LMFDB - Embedded newform 8043.2.a.t.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85290 q^{2} -1.00000 q^{3} +1.43325 q^{4} -3.21014 q^{5} +1.85290 q^{6} +1.00000 q^{7} +1.05014 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.85290 q^{2} -1.00000 q^{3} +1.43325 q^{4} -3.21014 q^{5} +1.85290 q^{6} +1.00000 q^{7} +1.05014 q^{8} +1.00000 q^{9} +5.94808 q^{10} +4.69097 q^{11} -1.43325 q^{12} +2.39172 q^{13} -1.85290 q^{14} +3.21014 q^{15} -4.81230 q^{16} -5.33525 q^{17} -1.85290 q^{18} -0.312316 q^{19} -4.60092 q^{20} -1.00000 q^{21} -8.69191 q^{22} -5.88569 q^{23} -1.05014 q^{24} +5.30500 q^{25} -4.43163 q^{26} -1.00000 q^{27} +1.43325 q^{28} +7.36152 q^{29} -5.94808 q^{30} +0.943195 q^{31} +6.81644 q^{32} -4.69097 q^{33} +9.88569 q^{34} -3.21014 q^{35} +1.43325 q^{36} +7.38664 q^{37} +0.578692 q^{38} -2.39172 q^{39} -3.37110 q^{40} +2.27743 q^{41} +1.85290 q^{42} +5.60881 q^{43} +6.72332 q^{44} -3.21014 q^{45} +10.9056 q^{46} +1.72173 q^{47} +4.81230 q^{48} +1.00000 q^{49} -9.82965 q^{50} +5.33525 q^{51} +3.42793 q^{52} +3.85567 q^{53} +1.85290 q^{54} -15.0587 q^{55} +1.05014 q^{56} +0.312316 q^{57} -13.6402 q^{58} -14.5600 q^{59} +4.60092 q^{60} +10.7348 q^{61} -1.74765 q^{62} +1.00000 q^{63} -3.00559 q^{64} -7.67777 q^{65} +8.69191 q^{66} -7.76670 q^{67} -7.64672 q^{68} +5.88569 q^{69} +5.94808 q^{70} -1.06851 q^{71} +1.05014 q^{72} +15.6913 q^{73} -13.6867 q^{74} -5.30500 q^{75} -0.447626 q^{76} +4.69097 q^{77} +4.43163 q^{78} -8.92717 q^{79} +15.4482 q^{80} +1.00000 q^{81} -4.21985 q^{82} +12.7810 q^{83} -1.43325 q^{84} +17.1269 q^{85} -10.3926 q^{86} -7.36152 q^{87} +4.92618 q^{88} +18.7109 q^{89} +5.94808 q^{90} +2.39172 q^{91} -8.43564 q^{92} -0.943195 q^{93} -3.19020 q^{94} +1.00258 q^{95} -6.81644 q^{96} +6.81283 q^{97} -1.85290 q^{98} +4.69097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.85290	−1.31020	−0.655100	−	0.755542i	$-0.727373\pi$
$2$	−1.85290	−1.31020	−0.655100	+	0.755542i	$0.727373\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.43325	0.716623
$5$	−3.21014	−1.43562	−0.717809	−	0.696240i	$-0.754855\pi$
$5$	−3.21014	−1.43562	−0.717809	+	0.696240i	$0.754855\pi$
$6$	1.85290	0.756444
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.05014	0.371281
$9$	1.00000	0.333333
$10$	5.94808	1.88095
$11$	4.69097	1.41438	0.707191	−	0.707023i	$-0.249962\pi$
$11$	4.69097	1.41438	0.707191	+	0.707023i	$0.249962\pi$
$12$	−1.43325	−0.413742
$13$	2.39172	0.663345	0.331672	−	0.943395i	$-0.392387\pi$
$13$	2.39172	0.663345	0.331672	+	0.943395i	$0.392387\pi$
$14$	−1.85290	−0.495209
$15$	3.21014	0.828855
$16$	−4.81230	−1.20307
$17$	−5.33525	−1.29399	−0.646994	−	0.762495i	$-0.723974\pi$
$17$	−5.33525	−1.29399	−0.646994	+	0.762495i	$0.723974\pi$
$18$	−1.85290	−0.436733
$19$	−0.312316	−0.0716503	−0.0358252	−	0.999358i	$-0.511406\pi$
$19$	−0.312316	−0.0716503	−0.0358252	+	0.999358i	$0.511406\pi$
$20$	−4.60092	−1.02880
$21$	−1.00000	−0.218218
$22$	−8.69191	−1.85312
$23$	−5.88569	−1.22725	−0.613625	−	0.789597i	$-0.710289\pi$
$23$	−5.88569	−1.22725	−0.613625	+	0.789597i	$0.710289\pi$
$24$	−1.05014	−0.214359
$25$	5.30500	1.06100
$26$	−4.43163	−0.869114
$27$	−1.00000	−0.192450
$28$	1.43325	0.270858
$29$	7.36152	1.36700	0.683500	−	0.729951i	$-0.260457\pi$
$29$	7.36152	1.36700	0.683500	+	0.729951i	$0.260457\pi$
$30$	−5.94808	−1.08597
$31$	0.943195	0.169403	0.0847014	−	0.996406i	$-0.473006\pi$
$31$	0.943195	0.169403	0.0847014	+	0.996406i	$0.473006\pi$
$32$	6.81644	1.20499
$33$	−4.69097	−0.816594
$34$	9.88569	1.69538
$35$	−3.21014	−0.542613
$36$	1.43325	0.238874
$37$	7.38664	1.21436	0.607178	−	0.794566i	$-0.292301\pi$
$37$	7.38664	1.21436	0.607178	+	0.794566i	$0.292301\pi$
$38$	0.578692	0.0938762
$39$	−2.39172	−0.382982
$40$	−3.37110	−0.533017
$41$	2.27743	0.355674	0.177837	−	0.984060i	$-0.443090\pi$
$41$	2.27743	0.355674	0.177837	+	0.984060i	$0.443090\pi$
$42$	1.85290	0.285909
$43$	5.60881	0.855336	0.427668	−	0.903936i	$-0.359335\pi$
$43$	5.60881	0.855336	0.427668	+	0.903936i	$0.359335\pi$
$44$	6.72332	1.01358
$45$	−3.21014	−0.478539
$46$	10.9056	1.60794
$47$	1.72173	0.251140	0.125570	−	0.992085i	$-0.459924\pi$
$47$	1.72173	0.251140	0.125570	+	0.992085i	$0.459924\pi$
$48$	4.81230	0.694595
$49$	1.00000	0.142857
$50$	−9.82965	−1.39012
$51$	5.33525	0.747084
$52$	3.42793	0.475368
$53$	3.85567	0.529617	0.264808	−	0.964301i	$-0.414691\pi$
$53$	3.85567	0.529617	0.264808	+	0.964301i	$0.414691\pi$
$54$	1.85290	0.252148
$55$	−15.0587	−2.03051
$56$	1.05014	0.140331
$57$	0.312316	0.0413673
$58$	−13.6402	−1.79104
$59$	−14.5600	−1.89556	−0.947778	−	0.318932i	$-0.896676\pi$
$59$	−14.5600	−1.89556	−0.947778	+	0.318932i	$0.896676\pi$
$60$	4.60092	0.593976
$61$	10.7348	1.37445	0.687224	−	0.726446i	$-0.258829\pi$
$61$	10.7348	1.37445	0.687224	+	0.726446i	$0.258829\pi$
$62$	−1.74765	−0.221951
$63$	1.00000	0.125988
$64$	−3.00559	−0.375699
$65$	−7.67777	−0.952310
$66$	8.69191	1.06990
$67$	−7.76670	−0.948853	−0.474426	−	0.880295i	$-0.657345\pi$
$67$	−7.76670	−0.948853	−0.474426	+	0.880295i	$0.657345\pi$
$68$	−7.64672	−0.927301
$69$	5.88569	0.708553
$70$	5.94808	0.710931
$71$	−1.06851	−0.126809	−0.0634044	−	0.997988i	$-0.520196\pi$
$71$	−1.06851	−0.126809	−0.0634044	+	0.997988i	$0.520196\pi$
$72$	1.05014	0.123760
$73$	15.6913	1.83653	0.918266	−	0.395964i	$-0.129589\pi$
$73$	15.6913	1.83653	0.918266	+	0.395964i	$0.129589\pi$
$74$	−13.6867	−1.59105
$75$	−5.30500	−0.612569
$76$	−0.447626	−0.0513463
$77$	4.69097	0.534586
$78$	4.43163	0.501783
$79$	−8.92717	−1.00438	−0.502192	−	0.864756i	$-0.667473\pi$
$79$	−8.92717	−1.00438	−0.502192	+	0.864756i	$0.667473\pi$
$80$	15.4482	1.72716
$81$	1.00000	0.111111
$82$	−4.21985	−0.466004
$83$	12.7810	1.40289	0.701447	−	0.712722i	$-0.252538\pi$
$83$	12.7810	1.40289	0.701447	+	0.712722i	$0.252538\pi$
$84$	−1.43325	−0.156380
$85$	17.1269	1.85767
$86$	−10.3926	−1.12066
$87$	−7.36152	−0.789237
$88$	4.92618	0.525132
$89$	18.7109	1.98335	0.991674	−	0.128776i	$-0.0411047\pi$
$89$	18.7109	1.98335	0.991674	+	0.128776i	$0.0411047\pi$
$90$	5.94808	0.626982
$91$	2.39172	0.250721
$92$	−8.43564	−0.879476
$93$	−0.943195	−0.0978047
$94$	−3.19020	−0.329044
$95$	1.00258	0.102863
$96$	−6.81644	−0.695700
$97$	6.81283	0.691738	0.345869	−	0.938283i	$-0.387584\pi$
$97$	6.81283	0.691738	0.345869	+	0.938283i	$0.387584\pi$
$98$	−1.85290	−0.187171
$99$	4.69097	0.471461
$100$	7.60337	0.760337
$101$	−13.6015	−1.35340	−0.676702	−	0.736257i	$-0.736592\pi$
$101$	−13.6015	−1.35340	−0.676702	+	0.736257i	$0.736592\pi$
$102$	−9.88569	−0.978830
$103$	−4.83718	−0.476621	−0.238311	−	0.971189i	$-0.576594\pi$
$103$	−4.83718	−0.476621	−0.238311	+	0.971189i	$0.576594\pi$
$104$	2.51165	0.246287
$105$	3.21014	0.313278
$106$	−7.14417	−0.693903
$107$	−12.9339	−1.25037	−0.625184	−	0.780477i	$-0.714976\pi$
$107$	−12.9339	−1.25037	−0.625184	+	0.780477i	$0.714976\pi$
$108$	−1.43325	−0.137914
$109$	5.11701	0.490121	0.245061	−	0.969508i	$-0.421192\pi$
$109$	5.11701	0.490121	0.245061	+	0.969508i	$0.421192\pi$
$110$	27.9023	2.66038
$111$	−7.38664	−0.701109
$112$	−4.81230	−0.454719
$113$	13.5759	1.27711	0.638554	−	0.769577i	$-0.279533\pi$
$113$	13.5759	1.27711	0.638554	+	0.769577i	$0.279533\pi$
$114$	−0.578692	−0.0541995
$115$	18.8939	1.76186
$116$	10.5509	0.979623
$117$	2.39172	0.221115
$118$	26.9783	2.48356
$119$	−5.33525	−0.489081
$120$	3.37110	0.307738
$121$	11.0052	1.00048
$122$	−19.8905	−1.80080
$123$	−2.27743	−0.205349
$124$	1.35183	0.121398
$125$	−0.979095	−0.0875729
$126$	−1.85290	−0.165070
$127$	17.8346	1.58256	0.791282	−	0.611451i	$-0.209414\pi$
$127$	17.8346	1.58256	0.791282	+	0.611451i	$0.209414\pi$
$128$	−8.06380	−0.712746
$129$	−5.60881	−0.493828
$130$	14.2262	1.24772
$131$	−21.6482	−1.89142	−0.945708	−	0.325018i	$-0.894630\pi$
$131$	−21.6482	−1.89142	−0.945708	+	0.325018i	$0.894630\pi$
$132$	−6.72332	−0.585190
$133$	−0.312316	−0.0270813
$134$	14.3909	1.24319
$135$	3.21014	0.276285
$136$	−5.60276	−0.480433
$137$	−2.09823	−0.179264	−0.0896320	−	0.995975i	$-0.528569\pi$
$137$	−2.09823	−0.179264	−0.0896320	+	0.995975i	$0.528569\pi$
$138$	−10.9056	−0.928346
$139$	−18.1952	−1.54330	−0.771650	−	0.636048i	$-0.780568\pi$
$139$	−18.1952	−1.54330	−0.771650	+	0.636048i	$0.780568\pi$
$140$	−4.60092	−0.388849
$141$	−1.72173	−0.144996
$142$	1.97985	0.166145
$143$	11.2195	0.938223
$144$	−4.81230	−0.401025
$145$	−23.6315	−1.96249
$146$	−29.0745	−2.40622
$147$	−1.00000	−0.0824786
$148$	10.5869	0.870235
$149$	−17.8336	−1.46098	−0.730492	−	0.682922i	$-0.760709\pi$
$149$	−17.8336	−1.46098	−0.730492	+	0.682922i	$0.760709\pi$
$150$	9.82965	0.802587
$151$	9.35590	0.761372	0.380686	−	0.924704i	$-0.375688\pi$
$151$	9.35590	0.761372	0.380686	+	0.924704i	$0.375688\pi$
$152$	−0.327976	−0.0266024
$153$	−5.33525	−0.431329
$154$	−8.69191	−0.700414
$155$	−3.02779	−0.243198
$156$	−3.42793	−0.274454
$157$	−23.3467	−1.86327	−0.931635	−	0.363396i	$-0.881617\pi$
$157$	−23.3467	−1.86327	−0.931635	+	0.363396i	$0.881617\pi$
$158$	16.5412	1.31594
$159$	−3.85567	−0.305774
$160$	−21.8817	−1.72990
$161$	−5.88569	−0.463857
$162$	−1.85290	−0.145578
$163$	18.9277	1.48254	0.741268	−	0.671210i	$-0.234225\pi$
$163$	18.9277	1.48254	0.741268	+	0.671210i	$0.234225\pi$
$164$	3.26411	0.254884
$165$	15.0587	1.17232
$166$	−23.6819	−1.83807
$167$	6.43574	0.498012	0.249006	−	0.968502i	$-0.419896\pi$
$167$	6.43574	0.498012	0.249006	+	0.968502i	$0.419896\pi$
$168$	−1.05014	−0.0810201
$169$	−7.27966	−0.559973
$170$	−31.7345	−2.43392
$171$	−0.312316	−0.0238834
$172$	8.03881	0.612953
$173$	−15.7641	−1.19852	−0.599261	−	0.800554i	$-0.704539\pi$
$173$	−15.7641	−1.19852	−0.599261	+	0.800554i	$0.704539\pi$
$174$	13.6402	1.03406
$175$	5.30500	0.401020
$176$	−22.5744	−1.70161
$177$	14.5600	1.09440
$178$	−34.6694	−2.59858
$179$	−7.14886	−0.534331	−0.267166	−	0.963651i	$-0.586087\pi$
$179$	−7.14886	−0.534331	−0.267166	+	0.963651i	$0.586087\pi$
$180$	−4.60092	−0.342932
$181$	−9.10549	−0.676806	−0.338403	−	0.941001i	$-0.609887\pi$
$181$	−9.10549	−0.676806	−0.338403	+	0.941001i	$0.609887\pi$
$182$	−4.43163	−0.328494
$183$	−10.7348	−0.793538
$184$	−6.18079	−0.455654
$185$	−23.7122	−1.74335
$186$	1.74765	0.128144
$187$	−25.0275	−1.83019
$188$	2.46766	0.179973
$189$	−1.00000	−0.0727393
$190$	−1.85768	−0.134770
$191$	−19.5972	−1.41800	−0.709001	−	0.705207i	$-0.750854\pi$
$191$	−19.5972	−1.41800	−0.709001	+	0.705207i	$0.750854\pi$
$192$	3.00559	0.216910
$193$	−5.18417	−0.373165	−0.186582	−	0.982439i	$-0.559741\pi$
$193$	−5.18417	−0.373165	−0.186582	+	0.982439i	$0.559741\pi$
$194$	−12.6235	−0.906314
$195$	7.67777	0.549817
$196$	1.43325	0.102375
$197$	16.7284	1.19185	0.595926	−	0.803040i	$-0.296785\pi$
$197$	16.7284	1.19185	0.595926	+	0.803040i	$0.296785\pi$
$198$	−8.69191	−0.617707
$199$	20.7020	1.46752	0.733762	−	0.679406i	$-0.237763\pi$
$199$	20.7020	1.46752	0.733762	+	0.679406i	$0.237763\pi$
$200$	5.57099	0.393929
$201$	7.76670	0.547820
$202$	25.2023	1.77323
$203$	7.36152	0.516677
$204$	7.64672	0.535378
$205$	−7.31086	−0.510613
$206$	8.96281	0.624469
$207$	−5.88569	−0.409083
$208$	−11.5097	−0.798053
$209$	−1.46507	−0.101341
$210$	−5.94808	−0.410456
$211$	16.8083	1.15713	0.578567	−	0.815635i	$-0.303612\pi$
$211$	16.8083	1.15713	0.578567	+	0.815635i	$0.303612\pi$
$212$	5.52612	0.379535
$213$	1.06851	0.0732131
$214$	23.9653	1.63823
$215$	−18.0051	−1.22794
$216$	−1.05014	−0.0714530
$217$	0.943195	0.0640282
$218$	−9.48132	−0.642156
$219$	−15.6913	−1.06032
$220$	−21.5828	−1.45511
$221$	−12.7604	−0.858360
$222$	13.6867	0.918592
$223$	−21.3467	−1.42948	−0.714739	−	0.699392i	$-0.753454\pi$
$223$	−21.3467	−1.42948	−0.714739	+	0.699392i	$0.753454\pi$
$224$	6.81644	0.455442
$225$	5.30500	0.353667
$226$	−25.1547	−1.67327
$227$	3.72777	0.247421	0.123711	−	0.992318i	$-0.460521\pi$
$227$	3.72777	0.247421	0.123711	+	0.992318i	$0.460521\pi$
$228$	0.447626	0.0296448
$229$	−14.4009	−0.951640	−0.475820	−	0.879543i	$-0.657849\pi$
$229$	−14.4009	−0.951640	−0.475820	+	0.879543i	$0.657849\pi$
$230$	−35.0085	−2.30839
$231$	−4.69097	−0.308643
$232$	7.73062	0.507540
$233$	26.9701	1.76687	0.883435	−	0.468553i	$-0.155225\pi$
$233$	26.9701	1.76687	0.883435	+	0.468553i	$0.155225\pi$
$234$	−4.43163	−0.289705
$235$	−5.52699	−0.360541
$236$	−20.8681	−1.35840
$237$	8.92717	0.579882
$238$	9.88569	0.640794
$239$	−8.73652	−0.565119	−0.282559	−	0.959250i	$-0.591183\pi$
$239$	−8.73652	−0.565119	−0.282559	+	0.959250i	$0.591183\pi$
$240$	−15.4482	−0.997174
$241$	−6.09077	−0.392341	−0.196171	−	0.980570i	$-0.562851\pi$
$241$	−6.09077	−0.392341	−0.196171	+	0.980570i	$0.562851\pi$
$242$	−20.3916	−1.31082
$243$	−1.00000	−0.0641500
$244$	15.3856	0.984961
$245$	−3.21014	−0.205088
$246$	4.21985	0.269048
$247$	−0.746975	−0.0475289
$248$	0.990486	0.0628959
$249$	−12.7810	−0.809961
$250$	1.81417	0.114738
$251$	−25.2040	−1.59086	−0.795431	−	0.606044i	$-0.792756\pi$
$251$	−25.2040	−1.59086	−0.795431	+	0.606044i	$0.792756\pi$
$252$	1.43325	0.0902860
$253$	−27.6096	−1.73580
$254$	−33.0458	−2.07347
$255$	−17.1269	−1.07253
$256$	20.9526	1.30954
$257$	7.18529	0.448206	0.224103	−	0.974565i	$-0.428055\pi$
$257$	7.18529	0.448206	0.224103	+	0.974565i	$0.428055\pi$
$258$	10.3926	0.647014
$259$	7.38664	0.458983
$260$	−11.0041	−0.682447
$261$	7.36152	0.455666
$262$	40.1121	2.47813
$263$	1.08053	0.0666282	0.0333141	−	0.999445i	$-0.489394\pi$
$263$	1.08053	0.0666282	0.0333141	+	0.999445i	$0.489394\pi$
$264$	−4.92618	−0.303185
$265$	−12.3772	−0.760327
$266$	0.578692	0.0354819
$267$	−18.7109	−1.14509
$268$	−11.1316	−0.679970
$269$	−2.00098	−0.122002	−0.0610009	−	0.998138i	$-0.519429\pi$
$269$	−2.00098	−0.122002	−0.0610009	+	0.998138i	$0.519429\pi$
$270$	−5.94808	−0.361988
$271$	22.8381	1.38732	0.693659	−	0.720304i	$-0.255998\pi$
$271$	22.8381	1.38732	0.693659	+	0.720304i	$0.255998\pi$
$272$	25.6748	1.55676
$273$	−2.39172	−0.144754
$274$	3.88782	0.234872
$275$	24.8856	1.50066
$276$	8.43564	0.507766
$277$	17.6647	1.06137	0.530686	−	0.847569i	$-0.321934\pi$
$277$	17.6647	1.06137	0.530686	+	0.847569i	$0.321934\pi$
$278$	33.7140	2.02203
$279$	0.943195	0.0564676
$280$	−3.37110	−0.201462
$281$	−8.23815	−0.491447	−0.245724	−	0.969340i	$-0.579026\pi$
$281$	−8.23815	−0.491447	−0.245724	+	0.969340i	$0.579026\pi$
$282$	3.19020	0.189973
$283$	19.0525	1.13255	0.566277	−	0.824215i	$-0.308383\pi$
$283$	19.0525	1.13255	0.566277	+	0.824215i	$0.308383\pi$
$284$	−1.53144	−0.0908741
$285$	−1.00258	−0.0593877
$286$	−20.7887	−1.22926
$287$	2.27743	0.134432
$288$	6.81644	0.401662
$289$	11.4649	0.674405
$290$	43.7868	2.57125
$291$	−6.81283	−0.399375
$292$	22.4895	1.31610
$293$	14.1130	0.824490	0.412245	−	0.911073i	$-0.364745\pi$
$293$	14.1130	0.824490	0.412245	+	0.911073i	$0.364745\pi$
$294$	1.85290	0.108063
$295$	46.7398	2.72129
$296$	7.75701	0.450867
$297$	−4.69097	−0.272198
$298$	33.0439	1.91418
$299$	−14.0769	−0.814090
$300$	−7.60337	−0.438981
$301$	5.60881	0.323287
$302$	−17.3356	−0.997550
$303$	13.6015	0.781389
$304$	1.50296	0.0862007
$305$	−34.4601	−1.97318
$306$	9.88569	0.565128
$307$	3.92129	0.223800	0.111900	−	0.993719i	$-0.464306\pi$
$307$	3.92129	0.223800	0.111900	+	0.993719i	$0.464306\pi$
$308$	6.72332	0.383097
$309$	4.83718	0.275177
$310$	5.61019	0.318638
$311$	−2.79178	−0.158307	−0.0791536	−	0.996862i	$-0.525222\pi$
$311$	−2.79178	−0.158307	−0.0791536	+	0.996862i	$0.525222\pi$
$312$	−2.51165	−0.142194
$313$	3.95575	0.223592	0.111796	−	0.993731i	$-0.464340\pi$
$313$	3.95575	0.223592	0.111796	+	0.993731i	$0.464340\pi$
$314$	43.2591	2.44125
$315$	−3.21014	−0.180871
$316$	−12.7948	−0.719765
$317$	5.47919	0.307742	0.153871	−	0.988091i	$-0.450826\pi$
$317$	5.47919	0.307742	0.153871	+	0.988091i	$0.450826\pi$
$318$	7.14417	0.400625
$319$	34.5327	1.93346
$320$	9.64838	0.539361
$321$	12.9339	0.721901
$322$	10.9056	0.607745
$323$	1.66629	0.0927147
$324$	1.43325	0.0796248
$325$	12.6881	0.703809
$326$	−35.0713	−1.94242
$327$	−5.11701	−0.282971
$328$	2.39162	0.132055
$329$	1.72173	0.0949220
$330$	−27.9023	−1.53597
$331$	2.77529	0.152544	0.0762719	−	0.997087i	$-0.475698\pi$
$331$	2.77529	0.152544	0.0762719	+	0.997087i	$0.475698\pi$
$332$	18.3183	1.00535
$333$	7.38664	0.404785
$334$	−11.9248	−0.652496
$335$	24.9322	1.36219
$336$	4.81230	0.262532
$337$	−26.2917	−1.43220	−0.716101	−	0.697997i	$-0.754075\pi$
$337$	−26.2917	−1.43220	−0.716101	+	0.697997i	$0.754075\pi$
$338$	13.4885	0.733677
$339$	−13.5759	−0.737339
$340$	24.5471	1.33125
$341$	4.42450	0.239600
$342$	0.578692	0.0312921
$343$	1.00000	0.0539949
$344$	5.89004	0.317570
$345$	−18.8939	−1.01721
$346$	29.2093	1.57030
$347$	−30.0569	−1.61354	−0.806769	−	0.590867i	$-0.798786\pi$
$347$	−30.0569	−1.61354	−0.806769	+	0.590867i	$0.798786\pi$
$348$	−10.5509	−0.565586
$349$	−10.6376	−0.569417	−0.284708	−	0.958614i	$-0.591897\pi$
$349$	−10.6376	−0.569417	−0.284708	+	0.958614i	$0.591897\pi$
$350$	−9.82965	−0.525417
$351$	−2.39172	−0.127661
$352$	31.9757	1.70431
$353$	−22.0385	−1.17299	−0.586495	−	0.809953i	$-0.699493\pi$
$353$	−22.0385	−1.17299	−0.586495	+	0.809953i	$0.699493\pi$
$354$	−26.9783	−1.43388
$355$	3.43007	0.182049
$356$	26.8173	1.42131
$357$	5.33525	0.282371
$358$	13.2461	0.700080
$359$	2.56691	0.135476	0.0677382	−	0.997703i	$-0.478422\pi$
$359$	2.56691	0.135476	0.0677382	+	0.997703i	$0.478422\pi$
$360$	−3.37110	−0.177672
$361$	−18.9025	−0.994866
$362$	16.8716	0.886750
$363$	−11.0052	−0.577625
$364$	3.42793	0.179672
$365$	−50.3714	−2.63656
$366$	19.8905	1.03969
$367$	5.51924	0.288102	0.144051	−	0.989570i	$-0.453987\pi$
$367$	5.51924	0.288102	0.144051	+	0.989570i	$0.453987\pi$
$368$	28.3237	1.47647
$369$	2.27743	0.118558
$370$	43.9363	2.28414
$371$	3.85567	0.200176
$372$	−1.35183	−0.0700891
$373$	−4.48940	−0.232453	−0.116226	−	0.993223i	$-0.537080\pi$
$373$	−4.48940	−0.232453	−0.116226	+	0.993223i	$0.537080\pi$
$374$	46.3735	2.39792
$375$	0.979095	0.0505602
$376$	1.80806	0.0932434
$377$	17.6067	0.906792
$378$	1.85290	0.0953030
$379$	31.9282	1.64004	0.820021	−	0.572334i	$-0.193962\pi$
$379$	31.9282	1.64004	0.820021	+	0.572334i	$0.193962\pi$
$380$	1.43694	0.0737136
$381$	−17.8346	−0.913694
$382$	36.3117	1.85787
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	8.06380	0.411504
$385$	−15.0587	−0.767462
$386$	9.60576	0.488920
$387$	5.60881	0.285112
$388$	9.76445	0.495715
$389$	25.8081	1.30852	0.654260	−	0.756270i	$-0.272980\pi$
$389$	25.8081	1.30852	0.654260	+	0.756270i	$0.272980\pi$
$390$	−14.2262	−0.720369
$391$	31.4016	1.58805
$392$	1.05014	0.0530401
$393$	21.6482	1.09201
$394$	−30.9961	−1.56156
$395$	28.6575	1.44191
$396$	6.72332	0.337859
$397$	−9.61054	−0.482339	−0.241170	−	0.970483i	$-0.577531\pi$
$397$	−9.61054	−0.482339	−0.241170	+	0.970483i	$0.577531\pi$
$398$	−38.3587	−1.92275
$399$	0.312316	0.0156354
$400$	−25.5292	−1.27646
$401$	−11.7868	−0.588606	−0.294303	−	0.955712i	$-0.595087\pi$
$401$	−11.7868	−0.588606	−0.294303	+	0.955712i	$0.595087\pi$
$402$	−14.3909	−0.717754
$403$	2.25586	0.112372
$404$	−19.4944	−0.969881
$405$	−3.21014	−0.159513
$406$	−13.6402	−0.676950
$407$	34.6505	1.71756
$408$	5.60276	0.277378
$409$	20.1698	0.997333	0.498667	−	0.866794i	$-0.333823\pi$
$409$	20.1698	0.997333	0.498667	+	0.866794i	$0.333823\pi$
$410$	13.5463	0.669005
$411$	2.09823	0.103498
$412$	−6.93286	−0.341558
$413$	−14.5600	−0.716453
$414$	10.9056	0.535981
$415$	−41.0287	−2.01402
$416$	16.3030	0.799322
$417$	18.1952	0.891024
$418$	2.71463	0.132777
$419$	10.2205	0.499303	0.249651	−	0.968336i	$-0.419684\pi$
$419$	10.2205	0.499303	0.249651	+	0.968336i	$0.419684\pi$
$420$	4.60092	0.224502
$421$	8.76855	0.427353	0.213677	−	0.976904i	$-0.431456\pi$
$421$	8.76855	0.427353	0.213677	+	0.976904i	$0.431456\pi$
$422$	−31.1442	−1.51608
$423$	1.72173	0.0837134
$424$	4.04899	0.196636
$425$	−28.3035	−1.37292
$426$	−1.97985	−0.0959238
$427$	10.7348	0.519492
$428$	−18.5375	−0.896043
$429$	−11.2195	−0.541683
$430$	33.3616	1.60884
$431$	20.8702	1.00528	0.502642	−	0.864495i	$-0.332362\pi$
$431$	20.8702	1.00528	0.502642	+	0.864495i	$0.332362\pi$
$432$	4.81230	0.231532
$433$	−4.67650	−0.224738	−0.112369	−	0.993667i	$-0.535844\pi$
$433$	−4.67650	−0.224738	−0.112369	+	0.993667i	$0.535844\pi$
$434$	−1.74765	−0.0838897
$435$	23.6315	1.13304
$436$	7.33394	0.351232
$437$	1.83820	0.0879329
$438$	29.0745	1.38923
$439$	−25.5135	−1.21769	−0.608847	−	0.793288i	$-0.708368\pi$
$439$	−25.5135	−1.21769	−0.608847	+	0.793288i	$0.708368\pi$
$440$	−15.8137	−0.753890
$441$	1.00000	0.0476190
$442$	23.6439	1.12462
$443$	−28.1711	−1.33845	−0.669224	−	0.743060i	$-0.733373\pi$
$443$	−28.1711	−1.33845	−0.669224	+	0.743060i	$0.733373\pi$
$444$	−10.5869	−0.502431
$445$	−60.0645	−2.84733
$446$	39.5533	1.87290
$447$	17.8336	0.843499
$448$	−3.00559	−0.142001
$449$	−32.6607	−1.54135	−0.770677	−	0.637226i	$-0.780082\pi$
$449$	−32.6607	−1.54135	−0.770677	+	0.637226i	$0.780082\pi$
$450$	−9.82965	−0.463374
$451$	10.6834	0.503059
$452$	19.4575	0.915205
$453$	−9.35590	−0.439578
$454$	−6.90720	−0.324171
$455$	−7.67777	−0.359939
$456$	0.327976	0.0153589
$457$	24.4618	1.14428	0.572138	−	0.820158i	$-0.306114\pi$
$457$	24.4618	1.14428	0.572138	+	0.820158i	$0.306114\pi$
$458$	26.6835	1.24684
$459$	5.33525	0.249028
$460$	27.0796	1.26259
$461$	26.0424	1.21292	0.606459	−	0.795115i	$-0.292590\pi$
$461$	26.0424	1.21292	0.606459	+	0.795115i	$0.292590\pi$
$462$	8.69191	0.404384
$463$	29.2747	1.36051	0.680256	−	0.732975i	$-0.261869\pi$
$463$	29.2747	1.36051	0.680256	+	0.732975i	$0.261869\pi$
$464$	−35.4258	−1.64460
$465$	3.02779	0.140410
$466$	−49.9730	−2.31495
$467$	7.39736	0.342309	0.171155	−	0.985244i	$-0.445250\pi$
$467$	7.39736	0.342309	0.171155	+	0.985244i	$0.445250\pi$
$468$	3.42793	0.158456
$469$	−7.76670	−0.358633
$470$	10.2410	0.472381
$471$	23.3467	1.07576
$472$	−15.2901	−0.703783
$473$	26.3108	1.20977
$474$	−16.5412	−0.759761
$475$	−1.65684	−0.0760210
$476$	−7.64672	−0.350487
$477$	3.85567	0.176539
$478$	16.1879	0.740418
$479$	−27.2961	−1.24719	−0.623596	−	0.781746i	$-0.714329\pi$
$479$	−27.2961	−1.24719	−0.623596	+	0.781746i	$0.714329\pi$
$480$	21.8817	0.998759
$481$	17.6668	0.805537
$482$	11.2856	0.514045
$483$	5.88569	0.267808
$484$	15.7732	0.716964
$485$	−21.8701	−0.993071
$486$	1.85290	0.0840493
$487$	−3.17351	−0.143805	−0.0719026	−	0.997412i	$-0.522907\pi$
$487$	−3.17351	−0.143805	−0.0719026	+	0.997412i	$0.522907\pi$
$488$	11.2730	0.510306
$489$	−18.9277	−0.855942
$490$	5.94808	0.268707
$491$	21.4652	0.968711	0.484355	−	0.874871i	$-0.339054\pi$
$491$	21.4652	0.968711	0.484355	+	0.874871i	$0.339054\pi$
$492$	−3.26411	−0.147158
$493$	−39.2755	−1.76888
$494$	1.38407	0.0622723
$495$	−15.0587	−0.676837
$496$	−4.53893	−0.203804
$497$	−1.06851	−0.0479292
$498$	23.6819	1.06121
$499$	42.1584	1.88727	0.943634	−	0.330990i	$-0.107383\pi$
$499$	42.1584	1.88727	0.943634	+	0.330990i	$0.107383\pi$
$500$	−1.40328	−0.0627568
$501$	−6.43574	−0.287528
$502$	46.7005	2.08435
$503$	−24.3838	−1.08722	−0.543610	−	0.839338i	$-0.682943\pi$
$503$	−24.3838	−1.08722	−0.543610	+	0.839338i	$0.682943\pi$
$504$	1.05014	0.0467769
$505$	43.6629	1.94297
$506$	51.1579	2.27425
$507$	7.27966	0.323301
$508$	25.5614	1.13410
$509$	−11.0516	−0.489854	−0.244927	−	0.969541i	$-0.578764\pi$
$509$	−11.0516	−0.489854	−0.244927	+	0.969541i	$0.578764\pi$
$510$	31.7345	1.40523
$511$	15.6913	0.694144
$512$	−22.6956	−1.00301
$513$	0.312316	0.0137891
$514$	−13.3136	−0.587240
$515$	15.5280	0.684246
$516$	−8.03881	−0.353889
$517$	8.07659	0.355208
$518$	−13.6867	−0.601360
$519$	15.7641	0.691966
$520$	−8.06273	−0.353574
$521$	38.0117	1.66532	0.832662	−	0.553781i	$-0.186816\pi$
$521$	38.0117	1.66532	0.832662	+	0.553781i	$0.186816\pi$
$522$	−13.6402	−0.597014
$523$	16.8756	0.737917	0.368959	−	0.929446i	$-0.379714\pi$
$523$	16.8756	0.737917	0.368959	+	0.929446i	$0.379714\pi$
$524$	−31.0272	−1.35543
$525$	−5.30500	−0.231529
$526$	−2.00211	−0.0872962
$527$	−5.03218	−0.219205
$528$	22.5744	0.982423
$529$	11.6413	0.506144
$530$	22.9338	0.996181
$531$	−14.5600	−0.631852
$532$	−0.447626	−0.0194071
$533$	5.44698	0.235935
$534$	34.6694	1.50029
$535$	41.5197	1.79505
$536$	−8.15612	−0.352291
$537$	7.14886	0.308496
$538$	3.70762	0.159847
$539$	4.69097	0.202055
$540$	4.60092	0.197992
$541$	31.3415	1.34748	0.673739	−	0.738970i	$-0.264687\pi$
$541$	31.3415	1.34748	0.673739	+	0.738970i	$0.264687\pi$
$542$	−42.3168	−1.81766
$543$	9.10549	0.390754
$544$	−36.3674	−1.55924
$545$	−16.4263	−0.703627
$546$	4.43163	0.189656
$547$	17.4234	0.744970	0.372485	−	0.928038i	$-0.378506\pi$
$547$	17.4234	0.744970	0.372485	+	0.928038i	$0.378506\pi$
$548$	−3.00728	−0.128465
$549$	10.7348	0.458149
$550$	−46.1106	−1.96616
$551$	−2.29912	−0.0979459
$552$	6.18079	0.263072
$553$	−8.92717	−0.379622
$554$	−32.7310	−1.39061
$555$	23.7122	1.00652
$556$	−26.0782	−1.10596
$557$	−0.331868	−0.0140617	−0.00703085	−	0.999975i	$-0.502238\pi$
$557$	−0.331868	−0.0140617	−0.00703085	+	0.999975i	$0.502238\pi$
$558$	−1.74765	−0.0739838
$559$	13.4147	0.567383
$560$	15.4482	0.652804
$561$	25.0275	1.05666
$562$	15.2645	0.643894
$563$	−43.0228	−1.81319	−0.906597	−	0.421997i	$-0.861329\pi$
$563$	−43.0228	−1.81319	−0.906597	+	0.421997i	$0.861329\pi$
$564$	−2.46766	−0.103907
$565$	−43.5804	−1.83344
$566$	−35.3024	−1.48387
$567$	1.00000	0.0419961
$568$	−1.12209	−0.0470817
$569$	41.3196	1.73221	0.866104	−	0.499864i	$-0.166617\pi$
$569$	41.3196	1.73221	0.866104	+	0.499864i	$0.166617\pi$
$570$	1.85768	0.0778097
$571$	2.11330	0.0884388	0.0442194	−	0.999022i	$-0.485920\pi$
$571$	2.11330	0.0884388	0.0442194	+	0.999022i	$0.485920\pi$
$572$	16.0803	0.672352
$573$	19.5972	0.818684
$574$	−4.21985	−0.176133
$575$	−31.2236	−1.30211
$576$	−3.00559	−0.125233
$577$	−32.0184	−1.33294	−0.666472	−	0.745530i	$-0.732196\pi$
$577$	−32.0184	−1.33294	−0.666472	+	0.745530i	$0.732196\pi$
$578$	−21.2433	−0.883605
$579$	5.18417	0.215447
$580$	−33.8697	−1.40636
$581$	12.7810	0.530244
$582$	12.6235	0.523261
$583$	18.0868	0.749080
$584$	16.4781	0.681869
$585$	−7.67777	−0.317437
$586$	−26.1500	−1.08025
$587$	43.7137	1.80426	0.902128	−	0.431469i	$-0.142005\pi$
$587$	43.7137	1.80426	0.902128	+	0.431469i	$0.142005\pi$
$588$	−1.43325	−0.0591061
$589$	−0.294575	−0.0121378
$590$	−86.6042	−3.56544
$591$	−16.7284	−0.688116
$592$	−35.5467	−1.46096
$593$	23.8069	0.977633	0.488816	−	0.872387i	$-0.337429\pi$
$593$	23.8069	0.977633	0.488816	+	0.872387i	$0.337429\pi$
$594$	8.69191	0.356634
$595$	17.1269	0.702134
$596$	−25.5599	−1.04697
$597$	−20.7020	−0.847276
$598$	26.0832	1.06662
$599$	26.4572	1.08101	0.540506	−	0.841340i	$-0.318233\pi$
$599$	26.4572	1.08101	0.540506	+	0.841340i	$0.318233\pi$
$600$	−5.57099	−0.227435
$601$	−42.2007	−1.72140	−0.860702	−	0.509109i	$-0.829975\pi$
$601$	−42.2007	−1.72140	−0.860702	+	0.509109i	$0.829975\pi$
$602$	−10.3926	−0.423570
$603$	−7.76670	−0.316284
$604$	13.4093	0.545617
$605$	−35.3283	−1.43630
$606$	−25.2023	−1.02377
$607$	24.0184	0.974879	0.487439	−	0.873157i	$-0.337931\pi$
$607$	24.0184	0.974879	0.487439	+	0.873157i	$0.337931\pi$
$608$	−2.12889	−0.0863377
$609$	−7.36152	−0.298304
$610$	63.8513	2.58526
$611$	4.11790	0.166593
$612$	−7.64672	−0.309100
$613$	43.6832	1.76435	0.882173	−	0.470925i	$-0.156080\pi$
$613$	43.6832	1.76435	0.882173	+	0.470925i	$0.156080\pi$
$614$	−7.26576	−0.293222
$615$	7.31086	0.294802
$616$	4.92618	0.198481
$617$	−3.55895	−0.143278	−0.0716389	−	0.997431i	$-0.522823\pi$
$617$	−3.55895	−0.143278	−0.0716389	+	0.997431i	$0.522823\pi$
$618$	−8.96281	−0.360537
$619$	−37.1304	−1.49240	−0.746199	−	0.665723i	$-0.768123\pi$
$619$	−37.1304	−1.49240	−0.746199	+	0.665723i	$0.768123\pi$
$620$	−4.33956	−0.174281
$621$	5.88569	0.236184
$622$	5.17289	0.207414
$623$	18.7109	0.749635
$624$	11.5097	0.460756
$625$	−23.3820	−0.935279
$626$	−7.32961	−0.292950
$627$	1.46507	0.0585092
$628$	−33.4616	−1.33526
$629$	−39.4096	−1.57136
$630$	5.94808	0.236977
$631$	−43.8209	−1.74448	−0.872240	−	0.489077i	$-0.837334\pi$
$631$	−43.8209	−1.74448	−0.872240	+	0.489077i	$0.837334\pi$
$632$	−9.37477	−0.372908
$633$	−16.8083	−0.668071
$634$	−10.1524	−0.403204
$635$	−57.2515	−2.27196
$636$	−5.52612	−0.219125
$637$	2.39172	0.0947636
$638$	−63.9857	−2.53322
$639$	−1.06851	−0.0422696
$640$	25.8859	1.02323
$641$	27.9201	1.10278	0.551389	−	0.834248i	$-0.314098\pi$
$641$	27.9201	1.10278	0.551389	+	0.834248i	$0.314098\pi$
$642$	−23.9653	−0.945834
$643$	−4.19824	−0.165562	−0.0827812	−	0.996568i	$-0.526380\pi$
$643$	−4.19824	−0.165562	−0.0827812	+	0.996568i	$0.526380\pi$
$644$	−8.43564	−0.332411
$645$	18.0051	0.708949
$646$	−3.08747	−0.121475
$647$	−37.2669	−1.46511	−0.732557	−	0.680706i	$-0.761673\pi$
$647$	−37.2669	−1.46511	−0.732557	+	0.680706i	$0.761673\pi$
$648$	1.05014	0.0412534
$649$	−68.3008	−2.68104
$650$	−23.5098	−0.922130
$651$	−0.943195	−0.0369667
$652$	27.1281	1.06242
$653$	−21.1806	−0.828862	−0.414431	−	0.910081i	$-0.636019\pi$
$653$	−21.1806	−0.828862	−0.414431	+	0.910081i	$0.636019\pi$
$654$	9.48132	0.370749
$655$	69.4939	2.71535
$656$	−10.9597	−0.427903
$657$	15.6913	0.612177
$658$	−3.19020	−0.124367
$659$	2.13751	0.0832657	0.0416328	−	0.999133i	$-0.486744\pi$
$659$	2.13751	0.0832657	0.0416328	+	0.999133i	$0.486744\pi$
$660$	21.5828	0.840109
$661$	18.8595	0.733551	0.366775	−	0.930310i	$-0.380462\pi$
$661$	18.8595	0.733551	0.366775	+	0.930310i	$0.380462\pi$
$662$	−5.14234	−0.199863
$663$	12.7604	0.495575
$664$	13.4218	0.520867
$665$	1.00258	0.0388784
$666$	−13.6867	−0.530350
$667$	−43.3276	−1.67765
$668$	9.22399	0.356887
$669$	21.3467	0.825309
$670$	−46.1969	−1.78474
$671$	50.3566	1.94399
$672$	−6.81644	−0.262950
$673$	−14.0290	−0.540777	−0.270389	−	0.962751i	$-0.587152\pi$
$673$	−14.0290	−0.540777	−0.270389	+	0.962751i	$0.587152\pi$
$674$	48.7160	1.87647
$675$	−5.30500	−0.204190
$676$	−10.4335	−0.401290
$677$	34.0790	1.30976	0.654881	−	0.755732i	$-0.272719\pi$
$677$	34.0790	1.30976	0.654881	+	0.755732i	$0.272719\pi$
$678$	25.1547	0.966061
$679$	6.81283	0.261452
$680$	17.9856	0.689718
$681$	−3.72777	−0.142849
$682$	−8.19817	−0.313924
$683$	36.4699	1.39548	0.697740	−	0.716351i	$-0.254189\pi$
$683$	36.4699	1.39548	0.697740	+	0.716351i	$0.254189\pi$
$684$	−0.447626	−0.0171154
$685$	6.73562	0.257355
$686$	−1.85290	−0.0707441
$687$	14.4009	0.549429
$688$	−26.9913	−1.02903
$689$	9.22169	0.351318
$690$	35.0085	1.33275
$691$	−7.13401	−0.271390	−0.135695	−	0.990751i	$-0.543327\pi$
$691$	−7.13401	−0.271390	−0.135695	+	0.990751i	$0.543327\pi$
$692$	−22.5938	−0.858888
$693$	4.69097	0.178195
$694$	55.6924	2.11406
$695$	58.4092	2.21559
$696$	−7.73062	−0.293028
$697$	−12.1506	−0.460238
$698$	19.7104	0.746050
$699$	−26.9701	−1.02010
$700$	7.60337	0.287380
$701$	−12.1932	−0.460533	−0.230266	−	0.973128i	$-0.573960\pi$
$701$	−12.1932	−0.460533	−0.230266	+	0.973128i	$0.573960\pi$
$702$	4.43163	0.167261
$703$	−2.30697	−0.0870090
$704$	−14.0992	−0.531382
$705$	5.52699	0.208159
$706$	40.8352	1.53685
$707$	−13.6015	−0.511539
$708$	20.8681	0.784272
$709$	19.9645	0.749782	0.374891	−	0.927069i	$-0.377680\pi$
$709$	19.9645	0.749782	0.374891	+	0.927069i	$0.377680\pi$
$710$	−6.35558	−0.238521
$711$	−8.92717	−0.334795
$712$	19.6490	0.736378
$713$	−5.55135	−0.207900
$714$	−9.88569	−0.369963
$715$	−36.0162	−1.34693
$716$	−10.2461	−0.382914
$717$	8.73652	0.326271
$718$	−4.75624	−0.177501
$719$	1.07483	0.0400843	0.0200422	−	0.999799i	$-0.493620\pi$
$719$	1.07483	0.0400843	0.0200422	+	0.999799i	$0.493620\pi$
$720$	15.4482	0.575719
$721$	−4.83718	−0.180146
$722$	35.0244	1.30347
$723$	6.09077	0.226518
$724$	−13.0504	−0.485014
$725$	39.0528	1.45039
$726$	20.3916	0.756804
$727$	−21.8309	−0.809665	−0.404832	−	0.914391i	$-0.632670\pi$
$727$	−21.8309	−0.809665	−0.404832	+	0.914391i	$0.632670\pi$
$728$	2.51165	0.0930878
$729$	1.00000	0.0370370
$730$	93.3333	3.45442
$731$	−29.9244	−1.10679
$732$	−15.3856	−0.568667
$733$	43.6954	1.61393	0.806964	−	0.590601i	$-0.201109\pi$
$733$	43.6954	1.61393	0.806964	+	0.590601i	$0.201109\pi$
$734$	−10.2266	−0.377471
$735$	3.21014	0.118408
$736$	−40.1194	−1.47882
$737$	−36.4334	−1.34204
$738$	−4.21985	−0.155335
$739$	−10.7849	−0.396729	−0.198364	−	0.980128i	$-0.563563\pi$
$739$	−10.7849	−0.396729	−0.198364	+	0.980128i	$0.563563\pi$
$740$	−33.9853	−1.24933
$741$	0.746975	0.0274408
$742$	−7.14417	−0.262271
$743$	0.991731	0.0363831	0.0181915	−	0.999835i	$-0.494209\pi$
$743$	0.991731	0.0363831	0.0181915	+	0.999835i	$0.494209\pi$
$744$	−0.990486	−0.0363130
$745$	57.2483	2.09741
$746$	8.31843	0.304559
$747$	12.7810	0.467631
$748$	−35.8706	−1.31156
$749$	−12.9339	−0.472595
$750$	−1.81417	−0.0662440
$751$	−31.0574	−1.13330	−0.566651	−	0.823958i	$-0.691761\pi$
$751$	−31.0574	−1.13330	−0.566651	+	0.823958i	$0.691761\pi$
$752$	−8.28548	−0.302140
$753$	25.2040	0.918485
$754$	−32.6235	−1.18808
$755$	−30.0337	−1.09304
$756$	−1.43325	−0.0521266
$757$	−22.7351	−0.826322	−0.413161	−	0.910658i	$-0.635575\pi$
$757$	−22.7351	−0.826322	−0.413161	+	0.910658i	$0.635575\pi$
$758$	−59.1598	−2.14878
$759$	27.6096	1.00216
$760$	1.05285	0.0381908
$761$	36.9060	1.33784	0.668920	−	0.743334i	$-0.266757\pi$
$761$	36.9060	1.33784	0.668920	+	0.743334i	$0.266757\pi$
$762$	33.0458	1.19712
$763$	5.11701	0.185248
$764$	−28.0876	−1.01617
$765$	17.1269	0.619224
$766$	1.85290	0.0669481
$767$	−34.8236	−1.25741
$768$	−20.9526	−0.756063
$769$	−41.7437	−1.50532	−0.752659	−	0.658411i	$-0.771229\pi$
$769$	−41.7437	−1.50532	−0.752659	+	0.658411i	$0.771229\pi$
$770$	27.9023	1.00553
$771$	−7.18529	−0.258772
$772$	−7.43019	−0.267418
$773$	12.5894	0.452808	0.226404	−	0.974033i	$-0.427303\pi$
$773$	12.5894	0.452808	0.226404	+	0.974033i	$0.427303\pi$
$774$	−10.3926	−0.373554
$775$	5.00365	0.179736
$776$	7.15442	0.256829
$777$	−7.38664	−0.264994
$778$	−47.8198	−1.71442
$779$	−0.711278	−0.0254842
$780$	11.0041	0.394011
$781$	−5.01235	−0.179356
$782$	−58.1841	−2.08066
$783$	−7.36152	−0.263079
$784$	−4.81230	−0.171868
$785$	74.9462	2.67494
$786$	−40.1121	−1.43075
$787$	−6.94407	−0.247530	−0.123765	−	0.992312i	$-0.539497\pi$
$787$	−6.94407	−0.247530	−0.123765	+	0.992312i	$0.539497\pi$
$788$	23.9760	0.854108
$789$	−1.08053	−0.0384678
$790$	−53.0995	−1.88919
$791$	13.5759	0.482702
$792$	4.92618	0.175044
$793$	25.6746	0.911733
$794$	17.8074	0.631960
$795$	12.3772	0.438975
$796$	29.6710	1.05166
$797$	−1.86467	−0.0660499	−0.0330249	−	0.999455i	$-0.510514\pi$
$797$	−1.86467	−0.0660499	−0.0330249	+	0.999455i	$0.510514\pi$
$798$	−0.578692	−0.0204855
$799$	−9.18586	−0.324972
$800$	36.1612	1.27849
$801$	18.7109	0.661116
$802$	21.8398	0.771191
$803$	73.6077	2.59756
$804$	11.1316	0.392581
$805$	18.8939	0.665922
$806$	−4.17989	−0.147230
$807$	2.00098	0.0704377
$808$	−14.2835	−0.502493
$809$	8.82350	0.310218	0.155109	−	0.987897i	$-0.450427\pi$
$809$	8.82350	0.310218	0.155109	+	0.987897i	$0.450427\pi$
$810$	5.94808	0.208994
$811$	−46.5161	−1.63340	−0.816701	−	0.577061i	$-0.804200\pi$
$811$	−46.5161	−1.63340	−0.816701	+	0.577061i	$0.804200\pi$
$812$	10.5509	0.370263
$813$	−22.8381	−0.800968
$814$	−64.2040	−2.25035
$815$	−60.7607	−2.12835
$816$	−25.6748	−0.898798
$817$	−1.75172	−0.0612851
$818$	−37.3727	−1.30671
$819$	2.39172	0.0835736
$820$	−10.4783	−0.365917
$821$	35.3062	1.23220	0.616098	−	0.787670i	$-0.288713\pi$
$821$	35.3062	1.23220	0.616098	+	0.787670i	$0.288713\pi$
$822$	−3.88782	−0.135603
$823$	31.8375	1.10979	0.554893	−	0.831922i	$-0.312759\pi$
$823$	31.8375	1.10979	0.554893	+	0.831922i	$0.312759\pi$
$824$	−5.07971	−0.176960
$825$	−24.8856	−0.866406
$826$	26.9783	0.938696
$827$	1.29171	0.0449172	0.0224586	−	0.999748i	$-0.492851\pi$
$827$	1.29171	0.0449172	0.0224586	+	0.999748i	$0.492851\pi$
$828$	−8.43564	−0.293159
$829$	53.0048	1.84093	0.920467	−	0.390821i	$-0.127809\pi$
$829$	53.0048	1.84093	0.920467	+	0.390821i	$0.127809\pi$
$830$	76.0221	2.63877
$831$	−17.6647	−0.612783
$832$	−7.18855	−0.249218
$833$	−5.33525	−0.184855
$834$	−33.7140	−1.16742
$835$	−20.6596	−0.714956
$836$	−2.09980	−0.0726232
$837$	−0.943195	−0.0326016
$838$	−18.9375	−0.654186
$839$	4.78091	0.165055	0.0825277	−	0.996589i	$-0.473701\pi$
$839$	4.78091	0.165055	0.0825277	+	0.996589i	$0.473701\pi$
$840$	3.37110	0.116314
$841$	25.1919	0.868686
$842$	−16.2473	−0.559918
$843$	8.23815	0.283737
$844$	24.0905	0.829228
$845$	23.3687	0.803908
$846$	−3.19020	−0.109681
$847$	11.0052	0.378144
$848$	−18.5546	−0.637168
$849$	−19.0525	−0.653880
$850$	52.4436	1.79880
$851$	−43.4754	−1.49032
$852$	1.53144	0.0524662
$853$	30.0506	1.02891	0.514457	−	0.857516i	$-0.327994\pi$
$853$	30.0506	1.02891	0.514457	+	0.857516i	$0.327994\pi$
$854$	−19.8905	−0.680639
$855$	1.00258	0.0342875
$856$	−13.5824	−0.464238
$857$	32.6428	1.11506	0.557529	−	0.830157i	$-0.311749\pi$
$857$	32.6428	1.11506	0.557529	+	0.830157i	$0.311749\pi$
$858$	20.7887	0.709713
$859$	41.5308	1.41701	0.708506	−	0.705705i	$-0.249370\pi$
$859$	41.5308	1.41701	0.708506	+	0.705705i	$0.249370\pi$
$860$	−25.8057	−0.879967
$861$	−2.27743	−0.0776145
$862$	−38.6705	−1.31712
$863$	25.8555	0.880132	0.440066	−	0.897965i	$-0.354955\pi$
$863$	25.8555	0.880132	0.440066	+	0.897965i	$0.354955\pi$
$864$	−6.81644	−0.231900
$865$	50.6049	1.72062
$866$	8.66509	0.294452
$867$	−11.4649	−0.389368
$868$	1.35183	0.0458841
$869$	−41.8771	−1.42058
$870$	−43.7868	−1.48451
$871$	−18.5758	−0.629417
$872$	5.37358	0.181972
$873$	6.81283	0.230579
$874$	−3.40600	−0.115210
$875$	−0.979095	−0.0330994
$876$	−22.4895	−0.759851
$877$	−16.7193	−0.564569	−0.282285	−	0.959331i	$-0.591092\pi$
$877$	−16.7193	−0.564569	−0.282285	+	0.959331i	$0.591092\pi$
$878$	47.2741	1.59542
$879$	−14.1130	−0.476019
$880$	72.4669	2.44286
$881$	−2.58708	−0.0871611	−0.0435805	−	0.999050i	$-0.513877\pi$
$881$	−2.58708	−0.0871611	−0.0435805	+	0.999050i	$0.513877\pi$
$882$	−1.85290	−0.0623905
$883$	−13.5192	−0.454957	−0.227478	−	0.973783i	$-0.573048\pi$
$883$	−13.5192	−0.454957	−0.227478	+	0.973783i	$0.573048\pi$
$884$	−18.2889	−0.615121
$885$	−46.7398	−1.57114
$886$	52.1983	1.75363
$887$	0.778491	0.0261392	0.0130696	−	0.999915i	$-0.495840\pi$
$887$	0.778491	0.0261392	0.0130696	+	0.999915i	$0.495840\pi$
$888$	−7.75701	−0.260308
$889$	17.8346	0.598153
$890$	111.294	3.73057
$891$	4.69097	0.157154
$892$	−30.5950	−1.02440
$893$	−0.537725	−0.0179943
$894$	−33.0439	−1.10515
$895$	22.9489	0.767096
$896$	−8.06380	−0.269393
$897$	14.0769	0.470015
$898$	60.5171	2.01948
$899$	6.94334	0.231573
$900$	7.60337	0.253446
$901$	−20.5709	−0.685318
$902$	−19.7952	−0.659108
$903$	−5.60881	−0.186650
$904$	14.2565	0.474166
$905$	29.2299	0.971635
$906$	17.3356	0.575935
$907$	4.86748	0.161622	0.0808110	−	0.996729i	$-0.474249\pi$
$907$	4.86748	0.161622	0.0808110	+	0.996729i	$0.474249\pi$
$908$	5.34282	0.177308
$909$	−13.6015	−0.451135
$910$	14.2262	0.471592
$911$	3.21058	0.106371	0.0531856	−	0.998585i	$-0.483063\pi$
$911$	3.21058	0.106371	0.0531856	+	0.998585i	$0.483063\pi$
$912$	−1.50296	−0.0497680
$913$	59.9552	1.98423
$914$	−45.3253	−1.49923
$915$	34.4601	1.13922
$916$	−20.6401	−0.681967
$917$	−21.6482	−0.714888
$918$	−9.88569	−0.326277
$919$	−5.49041	−0.181112	−0.0905559	−	0.995891i	$-0.528864\pi$
$919$	−5.49041	−0.181112	−0.0905559	+	0.995891i	$0.528864\pi$
$920$	19.8412	0.654146
$921$	−3.92129	−0.129211
$922$	−48.2541	−1.58916
$923$	−2.55558	−0.0841180
$924$	−6.72332	−0.221181
$925$	39.1861	1.28843
$926$	−54.2432	−1.78254
$927$	−4.83718	−0.158874
$928$	50.1793	1.64722
$929$	1.43430	0.0470580	0.0235290	−	0.999723i	$-0.492510\pi$
$929$	1.43430	0.0470580	0.0235290	+	0.999723i	$0.492510\pi$
$930$	−5.61019	−0.183965
$931$	−0.312316	−0.0102358
$932$	38.6548	1.26618
$933$	2.79178	0.0913987
$934$	−13.7066	−0.448493
$935$	80.3418	2.62746
$936$	2.51165	0.0820957
$937$	37.0831	1.21145	0.605726	−	0.795673i	$-0.292883\pi$
$937$	37.0831	1.21145	0.605726	+	0.795673i	$0.292883\pi$
$938$	14.3909	0.469880
$939$	−3.95575	−0.129091
$940$	−7.92154	−0.258372
$941$	−19.0673	−0.621575	−0.310787	−	0.950479i	$-0.600593\pi$
$941$	−19.0673	−0.621575	−0.310787	+	0.950479i	$0.600593\pi$
$942$	−43.2591	−1.40946
$943$	−13.4042	−0.436502
$944$	70.0672	2.28049
$945$	3.21014	0.104426
$946$	−48.7513	−1.58504
$947$	29.0946	0.945447	0.472724	−	0.881211i	$-0.343271\pi$
$947$	29.0946	0.945447	0.472724	+	0.881211i	$0.343271\pi$
$948$	12.7948	0.415557
$949$	37.5294	1.21825
$950$	3.06996	0.0996027
$951$	−5.47919	−0.177675
$952$	−5.60276	−0.181586
$953$	−13.9007	−0.450288	−0.225144	−	0.974325i	$-0.572285\pi$
$953$	−13.9007	−0.450288	−0.225144	+	0.974325i	$0.572285\pi$
$954$	−7.14417	−0.231301
$955$	62.9097	2.03571
$956$	−12.5216	−0.404977
$957$	−34.5327	−1.11628
$958$	50.5771	1.63407
$959$	−2.09823	−0.0677554
$960$	−9.64838	−0.311400
$961$	−30.1104	−0.971303
$962$	−32.7349	−1.05541
$963$	−12.9339	−0.416790
$964$	−8.72957	−0.281161
$965$	16.6419	0.535722
$966$	−10.9056	−0.350882
$967$	−17.9285	−0.576542	−0.288271	−	0.957549i	$-0.593080\pi$
$967$	−17.9285	−0.576542	−0.288271	+	0.957549i	$0.593080\pi$
$968$	11.5570	0.371457
$969$	−1.66629	−0.0535288
$970$	40.5232	1.30112
$971$	−58.9141	−1.89064	−0.945322	−	0.326139i	$-0.894252\pi$
$971$	−58.9141	−1.89064	−0.945322	+	0.326139i	$0.894252\pi$
$972$	−1.43325	−0.0459714
$973$	−18.1952	−0.583312
$974$	5.88019	0.188414
$975$	−12.6881	−0.406344
$976$	−51.6590	−1.65356
$977$	0.0288918	0.000924330 0	0.000462165	−	1.00000i	$-0.499853\pi$
$977$	0.0288918	0.000924330 0	0.000462165		1.00000i	$0.499853\pi$
$978$	35.0713	1.12146
$979$	87.7722	2.80521
$980$	−4.60092	−0.146971
$981$	5.11701	0.163374
$982$	−39.7729	−1.26920
$983$	55.3085	1.76407	0.882034	−	0.471185i	$-0.156174\pi$
$983$	55.3085	1.76407	0.882034	+	0.471185i	$0.156174\pi$
$984$	−2.39162	−0.0762420
$985$	−53.7006	−1.71104
$986$	72.7737	2.31759
$987$	−1.72173	−0.0548033
$988$	−1.07060	−0.0340603
$989$	−33.0117	−1.04971
$990$	27.9023	0.886792
$991$	−40.3241	−1.28094	−0.640468	−	0.767985i	$-0.721260\pi$
$991$	−40.3241	−1.28094	−0.640468	+	0.767985i	$0.721260\pi$
$992$	6.42923	0.204128
$993$	−2.77529	−0.0880712
$994$	1.97985	0.0627969
$995$	−66.4563	−2.10681
$996$	−18.3183	−0.580436
$997$	−31.5092	−0.997906	−0.498953	−	0.866629i	$-0.666282\pi$
$997$	−31.5092	−0.997906	−0.498953	+	0.866629i	$0.666282\pi$
$998$	−78.1154	−2.47270
$999$	−7.38664	−0.233703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.11	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85290 q^{2} -1.00000 q^{3} +1.43325 q^{4} -3.21014 q^{5} +1.85290 q^{6} +1.00000 q^{7} +1.05014 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.85290 q^{2} -1.00000 q^{3} +1.43325 q^{4} -3.21014 q^{5} +1.85290 q^{6} +1.00000 q^{7} +1.05014 q^{8} +1.00000 q^{9} +5.94808 q^{10} +4.69097 q^{11} -1.43325 q^{12} +2.39172 q^{13} -1.85290 q^{14} +3.21014 q^{15} -4.81230 q^{16} -5.33525 q^{17} -1.85290 q^{18} -0.312316 q^{19} -4.60092 q^{20} -1.00000 q^{21} -8.69191 q^{22} -5.88569 q^{23} -1.05014 q^{24} +5.30500 q^{25} -4.43163 q^{26} -1.00000 q^{27} +1.43325 q^{28} +7.36152 q^{29} -5.94808 q^{30} +0.943195 q^{31} +6.81644 q^{32} -4.69097 q^{33} +9.88569 q^{34} -3.21014 q^{35} +1.43325 q^{36} +7.38664 q^{37} +0.578692 q^{38} -2.39172 q^{39} -3.37110 q^{40} +2.27743 q^{41} +1.85290 q^{42} +5.60881 q^{43} +6.72332 q^{44} -3.21014 q^{45} +10.9056 q^{46} +1.72173 q^{47} +4.81230 q^{48} +1.00000 q^{49} -9.82965 q^{50} +5.33525 q^{51} +3.42793 q^{52} +3.85567 q^{53} +1.85290 q^{54} -15.0587 q^{55} +1.05014 q^{56} +0.312316 q^{57} -13.6402 q^{58} -14.5600 q^{59} +4.60092 q^{60} +10.7348 q^{61} -1.74765 q^{62} +1.00000 q^{63} -3.00559 q^{64} -7.67777 q^{65} +8.69191 q^{66} -7.76670 q^{67} -7.64672 q^{68} +5.88569 q^{69} +5.94808 q^{70} -1.06851 q^{71} +1.05014 q^{72} +15.6913 q^{73} -13.6867 q^{74} -5.30500 q^{75} -0.447626 q^{76} +4.69097 q^{77} +4.43163 q^{78} -8.92717 q^{79} +15.4482 q^{80} +1.00000 q^{81} -4.21985 q^{82} +12.7810 q^{83} -1.43325 q^{84} +17.1269 q^{85} -10.3926 q^{86} -7.36152 q^{87} +4.92618 q^{88} +18.7109 q^{89} +5.94808 q^{90} +2.39172 q^{91} -8.43564 q^{92} -0.943195 q^{93} -3.19020 q^{94} +1.00258 q^{95} -6.81644 q^{96} +6.81283 q^{97} -1.85290 q^{98} +4.69097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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