LMFDB - Embedded newform 8041.2.a.h.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.65828 q^{2} +2.25599 q^{3} +5.06647 q^{4} +2.74441 q^{5} -5.99706 q^{6} +1.84456 q^{7} -8.15154 q^{8} +2.08950 q^{9} +O(q^{10})$	\(q-2.65828 q^{2} +2.25599 q^{3} +5.06647 q^{4} +2.74441 q^{5} -5.99706 q^{6} +1.84456 q^{7} -8.15154 q^{8} +2.08950 q^{9} -7.29541 q^{10} -1.00000 q^{11} +11.4299 q^{12} -5.90020 q^{13} -4.90337 q^{14} +6.19135 q^{15} +11.5362 q^{16} -1.00000 q^{17} -5.55447 q^{18} -6.30370 q^{19} +13.9044 q^{20} +4.16132 q^{21} +2.65828 q^{22} +7.21197 q^{23} -18.3898 q^{24} +2.53176 q^{25} +15.6844 q^{26} -2.05409 q^{27} +9.34542 q^{28} -5.57082 q^{29} -16.4584 q^{30} -0.294044 q^{31} -14.3633 q^{32} -2.25599 q^{33} +2.65828 q^{34} +5.06223 q^{35} +10.5864 q^{36} -5.32041 q^{37} +16.7570 q^{38} -13.3108 q^{39} -22.3711 q^{40} -2.46037 q^{41} -11.0620 q^{42} -1.00000 q^{43} -5.06647 q^{44} +5.73443 q^{45} -19.1715 q^{46} -9.59119 q^{47} +26.0255 q^{48} -3.59759 q^{49} -6.73013 q^{50} -2.25599 q^{51} -29.8932 q^{52} +7.96143 q^{53} +5.46035 q^{54} -2.74441 q^{55} -15.0360 q^{56} -14.2211 q^{57} +14.8088 q^{58} -5.30229 q^{59} +31.3683 q^{60} +4.14825 q^{61} +0.781653 q^{62} +3.85421 q^{63} +15.1094 q^{64} -16.1925 q^{65} +5.99706 q^{66} +1.59057 q^{67} -5.06647 q^{68} +16.2701 q^{69} -13.4568 q^{70} +7.26949 q^{71} -17.0326 q^{72} -3.19520 q^{73} +14.1432 q^{74} +5.71163 q^{75} -31.9375 q^{76} -1.84456 q^{77} +35.3839 q^{78} +17.3824 q^{79} +31.6599 q^{80} -10.9025 q^{81} +6.54035 q^{82} +6.99529 q^{83} +21.0832 q^{84} -2.74441 q^{85} +2.65828 q^{86} -12.5677 q^{87} +8.15154 q^{88} -10.3573 q^{89} -15.2437 q^{90} -10.8833 q^{91} +36.5392 q^{92} -0.663361 q^{93} +25.4961 q^{94} -17.2999 q^{95} -32.4035 q^{96} -15.4225 q^{97} +9.56341 q^{98} -2.08950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65828	−1.87969	−0.939845	−	0.341601i	$-0.889031\pi$
$2$	−2.65828	−1.87969	−0.939845	+	0.341601i	$0.889031\pi$
$3$	2.25599	1.30250	0.651249	−	0.758864i	$-0.274246\pi$
$3$	2.25599	1.30250	0.651249	+	0.758864i	$0.274246\pi$
$4$	5.06647	2.53323
$5$	2.74441	1.22734	0.613668	−	0.789564i	$-0.289693\pi$
$5$	2.74441	1.22734	0.613668	+	0.789564i	$0.289693\pi$
$6$	−5.99706	−2.44829
$7$	1.84456	0.697179	0.348590	−	0.937275i	$-0.386661\pi$
$7$	1.84456	0.697179	0.348590	+	0.937275i	$0.386661\pi$
$8$	−8.15154	−2.88201
$9$	2.08950	0.696499
$10$	−7.29541	−2.30701
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	11.4299	3.29953
$13$	−5.90020	−1.63642	−0.818210	−	0.574919i	$-0.805034\pi$
$13$	−5.90020	−1.63642	−0.818210	+	0.574919i	$0.805034\pi$
$14$	−4.90337	−1.31048
$15$	6.19135	1.59860
$16$	11.5362	2.88404
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.55447	−1.30920
$19$	−6.30370	−1.44617	−0.723084	−	0.690760i	$-0.757276\pi$
$19$	−6.30370	−1.44617	−0.723084	+	0.690760i	$0.757276\pi$
$20$	13.9044	3.10913
$21$	4.16132	0.908074
$22$	2.65828	0.566748
$23$	7.21197	1.50380	0.751900	−	0.659277i	$-0.229138\pi$
$23$	7.21197	1.50380	0.751900	+	0.659277i	$0.229138\pi$
$24$	−18.3898	−3.75380
$25$	2.53176	0.506352
$26$	15.6844	3.07596
$27$	−2.05409	−0.395309
$28$	9.34542	1.76612
$29$	−5.57082	−1.03447	−0.517237	−	0.855842i	$-0.673040\pi$
$29$	−5.57082	−1.03447	−0.517237	+	0.855842i	$0.673040\pi$
$30$	−16.4584	−3.00487
$31$	−0.294044	−0.0528119	−0.0264060	−	0.999651i	$-0.508406\pi$
$31$	−0.294044	−0.0528119	−0.0264060	+	0.999651i	$0.508406\pi$
$32$	−14.3633	−2.53910
$33$	−2.25599	−0.392718
$34$	2.65828	0.455892
$35$	5.06223	0.855673
$36$	10.5864	1.76440
$37$	−5.32041	−0.874671	−0.437335	−	0.899299i	$-0.644078\pi$
$37$	−5.32041	−0.874671	−0.437335	+	0.899299i	$0.644078\pi$
$38$	16.7570	2.71835
$39$	−13.3108	−2.13143
$40$	−22.3711	−3.53719
$41$	−2.46037	−0.384245	−0.192122	−	0.981371i	$-0.561537\pi$
$41$	−2.46037	−0.384245	−0.192122	+	0.981371i	$0.561537\pi$
$42$	−11.0620	−1.70690
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−5.06647	−0.763799
$45$	5.73443	0.854838
$46$	−19.1715	−2.82668
$47$	−9.59119	−1.39902	−0.699509	−	0.714624i	$-0.746598\pi$
$47$	−9.59119	−1.39902	−0.699509	+	0.714624i	$0.746598\pi$
$48$	26.0255	3.75646
$49$	−3.59759	−0.513941
$50$	−6.73013	−0.951784
$51$	−2.25599	−0.315902
$52$	−29.8932	−4.14544
$53$	7.96143	1.09359	0.546793	−	0.837268i	$-0.315848\pi$
$53$	7.96143	1.09359	0.546793	+	0.837268i	$0.315848\pi$
$54$	5.46035	0.743059
$55$	−2.74441	−0.370056
$56$	−15.0360	−2.00927
$57$	−14.2211	−1.88363
$58$	14.8088	1.94449
$59$	−5.30229	−0.690300	−0.345150	−	0.938548i	$-0.612172\pi$
$59$	−5.30229	−0.690300	−0.345150	+	0.938548i	$0.612172\pi$
$60$	31.3683	4.04963
$61$	4.14825	0.531129	0.265564	−	0.964093i	$-0.414442\pi$
$61$	4.14825	0.531129	0.265564	+	0.964093i	$0.414442\pi$
$62$	0.781653	0.0992700
$63$	3.85421	0.485585
$64$	15.1094	1.88868
$65$	−16.1925	−2.00844
$66$	5.99706	0.738187
$67$	1.59057	0.194319	0.0971593	−	0.995269i	$-0.469024\pi$
$67$	1.59057	0.194319	0.0971593	+	0.995269i	$0.469024\pi$
$68$	−5.06647	−0.614400
$69$	16.2701	1.95870
$70$	−13.4568	−1.60840
$71$	7.26949	0.862729	0.431365	−	0.902178i	$-0.358032\pi$
$71$	7.26949	0.862729	0.431365	+	0.902178i	$0.358032\pi$
$72$	−17.0326	−2.00731
$73$	−3.19520	−0.373970	−0.186985	−	0.982363i	$-0.559872\pi$
$73$	−3.19520	−0.373970	−0.186985	+	0.982363i	$0.559872\pi$
$74$	14.1432	1.64411
$75$	5.71163	0.659522
$76$	−31.9375	−3.66348
$77$	−1.84456	−0.210207
$78$	35.3839	4.00643
$79$	17.3824	1.95567	0.977837	−	0.209369i	$-0.0671410\pi$
$79$	17.3824	1.95567	0.977837	+	0.209369i	$0.0671410\pi$
$80$	31.6599	3.53969
$81$	−10.9025	−1.21139
$82$	6.54035	0.722261
$83$	6.99529	0.767833	0.383916	−	0.923368i	$-0.374575\pi$
$83$	6.99529	0.767833	0.383916	+	0.923368i	$0.374575\pi$
$84$	21.0832	2.30036
$85$	−2.74441	−0.297673
$86$	2.65828	0.286650
$87$	−12.5677	−1.34740
$88$	8.15154	0.868957
$89$	−10.3573	−1.09788	−0.548938	−	0.835863i	$-0.684968\pi$
$89$	−10.3573	−1.09788	−0.548938	+	0.835863i	$0.684968\pi$
$90$	−15.2437	−1.60683
$91$	−10.8833	−1.14088
$92$	36.5392	3.80948
$93$	−0.663361	−0.0687874
$94$	25.4961	2.62972
$95$	−17.2999	−1.77493
$96$	−32.4035	−3.30717
$97$	−15.4225	−1.56592	−0.782959	−	0.622074i	$-0.786290\pi$
$97$	−15.4225	−1.56592	−0.782959	+	0.622074i	$0.786290\pi$
$98$	9.56341	0.966050
$99$	−2.08950	−0.210002
$100$	12.8271	1.28271
$101$	−2.57096	−0.255820	−0.127910	−	0.991786i	$-0.540827\pi$
$101$	−2.57096	−0.255820	−0.127910	+	0.991786i	$0.540827\pi$
$102$	5.99706	0.593798
$103$	17.2294	1.69767	0.848834	−	0.528660i	$-0.177305\pi$
$103$	17.2294	1.69767	0.848834	+	0.528660i	$0.177305\pi$
$104$	48.0957	4.71617
$105$	11.4203	1.11451
$106$	−21.1637	−2.05560
$107$	−14.9597	−1.44621	−0.723104	−	0.690739i	$-0.757285\pi$
$107$	−14.9597	−1.44621	−0.723104	+	0.690739i	$0.757285\pi$
$108$	−10.4070	−1.00141
$109$	9.12468	0.873985	0.436993	−	0.899465i	$-0.356044\pi$
$109$	9.12468	0.873985	0.436993	+	0.899465i	$0.356044\pi$
$110$	7.29541	0.695590
$111$	−12.0028	−1.13926
$112$	21.2792	2.01069
$113$	−1.91845	−0.180473	−0.0902363	−	0.995920i	$-0.528762\pi$
$113$	−1.91845	−0.180473	−0.0902363	+	0.995920i	$0.528762\pi$
$114$	37.8037	3.54064
$115$	19.7926	1.84567
$116$	−28.2244	−2.62057
$117$	−12.3284	−1.13977
$118$	14.0950	1.29755
$119$	−1.84456	−0.169091
$120$	−50.4691	−4.60718
$121$	1.00000	0.0909091
$122$	−11.0272	−0.998358
$123$	−5.55057	−0.500478
$124$	−1.48977	−0.133785
$125$	−6.77385	−0.605872
$126$	−10.2456	−0.912748
$127$	−0.570404	−0.0506152	−0.0253076	−	0.999680i	$-0.508057\pi$
$127$	−0.570404	−0.0506152	−0.0253076	+	0.999680i	$0.508057\pi$
$128$	−11.4385	−1.01103
$129$	−2.25599	−0.198629
$130$	43.0443	3.77524
$131$	4.85815	0.424459	0.212229	−	0.977220i	$-0.431928\pi$
$131$	4.85815	0.424459	0.212229	+	0.977220i	$0.431928\pi$
$132$	−11.4299	−0.994846
$133$	−11.6276	−1.00824
$134$	−4.22817	−0.365259
$135$	−5.63725	−0.485177
$136$	8.15154	0.698989
$137$	−16.2518	−1.38848	−0.694240	−	0.719743i	$-0.744260\pi$
$137$	−16.2518	−1.38848	−0.694240	+	0.719743i	$0.744260\pi$
$138$	−43.2507	−3.68174
$139$	13.5195	1.14671	0.573354	−	0.819308i	$-0.305642\pi$
$139$	13.5195	1.14671	0.573354	+	0.819308i	$0.305642\pi$
$140$	25.6476	2.16762
$141$	−21.6376	−1.82222
$142$	−19.3244	−1.62166
$143$	5.90020	0.493399
$144$	24.1048	2.00873
$145$	−15.2886	−1.26965
$146$	8.49375	0.702948
$147$	−8.11613	−0.669407
$148$	−26.9557	−2.21575
$149$	3.79098	0.310569	0.155285	−	0.987870i	$-0.450371\pi$
$149$	3.79098	0.310569	0.155285	+	0.987870i	$0.450371\pi$
$150$	−15.1831	−1.23970
$151$	−3.56443	−0.290069	−0.145035	−	0.989427i	$-0.546329\pi$
$151$	−3.56443	−0.290069	−0.145035	+	0.989427i	$0.546329\pi$
$152$	51.3849	4.16786
$153$	−2.08950	−0.168926
$154$	4.90337	0.395125
$155$	−0.806977	−0.0648179
$156$	−67.4387	−5.39942
$157$	3.56980	0.284901	0.142451	−	0.989802i	$-0.454502\pi$
$157$	3.56980	0.284901	0.142451	+	0.989802i	$0.454502\pi$
$158$	−46.2074	−3.67606
$159$	17.9609	1.42439
$160$	−39.4188	−3.11633
$161$	13.3029	1.04842
$162$	28.9819	2.27703
$163$	−0.207517	−0.0162540	−0.00812700	−	0.999967i	$-0.502587\pi$
$163$	−0.207517	−0.0162540	−0.00812700	+	0.999967i	$0.502587\pi$
$164$	−12.4654	−0.973383
$165$	−6.19135	−0.481996
$166$	−18.5955	−1.44329
$167$	−0.538258	−0.0416516	−0.0208258	−	0.999783i	$-0.506630\pi$
$167$	−0.538258	−0.0416516	−0.0208258	+	0.999783i	$0.506630\pi$
$168$	−33.9212	−2.61707
$169$	21.8123	1.67787
$170$	7.29541	0.559532
$171$	−13.1716	−1.00725
$172$	−5.06647	−0.386315
$173$	−4.08600	−0.310653	−0.155326	−	0.987863i	$-0.549643\pi$
$173$	−4.08600	−0.310653	−0.155326	+	0.987863i	$0.549643\pi$
$174$	33.4085	2.53269
$175$	4.66999	0.353018
$176$	−11.5362	−0.869571
$177$	−11.9619	−0.899114
$178$	27.5328	2.06367
$179$	−23.9955	−1.79351	−0.896753	−	0.442530i	$-0.854081\pi$
$179$	−23.9955	−1.79351	−0.896753	+	0.442530i	$0.854081\pi$
$180$	29.0533	2.16550
$181$	19.1206	1.42122	0.710611	−	0.703585i	$-0.248419\pi$
$181$	19.1206	1.42122	0.710611	+	0.703585i	$0.248419\pi$
$182$	28.9309	2.14450
$183$	9.35842	0.691794
$184$	−58.7887	−4.33396
$185$	−14.6014	−1.07351
$186$	1.76340	0.129299
$187$	1.00000	0.0731272
$188$	−48.5934	−3.54404
$189$	−3.78889	−0.275601
$190$	45.9881	3.33632
$191$	−11.5368	−0.834774	−0.417387	−	0.908729i	$-0.637054\pi$
$191$	−11.5368	−0.834774	−0.417387	+	0.908729i	$0.637054\pi$
$192$	34.0867	2.46000
$193$	1.01616	0.0731445	0.0365723	−	0.999331i	$-0.488356\pi$
$193$	1.01616	0.0731445	0.0365723	+	0.999331i	$0.488356\pi$
$194$	40.9974	2.94344
$195$	−36.5302	−2.61598
$196$	−18.2271	−1.30193
$197$	−10.3349	−0.736331	−0.368166	−	0.929760i	$-0.620014\pi$
$197$	−10.3349	−0.736331	−0.368166	+	0.929760i	$0.620014\pi$
$198$	5.55447	0.394739
$199$	−15.5068	−1.09925	−0.549625	−	0.835412i	$-0.685229\pi$
$199$	−15.5068	−1.09925	−0.549625	+	0.835412i	$0.685229\pi$
$200$	−20.6377	−1.45931
$201$	3.58830	0.253099
$202$	6.83433	0.480862
$203$	−10.2757	−0.721214
$204$	−11.4299	−0.800254
$205$	−6.75225	−0.471597
$206$	−45.8007	−3.19109
$207$	15.0694	1.04740
$208$	−68.0657	−4.71951
$209$	6.30370	0.436036
$210$	−30.3585	−2.09494
$211$	−2.64266	−0.181928	−0.0909642	−	0.995854i	$-0.528995\pi$
$211$	−2.64266	−0.181928	−0.0909642	+	0.995854i	$0.528995\pi$
$212$	40.3363	2.77031
$213$	16.3999	1.12370
$214$	39.7671	2.71842
$215$	−2.74441	−0.187167
$216$	16.7440	1.13928
$217$	−0.542383	−0.0368194
$218$	−24.2560	−1.64282
$219$	−7.20835	−0.487095
$220$	−13.9044	−0.937437
$221$	5.90020	0.396890
$222$	31.9069	2.14145
$223$	−12.4261	−0.832110	−0.416055	−	0.909339i	$-0.636588\pi$
$223$	−12.4261	−0.832110	−0.416055	+	0.909339i	$0.636588\pi$
$224$	−26.4940	−1.77021
$225$	5.29010	0.352674
$226$	5.09979	0.339233
$227$	−5.73684	−0.380768	−0.190384	−	0.981710i	$-0.560973\pi$
$227$	−5.73684	−0.380768	−0.190384	+	0.981710i	$0.560973\pi$
$228$	−72.0507	−4.77168
$229$	−25.4513	−1.68187	−0.840934	−	0.541138i	$-0.817994\pi$
$229$	−25.4513	−1.68187	−0.840934	+	0.541138i	$0.817994\pi$
$230$	−52.6143	−3.46928
$231$	−4.16132	−0.273795
$232$	45.4107	2.98136
$233$	−0.254189	−0.0166525	−0.00832624	−	0.999965i	$-0.502650\pi$
$233$	−0.254189	−0.0166525	−0.00832624	+	0.999965i	$0.502650\pi$
$234$	32.7725	2.14241
$235$	−26.3221	−1.71706
$236$	−26.8639	−1.74869
$237$	39.2146	2.54726
$238$	4.90337	0.317838
$239$	−12.0277	−0.778009	−0.389005	−	0.921236i	$-0.627181\pi$
$239$	−12.0277	−0.778009	−0.389005	+	0.921236i	$0.627181\pi$
$240$	71.4245	4.61043
$241$	−26.2729	−1.69239	−0.846194	−	0.532874i	$-0.821112\pi$
$241$	−26.2729	−1.69239	−0.846194	+	0.532874i	$0.821112\pi$
$242$	−2.65828	−0.170881
$243$	−18.4337	−1.18252
$244$	21.0170	1.34547
$245$	−9.87324	−0.630778
$246$	14.7550	0.940743
$247$	37.1931	2.36654
$248$	2.39691	0.152204
$249$	15.7813	1.00010
$250$	18.0068	1.13885
$251$	15.4518	0.975311	0.487656	−	0.873036i	$-0.337852\pi$
$251$	15.4518	0.975311	0.487656	+	0.873036i	$0.337852\pi$
$252$	19.5272	1.23010
$253$	−7.21197	−0.453413
$254$	1.51630	0.0951408
$255$	−6.19135	−0.387718
$256$	0.187910	0.0117444
$257$	−30.4661	−1.90042	−0.950211	−	0.311608i	$-0.899133\pi$
$257$	−30.4661	−1.90042	−0.950211	+	0.311608i	$0.899133\pi$
$258$	5.99706	0.373361
$259$	−9.81384	−0.609802
$260$	−82.0390	−5.08784
$261$	−11.6402	−0.720510
$262$	−12.9143	−0.797850
$263$	7.32453	0.451650	0.225825	−	0.974168i	$-0.427492\pi$
$263$	7.32453	0.451650	0.225825	+	0.974168i	$0.427492\pi$
$264$	18.3898	1.13181
$265$	21.8494	1.34220
$266$	30.9094	1.89518
$267$	−23.3661	−1.42998
$268$	8.05855	0.492254
$269$	−22.9826	−1.40127	−0.700637	−	0.713518i	$-0.747101\pi$
$269$	−22.9826	−1.40127	−0.700637	+	0.713518i	$0.747101\pi$
$270$	14.9854	0.911982
$271$	20.0223	1.21627	0.608135	−	0.793834i	$-0.291918\pi$
$271$	20.0223	1.21627	0.608135	+	0.793834i	$0.291918\pi$
$272$	−11.5362	−0.699483
$273$	−24.5526	−1.48599
$274$	43.2018	2.60991
$275$	−2.53176	−0.152671
$276$	82.4322	4.96183
$277$	21.4287	1.28753	0.643763	−	0.765225i	$-0.277372\pi$
$277$	21.4287	1.28753	0.643763	+	0.765225i	$0.277372\pi$
$278$	−35.9386	−2.15546
$279$	−0.614405	−0.0367834
$280$	−41.2650	−2.46605
$281$	−3.99772	−0.238484	−0.119242	−	0.992865i	$-0.538046\pi$
$281$	−3.99772	−0.238484	−0.119242	+	0.992865i	$0.538046\pi$
$282$	57.5190	3.42520
$283$	9.24586	0.549610	0.274805	−	0.961500i	$-0.411387\pi$
$283$	9.24586	0.549610	0.274805	+	0.961500i	$0.411387\pi$
$284$	36.8306	2.18550
$285$	−39.0284	−2.31185
$286$	−15.6844	−0.927438
$287$	−4.53830	−0.267888
$288$	−30.0121	−1.76848
$289$	1.00000	0.0588235
$290$	40.6414	2.38654
$291$	−34.7930	−2.03960
$292$	−16.1884	−0.947354
$293$	12.0941	0.706548	0.353274	−	0.935520i	$-0.385068\pi$
$293$	12.0941	0.706548	0.353274	+	0.935520i	$0.385068\pi$
$294$	21.5750	1.25828
$295$	−14.5516	−0.847229
$296$	43.3696	2.52081
$297$	2.05409	0.119190
$298$	−10.0775	−0.583774
$299$	−42.5521	−2.46085
$300$	28.9378	1.67072
$301$	−1.84456	−0.106319
$302$	9.47526	0.545240
$303$	−5.80005	−0.333204
$304$	−72.7206	−4.17081
$305$	11.3845	0.651873
$306$	5.55447	0.317528
$307$	−26.2024	−1.49545	−0.747724	−	0.664010i	$-0.768853\pi$
$307$	−26.2024	−1.49545	−0.747724	+	0.664010i	$0.768853\pi$
$308$	−9.34542	−0.532505
$309$	38.8695	2.21121
$310$	2.14517	0.121838
$311$	−13.9481	−0.790925	−0.395462	−	0.918482i	$-0.629416\pi$
$311$	−13.9481	−0.790925	−0.395462	+	0.918482i	$0.629416\pi$
$312$	108.504	6.14280
$313$	−3.78488	−0.213934	−0.106967	−	0.994263i	$-0.534114\pi$
$313$	−3.78488	−0.213934	−0.106967	+	0.994263i	$0.534114\pi$
$314$	−9.48954	−0.535526
$315$	10.5775	0.595975
$316$	88.0674	4.95418
$317$	−12.9268	−0.726041	−0.363021	−	0.931781i	$-0.618255\pi$
$317$	−12.9268	−0.726041	−0.363021	+	0.931781i	$0.618255\pi$
$318$	−47.7452	−2.67742
$319$	5.57082	0.311906
$320$	41.4664	2.31804
$321$	−33.7489	−1.88368
$322$	−35.3630	−1.97070
$323$	6.30370	0.350747
$324$	−55.2371	−3.06873
$325$	−14.9379	−0.828605
$326$	0.551639	0.0305525
$327$	20.5852	1.13836
$328$	20.0558	1.10740
$329$	−17.6915	−0.975366
$330$	16.4584	0.906004
$331$	9.81318	0.539381	0.269691	−	0.962947i	$-0.413079\pi$
$331$	9.81318	0.539381	0.269691	+	0.962947i	$0.413079\pi$
$332$	35.4414	1.94510
$333$	−11.1170	−0.609207
$334$	1.43084	0.0782921
$335$	4.36516	0.238494
$336$	48.0057	2.61892
$337$	−15.8043	−0.860914	−0.430457	−	0.902611i	$-0.641648\pi$
$337$	−15.8043	−0.860914	−0.430457	+	0.902611i	$0.641648\pi$
$338$	−57.9834	−3.15388
$339$	−4.32801	−0.235065
$340$	−13.9044	−0.754074
$341$	0.294044	0.0159234
$342$	35.0137	1.89333
$343$	−19.5479	−1.05549
$344$	8.15154	0.439502
$345$	44.6519	2.40398
$346$	10.8617	0.583931
$347$	−27.7741	−1.49099	−0.745495	−	0.666512i	$-0.767787\pi$
$347$	−27.7741	−1.49099	−0.745495	+	0.666512i	$0.767787\pi$
$348$	−63.6739	−3.41328
$349$	−10.5484	−0.564643	−0.282321	−	0.959320i	$-0.591104\pi$
$349$	−10.5484	−0.564643	−0.282321	+	0.959320i	$0.591104\pi$
$350$	−12.4142	−0.663564
$351$	12.1195	0.646892
$352$	14.3633	0.765567
$353$	−16.8250	−0.895503	−0.447751	−	0.894158i	$-0.647775\pi$
$353$	−16.8250	−0.895503	−0.447751	+	0.894158i	$0.647775\pi$
$354$	31.7982	1.69005
$355$	19.9504	1.05886
$356$	−52.4752	−2.78118
$357$	−4.16132	−0.220240
$358$	63.7868	3.37124
$359$	6.25343	0.330043	0.165022	−	0.986290i	$-0.447231\pi$
$359$	6.25343	0.330043	0.165022	+	0.986290i	$0.447231\pi$
$360$	−46.7444	−2.46365
$361$	20.7366	1.09140
$362$	−50.8279	−2.67146
$363$	2.25599	0.118409
$364$	−55.1398	−2.89011
$365$	−8.76893	−0.458987
$366$	−24.8773	−1.30036
$367$	−7.52179	−0.392634	−0.196317	−	0.980540i	$-0.562898\pi$
$367$	−7.52179	−0.392634	−0.196317	+	0.980540i	$0.562898\pi$
$368$	83.1985	4.33702
$369$	−5.14093	−0.267626
$370$	38.8146	2.01787
$371$	14.6854	0.762426
$372$	−3.36090	−0.174255
$373$	−13.8692	−0.718118	−0.359059	−	0.933315i	$-0.616902\pi$
$373$	−13.8692	−0.718118	−0.359059	+	0.933315i	$0.616902\pi$
$374$	−2.65828	−0.137457
$375$	−15.2818	−0.789146
$376$	78.1830	4.03198
$377$	32.8689	1.69284
$378$	10.0720	0.518045
$379$	2.08463	0.107080	0.0535402	−	0.998566i	$-0.482949\pi$
$379$	2.08463	0.107080	0.0535402	+	0.998566i	$0.482949\pi$
$380$	−87.6494	−4.49632
$381$	−1.28683	−0.0659261
$382$	30.6681	1.56912
$383$	23.4180	1.19660	0.598302	−	0.801271i	$-0.295842\pi$
$383$	23.4180	1.19660	0.598302	+	0.801271i	$0.295842\pi$
$384$	−25.8051	−1.31686
$385$	−5.06223	−0.257995
$386$	−2.70123	−0.137489
$387$	−2.08950	−0.106215
$388$	−78.1376	−3.96684
$389$	8.23336	0.417448	0.208724	−	0.977975i	$-0.433069\pi$
$389$	8.23336	0.417448	0.208724	+	0.977975i	$0.433069\pi$
$390$	97.1077	4.91724
$391$	−7.21197	−0.364725
$392$	29.3259	1.48118
$393$	10.9599	0.552856
$394$	27.4731	1.38407
$395$	47.7044	2.40027
$396$	−10.5864	−0.531985
$397$	27.2425	1.36726	0.683630	−	0.729829i	$-0.260400\pi$
$397$	27.2425	1.36726	0.683630	+	0.729829i	$0.260400\pi$
$398$	41.2215	2.06625
$399$	−26.2317	−1.31323
$400$	29.2068	1.46034
$401$	−31.8182	−1.58893	−0.794463	−	0.607313i	$-0.792247\pi$
$401$	−31.8182	−1.58893	−0.794463	+	0.607313i	$0.792247\pi$
$402$	−9.53873	−0.475748
$403$	1.73492	0.0864225
$404$	−13.0257	−0.648051
$405$	−29.9209	−1.48678
$406$	27.3158	1.35566
$407$	5.32041	0.263723
$408$	18.3898	0.910431
$409$	20.0035	0.989109	0.494554	−	0.869147i	$-0.335331\pi$
$409$	20.0035	0.989109	0.494554	+	0.869147i	$0.335331\pi$
$410$	17.9494	0.886457
$411$	−36.6638	−1.80849
$412$	87.2925	4.30059
$413$	−9.78041	−0.481263
$414$	−40.0587	−1.96878
$415$	19.1979	0.942388
$416$	84.7464	4.15504
$417$	30.4999	1.49358
$418$	−16.7570	−0.819613
$419$	−22.9358	−1.12049	−0.560243	−	0.828329i	$-0.689292\pi$
$419$	−22.9358	−1.12049	−0.560243	+	0.828329i	$0.689292\pi$
$420$	57.8608	2.82332
$421$	30.7051	1.49648	0.748238	−	0.663430i	$-0.230900\pi$
$421$	30.7051	1.49648	0.748238	+	0.663430i	$0.230900\pi$
$422$	7.02494	0.341969
$423$	−20.0408	−0.974415
$424$	−64.8979	−3.15172
$425$	−2.53176	−0.122808
$426$	−43.5956	−2.11221
$427$	7.65171	0.370292
$428$	−75.7928	−3.66358
$429$	13.3108	0.642651
$430$	7.29541	0.351816
$431$	18.2078	0.877039	0.438519	−	0.898722i	$-0.355503\pi$
$431$	18.2078	0.877039	0.438519	+	0.898722i	$0.355503\pi$
$432$	−23.6963	−1.14009
$433$	3.02039	0.145151	0.0725754	−	0.997363i	$-0.476878\pi$
$433$	3.02039	0.145151	0.0725754	+	0.997363i	$0.476878\pi$
$434$	1.44181	0.0692090
$435$	−34.4909	−1.65371
$436$	46.2299	2.21401
$437$	−45.4621	−2.17475
$438$	19.1618	0.915587
$439$	−10.7431	−0.512739	−0.256369	−	0.966579i	$-0.582526\pi$
$439$	−10.7431	−0.512739	−0.256369	+	0.966579i	$0.582526\pi$
$440$	22.3711	1.06650
$441$	−7.51715	−0.357959
$442$	−15.6844	−0.746031
$443$	9.17763	0.436042	0.218021	−	0.975944i	$-0.430040\pi$
$443$	9.17763	0.436042	0.218021	+	0.975944i	$0.430040\pi$
$444$	−60.8118	−2.88600
$445$	−28.4247	−1.34746
$446$	33.0320	1.56411
$447$	8.55242	0.404516
$448$	27.8703	1.31675
$449$	−33.1379	−1.56387	−0.781937	−	0.623358i	$-0.785768\pi$
$449$	−33.1379	−1.56387	−0.781937	+	0.623358i	$0.785768\pi$
$450$	−14.0626	−0.662917
$451$	2.46037	0.115854
$452$	−9.71977	−0.457180
$453$	−8.04132	−0.377814
$454$	15.2502	0.715725
$455$	−29.8681	−1.40024
$456$	115.924	5.42863
$457$	−2.05320	−0.0960449	−0.0480224	−	0.998846i	$-0.515292\pi$
$457$	−2.05320	−0.0960449	−0.0480224	+	0.998846i	$0.515292\pi$
$458$	67.6567	3.16139
$459$	2.05409	0.0958766
$460$	100.278	4.67551
$461$	24.5836	1.14497	0.572487	−	0.819914i	$-0.305979\pi$
$461$	24.5836	1.14497	0.572487	+	0.819914i	$0.305979\pi$
$462$	11.0620	0.514649
$463$	17.1696	0.797938	0.398969	−	0.916965i	$-0.369368\pi$
$463$	17.1696	0.797938	0.398969	+	0.916965i	$0.369368\pi$
$464$	−64.2659	−2.98347
$465$	−1.82053	−0.0844252
$466$	0.675706	0.0313015
$467$	9.35305	0.432807	0.216404	−	0.976304i	$-0.430567\pi$
$467$	9.35305	0.432807	0.216404	+	0.976304i	$0.430567\pi$
$468$	−62.4617	−2.88729
$469$	2.93390	0.135475
$470$	69.9716	3.22755
$471$	8.05344	0.371083
$472$	43.2219	1.98945
$473$	1.00000	0.0459800
$474$	−104.243	−4.78806
$475$	−15.9595	−0.732270
$476$	−9.34542	−0.428347
$477$	16.6354	0.761682
$478$	31.9731	1.46242
$479$	16.5710	0.757147	0.378573	−	0.925571i	$-0.376415\pi$
$479$	16.5710	0.757147	0.378573	+	0.925571i	$0.376415\pi$
$480$	−88.9284	−4.05901
$481$	31.3915	1.43133
$482$	69.8409	3.18117
$483$	30.0113	1.36556
$484$	5.06647	0.230294
$485$	−42.3256	−1.92191
$486$	49.0019	2.22277
$487$	39.3164	1.78160	0.890798	−	0.454400i	$-0.150146\pi$
$487$	39.3164	1.78160	0.890798	+	0.454400i	$0.150146\pi$
$488$	−33.8146	−1.53072
$489$	−0.468157	−0.0211708
$490$	26.2459	1.18567
$491$	−23.9760	−1.08202	−0.541010	−	0.841016i	$-0.681958\pi$
$491$	−23.9760	−1.08202	−0.541010	+	0.841016i	$0.681958\pi$
$492$	−28.1218	−1.26783
$493$	5.57082	0.250897
$494$	−98.8697	−4.44836
$495$	−5.73443	−0.257743
$496$	−3.39214	−0.152312
$497$	13.4090	0.601477
$498$	−41.9512	−1.87988
$499$	28.8605	1.29197	0.645986	−	0.763349i	$-0.276446\pi$
$499$	28.8605	1.29197	0.645986	+	0.763349i	$0.276446\pi$
$500$	−34.3195	−1.53482
$501$	−1.21430	−0.0542511
$502$	−41.0754	−1.83328
$503$	38.0662	1.69729	0.848643	−	0.528966i	$-0.177420\pi$
$503$	38.0662	1.69729	0.848643	+	0.528966i	$0.177420\pi$
$504$	−31.4177	−1.39946
$505$	−7.05574	−0.313977
$506$	19.1715	0.852275
$507$	49.2084	2.18542
$508$	−2.88993	−0.128220
$509$	−15.2040	−0.673906	−0.336953	−	0.941521i	$-0.609396\pi$
$509$	−15.2040	−0.673906	−0.336953	+	0.941521i	$0.609396\pi$
$510$	16.4584	0.728789
$511$	−5.89375	−0.260724
$512$	22.3775	0.988954
$513$	12.9484	0.571684
$514$	80.9875	3.57220
$515$	47.2846	2.08361
$516$	−11.4299	−0.503174
$517$	9.59119	0.421820
$518$	26.0880	1.14624
$519$	−9.21798	−0.404624
$520$	131.994	5.78833
$521$	40.0434	1.75433	0.877167	−	0.480185i	$-0.159431\pi$
$521$	40.0434	1.75433	0.877167	+	0.480185i	$0.159431\pi$
$522$	30.9429	1.35434
$523$	34.1034	1.49124	0.745619	−	0.666372i	$-0.232154\pi$
$523$	34.1034	1.49124	0.745619	+	0.666372i	$0.232154\pi$
$524$	24.6137	1.07525
$525$	10.5355	0.459805
$526$	−19.4707	−0.848962
$527$	0.294044	0.0128088
$528$	−26.0255	−1.13261
$529$	29.0125	1.26141
$530$	−58.0819	−2.52292
$531$	−11.0791	−0.480793
$532$	−58.9107	−2.55410
$533$	14.5167	0.628786
$534$	62.1136	2.68792
$535$	−41.0555	−1.77498
$536$	−12.9656	−0.560027
$537$	−54.1336	−2.33604
$538$	61.0942	2.63396
$539$	3.59759	0.154959
$540$	−28.5609	−1.22907
$541$	−33.9135	−1.45806	−0.729028	−	0.684484i	$-0.760028\pi$
$541$	−33.9135	−1.45806	−0.729028	+	0.684484i	$0.760028\pi$
$542$	−53.2250	−2.28621
$543$	43.1359	1.85114
$544$	14.3633	0.615822
$545$	25.0418	1.07267
$546$	65.2678	2.79320
$547$	−2.30935	−0.0987405	−0.0493703	−	0.998781i	$-0.515721\pi$
$547$	−2.30935	−0.0987405	−0.0493703	+	0.998781i	$0.515721\pi$
$548$	−82.3390	−3.51735
$549$	8.66775	0.369931
$550$	6.73013	0.286974
$551$	35.1168	1.49602
$552$	−132.627	−5.64497
$553$	32.0629	1.36345
$554$	−56.9636	−2.42015
$555$	−32.9406	−1.39825
$556$	68.4961	2.90488
$557$	6.61188	0.280154	0.140077	−	0.990141i	$-0.455265\pi$
$557$	6.61188	0.280154	0.140077	+	0.990141i	$0.455265\pi$
$558$	1.63326	0.0691415
$559$	5.90020	0.249552
$560$	58.3987	2.46780
$561$	2.25599	0.0952480
$562$	10.6271	0.448276
$563$	17.9353	0.755881	0.377940	−	0.925830i	$-0.376632\pi$
$563$	17.9353	0.755881	0.377940	+	0.925830i	$0.376632\pi$
$564$	−109.626	−4.61610
$565$	−5.26501	−0.221500
$566$	−24.5781	−1.03310
$567$	−20.1103	−0.844555
$568$	−59.2575	−2.48639
$569$	−32.0903	−1.34530	−0.672648	−	0.739963i	$-0.734843\pi$
$569$	−32.0903	−1.34530	−0.672648	+	0.739963i	$0.734843\pi$
$570$	103.749	4.34555
$571$	−43.8866	−1.83660	−0.918298	−	0.395890i	$-0.870436\pi$
$571$	−43.8866	−1.83660	−0.918298	+	0.395890i	$0.870436\pi$
$572$	29.8932	1.24990
$573$	−26.0269	−1.08729
$574$	12.0641	0.503546
$575$	18.2590	0.761452
$576$	31.5711	1.31546
$577$	9.67056	0.402591	0.201295	−	0.979531i	$-0.435485\pi$
$577$	9.67056	0.402591	0.201295	+	0.979531i	$0.435485\pi$
$578$	−2.65828	−0.110570
$579$	2.29244	0.0952706
$580$	−77.4591	−3.21631
$581$	12.9032	0.535317
$582$	92.4897	3.83382
$583$	−7.96143	−0.329729
$584$	26.0458	1.07778
$585$	−33.8342	−1.39887
$586$	−32.1497	−1.32809
$587$	38.9363	1.60707	0.803537	−	0.595254i	$-0.202949\pi$
$587$	38.9363	1.60707	0.803537	+	0.595254i	$0.202949\pi$
$588$	−41.1201	−1.69576
$589$	1.85357	0.0763749
$590$	38.6824	1.59253
$591$	−23.3155	−0.959069
$592$	−61.3772	−2.52259
$593$	−14.9208	−0.612726	−0.306363	−	0.951915i	$-0.599112\pi$
$593$	−14.9208	−0.612726	−0.306363	+	0.951915i	$0.599112\pi$
$594$	−5.46035	−0.224041
$595$	−5.06223	−0.207531
$596$	19.2069	0.786745
$597$	−34.9833	−1.43177
$598$	113.115	4.62563
$599$	−21.9083	−0.895151	−0.447575	−	0.894246i	$-0.647712\pi$
$599$	−21.9083	−0.895151	−0.447575	+	0.894246i	$0.647712\pi$
$600$	−46.5586	−1.90075
$601$	21.4192	0.873706	0.436853	−	0.899533i	$-0.356093\pi$
$601$	21.4192	0.873706	0.436853	+	0.899533i	$0.356093\pi$
$602$	4.90337	0.199846
$603$	3.32348	0.135343
$604$	−18.0591	−0.734813
$605$	2.74441	0.111576
$606$	15.4182	0.626321
$607$	−12.8298	−0.520746	−0.260373	−	0.965508i	$-0.583846\pi$
$607$	−12.8298	−0.520746	−0.260373	+	0.965508i	$0.583846\pi$
$608$	90.5421	3.67197
$609$	−23.1819	−0.939379
$610$	−30.2632	−1.22532
$611$	56.5899	2.28938
$612$	−10.5864	−0.427929
$613$	11.0324	0.445593	0.222796	−	0.974865i	$-0.428481\pi$
$613$	11.0324	0.445593	0.222796	+	0.974865i	$0.428481\pi$
$614$	69.6533	2.81098
$615$	−15.2330	−0.614254
$616$	15.0360	0.605819
$617$	31.8900	1.28384	0.641922	−	0.766770i	$-0.278137\pi$
$617$	31.8900	1.28384	0.641922	+	0.766770i	$0.278137\pi$
$618$	−103.326	−4.15638
$619$	−28.5217	−1.14639	−0.573193	−	0.819420i	$-0.694295\pi$
$619$	−28.5217	−1.14639	−0.573193	+	0.819420i	$0.694295\pi$
$620$	−4.08852	−0.164199
$621$	−14.8140	−0.594466
$622$	37.0780	1.48669
$623$	−19.1048	−0.765416
$624$	−153.556	−6.14714
$625$	−31.2490	−1.24996
$626$	10.0613	0.402129
$627$	14.2211	0.567936
$628$	18.0863	0.721721
$629$	5.32041	0.212139
$630$	−28.1180	−1.12025
$631$	21.8880	0.871349	0.435675	−	0.900104i	$-0.356510\pi$
$631$	21.8880	0.871349	0.435675	+	0.900104i	$0.356510\pi$
$632$	−141.693	−5.63626
$633$	−5.96182	−0.236961
$634$	34.3631	1.36473
$635$	−1.56542	−0.0621218
$636$	90.9984	3.60832
$637$	21.2265	0.841024
$638$	−14.8088	−0.586286
$639$	15.1896	0.600890
$640$	−31.3919	−1.24087
$641$	33.5200	1.32396	0.661980	−	0.749522i	$-0.269716\pi$
$641$	33.5200	1.32396	0.661980	+	0.749522i	$0.269716\pi$
$642$	89.7142	3.54074
$643$	−33.9518	−1.33893	−0.669464	−	0.742845i	$-0.733476\pi$
$643$	−33.9518	−1.33893	−0.669464	+	0.742845i	$0.733476\pi$
$644$	67.3989	2.65589
$645$	−6.19135	−0.243784
$646$	−16.7570	−0.659296
$647$	32.2788	1.26901	0.634505	−	0.772919i	$-0.281204\pi$
$647$	32.2788	1.26901	0.634505	+	0.772919i	$0.281204\pi$
$648$	88.8721	3.49123
$649$	5.30229	0.208133
$650$	39.7091	1.55752
$651$	−1.22361	−0.0479571
$652$	−1.05138	−0.0411752
$653$	17.6184	0.689463	0.344731	−	0.938701i	$-0.387970\pi$
$653$	17.6184	0.689463	0.344731	+	0.938701i	$0.387970\pi$
$654$	−54.7213	−2.13977
$655$	13.3327	0.520953
$656$	−28.3832	−1.10818
$657$	−6.67636	−0.260470
$658$	47.0291	1.83339
$659$	−17.7144	−0.690056	−0.345028	−	0.938592i	$-0.612131\pi$
$659$	−17.7144	−0.690056	−0.345028	+	0.938592i	$0.612131\pi$
$660$	−31.3683	−1.22101
$661$	0.506164	0.0196875	0.00984375	−	0.999952i	$-0.496867\pi$
$661$	0.506164	0.0196875	0.00984375	+	0.999952i	$0.496867\pi$
$662$	−26.0862	−1.01387
$663$	13.3108	0.516948
$664$	−57.0224	−2.21290
$665$	−31.9108	−1.23745
$666$	29.5521	1.14512
$667$	−40.1766	−1.55564
$668$	−2.72707	−0.105513
$669$	−28.0331	−1.08382
$670$	−11.6038	−0.448295
$671$	−4.14825	−0.160141
$672$	−59.7703	−2.30569
$673$	−26.4435	−1.01932	−0.509662	−	0.860375i	$-0.670230\pi$
$673$	−26.4435	−1.01932	−0.509662	+	0.860375i	$0.670230\pi$
$674$	42.0122	1.61825
$675$	−5.20045	−0.200166
$676$	110.512	4.25044
$677$	4.59098	0.176446	0.0882228	−	0.996101i	$-0.471881\pi$
$677$	4.59098	0.176446	0.0882228	+	0.996101i	$0.471881\pi$
$678$	11.5051	0.441850
$679$	−28.4478	−1.09172
$680$	22.3711	0.857894
$681$	−12.9423	−0.495949
$682$	−0.781653	−0.0299310
$683$	16.5453	0.633088	0.316544	−	0.948578i	$-0.397477\pi$
$683$	16.5453	0.633088	0.316544	+	0.948578i	$0.397477\pi$
$684$	−66.7333	−2.55161
$685$	−44.6014	−1.70413
$686$	51.9639	1.98399
$687$	−57.4179	−2.19063
$688$	−11.5362	−0.439812
$689$	−46.9740	−1.78957
$690$	−118.697	−4.51873
$691$	−1.56070	−0.0593719	−0.0296859	−	0.999559i	$-0.509451\pi$
$691$	−1.56070	−0.0593719	−0.0296859	+	0.999559i	$0.509451\pi$
$692$	−20.7016	−0.786956
$693$	−3.85421	−0.146409
$694$	73.8313	2.80260
$695$	37.1030	1.40740
$696$	102.446	3.88321
$697$	2.46037	0.0931931
$698$	28.0406	1.06135
$699$	−0.573448	−0.0216898
$700$	23.6604	0.894277
$701$	−24.0552	−0.908551	−0.454276	−	0.890861i	$-0.650102\pi$
$701$	−24.0552	−0.908551	−0.454276	+	0.890861i	$0.650102\pi$
$702$	−32.2171	−1.21596
$703$	33.5383	1.26492
$704$	−15.1094	−0.569458
$705$	−59.3824	−2.23647
$706$	44.7255	1.68327
$707$	−4.74229	−0.178352
$708$	−60.6047	−2.27767
$709$	25.0798	0.941893	0.470946	−	0.882162i	$-0.343913\pi$
$709$	25.0798	0.941893	0.470946	+	0.882162i	$0.343913\pi$
$710$	−53.0339	−1.99033
$711$	36.3205	1.36212
$712$	84.4283	3.16409
$713$	−2.12064	−0.0794186
$714$	11.0620	0.413983
$715$	16.1925	0.605566
$716$	−121.572	−4.54337
$717$	−27.1345	−1.01335
$718$	−16.6234	−0.620379
$719$	−29.0688	−1.08408	−0.542041	−	0.840352i	$-0.682348\pi$
$719$	−29.0688	−1.08408	−0.542041	+	0.840352i	$0.682348\pi$
$720$	66.1533	2.46539
$721$	31.7808	1.18358
$722$	−55.1239	−2.05150
$723$	−59.2715	−2.20433
$724$	96.8739	3.60029
$725$	−14.1040	−0.523808
$726$	−5.99706	−0.222572
$727$	40.5656	1.50449	0.752247	−	0.658881i	$-0.228970\pi$
$727$	40.5656	1.50449	0.752247	+	0.658881i	$0.228970\pi$
$728$	88.7156	3.28802
$729$	−8.87871	−0.328841
$730$	23.3103	0.862752
$731$	1.00000	0.0369863
$732$	47.4141	1.75248
$733$	−36.2908	−1.34043	−0.670216	−	0.742166i	$-0.733799\pi$
$733$	−36.2908	−1.34043	−0.670216	+	0.742166i	$0.733799\pi$
$734$	19.9951	0.738031
$735$	−22.2739	−0.821587
$736$	−103.588	−3.81830
$737$	−1.59057	−0.0585893
$738$	13.6661	0.503054
$739$	39.1549	1.44034	0.720168	−	0.693800i	$-0.244065\pi$
$739$	39.1549	1.44034	0.720168	+	0.693800i	$0.244065\pi$
$740$	−73.9774	−2.71946
$741$	83.9073	3.08241
$742$	−39.0378	−1.43312
$743$	−34.7666	−1.27546	−0.637731	−	0.770259i	$-0.720127\pi$
$743$	−34.7666	−1.27546	−0.637731	+	0.770259i	$0.720127\pi$
$744$	5.40742	0.198246
$745$	10.4040	0.381173
$746$	36.8682	1.34984
$747$	14.6166	0.534795
$748$	5.06647	0.185248
$749$	−27.5941	−1.00827
$750$	40.6232	1.48335
$751$	−41.8661	−1.52772	−0.763858	−	0.645384i	$-0.776697\pi$
$751$	−41.8661	−1.52772	−0.763858	+	0.645384i	$0.776697\pi$
$752$	−110.646	−4.03483
$753$	34.8592	1.27034
$754$	−87.3749	−3.18201
$755$	−9.78224	−0.356012
$756$	−19.1963	−0.698163
$757$	11.9521	0.434408	0.217204	−	0.976126i	$-0.430306\pi$
$757$	11.9521	0.434408	0.217204	+	0.976126i	$0.430306\pi$
$758$	−5.54155	−0.201278
$759$	−16.2701	−0.590569
$760$	141.021	5.11537
$761$	−10.1591	−0.368269	−0.184134	−	0.982901i	$-0.558948\pi$
$761$	−10.1591	−0.368269	−0.184134	+	0.982901i	$0.558948\pi$
$762$	3.42075	0.123921
$763$	16.8310	0.609324
$764$	−58.4508	−2.11468
$765$	−5.73443	−0.207329
$766$	−62.2517	−2.24924
$767$	31.2846	1.12962
$768$	0.423923	0.0152970
$769$	−10.7700	−0.388377	−0.194189	−	0.980964i	$-0.562207\pi$
$769$	−10.7700	−0.388377	−0.194189	+	0.980964i	$0.562207\pi$
$770$	13.4568	0.484951
$771$	−68.7312	−2.47529
$772$	5.14832	0.185292
$773$	−26.2977	−0.945863	−0.472932	−	0.881099i	$-0.656804\pi$
$773$	−26.2977	−0.945863	−0.472932	+	0.881099i	$0.656804\pi$
$774$	5.55447	0.199651
$775$	−0.744449	−0.0267414
$776$	125.717	4.51298
$777$	−22.1399	−0.794266
$778$	−21.8866	−0.784673
$779$	15.5094	0.555683
$780$	−185.079	−6.62690
$781$	−7.26949	−0.260123
$782$	19.1715	0.685570
$783$	11.4429	0.408937
$784$	−41.5024	−1.48223
$785$	9.79698	0.349669
$786$	−29.1346	−1.03920
$787$	6.01997	0.214589	0.107294	−	0.994227i	$-0.465781\pi$
$787$	6.01997	0.214589	0.107294	+	0.994227i	$0.465781\pi$
$788$	−52.3615	−1.86530
$789$	16.5241	0.588273
$790$	−126.812	−4.51176
$791$	−3.53870	−0.125822
$792$	17.0326	0.605228
$793$	−24.4755	−0.869150
$794$	−72.4182	−2.57002
$795$	49.2920	1.74821
$796$	−78.5648	−2.78466
$797$	8.48791	0.300657	0.150329	−	0.988636i	$-0.451967\pi$
$797$	8.48791	0.300657	0.150329	+	0.988636i	$0.451967\pi$
$798$	69.7313	2.46846
$799$	9.59119	0.339312
$800$	−36.3645	−1.28568
$801$	−21.6416	−0.764670
$802$	84.5818	2.98669
$803$	3.19520	0.112756
$804$	18.1800	0.641160
$805$	36.5086	1.28676
$806$	−4.61191	−0.162448
$807$	−51.8485	−1.82515
$808$	20.9573	0.737274
$809$	22.7508	0.799877	0.399939	−	0.916542i	$-0.369031\pi$
$809$	22.7508	0.799877	0.399939	+	0.916542i	$0.369031\pi$
$810$	79.5381	2.79468
$811$	−2.13588	−0.0750007	−0.0375004	−	0.999297i	$-0.511940\pi$
$811$	−2.13588	−0.0750007	−0.0375004	+	0.999297i	$0.511940\pi$
$812$	−52.0616	−1.82700
$813$	45.1702	1.58419
$814$	−14.1432	−0.495718
$815$	−0.569511	−0.0199491
$816$	−26.0255	−0.911075
$817$	6.30370	0.220539
$818$	−53.1749	−1.85922
$819$	−22.7406	−0.794621
$820$	−34.2100	−1.19467
$821$	45.1396	1.57538	0.787692	−	0.616069i	$-0.211276\pi$
$821$	45.1396	1.57538	0.787692	+	0.616069i	$0.211276\pi$
$822$	97.4628	3.39940
$823$	33.8258	1.17909	0.589547	−	0.807734i	$-0.299306\pi$
$823$	33.8258	1.17909	0.589547	+	0.807734i	$0.299306\pi$
$824$	−140.447	−4.89269
$825$	−5.71163	−0.198853
$826$	25.9991	0.904625
$827$	25.9695	0.903047	0.451524	−	0.892259i	$-0.350881\pi$
$827$	25.9695	0.903047	0.451524	+	0.892259i	$0.350881\pi$
$828$	76.3486	2.65330
$829$	−25.6368	−0.890404	−0.445202	−	0.895430i	$-0.646868\pi$
$829$	−25.6368	−0.890404	−0.445202	+	0.895430i	$0.646868\pi$
$830$	−51.0335	−1.77140
$831$	48.3430	1.67700
$832$	−89.1486	−3.09067
$833$	3.59759	0.124649
$834$	−81.0773	−2.80748
$835$	−1.47720	−0.0511205
$836$	31.9375	1.10458
$837$	0.603993	0.0208770
$838$	60.9698	2.10617
$839$	−16.2191	−0.559947	−0.279973	−	0.960008i	$-0.590326\pi$
$839$	−16.2191	−0.559947	−0.279973	+	0.960008i	$0.590326\pi$
$840$	−93.0934	−3.21203
$841$	2.03398	0.0701374
$842$	−81.6229	−2.81291
$843$	−9.01882	−0.310625
$844$	−13.3890	−0.460867
$845$	59.8619	2.05931
$846$	53.2740	1.83160
$847$	1.84456	0.0633799
$848$	91.8444	3.15395
$849$	20.8586	0.715865
$850$	6.73013	0.230842
$851$	−38.3707	−1.31533
$852$	83.0896	2.84660
$853$	−18.2701	−0.625555	−0.312777	−	0.949826i	$-0.601259\pi$
$853$	−18.2701	−0.625555	−0.312777	+	0.949826i	$0.601259\pi$
$854$	−20.3404	−0.696034
$855$	−36.1481	−1.23624
$856$	121.945	4.16798
$857$	51.1079	1.74581	0.872906	−	0.487888i	$-0.162233\pi$
$857$	51.1079	1.74581	0.872906	+	0.487888i	$0.162233\pi$
$858$	−35.3839	−1.20799
$859$	7.99077	0.272642	0.136321	−	0.990665i	$-0.456472\pi$
$859$	7.99077	0.272642	0.136321	+	0.990665i	$0.456472\pi$
$860$	−13.9044	−0.474138
$861$	−10.2384	−0.348923
$862$	−48.4015	−1.64856
$863$	−2.21821	−0.0755089	−0.0377544	−	0.999287i	$-0.512020\pi$
$863$	−2.21821	−0.0755089	−0.0377544	+	0.999287i	$0.512020\pi$
$864$	29.5035	1.00373
$865$	−11.2136	−0.381275
$866$	−8.02905	−0.272838
$867$	2.25599	0.0766175
$868$	−2.74797	−0.0932721
$869$	−17.3824	−0.589658
$870$	91.6865	3.10847
$871$	−9.38465	−0.317987
$872$	−74.3802	−2.51883
$873$	−32.2253	−1.09066
$874$	120.851	4.08785
$875$	−12.4948	−0.422401
$876$	−36.5209	−1.23393
$877$	34.2452	1.15638	0.578189	−	0.815903i	$-0.303760\pi$
$877$	34.2452	1.15638	0.578189	+	0.815903i	$0.303760\pi$
$878$	28.5581	0.963790
$879$	27.2843	0.920276
$880$	−31.6599	−1.06726
$881$	9.84346	0.331635	0.165817	−	0.986156i	$-0.446974\pi$
$881$	9.84346	0.331635	0.165817	+	0.986156i	$0.446974\pi$
$882$	19.9827	0.672853
$883$	1.69926	0.0571847	0.0285924	−	0.999591i	$-0.490898\pi$
$883$	1.69926	0.0571847	0.0285924	+	0.999591i	$0.490898\pi$
$884$	29.8932	1.00542
$885$	−32.8284	−1.10351
$886$	−24.3967	−0.819624
$887$	−37.3300	−1.25342	−0.626710	−	0.779252i	$-0.715599\pi$
$887$	−37.3300	−1.25342	−0.626710	+	0.779252i	$0.715599\pi$
$888$	97.8414	3.28334
$889$	−1.05215	−0.0352878
$890$	75.5610	2.53281
$891$	10.9025	0.365247
$892$	−62.9562	−2.10793
$893$	60.4600	2.02322
$894$	−22.7348	−0.760364
$895$	−65.8533	−2.20123
$896$	−21.0990	−0.704869
$897$	−95.9971	−3.20525
$898$	88.0899	2.93960
$899$	1.63807	0.0546326
$900$	26.8021	0.893405
$901$	−7.96143	−0.265234
$902$	−6.54035	−0.217770
$903$	−4.16132	−0.138480
$904$	15.6383	0.520123
$905$	52.4746	1.74432
$906$	21.3761	0.710174
$907$	31.5432	1.04737	0.523687	−	0.851911i	$-0.324556\pi$
$907$	31.5432	1.04737	0.523687	+	0.851911i	$0.324556\pi$
$908$	−29.0655	−0.964574
$909$	−5.37200	−0.178178
$910$	79.3980	2.63202
$911$	25.6223	0.848904	0.424452	−	0.905451i	$-0.360467\pi$
$911$	25.6223	0.848904	0.424452	+	0.905451i	$0.360467\pi$
$912$	−164.057	−5.43247
$913$	−6.99529	−0.231510
$914$	5.45800	0.180535
$915$	25.6833	0.849063
$916$	−128.948	−4.26057
$917$	8.96116	0.295924
$918$	−5.46035	−0.180218
$919$	5.24786	0.173111	0.0865554	−	0.996247i	$-0.472414\pi$
$919$	5.24786	0.173111	0.0865554	+	0.996247i	$0.472414\pi$
$920$	−161.340	−5.31922
$921$	−59.1123	−1.94782
$922$	−65.3503	−2.15220
$923$	−42.8914	−1.41179
$924$	−21.0832	−0.693586
$925$	−13.4700	−0.442891
$926$	−45.6416	−1.49988
$927$	36.0009	1.18242
$928$	80.0154	2.62663
$929$	34.2885	1.12497	0.562485	−	0.826807i	$-0.309845\pi$
$929$	34.2885	1.12497	0.562485	+	0.826807i	$0.309845\pi$
$930$	4.83949	0.158693
$931$	22.6781	0.743245
$932$	−1.28784	−0.0421846
$933$	−31.4668	−1.03018
$934$	−24.8630	−0.813544
$935$	2.74441	0.0897516
$936$	100.496	3.28481
$937$	49.8574	1.62877	0.814386	−	0.580324i	$-0.197074\pi$
$937$	49.8574	1.62877	0.814386	+	0.580324i	$0.197074\pi$
$938$	−7.79913	−0.254651
$939$	−8.53865	−0.278648
$940$	−133.360	−4.34973
$941$	−32.8326	−1.07031	−0.535157	−	0.844753i	$-0.679747\pi$
$941$	−32.8326	−1.07031	−0.535157	+	0.844753i	$0.679747\pi$
$942$	−21.4083	−0.697521
$943$	−17.7441	−0.577828
$944$	−61.1682	−1.99085
$945$	−10.3983	−0.338255
$946$	−2.65828	−0.0864282
$947$	45.4821	1.47797	0.738985	−	0.673722i	$-0.235305\pi$
$947$	45.4821	1.47797	0.738985	+	0.673722i	$0.235305\pi$
$948$	198.679	6.45280
$949$	18.8523	0.611972
$950$	42.4247	1.37644
$951$	−29.1627	−0.945666
$952$	15.0360	0.487321
$953$	−49.0118	−1.58765	−0.793824	−	0.608148i	$-0.791913\pi$
$953$	−49.0118	−1.58765	−0.793824	+	0.608148i	$0.791913\pi$
$954$	−44.2216	−1.43173
$955$	−31.6617	−1.02455
$956$	−60.9381	−1.97088
$957$	12.5677	0.406256
$958$	−44.0503	−1.42320
$959$	−29.9774	−0.968020
$960$	93.5478	3.01924
$961$	−30.9135	−0.997211
$962$	−83.4475	−2.69045
$963$	−31.2582	−1.00728
$964$	−133.111	−4.28722
$965$	2.78874	0.0897729
$966$	−79.7785	−2.56683
$967$	23.6854	0.761672	0.380836	−	0.924643i	$-0.375636\pi$
$967$	23.6854	0.761672	0.380836	+	0.924643i	$0.375636\pi$
$968$	−8.15154	−0.262000
$969$	14.2211	0.456847
$970$	112.513	3.61259
$971$	−11.0978	−0.356144	−0.178072	−	0.984017i	$-0.556986\pi$
$971$	−11.0978	−0.356144	−0.178072	+	0.984017i	$0.556986\pi$
$972$	−93.3936	−2.99560
$973$	24.9376	0.799461
$974$	−104.514	−3.34885
$975$	−33.6997	−1.07926
$976$	47.8549	1.53180
$977$	−34.4611	−1.10251	−0.551254	−	0.834338i	$-0.685850\pi$
$977$	−34.4611	−1.10251	−0.551254	+	0.834338i	$0.685850\pi$
$978$	1.24449	0.0397945
$979$	10.3573	0.331022
$980$	−50.0225	−1.59791
$981$	19.0660	0.608730
$982$	63.7349	2.03386
$983$	40.9038	1.30463	0.652314	−	0.757949i	$-0.273798\pi$
$983$	40.9038	1.30463	0.652314	+	0.757949i	$0.273798\pi$
$984$	45.2457	1.44238
$985$	−28.3632	−0.903725
$986$	−14.8088	−0.471608
$987$	−39.9120	−1.27041
$988$	188.438	5.99500
$989$	−7.21197	−0.229327
$990$	15.2437	0.484477
$991$	8.39725	0.266747	0.133374	−	0.991066i	$-0.457419\pi$
$991$	8.39725	0.266747	0.133374	+	0.991066i	$0.457419\pi$
$992$	4.22345	0.134095
$993$	22.1385	0.702543
$994$	−35.6450	−1.13059
$995$	−42.5570	−1.34915
$996$	79.9555	2.53349
$997$	−6.94153	−0.219840	−0.109920	−	0.993940i	$-0.535060\pi$
$997$	−6.94153	−0.219840	−0.109920	+	0.993940i	$0.535060\pi$
$998$	−76.7193	−2.42851
$999$	10.9286	0.345765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.4	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.65828 q^{2} +2.25599 q^{3} +5.06647 q^{4} +2.74441 q^{5} -5.99706 q^{6} +1.84456 q^{7} -8.15154 q^{8} +2.08950 q^{9} +O(q^{10})\)	\(q-2.65828 q^{2} +2.25599 q^{3} +5.06647 q^{4} +2.74441 q^{5} -5.99706 q^{6} +1.84456 q^{7} -8.15154 q^{8} +2.08950 q^{9} -7.29541 q^{10} -1.00000 q^{11} +11.4299 q^{12} -5.90020 q^{13} -4.90337 q^{14} +6.19135 q^{15} +11.5362 q^{16} -1.00000 q^{17} -5.55447 q^{18} -6.30370 q^{19} +13.9044 q^{20} +4.16132 q^{21} +2.65828 q^{22} +7.21197 q^{23} -18.3898 q^{24} +2.53176 q^{25} +15.6844 q^{26} -2.05409 q^{27} +9.34542 q^{28} -5.57082 q^{29} -16.4584 q^{30} -0.294044 q^{31} -14.3633 q^{32} -2.25599 q^{33} +2.65828 q^{34} +5.06223 q^{35} +10.5864 q^{36} -5.32041 q^{37} +16.7570 q^{38} -13.3108 q^{39} -22.3711 q^{40} -2.46037 q^{41} -11.0620 q^{42} -1.00000 q^{43} -5.06647 q^{44} +5.73443 q^{45} -19.1715 q^{46} -9.59119 q^{47} +26.0255 q^{48} -3.59759 q^{49} -6.73013 q^{50} -2.25599 q^{51} -29.8932 q^{52} +7.96143 q^{53} +5.46035 q^{54} -2.74441 q^{55} -15.0360 q^{56} -14.2211 q^{57} +14.8088 q^{58} -5.30229 q^{59} +31.3683 q^{60} +4.14825 q^{61} +0.781653 q^{62} +3.85421 q^{63} +15.1094 q^{64} -16.1925 q^{65} +5.99706 q^{66} +1.59057 q^{67} -5.06647 q^{68} +16.2701 q^{69} -13.4568 q^{70} +7.26949 q^{71} -17.0326 q^{72} -3.19520 q^{73} +14.1432 q^{74} +5.71163 q^{75} -31.9375 q^{76} -1.84456 q^{77} +35.3839 q^{78} +17.3824 q^{79} +31.6599 q^{80} -10.9025 q^{81} +6.54035 q^{82} +6.99529 q^{83} +21.0832 q^{84} -2.74441 q^{85} +2.65828 q^{86} -12.5677 q^{87} +8.15154 q^{88} -10.3573 q^{89} -15.2437 q^{90} -10.8833 q^{91} +36.5392 q^{92} -0.663361 q^{93} +25.4961 q^{94} -17.2999 q^{95} -32.4035 q^{96} -15.4225 q^{97} +9.56341 q^{98} -2.08950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 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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