LMFDB - Embedded newform 6047.2.a.a.1.18

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:	$1$
Dimension:	$217$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} +O(q^{10})$	\(q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} -0.510992 q^{10} +0.737352 q^{11} +11.0249 q^{12} -1.97568 q^{13} +5.61395 q^{14} +0.561963 q^{15} +4.42028 q^{16} -7.55846 q^{17} -10.6930 q^{18} +5.52880 q^{19} +0.844036 q^{20} -6.17394 q^{21} -1.81653 q^{22} +2.66109 q^{23} -13.8115 q^{24} -4.95698 q^{25} +4.86724 q^{26} +3.63170 q^{27} -9.27290 q^{28} +7.95097 q^{29} -1.38444 q^{30} -7.15763 q^{31} -0.694197 q^{32} +1.99773 q^{33} +18.6209 q^{34} -0.472659 q^{35} +17.6623 q^{36} +6.07020 q^{37} -13.6207 q^{38} -5.35275 q^{39} -1.05737 q^{40} -2.92883 q^{41} +15.2100 q^{42} +4.05631 q^{43} +3.00047 q^{44} +0.900287 q^{45} -6.55583 q^{46} -4.70183 q^{47} +11.9760 q^{48} -1.80719 q^{49} +12.2119 q^{50} -20.4783 q^{51} -8.03951 q^{52} -1.50496 q^{53} -8.94699 q^{54} +0.152940 q^{55} +11.6167 q^{56} +14.9793 q^{57} -19.5879 q^{58} +5.97409 q^{59} +2.28677 q^{60} +2.80794 q^{61} +17.6334 q^{62} -9.89089 q^{63} -7.13034 q^{64} -0.409791 q^{65} -4.92157 q^{66} +2.28444 q^{67} -30.7572 q^{68} +7.20977 q^{69} +1.16444 q^{70} -14.1479 q^{71} -22.1266 q^{72} +3.04156 q^{73} -14.9545 q^{74} -13.4301 q^{75} +22.4981 q^{76} -1.68026 q^{77} +13.1869 q^{78} -5.42532 q^{79} +0.916846 q^{80} -3.18188 q^{81} +7.21541 q^{82} +4.78846 q^{83} -25.1233 q^{84} -1.56776 q^{85} -9.99306 q^{86} +21.5418 q^{87} -3.75885 q^{88} -8.65761 q^{89} -2.21793 q^{90} +4.50212 q^{91} +10.8287 q^{92} -19.3923 q^{93} +11.5834 q^{94} +1.14677 q^{95} -1.88081 q^{96} -6.74444 q^{97} +4.45216 q^{98} +3.20043 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) $ 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * 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 $

$2$	−2.46358	−1.74202	−0.871009	−	0.491268i	$-0.836534\pi$
$2$	−2.46358	−1.74202	−0.871009	+	0.491268i	$0.836534\pi$
$3$	2.70933	1.56423	0.782115	−	0.623134i	$-0.214141\pi$
$3$	2.70933	1.56423	0.782115	+	0.623134i	$0.214141\pi$
$4$	4.06925	2.03462
$5$	0.207418	0.0927602	0.0463801	−	0.998924i	$-0.485231\pi$
$5$	0.207418	0.0927602	0.0463801	+	0.998924i	$0.485231\pi$
$6$	−6.67465	−2.72491
$7$	−2.27877	−0.861296	−0.430648	−	0.902520i	$-0.641715\pi$
$7$	−2.27877	−0.861296	−0.430648	+	0.902520i	$0.641715\pi$
$8$	−5.09776	−1.80233
$9$	4.34044	1.44681
$10$	−0.510992	−0.161590
$11$	0.737352	0.222320	0.111160	−	0.993803i	$-0.464543\pi$
$11$	0.737352	0.222320	0.111160	+	0.993803i	$0.464543\pi$
$12$	11.0249	3.18262
$13$	−1.97568	−0.547954	−0.273977	−	0.961736i	$-0.588339\pi$
$13$	−1.97568	−0.547954	−0.273977	+	0.961736i	$0.588339\pi$
$14$	5.61395	1.50039
$15$	0.561963	0.145098
$16$	4.42028	1.10507
$17$	−7.55846	−1.83319	−0.916597	−	0.399811i	$-0.869076\pi$
$17$	−7.55846	−1.83319	−0.916597	+	0.399811i	$0.869076\pi$
$18$	−10.6930	−2.52038
$19$	5.52880	1.26839	0.634197	−	0.773171i	$-0.281331\pi$
$19$	5.52880	1.26839	0.634197	+	0.773171i	$0.281331\pi$
$20$	0.844036	0.188732
$21$	−6.17394	−1.34726
$22$	−1.81653	−0.387285
$23$	2.66109	0.554877	0.277438	−	0.960743i	$-0.410515\pi$
$23$	2.66109	0.554877	0.277438	+	0.960743i	$0.410515\pi$
$24$	−13.8115	−2.81926
$25$	−4.95698	−0.991396
$26$	4.86724	0.954545
$27$	3.63170	0.698920
$28$	−9.27290	−1.75241
$29$	7.95097	1.47646	0.738229	−	0.674550i	$-0.235662\pi$
$29$	7.95097	1.47646	0.738229	+	0.674550i	$0.235662\pi$
$30$	−1.38444	−0.252764
$31$	−7.15763	−1.28555	−0.642774	−	0.766056i	$-0.722217\pi$
$31$	−7.15763	−1.28555	−0.642774	+	0.766056i	$0.722217\pi$
$32$	−0.694197	−0.122718
$33$	1.99773	0.347759
$34$	18.6209	3.19346
$35$	−0.472659	−0.0798940
$36$	17.6623	2.94372
$37$	6.07020	0.997935	0.498968	−	0.866621i	$-0.333713\pi$
$37$	6.07020	0.997935	0.498968	+	0.866621i	$0.333713\pi$
$38$	−13.6207	−2.20957
$39$	−5.35275	−0.857126
$40$	−1.05737	−0.167185
$41$	−2.92883	−0.457406	−0.228703	−	0.973496i	$-0.573448\pi$
$41$	−2.92883	−0.457406	−0.228703	+	0.973496i	$0.573448\pi$
$42$	15.2100	2.34696
$43$	4.05631	0.618581	0.309291	−	0.950968i	$-0.399908\pi$
$43$	4.05631	0.618581	0.309291	+	0.950968i	$0.399908\pi$
$44$	3.00047	0.452337
$45$	0.900287	0.134207
$46$	−6.55583	−0.966605
$47$	−4.70183	−0.685833	−0.342916	−	0.939366i	$-0.611415\pi$
$47$	−4.70183	−0.685833	−0.342916	+	0.939366i	$0.611415\pi$
$48$	11.9760	1.72858
$49$	−1.80719	−0.258170
$50$	12.2119	1.72703
$51$	−20.4783	−2.86754
$52$	−8.03951	−1.11488
$53$	−1.50496	−0.206722	−0.103361	−	0.994644i	$-0.532960\pi$
$53$	−1.50496	−0.206722	−0.103361	+	0.994644i	$0.532960\pi$
$54$	−8.94699	−1.21753
$55$	0.152940	0.0206224
$56$	11.6167	1.55234
$57$	14.9793	1.98406
$58$	−19.5879	−2.57202
$59$	5.97409	0.777760	0.388880	−	0.921288i	$-0.372862\pi$
$59$	5.97409	0.777760	0.388880	+	0.921288i	$0.372862\pi$
$60$	2.28677	0.295220
$61$	2.80794	0.359520	0.179760	−	0.983711i	$-0.442468\pi$
$61$	2.80794	0.359520	0.179760	+	0.983711i	$0.442468\pi$
$62$	17.6334	2.23945
$63$	−9.89089	−1.24614
$64$	−7.13034	−0.891293
$65$	−0.409791	−0.0508283
$66$	−4.92157	−0.605803
$67$	2.28444	0.279089	0.139545	−	0.990216i	$-0.455436\pi$
$67$	2.28444	0.279089	0.139545	+	0.990216i	$0.455436\pi$
$68$	−30.7572	−3.72986
$69$	7.20977	0.867955
$70$	1.16444	0.139177
$71$	−14.1479	−1.67904	−0.839522	−	0.543325i	$-0.817165\pi$
$71$	−14.1479	−1.67904	−0.839522	+	0.543325i	$0.817165\pi$
$72$	−22.1266	−2.60764
$73$	3.04156	0.355987	0.177994	−	0.984032i	$-0.443039\pi$
$73$	3.04156	0.355987	0.177994	+	0.984032i	$0.443039\pi$
$74$	−14.9545	−1.73842
$75$	−13.4301	−1.55077
$76$	22.4981	2.58071
$77$	−1.68026	−0.191483
$78$	13.1869	1.49313
$79$	−5.42532	−0.610396	−0.305198	−	0.952289i	$-0.598723\pi$
$79$	−5.42532	−0.610396	−0.305198	+	0.952289i	$0.598723\pi$
$80$	0.916846	0.102506
$81$	−3.18188	−0.353542
$82$	7.21541	0.796808
$83$	4.78846	0.525602	0.262801	−	0.964850i	$-0.415354\pi$
$83$	4.78846	0.525602	0.262801	+	0.964850i	$0.415354\pi$
$84$	−25.1233	−2.74118
$85$	−1.56776	−0.170048
$86$	−9.99306	−1.07758
$87$	21.5418	2.30952
$88$	−3.75885	−0.400694
$89$	−8.65761	−0.917705	−0.458852	−	0.888512i	$-0.651739\pi$
$89$	−8.65761	−0.917705	−0.458852	+	0.888512i	$0.651739\pi$
$90$	−2.21793	−0.233791
$91$	4.50212	0.471950
$92$	10.8287	1.12897
$93$	−19.3923	−2.01089
$94$	11.5834	1.19473
$95$	1.14677	0.117657
$96$	−1.88081	−0.191959
$97$	−6.74444	−0.684794	−0.342397	−	0.939555i	$-0.611239\pi$
$97$	−6.74444	−0.684794	−0.342397	+	0.939555i	$0.611239\pi$
$98$	4.45216	0.449736
$99$	3.20043	0.321656
$100$	−20.1712	−2.01712
$101$	18.0958	1.80060	0.900299	−	0.435272i	$-0.143348\pi$
$101$	18.0958	1.80060	0.900299	+	0.435272i	$0.143348\pi$
$102$	50.4501	4.99530
$103$	−15.7262	−1.54955	−0.774773	−	0.632239i	$-0.782136\pi$
$103$	−15.7262	−1.54955	−0.774773	+	0.632239i	$0.782136\pi$
$104$	10.0715	0.987595
$105$	−1.28059	−0.124973
$106$	3.70760	0.360114
$107$	−4.98626	−0.482040	−0.241020	−	0.970520i	$-0.577482\pi$
$107$	−4.98626	−0.482040	−0.241020	+	0.970520i	$0.577482\pi$
$108$	14.7783	1.42204
$109$	−11.2628	−1.07878	−0.539389	−	0.842057i	$-0.681345\pi$
$109$	−11.2628	−1.07878	−0.539389	+	0.842057i	$0.681345\pi$
$110$	−0.376781	−0.0359247
$111$	16.4462	1.56100
$112$	−10.0728	−0.951792
$113$	−0.733892	−0.0690388	−0.0345194	−	0.999404i	$-0.510990\pi$
$113$	−0.733892	−0.0690388	−0.0345194	+	0.999404i	$0.510990\pi$
$114$	−36.9028	−3.45627
$115$	0.551959	0.0514705
$116$	32.3545	3.00404
$117$	−8.57531	−0.792788
$118$	−14.7177	−1.35487
$119$	17.2240	1.57892
$120$	−2.86476	−0.261515
$121$	−10.4563	−0.950574
$122$	−6.91760	−0.626290
$123$	−7.93514	−0.715487
$124$	−29.1262	−2.61561
$125$	−2.06526	−0.184722
$126$	24.3670	2.17079
$127$	14.4144	1.27907	0.639534	−	0.768763i	$-0.279127\pi$
$127$	14.4144	1.27907	0.639534	+	0.768763i	$0.279127\pi$
$128$	18.9546	1.67537
$129$	10.9899	0.967603
$130$	1.00955	0.0885438
$131$	15.4389	1.34890	0.674452	−	0.738319i	$-0.264380\pi$
$131$	15.4389	1.34890	0.674452	+	0.738319i	$0.264380\pi$
$132$	8.12924	0.707560
$133$	−12.5989	−1.09246
$134$	−5.62792	−0.486178
$135$	0.753280	0.0648320
$136$	38.5312	3.30403
$137$	−12.3279	−1.05324	−0.526621	−	0.850100i	$-0.676541\pi$
$137$	−12.3279	−1.05324	−0.526621	+	0.850100i	$0.676541\pi$
$138$	−17.7619	−1.51199
$139$	7.49102	0.635380	0.317690	−	0.948195i	$-0.397093\pi$
$139$	7.49102	0.635380	0.317690	+	0.948195i	$0.397093\pi$
$140$	−1.92337	−0.162554
$141$	−12.7388	−1.07280
$142$	34.8545	2.92492
$143$	−1.45677	−0.121821
$144$	19.1860	1.59883
$145$	1.64918	0.136957
$146$	−7.49313	−0.620136
$147$	−4.89626	−0.403837
$148$	24.7012	2.03042
$149$	8.88590	0.727961	0.363981	−	0.931407i	$-0.381417\pi$
$149$	8.88590	0.727961	0.363981	+	0.931407i	$0.381417\pi$
$150$	33.0861	2.70147
$151$	−5.98210	−0.486816	−0.243408	−	0.969924i	$-0.578265\pi$
$151$	−5.98210	−0.486816	−0.243408	+	0.969924i	$0.578265\pi$
$152$	−28.1845	−2.28607
$153$	−32.8071	−2.65229
$154$	4.13946	0.333567
$155$	−1.48462	−0.119248
$156$	−21.7817	−1.74393
$157$	15.4856	1.23588	0.617942	−	0.786224i	$-0.287967\pi$
$157$	15.4856	1.23588	0.617942	+	0.786224i	$0.287967\pi$
$158$	13.3657	1.06332
$159$	−4.07743	−0.323361
$160$	−0.143989	−0.0113833
$161$	−6.06403	−0.477913
$162$	7.83883	0.615877
$163$	−22.5815	−1.76872	−0.884358	−	0.466810i	$-0.845403\pi$
$163$	−22.5815	−1.76872	−0.884358	+	0.466810i	$0.845403\pi$
$164$	−11.9181	−0.930648
$165$	0.414365	0.0322582
$166$	−11.7968	−0.915608
$167$	−6.24287	−0.483087	−0.241544	−	0.970390i	$-0.577654\pi$
$167$	−6.24287	−0.483087	−0.241544	+	0.970390i	$0.577654\pi$
$168$	31.4733	2.42822
$169$	−9.09670	−0.699746
$170$	3.86231	0.296226
$171$	23.9975	1.83513
$172$	16.5061	1.25858
$173$	−20.3542	−1.54750	−0.773749	−	0.633492i	$-0.781621\pi$
$173$	−20.3542	−1.54750	−0.773749	+	0.633492i	$0.781621\pi$
$174$	−53.0700	−4.02322
$175$	11.2958	0.853885
$176$	3.25930	0.245679
$177$	16.1857	1.21660
$178$	21.3288	1.59866
$179$	4.81935	0.360215	0.180108	−	0.983647i	$-0.442355\pi$
$179$	4.81935	0.360215	0.180108	+	0.983647i	$0.442355\pi$
$180$	3.66349	0.273060
$181$	−22.2852	−1.65645	−0.828225	−	0.560396i	$-0.810649\pi$
$181$	−22.2852	−1.65645	−0.828225	+	0.560396i	$0.810649\pi$
$182$	−11.0914	−0.822146
$183$	7.60762	0.562372
$184$	−13.5656	−1.00007
$185$	1.25907	0.0925687
$186$	47.7747	3.50301
$187$	−5.57324	−0.407556
$188$	−19.1329	−1.39541
$189$	−8.27582	−0.601977
$190$	−2.82518	−0.204960
$191$	−17.4157	−1.26016	−0.630080	−	0.776531i	$-0.716978\pi$
$191$	−17.4157	−1.26016	−0.630080	+	0.776531i	$0.716978\pi$
$192$	−19.3184	−1.39419
$193$	−19.1191	−1.37622	−0.688111	−	0.725605i	$-0.741560\pi$
$193$	−19.1191	−1.37622	−0.688111	+	0.725605i	$0.741560\pi$
$194$	16.6155	1.19292
$195$	−1.11026	−0.0795072
$196$	−7.35390	−0.525278
$197$	−22.1170	−1.57577	−0.787884	−	0.615824i	$-0.788823\pi$
$197$	−22.1170	−1.57577	−0.787884	+	0.615824i	$0.788823\pi$
$198$	−7.88454	−0.560330
$199$	−9.02073	−0.639463	−0.319731	−	0.947508i	$-0.603593\pi$
$199$	−9.02073	−0.639463	−0.319731	+	0.947508i	$0.603593\pi$
$200$	25.2695	1.78682
$201$	6.18930	0.436559
$202$	−44.5805	−3.13667
$203$	−18.1185	−1.27167
$204$	−83.3313	−5.83436
$205$	−0.607492	−0.0424290
$206$	38.7428	2.69934
$207$	11.5503	0.802804
$208$	−8.73304	−0.605527
$209$	4.07667	0.281989
$210$	3.15483	0.217704
$211$	−16.3882	−1.12821	−0.564104	−	0.825704i	$-0.690778\pi$
$211$	−16.3882	−1.12821	−0.564104	+	0.825704i	$0.690778\pi$
$212$	−6.12405	−0.420602
$213$	−38.3312	−2.62641
$214$	12.2841	0.839722
$215$	0.841352	0.0573797
$216$	−18.5135	−1.25969
$217$	16.3106	1.10724
$218$	27.7468	1.87925
$219$	8.24056	0.556846
$220$	0.622351	0.0419589
$221$	14.9331	1.00451
$222$	−40.5165	−2.71929
$223$	−5.27404	−0.353176	−0.176588	−	0.984285i	$-0.556506\pi$
$223$	−5.27404	−0.353176	−0.176588	+	0.984285i	$0.556506\pi$
$224$	1.58192	0.105696
$225$	−21.5155	−1.43437
$226$	1.80801	0.120267
$227$	−8.42635	−0.559276	−0.279638	−	0.960105i	$-0.590215\pi$
$227$	−8.42635	−0.559276	−0.279638	+	0.960105i	$0.590215\pi$
$228$	60.9546	4.03682
$229$	13.8065	0.912359	0.456179	−	0.889888i	$-0.349218\pi$
$229$	13.8065	0.912359	0.456179	+	0.889888i	$0.349218\pi$
$230$	−1.35980	−0.0896625
$231$	−4.55237	−0.299524
$232$	−40.5322	−2.66107
$233$	14.9144	0.977074	0.488537	−	0.872543i	$-0.337531\pi$
$233$	14.9144	0.977074	0.488537	+	0.872543i	$0.337531\pi$
$234$	21.1260	1.38105
$235$	−0.975245	−0.0636180
$236$	24.3100	1.58245
$237$	−14.6989	−0.954799
$238$	−42.4328	−2.75051
$239$	−8.71360	−0.563636	−0.281818	−	0.959468i	$-0.590937\pi$
$239$	−8.71360	−0.563636	−0.281818	+	0.959468i	$0.590937\pi$
$240$	2.48403	0.160344
$241$	−4.26170	−0.274520	−0.137260	−	0.990535i	$-0.543830\pi$
$241$	−4.26170	−0.274520	−0.137260	+	0.990535i	$0.543830\pi$
$242$	25.7600	1.65592
$243$	−19.5158	−1.25194
$244$	11.4262	0.731487
$245$	−0.374844	−0.0239479
$246$	19.5489	1.24639
$247$	−10.9231	−0.695022
$248$	36.4879	2.31698
$249$	12.9735	0.822162
$250$	5.08794	0.321789
$251$	−11.3520	−0.716534	−0.358267	−	0.933619i	$-0.616632\pi$
$251$	−11.3520	−0.716534	−0.358267	+	0.933619i	$0.616632\pi$
$252$	−40.2485	−2.53542
$253$	1.96216	0.123360
$254$	−35.5110	−2.22816
$255$	−4.24757	−0.265993
$256$	−32.4355	−2.02722
$257$	−3.48585	−0.217441	−0.108721	−	0.994072i	$-0.534675\pi$
$257$	−3.48585	−0.217441	−0.108721	+	0.994072i	$0.534675\pi$
$258$	−27.0744	−1.68558
$259$	−13.8326	−0.859517
$260$	−1.66754	−0.103417
$261$	34.5107	2.13616
$262$	−38.0350	−2.34981
$263$	−3.02880	−0.186764	−0.0933819	−	0.995630i	$-0.529768\pi$
$263$	−3.02880	−0.186764	−0.0933819	+	0.995630i	$0.529768\pi$
$264$	−10.1839	−0.626778
$265$	−0.312156	−0.0191756
$266$	31.0384	1.90309
$267$	−23.4563	−1.43550
$268$	9.29596	0.567841
$269$	11.3537	0.692249	0.346124	−	0.938189i	$-0.387498\pi$
$269$	11.3537	0.692249	0.346124	+	0.938189i	$0.387498\pi$
$270$	−1.85577	−0.112938
$271$	−12.1364	−0.737236	−0.368618	−	0.929581i	$-0.620169\pi$
$271$	−12.1364	−0.737236	−0.368618	+	0.929581i	$0.620169\pi$
$272$	−33.4105	−2.02581
$273$	12.1977	0.738239
$274$	30.3707	1.83476
$275$	−3.65504	−0.220407
$276$	29.3383	1.76596
$277$	−8.60539	−0.517048	−0.258524	−	0.966005i	$-0.583236\pi$
$277$	−8.60539	−0.517048	−0.258524	+	0.966005i	$0.583236\pi$
$278$	−18.4548	−1.10684
$279$	−31.0673	−1.85995
$280$	2.40951	0.143995
$281$	9.45790	0.564211	0.282105	−	0.959383i	$-0.408967\pi$
$281$	9.45790	0.564211	0.282105	+	0.959383i	$0.408967\pi$
$282$	31.3831	1.86884
$283$	−23.5494	−1.39987	−0.699934	−	0.714208i	$-0.746787\pi$
$283$	−23.5494	−1.39987	−0.699934	+	0.714208i	$0.746787\pi$
$284$	−57.5712	−3.41622
$285$	3.10698	0.184042
$286$	3.58887	0.212214
$287$	6.67413	0.393961
$288$	−3.01312	−0.177550
$289$	40.1303	2.36060
$290$	−4.06288	−0.238581
$291$	−18.2729	−1.07117
$292$	12.3768	0.724300
$293$	5.90558	0.345008	0.172504	−	0.985009i	$-0.444814\pi$
$293$	5.90558	0.345008	0.172504	+	0.985009i	$0.444814\pi$
$294$	12.0623	0.703491
$295$	1.23913	0.0721452
$296$	−30.9445	−1.79861
$297$	2.67784	0.155384
$298$	−21.8912	−1.26812
$299$	−5.25746	−0.304047
$300$	−54.6503	−3.15523
$301$	−9.24341	−0.532781
$302$	14.7374	0.848042
$303$	49.0274	2.81655
$304$	24.4388	1.40166
$305$	0.582418	0.0333491
$306$	80.8229	4.62034
$307$	−22.0290	−1.25726	−0.628632	−	0.777703i	$-0.716385\pi$
$307$	−22.0290	−1.25726	−0.628632	+	0.777703i	$0.716385\pi$
$308$	−6.83739	−0.389596
$309$	−42.6073	−2.42385
$310$	3.65749	0.207732
$311$	32.3394	1.83380	0.916899	−	0.399118i	$-0.130684\pi$
$311$	32.3394	1.83380	0.916899	+	0.399118i	$0.130684\pi$
$312$	27.2871	1.54483
$313$	−19.4592	−1.09990	−0.549950	−	0.835197i	$-0.685353\pi$
$313$	−19.4592	−1.09990	−0.549950	+	0.835197i	$0.685353\pi$
$314$	−38.1500	−2.15293
$315$	−2.05155	−0.115592
$316$	−22.0770	−1.24193
$317$	10.4087	0.584609	0.292305	−	0.956325i	$-0.405578\pi$
$317$	10.4087	0.584609	0.292305	+	0.956325i	$0.405578\pi$
$318$	10.0451	0.563300
$319$	5.86266	0.328246
$320$	−1.47896	−0.0826765
$321$	−13.5094	−0.754022
$322$	14.9393	0.832532
$323$	−41.7892	−2.32521
$324$	−12.9479	−0.719326
$325$	9.79338	0.543239
$326$	55.6313	3.08113
$327$	−30.5145	−1.68746
$328$	14.9305	0.824397
$329$	10.7144	0.590705
$330$	−1.02082	−0.0561944
$331$	−20.2037	−1.11050	−0.555248	−	0.831685i	$-0.687377\pi$
$331$	−20.2037	−1.11050	−0.555248	+	0.831685i	$0.687377\pi$
$332$	19.4854	1.06940
$333$	26.3474	1.44383
$334$	15.3798	0.841547
$335$	0.473835	0.0258884
$336$	−27.2905	−1.48882
$337$	−0.0108319	−0.000590049 0	−0.000295025	−	1.00000i	$-0.500094\pi$
$337$	−0.0108319	−0.000590049 0	−0.000295025		1.00000i	$0.500094\pi$
$338$	22.4105	1.21897
$339$	−1.98835	−0.107993
$340$	−6.37961	−0.345983
$341$	−5.27769	−0.285803
$342$	−59.1198	−3.19683
$343$	20.0696	1.08366
$344$	−20.6781	−1.11489
$345$	1.49544	0.0805117
$346$	50.1442	2.69577
$347$	−15.7900	−0.847654	−0.423827	−	0.905743i	$-0.639314\pi$
$347$	−15.7900	−0.847654	−0.423827	+	0.905743i	$0.639314\pi$
$348$	87.6588	4.69900
$349$	29.9566	1.60354	0.801770	−	0.597632i	$-0.203892\pi$
$349$	29.9566	1.60354	0.801770	+	0.597632i	$0.203892\pi$
$350$	−27.8282	−1.48748
$351$	−7.17506	−0.382976
$352$	−0.511868	−0.0272826
$353$	17.3623	0.924102	0.462051	−	0.886853i	$-0.347114\pi$
$353$	17.3623	0.924102	0.462051	+	0.886853i	$0.347114\pi$
$354$	−39.8749	−2.11933
$355$	−2.93453	−0.155749
$356$	−35.2300	−1.86718
$357$	46.6655	2.46980
$358$	−11.8729	−0.627501
$359$	20.2900	1.07086	0.535432	−	0.844578i	$-0.320149\pi$
$359$	20.2900	1.07086	0.535432	+	0.844578i	$0.320149\pi$
$360$	−4.58945	−0.241885
$361$	11.5677	0.608825
$362$	54.9016	2.88556
$363$	−28.3296	−1.48692
$364$	18.3202	0.960241
$365$	0.630874	0.0330215
$366$	−18.7420	−0.979661
$367$	14.1454	0.738384	0.369192	−	0.929353i	$-0.379634\pi$
$367$	14.1454	0.738384	0.369192	+	0.929353i	$0.379634\pi$
$368$	11.7628	0.613177
$369$	−12.7124	−0.661781
$370$	−3.10183	−0.161256
$371$	3.42946	0.178049
$372$	−78.9122	−4.09141
$373$	10.7290	0.555526	0.277763	−	0.960650i	$-0.410407\pi$
$373$	10.7290	0.555526	0.277763	+	0.960650i	$0.410407\pi$
$374$	13.7302	0.709969
$375$	−5.59546	−0.288948
$376$	23.9688	1.23610
$377$	−15.7085	−0.809031
$378$	20.3882	1.04865
$379$	16.1912	0.831684	0.415842	−	0.909437i	$-0.363487\pi$
$379$	16.1912	0.831684	0.415842	+	0.909437i	$0.363487\pi$
$380$	4.66651	0.239387
$381$	39.0532	2.00076
$382$	42.9052	2.19522
$383$	−17.0072	−0.869026	−0.434513	−	0.900666i	$-0.643079\pi$
$383$	−17.0072	−0.869026	−0.434513	+	0.900666i	$0.643079\pi$
$384$	51.3542	2.62066
$385$	−0.348516	−0.0177620
$386$	47.1015	2.39740
$387$	17.6062	0.894972
$388$	−27.4448	−1.39330
$389$	36.8718	1.86947	0.934736	−	0.355343i	$-0.115636\pi$
$389$	36.8718	1.86947	0.934736	+	0.355343i	$0.115636\pi$
$390$	2.73521	0.138503
$391$	−20.1138	−1.01720
$392$	9.21262	0.465308
$393$	41.8290	2.10999
$394$	54.4870	2.74501
$395$	−1.12531	−0.0566205
$396$	13.0234	0.654448
$397$	−24.4544	−1.22733	−0.613667	−	0.789565i	$-0.710306\pi$
$397$	−24.4544	−1.22733	−0.613667	+	0.789565i	$0.710306\pi$
$398$	22.2233	1.11395
$399$	−34.1345	−1.70886
$400$	−21.9112	−1.09556
$401$	1.24939	0.0623916	0.0311958	−	0.999513i	$-0.490068\pi$
$401$	1.24939	0.0623916	0.0311958	+	0.999513i	$0.490068\pi$
$402$	−15.2479	−0.760494
$403$	14.1412	0.704421
$404$	73.6362	3.66354
$405$	−0.659980	−0.0327947
$406$	44.6364	2.21527
$407$	4.47588	0.221861
$408$	104.394	5.16825
$409$	1.09338	0.0540644	0.0270322	−	0.999635i	$-0.491394\pi$
$409$	1.09338	0.0540644	0.0270322	+	0.999635i	$0.491394\pi$
$410$	1.49661	0.0739121
$411$	−33.4002	−1.64751
$412$	−63.9937	−3.15274
$413$	−13.6136	−0.669881
$414$	−28.4552	−1.39850
$415$	0.993214	0.0487550
$416$	1.37151	0.0672437
$417$	20.2956	0.993881
$418$	−10.0432	−0.491230
$419$	33.8754	1.65492	0.827460	−	0.561525i	$-0.189785\pi$
$419$	33.8754	1.65492	0.827460	+	0.561525i	$0.189785\pi$
$420$	−5.21103	−0.254272
$421$	36.1210	1.76043	0.880216	−	0.474574i	$-0.157398\pi$
$421$	36.1210	1.76043	0.880216	+	0.474574i	$0.157398\pi$
$422$	40.3736	1.96536
$423$	−20.4080	−0.992273
$424$	7.67193	0.372582
$425$	37.4671	1.81742
$426$	94.4322	4.57525
$427$	−6.39866	−0.309653
$428$	−20.2903	−0.980770
$429$	−3.94686	−0.190556
$430$	−2.07274	−0.0999565
$431$	10.5344	0.507425	0.253712	−	0.967280i	$-0.418348\pi$
$431$	10.5344	0.507425	0.253712	+	0.967280i	$0.418348\pi$
$432$	16.0531	0.772356
$433$	−32.7762	−1.57512	−0.787562	−	0.616235i	$-0.788657\pi$
$433$	−32.7762	−1.57512	−0.787562	+	0.616235i	$0.788657\pi$
$434$	−40.1826	−1.92883
$435$	4.46815	0.214232
$436$	−45.8310	−2.19491
$437$	14.7127	0.703803
$438$	−20.3013	−0.970035
$439$	−10.5311	−0.502623	−0.251312	−	0.967906i	$-0.580862\pi$
$439$	−10.5311	−0.502623	−0.251312	+	0.967906i	$0.580862\pi$
$440$	−0.779653	−0.0371685
$441$	−7.84400	−0.373524
$442$	−36.7889	−1.74987
$443$	6.98371	0.331806	0.165903	−	0.986142i	$-0.446946\pi$
$443$	6.98371	0.331806	0.165903	+	0.986142i	$0.446946\pi$
$444$	66.9235	3.17605
$445$	−1.79575	−0.0851265
$446$	12.9931	0.615239
$447$	24.0748	1.13870
$448$	16.2484	0.767667
$449$	1.16615	0.0550338	0.0275169	−	0.999621i	$-0.491240\pi$
$449$	1.16615	0.0550338	0.0275169	+	0.999621i	$0.491240\pi$
$450$	53.0052	2.49869
$451$	−2.15957	−0.101690
$452$	−2.98639	−0.140468
$453$	−16.2074	−0.761492
$454$	20.7590	0.974269
$455$	0.933821	0.0437782
$456$	−76.3611	−3.57594
$457$	−26.0996	−1.22089	−0.610444	−	0.792060i	$-0.709009\pi$
$457$	−26.0996	−1.22089	−0.610444	+	0.792060i	$0.709009\pi$
$458$	−34.0135	−1.58934
$459$	−27.4500	−1.28126
$460$	2.24606	0.104723
$461$	13.5240	0.629874	0.314937	−	0.949113i	$-0.398017\pi$
$461$	13.5240	0.629874	0.314937	+	0.949113i	$0.398017\pi$
$462$	11.2151	0.521775
$463$	24.6147	1.14394	0.571971	−	0.820274i	$-0.306179\pi$
$463$	24.6147	1.14394	0.571971	+	0.820274i	$0.306179\pi$
$464$	35.1455	1.63159
$465$	−4.02232	−0.186531
$466$	−36.7429	−1.70208
$467$	−9.72964	−0.450234	−0.225117	−	0.974332i	$-0.572276\pi$
$467$	−9.72964	−0.450234	−0.225117	+	0.974332i	$0.572276\pi$
$468$	−34.8951	−1.61302
$469$	−5.20573	−0.240378
$470$	2.40260	0.110824
$471$	41.9554	1.93320
$472$	−30.4545	−1.40178
$473$	2.99093	0.137523
$474$	36.2121	1.66328
$475$	−27.4062	−1.25748
$476$	70.0888	3.21251
$477$	−6.53219	−0.299089
$478$	21.4667	0.981864
$479$	−21.6866	−0.990885	−0.495443	−	0.868641i	$-0.664994\pi$
$479$	−21.6866	−0.990885	−0.495443	+	0.868641i	$0.664994\pi$
$480$	−0.390113	−0.0178062
$481$	−11.9928	−0.546822
$482$	10.4991	0.478219
$483$	−16.4294	−0.747566
$484$	−42.5493	−1.93406
$485$	−1.39892	−0.0635216
$486$	48.0789	2.18090
$487$	−4.13786	−0.187504	−0.0937522	−	0.995596i	$-0.529886\pi$
$487$	−4.13786	−0.187504	−0.0937522	+	0.995596i	$0.529886\pi$
$488$	−14.3142	−0.647974
$489$	−61.1805	−2.76668
$490$	0.923459	0.0417176
$491$	35.8806	1.61927	0.809634	−	0.586935i	$-0.199666\pi$
$491$	35.8806	1.61927	0.809634	+	0.586935i	$0.199666\pi$
$492$	−32.2900	−1.45575
$493$	−60.0971	−2.70664
$494$	26.9100	1.21074
$495$	0.663828	0.0298369
$496$	−31.6387	−1.42062
$497$	32.2398	1.44615
$498$	−31.9613	−1.43222
$499$	−4.99660	−0.223678	−0.111839	−	0.993726i	$-0.535674\pi$
$499$	−4.99660	−0.223678	−0.111839	+	0.993726i	$0.535674\pi$
$500$	−8.40405	−0.375840
$501$	−16.9140	−0.755660
$502$	27.9667	1.24821
$503$	21.6242	0.964176	0.482088	−	0.876123i	$-0.339879\pi$
$503$	21.6242	0.964176	0.482088	+	0.876123i	$0.339879\pi$
$504$	50.4214	2.24595
$505$	3.75340	0.167024
$506$	−4.83395	−0.214896
$507$	−24.6459	−1.09456
$508$	58.6556	2.60242
$509$	−37.6768	−1.66999	−0.834997	−	0.550254i	$-0.814531\pi$
$509$	−37.6768	−1.66999	−0.834997	+	0.550254i	$0.814531\pi$
$510$	10.4643	0.463365
$511$	−6.93102	−0.306610
$512$	41.9985	1.85609
$513$	20.0789	0.886507
$514$	8.58768	0.378786
$515$	−3.26189	−0.143736
$516$	44.7205	1.96871
$517$	−3.46691	−0.152474
$518$	34.0778	1.49729
$519$	−55.1461	−2.42064
$520$	2.08902	0.0916095
$521$	29.5897	1.29635	0.648174	−	0.761492i	$-0.275533\pi$
$521$	29.5897	1.29635	0.648174	+	0.761492i	$0.275533\pi$
$522$	−85.0201	−3.72123
$523$	−14.3667	−0.628213	−0.314106	−	0.949388i	$-0.601705\pi$
$523$	−14.3667	−0.628213	−0.314106	+	0.949388i	$0.601705\pi$
$524$	62.8247	2.74451
$525$	30.6041	1.33567
$526$	7.46170	0.325346
$527$	54.1006	2.35666
$528$	8.83050	0.384298
$529$	−15.9186	−0.692112
$530$	0.769023	0.0334042
$531$	25.9302	1.12527
$532$	−51.2680	−2.22275
$533$	5.78641	0.250637
$534$	57.7865	2.50067
$535$	−1.03424	−0.0447142
$536$	−11.6456	−0.503011
$537$	13.0572	0.563459
$538$	−27.9709	−1.20591
$539$	−1.33253	−0.0573963
$540$	3.06528	0.131909
$541$	−9.05680	−0.389382	−0.194691	−	0.980865i	$-0.562370\pi$
$541$	−9.05680	−0.389382	−0.194691	+	0.980865i	$0.562370\pi$
$542$	29.8991	1.28428
$543$	−60.3780	−2.59107
$544$	5.24706	0.224966
$545$	−2.33610	−0.100068
$546$	−30.0501	−1.28602
$547$	19.3570	0.827644	0.413822	−	0.910358i	$-0.364194\pi$
$547$	19.3570	0.827644	0.413822	+	0.910358i	$0.364194\pi$
$548$	−50.1651	−2.14295
$549$	12.1877	0.520158
$550$	9.00449	0.383953
$551$	43.9594	1.87273
$552$	−36.7537	−1.56434
$553$	12.3631	0.525731
$554$	21.2001	0.900707
$555$	3.41123	0.144799
$556$	30.4828	1.29276
$557$	−33.0231	−1.39923	−0.699616	−	0.714519i	$-0.746646\pi$
$557$	−33.0231	−1.39923	−0.699616	+	0.714519i	$0.746646\pi$
$558$	76.5369	3.24006
$559$	−8.01395	−0.338954
$560$	−2.08928	−0.0882884
$561$	−15.0997	−0.637511
$562$	−23.3003	−0.982865
$563$	−30.5218	−1.28634	−0.643171	−	0.765723i	$-0.722381\pi$
$563$	−30.5218	−1.28634	−0.643171	+	0.765723i	$0.722381\pi$
$564$	−51.8373	−2.18274
$565$	−0.152223	−0.00640405
$566$	58.0160	2.43859
$567$	7.25079	0.304504
$568$	72.1226	3.02620
$569$	17.7482	0.744042	0.372021	−	0.928224i	$-0.378665\pi$
$569$	17.7482	0.744042	0.372021	+	0.928224i	$0.378665\pi$
$570$	−7.65432	−0.320604
$571$	22.4174	0.938140	0.469070	−	0.883161i	$-0.344589\pi$
$571$	22.4174	0.938140	0.469070	+	0.883161i	$0.344589\pi$
$572$	−5.92795	−0.247860
$573$	−47.1849	−1.97118
$574$	−16.4423	−0.686288
$575$	−13.1910	−0.550102
$576$	−30.9488	−1.28954
$577$	26.7970	1.11557	0.557787	−	0.829984i	$-0.311651\pi$
$577$	26.7970	1.11557	0.557787	+	0.829984i	$0.311651\pi$
$578$	−98.8643	−4.11221
$579$	−51.7998	−2.15273
$580$	6.71090	0.278655
$581$	−10.9118	−0.452699
$582$	45.0168	1.86601
$583$	−1.10969	−0.0459585
$584$	−15.5051	−0.641607
$585$	−1.77868	−0.0735392
$586$	−14.5489	−0.601010
$587$	−15.1774	−0.626437	−0.313218	−	0.949681i	$-0.601407\pi$
$587$	−15.1774	−0.626437	−0.313218	+	0.949681i	$0.601407\pi$
$588$	−19.9241	−0.821656
$589$	−39.5731	−1.63058
$590$	−3.05271	−0.125678
$591$	−59.9220	−2.46486
$592$	26.8320	1.10279
$593$	30.2545	1.24240	0.621202	−	0.783650i	$-0.286645\pi$
$593$	30.2545	1.24240	0.621202	+	0.783650i	$0.286645\pi$
$594$	−6.59708	−0.270682
$595$	3.57257	0.146461
$596$	36.1589	1.48113
$597$	−24.4401	−1.00027
$598$	12.9522	0.529655
$599$	−46.9611	−1.91878	−0.959389	−	0.282088i	$-0.908973\pi$
$599$	−46.9611	−1.91878	−0.959389	+	0.282088i	$0.908973\pi$
$600$	68.4633	2.79500
$601$	39.2464	1.60089	0.800446	−	0.599405i	$-0.204596\pi$
$601$	39.2464	1.60089	0.800446	+	0.599405i	$0.204596\pi$
$602$	22.7719	0.928114
$603$	9.91549	0.403790
$604$	−24.3426	−0.990487
$605$	−2.16883	−0.0881754
$606$	−120.783	−4.90648
$607$	4.12177	0.167297	0.0836487	−	0.996495i	$-0.473343\pi$
$607$	4.12177	0.167297	0.0836487	+	0.996495i	$0.473343\pi$
$608$	−3.83808	−0.155655
$609$	−49.0888	−1.98918
$610$	−1.43483	−0.0580948
$611$	9.28930	0.375805
$612$	−133.500	−5.39642
$613$	−27.3466	−1.10452	−0.552260	−	0.833672i	$-0.686234\pi$
$613$	−27.3466	−1.10452	−0.552260	+	0.833672i	$0.686234\pi$
$614$	54.2704	2.19018
$615$	−1.64589	−0.0663688
$616$	8.56556	0.345116
$617$	−8.86438	−0.356867	−0.178433	−	0.983952i	$-0.557103\pi$
$617$	−8.86438	−0.356867	−0.178433	+	0.983952i	$0.557103\pi$
$618$	104.967	4.22238
$619$	−28.6808	−1.15278	−0.576388	−	0.817176i	$-0.695538\pi$
$619$	−28.6808	−1.15278	−0.576388	+	0.817176i	$0.695538\pi$
$620$	−6.04129	−0.242624
$621$	9.66429	0.387815
$622$	−79.6708	−3.19451
$623$	19.7287	0.790415
$624$	−23.6606	−0.947184
$625$	24.3565	0.974261
$626$	47.9395	1.91605
$627$	11.0450	0.441096
$628$	63.0146	2.51456
$629$	−45.8814	−1.82941
$630$	5.05417	0.201363
$631$	32.0498	1.27588	0.637940	−	0.770086i	$-0.279787\pi$
$631$	32.0498	1.27588	0.637940	+	0.770086i	$0.279787\pi$
$632$	27.6570	1.10014
$633$	−44.4009	−1.76478
$634$	−25.6426	−1.01840
$635$	2.98980	0.118647
$636$	−16.5921	−0.657918
$637$	3.57042	0.141465
$638$	−14.4432	−0.571810
$639$	−61.4081	−2.42927
$640$	3.93153	0.155407
$641$	−34.9964	−1.38227	−0.691137	−	0.722724i	$-0.742890\pi$
$641$	−34.9964	−1.38227	−0.691137	+	0.722724i	$0.742890\pi$
$642$	33.2816	1.31352
$643$	−21.8340	−0.861050	−0.430525	−	0.902579i	$-0.641672\pi$
$643$	−21.8340	−0.861050	−0.430525	+	0.902579i	$0.641672\pi$
$644$	−24.6761	−0.972373
$645$	2.27950	0.0897551
$646$	102.951	4.05056
$647$	−9.50571	−0.373708	−0.186854	−	0.982388i	$-0.559829\pi$
$647$	−9.50571	−0.373708	−0.186854	+	0.982388i	$0.559829\pi$
$648$	16.2205	0.637201
$649$	4.40500	0.172912
$650$	−24.1268	−0.946332
$651$	44.1908	1.73197
$652$	−91.8895	−3.59867
$653$	−4.17745	−0.163476	−0.0817382	−	0.996654i	$-0.526047\pi$
$653$	−4.17745	−0.163476	−0.0817382	+	0.996654i	$0.526047\pi$
$654$	75.1751	2.93958
$655$	3.20231	0.125125
$656$	−12.9462	−0.505465
$657$	13.2017	0.515047
$658$	−26.3959	−1.02902
$659$	33.0039	1.28565	0.642825	−	0.766013i	$-0.277762\pi$
$659$	33.0039	1.28565	0.642825	+	0.766013i	$0.277762\pi$
$660$	1.68615	0.0656334
$661$	20.9557	0.815083	0.407541	−	0.913187i	$-0.366386\pi$
$661$	20.9557	0.815083	0.407541	+	0.913187i	$0.366386\pi$
$662$	49.7735	1.93450
$663$	40.4585	1.57128
$664$	−24.4105	−0.947309
$665$	−2.61324	−0.101337
$666$	−64.9090	−2.51517
$667$	21.1583	0.819252
$668$	−25.4038	−0.982901
$669$	−14.2891	−0.552449
$670$	−1.16733	−0.0450980
$671$	2.07044	0.0799284
$672$	4.28593	0.165333
$673$	−7.61339	−0.293475	−0.146737	−	0.989175i	$-0.546877\pi$
$673$	−7.61339	−0.293475	−0.146737	+	0.989175i	$0.546877\pi$
$674$	0.0266852	0.00102788
$675$	−18.0022	−0.692907
$676$	−37.0167	−1.42372
$677$	30.0920	1.15653	0.578265	−	0.815849i	$-0.303730\pi$
$677$	30.0920	1.15653	0.578265	+	0.815849i	$0.303730\pi$
$678$	4.89848	0.188125
$679$	15.3691	0.589810
$680$	7.99208	0.306482
$681$	−22.8297	−0.874837
$682$	13.0020	0.497874
$683$	−10.3178	−0.394800	−0.197400	−	0.980323i	$-0.563250\pi$
$683$	−10.3178	−0.394800	−0.197400	+	0.980323i	$0.563250\pi$
$684$	97.6516	3.73380
$685$	−2.55702	−0.0976989
$686$	−49.4431	−1.88775
$687$	37.4063	1.42714
$688$	17.9300	0.683575
$689$	2.97331	0.113274
$690$	−3.68414	−0.140253
$691$	−37.2683	−1.41775	−0.708876	−	0.705333i	$-0.750797\pi$
$691$	−37.2683	−1.41775	−0.708876	+	0.705333i	$0.750797\pi$
$692$	−82.8261	−3.14858
$693$	−7.29307	−0.277041
$694$	38.9001	1.47663
$695$	1.55377	0.0589380
$696$	−109.815	−4.16252
$697$	22.1374	0.838514
$698$	−73.8006	−2.79340
$699$	40.4079	1.52837
$700$	45.9655	1.73733
$701$	−17.9837	−0.679234	−0.339617	−	0.940564i	$-0.610297\pi$
$701$	−17.9837	−0.679234	−0.339617	+	0.940564i	$0.610297\pi$
$702$	17.6764	0.667151
$703$	33.5610	1.26578
$704$	−5.25757	−0.198152
$705$	−2.64226	−0.0995132
$706$	−42.7735	−1.60980
$707$	−41.2362	−1.55085
$708$	65.8638	2.47531
$709$	−47.9511	−1.80084	−0.900420	−	0.435021i	$-0.856741\pi$
$709$	−47.9511	−1.80084	−0.900420	+	0.435021i	$0.856741\pi$
$710$	7.22946	0.271317
$711$	−23.5483	−0.883130
$712$	44.1345	1.65401
$713$	−19.0471	−0.713321
$714$	−114.964	−4.30243
$715$	−0.302160	−0.0113002
$716$	19.6111	0.732903
$717$	−23.6080	−0.881656
$718$	−49.9861	−1.86546
$719$	47.7537	1.78091	0.890456	−	0.455070i	$-0.150386\pi$
$719$	47.7537	1.78091	0.890456	+	0.455070i	$0.150386\pi$
$720$	3.97952	0.148308
$721$	35.8364	1.33462
$722$	−28.4979	−1.06058
$723$	−11.5463	−0.429413
$724$	−90.6842	−3.37025
$725$	−39.4128	−1.46375
$726$	69.7922	2.59023
$727$	−10.5311	−0.390578	−0.195289	−	0.980746i	$-0.562565\pi$
$727$	−10.5311	−0.390578	−0.195289	+	0.980746i	$0.562565\pi$
$728$	−22.9507	−0.850611
$729$	−43.3291	−1.60478
$730$	−1.55421	−0.0575239
$731$	−30.6594	−1.13398
$732$	30.9573	1.14421
$733$	26.1614	0.966295	0.483147	−	0.875539i	$-0.339494\pi$
$733$	26.1614	0.966295	0.483147	+	0.875539i	$0.339494\pi$
$734$	−34.8484	−1.28628
$735$	−1.01557	−0.0374600
$736$	−1.84732	−0.0680933
$737$	1.68444	0.0620471
$738$	31.3181	1.15283
$739$	23.6649	0.870526	0.435263	−	0.900303i	$-0.356655\pi$
$739$	23.6649	0.870526	0.435263	+	0.900303i	$0.356655\pi$
$740$	5.12347	0.188342
$741$	−29.5943	−1.08717
$742$	−8.44877	−0.310164
$743$	−30.4320	−1.11644	−0.558220	−	0.829693i	$-0.688516\pi$
$743$	−30.4320	−1.11644	−0.558220	+	0.829693i	$0.688516\pi$
$744$	98.8576	3.62430
$745$	1.84310	0.0675259
$746$	−26.4318	−0.967735
$747$	20.7841	0.760449
$748$	−22.6789	−0.829223
$749$	11.3626	0.415179
$750$	13.7849	0.503353
$751$	−22.0014	−0.802843	−0.401422	−	0.915893i	$-0.631484\pi$
$751$	−22.0014	−0.802843	−0.401422	+	0.915893i	$0.631484\pi$
$752$	−20.7834	−0.757893
$753$	−30.7563	−1.12082
$754$	38.6993	1.40935
$755$	−1.24080	−0.0451572
$756$	−33.6763	−1.22480
$757$	11.1472	0.405151	0.202576	−	0.979267i	$-0.435069\pi$
$757$	11.1472	0.405151	0.202576	+	0.979267i	$0.435069\pi$
$758$	−39.8883	−1.44881
$759$	5.31614	0.192964
$760$	−5.84599	−0.212056
$761$	14.2054	0.514945	0.257473	−	0.966286i	$-0.417110\pi$
$761$	14.2054	0.514945	0.257473	+	0.966286i	$0.417110\pi$
$762$	−96.2109	−3.48535
$763$	25.6653	0.929147
$764$	−70.8690	−2.56395
$765$	−6.80478	−0.246027
$766$	41.8986	1.51386
$767$	−11.8029	−0.426177
$768$	−87.8785	−3.17104
$769$	−26.2092	−0.945127	−0.472564	−	0.881297i	$-0.656671\pi$
$769$	−26.2092	−0.945127	−0.472564	+	0.881297i	$0.656671\pi$
$770$	0.858599	0.0309418
$771$	−9.44429	−0.340128
$772$	−77.8003	−2.80009
$773$	25.0060	0.899404	0.449702	−	0.893179i	$-0.351530\pi$
$773$	25.0060	0.899404	0.449702	+	0.893179i	$0.351530\pi$
$774$	−43.3743	−1.55906
$775$	35.4802	1.27449
$776$	34.3816	1.23423
$777$	−37.4771	−1.34448
$778$	−90.8367	−3.25665
$779$	−16.1929	−0.580171
$780$	−4.51791	−0.161767
$781$	−10.4320	−0.373285
$782$	49.5520	1.77197
$783$	28.8755	1.03193
$784$	−7.98827	−0.285295
$785$	3.21199	0.114641
$786$	−103.049	−3.67565
$787$	−27.2848	−0.972600	−0.486300	−	0.873792i	$-0.661654\pi$
$787$	−27.2848	−0.972600	−0.486300	+	0.873792i	$0.661654\pi$
$788$	−89.9994	−3.20609
$789$	−8.20600	−0.292141
$790$	2.77229	0.0986338
$791$	1.67238	0.0594628
$792$	−16.3151	−0.579730
$793$	−5.54758	−0.197000
$794$	60.2456	2.13804
$795$	−0.845732	−0.0299950
$796$	−36.7076	−1.30107
$797$	29.0781	1.03000	0.514999	−	0.857191i	$-0.327792\pi$
$797$	29.0781	1.03000	0.514999	+	0.857191i	$0.327792\pi$
$798$	84.0932	2.97687
$799$	35.5386	1.25727
$800$	3.44112	0.121662
$801$	−37.5779	−1.32775
$802$	−3.07798	−0.108687
$803$	2.24270	0.0791431
$804$	25.1858	0.888234
$805$	−1.25779	−0.0443313
$806$	−34.8379	−1.22711
$807$	30.7609	1.08284
$808$	−92.2481	−3.24528
$809$	9.73223	0.342167	0.171084	−	0.985257i	$-0.445273\pi$
$809$	9.73223	0.342167	0.171084	+	0.985257i	$0.445273\pi$
$810$	1.62592	0.0571289
$811$	−18.4772	−0.648821	−0.324411	−	0.945916i	$-0.605166\pi$
$811$	−18.4772	−0.648821	−0.324411	+	0.945916i	$0.605166\pi$
$812$	−73.7285	−2.58736
$813$	−32.8816	−1.15321
$814$	−11.0267	−0.386485
$815$	−4.68380	−0.164066
$816$	−90.5198	−3.16883
$817$	22.4265	0.784605
$818$	−2.69365	−0.0941811
$819$	19.5412	0.682825
$820$	−2.47203	−0.0863271
$821$	−12.6750	−0.442360	−0.221180	−	0.975233i	$-0.570991\pi$
$821$	−12.6750	−0.442360	−0.221180	+	0.975233i	$0.570991\pi$
$822$	82.2842	2.86999
$823$	9.04786	0.315389	0.157694	−	0.987488i	$-0.449594\pi$
$823$	9.04786	0.315389	0.157694	+	0.987488i	$0.449594\pi$
$824$	80.1683	2.79280
$825$	−9.90268	−0.344767
$826$	33.5382	1.16694
$827$	−22.9582	−0.798335	−0.399167	−	0.916878i	$-0.630701\pi$
$827$	−22.9582	−0.798335	−0.399167	+	0.916878i	$0.630701\pi$
$828$	47.0012	1.63340
$829$	45.7039	1.58736	0.793681	−	0.608334i	$-0.208162\pi$
$829$	45.7039	1.58736	0.793681	+	0.608334i	$0.208162\pi$
$830$	−2.44687	−0.0849320
$831$	−23.3148	−0.808782
$832$	14.0872	0.488387
$833$	13.6596	0.473275
$834$	−50.0000	−1.73136
$835$	−1.29488	−0.0448113
$836$	16.5890	0.573742
$837$	−25.9943	−0.898496
$838$	−83.4548	−2.88290
$839$	0.284620	0.00982618	0.00491309	−	0.999988i	$-0.498436\pi$
$839$	0.284620	0.00982618	0.00491309	+	0.999988i	$0.498436\pi$
$840$	6.52813	0.225242
$841$	34.2179	1.17993
$842$	−88.9872	−3.06670
$843$	25.6245	0.882555
$844$	−66.6875	−2.29548
$845$	−1.88682	−0.0649086
$846$	50.2769	1.72856
$847$	23.8276	0.818725
$848$	−6.65234	−0.228442
$849$	−63.8030	−2.18971
$850$	−92.3033	−3.16598
$851$	16.1534	0.553731
$852$	−155.979	−5.34376
$853$	20.2275	0.692575	0.346288	−	0.938128i	$-0.387442\pi$
$853$	20.2275	0.692575	0.346288	+	0.938128i	$0.387442\pi$
$854$	15.7636	0.539421
$855$	4.97751	0.170227
$856$	25.4188	0.868796
$857$	−8.92552	−0.304890	−0.152445	−	0.988312i	$-0.548715\pi$
$857$	−8.92552	−0.304890	−0.152445	+	0.988312i	$0.548715\pi$
$858$	9.72342	0.331952
$859$	−19.6422	−0.670183	−0.335092	−	0.942186i	$-0.608767\pi$
$859$	−19.6422	−0.670183	−0.335092	+	0.942186i	$0.608767\pi$
$860$	3.42367	0.116746
$861$	18.0824	0.616246
$862$	−25.9524	−0.883943
$863$	18.1000	0.616131	0.308066	−	0.951365i	$-0.400318\pi$
$863$	18.1000	0.616131	0.308066	+	0.951365i	$0.400318\pi$
$864$	−2.52111	−0.0857700
$865$	−4.22182	−0.143546
$866$	80.7469	2.74389
$867$	108.726	3.69253
$868$	66.3719	2.25281
$869$	−4.00037	−0.135703
$870$	−11.0077	−0.373195
$871$	−4.51332	−0.152928
$872$	57.4150	1.94432
$873$	−29.2739	−0.990770
$874$	−36.2459	−1.22604
$875$	4.70626	0.159101
$876$	33.5329	1.13297
$877$	9.15545	0.309158	0.154579	−	0.987980i	$-0.450598\pi$
$877$	9.15545	0.309158	0.154579	+	0.987980i	$0.450598\pi$
$878$	25.9443	0.875578
$879$	16.0001	0.539672
$880$	0.676038	0.0227892
$881$	−18.7061	−0.630224	−0.315112	−	0.949055i	$-0.602042\pi$
$881$	−18.7061	−0.630224	−0.315112	+	0.949055i	$0.602042\pi$
$882$	19.3243	0.650685
$883$	4.05251	0.136378	0.0681889	−	0.997672i	$-0.478278\pi$
$883$	4.05251	0.136378	0.0681889	+	0.997672i	$0.478278\pi$
$884$	60.7663	2.04379
$885$	3.35722	0.112852
$886$	−17.2050	−0.578012
$887$	37.0743	1.24483	0.622417	−	0.782686i	$-0.286151\pi$
$887$	37.0743	1.24483	0.622417	+	0.782686i	$0.286151\pi$
$888$	−83.8386	−2.81344
$889$	−32.8471	−1.10166
$890$	4.42397	0.148292
$891$	−2.34617	−0.0785995
$892$	−21.4614	−0.718580
$893$	−25.9955	−0.869907
$894$	−59.3103	−1.98363
$895$	0.999621	0.0334137
$896$	−43.1932	−1.44298
$897$	−14.2442	−0.475599
$898$	−2.87290	−0.0958699
$899$	−56.9101	−1.89806
$900$	−87.5518	−2.91839
$901$	11.3752	0.378962
$902$	5.32029	0.177146
$903$	−25.0434	−0.833393
$904$	3.74121	0.124431
$905$	−4.62236	−0.153653
$906$	39.9284	1.32653
$907$	36.4602	1.21064	0.605321	−	0.795981i	$-0.293045\pi$
$907$	36.4602	1.21064	0.605321	+	0.795981i	$0.293045\pi$
$908$	−34.2889	−1.13792
$909$	78.5438	2.60513
$910$	−2.30055	−0.0762624
$911$	44.5145	1.47483	0.737415	−	0.675440i	$-0.236046\pi$
$911$	44.5145	1.47483	0.737415	+	0.675440i	$0.236046\pi$
$912$	66.2128	2.19252
$913$	3.53078	0.116852
$914$	64.2985	2.12681
$915$	1.57796	0.0521657
$916$	56.1820	1.85631
$917$	−35.1818	−1.16180
$918$	67.6254	2.23197
$919$	−9.58116	−0.316053	−0.158027	−	0.987435i	$-0.550513\pi$
$919$	−9.58116	−0.316053	−0.158027	+	0.987435i	$0.550513\pi$
$920$	−2.81376	−0.0927669
$921$	−59.6839	−1.96665
$922$	−33.3174	−1.09725
$923$	27.9516	0.920039
$924$	−18.5247	−0.609418
$925$	−30.0899	−0.989348
$926$	−60.6404	−1.99277
$927$	−68.2586	−2.24191
$928$	−5.51954	−0.181188
$929$	42.3386	1.38908	0.694542	−	0.719452i	$-0.255607\pi$
$929$	42.3386	1.38908	0.694542	+	0.719452i	$0.255607\pi$
$930$	9.90933	0.324940
$931$	−9.99159	−0.327461
$932$	60.6904	1.98798
$933$	87.6179	2.86848
$934$	23.9698	0.784315
$935$	−1.15599	−0.0378050
$936$	43.7149	1.42887
$937$	−22.3169	−0.729061	−0.364531	−	0.931191i	$-0.618771\pi$
$937$	−22.3169	−0.729061	−0.364531	+	0.931191i	$0.618771\pi$
$938$	12.8248	0.418743
$939$	−52.7214	−1.72050
$940$	−3.96851	−0.129439
$941$	24.0424	0.783761	0.391880	−	0.920016i	$-0.371825\pi$
$941$	24.0424	0.783761	0.391880	+	0.920016i	$0.371825\pi$
$942$	−103.361	−3.36768
$943$	−7.79388	−0.253804
$944$	26.4071	0.859479
$945$	−1.71656	−0.0558395
$946$	−7.36840	−0.239567
$947$	−4.27489	−0.138915	−0.0694576	−	0.997585i	$-0.522127\pi$
$947$	−4.27489	−0.138915	−0.0694576	+	0.997585i	$0.522127\pi$
$948$	−59.8137	−1.94266
$949$	−6.00913	−0.195065
$950$	67.5174	2.19055
$951$	28.2005	0.914463
$952$	−87.8040	−2.84574
$953$	−39.3324	−1.27410	−0.637051	−	0.770822i	$-0.719846\pi$
$953$	−39.3324	−1.27410	−0.637051	+	0.770822i	$0.719846\pi$
$954$	16.0926	0.521018
$955$	−3.61234	−0.116893
$956$	−35.4578	−1.14679
$957$	15.8839	0.513452
$958$	53.4267	1.72614
$959$	28.0924	0.907152
$960$	−4.00699	−0.129325
$961$	20.2316	0.652634
$962$	29.5452	0.952574
$963$	−21.6426	−0.697423
$964$	−17.3419	−0.558546
$965$	−3.96565	−0.127659
$966$	40.4753	1.30227
$967$	42.9667	1.38172	0.690859	−	0.722990i	$-0.257233\pi$
$967$	42.9667	1.38172	0.690859	+	0.722990i	$0.257233\pi$
$968$	53.3038	1.71325
$969$	−113.221	−3.63717
$970$	3.44635	0.110656
$971$	36.2576	1.16356	0.581780	−	0.813346i	$-0.302356\pi$
$971$	36.2576	1.16356	0.581780	+	0.813346i	$0.302356\pi$
$972$	−79.4148	−2.54723
$973$	−17.0704	−0.547250
$974$	10.1940	0.326636
$975$	26.5335	0.849751
$976$	12.4119	0.397294
$977$	5.49274	0.175728	0.0878641	−	0.996132i	$-0.471996\pi$
$977$	5.49274	0.175728	0.0878641	+	0.996132i	$0.471996\pi$
$978$	150.723	4.81960
$979$	−6.38371	−0.204024
$980$	−1.52533	−0.0487249
$981$	−48.8854	−1.56079
$982$	−88.3948	−2.82079
$983$	−41.6338	−1.32791	−0.663956	−	0.747772i	$-0.731124\pi$
$983$	−41.6338	−1.32791	−0.663956	+	0.747772i	$0.731124\pi$
$984$	40.4515	1.28955
$985$	−4.58746	−0.146169
$986$	148.054	4.71500
$987$	29.0288	0.923998
$988$	−44.4489	−1.41411
$989$	10.7942	0.343236
$990$	−1.63540	−0.0519763
$991$	−39.7595	−1.26300	−0.631501	−	0.775375i	$-0.717561\pi$
$991$	−39.7595	−1.26300	−0.631501	+	0.775375i	$0.717561\pi$
$992$	4.96881	0.157760
$993$	−54.7384	−1.73707
$994$	−79.4255	−2.51923
$995$	−1.87106	−0.0593167
$996$	52.7924	1.67279
$997$	6.99188	0.221435	0.110718	−	0.993852i	$-0.464685\pi$
$997$	6.99188	0.221435	0.110718	+	0.993852i	$0.464685\pi$
$998$	12.3095	0.389652
$999$	22.0451	0.697477

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.a.1.18	✓	217

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.a.1.18	✓	217	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)

\(f(q)\)	\(=\)	\(q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} +O(q^{10})\)	\(q-2.46358 q^{2} +2.70933 q^{3} +4.06925 q^{4} +0.207418 q^{5} -6.67465 q^{6} -2.27877 q^{7} -5.09776 q^{8} +4.34044 q^{9} -0.510992 q^{10} +0.737352 q^{11} +11.0249 q^{12} -1.97568 q^{13} +5.61395 q^{14} +0.561963 q^{15} +4.42028 q^{16} -7.55846 q^{17} -10.6930 q^{18} +5.52880 q^{19} +0.844036 q^{20} -6.17394 q^{21} -1.81653 q^{22} +2.66109 q^{23} -13.8115 q^{24} -4.95698 q^{25} +4.86724 q^{26} +3.63170 q^{27} -9.27290 q^{28} +7.95097 q^{29} -1.38444 q^{30} -7.15763 q^{31} -0.694197 q^{32} +1.99773 q^{33} +18.6209 q^{34} -0.472659 q^{35} +17.6623 q^{36} +6.07020 q^{37} -13.6207 q^{38} -5.35275 q^{39} -1.05737 q^{40} -2.92883 q^{41} +15.2100 q^{42} +4.05631 q^{43} +3.00047 q^{44} +0.900287 q^{45} -6.55583 q^{46} -4.70183 q^{47} +11.9760 q^{48} -1.80719 q^{49} +12.2119 q^{50} -20.4783 q^{51} -8.03951 q^{52} -1.50496 q^{53} -8.94699 q^{54} +0.152940 q^{55} +11.6167 q^{56} +14.9793 q^{57} -19.5879 q^{58} +5.97409 q^{59} +2.28677 q^{60} +2.80794 q^{61} +17.6334 q^{62} -9.89089 q^{63} -7.13034 q^{64} -0.409791 q^{65} -4.92157 q^{66} +2.28444 q^{67} -30.7572 q^{68} +7.20977 q^{69} +1.16444 q^{70} -14.1479 q^{71} -22.1266 q^{72} +3.04156 q^{73} -14.9545 q^{74} -13.4301 q^{75} +22.4981 q^{76} -1.68026 q^{77} +13.1869 q^{78} -5.42532 q^{79} +0.916846 q^{80} -3.18188 q^{81} +7.21541 q^{82} +4.78846 q^{83} -25.1233 q^{84} -1.56776 q^{85} -9.99306 q^{86} +21.5418 q^{87} -3.75885 q^{88} -8.65761 q^{89} -2.21793 q^{90} +4.50212 q^{91} +10.8287 q^{92} -19.3923 q^{93} +11.5834 q^{94} +1.14677 q^{95} -1.88081 q^{96} -6.74444 q^{97} +4.45216 q^{98} +3.20043 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9}+O(q^{10}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9	\( 217 q - 20 q^{2} - 27 q^{3} + 184 q^{4} - 19 q^{5} - 17 q^{6} - 48 q^{7} - 57 q^{8} + 152 q^{9} - 46 q^{10} - 32 q^{11} - 72 q^{12} - 80 q^{13} - 22 q^{14} - 43 q^{15} + 122 q^{16} - 61 q^{17} - 88 q^{18} - 43 q^{19} - 41 q^{20} - 61 q^{21} - 93 q^{22} - 60 q^{23} - 41 q^{24} + 26 q^{25} - 9 q^{26} - 93 q^{27} - 126 q^{28} - 47 q^{29} - 36 q^{30} - 100 q^{31} - 114 q^{32} - 133 q^{33} - 75 q^{34} - 37 q^{35} + 75 q^{36} - 264 q^{37} - 35 q^{38} - 47 q^{39} - 118 q^{40} - 72 q^{41} - 64 q^{42} - 107 q^{43} - 59 q^{44} - 69 q^{45} - 111 q^{46} - 54 q^{47} - 135 q^{48} + 33 q^{49} - 42 q^{50} - 26 q^{51} - 173 q^{52} - 103 q^{53} - 28 q^{54} - 78 q^{55} - 44 q^{56} - 205 q^{57} - 189 q^{58} - 38 q^{59} - 105 q^{60} - 108 q^{61} - 14 q^{62} - 116 q^{63} + 39 q^{64} - 146 q^{65} + 5 q^{66} - 206 q^{67} - 62 q^{68} - 55 q^{69} - 125 q^{70} - 78 q^{71} - 225 q^{72} - 326 q^{73} + 3 q^{74} - 95 q^{75} - 84 q^{76} - 79 q^{77} - 86 q^{78} - 117 q^{79} - 39 q^{80} + q^{81} - 96 q^{82} - 23 q^{83} - 57 q^{84} - 224 q^{85} - 7 q^{86} - 45 q^{87} - 250 q^{88} - 104 q^{89} - 36 q^{90} - 96 q^{91} - 137 q^{92} - 155 q^{93} - 48 q^{94} - 38 q^{95} - 33 q^{96} - 447 q^{97} - 46 q^{98} - 94 q^{99}+O(q^{100}) \) 217 * q - 20 * q^2 - 27 * q^3 + 184 * q^4 - 19 * q^5 - 17 * q^6 - 48 * q^7 - 57 * q^8 + 152 * q^9 - 46 * q^10 - 32 * q^11 - 72 * q^12 - 80 * q^13 - 22 * q^14 - 43 * q^15 + 122 * q^16 - 61 * q^17 - 88 * q^18 - 43 * q^19 - 41 * q^20 - 61 * q^21 - 93 * q^22 - 60 * q^23 - 41 * q^24 + 26 * q^25 - 9 * q^26 - 93 * q^27 - 126 * q^28 - 47 * q^29 - 36 * q^30 - 100 * q^31 - 114 * q^32 - 133 * q^33 - 75 * q^34 - 37 * q^35 + 75 * q^36 - 264 * q^37 - 35 * q^38 - 47 * q^39 - 118 * q^40 - 72 * q^41 - 64 * q^42 - 107 * q^43 - 59 * q^44 - 69 * q^45 - 111 * q^46 - 54 * q^47 - 135 * q^48 + 33 * q^49 - 42 * q^50 - 26 * q^51 - 173 * q^52 - 103 * q^53 - 28 * q^54 - 78 * q^55 - 44 * q^56 - 205 * q^57 - 189 * q^58 - 38 * q^59 - 105 * q^60 - 108 * q^61 - 14 * q^62 - 116 * q^63 + 39 * q^64 - 146 * q^65 + 5 * q^66 - 206 * q^67 - 62 * q^68 - 55 * q^69 - 125 * q^70 - 78 * q^71 - 225 * q^72 - 326 * q^73 + 3 * q^74 - 95 * q^75 - 84 * q^76 - 79 * q^77 - 86 * q^78 - 117 * q^79 - 39 * q^80 + q^81 - 96 * q^82 - 23 * q^83 - 57 * q^84 - 224 * q^85 - 7 * q^86 - 45 * q^87 - 250 * q^88 - 104 * q^89 - 36 * q^90 - 96 * q^91 - 137 * q^92 - 155 * q^93 - 48 * q^94 - 38 * q^95 - 33 * q^96 - 447 * q^97 - 46 * q^98 - 94 * q^99

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