LMFDB - Embedded newform 8003.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30251 q^{2} -2.68436 q^{3} +3.30157 q^{4} -0.273715 q^{5} +6.18077 q^{6} +3.09928 q^{7} -2.99689 q^{8} +4.20577 q^{9} +O(q^{10})$	\(q-2.30251 q^{2} -2.68436 q^{3} +3.30157 q^{4} -0.273715 q^{5} +6.18077 q^{6} +3.09928 q^{7} -2.99689 q^{8} +4.20577 q^{9} +0.630233 q^{10} -3.14304 q^{11} -8.86260 q^{12} +2.17908 q^{13} -7.13614 q^{14} +0.734749 q^{15} +0.297236 q^{16} +3.02184 q^{17} -9.68384 q^{18} -3.38274 q^{19} -0.903690 q^{20} -8.31957 q^{21} +7.23690 q^{22} +5.84847 q^{23} +8.04472 q^{24} -4.92508 q^{25} -5.01737 q^{26} -3.23671 q^{27} +10.2325 q^{28} -2.11916 q^{29} -1.69177 q^{30} +6.92521 q^{31} +5.30939 q^{32} +8.43705 q^{33} -6.95782 q^{34} -0.848320 q^{35} +13.8856 q^{36} -2.61354 q^{37} +7.78881 q^{38} -5.84944 q^{39} +0.820294 q^{40} +3.80783 q^{41} +19.1559 q^{42} -11.2999 q^{43} -10.3770 q^{44} -1.15118 q^{45} -13.4662 q^{46} +7.72615 q^{47} -0.797887 q^{48} +2.60554 q^{49} +11.3401 q^{50} -8.11169 q^{51} +7.19441 q^{52} +1.00000 q^{53} +7.45257 q^{54} +0.860299 q^{55} -9.28820 q^{56} +9.08048 q^{57} +4.87939 q^{58} +7.82348 q^{59} +2.42583 q^{60} +1.48170 q^{61} -15.9454 q^{62} +13.0349 q^{63} -12.8194 q^{64} -0.596449 q^{65} -19.4264 q^{66} -4.94378 q^{67} +9.97682 q^{68} -15.6994 q^{69} +1.95327 q^{70} -1.14315 q^{71} -12.6042 q^{72} +9.02985 q^{73} +6.01770 q^{74} +13.2207 q^{75} -11.1684 q^{76} -9.74117 q^{77} +13.4684 q^{78} -7.66783 q^{79} -0.0813580 q^{80} -3.92883 q^{81} -8.76758 q^{82} -12.0096 q^{83} -27.4677 q^{84} -0.827123 q^{85} +26.0181 q^{86} +5.68857 q^{87} +9.41935 q^{88} -10.1479 q^{89} +2.65061 q^{90} +6.75360 q^{91} +19.3092 q^{92} -18.5897 q^{93} -17.7896 q^{94} +0.925907 q^{95} -14.2523 q^{96} -0.983964 q^{97} -5.99930 q^{98} -13.2189 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * 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 $

$2$	−2.30251	−1.62812	−0.814062	−	0.580778i	$-0.802748\pi$
$2$	−2.30251	−1.62812	−0.814062	+	0.580778i	$0.802748\pi$
$3$	−2.68436	−1.54981	−0.774907	−	0.632075i	$-0.782203\pi$
$3$	−2.68436	−1.54981	−0.774907	+	0.632075i	$0.782203\pi$
$4$	3.30157	1.65079
$5$	−0.273715	−0.122409	−0.0612046	−	0.998125i	$-0.519494\pi$
$5$	−0.273715	−0.122409	−0.0612046	+	0.998125i	$0.519494\pi$
$6$	6.18077	2.52329
$7$	3.09928	1.17142	0.585709	−	0.810521i	$-0.300816\pi$
$7$	3.09928	1.17142	0.585709	+	0.810521i	$0.300816\pi$
$8$	−2.99689	−1.05956
$9$	4.20577	1.40192
$10$	0.630233	0.199297
$11$	−3.14304	−0.947663	−0.473832	−	0.880615i	$-0.657129\pi$
$11$	−3.14304	−0.947663	−0.473832	+	0.880615i	$0.657129\pi$
$12$	−8.86260	−2.55841
$13$	2.17908	0.604369	0.302185	−	0.953249i	$-0.402284\pi$
$13$	2.17908	0.604369	0.302185	+	0.953249i	$0.402284\pi$
$14$	−7.13614	−1.90721
$15$	0.734749	0.189711
$16$	0.297236	0.0743090
$17$	3.02184	0.732903	0.366452	−	0.930437i	$-0.380573\pi$
$17$	3.02184	0.732903	0.366452	+	0.930437i	$0.380573\pi$
$18$	−9.68384	−2.28250
$19$	−3.38274	−0.776054	−0.388027	−	0.921648i	$-0.626843\pi$
$19$	−3.38274	−0.776054	−0.388027	+	0.921648i	$0.626843\pi$
$20$	−0.903690	−0.202071
$21$	−8.31957	−1.81548
$22$	7.23690	1.54291
$23$	5.84847	1.21949	0.609746	−	0.792597i	$-0.291272\pi$
$23$	5.84847	1.21949	0.609746	+	0.792597i	$0.291272\pi$
$24$	8.04472	1.64212
$25$	−4.92508	−0.985016
$26$	−5.01737	−0.983988
$27$	−3.23671	−0.622905
$28$	10.2325	1.93376
$29$	−2.11916	−0.393518	−0.196759	−	0.980452i	$-0.563042\pi$
$29$	−2.11916	−0.393518	−0.196759	+	0.980452i	$0.563042\pi$
$30$	−1.69177	−0.308874
$31$	6.92521	1.24381	0.621903	−	0.783095i	$-0.286360\pi$
$31$	6.92521	1.24381	0.621903	+	0.783095i	$0.286360\pi$
$32$	5.30939	0.938576
$33$	8.43705	1.46870
$34$	−6.95782	−1.19326
$35$	−0.848320	−0.143392
$36$	13.8856	2.31427
$37$	−2.61354	−0.429663	−0.214831	−	0.976651i	$-0.568920\pi$
$37$	−2.61354	−0.429663	−0.214831	+	0.976651i	$0.568920\pi$
$38$	7.78881	1.26351
$39$	−5.84944	−0.936660
$40$	0.820294	0.129700
$41$	3.80783	0.594683	0.297341	−	0.954771i	$-0.403900\pi$
$41$	3.80783	0.594683	0.297341	+	0.954771i	$0.403900\pi$
$42$	19.1559	2.95583
$43$	−11.2999	−1.72321	−0.861607	−	0.507576i	$-0.830541\pi$
$43$	−11.2999	−1.72321	−0.861607	+	0.507576i	$0.830541\pi$
$44$	−10.3770	−1.56439
$45$	−1.15118	−0.171608
$46$	−13.4662	−1.98548
$47$	7.72615	1.12698	0.563488	−	0.826124i	$-0.309459\pi$
$47$	7.72615	1.12698	0.563488	+	0.826124i	$0.309459\pi$
$48$	−0.797887	−0.115165
$49$	2.60554	0.372220
$50$	11.3401	1.60373
$51$	−8.11169	−1.13586
$52$	7.19441	0.997685
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	7.45257	1.01417
$55$	0.860299	0.116003
$56$	−9.28820	−1.24119
$57$	9.08048	1.20274
$58$	4.87939	0.640695
$59$	7.82348	1.01853	0.509265	−	0.860609i	$-0.329917\pi$
$59$	7.82348	1.01853	0.509265	+	0.860609i	$0.329917\pi$
$60$	2.42583	0.313173
$61$	1.48170	0.189712	0.0948559	−	0.995491i	$-0.469761\pi$
$61$	1.48170	0.189712	0.0948559	+	0.995491i	$0.469761\pi$
$62$	−15.9454	−2.02507
$63$	13.0349	1.64224
$64$	−12.8194	−1.60243
$65$	−0.596449	−0.0739803
$66$	−19.4264	−2.39123
$67$	−4.94378	−0.603979	−0.301989	−	0.953311i	$-0.597651\pi$
$67$	−4.94378	−0.603979	−0.301989	+	0.953311i	$0.597651\pi$
$68$	9.97682	1.20987
$69$	−15.6994	−1.88998
$70$	1.95327	0.233460
$71$	−1.14315	−0.135667	−0.0678333	−	0.997697i	$-0.521609\pi$
$71$	−1.14315	−0.135667	−0.0678333	+	0.997697i	$0.521609\pi$
$72$	−12.6042	−1.48542
$73$	9.02985	1.05686	0.528432	−	0.848976i	$-0.322780\pi$
$73$	9.02985	1.05686	0.528432	+	0.848976i	$0.322780\pi$
$74$	6.01770	0.699544
$75$	13.2207	1.52659
$76$	−11.1684	−1.28110
$77$	−9.74117	−1.11011
$78$	13.4684	1.52500
$79$	−7.66783	−0.862698	−0.431349	−	0.902185i	$-0.641962\pi$
$79$	−7.66783	−0.862698	−0.431349	+	0.902185i	$0.641962\pi$
$80$	−0.0813580	−0.00909610
$81$	−3.92883	−0.436536
$82$	−8.76758	−0.968217
$83$	−12.0096	−1.31822	−0.659111	−	0.752046i	$-0.729067\pi$
$83$	−12.0096	−1.31822	−0.659111	+	0.752046i	$0.729067\pi$
$84$	−27.4677	−2.99697
$85$	−0.827123	−0.0897141
$86$	26.0181	2.80560
$87$	5.68857	0.609879
$88$	9.41935	1.00411
$89$	−10.1479	−1.07568	−0.537839	−	0.843048i	$-0.680759\pi$
$89$	−10.1479	−1.07568	−0.537839	+	0.843048i	$0.680759\pi$
$90$	2.65061	0.279399
$91$	6.75360	0.707969
$92$	19.3092	2.01312
$93$	−18.5897	−1.92767
$94$	−17.7896	−1.83486
$95$	0.925907	0.0949960
$96$	−14.2523	−1.45462
$97$	−0.983964	−0.0999064	−0.0499532	−	0.998752i	$-0.515907\pi$
$97$	−0.983964	−0.0999064	−0.0499532	+	0.998752i	$0.515907\pi$
$98$	−5.99930	−0.606021
$99$	−13.2189	−1.32855
$100$	−16.2605	−1.62605
$101$	−10.2998	−1.02487	−0.512436	−	0.858726i	$-0.671257\pi$
$101$	−10.2998	−1.02487	−0.512436	+	0.858726i	$0.671257\pi$
$102$	18.6773	1.84933
$103$	5.09747	0.502268	0.251134	−	0.967952i	$-0.419196\pi$
$103$	5.09747	0.502268	0.251134	+	0.967952i	$0.419196\pi$
$104$	−6.53048	−0.640366
$105$	2.27719	0.222231
$106$	−2.30251	−0.223640
$107$	−4.80359	−0.464381	−0.232190	−	0.972670i	$-0.574589\pi$
$107$	−4.80359	−0.464381	−0.232190	+	0.972670i	$0.574589\pi$
$108$	−10.6862	−1.02828
$109$	−11.8903	−1.13888	−0.569442	−	0.822032i	$-0.692840\pi$
$109$	−11.8903	−1.13888	−0.569442	+	0.822032i	$0.692840\pi$
$110$	−1.98085	−0.188867
$111$	7.01566	0.665897
$112$	0.921218	0.0870469
$113$	2.08219	0.195876	0.0979378	−	0.995193i	$-0.468775\pi$
$113$	2.08219	0.195876	0.0979378	+	0.995193i	$0.468775\pi$
$114$	−20.9079	−1.95821
$115$	−1.60082	−0.149277
$116$	−6.99655	−0.649613
$117$	9.16472	0.847279
$118$	−18.0137	−1.65829
$119$	9.36552	0.858536
$120$	−2.20196	−0.201011
$121$	−1.12128	−0.101935
$122$	−3.41163	−0.308874
$123$	−10.2216	−0.921647
$124$	22.8641	2.05326
$125$	2.71664	0.242984
$126$	−30.0129	−2.67377
$127$	−20.8957	−1.85419	−0.927095	−	0.374825i	$-0.877703\pi$
$127$	−20.8957	−1.85419	−0.927095	+	0.374825i	$0.877703\pi$
$128$	18.8981	1.67037
$129$	30.3329	2.67066
$130$	1.37333	0.120449
$131$	12.7326	1.11246	0.556228	−	0.831030i	$-0.312248\pi$
$131$	12.7326	1.11246	0.556228	+	0.831030i	$0.312248\pi$
$132$	27.8555	2.42451
$133$	−10.4841	−0.909083
$134$	11.3831	0.983352
$135$	0.885936	0.0762492
$136$	−9.05611	−0.776555
$137$	18.2264	1.55719	0.778593	−	0.627530i	$-0.215934\pi$
$137$	18.2264	1.55719	0.778593	+	0.627530i	$0.215934\pi$
$138$	36.1481	3.07713
$139$	11.0207	0.934767	0.467384	−	0.884055i	$-0.345197\pi$
$139$	11.0207	0.934767	0.467384	+	0.884055i	$0.345197\pi$
$140$	−2.80079	−0.236710
$141$	−20.7397	−1.74660
$142$	2.63211	0.220882
$143$	−6.84896	−0.572739
$144$	1.25011	0.104175
$145$	0.580045	0.0481702
$146$	−20.7914	−1.72071
$147$	−6.99420	−0.576872
$148$	−8.62878	−0.709281
$149$	−15.2067	−1.24578	−0.622891	−	0.782308i	$-0.714042\pi$
$149$	−15.2067	−1.24578	−0.622891	+	0.782308i	$0.714042\pi$
$150$	−30.4408	−2.48548
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	10.1377	0.822276
$153$	12.7091	1.02747
$154$	22.4292	1.80740
$155$	−1.89554	−0.152253
$156$	−19.3123	−1.54623
$157$	−6.39224	−0.510157	−0.255078	−	0.966920i	$-0.582101\pi$
$157$	−6.39224	−0.510157	−0.255078	+	0.966920i	$0.582101\pi$
$158$	17.6553	1.40458
$159$	−2.68436	−0.212883
$160$	−1.45326	−0.114890
$161$	18.1261	1.42853
$162$	9.04618	0.710735
$163$	−14.8738	−1.16500	−0.582502	−	0.812829i	$-0.697926\pi$
$163$	−14.8738	−1.16500	−0.582502	+	0.812829i	$0.697926\pi$
$164$	12.5718	0.981694
$165$	−2.30935	−0.179782
$166$	27.6522	2.14623
$167$	0.976248	0.0755443	0.0377722	−	0.999286i	$-0.487974\pi$
$167$	0.976248	0.0755443	0.0377722	+	0.999286i	$0.487974\pi$
$168$	24.9328	1.92361
$169$	−8.25159	−0.634738
$170$	1.90446	0.146066
$171$	−14.2270	−1.08797
$172$	−37.3073	−2.84466
$173$	−2.22492	−0.169158	−0.0845789	−	0.996417i	$-0.526955\pi$
$173$	−2.22492	−0.169158	−0.0845789	+	0.996417i	$0.526955\pi$
$174$	−13.0980	−0.992958
$175$	−15.2642	−1.15387
$176$	−0.934226	−0.0704199
$177$	−21.0010	−1.57853
$178$	23.3657	1.75134
$179$	−7.38138	−0.551710	−0.275855	−	0.961199i	$-0.588961\pi$
$179$	−7.38138	−0.551710	−0.275855	+	0.961199i	$0.588961\pi$
$180$	−3.80071	−0.283288
$181$	−5.66733	−0.421249	−0.210625	−	0.977567i	$-0.567550\pi$
$181$	−5.66733	−0.421249	−0.210625	+	0.977567i	$0.567550\pi$
$182$	−15.5503	−1.15266
$183$	−3.97740	−0.294018
$184$	−17.5272	−1.29212
$185$	0.715365	0.0525946
$186$	42.8031	3.13848
$187$	−9.49777	−0.694545
$188$	25.5085	1.86040
$189$	−10.0315	−0.729682
$190$	−2.13191	−0.154665
$191$	−4.68809	−0.339218	−0.169609	−	0.985511i	$-0.554250\pi$
$191$	−4.68809	−0.339218	−0.169609	+	0.985511i	$0.554250\pi$
$192$	34.4119	2.48346
$193$	−3.48040	−0.250525	−0.125262	−	0.992124i	$-0.539977\pi$
$193$	−3.48040	−0.250525	−0.125262	+	0.992124i	$0.539977\pi$
$194$	2.26559	0.162660
$195$	1.60108	0.114656
$196$	8.60239	0.614456
$197$	−11.6106	−0.827220	−0.413610	−	0.910454i	$-0.635732\pi$
$197$	−11.6106	−0.827220	−0.413610	+	0.910454i	$0.635732\pi$
$198$	30.4367	2.16304
$199$	−10.2770	−0.728521	−0.364260	−	0.931297i	$-0.618678\pi$
$199$	−10.2770	−0.728521	−0.364260	+	0.931297i	$0.618678\pi$
$200$	14.7599	1.04368
$201$	13.2709	0.936055
$202$	23.7155	1.66862
$203$	−6.56786	−0.460974
$204$	−26.7813	−1.87507
$205$	−1.04226	−0.0727946
$206$	−11.7370	−0.817755
$207$	24.5973	1.70963
$208$	0.647703	0.0449101
$209$	10.6321	0.735437
$210$	−5.24327	−0.361820
$211$	26.9508	1.85537	0.927684	−	0.373365i	$-0.121796\pi$
$211$	26.9508	1.85537	0.927684	+	0.373365i	$0.121796\pi$
$212$	3.30157	0.226753
$213$	3.06862	0.210258
$214$	11.0603	0.756070
$215$	3.09294	0.210937
$216$	9.70005	0.660005
$217$	21.4632	1.45702
$218$	27.3776	1.85424
$219$	−24.2393	−1.63794
$220$	2.84034	0.191496
$221$	6.58484	0.442944
$222$	−16.1537	−1.08416
$223$	−28.1434	−1.88462	−0.942310	−	0.334741i	$-0.891351\pi$
$223$	−28.1434	−1.88462	−0.942310	+	0.334741i	$0.891351\pi$
$224$	16.4553	1.09947
$225$	−20.7137	−1.38092
$226$	−4.79426	−0.318910
$227$	−7.48542	−0.496825	−0.248412	−	0.968654i	$-0.579909\pi$
$227$	−7.48542	−0.496825	−0.248412	+	0.968654i	$0.579909\pi$
$228$	29.9798	1.98546
$229$	23.7983	1.57263	0.786317	−	0.617823i	$-0.211985\pi$
$229$	23.7983	1.57263	0.786317	+	0.617823i	$0.211985\pi$
$230$	3.68590	0.243041
$231$	26.1488	1.72046
$232$	6.35088	0.416956
$233$	16.2683	1.06577	0.532885	−	0.846188i	$-0.321108\pi$
$233$	16.2683	1.06577	0.532885	+	0.846188i	$0.321108\pi$
$234$	−21.1019	−1.37947
$235$	−2.11477	−0.137952
$236$	25.8298	1.68138
$237$	20.5832	1.33702
$238$	−21.5643	−1.39780
$239$	24.3550	1.57539	0.787697	−	0.616063i	$-0.211273\pi$
$239$	24.3550	1.57539	0.787697	+	0.616063i	$0.211273\pi$
$240$	0.218394	0.0140973
$241$	20.3864	1.31320	0.656602	−	0.754238i	$-0.271993\pi$
$241$	20.3864	1.31320	0.656602	+	0.754238i	$0.271993\pi$
$242$	2.58177	0.165962
$243$	20.2565	1.29945
$244$	4.89193	0.313174
$245$	−0.713177	−0.0455632
$246$	23.5353	1.50056
$247$	−7.37128	−0.469023
$248$	−20.7541	−1.31789
$249$	32.2379	2.04300
$250$	−6.25511	−0.395608
$251$	26.6816	1.68413	0.842064	−	0.539378i	$-0.181340\pi$
$251$	26.6816	1.68413	0.842064	+	0.539378i	$0.181340\pi$
$252$	43.0355	2.71098
$253$	−18.3820	−1.15567
$254$	48.1126	3.01885
$255$	2.22029	0.139040
$256$	−17.8743	−1.11715
$257$	27.9483	1.74337	0.871684	−	0.490068i	$-0.163028\pi$
$257$	27.9483	1.74337	0.871684	+	0.490068i	$0.163028\pi$
$258$	−69.8419	−4.34816
$259$	−8.10008	−0.503315
$260$	−1.96922	−0.122126
$261$	−8.91268	−0.551681
$262$	−29.3171	−1.81121
$263$	9.92310	0.611884	0.305942	−	0.952050i	$-0.401029\pi$
$263$	9.92310	0.611884	0.305942	+	0.952050i	$0.401029\pi$
$264$	−25.2849	−1.55618
$265$	−0.273715	−0.0168142
$266$	24.1397	1.48010
$267$	27.2406	1.66710
$268$	−16.3222	−0.997040
$269$	−18.8182	−1.14737	−0.573683	−	0.819077i	$-0.694486\pi$
$269$	−18.8182	−1.14737	−0.573683	+	0.819077i	$0.694486\pi$
$270$	−2.03988	−0.124143
$271$	5.41354	0.328849	0.164425	−	0.986390i	$-0.447423\pi$
$271$	5.41354	0.328849	0.164425	+	0.986390i	$0.447423\pi$
$272$	0.898199	0.0544613
$273$	−18.1291	−1.09722
$274$	−41.9665	−2.53529
$275$	15.4797	0.933463
$276$	−51.8327	−3.11996
$277$	−15.6502	−0.940332	−0.470166	−	0.882578i	$-0.655806\pi$
$277$	−15.6502	−0.940332	−0.470166	+	0.882578i	$0.655806\pi$
$278$	−25.3754	−1.52192
$279$	29.1258	1.74372
$280$	2.54232	0.151933
$281$	−0.187016	−0.0111564	−0.00557822	−	0.999984i	$-0.501776\pi$
$281$	−0.187016	−0.0111564	−0.00557822	+	0.999984i	$0.501776\pi$
$282$	47.7536	2.84368
$283$	8.57715	0.509859	0.254929	−	0.966960i	$-0.417948\pi$
$283$	8.57715	0.509859	0.254929	+	0.966960i	$0.417948\pi$
$284$	−3.77419	−0.223957
$285$	−2.48546	−0.147226
$286$	15.7698	0.932489
$287$	11.8015	0.696622
$288$	22.3301	1.31581
$289$	−7.86850	−0.462853
$290$	−1.33556	−0.0784270
$291$	2.64131	0.154836
$292$	29.8127	1.74466
$293$	19.5941	1.14470	0.572349	−	0.820010i	$-0.306032\pi$
$293$	19.5941	1.14470	0.572349	+	0.820010i	$0.306032\pi$
$294$	16.1043	0.939219
$295$	−2.14141	−0.124678
$296$	7.83248	0.455254
$297$	10.1731	0.590304
$298$	35.0137	2.02829
$299$	12.7443	0.737023
$300$	43.6490	2.52008
$301$	−35.0215	−2.01860
$302$	−2.30251	−0.132495
$303$	27.6484	1.58836
$304$	−1.00547	−0.0576678
$305$	−0.405563	−0.0232225
$306$	−29.2630	−1.67285
$307$	14.7529	0.841993	0.420996	−	0.907062i	$-0.361681\pi$
$307$	14.7529	0.841993	0.420996	+	0.907062i	$0.361681\pi$
$308$	−32.1612	−1.83255
$309$	−13.6834	−0.778422
$310$	4.36450	0.247887
$311$	0.701555	0.0397815	0.0198908	−	0.999802i	$-0.493668\pi$
$311$	0.701555	0.0397815	0.0198908	+	0.999802i	$0.493668\pi$
$312$	17.5301	0.992448
$313$	−25.5680	−1.44519	−0.722595	−	0.691272i	$-0.757051\pi$
$313$	−25.5680	−1.44519	−0.722595	+	0.691272i	$0.757051\pi$
$314$	14.7182	0.830598
$315$	−3.56784	−0.201025
$316$	−25.3159	−1.42413
$317$	−11.3553	−0.637780	−0.318890	−	0.947792i	$-0.603310\pi$
$317$	−11.3553	−0.637780	−0.318890	+	0.947792i	$0.603310\pi$
$318$	6.18077	0.346600
$319$	6.66060	0.372922
$320$	3.50887	0.196152
$321$	12.8946	0.719704
$322$	−41.7355	−2.32583
$323$	−10.2221	−0.568772
$324$	−12.9713	−0.720628
$325$	−10.7322	−0.595314
$326$	34.2471	1.89677
$327$	31.9178	1.76506
$328$	−11.4116	−0.630102
$329$	23.9455	1.32016
$330$	5.31731	0.292708
$331$	3.63741	0.199930	0.0999651	−	0.994991i	$-0.468127\pi$
$331$	3.63741	0.199930	0.0999651	+	0.994991i	$0.468127\pi$
$332$	−39.6505	−2.17610
$333$	−10.9919	−0.602354
$334$	−2.24782	−0.122995
$335$	1.35319	0.0739325
$336$	−2.47288	−0.134907
$337$	−7.29909	−0.397607	−0.198803	−	0.980039i	$-0.563705\pi$
$337$	−7.29909	−0.397607	−0.198803	+	0.980039i	$0.563705\pi$
$338$	18.9994	1.03343
$339$	−5.58933	−0.303571
$340$	−2.73081	−0.148099
$341$	−21.7662	−1.17871
$342$	32.7579	1.77134
$343$	−13.6197	−0.735392
$344$	33.8645	1.82585
$345$	4.29716	0.231351
$346$	5.12292	0.275410
$347$	−26.3516	−1.41463	−0.707313	−	0.706901i	$-0.750093\pi$
$347$	−26.3516	−1.41463	−0.707313	+	0.706901i	$0.750093\pi$
$348$	18.7812	1.00678
$349$	30.0607	1.60911	0.804557	−	0.593876i	$-0.202403\pi$
$349$	30.0607	1.60911	0.804557	+	0.593876i	$0.202403\pi$
$350$	35.1461	1.87864
$351$	−7.05306	−0.376465
$352$	−16.6876	−0.889454
$353$	19.9244	1.06047	0.530233	−	0.847852i	$-0.322104\pi$
$353$	19.9244	1.06047	0.530233	+	0.847852i	$0.322104\pi$
$354$	48.3551	2.57005
$355$	0.312897	0.0166068
$356$	−33.5041	−1.77571
$357$	−25.1404	−1.33057
$358$	16.9957	0.898252
$359$	18.7937	0.991896	0.495948	−	0.868352i	$-0.334821\pi$
$359$	18.7937	0.991896	0.495948	+	0.868352i	$0.334821\pi$
$360$	3.44997	0.181829
$361$	−7.55708	−0.397741
$362$	13.0491	0.685846
$363$	3.00992	0.157980
$364$	22.2975	1.16871
$365$	−2.47161	−0.129370
$366$	9.15803	0.478698
$367$	3.60248	0.188048	0.0940239	−	0.995570i	$-0.470027\pi$
$367$	3.60248	0.188048	0.0940239	+	0.995570i	$0.470027\pi$
$368$	1.73838	0.0906192
$369$	16.0148	0.833699
$370$	−1.64714	−0.0856306
$371$	3.09928	0.160907
$372$	−61.3754	−3.18216
$373$	−20.7055	−1.07209	−0.536045	−	0.844189i	$-0.680082\pi$
$373$	−20.7055	−1.07209	−0.536045	+	0.844189i	$0.680082\pi$
$374$	21.8687	1.13081
$375$	−7.29244	−0.376580
$376$	−23.1544	−1.19410
$377$	−4.61782	−0.237830
$378$	23.0976	1.18801
$379$	3.86848	0.198711	0.0993553	−	0.995052i	$-0.468322\pi$
$379$	3.86848	0.198711	0.0993553	+	0.995052i	$0.468322\pi$
$380$	3.05695	0.156818
$381$	56.0914	2.87365
$382$	10.7944	0.552289
$383$	0.0466249	0.00238242	0.00119121	−	0.999999i	$-0.499621\pi$
$383$	0.0466249	0.00238242	0.00119121	+	0.999999i	$0.499621\pi$
$384$	−50.7293	−2.58877
$385$	2.66631	0.135888
$386$	8.01367	0.407885
$387$	−47.5246	−2.41581
$388$	−3.24863	−0.164924
$389$	−11.4356	−0.579807	−0.289903	−	0.957056i	$-0.593623\pi$
$389$	−11.4356	−0.579807	−0.289903	+	0.957056i	$0.593623\pi$
$390$	−3.68651	−0.186674
$391$	17.6731	0.893769
$392$	−7.80852	−0.394390
$393$	−34.1789	−1.72410
$394$	26.7335	1.34682
$395$	2.09880	0.105602
$396$	−43.6432	−2.19315
$397$	−4.91097	−0.246475	−0.123237	−	0.992377i	$-0.539328\pi$
$397$	−4.91097	−0.246475	−0.123237	+	0.992377i	$0.539328\pi$
$398$	23.6631	1.18612
$399$	28.1429	1.40891
$400$	−1.46391	−0.0731956
$401$	−31.9582	−1.59592	−0.797958	−	0.602713i	$-0.794086\pi$
$401$	−31.9582	−1.59592	−0.797958	+	0.602713i	$0.794086\pi$
$402$	−30.5564	−1.52401
$403$	15.0906	0.751718
$404$	−34.0056	−1.69184
$405$	1.07538	0.0534360
$406$	15.1226	0.750522
$407$	8.21446	0.407175
$408$	24.3098	1.20352
$409$	−7.36544	−0.364197	−0.182099	−	0.983280i	$-0.558289\pi$
$409$	−7.36544	−0.364197	−0.182099	+	0.983280i	$0.558289\pi$
$410$	2.39982	0.118519
$411$	−48.9261	−2.41335
$412$	16.8297	0.829138
$413$	24.2472	1.19313
$414$	−56.6357	−2.78349
$415$	3.28720	0.161362
$416$	11.5696	0.567247
$417$	−29.5836	−1.44872
$418$	−24.4805	−1.19738
$419$	6.10451	0.298225	0.149112	−	0.988820i	$-0.452358\pi$
$419$	6.10451	0.298225	0.149112	+	0.988820i	$0.452358\pi$
$420$	7.51832	0.366856
$421$	10.4759	0.510565	0.255282	−	0.966867i	$-0.417832\pi$
$421$	10.4759	0.510565	0.255282	+	0.966867i	$0.417832\pi$
$422$	−62.0546	−3.02077
$423$	32.4944	1.57993
$424$	−2.99689	−0.145542
$425$	−14.8828	−0.721921
$426$	−7.06553	−0.342326
$427$	4.59220	0.222232
$428$	−15.8594	−0.766594
$429$	18.3850	0.887638
$430$	−7.12155	−0.343432
$431$	−5.80572	−0.279652	−0.139826	−	0.990176i	$-0.544654\pi$
$431$	−5.80572	−0.279652	−0.139826	+	0.990176i	$0.544654\pi$
$432$	−0.962066	−0.0462874
$433$	−29.1816	−1.40238	−0.701189	−	0.712976i	$-0.747347\pi$
$433$	−29.1816	−1.40238	−0.701189	+	0.712976i	$0.747347\pi$
$434$	−49.4193	−2.37220
$435$	−1.55705	−0.0746548
$436$	−39.2566	−1.88005
$437$	−19.7839	−0.946390
$438$	55.8114	2.66677
$439$	35.0665	1.67363	0.836817	−	0.547483i	$-0.184414\pi$
$439$	35.0665	1.67363	0.836817	+	0.547483i	$0.184414\pi$
$440$	−2.57822	−0.122912
$441$	10.9583	0.521824
$442$	−15.1617	−0.721168
$443$	5.16267	0.245286	0.122643	−	0.992451i	$-0.460863\pi$
$443$	5.16267	0.245286	0.122643	+	0.992451i	$0.460863\pi$
$444$	23.1627	1.09925
$445$	2.77764	0.131673
$446$	64.8005	3.06839
$447$	40.8202	1.93073
$448$	−39.7310	−1.87711
$449$	26.2717	1.23984	0.619920	−	0.784665i	$-0.287165\pi$
$449$	26.2717	1.23984	0.619920	+	0.784665i	$0.287165\pi$
$450$	47.6937	2.24830
$451$	−11.9682	−0.563559
$452$	6.87449	0.323349
$453$	−2.68436	−0.126122
$454$	17.2353	0.808892
$455$	−1.84856	−0.0866619
$456$	−27.2132	−1.27437
$457$	−29.2167	−1.36670	−0.683350	−	0.730091i	$-0.739478\pi$
$457$	−29.2167	−1.36670	−0.683350	+	0.730091i	$0.739478\pi$
$458$	−54.7959	−2.56044
$459$	−9.78080	−0.456529
$460$	−5.28521	−0.246424
$461$	7.24645	0.337501	0.168750	−	0.985659i	$-0.446027\pi$
$461$	7.24645	0.337501	0.168750	+	0.985659i	$0.446027\pi$
$462$	−60.2079	−2.80113
$463$	24.5830	1.14247	0.571235	−	0.820787i	$-0.306465\pi$
$463$	24.5830	1.14247	0.571235	+	0.820787i	$0.306465\pi$
$464$	−0.629890	−0.0292419
$465$	5.08829	0.235964
$466$	−37.4579	−1.73521
$467$	−21.8162	−1.00954	−0.504768	−	0.863255i	$-0.668422\pi$
$467$	−21.8162	−1.00954	−0.504768	+	0.863255i	$0.668422\pi$
$468$	30.2580	1.39868
$469$	−15.3222	−0.707512
$470$	4.86928	0.224603
$471$	17.1591	0.790648
$472$	−23.4461	−1.07920
$473$	35.5160	1.63303
$474$	−47.3931	−2.17684
$475$	16.6603	0.764425
$476$	30.9210	1.41726
$477$	4.20577	0.192569
$478$	−56.0777	−2.56494
$479$	−31.3410	−1.43201	−0.716003	−	0.698097i	$-0.754030\pi$
$479$	−31.3410	−1.43201	−0.716003	+	0.698097i	$0.754030\pi$
$480$	3.90107	0.178059
$481$	−5.69512	−0.259675
$482$	−46.9400	−2.13806
$483$	−48.6568	−2.21396
$484$	−3.70199	−0.168272
$485$	0.269326	0.0122295
$486$	−46.6409	−2.11567
$487$	−22.5886	−1.02359	−0.511795	−	0.859108i	$-0.671019\pi$
$487$	−22.5886	−1.02359	−0.511795	+	0.859108i	$0.671019\pi$
$488$	−4.44048	−0.201011
$489$	39.9265	1.80554
$490$	1.64210	0.0741825
$491$	−0.632130	−0.0285276	−0.0142638	−	0.999898i	$-0.504540\pi$
$491$	−0.632130	−0.0285276	−0.0142638	+	0.999898i	$0.504540\pi$
$492$	−33.7472	−1.52144
$493$	−6.40375	−0.288410
$494$	16.9725	0.763627
$495$	3.61822	0.162627
$496$	2.05842	0.0924259
$497$	−3.54294	−0.158922
$498$	−74.2283	−3.32625
$499$	5.26420	0.235658	0.117829	−	0.993034i	$-0.462407\pi$
$499$	5.26420	0.235658	0.117829	+	0.993034i	$0.462407\pi$
$500$	8.96920	0.401115
$501$	−2.62060	−0.117080
$502$	−61.4348	−2.74197
$503$	23.1130	1.03056	0.515279	−	0.857023i	$-0.327688\pi$
$503$	23.1130	1.03056	0.515279	+	0.857023i	$0.327688\pi$
$504$	−39.0640	−1.74005
$505$	2.81922	0.125454
$506$	42.3248	1.88157
$507$	22.1502	0.983725
$508$	−68.9886	−3.06087
$509$	−12.9410	−0.573599	−0.286799	−	0.957991i	$-0.592591\pi$
$509$	−12.9410	−0.573599	−0.286799	+	0.957991i	$0.592591\pi$
$510$	−5.11225	−0.226374
$511$	27.9861	1.23803
$512$	3.35971	0.148480
$513$	10.9489	0.483407
$514$	−64.3514	−2.83842
$515$	−1.39525	−0.0614822
$516$	100.146	4.40869
$517$	−24.2836	−1.06799
$518$	18.6506	0.819458
$519$	5.97249	0.262163
$520$	1.78749	0.0783866
$521$	−20.1184	−0.881402	−0.440701	−	0.897654i	$-0.645270\pi$
$521$	−20.1184	−0.881402	−0.440701	+	0.897654i	$0.645270\pi$
$522$	20.5216	0.898205
$523$	43.6511	1.90873	0.954364	−	0.298647i	$-0.0965352\pi$
$523$	43.6511	1.90873	0.954364	+	0.298647i	$0.0965352\pi$
$524$	42.0377	1.83643
$525$	40.9746	1.78828
$526$	−22.8481	−0.996224
$527$	20.9269	0.911589
$528$	2.50779	0.109138
$529$	11.2046	0.487158
$530$	0.630233	0.0273756
$531$	32.9038	1.42790
$532$	−34.6139	−1.50070
$533$	8.29758	0.359408
$534$	−62.7220	−2.71425
$535$	1.31482	0.0568445
$536$	14.8160	0.639952
$537$	19.8142	0.855048
$538$	43.3292	1.86805
$539$	−8.18933	−0.352740
$540$	2.92498	0.125871
$541$	6.46670	0.278025	0.139013	−	0.990291i	$-0.455607\pi$
$541$	6.46670	0.278025	0.139013	+	0.990291i	$0.455607\pi$
$542$	−12.4648	−0.535407
$543$	15.2131	0.652858
$544$	16.0441	0.687886
$545$	3.25455	0.139410
$546$	41.7424	1.78641
$547$	21.7690	0.930774	0.465387	−	0.885107i	$-0.345915\pi$
$547$	21.7690	0.930774	0.465387	+	0.885107i	$0.345915\pi$
$548$	60.1757	2.57058
$549$	6.23167	0.265961
$550$	−35.6423	−1.51979
$551$	7.16855	0.305391
$552$	47.0493	2.00255
$553$	−23.7648	−1.01058
$554$	36.0349	1.53098
$555$	−1.92029	−0.0815119
$556$	36.3858	1.54310
$557$	3.35865	0.142311	0.0711553	−	0.997465i	$-0.477331\pi$
$557$	3.35865	0.142311	0.0711553	+	0.997465i	$0.477331\pi$
$558$	−67.0627	−2.83899
$559$	−24.6234	−1.04146
$560$	−0.252151	−0.0106553
$561$	25.4954	1.07642
$562$	0.430607	0.0181641
$563$	−16.2825	−0.686226	−0.343113	−	0.939294i	$-0.611481\pi$
$563$	−16.2825	−0.686226	−0.343113	+	0.939294i	$0.611481\pi$
$564$	−68.4738	−2.88327
$565$	−0.569926	−0.0239770
$566$	−19.7490	−0.830113
$567$	−12.1765	−0.511366
$568$	3.42589	0.143747
$569$	−6.99578	−0.293278	−0.146639	−	0.989190i	$-0.546846\pi$
$569$	−6.99578	−0.293278	−0.146639	+	0.989190i	$0.546846\pi$
$570$	5.72282	0.239702
$571$	0.547338	0.0229054	0.0114527	−	0.999934i	$-0.496354\pi$
$571$	0.547338	0.0229054	0.0114527	+	0.999934i	$0.496354\pi$
$572$	−22.6123	−0.945469
$573$	12.5845	0.525725
$574$	−27.1732	−1.13419
$575$	−28.8042	−1.20122
$576$	−53.9155	−2.24648
$577$	−25.7821	−1.07332	−0.536661	−	0.843798i	$-0.680315\pi$
$577$	−25.7821	−1.07332	−0.536661	+	0.843798i	$0.680315\pi$
$578$	18.1173	0.753581
$579$	9.34263	0.388267
$580$	1.91506	0.0795186
$581$	−37.2210	−1.54419
$582$	−6.08166	−0.252093
$583$	−3.14304	−0.130172
$584$	−27.0615	−1.11981
$585$	−2.50852	−0.103715
$586$	−45.1157	−1.86371
$587$	1.74641	0.0720819	0.0360409	−	0.999350i	$-0.488525\pi$
$587$	1.74641	0.0720819	0.0360409	+	0.999350i	$0.488525\pi$
$588$	−23.0919	−0.952293
$589$	−23.4262	−0.965259
$590$	4.93062	0.202990
$591$	31.1669	1.28204
$592$	−0.776837	−0.0319278
$593$	12.0609	0.495280	0.247640	−	0.968852i	$-0.420345\pi$
$593$	12.0609	0.495280	0.247640	+	0.968852i	$0.420345\pi$
$594$	−23.4237	−0.961087
$595$	−2.56349	−0.105093
$596$	−50.2061	−2.05652
$597$	27.5873	1.12907
$598$	−29.3440	−1.19996
$599$	−9.52183	−0.389052	−0.194526	−	0.980897i	$-0.562317\pi$
$599$	−9.52183	−0.389052	−0.194526	+	0.980897i	$0.562317\pi$
$600$	−39.6209	−1.61752
$601$	−21.3737	−0.871852	−0.435926	−	0.899983i	$-0.643579\pi$
$601$	−21.3737	−0.871852	−0.435926	+	0.899983i	$0.643579\pi$
$602$	80.6374	3.28654
$603$	−20.7924	−0.846731
$604$	3.30157	0.134339
$605$	0.306912	0.0124777
$606$	−63.6608	−2.58604
$607$	−25.2754	−1.02590	−0.512949	−	0.858419i	$-0.671447\pi$
$607$	−25.2754	−1.02590	−0.512949	+	0.858419i	$0.671447\pi$
$608$	−17.9603	−0.728385
$609$	17.6305	0.714423
$610$	0.933815	0.0378090
$611$	16.8359	0.681109
$612$	41.9602	1.69614
$613$	−14.9350	−0.603221	−0.301610	−	0.953431i	$-0.597524\pi$
$613$	−14.9350	−0.603221	−0.301610	+	0.953431i	$0.597524\pi$
$614$	−33.9688	−1.37087
$615$	2.79780	0.112818
$616$	29.1932	1.17623
$617$	20.3876	0.820775	0.410387	−	0.911911i	$-0.365394\pi$
$617$	20.3876	0.820775	0.410387	+	0.911911i	$0.365394\pi$
$618$	31.5063	1.26737
$619$	−26.4939	−1.06488	−0.532439	−	0.846468i	$-0.678725\pi$
$619$	−26.4939	−1.06488	−0.532439	+	0.846468i	$0.678725\pi$
$620$	−6.25825	−0.251337
$621$	−18.9298	−0.759627
$622$	−1.61534	−0.0647693
$623$	−31.4513	−1.26007
$624$	−1.73866	−0.0696023
$625$	23.8818	0.955273
$626$	58.8707	2.35295
$627$	−28.5403	−1.13979
$628$	−21.1045	−0.842160
$629$	−7.89768	−0.314901
$630$	8.21500	0.327293
$631$	37.5273	1.49394	0.746969	−	0.664859i	$-0.231509\pi$
$631$	37.5273	1.49394	0.746969	+	0.664859i	$0.231509\pi$
$632$	22.9796	0.914081
$633$	−72.3455	−2.87548
$634$	26.1458	1.03838
$635$	5.71946	0.226970
$636$	−8.86260	−0.351425
$637$	5.67770	0.224959
$638$	−15.3361	−0.607163
$639$	−4.80781	−0.190194
$640$	−5.17270	−0.204469
$641$	−1.67457	−0.0661415	−0.0330708	−	0.999453i	$-0.510529\pi$
$641$	−1.67457	−0.0661415	−0.0330708	+	0.999453i	$0.510529\pi$
$642$	−29.6899	−1.17177
$643$	28.6971	1.13170	0.565852	−	0.824507i	$-0.308547\pi$
$643$	28.6971	1.13170	0.565852	+	0.824507i	$0.308547\pi$
$644$	59.8445	2.35820
$645$	−8.30256	−0.326913
$646$	23.5365	0.926031
$647$	−42.2522	−1.66110	−0.830552	−	0.556941i	$-0.811975\pi$
$647$	−42.2522	−1.66110	−0.830552	+	0.556941i	$0.811975\pi$
$648$	11.7743	0.462536
$649$	−24.5895	−0.965224
$650$	24.7110	0.969244
$651$	−57.6148	−2.25810
$652$	−49.1068	−1.92317
$653$	−34.2471	−1.34019	−0.670096	−	0.742274i	$-0.733747\pi$
$653$	−34.2471	−1.34019	−0.670096	+	0.742274i	$0.733747\pi$
$654$	−73.4911	−2.87373
$655$	−3.48511	−0.136175
$656$	1.13182	0.0441903
$657$	37.9775	1.48164
$658$	−55.1349	−2.14938
$659$	0.259796	0.0101202	0.00506010	−	0.999987i	$-0.498389\pi$
$659$	0.259796	0.0101202	0.00506010	+	0.999987i	$0.498389\pi$
$660$	−7.62448	−0.296782
$661$	11.5442	0.449018	0.224509	−	0.974472i	$-0.427922\pi$
$661$	11.5442	0.449018	0.224509	+	0.974472i	$0.427922\pi$
$662$	−8.37519	−0.325511
$663$	−17.6761	−0.686481
$664$	35.9913	1.39673
$665$	2.86965	0.111280
$666$	25.3091	0.980706
$667$	−12.3938	−0.479891
$668$	3.22315	0.124708
$669$	75.5469	2.92081
$670$	−3.11573	−0.120371
$671$	−4.65704	−0.179783
$672$	−44.1718	−1.70397
$673$	−31.8421	−1.22742	−0.613712	−	0.789530i	$-0.710324\pi$
$673$	−31.8421	−1.22742	−0.613712	+	0.789530i	$0.710324\pi$
$674$	16.8063	0.647353
$675$	15.9410	0.613571
$676$	−27.2432	−1.04782
$677$	−22.9634	−0.882555	−0.441278	−	0.897371i	$-0.645475\pi$
$677$	−22.9634	−0.882555	−0.441278	+	0.897371i	$0.645475\pi$
$678$	12.8695	0.494250
$679$	−3.04958	−0.117032
$680$	2.47880	0.0950575
$681$	20.0935	0.769986
$682$	50.1171	1.91908
$683$	−42.3094	−1.61893	−0.809463	−	0.587171i	$-0.800241\pi$
$683$	−42.3094	−1.61893	−0.809463	+	0.587171i	$0.800241\pi$
$684$	−46.9715	−1.79600
$685$	−4.98884	−0.190614
$686$	31.3595	1.19731
$687$	−63.8830	−2.43729
$688$	−3.35873	−0.128050
$689$	2.17908	0.0830165
$690$	−9.89427	−0.376669
$691$	52.0437	1.97984	0.989918	−	0.141639i	$-0.0452373\pi$
$691$	52.0437	1.97984	0.989918	+	0.141639i	$0.0452373\pi$
$692$	−7.34575	−0.279244
$693$	−40.9691	−1.55629
$694$	60.6748	2.30318
$695$	−3.01654	−0.114424
$696$	−17.0480	−0.646204
$697$	11.5066	0.435845
$698$	−69.2153	−2.61984
$699$	−43.6698	−1.65175
$700$	−50.3959	−1.90479
$701$	−17.2892	−0.653004	−0.326502	−	0.945196i	$-0.605870\pi$
$701$	−17.2892	−0.653004	−0.326502	+	0.945196i	$0.605870\pi$
$702$	16.2398	0.612931
$703$	8.84091	0.333441
$704$	40.2920	1.51856
$705$	5.67678	0.213800
$706$	−45.8761	−1.72657
$707$	−31.9221	−1.20055
$708$	−69.3364	−2.60582
$709$	−9.57171	−0.359473	−0.179737	−	0.983715i	$-0.557525\pi$
$709$	−9.57171	−0.359473	−0.179737	+	0.983715i	$0.557525\pi$
$710$	−0.720450	−0.0270380
$711$	−32.2491	−1.20944
$712$	30.4122	1.13975
$713$	40.5019	1.51681
$714$	57.8861	2.16633
$715$	1.87466	0.0701084
$716$	−24.3701	−0.910755
$717$	−65.3775	−2.44157
$718$	−43.2729	−1.61493
$719$	19.0031	0.708695	0.354348	−	0.935114i	$-0.384703\pi$
$719$	19.0031	0.708695	0.354348	+	0.935114i	$0.384703\pi$
$720$	−0.342173	−0.0127520
$721$	15.7985	0.588366
$722$	17.4003	0.647571
$723$	−54.7243	−2.03522
$724$	−18.7111	−0.695393
$725$	10.4370	0.387621
$726$	−6.93038	−0.257210
$727$	−14.4382	−0.535482	−0.267741	−	0.963491i	$-0.586277\pi$
$727$	−14.4382	−0.535482	−0.267741	+	0.963491i	$0.586277\pi$
$728$	−20.2398	−0.750136
$729$	−42.5891	−1.57738
$730$	5.69091	0.210630
$731$	−34.1464	−1.26295
$732$	−13.1317	−0.485361
$733$	16.9441	0.625845	0.312922	−	0.949779i	$-0.398692\pi$
$733$	16.9441	0.625845	0.312922	+	0.949779i	$0.398692\pi$
$734$	−8.29476	−0.306165
$735$	1.91442	0.0706144
$736$	31.0518	1.14459
$737$	15.5385	0.572369
$738$	−36.8744	−1.35736
$739$	1.18302	0.0435180	0.0217590	−	0.999763i	$-0.493073\pi$
$739$	1.18302	0.0435180	0.0217590	+	0.999763i	$0.493073\pi$
$740$	2.36183	0.0868225
$741$	19.7871	0.726898
$742$	−7.13614	−0.261976
$743$	34.3355	1.25965	0.629823	−	0.776738i	$-0.283127\pi$
$743$	34.3355	1.25965	0.629823	+	0.776738i	$0.283127\pi$
$744$	55.7114	2.04248
$745$	4.16231	0.152495
$746$	47.6747	1.74550
$747$	−50.5094	−1.84804
$748$	−31.3576	−1.14655
$749$	−14.8877	−0.543984
$750$	16.7910	0.613119
$751$	20.3281	0.741782	0.370891	−	0.928676i	$-0.379052\pi$
$751$	20.3281	0.741782	0.370891	+	0.928676i	$0.379052\pi$
$752$	2.29649	0.0837444
$753$	−71.6229	−2.61008
$754$	10.6326	0.387217
$755$	−0.273715	−0.00996151
$756$	−33.1196	−1.20455
$757$	−7.66799	−0.278698	−0.139349	−	0.990243i	$-0.544501\pi$
$757$	−7.66799	−0.278698	−0.139349	+	0.990243i	$0.544501\pi$
$758$	−8.90724	−0.323525
$759$	49.3438	1.79107
$760$	−2.77484	−0.100654
$761$	−4.85031	−0.175824	−0.0879119	−	0.996128i	$-0.528019\pi$
$761$	−4.85031	−0.175824	−0.0879119	+	0.996128i	$0.528019\pi$
$762$	−129.151	−4.67866
$763$	−36.8513	−1.33411
$764$	−15.4781	−0.559976
$765$	−3.47869	−0.125772
$766$	−0.107355	−0.00387888
$767$	17.0480	0.615569
$768$	47.9811	1.73137
$769$	49.6447	1.79023	0.895116	−	0.445833i	$-0.147092\pi$
$769$	49.6447	1.79023	0.895116	+	0.445833i	$0.147092\pi$
$770$	−6.13921	−0.221242
$771$	−75.0233	−2.70190
$772$	−11.4908	−0.413563
$773$	26.2744	0.945024	0.472512	−	0.881324i	$-0.343347\pi$
$773$	26.2744	0.945024	0.472512	+	0.881324i	$0.343347\pi$
$774$	109.426	3.93324
$775$	−34.1072	−1.22517
$776$	2.94883	0.105857
$777$	21.7435	0.780044
$778$	26.3306	0.943997
$779$	−12.8809	−0.461506
$780$	5.28608	0.189272
$781$	3.59296	0.128566
$782$	−40.6927	−1.45517
$783$	6.85909	0.245124
$784$	0.774461	0.0276593
$785$	1.74965	0.0624478
$786$	78.6975	2.80705
$787$	−19.8187	−0.706461	−0.353231	−	0.935536i	$-0.614917\pi$
$787$	−19.8187	−0.706461	−0.353231	+	0.935536i	$0.614917\pi$
$788$	−38.3332	−1.36556
$789$	−26.6371	−0.948307
$790$	−4.83252	−0.171933
$791$	6.45328	0.229452
$792$	39.6156	1.40768
$793$	3.22874	0.114656
$794$	11.3076	0.401291
$795$	0.734749	0.0260589
$796$	−33.9304	−1.20263
$797$	32.0835	1.13646	0.568228	−	0.822871i	$-0.307629\pi$
$797$	32.0835	1.13646	0.568228	+	0.822871i	$0.307629\pi$
$798$	−64.7995	−2.29388
$799$	23.3472	0.825964
$800$	−26.1492	−0.924513
$801$	−42.6798	−1.50802
$802$	73.5842	2.59835
$803$	−28.3812	−1.00155
$804$	43.8147	1.54523
$805$	−4.96138	−0.174866
$806$	−34.7464	−1.22389
$807$	50.5148	1.77820
$808$	30.8674	1.08591
$809$	−25.1561	−0.884441	−0.442220	−	0.896906i	$-0.645809\pi$
$809$	−25.1561	−0.884441	−0.442220	+	0.896906i	$0.645809\pi$
$810$	−2.47608	−0.0870004
$811$	−42.5295	−1.49341	−0.746706	−	0.665155i	$-0.768366\pi$
$811$	−42.5295	−1.49341	−0.746706	+	0.665155i	$0.768366\pi$
$812$	−21.6843	−0.760969
$813$	−14.5319	−0.509655
$814$	−18.9139	−0.662932
$815$	4.07118	0.142607
$816$	−2.41109	−0.0844049
$817$	38.2245	1.33731
$818$	16.9590	0.592959
$819$	28.4041	0.992518
$820$	−3.44110	−0.120168
$821$	35.1911	1.22818	0.614088	−	0.789237i	$-0.289524\pi$
$821$	35.1911	1.22818	0.614088	+	0.789237i	$0.289524\pi$
$822$	112.653	3.92923
$823$	1.19175	0.0415418	0.0207709	−	0.999784i	$-0.493388\pi$
$823$	1.19175	0.0415418	0.0207709	+	0.999784i	$0.493388\pi$
$824$	−15.2765	−0.532184
$825$	−41.5531	−1.44669
$826$	−55.8295	−1.94256
$827$	17.5663	0.610841	0.305421	−	0.952218i	$-0.401203\pi$
$827$	17.5663	0.610841	0.305421	+	0.952218i	$0.401203\pi$
$828$	81.2098	2.82224
$829$	1.35590	0.0470925	0.0235463	−	0.999723i	$-0.492504\pi$
$829$	1.35590	0.0470925	0.0235463	+	0.999723i	$0.492504\pi$
$830$	−7.56883	−0.262718
$831$	42.0108	1.45734
$832$	−27.9346	−0.968458
$833$	7.87353	0.272802
$834$	68.1167	2.35869
$835$	−0.267214	−0.00924732
$836$	35.1026	1.21405
$837$	−22.4149	−0.774772
$838$	−14.0557	−0.485547
$839$	44.8533	1.54851	0.774254	−	0.632875i	$-0.218125\pi$
$839$	44.8533	1.54851	0.774254	+	0.632875i	$0.218125\pi$
$840$	−6.82450	−0.235468
$841$	−24.5092	−0.845144
$842$	−24.1209	−0.831263
$843$	0.502017	0.0172904
$844$	88.9800	3.06282
$845$	2.25858	0.0776977
$846$	−74.8188	−2.57232
$847$	−3.47516	−0.119408
$848$	0.297236	0.0102071
$849$	−23.0241	−0.790186
$850$	34.2678	1.17538
$851$	−15.2852	−0.523970
$852$	10.1313	0.347091
$853$	6.26724	0.214586	0.107293	−	0.994227i	$-0.465782\pi$
$853$	6.26724	0.214586	0.107293	+	0.994227i	$0.465782\pi$
$854$	−10.5736	−0.361821
$855$	3.89415	0.133177
$856$	14.3958	0.492040
$857$	−45.0601	−1.53922	−0.769611	−	0.638513i	$-0.779550\pi$
$857$	−45.0601	−1.53922	−0.769611	+	0.638513i	$0.779550\pi$
$858$	−42.3318	−1.44518
$859$	−32.0892	−1.09487	−0.547434	−	0.836849i	$-0.684395\pi$
$859$	−32.0892	−1.09487	−0.547434	+	0.836849i	$0.684395\pi$
$860$	10.2116	0.348212
$861$	−31.6795	−1.07963
$862$	13.3678	0.455308
$863$	−15.2291	−0.518404	−0.259202	−	0.965823i	$-0.583460\pi$
$863$	−15.2291	−0.518404	−0.259202	+	0.965823i	$0.583460\pi$
$864$	−17.1849	−0.584643
$865$	0.608996	0.0207065
$866$	67.1910	2.28324
$867$	21.1218	0.717335
$868$	70.8623	2.40522
$869$	24.1003	0.817548
$870$	3.58513	0.121547
$871$	−10.7729	−0.365026
$872$	35.6339	1.20672
$873$	−4.13832	−0.140061
$874$	45.5526	1.54084
$875$	8.41965	0.284636
$876$	−80.0279	−2.70389
$877$	−4.02567	−0.135937	−0.0679686	−	0.997687i	$-0.521652\pi$
$877$	−4.02567	−0.135937	−0.0679686	+	0.997687i	$0.521652\pi$
$878$	−80.7411	−2.72488
$879$	−52.5975	−1.77407
$880$	0.255712	0.00862004
$881$	−7.46080	−0.251361	−0.125680	−	0.992071i	$-0.540111\pi$
$881$	−7.46080	−0.251361	−0.125680	+	0.992071i	$0.540111\pi$
$882$	−25.2317	−0.849594
$883$	−25.5475	−0.859741	−0.429871	−	0.902890i	$-0.641441\pi$
$883$	−25.5475	−0.859741	−0.429871	+	0.902890i	$0.641441\pi$
$884$	21.7403	0.731206
$885$	5.74830	0.193227
$886$	−11.8871	−0.399356
$887$	−36.7495	−1.23393	−0.616963	−	0.786992i	$-0.711637\pi$
$887$	−36.7495	−1.23393	−0.616963	+	0.786992i	$0.711637\pi$
$888$	−21.0252	−0.705558
$889$	−64.7616	−2.17203
$890$	−6.39556	−0.214380
$891$	12.3485	0.413689
$892$	−92.9174	−3.11111
$893$	−26.1356	−0.874593
$894$	−93.9892	−3.14347
$895$	2.02039	0.0675343
$896$	58.5706	1.95671
$897$	−34.2103	−1.14225
$898$	−60.4911	−2.01861
$899$	−14.6756	−0.489459
$900$	−68.3879	−2.27960
$901$	3.02184	0.100672
$902$	27.5569	0.917544
$903$	94.0101	3.12846
$904$	−6.24008	−0.207542
$905$	1.55123	0.0515648
$906$	6.18077	0.205342
$907$	−4.06383	−0.134937	−0.0674686	−	0.997721i	$-0.521492\pi$
$907$	−4.06383	−0.134937	−0.0674686	+	0.997721i	$0.521492\pi$
$908$	−24.7137	−0.820152
$909$	−43.3187	−1.43679
$910$	4.25634	0.141096
$911$	10.9572	0.363029	0.181515	−	0.983388i	$-0.441900\pi$
$911$	10.9572	0.363029	0.181515	+	0.983388i	$0.441900\pi$
$912$	2.69904	0.0893743
$913$	37.7466	1.24923
$914$	67.2719	2.22516
$915$	1.08868	0.0359905
$916$	78.5717	2.59608
$917$	39.4620	1.30315
$918$	22.5204	0.743285
$919$	−2.65289	−0.0875106	−0.0437553	−	0.999042i	$-0.513932\pi$
$919$	−2.65289	−0.0875106	−0.0437553	+	0.999042i	$0.513932\pi$
$920$	4.79747	0.158168
$921$	−39.6020	−1.30493
$922$	−16.6850	−0.549493
$923$	−2.49102	−0.0819928
$924$	86.3321	2.84012
$925$	12.8719	0.423225
$926$	−56.6027	−1.86008
$927$	21.4388	0.704141
$928$	−11.2514	−0.369346
$929$	−59.4707	−1.95117	−0.975585	−	0.219623i	$-0.929517\pi$
$929$	−59.4707	−1.95117	−0.975585	+	0.219623i	$0.929517\pi$
$930$	−11.7159	−0.384179
$931$	−8.81387	−0.288863
$932$	53.7109	1.75936
$933$	−1.88322	−0.0616540
$934$	50.2322	1.64365
$935$	2.59968	0.0850187
$936$	−27.4657	−0.897743
$937$	−54.2017	−1.77069	−0.885346	−	0.464933i	$-0.846078\pi$
$937$	−54.2017	−1.77069	−0.885346	+	0.464933i	$0.846078\pi$
$938$	35.2795	1.15192
$939$	68.6337	2.23977
$940$	−6.98205	−0.227729
$941$	−43.5369	−1.41926	−0.709632	−	0.704573i	$-0.751139\pi$
$941$	−43.5369	−1.41926	−0.709632	+	0.704573i	$0.751139\pi$
$942$	−39.5090	−1.28727
$943$	22.2700	0.725210
$944$	2.32542	0.0756860
$945$	2.74576	0.0893197
$946$	−81.7760	−2.65877
$947$	34.1513	1.10977	0.554884	−	0.831928i	$-0.312763\pi$
$947$	34.1513	1.10977	0.554884	+	0.831928i	$0.312763\pi$
$948$	67.9569	2.20714
$949$	19.6768	0.638737
$950$	−38.3605	−1.24458
$951$	30.4818	0.988439
$952$	−28.0674	−0.909671
$953$	47.9124	1.55204	0.776018	−	0.630711i	$-0.217236\pi$
$953$	47.9124	1.55204	0.776018	+	0.630711i	$0.217236\pi$
$954$	−9.68384	−0.313526
$955$	1.28320	0.0415234
$956$	80.4098	2.60064
$957$	−17.8794	−0.577960
$958$	72.1631	2.33148
$959$	56.4887	1.82412
$960$	−9.41905	−0.303999
$961$	16.9586	0.547051
$962$	13.1131	0.422783
$963$	−20.2028	−0.651026
$964$	67.3072	2.16782
$965$	0.952638	0.0306665
$966$	112.033	3.60460
$967$	−2.33827	−0.0751936	−0.0375968	−	0.999293i	$-0.511970\pi$
$967$	−2.33827	−0.0751936	−0.0375968	+	0.999293i	$0.511970\pi$
$968$	3.36036	0.108006
$969$	27.4397	0.881491
$970$	−0.620127	−0.0199111
$971$	30.1194	0.966577	0.483288	−	0.875461i	$-0.339442\pi$
$971$	30.1194	0.966577	0.483288	+	0.875461i	$0.339442\pi$
$972$	66.8783	2.14512
$973$	34.1564	1.09500
$974$	52.0107	1.66653
$975$	28.8090	0.922625
$976$	0.440414	0.0140973
$977$	−35.7212	−1.14282	−0.571411	−	0.820664i	$-0.693604\pi$
$977$	−35.7212	−1.14282	−0.571411	+	0.820664i	$0.693604\pi$
$978$	−91.9313	−2.93964
$979$	31.8954	1.01938
$980$	−2.35460	−0.0752151
$981$	−50.0078	−1.59663
$982$	1.45549	0.0464465
$983$	−32.2626	−1.02902	−0.514508	−	0.857485i	$-0.672026\pi$
$983$	−32.2626	−1.02902	−0.514508	+	0.857485i	$0.672026\pi$
$984$	30.6329	0.976541
$985$	3.17799	0.101259
$986$	14.7447	0.469568
$987$	−64.2783	−2.04600
$988$	−24.3368	−0.774257
$989$	−66.0870	−2.10144
$990$	−8.33099	−0.264776
$991$	4.39118	0.139491	0.0697453	−	0.997565i	$-0.477781\pi$
$991$	4.39118	0.139491	0.0697453	+	0.997565i	$0.477781\pi$
$992$	36.7687	1.16741
$993$	−9.76411	−0.309855
$994$	8.15766	0.258745
$995$	2.81298	0.0891776
$996$	106.436	3.37255
$997$	−17.4750	−0.553440	−0.276720	−	0.960951i	$-0.589247\pi$
$997$	−17.4750	−0.553440	−0.276720	+	0.960951i	$0.589247\pi$
$998$	−12.1209	−0.383680
$999$	8.45925	0.267639

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.18	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.18	✓	147	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30251 q^{2} -2.68436 q^{3} +3.30157 q^{4} -0.273715 q^{5} +6.18077 q^{6} +3.09928 q^{7} -2.99689 q^{8} +4.20577 q^{9} +O(q^{10})\)	\(q-2.30251 q^{2} -2.68436 q^{3} +3.30157 q^{4} -0.273715 q^{5} +6.18077 q^{6} +3.09928 q^{7} -2.99689 q^{8} +4.20577 q^{9} +0.630233 q^{10} -3.14304 q^{11} -8.86260 q^{12} +2.17908 q^{13} -7.13614 q^{14} +0.734749 q^{15} +0.297236 q^{16} +3.02184 q^{17} -9.68384 q^{18} -3.38274 q^{19} -0.903690 q^{20} -8.31957 q^{21} +7.23690 q^{22} +5.84847 q^{23} +8.04472 q^{24} -4.92508 q^{25} -5.01737 q^{26} -3.23671 q^{27} +10.2325 q^{28} -2.11916 q^{29} -1.69177 q^{30} +6.92521 q^{31} +5.30939 q^{32} +8.43705 q^{33} -6.95782 q^{34} -0.848320 q^{35} +13.8856 q^{36} -2.61354 q^{37} +7.78881 q^{38} -5.84944 q^{39} +0.820294 q^{40} +3.80783 q^{41} +19.1559 q^{42} -11.2999 q^{43} -10.3770 q^{44} -1.15118 q^{45} -13.4662 q^{46} +7.72615 q^{47} -0.797887 q^{48} +2.60554 q^{49} +11.3401 q^{50} -8.11169 q^{51} +7.19441 q^{52} +1.00000 q^{53} +7.45257 q^{54} +0.860299 q^{55} -9.28820 q^{56} +9.08048 q^{57} +4.87939 q^{58} +7.82348 q^{59} +2.42583 q^{60} +1.48170 q^{61} -15.9454 q^{62} +13.0349 q^{63} -12.8194 q^{64} -0.596449 q^{65} -19.4264 q^{66} -4.94378 q^{67} +9.97682 q^{68} -15.6994 q^{69} +1.95327 q^{70} -1.14315 q^{71} -12.6042 q^{72} +9.02985 q^{73} +6.01770 q^{74} +13.2207 q^{75} -11.1684 q^{76} -9.74117 q^{77} +13.4684 q^{78} -7.66783 q^{79} -0.0813580 q^{80} -3.92883 q^{81} -8.76758 q^{82} -12.0096 q^{83} -27.4677 q^{84} -0.827123 q^{85} +26.0181 q^{86} +5.68857 q^{87} +9.41935 q^{88} -10.1479 q^{89} +2.65061 q^{90} +6.75360 q^{91} +19.3092 q^{92} -18.5897 q^{93} -17.7896 q^{94} +0.925907 q^{95} -14.2523 q^{96} -0.983964 q^{97} -5.99930 q^{98} -13.2189 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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