LMFDB - Embedded newform 6007.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$0$
Dimension:	$261$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66623 q^{2} -2.56917 q^{3} +5.10878 q^{4} +0.348811 q^{5} +6.85001 q^{6} +3.60714 q^{7} -8.28872 q^{8} +3.60066 q^{9} +O(q^{10})$	\(q-2.66623 q^{2} -2.56917 q^{3} +5.10878 q^{4} +0.348811 q^{5} +6.85001 q^{6} +3.60714 q^{7} -8.28872 q^{8} +3.60066 q^{9} -0.930012 q^{10} +0.0511287 q^{11} -13.1253 q^{12} -5.20251 q^{13} -9.61745 q^{14} -0.896158 q^{15} +11.8821 q^{16} +5.68173 q^{17} -9.60018 q^{18} +7.79585 q^{19} +1.78200 q^{20} -9.26736 q^{21} -0.136321 q^{22} +8.63215 q^{23} +21.2952 q^{24} -4.87833 q^{25} +13.8711 q^{26} -1.54320 q^{27} +18.4281 q^{28} -10.2013 q^{29} +2.38936 q^{30} -10.2105 q^{31} -15.1029 q^{32} -0.131359 q^{33} -15.1488 q^{34} +1.25821 q^{35} +18.3950 q^{36} -6.19651 q^{37} -20.7855 q^{38} +13.3662 q^{39} -2.89120 q^{40} +7.17285 q^{41} +24.7089 q^{42} +9.15764 q^{43} +0.261205 q^{44} +1.25595 q^{45} -23.0153 q^{46} +7.22824 q^{47} -30.5271 q^{48} +6.01143 q^{49} +13.0067 q^{50} -14.5973 q^{51} -26.5785 q^{52} -4.47877 q^{53} +4.11452 q^{54} +0.0178343 q^{55} -29.8985 q^{56} -20.0289 q^{57} +27.1991 q^{58} +7.93411 q^{59} -4.57827 q^{60} -12.5969 q^{61} +27.2236 q^{62} +12.9881 q^{63} +16.5036 q^{64} -1.81470 q^{65} +0.350232 q^{66} -5.31443 q^{67} +29.0267 q^{68} -22.1775 q^{69} -3.35468 q^{70} +10.8175 q^{71} -29.8449 q^{72} +1.02710 q^{73} +16.5213 q^{74} +12.5333 q^{75} +39.8273 q^{76} +0.184428 q^{77} -35.6373 q^{78} -2.97160 q^{79} +4.14460 q^{80} -6.83723 q^{81} -19.1245 q^{82} +6.54913 q^{83} -47.3449 q^{84} +1.98185 q^{85} -24.4164 q^{86} +26.2090 q^{87} -0.423791 q^{88} +6.84015 q^{89} -3.34865 q^{90} -18.7662 q^{91} +44.0997 q^{92} +26.2327 q^{93} -19.2721 q^{94} +2.71928 q^{95} +38.8020 q^{96} +16.1671 q^{97} -16.0278 q^{98} +0.184097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) $ 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * 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 $

$2$	−2.66623	−1.88531	−0.942654	−	0.333770i	$-0.891679\pi$
$2$	−2.66623	−1.88531	−0.942654	+	0.333770i	$0.891679\pi$
$3$	−2.56917	−1.48331	−0.741657	−	0.670779i	$-0.765960\pi$
$3$	−2.56917	−1.48331	−0.741657	+	0.670779i	$0.765960\pi$
$4$	5.10878	2.55439
$5$	0.348811	0.155993	0.0779966	−	0.996954i	$-0.475148\pi$
$5$	0.348811	0.155993	0.0779966	+	0.996954i	$0.475148\pi$
$6$	6.85001	2.79650
$7$	3.60714	1.36337	0.681685	−	0.731646i	$-0.261248\pi$
$7$	3.60714	1.36337	0.681685	+	0.731646i	$0.261248\pi$
$8$	−8.28872	−2.93051
$9$	3.60066	1.20022
$10$	−0.930012	−0.294095
$11$	0.0511287	0.0154159	0.00770794	−	0.999970i	$-0.497546\pi$
$11$	0.0511287	0.0154159	0.00770794	+	0.999970i	$0.497546\pi$
$12$	−13.1253	−3.78896
$13$	−5.20251	−1.44292	−0.721459	−	0.692457i	$-0.756528\pi$
$13$	−5.20251	−1.44292	−0.721459	+	0.692457i	$0.756528\pi$
$14$	−9.61745	−2.57037
$15$	−0.896158	−0.231387
$16$	11.8821	2.97052
$17$	5.68173	1.37802	0.689010	−	0.724751i	$-0.258045\pi$
$17$	5.68173	1.37802	0.689010	+	0.724751i	$0.258045\pi$
$18$	−9.60018	−2.26278
$19$	7.79585	1.78849	0.894246	−	0.447577i	$-0.147713\pi$
$19$	7.79585	1.78849	0.894246	+	0.447577i	$0.147713\pi$
$20$	1.78200	0.398468
$21$	−9.26736	−2.02230
$22$	−0.136321	−0.0290637
$23$	8.63215	1.79993	0.899963	−	0.435965i	$-0.143593\pi$
$23$	8.63215	1.79993	0.899963	+	0.435965i	$0.143593\pi$
$24$	21.2952	4.34686
$25$	−4.87833	−0.975666
$26$	13.8711	2.72035
$27$	−1.54320	−0.296988
$28$	18.4281	3.48258
$29$	−10.2013	−1.89434	−0.947169	−	0.320735i	$-0.896070\pi$
$29$	−10.2013	−1.89434	−0.947169	+	0.320735i	$0.896070\pi$
$30$	2.38936	0.436236
$31$	−10.2105	−1.83387	−0.916933	−	0.399040i	$-0.869343\pi$
$31$	−10.2105	−1.83387	−0.916933	+	0.399040i	$0.869343\pi$
$32$	−15.1029	−2.66984
$33$	−0.131359	−0.0228666
$34$	−15.1488	−2.59799
$35$	1.25821	0.212676
$36$	18.3950	3.06583
$37$	−6.19651	−1.01870	−0.509350	−	0.860559i	$-0.670114\pi$
$37$	−6.19651	−1.01870	−0.509350	+	0.860559i	$0.670114\pi$
$38$	−20.7855	−3.37186
$39$	13.3662	2.14030
$40$	−2.89120	−0.457139
$41$	7.17285	1.12021	0.560105	−	0.828421i	$-0.310761\pi$
$41$	7.17285	1.12021	0.560105	+	0.828421i	$0.310761\pi$
$42$	24.7089	3.81267
$43$	9.15764	1.39653	0.698263	−	0.715841i	$-0.253956\pi$
$43$	9.15764	1.39653	0.698263	+	0.715841i	$0.253956\pi$
$44$	0.261205	0.0393782
$45$	1.25595	0.187226
$46$	−23.0153	−3.39342
$47$	7.22824	1.05435	0.527173	−	0.849758i	$-0.323252\pi$
$47$	7.22824	1.05435	0.527173	+	0.849758i	$0.323252\pi$
$48$	−30.5271	−4.40621
$49$	6.01143	0.858775
$50$	13.0067	1.83943
$51$	−14.5973	−2.04404
$52$	−26.5785	−3.68577
$53$	−4.47877	−0.615206	−0.307603	−	0.951515i	$-0.599527\pi$
$53$	−4.47877	−0.615206	−0.307603	+	0.951515i	$0.599527\pi$
$54$	4.11452	0.559915
$55$	0.0178343	0.00240477
$56$	−29.8985	−3.99536
$57$	−20.0289	−2.65289
$58$	27.1991	3.57141
$59$	7.93411	1.03293	0.516467	−	0.856307i	$-0.327247\pi$
$59$	7.93411	1.03293	0.516467	+	0.856307i	$0.327247\pi$
$60$	−4.57827	−0.591052
$61$	−12.5969	−1.61287	−0.806433	−	0.591325i	$-0.798605\pi$
$61$	−12.5969	−1.61287	−0.806433	+	0.591325i	$0.798605\pi$
$62$	27.2236	3.45741
$63$	12.9881	1.63634
$64$	16.5036	2.06295
$65$	−1.81470	−0.225085
$66$	0.350232	0.0431106
$67$	−5.31443	−0.649261	−0.324630	−	0.945841i	$-0.605240\pi$
$67$	−5.31443	−0.649261	−0.324630	+	0.945841i	$0.605240\pi$
$68$	29.0267	3.52000
$69$	−22.1775	−2.66986
$70$	−3.35468	−0.400961
$71$	10.8175	1.28381	0.641903	−	0.766786i	$-0.278145\pi$
$71$	10.8175	1.28381	0.641903	+	0.766786i	$0.278145\pi$
$72$	−29.8449	−3.51725
$73$	1.02710	0.120213	0.0601063	−	0.998192i	$-0.480856\pi$
$73$	1.02710	0.120213	0.0601063	+	0.998192i	$0.480856\pi$
$74$	16.5213	1.92057
$75$	12.5333	1.44722
$76$	39.8273	4.56850
$77$	0.184428	0.0210175
$78$	−35.6373	−4.03513
$79$	−2.97160	−0.334331	−0.167166	−	0.985929i	$-0.553461\pi$
$79$	−2.97160	−0.334331	−0.167166	+	0.985929i	$0.553461\pi$
$80$	4.14460	0.463381
$81$	−6.83723	−0.759693
$82$	−19.1245	−2.11194
$83$	6.54913	0.718860	0.359430	−	0.933172i	$-0.382971\pi$
$83$	6.54913	0.718860	0.359430	+	0.933172i	$0.382971\pi$
$84$	−47.3449	−5.16575
$85$	1.98185	0.214962
$86$	−24.4164	−2.63288
$87$	26.2090	2.80990
$88$	−0.423791	−0.0451763
$89$	6.84015	0.725054	0.362527	−	0.931973i	$-0.381914\pi$
$89$	6.84015	0.725054	0.362527	+	0.931973i	$0.381914\pi$
$90$	−3.34865	−0.352979
$91$	−18.7662	−1.96723
$92$	44.0997	4.59772
$93$	26.2327	2.72020
$94$	−19.2721	−1.98777
$95$	2.71928	0.278993
$96$	38.8020	3.96021
$97$	16.1671	1.64152	0.820758	−	0.571276i	$-0.193552\pi$
$97$	16.1671	1.64152	0.820758	+	0.571276i	$0.193552\pi$
$98$	−16.0278	−1.61906
$99$	0.184097	0.0185024
$100$	−24.9223	−2.49223
$101$	−1.71341	−0.170490	−0.0852452	−	0.996360i	$-0.527167\pi$
$101$	−1.71341	−0.170490	−0.0852452	+	0.996360i	$0.527167\pi$
$102$	38.9199	3.85364
$103$	1.74575	0.172014	0.0860069	−	0.996295i	$-0.472589\pi$
$103$	1.74575	0.172014	0.0860069	+	0.996295i	$0.472589\pi$
$104$	43.1222	4.22848
$105$	−3.23256	−0.315466
$106$	11.9414	1.15985
$107$	11.3317	1.09548	0.547739	−	0.836649i	$-0.315489\pi$
$107$	11.3317	1.09548	0.547739	+	0.836649i	$0.315489\pi$
$108$	−7.88385	−0.758624
$109$	15.9866	1.53124	0.765618	−	0.643296i	$-0.222433\pi$
$109$	15.9866	1.53124	0.765618	+	0.643296i	$0.222433\pi$
$110$	−0.0475503	−0.00453374
$111$	15.9199	1.51105
$112$	42.8602	4.04991
$113$	16.5834	1.56004	0.780018	−	0.625757i	$-0.215210\pi$
$113$	16.5834	1.56004	0.780018	+	0.625757i	$0.215210\pi$
$114$	53.4017	5.00152
$115$	3.01099	0.280776
$116$	−52.1163	−4.83888
$117$	−18.7325	−1.73182
$118$	−21.1542	−1.94740
$119$	20.4948	1.87875
$120$	7.42800	0.678081
$121$	−10.9974	−0.999762
$122$	33.5862	3.04075
$123$	−18.4283	−1.66162
$124$	−52.1634	−4.68441
$125$	−3.44568	−0.308191
$126$	−34.6292	−3.08501
$127$	7.96535	0.706811	0.353405	−	0.935470i	$-0.385024\pi$
$127$	7.96535	0.706811	0.353405	+	0.935470i	$0.385024\pi$
$128$	−13.7967	−1.21947
$129$	−23.5276	−2.07149
$130$	4.83840	0.424356
$131$	−18.6641	−1.63069	−0.815347	−	0.578973i	$-0.803454\pi$
$131$	−18.6641	−1.63069	−0.815347	+	0.578973i	$0.803454\pi$
$132$	−0.671082	−0.0584102
$133$	28.1207	2.43837
$134$	14.1695	1.22406
$135$	−0.538285	−0.0463282
$136$	−47.0942	−4.03830
$137$	−0.0676885	−0.00578302	−0.00289151	−	0.999996i	$-0.500920\pi$
$137$	−0.0676885	−0.00578302	−0.00289151	+	0.999996i	$0.500920\pi$
$138$	59.1303	5.03350
$139$	−10.1713	−0.862717	−0.431358	−	0.902181i	$-0.641966\pi$
$139$	−10.1713	−0.862717	−0.431358	+	0.902181i	$0.641966\pi$
$140$	6.42792	0.543258
$141$	−18.5706	−1.56393
$142$	−28.8420	−2.42037
$143$	−0.265998	−0.0222438
$144$	42.7833	3.56527
$145$	−3.55834	−0.295504
$146$	−2.73848	−0.226638
$147$	−15.4444	−1.27383
$148$	−31.6566	−2.60216
$149$	1.59105	0.130344	0.0651718	−	0.997874i	$-0.479240\pi$
$149$	1.59105	0.130344	0.0651718	+	0.997874i	$0.479240\pi$
$150$	−33.4166	−2.72845
$151$	20.9013	1.70093	0.850464	−	0.526034i	$-0.176322\pi$
$151$	20.9013	1.70093	0.850464	+	0.526034i	$0.176322\pi$
$152$	−64.6176	−5.24118
$153$	20.4580	1.65393
$154$	−0.491728	−0.0396245
$155$	−3.56155	−0.286071
$156$	68.2848	5.46716
$157$	−9.25833	−0.738895	−0.369448	−	0.929252i	$-0.620453\pi$
$157$	−9.25833	−0.738895	−0.369448	+	0.929252i	$0.620453\pi$
$158$	7.92298	0.630318
$159$	11.5067	0.912543
$160$	−5.26806	−0.416477
$161$	31.1373	2.45396
$162$	18.2296	1.43226
$163$	3.02114	0.236634	0.118317	−	0.992976i	$-0.462250\pi$
$163$	3.02114	0.236634	0.118317	+	0.992976i	$0.462250\pi$
$164$	36.6445	2.86146
$165$	−0.0458194	−0.00356703
$166$	−17.4615	−1.35527
$167$	−16.5016	−1.27693	−0.638467	−	0.769650i	$-0.720431\pi$
$167$	−16.5016	−1.27693	−0.638467	+	0.769650i	$0.720431\pi$
$168$	76.8146	5.92637
$169$	14.0662	1.08201
$170$	−5.28407	−0.405270
$171$	28.0702	2.14658
$172$	46.7844	3.56727
$173$	11.8471	0.900717	0.450358	−	0.892848i	$-0.351296\pi$
$173$	11.8471	0.900717	0.450358	+	0.892848i	$0.351296\pi$
$174$	−69.8792	−5.29753
$175$	−17.5968	−1.33019
$176$	0.607515	0.0457931
$177$	−20.3841	−1.53216
$178$	−18.2374	−1.36695
$179$	−7.27477	−0.543742	−0.271871	−	0.962334i	$-0.587642\pi$
$179$	−7.27477	−0.543742	−0.271871	+	0.962334i	$0.587642\pi$
$180$	6.41638	0.478249
$181$	−8.75010	−0.650390	−0.325195	−	0.945647i	$-0.605430\pi$
$181$	−8.75010	−0.650390	−0.325195	+	0.945647i	$0.605430\pi$
$182$	50.0349	3.70884
$183$	32.3636	2.39239
$184$	−71.5494	−5.27470
$185$	−2.16141	−0.158910
$186$	−69.9423	−5.12842
$187$	0.290499	0.0212434
$188$	36.9275	2.69321
$189$	−5.56652	−0.404905
$190$	−7.25023	−0.525987
$191$	0.422808	0.0305933	0.0152966	−	0.999883i	$-0.495131\pi$
$191$	0.422808	0.0305933	0.0152966	+	0.999883i	$0.495131\pi$
$192$	−42.4007	−3.06001
$193$	−5.19612	−0.374025	−0.187013	−	0.982358i	$-0.559881\pi$
$193$	−5.19612	−0.374025	−0.187013	+	0.982358i	$0.559881\pi$
$194$	−43.1051	−3.09476
$195$	4.66227	0.333872
$196$	30.7111	2.19365
$197$	4.78794	0.341126	0.170563	−	0.985347i	$-0.445441\pi$
$197$	4.78794	0.341126	0.170563	+	0.985347i	$0.445441\pi$
$198$	−0.490845	−0.0348828
$199$	12.3121	0.872783	0.436392	−	0.899757i	$-0.356256\pi$
$199$	12.3121	0.872783	0.436392	+	0.899757i	$0.356256\pi$
$200$	40.4351	2.85919
$201$	13.6537	0.963057
$202$	4.56834	0.321427
$203$	−36.7976	−2.58268
$204$	−74.5746	−5.22127
$205$	2.50197	0.174745
$206$	−4.65457	−0.324299
$207$	31.0814	2.16031
$208$	−61.8166	−4.28621
$209$	0.398592	0.0275712
$210$	8.61875	0.594750
$211$	1.90337	0.131034	0.0655169	−	0.997851i	$-0.479130\pi$
$211$	1.90337	0.131034	0.0655169	+	0.997851i	$0.479130\pi$
$212$	−22.8810	−1.57148
$213$	−27.7922	−1.90429
$214$	−30.2129	−2.06531
$215$	3.19429	0.217849
$216$	12.7911	0.870326
$217$	−36.8308	−2.50024
$218$	−42.6239	−2.88685
$219$	−2.63879	−0.178313
$220$	0.0911114	0.00614273
$221$	−29.5593	−1.98837
$222$	−42.4462	−2.84880
$223$	−3.26908	−0.218913	−0.109457	−	0.993992i	$-0.534911\pi$
$223$	−3.26908	−0.218913	−0.109457	+	0.993992i	$0.534911\pi$
$224$	−54.4782	−3.63998
$225$	−17.5652	−1.17101
$226$	−44.2152	−2.94115
$227$	9.61264	0.638013	0.319007	−	0.947753i	$-0.396651\pi$
$227$	9.61264	0.638013	0.319007	+	0.947753i	$0.396651\pi$
$228$	−102.323	−6.77652
$229$	−15.2652	−1.00875	−0.504376	−	0.863484i	$-0.668278\pi$
$229$	−15.2652	−1.00875	−0.504376	+	0.863484i	$0.668278\pi$
$230$	−8.02800	−0.529350
$231$	−0.473828	−0.0311756
$232$	84.5559	5.55137
$233$	−21.2888	−1.39467	−0.697337	−	0.716744i	$-0.745632\pi$
$233$	−21.2888	−1.39467	−0.697337	+	0.716744i	$0.745632\pi$
$234$	49.9451	3.26501
$235$	2.52129	0.164471
$236$	40.5336	2.63851
$237$	7.63457	0.495918
$238$	−54.6437	−3.54203
$239$	11.0483	0.714653	0.357326	−	0.933980i	$-0.383688\pi$
$239$	11.0483	0.714653	0.357326	+	0.933980i	$0.383688\pi$
$240$	−10.6482	−0.687339
$241$	−13.3386	−0.859214	−0.429607	−	0.903016i	$-0.641348\pi$
$241$	−13.3386	−0.859214	−0.429607	+	0.903016i	$0.641348\pi$
$242$	29.3216	1.88486
$243$	22.1956	1.42385
$244$	−64.3547	−4.11989
$245$	2.09685	0.133963
$246$	49.1341	3.13268
$247$	−40.5580	−2.58065
$248$	84.6323	5.37416
$249$	−16.8258	−1.06629
$250$	9.18696	0.581034
$251$	−9.87507	−0.623309	−0.311654	−	0.950196i	$-0.600883\pi$
$251$	−9.87507	−0.623309	−0.311654	+	0.950196i	$0.600883\pi$
$252$	66.3532	4.17986
$253$	0.441350	0.0277475
$254$	−21.2375	−1.33256
$255$	−5.09172	−0.318856
$256$	3.77786	0.236116
$257$	2.50563	0.156297	0.0781484	−	0.996942i	$-0.475099\pi$
$257$	2.50563	0.156297	0.0781484	+	0.996942i	$0.475099\pi$
$258$	62.7299	3.90539
$259$	−22.3517	−1.38886
$260$	−9.27089	−0.574956
$261$	−36.7315	−2.27362
$262$	49.7629	3.07436
$263$	−8.73654	−0.538718	−0.269359	−	0.963040i	$-0.586812\pi$
$263$	−8.73654	−0.538718	−0.269359	+	0.963040i	$0.586812\pi$
$264$	1.08879	0.0670106
$265$	−1.56224	−0.0959679
$266$	−74.9762	−4.59709
$267$	−17.5735	−1.07548
$268$	−27.1502	−1.65846
$269$	−24.0317	−1.46524	−0.732618	−	0.680640i	$-0.761702\pi$
$269$	−24.0317	−1.46524	−0.732618	+	0.680640i	$0.761702\pi$
$270$	1.43519	0.0873429
$271$	4.11319	0.249858	0.124929	−	0.992166i	$-0.460130\pi$
$271$	4.11319	0.249858	0.124929	+	0.992166i	$0.460130\pi$
$272$	67.5107	4.09344
$273$	48.2136	2.91802
$274$	0.180473	0.0109028
$275$	−0.249423	−0.0150407
$276$	−113.300	−6.81985
$277$	−7.20970	−0.433189	−0.216595	−	0.976262i	$-0.569495\pi$
$277$	−7.20970	−0.433189	−0.216595	+	0.976262i	$0.569495\pi$
$278$	27.1190	1.62649
$279$	−36.7647	−2.20104
$280$	−10.4290	−0.623249
$281$	7.42624	0.443013	0.221506	−	0.975159i	$-0.428903\pi$
$281$	7.42624	0.443013	0.221506	+	0.975159i	$0.428903\pi$
$282$	49.5135	2.94848
$283$	−1.30259	−0.0774307	−0.0387153	−	0.999250i	$-0.512327\pi$
$283$	−1.30259	−0.0774307	−0.0387153	+	0.999250i	$0.512327\pi$
$284$	55.2644	3.27934
$285$	−6.98631	−0.413833
$286$	0.709211	0.0419365
$287$	25.8734	1.52726
$288$	−54.3804	−3.20439
$289$	15.2820	0.898941
$290$	9.48735	0.557116
$291$	−41.5360	−2.43488
$292$	5.24721	0.307070
$293$	17.5218	1.02364	0.511819	−	0.859094i	$-0.328972\pi$
$293$	17.5218	1.02364	0.511819	+	0.859094i	$0.328972\pi$
$294$	41.1783	2.40157
$295$	2.76751	0.161131
$296$	51.3612	2.98531
$297$	−0.0789016	−0.00457834
$298$	−4.24209	−0.245738
$299$	−44.9089	−2.59715
$300$	64.0298	3.69676
$301$	33.0328	1.90398
$302$	−55.7278	−3.20677
$303$	4.40204	0.252891
$304$	92.6309	5.31275
$305$	−4.39394	−0.251596
$306$	−54.5456	−3.11816
$307$	−11.3753	−0.649222	−0.324611	−	0.945848i	$-0.605233\pi$
$307$	−11.3753	−0.649222	−0.324611	+	0.945848i	$0.605233\pi$
$308$	0.942202	0.0536870
$309$	−4.48514	−0.255150
$310$	9.49592	0.539332
$311$	−3.40638	−0.193158	−0.0965792	−	0.995325i	$-0.530790\pi$
$311$	−3.40638	−0.193158	−0.0965792	+	0.995325i	$0.530790\pi$
$312$	−110.788	−6.27216
$313$	18.1585	1.02638	0.513190	−	0.858275i	$-0.328464\pi$
$313$	18.1585	1.02638	0.513190	+	0.858275i	$0.328464\pi$
$314$	24.6848	1.39305
$315$	4.53039	0.255258
$316$	−15.1813	−0.854013
$317$	19.3150	1.08484	0.542419	−	0.840108i	$-0.317508\pi$
$317$	19.3150	1.08484	0.542419	+	0.840108i	$0.317508\pi$
$318$	−30.6796	−1.72043
$319$	−0.521580	−0.0292029
$320$	5.75666	0.321807
$321$	−29.1131	−1.62494
$322$	−83.0192	−4.62648
$323$	44.2939	2.46458
$324$	−34.9299	−1.94055
$325$	25.3796	1.40781
$326$	−8.05506	−0.446128
$327$	−41.0723	−2.27130
$328$	−59.4537	−3.28278
$329$	26.0732	1.43746
$330$	0.122165	0.00672496
$331$	25.4737	1.40016	0.700081	−	0.714064i	$-0.253147\pi$
$331$	25.4737	1.40016	0.700081	+	0.714064i	$0.253147\pi$
$332$	33.4580	1.83625
$333$	−22.3115	−1.22266
$334$	43.9971	2.40741
$335$	−1.85373	−0.101280
$336$	−110.115	−6.00729
$337$	−8.71664	−0.474826	−0.237413	−	0.971409i	$-0.576299\pi$
$337$	−8.71664	−0.474826	−0.237413	+	0.971409i	$0.576299\pi$
$338$	−37.5036	−2.03993
$339$	−42.6057	−2.31402
$340$	10.1248	0.549097
$341$	−0.522051	−0.0282707
$342$	−74.8416	−4.04697
$343$	−3.56592	−0.192542
$344$	−75.9051	−4.09253
$345$	−7.73576	−0.416480
$346$	−31.5870	−1.69813
$347$	−14.0508	−0.754288	−0.377144	−	0.926155i	$-0.623094\pi$
$347$	−14.0508	−0.754288	−0.377144	+	0.926155i	$0.623094\pi$
$348$	133.896	7.17757
$349$	30.0074	1.60626	0.803129	−	0.595805i	$-0.203167\pi$
$349$	30.0074	1.60626	0.803129	+	0.595805i	$0.203167\pi$
$350$	46.9171	2.50782
$351$	8.02850	0.428530
$352$	−0.772191	−0.0411579
$353$	3.54394	0.188625	0.0943123	−	0.995543i	$-0.469935\pi$
$353$	3.54394	0.188625	0.0943123	+	0.995543i	$0.469935\pi$
$354$	54.3487	2.88860
$355$	3.77328	0.200265
$356$	34.9448	1.85207
$357$	−52.6546	−2.78678
$358$	19.3962	1.02512
$359$	−2.52731	−0.133386	−0.0666932	−	0.997774i	$-0.521245\pi$
$359$	−2.52731	−0.133386	−0.0666932	+	0.997774i	$0.521245\pi$
$360$	−10.4102	−0.548667
$361$	41.7753	2.19870
$362$	23.3298	1.22619
$363$	28.2542	1.48296
$364$	−95.8722	−5.02507
$365$	0.358263	0.0187524
$366$	−86.2888	−4.51039
$367$	−7.16206	−0.373856	−0.186928	−	0.982374i	$-0.559853\pi$
$367$	−7.16206	−0.373856	−0.186928	+	0.982374i	$0.559853\pi$
$368$	102.568	5.34672
$369$	25.8270	1.34450
$370$	5.76283	0.299595
$371$	−16.1555	−0.838752
$372$	134.017	6.94845
$373$	−23.5767	−1.22075	−0.610377	−	0.792111i	$-0.708982\pi$
$373$	−23.5767	−1.22075	−0.610377	+	0.792111i	$0.708982\pi$
$374$	−0.774537	−0.0400504
$375$	8.85254	0.457143
$376$	−59.9128	−3.08977
$377$	53.0725	2.73337
$378$	14.8416	0.763370
$379$	−1.95675	−0.100511	−0.0502556	−	0.998736i	$-0.516004\pi$
$379$	−1.95675	−0.100511	−0.0502556	+	0.998736i	$0.516004\pi$
$380$	13.8922	0.712656
$381$	−20.4644	−1.04842
$382$	−1.12730	−0.0576778
$383$	−26.5091	−1.35455	−0.677276	−	0.735729i	$-0.736840\pi$
$383$	−26.5091	−1.35455	−0.677276	+	0.735729i	$0.736840\pi$
$384$	35.4461	1.80885
$385$	0.0643306	0.00327859
$386$	13.8541	0.705153
$387$	32.9735	1.67614
$388$	82.5939	4.19307
$389$	−12.7893	−0.648444	−0.324222	−	0.945981i	$-0.605103\pi$
$389$	−12.7893	−0.648444	−0.324222	+	0.945981i	$0.605103\pi$
$390$	−12.4307	−0.629452
$391$	49.0455	2.48034
$392$	−49.8270	−2.51665
$393$	47.9514	2.41883
$394$	−12.7657	−0.643129
$395$	−1.03653	−0.0521534
$396$	0.940511	0.0472624
$397$	6.45772	0.324104	0.162052	−	0.986782i	$-0.448189\pi$
$397$	6.45772	0.324104	0.162052	+	0.986782i	$0.448189\pi$
$398$	−32.8269	−1.64547
$399$	−72.2470	−3.61687
$400$	−57.9647	−2.89823
$401$	9.84710	0.491741	0.245870	−	0.969303i	$-0.420926\pi$
$401$	9.84710	0.491741	0.245870	+	0.969303i	$0.420926\pi$
$402$	−36.4039	−1.81566
$403$	53.1205	2.64612
$404$	−8.75342	−0.435499
$405$	−2.38491	−0.118507
$406$	98.1107	4.86915
$407$	−0.316820	−0.0157042
$408$	120.993	5.99006
$409$	−17.6998	−0.875197	−0.437598	−	0.899171i	$-0.644171\pi$
$409$	−17.6998	−0.875197	−0.437598	+	0.899171i	$0.644171\pi$
$410$	−6.67083	−0.329449
$411$	0.173904	0.00857803
$412$	8.91865	0.439390
$413$	28.6194	1.40827
$414$	−82.8702	−4.07285
$415$	2.28441	0.112137
$416$	78.5730	3.85236
$417$	26.1318	1.27968
$418$	−1.06274	−0.0519802
$419$	24.1444	1.17953	0.589765	−	0.807575i	$-0.299220\pi$
$419$	24.1444	1.17953	0.589765	+	0.807575i	$0.299220\pi$
$420$	−16.5144	−0.805823
$421$	25.8420	1.25946	0.629732	−	0.776813i	$-0.283165\pi$
$421$	25.8420	1.25946	0.629732	+	0.776813i	$0.283165\pi$
$422$	−5.07483	−0.247039
$423$	26.0264	1.26545
$424$	37.1232	1.80286
$425$	−27.7173	−1.34449
$426$	74.1003	3.59017
$427$	−45.4387	−2.19893
$428$	57.8912	2.79828
$429$	0.683395	0.0329946
$430$	−8.51671	−0.410712
$431$	−8.18874	−0.394438	−0.197219	−	0.980359i	$-0.563191\pi$
$431$	−8.18874	−0.394438	−0.197219	+	0.980359i	$0.563191\pi$
$432$	−18.3364	−0.882209
$433$	17.5362	0.842736	0.421368	−	0.906890i	$-0.361550\pi$
$433$	17.5362	0.842736	0.421368	+	0.906890i	$0.361550\pi$
$434$	98.1994	4.71372
$435$	9.14199	0.438325
$436$	81.6719	3.91137
$437$	67.2949	3.21915
$438$	7.03563	0.336175
$439$	2.15547	0.102875	0.0514375	−	0.998676i	$-0.483620\pi$
$439$	2.15547	0.102875	0.0514375	+	0.998676i	$0.483620\pi$
$440$	−0.147823	−0.00704720
$441$	21.6451	1.03072
$442$	78.8118	3.74869
$443$	13.4907	0.640964	0.320482	−	0.947255i	$-0.396155\pi$
$443$	13.4907	0.640964	0.320482	+	0.947255i	$0.396155\pi$
$444$	81.3314	3.85982
$445$	2.38592	0.113104
$446$	8.71611	0.412720
$447$	−4.08767	−0.193340
$448$	59.5308	2.81257
$449$	−12.1385	−0.572854	−0.286427	−	0.958102i	$-0.592468\pi$
$449$	−12.1385	−0.572854	−0.286427	+	0.958102i	$0.592468\pi$
$450$	46.8329	2.20772
$451$	0.366738	0.0172690
$452$	84.7210	3.98494
$453$	−53.6992	−2.52301
$454$	−25.6295	−1.20285
$455$	−6.54586	−0.306875
$456$	166.014	7.77432
$457$	−11.6518	−0.545047	−0.272523	−	0.962149i	$-0.587858\pi$
$457$	−11.6518	−0.545047	−0.272523	+	0.962149i	$0.587858\pi$
$458$	40.7005	1.90181
$459$	−8.76802	−0.409256
$460$	15.3825	0.717213
$461$	4.78062	0.222656	0.111328	−	0.993784i	$-0.464490\pi$
$461$	4.78062	0.222656	0.111328	+	0.993784i	$0.464490\pi$
$462$	1.26333	0.0587756
$463$	−12.8833	−0.598738	−0.299369	−	0.954137i	$-0.596776\pi$
$463$	−12.8833	−0.598738	−0.299369	+	0.954137i	$0.596776\pi$
$464$	−121.213	−5.62717
$465$	9.15025	0.424333
$466$	56.7607	2.62939
$467$	−13.9779	−0.646822	−0.323411	−	0.946259i	$-0.604830\pi$
$467$	−13.9779	−0.646822	−0.323411	+	0.946259i	$0.604830\pi$
$468$	−95.7001	−4.42374
$469$	−19.1699	−0.885182
$470$	−6.72234	−0.310079
$471$	23.7863	1.09601
$472$	−65.7636	−3.02702
$473$	0.468218	0.0215287
$474$	−20.3555	−0.934959
$475$	−38.0307	−1.74497
$476$	104.703	4.79906
$477$	−16.1265	−0.738382
$478$	−29.4572	−1.34734
$479$	−23.8032	−1.08760	−0.543799	−	0.839216i	$-0.683014\pi$
$479$	−23.8032	−1.08760	−0.543799	+	0.839216i	$0.683014\pi$
$480$	13.5346	0.617766
$481$	32.2374	1.46990
$482$	35.5637	1.61988
$483$	−79.9972	−3.64000
$484$	−56.1832	−2.55378
$485$	5.63925	0.256065
$486$	−59.1787	−2.68440
$487$	25.0579	1.13548	0.567742	−	0.823207i	$-0.307817\pi$
$487$	25.0579	1.13548	0.567742	+	0.823207i	$0.307817\pi$
$488$	104.412	4.72651
$489$	−7.76184	−0.351003
$490$	−5.59070	−0.252562
$491$	−22.7814	−1.02811	−0.514055	−	0.857757i	$-0.671857\pi$
$491$	−22.7814	−1.02811	−0.514055	+	0.857757i	$0.671857\pi$
$492$	−94.1461	−4.24444
$493$	−57.9611	−2.61044
$494$	108.137	4.86531
$495$	0.0642151	0.00288626
$496$	−121.322	−5.44753
$497$	39.0203	1.75030
$498$	44.8616	2.01030
$499$	21.4745	0.961329	0.480665	−	0.876904i	$-0.340395\pi$
$499$	21.4745	0.961329	0.480665	+	0.876904i	$0.340395\pi$
$500$	−17.6032	−0.787239
$501$	42.3955	1.89409
$502$	26.3292	1.17513
$503$	2.69357	0.120100	0.0600501	−	0.998195i	$-0.480874\pi$
$503$	2.69357	0.120100	0.0600501	+	0.998195i	$0.480874\pi$
$504$	−107.654	−4.79531
$505$	−0.597656	−0.0265954
$506$	−1.17674	−0.0523125
$507$	−36.1384	−1.60496
$508$	40.6932	1.80547
$509$	−28.3687	−1.25742	−0.628710	−	0.777640i	$-0.716417\pi$
$509$	−28.3687	−1.25742	−0.628710	+	0.777640i	$0.716417\pi$
$510$	13.5757	0.601142
$511$	3.70488	0.163894
$512$	17.5207	0.774314
$513$	−12.0305	−0.531161
$514$	−6.68058	−0.294668
$515$	0.608937	0.0268330
$516$	−120.197	−5.29139
$517$	0.369570	0.0162537
$518$	59.5947	2.61844
$519$	−30.4372	−1.33605
$520$	15.0415	0.659614
$521$	−23.5574	−1.03207	−0.516034	−	0.856568i	$-0.672592\pi$
$521$	−23.5574	−1.03207	−0.516034	+	0.856568i	$0.672592\pi$
$522$	97.9346	4.28648
$523$	0.0509974	0.00222996	0.00111498	−	0.999999i	$-0.499645\pi$
$523$	0.0509974	0.00222996	0.00111498	+	0.999999i	$0.499645\pi$
$524$	−95.3510	−4.16543
$525$	45.2093	1.97309
$526$	23.2936	1.01565
$527$	−58.0135	−2.52711
$528$	−1.56081	−0.0679256
$529$	51.5139	2.23974
$530$	4.16530	0.180929
$531$	28.5680	1.23975
$532$	143.662	6.22856
$533$	−37.3169	−1.61637
$534$	46.8551	2.02762
$535$	3.95263	0.170887
$536$	44.0498	1.90266
$537$	18.6902	0.806540
$538$	64.0739	2.76242
$539$	0.307356	0.0132388
$540$	−2.74998	−0.118340
$541$	4.06170	0.174626	0.0873130	−	0.996181i	$-0.472172\pi$
$541$	4.06170	0.174626	0.0873130	+	0.996181i	$0.472172\pi$
$542$	−10.9667	−0.471060
$543$	22.4805	0.964732
$544$	−85.8105	−3.67909
$545$	5.57630	0.238862
$546$	−128.548	−5.50137
$547$	19.5815	0.837243	0.418622	−	0.908161i	$-0.362513\pi$
$547$	19.5815	0.837243	0.418622	+	0.908161i	$0.362513\pi$
$548$	−0.345806	−0.0147721
$549$	−45.3571	−1.93579
$550$	0.665018	0.0283565
$551$	−79.5280	−3.38801
$552$	183.823	7.82403
$553$	−10.7190	−0.455817
$554$	19.2227	0.816695
$555$	5.55305	0.235714
$556$	−51.9628	−2.20372
$557$	−15.2112	−0.644521	−0.322260	−	0.946651i	$-0.604443\pi$
$557$	−15.2112	−0.644521	−0.322260	+	0.946651i	$0.604443\pi$
$558$	98.0230	4.14965
$559$	−47.6427	−2.01507
$560$	14.9501	0.631759
$561$	−0.746343	−0.0315106
$562$	−19.8001	−0.835215
$563$	31.0075	1.30681	0.653404	−	0.757009i	$-0.273340\pi$
$563$	31.0075	1.30681	0.653404	+	0.757009i	$0.273340\pi$
$564$	−94.8731	−3.99488
$565$	5.78448	0.243355
$566$	3.47299	0.145981
$567$	−24.6628	−1.03574
$568$	−89.6636	−3.76220
$569$	6.15156	0.257887	0.128943	−	0.991652i	$-0.458841\pi$
$569$	6.15156	0.257887	0.128943	+	0.991652i	$0.458841\pi$
$570$	18.6271	0.780204
$571$	12.9365	0.541376	0.270688	−	0.962667i	$-0.412749\pi$
$571$	12.9365	0.541376	0.270688	+	0.962667i	$0.412749\pi$
$572$	−1.35892	−0.0568195
$573$	−1.08627	−0.0453795
$574$	−68.9845	−2.87936
$575$	−42.1105	−1.75613
$576$	59.4239	2.47600
$577$	−37.2088	−1.54902	−0.774512	−	0.632559i	$-0.782004\pi$
$577$	−37.2088	−1.54902	−0.774512	+	0.632559i	$0.782004\pi$
$578$	−40.7453	−1.69478
$579$	13.3497	0.554796
$580$	−18.1788	−0.754832
$581$	23.6236	0.980071
$582$	110.744	4.59051
$583$	−0.228993	−0.00948394
$584$	−8.51332	−0.352284
$585$	−6.53410	−0.270152
$586$	−46.7173	−1.92987
$587$	33.4920	1.38236	0.691181	−	0.722682i	$-0.257091\pi$
$587$	33.4920	1.38236	0.691181	+	0.722682i	$0.257091\pi$
$588$	−78.9021	−3.25387
$589$	−79.5998	−3.27985
$590$	−7.37882	−0.303781
$591$	−12.3010	−0.505997
$592$	−73.6274	−3.02607
$593$	46.2552	1.89947	0.949737	−	0.313049i	$-0.101351\pi$
$593$	46.2552	1.89947	0.949737	+	0.313049i	$0.101351\pi$
$594$	0.210370	0.00863158
$595$	7.14881	0.293072
$596$	8.12830	0.332948
$597$	−31.6320	−1.29461
$598$	119.737	4.89642
$599$	12.1095	0.494780	0.247390	−	0.968916i	$-0.420427\pi$
$599$	12.1095	0.494780	0.247390	+	0.968916i	$0.420427\pi$
$600$	−103.885	−4.24108
$601$	27.3705	1.11647	0.558234	−	0.829684i	$-0.311479\pi$
$601$	27.3705	1.11647	0.558234	+	0.829684i	$0.311479\pi$
$602$	−88.0731	−3.58959
$603$	−19.1354	−0.779255
$604$	106.780	4.34483
$605$	−3.83601	−0.155956
$606$	−11.7369	−0.476777
$607$	−15.1152	−0.613509	−0.306754	−	0.951789i	$-0.599243\pi$
$607$	−15.1152	−0.613509	−0.306754	+	0.951789i	$0.599243\pi$
$608$	−117.740	−4.77498
$609$	94.5393	3.83093
$610$	11.7152	0.474337
$611$	−37.6050	−1.52134
$612$	104.515	4.22478
$613$	45.0829	1.82088	0.910440	−	0.413641i	$-0.135743\pi$
$613$	45.0829	1.82088	0.910440	+	0.413641i	$0.135743\pi$
$614$	30.3292	1.22399
$615$	−6.42800	−0.259202
$616$	−1.52867	−0.0615920
$617$	−9.04881	−0.364291	−0.182146	−	0.983272i	$-0.558304\pi$
$617$	−9.04881	−0.364291	−0.182146	+	0.983272i	$0.558304\pi$
$618$	11.9584	0.481037
$619$	−17.6213	−0.708260	−0.354130	−	0.935196i	$-0.615223\pi$
$619$	−17.6213	−0.708260	−0.354130	+	0.935196i	$0.615223\pi$
$620$	−18.1952	−0.730736
$621$	−13.3211	−0.534557
$622$	9.08220	0.364163
$623$	24.6733	0.988516
$624$	158.818	6.35780
$625$	23.1898	0.927590
$626$	−48.4148	−1.93504
$627$	−1.02405	−0.0408967
$628$	−47.2988	−1.88743
$629$	−35.2069	−1.40379
$630$	−12.0790	−0.481241
$631$	−3.33334	−0.132698	−0.0663491	−	0.997796i	$-0.521135\pi$
$631$	−3.33334	−0.132698	−0.0663491	+	0.997796i	$0.521135\pi$
$632$	24.6308	0.979760
$633$	−4.89010	−0.194364
$634$	−51.4982	−2.04526
$635$	2.77841	0.110258
$636$	58.7854	2.33099
$637$	−31.2745	−1.23914
$638$	1.39065	0.0550565
$639$	38.9503	1.54085
$640$	−4.81244	−0.190228
$641$	−30.7572	−1.21484	−0.607418	−	0.794383i	$-0.707794\pi$
$641$	−30.7572	−1.21484	−0.607418	+	0.794383i	$0.707794\pi$
$642$	77.6223	3.06351
$643$	47.6666	1.87979	0.939893	−	0.341469i	$-0.110924\pi$
$643$	47.6666	1.87979	0.939893	+	0.341469i	$0.110924\pi$
$644$	159.074	6.26838
$645$	−8.20669	−0.323138
$646$	−118.098	−4.64649
$647$	29.7313	1.16886	0.584428	−	0.811445i	$-0.301319\pi$
$647$	29.7313	1.16886	0.584428	+	0.811445i	$0.301319\pi$
$648$	56.6719	2.22628
$649$	0.405661	0.0159236
$650$	−67.6678	−2.65415
$651$	94.6247	3.70864
$652$	15.4344	0.604456
$653$	28.1238	1.10057	0.550284	−	0.834978i	$-0.314519\pi$
$653$	28.1238	1.10057	0.550284	+	0.834978i	$0.314519\pi$
$654$	109.508	4.28211
$655$	−6.51027	−0.254377
$656$	85.2283	3.32761
$657$	3.69823	0.144282
$658$	−69.5172	−2.71006
$659$	3.37599	0.131510	0.0657549	−	0.997836i	$-0.479054\pi$
$659$	3.37599	0.131510	0.0657549	+	0.997836i	$0.479054\pi$
$660$	−0.234081	−0.00911159
$661$	−23.1864	−0.901845	−0.450922	−	0.892563i	$-0.648905\pi$
$661$	−23.1864	−0.901845	−0.450922	+	0.892563i	$0.648905\pi$
$662$	−67.9188	−2.63974
$663$	75.9429	2.94938
$664$	−54.2839	−2.10662
$665$	9.80882	0.380370
$666$	59.4877	2.30510
$667$	−88.0593	−3.40967
$668$	−84.3031	−3.26178
$669$	8.39883	0.324717
$670$	4.94248	0.190945
$671$	−0.644062	−0.0248637
$672$	139.964	5.39923
$673$	−39.7802	−1.53341	−0.766707	−	0.641997i	$-0.778106\pi$
$673$	−39.7802	−1.53341	−0.766707	+	0.641997i	$0.778106\pi$
$674$	23.2406	0.895193
$675$	7.52822	0.289761
$676$	71.8609	2.76388
$677$	32.7202	1.25754	0.628770	−	0.777591i	$-0.283559\pi$
$677$	32.7202	1.25754	0.628770	+	0.777591i	$0.283559\pi$
$678$	113.596	4.36265
$679$	58.3167	2.23799
$680$	−16.4270	−0.629947
$681$	−24.6965	−0.946373
$682$	1.39191	0.0532989
$683$	23.6511	0.904984	0.452492	−	0.891769i	$-0.350535\pi$
$683$	23.6511	0.904984	0.452492	+	0.891769i	$0.350535\pi$
$684$	143.404	5.48321
$685$	−0.0236105	−0.000902111 0
$686$	9.50756	0.363000
$687$	39.2190	1.49630
$688$	108.812	4.14841
$689$	23.3008	0.887691
$690$	20.6253	0.785193
$691$	−19.3385	−0.735673	−0.367836	−	0.929891i	$-0.619901\pi$
$691$	−19.3385	−0.735673	−0.367836	+	0.929891i	$0.619901\pi$
$692$	60.5241	2.30078
$693$	0.664063	0.0252256
$694$	37.4627	1.42207
$695$	−3.54786	−0.134578
$696$	−217.239	−8.23442
$697$	40.7542	1.54367
$698$	−80.0065	−3.02829
$699$	54.6945	2.06874
$700$	−89.8982	−3.39783
$701$	−3.50471	−0.132371	−0.0661856	−	0.997807i	$-0.521083\pi$
$701$	−3.50471	−0.132371	−0.0661856	+	0.997807i	$0.521083\pi$
$702$	−21.4058	−0.807911
$703$	−48.3071	−1.82194
$704$	0.843809	0.0318022
$705$	−6.47764	−0.243962
$706$	−9.44894	−0.355616
$707$	−6.18049	−0.232441
$708$	−104.138	−3.91374
$709$	4.33785	0.162912	0.0814558	−	0.996677i	$-0.474043\pi$
$709$	4.33785	0.162912	0.0814558	+	0.996677i	$0.474043\pi$
$710$	−10.0604	−0.377562
$711$	−10.6997	−0.401271
$712$	−56.6961	−2.12477
$713$	−88.1389	−3.30083
$714$	140.389	5.25394
$715$	−0.0927830	−0.00346989
$716$	−37.1652	−1.38893
$717$	−28.3849	−1.06005
$718$	6.73840	0.251475
$719$	23.4378	0.874083	0.437042	−	0.899441i	$-0.356026\pi$
$719$	23.4378	0.874083	0.437042	+	0.899441i	$0.356026\pi$
$720$	14.9233	0.556159
$721$	6.29715	0.234518
$722$	−111.383	−4.14523
$723$	34.2692	1.27448
$724$	−44.7023	−1.66135
$725$	49.7654	1.84824
$726$	−75.3322	−2.79584
$727$	20.3593	0.755084	0.377542	−	0.925992i	$-0.376769\pi$
$727$	20.3593	0.755084	0.377542	+	0.925992i	$0.376769\pi$
$728$	155.548	5.76498
$729$	−36.5128	−1.35232
$730$	−0.955212	−0.0353540
$731$	52.0312	1.92444
$732$	165.339	6.11109
$733$	−12.6860	−0.468569	−0.234284	−	0.972168i	$-0.575275\pi$
$733$	−12.6860	−0.468569	−0.234284	+	0.972168i	$0.575275\pi$
$734$	19.0957	0.704835
$735$	−5.38719	−0.198709
$736$	−130.370	−4.80552
$737$	−0.271720	−0.0100089
$738$	−68.8607	−2.53480
$739$	−22.6374	−0.832730	−0.416365	−	0.909197i	$-0.636696\pi$
$739$	−22.6374	−0.832730	−0.416365	+	0.909197i	$0.636696\pi$
$740$	−11.0422	−0.405919
$741$	104.201	3.82791
$742$	43.0743	1.58131
$743$	13.2850	0.487380	0.243690	−	0.969853i	$-0.421642\pi$
$743$	13.2850	0.487380	0.243690	+	0.969853i	$0.421642\pi$
$744$	−217.435	−7.97156
$745$	0.554975	0.0203327
$746$	62.8608	2.30150
$747$	23.5812	0.862790
$748$	1.48410	0.0542639
$749$	40.8750	1.49354
$750$	−23.6029	−0.861856
$751$	24.8309	0.906093	0.453047	−	0.891487i	$-0.350337\pi$
$751$	24.8309	0.906093	0.453047	+	0.891487i	$0.350337\pi$
$752$	85.8864	3.13196
$753$	25.3708	0.924562
$754$	−141.504	−5.15325
$755$	7.29063	0.265333
$756$	−28.4381	−1.03428
$757$	−20.6493	−0.750512	−0.375256	−	0.926921i	$-0.622445\pi$
$757$	−20.6493	−0.750512	−0.375256	+	0.926921i	$0.622445\pi$
$758$	5.21713	0.189495
$759$	−1.13391	−0.0411582
$760$	−22.5394	−0.817589
$761$	−4.43067	−0.160612	−0.0803059	−	0.996770i	$-0.525590\pi$
$761$	−4.43067	−0.160612	−0.0803059	+	0.996770i	$0.525590\pi$
$762$	54.5627	1.97660
$763$	57.6657	2.08764
$764$	2.16003	0.0781472
$765$	7.13597	0.258002
$766$	70.6794	2.55375
$767$	−41.2773	−1.49044
$768$	−9.70598	−0.350234
$769$	4.96049	0.178880	0.0894399	−	0.995992i	$-0.471492\pi$
$769$	4.96049	0.178880	0.0894399	+	0.995992i	$0.471492\pi$
$770$	−0.171520	−0.00618116
$771$	−6.43739	−0.231837
$772$	−26.5458	−0.955406
$773$	−23.6985	−0.852375	−0.426187	−	0.904635i	$-0.640144\pi$
$773$	−23.6985	−0.852375	−0.426187	+	0.904635i	$0.640144\pi$
$774$	−87.9150	−3.16004
$775$	49.8104	1.78924
$776$	−134.004	−4.81047
$777$	57.4253	2.06012
$778$	34.0993	1.22252
$779$	55.9185	2.00349
$780$	23.8185	0.852840
$781$	0.553087	0.0197910
$782$	−130.767	−4.67620
$783$	15.7426	0.562596
$784$	71.4282	2.55101
$785$	−3.22941	−0.115263
$786$	−127.850	−4.56024
$787$	−8.62123	−0.307314	−0.153657	−	0.988124i	$-0.549105\pi$
$787$	−8.62123	−0.307314	−0.153657	+	0.988124i	$0.549105\pi$
$788$	24.4605	0.871370
$789$	22.4457	0.799088
$790$	2.76362	0.0983254
$791$	59.8186	2.12690
$792$	−1.52593	−0.0542215
$793$	65.5355	2.32723
$794$	−17.2178	−0.611036
$795$	4.01368	0.142351
$796$	62.8999	2.22943
$797$	36.1260	1.27965	0.639824	−	0.768521i	$-0.279007\pi$
$797$	36.1260	1.27965	0.639824	+	0.768521i	$0.279007\pi$
$798$	192.627	6.81892
$799$	41.0688	1.45291
$800$	73.6769	2.60487
$801$	24.6290	0.870224
$802$	−26.2546	−0.927083
$803$	0.0525141	0.00185318
$804$	69.7537	2.46002
$805$	10.8611	0.382802
$806$	−141.631	−4.98875
$807$	61.7415	2.17341
$808$	14.2020	0.499623
$809$	−14.8011	−0.520377	−0.260189	−	0.965558i	$-0.583785\pi$
$809$	−14.8011	−0.520377	−0.260189	+	0.965558i	$0.583785\pi$
$810$	6.35871	0.223422
$811$	−27.1415	−0.953066	−0.476533	−	0.879157i	$-0.658107\pi$
$811$	−27.1415	−0.953066	−0.476533	+	0.879157i	$0.658107\pi$
$812$	−187.991	−6.59718
$813$	−10.5675	−0.370618
$814$	0.844714	0.0296072
$815$	1.05381	0.0369133
$816$	−173.447	−6.07185
$817$	71.3916	2.49768
$818$	47.1916	1.65002
$819$	−67.5706	−2.36111
$820$	12.7820	0.446368
$821$	51.6380	1.80218	0.901089	−	0.433635i	$-0.142769\pi$
$821$	51.6380	1.80218	0.901089	+	0.433635i	$0.142769\pi$
$822$	−0.463667	−0.0161722
$823$	−40.7248	−1.41958	−0.709789	−	0.704414i	$-0.751210\pi$
$823$	−40.7248	−1.41958	−0.709789	+	0.704414i	$0.751210\pi$
$824$	−14.4700	−0.504087
$825$	0.640810	0.0223101
$826$	−76.3059	−2.65502
$827$	5.22723	0.181769	0.0908843	−	0.995861i	$-0.471031\pi$
$827$	5.22723	0.181769	0.0908843	+	0.995861i	$0.471031\pi$
$828$	158.788	5.51827
$829$	−18.3040	−0.635723	−0.317861	−	0.948137i	$-0.602965\pi$
$829$	−18.3040	−0.635723	−0.317861	+	0.948137i	$0.602965\pi$
$830$	−6.09076	−0.211413
$831$	18.5230	0.642555
$832$	−85.8604	−2.97667
$833$	34.1553	1.18341
$834$	−69.6734	−2.41259
$835$	−5.75595	−0.199193
$836$	2.03632	0.0704275
$837$	15.7569	0.544637
$838$	−64.3744	−2.22378
$839$	7.02766	0.242622	0.121311	−	0.992615i	$-0.461290\pi$
$839$	7.02766	0.242622	0.121311	+	0.992615i	$0.461290\pi$
$840$	26.7938	0.924474
$841$	75.0670	2.58852
$842$	−68.9008	−2.37448
$843$	−19.0793	−0.657127
$844$	9.72392	0.334711
$845$	4.90644	0.168787
$846$	−69.3924	−2.38576
$847$	−39.6691	−1.36305
$848$	−53.2170	−1.82748
$849$	3.34657	0.114854
$850$	73.9008	2.53478
$851$	−53.4892	−1.83359
$852$	−141.984	−4.86429
$853$	2.29206	0.0784788	0.0392394	−	0.999230i	$-0.487507\pi$
$853$	2.29206	0.0784788	0.0392394	+	0.999230i	$0.487507\pi$
$854$	121.150	4.14567
$855$	9.79121	0.334852
$856$	−93.9254	−3.21030
$857$	31.8908	1.08937	0.544684	−	0.838641i	$-0.316650\pi$
$857$	31.8908	1.08937	0.544684	+	0.838641i	$0.316650\pi$
$858$	−1.82209	−0.0622050
$859$	42.2343	1.44102	0.720508	−	0.693446i	$-0.243909\pi$
$859$	42.2343	1.44102	0.720508	+	0.693446i	$0.243909\pi$
$860$	16.3189	0.556471
$861$	−66.4734	−2.26541
$862$	21.8331	0.743637
$863$	18.8985	0.643311	0.321656	−	0.946857i	$-0.395761\pi$
$863$	18.8985	0.643311	0.321656	+	0.946857i	$0.395761\pi$
$864$	23.3067	0.792911
$865$	4.13240	0.140506
$866$	−46.7555	−1.58882
$867$	−39.2621	−1.33341
$868$	−188.160	−6.38658
$869$	−0.151934	−0.00515401
$870$	−24.3747	−0.826378
$871$	27.6484	0.936830
$872$	−132.508	−4.48729
$873$	58.2120	1.97018
$874$	−179.424	−6.06910
$875$	−12.4290	−0.420177
$876$	−13.4810	−0.455481
$877$	12.0075	0.405464	0.202732	−	0.979234i	$-0.435018\pi$
$877$	12.0075	0.405464	0.202732	+	0.979234i	$0.435018\pi$
$878$	−5.74698	−0.193951
$879$	−45.0167	−1.51837
$880$	0.211908	0.00714342
$881$	15.8019	0.532378	0.266189	−	0.963921i	$-0.414235\pi$
$881$	15.8019	0.532378	0.266189	+	0.963921i	$0.414235\pi$
$882$	−57.7108	−1.94322
$883$	10.0380	0.337806	0.168903	−	0.985633i	$-0.445978\pi$
$883$	10.0380	0.337806	0.168903	+	0.985633i	$0.445978\pi$
$884$	−151.012	−5.07907
$885$	−7.11022	−0.239007
$886$	−35.9694	−1.20842
$887$	−19.3367	−0.649263	−0.324631	−	0.945841i	$-0.605240\pi$
$887$	−19.3367	−0.649263	−0.324631	+	0.945841i	$0.605240\pi$
$888$	−131.956	−4.42815
$889$	28.7321	0.963644
$890$	−6.36142	−0.213235
$891$	−0.349579	−0.0117113
$892$	−16.7010	−0.559190
$893$	56.3503	1.88569
$894$	10.8987	0.364506
$895$	−2.53752	−0.0848201
$896$	−49.7665	−1.66258
$897$	115.379	3.85238
$898$	32.3642	1.08001
$899$	104.161	3.47396
$900$	−89.7368	−2.99123
$901$	−25.4471	−0.847766
$902$	−0.977809	−0.0325575
$903$	−84.8671	−2.82420
$904$	−137.455	−4.57169
$905$	−3.05214	−0.101456
$906$	143.174	4.75665
$907$	19.9962	0.663962	0.331981	−	0.943286i	$-0.392283\pi$
$907$	19.9962	0.663962	0.331981	+	0.943286i	$0.392283\pi$
$908$	49.1088	1.62973
$909$	−6.16940	−0.204626
$910$	17.4528	0.578553
$911$	−46.8396	−1.55187	−0.775933	−	0.630816i	$-0.782720\pi$
$911$	−46.8396	−1.55187	−0.775933	+	0.630816i	$0.782720\pi$
$912$	−237.985	−7.88047
$913$	0.334848	0.0110819
$914$	31.0663	1.02758
$915$	11.2888	0.373196
$916$	−77.9866	−2.57675
$917$	−67.3241	−2.22324
$918$	23.3776	0.771574
$919$	−4.75727	−0.156928	−0.0784639	−	0.996917i	$-0.525002\pi$
$919$	−4.75727	−0.156928	−0.0784639	+	0.996917i	$0.525002\pi$
$920$	−24.9573	−0.822817
$921$	29.2251	0.963001
$922$	−12.7462	−0.419775
$923$	−56.2784	−1.85243
$924$	−2.42068	−0.0796346
$925$	30.2286	0.993911
$926$	34.3499	1.12881
$927$	6.28585	0.206454
$928$	154.069	5.05758
$929$	−7.15602	−0.234782	−0.117391	−	0.993086i	$-0.537453\pi$
$929$	−7.15602	−0.234782	−0.117391	+	0.993086i	$0.537453\pi$
$930$	−24.3967	−0.799998
$931$	46.8642	1.53591
$932$	−108.760	−3.56254
$933$	8.75160	0.286514
$934$	37.2684	1.21946
$935$	0.101329	0.00331383
$936$	155.268	5.07510
$937$	−21.6908	−0.708608	−0.354304	−	0.935130i	$-0.615282\pi$
$937$	−21.6908	−0.708608	−0.354304	+	0.935130i	$0.615282\pi$
$938$	51.1112	1.66884
$939$	−46.6524	−1.52244
$940$	12.8807	0.420123
$941$	32.1197	1.04707	0.523537	−	0.852003i	$-0.324612\pi$
$941$	32.1197	1.04707	0.523537	+	0.852003i	$0.324612\pi$
$942$	−63.4197	−2.06632
$943$	61.9171	2.01630
$944$	94.2737	3.06835
$945$	−1.94167	−0.0631624
$946$	−1.24838	−0.0405882
$947$	−41.7354	−1.35622	−0.678108	−	0.734962i	$-0.737200\pi$
$947$	−41.7354	−1.35622	−0.678108	+	0.734962i	$0.737200\pi$
$948$	39.0033	1.26677
$949$	−5.34349	−0.173457
$950$	101.399	3.28981
$951$	−49.6236	−1.60916
$952$	−169.875	−5.50569
$953$	−11.4501	−0.370904	−0.185452	−	0.982653i	$-0.559375\pi$
$953$	−11.4501	−0.370904	−0.185452	+	0.982653i	$0.559375\pi$
$954$	42.9970	1.39208
$955$	0.147480	0.00477235
$956$	56.4431	1.82550
$957$	1.34003	0.0433170
$958$	63.4649	2.05046
$959$	−0.244161	−0.00788439
$960$	−14.7899	−0.477340
$961$	73.2551	2.36307
$962$	−85.9524	−2.77122
$963$	40.8016	1.31481
$964$	−68.1439	−2.19477
$965$	−1.81247	−0.0583454
$966$	213.291	6.86252
$967$	−33.7597	−1.08564	−0.542820	−	0.839849i	$-0.682643\pi$
$967$	−33.7597	−1.08564	−0.542820	+	0.839849i	$0.682643\pi$
$968$	91.1543	2.92981
$969$	−113.799	−3.65574
$970$	−15.0355	−0.482762
$971$	24.2981	0.779764	0.389882	−	0.920865i	$-0.372516\pi$
$971$	24.2981	0.779764	0.389882	+	0.920865i	$0.372516\pi$
$972$	113.393	3.63707
$973$	−36.6892	−1.17620
$974$	−66.8102	−2.14074
$975$	−65.2046	−2.08822
$976$	−149.677	−4.79105
$977$	−48.7291	−1.55898	−0.779491	−	0.626413i	$-0.784522\pi$
$977$	−48.7291	−1.55898	−0.779491	+	0.626413i	$0.784522\pi$
$978$	20.6949	0.661748
$979$	0.349728	0.0111773
$980$	10.7124	0.342194
$981$	57.5622	1.83782
$982$	60.7404	1.93831
$983$	17.9794	0.573452	0.286726	−	0.958013i	$-0.407433\pi$
$983$	17.9794	0.573452	0.286726	+	0.958013i	$0.407433\pi$
$984$	152.747	4.86940
$985$	1.67009	0.0532134
$986$	154.538	4.92148
$987$	−66.9867	−2.13221
$988$	−207.202	−6.59198
$989$	79.0501	2.51365
$990$	−0.171212	−0.00544148
$991$	35.3017	1.12139	0.560697	−	0.828021i	$-0.310533\pi$
$991$	35.3017	1.12139	0.560697	+	0.828021i	$0.310533\pi$
$992$	154.209	4.89613
$993$	−65.4464	−2.07688
$994$	−104.037	−3.29986
$995$	4.29461	0.136148
$996$	−85.9596	−2.72373
$997$	10.3589	0.328071	0.164035	−	0.986454i	$-0.447549\pi$
$997$	10.3589	0.328071	0.164035	+	0.986454i	$0.447549\pi$
$998$	−57.2559	−1.81240
$999$	9.56244	0.302542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.c.1.5	✓	261

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.c.1.5	✓	261	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66623 q^{2} -2.56917 q^{3} +5.10878 q^{4} +0.348811 q^{5} +6.85001 q^{6} +3.60714 q^{7} -8.28872 q^{8} +3.60066 q^{9} +O(q^{10})\)	\(q-2.66623 q^{2} -2.56917 q^{3} +5.10878 q^{4} +0.348811 q^{5} +6.85001 q^{6} +3.60714 q^{7} -8.28872 q^{8} +3.60066 q^{9} -0.930012 q^{10} +0.0511287 q^{11} -13.1253 q^{12} -5.20251 q^{13} -9.61745 q^{14} -0.896158 q^{15} +11.8821 q^{16} +5.68173 q^{17} -9.60018 q^{18} +7.79585 q^{19} +1.78200 q^{20} -9.26736 q^{21} -0.136321 q^{22} +8.63215 q^{23} +21.2952 q^{24} -4.87833 q^{25} +13.8711 q^{26} -1.54320 q^{27} +18.4281 q^{28} -10.2013 q^{29} +2.38936 q^{30} -10.2105 q^{31} -15.1029 q^{32} -0.131359 q^{33} -15.1488 q^{34} +1.25821 q^{35} +18.3950 q^{36} -6.19651 q^{37} -20.7855 q^{38} +13.3662 q^{39} -2.89120 q^{40} +7.17285 q^{41} +24.7089 q^{42} +9.15764 q^{43} +0.261205 q^{44} +1.25595 q^{45} -23.0153 q^{46} +7.22824 q^{47} -30.5271 q^{48} +6.01143 q^{49} +13.0067 q^{50} -14.5973 q^{51} -26.5785 q^{52} -4.47877 q^{53} +4.11452 q^{54} +0.0178343 q^{55} -29.8985 q^{56} -20.0289 q^{57} +27.1991 q^{58} +7.93411 q^{59} -4.57827 q^{60} -12.5969 q^{61} +27.2236 q^{62} +12.9881 q^{63} +16.5036 q^{64} -1.81470 q^{65} +0.350232 q^{66} -5.31443 q^{67} +29.0267 q^{68} -22.1775 q^{69} -3.35468 q^{70} +10.8175 q^{71} -29.8449 q^{72} +1.02710 q^{73} +16.5213 q^{74} +12.5333 q^{75} +39.8273 q^{76} +0.184428 q^{77} -35.6373 q^{78} -2.97160 q^{79} +4.14460 q^{80} -6.83723 q^{81} -19.1245 q^{82} +6.54913 q^{83} -47.3449 q^{84} +1.98185 q^{85} -24.4164 q^{86} +26.2090 q^{87} -0.423791 q^{88} +6.84015 q^{89} -3.34865 q^{90} -18.7662 q^{91} +44.0997 q^{92} +26.2327 q^{93} -19.2721 q^{94} +2.71928 q^{95} +38.8020 q^{96} +16.1671 q^{97} -16.0278 q^{98} +0.184097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9}+O(q^{10}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9	\( 261 q + 26 q^{2} + 25 q^{3} + 274 q^{4} + 66 q^{5} + 25 q^{6} + 37 q^{7} + 72 q^{8} + 310 q^{9} + 35 q^{10} + 32 q^{11} + 51 q^{12} + 60 q^{13} + 55 q^{14} + 16 q^{15} + 288 q^{16} + 270 q^{17} + 45 q^{18} + 34 q^{19} + 157 q^{20} + 27 q^{21} + 38 q^{22} + 116 q^{23} + 48 q^{24} + 335 q^{25} + 46 q^{26} + 73 q^{27} + 70 q^{28} + 99 q^{29} + 33 q^{30} + 33 q^{31} + 150 q^{32} + 172 q^{33} + 24 q^{34} + 114 q^{35} + 339 q^{36} + 36 q^{37} + 112 q^{38} + 30 q^{39} + 106 q^{40} + 209 q^{41} + 64 q^{42} + 64 q^{43} + 65 q^{44} + 153 q^{45} + 135 q^{47} + 87 q^{48} + 332 q^{49} + 82 q^{50} + 52 q^{51} + 102 q^{52} + 163 q^{53} + 52 q^{54} + 56 q^{55} + 134 q^{56} + 181 q^{57} + q^{58} + 89 q^{59} - 43 q^{60} + 112 q^{61} + 228 q^{62} + 130 q^{63} + 268 q^{64} + 248 q^{65} + 5 q^{66} + 42 q^{67} + 453 q^{68} + 51 q^{69} - 22 q^{70} + 98 q^{71} + 113 q^{72} + 206 q^{73} + 81 q^{74} + 29 q^{75} + 62 q^{76} + 185 q^{77} - 25 q^{78} + 29 q^{79} + 258 q^{80} + 393 q^{81} + 79 q^{82} + 265 q^{83} - 25 q^{84} + 84 q^{85} + 36 q^{86} + 131 q^{87} + 24 q^{88} + 195 q^{89} + 89 q^{90} - 18 q^{91} + 261 q^{92} + 52 q^{93} + 3 q^{94} + 104 q^{95} + 92 q^{96} + 213 q^{97} + 156 q^{98} + 47 q^{99}+O(q^{100}) \) 261 * q + 26 * q^2 + 25 * q^3 + 274 * q^4 + 66 * q^5 + 25 * q^6 + 37 * q^7 + 72 * q^8 + 310 * q^9 + 35 * q^10 + 32 * q^11 + 51 * q^12 + 60 * q^13 + 55 * q^14 + 16 * q^15 + 288 * q^16 + 270 * q^17 + 45 * q^18 + 34 * q^19 + 157 * q^20 + 27 * q^21 + 38 * q^22 + 116 * q^23 + 48 * q^24 + 335 * q^25 + 46 * q^26 + 73 * q^27 + 70 * q^28 + 99 * q^29 + 33 * q^30 + 33 * q^31 + 150 * q^32 + 172 * q^33 + 24 * q^34 + 114 * q^35 + 339 * q^36 + 36 * q^37 + 112 * q^38 + 30 * q^39 + 106 * q^40 + 209 * q^41 + 64 * q^42 + 64 * q^43 + 65 * q^44 + 153 * q^45 + 135 * q^47 + 87 * q^48 + 332 * q^49 + 82 * q^50 + 52 * q^51 + 102 * q^52 + 163 * q^53 + 52 * q^54 + 56 * q^55 + 134 * q^56 + 181 * q^57 + q^58 + 89 * q^59 - 43 * q^60 + 112 * q^61 + 228 * q^62 + 130 * q^63 + 268 * q^64 + 248 * q^65 + 5 * q^66 + 42 * q^67 + 453 * q^68 + 51 * q^69 - 22 * q^70 + 98 * q^71 + 113 * q^72 + 206 * q^73 + 81 * q^74 + 29 * q^75 + 62 * q^76 + 185 * q^77 - 25 * q^78 + 29 * q^79 + 258 * q^80 + 393 * q^81 + 79 * q^82 + 265 * q^83 - 25 * q^84 + 84 * q^85 + 36 * q^86 + 131 * q^87 + 24 * q^88 + 195 * q^89 + 89 * q^90 - 18 * q^91 + 261 * q^92 + 52 * q^93 + 3 * q^94 + 104 * q^95 + 92 * q^96 + 213 * q^97 + 156 * q^98 + 47 * q^99

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