LMFDB - Embedded newform 8039.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65513 q^{2} -1.36605 q^{3} +5.04972 q^{4} +2.66534 q^{5} +3.62703 q^{6} -0.858733 q^{7} -8.09741 q^{8} -1.13392 q^{9} +O(q^{10})$	\(q-2.65513 q^{2} -1.36605 q^{3} +5.04972 q^{4} +2.66534 q^{5} +3.62703 q^{6} -0.858733 q^{7} -8.09741 q^{8} -1.13392 q^{9} -7.07683 q^{10} +2.44166 q^{11} -6.89815 q^{12} +2.58829 q^{13} +2.28005 q^{14} -3.64098 q^{15} +11.4002 q^{16} +0.199755 q^{17} +3.01070 q^{18} -2.30305 q^{19} +13.4592 q^{20} +1.17307 q^{21} -6.48292 q^{22} -4.05742 q^{23} +11.0614 q^{24} +2.10405 q^{25} -6.87226 q^{26} +5.64712 q^{27} -4.33636 q^{28} +3.88125 q^{29} +9.66728 q^{30} +0.530304 q^{31} -14.0743 q^{32} -3.33542 q^{33} -0.530374 q^{34} -2.28882 q^{35} -5.72598 q^{36} -4.95621 q^{37} +6.11491 q^{38} -3.53573 q^{39} -21.5824 q^{40} -4.34922 q^{41} -3.11465 q^{42} +7.37533 q^{43} +12.3297 q^{44} -3.02228 q^{45} +10.7730 q^{46} -1.79772 q^{47} -15.5733 q^{48} -6.26258 q^{49} -5.58653 q^{50} -0.272874 q^{51} +13.0702 q^{52} -0.981512 q^{53} -14.9939 q^{54} +6.50785 q^{55} +6.95351 q^{56} +3.14608 q^{57} -10.3052 q^{58} -7.29190 q^{59} -18.3859 q^{60} -9.37939 q^{61} -1.40803 q^{62} +0.973734 q^{63} +14.5687 q^{64} +6.89869 q^{65} +8.85597 q^{66} +12.1368 q^{67} +1.00870 q^{68} +5.54262 q^{69} +6.07711 q^{70} -1.88017 q^{71} +9.18181 q^{72} +8.21292 q^{73} +13.1594 q^{74} -2.87423 q^{75} -11.6298 q^{76} -2.09673 q^{77} +9.38781 q^{78} -9.14254 q^{79} +30.3855 q^{80} -4.31247 q^{81} +11.5477 q^{82} +13.7110 q^{83} +5.92367 q^{84} +0.532414 q^{85} -19.5825 q^{86} -5.30197 q^{87} -19.7711 q^{88} +5.79577 q^{89} +8.02456 q^{90} -2.22265 q^{91} -20.4888 q^{92} -0.724419 q^{93} +4.77318 q^{94} -6.13843 q^{95} +19.2262 q^{96} +6.50388 q^{97} +16.6280 q^{98} -2.76864 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.65513	−1.87746	−0.938731	−	0.344652i	$-0.887997\pi$
$2$	−2.65513	−1.87746	−0.938731	+	0.344652i	$0.887997\pi$
$3$	−1.36605	−0.788687	−0.394343	−	0.918963i	$-0.629028\pi$
$3$	−1.36605	−0.788687	−0.394343	+	0.918963i	$0.629028\pi$
$4$	5.04972	2.52486
$5$	2.66534	1.19198	0.595989	−	0.802993i	$-0.296760\pi$
$5$	2.66534	1.19198	0.595989	+	0.802993i	$0.296760\pi$
$6$	3.62703	1.48073
$7$	−0.858733	−0.324571	−0.162285	−	0.986744i	$-0.551886\pi$
$7$	−0.858733	−0.324571	−0.162285	+	0.986744i	$0.551886\pi$
$8$	−8.09741	−2.86287
$9$	−1.13392	−0.377973
$10$	−7.07683	−2.23789
$11$	2.44166	0.736187	0.368094	−	0.929789i	$-0.380011\pi$
$11$	2.44166	0.736187	0.368094	+	0.929789i	$0.380011\pi$
$12$	−6.89815	−1.99132
$13$	2.58829	0.717863	0.358932	−	0.933364i	$-0.383141\pi$
$13$	2.58829	0.717863	0.358932	+	0.933364i	$0.383141\pi$
$14$	2.28005	0.609369
$15$	−3.64098	−0.940097
$16$	11.4002	2.85006
$17$	0.199755	0.0484476	0.0242238	−	0.999707i	$-0.492289\pi$
$17$	0.199755	0.0484476	0.0242238	+	0.999707i	$0.492289\pi$
$18$	3.01070	0.709630
$19$	−2.30305	−0.528357	−0.264178	−	0.964474i	$-0.585101\pi$
$19$	−2.30305	−0.528357	−0.264178	+	0.964474i	$0.585101\pi$
$20$	13.4592	3.00958
$21$	1.17307	0.255985
$22$	−6.48292	−1.38216
$23$	−4.05742	−0.846030	−0.423015	−	0.906123i	$-0.639028\pi$
$23$	−4.05742	−0.846030	−0.423015	+	0.906123i	$0.639028\pi$
$24$	11.0614	2.25791
$25$	2.10405	0.420810
$26$	−6.87226	−1.34776
$27$	5.64712	1.08679
$28$	−4.33636	−0.819496
$29$	3.88125	0.720731	0.360365	−	0.932811i	$-0.382652\pi$
$29$	3.88125	0.720731	0.360365	+	0.932811i	$0.382652\pi$
$30$	9.66728	1.76500
$31$	0.530304	0.0952454	0.0476227	−	0.998865i	$-0.484835\pi$
$31$	0.530304	0.0952454	0.0476227	+	0.998865i	$0.484835\pi$
$32$	−14.0743	−2.48801
$33$	−3.33542	−0.580621
$34$	−0.530374	−0.0909585
$35$	−2.28882	−0.386881
$36$	−5.72598	−0.954330
$37$	−4.95621	−0.814796	−0.407398	−	0.913251i	$-0.633564\pi$
$37$	−4.95621	−0.814796	−0.407398	+	0.913251i	$0.633564\pi$
$38$	6.11491	0.991969
$39$	−3.53573	−0.566169
$40$	−21.5824	−3.41247
$41$	−4.34922	−0.679234	−0.339617	−	0.940564i	$-0.610297\pi$
$41$	−4.34922	−0.679234	−0.339617	+	0.940564i	$0.610297\pi$
$42$	−3.11465	−0.480601
$43$	7.37533	1.12473	0.562363	−	0.826890i	$-0.309892\pi$
$43$	7.37533	1.12473	0.562363	+	0.826890i	$0.309892\pi$
$44$	12.3297	1.85877
$45$	−3.02228	−0.450535
$46$	10.7730	1.58839
$47$	−1.79772	−0.262224	−0.131112	−	0.991368i	$-0.541855\pi$
$47$	−1.79772	−0.262224	−0.131112	+	0.991368i	$0.541855\pi$
$48$	−15.5733	−2.24781
$49$	−6.26258	−0.894654
$50$	−5.58653	−0.790054
$51$	−0.272874	−0.0382100
$52$	13.0702	1.81250
$53$	−0.981512	−0.134821	−0.0674105	−	0.997725i	$-0.521474\pi$
$53$	−0.981512	−0.134821	−0.0674105	+	0.997725i	$0.521474\pi$
$54$	−14.9939	−2.04040
$55$	6.50785	0.877519
$56$	6.95351	0.929202
$57$	3.14608	0.416708
$58$	−10.3052	−1.35314
$59$	−7.29190	−0.949324	−0.474662	−	0.880168i	$-0.657430\pi$
$59$	−7.29190	−0.949324	−0.474662	+	0.880168i	$0.657430\pi$
$60$	−18.3859	−2.37361
$61$	−9.37939	−1.20091	−0.600454	−	0.799659i	$-0.705013\pi$
$61$	−9.37939	−1.20091	−0.600454	+	0.799659i	$0.705013\pi$
$62$	−1.40803	−0.178820
$63$	0.973734	0.122679
$64$	14.5687	1.82108
$65$	6.89869	0.855677
$66$	8.85597	1.09009
$67$	12.1368	1.48274	0.741371	−	0.671095i	$-0.234176\pi$
$67$	12.1368	1.48274	0.741371	+	0.671095i	$0.234176\pi$
$68$	1.00870	0.122323
$69$	5.54262	0.667253
$70$	6.07711	0.726354
$71$	−1.88017	−0.223135	−0.111568	−	0.993757i	$-0.535587\pi$
$71$	−1.88017	−0.223135	−0.111568	+	0.993757i	$0.535587\pi$
$72$	9.18181	1.08209
$73$	8.21292	0.961250	0.480625	−	0.876926i	$-0.340410\pi$
$73$	8.21292	0.961250	0.480625	+	0.876926i	$0.340410\pi$
$74$	13.1594	1.52975
$75$	−2.87423	−0.331887
$76$	−11.6298	−1.33403
$77$	−2.09673	−0.238945
$78$	9.38781	1.06296
$79$	−9.14254	−1.02862	−0.514308	−	0.857606i	$-0.671951\pi$
$79$	−9.14254	−1.02862	−0.514308	+	0.857606i	$0.671951\pi$
$80$	30.3855	3.39721
$81$	−4.31247	−0.479163
$82$	11.5477	1.27523
$83$	13.7110	1.50498	0.752491	−	0.658603i	$-0.228852\pi$
$83$	13.7110	1.50498	0.752491	+	0.658603i	$0.228852\pi$
$84$	5.92367	0.646325
$85$	0.532414	0.0577484
$86$	−19.5825	−2.11163
$87$	−5.30197	−0.568431
$88$	−19.7711	−2.10761
$89$	5.79577	0.614351	0.307175	−	0.951653i	$-0.400616\pi$
$89$	5.79577	0.614351	0.307175	+	0.951653i	$0.400616\pi$
$90$	8.02456	0.845863
$91$	−2.22265	−0.232997
$92$	−20.4888	−2.13611
$93$	−0.724419	−0.0751188
$94$	4.77318	0.492316
$95$	−6.13843	−0.629789
$96$	19.2262	1.96226
$97$	6.50388	0.660369	0.330184	−	0.943916i	$-0.392889\pi$
$97$	6.50388	0.660369	0.330184	+	0.943916i	$0.392889\pi$
$98$	16.6280	1.67968
$99$	−2.76864	−0.278259
$100$	10.6249	1.06249
$101$	2.43832	0.242622	0.121311	−	0.992615i	$-0.461290\pi$
$101$	2.43832	0.242622	0.121311	+	0.992615i	$0.461290\pi$
$102$	0.724516	0.0717377
$103$	−7.22073	−0.711480	−0.355740	−	0.934585i	$-0.615771\pi$
$103$	−7.22073	−0.711480	−0.355740	+	0.934585i	$0.615771\pi$
$104$	−20.9585	−2.05515
$105$	3.12663	0.305128
$106$	2.60604	0.253121
$107$	20.0421	1.93754	0.968770	−	0.247960i	$-0.0797600\pi$
$107$	20.0421	1.93754	0.968770	+	0.247960i	$0.0797600\pi$
$108$	28.5164	2.74399
$109$	4.34829	0.416491	0.208245	−	0.978077i	$-0.433225\pi$
$109$	4.34829	0.416491	0.208245	+	0.978077i	$0.433225\pi$
$110$	−17.2792	−1.64751
$111$	6.77041	0.642619
$112$	−9.78977	−0.925046
$113$	−9.85520	−0.927099	−0.463550	−	0.886071i	$-0.653424\pi$
$113$	−9.85520	−0.927099	−0.463550	+	0.886071i	$0.653424\pi$
$114$	−8.35324	−0.782353
$115$	−10.8144	−1.00845
$116$	19.5992	1.81974
$117$	−2.93492	−0.271333
$118$	19.3609	1.78232
$119$	−0.171536	−0.0157247
$120$	29.4825	2.69137
$121$	−5.03831	−0.458028
$122$	24.9035	2.25466
$123$	5.94123	0.535703
$124$	2.67789	0.240481
$125$	−7.71870	−0.690381
$126$	−2.58539	−0.230325
$127$	−18.0204	−1.59905	−0.799527	−	0.600630i	$-0.794916\pi$
$127$	−18.0204	−1.59905	−0.799527	+	0.600630i	$0.794916\pi$
$128$	−10.5331	−0.931004
$129$	−10.0750	−0.887057
$130$	−18.3169	−1.60650
$131$	−17.6416	−1.54135	−0.770677	−	0.637226i	$-0.780082\pi$
$131$	−17.6416	−1.54135	−0.770677	+	0.637226i	$0.780082\pi$
$132$	−16.8429	−1.46599
$133$	1.97771	0.171489
$134$	−32.2247	−2.78379
$135$	15.0515	1.29543
$136$	−1.61749	−0.138699
$137$	−5.95486	−0.508758	−0.254379	−	0.967105i	$-0.581871\pi$
$137$	−5.95486	−0.508758	−0.254379	+	0.967105i	$0.581871\pi$
$138$	−14.7164	−1.25274
$139$	−11.1898	−0.949104	−0.474552	−	0.880228i	$-0.657390\pi$
$139$	−11.1898	−0.949104	−0.474552	+	0.880228i	$0.657390\pi$
$140$	−11.5579	−0.976820
$141$	2.45577	0.206813
$142$	4.99210	0.418928
$143$	6.31972	0.528482
$144$	−12.9270	−1.07725
$145$	10.3449	0.859095
$146$	−21.8064	−1.80471
$147$	8.55497	0.705602
$148$	−25.0275	−2.05725
$149$	−10.2456	−0.839352	−0.419676	−	0.907674i	$-0.637856\pi$
$149$	−10.2456	−0.839352	−0.419676	+	0.907674i	$0.637856\pi$
$150$	7.63145	0.623105
$151$	4.84205	0.394040	0.197020	−	0.980399i	$-0.436874\pi$
$151$	4.84205	0.394040	0.197020	+	0.980399i	$0.436874\pi$
$152$	18.6488	1.51261
$153$	−0.226506	−0.0183119
$154$	5.56710	0.448610
$155$	1.41344	0.113530
$156$	−17.8544	−1.42950
$157$	−1.59080	−0.126959	−0.0634797	−	0.997983i	$-0.520220\pi$
$157$	−1.59080	−0.126959	−0.0634797	+	0.997983i	$0.520220\pi$
$158$	24.2746	1.93119
$159$	1.34079	0.106332
$160$	−37.5129	−2.96565
$161$	3.48424	0.274596
$162$	11.4502	0.899610
$163$	6.59527	0.516582	0.258291	−	0.966067i	$-0.416841\pi$
$163$	6.59527	0.516582	0.258291	+	0.966067i	$0.416841\pi$
$164$	−21.9623	−1.71497
$165$	−8.89002	−0.692087
$166$	−36.4046	−2.82554
$167$	−2.50674	−0.193978	−0.0969888	−	0.995285i	$-0.530921\pi$
$167$	−2.50674	−0.193978	−0.0969888	+	0.995285i	$0.530921\pi$
$168$	−9.49882	−0.732850
$169$	−6.30074	−0.484672
$170$	−1.41363	−0.108420
$171$	2.61148	0.199705
$172$	37.2433	2.83978
$173$	−9.70576	−0.737916	−0.368958	−	0.929446i	$-0.620285\pi$
$173$	−9.70576	−0.737916	−0.368958	+	0.929446i	$0.620285\pi$
$174$	14.0774	1.06721
$175$	−1.80682	−0.136583
$176$	27.8355	2.09818
$177$	9.96107	0.748720
$178$	−15.3885	−1.15342
$179$	−7.70734	−0.576074	−0.288037	−	0.957619i	$-0.593003\pi$
$179$	−7.70734	−0.576074	−0.288037	+	0.957619i	$0.593003\pi$
$180$	−15.2617	−1.13754
$181$	−19.0360	−1.41494	−0.707468	−	0.706746i	$-0.750163\pi$
$181$	−19.0360	−1.41494	−0.707468	+	0.706746i	$0.750163\pi$
$182$	5.90143	0.437443
$183$	12.8127	0.947140
$184$	32.8546	2.42207
$185$	−13.2100	−0.971219
$186$	1.92343	0.141033
$187$	0.487732	0.0356665
$188$	−9.07798	−0.662080
$189$	−4.84937	−0.352740
$190$	16.2983	1.18240
$191$	9.08475	0.657349	0.328675	−	0.944443i	$-0.393398\pi$
$191$	9.08475	0.657349	0.328675	+	0.944443i	$0.393398\pi$
$192$	−19.9015	−1.43627
$193$	−4.04564	−0.291212	−0.145606	−	0.989343i	$-0.546513\pi$
$193$	−4.04564	−0.291212	−0.145606	+	0.989343i	$0.546513\pi$
$194$	−17.2686	−1.23982
$195$	−9.42392	−0.674861
$196$	−31.6243	−2.25888
$197$	9.12227	0.649935	0.324967	−	0.945725i	$-0.394647\pi$
$197$	9.12227	0.649935	0.324967	+	0.945725i	$0.394647\pi$
$198$	7.35111	0.522421
$199$	8.92338	0.632561	0.316281	−	0.948666i	$-0.397566\pi$
$199$	8.92338	0.632561	0.316281	+	0.948666i	$0.397566\pi$
$200$	−17.0374	−1.20472
$201$	−16.5794	−1.16942
$202$	−6.47405	−0.455513
$203$	−3.33296	−0.233928
$204$	−1.37794	−0.0964749
$205$	−11.5922	−0.809631
$206$	19.1720	1.33578
$207$	4.60078	0.319777
$208$	29.5072	2.04595
$209$	−5.62327	−0.388970
$210$	−8.30161	−0.572866
$211$	−15.6589	−1.07801	−0.539003	−	0.842304i	$-0.681199\pi$
$211$	−15.6589	−1.07801	−0.539003	+	0.842304i	$0.681199\pi$
$212$	−4.95636	−0.340404
$213$	2.56840	0.175984
$214$	−53.2143	−3.63766
$215$	19.6578	1.34065
$216$	−45.7271	−3.11133
$217$	−0.455390	−0.0309139
$218$	−11.5453	−0.781945
$219$	−11.2192	−0.758125
$220$	32.8628	2.21561
$221$	0.517023	0.0347787
$222$	−17.9763	−1.20649
$223$	4.88259	0.326962	0.163481	−	0.986546i	$-0.447728\pi$
$223$	4.88259	0.326962	0.163481	+	0.986546i	$0.447728\pi$
$224$	12.0861	0.807535
$225$	−2.38582	−0.159055
$226$	26.1668	1.74059
$227$	−16.6819	−1.10721	−0.553607	−	0.832778i	$-0.686749\pi$
$227$	−16.6819	−1.10721	−0.553607	+	0.832778i	$0.686749\pi$
$228$	15.8868	1.05213
$229$	−4.26502	−0.281841	−0.140920	−	0.990021i	$-0.545006\pi$
$229$	−4.26502	−0.281841	−0.140920	+	0.990021i	$0.545006\pi$
$230$	28.7137	1.89332
$231$	2.86423	0.188453
$232$	−31.4281	−2.06336
$233$	−4.03064	−0.264056	−0.132028	−	0.991246i	$-0.542149\pi$
$233$	−4.03064	−0.264056	−0.132028	+	0.991246i	$0.542149\pi$
$234$	7.79258	0.509417
$235$	−4.79154	−0.312565
$236$	−36.8221	−2.39691
$237$	12.4891	0.811256
$238$	0.455450	0.0295224
$239$	−24.3155	−1.57284	−0.786420	−	0.617693i	$-0.788068\pi$
$239$	−24.3155	−1.57284	−0.786420	+	0.617693i	$0.788068\pi$
$240$	−41.5080	−2.67933
$241$	8.97926	0.578405	0.289202	−	0.957268i	$-0.406610\pi$
$241$	8.97926	0.578405	0.289202	+	0.957268i	$0.406610\pi$
$242$	13.3774	0.859930
$243$	−11.0503	−0.708880
$244$	−47.3633	−3.03213
$245$	−16.6919	−1.06641
$246$	−15.7747	−1.00576
$247$	−5.96098	−0.379288
$248$	−4.29409	−0.272675
$249$	−18.7299	−1.18696
$250$	20.4942	1.29616
$251$	22.8278	1.44088	0.720438	−	0.693519i	$-0.243941\pi$
$251$	22.8278	1.44088	0.720438	+	0.693519i	$0.243941\pi$
$252$	4.91709	0.309747
$253$	−9.90682	−0.622837
$254$	47.8466	3.00216
$255$	−0.727302	−0.0455454
$256$	−1.17057	−0.0731607
$257$	24.3022	1.51593	0.757963	−	0.652297i	$-0.226195\pi$
$257$	24.3022	1.51593	0.757963	+	0.652297i	$0.226195\pi$
$258$	26.7505	1.66542
$259$	4.25606	0.264459
$260$	34.8364	2.16046
$261$	−4.40103	−0.272417
$262$	46.8407	2.89383
$263$	20.6574	1.27379	0.636895	−	0.770950i	$-0.280218\pi$
$263$	20.6574	1.27379	0.636895	+	0.770950i	$0.280218\pi$
$264$	27.0082	1.66224
$265$	−2.61606	−0.160704
$266$	−5.25107	−0.321964
$267$	−7.91729	−0.484530
$268$	61.2873	3.74372
$269$	25.3822	1.54758	0.773791	−	0.633441i	$-0.218358\pi$
$269$	25.3822	1.54758	0.773791	+	0.633441i	$0.218358\pi$
$270$	−39.9637	−2.43212
$271$	−1.21951	−0.0740799	−0.0370400	−	0.999314i	$-0.511793\pi$
$271$	−1.21951	−0.0740799	−0.0370400	+	0.999314i	$0.511793\pi$
$272$	2.27725	0.138079
$273$	3.03624	0.183762
$274$	15.8109	0.955173
$275$	5.13737	0.309795
$276$	27.9887	1.68472
$277$	11.1574	0.670383	0.335192	−	0.942150i	$-0.391199\pi$
$277$	11.1574	0.670383	0.335192	+	0.942150i	$0.391199\pi$
$278$	29.7103	1.78191
$279$	−0.601322	−0.0360002
$280$	18.5335	1.10759
$281$	7.53157	0.449296	0.224648	−	0.974440i	$-0.427877\pi$
$281$	7.53157	0.449296	0.224648	+	0.974440i	$0.427877\pi$
$282$	−6.52038	−0.388283
$283$	−11.1646	−0.663666	−0.331833	−	0.943338i	$-0.607667\pi$
$283$	−11.1646	−0.663666	−0.331833	+	0.943338i	$0.607667\pi$
$284$	−9.49435	−0.563386
$285$	8.38537	0.496706
$286$	−16.7797	−0.992204
$287$	3.73482	0.220459
$288$	15.9591	0.940401
$289$	−16.9601	−0.997653
$290$	−27.4670	−1.61292
$291$	−8.88459	−0.520824
$292$	41.4730	2.42702
$293$	−11.5333	−0.673781	−0.336890	−	0.941544i	$-0.609375\pi$
$293$	−11.5333	−0.673781	−0.336890	+	0.941544i	$0.609375\pi$
$294$	−22.7146	−1.32474
$295$	−19.4354	−1.13157
$296$	40.1325	2.33265
$297$	13.7883	0.800081
$298$	27.2034	1.57585
$299$	−10.5018	−0.607334
$300$	−14.5140	−0.837969
$301$	−6.33344	−0.365053
$302$	−12.8563	−0.739795
$303$	−3.33085	−0.191352
$304$	−26.2554	−1.50585
$305$	−24.9993	−1.43146
$306$	0.601402	0.0343799
$307$	−11.4585	−0.653973	−0.326987	−	0.945029i	$-0.606033\pi$
$307$	−11.4585	−0.653973	−0.326987	+	0.945029i	$0.606033\pi$
$308$	−10.5879	−0.603302
$309$	9.86385	0.561135
$310$	−3.75287	−0.213149
$311$	17.0223	0.965249	0.482624	−	0.875827i	$-0.339684\pi$
$311$	17.0223	0.965249	0.482624	+	0.875827i	$0.339684\pi$
$312$	28.6302	1.62087
$313$	−24.4630	−1.38273	−0.691365	−	0.722506i	$-0.742990\pi$
$313$	−24.4630	−1.38273	−0.691365	+	0.722506i	$0.742990\pi$
$314$	4.22377	0.238361
$315$	2.59533	0.146231
$316$	−46.1673	−2.59711
$317$	1.27585	0.0716589	0.0358295	−	0.999358i	$-0.488593\pi$
$317$	1.27585	0.0716589	0.0358295	+	0.999358i	$0.488593\pi$
$318$	−3.55997	−0.199633
$319$	9.47669	0.530593
$320$	38.8305	2.17069
$321$	−27.3784	−1.52811
$322$	−9.25111	−0.515544
$323$	−0.460045	−0.0255976
$324$	−21.7768	−1.20982
$325$	5.44590	0.302084
$326$	−17.5113	−0.969862
$327$	−5.93997	−0.328481
$328$	35.2174	1.94456
$329$	1.54376	0.0851103
$330$	23.6042	1.29937
$331$	8.60947	0.473220	0.236610	−	0.971605i	$-0.423964\pi$
$331$	8.60947	0.473220	0.236610	+	0.971605i	$0.423964\pi$
$332$	69.2369	3.79987
$333$	5.61995	0.307971
$334$	6.65573	0.364185
$335$	32.3486	1.76739
$336$	13.3733	0.729571
$337$	−15.8770	−0.864877	−0.432439	−	0.901663i	$-0.642347\pi$
$337$	−15.8770	−0.864877	−0.432439	+	0.901663i	$0.642347\pi$
$338$	16.7293	0.909954
$339$	13.4627	0.731191
$340$	2.68854	0.145807
$341$	1.29482	0.0701185
$342$	−6.93381	−0.374938
$343$	11.3890	0.614949
$344$	−59.7210	−3.21994
$345$	14.7730	0.795350
$346$	25.7701	1.38541
$347$	−32.5951	−1.74980	−0.874898	−	0.484306i	$-0.839072\pi$
$347$	−32.5951	−1.74980	−0.874898	+	0.484306i	$0.839072\pi$
$348$	−26.7735	−1.43521
$349$	7.12471	0.381377	0.190688	−	0.981651i	$-0.438928\pi$
$349$	7.12471	0.381377	0.190688	+	0.981651i	$0.438928\pi$
$350$	4.79734	0.256428
$351$	14.6164	0.780166
$352$	−34.3647	−1.83164
$353$	−13.2399	−0.704689	−0.352345	−	0.935870i	$-0.614616\pi$
$353$	−13.2399	−0.704689	−0.352345	+	0.935870i	$0.614616\pi$
$354$	−26.4479	−1.40569
$355$	−5.01130	−0.265972
$356$	29.2670	1.55115
$357$	0.234326	0.0124018
$358$	20.4640	1.08156
$359$	11.1081	0.586264	0.293132	−	0.956072i	$-0.405303\pi$
$359$	11.1081	0.586264	0.293132	+	0.956072i	$0.405303\pi$
$360$	24.4727	1.28982
$361$	−13.6959	−0.720839
$362$	50.5431	2.65649
$363$	6.88256	0.361241
$364$	−11.2238	−0.588286
$365$	21.8902	1.14579
$366$	−34.0193	−1.77822
$367$	30.9697	1.61660	0.808301	−	0.588769i	$-0.200387\pi$
$367$	30.9697	1.61660	0.808301	+	0.588769i	$0.200387\pi$
$368$	−46.2555	−2.41124
$369$	4.93166	0.256732
$370$	35.0743	1.82343
$371$	0.842857	0.0437589
$372$	−3.65812	−0.189664
$373$	1.81202	0.0938229	0.0469114	−	0.998899i	$-0.485062\pi$
$373$	1.81202	0.0938229	0.0469114	+	0.998899i	$0.485062\pi$
$374$	−1.29499	−0.0669625
$375$	10.5441	0.544495
$376$	14.5569	0.750713
$377$	10.0458	0.517386
$378$	12.8757	0.662255
$379$	−10.6067	−0.544832	−0.272416	−	0.962180i	$-0.587823\pi$
$379$	−10.6067	−0.544832	−0.272416	+	0.962180i	$0.587823\pi$
$380$	−30.9973	−1.59013
$381$	24.6167	1.26115
$382$	−24.1212	−1.23415
$383$	24.5943	1.25671	0.628355	−	0.777927i	$-0.283729\pi$
$383$	24.5943	1.25671	0.628355	+	0.777927i	$0.283729\pi$
$384$	14.3887	0.734270
$385$	−5.58851	−0.284817
$386$	10.7417	0.546739
$387$	−8.36303	−0.425117
$388$	32.8428	1.66734
$389$	15.2816	0.774810	0.387405	−	0.921910i	$-0.373371\pi$
$389$	15.2816	0.774810	0.387405	+	0.921910i	$0.373371\pi$
$390$	25.0217	1.26703
$391$	−0.810488	−0.0409881
$392$	50.7107	2.56127
$393$	24.0992	1.21564
$394$	−24.2208	−1.22023
$395$	−24.3680	−1.22609
$396$	−13.9809	−0.702565
$397$	0.740702	0.0371747	0.0185874	−	0.999827i	$-0.494083\pi$
$397$	0.740702	0.0371747	0.0185874	+	0.999827i	$0.494083\pi$
$398$	−23.6927	−1.18761
$399$	−2.70164	−0.135251
$400$	23.9867	1.19933
$401$	4.69710	0.234562	0.117281	−	0.993099i	$-0.462582\pi$
$401$	4.69710	0.234562	0.117281	+	0.993099i	$0.462582\pi$
$402$	44.0204	2.19554
$403$	1.37258	0.0683732
$404$	12.3128	0.612586
$405$	−11.4942	−0.571152
$406$	8.84945	0.439191
$407$	−12.1014	−0.599843
$408$	2.20957	0.109390
$409$	19.3674	0.957655	0.478828	−	0.877909i	$-0.341062\pi$
$409$	19.3674	0.957655	0.478828	+	0.877909i	$0.341062\pi$
$410$	30.7787	1.52005
$411$	8.13461	0.401251
$412$	−36.4627	−1.79639
$413$	6.26180	0.308123
$414$	−12.2157	−0.600368
$415$	36.5446	1.79390
$416$	−36.4285	−1.78605
$417$	15.2857	0.748546
$418$	14.9305	0.730275
$419$	−7.08663	−0.346204	−0.173102	−	0.984904i	$-0.555379\pi$
$419$	−7.08663	−0.346204	−0.173102	+	0.984904i	$0.555379\pi$
$420$	15.7886	0.770405
$421$	−12.3592	−0.602353	−0.301176	−	0.953568i	$-0.597379\pi$
$421$	−12.3592	−0.602353	−0.301176	+	0.953568i	$0.597379\pi$
$422$	41.5766	2.02392
$423$	2.03847	0.0991137
$424$	7.94770	0.385975
$425$	0.420293	0.0203872
$426$	−6.81944	−0.330403
$427$	8.05439	0.389779
$428$	101.207	4.89202
$429$	−8.63303	−0.416807
$430$	−52.1940	−2.51702
$431$	15.7887	0.760516	0.380258	−	0.924881i	$-0.375835\pi$
$431$	15.7887	0.760516	0.380258	+	0.924881i	$0.375835\pi$
$432$	64.3786	3.09741
$433$	−19.7091	−0.947157	−0.473579	−	0.880752i	$-0.657038\pi$
$433$	−19.7091	−0.947157	−0.473579	+	0.880752i	$0.657038\pi$
$434$	1.20912	0.0580396
$435$	−14.1316	−0.677557
$436$	21.9577	1.05158
$437$	9.34445	0.447006
$438$	29.7885	1.42335
$439$	−15.9126	−0.759465	−0.379733	−	0.925096i	$-0.623984\pi$
$439$	−15.9126	−0.759465	−0.379733	+	0.925096i	$0.623984\pi$
$440$	−52.6968	−2.51222
$441$	7.10126	0.338155
$442$	−1.37276	−0.0652957
$443$	29.0865	1.38194	0.690970	−	0.722883i	$-0.257184\pi$
$443$	29.0865	1.38194	0.690970	+	0.722883i	$0.257184\pi$
$444$	34.1887	1.62252
$445$	15.4477	0.732292
$446$	−12.9639	−0.613859
$447$	13.9959	0.661986
$448$	−12.5106	−0.591070
$449$	−22.0315	−1.03973	−0.519866	−	0.854248i	$-0.674018\pi$
$449$	−22.0315	−1.03973	−0.519866	+	0.854248i	$0.674018\pi$
$450$	6.33467	0.298619
$451$	−10.6193	−0.500043
$452$	−49.7660	−2.34080
$453$	−6.61446	−0.310774
$454$	44.2925	2.07875
$455$	−5.92413	−0.277727
$456$	−25.4751	−1.19298
$457$	−6.54543	−0.306182	−0.153091	−	0.988212i	$-0.548923\pi$
$457$	−6.54543	−0.306182	−0.153091	+	0.988212i	$0.548923\pi$
$458$	11.3242	0.529145
$459$	1.12804	0.0526523
$460$	−54.6097	−2.54619
$461$	−5.86292	−0.273063	−0.136532	−	0.990636i	$-0.543596\pi$
$461$	−5.86292	−0.273063	−0.136532	+	0.990636i	$0.543596\pi$
$462$	−7.60491	−0.353812
$463$	10.4157	0.484059	0.242029	−	0.970269i	$-0.422187\pi$
$463$	10.4157	0.484059	0.242029	+	0.970269i	$0.422187\pi$
$464$	44.2472	2.05413
$465$	−1.93083	−0.0895399
$466$	10.7019	0.495754
$467$	−15.8687	−0.734316	−0.367158	−	0.930159i	$-0.619669\pi$
$467$	−15.8687	−0.734316	−0.367158	+	0.930159i	$0.619669\pi$
$468$	−14.8205	−0.685078
$469$	−10.4222	−0.481254
$470$	12.7222	0.586829
$471$	2.17310	0.100131
$472$	59.0455	2.71779
$473$	18.0080	0.828010
$474$	−33.1603	−1.52310
$475$	−4.84574	−0.222338
$476$	−0.866208	−0.0397026
$477$	1.11296	0.0509587
$478$	64.5608	2.95294
$479$	16.9814	0.775901	0.387950	−	0.921680i	$-0.373183\pi$
$479$	16.9814	0.775901	0.387950	+	0.921680i	$0.373183\pi$
$480$	51.2443	2.33897
$481$	−12.8281	−0.584912
$482$	−23.8411	−1.08593
$483$	−4.75963	−0.216571
$484$	−25.4421	−1.15646
$485$	17.3351	0.787144
$486$	29.3401	1.33089
$487$	18.2763	0.828177	0.414089	−	0.910237i	$-0.364100\pi$
$487$	18.2763	0.828177	0.414089	+	0.910237i	$0.364100\pi$
$488$	75.9488	3.43804
$489$	−9.00944	−0.407421
$490$	44.3192	2.00214
$491$	34.0273	1.53563	0.767815	−	0.640671i	$-0.221344\pi$
$491$	34.0273	1.53563	0.767815	+	0.640671i	$0.221344\pi$
$492$	30.0016	1.35257
$493$	0.775298	0.0349177
$494$	15.8272	0.712098
$495$	−7.37938	−0.331679
$496$	6.04559	0.271455
$497$	1.61457	0.0724232
$498$	49.7303	2.22847
$499$	7.94564	0.355696	0.177848	−	0.984058i	$-0.443086\pi$
$499$	7.94564	0.355696	0.177848	+	0.984058i	$0.443086\pi$
$500$	−38.9773	−1.74312
$501$	3.42432	0.152988
$502$	−60.6107	−2.70519
$503$	−38.5750	−1.71998	−0.859988	−	0.510315i	$-0.829529\pi$
$503$	−38.5750	−1.71998	−0.859988	+	0.510315i	$0.829529\pi$
$504$	−7.88472	−0.351214
$505$	6.49895	0.289199
$506$	26.3039	1.16935
$507$	8.60710	0.382255
$508$	−90.9981	−4.03739
$509$	−29.3962	−1.30296	−0.651482	−	0.758664i	$-0.725852\pi$
$509$	−29.3962	−1.30296	−0.651482	+	0.758664i	$0.725852\pi$
$510$	1.93108	0.0855098
$511$	−7.05271	−0.311993
$512$	24.1742	1.06836
$513$	−13.0056	−0.574212
$514$	−64.5254	−2.84609
$515$	−19.2457	−0.848068
$516$	−50.8761	−2.23970
$517$	−4.38941	−0.193046
$518$	−11.3004	−0.496511
$519$	13.2585	0.581984
$520$	−55.8615	−2.44969
$521$	5.14676	0.225484	0.112742	−	0.993624i	$-0.464037\pi$
$521$	5.14676	0.225484	0.112742	+	0.993624i	$0.464037\pi$
$522$	11.6853	0.511452
$523$	−22.4874	−0.983306	−0.491653	−	0.870791i	$-0.663607\pi$
$523$	−22.4874	−0.983306	−0.491653	+	0.870791i	$0.663607\pi$
$524$	−89.0851	−3.89170
$525$	2.46819	0.107721
$526$	−54.8482	−2.39149
$527$	0.105931	0.00461441
$528$	−38.0245	−1.65481
$529$	−6.53736	−0.284233
$530$	6.94599	0.301715
$531$	8.26843	0.358819
$532$	9.98688	0.432986
$533$	−11.2570	−0.487597
$534$	21.0214	0.909687
$535$	53.4190	2.30950
$536$	−98.2764	−4.24489
$537$	10.5286	0.454342
$538$	−67.3931	−2.90552
$539$	−15.2911	−0.658633
$540$	76.0060	3.27078
$541$	−16.8704	−0.725315	−0.362657	−	0.931923i	$-0.618130\pi$
$541$	−16.8704	−0.725315	−0.362657	+	0.931923i	$0.618130\pi$
$542$	3.23796	0.139082
$543$	26.0041	1.11594
$544$	−2.81141	−0.120538
$545$	11.5897	0.496448
$546$	−8.06163	−0.345006
$547$	−0.0730159	−0.00312193	−0.00156097	−	0.999999i	$-0.500497\pi$
$547$	−0.0730159	−0.00312193	−0.00156097	+	0.999999i	$0.500497\pi$
$548$	−30.0704	−1.28454
$549$	10.6355	0.453911
$550$	−13.6404	−0.581628
$551$	−8.93873	−0.380803
$552$	−44.8808	−1.91026
$553$	7.85100	0.333858
$554$	−29.6244	−1.25862
$555$	18.0455	0.765987
$556$	−56.5052	−2.39635
$557$	−6.65531	−0.281995	−0.140997	−	0.990010i	$-0.545031\pi$
$557$	−6.65531	−0.281995	−0.140997	+	0.990010i	$0.545031\pi$
$558$	1.59659	0.0675890
$559$	19.0895	0.807400
$560$	−26.0931	−1.10263
$561$	−0.666264	−0.0281297
$562$	−19.9973	−0.843535
$563$	28.7108	1.21002	0.605008	−	0.796219i	$-0.293170\pi$
$563$	28.7108	1.21002	0.605008	+	0.796219i	$0.293170\pi$
$564$	12.4009	0.522173
$565$	−26.2675	−1.10508
$566$	29.6435	1.24601
$567$	3.70326	0.155522
$568$	15.2245	0.638807
$569$	16.8574	0.706698	0.353349	−	0.935492i	$-0.385043\pi$
$569$	16.8574	0.706698	0.353349	+	0.935492i	$0.385043\pi$
$570$	−22.2643	−0.932547
$571$	10.4009	0.435265	0.217632	−	0.976031i	$-0.430167\pi$
$571$	10.4009	0.435265	0.217632	+	0.976031i	$0.430167\pi$
$572$	31.9128	1.33434
$573$	−12.4102	−0.518443
$574$	−9.91643	−0.413904
$575$	−8.53701	−0.356018
$576$	−16.5197	−0.688321
$577$	−38.7078	−1.61143	−0.805714	−	0.592304i	$-0.798218\pi$
$577$	−38.7078	−1.61143	−0.805714	+	0.592304i	$0.798218\pi$
$578$	45.0313	1.87305
$579$	5.52653	0.229675
$580$	52.2387	2.16909
$581$	−11.7741	−0.488473
$582$	23.5898	0.977827
$583$	−2.39652	−0.0992535
$584$	−66.5034	−2.75193
$585$	−7.82255	−0.323423
$586$	30.6223	1.26500
$587$	30.8576	1.27363	0.636815	−	0.771017i	$-0.280252\pi$
$587$	30.8576	1.27363	0.636815	+	0.771017i	$0.280252\pi$
$588$	43.2002	1.78155
$589$	−1.22132	−0.0503235
$590$	51.6036	2.12448
$591$	−12.4614	−0.512595
$592$	−56.5020	−2.32222
$593$	−11.4906	−0.471861	−0.235930	−	0.971770i	$-0.575814\pi$
$593$	−11.4906	−0.471861	−0.235930	+	0.971770i	$0.575814\pi$
$594$	−36.6098	−1.50212
$595$	−0.457202	−0.0187434
$596$	−51.7374	−2.11925
$597$	−12.1897	−0.498893
$598$	27.8836	1.14025
$599$	8.80795	0.359883	0.179942	−	0.983677i	$-0.442409\pi$
$599$	8.80795	0.359883	0.179942	+	0.983677i	$0.442409\pi$
$600$	23.2738	0.950149
$601$	34.2605	1.39751	0.698757	−	0.715359i	$-0.253737\pi$
$601$	34.2605	1.39751	0.698757	+	0.715359i	$0.253737\pi$
$602$	16.8161	0.685373
$603$	−13.7621	−0.560437
$604$	24.4510	0.994897
$605$	−13.4288	−0.545959
$606$	8.84385	0.359257
$607$	−13.4608	−0.546356	−0.273178	−	0.961963i	$-0.588075\pi$
$607$	−13.4608	−0.546356	−0.273178	+	0.961963i	$0.588075\pi$
$608$	32.4139	1.31456
$609$	4.55298	0.184496
$610$	66.3764	2.68750
$611$	−4.65302	−0.188241
$612$	−1.14379	−0.0462350
$613$	−27.8200	−1.12364	−0.561820	−	0.827259i	$-0.689899\pi$
$613$	−27.8200	−1.12364	−0.561820	+	0.827259i	$0.689899\pi$
$614$	30.4239	1.22781
$615$	15.8354	0.638545
$616$	16.9781	0.684067
$617$	−9.36470	−0.377009	−0.188504	−	0.982072i	$-0.560364\pi$
$617$	−9.36470	−0.377009	−0.188504	+	0.982072i	$0.560364\pi$
$618$	−26.1898	−1.05351
$619$	−13.9673	−0.561393	−0.280697	−	0.959797i	$-0.590565\pi$
$619$	−13.9673	−0.561393	−0.280697	+	0.959797i	$0.590565\pi$
$620$	7.13749	0.286648
$621$	−22.9127	−0.919456
$622$	−45.1966	−1.81222
$623$	−4.97702	−0.199400
$624$	−40.3081	−1.61362
$625$	−31.0932	−1.24373
$626$	64.9524	2.59602
$627$	7.68164	0.306775
$628$	−8.03307	−0.320555
$629$	−0.990026	−0.0394749
$630$	−6.89095	−0.274542
$631$	5.03417	0.200407	0.100204	−	0.994967i	$-0.468051\pi$
$631$	5.03417	0.200407	0.100204	+	0.994967i	$0.468051\pi$
$632$	74.0309	2.94479
$633$	21.3908	0.850209
$634$	−3.38755	−0.134537
$635$	−48.0306	−1.90604
$636$	6.77061	0.268472
$637$	−16.2094	−0.642239
$638$	−25.1619	−0.996168
$639$	2.13196	0.0843392
$640$	−28.0743	−1.10974
$641$	−25.6571	−1.01339	−0.506697	−	0.862124i	$-0.669134\pi$
$641$	−25.6571	−1.01339	−0.506697	+	0.862124i	$0.669134\pi$
$642$	72.6932	2.86897
$643$	2.69819	0.106406	0.0532032	−	0.998584i	$-0.483057\pi$
$643$	2.69819	0.106406	0.0532032	+	0.998584i	$0.483057\pi$
$644$	17.5944	0.693318
$645$	−26.8534	−1.05735
$646$	1.22148	0.0480585
$647$	19.3180	0.759468	0.379734	−	0.925096i	$-0.376016\pi$
$647$	19.3180	0.759468	0.379734	+	0.925096i	$0.376016\pi$
$648$	34.9198	1.37178
$649$	−17.8043	−0.698881
$650$	−14.4596	−0.567151
$651$	0.622083	0.0243814
$652$	33.3043	1.30430
$653$	−26.0762	−1.02044	−0.510220	−	0.860044i	$-0.670436\pi$
$653$	−26.0762	−1.02044	−0.510220	+	0.860044i	$0.670436\pi$
$654$	15.7714	0.616710
$655$	−47.0209	−1.83726
$656$	−49.5821	−1.93586
$657$	−9.31279	−0.363327
$658$	−4.09889	−0.159791
$659$	14.3977	0.560856	0.280428	−	0.959875i	$-0.409524\pi$
$659$	14.3977	0.560856	0.280428	+	0.959875i	$0.409524\pi$
$660$	−44.8921	−1.74742
$661$	3.06784	0.119325	0.0596626	−	0.998219i	$-0.480998\pi$
$661$	3.06784	0.119325	0.0596626	+	0.998219i	$0.480998\pi$
$662$	−22.8593	−0.888451
$663$	−0.706277	−0.0274295
$664$	−111.024	−4.30856
$665$	5.27127	0.204411
$666$	−14.9217	−0.578204
$667$	−15.7479	−0.609760
$668$	−12.6584	−0.489766
$669$	−6.66983	−0.257871
$670$	−85.8899	−3.31822
$671$	−22.9013	−0.884093
$672$	−16.5101	−0.636892
$673$	13.0495	0.503020	0.251510	−	0.967855i	$-0.419073\pi$
$673$	13.0495	0.503020	0.251510	+	0.967855i	$0.419073\pi$
$674$	42.1556	1.62377
$675$	11.8818	0.457332
$676$	−31.8170	−1.22373
$677$	24.3673	0.936510	0.468255	−	0.883593i	$-0.344883\pi$
$677$	24.3673	0.936510	0.468255	+	0.883593i	$0.344883\pi$
$678$	−35.7451	−1.37278
$679$	−5.58509	−0.214336
$680$	−4.31118	−0.165326
$681$	22.7882	0.873245
$682$	−3.43792	−0.131645
$683$	24.3507	0.931754	0.465877	−	0.884850i	$-0.345739\pi$
$683$	24.3507	0.931754	0.465877	+	0.884850i	$0.345739\pi$
$684$	13.1872	0.504226
$685$	−15.8717	−0.606428
$686$	−30.2393	−1.15454
$687$	5.82622	0.222284
$688$	84.0805	3.20554
$689$	−2.54044	−0.0967830
$690$	−39.2242	−1.49324
$691$	36.4869	1.38803	0.694013	−	0.719963i	$-0.255841\pi$
$691$	36.4869	1.38803	0.694013	+	0.719963i	$0.255841\pi$
$692$	−49.0114	−1.86313
$693$	2.37753	0.0903147
$694$	86.5443	3.28518
$695$	−29.8246	−1.13131
$696$	42.9322	1.62734
$697$	−0.868776	−0.0329072
$698$	−18.9170	−0.716020
$699$	5.50603	0.208257
$700$	−9.12392	−0.344852
$701$	1.02568	0.0387392	0.0193696	−	0.999812i	$-0.493834\pi$
$701$	1.02568	0.0387392	0.0193696	+	0.999812i	$0.493834\pi$
$702$	−38.8085	−1.46473
$703$	11.4144	0.430503
$704$	35.5717	1.34066
$705$	6.54546	0.246516
$706$	35.1537	1.32303
$707$	−2.09386	−0.0787478
$708$	50.3006	1.89041
$709$	−35.2150	−1.32253	−0.661263	−	0.750154i	$-0.729979\pi$
$709$	−35.2150	−1.32253	−0.661263	+	0.750154i	$0.729979\pi$
$710$	13.3057	0.499353
$711$	10.3669	0.388789
$712$	−46.9307	−1.75880
$713$	−2.15166	−0.0805805
$714$	−0.622166	−0.0232840
$715$	16.8442	0.629938
$716$	−38.9199	−1.45451
$717$	33.2161	1.24048
$718$	−29.4935	−1.10069
$719$	11.3329	0.422647	0.211323	−	0.977416i	$-0.432223\pi$
$719$	11.3329	0.422647	0.211323	+	0.977416i	$0.432223\pi$
$720$	−34.4548	−1.28405
$721$	6.20068	0.230925
$722$	36.3645	1.35335
$723$	−12.2661	−0.456180
$724$	−96.1265	−3.57252
$725$	8.16635	0.303291
$726$	−18.2741	−0.678215
$727$	−27.9109	−1.03516	−0.517578	−	0.855636i	$-0.673166\pi$
$727$	−27.9109	−1.03516	−0.517578	+	0.855636i	$0.673166\pi$
$728$	17.9977	0.667040
$729$	28.0327	1.03825
$730$	−58.1215	−2.15117
$731$	1.47325	0.0544903
$732$	64.7004	2.39140
$733$	−16.6997	−0.616817	−0.308409	−	0.951254i	$-0.599796\pi$
$733$	−16.6997	−0.616817	−0.308409	+	0.951254i	$0.599796\pi$
$734$	−82.2285	−3.03511
$735$	22.8019	0.841061
$736$	57.1054	2.10493
$737$	29.6338	1.09158
$738$	−13.0942	−0.482005
$739$	−37.3104	−1.37249	−0.686243	−	0.727372i	$-0.740742\pi$
$739$	−37.3104	−1.37249	−0.686243	+	0.727372i	$0.740742\pi$
$740$	−66.7068	−2.45219
$741$	8.14296	0.299139
$742$	−2.23789	−0.0821557
$743$	42.6362	1.56417	0.782085	−	0.623172i	$-0.214156\pi$
$743$	42.6362	1.56417	0.782085	+	0.623172i	$0.214156\pi$
$744$	5.86592	0.215055
$745$	−27.3080	−1.00049
$746$	−4.81115	−0.176149
$747$	−15.5472	−0.568842
$748$	2.46291	0.0900530
$749$	−17.2108	−0.628869
$750$	−27.9960	−1.02227
$751$	−21.7452	−0.793493	−0.396746	−	0.917928i	$-0.629861\pi$
$751$	−21.7452	−0.793493	−0.396746	+	0.917928i	$0.629861\pi$
$752$	−20.4944	−0.747355
$753$	−31.1838	−1.13640
$754$	−26.6730	−0.971372
$755$	12.9057	0.469687
$756$	−24.4880	−0.890619
$757$	−27.3253	−0.993154	−0.496577	−	0.867993i	$-0.665410\pi$
$757$	−27.3253	−0.993154	−0.496577	+	0.867993i	$0.665410\pi$
$758$	28.1623	1.02290
$759$	13.5332	0.491223
$760$	49.7053	1.80300
$761$	−29.5739	−1.07205	−0.536027	−	0.844201i	$-0.680076\pi$
$761$	−29.5739	−1.07205	−0.536027	+	0.844201i	$0.680076\pi$
$762$	−65.3606	−2.36776
$763$	−3.73402	−0.135181
$764$	45.8754	1.65971
$765$	−0.603715	−0.0218274
$766$	−65.3011	−2.35942
$767$	−18.8736	−0.681485
$768$	1.59905	0.0577009
$769$	−16.3839	−0.590820	−0.295410	−	0.955371i	$-0.595456\pi$
$769$	−16.3839	−0.590820	−0.295410	+	0.955371i	$0.595456\pi$
$770$	14.8382	0.534732
$771$	−33.1979	−1.19559
$772$	−20.4294	−0.735269
$773$	−42.6103	−1.53259	−0.766294	−	0.642490i	$-0.777901\pi$
$773$	−42.6103	−1.53259	−0.766294	+	0.642490i	$0.777901\pi$
$774$	22.2049	0.798140
$775$	1.11579	0.0400802
$776$	−52.6646	−1.89055
$777$	−5.81398	−0.208575
$778$	−40.5748	−1.45468
$779$	10.0165	0.358878
$780$	−47.5882	−1.70393
$781$	−4.59074	−0.164269
$782$	2.15195	0.0769536
$783$	21.9179	0.783282
$784$	−71.3949	−2.54982
$785$	−4.24001	−0.151333
$786$	−63.9866	−2.28233
$787$	9.66092	0.344375	0.172187	−	0.985064i	$-0.444917\pi$
$787$	9.66092	0.344375	0.172187	+	0.985064i	$0.444917\pi$
$788$	46.0649	1.64099
$789$	−28.2190	−1.00462
$790$	64.7002	2.30193
$791$	8.46299	0.300909
$792$	22.4188	0.796619
$793$	−24.2766	−0.862088
$794$	−1.96666	−0.0697941
$795$	3.57366	0.126745
$796$	45.0606	1.59713
$797$	−29.6458	−1.05011	−0.525054	−	0.851069i	$-0.675955\pi$
$797$	−29.6458	−1.05011	−0.525054	+	0.851069i	$0.675955\pi$
$798$	7.17321	0.253929
$799$	−0.359102	−0.0127041
$800$	−29.6131	−1.04698
$801$	−6.57194	−0.232208
$802$	−12.4714	−0.440381
$803$	20.0531	0.707660
$804$	−83.7212	−2.95262
$805$	9.28669	0.327313
$806$	−3.64438	−0.128368
$807$	−34.6733	−1.22056
$808$	−19.7441	−0.694593
$809$	−19.6671	−0.691460	−0.345730	−	0.938334i	$-0.612369\pi$
$809$	−19.6671	−0.691460	−0.345730	+	0.938334i	$0.612369\pi$
$810$	30.5186	1.07231
$811$	−6.92462	−0.243156	−0.121578	−	0.992582i	$-0.538796\pi$
$811$	−6.92462	−0.243156	−0.121578	+	0.992582i	$0.538796\pi$
$812$	−16.8305	−0.590636
$813$	1.66591	0.0584258
$814$	32.1307	1.12618
$815$	17.5787	0.615754
$816$	−3.11083	−0.108901
$817$	−16.9858	−0.594257
$818$	−51.4229	−1.79796
$819$	2.52031	0.0880667
$820$	−58.5371	−2.04421
$821$	−41.0082	−1.43120	−0.715599	−	0.698512i	$-0.753846\pi$
$821$	−41.0082	−1.43120	−0.715599	+	0.698512i	$0.753846\pi$
$822$	−21.5984	−0.753332
$823$	−3.46851	−0.120905	−0.0604523	−	0.998171i	$-0.519254\pi$
$823$	−3.46851	−0.120905	−0.0604523	+	0.998171i	$0.519254\pi$
$824$	58.4692	2.03687
$825$	−7.01788	−0.244331
$826$	−16.6259	−0.578489
$827$	−48.2864	−1.67908	−0.839541	−	0.543297i	$-0.817176\pi$
$827$	−48.2864	−1.67908	−0.839541	+	0.543297i	$0.817176\pi$
$828$	23.2327	0.807391
$829$	2.66116	0.0924260	0.0462130	−	0.998932i	$-0.485285\pi$
$829$	2.66116	0.0924260	0.0462130	+	0.998932i	$0.485285\pi$
$830$	−97.0307	−3.36798
$831$	−15.2415	−0.528722
$832$	37.7080	1.30729
$833$	−1.25098	−0.0433438
$834$	−40.5856	−1.40537
$835$	−6.68133	−0.231217
$836$	−28.3959	−0.982094
$837$	2.99469	0.103512
$838$	18.8159	0.649985
$839$	12.0842	0.417195	0.208597	−	0.978002i	$-0.433110\pi$
$839$	12.0842	0.417195	0.208597	+	0.978002i	$0.433110\pi$
$840$	−25.3176	−0.873540
$841$	−13.9359	−0.480547
$842$	32.8154	1.13089
$843$	−10.2885	−0.354353
$844$	−79.0733	−2.72182
$845$	−16.7936	−0.577719
$846$	−5.41240	−0.186082
$847$	4.32656	0.148662
$848$	−11.1895	−0.384248
$849$	15.2513	0.523425
$850$	−1.11593	−0.0382762
$851$	20.1094	0.689342
$852$	12.9697	0.444335
$853$	−8.26617	−0.283028	−0.141514	−	0.989936i	$-0.545197\pi$
$853$	−8.26617	−0.283028	−0.141514	+	0.989936i	$0.545197\pi$
$854$	−21.3855	−0.731796
$855$	6.96048	0.238043
$856$	−162.289	−5.54692
$857$	−16.4357	−0.561431	−0.280716	−	0.959791i	$-0.590572\pi$
$857$	−16.4357	−0.561431	−0.280716	+	0.959791i	$0.590572\pi$
$858$	22.9218	0.782538
$859$	−29.1066	−0.993104	−0.496552	−	0.868007i	$-0.665401\pi$
$859$	−29.1066	−0.993104	−0.496552	+	0.868007i	$0.665401\pi$
$860$	99.2663	3.38495
$861$	−5.10193	−0.173873
$862$	−41.9211	−1.42784
$863$	41.3100	1.40621	0.703105	−	0.711086i	$-0.251796\pi$
$863$	41.3100	1.40621	0.703105	+	0.711086i	$0.251796\pi$
$864$	−79.4794	−2.70394
$865$	−25.8692	−0.879579
$866$	52.3302	1.77825
$867$	23.1683	0.786836
$868$	−2.29959	−0.0780532
$869$	−22.3229	−0.757254
$870$	37.5212	1.27209
$871$	31.4135	1.06441
$872$	−35.2099	−1.19236
$873$	−7.37487	−0.249602
$874$	−24.8107	−0.839236
$875$	6.62830	0.224078
$876$	−56.6539	−1.91416
$877$	−22.7487	−0.768168	−0.384084	−	0.923298i	$-0.625483\pi$
$877$	−22.7487	−0.768168	−0.384084	+	0.923298i	$0.625483\pi$
$878$	42.2499	1.42587
$879$	15.7550	0.531402
$880$	74.1911	2.50098
$881$	37.4653	1.26224	0.631119	−	0.775686i	$-0.282596\pi$
$881$	37.4653	1.26224	0.631119	+	0.775686i	$0.282596\pi$
$882$	−18.8548	−0.634873
$883$	−18.1628	−0.611227	−0.305613	−	0.952156i	$-0.598861\pi$
$883$	−18.1628	−0.611227	−0.305613	+	0.952156i	$0.598861\pi$
$884$	2.61082	0.0878115
$885$	26.5497	0.892457
$886$	−77.2284	−2.59454
$887$	−24.8185	−0.833322	−0.416661	−	0.909062i	$-0.636800\pi$
$887$	−24.8185	−0.833322	−0.416661	+	0.909062i	$0.636800\pi$
$888$	−54.8228	−1.83973
$889$	15.4747	0.519006
$890$	−41.0157	−1.37485
$891$	−10.5296	−0.352754
$892$	24.6557	0.825534
$893$	4.14024	0.138548
$894$	−37.1611	−1.24285
$895$	−20.5427	−0.686667
$896$	9.04513	0.302176
$897$	14.3459	0.478996
$898$	58.4966	1.95206
$899$	2.05824	0.0686463
$900$	−12.0477	−0.401591
$901$	−0.196061	−0.00653175
$902$	28.1956	0.938812
$903$	8.65176	0.287913
$904$	79.8016	2.65416
$905$	−50.7375	−1.68657
$906$	17.5623	0.583467
$907$	−49.5646	−1.64577	−0.822883	−	0.568211i	$-0.807636\pi$
$907$	−49.5646	−1.64577	−0.822883	+	0.568211i	$0.807636\pi$
$908$	−84.2387	−2.79556
$909$	−2.76486	−0.0917045
$910$	15.7293	0.521423
$911$	22.9117	0.759098	0.379549	−	0.925172i	$-0.376079\pi$
$911$	22.9117	0.759098	0.379549	+	0.925172i	$0.376079\pi$
$912$	35.8660	1.18764
$913$	33.4776	1.10795
$914$	17.3790	0.574845
$915$	34.1502	1.12897
$916$	−21.5372	−0.711609
$917$	15.1494	0.500278
$918$	−2.99509	−0.0988527
$919$	−41.9176	−1.38273	−0.691367	−	0.722504i	$-0.742991\pi$
$919$	−41.9176	−1.38273	−0.691367	+	0.722504i	$0.742991\pi$
$920$	87.5687	2.88705
$921$	15.6529	0.515780
$922$	15.5668	0.512666
$923$	−4.86644	−0.160181
$924$	14.4636	0.475817
$925$	−10.4281	−0.342874
$926$	−27.6551	−0.908802
$927$	8.18773	0.268920
$928$	−54.6260	−1.79319
$929$	19.5862	0.642603	0.321301	−	0.946977i	$-0.395880\pi$
$929$	19.5862	0.642603	0.321301	+	0.946977i	$0.395880\pi$
$930$	5.12659	0.168108
$931$	14.4231	0.472696
$932$	−20.3536	−0.666704
$933$	−23.2533	−0.761279
$934$	42.1335	1.37865
$935$	1.29997	0.0425137
$936$	23.7652	0.776790
$937$	−10.7819	−0.352231	−0.176115	−	0.984370i	$-0.556353\pi$
$937$	−10.7819	−0.352231	−0.176115	+	0.984370i	$0.556353\pi$
$938$	27.6724	0.903537
$939$	33.4175	1.09054
$940$	−24.1959	−0.789184
$941$	−21.0437	−0.686005	−0.343002	−	0.939334i	$-0.611444\pi$
$941$	−21.0437	−0.686005	−0.343002	+	0.939334i	$0.611444\pi$
$942$	−5.76986	−0.187992
$943$	17.6466	0.574652
$944$	−83.1294	−2.70563
$945$	−12.9252	−0.420458
$946$	−47.8137	−1.55456
$947$	29.9237	0.972389	0.486194	−	0.873851i	$-0.338385\pi$
$947$	29.9237	0.972389	0.486194	+	0.873851i	$0.338385\pi$
$948$	63.0666	2.04831
$949$	21.2574	0.690046
$950$	12.8661	0.417430
$951$	−1.74287	−0.0565165
$952$	1.38900	0.0450176
$953$	39.8198	1.28989	0.644945	−	0.764229i	$-0.276880\pi$
$953$	39.8198	1.28989	0.644945	+	0.764229i	$0.276880\pi$
$954$	−2.95504	−0.0956730
$955$	24.2140	0.783545
$956$	−122.787	−3.97120
$957$	−12.9456	−0.418472
$958$	−45.0879	−1.45672
$959$	5.11363	0.165128
$960$	−53.0442	−1.71200
$961$	−30.7188	−0.990928
$962$	34.0604	1.09815
$963$	−22.7261	−0.732338
$964$	45.3427	1.46039
$965$	−10.7830	−0.347118
$966$	12.6374	0.406603
$967$	−41.9306	−1.34840	−0.674198	−	0.738550i	$-0.735511\pi$
$967$	−41.9306	−1.34840	−0.674198	+	0.738550i	$0.735511\pi$
$968$	40.7972	1.31127
$969$	0.628443	0.0201885
$970$	−46.0269	−1.47783
$971$	−9.56686	−0.307015	−0.153508	−	0.988147i	$-0.549057\pi$
$971$	−9.56686	−0.307015	−0.153508	+	0.988147i	$0.549057\pi$
$972$	−55.8011	−1.78982
$973$	9.60903	0.308051
$974$	−48.5259	−1.55487
$975$	−7.43934	−0.238250
$976$	−106.927	−3.42266
$977$	30.2307	0.967166	0.483583	−	0.875299i	$-0.339335\pi$
$977$	30.2307	0.967166	0.483583	+	0.875299i	$0.339335\pi$
$978$	23.9213	0.764917
$979$	14.1513	0.452277
$980$	−84.2895	−2.69253
$981$	−4.93061	−0.157422
$982$	−90.3469	−2.88309
$983$	8.19510	0.261383	0.130692	−	0.991423i	$-0.458280\pi$
$983$	8.19510	0.261383	0.130692	+	0.991423i	$0.458280\pi$
$984$	−48.1086	−1.53365
$985$	24.3140	0.774708
$986$	−2.05852	−0.0655566
$987$	−2.10885	−0.0671253
$988$	−30.1013	−0.957649
$989$	−29.9248	−0.951553
$990$	19.5932	0.622714
$991$	−21.0347	−0.668188	−0.334094	−	0.942540i	$-0.608430\pi$
$991$	−21.0347	−0.668188	−0.334094	+	0.942540i	$0.608430\pi$
$992$	−7.46367	−0.236972
$993$	−11.7609	−0.373222
$994$	−4.28689	−0.135972
$995$	23.7839	0.753999
$996$	−94.5807	−2.99691
$997$	−22.4707	−0.711654	−0.355827	−	0.934552i	$-0.615801\pi$
$997$	−22.4707	−0.711654	−0.355827	+	0.934552i	$0.615801\pi$
$998$	−21.0967	−0.667805
$999$	−27.9883	−0.885512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.7	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.7	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65513 q^{2} -1.36605 q^{3} +5.04972 q^{4} +2.66534 q^{5} +3.62703 q^{6} -0.858733 q^{7} -8.09741 q^{8} -1.13392 q^{9} +O(q^{10})\)	\(q-2.65513 q^{2} -1.36605 q^{3} +5.04972 q^{4} +2.66534 q^{5} +3.62703 q^{6} -0.858733 q^{7} -8.09741 q^{8} -1.13392 q^{9} -7.07683 q^{10} +2.44166 q^{11} -6.89815 q^{12} +2.58829 q^{13} +2.28005 q^{14} -3.64098 q^{15} +11.4002 q^{16} +0.199755 q^{17} +3.01070 q^{18} -2.30305 q^{19} +13.4592 q^{20} +1.17307 q^{21} -6.48292 q^{22} -4.05742 q^{23} +11.0614 q^{24} +2.10405 q^{25} -6.87226 q^{26} +5.64712 q^{27} -4.33636 q^{28} +3.88125 q^{29} +9.66728 q^{30} +0.530304 q^{31} -14.0743 q^{32} -3.33542 q^{33} -0.530374 q^{34} -2.28882 q^{35} -5.72598 q^{36} -4.95621 q^{37} +6.11491 q^{38} -3.53573 q^{39} -21.5824 q^{40} -4.34922 q^{41} -3.11465 q^{42} +7.37533 q^{43} +12.3297 q^{44} -3.02228 q^{45} +10.7730 q^{46} -1.79772 q^{47} -15.5733 q^{48} -6.26258 q^{49} -5.58653 q^{50} -0.272874 q^{51} +13.0702 q^{52} -0.981512 q^{53} -14.9939 q^{54} +6.50785 q^{55} +6.95351 q^{56} +3.14608 q^{57} -10.3052 q^{58} -7.29190 q^{59} -18.3859 q^{60} -9.37939 q^{61} -1.40803 q^{62} +0.973734 q^{63} +14.5687 q^{64} +6.89869 q^{65} +8.85597 q^{66} +12.1368 q^{67} +1.00870 q^{68} +5.54262 q^{69} +6.07711 q^{70} -1.88017 q^{71} +9.18181 q^{72} +8.21292 q^{73} +13.1594 q^{74} -2.87423 q^{75} -11.6298 q^{76} -2.09673 q^{77} +9.38781 q^{78} -9.14254 q^{79} +30.3855 q^{80} -4.31247 q^{81} +11.5477 q^{82} +13.7110 q^{83} +5.92367 q^{84} +0.532414 q^{85} -19.5825 q^{86} -5.30197 q^{87} -19.7711 q^{88} +5.79577 q^{89} +8.02456 q^{90} -2.22265 q^{91} -20.4888 q^{92} -0.724419 q^{93} +4.77318 q^{94} -6.13843 q^{95} +19.2262 q^{96} +6.50388 q^{97} +16.6280 q^{98} -2.76864 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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