LMFDB - Embedded newform 8041.2.a.h.1.32

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			1.32
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)

$f(q)$	$=$	$q-0.617901 q^{2} -1.30117 q^{3} -1.61820 q^{4} -2.62644 q^{5} +0.803994 q^{6} -2.04592 q^{7} +2.23569 q^{8} -1.30696 q^{9} +O(q^{10})$	\(q-0.617901 q^{2} -1.30117 q^{3} -1.61820 q^{4} -2.62644 q^{5} +0.803994 q^{6} -2.04592 q^{7} +2.23569 q^{8} -1.30696 q^{9} +1.62288 q^{10} -1.00000 q^{11} +2.10555 q^{12} -4.80263 q^{13} +1.26418 q^{14} +3.41744 q^{15} +1.85496 q^{16} -1.00000 q^{17} +0.807571 q^{18} -7.54774 q^{19} +4.25010 q^{20} +2.66209 q^{21} +0.617901 q^{22} -7.95372 q^{23} -2.90901 q^{24} +1.89817 q^{25} +2.96755 q^{26} +5.60408 q^{27} +3.31071 q^{28} +5.01071 q^{29} -2.11164 q^{30} +6.89364 q^{31} -5.61756 q^{32} +1.30117 q^{33} +0.617901 q^{34} +5.37349 q^{35} +2.11492 q^{36} +8.76905 q^{37} +4.66375 q^{38} +6.24904 q^{39} -5.87190 q^{40} -6.26226 q^{41} -1.64491 q^{42} -1.00000 q^{43} +1.61820 q^{44} +3.43265 q^{45} +4.91461 q^{46} +4.77275 q^{47} -2.41362 q^{48} -2.81420 q^{49} -1.17288 q^{50} +1.30117 q^{51} +7.77161 q^{52} -6.97927 q^{53} -3.46277 q^{54} +2.62644 q^{55} -4.57405 q^{56} +9.82088 q^{57} -3.09612 q^{58} -10.5990 q^{59} -5.53009 q^{60} +12.1667 q^{61} -4.25959 q^{62} +2.67394 q^{63} -0.238827 q^{64} +12.6138 q^{65} -0.803994 q^{66} +6.47942 q^{67} +1.61820 q^{68} +10.3491 q^{69} -3.32029 q^{70} +12.1817 q^{71} -2.92195 q^{72} -6.48678 q^{73} -5.41841 q^{74} -2.46984 q^{75} +12.2137 q^{76} +2.04592 q^{77} -3.86129 q^{78} -10.5592 q^{79} -4.87194 q^{80} -3.37098 q^{81} +3.86945 q^{82} -3.63871 q^{83} -4.30779 q^{84} +2.62644 q^{85} +0.617901 q^{86} -6.51978 q^{87} -2.23569 q^{88} +14.5026 q^{89} -2.12104 q^{90} +9.82582 q^{91} +12.8707 q^{92} -8.96979 q^{93} -2.94908 q^{94} +19.8237 q^{95} +7.30940 q^{96} +3.61681 q^{97} +1.73890 q^{98} +1.30696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.617901	−0.436922	−0.218461	−	0.975846i	$-0.570104\pi$
$2$	−0.617901	−0.436922	−0.218461	+	0.975846i	$0.570104\pi$
$3$	−1.30117	−0.751230	−0.375615	−	0.926776i	$-0.622569\pi$
$3$	−1.30117	−0.751230	−0.375615	+	0.926776i	$0.622569\pi$
$4$	−1.61820	−0.809099
$5$	−2.62644	−1.17458	−0.587289	−	0.809377i	$-0.699805\pi$
$5$	−2.62644	−1.17458	−0.587289	+	0.809377i	$0.699805\pi$
$6$	0.803994	0.328229
$7$	−2.04592	−0.773286	−0.386643	−	0.922229i	$-0.626365\pi$
$7$	−2.04592	−0.773286	−0.386643	+	0.922229i	$0.626365\pi$
$8$	2.23569	0.790435
$9$	−1.30696	−0.435653
$10$	1.62288	0.513199
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.10555	0.607820
$13$	−4.80263	−1.33201	−0.666006	−	0.745947i	$-0.731997\pi$
$13$	−4.80263	−1.33201	−0.666006	+	0.745947i	$0.731997\pi$
$14$	1.26418	0.337866
$15$	3.41744	0.882379
$16$	1.85496	0.463740
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.807571	0.190346
$19$	−7.54774	−1.73157	−0.865785	−	0.500417i	$-0.833180\pi$
$19$	−7.54774	−1.73157	−0.865785	+	0.500417i	$0.833180\pi$
$20$	4.25010	0.950350
$21$	2.66209	0.580916
$22$	0.617901	0.131737
$23$	−7.95372	−1.65847	−0.829233	−	0.558904i	$-0.811222\pi$
$23$	−7.95372	−1.65847	−0.829233	+	0.558904i	$0.811222\pi$
$24$	−2.90901	−0.593799
$25$	1.89817	0.379634
$26$	2.96755	0.581985
$27$	5.60408	1.07851
$28$	3.31071	0.625665
$29$	5.01071	0.930465	0.465233	−	0.885188i	$-0.345971\pi$
$29$	5.01071	0.930465	0.465233	+	0.885188i	$0.345971\pi$
$30$	−2.11164	−0.385531
$31$	6.89364	1.23813	0.619067	−	0.785338i	$-0.287511\pi$
$31$	6.89364	1.23813	0.619067	+	0.785338i	$0.287511\pi$
$32$	−5.61756	−0.993054
$33$	1.30117	0.226504
$34$	0.617901	0.105969
$35$	5.37349	0.908285
$36$	2.11492	0.352486
$37$	8.76905	1.44162	0.720812	−	0.693131i	$-0.243769\pi$
$37$	8.76905	1.44162	0.720812	+	0.693131i	$0.243769\pi$
$38$	4.66375	0.756561
$39$	6.24904	1.00065
$40$	−5.87190	−0.928428
$41$	−6.26226	−0.978000	−0.489000	−	0.872284i	$-0.662638\pi$
$41$	−6.26226	−0.978000	−0.489000	+	0.872284i	$0.662638\pi$
$42$	−1.64491	−0.253815
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.61820	0.243953
$45$	3.43265	0.511709
$46$	4.91461	0.724620
$47$	4.77275	0.696176	0.348088	−	0.937462i	$-0.386831\pi$
$47$	4.77275	0.696176	0.348088	+	0.937462i	$0.386831\pi$
$48$	−2.41362	−0.348376
$49$	−2.81420	−0.402028
$50$	−1.17288	−0.165871
$51$	1.30117	0.182200
$52$	7.77161	1.07773
$53$	−6.97927	−0.958677	−0.479338	−	0.877630i	$-0.659123\pi$
$53$	−6.97927	−0.958677	−0.479338	+	0.877630i	$0.659123\pi$
$54$	−3.46277	−0.471223
$55$	2.62644	0.354149
$56$	−4.57405	−0.611233
$57$	9.82088	1.30081
$58$	−3.09612	−0.406541
$59$	−10.5990	−1.37987	−0.689934	−	0.723872i	$-0.742360\pi$
$59$	−10.5990	−1.37987	−0.689934	+	0.723872i	$0.742360\pi$
$60$	−5.53009	−0.713932
$61$	12.1667	1.55778	0.778890	−	0.627161i	$-0.215783\pi$
$61$	12.1667	1.55778	0.778890	+	0.627161i	$0.215783\pi$
$62$	−4.25959	−0.540968
$63$	2.67394	0.336885
$64$	−0.238827	−0.0298533
$65$	12.6138	1.56455
$66$	−0.803994	−0.0989648
$67$	6.47942	0.791588	0.395794	−	0.918339i	$-0.370469\pi$
$67$	6.47942	0.791588	0.395794	+	0.918339i	$0.370469\pi$
$68$	1.61820	0.196235
$69$	10.3491	1.24589
$70$	−3.32029	−0.396850
$71$	12.1817	1.44570	0.722849	−	0.691006i	$-0.242832\pi$
$71$	12.1817	1.44570	0.722849	+	0.691006i	$0.242832\pi$
$72$	−2.92195	−0.344356
$73$	−6.48678	−0.759220	−0.379610	−	0.925147i	$-0.623942\pi$
$73$	−6.48678	−0.759220	−0.379610	+	0.925147i	$0.623942\pi$
$74$	−5.41841	−0.629877
$75$	−2.46984	−0.285193
$76$	12.2137	1.40101
$77$	2.04592	0.233155
$78$	−3.86129	−0.437205
$79$	−10.5592	−1.18801	−0.594003	−	0.804463i	$-0.702453\pi$
$79$	−10.5592	−1.18801	−0.594003	+	0.804463i	$0.702453\pi$
$80$	−4.87194	−0.544699
$81$	−3.37098	−0.374553
$82$	3.86945	0.427310
$83$	−3.63871	−0.399400	−0.199700	−	0.979857i	$-0.563997\pi$
$83$	−3.63871	−0.399400	−0.199700	+	0.979857i	$0.563997\pi$
$84$	−4.30779	−0.470019
$85$	2.62644	0.284877
$86$	0.617901	0.0666300
$87$	−6.51978	−0.698994
$88$	−2.23569	−0.238325
$89$	14.5026	1.53727	0.768636	−	0.639686i	$-0.220936\pi$
$89$	14.5026	1.53727	0.768636	+	0.639686i	$0.220936\pi$
$90$	−2.12104	−0.223577
$91$	9.82582	1.03003
$92$	12.8707	1.34186
$93$	−8.96979	−0.930124
$94$	−2.94908	−0.304175
$95$	19.8237	2.03386
$96$	7.30940	0.746012
$97$	3.61681	0.367232	0.183616	−	0.982998i	$-0.441220\pi$
$97$	3.61681	0.367232	0.183616	+	0.982998i	$0.441220\pi$
$98$	1.73890	0.175655
$99$	1.30696	0.131354
$100$	−3.07162	−0.307162
$101$	5.18546	0.515973	0.257986	−	0.966149i	$-0.416941\pi$
$101$	5.18546	0.515973	0.257986	+	0.966149i	$0.416941\pi$
$102$	−0.803994	−0.0796073
$103$	0.170452	0.0167951	0.00839756	−	0.999965i	$-0.497327\pi$
$103$	0.170452	0.0167951	0.00839756	+	0.999965i	$0.497327\pi$
$104$	−10.7372	−1.05287
$105$	−6.99182	−0.682332
$106$	4.31250	0.418867
$107$	−8.93204	−0.863493	−0.431746	−	0.901995i	$-0.642102\pi$
$107$	−8.93204	−0.863493	−0.431746	+	0.901995i	$0.642102\pi$
$108$	−9.06852	−0.872618
$109$	−5.06771	−0.485399	−0.242699	−	0.970102i	$-0.578033\pi$
$109$	−5.06771	−0.485399	−0.242699	+	0.970102i	$0.578033\pi$
$110$	−1.62288	−0.154735
$111$	−11.4100	−1.08299
$112$	−3.79511	−0.358604
$113$	9.05239	0.851577	0.425788	−	0.904823i	$-0.359997\pi$
$113$	9.05239	0.851577	0.425788	+	0.904823i	$0.359997\pi$
$114$	−6.06833	−0.568351
$115$	20.8899	1.94800
$116$	−8.10832	−0.752839
$117$	6.27685	0.580295
$118$	6.54911	0.602895
$119$	2.04592	0.187549
$120$	7.64033	0.697463
$121$	1.00000	0.0909091
$122$	−7.51779	−0.680628
$123$	8.14825	0.734703
$124$	−11.1553	−1.00177
$125$	8.14676	0.728668
$126$	−1.65223	−0.147192
$127$	0.354797	0.0314831	0.0157416	−	0.999876i	$-0.494989\pi$
$127$	0.354797	0.0314831	0.0157416	+	0.999876i	$0.494989\pi$
$128$	11.3827	1.00610
$129$	1.30117	0.114562
$130$	−7.79409	−0.683587
$131$	−11.4319	−0.998813	−0.499406	−	0.866368i	$-0.666449\pi$
$131$	−11.4319	−0.998813	−0.499406	+	0.866368i	$0.666449\pi$
$132$	−2.10555	−0.183265
$133$	15.4421	1.33900
$134$	−4.00364	−0.345862
$135$	−14.7188	−1.26679
$136$	−2.23569	−0.191709
$137$	−2.73657	−0.233801	−0.116900	−	0.993144i	$-0.537296\pi$
$137$	−2.73657	−0.233801	−0.116900	+	0.993144i	$0.537296\pi$
$138$	−6.39474	−0.544357
$139$	−10.1084	−0.857385	−0.428692	−	0.903451i	$-0.641026\pi$
$139$	−10.1084	−0.857385	−0.428692	+	0.903451i	$0.641026\pi$
$140$	−8.69537	−0.734893
$141$	−6.21015	−0.522989
$142$	−7.52707	−0.631657
$143$	4.80263	0.401616
$144$	−2.42436	−0.202030
$145$	−13.1603	−1.09290
$146$	4.00819	0.331720
$147$	3.66175	0.302016
$148$	−14.1901	−1.16642
$149$	−12.4365	−1.01884	−0.509419	−	0.860519i	$-0.670140\pi$
$149$	−12.4365	−1.01884	−0.509419	+	0.860519i	$0.670140\pi$
$150$	1.52612	0.124607
$151$	−1.27853	−0.104045	−0.0520225	−	0.998646i	$-0.516567\pi$
$151$	−1.27853	−0.104045	−0.0520225	+	0.998646i	$0.516567\pi$
$152$	−16.8744	−1.36869
$153$	1.30696	0.105661
$154$	−1.26418	−0.101870
$155$	−18.1057	−1.45429
$156$	−10.1122	−0.809623
$157$	16.1480	1.28875	0.644374	−	0.764711i	$-0.277118\pi$
$157$	16.1480	1.28875	0.644374	+	0.764711i	$0.277118\pi$
$158$	6.52455	0.519066
$159$	9.08121	0.720187
$160$	14.7542	1.16642
$161$	16.2727	1.28247
$162$	2.08293	0.163651
$163$	20.4862	1.60460	0.802300	−	0.596920i	$-0.203609\pi$
$163$	20.4862	1.60460	0.802300	+	0.596920i	$0.203609\pi$
$164$	10.1336	0.791299
$165$	−3.41744	−0.266047
$166$	2.24836	0.174507
$167$	17.3215	1.34038	0.670191	−	0.742189i	$-0.266212\pi$
$167$	17.3215	1.34038	0.670191	+	0.742189i	$0.266212\pi$
$168$	5.95161	0.459177
$169$	10.0653	0.774254
$170$	−1.62288	−0.124469
$171$	9.86458	0.754363
$172$	1.61820	0.123386
$173$	15.2139	1.15669	0.578345	−	0.815792i	$-0.303699\pi$
$173$	15.2139	1.15669	0.578345	+	0.815792i	$0.303699\pi$
$174$	4.02858	0.305406
$175$	−3.88351	−0.293566
$176$	−1.85496	−0.139823
$177$	13.7910	1.03660
$178$	−8.96117	−0.671668
$179$	15.3618	1.14820	0.574099	−	0.818786i	$-0.305353\pi$
$179$	15.3618	1.14820	0.574099	+	0.818786i	$0.305353\pi$
$180$	−5.55470	−0.414023
$181$	23.4554	1.74342	0.871712	−	0.490019i	$-0.163010\pi$
$181$	23.4554	1.74342	0.871712	+	0.490019i	$0.163010\pi$
$182$	−6.07139	−0.450041
$183$	−15.8309	−1.17025
$184$	−17.7820	−1.31091
$185$	−23.0314	−1.69330
$186$	5.54244	0.406392
$187$	1.00000	0.0731272
$188$	−7.72325	−0.563276
$189$	−11.4655	−0.833994
$190$	−12.2491	−0.888640
$191$	25.4428	1.84098	0.920490	−	0.390766i	$-0.127790\pi$
$191$	25.4428	1.84098	0.920490	+	0.390766i	$0.127790\pi$
$192$	0.310754	0.0224267
$193$	−11.2646	−0.810840	−0.405420	−	0.914130i	$-0.632875\pi$
$193$	−11.2646	−0.810840	−0.405420	+	0.914130i	$0.632875\pi$
$194$	−2.23483	−0.160452
$195$	−16.4127	−1.17534
$196$	4.55393	0.325281
$197$	3.33575	0.237662	0.118831	−	0.992914i	$-0.462085\pi$
$197$	3.33575	0.237662	0.118831	+	0.992914i	$0.462085\pi$
$198$	−0.807571	−0.0573916
$199$	3.00069	0.212713	0.106356	−	0.994328i	$-0.466082\pi$
$199$	3.00069	0.212713	0.106356	+	0.994328i	$0.466082\pi$
$200$	4.24372	0.300076
$201$	−8.43083	−0.594665
$202$	−3.20410	−0.225440
$203$	−10.2515	−0.719516
$204$	−2.10555	−0.147418
$205$	16.4474	1.14874
$206$	−0.105322	−0.00733816
$207$	10.3952	0.722515
$208$	−8.90870	−0.617707
$209$	7.54774	0.522088
$210$	4.32025	0.298126
$211$	−17.8539	−1.22911	−0.614557	−	0.788872i	$-0.710665\pi$
$211$	−17.8539	−1.22911	−0.614557	+	0.788872i	$0.710665\pi$
$212$	11.2938	0.775664
$213$	−15.8504	−1.08605
$214$	5.51912	0.377279
$215$	2.62644	0.179122
$216$	12.5290	0.852489
$217$	−14.1039	−0.957433
$218$	3.13134	0.212081
$219$	8.44040	0.570349
$220$	−4.25010	−0.286541
$221$	4.80263	0.323060
$222$	7.05027	0.473183
$223$	26.6406	1.78399	0.891995	−	0.452045i	$-0.149306\pi$
$223$	26.6406	1.78399	0.891995	+	0.452045i	$0.149306\pi$
$224$	11.4931	0.767915
$225$	−2.48083	−0.165389
$226$	−5.59348	−0.372073
$227$	−0.153828	−0.0102099	−0.00510496	−	0.999987i	$-0.501625\pi$
$227$	−0.153828	−0.0102099	−0.00510496	+	0.999987i	$0.501625\pi$
$228$	−15.8921	−1.05248
$229$	−18.2301	−1.20468	−0.602339	−	0.798240i	$-0.705765\pi$
$229$	−18.2301	−1.20468	−0.602339	+	0.798240i	$0.705765\pi$
$230$	−12.9079	−0.851123
$231$	−2.66209	−0.175153
$232$	11.2024	0.735473
$233$	13.2956	0.871021	0.435511	−	0.900184i	$-0.356568\pi$
$233$	13.2956	0.871021	0.435511	+	0.900184i	$0.356568\pi$
$234$	−3.87847	−0.253544
$235$	−12.5353	−0.817714
$236$	17.1512	1.11645
$237$	13.7393	0.892465
$238$	−1.26418	−0.0819445
$239$	−26.5097	−1.71477	−0.857385	−	0.514675i	$-0.827913\pi$
$239$	−26.5097	−1.71477	−0.857385	+	0.514675i	$0.827913\pi$
$240$	6.33922	0.409195
$241$	−29.1411	−1.87714	−0.938570	−	0.345088i	$-0.887849\pi$
$241$	−29.1411	−1.87714	−0.938570	+	0.345088i	$0.887849\pi$
$242$	−0.617901	−0.0397202
$243$	−12.4260	−0.797130
$244$	−19.6881	−1.26040
$245$	7.39131	0.472214
$246$	−5.03481	−0.321008
$247$	36.2490	2.30647
$248$	15.4120	0.978665
$249$	4.73457	0.300041
$250$	−5.03389	−0.318371
$251$	30.1624	1.90383	0.951917	−	0.306357i	$-0.0991100\pi$
$251$	30.1624	1.90383	0.951917	+	0.306357i	$0.0991100\pi$
$252$	−4.32696	−0.272573
$253$	7.95372	0.500046
$254$	−0.219229	−0.0137557
$255$	−3.41744	−0.214008
$256$	−6.55573	−0.409733
$257$	−12.9747	−0.809337	−0.404668	−	0.914463i	$-0.632613\pi$
$257$	−12.9747	−0.809337	−0.404668	+	0.914463i	$0.632613\pi$
$258$	−0.803994	−0.0500545
$259$	−17.9408	−1.11479
$260$	−20.4117	−1.26588
$261$	−6.54879	−0.405360
$262$	7.06381	0.436403
$263$	−7.82844	−0.482723	−0.241361	−	0.970435i	$-0.577594\pi$
$263$	−7.82844	−0.482723	−0.241361	+	0.970435i	$0.577594\pi$
$264$	2.90901	0.179037
$265$	18.3306	1.12604
$266$	−9.54168	−0.585038
$267$	−18.8703	−1.15485
$268$	−10.4850	−0.640473
$269$	8.22717	0.501620	0.250810	−	0.968036i	$-0.419303\pi$
$269$	8.22717	0.501620	0.250810	+	0.968036i	$0.419303\pi$
$270$	9.09474	0.553488
$271$	−21.1823	−1.28673	−0.643367	−	0.765558i	$-0.722463\pi$
$271$	−21.1823	−1.28673	−0.643367	+	0.765558i	$0.722463\pi$
$272$	−1.85496	−0.112474
$273$	−12.7851	−0.773787
$274$	1.69093	0.102153
$275$	−1.89817	−0.114464
$276$	−16.7470	−1.00805
$277$	1.02465	0.0615653	0.0307827	−	0.999526i	$-0.490200\pi$
$277$	1.02465	0.0615653	0.0307827	+	0.999526i	$0.490200\pi$
$278$	6.24600	0.374610
$279$	−9.00971	−0.539397
$280$	12.0134	0.717941
$281$	14.3026	0.853224	0.426612	−	0.904435i	$-0.359707\pi$
$281$	14.3026	0.853224	0.426612	+	0.904435i	$0.359707\pi$
$282$	3.83726	0.228505
$283$	25.9958	1.54529	0.772644	−	0.634840i	$-0.218934\pi$
$283$	25.9958	1.54529	0.772644	+	0.634840i	$0.218934\pi$
$284$	−19.7124	−1.16971
$285$	−25.7939	−1.52790
$286$	−2.96755	−0.175475
$287$	12.8121	0.756274
$288$	7.34192	0.432627
$289$	1.00000	0.0588235
$290$	8.13177	0.477514
$291$	−4.70608	−0.275875
$292$	10.4969	0.614285
$293$	0.0230942	0.00134918	0.000674588	−	1.00000i	$-0.499785\pi$
$293$	0.0230942	0.00134918	0.000674588		1.00000i	$0.499785\pi$
$294$	−2.26260	−0.131957
$295$	27.8375	1.62076
$296$	19.6049	1.13951
$297$	−5.60408	−0.325182
$298$	7.68453	0.445153
$299$	38.1988	2.20909
$300$	3.99669	0.230749
$301$	2.04592	0.117925
$302$	0.790003	0.0454596
$303$	−6.74716	−0.387614
$304$	−14.0008	−0.802999
$305$	−31.9549	−1.82973
$306$	−0.807571	−0.0461658
$307$	−13.7967	−0.787417	−0.393709	−	0.919235i	$-0.628808\pi$
$307$	−13.7967	−0.787417	−0.393709	+	0.919235i	$0.628808\pi$
$308$	−3.31071	−0.188645
$309$	−0.221787	−0.0126170
$310$	11.1875	0.635410
$311$	1.40256	0.0795321	0.0397661	−	0.999209i	$-0.487339\pi$
$311$	1.40256	0.0795321	0.0397661	+	0.999209i	$0.487339\pi$
$312$	13.9709	0.790947
$313$	−25.7821	−1.45729	−0.728644	−	0.684892i	$-0.759849\pi$
$313$	−25.7821	−1.45729	−0.728644	+	0.684892i	$0.759849\pi$
$314$	−9.97785	−0.563082
$315$	−7.02293	−0.395697
$316$	17.0869	0.961214
$317$	−24.7311	−1.38904	−0.694518	−	0.719475i	$-0.744382\pi$
$317$	−24.7311	−1.38904	−0.694518	+	0.719475i	$0.744382\pi$
$318$	−5.61129	−0.314666
$319$	−5.01071	−0.280546
$320$	0.627263	0.0350651
$321$	11.6221	0.648682
$322$	−10.0549	−0.560339
$323$	7.54774	0.419967
$324$	5.45492	0.303051
$325$	−9.11622	−0.505677
$326$	−12.6584	−0.701086
$327$	6.59395	0.364646
$328$	−14.0005	−0.773046
$329$	−9.76467	−0.538344
$330$	2.11164	0.116242
$331$	−16.3692	−0.899734	−0.449867	−	0.893096i	$-0.648529\pi$
$331$	−16.3692	−0.899734	−0.449867	+	0.893096i	$0.648529\pi$
$332$	5.88815	0.323154
$333$	−11.4608	−0.628048
$334$	−10.7030	−0.585642
$335$	−17.0178	−0.929782
$336$	4.93808	0.269394
$337$	9.03246	0.492029	0.246015	−	0.969266i	$-0.420879\pi$
$337$	9.03246	0.492029	0.246015	+	0.969266i	$0.420879\pi$
$338$	−6.21936	−0.338289
$339$	−11.7787	−0.639730
$340$	−4.25010	−0.230494
$341$	−6.89364	−0.373312
$342$	−6.09534	−0.329598
$343$	20.0791	1.08417
$344$	−2.23569	−0.120540
$345$	−27.1814	−1.46339
$346$	−9.40068	−0.505383
$347$	−28.7474	−1.54324	−0.771622	−	0.636082i	$-0.780554\pi$
$347$	−28.7474	−1.54324	−0.771622	+	0.636082i	$0.780554\pi$
$348$	10.5503	0.565555
$349$	−14.4815	−0.775177	−0.387588	−	0.921833i	$-0.626692\pi$
$349$	−14.4815	−0.775177	−0.387588	+	0.921833i	$0.626692\pi$
$350$	2.39963	0.128265
$351$	−26.9144	−1.43658
$352$	5.61756	0.299417
$353$	−14.1779	−0.754614	−0.377307	−	0.926088i	$-0.623150\pi$
$353$	−14.1779	−0.754614	−0.377307	+	0.926088i	$0.623150\pi$
$354$	−8.52150	−0.452913
$355$	−31.9944	−1.69809
$356$	−23.4681	−1.24381
$357$	−2.66209	−0.140893
$358$	−9.49210	−0.501673
$359$	17.8781	0.943572	0.471786	−	0.881713i	$-0.343610\pi$
$359$	17.8781	0.943572	0.471786	+	0.881713i	$0.343610\pi$
$360$	7.67433	0.404473
$361$	37.9683	1.99833
$362$	−14.4931	−0.761740
$363$	−1.30117	−0.0682937
$364$	−15.9001	−0.833393
$365$	17.0371	0.891764
$366$	9.78191	0.511309
$367$	−34.9109	−1.82233	−0.911167	−	0.412038i	$-0.864817\pi$
$367$	−34.9109	−1.82233	−0.911167	+	0.412038i	$0.864817\pi$
$368$	−14.7538	−0.769097
$369$	8.18451	0.426069
$370$	14.2311	0.739840
$371$	14.2791	0.741332
$372$	14.5149	0.752563
$373$	−6.46868	−0.334936	−0.167468	−	0.985878i	$-0.553559\pi$
$373$	−6.46868	−0.334936	−0.167468	+	0.985878i	$0.553559\pi$
$374$	−0.617901	−0.0319509
$375$	−10.6003	−0.547398
$376$	10.6704	0.550282
$377$	−24.0646	−1.23939
$378$	7.08456	0.364390
$379$	−8.64426	−0.444026	−0.222013	−	0.975044i	$-0.571263\pi$
$379$	−8.64426	−0.444026	−0.222013	+	0.975044i	$0.571263\pi$
$380$	−32.0786	−1.64560
$381$	−0.461651	−0.0236511
$382$	−15.7212	−0.804365
$383$	−25.7377	−1.31514	−0.657568	−	0.753395i	$-0.728415\pi$
$383$	−25.7377	−1.31514	−0.657568	+	0.753395i	$0.728415\pi$
$384$	−14.8108	−0.755811
$385$	−5.37349	−0.273858
$386$	6.96038	0.354274
$387$	1.30696	0.0664365
$388$	−5.85272	−0.297127
$389$	−38.0989	−1.93169	−0.965845	−	0.259119i	$-0.916568\pi$
$389$	−38.0989	−1.93169	−0.965845	+	0.259119i	$0.916568\pi$
$390$	10.1414	0.513531
$391$	7.95372	0.402237
$392$	−6.29167	−0.317777
$393$	14.8749	0.750338
$394$	−2.06116	−0.103840
$395$	27.7331	1.39541
$396$	−2.11492	−0.106279
$397$	6.36494	0.319447	0.159724	−	0.987162i	$-0.448940\pi$
$397$	6.36494	0.319447	0.159724	+	0.987162i	$0.448940\pi$
$398$	−1.85413	−0.0929390
$399$	−20.0928	−1.00590
$400$	3.52104	0.176052
$401$	−21.7451	−1.08590	−0.542950	−	0.839765i	$-0.682693\pi$
$401$	−21.7451	−1.08590	−0.542950	+	0.839765i	$0.682693\pi$
$402$	5.20942	0.259822
$403$	−33.1076	−1.64921
$404$	−8.39110	−0.417473
$405$	8.85367	0.439942
$406$	6.33443	0.314373
$407$	−8.76905	−0.434666
$408$	2.90901	0.144017
$409$	−6.78297	−0.335396	−0.167698	−	0.985838i	$-0.553633\pi$
$409$	−6.78297	−0.335396	−0.167698	+	0.985838i	$0.553633\pi$
$410$	−10.1629	−0.501909
$411$	3.56074	0.175638
$412$	−0.275825	−0.0135889
$413$	21.6847	1.06703
$414$	−6.42320	−0.315683
$415$	9.55683	0.469126
$416$	26.9791	1.32276
$417$	13.1528	0.644093
$418$	−4.66375	−0.228112
$419$	7.67174	0.374789	0.187394	−	0.982285i	$-0.439996\pi$
$419$	7.67174	0.374789	0.187394	+	0.982285i	$0.439996\pi$
$420$	11.3141	0.552074
$421$	−1.05801	−0.0515642	−0.0257821	−	0.999668i	$-0.508208\pi$
$421$	−1.05801	−0.0515642	−0.0257821	+	0.999668i	$0.508208\pi$
$422$	11.0320	0.537027
$423$	−6.23778	−0.303291
$424$	−15.6035	−0.757772
$425$	−1.89817	−0.0920748
$426$	9.79399	0.474520
$427$	−24.8920	−1.20461
$428$	14.4538	0.698651
$429$	−6.24904	−0.301706
$430$	−1.62288	−0.0782621
$431$	−10.4491	−0.503317	−0.251659	−	0.967816i	$-0.580976\pi$
$431$	−10.4491	−0.503317	−0.251659	+	0.967816i	$0.580976\pi$
$432$	10.3954	0.500147
$433$	−5.71185	−0.274494	−0.137247	−	0.990537i	$-0.543825\pi$
$433$	−5.71185	−0.274494	−0.137247	+	0.990537i	$0.543825\pi$
$434$	8.71479	0.418323
$435$	17.1238	0.821023
$436$	8.20056	0.392735
$437$	60.0326	2.87175
$438$	−5.21533	−0.249198
$439$	−14.2638	−0.680774	−0.340387	−	0.940286i	$-0.610558\pi$
$439$	−14.2638	−0.680774	−0.340387	+	0.940286i	$0.610558\pi$
$440$	5.87190	0.279932
$441$	3.67804	0.175145
$442$	−2.96755	−0.141152
$443$	3.26040	0.154906	0.0774532	−	0.996996i	$-0.475321\pi$
$443$	3.26040	0.154906	0.0774532	+	0.996996i	$0.475321\pi$
$444$	18.4637	0.876247
$445$	−38.0902	−1.80565
$446$	−16.4613	−0.779465
$447$	16.1820	0.765382
$448$	0.488621	0.0230852
$449$	33.6289	1.58705	0.793524	−	0.608539i	$-0.208244\pi$
$449$	33.6289	1.58705	0.793524	+	0.608539i	$0.208244\pi$
$450$	1.53291	0.0722620
$451$	6.26226	0.294878
$452$	−14.6486	−0.689010
$453$	1.66358	0.0781618
$454$	0.0950504	0.00446094
$455$	−25.8069	−1.20985
$456$	21.9564	1.02820
$457$	8.51316	0.398229	0.199115	−	0.979976i	$-0.436193\pi$
$457$	8.51316	0.398229	0.199115	+	0.979976i	$0.436193\pi$
$458$	11.2644	0.526351
$459$	−5.60408	−0.261576
$460$	−33.8041	−1.57612
$461$	−9.62466	−0.448265	−0.224133	−	0.974559i	$-0.571955\pi$
$461$	−9.62466	−0.448265	−0.224133	+	0.974559i	$0.571955\pi$
$462$	1.64491	0.0765281
$463$	11.3627	0.528069	0.264034	−	0.964513i	$-0.414947\pi$
$463$	11.3627	0.528069	0.264034	+	0.964513i	$0.414947\pi$
$464$	9.29467	0.431494
$465$	23.5586	1.09250
$466$	−8.21534	−0.380568
$467$	16.8005	0.777435	0.388717	−	0.921357i	$-0.372918\pi$
$467$	16.8005	0.777435	0.388717	+	0.921357i	$0.372918\pi$
$468$	−10.1572	−0.469516
$469$	−13.2564	−0.612124
$470$	7.74559	0.357277
$471$	−21.0112	−0.968146
$472$	−23.6960	−1.09070
$473$	1.00000	0.0459800
$474$	−8.48955	−0.389938
$475$	−14.3269	−0.657363
$476$	−3.31071	−0.151746
$477$	9.12162	0.417650
$478$	16.3804	0.749221
$479$	12.8562	0.587416	0.293708	−	0.955895i	$-0.405111\pi$
$479$	12.8562	0.587416	0.293708	+	0.955895i	$0.405111\pi$
$480$	−19.1977	−0.876250
$481$	−42.1146	−1.92026
$482$	18.0063	0.820164
$483$	−21.1735	−0.963429
$484$	−1.61820	−0.0735545
$485$	−9.49933	−0.431342
$486$	7.67806	0.348284
$487$	−18.1618	−0.822991	−0.411495	−	0.911412i	$-0.634993\pi$
$487$	−18.1618	−0.822991	−0.411495	+	0.911412i	$0.634993\pi$
$488$	27.2008	1.23132
$489$	−26.6560	−1.20542
$490$	−4.56710	−0.206321
$491$	−17.5663	−0.792758	−0.396379	−	0.918087i	$-0.629733\pi$
$491$	−17.5663	−0.792758	−0.396379	+	0.918087i	$0.629733\pi$
$492$	−13.1855	−0.594448
$493$	−5.01071	−0.225671
$494$	−22.3983	−1.00775
$495$	−3.43265	−0.154286
$496$	12.7874	0.574173
$497$	−24.9228	−1.11794
$498$	−2.92550	−0.131095
$499$	−15.3723	−0.688160	−0.344080	−	0.938940i	$-0.611809\pi$
$499$	−15.3723	−0.688160	−0.344080	+	0.938940i	$0.611809\pi$
$500$	−13.1831	−0.589565
$501$	−22.5383	−1.00693
$502$	−18.6374	−0.831827
$503$	9.09715	0.405622	0.202811	−	0.979218i	$-0.434992\pi$
$503$	9.09715	0.405622	0.202811	+	0.979218i	$0.434992\pi$
$504$	5.97809	0.266285
$505$	−13.6193	−0.606050
$506$	−4.91461	−0.218481
$507$	−13.0967	−0.581643
$508$	−0.574132	−0.0254730
$509$	23.6286	1.04732	0.523659	−	0.851928i	$-0.324567\pi$
$509$	23.6286	1.04732	0.523659	+	0.851928i	$0.324567\pi$
$510$	2.11164	0.0935050
$511$	13.2715	0.587095
$512$	−18.7146	−0.827076
$513$	−42.2981	−1.86751
$514$	8.01706	0.353617
$515$	−0.447681	−0.0197272
$516$	−2.10555	−0.0926916
$517$	−4.77275	−0.209905
$518$	11.0856	0.487075
$519$	−19.7958	−0.868941
$520$	28.2006	1.23668
$521$	−6.21703	−0.272373	−0.136186	−	0.990683i	$-0.543485\pi$
$521$	−6.21703	−0.272373	−0.136186	+	0.990683i	$0.543485\pi$
$522$	4.04651	0.177111
$523$	29.2151	1.27749	0.638743	−	0.769420i	$-0.279455\pi$
$523$	29.2151	1.27749	0.638743	+	0.769420i	$0.279455\pi$
$524$	18.4991	0.808139
$525$	5.05311	0.220536
$526$	4.83720	0.210912
$527$	−6.89364	−0.300292
$528$	2.41362	0.105039
$529$	40.2617	1.75051
$530$	−11.3265	−0.491992
$531$	13.8524	0.601144
$532$	−24.9884	−1.08338
$533$	30.0753	1.30271
$534$	11.6600	0.504578
$535$	23.4594	1.01424
$536$	14.4860	0.625699
$537$	−19.9883	−0.862561
$538$	−5.08358	−0.219169
$539$	2.81420	0.121216
$540$	23.8179	1.02496
$541$	−0.345274	−0.0148445	−0.00742224	−	0.999972i	$-0.502363\pi$
$541$	−0.345274	−0.0148445	−0.00742224	+	0.999972i	$0.502363\pi$
$542$	13.0886	0.562203
$543$	−30.5194	−1.30971
$544$	5.61756	0.240851
$545$	13.3100	0.570139
$546$	7.89990	0.338085
$547$	32.5804	1.39304	0.696519	−	0.717539i	$-0.254731\pi$
$547$	32.5804	1.39304	0.696519	+	0.717539i	$0.254731\pi$
$548$	4.42831	0.189168
$549$	−15.9013	−0.678652
$550$	1.17288	0.0500119
$551$	−37.8195	−1.61117
$552$	23.1374	0.984795
$553$	21.6034	0.918668
$554$	−0.633133	−0.0268993
$555$	29.9677	1.27206
$556$	16.3574	0.693709
$557$	15.6558	0.663359	0.331680	−	0.943392i	$-0.392385\pi$
$557$	15.6558	0.663359	0.331680	+	0.943392i	$0.392385\pi$
$558$	5.56711	0.235674
$559$	4.80263	0.203130
$560$	9.96762	0.421209
$561$	−1.30117	−0.0549354
$562$	−8.83762	−0.372792
$563$	−29.0284	−1.22340	−0.611701	−	0.791089i	$-0.709515\pi$
$563$	−29.0284	−1.22340	−0.611701	+	0.791089i	$0.709515\pi$
$564$	10.0493	0.423150
$565$	−23.7755	−1.00024
$566$	−16.0628	−0.675170
$567$	6.89677	0.289637
$568$	27.2344	1.14273
$569$	41.1867	1.72664	0.863319	−	0.504658i	$-0.168382\pi$
$569$	41.1867	1.72664	0.863319	+	0.504658i	$0.168382\pi$
$570$	15.9381	0.667573
$571$	−17.1746	−0.718735	−0.359368	−	0.933196i	$-0.617008\pi$
$571$	−17.1746	−0.718735	−0.359368	+	0.933196i	$0.617008\pi$
$572$	−7.77161	−0.324948
$573$	−33.1054	−1.38300
$574$	−7.91661	−0.330433
$575$	−15.0975	−0.629610
$576$	0.312137	0.0130057
$577$	38.4080	1.59894	0.799472	−	0.600703i	$-0.205113\pi$
$577$	38.4080	1.59894	0.799472	+	0.600703i	$0.205113\pi$
$578$	−0.617901	−0.0257013
$579$	14.6571	0.609128
$580$	21.2960	0.884268
$581$	7.44451	0.308850
$582$	2.90789	0.120536
$583$	6.97927	0.289052
$584$	−14.5024	−0.600115
$585$	−16.4857	−0.681602
$586$	−0.0142699	−0.000589485 0
$587$	−22.4347	−0.925980	−0.462990	−	0.886364i	$-0.653223\pi$
$587$	−22.4347	−0.925980	−0.462990	+	0.886364i	$0.653223\pi$
$588$	−5.92543	−0.244361
$589$	−52.0314	−2.14392
$590$	−17.2008	−0.708147
$591$	−4.34037	−0.178539
$592$	16.2663	0.668539
$593$	−23.6050	−0.969342	−0.484671	−	0.874696i	$-0.661061\pi$
$593$	−23.6050	−0.969342	−0.484671	+	0.874696i	$0.661061\pi$
$594$	3.46277	0.142079
$595$	−5.37349	−0.220292
$596$	20.1247	0.824341
$597$	−3.90440	−0.159796
$598$	−23.6031	−0.965202
$599$	−23.2707	−0.950814	−0.475407	−	0.879766i	$-0.657699\pi$
$599$	−23.2707	−0.950814	−0.475407	+	0.879766i	$0.657699\pi$
$600$	−5.52180	−0.225426
$601$	9.38278	0.382731	0.191366	−	0.981519i	$-0.438708\pi$
$601$	9.38278	0.382731	0.191366	+	0.981519i	$0.438708\pi$
$602$	−1.26418	−0.0515241
$603$	−8.46834	−0.344858
$604$	2.06891	0.0841828
$605$	−2.62644	−0.106780
$606$	4.16908	0.169357
$607$	31.5983	1.28253	0.641267	−	0.767318i	$-0.278409\pi$
$607$	31.5983	1.28253	0.641267	+	0.767318i	$0.278409\pi$
$608$	42.3999	1.71954
$609$	13.3390	0.540522
$610$	19.7450	0.799451
$611$	−22.9218	−0.927315
$612$	−2.11492	−0.0854905
$613$	39.2711	1.58615	0.793073	−	0.609126i	$-0.208480\pi$
$613$	39.2711	1.58615	0.793073	+	0.609126i	$0.208480\pi$
$614$	8.52498	0.344040
$615$	−21.4009	−0.862966
$616$	4.57405	0.184294
$617$	−32.3902	−1.30398	−0.651990	−	0.758228i	$-0.726066\pi$
$617$	−32.3902	−1.30398	−0.651990	+	0.758228i	$0.726066\pi$
$618$	0.137042	0.00551265
$619$	31.3949	1.26187	0.630933	−	0.775837i	$-0.282672\pi$
$619$	31.3949	1.26187	0.630933	+	0.775837i	$0.282672\pi$
$620$	29.2986	1.17666
$621$	−44.5733	−1.78866
$622$	−0.866646	−0.0347493
$623$	−29.6712	−1.18875
$624$	11.5917	0.464041
$625$	−30.8878	−1.23551
$626$	15.9308	0.636722
$627$	−9.82088	−0.392208
$628$	−26.1306	−1.04272
$629$	−8.76905	−0.349645
$630$	4.33948	0.172889
$631$	−15.9637	−0.635505	−0.317753	−	0.948174i	$-0.602928\pi$
$631$	−15.9637	−0.635505	−0.317753	+	0.948174i	$0.602928\pi$
$632$	−23.6071	−0.939041
$633$	23.2310	0.923348
$634$	15.2814	0.606901
$635$	−0.931852	−0.0369794
$636$	−14.6952	−0.582703
$637$	13.5156	0.535506
$638$	3.09612	0.122577
$639$	−15.9209	−0.629823
$640$	−29.8959	−1.18174
$641$	−11.2990	−0.446285	−0.223142	−	0.974786i	$-0.571632\pi$
$641$	−11.2990	−0.446285	−0.223142	+	0.974786i	$0.571632\pi$
$642$	−7.18130	−0.283423
$643$	14.0067	0.552372	0.276186	−	0.961104i	$-0.410929\pi$
$643$	14.0067	0.552372	0.276186	+	0.961104i	$0.410929\pi$
$644$	−26.3325	−1.03764
$645$	−3.41744	−0.134562
$646$	−4.66375	−0.183493
$647$	28.2872	1.11208	0.556042	−	0.831154i	$-0.312319\pi$
$647$	28.2872	1.11208	0.556042	+	0.831154i	$0.312319\pi$
$648$	−7.53646	−0.296060
$649$	10.5990	0.416046
$650$	5.63292	0.220941
$651$	18.3515	0.719252
$652$	−33.1507	−1.29828
$653$	−42.8327	−1.67617	−0.838086	−	0.545538i	$-0.816325\pi$
$653$	−42.8327	−1.67617	−0.838086	+	0.545538i	$0.816325\pi$
$654$	−4.07441	−0.159322
$655$	30.0253	1.17318
$656$	−11.6162	−0.453538
$657$	8.47796	0.330757
$658$	6.03360	0.235214
$659$	5.65284	0.220203	0.110102	−	0.993920i	$-0.464882\pi$
$659$	5.65284	0.220203	0.110102	+	0.993920i	$0.464882\pi$
$660$	5.53009	0.215259
$661$	6.33559	0.246426	0.123213	−	0.992380i	$-0.460680\pi$
$661$	6.33559	0.246426	0.123213	+	0.992380i	$0.460680\pi$
$662$	10.1146	0.393114
$663$	−6.24904	−0.242693
$664$	−8.13501	−0.315700
$665$	−40.5577	−1.57276
$666$	7.08164	0.274408
$667$	−39.8538	−1.54314
$668$	−28.0297	−1.08450
$669$	−34.6640	−1.34019
$670$	10.5153	0.406242
$671$	−12.1667	−0.469688
$672$	−14.9545	−0.576881
$673$	11.5829	0.446489	0.223244	−	0.974763i	$-0.428335\pi$
$673$	11.5829	0.446489	0.223244	+	0.974763i	$0.428335\pi$
$674$	−5.58117	−0.214979
$675$	10.6375	0.409438
$676$	−16.2876	−0.626448
$677$	−39.2229	−1.50746	−0.753730	−	0.657184i	$-0.771747\pi$
$677$	−39.2229	−1.50746	−0.753730	+	0.657184i	$0.771747\pi$
$678$	7.27806	0.279512
$679$	−7.39972	−0.283975
$680$	5.87190	0.225177
$681$	0.200156	0.00766999
$682$	4.25959	0.163108
$683$	−41.8260	−1.60043	−0.800213	−	0.599716i	$-0.795280\pi$
$683$	−41.8260	−1.60043	−0.800213	+	0.599716i	$0.795280\pi$
$684$	−15.9628	−0.610355
$685$	7.18743	0.274617
$686$	−12.4069	−0.473698
$687$	23.7204	0.904991
$688$	−1.85496	−0.0707198
$689$	33.5189	1.27697
$690$	16.7954	0.639389
$691$	22.9989	0.874920	0.437460	−	0.899238i	$-0.355878\pi$
$691$	22.9989	0.874920	0.437460	+	0.899238i	$0.355878\pi$
$692$	−24.6191	−0.935877
$693$	−2.67394	−0.101575
$694$	17.7631	0.674277
$695$	26.5491	1.00707
$696$	−14.5762	−0.552509
$697$	6.26226	0.237200
$698$	8.94813	0.338692
$699$	−17.2998	−0.654338
$700$	6.28429	0.237524
$701$	−5.43374	−0.205230	−0.102615	−	0.994721i	$-0.532721\pi$
$701$	−5.43374	−0.205230	−0.102615	+	0.994721i	$0.532721\pi$
$702$	16.6304	0.627674
$703$	−66.1865	−2.49627
$704$	0.238827	0.00900112
$705$	16.3106	0.614291
$706$	8.76054	0.329707
$707$	−10.6091	−0.398995
$708$	−22.3166	−0.838711
$709$	16.0432	0.602515	0.301258	−	0.953543i	$-0.402594\pi$
$709$	16.0432	0.602515	0.301258	+	0.953543i	$0.402594\pi$
$710$	19.7694	0.741931
$711$	13.8005	0.517558
$712$	32.4233	1.21511
$713$	−54.8301	−2.05340
$714$	1.64491	0.0615592
$715$	−12.6138	−0.471730
$716$	−24.8585	−0.929006
$717$	34.4936	1.28819
$718$	−11.0469	−0.412267
$719$	39.7109	1.48097	0.740483	−	0.672075i	$-0.234597\pi$
$719$	39.7109	1.48097	0.740483	+	0.672075i	$0.234597\pi$
$720$	6.36743	0.237300
$721$	−0.348731	−0.0129874
$722$	−23.4607	−0.873116
$723$	37.9174	1.41016
$724$	−37.9554	−1.41060
$725$	9.51119	0.353237
$726$	0.803994	0.0298390
$727$	−7.25142	−0.268940	−0.134470	−	0.990918i	$-0.542933\pi$
$727$	−7.25142	−0.268940	−0.134470	+	0.990918i	$0.542933\pi$
$728$	21.9675	0.814169
$729$	26.2813	0.973382
$730$	−10.5273	−0.389631
$731$	1.00000	0.0369863
$732$	25.6175	0.946849
$733$	33.9083	1.25243	0.626215	−	0.779650i	$-0.284603\pi$
$733$	33.9083	1.25243	0.626215	+	0.779650i	$0.284603\pi$
$734$	21.5715	0.796218
$735$	−9.61735	−0.354741
$736$	44.6805	1.64695
$737$	−6.47942	−0.238673
$738$	−5.05722	−0.186159
$739$	−20.8217	−0.765938	−0.382969	−	0.923761i	$-0.625098\pi$
$739$	−20.8217	−0.765938	−0.382969	+	0.923761i	$0.625098\pi$
$740$	37.2693	1.37005
$741$	−47.1661	−1.73269
$742$	−8.82305	−0.323904
$743$	−30.9368	−1.13496	−0.567480	−	0.823387i	$-0.692082\pi$
$743$	−30.9368	−1.13496	−0.567480	+	0.823387i	$0.692082\pi$
$744$	−20.0537	−0.735203
$745$	32.6637	1.19671
$746$	3.99700	0.146341
$747$	4.75564	0.174000
$748$	−1.61820	−0.0591672
$749$	18.2743	0.667727
$750$	6.54994	0.239170
$751$	17.7268	0.646860	0.323430	−	0.946252i	$-0.395164\pi$
$751$	17.7268	0.646860	0.323430	+	0.946252i	$0.395164\pi$
$752$	8.85326	0.322845
$753$	−39.2464	−1.43022
$754$	14.8695	0.541517
$755$	3.35797	0.122209
$756$	18.5535	0.674784
$757$	7.60882	0.276547	0.138274	−	0.990394i	$-0.455845\pi$
$757$	7.60882	0.276547	0.138274	+	0.990394i	$0.455845\pi$
$758$	5.34130	0.194005
$759$	−10.3491	−0.375650
$760$	44.3195	1.60764
$761$	−9.92152	−0.359655	−0.179827	−	0.983698i	$-0.557554\pi$
$761$	−9.92152	−0.359655	−0.179827	+	0.983698i	$0.557554\pi$
$762$	0.285254	0.0103337
$763$	10.3681	0.375352
$764$	−41.1716	−1.48954
$765$	−3.43265	−0.124108
$766$	15.9034	0.574612
$767$	50.9030	1.83800
$768$	8.53011	0.307804
$769$	43.2831	1.56083	0.780414	−	0.625263i	$-0.215008\pi$
$769$	43.2831	1.56083	0.780414	+	0.625263i	$0.215008\pi$
$770$	3.32029	0.119655
$771$	16.8822	0.607998
$772$	18.2283	0.656050
$773$	20.8103	0.748493	0.374247	−	0.927329i	$-0.377901\pi$
$773$	20.8103	0.748493	0.374247	+	0.927329i	$0.377901\pi$
$774$	−0.807571	−0.0290276
$775$	13.0853	0.470038
$776$	8.08606	0.290273
$777$	23.3440	0.837462
$778$	23.5413	0.843998
$779$	47.2658	1.69347
$780$	26.5590	0.950965
$781$	−12.1817	−0.435894
$782$	−4.91461	−0.175746
$783$	28.0804	1.00351
$784$	−5.22023	−0.186437
$785$	−42.4116	−1.51374
$786$	−9.19121	−0.327839
$787$	−9.13009	−0.325453	−0.162726	−	0.986671i	$-0.552029\pi$
$787$	−9.13009	−0.325453	−0.162726	+	0.986671i	$0.552029\pi$
$788$	−5.39790	−0.192292
$789$	10.1861	0.362636
$790$	−17.1363	−0.609683
$791$	−18.5205	−0.658513
$792$	2.92195	0.103827
$793$	−58.4320	−2.07498
$794$	−3.93290	−0.139574
$795$	−23.8512	−0.845916
$796$	−4.85570	−0.172106
$797$	47.3835	1.67841	0.839205	−	0.543815i	$-0.183021\pi$
$797$	47.3835	1.67841	0.839205	+	0.543815i	$0.183021\pi$
$798$	12.4153	0.439498
$799$	−4.77275	−0.168848
$800$	−10.6631	−0.376997
$801$	−18.9543	−0.669718
$802$	13.4363	0.474453
$803$	6.48678	0.228914
$804$	13.6427	0.481143
$805$	−42.7392	−1.50636
$806$	20.4572	0.720576
$807$	−10.7049	−0.376832
$808$	11.5931	0.407843
$809$	−14.1419	−0.497204	−0.248602	−	0.968606i	$-0.579971\pi$
$809$	−14.1419	−0.497204	−0.248602	+	0.968606i	$0.579971\pi$
$810$	−5.47069	−0.192221
$811$	45.3734	1.59328	0.796638	−	0.604457i	$-0.206610\pi$
$811$	45.3734	1.59328	0.796638	+	0.604457i	$0.206610\pi$
$812$	16.5890	0.582160
$813$	27.5618	0.966634
$814$	5.41841	0.189915
$815$	−53.8056	−1.88473
$816$	2.41362	0.0844936
$817$	7.54774	0.264062
$818$	4.19120	0.146542
$819$	−12.8419	−0.448734
$820$	−26.6152	−0.929443
$821$	36.2960	1.26674	0.633370	−	0.773849i	$-0.281671\pi$
$821$	36.2960	1.26674	0.633370	+	0.773849i	$0.281671\pi$
$822$	−2.20018	−0.0767403
$823$	31.7978	1.10840	0.554201	−	0.832383i	$-0.313024\pi$
$823$	31.7978	1.10840	0.554201	+	0.832383i	$0.313024\pi$
$824$	0.381077	0.0132755
$825$	2.46984	0.0859889
$826$	−13.3990	−0.466210
$827$	−12.1290	−0.421766	−0.210883	−	0.977511i	$-0.567634\pi$
$827$	−12.1290	−0.421766	−0.210883	+	0.977511i	$0.567634\pi$
$828$	−16.8215	−0.584587
$829$	33.8633	1.17612	0.588061	−	0.808817i	$-0.299892\pi$
$829$	33.8633	1.17612	0.588061	+	0.808817i	$0.299892\pi$
$830$	−5.90518	−0.204972
$831$	−1.33324	−0.0462497
$832$	1.14700	0.0397650
$833$	2.81420	0.0975062
$834$	−8.12710	−0.281419
$835$	−45.4939	−1.57438
$836$	−12.2137	−0.422421
$837$	38.6325	1.33534
$838$	−4.74037	−0.163753
$839$	−12.8010	−0.441938	−0.220969	−	0.975281i	$-0.570922\pi$
$839$	−12.8010	−0.441938	−0.220969	+	0.975281i	$0.570922\pi$
$840$	−15.6315	−0.539339
$841$	−3.89279	−0.134234
$842$	0.653745	0.0225295
$843$	−18.6102	−0.640968
$844$	28.8912	0.994476
$845$	−26.4359	−0.909422
$846$	3.85433	0.132515
$847$	−2.04592	−0.0702988
$848$	−12.9463	−0.444577
$849$	−33.8249	−1.16087
$850$	1.17288	0.0402295
$851$	−69.7466	−2.39088
$852$	25.6491	0.878724
$853$	20.4429	0.699950	0.349975	−	0.936759i	$-0.386190\pi$
$853$	20.4429	0.699950	0.349975	+	0.936759i	$0.386190\pi$
$854$	15.3808	0.526321
$855$	−25.9087	−0.886059
$856$	−19.9693	−0.682535
$857$	4.55245	0.155509	0.0777544	−	0.996973i	$-0.475225\pi$
$857$	4.55245	0.155509	0.0777544	+	0.996973i	$0.475225\pi$
$858$	3.86129	0.131822
$859$	9.56494	0.326352	0.163176	−	0.986597i	$-0.447826\pi$
$859$	9.56494	0.326352	0.163176	+	0.986597i	$0.447826\pi$
$860$	−4.25010	−0.144927
$861$	−16.6707	−0.568136
$862$	6.45653	0.219910
$863$	51.1745	1.74200	0.871000	−	0.491282i	$-0.163472\pi$
$863$	51.1745	1.74200	0.871000	+	0.491282i	$0.163472\pi$
$864$	−31.4813	−1.07101
$865$	−39.9583	−1.35862
$866$	3.52936	0.119933
$867$	−1.30117	−0.0441900
$868$	22.8228	0.774658
$869$	10.5592	0.358197
$870$	−10.5808	−0.358723
$871$	−31.1183	−1.05440
$872$	−11.3298	−0.383676
$873$	−4.72702	−0.159986
$874$	−37.0942	−1.25473
$875$	−16.6676	−0.563469
$876$	−13.6582	−0.461469
$877$	38.0196	1.28383	0.641915	−	0.766776i	$-0.278140\pi$
$877$	38.0196	1.28383	0.641915	+	0.766776i	$0.278140\pi$
$878$	8.81361	0.297445
$879$	−0.0300494	−0.00101354
$880$	4.87194	0.164233
$881$	−43.0465	−1.45027	−0.725137	−	0.688605i	$-0.758224\pi$
$881$	−43.0465	−1.45027	−0.725137	+	0.688605i	$0.758224\pi$
$882$	−2.27267	−0.0765246
$883$	−20.7605	−0.698645	−0.349323	−	0.937003i	$-0.613588\pi$
$883$	−20.7605	−0.698645	−0.349323	+	0.937003i	$0.613588\pi$
$884$	−7.77161	−0.261388
$885$	−36.2213	−1.21757
$886$	−2.01461	−0.0676820
$887$	−51.7960	−1.73914	−0.869570	−	0.493810i	$-0.835604\pi$
$887$	−51.7960	−1.73914	−0.869570	+	0.493810i	$0.835604\pi$
$888$	−25.5093	−0.856035
$889$	−0.725887	−0.0243455
$890$	23.5360	0.788927
$891$	3.37098	0.112932
$892$	−43.1098	−1.44342
$893$	−36.0234	−1.20548
$894$	−9.99887	−0.334412
$895$	−40.3469	−1.34865
$896$	−23.2881	−0.778001
$897$	−49.7031	−1.65954
$898$	−20.7794	−0.693416
$899$	34.5420	1.15204
$900$	4.01448	0.133816
$901$	6.97927	0.232513
$902$	−3.86945	−0.128839
$903$	−2.66209	−0.0885889
$904$	20.2383	0.673117
$905$	−61.6040	−2.04779
$906$	−1.02793	−0.0341506
$907$	35.5126	1.17918	0.589589	−	0.807704i	$-0.299290\pi$
$907$	35.5126	1.17918	0.589589	+	0.807704i	$0.299290\pi$
$908$	0.248924	0.00826083
$909$	−6.77719	−0.224785
$910$	15.9461	0.528609
$911$	9.54375	0.316198	0.158099	−	0.987423i	$-0.449463\pi$
$911$	9.54375	0.316198	0.158099	+	0.987423i	$0.449463\pi$
$912$	18.2174	0.603237
$913$	3.63871	0.120424
$914$	−5.26029	−0.173995
$915$	41.5788	1.37455
$916$	29.4999	0.974704
$917$	23.3889	0.772368
$918$	3.46277	0.114288
$919$	−43.8152	−1.44533	−0.722665	−	0.691198i	$-0.757083\pi$
$919$	−43.8152	−1.44533	−0.722665	+	0.691198i	$0.757083\pi$
$920$	46.7034	1.53977
$921$	17.9518	0.591532
$922$	5.94709	0.195857
$923$	−58.5041	−1.92569
$924$	4.30779	0.141716
$925$	16.6452	0.547290
$926$	−7.02102	−0.230725
$927$	−0.222774	−0.00731684
$928$	−28.1480	−0.924002
$929$	49.9408	1.63850	0.819252	−	0.573434i	$-0.194389\pi$
$929$	49.9408	1.63850	0.819252	+	0.573434i	$0.194389\pi$
$930$	−14.5569	−0.477339
$931$	21.2408	0.696140
$932$	−21.5149	−0.704743
$933$	−1.82497	−0.0597469
$934$	−10.3811	−0.339678
$935$	−2.62644	−0.0858937
$936$	14.0331	0.458685
$937$	23.9449	0.782245	0.391123	−	0.920339i	$-0.372087\pi$
$937$	23.9449	0.782245	0.391123	+	0.920339i	$0.372087\pi$
$938$	8.19115	0.267450
$939$	33.5468	1.09476
$940$	20.2846	0.661612
$941$	−6.26077	−0.204095	−0.102048	−	0.994780i	$-0.532539\pi$
$941$	−6.26077	−0.204095	−0.102048	+	0.994780i	$0.532539\pi$
$942$	12.9829	0.423005
$943$	49.8082	1.62198
$944$	−19.6607	−0.639901
$945$	30.1135	0.979591
$946$	−0.617901	−0.0200897
$947$	4.99417	0.162289	0.0811444	−	0.996702i	$-0.474143\pi$
$947$	4.99417	0.162289	0.0811444	+	0.996702i	$0.474143\pi$
$948$	−22.2330	−0.722093
$949$	31.1536	1.01129
$950$	8.85261	0.287216
$951$	32.1793	1.04349
$952$	4.57405	0.148246
$953$	−14.3212	−0.463910	−0.231955	−	0.972727i	$-0.574512\pi$
$953$	−14.3212	−0.463910	−0.231955	+	0.972727i	$0.574512\pi$
$954$	−5.63626	−0.182481
$955$	−66.8240	−2.16238
$956$	42.8980	1.38742
$957$	6.51978	0.210755
$958$	−7.94387	−0.256655
$959$	5.59881	0.180795
$960$	−0.816175	−0.0263419
$961$	16.5223	0.532977
$962$	26.0226	0.839003
$963$	11.6738	0.376183
$964$	47.1560	1.51879
$965$	29.5856	0.952396
$966$	13.0832	0.420944
$967$	24.5361	0.789027	0.394513	−	0.918890i	$-0.370913\pi$
$967$	24.5361	0.789027	0.394513	+	0.918890i	$0.370913\pi$
$968$	2.23569	0.0718578
$969$	−9.82088	−0.315492
$970$	5.86964	0.188463
$971$	−45.3905	−1.45665	−0.728325	−	0.685231i	$-0.759701\pi$
$971$	−45.3905	−1.45665	−0.728325	+	0.685231i	$0.759701\pi$
$972$	20.1078	0.644957
$973$	20.6810	0.663004
$974$	11.2222	0.359583
$975$	11.8617	0.379880
$976$	22.5687	0.722406
$977$	22.2297	0.711192	0.355596	−	0.934640i	$-0.384278\pi$
$977$	22.2297	0.711192	0.355596	+	0.934640i	$0.384278\pi$
$978$	16.4708	0.526677
$979$	−14.5026	−0.463505
$980$	−11.9606	−0.382068
$981$	6.62329	0.211465
$982$	10.8543	0.346374
$983$	1.87347	0.0597545	0.0298773	−	0.999554i	$-0.490488\pi$
$983$	1.87347	0.0597545	0.0298773	+	0.999554i	$0.490488\pi$
$984$	18.2170	0.580735
$985$	−8.76113	−0.279153
$986$	3.09612	0.0986006
$987$	12.7055	0.404420
$988$	−58.6581	−1.86616
$989$	7.95372	0.252914
$990$	2.12104	0.0674109
$991$	−13.5265	−0.429683	−0.214841	−	0.976649i	$-0.568923\pi$
$991$	−13.5265	−0.429683	−0.214841	+	0.976649i	$0.568923\pi$
$992$	−38.7254	−1.22953
$993$	21.2991	0.675907
$994$	15.3998	0.488452
$995$	−7.88111	−0.249848
$996$	−7.66148	−0.242763
$997$	15.5351	0.492002	0.246001	−	0.969270i	$-0.420883\pi$
$997$	15.5351	0.492002	0.246001	+	0.969270i	$0.420883\pi$
$998$	9.49858	0.300672
$999$	49.1425	1.55480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.32	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.32	✓	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)

\(f(q)\)	\(=\)	\(q-0.617901 q^{2} -1.30117 q^{3} -1.61820 q^{4} -2.62644 q^{5} +0.803994 q^{6} -2.04592 q^{7} +2.23569 q^{8} -1.30696 q^{9} +O(q^{10})\)	\(q-0.617901 q^{2} -1.30117 q^{3} -1.61820 q^{4} -2.62644 q^{5} +0.803994 q^{6} -2.04592 q^{7} +2.23569 q^{8} -1.30696 q^{9} +1.62288 q^{10} -1.00000 q^{11} +2.10555 q^{12} -4.80263 q^{13} +1.26418 q^{14} +3.41744 q^{15} +1.85496 q^{16} -1.00000 q^{17} +0.807571 q^{18} -7.54774 q^{19} +4.25010 q^{20} +2.66209 q^{21} +0.617901 q^{22} -7.95372 q^{23} -2.90901 q^{24} +1.89817 q^{25} +2.96755 q^{26} +5.60408 q^{27} +3.31071 q^{28} +5.01071 q^{29} -2.11164 q^{30} +6.89364 q^{31} -5.61756 q^{32} +1.30117 q^{33} +0.617901 q^{34} +5.37349 q^{35} +2.11492 q^{36} +8.76905 q^{37} +4.66375 q^{38} +6.24904 q^{39} -5.87190 q^{40} -6.26226 q^{41} -1.64491 q^{42} -1.00000 q^{43} +1.61820 q^{44} +3.43265 q^{45} +4.91461 q^{46} +4.77275 q^{47} -2.41362 q^{48} -2.81420 q^{49} -1.17288 q^{50} +1.30117 q^{51} +7.77161 q^{52} -6.97927 q^{53} -3.46277 q^{54} +2.62644 q^{55} -4.57405 q^{56} +9.82088 q^{57} -3.09612 q^{58} -10.5990 q^{59} -5.53009 q^{60} +12.1667 q^{61} -4.25959 q^{62} +2.67394 q^{63} -0.238827 q^{64} +12.6138 q^{65} -0.803994 q^{66} +6.47942 q^{67} +1.61820 q^{68} +10.3491 q^{69} -3.32029 q^{70} +12.1817 q^{71} -2.92195 q^{72} -6.48678 q^{73} -5.41841 q^{74} -2.46984 q^{75} +12.2137 q^{76} +2.04592 q^{77} -3.86129 q^{78} -10.5592 q^{79} -4.87194 q^{80} -3.37098 q^{81} +3.86945 q^{82} -3.63871 q^{83} -4.30779 q^{84} +2.62644 q^{85} +0.617901 q^{86} -6.51978 q^{87} -2.23569 q^{88} +14.5026 q^{89} -2.12104 q^{90} +9.82582 q^{91} +12.8707 q^{92} -8.96979 q^{93} -2.94908 q^{94} +19.8237 q^{95} +7.30940 q^{96} +3.61681 q^{97} +1.73890 q^{98} +1.30696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 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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