LMFDB - Embedded newform 6023.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30301 q^{2} -0.172789 q^{3} +3.30385 q^{4} -0.809544 q^{5} +0.397934 q^{6} +0.778568 q^{7} -3.00278 q^{8} -2.97014 q^{9} +O(q^{10})$	\(q-2.30301 q^{2} -0.172789 q^{3} +3.30385 q^{4} -0.809544 q^{5} +0.397934 q^{6} +0.778568 q^{7} -3.00278 q^{8} -2.97014 q^{9} +1.86439 q^{10} -2.21703 q^{11} -0.570868 q^{12} -2.37373 q^{13} -1.79305 q^{14} +0.139880 q^{15} +0.307729 q^{16} +6.20859 q^{17} +6.84027 q^{18} +1.00000 q^{19} -2.67461 q^{20} -0.134528 q^{21} +5.10584 q^{22} -5.76630 q^{23} +0.518847 q^{24} -4.34464 q^{25} +5.46673 q^{26} +1.03157 q^{27} +2.57227 q^{28} +4.78038 q^{29} -0.322145 q^{30} -2.30252 q^{31} +5.29686 q^{32} +0.383078 q^{33} -14.2984 q^{34} -0.630285 q^{35} -9.81291 q^{36} +4.83358 q^{37} -2.30301 q^{38} +0.410155 q^{39} +2.43088 q^{40} +3.52523 q^{41} +0.309819 q^{42} +5.65688 q^{43} -7.32473 q^{44} +2.40446 q^{45} +13.2798 q^{46} +5.68982 q^{47} -0.0531721 q^{48} -6.39383 q^{49} +10.0057 q^{50} -1.07277 q^{51} -7.84246 q^{52} -1.90176 q^{53} -2.37572 q^{54} +1.79478 q^{55} -2.33787 q^{56} -0.172789 q^{57} -11.0093 q^{58} -7.22746 q^{59} +0.462143 q^{60} +0.737066 q^{61} +5.30272 q^{62} -2.31246 q^{63} -12.8142 q^{64} +1.92164 q^{65} -0.882231 q^{66} +14.6490 q^{67} +20.5122 q^{68} +0.996352 q^{69} +1.45155 q^{70} +12.0910 q^{71} +8.91869 q^{72} +5.37051 q^{73} -11.1318 q^{74} +0.750705 q^{75} +3.30385 q^{76} -1.72611 q^{77} -0.944590 q^{78} +2.39587 q^{79} -0.249120 q^{80} +8.73219 q^{81} -8.11863 q^{82} -6.06346 q^{83} -0.444460 q^{84} -5.02612 q^{85} -13.0278 q^{86} -0.825996 q^{87} +6.65725 q^{88} -9.65826 q^{89} -5.53750 q^{90} -1.84811 q^{91} -19.0510 q^{92} +0.397849 q^{93} -13.1037 q^{94} -0.809544 q^{95} -0.915238 q^{96} +2.54246 q^{97} +14.7251 q^{98} +6.58489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.30301	−1.62847	−0.814237	−	0.580533i	$-0.802844\pi$
$2$	−2.30301	−1.62847	−0.814237	+	0.580533i	$0.802844\pi$
$3$	−0.172789	−0.0997596	−0.0498798	−	0.998755i	$-0.515884\pi$
$3$	−0.172789	−0.0997596	−0.0498798	+	0.998755i	$0.515884\pi$
$4$	3.30385	1.65193
$5$	−0.809544	−0.362039	−0.181019	−	0.983480i	$-0.557940\pi$
$5$	−0.809544	−0.362039	−0.181019	+	0.983480i	$0.557940\pi$
$6$	0.397934	0.162456
$7$	0.778568	0.294271	0.147135	−	0.989116i	$-0.452995\pi$
$7$	0.778568	0.294271	0.147135	+	0.989116i	$0.452995\pi$
$8$	−3.00278	−1.06164
$9$	−2.97014	−0.990048
$10$	1.86439	0.589571
$11$	−2.21703	−0.668459	−0.334230	−	0.942492i	$-0.608476\pi$
$11$	−2.21703	−0.668459	−0.334230	+	0.942492i	$0.608476\pi$
$12$	−0.570868	−0.164795
$13$	−2.37373	−0.658355	−0.329178	−	0.944268i	$-0.606771\pi$
$13$	−2.37373	−0.658355	−0.329178	+	0.944268i	$0.606771\pi$
$14$	−1.79305	−0.479212
$15$	0.139880	0.0361169
$16$	0.307729	0.0769323
$17$	6.20859	1.50580	0.752902	−	0.658133i	$-0.228653\pi$
$17$	6.20859	1.50580	0.752902	+	0.658133i	$0.228653\pi$
$18$	6.84027	1.61227
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.67461	−0.598061
$21$	−0.134528	−0.0293564
$22$	5.10584	1.08857
$23$	−5.76630	−1.20236	−0.601178	−	0.799115i	$-0.705302\pi$
$23$	−5.76630	−1.20236	−0.601178	+	0.799115i	$0.705302\pi$
$24$	0.518847	0.105909
$25$	−4.34464	−0.868928
$26$	5.46673	1.07211
$27$	1.03157	0.198526
$28$	2.57227	0.486114
$29$	4.78038	0.887694	0.443847	−	0.896103i	$-0.353613\pi$
$29$	4.78038	0.887694	0.443847	+	0.896103i	$0.353613\pi$
$30$	−0.322145	−0.0588154
$31$	−2.30252	−0.413544	−0.206772	−	0.978389i	$-0.566296\pi$
$31$	−2.30252	−0.413544	−0.206772	+	0.978389i	$0.566296\pi$
$32$	5.29686	0.936361
$33$	0.383078	0.0666852
$34$	−14.2984	−2.45216
$35$	−0.630285	−0.106538
$36$	−9.81291	−1.63549
$37$	4.83358	0.794636	0.397318	−	0.917681i	$-0.369941\pi$
$37$	4.83358	0.794636	0.397318	+	0.917681i	$0.369941\pi$
$38$	−2.30301	−0.373597
$39$	0.410155	0.0656773
$40$	2.43088	0.384356
$41$	3.52523	0.550548	0.275274	−	0.961366i	$-0.411231\pi$
$41$	3.52523	0.550548	0.275274	+	0.961366i	$0.411231\pi$
$42$	0.309819	0.0478061
$43$	5.65688	0.862666	0.431333	−	0.902193i	$-0.358043\pi$
$43$	5.65688	0.862666	0.431333	+	0.902193i	$0.358043\pi$
$44$	−7.32473	−1.10424
$45$	2.40446	0.358436
$46$	13.2798	1.95801
$47$	5.68982	0.829945	0.414973	−	0.909834i	$-0.363791\pi$
$47$	5.68982	0.829945	0.414973	+	0.909834i	$0.363791\pi$
$48$	−0.0531721	−0.00767473
$49$	−6.39383	−0.913405
$50$	10.0057	1.41503
$51$	−1.07277	−0.150218
$52$	−7.84246	−1.08755
$53$	−1.90176	−0.261227	−0.130613	−	0.991433i	$-0.541695\pi$
$53$	−1.90176	−0.261227	−0.130613	+	0.991433i	$0.541695\pi$
$54$	−2.37572	−0.323295
$55$	1.79478	0.242008
$56$	−2.33787	−0.312411
$57$	−0.172789	−0.0228864
$58$	−11.0093	−1.44559
$59$	−7.22746	−0.940935	−0.470468	−	0.882417i	$-0.655915\pi$
$59$	−7.22746	−0.940935	−0.470468	+	0.882417i	$0.655915\pi$
$60$	0.462143	0.0596624
$61$	0.737066	0.0943716	0.0471858	−	0.998886i	$-0.484975\pi$
$61$	0.737066	0.0943716	0.0471858	+	0.998886i	$0.484975\pi$
$62$	5.30272	0.673446
$63$	−2.31246	−0.291342
$64$	−12.8142	−1.60177
$65$	1.92164	0.238350
$66$	−0.882231	−0.108595
$67$	14.6490	1.78966	0.894828	−	0.446411i	$-0.147298\pi$
$67$	14.6490	1.78966	0.894828	+	0.446411i	$0.147298\pi$
$68$	20.5122	2.48748
$69$	0.996352	0.119947
$70$	1.45155	0.173494
$71$	12.0910	1.43494	0.717469	−	0.696590i	$-0.245301\pi$
$71$	12.0910	1.43494	0.717469	+	0.696590i	$0.245301\pi$
$72$	8.91869	1.05108
$73$	5.37051	0.628570	0.314285	−	0.949329i	$-0.398235\pi$
$73$	5.37051	0.628570	0.314285	+	0.949329i	$0.398235\pi$
$74$	−11.1318	−1.29404
$75$	0.750705	0.0866839
$76$	3.30385	0.378978
$77$	−1.72611	−0.196708
$78$	−0.944590	−0.106954
$79$	2.39587	0.269556	0.134778	−	0.990876i	$-0.456968\pi$
$79$	2.39587	0.269556	0.134778	+	0.990876i	$0.456968\pi$
$80$	−0.249120	−0.0278525
$81$	8.73219	0.970243
$82$	−8.11863	−0.896553
$83$	−6.06346	−0.665551	−0.332775	−	0.943006i	$-0.607985\pi$
$83$	−6.06346	−0.665551	−0.332775	+	0.943006i	$0.607985\pi$
$84$	−0.444460	−0.0484945
$85$	−5.02612	−0.545160
$86$	−13.0278	−1.40483
$87$	−0.825996	−0.0885560
$88$	6.65725	0.709665
$89$	−9.65826	−1.02377	−0.511887	−	0.859053i	$-0.671053\pi$
$89$	−9.65826	−1.02377	−0.511887	+	0.859053i	$0.671053\pi$
$90$	−5.53750	−0.583703
$91$	−1.84811	−0.193735
$92$	−19.0510	−1.98620
$93$	0.397849	0.0412550
$94$	−13.1037	−1.35154
$95$	−0.809544	−0.0830574
$96$	−0.915238	−0.0934110
$97$	2.54246	0.258148	0.129074	−	0.991635i	$-0.458800\pi$
$97$	2.54246	0.258148	0.129074	+	0.991635i	$0.458800\pi$
$98$	14.7251	1.48746
$99$	6.58489	0.661807
$100$	−14.3540	−1.43540
$101$	13.6179	1.35503	0.677516	−	0.735508i	$-0.263056\pi$
$101$	13.6179	1.35503	0.677516	+	0.735508i	$0.263056\pi$
$102$	2.47061	0.244627
$103$	11.3724	1.12056	0.560280	−	0.828303i	$-0.310694\pi$
$103$	11.3724	1.12056	0.560280	+	0.828303i	$0.310694\pi$
$104$	7.12780	0.698938
$105$	0.108906	0.0106281
$106$	4.37977	0.425401
$107$	−18.5859	−1.79677	−0.898384	−	0.439211i	$-0.855258\pi$
$107$	−18.5859	−1.79677	−0.898384	+	0.439211i	$0.855258\pi$
$108$	3.40817	0.327951
$109$	−16.2514	−1.55660	−0.778302	−	0.627890i	$-0.783919\pi$
$109$	−16.2514	−1.55660	−0.778302	+	0.627890i	$0.783919\pi$
$110$	−4.13340	−0.394104
$111$	−0.835188	−0.0792726
$112$	0.239588	0.0226389
$113$	1.89395	0.178168	0.0890840	−	0.996024i	$-0.471606\pi$
$113$	1.89395	0.178168	0.0890840	+	0.996024i	$0.471606\pi$
$114$	0.397934	0.0372699
$115$	4.66807	0.435300
$116$	15.7937	1.46640
$117$	7.05033	0.651803
$118$	16.6449	1.53229
$119$	4.83381	0.443114
$120$	−0.420029	−0.0383432
$121$	−6.08479	−0.553162
$122$	−1.69747	−0.153682
$123$	−0.609120	−0.0549225
$124$	−7.60717	−0.683144
$125$	7.56489	0.676625
$126$	5.32561	0.474443
$127$	−18.7924	−1.66756	−0.833779	−	0.552098i	$-0.813828\pi$
$127$	−18.7924	−1.66756	−0.833779	+	0.552098i	$0.813828\pi$
$128$	18.9174	1.67208
$129$	−0.977445	−0.0860593
$130$	−4.42556	−0.388147
$131$	18.8803	1.64958	0.824791	−	0.565438i	$-0.191293\pi$
$131$	18.8803	1.64958	0.824791	+	0.565438i	$0.191293\pi$
$132$	1.26563	0.110159
$133$	0.778568	0.0675104
$134$	−33.7367	−2.91441
$135$	−0.835104	−0.0718743
$136$	−18.6430	−1.59863
$137$	6.77648	0.578954	0.289477	−	0.957185i	$-0.406519\pi$
$137$	6.77648	0.578954	0.289477	+	0.957185i	$0.406519\pi$
$138$	−2.29461	−0.195330
$139$	−4.08150	−0.346188	−0.173094	−	0.984905i	$-0.555376\pi$
$139$	−4.08150	−0.346188	−0.173094	+	0.984905i	$0.555376\pi$
$140$	−2.08237	−0.175992
$141$	−0.983137	−0.0827950
$142$	−27.8457	−2.33676
$143$	5.26263	0.440084
$144$	−0.913999	−0.0761666
$145$	−3.86993	−0.321380
$146$	−12.3683	−1.02361
$147$	1.10478	0.0911209
$148$	15.9694	1.31268
$149$	−18.0440	−1.47823	−0.739113	−	0.673582i	$-0.764755\pi$
$149$	−18.0440	−1.47823	−0.739113	+	0.673582i	$0.764755\pi$
$150$	−1.72888	−0.141162
$151$	−13.4346	−1.09329	−0.546645	−	0.837365i	$-0.684095\pi$
$151$	−13.4346	−1.09329	−0.546645	+	0.837365i	$0.684095\pi$
$152$	−3.00278	−0.243558
$153$	−18.4404	−1.49082
$154$	3.97524	0.320334
$155$	1.86399	0.149719
$156$	1.35509	0.108494
$157$	−7.22935	−0.576965	−0.288483	−	0.957485i	$-0.593151\pi$
$157$	−7.22935	−0.576965	−0.288483	+	0.957485i	$0.593151\pi$
$158$	−5.51771	−0.438965
$159$	0.328603	0.0260599
$160$	−4.28804	−0.338999
$161$	−4.48946	−0.353819
$162$	−20.1103	−1.58002
$163$	−23.5012	−1.84075	−0.920377	−	0.391031i	$-0.872118\pi$
$163$	−23.5012	−1.84075	−0.920377	+	0.391031i	$0.872118\pi$
$164$	11.6468	0.909465
$165$	−0.310118	−0.0241427
$166$	13.9642	1.08383
$167$	−14.5880	−1.12885	−0.564427	−	0.825483i	$-0.690903\pi$
$167$	−14.5880	−1.12885	−0.564427	+	0.825483i	$0.690903\pi$
$168$	0.403957	0.0311660
$169$	−7.36539	−0.566568
$170$	11.5752	0.887778
$171$	−2.97014	−0.227133
$172$	18.6895	1.42506
$173$	4.74066	0.360425	0.180213	−	0.983628i	$-0.442321\pi$
$173$	4.74066	0.360425	0.180213	+	0.983628i	$0.442321\pi$
$174$	1.90228	0.144211
$175$	−3.38260	−0.255700
$176$	−0.682244	−0.0514261
$177$	1.24882	0.0938674
$178$	22.2431	1.66719
$179$	14.5366	1.08652	0.543260	−	0.839565i	$-0.317190\pi$
$179$	14.5366	1.08652	0.543260	+	0.839565i	$0.317190\pi$
$180$	7.94398	0.592110
$181$	−0.149409	−0.0111055	−0.00555273	−	0.999985i	$-0.501767\pi$
$181$	−0.149409	−0.0111055	−0.00555273	+	0.999985i	$0.501767\pi$
$182$	4.25622	0.315492
$183$	−0.127357	−0.00941448
$184$	17.3149	1.27647
$185$	−3.91299	−0.287689
$186$	−0.916250	−0.0671827
$187$	−13.7646	−1.00657
$188$	18.7983	1.37101
$189$	0.803150	0.0584206
$190$	1.86439	0.135257
$191$	20.0644	1.45181	0.725904	−	0.687796i	$-0.241422\pi$
$191$	20.0644	1.45181	0.725904	+	0.687796i	$0.241422\pi$
$192$	2.21414	0.159792
$193$	10.1723	0.732220	0.366110	−	0.930572i	$-0.380689\pi$
$193$	10.1723	0.732220	0.366110	+	0.930572i	$0.380689\pi$
$194$	−5.85531	−0.420387
$195$	−0.332038	−0.0237777
$196$	−21.1243	−1.50888
$197$	12.0067	0.855444	0.427722	−	0.903910i	$-0.359316\pi$
$197$	12.0067	0.855444	0.427722	+	0.903910i	$0.359316\pi$
$198$	−15.1651	−1.07773
$199$	1.51651	0.107503	0.0537514	−	0.998554i	$-0.482882\pi$
$199$	1.51651	0.107503	0.0537514	+	0.998554i	$0.482882\pi$
$200$	13.0460	0.922491
$201$	−2.53118	−0.178535
$202$	−31.3622	−2.20663
$203$	3.72185	0.261223
$204$	−3.54429	−0.248150
$205$	−2.85383	−0.199320
$206$	−26.1908	−1.82480
$207$	17.1267	1.19039
$208$	−0.730467	−0.0506488
$209$	−2.21703	−0.153355
$210$	−0.250812	−0.0173077
$211$	13.8124	0.950887	0.475443	−	0.879746i	$-0.342288\pi$
$211$	13.8124	0.950887	0.475443	+	0.879746i	$0.342288\pi$
$212$	−6.28313	−0.431527
$213$	−2.08919	−0.143149
$214$	42.8035	2.92599
$215$	−4.57949	−0.312319
$216$	−3.09759	−0.210764
$217$	−1.79266	−0.121694
$218$	37.4272	2.53489
$219$	−0.927963	−0.0627059
$220$	5.92969	0.399780
$221$	−14.7375	−0.991354
$222$	1.92345	0.129093
$223$	7.57198	0.507057	0.253529	−	0.967328i	$-0.418409\pi$
$223$	7.57198	0.507057	0.253529	+	0.967328i	$0.418409\pi$
$224$	4.12396	0.275544
$225$	12.9042	0.860280
$226$	−4.36179	−0.290142
$227$	17.2656	1.14596	0.572978	−	0.819571i	$-0.305788\pi$
$227$	17.2656	1.14596	0.572978	+	0.819571i	$0.305788\pi$
$228$	−0.570868	−0.0378067
$229$	−9.22487	−0.609596	−0.304798	−	0.952417i	$-0.598589\pi$
$229$	−9.22487	−0.609596	−0.304798	+	0.952417i	$0.598589\pi$
$230$	−10.7506	−0.708875
$231$	0.298252	0.0196235
$232$	−14.3544	−0.942414
$233$	0.839263	0.0549820	0.0274910	−	0.999622i	$-0.491248\pi$
$233$	0.839263	0.0549820	0.0274910	+	0.999622i	$0.491248\pi$
$234$	−16.2370	−1.06144
$235$	−4.60616	−0.300473
$236$	−23.8785	−1.55436
$237$	−0.413979	−0.0268909
$238$	−11.1323	−0.721600
$239$	2.03456	0.131605	0.0658023	−	0.997833i	$-0.479039\pi$
$239$	2.03456	0.131605	0.0658023	+	0.997833i	$0.479039\pi$
$240$	0.0430452	0.00277855
$241$	−19.7562	−1.27261	−0.636304	−	0.771438i	$-0.719538\pi$
$241$	−19.7562	−1.27261	−0.636304	+	0.771438i	$0.719538\pi$
$242$	14.0133	0.900810
$243$	−4.60355	−0.295318
$244$	2.43516	0.155895
$245$	5.17609	0.330688
$246$	1.40281	0.0894398
$247$	−2.37373	−0.151037
$248$	6.91395	0.439036
$249$	1.04770	0.0663951
$250$	−17.4220	−1.10187
$251$	4.80840	0.303504	0.151752	−	0.988419i	$-0.451509\pi$
$251$	4.80840	0.303504	0.151752	+	0.988419i	$0.451509\pi$
$252$	−7.64002	−0.481276
$253$	12.7841	0.803726
$254$	43.2791	2.71558
$255$	0.868458	0.0543849
$256$	−17.9387	−1.12117
$257$	0.374448	0.0233574	0.0116787	−	0.999932i	$-0.496282\pi$
$257$	0.374448	0.0233574	0.0116787	+	0.999932i	$0.496282\pi$
$258$	2.25107	0.140145
$259$	3.76327	0.233838
$260$	6.34882	0.393737
$261$	−14.1984	−0.878860
$262$	−43.4816	−2.68630
$263$	−24.1692	−1.49034	−0.745170	−	0.666875i	$-0.767631\pi$
$263$	−24.1692	−1.49034	−0.745170	+	0.666875i	$0.767631\pi$
$264$	−1.15030	−0.0707959
$265$	1.53956	0.0945742
$266$	−1.79305	−0.109939
$267$	1.66884	0.102131
$268$	48.3980	2.95638
$269$	−30.3373	−1.84970	−0.924848	−	0.380338i	$-0.875808\pi$
$269$	−30.3373	−1.84970	−0.924848	+	0.380338i	$0.875808\pi$
$270$	1.92325	0.117045
$271$	−17.8794	−1.08610	−0.543049	−	0.839701i	$-0.682730\pi$
$271$	−17.8794	−1.08610	−0.543049	+	0.839701i	$0.682730\pi$
$272$	1.91056	0.115845
$273$	0.319333	0.0193269
$274$	−15.6063	−0.942811
$275$	9.63219	0.580843
$276$	3.29180	0.198143
$277$	6.94992	0.417580	0.208790	−	0.977960i	$-0.433047\pi$
$277$	6.94992	0.417580	0.208790	+	0.977960i	$0.433047\pi$
$278$	9.39973	0.563758
$279$	6.83880	0.409429
$280$	1.89261	0.113105
$281$	21.0988	1.25865	0.629325	−	0.777142i	$-0.283331\pi$
$281$	21.0988	1.25865	0.629325	+	0.777142i	$0.283331\pi$
$282$	2.26417	0.134830
$283$	−16.7973	−0.998493	−0.499247	−	0.866460i	$-0.666390\pi$
$283$	−16.7973	−0.998493	−0.499247	+	0.866460i	$0.666390\pi$
$284$	39.9469	2.37041
$285$	0.139880	0.00828578
$286$	−12.1199	−0.716664
$287$	2.74463	0.162010
$288$	−15.7324	−0.927042
$289$	21.5466	1.26744
$290$	8.91247	0.523359
$291$	−0.439309	−0.0257527
$292$	17.7434	1.03835
$293$	4.38566	0.256213	0.128106	−	0.991760i	$-0.459110\pi$
$293$	4.38566	0.256213	0.128106	+	0.991760i	$0.459110\pi$
$294$	−2.54432	−0.148388
$295$	5.85095	0.340655
$296$	−14.5142	−0.843619
$297$	−2.28703	−0.132707
$298$	41.5556	2.40725
$299$	13.6877	0.791578
$300$	2.48022	0.143195
$301$	4.40426	0.253858
$302$	30.9399	1.78039
$303$	−2.35302	−0.135178
$304$	0.307729	0.0176495
$305$	−0.596687	−0.0341662
$306$	42.4684	2.42776
$307$	−25.5625	−1.45893	−0.729463	−	0.684020i	$-0.760230\pi$
$307$	−25.5625	−1.45893	−0.729463	+	0.684020i	$0.760230\pi$
$308$	−5.70280	−0.324947
$309$	−1.96503	−0.111787
$310$	−4.29278	−0.243814
$311$	8.22535	0.466417	0.233208	−	0.972427i	$-0.425078\pi$
$311$	8.22535	0.466417	0.233208	+	0.972427i	$0.425078\pi$
$312$	−1.23160	−0.0697258
$313$	16.7137	0.944713	0.472356	−	0.881408i	$-0.343403\pi$
$313$	16.7137	0.944713	0.472356	+	0.881408i	$0.343403\pi$
$314$	16.6493	0.939573
$315$	1.87204	0.105477
$316$	7.91560	0.445287
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−0.756775	−0.0424378
$319$	−10.5982	−0.593387
$320$	10.3736	0.579904
$321$	3.21144	0.179245
$322$	10.3393	0.576184
$323$	6.20859	0.345455
$324$	28.8498	1.60277
$325$	10.3130	0.572063
$326$	54.1234	2.99762
$327$	2.80806	0.155286
$328$	−10.5855	−0.584486
$329$	4.42991	0.244229
$330$	0.714205	0.0393157
$331$	−16.6451	−0.914896	−0.457448	−	0.889236i	$-0.651236\pi$
$331$	−16.6451	−0.914896	−0.457448	+	0.889236i	$0.651236\pi$
$332$	−20.0328	−1.09944
$333$	−14.3564	−0.786727
$334$	33.5963	1.83831
$335$	−11.8590	−0.647925
$336$	−0.0413981	−0.00225845
$337$	−0.416497	−0.0226880	−0.0113440	−	0.999936i	$-0.503611\pi$
$337$	−0.416497	−0.0226880	−0.0113440	+	0.999936i	$0.503611\pi$
$338$	16.9626	0.922641
$339$	−0.327253	−0.0177740
$340$	−16.6056	−0.900563
$341$	5.10474	0.276437
$342$	6.84027	0.369879
$343$	−10.4280	−0.563059
$344$	−16.9864	−0.915844
$345$	−0.806591	−0.0434254
$346$	−10.9178	−0.586943
$347$	11.3700	0.610374	0.305187	−	0.952292i	$-0.401281\pi$
$347$	11.3700	0.610374	0.305187	+	0.952292i	$0.401281\pi$
$348$	−2.72897	−0.146288
$349$	−7.09875	−0.379988	−0.189994	−	0.981785i	$-0.560847\pi$
$349$	−7.09875	−0.379988	−0.189994	+	0.981785i	$0.560847\pi$
$350$	7.79015	0.416401
$351$	−2.44868	−0.130701
$352$	−11.7433	−0.625919
$353$	10.6363	0.566111	0.283055	−	0.959104i	$-0.408652\pi$
$353$	10.6363	0.566111	0.283055	+	0.959104i	$0.408652\pi$
$354$	−2.87605	−0.152861
$355$	−9.78820	−0.519503
$356$	−31.9095	−1.69120
$357$	−0.835227	−0.0442049
$358$	−33.4780	−1.76937
$359$	17.9666	0.948241	0.474121	−	0.880460i	$-0.342766\pi$
$359$	17.9666	0.948241	0.474121	+	0.880460i	$0.342766\pi$
$360$	−7.22007	−0.380531
$361$	1.00000	0.0526316
$362$	0.344090	0.0180850
$363$	1.05138	0.0551833
$364$	−6.10589	−0.320035
$365$	−4.34766	−0.227567
$366$	0.293304	0.0153312
$367$	33.2349	1.73485	0.867425	−	0.497568i	$-0.165774\pi$
$367$	33.2349	1.73485	0.867425	+	0.497568i	$0.165774\pi$
$368$	−1.77446	−0.0925000
$369$	−10.4704	−0.545069
$370$	9.01166	0.468494
$371$	−1.48065	−0.0768714
$372$	1.31443	0.0681502
$373$	−24.1044	−1.24808	−0.624038	−	0.781394i	$-0.714509\pi$
$373$	−24.1044	−1.24808	−0.624038	+	0.781394i	$0.714509\pi$
$374$	31.7000	1.63917
$375$	−1.30713	−0.0674998
$376$	−17.0853	−0.881106
$377$	−11.3473	−0.584418
$378$	−1.84966	−0.0951363
$379$	3.54637	0.182165	0.0910823	−	0.995843i	$-0.470967\pi$
$379$	3.54637	0.182165	0.0910823	+	0.995843i	$0.470967\pi$
$380$	−2.67461	−0.137205
$381$	3.24712	0.166355
$382$	−46.2085	−2.36423
$383$	−21.7660	−1.11219	−0.556096	−	0.831118i	$-0.687701\pi$
$383$	−21.7660	−1.11219	−0.556096	+	0.831118i	$0.687701\pi$
$384$	−3.26872	−0.166806
$385$	1.39736	0.0712160
$386$	−23.4270	−1.19240
$387$	−16.8018	−0.854081
$388$	8.39991	0.426441
$389$	18.5828	0.942184	0.471092	−	0.882084i	$-0.343860\pi$
$389$	18.5828	0.942184	0.471092	+	0.882084i	$0.343860\pi$
$390$	0.764687	0.0387214
$391$	−35.8006	−1.81051
$392$	19.1993	0.969710
$393$	−3.26231	−0.164562
$394$	−27.6516	−1.39307
$395$	−1.93956	−0.0975899
$396$	21.7555	1.09326
$397$	−11.5151	−0.577928	−0.288964	−	0.957340i	$-0.593311\pi$
$397$	−11.5151	−0.577928	−0.288964	+	0.957340i	$0.593311\pi$
$398$	−3.49255	−0.175066
$399$	−0.134528	−0.00673481
$400$	−1.33697	−0.0668486
$401$	4.49865	0.224652	0.112326	−	0.993671i	$-0.464170\pi$
$401$	4.49865	0.224652	0.112326	+	0.993671i	$0.464170\pi$
$402$	5.82932	0.290740
$403$	5.46556	0.272259
$404$	44.9915	2.23841
$405$	−7.06909	−0.351266
$406$	−8.57145	−0.425394
$407$	−10.7162	−0.531181
$408$	3.22131	0.159478
$409$	−30.4754	−1.50691	−0.753457	−	0.657498i	$-0.771615\pi$
$409$	−30.4754	−1.50691	−0.753457	+	0.657498i	$0.771615\pi$
$410$	6.57239	0.324587
$411$	−1.17090	−0.0577562
$412$	37.5729	1.85108
$413$	−5.62707	−0.276890
$414$	−39.4431	−1.93852
$415$	4.90863	0.240955
$416$	−12.5733	−0.616458
$417$	0.705237	0.0345356
$418$	5.10584	0.249735
$419$	23.4691	1.14654	0.573271	−	0.819366i	$-0.305674\pi$
$419$	23.4691	1.14654	0.573271	+	0.819366i	$0.305674\pi$
$420$	0.359810	0.0175569
$421$	−20.4546	−0.996896	−0.498448	−	0.866920i	$-0.666097\pi$
$421$	−20.4546	−0.996896	−0.498448	+	0.866920i	$0.666097\pi$
$422$	−31.8101	−1.54849
$423$	−16.8996	−0.821686
$424$	5.71056	0.277329
$425$	−26.9741	−1.30843
$426$	4.81142	0.233114
$427$	0.573856	0.0277708
$428$	−61.4051	−2.96813
$429$	−0.909324	−0.0439026
$430$	10.5466	0.508603
$431$	39.4720	1.90130	0.950650	−	0.310267i	$-0.100418\pi$
$431$	39.4720	1.90130	0.950650	+	0.310267i	$0.100418\pi$
$432$	0.317445	0.0152731
$433$	−15.7395	−0.756393	−0.378196	−	0.925725i	$-0.623456\pi$
$433$	−15.7395	−0.756393	−0.378196	+	0.925725i	$0.623456\pi$
$434$	4.12852	0.198175
$435$	0.668680	0.0320607
$436$	−53.6923	−2.57139
$437$	−5.76630	−0.275840
$438$	2.13711	0.102115
$439$	−4.34675	−0.207459	−0.103730	−	0.994606i	$-0.533078\pi$
$439$	−4.34675	−0.207459	−0.103730	+	0.994606i	$0.533078\pi$
$440$	−5.38933	−0.256926
$441$	18.9906	0.904314
$442$	33.9407	1.61439
$443$	31.9447	1.51774	0.758870	−	0.651242i	$-0.225752\pi$
$443$	31.9447	1.51774	0.758870	+	0.651242i	$0.225752\pi$
$444$	−2.75934	−0.130952
$445$	7.81879	0.370646
$446$	−17.4383	−0.825730
$447$	3.11781	0.147467
$448$	−9.97670	−0.471355
$449$	2.47155	0.116640	0.0583198	−	0.998298i	$-0.481426\pi$
$449$	2.47155	0.116640	0.0583198	+	0.998298i	$0.481426\pi$
$450$	−29.7185	−1.40094
$451$	−7.81553	−0.368019
$452$	6.25733	0.294320
$453$	2.32134	0.109066
$454$	−39.7627	−1.86616
$455$	1.49613	0.0701396
$456$	0.518847	0.0242972
$457$	−37.2264	−1.74138	−0.870690	−	0.491833i	$-0.836327\pi$
$457$	−37.2264	−1.74138	−0.870690	+	0.491833i	$0.836327\pi$
$458$	21.2449	0.992711
$459$	6.40462	0.298942
$460$	15.4226	0.719083
$461$	−9.21963	−0.429401	−0.214701	−	0.976680i	$-0.568878\pi$
$461$	−9.21963	−0.429401	−0.214701	+	0.976680i	$0.568878\pi$
$462$	−0.686877	−0.0319564
$463$	−15.7439	−0.731681	−0.365840	−	0.930678i	$-0.619218\pi$
$463$	−15.7439	−0.731681	−0.365840	+	0.930678i	$0.619218\pi$
$464$	1.47106	0.0682923
$465$	−0.322076	−0.0149359
$466$	−1.93283	−0.0895367
$467$	−24.0830	−1.11443	−0.557215	−	0.830368i	$-0.688130\pi$
$467$	−24.0830	−1.11443	−0.557215	+	0.830368i	$0.688130\pi$
$468$	23.2932	1.07673
$469$	11.4052	0.526644
$470$	10.6080	0.489312
$471$	1.24915	0.0575578
$472$	21.7025	0.998938
$473$	−12.5415	−0.576657
$474$	0.953398	0.0437910
$475$	−4.34464	−0.199346
$476$	15.9702	0.731992
$477$	5.64850	0.258627
$478$	−4.68561	−0.214315
$479$	0.664923	0.0303811	0.0151905	−	0.999885i	$-0.495165\pi$
$479$	0.664923	0.0303811	0.0151905	+	0.999885i	$0.495165\pi$
$480$	0.740925	0.0338184
$481$	−11.4736	−0.523153
$482$	45.4987	2.07241
$483$	0.775728	0.0352968
$484$	−20.1032	−0.913783
$485$	−2.05823	−0.0934596
$486$	10.6020	0.480917
$487$	−38.9692	−1.76586	−0.882932	−	0.469501i	$-0.844434\pi$
$487$	−38.9692	−1.76586	−0.882932	+	0.469501i	$0.844434\pi$
$488$	−2.21325	−0.100189
$489$	4.06074	0.183633
$490$	−11.9206	−0.538517
$491$	−30.7955	−1.38978	−0.694892	−	0.719115i	$-0.744548\pi$
$491$	−30.7955	−1.38978	−0.694892	+	0.719115i	$0.744548\pi$
$492$	−2.01244	−0.0907279
$493$	29.6794	1.33669
$494$	5.46673	0.245960
$495$	−5.33076	−0.239600
$496$	−0.708551	−0.0318149
$497$	9.41366	0.422261
$498$	−2.41286	−0.108123
$499$	21.5540	0.964890	0.482445	−	0.875926i	$-0.339749\pi$
$499$	21.5540	0.964890	0.482445	+	0.875926i	$0.339749\pi$
$500$	24.9933	1.11773
$501$	2.52065	0.112614
$502$	−11.0738	−0.494248
$503$	39.9805	1.78264	0.891321	−	0.453374i	$-0.149780\pi$
$503$	39.9805	1.78264	0.891321	+	0.453374i	$0.149780\pi$
$504$	6.94380	0.309302
$505$	−11.0243	−0.490574
$506$	−29.4418	−1.30885
$507$	1.27266	0.0565207
$508$	−62.0874	−2.75468
$509$	−11.2161	−0.497144	−0.248572	−	0.968613i	$-0.579961\pi$
$509$	−11.2161	−0.497144	−0.248572	+	0.968613i	$0.579961\pi$
$510$	−2.00007	−0.0885644
$511$	4.18130	0.184970
$512$	3.47808	0.153711
$513$	1.03157	0.0455451
$514$	−0.862358	−0.0380370
$515$	−9.20649	−0.405686
$516$	−3.22933	−0.142164
$517$	−12.6145	−0.554785
$518$	−8.66684	−0.380799
$519$	−0.819132	−0.0359559
$520$	−5.77027	−0.253043
$521$	−1.90416	−0.0834227	−0.0417114	−	0.999130i	$-0.513281\pi$
$521$	−1.90416	−0.0834227	−0.0417114	+	0.999130i	$0.513281\pi$
$522$	32.6991	1.43120
$523$	−25.8152	−1.12882	−0.564410	−	0.825495i	$-0.690896\pi$
$523$	−25.8152	−1.12882	−0.564410	+	0.825495i	$0.690896\pi$
$524$	62.3778	2.72499
$525$	0.584475	0.0255086
$526$	55.6620	2.42698
$527$	−14.2954	−0.622716
$528$	0.117884	0.00513025
$529$	10.2502	0.445662
$530$	−3.54561	−0.154012
$531$	21.4666	0.931571
$532$	2.57227	0.111522
$533$	−8.36795	−0.362456
$534$	−3.84335	−0.166318
$535$	15.0461	0.650500
$536$	−43.9876	−1.89998
$537$	−2.51177	−0.108391
$538$	69.8670	3.01218
$539$	14.1753	0.610574
$540$	−2.75906	−0.118731
$541$	−27.8145	−1.19584	−0.597918	−	0.801557i	$-0.704005\pi$
$541$	−27.8145	−1.19584	−0.597918	+	0.801557i	$0.704005\pi$
$542$	41.1765	1.76868
$543$	0.0258162	0.00110788
$544$	32.8860	1.40998
$545$	13.1562	0.563552
$546$	−0.735427	−0.0314734
$547$	10.8330	0.463186	0.231593	−	0.972813i	$-0.425606\pi$
$547$	10.8330	0.463186	0.231593	+	0.972813i	$0.425606\pi$
$548$	22.3885	0.956389
$549$	−2.18919	−0.0934324
$550$	−22.1830	−0.945887
$551$	4.78038	0.203651
$552$	−2.99183	−0.127341
$553$	1.86535	0.0793226
$554$	−16.0057	−0.680018
$555$	0.676121	0.0286998
$556$	−13.4847	−0.571877
$557$	−13.1825	−0.558559	−0.279279	−	0.960210i	$-0.590096\pi$
$557$	−13.1825	−0.558559	−0.279279	+	0.960210i	$0.590096\pi$
$558$	−15.7498	−0.666743
$559$	−13.4279	−0.567941
$560$	−0.193957	−0.00819617
$561$	2.37837	0.100415
$562$	−48.5908	−2.04968
$563$	−45.4004	−1.91340	−0.956699	−	0.291080i	$-0.905985\pi$
$563$	−45.4004	−1.91340	−0.956699	+	0.291080i	$0.905985\pi$
$564$	−3.24814	−0.136771
$565$	−1.53324	−0.0645037
$566$	38.6842	1.62602
$567$	6.79860	0.285514
$568$	−36.3066	−1.52339
$569$	−45.1560	−1.89304	−0.946520	−	0.322645i	$-0.895428\pi$
$569$	−45.1560	−1.89304	−0.946520	+	0.322645i	$0.895428\pi$
$570$	−0.322145	−0.0134932
$571$	17.5149	0.732977	0.366488	−	0.930423i	$-0.380560\pi$
$571$	17.5149	0.732977	0.366488	+	0.930423i	$0.380560\pi$
$572$	17.3870	0.726985
$573$	−3.46690	−0.144832
$574$	−6.32091	−0.263830
$575$	25.0525	1.04476
$576$	38.0599	1.58583
$577$	23.0446	0.959359	0.479680	−	0.877444i	$-0.340753\pi$
$577$	23.0446	0.959359	0.479680	+	0.877444i	$0.340753\pi$
$578$	−49.6219	−2.06400
$579$	−1.75766	−0.0730460
$580$	−12.7857	−0.530896
$581$	−4.72081	−0.195852
$582$	1.01173	0.0419376
$583$	4.21625	0.174619
$584$	−16.1265	−0.667317
$585$	−5.70755	−0.235978
$586$	−10.1002	−0.417236
$587$	−33.5029	−1.38281	−0.691407	−	0.722465i	$-0.743009\pi$
$587$	−33.5029	−1.38281	−0.691407	+	0.722465i	$0.743009\pi$
$588$	3.65004	0.150525
$589$	−2.30252	−0.0948735
$590$	−13.4748	−0.554748
$591$	−2.07463	−0.0853388
$592$	1.48743	0.0611331
$593$	−14.7128	−0.604182	−0.302091	−	0.953279i	$-0.597685\pi$
$593$	−14.7128	−0.604182	−0.302091	+	0.953279i	$0.597685\pi$
$594$	5.26705	0.216110
$595$	−3.91318	−0.160425
$596$	−59.6148	−2.44192
$597$	−0.262037	−0.0107244
$598$	−31.5228	−1.28906
$599$	−24.0842	−0.984054	−0.492027	−	0.870580i	$-0.663744\pi$
$599$	−24.0842	−0.984054	−0.492027	+	0.870580i	$0.663744\pi$
$600$	−2.25420	−0.0920274
$601$	23.4287	0.955675	0.477838	−	0.878448i	$-0.341421\pi$
$601$	23.4287	0.955675	0.477838	+	0.878448i	$0.341421\pi$
$602$	−10.1431	−0.413400
$603$	−43.5095	−1.77185
$604$	−44.3858	−1.80603
$605$	4.92590	0.200266
$606$	5.41903	0.220133
$607$	−32.5909	−1.32282	−0.661412	−	0.750023i	$-0.730042\pi$
$607$	−32.5909	−1.32282	−0.661412	+	0.750023i	$0.730042\pi$
$608$	5.29686	0.214816
$609$	−0.643094	−0.0260595
$610$	1.37418	0.0556388
$611$	−13.5061	−0.546399
$612$	−60.9243	−2.46272
$613$	26.5352	1.07175	0.535873	−	0.844299i	$-0.319983\pi$
$613$	26.5352	1.07175	0.535873	+	0.844299i	$0.319983\pi$
$614$	58.8706	2.37582
$615$	0.493109	0.0198841
$616$	5.18312	0.208834
$617$	−25.9242	−1.04367	−0.521834	−	0.853047i	$-0.674752\pi$
$617$	−25.9242	−1.04367	−0.521834	+	0.853047i	$0.674752\pi$
$618$	4.52548	0.182042
$619$	−41.8687	−1.68285	−0.841423	−	0.540377i	$-0.818282\pi$
$619$	−41.8687	−1.68285	−0.841423	+	0.540377i	$0.818282\pi$
$620$	6.15834	0.247325
$621$	−5.94837	−0.238700
$622$	−18.9430	−0.759547
$623$	−7.51961	−0.301267
$624$	0.126216	0.00505270
$625$	15.5991	0.623963
$626$	−38.4918	−1.53844
$627$	0.383078	0.0152986
$628$	−23.8847	−0.953104
$629$	30.0097	1.19657
$630$	−4.31132	−0.171767
$631$	22.3148	0.888340	0.444170	−	0.895943i	$-0.353499\pi$
$631$	22.3148	0.888340	0.444170	+	0.895943i	$0.353499\pi$
$632$	−7.19427	−0.286173
$633$	−2.38663	−0.0948601
$634$	−2.30301	−0.0914642
$635$	15.2133	0.603721
$636$	1.08565	0.0430490
$637$	15.1773	0.601345
$638$	24.4078	0.966315
$639$	−35.9120	−1.42066
$640$	−15.3145	−0.605358
$641$	7.89144	0.311693	0.155847	−	0.987781i	$-0.450189\pi$
$641$	7.89144	0.311693	0.155847	+	0.987781i	$0.450189\pi$
$642$	−7.39597	−0.291896
$643$	−29.3531	−1.15757	−0.578787	−	0.815479i	$-0.696474\pi$
$643$	−29.3531	−1.15757	−0.578787	+	0.815479i	$0.696474\pi$
$644$	−14.8325	−0.584482
$645$	0.791285	0.0311568
$646$	−14.2984	−0.562564
$647$	−18.0912	−0.711240	−0.355620	−	0.934631i	$-0.615730\pi$
$647$	−18.0912	−0.711240	−0.355620	+	0.934631i	$0.615730\pi$
$648$	−26.2208	−1.03005
$649$	16.0235	0.628977
$650$	−23.7510	−0.931590
$651$	0.309752	0.0121402
$652$	−77.6444	−3.04079
$653$	−4.79177	−0.187516	−0.0937582	−	0.995595i	$-0.529888\pi$
$653$	−4.79177	−0.187516	−0.0937582	+	0.995595i	$0.529888\pi$
$654$	−6.46700	−0.252880
$655$	−15.2844	−0.597213
$656$	1.08482	0.0423549
$657$	−15.9512	−0.622315
$658$	−10.2021	−0.397720
$659$	−16.4878	−0.642275	−0.321137	−	0.947033i	$-0.604065\pi$
$659$	−16.4878	−0.642275	−0.321137	+	0.947033i	$0.604065\pi$
$660$	−1.02458	−0.0398819
$661$	44.8367	1.74394	0.871972	−	0.489556i	$-0.162841\pi$
$661$	44.8367	1.74394	0.871972	+	0.489556i	$0.162841\pi$
$662$	38.3338	1.48988
$663$	2.54648	0.0988971
$664$	18.2072	0.706578
$665$	−0.630285	−0.0244414
$666$	33.0630	1.28116
$667$	−27.5651	−1.06733
$668$	−48.1966	−1.86478
$669$	−1.30835	−0.0505839
$670$	27.3113	1.05513
$671$	−1.63410	−0.0630836
$672$	−0.712574	−0.0274882
$673$	−5.06678	−0.195310	−0.0976549	−	0.995220i	$-0.531134\pi$
$673$	−5.06678	−0.195310	−0.0976549	+	0.995220i	$0.531134\pi$
$674$	0.959195	0.0369468
$675$	−4.48182	−0.172505
$676$	−24.3341	−0.935929
$677$	−27.6467	−1.06255	−0.531275	−	0.847199i	$-0.678287\pi$
$677$	−27.6467	−1.06255	−0.531275	+	0.847199i	$0.678287\pi$
$678$	0.753668	0.0289444
$679$	1.97948	0.0759654
$680$	15.0923	0.578765
$681$	−2.98329	−0.114320
$682$	−11.7563	−0.450171
$683$	−19.6449	−0.751690	−0.375845	−	0.926683i	$-0.622647\pi$
$683$	−19.6449	−0.751690	−0.375845	+	0.926683i	$0.622647\pi$
$684$	−9.81291	−0.375206
$685$	−5.48586	−0.209604
$686$	24.0158	0.916927
$687$	1.59395	0.0608131
$688$	1.74079	0.0663669
$689$	4.51427	0.171980
$690$	1.85759	0.0707171
$691$	23.4395	0.891679	0.445840	−	0.895113i	$-0.352905\pi$
$691$	23.4395	0.891679	0.445840	+	0.895113i	$0.352905\pi$
$692$	15.6624	0.595396
$693$	5.12678	0.194750
$694$	−26.1852	−0.993977
$695$	3.30415	0.125334
$696$	2.48028	0.0940149
$697$	21.8867	0.829018
$698$	16.3485	0.618800
$699$	−0.145015	−0.00548498
$700$	−11.1756	−0.422398
$701$	14.8263	0.559981	0.279990	−	0.960003i	$-0.409669\pi$
$701$	14.8263	0.559981	0.279990	+	0.960003i	$0.409669\pi$
$702$	5.63934	0.212843
$703$	4.83358	0.182302
$704$	28.4094	1.07072
$705$	0.795892	0.0299750
$706$	−24.4954	−0.921896
$707$	10.6025	0.398747
$708$	4.12593	0.155062
$709$	27.9832	1.05093	0.525465	−	0.850815i	$-0.323891\pi$
$709$	27.9832	1.05093	0.525465	+	0.850815i	$0.323891\pi$
$710$	22.5423	0.845998
$711$	−7.11608	−0.266874
$712$	29.0016	1.08688
$713$	13.2770	0.497228
$714$	1.92354	0.0719865
$715$	−4.26033	−0.159327
$716$	48.0269	1.79485
$717$	−0.351549	−0.0131288
$718$	−41.3773	−1.54419
$719$	−11.0739	−0.412988	−0.206494	−	0.978448i	$-0.566205\pi$
$719$	−11.0739	−0.412988	−0.206494	+	0.978448i	$0.566205\pi$
$720$	0.739923	0.0275753
$721$	8.85422	0.329748
$722$	−2.30301	−0.0857091
$723$	3.41365	0.126955
$724$	−0.493624	−0.0183454
$725$	−20.7690	−0.771342
$726$	−2.42134	−0.0898645
$727$	36.7626	1.36345	0.681724	−	0.731610i	$-0.261231\pi$
$727$	36.7626	1.36345	0.681724	+	0.731610i	$0.261231\pi$
$728$	5.54948	0.205677
$729$	−25.4011	−0.940782
$730$	10.0127	0.370587
$731$	35.1212	1.29901
$732$	−0.420768	−0.0155520
$733$	21.0937	0.779114	0.389557	−	0.921002i	$-0.372628\pi$
$733$	21.0937	0.779114	0.389557	+	0.921002i	$0.372628\pi$
$734$	−76.5404	−2.82516
$735$	−0.894370	−0.0329893
$736$	−30.5433	−1.12584
$737$	−32.4772	−1.19631
$738$	24.1135	0.887631
$739$	−16.2816	−0.598928	−0.299464	−	0.954108i	$-0.596808\pi$
$739$	−16.2816	−0.598928	−0.299464	+	0.954108i	$0.596808\pi$
$740$	−12.9279	−0.475241
$741$	0.410155	0.0150674
$742$	3.40995	0.125183
$743$	−27.2198	−0.998598	−0.499299	−	0.866430i	$-0.666409\pi$
$743$	−27.2198	−0.998598	−0.499299	+	0.866430i	$0.666409\pi$
$744$	−1.19465	−0.0437981
$745$	14.6074	0.535175
$746$	55.5126	2.03246
$747$	18.0093	0.658927
$748$	−45.4762	−1.66278
$749$	−14.4704	−0.528737
$750$	3.01033	0.109922
$751$	−20.8932	−0.762405	−0.381203	−	0.924492i	$-0.624490\pi$
$751$	−20.8932	−0.762405	−0.381203	+	0.924492i	$0.624490\pi$
$752$	1.75092	0.0638496
$753$	−0.830838	−0.0302774
$754$	26.1330	0.951709
$755$	10.8759	0.395813
$756$	2.65349	0.0965064
$757$	−4.58123	−0.166508	−0.0832538	−	0.996528i	$-0.526531\pi$
$757$	−4.58123	−0.166508	−0.0832538	+	0.996528i	$0.526531\pi$
$758$	−8.16732	−0.296650
$759$	−2.20894	−0.0801795
$760$	2.43088	0.0881774
$761$	−30.1562	−1.09316	−0.546582	−	0.837406i	$-0.684071\pi$
$761$	−30.1562	−1.09316	−0.546582	+	0.837406i	$0.684071\pi$
$762$	−7.47815	−0.270905
$763$	−12.6528	−0.458063
$764$	66.2898	2.39828
$765$	14.9283	0.539734
$766$	50.1274	1.81117
$767$	17.1561	0.619470
$768$	3.09960	0.111847
$769$	1.56136	0.0563040	0.0281520	−	0.999604i	$-0.491038\pi$
$769$	1.56136	0.0563040	0.0281520	+	0.999604i	$0.491038\pi$
$770$	−3.21813	−0.115973
$771$	−0.0647005	−0.00233013
$772$	33.6079	1.20957
$773$	−15.3816	−0.553237	−0.276619	−	0.960980i	$-0.589214\pi$
$773$	−15.3816	−0.553237	−0.276619	+	0.960980i	$0.589214\pi$
$774$	38.6946	1.39085
$775$	10.0036	0.359340
$776$	−7.63445	−0.274061
$777$	−0.650251	−0.0233276
$778$	−42.7963	−1.53432
$779$	3.52523	0.126304
$780$	−1.09700	−0.0392791
$781$	−26.8061	−0.959197
$782$	82.4491	2.94837
$783$	4.93131	0.176231
$784$	−1.96757	−0.0702703
$785$	5.85248	0.208884
$786$	7.51312	0.267984
$787$	6.27056	0.223521	0.111761	−	0.993735i	$-0.464351\pi$
$787$	6.27056	0.223521	0.111761	+	0.993735i	$0.464351\pi$
$788$	39.6685	1.41313
$789$	4.17617	0.148676
$790$	4.46683	0.158923
$791$	1.47457	0.0524296
$792$	−19.7730	−0.702602
$793$	−1.74960	−0.0621301
$794$	26.5195	0.941140
$795$	−0.266018	−0.00943469
$796$	5.01034	0.177587
$797$	−47.3906	−1.67866	−0.839330	−	0.543622i	$-0.817052\pi$
$797$	−47.3906	−1.67866	−0.839330	+	0.543622i	$0.817052\pi$
$798$	0.309819	0.0109675
$799$	35.3257	1.24973
$800$	−23.0129	−0.813630
$801$	28.6864	1.01359
$802$	−10.3604	−0.365839
$803$	−11.9066	−0.420173
$804$	−8.36263	−0.294927
$805$	3.63441	0.128096
$806$	−12.5872	−0.443366
$807$	5.24194	0.184525
$808$	−40.8916	−1.43856
$809$	15.5910	0.548151	0.274075	−	0.961708i	$-0.411628\pi$
$809$	15.5910	0.548151	0.274075	+	0.961708i	$0.411628\pi$
$810$	16.2802	0.572027
$811$	−2.49091	−0.0874678	−0.0437339	−	0.999043i	$-0.513925\pi$
$811$	−2.49091	−0.0874678	−0.0437339	+	0.999043i	$0.513925\pi$
$812$	12.2964	0.431520
$813$	3.08936	0.108349
$814$	24.6795	0.865015
$815$	19.0252	0.666425
$816$	−0.330124	−0.0115566
$817$	5.65688	0.197909
$818$	70.1852	2.45397
$819$	5.48916	0.191807
$820$	−9.42862	−0.329262
$821$	38.8784	1.35687	0.678433	−	0.734662i	$-0.262659\pi$
$821$	38.8784	1.35687	0.678433	+	0.734662i	$0.262659\pi$
$822$	2.69659	0.0940545
$823$	−48.6131	−1.69455	−0.847274	−	0.531157i	$-0.821757\pi$
$823$	−48.6131	−1.69455	−0.847274	+	0.531157i	$0.821757\pi$
$824$	−34.1490	−1.18964
$825$	−1.66433	−0.0579447
$826$	12.9592	0.450908
$827$	9.51843	0.330988	0.165494	−	0.986211i	$-0.447078\pi$
$827$	9.51843	0.330988	0.165494	+	0.986211i	$0.447078\pi$
$828$	56.5842	1.96644
$829$	−32.0036	−1.11153	−0.555765	−	0.831339i	$-0.687575\pi$
$829$	−32.0036	−1.11153	−0.555765	+	0.831339i	$0.687575\pi$
$830$	−11.3046	−0.392389
$831$	−1.20087	−0.0416577
$832$	30.4174	1.05453
$833$	−39.6967	−1.37541
$834$	−1.62417	−0.0562403
$835$	11.8096	0.408689
$836$	−7.32473	−0.253331
$837$	−2.37522	−0.0820994
$838$	−54.0497	−1.86711
$839$	−21.5610	−0.744368	−0.372184	−	0.928159i	$-0.621391\pi$
$839$	−21.5610	−0.744368	−0.372184	+	0.928159i	$0.621391\pi$
$840$	−0.327021	−0.0112833
$841$	−6.14798	−0.211999
$842$	47.1071	1.62342
$843$	−3.64564	−0.125562
$844$	45.6342	1.57079
$845$	5.96260	0.205120
$846$	38.9199	1.33809
$847$	−4.73742	−0.162780
$848$	−0.585226	−0.0200968
$849$	2.90238	0.0996093
$850$	62.1215	2.13075
$851$	−27.8719	−0.955436
$852$	−6.90237	−0.236471
$853$	12.4691	0.426935	0.213467	−	0.976950i	$-0.431524\pi$
$853$	12.4691	0.426935	0.213467	+	0.976950i	$0.431524\pi$
$854$	−1.32159	−0.0452240
$855$	2.40446	0.0822309
$856$	55.8094	1.90753
$857$	7.26227	0.248074	0.124037	−	0.992278i	$-0.460416\pi$
$857$	7.26227	0.248074	0.124037	+	0.992278i	$0.460416\pi$
$858$	2.09418	0.0714942
$859$	−31.7416	−1.08301	−0.541504	−	0.840698i	$-0.682145\pi$
$859$	−31.7416	−1.08301	−0.541504	+	0.840698i	$0.682145\pi$
$860$	−15.1300	−0.515927
$861$	−0.474241	−0.0161621
$862$	−90.9044	−3.09621
$863$	7.77045	0.264509	0.132255	−	0.991216i	$-0.457778\pi$
$863$	7.77045	0.264509	0.132255	+	0.991216i	$0.457778\pi$
$864$	5.46410	0.185892
$865$	−3.83777	−0.130488
$866$	36.2482	1.23177
$867$	−3.72300	−0.126440
$868$	−5.92270	−0.201029
$869$	−5.31171	−0.180187
$870$	−1.53998	−0.0522101
$871$	−34.7727	−1.17823
$872$	48.7995	1.65256
$873$	−7.55148	−0.255579
$874$	13.2798	0.449197
$875$	5.88978	0.199111
$876$	−3.06585	−0.103586
$877$	20.2031	0.682209	0.341105	−	0.940025i	$-0.389199\pi$
$877$	20.2031	0.682209	0.341105	+	0.940025i	$0.389199\pi$
$878$	10.0106	0.337842
$879$	−0.757793	−0.0255597
$880$	0.552306	0.0186182
$881$	−56.7964	−1.91352	−0.956759	−	0.290882i	$-0.906051\pi$
$881$	−56.7964	−1.91352	−0.956759	+	0.290882i	$0.906051\pi$
$882$	−43.7355	−1.47265
$883$	−41.5493	−1.39825	−0.699123	−	0.715002i	$-0.746426\pi$
$883$	−41.5493	−1.39825	−0.699123	+	0.715002i	$0.746426\pi$
$884$	−48.6906	−1.63764
$885$	−1.01098	−0.0339836
$886$	−73.5690	−2.47160
$887$	−16.9596	−0.569446	−0.284723	−	0.958610i	$-0.591902\pi$
$887$	−16.9596	−0.569446	−0.284723	+	0.958610i	$0.591902\pi$
$888$	2.50789	0.0841592
$889$	−14.6312	−0.490714
$890$	−18.0067	−0.603587
$891$	−19.3595	−0.648568
$892$	25.0167	0.837621
$893$	5.68982	0.190403
$894$	−7.18034	−0.240146
$895$	−11.7681	−0.393363
$896$	14.7285	0.492045
$897$	−2.36507	−0.0789675
$898$	−5.69200	−0.189945
$899$	−11.0069	−0.367101
$900$	42.6336	1.42112
$901$	−11.8072	−0.393356
$902$	17.9992	0.599309
$903$	−0.761007	−0.0253247
$904$	−5.68712	−0.189151
$905$	0.120953	0.00402061
$906$	−5.34607	−0.177611
$907$	−19.4393	−0.645472	−0.322736	−	0.946489i	$-0.604603\pi$
$907$	−19.4393	−0.645472	−0.322736	+	0.946489i	$0.604603\pi$
$908$	57.0428	1.89303
$909$	−40.4471	−1.34155
$910$	−3.44560	−0.114220
$911$	−48.6772	−1.61275	−0.806374	−	0.591406i	$-0.798573\pi$
$911$	−48.6772	−1.61275	−0.806374	+	0.591406i	$0.798573\pi$
$912$	−0.0531721	−0.00176070
$913$	13.4429	0.444894
$914$	85.7328	2.83579
$915$	0.103101	0.00340841
$916$	−30.4776	−1.00701
$917$	14.6996	0.485424
$918$	−14.7499	−0.486819
$919$	−11.2115	−0.369832	−0.184916	−	0.982754i	$-0.559201\pi$
$919$	−11.2115	−0.369832	−0.184916	+	0.982754i	$0.559201\pi$
$920$	−14.0172	−0.462133
$921$	4.41690	0.145542
$922$	21.2329	0.699268
$923$	−28.7008	−0.944699
$924$	0.985379	0.0324166
$925$	−21.0002	−0.690481
$926$	36.2583	1.19152
$927$	−33.7778	−1.10941
$928$	25.3210	0.831202
$929$	−29.5705	−0.970175	−0.485088	−	0.874466i	$-0.661212\pi$
$929$	−29.5705	−0.970175	−0.485088	+	0.874466i	$0.661212\pi$
$930$	0.741744	0.0243228
$931$	−6.39383	−0.209549
$932$	2.77280	0.0908261
$933$	−1.42125	−0.0465296
$934$	55.4635	1.81482
$935$	11.1431	0.364417
$936$	−21.1706	−0.691983
$937$	−18.3092	−0.598136	−0.299068	−	0.954232i	$-0.596676\pi$
$937$	−18.3092	−0.598136	−0.299068	+	0.954232i	$0.596676\pi$
$938$	−26.2663	−0.857625
$939$	−2.88794	−0.0942442
$940$	−15.2181	−0.496358
$941$	−19.5955	−0.638795	−0.319398	−	0.947621i	$-0.603481\pi$
$941$	−19.5955	−0.638795	−0.319398	+	0.947621i	$0.603481\pi$
$942$	−2.87681	−0.0937314
$943$	−20.3275	−0.661956
$944$	−2.22410	−0.0723883
$945$	−0.650185	−0.0211505
$946$	28.8831	0.939071
$947$	−14.8001	−0.480937	−0.240469	−	0.970657i	$-0.577301\pi$
$947$	−14.8001	−0.480937	−0.240469	+	0.970657i	$0.577301\pi$
$948$	−1.36773	−0.0444217
$949$	−12.7482	−0.413823
$950$	10.0057	0.324629
$951$	−0.172789	−0.00560306
$952$	−14.5149	−0.470429
$953$	−40.2466	−1.30372	−0.651858	−	0.758341i	$-0.726010\pi$
$953$	−40.2466	−1.30372	−0.651858	+	0.758341i	$0.726010\pi$
$954$	−13.0085	−0.421167
$955$	−16.2430	−0.525611
$956$	6.72188	0.217401
$957$	1.83126	0.0591961
$958$	−1.53132	−0.0494748
$959$	5.27595	0.170369
$960$	−1.79245	−0.0578510
$961$	−25.6984	−0.828981
$962$	26.4239	0.851940
$963$	55.2028	1.77889
$964$	−65.2716	−2.10226
$965$	−8.23495	−0.265092
$966$	−1.78651	−0.0574799
$967$	−18.1049	−0.582215	−0.291107	−	0.956690i	$-0.594024\pi$
$967$	−18.1049	−0.582215	−0.291107	+	0.956690i	$0.594024\pi$
$968$	18.2713	0.587261
$969$	−1.07277	−0.0344625
$970$	4.74013	0.152196
$971$	34.2939	1.10054	0.550271	−	0.834986i	$-0.314524\pi$
$971$	34.2939	1.10054	0.550271	+	0.834986i	$0.314524\pi$
$972$	−15.2094	−0.487843
$973$	−3.17772	−0.101873
$974$	89.7465	2.87566
$975$	−1.78197	−0.0570688
$976$	0.226817	0.00726022
$977$	40.8171	1.30586	0.652928	−	0.757420i	$-0.273540\pi$
$977$	40.8171	1.30586	0.652928	+	0.757420i	$0.273540\pi$
$978$	−9.35192	−0.299042
$979$	21.4126	0.684351
$980$	17.1010	0.546272
$981$	48.2691	1.54111
$982$	70.9224	2.26322
$983$	40.2191	1.28279	0.641395	−	0.767211i	$-0.278356\pi$
$983$	40.2191	1.28279	0.641395	+	0.767211i	$0.278356\pi$
$984$	1.82905	0.0583081
$985$	−9.71998	−0.309704
$986$	−68.3519	−2.17677
$987$	−0.765439	−0.0243642
$988$	−7.84246	−0.249502
$989$	−32.6193	−1.03723
$990$	12.2768	0.390182
$991$	16.5642	0.526178	0.263089	−	0.964772i	$-0.415259\pi$
$991$	16.5642	0.526178	0.263089	+	0.964772i	$0.415259\pi$
$992$	−12.1961	−0.387227
$993$	2.87608	0.0912697
$994$	−21.6798	−0.687640
$995$	−1.22768	−0.0389202
$996$	3.46144	0.109680
$997$	−9.13221	−0.289220	−0.144610	−	0.989489i	$-0.546193\pi$
$997$	−9.13221	−0.289220	−0.144610	+	0.989489i	$0.546193\pi$
$998$	−49.6391	−1.57130
$999$	4.98619	0.157756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.11	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.11	✓	98	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30301 q^{2} -0.172789 q^{3} +3.30385 q^{4} -0.809544 q^{5} +0.397934 q^{6} +0.778568 q^{7} -3.00278 q^{8} -2.97014 q^{9} +O(q^{10})\)	\(q-2.30301 q^{2} -0.172789 q^{3} +3.30385 q^{4} -0.809544 q^{5} +0.397934 q^{6} +0.778568 q^{7} -3.00278 q^{8} -2.97014 q^{9} +1.86439 q^{10} -2.21703 q^{11} -0.570868 q^{12} -2.37373 q^{13} -1.79305 q^{14} +0.139880 q^{15} +0.307729 q^{16} +6.20859 q^{17} +6.84027 q^{18} +1.00000 q^{19} -2.67461 q^{20} -0.134528 q^{21} +5.10584 q^{22} -5.76630 q^{23} +0.518847 q^{24} -4.34464 q^{25} +5.46673 q^{26} +1.03157 q^{27} +2.57227 q^{28} +4.78038 q^{29} -0.322145 q^{30} -2.30252 q^{31} +5.29686 q^{32} +0.383078 q^{33} -14.2984 q^{34} -0.630285 q^{35} -9.81291 q^{36} +4.83358 q^{37} -2.30301 q^{38} +0.410155 q^{39} +2.43088 q^{40} +3.52523 q^{41} +0.309819 q^{42} +5.65688 q^{43} -7.32473 q^{44} +2.40446 q^{45} +13.2798 q^{46} +5.68982 q^{47} -0.0531721 q^{48} -6.39383 q^{49} +10.0057 q^{50} -1.07277 q^{51} -7.84246 q^{52} -1.90176 q^{53} -2.37572 q^{54} +1.79478 q^{55} -2.33787 q^{56} -0.172789 q^{57} -11.0093 q^{58} -7.22746 q^{59} +0.462143 q^{60} +0.737066 q^{61} +5.30272 q^{62} -2.31246 q^{63} -12.8142 q^{64} +1.92164 q^{65} -0.882231 q^{66} +14.6490 q^{67} +20.5122 q^{68} +0.996352 q^{69} +1.45155 q^{70} +12.0910 q^{71} +8.91869 q^{72} +5.37051 q^{73} -11.1318 q^{74} +0.750705 q^{75} +3.30385 q^{76} -1.72611 q^{77} -0.944590 q^{78} +2.39587 q^{79} -0.249120 q^{80} +8.73219 q^{81} -8.11863 q^{82} -6.06346 q^{83} -0.444460 q^{84} -5.02612 q^{85} -13.0278 q^{86} -0.825996 q^{87} +6.65725 q^{88} -9.65826 q^{89} -5.53750 q^{90} -1.84811 q^{91} -19.0510 q^{92} +0.397849 q^{93} -13.1037 q^{94} -0.809544 q^{95} -0.915238 q^{96} +2.54246 q^{97} +14.7251 q^{98} +6.58489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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