LMFDB - Embedded newform 4011.2.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.797866 q^{2} +1.00000 q^{3} -1.36341 q^{4} +0.229986 q^{5} +0.797866 q^{6} -1.00000 q^{7} -2.68355 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.797866 q^{2} +1.00000 q^{3} -1.36341 q^{4} +0.229986 q^{5} +0.797866 q^{6} -1.00000 q^{7} -2.68355 q^{8} +1.00000 q^{9} +0.183498 q^{10} -2.28169 q^{11} -1.36341 q^{12} -2.54945 q^{13} -0.797866 q^{14} +0.229986 q^{15} +0.585709 q^{16} -5.30219 q^{17} +0.797866 q^{18} +3.06834 q^{19} -0.313565 q^{20} -1.00000 q^{21} -1.82049 q^{22} +4.59878 q^{23} -2.68355 q^{24} -4.94711 q^{25} -2.03412 q^{26} +1.00000 q^{27} +1.36341 q^{28} +5.18446 q^{29} +0.183498 q^{30} +10.1171 q^{31} +5.83442 q^{32} -2.28169 q^{33} -4.23043 q^{34} -0.229986 q^{35} -1.36341 q^{36} -7.95934 q^{37} +2.44812 q^{38} -2.54945 q^{39} -0.617178 q^{40} +7.00076 q^{41} -0.797866 q^{42} +12.4299 q^{43} +3.11089 q^{44} +0.229986 q^{45} +3.66921 q^{46} +2.89044 q^{47} +0.585709 q^{48} +1.00000 q^{49} -3.94713 q^{50} -5.30219 q^{51} +3.47595 q^{52} +4.76331 q^{53} +0.797866 q^{54} -0.524757 q^{55} +2.68355 q^{56} +3.06834 q^{57} +4.13650 q^{58} -5.54577 q^{59} -0.313565 q^{60} -3.81319 q^{61} +8.07210 q^{62} -1.00000 q^{63} +3.48366 q^{64} -0.586337 q^{65} -1.82049 q^{66} +11.5047 q^{67} +7.22906 q^{68} +4.59878 q^{69} -0.183498 q^{70} +3.02367 q^{71} -2.68355 q^{72} +10.4280 q^{73} -6.35049 q^{74} -4.94711 q^{75} -4.18341 q^{76} +2.28169 q^{77} -2.03412 q^{78} -6.36311 q^{79} +0.134705 q^{80} +1.00000 q^{81} +5.58567 q^{82} +14.1379 q^{83} +1.36341 q^{84} -1.21943 q^{85} +9.91737 q^{86} +5.18446 q^{87} +6.12304 q^{88} -7.60469 q^{89} +0.183498 q^{90} +2.54945 q^{91} -6.27002 q^{92} +10.1171 q^{93} +2.30618 q^{94} +0.705674 q^{95} +5.83442 q^{96} -14.5618 q^{97} +0.797866 q^{98} -2.28169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	0.797866	0.564176	0.282088	−	0.959389i	$-0.408973\pi$
$2$	0.797866	0.564176	0.282088	+	0.959389i	$0.408973\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.36341	−0.681705
$5$	0.229986	0.102853	0.0514263	−	0.998677i	$-0.483623\pi$
$5$	0.229986	0.102853	0.0514263	+	0.998677i	$0.483623\pi$
$6$	0.797866	0.325727
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.68355	−0.948778
$9$	1.00000	0.333333
$10$	0.183498	0.0580270
$11$	−2.28169	−0.687957	−0.343978	−	0.938978i	$-0.611775\pi$
$11$	−2.28169	−0.687957	−0.343978	+	0.938978i	$0.611775\pi$
$12$	−1.36341	−0.393583
$13$	−2.54945	−0.707091	−0.353545	−	0.935417i	$-0.615024\pi$
$13$	−2.54945	−0.707091	−0.353545	+	0.935417i	$0.615024\pi$
$14$	−0.797866	−0.213239
$15$	0.229986	0.0593820
$16$	0.585709	0.146427
$17$	−5.30219	−1.28597	−0.642985	−	0.765879i	$-0.722304\pi$
$17$	−5.30219	−1.28597	−0.642985	+	0.765879i	$0.722304\pi$
$18$	0.797866	0.188059
$19$	3.06834	0.703926	0.351963	−	0.936014i	$-0.385514\pi$
$19$	3.06834	0.703926	0.351963	+	0.936014i	$0.385514\pi$
$20$	−0.313565	−0.0701152
$21$	−1.00000	−0.218218
$22$	−1.82049	−0.388129
$23$	4.59878	0.958912	0.479456	−	0.877566i	$-0.340834\pi$
$23$	4.59878	0.958912	0.479456	+	0.877566i	$0.340834\pi$
$24$	−2.68355	−0.547777
$25$	−4.94711	−0.989421
$26$	−2.03412	−0.398924
$27$	1.00000	0.192450
$28$	1.36341	0.257660
$29$	5.18446	0.962730	0.481365	−	0.876520i	$-0.340141\pi$
$29$	5.18446	0.962730	0.481365	+	0.876520i	$0.340141\pi$
$30$	0.183498	0.0335019
$31$	10.1171	1.81709	0.908544	−	0.417789i	$-0.137195\pi$
$31$	10.1171	1.81709	0.908544	+	0.417789i	$0.137195\pi$
$32$	5.83442	1.03139
$33$	−2.28169	−0.397192
$34$	−4.23043	−0.725513
$35$	−0.229986	−0.0388747
$36$	−1.36341	−0.227235
$37$	−7.95934	−1.30851	−0.654254	−	0.756275i	$-0.727017\pi$
$37$	−7.95934	−1.30851	−0.654254	+	0.756275i	$0.727017\pi$
$38$	2.44812	0.397138
$39$	−2.54945	−0.408239
$40$	−0.617178	−0.0975844
$41$	7.00076	1.09334	0.546668	−	0.837350i	$-0.315896\pi$
$41$	7.00076	1.09334	0.546668	+	0.837350i	$0.315896\pi$
$42$	−0.797866	−0.123113
$43$	12.4299	1.89554	0.947769	−	0.318958i	$-0.103333\pi$
$43$	12.4299	1.89554	0.947769	+	0.318958i	$0.103333\pi$
$44$	3.11089	0.468984
$45$	0.229986	0.0342842
$46$	3.66921	0.540995
$47$	2.89044	0.421614	0.210807	−	0.977528i	$-0.432391\pi$
$47$	2.89044	0.421614	0.210807	+	0.977528i	$0.432391\pi$
$48$	0.585709	0.0845398
$49$	1.00000	0.142857
$50$	−3.94713	−0.558208
$51$	−5.30219	−0.742455
$52$	3.47595	0.482027
$53$	4.76331	0.654291	0.327145	−	0.944974i	$-0.393913\pi$
$53$	4.76331	0.654291	0.327145	+	0.944974i	$0.393913\pi$
$54$	0.797866	0.108576
$55$	−0.524757	−0.0707582
$56$	2.68355	0.358604
$57$	3.06834	0.406412
$58$	4.13650	0.543149
$59$	−5.54577	−0.721998	−0.360999	−	0.932566i	$-0.617564\pi$
$59$	−5.54577	−0.721998	−0.360999	+	0.932566i	$0.617564\pi$
$60$	−0.313565	−0.0404810
$61$	−3.81319	−0.488229	−0.244114	−	0.969746i	$-0.578497\pi$
$61$	−3.81319	−0.488229	−0.244114	+	0.969746i	$0.578497\pi$
$62$	8.07210	1.02516
$63$	−1.00000	−0.125988
$64$	3.48366	0.435458
$65$	−0.586337	−0.0727262
$66$	−1.82049	−0.224086
$67$	11.5047	1.40553	0.702763	−	0.711424i	$-0.251949\pi$
$67$	11.5047	1.40553	0.702763	+	0.711424i	$0.251949\pi$
$68$	7.22906	0.876652
$69$	4.59878	0.553628
$70$	−0.183498	−0.0219322
$71$	3.02367	0.358844	0.179422	−	0.983772i	$-0.442577\pi$
$71$	3.02367	0.358844	0.179422	+	0.983772i	$0.442577\pi$
$72$	−2.68355	−0.316259
$73$	10.4280	1.22050	0.610251	−	0.792208i	$-0.291069\pi$
$73$	10.4280	1.22050	0.610251	+	0.792208i	$0.291069\pi$
$74$	−6.35049	−0.738229
$75$	−4.94711	−0.571243
$76$	−4.18341	−0.479870
$77$	2.28169	0.260023
$78$	−2.03412	−0.230319
$79$	−6.36311	−0.715906	−0.357953	−	0.933740i	$-0.616525\pi$
$79$	−6.36311	−0.715906	−0.357953	+	0.933740i	$0.616525\pi$
$80$	0.134705	0.0150604
$81$	1.00000	0.111111
$82$	5.58567	0.616834
$83$	14.1379	1.55183	0.775917	−	0.630835i	$-0.217287\pi$
$83$	14.1379	1.55183	0.775917	+	0.630835i	$0.217287\pi$
$84$	1.36341	0.148760
$85$	−1.21943	−0.132265
$86$	9.91737	1.06942
$87$	5.18446	0.555832
$88$	6.12304	0.652718
$89$	−7.60469	−0.806096	−0.403048	−	0.915179i	$-0.632049\pi$
$89$	−7.60469	−0.806096	−0.403048	+	0.915179i	$0.632049\pi$
$90$	0.183498	0.0193423
$91$	2.54945	0.267255
$92$	−6.27002	−0.653695
$93$	10.1171	1.04910
$94$	2.30618	0.237865
$95$	0.705674	0.0724007
$96$	5.83442	0.595473
$97$	−14.5618	−1.47852	−0.739261	−	0.673419i	$-0.764825\pi$
$97$	−14.5618	−1.47852	−0.739261	+	0.673419i	$0.764825\pi$
$98$	0.797866	0.0805966
$99$	−2.28169	−0.229319
$100$	6.74494	0.674494
$101$	7.33332	0.729692	0.364846	−	0.931068i	$-0.381122\pi$
$101$	7.33332	0.729692	0.364846	+	0.931068i	$0.381122\pi$
$102$	−4.23043	−0.418875
$103$	0.522380	0.0514716	0.0257358	−	0.999669i	$-0.491807\pi$
$103$	0.522380	0.0514716	0.0257358	+	0.999669i	$0.491807\pi$
$104$	6.84158	0.670872
$105$	−0.229986	−0.0224443
$106$	3.80048	0.369135
$107$	2.36724	0.228850	0.114425	−	0.993432i	$-0.463497\pi$
$107$	2.36724	0.228850	0.114425	+	0.993432i	$0.463497\pi$
$108$	−1.36341	−0.131194
$109$	−15.8614	−1.51924	−0.759622	−	0.650365i	$-0.774616\pi$
$109$	−15.8614	−1.51924	−0.759622	+	0.650365i	$0.774616\pi$
$110$	−0.418685	−0.0399201
$111$	−7.95934	−0.755467
$112$	−0.585709	−0.0553443
$113$	16.9979	1.59902	0.799512	−	0.600650i	$-0.205092\pi$
$113$	16.9979	1.59902	0.799512	+	0.600650i	$0.205092\pi$
$114$	2.44812	0.229288
$115$	1.05765	0.0986266
$116$	−7.06855	−0.656298
$117$	−2.54945	−0.235697
$118$	−4.42478	−0.407334
$119$	5.30219	0.486051
$120$	−0.617178	−0.0563404
$121$	−5.79387	−0.526716
$122$	−3.04241	−0.275447
$123$	7.00076	0.631238
$124$	−13.7938	−1.23872
$125$	−2.28769	−0.204617
$126$	−0.797866	−0.0710795
$127$	18.5990	1.65039	0.825197	−	0.564845i	$-0.191064\pi$
$127$	18.5990	1.65039	0.825197	+	0.564845i	$0.191064\pi$
$128$	−8.88934	−0.785714
$129$	12.4299	1.09439
$130$	−0.467818	−0.0410304
$131$	−15.3370	−1.34000	−0.670000	−	0.742361i	$-0.733706\pi$
$131$	−15.3370	−1.34000	−0.670000	+	0.742361i	$0.733706\pi$
$132$	3.11089	0.270768
$133$	−3.06834	−0.266059
$134$	9.17923	0.792965
$135$	0.229986	0.0197940
$136$	14.2287	1.22010
$137$	3.53453	0.301975	0.150988	−	0.988536i	$-0.451755\pi$
$137$	3.53453	0.301975	0.150988	+	0.988536i	$0.451755\pi$
$138$	3.66921	0.312344
$139$	12.1048	1.02671	0.513357	−	0.858175i	$-0.328402\pi$
$139$	12.1048	1.02671	0.513357	+	0.858175i	$0.328402\pi$
$140$	0.313565	0.0265011
$141$	2.89044	0.243419
$142$	2.41248	0.202451
$143$	5.81707	0.486448
$144$	0.585709	0.0488091
$145$	1.19235	0.0990194
$146$	8.32012	0.688578
$147$	1.00000	0.0824786
$148$	10.8519	0.892017
$149$	−11.9796	−0.981408	−0.490704	−	0.871326i	$-0.663260\pi$
$149$	−11.9796	−0.981408	−0.490704	+	0.871326i	$0.663260\pi$
$150$	−3.94713	−0.322282
$151$	3.38423	0.275405	0.137702	−	0.990474i	$-0.456028\pi$
$151$	3.38423	0.275405	0.137702	+	0.990474i	$0.456028\pi$
$152$	−8.23405	−0.667870
$153$	−5.30219	−0.428656
$154$	1.82049	0.146699
$155$	2.32679	0.186892
$156$	3.47595	0.278299
$157$	9.42430	0.752141	0.376070	−	0.926591i	$-0.377275\pi$
$157$	9.42430	0.752141	0.376070	+	0.926591i	$0.377275\pi$
$158$	−5.07691	−0.403897
$159$	4.76331	0.377755
$160$	1.34183	0.106081
$161$	−4.59878	−0.362435
$162$	0.797866	0.0626862
$163$	−13.4477	−1.05330	−0.526652	−	0.850081i	$-0.676553\pi$
$163$	−13.4477	−1.05330	−0.526652	+	0.850081i	$0.676553\pi$
$164$	−9.54492	−0.745333
$165$	−0.524757	−0.0408523
$166$	11.2801	0.875508
$167$	−10.5943	−0.819811	−0.409905	−	0.912128i	$-0.634438\pi$
$167$	−10.5943	−0.819811	−0.409905	+	0.912128i	$0.634438\pi$
$168$	2.68355	0.207040
$169$	−6.50029	−0.500023
$170$	−0.972938	−0.0746210
$171$	3.06834	0.234642
$172$	−16.9470	−1.29220
$173$	−8.93202	−0.679089	−0.339544	−	0.940590i	$-0.610273\pi$
$173$	−8.93202	−0.679089	−0.339544	+	0.940590i	$0.610273\pi$
$174$	4.13650	0.313587
$175$	4.94711	0.373966
$176$	−1.33641	−0.100736
$177$	−5.54577	−0.416846
$178$	−6.06752	−0.454780
$179$	11.7675	0.879545	0.439772	−	0.898109i	$-0.355059\pi$
$179$	11.7675	0.879545	0.439772	+	0.898109i	$0.355059\pi$
$180$	−0.313565	−0.0233717
$181$	11.4238	0.849125	0.424563	−	0.905399i	$-0.360428\pi$
$181$	11.4238	0.849125	0.424563	+	0.905399i	$0.360428\pi$
$182$	2.03412	0.150779
$183$	−3.81319	−0.281879
$184$	−12.3411	−0.909794
$185$	−1.83053	−0.134584
$186$	8.07210	0.591875
$187$	12.0980	0.884691
$188$	−3.94086	−0.287417
$189$	−1.00000	−0.0727393
$190$	0.563033	0.0408467
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	3.48366	0.251412
$193$	3.50957	0.252624	0.126312	−	0.991991i	$-0.459686\pi$
$193$	3.50957	0.252624	0.126312	+	0.991991i	$0.459686\pi$
$194$	−11.6183	−0.834147
$195$	−0.586337	−0.0419885
$196$	−1.36341	−0.0973865
$197$	−3.19611	−0.227714	−0.113857	−	0.993497i	$-0.536321\pi$
$197$	−3.19611	−0.227714	−0.113857	+	0.993497i	$0.536321\pi$
$198$	−1.82049	−0.129376
$199$	21.0984	1.49562	0.747812	−	0.663911i	$-0.231104\pi$
$199$	21.0984	1.49562	0.747812	+	0.663911i	$0.231104\pi$
$200$	13.2758	0.938741
$201$	11.5047	0.811481
$202$	5.85100	0.411675
$203$	−5.18446	−0.363878
$204$	7.22906	0.506135
$205$	1.61007	0.112453
$206$	0.416789	0.0290391
$207$	4.59878	0.319637
$208$	−1.49324	−0.103537
$209$	−7.00102	−0.484271
$210$	−0.183498	−0.0126625
$211$	−1.25014	−0.0860630	−0.0430315	−	0.999074i	$-0.513702\pi$
$211$	−1.25014	−0.0860630	−0.0430315	+	0.999074i	$0.513702\pi$
$212$	−6.49435	−0.446034
$213$	3.02367	0.207178
$214$	1.88874	0.129112
$215$	2.85869	0.194961
$216$	−2.68355	−0.182592
$217$	−10.1171	−0.686795
$218$	−12.6552	−0.857121
$219$	10.4280	0.704657
$220$	0.715459	0.0482362
$221$	13.5177	0.909297
$222$	−6.35049	−0.426217
$223$	−0.302539	−0.0202595	−0.0101297	−	0.999949i	$-0.503224\pi$
$223$	−0.302539	−0.0202595	−0.0101297	+	0.999949i	$0.503224\pi$
$224$	−5.83442	−0.389828
$225$	−4.94711	−0.329807
$226$	13.5620	0.902131
$227$	22.8785	1.51850	0.759249	−	0.650800i	$-0.225566\pi$
$227$	22.8785	1.51850	0.759249	+	0.650800i	$0.225566\pi$
$228$	−4.18341	−0.277053
$229$	20.4787	1.35327	0.676634	−	0.736319i	$-0.263438\pi$
$229$	20.4787	1.35327	0.676634	+	0.736319i	$0.263438\pi$
$230$	0.843865	0.0556428
$231$	2.28169	0.150124
$232$	−13.9128	−0.913417
$233$	−9.64060	−0.631577	−0.315788	−	0.948830i	$-0.602269\pi$
$233$	−9.64060	−0.631577	−0.315788	+	0.948830i	$0.602269\pi$
$234$	−2.03412	−0.132975
$235$	0.664760	0.0433641
$236$	7.56116	0.492190
$237$	−6.36311	−0.413328
$238$	4.23043	0.274218
$239$	12.5265	0.810272	0.405136	−	0.914256i	$-0.367224\pi$
$239$	12.5265	0.810272	0.405136	+	0.914256i	$0.367224\pi$
$240$	0.134705	0.00869514
$241$	−14.0251	−0.903435	−0.451718	−	0.892161i	$-0.649189\pi$
$241$	−14.0251	−0.903435	−0.451718	+	0.892161i	$0.649189\pi$
$242$	−4.62273	−0.297160
$243$	1.00000	0.0641500
$244$	5.19894	0.332828
$245$	0.229986	0.0146932
$246$	5.58567	0.356129
$247$	−7.82259	−0.497740
$248$	−27.1498	−1.72401
$249$	14.1379	0.895952
$250$	−1.82527	−0.115440
$251$	−17.0848	−1.07838	−0.539190	−	0.842184i	$-0.681270\pi$
$251$	−17.0848	−1.07838	−0.539190	+	0.842184i	$0.681270\pi$
$252$	1.36341	0.0858868
$253$	−10.4930	−0.659690
$254$	14.8395	0.931113
$255$	−1.21943	−0.0763634
$256$	−14.0598	−0.878739
$257$	7.66264	0.477982	0.238991	−	0.971022i	$-0.423183\pi$
$257$	7.66264	0.477982	0.238991	+	0.971022i	$0.423183\pi$
$258$	9.91737	0.617428
$259$	7.95934	0.494570
$260$	0.799418	0.0495778
$261$	5.18446	0.320910
$262$	−12.2369	−0.755996
$263$	−27.8460	−1.71706	−0.858529	−	0.512765i	$-0.828621\pi$
$263$	−27.8460	−1.71706	−0.858529	+	0.512765i	$0.828621\pi$
$264$	6.12304	0.376847
$265$	1.09549	0.0672956
$266$	−2.44812	−0.150104
$267$	−7.60469	−0.465400
$268$	−15.6857	−0.958155
$269$	18.3880	1.12114	0.560568	−	0.828108i	$-0.310583\pi$
$269$	18.3880	1.12114	0.560568	+	0.828108i	$0.310583\pi$
$270$	0.183498	0.0111673
$271$	19.3264	1.17399	0.586997	−	0.809589i	$-0.300310\pi$
$271$	19.3264	1.17399	0.586997	+	0.809589i	$0.300310\pi$
$272$	−3.10554	−0.188301
$273$	2.54945	0.154300
$274$	2.82008	0.170367
$275$	11.2878	0.680679
$276$	−6.27002	−0.377411
$277$	−21.4279	−1.28748	−0.643738	−	0.765246i	$-0.722617\pi$
$277$	−21.4279	−1.28748	−0.643738	+	0.765246i	$0.722617\pi$
$278$	9.65799	0.579248
$279$	10.1171	0.605696
$280$	0.617178	0.0368834
$281$	19.9431	1.18970	0.594852	−	0.803835i	$-0.297211\pi$
$281$	19.9431	1.18970	0.594852	+	0.803835i	$0.297211\pi$
$282$	2.30618	0.137331
$283$	−15.1073	−0.898034	−0.449017	−	0.893523i	$-0.648226\pi$
$283$	−15.1073	−0.898034	−0.449017	+	0.893523i	$0.648226\pi$
$284$	−4.12250	−0.244626
$285$	0.705674	0.0418005
$286$	4.64124	0.274442
$287$	−7.00076	−0.413242
$288$	5.83442	0.343796
$289$	11.1132	0.653716
$290$	0.951336	0.0558644
$291$	−14.5618	−0.853626
$292$	−14.2176	−0.832023
$293$	18.5883	1.08594	0.542971	−	0.839752i	$-0.317299\pi$
$293$	18.5883	1.08594	0.542971	+	0.839752i	$0.317299\pi$
$294$	0.797866	0.0465325
$295$	−1.27545	−0.0742594
$296$	21.3593	1.24148
$297$	−2.28169	−0.132397
$298$	−9.55812	−0.553687
$299$	−11.7244	−0.678038
$300$	6.74494	0.389419
$301$	−12.4299	−0.716446
$302$	2.70016	0.155377
$303$	7.33332	0.421288
$304$	1.79716	0.103074
$305$	−0.876979	−0.0502157
$306$	−4.23043	−0.241838
$307$	25.9647	1.48188	0.740942	−	0.671570i	$-0.234380\pi$
$307$	25.9647	1.48188	0.740942	+	0.671570i	$0.234380\pi$
$308$	−3.11089	−0.177259
$309$	0.522380	0.0297171
$310$	1.85647	0.105440
$311$	−13.1107	−0.743441	−0.371720	−	0.928345i	$-0.621232\pi$
$311$	−13.1107	−0.743441	−0.371720	+	0.928345i	$0.621232\pi$
$312$	6.84158	0.387328
$313$	12.4180	0.701907	0.350953	−	0.936393i	$-0.385858\pi$
$313$	12.4180	0.701907	0.350953	+	0.936393i	$0.385858\pi$
$314$	7.51932	0.424340
$315$	−0.229986	−0.0129582
$316$	8.67553	0.488037
$317$	3.51517	0.197432	0.0987159	−	0.995116i	$-0.468527\pi$
$317$	3.51517	0.197432	0.0987159	+	0.995116i	$0.468527\pi$
$318$	3.80048	0.213120
$319$	−11.8294	−0.662317
$320$	0.801192	0.0447880
$321$	2.36724	0.132127
$322$	−3.66921	−0.204477
$323$	−16.2689	−0.905227
$324$	−1.36341	−0.0757450
$325$	12.6124	0.699611
$326$	−10.7294	−0.594249
$327$	−15.8614	−0.877136
$328$	−18.7869	−1.03733
$329$	−2.89044	−0.159355
$330$	−0.418685	−0.0230479
$331$	26.3433	1.44796	0.723981	−	0.689820i	$-0.242310\pi$
$331$	26.3433	1.44796	0.723981	+	0.689820i	$0.242310\pi$
$332$	−19.2757	−1.05789
$333$	−7.95934	−0.436169
$334$	−8.45282	−0.462518
$335$	2.64592	0.144562
$336$	−0.585709	−0.0319530
$337$	19.3083	1.05179	0.525894	−	0.850550i	$-0.323731\pi$
$337$	19.3083	1.05179	0.525894	+	0.850550i	$0.323731\pi$
$338$	−5.18636	−0.282101
$339$	16.9979	0.923197
$340$	1.66258	0.0901660
$341$	−23.0842	−1.25008
$342$	2.44812	0.132379
$343$	−1.00000	−0.0539949
$344$	−33.3562	−1.79844
$345$	1.05765	0.0569421
$346$	−7.12655	−0.383126
$347$	4.20888	0.225944	0.112972	−	0.993598i	$-0.463963\pi$
$347$	4.20888	0.225944	0.112972	+	0.993598i	$0.463963\pi$
$348$	−7.06855	−0.378914
$349$	−33.3592	−1.78568	−0.892839	−	0.450376i	$-0.851290\pi$
$349$	−33.3592	−1.78568	−0.892839	+	0.450376i	$0.851290\pi$
$350$	3.94713	0.210983
$351$	−2.54945	−0.136080
$352$	−13.3124	−0.709551
$353$	24.1892	1.28746	0.643731	−	0.765252i	$-0.277386\pi$
$353$	24.1892	1.28746	0.643731	+	0.765252i	$0.277386\pi$
$354$	−4.42478	−0.235174
$355$	0.695400	0.0369080
$356$	10.3683	0.549520
$357$	5.30219	0.280621
$358$	9.38889	0.496218
$359$	32.7530	1.72864	0.864319	−	0.502943i	$-0.167749\pi$
$359$	32.7530	1.72864	0.864319	+	0.502943i	$0.167749\pi$
$360$	−0.617178	−0.0325281
$361$	−9.58527	−0.504488
$362$	9.11467	0.479056
$363$	−5.79387	−0.304099
$364$	−3.47595	−0.182189
$365$	2.39828	0.125532
$366$	−3.04241	−0.159030
$367$	−13.3602	−0.697396	−0.348698	−	0.937235i	$-0.613376\pi$
$367$	−13.3602	−0.697396	−0.348698	+	0.937235i	$0.613376\pi$
$368$	2.69354	0.140411
$369$	7.00076	0.364445
$370$	−1.46052	−0.0759288
$371$	−4.76331	−0.247299
$372$	−13.7938	−0.715174
$373$	16.1673	0.837110	0.418555	−	0.908191i	$-0.362537\pi$
$373$	16.1673	0.837110	0.418555	+	0.908191i	$0.362537\pi$
$374$	9.65255	0.499122
$375$	−2.28769	−0.118136
$376$	−7.75664	−0.400018
$377$	−13.2175	−0.680738
$378$	−0.797866	−0.0410378
$379$	−20.5917	−1.05772	−0.528862	−	0.848708i	$-0.677381\pi$
$379$	−20.5917	−1.05772	−0.528862	+	0.848708i	$0.677381\pi$
$380$	−0.962124	−0.0493559
$381$	18.5990	0.952855
$382$	−0.797866	−0.0408224
$383$	16.6339	0.849955	0.424977	−	0.905204i	$-0.360282\pi$
$383$	16.6339	0.849955	0.424977	+	0.905204i	$0.360282\pi$
$384$	−8.88934	−0.453632
$385$	0.524757	0.0267441
$386$	2.80017	0.142525
$387$	12.4299	0.631846
$388$	19.8537	1.00792
$389$	31.7806	1.61134	0.805669	−	0.592366i	$-0.201806\pi$
$389$	31.7806	1.61134	0.805669	+	0.592366i	$0.201806\pi$
$390$	−0.467818	−0.0236889
$391$	−24.3836	−1.23313
$392$	−2.68355	−0.135540
$393$	−15.3370	−0.773649
$394$	−2.55007	−0.128471
$395$	−1.46342	−0.0736328
$396$	3.11089	0.156328
$397$	−23.1669	−1.16272	−0.581358	−	0.813648i	$-0.697478\pi$
$397$	−23.1669	−1.16272	−0.581358	+	0.813648i	$0.697478\pi$
$398$	16.8337	0.843795
$399$	−3.06834	−0.153609
$400$	−2.89756	−0.144878
$401$	−4.06506	−0.203000	−0.101500	−	0.994836i	$-0.532364\pi$
$401$	−4.06506	−0.203000	−0.101500	+	0.994836i	$0.532364\pi$
$402$	9.17923	0.457818
$403$	−25.7931	−1.28485
$404$	−9.99832	−0.497435
$405$	0.229986	0.0114281
$406$	−4.13650	−0.205291
$407$	18.1608	0.900197
$408$	14.2287	0.704425
$409$	1.30015	0.0642885	0.0321443	−	0.999483i	$-0.489766\pi$
$409$	1.30015	0.0642885	0.0321443	+	0.999483i	$0.489766\pi$
$410$	1.28462	0.0634430
$411$	3.53453	0.174345
$412$	−0.712218	−0.0350885
$413$	5.54577	0.272890
$414$	3.66921	0.180332
$415$	3.25151	0.159610
$416$	−14.8746	−0.729285
$417$	12.1048	0.592774
$418$	−5.58587	−0.273214
$419$	−25.1602	−1.22916	−0.614579	−	0.788856i	$-0.710674\pi$
$419$	−25.1602	−1.22916	−0.614579	+	0.788856i	$0.710674\pi$
$420$	0.313565	0.0153004
$421$	21.1854	1.03251	0.516257	−	0.856434i	$-0.327325\pi$
$421$	21.1854	1.03251	0.516257	+	0.856434i	$0.327325\pi$
$422$	−0.997441	−0.0485547
$423$	2.89044	0.140538
$424$	−12.7826	−0.620777
$425$	26.2305	1.27237
$426$	2.41248	0.116885
$427$	3.81319	0.184533
$428$	−3.22752	−0.156008
$429$	5.81707	0.280851
$430$	2.28085	0.109992
$431$	−21.8763	−1.05375	−0.526873	−	0.849944i	$-0.676636\pi$
$431$	−21.8763	−1.05375	−0.526873	+	0.849944i	$0.676636\pi$
$432$	0.585709	0.0281799
$433$	6.67240	0.320655	0.160328	−	0.987064i	$-0.448745\pi$
$433$	6.67240	0.320655	0.160328	+	0.987064i	$0.448745\pi$
$434$	−8.07210	−0.387473
$435$	1.19235	0.0571689
$436$	21.6256	1.03568
$437$	14.1106	0.675003
$438$	8.32012	0.397551
$439$	−24.6998	−1.17886	−0.589428	−	0.807821i	$-0.700647\pi$
$439$	−24.6998	−1.17886	−0.589428	+	0.807821i	$0.700647\pi$
$440$	1.40821	0.0671338
$441$	1.00000	0.0476190
$442$	10.7853	0.513004
$443$	−12.7825	−0.607316	−0.303658	−	0.952781i	$-0.598208\pi$
$443$	−12.7825	−0.607316	−0.303658	+	0.952781i	$0.598208\pi$
$444$	10.8519	0.515006
$445$	−1.74897	−0.0829091
$446$	−0.241385	−0.0114299
$447$	−11.9796	−0.566616
$448$	−3.48366	−0.164588
$449$	4.91907	0.232145	0.116073	−	0.993241i	$-0.462969\pi$
$449$	4.91907	0.232145	0.116073	+	0.993241i	$0.462969\pi$
$450$	−3.94713	−0.186069
$451$	−15.9736	−0.752168
$452$	−23.1751	−1.09006
$453$	3.38423	0.159005
$454$	18.2540	0.856701
$455$	0.586337	0.0274879
$456$	−8.23405	−0.385595
$457$	−35.2766	−1.65017	−0.825086	−	0.565007i	$-0.808873\pi$
$457$	−35.2766	−1.65017	−0.825086	+	0.565007i	$0.808873\pi$
$458$	16.3392	0.763482
$459$	−5.30219	−0.247485
$460$	−1.44201	−0.0672343
$461$	40.8261	1.90146	0.950731	−	0.310019i	$-0.100335\pi$
$461$	40.8261	1.90146	0.950731	+	0.310019i	$0.100335\pi$
$462$	1.82049	0.0846966
$463$	−31.7698	−1.47647	−0.738234	−	0.674545i	$-0.764340\pi$
$463$	−31.7698	−1.47647	−0.738234	+	0.674545i	$0.764340\pi$
$464$	3.03658	0.140970
$465$	2.32679	0.107902
$466$	−7.69190	−0.356320
$467$	3.61992	0.167510	0.0837550	−	0.996486i	$-0.473309\pi$
$467$	3.61992	0.167510	0.0837550	+	0.996486i	$0.473309\pi$
$468$	3.47595	0.160676
$469$	−11.5047	−0.531239
$470$	0.530389	0.0244650
$471$	9.42430	0.434249
$472$	14.8824	0.685016
$473$	−28.3612	−1.30405
$474$	−5.07691	−0.233190
$475$	−15.1794	−0.696479
$476$	−7.22906	−0.331343
$477$	4.76331	0.218097
$478$	9.99447	0.457136
$479$	3.73399	0.170610	0.0853051	−	0.996355i	$-0.472814\pi$
$479$	3.73399	0.170610	0.0853051	+	0.996355i	$0.472814\pi$
$480$	1.34183	0.0612459
$481$	20.2920	0.925234
$482$	−11.1901	−0.509697
$483$	−4.59878	−0.209252
$484$	7.89942	0.359065
$485$	−3.34900	−0.152070
$486$	0.797866	0.0361919
$487$	33.1603	1.50264	0.751318	−	0.659941i	$-0.229419\pi$
$487$	33.1603	1.50264	0.751318	+	0.659941i	$0.229419\pi$
$488$	10.2329	0.463221
$489$	−13.4477	−0.608125
$490$	0.183498	0.00828958
$491$	24.3701	1.09981	0.549904	−	0.835228i	$-0.314664\pi$
$491$	24.3701	1.09981	0.549904	+	0.835228i	$0.314664\pi$
$492$	−9.54492	−0.430318
$493$	−27.4890	−1.23804
$494$	−6.24138	−0.280813
$495$	−0.524757	−0.0235861
$496$	5.92569	0.266071
$497$	−3.02367	−0.135630
$498$	11.2801	0.505475
$499$	13.4765	0.603291	0.301646	−	0.953420i	$-0.402464\pi$
$499$	13.4765	0.603291	0.301646	+	0.953420i	$0.402464\pi$
$500$	3.11906	0.139489
$501$	−10.5943	−0.473318
$502$	−13.6313	−0.608396
$503$	7.56205	0.337175	0.168588	−	0.985687i	$-0.446079\pi$
$503$	7.56205	0.337175	0.168588	+	0.985687i	$0.446079\pi$
$504$	2.68355	0.119535
$505$	1.68656	0.0750508
$506$	−8.37201	−0.372181
$507$	−6.50029	−0.288688
$508$	−25.3581	−1.12508
$509$	−15.6700	−0.694559	−0.347279	−	0.937762i	$-0.612894\pi$
$509$	−15.6700	−0.694559	−0.347279	+	0.937762i	$0.612894\pi$
$510$	−0.972938	−0.0430824
$511$	−10.4280	−0.461307
$512$	6.56083	0.289950
$513$	3.06834	0.135471
$514$	6.11375	0.269666
$515$	0.120140	0.00529399
$516$	−16.9470	−0.746051
$517$	−6.59510	−0.290052
$518$	6.35049	0.279024
$519$	−8.93202	−0.392072
$520$	1.57346	0.0690010
$521$	−28.8646	−1.26458	−0.632291	−	0.774731i	$-0.717885\pi$
$521$	−28.8646	−1.26458	−0.632291	+	0.774731i	$0.717885\pi$
$522$	4.13650	0.181050
$523$	−39.0237	−1.70639	−0.853194	−	0.521594i	$-0.825338\pi$
$523$	−39.0237	−1.70639	−0.853194	+	0.521594i	$0.825338\pi$
$524$	20.9106	0.913484
$525$	4.94711	0.215909
$526$	−22.2174	−0.968724
$527$	−53.6428	−2.33672
$528$	−1.33641	−0.0581597
$529$	−1.85123	−0.0804884
$530$	0.874056	0.0379666
$531$	−5.54577	−0.240666
$532$	4.18341	0.181374
$533$	−17.8481	−0.773088
$534$	−6.06752	−0.262567
$535$	0.544432	0.0235378
$536$	−30.8735	−1.33353
$537$	11.7675	0.507805
$538$	14.6712	0.632518
$539$	−2.28169	−0.0982795
$540$	−0.313565	−0.0134937
$541$	4.08674	0.175703	0.0878514	−	0.996134i	$-0.472000\pi$
$541$	4.08674	0.175703	0.0878514	+	0.996134i	$0.472000\pi$
$542$	15.4198	0.662339
$543$	11.4238	0.490243
$544$	−30.9352	−1.32633
$545$	−3.64789	−0.156258
$546$	2.03412	0.0870523
$547$	−9.28441	−0.396973	−0.198486	−	0.980104i	$-0.563603\pi$
$547$	−9.28441	−0.396973	−0.198486	+	0.980104i	$0.563603\pi$
$548$	−4.81901	−0.205858
$549$	−3.81319	−0.162743
$550$	9.00614	0.384023
$551$	15.9077	0.677691
$552$	−12.3411	−0.525270
$553$	6.36311	0.270587
$554$	−17.0966	−0.726363
$555$	−1.83053	−0.0777018
$556$	−16.5038	−0.699916
$557$	16.7240	0.708617	0.354309	−	0.935129i	$-0.384716\pi$
$557$	16.7240	0.708617	0.354309	+	0.935129i	$0.384716\pi$
$558$	8.07210	0.341719
$559$	−31.6894	−1.34032
$560$	−0.134705	−0.00569231
$561$	12.0980	0.510777
$562$	15.9119	0.671203
$563$	10.9566	0.461768	0.230884	−	0.972981i	$-0.425838\pi$
$563$	10.9566	0.461768	0.230884	+	0.972981i	$0.425838\pi$
$564$	−3.94086	−0.165940
$565$	3.90926	0.164464
$566$	−12.0536	−0.506650
$567$	−1.00000	−0.0419961
$568$	−8.11417	−0.340463
$569$	37.8348	1.58612	0.793059	−	0.609145i	$-0.208487\pi$
$569$	37.8348	1.58612	0.793059	+	0.609145i	$0.208487\pi$
$570$	0.563033	0.0235829
$571$	2.64671	0.110761	0.0553806	−	0.998465i	$-0.482363\pi$
$571$	2.64671	0.110761	0.0553806	+	0.998465i	$0.482363\pi$
$572$	−7.93105	−0.331614
$573$	−1.00000	−0.0417756
$574$	−5.58567	−0.233141
$575$	−22.7506	−0.948768
$576$	3.48366	0.145153
$577$	−12.7664	−0.531474	−0.265737	−	0.964046i	$-0.585615\pi$
$577$	−12.7664	−0.531474	−0.265737	+	0.964046i	$0.585615\pi$
$578$	8.86682	0.368811
$579$	3.50957	0.145853
$580$	−1.62566	−0.0675020
$581$	−14.1379	−0.586538
$582$	−11.6183	−0.481595
$583$	−10.8684	−0.450124
$584$	−27.9840	−1.15799
$585$	−0.586337	−0.0242421
$586$	14.8310	0.612663
$587$	−20.0260	−0.826562	−0.413281	−	0.910603i	$-0.635617\pi$
$587$	−20.0260	−0.826562	−0.413281	+	0.910603i	$0.635617\pi$
$588$	−1.36341	−0.0562261
$589$	31.0428	1.27910
$590$	−1.01764	−0.0418954
$591$	−3.19611	−0.131471
$592$	−4.66186	−0.191601
$593$	−32.2699	−1.32517	−0.662584	−	0.748988i	$-0.730540\pi$
$593$	−32.2699	−1.32517	−0.662584	+	0.748988i	$0.730540\pi$
$594$	−1.82049	−0.0746954
$595$	1.21943	0.0499916
$596$	16.3331	0.669031
$597$	21.0984	0.863499
$598$	−9.35447	−0.382533
$599$	−11.6712	−0.476871	−0.238435	−	0.971158i	$-0.576634\pi$
$599$	−11.6712	−0.476871	−0.238435	+	0.971158i	$0.576634\pi$
$600$	13.2758	0.541983
$601$	33.7755	1.37773	0.688865	−	0.724890i	$-0.258109\pi$
$601$	33.7755	1.37773	0.688865	+	0.724890i	$0.258109\pi$
$602$	−9.91737	−0.404202
$603$	11.5047	0.468509
$604$	−4.61410	−0.187745
$605$	−1.33251	−0.0541741
$606$	5.85100	0.237681
$607$	−12.2933	−0.498971	−0.249485	−	0.968379i	$-0.580261\pi$
$607$	−12.2933	−0.498971	−0.249485	+	0.968379i	$0.580261\pi$
$608$	17.9020	0.726021
$609$	−5.18446	−0.210085
$610$	−0.699711	−0.0283305
$611$	−7.36904	−0.298119
$612$	7.22906	0.292217
$613$	−22.2052	−0.896860	−0.448430	−	0.893818i	$-0.648017\pi$
$613$	−22.2052	−0.896860	−0.448430	+	0.893818i	$0.648017\pi$
$614$	20.7163	0.836043
$615$	1.61007	0.0649245
$616$	−6.12304	−0.246704
$617$	17.1016	0.688483	0.344242	−	0.938881i	$-0.388136\pi$
$617$	17.1016	0.688483	0.344242	+	0.938881i	$0.388136\pi$
$618$	0.416789	0.0167657
$619$	9.10893	0.366119	0.183059	−	0.983102i	$-0.441400\pi$
$619$	9.10893	0.366119	0.183059	+	0.983102i	$0.441400\pi$
$620$	−3.17237	−0.127406
$621$	4.59878	0.184543
$622$	−10.4606	−0.419431
$623$	7.60469	0.304676
$624$	−1.49324	−0.0597773
$625$	24.2094	0.968376
$626$	9.90789	0.395999
$627$	−7.00102	−0.279594
$628$	−12.8492	−0.512738
$629$	42.2019	1.68270
$630$	−0.183498	−0.00731072
$631$	3.97209	0.158126	0.0790631	−	0.996870i	$-0.474807\pi$
$631$	3.97209	0.158126	0.0790631	+	0.996870i	$0.474807\pi$
$632$	17.0757	0.679236
$633$	−1.25014	−0.0496885
$634$	2.80463	0.111386
$635$	4.27750	0.169747
$636$	−6.49435	−0.257518
$637$	−2.54945	−0.101013
$638$	−9.43823	−0.373663
$639$	3.02367	0.119615
$640$	−2.04442	−0.0808128
$641$	27.7193	1.09485	0.547424	−	0.836856i	$-0.315609\pi$
$641$	27.7193	1.09485	0.547424	+	0.836856i	$0.315609\pi$
$642$	1.88874	0.0745427
$643$	−24.5068	−0.966452	−0.483226	−	0.875496i	$-0.660535\pi$
$643$	−24.5068	−0.966452	−0.483226	+	0.875496i	$0.660535\pi$
$644$	6.27002	0.247074
$645$	2.85869	0.112561
$646$	−12.9804	−0.510708
$647$	19.9024	0.782443	0.391222	−	0.920297i	$-0.372053\pi$
$647$	19.9024	0.782443	0.391222	+	0.920297i	$0.372053\pi$
$648$	−2.68355	−0.105420
$649$	12.6538	0.496703
$650$	10.0630	0.394704
$651$	−10.1171	−0.396521
$652$	18.3347	0.718043
$653$	17.7429	0.694334	0.347167	−	0.937803i	$-0.387144\pi$
$653$	17.7429	0.694334	0.347167	+	0.937803i	$0.387144\pi$
$654$	−12.6552	−0.494859
$655$	−3.52729	−0.137823
$656$	4.10041	0.160094
$657$	10.4280	0.406834
$658$	−2.30618	−0.0899044
$659$	47.2726	1.84148	0.920739	−	0.390178i	$-0.127587\pi$
$659$	47.2726	1.84148	0.920739	+	0.390178i	$0.127587\pi$
$660$	0.715459	0.0278492
$661$	−11.0825	−0.431058	−0.215529	−	0.976497i	$-0.569148\pi$
$661$	−11.0825	−0.431058	−0.215529	+	0.976497i	$0.569148\pi$
$662$	21.0185	0.816905
$663$	13.5177	0.524983
$664$	−37.9397	−1.47235
$665$	−0.705674	−0.0273649
$666$	−6.35049	−0.246076
$667$	23.8422	0.923173
$668$	14.4444	0.558869
$669$	−0.302539	−0.0116968
$670$	2.11109	0.0815585
$671$	8.70053	0.335880
$672$	−5.83442	−0.225067
$673$	12.8419	0.495019	0.247510	−	0.968885i	$-0.420388\pi$
$673$	12.8419	0.495019	0.247510	+	0.968885i	$0.420388\pi$
$674$	15.4054	0.593394
$675$	−4.94711	−0.190414
$676$	8.86257	0.340868
$677$	−13.3841	−0.514391	−0.257196	−	0.966359i	$-0.582798\pi$
$677$	−13.3841	−0.514391	−0.257196	+	0.966359i	$0.582798\pi$
$678$	13.5620	0.520846
$679$	14.5618	0.558829
$680$	3.27239	0.125490
$681$	22.8785	0.876706
$682$	−18.4181	−0.705264
$683$	15.3899	0.588880	0.294440	−	0.955670i	$-0.404867\pi$
$683$	15.3899	0.588880	0.294440	+	0.955670i	$0.404867\pi$
$684$	−4.18341	−0.159957
$685$	0.812891	0.0310590
$686$	−0.797866	−0.0304627
$687$	20.4787	0.781310
$688$	7.28028	0.277558
$689$	−12.1438	−0.462643
$690$	0.843865	0.0321254
$691$	−7.69163	−0.292603	−0.146302	−	0.989240i	$-0.546737\pi$
$691$	−7.69163	−0.292603	−0.146302	+	0.989240i	$0.546737\pi$
$692$	12.1780	0.462938
$693$	2.28169	0.0866744
$694$	3.35812	0.127472
$695$	2.78392	0.105600
$696$	−13.9128	−0.527362
$697$	−37.1194	−1.40600
$698$	−26.6162	−1.00744
$699$	−9.64060	−0.364641
$700$	−6.74494	−0.254935
$701$	−35.8412	−1.35370	−0.676851	−	0.736120i	$-0.736656\pi$
$701$	−35.8412	−1.35370	−0.676851	+	0.736120i	$0.736656\pi$
$702$	−2.03412	−0.0767729
$703$	−24.4220	−0.921093
$704$	−7.94865	−0.299576
$705$	0.664760	0.0250363
$706$	19.2997	0.726355
$707$	−7.33332	−0.275798
$708$	7.56116	0.284166
$709$	38.8943	1.46071	0.730354	−	0.683069i	$-0.239355\pi$
$709$	38.8943	1.46071	0.730354	+	0.683069i	$0.239355\pi$
$710$	0.554836	0.0208226
$711$	−6.36311	−0.238635
$712$	20.4076	0.764806
$713$	46.5264	1.74243
$714$	4.23043	0.158320
$715$	1.33784	0.0500325
$716$	−16.0439	−0.599590
$717$	12.5265	0.467811
$718$	26.1325	0.975257
$719$	−42.9483	−1.60170	−0.800851	−	0.598863i	$-0.795619\pi$
$719$	−42.9483	−1.60170	−0.800851	+	0.598863i	$0.795619\pi$
$720$	0.134705	0.00502014
$721$	−0.522380	−0.0194544
$722$	−7.64776	−0.284620
$723$	−14.0251	−0.521599
$724$	−15.5753	−0.578853
$725$	−25.6481	−0.952546
$726$	−4.62273	−0.171566
$727$	−43.8670	−1.62694	−0.813469	−	0.581608i	$-0.802424\pi$
$727$	−43.8670	−1.62694	−0.813469	+	0.581608i	$0.802424\pi$
$728$	−6.84158	−0.253566
$729$	1.00000	0.0370370
$730$	1.91351	0.0708221
$731$	−65.9055	−2.43760
$732$	5.19894	0.192158
$733$	−11.9295	−0.440627	−0.220314	−	0.975429i	$-0.570708\pi$
$733$	−11.9295	−0.440627	−0.220314	+	0.975429i	$0.570708\pi$
$734$	−10.6596	−0.393454
$735$	0.229986	0.00848315
$736$	26.8312	0.989011
$737$	−26.2503	−0.966941
$738$	5.58567	0.205611
$739$	18.6065	0.684450	0.342225	−	0.939618i	$-0.388820\pi$
$739$	18.6065	0.684450	0.342225	+	0.939618i	$0.388820\pi$
$740$	2.49577	0.0917463
$741$	−7.82259	−0.287370
$742$	−3.80048	−0.139520
$743$	43.7949	1.60668	0.803340	−	0.595520i	$-0.203054\pi$
$743$	43.7949	1.60668	0.803340	+	0.595520i	$0.203054\pi$
$744$	−27.1498	−0.995360
$745$	−2.75514	−0.100940
$746$	12.8993	0.472278
$747$	14.1379	0.517278
$748$	−16.4945	−0.603098
$749$	−2.36724	−0.0864972
$750$	−1.82527	−0.0666494
$751$	−31.1012	−1.13490	−0.567450	−	0.823408i	$-0.692070\pi$
$751$	−31.1012	−1.13490	−0.567450	+	0.823408i	$0.692070\pi$
$752$	1.69296	0.0617358
$753$	−17.0848	−0.622603
$754$	−10.5458	−0.384056
$755$	0.778325	0.0283261
$756$	1.36341	0.0495868
$757$	−39.6090	−1.43961	−0.719806	−	0.694175i	$-0.755769\pi$
$757$	−39.6090	−1.43961	−0.719806	+	0.694175i	$0.755769\pi$
$758$	−16.4294	−0.596743
$759$	−10.4930	−0.380872
$760$	−1.89371	−0.0686922
$761$	−23.1956	−0.840841	−0.420421	−	0.907329i	$-0.638117\pi$
$761$	−23.1956	−0.840841	−0.420421	+	0.907329i	$0.638117\pi$
$762$	14.8395	0.537578
$763$	15.8614	0.574220
$764$	1.36341	0.0493265
$765$	−1.21943	−0.0440884
$766$	13.2717	0.479524
$767$	14.1387	0.510518
$768$	−14.0598	−0.507340
$769$	21.7193	0.783217	0.391608	−	0.920132i	$-0.371919\pi$
$769$	21.7193	0.783217	0.391608	+	0.920132i	$0.371919\pi$
$770$	0.418685	0.0150884
$771$	7.66264	0.275963
$772$	−4.78499	−0.172215
$773$	47.7528	1.71755	0.858775	−	0.512353i	$-0.171226\pi$
$773$	47.7528	1.71755	0.858775	+	0.512353i	$0.171226\pi$
$774$	9.91737	0.356472
$775$	−50.0505	−1.79787
$776$	39.0772	1.40279
$777$	7.95934	0.285540
$778$	25.3566	0.909079
$779$	21.4807	0.769627
$780$	0.799418	0.0286238
$781$	−6.89909	−0.246869
$782$	−19.4548	−0.695703
$783$	5.18446	0.185277
$784$	0.585709	0.0209182
$785$	2.16745	0.0773597
$786$	−12.2369	−0.436474
$787$	−43.4324	−1.54820	−0.774098	−	0.633065i	$-0.781796\pi$
$787$	−43.4324	−1.54820	−0.774098	+	0.633065i	$0.781796\pi$
$788$	4.35762	0.155234
$789$	−27.8460	−0.991344
$790$	−1.16762	−0.0415419
$791$	−16.9979	−0.604374
$792$	6.12304	0.217573
$793$	9.72155	0.345222
$794$	−18.4841	−0.655977
$795$	1.09549	0.0388531
$796$	−28.7657	−1.01957
$797$	6.72431	0.238187	0.119094	−	0.992883i	$-0.462001\pi$
$797$	6.72431	0.238187	0.119094	+	0.992883i	$0.462001\pi$
$798$	−2.44812	−0.0866627
$799$	−15.3257	−0.542183
$800$	−28.8635	−1.02048
$801$	−7.60469	−0.268699
$802$	−3.24337	−0.114528
$803$	−23.7935	−0.839653
$804$	−15.6857	−0.553191
$805$	−1.05765	−0.0372774
$806$	−20.5794	−0.724880
$807$	18.3880	0.647288
$808$	−19.6793	−0.692316
$809$	34.0304	1.19645	0.598223	−	0.801329i	$-0.295874\pi$
$809$	34.0304	1.19645	0.598223	+	0.801329i	$0.295874\pi$
$810$	0.183498	0.00644745
$811$	−15.4538	−0.542655	−0.271328	−	0.962487i	$-0.587463\pi$
$811$	−15.4538	−0.542655	−0.271328	+	0.962487i	$0.587463\pi$
$812$	7.06855	0.248057
$813$	19.3264	0.677805
$814$	14.4899	0.507870
$815$	−3.09277	−0.108335
$816$	−3.10554	−0.108716
$817$	38.1391	1.33432
$818$	1.03735	0.0362701
$819$	2.54945	0.0890851
$820$	−2.19519	−0.0766595
$821$	−19.7040	−0.687675	−0.343838	−	0.939029i	$-0.611727\pi$
$821$	−19.7040	−0.687675	−0.343838	+	0.939029i	$0.611727\pi$
$822$	2.82008	0.0983616
$823$	−27.2909	−0.951303	−0.475651	−	0.879634i	$-0.657788\pi$
$823$	−27.2909	−0.951303	−0.475651	+	0.879634i	$0.657788\pi$
$824$	−1.40183	−0.0488351
$825$	11.2878	0.392990
$826$	4.42478	0.153958
$827$	−31.0822	−1.08083	−0.540417	−	0.841397i	$-0.681734\pi$
$827$	−31.0822	−1.08083	−0.540417	+	0.841397i	$0.681734\pi$
$828$	−6.27002	−0.217898
$829$	−11.5497	−0.401136	−0.200568	−	0.979680i	$-0.564279\pi$
$829$	−11.5497	−0.401136	−0.200568	+	0.979680i	$0.564279\pi$
$830$	2.59427	0.0900483
$831$	−21.4279	−0.743324
$832$	−8.88143	−0.307908
$833$	−5.30219	−0.183710
$834$	9.65799	0.334429
$835$	−2.43653	−0.0843197
$836$	9.54526	0.330130
$837$	10.1171	0.349699
$838$	−20.0745	−0.693461
$839$	24.6747	0.851866	0.425933	−	0.904755i	$-0.359946\pi$
$839$	24.6747	0.851866	0.425933	+	0.904755i	$0.359946\pi$
$840$	0.617178	0.0212947
$841$	−2.12137	−0.0731508
$842$	16.9031	0.582520
$843$	19.9431	0.686876
$844$	1.70445	0.0586696
$845$	−1.49497	−0.0514287
$846$	2.30618	0.0792882
$847$	5.79387	0.199080
$848$	2.78991	0.0958060
$849$	−15.1073	−0.518480
$850$	20.9284	0.717838
$851$	−36.6033	−1.25474
$852$	−4.12250	−0.141235
$853$	−2.65071	−0.0907586	−0.0453793	−	0.998970i	$-0.514450\pi$
$853$	−2.65071	−0.0907586	−0.0453793	+	0.998970i	$0.514450\pi$
$854$	3.04241	0.104109
$855$	0.705674	0.0241336
$856$	−6.35262	−0.217128
$857$	−43.6831	−1.49219	−0.746093	−	0.665842i	$-0.768072\pi$
$857$	−43.6831	−1.49219	−0.746093	+	0.665842i	$0.768072\pi$
$858$	4.64124	0.158449
$859$	−20.8797	−0.712407	−0.356203	−	0.934408i	$-0.615929\pi$
$859$	−20.8797	−0.712407	−0.356203	+	0.934408i	$0.615929\pi$
$860$	−3.89757	−0.132906
$861$	−7.00076	−0.238585
$862$	−17.4544	−0.594498
$863$	4.06171	0.138262	0.0691312	−	0.997608i	$-0.477977\pi$
$863$	4.06171	0.138262	0.0691312	+	0.997608i	$0.477977\pi$
$864$	5.83442	0.198491
$865$	−2.05424	−0.0698461
$866$	5.32368	0.180906
$867$	11.1132	0.377423
$868$	13.7938	0.468192
$869$	14.5187	0.492512
$870$	0.951336	0.0322533
$871$	−29.3308	−0.993835
$872$	42.5648	1.44142
$873$	−14.5618	−0.492841
$874$	11.2584	0.380821
$875$	2.28769	0.0773381
$876$	−14.2176	−0.480369
$877$	−36.0846	−1.21849	−0.609245	−	0.792982i	$-0.708527\pi$
$877$	−36.0846	−1.21849	−0.609245	+	0.792982i	$0.708527\pi$
$878$	−19.7071	−0.665083
$879$	18.5883	0.626969
$880$	−0.307355	−0.0103609
$881$	6.51380	0.219455	0.109728	−	0.993962i	$-0.465002\pi$
$881$	6.51380	0.219455	0.109728	+	0.993962i	$0.465002\pi$
$882$	0.797866	0.0268655
$883$	47.5912	1.60157	0.800786	−	0.598950i	$-0.204415\pi$
$883$	47.5912	1.60157	0.800786	+	0.598950i	$0.204415\pi$
$884$	−18.4301	−0.619872
$885$	−1.27545	−0.0428737
$886$	−10.1987	−0.342633
$887$	23.8012	0.799165	0.399582	−	0.916697i	$-0.369155\pi$
$887$	23.8012	0.799165	0.399582	+	0.916697i	$0.369155\pi$
$888$	21.3593	0.716771
$889$	−18.5990	−0.623790
$890$	−1.39544	−0.0467754
$891$	−2.28169	−0.0764396
$892$	0.412485	0.0138110
$893$	8.86886	0.296785
$894$	−9.55812	−0.319671
$895$	2.70636	0.0904635
$896$	8.88934	0.296972
$897$	−11.7244	−0.391465
$898$	3.92476	0.130971
$899$	52.4518	1.74937
$900$	6.74494	0.224831
$901$	−25.2560	−0.841398
$902$	−12.7448	−0.424355
$903$	−12.4299	−0.413640
$904$	−45.6146	−1.51712
$905$	2.62731	0.0873348
$906$	2.70016	0.0897069
$907$	39.4009	1.30829	0.654143	−	0.756371i	$-0.273030\pi$
$907$	39.4009	1.30829	0.654143	+	0.756371i	$0.273030\pi$
$908$	−31.1928	−1.03517
$909$	7.33332	0.243231
$910$	0.467818	0.0155080
$911$	35.9828	1.19216	0.596082	−	0.802923i	$-0.296723\pi$
$911$	35.9828	1.19216	0.596082	+	0.802923i	$0.296723\pi$
$912$	1.79716	0.0595097
$913$	−32.2583	−1.06759
$914$	−28.1460	−0.930988
$915$	−0.876979	−0.0289920
$916$	−27.9208	−0.922530
$917$	15.3370	0.506472
$918$	−4.23043	−0.139625
$919$	43.0287	1.41939	0.709693	−	0.704511i	$-0.248833\pi$
$919$	43.0287	1.41939	0.709693	+	0.704511i	$0.248833\pi$
$920$	−2.83826	−0.0935748
$921$	25.9647	0.855566
$922$	32.5737	1.07276
$923$	−7.70870	−0.253735
$924$	−3.11089	−0.102341
$925$	39.3757	1.29467
$926$	−25.3480	−0.832988
$927$	0.522380	0.0171572
$928$	30.2483	0.992949
$929$	−2.72038	−0.0892528	−0.0446264	−	0.999004i	$-0.514210\pi$
$929$	−2.72038	−0.0892528	−0.0446264	+	0.999004i	$0.514210\pi$
$930$	1.85647	0.0608759
$931$	3.06834	0.100561
$932$	13.1441	0.430549
$933$	−13.1107	−0.429226
$934$	2.88821	0.0945052
$935$	2.78236	0.0909928
$936$	6.84158	0.223624
$937$	−52.2064	−1.70551	−0.852754	−	0.522312i	$-0.825070\pi$
$937$	−52.2064	−1.70551	−0.852754	+	0.522312i	$0.825070\pi$
$938$	−9.17923	−0.299712
$939$	12.4180	0.405246
$940$	−0.906340	−0.0295616
$941$	−9.09454	−0.296474	−0.148237	−	0.988952i	$-0.547360\pi$
$941$	−9.09454	−0.296474	−0.148237	+	0.988952i	$0.547360\pi$
$942$	7.51932	0.244993
$943$	32.1950	1.04841
$944$	−3.24821	−0.105720
$945$	−0.229986	−0.00748143
$946$	−22.6284	−0.735713
$947$	−12.1208	−0.393873	−0.196937	−	0.980416i	$-0.563099\pi$
$947$	−12.1208	−0.393873	−0.196937	+	0.980416i	$0.563099\pi$
$948$	8.67553	0.281768
$949$	−26.5856	−0.863006
$950$	−12.1111	−0.392937
$951$	3.51517	0.113987
$952$	−14.2287	−0.461154
$953$	26.8737	0.870524	0.435262	−	0.900304i	$-0.356656\pi$
$953$	26.8737	0.870524	0.435262	+	0.900304i	$0.356656\pi$
$954$	3.80048	0.123045
$955$	−0.229986	−0.00744216
$956$	−17.0788	−0.552367
$957$	−11.8294	−0.382389
$958$	2.97922	0.0962542
$959$	−3.53453	−0.114136
$960$	0.801192	0.0258584
$961$	71.3561	2.30181
$962$	16.1903	0.521995
$963$	2.36724	0.0762834
$964$	19.1220	0.615877
$965$	0.807151	0.0259831
$966$	−3.66921	−0.118055
$967$	5.11063	0.164347	0.0821734	−	0.996618i	$-0.473814\pi$
$967$	5.11063	0.164347	0.0821734	+	0.996618i	$0.473814\pi$
$968$	15.5481	0.499736
$969$	−16.2689	−0.522633
$970$	−2.67205	−0.0857943
$971$	26.1095	0.837895	0.418948	−	0.908010i	$-0.362399\pi$
$971$	26.1095	0.837895	0.418948	+	0.908010i	$0.362399\pi$
$972$	−1.36341	−0.0437314
$973$	−12.1048	−0.388061
$974$	26.4574	0.847751
$975$	12.6124	0.403920
$976$	−2.23342	−0.0714900
$977$	−20.2721	−0.648563	−0.324281	−	0.945961i	$-0.605122\pi$
$977$	−20.2721	−0.648563	−0.324281	+	0.945961i	$0.605122\pi$
$978$	−10.7294	−0.343090
$979$	17.3516	0.554559
$980$	−0.313565	−0.0100165
$981$	−15.8614	−0.506415
$982$	19.4441	0.620485
$983$	49.7697	1.58741	0.793704	−	0.608304i	$-0.208150\pi$
$983$	49.7697	1.58741	0.793704	+	0.608304i	$0.208150\pi$
$984$	−18.7869	−0.598904
$985$	−0.735060	−0.0234210
$986$	−21.9325	−0.698473
$987$	−2.89044	−0.0920038
$988$	10.6654	0.339312
$989$	57.1622	1.81765
$990$	−0.418685	−0.0133067
$991$	−37.4752	−1.19044	−0.595220	−	0.803563i	$-0.702935\pi$
$991$	−37.4752	−1.19044	−0.595220	+	0.803563i	$0.702935\pi$
$992$	59.0275	1.87412
$993$	26.3433	0.835981
$994$	−2.41248	−0.0765193
$995$	4.85232	0.153829
$996$	−19.2757	−0.610775
$997$	−13.6906	−0.433587	−0.216794	−	0.976217i	$-0.569560\pi$
$997$	−13.6906	−0.433587	−0.216794	+	0.976217i	$0.569560\pi$
$998$	10.7524	0.340363
$999$	−7.95934	−0.251822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.16	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.16	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.797866 q^{2} +1.00000 q^{3} -1.36341 q^{4} +0.229986 q^{5} +0.797866 q^{6} -1.00000 q^{7} -2.68355 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.797866 q^{2} +1.00000 q^{3} -1.36341 q^{4} +0.229986 q^{5} +0.797866 q^{6} -1.00000 q^{7} -2.68355 q^{8} +1.00000 q^{9} +0.183498 q^{10} -2.28169 q^{11} -1.36341 q^{12} -2.54945 q^{13} -0.797866 q^{14} +0.229986 q^{15} +0.585709 q^{16} -5.30219 q^{17} +0.797866 q^{18} +3.06834 q^{19} -0.313565 q^{20} -1.00000 q^{21} -1.82049 q^{22} +4.59878 q^{23} -2.68355 q^{24} -4.94711 q^{25} -2.03412 q^{26} +1.00000 q^{27} +1.36341 q^{28} +5.18446 q^{29} +0.183498 q^{30} +10.1171 q^{31} +5.83442 q^{32} -2.28169 q^{33} -4.23043 q^{34} -0.229986 q^{35} -1.36341 q^{36} -7.95934 q^{37} +2.44812 q^{38} -2.54945 q^{39} -0.617178 q^{40} +7.00076 q^{41} -0.797866 q^{42} +12.4299 q^{43} +3.11089 q^{44} +0.229986 q^{45} +3.66921 q^{46} +2.89044 q^{47} +0.585709 q^{48} +1.00000 q^{49} -3.94713 q^{50} -5.30219 q^{51} +3.47595 q^{52} +4.76331 q^{53} +0.797866 q^{54} -0.524757 q^{55} +2.68355 q^{56} +3.06834 q^{57} +4.13650 q^{58} -5.54577 q^{59} -0.313565 q^{60} -3.81319 q^{61} +8.07210 q^{62} -1.00000 q^{63} +3.48366 q^{64} -0.586337 q^{65} -1.82049 q^{66} +11.5047 q^{67} +7.22906 q^{68} +4.59878 q^{69} -0.183498 q^{70} +3.02367 q^{71} -2.68355 q^{72} +10.4280 q^{73} -6.35049 q^{74} -4.94711 q^{75} -4.18341 q^{76} +2.28169 q^{77} -2.03412 q^{78} -6.36311 q^{79} +0.134705 q^{80} +1.00000 q^{81} +5.58567 q^{82} +14.1379 q^{83} +1.36341 q^{84} -1.21943 q^{85} +9.91737 q^{86} +5.18446 q^{87} +6.12304 q^{88} -7.60469 q^{89} +0.183498 q^{90} +2.54945 q^{91} -6.27002 q^{92} +10.1171 q^{93} +2.30618 q^{94} +0.705674 q^{95} +5.83442 q^{96} -14.5618 q^{97} +0.797866 q^{98} -2.28169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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