170	−0.478369	−0.239184	−	0.970974i	$-0.576880\pi$
$307$	−8.38170	−0.478369	−0.239184	+	0.970974i	$0.576880\pi$
$308$	−13.2600	−0.755558
$309$	−9.55190	−0.543389
$310$	7.03756	0.399706
$311$	19.2840	1.09349	0.546746	−	0.837298i	$-0.315866\pi$
$311$	19.2840	1.09349	0.546746	+	0.837298i	$0.315866\pi$
$312$	3.50247	0.198288
$313$	7.23827	0.409131	0.204566	−	0.978853i	$-0.434422\pi$
$313$	7.23827	0.409131	0.204566	+	0.978853i	$0.434422\pi$
$314$	21.2692	1.20029
$315$	12.4760	0.702946
$316$	−7.85870	−0.442086
$317$	−28.9216	−1.62440	−0.812201	−	0.583378i	$-0.801731\pi$
$317$	−28.9216	−1.62440	−0.812201	+	0.583378i	$0.801731\pi$
$318$	8.05315	0.451598
$319$	−13.3526	−0.747602
$320$	−1.00000	−0.0559017
$321$	−12.0614	−0.673204
$322$	33.1237	1.84591
$323$	26.6160	1.48096
$324$	5.29348	0.294082
$325$	5.32494	0.295375
$326$	−2.61197	−0.144664
$327$	2.82644	0.156302
$328$	8.54534	0.471837
$329$	59.4411	3.27710
$330$	1.79479	0.0987999
$331$	−35.5094	−1.95177	−0.975885	−	0.218284i	$-0.929954\pi$
$331$	−35.5094	−1.95177	−0.975885	+	0.218284i	$0.929954\pi$
$332$	7.47633	0.410317
$333$	−18.9851	−1.04038
$334$	8.38548	0.458833
$335$	−9.57732	−0.523265
$336$	3.19630	0.174373
$337$	−19.4402	−1.05898	−0.529488	−	0.848318i	$-0.677616\pi$
$337$	−19.4402	−1.05898	−0.529488	+	0.848318i	$0.677616\pi$
$338$	15.3550	0.835204
$339$	2.76390	0.150114
$340$	4.78932	0.259737
$341$	19.2033	1.03992
$342$	14.2678	0.771516
$343$	46.7211	2.52270
$344$	−6.13645	−0.330855
$345$	−4.48342	−0.241379
$346$	6.46330	0.347469
$347$	4.83666	0.259646	0.129823	−	0.991537i	$-0.458559\pi$
$347$	4.83666	0.259646	0.129823	+	0.991537i	$0.458559\pi$
$348$	3.21863	0.172537
$349$	−36.2499	−1.94041	−0.970207	−	0.242277i	$-0.922106\pi$
$349$	−36.2499	−1.94041	−0.970207	+	0.242277i	$0.922106\pi$
$350$	4.85947	0.259750
$351$	−19.4995	−1.04081
$352$	−2.72869	−0.145440
$353$	8.24259	0.438709	0.219354	−	0.975645i	$-0.429605\pi$
$353$	8.24259	0.438709	0.219354	+	0.975645i	$0.429605\pi$
$354$	4.84797	0.257667
$355$	−5.46888	−0.290258
$356$	−3.80208	−0.201510
$357$	−15.3081	−0.810191
$358$	18.2236	0.963145
$359$	−10.8816	−0.574307	−0.287153	−	0.957885i	$-0.592709\pi$
$359$	−10.8816	−0.574307	−0.287153	+	0.957885i	$0.592709\pi$
$360$	2.56737	0.135312
$361$	11.8845	0.625498
$362$	13.3120	0.699663
$363$	−2.33780	−0.122703
$364$	25.8764	1.35629
$365$	10.1972	0.533747
$366$	2.84568	0.148746
$367$	−26.4108	−1.37863	−0.689317	−	0.724460i	$-0.742089\pi$
$367$	−26.4108	−1.37863	−0.689317	+	0.724460i	$0.742089\pi$
$368$	6.81632	0.355325
$369$	−21.9390	−1.14210
$370$	−7.39479	−0.384437
$371$	59.4970	3.08893
$372$	−4.62894	−0.239999
$373$	9.00937	0.466488	0.233244	−	0.972418i	$-0.425066\pi$
$373$	9.00937	0.466488	0.233244	+	0.972418i	$0.425066\pi$
$374$	13.0686	0.675759
$375$	−0.657748	−0.0339659
$376$	12.2320	0.630818
$377$	26.0571	1.34201
$378$	−17.7950	−0.915276
$379$	−6.55610	−0.336764	−0.168382	−	0.985722i	$-0.553854\pi$
$379$	−6.55610	−0.336764	−0.168382	+	0.985722i	$0.553854\pi$
$380$	5.55738	0.285088
$381$	−10.8466	−0.555686
$382$	−24.9236	−1.27520
$383$	29.7550	1.52041	0.760206	−	0.649682i	$-0.225098\pi$
$383$	29.7550	1.52041	0.760206	+	0.649682i	$0.225098\pi$
$384$	0.657748	0.0335655
$385$	13.2600	0.675792
$386$	1.42758	0.0726617
$387$	15.7545	0.800848
$388$	−0.524453	−0.0266251
$389$	−26.6722	−1.35233	−0.676167	−	0.736748i	$-0.736360\pi$
$389$	−26.6722	−1.35233	−0.676167	+	0.736748i	$0.736360\pi$
$390$	−3.50247	−0.177354
$391$	−32.6455	−1.65095
$392$	16.6144	0.839156
$393$	−2.41814	−0.121979
$394$	−24.5490	−1.23676
$395$	7.85870	0.395414
$396$	7.00555	0.352042
$397$	−10.3535	−0.519628	−0.259814	−	0.965659i	$-0.583661\pi$
$397$	−10.3535	−0.519628	−0.259814	+	0.965659i	$0.583661\pi$
$398$	0.269032	0.0134854
$399$	−17.7631	−0.889266
$400$	1.00000	0.0500000
$401$	0.100662	0.00502682	0.00251341	−	0.999997i	$-0.499200\pi$
$401$	0.100662	0.00502682	0.00251341	+	0.999997i	$0.499200\pi$
$402$	6.29946	0.314189
$403$	−37.4746	−1.86674
$404$	13.8123	0.687187
$405$	−5.29348	−0.263035
$406$	23.7794	1.18015
$407$	−20.1781	−1.00019
$408$	−3.15016	−0.155956
$409$	27.9049	1.37981	0.689904	−	0.723900i	$-0.257653\pi$
$409$	27.9049	1.37981	0.689904	+	0.723900i	$0.257653\pi$
$410$	−8.54534	−0.422024
$411$	5.56106	0.274307
$412$	−14.5221	−0.715454
$413$	35.8170	1.76244
$414$	−17.5000	−0.860078
$415$	−7.47633	−0.366999
$416$	5.32494	0.261077
$417$	3.22300	0.157831
$418$	15.1644	0.741714
$419$	−19.5961	−0.957330	−0.478665	−	0.877998i	$-0.658879\pi$
$419$	−19.5961	−0.957330	−0.478665	+	0.877998i	$0.658879\pi$
$420$	−3.19630	−0.155964
$421$	10.8798	0.530249	0.265125	−	0.964214i	$-0.414587\pi$
$421$	10.8798	0.530249	0.265125	+	0.964214i	$0.414587\pi$
$422$	13.7218	0.667968
$423$	−31.4041	−1.52692
$424$	12.2435	0.594598
$425$	−4.78932	−0.232316
$426$	3.59714	0.174282
$427$	21.0240	1.01742
$428$	−18.3375	−0.886376
$429$	−9.55716	−0.461424
$430$	6.13645	0.295926
$431$	38.8093	1.86938	0.934690	−	0.355465i	$-0.115677\pi$
$431$	38.8093	1.86938	0.934690	+	0.355465i	$0.115677\pi$
$432$	−3.66192	−0.176184
$433$	−22.7471	−1.09316	−0.546578	−	0.837408i	$-0.684070\pi$
$433$	−22.7471	−1.09316	−0.546578	+	0.837408i	$0.684070\pi$
$434$	−34.1988	−1.64159
$435$	−3.21863	−0.154321
$436$	4.29714	0.205796
$437$	−37.8809	−1.81209
$438$	−6.70720	−0.320483
$439$	7.64932	0.365082	0.182541	−	0.983198i	$-0.441568\pi$
$439$	7.64932	0.365082	0.182541	+	0.983198i	$0.441568\pi$
$440$	2.72869	0.130085
$441$	−42.6554	−2.03121
$442$	−25.5028	−1.21305
$443$	−7.21100	−0.342605	−0.171302	−	0.985218i	$-0.554798\pi$
$443$	−7.21100	−0.342605	−0.171302	+	0.985218i	$0.554798\pi$
$444$	4.86390	0.230831
$445$	3.80208	0.180236
$446$	−4.50229	−0.213189
$447$	−7.92300	−0.374745
$448$	4.85947	0.229588
$449$	10.9506	0.516790	0.258395	−	0.966039i	$-0.416806\pi$
$449$	10.9506	0.516790	0.258395	+	0.966039i	$0.416806\pi$
$450$	−2.56737	−0.121027
$451$	−23.3176	−1.09798
$452$	4.20207	0.197649
$453$	−14.8272	−0.696644
$454$	−2.70149	−0.126787
$455$	−25.8764	−1.21310
$456$	−3.65535	−0.171178
$457$	−5.83558	−0.272977	−0.136488	−	0.990642i	$-0.543582\pi$
$457$	−5.83558	−0.272977	−0.136488	+	0.990642i	$0.543582\pi$
$458$	−0.304049	−0.0142073
$459$	17.5381	0.818609
$460$	−6.81632	−0.317812
$461$	1.59905	0.0744751	0.0372376	−	0.999306i	$-0.488144\pi$
$461$	1.59905	0.0744751	0.0372376	+	0.999306i	$0.488144\pi$
$462$	−8.72173	−0.405771
$463$	22.0566	1.02506	0.512528	−	0.858671i	$-0.328709\pi$
$463$	22.0566	1.02506	0.512528	+	0.858671i	$0.328709\pi$
$464$	4.89341	0.227171
$465$	4.62894	0.214662
$466$	−2.17852	−0.100918
$467$	14.4621	0.669228	0.334614	−	0.942355i	$-0.391394\pi$
$467$	14.4621	0.669228	0.334614	+	0.942355i	$0.391394\pi$
$468$	−13.6711	−0.631947
$469$	46.5407	2.14905
$470$	−12.2320	−0.564221
$471$	13.9898	0.644615
$472$	7.37057	0.339258
$473$	16.7445	0.769912
$474$	−5.16904	−0.237422
$475$	−5.55738	−0.254990
$476$	−23.2735	−1.06674
$477$	−31.4336	−1.43925
$478$	23.0705	1.05522
$479$	−18.3844	−0.840004	−0.420002	−	0.907523i	$-0.637971\pi$
$479$	−18.3844	−0.840004	−0.420002	+	0.907523i	$0.637971\pi$
$480$	−0.657748	−0.0300219
$481$	39.3768	1.79543
$482$	24.1372	1.09942
$483$	21.7870	0.991344
$484$	−3.55425	−0.161557
$485$	0.524453	0.0238142
$486$	14.4675	0.656261
$487$	16.8715	0.764521	0.382260	−	0.924055i	$-0.375146\pi$
$487$	16.8715	0.764521	0.382260	+	0.924055i	$0.375146\pi$
$488$	4.32641	0.195847
$489$	−1.71802	−0.0776914
$490$	−16.6144	−0.750564
$491$	−28.9865	−1.30814	−0.654072	−	0.756433i	$-0.726940\pi$
$491$	−28.9865	−1.30814	−0.654072	+	0.756433i	$0.726940\pi$
$492$	5.62068	0.253400
$493$	−23.4361	−1.05551
$494$	−29.5927	−1.33144
$495$	−7.00555	−0.314876
$496$	−7.03756	−0.315996
$497$	26.5759	1.19209
$498$	4.91754	0.220360
$499$	22.1514	0.991634	0.495817	−	0.868427i	$-0.334869\pi$
$499$	22.1514	0.991634	0.495817	+	0.868427i	$0.334869\pi$
$500$	−1.00000	−0.0447214
$501$	5.51553	0.246416
$502$	−24.2163	−1.08083
$503$	13.5817	0.605579	0.302790	−	0.953057i	$-0.402082\pi$
$503$	13.5817	0.605579	0.302790	+	0.953057i	$0.402082\pi$
$504$	−12.4760	−0.555727
$505$	−13.8123	−0.614639
$506$	−18.5996	−0.826854
$507$	10.0997	0.448545
$508$	−16.4905	−0.731645
$509$	−22.9558	−1.01750	−0.508749	−	0.860915i	$-0.669892\pi$
$509$	−22.9558	−1.01750	−0.508749	+	0.860915i	$0.669892\pi$
$510$	3.15016	0.139491
$511$	−49.5531	−2.19210
$512$	1.00000	0.0441942
$513$	20.3507	0.898505
$514$	−28.3103	−1.24871
$515$	14.5221	0.639922
$516$	−4.03624	−0.177685
$517$	−33.3774	−1.46794
$518$	35.9348	1.57888
$519$	4.25122	0.186608
$520$	−5.32494	−0.233514
$521$	−21.8511	−0.957315	−0.478658	−	0.878002i	$-0.658876\pi$
$521$	−21.8511	−0.957315	−0.478658	+	0.878002i	$0.658876\pi$
$522$	−12.5632	−0.549875
$523$	−28.8733	−1.26254	−0.631271	−	0.775563i	$-0.717466\pi$
$523$	−28.8733	−1.26254	−0.631271	+	0.775563i	$0.717466\pi$
$524$	−3.67639	−0.160604
$525$	3.19630	0.139498
$526$	23.0401	1.00460
$527$	33.7051	1.46822
$528$	−1.79479	−0.0781082
$529$	23.4622	1.02009
$530$	−12.2435	−0.531825
$531$	−18.9230	−0.821186
$532$	−27.0059	−1.17086
$533$	45.5035	1.97097
$534$	−2.50081	−0.108221
$535$	18.3375	0.792798
$536$	9.57732	0.413677
$537$	11.9865	0.517256
$538$	−6.37155	−0.274697
$539$	−45.3357	−1.95275
$540$	3.66192	0.157584
$541$	3.24806	0.139645	0.0698225	−	0.997559i	$-0.477757\pi$
$541$	3.24806	0.139645	0.0698225	+	0.997559i	$0.477757\pi$
$542$	21.9663	0.943533
$543$	8.75593	0.375753
$544$	−4.78932	−0.205340
$545$	−4.29714	−0.184069
$546$	17.0201	0.728395
$547$	−32.2226	−1.37774	−0.688870	−	0.724885i	$-0.741893\pi$
$547$	−32.2226	−1.37774	−0.688870	+	0.724885i	$0.741893\pi$
$548$	8.45470	0.361167
$549$	−11.1075	−0.474055
$550$	−2.72869	−0.116352
$551$	−27.1945	−1.15853
$552$	4.48342	0.190827
$553$	−38.1891	−1.62397
$554$	−28.7993	−1.22356
$555$	−4.86390	−0.206461
$556$	4.90005	0.207808
$557$	−14.1314	−0.598767	−0.299383	−	0.954133i	$-0.596781\pi$
$557$	−14.1314	−0.598767	−0.299383	+	0.954133i	$0.596781\pi$
$558$	18.0680	0.764879
$559$	−32.6763	−1.38206
$560$	−4.85947	−0.205350
$561$	8.59581	0.362916
$562$	18.5761	0.783587
$563$	−4.69434	−0.197843	−0.0989215	−	0.995095i	$-0.531539\pi$
$563$	−4.69434	−0.197843	−0.0989215	+	0.995095i	$0.531539\pi$
$564$	8.04558	0.338780
$565$	−4.20207	−0.176782
$566$	6.54014	0.274903
$567$	25.7235	1.08029
$568$	5.46888	0.229469
$569$	−13.5870	−0.569597	−0.284799	−	0.958587i	$-0.591927\pi$
$569$	−13.5870	−0.569597	−0.284799	+	0.958587i	$0.591927\pi$
$570$	3.65535	0.153106
$571$	14.7679	0.618015	0.309008	−	0.951060i	$-0.400003\pi$
$571$	14.7679	0.618015	0.309008	+	0.951060i	$0.400003\pi$
$572$	−14.5301	−0.607535
$573$	−16.3935	−0.684847
$574$	41.5258	1.73325
$575$	6.81632	0.284260
$576$	−2.56737	−0.106974
$577$	−8.70775	−0.362508	−0.181254	−	0.983436i	$-0.558016\pi$
$577$	−8.70775	−0.362508	−0.181254	+	0.983436i	$0.558016\pi$
$578$	5.93754	0.246969
$579$	0.938985	0.0390229
$580$	−4.89341	−0.203188
$581$	36.3310	1.50726
$582$	−0.344958	−0.0142990
$583$	−33.4088	−1.38365
$584$	−10.1972	−0.421964
$585$	13.6711	0.565230
$586$	1.40658	0.0581054
$587$	−9.99014	−0.412337	−0.206169	−	0.978516i	$-0.566100\pi$
$587$	−9.99014	−0.412337	−0.206169	+	0.978516i	$0.566100\pi$
$588$	10.9281	0.450668
$589$	39.1104	1.61152
$590$	−7.37057	−0.303441
$591$	−16.1471	−0.664201
$592$	7.39479	0.303924
$593$	46.2832	1.90063	0.950313	−	0.311297i	$-0.100764\pi$
$593$	46.2832	1.90063	0.950313	+	0.311297i	$0.100764\pi$
$594$	9.99226	0.409987
$595$	23.2735	0.954122
$596$	−12.0456	−0.493409
$597$	0.176955	0.00724230
$598$	36.2965	1.48427
$599$	42.6438	1.74238	0.871189	−	0.490948i	$-0.163350\pi$
$599$	42.6438	1.74238	0.871189	+	0.490948i	$0.163350\pi$
$600$	0.657748	0.0268524
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−29.8199	−1.21537
$603$	−24.5885	−1.00132
$604$	−22.5424	−0.917238
$605$	3.55425	0.144501
$606$	9.08500	0.369053
$607$	−17.3953	−0.706054	−0.353027	−	0.935613i	$-0.614848\pi$
$607$	−17.3953	−0.706054	−0.353027	+	0.935613i	$0.614848\pi$
$608$	−5.55738	−0.225382
$609$	15.6408	0.633798
$610$	−4.32641	−0.175171
$611$	65.1348	2.63507
$612$	12.2959	0.497034
$613$	−1.14969	−0.0464355	−0.0232177	−	0.999730i	$-0.507391\pi$
$613$	−1.14969	−0.0464355	−0.0232177	+	0.999730i	$0.507391\pi$
$614$	−8.38170	−0.338258
$615$	−5.62068	−0.226648
$616$	−13.2600	−0.534260
$617$	15.0369	0.605363	0.302682	−	0.953092i	$-0.402118\pi$
$617$	15.0369	0.605363	0.302682	+	0.953092i	$0.402118\pi$
$618$	−9.55190	−0.384234
$619$	−27.7477	−1.11527	−0.557637	−	0.830085i	$-0.688292\pi$
$619$	−27.7477	−1.11527	−0.557637	+	0.830085i	$0.688292\pi$
$620$	7.03756	0.282635
$621$	−24.9608	−1.00164
$622$	19.2840	0.773216
$623$	−18.4761	−0.740230
$624$	3.50247	0.140211
$625$	1.00000	0.0400000
$626$	7.23827	0.289299
$627$	9.97433	0.398336
$628$	21.2692	0.848734
$629$	−35.4160	−1.41213
$630$	12.4760	0.497058
$631$	−14.9967	−0.597010	−0.298505	−	0.954408i	$-0.596488\pi$
$631$	−14.9967	−0.597010	−0.298505	+	0.954408i	$0.596488\pi$
$632$	−7.85870	−0.312602
$633$	9.02550	0.358731
$634$	−28.9216	−1.14863
$635$	16.4905	0.654404
$636$	8.05315	0.319328
$637$	88.4710	3.50535
$638$	−13.3526	−0.528634
$639$	−14.0406	−0.555439
$640$	−1.00000	−0.0395285
$641$	−0.940211	−0.0371361	−0.0185681	−	0.999828i	$-0.505911\pi$
$641$	−0.940211	−0.0371361	−0.0185681	+	0.999828i	$0.505911\pi$
$642$	−12.0614	−0.476027
$643$	−30.1445	−1.18878	−0.594391	−	0.804176i	$-0.702607\pi$
$643$	−30.1445	−1.18878	−0.594391	+	0.804176i	$0.702607\pi$
$644$	33.1237	1.30526
$645$	4.03624	0.158927
$646$	26.6160	1.04719
$647$	37.1402	1.46013	0.730067	−	0.683376i	$-0.239489\pi$
$647$	37.1402	1.46013	0.730067	+	0.683376i	$0.239489\pi$
$648$	5.29348	0.207948
$649$	−20.1120	−0.789465
$650$	5.32494	0.208862
$651$	−22.4942	−0.881616
$652$	−2.61197	−0.102293
$653$	−3.16247	−0.123757	−0.0618785	−	0.998084i	$-0.519709\pi$
$653$	−3.16247	−0.123757	−0.0618785	+	0.998084i	$0.519709\pi$
$654$	2.82644	0.110522
$655$	3.67639	0.143648
$656$	8.54534	0.333639
$657$	26.1800	1.02138
$658$	59.4411	2.31726
$659$	14.2324	0.554415	0.277208	−	0.960810i	$-0.410591\pi$
$659$	14.2324	0.554415	0.277208	+	0.960810i	$0.410591\pi$
$660$	1.79479	0.0698621
$661$	8.95079	0.348145	0.174073	−	0.984733i	$-0.444307\pi$
$661$	8.95079	0.348145	0.174073	+	0.984733i	$0.444307\pi$
$662$	−35.5094	−1.38011
$663$	−16.7744	−0.651465
$664$	7.47633	0.290138
$665$	27.0059	1.04724
$666$	−18.9851	−0.735659
$667$	33.3550	1.29151
$668$	8.38548	0.324444
$669$	−2.96137	−0.114493
$670$	−9.57732	−0.370004
$671$	−11.8054	−0.455743
$672$	3.19630	0.123300
$673$	−11.7126	−0.451486	−0.225743	−	0.974187i	$-0.572481\pi$
$673$	−11.7126	−0.451486	−0.225743	+	0.974187i	$0.572481\pi$
$674$	−19.4402	−0.748808
$675$	−3.66192	−0.140947
$676$	15.3550	0.590578
$677$	−21.0433	−0.808760	−0.404380	−	0.914591i	$-0.632513\pi$
$677$	−21.0433	−0.808760	−0.404380	+	0.914591i	$0.632513\pi$
$678$	2.76390	0.106147
$679$	−2.54856	−0.0978049
$680$	4.78932	0.183662
$681$	−1.77690	−0.0680909
$682$	19.2033	0.735333
$683$	−22.4559	−0.859250	−0.429625	−	0.903007i	$-0.641354\pi$
$683$	−22.4559	−0.859250	−0.429625	+	0.903007i	$0.641354\pi$
$684$	14.2678	0.545544
$685$	−8.45470	−0.323037
$686$	46.7211	1.78382
$687$	−0.199987	−0.00763000
$688$	−6.13645	−0.233950
$689$	65.1961	2.48377
$690$	−4.48342	−0.170681
$691$	−31.4059	−1.19474	−0.597369	−	0.801966i	$-0.703787\pi$
$691$	−31.4059	−1.19474	−0.597369	+	0.801966i	$0.703787\pi$
$692$	6.46330	0.245698
$693$	34.0433	1.29320
$694$	4.83666	0.183597
$695$	−4.90005	−0.185869
$696$	3.21863	0.122002
$697$	−40.9263	−1.55019
$698$	−36.2499	−1.37208
$699$	−1.43292	−0.0541979
$700$	4.85947	0.183671
$701$	19.6558	0.742391	0.371196	−	0.928555i	$-0.378948\pi$
$701$	19.6558	0.742391	0.371196	+	0.928555i	$0.378948\pi$
$702$	−19.4995	−0.735963
$703$	−41.0956	−1.54995
$704$	−2.72869	−0.102841
$705$	−8.04558	−0.303014
$706$	8.24259	0.310214
$707$	67.1204	2.52432
$708$	4.84797	0.182198
$709$	−10.4000	−0.390581	−0.195291	−	0.980745i	$-0.562565\pi$
$709$	−10.4000	−0.390581	−0.195291	+	0.980745i	$0.562565\pi$
$710$	−5.46888	−0.205243
$711$	20.1762	0.756666
$712$	−3.80208	−0.142489
$713$	−47.9702	−1.79650
$714$	−15.3081	−0.572892
$715$	14.5301	0.543396
$716$	18.2236	0.681047
$717$	15.1746	0.566705
$718$	−10.8816	−0.406096
$719$	−23.1783	−0.864405	−0.432203	−	0.901777i	$-0.642263\pi$
$719$	−23.1783	−0.864405	−0.432203	+	0.901777i	$0.642263\pi$
$720$	2.56737	0.0956802
$721$	−70.5699	−2.62816
$722$	11.8845	0.442294
$723$	15.8762	0.590441
$724$	13.3120	0.494736
$725$	4.89341	0.181737
$726$	−2.33780	−0.0867638
$727$	34.5821	1.28258	0.641289	−	0.767299i	$-0.278400\pi$
$727$	34.5821	1.28258	0.641289	+	0.767299i	$0.278400\pi$
$728$	25.8764	0.959043
$729$	−6.36445	−0.235721
$730$	10.1972	0.377416
$731$	29.3894	1.08701
$732$	2.84568	0.105179
$733$	35.8091	1.32264	0.661320	−	0.750104i	$-0.269997\pi$
$733$	35.8091	1.32264	0.661320	+	0.750104i	$0.269997\pi$
$734$	−26.4108	−0.974841
$735$	−10.9281	−0.403089
$736$	6.81632	0.251253
$737$	−26.1335	−0.962642
$738$	−21.9390	−0.807587
$739$	−31.9471	−1.17519	−0.587597	−	0.809154i	$-0.699926\pi$
$739$	−31.9471	−1.17519	−0.587597	+	0.809154i	$0.699926\pi$
$740$	−7.39479	−0.271838
$741$	−19.4646	−0.715048
$742$	59.4970	2.18420
$743$	−15.4672	−0.567437	−0.283719	−	0.958908i	$-0.591568\pi$
$743$	−15.4672	−0.567437	−0.283719	+	0.958908i	$0.591568\pi$
$744$	−4.62894	−0.169705
$745$	12.0456	0.441318
$746$	9.00937	0.329857
$747$	−19.1945	−0.702290
$748$	13.0686	0.477834
$749$	−89.1104	−3.25602
$750$	−0.657748	−0.0240175
$751$	−7.88268	−0.287643	−0.143822	−	0.989604i	$-0.545939\pi$
$751$	−7.88268	−0.287643	−0.143822	+	0.989604i	$0.545939\pi$
$752$	12.2320	0.446056
$753$	−15.9282	−0.580457
$754$	26.0571	0.948945
$755$	22.5424	0.820403
$756$	−17.7950	−0.647198
$757$	−36.0950	−1.31190	−0.655948	−	0.754806i	$-0.727731\pi$
$757$	−36.0950	−1.31190	−0.655948	+	0.754806i	$0.727731\pi$
$758$	−6.55610	−0.238128
$759$	−12.2339	−0.444061
$760$	5.55738	0.201587
$761$	12.4614	0.451725	0.225863	−	0.974159i	$-0.427480\pi$
$761$	12.4614	0.451725	0.225863	+	0.974159i	$0.427480\pi$
$762$	−10.8466	−0.392929
$763$	20.8818	0.755973
$764$	−24.9236	−0.901705
$765$	−12.2959	−0.444560
$766$	29.7550	1.07509
$767$	39.2479	1.41716
$768$	0.657748	0.0237344
$769$	2.08511	0.0751912	0.0375956	−	0.999293i	$-0.488030\pi$
$769$	2.08511	0.0751912	0.0375956	+	0.999293i	$0.488030\pi$
$770$	13.2600	0.477857
$771$	−18.6210	−0.670620
$772$	1.42758	0.0513796
$773$	33.6820	1.21146	0.605729	−	0.795671i	$-0.292881\pi$
$773$	33.6820	1.21146	0.605729	+	0.795671i	$0.292881\pi$
$774$	15.7545	0.566285
$775$	−7.03756	−0.252797
$776$	−0.524453	−0.0188268
$777$	23.6360	0.847937
$778$	−26.6722	−0.956245
$779$	−47.4897	−1.70149
$780$	−3.50247	−0.125409
$781$	−14.9229	−0.533983
$782$	−32.6455	−1.16740
$783$	−17.9193	−0.640383
$784$	16.6144	0.593373
$785$	−21.2692	−0.759131
$786$	−2.41814	−0.0862521
$787$	10.5096	0.374626	0.187313	−	0.982300i	$-0.440022\pi$
$787$	10.5096	0.374626	0.187313	+	0.982300i	$0.440022\pi$
$788$	−24.5490	−0.874523
$789$	15.1546	0.539517
$790$	7.85870	0.279600
$791$	20.4198	0.726045
$792$	7.00555	0.248931
$793$	23.0379	0.818099
$794$	−10.3535	−0.367432
$795$	−8.05315	−0.285616
$796$	0.269032	0.00953559
$797$	−18.0190	−0.638264	−0.319132	−	0.947710i	$-0.603391\pi$
$797$	−18.0190	−0.638264	−0.319132	+	0.947710i	$0.603391\pi$
$798$	−17.7631	−0.628806
$799$	−58.5830	−2.07252
$800$	1.00000	0.0353553
$801$	9.76135	0.344900
$802$	0.100662	0.00355450
$803$	27.8251	0.981926
$804$	6.29946	0.222165
$805$	−33.1237	−1.16746
$806$	−37.4746	−1.31999
$807$	−4.19087	−0.147526
$808$	13.8123	0.485915
$809$	−18.9215	−0.665246	−0.332623	−	0.943060i	$-0.607934\pi$
$809$	−18.9215	−0.665246	−0.332623	+	0.943060i	$0.607934\pi$
$810$	−5.29348	−0.185994
$811$	−2.80670	−0.0985564	−0.0492782	−	0.998785i	$-0.515692\pi$
$811$	−2.80670	−0.0985564	−0.0492782	+	0.998785i	$0.515692\pi$
$812$	23.7794	0.834492
$813$	14.4483	0.506723
$814$	−20.1781	−0.707242
$815$	2.61197	0.0914933
$816$	−3.15016	−0.110278
$817$	34.1026	1.19310
$818$	27.9049	0.975672
$819$	−66.4343	−2.32140
$820$	−8.54534	−0.298416
$821$	8.86577	0.309417	0.154709	−	0.987960i	$-0.450556\pi$
$821$	8.86577	0.309417	0.154709	+	0.987960i	$0.450556\pi$
$822$	5.56106	0.193964
$823$	23.4106	0.816044	0.408022	−	0.912972i	$-0.366219\pi$
$823$	23.4106	0.816044	0.408022	+	0.912972i	$0.366219\pi$
$824$	−14.5221	−0.505903
$825$	−1.79479	−0.0624866
$826$	35.8170	1.24623
$827$	−50.4786	−1.75531	−0.877657	−	0.479289i	$-0.840895\pi$
$827$	−50.4786	−1.75531	−0.877657	+	0.479289i	$0.840895\pi$
$828$	−17.5000	−0.608167
$829$	42.0759	1.46136	0.730679	−	0.682721i	$-0.239204\pi$
$829$	42.0759	1.46136	0.730679	+	0.682721i	$0.239204\pi$
$830$	−7.47633	−0.259507
$831$	−18.9426	−0.657113
$832$	5.32494	0.184609
$833$	−79.5718	−2.75700
$834$	3.22300	0.111603
$835$	−8.38548	−0.290191
$836$	15.1644	0.524471
$837$	25.7710	0.890776
$838$	−19.5961	−0.676935
$839$	17.8596	0.616583	0.308291	−	0.951292i	$-0.400243\pi$
$839$	17.8596	0.616583	0.308291	+	0.951292i	$0.400243\pi$
$840$	−3.19630	−0.110283
$841$	−5.05455	−0.174295
$842$	10.8798	0.374943
$843$	12.2184	0.420824
$844$	13.7218	0.472325
$845$	−15.3550	−0.528229
$846$	−31.4041	−1.07970
$847$	−17.2718	−0.593465
$848$	12.2435	0.420444
$849$	4.30176	0.147636
$850$	−4.78932	−0.164272
$851$	50.4052	1.72787
$852$	3.59714	0.123236
$853$	−5.56569	−0.190566	−0.0952829	−	0.995450i	$-0.530376\pi$
$853$	−5.56569	−0.190566	−0.0952829	+	0.995450i	$0.530376\pi$
$854$	21.0240	0.719428
$855$	−14.2678	−0.487950
$856$	−18.3375	−0.626762
$857$	−31.3109	−1.06956	−0.534780	−	0.844991i	$-0.679606\pi$
$857$	−31.3109	−1.06956	−0.534780	+	0.844991i	$0.679606\pi$
$858$	−9.55716	−0.326276
$859$	−43.3635	−1.47954	−0.739771	−	0.672859i	$-0.765066\pi$
$859$	−43.3635	−1.47954	−0.739771	+	0.672859i	$0.765066\pi$
$860$	6.13645	0.209251
$861$	27.3135	0.930842
$862$	38.8093	1.32185
$863$	−1.58564	−0.0539759	−0.0269880	−	0.999636i	$-0.508592\pi$
$863$	−1.58564	−0.0539759	−0.0269880	+	0.999636i	$0.508592\pi$
$864$	−3.66192	−0.124581
$865$	−6.46330	−0.219759
$866$	−22.7471	−0.772979
$867$	3.90540	0.132634
$868$	−34.1988	−1.16078
$869$	21.4440	0.727436
$870$	−3.21863	−0.109122
$871$	50.9987	1.72803
$872$	4.29714	0.145520
$873$	1.34646	0.0455709
$874$	−37.8809	−1.28134
$875$	−4.85947	−0.164280
$876$	−6.70720	−0.226615
$877$	16.1462	0.545218	0.272609	−	0.962125i	$-0.412114\pi$
$877$	16.1462	0.545218	0.272609	+	0.962125i	$0.412114\pi$
$878$	7.64932	0.258152
$879$	0.925177	0.0312054
$880$	2.72869	0.0919841
$881$	13.7037	0.461690	0.230845	−	0.972991i	$-0.425851\pi$
$881$	13.7037	0.461690	0.230845	+	0.972991i	$0.425851\pi$
$882$	−42.6554	−1.43628
$883$	19.7184	0.663579	0.331789	−	0.943354i	$-0.392348\pi$
$883$	19.7184	0.663579	0.331789	+	0.943354i	$0.392348\pi$
$884$	−25.5028	−0.857753
$885$	−4.84797	−0.162963
$886$	−7.21100	−0.242258
$887$	25.0435	0.840877	0.420438	−	0.907321i	$-0.361876\pi$
$887$	25.0435	0.840877	0.420438	+	0.907321i	$0.361876\pi$
$888$	4.86390	0.163222
$889$	−80.1348	−2.68764
$890$	3.80208	0.127446
$891$	−14.4443	−0.483901
$892$	−4.50229	−0.150748
$893$	−67.9780	−2.27480
$894$	−7.92300	−0.264985
$895$	−18.2236	−0.609147
$896$	4.85947	0.162343
$897$	23.8739	0.797128
$898$	10.9506	0.365426
$899$	−34.4376	−1.14856
$900$	−2.56737	−0.0855789
$901$	−58.6381	−1.95352
$902$	−23.3176	−0.776391
$903$	−19.6140	−0.652712
$904$	4.20207	0.139759
$905$	−13.3120	−0.442506
$906$	−14.8272	−0.492602
$907$	−31.7505	−1.05426	−0.527129	−	0.849785i	$-0.676732\pi$
$907$	−31.7505	−1.05426	−0.527129	+	0.849785i	$0.676732\pi$
$908$	−2.70149	−0.0896521
$909$	−35.4612	−1.17618
$910$	−25.8764	−0.857795
$911$	−57.5107	−1.90542	−0.952708	−	0.303888i	$-0.901715\pi$
$911$	−57.5107	−1.90542	−0.952708	+	0.303888i	$0.901715\pi$
$912$	−3.65535	−0.121041
$913$	−20.4006	−0.675161
$914$	−5.83558	−0.193024
$915$	−2.84568	−0.0940754
$916$	−0.304049	−0.0100461
$917$	−17.8653	−0.589965
$918$	17.5381	0.578844
$919$	−4.61408	−0.152205	−0.0761023	−	0.997100i	$-0.524248\pi$
$919$	−4.61408	−0.152205	−0.0761023	+	0.997100i	$0.524248\pi$
$920$	−6.81632	−0.224727
$921$	−5.51304	−0.181661
$922$	1.59905	0.0526619
$923$	29.1215	0.958545
$924$	−8.72173	−0.286924
$925$	7.39479	0.243139
$926$	22.0566	0.724824
$927$	37.2837	1.22456
$928$	4.89341	0.160634
$929$	−9.97455	−0.327254	−0.163627	−	0.986522i	$-0.552319\pi$
$929$	−9.97455	−0.327254	−0.163627	+	0.986522i	$0.552319\pi$
$930$	4.62894	0.151789
$931$	−92.3328	−3.02608
$932$	−2.17852	−0.0713598
$933$	12.6840	0.415255
$934$	14.4621	0.473216
$935$	−13.0686	−0.427388
$936$	−13.6711	−0.446854
$937$	−12.8754	−0.420622	−0.210311	−	0.977635i	$-0.567448\pi$
$937$	−12.8754	−0.420622	−0.210311	+	0.977635i	$0.567448\pi$
$938$	46.5407	1.51961
$939$	4.76095	0.155368
$940$	−12.2320	−0.398964
$941$	−22.2813	−0.726350	−0.363175	−	0.931721i	$-0.618307\pi$
$941$	−22.2813	−0.726350	−0.363175	+	0.931721i	$0.618307\pi$
$942$	13.9898	0.455811
$943$	58.2477	1.89681
$944$	7.37057	0.239891
$945$	17.7950	0.578872
$946$	16.7445	0.544410
$947$	−13.2038	−0.429066	−0.214533	−	0.976717i	$-0.568823\pi$
$947$	−13.2038	−0.429066	−0.214533	+	0.976717i	$0.568823\pi$
$948$	−5.16904	−0.167883
$949$	−54.2997	−1.76264
$950$	−5.55738	−0.180305
$951$	−19.0231	−0.616868
$952$	−23.2735	−0.754299
$953$	57.8179	1.87291	0.936453	−	0.350792i	$-0.114088\pi$
$953$	57.8179	1.87291	0.936453	+	0.350792i	$0.114088\pi$
$954$	−31.4336	−1.01770
$955$	24.9236	0.806510
$956$	23.0705	0.746154
$957$	−8.78264	−0.283902
$958$	−18.3844	−0.593972
$959$	41.0853	1.32672
$960$	−0.657748	−0.0212287
$961$	18.5272	0.597652
$962$	39.3768	1.26956
$963$	47.0791	1.51710
$964$	24.1372	0.777406
$965$	−1.42758	−0.0459553
$966$	21.7870	0.700986
$967$	−39.3175	−1.26437	−0.632183	−	0.774819i	$-0.717841\pi$
$967$	−39.3175	−1.26437	−0.632183	+	0.774819i	$0.717841\pi$
$968$	−3.55425	−0.114238
$969$	17.5066	0.562394
$970$	0.524453	0.0168392
$971$	5.73680	0.184103	0.0920514	−	0.995754i	$-0.470658\pi$
$971$	5.73680	0.184103	0.0920514	+	0.995754i	$0.470658\pi$
$972$	14.4675	0.464047
$973$	23.8116	0.763366
$974$	16.8715	0.540598
$975$	3.50247	0.112169
$976$	4.32641	0.138485
$977$	21.0015	0.671898	0.335949	−	0.941880i	$-0.390943\pi$
$977$	21.0015	0.671898	0.335949	+	0.941880i	$0.390943\pi$
$978$	−1.71802	−0.0549361
$979$	10.3747	0.331577
$980$	−16.6144	−0.530729
$981$	−11.0323	−0.352236
$982$	−28.9865	−0.924997
$983$	−35.1807	−1.12209	−0.561045	−	0.827785i	$-0.689601\pi$
$983$	−35.1807	−1.12209	−0.561045	+	0.827785i	$0.689601\pi$
$984$	5.62068	0.179181
$985$	24.5490	0.782197
$986$	−23.4361	−0.746357
$987$	39.0973	1.24448
$988$	−29.5927	−0.941470
$989$	−41.8280	−1.33005
$990$	−7.00555	−0.222651
$991$	2.97065	0.0943659	0.0471829	−	0.998886i	$-0.484976\pi$
$991$	2.97065	0.0943659	0.0471829	+	0.998886i	$0.484976\pi$
$992$	−7.03756	−0.223443
$993$	−23.3562	−0.741186
$994$	26.5759	0.842935
$995$	−0.269032	−0.00852889
$996$	4.91754	0.155818
$997$	33.2478	1.05297	0.526484	−	0.850185i	$-0.323510\pi$
$997$	33.2478	1.05297	0.526484	+	0.850185i	$0.323510\pi$
$998$	22.1514	0.701191
$999$	−27.0791	−0.856746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.657748 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.657748 q^{6} +4.85947 q^{7} +1.00000 q^{8} -2.56737 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.657748 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.657748 q^{6} +4.85947 q^{7} +1.00000 q^{8} -2.56737 q^{9} -1.00000 q^{10} -2.72869 q^{11} +0.657748 q^{12} +5.32494 q^{13} +4.85947 q^{14} -0.657748 q^{15} +1.00000 q^{16} -4.78932 q^{17} -2.56737 q^{18} -5.55738 q^{19} -1.00000 q^{20} +3.19630 q^{21} -2.72869 q^{22} +6.81632 q^{23} +0.657748 q^{24} +1.00000 q^{25} +5.32494 q^{26} -3.66192 q^{27} +4.85947 q^{28} +4.89341 q^{29} -0.657748 q^{30} -7.03756 q^{31} +1.00000 q^{32} -1.79479 q^{33} -4.78932 q^{34} -4.85947 q^{35} -2.56737 q^{36} +7.39479 q^{37} -5.55738 q^{38} +3.50247 q^{39} -1.00000 q^{40} +8.54534 q^{41} +3.19630 q^{42} -6.13645 q^{43} -2.72869 q^{44} +2.56737 q^{45} +6.81632 q^{46} +12.2320 q^{47} +0.657748 q^{48} +16.6144 q^{49} +1.00000 q^{50} -3.15016 q^{51} +5.32494 q^{52} +12.2435 q^{53} -3.66192 q^{54} +2.72869 q^{55} +4.85947 q^{56} -3.65535 q^{57} +4.89341 q^{58} +7.37057 q^{59} -0.657748 q^{60} +4.32641 q^{61} -7.03756 q^{62} -12.4760 q^{63} +1.00000 q^{64} -5.32494 q^{65} -1.79479 q^{66} +9.57732 q^{67} -4.78932 q^{68} +4.48342 q^{69} -4.85947 q^{70} +5.46888 q^{71} -2.56737 q^{72} -10.1972 q^{73} +7.39479 q^{74} +0.657748 q^{75} -5.55738 q^{76} -13.2600 q^{77} +3.50247 q^{78} -7.85870 q^{79} -1.00000 q^{80} +5.29348 q^{81} +8.54534 q^{82} +7.47633 q^{83} +3.19630 q^{84} +4.78932 q^{85} -6.13645 q^{86} +3.21863 q^{87} -2.72869 q^{88} -3.80208 q^{89} +2.56737 q^{90} +25.8764 q^{91} +6.81632 q^{92} -4.62894 q^{93} +12.2320 q^{94} +5.55738 q^{95} +0.657748 q^{96} -0.524453 q^{97} +16.6144 q^{98} +7.00555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 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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