LMFDB - Embedded newform 6005.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9501664138$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41534 q^{2} +2.54592 q^{3} +3.83384 q^{4} -1.00000 q^{5} -6.14926 q^{6} -0.649970 q^{7} -4.42935 q^{8} +3.48173 q^{9} +O(q^{10})$	\(q-2.41534 q^{2} +2.54592 q^{3} +3.83384 q^{4} -1.00000 q^{5} -6.14926 q^{6} -0.649970 q^{7} -4.42935 q^{8} +3.48173 q^{9} +2.41534 q^{10} +2.60440 q^{11} +9.76067 q^{12} -1.35325 q^{13} +1.56990 q^{14} -2.54592 q^{15} +3.03067 q^{16} +0.548495 q^{17} -8.40953 q^{18} -3.64119 q^{19} -3.83384 q^{20} -1.65477 q^{21} -6.29050 q^{22} -7.35794 q^{23} -11.2768 q^{24} +1.00000 q^{25} +3.26855 q^{26} +1.22644 q^{27} -2.49188 q^{28} +3.66627 q^{29} +6.14926 q^{30} +2.02141 q^{31} +1.53861 q^{32} +6.63061 q^{33} -1.32480 q^{34} +0.649970 q^{35} +13.3484 q^{36} +3.56324 q^{37} +8.79469 q^{38} -3.44527 q^{39} +4.42935 q^{40} -11.3995 q^{41} +3.99683 q^{42} +9.18007 q^{43} +9.98487 q^{44} -3.48173 q^{45} +17.7719 q^{46} +7.78559 q^{47} +7.71585 q^{48} -6.57754 q^{49} -2.41534 q^{50} +1.39643 q^{51} -5.18815 q^{52} -1.13133 q^{53} -2.96226 q^{54} -2.60440 q^{55} +2.87894 q^{56} -9.27018 q^{57} -8.85528 q^{58} +1.74890 q^{59} -9.76067 q^{60} -10.1533 q^{61} -4.88239 q^{62} -2.26302 q^{63} -9.77760 q^{64} +1.35325 q^{65} -16.0151 q^{66} -10.8059 q^{67} +2.10284 q^{68} -18.7328 q^{69} -1.56990 q^{70} +4.49730 q^{71} -15.4218 q^{72} +5.49103 q^{73} -8.60642 q^{74} +2.54592 q^{75} -13.9597 q^{76} -1.69278 q^{77} +8.32148 q^{78} -11.3104 q^{79} -3.03067 q^{80} -7.32276 q^{81} +27.5335 q^{82} +9.61816 q^{83} -6.34414 q^{84} -0.548495 q^{85} -22.1729 q^{86} +9.33405 q^{87} -11.5358 q^{88} -9.94983 q^{89} +8.40953 q^{90} +0.879571 q^{91} -28.2092 q^{92} +5.14636 q^{93} -18.8048 q^{94} +3.64119 q^{95} +3.91719 q^{96} -5.78416 q^{97} +15.8870 q^{98} +9.06781 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) $ 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * 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 $

$2$	−2.41534	−1.70790	−0.853950	−	0.520355i	$-0.825800\pi$
$2$	−2.41534	−1.70790	−0.853950	+	0.520355i	$0.825800\pi$
$3$	2.54592	1.46989	0.734945	−	0.678127i	$-0.237208\pi$
$3$	2.54592	1.46989	0.734945	+	0.678127i	$0.237208\pi$
$4$	3.83384	1.91692
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.14926	−2.51042
$7$	−0.649970	−0.245666	−0.122833	−	0.992427i	$-0.539198\pi$
$7$	−0.649970	−0.245666	−0.122833	+	0.992427i	$0.539198\pi$
$8$	−4.42935	−1.56601
$9$	3.48173	1.16058
$10$	2.41534	0.763796
$11$	2.60440	0.785257	0.392628	−	0.919697i	$-0.371566\pi$
$11$	2.60440	0.785257	0.392628	+	0.919697i	$0.371566\pi$
$12$	9.76067	2.81766
$13$	−1.35325	−0.375324	−0.187662	−	0.982234i	$-0.560091\pi$
$13$	−1.35325	−0.375324	−0.187662	+	0.982234i	$0.560091\pi$
$14$	1.56990	0.419572
$15$	−2.54592	−0.657355
$16$	3.03067	0.757667
$17$	0.548495	0.133030	0.0665148	−	0.997785i	$-0.478812\pi$
$17$	0.548495	0.133030	0.0665148	+	0.997785i	$0.478812\pi$
$18$	−8.40953	−1.98215
$19$	−3.64119	−0.835346	−0.417673	−	0.908597i	$-0.637154\pi$
$19$	−3.64119	−0.835346	−0.417673	+	0.908597i	$0.637154\pi$
$20$	−3.83384	−0.857273
$21$	−1.65477	−0.361101
$22$	−6.29050	−1.34114
$23$	−7.35794	−1.53424	−0.767118	−	0.641506i	$-0.778310\pi$
$23$	−7.35794	−1.53424	−0.767118	+	0.641506i	$0.778310\pi$
$24$	−11.2768	−2.30186
$25$	1.00000	0.200000
$26$	3.26855	0.641015
$27$	1.22644	0.236028
$28$	−2.49188	−0.470922
$29$	3.66627	0.680810	0.340405	−	0.940279i	$-0.389436\pi$
$29$	3.66627	0.680810	0.340405	+	0.940279i	$0.389436\pi$
$30$	6.14926	1.12270
$31$	2.02141	0.363056	0.181528	−	0.983386i	$-0.441896\pi$
$31$	2.02141	0.363056	0.181528	+	0.983386i	$0.441896\pi$
$32$	1.53861	0.271991
$33$	6.63061	1.15424
$34$	−1.32480	−0.227201
$35$	0.649970	0.109865
$36$	13.3484	2.22473
$37$	3.56324	0.585793	0.292897	−	0.956144i	$-0.405381\pi$
$37$	3.56324	0.585793	0.292897	+	0.956144i	$0.405381\pi$
$38$	8.79469	1.42669
$39$	−3.44527	−0.551684
$40$	4.42935	0.700341
$41$	−11.3995	−1.78030	−0.890149	−	0.455669i	$-0.849400\pi$
$41$	−11.3995	−1.78030	−0.890149	+	0.455669i	$0.849400\pi$
$42$	3.99683	0.616725
$43$	9.18007	1.39995	0.699974	−	0.714168i	$-0.253195\pi$
$43$	9.18007	1.39995	0.699974	+	0.714168i	$0.253195\pi$
$44$	9.98487	1.50528
$45$	−3.48173	−0.519025
$46$	17.7719	2.62032
$47$	7.78559	1.13564	0.567822	−	0.823151i	$-0.307786\pi$
$47$	7.78559	1.13564	0.567822	+	0.823151i	$0.307786\pi$
$48$	7.71585	1.11369
$49$	−6.57754	−0.939648
$50$	−2.41534	−0.341580
$51$	1.39643	0.195539
$52$	−5.18815	−0.719466
$53$	−1.13133	−0.155400	−0.0777001	−	0.996977i	$-0.524758\pi$
$53$	−1.13133	−0.155400	−0.0777001	+	0.996977i	$0.524758\pi$
$54$	−2.96226	−0.403112
$55$	−2.60440	−0.351177
$56$	2.87894	0.384715
$57$	−9.27018	−1.22787
$58$	−8.85528	−1.16276
$59$	1.74890	0.227687	0.113844	−	0.993499i	$-0.463684\pi$
$59$	1.74890	0.227687	0.113844	+	0.993499i	$0.463684\pi$
$60$	−9.76067	−1.26010
$61$	−10.1533	−1.29999	−0.649996	−	0.759938i	$-0.725229\pi$
$61$	−10.1533	−1.29999	−0.649996	+	0.759938i	$0.725229\pi$
$62$	−4.88239	−0.620064
$63$	−2.26302	−0.285113
$64$	−9.77760	−1.22220
$65$	1.35325	0.167850
$66$	−16.0151	−1.97133
$67$	−10.8059	−1.32015	−0.660076	−	0.751199i	$-0.729476\pi$
$67$	−10.8059	−1.32015	−0.660076	+	0.751199i	$0.729476\pi$
$68$	2.10284	0.255007
$69$	−18.7328	−2.25516
$70$	−1.56990	−0.187638
$71$	4.49730	0.533732	0.266866	−	0.963734i	$-0.414012\pi$
$71$	4.49730	0.533732	0.266866	+	0.963734i	$0.414012\pi$
$72$	−15.4218	−1.81747
$73$	5.49103	0.642676	0.321338	−	0.946965i	$-0.395867\pi$
$73$	5.49103	0.642676	0.321338	+	0.946965i	$0.395867\pi$
$74$	−8.60642	−1.00048
$75$	2.54592	0.293978
$76$	−13.9597	−1.60129
$77$	−1.69278	−0.192911
$78$	8.32148	0.942222
$79$	−11.3104	−1.27251	−0.636257	−	0.771477i	$-0.719518\pi$
$79$	−11.3104	−1.27251	−0.636257	+	0.771477i	$0.719518\pi$
$80$	−3.03067	−0.338839
$81$	−7.32276	−0.813640
$82$	27.5335	3.04057
$83$	9.61816	1.05573	0.527865	−	0.849328i	$-0.322993\pi$
$83$	9.61816	1.05573	0.527865	+	0.849328i	$0.322993\pi$
$84$	−6.34414	−0.692203
$85$	−0.548495	−0.0594927
$86$	−22.1729	−2.39097
$87$	9.33405	1.00072
$88$	−11.5358	−1.22972
$89$	−9.94983	−1.05468	−0.527340	−	0.849654i	$-0.676811\pi$
$89$	−9.94983	−1.05468	−0.527340	+	0.849654i	$0.676811\pi$
$90$	8.40953	0.886443
$91$	0.879571	0.0922041
$92$	−28.2092	−2.94101
$93$	5.14636	0.533653
$94$	−18.8048	−1.93957
$95$	3.64119	0.373578
$96$	3.91719	0.399796
$97$	−5.78416	−0.587292	−0.293646	−	0.955914i	$-0.594869\pi$
$97$	−5.78416	−0.587292	−0.293646	+	0.955914i	$0.594869\pi$
$98$	15.8870	1.60483
$99$	9.06781	0.911350
$100$	3.83384	0.383384
$101$	11.2396	1.11838	0.559190	−	0.829040i	$-0.311112\pi$
$101$	11.2396	1.11838	0.559190	+	0.829040i	$0.311112\pi$
$102$	−3.37284	−0.333961
$103$	10.0969	0.994881	0.497441	−	0.867498i	$-0.334273\pi$
$103$	10.0969	0.994881	0.497441	+	0.867498i	$0.334273\pi$
$104$	5.99401	0.587761
$105$	1.65477	0.161489
$106$	2.73254	0.265408
$107$	−8.69078	−0.840169	−0.420085	−	0.907485i	$-0.638000\pi$
$107$	−8.69078	−0.840169	−0.420085	+	0.907485i	$0.638000\pi$
$108$	4.70197	0.452447
$109$	−6.58037	−0.630285	−0.315142	−	0.949044i	$-0.602052\pi$
$109$	−6.58037	−0.630285	−0.315142	+	0.949044i	$0.602052\pi$
$110$	6.29050	0.599776
$111$	9.07174	0.861051
$112$	−1.96984	−0.186133
$113$	−8.97701	−0.844486	−0.422243	−	0.906483i	$-0.638757\pi$
$113$	−8.97701	−0.844486	−0.422243	+	0.906483i	$0.638757\pi$
$114$	22.3906	2.09707
$115$	7.35794	0.686132
$116$	14.0559	1.30506
$117$	−4.71164	−0.435591
$118$	−4.22418	−0.388867
$119$	−0.356505	−0.0326808
$120$	11.2768	1.02942
$121$	−4.21709	−0.383372
$122$	24.5235	2.22026
$123$	−29.0222	−2.61684
$124$	7.74978	0.695951
$125$	−1.00000	−0.0894427
$126$	5.46595	0.486945
$127$	−8.50778	−0.754943	−0.377472	−	0.926021i	$-0.623206\pi$
$127$	−8.50778	−0.754943	−0.377472	+	0.926021i	$0.623206\pi$
$128$	20.5390	1.81540
$129$	23.3718	2.05777
$130$	−3.26855	−0.286671
$131$	16.2365	1.41859	0.709294	−	0.704913i	$-0.249014\pi$
$131$	16.2365	1.41859	0.709294	+	0.704913i	$0.249014\pi$
$132$	25.4207	2.21259
$133$	2.36666	0.205216
$134$	26.0999	2.25469
$135$	−1.22644	−0.105555
$136$	−2.42948	−0.208326
$137$	−18.7107	−1.59856	−0.799282	−	0.600956i	$-0.794787\pi$
$137$	−18.7107	−1.59856	−0.799282	+	0.600956i	$0.794787\pi$
$138$	45.2459	3.85158
$139$	−9.64975	−0.818481	−0.409241	−	0.912426i	$-0.634206\pi$
$139$	−9.64975	−0.818481	−0.409241	+	0.912426i	$0.634206\pi$
$140$	2.49188	0.210603
$141$	19.8215	1.66927
$142$	−10.8625	−0.911560
$143$	−3.52440	−0.294726
$144$	10.5520	0.879330
$145$	−3.66627	−0.304467
$146$	−13.2627	−1.09763
$147$	−16.7459	−1.38118
$148$	13.6609	1.12292
$149$	−9.78334	−0.801483	−0.400741	−	0.916191i	$-0.631247\pi$
$149$	−9.78334	−0.801483	−0.400741	+	0.916191i	$0.631247\pi$
$150$	−6.14926	−0.502085
$151$	0.245726	0.0199969	0.00999846	−	0.999950i	$-0.496817\pi$
$151$	0.245726	0.0199969	0.00999846	+	0.999950i	$0.496817\pi$
$152$	16.1281	1.30816
$153$	1.90971	0.154391
$154$	4.08864	0.329472
$155$	−2.02141	−0.162364
$156$	−13.2086	−1.05754
$157$	−4.38577	−0.350022	−0.175011	−	0.984566i	$-0.555996\pi$
$157$	−4.38577	−0.350022	−0.175011	+	0.984566i	$0.555996\pi$
$158$	27.3183	2.17333
$159$	−2.88028	−0.228421
$160$	−1.53861	−0.121638
$161$	4.78244	0.376909
$162$	17.6869	1.38962
$163$	16.8697	1.32134	0.660669	−	0.750677i	$-0.270273\pi$
$163$	16.8697	1.32134	0.660669	+	0.750677i	$0.270273\pi$
$164$	−43.7038	−3.41269
$165$	−6.63061	−0.516192
$166$	−23.2311	−1.80308
$167$	−4.17601	−0.323149	−0.161575	−	0.986860i	$-0.551657\pi$
$167$	−4.17601	−0.323149	−0.161575	+	0.986860i	$0.551657\pi$
$168$	7.32957	0.565488
$169$	−11.1687	−0.859132
$170$	1.32480	0.101607
$171$	−12.6776	−0.969481
$172$	35.1950	2.68359
$173$	10.2632	0.780296	0.390148	−	0.920752i	$-0.372424\pi$
$173$	10.2632	0.780296	0.390148	+	0.920752i	$0.372424\pi$
$174$	−22.5449	−1.70912
$175$	−0.649970	−0.0491331
$176$	7.89308	0.594963
$177$	4.45257	0.334675
$178$	24.0322	1.80129
$179$	18.6191	1.39166	0.695828	−	0.718209i	$-0.255038\pi$
$179$	18.6191	1.39166	0.695828	+	0.718209i	$0.255038\pi$
$180$	−13.3484	−0.994930
$181$	10.9258	0.812106	0.406053	−	0.913850i	$-0.366905\pi$
$181$	10.9258	0.812106	0.406053	+	0.913850i	$0.366905\pi$
$182$	−2.12446	−0.157475
$183$	−25.8494	−1.91084
$184$	32.5909	2.40263
$185$	−3.56324	−0.261975
$186$	−12.4302	−0.911426
$187$	1.42850	0.104462
$188$	29.8487	2.17694
$189$	−0.797147	−0.0579839
$190$	−8.79469	−0.638034
$191$	−11.4907	−0.831440	−0.415720	−	0.909493i	$-0.636470\pi$
$191$	−11.4907	−0.831440	−0.415720	+	0.909493i	$0.636470\pi$
$192$	−24.8930	−1.79650
$193$	−21.6226	−1.55643	−0.778213	−	0.628000i	$-0.783874\pi$
$193$	−21.6226	−1.55643	−0.778213	+	0.628000i	$0.783874\pi$
$194$	13.9707	1.00304
$195$	3.44527	0.246721
$196$	−25.2173	−1.80123
$197$	11.4908	0.818687	0.409344	−	0.912380i	$-0.365758\pi$
$197$	11.4908	0.818687	0.409344	+	0.912380i	$0.365758\pi$
$198$	−21.9018	−1.55649
$199$	−16.3365	−1.15806	−0.579032	−	0.815305i	$-0.696569\pi$
$199$	−16.3365	−1.15806	−0.579032	+	0.815305i	$0.696569\pi$
$200$	−4.42935	−0.313202
$201$	−27.5110	−1.94048
$202$	−27.1473	−1.91008
$203$	−2.38297	−0.167252
$204$	5.35368	0.374833
$205$	11.3995	0.796174
$206$	−24.3875	−1.69916
$207$	−25.6183	−1.78060
$208$	−4.10125	−0.284371
$209$	−9.48312	−0.655961
$210$	−3.99683	−0.275808
$211$	−23.3676	−1.60869	−0.804345	−	0.594163i	$-0.797483\pi$
$211$	−23.3676	−1.60869	−0.804345	+	0.594163i	$0.797483\pi$
$212$	−4.33735	−0.297890
$213$	11.4498	0.784527
$214$	20.9911	1.43492
$215$	−9.18007	−0.626076
$216$	−5.43231	−0.369622
$217$	−1.31386	−0.0891905
$218$	15.8938	1.07646
$219$	13.9797	0.944663
$220$	−9.98487	−0.673180
$221$	−0.742251	−0.0499292
$222$	−21.9113	−1.47059
$223$	−12.6861	−0.849527	−0.424763	−	0.905304i	$-0.639643\pi$
$223$	−12.6861	−0.849527	−0.424763	+	0.905304i	$0.639643\pi$
$224$	−1.00005	−0.0668187
$225$	3.48173	0.232115
$226$	21.6825	1.44230
$227$	−26.2881	−1.74480	−0.872400	−	0.488793i	$-0.837437\pi$
$227$	−26.2881	−1.74480	−0.872400	+	0.488793i	$0.837437\pi$
$228$	−35.5404	−2.35372
$229$	−15.9102	−1.05138	−0.525688	−	0.850677i	$-0.676192\pi$
$229$	−15.9102	−1.05138	−0.525688	+	0.850677i	$0.676192\pi$
$230$	−17.7719	−1.17184
$231$	−4.30970	−0.283557
$232$	−16.2392	−1.06616
$233$	15.5351	1.01774	0.508868	−	0.860845i	$-0.330064\pi$
$233$	15.5351	1.01774	0.508868	+	0.860845i	$0.330064\pi$
$234$	11.3802	0.743947
$235$	−7.78559	−0.507876
$236$	6.70501	0.436459
$237$	−28.7953	−1.87046
$238$	0.861080	0.0558155
$239$	10.5320	0.681260	0.340630	−	0.940198i	$-0.389360\pi$
$239$	10.5320	0.681260	0.340630	+	0.940198i	$0.389360\pi$
$240$	−7.71585	−0.498056
$241$	5.34232	0.344129	0.172065	−	0.985086i	$-0.444956\pi$
$241$	5.34232	0.344129	0.172065	+	0.985086i	$0.444956\pi$
$242$	10.1857	0.654761
$243$	−22.3225	−1.43199
$244$	−38.9260	−2.49198
$245$	6.57754	0.420224
$246$	70.0983	4.46930
$247$	4.92743	0.313525
$248$	−8.95354	−0.568550
$249$	24.4871	1.55181
$250$	2.41534	0.152759
$251$	−30.4516	−1.92209	−0.961044	−	0.276397i	$-0.910860\pi$
$251$	−30.4516	−1.92209	−0.961044	+	0.276397i	$0.910860\pi$
$252$	−8.67606	−0.546540
$253$	−19.1630	−1.20477
$254$	20.5491	1.28937
$255$	−1.39643	−0.0874476
$256$	−30.0533	−1.87833
$257$	5.18549	0.323462	0.161731	−	0.986835i	$-0.448292\pi$
$257$	5.18549	0.323462	0.161731	+	0.986835i	$0.448292\pi$
$258$	−56.4506	−3.51446
$259$	−2.31600	−0.143909
$260$	5.18815	0.321755
$261$	12.7650	0.790131
$262$	−39.2165	−2.42280
$263$	−10.1000	−0.622790	−0.311395	−	0.950281i	$-0.600796\pi$
$263$	−10.1000	−0.622790	−0.311395	+	0.950281i	$0.600796\pi$
$264$	−29.3693	−1.80755
$265$	1.13133	0.0694971
$266$	−5.71628	−0.350488
$267$	−25.3315	−1.55026
$268$	−41.4282	−2.53063
$269$	32.2486	1.96623	0.983117	−	0.182979i	$-0.0585739\pi$
$269$	32.2486	1.96623	0.983117	+	0.182979i	$0.0585739\pi$
$270$	2.96226	0.180277
$271$	−14.0294	−0.852226	−0.426113	−	0.904670i	$-0.640117\pi$
$271$	−14.0294	−0.852226	−0.426113	+	0.904670i	$0.640117\pi$
$272$	1.66231	0.100792
$273$	2.23932	0.135530
$274$	45.1926	2.73019
$275$	2.60440	0.157051
$276$	−71.8184	−4.32296
$277$	25.4561	1.52951	0.764755	−	0.644321i	$-0.222860\pi$
$277$	25.4561	1.52951	0.764755	+	0.644321i	$0.222860\pi$
$278$	23.3074	1.39788
$279$	7.03801	0.421354
$280$	−2.87894	−0.172050
$281$	31.6816	1.88997	0.944983	−	0.327120i	$-0.106078\pi$
$281$	31.6816	1.88997	0.944983	+	0.327120i	$0.106078\pi$
$282$	−47.8756	−2.85095
$283$	26.6815	1.58605	0.793025	−	0.609189i	$-0.208505\pi$
$283$	26.6815	1.58605	0.793025	+	0.609189i	$0.208505\pi$
$284$	17.2420	1.02312
$285$	9.27018	0.549118
$286$	8.51262	0.503362
$287$	7.40932	0.437358
$288$	5.35702	0.315666
$289$	−16.6992	−0.982303
$290$	8.85528	0.520000
$291$	−14.7260	−0.863255
$292$	21.0517	1.23196
$293$	−17.8700	−1.04398	−0.521989	−	0.852952i	$-0.674810\pi$
$293$	−17.8700	−1.04398	−0.521989	+	0.852952i	$0.674810\pi$
$294$	40.4470	2.35892
$295$	−1.74890	−0.101825
$296$	−15.7828	−0.917358
$297$	3.19413	0.185342
$298$	23.6300	1.36885
$299$	9.95713	0.575836
$300$	9.76067	0.563533
$301$	−5.96677	−0.343919
$302$	−0.593511	−0.0341527
$303$	28.6151	1.64389
$304$	−11.0352	−0.632914
$305$	10.1533	0.581374
$306$	−4.61259	−0.263684
$307$	21.3267	1.21718	0.608588	−	0.793486i	$-0.291736\pi$
$307$	21.3267	1.21718	0.608588	+	0.793486i	$0.291736\pi$
$308$	−6.48987	−0.369794
$309$	25.7060	1.46237
$310$	4.88239	0.277301
$311$	−33.5826	−1.90430	−0.952148	−	0.305639i	$-0.901130\pi$
$311$	−33.5826	−1.90430	−0.952148	+	0.305639i	$0.901130\pi$
$312$	15.2603	0.863944
$313$	−21.0664	−1.19074	−0.595372	−	0.803450i	$-0.702995\pi$
$313$	−21.0664	−1.19074	−0.595372	+	0.803450i	$0.702995\pi$
$314$	10.5931	0.597803
$315$	2.26302	0.127507
$316$	−43.3621	−2.43931
$317$	−7.48574	−0.420441	−0.210221	−	0.977654i	$-0.567418\pi$
$317$	−7.48574	−0.420441	−0.210221	+	0.977654i	$0.567418\pi$
$318$	6.95685	0.390121
$319$	9.54845	0.534611
$320$	9.77760	0.546584
$321$	−22.1261	−1.23496
$322$	−11.5512	−0.643723
$323$	−1.99717	−0.111126
$324$	−28.0743	−1.55968
$325$	−1.35325	−0.0750648
$326$	−40.7460	−2.25671
$327$	−16.7531	−0.926449
$328$	50.4922	2.78797
$329$	−5.06040	−0.278989
$330$	16.0151	0.881604
$331$	11.1700	0.613960	0.306980	−	0.951716i	$-0.400682\pi$
$331$	11.1700	0.613960	0.306980	+	0.951716i	$0.400682\pi$
$332$	36.8745	2.02375
$333$	12.4062	0.679857
$334$	10.0865	0.551907
$335$	10.8059	0.590390
$336$	−5.01507	−0.273595
$337$	7.69421	0.419130	0.209565	−	0.977795i	$-0.432795\pi$
$337$	7.69421	0.419130	0.209565	+	0.977795i	$0.432795\pi$
$338$	26.9762	1.46731
$339$	−22.8548	−1.24130
$340$	−2.10284	−0.114043
$341$	5.26457	0.285093
$342$	30.6207	1.65578
$343$	8.82499	0.476505
$344$	−40.6617	−2.19233
$345$	18.7328	1.00854
$346$	−24.7891	−1.33267
$347$	−25.4647	−1.36702	−0.683508	−	0.729943i	$-0.739547\pi$
$347$	−25.4647	−1.36702	−0.683508	+	0.729943i	$0.739547\pi$
$348$	35.7853	1.91829
$349$	5.51253	0.295079	0.147540	−	0.989056i	$-0.452865\pi$
$349$	5.51253	0.295079	0.147540	+	0.989056i	$0.452865\pi$
$350$	1.56990	0.0839145
$351$	−1.65967	−0.0885869
$352$	4.00716	0.213582
$353$	7.94911	0.423088	0.211544	−	0.977368i	$-0.432151\pi$
$353$	7.94911	0.423088	0.211544	+	0.977368i	$0.432151\pi$
$354$	−10.7544	−0.571592
$355$	−4.49730	−0.238692
$356$	−38.1461	−2.02174
$357$	−0.907636	−0.0480372
$358$	−44.9713	−2.37681
$359$	18.5575	0.979427	0.489714	−	0.871883i	$-0.337101\pi$
$359$	18.5575	0.979427	0.489714	+	0.871883i	$0.337101\pi$
$360$	15.4218	0.812799
$361$	−5.74176	−0.302198
$362$	−26.3894	−1.38700
$363$	−10.7364	−0.563514
$364$	3.37214	0.176748
$365$	−5.49103	−0.287413
$366$	62.4350	3.26353
$367$	−16.1304	−0.842001	−0.421000	−	0.907060i	$-0.638321\pi$
$367$	−16.1304	−0.842001	−0.421000	+	0.907060i	$0.638321\pi$
$368$	−22.2995	−1.16244
$369$	−39.6898	−2.06617
$370$	8.60642	0.447426
$371$	0.735331	0.0381765
$372$	19.7303	1.02297
$373$	−3.24989	−0.168273	−0.0841364	−	0.996454i	$-0.526813\pi$
$373$	−3.24989	−0.168273	−0.0841364	+	0.996454i	$0.526813\pi$
$374$	−3.45031	−0.178411
$375$	−2.54592	−0.131471
$376$	−34.4851	−1.77843
$377$	−4.96138	−0.255524
$378$	1.92538	0.0990307
$379$	−9.88319	−0.507665	−0.253833	−	0.967248i	$-0.581691\pi$
$379$	−9.88319	−0.507665	−0.253833	+	0.967248i	$0.581691\pi$
$380$	13.9597	0.716120
$381$	−21.6601	−1.10968
$382$	27.7540	1.42002
$383$	16.4148	0.838755	0.419377	−	0.907812i	$-0.362248\pi$
$383$	16.4148	0.838755	0.419377	+	0.907812i	$0.362248\pi$
$384$	52.2906	2.66844
$385$	1.69278	0.0862722
$386$	52.2257	2.65822
$387$	31.9625	1.62474
$388$	−22.1756	−1.12579
$389$	−19.3781	−0.982509	−0.491255	−	0.871016i	$-0.663462\pi$
$389$	−19.3781	−0.982509	−0.491255	+	0.871016i	$0.663462\pi$
$390$	−8.32148	−0.421374
$391$	−4.03580	−0.204099
$392$	29.1342	1.47150
$393$	41.3368	2.08517
$394$	−27.7542	−1.39824
$395$	11.3104	0.569086
$396$	34.7646	1.74699
$397$	26.8379	1.34695	0.673477	−	0.739208i	$-0.264800\pi$
$397$	26.8379	1.34695	0.673477	+	0.739208i	$0.264800\pi$
$398$	39.4581	1.97786
$399$	6.02534	0.301644
$400$	3.03067	0.151533
$401$	−0.818202	−0.0408591	−0.0204295	−	0.999791i	$-0.506503\pi$
$401$	−0.818202	−0.0408591	−0.0204295	+	0.999791i	$0.506503\pi$
$402$	66.4483	3.31414
$403$	−2.73548	−0.136264
$404$	43.0908	2.14385
$405$	7.32276	0.363871
$406$	5.75567	0.285649
$407$	9.28011	0.459998
$408$	−6.18526	−0.306216
$409$	−35.8829	−1.77430	−0.887148	−	0.461484i	$-0.847317\pi$
$409$	−35.8829	−1.77430	−0.887148	+	0.461484i	$0.847317\pi$
$410$	−27.5335	−1.35978
$411$	−47.6360	−2.34971
$412$	38.7101	1.90711
$413$	−1.13673	−0.0559350
$414$	61.8769	3.04108
$415$	−9.61816	−0.472137
$416$	−2.08212	−0.102085
$417$	−24.5675	−1.20308
$418$	22.9049	1.12032
$419$	17.4243	0.851231	0.425616	−	0.904904i	$-0.360058\pi$
$419$	17.4243	0.851231	0.425616	+	0.904904i	$0.360058\pi$
$420$	6.34414	0.309563
$421$	−34.9297	−1.70237	−0.851185	−	0.524865i	$-0.824116\pi$
$421$	−34.9297	−1.70237	−0.851185	+	0.524865i	$0.824116\pi$
$422$	56.4405	2.74748
$423$	27.1073	1.31800
$424$	5.01106	0.243358
$425$	0.548495	0.0266059
$426$	−27.6551	−1.33989
$427$	6.59932	0.319363
$428$	−33.3191	−1.61054
$429$	−8.97286	−0.433214
$430$	22.1729	1.06927
$431$	30.3948	1.46407	0.732033	−	0.681269i	$-0.238572\pi$
$431$	30.3948	1.46407	0.732033	+	0.681269i	$0.238572\pi$
$432$	3.71692	0.178831
$433$	−21.2783	−1.02257	−0.511285	−	0.859411i	$-0.670830\pi$
$433$	−21.2783	−1.02257	−0.511285	+	0.859411i	$0.670830\pi$
$434$	3.17341	0.152328
$435$	−9.33405	−0.447534
$436$	−25.2281	−1.20821
$437$	26.7916	1.28162
$438$	−33.7657	−1.61339
$439$	2.95231	0.140906	0.0704531	−	0.997515i	$-0.477555\pi$
$439$	2.95231	0.140906	0.0704531	+	0.997515i	$0.477555\pi$
$440$	11.5358	0.549948
$441$	−22.9012	−1.09053
$442$	1.79278	0.0852740
$443$	18.4894	0.878456	0.439228	−	0.898376i	$-0.355252\pi$
$443$	18.4894	0.878456	0.439228	+	0.898376i	$0.355252\pi$
$444$	34.7796	1.65057
$445$	9.94983	0.471667
$446$	30.6413	1.45091
$447$	−24.9076	−1.17809
$448$	6.35515	0.300253
$449$	10.5991	0.500202	0.250101	−	0.968220i	$-0.419536\pi$
$449$	10.5991	0.500202	0.250101	+	0.968220i	$0.419536\pi$
$450$	−8.40953	−0.396429
$451$	−29.6888	−1.39799
$452$	−34.4164	−1.61881
$453$	0.625600	0.0293933
$454$	63.4945	2.97994
$455$	−0.879571	−0.0412349
$456$	41.0609	1.92285
$457$	31.3784	1.46782	0.733910	−	0.679247i	$-0.237693\pi$
$457$	31.3784	1.46782	0.733910	+	0.679247i	$0.237693\pi$
$458$	38.4285	1.79565
$459$	0.672695	0.0313987
$460$	28.2092	1.31526
$461$	−30.2511	−1.40894	−0.704468	−	0.709736i	$-0.748814\pi$
$461$	−30.2511	−1.40894	−0.704468	+	0.709736i	$0.748814\pi$
$462$	10.4094	0.484287
$463$	10.5481	0.490213	0.245106	−	0.969496i	$-0.421177\pi$
$463$	10.5481	0.490213	0.245106	+	0.969496i	$0.421177\pi$
$464$	11.1113	0.515827
$465$	−5.14636	−0.238657
$466$	−37.5224	−1.73819
$467$	6.22279	0.287957	0.143978	−	0.989581i	$-0.454010\pi$
$467$	6.22279	0.287957	0.143978	+	0.989581i	$0.454010\pi$
$468$	−18.0637	−0.834995
$469$	7.02352	0.324316
$470$	18.8048	0.867401
$471$	−11.1658	−0.514494
$472$	−7.74648	−0.356561
$473$	23.9086	1.09932
$474$	69.5503	3.19455
$475$	−3.64119	−0.167069
$476$	−1.36679	−0.0626465
$477$	−3.93898	−0.180354
$478$	−25.4384	−1.16352
$479$	22.2873	1.01833	0.509166	−	0.860668i	$-0.329954\pi$
$479$	22.2873	1.01833	0.509166	+	0.860668i	$0.329954\pi$
$480$	−3.91719	−0.178794
$481$	−4.82195	−0.219862
$482$	−12.9035	−0.587738
$483$	12.1757	0.554015
$484$	−16.1677	−0.734894
$485$	5.78416	0.262645
$486$	53.9163	2.44569
$487$	−27.0097	−1.22393	−0.611963	−	0.790887i	$-0.709620\pi$
$487$	−27.0097	−1.22393	−0.611963	+	0.790887i	$0.709620\pi$
$488$	44.9723	2.03580
$489$	42.9490	1.94222
$490$	−15.8870	−0.717700
$491$	−12.0362	−0.543188	−0.271594	−	0.962412i	$-0.587551\pi$
$491$	−12.0362	−0.543188	−0.271594	+	0.962412i	$0.587551\pi$
$492$	−111.267	−5.01628
$493$	2.01093	0.0905679
$494$	−11.9014	−0.535469
$495$	−9.06781	−0.407568
$496$	6.12623	0.275076
$497$	−2.92311	−0.131120
$498$	−59.1445	−2.65033
$499$	29.3651	1.31456	0.657281	−	0.753646i	$-0.271706\pi$
$499$	29.3651	1.31456	0.657281	+	0.753646i	$0.271706\pi$
$500$	−3.83384	−0.171455
$501$	−10.6318	−0.474994
$502$	73.5508	3.28273
$503$	−7.54935	−0.336609	−0.168304	−	0.985735i	$-0.553829\pi$
$503$	−7.54935	−0.336609	−0.168304	+	0.985735i	$0.553829\pi$
$504$	10.0237	0.446491
$505$	−11.2396	−0.500155
$506$	46.2852	2.05763
$507$	−28.4347	−1.26283
$508$	−32.6175	−1.44717
$509$	−6.79321	−0.301104	−0.150552	−	0.988602i	$-0.548105\pi$
$509$	−6.79321	−0.301104	−0.150552	+	0.988602i	$0.548105\pi$
$510$	3.37284	0.149352
$511$	−3.56900	−0.157883
$512$	31.5108	1.39259
$513$	−4.46569	−0.197165
$514$	−12.5247	−0.552441
$515$	−10.0969	−0.444924
$516$	89.6037	3.94458
$517$	20.2768	0.891773
$518$	5.59392	0.245783
$519$	26.1293	1.14695
$520$	−5.99401	−0.262855
$521$	−20.2983	−0.889286	−0.444643	−	0.895708i	$-0.646669\pi$
$521$	−20.2983	−0.889286	−0.444643	+	0.895708i	$0.646669\pi$
$522$	−30.8317	−1.34946
$523$	2.18168	0.0953981	0.0476991	−	0.998862i	$-0.484811\pi$
$523$	2.18168	0.0953981	0.0476991	+	0.998862i	$0.484811\pi$
$524$	62.2481	2.71932
$525$	−1.65477	−0.0722203
$526$	24.3948	1.06366
$527$	1.10874	0.0482973
$528$	20.0952	0.874530
$529$	31.1393	1.35388
$530$	−2.73254	−0.118694
$531$	6.08919	0.264248
$532$	9.07342	0.393382
$533$	15.4263	0.668188
$534$	61.1841	2.64769
$535$	8.69078	0.375735
$536$	47.8631	2.06737
$537$	47.4027	2.04558
$538$	−77.8913	−3.35813
$539$	−17.1306	−0.737865
$540$	−4.70197	−0.202340
$541$	20.5038	0.881528	0.440764	−	0.897623i	$-0.354708\pi$
$541$	20.5038	0.881528	0.440764	+	0.897623i	$0.354708\pi$
$542$	33.8857	1.45552
$543$	27.8162	1.19371
$544$	0.843921	0.0361828
$545$	6.58037	0.281872
$546$	−5.40871	−0.231471
$547$	−39.6923	−1.69712	−0.848561	−	0.529098i	$-0.822530\pi$
$547$	−39.6923	−1.69712	−0.848561	+	0.529098i	$0.822530\pi$
$548$	−71.7339	−3.06432
$549$	−35.3509	−1.50874
$550$	−6.29050	−0.268228
$551$	−13.3496	−0.568712
$552$	82.9739	3.53160
$553$	7.35139	0.312613
$554$	−61.4850	−2.61225
$555$	−9.07174	−0.385074
$556$	−36.9956	−1.56896
$557$	8.60641	0.364665	0.182333	−	0.983237i	$-0.441635\pi$
$557$	8.60641	0.364665	0.182333	+	0.983237i	$0.441635\pi$
$558$	−16.9991	−0.719631
$559$	−12.4229	−0.525434
$560$	1.96984	0.0832411
$561$	3.63686	0.153548
$562$	−76.5217	−3.22787
$563$	21.7871	0.918219	0.459109	−	0.888380i	$-0.348169\pi$
$563$	21.7871	0.918219	0.459109	+	0.888380i	$0.348169\pi$
$564$	75.9926	3.19987
$565$	8.97701	0.377665
$566$	−64.4448	−2.70882
$567$	4.75958	0.199883
$568$	−19.9201	−0.835830
$569$	−27.1315	−1.13741	−0.568707	−	0.822540i	$-0.692556\pi$
$569$	−27.1315	−1.13741	−0.568707	+	0.822540i	$0.692556\pi$
$570$	−22.3906	−0.937839
$571$	−31.9706	−1.33793	−0.668964	−	0.743295i	$-0.733262\pi$
$571$	−31.9706	−1.33793	−0.668964	+	0.743295i	$0.733262\pi$
$572$	−13.5120	−0.564966
$573$	−29.2545	−1.22213
$574$	−17.8960	−0.746964
$575$	−7.35794	−0.306847
$576$	−34.0429	−1.41846
$577$	−16.9908	−0.707338	−0.353669	−	0.935371i	$-0.615066\pi$
$577$	−16.9908	−0.707338	−0.353669	+	0.935371i	$0.615066\pi$
$578$	40.3341	1.67768
$579$	−55.0494	−2.28777
$580$	−14.0559	−0.583640
$581$	−6.25152	−0.259357
$582$	35.5683	1.47435
$583$	−2.94644	−0.122029
$584$	−24.3217	−1.00644
$585$	4.71164	0.194802
$586$	43.1621	1.78301
$587$	31.9638	1.31929	0.659644	−	0.751578i	$-0.270707\pi$
$587$	31.9638	1.31929	0.659644	+	0.751578i	$0.270707\pi$
$588$	−64.2012	−2.64761
$589$	−7.36034	−0.303278
$590$	4.22418	0.173907
$591$	29.2547	1.20338
$592$	10.7990	0.443836
$593$	−15.7983	−0.648760	−0.324380	−	0.945927i	$-0.605156\pi$
$593$	−15.7983	−0.648760	−0.324380	+	0.945927i	$0.605156\pi$
$594$	−7.71490	−0.316546
$595$	0.356505	0.0146153
$596$	−37.5078	−1.53638
$597$	−41.5915	−1.70223
$598$	−24.0498	−0.983469
$599$	−0.242346	−0.00990197	−0.00495099	−	0.999988i	$-0.501576\pi$
$599$	−0.242346	−0.00990197	−0.00495099	+	0.999988i	$0.501576\pi$
$600$	−11.2768	−0.460373
$601$	2.19984	0.0897333	0.0448667	−	0.998993i	$-0.485714\pi$
$601$	2.19984	0.0897333	0.0448667	+	0.998993i	$0.485714\pi$
$602$	14.4118	0.587379
$603$	−37.6232	−1.53214
$604$	0.942076	0.0383325
$605$	4.21709	0.171449
$606$	−69.1151	−2.80761
$607$	−11.1417	−0.452228	−0.226114	−	0.974101i	$-0.572602\pi$
$607$	−11.1417	−0.452228	−0.226114	+	0.974101i	$0.572602\pi$
$608$	−5.60237	−0.227206
$609$	−6.06685	−0.245841
$610$	−24.5235	−0.992929
$611$	−10.5358	−0.426235
$612$	7.32153	0.295955
$613$	32.9660	1.33149	0.665743	−	0.746181i	$-0.268115\pi$
$613$	32.9660	1.33149	0.665743	+	0.746181i	$0.268115\pi$
$614$	−51.5110	−2.07882
$615$	29.0222	1.17029
$616$	7.49792	0.302100
$617$	−32.6291	−1.31360	−0.656798	−	0.754066i	$-0.728090\pi$
$617$	−32.6291	−1.31360	−0.656798	+	0.754066i	$0.728090\pi$
$618$	−62.0887	−2.49757
$619$	−20.3234	−0.816865	−0.408432	−	0.912789i	$-0.633924\pi$
$619$	−20.3234	−0.816865	−0.408432	+	0.912789i	$0.633924\pi$
$620$	−7.74978	−0.311239
$621$	−9.02405	−0.362123
$622$	81.1133	3.25235
$623$	6.46709	0.259099
$624$	−10.4415	−0.417993
$625$	1.00000	0.0400000
$626$	50.8825	2.03367
$627$	−24.1433	−0.964190
$628$	−16.8143	−0.670965
$629$	1.95442	0.0779278
$630$	−5.46595	−0.217768
$631$	1.91308	0.0761584	0.0380792	−	0.999275i	$-0.487876\pi$
$631$	1.91308	0.0761584	0.0380792	+	0.999275i	$0.487876\pi$
$632$	50.0975	1.99277
$633$	−59.4920	−2.36460
$634$	18.0806	0.718071
$635$	8.50778	0.337621
$636$	−11.0425	−0.437866
$637$	8.90105	0.352672
$638$	−23.0627	−0.913061
$639$	15.6584	0.619436
$640$	−20.5390	−0.811874
$641$	−34.8603	−1.37690	−0.688450	−	0.725284i	$-0.741709\pi$
$641$	−34.8603	−1.37690	−0.688450	+	0.725284i	$0.741709\pi$
$642$	53.4418	2.10918
$643$	0.819119	0.0323029	0.0161515	−	0.999870i	$-0.494859\pi$
$643$	0.819119	0.0323029	0.0161515	+	0.999870i	$0.494859\pi$
$644$	18.3351	0.722505
$645$	−23.3718	−0.920262
$646$	4.82384	0.189792
$647$	32.8064	1.28975	0.644876	−	0.764287i	$-0.276909\pi$
$647$	32.8064	1.28975	0.644876	+	0.764287i	$0.276909\pi$
$648$	32.4351	1.27417
$649$	4.55484	0.178793
$650$	3.26855	0.128203
$651$	−3.34498	−0.131100
$652$	64.6759	2.53290
$653$	40.6274	1.58987	0.794936	−	0.606694i	$-0.207505\pi$
$653$	40.6274	1.58987	0.794936	+	0.606694i	$0.207505\pi$
$654$	40.4644	1.58228
$655$	−16.2365	−0.634411
$656$	−34.5480	−1.34887
$657$	19.1182	0.745874
$658$	12.2226	0.476485
$659$	33.9027	1.32066	0.660331	−	0.750975i	$-0.270416\pi$
$659$	33.9027	1.32066	0.660331	+	0.750975i	$0.270416\pi$
$660$	−25.4207	−0.989500
$661$	−11.1550	−0.433878	−0.216939	−	0.976185i	$-0.569607\pi$
$661$	−11.1550	−0.433878	−0.216939	+	0.976185i	$0.569607\pi$
$662$	−26.9793	−1.04858
$663$	−1.88971	−0.0733904
$664$	−42.6022	−1.65328
$665$	−2.36666	−0.0917753
$666$	−29.9652	−1.16113
$667$	−26.9762	−1.04452
$668$	−16.0102	−0.619452
$669$	−32.2979	−1.24871
$670$	−26.0999	−1.00833
$671$	−26.4432	−1.02083
$672$	−2.54605	−0.0982162
$673$	−34.5212	−1.33069	−0.665347	−	0.746534i	$-0.731717\pi$
$673$	−34.5212	−1.33069	−0.665347	+	0.746534i	$0.731717\pi$
$674$	−18.5841	−0.715833
$675$	1.22644	0.0472056
$676$	−42.8191	−1.64689
$677$	−31.4029	−1.20691	−0.603456	−	0.797396i	$-0.706210\pi$
$677$	−31.4029	−1.20691	−0.603456	+	0.797396i	$0.706210\pi$
$678$	55.2019	2.12002
$679$	3.75953	0.144278
$680$	2.42948	0.0931661
$681$	−66.9274	−2.56466
$682$	−12.7157	−0.486910
$683$	14.8010	0.566345	0.283173	−	0.959069i	$-0.408613\pi$
$683$	14.8010	0.566345	0.283173	+	0.959069i	$0.408613\pi$
$684$	−48.6040	−1.85842
$685$	18.7107	0.714900
$686$	−21.3153	−0.813823
$687$	−40.5062	−1.54541
$688$	27.8218	1.06069
$689$	1.53097	0.0583254
$690$	−45.2459	−1.72248
$691$	29.0202	1.10398	0.551990	−	0.833851i	$-0.313869\pi$
$691$	29.0202	1.10398	0.551990	+	0.833851i	$0.313869\pi$
$692$	39.3475	1.49577
$693$	−5.89381	−0.223887
$694$	61.5058	2.33473
$695$	9.64975	0.366036
$696$	−41.3438	−1.56713
$697$	−6.25256	−0.236832
$698$	−13.3146	−0.503966
$699$	39.5511	1.49596
$700$	−2.49188	−0.0941844
$701$	19.7064	0.744301	0.372151	−	0.928172i	$-0.378620\pi$
$701$	19.7064	0.744301	0.372151	+	0.928172i	$0.378620\pi$
$702$	4.00867	0.151297
$703$	−12.9744	−0.489340
$704$	−25.4648	−0.959741
$705$	−19.8215	−0.746521
$706$	−19.1998	−0.722592
$707$	−7.30539	−0.274747
$708$	17.0704	0.641546
$709$	−32.7400	−1.22958	−0.614788	−	0.788692i	$-0.710759\pi$
$709$	−32.7400	−1.22958	−0.614788	+	0.788692i	$0.710759\pi$
$710$	10.8625	0.407662
$711$	−39.3796	−1.47685
$712$	44.0713	1.65164
$713$	−14.8734	−0.557015
$714$	2.19224	0.0820427
$715$	3.52440	0.131805
$716$	71.3826	2.66769
$717$	26.8137	1.00138
$718$	−44.8226	−1.67276
$719$	−0.146510	−0.00546392	−0.00273196	−	0.999996i	$-0.500870\pi$
$719$	−0.146510	−0.00546392	−0.00273196	+	0.999996i	$0.500870\pi$
$720$	−10.5520	−0.393248
$721$	−6.56271	−0.244408
$722$	13.8683	0.516123
$723$	13.6011	0.505832
$724$	41.8877	1.55674
$725$	3.66627	0.136162
$726$	25.9320	0.962426
$727$	15.1349	0.561324	0.280662	−	0.959807i	$-0.409446\pi$
$727$	15.1349	0.561324	0.280662	+	0.959807i	$0.409446\pi$
$728$	−3.89593	−0.144393
$729$	−34.8631	−1.29123
$730$	13.2627	0.490873
$731$	5.03523	0.186235
$732$	−99.1027	−3.66294
$733$	48.7555	1.80082	0.900412	−	0.435039i	$-0.143265\pi$
$733$	48.7555	1.80082	0.900412	+	0.435039i	$0.143265\pi$
$734$	38.9604	1.43805
$735$	16.7459	0.617682
$736$	−11.3210	−0.417298
$737$	−28.1429	−1.03666
$738$	95.8643	3.52881
$739$	−25.7646	−0.947767	−0.473884	−	0.880587i	$-0.657148\pi$
$739$	−25.7646	−0.947767	−0.473884	+	0.880587i	$0.657148\pi$
$740$	−13.6609	−0.502185
$741$	12.5449	0.460847
$742$	−1.77607	−0.0652016
$743$	24.9357	0.914802	0.457401	−	0.889260i	$-0.348780\pi$
$743$	24.9357	0.914802	0.457401	+	0.889260i	$0.348780\pi$
$744$	−22.7950	−0.835706
$745$	9.78334	0.358434
$746$	7.84956	0.287393
$747$	33.4878	1.22525
$748$	5.47665	0.200246
$749$	5.64874	0.206401
$750$	6.14926	0.224539
$751$	−16.9140	−0.617202	−0.308601	−	0.951192i	$-0.599861\pi$
$751$	−16.9140	−0.617202	−0.308601	+	0.951192i	$0.599861\pi$
$752$	23.5955	0.860441
$753$	−77.5274	−2.82526
$754$	11.9834	0.436410
$755$	−0.245726	−0.00894289
$756$	−3.05614	−0.111151
$757$	−5.33625	−0.193949	−0.0969747	−	0.995287i	$-0.530917\pi$
$757$	−5.33625	−0.193949	−0.0969747	+	0.995287i	$0.530917\pi$
$758$	23.8712	0.867042
$759$	−48.7876	−1.77088
$760$	−16.1281	−0.585027
$761$	−26.9139	−0.975629	−0.487815	−	0.872947i	$-0.662206\pi$
$761$	−26.9139	−0.975629	−0.487815	+	0.872947i	$0.662206\pi$
$762$	52.3165	1.89523
$763$	4.27704	0.154839
$764$	−44.0537	−1.59381
$765$	−1.90971	−0.0690457
$766$	−39.6471	−1.43251
$767$	−2.36670	−0.0854565
$768$	−76.5133	−2.76094
$769$	−4.68569	−0.168970	−0.0844852	−	0.996425i	$-0.526925\pi$
$769$	−4.68569	−0.168970	−0.0844852	+	0.996425i	$0.526925\pi$
$770$	−4.08864	−0.147344
$771$	13.2019	0.475454
$772$	−82.8975	−2.98355
$773$	−27.3583	−0.984010	−0.492005	−	0.870592i	$-0.663736\pi$
$773$	−27.3583	−0.984010	−0.492005	+	0.870592i	$0.663736\pi$
$774$	−77.2001	−2.77490
$775$	2.02141	0.0726113
$776$	25.6200	0.919706
$777$	−5.89636	−0.211531
$778$	46.8046	1.67803
$779$	41.5076	1.48716
$780$	13.2086	0.472944
$781$	11.7128	0.419116
$782$	9.74780	0.348581
$783$	4.49645	0.160690
$784$	−19.9343	−0.711941
$785$	4.38577	0.156535
$786$	−99.8423	−3.56126
$787$	−34.3168	−1.22326	−0.611631	−	0.791143i	$-0.709486\pi$
$787$	−34.3168	−1.22326	−0.611631	+	0.791143i	$0.709486\pi$
$788$	44.0540	1.56936
$789$	−25.7137	−0.915433
$790$	−27.3183	−0.971941
$791$	5.83479	0.207461
$792$	−40.1645	−1.42718
$793$	13.7399	0.487918
$794$	−64.8225	−2.30046
$795$	2.88028	0.102153
$796$	−62.6316	−2.21992
$797$	2.66091	0.0942544	0.0471272	−	0.998889i	$-0.484993\pi$
$797$	2.66091	0.0942544	0.0471272	+	0.998889i	$0.484993\pi$
$798$	−14.5532	−0.515178
$799$	4.27036	0.151074
$800$	1.53861	0.0543981
$801$	−34.6426	−1.22404
$802$	1.97623	0.0697832
$803$	14.3008	0.504666
$804$	−105.473	−3.71974
$805$	−4.78244	−0.168559
$806$	6.60709	0.232725
$807$	82.1025	2.89015
$808$	−49.7840	−1.75139
$809$	30.8343	1.08407	0.542037	−	0.840354i	$-0.317653\pi$
$809$	30.8343	1.08407	0.542037	+	0.840354i	$0.317653\pi$
$810$	−17.6869	−0.621455
$811$	−51.0190	−1.79152	−0.895759	−	0.444539i	$-0.853367\pi$
$811$	−51.0190	−1.79152	−0.895759	+	0.444539i	$0.853367\pi$
$812$	−9.13593	−0.320608
$813$	−35.7178	−1.25268
$814$	−22.4146	−0.785631
$815$	−16.8697	−0.590921
$816$	4.23211	0.148153
$817$	−33.4264	−1.16944
$818$	86.6693	3.03032
$819$	3.06243	0.107010
$820$	43.7038	1.52620
$821$	50.4648	1.76123	0.880617	−	0.473828i	$-0.157128\pi$
$821$	50.4648	1.76123	0.880617	+	0.473828i	$0.157128\pi$
$822$	115.057	4.01307
$823$	−53.7288	−1.87287	−0.936434	−	0.350844i	$-0.885895\pi$
$823$	−53.7288	−1.87287	−0.936434	+	0.350844i	$0.885895\pi$
$824$	−44.7229	−1.55799
$825$	6.63061	0.230848
$826$	2.74559	0.0955313
$827$	48.6240	1.69082	0.845410	−	0.534117i	$-0.179356\pi$
$827$	48.6240	1.69082	0.845410	+	0.534117i	$0.179356\pi$
$828$	−98.2167	−3.41327
$829$	−23.6916	−0.822844	−0.411422	−	0.911445i	$-0.634968\pi$
$829$	−23.6916	−0.822844	−0.411422	+	0.911445i	$0.634968\pi$
$830$	23.2311	0.806362
$831$	64.8093	2.24821
$832$	13.2315	0.458721
$833$	−3.60775	−0.125001
$834$	59.3388	2.05474
$835$	4.17601	0.144517
$836$	−36.3568	−1.25743
$837$	2.47914	0.0856914
$838$	−42.0855	−1.45382
$839$	−26.8113	−0.925628	−0.462814	−	0.886455i	$-0.653160\pi$
$839$	−26.8113	−0.925628	−0.462814	+	0.886455i	$0.653160\pi$
$840$	−7.32957	−0.252894
$841$	−15.5584	−0.536498
$842$	84.3670	2.90748
$843$	80.6589	2.77804
$844$	−89.5876	−3.08373
$845$	11.1687	0.384216
$846$	−65.4732	−2.25101
$847$	2.74098	0.0941813
$848$	−3.42869	−0.117742
$849$	67.9291	2.33132
$850$	−1.32480	−0.0454403
$851$	−26.2181	−0.898745
$852$	43.8967	1.50388
$853$	6.80412	0.232969	0.116484	−	0.993193i	$-0.462837\pi$
$853$	6.80412	0.232969	0.116484	+	0.993193i	$0.462837\pi$
$854$	−15.9396	−0.545441
$855$	12.6776	0.433565
$856$	38.4945	1.31571
$857$	−27.6904	−0.945885	−0.472942	−	0.881093i	$-0.656808\pi$
$857$	−27.6904	−0.945885	−0.472942	+	0.881093i	$0.656808\pi$
$858$	21.6725	0.739886
$859$	−5.65962	−0.193104	−0.0965518	−	0.995328i	$-0.530781\pi$
$859$	−5.65962	−0.193104	−0.0965518	+	0.995328i	$0.530781\pi$
$860$	−35.1950	−1.20014
$861$	18.8636	0.642868
$862$	−73.4136	−2.50048
$863$	6.62902	0.225654	0.112827	−	0.993615i	$-0.464009\pi$
$863$	6.62902	0.225654	0.112827	+	0.993615i	$0.464009\pi$
$864$	1.88701	0.0641974
$865$	−10.2632	−0.348959
$866$	51.3943	1.74645
$867$	−42.5148	−1.44388
$868$	−5.03713	−0.170971
$869$	−29.4567	−0.999250
$870$	22.5449	0.764342
$871$	14.6231	0.495484
$872$	29.1467	0.987032
$873$	−20.1389	−0.681597
$874$	−64.7108	−2.18888
$875$	0.649970	0.0219730
$876$	53.5961	1.81084
$877$	29.2335	0.987144	0.493572	−	0.869705i	$-0.335691\pi$
$877$	29.2335	0.987144	0.493572	+	0.869705i	$0.335691\pi$
$878$	−7.13082	−0.240654
$879$	−45.4957	−1.53453
$880$	−7.89308	−0.266076
$881$	5.90024	0.198784	0.0993921	−	0.995048i	$-0.468310\pi$
$881$	5.90024	0.198784	0.0993921	+	0.995048i	$0.468310\pi$
$882$	55.3140	1.86252
$883$	−10.1362	−0.341109	−0.170554	−	0.985348i	$-0.554556\pi$
$883$	−10.1362	−0.341109	−0.170554	+	0.985348i	$0.554556\pi$
$884$	−2.84567	−0.0957103
$885$	−4.45257	−0.149671
$886$	−44.6580	−1.50031
$887$	−7.64340	−0.256640	−0.128320	−	0.991733i	$-0.540958\pi$
$887$	−7.64340	−0.256640	−0.128320	+	0.991733i	$0.540958\pi$
$888$	−40.1819	−1.34842
$889$	5.52980	0.185464
$890$	−24.0322	−0.805561
$891$	−19.0714	−0.638917
$892$	−48.6367	−1.62848
$893$	−28.3488	−0.948656
$894$	60.1603	2.01206
$895$	−18.6191	−0.622367
$896$	−13.3497	−0.445982
$897$	25.3501	0.846415
$898$	−25.6003	−0.854294
$899$	7.41105	0.247172
$900$	13.3484	0.444946
$901$	−0.620530	−0.0206728
$902$	71.7084	2.38763
$903$	−15.1909	−0.505523
$904$	39.7623	1.32247
$905$	−10.9258	−0.363185
$906$	−1.51103	−0.0502007
$907$	−28.1826	−0.935786	−0.467893	−	0.883785i	$-0.654987\pi$
$907$	−28.1826	−0.935786	−0.467893	+	0.883785i	$0.654987\pi$
$908$	−100.784	−3.34464
$909$	39.1331	1.29796
$910$	2.12446	0.0704252
$911$	19.5344	0.647203	0.323601	−	0.946194i	$-0.395106\pi$
$911$	19.5344	0.647203	0.323601	+	0.946194i	$0.395106\pi$
$912$	−28.0949	−0.930314
$913$	25.0496	0.829019
$914$	−75.7894	−2.50689
$915$	25.8494	0.854556
$916$	−60.9973	−2.01541
$917$	−10.5532	−0.348498
$918$	−1.62478	−0.0536258
$919$	−2.68556	−0.0885886	−0.0442943	−	0.999019i	$-0.514104\pi$
$919$	−2.68556	−0.0885886	−0.0442943	+	0.999019i	$0.514104\pi$
$920$	−32.5909	−1.07449
$921$	54.2960	1.78912
$922$	73.0666	2.40632
$923$	−6.08597	−0.200322
$924$	−16.5227	−0.543557
$925$	3.56324	0.117159
$926$	−25.4772	−0.837234
$927$	35.1548	1.15463
$928$	5.64097	0.185174
$929$	28.5598	0.937016	0.468508	−	0.883459i	$-0.344792\pi$
$929$	28.5598	0.937016	0.468508	+	0.883459i	$0.344792\pi$
$930$	12.4302	0.407602
$931$	23.9501	0.784931
$932$	59.5590	1.95092
$933$	−85.4988	−2.79910
$934$	−15.0301	−0.491801
$935$	−1.42850	−0.0467170
$936$	20.8695	0.682141
$937$	−48.3536	−1.57964	−0.789822	−	0.613337i	$-0.789827\pi$
$937$	−48.3536	−1.57964	−0.789822	+	0.613337i	$0.789827\pi$
$938$	−16.9641	−0.553899
$939$	−53.6335	−1.75026
$940$	−29.8487	−0.973558
$941$	34.8758	1.13692	0.568459	−	0.822712i	$-0.307540\pi$
$941$	34.8758	1.13692	0.568459	+	0.822712i	$0.307540\pi$
$942$	26.9692	0.878704
$943$	83.8766	2.73140
$944$	5.30034	0.172511
$945$	0.797147	0.0259312
$946$	−57.7473	−1.87753
$947$	25.5977	0.831814	0.415907	−	0.909407i	$-0.363464\pi$
$947$	25.5977	0.831814	0.415907	+	0.909407i	$0.363464\pi$
$948$	−110.397	−3.58552
$949$	−7.43073	−0.241212
$950$	8.79469	0.285337
$951$	−19.0581	−0.618002
$952$	1.57909	0.0511785
$953$	−34.9598	−1.13246	−0.566229	−	0.824248i	$-0.691598\pi$
$953$	−34.9598	−1.13246	−0.566229	+	0.824248i	$0.691598\pi$
$954$	9.51397	0.308026
$955$	11.4907	0.371831
$956$	40.3781	1.30592
$957$	24.3096	0.785818
$958$	−53.8313	−1.73921
$959$	12.1614	0.392712
$960$	24.8930	0.803419
$961$	−26.9139	−0.868190
$962$	11.6466	0.375502
$963$	−30.2589	−0.975079
$964$	20.4816	0.659668
$965$	21.6226	0.696055
$966$	−29.4085	−0.946202
$967$	−15.1386	−0.486824	−0.243412	−	0.969923i	$-0.578267\pi$
$967$	−15.1386	−0.486824	−0.243412	+	0.969923i	$0.578267\pi$
$968$	18.6790	0.600364
$969$	−5.08465	−0.163343
$970$	−13.9707	−0.448572
$971$	−38.1177	−1.22326	−0.611628	−	0.791145i	$-0.709485\pi$
$971$	−38.1177	−1.22326	−0.611628	+	0.791145i	$0.709485\pi$
$972$	−85.5810	−2.74501
$973$	6.27205	0.201073
$974$	65.2374	2.09034
$975$	−3.44527	−0.110337
$976$	−30.7712	−0.984962
$977$	−24.5673	−0.785978	−0.392989	−	0.919543i	$-0.628559\pi$
$977$	−24.5673	−0.785978	−0.392989	+	0.919543i	$0.628559\pi$
$978$	−103.736	−3.31712
$979$	−25.9134	−0.828195
$980$	25.2173	0.805536
$981$	−22.9110	−0.731493
$982$	29.0716	0.927711
$983$	53.6080	1.70983	0.854916	−	0.518767i	$-0.173609\pi$
$983$	53.6080	1.70983	0.854916	+	0.518767i	$0.173609\pi$
$984$	128.549	4.09800
$985$	−11.4908	−0.366128
$986$	−4.85708	−0.154681
$987$	−12.8834	−0.410083
$988$	18.8910	0.601003
$989$	−67.5464	−2.14785
$990$	21.9018	0.696085
$991$	12.3240	0.391483	0.195742	−	0.980655i	$-0.437289\pi$
$991$	12.3240	0.391483	0.195742	+	0.980655i	$0.437289\pi$
$992$	3.11017	0.0987480
$993$	28.4380	0.902453
$994$	7.06030	0.223939
$995$	16.3365	0.517902
$996$	93.8797	2.97469
$997$	−41.7972	−1.32373	−0.661865	−	0.749623i	$-0.730235\pi$
$997$	−41.7972	−1.32373	−0.661865	+	0.749623i	$0.730235\pi$
$998$	−70.9265	−2.24514
$999$	4.37009	0.138263

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.d.1.6	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.d.1.6	✓	83	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41534 q^{2} +2.54592 q^{3} +3.83384 q^{4} -1.00000 q^{5} -6.14926 q^{6} -0.649970 q^{7} -4.42935 q^{8} +3.48173 q^{9} +O(q^{10})\)	\(q-2.41534 q^{2} +2.54592 q^{3} +3.83384 q^{4} -1.00000 q^{5} -6.14926 q^{6} -0.649970 q^{7} -4.42935 q^{8} +3.48173 q^{9} +2.41534 q^{10} +2.60440 q^{11} +9.76067 q^{12} -1.35325 q^{13} +1.56990 q^{14} -2.54592 q^{15} +3.03067 q^{16} +0.548495 q^{17} -8.40953 q^{18} -3.64119 q^{19} -3.83384 q^{20} -1.65477 q^{21} -6.29050 q^{22} -7.35794 q^{23} -11.2768 q^{24} +1.00000 q^{25} +3.26855 q^{26} +1.22644 q^{27} -2.49188 q^{28} +3.66627 q^{29} +6.14926 q^{30} +2.02141 q^{31} +1.53861 q^{32} +6.63061 q^{33} -1.32480 q^{34} +0.649970 q^{35} +13.3484 q^{36} +3.56324 q^{37} +8.79469 q^{38} -3.44527 q^{39} +4.42935 q^{40} -11.3995 q^{41} +3.99683 q^{42} +9.18007 q^{43} +9.98487 q^{44} -3.48173 q^{45} +17.7719 q^{46} +7.78559 q^{47} +7.71585 q^{48} -6.57754 q^{49} -2.41534 q^{50} +1.39643 q^{51} -5.18815 q^{52} -1.13133 q^{53} -2.96226 q^{54} -2.60440 q^{55} +2.87894 q^{56} -9.27018 q^{57} -8.85528 q^{58} +1.74890 q^{59} -9.76067 q^{60} -10.1533 q^{61} -4.88239 q^{62} -2.26302 q^{63} -9.77760 q^{64} +1.35325 q^{65} -16.0151 q^{66} -10.8059 q^{67} +2.10284 q^{68} -18.7328 q^{69} -1.56990 q^{70} +4.49730 q^{71} -15.4218 q^{72} +5.49103 q^{73} -8.60642 q^{74} +2.54592 q^{75} -13.9597 q^{76} -1.69278 q^{77} +8.32148 q^{78} -11.3104 q^{79} -3.03067 q^{80} -7.32276 q^{81} +27.5335 q^{82} +9.61816 q^{83} -6.34414 q^{84} -0.548495 q^{85} -22.1729 q^{86} +9.33405 q^{87} -11.5358 q^{88} -9.94983 q^{89} +8.40953 q^{90} +0.879571 q^{91} -28.2092 q^{92} +5.14636 q^{93} -18.8048 q^{94} +3.64119 q^{95} +3.91719 q^{96} -5.78416 q^{97} +15.8870 q^{98} +9.06781 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9}+O(q^{10}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9	\( 83 q + q^{2} - 4 q^{3} + 61 q^{4} - 83 q^{5} - 6 q^{6} + 2 q^{7} - 3 q^{8} + 61 q^{9} - q^{10} - 26 q^{11} - 12 q^{12} - 15 q^{13} - 21 q^{14} + 4 q^{15} + 5 q^{16} + 8 q^{17} - 12 q^{18} - 79 q^{19} - 61 q^{20} - 34 q^{21} - 25 q^{22} + 31 q^{23} - 42 q^{24} + 83 q^{25} - 13 q^{26} - 25 q^{27} - 16 q^{28} - 16 q^{29} + 6 q^{30} - 40 q^{31} + 15 q^{32} - 33 q^{33} - 54 q^{34} - 2 q^{35} + 11 q^{36} - 45 q^{37} + 10 q^{38} - 54 q^{39} + 3 q^{40} - 27 q^{41} - 28 q^{42} - 101 q^{43} - 51 q^{44} - 61 q^{45} - 46 q^{46} + 71 q^{47} - 14 q^{48} + 23 q^{49} + q^{50} - 71 q^{51} - 34 q^{52} - 49 q^{53} - 25 q^{54} + 26 q^{55} - 41 q^{56} - 20 q^{57} - 43 q^{58} - 60 q^{59} + 12 q^{60} - 38 q^{61} - 2 q^{62} + 36 q^{63} - 113 q^{64} + 15 q^{65} - 42 q^{66} - 164 q^{67} + 10 q^{68} - 93 q^{69} + 21 q^{70} - 78 q^{71} + q^{72} - 18 q^{73} - 23 q^{74} - 4 q^{75} - 112 q^{76} - 35 q^{77} - 44 q^{78} - 124 q^{79} - 5 q^{80} - 45 q^{81} - 34 q^{82} + 5 q^{83} - 60 q^{84} - 8 q^{85} - 25 q^{86} + 12 q^{87} - 149 q^{88} - 44 q^{89} + 12 q^{90} - 192 q^{91} + 35 q^{92} - 13 q^{93} - 32 q^{94} + 79 q^{95} - 59 q^{96} - 31 q^{97} + 25 q^{98} - 134 q^{99}+O(q^{100}) \) 83 * q + q^2 - 4 * q^3 + 61 * q^4 - 83 * q^5 - 6 * q^6 + 2 * q^7 - 3 * q^8 + 61 * q^9 - q^10 - 26 * q^11 - 12 * q^12 - 15 * q^13 - 21 * q^14 + 4 * q^15 + 5 * q^16 + 8 * q^17 - 12 * q^18 - 79 * q^19 - 61 * q^20 - 34 * q^21 - 25 * q^22 + 31 * q^23 - 42 * q^24 + 83 * q^25 - 13 * q^26 - 25 * q^27 - 16 * q^28 - 16 * q^29 + 6 * q^30 - 40 * q^31 + 15 * q^32 - 33 * q^33 - 54 * q^34 - 2 * q^35 + 11 * q^36 - 45 * q^37 + 10 * q^38 - 54 * q^39 + 3 * q^40 - 27 * q^41 - 28 * q^42 - 101 * q^43 - 51 * q^44 - 61 * q^45 - 46 * q^46 + 71 * q^47 - 14 * q^48 + 23 * q^49 + q^50 - 71 * q^51 - 34 * q^52 - 49 * q^53 - 25 * q^54 + 26 * q^55 - 41 * q^56 - 20 * q^57 - 43 * q^58 - 60 * q^59 + 12 * q^60 - 38 * q^61 - 2 * q^62 + 36 * q^63 - 113 * q^64 + 15 * q^65 - 42 * q^66 - 164 * q^67 + 10 * q^68 - 93 * q^69 + 21 * q^70 - 78 * q^71 + q^72 - 18 * q^73 - 23 * q^74 - 4 * q^75 - 112 * q^76 - 35 * q^77 - 44 * q^78 - 124 * q^79 - 5 * q^80 - 45 * q^81 - 34 * q^82 + 5 * q^83 - 60 * q^84 - 8 * q^85 - 25 * q^86 + 12 * q^87 - 149 * q^88 - 44 * q^89 + 12 * q^90 - 192 * q^91 + 35 * q^92 - 13 * q^93 - 32 * q^94 + 79 * q^95 - 59 * q^96 - 31 * q^97 + 25 * q^98 - 134 * q^99

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