LMFDB - Embedded newform 6017.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.98872 q^{2} +0.557360 q^{3} +1.95500 q^{4} +0.637327 q^{5} -1.10843 q^{6} +2.66044 q^{7} +0.0894893 q^{8} -2.68935 q^{9} +O(q^{10})$	\(q-1.98872 q^{2} +0.557360 q^{3} +1.95500 q^{4} +0.637327 q^{5} -1.10843 q^{6} +2.66044 q^{7} +0.0894893 q^{8} -2.68935 q^{9} -1.26746 q^{10} +1.00000 q^{11} +1.08964 q^{12} -6.64896 q^{13} -5.29087 q^{14} +0.355221 q^{15} -4.08797 q^{16} -1.69546 q^{17} +5.34836 q^{18} +5.09154 q^{19} +1.24597 q^{20} +1.48283 q^{21} -1.98872 q^{22} -4.12846 q^{23} +0.0498778 q^{24} -4.59381 q^{25} +13.2229 q^{26} -3.17102 q^{27} +5.20117 q^{28} -6.61614 q^{29} -0.706434 q^{30} +9.36377 q^{31} +7.95085 q^{32} +0.557360 q^{33} +3.37179 q^{34} +1.69557 q^{35} -5.25768 q^{36} -3.79796 q^{37} -10.1256 q^{38} -3.70587 q^{39} +0.0570339 q^{40} -2.40641 q^{41} -2.94892 q^{42} -6.86867 q^{43} +1.95500 q^{44} -1.71399 q^{45} +8.21035 q^{46} +6.93512 q^{47} -2.27847 q^{48} +0.0779608 q^{49} +9.13580 q^{50} -0.944981 q^{51} -12.9987 q^{52} +3.41330 q^{53} +6.30626 q^{54} +0.637327 q^{55} +0.238081 q^{56} +2.83782 q^{57} +13.1576 q^{58} -12.2342 q^{59} +0.694457 q^{60} -5.24970 q^{61} -18.6219 q^{62} -7.15486 q^{63} -7.63605 q^{64} -4.23756 q^{65} -1.10843 q^{66} +9.65711 q^{67} -3.31462 q^{68} -2.30104 q^{69} -3.37202 q^{70} +5.16798 q^{71} -0.240668 q^{72} +15.8652 q^{73} +7.55308 q^{74} -2.56041 q^{75} +9.95396 q^{76} +2.66044 q^{77} +7.36993 q^{78} +7.53184 q^{79} -2.60537 q^{80} +6.30065 q^{81} +4.78568 q^{82} -4.10948 q^{83} +2.89893 q^{84} -1.08056 q^{85} +13.6599 q^{86} -3.68757 q^{87} +0.0894893 q^{88} +15.0899 q^{89} +3.40865 q^{90} -17.6892 q^{91} -8.07115 q^{92} +5.21899 q^{93} -13.7920 q^{94} +3.24497 q^{95} +4.43149 q^{96} +13.1390 q^{97} -0.155042 q^{98} -2.68935 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.98872	−1.40624	−0.703118	−	0.711073i	$-0.748210\pi$
$2$	−1.98872	−1.40624	−0.703118	+	0.711073i	$0.748210\pi$
$3$	0.557360	0.321792	0.160896	−	0.986971i	$-0.448562\pi$
$3$	0.557360	0.321792	0.160896	+	0.986971i	$0.448562\pi$
$4$	1.95500	0.977501
$5$	0.637327	0.285021	0.142511	−	0.989793i	$-0.454483\pi$
$5$	0.637327	0.285021	0.142511	+	0.989793i	$0.454483\pi$
$6$	−1.10843	−0.452516
$7$	2.66044	1.00555	0.502777	−	0.864416i	$-0.332312\pi$
$7$	2.66044	1.00555	0.502777	+	0.864416i	$0.332312\pi$
$8$	0.0894893	0.0316393
$9$	−2.68935	−0.896450
$10$	−1.26746	−0.400807
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.08964	0.314552
$13$	−6.64896	−1.84409	−0.922045	−	0.387084i	$-0.873482\pi$
$13$	−6.64896	−1.84409	−0.922045	+	0.387084i	$0.873482\pi$
$14$	−5.29087	−1.41405
$15$	0.355221	0.0917176
$16$	−4.08797	−1.02199
$17$	−1.69546	−0.411209	−0.205604	−	0.978635i	$-0.565916\pi$
$17$	−1.69546	−0.411209	−0.205604	+	0.978635i	$0.565916\pi$
$18$	5.34836	1.26062
$19$	5.09154	1.16808	0.584039	−	0.811725i	$-0.301471\pi$
$19$	5.09154	1.16808	0.584039	+	0.811725i	$0.301471\pi$
$20$	1.24597	0.278608
$21$	1.48283	0.323579
$22$	−1.98872	−0.423996
$23$	−4.12846	−0.860844	−0.430422	−	0.902628i	$-0.641635\pi$
$23$	−4.12846	−0.860844	−0.430422	+	0.902628i	$0.641635\pi$
$24$	0.0498778	0.0101813
$25$	−4.59381	−0.918763
$26$	13.2229	2.59323
$27$	−3.17102	−0.610263
$28$	5.20117	0.982929
$29$	−6.61614	−1.22859	−0.614293	−	0.789078i	$-0.710559\pi$
$29$	−6.61614	−1.22859	−0.614293	+	0.789078i	$0.710559\pi$
$30$	−0.706434	−0.128977
$31$	9.36377	1.68178	0.840891	−	0.541205i	$-0.182032\pi$
$31$	9.36377	1.68178	0.840891	+	0.541205i	$0.182032\pi$
$32$	7.95085	1.40552
$33$	0.557360	0.0970240
$34$	3.37179	0.578257
$35$	1.69557	0.286604
$36$	−5.25768	−0.876280
$37$	−3.79796	−0.624381	−0.312190	−	0.950020i	$-0.601063\pi$
$37$	−3.79796	−0.624381	−0.312190	+	0.950020i	$0.601063\pi$
$38$	−10.1256	−1.64259
$39$	−3.70587	−0.593414
$40$	0.0570339	0.00901786
$41$	−2.40641	−0.375818	−0.187909	−	0.982186i	$-0.560171\pi$
$41$	−2.40641	−0.375818	−0.187909	+	0.982186i	$0.560171\pi$
$42$	−2.94892	−0.455029
$43$	−6.86867	−1.04746	−0.523731	−	0.851884i	$-0.675460\pi$
$43$	−6.86867	−1.04746	−0.523731	+	0.851884i	$0.675460\pi$
$44$	1.95500	0.294728
$45$	−1.71399	−0.255507
$46$	8.21035	1.21055
$47$	6.93512	1.01159	0.505796	−	0.862653i	$-0.331199\pi$
$47$	6.93512	1.01159	0.505796	+	0.862653i	$0.331199\pi$
$48$	−2.27847	−0.328869
$49$	0.0779608	0.0111373
$50$	9.13580	1.29200
$51$	−0.944981	−0.132324
$52$	−12.9987	−1.80260
$53$	3.41330	0.468853	0.234427	−	0.972134i	$-0.424679\pi$
$53$	3.41330	0.468853	0.234427	+	0.972134i	$0.424679\pi$
$54$	6.30626	0.858174
$55$	0.637327	0.0859371
$56$	0.238081	0.0318150
$57$	2.83782	0.375879
$58$	13.1576	1.72768
$59$	−12.2342	−1.59276	−0.796381	−	0.604795i	$-0.793255\pi$
$59$	−12.2342	−1.59276	−0.796381	+	0.604795i	$0.793255\pi$
$60$	0.694457	0.0896540
$61$	−5.24970	−0.672155	−0.336078	−	0.941834i	$-0.609100\pi$
$61$	−5.24970	−0.672155	−0.336078	+	0.941834i	$0.609100\pi$
$62$	−18.6219	−2.36498
$63$	−7.15486	−0.901428
$64$	−7.63605	−0.954507
$65$	−4.23756	−0.525604
$66$	−1.10843	−0.136439
$67$	9.65711	1.17980	0.589902	−	0.807475i	$-0.299166\pi$
$67$	9.65711	1.17980	0.589902	+	0.807475i	$0.299166\pi$
$68$	−3.31462	−0.401957
$69$	−2.30104	−0.277013
$70$	−3.37202	−0.403033
$71$	5.16798	0.613326	0.306663	−	0.951818i	$-0.400788\pi$
$71$	5.16798	0.613326	0.306663	+	0.951818i	$0.400788\pi$
$72$	−0.240668	−0.0283630
$73$	15.8652	1.85688	0.928441	−	0.371479i	$-0.121149\pi$
$73$	15.8652	1.85688	0.928441	+	0.371479i	$0.121149\pi$
$74$	7.55308	0.878027
$75$	−2.56041	−0.295651
$76$	9.95396	1.14180
$77$	2.66044	0.303186
$78$	7.36993	0.834480
$79$	7.53184	0.847398	0.423699	−	0.905803i	$-0.360731\pi$
$79$	7.53184	0.847398	0.423699	+	0.905803i	$0.360731\pi$
$80$	−2.60537	−0.291290
$81$	6.30065	0.700072
$82$	4.78568	0.528490
$83$	−4.10948	−0.451074	−0.225537	−	0.974235i	$-0.572414\pi$
$83$	−4.10948	−0.451074	−0.225537	+	0.974235i	$0.572414\pi$
$84$	2.89893	0.316299
$85$	−1.08056	−0.117203
$86$	13.6599	1.47298
$87$	−3.68757	−0.395349
$88$	0.0894893	0.00953959
$89$	15.0899	1.59952	0.799762	−	0.600317i	$-0.204959\pi$
$89$	15.0899	1.59952	0.799762	+	0.600317i	$0.204959\pi$
$90$	3.40865	0.359303
$91$	−17.6892	−1.85433
$92$	−8.07115	−0.841476
$93$	5.21899	0.541184
$94$	−13.7920	−1.42254
$95$	3.24497	0.332927
$96$	4.43149	0.452287
$97$	13.1390	1.33407	0.667034	−	0.745027i	$-0.267564\pi$
$97$	13.1390	1.33407	0.667034	+	0.745027i	$0.267564\pi$
$98$	−0.155042	−0.0156616
$99$	−2.68935	−0.270290
$100$	−8.98091	−0.898091
$101$	13.9171	1.38481	0.692403	−	0.721511i	$-0.256552\pi$
$101$	13.9171	1.38481	0.692403	+	0.721511i	$0.256552\pi$
$102$	1.87930	0.186079
$103$	−3.67193	−0.361806	−0.180903	−	0.983501i	$-0.557902\pi$
$103$	−3.67193	−0.361806	−0.180903	+	0.983501i	$0.557902\pi$
$104$	−0.595011	−0.0583456
$105$	0.945045	0.0922269
$106$	−6.78810	−0.659318
$107$	15.7010	1.51788	0.758938	−	0.651163i	$-0.225718\pi$
$107$	15.7010	1.51788	0.758938	+	0.651163i	$0.225718\pi$
$108$	−6.19935	−0.596532
$109$	3.25590	0.311859	0.155929	−	0.987768i	$-0.450163\pi$
$109$	3.25590	0.311859	0.155929	+	0.987768i	$0.450163\pi$
$110$	−1.26746	−0.120848
$111$	−2.11683	−0.200921
$112$	−10.8758	−1.02767
$113$	11.8268	1.11257	0.556285	−	0.830991i	$-0.312226\pi$
$113$	11.8268	1.11257	0.556285	+	0.830991i	$0.312226\pi$
$114$	−5.64363	−0.528574
$115$	−2.63118	−0.245359
$116$	−12.9346	−1.20094
$117$	17.8814	1.65313
$118$	24.3305	2.23980
$119$	−4.51067	−0.413492
$120$	0.0317885	0.00290188
$121$	1.00000	0.0909091
$122$	10.4402	0.945209
$123$	−1.34124	−0.120935
$124$	18.3062	1.64394
$125$	−6.11439	−0.546888
$126$	14.2290	1.26762
$127$	8.88592	0.788498	0.394249	−	0.919004i	$-0.371005\pi$
$127$	8.88592	0.788498	0.394249	+	0.919004i	$0.371005\pi$
$128$	−0.715733	−0.0632625
$129$	−3.82833	−0.337065
$130$	8.42731	0.739124
$131$	17.4154	1.52159	0.760796	−	0.648991i	$-0.224809\pi$
$131$	17.4154	1.52159	0.760796	+	0.648991i	$0.224809\pi$
$132$	1.08964	0.0948410
$133$	13.5457	1.17457
$134$	−19.2053	−1.65908
$135$	−2.02097	−0.173938
$136$	−0.151725	−0.0130103
$137$	−3.63623	−0.310664	−0.155332	−	0.987862i	$-0.549645\pi$
$137$	−3.63623	−0.310664	−0.155332	+	0.987862i	$0.549645\pi$
$138$	4.57613	0.389546
$139$	−20.6615	−1.75249	−0.876243	−	0.481870i	$-0.839958\pi$
$139$	−20.6615	−1.75249	−0.876243	+	0.481870i	$0.839958\pi$
$140$	3.31485	0.280156
$141$	3.86536	0.325522
$142$	−10.2776	−0.862481
$143$	−6.64896	−0.556014
$144$	10.9940	0.916165
$145$	−4.21664	−0.350173
$146$	−31.5514	−2.61122
$147$	0.0434523	0.00358388
$148$	−7.42502	−0.610333
$149$	1.26223	0.103406	0.0517031	−	0.998663i	$-0.483535\pi$
$149$	1.26223	0.103406	0.0517031	+	0.998663i	$0.483535\pi$
$150$	5.09194	0.415755
$151$	15.7179	1.27911	0.639553	−	0.768747i	$-0.279119\pi$
$151$	15.7179	1.27911	0.639553	+	0.768747i	$0.279119\pi$
$152$	0.455638	0.0369571
$153$	4.55968	0.368628
$154$	−5.29087	−0.426351
$155$	5.96778	0.479343
$156$	−7.24497	−0.580062
$157$	24.6060	1.96377	0.981886	−	0.189474i	$-0.0606783\pi$
$157$	24.6060	1.96377	0.981886	+	0.189474i	$0.0606783\pi$
$158$	−14.9787	−1.19164
$159$	1.90244	0.150873
$160$	5.06729	0.400604
$161$	−10.9835	−0.865625
$162$	−12.5302	−0.984467
$163$	−0.500833	−0.0392283	−0.0196141	−	0.999808i	$-0.506244\pi$
$163$	−0.500833	−0.0392283	−0.0196141	+	0.999808i	$0.506244\pi$
$164$	−4.70454	−0.367363
$165$	0.355221	0.0276539
$166$	8.17260	0.634317
$167$	−2.16239	−0.167331	−0.0836654	−	0.996494i	$-0.526663\pi$
$167$	−2.16239	−0.167331	−0.0836654	+	0.996494i	$0.526663\pi$
$168$	0.132697	0.0102378
$169$	31.2086	2.40067
$170$	2.14893	0.164815
$171$	−13.6929	−1.04712
$172$	−13.4283	−1.02390
$173$	21.2577	1.61619	0.808096	−	0.589051i	$-0.200498\pi$
$173$	21.2577	1.61619	0.808096	+	0.589051i	$0.200498\pi$
$174$	7.33354	0.555954
$175$	−12.2216	−0.923865
$176$	−4.08797	−0.308142
$177$	−6.81888	−0.512538
$178$	−30.0095	−2.24931
$179$	−21.6590	−1.61887	−0.809433	−	0.587212i	$-0.800225\pi$
$179$	−21.6590	−1.61887	−0.809433	+	0.587212i	$0.800225\pi$
$180$	−3.35086	−0.249758
$181$	−20.5550	−1.52784	−0.763919	−	0.645312i	$-0.776728\pi$
$181$	−20.5550	−1.52784	−0.763919	+	0.645312i	$0.776728\pi$
$182$	35.1788	2.60763
$183$	−2.92598	−0.216294
$184$	−0.369453	−0.0272365
$185$	−2.42054	−0.177962
$186$	−10.3791	−0.761033
$187$	−1.69546	−0.123984
$188$	13.5582	0.988832
$189$	−8.43632	−0.613652
$190$	−6.45334	−0.468174
$191$	−10.6989	−0.774148	−0.387074	−	0.922049i	$-0.626514\pi$
$191$	−10.6989	−0.774148	−0.387074	+	0.922049i	$0.626514\pi$
$192$	−4.25603	−0.307153
$193$	16.2657	1.17083	0.585416	−	0.810733i	$-0.300931\pi$
$193$	16.2657	1.17083	0.585416	+	0.810733i	$0.300931\pi$
$194$	−26.1299	−1.87601
$195$	−2.36185	−0.169135
$196$	0.152414	0.0108867
$197$	−10.1570	−0.723653	−0.361827	−	0.932245i	$-0.617847\pi$
$197$	−10.1570	−0.723653	−0.361827	+	0.932245i	$0.617847\pi$
$198$	5.34836	0.380091
$199$	13.6754	0.969421	0.484710	−	0.874675i	$-0.338925\pi$
$199$	13.6754	0.969421	0.484710	+	0.874675i	$0.338925\pi$
$200$	−0.411097	−0.0290690
$201$	5.38249	0.379652
$202$	−27.6773	−1.94737
$203$	−17.6019	−1.23541
$204$	−1.84744	−0.129347
$205$	−1.53367	−0.107116
$206$	7.30243	0.508785
$207$	11.1029	0.771704
$208$	27.1808	1.88465
$209$	5.09154	0.352189
$210$	−1.87943	−0.129693
$211$	−12.9059	−0.888480	−0.444240	−	0.895908i	$-0.646526\pi$
$211$	−12.9059	−0.888480	−0.444240	+	0.895908i	$0.646526\pi$
$212$	6.67301	0.458304
$213$	2.88043	0.197363
$214$	−31.2249	−2.13449
$215$	−4.37759	−0.298549
$216$	−0.283772	−0.0193083
$217$	24.9118	1.69112
$218$	−6.47507	−0.438547
$219$	8.84264	0.597530
$220$	1.24597	0.0840036
$221$	11.2730	0.758306
$222$	4.20979	0.282542
$223$	14.4656	0.968686	0.484343	−	0.874878i	$-0.339059\pi$
$223$	14.4656	0.968686	0.484343	+	0.874878i	$0.339059\pi$
$224$	21.1528	1.41333
$225$	12.3544	0.823625
$226$	−23.5202	−1.56454
$227$	−11.4424	−0.759457	−0.379729	−	0.925098i	$-0.623983\pi$
$227$	−11.4424	−0.759457	−0.379729	+	0.925098i	$0.623983\pi$
$228$	5.54794	0.367422
$229$	−15.6770	−1.03597	−0.517983	−	0.855391i	$-0.673317\pi$
$229$	−15.6770	−1.03597	−0.517983	+	0.855391i	$0.673317\pi$
$230$	5.23268	0.345032
$231$	1.48283	0.0975628
$232$	−0.592074	−0.0388715
$233$	21.9381	1.43721	0.718605	−	0.695418i	$-0.244781\pi$
$233$	21.9381	1.43721	0.718605	+	0.695418i	$0.244781\pi$
$234$	−35.5610	−2.32470
$235$	4.41994	0.288325
$236$	−23.9180	−1.55693
$237$	4.19795	0.272686
$238$	8.97045	0.581468
$239$	−8.77130	−0.567368	−0.283684	−	0.958918i	$-0.591557\pi$
$239$	−8.77130	−0.567368	−0.283684	+	0.958918i	$0.591557\pi$
$240$	−1.45213	−0.0937347
$241$	9.11202	0.586957	0.293479	−	0.955966i	$-0.405187\pi$
$241$	9.11202	0.586957	0.293479	+	0.955966i	$0.405187\pi$
$242$	−1.98872	−0.127840
$243$	13.0248	0.835540
$244$	−10.2632	−0.657032
$245$	0.0496865	0.00317435
$246$	2.66735	0.170064
$247$	−33.8534	−2.15404
$248$	0.837957	0.0532103
$249$	−2.29046	−0.145152
$250$	12.1598	0.769054
$251$	−2.86403	−0.180776	−0.0903880	−	0.995907i	$-0.528811\pi$
$251$	−2.86403	−0.180776	−0.0903880	+	0.995907i	$0.528811\pi$
$252$	−13.9878	−0.881147
$253$	−4.12846	−0.259554
$254$	−17.6716	−1.10881
$255$	−0.602262	−0.0377151
$256$	16.6955	1.04347
$257$	−28.0817	−1.75169	−0.875844	−	0.482594i	$-0.839695\pi$
$257$	−28.0817	−1.75169	−0.875844	+	0.482594i	$0.839695\pi$
$258$	7.61346	0.473993
$259$	−10.1043	−0.627848
$260$	−8.28443	−0.513779
$261$	17.7931	1.10137
$262$	−34.6344	−2.13972
$263$	−27.6892	−1.70739	−0.853695	−	0.520774i	$-0.825644\pi$
$263$	−27.6892	−1.70739	−0.853695	+	0.520774i	$0.825644\pi$
$264$	0.0498778	0.00306977
$265$	2.17539	0.133633
$266$	−26.9387	−1.65172
$267$	8.41051	0.514715
$268$	18.8797	1.15326
$269$	1.63171	0.0994874	0.0497437	−	0.998762i	$-0.484160\pi$
$269$	1.63171	0.0994874	0.0497437	+	0.998762i	$0.484160\pi$
$270$	4.01915	0.244598
$271$	15.1778	0.921988	0.460994	−	0.887403i	$-0.347493\pi$
$271$	15.1778	0.921988	0.460994	+	0.887403i	$0.347493\pi$
$272$	6.93098	0.420253
$273$	−9.85925	−0.596709
$274$	7.23144	0.436868
$275$	−4.59381	−0.277017
$276$	−4.49854	−0.270780
$277$	−2.22873	−0.133911	−0.0669556	−	0.997756i	$-0.521329\pi$
$277$	−2.22873	−0.133911	−0.0669556	+	0.997756i	$0.521329\pi$
$278$	41.0899	2.46441
$279$	−25.1824	−1.50763
$280$	0.151736	0.00906794
$281$	32.4821	1.93772	0.968858	−	0.247615i	$-0.0796470\pi$
$281$	32.4821	1.93772	0.968858	+	0.247615i	$0.0796470\pi$
$282$	−7.68712	−0.457761
$283$	−6.39882	−0.380371	−0.190185	−	0.981748i	$-0.560909\pi$
$283$	−6.39882	−0.380371	−0.190185	+	0.981748i	$0.560909\pi$
$284$	10.1034	0.599527
$285$	1.80862	0.107133
$286$	13.2229	0.781887
$287$	−6.40212	−0.377905
$288$	−21.3826	−1.25998
$289$	−14.1254	−0.830907
$290$	8.38571	0.492426
$291$	7.32318	0.429293
$292$	31.0165	1.81510
$293$	−14.3919	−0.840782	−0.420391	−	0.907343i	$-0.638107\pi$
$293$	−14.3919	−0.840782	−0.420391	+	0.907343i	$0.638107\pi$
$294$	−0.0864143	−0.00503979
$295$	−7.79721	−0.453971
$296$	−0.339877	−0.0197550
$297$	−3.17102	−0.184001
$298$	−2.51023	−0.145413
$299$	27.4500	1.58747
$300$	−5.00561	−0.288999
$301$	−18.2737	−1.05328
$302$	−31.2585	−1.79873
$303$	7.75686	0.445620
$304$	−20.8141	−1.19377
$305$	−3.34577	−0.191578
$306$	−9.06792	−0.518378
$307$	2.30208	0.131387	0.0656934	−	0.997840i	$-0.479074\pi$
$307$	2.30208	0.131387	0.0656934	+	0.997840i	$0.479074\pi$
$308$	5.20117	0.296364
$309$	−2.04659	−0.116426
$310$	−11.8682	−0.674070
$311$	19.5970	1.11124	0.555621	−	0.831435i	$-0.312480\pi$
$311$	19.5970	1.11124	0.555621	+	0.831435i	$0.312480\pi$
$312$	−0.331636	−0.0187752
$313$	0.990127	0.0559653	0.0279826	−	0.999608i	$-0.491092\pi$
$313$	0.990127	0.0559653	0.0279826	+	0.999608i	$0.491092\pi$
$314$	−48.9344	−2.76153
$315$	−4.55998	−0.256926
$316$	14.7248	0.828332
$317$	−25.5806	−1.43675	−0.718374	−	0.695657i	$-0.755113\pi$
$317$	−25.5806	−1.43675	−0.718374	+	0.695657i	$0.755113\pi$
$318$	−3.78342	−0.212164
$319$	−6.61614	−0.370432
$320$	−4.86666	−0.272055
$321$	8.75113	0.488441
$322$	21.8432	1.21727
$323$	−8.63248	−0.480324
$324$	12.3178	0.684321
$325$	30.5441	1.69428
$326$	0.996015	0.0551642
$327$	1.81471	0.100354
$328$	−0.215348	−0.0118906
$329$	18.4505	1.01721
$330$	−0.706434	−0.0388879
$331$	28.1634	1.54800	0.774001	−	0.633184i	$-0.218252\pi$
$331$	28.1634	1.54800	0.774001	+	0.633184i	$0.218252\pi$
$332$	−8.03404	−0.440925
$333$	10.2140	0.559726
$334$	4.30039	0.235307
$335$	6.15474	0.336269
$336$	−6.06175	−0.330696
$337$	2.18659	0.119111	0.0595556	−	0.998225i	$-0.481032\pi$
$337$	2.18659	0.119111	0.0595556	+	0.998225i	$0.481032\pi$
$338$	−62.0652	−3.37590
$339$	6.59179	0.358017
$340$	−2.11250	−0.114566
$341$	9.36377	0.507076
$342$	27.2314	1.47250
$343$	−18.4157	−0.994354
$344$	−0.614673	−0.0331409
$345$	−1.46652	−0.0789546
$346$	−42.2755	−2.27275
$347$	16.7415	0.898731	0.449365	−	0.893348i	$-0.351650\pi$
$347$	16.7415	0.898731	0.449365	+	0.893348i	$0.351650\pi$
$348$	−7.20921	−0.386454
$349$	−7.24297	−0.387707	−0.193854	−	0.981030i	$-0.562099\pi$
$349$	−7.24297	−0.387707	−0.193854	+	0.981030i	$0.562099\pi$
$350$	24.3053	1.29917
$351$	21.0840	1.12538
$352$	7.95085	0.423782
$353$	5.03337	0.267899	0.133950	−	0.990988i	$-0.457234\pi$
$353$	5.03337	0.267899	0.133950	+	0.990988i	$0.457234\pi$
$354$	13.5608	0.720750
$355$	3.29369	0.174811
$356$	29.5008	1.56354
$357$	−2.51407	−0.133059
$358$	43.0736	2.27651
$359$	4.20857	0.222120	0.111060	−	0.993814i	$-0.464575\pi$
$359$	4.20857	0.222120	0.111060	+	0.993814i	$0.464575\pi$
$360$	−0.153384	−0.00808406
$361$	6.92374	0.364408
$362$	40.8781	2.14850
$363$	0.557360	0.0292538
$364$	−34.5824	−1.81261
$365$	10.1113	0.529251
$366$	5.81894	0.304161
$367$	−6.82458	−0.356240	−0.178120	−	0.984009i	$-0.557002\pi$
$367$	−6.82458	−0.356240	−0.178120	+	0.984009i	$0.557002\pi$
$368$	16.8770	0.879777
$369$	6.47168	0.336902
$370$	4.81378	0.250256
$371$	9.08090	0.471457
$372$	10.2031	0.529008
$373$	7.43841	0.385146	0.192573	−	0.981283i	$-0.438317\pi$
$373$	7.43841	0.385146	0.192573	+	0.981283i	$0.438317\pi$
$374$	3.37179	0.174351
$375$	−3.40792	−0.175984
$376$	0.620620	0.0320060
$377$	43.9904	2.26562
$378$	16.7775	0.862939
$379$	18.2056	0.935161	0.467580	−	0.883951i	$-0.345126\pi$
$379$	18.2056	0.935161	0.467580	+	0.883951i	$0.345126\pi$
$380$	6.34393	0.325437
$381$	4.95266	0.253732
$382$	21.2772	1.08864
$383$	−21.2802	−1.08737	−0.543685	−	0.839290i	$-0.682971\pi$
$383$	−21.2802	−1.08737	−0.543685	+	0.839290i	$0.682971\pi$
$384$	−0.398922	−0.0203574
$385$	1.69557	0.0864143
$386$	−32.3479	−1.64647
$387$	18.4723	0.938998
$388$	25.6869	1.30405
$389$	21.7626	1.10341	0.551703	−	0.834041i	$-0.313978\pi$
$389$	21.7626	1.10341	0.551703	+	0.834041i	$0.313978\pi$
$390$	4.69705	0.237844
$391$	6.99963	0.353987
$392$	0.00697666	0.000352375 0
$393$	9.70667	0.489637
$394$	20.1993	1.01763
$395$	4.80024	0.241526
$396$	−5.25768	−0.264208
$397$	8.75517	0.439409	0.219705	−	0.975566i	$-0.429491\pi$
$397$	8.75517	0.439409	0.219705	+	0.975566i	$0.429491\pi$
$398$	−27.1964	−1.36323
$399$	7.54986	0.377966
$400$	18.7794	0.938969
$401$	4.87154	0.243273	0.121636	−	0.992575i	$-0.461186\pi$
$401$	4.87154	0.243273	0.121636	+	0.992575i	$0.461186\pi$
$402$	−10.7043	−0.533880
$403$	−62.2593	−3.10136
$404$	27.2080	1.35365
$405$	4.01557	0.199535
$406$	35.0051	1.73728
$407$	−3.79796	−0.188258
$408$	−0.0845657	−0.00418663
$409$	5.47982	0.270960	0.135480	−	0.990780i	$-0.456742\pi$
$409$	5.47982	0.270960	0.135480	+	0.990780i	$0.456742\pi$
$410$	3.05004	0.150631
$411$	−2.02669	−0.0999694
$412$	−7.17863	−0.353666
$413$	−32.5485	−1.60161
$414$	−22.0805	−1.08520
$415$	−2.61908	−0.128566
$416$	−52.8649	−2.59191
$417$	−11.5159	−0.563936
$418$	−10.1256	−0.495261
$419$	−14.7224	−0.719235	−0.359618	−	0.933100i	$-0.617093\pi$
$419$	−14.7224	−0.719235	−0.359618	+	0.933100i	$0.617093\pi$
$420$	1.84756	0.0901519
$421$	1.10731	0.0539671	0.0269836	−	0.999636i	$-0.491410\pi$
$421$	1.10731	0.0539671	0.0269836	+	0.999636i	$0.491410\pi$
$422$	25.6662	1.24941
$423$	−18.6510	−0.906841
$424$	0.305454	0.0148342
$425$	7.78862	0.377803
$426$	−5.72836	−0.277540
$427$	−13.9665	−0.675888
$428$	30.6955	1.48373
$429$	−3.70587	−0.178921
$430$	8.70579	0.419830
$431$	23.0111	1.10841	0.554203	−	0.832381i	$-0.313023\pi$
$431$	23.0111	1.10841	0.554203	+	0.832381i	$0.313023\pi$
$432$	12.9630	0.623684
$433$	11.0756	0.532260	0.266130	−	0.963937i	$-0.414255\pi$
$433$	11.0756	0.532260	0.266130	+	0.963937i	$0.414255\pi$
$434$	−49.5425	−2.37812
$435$	−2.35019	−0.112683
$436$	6.36529	0.304842
$437$	−21.0202	−1.00553
$438$	−17.5855	−0.840269
$439$	32.4582	1.54914	0.774572	−	0.632485i	$-0.217965\pi$
$439$	32.4582	1.54914	0.774572	+	0.632485i	$0.217965\pi$
$440$	0.0570339	0.00271899
$441$	−0.209664	−0.00998399
$442$	−22.4189	−1.06636
$443$	−40.2683	−1.91320	−0.956601	−	0.291400i	$-0.905879\pi$
$443$	−40.2683	−1.91320	−0.956601	+	0.291400i	$0.905879\pi$
$444$	−4.13841	−0.196400
$445$	9.61719	0.455898
$446$	−28.7679	−1.36220
$447$	0.703519	0.0332753
$448$	−20.3153	−0.959807
$449$	−26.7364	−1.26177	−0.630885	−	0.775877i	$-0.717308\pi$
$449$	−26.7364	−1.26177	−0.630885	+	0.775877i	$0.717308\pi$
$450$	−24.5694	−1.15821
$451$	−2.40641	−0.113314
$452$	23.1214	1.08754
$453$	8.76055	0.411607
$454$	22.7557	1.06798
$455$	−11.2738	−0.528523
$456$	0.253955	0.0118925
$457$	−18.9210	−0.885086	−0.442543	−	0.896747i	$-0.645924\pi$
$457$	−18.9210	−0.885086	−0.442543	+	0.896747i	$0.645924\pi$
$458$	31.1772	1.45681
$459$	5.37633	0.250945
$460$	−5.14396	−0.239838
$461$	−30.5521	−1.42295	−0.711476	−	0.702710i	$-0.751973\pi$
$461$	−30.5521	−1.42295	−0.711476	+	0.702710i	$0.751973\pi$
$462$	−2.94892	−0.137196
$463$	9.35031	0.434546	0.217273	−	0.976111i	$-0.430284\pi$
$463$	9.35031	0.434546	0.217273	+	0.976111i	$0.430284\pi$
$464$	27.0466	1.25561
$465$	3.32620	0.154249
$466$	−43.6286	−2.02106
$467$	9.13970	0.422935	0.211467	−	0.977385i	$-0.432176\pi$
$467$	9.13970	0.422935	0.211467	+	0.977385i	$0.432176\pi$
$468$	34.9581	1.61594
$469$	25.6922	1.18636
$470$	−8.79002	−0.405453
$471$	13.7144	0.631926
$472$	−1.09483	−0.0503938
$473$	−6.86867	−0.315822
$474$	−8.34854	−0.383461
$475$	−23.3896	−1.07319
$476$	−8.81837	−0.404189
$477$	−9.17956	−0.420303
$478$	17.4437	0.797854
$479$	5.97185	0.272861	0.136430	−	0.990650i	$-0.456437\pi$
$479$	5.97185	0.272861	0.136430	+	0.990650i	$0.456437\pi$
$480$	2.82431	0.128911
$481$	25.2525	1.15141
$482$	−18.1213	−0.825400
$483$	−6.12179	−0.278551
$484$	1.95500	0.0888637
$485$	8.37386	0.380238
$486$	−25.9026	−1.17497
$487$	12.4993	0.566398	0.283199	−	0.959061i	$-0.408604\pi$
$487$	12.4993	0.566398	0.283199	+	0.959061i	$0.408604\pi$
$488$	−0.469792	−0.0212665
$489$	−0.279144	−0.0126233
$490$	−0.0988125	−0.00446389
$491$	−16.7488	−0.755864	−0.377932	−	0.925833i	$-0.623365\pi$
$491$	−16.7488	−0.755864	−0.377932	+	0.925833i	$0.623365\pi$
$492$	−2.62212	−0.118215
$493$	11.2174	0.505205
$494$	67.3249	3.02909
$495$	−1.71399	−0.0770383
$496$	−38.2788	−1.71877
$497$	13.7491	0.616732
$498$	4.55508	0.204118
$499$	22.7869	1.02008	0.510041	−	0.860150i	$-0.329630\pi$
$499$	22.7869	1.02008	0.510041	+	0.860150i	$0.329630\pi$
$500$	−11.9536	−0.534583
$501$	−1.20523	−0.0538458
$502$	5.69575	0.254214
$503$	7.82051	0.348699	0.174350	−	0.984684i	$-0.444218\pi$
$503$	7.82051	0.348699	0.174350	+	0.984684i	$0.444218\pi$
$504$	−0.640284	−0.0285205
$505$	8.86976	0.394699
$506$	8.21035	0.364995
$507$	17.3945	0.772515
$508$	17.3720	0.770757
$509$	−42.4643	−1.88220	−0.941098	−	0.338133i	$-0.890205\pi$
$509$	−42.4643	−1.88220	−0.941098	+	0.338133i	$0.890205\pi$
$510$	1.19773	0.0530363
$511$	42.2085	1.86719
$512$	−31.7712	−1.40410
$513$	−16.1454	−0.712835
$514$	55.8466	2.46329
$515$	−2.34022	−0.103122
$516$	−7.48438	−0.329482
$517$	6.93512	0.305006
$518$	20.0945	0.882903
$519$	11.8482	0.520078
$520$	−0.379216	−0.0166297
$521$	−24.5625	−1.07610	−0.538051	−	0.842912i	$-0.680839\pi$
$521$	−24.5625	−1.07610	−0.538051	+	0.842912i	$0.680839\pi$
$522$	−35.3855	−1.54878
$523$	34.9849	1.52978	0.764892	−	0.644158i	$-0.222792\pi$
$523$	34.9849	1.52978	0.764892	+	0.644158i	$0.222792\pi$
$524$	34.0472	1.48736
$525$	−6.81183	−0.297293
$526$	55.0660	2.40099
$527$	−15.8759	−0.691564
$528$	−2.27847	−0.0991579
$529$	−5.95579	−0.258947
$530$	−4.32624	−0.187920
$531$	32.9021	1.42783
$532$	26.4820	1.14814
$533$	16.0001	0.693043
$534$	−16.7261	−0.723810
$535$	10.0067	0.432627
$536$	0.864209	0.0373281
$537$	−12.0718	−0.520938
$538$	−3.24502	−0.139903
$539$	0.0779608	0.00335801
$540$	−3.95101	−0.170024
$541$	21.7524	0.935210	0.467605	−	0.883937i	$-0.345117\pi$
$541$	21.7524	0.935210	0.467605	+	0.883937i	$0.345117\pi$
$542$	−30.1844	−1.29653
$543$	−11.4565	−0.491647
$544$	−13.4803	−0.577964
$545$	2.07507	0.0888863
$546$	19.6073	0.839114
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−7.10884	−0.303675
$549$	14.1183	0.602553
$550$	9.13580	0.389552
$551$	−33.6863	−1.43508
$552$	−0.205919	−0.00876448
$553$	20.0380	0.852104
$554$	4.43231	0.188311
$555$	−1.34911	−0.0572667
$556$	−40.3933	−1.71306
$557$	18.2444	0.773039	0.386519	−	0.922281i	$-0.373677\pi$
$557$	18.2444	0.773039	0.386519	+	0.922281i	$0.373677\pi$
$558$	50.0808	2.12009
$559$	45.6695	1.93161
$560$	−6.93145	−0.292907
$561$	−0.944981	−0.0398971
$562$	−64.5977	−2.72489
$563$	−8.94494	−0.376984	−0.188492	−	0.982075i	$-0.560360\pi$
$563$	−8.94494	−0.376984	−0.188492	+	0.982075i	$0.560360\pi$
$564$	7.55679	0.318198
$565$	7.53753	0.317106
$566$	12.7255	0.534891
$567$	16.7625	0.703960
$568$	0.462479	0.0194052
$569$	−12.5649	−0.526748	−0.263374	−	0.964694i	$-0.584835\pi$
$569$	−12.5649	−0.526748	−0.263374	+	0.964694i	$0.584835\pi$
$570$	−3.59683	−0.150655
$571$	26.8084	1.12190	0.560948	−	0.827851i	$-0.310437\pi$
$571$	26.8084	1.12190	0.560948	+	0.827851i	$0.310437\pi$
$572$	−12.9987	−0.543504
$573$	−5.96317	−0.249115
$574$	12.7320	0.531424
$575$	18.9654	0.790912
$576$	20.5360	0.855667
$577$	−7.61992	−0.317221	−0.158611	−	0.987341i	$-0.550701\pi$
$577$	−7.61992	−0.317221	−0.158611	+	0.987341i	$0.550701\pi$
$578$	28.0915	1.16845
$579$	9.06587	0.376765
$580$	−8.24354	−0.342294
$581$	−10.9330	−0.453579
$582$	−14.5638	−0.603687
$583$	3.41330	0.141365
$584$	1.41977	0.0587504
$585$	11.3963	0.471178
$586$	28.6214	1.18234
$587$	−8.86801	−0.366022	−0.183011	−	0.983111i	$-0.558584\pi$
$587$	−8.86801	−0.366022	−0.183011	+	0.983111i	$0.558584\pi$
$588$	0.0849493	0.00350325
$589$	47.6760	1.96445
$590$	15.5064	0.638390
$591$	−5.66109	−0.232866
$592$	15.5260	0.638113
$593$	31.3248	1.28635	0.643177	−	0.765717i	$-0.277616\pi$
$593$	31.3248	1.28635	0.643177	+	0.765717i	$0.277616\pi$
$594$	6.30626	0.258749
$595$	−2.87477	−0.117854
$596$	2.46767	0.101080
$597$	7.62211	0.311952
$598$	−54.5903	−2.23236
$599$	−23.3767	−0.955146	−0.477573	−	0.878592i	$-0.658483\pi$
$599$	−23.3767	−0.955146	−0.477573	+	0.878592i	$0.658483\pi$
$600$	−0.229129	−0.00935417
$601$	35.4599	1.44644	0.723219	−	0.690619i	$-0.242662\pi$
$601$	35.4599	1.44644	0.723219	+	0.690619i	$0.242662\pi$
$602$	36.3413	1.48116
$603$	−25.9714	−1.05764
$604$	30.7286	1.25033
$605$	0.637327	0.0259110
$606$	−15.4262	−0.626647
$607$	2.98068	0.120982	0.0604911	−	0.998169i	$-0.480733\pi$
$607$	2.98068	0.120982	0.0604911	+	0.998169i	$0.480733\pi$
$608$	40.4820	1.64176
$609$	−9.81058	−0.397545
$610$	6.65380	0.269405
$611$	−46.1114	−1.86547
$612$	8.91418	0.360334
$613$	16.7442	0.676294	0.338147	−	0.941093i	$-0.390200\pi$
$613$	16.7442	0.676294	0.338147	+	0.941093i	$0.390200\pi$
$614$	−4.57819	−0.184761
$615$	−0.854807	−0.0344692
$616$	0.238081	0.00959257
$617$	−20.6641	−0.831905	−0.415953	−	0.909386i	$-0.636552\pi$
$617$	−20.6641	−0.831905	−0.415953	+	0.909386i	$0.636552\pi$
$618$	4.07009	0.163723
$619$	−31.0978	−1.24993	−0.624963	−	0.780654i	$-0.714886\pi$
$619$	−31.0978	−1.24993	−0.624963	+	0.780654i	$0.714886\pi$
$620$	11.6670	0.468559
$621$	13.0914	0.525341
$622$	−38.9729	−1.56267
$623$	40.1458	1.60841
$624$	15.1495	0.606465
$625$	19.0722	0.762888
$626$	−1.96908	−0.0787004
$627$	2.83782	0.113332
$628$	48.1047	1.91959
$629$	6.43928	0.256751
$630$	9.06853	0.361299
$631$	7.63376	0.303895	0.151948	−	0.988389i	$-0.451446\pi$
$631$	7.63376	0.303895	0.151948	+	0.988389i	$0.451446\pi$
$632$	0.674019	0.0268111
$633$	−7.19325	−0.285906
$634$	50.8726	2.02041
$635$	5.66323	0.224739
$636$	3.71927	0.147479
$637$	−0.518358	−0.0205381
$638$	13.1576	0.520916
$639$	−13.8985	−0.549816
$640$	−0.456156	−0.0180312
$641$	−35.5184	−1.40289	−0.701447	−	0.712722i	$-0.747462\pi$
$641$	−35.5184	−1.40289	−0.701447	+	0.712722i	$0.747462\pi$
$642$	−17.4035	−0.686863
$643$	−7.51878	−0.296512	−0.148256	−	0.988949i	$-0.547366\pi$
$643$	−7.51878	−0.296512	−0.148256	+	0.988949i	$0.547366\pi$
$644$	−21.4728	−0.846149
$645$	−2.43989	−0.0960707
$646$	17.1676	0.675449
$647$	27.3499	1.07523	0.537617	−	0.843189i	$-0.319325\pi$
$647$	27.3499	1.07523	0.537617	+	0.843189i	$0.319325\pi$
$648$	0.563841	0.0221498
$649$	−12.2342	−0.480236
$650$	−60.7436	−2.38256
$651$	13.8848	0.544190
$652$	−0.979129	−0.0383456
$653$	−17.1987	−0.673038	−0.336519	−	0.941677i	$-0.609250\pi$
$653$	−17.1987	−0.673038	−0.336519	+	0.941677i	$0.609250\pi$
$654$	−3.60895	−0.141121
$655$	11.0993	0.433686
$656$	9.83735	0.384084
$657$	−42.6671	−1.66460
$658$	−36.6929	−1.43044
$659$	−10.6724	−0.415737	−0.207869	−	0.978157i	$-0.566653\pi$
$659$	−10.6724	−0.415737	−0.207869	+	0.978157i	$0.566653\pi$
$660$	0.694457	0.0270317
$661$	−43.3488	−1.68607	−0.843036	−	0.537857i	$-0.819234\pi$
$661$	−43.3488	−1.68607	−0.843036	+	0.537857i	$0.819234\pi$
$662$	−56.0091	−2.17686
$663$	6.28314	0.244017
$664$	−0.367755	−0.0142717
$665$	8.63307	0.334776
$666$	−20.3129	−0.787107
$667$	27.3145	1.05762
$668$	−4.22748	−0.163566
$669$	8.06254	0.311716
$670$	−12.2400	−0.472874
$671$	−5.24970	−0.202662
$672$	11.7897	0.454798
$673$	26.8881	1.03646	0.518230	−	0.855241i	$-0.326591\pi$
$673$	26.8881	1.03646	0.518230	+	0.855241i	$0.326591\pi$
$674$	−4.34851	−0.167499
$675$	14.5671	0.560687
$676$	61.0130	2.34665
$677$	15.6773	0.602527	0.301263	−	0.953541i	$-0.402592\pi$
$677$	15.6773	0.602527	0.301263	+	0.953541i	$0.402592\pi$
$678$	−13.1092	−0.503456
$679$	34.9557	1.34148
$680$	−0.0966986	−0.00370822
$681$	−6.37753	−0.244387
$682$	−18.6219	−0.713069
$683$	−21.5979	−0.826422	−0.413211	−	0.910635i	$-0.635593\pi$
$683$	−21.5979	−0.826422	−0.413211	+	0.910635i	$0.635593\pi$
$684$	−26.7697	−1.02356
$685$	−2.31747	−0.0885459
$686$	36.6236	1.39830
$687$	−8.73775	−0.333366
$688$	28.0789	1.07050
$689$	−22.6949	−0.864607
$690$	2.91649	0.111029
$691$	12.4230	0.472593	0.236296	−	0.971681i	$-0.424066\pi$
$691$	12.4230	0.472593	0.236296	+	0.971681i	$0.424066\pi$
$692$	41.5588	1.57983
$693$	−7.15486	−0.271791
$694$	−33.2941	−1.26383
$695$	−13.1681	−0.499496
$696$	−0.329998	−0.0125086
$697$	4.07997	0.154540
$698$	14.4042	0.545208
$699$	12.2274	0.462483
$700$	−23.8932	−0.903079
$701$	−2.69590	−0.101823	−0.0509113	−	0.998703i	$-0.516213\pi$
$701$	−2.69590	−0.101823	−0.0509113	+	0.998703i	$0.516213\pi$
$702$	−41.9301	−1.58255
$703$	−19.3375	−0.729326
$704$	−7.63605	−0.287795
$705$	2.46350	0.0927808
$706$	−10.0100	−0.376730
$707$	37.0258	1.39250
$708$	−13.3309	−0.501007
$709$	−34.7229	−1.30405	−0.652024	−	0.758199i	$-0.726080\pi$
$709$	−34.7229	−1.30405	−0.652024	+	0.758199i	$0.726080\pi$
$710$	−6.55022	−0.245825
$711$	−20.2558	−0.759650
$712$	1.35038	0.0506078
$713$	−38.6580	−1.44775
$714$	4.99977	0.187112
$715$	−4.23756	−0.158476
$716$	−42.3433	−1.58244
$717$	−4.88878	−0.182575
$718$	−8.36966	−0.312353
$719$	16.5289	0.616425	0.308212	−	0.951318i	$-0.400269\pi$
$719$	16.5289	0.616425	0.308212	+	0.951318i	$0.400269\pi$
$720$	7.00676	0.261127
$721$	−9.76896	−0.363815
$722$	−13.7694	−0.512443
$723$	5.07868	0.188878
$724$	−40.1850	−1.49346
$725$	30.3933	1.12878
$726$	−1.10843	−0.0411378
$727$	−10.0713	−0.373524	−0.186762	−	0.982405i	$-0.559799\pi$
$727$	−10.0713	−0.373524	−0.186762	+	0.982405i	$0.559799\pi$
$728$	−1.58299	−0.0586696
$729$	−11.6424	−0.431202
$730$	−20.1086	−0.744252
$731$	11.6455	0.430726
$732$	−5.72029	−0.211428
$733$	12.3008	0.454339	0.227169	−	0.973855i	$-0.427053\pi$
$733$	12.3008	0.454339	0.227169	+	0.973855i	$0.427053\pi$
$734$	13.5722	0.500958
$735$	0.0276933	0.00102148
$736$	−32.8248	−1.20994
$737$	9.65711	0.355724
$738$	−12.8704	−0.473764
$739$	−10.7678	−0.396101	−0.198050	−	0.980192i	$-0.563461\pi$
$739$	−10.7678	−0.396101	−0.198050	+	0.980192i	$0.563461\pi$
$740$	−4.73216	−0.173958
$741$	−18.8686	−0.693154
$742$	−18.0594	−0.662980
$743$	28.2405	1.03604	0.518021	−	0.855368i	$-0.326669\pi$
$743$	28.2405	1.03604	0.518021	+	0.855368i	$0.326669\pi$
$744$	0.467044	0.0171227
$745$	0.804455	0.0294729
$746$	−14.7929	−0.541607
$747$	11.0518	0.404365
$748$	−3.31462	−0.121195
$749$	41.7717	1.52631
$750$	6.77740	0.247476
$751$	9.04171	0.329937	0.164968	−	0.986299i	$-0.447248\pi$
$751$	9.04171	0.329937	0.164968	+	0.986299i	$0.447248\pi$
$752$	−28.3506	−1.03384
$753$	−1.59630	−0.0581723
$754$	−87.4845	−3.18600
$755$	10.0175	0.364573
$756$	−16.4930	−0.599845
$757$	17.2704	0.627704	0.313852	−	0.949472i	$-0.398380\pi$
$757$	17.2704	0.627704	0.313852	+	0.949472i	$0.398380\pi$
$758$	−36.2059	−1.31506
$759$	−2.30104	−0.0835225
$760$	0.290390	0.0105336
$761$	−50.8255	−1.84242	−0.921211	−	0.389064i	$-0.872798\pi$
$761$	−50.8255	−1.84242	−0.921211	+	0.389064i	$0.872798\pi$
$762$	−9.84945	−0.356808
$763$	8.66214	0.313590
$764$	−20.9164	−0.756730
$765$	2.90600	0.105067
$766$	42.3204	1.52910
$767$	81.3449	2.93720
$768$	9.30541	0.335780
$769$	8.10085	0.292124	0.146062	−	0.989275i	$-0.453340\pi$
$769$	8.10085	0.292124	0.146062	+	0.989275i	$0.453340\pi$
$770$	−3.37202	−0.121519
$771$	−15.6516	−0.563680
$772$	31.7995	1.14449
$773$	−40.5190	−1.45737	−0.728683	−	0.684851i	$-0.759867\pi$
$773$	−40.5190	−1.45737	−0.728683	+	0.684851i	$0.759867\pi$
$774$	−36.7361	−1.32045
$775$	−43.0154	−1.54516
$776$	1.17580	0.0422089
$777$	−5.63172	−0.202037
$778$	−43.2796	−1.55165
$779$	−12.2523	−0.438986
$780$	−4.61742	−0.165330
$781$	5.16798	0.184925
$782$	−13.9203	−0.497789
$783$	20.9799	0.749760
$784$	−0.318702	−0.0113822
$785$	15.6821	0.559716
$786$	−19.3038	−0.688545
$787$	3.03680	0.108250	0.0541252	−	0.998534i	$-0.482763\pi$
$787$	3.03680	0.108250	0.0541252	+	0.998534i	$0.482763\pi$
$788$	−19.8569	−0.707371
$789$	−15.4329	−0.549425
$790$	−9.54633	−0.339643
$791$	31.4645	1.11875
$792$	−0.240668	−0.00855177
$793$	34.9050	1.23951
$794$	−17.4116	−0.617913
$795$	1.21248	0.0430021
$796$	26.7354	0.947610
$797$	45.6769	1.61796	0.808980	−	0.587836i	$-0.200020\pi$
$797$	45.6769	1.61796	0.808980	+	0.587836i	$0.200020\pi$
$798$	−15.0146	−0.531509
$799$	−11.7582	−0.415976
$800$	−36.5247	−1.29134
$801$	−40.5820	−1.43389
$802$	−9.68812	−0.342099
$803$	15.8652	0.559871
$804$	10.5228	0.371110
$805$	−7.00011	−0.246721
$806$	123.816	4.36124
$807$	0.909453	0.0320143
$808$	1.24544	0.0438143
$809$	17.9863	0.632366	0.316183	−	0.948698i	$-0.397599\pi$
$809$	17.9863	0.632366	0.316183	+	0.948698i	$0.397599\pi$
$810$	−7.98584	−0.280594
$811$	−2.38202	−0.0836439	−0.0418219	−	0.999125i	$-0.513316\pi$
$811$	−2.38202	−0.0836439	−0.0418219	+	0.999125i	$0.513316\pi$
$812$	−34.4117	−1.20761
$813$	8.45952	0.296688
$814$	7.55308	0.264735
$815$	−0.319194	−0.0111809
$816$	3.86306	0.135234
$817$	−34.9721	−1.22352
$818$	−10.8978	−0.381033
$819$	47.5724	1.66231
$820$	−2.99833	−0.104706
$821$	23.4551	0.818589	0.409295	−	0.912402i	$-0.365775\pi$
$821$	23.4551	0.818589	0.409295	+	0.912402i	$0.365775\pi$
$822$	4.03052	0.140581
$823$	7.37486	0.257072	0.128536	−	0.991705i	$-0.458972\pi$
$823$	7.37486	0.257072	0.128536	+	0.991705i	$0.458972\pi$
$824$	−0.328599	−0.0114473
$825$	−2.56041	−0.0891421
$826$	64.7298	2.25224
$827$	43.8506	1.52483	0.762417	−	0.647086i	$-0.224012\pi$
$827$	43.8506	1.52483	0.762417	+	0.647086i	$0.224012\pi$
$828$	21.7061	0.754341
$829$	20.4586	0.710556	0.355278	−	0.934761i	$-0.384386\pi$
$829$	20.4586	0.710556	0.355278	+	0.934761i	$0.384386\pi$
$830$	5.20862	0.180794
$831$	−1.24220	−0.0430916
$832$	50.7718	1.76020
$833$	−0.132179	−0.00457974
$834$	22.9019	0.793028
$835$	−1.37815	−0.0476928
$836$	9.95396	0.344265
$837$	−29.6927	−1.02633
$838$	29.2787	1.01141
$839$	−7.74964	−0.267547	−0.133774	−	0.991012i	$-0.542709\pi$
$839$	−7.74964	−0.267547	−0.133774	+	0.991012i	$0.542709\pi$
$840$	0.0845714	0.00291799
$841$	14.7733	0.509422
$842$	−2.20213	−0.0758906
$843$	18.1042	0.623542
$844$	−25.2311	−0.868490
$845$	19.8901	0.684240
$846$	37.0915	1.27523
$847$	2.66044	0.0914139
$848$	−13.9535	−0.479165
$849$	−3.56645	−0.122400
$850$	−15.4894	−0.531281
$851$	15.6797	0.537495
$852$	5.63124	0.192923
$853$	37.7481	1.29247	0.646235	−	0.763138i	$-0.276343\pi$
$853$	37.7481	1.29247	0.646235	+	0.763138i	$0.276343\pi$
$854$	27.7755	0.950458
$855$	−8.72686	−0.298452
$856$	1.40507	0.0480245
$857$	35.0874	1.19856	0.599282	−	0.800538i	$-0.295453\pi$
$857$	35.0874	1.19856	0.599282	+	0.800538i	$0.295453\pi$
$858$	7.36993	0.251605
$859$	54.3345	1.85387	0.926935	−	0.375223i	$-0.122434\pi$
$859$	54.3345	1.85387	0.926935	+	0.375223i	$0.122434\pi$
$860$	−8.55819	−0.291832
$861$	−3.56829	−0.121607
$862$	−45.7627	−1.55868
$863$	29.8003	1.01442	0.507208	−	0.861824i	$-0.330678\pi$
$863$	29.8003	1.01442	0.507208	+	0.861824i	$0.330678\pi$
$864$	−25.2123	−0.857739
$865$	13.5481	0.460649
$866$	−22.0263	−0.748483
$867$	−7.87295	−0.267379
$868$	48.7025	1.65307
$869$	7.53184	0.255500
$870$	4.67386	0.158459
$871$	−64.2097	−2.17566
$872$	0.291368	0.00986697
$873$	−35.3355	−1.19592
$874$	41.8033	1.41402
$875$	−16.2670	−0.549925
$876$	17.2874	0.584086
$877$	14.9196	0.503801	0.251900	−	0.967753i	$-0.418944\pi$
$877$	14.9196	0.503801	0.251900	+	0.967753i	$0.418944\pi$
$878$	−64.5502	−2.17846
$879$	−8.02146	−0.270557
$880$	−2.60537	−0.0878271
$881$	16.4129	0.552965	0.276482	−	0.961019i	$-0.410831\pi$
$881$	16.4129	0.552965	0.276482	+	0.961019i	$0.410831\pi$
$882$	0.416962	0.0140399
$883$	−25.2076	−0.848304	−0.424152	−	0.905591i	$-0.639428\pi$
$883$	−25.2076	−0.848304	−0.424152	+	0.905591i	$0.639428\pi$
$884$	22.0388	0.741245
$885$	−4.34585	−0.146084
$886$	80.0822	2.69041
$887$	−2.96786	−0.0996511	−0.0498255	−	0.998758i	$-0.515867\pi$
$887$	−2.96786	−0.0996511	−0.0498255	+	0.998758i	$0.515867\pi$
$888$	−0.189434	−0.00635699
$889$	23.6405	0.792877
$890$	−19.1259	−0.641101
$891$	6.30065	0.211080
$892$	28.2802	0.946892
$893$	35.3104	1.18162
$894$	−1.39910	−0.0467929
$895$	−13.8038	−0.461411
$896$	−1.90417	−0.0636138
$897$	15.2995	0.510837
$898$	53.1712	1.77435
$899$	−61.9519	−2.06621
$900$	24.1528	0.805094
$901$	−5.78711	−0.192797
$902$	4.78568	0.159346
$903$	−10.1850	−0.338937
$904$	1.05837	0.0352009
$905$	−13.1002	−0.435466
$906$	−17.4223	−0.578816
$907$	14.4832	0.480907	0.240454	−	0.970661i	$-0.422704\pi$
$907$	14.4832	0.480907	0.240454	+	0.970661i	$0.422704\pi$
$908$	−22.3699	−0.742370
$909$	−37.4280	−1.24141
$910$	22.4204	0.743229
$911$	−26.9601	−0.893229	−0.446614	−	0.894727i	$-0.647370\pi$
$911$	−26.9601	−0.893229	−0.446614	+	0.894727i	$0.647370\pi$
$912$	−11.6009	−0.384145
$913$	−4.10948	−0.136004
$914$	37.6285	1.24464
$915$	−1.86480	−0.0616485
$916$	−30.6486	−1.01266
$917$	46.3327	1.53004
$918$	−10.6920	−0.352889
$919$	−3.52484	−0.116274	−0.0581369	−	0.998309i	$-0.518516\pi$
$919$	−3.52484	−0.116274	−0.0581369	+	0.998309i	$0.518516\pi$
$920$	−0.235463	−0.00776297
$921$	1.28309	0.0422792
$922$	60.7595	2.00101
$923$	−34.3617	−1.13103
$924$	2.89893	0.0953677
$925$	17.4471	0.573658
$926$	−18.5951	−0.611074
$927$	9.87510	0.324341
$928$	−52.6039	−1.72681
$929$	17.0727	0.560137	0.280068	−	0.959980i	$-0.409643\pi$
$929$	17.0727	0.560137	0.280068	+	0.959980i	$0.409643\pi$
$930$	−6.61488	−0.216911
$931$	0.396940	0.0130092
$932$	42.8890	1.40487
$933$	10.9226	0.357589
$934$	−18.1763	−0.594746
$935$	−1.08056	−0.0353381
$936$	1.60019	0.0523039
$937$	21.3284	0.696768	0.348384	−	0.937352i	$-0.386731\pi$
$937$	21.3284	0.696768	0.348384	+	0.937352i	$0.386731\pi$
$938$	−51.0946	−1.66830
$939$	0.551858	0.0180092
$940$	8.64099	0.281838
$941$	55.3431	1.80413	0.902066	−	0.431598i	$-0.142050\pi$
$941$	55.3431	1.80413	0.902066	+	0.431598i	$0.142050\pi$
$942$	−27.2741	−0.888638
$943$	9.93479	0.323521
$944$	50.0132	1.62779
$945$	−5.37669	−0.174904
$946$	13.6599	0.444120
$947$	9.95905	0.323625	0.161813	−	0.986821i	$-0.448266\pi$
$947$	9.95905	0.323625	0.161813	+	0.986821i	$0.448266\pi$
$948$	8.20700	0.266551
$949$	−105.487	−3.42426
$950$	46.5153	1.50916
$951$	−14.2576	−0.462335
$952$	−0.403657	−0.0130826
$953$	−39.4037	−1.27641	−0.638206	−	0.769866i	$-0.720323\pi$
$953$	−39.4037	−1.27641	−0.638206	+	0.769866i	$0.720323\pi$
$954$	18.2556	0.591046
$955$	−6.81872	−0.220649
$956$	−17.1479	−0.554603
$957$	−3.68757	−0.119202
$958$	−11.8763	−0.383707
$959$	−9.67399	−0.312390
$960$	−2.71248	−0.0875451
$961$	56.6801	1.82839
$962$	−50.2201	−1.61916
$963$	−42.2256	−1.36070
$964$	17.8140	0.573751
$965$	10.3666	0.333712
$966$	12.1745	0.391709
$967$	8.82420	0.283767	0.141884	−	0.989883i	$-0.454684\pi$
$967$	8.82420	0.283767	0.141884	+	0.989883i	$0.454684\pi$
$968$	0.0894893	0.00287630
$969$	−4.81140	−0.154565
$970$	−16.6533	−0.534704
$971$	−8.72600	−0.280031	−0.140015	−	0.990149i	$-0.544715\pi$
$971$	−8.72600	−0.280031	−0.140015	+	0.990149i	$0.544715\pi$
$972$	25.4635	0.816741
$973$	−54.9688	−1.76222
$974$	−24.8576	−0.796490
$975$	17.0241	0.545206
$976$	21.4606	0.686938
$977$	61.5755	1.96998	0.984988	−	0.172624i	$-0.0552246\pi$
$977$	61.5755	1.96998	0.984988	+	0.172624i	$0.0552246\pi$
$978$	0.555140	0.0177514
$979$	15.0899	0.482275
$980$	0.0971372	0.00310293
$981$	−8.75625	−0.279566
$982$	33.3087	1.06292
$983$	16.9934	0.542005	0.271003	−	0.962579i	$-0.412645\pi$
$983$	16.9934	0.542005	0.271003	+	0.962579i	$0.412645\pi$
$984$	−0.120027	−0.00382631
$985$	−6.47330	−0.206256
$986$	−22.3082	−0.710438
$987$	10.2836	0.327330
$988$	−66.1835	−2.10558
$989$	28.3571	0.901702
$990$	3.40865	0.108334
$991$	9.63946	0.306207	0.153104	−	0.988210i	$-0.451073\pi$
$991$	9.63946	0.306207	0.153104	+	0.988210i	$0.451073\pi$
$992$	74.4499	2.36379
$993$	15.6972	0.498135
$994$	−27.3431	−0.867271
$995$	8.71567	0.276305
$996$	−4.47786	−0.141886
$997$	10.5842	0.335206	0.167603	−	0.985855i	$-0.446397\pi$
$997$	10.5842	0.335206	0.167603	+	0.985855i	$0.446397\pi$
$998$	−45.3168	−1.43448
$999$	12.0434	0.381036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.18	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.18	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.98872 q^{2} +0.557360 q^{3} +1.95500 q^{4} +0.637327 q^{5} -1.10843 q^{6} +2.66044 q^{7} +0.0894893 q^{8} -2.68935 q^{9} +O(q^{10})\)	\(q-1.98872 q^{2} +0.557360 q^{3} +1.95500 q^{4} +0.637327 q^{5} -1.10843 q^{6} +2.66044 q^{7} +0.0894893 q^{8} -2.68935 q^{9} -1.26746 q^{10} +1.00000 q^{11} +1.08964 q^{12} -6.64896 q^{13} -5.29087 q^{14} +0.355221 q^{15} -4.08797 q^{16} -1.69546 q^{17} +5.34836 q^{18} +5.09154 q^{19} +1.24597 q^{20} +1.48283 q^{21} -1.98872 q^{22} -4.12846 q^{23} +0.0498778 q^{24} -4.59381 q^{25} +13.2229 q^{26} -3.17102 q^{27} +5.20117 q^{28} -6.61614 q^{29} -0.706434 q^{30} +9.36377 q^{31} +7.95085 q^{32} +0.557360 q^{33} +3.37179 q^{34} +1.69557 q^{35} -5.25768 q^{36} -3.79796 q^{37} -10.1256 q^{38} -3.70587 q^{39} +0.0570339 q^{40} -2.40641 q^{41} -2.94892 q^{42} -6.86867 q^{43} +1.95500 q^{44} -1.71399 q^{45} +8.21035 q^{46} +6.93512 q^{47} -2.27847 q^{48} +0.0779608 q^{49} +9.13580 q^{50} -0.944981 q^{51} -12.9987 q^{52} +3.41330 q^{53} +6.30626 q^{54} +0.637327 q^{55} +0.238081 q^{56} +2.83782 q^{57} +13.1576 q^{58} -12.2342 q^{59} +0.694457 q^{60} -5.24970 q^{61} -18.6219 q^{62} -7.15486 q^{63} -7.63605 q^{64} -4.23756 q^{65} -1.10843 q^{66} +9.65711 q^{67} -3.31462 q^{68} -2.30104 q^{69} -3.37202 q^{70} +5.16798 q^{71} -0.240668 q^{72} +15.8652 q^{73} +7.55308 q^{74} -2.56041 q^{75} +9.95396 q^{76} +2.66044 q^{77} +7.36993 q^{78} +7.53184 q^{79} -2.60537 q^{80} +6.30065 q^{81} +4.78568 q^{82} -4.10948 q^{83} +2.89893 q^{84} -1.08056 q^{85} +13.6599 q^{86} -3.68757 q^{87} +0.0894893 q^{88} +15.0899 q^{89} +3.40865 q^{90} -17.6892 q^{91} -8.07115 q^{92} +5.21899 q^{93} -13.7920 q^{94} +3.24497 q^{95} +4.43149 q^{96} +13.1390 q^{97} -0.155042 q^{98} -2.68935 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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