LMFDB - Embedded newform 8003.2.a.c.1.9

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:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.58576 q^{2} +1.51660 q^{3} +4.68613 q^{4} -3.91728 q^{5} -3.92157 q^{6} -1.90750 q^{7} -6.94569 q^{8} -0.699911 q^{9} +O(q^{10})$	\(q-2.58576 q^{2} +1.51660 q^{3} +4.68613 q^{4} -3.91728 q^{5} -3.92157 q^{6} -1.90750 q^{7} -6.94569 q^{8} -0.699911 q^{9} +10.1291 q^{10} +3.75612 q^{11} +7.10701 q^{12} +0.142589 q^{13} +4.93232 q^{14} -5.94096 q^{15} +8.58758 q^{16} +0.966060 q^{17} +1.80980 q^{18} +3.91278 q^{19} -18.3569 q^{20} -2.89292 q^{21} -9.71241 q^{22} +8.94661 q^{23} -10.5339 q^{24} +10.3451 q^{25} -0.368700 q^{26} -5.61130 q^{27} -8.93879 q^{28} -1.33204 q^{29} +15.3619 q^{30} +5.78221 q^{31} -8.31402 q^{32} +5.69655 q^{33} -2.49799 q^{34} +7.47220 q^{35} -3.27988 q^{36} +8.39609 q^{37} -10.1175 q^{38} +0.216251 q^{39} +27.2082 q^{40} -7.06425 q^{41} +7.48038 q^{42} -10.2633 q^{43} +17.6017 q^{44} +2.74175 q^{45} -23.1338 q^{46} -5.88279 q^{47} +13.0240 q^{48} -3.36145 q^{49} -26.7498 q^{50} +1.46513 q^{51} +0.668190 q^{52} -1.00000 q^{53} +14.5095 q^{54} -14.7138 q^{55} +13.2489 q^{56} +5.93414 q^{57} +3.44432 q^{58} +10.5720 q^{59} -27.8401 q^{60} +10.9931 q^{61} -14.9514 q^{62} +1.33508 q^{63} +4.32286 q^{64} -0.558560 q^{65} -14.7299 q^{66} +4.88864 q^{67} +4.52709 q^{68} +13.5685 q^{69} -19.3213 q^{70} -5.62361 q^{71} +4.86136 q^{72} +2.67486 q^{73} -21.7102 q^{74} +15.6894 q^{75} +18.3358 q^{76} -7.16479 q^{77} -0.559172 q^{78} -12.4486 q^{79} -33.6400 q^{80} -6.41039 q^{81} +18.2664 q^{82} -4.48555 q^{83} -13.5566 q^{84} -3.78433 q^{85} +26.5383 q^{86} -2.02017 q^{87} -26.0888 q^{88} -4.37845 q^{89} -7.08949 q^{90} -0.271988 q^{91} +41.9250 q^{92} +8.76932 q^{93} +15.2114 q^{94} -15.3274 q^{95} -12.6091 q^{96} +7.22950 q^{97} +8.69190 q^{98} -2.62895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.58576	−1.82841	−0.914203	−	0.405257i	$-0.867182\pi$
$2$	−2.58576	−1.82841	−0.914203	+	0.405257i	$0.867182\pi$
$3$	1.51660	0.875612	0.437806	−	0.899069i	$-0.355756\pi$
$3$	1.51660	0.875612	0.437806	+	0.899069i	$0.355756\pi$
$4$	4.68613	2.34307
$5$	−3.91728	−1.75186	−0.875930	−	0.482438i	$-0.839751\pi$
$5$	−3.91728	−1.75186	−0.875930	+	0.482438i	$0.839751\pi$
$6$	−3.92157	−1.60097
$7$	−1.90750	−0.720966	−0.360483	−	0.932766i	$-0.617388\pi$
$7$	−1.90750	−0.720966	−0.360483	+	0.932766i	$0.617388\pi$
$8$	−6.94569	−2.45567
$9$	−0.699911	−0.233304
$10$	10.1291	3.20311
$11$	3.75612	1.13251	0.566256	−	0.824229i	$-0.308391\pi$
$11$	3.75612	1.13251	0.566256	+	0.824229i	$0.308391\pi$
$12$	7.10701	2.05162
$13$	0.142589	0.0395470	0.0197735	−	0.999804i	$-0.493705\pi$
$13$	0.142589	0.0395470	0.0197735	+	0.999804i	$0.493705\pi$
$14$	4.93232	1.31822
$15$	−5.94096	−1.53395
$16$	8.58758	2.14690
$17$	0.966060	0.234304	0.117152	−	0.993114i	$-0.462624\pi$
$17$	0.966060	0.234304	0.117152	+	0.993114i	$0.462624\pi$
$18$	1.80980	0.426574
$19$	3.91278	0.897653	0.448826	−	0.893619i	$-0.351842\pi$
$19$	3.91278	0.897653	0.448826	+	0.893619i	$0.351842\pi$
$20$	−18.3569	−4.10473
$21$	−2.89292	−0.631287
$22$	−9.71241	−2.07069
$23$	8.94661	1.86550	0.932749	−	0.360527i	$-0.117403\pi$
$23$	8.94661	1.86550	0.932749	+	0.360527i	$0.117403\pi$
$24$	−10.5339	−2.15021
$25$	10.3451	2.06901
$26$	−0.368700	−0.0723080
$27$	−5.61130	−1.07990
$28$	−8.93879	−1.68927
$29$	−1.33204	−0.247353	−0.123677	−	0.992323i	$-0.539469\pi$
$29$	−1.33204	−0.247353	−0.123677	+	0.992323i	$0.539469\pi$
$30$	15.3619	2.80468
$31$	5.78221	1.03851	0.519257	−	0.854618i	$-0.326209\pi$
$31$	5.78221	1.03851	0.519257	+	0.854618i	$0.326209\pi$
$32$	−8.31402	−1.46972
$33$	5.69655	0.991641
$34$	−2.49799	−0.428403
$35$	7.47220	1.26303
$36$	−3.27988	−0.546646
$37$	8.39609	1.38031	0.690155	−	0.723662i	$-0.257543\pi$
$37$	8.39609	1.38031	0.690155	+	0.723662i	$0.257543\pi$
$38$	−10.1175	−1.64127
$39$	0.216251	0.0346278
$40$	27.2082	4.30199
$41$	−7.06425	−1.10325	−0.551626	−	0.834092i	$-0.685992\pi$
$41$	−7.06425	−1.10325	−0.551626	+	0.834092i	$0.685992\pi$
$42$	7.48038	1.15425
$43$	−10.2633	−1.56514	−0.782568	−	0.622565i	$-0.786091\pi$
$43$	−10.2633	−1.56514	−0.782568	+	0.622565i	$0.786091\pi$
$44$	17.6017	2.65355
$45$	2.74175	0.408716
$46$	−23.1338	−3.41089
$47$	−5.88279	−0.858092	−0.429046	−	0.903283i	$-0.641150\pi$
$47$	−5.88279	−0.858092	−0.429046	+	0.903283i	$0.641150\pi$
$48$	13.0240	1.87985
$49$	−3.36145	−0.480207
$50$	−26.7498	−3.78300
$51$	1.46513	0.205159
$52$	0.668190	0.0926613
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	14.5095	1.97449
$55$	−14.7138	−1.98400
$56$	13.2489	1.77046
$57$	5.93414	0.785995
$58$	3.44432	0.452262
$59$	10.5720	1.37636	0.688179	−	0.725541i	$-0.258411\pi$
$59$	10.5720	1.37636	0.688179	+	0.725541i	$0.258411\pi$
$60$	−27.8401	−3.59415
$61$	10.9931	1.40752	0.703761	−	0.710437i	$-0.251503\pi$
$61$	10.9931	1.40752	0.703761	+	0.710437i	$0.251503\pi$
$62$	−14.9514	−1.89883
$63$	1.33508	0.168204
$64$	4.32286	0.540357
$65$	−0.558560	−0.0692808
$66$	−14.7299	−1.81312
$67$	4.88864	0.597243	0.298621	−	0.954372i	$-0.403473\pi$
$67$	4.88864	0.597243	0.298621	+	0.954372i	$0.403473\pi$
$68$	4.52709	0.548990
$69$	13.5685	1.63345
$70$	−19.3213	−2.30934
$71$	−5.62361	−0.667400	−0.333700	−	0.942679i	$-0.608297\pi$
$71$	−5.62361	−0.667400	−0.333700	+	0.942679i	$0.608297\pi$
$72$	4.86136	0.572917
$73$	2.67486	0.313068	0.156534	−	0.987673i	$-0.449968\pi$
$73$	2.67486	0.313068	0.156534	+	0.987673i	$0.449968\pi$
$74$	−21.7102	−2.52377
$75$	15.6894	1.81165
$76$	18.3358	2.10326
$77$	−7.16479	−0.816503
$78$	−0.559172	−0.0633137
$79$	−12.4486	−1.40058	−0.700288	−	0.713860i	$-0.746945\pi$
$79$	−12.4486	−1.40058	−0.700288	+	0.713860i	$0.746945\pi$
$80$	−33.6400	−3.76106
$81$	−6.41039	−0.712266
$82$	18.2664	2.01719
$83$	−4.48555	−0.492353	−0.246177	−	0.969225i	$-0.579174\pi$
$83$	−4.48555	−0.492353	−0.246177	+	0.969225i	$0.579174\pi$
$84$	−13.5566	−1.47915
$85$	−3.78433	−0.410468
$86$	26.5383	2.86170
$87$	−2.02017	−0.216585
$88$	−26.0888	−2.78108
$89$	−4.37845	−0.464115	−0.232057	−	0.972702i	$-0.574546\pi$
$89$	−4.37845	−0.464115	−0.232057	+	0.972702i	$0.574546\pi$
$90$	−7.08949	−0.747298
$91$	−0.271988	−0.0285121
$92$	41.9250	4.37099
$93$	8.76932	0.909336
$94$	15.2114	1.56894
$95$	−15.3274	−1.57256
$96$	−12.6091	−1.28691
$97$	7.22950	0.734045	0.367022	−	0.930212i	$-0.380377\pi$
$97$	7.22950	0.734045	0.367022	+	0.930212i	$0.380377\pi$
$98$	8.69190	0.878014
$99$	−2.62895	−0.264219
$100$	48.4784	4.84784
$101$	−12.0889	−1.20289	−0.601446	−	0.798913i	$-0.705409\pi$
$101$	−12.0889	−1.20289	−0.601446	+	0.798913i	$0.705409\pi$
$102$	−3.78847	−0.375114
$103$	2.36405	0.232937	0.116468	−	0.993194i	$-0.462843\pi$
$103$	2.36405	0.232937	0.116468	+	0.993194i	$0.462843\pi$
$104$	−0.990377	−0.0971144
$105$	11.3324	1.10593
$106$	2.58576	0.251151
$107$	9.13710	0.883317	0.441658	−	0.897183i	$-0.354390\pi$
$107$	9.13710	0.883317	0.441658	+	0.897183i	$0.354390\pi$
$108$	−26.2953	−2.53027
$109$	9.16055	0.877422	0.438711	−	0.898628i	$-0.355435\pi$
$109$	9.16055	0.877422	0.438711	+	0.898628i	$0.355435\pi$
$110$	38.0462	3.62756
$111$	12.7336	1.20862
$112$	−16.3808	−1.54784
$113$	5.92505	0.557382	0.278691	−	0.960381i	$-0.410100\pi$
$113$	5.92505	0.557382	0.278691	+	0.960381i	$0.410100\pi$
$114$	−15.3442	−1.43712
$115$	−35.0464	−3.26809
$116$	−6.24211	−0.579565
$117$	−0.0997995	−0.00922647
$118$	−27.3366	−2.51654
$119$	−1.84276	−0.168925
$120$	41.2641	3.76688
$121$	3.10843	0.282584
$122$	−28.4255	−2.57352
$123$	−10.7137	−0.966020
$124$	27.0962	2.43331
$125$	−20.9381	−1.87276
$126$	−3.45219	−0.307545
$127$	17.4134	1.54519	0.772595	−	0.634899i	$-0.218958\pi$
$127$	17.4134	1.54519	0.772595	+	0.634899i	$0.218958\pi$
$128$	5.45018	0.481732
$129$	−15.5653	−1.37045
$130$	1.44430	0.126673
$131$	−12.0533	−1.05310	−0.526550	−	0.850144i	$-0.676515\pi$
$131$	−12.0533	−1.05310	−0.526550	+	0.850144i	$0.676515\pi$
$132$	26.6948	2.32348
$133$	−7.46361	−0.647177
$134$	−12.6408	−1.09200
$135$	21.9810	1.89183
$136$	−6.70995	−0.575373
$137$	−5.13529	−0.438737	−0.219369	−	0.975642i	$-0.570400\pi$
$137$	−5.13529	−0.438737	−0.219369	+	0.975642i	$0.570400\pi$
$138$	−35.0848	−2.98661
$139$	−15.2916	−1.29702	−0.648509	−	0.761207i	$-0.724607\pi$
$139$	−15.2916	−1.29702	−0.648509	+	0.761207i	$0.724607\pi$
$140$	35.0157	2.95937
$141$	−8.92186	−0.751356
$142$	14.5413	1.22028
$143$	0.535580	0.0447875
$144$	−6.01055	−0.500879
$145$	5.21796	0.433328
$146$	−6.91653	−0.572416
$147$	−5.09799	−0.420475
$148$	39.3452	3.23416
$149$	−22.5918	−1.85079	−0.925395	−	0.379005i	$-0.876266\pi$
$149$	−22.5918	−1.85079	−0.925395	+	0.379005i	$0.876266\pi$
$150$	−40.5689	−3.31244
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−27.1769	−2.20434
$153$	−0.676156	−0.0546640
$154$	18.5264	1.49290
$155$	−22.6505	−1.81933
$156$	1.01338	0.0811353
$157$	7.94569	0.634135	0.317067	−	0.948403i	$-0.397302\pi$
$157$	7.94569	0.634135	0.317067	+	0.948403i	$0.397302\pi$
$158$	32.1890	2.56082
$159$	−1.51660	−0.120275
$160$	32.5683	2.57475
$161$	−17.0656	−1.34496
$162$	16.5757	1.30231
$163$	16.5204	1.29398	0.646989	−	0.762499i	$-0.276028\pi$
$163$	16.5204	1.29398	0.646989	+	0.762499i	$0.276028\pi$
$164$	−33.1040	−2.58499
$165$	−22.3150	−1.73722
$166$	11.5985	0.900221
$167$	−25.1452	−1.94579	−0.972897	−	0.231240i	$-0.925722\pi$
$167$	−25.1452	−1.94579	−0.972897	+	0.231240i	$0.925722\pi$
$168$	20.0933	1.55023
$169$	−12.9797	−0.998436
$170$	9.78534	0.750501
$171$	−2.73860	−0.209426
$172$	−48.0951	−3.66722
$173$	−10.5848	−0.804745	−0.402372	−	0.915476i	$-0.631814\pi$
$173$	−10.5848	−0.804745	−0.402372	+	0.915476i	$0.631814\pi$
$174$	5.22368	0.396006
$175$	−19.7332	−1.49169
$176$	32.2560	2.43139
$177$	16.0335	1.20515
$178$	11.3216	0.848590
$179$	−24.0504	−1.79761	−0.898807	−	0.438344i	$-0.855565\pi$
$179$	−24.0504	−1.79761	−0.898807	+	0.438344i	$0.855565\pi$
$180$	12.8482	0.957648
$181$	6.86739	0.510449	0.255225	−	0.966882i	$-0.417851\pi$
$181$	6.86739	0.510449	0.255225	+	0.966882i	$0.417851\pi$
$182$	0.703294	0.0521316
$183$	16.6722	1.23244
$184$	−62.1404	−4.58105
$185$	−32.8898	−2.41811
$186$	−22.6753	−1.66264
$187$	3.62863	0.265352
$188$	−27.5675	−2.01057
$189$	10.7035	0.778568
$190$	39.6330	2.87528
$191$	15.7699	1.14107	0.570533	−	0.821275i	$-0.306737\pi$
$191$	15.7699	1.14107	0.570533	+	0.821275i	$0.306737\pi$
$192$	6.55607	0.473143
$193$	18.8268	1.35519	0.677593	−	0.735437i	$-0.263023\pi$
$193$	18.8268	1.35519	0.677593	+	0.735437i	$0.263023\pi$
$194$	−18.6937	−1.34213
$195$	−0.847114	−0.0606631
$196$	−15.7522	−1.12516
$197$	−6.29805	−0.448718	−0.224359	−	0.974507i	$-0.572029\pi$
$197$	−6.29805	−0.448718	−0.224359	+	0.974507i	$0.572029\pi$
$198$	6.79782	0.483100
$199$	17.5297	1.24265	0.621325	−	0.783553i	$-0.286595\pi$
$199$	17.5297	1.24265	0.621325	+	0.783553i	$0.286595\pi$
$200$	−71.8536	−5.08082
$201$	7.41414	0.522953
$202$	31.2590	2.19937
$203$	2.54086	0.178333
$204$	6.86580	0.480702
$205$	27.6727	1.93274
$206$	−6.11285	−0.425902
$207$	−6.26184	−0.435228
$208$	1.22449	0.0849033
$209$	14.6969	1.01660
$210$	−29.3027	−2.02208
$211$	−16.3640	−1.12654	−0.563271	−	0.826273i	$-0.690457\pi$
$211$	−16.3640	−1.12654	−0.563271	+	0.826273i	$0.690457\pi$
$212$	−4.68613	−0.321845
$213$	−8.52879	−0.584383
$214$	−23.6263	−1.61506
$215$	40.2041	2.74190
$216$	38.9743	2.65187
$217$	−11.0295	−0.748734
$218$	−23.6870	−1.60428
$219$	4.05670	0.274126
$220$	−68.9507	−4.64865
$221$	0.137749	0.00926602
$222$	−32.9259	−2.20984
$223$	−14.1502	−0.947565	−0.473782	−	0.880642i	$-0.657112\pi$
$223$	−14.1502	−0.947565	−0.473782	+	0.880642i	$0.657112\pi$
$224$	15.8590	1.05962
$225$	−7.24063	−0.482709
$226$	−15.3207	−1.01912
$227$	25.6179	1.70032	0.850160	−	0.526525i	$-0.176505\pi$
$227$	25.6179	1.70032	0.850160	+	0.526525i	$0.176505\pi$
$228$	27.8082	1.84164
$229$	21.4403	1.41681	0.708407	−	0.705804i	$-0.249414\pi$
$229$	21.4403	1.41681	0.708407	+	0.705804i	$0.249414\pi$
$230$	90.6214	5.97540
$231$	−10.8661	−0.714940
$232$	9.25192	0.607418
$233$	5.55659	0.364025	0.182012	−	0.983296i	$-0.441739\pi$
$233$	5.55659	0.364025	0.182012	+	0.983296i	$0.441739\pi$
$234$	0.258057	0.0168697
$235$	23.0445	1.50326
$236$	49.5418	3.22490
$237$	−18.8796	−1.22636
$238$	4.76492	0.308864
$239$	3.49503	0.226075	0.113037	−	0.993591i	$-0.463942\pi$
$239$	3.49503	0.226075	0.113037	+	0.993591i	$0.463942\pi$
$240$	−51.0185	−3.29323
$241$	27.1249	1.74727	0.873633	−	0.486585i	$-0.161758\pi$
$241$	27.1249	1.74727	0.873633	+	0.486585i	$0.161758\pi$
$242$	−8.03763	−0.516679
$243$	7.11188	0.456227
$244$	51.5151	3.29792
$245$	13.1677	0.841256
$246$	27.7030	1.76628
$247$	0.557918	0.0354995
$248$	−40.1614	−2.55025
$249$	−6.80280	−0.431110
$250$	54.1409	3.42417
$251$	−2.17259	−0.137132	−0.0685662	−	0.997647i	$-0.521842\pi$
$251$	−2.17259	−0.137132	−0.0685662	+	0.997647i	$0.521842\pi$
$252$	6.25636	0.394114
$253$	33.6045	2.11270
$254$	−45.0268	−2.82524
$255$	−5.73932	−0.359410
$256$	−22.7386	−1.42116
$257$	−5.50631	−0.343474	−0.171737	−	0.985143i	$-0.554938\pi$
$257$	−5.50631	−0.343474	−0.171737	+	0.985143i	$0.554938\pi$
$258$	40.2482	2.50574
$259$	−16.0155	−0.995157
$260$	−2.61749	−0.162330
$261$	0.932308	0.0577084
$262$	31.1668	1.92549
$263$	−4.71111	−0.290499	−0.145250	−	0.989395i	$-0.546399\pi$
$263$	−4.71111	−0.290499	−0.145250	+	0.989395i	$0.546399\pi$
$264$	−39.5664	−2.43514
$265$	3.91728	0.240637
$266$	19.2991	1.18330
$267$	−6.64037	−0.406384
$268$	22.9088	1.39938
$269$	−4.71700	−0.287601	−0.143800	−	0.989607i	$-0.545932\pi$
$269$	−4.71700	−0.287601	−0.143800	+	0.989607i	$0.545932\pi$
$270$	−56.8376	−3.45903
$271$	18.7886	1.14132	0.570662	−	0.821185i	$-0.306687\pi$
$271$	18.7886	1.14132	0.570662	+	0.821185i	$0.306687\pi$
$272$	8.29612	0.503026
$273$	−0.412498	−0.0249655
$274$	13.2786	0.802190
$275$	38.8573	2.34318
$276$	63.5837	3.82729
$277$	26.3472	1.58305	0.791526	−	0.611136i	$-0.209287\pi$
$277$	26.3472	1.58305	0.791526	+	0.611136i	$0.209287\pi$
$278$	39.5404	2.37147
$279$	−4.04703	−0.242289
$280$	−51.8996	−3.10159
$281$	−4.57799	−0.273100	−0.136550	−	0.990633i	$-0.543601\pi$
$281$	−4.57799	−0.273100	−0.136550	+	0.990633i	$0.543601\pi$
$282$	23.0697	1.37378
$283$	−19.9392	−1.18526	−0.592631	−	0.805474i	$-0.701911\pi$
$283$	−19.9392	−1.18526	−0.592631	+	0.805474i	$0.701911\pi$
$284$	−26.3530	−1.56376
$285$	−23.2457	−1.37695
$286$	−1.38488	−0.0818897
$287$	13.4751	0.795407
$288$	5.81908	0.342892
$289$	−16.0667	−0.945102
$290$	−13.4924	−0.792300
$291$	10.9643	0.642738
$292$	12.5347	0.733540
$293$	17.2198	1.00599	0.502996	−	0.864289i	$-0.332231\pi$
$293$	17.2198	1.00599	0.502996	+	0.864289i	$0.332231\pi$
$294$	13.1822	0.768800
$295$	−41.4135	−2.41119
$296$	−58.3166	−3.38959
$297$	−21.0767	−1.22299
$298$	58.4168	3.38399
$299$	1.27569	0.0737749
$300$	73.5225	4.24483
$301$	19.5772	1.12841
$302$	−2.58576	−0.148794
$303$	−18.3341	−1.05327
$304$	33.6013	1.92717
$305$	−43.0630	−2.46578
$306$	1.74837	0.0999479
$307$	24.9304	1.42286	0.711428	−	0.702759i	$-0.248049\pi$
$307$	24.9304	1.42286	0.711428	+	0.702759i	$0.248049\pi$
$308$	−33.5752	−1.91312
$309$	3.58532	0.203962
$310$	58.5687	3.32648
$311$	23.5635	1.33616	0.668081	−	0.744088i	$-0.267116\pi$
$311$	23.5635	1.33616	0.668081	+	0.744088i	$0.267116\pi$
$312$	−1.50201	−0.0850346
$313$	0.606690	0.0342922	0.0171461	−	0.999853i	$-0.494542\pi$
$313$	0.606690	0.0342922	0.0171461	+	0.999853i	$0.494542\pi$
$314$	−20.5456	−1.15946
$315$	−5.22988	−0.294670
$316$	−58.3358	−3.28164
$317$	−3.08402	−0.173216	−0.0866080	−	0.996242i	$-0.527603\pi$
$317$	−3.08402	−0.173216	−0.0866080	+	0.996242i	$0.527603\pi$
$318$	3.92157	0.219911
$319$	−5.00329	−0.280131
$320$	−16.9338	−0.946631
$321$	13.8574	0.773443
$322$	44.1276	2.45913
$323$	3.77998	0.210324
$324$	−30.0399	−1.66889
$325$	1.47509	0.0818233
$326$	−42.7177	−2.36592
$327$	13.8929	0.768281
$328$	49.0661	2.70922
$329$	11.2214	0.618656
$330$	57.7010	3.17634
$331$	−3.76482	−0.206933	−0.103467	−	0.994633i	$-0.532993\pi$
$331$	−3.76482	−0.206933	−0.103467	+	0.994633i	$0.532993\pi$
$332$	−21.0199	−1.15362
$333$	−5.87652	−0.322031
$334$	65.0193	3.55770
$335$	−19.1502	−1.04629
$336$	−24.8432	−1.35531
$337$	30.3197	1.65162	0.825810	−	0.563948i	$-0.190718\pi$
$337$	30.3197	1.65162	0.825810	+	0.563948i	$0.190718\pi$
$338$	33.5623	1.82555
$339$	8.98595	0.488050
$340$	−17.7339	−0.961753
$341$	21.7187	1.17613
$342$	7.08135	0.382915
$343$	19.7644	1.06718
$344$	71.2855	3.84346
$345$	−53.1515	−2.86158
$346$	27.3696	1.47140
$347$	−7.44001	−0.399401	−0.199700	−	0.979857i	$-0.563997\pi$
$347$	−7.44001	−0.399401	−0.199700	+	0.979857i	$0.563997\pi$
$348$	−9.46681	−0.507474
$349$	−8.69386	−0.465372	−0.232686	−	0.972552i	$-0.574751\pi$
$349$	−8.69386	−0.465372	−0.232686	+	0.972552i	$0.574751\pi$
$350$	51.0252	2.72741
$351$	−0.800109	−0.0427066
$352$	−31.2284	−1.66448
$353$	18.5627	0.987991	0.493995	−	0.869464i	$-0.335536\pi$
$353$	18.5627	0.987991	0.493995	+	0.869464i	$0.335536\pi$
$354$	−41.4588	−2.20351
$355$	22.0292	1.16919
$356$	−20.5180	−1.08745
$357$	−2.79473	−0.147913
$358$	62.1886	3.28677
$359$	28.2132	1.48904	0.744519	−	0.667602i	$-0.232679\pi$
$359$	28.2132	1.48904	0.744519	+	0.667602i	$0.232679\pi$
$360$	−19.0433	−1.00367
$361$	−3.69017	−0.194219
$362$	−17.7574	−0.933308
$363$	4.71425	0.247434
$364$	−1.27457	−0.0668057
$365$	−10.4782	−0.548452
$366$	−43.1102	−2.25340
$367$	3.67470	0.191818	0.0959089	−	0.995390i	$-0.469424\pi$
$367$	3.67470	0.191818	0.0959089	+	0.995390i	$0.469424\pi$
$368$	76.8298	4.00503
$369$	4.94435	0.257393
$370$	85.0451	4.42128
$371$	1.90750	0.0990323
$372$	41.0942	2.13064
$373$	−31.7582	−1.64438	−0.822189	−	0.569215i	$-0.807247\pi$
$373$	−31.7582	−1.64438	−0.822189	+	0.569215i	$0.807247\pi$
$374$	−9.38276	−0.485171
$375$	−31.7549	−1.63981
$376$	40.8600	2.10719
$377$	−0.189934	−0.00978208
$378$	−27.6768	−1.42354
$379$	6.69828	0.344068	0.172034	−	0.985091i	$-0.444966\pi$
$379$	6.69828	0.344068	0.172034	+	0.985091i	$0.444966\pi$
$380$	−71.8264	−3.68462
$381$	26.4093	1.35299
$382$	−40.7770	−2.08633
$383$	18.4508	0.942793	0.471396	−	0.881921i	$-0.343750\pi$
$383$	18.4508	0.942793	0.471396	+	0.881921i	$0.343750\pi$
$384$	8.26577	0.421811
$385$	28.0665	1.43040
$386$	−48.6816	−2.47783
$387$	7.18339	0.365152
$388$	33.8784	1.71992
$389$	31.1220	1.57795	0.788974	−	0.614427i	$-0.210613\pi$
$389$	31.1220	1.57795	0.788974	+	0.614427i	$0.210613\pi$
$390$	2.19043	0.110917
$391$	8.64296	0.437093
$392$	23.3476	1.17923
$393$	−18.2801	−0.922107
$394$	16.2852	0.820438
$395$	48.7646	2.45361
$396$	−12.3196	−0.619084
$397$	5.73702	0.287933	0.143966	−	0.989583i	$-0.454014\pi$
$397$	5.73702	0.287933	0.143966	+	0.989583i	$0.454014\pi$
$398$	−45.3276	−2.27207
$399$	−11.3194	−0.566676
$400$	88.8392	4.44196
$401$	−0.256250	−0.0127965	−0.00639826	−	0.999980i	$-0.502037\pi$
$401$	−0.256250	−0.0127965	−0.00639826	+	0.999980i	$0.502037\pi$
$402$	−19.1712	−0.956170
$403$	0.824478	0.0410702
$404$	−56.6503	−2.81846
$405$	25.1113	1.24779
$406$	−6.57004	−0.326066
$407$	31.5367	1.56322
$408$	−10.1763	−0.503804
$409$	−38.3070	−1.89416	−0.947079	−	0.321002i	$-0.895980\pi$
$409$	−38.3070	−1.89416	−0.947079	+	0.321002i	$0.895980\pi$
$410$	−71.5547	−3.53384
$411$	−7.78820	−0.384164
$412$	11.0782	0.545786
$413$	−20.1661	−0.992307
$414$	16.1916	0.795773
$415$	17.5711	0.862534
$416$	−1.18549	−0.0581232
$417$	−23.1913	−1.13568
$418$	−38.0025	−1.85876
$419$	34.8432	1.70220	0.851101	−	0.525002i	$-0.175936\pi$
$419$	34.8432	1.70220	0.851101	+	0.525002i	$0.175936\pi$
$420$	53.1050	2.59126
$421$	2.30563	0.112370	0.0561848	−	0.998420i	$-0.482106\pi$
$421$	2.30563	0.112370	0.0561848	+	0.998420i	$0.482106\pi$
$422$	42.3132	2.05977
$423$	4.11743	0.200196
$424$	6.94569	0.337312
$425$	9.99396	0.484778
$426$	22.0534	1.06849
$427$	−20.9693	−1.01478
$428$	42.8177	2.06967
$429$	0.812263	0.0392164
$430$	−103.958	−5.01330
$431$	−3.04894	−0.146862	−0.0734312	−	0.997300i	$-0.523395\pi$
$431$	−3.04894	−0.146862	−0.0734312	+	0.997300i	$0.523395\pi$
$432$	−48.1875	−2.31842
$433$	−16.6336	−0.799358	−0.399679	−	0.916655i	$-0.630878\pi$
$433$	−16.6336	−0.799358	−0.399679	+	0.916655i	$0.630878\pi$
$434$	28.5197	1.36899
$435$	7.91358	0.379427
$436$	42.9276	2.05586
$437$	35.0061	1.67457
$438$	−10.4896	−0.501214
$439$	−15.1998	−0.725447	−0.362724	−	0.931897i	$-0.618153\pi$
$439$	−15.1998	−0.725447	−0.362724	+	0.931897i	$0.618153\pi$
$440$	102.197	4.87206
$441$	2.35272	0.112034
$442$	−0.356186	−0.0169420
$443$	−5.99981	−0.285060	−0.142530	−	0.989791i	$-0.545524\pi$
$443$	−5.99981	−0.285060	−0.142530	+	0.989791i	$0.545524\pi$
$444$	59.6711	2.83187
$445$	17.1516	0.813064
$446$	36.5889	1.73253
$447$	−34.2628	−1.62057
$448$	−8.24584	−0.389579
$449$	−28.4475	−1.34252	−0.671260	−	0.741222i	$-0.734247\pi$
$449$	−28.4475	−1.34252	−0.671260	+	0.741222i	$0.734247\pi$
$450$	18.7225	0.882588
$451$	−26.5342	−1.24945
$452$	27.7656	1.30598
$453$	1.51660	0.0712563
$454$	−66.2416	−3.10887
$455$	1.06545	0.0499491
$456$	−41.2166	−1.93015
$457$	−17.1863	−0.803942	−0.401971	−	0.915653i	$-0.631675\pi$
$457$	−17.1863	−0.803942	−0.401971	+	0.915653i	$0.631675\pi$
$458$	−55.4393	−2.59051
$459$	−5.42085	−0.253024
$460$	−164.232	−7.65736
$461$	0.275645	0.0128381	0.00641904	−	0.999979i	$-0.497957\pi$
$461$	0.275645	0.0128381	0.00641904	+	0.999979i	$0.497957\pi$
$462$	28.0972	1.30720
$463$	0.821586	0.0381823	0.0190912	−	0.999818i	$-0.493923\pi$
$463$	0.821586	0.0381823	0.0190912	+	0.999818i	$0.493923\pi$
$464$	−11.4390	−0.531041
$465$	−34.3519	−1.59303
$466$	−14.3680	−0.665585
$467$	18.6468	0.862872	0.431436	−	0.902144i	$-0.358007\pi$
$467$	18.6468	0.862872	0.431436	+	0.902144i	$0.358007\pi$
$468$	−0.467674	−0.0216182
$469$	−9.32508	−0.430592
$470$	−59.5875	−2.74857
$471$	12.0505	0.555256
$472$	−73.4298	−3.37988
$473$	−38.5501	−1.77254
$474$	48.8180	2.24229
$475$	40.4780	1.85726
$476$	−8.63540	−0.395803
$477$	0.699911	0.0320467
$478$	−9.03730	−0.413356
$479$	18.2930	0.835828	0.417914	−	0.908487i	$-0.362761\pi$
$479$	18.2930	0.835828	0.417914	+	0.908487i	$0.362761\pi$
$480$	49.3933	2.25448
$481$	1.19719	0.0545871
$482$	−70.1383	−3.19471
$483$	−25.8818	−1.17766
$484$	14.5665	0.662114
$485$	−28.3200	−1.28594
$486$	−18.3896	−0.834169
$487$	26.4988	1.20077	0.600387	−	0.799709i	$-0.295013\pi$
$487$	26.4988	1.20077	0.600387	+	0.799709i	$0.295013\pi$
$488$	−76.3546	−3.45641
$489$	25.0549	1.13302
$490$	−34.0486	−1.53816
$491$	27.5508	1.24335	0.621675	−	0.783276i	$-0.286453\pi$
$491$	27.5508	1.24335	0.621675	+	0.783276i	$0.286453\pi$
$492$	−50.2057	−2.26345
$493$	−1.28683	−0.0579558
$494$	−1.44264	−0.0649074
$495$	10.2983	0.462876
$496$	49.6552	2.22958
$497$	10.7270	0.481173
$498$	17.5904	0.788244
$499$	7.01388	0.313984	0.156992	−	0.987600i	$-0.449820\pi$
$499$	7.01388	0.313984	0.156992	+	0.987600i	$0.449820\pi$
$500$	−98.1189	−4.38801
$501$	−38.1353	−1.70376
$502$	5.61778	0.250734
$503$	16.2687	0.725385	0.362693	−	0.931909i	$-0.381857\pi$
$503$	16.2687	0.725385	0.362693	+	0.931909i	$0.381857\pi$
$504$	−9.27304	−0.413054
$505$	47.3557	2.10730
$506$	−86.8931	−3.86287
$507$	−19.6850	−0.874242
$508$	81.6016	3.62049
$509$	−7.12948	−0.316009	−0.158004	−	0.987438i	$-0.550506\pi$
$509$	−7.12948	−0.316009	−0.158004	+	0.987438i	$0.550506\pi$
$510$	14.8405	0.657148
$511$	−5.10229	−0.225712
$512$	47.8960	2.11672
$513$	−21.9558	−0.969371
$514$	14.2380	0.628011
$515$	−9.26063	−0.408072
$516$	−72.9413	−3.21106
$517$	−22.0964	−0.971800
$518$	41.4122	1.81955
$519$	−16.0529	−0.704644
$520$	3.87958	0.170131
$521$	29.9032	1.31008	0.655041	−	0.755593i	$-0.272651\pi$
$521$	29.9032	1.31008	0.655041	+	0.755593i	$0.272651\pi$
$522$	−2.41072	−0.105514
$523$	−15.4246	−0.674471	−0.337235	−	0.941420i	$-0.609492\pi$
$523$	−15.4246	−0.674471	−0.337235	+	0.941420i	$0.609492\pi$
$524$	−56.4833	−2.46748
$525$	−29.9275	−1.30614
$526$	12.1818	0.531151
$527$	5.58596	0.243328
$528$	48.9196	2.12895
$529$	57.0419	2.48008
$530$	−10.1291	−0.439981
$531$	−7.39946	−0.321109
$532$	−34.9755	−1.51638
$533$	−1.00728	−0.0436303
$534$	17.1704	0.743035
$535$	−35.7926	−1.54745
$536$	−33.9550	−1.46663
$537$	−36.4750	−1.57401
$538$	12.1970	0.525851
$539$	−12.6260	−0.543841
$540$	103.006	4.43267
$541$	−22.2568	−0.956894	−0.478447	−	0.878116i	$-0.658800\pi$
$541$	−22.2568	−0.956894	−0.478447	+	0.878116i	$0.658800\pi$
$542$	−48.5826	−2.08680
$543$	10.4151	0.446956
$544$	−8.03184	−0.344362
$545$	−35.8844	−1.53712
$546$	1.06662	0.0456471
$547$	−35.8183	−1.53148	−0.765740	−	0.643150i	$-0.777627\pi$
$547$	−35.8183	−1.53148	−0.765740	+	0.643150i	$0.777627\pi$
$548$	−24.0646	−1.02799
$549$	−7.69419	−0.328380
$550$	−100.476	−4.28429
$551$	−5.21197	−0.222037
$552$	−94.2424	−4.01122
$553$	23.7457	1.00977
$554$	−68.1275	−2.89446
$555$	−49.8809	−2.11732
$556$	−71.6585	−3.03900
$557$	−9.46947	−0.401234	−0.200617	−	0.979670i	$-0.564295\pi$
$557$	−9.46947	−0.401234	−0.200617	+	0.979670i	$0.564295\pi$
$558$	10.4646	0.443003
$559$	−1.46343	−0.0618964
$560$	64.1681	2.71160
$561$	5.50320	0.232345
$562$	11.8376	0.499337
$563$	16.6832	0.703115	0.351558	−	0.936166i	$-0.385652\pi$
$563$	16.6832	0.703115	0.351558	+	0.936166i	$0.385652\pi$
$564$	−41.8090	−1.76048
$565$	−23.2101	−0.976455
$566$	51.5579	2.16714
$567$	12.2278	0.513520
$568$	39.0598	1.63891
$569$	−46.6921	−1.95743	−0.978717	−	0.205216i	$-0.934210\pi$
$569$	−46.6921	−1.95743	−0.978717	+	0.205216i	$0.934210\pi$
$570$	60.1076	2.51763
$571$	17.6507	0.738658	0.369329	−	0.929299i	$-0.379587\pi$
$571$	17.6507	0.738658	0.369329	+	0.929299i	$0.379587\pi$
$572$	2.50980	0.104940
$573$	23.9166	0.999131
$574$	−34.8432	−1.45433
$575$	92.5534	3.85974
$576$	−3.02562	−0.126067
$577$	−7.85004	−0.326802	−0.163401	−	0.986560i	$-0.552246\pi$
$577$	−7.85004	−0.326802	−0.163401	+	0.986560i	$0.552246\pi$
$578$	41.5446	1.72803
$579$	28.5529	1.18662
$580$	24.4521	1.01532
$581$	8.55618	0.354970
$582$	−28.3510	−1.17519
$583$	−3.75612	−0.155563
$584$	−18.5787	−0.768793
$585$	0.390942	0.0161635
$586$	−44.5262	−1.83936
$587$	−34.9831	−1.44391	−0.721954	−	0.691941i	$-0.756756\pi$
$587$	−34.9831	−1.44391	−0.721954	+	0.691941i	$0.756756\pi$
$588$	−23.8899	−0.985202
$589$	22.6245	0.932226
$590$	107.085	4.40863
$591$	−9.55165	−0.392902
$592$	72.1021	2.96338
$593$	−8.61073	−0.353600	−0.176800	−	0.984247i	$-0.556575\pi$
$593$	−8.61073	−0.353600	−0.176800	+	0.984247i	$0.556575\pi$
$594$	54.4992	2.23613
$595$	7.21859	0.295933
$596$	−105.868	−4.33652
$597$	26.5857	1.08808
$598$	−3.29861	−0.134890
$599$	−19.6518	−0.802950	−0.401475	−	0.915870i	$-0.631502\pi$
$599$	−19.6518	−0.802950	−0.401475	+	0.915870i	$0.631502\pi$
$600$	−108.974	−4.44883
$601$	−27.8365	−1.13547	−0.567737	−	0.823210i	$-0.692181\pi$
$601$	−27.8365	−1.13547	−0.567737	+	0.823210i	$0.692181\pi$
$602$	−50.6218	−2.06319
$603$	−3.42162	−0.139339
$604$	4.68613	0.190676
$605$	−12.1766	−0.495048
$606$	47.4075	1.92580
$607$	28.8503	1.17100	0.585499	−	0.810673i	$-0.300898\pi$
$607$	28.8503	1.17100	0.585499	+	0.810673i	$0.300898\pi$
$608$	−32.5309	−1.31930
$609$	3.85348	0.156151
$610$	111.350	4.50845
$611$	−0.838819	−0.0339350
$612$	−3.16856	−0.128081
$613$	45.9035	1.85402	0.927012	−	0.375033i	$-0.122369\pi$
$613$	45.9035	1.85402	0.927012	+	0.375033i	$0.122369\pi$
$614$	−64.4640	−2.60156
$615$	41.9685	1.69233
$616$	49.7644	2.00506
$617$	30.4913	1.22753	0.613766	−	0.789488i	$-0.289654\pi$
$617$	30.4913	1.22753	0.613766	+	0.789488i	$0.289654\pi$
$618$	−9.27077	−0.372925
$619$	31.7620	1.27662	0.638311	−	0.769779i	$-0.279634\pi$
$619$	31.7620	1.27662	0.638311	+	0.769779i	$0.279634\pi$
$620$	−106.143	−4.26282
$621$	−50.2021	−2.01454
$622$	−60.9294	−2.44305
$623$	8.35188	0.334611
$624$	1.85707	0.0743423
$625$	30.2952	1.21181
$626$	−1.56875	−0.0627000
$627$	22.2893	0.890150
$628$	37.2345	1.48582
$629$	8.11113	0.323412
$630$	13.5232	0.538777
$631$	−10.4816	−0.417265	−0.208632	−	0.977994i	$-0.566901\pi$
$631$	−10.4816	−0.417265	−0.208632	+	0.977994i	$0.566901\pi$
$632$	86.4641	3.43936
$633$	−24.8176	−0.986413
$634$	7.97453	0.316709
$635$	−68.2132	−2.70696
$636$	−7.10701	−0.281811
$637$	−0.479305	−0.0189908
$638$	12.9373	0.512192
$639$	3.93603	0.155707
$640$	−21.3499	−0.843928
$641$	6.16145	0.243363	0.121681	−	0.992569i	$-0.461171\pi$
$641$	6.16145	0.243363	0.121681	+	0.992569i	$0.461171\pi$
$642$	−35.8318	−1.41417
$643$	−11.0271	−0.434866	−0.217433	−	0.976075i	$-0.569768\pi$
$643$	−11.0271	−0.434866	−0.217433	+	0.976075i	$0.569768\pi$
$644$	−79.9719	−3.15133
$645$	60.9738	2.40084
$646$	−9.77410	−0.384557
$647$	20.1232	0.791125	0.395562	−	0.918439i	$-0.370550\pi$
$647$	20.1232	0.791125	0.395562	+	0.918439i	$0.370550\pi$
$648$	44.5246	1.74909
$649$	39.7097	1.55874
$650$	−3.81423	−0.149606
$651$	−16.7275	−0.655601
$652$	77.4169	3.03188
$653$	−17.9445	−0.702224	−0.351112	−	0.936333i	$-0.614196\pi$
$653$	−17.9445	−0.702224	−0.351112	+	0.936333i	$0.614196\pi$
$654$	−35.9237	−1.40473
$655$	47.2161	1.84488
$656$	−60.6649	−2.36857
$657$	−1.87216	−0.0730401
$658$	−29.0158	−1.13115
$659$	−8.14962	−0.317464	−0.158732	−	0.987322i	$-0.550741\pi$
$659$	−8.14962	−0.317464	−0.158732	+	0.987322i	$0.550741\pi$
$660$	−104.571	−4.07042
$661$	4.92480	0.191553	0.0957763	−	0.995403i	$-0.469467\pi$
$661$	4.92480	0.191553	0.0957763	+	0.995403i	$0.469467\pi$
$662$	9.73490	0.378358
$663$	0.208911	0.00811344
$664$	31.1552	1.20906
$665$	29.2371	1.13376
$666$	15.1952	0.588804
$667$	−11.9172	−0.461437
$668$	−117.834	−4.55912
$669$	−21.4602	−0.829699
$670$	49.5177	1.91304
$671$	41.2914	1.59404
$672$	24.0518	0.927818
$673$	−10.5249	−0.405704	−0.202852	−	0.979209i	$-0.565021\pi$
$673$	−10.5249	−0.405704	−0.202852	+	0.979209i	$0.565021\pi$
$674$	−78.3994	−3.01983
$675$	−58.0493	−2.23432
$676$	−60.8245	−2.33940
$677$	18.6657	0.717381	0.358691	−	0.933457i	$-0.383223\pi$
$677$	18.6657	0.717381	0.358691	+	0.933457i	$0.383223\pi$
$678$	−23.2355	−0.892353
$679$	−13.7903	−0.529222
$680$	26.2847	1.00797
$681$	38.8522	1.48882
$682$	−56.1591	−2.15044
$683$	−37.7647	−1.44503	−0.722513	−	0.691357i	$-0.757013\pi$
$683$	−37.7647	−1.44503	−0.722513	+	0.691357i	$0.757013\pi$
$684$	−12.8334	−0.490699
$685$	20.1164	0.768606
$686$	−51.1060	−1.95124
$687$	32.5164	1.24058
$688$	−88.1368	−3.36018
$689$	−0.142589	−0.00543220
$690$	137.437	5.23213
$691$	−9.96020	−0.378904	−0.189452	−	0.981890i	$-0.560671\pi$
$691$	−9.96020	−0.378904	−0.189452	+	0.981890i	$0.560671\pi$
$692$	−49.6016	−1.88557
$693$	5.01472	0.190493
$694$	19.2380	0.730266
$695$	59.9015	2.27219
$696$	14.0315	0.531862
$697$	−6.82449	−0.258496
$698$	22.4802	0.850888
$699$	8.42715	0.318744
$700$	−92.4724	−3.49513
$701$	−8.51557	−0.321629	−0.160814	−	0.986985i	$-0.551412\pi$
$701$	−8.51557	−0.321629	−0.160814	+	0.986985i	$0.551412\pi$
$702$	2.06889	0.0780850
$703$	32.8520	1.23904
$704$	16.2372	0.611961
$705$	34.9494	1.31627
$706$	−47.9985	−1.80645
$707$	23.0596	0.867245
$708$	75.1353	2.82376
$709$	14.2980	0.536973	0.268487	−	0.963283i	$-0.413476\pi$
$709$	14.2980	0.536973	0.268487	+	0.963283i	$0.413476\pi$
$710$	−56.9623	−2.13776
$711$	8.71291	0.326760
$712$	30.4113	1.13971
$713$	51.7312	1.93735
$714$	7.22650	0.270445
$715$	−2.09802	−0.0784614
$716$	−112.704	−4.21193
$717$	5.30058	0.197954
$718$	−72.9525	−2.72256
$719$	−8.40001	−0.313268	−0.156634	−	0.987657i	$-0.550064\pi$
$719$	−8.40001	−0.313268	−0.156634	+	0.987657i	$0.550064\pi$
$720$	23.5450	0.877470
$721$	−4.50942	−0.167939
$722$	9.54188	0.355112
$723$	41.1377	1.52993
$724$	32.1815	1.19602
$725$	−13.7800	−0.511777
$726$	−12.1899	−0.452410
$727$	27.9374	1.03614	0.518069	−	0.855339i	$-0.326651\pi$
$727$	27.9374	1.03614	0.518069	+	0.855339i	$0.326651\pi$
$728$	1.88914	0.0700162
$729$	30.0171	1.11174
$730$	27.0940	1.00279
$731$	−9.91495	−0.366718
$732$	78.1280	2.88770
$733$	−43.6711	−1.61303	−0.806514	−	0.591215i	$-0.798648\pi$
$733$	−43.6711	−1.61303	−0.806514	+	0.591215i	$0.798648\pi$
$734$	−9.50188	−0.350721
$735$	19.9703	0.736614
$736$	−74.3823	−2.74177
$737$	18.3623	0.676385
$738$	−12.7849	−0.470618
$739$	2.08967	0.0768698	0.0384349	−	0.999261i	$-0.487763\pi$
$739$	2.08967	0.0768698	0.0384349	+	0.999261i	$0.487763\pi$
$740$	−154.126	−5.66579
$741$	0.846141	0.0310838
$742$	−4.93232	−0.181071
$743$	18.9152	0.693931	0.346965	−	0.937878i	$-0.387212\pi$
$743$	18.9152	0.693931	0.346965	+	0.937878i	$0.387212\pi$
$744$	−60.9089	−2.23303
$745$	88.4982	3.24232
$746$	82.1190	3.00659
$747$	3.13949	0.114868
$748$	17.0043	0.621738
$749$	−17.4290	−0.636842
$750$	82.1103	2.99825
$751$	0.164356	0.00599743	0.00299871	−	0.999996i	$-0.499045\pi$
$751$	0.164356	0.00599743	0.00299871	+	0.999996i	$0.499045\pi$
$752$	−50.5189	−1.84223
$753$	−3.29495	−0.120075
$754$	0.491122	0.0178856
$755$	−3.91728	−0.142564
$756$	50.1582	1.82424
$757$	−41.5741	−1.51104	−0.755518	−	0.655128i	$-0.772615\pi$
$757$	−41.5741	−1.51104	−0.755518	+	0.655128i	$0.772615\pi$
$758$	−17.3201	−0.629095
$759$	50.9648	1.84990
$760$	106.460	3.86170
$761$	−6.44288	−0.233554	−0.116777	−	0.993158i	$-0.537256\pi$
$761$	−6.44288	−0.233554	−0.116777	+	0.993158i	$0.537256\pi$
$762$	−68.2879	−2.47381
$763$	−17.4737	−0.632592
$764$	73.8996	2.67359
$765$	2.64869	0.0957637
$766$	−47.7093	−1.72381
$767$	1.50745	0.0544308
$768$	−34.4854	−1.24438
$769$	38.0509	1.37215	0.686075	−	0.727531i	$-0.259332\pi$
$769$	38.0509	1.37215	0.686075	+	0.727531i	$0.259332\pi$
$770$	−72.5730	−2.61535
$771$	−8.35090	−0.300750
$772$	88.2251	3.17529
$773$	26.9944	0.970921	0.485460	−	0.874259i	$-0.338652\pi$
$773$	26.9944	0.970921	0.485460	+	0.874259i	$0.338652\pi$
$774$	−18.5745	−0.667646
$775$	59.8173	2.14870
$776$	−50.2139	−1.80257
$777$	−24.2892	−0.871371
$778$	−80.4739	−2.88513
$779$	−27.6409	−0.990337
$780$	−3.96969	−0.142138
$781$	−21.1229	−0.755838
$782$	−22.3486	−0.799184
$783$	7.47446	0.267116
$784$	−28.8667	−1.03096
$785$	−31.1255	−1.11092
$786$	47.2678	1.68599
$787$	5.34202	0.190423	0.0952113	−	0.995457i	$-0.469647\pi$
$787$	5.34202	0.190423	0.0952113	+	0.995457i	$0.469647\pi$
$788$	−29.5135	−1.05138
$789$	−7.14489	−0.254365
$790$	−126.093	−4.48620
$791$	−11.3020	−0.401853
$792$	18.2599	0.648836
$793$	1.56749	0.0556633
$794$	−14.8345	−0.526458
$795$	5.94096	0.210704
$796$	82.1467	2.91161
$797$	23.2653	0.824101	0.412050	−	0.911161i	$-0.364813\pi$
$797$	23.2653	0.824101	0.412050	+	0.911161i	$0.364813\pi$
$798$	29.2691	1.03611
$799$	−5.68312	−0.201054
$800$	−86.0091	−3.04088
$801$	3.06453	0.108280
$802$	0.662600	0.0233972
$803$	10.0471	0.354554
$804$	34.7436	1.22531
$805$	66.8509	2.35618
$806$	−2.13190	−0.0750929
$807$	−7.15382	−0.251827
$808$	83.9658	2.95391
$809$	14.1968	0.499134	0.249567	−	0.968358i	$-0.419712\pi$
$809$	14.1968	0.499134	0.249567	+	0.968358i	$0.419712\pi$
$810$	−64.9317	−2.28147
$811$	37.6255	1.32121	0.660604	−	0.750734i	$-0.270300\pi$
$811$	37.6255	1.32121	0.660604	+	0.750734i	$0.270300\pi$
$812$	11.9068	0.417847
$813$	28.4948	0.999357
$814$	−81.5463	−2.85820
$815$	−64.7151	−2.26687
$816$	12.5819	0.440456
$817$	−40.1579	−1.40495
$818$	99.0524	3.46329
$819$	0.190367	0.00665197
$820$	129.678	4.52854
$821$	49.9913	1.74471	0.872354	−	0.488875i	$-0.162593\pi$
$821$	49.9913	1.74471	0.872354	+	0.488875i	$0.162593\pi$
$822$	20.1384	0.702407
$823$	40.3708	1.40724	0.703619	−	0.710578i	$-0.251566\pi$
$823$	40.3708	1.40724	0.703619	+	0.710578i	$0.251566\pi$
$824$	−16.4199	−0.572015
$825$	58.9312	2.05172
$826$	52.1445	1.81434
$827$	18.0366	0.627195	0.313598	−	0.949556i	$-0.398466\pi$
$827$	18.0366	0.627195	0.313598	+	0.949556i	$0.398466\pi$
$828$	−29.3438	−1.01977
$829$	−23.6846	−0.822601	−0.411300	−	0.911500i	$-0.634925\pi$
$829$	−23.6846	−0.822601	−0.411300	+	0.911500i	$0.634925\pi$
$830$	−45.4347	−1.57706
$831$	39.9583	1.38614
$832$	0.616391	0.0213695
$833$	−3.24736	−0.112514
$834$	59.9671	2.07649
$835$	98.5007	3.40876
$836$	68.8714	2.38197
$837$	−32.4457	−1.12149
$838$	−90.0960	−3.11232
$839$	21.8035	0.752739	0.376370	−	0.926470i	$-0.377172\pi$
$839$	21.8035	0.752739	0.376370	+	0.926470i	$0.377172\pi$
$840$	−78.7111	−2.71579
$841$	−27.2257	−0.938816
$842$	−5.96180	−0.205457
$843$	−6.94300	−0.239130
$844$	−76.6837	−2.63956
$845$	50.8450	1.74912
$846$	−10.6467	−0.366040
$847$	−5.92932	−0.203734
$848$	−8.58758	−0.294899
$849$	−30.2399	−1.03783
$850$	−25.8419	−0.886371
$851$	75.1166	2.57496
$852$	−39.9671	−1.36925
$853$	32.2129	1.10295	0.551474	−	0.834192i	$-0.314065\pi$
$853$	32.2129	1.10295	0.551474	+	0.834192i	$0.314065\pi$
$854$	54.2215	1.85542
$855$	10.7279	0.366885
$856$	−63.4634	−2.16914
$857$	41.0072	1.40078	0.700390	−	0.713760i	$-0.253009\pi$
$857$	41.0072	1.40078	0.700390	+	0.713760i	$0.253009\pi$
$858$	−2.10031	−0.0717036
$859$	−24.6072	−0.839588	−0.419794	−	0.907619i	$-0.637898\pi$
$859$	−24.6072	−0.839588	−0.419794	+	0.907619i	$0.637898\pi$
$860$	188.402	6.42445
$861$	20.4363	0.696468
$862$	7.88382	0.268524
$863$	−20.0106	−0.681170	−0.340585	−	0.940214i	$-0.610625\pi$
$863$	−20.0106	−0.681170	−0.340585	+	0.940214i	$0.610625\pi$
$864$	46.6525	1.58715
$865$	41.4635	1.40980
$866$	43.0103	1.46155
$867$	−24.3669	−0.827542
$868$	−51.6859	−1.75433
$869$	−46.7584	−1.58617
$870$	−20.4626	−0.693747
$871$	0.697066	0.0236192
$872$	−63.6263	−2.15466
$873$	−5.06001	−0.171255
$874$	−90.5173	−3.06179
$875$	39.9395	1.35020
$876$	19.0102	0.642297
$877$	48.7666	1.64673	0.823366	−	0.567511i	$-0.192094\pi$
$877$	48.7666	1.64673	0.823366	+	0.567511i	$0.192094\pi$
$878$	39.3030	1.32641
$879$	26.1156	0.880858
$880$	−126.356	−4.25945
$881$	40.1845	1.35385	0.676925	−	0.736052i	$-0.263312\pi$
$881$	40.1845	1.35385	0.676925	+	0.736052i	$0.263312\pi$
$882$	−6.08356	−0.204844
$883$	−15.2135	−0.511977	−0.255988	−	0.966680i	$-0.582401\pi$
$883$	−15.2135	−0.511977	−0.255988	+	0.966680i	$0.582401\pi$
$884$	0.645511	0.0217109
$885$	−62.8079	−2.11126
$886$	15.5140	0.521204
$887$	41.2413	1.38475	0.692374	−	0.721539i	$-0.256565\pi$
$887$	41.2413	1.38475	0.692374	+	0.721539i	$0.256565\pi$
$888$	−88.4433	−2.96796
$889$	−33.2161	−1.11403
$890$	−44.3499	−1.48661
$891$	−24.0782	−0.806650
$892$	−66.3095	−2.22021
$893$	−23.0180	−0.770269
$894$	88.5951	2.96306
$895$	94.2123	3.14917
$896$	−10.3962	−0.347313
$897$	1.93471	0.0645981
$898$	73.5583	2.45467
$899$	−7.70212	−0.256880
$900$	−33.9306	−1.13102
$901$	−0.966060	−0.0321841
$902$	68.6109	2.28449
$903$	29.6909	0.988050
$904$	−41.1535	−1.36875
$905$	−26.9015	−0.894236
$906$	−3.92157	−0.130285
$907$	−11.4689	−0.380819	−0.190409	−	0.981705i	$-0.560982\pi$
$907$	−11.4689	−0.380819	−0.190409	+	0.981705i	$0.560982\pi$
$908$	120.049	3.98396
$909$	8.46117	0.280639
$910$	−2.75500	−0.0913273
$911$	−12.6546	−0.419265	−0.209632	−	0.977780i	$-0.567227\pi$
$911$	−12.6546	−0.419265	−0.209632	+	0.977780i	$0.567227\pi$
$912$	50.9599	1.68745
$913$	−16.8483	−0.557596
$914$	44.4396	1.46993
$915$	−65.3095	−2.15907
$916$	100.472	3.31969
$917$	22.9916	0.759250
$918$	14.0170	0.462630
$919$	−5.85207	−0.193042	−0.0965209	−	0.995331i	$-0.530771\pi$
$919$	−5.85207	−0.193042	−0.0965209	+	0.995331i	$0.530771\pi$
$920$	243.421	8.02536
$921$	37.8096	1.24587
$922$	−0.712751	−0.0234732
$923$	−0.801863	−0.0263937
$924$	−50.9202	−1.67515
$925$	86.8582	2.85588
$926$	−2.12442	−0.0698128
$927$	−1.65462	−0.0543450
$928$	11.0746	0.363541
$929$	−12.8196	−0.420596	−0.210298	−	0.977637i	$-0.567443\pi$
$929$	−12.8196	−0.420596	−0.210298	+	0.977637i	$0.567443\pi$
$930$	88.8255	2.91270
$931$	−13.1526	−0.431060
$932$	26.0389	0.852934
$933$	35.7365	1.16996
$934$	−48.2161	−1.57768
$935$	−14.2144	−0.464860
$936$	0.693176	0.0226572
$937$	−35.8178	−1.17012	−0.585058	−	0.810992i	$-0.698928\pi$
$937$	−35.8178	−1.17012	−0.585058	+	0.810992i	$0.698928\pi$
$938$	24.1124	0.787297
$939$	0.920109	0.0300266
$940$	107.990	3.52223
$941$	52.9402	1.72580	0.862900	−	0.505375i	$-0.168646\pi$
$941$	52.9402	1.72580	0.862900	+	0.505375i	$0.168646\pi$
$942$	−31.1596	−1.01523
$943$	−63.2012	−2.05811
$944$	90.7879	2.95490
$945$	−41.9288	−1.36394
$946$	99.6812	3.24091
$947$	−26.0614	−0.846883	−0.423441	−	0.905924i	$-0.639178\pi$
$947$	−26.0614	−0.846883	−0.423441	+	0.905924i	$0.639178\pi$
$948$	−88.4723	−2.87345
$949$	0.381405	0.0123809
$950$	−104.666	−3.39582
$951$	−4.67724	−0.151670
$952$	12.7992	0.414825
$953$	−30.6756	−0.993679	−0.496839	−	0.867843i	$-0.665506\pi$
$953$	−30.6756	−0.993679	−0.496839	+	0.867843i	$0.665506\pi$
$954$	−1.80980	−0.0585944
$955$	−61.7749	−1.99899
$956$	16.3782	0.529708
$957$	−7.58801	−0.245286
$958$	−47.3012	−1.52823
$959$	9.79555	0.316315
$960$	−25.6819	−0.828881
$961$	2.43391	0.0785132
$962$	−3.09564	−0.0998073
$963$	−6.39516	−0.206081
$964$	127.111	4.09396
$965$	−73.7500	−2.37410
$966$	66.9241	2.15325
$967$	−17.3466	−0.557830	−0.278915	−	0.960316i	$-0.589975\pi$
$967$	−17.3466	−0.557830	−0.278915	+	0.960316i	$0.589975\pi$
$968$	−21.5902	−0.693934
$969$	5.73273	0.184162
$970$	73.2286	2.35123
$971$	14.9833	0.480838	0.240419	−	0.970669i	$-0.422715\pi$
$971$	14.9833	0.480838	0.240419	+	0.970669i	$0.422715\pi$
$972$	33.3272	1.06897
$973$	29.1687	0.935106
$974$	−68.5194	−2.19550
$975$	2.23713	0.0716455
$976$	94.4041	3.02180
$977$	41.3195	1.32193	0.660964	−	0.750417i	$-0.270148\pi$
$977$	41.3195	1.32193	0.660964	+	0.750417i	$0.270148\pi$
$978$	−64.7859	−2.07163
$979$	−16.4460	−0.525615
$980$	61.7058	1.97112
$981$	−6.41158	−0.204706
$982$	−71.2396	−2.27335
$983$	−49.6718	−1.58429	−0.792143	−	0.610336i	$-0.791034\pi$
$983$	−49.6718	−1.58429	−0.792143	+	0.610336i	$0.791034\pi$
$984$	74.4139	2.37223
$985$	24.6712	0.786091
$986$	3.32742	0.105967
$987$	17.0184	0.541702
$988$	2.61448	0.0831777
$989$	−91.8216	−2.91976
$990$	−26.6290	−0.846324
$991$	−4.59118	−0.145844	−0.0729219	−	0.997338i	$-0.523232\pi$
$991$	−4.59118	−0.145844	−0.0729219	+	0.997338i	$0.523232\pi$
$992$	−48.0734	−1.52633
$993$	−5.70974	−0.181193
$994$	−27.7375	−0.879779
$995$	−68.6688	−2.17695
$996$	−31.8789	−1.01012
$997$	−7.02084	−0.222352	−0.111176	−	0.993801i	$-0.535462\pi$
$997$	−7.02084	−0.222352	−0.111176	+	0.993801i	$0.535462\pi$
$998$	−18.1362	−0.574091
$999$	−47.1130	−1.49059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.9	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.9	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.58576 q^{2} +1.51660 q^{3} +4.68613 q^{4} -3.91728 q^{5} -3.92157 q^{6} -1.90750 q^{7} -6.94569 q^{8} -0.699911 q^{9} +O(q^{10})\)	\(q-2.58576 q^{2} +1.51660 q^{3} +4.68613 q^{4} -3.91728 q^{5} -3.92157 q^{6} -1.90750 q^{7} -6.94569 q^{8} -0.699911 q^{9} +10.1291 q^{10} +3.75612 q^{11} +7.10701 q^{12} +0.142589 q^{13} +4.93232 q^{14} -5.94096 q^{15} +8.58758 q^{16} +0.966060 q^{17} +1.80980 q^{18} +3.91278 q^{19} -18.3569 q^{20} -2.89292 q^{21} -9.71241 q^{22} +8.94661 q^{23} -10.5339 q^{24} +10.3451 q^{25} -0.368700 q^{26} -5.61130 q^{27} -8.93879 q^{28} -1.33204 q^{29} +15.3619 q^{30} +5.78221 q^{31} -8.31402 q^{32} +5.69655 q^{33} -2.49799 q^{34} +7.47220 q^{35} -3.27988 q^{36} +8.39609 q^{37} -10.1175 q^{38} +0.216251 q^{39} +27.2082 q^{40} -7.06425 q^{41} +7.48038 q^{42} -10.2633 q^{43} +17.6017 q^{44} +2.74175 q^{45} -23.1338 q^{46} -5.88279 q^{47} +13.0240 q^{48} -3.36145 q^{49} -26.7498 q^{50} +1.46513 q^{51} +0.668190 q^{52} -1.00000 q^{53} +14.5095 q^{54} -14.7138 q^{55} +13.2489 q^{56} +5.93414 q^{57} +3.44432 q^{58} +10.5720 q^{59} -27.8401 q^{60} +10.9931 q^{61} -14.9514 q^{62} +1.33508 q^{63} +4.32286 q^{64} -0.558560 q^{65} -14.7299 q^{66} +4.88864 q^{67} +4.52709 q^{68} +13.5685 q^{69} -19.3213 q^{70} -5.62361 q^{71} +4.86136 q^{72} +2.67486 q^{73} -21.7102 q^{74} +15.6894 q^{75} +18.3358 q^{76} -7.16479 q^{77} -0.559172 q^{78} -12.4486 q^{79} -33.6400 q^{80} -6.41039 q^{81} +18.2664 q^{82} -4.48555 q^{83} -13.5566 q^{84} -3.78433 q^{85} +26.5383 q^{86} -2.02017 q^{87} -26.0888 q^{88} -4.37845 q^{89} -7.08949 q^{90} -0.271988 q^{91} +41.9250 q^{92} +8.76932 q^{93} +15.2114 q^{94} -15.3274 q^{95} -12.6091 q^{96} +7.22950 q^{97} +8.69190 q^{98} -2.62895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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