LMFDB - Embedded newform 6023.2.a.a.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.11992 q^{2} +0.896090 q^{3} +2.49404 q^{4} +2.73729 q^{5} -1.89963 q^{6} -3.12431 q^{7} -1.04733 q^{8} -2.19702 q^{9} +O(q^{10})$	\(q-2.11992 q^{2} +0.896090 q^{3} +2.49404 q^{4} +2.73729 q^{5} -1.89963 q^{6} -3.12431 q^{7} -1.04733 q^{8} -2.19702 q^{9} -5.80282 q^{10} -3.68688 q^{11} +2.23489 q^{12} +2.88557 q^{13} +6.62328 q^{14} +2.45285 q^{15} -2.76783 q^{16} +3.95274 q^{17} +4.65750 q^{18} +1.00000 q^{19} +6.82691 q^{20} -2.79966 q^{21} +7.81587 q^{22} +1.84581 q^{23} -0.938503 q^{24} +2.49274 q^{25} -6.11716 q^{26} -4.65700 q^{27} -7.79217 q^{28} -2.64707 q^{29} -5.19985 q^{30} +2.61634 q^{31} +7.96224 q^{32} -3.30377 q^{33} -8.37948 q^{34} -8.55214 q^{35} -5.47947 q^{36} -2.33001 q^{37} -2.11992 q^{38} +2.58573 q^{39} -2.86685 q^{40} -7.72654 q^{41} +5.93505 q^{42} +9.00399 q^{43} -9.19523 q^{44} -6.01388 q^{45} -3.91297 q^{46} -8.86630 q^{47} -2.48023 q^{48} +2.76133 q^{49} -5.28440 q^{50} +3.54201 q^{51} +7.19673 q^{52} +12.7220 q^{53} +9.87245 q^{54} -10.0920 q^{55} +3.27219 q^{56} +0.896090 q^{57} +5.61156 q^{58} +4.98471 q^{59} +6.11753 q^{60} -6.55802 q^{61} -5.54642 q^{62} +6.86419 q^{63} -11.3436 q^{64} +7.89862 q^{65} +7.00372 q^{66} +1.54885 q^{67} +9.85831 q^{68} +1.65401 q^{69} +18.1298 q^{70} +4.02083 q^{71} +2.30101 q^{72} -5.80545 q^{73} +4.93943 q^{74} +2.23372 q^{75} +2.49404 q^{76} +11.5190 q^{77} -5.48152 q^{78} -6.95203 q^{79} -7.57635 q^{80} +2.41798 q^{81} +16.3796 q^{82} +14.8934 q^{83} -6.98249 q^{84} +10.8198 q^{85} -19.0877 q^{86} -2.37201 q^{87} +3.86138 q^{88} -7.21817 q^{89} +12.7489 q^{90} -9.01541 q^{91} +4.60354 q^{92} +2.34447 q^{93} +18.7958 q^{94} +2.73729 q^{95} +7.13488 q^{96} +1.20280 q^{97} -5.85378 q^{98} +8.10015 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.11992	−1.49901	−0.749503	−	0.662000i	$-0.769708\pi$
$2$	−2.11992	−1.49901	−0.749503	+	0.662000i	$0.769708\pi$
$3$	0.896090	0.517358	0.258679	−	0.965963i	$-0.416713\pi$
$3$	0.896090	0.517358	0.258679	+	0.965963i	$0.416713\pi$
$4$	2.49404	1.24702
$5$	2.73729	1.22415	0.612076	−	0.790799i	$-0.290335\pi$
$5$	2.73729	1.22415	0.612076	+	0.790799i	$0.290335\pi$
$6$	−1.89963	−0.775523
$7$	−3.12431	−1.18088	−0.590440	−	0.807082i	$-0.701046\pi$
$7$	−3.12431	−1.18088	−0.590440	+	0.807082i	$0.701046\pi$
$8$	−1.04733	−0.370288
$9$	−2.19702	−0.732341
$10$	−5.80282	−1.83501
$11$	−3.68688	−1.11163	−0.555817	−	0.831304i	$-0.687595\pi$
$11$	−3.68688	−1.11163	−0.555817	+	0.831304i	$0.687595\pi$
$12$	2.23489	0.645156
$13$	2.88557	0.800312	0.400156	−	0.916447i	$-0.368956\pi$
$13$	2.88557	0.800312	0.400156	+	0.916447i	$0.368956\pi$
$14$	6.62328	1.77015
$15$	2.45285	0.633324
$16$	−2.76783	−0.691958
$17$	3.95274	0.958680	0.479340	−	0.877629i	$-0.340876\pi$
$17$	3.95274	0.958680	0.479340	+	0.877629i	$0.340876\pi$
$18$	4.65750	1.09778
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	6.82691	1.52654
$21$	−2.79966	−0.610937
$22$	7.81587	1.66635
$23$	1.84581	0.384879	0.192439	−	0.981309i	$-0.438360\pi$
$23$	1.84581	0.384879	0.192439	+	0.981309i	$0.438360\pi$
$24$	−0.938503	−0.191571
$25$	2.49274	0.498548
$26$	−6.11716	−1.19967
$27$	−4.65700	−0.896240
$28$	−7.79217	−1.47258
$29$	−2.64707	−0.491548	−0.245774	−	0.969327i	$-0.579042\pi$
$29$	−2.64707	−0.491548	−0.245774	+	0.969327i	$0.579042\pi$
$30$	−5.19985	−0.949358
$31$	2.61634	0.469908	0.234954	−	0.972006i	$-0.424506\pi$
$31$	2.61634	0.469908	0.234954	+	0.972006i	$0.424506\pi$
$32$	7.96224	1.40754
$33$	−3.30377	−0.575113
$34$	−8.37948	−1.43707
$35$	−8.55214	−1.44558
$36$	−5.47947	−0.913245
$37$	−2.33001	−0.383052	−0.191526	−	0.981488i	$-0.561344\pi$
$37$	−2.33001	−0.383052	−0.191526	+	0.981488i	$0.561344\pi$
$38$	−2.11992	−0.343896
$39$	2.58573	0.414048
$40$	−2.86685	−0.453288
$41$	−7.72654	−1.20668	−0.603341	−	0.797483i	$-0.706164\pi$
$41$	−7.72654	−1.20668	−0.603341	+	0.797483i	$0.706164\pi$
$42$	5.93505	0.915799
$43$	9.00399	1.37310	0.686548	−	0.727084i	$-0.259125\pi$
$43$	9.00399	1.37310	0.686548	+	0.727084i	$0.259125\pi$
$44$	−9.19523	−1.38623
$45$	−6.01388	−0.896497
$46$	−3.91297	−0.576936
$47$	−8.86630	−1.29328	−0.646641	−	0.762794i	$-0.723827\pi$
$47$	−8.86630	−1.29328	−0.646641	+	0.762794i	$0.723827\pi$
$48$	−2.48023	−0.357990
$49$	2.76133	0.394475
$50$	−5.28440	−0.747326
$51$	3.54201	0.495981
$52$	7.19673	0.998007
$53$	12.7220	1.74750	0.873751	−	0.486374i	$-0.161681\pi$
$53$	12.7220	1.74750	0.873751	+	0.486374i	$0.161681\pi$
$54$	9.87245	1.34347
$55$	−10.0920	−1.36081
$56$	3.27219	0.437265
$57$	0.896090	0.118690
$58$	5.61156	0.736834
$59$	4.98471	0.648954	0.324477	−	0.945894i	$-0.394812\pi$
$59$	4.98471	0.648954	0.324477	+	0.945894i	$0.394812\pi$
$60$	6.11753	0.789769
$61$	−6.55802	−0.839669	−0.419834	−	0.907601i	$-0.637912\pi$
$61$	−6.55802	−0.839669	−0.419834	+	0.907601i	$0.637912\pi$
$62$	−5.54642	−0.704396
$63$	6.86419	0.864806
$64$	−11.3436	−1.41795
$65$	7.89862	0.979703
$66$	7.00372	0.862098
$67$	1.54885	0.189222	0.0946109	−	0.995514i	$-0.469839\pi$
$67$	1.54885	0.189222	0.0946109	+	0.995514i	$0.469839\pi$
$68$	9.85831	1.19550
$69$	1.65401	0.199120
$70$	18.1298	2.16693
$71$	4.02083	0.477184	0.238592	−	0.971120i	$-0.423314\pi$
$71$	4.02083	0.477184	0.238592	+	0.971120i	$0.423314\pi$
$72$	2.30101	0.271177
$73$	−5.80545	−0.679477	−0.339738	−	0.940520i	$-0.610339\pi$
$73$	−5.80545	−0.679477	−0.339738	+	0.940520i	$0.610339\pi$
$74$	4.93943	0.574197
$75$	2.23372	0.257927
$76$	2.49404	0.286086
$77$	11.5190	1.31271
$78$	−5.48152	−0.620660
$79$	−6.95203	−0.782164	−0.391082	−	0.920356i	$-0.627899\pi$
$79$	−6.95203	−0.782164	−0.391082	+	0.920356i	$0.627899\pi$
$80$	−7.57635	−0.847062
$81$	2.41798	0.268665
$82$	16.3796	1.80883
$83$	14.8934	1.63476	0.817381	−	0.576097i	$-0.195425\pi$
$83$	14.8934	1.63476	0.817381	+	0.576097i	$0.195425\pi$
$84$	−6.98249	−0.761852
$85$	10.8198	1.17357
$86$	−19.0877	−2.05828
$87$	−2.37201	−0.254306
$88$	3.86138	0.411625
$89$	−7.21817	−0.765124	−0.382562	−	0.923930i	$-0.624958\pi$
$89$	−7.21817	−0.765124	−0.382562	+	0.923930i	$0.624958\pi$
$90$	12.7489	1.34385
$91$	−9.01541	−0.945072
$92$	4.60354	0.479952
$93$	2.34447	0.243111
$94$	18.7958	1.93864
$95$	2.73729	0.280840
$96$	7.13488	0.728200
$97$	1.20280	0.122126	0.0610629	−	0.998134i	$-0.480551\pi$
$97$	1.20280	0.122126	0.0610629	+	0.998134i	$0.480551\pi$
$98$	−5.85378	−0.591321
$99$	8.10015	0.814096
$100$	6.21700	0.621700
$101$	−19.3303	−1.92344	−0.961721	−	0.274032i	$-0.911643\pi$
$101$	−19.3303	−1.92344	−0.961721	+	0.274032i	$0.911643\pi$
$102$	−7.50876	−0.743478
$103$	14.6768	1.44615	0.723075	−	0.690770i	$-0.242728\pi$
$103$	14.6768	1.44615	0.723075	+	0.690770i	$0.242728\pi$
$104$	−3.02214	−0.296346
$105$	−7.66348	−0.747879
$106$	−26.9696	−2.61952
$107$	−7.00485	−0.677185	−0.338592	−	0.940933i	$-0.609951\pi$
$107$	−7.00485	−0.677185	−0.338592	+	0.940933i	$0.609951\pi$
$108$	−11.6148	−1.11763
$109$	7.08070	0.678208	0.339104	−	0.940749i	$-0.389876\pi$
$109$	7.08070	0.678208	0.339104	+	0.940749i	$0.389876\pi$
$110$	21.3943	2.03986
$111$	−2.08790	−0.198175
$112$	8.64758	0.817119
$113$	−10.0482	−0.945251	−0.472626	−	0.881263i	$-0.656694\pi$
$113$	−10.0482	−0.945251	−0.472626	+	0.881263i	$0.656694\pi$
$114$	−1.89963	−0.177917
$115$	5.05252	0.471150
$116$	−6.60190	−0.612971
$117$	−6.33966	−0.586101
$118$	−10.5672	−0.972787
$119$	−12.3496	−1.13209
$120$	−2.56895	−0.234512
$121$	2.59306	0.235732
$122$	13.9025	1.25867
$123$	−6.92367	−0.624287
$124$	6.52526	0.585986
$125$	−6.86309	−0.613854
$126$	−14.5515	−1.29635
$127$	10.4984	0.931579	0.465790	−	0.884895i	$-0.345770\pi$
$127$	10.4984	0.931579	0.465790	+	0.884895i	$0.345770\pi$
$128$	8.12302	0.717980
$129$	8.06839	0.710382
$130$	−16.7444	−1.46858
$131$	−3.70523	−0.323727	−0.161864	−	0.986813i	$-0.551750\pi$
$131$	−3.70523	−0.323727	−0.161864	+	0.986813i	$0.551750\pi$
$132$	−8.23975	−0.717178
$133$	−3.12431	−0.270912
$134$	−3.28343	−0.283645
$135$	−12.7475	−1.09713
$136$	−4.13983	−0.354987
$137$	0.298109	0.0254692	0.0127346	−	0.999919i	$-0.495946\pi$
$137$	0.298109	0.0254692	0.0127346	+	0.999919i	$0.495946\pi$
$138$	−3.50637	−0.298482
$139$	−10.9080	−0.925208	−0.462604	−	0.886565i	$-0.653085\pi$
$139$	−10.9080	−0.925208	−0.462604	+	0.886565i	$0.653085\pi$
$140$	−21.3294	−1.80266
$141$	−7.94500	−0.669090
$142$	−8.52381	−0.715303
$143$	−10.6387	−0.889655
$144$	6.08099	0.506749
$145$	−7.24578	−0.601730
$146$	12.3071	1.01854
$147$	2.47440	0.204085
$148$	−5.81115	−0.477674
$149$	−20.2302	−1.65733	−0.828663	−	0.559748i	$-0.810898\pi$
$149$	−20.2302	−1.65733	−0.828663	+	0.559748i	$0.810898\pi$
$150$	−4.73529	−0.386635
$151$	6.41498	0.522044	0.261022	−	0.965333i	$-0.415941\pi$
$151$	6.41498	0.522044	0.261022	+	0.965333i	$0.415941\pi$
$152$	−1.04733	−0.0849498
$153$	−8.68426	−0.702081
$154$	−24.4192	−1.96776
$155$	7.16167	0.575239
$156$	6.44891	0.516326
$157$	−8.51345	−0.679448	−0.339724	−	0.940525i	$-0.610334\pi$
$157$	−8.51345	−0.679448	−0.339724	+	0.940525i	$0.610334\pi$
$158$	14.7377	1.17247
$159$	11.4001	0.904083
$160$	21.7949	1.72304
$161$	−5.76690	−0.454495
$162$	−5.12592	−0.402730
$163$	−15.4609	−1.21099	−0.605496	−	0.795848i	$-0.707025\pi$
$163$	−15.4609	−1.21099	−0.605496	+	0.795848i	$0.707025\pi$
$164$	−19.2703	−1.50476
$165$	−9.04337	−0.704025
$166$	−31.5727	−2.45052
$167$	0.689554	0.0533593	0.0266797	−	0.999644i	$-0.491507\pi$
$167$	0.689554	0.0533593	0.0266797	+	0.999644i	$0.491507\pi$
$168$	2.93218	0.226222
$169$	−4.67351	−0.359501
$170$	−22.9370	−1.75919
$171$	−2.19702	−0.168011
$172$	22.4564	1.71228
$173$	−0.152291	−0.0115785	−0.00578924	−	0.999983i	$-0.501843\pi$
$173$	−0.152291	−0.0115785	−0.00578924	+	0.999983i	$0.501843\pi$
$174$	5.02846	0.381207
$175$	−7.78809	−0.588724
$176$	10.2047	0.769205
$177$	4.46675	0.335741
$178$	15.3019	1.14693
$179$	−10.3101	−0.770610	−0.385305	−	0.922789i	$-0.625904\pi$
$179$	−10.3101	−0.770610	−0.385305	+	0.922789i	$0.625904\pi$
$180$	−14.9989	−1.11795
$181$	−15.6852	−1.16588	−0.582938	−	0.812517i	$-0.698097\pi$
$181$	−15.6852	−1.16588	−0.582938	+	0.812517i	$0.698097\pi$
$182$	19.1119	1.41667
$183$	−5.87658	−0.434409
$184$	−1.93318	−0.142516
$185$	−6.37791	−0.468913
$186$	−4.97009	−0.364425
$187$	−14.5733	−1.06570
$188$	−22.1129	−1.61275
$189$	14.5499	1.05835
$190$	−5.80282	−0.420981
$191$	3.15754	0.228472	0.114236	−	0.993454i	$-0.463558\pi$
$191$	3.15754	0.228472	0.114236	+	0.993454i	$0.463558\pi$
$192$	−10.1649	−0.733588
$193$	2.92671	0.210669	0.105334	−	0.994437i	$-0.466409\pi$
$193$	2.92671	0.210669	0.105334	+	0.994437i	$0.466409\pi$
$194$	−2.54983	−0.183067
$195$	7.07787	0.506857
$196$	6.88687	0.491920
$197$	−15.6474	−1.11483	−0.557415	−	0.830234i	$-0.688207\pi$
$197$	−15.6474	−1.11483	−0.557415	+	0.830234i	$0.688207\pi$
$198$	−17.1716	−1.22034
$199$	−0.485184	−0.0343938	−0.0171969	−	0.999852i	$-0.505474\pi$
$199$	−0.485184	−0.0343938	−0.0171969	+	0.999852i	$0.505474\pi$
$200$	−2.61072	−0.184606
$201$	1.38791	0.0978953
$202$	40.9787	2.88325
$203$	8.27027	0.580459
$204$	8.83393	0.618499
$205$	−21.1498	−1.47716
$206$	−31.1136	−2.16779
$207$	−4.05530	−0.281863
$208$	−7.98677	−0.553783
$209$	−3.68688	−0.255027
$210$	16.2459	1.12108
$211$	6.68869	0.460468	0.230234	−	0.973135i	$-0.426051\pi$
$211$	6.68869	0.460468	0.230234	+	0.973135i	$0.426051\pi$
$212$	31.7292	2.17917
$213$	3.60302	0.246875
$214$	14.8497	1.01510
$215$	24.6465	1.68088
$216$	4.87742	0.331866
$217$	−8.17426	−0.554905
$218$	−15.0105	−1.01664
$219$	−5.20221	−0.351532
$220$	−25.1700	−1.69696
$221$	11.4059	0.767243
$222$	4.42617	0.297065
$223$	−20.9347	−1.40189	−0.700944	−	0.713216i	$-0.747238\pi$
$223$	−20.9347	−1.40189	−0.700944	+	0.713216i	$0.747238\pi$
$224$	−24.8765	−1.66213
$225$	−5.47660	−0.365107
$226$	21.3013	1.41694
$227$	8.01312	0.531850	0.265925	−	0.963994i	$-0.414323\pi$
$227$	8.01312	0.531850	0.265925	+	0.963994i	$0.414323\pi$
$228$	2.23489	0.148009
$229$	18.8728	1.24715	0.623575	−	0.781764i	$-0.285680\pi$
$229$	18.8728	1.24715	0.623575	+	0.781764i	$0.285680\pi$
$230$	−10.7109	−0.706257
$231$	10.3220	0.679139
$232$	2.77236	0.182014
$233$	1.50719	0.0987391	0.0493695	−	0.998781i	$-0.484279\pi$
$233$	1.50719	0.0987391	0.0493695	+	0.998781i	$0.484279\pi$
$234$	13.4395	0.878570
$235$	−24.2696	−1.58317
$236$	12.4321	0.809260
$237$	−6.22964	−0.404659
$238$	26.1801	1.69700
$239$	8.56910	0.554289	0.277144	−	0.960828i	$-0.410612\pi$
$239$	8.56910	0.554289	0.277144	+	0.960828i	$0.410612\pi$
$240$	−6.78909	−0.438234
$241$	−7.10341	−0.457571	−0.228785	−	0.973477i	$-0.573475\pi$
$241$	−7.10341	−0.457571	−0.228785	+	0.973477i	$0.573475\pi$
$242$	−5.49706	−0.353364
$243$	16.1377	1.03524
$244$	−16.3560	−1.04709
$245$	7.55855	0.482898
$246$	14.6776	0.935810
$247$	2.88557	0.183604
$248$	−2.74017	−0.174001
$249$	13.3458	0.845757
$250$	14.5492	0.920171
$251$	−8.88454	−0.560787	−0.280394	−	0.959885i	$-0.590465\pi$
$251$	−8.88454	−0.560787	−0.280394	+	0.959885i	$0.590465\pi$
$252$	17.1196	1.07843
$253$	−6.80529	−0.427845
$254$	−22.2557	−1.39644
$255$	9.69550	0.607156
$256$	5.46709	0.341693
$257$	−18.2364	−1.13755	−0.568777	−	0.822492i	$-0.692583\pi$
$257$	−18.2364	−1.13755	−0.568777	+	0.822492i	$0.692583\pi$
$258$	−17.1043	−1.06487
$259$	7.27969	0.452338
$260$	19.6995	1.22171
$261$	5.81567	0.359981
$262$	7.85477	0.485269
$263$	−17.5569	−1.08260	−0.541302	−	0.840828i	$-0.682069\pi$
$263$	−17.5569	−1.08260	−0.541302	+	0.840828i	$0.682069\pi$
$264$	3.46014	0.212957
$265$	34.8238	2.13921
$266$	6.62328	0.406099
$267$	−6.46813	−0.395843
$268$	3.86289	0.235964
$269$	7.58831	0.462667	0.231334	−	0.972874i	$-0.425691\pi$
$269$	7.58831	0.462667	0.231334	+	0.972874i	$0.425691\pi$
$270$	27.0237	1.64461
$271$	−7.16063	−0.434977	−0.217489	−	0.976063i	$-0.569786\pi$
$271$	−7.16063	−0.434977	−0.217489	+	0.976063i	$0.569786\pi$
$272$	−10.9405	−0.663367
$273$	−8.07862	−0.488940
$274$	−0.631966	−0.0381785
$275$	−9.19042	−0.554203
$276$	4.12519	0.248307
$277$	−21.9107	−1.31648	−0.658242	−	0.752807i	$-0.728700\pi$
$277$	−21.9107	−1.31648	−0.658242	+	0.752807i	$0.728700\pi$
$278$	23.1241	1.38689
$279$	−5.74816	−0.344133
$280$	8.95692	0.535278
$281$	−16.8044	−1.00247	−0.501234	−	0.865312i	$-0.667121\pi$
$281$	−16.8044	−1.00247	−0.501234	+	0.865312i	$0.667121\pi$
$282$	16.8427	1.00297
$283$	23.1600	1.37672	0.688359	−	0.725370i	$-0.258331\pi$
$283$	23.1600	1.37672	0.688359	+	0.725370i	$0.258331\pi$
$284$	10.0281	0.595059
$285$	2.45285	0.145295
$286$	22.5532	1.33360
$287$	24.1401	1.42495
$288$	−17.4932	−1.03080
$289$	−1.37584	−0.0809320
$290$	15.3605	0.901997
$291$	1.07782	0.0631827
$292$	−14.4791	−0.847322
$293$	23.9512	1.39925	0.699623	−	0.714512i	$-0.253351\pi$
$293$	23.9512	1.39925	0.699623	+	0.714512i	$0.253351\pi$
$294$	−5.24552	−0.305925
$295$	13.6446	0.794419
$296$	2.44029	0.141839
$297$	17.1698	0.996292
$298$	42.8864	2.48434
$299$	5.32622	0.308023
$300$	5.57099	0.321641
$301$	−28.1313	−1.62146
$302$	−13.5992	−0.782547
$303$	−17.3217	−0.995107
$304$	−2.76783	−0.158746
$305$	−17.9512	−1.02788
$306$	18.4099	1.05242
$307$	−10.5008	−0.599310	−0.299655	−	0.954048i	$-0.596872\pi$
$307$	−10.5008	−0.599310	−0.299655	+	0.954048i	$0.596872\pi$
$308$	28.7288	1.63697
$309$	13.1517	0.748177
$310$	−15.1821	−0.862288
$311$	0.565761	0.0320814	0.0160407	−	0.999871i	$-0.494894\pi$
$311$	0.565761	0.0320814	0.0160407	+	0.999871i	$0.494894\pi$
$312$	−2.70811	−0.153317
$313$	−32.7002	−1.84833	−0.924164	−	0.381997i	$-0.875237\pi$
$313$	−32.7002	−1.84833	−0.924164	+	0.381997i	$0.875237\pi$
$314$	18.0478	1.01850
$315$	18.7892	1.05865
$316$	−17.3387	−0.975376
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−24.1672	−1.35523
$319$	9.75941	0.546422
$320$	−31.0507	−1.73579
$321$	−6.27698	−0.350347
$322$	12.2253	0.681292
$323$	3.95274	0.219936
$324$	6.03055	0.335031
$325$	7.19296	0.398994
$326$	32.7758	1.81529
$327$	6.34495	0.350876
$328$	8.09225	0.446820
$329$	27.7011	1.52721
$330$	19.1712	1.05534
$331$	4.58279	0.251893	0.125947	−	0.992037i	$-0.459803\pi$
$331$	4.58279	0.251893	0.125947	+	0.992037i	$0.459803\pi$
$332$	37.1448	2.03858
$333$	5.11909	0.280524
$334$	−1.46180	−0.0799860
$335$	4.23964	0.231636
$336$	7.74900	0.422743
$337$	−24.3454	−1.32618	−0.663089	−	0.748541i	$-0.730755\pi$
$337$	−24.3454	−1.32618	−0.663089	+	0.748541i	$0.730755\pi$
$338$	9.90745	0.538894
$339$	−9.00405	−0.489033
$340$	26.9850	1.46347
$341$	−9.64612	−0.522367
$342$	4.65750	0.251849
$343$	13.2429	0.715051
$344$	−9.43017	−0.508440
$345$	4.52751	0.243753
$346$	0.322845	0.0173562
$347$	17.8670	0.959150	0.479575	−	0.877501i	$-0.340791\pi$
$347$	17.8670	0.959150	0.479575	+	0.877501i	$0.340791\pi$
$348$	−5.91590	−0.317125
$349$	−5.94716	−0.318344	−0.159172	−	0.987251i	$-0.550882\pi$
$349$	−5.94716	−0.318344	−0.159172	+	0.987251i	$0.550882\pi$
$350$	16.5101	0.882502
$351$	−13.4381	−0.717272
$352$	−29.3558	−1.56467
$353$	37.3874	1.98993	0.994966	−	0.100213i	$-0.0319525\pi$
$353$	37.3874	1.98993	0.994966	+	0.100213i	$0.0319525\pi$
$354$	−9.46913	−0.503279
$355$	11.0062	0.584146
$356$	−18.0024	−0.954127
$357$	−11.0663	−0.585693
$358$	21.8565	1.15515
$359$	10.0029	0.527933	0.263967	−	0.964532i	$-0.414969\pi$
$359$	10.0029	0.527933	0.263967	+	0.964532i	$0.414969\pi$
$360$	6.29853	0.331962
$361$	1.00000	0.0526316
$362$	33.2514	1.74766
$363$	2.32361	0.121958
$364$	−22.4848	−1.17853
$365$	−15.8912	−0.831783
$366$	12.4579	0.651182
$367$	−7.74629	−0.404353	−0.202176	−	0.979349i	$-0.564801\pi$
$367$	−7.74629	−0.404353	−0.202176	+	0.979349i	$0.564801\pi$
$368$	−5.10890	−0.266320
$369$	16.9754	0.883703
$370$	13.5206	0.702904
$371$	−39.7475	−2.06359
$372$	5.84722	0.303164
$373$	−15.5834	−0.806879	−0.403440	−	0.915006i	$-0.632185\pi$
$373$	−15.5834	−0.806879	−0.403440	+	0.915006i	$0.632185\pi$
$374$	30.8941	1.59750
$375$	−6.14995	−0.317582
$376$	9.28595	0.478886
$377$	−7.63829	−0.393392
$378$	−30.8446	−1.58648
$379$	−6.19440	−0.318185	−0.159092	−	0.987264i	$-0.550857\pi$
$379$	−6.19440	−0.318185	−0.159092	+	0.987264i	$0.550857\pi$
$380$	6.82691	0.350213
$381$	9.40748	0.481960
$382$	−6.69373	−0.342481
$383$	−8.59057	−0.438958	−0.219479	−	0.975617i	$-0.570436\pi$
$383$	−8.59057	−0.438958	−0.219479	+	0.975617i	$0.570436\pi$
$384$	7.27895	0.371453
$385$	31.5307	1.60695
$386$	−6.20437	−0.315794
$387$	−19.7820	−1.00557
$388$	2.99983	0.152293
$389$	7.65552	0.388150	0.194075	−	0.980987i	$-0.437829\pi$
$389$	7.65552	0.388150	0.194075	+	0.980987i	$0.437829\pi$
$390$	−15.0045	−0.759782
$391$	7.29602	0.368976
$392$	−2.89203	−0.146069
$393$	−3.32022	−0.167483
$394$	33.1711	1.67114
$395$	−19.0297	−0.957488
$396$	20.2021	1.01520
$397$	9.14034	0.458740	0.229370	−	0.973339i	$-0.426333\pi$
$397$	9.14034	0.458740	0.229370	+	0.973339i	$0.426333\pi$
$398$	1.02855	0.0515565
$399$	−2.79966	−0.140159
$400$	−6.89948	−0.344974
$401$	−28.5188	−1.42416	−0.712081	−	0.702097i	$-0.752247\pi$
$401$	−28.5188	−1.42416	−0.712081	+	0.702097i	$0.752247\pi$
$402$	−2.94224	−0.146746
$403$	7.54962	0.376073
$404$	−48.2107	−2.39857
$405$	6.61871	0.328886
$406$	−17.5323	−0.870112
$407$	8.59047	0.425814
$408$	−3.70966	−0.183655
$409$	−5.84806	−0.289168	−0.144584	−	0.989493i	$-0.546184\pi$
$409$	−5.84806	−0.289168	−0.144584	+	0.989493i	$0.546184\pi$
$410$	44.8357	2.21428
$411$	0.267132	0.0131767
$412$	36.6046	1.80338
$413$	−15.5738	−0.766337
$414$	8.59689	0.422514
$415$	40.7675	2.00120
$416$	22.9756	1.12647
$417$	−9.77458	−0.478663
$418$	7.81587	0.382287
$419$	1.23016	0.0600972	0.0300486	−	0.999548i	$-0.490434\pi$
$419$	1.23016	0.0600972	0.0300486	+	0.999548i	$0.490434\pi$
$420$	−19.1131	−0.932622
$421$	2.70647	0.131905	0.0659527	−	0.997823i	$-0.478991\pi$
$421$	2.70647	0.131905	0.0659527	+	0.997823i	$0.478991\pi$
$422$	−14.1795	−0.690245
$423$	19.4795	0.947124
$424$	−13.3241	−0.647078
$425$	9.85315	0.477948
$426$	−7.63810	−0.370067
$427$	20.4893	0.991547
$428$	−17.4704	−0.844464
$429$	−9.53325	−0.460270
$430$	−52.2485	−2.51965
$431$	−31.2227	−1.50394	−0.751972	−	0.659195i	$-0.770897\pi$
$431$	−31.2227	−1.50394	−0.751972	+	0.659195i	$0.770897\pi$
$432$	12.8898	0.620161
$433$	−18.3588	−0.882267	−0.441133	−	0.897442i	$-0.645423\pi$
$433$	−18.3588	−0.882267	−0.441133	+	0.897442i	$0.645423\pi$
$434$	17.3287	0.831807
$435$	−6.49287	−0.311309
$436$	17.6596	0.845741
$437$	1.84581	0.0882972
$438$	11.0282	0.526950
$439$	−8.00073	−0.381854	−0.190927	−	0.981604i	$-0.561149\pi$
$439$	−8.00073	−0.381854	−0.190927	+	0.981604i	$0.561149\pi$
$440$	10.5697	0.503891
$441$	−6.06670	−0.288891
$442$	−24.1795	−1.15010
$443$	16.8183	0.799062	0.399531	−	0.916720i	$-0.369173\pi$
$443$	16.8183	0.799062	0.399531	+	0.916720i	$0.369173\pi$
$444$	−5.20731	−0.247128
$445$	−19.7582	−0.936629
$446$	44.3797	2.10144
$447$	−18.1281	−0.857430
$448$	35.4410	1.67443
$449$	38.5350	1.81858	0.909289	−	0.416166i	$-0.136627\pi$
$449$	38.5350	1.81858	0.909289	+	0.416166i	$0.136627\pi$
$450$	11.6099	0.547298
$451$	28.4868	1.34139
$452$	−25.0605	−1.17875
$453$	5.74840	0.270083
$454$	−16.9872	−0.797246
$455$	−24.6778	−1.15691
$456$	−0.938503	−0.0439494
$457$	−1.82300	−0.0852766	−0.0426383	−	0.999091i	$-0.513576\pi$
$457$	−1.82300	−0.0852766	−0.0426383	+	0.999091i	$0.513576\pi$
$458$	−40.0087	−1.86949
$459$	−18.4079	−0.859208
$460$	12.6012	0.587534
$461$	−6.47528	−0.301584	−0.150792	−	0.988566i	$-0.548182\pi$
$461$	−6.47528	−0.301584	−0.150792	+	0.988566i	$0.548182\pi$
$462$	−21.8818	−1.01803
$463$	−5.38407	−0.250219	−0.125109	−	0.992143i	$-0.539928\pi$
$463$	−5.38407	−0.250219	−0.125109	+	0.992143i	$0.539928\pi$
$464$	7.32664	0.340131
$465$	6.41750	0.297604
$466$	−3.19511	−0.148011
$467$	4.15465	0.192254	0.0961272	−	0.995369i	$-0.469354\pi$
$467$	4.15465	0.192254	0.0961272	+	0.995369i	$0.469354\pi$
$468$	−15.8114	−0.730881
$469$	−4.83908	−0.223448
$470$	51.4495	2.37319
$471$	−7.62882	−0.351517
$472$	−5.22065	−0.240300
$473$	−33.1966	−1.52638
$474$	13.2063	0.606586
$475$	2.49274	0.114375
$476$	−30.8004	−1.41174
$477$	−27.9505	−1.27977
$478$	−18.1658	−0.830883
$479$	21.3573	0.975842	0.487921	−	0.872888i	$-0.337755\pi$
$479$	21.3573	0.975842	0.487921	+	0.872888i	$0.337755\pi$
$480$	19.5302	0.891428
$481$	−6.72340	−0.306561
$482$	15.0586	0.685902
$483$	−5.16766	−0.235137
$484$	6.46719	0.293963
$485$	3.29241	0.149500
$486$	−34.2106	−1.55183
$487$	−24.2016	−1.09668	−0.548339	−	0.836256i	$-0.684740\pi$
$487$	−24.2016	−1.09668	−0.548339	+	0.836256i	$0.684740\pi$
$488$	6.86842	0.310919
$489$	−13.8544	−0.626516
$490$	−16.0235	−0.723867
$491$	2.49575	0.112632	0.0563158	−	0.998413i	$-0.482065\pi$
$491$	2.49575	0.112632	0.0563158	+	0.998413i	$0.482065\pi$
$492$	−17.2679	−0.778499
$493$	−10.4632	−0.471238
$494$	−6.11716	−0.275224
$495$	22.1724	0.996577
$496$	−7.24159	−0.325157
$497$	−12.5623	−0.563497
$498$	−28.2920	−1.26780
$499$	−15.9018	−0.711862	−0.355931	−	0.934512i	$-0.615836\pi$
$499$	−15.9018	−0.711862	−0.355931	+	0.934512i	$0.615836\pi$
$500$	−17.1169	−0.765489
$501$	0.617902	0.0276058
$502$	18.8345	0.840624
$503$	2.73136	0.121785	0.0608927	−	0.998144i	$-0.480605\pi$
$503$	2.73136	0.121785	0.0608927	+	0.998144i	$0.480605\pi$
$504$	−7.18908	−0.320227
$505$	−52.9127	−2.35458
$506$	14.4266	0.641342
$507$	−4.18788	−0.185990
$508$	26.1834	1.16170
$509$	−30.3397	−1.34478	−0.672392	−	0.740195i	$-0.734733\pi$
$509$	−30.3397	−1.34478	−0.672392	+	0.740195i	$0.734733\pi$
$510$	−20.5536	−0.910130
$511$	18.1380	0.802380
$512$	−27.8358	−1.23018
$513$	−4.65700	−0.205612
$514$	38.6596	1.70520
$515$	40.1747	1.77031
$516$	20.1229	0.885862
$517$	32.6889	1.43766
$518$	−15.4323	−0.678057
$519$	−0.136467	−0.00599022
$520$	−8.27247	−0.362772
$521$	−31.8065	−1.39347	−0.696733	−	0.717330i	$-0.745364\pi$
$521$	−31.8065	−1.39347	−0.696733	+	0.717330i	$0.745364\pi$
$522$	−12.3287	−0.539614
$523$	−1.91857	−0.0838932	−0.0419466	−	0.999120i	$-0.513356\pi$
$523$	−1.91857	−0.0838932	−0.0419466	+	0.999120i	$0.513356\pi$
$524$	−9.24100	−0.403695
$525$	−6.97883	−0.304581
$526$	37.2191	1.62283
$527$	10.3417	0.450492
$528$	9.14429	0.397954
$529$	−19.5930	−0.851868
$530$	−73.8234	−3.20669
$531$	−10.9515	−0.475256
$532$	−7.79217	−0.337834
$533$	−22.2954	−0.965723
$534$	13.7119	0.593371
$535$	−19.1743	−0.828977
$536$	−1.62216	−0.0700665
$537$	−9.23874	−0.398681
$538$	−16.0866	−0.693542
$539$	−10.1807	−0.438513
$540$	−31.7929	−1.36815
$541$	−29.9506	−1.28768	−0.643838	−	0.765162i	$-0.722659\pi$
$541$	−29.9506	−1.28768	−0.643838	+	0.765162i	$0.722659\pi$
$542$	15.1799	0.652034
$543$	−14.0554	−0.603175
$544$	31.4727	1.34938
$545$	19.3819	0.830230
$546$	17.1260	0.732925
$547$	−36.6891	−1.56871	−0.784357	−	0.620310i	$-0.787007\pi$
$547$	−36.6891	−1.56871	−0.784357	+	0.620310i	$0.787007\pi$
$548$	0.743497	0.0317606
$549$	14.4081	0.614924
$550$	19.4829	0.830754
$551$	−2.64707	−0.112769
$552$	−1.73230	−0.0737316
$553$	21.7203	0.923642
$554$	46.4487	1.97342
$555$	−5.71518	−0.242596
$556$	−27.2051	−1.15375
$557$	15.9343	0.675158	0.337579	−	0.941297i	$-0.390392\pi$
$557$	15.9343	0.675158	0.337579	+	0.941297i	$0.390392\pi$
$558$	12.1856	0.515858
$559$	25.9816	1.09891
$560$	23.6709	1.00028
$561$	−13.0590	−0.551349
$562$	35.6240	1.50271
$563$	16.5608	0.697953	0.348976	−	0.937132i	$-0.386529\pi$
$563$	16.5608	0.697953	0.348976	+	0.937132i	$0.386529\pi$
$564$	−19.8152	−0.834369
$565$	−27.5047	−1.15713
$566$	−49.0972	−2.06371
$567$	−7.55453	−0.317260
$568$	−4.21114	−0.176695
$569$	14.9996	0.628817	0.314409	−	0.949288i	$-0.398194\pi$
$569$	14.9996	0.628817	0.314409	+	0.949288i	$0.398194\pi$
$570$	−5.19985	−0.217798
$571$	26.2370	1.09799	0.548993	−	0.835827i	$-0.315011\pi$
$571$	26.2370	1.09799	0.548993	+	0.835827i	$0.315011\pi$
$572$	−26.5334	−1.10942
$573$	2.82944	0.118202
$574$	−51.1750	−2.13600
$575$	4.60113	0.191880
$576$	24.9222	1.03842
$577$	1.37843	0.0573848	0.0286924	−	0.999588i	$-0.490866\pi$
$577$	1.37843	0.0573848	0.0286924	+	0.999588i	$0.490866\pi$
$578$	2.91667	0.121318
$579$	2.62259	0.108991
$580$	−18.0713	−0.750370
$581$	−46.5316	−1.93046
$582$	−2.28488	−0.0947113
$583$	−46.9044	−1.94258
$584$	6.08023	0.251602
$585$	−17.3535	−0.717477
$586$	−50.7746	−2.09748
$587$	−13.7533	−0.567660	−0.283830	−	0.958875i	$-0.591605\pi$
$587$	−13.7533	−0.567660	−0.283830	+	0.958875i	$0.591605\pi$
$588$	6.17126	0.254498
$589$	2.61634	0.107804
$590$	−28.9254	−1.19084
$591$	−14.0215	−0.576766
$592$	6.44908	0.265056
$593$	33.2022	1.36345	0.681725	−	0.731608i	$-0.261230\pi$
$593$	33.2022	1.36345	0.681725	+	0.731608i	$0.261230\pi$
$594$	−36.3985	−1.49345
$595$	−33.8044	−1.38584
$596$	−50.4551	−2.06672
$597$	−0.434769	−0.0177939
$598$	−11.2911	−0.461729
$599$	13.4818	0.550852	0.275426	−	0.961322i	$-0.411181\pi$
$599$	13.4818	0.550852	0.275426	+	0.961322i	$0.411181\pi$
$600$	−2.33944	−0.0955073
$601$	29.9566	1.22195	0.610977	−	0.791648i	$-0.290777\pi$
$601$	29.9566	1.22195	0.610977	+	0.791648i	$0.290777\pi$
$602$	59.6360	2.43058
$603$	−3.40285	−0.138575
$604$	15.9992	0.651000
$605$	7.09793	0.288572
$606$	36.7206	1.49167
$607$	26.4256	1.07258	0.536291	−	0.844033i	$-0.319825\pi$
$607$	26.4256	1.07258	0.536291	+	0.844033i	$0.319825\pi$
$608$	7.96224	0.322911
$609$	7.41090	0.300305
$610$	38.0550	1.54080
$611$	−25.5843	−1.03503
$612$	−21.6589	−0.875510
$613$	12.0532	0.486824	0.243412	−	0.969923i	$-0.421733\pi$
$613$	12.0532	0.486824	0.243412	+	0.969923i	$0.421733\pi$
$614$	22.2607	0.898370
$615$	−18.9521	−0.764222
$616$	−12.0642	−0.486079
$617$	8.62742	0.347327	0.173664	−	0.984805i	$-0.444439\pi$
$617$	8.62742	0.347327	0.173664	+	0.984805i	$0.444439\pi$
$618$	−27.8806	−1.12152
$619$	14.2630	0.573280	0.286640	−	0.958038i	$-0.407462\pi$
$619$	14.2630	0.573280	0.286640	+	0.958038i	$0.407462\pi$
$620$	17.8615	0.717336
$621$	−8.59595	−0.344944
$622$	−1.19937	−0.0480902
$623$	22.5518	0.903520
$624$	−7.15686	−0.286504
$625$	−31.2499	−1.25000
$626$	69.3218	2.77066
$627$	−3.30377	−0.131940
$628$	−21.2329	−0.847286
$629$	−9.20993	−0.367224
$630$	−39.8316	−1.58693
$631$	−32.3036	−1.28599	−0.642994	−	0.765872i	$-0.722308\pi$
$631$	−32.3036	−1.28599	−0.642994	+	0.765872i	$0.722308\pi$
$632$	7.28108	0.289626
$633$	5.99366	0.238227
$634$	−2.11992	−0.0841926
$635$	28.7370	1.14039
$636$	28.4322	1.12741
$637$	7.96800	0.315703
$638$	−20.6891	−0.819091
$639$	−8.83385	−0.349462
$640$	22.2350	0.878917
$641$	−32.4646	−1.28227	−0.641136	−	0.767427i	$-0.721537\pi$
$641$	−32.4646	−1.28227	−0.641136	+	0.767427i	$0.721537\pi$
$642$	13.3067	0.525172
$643$	−11.1890	−0.441253	−0.220627	−	0.975358i	$-0.570810\pi$
$643$	−11.1890	−0.441253	−0.220627	+	0.975358i	$0.570810\pi$
$644$	−14.3829	−0.566766
$645$	22.0855	0.869615
$646$	−8.37948	−0.329686
$647$	−28.9443	−1.13792	−0.568960	−	0.822365i	$-0.692654\pi$
$647$	−28.9443	−1.13792	−0.568960	+	0.822365i	$0.692654\pi$
$648$	−2.53243	−0.0994831
$649$	−18.3780	−0.721400
$650$	−15.2485	−0.598094
$651$	−7.32487	−0.287084
$652$	−38.5602	−1.51013
$653$	−7.28374	−0.285035	−0.142517	−	0.989792i	$-0.545520\pi$
$653$	−7.28374	−0.285035	−0.142517	+	0.989792i	$0.545520\pi$
$654$	−13.4508	−0.525966
$655$	−10.1423	−0.396291
$656$	21.3858	0.834974
$657$	12.7547	0.497609
$658$	−58.7240	−2.28930
$659$	−25.6631	−0.999692	−0.499846	−	0.866114i	$-0.666610\pi$
$659$	−25.6631	−0.999692	−0.499846	+	0.866114i	$0.666610\pi$
$660$	−22.5546	−0.877935
$661$	−27.4206	−1.06654	−0.533268	−	0.845946i	$-0.679036\pi$
$661$	−27.4206	−1.06654	−0.533268	+	0.845946i	$0.679036\pi$
$662$	−9.71514	−0.377589
$663$	10.2207	0.396939
$664$	−15.5983	−0.605332
$665$	−8.55214	−0.331638
$666$	−10.8520	−0.420508
$667$	−4.88600	−0.189186
$668$	1.71978	0.0665402
$669$	−18.7593	−0.725277
$670$	−8.98768	−0.347224
$671$	24.1786	0.933405
$672$	−22.2916	−0.859917
$673$	20.0094	0.771306	0.385653	−	0.922644i	$-0.373976\pi$
$673$	20.0094	0.771306	0.385653	+	0.922644i	$0.373976\pi$
$674$	51.6102	1.98795
$675$	−11.6087	−0.446818
$676$	−11.6559	−0.448305
$677$	28.4726	1.09429	0.547144	−	0.837038i	$-0.315715\pi$
$677$	28.4726	1.09429	0.547144	+	0.837038i	$0.315715\pi$
$678$	19.0878	0.733064
$679$	−3.75792	−0.144216
$680$	−11.3319	−0.434558
$681$	7.18048	0.275157
$682$	20.4490	0.783031
$683$	−5.97112	−0.228479	−0.114239	−	0.993453i	$-0.536443\pi$
$683$	−5.97112	−0.228479	−0.114239	+	0.993453i	$0.536443\pi$
$684$	−5.47947	−0.209513
$685$	0.816010	0.0311781
$686$	−28.0739	−1.07187
$687$	16.9117	0.645222
$688$	−24.9216	−0.950125
$689$	36.7102	1.39855
$690$	−9.59795	−0.365388
$691$	21.5596	0.820166	0.410083	−	0.912048i	$-0.365500\pi$
$691$	21.5596	0.820166	0.410083	+	0.912048i	$0.365500\pi$
$692$	−0.379821	−0.0144386
$693$	−25.3074	−0.961349
$694$	−37.8765	−1.43777
$695$	−29.8584	−1.13259
$696$	2.48428	0.0941664
$697$	−30.5410	−1.15682
$698$	12.6075	0.477200
$699$	1.35057	0.0510834
$700$	−19.4238	−0.734152
$701$	−34.6228	−1.30768	−0.653842	−	0.756631i	$-0.726844\pi$
$701$	−34.6228	−1.30768	−0.653842	+	0.756631i	$0.726844\pi$
$702$	28.4876	1.07520
$703$	−2.33001	−0.0878781
$704$	41.8225	1.57624
$705$	−21.7477	−0.819067
$706$	−79.2582	−2.98292
$707$	60.3940	2.27135
$708$	11.1403	0.418677
$709$	5.16853	0.194108	0.0970540	−	0.995279i	$-0.469058\pi$
$709$	5.16853	0.194108	0.0970540	+	0.995279i	$0.469058\pi$
$710$	−23.3321	−0.875639
$711$	15.2738	0.572811
$712$	7.55982	0.283316
$713$	4.82928	0.180858
$714$	23.4597	0.877958
$715$	−29.1212	−1.08907
$716$	−25.7137	−0.960968
$717$	7.67868	0.286766
$718$	−21.2053	−0.791376
$719$	38.6399	1.44103	0.720513	−	0.693441i	$-0.243906\pi$
$719$	38.6399	1.44103	0.720513	+	0.693441i	$0.243906\pi$
$720$	16.6454	0.620338
$721$	−45.8550	−1.70773
$722$	−2.11992	−0.0788951
$723$	−6.36529	−0.236728
$724$	−39.1197	−1.45387
$725$	−6.59845	−0.245060
$726$	−4.92586	−0.182816
$727$	−13.7127	−0.508574	−0.254287	−	0.967129i	$-0.581841\pi$
$727$	−13.7127	−0.508574	−0.254287	+	0.967129i	$0.581841\pi$
$728$	9.44212	0.349948
$729$	7.20691	0.266923
$730$	33.6880	1.24685
$731$	35.5905	1.31636
$732$	−14.6564	−0.541718
$733$	−36.6182	−1.35252	−0.676262	−	0.736661i	$-0.736401\pi$
$733$	−36.6182	−1.35252	−0.676262	+	0.736661i	$0.736401\pi$
$734$	16.4215	0.606128
$735$	6.77314	0.249831
$736$	14.6968	0.541731
$737$	−5.71041	−0.210346
$738$	−35.9864	−1.32468
$739$	39.0637	1.43698	0.718490	−	0.695537i	$-0.244834\pi$
$739$	39.0637	1.43698	0.718490	+	0.695537i	$0.244834\pi$
$740$	−15.9068	−0.584745
$741$	2.58573	0.0949890
$742$	84.2614	3.09333
$743$	36.6134	1.34322	0.671608	−	0.740907i	$-0.265604\pi$
$743$	36.6134	1.34322	0.671608	+	0.740907i	$0.265604\pi$
$744$	−2.45544	−0.0900209
$745$	−55.3760	−2.02882
$746$	33.0356	1.20952
$747$	−32.7211	−1.19720
$748$	−36.3464	−1.32895
$749$	21.8854	0.799673
$750$	13.0374	0.476058
$751$	−13.7534	−0.501869	−0.250935	−	0.968004i	$-0.580738\pi$
$751$	−13.7534	−0.501869	−0.250935	+	0.968004i	$0.580738\pi$
$752$	24.5404	0.894898
$753$	−7.96134	−0.290128
$754$	16.1925	0.589697
$755$	17.5596	0.639061
$756$	36.2881	1.31979
$757$	−21.3235	−0.775016	−0.387508	−	0.921866i	$-0.626664\pi$
$757$	−21.3235	−0.775016	−0.387508	+	0.921866i	$0.626664\pi$
$758$	13.1316	0.476961
$759$	−6.09815	−0.221349
$760$	−2.86685	−0.103991
$761$	29.9282	1.08490	0.542448	−	0.840089i	$-0.317497\pi$
$761$	29.9282	1.08490	0.542448	+	0.840089i	$0.317497\pi$
$762$	−19.9431	−0.722461
$763$	−22.1223	−0.800882
$764$	7.87505	0.284909
$765$	−23.7713	−0.859454
$766$	18.2113	0.658001
$767$	14.3837	0.519366
$768$	4.89901	0.176778
$769$	−18.3873	−0.663063	−0.331532	−	0.943444i	$-0.607565\pi$
$769$	−18.3873	−0.663063	−0.331532	+	0.943444i	$0.607565\pi$
$770$	−66.8424	−2.40883
$771$	−16.3414	−0.588522
$772$	7.29934	0.262709
$773$	−21.0056	−0.755517	−0.377759	−	0.925904i	$-0.623305\pi$
$773$	−21.0056	−0.755517	−0.377759	+	0.925904i	$0.623305\pi$
$774$	41.9361	1.50736
$775$	6.52185	0.234272
$776$	−1.25973	−0.0452216
$777$	6.52325	0.234020
$778$	−16.2290	−0.581840
$779$	−7.72654	−0.276832
$780$	17.6525	0.632062
$781$	−14.8243	−0.530455
$782$	−15.4670	−0.553097
$783$	12.3274	0.440545
$784$	−7.64290	−0.272961
$785$	−23.3038	−0.831747
$786$	7.03858	0.251058
$787$	12.1097	0.431663	0.215831	−	0.976431i	$-0.430754\pi$
$787$	12.1097	0.431663	0.215831	+	0.976431i	$0.430754\pi$
$788$	−39.0252	−1.39022
$789$	−15.7326	−0.560094
$790$	40.3414	1.43528
$791$	31.3936	1.11623
$792$	−8.48354	−0.301450
$793$	−18.9236	−0.671997
$794$	−19.3767	−0.687655
$795$	31.2052	1.10673
$796$	−1.21007	−0.0428898
$797$	−24.6069	−0.871623	−0.435811	−	0.900038i	$-0.643539\pi$
$797$	−24.6069	−0.871623	−0.435811	+	0.900038i	$0.643539\pi$
$798$	5.93505	0.210099
$799$	−35.0462	−1.23984
$800$	19.8478	0.701725
$801$	15.8585	0.560332
$802$	60.4575	2.13483
$803$	21.4040	0.755330
$804$	3.46150	0.122078
$805$	−15.7857	−0.556371
$806$	−16.0046	−0.563737
$807$	6.79981	0.239365
$808$	20.2453	0.712226
$809$	−18.0003	−0.632858	−0.316429	−	0.948616i	$-0.602484\pi$
$809$	−18.0003	−0.632858	−0.316429	+	0.948616i	$0.602484\pi$
$810$	−14.0311	−0.493003
$811$	−34.5492	−1.21319	−0.606593	−	0.795012i	$-0.707464\pi$
$811$	−34.5492	−1.21319	−0.606593	+	0.795012i	$0.707464\pi$
$812$	20.6264	0.723845
$813$	−6.41657	−0.225039
$814$	−18.2111	−0.638297
$815$	−42.3210	−1.48244
$816$	−9.80369	−0.343198
$817$	9.00399	0.315010
$818$	12.3974	0.433465
$819$	19.8071	0.692115
$820$	−52.7484	−1.84205
$821$	29.0302	1.01316	0.506580	−	0.862193i	$-0.330910\pi$
$821$	29.0302	1.01316	0.506580	+	0.862193i	$0.330910\pi$
$822$	−0.566298	−0.0197519
$823$	−27.4393	−0.956475	−0.478238	−	0.878230i	$-0.658724\pi$
$823$	−27.4393	−0.956475	−0.478238	+	0.878230i	$0.658724\pi$
$824$	−15.3715	−0.535491
$825$	−8.23544	−0.286721
$826$	33.0151	1.14874
$827$	27.7489	0.964925	0.482463	−	0.875917i	$-0.339742\pi$
$827$	27.7489	0.964925	0.482463	+	0.875917i	$0.339742\pi$
$828$	−10.1141	−0.351489
$829$	−24.6494	−0.856110	−0.428055	−	0.903753i	$-0.640801\pi$
$829$	−24.6494	−0.856110	−0.428055	+	0.903753i	$0.640801\pi$
$830$	−86.4237	−2.99981
$831$	−19.6339	−0.681093
$832$	−32.7327	−1.13480
$833$	10.9148	0.378176
$834$	20.7213	0.717520
$835$	1.88751	0.0653199
$836$	−9.19523	−0.318024
$837$	−12.1843	−0.421151
$838$	−2.60783	−0.0900861
$839$	19.5185	0.673854	0.336927	−	0.941531i	$-0.390613\pi$
$839$	19.5185	0.673854	0.336927	+	0.941531i	$0.390613\pi$
$840$	8.02621	0.276930
$841$	−21.9930	−0.758380
$842$	−5.73750	−0.197727
$843$	−15.0583	−0.518635
$844$	16.6819	0.574214
$845$	−12.7927	−0.440083
$846$	−41.2948	−1.41975
$847$	−8.10151	−0.278371
$848$	−35.2124	−1.20920
$849$	20.7534	0.712256
$850$	−20.8878	−0.716447
$851$	−4.30077	−0.147428
$852$	8.98609	0.307858
$853$	−12.1243	−0.415129	−0.207564	−	0.978221i	$-0.566554\pi$
$853$	−12.1243	−0.415129	−0.207564	+	0.978221i	$0.566554\pi$
$854$	−43.4356	−1.48634
$855$	−6.01388	−0.205670
$856$	7.33640	0.250753
$857$	−10.9416	−0.373757	−0.186878	−	0.982383i	$-0.559837\pi$
$857$	−10.9416	−0.373757	−0.186878	+	0.982383i	$0.559837\pi$
$858$	20.2097	0.689948
$859$	24.0885	0.821890	0.410945	−	0.911660i	$-0.365199\pi$
$859$	24.0885	0.821890	0.410945	+	0.911660i	$0.365199\pi$
$860$	61.4695	2.09609
$861$	21.6317	0.737207
$862$	66.1895	2.25442
$863$	−12.3840	−0.421556	−0.210778	−	0.977534i	$-0.567600\pi$
$863$	−12.3840	−0.421556	−0.210778	+	0.977534i	$0.567600\pi$
$864$	−37.0801	−1.26149
$865$	−0.416865	−0.0141738
$866$	38.9191	1.32252
$867$	−1.23288	−0.0418708
$868$	−20.3870	−0.691979
$869$	25.6313	0.869481
$870$	13.7643	0.466655
$871$	4.46930	0.151436
$872$	−7.41584	−0.251132
$873$	−2.64258	−0.0894377
$874$	−3.91297	−0.132358
$875$	21.4425	0.724887
$876$	−12.9745	−0.438369
$877$	4.83926	0.163410	0.0817051	−	0.996657i	$-0.473963\pi$
$877$	4.83926	0.163410	0.0817051	+	0.996657i	$0.473963\pi$
$878$	16.9609	0.572402
$879$	21.4625	0.723911
$880$	27.9331	0.941624
$881$	25.0017	0.842329	0.421164	−	0.906984i	$-0.361622\pi$
$881$	25.0017	0.842329	0.421164	+	0.906984i	$0.361622\pi$
$882$	12.8609	0.433049
$883$	−8.38449	−0.282161	−0.141080	−	0.989998i	$-0.545058\pi$
$883$	−8.38449	−0.282161	−0.141080	+	0.989998i	$0.545058\pi$
$884$	28.4468	0.956769
$885$	12.2268	0.410999
$886$	−35.6534	−1.19780
$887$	16.9400	0.568790	0.284395	−	0.958707i	$-0.408207\pi$
$887$	16.9400	0.568790	0.284395	+	0.958707i	$0.408207\pi$
$888$	2.18672	0.0733816
$889$	−32.8002	−1.10008
$890$	41.8857	1.40401
$891$	−8.91479	−0.298657
$892$	−52.2119	−1.74819
$893$	−8.86630	−0.296699
$894$	38.4301	1.28529
$895$	−28.2216	−0.943344
$896$	−25.3788	−0.847848
$897$	4.77277	0.159358
$898$	−81.6909	−2.72606
$899$	−6.92563	−0.230983
$900$	−13.6589	−0.455296
$901$	50.2868	1.67529
$902$	−60.3896	−2.01075
$903$	−25.2082	−0.838875
$904$	10.5238	0.350015
$905$	−42.9350	−1.42721
$906$	−12.1861	−0.404857
$907$	−58.2231	−1.93327	−0.966633	−	0.256164i	$-0.917541\pi$
$907$	−58.2231	−1.93327	−0.966633	+	0.256164i	$0.917541\pi$
$908$	19.9851	0.663228
$909$	42.4692	1.40862
$910$	52.3148	1.73422
$911$	9.68896	0.321010	0.160505	−	0.987035i	$-0.448688\pi$
$911$	9.68896	0.321010	0.160505	+	0.987035i	$0.448688\pi$
$912$	−2.48023	−0.0821285
$913$	−54.9101	−1.81726
$914$	3.86462	0.127830
$915$	−16.0859	−0.531783
$916$	47.0696	1.55522
$917$	11.5763	0.382283
$918$	39.0232	1.28796
$919$	−33.4832	−1.10451	−0.552255	−	0.833675i	$-0.686233\pi$
$919$	−33.4832	−1.10451	−0.552255	+	0.833675i	$0.686233\pi$
$920$	−5.29166	−0.174461
$921$	−9.40962	−0.310058
$922$	13.7270	0.452076
$923$	11.6024	0.381896
$924$	25.7436	0.846901
$925$	−5.80811	−0.190969
$926$	11.4138	0.375080
$927$	−32.2453	−1.05908
$928$	−21.0766	−0.691873
$929$	16.2520	0.533212	0.266606	−	0.963806i	$-0.414098\pi$
$929$	16.2520	0.533212	0.266606	+	0.963806i	$0.414098\pi$
$930$	−13.6046	−0.446111
$931$	2.76133	0.0904989
$932$	3.75899	0.123130
$933$	0.506972	0.0165975
$934$	−8.80751	−0.288191
$935$	−39.8912	−1.30458
$936$	6.63972	0.217026
$937$	28.8685	0.943092	0.471546	−	0.881841i	$-0.343696\pi$
$937$	28.8685	0.943092	0.471546	+	0.881841i	$0.343696\pi$
$938$	10.2584	0.334950
$939$	−29.3024	−0.956246
$940$	−60.5294	−1.97425
$941$	1.57373	0.0513023	0.0256511	−	0.999671i	$-0.491834\pi$
$941$	1.57373	0.0513023	0.0256511	+	0.999671i	$0.491834\pi$
$942$	16.1725	0.526927
$943$	−14.2618	−0.464427
$944$	−13.7969	−0.449049
$945$	39.8273	1.29558
$946$	70.3740	2.28806
$947$	47.2058	1.53398	0.766991	−	0.641657i	$-0.221753\pi$
$947$	47.2058	1.53398	0.766991	+	0.641657i	$0.221753\pi$
$948$	−15.5370	−0.504618
$949$	−16.7520	−0.543793
$950$	−5.28440	−0.171448
$951$	0.896090	0.0290577
$952$	12.9341	0.419197
$953$	39.5327	1.28059	0.640294	−	0.768130i	$-0.278812\pi$
$953$	39.5327	1.28059	0.640294	+	0.768130i	$0.278812\pi$
$954$	59.2528	1.91838
$955$	8.64310	0.279684
$956$	21.3717	0.691210
$957$	8.74531	0.282696
$958$	−45.2758	−1.46279
$959$	−0.931386	−0.0300760
$960$	−27.8242	−0.898023
$961$	−24.1548	−0.779186
$962$	14.2531	0.459537
$963$	15.3898	0.495930
$964$	−17.7162	−0.570601
$965$	8.01124	0.257891
$966$	10.9550	0.352471
$967$	−36.6567	−1.17880	−0.589400	−	0.807842i	$-0.700636\pi$
$967$	−36.6567	−1.17880	−0.589400	+	0.807842i	$0.700636\pi$
$968$	−2.71579	−0.0872887
$969$	3.54201	0.113786
$970$	−6.97962	−0.224102
$971$	17.2027	0.552060	0.276030	−	0.961149i	$-0.410981\pi$
$971$	17.2027	0.552060	0.276030	+	0.961149i	$0.410981\pi$
$972$	40.2482	1.29096
$973$	34.0801	1.09256
$974$	51.3053	1.64393
$975$	6.44554	0.206422
$976$	18.1515	0.581016
$977$	29.3796	0.939937	0.469968	−	0.882683i	$-0.344265\pi$
$977$	29.3796	0.939937	0.469968	+	0.882683i	$0.344265\pi$
$978$	29.3701	0.939152
$979$	26.6125	0.850539
$980$	18.8513	0.602184
$981$	−15.5565	−0.496680
$982$	−5.29078	−0.168835
$983$	10.8387	0.345700	0.172850	−	0.984948i	$-0.444702\pi$
$983$	10.8387	0.345700	0.172850	+	0.984948i	$0.444702\pi$
$984$	7.25138	0.231166
$985$	−42.8314	−1.36472
$986$	22.1810	0.706389
$987$	24.8227	0.790114
$988$	7.19673	0.228958
$989$	16.6197	0.528476
$990$	−47.0037	−1.49388
$991$	4.22247	0.134131	0.0670656	−	0.997749i	$-0.478636\pi$
$991$	4.22247	0.134131	0.0670656	+	0.997749i	$0.478636\pi$
$992$	20.8319	0.661414
$993$	4.10659	0.130319
$994$	26.6311	0.844686
$995$	−1.32809	−0.0421032
$996$	33.2851	1.05468
$997$	3.78488	0.119868	0.0599341	−	0.998202i	$-0.480911\pi$
$997$	3.78488	0.119868	0.0599341	+	0.998202i	$0.480911\pi$
$998$	33.7105	1.06709
$999$	10.8509	0.343306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.16	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.11992 q^{2} +0.896090 q^{3} +2.49404 q^{4} +2.73729 q^{5} -1.89963 q^{6} -3.12431 q^{7} -1.04733 q^{8} -2.19702 q^{9} +O(q^{10})\)	\(q-2.11992 q^{2} +0.896090 q^{3} +2.49404 q^{4} +2.73729 q^{5} -1.89963 q^{6} -3.12431 q^{7} -1.04733 q^{8} -2.19702 q^{9} -5.80282 q^{10} -3.68688 q^{11} +2.23489 q^{12} +2.88557 q^{13} +6.62328 q^{14} +2.45285 q^{15} -2.76783 q^{16} +3.95274 q^{17} +4.65750 q^{18} +1.00000 q^{19} +6.82691 q^{20} -2.79966 q^{21} +7.81587 q^{22} +1.84581 q^{23} -0.938503 q^{24} +2.49274 q^{25} -6.11716 q^{26} -4.65700 q^{27} -7.79217 q^{28} -2.64707 q^{29} -5.19985 q^{30} +2.61634 q^{31} +7.96224 q^{32} -3.30377 q^{33} -8.37948 q^{34} -8.55214 q^{35} -5.47947 q^{36} -2.33001 q^{37} -2.11992 q^{38} +2.58573 q^{39} -2.86685 q^{40} -7.72654 q^{41} +5.93505 q^{42} +9.00399 q^{43} -9.19523 q^{44} -6.01388 q^{45} -3.91297 q^{46} -8.86630 q^{47} -2.48023 q^{48} +2.76133 q^{49} -5.28440 q^{50} +3.54201 q^{51} +7.19673 q^{52} +12.7220 q^{53} +9.87245 q^{54} -10.0920 q^{55} +3.27219 q^{56} +0.896090 q^{57} +5.61156 q^{58} +4.98471 q^{59} +6.11753 q^{60} -6.55802 q^{61} -5.54642 q^{62} +6.86419 q^{63} -11.3436 q^{64} +7.89862 q^{65} +7.00372 q^{66} +1.54885 q^{67} +9.85831 q^{68} +1.65401 q^{69} +18.1298 q^{70} +4.02083 q^{71} +2.30101 q^{72} -5.80545 q^{73} +4.93943 q^{74} +2.23372 q^{75} +2.49404 q^{76} +11.5190 q^{77} -5.48152 q^{78} -6.95203 q^{79} -7.57635 q^{80} +2.41798 q^{81} +16.3796 q^{82} +14.8934 q^{83} -6.98249 q^{84} +10.8198 q^{85} -19.0877 q^{86} -2.37201 q^{87} +3.86138 q^{88} -7.21817 q^{89} +12.7489 q^{90} -9.01541 q^{91} +4.60354 q^{92} +2.34447 q^{93} +18.7958 q^{94} +2.73729 q^{95} +7.13488 q^{96} +1.20280 q^{97} -5.85378 q^{98} +8.10015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 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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