LMFDB - Embedded newform 6047.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69892 q^{2} +0.321066 q^{3} +5.28419 q^{4} -2.61974 q^{5} -0.866532 q^{6} -2.02949 q^{7} -8.86379 q^{8} -2.89692 q^{9} +O(q^{10})$	\(q-2.69892 q^{2} +0.321066 q^{3} +5.28419 q^{4} -2.61974 q^{5} -0.866532 q^{6} -2.02949 q^{7} -8.86379 q^{8} -2.89692 q^{9} +7.07048 q^{10} +0.150891 q^{11} +1.69657 q^{12} +3.48633 q^{13} +5.47745 q^{14} -0.841109 q^{15} +13.3543 q^{16} -3.50370 q^{17} +7.81856 q^{18} -1.49640 q^{19} -13.8432 q^{20} -0.651600 q^{21} -0.407242 q^{22} -3.96165 q^{23} -2.84586 q^{24} +1.86304 q^{25} -9.40934 q^{26} -1.89330 q^{27} -10.7242 q^{28} -7.85969 q^{29} +2.27009 q^{30} +1.13379 q^{31} -18.3147 q^{32} +0.0484458 q^{33} +9.45623 q^{34} +5.31674 q^{35} -15.3079 q^{36} -2.38120 q^{37} +4.03867 q^{38} +1.11934 q^{39} +23.2208 q^{40} -9.49234 q^{41} +1.75862 q^{42} +10.8831 q^{43} +0.797335 q^{44} +7.58917 q^{45} +10.6922 q^{46} -0.888951 q^{47} +4.28761 q^{48} -2.88116 q^{49} -5.02821 q^{50} -1.12492 q^{51} +18.4224 q^{52} -4.27646 q^{53} +5.10987 q^{54} -0.395294 q^{55} +17.9890 q^{56} -0.480443 q^{57} +21.2127 q^{58} +9.55046 q^{59} -4.44458 q^{60} -11.6987 q^{61} -3.06002 q^{62} +5.87927 q^{63} +22.7213 q^{64} -9.13328 q^{65} -0.130752 q^{66} -7.26318 q^{67} -18.5142 q^{68} -1.27195 q^{69} -14.3495 q^{70} +3.81577 q^{71} +25.6777 q^{72} -14.3665 q^{73} +6.42668 q^{74} +0.598159 q^{75} -7.90727 q^{76} -0.306231 q^{77} -3.02102 q^{78} +3.40307 q^{79} -34.9848 q^{80} +8.08288 q^{81} +25.6191 q^{82} +13.7854 q^{83} -3.44318 q^{84} +9.17880 q^{85} -29.3726 q^{86} -2.52348 q^{87} -1.33746 q^{88} -15.9395 q^{89} -20.4826 q^{90} -7.07548 q^{91} -20.9341 q^{92} +0.364022 q^{93} +2.39921 q^{94} +3.92018 q^{95} -5.88021 q^{96} -3.01739 q^{97} +7.77603 q^{98} -0.437118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.69892	−1.90843	−0.954214	−	0.299125i	$-0.903305\pi$
$2$	−2.69892	−1.90843	−0.954214	+	0.299125i	$0.903305\pi$
$3$	0.321066	0.185367	0.0926837	−	0.995696i	$-0.470455\pi$
$3$	0.321066	0.185367	0.0926837	+	0.995696i	$0.470455\pi$
$4$	5.28419	2.64210
$5$	−2.61974	−1.17158	−0.585792	−	0.810461i	$-0.699216\pi$
$5$	−2.61974	−1.17158	−0.585792	+	0.810461i	$0.699216\pi$
$6$	−0.866532	−0.353760
$7$	−2.02949	−0.767076	−0.383538	−	0.923525i	$-0.625294\pi$
$7$	−2.02949	−0.767076	−0.383538	+	0.923525i	$0.625294\pi$
$8$	−8.86379	−3.13382
$9$	−2.89692	−0.965639
$10$	7.07048	2.23588
$11$	0.150891	0.0454952	0.0227476	−	0.999741i	$-0.492759\pi$
$11$	0.150891	0.0454952	0.0227476	+	0.999741i	$0.492759\pi$
$12$	1.69657	0.489758
$13$	3.48633	0.966934	0.483467	−	0.875363i	$-0.339377\pi$
$13$	3.48633	0.966934	0.483467	+	0.875363i	$0.339377\pi$
$14$	5.47745	1.46391
$15$	−0.841109	−0.217173
$16$	13.3543	3.33858
$17$	−3.50370	−0.849773	−0.424887	−	0.905247i	$-0.639686\pi$
$17$	−3.50370	−0.849773	−0.424887	+	0.905247i	$0.639686\pi$
$18$	7.81856	1.84285
$19$	−1.49640	−0.343298	−0.171649	−	0.985158i	$-0.554909\pi$
$19$	−1.49640	−0.343298	−0.171649	+	0.985158i	$0.554909\pi$
$20$	−13.8432	−3.09544
$21$	−0.651600	−0.142191
$22$	−0.407242	−0.0868244
$23$	−3.96165	−0.826061	−0.413031	−	0.910717i	$-0.635530\pi$
$23$	−3.96165	−0.826061	−0.413031	+	0.910717i	$0.635530\pi$
$24$	−2.84586	−0.580908
$25$	1.86304	0.372609
$26$	−9.40934	−1.84532
$27$	−1.89330	−0.364365
$28$	−10.7242	−2.02669
$29$	−7.85969	−1.45951	−0.729754	−	0.683710i	$-0.760365\pi$
$29$	−7.85969	−1.45951	−0.729754	+	0.683710i	$0.760365\pi$
$30$	2.27009	0.414460
$31$	1.13379	0.203635	0.101818	−	0.994803i	$-0.467534\pi$
$31$	1.13379	0.203635	0.101818	+	0.994803i	$0.467534\pi$
$32$	−18.3147	−3.23761
$33$	0.0484458	0.00843333
$34$	9.45623	1.62173
$35$	5.31674	0.898694
$36$	−15.3079	−2.55131
$37$	−2.38120	−0.391467	−0.195733	−	0.980657i	$-0.562709\pi$
$37$	−2.38120	−0.391467	−0.195733	+	0.980657i	$0.562709\pi$
$38$	4.03867	0.655159
$39$	1.11934	0.179238
$40$	23.2208	3.67153
$41$	−9.49234	−1.48245	−0.741227	−	0.671254i	$-0.765756\pi$
$41$	−9.49234	−1.48245	−0.741227	+	0.671254i	$0.765756\pi$
$42$	1.75862	0.271361
$43$	10.8831	1.65965	0.829827	−	0.558021i	$-0.188439\pi$
$43$	10.8831	1.65965	0.829827	+	0.558021i	$0.188439\pi$
$44$	0.797335	0.120203
$45$	7.58917	1.13133
$46$	10.6922	1.57648
$47$	−0.888951	−0.129667	−0.0648334	−	0.997896i	$-0.520652\pi$
$47$	−0.888951	−0.129667	−0.0648334	+	0.997896i	$0.520652\pi$
$48$	4.28761	0.618863
$49$	−2.88116	−0.411594
$50$	−5.02821	−0.711097
$51$	−1.12492	−0.157520
$52$	18.4224	2.55473
$53$	−4.27646	−0.587417	−0.293708	−	0.955895i	$-0.594889\pi$
$53$	−4.27646	−0.587417	−0.293708	+	0.955895i	$0.594889\pi$
$54$	5.10987	0.695365
$55$	−0.395294	−0.0533015
$56$	17.9890	2.40388
$57$	−0.480443	−0.0636362
$58$	21.2127	2.78536
$59$	9.55046	1.24336	0.621682	−	0.783270i	$-0.286450\pi$
$59$	9.55046	1.24336	0.621682	+	0.783270i	$0.286450\pi$
$60$	−4.44458	−0.573793
$61$	−11.6987	−1.49786	−0.748931	−	0.662648i	$-0.769433\pi$
$61$	−11.6987	−1.49786	−0.748931	+	0.662648i	$0.769433\pi$
$62$	−3.06002	−0.388623
$63$	5.87927	0.740718
$64$	22.7213	2.84017
$65$	−9.13328	−1.13284
$66$	−0.130752	−0.0160944
$67$	−7.26318	−0.887339	−0.443670	−	0.896190i	$-0.646324\pi$
$67$	−7.26318	−0.887339	−0.443670	+	0.896190i	$0.646324\pi$
$68$	−18.5142	−2.24518
$69$	−1.27195	−0.153125
$70$	−14.3495	−1.71509
$71$	3.81577	0.452848	0.226424	−	0.974029i	$-0.427296\pi$
$71$	3.81577	0.452848	0.226424	+	0.974029i	$0.427296\pi$
$72$	25.6777	3.02614
$73$	−14.3665	−1.68147	−0.840735	−	0.541448i	$-0.817876\pi$
$73$	−14.3665	−1.68147	−0.840735	+	0.541448i	$0.817876\pi$
$74$	6.42668	0.747086
$75$	0.598159	0.0690695
$76$	−7.90727	−0.907026
$77$	−0.306231	−0.0348983
$78$	−3.02102	−0.342063
$79$	3.40307	0.382875	0.191438	−	0.981505i	$-0.438685\pi$
$79$	3.40307	0.382875	0.191438	+	0.981505i	$0.438685\pi$
$80$	−34.9848	−3.91142
$81$	8.08288	0.898098
$82$	25.6191	2.82916
$83$	13.7854	1.51315	0.756574	−	0.653908i	$-0.226872\pi$
$83$	13.7854	1.51315	0.756574	+	0.653908i	$0.226872\pi$
$84$	−3.44318	−0.375682
$85$	9.17880	0.995581
$86$	−29.3726	−3.16733
$87$	−2.52348	−0.270545
$88$	−1.33746	−0.142574
$89$	−15.9395	−1.68959	−0.844794	−	0.535092i	$-0.820277\pi$
$89$	−15.9395	−1.68959	−0.844794	+	0.535092i	$0.820277\pi$
$90$	−20.4826	−2.15906
$91$	−7.07548	−0.741712
$92$	−20.9341	−2.18253
$93$	0.364022	0.0377473
$94$	2.39921	0.247460
$95$	3.92018	0.402202
$96$	−5.88021	−0.600147
$97$	−3.01739	−0.306370	−0.153185	−	0.988198i	$-0.548953\pi$
$97$	−3.01739	−0.306370	−0.153185	+	0.988198i	$0.548953\pi$
$98$	7.77603	0.785498
$99$	−0.437118	−0.0439320
$100$	9.84468	0.984468
$101$	−19.8028	−1.97045	−0.985224	−	0.171268i	$-0.945214\pi$
$101$	−19.8028	−1.97045	−0.985224	+	0.171268i	$0.945214\pi$
$102$	3.03607	0.300616
$103$	−16.1127	−1.58764	−0.793818	−	0.608156i	$-0.791910\pi$
$103$	−16.1127	−1.58764	−0.793818	+	0.608156i	$0.791910\pi$
$104$	−30.9021	−3.03020
$105$	1.70702	0.166588
$106$	11.5418	1.12104
$107$	0.218465	0.0211198	0.0105599	−	0.999944i	$-0.496639\pi$
$107$	0.218465	0.0211198	0.0105599	+	0.999944i	$0.496639\pi$
$108$	−10.0045	−0.962688
$109$	1.59501	0.152775	0.0763873	−	0.997078i	$-0.475661\pi$
$109$	1.59501	0.152775	0.0763873	+	0.997078i	$0.475661\pi$
$110$	1.06687	0.101722
$111$	−0.764521	−0.0725652
$112$	−27.1025	−2.56094
$113$	−5.92403	−0.557286	−0.278643	−	0.960395i	$-0.589885\pi$
$113$	−5.92403	−0.557286	−0.278643	+	0.960395i	$0.589885\pi$
$114$	1.29668	0.121445
$115$	10.3785	0.967800
$116$	−41.5321	−3.85616
$117$	−10.0996	−0.933709
$118$	−25.7760	−2.37287
$119$	7.11074	0.651841
$120$	7.45541	0.680583
$121$	−10.9772	−0.997930
$122$	31.5738	2.85856
$123$	−3.04766	−0.274799
$124$	5.99118	0.538024
$125$	8.21801	0.735042
$126$	−15.8677	−1.41361
$127$	8.29976	0.736484	0.368242	−	0.929730i	$-0.379960\pi$
$127$	8.29976	0.736484	0.368242	+	0.929730i	$0.379960\pi$
$128$	−24.6938	−2.18264
$129$	3.49418	0.307646
$130$	24.6500	2.16195
$131$	−4.10600	−0.358743	−0.179371	−	0.983781i	$-0.557406\pi$
$131$	−4.10600	−0.358743	−0.179371	+	0.983781i	$0.557406\pi$
$132$	0.255997	0.0222817
$133$	3.03694	0.263336
$134$	19.6028	1.69342
$135$	4.95995	0.426884
$136$	31.0561	2.66304
$137$	−12.4565	−1.06423	−0.532115	−	0.846672i	$-0.678603\pi$
$137$	−12.4565	−1.06423	−0.532115	+	0.846672i	$0.678603\pi$
$138$	3.43290	0.292228
$139$	1.93680	0.164278	0.0821388	−	0.996621i	$-0.473825\pi$
$139$	1.93680	0.164278	0.0821388	+	0.996621i	$0.473825\pi$
$140$	28.0947	2.37444
$141$	−0.285412	−0.0240360
$142$	−10.2985	−0.864228
$143$	0.526055	0.0439909
$144$	−38.6863	−3.22386
$145$	20.5903	1.70994
$146$	38.7740	3.20896
$147$	−0.925042	−0.0762962
$148$	−12.5827	−1.03429
$149$	−0.825387	−0.0676183	−0.0338092	−	0.999428i	$-0.510764\pi$
$149$	−0.825387	−0.0676183	−0.0338092	+	0.999428i	$0.510764\pi$
$150$	−1.61439	−0.131814
$151$	−9.13818	−0.743655	−0.371827	−	0.928302i	$-0.621269\pi$
$151$	−9.13818	−0.743655	−0.371827	+	0.928302i	$0.621269\pi$
$152$	13.2638	1.07583
$153$	10.1499	0.820574
$154$	0.826495	0.0666009
$155$	−2.97024	−0.238576
$156$	5.91481	0.473564
$157$	5.68830	0.453976	0.226988	−	0.973898i	$-0.427112\pi$
$157$	5.68830	0.453976	0.226988	+	0.973898i	$0.427112\pi$
$158$	−9.18462	−0.730689
$159$	−1.37302	−0.108888
$160$	47.9797	3.79313
$161$	8.04014	0.633652
$162$	−21.8151	−1.71395
$163$	6.90941	0.541187	0.270594	−	0.962694i	$-0.412780\pi$
$163$	6.90941	0.541187	0.270594	+	0.962694i	$0.412780\pi$
$164$	−50.1593	−3.91679
$165$	−0.126915	−0.00988036
$166$	−37.2058	−2.88773
$167$	−3.56096	−0.275555	−0.137778	−	0.990463i	$-0.543996\pi$
$167$	−3.56096	−0.275555	−0.137778	+	0.990463i	$0.543996\pi$
$168$	5.77565	0.445601
$169$	−0.845500	−0.0650384
$170$	−24.7729	−1.89999
$171$	4.33495	0.331502
$172$	57.5083	4.38497
$173$	−12.3995	−0.942716	−0.471358	−	0.881942i	$-0.656236\pi$
$173$	−12.3995	−0.942716	−0.471358	+	0.881942i	$0.656236\pi$
$174$	6.81067	0.516316
$175$	−3.78103	−0.285819
$176$	2.01504	0.151889
$177$	3.06632	0.230479
$178$	43.0196	3.22445
$179$	14.1371	1.05665	0.528327	−	0.849041i	$-0.322819\pi$
$179$	14.1371	1.05665	0.528327	+	0.849041i	$0.322819\pi$
$180$	40.1026	2.98907
$181$	11.3858	0.846300	0.423150	−	0.906060i	$-0.360924\pi$
$181$	11.3858	0.846300	0.423150	+	0.906060i	$0.360924\pi$
$182$	19.0962	1.41550
$183$	−3.75604	−0.277655
$184$	35.1152	2.58873
$185$	6.23813	0.458636
$186$	−0.982468	−0.0720380
$187$	−0.528676	−0.0386606
$188$	−4.69739	−0.342592
$189$	3.84243	0.279496
$190$	−10.5803	−0.767574
$191$	−19.1249	−1.38383	−0.691914	−	0.721980i	$-0.743232\pi$
$191$	−19.1249	−1.38383	−0.691914	+	0.721980i	$0.743232\pi$
$192$	7.29504	0.526474
$193$	18.3081	1.31784	0.658921	−	0.752212i	$-0.271013\pi$
$193$	18.3081	1.31784	0.658921	+	0.752212i	$0.271013\pi$
$194$	8.14371	0.584684
$195$	−2.93238	−0.209992
$196$	−15.2246	−1.08747
$197$	−3.84972	−0.274281	−0.137140	−	0.990552i	$-0.543791\pi$
$197$	−3.84972	−0.274281	−0.137140	+	0.990552i	$0.543791\pi$
$198$	1.17975	0.0838410
$199$	−16.7193	−1.18520	−0.592601	−	0.805496i	$-0.701899\pi$
$199$	−16.7193	−1.18520	−0.592601	+	0.805496i	$0.701899\pi$
$200$	−16.5136	−1.16769
$201$	−2.33196	−0.164484
$202$	53.4462	3.76046
$203$	15.9512	1.11955
$204$	−5.94429	−0.416184
$205$	24.8675	1.73682
$206$	43.4871	3.02989
$207$	11.4766	0.797677
$208$	46.5575	3.22818
$209$	−0.225793	−0.0156184
$210$	−4.60713	−0.317922
$211$	7.06473	0.486356	0.243178	−	0.969982i	$-0.421810\pi$
$211$	7.06473	0.486356	0.243178	+	0.969982i	$0.421810\pi$
$212$	−22.5976	−1.55201
$213$	1.22511	0.0839432
$214$	−0.589620	−0.0403056
$215$	−28.5108	−1.94442
$216$	16.7818	1.14186
$217$	−2.30102	−0.156204
$218$	−4.30482	−0.291559
$219$	−4.61258	−0.311689
$220$	−2.08881	−0.140828
$221$	−12.2151	−0.821675
$222$	2.06339	0.138485
$223$	−6.60472	−0.442285	−0.221142	−	0.975242i	$-0.570979\pi$
$223$	−6.60472	−0.442285	−0.221142	+	0.975242i	$0.570979\pi$
$224$	37.1695	2.48349
$225$	−5.39708	−0.359805
$226$	15.9885	1.06354
$227$	25.9948	1.72534	0.862668	−	0.505771i	$-0.168792\pi$
$227$	25.9948	1.72534	0.862668	+	0.505771i	$0.168792\pi$
$228$	−2.53875	−0.168133
$229$	−1.96242	−0.129680	−0.0648400	−	0.997896i	$-0.520654\pi$
$229$	−1.96242	−0.129680	−0.0648400	+	0.997896i	$0.520654\pi$
$230$	−28.0108	−1.84698
$231$	−0.0983204	−0.00646901
$232$	69.6666	4.57384
$233$	5.11916	0.335367	0.167684	−	0.985841i	$-0.446371\pi$
$233$	5.11916	0.335367	0.167684	+	0.985841i	$0.446371\pi$
$234$	27.2581	1.78192
$235$	2.32882	0.151916
$236$	50.4665	3.28509
$237$	1.09261	0.0709725
$238$	−19.1914	−1.24399
$239$	−8.17753	−0.528960	−0.264480	−	0.964391i	$-0.585200\pi$
$239$	−8.17753	−0.528960	−0.264480	+	0.964391i	$0.585200\pi$
$240$	−11.2324	−0.725050
$241$	−19.4770	−1.25462	−0.627312	−	0.778768i	$-0.715845\pi$
$241$	−19.4770	−1.25462	−0.627312	+	0.778768i	$0.715845\pi$
$242$	29.6267	1.90448
$243$	8.27503	0.530843
$244$	−61.8181	−3.95750
$245$	7.54789	0.482217
$246$	8.22541	0.524433
$247$	−5.21695	−0.331947
$248$	−10.0497	−0.638157
$249$	4.42603	0.280488
$250$	−22.1798	−1.40277
$251$	−11.5525	−0.729190	−0.364595	−	0.931166i	$-0.618793\pi$
$251$	−11.5525	−0.729190	−0.364595	+	0.931166i	$0.618793\pi$
$252$	31.0672	1.95705
$253$	−0.597776	−0.0375819
$254$	−22.4004	−1.40553
$255$	2.94700	0.184548
$256$	21.2040	1.32525
$257$	13.3817	0.834725	0.417363	−	0.908740i	$-0.362954\pi$
$257$	13.3817	0.834725	0.417363	+	0.908740i	$0.362954\pi$
$258$	−9.43053	−0.587119
$259$	4.83263	0.300285
$260$	−48.2620	−2.99308
$261$	22.7689	1.40936
$262$	11.0818	0.684635
$263$	1.06515	0.0656799	0.0328399	−	0.999461i	$-0.489545\pi$
$263$	1.06515	0.0656799	0.0328399	+	0.999461i	$0.489545\pi$
$264$	−0.429413	−0.0264286
$265$	11.2032	0.688208
$266$	−8.19646	−0.502557
$267$	−5.11764	−0.313194
$268$	−38.3801	−2.34444
$269$	28.8216	1.75729	0.878643	−	0.477480i	$-0.158450\pi$
$269$	28.8216	1.75729	0.878643	+	0.477480i	$0.158450\pi$
$270$	−13.3865	−0.814678
$271$	25.9706	1.57760	0.788802	−	0.614647i	$-0.210702\pi$
$271$	25.9706	1.57760	0.788802	+	0.614647i	$0.210702\pi$
$272$	−46.7895	−2.83703
$273$	−2.27169	−0.137489
$274$	33.6191	2.03101
$275$	0.281116	0.0169519
$276$	−6.72123	−0.404570
$277$	−9.11553	−0.547699	−0.273850	−	0.961773i	$-0.588297\pi$
$277$	−9.11553	−0.547699	−0.273850	+	0.961773i	$0.588297\pi$
$278$	−5.22729	−0.313512
$279$	−3.28450	−0.196638
$280$	−47.1265	−2.81635
$281$	−15.6130	−0.931395	−0.465697	−	0.884944i	$-0.654196\pi$
$281$	−15.6130	−0.931395	−0.465697	+	0.884944i	$0.654196\pi$
$282$	0.770305	0.0458710
$283$	−7.36902	−0.438043	−0.219021	−	0.975720i	$-0.570286\pi$
$283$	−7.36902	−0.438043	−0.219021	+	0.975720i	$0.570286\pi$
$284$	20.1632	1.19647
$285$	1.25864	0.0745552
$286$	−1.41978	−0.0839535
$287$	19.2646	1.13715
$288$	53.0561	3.12636
$289$	−4.72405	−0.277885
$290$	−55.5718	−3.26329
$291$	−0.968780	−0.0567909
$292$	−75.9152	−4.44260
$293$	−8.21519	−0.479936	−0.239968	−	0.970781i	$-0.577137\pi$
$293$	−8.21519	−0.479936	−0.239968	+	0.970781i	$0.577137\pi$
$294$	2.49662	0.145606
$295$	−25.0197	−1.45670
$296$	21.1064	1.22679
$297$	−0.285681	−0.0165769
$298$	2.22766	0.129045
$299$	−13.8116	−0.798747
$300$	3.16079	0.182488
$301$	−22.0871	−1.27308
$302$	24.6633	1.41921
$303$	−6.35799	−0.365257
$304$	−19.9834	−1.14613
$305$	30.6475	1.75487
$306$	−27.3939	−1.56601
$307$	−19.0269	−1.08592	−0.542960	−	0.839759i	$-0.682697\pi$
$307$	−19.0269	−1.08592	−0.542960	+	0.839759i	$0.682697\pi$
$308$	−1.61819	−0.0922047
$309$	−5.17325	−0.294296
$310$	8.01646	0.455305
$311$	0.268523	0.0152265	0.00761326	−	0.999971i	$-0.497577\pi$
$311$	0.268523	0.0152265	0.00761326	+	0.999971i	$0.497577\pi$
$312$	−9.92160	−0.561700
$313$	−21.2263	−1.19978	−0.599892	−	0.800081i	$-0.704790\pi$
$313$	−21.2263	−1.19978	−0.599892	+	0.800081i	$0.704790\pi$
$314$	−15.3523	−0.866380
$315$	−15.4022	−0.867814
$316$	17.9825	1.01159
$317$	3.28812	0.184679	0.0923396	−	0.995728i	$-0.470565\pi$
$317$	3.28812	0.184679	0.0923396	+	0.995728i	$0.470565\pi$
$318$	3.70569	0.207805
$319$	−1.18595	−0.0664006
$320$	−59.5240	−3.32749
$321$	0.0701415	0.00391492
$322$	−21.6997	−1.20928
$323$	5.24295	0.291725
$324$	42.7115	2.37286
$325$	6.49518	0.360288
$326$	−18.6480	−1.03282
$327$	0.512104	0.0283194
$328$	84.1380	4.64575
$329$	1.80412	0.0994643
$330$	0.342535	0.0188559
$331$	−19.2202	−1.05644	−0.528219	−	0.849108i	$-0.677140\pi$
$331$	−19.2202	−1.05644	−0.528219	+	0.849108i	$0.677140\pi$
$332$	72.8449	3.99788
$333$	6.89814	0.378016
$334$	9.61076	0.525877
$335$	19.0277	1.03959
$336$	−8.70167	−0.474715
$337$	9.01642	0.491155	0.245578	−	0.969377i	$-0.421022\pi$
$337$	9.01642	0.491155	0.245578	+	0.969377i	$0.421022\pi$
$338$	2.28194	0.124121
$339$	−1.90200	−0.103303
$340$	48.5025	2.63042
$341$	0.171079	0.00926443
$342$	−11.6997	−0.632647
$343$	20.0537	1.08280
$344$	−96.4653	−5.20106
$345$	3.33218	0.179399
$346$	33.4653	1.79911
$347$	−11.1957	−0.601019	−0.300509	−	0.953779i	$-0.597157\pi$
$347$	−11.1957	−0.601019	−0.300509	+	0.953779i	$0.597157\pi$
$348$	−13.3345	−0.714806
$349$	−22.4501	−1.20172	−0.600862	−	0.799352i	$-0.705176\pi$
$349$	−22.4501	−1.20172	−0.600862	+	0.799352i	$0.705176\pi$
$350$	10.2047	0.545465
$351$	−6.60066	−0.352317
$352$	−2.76351	−0.147296
$353$	27.9339	1.48677	0.743385	−	0.668864i	$-0.233219\pi$
$353$	27.9339	1.48677	0.743385	+	0.668864i	$0.233219\pi$
$354$	−8.27578	−0.439853
$355$	−9.99632	−0.530549
$356$	−84.2276	−4.46405
$357$	2.28302	0.120830
$358$	−38.1549	−2.01655
$359$	−12.4775	−0.658535	−0.329268	−	0.944237i	$-0.606802\pi$
$359$	−12.4775	−0.658535	−0.329268	+	0.944237i	$0.606802\pi$
$360$	−67.2688	−3.54538
$361$	−16.7608	−0.882146
$362$	−30.7294	−1.61510
$363$	−3.52441	−0.184984
$364$	−37.3882	−1.95967
$365$	37.6365	1.96998
$366$	10.1373	0.529884
$367$	14.0317	0.732448	0.366224	−	0.930527i	$-0.380650\pi$
$367$	14.0317	0.732448	0.366224	+	0.930527i	$0.380650\pi$
$368$	−52.9051	−2.75787
$369$	27.4985	1.43152
$370$	−16.8362	−0.875274
$371$	8.67904	0.450593
$372$	1.92356	0.0997321
$373$	4.17402	0.216122	0.108061	−	0.994144i	$-0.465536\pi$
$373$	4.17402	0.216122	0.108061	+	0.994144i	$0.465536\pi$
$374$	1.42686	0.0737810
$375$	2.63852	0.136253
$376$	7.87947	0.406353
$377$	−27.4015	−1.41125
$378$	−10.3704	−0.533398
$379$	−0.810957	−0.0416560	−0.0208280	−	0.999783i	$-0.506630\pi$
$379$	−0.810957	−0.0416560	−0.0208280	+	0.999783i	$0.506630\pi$
$380$	20.7150	1.06266
$381$	2.66477	0.136520
$382$	51.6166	2.64094
$383$	−17.1420	−0.875914	−0.437957	−	0.898996i	$-0.644298\pi$
$383$	−17.1420	−0.875914	−0.437957	+	0.898996i	$0.644298\pi$
$384$	−7.92833	−0.404591
$385$	0.802247	0.0408863
$386$	−49.4121	−2.51501
$387$	−31.5274	−1.60263
$388$	−15.9445	−0.809458
$389$	30.1258	1.52744	0.763720	−	0.645548i	$-0.223371\pi$
$389$	30.1258	1.52744	0.763720	+	0.645548i	$0.223371\pi$
$390$	7.91428	0.400755
$391$	13.8805	0.701965
$392$	25.5380	1.28986
$393$	−1.31830	−0.0664992
$394$	10.3901	0.523445
$395$	−8.91516	−0.448570
$396$	−2.30981	−0.116073
$397$	27.5147	1.38092	0.690461	−	0.723370i	$-0.257408\pi$
$397$	27.5147	1.38092	0.690461	+	0.723370i	$0.257408\pi$
$398$	45.1242	2.26187
$399$	0.975056	0.0488138
$400$	24.8796	1.24398
$401$	0.582299	0.0290786	0.0145393	−	0.999894i	$-0.495372\pi$
$401$	0.582299	0.0290786	0.0145393	+	0.999894i	$0.495372\pi$
$402$	6.29378	0.313905
$403$	3.95278	0.196902
$404$	−104.642	−5.20612
$405$	−21.1750	−1.05220
$406$	−43.0510	−2.13659
$407$	−0.359301	−0.0178099
$408$	9.97104	0.493640
$409$	−1.33729	−0.0661249	−0.0330624	−	0.999453i	$-0.510526\pi$
$409$	−1.33729	−0.0661249	−0.0330624	+	0.999453i	$0.510526\pi$
$410$	−67.1154	−3.31459
$411$	−3.99935	−0.197274
$412$	−85.1428	−4.19469
$413$	−19.3826	−0.953755
$414$	−30.9744	−1.52231
$415$	−36.1143	−1.77278
$416$	−63.8510	−3.13055
$417$	0.621842	0.0304517
$418$	0.609398	0.0298066
$419$	24.4002	1.19203	0.596013	−	0.802975i	$-0.296751\pi$
$419$	24.4002	1.19203	0.596013	+	0.802975i	$0.296751\pi$
$420$	9.02024	0.440143
$421$	35.0410	1.70779	0.853896	−	0.520444i	$-0.174233\pi$
$421$	35.0410	1.70779	0.853896	+	0.520444i	$0.174233\pi$
$422$	−19.0672	−0.928176
$423$	2.57522	0.125211
$424$	37.9056	1.84086
$425$	−6.52755	−0.316633
$426$	−3.30648	−0.160200
$427$	23.7424	1.14897
$428$	1.15441	0.0558005
$429$	0.168898	0.00815448
$430$	76.9486	3.71079
$431$	24.9028	1.19952	0.599762	−	0.800178i	$-0.295262\pi$
$431$	24.9028	1.19952	0.599762	+	0.800178i	$0.295262\pi$
$432$	−25.2837	−1.21646
$433$	5.34569	0.256897	0.128449	−	0.991716i	$-0.459000\pi$
$433$	5.34569	0.256897	0.128449	+	0.991716i	$0.459000\pi$
$434$	6.21029	0.298103
$435$	6.61085	0.316966
$436$	8.42835	0.403645
$437$	5.92822	0.283585
$438$	12.4490	0.594837
$439$	−5.57270	−0.265971	−0.132985	−	0.991118i	$-0.542456\pi$
$439$	−5.57270	−0.265971	−0.132985	+	0.991118i	$0.542456\pi$
$440$	3.50381	0.167037
$441$	8.34648	0.397452
$442$	32.9676	1.56811
$443$	35.9211	1.70666	0.853330	−	0.521370i	$-0.174579\pi$
$443$	35.9211	1.70666	0.853330	+	0.521370i	$0.174579\pi$
$444$	−4.03988	−0.191724
$445$	41.7574	1.97949
$446$	17.8256	0.844069
$447$	−0.265003	−0.0125342
$448$	−46.1128	−2.17862
$449$	−18.0345	−0.851101	−0.425550	−	0.904935i	$-0.639920\pi$
$449$	−18.0345	−0.851101	−0.425550	+	0.904935i	$0.639920\pi$
$450$	14.5663	0.686663
$451$	−1.43230	−0.0674446
$452$	−31.3037	−1.47240
$453$	−2.93396	−0.137849
$454$	−70.1580	−3.29268
$455$	18.5359	0.868978
$456$	4.25854	0.199425
$457$	30.3530	1.41985	0.709927	−	0.704275i	$-0.248728\pi$
$457$	30.3530	1.41985	0.709927	+	0.704275i	$0.248728\pi$
$458$	5.29641	0.247485
$459$	6.63356	0.309628
$460$	54.8420	2.55702
$461$	−14.4558	−0.673273	−0.336636	−	0.941635i	$-0.609289\pi$
$461$	−14.4558	−0.673273	−0.336636	+	0.941635i	$0.609289\pi$
$462$	0.265359	0.0123456
$463$	23.0813	1.07268	0.536340	−	0.844002i	$-0.319806\pi$
$463$	23.0813	1.07268	0.536340	+	0.844002i	$0.319806\pi$
$464$	−104.961	−4.87268
$465$	−0.953643	−0.0442242
$466$	−13.8162	−0.640024
$467$	25.1060	1.16177	0.580884	−	0.813986i	$-0.302707\pi$
$467$	25.1060	1.16177	0.580884	+	0.813986i	$0.302707\pi$
$468$	−53.3683	−2.46695
$469$	14.7406	0.680657
$470$	−6.28531	−0.289920
$471$	1.82632	0.0841523
$472$	−84.6532	−3.89648
$473$	1.64215	0.0755064
$474$	−2.94887	−0.135446
$475$	−2.78786	−0.127916
$476$	37.5745	1.72223
$477$	12.3885	0.567233
$478$	22.0705	1.00948
$479$	−6.37443	−0.291255	−0.145628	−	0.989339i	$-0.546520\pi$
$479$	−6.37443	−0.291255	−0.145628	+	0.989339i	$0.546520\pi$
$480$	15.4046	0.703122
$481$	−8.30165	−0.378523
$482$	52.5669	2.39436
$483$	2.58141	0.117458
$484$	−58.0058	−2.63663
$485$	7.90478	0.358938
$486$	−22.3337	−1.01308
$487$	30.9180	1.40103	0.700514	−	0.713639i	$-0.252954\pi$
$487$	30.9180	1.40103	0.700514	+	0.713639i	$0.252954\pi$
$488$	103.695	4.69403
$489$	2.21838	0.100318
$490$	−20.3712	−0.920277
$491$	26.9153	1.21467	0.607335	−	0.794446i	$-0.292239\pi$
$491$	26.9153	1.21467	0.607335	+	0.794446i	$0.292239\pi$
$492$	−16.1044	−0.726044
$493$	27.5380	1.24025
$494$	14.0802	0.633496
$495$	1.14514	0.0514700
$496$	15.1410	0.679852
$497$	−7.74407	−0.347369
$498$	−11.9455	−0.535291
$499$	−15.7800	−0.706408	−0.353204	−	0.935546i	$-0.614908\pi$
$499$	−15.7800	−0.706408	−0.353204	+	0.935546i	$0.614908\pi$
$500$	43.4256	1.94205
$501$	−1.14330	−0.0510789
$502$	31.1794	1.39161
$503$	−41.0705	−1.83124	−0.915621	−	0.402043i	$-0.868300\pi$
$503$	−41.0705	−1.83124	−0.915621	+	0.402043i	$0.868300\pi$
$504$	−52.1126	−2.32128
$505$	51.8781	2.30855
$506$	1.61335	0.0717223
$507$	−0.271461	−0.0120560
$508$	43.8575	1.94586
$509$	−14.8275	−0.657220	−0.328610	−	0.944466i	$-0.606580\pi$
$509$	−14.8275	−0.657220	−0.328610	+	0.944466i	$0.606580\pi$
$510$	−7.95372	−0.352197
$511$	29.1567	1.28981
$512$	−7.84041	−0.346501
$513$	2.83313	0.125086
$514$	−36.1161	−1.59301
$515$	42.2112	1.86005
$516$	18.4639	0.812829
$517$	−0.134134	−0.00589923
$518$	−13.0429	−0.573072
$519$	−3.98105	−0.174749
$520$	80.9555	3.55013
$521$	−29.9782	−1.31337	−0.656683	−	0.754166i	$-0.728041\pi$
$521$	−29.9782	−1.31337	−0.656683	+	0.754166i	$0.728041\pi$
$522$	−61.4514	−2.68966
$523$	−22.3504	−0.977315	−0.488657	−	0.872476i	$-0.662513\pi$
$523$	−22.3504	−0.977315	−0.488657	+	0.872476i	$0.662513\pi$
$524$	−21.6969	−0.947833
$525$	−1.21396	−0.0529815
$526$	−2.87476	−0.125345
$527$	−3.97248	−0.173044
$528$	0.646960	0.0281553
$529$	−7.30532	−0.317623
$530$	−30.2366	−1.31340
$531$	−27.6669	−1.20064
$532$	16.0477	0.695758
$533$	−33.0934	−1.43344
$534$	13.8121	0.597709
$535$	−0.572321	−0.0247436
$536$	64.3793	2.78076
$537$	4.53893	0.195869
$538$	−77.7874	−3.35365
$539$	−0.434740	−0.0187256
$540$	26.2093	1.12787
$541$	−4.10382	−0.176437	−0.0882185	−	0.996101i	$-0.528117\pi$
$541$	−4.10382	−0.176437	−0.0882185	+	0.996101i	$0.528117\pi$
$542$	−70.0928	−3.01074
$543$	3.65559	0.156876
$544$	64.1692	2.75123
$545$	−4.17852	−0.178988
$546$	6.13113	0.262388
$547$	−18.2627	−0.780858	−0.390429	−	0.920633i	$-0.627673\pi$
$547$	−18.2627	−0.780858	−0.390429	+	0.920633i	$0.627673\pi$
$548$	−65.8225	−2.81180
$549$	33.8901	1.44639
$550$	−0.758710	−0.0323515
$551$	11.7612	0.501046
$552$	11.2743	0.479866
$553$	−6.90650	−0.293694
$554$	24.6021	1.04524
$555$	2.00285	0.0850162
$556$	10.2344	0.434037
$557$	−40.0463	−1.69682	−0.848409	−	0.529342i	$-0.822439\pi$
$557$	−40.0463	−1.69682	−0.848409	+	0.529342i	$0.822439\pi$
$558$	8.86463	0.375270
$559$	37.9420	1.60478
$560$	71.0014	3.00036
$561$	−0.169740	−0.00716642
$562$	42.1384	1.77750
$563$	20.1687	0.850007	0.425004	−	0.905192i	$-0.360273\pi$
$563$	20.1687	0.850007	0.425004	+	0.905192i	$0.360273\pi$
$564$	−1.50817	−0.0635054
$565$	15.5194	0.652907
$566$	19.8884	0.835973
$567$	−16.4041	−0.688909
$568$	−33.8221	−1.41915
$569$	−16.7148	−0.700720	−0.350360	−	0.936615i	$-0.613941\pi$
$569$	−16.7148	−0.700720	−0.350360	+	0.936615i	$0.613941\pi$
$570$	−3.39696	−0.142283
$571$	4.23284	0.177139	0.0885693	−	0.996070i	$-0.471771\pi$
$571$	4.23284	0.177139	0.0885693	+	0.996070i	$0.471771\pi$
$572$	2.77977	0.116228
$573$	−6.14035	−0.256517
$574$	−51.9938	−2.17018
$575$	−7.38073	−0.307798
$576$	−65.8218	−2.74257
$577$	−21.5958	−0.899045	−0.449522	−	0.893269i	$-0.648406\pi$
$577$	−21.5958	−0.899045	−0.449522	+	0.893269i	$0.648406\pi$
$578$	12.7499	0.530324
$579$	5.87809	0.244285
$580$	108.803	4.51781
$581$	−27.9774	−1.16070
$582$	2.61466	0.108381
$583$	−0.645278	−0.0267247
$584$	127.341	5.26942
$585$	26.4584	1.09392
$586$	22.1722	0.915924
$587$	−13.0995	−0.540672	−0.270336	−	0.962766i	$-0.587135\pi$
$587$	−13.0995	−0.540672	−0.270336	+	0.962766i	$0.587135\pi$
$588$	−4.88810	−0.201582
$589$	−1.69661	−0.0699076
$590$	67.5264	2.78002
$591$	−1.23601	−0.0508427
$592$	−31.7993	−1.30694
$593$	−8.44535	−0.346809	−0.173404	−	0.984851i	$-0.555477\pi$
$593$	−8.44535	−0.346809	−0.173404	+	0.984851i	$0.555477\pi$
$594$	0.771031	0.0316358
$595$	−18.6283	−0.763686
$596$	−4.36150	−0.178654
$597$	−5.36801	−0.219698
$598$	37.2765	1.52435
$599$	−12.3576	−0.504918	−0.252459	−	0.967608i	$-0.581239\pi$
$599$	−12.3576	−0.504918	−0.252459	+	0.967608i	$0.581239\pi$
$600$	−5.30195	−0.216451
$601$	−12.5192	−0.510671	−0.255335	−	0.966853i	$-0.582186\pi$
$601$	−12.5192	−0.510671	−0.255335	+	0.966853i	$0.582186\pi$
$602$	59.6115	2.42958
$603$	21.0408	0.856849
$604$	−48.2879	−1.96481
$605$	28.7575	1.16916
$606$	17.1597	0.697066
$607$	13.2252	0.536794	0.268397	−	0.963308i	$-0.413506\pi$
$607$	13.2252	0.536794	0.268397	+	0.963308i	$0.413506\pi$
$608$	27.4061	1.11146
$609$	5.12138	0.207529
$610$	−82.7153	−3.34904
$611$	−3.09918	−0.125379
$612$	53.6342	2.16804
$613$	32.2352	1.30197	0.650984	−	0.759091i	$-0.274356\pi$
$613$	32.2352	1.30197	0.650984	+	0.759091i	$0.274356\pi$
$614$	51.3520	2.07240
$615$	7.98409	0.321950
$616$	2.71437	0.109365
$617$	40.2697	1.62120	0.810598	−	0.585603i	$-0.199142\pi$
$617$	40.2697	1.62120	0.810598	+	0.585603i	$0.199142\pi$
$618$	13.9622	0.561642
$619$	37.3605	1.50165	0.750823	−	0.660503i	$-0.229657\pi$
$619$	37.3605	1.50165	0.750823	+	0.660503i	$0.229657\pi$
$620$	−15.6953	−0.630340
$621$	7.50058	0.300988
$622$	−0.724723	−0.0290587
$623$	32.3492	1.29604
$624$	14.9480	0.598400
$625$	−30.8443	−1.23377
$626$	57.2883	2.28970
$627$	−0.0724944	−0.00289515
$628$	30.0581	1.19945
$629$	8.34302	0.332658
$630$	41.5693	1.65616
$631$	−26.8311	−1.06813	−0.534065	−	0.845443i	$-0.679336\pi$
$631$	−26.8311	−1.06813	−0.534065	+	0.845443i	$0.679336\pi$
$632$	−30.1641	−1.19986
$633$	2.26824	0.0901546
$634$	−8.87439	−0.352447
$635$	−21.7432	−0.862853
$636$	−7.25532	−0.287692
$637$	−10.0447	−0.397985
$638$	3.20080	0.126721
$639$	−11.0540	−0.437288
$640$	64.6913	2.55715
$641$	−7.11609	−0.281069	−0.140534	−	0.990076i	$-0.544882\pi$
$641$	−7.11609	−0.281069	−0.140534	+	0.990076i	$0.544882\pi$
$642$	−0.189307	−0.00747134
$643$	6.71188	0.264691	0.132345	−	0.991204i	$-0.457749\pi$
$643$	6.71188	0.264691	0.132345	+	0.991204i	$0.457749\pi$
$644$	42.4856	1.67417
$645$	−9.15385	−0.360433
$646$	−14.1503	−0.556737
$647$	39.2170	1.54178	0.770890	−	0.636968i	$-0.219812\pi$
$647$	39.2170	1.54178	0.770890	+	0.636968i	$0.219812\pi$
$648$	−71.6449	−2.81448
$649$	1.44107	0.0565671
$650$	−17.5300	−0.687584
$651$	−0.738780	−0.0289551
$652$	36.5107	1.42987
$653$	17.2677	0.675736	0.337868	−	0.941193i	$-0.390294\pi$
$653$	17.2677	0.675736	0.337868	+	0.941193i	$0.390294\pi$
$654$	−1.38213	−0.0540455
$655$	10.7567	0.420297
$656$	−126.764	−4.94928
$657$	41.6185	1.62369
$658$	−4.86918	−0.189820
$659$	−21.8381	−0.850693	−0.425347	−	0.905030i	$-0.639848\pi$
$659$	−21.8381	−0.850693	−0.425347	+	0.905030i	$0.639848\pi$
$660$	−0.670646	−0.0261048
$661$	12.9042	0.501915	0.250957	−	0.967998i	$-0.419255\pi$
$661$	12.9042	0.501915	0.250957	+	0.967998i	$0.419255\pi$
$662$	51.8739	2.01614
$663$	−3.92184	−0.152312
$664$	−122.191	−4.74194
$665$	−7.95598	−0.308520
$666$	−18.6175	−0.721415
$667$	31.1373	1.20564
$668$	−18.8168	−0.728043
$669$	−2.12055	−0.0819852
$670$	−51.3542	−1.98399
$671$	−1.76522	−0.0681456
$672$	11.9339	0.460358
$673$	10.2609	0.395529	0.197765	−	0.980250i	$-0.436632\pi$
$673$	10.2609	0.395529	0.197765	+	0.980250i	$0.436632\pi$
$674$	−24.3346	−0.937335
$675$	−3.52729	−0.135766
$676$	−4.46778	−0.171838
$677$	−34.4667	−1.32466	−0.662331	−	0.749211i	$-0.730433\pi$
$677$	−34.4667	−1.32466	−0.662331	+	0.749211i	$0.730433\pi$
$678$	5.13336	0.197146
$679$	6.12377	0.235009
$680$	−81.3589	−3.11997
$681$	8.34604	0.319821
$682$	−0.461729	−0.0176805
$683$	20.5183	0.785111	0.392556	−	0.919728i	$-0.371591\pi$
$683$	20.5183	0.785111	0.392556	+	0.919728i	$0.371591\pi$
$684$	22.9067	0.875860
$685$	32.6328	1.24684
$686$	−54.1235	−2.06645
$687$	−0.630064	−0.0240385
$688$	145.336	5.54088
$689$	−14.9091	−0.567993
$690$	−8.99330	−0.342369
$691$	13.2697	0.504805	0.252402	−	0.967622i	$-0.418779\pi$
$691$	13.2697	0.504805	0.252402	+	0.967622i	$0.418779\pi$
$692$	−65.5213	−2.49075
$693$	0.887127	0.0336992
$694$	30.2164	1.14700
$695$	−5.07393	−0.192465
$696$	22.3675	0.847840
$697$	33.2583	1.25975
$698$	60.5911	2.29341
$699$	1.64359	0.0621661
$700$	−19.9797	−0.755162
$701$	−23.7637	−0.897542	−0.448771	−	0.893647i	$-0.648138\pi$
$701$	−23.7637	−0.897542	−0.448771	+	0.893647i	$0.648138\pi$
$702$	17.8147	0.672372
$703$	3.56323	0.134390
$704$	3.42844	0.129214
$705$	0.747705	0.0281602
$706$	−75.3914	−2.83739
$707$	40.1896	1.51148
$708$	16.2030	0.608948
$709$	26.5440	0.996883	0.498441	−	0.866923i	$-0.333906\pi$
$709$	26.5440	0.996883	0.498441	+	0.866923i	$0.333906\pi$
$710$	26.9793	1.01252
$711$	−9.85840	−0.369719
$712$	141.285	5.29486
$713$	−4.49169	−0.168215
$714$	−6.16168	−0.230595
$715$	−1.37813	−0.0515390
$716$	74.7030	2.79178
$717$	−2.62552	−0.0980520
$718$	33.6757	1.25677
$719$	49.2247	1.83577	0.917886	−	0.396844i	$-0.129895\pi$
$719$	49.2247	1.83577	0.917886	+	0.396844i	$0.129895\pi$
$720$	101.348	3.77702
$721$	32.7007	1.21784
$722$	45.2361	1.68351
$723$	−6.25339	−0.232566
$724$	60.1647	2.23600
$725$	−14.6429	−0.543825
$726$	9.51212	0.353028
$727$	−1.83788	−0.0681631	−0.0340815	−	0.999419i	$-0.510851\pi$
$727$	−1.83788	−0.0681631	−0.0340815	+	0.999419i	$0.510851\pi$
$728$	62.7156	2.32439
$729$	−21.5918	−0.799697
$730$	−101.578	−3.75957
$731$	−38.1311	−1.41033
$732$	−19.8477	−0.733591
$733$	37.4778	1.38428	0.692138	−	0.721765i	$-0.256669\pi$
$733$	37.4778	1.38428	0.692138	+	0.721765i	$0.256669\pi$
$734$	−37.8705	−1.39782
$735$	2.42337	0.0893873
$736$	72.5564	2.67446
$737$	−1.09595	−0.0403697
$738$	−74.2164	−2.73194
$739$	31.9704	1.17605	0.588024	−	0.808843i	$-0.299906\pi$
$739$	31.9704	1.17605	0.588024	+	0.808843i	$0.299906\pi$
$740$	32.9635	1.21176
$741$	−1.67498	−0.0615320
$742$	−23.4241	−0.859925
$743$	25.3046	0.928334	0.464167	−	0.885748i	$-0.346354\pi$
$743$	25.3046	0.928334	0.464167	+	0.885748i	$0.346354\pi$
$744$	−3.22661	−0.118293
$745$	2.16230	0.0792205
$746$	−11.2654	−0.412454
$747$	−39.9353	−1.46115
$748$	−2.79363	−0.102145
$749$	−0.443373	−0.0162005
$750$	−7.12117	−0.260028
$751$	−42.4211	−1.54797	−0.773984	−	0.633205i	$-0.781739\pi$
$751$	−42.4211	−1.54797	−0.773984	+	0.633205i	$0.781739\pi$
$752$	−11.8713	−0.432903
$753$	−3.70913	−0.135168
$754$	73.9545	2.69326
$755$	23.9397	0.871254
$756$	20.3042	0.738455
$757$	11.2347	0.408331	0.204165	−	0.978936i	$-0.434552\pi$
$757$	11.2347	0.408331	0.204165	+	0.978936i	$0.434552\pi$
$758$	2.18871	0.0794975
$759$	−0.191925	−0.00696645
$760$	−34.7477	−1.26043
$761$	−2.74228	−0.0994077	−0.0497039	−	0.998764i	$-0.515828\pi$
$761$	−2.74228	−0.0994077	−0.0497039	+	0.998764i	$0.515828\pi$
$762$	−7.19200	−0.260539
$763$	−3.23707	−0.117190
$764$	−101.060	−3.65621
$765$	−26.5902	−0.961371
$766$	46.2649	1.67162
$767$	33.2961	1.20225
$768$	6.80787	0.245658
$769$	46.7099	1.68440	0.842202	−	0.539163i	$-0.181259\pi$
$769$	46.7099	1.68440	0.842202	+	0.539163i	$0.181259\pi$
$770$	−2.16520	−0.0780285
$771$	4.29639	0.154731
$772$	96.7433	3.48187
$773$	5.36970	0.193135	0.0965673	−	0.995326i	$-0.469214\pi$
$773$	5.36970	0.193135	0.0965673	+	0.995326i	$0.469214\pi$
$774$	85.0900	3.05850
$775$	2.11231	0.0758762
$776$	26.7455	0.960108
$777$	1.55159	0.0556630
$778$	−81.3073	−2.91501
$779$	14.2043	0.508924
$780$	−15.4953	−0.554820
$781$	0.575763	0.0206024
$782$	−37.4623	−1.33965
$783$	14.8807	0.531794
$784$	−38.4759	−1.37414
$785$	−14.9019	−0.531871
$786$	3.55798	0.126909
$787$	−27.7111	−0.987795	−0.493897	−	0.869520i	$-0.664428\pi$
$787$	−27.7111	−0.987795	−0.493897	+	0.869520i	$0.664428\pi$
$788$	−20.3426	−0.724677
$789$	0.341983	0.0121749
$790$	24.0613	0.856064
$791$	12.0228	0.427481
$792$	3.87452	0.137675
$793$	−40.7855	−1.44833
$794$	−74.2600	−2.63539
$795$	3.59697	0.127571
$796$	−88.3482	−3.13142
$797$	21.4896	0.761202	0.380601	−	0.924739i	$-0.375717\pi$
$797$	21.4896	0.761202	0.380601	+	0.924739i	$0.375717\pi$
$798$	−2.63160	−0.0931577
$799$	3.11462	0.110187
$800$	−34.1210	−1.20636
$801$	46.1755	1.63153
$802$	−1.57158	−0.0554945
$803$	−2.16777	−0.0764988
$804$	−12.3225	−0.434582
$805$	−21.0631	−0.742376
$806$	−10.6682	−0.375773
$807$	9.25363	0.325743
$808$	175.527	6.17504
$809$	37.9692	1.33493	0.667464	−	0.744642i	$-0.267380\pi$
$809$	37.9692	1.33493	0.667464	+	0.744642i	$0.267380\pi$
$810$	57.1498	2.00804
$811$	39.2690	1.37892	0.689460	−	0.724323i	$-0.257848\pi$
$811$	39.2690	1.37892	0.689460	+	0.724323i	$0.257848\pi$
$812$	84.2891	2.95797
$813$	8.33828	0.292436
$814$	0.969725	0.0339889
$815$	−18.1009	−0.634046
$816$	−15.0225	−0.525893
$817$	−16.2855	−0.569756
$818$	3.60925	0.126195
$819$	20.4971	0.716226
$820$	131.404	4.58884
$821$	−33.8762	−1.18229	−0.591144	−	0.806566i	$-0.701323\pi$
$821$	−33.8762	−1.18229	−0.591144	+	0.806566i	$0.701323\pi$
$822$	10.7940	0.376482
$823$	−39.5791	−1.37964	−0.689820	−	0.723981i	$-0.742310\pi$
$823$	−39.5791	−1.37964	−0.689820	+	0.723981i	$0.742310\pi$
$824$	142.820	4.97537
$825$	0.0902566	0.00314233
$826$	52.3121	1.82017
$827$	18.2126	0.633314	0.316657	−	0.948540i	$-0.397440\pi$
$827$	18.2126	0.633314	0.316657	+	0.948540i	$0.397440\pi$
$828$	60.6444	2.10754
$829$	−37.7346	−1.31058	−0.655288	−	0.755379i	$-0.727453\pi$
$829$	−37.7346	−1.31058	−0.655288	+	0.755379i	$0.727453\pi$
$830$	97.4697	3.38322
$831$	−2.92668	−0.101526
$832$	79.2141	2.74625
$833$	10.0947	0.349762
$834$	−1.67830	−0.0581149
$835$	9.32879	0.322836
$836$	−1.19313	−0.0412654
$837$	−2.14661	−0.0741976
$838$	−65.8542	−2.27490
$839$	−35.3946	−1.22196	−0.610978	−	0.791647i	$-0.709224\pi$
$839$	−35.3946	−1.22196	−0.610978	+	0.791647i	$0.709224\pi$
$840$	−15.1307	−0.522059
$841$	32.7747	1.13016
$842$	−94.5729	−3.25920
$843$	−5.01281	−0.172650
$844$	37.3314	1.28500
$845$	2.21499	0.0761980
$846$	−6.95032	−0.238957
$847$	22.2782	0.765488
$848$	−57.1091	−1.96114
$849$	−2.36594	−0.0811988
$850$	17.6174	0.604271
$851$	9.43348	0.323376
$852$	6.47372	0.221786
$853$	39.9327	1.36727	0.683635	−	0.729824i	$-0.260398\pi$
$853$	39.9327	1.36727	0.683635	+	0.729824i	$0.260398\pi$
$854$	−64.0789	−2.19273
$855$	−11.3564	−0.388382
$856$	−1.93642	−0.0661856
$857$	−27.1751	−0.928283	−0.464142	−	0.885761i	$-0.653637\pi$
$857$	−27.1751	−0.928283	−0.464142	+	0.885761i	$0.653637\pi$
$858$	−0.455843	−0.0155622
$859$	−18.0226	−0.614923	−0.307462	−	0.951560i	$-0.599480\pi$
$859$	−18.0226	−0.614923	−0.307462	+	0.951560i	$0.599480\pi$
$860$	−150.657	−5.13735
$861$	6.18521	0.210791
$862$	−67.2107	−2.28921
$863$	−47.7757	−1.62630	−0.813152	−	0.582051i	$-0.802250\pi$
$863$	−47.7757	−1.62630	−0.813152	+	0.582051i	$0.802250\pi$
$864$	34.6751	1.17967
$865$	32.4835	1.10447
$866$	−14.4276	−0.490270
$867$	−1.51673	−0.0515109
$868$	−12.1591	−0.412705
$869$	0.513491	0.0174190
$870$	−17.8422	−0.604907
$871$	−25.3219	−0.857998
$872$	−14.1379	−0.478768
$873$	8.74113	0.295842
$874$	−15.9998	−0.541202
$875$	−16.6784	−0.563833
$876$	−24.3738	−0.823513
$877$	22.6238	0.763952	0.381976	−	0.924172i	$-0.375244\pi$
$877$	22.6238	0.763952	0.381976	+	0.924172i	$0.375244\pi$
$878$	15.0403	0.507586
$879$	−2.63761	−0.0889645
$880$	−5.27888	−0.177951
$881$	4.13858	0.139432	0.0697162	−	0.997567i	$-0.477791\pi$
$881$	4.13858	0.139432	0.0697162	+	0.997567i	$0.477791\pi$
$882$	−22.5265	−0.758508
$883$	16.8129	0.565801	0.282900	−	0.959149i	$-0.408703\pi$
$883$	16.8129	0.565801	0.282900	+	0.959149i	$0.408703\pi$
$884$	−64.5468	−2.17094
$885$	−8.03298	−0.270026
$886$	−96.9482	−3.25704
$887$	15.6404	0.525152	0.262576	−	0.964911i	$-0.415428\pi$
$887$	15.6404	0.525152	0.262576	+	0.964911i	$0.415428\pi$
$888$	6.77655	0.227406
$889$	−16.8443	−0.564939
$890$	−112.700	−3.77772
$891$	1.21963	0.0408592
$892$	−34.9006	−1.16856
$893$	1.33023	0.0445144
$894$	0.715224	0.0239207
$895$	−37.0355	−1.23796
$896$	50.1158	1.67425
$897$	−4.43444	−0.148062
$898$	48.6738	1.62426
$899$	−8.91126	−0.297207
$900$	−28.5192	−0.950640
$901$	14.9834	0.499171
$902$	3.86568	0.128713
$903$	−7.09142	−0.235988
$904$	52.5093	1.74643
$905$	−29.8278	−0.991511
$906$	7.91853	0.263075
$907$	49.8762	1.65611	0.828057	−	0.560644i	$-0.189447\pi$
$907$	49.8762	1.65611	0.828057	+	0.560644i	$0.189447\pi$
$908$	137.361	4.55850
$909$	57.3670	1.90274
$910$	−50.0271	−1.65838
$911$	−23.7373	−0.786453	−0.393226	−	0.919442i	$-0.628641\pi$
$911$	−23.7373	−0.786453	−0.393226	+	0.919442i	$0.628641\pi$
$912$	−6.41598	−0.212454
$913$	2.08009	0.0688410
$914$	−81.9205	−2.70969
$915$	9.83986	0.325296
$916$	−10.3698	−0.342627
$917$	8.33309	0.275183
$918$	−17.9035	−0.590902
$919$	−37.2320	−1.22817	−0.614085	−	0.789240i	$-0.710475\pi$
$919$	−37.2320	−1.22817	−0.614085	+	0.789240i	$0.710475\pi$
$920$	−91.9928	−3.03291
$921$	−6.10887	−0.201294
$922$	39.0151	1.28489
$923$	13.3030	0.437874
$924$	−0.519544	−0.0170917
$925$	−4.43628	−0.145864
$926$	−62.2948	−2.04713
$927$	46.6773	1.53308
$928$	143.948	4.72531
$929$	5.40545	0.177347	0.0886736	−	0.996061i	$-0.471737\pi$
$929$	5.40545	0.177347	0.0886736	+	0.996061i	$0.471737\pi$
$930$	2.57381	0.0843986
$931$	4.31137	0.141300
$932$	27.0506	0.886072
$933$	0.0862134	0.00282250
$934$	−67.7593	−2.21715
$935$	1.38500	0.0452942
$936$	89.5208	2.92608
$937$	−8.17427	−0.267042	−0.133521	−	0.991046i	$-0.542628\pi$
$937$	−8.17427	−0.267042	−0.133521	+	0.991046i	$0.542628\pi$
$938$	−39.7837	−1.29898
$939$	−6.81505	−0.222401
$940$	12.3059	0.401376
$941$	34.2419	1.11625	0.558127	−	0.829756i	$-0.311520\pi$
$941$	34.2419	1.11625	0.558127	+	0.829756i	$0.311520\pi$
$942$	−4.92909	−0.160598
$943$	37.6053	1.22460
$944$	127.540	4.15106
$945$	−10.0662	−0.327453
$946$	−4.43205	−0.144098
$947$	4.85211	0.157672	0.0788362	−	0.996888i	$-0.474880\pi$
$947$	4.85211	0.157672	0.0788362	+	0.996888i	$0.474880\pi$
$948$	5.77355	0.187516
$949$	−50.0863	−1.62587
$950$	7.52422	0.244118
$951$	1.05570	0.0342335
$952$	−63.0281	−2.04275
$953$	−29.8960	−0.968427	−0.484214	−	0.874950i	$-0.660894\pi$
$953$	−29.8960	−0.968427	−0.484214	+	0.874950i	$0.660894\pi$
$954$	−33.4357	−1.08252
$955$	50.1023	1.62127
$956$	−43.2116	−1.39756
$957$	−0.380769	−0.0123085
$958$	17.2041	0.555840
$959$	25.2804	0.816346
$960$	−19.1111	−0.616808
$961$	−29.7145	−0.958533
$962$	22.4055	0.722383
$963$	−0.632874	−0.0203941
$964$	−102.920	−3.31483
$965$	−47.9624	−1.54396
$966$	−6.96704	−0.224161
$967$	−41.7370	−1.34217	−0.671085	−	0.741380i	$-0.734171\pi$
$967$	−41.7370	−1.34217	−0.671085	+	0.741380i	$0.734171\pi$
$968$	97.2998	3.12734
$969$	1.68333	0.0540764
$970$	−21.3344	−0.685006
$971$	−18.5172	−0.594247	−0.297123	−	0.954839i	$-0.596027\pi$
$971$	−18.5172	−0.594247	−0.297123	+	0.954839i	$0.596027\pi$
$972$	43.7268	1.40254
$973$	−3.93073	−0.126013
$974$	−83.4453	−2.67376
$975$	2.08538	0.0667856
$976$	−156.228	−5.00073
$977$	8.81528	0.282026	0.141013	−	0.990008i	$-0.454964\pi$
$977$	8.81528	0.282026	0.141013	+	0.990008i	$0.454964\pi$
$978$	−5.98723	−0.191450
$979$	−2.40513	−0.0768682
$980$	39.8845	1.27406
$981$	−4.62062	−0.147525
$982$	−72.6423	−2.31811
$983$	52.1689	1.66393	0.831965	−	0.554828i	$-0.187216\pi$
$983$	52.1689	1.66393	0.831965	+	0.554828i	$0.187216\pi$
$984$	27.0138	0.861170
$985$	10.0853	0.321343
$986$	−74.3230	−2.36693
$987$	0.579241	0.0184374
$988$	−27.5674	−0.877035
$989$	−43.1150	−1.37098
$990$	−3.09063	−0.0982268
$991$	23.2262	0.737804	0.368902	−	0.929468i	$-0.379734\pi$
$991$	23.2262	0.737804	0.368902	+	0.929468i	$0.379734\pi$
$992$	−20.7651	−0.659291
$993$	−6.17095	−0.195829
$994$	20.9007	0.662928
$995$	43.8003	1.38856
$996$	23.3880	0.741077
$997$	0.0137954	0.000436903 0	0.000218452	−	1.00000i	$-0.499930\pi$
$997$	0.0137954	0.000436903 0	0.000218452		1.00000i	$0.499930\pi$
$998$	42.5889	1.34813
$999$	4.50832	0.142637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.6	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.6	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69892 q^{2} +0.321066 q^{3} +5.28419 q^{4} -2.61974 q^{5} -0.866532 q^{6} -2.02949 q^{7} -8.86379 q^{8} -2.89692 q^{9} +O(q^{10})\)	\(q-2.69892 q^{2} +0.321066 q^{3} +5.28419 q^{4} -2.61974 q^{5} -0.866532 q^{6} -2.02949 q^{7} -8.86379 q^{8} -2.89692 q^{9} +7.07048 q^{10} +0.150891 q^{11} +1.69657 q^{12} +3.48633 q^{13} +5.47745 q^{14} -0.841109 q^{15} +13.3543 q^{16} -3.50370 q^{17} +7.81856 q^{18} -1.49640 q^{19} -13.8432 q^{20} -0.651600 q^{21} -0.407242 q^{22} -3.96165 q^{23} -2.84586 q^{24} +1.86304 q^{25} -9.40934 q^{26} -1.89330 q^{27} -10.7242 q^{28} -7.85969 q^{29} +2.27009 q^{30} +1.13379 q^{31} -18.3147 q^{32} +0.0484458 q^{33} +9.45623 q^{34} +5.31674 q^{35} -15.3079 q^{36} -2.38120 q^{37} +4.03867 q^{38} +1.11934 q^{39} +23.2208 q^{40} -9.49234 q^{41} +1.75862 q^{42} +10.8831 q^{43} +0.797335 q^{44} +7.58917 q^{45} +10.6922 q^{46} -0.888951 q^{47} +4.28761 q^{48} -2.88116 q^{49} -5.02821 q^{50} -1.12492 q^{51} +18.4224 q^{52} -4.27646 q^{53} +5.10987 q^{54} -0.395294 q^{55} +17.9890 q^{56} -0.480443 q^{57} +21.2127 q^{58} +9.55046 q^{59} -4.44458 q^{60} -11.6987 q^{61} -3.06002 q^{62} +5.87927 q^{63} +22.7213 q^{64} -9.13328 q^{65} -0.130752 q^{66} -7.26318 q^{67} -18.5142 q^{68} -1.27195 q^{69} -14.3495 q^{70} +3.81577 q^{71} +25.6777 q^{72} -14.3665 q^{73} +6.42668 q^{74} +0.598159 q^{75} -7.90727 q^{76} -0.306231 q^{77} -3.02102 q^{78} +3.40307 q^{79} -34.9848 q^{80} +8.08288 q^{81} +25.6191 q^{82} +13.7854 q^{83} -3.44318 q^{84} +9.17880 q^{85} -29.3726 q^{86} -2.52348 q^{87} -1.33746 q^{88} -15.9395 q^{89} -20.4826 q^{90} -7.07548 q^{91} -20.9341 q^{92} +0.364022 q^{93} +2.39921 q^{94} +3.92018 q^{95} -5.88021 q^{96} -3.01739 q^{97} +7.77603 q^{98} -0.437118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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