LMFDB - Embedded newform 8041.2.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85483 q^{2} +0.655235 q^{3} +1.44041 q^{4} +4.10800 q^{5} -1.21535 q^{6} -1.24342 q^{7} +1.03795 q^{8} -2.57067 q^{9} +O(q^{10})$	\(q-1.85483 q^{2} +0.655235 q^{3} +1.44041 q^{4} +4.10800 q^{5} -1.21535 q^{6} -1.24342 q^{7} +1.03795 q^{8} -2.57067 q^{9} -7.61965 q^{10} -1.00000 q^{11} +0.943805 q^{12} +2.04423 q^{13} +2.30634 q^{14} +2.69170 q^{15} -4.80604 q^{16} -1.00000 q^{17} +4.76816 q^{18} +5.72719 q^{19} +5.91719 q^{20} -0.814734 q^{21} +1.85483 q^{22} -5.52036 q^{23} +0.680101 q^{24} +11.8757 q^{25} -3.79171 q^{26} -3.65009 q^{27} -1.79104 q^{28} -8.74117 q^{29} -4.99266 q^{30} +2.93216 q^{31} +6.83850 q^{32} -0.655235 q^{33} +1.85483 q^{34} -5.10798 q^{35} -3.70281 q^{36} +1.56239 q^{37} -10.6230 q^{38} +1.33945 q^{39} +4.26390 q^{40} -6.25556 q^{41} +1.51120 q^{42} -1.00000 q^{43} -1.44041 q^{44} -10.5603 q^{45} +10.2393 q^{46} -7.49069 q^{47} -3.14909 q^{48} -5.45390 q^{49} -22.0274 q^{50} -0.655235 q^{51} +2.94453 q^{52} +1.86093 q^{53} +6.77032 q^{54} -4.10800 q^{55} -1.29061 q^{56} +3.75266 q^{57} +16.2134 q^{58} -8.57050 q^{59} +3.87715 q^{60} +6.86031 q^{61} -5.43867 q^{62} +3.19643 q^{63} -3.07221 q^{64} +8.39770 q^{65} +1.21535 q^{66} +11.6268 q^{67} -1.44041 q^{68} -3.61713 q^{69} +9.47446 q^{70} -7.96033 q^{71} -2.66823 q^{72} -12.0888 q^{73} -2.89797 q^{74} +7.78134 q^{75} +8.24949 q^{76} +1.24342 q^{77} -2.48446 q^{78} +6.30339 q^{79} -19.7432 q^{80} +5.32033 q^{81} +11.6030 q^{82} -7.80352 q^{83} -1.17355 q^{84} -4.10800 q^{85} +1.85483 q^{86} -5.72752 q^{87} -1.03795 q^{88} +2.05894 q^{89} +19.5876 q^{90} -2.54184 q^{91} -7.95156 q^{92} +1.92125 q^{93} +13.8940 q^{94} +23.5273 q^{95} +4.48083 q^{96} -6.35396 q^{97} +10.1161 q^{98} +2.57067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * 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 $

$2$	−1.85483	−1.31157	−0.655783	−	0.754950i	$-0.727661\pi$
$2$	−1.85483	−1.31157	−0.655783	+	0.754950i	$0.727661\pi$
$3$	0.655235	0.378300	0.189150	−	0.981948i	$-0.439427\pi$
$3$	0.655235	0.378300	0.189150	+	0.981948i	$0.439427\pi$
$4$	1.44041	0.720204
$5$	4.10800	1.83715	0.918576	−	0.395243i	$-0.129340\pi$
$5$	4.10800	1.83715	0.918576	+	0.395243i	$0.129340\pi$
$6$	−1.21535	−0.496165
$7$	−1.24342	−0.469970	−0.234985	−	0.971999i	$-0.575504\pi$
$7$	−1.24342	−0.469970	−0.234985	+	0.971999i	$0.575504\pi$
$8$	1.03795	0.366971
$9$	−2.57067	−0.856889
$10$	−7.61965	−2.40955
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.943805	0.272453
$13$	2.04423	0.566968	0.283484	−	0.958977i	$-0.408510\pi$
$13$	2.04423	0.566968	0.283484	+	0.958977i	$0.408510\pi$
$14$	2.30634	0.616396
$15$	2.69170	0.694995
$16$	−4.80604	−1.20151
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.76816	1.12387
$19$	5.72719	1.31391	0.656954	−	0.753930i	$-0.271844\pi$
$19$	5.72719	1.31391	0.656954	+	0.753930i	$0.271844\pi$
$20$	5.91719	1.32312
$21$	−0.814734	−0.177790
$22$	1.85483	0.395452
$23$	−5.52036	−1.15107	−0.575537	−	0.817776i	$-0.695207\pi$
$23$	−5.52036	−1.15107	−0.575537	+	0.817776i	$0.695207\pi$
$24$	0.680101	0.138825
$25$	11.8757	2.37513
$26$	−3.79171	−0.743615
$27$	−3.65009	−0.702461
$28$	−1.79104	−0.338474
$29$	−8.74117	−1.62319	−0.811597	−	0.584217i	$-0.801402\pi$
$29$	−8.74117	−1.62319	−0.811597	+	0.584217i	$0.801402\pi$
$30$	−4.99266	−0.911531
$31$	2.93216	0.526631	0.263316	−	0.964710i	$-0.415184\pi$
$31$	2.93216	0.526631	0.263316	+	0.964710i	$0.415184\pi$
$32$	6.83850	1.20889
$33$	−0.655235	−0.114062
$34$	1.85483	0.318101
$35$	−5.10798	−0.863407
$36$	−3.70281	−0.617135
$37$	1.56239	0.256855	0.128427	−	0.991719i	$-0.459007\pi$
$37$	1.56239	0.256855	0.128427	+	0.991719i	$0.459007\pi$
$38$	−10.6230	−1.72328
$39$	1.33945	0.214484
$40$	4.26390	0.674182
$41$	−6.25556	−0.976954	−0.488477	−	0.872577i	$-0.662447\pi$
$41$	−6.25556	−0.976954	−0.488477	+	0.872577i	$0.662447\pi$
$42$	1.51120	0.233183
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.44041	−0.217150
$45$	−10.5603	−1.57424
$46$	10.2393	1.50971
$47$	−7.49069	−1.09263	−0.546314	−	0.837580i	$-0.683970\pi$
$47$	−7.49069	−1.09263	−0.546314	+	0.837580i	$0.683970\pi$
$48$	−3.14909	−0.454531
$49$	−5.45390	−0.779128
$50$	−22.0274	−3.11514
$51$	−0.655235	−0.0917512
$52$	2.94453	0.408332
$53$	1.86093	0.255618	0.127809	−	0.991799i	$-0.459206\pi$
$53$	1.86093	0.255618	0.127809	+	0.991799i	$0.459206\pi$
$54$	6.77032	0.921324
$55$	−4.10800	−0.553922
$56$	−1.29061	−0.172465
$57$	3.75266	0.497052
$58$	16.2134	2.12893
$59$	−8.57050	−1.11578	−0.557892	−	0.829914i	$-0.688390\pi$
$59$	−8.57050	−1.11578	−0.557892	+	0.829914i	$0.688390\pi$
$60$	3.87715	0.500538
$61$	6.86031	0.878373	0.439187	−	0.898396i	$-0.355267\pi$
$61$	6.86031	0.878373	0.439187	+	0.898396i	$0.355267\pi$
$62$	−5.43867	−0.690712
$63$	3.19643	0.402712
$64$	−3.07221	−0.384026
$65$	8.39770	1.04161
$66$	1.21535	0.149599
$67$	11.6268	1.42044	0.710221	−	0.703979i	$-0.248595\pi$
$67$	11.6268	1.42044	0.710221	+	0.703979i	$0.248595\pi$
$68$	−1.44041	−0.174675
$69$	−3.61713	−0.435451
$70$	9.47446	1.13241
$71$	−7.96033	−0.944717	−0.472358	−	0.881407i	$-0.656597\pi$
$71$	−7.96033	−0.944717	−0.472358	+	0.881407i	$0.656597\pi$
$72$	−2.66823	−0.314453
$73$	−12.0888	−1.41488	−0.707441	−	0.706772i	$-0.750151\pi$
$73$	−12.0888	−1.41488	−0.707441	+	0.706772i	$0.750151\pi$
$74$	−2.89797	−0.336882
$75$	7.78134	0.898512
$76$	8.24949	0.946282
$77$	1.24342	0.141701
$78$	−2.48446	−0.281310
$79$	6.30339	0.709187	0.354594	−	0.935021i	$-0.384619\pi$
$79$	6.30339	0.709187	0.354594	+	0.935021i	$0.384619\pi$
$80$	−19.7432	−2.20736
$81$	5.32033	0.591148
$82$	11.6030	1.28134
$83$	−7.80352	−0.856547	−0.428274	−	0.903649i	$-0.640878\pi$
$83$	−7.80352	−0.856547	−0.428274	+	0.903649i	$0.640878\pi$
$84$	−1.17355	−0.128045
$85$	−4.10800	−0.445575
$86$	1.85483	0.200012
$87$	−5.72752	−0.614054
$88$	−1.03795	−0.110646
$89$	2.05894	0.218248	0.109124	−	0.994028i	$-0.465196\pi$
$89$	2.05894	0.218248	0.109124	+	0.994028i	$0.465196\pi$
$90$	19.5876	2.06471
$91$	−2.54184	−0.266458
$92$	−7.95156	−0.829008
$93$	1.92125	0.199225
$94$	13.8940	1.43305
$95$	23.5273	2.41385
$96$	4.48083	0.457322
$97$	−6.35396	−0.645147	−0.322573	−	0.946544i	$-0.604548\pi$
$97$	−6.35396	−0.645147	−0.322573	+	0.946544i	$0.604548\pi$
$98$	10.1161	1.02188
$99$	2.57067	0.258362
$100$	17.1058	1.71058
$101$	8.07955	0.803945	0.401973	−	0.915652i	$-0.368325\pi$
$101$	8.07955	0.803945	0.401973	+	0.915652i	$0.368325\pi$
$102$	1.21535	0.120338
$103$	−3.52162	−0.346995	−0.173498	−	0.984834i	$-0.555507\pi$
$103$	−3.52162	−0.346995	−0.173498	+	0.984834i	$0.555507\pi$
$104$	2.12181	0.208061
$105$	−3.34693	−0.326627
$106$	−3.45171	−0.335260
$107$	−9.71384	−0.939072	−0.469536	−	0.882913i	$-0.655579\pi$
$107$	−9.71384	−0.939072	−0.469536	+	0.882913i	$0.655579\pi$
$108$	−5.25762	−0.505915
$109$	3.86982	0.370661	0.185331	−	0.982676i	$-0.440664\pi$
$109$	3.86982	0.370661	0.185331	+	0.982676i	$0.440664\pi$
$110$	7.61965	0.726505
$111$	1.02373	0.0971682
$112$	5.97595	0.564674
$113$	16.2691	1.53047	0.765233	−	0.643754i	$-0.222624\pi$
$113$	16.2691	1.53047	0.765233	+	0.643754i	$0.222624\pi$
$114$	−6.96055	−0.651916
$115$	−22.6776	−2.11470
$116$	−12.5908	−1.16903
$117$	−5.25504	−0.485828
$118$	15.8968	1.46342
$119$	1.24342	0.113984
$120$	2.79386	0.255043
$121$	1.00000	0.0909091
$122$	−12.7247	−1.15204
$123$	−4.09886	−0.369582
$124$	4.22351	0.379282
$125$	28.2452	2.52632
$126$	−5.92884	−0.528183
$127$	−10.7446	−0.953426	−0.476713	−	0.879059i	$-0.658172\pi$
$127$	−10.7446	−0.953426	−0.476713	+	0.879059i	$0.658172\pi$
$128$	−7.97858	−0.705213
$129$	−0.655235	−0.0576902
$130$	−15.5763	−1.36613
$131$	−14.5595	−1.27207	−0.636034	−	0.771661i	$-0.719426\pi$
$131$	−14.5595	−1.27207	−0.636034	+	0.771661i	$0.719426\pi$
$132$	−0.943805	−0.0821477
$133$	−7.12133	−0.617498
$134$	−21.5658	−1.86300
$135$	−14.9946	−1.29053
$136$	−1.03795	−0.0890035
$137$	−2.59301	−0.221536	−0.110768	−	0.993846i	$-0.535331\pi$
$137$	−2.59301	−0.221536	−0.110768	+	0.993846i	$0.535331\pi$
$138$	6.70917	0.571123
$139$	−20.0709	−1.70239	−0.851194	−	0.524851i	$-0.824121\pi$
$139$	−20.0709	−1.70239	−0.851194	+	0.524851i	$0.824121\pi$
$140$	−7.35758	−0.621829
$141$	−4.90816	−0.413341
$142$	14.7651	1.23906
$143$	−2.04423	−0.170947
$144$	12.3547	1.02956
$145$	−35.9087	−2.98206
$146$	22.4226	1.85571
$147$	−3.57358	−0.294744
$148$	2.25048	0.184988
$149$	−11.8744	−0.972790	−0.486395	−	0.873739i	$-0.661688\pi$
$149$	−11.8744	−0.972790	−0.486395	+	0.873739i	$0.661688\pi$
$150$	−14.4331	−1.17846
$151$	−2.43319	−0.198010	−0.0990051	−	0.995087i	$-0.531566\pi$
$151$	−2.43319	−0.198010	−0.0990051	+	0.995087i	$0.531566\pi$
$152$	5.94455	0.482166
$153$	2.57067	0.207826
$154$	−2.30634	−0.185850
$155$	12.0453	0.967502
$156$	1.92936	0.154472
$157$	3.77020	0.300895	0.150447	−	0.988618i	$-0.451929\pi$
$157$	3.77020	0.300895	0.150447	+	0.988618i	$0.451929\pi$
$158$	−11.6917	−0.930145
$159$	1.21934	0.0967003
$160$	28.0926	2.22091
$161$	6.86414	0.540970
$162$	−9.86833	−0.775329
$163$	21.8095	1.70825	0.854127	−	0.520065i	$-0.174092\pi$
$163$	21.8095	1.70825	0.854127	+	0.520065i	$0.174092\pi$
$164$	−9.01056	−0.703606
$165$	−2.69170	−0.209549
$166$	14.4742	1.12342
$167$	1.35784	0.105073	0.0525363	−	0.998619i	$-0.483269\pi$
$167$	1.35784	0.105073	0.0525363	+	0.998619i	$0.483269\pi$
$168$	−0.845654	−0.0652436
$169$	−8.82112	−0.678548
$170$	7.61965	0.584401
$171$	−14.7227	−1.12587
$172$	−1.44041	−0.109830
$173$	−22.7356	−1.72856	−0.864279	−	0.503013i	$-0.832225\pi$
$173$	−22.7356	−1.72856	−0.864279	+	0.503013i	$0.832225\pi$
$174$	10.6236	0.805372
$175$	−14.7665	−1.11624
$176$	4.80604	0.362269
$177$	−5.61569	−0.422101
$178$	−3.81900	−0.286246
$179$	5.44221	0.406770	0.203385	−	0.979099i	$-0.434806\pi$
$179$	5.44221	0.406770	0.203385	+	0.979099i	$0.434806\pi$
$180$	−15.2111	−1.13377
$181$	0.553468	0.0411389	0.0205695	−	0.999788i	$-0.493452\pi$
$181$	0.553468	0.0411389	0.0205695	+	0.999788i	$0.493452\pi$
$182$	4.71470	0.349477
$183$	4.49512	0.332288
$184$	−5.72986	−0.422411
$185$	6.41829	0.471882
$186$	−3.56360	−0.261296
$187$	1.00000	0.0731272
$188$	−10.7896	−0.786915
$189$	4.53861	0.330136
$190$	−43.6392	−3.16592
$191$	0.792894	0.0573718	0.0286859	−	0.999588i	$-0.490868\pi$
$191$	0.792894	0.0573718	0.0286859	+	0.999588i	$0.490868\pi$
$192$	−2.01302	−0.145277
$193$	3.29520	0.237194	0.118597	−	0.992942i	$-0.462160\pi$
$193$	3.29520	0.237194	0.118597	+	0.992942i	$0.462160\pi$
$194$	11.7855	0.846152
$195$	5.50246	0.394039
$196$	−7.85584	−0.561131
$197$	2.62816	0.187248	0.0936242	−	0.995608i	$-0.470155\pi$
$197$	2.62816	0.187248	0.0936242	+	0.995608i	$0.470155\pi$
$198$	−4.76816	−0.338858
$199$	16.9415	1.20095	0.600475	−	0.799643i	$-0.294978\pi$
$199$	16.9415	1.20095	0.600475	+	0.799643i	$0.294978\pi$
$200$	12.3263	0.871604
$201$	7.61830	0.537353
$202$	−14.9862	−1.05443
$203$	10.8690	0.762853
$204$	−0.943805	−0.0660796
$205$	−25.6978	−1.79481
$206$	6.53201	0.455107
$207$	14.1910	0.986343
$208$	−9.82466	−0.681217
$209$	−5.72719	−0.396158
$210$	6.20799	0.428392
$211$	−9.12966	−0.628512	−0.314256	−	0.949338i	$-0.601755\pi$
$211$	−9.12966	−0.628512	−0.314256	+	0.949338i	$0.601755\pi$
$212$	2.68049	0.184097
$213$	−5.21588	−0.357386
$214$	18.0176	1.23165
$215$	−4.10800	−0.280163
$216$	−3.78862	−0.257783
$217$	−3.64592	−0.247501
$218$	−7.17787	−0.486147
$219$	−7.92098	−0.535250
$220$	−5.91719	−0.398937
$221$	−2.04423	−0.137510
$222$	−1.89885	−0.127442
$223$	−28.5249	−1.91017	−0.955084	−	0.296334i	$-0.904236\pi$
$223$	−28.5249	−1.91017	−0.955084	+	0.296334i	$0.904236\pi$
$224$	−8.50316	−0.568141
$225$	−30.5284	−2.03522
$226$	−30.1764	−2.00731
$227$	3.68379	0.244502	0.122251	−	0.992499i	$-0.460989\pi$
$227$	3.68379	0.244502	0.122251	+	0.992499i	$0.460989\pi$
$228$	5.40536	0.357978
$229$	9.32019	0.615896	0.307948	−	0.951403i	$-0.400358\pi$
$229$	9.32019	0.615896	0.307948	+	0.951403i	$0.400358\pi$
$230$	42.0632	2.77357
$231$	0.814734	0.0536056
$232$	−9.07290	−0.595665
$233$	−21.4356	−1.40429	−0.702146	−	0.712033i	$-0.747775\pi$
$233$	−21.4356	−1.40429	−0.702146	+	0.712033i	$0.747775\pi$
$234$	9.74722	0.637196
$235$	−30.7717	−2.00733
$236$	−12.3450	−0.803592
$237$	4.13020	0.268285
$238$	−2.30634	−0.149498
$239$	−25.6556	−1.65952	−0.829760	−	0.558121i	$-0.811523\pi$
$239$	−25.6556	−1.65952	−0.829760	+	0.558121i	$0.811523\pi$
$240$	−12.9364	−0.835043
$241$	−12.0090	−0.773568	−0.386784	−	0.922170i	$-0.626414\pi$
$241$	−12.0090	−0.773568	−0.386784	+	0.922170i	$0.626414\pi$
$242$	−1.85483	−0.119233
$243$	14.4364	0.926092
$244$	9.88165	0.632608
$245$	−22.4046	−1.43138
$246$	7.60270	0.484731
$247$	11.7077	0.744943
$248$	3.04344	0.193258
$249$	−5.11314	−0.324032
$250$	−52.3901	−3.31344
$251$	2.62589	0.165744	0.0828722	−	0.996560i	$-0.473591\pi$
$251$	2.62589	0.165744	0.0828722	+	0.996560i	$0.473591\pi$
$252$	4.60416	0.290035
$253$	5.52036	0.347062
$254$	19.9294	1.25048
$255$	−2.69170	−0.168561
$256$	20.9433	1.30896
$257$	−13.6681	−0.852594	−0.426297	−	0.904583i	$-0.640182\pi$
$257$	−13.6681	−0.852594	−0.426297	+	0.904583i	$0.640182\pi$
$258$	1.21535	0.0756645
$259$	−1.94271	−0.120714
$260$	12.0961	0.750169
$261$	22.4706	1.39090
$262$	27.0054	1.66840
$263$	−5.68662	−0.350652	−0.175326	−	0.984510i	$-0.556098\pi$
$263$	−5.68662	−0.350652	−0.175326	+	0.984510i	$0.556098\pi$
$264$	−0.680101	−0.0418574
$265$	7.64468	0.469609
$266$	13.2089	0.809888
$267$	1.34909	0.0825630
$268$	16.7474	1.02301
$269$	25.8214	1.57436	0.787179	−	0.616724i	$-0.211541\pi$
$269$	25.8214	1.57436	0.787179	+	0.616724i	$0.211541\pi$
$270$	27.8125	1.69261
$271$	−4.37192	−0.265575	−0.132787	−	0.991145i	$-0.542393\pi$
$271$	−4.37192	−0.265575	−0.132787	+	0.991145i	$0.542393\pi$
$272$	4.80604	0.291409
$273$	−1.66550	−0.100801
$274$	4.80961	0.290559
$275$	−11.8757	−0.716129
$276$	−5.21014	−0.313614
$277$	−15.4016	−0.925390	−0.462695	−	0.886518i	$-0.653117\pi$
$277$	−15.4016	−0.925390	−0.462695	+	0.886518i	$0.653117\pi$
$278$	37.2281	2.23279
$279$	−7.53761	−0.451265
$280$	−5.30183	−0.316845
$281$	−24.2974	−1.44946	−0.724730	−	0.689033i	$-0.758036\pi$
$281$	−24.2974	−1.44946	−0.724730	+	0.689033i	$0.758036\pi$
$282$	9.10382	0.542124
$283$	−12.5168	−0.744046	−0.372023	−	0.928224i	$-0.621336\pi$
$283$	−12.5168	−0.744046	−0.372023	+	0.928224i	$0.621336\pi$
$284$	−11.4661	−0.680389
$285$	15.4159	0.913160
$286$	3.79171	0.224208
$287$	7.77831	0.459139
$288$	−17.5795	−1.03588
$289$	1.00000	0.0588235
$290$	66.6047	3.91116
$291$	−4.16333	−0.244059
$292$	−17.4127	−1.01900
$293$	28.7021	1.67680	0.838398	−	0.545058i	$-0.183492\pi$
$293$	28.7021	1.67680	0.838398	+	0.545058i	$0.183492\pi$
$294$	6.62840	0.386576
$295$	−35.2076	−2.04986
$296$	1.62168	0.0942583
$297$	3.65009	0.211800
$298$	22.0251	1.27588
$299$	−11.2849	−0.652621
$300$	11.2083	0.647112
$301$	1.24342	0.0716697
$302$	4.51316	0.259703
$303$	5.29400	0.304132
$304$	−27.5251	−1.57867
$305$	28.1822	1.61371
$306$	−4.76816	−0.272578
$307$	−0.184798	−0.0105470	−0.00527350	−	0.999986i	$-0.501679\pi$
$307$	−0.184798	−0.0105470	−0.00527350	+	0.999986i	$0.501679\pi$
$308$	1.79104	0.102054
$309$	−2.30749	−0.131268
$310$	−22.3420	−1.26894
$311$	14.8388	0.841430	0.420715	−	0.907193i	$-0.361779\pi$
$311$	14.8388	0.841430	0.420715	+	0.907193i	$0.361779\pi$
$312$	1.39028	0.0787093
$313$	14.3331	0.810154	0.405077	−	0.914283i	$-0.367245\pi$
$313$	14.3331	0.810154	0.405077	+	0.914283i	$0.367245\pi$
$314$	−6.99310	−0.394643
$315$	13.1309	0.739844
$316$	9.07946	0.510759
$317$	2.98640	0.167733	0.0838666	−	0.996477i	$-0.473273\pi$
$317$	2.98640	0.167733	0.0838666	+	0.996477i	$0.473273\pi$
$318$	−2.26168	−0.126829
$319$	8.74117	0.489412
$320$	−12.6206	−0.705514
$321$	−6.36485	−0.355251
$322$	−12.7318	−0.709518
$323$	−5.72719	−0.318670
$324$	7.66345	0.425747
$325$	24.2766	1.34662
$326$	−40.4530	−2.24049
$327$	2.53564	0.140221
$328$	−6.49296	−0.358514
$329$	9.31410	0.513503
$330$	4.99266	0.274837
$331$	27.5579	1.51472	0.757359	−	0.652999i	$-0.226490\pi$
$331$	27.5579	1.51472	0.757359	+	0.652999i	$0.226490\pi$
$332$	−11.2402	−0.616889
$333$	−4.01638	−0.220096
$334$	−2.51856	−0.137809
$335$	47.7630	2.60957
$336$	3.91565	0.213616
$337$	−0.282699	−0.0153996	−0.00769979	−	0.999970i	$-0.502451\pi$
$337$	−0.282699	−0.0153996	−0.00769979	+	0.999970i	$0.502451\pi$
$338$	16.3617	0.889960
$339$	10.6601	0.578975
$340$	−5.91719	−0.320905
$341$	−2.93216	−0.158785
$342$	27.3082	1.47666
$343$	15.4855	0.836137
$344$	−1.03795	−0.0559626
$345$	−14.8592	−0.799990
$346$	42.1708	2.26712
$347$	−5.85346	−0.314230	−0.157115	−	0.987580i	$-0.550219\pi$
$347$	−5.85346	−0.314230	−0.157115	+	0.987580i	$0.550219\pi$
$348$	−8.24996	−0.442244
$349$	12.6721	0.678321	0.339160	−	0.940729i	$-0.389857\pi$
$349$	12.6721	0.678321	0.339160	+	0.940729i	$0.389857\pi$
$350$	27.3893	1.46402
$351$	−7.46164	−0.398273
$352$	−6.83850	−0.364494
$353$	2.31261	0.123088	0.0615438	−	0.998104i	$-0.480398\pi$
$353$	2.31261	0.123088	0.0615438	+	0.998104i	$0.480398\pi$
$354$	10.4162	0.553613
$355$	−32.7010	−1.73559
$356$	2.96572	0.157183
$357$	0.814734	0.0431203
$358$	−10.0944	−0.533505
$359$	8.35980	0.441214	0.220607	−	0.975363i	$-0.429196\pi$
$359$	8.35980	0.441214	0.220607	+	0.975363i	$0.429196\pi$
$360$	−10.9611	−0.577699
$361$	13.8008	0.726356
$362$	−1.02659	−0.0539564
$363$	0.655235	0.0343909
$364$	−3.66129	−0.191904
$365$	−49.6606	−2.59936
$366$	−8.33769	−0.435818
$367$	−29.1041	−1.51922	−0.759611	−	0.650377i	$-0.774611\pi$
$367$	−29.1041	−1.51922	−0.759611	+	0.650377i	$0.774611\pi$
$368$	26.5311	1.38303
$369$	16.0810	0.837142
$370$	−11.9049	−0.618904
$371$	−2.31392	−0.120133
$372$	2.76739	0.143482
$373$	−2.83225	−0.146648	−0.0733242	−	0.997308i	$-0.523361\pi$
$373$	−2.83225	−0.146648	−0.0733242	+	0.997308i	$0.523361\pi$
$374$	−1.85483	−0.0959112
$375$	18.5072	0.955708
$376$	−7.77496	−0.400963
$377$	−17.8690	−0.920298
$378$	−8.41837	−0.432994
$379$	17.6568	0.906969	0.453484	−	0.891264i	$-0.350181\pi$
$379$	17.6568	0.906969	0.453484	+	0.891264i	$0.350181\pi$
$380$	33.8889	1.73846
$381$	−7.04022	−0.360681
$382$	−1.47069	−0.0752469
$383$	22.0366	1.12602	0.563010	−	0.826450i	$-0.309643\pi$
$383$	22.0366	1.12602	0.563010	+	0.826450i	$0.309643\pi$
$384$	−5.22784	−0.266782
$385$	5.10798	0.260327
$386$	−6.11205	−0.311095
$387$	2.57067	0.130674
$388$	−9.15229	−0.464637
$389$	6.60282	0.334777	0.167388	−	0.985891i	$-0.446467\pi$
$389$	6.60282	0.334777	0.167388	+	0.985891i	$0.446467\pi$
$390$	−10.2062	−0.516809
$391$	5.52036	0.279176
$392$	−5.66088	−0.285917
$393$	−9.53988	−0.481223
$394$	−4.87479	−0.245588
$395$	25.8943	1.30289
$396$	3.70281	0.186073
$397$	2.00210	0.100482	0.0502412	−	0.998737i	$-0.484001\pi$
$397$	2.00210	0.100482	0.0502412	+	0.998737i	$0.484001\pi$
$398$	−31.4237	−1.57513
$399$	−4.66614	−0.233599
$400$	−57.0749	−2.85374
$401$	−9.69953	−0.484371	−0.242186	−	0.970230i	$-0.577864\pi$
$401$	−9.69953	−0.484371	−0.242186	+	0.970230i	$0.577864\pi$
$402$	−14.1307	−0.704774
$403$	5.99401	0.298583
$404$	11.6378	0.579004
$405$	21.8559	1.08603
$406$	−20.1601	−1.00053
$407$	−1.56239	−0.0774447
$408$	−0.680101	−0.0336700
$409$	27.9924	1.38413	0.692067	−	0.721833i	$-0.256700\pi$
$409$	27.9924	1.38413	0.692067	+	0.721833i	$0.256700\pi$
$410$	47.6652	2.35402
$411$	−1.69903	−0.0838071
$412$	−5.07256	−0.249907
$413$	10.6568	0.524385
$414$	−26.3219	−1.29365
$415$	−32.0568	−1.57361
$416$	13.9795	0.685400
$417$	−13.1511	−0.644013
$418$	10.6230	0.519588
$419$	5.97522	0.291908	0.145954	−	0.989291i	$-0.453375\pi$
$419$	5.97522	0.291908	0.145954	+	0.989291i	$0.453375\pi$
$420$	−4.82094	−0.235238
$421$	−35.5002	−1.73017	−0.865087	−	0.501622i	$-0.832737\pi$
$421$	−35.5002	−1.73017	−0.865087	+	0.501622i	$0.832737\pi$
$422$	16.9340	0.824334
$423$	19.2561	0.936262
$424$	1.93155	0.0938044
$425$	−11.8757	−0.576054
$426$	9.67459	0.468736
$427$	−8.53028	−0.412809
$428$	−13.9919	−0.676324
$429$	−1.33945	−0.0646693
$430$	7.61965	0.367452
$431$	3.16422	0.152415	0.0762074	−	0.997092i	$-0.475719\pi$
$431$	3.16422	0.152415	0.0762074	+	0.997092i	$0.475719\pi$
$432$	17.5425	0.844014
$433$	34.2592	1.64639	0.823196	−	0.567758i	$-0.192189\pi$
$433$	34.2592	1.64639	0.823196	+	0.567758i	$0.192189\pi$
$434$	6.76257	0.324614
$435$	−23.5286	−1.12811
$436$	5.57412	0.266952
$437$	−31.6162	−1.51241
$438$	14.6921	0.702016
$439$	−10.9894	−0.524497	−0.262249	−	0.965000i	$-0.584464\pi$
$439$	−10.9894	−0.524497	−0.262249	+	0.965000i	$0.584464\pi$
$440$	−4.26390	−0.203273
$441$	14.0202	0.667627
$442$	3.79171	0.180353
$443$	−25.4110	−1.20731	−0.603657	−	0.797245i	$-0.706290\pi$
$443$	−25.4110	−1.20731	−0.603657	+	0.797245i	$0.706290\pi$
$444$	1.47459	0.0699809
$445$	8.45814	0.400954
$446$	52.9090	2.50531
$447$	−7.78053	−0.368007
$448$	3.82005	0.180481
$449$	16.7522	0.790584	0.395292	−	0.918556i	$-0.370643\pi$
$449$	16.7522	0.790584	0.395292	+	0.918556i	$0.370643\pi$
$450$	56.6250	2.66933
$451$	6.25556	0.294563
$452$	23.4341	1.10225
$453$	−1.59431	−0.0749072
$454$	−6.83282	−0.320680
$455$	−10.4419	−0.489524
$456$	3.89507	0.182404
$457$	0.243385	0.0113851	0.00569254	−	0.999984i	$-0.498188\pi$
$457$	0.243385	0.0113851	0.00569254	+	0.999984i	$0.498188\pi$
$458$	−17.2874	−0.807788
$459$	3.65009	0.170372
$460$	−32.6650	−1.52301
$461$	29.2917	1.36425	0.682125	−	0.731236i	$-0.261056\pi$
$461$	29.2917	1.36425	0.682125	+	0.731236i	$0.261056\pi$
$462$	−1.51120	−0.0703072
$463$	−18.0454	−0.838641	−0.419321	−	0.907838i	$-0.637732\pi$
$463$	−18.0454	−0.838641	−0.419321	+	0.907838i	$0.637732\pi$
$464$	42.0104	1.95028
$465$	7.89250	0.366006
$466$	39.7595	1.84182
$467$	17.1839	0.795176	0.397588	−	0.917564i	$-0.369847\pi$
$467$	17.1839	0.795176	0.397588	+	0.917564i	$0.369847\pi$
$468$	−7.56939	−0.349895
$469$	−14.4571	−0.667565
$470$	57.0764	2.63274
$471$	2.47037	0.113829
$472$	−8.89575	−0.409460
$473$	1.00000	0.0459800
$474$	−7.66084	−0.351874
$475$	68.0142	3.12070
$476$	1.79104	0.0820920
$477$	−4.78382	−0.219036
$478$	47.5868	2.17657
$479$	−22.8204	−1.04269	−0.521345	−	0.853346i	$-0.674570\pi$
$479$	−22.8204	−1.04269	−0.521345	+	0.853346i	$0.674570\pi$
$480$	18.4072	0.840171
$481$	3.19388	0.145628
$482$	22.2747	1.01458
$483$	4.49762	0.204649
$484$	1.44041	0.0654731
$485$	−26.1021	−1.18523
$486$	−26.7770	−1.21463
$487$	−39.4780	−1.78892	−0.894459	−	0.447149i	$-0.852439\pi$
$487$	−39.4780	−1.78892	−0.894459	+	0.447149i	$0.852439\pi$
$488$	7.12067	0.322337
$489$	14.2904	0.646232
$490$	41.5568	1.87735
$491$	−15.8012	−0.713099	−0.356549	−	0.934277i	$-0.616047\pi$
$491$	−15.8012	−0.713099	−0.356549	+	0.934277i	$0.616047\pi$
$492$	−5.90403	−0.266174
$493$	8.74117	0.393682
$494$	−21.7158	−0.977042
$495$	10.5603	0.474650
$496$	−14.0921	−0.632753
$497$	9.89806	0.443989
$498$	9.48402	0.424989
$499$	18.2453	0.816772	0.408386	−	0.912809i	$-0.366092\pi$
$499$	18.2453	0.816772	0.408386	+	0.912809i	$0.366092\pi$
$500$	40.6846	1.81947
$501$	0.889701	0.0397489
$502$	−4.87058	−0.217385
$503$	29.5953	1.31959	0.659795	−	0.751446i	$-0.270643\pi$
$503$	29.5953	1.31959	0.659795	+	0.751446i	$0.270643\pi$
$504$	3.31774	0.147784
$505$	33.1908	1.47697
$506$	−10.2393	−0.455194
$507$	−5.77991	−0.256695
$508$	−15.4766	−0.686661
$509$	−34.0495	−1.50922	−0.754608	−	0.656176i	$-0.772173\pi$
$509$	−34.0495	−1.50922	−0.754608	+	0.656176i	$0.772173\pi$
$510$	4.99266	0.221079
$511$	15.0315	0.664952
$512$	−22.8893	−1.01157
$513$	−20.9048	−0.922970
$514$	25.3521	1.11823
$515$	−14.4668	−0.637483
$516$	−0.943805	−0.0415487
$517$	7.49069	0.329440
$518$	3.60340	0.158324
$519$	−14.8972	−0.653913
$520$	8.71640	0.382239
$521$	−3.89218	−0.170520	−0.0852599	−	0.996359i	$-0.527172\pi$
$521$	−3.89218	−0.170520	−0.0852599	+	0.996359i	$0.527172\pi$
$522$	−41.6793	−1.82425
$523$	37.8610	1.65555	0.827774	−	0.561062i	$-0.189607\pi$
$523$	37.8610	1.65555	0.827774	+	0.561062i	$0.189607\pi$
$524$	−20.9716	−0.916148
$525$	−9.67550	−0.422274
$526$	10.5477	0.459903
$527$	−2.93216	−0.127727
$528$	3.14909	0.137046
$529$	7.47433	0.324971
$530$	−14.1796	−0.615923
$531$	22.0319	0.956103
$532$	−10.2576	−0.444724
$533$	−12.7878	−0.553901
$534$	−2.50234	−0.108287
$535$	−39.9044	−1.72522
$536$	12.0681	0.521261
$537$	3.56593	0.153881
$538$	−47.8944	−2.06487
$539$	5.45390	0.234916
$540$	−21.5983	−0.929443
$541$	−34.0047	−1.46198	−0.730988	−	0.682390i	$-0.760941\pi$
$541$	−34.0047	−1.46198	−0.730988	+	0.682390i	$0.760941\pi$
$542$	8.10917	0.348319
$543$	0.362651	0.0155629
$544$	−6.83850	−0.293198
$545$	15.8972	0.680962
$546$	3.08923	0.132207
$547$	−13.2042	−0.564570	−0.282285	−	0.959331i	$-0.591092\pi$
$547$	−13.2042	−0.564570	−0.282285	+	0.959331i	$0.591092\pi$
$548$	−3.73500	−0.159551
$549$	−17.6356	−0.752668
$550$	22.0274	0.939250
$551$	−50.0624	−2.13273
$552$	−3.75440	−0.159798
$553$	−7.83779	−0.333297
$554$	28.5673	1.21371
$555$	4.20548	0.178513
$556$	−28.9102	−1.22607
$557$	−10.2731	−0.435284	−0.217642	−	0.976029i	$-0.569836\pi$
$557$	−10.2731	−0.435284	−0.217642	+	0.976029i	$0.569836\pi$
$558$	13.9810	0.591863
$559$	−2.04423	−0.0864617
$560$	24.5492	1.03739
$561$	0.655235	0.0276640
$562$	45.0676	1.90106
$563$	−18.8701	−0.795280	−0.397640	−	0.917542i	$-0.630171\pi$
$563$	−18.8701	−0.795280	−0.397640	+	0.917542i	$0.630171\pi$
$564$	−7.06975	−0.297690
$565$	66.8333	2.81170
$566$	23.2165	0.975864
$567$	−6.61543	−0.277822
$568$	−8.26243	−0.346684
$569$	21.0006	0.880391	0.440195	−	0.897902i	$-0.354909\pi$
$569$	21.0006	0.880391	0.440195	+	0.897902i	$0.354909\pi$
$570$	−28.5939	−1.19767
$571$	−10.4340	−0.436649	−0.218324	−	0.975876i	$-0.570059\pi$
$571$	−10.4340	−0.436649	−0.218324	+	0.975876i	$0.570059\pi$
$572$	−2.94453	−0.123117
$573$	0.519532	0.0217038
$574$	−14.4275	−0.602191
$575$	−65.5578	−2.73395
$576$	7.89762	0.329068
$577$	−32.8945	−1.36941	−0.684707	−	0.728818i	$-0.740070\pi$
$577$	−32.8945	−1.36941	−0.684707	+	0.728818i	$0.740070\pi$
$578$	−1.85483	−0.0771509
$579$	2.15913	0.0897304
$580$	−51.7232	−2.14769
$581$	9.70308	0.402552
$582$	7.72229	0.320099
$583$	−1.86093	−0.0770717
$584$	−12.5475	−0.519221
$585$	−21.5877	−0.892541
$586$	−53.2377	−2.19923
$587$	2.85287	0.117751	0.0588753	−	0.998265i	$-0.481249\pi$
$587$	2.85287	0.117751	0.0588753	+	0.998265i	$0.481249\pi$
$588$	−5.14742	−0.212276
$589$	16.7931	0.691946
$590$	65.3042	2.68853
$591$	1.72206	0.0708360
$592$	−7.50890	−0.308614
$593$	9.04829	0.371569	0.185784	−	0.982591i	$-0.440517\pi$
$593$	9.04829	0.371569	0.185784	+	0.982591i	$0.440517\pi$
$594$	−6.77032	−0.277790
$595$	5.10798	0.209407
$596$	−17.1040	−0.700607
$597$	11.1007	0.454320
$598$	20.9316	0.855956
$599$	−4.43690	−0.181287	−0.0906434	−	0.995883i	$-0.528892\pi$
$599$	−4.43690	−0.181287	−0.0906434	+	0.995883i	$0.528892\pi$
$600$	8.07665	0.329728
$601$	5.40516	0.220481	0.110240	−	0.993905i	$-0.464838\pi$
$601$	5.40516	0.220481	0.110240	+	0.993905i	$0.464838\pi$
$602$	−2.30634	−0.0939996
$603$	−29.8887	−1.21716
$604$	−3.50478	−0.142608
$605$	4.10800	0.167014
$606$	−9.81949	−0.398890
$607$	30.9503	1.25623	0.628117	−	0.778119i	$-0.283826\pi$
$607$	30.9503	1.25623	0.628117	+	0.778119i	$0.283826\pi$
$608$	39.1654	1.58837
$609$	7.12173	0.288587
$610$	−52.2732	−2.11648
$611$	−15.3127	−0.619485
$612$	3.70281	0.149677
$613$	41.1320	1.66130	0.830652	−	0.556792i	$-0.187968\pi$
$613$	41.1320	1.66130	0.830652	+	0.556792i	$0.187968\pi$
$614$	0.342770	0.0138331
$615$	−16.8381	−0.678978
$616$	1.29061	0.0520003
$617$	9.43884	0.379993	0.189997	−	0.981785i	$-0.439152\pi$
$617$	9.43884	0.379993	0.189997	+	0.981785i	$0.439152\pi$
$618$	4.28000	0.172167
$619$	−18.4197	−0.740349	−0.370175	−	0.928962i	$-0.620702\pi$
$619$	−18.4197	−0.740349	−0.370175	+	0.928962i	$0.620702\pi$
$620$	17.3502	0.696799
$621$	20.1498	0.808585
$622$	−27.5235	−1.10359
$623$	−2.56014	−0.102570
$624$	−6.43746	−0.257704
$625$	56.6528	2.26611
$626$	−26.5855	−1.06257
$627$	−3.75266	−0.149867
$628$	5.43063	0.216706
$629$	−1.56239	−0.0622965
$630$	−24.3557	−0.970353
$631$	4.51522	0.179748	0.0898739	−	0.995953i	$-0.471354\pi$
$631$	4.51522	0.179748	0.0898739	+	0.995953i	$0.471354\pi$
$632$	6.54261	0.260251
$633$	−5.98207	−0.237766
$634$	−5.53928	−0.219993
$635$	−44.1387	−1.75159
$636$	1.75635	0.0696439
$637$	−11.1490	−0.441740
$638$	−16.2134	−0.641895
$639$	20.4633	0.809518
$640$	−32.7760	−1.29558
$641$	−41.7113	−1.64750	−0.823748	−	0.566956i	$-0.808121\pi$
$641$	−41.7113	−1.64750	−0.823748	+	0.566956i	$0.808121\pi$
$642$	11.8057	0.465935
$643$	−33.9006	−1.33691	−0.668454	−	0.743753i	$-0.733044\pi$
$643$	−33.9006	−1.33691	−0.668454	+	0.743753i	$0.733044\pi$
$644$	9.88716	0.389609
$645$	−2.69170	−0.105986
$646$	10.6230	0.417956
$647$	−36.7380	−1.44432	−0.722161	−	0.691725i	$-0.756851\pi$
$647$	−36.7380	−1.44432	−0.722161	+	0.691725i	$0.756851\pi$
$648$	5.52224	0.216934
$649$	8.57050	0.336421
$650$	−45.0290	−1.76618
$651$	−2.38893	−0.0936296
$652$	31.4146	1.23029
$653$	−41.3608	−1.61857	−0.809287	−	0.587413i	$-0.800146\pi$
$653$	−41.3608	−1.61857	−0.809287	+	0.587413i	$0.800146\pi$
$654$	−4.70319	−0.183909
$655$	−59.8103	−2.33698
$656$	30.0645	1.17382
$657$	31.0762	1.21240
$658$	−17.2761	−0.673492
$659$	24.9762	0.972936	0.486468	−	0.873698i	$-0.338285\pi$
$659$	24.9762	0.972936	0.486468	+	0.873698i	$0.338285\pi$
$660$	−3.87715	−0.150918
$661$	8.75996	0.340723	0.170361	−	0.985382i	$-0.445506\pi$
$661$	8.75996	0.340723	0.170361	+	0.985382i	$0.445506\pi$
$662$	−51.1153	−1.98665
$663$	−1.33945	−0.0520200
$664$	−8.09967	−0.314328
$665$	−29.2544	−1.13444
$666$	7.44972	0.288671
$667$	48.2544	1.86842
$668$	1.95584	0.0756736
$669$	−18.6905	−0.722617
$670$	−88.5923	−3.42262
$671$	−6.86031	−0.264839
$672$	−5.57156	−0.214928
$673$	13.3231	0.513570	0.256785	−	0.966469i	$-0.417337\pi$
$673$	13.3231	0.513570	0.256785	+	0.966469i	$0.417337\pi$
$674$	0.524359	0.0201976
$675$	−43.3473	−1.66844
$676$	−12.7060	−0.488693
$677$	4.86560	0.187000	0.0935001	−	0.995619i	$-0.470194\pi$
$677$	4.86560	0.187000	0.0935001	+	0.995619i	$0.470194\pi$
$678$	−19.7726	−0.759364
$679$	7.90066	0.303200
$680$	−4.26390	−0.163513
$681$	2.41375	0.0924951
$682$	5.43867	0.208257
$683$	15.1521	0.579780	0.289890	−	0.957060i	$-0.406381\pi$
$683$	15.1521	0.579780	0.289890	+	0.957060i	$0.406381\pi$
$684$	−21.2067	−0.810859
$685$	−10.6521	−0.406996
$686$	−28.7230	−1.09665
$687$	6.10692	0.232993
$688$	4.80604	0.183229
$689$	3.80416	0.144927
$690$	27.5613	1.04924
$691$	0.533417	0.0202921	0.0101461	−	0.999949i	$-0.496770\pi$
$691$	0.533417	0.0202921	0.0101461	+	0.999949i	$0.496770\pi$
$692$	−32.7486	−1.24491
$693$	−3.19643	−0.121422
$694$	10.8572	0.412134
$695$	−82.4511	−3.12755
$696$	−5.94488	−0.225340
$697$	6.25556	0.236946
$698$	−23.5046	−0.889662
$699$	−14.0454	−0.531244
$700$	−21.2697	−0.803920
$701$	−15.2661	−0.576594	−0.288297	−	0.957541i	$-0.593089\pi$
$701$	−15.2661	−0.576594	−0.288297	+	0.957541i	$0.593089\pi$
$702$	13.8401	0.522361
$703$	8.94810	0.337484
$704$	3.07221	0.115788
$705$	−20.1627	−0.759371
$706$	−4.28950	−0.161437
$707$	−10.0463	−0.377830
$708$	−8.08888	−0.303999
$709$	23.1022	0.867621	0.433811	−	0.901004i	$-0.357169\pi$
$709$	23.1022	0.867621	0.433811	+	0.901004i	$0.357169\pi$
$710$	60.6549	2.27634
$711$	−16.2039	−0.607695
$712$	2.13708	0.0800905
$713$	−16.1866	−0.606192
$714$	−1.51120	−0.0565551
$715$	−8.39770	−0.314056
$716$	7.83900	0.292957
$717$	−16.8104	−0.627796
$718$	−15.5060	−0.578680
$719$	−16.1498	−0.602285	−0.301143	−	0.953579i	$-0.597368\pi$
$719$	−16.1498	−0.602285	−0.301143	+	0.953579i	$0.597368\pi$
$720$	50.7532	1.89146
$721$	4.37886	0.163077
$722$	−25.5981	−0.952663
$723$	−7.86872	−0.292641
$724$	0.797219	0.0296284
$725$	−103.807	−3.85530
$726$	−1.21535	−0.0451059
$727$	8.82634	0.327351	0.163675	−	0.986514i	$-0.447665\pi$
$727$	8.82634	0.327351	0.163675	+	0.986514i	$0.447665\pi$
$728$	−2.63831	−0.0977823
$729$	−6.50180	−0.240807
$730$	92.1122	3.40923
$731$	1.00000	0.0369863
$732$	6.47480	0.239315
$733$	48.1676	1.77911	0.889555	−	0.456829i	$-0.151015\pi$
$733$	48.1676	1.77911	0.889555	+	0.456829i	$0.151015\pi$
$734$	53.9833	1.99256
$735$	−14.6803	−0.541490
$736$	−37.7510	−1.39152
$737$	−11.6268	−0.428279
$738$	−29.8275	−1.09797
$739$	30.3296	1.11569	0.557846	−	0.829944i	$-0.311628\pi$
$739$	30.3296	1.11569	0.557846	+	0.829944i	$0.311628\pi$
$740$	9.24495	0.339851
$741$	7.67130	0.281812
$742$	4.29194	0.157562
$743$	4.69039	0.172074	0.0860368	−	0.996292i	$-0.472580\pi$
$743$	4.69039	0.172074	0.0860368	+	0.996292i	$0.472580\pi$
$744$	1.99417	0.0731097
$745$	−48.7801	−1.78716
$746$	5.25336	0.192339
$747$	20.0602	0.733966
$748$	1.44041	0.0526665
$749$	12.0784	0.441336
$750$	−34.3278	−1.25347
$751$	−41.7424	−1.52320	−0.761601	−	0.648046i	$-0.775587\pi$
$751$	−41.7424	−1.52320	−0.761601	+	0.648046i	$0.775587\pi$
$752$	36.0005	1.31280
$753$	1.72057	0.0627011
$754$	33.1440	1.20703
$755$	−9.99554	−0.363775
$756$	6.53745	0.237765
$757$	40.7576	1.48136	0.740680	−	0.671858i	$-0.234503\pi$
$757$	40.7576	1.48136	0.740680	+	0.671858i	$0.234503\pi$
$758$	−32.7504	−1.18955
$759$	3.61713	0.131293
$760$	24.4202	0.885813
$761$	−24.3814	−0.883824	−0.441912	−	0.897059i	$-0.645700\pi$
$761$	−24.3814	−0.883824	−0.441912	+	0.897059i	$0.645700\pi$
$762$	13.0584	0.473057
$763$	−4.81182	−0.174200
$764$	1.14209	0.0413194
$765$	10.5603	0.381808
$766$	−40.8743	−1.47685
$767$	−17.5201	−0.632613
$768$	13.7228	0.495179
$769$	−17.8909	−0.645162	−0.322581	−	0.946542i	$-0.604551\pi$
$769$	−17.8909	−0.645162	−0.322581	+	0.946542i	$0.604551\pi$
$770$	−9.47446	−0.341436
$771$	−8.95583	−0.322536
$772$	4.74643	0.170828
$773$	37.3850	1.34464	0.672322	−	0.740259i	$-0.265297\pi$
$773$	37.3850	1.34464	0.672322	+	0.740259i	$0.265297\pi$
$774$	−4.76816	−0.171388
$775$	34.8213	1.25082
$776$	−6.59510	−0.236750
$777$	−1.27293	−0.0456661
$778$	−12.2471	−0.439081
$779$	−35.8268	−1.28363
$780$	7.92579	0.283789
$781$	7.96033	0.284843
$782$	−10.2393	−0.366158
$783$	31.9061	1.14023
$784$	26.2117	0.936131
$785$	15.4880	0.552790
$786$	17.6949	0.631156
$787$	−42.9548	−1.53117	−0.765586	−	0.643333i	$-0.777551\pi$
$787$	−42.9548	−1.53117	−0.765586	+	0.643333i	$0.777551\pi$
$788$	3.78562	0.134857
$789$	−3.72607	−0.132652
$790$	−48.0297	−1.70882
$791$	−20.2294	−0.719273
$792$	2.66823	0.0948113
$793$	14.0241	0.498009
$794$	−3.71355	−0.131789
$795$	5.00906	0.177653
$796$	24.4027	0.864929
$797$	−38.1922	−1.35284	−0.676418	−	0.736518i	$-0.736469\pi$
$797$	−38.1922	−1.35284	−0.676418	+	0.736518i	$0.736469\pi$
$798$	8.65492	0.306381
$799$	7.49069	0.265001
$800$	81.2117	2.87127
$801$	−5.29286	−0.187014
$802$	17.9910	0.635285
$803$	12.0888	0.426603
$804$	10.9735	0.387004
$805$	28.1979	0.993845
$806$	−11.1179	−0.391611
$807$	16.9191	0.595580
$808$	8.38617	0.295025
$809$	−22.2887	−0.783629	−0.391814	−	0.920044i	$-0.628152\pi$
$809$	−22.2887	−0.783629	−0.391814	+	0.920044i	$0.628152\pi$
$810$	−40.5391	−1.42440
$811$	11.7272	0.411799	0.205899	−	0.978573i	$-0.433988\pi$
$811$	11.7272	0.411799	0.205899	+	0.978573i	$0.433988\pi$
$812$	15.6558	0.549409
$813$	−2.86463	−0.100467
$814$	2.89797	0.101574
$815$	89.5935	3.13832
$816$	3.14909	0.110240
$817$	−5.72719	−0.200369
$818$	−51.9212	−1.81538
$819$	6.53424	0.228325
$820$	−37.0154	−1.29263
$821$	−45.5258	−1.58886	−0.794430	−	0.607355i	$-0.792230\pi$
$821$	−45.5258	−1.58886	−0.794430	+	0.607355i	$0.792230\pi$
$822$	3.15142	0.109918
$823$	−48.1450	−1.67823	−0.839115	−	0.543955i	$-0.816926\pi$
$823$	−48.1450	−1.67823	−0.839115	+	0.543955i	$0.816926\pi$
$824$	−3.65527	−0.127337
$825$	−7.78134	−0.270911
$826$	−19.7665	−0.687765
$827$	−16.2434	−0.564838	−0.282419	−	0.959291i	$-0.591137\pi$
$827$	−16.2434	−0.564838	−0.282419	+	0.959291i	$0.591137\pi$
$828$	20.4408	0.710368
$829$	19.7099	0.684552	0.342276	−	0.939599i	$-0.388802\pi$
$829$	19.7099	0.684552	0.342276	+	0.939599i	$0.388802\pi$
$830$	59.4601	2.06389
$831$	−10.0916	−0.350075
$832$	−6.28030	−0.217730
$833$	5.45390	0.188966
$834$	24.3932	0.844666
$835$	5.57799	0.193034
$836$	−8.24949	−0.285315
$837$	−10.7027	−0.369938
$838$	−11.0830	−0.382857
$839$	−21.7476	−0.750811	−0.375406	−	0.926861i	$-0.622497\pi$
$839$	−21.7476	−0.750811	−0.375406	+	0.926861i	$0.622497\pi$
$840$	−3.47395	−0.119863
$841$	47.4080	1.63476
$842$	65.8470	2.26924
$843$	−15.9205	−0.548331
$844$	−13.1504	−0.452656
$845$	−36.2372	−1.24660
$846$	−35.7168	−1.22797
$847$	−1.24342	−0.0427245
$848$	−8.94369	−0.307128
$849$	−8.20143	−0.281472
$850$	22.0274	0.755532
$851$	−8.62494	−0.295659
$852$	−7.51300	−0.257391
$853$	2.31018	0.0790989	0.0395494	−	0.999218i	$-0.487408\pi$
$853$	2.31018	0.0790989	0.0395494	+	0.999218i	$0.487408\pi$
$854$	15.8222	0.541426
$855$	−60.4809	−2.06840
$856$	−10.0825	−0.344612
$857$	30.6874	1.04826	0.524131	−	0.851638i	$-0.324390\pi$
$857$	30.6874	1.04826	0.524131	+	0.851638i	$0.324390\pi$
$858$	2.48446	0.0848180
$859$	−25.5723	−0.872516	−0.436258	−	0.899822i	$-0.643697\pi$
$859$	−25.5723	−0.872516	−0.436258	+	0.899822i	$0.643697\pi$
$860$	−5.91719	−0.201775
$861$	5.09662	0.173692
$862$	−5.86909	−0.199902
$863$	36.6473	1.24749	0.623745	−	0.781628i	$-0.285610\pi$
$863$	36.6473	1.24749	0.623745	+	0.781628i	$0.285610\pi$
$864$	−24.9612	−0.849197
$865$	−93.3979	−3.17562
$866$	−63.5451	−2.15935
$867$	0.655235	0.0222529
$868$	−5.25161	−0.178251
$869$	−6.30339	−0.213828
$870$	43.6417	1.47959
$871$	23.7679	0.805344
$872$	4.01668	0.136022
$873$	16.3339	0.552819
$874$	58.6427	1.98362
$875$	−35.1207	−1.18730
$876$	−11.4094	−0.385489
$877$	−39.7705	−1.34296	−0.671478	−	0.741025i	$-0.734340\pi$
$877$	−39.7705	−1.34296	−0.671478	+	0.741025i	$0.734340\pi$
$878$	20.3836	0.687912
$879$	18.8066	0.634332
$880$	19.7432	0.665543
$881$	−34.4179	−1.15957	−0.579783	−	0.814771i	$-0.696863\pi$
$881$	−34.4179	−1.15957	−0.579783	+	0.814771i	$0.696863\pi$
$882$	−26.0051	−0.875636
$883$	−40.8671	−1.37529	−0.687643	−	0.726049i	$-0.741355\pi$
$883$	−40.8671	−1.37529	−0.687643	+	0.726049i	$0.741355\pi$
$884$	−2.94453	−0.0990351
$885$	−23.0692	−0.775464
$886$	47.1332	1.58347
$887$	−5.93180	−0.199170	−0.0995852	−	0.995029i	$-0.531752\pi$
$887$	−5.93180	−0.199170	−0.0995852	+	0.995029i	$0.531752\pi$
$888$	1.06258	0.0356579
$889$	13.3601	0.448082
$890$	−15.6884	−0.525877
$891$	−5.32033	−0.178238
$892$	−41.0875	−1.37571
$893$	−42.9006	−1.43561
$894$	14.4316	0.482665
$895$	22.3566	0.747299
$896$	9.92075	0.331429
$897$	−7.39425	−0.246887
$898$	−31.0725	−1.03690
$899$	−25.6305	−0.854825
$900$	−43.9733	−1.46578
$901$	−1.86093	−0.0619965
$902$	−11.6030	−0.386338
$903$	0.814734	0.0271127
$904$	16.8865	0.561637
$905$	2.27364	0.0755785
$906$	2.95718	0.0982457
$907$	−15.7301	−0.522311	−0.261155	−	0.965297i	$-0.584103\pi$
$907$	−15.7301	−0.522311	−0.261155	+	0.965297i	$0.584103\pi$
$908$	5.30616	0.176091
$909$	−20.7698	−0.688892
$910$	19.3680	0.642042
$911$	54.9890	1.82187	0.910934	−	0.412552i	$-0.135363\pi$
$911$	54.9890	1.82187	0.910934	+	0.412552i	$0.135363\pi$
$912$	−18.0354	−0.597213
$913$	7.80352	0.258259
$914$	−0.451439	−0.0149323
$915$	18.4659	0.610465
$916$	13.4249	0.443570
$917$	18.1036	0.597834
$918$	−6.77032	−0.223454
$919$	−11.4712	−0.378399	−0.189199	−	0.981939i	$-0.560589\pi$
$919$	−11.4712	−0.378399	−0.189199	+	0.981939i	$0.560589\pi$
$920$	−23.5382	−0.776033
$921$	−0.121086	−0.00398993
$922$	−54.3312	−1.78930
$923$	−16.2727	−0.535624
$924$	1.17355	0.0386069
$925$	18.5544	0.610064
$926$	33.4712	1.09993
$927$	9.05291	0.297337
$928$	−59.7765	−1.96226
$929$	49.9260	1.63802	0.819009	−	0.573781i	$-0.194524\pi$
$929$	49.9260	1.63802	0.819009	+	0.573781i	$0.194524\pi$
$930$	−14.6393	−0.480041
$931$	−31.2355	−1.02370
$932$	−30.8760	−1.01138
$933$	9.72288	0.318313
$934$	−31.8733	−1.04293
$935$	4.10800	0.134346
$936$	−5.45447	−0.178285
$937$	−26.9071	−0.879018	−0.439509	−	0.898238i	$-0.644848\pi$
$937$	−26.9071	−0.879018	−0.439509	+	0.898238i	$0.644848\pi$
$938$	26.8154	0.875555
$939$	9.39154	0.306481
$940$	−44.3238	−1.44568
$941$	−21.3862	−0.697169	−0.348585	−	0.937277i	$-0.613338\pi$
$941$	−21.3862	−0.697169	−0.348585	+	0.937277i	$0.613338\pi$
$942$	−4.58212	−0.149294
$943$	34.5329	1.12455
$944$	41.1902	1.34063
$945$	18.6446	0.606510
$946$	−1.85483	−0.0603058
$947$	−2.58087	−0.0838670	−0.0419335	−	0.999120i	$-0.513352\pi$
$947$	−2.58087	−0.0838670	−0.0419335	+	0.999120i	$0.513352\pi$
$948$	5.94917	0.193220
$949$	−24.7122	−0.802193
$950$	−126.155	−4.09301
$951$	1.95680	0.0634534
$952$	1.29061	0.0418290
$953$	−23.1739	−0.750677	−0.375338	−	0.926888i	$-0.622473\pi$
$953$	−23.1739	−0.750677	−0.375338	+	0.926888i	$0.622473\pi$
$954$	8.87320	0.287280
$955$	3.25721	0.105401
$956$	−36.9545	−1.19519
$957$	5.72752	0.185144
$958$	42.3280	1.36756
$959$	3.22421	0.104115
$960$	−8.26947	−0.266896
$961$	−22.4024	−0.722659
$962$	−5.92412	−0.191001
$963$	24.9711	0.804681
$964$	−17.2979	−0.557127
$965$	13.5367	0.435761
$966$	−8.34234	−0.268410
$967$	33.9606	1.09210	0.546050	−	0.837752i	$-0.316131\pi$
$967$	33.9606	1.09210	0.546050	+	0.837752i	$0.316131\pi$
$968$	1.03795	0.0333610
$969$	−3.75266	−0.120553
$970$	48.4150	1.55451
$971$	−10.4918	−0.336698	−0.168349	−	0.985727i	$-0.553844\pi$
$971$	−10.4918	−0.336698	−0.168349	+	0.985727i	$0.553844\pi$
$972$	20.7942	0.666975
$973$	24.9566	0.800071
$974$	73.2251	2.34628
$975$	15.9069	0.509427
$976$	−32.9709	−1.05537
$977$	24.1691	0.773238	0.386619	−	0.922240i	$-0.373643\pi$
$977$	24.1691	0.773238	0.386619	+	0.922240i	$0.373643\pi$
$978$	−26.5062	−0.847576
$979$	−2.05894	−0.0658041
$980$	−32.2718	−1.03088
$981$	−9.94802	−0.317616
$982$	29.3086	0.935275
$983$	−36.9801	−1.17948	−0.589740	−	0.807593i	$-0.700770\pi$
$983$	−36.9801	−1.17948	−0.589740	+	0.807593i	$0.700770\pi$
$984$	−4.25442	−0.135626
$985$	10.7965	0.344004
$986$	−16.2134	−0.516340
$987$	6.10292	0.194258
$988$	16.8639	0.536511
$989$	5.52036	0.175537
$990$	−19.5876	−0.622535
$991$	−29.4127	−0.934325	−0.467162	−	0.884172i	$-0.654724\pi$
$991$	−29.4127	−0.934325	−0.467162	+	0.884172i	$0.654724\pi$
$992$	20.0516	0.636639
$993$	18.0569	0.573017
$994$	−18.3592	−0.582320
$995$	69.5956	2.20633
$996$	−7.36500	−0.233369
$997$	11.5880	0.366997	0.183499	−	0.983020i	$-0.441258\pi$
$997$	11.5880	0.366997	0.183499	+	0.983020i	$0.441258\pi$
$998$	−33.8420	−1.07125
$999$	−5.70286	−0.180431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.17	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.17	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85483 q^{2} +0.655235 q^{3} +1.44041 q^{4} +4.10800 q^{5} -1.21535 q^{6} -1.24342 q^{7} +1.03795 q^{8} -2.57067 q^{9} +O(q^{10})\)	\(q-1.85483 q^{2} +0.655235 q^{3} +1.44041 q^{4} +4.10800 q^{5} -1.21535 q^{6} -1.24342 q^{7} +1.03795 q^{8} -2.57067 q^{9} -7.61965 q^{10} -1.00000 q^{11} +0.943805 q^{12} +2.04423 q^{13} +2.30634 q^{14} +2.69170 q^{15} -4.80604 q^{16} -1.00000 q^{17} +4.76816 q^{18} +5.72719 q^{19} +5.91719 q^{20} -0.814734 q^{21} +1.85483 q^{22} -5.52036 q^{23} +0.680101 q^{24} +11.8757 q^{25} -3.79171 q^{26} -3.65009 q^{27} -1.79104 q^{28} -8.74117 q^{29} -4.99266 q^{30} +2.93216 q^{31} +6.83850 q^{32} -0.655235 q^{33} +1.85483 q^{34} -5.10798 q^{35} -3.70281 q^{36} +1.56239 q^{37} -10.6230 q^{38} +1.33945 q^{39} +4.26390 q^{40} -6.25556 q^{41} +1.51120 q^{42} -1.00000 q^{43} -1.44041 q^{44} -10.5603 q^{45} +10.2393 q^{46} -7.49069 q^{47} -3.14909 q^{48} -5.45390 q^{49} -22.0274 q^{50} -0.655235 q^{51} +2.94453 q^{52} +1.86093 q^{53} +6.77032 q^{54} -4.10800 q^{55} -1.29061 q^{56} +3.75266 q^{57} +16.2134 q^{58} -8.57050 q^{59} +3.87715 q^{60} +6.86031 q^{61} -5.43867 q^{62} +3.19643 q^{63} -3.07221 q^{64} +8.39770 q^{65} +1.21535 q^{66} +11.6268 q^{67} -1.44041 q^{68} -3.61713 q^{69} +9.47446 q^{70} -7.96033 q^{71} -2.66823 q^{72} -12.0888 q^{73} -2.89797 q^{74} +7.78134 q^{75} +8.24949 q^{76} +1.24342 q^{77} -2.48446 q^{78} +6.30339 q^{79} -19.7432 q^{80} +5.32033 q^{81} +11.6030 q^{82} -7.80352 q^{83} -1.17355 q^{84} -4.10800 q^{85} +1.85483 q^{86} -5.72752 q^{87} -1.03795 q^{88} +2.05894 q^{89} +19.5876 q^{90} -2.54184 q^{91} -7.95156 q^{92} +1.92125 q^{93} +13.8940 q^{94} +23.5273 q^{95} +4.48083 q^{96} -6.35396 q^{97} +10.1161 q^{98} +2.57067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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