LMFDB - Embedded newform 6015.2.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.76442 q^{2} +1.00000 q^{3} +1.11320 q^{4} -1.00000 q^{5} -1.76442 q^{6} -1.91400 q^{7} +1.56470 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.76442 q^{2} +1.00000 q^{3} +1.11320 q^{4} -1.00000 q^{5} -1.76442 q^{6} -1.91400 q^{7} +1.56470 q^{8} +1.00000 q^{9} +1.76442 q^{10} +5.51678 q^{11} +1.11320 q^{12} -4.53295 q^{13} +3.37710 q^{14} -1.00000 q^{15} -4.98719 q^{16} +2.79159 q^{17} -1.76442 q^{18} +1.46521 q^{19} -1.11320 q^{20} -1.91400 q^{21} -9.73394 q^{22} -1.00681 q^{23} +1.56470 q^{24} +1.00000 q^{25} +7.99804 q^{26} +1.00000 q^{27} -2.13065 q^{28} +2.69631 q^{29} +1.76442 q^{30} -8.25999 q^{31} +5.67012 q^{32} +5.51678 q^{33} -4.92555 q^{34} +1.91400 q^{35} +1.11320 q^{36} +9.26785 q^{37} -2.58526 q^{38} -4.53295 q^{39} -1.56470 q^{40} +0.208915 q^{41} +3.37710 q^{42} -0.755852 q^{43} +6.14125 q^{44} -1.00000 q^{45} +1.77644 q^{46} -2.44722 q^{47} -4.98719 q^{48} -3.33662 q^{49} -1.76442 q^{50} +2.79159 q^{51} -5.04605 q^{52} +9.12954 q^{53} -1.76442 q^{54} -5.51678 q^{55} -2.99483 q^{56} +1.46521 q^{57} -4.75744 q^{58} -8.33486 q^{59} -1.11320 q^{60} +9.21208 q^{61} +14.5741 q^{62} -1.91400 q^{63} -0.0301181 q^{64} +4.53295 q^{65} -9.73394 q^{66} +3.37255 q^{67} +3.10758 q^{68} -1.00681 q^{69} -3.37710 q^{70} -8.68636 q^{71} +1.56470 q^{72} +16.8266 q^{73} -16.3524 q^{74} +1.00000 q^{75} +1.63107 q^{76} -10.5591 q^{77} +7.99804 q^{78} -15.0131 q^{79} +4.98719 q^{80} +1.00000 q^{81} -0.368615 q^{82} +16.0636 q^{83} -2.13065 q^{84} -2.79159 q^{85} +1.33364 q^{86} +2.69631 q^{87} +8.63210 q^{88} -0.609573 q^{89} +1.76442 q^{90} +8.67604 q^{91} -1.12078 q^{92} -8.25999 q^{93} +4.31793 q^{94} -1.46521 q^{95} +5.67012 q^{96} +14.1259 q^{97} +5.88722 q^{98} +5.51678 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−1.76442	−1.24764	−0.623818	−	0.781569i	$-0.714420\pi$
$2$	−1.76442	−1.24764	−0.623818	+	0.781569i	$0.714420\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.11320	0.556598
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.76442	−0.720323
$7$	−1.91400	−0.723422	−0.361711	−	0.932290i	$-0.617807\pi$
$7$	−1.91400	−0.723422	−0.361711	+	0.932290i	$0.617807\pi$
$8$	1.56470	0.553205
$9$	1.00000	0.333333
$10$	1.76442	0.557960
$11$	5.51678	1.66337	0.831685	−	0.555247i	$-0.187376\pi$
$11$	5.51678	1.66337	0.831685	+	0.555247i	$0.187376\pi$
$12$	1.11320	0.321352
$13$	−4.53295	−1.25721	−0.628606	−	0.777724i	$-0.716374\pi$
$13$	−4.53295	−1.25721	−0.628606	+	0.777724i	$0.716374\pi$
$14$	3.37710	0.902568
$15$	−1.00000	−0.258199
$16$	−4.98719	−1.24680
$17$	2.79159	0.677059	0.338530	−	0.940956i	$-0.390070\pi$
$17$	2.79159	0.677059	0.338530	+	0.940956i	$0.390070\pi$
$18$	−1.76442	−0.415879
$19$	1.46521	0.336143	0.168071	−	0.985775i	$-0.446246\pi$
$19$	1.46521	0.336143	0.168071	+	0.985775i	$0.446246\pi$
$20$	−1.11320	−0.248918
$21$	−1.91400	−0.417668
$22$	−9.73394	−2.07528
$23$	−1.00681	−0.209935	−0.104967	−	0.994476i	$-0.533474\pi$
$23$	−1.00681	−0.209935	−0.104967	+	0.994476i	$0.533474\pi$
$24$	1.56470	0.319393
$25$	1.00000	0.200000
$26$	7.99804	1.56854
$27$	1.00000	0.192450
$28$	−2.13065	−0.402655
$29$	2.69631	0.500693	0.250346	−	0.968156i	$-0.419455\pi$
$29$	2.69631	0.500693	0.250346	+	0.968156i	$0.419455\pi$
$30$	1.76442	0.322138
$31$	−8.25999	−1.48354	−0.741769	−	0.670655i	$-0.766013\pi$
$31$	−8.25999	−1.48354	−0.741769	+	0.670655i	$0.766013\pi$
$32$	5.67012	1.00234
$33$	5.51678	0.960348
$34$	−4.92555	−0.844724
$35$	1.91400	0.323524
$36$	1.11320	0.185533
$37$	9.26785	1.52362	0.761812	−	0.647798i	$-0.224310\pi$
$37$	9.26785	1.52362	0.761812	+	0.647798i	$0.224310\pi$
$38$	−2.58526	−0.419384
$39$	−4.53295	−0.725852
$40$	−1.56470	−0.247401
$41$	0.208915	0.0326271	0.0163135	−	0.999867i	$-0.494807\pi$
$41$	0.208915	0.0326271	0.0163135	+	0.999867i	$0.494807\pi$
$42$	3.37710	0.521098
$43$	−0.755852	−0.115266	−0.0576332	−	0.998338i	$-0.518355\pi$
$43$	−0.755852	−0.115266	−0.0576332	+	0.998338i	$0.518355\pi$
$44$	6.14125	0.925828
$45$	−1.00000	−0.149071
$46$	1.77644	0.261922
$47$	−2.44722	−0.356963	−0.178482	−	0.983943i	$-0.557119\pi$
$47$	−2.44722	−0.356963	−0.178482	+	0.983943i	$0.557119\pi$
$48$	−4.98719	−0.719838
$49$	−3.33662	−0.476660
$50$	−1.76442	−0.249527
$51$	2.79159	0.390900
$52$	−5.04605	−0.699762
$53$	9.12954	1.25404	0.627019	−	0.779004i	$-0.284275\pi$
$53$	9.12954	1.25404	0.627019	+	0.779004i	$0.284275\pi$
$54$	−1.76442	−0.240108
$55$	−5.51678	−0.743882
$56$	−2.99483	−0.400201
$57$	1.46521	0.194072
$58$	−4.75744	−0.624683
$59$	−8.33486	−1.08511	−0.542553	−	0.840021i	$-0.682542\pi$
$59$	−8.33486	−1.08511	−0.542553	+	0.840021i	$0.682542\pi$
$60$	−1.11320	−0.143713
$61$	9.21208	1.17949	0.589743	−	0.807591i	$-0.299229\pi$
$61$	9.21208	1.17949	0.589743	+	0.807591i	$0.299229\pi$
$62$	14.5741	1.85092
$63$	−1.91400	−0.241141
$64$	−0.0301181	−0.00376476
$65$	4.53295	0.562243
$66$	−9.73394	−1.19816
$67$	3.37255	0.412022	0.206011	−	0.978550i	$-0.433952\pi$
$67$	3.37255	0.412022	0.206011	+	0.978550i	$0.433952\pi$
$68$	3.10758	0.376850
$69$	−1.00681	−0.121206
$70$	−3.37710	−0.403641
$71$	−8.68636	−1.03088	−0.515441	−	0.856925i	$-0.672372\pi$
$71$	−8.68636	−1.03088	−0.515441	+	0.856925i	$0.672372\pi$
$72$	1.56470	0.184402
$73$	16.8266	1.96941	0.984705	−	0.174229i	$-0.0557432\pi$
$73$	16.8266	1.96941	0.984705	+	0.174229i	$0.0557432\pi$
$74$	−16.3524	−1.90093
$75$	1.00000	0.115470
$76$	1.63107	0.187096
$77$	−10.5591	−1.20332
$78$	7.99804	0.905600
$79$	−15.0131	−1.68911	−0.844554	−	0.535470i	$-0.820135\pi$
$79$	−15.0131	−1.68911	−0.844554	+	0.535470i	$0.820135\pi$
$80$	4.98719	0.557584
$81$	1.00000	0.111111
$82$	−0.368615	−0.0407068
$83$	16.0636	1.76321	0.881605	−	0.471987i	$-0.156463\pi$
$83$	16.0636	1.76321	0.881605	+	0.471987i	$0.156463\pi$
$84$	−2.13065	−0.232473
$85$	−2.79159	−0.302790
$86$	1.33364	0.143811
$87$	2.69631	0.289075
$88$	8.63210	0.920185
$89$	−0.609573	−0.0646146	−0.0323073	−	0.999478i	$-0.510286\pi$
$89$	−0.609573	−0.0646146	−0.0323073	+	0.999478i	$0.510286\pi$
$90$	1.76442	0.185987
$91$	8.67604	0.909496
$92$	−1.12078	−0.116849
$93$	−8.25999	−0.856521
$94$	4.31793	0.445361
$95$	−1.46521	−0.150328
$96$	5.67012	0.578704
$97$	14.1259	1.43427	0.717133	−	0.696936i	$-0.245454\pi$
$97$	14.1259	1.43427	0.717133	+	0.696936i	$0.245454\pi$
$98$	5.88722	0.594699
$99$	5.51678	0.554457
$100$	1.11320	0.111320
$101$	−3.20032	−0.318444	−0.159222	−	0.987243i	$-0.550899\pi$
$101$	−3.20032	−0.318444	−0.159222	+	0.987243i	$0.550899\pi$
$102$	−4.92555	−0.487702
$103$	−3.48278	−0.343169	−0.171584	−	0.985169i	$-0.554889\pi$
$103$	−3.48278	−0.343169	−0.171584	+	0.985169i	$0.554889\pi$
$104$	−7.09270	−0.695497
$105$	1.91400	0.186787
$106$	−16.1084	−1.56458
$107$	−11.0942	−1.07252	−0.536260	−	0.844053i	$-0.680163\pi$
$107$	−11.0942	−1.07252	−0.536260	+	0.844053i	$0.680163\pi$
$108$	1.11320	0.107117
$109$	−10.5637	−1.01182	−0.505908	−	0.862587i	$-0.668842\pi$
$109$	−10.5637	−1.01182	−0.505908	+	0.862587i	$0.668842\pi$
$110$	9.73394	0.928095
$111$	9.26785	0.879665
$112$	9.54545	0.901960
$113$	4.93477	0.464224	0.232112	−	0.972689i	$-0.425436\pi$
$113$	4.93477	0.464224	0.232112	+	0.972689i	$0.425436\pi$
$114$	−2.58526	−0.242132
$115$	1.00681	0.0938856
$116$	3.00152	0.278684
$117$	−4.53295	−0.419071
$118$	14.7062	1.35382
$119$	−5.34309	−0.489800
$120$	−1.56470	−0.142837
$121$	19.4348	1.76680
$122$	−16.2540	−1.47157
$123$	0.208915	0.0188373
$124$	−9.19498	−0.825734
$125$	−1.00000	−0.0894427
$126$	3.37710	0.300856
$127$	−6.62638	−0.587996	−0.293998	−	0.955806i	$-0.594986\pi$
$127$	−6.62638	−0.587996	−0.293998	+	0.955806i	$0.594986\pi$
$128$	−11.2871	−0.997647
$129$	−0.755852	−0.0665491
$130$	−7.99804	−0.701475
$131$	−20.7254	−1.81079	−0.905393	−	0.424574i	$-0.860424\pi$
$131$	−20.7254	−1.81079	−0.905393	+	0.424574i	$0.860424\pi$
$132$	6.14125	0.534527
$133$	−2.80441	−0.243173
$134$	−5.95061	−0.514054
$135$	−1.00000	−0.0860663
$136$	4.36800	0.374553
$137$	1.38507	0.118334	0.0591672	−	0.998248i	$-0.481156\pi$
$137$	1.38507	0.118334	0.0591672	+	0.998248i	$0.481156\pi$
$138$	1.77644	0.151221
$139$	5.14462	0.436361	0.218181	−	0.975908i	$-0.429988\pi$
$139$	5.14462	0.436361	0.218181	+	0.975908i	$0.429988\pi$
$140$	2.13065	0.180073
$141$	−2.44722	−0.206093
$142$	15.3264	1.28617
$143$	−25.0072	−2.09121
$144$	−4.98719	−0.415599
$145$	−2.69631	−0.223917
$146$	−29.6894	−2.45711
$147$	−3.33662	−0.275200
$148$	10.3169	0.848046
$149$	8.31227	0.680967	0.340484	−	0.940250i	$-0.389409\pi$
$149$	8.31227	0.680967	0.340484	+	0.940250i	$0.389409\pi$
$150$	−1.76442	−0.144065
$151$	−9.30529	−0.757253	−0.378627	−	0.925549i	$-0.623604\pi$
$151$	−9.30529	−0.757253	−0.378627	+	0.925549i	$0.623604\pi$
$152$	2.29262	0.185956
$153$	2.79159	0.225686
$154$	18.6307	1.50131
$155$	8.25999	0.663459
$156$	−5.04605	−0.404007
$157$	−16.5714	−1.32254	−0.661272	−	0.750146i	$-0.729983\pi$
$157$	−16.5714	−1.32254	−0.661272	+	0.750146i	$0.729983\pi$
$158$	26.4895	2.10739
$159$	9.12954	0.724019
$160$	−5.67012	−0.448262
$161$	1.92703	0.151871
$162$	−1.76442	−0.138626
$163$	14.1922	1.11162	0.555808	−	0.831311i	$-0.312409\pi$
$163$	14.1922	1.11162	0.555808	+	0.831311i	$0.312409\pi$
$164$	0.232564	0.0181602
$165$	−5.51678	−0.429481
$166$	−28.3430	−2.19985
$167$	−0.771018	−0.0596631	−0.0298316	−	0.999555i	$-0.509497\pi$
$167$	−0.771018	−0.0596631	−0.0298316	+	0.999555i	$0.509497\pi$
$168$	−2.99483	−0.231056
$169$	7.54759	0.580584
$170$	4.92555	0.377772
$171$	1.46521	0.112048
$172$	−0.841411	−0.0641570
$173$	4.53635	0.344892	0.172446	−	0.985019i	$-0.444833\pi$
$173$	4.53635	0.344892	0.172446	+	0.985019i	$0.444833\pi$
$174$	−4.75744	−0.360661
$175$	−1.91400	−0.144684
$176$	−27.5132	−2.07389
$177$	−8.33486	−0.626486
$178$	1.07555	0.0806156
$179$	16.2572	1.21512	0.607560	−	0.794274i	$-0.292148\pi$
$179$	16.2572	1.21512	0.607560	+	0.794274i	$0.292148\pi$
$180$	−1.11320	−0.0829727
$181$	8.74920	0.650323	0.325161	−	0.945659i	$-0.394581\pi$
$181$	8.74920	0.650323	0.325161	+	0.945659i	$0.394581\pi$
$182$	−15.3082	−1.13472
$183$	9.21208	0.680976
$184$	−1.57536	−0.116137
$185$	−9.26785	−0.681386
$186$	14.5741	1.06863
$187$	15.4006	1.12620
$188$	−2.72423	−0.198685
$189$	−1.91400	−0.139223
$190$	2.58526	0.187554
$191$	−5.89561	−0.426591	−0.213296	−	0.976988i	$-0.568420\pi$
$191$	−5.89561	−0.426591	−0.213296	+	0.976988i	$0.568420\pi$
$192$	−0.0301181	−0.00217359
$193$	−16.5469	−1.19107	−0.595534	−	0.803330i	$-0.703060\pi$
$193$	−16.5469	−1.19107	−0.595534	+	0.803330i	$0.703060\pi$
$194$	−24.9241	−1.78944
$195$	4.53295	0.324611
$196$	−3.71431	−0.265308
$197$	4.00431	0.285296	0.142648	−	0.989774i	$-0.454438\pi$
$197$	4.00431	0.285296	0.142648	+	0.989774i	$0.454438\pi$
$198$	−9.73394	−0.691761
$199$	14.1203	1.00096	0.500480	−	0.865748i	$-0.333157\pi$
$199$	14.1203	1.00096	0.500480	+	0.865748i	$0.333157\pi$
$200$	1.56470	0.110641
$201$	3.37255	0.237881
$202$	5.64673	0.397302
$203$	−5.16073	−0.362212
$204$	3.10758	0.217574
$205$	−0.208915	−0.0145913
$206$	6.14510	0.428150
$207$	−1.00681	−0.0699782
$208$	22.6066	1.56749
$209$	8.08325	0.559130
$210$	−3.37710	−0.233042
$211$	22.6867	1.56182	0.780908	−	0.624645i	$-0.214756\pi$
$211$	22.6867	1.56182	0.780908	+	0.624645i	$0.214756\pi$
$212$	10.1630	0.697995
$213$	−8.68636	−0.595180
$214$	19.5749	1.33811
$215$	0.755852	0.0515487
$216$	1.56470	0.106464
$217$	15.8096	1.07322
$218$	18.6388	1.26238
$219$	16.8266	1.13704
$220$	−6.14125	−0.414043
$221$	−12.6541	−0.851208
$222$	−16.3524	−1.09750
$223$	14.1925	0.950398	0.475199	−	0.879878i	$-0.342376\pi$
$223$	14.1925	0.950398	0.475199	+	0.879878i	$0.342376\pi$
$224$	−10.8526	−0.725118
$225$	1.00000	0.0666667
$226$	−8.70703	−0.579183
$227$	−13.5947	−0.902311	−0.451156	−	0.892445i	$-0.648988\pi$
$227$	−13.5947	−0.902311	−0.451156	+	0.892445i	$0.648988\pi$
$228$	1.63107	0.108020
$229$	4.12183	0.272378	0.136189	−	0.990683i	$-0.456514\pi$
$229$	4.12183	0.272378	0.136189	+	0.990683i	$0.456514\pi$
$230$	−1.77644	−0.117135
$231$	−10.5591	−0.694737
$232$	4.21892	0.276986
$233$	14.2307	0.932284	0.466142	−	0.884710i	$-0.345644\pi$
$233$	14.2307	0.932284	0.466142	+	0.884710i	$0.345644\pi$
$234$	7.99804	0.522848
$235$	2.44722	0.159639
$236$	−9.27832	−0.603967
$237$	−15.0131	−0.975207
$238$	9.42747	0.611092
$239$	−20.5401	−1.32863	−0.664314	−	0.747454i	$-0.731276\pi$
$239$	−20.5401	−1.32863	−0.664314	+	0.747454i	$0.731276\pi$
$240$	4.98719	0.321922
$241$	5.12578	0.330180	0.165090	−	0.986278i	$-0.447208\pi$
$241$	5.12578	0.330180	0.165090	+	0.986278i	$0.447208\pi$
$242$	−34.2913	−2.20433
$243$	1.00000	0.0641500
$244$	10.2548	0.656499
$245$	3.33662	0.213169
$246$	−0.368615	−0.0235021
$247$	−6.64173	−0.422603
$248$	−12.9244	−0.820701
$249$	16.0636	1.01799
$250$	1.76442	0.111592
$251$	9.83652	0.620876	0.310438	−	0.950594i	$-0.399524\pi$
$251$	9.83652	0.620876	0.310438	+	0.950594i	$0.399524\pi$
$252$	−2.13065	−0.134218
$253$	−5.55435	−0.349199
$254$	11.6917	0.733606
$255$	−2.79159	−0.174816
$256$	19.9755	1.24847
$257$	0.111824	0.00697540	0.00348770	−	0.999994i	$-0.498890\pi$
$257$	0.111824	0.00697540	0.00348770	+	0.999994i	$0.498890\pi$
$258$	1.33364	0.0830291
$259$	−17.7386	−1.10222
$260$	5.04605	0.312943
$261$	2.69631	0.166898
$262$	36.5684	2.25920
$263$	15.1217	0.932446	0.466223	−	0.884667i	$-0.345614\pi$
$263$	15.1217	0.932446	0.466223	+	0.884667i	$0.345614\pi$
$264$	8.63210	0.531269
$265$	−9.12954	−0.560823
$266$	4.94817	0.303392
$267$	−0.609573	−0.0373053
$268$	3.75430	0.229331
$269$	14.4806	0.882901	0.441450	−	0.897286i	$-0.354464\pi$
$269$	14.4806	0.882901	0.441450	+	0.897286i	$0.354464\pi$
$270$	1.76442	0.107379
$271$	21.8288	1.32600	0.663001	−	0.748618i	$-0.269282\pi$
$271$	21.8288	1.32600	0.663001	+	0.748618i	$0.269282\pi$
$272$	−13.9222	−0.844155
$273$	8.67604	0.525098
$274$	−2.44385	−0.147638
$275$	5.51678	0.332674
$276$	−1.12078	−0.0674628
$277$	−16.3611	−0.983041	−0.491521	−	0.870866i	$-0.663559\pi$
$277$	−16.3611	−0.983041	−0.491521	+	0.870866i	$0.663559\pi$
$278$	−9.07730	−0.544420
$279$	−8.25999	−0.494513
$280$	2.99483	0.178975
$281$	−12.3893	−0.739085	−0.369543	−	0.929214i	$-0.620486\pi$
$281$	−12.3893	−0.739085	−0.369543	+	0.929214i	$0.620486\pi$
$282$	4.31793	0.257129
$283$	12.2457	0.727931	0.363966	−	0.931412i	$-0.381423\pi$
$283$	12.2457	0.727931	0.363966	+	0.931412i	$0.381423\pi$
$284$	−9.66962	−0.573786
$285$	−1.46521	−0.0867917
$286$	44.1234	2.60907
$287$	−0.399863	−0.0236032
$288$	5.67012	0.334115
$289$	−9.20704	−0.541591
$290$	4.75744	0.279367
$291$	14.1259	0.828074
$292$	18.7313	1.09617
$293$	29.9363	1.74890	0.874450	−	0.485116i	$-0.161223\pi$
$293$	29.9363	1.74890	0.874450	+	0.485116i	$0.161223\pi$
$294$	5.88722	0.343350
$295$	8.33486	0.485274
$296$	14.5014	0.842877
$297$	5.51678	0.320116
$298$	−14.6664	−0.849600
$299$	4.56382	0.263932
$300$	1.11320	0.0642703
$301$	1.44670	0.0833862
$302$	16.4185	0.944777
$303$	−3.20032	−0.183854
$304$	−7.30729	−0.419102
$305$	−9.21208	−0.527482
$306$	−4.92555	−0.281575
$307$	20.3577	1.16188	0.580938	−	0.813948i	$-0.302686\pi$
$307$	20.3577	1.16188	0.580938	+	0.813948i	$0.302686\pi$
$308$	−11.7543	−0.669765
$309$	−3.48278	−0.198128
$310$	−14.5741	−0.827755
$311$	12.3998	0.703128	0.351564	−	0.936164i	$-0.385650\pi$
$311$	12.3998	0.703128	0.351564	+	0.936164i	$0.385650\pi$
$312$	−7.09270	−0.401545
$313$	−1.28340	−0.0725423	−0.0362711	−	0.999342i	$-0.511548\pi$
$313$	−1.28340	−0.0725423	−0.0362711	+	0.999342i	$0.511548\pi$
$314$	29.2391	1.65006
$315$	1.91400	0.107841
$316$	−16.7125	−0.940154
$317$	21.0435	1.18192	0.590960	−	0.806701i	$-0.298749\pi$
$317$	21.0435	1.18192	0.590960	+	0.806701i	$0.298749\pi$
$318$	−16.1084	−0.903313
$319$	14.8750	0.832838
$320$	0.0301181	0.00168365
$321$	−11.0942	−0.619219
$322$	−3.40010	−0.189480
$323$	4.09027	0.227589
$324$	1.11320	0.0618442
$325$	−4.53295	−0.251443
$326$	−25.0410	−1.38689
$327$	−10.5637	−0.584172
$328$	0.326890	0.0180495
$329$	4.68396	0.258235
$330$	9.73394	0.535836
$331$	6.72481	0.369629	0.184815	−	0.982773i	$-0.440832\pi$
$331$	6.72481	0.369629	0.184815	+	0.982773i	$0.440832\pi$
$332$	17.8819	0.981399
$333$	9.26785	0.507875
$334$	1.36040	0.0744379
$335$	−3.37255	−0.184262
$336$	9.54545	0.520747
$337$	22.6640	1.23459	0.617294	−	0.786733i	$-0.288229\pi$
$337$	22.6640	1.23459	0.617294	+	0.786733i	$0.288229\pi$
$338$	−13.3172	−0.724358
$339$	4.93477	0.268020
$340$	−3.10758	−0.168532
$341$	−45.5685	−2.46768
$342$	−2.58526	−0.139795
$343$	19.7842	1.06825
$344$	−1.18268	−0.0637659
$345$	1.00681	0.0542049
$346$	−8.00404	−0.430300
$347$	−18.4609	−0.991034	−0.495517	−	0.868598i	$-0.665021\pi$
$347$	−18.4609	−0.991034	−0.495517	+	0.868598i	$0.665021\pi$
$348$	3.00152	0.160899
$349$	−9.48896	−0.507932	−0.253966	−	0.967213i	$-0.581735\pi$
$349$	−9.48896	−0.507932	−0.253966	+	0.967213i	$0.581735\pi$
$350$	3.37710	0.180514
$351$	−4.53295	−0.241951
$352$	31.2808	1.66727
$353$	10.6261	0.565569	0.282785	−	0.959183i	$-0.408742\pi$
$353$	10.6261	0.565569	0.282785	+	0.959183i	$0.408742\pi$
$354$	14.7062	0.781628
$355$	8.68636	0.461024
$356$	−0.678574	−0.0359643
$357$	−5.34309	−0.282786
$358$	−28.6846	−1.51603
$359$	−12.2534	−0.646712	−0.323356	−	0.946277i	$-0.604811\pi$
$359$	−12.2534	−0.646712	−0.323356	+	0.946277i	$0.604811\pi$
$360$	−1.56470	−0.0824670
$361$	−16.8532	−0.887008
$362$	−15.4373	−0.811367
$363$	19.4348	1.02006
$364$	9.65812	0.506223
$365$	−16.8266	−0.880747
$366$	−16.2540	−0.849611
$367$	−15.5142	−0.809833	−0.404917	−	0.914354i	$-0.632699\pi$
$367$	−15.5142	−0.809833	−0.404917	+	0.914354i	$0.632699\pi$
$368$	5.02115	0.261746
$369$	0.208915	0.0108757
$370$	16.3524	0.850122
$371$	−17.4739	−0.907199
$372$	−9.19498	−0.476738
$373$	33.1545	1.71667	0.858337	−	0.513086i	$-0.171498\pi$
$373$	33.1545	1.71667	0.858337	+	0.513086i	$0.171498\pi$
$374$	−27.1731	−1.40509
$375$	−1.00000	−0.0516398
$376$	−3.82916	−0.197474
$377$	−12.2222	−0.629477
$378$	3.37710	0.173699
$379$	32.8790	1.68888	0.844441	−	0.535649i	$-0.179933\pi$
$379$	32.8790	1.68888	0.844441	+	0.535649i	$0.179933\pi$
$380$	−1.63107	−0.0836720
$381$	−6.62638	−0.339480
$382$	10.4024	0.532231
$383$	6.37217	0.325603	0.162801	−	0.986659i	$-0.447947\pi$
$383$	6.37217	0.325603	0.162801	+	0.986659i	$0.447947\pi$
$384$	−11.2871	−0.575992
$385$	10.5591	0.538141
$386$	29.1957	1.48602
$387$	−0.755852	−0.0384221
$388$	15.7249	0.798309
$389$	8.67330	0.439754	0.219877	−	0.975528i	$-0.429434\pi$
$389$	8.67330	0.439754	0.219877	+	0.975528i	$0.429434\pi$
$390$	−7.99804	−0.404997
$391$	−2.81060	−0.142138
$392$	−5.22081	−0.263691
$393$	−20.7254	−1.04546
$394$	−7.06531	−0.355945
$395$	15.0131	0.755392
$396$	6.14125	0.308609
$397$	−20.7911	−1.04347	−0.521737	−	0.853106i	$-0.674716\pi$
$397$	−20.7911	−1.04347	−0.521737	+	0.853106i	$0.674716\pi$
$398$	−24.9142	−1.24883
$399$	−2.80441	−0.140396
$400$	−4.98719	−0.249359
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−5.95061	−0.296789
$403$	37.4421	1.86512
$404$	−3.56258	−0.177245
$405$	−1.00000	−0.0496904
$406$	9.10572	0.451909
$407$	51.1287	2.53435
$408$	4.36800	0.216248
$409$	14.4009	0.712079	0.356040	−	0.934471i	$-0.384127\pi$
$409$	14.4009	0.712079	0.356040	+	0.934471i	$0.384127\pi$
$410$	0.368615	0.0182046
$411$	1.38507	0.0683203
$412$	−3.87701	−0.191007
$413$	15.9529	0.784990
$414$	1.77644	0.0873074
$415$	−16.0636	−0.788532
$416$	−25.7023	−1.26016
$417$	5.14462	0.251933
$418$	−14.2623	−0.697591
$419$	20.0423	0.979130	0.489565	−	0.871967i	$-0.337156\pi$
$419$	20.0423	0.979130	0.489565	+	0.871967i	$0.337156\pi$
$420$	2.13065	0.103965
$421$	11.8595	0.577998	0.288999	−	0.957329i	$-0.406678\pi$
$421$	11.8595	0.577998	0.288999	+	0.957329i	$0.406678\pi$
$422$	−40.0290	−1.94858
$423$	−2.44722	−0.118988
$424$	14.2850	0.693740
$425$	2.79159	0.135412
$426$	15.3264	0.742568
$427$	−17.6319	−0.853266
$428$	−12.3500	−0.596962
$429$	−25.0072	−1.20736
$430$	−1.33364	−0.0643140
$431$	−19.0739	−0.918755	−0.459378	−	0.888241i	$-0.651927\pi$
$431$	−19.0739	−0.918755	−0.459378	+	0.888241i	$0.651927\pi$
$432$	−4.98719	−0.239946
$433$	−0.861488	−0.0414005	−0.0207002	−	0.999786i	$-0.506590\pi$
$433$	−0.861488	−0.0414005	−0.0207002	+	0.999786i	$0.506590\pi$
$434$	−27.8948	−1.33899
$435$	−2.69631	−0.129278
$436$	−11.7594	−0.563174
$437$	−1.47519	−0.0705680
$438$	−29.6894	−1.41861
$439$	−5.17437	−0.246959	−0.123480	−	0.992347i	$-0.539405\pi$
$439$	−5.17437	−0.246959	−0.123480	+	0.992347i	$0.539405\pi$
$440$	−8.63210	−0.411519
$441$	−3.33662	−0.158887
$442$	22.3272	1.06200
$443$	15.8194	0.751604	0.375802	−	0.926700i	$-0.377367\pi$
$443$	15.8194	0.751604	0.375802	+	0.926700i	$0.377367\pi$
$444$	10.3169	0.489619
$445$	0.609573	0.0288965
$446$	−25.0415	−1.18575
$447$	8.31227	0.393157
$448$	0.0576459	0.00272351
$449$	−23.8877	−1.12733	−0.563665	−	0.826003i	$-0.690609\pi$
$449$	−23.8877	−1.12733	−0.563665	+	0.826003i	$0.690609\pi$
$450$	−1.76442	−0.0831758
$451$	1.15254	0.0542710
$452$	5.49336	0.258386
$453$	−9.30529	−0.437201
$454$	23.9868	1.12576
$455$	−8.67604	−0.406739
$456$	2.29262	0.107362
$457$	−29.0142	−1.35723	−0.678613	−	0.734496i	$-0.737419\pi$
$457$	−29.0142	−1.35723	−0.678613	+	0.734496i	$0.737419\pi$
$458$	−7.27267	−0.339829
$459$	2.79159	0.130300
$460$	1.12078	0.0522565
$461$	29.4404	1.37118	0.685589	−	0.727989i	$-0.259545\pi$
$461$	29.4404	1.37118	0.685589	+	0.727989i	$0.259545\pi$
$462$	18.6307	0.866779
$463$	−32.3485	−1.50336	−0.751682	−	0.659526i	$-0.770757\pi$
$463$	−32.3485	−1.50336	−0.751682	+	0.659526i	$0.770757\pi$
$464$	−13.4470	−0.624262
$465$	8.25999	0.383048
$466$	−25.1090	−1.16315
$467$	−3.41752	−0.158144	−0.0790719	−	0.996869i	$-0.525196\pi$
$467$	−3.41752	−0.158144	−0.0790719	+	0.996869i	$0.525196\pi$
$468$	−5.04605	−0.233254
$469$	−6.45504	−0.298066
$470$	−4.31793	−0.199171
$471$	−16.5714	−0.763571
$472$	−13.0416	−0.600287
$473$	−4.16987	−0.191731
$474$	26.4895	1.21670
$475$	1.46521	0.0672286
$476$	−5.94790	−0.272621
$477$	9.12954	0.418013
$478$	36.2414	1.65764
$479$	−20.8445	−0.952409	−0.476205	−	0.879334i	$-0.657988\pi$
$479$	−20.8445	−0.952409	−0.476205	+	0.879334i	$0.657988\pi$
$480$	−5.67012	−0.258804
$481$	−42.0106	−1.91552
$482$	−9.04405	−0.411945
$483$	1.92703	0.0876830
$484$	21.6348	0.983398
$485$	−14.1259	−0.641423
$486$	−1.76442	−0.0800359
$487$	26.7772	1.21339	0.606696	−	0.794934i	$-0.292495\pi$
$487$	26.7772	1.21339	0.606696	+	0.794934i	$0.292495\pi$
$488$	14.4141	0.652498
$489$	14.1922	0.641792
$490$	−5.88722	−0.265957
$491$	28.5898	1.29024	0.645120	−	0.764081i	$-0.276807\pi$
$491$	28.5898	1.29024	0.645120	+	0.764081i	$0.276807\pi$
$492$	0.232564	0.0104848
$493$	7.52699	0.338999
$494$	11.7188	0.527255
$495$	−5.51678	−0.247961
$496$	41.1941	1.84967
$497$	16.6257	0.745763
$498$	−28.3430	−1.27008
$499$	17.1821	0.769177	0.384589	−	0.923088i	$-0.374343\pi$
$499$	17.1821	0.769177	0.384589	+	0.923088i	$0.374343\pi$
$500$	−1.11320	−0.0497836
$501$	−0.771018	−0.0344465
$502$	−17.3558	−0.774627
$503$	26.2077	1.16854	0.584271	−	0.811558i	$-0.301380\pi$
$503$	26.2077	1.16854	0.584271	+	0.811558i	$0.301380\pi$
$504$	−2.99483	−0.133400
$505$	3.20032	0.142412
$506$	9.80023	0.435674
$507$	7.54759	0.335200
$508$	−7.37645	−0.327277
$509$	17.1714	0.761107	0.380553	−	0.924759i	$-0.375734\pi$
$509$	17.1714	0.761107	0.380553	+	0.924759i	$0.375734\pi$
$510$	4.92555	0.218107
$511$	−32.2061	−1.42472
$512$	−12.6710	−0.559985
$513$	1.46521	0.0646907
$514$	−0.197305	−0.00870277
$515$	3.48278	0.153470
$516$	−0.841411	−0.0370410
$517$	−13.5008	−0.593762
$518$	31.2985	1.37518
$519$	4.53635	0.199124
$520$	7.09270	0.311036
$521$	25.9610	1.13737	0.568685	−	0.822555i	$-0.307452\pi$
$521$	25.9610	1.13737	0.568685	+	0.822555i	$0.307452\pi$
$522$	−4.75744	−0.208228
$523$	14.5422	0.635887	0.317943	−	0.948110i	$-0.397008\pi$
$523$	14.5422	0.635887	0.317943	+	0.948110i	$0.397008\pi$
$524$	−23.0714	−1.00788
$525$	−1.91400	−0.0835336
$526$	−26.6812	−1.16335
$527$	−23.0585	−1.00444
$528$	−27.5132	−1.19736
$529$	−21.9863	−0.955927
$530$	16.1084	0.699703
$531$	−8.33486	−0.361702
$532$	−3.12185	−0.135350
$533$	−0.947002	−0.0410192
$534$	1.07555	0.0465434
$535$	11.0942	0.479645
$536$	5.27703	0.227933
$537$	16.2572	0.701550
$538$	−25.5500	−1.10154
$539$	−18.4074	−0.792863
$540$	−1.11320	−0.0479043
$541$	30.0381	1.29144	0.645719	−	0.763575i	$-0.276558\pi$
$541$	30.0381	1.29144	0.645719	+	0.763575i	$0.276558\pi$
$542$	−38.5152	−1.65437
$543$	8.74920	0.375464
$544$	15.8286	0.678647
$545$	10.5637	0.452498
$546$	−15.3082	−0.655131
$547$	1.03158	0.0441070	0.0220535	−	0.999757i	$-0.492980\pi$
$547$	1.03158	0.0441070	0.0220535	+	0.999757i	$0.492980\pi$
$548$	1.54185	0.0658646
$549$	9.21208	0.393162
$550$	−9.73394	−0.415057
$551$	3.95067	0.168304
$552$	−1.57536	−0.0670517
$553$	28.7351	1.22194
$554$	28.8679	1.22648
$555$	−9.26785	−0.393398
$556$	5.72697	0.242878
$557$	−43.5065	−1.84343	−0.921714	−	0.387871i	$-0.873211\pi$
$557$	−43.5065	−1.84343	−0.921714	+	0.387871i	$0.873211\pi$
$558$	14.5741	0.616972
$559$	3.42624	0.144914
$560$	−9.54545	−0.403369
$561$	15.4006	0.650212
$562$	21.8600	0.922110
$563$	11.1776	0.471078	0.235539	−	0.971865i	$-0.424314\pi$
$563$	11.1776	0.471078	0.235539	+	0.971865i	$0.424314\pi$
$564$	−2.72423	−0.114711
$565$	−4.93477	−0.207607
$566$	−21.6066	−0.908194
$567$	−1.91400	−0.0803802
$568$	−13.5916	−0.570289
$569$	−1.82350	−0.0764450	−0.0382225	−	0.999269i	$-0.512170\pi$
$569$	−1.82350	−0.0764450	−0.0382225	+	0.999269i	$0.512170\pi$
$570$	2.58526	0.108285
$571$	−35.1063	−1.46915	−0.734576	−	0.678526i	$-0.762619\pi$
$571$	−35.1063	−1.46915	−0.734576	+	0.678526i	$0.762619\pi$
$572$	−27.8379	−1.16396
$573$	−5.89561	−0.246292
$574$	0.705528	0.0294482
$575$	−1.00681	−0.0419869
$576$	−0.0301181	−0.00125492
$577$	−0.905734	−0.0377062	−0.0188531	−	0.999822i	$-0.506001\pi$
$577$	−0.905734	−0.0377062	−0.0188531	+	0.999822i	$0.506001\pi$
$578$	16.2451	0.675708
$579$	−16.5469	−0.687664
$580$	−3.00152	−0.124631
$581$	−30.7457	−1.27555
$582$	−24.9241	−1.03314
$583$	50.3656	2.08593
$584$	26.3287	1.08949
$585$	4.53295	0.187414
$586$	−52.8204	−2.18199
$587$	−1.69529	−0.0699723	−0.0349862	−	0.999388i	$-0.511139\pi$
$587$	−1.69529	−0.0699723	−0.0349862	+	0.999388i	$0.511139\pi$
$588$	−3.71431	−0.153176
$589$	−12.1026	−0.498681
$590$	−14.7062	−0.605446
$591$	4.00431	0.164715
$592$	−46.2205	−1.89965
$593$	−6.63548	−0.272487	−0.136243	−	0.990675i	$-0.543503\pi$
$593$	−6.63548	−0.272487	−0.136243	+	0.990675i	$0.543503\pi$
$594$	−9.73394	−0.399388
$595$	5.34309	0.219045
$596$	9.25318	0.379025
$597$	14.1203	0.577904
$598$	−8.05251	−0.329292
$599$	30.5749	1.24926	0.624629	−	0.780922i	$-0.285250\pi$
$599$	30.5749	1.24926	0.624629	+	0.780922i	$0.285250\pi$
$600$	1.56470	0.0638786
$601$	12.3256	0.502772	0.251386	−	0.967887i	$-0.419114\pi$
$601$	12.3256	0.502772	0.251386	+	0.967887i	$0.419114\pi$
$602$	−2.55259	−0.104036
$603$	3.37255	0.137341
$604$	−10.3586	−0.421485
$605$	−19.4348	−0.790138
$606$	5.64673	0.229383
$607$	−7.50828	−0.304752	−0.152376	−	0.988323i	$-0.548692\pi$
$607$	−7.50828	−0.304752	−0.152376	+	0.988323i	$0.548692\pi$
$608$	8.30792	0.336931
$609$	−5.16073	−0.209123
$610$	16.2540	0.658106
$611$	11.0931	0.448779
$612$	3.10758	0.125617
$613$	2.40230	0.0970279	0.0485139	−	0.998823i	$-0.484551\pi$
$613$	2.40230	0.0970279	0.0485139	+	0.998823i	$0.484551\pi$
$614$	−35.9197	−1.44960
$615$	−0.208915	−0.00842428
$616$	−16.5218	−0.665683
$617$	−39.5177	−1.59092	−0.795461	−	0.606005i	$-0.792771\pi$
$617$	−39.5177	−1.59092	−0.795461	+	0.606005i	$0.792771\pi$
$618$	6.14510	0.247192
$619$	40.1920	1.61545	0.807726	−	0.589558i	$-0.200698\pi$
$619$	40.1920	1.61545	0.807726	+	0.589558i	$0.200698\pi$
$620$	9.19498	0.369279
$621$	−1.00681	−0.0404019
$622$	−21.8785	−0.877248
$623$	1.16672	0.0467437
$624$	22.6066	0.904990
$625$	1.00000	0.0400000
$626$	2.26447	0.0905064
$627$	8.08325	0.322814
$628$	−18.4472	−0.736125
$629$	25.8720	1.03158
$630$	−3.37710	−0.134547
$631$	17.7863	0.708060	0.354030	−	0.935234i	$-0.384811\pi$
$631$	17.7863	0.708060	0.354030	+	0.935234i	$0.384811\pi$
$632$	−23.4911	−0.934424
$633$	22.6867	0.901715
$634$	−37.1296	−1.47461
$635$	6.62638	0.262960
$636$	10.1630	0.402987
$637$	15.1247	0.599263
$638$	−26.2457	−1.03908
$639$	−8.68636	−0.343627
$640$	11.2871	0.446161
$641$	−0.421529	−0.0166494	−0.00832469	−	0.999965i	$-0.502650\pi$
$641$	−0.421529	−0.0166494	−0.00832469	+	0.999965i	$0.502650\pi$
$642$	19.5749	0.772561
$643$	39.8715	1.57238	0.786189	−	0.617986i	$-0.212051\pi$
$643$	39.8715	1.57238	0.786189	+	0.617986i	$0.212051\pi$
$644$	2.14516	0.0845312
$645$	0.755852	0.0297616
$646$	−7.21697	−0.283948
$647$	−6.62671	−0.260523	−0.130261	−	0.991480i	$-0.541582\pi$
$647$	−6.62671	−0.260523	−0.130261	+	0.991480i	$0.541582\pi$
$648$	1.56470	0.0614672
$649$	−45.9816	−1.80493
$650$	7.99804	0.313709
$651$	15.8096	0.619627
$652$	15.7986	0.618723
$653$	27.7767	1.08699	0.543493	−	0.839414i	$-0.317101\pi$
$653$	27.7767	1.08699	0.543493	+	0.839414i	$0.317101\pi$
$654$	18.6388	0.728835
$655$	20.7254	0.809808
$656$	−1.04190	−0.0406794
$657$	16.8266	0.656470
$658$	−8.26450	−0.322184
$659$	28.7295	1.11914	0.559570	−	0.828783i	$-0.310966\pi$
$659$	28.7295	1.11914	0.559570	+	0.828783i	$0.310966\pi$
$660$	−6.14125	−0.239048
$661$	30.9291	1.20300	0.601502	−	0.798871i	$-0.294569\pi$
$661$	30.9291	1.20300	0.601502	+	0.798871i	$0.294569\pi$
$662$	−11.8654	−0.461163
$663$	−12.6541	−0.491445
$664$	25.1347	0.975417
$665$	2.80441	0.108750
$666$	−16.3524	−0.633643
$667$	−2.71468	−0.105113
$668$	−0.858293	−0.0332084
$669$	14.1925	0.548712
$670$	5.95061	0.229892
$671$	50.8210	1.96192
$672$	−10.8526	−0.418647
$673$	37.1850	1.43338	0.716689	−	0.697393i	$-0.245657\pi$
$673$	37.1850	1.43338	0.716689	+	0.697393i	$0.245657\pi$
$674$	−39.9890	−1.54032
$675$	1.00000	0.0384900
$676$	8.40194	0.323152
$677$	5.63593	0.216607	0.108303	−	0.994118i	$-0.465458\pi$
$677$	5.63593	0.216607	0.108303	+	0.994118i	$0.465458\pi$
$678$	−8.70703	−0.334391
$679$	−27.0369	−1.03758
$680$	−4.36800	−0.167505
$681$	−13.5947	−0.520950
$682$	80.4023	3.07876
$683$	−49.6482	−1.89974	−0.949868	−	0.312650i	$-0.898783\pi$
$683$	−49.6482	−1.89974	−0.949868	+	0.312650i	$0.898783\pi$
$684$	1.63107	0.0623654
$685$	−1.38507	−0.0529207
$686$	−34.9078	−1.33279
$687$	4.12183	0.157258
$688$	3.76958	0.143714
$689$	−41.3837	−1.57659
$690$	−1.77644	−0.0676280
$691$	21.8362	0.830688	0.415344	−	0.909664i	$-0.363661\pi$
$691$	21.8362	0.830688	0.415344	+	0.909664i	$0.363661\pi$
$692$	5.04984	0.191966
$693$	−10.5591	−0.401106
$694$	32.5729	1.23645
$695$	−5.14462	−0.195147
$696$	4.21892	0.159918
$697$	0.583205	0.0220905
$698$	16.7426	0.633715
$699$	14.2307	0.538254
$700$	−2.13065	−0.0805310
$701$	41.3981	1.56358	0.781792	−	0.623539i	$-0.214306\pi$
$701$	41.3981	1.56358	0.781792	+	0.623539i	$0.214306\pi$
$702$	7.99804	0.301867
$703$	13.5794	0.512155
$704$	−0.166155	−0.00626219
$705$	2.44722	0.0921675
$706$	−18.7489	−0.705625
$707$	6.12540	0.230369
$708$	−9.27832	−0.348701
$709$	20.8087	0.781488	0.390744	−	0.920499i	$-0.372218\pi$
$709$	20.8087	0.781488	0.390744	+	0.920499i	$0.372218\pi$
$710$	−15.3264	−0.575191
$711$	−15.0131	−0.563036
$712$	−0.953800	−0.0357452
$713$	8.31625	0.311446
$714$	9.42747	0.352814
$715$	25.0072	0.935218
$716$	18.0974	0.676333
$717$	−20.5401	−0.767083
$718$	21.6203	0.806861
$719$	−4.30297	−0.160474	−0.0802369	−	0.996776i	$-0.525568\pi$
$719$	−4.30297	−0.160474	−0.0802369	+	0.996776i	$0.525568\pi$
$720$	4.98719	0.185861
$721$	6.66603	0.248256
$722$	29.7361	1.10666
$723$	5.12578	0.190630
$724$	9.73956	0.361968
$725$	2.69631	0.100139
$726$	−34.2913	−1.27267
$727$	−14.3110	−0.530765	−0.265383	−	0.964143i	$-0.585498\pi$
$727$	−14.3110	−0.530765	−0.265383	+	0.964143i	$0.585498\pi$
$728$	13.5754	0.503138
$729$	1.00000	0.0370370
$730$	29.6894	1.09885
$731$	−2.11003	−0.0780422
$732$	10.2548	0.379030
$733$	−2.70287	−0.0998329	−0.0499165	−	0.998753i	$-0.515896\pi$
$733$	−2.70287	−0.0998329	−0.0499165	+	0.998753i	$0.515896\pi$
$734$	27.3736	1.01038
$735$	3.33662	0.123073
$736$	−5.70873	−0.210427
$737$	18.6056	0.685346
$738$	−0.368615	−0.0135689
$739$	−33.5650	−1.23471	−0.617355	−	0.786685i	$-0.711796\pi$
$739$	−33.5650	−1.23471	−0.617355	+	0.786685i	$0.711796\pi$
$740$	−10.3169	−0.379258
$741$	−6.64173	−0.243990
$742$	30.8314	1.13185
$743$	18.9514	0.695260	0.347630	−	0.937632i	$-0.386987\pi$
$743$	18.9514	0.695260	0.347630	+	0.937632i	$0.386987\pi$
$744$	−12.9244	−0.473832
$745$	−8.31227	−0.304538
$746$	−58.4986	−2.14179
$747$	16.0636	0.587737
$748$	17.1438	0.626841
$749$	21.2343	0.775884
$750$	1.76442	0.0644277
$751$	−38.8870	−1.41901	−0.709504	−	0.704701i	$-0.751081\pi$
$751$	−38.8870	−1.41901	−0.709504	+	0.704701i	$0.751081\pi$
$752$	12.2047	0.445061
$753$	9.83652	0.358463
$754$	21.5652	0.785359
$755$	9.30529	0.338654
$756$	−2.13065	−0.0774910
$757$	15.4873	0.562894	0.281447	−	0.959577i	$-0.409186\pi$
$757$	15.4873	0.562894	0.281447	+	0.959577i	$0.409186\pi$
$758$	−58.0125	−2.10711
$759$	−5.55435	−0.201610
$760$	−2.29262	−0.0831620
$761$	6.69680	0.242759	0.121379	−	0.992606i	$-0.461268\pi$
$761$	6.69680	0.242759	0.121379	+	0.992606i	$0.461268\pi$
$762$	11.6917	0.423547
$763$	20.2188	0.731970
$764$	−6.56296	−0.237440
$765$	−2.79159	−0.100930
$766$	−11.2432	−0.406234
$767$	37.7815	1.36421
$768$	19.9755	0.720802
$769$	26.5871	0.958755	0.479377	−	0.877609i	$-0.340862\pi$
$769$	26.5871	0.958755	0.479377	+	0.877609i	$0.340862\pi$
$770$	−18.6307	−0.671404
$771$	0.111824	0.00402725
$772$	−18.4199	−0.662946
$773$	−24.9979	−0.899113	−0.449557	−	0.893252i	$-0.648418\pi$
$773$	−24.9979	−0.899113	−0.449557	+	0.893252i	$0.648418\pi$
$774$	1.33364	0.0479368
$775$	−8.25999	−0.296708
$776$	22.1028	0.793444
$777$	−17.7386	−0.636369
$778$	−15.3034	−0.548653
$779$	0.306105	0.0109674
$780$	5.04605	0.180678
$781$	−47.9207	−1.71474
$782$	4.95909	0.177337
$783$	2.69631	0.0963584
$784$	16.6404	0.594298
$785$	16.5714	0.591460
$786$	36.5684	1.30435
$787$	40.7506	1.45260	0.726301	−	0.687377i	$-0.241238\pi$
$787$	40.7506	1.45260	0.726301	+	0.687377i	$0.241238\pi$
$788$	4.45758	0.158795
$789$	15.1217	0.538348
$790$	−26.4895	−0.942455
$791$	−9.44512	−0.335830
$792$	8.63210	0.306728
$793$	−41.7578	−1.48286
$794$	36.6843	1.30188
$795$	−9.12954	−0.323791
$796$	15.7186	0.557132
$797$	32.6324	1.15590	0.577949	−	0.816073i	$-0.303853\pi$
$797$	32.6324	1.15590	0.577949	+	0.816073i	$0.303853\pi$
$798$	4.94817	0.175163
$799$	−6.83162	−0.241685
$800$	5.67012	0.200469
$801$	−0.609573	−0.0215382
$802$	1.76442	0.0623040
$803$	92.8289	3.27586
$804$	3.75430	0.132404
$805$	−1.92703	−0.0679189
$806$	−66.0638	−2.32700
$807$	14.4806	0.509743
$808$	−5.00754	−0.176165
$809$	−31.1002	−1.09342	−0.546712	−	0.837321i	$-0.684121\pi$
$809$	−31.1002	−1.09342	−0.546712	+	0.837321i	$0.684121\pi$
$810$	1.76442	0.0619956
$811$	−55.0127	−1.93176	−0.965879	−	0.258993i	$-0.916609\pi$
$811$	−55.0127	−1.93176	−0.965879	+	0.258993i	$0.916609\pi$
$812$	−5.74490	−0.201606
$813$	21.8288	0.765568
$814$	−90.2127	−3.16195
$815$	−14.1922	−0.497130
$816$	−13.9222	−0.487373
$817$	−1.10748	−0.0387459
$818$	−25.4093	−0.888416
$819$	8.67604	0.303165
$820$	−0.232564	−0.00812147
$821$	23.4098	0.817008	0.408504	−	0.912757i	$-0.366051\pi$
$821$	23.4098	0.817008	0.408504	+	0.912757i	$0.366051\pi$
$822$	−2.44385	−0.0852390
$823$	31.2160	1.08812	0.544061	−	0.839046i	$-0.316886\pi$
$823$	31.2160	1.08812	0.544061	+	0.839046i	$0.316886\pi$
$824$	−5.44951	−0.189843
$825$	5.51678	0.192070
$826$	−28.1477	−0.979382
$827$	45.2103	1.57212	0.786059	−	0.618152i	$-0.212118\pi$
$827$	45.2103	1.57212	0.786059	+	0.618152i	$0.212118\pi$
$828$	−1.12078	−0.0389497
$829$	−9.91807	−0.344469	−0.172234	−	0.985056i	$-0.555099\pi$
$829$	−9.91807	−0.344469	−0.172234	+	0.985056i	$0.555099\pi$
$830$	28.3430	0.983801
$831$	−16.3611	−0.567559
$832$	0.136524	0.00473311
$833$	−9.31447	−0.322727
$834$	−9.07730	−0.314321
$835$	0.771018	0.0266822
$836$	8.99823	0.311210
$837$	−8.25999	−0.285507
$838$	−35.3631	−1.22160
$839$	8.20024	0.283104	0.141552	−	0.989931i	$-0.454791\pi$
$839$	8.20024	0.283104	0.141552	+	0.989931i	$0.454791\pi$
$840$	2.99483	0.103331
$841$	−21.7299	−0.749307
$842$	−20.9252	−0.721132
$843$	−12.3893	−0.426711
$844$	25.2547	0.869303
$845$	−7.54759	−0.259645
$846$	4.31793	0.148454
$847$	−37.1982	−1.27814
$848$	−45.5307	−1.56353
$849$	12.2457	0.420271
$850$	−4.92555	−0.168945
$851$	−9.33097	−0.319862
$852$	−9.66962	−0.331276
$853$	17.0009	0.582101	0.291050	−	0.956708i	$-0.405995\pi$
$853$	17.0009	0.582101	0.291050	+	0.956708i	$0.405995\pi$
$854$	31.1101	1.06457
$855$	−1.46521	−0.0501092
$856$	−17.3591	−0.593323
$857$	−8.32355	−0.284327	−0.142163	−	0.989843i	$-0.545406\pi$
$857$	−8.32355	−0.284327	−0.142163	+	0.989843i	$0.545406\pi$
$858$	44.1234	1.50635
$859$	−18.0073	−0.614402	−0.307201	−	0.951645i	$-0.599392\pi$
$859$	−18.0073	−0.614402	−0.307201	+	0.951645i	$0.599392\pi$
$860$	0.841411	0.0286919
$861$	−0.399863	−0.0136273
$862$	33.6544	1.14627
$863$	35.0744	1.19395	0.596974	−	0.802261i	$-0.296370\pi$
$863$	35.0744	1.19395	0.596974	+	0.802261i	$0.296370\pi$
$864$	5.67012	0.192901
$865$	−4.53635	−0.154240
$866$	1.52003	0.0516527
$867$	−9.20704	−0.312687
$868$	17.5992	0.597354
$869$	−82.8241	−2.80961
$870$	4.75744	0.161292
$871$	−15.2876	−0.518000
$872$	−16.5290	−0.559742
$873$	14.1259	0.478089
$874$	2.60286	0.0880432
$875$	1.91400	0.0647049
$876$	18.7313	0.632873
$877$	−0.00729731	−0.000246413 0	−0.000123206	−	1.00000i	$-0.500039\pi$
$877$	−0.00729731	−0.000246413 0	−0.000123206		1.00000i	$0.500039\pi$
$878$	9.12978	0.308115
$879$	29.9363	1.00973
$880$	27.5132	0.927470
$881$	18.2675	0.615448	0.307724	−	0.951476i	$-0.400433\pi$
$881$	18.2675	0.615448	0.307724	+	0.951476i	$0.400433\pi$
$882$	5.88722	0.198233
$883$	−20.6280	−0.694187	−0.347094	−	0.937830i	$-0.612831\pi$
$883$	−20.6280	−0.694187	−0.347094	+	0.937830i	$0.612831\pi$
$884$	−14.0865	−0.473780
$885$	8.33486	0.280173
$886$	−27.9122	−0.937729
$887$	8.29964	0.278675	0.139337	−	0.990245i	$-0.455503\pi$
$887$	8.29964	0.278675	0.139337	+	0.990245i	$0.455503\pi$
$888$	14.5014	0.486635
$889$	12.6829	0.425369
$890$	−1.07555	−0.0360524
$891$	5.51678	0.184819
$892$	15.7990	0.528989
$893$	−3.58569	−0.119991
$894$	−14.6664	−0.490517
$895$	−16.2572	−0.543418
$896$	21.6034	0.721720
$897$	4.56382	0.152381
$898$	42.1480	1.40650
$899$	−22.2715	−0.742797
$900$	1.11320	0.0371065
$901$	25.4859	0.849058
$902$	−2.03357	−0.0677105
$903$	1.44670	0.0481431
$904$	7.72143	0.256811
$905$	−8.74920	−0.290833
$906$	16.4185	0.545467
$907$	5.84545	0.194095	0.0970475	−	0.995280i	$-0.469060\pi$
$907$	5.84545	0.194095	0.0970475	+	0.995280i	$0.469060\pi$
$908$	−15.1335	−0.502224
$909$	−3.20032	−0.106148
$910$	15.3082	0.507462
$911$	19.8540	0.657793	0.328896	−	0.944366i	$-0.393323\pi$
$911$	19.8540	0.657793	0.328896	+	0.944366i	$0.393323\pi$
$912$	−7.30729	−0.241968
$913$	88.6194	2.93287
$914$	51.1933	1.69332
$915$	−9.21208	−0.304542
$916$	4.58841	0.151605
$917$	39.6683	1.30996
$918$	−4.92555	−0.162567
$919$	0.484043	0.0159671	0.00798355	−	0.999968i	$-0.497459\pi$
$919$	0.484043	0.0159671	0.00798355	+	0.999968i	$0.497459\pi$
$920$	1.57536	0.0519380
$921$	20.3577	0.670810
$922$	−51.9454	−1.71073
$923$	39.3748	1.29604
$924$	−11.7543	−0.386689
$925$	9.26785	0.304725
$926$	57.0765	1.87565
$927$	−3.48278	−0.114390
$928$	15.2884	0.501867
$929$	−50.1817	−1.64641	−0.823204	−	0.567746i	$-0.807815\pi$
$929$	−50.1817	−1.64641	−0.823204	+	0.567746i	$0.807815\pi$
$930$	−14.5741	−0.477905
$931$	−4.88886	−0.160226
$932$	15.8415	0.518907
$933$	12.3998	0.405951
$934$	6.02995	0.197306
$935$	−15.4006	−0.503652
$936$	−7.09270	−0.231832
$937$	−8.69810	−0.284154	−0.142077	−	0.989856i	$-0.545378\pi$
$937$	−8.69810	−0.284154	−0.142077	+	0.989856i	$0.545378\pi$
$938$	11.3894	0.371878
$939$	−1.28340	−0.0418823
$940$	2.72423	0.0888546
$941$	51.1382	1.66706	0.833529	−	0.552476i	$-0.186317\pi$
$941$	51.1382	1.66706	0.833529	+	0.552476i	$0.186317\pi$
$942$	29.2391	0.952660
$943$	−0.210338	−0.00684956
$944$	41.5675	1.35291
$945$	1.91400	0.0622623
$946$	7.35742	0.239210
$947$	−56.4896	−1.83566	−0.917832	−	0.396968i	$-0.870062\pi$
$947$	−56.4896	−1.83566	−0.917832	+	0.396968i	$0.870062\pi$
$948$	−16.7125	−0.542798
$949$	−76.2743	−2.47597
$950$	−2.58526	−0.0838768
$951$	21.0435	0.682381
$952$	−8.36033	−0.270960
$953$	−10.6871	−0.346190	−0.173095	−	0.984905i	$-0.555377\pi$
$953$	−10.6871	−0.346190	−0.173095	+	0.984905i	$0.555377\pi$
$954$	−16.1084	−0.521528
$955$	5.89561	0.190777
$956$	−22.8651	−0.739511
$957$	14.8750	0.480839
$958$	36.7785	1.18826
$959$	−2.65101	−0.0856057
$960$	0.0301181	0.000972057 0
$961$	37.2275	1.20089
$962$	74.1246	2.38987
$963$	−11.0942	−0.357507
$964$	5.70599	0.183778
$965$	16.5469	0.532662
$966$	−3.40010	−0.109396
$967$	9.65926	0.310621	0.155310	−	0.987866i	$-0.450362\pi$
$967$	9.65926	0.310621	0.155310	+	0.987866i	$0.450362\pi$
$968$	30.4097	0.977404
$969$	4.09027	0.131398
$970$	24.9241	0.800263
$971$	−59.9749	−1.92469	−0.962343	−	0.271840i	$-0.912368\pi$
$971$	−59.9749	−1.92469	−0.962343	+	0.271840i	$0.912368\pi$
$972$	1.11320	0.0357057
$973$	−9.84679	−0.315673
$974$	−47.2464	−1.51387
$975$	−4.53295	−0.145170
$976$	−45.9424	−1.47058
$977$	32.8795	1.05191	0.525954	−	0.850513i	$-0.323708\pi$
$977$	32.8795	1.05191	0.525954	+	0.850513i	$0.323708\pi$
$978$	−25.0410	−0.800723
$979$	−3.36288	−0.107478
$980$	3.71431	0.118649
$981$	−10.5637	−0.337272
$982$	−50.4446	−1.60975
$983$	−27.2072	−0.867776	−0.433888	−	0.900967i	$-0.642859\pi$
$983$	−27.2072	−0.867776	−0.433888	+	0.900967i	$0.642859\pi$
$984$	0.326890	0.0104209
$985$	−4.00431	−0.127588
$986$	−13.2808	−0.422947
$987$	4.68396	0.149092
$988$	−7.39354	−0.235220
$989$	0.761000	0.0241984
$990$	9.73394	0.309365
$991$	15.2003	0.482852	0.241426	−	0.970419i	$-0.422385\pi$
$991$	15.2003	0.482852	0.241426	+	0.970419i	$0.422385\pi$
$992$	−46.8351	−1.48702
$993$	6.72481	0.213406
$994$	−29.3347	−0.930441
$995$	−14.1203	−0.447643
$996$	17.8819	0.566611
$997$	22.8233	0.722820	0.361410	−	0.932407i	$-0.382295\pi$
$997$	22.8233	0.722820	0.361410	+	0.932407i	$0.382295\pi$
$998$	−30.3165	−0.959654
$999$	9.26785	0.293222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.9	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.9	✓	39	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.76442 q^{2} +1.00000 q^{3} +1.11320 q^{4} -1.00000 q^{5} -1.76442 q^{6} -1.91400 q^{7} +1.56470 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.76442 q^{2} +1.00000 q^{3} +1.11320 q^{4} -1.00000 q^{5} -1.76442 q^{6} -1.91400 q^{7} +1.56470 q^{8} +1.00000 q^{9} +1.76442 q^{10} +5.51678 q^{11} +1.11320 q^{12} -4.53295 q^{13} +3.37710 q^{14} -1.00000 q^{15} -4.98719 q^{16} +2.79159 q^{17} -1.76442 q^{18} +1.46521 q^{19} -1.11320 q^{20} -1.91400 q^{21} -9.73394 q^{22} -1.00681 q^{23} +1.56470 q^{24} +1.00000 q^{25} +7.99804 q^{26} +1.00000 q^{27} -2.13065 q^{28} +2.69631 q^{29} +1.76442 q^{30} -8.25999 q^{31} +5.67012 q^{32} +5.51678 q^{33} -4.92555 q^{34} +1.91400 q^{35} +1.11320 q^{36} +9.26785 q^{37} -2.58526 q^{38} -4.53295 q^{39} -1.56470 q^{40} +0.208915 q^{41} +3.37710 q^{42} -0.755852 q^{43} +6.14125 q^{44} -1.00000 q^{45} +1.77644 q^{46} -2.44722 q^{47} -4.98719 q^{48} -3.33662 q^{49} -1.76442 q^{50} +2.79159 q^{51} -5.04605 q^{52} +9.12954 q^{53} -1.76442 q^{54} -5.51678 q^{55} -2.99483 q^{56} +1.46521 q^{57} -4.75744 q^{58} -8.33486 q^{59} -1.11320 q^{60} +9.21208 q^{61} +14.5741 q^{62} -1.91400 q^{63} -0.0301181 q^{64} +4.53295 q^{65} -9.73394 q^{66} +3.37255 q^{67} +3.10758 q^{68} -1.00681 q^{69} -3.37710 q^{70} -8.68636 q^{71} +1.56470 q^{72} +16.8266 q^{73} -16.3524 q^{74} +1.00000 q^{75} +1.63107 q^{76} -10.5591 q^{77} +7.99804 q^{78} -15.0131 q^{79} +4.98719 q^{80} +1.00000 q^{81} -0.368615 q^{82} +16.0636 q^{83} -2.13065 q^{84} -2.79159 q^{85} +1.33364 q^{86} +2.69631 q^{87} +8.63210 q^{88} -0.609573 q^{89} +1.76442 q^{90} +8.67604 q^{91} -1.12078 q^{92} -8.25999 q^{93} +4.31793 q^{94} -1.46521 q^{95} +5.67012 q^{96} +14.1259 q^{97} +5.88722 q^{98} +5.51678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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