LMFDB - Embedded newform 2011.2.a.a.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.16126 q^{2} -0.721683 q^{3} -0.651472 q^{4} +1.92946 q^{5} +0.838063 q^{6} +2.47621 q^{7} +3.07905 q^{8} -2.47917 q^{9} +O(q^{10})$	\(q-1.16126 q^{2} -0.721683 q^{3} -0.651472 q^{4} +1.92946 q^{5} +0.838063 q^{6} +2.47621 q^{7} +3.07905 q^{8} -2.47917 q^{9} -2.24061 q^{10} +1.74116 q^{11} +0.470157 q^{12} -5.52244 q^{13} -2.87553 q^{14} -1.39246 q^{15} -2.27264 q^{16} +5.40108 q^{17} +2.87897 q^{18} -3.91744 q^{19} -1.25699 q^{20} -1.78704 q^{21} -2.02194 q^{22} -3.25420 q^{23} -2.22210 q^{24} -1.27718 q^{25} +6.41299 q^{26} +3.95423 q^{27} -1.61318 q^{28} -0.523693 q^{29} +1.61701 q^{30} -5.17744 q^{31} -3.51898 q^{32} -1.25656 q^{33} -6.27207 q^{34} +4.77776 q^{35} +1.61511 q^{36} -1.20376 q^{37} +4.54917 q^{38} +3.98545 q^{39} +5.94091 q^{40} -0.451616 q^{41} +2.07522 q^{42} -9.83978 q^{43} -1.13431 q^{44} -4.78347 q^{45} +3.77897 q^{46} +7.23941 q^{47} +1.64013 q^{48} -0.868374 q^{49} +1.48314 q^{50} -3.89787 q^{51} +3.59771 q^{52} -5.58256 q^{53} -4.59189 q^{54} +3.35949 q^{55} +7.62439 q^{56} +2.82715 q^{57} +0.608145 q^{58} +2.47408 q^{59} +0.907149 q^{60} +14.0548 q^{61} +6.01236 q^{62} -6.13896 q^{63} +8.63173 q^{64} -10.6553 q^{65} +1.45920 q^{66} -11.4562 q^{67} -3.51866 q^{68} +2.34850 q^{69} -5.54822 q^{70} +7.81214 q^{71} -7.63350 q^{72} +1.16866 q^{73} +1.39788 q^{74} +0.921719 q^{75} +2.55210 q^{76} +4.31147 q^{77} -4.62815 q^{78} -7.82680 q^{79} -4.38497 q^{80} +4.58382 q^{81} +0.524444 q^{82} +8.11311 q^{83} +1.16421 q^{84} +10.4212 q^{85} +11.4266 q^{86} +0.377941 q^{87} +5.36111 q^{88} -0.372439 q^{89} +5.55486 q^{90} -13.6747 q^{91} +2.12002 q^{92} +3.73647 q^{93} -8.40685 q^{94} -7.55854 q^{95} +2.53959 q^{96} +1.21641 q^{97} +1.00841 q^{98} -4.31663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) $ 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * 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 $

$2$	−1.16126	−0.821136	−0.410568	−	0.911830i	$-0.634670\pi$
$2$	−1.16126	−0.821136	−0.410568	+	0.911830i	$0.634670\pi$
$3$	−0.721683	−0.416664	−0.208332	−	0.978058i	$-0.566803\pi$
$3$	−0.721683	−0.416664	−0.208332	+	0.978058i	$0.566803\pi$
$4$	−0.651472	−0.325736
$5$	1.92946	0.862881	0.431441	−	0.902141i	$-0.358005\pi$
$5$	1.92946	0.862881	0.431441	+	0.902141i	$0.358005\pi$
$6$	0.838063	0.342138
$7$	2.47621	0.935920	0.467960	−	0.883750i	$-0.344989\pi$
$7$	2.47621	0.935920	0.467960	+	0.883750i	$0.344989\pi$
$8$	3.07905	1.08861
$9$	−2.47917	−0.826391
$10$	−2.24061	−0.708543
$11$	1.74116	0.524978	0.262489	−	0.964935i	$-0.415457\pi$
$11$	1.74116	0.524978	0.262489	+	0.964935i	$0.415457\pi$
$12$	0.470157	0.135723
$13$	−5.52244	−1.53165	−0.765824	−	0.643050i	$-0.777669\pi$
$13$	−5.52244	−1.53165	−0.765824	+	0.643050i	$0.777669\pi$
$14$	−2.87553	−0.768518
$15$	−1.39246	−0.359532
$16$	−2.27264	−0.568160
$17$	5.40108	1.30996	0.654978	−	0.755648i	$-0.272678\pi$
$17$	5.40108	1.30996	0.654978	+	0.755648i	$0.272678\pi$
$18$	2.87897	0.678579
$19$	−3.91744	−0.898722	−0.449361	−	0.893350i	$-0.648348\pi$
$19$	−3.91744	−0.898722	−0.449361	+	0.893350i	$0.648348\pi$
$20$	−1.25699	−0.281072
$21$	−1.78704	−0.389964
$22$	−2.02194	−0.431078
$23$	−3.25420	−0.678547	−0.339273	−	0.940688i	$-0.610181\pi$
$23$	−3.25420	−0.678547	−0.339273	+	0.940688i	$0.610181\pi$
$24$	−2.22210	−0.453584
$25$	−1.27718	−0.255436
$26$	6.41299	1.25769
$27$	3.95423	0.760992
$28$	−1.61318	−0.304863
$29$	−0.523693	−0.0972474	−0.0486237	−	0.998817i	$-0.515484\pi$
$29$	−0.523693	−0.0972474	−0.0486237	+	0.998817i	$0.515484\pi$
$30$	1.61701	0.295224
$31$	−5.17744	−0.929896	−0.464948	−	0.885338i	$-0.653927\pi$
$31$	−5.17744	−0.929896	−0.464948	+	0.885338i	$0.653927\pi$
$32$	−3.51898	−0.622073
$33$	−1.25656	−0.218740
$34$	−6.27207	−1.07565
$35$	4.77776	0.807588
$36$	1.61511	0.269185
$37$	−1.20376	−0.197897	−0.0989486	−	0.995093i	$-0.531548\pi$
$37$	−1.20376	−0.197897	−0.0989486	+	0.995093i	$0.531548\pi$
$38$	4.54917	0.737972
$39$	3.98545	0.638183
$40$	5.94091	0.939341
$41$	−0.451616	−0.0705305	−0.0352653	−	0.999378i	$-0.511228\pi$
$41$	−0.451616	−0.0705305	−0.0352653	+	0.999378i	$0.511228\pi$
$42$	2.07522	0.320214
$43$	−9.83978	−1.50055	−0.750276	−	0.661124i	$-0.770080\pi$
$43$	−9.83978	−1.50055	−0.750276	+	0.661124i	$0.770080\pi$
$44$	−1.13431	−0.171004
$45$	−4.78347	−0.713077
$46$	3.77897	0.557179
$47$	7.23941	1.05598	0.527988	−	0.849252i	$-0.322946\pi$
$47$	7.23941	1.05598	0.527988	+	0.849252i	$0.322946\pi$
$48$	1.64013	0.236732
$49$	−0.868374	−0.124053
$50$	1.48314	0.209748
$51$	−3.89787	−0.545811
$52$	3.59771	0.498913
$53$	−5.58256	−0.766823	−0.383412	−	0.923578i	$-0.625251\pi$
$53$	−5.58256	−0.766823	−0.383412	+	0.923578i	$0.625251\pi$
$54$	−4.59189	−0.624877
$55$	3.35949	0.452994
$56$	7.62439	1.01885
$57$	2.82715	0.374465
$58$	0.608145	0.0798533
$59$	2.47408	0.322098	0.161049	−	0.986946i	$-0.448512\pi$
$59$	2.47408	0.322098	0.161049	+	0.986946i	$0.448512\pi$
$60$	0.907149	0.117112
$61$	14.0548	1.79953	0.899765	−	0.436375i	$-0.143738\pi$
$61$	14.0548	1.79953	0.899765	+	0.436375i	$0.143738\pi$
$62$	6.01236	0.763571
$63$	−6.13896	−0.773436
$64$	8.63173	1.07897
$65$	−10.6553	−1.32163
$66$	1.45920	0.179615
$67$	−11.4562	−1.39960	−0.699801	−	0.714338i	$-0.746728\pi$
$67$	−11.4562	−1.39960	−0.699801	+	0.714338i	$0.746728\pi$
$68$	−3.51866	−0.426700
$69$	2.34850	0.282726
$70$	−5.54822	−0.663139
$71$	7.81214	0.927130	0.463565	−	0.886063i	$-0.346570\pi$
$71$	7.81214	0.927130	0.463565	+	0.886063i	$0.346570\pi$
$72$	−7.63350	−0.899617
$73$	1.16866	0.136781	0.0683906	−	0.997659i	$-0.478214\pi$
$73$	1.16866	0.136781	0.0683906	+	0.997659i	$0.478214\pi$
$74$	1.39788	0.162500
$75$	0.921719	0.106431
$76$	2.55210	0.292746
$77$	4.31147	0.491338
$78$	−4.62815	−0.524035
$79$	−7.82680	−0.880584	−0.440292	−	0.897855i	$-0.645125\pi$
$79$	−7.82680	−0.880584	−0.440292	+	0.897855i	$0.645125\pi$
$80$	−4.38497	−0.490255
$81$	4.58382	0.509313
$82$	0.524444	0.0579151
$83$	8.11311	0.890530	0.445265	−	0.895399i	$-0.353110\pi$
$83$	8.11311	0.890530	0.445265	+	0.895399i	$0.353110\pi$
$84$	1.16421	0.127025
$85$	10.4212	1.13034
$86$	11.4266	1.23216
$87$	0.377941	0.0405195
$88$	5.36111	0.571496
$89$	−0.372439	−0.0394785	−0.0197392	−	0.999805i	$-0.506284\pi$
$89$	−0.372439	−0.0394785	−0.0197392	+	0.999805i	$0.506284\pi$
$90$	5.55486	0.585533
$91$	−13.6747	−1.43350
$92$	2.12002	0.221027
$93$	3.73647	0.387454
$94$	−8.40685	−0.867100
$95$	−7.55854	−0.775490
$96$	2.53959	0.259195
$97$	1.21641	0.123508	0.0617541	−	0.998091i	$-0.480331\pi$
$97$	1.21641	0.123508	0.0617541	+	0.998091i	$0.480331\pi$
$98$	1.00841	0.101865
$99$	−4.31663	−0.433837
$100$	0.832047	0.0832047
$101$	10.5220	1.04698	0.523489	−	0.852033i	$-0.324630\pi$
$101$	10.5220	1.04698	0.523489	+	0.852033i	$0.324630\pi$
$102$	4.52645	0.448185
$103$	9.15192	0.901765	0.450883	−	0.892583i	$-0.351109\pi$
$103$	9.15192	0.901765	0.450883	+	0.892583i	$0.351109\pi$
$104$	−17.0039	−1.66737
$105$	−3.44803	−0.336493
$106$	6.48281	0.629666
$107$	−13.2025	−1.27634	−0.638168	−	0.769897i	$-0.720308\pi$
$107$	−13.2025	−1.27634	−0.638168	+	0.769897i	$0.720308\pi$
$108$	−2.57607	−0.247882
$109$	−17.2681	−1.65398	−0.826990	−	0.562216i	$-0.809949\pi$
$109$	−17.2681	−1.65398	−0.826990	+	0.562216i	$0.809949\pi$
$110$	−3.90125	−0.371970
$111$	0.868735	0.0824566
$112$	−5.62754	−0.531752
$113$	−18.6983	−1.75899	−0.879494	−	0.475910i	$-0.842119\pi$
$113$	−18.6983	−1.75899	−0.879494	+	0.475910i	$0.842119\pi$
$114$	−3.28306	−0.307487
$115$	−6.27884	−0.585505
$116$	0.341172	0.0316770
$117$	13.6911	1.26574
$118$	−2.87306	−0.264486
$119$	13.3742	1.22601
$120$	−4.28746	−0.391389
$121$	−7.96838	−0.724398
$122$	−16.3213	−1.47766
$123$	0.325923	0.0293875
$124$	3.37296	0.302901
$125$	−12.1116	−1.08329
$126$	7.12893	0.635096
$127$	−12.5547	−1.11405	−0.557024	−	0.830497i	$-0.688057\pi$
$127$	−12.5547	−1.11405	−0.557024	+	0.830497i	$0.688057\pi$
$128$	−2.98574	−0.263905
$129$	7.10121	0.625226
$130$	12.3736	1.08524
$131$	0.612407	0.0535063	0.0267531	−	0.999642i	$-0.491483\pi$
$131$	0.612407	0.0535063	0.0267531	+	0.999642i	$0.491483\pi$
$132$	0.818616	0.0712514
$133$	−9.70040	−0.841132
$134$	13.3037	1.14926
$135$	7.62953	0.656645
$136$	16.6302	1.42603
$137$	−9.97081	−0.851863	−0.425932	−	0.904755i	$-0.640054\pi$
$137$	−9.97081	−0.851863	−0.425932	+	0.904755i	$0.640054\pi$
$138$	−2.72722	−0.232156
$139$	4.57631	0.388157	0.194079	−	0.980986i	$-0.437828\pi$
$139$	4.57631	0.388157	0.194079	+	0.980986i	$0.437828\pi$
$140$	−3.11257	−0.263061
$141$	−5.22456	−0.439988
$142$	−9.07193	−0.761300
$143$	−9.61542	−0.804082
$144$	5.63427	0.469522
$145$	−1.01045	−0.0839130
$146$	−1.35712	−0.112316
$147$	0.626691	0.0516886
$148$	0.784217	0.0644623
$149$	−11.6040	−0.950636	−0.475318	−	0.879814i	$-0.657667\pi$
$149$	−11.6040	−0.950636	−0.475318	+	0.879814i	$0.657667\pi$
$150$	−1.07036	−0.0873943
$151$	−21.9675	−1.78769	−0.893846	−	0.448374i	$-0.852003\pi$
$151$	−21.9675	−1.78769	−0.893846	+	0.448374i	$0.852003\pi$
$152$	−12.0620	−0.978357
$153$	−13.3902	−1.08254
$154$	−5.00674	−0.403455
$155$	−9.98967	−0.802390
$156$	−2.59641	−0.207879
$157$	8.45146	0.674500	0.337250	−	0.941415i	$-0.390503\pi$
$157$	8.45146	0.674500	0.337250	+	0.941415i	$0.390503\pi$
$158$	9.08896	0.723079
$159$	4.02884	0.319508
$160$	−6.78973	−0.536775
$161$	−8.05808	−0.635065
$162$	−5.32301	−0.418215
$163$	−4.63922	−0.363372	−0.181686	−	0.983357i	$-0.558155\pi$
$163$	−4.63922	−0.363372	−0.181686	+	0.983357i	$0.558155\pi$
$164$	0.294215	0.0229743
$165$	−2.42449	−0.188746
$166$	−9.42144	−0.731246
$167$	−10.4063	−0.805263	−0.402632	−	0.915362i	$-0.631904\pi$
$167$	−10.4063	−0.805263	−0.402632	+	0.915362i	$0.631904\pi$
$168$	−5.50239	−0.424519
$169$	17.4973	1.34595
$170$	−12.1017	−0.928159
$171$	9.71200	0.742695
$172$	6.41034	0.488784
$173$	−15.8135	−1.20228	−0.601140	−	0.799144i	$-0.705287\pi$
$173$	−15.8135	−1.20228	−0.601140	+	0.799144i	$0.705287\pi$
$174$	−0.438888	−0.0332720
$175$	−3.16257	−0.239068
$176$	−3.95702	−0.298272
$177$	−1.78550	−0.134207
$178$	0.432499	0.0324172
$179$	−12.3539	−0.923370	−0.461685	−	0.887044i	$-0.652755\pi$
$179$	−12.3539	−0.923370	−0.461685	+	0.887044i	$0.652755\pi$
$180$	3.11630	0.232275
$181$	−22.6371	−1.68260	−0.841302	−	0.540566i	$-0.818210\pi$
$181$	−22.6371	−1.68260	−0.841302	+	0.540566i	$0.818210\pi$
$182$	15.8799	1.17710
$183$	−10.1431	−0.749799
$184$	−10.0198	−0.738672
$185$	−2.32261	−0.170762
$186$	−4.33902	−0.318153
$187$	9.40413	0.687698
$188$	−4.71628	−0.343970
$189$	9.79151	0.712227
$190$	8.77744	0.636783
$191$	16.1004	1.16499	0.582493	−	0.812836i	$-0.302077\pi$
$191$	16.1004	1.16499	0.582493	+	0.812836i	$0.302077\pi$
$192$	−6.22938	−0.449566
$193$	20.1110	1.44762	0.723811	−	0.689999i	$-0.242389\pi$
$193$	20.1110	1.44762	0.723811	+	0.689999i	$0.242389\pi$
$194$	−1.41257	−0.101417
$195$	7.68977	0.550676
$196$	0.565721	0.0404087
$197$	−2.89584	−0.206320	−0.103160	−	0.994665i	$-0.532895\pi$
$197$	−2.89584	−0.206320	−0.103160	+	0.994665i	$0.532895\pi$
$198$	5.01273	0.356239
$199$	−10.9464	−0.775970	−0.387985	−	0.921666i	$-0.626829\pi$
$199$	−10.9464	−0.775970	−0.387985	+	0.921666i	$0.626829\pi$
$200$	−3.93250	−0.278070
$201$	8.26777	0.583164
$202$	−12.2188	−0.859711
$203$	−1.29678	−0.0910158
$204$	2.53936	0.177790
$205$	−0.871375	−0.0608595
$206$	−10.6278	−0.740471
$207$	8.06771	0.560745
$208$	12.5505	0.870221
$209$	−6.82087	−0.471809
$210$	4.00406	0.276306
$211$	1.91684	0.131961	0.0659804	−	0.997821i	$-0.478983\pi$
$211$	1.91684	0.131961	0.0659804	+	0.997821i	$0.478983\pi$
$212$	3.63688	0.249782
$213$	−5.63789	−0.386302
$214$	15.3316	1.04805
$215$	−18.9855	−1.29480
$216$	12.1753	0.828422
$217$	−12.8204	−0.870308
$218$	20.0527	1.35814
$219$	−0.843402	−0.0569918
$220$	−2.18862	−0.147556
$221$	−29.8271	−2.00639
$222$	−1.00883	−0.0677081
$223$	11.1916	0.749444	0.374722	−	0.927137i	$-0.377738\pi$
$223$	11.1916	0.749444	0.374722	+	0.927137i	$0.377738\pi$
$224$	−8.71373	−0.582211
$225$	3.16635	0.211090
$226$	21.7136	1.44437
$227$	11.1091	0.737335	0.368668	−	0.929561i	$-0.379814\pi$
$227$	11.1091	0.737335	0.368668	+	0.929561i	$0.379814\pi$
$228$	−1.84181	−0.121977
$229$	−3.68040	−0.243208	−0.121604	−	0.992579i	$-0.538804\pi$
$229$	−3.68040	−0.243208	−0.121604	+	0.992579i	$0.538804\pi$
$230$	7.29138	0.480779
$231$	−3.11152	−0.204723
$232$	−1.61248	−0.105864
$233$	−10.6432	−0.697261	−0.348631	−	0.937260i	$-0.613353\pi$
$233$	−10.6432	−0.697261	−0.348631	+	0.937260i	$0.613353\pi$
$234$	−15.8989	−1.03934
$235$	13.9682	0.911183
$236$	−1.61180	−0.104919
$237$	5.64847	0.366908
$238$	−15.5310	−1.00672
$239$	10.7401	0.694721	0.347361	−	0.937732i	$-0.387078\pi$
$239$	10.7401	0.694721	0.347361	+	0.937732i	$0.387078\pi$
$240$	3.16456	0.204271
$241$	18.7148	1.20553	0.602764	−	0.797919i	$-0.294066\pi$
$241$	18.7148	1.20553	0.602764	+	0.797919i	$0.294066\pi$
$242$	9.25337	0.594829
$243$	−15.1707	−0.973204
$244$	−9.15629	−0.586172
$245$	−1.67549	−0.107043
$246$	−0.378482	−0.0241311
$247$	21.6338	1.37652
$248$	−15.9416	−1.01229
$249$	−5.85510	−0.371052
$250$	14.0647	0.889530
$251$	11.2604	0.710753	0.355377	−	0.934723i	$-0.384353\pi$
$251$	11.2604	0.710753	0.355377	+	0.934723i	$0.384353\pi$
$252$	3.99936	0.251936
$253$	−5.66606	−0.356222
$254$	14.5793	0.914784
$255$	−7.52079	−0.470970
$256$	−13.7962	−0.862264
$257$	8.98865	0.560696	0.280348	−	0.959898i	$-0.409550\pi$
$257$	8.98865	0.560696	0.280348	+	0.959898i	$0.409550\pi$
$258$	−8.24636	−0.513396
$259$	−2.98077	−0.185216
$260$	6.94165	0.430503
$261$	1.29833	0.0803644
$262$	−0.711165	−0.0439359
$263$	5.01655	0.309334	0.154667	−	0.987967i	$-0.450570\pi$
$263$	5.01655	0.309334	0.154667	+	0.987967i	$0.450570\pi$
$264$	−3.86902	−0.238122
$265$	−10.7713	−0.661678
$266$	11.2647	0.690683
$267$	0.268783	0.0164493
$268$	7.46341	0.455901
$269$	−18.5662	−1.13200	−0.566002	−	0.824404i	$-0.691511\pi$
$269$	−18.5662	−1.13200	−0.566002	+	0.824404i	$0.691511\pi$
$270$	−8.85988	−0.539195
$271$	0.502577	0.0305294	0.0152647	−	0.999883i	$-0.495141\pi$
$271$	0.502577	0.0305294	0.0152647	+	0.999883i	$0.495141\pi$
$272$	−12.2747	−0.744264
$273$	9.86882	0.597288
$274$	11.5787	0.699496
$275$	−2.22377	−0.134098
$276$	−1.52998	−0.0920941
$277$	26.0788	1.56692	0.783461	−	0.621441i	$-0.213452\pi$
$277$	26.0788	1.56692	0.783461	+	0.621441i	$0.213452\pi$
$278$	−5.31429	−0.318730
$279$	12.8358	0.768458
$280$	14.7110	0.879148
$281$	17.4136	1.03881	0.519405	−	0.854528i	$-0.326154\pi$
$281$	17.4136	1.03881	0.519405	+	0.854528i	$0.326154\pi$
$282$	6.06708	0.361290
$283$	−30.0586	−1.78680	−0.893399	−	0.449264i	$-0.851686\pi$
$283$	−30.0586	−1.78680	−0.893399	+	0.449264i	$0.851686\pi$
$284$	−5.08939	−0.302000
$285$	5.45487	0.323119
$286$	11.1660	0.660260
$287$	−1.11830	−0.0660109
$288$	8.72415	0.514075
$289$	12.1717	0.715983
$290$	1.17339	0.0689040
$291$	−0.877866	−0.0514614
$292$	−0.761349	−0.0445546
$293$	11.9689	0.699232	0.349616	−	0.936893i	$-0.386312\pi$
$293$	11.9689	0.699232	0.349616	+	0.936893i	$0.386312\pi$
$294$	−0.727752	−0.0424434
$295$	4.77365	0.277932
$296$	−3.70644	−0.215433
$297$	6.88493	0.399504
$298$	13.4753	0.780601
$299$	17.9711	1.03929
$300$	−0.600474	−0.0346684
$301$	−24.3654	−1.40440
$302$	25.5100	1.46794
$303$	−7.59355	−0.436238
$304$	8.90292	0.510618
$305$	27.1181	1.55278
$306$	15.5495	0.888908
$307$	30.4348	1.73700	0.868502	−	0.495686i	$-0.165083\pi$
$307$	30.4348	1.73700	0.868502	+	0.495686i	$0.165083\pi$
$308$	−2.80880	−0.160046
$309$	−6.60478	−0.375733
$310$	11.6006	0.658871
$311$	7.45360	0.422655	0.211327	−	0.977415i	$-0.432221\pi$
$311$	7.45360	0.422655	0.211327	+	0.977415i	$0.432221\pi$
$312$	12.2714	0.694732
$313$	−8.96603	−0.506790	−0.253395	−	0.967363i	$-0.581547\pi$
$313$	−8.96603	−0.506790	−0.253395	+	0.967363i	$0.581547\pi$
$314$	−9.81435	−0.553856
$315$	−11.8449	−0.667384
$316$	5.09894	0.286838
$317$	−32.4956	−1.82513	−0.912567	−	0.408927i	$-0.865903\pi$
$317$	−32.4956	−1.82513	−0.912567	+	0.408927i	$0.865903\pi$
$318$	−4.67854	−0.262359
$319$	−0.911832	−0.0510528
$320$	16.6546	0.931020
$321$	9.52805	0.531804
$322$	9.35753	0.521475
$323$	−21.1584	−1.17729
$324$	−2.98623	−0.165902
$325$	7.05314	0.391238
$326$	5.38735	0.298378
$327$	12.4621	0.689154
$328$	−1.39055	−0.0767802
$329$	17.9263	0.988310
$330$	2.81547	0.154986
$331$	−7.15719	−0.393395	−0.196697	−	0.980464i	$-0.563022\pi$
$331$	−7.15719	−0.393395	−0.196697	+	0.980464i	$0.563022\pi$
$332$	−5.28547	−0.290078
$333$	2.98433	0.163540
$334$	12.0844	0.661230
$335$	−22.1044	−1.20769
$336$	4.06130	0.221562
$337$	−23.1974	−1.26364	−0.631821	−	0.775114i	$-0.717692\pi$
$337$	−23.1974	−1.26364	−0.631821	+	0.775114i	$0.717692\pi$
$338$	−20.3189	−1.10520
$339$	13.4942	0.732907
$340$	−6.78911	−0.368191
$341$	−9.01473	−0.488175
$342$	−11.2782	−0.609854
$343$	−19.4838	−1.05202
$344$	−30.2972	−1.63352
$345$	4.53134	0.243959
$346$	18.3636	0.987235
$347$	16.1370	0.866277	0.433139	−	0.901327i	$-0.357406\pi$
$347$	16.1370	0.866277	0.433139	+	0.901327i	$0.357406\pi$
$348$	−0.246218	−0.0131987
$349$	−16.6854	−0.893146	−0.446573	−	0.894747i	$-0.647356\pi$
$349$	−16.6854	−0.893146	−0.446573	+	0.894747i	$0.647356\pi$
$350$	3.67257	0.196307
$351$	−21.8370	−1.16557
$352$	−6.12709	−0.326575
$353$	−3.98824	−0.212273	−0.106136	−	0.994352i	$-0.533848\pi$
$353$	−3.98824	−0.212273	−0.106136	+	0.994352i	$0.533848\pi$
$354$	2.07344	0.110202
$355$	15.0732	0.800003
$356$	0.242634	0.0128596
$357$	−9.65196	−0.510836
$358$	14.3460	0.758212
$359$	12.6475	0.667509	0.333755	−	0.942660i	$-0.391684\pi$
$359$	12.6475	0.667509	0.333755	+	0.942660i	$0.391684\pi$
$360$	−14.7285	−0.776263
$361$	−3.65369	−0.192300
$362$	26.2876	1.38165
$363$	5.75064	0.301831
$364$	8.90870	0.466943
$365$	2.25488	0.118026
$366$	11.7788	0.615687
$367$	−18.3891	−0.959904	−0.479952	−	0.877295i	$-0.659346\pi$
$367$	−18.3891	−0.959904	−0.479952	+	0.877295i	$0.659346\pi$
$368$	7.39561	0.385523
$369$	1.11963	0.0582858
$370$	2.69716	0.140219
$371$	−13.8236	−0.717686
$372$	−2.43421	−0.126208
$373$	−1.74443	−0.0903230	−0.0451615	−	0.998980i	$-0.514380\pi$
$373$	−1.74443	−0.0903230	−0.0451615	+	0.998980i	$0.514380\pi$
$374$	−10.9207	−0.564693
$375$	8.74072	0.451369
$376$	22.2905	1.14955
$377$	2.89206	0.148949
$378$	−11.3705	−0.584835
$379$	−17.3083	−0.889066	−0.444533	−	0.895762i	$-0.646630\pi$
$379$	−17.3083	−0.889066	−0.444533	+	0.895762i	$0.646630\pi$
$380$	4.92418	0.252605
$381$	9.06050	0.464184
$382$	−18.6968	−0.956612
$383$	0.647252	0.0330730	0.0165365	−	0.999863i	$-0.494736\pi$
$383$	0.647252	0.0330730	0.0165365	+	0.999863i	$0.494736\pi$
$384$	2.15476	0.109960
$385$	8.31882	0.423966
$386$	−23.3541	−1.18869
$387$	24.3945	1.24004
$388$	−0.792460	−0.0402311
$389$	0.534527	0.0271016	0.0135508	−	0.999908i	$-0.495687\pi$
$389$	0.534527	0.0271016	0.0135508	+	0.999908i	$0.495687\pi$
$390$	−8.92983	−0.452180
$391$	−17.5762	−0.888866
$392$	−2.67377	−0.135046
$393$	−0.441964	−0.0222941
$394$	3.36282	0.169417
$395$	−15.1015	−0.759839
$396$	2.81216	0.141316
$397$	33.1744	1.66497	0.832487	−	0.554044i	$-0.186916\pi$
$397$	33.1744	1.66497	0.832487	+	0.554044i	$0.186916\pi$
$398$	12.7116	0.637176
$399$	7.00062	0.350469
$400$	2.90257	0.145128
$401$	4.42314	0.220881	0.110440	−	0.993883i	$-0.464774\pi$
$401$	4.42314	0.220881	0.110440	+	0.993883i	$0.464774\pi$
$402$	−9.60104	−0.478856
$403$	28.5921	1.42427
$404$	−6.85479	−0.341038
$405$	8.84430	0.439477
$406$	1.50590	0.0747364
$407$	−2.09594	−0.103892
$408$	−12.0018	−0.594175
$409$	21.8541	1.08061	0.540307	−	0.841468i	$-0.318308\pi$
$409$	21.8541	1.08061	0.540307	+	0.841468i	$0.318308\pi$
$410$	1.01189	0.0499739
$411$	7.19576	0.354941
$412$	−5.96222	−0.293737
$413$	6.12635	0.301458
$414$	−9.36872	−0.460448
$415$	15.6539	0.768421
$416$	19.4333	0.952797
$417$	−3.30264	−0.161731
$418$	7.92081	0.387419
$419$	−35.7884	−1.74838	−0.874190	−	0.485585i	$-0.838607\pi$
$419$	−35.7884	−1.74838	−0.874190	+	0.485585i	$0.838607\pi$
$420$	2.24629	0.109608
$421$	−12.9125	−0.629318	−0.314659	−	0.949205i	$-0.601890\pi$
$421$	−12.9125	−0.629318	−0.314659	+	0.949205i	$0.601890\pi$
$422$	−2.22595	−0.108358
$423$	−17.9478	−0.872650
$424$	−17.1890	−0.834771
$425$	−6.89815	−0.334610
$426$	6.54706	0.317206
$427$	34.8026	1.68422
$428$	8.60108	0.415749
$429$	6.93929	0.335032
$430$	22.0471	1.06321
$431$	−36.4217	−1.75437	−0.877186	−	0.480151i	$-0.840582\pi$
$431$	−36.4217	−1.75437	−0.877186	+	0.480151i	$0.840582\pi$
$432$	−8.98654	−0.432365
$433$	4.95585	0.238163	0.119081	−	0.992884i	$-0.462005\pi$
$433$	4.95585	0.238163	0.119081	+	0.992884i	$0.462005\pi$
$434$	14.8879	0.714641
$435$	0.729222	0.0349635
$436$	11.2497	0.538761
$437$	12.7481	0.609824
$438$	0.979410	0.0467980
$439$	21.4479	1.02365	0.511825	−	0.859089i	$-0.328969\pi$
$439$	21.4479	1.02365	0.511825	+	0.859089i	$0.328969\pi$
$440$	10.3441	0.493133
$441$	2.15285	0.102517
$442$	34.6371	1.64752
$443$	15.3537	0.729476	0.364738	−	0.931110i	$-0.381159\pi$
$443$	15.3537	0.729476	0.364738	+	0.931110i	$0.381159\pi$
$444$	−0.565956	−0.0268591
$445$	−0.718607	−0.0340652
$446$	−12.9964	−0.615395
$447$	8.37440	0.396096
$448$	21.3740	1.00983
$449$	34.8050	1.64255	0.821275	−	0.570532i	$-0.193263\pi$
$449$	34.8050	1.64255	0.821275	+	0.570532i	$0.193263\pi$
$450$	−3.67696	−0.173333
$451$	−0.786333	−0.0370270
$452$	12.1814	0.572966
$453$	15.8536	0.744867
$454$	−12.9005	−0.605452
$455$	−26.3848	−1.23694
$456$	8.70494	0.407646
$457$	−15.3510	−0.718090	−0.359045	−	0.933320i	$-0.616898\pi$
$457$	−15.3510	−0.718090	−0.359045	+	0.933320i	$0.616898\pi$
$458$	4.27391	0.199707
$459$	21.3571	0.996865
$460$	4.09049	0.190720
$461$	−26.4214	−1.23057	−0.615284	−	0.788306i	$-0.710959\pi$
$461$	−26.4214	−1.23057	−0.615284	+	0.788306i	$0.710959\pi$
$462$	3.61328	0.168105
$463$	40.3831	1.87676	0.938382	−	0.345601i	$-0.112325\pi$
$463$	40.3831	1.87676	0.938382	+	0.345601i	$0.112325\pi$
$464$	1.19017	0.0552521
$465$	7.20938	0.334327
$466$	12.3596	0.572546
$467$	−18.6440	−0.862743	−0.431371	−	0.902174i	$-0.641970\pi$
$467$	−18.6440	−0.862743	−0.431371	+	0.902174i	$0.641970\pi$
$468$	−8.91935	−0.412297
$469$	−28.3681	−1.30992
$470$	−16.2207	−0.748205
$471$	−6.09928	−0.281040
$472$	7.61783	0.350639
$473$	−17.1326	−0.787758
$474$	−6.55935	−0.301281
$475$	5.00327	0.229566
$476$	−8.71294	−0.399357
$477$	13.8401	0.633696
$478$	−12.4721	−0.570461
$479$	28.1873	1.28791	0.643956	−	0.765062i	$-0.277292\pi$
$479$	28.1873	1.28791	0.643956	+	0.765062i	$0.277292\pi$
$480$	4.90003	0.223655
$481$	6.64770	0.303109
$482$	−21.7328	−0.989903
$483$	5.81538	0.264609
$484$	5.19118	0.235963
$485$	2.34702	0.106573
$486$	17.6172	0.799133
$487$	−5.92728	−0.268591	−0.134295	−	0.990941i	$-0.542877\pi$
$487$	−5.92728	−0.268591	−0.134295	+	0.990941i	$0.542877\pi$
$488$	43.2754	1.95898
$489$	3.34805	0.151404
$490$	1.94569	0.0878971
$491$	13.0288	0.587982	0.293991	−	0.955808i	$-0.405016\pi$
$491$	13.0288	0.587982	0.293991	+	0.955808i	$0.405016\pi$
$492$	−0.212330	−0.00957258
$493$	−2.82851	−0.127390
$494$	−25.1225	−1.13031
$495$	−8.32876	−0.374350
$496$	11.7665	0.528330
$497$	19.3445	0.867720
$498$	6.79930	0.304684
$499$	0.285765	0.0127926	0.00639629	−	0.999980i	$-0.497964\pi$
$499$	0.285765	0.0127926	0.00639629	+	0.999980i	$0.497964\pi$
$500$	7.89035	0.352867
$501$	7.51005	0.335524
$502$	−13.0763	−0.583625
$503$	24.3016	1.08356	0.541779	−	0.840521i	$-0.317751\pi$
$503$	24.3016	1.08356	0.541779	+	0.840521i	$0.317751\pi$
$504$	−18.9022	−0.841970
$505$	20.3018	0.903417
$506$	6.57978	0.292507
$507$	−12.6275	−0.560807
$508$	8.17902	0.362885
$509$	−25.5176	−1.13105	−0.565523	−	0.824732i	$-0.691326\pi$
$509$	−25.5176	−1.13105	−0.565523	+	0.824732i	$0.691326\pi$
$510$	8.73361	0.386731
$511$	2.89385	0.128016
$512$	21.9925	0.971941
$513$	−15.4904	−0.683919
$514$	−10.4382	−0.460408
$515$	17.6583	0.778116
$516$	−4.62624	−0.203659
$517$	12.6049	0.554365
$518$	3.46145	0.152087
$519$	11.4124	0.500947
$520$	−32.8083	−1.43874
$521$	−40.0968	−1.75667	−0.878336	−	0.478043i	$-0.841346\pi$
$521$	−40.0968	−1.75667	−0.878336	+	0.478043i	$0.841346\pi$
$522$	−1.50770	−0.0659901
$523$	29.1540	1.27482	0.637408	−	0.770527i	$-0.280007\pi$
$523$	29.1540	1.27482	0.637408	+	0.770527i	$0.280007\pi$
$524$	−0.398966	−0.0174289
$525$	2.28237	0.0996109
$526$	−5.82553	−0.254005
$527$	−27.9638	−1.21812
$528$	2.85572	0.124279
$529$	−12.4102	−0.539575
$530$	12.5083	0.543327
$531$	−6.13368	−0.266179
$532$	6.31954	0.273987
$533$	2.49402	0.108028
$534$	−0.312127	−0.0135071
$535$	−25.4738	−1.10133
$536$	−35.2743	−1.52362
$537$	8.91557	0.384735
$538$	21.5603	0.929529
$539$	−1.51197	−0.0651254
$540$	−4.97043	−0.213893
$541$	9.28870	0.399353	0.199676	−	0.979862i	$-0.436011\pi$
$541$	9.28870	0.399353	0.199676	+	0.979862i	$0.436011\pi$
$542$	−0.583624	−0.0250688
$543$	16.3368	0.701080
$544$	−19.0063	−0.814888
$545$	−33.3181	−1.42719
$546$	−11.4603	−0.490455
$547$	25.5340	1.09175	0.545877	−	0.837865i	$-0.316197\pi$
$547$	25.5340	1.09175	0.545877	+	0.837865i	$0.316197\pi$
$548$	6.49570	0.277483
$549$	−34.8442	−1.48712
$550$	2.58238	0.110113
$551$	2.05154	0.0873984
$552$	7.23115	0.307778
$553$	−19.3808	−0.824156
$554$	−30.2843	−1.28666
$555$	1.67619	0.0711503
$556$	−2.98134	−0.126437
$557$	−32.0849	−1.35948	−0.679741	−	0.733452i	$-0.737908\pi$
$557$	−32.0849	−1.35948	−0.679741	+	0.733452i	$0.737908\pi$
$558$	−14.9057	−0.631008
$559$	54.3396	2.29832
$560$	−10.8581	−0.458839
$561$	−6.78680	−0.286539
$562$	−20.2218	−0.853004
$563$	−6.79017	−0.286172	−0.143086	−	0.989710i	$-0.545702\pi$
$563$	−6.79017	−0.286172	−0.143086	+	0.989710i	$0.545702\pi$
$564$	3.40366	0.143320
$565$	−36.0776	−1.51780
$566$	34.9059	1.46720
$567$	11.3505	0.476677
$568$	24.0540	1.00928
$569$	−29.3647	−1.23103	−0.615517	−	0.788124i	$-0.711053\pi$
$569$	−29.3647	−1.23103	−0.615517	+	0.788124i	$0.711053\pi$
$570$	−6.33453	−0.265324
$571$	−19.2193	−0.804302	−0.402151	−	0.915573i	$-0.631737\pi$
$571$	−19.2193	−0.804302	−0.402151	+	0.915573i	$0.631737\pi$
$572$	6.26418	0.261918
$573$	−11.6194	−0.485408
$574$	1.29863	0.0542039
$575$	4.15619	0.173325
$576$	−21.3996	−0.891648
$577$	−30.0600	−1.25141	−0.625707	−	0.780058i	$-0.715189\pi$
$577$	−30.0600	−1.25141	−0.625707	+	0.780058i	$0.715189\pi$
$578$	−14.1345	−0.587919
$579$	−14.5138	−0.603172
$580$	0.658278	0.0273335
$581$	20.0898	0.833465
$582$	1.01943	0.0422568
$583$	−9.72011	−0.402566
$584$	3.59836	0.148901
$585$	26.4164	1.09218
$586$	−13.8990	−0.574164
$587$	24.0162	0.991254	0.495627	−	0.868536i	$-0.334938\pi$
$587$	24.0162	0.991254	0.495627	+	0.868536i	$0.334938\pi$
$588$	−0.408272	−0.0168368
$589$	20.2823	0.835717
$590$	−5.54345	−0.228220
$591$	2.08988	0.0859661
$592$	2.73572	0.112437
$593$	−31.1770	−1.28029	−0.640143	−	0.768256i	$-0.721125\pi$
$593$	−31.1770	−1.28029	−0.640143	+	0.768256i	$0.721125\pi$
$594$	−7.99520	−0.328047
$595$	25.8051	1.05790
$596$	7.55967	0.309656
$597$	7.89983	0.323319
$598$	−20.8691	−0.853402
$599$	38.7770	1.58438	0.792192	−	0.610271i	$-0.208940\pi$
$599$	38.7770	1.58438	0.792192	+	0.610271i	$0.208940\pi$
$600$	2.83802	0.115862
$601$	−5.32621	−0.217261	−0.108630	−	0.994082i	$-0.534646\pi$
$601$	−5.32621	−0.217261	−0.108630	+	0.994082i	$0.534646\pi$
$602$	28.2946	1.15320
$603$	28.4020	1.15662
$604$	14.3112	0.582316
$605$	−15.3747	−0.625069
$606$	8.81809	0.358211
$607$	22.6035	0.917449	0.458725	−	0.888578i	$-0.348306\pi$
$607$	22.6035	0.917449	0.458725	+	0.888578i	$0.348306\pi$
$608$	13.7854	0.559070
$609$	0.935862	0.0379230
$610$	−31.4912	−1.27504
$611$	−39.9792	−1.61738
$612$	8.72336	0.352621
$613$	12.7738	0.515929	0.257965	−	0.966154i	$-0.416948\pi$
$613$	12.7738	0.515929	0.257965	+	0.966154i	$0.416948\pi$
$614$	−35.3427	−1.42632
$615$	0.628857	0.0253579
$616$	13.2752	0.534875
$617$	31.0873	1.25153	0.625764	−	0.780012i	$-0.284787\pi$
$617$	31.0873	1.25153	0.625764	+	0.780012i	$0.284787\pi$
$618$	7.66988	0.308528
$619$	−8.34550	−0.335434	−0.167717	−	0.985835i	$-0.553640\pi$
$619$	−8.34550	−0.335434	−0.167717	+	0.985835i	$0.553640\pi$
$620$	6.50799	0.261367
$621$	−12.8678	−0.516368
$622$	−8.65558	−0.347057
$623$	−0.922238	−0.0369487
$624$	−9.05749	−0.362590
$625$	−16.9829	−0.679317
$626$	10.4119	0.416143
$627$	4.92251	0.196586
$628$	−5.50589	−0.219709
$629$	−6.50162	−0.259236
$630$	13.7550	0.548012
$631$	1.26410	0.0503229	0.0251615	−	0.999683i	$-0.491990\pi$
$631$	1.26410	0.0503229	0.0251615	+	0.999683i	$0.491990\pi$
$632$	−24.0991	−0.958612
$633$	−1.38335	−0.0549833
$634$	37.7359	1.49868
$635$	−24.2238	−0.961291
$636$	−2.62468	−0.104075
$637$	4.79554	0.190006
$638$	1.05888	0.0419213
$639$	−19.3676	−0.766172
$640$	−5.76087	−0.227719
$641$	16.0445	0.633721	0.316861	−	0.948472i	$-0.397371\pi$
$641$	16.0445	0.633721	0.316861	+	0.948472i	$0.397371\pi$
$642$	−11.0646	−0.436683
$643$	27.4775	1.08361	0.541804	−	0.840505i	$-0.317741\pi$
$643$	27.4775	1.08361	0.541804	+	0.840505i	$0.317741\pi$
$644$	5.24961	0.206864
$645$	13.7015	0.539496
$646$	24.5704	0.966711
$647$	25.6237	1.00737	0.503685	−	0.863887i	$-0.331977\pi$
$647$	25.6237	1.00737	0.503685	+	0.863887i	$0.331977\pi$
$648$	14.1138	0.554443
$649$	4.30776	0.169095
$650$	−8.19054	−0.321259
$651$	9.25230	0.362626
$652$	3.02232	0.118363
$653$	6.18521	0.242046	0.121023	−	0.992650i	$-0.461382\pi$
$653$	6.18521	0.242046	0.121023	+	0.992650i	$0.461382\pi$
$654$	−14.4717	−0.565889
$655$	1.18162	0.0461696
$656$	1.02636	0.0400726
$657$	−2.89731	−0.113035
$658$	−20.8171	−0.811537
$659$	35.6102	1.38718	0.693588	−	0.720372i	$-0.256029\pi$
$659$	35.6102	1.38718	0.693588	+	0.720372i	$0.256029\pi$
$660$	1.57949	0.0614815
$661$	28.0411	1.09067	0.545336	−	0.838217i	$-0.316402\pi$
$661$	28.0411	1.09067	0.545336	+	0.838217i	$0.316402\pi$
$662$	8.31136	0.323030
$663$	21.5257	0.835991
$664$	24.9807	0.969439
$665$	−18.7166	−0.725797
$666$	−3.46559	−0.134289
$667$	1.70420	0.0659869
$668$	6.77941	0.262303
$669$	−8.07678	−0.312266
$670$	25.6689	0.991677
$671$	24.4716	0.944714
$672$	6.28855	0.242586
$673$	−22.8129	−0.879375	−0.439687	−	0.898151i	$-0.644911\pi$
$673$	−22.8129	−0.879375	−0.439687	+	0.898151i	$0.644911\pi$
$674$	26.9382	1.03762
$675$	−5.05026	−0.194385
$676$	−11.3990	−0.438423
$677$	31.7364	1.21973	0.609865	−	0.792505i	$-0.291224\pi$
$677$	31.7364	1.21973	0.609865	+	0.792505i	$0.291224\pi$
$678$	−15.6703	−0.601816
$679$	3.01210	0.115594
$680$	32.0874	1.23049
$681$	−8.01724	−0.307221
$682$	10.4685	0.400858
$683$	−24.2509	−0.927934	−0.463967	−	0.885853i	$-0.653574\pi$
$683$	−24.2509	−0.927934	−0.463967	+	0.885853i	$0.653574\pi$
$684$	−6.32710	−0.241923
$685$	−19.2383	−0.735057
$686$	22.6257	0.863855
$687$	2.65608	0.101336
$688$	22.3623	0.852554
$689$	30.8293	1.17450
$690$	−5.26207	−0.200323
$691$	−25.6982	−0.977605	−0.488803	−	0.872394i	$-0.662566\pi$
$691$	−25.6982	−0.977605	−0.488803	+	0.872394i	$0.662566\pi$
$692$	10.3021	0.391626
$693$	−10.6889	−0.406037
$694$	−18.7392	−0.711331
$695$	8.82981	0.334934
$696$	1.16370	0.0441099
$697$	−2.43921	−0.0923918
$698$	19.3761	0.733394
$699$	7.68104	0.290524
$700$	2.06032	0.0778729
$701$	−11.1124	−0.419709	−0.209854	−	0.977733i	$-0.567299\pi$
$701$	−11.1124	−0.419709	−0.209854	+	0.977733i	$0.567299\pi$
$702$	25.3584	0.957092
$703$	4.71566	0.177854
$704$	15.0292	0.566434
$705$	−10.0806	−0.379657
$706$	4.63139	0.174305
$707$	26.0547	0.979887
$708$	1.16321	0.0437160
$709$	−15.1180	−0.567769	−0.283884	−	0.958859i	$-0.591623\pi$
$709$	−15.1180	−0.567769	−0.283884	+	0.958859i	$0.591623\pi$
$710$	−17.5039	−0.656911
$711$	19.4040	0.727707
$712$	−1.14676	−0.0429766
$713$	16.8484	0.630978
$714$	11.2084	0.419466
$715$	−18.5526	−0.693827
$716$	8.04819	0.300775
$717$	−7.75097	−0.289465
$718$	−14.6870	−0.548116
$719$	12.9226	0.481932	0.240966	−	0.970534i	$-0.422536\pi$
$719$	12.9226	0.481932	0.240966	+	0.970534i	$0.422536\pi$
$720$	10.8711	0.405142
$721$	22.6621	0.843980
$722$	4.24289	0.157904
$723$	−13.5062	−0.502301
$724$	14.7475	0.548085
$725$	0.668850	0.0248405
$726$	−6.67800	−0.247844
$727$	0.296840	0.0110092	0.00550460	−	0.999985i	$-0.498248\pi$
$727$	0.296840	0.0110092	0.00550460	+	0.999985i	$0.498248\pi$
$728$	−42.1052	−1.56052
$729$	−2.80298	−0.103814
$730$	−2.61851	−0.0969153
$731$	−53.1455	−1.96566
$732$	6.60795	0.244237
$733$	−20.5716	−0.759831	−0.379915	−	0.925021i	$-0.624047\pi$
$733$	−20.5716	−0.759831	−0.379915	+	0.925021i	$0.624047\pi$
$734$	21.3546	0.788212
$735$	1.20918	0.0446011
$736$	11.4514	0.422105
$737$	−19.9471	−0.734760
$738$	−1.30019	−0.0478605
$739$	33.0263	1.21489	0.607446	−	0.794361i	$-0.292194\pi$
$739$	33.0263	1.21489	0.607446	+	0.794361i	$0.292194\pi$
$740$	1.51312	0.0556233
$741$	−15.6127	−0.573548
$742$	16.0528	0.589317
$743$	−16.8403	−0.617812	−0.308906	−	0.951093i	$-0.599963\pi$
$743$	−16.8403	−0.617812	−0.308906	+	0.951093i	$0.599963\pi$
$744$	11.5048	0.421786
$745$	−22.3894	−0.820286
$746$	2.02573	0.0741674
$747$	−20.1138	−0.735926
$748$	−6.12653	−0.224008
$749$	−32.6923	−1.19455
$750$	−10.1503	−0.370635
$751$	−0.585382	−0.0213609	−0.0106805	−	0.999943i	$-0.503400\pi$
$751$	−0.585382	−0.0213609	−0.0106805	+	0.999943i	$0.503400\pi$
$752$	−16.4526	−0.599964
$753$	−8.12648	−0.296145
$754$	−3.35844	−0.122307
$755$	−42.3855	−1.54257
$756$	−6.37889	−0.231998
$757$	43.2676	1.57259	0.786294	−	0.617852i	$-0.211997\pi$
$757$	43.2676	1.57259	0.786294	+	0.617852i	$0.211997\pi$
$758$	20.0994	0.730044
$759$	4.08910	0.148425
$760$	−23.2731	−0.844206
$761$	−43.4398	−1.57469	−0.787345	−	0.616512i	$-0.788545\pi$
$761$	−43.4398	−1.57469	−0.787345	+	0.616512i	$0.788545\pi$
$762$	−10.5216	−0.381158
$763$	−42.7594	−1.54799
$764$	−10.4890	−0.379478
$765$	−25.8359	−0.934100
$766$	−0.751629	−0.0271575
$767$	−13.6630	−0.493341
$768$	9.95651	0.359275
$769$	−49.3028	−1.77790	−0.888952	−	0.458001i	$-0.848566\pi$
$769$	−49.3028	−1.77790	−0.888952	+	0.458001i	$0.848566\pi$
$770$	−9.66032	−0.348134
$771$	−6.48696	−0.233622
$772$	−13.1018	−0.471542
$773$	−7.98486	−0.287196	−0.143598	−	0.989636i	$-0.545867\pi$
$773$	−7.98486	−0.287196	−0.143598	+	0.989636i	$0.545867\pi$
$774$	−28.3284	−1.01824
$775$	6.61252	0.237529
$776$	3.74540	0.134452
$777$	2.15117	0.0771728
$778$	−0.620726	−0.0222541
$779$	1.76918	0.0633873
$780$	−5.00967	−0.179375
$781$	13.6022	0.486723
$782$	20.4105	0.729879
$783$	−2.07080	−0.0740045
$784$	1.97350	0.0704822
$785$	16.3068	0.582013
$786$	0.513236	0.0183065
$787$	−8.38025	−0.298724	−0.149362	−	0.988783i	$-0.547722\pi$
$787$	−8.38025	−0.298724	−0.149362	+	0.988783i	$0.547722\pi$
$788$	1.88656	0.0672058
$789$	−3.62036	−0.128888
$790$	17.5368	0.623931
$791$	−46.3009	−1.64627
$792$	−13.2911	−0.472279
$793$	−77.6166	−2.75625
$794$	−38.5241	−1.36717
$795$	7.77349	0.275697
$796$	7.13127	0.252761
$797$	32.6464	1.15640	0.578198	−	0.815897i	$-0.303756\pi$
$797$	32.6464	1.15640	0.578198	+	0.815897i	$0.303756\pi$
$798$	−8.12955	−0.287783
$799$	39.1007	1.38328
$800$	4.49436	0.158900
$801$	0.923341	0.0326246
$802$	−5.13642	−0.181373
$803$	2.03482	0.0718071
$804$	−5.38622	−0.189957
$805$	−15.5477	−0.547986
$806$	−33.2029	−1.16952
$807$	13.3990	0.471665
$808$	32.3978	1.13975
$809$	11.1591	0.392334	0.196167	−	0.980571i	$-0.437151\pi$
$809$	11.1591	0.392334	0.196167	+	0.980571i	$0.437151\pi$
$810$	−10.2705	−0.360870
$811$	55.3167	1.94243	0.971216	−	0.238202i	$-0.0765580\pi$
$811$	55.3167	1.94243	0.971216	+	0.238202i	$0.0765580\pi$
$812$	0.844813	0.0296471
$813$	−0.362702	−0.0127205
$814$	2.43393	0.0853092
$815$	−8.95120	−0.313547
$816$	8.85846	0.310108
$817$	38.5467	1.34858
$818$	−25.3783	−0.887331
$819$	33.9020	1.18463
$820$	0.567676	0.0198241
$821$	2.81352	0.0981925	0.0490963	−	0.998794i	$-0.484366\pi$
$821$	2.81352	0.0981925	0.0490963	+	0.998794i	$0.484366\pi$
$822$	−8.35616	−0.291455
$823$	−1.75483	−0.0611696	−0.0305848	−	0.999532i	$-0.509737\pi$
$823$	−1.75483	−0.0611696	−0.0305848	+	0.999532i	$0.509737\pi$
$824$	28.1792	0.981670
$825$	1.60486	0.0558739
$826$	−7.11430	−0.247538
$827$	10.5617	0.367265	0.183633	−	0.982995i	$-0.441214\pi$
$827$	10.5617	0.367265	0.183633	+	0.982995i	$0.441214\pi$
$828$	−5.25589	−0.182655
$829$	14.2836	0.496090	0.248045	−	0.968749i	$-0.420212\pi$
$829$	14.2836	0.496090	0.248045	+	0.968749i	$0.420212\pi$
$830$	−18.1783	−0.630978
$831$	−18.8206	−0.652880
$832$	−47.6682	−1.65260
$833$	−4.69016	−0.162504
$834$	3.83523	0.132803
$835$	−20.0785	−0.694846
$836$	4.44361	0.153685
$837$	−20.4728	−0.707643
$838$	41.5597	1.43566
$839$	56.7967	1.96084	0.980420	−	0.196919i	$-0.0630935\pi$
$839$	56.7967	1.96084	0.980420	+	0.196919i	$0.0630935\pi$
$840$	−10.6167	−0.366309
$841$	−28.7257	−0.990543
$842$	14.9948	0.516756
$843$	−12.5671	−0.432835
$844$	−1.24877	−0.0429844
$845$	33.7603	1.16139
$846$	20.8420	0.716564
$847$	−19.7314	−0.677979
$848$	12.6871	0.435678
$849$	21.6928	0.744495
$850$	8.01056	0.274760
$851$	3.91728	0.134282
$852$	3.67293	0.125832
$853$	46.6609	1.59764	0.798819	−	0.601572i	$-0.205459\pi$
$853$	46.6609	1.59764	0.798819	+	0.601572i	$0.205459\pi$
$854$	−40.4149	−1.38297
$855$	18.7389	0.640858
$856$	−40.6513	−1.38943
$857$	−20.6518	−0.705452	−0.352726	−	0.935727i	$-0.614745\pi$
$857$	−20.6518	−0.705452	−0.352726	+	0.935727i	$0.614745\pi$
$858$	−8.05833	−0.275107
$859$	29.1454	0.994430	0.497215	−	0.867627i	$-0.334356\pi$
$859$	29.1454	0.994430	0.497215	+	0.867627i	$0.334356\pi$
$860$	12.3685	0.421763
$861$	0.807056	0.0275044
$862$	42.2951	1.44058
$863$	−5.82871	−0.198412	−0.0992059	−	0.995067i	$-0.531630\pi$
$863$	−5.82871	−0.198412	−0.0992059	+	0.995067i	$0.531630\pi$
$864$	−13.9148	−0.473392
$865$	−30.5116	−1.03742
$866$	−5.75504	−0.195564
$867$	−8.78412	−0.298324
$868$	8.35216	0.283491
$869$	−13.6277	−0.462287
$870$	−0.846817	−0.0287098
$871$	63.2663	2.14370
$872$	−53.1693	−1.80054
$873$	−3.01570	−0.102066
$874$	−14.8039	−0.500749
$875$	−29.9908	−1.01387
$876$	0.549453	0.0185643
$877$	−40.8433	−1.37918	−0.689590	−	0.724200i	$-0.742209\pi$
$877$	−40.8433	−1.37918	−0.689590	+	0.724200i	$0.742209\pi$
$878$	−24.9066	−0.840556
$879$	−8.63777	−0.291345
$880$	−7.63492	−0.257373
$881$	−25.3608	−0.854425	−0.427213	−	0.904151i	$-0.640504\pi$
$881$	−25.3608	−0.854425	−0.427213	+	0.904151i	$0.640504\pi$
$882$	−2.50002	−0.0841801
$883$	32.9763	1.10974	0.554870	−	0.831937i	$-0.312768\pi$
$883$	32.9763	1.10974	0.554870	+	0.831937i	$0.312768\pi$
$884$	19.4315	0.653554
$885$	−3.44506	−0.115804
$886$	−17.8296	−0.598999
$887$	11.2155	0.376579	0.188289	−	0.982114i	$-0.439706\pi$
$887$	11.2155	0.376579	0.188289	+	0.982114i	$0.439706\pi$
$888$	2.67488	0.0897631
$889$	−31.0880	−1.04266
$890$	0.834490	0.0279722
$891$	7.98114	0.267378
$892$	−7.29101	−0.244121
$893$	−28.3599	−0.949029
$894$	−9.72487	−0.325248
$895$	−23.8363	−0.796759
$896$	−7.39333	−0.246994
$897$	−12.9694	−0.433037
$898$	−40.4177	−1.34876
$899$	2.71139	0.0904300
$900$	−2.06279	−0.0687596
$901$	−30.1519	−1.00450
$902$	0.913138	0.0304042
$903$	17.5841	0.585162
$904$	−57.5730	−1.91485
$905$	−43.6774	−1.45189
$906$	−18.4102	−0.611637
$907$	−26.6790	−0.885863	−0.442931	−	0.896556i	$-0.646061\pi$
$907$	−26.6790	−0.885863	−0.442931	+	0.896556i	$0.646061\pi$
$908$	−7.23725	−0.240177
$909$	−26.0858	−0.865213
$910$	30.6397	1.01570
$911$	−8.59455	−0.284750	−0.142375	−	0.989813i	$-0.545474\pi$
$911$	−8.59455	−0.284750	−0.142375	+	0.989813i	$0.545474\pi$
$912$	−6.42509	−0.212756
$913$	14.1262	0.467509
$914$	17.8265	0.589649
$915$	−19.5707	−0.646988
$916$	2.39768	0.0792215
$917$	1.51645	0.0500776
$918$	−24.8012	−0.818561
$919$	7.41874	0.244722	0.122361	−	0.992486i	$-0.460953\pi$
$919$	7.41874	0.244722	0.122361	+	0.992486i	$0.460953\pi$
$920$	−19.3329	−0.637386
$921$	−21.9643	−0.723747
$922$	30.6822	1.01046
$923$	−43.1420	−1.42004
$924$	2.02707	0.0666856
$925$	1.53742	0.0505500
$926$	−46.8954	−1.54108
$927$	−22.6892	−0.745211
$928$	1.84286	0.0604950
$929$	−45.6615	−1.49810	−0.749052	−	0.662511i	$-0.769491\pi$
$929$	−45.6615	−1.49810	−0.749052	+	0.662511i	$0.769491\pi$
$930$	−8.37197	−0.274528
$931$	3.40180	0.111489
$932$	6.93377	0.227123
$933$	−5.37914	−0.176105
$934$	21.6506	0.708429
$935$	18.1449	0.593402
$936$	42.1555	1.37790
$937$	48.2824	1.57732	0.788658	−	0.614832i	$-0.210776\pi$
$937$	48.2824	1.57732	0.788658	+	0.614832i	$0.210776\pi$
$938$	32.9427	1.07562
$939$	6.47063	0.211161
$940$	−9.09987	−0.296805
$941$	−36.8489	−1.20124	−0.600620	−	0.799535i	$-0.705079\pi$
$941$	−36.8489	−1.20124	−0.600620	+	0.799535i	$0.705079\pi$
$942$	7.08285	0.230772
$943$	1.46965	0.0478582
$944$	−5.62270	−0.183003
$945$	18.8923	0.614568
$946$	19.8954	0.646856
$947$	−17.9078	−0.581927	−0.290963	−	0.956734i	$-0.593976\pi$
$947$	−17.9078	−0.581927	−0.290963	+	0.956734i	$0.593976\pi$
$948$	−3.67982	−0.119515
$949$	−6.45384	−0.209501
$950$	−5.81010	−0.188505
$951$	23.4515	0.760468
$952$	41.1799	1.33465
$953$	59.4441	1.92558	0.962792	−	0.270245i	$-0.0871046\pi$
$953$	59.4441	1.92558	0.962792	+	0.270245i	$0.0871046\pi$
$954$	−16.0720	−0.520351
$955$	31.0652	1.00525
$956$	−6.99690	−0.226296
$957$	0.658054	0.0212719
$958$	−32.7329	−1.05755
$959$	−24.6898	−0.797276
$960$	−12.0193	−0.387922
$961$	−4.19410	−0.135294
$962$	−7.71971	−0.248893
$963$	32.7314	1.05475
$964$	−12.1922	−0.392684
$965$	38.8034	1.24913
$966$	−6.75318	−0.217280
$967$	16.8752	0.542669	0.271334	−	0.962485i	$-0.412535\pi$
$967$	16.8752	0.542669	0.271334	+	0.962485i	$0.412535\pi$
$968$	−24.5350	−0.788586
$969$	15.2697	0.490532
$970$	−2.72551	−0.0875108
$971$	41.3567	1.32720	0.663600	−	0.748087i	$-0.269028\pi$
$971$	41.3567	1.32720	0.663600	+	0.748087i	$0.269028\pi$
$972$	9.88332	0.317008
$973$	11.3319	0.363284
$974$	6.88313	0.220550
$975$	−5.09013	−0.163015
$976$	−31.9414	−1.02242
$977$	1.00276	0.0320811	0.0160405	−	0.999871i	$-0.494894\pi$
$977$	1.00276	0.0320811	0.0160405	+	0.999871i	$0.494894\pi$
$978$	−3.88796	−0.124323
$979$	−0.648474	−0.0207253
$980$	1.09154	0.0348679
$981$	42.8105	1.36683
$982$	−15.1298	−0.482813
$983$	7.90710	0.252197	0.126099	−	0.992018i	$-0.459754\pi$
$983$	7.90710	0.252197	0.126099	+	0.992018i	$0.459754\pi$
$984$	1.00354	0.0319915
$985$	−5.58740	−0.178030
$986$	3.28464	0.104604
$987$	−12.9371	−0.411793
$988$	−14.0938	−0.448384
$989$	32.0206	1.01820
$990$	9.67187	0.307392
$991$	11.9119	0.378395	0.189197	−	0.981939i	$-0.439411\pi$
$991$	11.9119	0.378395	0.189197	+	0.981939i	$0.439411\pi$
$992$	18.2193	0.578463
$993$	5.16522	0.163913
$994$	−22.4640	−0.712516
$995$	−21.1207	−0.669570
$996$	3.81443	0.120865
$997$	−41.4093	−1.31145	−0.655724	−	0.755001i	$-0.727636\pi$
$997$	−41.4093	−1.31145	−0.655724	+	0.755001i	$0.727636\pi$
$998$	−0.331847	−0.0105044
$999$	−4.75995	−0.150598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.a.1.28	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.a.1.28	✓	77	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.16126 q^{2} -0.721683 q^{3} -0.651472 q^{4} +1.92946 q^{5} +0.838063 q^{6} +2.47621 q^{7} +3.07905 q^{8} -2.47917 q^{9} +O(q^{10})\)	\(q-1.16126 q^{2} -0.721683 q^{3} -0.651472 q^{4} +1.92946 q^{5} +0.838063 q^{6} +2.47621 q^{7} +3.07905 q^{8} -2.47917 q^{9} -2.24061 q^{10} +1.74116 q^{11} +0.470157 q^{12} -5.52244 q^{13} -2.87553 q^{14} -1.39246 q^{15} -2.27264 q^{16} +5.40108 q^{17} +2.87897 q^{18} -3.91744 q^{19} -1.25699 q^{20} -1.78704 q^{21} -2.02194 q^{22} -3.25420 q^{23} -2.22210 q^{24} -1.27718 q^{25} +6.41299 q^{26} +3.95423 q^{27} -1.61318 q^{28} -0.523693 q^{29} +1.61701 q^{30} -5.17744 q^{31} -3.51898 q^{32} -1.25656 q^{33} -6.27207 q^{34} +4.77776 q^{35} +1.61511 q^{36} -1.20376 q^{37} +4.54917 q^{38} +3.98545 q^{39} +5.94091 q^{40} -0.451616 q^{41} +2.07522 q^{42} -9.83978 q^{43} -1.13431 q^{44} -4.78347 q^{45} +3.77897 q^{46} +7.23941 q^{47} +1.64013 q^{48} -0.868374 q^{49} +1.48314 q^{50} -3.89787 q^{51} +3.59771 q^{52} -5.58256 q^{53} -4.59189 q^{54} +3.35949 q^{55} +7.62439 q^{56} +2.82715 q^{57} +0.608145 q^{58} +2.47408 q^{59} +0.907149 q^{60} +14.0548 q^{61} +6.01236 q^{62} -6.13896 q^{63} +8.63173 q^{64} -10.6553 q^{65} +1.45920 q^{66} -11.4562 q^{67} -3.51866 q^{68} +2.34850 q^{69} -5.54822 q^{70} +7.81214 q^{71} -7.63350 q^{72} +1.16866 q^{73} +1.39788 q^{74} +0.921719 q^{75} +2.55210 q^{76} +4.31147 q^{77} -4.62815 q^{78} -7.82680 q^{79} -4.38497 q^{80} +4.58382 q^{81} +0.524444 q^{82} +8.11311 q^{83} +1.16421 q^{84} +10.4212 q^{85} +11.4266 q^{86} +0.377941 q^{87} +5.36111 q^{88} -0.372439 q^{89} +5.55486 q^{90} -13.6747 q^{91} +2.12002 q^{92} +3.73647 q^{93} -8.40685 q^{94} -7.55854 q^{95} +2.53959 q^{96} +1.21641 q^{97} +1.00841 q^{98} -4.31663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * q^99

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