LMFDB - Embedded newform 6023.2.a.a.1.7

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			1.7
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)

$f(q)$	$=$	$q-2.51733 q^{2} -2.83375 q^{3} +4.33693 q^{4} +3.33686 q^{5} +7.13347 q^{6} +2.06105 q^{7} -5.88281 q^{8} +5.03014 q^{9} +O(q^{10})$	\(q-2.51733 q^{2} -2.83375 q^{3} +4.33693 q^{4} +3.33686 q^{5} +7.13347 q^{6} +2.06105 q^{7} -5.88281 q^{8} +5.03014 q^{9} -8.39997 q^{10} +2.85602 q^{11} -12.2898 q^{12} -2.37787 q^{13} -5.18833 q^{14} -9.45584 q^{15} +6.13510 q^{16} -7.23109 q^{17} -12.6625 q^{18} +1.00000 q^{19} +14.4717 q^{20} -5.84049 q^{21} -7.18954 q^{22} -0.316032 q^{23} +16.6704 q^{24} +6.13466 q^{25} +5.98587 q^{26} -5.75290 q^{27} +8.93861 q^{28} +1.19180 q^{29} +23.8034 q^{30} -1.45736 q^{31} -3.67842 q^{32} -8.09326 q^{33} +18.2030 q^{34} +6.87743 q^{35} +21.8153 q^{36} +3.37994 q^{37} -2.51733 q^{38} +6.73829 q^{39} -19.6302 q^{40} +4.39884 q^{41} +14.7024 q^{42} -5.62271 q^{43} +12.3864 q^{44} +16.7849 q^{45} +0.795555 q^{46} +4.07583 q^{47} -17.3853 q^{48} -2.75209 q^{49} -15.4429 q^{50} +20.4911 q^{51} -10.3127 q^{52} -4.80591 q^{53} +14.4819 q^{54} +9.53016 q^{55} -12.1248 q^{56} -2.83375 q^{57} -3.00014 q^{58} -6.63239 q^{59} -41.0093 q^{60} +10.0291 q^{61} +3.66864 q^{62} +10.3673 q^{63} -3.01042 q^{64} -7.93463 q^{65} +20.3734 q^{66} -13.8874 q^{67} -31.3607 q^{68} +0.895555 q^{69} -17.3127 q^{70} +0.389297 q^{71} -29.5914 q^{72} -5.58782 q^{73} -8.50841 q^{74} -17.3841 q^{75} +4.33693 q^{76} +5.88640 q^{77} -16.9625 q^{78} -5.67422 q^{79} +20.4720 q^{80} +1.21186 q^{81} -11.0733 q^{82} +5.23670 q^{83} -25.3298 q^{84} -24.1291 q^{85} +14.1542 q^{86} -3.37725 q^{87} -16.8015 q^{88} -5.10319 q^{89} -42.2530 q^{90} -4.90090 q^{91} -1.37061 q^{92} +4.12978 q^{93} -10.2602 q^{94} +3.33686 q^{95} +10.4237 q^{96} +10.3654 q^{97} +6.92790 q^{98} +14.3662 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.51733	−1.78002	−0.890009	−	0.455943i	$-0.849302\pi$
$2$	−2.51733	−1.78002	−0.890009	+	0.455943i	$0.849302\pi$
$3$	−2.83375	−1.63607	−0.818033	−	0.575171i	$-0.804935\pi$
$3$	−2.83375	−1.63607	−0.818033	+	0.575171i	$0.804935\pi$
$4$	4.33693	2.16846
$5$	3.33686	1.49229	0.746145	−	0.665783i	$-0.231902\pi$
$5$	3.33686	1.49229	0.746145	+	0.665783i	$0.231902\pi$
$6$	7.13347	2.91223
$7$	2.06105	0.779002	0.389501	−	0.921026i	$-0.372647\pi$
$7$	2.06105	0.779002	0.389501	+	0.921026i	$0.372647\pi$
$8$	−5.88281	−2.07989
$9$	5.03014	1.67671
$10$	−8.39997	−2.65630
$11$	2.85602	0.861124	0.430562	−	0.902561i	$-0.358315\pi$
$11$	2.85602	0.861124	0.430562	+	0.902561i	$0.358315\pi$
$12$	−12.2898	−3.54775
$13$	−2.37787	−0.659502	−0.329751	−	0.944068i	$-0.606965\pi$
$13$	−2.37787	−0.659502	−0.329751	+	0.944068i	$0.606965\pi$
$14$	−5.18833	−1.38664
$15$	−9.45584	−2.44149
$16$	6.13510	1.53378
$17$	−7.23109	−1.75380	−0.876898	−	0.480677i	$-0.840391\pi$
$17$	−7.23109	−1.75380	−0.876898	+	0.480677i	$0.840391\pi$
$18$	−12.6625	−2.98458
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	14.4717	3.23598
$21$	−5.84049	−1.27450
$22$	−7.18954	−1.53282
$23$	−0.316032	−0.0658972	−0.0329486	−	0.999457i	$-0.510490\pi$
$23$	−0.316032	−0.0658972	−0.0329486	+	0.999457i	$0.510490\pi$
$24$	16.6704	3.40284
$25$	6.13466	1.22693
$26$	5.98587	1.17393
$27$	−5.75290	−1.10715
$28$	8.93861	1.68924
$29$	1.19180	0.221311	0.110655	−	0.993859i	$-0.464705\pi$
$29$	1.19180	0.221311	0.110655	+	0.993859i	$0.464705\pi$
$30$	23.8034	4.34589
$31$	−1.45736	−0.261749	−0.130874	−	0.991399i	$-0.541778\pi$
$31$	−1.45736	−0.261749	−0.130874	+	0.991399i	$0.541778\pi$
$32$	−3.67842	−0.650259
$33$	−8.09326	−1.40886
$34$	18.2030	3.12179
$35$	6.87743	1.16250
$36$	21.8153	3.63589
$37$	3.37994	0.555658	0.277829	−	0.960630i	$-0.410385\pi$
$37$	3.37994	0.555658	0.277829	+	0.960630i	$0.410385\pi$
$38$	−2.51733	−0.408364
$39$	6.73829	1.07899
$40$	−19.6302	−3.10380
$41$	4.39884	0.686984	0.343492	−	0.939156i	$-0.388390\pi$
$41$	4.39884	0.686984	0.343492	+	0.939156i	$0.388390\pi$
$42$	14.7024	2.26863
$43$	−5.62271	−0.857455	−0.428728	−	0.903434i	$-0.641038\pi$
$43$	−5.62271	−0.857455	−0.428728	+	0.903434i	$0.641038\pi$
$44$	12.3864	1.86732
$45$	16.7849	2.50214
$46$	0.795555	0.117298
$47$	4.07583	0.594520	0.297260	−	0.954797i	$-0.403927\pi$
$47$	4.07583	0.594520	0.297260	+	0.954797i	$0.403927\pi$
$48$	−17.3853	−2.50936
$49$	−2.75209	−0.393155
$50$	−15.4429	−2.18396
$51$	20.4911	2.86933
$52$	−10.3127	−1.43011
$53$	−4.80591	−0.660143	−0.330071	−	0.943956i	$-0.607073\pi$
$53$	−4.80591	−0.660143	−0.330071	+	0.943956i	$0.607073\pi$
$54$	14.4819	1.97074
$55$	9.53016	1.28505
$56$	−12.1248	−1.62024
$57$	−2.83375	−0.375339
$58$	−3.00014	−0.393938
$59$	−6.63239	−0.863464	−0.431732	−	0.902002i	$-0.642097\pi$
$59$	−6.63239	−0.863464	−0.431732	+	0.902002i	$0.642097\pi$
$60$	−41.0093	−5.29428
$61$	10.0291	1.28409	0.642046	−	0.766666i	$-0.278086\pi$
$61$	10.0291	1.28409	0.642046	+	0.766666i	$0.278086\pi$
$62$	3.66864	0.465918
$63$	10.3673	1.30616
$64$	−3.01042	−0.376302
$65$	−7.93463	−0.984169
$66$	20.3734	2.50779
$67$	−13.8874	−1.69662	−0.848309	−	0.529502i	$-0.822379\pi$
$67$	−13.8874	−1.69662	−0.848309	+	0.529502i	$0.822379\pi$
$68$	−31.3607	−3.80304
$69$	0.895555	0.107812
$70$	−17.3127	−2.06927
$71$	0.389297	0.0462010	0.0231005	−	0.999733i	$-0.492646\pi$
$71$	0.389297	0.0462010	0.0231005	+	0.999733i	$0.492646\pi$
$72$	−29.5914	−3.48737
$73$	−5.58782	−0.654004	−0.327002	−	0.945024i	$-0.606038\pi$
$73$	−5.58782	−0.654004	−0.327002	+	0.945024i	$0.606038\pi$
$74$	−8.50841	−0.989082
$75$	−17.3841	−2.00734
$76$	4.33693	0.497480
$77$	5.88640	0.670817
$78$	−16.9625	−1.92062
$79$	−5.67422	−0.638400	−0.319200	−	0.947687i	$-0.603414\pi$
$79$	−5.67422	−0.638400	−0.319200	+	0.947687i	$0.603414\pi$
$80$	20.4720	2.28884
$81$	1.21186	0.134651
$82$	−11.0733	−1.22284
$83$	5.23670	0.574803	0.287401	−	0.957810i	$-0.407209\pi$
$83$	5.23670	0.574803	0.287401	+	0.957810i	$0.407209\pi$
$84$	−25.3298	−2.76371
$85$	−24.1291	−2.61717
$86$	14.1542	1.52629
$87$	−3.37725	−0.362079
$88$	−16.8015	−1.79104
$89$	−5.10319	−0.540937	−0.270469	−	0.962729i	$-0.587179\pi$
$89$	−5.10319	−0.540937	−0.270469	+	0.962729i	$0.587179\pi$
$90$	−42.2530	−4.45386
$91$	−4.90090	−0.513754
$92$	−1.37061	−0.142896
$93$	4.12978	0.428239
$94$	−10.2602	−1.05826
$95$	3.33686	0.342355
$96$	10.4237	1.06387
$97$	10.3654	1.05245	0.526226	−	0.850345i	$-0.323607\pi$
$97$	10.3654	1.05245	0.526226	+	0.850345i	$0.323607\pi$
$98$	6.92790	0.699824
$99$	14.3662	1.44386
$100$	26.6056	2.66056
$101$	8.88169	0.883761	0.441881	−	0.897074i	$-0.354311\pi$
$101$	8.88169	0.883761	0.441881	+	0.897074i	$0.354311\pi$
$102$	−51.5827	−5.10745
$103$	−7.39367	−0.728520	−0.364260	−	0.931297i	$-0.618678\pi$
$103$	−7.39367	−0.728520	−0.364260	+	0.931297i	$0.618678\pi$
$104$	13.9886	1.37169
$105$	−19.4889	−1.90192
$106$	12.0980	1.17507
$107$	−4.64578	−0.449125	−0.224562	−	0.974460i	$-0.572095\pi$
$107$	−4.64578	−0.449125	−0.224562	+	0.974460i	$0.572095\pi$
$108$	−24.9499	−2.40081
$109$	4.02643	0.385662	0.192831	−	0.981232i	$-0.438233\pi$
$109$	4.02643	0.385662	0.192831	+	0.981232i	$0.438233\pi$
$110$	−23.9905	−2.28741
$111$	−9.57790	−0.909094
$112$	12.6447	1.19481
$113$	−8.81378	−0.829130	−0.414565	−	0.910020i	$-0.636066\pi$
$113$	−8.81378	−0.829130	−0.414565	+	0.910020i	$0.636066\pi$
$114$	7.13347	0.668111
$115$	−1.05455	−0.0983377
$116$	5.16874	0.479905
$117$	−11.9610	−1.10580
$118$	16.6959	1.53698
$119$	−14.9036	−1.36621
$120$	55.6269	5.07802
$121$	−2.84313	−0.258466
$122$	−25.2465	−2.28571
$123$	−12.4652	−1.12395
$124$	−6.32045	−0.567593
$125$	3.78621	0.338649
$126$	−26.0980	−2.32499
$127$	1.83568	0.162891	0.0814453	−	0.996678i	$-0.474046\pi$
$127$	1.83568	0.162891	0.0814453	+	0.996678i	$0.474046\pi$
$128$	14.9350	1.32008
$129$	15.9333	1.40285
$130$	19.9740	1.75184
$131$	−3.91589	−0.342133	−0.171067	−	0.985259i	$-0.554721\pi$
$131$	−3.91589	−0.342133	−0.171067	+	0.985259i	$0.554721\pi$
$132$	−35.0999	−3.05505
$133$	2.06105	0.178715
$134$	34.9591	3.02001
$135$	−19.1966	−1.65218
$136$	42.5391	3.64770
$137$	−14.2888	−1.22077	−0.610386	−	0.792104i	$-0.708986\pi$
$137$	−14.2888	−1.22077	−0.610386	+	0.792104i	$0.708986\pi$
$138$	−2.25440	−0.191908
$139$	−5.96373	−0.505837	−0.252919	−	0.967488i	$-0.581390\pi$
$139$	−5.96373	−0.505837	−0.252919	+	0.967488i	$0.581390\pi$
$140$	29.8269	2.52084
$141$	−11.5499	−0.972675
$142$	−0.979987	−0.0822387
$143$	−6.79125	−0.567913
$144$	30.8604	2.57170
$145$	3.97686	0.330260
$146$	14.0664	1.16414
$147$	7.79873	0.643228
$148$	14.6586	1.20493
$149$	−6.15091	−0.503902	−0.251951	−	0.967740i	$-0.581072\pi$
$149$	−6.15091	−0.503902	−0.251951	+	0.967740i	$0.581072\pi$
$150$	43.7614	3.57310
$151$	0.472396	0.0384431	0.0192215	−	0.999815i	$-0.493881\pi$
$151$	0.472396	0.0384431	0.0192215	+	0.999815i	$0.493881\pi$
$152$	−5.88281	−0.477159
$153$	−36.3733	−2.94061
$154$	−14.8180	−1.19407
$155$	−4.86300	−0.390606
$156$	29.2235	2.33975
$157$	−21.6085	−1.72455	−0.862273	−	0.506444i	$-0.830960\pi$
$157$	−21.6085	−1.72455	−0.862273	+	0.506444i	$0.830960\pi$
$158$	14.2839	1.13636
$159$	13.6187	1.08004
$160$	−12.2744	−0.970376
$161$	−0.651356	−0.0513340
$162$	−3.05064	−0.239681
$163$	15.7319	1.23221	0.616107	−	0.787663i	$-0.288709\pi$
$163$	15.7319	1.23221	0.616107	+	0.787663i	$0.288709\pi$
$164$	19.0775	1.48970
$165$	−27.0061	−2.10242
$166$	−13.1825	−1.02316
$167$	14.8716	1.15080	0.575399	−	0.817873i	$-0.304847\pi$
$167$	14.8716	1.15080	0.575399	+	0.817873i	$0.304847\pi$
$168$	34.3585	2.65082
$169$	−7.34574	−0.565057
$170$	60.7409	4.65862
$171$	5.03014	0.384664
$172$	−24.3853	−1.85936
$173$	−11.6698	−0.887241	−0.443620	−	0.896215i	$-0.646306\pi$
$173$	−11.6698	−0.887241	−0.443620	+	0.896215i	$0.646306\pi$
$174$	8.50164	0.644508
$175$	12.6438	0.955783
$176$	17.5220	1.32077
$177$	18.7945	1.41268
$178$	12.8464	0.962878
$179$	−3.18464	−0.238031	−0.119016	−	0.992892i	$-0.537974\pi$
$179$	−3.18464	−0.238031	−0.119016	+	0.992892i	$0.537974\pi$
$180$	72.7948	5.42581
$181$	−13.4223	−0.997673	−0.498836	−	0.866696i	$-0.666239\pi$
$181$	−13.4223	−0.997673	−0.498836	+	0.866696i	$0.666239\pi$
$182$	12.3372	0.914491
$183$	−28.4199	−2.10086
$184$	1.85916	0.137059
$185$	11.2784	0.829204
$186$	−10.3960	−0.762272
$187$	−20.6522	−1.51024
$188$	17.6766	1.28920
$189$	−11.8570	−0.862469
$190$	−8.39997	−0.609398
$191$	23.5050	1.70076	0.850381	−	0.526168i	$-0.176372\pi$
$191$	23.5050	1.70076	0.850381	+	0.526168i	$0.176372\pi$
$192$	8.53077	0.615655
$193$	2.96010	0.213073	0.106536	−	0.994309i	$-0.466024\pi$
$193$	2.96010	0.213073	0.106536	+	0.994309i	$0.466024\pi$
$194$	−26.0932	−1.87338
$195$	22.4847	1.61017
$196$	−11.9356	−0.852544
$197$	−8.79362	−0.626520	−0.313260	−	0.949667i	$-0.601421\pi$
$197$	−8.79362	−0.626520	−0.313260	+	0.949667i	$0.601421\pi$
$198$	−36.1644	−2.57009
$199$	−5.90604	−0.418668	−0.209334	−	0.977844i	$-0.567130\pi$
$199$	−5.90604	−0.418668	−0.209334	+	0.977844i	$0.567130\pi$
$200$	−36.0891	−2.55188
$201$	39.3534	2.77578
$202$	−22.3581	−1.57311
$203$	2.45635	0.172402
$204$	88.8684	6.22203
$205$	14.6783	1.02518
$206$	18.6123	1.29678
$207$	−1.58968	−0.110491
$208$	−14.5885	−1.01153
$209$	2.85602	0.197555
$210$	49.0600	3.38546
$211$	−12.2752	−0.845062	−0.422531	−	0.906349i	$-0.638858\pi$
$211$	−12.2752	−0.845062	−0.422531	+	0.906349i	$0.638858\pi$
$212$	−20.8429	−1.43150
$213$	−1.10317	−0.0755880
$214$	11.6949	0.799450
$215$	−18.7622	−1.27957
$216$	33.8432	2.30274
$217$	−3.00368	−0.203903
$218$	−10.1358	−0.686485
$219$	15.8345	1.06999
$220$	41.3317	2.78658
$221$	17.1946	1.15663
$222$	24.1107	1.61820
$223$	20.6539	1.38308	0.691542	−	0.722336i	$-0.256932\pi$
$223$	20.6539	1.38308	0.691542	+	0.722336i	$0.256932\pi$
$224$	−7.58140	−0.506553
$225$	30.8582	2.05721
$226$	22.1871	1.47587
$227$	−20.7902	−1.37989	−0.689947	−	0.723860i	$-0.742366\pi$
$227$	−20.7902	−1.37989	−0.689947	+	0.723860i	$0.742366\pi$
$228$	−12.2898	−0.813910
$229$	−8.89808	−0.588002	−0.294001	−	0.955805i	$-0.594987\pi$
$229$	−8.89808	−0.588002	−0.294001	+	0.955805i	$0.594987\pi$
$230$	2.65466	0.175043
$231$	−16.6806	−1.09750
$232$	−7.01111	−0.460302
$233$	1.26813	0.0830782	0.0415391	−	0.999137i	$-0.486774\pi$
$233$	1.26813	0.0830782	0.0415391	+	0.999137i	$0.486774\pi$
$234$	30.1098	1.96834
$235$	13.6005	0.887197
$236$	−28.7642	−1.87239
$237$	16.0793	1.04446
$238$	37.5172	2.43188
$239$	11.8724	0.767964	0.383982	−	0.923340i	$-0.374552\pi$
$239$	11.8724	0.767964	0.383982	+	0.923340i	$0.374552\pi$
$240$	−58.0125	−3.74469
$241$	−19.5005	−1.25614	−0.628069	−	0.778157i	$-0.716155\pi$
$241$	−19.5005	−1.25614	−0.628069	+	0.778157i	$0.716155\pi$
$242$	7.15708	0.460074
$243$	13.8246	0.886848
$244$	43.4954	2.78451
$245$	−9.18334	−0.586702
$246$	31.3790	2.00065
$247$	−2.37787	−0.151300
$248$	8.57336	0.544409
$249$	−14.8395	−0.940415
$250$	−9.53112	−0.602801
$251$	19.9553	1.25956	0.629782	−	0.776772i	$-0.283144\pi$
$251$	19.9553	1.25956	0.629782	+	0.776772i	$0.283144\pi$
$252$	44.9624	2.83237
$253$	−0.902594	−0.0567456
$254$	−4.62101	−0.289948
$255$	68.3760	4.28187
$256$	−31.5755	−1.97347
$257$	6.09802	0.380384	0.190192	−	0.981747i	$-0.439089\pi$
$257$	6.09802	0.380384	0.190192	+	0.981747i	$0.439089\pi$
$258$	−40.1094	−2.49710
$259$	6.96621	0.432859
$260$	−34.4119	−2.13414
$261$	5.99490	0.371075
$262$	9.85758	0.609003
$263$	2.64163	0.162890	0.0814449	−	0.996678i	$-0.474047\pi$
$263$	2.64163	0.162890	0.0814449	+	0.996678i	$0.474047\pi$
$264$	47.6111	2.93026
$265$	−16.0367	−0.985125
$266$	−5.18833	−0.318117
$267$	14.4612	0.885009
$268$	−60.2287	−3.67906
$269$	−16.1719	−0.986020	−0.493010	−	0.870024i	$-0.664103\pi$
$269$	−16.1719	−0.986020	−0.493010	+	0.870024i	$0.664103\pi$
$270$	48.3242	2.94092
$271$	−14.5880	−0.886160	−0.443080	−	0.896482i	$-0.646114\pi$
$271$	−14.5880	−0.886160	−0.443080	+	0.896482i	$0.646114\pi$
$272$	−44.3634	−2.68993
$273$	13.8879	0.840535
$274$	35.9695	2.17300
$275$	17.5207	1.05654
$276$	3.88396	0.233787
$277$	−10.7221	−0.644226	−0.322113	−	0.946701i	$-0.604393\pi$
$277$	−10.7221	−0.644226	−0.322113	+	0.946701i	$0.604393\pi$
$278$	15.0127	0.900400
$279$	−7.33070	−0.438878
$280$	−40.4587	−2.41787
$281$	14.6542	0.874194	0.437097	−	0.899414i	$-0.356007\pi$
$281$	14.6542	0.874194	0.437097	+	0.899414i	$0.356007\pi$
$282$	29.0748	1.73138
$283$	−12.9458	−0.769551	−0.384775	−	0.923010i	$-0.625721\pi$
$283$	−12.9458	−0.769551	−0.384775	+	0.923010i	$0.625721\pi$
$284$	1.68835	0.100185
$285$	−9.45584	−0.560115
$286$	17.0958	1.01090
$287$	9.06622	0.535162
$288$	−18.5030	−1.09030
$289$	35.2886	2.07580
$290$	−10.0111	−0.587869
$291$	−29.3731	−1.72188
$292$	−24.2340	−1.41819
$293$	16.5919	0.969307	0.484654	−	0.874706i	$-0.338946\pi$
$293$	16.5919	0.969307	0.484654	+	0.874706i	$0.338946\pi$
$294$	−19.6319	−1.14496
$295$	−22.1314	−1.28854
$296$	−19.8835	−1.15571
$297$	−16.4304	−0.953389
$298$	15.4839	0.896955
$299$	0.751482	0.0434593
$300$	−75.3936	−4.35285
$301$	−11.5887	−0.667959
$302$	−1.18918	−0.0684294
$303$	−25.1685	−1.44589
$304$	6.13510	0.351872
$305$	33.4657	1.91624
$306$	91.5636	5.23434
$307$	11.9141	0.679976	0.339988	−	0.940430i	$-0.389577\pi$
$307$	11.9141	0.679976	0.339988	+	0.940430i	$0.389577\pi$
$308$	25.5289	1.45464
$309$	20.9518	1.19191
$310$	12.2418	0.695285
$311$	4.33724	0.245942	0.122971	−	0.992410i	$-0.460758\pi$
$311$	4.33724	0.245942	0.122971	+	0.992410i	$0.460758\pi$
$312$	−39.6401	−2.24418
$313$	−18.2650	−1.03240	−0.516199	−	0.856469i	$-0.672653\pi$
$313$	−18.2650	−1.03240	−0.516199	+	0.856469i	$0.672653\pi$
$314$	54.3956	3.06972
$315$	34.5944	1.94917
$316$	−24.6087	−1.38435
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−34.2828	−1.92249
$319$	3.40380	0.190576
$320$	−10.0454	−0.561552
$321$	13.1650	0.734797
$322$	1.63968	0.0913755
$323$	−7.23109	−0.402348
$324$	5.25574	0.291986
$325$	−14.5874	−0.809165
$326$	−39.6022	−2.19336
$327$	−11.4099	−0.630968
$328$	−25.8776	−1.42885
$329$	8.40047	0.463133
$330$	67.9831	3.74235
$331$	6.02470	0.331147	0.165574	−	0.986197i	$-0.447052\pi$
$331$	6.02470	0.331147	0.165574	+	0.986197i	$0.447052\pi$
$332$	22.7112	1.24644
$333$	17.0015	0.931679
$334$	−37.4366	−2.04844
$335$	−46.3404	−2.53185
$336$	−35.8320	−1.95480
$337$	−10.7988	−0.588250	−0.294125	−	0.955767i	$-0.595028\pi$
$337$	−10.7988	−0.588250	−0.294125	+	0.955767i	$0.595028\pi$
$338$	18.4916	1.00581
$339$	24.9760	1.35651
$340$	−104.646	−5.67525
$341$	−4.16225	−0.225398
$342$	−12.6625	−0.684709
$343$	−20.0995	−1.08527
$344$	33.0774	1.78341
$345$	2.98834	0.160887
$346$	29.3768	1.57930
$347$	−16.6283	−0.892654	−0.446327	−	0.894870i	$-0.647268\pi$
$347$	−16.6283	−0.892654	−0.446327	+	0.894870i	$0.647268\pi$
$348$	−14.6469	−0.785156
$349$	−12.2205	−0.654148	−0.327074	−	0.944999i	$-0.606063\pi$
$349$	−12.2205	−0.654148	−0.327074	+	0.944999i	$0.606063\pi$
$350$	−31.8286	−1.70131
$351$	13.6796	0.730165
$352$	−10.5057	−0.559953
$353$	16.1899	0.861700	0.430850	−	0.902424i	$-0.358214\pi$
$353$	16.1899	0.861700	0.430850	+	0.902424i	$0.358214\pi$
$354$	−47.3120	−2.51460
$355$	1.29903	0.0689454
$356$	−22.1322	−1.17300
$357$	42.2331	2.23521
$358$	8.01677	0.423700
$359$	−10.5160	−0.555013	−0.277507	−	0.960724i	$-0.589508\pi$
$359$	−10.5160	−0.555013	−0.277507	+	0.960724i	$0.589508\pi$
$360$	−98.7423	−5.20418
$361$	1.00000	0.0526316
$362$	33.7883	1.77588
$363$	8.05671	0.422868
$364$	−21.2549	−1.11406
$365$	−18.6458	−0.975965
$366$	71.5422	3.73957
$367$	8.93005	0.466145	0.233072	−	0.972459i	$-0.425122\pi$
$367$	8.93005	0.466145	0.233072	+	0.972459i	$0.425122\pi$
$368$	−1.93889	−0.101071
$369$	22.1268	1.15187
$370$	−28.3914	−1.47600
$371$	−9.90521	−0.514253
$372$	17.9106	0.928620
$373$	−25.2771	−1.30880	−0.654399	−	0.756149i	$-0.727078\pi$
$373$	−25.2771	−1.30880	−0.654399	+	0.756149i	$0.727078\pi$
$374$	51.9882	2.68825
$375$	−10.7292	−0.554051
$376$	−23.9773	−1.23654
$377$	−2.83394	−0.145955
$378$	29.8479	1.53521
$379$	27.8727	1.43172	0.715862	−	0.698242i	$-0.246034\pi$
$379$	27.8727	1.43172	0.715862	+	0.698242i	$0.246034\pi$
$380$	14.4717	0.742385
$381$	−5.20187	−0.266500
$382$	−59.1697	−3.02739
$383$	17.8849	0.913876	0.456938	−	0.889499i	$-0.348946\pi$
$383$	17.8849	0.913876	0.456938	+	0.889499i	$0.348946\pi$
$384$	−42.3222	−2.15974
$385$	19.6421	1.00105
$386$	−7.45154	−0.379274
$387$	−28.2830	−1.43771
$388$	44.9542	2.28220
$389$	−30.8292	−1.56310	−0.781550	−	0.623842i	$-0.785571\pi$
$389$	−30.8292	−1.56310	−0.781550	+	0.623842i	$0.785571\pi$
$390$	−56.6014	−2.86613
$391$	2.28525	0.115570
$392$	16.1900	0.817720
$393$	11.0967	0.559752
$394$	22.1364	1.11522
$395$	−18.9341	−0.952678
$396$	62.3052	3.13095
$397$	4.97645	0.249761	0.124881	−	0.992172i	$-0.460145\pi$
$397$	4.97645	0.249761	0.124881	+	0.992172i	$0.460145\pi$
$398$	14.8674	0.745237
$399$	−5.84049	−0.292390
$400$	37.6368	1.88184
$401$	−30.7182	−1.53400	−0.766998	−	0.641650i	$-0.778250\pi$
$401$	−30.7182	−1.53400	−0.766998	+	0.641650i	$0.778250\pi$
$402$	−99.0654	−4.94094
$403$	3.46540	0.172624
$404$	38.5193	1.91641
$405$	4.04381	0.200938
$406$	−6.18343	−0.306878
$407$	9.65318	0.478491
$408$	−120.545	−5.96788
$409$	−23.1097	−1.14270	−0.571351	−	0.820706i	$-0.693580\pi$
$409$	−23.1097	−1.14270	−0.571351	+	0.820706i	$0.693580\pi$
$410$	−36.9502	−1.82484
$411$	40.4908	1.99726
$412$	−32.0658	−1.57977
$413$	−13.6697	−0.672640
$414$	4.00175	0.196675
$415$	17.4742	0.857773
$416$	8.74681	0.428847
$417$	16.8997	0.827583
$418$	−7.18954	−0.351652
$419$	38.1024	1.86142	0.930712	−	0.365754i	$-0.119189\pi$
$419$	38.1024	1.86142	0.930712	+	0.365754i	$0.119189\pi$
$420$	−84.5221	−4.12425
$421$	8.85662	0.431645	0.215823	−	0.976433i	$-0.430757\pi$
$421$	8.85662	0.431645	0.215823	+	0.976433i	$0.430757\pi$
$422$	30.9008	1.50423
$423$	20.5020	0.996839
$424$	28.2723	1.37302
$425$	−44.3603	−2.15179
$426$	2.77704	0.134548
$427$	20.6704	1.00031
$428$	−20.1484	−0.973911
$429$	19.2447	0.929143
$430$	47.2306	2.27766
$431$	29.0196	1.39782	0.698912	−	0.715208i	$-0.253668\pi$
$431$	29.0196	1.39782	0.698912	+	0.715208i	$0.253668\pi$
$432$	−35.2946	−1.69811
$433$	33.4243	1.60627	0.803134	−	0.595799i	$-0.203164\pi$
$433$	33.4243	1.60627	0.803134	+	0.595799i	$0.203164\pi$
$434$	7.56124	0.362951
$435$	−11.2694	−0.540328
$436$	17.4623	0.836294
$437$	−0.316032	−0.0151178
$438$	−39.8605	−1.90461
$439$	−4.05763	−0.193660	−0.0968301	−	0.995301i	$-0.530870\pi$
$439$	−4.05763	−0.193660	−0.0968301	+	0.995301i	$0.530870\pi$
$440$	−56.0642	−2.67275
$441$	−13.8434	−0.659208
$442$	−43.2844	−2.05883
$443$	−6.40351	−0.304240	−0.152120	−	0.988362i	$-0.548610\pi$
$443$	−6.40351	−0.304240	−0.152120	+	0.988362i	$0.548610\pi$
$444$	−41.5387	−1.97134
$445$	−17.0287	−0.807236
$446$	−51.9925	−2.46192
$447$	17.4301	0.824418
$448$	−6.20461	−0.293140
$449$	5.23650	0.247126	0.123563	−	0.992337i	$-0.460568\pi$
$449$	5.23650	0.247126	0.123563	+	0.992337i	$0.460568\pi$
$450$	−77.6801	−3.66187
$451$	12.5632	0.591578
$452$	−38.2247	−1.79794
$453$	−1.33865	−0.0628954
$454$	52.3357	2.45624
$455$	−16.3536	−0.766670
$456$	16.6704	0.780664
$457$	−35.7811	−1.67377	−0.836885	−	0.547379i	$-0.815626\pi$
$457$	−35.7811	−1.67377	−0.836885	+	0.547379i	$0.815626\pi$
$458$	22.3994	1.04665
$459$	41.5997	1.94171
$460$	−4.57353	−0.213242
$461$	−24.3719	−1.13511	−0.567555	−	0.823335i	$-0.692111\pi$
$461$	−24.3719	−1.13511	−0.567555	+	0.823335i	$0.692111\pi$
$462$	41.9904	1.95357
$463$	−21.6557	−1.00642	−0.503212	−	0.864163i	$-0.667848\pi$
$463$	−21.6557	−1.00642	−0.503212	+	0.864163i	$0.667848\pi$
$464$	7.31179	0.339441
$465$	13.7805	0.639056
$466$	−3.19231	−0.147881
$467$	0.443365	0.0205165	0.0102582	−	0.999947i	$-0.496735\pi$
$467$	0.443365	0.0205165	0.0102582	+	0.999947i	$0.496735\pi$
$468$	−51.8741	−2.39788
$469$	−28.6226	−1.32167
$470$	−34.2368	−1.57923
$471$	61.2331	2.82147
$472$	39.0171	1.79591
$473$	−16.0586	−0.738375
$474$	−40.4769	−1.85916
$475$	6.13466	0.281478
$476$	−64.6359	−2.96258
$477$	−24.1744	−1.10687
$478$	−29.8868	−1.36699
$479$	4.23704	0.193595	0.0967977	−	0.995304i	$-0.469140\pi$
$479$	4.23704	0.193595	0.0967977	+	0.995304i	$0.469140\pi$
$480$	34.7825	1.58760
$481$	−8.03705	−0.366458
$482$	49.0892	2.23595
$483$	1.84578	0.0839859
$484$	−12.3304	−0.560475
$485$	34.5881	1.57056
$486$	−34.8010	−1.57860
$487$	15.1256	0.685406	0.342703	−	0.939444i	$-0.388657\pi$
$487$	15.1256	0.685406	0.342703	+	0.939444i	$0.388657\pi$
$488$	−58.9992	−2.67077
$489$	−44.5801	−2.01598
$490$	23.1175	1.04434
$491$	28.9013	1.30430	0.652149	−	0.758091i	$-0.273868\pi$
$491$	28.9013	1.30430	0.652149	+	0.758091i	$0.273868\pi$
$492$	−54.0608	−2.43725
$493$	−8.61798	−0.388134
$494$	5.98587	0.269317
$495$	47.9380	2.15465
$496$	−8.94103	−0.401464
$497$	0.802359	0.0359907
$498$	37.3559	1.67396
$499$	18.3325	0.820677	0.410339	−	0.911933i	$-0.365410\pi$
$499$	18.3325	0.820677	0.410339	+	0.911933i	$0.365410\pi$
$500$	16.4205	0.734348
$501$	−42.1423	−1.88278
$502$	−50.2339	−2.24205
$503$	−17.1589	−0.765078	−0.382539	−	0.923939i	$-0.624950\pi$
$503$	−17.1589	−0.765078	−0.382539	+	0.923939i	$0.624950\pi$
$504$	−60.9892	−2.71667
$505$	29.6370	1.31883
$506$	2.27212	0.101008
$507$	20.8160	0.924470
$508$	7.96123	0.353223
$509$	−12.6983	−0.562843	−0.281421	−	0.959584i	$-0.590806\pi$
$509$	−12.6983	−0.562843	−0.281421	+	0.959584i	$0.590806\pi$
$510$	−172.125	−7.62180
$511$	−11.5167	−0.509471
$512$	49.6158	2.19273
$513$	−5.75290	−0.253997
$514$	−15.3507	−0.677090
$515$	−24.6717	−1.08716
$516$	69.1018	3.04204
$517$	11.6407	0.511956
$518$	−17.5362	−0.770497
$519$	33.0694	1.45158
$520$	46.6779	2.04696
$521$	−25.7858	−1.12970	−0.564849	−	0.825194i	$-0.691066\pi$
$521$	−25.7858	−1.12970	−0.564849	+	0.825194i	$0.691066\pi$
$522$	−15.0911	−0.660520
$523$	21.0851	0.921989	0.460994	−	0.887403i	$-0.347493\pi$
$523$	21.0851	0.921989	0.460994	+	0.887403i	$0.347493\pi$
$524$	−16.9829	−0.741904
$525$	−35.8294	−1.56372
$526$	−6.64984	−0.289947
$527$	10.5383	0.459054
$528$	−49.6529	−2.16087
$529$	−22.9001	−0.995658
$530$	40.3695	1.75354
$531$	−33.3618	−1.44778
$532$	8.93861	0.387538
$533$	−10.4599	−0.453068
$534$	−36.4035	−1.57533
$535$	−15.5023	−0.670224
$536$	81.6971	3.52878
$537$	9.02447	0.389435
$538$	40.7100	1.75513
$539$	−7.86003	−0.338555
$540$	−83.2544	−3.58270
$541$	15.1819	0.652719	0.326360	−	0.945246i	$-0.394178\pi$
$541$	15.1819	0.652719	0.326360	+	0.945246i	$0.394178\pi$
$542$	36.7228	1.57738
$543$	38.0355	1.63226
$544$	26.5990	1.14042
$545$	13.4356	0.575520
$546$	−34.9604	−1.49617
$547$	30.5004	1.30410	0.652052	−	0.758174i	$-0.273908\pi$
$547$	30.5004	1.30410	0.652052	+	0.758174i	$0.273908\pi$
$548$	−61.9694	−2.64720
$549$	50.4476	2.15305
$550$	−44.1054	−1.88066
$551$	1.19180	0.0507722
$552$	−5.26838	−0.224237
$553$	−11.6948	−0.497315
$554$	26.9909	1.14673
$555$	−31.9601	−1.35663
$556$	−25.8643	−1.09689
$557$	22.1642	0.939128	0.469564	−	0.882899i	$-0.344411\pi$
$557$	22.1642	0.939128	0.469564	+	0.882899i	$0.344411\pi$
$558$	18.4538	0.781210
$559$	13.3701	0.565494
$560$	42.1937	1.78301
$561$	58.5230	2.47084
$562$	−36.8893	−1.55608
$563$	−18.4363	−0.776999	−0.388499	−	0.921449i	$-0.627006\pi$
$563$	−18.4363	−0.776999	−0.388499	+	0.921449i	$0.627006\pi$
$564$	−50.0910	−2.10921
$565$	−29.4104	−1.23730
$566$	32.5889	1.36981
$567$	2.49770	0.104893
$568$	−2.29016	−0.0960930
$569$	44.0428	1.84637	0.923186	−	0.384354i	$-0.125576\pi$
$569$	44.0428	1.84637	0.923186	+	0.384354i	$0.125576\pi$
$570$	23.8034	0.997016
$571$	2.67850	0.112092	0.0560459	−	0.998428i	$-0.482151\pi$
$571$	2.67850	0.112092	0.0560459	+	0.998428i	$0.482151\pi$
$572$	−29.4532	−1.23150
$573$	−66.6073	−2.78256
$574$	−22.8226	−0.952598
$575$	−1.93875	−0.0808513
$576$	−15.1428	−0.630950
$577$	−37.3972	−1.55687	−0.778433	−	0.627728i	$-0.783985\pi$
$577$	−37.3972	−1.55687	−0.778433	+	0.627728i	$0.783985\pi$
$578$	−88.8329	−3.69496
$579$	−8.38819	−0.348601
$580$	17.2474	0.716158
$581$	10.7931	0.447773
$582$	73.9416	3.06498
$583$	−13.7258	−0.568464
$584$	32.8721	1.36026
$585$	−39.9123	−1.65017
$586$	−41.7671	−1.72538
$587$	−0.859580	−0.0354787	−0.0177393	−	0.999843i	$-0.505647\pi$
$587$	−0.859580	−0.0354787	−0.0177393	+	0.999843i	$0.505647\pi$
$588$	33.8225	1.39482
$589$	−1.45736	−0.0600493
$590$	55.7119	2.29362
$591$	24.9189	1.02503
$592$	20.7363	0.852255
$593$	47.1068	1.93444	0.967222	−	0.253931i	$-0.0817235\pi$
$593$	47.1068	1.93444	0.967222	+	0.253931i	$0.0817235\pi$
$594$	41.3607	1.69705
$595$	−49.7313	−2.03878
$596$	−26.6761	−1.09269
$597$	16.7362	0.684968
$598$	−1.89173	−0.0773584
$599$	−8.04107	−0.328549	−0.164275	−	0.986415i	$-0.552528\pi$
$599$	−8.04107	−0.328549	−0.164275	+	0.986415i	$0.552528\pi$
$600$	102.267	4.17505
$601$	−7.59123	−0.309653	−0.154826	−	0.987942i	$-0.549482\pi$
$601$	−7.59123	−0.309653	−0.154826	+	0.987942i	$0.549482\pi$
$602$	29.1724	1.18898
$603$	−69.8556	−2.84474
$604$	2.04875	0.0833625
$605$	−9.48713	−0.385707
$606$	63.3573	2.57371
$607$	−10.7070	−0.434582	−0.217291	−	0.976107i	$-0.569722\pi$
$607$	−10.7070	−0.434582	−0.217291	+	0.976107i	$0.569722\pi$
$608$	−3.67842	−0.149180
$609$	−6.96067	−0.282061
$610$	−84.2440	−3.41094
$611$	−9.69178	−0.392088
$612$	−157.749	−6.37661
$613$	−12.2557	−0.495002	−0.247501	−	0.968888i	$-0.579609\pi$
$613$	−12.2557	−0.495002	−0.247501	+	0.968888i	$0.579609\pi$
$614$	−29.9918	−1.21037
$615$	−41.5947	−1.67726
$616$	−34.6286	−1.39523
$617$	−13.3135	−0.535983	−0.267992	−	0.963421i	$-0.586360\pi$
$617$	−13.3135	−0.535983	−0.267992	+	0.963421i	$0.586360\pi$
$618$	−52.7425	−2.12161
$619$	−46.3705	−1.86379	−0.931895	−	0.362729i	$-0.881845\pi$
$619$	−46.3705	−1.86379	−0.931895	+	0.362729i	$0.881845\pi$
$620$	−21.0905	−0.847014
$621$	1.81810	0.0729577
$622$	−10.9182	−0.437782
$623$	−10.5179	−0.421391
$624$	41.3401	1.65493
$625$	−18.0392	−0.721570
$626$	45.9789	1.83769
$627$	−8.09326	−0.323214
$628$	−93.7146	−3.73962
$629$	−24.4406	−0.974511
$630$	−87.0854	−3.46957
$631$	5.27488	0.209990	0.104995	−	0.994473i	$-0.466517\pi$
$631$	5.27488	0.209990	0.104995	+	0.994473i	$0.466517\pi$
$632$	33.3804	1.32780
$633$	34.7849	1.38258
$634$	−2.51733	−0.0999758
$635$	6.12543	0.243080
$636$	59.0636	2.34202
$637$	6.54411	0.259287
$638$	−8.56847	−0.339229
$639$	1.95822	0.0774658
$640$	49.8362	1.96995
$641$	11.3882	0.449806	0.224903	−	0.974381i	$-0.427794\pi$
$641$	11.3882	0.449806	0.224903	+	0.974381i	$0.427794\pi$
$642$	−33.1405	−1.30795
$643$	−45.6395	−1.79985	−0.899923	−	0.436048i	$-0.856378\pi$
$643$	−45.6395	−1.79985	−0.899923	+	0.436048i	$0.856378\pi$
$644$	−2.82489	−0.111316
$645$	53.1674	2.09346
$646$	18.2030	0.716187
$647$	−27.7866	−1.09240	−0.546201	−	0.837654i	$-0.683927\pi$
$647$	−27.7866	−1.09240	−0.546201	+	0.837654i	$0.683927\pi$
$648$	−7.12914	−0.280059
$649$	−18.9423	−0.743549
$650$	36.7213	1.44033
$651$	8.51167	0.333599
$652$	68.2279	2.67201
$653$	5.26525	0.206045	0.103023	−	0.994679i	$-0.467149\pi$
$653$	5.26525	0.206045	0.103023	+	0.994679i	$0.467149\pi$
$654$	28.7224	1.12313
$655$	−13.0668	−0.510562
$656$	26.9873	1.05368
$657$	−28.1075	−1.09658
$658$	−21.1467	−0.824385
$659$	−8.62009	−0.335791	−0.167895	−	0.985805i	$-0.553697\pi$
$659$	−8.62009	−0.335791	−0.167895	+	0.985805i	$0.553697\pi$
$660$	−117.124	−4.55903
$661$	−16.9211	−0.658155	−0.329078	−	0.944303i	$-0.606738\pi$
$661$	−16.9211	−0.658155	−0.329078	+	0.944303i	$0.606738\pi$
$662$	−15.1661	−0.589448
$663$	−48.7251	−1.89233
$664$	−30.8066	−1.19553
$665$	6.87743	0.266695
$666$	−42.7984	−1.65841
$667$	−0.376645	−0.0145838
$668$	64.4970	2.49546
$669$	−58.5279	−2.26282
$670$	116.654	4.50673
$671$	28.6433	1.10576
$672$	21.4838	0.828755
$673$	−33.9234	−1.30765	−0.653825	−	0.756646i	$-0.726837\pi$
$673$	−33.9234	−1.30765	−0.653825	+	0.756646i	$0.726837\pi$
$674$	27.1842	1.04710
$675$	−35.2921	−1.35839
$676$	−31.8579	−1.22531
$677$	39.3006	1.51045	0.755223	−	0.655468i	$-0.227528\pi$
$677$	39.3006	1.51045	0.755223	+	0.655468i	$0.227528\pi$
$678$	−62.8728	−2.41462
$679$	21.3637	0.819862
$680$	141.947	5.44343
$681$	58.9142	2.25760
$682$	10.4777	0.401213
$683$	51.8986	1.98584	0.992922	−	0.118772i	$-0.0378958\pi$
$683$	51.8986	1.98584	0.992922	+	0.118772i	$0.0378958\pi$
$684$	21.8153	0.834131
$685$	−47.6797	−1.82175
$686$	50.5970	1.93180
$687$	25.2149	0.962009
$688$	−34.4959	−1.31514
$689$	11.4278	0.435366
$690$	−7.52264	−0.286382
$691$	−20.6616	−0.786003	−0.393002	−	0.919538i	$-0.628563\pi$
$691$	−20.6616	−0.786003	−0.393002	+	0.919538i	$0.628563\pi$
$692$	−50.6112	−1.92395
$693$	29.6094	1.12477
$694$	41.8588	1.58894
$695$	−19.9002	−0.754856
$696$	19.8677	0.753085
$697$	−31.8084	−1.20483
$698$	30.7630	1.16439
$699$	−3.59357	−0.135921
$700$	54.8354	2.07258
$701$	12.2817	0.463875	0.231937	−	0.972731i	$-0.425494\pi$
$701$	12.2817	0.463875	0.231937	+	0.972731i	$0.425494\pi$
$702$	−34.4361	−1.29971
$703$	3.37994	0.127477
$704$	−8.59783	−0.324043
$705$	−38.5403	−1.45151
$706$	−40.7552	−1.53384
$707$	18.3056	0.688452
$708$	81.5106	3.06335
$709$	−3.41006	−0.128067	−0.0640337	−	0.997948i	$-0.520397\pi$
$709$	−3.41006	−0.128067	−0.0640337	+	0.997948i	$0.520397\pi$
$710$	−3.27008	−0.122724
$711$	−28.5421	−1.07041
$712$	30.0211	1.12509
$713$	0.460571	0.0172485
$714$	−106.314	−3.97872
$715$	−22.6615	−0.847492
$716$	−13.8116	−0.516162
$717$	−33.6435	−1.25644
$718$	26.4722	0.987934
$719$	−37.4928	−1.39824	−0.699122	−	0.715002i	$-0.746426\pi$
$719$	−37.4928	−1.39824	−0.699122	+	0.715002i	$0.746426\pi$
$720$	102.977	3.83772
$721$	−15.2387	−0.567518
$722$	−2.51733	−0.0936852
$723$	55.2596	2.05513
$724$	−58.2116	−2.16342
$725$	7.31126	0.271534
$726$	−20.2814	−0.752712
$727$	21.9878	0.815483	0.407742	−	0.913097i	$-0.366316\pi$
$727$	21.9878	0.815483	0.407742	+	0.913097i	$0.366316\pi$
$728$	28.8311	1.06855
$729$	−42.8110	−1.58559
$730$	46.9375	1.73724
$731$	40.6583	1.50380
$732$	−123.255	−4.55564
$733$	52.6812	1.94582	0.972912	−	0.231174i	$-0.0742568\pi$
$733$	52.6812	1.94582	0.972912	+	0.231174i	$0.0742568\pi$
$734$	−22.4799	−0.829747
$735$	26.0233	0.959884
$736$	1.16250	0.0428502
$737$	−39.6628	−1.46100
$738$	−55.7003	−2.05036
$739$	−6.87693	−0.252972	−0.126486	−	0.991968i	$-0.540370\pi$
$739$	−6.87693	−0.252972	−0.126486	+	0.991968i	$0.540370\pi$
$740$	48.9136	1.79810
$741$	6.73829	0.247537
$742$	24.9346	0.915379
$743$	7.92730	0.290825	0.145412	−	0.989371i	$-0.453549\pi$
$743$	7.92730	0.290825	0.145412	+	0.989371i	$0.453549\pi$
$744$	−24.2947	−0.890689
$745$	−20.5248	−0.751969
$746$	63.6307	2.32969
$747$	26.3413	0.963779
$748$	−89.5669	−3.27489
$749$	−9.57517	−0.349869
$750$	27.0088	0.986222
$751$	−38.6399	−1.40999	−0.704996	−	0.709212i	$-0.749051\pi$
$751$	−38.6399	−1.40999	−0.704996	+	0.709212i	$0.749051\pi$
$752$	25.0056	0.911861
$753$	−56.5482	−2.06073
$754$	7.13394	0.259803
$755$	1.57632	0.0573683
$756$	−51.4229	−1.87023
$757$	−49.8983	−1.81359	−0.906793	−	0.421577i	$-0.861477\pi$
$757$	−49.8983	−1.81359	−0.906793	+	0.421577i	$0.861477\pi$
$758$	−70.1647	−2.54850
$759$	2.55773	0.0928396
$760$	−19.6302	−0.712060
$761$	26.6253	0.965166	0.482583	−	0.875850i	$-0.339699\pi$
$761$	26.6253	0.965166	0.482583	+	0.875850i	$0.339699\pi$
$762$	13.0948	0.474374
$763$	8.29865	0.300431
$764$	101.940	3.68804
$765$	−121.373	−4.38825
$766$	−45.0221	−1.62672
$767$	15.7710	0.569456
$768$	89.4772	3.22873
$769$	2.49845	0.0900964	0.0450482	−	0.998985i	$-0.485656\pi$
$769$	2.49845	0.0900964	0.0450482	+	0.998985i	$0.485656\pi$
$770$	−49.4456	−1.78190
$771$	−17.2803	−0.622333
$772$	12.8378	0.462041
$773$	−23.9055	−0.859823	−0.429911	−	0.902871i	$-0.641455\pi$
$773$	−23.9055	−0.859823	−0.429911	+	0.902871i	$0.641455\pi$
$774$	71.1975	2.55914
$775$	−8.94039	−0.321148
$776$	−60.9780	−2.18898
$777$	−19.7405	−0.708186
$778$	77.6070	2.78235
$779$	4.39884	0.157605
$780$	97.5148	3.49159
$781$	1.11184	0.0397848
$782$	−5.75272	−0.205717
$783$	−6.85628	−0.245023
$784$	−16.8843	−0.603012
$785$	−72.1046	−2.57352
$786$	−27.9339	−0.996369
$787$	2.59805	0.0926106	0.0463053	−	0.998927i	$-0.485255\pi$
$787$	2.59805	0.0926106	0.0463053	+	0.998927i	$0.485255\pi$
$788$	−38.1373	−1.35859
$789$	−7.48571	−0.266498
$790$	47.6633	1.69578
$791$	−18.1656	−0.645894
$792$	−84.5136	−3.00306
$793$	−23.8479	−0.846862
$794$	−12.5274	−0.444579
$795$	45.4439	1.61173
$796$	−25.6141	−0.907867
$797$	−55.4396	−1.96377	−0.981886	−	0.189471i	$-0.939323\pi$
$797$	−55.4396	−1.96377	−0.981886	+	0.189471i	$0.939323\pi$
$798$	14.7024	0.520460
$799$	−29.4726	−1.04267
$800$	−22.5659	−0.797824
$801$	−25.6697	−0.906996
$802$	77.3278	2.73054
$803$	−15.9589	−0.563179
$804$	170.673	6.01918
$805$	−2.17349	−0.0766053
$806$	−8.72355	−0.307274
$807$	45.8272	1.61319
$808$	−52.2493	−1.83813
$809$	19.0125	0.668443	0.334222	−	0.942494i	$-0.391527\pi$
$809$	19.0125	0.668443	0.334222	+	0.942494i	$0.391527\pi$
$810$	−10.1796	−0.357674
$811$	24.5086	0.860615	0.430307	−	0.902682i	$-0.358405\pi$
$811$	24.5086	0.860615	0.430307	+	0.902682i	$0.358405\pi$
$812$	10.6530	0.373847
$813$	41.3388	1.44982
$814$	−24.3002	−0.851722
$815$	52.4950	1.83882
$816$	125.715	4.40090
$817$	−5.62271	−0.196714
$818$	58.1747	2.03403
$819$	−24.6522	−0.861417
$820$	63.6589	2.22307
$821$	22.3415	0.779724	0.389862	−	0.920873i	$-0.372523\pi$
$821$	22.3415	0.779724	0.389862	+	0.920873i	$0.372523\pi$
$822$	−101.929	−3.55517
$823$	38.1711	1.33056	0.665280	−	0.746594i	$-0.268312\pi$
$823$	38.1711	1.33056	0.665280	+	0.746594i	$0.268312\pi$
$824$	43.4956	1.51524
$825$	−49.6494	−1.72857
$826$	34.4110	1.19731
$827$	15.3735	0.534589	0.267295	−	0.963615i	$-0.413870\pi$
$827$	15.3735	0.534589	0.267295	+	0.963615i	$0.413870\pi$
$828$	−6.89434	−0.239595
$829$	31.7240	1.10182	0.550910	−	0.834565i	$-0.314281\pi$
$829$	31.7240	1.10182	0.550910	+	0.834565i	$0.314281\pi$
$830$	−43.9882	−1.52685
$831$	30.3836	1.05400
$832$	7.15838	0.248172
$833$	19.9006	0.689514
$834$	−42.5421	−1.47311
$835$	49.6244	1.71732
$836$	12.3864	0.428392
$837$	8.38402	0.289794
$838$	−95.9161	−3.31337
$839$	5.81725	0.200834	0.100417	−	0.994945i	$-0.467982\pi$
$839$	5.81725	0.200834	0.100417	+	0.994945i	$0.467982\pi$
$840$	114.650	3.95579
$841$	−27.5796	−0.951021
$842$	−22.2950	−0.768337
$843$	−41.5262	−1.43024
$844$	−53.2368	−1.83249
$845$	−24.5117	−0.843229
$846$	−51.6101	−1.77439
$847$	−5.85982	−0.201346
$848$	−29.4847	−1.01251
$849$	36.6853	1.25904
$850$	111.669	3.83022
$851$	−1.06817	−0.0366163
$852$	−4.78437	−0.163910
$853$	32.1403	1.10046	0.550231	−	0.835012i	$-0.314540\pi$
$853$	32.1403	1.10046	0.550231	+	0.835012i	$0.314540\pi$
$854$	−52.0341	−1.78057
$855$	16.7849	0.574031
$856$	27.3303	0.934129
$857$	54.8195	1.87260	0.936299	−	0.351205i	$-0.114228\pi$
$857$	54.8195	1.87260	0.936299	+	0.351205i	$0.114228\pi$
$858$	−48.4452	−1.65389
$859$	−10.0130	−0.341639	−0.170820	−	0.985302i	$-0.554642\pi$
$859$	−10.0130	−0.341639	−0.170820	+	0.985302i	$0.554642\pi$
$860$	−81.3704	−2.77471
$861$	−25.6914	−0.875560
$862$	−73.0517	−2.48815
$863$	−8.17804	−0.278384	−0.139192	−	0.990265i	$-0.544450\pi$
$863$	−8.17804	−0.278384	−0.139192	+	0.990265i	$0.544450\pi$
$864$	21.1616	0.719931
$865$	−38.9406	−1.32402
$866$	−84.1398	−2.85919
$867$	−99.9990	−3.39615
$868$	−13.0267	−0.442157
$869$	−16.2057	−0.549741
$870$	28.3688	0.961793
$871$	33.0225	1.11892
$872$	−23.6867	−0.802134
$873$	52.1396	1.76466
$874$	0.795555	0.0269100
$875$	7.80355	0.263808
$876$	68.6730	2.32025
$877$	−28.4073	−0.959247	−0.479624	−	0.877474i	$-0.659227\pi$
$877$	−28.4073	−0.959247	−0.479624	+	0.877474i	$0.659227\pi$
$878$	10.2144	0.344719
$879$	−47.0172	−1.58585
$880$	58.4685	1.97097
$881$	45.5256	1.53379	0.766897	−	0.641770i	$-0.221799\pi$
$881$	45.5256	1.53379	0.766897	+	0.641770i	$0.221799\pi$
$882$	34.8483	1.17340
$883$	46.6946	1.57140	0.785699	−	0.618609i	$-0.212303\pi$
$883$	46.6946	1.57140	0.785699	+	0.618609i	$0.212303\pi$
$884$	74.5717	2.50812
$885$	62.7148	2.10813
$886$	16.1197	0.541552
$887$	9.37380	0.314741	0.157371	−	0.987540i	$-0.449698\pi$
$887$	9.37380	0.314741	0.157371	+	0.987540i	$0.449698\pi$
$888$	56.3450	1.89081
$889$	3.78343	0.126892
$890$	42.8667	1.43689
$891$	3.46110	0.115951
$892$	89.5743	2.99917
$893$	4.07583	0.136392
$894$	−43.8774	−1.46748
$895$	−10.6267	−0.355212
$896$	30.7818	1.02835
$897$	−2.12951	−0.0711024
$898$	−13.1820	−0.439888
$899$	−1.73687	−0.0579279
$900$	133.830	4.46099
$901$	34.7520	1.15776
$902$	−31.6257	−1.05302
$903$	32.8394	1.09283
$904$	51.8498	1.72450
$905$	−44.7884	−1.48882
$906$	3.36983	0.111955
$907$	−51.2953	−1.70323	−0.851616	−	0.524167i	$-0.824377\pi$
$907$	−51.2953	−1.70323	−0.851616	+	0.524167i	$0.824377\pi$
$908$	−90.1656	−2.99225
$909$	44.6761	1.48181
$910$	41.1674	1.36469
$911$	−19.3696	−0.641743	−0.320872	−	0.947123i	$-0.603976\pi$
$911$	−19.3696	−0.641743	−0.320872	+	0.947123i	$0.603976\pi$
$912$	−17.3853	−0.575686
$913$	14.9562	0.494976
$914$	90.0727	2.97934
$915$	−94.8333	−3.13509
$916$	−38.5903	−1.27506
$917$	−8.07084	−0.266522
$918$	−104.720	−3.45627
$919$	−29.4985	−0.973064	−0.486532	−	0.873663i	$-0.661738\pi$
$919$	−29.4985	−0.973064	−0.486532	+	0.873663i	$0.661738\pi$
$920$	6.20375	0.204532
$921$	−33.7617	−1.11249
$922$	61.3519	2.02052
$923$	−0.925697	−0.0304697
$924$	−72.3425	−2.37989
$925$	20.7348	0.681755
$926$	54.5144	1.79145
$927$	−37.1911	−1.22152
$928$	−4.38393	−0.143909
$929$	22.5855	0.741007	0.370504	−	0.928831i	$-0.379185\pi$
$929$	22.5855	0.741007	0.370504	+	0.928831i	$0.379185\pi$
$930$	−34.6901	−1.13753
$931$	−2.75209	−0.0901960
$932$	5.49981	0.180152
$933$	−12.2906	−0.402378
$934$	−1.11609	−0.0365197
$935$	−68.9134	−2.25371
$936$	70.3644	2.29993
$937$	−13.6867	−0.447125	−0.223563	−	0.974690i	$-0.571769\pi$
$937$	−13.6867	−0.447125	−0.223563	+	0.974690i	$0.571769\pi$
$938$	72.0524	2.35259
$939$	51.7584	1.68907
$940$	58.9843	1.92386
$941$	−14.1083	−0.459918	−0.229959	−	0.973200i	$-0.573859\pi$
$941$	−14.1083	−0.459918	−0.229959	+	0.973200i	$0.573859\pi$
$942$	−154.144	−5.02227
$943$	−1.39017	−0.0452703
$944$	−40.6904	−1.32436
$945$	−39.5651	−1.28705
$946$	40.4247	1.31432
$947$	−6.99192	−0.227207	−0.113603	−	0.993526i	$-0.536239\pi$
$947$	−6.99192	−0.227207	−0.113603	+	0.993526i	$0.536239\pi$
$948$	69.7349	2.26488
$949$	13.2871	0.431318
$950$	−15.4429	−0.501035
$951$	−2.83375	−0.0918906
$952$	87.6751	2.84157
$953$	−16.4224	−0.531973	−0.265986	−	0.963977i	$-0.585698\pi$
$953$	−16.4224	−0.531973	−0.265986	+	0.963977i	$0.585698\pi$
$954$	60.8548	1.97025
$955$	78.4330	2.53803
$956$	51.4899	1.66530
$957$	−9.64551	−0.311795
$958$	−10.6660	−0.344603
$959$	−29.4498	−0.950984
$960$	28.4660	0.918737
$961$	−28.8761	−0.931487
$962$	20.2319	0.652302
$963$	−23.3689	−0.753052
$964$	−84.5724	−2.72389
$965$	9.87746	0.317967
$966$	−4.64643	−0.149496
$967$	11.8438	0.380870	0.190435	−	0.981700i	$-0.439010\pi$
$967$	11.8438	0.380870	0.190435	+	0.981700i	$0.439010\pi$
$968$	16.7256	0.537581
$969$	20.4911	0.658268
$970$	−87.0694	−2.79563
$971$	2.88057	0.0924420	0.0462210	−	0.998931i	$-0.485282\pi$
$971$	2.88057	0.0924420	0.0462210	+	0.998931i	$0.485282\pi$
$972$	59.9563	1.92310
$973$	−12.2915	−0.394048
$974$	−38.0761	−1.22004
$975$	41.3371	1.32385
$976$	61.5294	1.96951
$977$	6.43191	0.205775	0.102887	−	0.994693i	$-0.467192\pi$
$977$	6.43191	0.205775	0.102887	+	0.994693i	$0.467192\pi$
$978$	112.223	3.58849
$979$	−14.5748	−0.465814
$980$	−39.8275	−1.27224
$981$	20.2535	0.646644
$982$	−72.7540	−2.32167
$983$	43.1600	1.37659	0.688295	−	0.725431i	$-0.258360\pi$
$983$	43.1600	1.37659	0.688295	+	0.725431i	$0.258360\pi$
$984$	73.3306	2.33769
$985$	−29.3431	−0.934950
$986$	21.6943	0.690886
$987$	−23.8048	−0.757716
$988$	−10.3127	−0.328089
$989$	1.77695	0.0565039
$990$	−120.676	−3.83532
$991$	−13.8840	−0.441041	−0.220520	−	0.975382i	$-0.570776\pi$
$991$	−13.8840	−0.441041	−0.220520	+	0.975382i	$0.570776\pi$
$992$	5.36077	0.170205
$993$	−17.0725	−0.541779
$994$	−2.01980	−0.0640641
$995$	−19.7076	−0.624774
$996$	−64.3579	−2.03926
$997$	43.1791	1.36750	0.683748	−	0.729718i	$-0.260349\pi$
$997$	43.1791	1.36750	0.683748	+	0.729718i	$0.260349\pi$
$998$	−46.1490	−1.46082
$999$	−19.4444	−0.615195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.7	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-2.51733 q^{2} -2.83375 q^{3} +4.33693 q^{4} +3.33686 q^{5} +7.13347 q^{6} +2.06105 q^{7} -5.88281 q^{8} +5.03014 q^{9} +O(q^{10})\)	\(q-2.51733 q^{2} -2.83375 q^{3} +4.33693 q^{4} +3.33686 q^{5} +7.13347 q^{6} +2.06105 q^{7} -5.88281 q^{8} +5.03014 q^{9} -8.39997 q^{10} +2.85602 q^{11} -12.2898 q^{12} -2.37787 q^{13} -5.18833 q^{14} -9.45584 q^{15} +6.13510 q^{16} -7.23109 q^{17} -12.6625 q^{18} +1.00000 q^{19} +14.4717 q^{20} -5.84049 q^{21} -7.18954 q^{22} -0.316032 q^{23} +16.6704 q^{24} +6.13466 q^{25} +5.98587 q^{26} -5.75290 q^{27} +8.93861 q^{28} +1.19180 q^{29} +23.8034 q^{30} -1.45736 q^{31} -3.67842 q^{32} -8.09326 q^{33} +18.2030 q^{34} +6.87743 q^{35} +21.8153 q^{36} +3.37994 q^{37} -2.51733 q^{38} +6.73829 q^{39} -19.6302 q^{40} +4.39884 q^{41} +14.7024 q^{42} -5.62271 q^{43} +12.3864 q^{44} +16.7849 q^{45} +0.795555 q^{46} +4.07583 q^{47} -17.3853 q^{48} -2.75209 q^{49} -15.4429 q^{50} +20.4911 q^{51} -10.3127 q^{52} -4.80591 q^{53} +14.4819 q^{54} +9.53016 q^{55} -12.1248 q^{56} -2.83375 q^{57} -3.00014 q^{58} -6.63239 q^{59} -41.0093 q^{60} +10.0291 q^{61} +3.66864 q^{62} +10.3673 q^{63} -3.01042 q^{64} -7.93463 q^{65} +20.3734 q^{66} -13.8874 q^{67} -31.3607 q^{68} +0.895555 q^{69} -17.3127 q^{70} +0.389297 q^{71} -29.5914 q^{72} -5.58782 q^{73} -8.50841 q^{74} -17.3841 q^{75} +4.33693 q^{76} +5.88640 q^{77} -16.9625 q^{78} -5.67422 q^{79} +20.4720 q^{80} +1.21186 q^{81} -11.0733 q^{82} +5.23670 q^{83} -25.3298 q^{84} -24.1291 q^{85} +14.1542 q^{86} -3.37725 q^{87} -16.8015 q^{88} -5.10319 q^{89} -42.2530 q^{90} -4.90090 q^{91} -1.37061 q^{92} +4.12978 q^{93} -10.2602 q^{94} +3.33686 q^{95} +10.4237 q^{96} +10.3654 q^{97} +6.92790 q^{98} +14.3662 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 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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