LMFDB - Embedded newform 8003.2.a.b.1.6

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:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +O(q^{10})$	\(q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +8.55094 q^{10} +6.56696 q^{11} -12.1272 q^{12} -0.553887 q^{13} -1.60302 q^{14} +8.08846 q^{15} +10.0993 q^{16} +6.81718 q^{17} -8.29493 q^{18} +7.03627 q^{19} -15.9210 q^{20} -1.51632 q^{21} -17.2322 q^{22} -1.85353 q^{23} +18.7961 q^{24} +5.61878 q^{25} +1.45344 q^{26} -0.399838 q^{27} +2.98466 q^{28} +6.42256 q^{29} -21.2247 q^{30} -1.64144 q^{31} -11.3562 q^{32} -16.3002 q^{33} -17.8888 q^{34} -1.99067 q^{35} +15.4444 q^{36} -2.92399 q^{37} -18.4637 q^{38} +1.37483 q^{39} +24.6761 q^{40} +4.41849 q^{41} +3.97893 q^{42} -2.75943 q^{43} +32.0847 q^{44} -10.3009 q^{45} +4.86381 q^{46} +0.122965 q^{47} -25.0679 q^{48} -6.62682 q^{49} -14.7441 q^{50} -16.9213 q^{51} -2.70617 q^{52} -1.00000 q^{53} +1.04920 q^{54} -21.3994 q^{55} -4.62595 q^{56} -17.4651 q^{57} -16.8533 q^{58} +2.05909 q^{59} +39.5184 q^{60} -8.14786 q^{61} +4.30725 q^{62} +1.93107 q^{63} +9.60108 q^{64} +1.80492 q^{65} +42.7729 q^{66} -5.00407 q^{67} +33.3072 q^{68} +4.60075 q^{69} +5.22366 q^{70} +0.658063 q^{71} -23.9373 q^{72} +5.08046 q^{73} +7.67277 q^{74} -13.9467 q^{75} +34.3777 q^{76} +4.01167 q^{77} -3.60767 q^{78} -9.53151 q^{79} -32.9099 q^{80} -8.49080 q^{81} -11.5945 q^{82} -0.567433 q^{83} -7.40839 q^{84} -22.2148 q^{85} +7.24097 q^{86} -15.9418 q^{87} -49.7282 q^{88} -2.38038 q^{89} +27.0302 q^{90} -0.338363 q^{91} -9.05594 q^{92} +4.07430 q^{93} -0.322669 q^{94} -22.9287 q^{95} +28.1879 q^{96} -12.0139 q^{97} +17.3893 q^{98} +20.7587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.62408	−1.85550	−0.927751	−	0.373200i	$-0.878261\pi$
$2$	−2.62408	−1.85550	−0.927751	+	0.373200i	$0.878261\pi$
$3$	−2.48215	−1.43307	−0.716536	−	0.697550i	$-0.754273\pi$
$3$	−2.48215	−1.43307	−0.716536	+	0.697550i	$0.754273\pi$
$4$	4.88578	2.44289
$5$	−3.25865	−1.45731	−0.728656	−	0.684880i	$-0.759855\pi$
$5$	−3.25865	−1.45731	−0.728656	+	0.684880i	$0.759855\pi$
$6$	6.51336	2.65907
$7$	0.610888	0.230894	0.115447	−	0.993314i	$-0.463170\pi$
$7$	0.610888	0.230894	0.115447	+	0.993314i	$0.463170\pi$
$8$	−7.57250	−2.67728
$9$	3.16108	1.05369
$10$	8.55094	2.70404
$11$	6.56696	1.98001	0.990006	−	0.141027i	$-0.0450403\pi$
$11$	6.56696	1.98001	0.990006	+	0.141027i	$0.0450403\pi$
$12$	−12.1272	−3.50083
$13$	−0.553887	−0.153621	−0.0768104	−	0.997046i	$-0.524474\pi$
$13$	−0.553887	−0.153621	−0.0768104	+	0.997046i	$0.524474\pi$
$14$	−1.60302	−0.428424
$15$	8.08846	2.08843
$16$	10.0993	2.52481
$17$	6.81718	1.65341	0.826705	−	0.562636i	$-0.190213\pi$
$17$	6.81718	1.65341	0.826705	+	0.562636i	$0.190213\pi$
$18$	−8.29493	−1.95513
$19$	7.03627	1.61423	0.807116	−	0.590393i	$-0.201027\pi$
$19$	7.03627	1.61423	0.807116	+	0.590393i	$0.201027\pi$
$20$	−15.9210	−3.56005
$21$	−1.51632	−0.330888
$22$	−17.2322	−3.67392
$23$	−1.85353	−0.386488	−0.193244	−	0.981151i	$-0.561901\pi$
$23$	−1.85353	−0.386488	−0.193244	+	0.981151i	$0.561901\pi$
$24$	18.7961	3.83674
$25$	5.61878	1.12376
$26$	1.45344	0.285044
$27$	−0.399838	−0.0769488
$28$	2.98466	0.564048
$29$	6.42256	1.19264	0.596320	−	0.802747i	$-0.296629\pi$
$29$	6.42256	1.19264	0.596320	+	0.802747i	$0.296629\pi$
$30$	−21.2247	−3.87509
$31$	−1.64144	−0.294811	−0.147405	−	0.989076i	$-0.547092\pi$
$31$	−1.64144	−0.294811	−0.147405	+	0.989076i	$0.547092\pi$
$32$	−11.3562	−2.00752
$33$	−16.3002	−2.83750
$34$	−17.8888	−3.06791
$35$	−1.99067	−0.336484
$36$	15.4444	2.57406
$37$	−2.92399	−0.480701	−0.240350	−	0.970686i	$-0.577262\pi$
$37$	−2.92399	−0.480701	−0.240350	+	0.970686i	$0.577262\pi$
$38$	−18.4637	−2.99521
$39$	1.37483	0.220150
$40$	24.6761	3.90163
$41$	4.41849	0.690053	0.345026	−	0.938593i	$-0.387870\pi$
$41$	4.41849	0.690053	0.345026	+	0.938593i	$0.387870\pi$
$42$	3.97893	0.613963
$43$	−2.75943	−0.420810	−0.210405	−	0.977614i	$-0.567478\pi$
$43$	−2.75943	−0.420810	−0.210405	+	0.977614i	$0.567478\pi$
$44$	32.0847	4.83695
$45$	−10.3009	−1.53556
$46$	4.86381	0.717129
$47$	0.122965	0.0179362	0.00896812	−	0.999960i	$-0.497145\pi$
$47$	0.122965	0.0179362	0.00896812	+	0.999960i	$0.497145\pi$
$48$	−25.0679	−3.61824
$49$	−6.62682	−0.946688
$50$	−14.7441	−2.08513
$51$	−16.9213	−2.36946
$52$	−2.70617	−0.375278
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.04920	0.142779
$55$	−21.3994	−2.88549
$56$	−4.62595	−0.618168
$57$	−17.4651	−2.31331
$58$	−16.8533	−2.21295
$59$	2.05909	0.268071	0.134035	−	0.990977i	$-0.457206\pi$
$59$	2.05909	0.268071	0.134035	+	0.990977i	$0.457206\pi$
$60$	39.5184	5.10181
$61$	−8.14786	−1.04323	−0.521613	−	0.853182i	$-0.674670\pi$
$61$	−8.14786	−1.04323	−0.521613	+	0.853182i	$0.674670\pi$
$62$	4.30725	0.547022
$63$	1.93107	0.243292
$64$	9.60108	1.20014
$65$	1.80492	0.223873
$66$	42.7729	5.26499
$67$	−5.00407	−0.611344	−0.305672	−	0.952137i	$-0.598881\pi$
$67$	−5.00407	−0.611344	−0.305672	+	0.952137i	$0.598881\pi$
$68$	33.3072	4.03910
$69$	4.60075	0.553865
$70$	5.22366	0.624347
$71$	0.658063	0.0780977	0.0390488	−	0.999237i	$-0.487567\pi$
$71$	0.658063	0.0780977	0.0390488	+	0.999237i	$0.487567\pi$
$72$	−23.9373	−2.82104
$73$	5.08046	0.594622	0.297311	−	0.954781i	$-0.403910\pi$
$73$	5.08046	0.594622	0.297311	+	0.954781i	$0.403910\pi$
$74$	7.67277	0.891942
$75$	−13.9467	−1.61042
$76$	34.3777	3.94339
$77$	4.01167	0.457173
$78$	−3.60767	−0.408488
$79$	−9.53151	−1.07238	−0.536189	−	0.844098i	$-0.680137\pi$
$79$	−9.53151	−1.07238	−0.536189	+	0.844098i	$0.680137\pi$
$80$	−32.9099	−3.67944
$81$	−8.49080	−0.943422
$82$	−11.5945	−1.28039
$83$	−0.567433	−0.0622839	−0.0311419	−	0.999515i	$-0.509914\pi$
$83$	−0.567433	−0.0622839	−0.0311419	+	0.999515i	$0.509914\pi$
$84$	−7.40839	−0.808321
$85$	−22.2148	−2.40953
$86$	7.24097	0.780814
$87$	−15.9418	−1.70914
$88$	−49.7282	−5.30105
$89$	−2.38038	−0.252320	−0.126160	−	0.992010i	$-0.540265\pi$
$89$	−2.38038	−0.252320	−0.126160	+	0.992010i	$0.540265\pi$
$90$	27.0302	2.84924
$91$	−0.338363	−0.0354701
$92$	−9.05594	−0.944147
$93$	4.07430	0.422485
$94$	−0.322669	−0.0332807
$95$	−22.9287	−2.35244
$96$	28.1879	2.87691
$97$	−12.0139	−1.21982	−0.609911	−	0.792470i	$-0.708795\pi$
$97$	−12.0139	−1.21982	−0.609911	+	0.792470i	$0.708795\pi$
$98$	17.3893	1.75658
$99$	20.7587	2.08633
$100$	27.4521	2.74521
$101$	7.81888	0.778007	0.389004	−	0.921236i	$-0.372819\pi$
$101$	7.81888	0.778007	0.389004	+	0.921236i	$0.372819\pi$
$102$	44.4028	4.39653
$103$	−4.44738	−0.438213	−0.219107	−	0.975701i	$-0.570314\pi$
$103$	−4.44738	−0.438213	−0.219107	+	0.975701i	$0.570314\pi$
$104$	4.19431	0.411286
$105$	4.94114	0.482206
$106$	2.62408	0.254873
$107$	1.68699	0.163088	0.0815439	−	0.996670i	$-0.474015\pi$
$107$	1.68699	0.163088	0.0815439	+	0.996670i	$0.474015\pi$
$108$	−1.95352	−0.187977
$109$	−7.52303	−0.720575	−0.360288	−	0.932841i	$-0.617321\pi$
$109$	−7.52303	−0.720575	−0.360288	+	0.932841i	$0.617321\pi$
$110$	56.1536	5.35404
$111$	7.25779	0.688879
$112$	6.16951	0.582964
$113$	−9.84428	−0.926072	−0.463036	−	0.886340i	$-0.653240\pi$
$113$	−9.84428	−0.926072	−0.463036	+	0.886340i	$0.653240\pi$
$114$	45.8298	4.29235
$115$	6.04000	0.563233
$116$	31.3792	2.91349
$117$	−1.75088	−0.161869
$118$	−5.40321	−0.497406
$119$	4.16454	0.381762
$120$	−61.2498	−5.59132
$121$	32.1249	2.92045
$122$	21.3806	1.93571
$123$	−10.9674	−0.988896
$124$	−8.01969	−0.720189
$125$	−2.01640	−0.180352
$126$	−5.06727	−0.451428
$127$	−18.4441	−1.63665	−0.818323	−	0.574758i	$-0.805096\pi$
$127$	−18.4441	−1.63665	−0.818323	+	0.574758i	$0.805096\pi$
$128$	−2.48153	−0.219338
$129$	6.84934	0.603051
$130$	−4.73626	−0.415397
$131$	7.41549	0.647894	0.323947	−	0.946075i	$-0.394990\pi$
$131$	7.41549	0.647894	0.323947	+	0.946075i	$0.394990\pi$
$132$	−79.6391	−6.93169
$133$	4.29837	0.372716
$134$	13.1310	1.13435
$135$	1.30293	0.112138
$136$	−51.6231	−4.42664
$137$	6.68839	0.571428	0.285714	−	0.958315i	$-0.407769\pi$
$137$	6.68839	0.571428	0.285714	+	0.958315i	$0.407769\pi$
$138$	−12.0727	−1.02770
$139$	−5.83713	−0.495099	−0.247549	−	0.968875i	$-0.579625\pi$
$139$	−5.83713	−0.495099	−0.247549	+	0.968875i	$0.579625\pi$
$140$	−9.72596	−0.821993
$141$	−0.305217	−0.0257039
$142$	−1.72681	−0.144910
$143$	−3.63735	−0.304171
$144$	31.9246	2.66038
$145$	−20.9289	−1.73805
$146$	−13.3315	−1.10332
$147$	16.4488	1.35667
$148$	−14.2860	−1.17430
$149$	−19.5185	−1.59902	−0.799508	−	0.600656i	$-0.794906\pi$
$149$	−19.5185	−1.59902	−0.799508	+	0.600656i	$0.794906\pi$
$150$	36.5972	2.98815
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−53.2821	−4.32175
$153$	21.5497	1.74219
$154$	−10.5269	−0.848285
$155$	5.34886	0.429631
$156$	6.71713	0.537801
$157$	−3.54755	−0.283125	−0.141563	−	0.989929i	$-0.545213\pi$
$157$	−3.54755	−0.283125	−0.141563	+	0.989929i	$0.545213\pi$
$158$	25.0114	1.98980
$159$	2.48215	0.196848
$160$	37.0059	2.92558
$161$	−1.13230	−0.0892377
$162$	22.2805	1.75052
$163$	−0.226666	−0.0177539	−0.00887693	−	0.999961i	$-0.502826\pi$
$163$	−0.226666	−0.0177539	−0.00887693	+	0.999961i	$0.502826\pi$
$164$	21.5878	1.68572
$165$	53.1166	4.13512
$166$	1.48899	0.115568
$167$	−7.25741	−0.561595	−0.280797	−	0.959767i	$-0.590599\pi$
$167$	−7.25741	−0.561595	−0.280797	+	0.959767i	$0.590599\pi$
$168$	11.4823	0.885879
$169$	−12.6932	−0.976401
$170$	58.2933	4.47089
$171$	22.2423	1.70091
$172$	−13.4820	−1.02799
$173$	−22.8210	−1.73505	−0.867525	−	0.497393i	$-0.834291\pi$
$173$	−22.8210	−1.73505	−0.867525	+	0.497393i	$0.834291\pi$
$174$	41.8324	3.17131
$175$	3.43245	0.259469
$176$	66.3214	4.99916
$177$	−5.11098	−0.384164
$178$	6.24630	0.468180
$179$	11.8175	0.883284	0.441642	−	0.897191i	$-0.354396\pi$
$179$	11.8175	0.883284	0.441642	+	0.897191i	$0.354396\pi$
$180$	−50.3277	−3.75121
$181$	0.285597	0.0212282	0.0106141	−	0.999944i	$-0.496621\pi$
$181$	0.285597	0.0212282	0.0106141	+	0.999944i	$0.496621\pi$
$182$	0.887890	0.0658148
$183$	20.2242	1.49502
$184$	14.0359	1.03474
$185$	9.52825	0.700531
$186$	−10.6913	−0.783921
$187$	44.7681	3.27377
$188$	0.600778	0.0438162
$189$	−0.244256	−0.0177670
$190$	60.1667	4.36495
$191$	−25.2649	−1.82810	−0.914052	−	0.405596i	$-0.867064\pi$
$191$	−25.2649	−1.82810	−0.914052	+	0.405596i	$0.867064\pi$
$192$	−23.8314	−1.71988
$193$	3.29886	0.237457	0.118729	−	0.992927i	$-0.462118\pi$
$193$	3.29886	0.237457	0.118729	+	0.992927i	$0.462118\pi$
$194$	31.5253	2.26338
$195$	−4.48010	−0.320826
$196$	−32.3771	−2.31265
$197$	−2.84106	−0.202417	−0.101209	−	0.994865i	$-0.532271\pi$
$197$	−2.84106	−0.202417	−0.101209	+	0.994865i	$0.532271\pi$
$198$	−54.4724	−3.87119
$199$	−13.3172	−0.944034	−0.472017	−	0.881589i	$-0.656474\pi$
$199$	−13.3172	−0.944034	−0.472017	+	0.881589i	$0.656474\pi$
$200$	−42.5482	−3.00861
$201$	12.4209	0.876100
$202$	−20.5173	−1.44359
$203$	3.92346	0.275373
$204$	−82.6737	−5.78831
$205$	−14.3983	−1.00562
$206$	11.6703	0.813105
$207$	−5.85917	−0.407240
$208$	−5.59385	−0.387864
$209$	46.2069	3.19620
$210$	−12.9659	−0.894735
$211$	8.10242	0.557794	0.278897	−	0.960321i	$-0.410031\pi$
$211$	8.10242	0.557794	0.278897	+	0.960321i	$0.410031\pi$
$212$	−4.88578	−0.335556
$213$	−1.63341	−0.111920
$214$	−4.42680	−0.302610
$215$	8.99203	0.613251
$216$	3.02777	0.206014
$217$	−1.00273	−0.0680700
$218$	19.7410	1.33703
$219$	−12.6105	−0.852137
$220$	−104.553	−7.04894
$221$	−3.77595	−0.253998
$222$	−19.0450	−1.27822
$223$	−12.9999	−0.870536	−0.435268	−	0.900301i	$-0.643346\pi$
$223$	−12.9999	−0.870536	−0.435268	+	0.900301i	$0.643346\pi$
$224$	−6.93738	−0.463523
$225$	17.7615	1.18410
$226$	25.8321	1.71833
$227$	−19.2694	−1.27895	−0.639476	−	0.768811i	$-0.720849\pi$
$227$	−19.2694	−1.27895	−0.639476	+	0.768811i	$0.720849\pi$
$228$	−85.3306	−5.65116
$229$	−10.3824	−0.686090	−0.343045	−	0.939319i	$-0.611458\pi$
$229$	−10.3824	−0.686090	−0.343045	+	0.939319i	$0.611458\pi$
$230$	−15.8494	−1.04508
$231$	−9.95759	−0.655161
$232$	−48.6348	−3.19303
$233$	12.6518	0.828846	0.414423	−	0.910084i	$-0.363983\pi$
$233$	12.6518	0.828846	0.414423	+	0.910084i	$0.363983\pi$
$234$	4.59446	0.300349
$235$	−0.400699	−0.0261387
$236$	10.0602	0.654866
$237$	23.6587	1.53680
$238$	−10.9281	−0.708361
$239$	0.236038	0.0152680	0.00763402	−	0.999971i	$-0.497570\pi$
$239$	0.236038	0.0152680	0.00763402	+	0.999971i	$0.497570\pi$
$240$	81.6874	5.27290
$241$	11.9739	0.771304	0.385652	−	0.922644i	$-0.373976\pi$
$241$	11.9739	0.771304	0.385652	+	0.922644i	$0.373976\pi$
$242$	−84.2982	−5.41889
$243$	22.2750	1.42894
$244$	−39.8086	−2.54849
$245$	21.5945	1.37962
$246$	28.7792	1.83490
$247$	−3.89730	−0.247979
$248$	12.4298	0.789291
$249$	1.40846	0.0892573
$250$	5.29118	0.334643
$251$	−23.0954	−1.45777	−0.728885	−	0.684636i	$-0.759961\pi$
$251$	−23.0954	−1.45777	−0.728885	+	0.684636i	$0.759961\pi$
$252$	9.43477	0.594334
$253$	−12.1721	−0.765251
$254$	48.3987	3.03680
$255$	55.1405	3.45303
$256$	−12.6904	−0.793153
$257$	−13.6842	−0.853599	−0.426800	−	0.904346i	$-0.640359\pi$
$257$	−13.6842	−0.853599	−0.426800	+	0.904346i	$0.640359\pi$
$258$	−17.9732	−1.11896
$259$	−1.78623	−0.110991
$260$	8.81845	0.546897
$261$	20.3023	1.25668
$262$	−19.4588	−1.20217
$263$	25.8285	1.59266	0.796328	−	0.604865i	$-0.206773\pi$
$263$	25.8285	1.59266	0.796328	+	0.604865i	$0.206773\pi$
$264$	123.433	7.59678
$265$	3.25865	0.200177
$266$	−11.2793	−0.691576
$267$	5.90847	0.361592
$268$	−24.4487	−1.49344
$269$	−11.7068	−0.713779	−0.356889	−	0.934147i	$-0.616163\pi$
$269$	−11.7068	−0.713779	−0.356889	+	0.934147i	$0.616163\pi$
$270$	−3.41899	−0.208073
$271$	26.6988	1.62184	0.810918	−	0.585159i	$-0.198968\pi$
$271$	26.6988	1.62184	0.810918	+	0.585159i	$0.198968\pi$
$272$	68.8485	4.17455
$273$	0.839869	0.0508312
$274$	−17.5509	−1.06029
$275$	36.8983	2.22505
$276$	22.4782	1.35303
$277$	2.31899	0.139335	0.0696674	−	0.997570i	$-0.477806\pi$
$277$	2.31899	0.139335	0.0696674	+	0.997570i	$0.477806\pi$
$278$	15.3171	0.918656
$279$	−5.18872	−0.310640
$280$	15.0743	0.900863
$281$	13.0713	0.779770	0.389885	−	0.920864i	$-0.372515\pi$
$281$	13.0713	0.779770	0.389885	+	0.920864i	$0.372515\pi$
$282$	0.800913	0.0476937
$283$	−31.7668	−1.88834	−0.944170	−	0.329460i	$-0.893133\pi$
$283$	−31.7668	−1.88834	−0.944170	+	0.329460i	$0.893133\pi$
$284$	3.21515	0.190784
$285$	56.9126	3.37121
$286$	9.54469	0.564390
$287$	2.69920	0.159329
$288$	−35.8980	−2.11531
$289$	29.4740	1.73377
$290$	54.9189	3.22495
$291$	29.8202	1.74809
$292$	24.8220	1.45260
$293$	−26.8730	−1.56994	−0.784969	−	0.619535i	$-0.787321\pi$
$293$	−26.8730	−1.56994	−0.784969	+	0.619535i	$0.787321\pi$
$294$	−43.1628	−2.51731
$295$	−6.70985	−0.390662
$296$	22.1419	1.28697
$297$	−2.62572	−0.152359
$298$	51.2180	2.96698
$299$	1.02665	0.0593725
$300$	−68.1404	−3.93409
$301$	−1.68571	−0.0971624
$302$	2.62408	0.150999
$303$	−19.4077	−1.11494
$304$	71.0611	4.07563
$305$	26.5510	1.52031
$306$	−56.5481	−3.23264
$307$	−30.9630	−1.76715	−0.883576	−	0.468288i	$-0.844871\pi$
$307$	−30.9630	−1.76715	−0.883576	+	0.468288i	$0.844871\pi$
$308$	19.6001	1.11682
$309$	11.0391	0.627991
$310$	−14.0358	−0.797181
$311$	−14.7720	−0.837643	−0.418821	−	0.908069i	$-0.637557\pi$
$311$	−14.7720	−0.837643	−0.418821	+	0.908069i	$0.637557\pi$
$312$	−10.4109	−0.589402
$313$	25.1441	1.42123	0.710615	−	0.703581i	$-0.248417\pi$
$313$	25.1441	1.42123	0.710615	+	0.703581i	$0.248417\pi$
$314$	9.30903	0.525339
$315$	−6.29267	−0.354552
$316$	−46.5688	−2.61970
$317$	−18.9254	−1.06296	−0.531479	−	0.847071i	$-0.678364\pi$
$317$	−18.9254	−1.06296	−0.531479	+	0.847071i	$0.678364\pi$
$318$	−6.51336	−0.365251
$319$	42.1767	2.36144
$320$	−31.2865	−1.74897
$321$	−4.18738	−0.233716
$322$	2.97124	0.165581
$323$	47.9676	2.66899
$324$	−41.4841	−2.30467
$325$	−3.11217	−0.172632
$326$	0.594789	0.0329423
$327$	18.6733	1.03264
$328$	−33.4590	−1.84747
$329$	0.0751177	0.00414137
$330$	−139.382	−7.67272
$331$	−3.59576	−0.197641	−0.0988205	−	0.995105i	$-0.531507\pi$
$331$	−3.59576	−0.197641	−0.0988205	+	0.995105i	$0.531507\pi$
$332$	−2.77235	−0.152153
$333$	−9.24298	−0.506512
$334$	19.0440	1.04204
$335$	16.3065	0.890918
$336$	−15.3137	−0.835429
$337$	−19.9423	−1.08633	−0.543163	−	0.839627i	$-0.682774\pi$
$337$	−19.9423	−1.08633	−0.543163	+	0.839627i	$0.682774\pi$
$338$	33.3079	1.81171
$339$	24.4350	1.32713
$340$	−108.537	−5.88622
$341$	−10.7792	−0.583728
$342$	−58.3654	−3.15604
$343$	−8.32446	−0.449478
$344$	20.8958	1.12663
$345$	−14.9922	−0.807154
$346$	59.8841	3.21939
$347$	−12.8463	−0.689624	−0.344812	−	0.938672i	$-0.612057\pi$
$347$	−12.8463	−0.689624	−0.344812	+	0.938672i	$0.612057\pi$
$348$	−77.8880	−4.17523
$349$	−14.6891	−0.786288	−0.393144	−	0.919477i	$-0.628613\pi$
$349$	−14.6891	−0.786288	−0.393144	+	0.919477i	$0.628613\pi$
$350$	−9.00700	−0.481444
$351$	0.221465	0.0118209
$352$	−74.5758	−3.97490
$353$	31.0255	1.65132	0.825660	−	0.564168i	$-0.190803\pi$
$353$	31.0255	1.65132	0.825660	+	0.564168i	$0.190803\pi$
$354$	13.4116	0.712818
$355$	−2.14439	−0.113813
$356$	−11.6300	−0.616389
$357$	−10.3370	−0.547093
$358$	−31.0101	−1.63894
$359$	−0.915912	−0.0483400	−0.0241700	−	0.999708i	$-0.507694\pi$
$359$	−0.915912	−0.0483400	−0.0241700	+	0.999708i	$0.507694\pi$
$360$	78.0032	4.11113
$361$	30.5091	1.60574
$362$	−0.749427	−0.0393890
$363$	−79.7389	−4.18521
$364$	−1.65317	−0.0866494
$365$	−16.5554	−0.866550
$366$	−53.0700	−2.77401
$367$	−20.3916	−1.06443	−0.532217	−	0.846608i	$-0.678641\pi$
$367$	−20.3916	−1.06443	−0.532217	+	0.846608i	$0.678641\pi$
$368$	−18.7193	−0.975810
$369$	13.9672	0.727105
$370$	−25.0029	−1.29984
$371$	−0.610888	−0.0317157
$372$	19.9061	1.03208
$373$	27.9887	1.44920	0.724601	−	0.689169i	$-0.242024\pi$
$373$	27.9887	1.44920	0.724601	+	0.689169i	$0.242024\pi$
$374$	−117.475	−6.07449
$375$	5.00500	0.258457
$376$	−0.931150	−0.0480204
$377$	−3.55738	−0.183214
$378$	0.640946	0.0329667
$379$	2.93247	0.150631	0.0753155	−	0.997160i	$-0.476004\pi$
$379$	2.93247	0.150631	0.0753155	+	0.997160i	$0.476004\pi$
$380$	−112.025	−5.74674
$381$	45.7810	2.34543
$382$	66.2970	3.39205
$383$	−28.5613	−1.45942	−0.729708	−	0.683759i	$-0.760344\pi$
$383$	−28.5613	−1.45942	−0.729708	+	0.683759i	$0.760344\pi$
$384$	6.15953	0.314327
$385$	−13.0726	−0.666243
$386$	−8.65647	−0.440603
$387$	−8.72281	−0.443405
$388$	−58.6970	−2.97989
$389$	24.0747	1.22064	0.610318	−	0.792156i	$-0.291041\pi$
$389$	24.0747	1.22064	0.610318	+	0.792156i	$0.291041\pi$
$390$	11.7561	0.595294
$391$	−12.6359	−0.639023
$392$	50.1815	2.53455
$393$	−18.4064	−0.928479
$394$	7.45516	0.375586
$395$	31.0598	1.56279
$396$	101.422	5.09667
$397$	10.1374	0.508782	0.254391	−	0.967101i	$-0.418125\pi$
$397$	10.1374	0.508782	0.254391	+	0.967101i	$0.418125\pi$
$398$	34.9455	1.75166
$399$	−10.6692	−0.534129
$400$	56.7455	2.83728
$401$	4.33304	0.216382	0.108191	−	0.994130i	$-0.465494\pi$
$401$	4.33304	0.216382	0.108191	+	0.994130i	$0.465494\pi$
$402$	−32.5933	−1.62560
$403$	0.909171	0.0452890
$404$	38.2013	1.90058
$405$	27.6685	1.37486
$406$	−10.2955	−0.510956
$407$	−19.2017	−0.951794
$408$	128.136	6.34370
$409$	8.95975	0.443031	0.221516	−	0.975157i	$-0.428900\pi$
$409$	8.95975	0.443031	0.221516	+	0.975157i	$0.428900\pi$
$410$	37.7823	1.86593
$411$	−16.6016	−0.818898
$412$	−21.7289	−1.07051
$413$	1.25787	0.0618959
$414$	15.3749	0.755635
$415$	1.84906	0.0907670
$416$	6.29007	0.308396
$417$	14.4886	0.709512
$418$	−121.250	−5.93055
$419$	−33.1607	−1.62001	−0.810003	−	0.586425i	$-0.800535\pi$
$419$	−33.1607	−1.62001	−0.810003	+	0.586425i	$0.800535\pi$
$420$	24.1413	1.17798
$421$	25.2215	1.22922	0.614611	−	0.788830i	$-0.289313\pi$
$421$	25.2215	1.22922	0.614611	+	0.788830i	$0.289313\pi$
$422$	−21.2614	−1.03499
$423$	0.388702	0.0188993
$424$	7.57250	0.367753
$425$	38.3043	1.85803
$426$	4.28620	0.207667
$427$	−4.97743	−0.240875
$428$	8.24227	0.398405
$429$	9.02847	0.435899
$430$	−23.5958	−1.13789
$431$	−18.3840	−0.885527	−0.442763	−	0.896638i	$-0.646002\pi$
$431$	−18.3840	−0.885527	−0.442763	+	0.896638i	$0.646002\pi$
$432$	−4.03806	−0.194281
$433$	21.5689	1.03653	0.518267	−	0.855219i	$-0.326577\pi$
$433$	21.5689	1.03653	0.518267	+	0.855219i	$0.326577\pi$
$434$	2.63125	0.126304
$435$	51.9486	2.49075
$436$	−36.7558	−1.76028
$437$	−13.0419	−0.623881
$438$	33.0908	1.58114
$439$	29.1914	1.39323	0.696616	−	0.717444i	$-0.254688\pi$
$439$	29.1914	1.39323	0.696616	+	0.717444i	$0.254688\pi$
$440$	162.047	7.72528
$441$	−20.9479	−0.997520
$442$	9.90839	0.471294
$443$	29.4471	1.39908	0.699538	−	0.714596i	$-0.253389\pi$
$443$	29.4471	1.39908	0.699538	+	0.714596i	$0.253389\pi$
$444$	35.4599	1.68285
$445$	7.75682	0.367709
$446$	34.1127	1.61528
$447$	48.4478	2.29150
$448$	5.86518	0.277104
$449$	−31.0829	−1.46689	−0.733446	−	0.679748i	$-0.762089\pi$
$449$	−31.0829	−1.46689	−0.733446	+	0.679748i	$0.762089\pi$
$450$	−46.6074	−2.19709
$451$	29.0161	1.36631
$452$	−48.0969	−2.26229
$453$	2.48215	0.116622
$454$	50.5643	2.37310
$455$	1.10261	0.0516910
$456$	132.254	6.19338
$457$	8.29414	0.387984	0.193992	−	0.981003i	$-0.437856\pi$
$457$	8.29414	0.387984	0.193992	+	0.981003i	$0.437856\pi$
$458$	27.2443	1.27304
$459$	−2.72577	−0.127228
$460$	29.5101	1.37592
$461$	−15.1643	−0.706271	−0.353135	−	0.935572i	$-0.614885\pi$
$461$	−15.1643	−0.706271	−0.353135	+	0.935572i	$0.614885\pi$
$462$	26.1295	1.21565
$463$	−13.0326	−0.605677	−0.302838	−	0.953042i	$-0.597934\pi$
$463$	−13.0326	−0.605677	−0.302838	+	0.953042i	$0.597934\pi$
$464$	64.8631	3.01119
$465$	−13.2767	−0.615692
$466$	−33.1992	−1.53792
$467$	−1.15375	−0.0533891	−0.0266946	−	0.999644i	$-0.508498\pi$
$467$	−1.15375	−0.0533891	−0.0266946	+	0.999644i	$0.508498\pi$
$468$	−8.55443	−0.395429
$469$	−3.05692	−0.141156
$470$	1.05146	0.0485004
$471$	8.80556	0.405739
$472$	−15.5924	−0.717700
$473$	−18.1211	−0.833208
$474$	−62.0821	−2.85153
$475$	39.5353	1.81400
$476$	20.3470	0.932603
$477$	−3.16108	−0.144736
$478$	−0.619382	−0.0283299
$479$	−29.9037	−1.36634	−0.683168	−	0.730262i	$-0.739398\pi$
$479$	−29.9037	−1.36634	−0.683168	+	0.730262i	$0.739398\pi$
$480$	−91.8544	−4.19256
$481$	1.61956	0.0738456
$482$	−31.4203	−1.43116
$483$	2.81054	0.127884
$484$	156.955	7.13432
$485$	39.1489	1.77766
$486$	−58.4512	−2.65140
$487$	−7.16599	−0.324722	−0.162361	−	0.986731i	$-0.551911\pi$
$487$	−7.16599	−0.324722	−0.162361	+	0.986731i	$0.551911\pi$
$488$	61.6996	2.79301
$489$	0.562620	0.0254425
$490$	−56.6655	−2.55989
$491$	−18.0096	−0.812762	−0.406381	−	0.913704i	$-0.633209\pi$
$491$	−18.0096	−0.812762	−0.406381	+	0.913704i	$0.633209\pi$
$492$	−53.5842	−2.41576
$493$	43.7838	1.97192
$494$	10.2268	0.460126
$495$	−67.6453	−3.04043
$496$	−16.5773	−0.744342
$497$	0.402002	0.0180323
$498$	−3.69590	−0.165617
$499$	33.9682	1.52062	0.760312	−	0.649558i	$-0.225046\pi$
$499$	33.9682	1.52062	0.760312	+	0.649558i	$0.225046\pi$
$500$	−9.85166	−0.440579
$501$	18.0140	0.804806
$502$	60.6042	2.70490
$503$	34.9480	1.55825	0.779126	−	0.626867i	$-0.215663\pi$
$503$	34.9480	1.55825	0.779126	+	0.626867i	$0.215663\pi$
$504$	−14.6230	−0.651361
$505$	−25.4790	−1.13380
$506$	31.9404	1.41992
$507$	31.5065	1.39925
$508$	−90.1136	−3.99814
$509$	−18.3056	−0.811382	−0.405691	−	0.914010i	$-0.632969\pi$
$509$	−18.3056	−0.811382	−0.405691	+	0.914010i	$0.632969\pi$
$510$	−144.693	−6.40711
$511$	3.10359	0.137295
$512$	38.2638	1.69104
$513$	−2.81337	−0.124213
$514$	35.9085	1.58386
$515$	14.4924	0.638613
$516$	33.4643	1.47319
$517$	0.807504	0.0355140
$518$	4.68720	0.205944
$519$	56.6453	2.48645
$520$	−13.6678	−0.599372
$521$	−36.0676	−1.58015	−0.790076	−	0.613009i	$-0.789959\pi$
$521$	−36.0676	−1.58015	−0.790076	+	0.613009i	$0.789959\pi$
$522$	−53.2747	−2.33177
$523$	−35.3948	−1.54771	−0.773853	−	0.633365i	$-0.781673\pi$
$523$	−35.3948	−1.54771	−0.773853	+	0.633365i	$0.781673\pi$
$524$	36.2304	1.58273
$525$	−8.51986	−0.371837
$526$	−67.7761	−2.95518
$527$	−11.1900	−0.487443
$528$	−164.620	−7.16416
$529$	−19.5644	−0.850627
$530$	−8.55094	−0.371429
$531$	6.50896	0.282465
$532$	21.0009	0.910504
$533$	−2.44735	−0.106006
$534$	−15.5043	−0.670936
$535$	−5.49732	−0.237670
$536$	37.8933	1.63674
$537$	−29.3329	−1.26581
$538$	30.7196	1.32442
$539$	−43.5180	−1.87445
$540$	6.36582	0.273941
$541$	31.9562	1.37390	0.686952	−	0.726703i	$-0.258948\pi$
$541$	31.9562	1.37390	0.686952	+	0.726703i	$0.258948\pi$
$542$	−70.0597	−3.00932
$543$	−0.708895	−0.0304216
$544$	−77.4175	−3.31925
$545$	24.5149	1.05010
$546$	−2.20388	−0.0943174
$547$	−15.7117	−0.671784	−0.335892	−	0.941900i	$-0.609038\pi$
$547$	−15.7117	−0.671784	−0.335892	+	0.941900i	$0.609038\pi$
$548$	32.6780	1.39593
$549$	−25.7561	−1.09924
$550$	−96.8239	−4.12859
$551$	45.1909	1.92520
$552$	−34.8391	−1.48285
$553$	−5.82268	−0.247606
$554$	−6.08522	−0.258536
$555$	−23.6506	−1.00391
$556$	−28.5189	−1.20947
$557$	26.5186	1.12363	0.561814	−	0.827264i	$-0.310104\pi$
$557$	26.5186	1.12363	0.561814	+	0.827264i	$0.310104\pi$
$558$	13.6156	0.576394
$559$	1.52842	0.0646451
$560$	−20.1043	−0.849560
$561$	−111.121	−4.69155
$562$	−34.3002	−1.44687
$563$	8.16045	0.343922	0.171961	−	0.985104i	$-0.444990\pi$
$563$	8.16045	0.343922	0.171961	+	0.985104i	$0.444990\pi$
$564$	−1.49122	−0.0627918
$565$	32.0790	1.34957
$566$	83.3585	3.50382
$567$	−5.18692	−0.217830
$568$	−4.98318	−0.209089
$569$	−43.7433	−1.83381	−0.916907	−	0.399101i	$-0.869322\pi$
$569$	−43.7433	−1.83381	−0.916907	+	0.399101i	$0.869322\pi$
$570$	−149.343	−6.25529
$571$	−8.93501	−0.373919	−0.186959	−	0.982368i	$-0.559863\pi$
$571$	−8.93501	−0.373919	−0.186959	+	0.982368i	$0.559863\pi$
$572$	−17.7713	−0.743055
$573$	62.7114	2.61981
$574$	−7.08292	−0.295635
$575$	−10.4146	−0.434318
$576$	30.3498	1.26458
$577$	−32.6009	−1.35720	−0.678598	−	0.734510i	$-0.737412\pi$
$577$	−32.6009	−1.35720	−0.678598	+	0.734510i	$0.737412\pi$
$578$	−77.3420	−3.21700
$579$	−8.18829	−0.340294
$580$	−102.254	−4.24586
$581$	−0.346638	−0.0143810
$582$	−78.2506	−3.24359
$583$	−6.56696	−0.271976
$584$	−38.4717	−1.59197
$585$	5.70552	0.235894
$586$	70.5168	2.91302
$587$	23.2205	0.958414	0.479207	−	0.877702i	$-0.340924\pi$
$587$	23.2205	0.958414	0.479207	+	0.877702i	$0.340924\pi$
$588$	80.3650	3.31420
$589$	−11.5496	−0.475893
$590$	17.6071	0.724875
$591$	7.05195	0.290078
$592$	−29.5301	−1.21368
$593$	−7.00612	−0.287707	−0.143853	−	0.989599i	$-0.545949\pi$
$593$	−7.00612	−0.287707	−0.143853	+	0.989599i	$0.545949\pi$
$594$	6.89008	0.282703
$595$	−13.5708	−0.556347
$596$	−95.3629	−3.90622
$597$	33.0554	1.35287
$598$	−2.69400	−0.110166
$599$	−33.3961	−1.36453	−0.682264	−	0.731106i	$-0.739004\pi$
$599$	−33.3961	−1.36453	−0.682264	+	0.731106i	$0.739004\pi$
$600$	105.611	4.31156
$601$	37.4337	1.52695	0.763476	−	0.645836i	$-0.223491\pi$
$601$	37.4337	1.52695	0.763476	+	0.645836i	$0.223491\pi$
$602$	4.42342	0.180285
$603$	−15.8183	−0.644170
$604$	−4.88578	−0.198799
$605$	−104.684	−4.25600
$606$	50.9272	2.06877
$607$	4.71995	0.191577	0.0957885	−	0.995402i	$-0.469463\pi$
$607$	4.71995	0.191577	0.0957885	+	0.995402i	$0.469463\pi$
$608$	−79.9055	−3.24059
$609$	−9.73864	−0.394630
$610$	−69.6719	−2.82093
$611$	−0.0681086	−0.00275538
$612$	105.287	4.25597
$613$	−21.0932	−0.851946	−0.425973	−	0.904736i	$-0.640068\pi$
$613$	−21.0932	−0.851946	−0.425973	+	0.904736i	$0.640068\pi$
$614$	81.2493	3.27895
$615$	35.7388	1.44113
$616$	−30.3784	−1.22398
$617$	36.2892	1.46095	0.730473	−	0.682941i	$-0.239299\pi$
$617$	36.2892	1.46095	0.730473	+	0.682941i	$0.239299\pi$
$618$	−28.9674	−1.16524
$619$	−43.3640	−1.74295	−0.871473	−	0.490444i	$-0.836835\pi$
$619$	−43.3640	−1.74295	−0.871473	+	0.490444i	$0.836835\pi$
$620$	26.1333	1.04954
$621$	0.741111	0.0297398
$622$	38.7628	1.55425
$623$	−1.45415	−0.0582591
$624$	13.8848	0.555837
$625$	−21.5232	−0.860928
$626$	−65.9801	−2.63710
$627$	−114.693	−4.58038
$628$	−17.3325	−0.691643
$629$	−19.9334	−0.794796
$630$	16.5124	0.657872
$631$	−22.2315	−0.885022	−0.442511	−	0.896763i	$-0.645912\pi$
$631$	−22.2315	−0.885022	−0.442511	+	0.896763i	$0.645912\pi$
$632$	72.1773	2.87106
$633$	−20.1115	−0.799358
$634$	49.6618	1.97232
$635$	60.1027	2.38510
$636$	12.1272	0.480877
$637$	3.67051	0.145431
$638$	−110.675	−4.38166
$639$	2.08019	0.0822911
$640$	8.08642	0.319644
$641$	26.9528	1.06457	0.532285	−	0.846565i	$-0.321333\pi$
$641$	26.9528	1.06457	0.532285	+	0.846565i	$0.321333\pi$
$642$	10.9880	0.433661
$643$	6.94492	0.273881	0.136941	−	0.990579i	$-0.456273\pi$
$643$	6.94492	0.273881	0.136941	+	0.990579i	$0.456273\pi$
$644$	−5.53216	−0.217998
$645$	−22.3196	−0.878833
$646$	−125.871	−4.95231
$647$	−2.19558	−0.0863171	−0.0431586	−	0.999068i	$-0.513742\pi$
$647$	−2.19558	−0.0863171	−0.0431586	+	0.999068i	$0.513742\pi$
$648$	64.2965	2.52581
$649$	13.5219	0.530783
$650$	8.16658	0.320320
$651$	2.48894	0.0975492
$652$	−1.10744	−0.0433707
$653$	−15.9755	−0.625168	−0.312584	−	0.949890i	$-0.601195\pi$
$653$	−15.9755	−0.625168	−0.312584	+	0.949890i	$0.601195\pi$
$654$	−49.0002	−1.91606
$655$	−24.1645	−0.944183
$656$	44.6235	1.74226
$657$	16.0598	0.626551
$658$	−0.197114	−0.00768432
$659$	−31.7292	−1.23599	−0.617996	−	0.786181i	$-0.712055\pi$
$659$	−31.7292	−1.23599	−0.617996	+	0.786181i	$0.712055\pi$
$660$	259.516	10.1016
$661$	8.11186	0.315515	0.157757	−	0.987478i	$-0.449574\pi$
$661$	8.11186	0.315515	0.157757	+	0.987478i	$0.449574\pi$
$662$	9.43556	0.366723
$663$	9.37249	0.363997
$664$	4.29688	0.166751
$665$	−14.0069	−0.543164
$666$	24.2543	0.939834
$667$	−11.9044	−0.460941
$668$	−35.4581	−1.37191
$669$	32.2677	1.24754
$670$	−42.7895	−1.65310
$671$	−53.5066	−2.06560
$672$	17.2196	0.664262
$673$	−33.1516	−1.27790	−0.638949	−	0.769249i	$-0.720631\pi$
$673$	−33.1516	−1.27790	−0.638949	+	0.769249i	$0.720631\pi$
$674$	52.3301	2.01568
$675$	−2.24660	−0.0864717
$676$	−62.0162	−2.38524
$677$	−23.4270	−0.900372	−0.450186	−	0.892935i	$-0.648642\pi$
$677$	−23.4270	−0.900372	−0.450186	+	0.892935i	$0.648642\pi$
$678$	−64.1193	−2.46249
$679$	−7.33912	−0.281650
$680$	168.221	6.45100
$681$	47.8295	1.83283
$682$	28.2855	1.08311
$683$	9.70710	0.371432	0.185716	−	0.982603i	$-0.440540\pi$
$683$	9.70710	0.371432	0.185716	+	0.982603i	$0.440540\pi$
$684$	108.671	4.15513
$685$	−21.7951	−0.832749
$686$	21.8440	0.834008
$687$	25.7708	0.983217
$688$	−27.8682	−1.06247
$689$	0.553887	0.0211014
$690$	39.3407	1.49768
$691$	−16.7230	−0.636172	−0.318086	−	0.948062i	$-0.603040\pi$
$691$	−16.7230	−0.636172	−0.318086	+	0.948062i	$0.603040\pi$
$692$	−111.498	−4.23853
$693$	12.6812	0.481720
$694$	33.7096	1.27960
$695$	19.0211	0.721513
$696$	120.719	4.57584
$697$	30.1217	1.14094
$698$	38.5453	1.45896
$699$	−31.4037	−1.18780
$700$	16.7702	0.633853
$701$	−14.6816	−0.554517	−0.277259	−	0.960795i	$-0.589426\pi$
$701$	−14.6816	−0.554517	−0.277259	+	0.960795i	$0.589426\pi$
$702$	−0.581141	−0.0219338
$703$	−20.5740	−0.775963
$704$	63.0499	2.37628
$705$	0.994596	0.0374586
$706$	−81.4132	−3.06403
$707$	4.77646	0.179637
$708$	−24.9711	−0.938471
$709$	−23.2063	−0.871531	−0.435766	−	0.900060i	$-0.643522\pi$
$709$	−23.2063	−0.871531	−0.435766	+	0.900060i	$0.643522\pi$
$710$	5.62705	0.211180
$711$	−30.1299	−1.12996
$712$	18.0254	0.675531
$713$	3.04245	0.113941
$714$	27.1251	1.01513
$715$	11.8529	0.443272
$716$	57.7379	2.15776
$717$	−0.585883	−0.0218802
$718$	2.40342	0.0896950
$719$	50.5760	1.88617	0.943083	−	0.332556i	$-0.107911\pi$
$719$	50.5760	1.88617	0.943083	+	0.332556i	$0.107911\pi$
$720$	−104.031	−3.87701
$721$	−2.71685	−0.101181
$722$	−80.0583	−2.97946
$723$	−29.7210	−1.10533
$724$	1.39536	0.0518582
$725$	36.0870	1.34024
$726$	209.241	7.76566
$727$	25.1604	0.933148	0.466574	−	0.884482i	$-0.345488\pi$
$727$	25.1604	0.933148	0.466574	+	0.884482i	$0.345488\pi$
$728$	2.56225	0.0949634
$729$	−29.8175	−1.10435
$730$	43.4427	1.60789
$731$	−18.8116	−0.695771
$732$	98.8111	3.65216
$733$	−43.2926	−1.59905	−0.799524	−	0.600635i	$-0.794915\pi$
$733$	−43.2926	−1.59905	−0.799524	+	0.600635i	$0.794915\pi$
$734$	53.5092	1.97506
$735$	−53.6008	−1.97709
$736$	21.0491	0.775880
$737$	−32.8615	−1.21047
$738$	−36.6511	−1.34915
$739$	−47.3007	−1.73998	−0.869992	−	0.493065i	$-0.835876\pi$
$739$	−47.3007	−1.73998	−0.869992	+	0.493065i	$0.835876\pi$
$740$	46.5529	1.71132
$741$	9.67370	0.355372
$742$	1.60302	0.0588486
$743$	4.94915	0.181567	0.0907834	−	0.995871i	$-0.471063\pi$
$743$	4.94915	0.181567	0.0907834	+	0.995871i	$0.471063\pi$
$744$	−30.8526	−1.13111
$745$	63.6038	2.33026
$746$	−73.4446	−2.68900
$747$	−1.79370	−0.0656282
$748$	218.727	7.99746
$749$	1.03056	0.0376560
$750$	−13.1335	−0.479568
$751$	1.07182	0.0391112	0.0195556	−	0.999809i	$-0.493775\pi$
$751$	1.07182	0.0391112	0.0195556	+	0.999809i	$0.493775\pi$
$752$	1.24185	0.0452857
$753$	57.3264	2.08909
$754$	9.33482	0.339954
$755$	3.25865	0.118594
$756$	−1.19338	−0.0434028
$757$	24.3791	0.886075	0.443037	−	0.896503i	$-0.353901\pi$
$757$	24.3791	0.886075	0.443037	+	0.896503i	$0.353901\pi$
$758$	−7.69504	−0.279496
$759$	30.2129	1.09666
$760$	173.628	6.29814
$761$	−5.04882	−0.183020	−0.0915098	−	0.995804i	$-0.529169\pi$
$761$	−5.04882	−0.183020	−0.0915098	+	0.995804i	$0.529169\pi$
$762$	−120.133	−4.35195
$763$	−4.59572	−0.166376
$764$	−123.439	−4.46585
$765$	−70.2229	−2.53891
$766$	74.9471	2.70795
$767$	−1.14050	−0.0411812
$768$	31.4996	1.13665
$769$	−22.2005	−0.800572	−0.400286	−	0.916390i	$-0.631089\pi$
$769$	−22.2005	−0.800572	−0.400286	+	0.916390i	$0.631089\pi$
$770$	34.3036	1.23622
$771$	33.9664	1.22327
$772$	16.1175	0.580082
$773$	15.3380	0.551668	0.275834	−	0.961205i	$-0.411046\pi$
$773$	15.3380	0.551668	0.275834	+	0.961205i	$0.411046\pi$
$774$	22.8893	0.822739
$775$	−9.22287	−0.331295
$776$	90.9749	3.26581
$777$	4.43370	0.159058
$778$	−63.1739	−2.26489
$779$	31.0897	1.11391
$780$	−21.8888	−0.783743
$781$	4.32147	0.154634
$782$	33.1575	1.18571
$783$	−2.56798	−0.0917722
$784$	−66.9259	−2.39021
$785$	11.5602	0.412601
$786$	48.2997	1.72279
$787$	−16.4908	−0.587832	−0.293916	−	0.955831i	$-0.594959\pi$
$787$	−16.4908	−0.587832	−0.293916	+	0.955831i	$0.594959\pi$
$788$	−13.8808	−0.494483
$789$	−64.1104	−2.28239
$790$	−81.5033	−2.89976
$791$	−6.01375	−0.213824
$792$	−157.195	−5.58569
$793$	4.51300	0.160261
$794$	−26.6014	−0.944047
$795$	−8.08846	−0.286868
$796$	−65.0651	−2.30617
$797$	−16.1067	−0.570528	−0.285264	−	0.958449i	$-0.592081\pi$
$797$	−16.1067	−0.570528	−0.285264	+	0.958449i	$0.592081\pi$
$798$	27.9968	0.991078
$799$	0.838273	0.0296560
$800$	−63.8081	−2.25596
$801$	−7.52458	−0.265868
$802$	−11.3702	−0.401497
$803$	33.3631	1.17736
$804$	60.6855	2.14021
$805$	3.68976	0.130047
$806$	−2.38573	−0.0840339
$807$	29.0582	1.02290
$808$	−59.2084	−2.08295
$809$	−35.3972	−1.24450	−0.622250	−	0.782819i	$-0.713781\pi$
$809$	−35.3972	−1.24450	−0.622250	+	0.782819i	$0.713781\pi$
$810$	−72.6043	−2.55105
$811$	16.7415	0.587874	0.293937	−	0.955825i	$-0.405034\pi$
$811$	16.7415	0.587874	0.293937	+	0.955825i	$0.405034\pi$
$812$	19.1692	0.672706
$813$	−66.2705	−2.32421
$814$	50.3868	1.76605
$815$	0.738625	0.0258729
$816$	−170.892	−5.98243
$817$	−19.4161	−0.679285
$818$	−23.5111	−0.822046
$819$	−1.06959	−0.0373747
$820$	−70.3470	−2.45662
$821$	−17.7154	−0.618272	−0.309136	−	0.951018i	$-0.600040\pi$
$821$	−17.7154	−0.618272	−0.309136	+	0.951018i	$0.600040\pi$
$822$	43.5639	1.51947
$823$	21.3083	0.742759	0.371379	−	0.928481i	$-0.378885\pi$
$823$	21.3083	0.742759	0.371379	+	0.928481i	$0.378885\pi$
$824$	33.6777	1.17322
$825$	−91.5872	−3.18866
$826$	−3.30075	−0.114848
$827$	−19.6490	−0.683262	−0.341631	−	0.939834i	$-0.610979\pi$
$827$	−19.6490	−0.683262	−0.341631	+	0.939834i	$0.610979\pi$
$828$	−28.6266	−0.994843
$829$	−39.7903	−1.38197	−0.690987	−	0.722867i	$-0.742824\pi$
$829$	−39.7903	−1.38197	−0.690987	+	0.722867i	$0.742824\pi$
$830$	−4.85209	−0.168418
$831$	−5.75610	−0.199677
$832$	−5.31792	−0.184366
$833$	−45.1762	−1.56526
$834$	−38.0193	−1.31650
$835$	23.6493	0.818419
$836$	225.757	7.80795
$837$	0.656308	0.0226853
$838$	87.0162	3.00593
$839$	10.5594	0.364552	0.182276	−	0.983247i	$-0.441654\pi$
$839$	10.5594	0.364552	0.182276	+	0.983247i	$0.441654\pi$
$840$	−37.4168	−1.29100
$841$	12.2493	0.422389
$842$	−66.1832	−2.28082
$843$	−32.4450	−1.11747
$844$	39.5866	1.36263
$845$	41.3627	1.42292
$846$	−1.01998	−0.0350678
$847$	19.6247	0.674313
$848$	−10.0993	−0.346810
$849$	78.8500	2.70613
$850$	−100.513	−3.44758
$851$	5.41971	0.185785
$852$	−7.98049	−0.273407
$853$	−40.7463	−1.39513	−0.697563	−	0.716523i	$-0.745732\pi$
$853$	−40.7463	−1.39513	−0.697563	+	0.716523i	$0.745732\pi$
$854$	13.0612	0.446943
$855$	−72.4797	−2.47875
$856$	−12.7747	−0.436632
$857$	30.8214	1.05284	0.526420	−	0.850225i	$-0.323534\pi$
$857$	30.8214	1.05284	0.526420	+	0.850225i	$0.323534\pi$
$858$	−23.6914	−0.808811
$859$	−14.8826	−0.507789	−0.253895	−	0.967232i	$-0.581712\pi$
$859$	−14.8826	−0.507789	−0.253895	+	0.967232i	$0.581712\pi$
$860$	43.9330	1.49810
$861$	−6.69984	−0.228330
$862$	48.2411	1.64310
$863$	43.9674	1.49667	0.748333	−	0.663323i	$-0.230854\pi$
$863$	43.9674	1.49667	0.748333	+	0.663323i	$0.230854\pi$
$864$	4.54064	0.154476
$865$	74.3657	2.52851
$866$	−56.5984	−1.92329
$867$	−73.1590	−2.48461
$868$	−4.89913	−0.166287
$869$	−62.5930	−2.12332
$870$	−136.317	−4.62159
$871$	2.77169	0.0939151
$872$	56.9681	1.92918
$873$	−37.9768	−1.28532
$874$	34.2231	1.15761
$875$	−1.23179	−0.0416422
$876$	−61.6119	−2.08167
$877$	−28.9962	−0.979133	−0.489567	−	0.871966i	$-0.662845\pi$
$877$	−28.9962	−0.979133	−0.489567	+	0.871966i	$0.662845\pi$
$878$	−76.6006	−2.58514
$879$	66.7029	2.24983
$880$	−216.118	−7.28533
$881$	−6.97946	−0.235144	−0.117572	−	0.993064i	$-0.537511\pi$
$881$	−6.97946	−0.235144	−0.117572	+	0.993064i	$0.537511\pi$
$882$	54.9690	1.85090
$883$	52.4084	1.76368	0.881841	−	0.471547i	$-0.156304\pi$
$883$	52.4084	1.76368	0.881841	+	0.471547i	$0.156304\pi$
$884$	−18.4485	−0.620489
$885$	16.6549	0.559847
$886$	−77.2715	−2.59599
$887$	−20.4074	−0.685215	−0.342607	−	0.939479i	$-0.611310\pi$
$887$	−20.4074	−0.685215	−0.342607	+	0.939479i	$0.611310\pi$
$888$	−54.9596	−1.84432
$889$	−11.2673	−0.377892
$890$	−20.3545	−0.682284
$891$	−55.7587	−1.86799
$892$	−63.5145	−2.12662
$893$	0.865213	0.0289533
$894$	−127.131	−4.25189
$895$	−38.5092	−1.28722
$896$	−1.51593	−0.0506438
$897$	−2.54830	−0.0850851
$898$	81.5638	2.72182
$899$	−10.5422	−0.351603
$900$	86.7785	2.89262
$901$	−6.81718	−0.227113
$902$	−76.1404	−2.53520
$903$	4.18418	0.139241
$904$	74.5457	2.47935
$905$	−0.930659	−0.0309361
$906$	−6.51336	−0.216392
$907$	−10.9648	−0.364081	−0.182040	−	0.983291i	$-0.558270\pi$
$907$	−10.9648	−0.364081	−0.182040	+	0.983291i	$0.558270\pi$
$908$	−94.1458	−3.12434
$909$	24.7161	0.819783
$910$	−2.89332	−0.0959127
$911$	0.704225	0.0233320	0.0116660	−	0.999932i	$-0.496287\pi$
$911$	0.704225	0.0233320	0.0116660	+	0.999932i	$0.496287\pi$
$912$	−176.385	−5.84068
$913$	−3.72631	−0.123323
$914$	−21.7645	−0.719904
$915$	−65.9037	−2.17871
$916$	−50.7262	−1.67604
$917$	4.53003	0.149595
$918$	7.15262	0.236072
$919$	24.9517	0.823081	0.411540	−	0.911392i	$-0.364991\pi$
$919$	24.9517	0.823081	0.411540	+	0.911392i	$0.364991\pi$
$920$	−45.7379	−1.50793
$921$	76.8549	2.53245
$922$	39.7922	1.31049
$923$	−0.364493	−0.0119974
$924$	−48.6505	−1.60049
$925$	−16.4293	−0.540191
$926$	34.1986	1.12383
$927$	−14.0585	−0.461743
$928$	−72.9360	−2.39424
$929$	49.3087	1.61777	0.808883	−	0.587970i	$-0.200073\pi$
$929$	49.3087	1.61777	0.808883	+	0.587970i	$0.200073\pi$
$930$	34.8391	1.14242
$931$	−46.6281	−1.52817
$932$	61.8138	2.02478
$933$	36.6664	1.20040
$934$	3.02752	0.0990636
$935$	−145.884	−4.77090
$936$	13.2586	0.433370
$937$	−40.0037	−1.30686	−0.653432	−	0.756985i	$-0.726671\pi$
$937$	−40.0037	−1.30686	−0.653432	+	0.756985i	$0.726671\pi$
$938$	8.02160	0.261914
$939$	−62.4116	−2.03673
$940$	−1.95772	−0.0638539
$941$	13.6800	0.445955	0.222977	−	0.974824i	$-0.428422\pi$
$941$	13.6800	0.445955	0.222977	+	0.974824i	$0.428422\pi$
$942$	−23.1065	−0.752849
$943$	−8.18982	−0.266697
$944$	20.7953	0.676828
$945$	0.795944	0.0258921
$946$	47.5511	1.54602
$947$	45.8467	1.48982	0.744908	−	0.667167i	$-0.232493\pi$
$947$	45.8467	1.48982	0.744908	+	0.667167i	$0.232493\pi$
$948$	115.591	3.75422
$949$	−2.81400	−0.0913463
$950$	−103.744	−3.36589
$951$	46.9758	1.52330
$952$	−31.5359	−1.02209
$953$	56.5045	1.83036	0.915179	−	0.403047i	$-0.132049\pi$
$953$	56.5045	1.83036	0.915179	+	0.403047i	$0.132049\pi$
$954$	8.29493	0.268558
$955$	82.3294	2.66412
$956$	1.15323	0.0372981
$957$	−104.689	−3.38411
$958$	78.4696	2.53524
$959$	4.08586	0.131939
$960$	77.6580	2.50640
$961$	−28.3057	−0.913087
$962$	−4.24985	−0.137021
$963$	5.33273	0.171845
$964$	58.5016	1.88421
$965$	−10.7498	−0.346049
$966$	−7.37507	−0.237289
$967$	−7.79697	−0.250734	−0.125367	−	0.992110i	$-0.540011\pi$
$967$	−7.79697	−0.250734	−0.125367	+	0.992110i	$0.540011\pi$
$968$	−243.266	−7.81886
$969$	−119.063	−3.82485
$970$	−102.730	−3.29845
$971$	−36.8392	−1.18223	−0.591113	−	0.806589i	$-0.701311\pi$
$971$	−36.8392	−1.18223	−0.591113	+	0.806589i	$0.701311\pi$
$972$	108.831	3.49074
$973$	−3.56583	−0.114315
$974$	18.8041	0.602522
$975$	7.72489	0.247394
$976$	−82.2873	−2.63395
$977$	11.3592	0.363412	0.181706	−	0.983353i	$-0.441838\pi$
$977$	11.3592	0.363412	0.181706	+	0.983353i	$0.441838\pi$
$978$	−1.47636	−0.0472087
$979$	−15.6319	−0.499596
$980$	105.506	3.37026
$981$	−23.7809	−0.759266
$982$	47.2585	1.50808
$983$	3.31628	0.105773	0.0528864	−	0.998601i	$-0.483158\pi$
$983$	3.31628	0.105773	0.0528864	+	0.998601i	$0.483158\pi$
$984$	83.0505	2.64755
$985$	9.25802	0.294985
$986$	−114.892	−3.65891
$987$	−0.186454	−0.00593488
$988$	−19.0413	−0.605786
$989$	5.11470	0.162638
$990$	177.506	5.64152
$991$	44.0319	1.39872	0.699360	−	0.714770i	$-0.253468\pi$
$991$	44.0319	1.39872	0.699360	+	0.714770i	$0.253468\pi$
$992$	18.6405	0.591837
$993$	8.92524	0.283234
$994$	−1.05488	−0.0334589
$995$	43.3962	1.37575
$996$	6.88140	0.218045
$997$	−30.5965	−0.969002	−0.484501	−	0.874791i	$-0.660999\pi$
$997$	−30.5965	−0.969002	−0.484501	+	0.874791i	$0.660999\pi$
$998$	−89.1351	−2.82152
$999$	1.16912	0.0369894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.6	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.6	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +O(q^{10})\)	\(q-2.62408 q^{2} -2.48215 q^{3} +4.88578 q^{4} -3.25865 q^{5} +6.51336 q^{6} +0.610888 q^{7} -7.57250 q^{8} +3.16108 q^{9} +8.55094 q^{10} +6.56696 q^{11} -12.1272 q^{12} -0.553887 q^{13} -1.60302 q^{14} +8.08846 q^{15} +10.0993 q^{16} +6.81718 q^{17} -8.29493 q^{18} +7.03627 q^{19} -15.9210 q^{20} -1.51632 q^{21} -17.2322 q^{22} -1.85353 q^{23} +18.7961 q^{24} +5.61878 q^{25} +1.45344 q^{26} -0.399838 q^{27} +2.98466 q^{28} +6.42256 q^{29} -21.2247 q^{30} -1.64144 q^{31} -11.3562 q^{32} -16.3002 q^{33} -17.8888 q^{34} -1.99067 q^{35} +15.4444 q^{36} -2.92399 q^{37} -18.4637 q^{38} +1.37483 q^{39} +24.6761 q^{40} +4.41849 q^{41} +3.97893 q^{42} -2.75943 q^{43} +32.0847 q^{44} -10.3009 q^{45} +4.86381 q^{46} +0.122965 q^{47} -25.0679 q^{48} -6.62682 q^{49} -14.7441 q^{50} -16.9213 q^{51} -2.70617 q^{52} -1.00000 q^{53} +1.04920 q^{54} -21.3994 q^{55} -4.62595 q^{56} -17.4651 q^{57} -16.8533 q^{58} +2.05909 q^{59} +39.5184 q^{60} -8.14786 q^{61} +4.30725 q^{62} +1.93107 q^{63} +9.60108 q^{64} +1.80492 q^{65} +42.7729 q^{66} -5.00407 q^{67} +33.3072 q^{68} +4.60075 q^{69} +5.22366 q^{70} +0.658063 q^{71} -23.9373 q^{72} +5.08046 q^{73} +7.67277 q^{74} -13.9467 q^{75} +34.3777 q^{76} +4.01167 q^{77} -3.60767 q^{78} -9.53151 q^{79} -32.9099 q^{80} -8.49080 q^{81} -11.5945 q^{82} -0.567433 q^{83} -7.40839 q^{84} -22.2148 q^{85} +7.24097 q^{86} -15.9418 q^{87} -49.7282 q^{88} -2.38038 q^{89} +27.0302 q^{90} -0.338363 q^{91} -9.05594 q^{92} +4.07430 q^{93} -0.322669 q^{94} -22.9287 q^{95} +28.1879 q^{96} -12.0139 q^{97} +17.3893 q^{98} +20.7587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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