LMFDB - Embedded newform 8003.2.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +O(q^{10})$	\(q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +0.567192 q^{10} -3.85911 q^{11} -10.9079 q^{12} +2.35317 q^{13} +5.49587 q^{14} +0.398382 q^{15} +16.3844 q^{16} +6.01787 q^{17} -2.10220 q^{18} -0.129844 q^{19} -1.15531 q^{20} +3.86017 q^{21} +10.6558 q^{22} +3.90927 q^{23} +19.4088 q^{24} -4.95781 q^{25} -6.49761 q^{26} +4.34171 q^{27} -11.1945 q^{28} +0.957838 q^{29} -1.10002 q^{30} -1.15433 q^{31} -25.2257 q^{32} +7.48442 q^{33} -16.6167 q^{34} +0.408851 q^{35} +4.28197 q^{36} -7.73361 q^{37} +0.358529 q^{38} -4.56377 q^{39} +2.05569 q^{40} -4.49823 q^{41} -10.6588 q^{42} -0.734170 q^{43} -21.7049 q^{44} -0.156388 q^{45} -10.7944 q^{46} +0.262826 q^{47} -31.7761 q^{48} -3.03840 q^{49} +13.6896 q^{50} -11.6712 q^{51} +13.2350 q^{52} -1.00000 q^{53} -11.9884 q^{54} +0.792714 q^{55} +19.9188 q^{56} +0.251822 q^{57} -2.64480 q^{58} +11.0473 q^{59} +2.24063 q^{60} -3.50583 q^{61} +3.18737 q^{62} -1.51534 q^{63} +36.8850 q^{64} -0.483373 q^{65} -20.6661 q^{66} -14.4410 q^{67} +33.8465 q^{68} -7.58170 q^{69} -1.12893 q^{70} +14.4755 q^{71} -7.61905 q^{72} -11.8770 q^{73} +21.3542 q^{74} +9.61524 q^{75} -0.730288 q^{76} +7.68109 q^{77} +12.6016 q^{78} +8.94065 q^{79} -3.36558 q^{80} -10.7044 q^{81} +12.4206 q^{82} -9.37659 q^{83} +21.7108 q^{84} -1.23615 q^{85} +2.02720 q^{86} -1.85764 q^{87} +38.6202 q^{88} +5.83301 q^{89} +0.431820 q^{90} -4.68370 q^{91} +21.9870 q^{92} +2.23873 q^{93} -0.725720 q^{94} +0.0266718 q^{95} +48.9232 q^{96} -8.77372 q^{97} +8.38967 q^{98} -2.93806 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76122	−1.95248	−0.976238	−	0.216701i	$-0.930470\pi$
$2$	−2.76122	−1.95248	−0.976238	+	0.216701i	$0.930470\pi$
$3$	−1.93941	−1.11972	−0.559861	−	0.828587i	$-0.689145\pi$
$3$	−1.93941	−1.11972	−0.559861	+	0.828587i	$0.689145\pi$
$4$	5.62432	2.81216
$5$	−0.205414	−0.0918638	−0.0459319	−	0.998945i	$-0.514626\pi$
$5$	−0.205414	−0.0918638	−0.0459319	+	0.998945i	$0.514626\pi$
$6$	5.35515	2.18623
$7$	−1.99038	−0.752292	−0.376146	−	0.926560i	$-0.622751\pi$
$7$	−1.99038	−0.752292	−0.376146	+	0.926560i	$0.622751\pi$
$8$	−10.0076	−3.53820
$9$	0.761331	0.253777
$10$	0.567192	0.179362
$11$	−3.85911	−1.16357	−0.581783	−	0.813344i	$-0.697645\pi$
$11$	−3.85911	−1.16357	−0.581783	+	0.813344i	$0.697645\pi$
$12$	−10.9079	−3.14884
$13$	2.35317	0.652652	0.326326	−	0.945257i	$-0.394189\pi$
$13$	2.35317	0.652652	0.326326	+	0.945257i	$0.394189\pi$
$14$	5.49587	1.46883
$15$	0.398382	0.102862
$16$	16.3844	4.09610
$17$	6.01787	1.45955	0.729774	−	0.683688i	$-0.239625\pi$
$17$	6.01787	1.45955	0.729774	+	0.683688i	$0.239625\pi$
$18$	−2.10220	−0.495493
$19$	−0.129844	−0.0297884	−0.0148942	−	0.999889i	$-0.504741\pi$
$19$	−0.129844	−0.0297884	−0.0148942	+	0.999889i	$0.504741\pi$
$20$	−1.15531	−0.258336
$21$	3.86017	0.842358
$22$	10.6558	2.27183
$23$	3.90927	0.815140	0.407570	−	0.913174i	$-0.366376\pi$
$23$	3.90927	0.815140	0.407570	+	0.913174i	$0.366376\pi$
$24$	19.4088	3.96180
$25$	−4.95781	−0.991561
$26$	−6.49761	−1.27429
$27$	4.34171	0.835562
$28$	−11.1945	−2.11557
$29$	0.957838	0.177866	0.0889330	−	0.996038i	$-0.471654\pi$
$29$	0.957838	0.177866	0.0889330	+	0.996038i	$0.471654\pi$
$30$	−1.10002	−0.200835
$31$	−1.15433	−0.207324	−0.103662	−	0.994613i	$-0.533056\pi$
$31$	−1.15433	−0.207324	−0.103662	+	0.994613i	$0.533056\pi$
$32$	−25.2257	−4.45932
$33$	7.48442	1.30287
$34$	−16.6167	−2.84973
$35$	0.408851	0.0691084
$36$	4.28197	0.713662
$37$	−7.73361	−1.27140	−0.635699	−	0.771937i	$-0.719288\pi$
$37$	−7.73361	−1.27140	−0.635699	+	0.771937i	$0.719288\pi$
$38$	0.358529	0.0581611
$39$	−4.56377	−0.730788
$40$	2.05569	0.325033
$41$	−4.49823	−0.702506	−0.351253	−	0.936281i	$-0.614244\pi$
$41$	−4.49823	−0.702506	−0.351253	+	0.936281i	$0.614244\pi$
$42$	−10.6588	−1.64468
$43$	−0.734170	−0.111960	−0.0559800	−	0.998432i	$-0.517828\pi$
$43$	−0.734170	−0.111960	−0.0559800	+	0.998432i	$0.517828\pi$
$44$	−21.7049	−3.27214
$45$	−0.156388	−0.0233129
$46$	−10.7944	−1.59154
$47$	0.262826	0.0383371	0.0191686	−	0.999816i	$-0.493898\pi$
$47$	0.262826	0.0383371	0.0191686	+	0.999816i	$0.493898\pi$
$48$	−31.7761	−4.58649
$49$	−3.03840	−0.434057
$50$	13.6896	1.93600
$51$	−11.6712	−1.63429
$52$	13.2350	1.83536
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−11.9884	−1.63142
$55$	0.792714	0.106890
$56$	19.9188	2.66176
$57$	0.251822	0.0333547
$58$	−2.64480	−0.347279
$59$	11.0473	1.43824	0.719121	−	0.694885i	$-0.244545\pi$
$59$	11.0473	1.43824	0.719121	+	0.694885i	$0.244545\pi$
$60$	2.24063	0.289264
$61$	−3.50583	−0.448876	−0.224438	−	0.974488i	$-0.572055\pi$
$61$	−3.50583	−0.448876	−0.224438	+	0.974488i	$0.572055\pi$
$62$	3.18737	0.404796
$63$	−1.51534	−0.190914
$64$	36.8850	4.61063
$65$	−0.483373	−0.0599551
$66$	−20.6661	−2.54382
$67$	−14.4410	−1.76425	−0.882126	−	0.471013i	$-0.843889\pi$
$67$	−14.4410	−1.76425	−0.882126	+	0.471013i	$0.843889\pi$
$68$	33.8465	4.10449
$69$	−7.58170	−0.912730
$70$	−1.12893	−0.134932
$71$	14.4755	1.71792	0.858961	−	0.512041i	$-0.171110\pi$
$71$	14.4755	1.71792	0.858961	+	0.512041i	$0.171110\pi$
$72$	−7.61905	−0.897914
$73$	−11.8770	−1.39010	−0.695051	−	0.718960i	$-0.744618\pi$
$73$	−11.8770	−1.39010	−0.695051	+	0.718960i	$0.744618\pi$
$74$	21.3542	2.48237
$75$	9.61524	1.11027
$76$	−0.730288	−0.0837697
$77$	7.68109	0.875341
$78$	12.6016	1.42685
$79$	8.94065	1.00590	0.502951	−	0.864315i	$-0.332248\pi$
$79$	8.94065	1.00590	0.502951	+	0.864315i	$0.332248\pi$
$80$	−3.36558	−0.376283
$81$	−10.7044	−1.18937
$82$	12.4206	1.37163
$83$	−9.37659	−1.02921	−0.514607	−	0.857426i	$-0.672062\pi$
$83$	−9.37659	−1.02921	−0.514607	+	0.857426i	$0.672062\pi$
$84$	21.7108	2.36885
$85$	−1.23615	−0.134080
$86$	2.02720	0.218599
$87$	−1.85764	−0.199160
$88$	38.6202	4.11693
$89$	5.83301	0.618298	0.309149	−	0.951014i	$-0.399956\pi$
$89$	5.83301	0.618298	0.309149	+	0.951014i	$0.399956\pi$
$90$	0.431820	0.0455179
$91$	−4.68370	−0.490985
$92$	21.9870	2.29231
$93$	2.23873	0.232146
$94$	−0.725720	−0.0748523
$95$	0.0266718	0.00273647
$96$	48.9232	4.99320
$97$	−8.77372	−0.890836	−0.445418	−	0.895323i	$-0.646945\pi$
$97$	−8.77372	−0.890836	−0.445418	+	0.895323i	$0.646945\pi$
$98$	8.38967	0.847485
$99$	−2.93806	−0.295286
$100$	−27.8843	−2.78843
$101$	2.64614	0.263301	0.131651	−	0.991296i	$-0.457972\pi$
$101$	2.64614	0.263301	0.131651	+	0.991296i	$0.457972\pi$
$102$	32.2266	3.19091
$103$	−2.24563	−0.221269	−0.110634	−	0.993861i	$-0.535288\pi$
$103$	−2.24563	−0.221269	−0.110634	+	0.993861i	$0.535288\pi$
$104$	−23.5495	−2.30921
$105$	−0.792931	−0.0773822
$106$	2.76122	0.268193
$107$	1.50317	0.145317	0.0726587	−	0.997357i	$-0.476852\pi$
$107$	1.50317	0.145317	0.0726587	+	0.997357i	$0.476852\pi$
$108$	24.4192	2.34974
$109$	15.4062	1.47565	0.737823	−	0.674995i	$-0.235854\pi$
$109$	15.4062	1.47565	0.737823	+	0.674995i	$0.235854\pi$
$110$	−2.18886	−0.208699
$111$	14.9987	1.42361
$112$	−32.6111	−3.08146
$113$	19.0646	1.79344	0.896721	−	0.442595i	$-0.145942\pi$
$113$	19.0646	1.79344	0.896721	+	0.442595i	$0.145942\pi$
$114$	−0.695336	−0.0651242
$115$	−0.803018	−0.0748818
$116$	5.38719	0.500188
$117$	1.79154	0.165628
$118$	−30.5041	−2.80813
$119$	−11.9778	−1.09801
$120$	−3.98683	−0.363946
$121$	3.89273	0.353885
$122$	9.68036	0.876419
$123$	8.72394	0.786611
$124$	−6.49235	−0.583030
$125$	2.04547	0.182952
$126$	4.18417	0.372756
$127$	11.8907	1.05513	0.527565	−	0.849515i	$-0.323105\pi$
$127$	11.8907	1.05513	0.527565	+	0.849515i	$0.323105\pi$
$128$	−51.3961	−4.54282
$129$	1.42386	0.125364
$130$	1.33470	0.117061
$131$	11.5171	1.00626	0.503129	−	0.864211i	$-0.332182\pi$
$131$	11.5171	1.00626	0.503129	+	0.864211i	$0.332182\pi$
$132$	42.0948	3.66388
$133$	0.258440	0.0224096
$134$	39.8748	3.44466
$135$	−0.891846	−0.0767579
$136$	−60.2242	−5.16418
$137$	−10.8520	−0.927149	−0.463575	−	0.886058i	$-0.653433\pi$
$137$	−10.8520	−0.927149	−0.463575	+	0.886058i	$0.653433\pi$
$138$	20.9347	1.78208
$139$	6.10227	0.517588	0.258794	−	0.965933i	$-0.416675\pi$
$139$	6.10227	0.517588	0.258794	+	0.965933i	$0.416675\pi$
$140$	2.29951	0.194344
$141$	−0.509729	−0.0429269
$142$	−39.9699	−3.35420
$143$	−9.08114	−0.759403
$144$	12.4739	1.03949
$145$	−0.196753	−0.0163394
$146$	32.7951	2.71414
$147$	5.89271	0.486023
$148$	−43.4964	−3.57538
$149$	9.37744	0.768230	0.384115	−	0.923285i	$-0.374507\pi$
$149$	9.37744	0.768230	0.384115	+	0.923285i	$0.374507\pi$
$150$	−26.5498	−2.16778
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	1.29943	0.105397
$153$	4.58159	0.370400
$154$	−21.2092	−1.70908
$155$	0.237116	0.0190456
$156$	−25.6681	−2.05510
$157$	6.80516	0.543111	0.271555	−	0.962423i	$-0.412462\pi$
$157$	6.80516	0.543111	0.271555	+	0.962423i	$0.412462\pi$
$158$	−24.6871	−1.96400
$159$	1.93941	0.153806
$160$	5.18171	0.409650
$161$	−7.78093	−0.613223
$162$	29.5571	2.32222
$163$	6.50108	0.509204	0.254602	−	0.967046i	$-0.418056\pi$
$163$	6.50108	0.509204	0.254602	+	0.967046i	$0.418056\pi$
$164$	−25.2995	−1.97556
$165$	−1.53740	−0.119687
$166$	25.8908	2.00952
$167$	−19.4983	−1.50882	−0.754410	−	0.656403i	$-0.772077\pi$
$167$	−19.4983	−1.50882	−0.754410	+	0.656403i	$0.772077\pi$
$168$	−38.6308	−2.98043
$169$	−7.46259	−0.574046
$170$	3.41329	0.261787
$171$	−0.0988546	−0.00755960
$172$	−4.12921	−0.314849
$173$	−2.38549	−0.181365	−0.0906827	−	0.995880i	$-0.528905\pi$
$173$	−2.38549	−0.181365	−0.0906827	+	0.995880i	$0.528905\pi$
$174$	5.12936	0.388856
$175$	9.86791	0.745944
$176$	−63.2291	−4.76607
$177$	−21.4254	−1.61043
$178$	−16.1062	−1.20721
$179$	−8.75832	−0.654628	−0.327314	−	0.944916i	$-0.606143\pi$
$179$	−8.75832	−0.654628	−0.327314	+	0.944916i	$0.606143\pi$
$180$	−0.879575	−0.0655596
$181$	−12.2071	−0.907344	−0.453672	−	0.891169i	$-0.649886\pi$
$181$	−12.2071	−0.907344	−0.453672	+	0.891169i	$0.649886\pi$
$182$	12.9327	0.958636
$183$	6.79926	0.502616
$184$	−39.1223	−2.88413
$185$	1.58859	0.116795
$186$	−6.18163	−0.453259
$187$	−23.2236	−1.69828
$188$	1.47822	0.107810
$189$	−8.64164	−0.628587
$190$	−0.0736467	−0.00534290
$191$	21.0990	1.52667	0.763336	−	0.646002i	$-0.223560\pi$
$191$	21.0990	1.52667	0.763336	+	0.646002i	$0.223560\pi$
$192$	−71.5354	−5.16262
$193$	−9.37943	−0.675146	−0.337573	−	0.941299i	$-0.609606\pi$
$193$	−9.37943	−0.675146	−0.337573	+	0.941299i	$0.609606\pi$
$194$	24.2261	1.73934
$195$	0.937461	0.0671330
$196$	−17.0889	−1.22064
$197$	8.20728	0.584744	0.292372	−	0.956305i	$-0.405555\pi$
$197$	8.20728	0.584744	0.292372	+	0.956305i	$0.405555\pi$
$198$	8.11262	0.576539
$199$	23.4110	1.65956	0.829780	−	0.558091i	$-0.188466\pi$
$199$	23.4110	1.65956	0.829780	+	0.558091i	$0.188466\pi$
$200$	49.6155	3.50834
$201$	28.0072	1.97547
$202$	−7.30658	−0.514089
$203$	−1.90646	−0.133807
$204$	−65.6424	−4.59589
$205$	0.923998	0.0645349
$206$	6.20069	0.432022
$207$	2.97625	0.206864
$208$	38.5552	2.67332
$209$	0.501084	0.0346607
$210$	2.18946	0.151087
$211$	−13.6393	−0.938969	−0.469485	−	0.882941i	$-0.655560\pi$
$211$	−13.6393	−0.938969	−0.469485	+	0.882941i	$0.655560\pi$
$212$	−5.62432	−0.386280
$213$	−28.0739	−1.92359
$214$	−4.15059	−0.283729
$215$	0.150809	0.0102851
$216$	−43.4499	−2.95639
$217$	2.29756	0.155969
$218$	−42.5398	−2.88116
$219$	23.0345	1.55653
$220$	4.45848	0.300591
$221$	14.1611	0.952577
$222$	−41.4146	−2.77957
$223$	7.66713	0.513429	0.256715	−	0.966487i	$-0.417360\pi$
$223$	7.66713	0.513429	0.256715	+	0.966487i	$0.417360\pi$
$224$	50.2088	3.35471
$225$	−3.77453	−0.251635
$226$	−52.6414	−3.50165
$227$	−3.45779	−0.229501	−0.114751	−	0.993394i	$-0.536607\pi$
$227$	−3.45779	−0.229501	−0.114751	+	0.993394i	$0.536607\pi$
$228$	1.41633	0.0937988
$229$	12.9231	0.853984	0.426992	−	0.904255i	$-0.359573\pi$
$229$	12.9231	0.853984	0.426992	+	0.904255i	$0.359573\pi$
$230$	2.21731	0.146205
$231$	−14.8968	−0.980139
$232$	−9.58561	−0.629326
$233$	−27.0050	−1.76916	−0.884578	−	0.466393i	$-0.845553\pi$
$233$	−27.0050	−1.76916	−0.884578	+	0.466393i	$0.845553\pi$
$234$	−4.94683	−0.323385
$235$	−0.0539880	−0.00352179
$236$	62.1339	4.04457
$237$	−17.3396	−1.12633
$238$	33.0734	2.14383
$239$	23.1943	1.50031	0.750157	−	0.661260i	$-0.229978\pi$
$239$	23.1943	1.50031	0.750157	+	0.661260i	$0.229978\pi$
$240$	6.52725	0.421332
$241$	15.4009	0.992058	0.496029	−	0.868306i	$-0.334791\pi$
$241$	15.4009	0.992058	0.496029	+	0.868306i	$0.334791\pi$
$242$	−10.7487	−0.690951
$243$	7.73508	0.496206
$244$	−19.7179	−1.26231
$245$	0.624128	0.0398741
$246$	−24.0887	−1.53584
$247$	−0.305546	−0.0194414
$248$	11.5521	0.733556
$249$	18.1851	1.15243
$250$	−5.64799	−0.357210
$251$	10.2340	0.645966	0.322983	−	0.946405i	$-0.395314\pi$
$251$	10.2340	0.645966	0.322983	+	0.946405i	$0.395314\pi$
$252$	−8.52274	−0.536882
$253$	−15.0863	−0.948469
$254$	−32.8328	−2.06012
$255$	2.39741	0.150132
$256$	68.1458	4.25911
$257$	10.4985	0.654878	0.327439	−	0.944872i	$-0.393814\pi$
$257$	10.4985	0.654878	0.327439	+	0.944872i	$0.393814\pi$
$258$	−3.93159	−0.244770
$259$	15.3928	0.956463
$260$	−2.71865	−0.168603
$261$	0.729231	0.0451383
$262$	−31.8014	−1.96469
$263$	15.4749	0.954224	0.477112	−	0.878842i	$-0.341684\pi$
$263$	15.4749	0.954224	0.477112	+	0.878842i	$0.341684\pi$
$264$	−74.9007	−4.60982
$265$	0.205414	0.0126185
$266$	−0.713608	−0.0437541
$267$	−11.3126	−0.692321
$268$	−81.2211	−4.96137
$269$	7.60631	0.463765	0.231882	−	0.972744i	$-0.425512\pi$
$269$	7.60631	0.463765	0.231882	+	0.972744i	$0.425512\pi$
$270$	2.46258	0.149868
$271$	9.13029	0.554626	0.277313	−	0.960780i	$-0.410556\pi$
$271$	9.13029	0.554626	0.277313	+	0.960780i	$0.410556\pi$
$272$	98.5991	5.97845
$273$	9.08363	0.549766
$274$	29.9647	1.81024
$275$	19.1327	1.15375
$276$	−42.6420	−2.56674
$277$	−22.8088	−1.37045	−0.685224	−	0.728332i	$-0.740296\pi$
$277$	−22.8088	−1.37045	−0.685224	+	0.728332i	$0.740296\pi$
$278$	−16.8497	−1.01058
$279$	−0.878829	−0.0526141
$280$	−4.09159	−0.244520
$281$	−4.99900	−0.298215	−0.149108	−	0.988821i	$-0.547640\pi$
$281$	−4.99900	−0.298215	−0.149108	+	0.988821i	$0.547640\pi$
$282$	1.40747	0.0838137
$283$	−19.5383	−1.16143	−0.580717	−	0.814106i	$-0.697228\pi$
$283$	−19.5383	−1.16143	−0.580717	+	0.814106i	$0.697228\pi$
$284$	81.4147	4.83108
$285$	−0.0517277	−0.00306409
$286$	25.0750	1.48272
$287$	8.95318	0.528490
$288$	−19.2051	−1.13167
$289$	19.2148	1.13028
$290$	0.543278	0.0319024
$291$	17.0159	0.997488
$292$	−66.8003	−3.90919
$293$	16.1349	0.942609	0.471304	−	0.881971i	$-0.343783\pi$
$293$	16.1349	0.942609	0.471304	+	0.881971i	$0.343783\pi$
$294$	−16.2711	−0.948947
$295$	−2.26928	−0.132122
$296$	77.3945	4.49847
$297$	−16.7551	−0.972231
$298$	−25.8932	−1.49995
$299$	9.19918	0.532002
$300$	54.0792	3.12227
$301$	1.46128	0.0842266
$302$	2.76122	0.158890
$303$	−5.13197	−0.294824
$304$	−2.12742	−0.122016
$305$	0.720145	0.0412354
$306$	−12.6508	−0.723197
$307$	21.1283	1.20586	0.602928	−	0.797796i	$-0.294001\pi$
$307$	21.1283	1.20586	0.602928	+	0.797796i	$0.294001\pi$
$308$	43.2009	2.46160
$309$	4.35522	0.247760
$310$	−0.654729	−0.0371861
$311$	17.0463	0.966609	0.483305	−	0.875452i	$-0.339436\pi$
$311$	17.0463	0.966609	0.483305	+	0.875452i	$0.339436\pi$
$312$	45.6722	2.58568
$313$	13.2234	0.747432	0.373716	−	0.927543i	$-0.378083\pi$
$313$	13.2234	0.747432	0.373716	+	0.927543i	$0.378083\pi$
$314$	−18.7905	−1.06041
$315$	0.311271	0.0175381
$316$	50.2851	2.82876
$317$	−15.3395	−0.861553	−0.430776	−	0.902459i	$-0.641760\pi$
$317$	−15.3395	−0.861553	−0.430776	+	0.902459i	$0.641760\pi$
$318$	−5.35515	−0.300302
$319$	−3.69640	−0.206959
$320$	−7.57669	−0.423550
$321$	−2.91528	−0.162715
$322$	21.4848	1.19730
$323$	−0.781388	−0.0434776
$324$	−60.2048	−3.34471
$325$	−11.6666	−0.647144
$326$	−17.9509	−0.994208
$327$	−29.8790	−1.65231
$328$	45.0163	2.48561
$329$	−0.523123	−0.0288407
$330$	4.24510	0.233685
$331$	0.301712	0.0165836	0.00829180	−	0.999966i	$-0.497361\pi$
$331$	0.301712	0.0165836	0.00829180	+	0.999966i	$0.497361\pi$
$332$	−52.7370	−2.89432
$333$	−5.88784	−0.322651
$334$	53.8389	2.94594
$335$	2.96638	0.162071
$336$	63.2465	3.45038
$337$	3.99156	0.217434	0.108717	−	0.994073i	$-0.465326\pi$
$337$	3.99156	0.217434	0.108717	+	0.994073i	$0.465326\pi$
$338$	20.6058	1.12081
$339$	−36.9741	−2.00816
$340$	−6.95253	−0.377054
$341$	4.45470	0.241236
$342$	0.272959	0.0147599
$343$	19.9802	1.07883
$344$	7.34725	0.396137
$345$	1.55739	0.0838468
$346$	6.58685	0.354111
$347$	−0.796848	−0.0427771	−0.0213885	−	0.999771i	$-0.506809\pi$
$347$	−0.796848	−0.0427771	−0.0213885	+	0.999771i	$0.506809\pi$
$348$	−10.4480	−0.560071
$349$	14.7230	0.788105	0.394052	−	0.919088i	$-0.371073\pi$
$349$	14.7230	0.788105	0.394052	+	0.919088i	$0.371073\pi$
$350$	−27.2474	−1.45644
$351$	10.2168	0.545331
$352$	97.3489	5.18872
$353$	−1.24726	−0.0663852	−0.0331926	−	0.999449i	$-0.510567\pi$
$353$	−1.24726	−0.0663852	−0.0331926	+	0.999449i	$0.510567\pi$
$354$	59.1602	3.14433
$355$	−2.97346	−0.157815
$356$	32.8067	1.73875
$357$	23.2300	1.22946
$358$	24.1836	1.27814
$359$	−15.1924	−0.801827	−0.400913	−	0.916116i	$-0.631307\pi$
$359$	−15.1924	−0.801827	−0.400913	+	0.916116i	$0.631307\pi$
$360$	1.56506	0.0824858
$361$	−18.9831	−0.999113
$362$	33.7064	1.77157
$363$	−7.54962	−0.396252
$364$	−26.3426	−1.38073
$365$	2.43971	0.127700
$366$	−18.7742	−0.981345
$367$	−3.74708	−0.195596	−0.0977981	−	0.995206i	$-0.531180\pi$
$367$	−3.74708	−0.195596	−0.0977981	+	0.995206i	$0.531180\pi$
$368$	64.0510	3.33889
$369$	−3.42464	−0.178280
$370$	−4.38644	−0.228040
$371$	1.99038	0.103335
$372$	12.5914	0.652831
$373$	19.3559	1.00221	0.501104	−	0.865387i	$-0.332927\pi$
$373$	19.3559	1.00221	0.501104	+	0.865387i	$0.332927\pi$
$374$	64.1255	3.31585
$375$	−3.96701	−0.204856
$376$	−2.63024	−0.135645
$377$	2.25395	0.116085
$378$	23.8615	1.22730
$379$	−35.5976	−1.82853	−0.914264	−	0.405119i	$-0.867230\pi$
$379$	−35.5976	−1.82853	−0.914264	+	0.405119i	$0.867230\pi$
$380$	0.150011	0.00769540
$381$	−23.0610	−1.18145
$382$	−58.2590	−2.98079
$383$	6.94785	0.355019	0.177509	−	0.984119i	$-0.443196\pi$
$383$	6.94785	0.355019	0.177509	+	0.984119i	$0.443196\pi$
$384$	99.6783	5.08669
$385$	−1.57780	−0.0804121
$386$	25.8986	1.31821
$387$	−0.558946	−0.0284128
$388$	−49.3462	−2.50518
$389$	−38.7304	−1.96371	−0.981855	−	0.189632i	$-0.939270\pi$
$389$	−38.7304	−1.96371	−0.981855	+	0.189632i	$0.939270\pi$
$390$	−2.58853	−0.131076
$391$	23.5255	1.18974
$392$	30.4069	1.53578
$393$	−22.3365	−1.12673
$394$	−22.6621	−1.14170
$395$	−1.83653	−0.0924059
$396$	−16.5246	−0.830392
$397$	−3.78207	−0.189817	−0.0949083	−	0.995486i	$-0.530256\pi$
$397$	−3.78207	−0.189817	−0.0949083	+	0.995486i	$0.530256\pi$
$398$	−64.6428	−3.24025
$399$	−0.501222	−0.0250925
$400$	−81.2306	−4.06153
$401$	7.15639	0.357373	0.178687	−	0.983906i	$-0.442815\pi$
$401$	7.15639	0.357373	0.178687	+	0.983906i	$0.442815\pi$
$402$	−77.3339	−3.85706
$403$	−2.71634	−0.135311
$404$	14.8828	0.740446
$405$	2.19882	0.109260
$406$	5.26415	0.261255
$407$	29.8449	1.47936
$408$	116.800	5.78245
$409$	22.5027	1.11269	0.556344	−	0.830952i	$-0.312204\pi$
$409$	22.5027	1.11269	0.556344	+	0.830952i	$0.312204\pi$
$410$	−2.55136	−0.126003
$411$	21.0465	1.03815
$412$	−12.6302	−0.622244
$413$	−21.9884	−1.08198
$414$	−8.21807	−0.403896
$415$	1.92608	0.0945475
$416$	−59.3605	−2.91039
$417$	−11.8348	−0.579555
$418$	−1.38360	−0.0676742
$419$	−23.9718	−1.17110	−0.585550	−	0.810636i	$-0.699121\pi$
$419$	−23.9718	−1.17110	−0.585550	+	0.810636i	$0.699121\pi$
$420$	−4.45970	−0.217611
$421$	16.1850	0.788809	0.394404	−	0.918937i	$-0.370951\pi$
$421$	16.1850	0.788809	0.394404	+	0.918937i	$0.370951\pi$
$422$	37.6611	1.83331
$423$	0.200097	0.00972907
$424$	10.0076	0.486010
$425$	−29.8354	−1.44723
$426$	77.5183	3.75577
$427$	6.97793	0.337686
$428$	8.45434	0.408656
$429$	17.6121	0.850320
$430$	−0.416415	−0.0200813
$431$	−29.3626	−1.41435	−0.707173	−	0.707040i	$-0.750030\pi$
$431$	−29.3626	−1.41435	−0.707173	+	0.707040i	$0.750030\pi$
$432$	71.1362	3.42254
$433$	8.93518	0.429398	0.214699	−	0.976680i	$-0.431123\pi$
$433$	8.93518	0.429398	0.214699	+	0.976680i	$0.431123\pi$
$434$	−6.34406	−0.304525
$435$	0.381586	0.0182956
$436$	86.6494	4.14975
$437$	−0.507598	−0.0242817
$438$	−63.6033	−3.03908
$439$	19.0134	0.907461	0.453731	−	0.891139i	$-0.350093\pi$
$439$	19.0134	0.907461	0.453731	+	0.891139i	$0.350093\pi$
$440$	−7.93312	−0.378197
$441$	−2.31322	−0.110154
$442$	−39.1018	−1.85988
$443$	6.10126	0.289879	0.144940	−	0.989440i	$-0.453701\pi$
$443$	6.10126	0.289879	0.144940	+	0.989440i	$0.453701\pi$
$444$	84.3575	4.00343
$445$	−1.19818	−0.0567991
$446$	−21.1706	−1.00246
$447$	−18.1867	−0.860204
$448$	−73.4151	−3.46854
$449$	−32.0433	−1.51222	−0.756109	−	0.654446i	$-0.772902\pi$
$449$	−32.0433	−1.51222	−0.756109	+	0.654446i	$0.772902\pi$
$450$	10.4223	0.491312
$451$	17.3592	0.817412
$452$	107.225	5.04345
$453$	1.93941	0.0911217
$454$	9.54771	0.448096
$455$	0.962095	0.0451037
$456$	−2.52013	−0.118016
$457$	−34.2680	−1.60299	−0.801495	−	0.598002i	$-0.795961\pi$
$457$	−34.2680	−1.60299	−0.801495	+	0.598002i	$0.795961\pi$
$458$	−35.6836	−1.66738
$459$	26.1279	1.21954
$460$	−4.51643	−0.210580
$461$	−13.3395	−0.621281	−0.310640	−	0.950527i	$-0.600544\pi$
$461$	−13.3395	−0.621281	−0.310640	+	0.950527i	$0.600544\pi$
$462$	41.1334	1.91370
$463$	−19.7956	−0.919981	−0.459991	−	0.887924i	$-0.652147\pi$
$463$	−19.7956	−0.919981	−0.459991	+	0.887924i	$0.652147\pi$
$464$	15.6936	0.728556
$465$	−0.459866	−0.0213258
$466$	74.5666	3.45423
$467$	41.1409	1.90377	0.951886	−	0.306451i	$-0.0991415\pi$
$467$	41.1409	1.90377	0.951886	+	0.306451i	$0.0991415\pi$
$468$	10.0762	0.465773
$469$	28.7431	1.32723
$470$	0.149073	0.00687621
$471$	−13.1980	−0.608133
$472$	−110.557	−5.08879
$473$	2.83324	0.130273
$474$	47.8785	2.19913
$475$	0.643744	0.0295370
$476$	−67.3673	−3.08777
$477$	−0.761331	−0.0348589
$478$	−64.0445	−2.92933
$479$	11.1634	0.510070	0.255035	−	0.966932i	$-0.417913\pi$
$479$	11.1634	0.510070	0.255035	+	0.966932i	$0.417913\pi$
$480$	−10.0495	−0.458694
$481$	−18.1985	−0.829780
$482$	−42.5252	−1.93697
$483$	15.0905	0.686639
$484$	21.8940	0.995181
$485$	1.80224	0.0818355
$486$	−21.3583	−0.968830
$487$	25.1289	1.13870	0.569350	−	0.822096i	$-0.307195\pi$
$487$	25.1289	1.13870	0.569350	+	0.822096i	$0.307195\pi$
$488$	35.0848	1.58821
$489$	−12.6083	−0.570167
$490$	−1.72335	−0.0778532
$491$	3.18771	0.143859	0.0719297	−	0.997410i	$-0.477084\pi$
$491$	3.18771	0.143859	0.0719297	+	0.997410i	$0.477084\pi$
$492$	49.0663	2.21208
$493$	5.76415	0.259604
$494$	0.843679	0.0379589
$495$	0.603517	0.0271261
$496$	−18.9130	−0.849221
$497$	−28.8116	−1.29238
$498$	−50.2130	−2.25010
$499$	29.8587	1.33666	0.668330	−	0.743865i	$-0.267009\pi$
$499$	29.8587	1.33666	0.668330	+	0.743865i	$0.267009\pi$
$500$	11.5044	0.514492
$501$	37.8152	1.68946
$502$	−28.2584	−1.26123
$503$	26.1012	1.16379	0.581897	−	0.813262i	$-0.302311\pi$
$503$	26.1012	1.16379	0.581897	+	0.813262i	$0.302311\pi$
$504$	15.1648	0.675494
$505$	−0.543554	−0.0241878
$506$	41.6566	1.85186
$507$	14.4731	0.642771
$508$	66.8772	2.96720
$509$	−20.4312	−0.905599	−0.452799	−	0.891612i	$-0.649575\pi$
$509$	−20.4312	−0.905599	−0.452799	+	0.891612i	$0.649575\pi$
$510$	−6.61978	−0.293129
$511$	23.6398	1.04576
$512$	−85.3731	−3.77300
$513$	−0.563747	−0.0248900
$514$	−28.9886	−1.27863
$515$	0.461284	0.0203266
$516$	8.00826	0.352544
$517$	−1.01427	−0.0446077
$518$	−42.5029	−1.86747
$519$	4.62645	0.203079
$520$	4.83738	0.212133
$521$	−14.7118	−0.644535	−0.322268	−	0.946649i	$-0.604445\pi$
$521$	−14.7118	−0.644535	−0.322268	+	0.946649i	$0.604445\pi$
$522$	−2.01357	−0.0881314
$523$	−17.9535	−0.785051	−0.392525	−	0.919741i	$-0.628398\pi$
$523$	−17.9535	−0.785051	−0.392525	+	0.919741i	$0.628398\pi$
$524$	64.7762	2.82976
$525$	−19.1380	−0.835249
$526$	−42.7296	−1.86310
$527$	−6.94663	−0.302600
$528$	122.628	5.33668
$529$	−7.71758	−0.335547
$530$	−0.567192	−0.0246372
$531$	8.41068	0.364992
$532$	1.45355	0.0630193
$533$	−10.5851	−0.458492
$534$	31.2366	1.35174
$535$	−0.308772	−0.0133494
$536$	144.519	6.24229
$537$	16.9860	0.733001
$538$	−21.0027	−0.905490
$539$	11.7255	0.505053
$540$	−5.01603	−0.215856
$541$	36.0689	1.55072	0.775361	−	0.631519i	$-0.217568\pi$
$541$	36.0689	1.55072	0.775361	+	0.631519i	$0.217568\pi$
$542$	−25.2107	−1.08289
$543$	23.6746	1.01597
$544$	−151.805	−6.50860
$545$	−3.16464	−0.135558
$546$	−25.0819	−1.07341
$547$	−33.7246	−1.44196	−0.720979	−	0.692957i	$-0.756308\pi$
$547$	−33.7246	−1.44196	−0.720979	+	0.692957i	$0.756308\pi$
$548$	−61.0352	−2.60729
$549$	−2.66910	−0.113914
$550$	−52.8296	−2.25266
$551$	−0.124370	−0.00529834
$552$	75.8743	3.22942
$553$	−17.7953	−0.756732
$554$	62.9801	2.67577
$555$	−3.08094	−0.130778
$556$	34.3212	1.45554
$557$	−19.1321	−0.810654	−0.405327	−	0.914172i	$-0.632842\pi$
$557$	−19.1321	−0.810654	−0.405327	+	0.914172i	$0.632842\pi$
$558$	2.42664	0.102728
$559$	−1.72763	−0.0730708
$560$	6.69877	0.283075
$561$	45.0403	1.90160
$562$	13.8033	0.582258
$563$	23.0855	0.972940	0.486470	−	0.873697i	$-0.338284\pi$
$563$	23.0855	0.972940	0.486470	+	0.873697i	$0.338284\pi$
$564$	−2.86688	−0.120717
$565$	−3.91612	−0.164752
$566$	53.9496	2.26767
$567$	21.3057	0.894757
$568$	−144.864	−6.07836
$569$	−31.9175	−1.33805	−0.669027	−	0.743238i	$-0.733289\pi$
$569$	−31.9175	−1.33805	−0.669027	+	0.743238i	$0.733289\pi$
$570$	0.142832	0.00598256
$571$	34.0889	1.42658	0.713289	−	0.700870i	$-0.247205\pi$
$571$	34.0889	1.42658	0.713289	+	0.700870i	$0.247205\pi$
$572$	−51.0753	−2.13556
$573$	−40.9198	−1.70945
$574$	−24.7217	−1.03186
$575$	−19.3814	−0.808261
$576$	28.0817	1.17007
$577$	1.59831	0.0665384	0.0332692	−	0.999446i	$-0.489408\pi$
$577$	1.59831	0.0665384	0.0332692	+	0.999446i	$0.489408\pi$
$578$	−53.0563	−2.20685
$579$	18.1906	0.755976
$580$	−1.10660	−0.0459492
$581$	18.6630	0.774270
$582$	−46.9845	−1.94757
$583$	3.85911	0.159828
$584$	118.860	4.91847
$585$	−0.368007	−0.0152152
$586$	−44.5519	−1.84042
$587$	−26.2172	−1.08210	−0.541050	−	0.840990i	$-0.681973\pi$
$587$	−26.2172	−1.08210	−0.541050	+	0.840990i	$0.681973\pi$
$588$	33.1425	1.36677
$589$	0.149884	0.00617586
$590$	6.26596	0.257966
$591$	−15.9173	−0.654751
$592$	−126.710	−5.20777
$593$	−32.6121	−1.33922	−0.669610	−	0.742713i	$-0.733539\pi$
$593$	−32.6121	−1.33922	−0.669610	+	0.742713i	$0.733539\pi$
$594$	46.2646	1.89826
$595$	2.46041	0.100867
$596$	52.7418	2.16039
$597$	−45.4036	−1.85825
$598$	−25.4009	−1.03872
$599$	17.7319	0.724506	0.362253	−	0.932080i	$-0.382008\pi$
$599$	17.7319	0.724506	0.362253	+	0.932080i	$0.382008\pi$
$600$	−96.2250	−3.92837
$601$	−26.0475	−1.06250	−0.531250	−	0.847215i	$-0.678278\pi$
$601$	−26.0475	−1.06250	−0.531250	+	0.847215i	$0.678278\pi$
$602$	−4.03490	−0.164450
$603$	−10.9944	−0.447726
$604$	−5.62432	−0.228851
$605$	−0.799620	−0.0325092
$606$	14.1705	0.575637
$607$	−29.9550	−1.21584	−0.607918	−	0.794000i	$-0.707995\pi$
$607$	−29.9550	−1.21584	−0.607918	+	0.794000i	$0.707995\pi$
$608$	3.27542	0.132836
$609$	3.69741	0.149827
$610$	−1.98848	−0.0805111
$611$	0.618474	0.0250208
$612$	25.7684	1.04162
$613$	−22.3007	−0.900715	−0.450358	−	0.892848i	$-0.648704\pi$
$613$	−22.3007	−0.900715	−0.450358	+	0.892848i	$0.648704\pi$
$614$	−58.3399	−2.35440
$615$	−1.79202	−0.0722611
$616$	−76.8689	−3.09714
$617$	−10.5056	−0.422939	−0.211470	−	0.977385i	$-0.567825\pi$
$617$	−10.5056	−0.422939	−0.211470	+	0.977385i	$0.567825\pi$
$618$	−12.0257	−0.483745
$619$	36.1598	1.45339	0.726693	−	0.686963i	$-0.241056\pi$
$619$	36.1598	1.45339	0.726693	+	0.686963i	$0.241056\pi$
$620$	1.33362	0.0535593
$621$	16.9729	0.681100
$622$	−47.0687	−1.88728
$623$	−11.6099	−0.465140
$624$	−74.7746	−2.99338
$625$	24.3689	0.974754
$626$	−36.5128	−1.45934
$627$	−0.971810	−0.0388104
$628$	38.2744	1.52732
$629$	−46.5399	−1.85567
$630$	−0.859486	−0.0342427
$631$	0.817036	0.0325257	0.0162628	−	0.999868i	$-0.494823\pi$
$631$	0.817036	0.0325257	0.0162628	+	0.999868i	$0.494823\pi$
$632$	−89.4740	−3.55909
$633$	26.4523	1.05138
$634$	42.3557	1.68216
$635$	−2.44251	−0.0969282
$636$	10.9079	0.432526
$637$	−7.14986	−0.283288
$638$	10.2066	0.404082
$639$	11.0206	0.435969
$640$	10.5575	0.417320
$641$	−30.2915	−1.19644	−0.598221	−	0.801331i	$-0.704125\pi$
$641$	−30.2915	−1.19644	−0.598221	+	0.801331i	$0.704125\pi$
$642$	8.04972	0.317697
$643$	−32.3198	−1.27457	−0.637285	−	0.770628i	$-0.719943\pi$
$643$	−32.3198	−1.27457	−0.637285	+	0.770628i	$0.719943\pi$
$644$	−43.7625	−1.72448
$645$	−0.292480	−0.0115164
$646$	2.15758	0.0848889
$647$	13.9782	0.549540	0.274770	−	0.961510i	$-0.411398\pi$
$647$	13.9782	0.549540	0.274770	+	0.961510i	$0.411398\pi$
$648$	107.125	4.20825
$649$	−42.6329	−1.67349
$650$	32.2139	1.26353
$651$	−4.45592	−0.174641
$652$	36.5642	1.43196
$653$	0.497245	0.0194587	0.00972935	−	0.999953i	$-0.496903\pi$
$653$	0.497245	0.0194587	0.00972935	+	0.999953i	$0.496903\pi$
$654$	82.5024	3.22610
$655$	−2.36578	−0.0924387
$656$	−73.7008	−2.87753
$657$	−9.04235	−0.352776
$658$	1.44446	0.0563108
$659$	−2.10716	−0.0820832	−0.0410416	−	0.999157i	$-0.513068\pi$
$659$	−2.10716	−0.0820832	−0.0410416	+	0.999157i	$0.513068\pi$
$660$	−8.64684	−0.336578
$661$	−32.4626	−1.26265	−0.631325	−	0.775518i	$-0.717489\pi$
$661$	−32.4626	−1.26265	−0.631325	+	0.775518i	$0.717489\pi$
$662$	−0.833093	−0.0323791
$663$	−27.4642	−1.06662
$664$	93.8367	3.64157
$665$	−0.0530870	−0.00205863
$666$	16.2576	0.629969
$667$	3.74445	0.144986
$668$	−109.665	−4.24305
$669$	−14.8697	−0.574898
$670$	−8.19083	−0.316440
$671$	13.5294	0.522296
$672$	−97.3756	−3.75635
$673$	42.6044	1.64228	0.821140	−	0.570726i	$-0.193338\pi$
$673$	42.6044	1.64228	0.821140	+	0.570726i	$0.193338\pi$
$674$	−11.0216	−0.424535
$675$	−21.5253	−0.828511
$676$	−41.9720	−1.61431
$677$	20.8069	0.799675	0.399838	−	0.916586i	$-0.369066\pi$
$677$	20.8069	0.799675	0.399838	+	0.916586i	$0.369066\pi$
$678$	102.094	3.92088
$679$	17.4630	0.670169
$680$	12.3709	0.474401
$681$	6.70609	0.256978
$682$	−12.3004	−0.471007
$683$	20.2171	0.773585	0.386792	−	0.922167i	$-0.373583\pi$
$683$	20.2171	0.773585	0.386792	+	0.922167i	$0.373583\pi$
$684$	−0.555990	−0.0212588
$685$	2.22915	0.0851714
$686$	−55.1697	−2.10639
$687$	−25.0633	−0.956224
$688$	−12.0289	−0.458598
$689$	−2.35317	−0.0896486
$690$	−4.30028	−0.163709
$691$	−45.4363	−1.72848	−0.864239	−	0.503081i	$-0.832200\pi$
$691$	−45.4363	−1.72848	−0.864239	+	0.503081i	$0.832200\pi$
$692$	−13.4168	−0.510029
$693$	5.84785	0.222141
$694$	2.20027	0.0835212
$695$	−1.25349	−0.0475476
$696$	18.5905	0.704670
$697$	−27.0698	−1.02534
$698$	−40.6535	−1.53876
$699$	52.3739	1.98096
$700$	55.5003	2.09771
$701$	−19.2151	−0.725744	−0.362872	−	0.931839i	$-0.618204\pi$
$701$	−19.2151	−0.725744	−0.362872	+	0.931839i	$0.618204\pi$
$702$	−28.2108	−1.06475
$703$	1.00417	0.0378729
$704$	−142.343	−5.36477
$705$	0.104705	0.00394343
$706$	3.44397	0.129616
$707$	−5.26683	−0.198079
$708$	−120.503	−4.52879
$709$	2.98664	0.112166	0.0560828	−	0.998426i	$-0.482139\pi$
$709$	2.98664	0.112166	0.0560828	+	0.998426i	$0.482139\pi$
$710$	8.21037	0.308130
$711$	6.80679	0.255275
$712$	−58.3741	−2.18766
$713$	−4.51261	−0.168998
$714$	−64.1431	−2.40050
$715$	1.86539	0.0697616
$716$	−49.2597	−1.84092
$717$	−44.9833	−1.67993
$718$	41.9497	1.56555
$719$	−18.5296	−0.691038	−0.345519	−	0.938412i	$-0.612297\pi$
$719$	−18.5296	−0.691038	−0.345519	+	0.938412i	$0.612297\pi$
$720$	−2.56231	−0.0954918
$721$	4.46966	0.166459
$722$	52.4166	1.95074
$723$	−29.8687	−1.11083
$724$	−68.6565	−2.55160
$725$	−4.74877	−0.176365
$726$	20.8462	0.773673
$727$	−8.40272	−0.311640	−0.155820	−	0.987786i	$-0.549802\pi$
$727$	−8.40272	−0.311640	−0.155820	+	0.987786i	$0.549802\pi$
$728$	46.8723	1.73720
$729$	17.1116	0.633762
$730$	−6.73656	−0.249331
$731$	−4.41814	−0.163411
$732$	38.2413	1.41344
$733$	31.7577	1.17300	0.586499	−	0.809950i	$-0.300506\pi$
$733$	31.7577	1.17300	0.586499	+	0.809950i	$0.300506\pi$
$734$	10.3465	0.381897
$735$	−1.21044	−0.0446479
$736$	−98.6143	−3.63497
$737$	55.7295	2.05282
$738$	9.45618	0.348087
$739$	−18.9067	−0.695495	−0.347747	−	0.937588i	$-0.613053\pi$
$739$	−18.9067	−0.695495	−0.347747	+	0.937588i	$0.613053\pi$
$740$	8.93475	0.328448
$741$	0.592581	0.0217690
$742$	−5.49587	−0.201760
$743$	−37.1631	−1.36338	−0.681691	−	0.731640i	$-0.738755\pi$
$743$	−37.1631	−1.36338	−0.681691	+	0.731640i	$0.738755\pi$
$744$	−22.4042	−0.821379
$745$	−1.92625	−0.0705725
$746$	−53.4458	−1.95679
$747$	−7.13868	−0.261191
$748$	−130.617	−4.77584
$749$	−2.99188	−0.109321
$750$	10.9538	0.399976
$751$	4.75509	0.173516	0.0867578	−	0.996229i	$-0.472349\pi$
$751$	4.75509	0.173516	0.0867578	+	0.996229i	$0.472349\pi$
$752$	4.30624	0.157032
$753$	−19.8480	−0.723302
$754$	−6.22366	−0.226652
$755$	0.205414	0.00747577
$756$	−48.6034	−1.76769
$757$	15.1677	0.551278	0.275639	−	0.961261i	$-0.411111\pi$
$757$	15.1677	0.551278	0.275639	+	0.961261i	$0.411111\pi$
$758$	98.2929	3.57016
$759$	29.2586	1.06202
$760$	−0.266920	−0.00968219
$761$	0.618791	0.0224312	0.0112156	−	0.999937i	$-0.496430\pi$
$761$	0.618791	0.0224312	0.0112156	+	0.999937i	$0.496430\pi$
$762$	63.6765	2.30676
$763$	−30.6641	−1.11012
$764$	118.668	4.29325
$765$	−0.941121	−0.0340263
$766$	−19.1845	−0.693166
$767$	25.9963	0.938671
$768$	−132.163	−4.76902
$769$	40.8060	1.47150	0.735751	−	0.677253i	$-0.236830\pi$
$769$	40.8060	1.47150	0.735751	+	0.677253i	$0.236830\pi$
$770$	4.35665	0.157003
$771$	−20.3609	−0.733281
$772$	−52.7529	−1.89862
$773$	6.92057	0.248916	0.124458	−	0.992225i	$-0.460281\pi$
$773$	6.92057	0.248916	0.124458	+	0.992225i	$0.460281\pi$
$774$	1.54337	0.0554754
$775$	5.72296	0.205575
$776$	87.8034	3.15196
$777$	−29.8531	−1.07097
$778$	106.943	3.83410
$779$	0.584071	0.0209265
$780$	5.27259	0.188789
$781$	−55.8624	−1.99891
$782$	−64.9591	−2.32293
$783$	4.15865	0.148618
$784$	−49.7822	−1.77794
$785$	−1.39787	−0.0498922
$786$	61.6760	2.19991
$787$	3.63883	0.129710	0.0648551	−	0.997895i	$-0.479341\pi$
$787$	3.63883	0.129710	0.0648551	+	0.997895i	$0.479341\pi$
$788$	46.1604	1.64440
$789$	−30.0123	−1.06847
$790$	5.07106	0.180420
$791$	−37.9457	−1.34919
$792$	29.4028	1.04478
$793$	−8.24981	−0.292960
$794$	10.4431	0.370612
$795$	−0.398382	−0.0141292
$796$	131.671	4.66695
$797$	4.06092	0.143845	0.0719226	−	0.997410i	$-0.477087\pi$
$797$	4.06092	0.143845	0.0719226	+	0.997410i	$0.477087\pi$
$798$	1.38398	0.0489924
$799$	1.58165	0.0559549
$800$	125.064	4.42169
$801$	4.44085	0.156910
$802$	−19.7604	−0.697763
$803$	45.8348	1.61748
$804$	157.521	5.55535
$805$	1.59831	0.0563330
$806$	7.50041	0.264191
$807$	−14.7518	−0.519287
$808$	−26.4814	−0.931613
$809$	−3.51399	−0.123545	−0.0617727	−	0.998090i	$-0.519675\pi$
$809$	−3.51399	−0.123545	−0.0617727	+	0.998090i	$0.519675\pi$
$810$	−6.07143	−0.213328
$811$	−49.0909	−1.72381	−0.861907	−	0.507067i	$-0.830730\pi$
$811$	−49.0909	−1.72381	−0.861907	+	0.507067i	$0.830730\pi$
$812$	−10.7225	−0.376288
$813$	−17.7074	−0.621027
$814$	−82.4082	−2.88841
$815$	−1.33541	−0.0467774
$816$	−191.225	−6.69420
$817$	0.0953280	0.00333510
$818$	−62.1349	−2.17250
$819$	−3.56584	−0.124601
$820$	5.19687	0.181482
$821$	4.25551	0.148518	0.0742592	−	0.997239i	$-0.476341\pi$
$821$	4.25551	0.148518	0.0742592	+	0.997239i	$0.476341\pi$
$822$	−58.1141	−2.02696
$823$	37.5323	1.30829	0.654147	−	0.756367i	$-0.273028\pi$
$823$	37.5323	1.30829	0.654147	+	0.756367i	$0.273028\pi$
$824$	22.4733	0.782895
$825$	−37.1063	−1.29187
$826$	60.7147	2.11254
$827$	−36.5650	−1.27149	−0.635744	−	0.771900i	$-0.719307\pi$
$827$	−36.5650	−1.27149	−0.635744	+	0.771900i	$0.719307\pi$
$828$	16.7394	0.581734
$829$	−0.910563	−0.0316252	−0.0158126	−	0.999875i	$-0.505034\pi$
$829$	−0.910563	−0.0316252	−0.0158126	+	0.999875i	$0.505034\pi$
$830$	−5.31833	−0.184602
$831$	44.2357	1.53452
$832$	86.7967	3.00913
$833$	−18.2847	−0.633527
$834$	32.6786	1.13157
$835$	4.00521	0.138606
$836$	2.81826	0.0974716
$837$	−5.01178	−0.173232
$838$	66.1914	2.28655
$839$	42.7814	1.47698	0.738489	−	0.674265i	$-0.235539\pi$
$839$	42.7814	1.47698	0.738489	+	0.674265i	$0.235539\pi$
$840$	7.93530	0.273794
$841$	−28.0825	−0.968364
$842$	−44.6903	−1.54013
$843$	9.69514	0.333918
$844$	−76.7119	−2.64053
$845$	1.53292	0.0527340
$846$	−0.552513	−0.0189958
$847$	−7.74801	−0.266225
$848$	−16.3844	−0.562642
$849$	37.8929	1.30048
$850$	82.3822	2.82569
$851$	−30.2328	−1.03637
$852$	−157.897	−5.40946
$853$	−4.97060	−0.170190	−0.0850951	−	0.996373i	$-0.527119\pi$
$853$	−4.97060	−0.170190	−0.0850951	+	0.996373i	$0.527119\pi$
$854$	−19.2676	−0.659323
$855$	0.0203061	0.000694453 0
$856$	−15.0431	−0.514162
$857$	15.1043	0.515953	0.257976	−	0.966151i	$-0.416944\pi$
$857$	15.1043	0.515953	0.257976	+	0.966151i	$0.416944\pi$
$858$	−48.6308	−1.66023
$859$	0.172905	0.00589943	0.00294971	−	0.999996i	$-0.499061\pi$
$859$	0.172905	0.00589943	0.00294971	+	0.999996i	$0.499061\pi$
$860$	0.848196	0.0289233
$861$	−17.3639	−0.591762
$862$	81.0765	2.76148
$863$	−10.6838	−0.363680	−0.181840	−	0.983328i	$-0.558205\pi$
$863$	−10.6838	−0.363680	−0.181840	+	0.983328i	$0.558205\pi$
$864$	−109.523	−3.72604
$865$	0.490012	0.0166609
$866$	−24.6720	−0.838388
$867$	−37.2655	−1.26560
$868$	12.9222	0.438609
$869$	−34.5030	−1.17043
$870$	−1.05364	−0.0357218
$871$	−33.9822	−1.15144
$872$	−154.178	−5.22113
$873$	−6.67970	−0.226074
$874$	1.40159	0.0474094
$875$	−4.07126	−0.137634
$876$	129.554	4.37721
$877$	25.2885	0.853931	0.426966	−	0.904268i	$-0.359583\pi$
$877$	25.2885	0.853931	0.426966	+	0.904268i	$0.359583\pi$
$878$	−52.5002	−1.77180
$879$	−31.2922	−1.05546
$880$	12.9881	0.437830
$881$	1.33758	0.0450644	0.0225322	−	0.999746i	$-0.492827\pi$
$881$	1.33758	0.0450644	0.0225322	+	0.999746i	$0.492827\pi$
$882$	6.38731	0.215072
$883$	−23.2230	−0.781516	−0.390758	−	0.920494i	$-0.627787\pi$
$883$	−23.2230	−0.781516	−0.390758	+	0.920494i	$0.627787\pi$
$884$	79.6465	2.67880
$885$	4.40107	0.147940
$886$	−16.8469	−0.565983
$887$	33.5458	1.12636	0.563178	−	0.826335i	$-0.309578\pi$
$887$	33.5458	1.12636	0.563178	+	0.826335i	$0.309578\pi$
$888$	−150.100	−5.03703
$889$	−23.6670	−0.793766
$890$	3.30843	0.110899
$891$	41.3093	1.38391
$892$	43.1224	1.44385
$893$	−0.0341265	−0.00114200
$894$	50.2176	1.67953
$895$	1.79908	0.0601366
$896$	102.298	3.41752
$897$	−17.8410	−0.595695
$898$	88.4786	2.95257
$899$	−1.10566	−0.0368760
$900$	−21.2292	−0.707639
$901$	−6.01787	−0.200484
$902$	−47.9325	−1.59598
$903$	−2.83402	−0.0943103
$904$	−190.790	−6.34557
$905$	2.50750	0.0833520
$906$	−5.35515	−0.177913
$907$	−0.884477	−0.0293686	−0.0146843	−	0.999892i	$-0.504674\pi$
$907$	−0.884477	−0.0293686	−0.0146843	+	0.999892i	$0.504674\pi$
$908$	−19.4477	−0.645395
$909$	2.01459	0.0668197
$910$	−2.65655	−0.0880639
$911$	−52.5849	−1.74221	−0.871107	−	0.491093i	$-0.836598\pi$
$911$	−52.5849	−1.74221	−0.871107	+	0.491093i	$0.836598\pi$
$912$	4.12595	0.136624
$913$	36.1853	1.19756
$914$	94.6214	3.12980
$915$	−1.39666	−0.0461722
$916$	72.6838	2.40154
$917$	−22.9235	−0.757000
$918$	−72.1447	−2.38113
$919$	−8.03210	−0.264954	−0.132477	−	0.991186i	$-0.542293\pi$
$919$	−8.03210	−0.264954	−0.132477	+	0.991186i	$0.542293\pi$
$920$	8.03624	0.264947
$921$	−40.9765	−1.35022
$922$	36.8332	1.21304
$923$	34.0632	1.12120
$924$	−83.7845	−2.75631
$925$	38.3418	1.26067
$926$	54.6601	1.79624
$927$	−1.70967	−0.0561529
$928$	−24.1622	−0.793162
$929$	17.0027	0.557839	0.278920	−	0.960314i	$-0.410024\pi$
$929$	17.0027	0.557839	0.278920	+	0.960314i	$0.410024\pi$
$930$	1.26979	0.0416381
$931$	0.394519	0.0129298
$932$	−151.885	−4.97515
$933$	−33.0599	−1.08233
$934$	−113.599	−3.71707
$935$	4.77045	0.156010
$936$	−17.9289	−0.586025
$937$	−4.25305	−0.138941	−0.0694706	−	0.997584i	$-0.522131\pi$
$937$	−4.25305	−0.138941	−0.0694706	+	0.997584i	$0.522131\pi$
$938$	−79.3660	−2.59139
$939$	−25.6457	−0.836916
$940$	−0.303646	−0.00990385
$941$	−3.40934	−0.111141	−0.0555707	−	0.998455i	$-0.517698\pi$
$941$	−3.40934	−0.111141	−0.0555707	+	0.998455i	$0.517698\pi$
$942$	36.4426	1.18737
$943$	−17.5848	−0.572641
$944$	181.004	5.89118
$945$	1.77511	0.0577444
$946$	−7.82320	−0.254354
$947$	−39.1120	−1.27097	−0.635485	−	0.772113i	$-0.719200\pi$
$947$	−39.1120	−1.27097	−0.635485	+	0.772113i	$0.719200\pi$
$948$	−97.5237	−3.16742
$949$	−27.9487	−0.907253
$950$	−1.77752	−0.0576703
$951$	29.7497	0.964699
$952$	119.869	3.88497
$953$	8.90018	0.288305	0.144153	−	0.989555i	$-0.453954\pi$
$953$	8.90018	0.288305	0.144153	+	0.989555i	$0.453954\pi$
$954$	2.10220	0.0680612
$955$	−4.33403	−0.140246
$956$	130.452	4.21912
$957$	7.16886	0.231736
$958$	−30.8246	−0.995899
$959$	21.5996	0.697487
$960$	14.6943	0.474258
$961$	−29.6675	−0.957017
$962$	50.2500	1.62013
$963$	1.14441	0.0368782
$964$	86.6195	2.78983
$965$	1.92666	0.0620214
$966$	−41.6680	−1.34065
$967$	−20.8010	−0.668915	−0.334457	−	0.942411i	$-0.608553\pi$
$967$	−20.8010	−0.668915	−0.334457	+	0.942411i	$0.608553\pi$
$968$	−38.9567	−1.25212
$969$	1.51544	0.0486828
$970$	−4.97638	−0.159782
$971$	8.61610	0.276504	0.138252	−	0.990397i	$-0.455852\pi$
$971$	8.61610	0.276504	0.138252	+	0.990397i	$0.455852\pi$
$972$	43.5046	1.39541
$973$	−12.1458	−0.389377
$974$	−69.3864	−2.22328
$975$	22.6263	0.724621
$976$	−57.4409	−1.83864
$977$	−5.01933	−0.160582	−0.0802912	−	0.996771i	$-0.525585\pi$
$977$	−5.01933	−0.160582	−0.0802912	+	0.996771i	$0.525585\pi$
$978$	34.8142	1.11324
$979$	−22.5102	−0.719430
$980$	3.51030	0.112132
$981$	11.7292	0.374485
$982$	−8.80197	−0.280882
$983$	33.6877	1.07447	0.537236	−	0.843432i	$-0.319468\pi$
$983$	33.6877	1.07447	0.537236	+	0.843432i	$0.319468\pi$
$984$	−87.3053	−2.78319
$985$	−1.68589	−0.0537168
$986$	−15.9161	−0.506871
$987$	1.01455	0.0322936
$988$	−1.71849	−0.0546725
$989$	−2.87007	−0.0912630
$990$	−1.66644	−0.0529630
$991$	15.4063	0.489397	0.244699	−	0.969599i	$-0.421311\pi$
$991$	15.4063	0.489397	0.244699	+	0.969599i	$0.421311\pi$
$992$	29.1189	0.924527
$993$	−0.585145	−0.0185690
$994$	79.5552	2.52334
$995$	−4.80893	−0.152453
$996$	102.279	3.24083
$997$	−22.7283	−0.719813	−0.359907	−	0.932988i	$-0.617191\pi$
$997$	−22.7283	−0.719813	−0.359907	+	0.932988i	$0.617191\pi$
$998$	−82.4464	−2.60980
$999$	−33.5771	−1.06233

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.2	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +O(q^{10})\)	\(q-2.76122 q^{2} -1.93941 q^{3} +5.62432 q^{4} -0.205414 q^{5} +5.35515 q^{6} -1.99038 q^{7} -10.0076 q^{8} +0.761331 q^{9} +0.567192 q^{10} -3.85911 q^{11} -10.9079 q^{12} +2.35317 q^{13} +5.49587 q^{14} +0.398382 q^{15} +16.3844 q^{16} +6.01787 q^{17} -2.10220 q^{18} -0.129844 q^{19} -1.15531 q^{20} +3.86017 q^{21} +10.6558 q^{22} +3.90927 q^{23} +19.4088 q^{24} -4.95781 q^{25} -6.49761 q^{26} +4.34171 q^{27} -11.1945 q^{28} +0.957838 q^{29} -1.10002 q^{30} -1.15433 q^{31} -25.2257 q^{32} +7.48442 q^{33} -16.6167 q^{34} +0.408851 q^{35} +4.28197 q^{36} -7.73361 q^{37} +0.358529 q^{38} -4.56377 q^{39} +2.05569 q^{40} -4.49823 q^{41} -10.6588 q^{42} -0.734170 q^{43} -21.7049 q^{44} -0.156388 q^{45} -10.7944 q^{46} +0.262826 q^{47} -31.7761 q^{48} -3.03840 q^{49} +13.6896 q^{50} -11.6712 q^{51} +13.2350 q^{52} -1.00000 q^{53} -11.9884 q^{54} +0.792714 q^{55} +19.9188 q^{56} +0.251822 q^{57} -2.64480 q^{58} +11.0473 q^{59} +2.24063 q^{60} -3.50583 q^{61} +3.18737 q^{62} -1.51534 q^{63} +36.8850 q^{64} -0.483373 q^{65} -20.6661 q^{66} -14.4410 q^{67} +33.8465 q^{68} -7.58170 q^{69} -1.12893 q^{70} +14.4755 q^{71} -7.61905 q^{72} -11.8770 q^{73} +21.3542 q^{74} +9.61524 q^{75} -0.730288 q^{76} +7.68109 q^{77} +12.6016 q^{78} +8.94065 q^{79} -3.36558 q^{80} -10.7044 q^{81} +12.4206 q^{82} -9.37659 q^{83} +21.7108 q^{84} -1.23615 q^{85} +2.02720 q^{86} -1.85764 q^{87} +38.6202 q^{88} +5.83301 q^{89} +0.431820 q^{90} -4.68370 q^{91} +21.9870 q^{92} +2.23873 q^{93} -0.725720 q^{94} +0.0266718 q^{95} +48.9232 q^{96} -8.77372 q^{97} +8.38967 q^{98} -2.93806 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 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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