LMFDB - Embedded newform 8041.2.a.e.1.18

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:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.32441 q^{2} -2.65196 q^{3} -0.245926 q^{4} -0.221912 q^{5} +3.51229 q^{6} +0.607593 q^{7} +2.97454 q^{8} +4.03289 q^{9} +O(q^{10})$	\(q-1.32441 q^{2} -2.65196 q^{3} -0.245926 q^{4} -0.221912 q^{5} +3.51229 q^{6} +0.607593 q^{7} +2.97454 q^{8} +4.03289 q^{9} +0.293903 q^{10} -1.00000 q^{11} +0.652185 q^{12} -1.48759 q^{13} -0.804705 q^{14} +0.588501 q^{15} -3.44767 q^{16} -1.00000 q^{17} -5.34122 q^{18} +6.75581 q^{19} +0.0545738 q^{20} -1.61131 q^{21} +1.32441 q^{22} -8.80290 q^{23} -7.88835 q^{24} -4.95076 q^{25} +1.97018 q^{26} -2.73919 q^{27} -0.149423 q^{28} -2.51469 q^{29} -0.779420 q^{30} -3.76664 q^{31} -1.38293 q^{32} +2.65196 q^{33} +1.32441 q^{34} -0.134832 q^{35} -0.991792 q^{36} +0.973107 q^{37} -8.94749 q^{38} +3.94502 q^{39} -0.660085 q^{40} +6.35263 q^{41} +2.13404 q^{42} +1.00000 q^{43} +0.245926 q^{44} -0.894946 q^{45} +11.6587 q^{46} +0.412911 q^{47} +9.14308 q^{48} -6.63083 q^{49} +6.55685 q^{50} +2.65196 q^{51} +0.365836 q^{52} +2.59789 q^{53} +3.62782 q^{54} +0.221912 q^{55} +1.80731 q^{56} -17.9161 q^{57} +3.33049 q^{58} +14.1945 q^{59} -0.144728 q^{60} +8.73637 q^{61} +4.98859 q^{62} +2.45035 q^{63} +8.72691 q^{64} +0.330113 q^{65} -3.51229 q^{66} -9.51349 q^{67} +0.245926 q^{68} +23.3449 q^{69} +0.178573 q^{70} +10.0855 q^{71} +11.9960 q^{72} +4.40274 q^{73} -1.28880 q^{74} +13.1292 q^{75} -1.66143 q^{76} -0.607593 q^{77} -5.22485 q^{78} -6.39281 q^{79} +0.765078 q^{80} -4.83446 q^{81} -8.41352 q^{82} -8.28187 q^{83} +0.396263 q^{84} +0.221912 q^{85} -1.32441 q^{86} +6.66885 q^{87} -2.97454 q^{88} +5.07709 q^{89} +1.18528 q^{90} -0.903848 q^{91} +2.16486 q^{92} +9.98898 q^{93} -0.546865 q^{94} -1.49919 q^{95} +3.66748 q^{96} +5.09799 q^{97} +8.78197 q^{98} -4.03289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−1.32441	−0.936503	−0.468251	−	0.883595i	$-0.655116\pi$
$2$	−1.32441	−0.936503	−0.468251	+	0.883595i	$0.655116\pi$
$3$	−2.65196	−1.53111	−0.765555	−	0.643371i	$-0.777535\pi$
$3$	−2.65196	−1.53111	−0.765555	+	0.643371i	$0.777535\pi$
$4$	−0.245926	−0.122963
$5$	−0.221912	−0.0992420	−0.0496210	−	0.998768i	$-0.515801\pi$
$5$	−0.221912	−0.0992420	−0.0496210	+	0.998768i	$0.515801\pi$
$6$	3.51229	1.43389
$7$	0.607593	0.229648	0.114824	−	0.993386i	$-0.463370\pi$
$7$	0.607593	0.229648	0.114824	+	0.993386i	$0.463370\pi$
$8$	2.97454	1.05166
$9$	4.03289	1.34430
$10$	0.293903	0.0929404
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.652185	0.188270
$13$	−1.48759	−0.412583	−0.206291	−	0.978491i	$-0.566139\pi$
$13$	−1.48759	−0.412583	−0.206291	+	0.978491i	$0.566139\pi$
$14$	−0.804705	−0.215066
$15$	0.588501	0.151950
$16$	−3.44767	−0.861917
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−5.34122	−1.25894
$19$	6.75581	1.54989	0.774944	−	0.632030i	$-0.217778\pi$
$19$	6.75581	1.54989	0.774944	+	0.632030i	$0.217778\pi$
$20$	0.0545738	0.0122031
$21$	−1.61131	−0.351617
$22$	1.32441	0.282366
$23$	−8.80290	−1.83553	−0.917765	−	0.397123i	$-0.870009\pi$
$23$	−8.80290	−1.83553	−0.917765	+	0.397123i	$0.870009\pi$
$24$	−7.88835	−1.61020
$25$	−4.95076	−0.990151
$26$	1.97018	0.386385
$27$	−2.73919	−0.527156
$28$	−0.149423	−0.0282382
$29$	−2.51469	−0.466966	−0.233483	−	0.972361i	$-0.575012\pi$
$29$	−2.51469	−0.466966	−0.233483	+	0.972361i	$0.575012\pi$
$30$	−0.779420	−0.142302
$31$	−3.76664	−0.676509	−0.338254	−	0.941055i	$-0.609836\pi$
$31$	−3.76664	−0.676509	−0.338254	+	0.941055i	$0.609836\pi$
$32$	−1.38293	−0.244470
$33$	2.65196	0.461647
$34$	1.32441	0.227135
$35$	−0.134832	−0.0227908
$36$	−0.991792	−0.165299
$37$	0.973107	0.159978	0.0799889	−	0.996796i	$-0.474512\pi$
$37$	0.973107	0.159978	0.0799889	+	0.996796i	$0.474512\pi$
$38$	−8.94749	−1.45147
$39$	3.94502	0.631710
$40$	−0.660085	−0.104369
$41$	6.35263	0.992115	0.496057	−	0.868290i	$-0.334781\pi$
$41$	6.35263	0.992115	0.496057	+	0.868290i	$0.334781\pi$
$42$	2.13404	0.329290
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.245926	0.0370747
$45$	−0.894946	−0.133411
$46$	11.6587	1.71898
$47$	0.412911	0.0602292	0.0301146	−	0.999546i	$-0.490413\pi$
$47$	0.412911	0.0602292	0.0301146	+	0.999546i	$0.490413\pi$
$48$	9.14308	1.31969
$49$	−6.63083	−0.947262
$50$	6.55685	0.927279
$51$	2.65196	0.371349
$52$	0.365836	0.0507324
$53$	2.59789	0.356848	0.178424	−	0.983954i	$-0.442900\pi$
$53$	2.59789	0.356848	0.178424	+	0.983954i	$0.442900\pi$
$54$	3.62782	0.493683
$55$	0.221912	0.0299226
$56$	1.80731	0.241512
$57$	−17.9161	−2.37305
$58$	3.33049	0.437315
$59$	14.1945	1.84796	0.923980	−	0.382441i	$-0.124916\pi$
$59$	14.1945	1.84796	0.923980	+	0.382441i	$0.124916\pi$
$60$	−0.144728	−0.0186843
$61$	8.73637	1.11858	0.559288	−	0.828973i	$-0.311074\pi$
$61$	8.73637	1.11858	0.559288	+	0.828973i	$0.311074\pi$
$62$	4.98859	0.633552
$63$	2.45035	0.308716
$64$	8.72691	1.09086
$65$	0.330113	0.0409455
$66$	−3.51229	−0.432334
$67$	−9.51349	−1.16226	−0.581129	−	0.813811i	$-0.697389\pi$
$67$	−9.51349	−1.16226	−0.581129	+	0.813811i	$0.697389\pi$
$68$	0.245926	0.0298229
$69$	23.3449	2.81040
$70$	0.178573	0.0213436
$71$	10.0855	1.19692	0.598462	−	0.801151i	$-0.295779\pi$
$71$	10.0855	1.19692	0.598462	+	0.801151i	$0.295779\pi$
$72$	11.9960	1.41374
$73$	4.40274	0.515302	0.257651	−	0.966238i	$-0.417052\pi$
$73$	4.40274	0.515302	0.257651	+	0.966238i	$0.417052\pi$
$74$	−1.28880	−0.149820
$75$	13.1292	1.51603
$76$	−1.66143	−0.190579
$77$	−0.607593	−0.0692416
$78$	−5.22485	−0.591598
$79$	−6.39281	−0.719248	−0.359624	−	0.933097i	$-0.617095\pi$
$79$	−6.39281	−0.719248	−0.359624	+	0.933097i	$0.617095\pi$
$80$	0.765078	0.0855384
$81$	−4.83446	−0.537163
$82$	−8.41352	−0.929118
$83$	−8.28187	−0.909054	−0.454527	−	0.890733i	$-0.650192\pi$
$83$	−8.28187	−0.909054	−0.454527	+	0.890733i	$0.650192\pi$
$84$	0.396263	0.0432358
$85$	0.221912	0.0240697
$86$	−1.32441	−0.142815
$87$	6.66885	0.714976
$88$	−2.97454	−0.317087
$89$	5.07709	0.538171	0.269085	−	0.963116i	$-0.413279\pi$
$89$	5.07709	0.538171	0.269085	+	0.963116i	$0.413279\pi$
$90$	1.18528	0.124939
$91$	−0.903848	−0.0947490
$92$	2.16486	0.225702
$93$	9.98898	1.03581
$94$	−0.546865	−0.0564048
$95$	−1.49919	−0.153814
$96$	3.66748	0.374310
$97$	5.09799	0.517623	0.258811	−	0.965928i	$-0.416669\pi$
$97$	5.09799	0.517623	0.258811	+	0.965928i	$0.416669\pi$
$98$	8.78197	0.887113
$99$	−4.03289	−0.405321
$100$	1.21752	0.121752
$101$	−13.9102	−1.38412	−0.692061	−	0.721839i	$-0.743297\pi$
$101$	−13.9102	−1.38412	−0.692061	+	0.721839i	$0.743297\pi$
$102$	−3.51229	−0.347769
$103$	−7.26983	−0.716318	−0.358159	−	0.933661i	$-0.616595\pi$
$103$	−7.26983	−0.716318	−0.358159	+	0.933661i	$0.616595\pi$
$104$	−4.42489	−0.433896
$105$	0.357569	0.0348952
$106$	−3.44069	−0.334189
$107$	2.77235	0.268013	0.134007	−	0.990980i	$-0.457216\pi$
$107$	2.77235	0.268013	0.134007	+	0.990980i	$0.457216\pi$
$108$	0.673636	0.0648207
$109$	0.658171	0.0630414	0.0315207	−	0.999503i	$-0.489965\pi$
$109$	0.658171	0.0630414	0.0315207	+	0.999503i	$0.489965\pi$
$110$	−0.293903	−0.0280226
$111$	−2.58064	−0.244943
$112$	−2.09478	−0.197938
$113$	−19.3203	−1.81750	−0.908749	−	0.417344i	$-0.862961\pi$
$113$	−19.3203	−1.81750	−0.908749	+	0.417344i	$0.862961\pi$
$114$	23.7284	2.22237
$115$	1.95347	0.182162
$116$	0.618427	0.0574195
$117$	−5.99928	−0.554634
$118$	−18.7993	−1.73062
$119$	−0.607593	−0.0556979
$120$	1.75052	0.159800
$121$	1.00000	0.0909091
$122$	−11.5706	−1.04755
$123$	−16.8469	−1.51904
$124$	0.926314	0.0831855
$125$	2.20819	0.197507
$126$	−3.24529	−0.289113
$127$	−18.7177	−1.66093	−0.830464	−	0.557072i	$-0.811925\pi$
$127$	−18.7177	−1.66093	−0.830464	+	0.557072i	$0.811925\pi$
$128$	−8.79219	−0.777127
$129$	−2.65196	−0.233492
$130$	−0.437207	−0.0383456
$131$	−1.21438	−0.106100	−0.0530502	−	0.998592i	$-0.516894\pi$
$131$	−1.21438	−0.106100	−0.0530502	+	0.998592i	$0.516894\pi$
$132$	−0.652185	−0.0567654
$133$	4.10478	0.355930
$134$	12.5998	1.08846
$135$	0.607857	0.0523160
$136$	−2.97454	−0.255064
$137$	−3.09573	−0.264486	−0.132243	−	0.991217i	$-0.542218\pi$
$137$	−3.09573	−0.264486	−0.132243	+	0.991217i	$0.542218\pi$
$138$	−30.9184	−2.63195
$139$	−2.12113	−0.179912	−0.0899558	−	0.995946i	$-0.528673\pi$
$139$	−2.12113	−0.179912	−0.0899558	+	0.995946i	$0.528673\pi$
$140$	0.0331587	0.00280242
$141$	−1.09502	−0.0922175
$142$	−13.3573	−1.12092
$143$	1.48759	0.124398
$144$	−13.9041	−1.15867
$145$	0.558039	0.0463426
$146$	−5.83106	−0.482582
$147$	17.5847	1.45036
$148$	−0.239312	−0.0196713
$149$	12.3279	1.00994	0.504969	−	0.863137i	$-0.331504\pi$
$149$	12.3279	1.00994	0.504969	+	0.863137i	$0.331504\pi$
$150$	−17.3885	−1.41977
$151$	−11.9777	−0.974732	−0.487366	−	0.873198i	$-0.662042\pi$
$151$	−11.9777	−0.974732	−0.487366	+	0.873198i	$0.662042\pi$
$152$	20.0954	1.62995
$153$	−4.03289	−0.326040
$154$	0.804705	0.0648449
$155$	0.835862	0.0671380
$156$	−0.970183	−0.0776768
$157$	18.4716	1.47419	0.737097	−	0.675787i	$-0.236196\pi$
$157$	18.4716	1.47419	0.737097	+	0.675787i	$0.236196\pi$
$158$	8.46674	0.673577
$159$	−6.88951	−0.546374
$160$	0.306889	0.0242617
$161$	−5.34858	−0.421527
$162$	6.40283	0.503054
$163$	13.1413	1.02931	0.514654	−	0.857398i	$-0.327920\pi$
$163$	13.1413	1.02931	0.514654	+	0.857398i	$0.327920\pi$
$164$	−1.56228	−0.121993
$165$	−0.588501	−0.0458148
$166$	10.9686	0.851331
$167$	17.3299	1.34103	0.670514	−	0.741897i	$-0.266074\pi$
$167$	17.3299	1.34103	0.670514	+	0.741897i	$0.266074\pi$
$168$	−4.79291	−0.369781
$169$	−10.7871	−0.829775
$170$	−0.293903	−0.0225413
$171$	27.2454	2.08351
$172$	−0.245926	−0.0187517
$173$	−14.8756	−1.13097	−0.565486	−	0.824758i	$-0.691311\pi$
$173$	−14.8756	−1.13097	−0.565486	+	0.824758i	$0.691311\pi$
$174$	−8.83233	−0.669577
$175$	−3.00804	−0.227387
$176$	3.44767	0.259878
$177$	−37.6431	−2.82943
$178$	−6.72418	−0.503998
$179$	−9.34096	−0.698176	−0.349088	−	0.937090i	$-0.613509\pi$
$179$	−9.34096	−0.698176	−0.349088	+	0.937090i	$0.613509\pi$
$180$	0.220090	0.0164046
$181$	−21.7251	−1.61481	−0.807405	−	0.589997i	$-0.799129\pi$
$181$	−21.7251	−1.61481	−0.807405	+	0.589997i	$0.799129\pi$
$182$	1.19707	0.0887327
$183$	−23.1685	−1.71266
$184$	−26.1845	−1.93035
$185$	−0.215944	−0.0158765
$186$	−13.2296	−0.970038
$187$	1.00000	0.0731272
$188$	−0.101545	−0.00740596
$189$	−1.66431	−0.121061
$190$	1.98555	0.144047
$191$	8.62216	0.623878	0.311939	−	0.950102i	$-0.399022\pi$
$191$	8.62216	0.623878	0.311939	+	0.950102i	$0.399022\pi$
$192$	−23.1434	−1.67023
$193$	−2.89426	−0.208333	−0.104167	−	0.994560i	$-0.533218\pi$
$193$	−2.89426	−0.208333	−0.104167	+	0.994560i	$0.533218\pi$
$194$	−6.75186	−0.484755
$195$	−0.875448	−0.0626921
$196$	1.63069	0.116478
$197$	1.08486	0.0772931	0.0386465	−	0.999253i	$-0.487695\pi$
$197$	1.08486	0.0772931	0.0386465	+	0.999253i	$0.487695\pi$
$198$	5.34122	0.379584
$199$	12.6021	0.893340	0.446670	−	0.894699i	$-0.352610\pi$
$199$	12.6021	0.893340	0.446670	+	0.894699i	$0.352610\pi$
$200$	−14.7262	−1.04130
$201$	25.2294	1.77954
$202$	18.4229	1.29623
$203$	−1.52791	−0.107238
$204$	−0.652185	−0.0456621
$205$	−1.40972	−0.0984594
$206$	9.62827	0.670833
$207$	−35.5011	−2.46750
$208$	5.12871	0.355612
$209$	−6.75581	−0.467309
$210$	−0.473570	−0.0326794
$211$	−9.02178	−0.621085	−0.310543	−	0.950559i	$-0.600511\pi$
$211$	−9.02178	−0.621085	−0.310543	+	0.950559i	$0.600511\pi$
$212$	−0.638889	−0.0438791
$213$	−26.7462	−1.83262
$214$	−3.67174	−0.250995
$215$	−0.221912	−0.0151343
$216$	−8.14781	−0.554388
$217$	−2.28858	−0.155359
$218$	−0.871692	−0.0590384
$219$	−11.6759	−0.788984
$220$	−0.0545738	−0.00367937
$221$	1.48759	0.100066
$222$	3.41784	0.229390
$223$	1.40566	0.0941302	0.0470651	−	0.998892i	$-0.485013\pi$
$223$	1.40566	0.0941302	0.0470651	+	0.998892i	$0.485013\pi$
$224$	−0.840259	−0.0561421
$225$	−19.9659	−1.33106
$226$	25.5880	1.70209
$227$	17.3532	1.15177	0.575886	−	0.817530i	$-0.304657\pi$
$227$	17.3532	1.15177	0.575886	+	0.817530i	$0.304657\pi$
$228$	4.40604	0.291797
$229$	−5.80933	−0.383891	−0.191946	−	0.981406i	$-0.561480\pi$
$229$	−5.80933	−0.383891	−0.191946	+	0.981406i	$0.561480\pi$
$230$	−2.58720	−0.170595
$231$	1.61131	0.106017
$232$	−7.48004	−0.491088
$233$	−3.79109	−0.248362	−0.124181	−	0.992260i	$-0.539630\pi$
$233$	−3.79109	−0.248362	−0.124181	+	0.992260i	$0.539630\pi$
$234$	7.94554	0.519416
$235$	−0.0916297	−0.00597726
$236$	−3.49078	−0.227231
$237$	16.9535	1.10125
$238$	0.804705	0.0521613
$239$	−16.2373	−1.05031	−0.525153	−	0.851008i	$-0.675992\pi$
$239$	−16.2373	−1.05031	−0.525153	+	0.851008i	$0.675992\pi$
$240$	−2.02896	−0.130969
$241$	9.90711	0.638173	0.319087	−	0.947726i	$-0.396624\pi$
$241$	9.90711	0.638173	0.319087	+	0.947726i	$0.396624\pi$
$242$	−1.32441	−0.0851366
$243$	21.0384	1.34961
$244$	−2.14850	−0.137543
$245$	1.47146	0.0940081
$246$	22.3123	1.42258
$247$	−10.0499	−0.639457
$248$	−11.2040	−0.711455
$249$	21.9632	1.39186
$250$	−2.92456	−0.184965
$251$	2.19577	0.138596	0.0692979	−	0.997596i	$-0.477924\pi$
$251$	2.19577	0.138596	0.0692979	+	0.997596i	$0.477924\pi$
$252$	−0.602606	−0.0379606
$253$	8.80290	0.553433
$254$	24.7900	1.55546
$255$	−0.588501	−0.0368534
$256$	−5.80932	−0.363083
$257$	6.36871	0.397269	0.198635	−	0.980074i	$-0.436349\pi$
$257$	6.36871	0.397269	0.198635	+	0.980074i	$0.436349\pi$
$258$	3.51229	0.218666
$259$	0.591252	0.0367386
$260$	−0.0811834	−0.00503478
$261$	−10.1415	−0.627741
$262$	1.60834	0.0993634
$263$	4.11172	0.253540	0.126770	−	0.991932i	$-0.459539\pi$
$263$	4.11172	0.253540	0.126770	+	0.991932i	$0.459539\pi$
$264$	7.88835	0.485495
$265$	−0.576504	−0.0354143
$266$	−5.43643	−0.333329
$267$	−13.4643	−0.823999
$268$	2.33961	0.142915
$269$	17.0490	1.03950	0.519749	−	0.854319i	$-0.326025\pi$
$269$	17.0490	1.03950	0.519749	+	0.854319i	$0.326025\pi$
$270$	−0.805055	−0.0489941
$271$	13.2510	0.804939	0.402470	−	0.915433i	$-0.368152\pi$
$271$	13.2510	0.804939	0.402470	+	0.915433i	$0.368152\pi$
$272$	3.44767	0.209046
$273$	2.39697	0.145071
$274$	4.10003	0.247692
$275$	4.95076	0.298542
$276$	−5.74112	−0.345575
$277$	−29.8432	−1.79311	−0.896553	−	0.442936i	$-0.853937\pi$
$277$	−29.8432	−1.79311	−0.896553	+	0.442936i	$0.853937\pi$
$278$	2.80925	0.168488
$279$	−15.1904	−0.909428
$280$	−0.401063	−0.0239681
$281$	−8.34534	−0.497841	−0.248920	−	0.968524i	$-0.580076\pi$
$281$	−8.34534	−0.497841	−0.248920	+	0.968524i	$0.580076\pi$
$282$	1.45026	0.0863619
$283$	−5.09857	−0.303079	−0.151539	−	0.988451i	$-0.548423\pi$
$283$	−5.09857	−0.303079	−0.151539	+	0.988451i	$0.548423\pi$
$284$	−2.48028	−0.147177
$285$	3.97580	0.235506
$286$	−1.97018	−0.116499
$287$	3.85981	0.227838
$288$	−5.57721	−0.328640
$289$	1.00000	0.0588235
$290$	−0.739075	−0.0434000
$291$	−13.5197	−0.792537
$292$	−1.08275	−0.0633630
$293$	−23.6809	−1.38345	−0.691726	−	0.722160i	$-0.743149\pi$
$293$	−23.6809	−1.38345	−0.691726	+	0.722160i	$0.743149\pi$
$294$	−23.2894	−1.35827
$295$	−3.14992	−0.183395
$296$	2.89454	0.168242
$297$	2.73919	0.158944
$298$	−16.3272	−0.945810
$299$	13.0951	0.757309
$300$	−3.22881	−0.186415
$301$	0.607593	0.0350211
$302$	15.8635	0.912839
$303$	36.8894	2.11924
$304$	−23.2918	−1.33588
$305$	−1.93870	−0.111010
$306$	5.34122	0.305337
$307$	−10.2397	−0.584412	−0.292206	−	0.956355i	$-0.594389\pi$
$307$	−10.2397	−0.584412	−0.292206	+	0.956355i	$0.594389\pi$
$308$	0.149423	0.00851415
$309$	19.2793	1.09676
$310$	−1.10703	−0.0628750
$311$	14.3080	0.811333	0.405666	−	0.914021i	$-0.367039\pi$
$311$	14.3080	0.811333	0.405666	+	0.914021i	$0.367039\pi$
$312$	11.7346	0.664342
$313$	5.49671	0.310692	0.155346	−	0.987860i	$-0.450351\pi$
$313$	5.49671	0.310692	0.155346	+	0.987860i	$0.450351\pi$
$314$	−24.4641	−1.38059
$315$	−0.543763	−0.0306376
$316$	1.57216	0.0884408
$317$	10.8554	0.609703	0.304851	−	0.952400i	$-0.401393\pi$
$317$	10.8554	0.609703	0.304851	+	0.952400i	$0.401393\pi$
$318$	9.12457	0.511681
$319$	2.51469	0.140796
$320$	−1.93660	−0.108259
$321$	−7.35217	−0.410358
$322$	7.08373	0.394761
$323$	−6.75581	−0.375903
$324$	1.18892	0.0660511
$325$	7.36469	0.408519
$326$	−17.4046	−0.963950
$327$	−1.74544	−0.0965233
$328$	18.8961	1.04337
$329$	0.250881	0.0138315
$330$	0.779420	0.0429056
$331$	−23.8647	−1.31172	−0.655861	−	0.754882i	$-0.727694\pi$
$331$	−23.8647	−1.31172	−0.655861	+	0.754882i	$0.727694\pi$
$332$	2.03673	0.111780
$333$	3.92443	0.215058
$334$	−22.9520	−1.25588
$335$	2.11116	0.115345
$336$	5.55527	0.303065
$337$	−5.15647	−0.280891	−0.140445	−	0.990088i	$-0.544853\pi$
$337$	−5.15647	−0.280891	−0.140445	+	0.990088i	$0.544853\pi$
$338$	14.2866	0.777087
$339$	51.2366	2.78279
$340$	−0.0545738	−0.00295968
$341$	3.76664	0.203975
$342$	−36.0843	−1.95121
$343$	−8.28199	−0.447186
$344$	2.97454	0.160376
$345$	−5.18052	−0.278910
$346$	19.7015	1.05916
$347$	−1.28152	−0.0687954	−0.0343977	−	0.999408i	$-0.510951\pi$
$347$	−1.28152	−0.0687954	−0.0343977	+	0.999408i	$0.510951\pi$
$348$	−1.64004	−0.0879155
$349$	−11.5823	−0.619985	−0.309993	−	0.950739i	$-0.600327\pi$
$349$	−11.5823	−0.619985	−0.309993	+	0.950739i	$0.600327\pi$
$350$	3.98390	0.212948
$351$	4.07478	0.217496
$352$	1.38293	0.0737105
$353$	−29.7247	−1.58208	−0.791042	−	0.611761i	$-0.790461\pi$
$353$	−29.7247	−1.58208	−0.791042	+	0.611761i	$0.790461\pi$
$354$	49.8551	2.64977
$355$	−2.23808	−0.118785
$356$	−1.24859	−0.0661751
$357$	1.61131	0.0852796
$358$	12.3713	0.653843
$359$	−25.7799	−1.36061	−0.680306	−	0.732928i	$-0.738153\pi$
$359$	−25.7799	−1.36061	−0.680306	+	0.732928i	$0.738153\pi$
$360$	−2.66205	−0.140302
$361$	26.6409	1.40215
$362$	28.7730	1.51227
$363$	−2.65196	−0.139192
$364$	0.222280	0.0116506
$365$	−0.977020	−0.0511396
$366$	30.6847	1.60391
$367$	−22.8009	−1.19020	−0.595100	−	0.803652i	$-0.702887\pi$
$367$	−22.8009	−1.19020	−0.595100	+	0.803652i	$0.702887\pi$
$368$	30.3495	1.58208
$369$	25.6195	1.33370
$370$	0.285999	0.0148684
$371$	1.57846	0.0819497
$372$	−2.45655	−0.127366
$373$	33.9465	1.75768	0.878842	−	0.477112i	$-0.158316\pi$
$373$	33.9465	1.75768	0.878842	+	0.477112i	$0.158316\pi$
$374$	−1.32441	−0.0684839
$375$	−5.85603	−0.302404
$376$	1.22822	0.0633405
$377$	3.74082	0.192662
$378$	2.20423	0.113374
$379$	0.194765	0.0100044	0.00500220	−	0.999987i	$-0.498408\pi$
$379$	0.194765	0.0100044	0.00500220	+	0.999987i	$0.498408\pi$
$380$	0.368690	0.0189134
$381$	49.6386	2.54306
$382$	−11.4193	−0.584263
$383$	−21.3337	−1.09010	−0.545051	−	0.838403i	$-0.683490\pi$
$383$	−21.3337	−1.09010	−0.545051	+	0.838403i	$0.683490\pi$
$384$	23.3165	1.18987
$385$	0.134832	0.00687167
$386$	3.83320	0.195105
$387$	4.03289	0.205003
$388$	−1.25373	−0.0636484
$389$	−36.5107	−1.85117	−0.925584	−	0.378542i	$-0.876425\pi$
$389$	−36.5107	−1.85117	−0.925584	+	0.378542i	$0.876425\pi$
$390$	1.15946	0.0587113
$391$	8.80290	0.445182
$392$	−19.7237	−0.996195
$393$	3.22048	0.162451
$394$	−1.43680	−0.0723852
$395$	1.41864	0.0713796
$396$	0.991792	0.0498394
$397$	7.08224	0.355448	0.177724	−	0.984080i	$-0.443127\pi$
$397$	7.08224	0.355448	0.177724	+	0.984080i	$0.443127\pi$
$398$	−16.6904	−0.836615
$399$	−10.8857	−0.544967
$400$	17.0686	0.853428
$401$	2.36907	0.118306	0.0591528	−	0.998249i	$-0.481160\pi$
$401$	2.36907	0.118306	0.0591528	+	0.998249i	$0.481160\pi$
$402$	−33.4142	−1.66655
$403$	5.60321	0.279116
$404$	3.42089	0.170196
$405$	1.07282	0.0533091
$406$	2.02358	0.100429
$407$	−0.973107	−0.0482351
$408$	7.88835	0.390532
$409$	14.6982	0.726780	0.363390	−	0.931637i	$-0.381619\pi$
$409$	14.6982	0.726780	0.363390	+	0.931637i	$0.381619\pi$
$410$	1.86706	0.0922075
$411$	8.20974	0.404957
$412$	1.78784	0.0880805
$413$	8.62444	0.424381
$414$	47.0182	2.31082
$415$	1.83785	0.0902163
$416$	2.05723	0.100864
$417$	5.62514	0.275465
$418$	8.94749	0.437636
$419$	−21.6411	−1.05724	−0.528619	−	0.848859i	$-0.677290\pi$
$419$	−21.6411	−1.05724	−0.528619	+	0.848859i	$0.677290\pi$
$420$	−0.0879354	−0.00429081
$421$	−30.9897	−1.51034	−0.755172	−	0.655527i	$-0.772447\pi$
$421$	−30.9897	−1.51034	−0.755172	+	0.655527i	$0.772447\pi$
$422$	11.9486	0.581648
$423$	1.66522	0.0809659
$424$	7.72753	0.375282
$425$	4.95076	0.240147
$426$	35.4231	1.71626
$427$	5.30815	0.256879
$428$	−0.681793	−0.0329557
$429$	−3.94502	−0.190468
$430$	0.293903	0.0141733
$431$	3.72901	0.179620	0.0898101	−	0.995959i	$-0.471374\pi$
$431$	3.72901	0.179620	0.0898101	+	0.995959i	$0.471374\pi$
$432$	9.44380	0.454365
$433$	−29.5852	−1.42178	−0.710888	−	0.703305i	$-0.751707\pi$
$433$	−29.5852	−1.42178	−0.710888	+	0.703305i	$0.751707\pi$
$434$	3.03103	0.145494
$435$	−1.47990	−0.0709556
$436$	−0.161861	−0.00775175
$437$	−59.4707	−2.84487
$438$	15.4637	0.738886
$439$	11.6524	0.556141	0.278070	−	0.960561i	$-0.410305\pi$
$439$	11.6524	0.556141	0.278070	+	0.960561i	$0.410305\pi$
$440$	0.660085	0.0314683
$441$	−26.7414	−1.27340
$442$	−1.97018	−0.0937121
$443$	−0.983291	−0.0467176	−0.0233588	−	0.999727i	$-0.507436\pi$
$443$	−0.983291	−0.0467176	−0.0233588	+	0.999727i	$0.507436\pi$
$444$	0.634646	0.0301190
$445$	−1.12667	−0.0534091
$446$	−1.86168	−0.0881532
$447$	−32.6930	−1.54633
$448$	5.30241	0.250515
$449$	42.2750	1.99508	0.997540	−	0.0700952i	$-0.0223303\pi$
$449$	42.2750	1.99508	0.997540	+	0.0700952i	$0.0223303\pi$
$450$	26.4431	1.24654
$451$	−6.35263	−0.299134
$452$	4.75135	0.223485
$453$	31.7644	1.49242
$454$	−22.9828	−1.07864
$455$	0.200574	0.00940308
$456$	−53.2922	−2.49564
$457$	−28.1450	−1.31657	−0.658283	−	0.752770i	$-0.728717\pi$
$457$	−28.1450	−1.31657	−0.658283	+	0.752770i	$0.728717\pi$
$458$	7.69396	0.359515
$459$	2.73919	0.127854
$460$	−0.480408	−0.0223991
$461$	18.7709	0.874248	0.437124	−	0.899401i	$-0.355997\pi$
$461$	18.7709	0.874248	0.437124	+	0.899401i	$0.355997\pi$
$462$	−2.13404	−0.0992847
$463$	34.1970	1.58927	0.794634	−	0.607089i	$-0.207663\pi$
$463$	34.1970	1.58927	0.794634	+	0.607089i	$0.207663\pi$
$464$	8.66981	0.402486
$465$	−2.21667	−0.102796
$466$	5.02097	0.232592
$467$	27.7449	1.28388	0.641940	−	0.766754i	$-0.278130\pi$
$467$	27.7449	1.28388	0.641940	+	0.766754i	$0.278130\pi$
$468$	1.47538	0.0681994
$469$	−5.78033	−0.266911
$470$	0.121356	0.00559772
$471$	−48.9859	−2.25715
$472$	42.2219	1.94342
$473$	−1.00000	−0.0459800
$474$	−22.4534	−1.03132
$475$	−33.4464	−1.53462
$476$	0.149423	0.00684878
$477$	10.4770	0.479710
$478$	21.5050	0.983614
$479$	27.7131	1.26625	0.633123	−	0.774052i	$-0.281773\pi$
$479$	27.7131	1.26625	0.633123	+	0.774052i	$0.281773\pi$
$480$	−0.813856	−0.0371473
$481$	−1.44758	−0.0660041
$482$	−13.1211	−0.597651
$483$	14.1842	0.645404
$484$	−0.245926	−0.0111784
$485$	−1.13130	−0.0513699
$486$	−27.8635	−1.26391
$487$	18.3443	0.831261	0.415630	−	0.909534i	$-0.363561\pi$
$487$	18.3443	0.831261	0.415630	+	0.909534i	$0.363561\pi$
$488$	25.9866	1.17636
$489$	−34.8503	−1.57598
$490$	−1.94882	−0.0880388
$491$	9.78312	0.441506	0.220753	−	0.975330i	$-0.429149\pi$
$491$	9.78312	0.441506	0.220753	+	0.975330i	$0.429149\pi$
$492$	4.14310	0.186785
$493$	2.51469	0.113256
$494$	13.3102	0.598854
$495$	0.894946	0.0402248
$496$	12.9861	0.583094
$497$	6.12785	0.274872
$498$	−29.0884	−1.30348
$499$	30.1145	1.34811	0.674054	−	0.738682i	$-0.264551\pi$
$499$	30.1145	1.34811	0.674054	+	0.738682i	$0.264551\pi$
$500$	−0.543051	−0.0242860
$501$	−45.9582	−2.05326
$502$	−2.90811	−0.129795
$503$	33.8328	1.50853	0.754265	−	0.656570i	$-0.227993\pi$
$503$	33.8328	1.50853	0.754265	+	0.656570i	$0.227993\pi$
$504$	7.28867	0.324663
$505$	3.08685	0.137363
$506$	−11.6587	−0.518292
$507$	28.6069	1.27048
$508$	4.60317	0.204233
$509$	38.0253	1.68544	0.842721	−	0.538351i	$-0.180952\pi$
$509$	38.0253	1.68544	0.842721	+	0.538351i	$0.180952\pi$
$510$	0.779420	0.0345133
$511$	2.67507	0.118338
$512$	25.2783	1.11715
$513$	−18.5054	−0.817034
$514$	−8.43481	−0.372044
$515$	1.61326	0.0710888
$516$	0.652185	0.0287109
$517$	−0.412911	−0.0181598
$518$	−0.783063	−0.0344058
$519$	39.4495	1.73164
$520$	0.981935	0.0430607
$521$	−24.3263	−1.06576	−0.532878	−	0.846192i	$-0.678889\pi$
$521$	−24.3263	−1.06576	−0.532878	+	0.846192i	$0.678889\pi$
$522$	13.4315	0.587881
$523$	−44.4598	−1.94409	−0.972046	−	0.234792i	$-0.924559\pi$
$523$	−44.4598	−1.94409	−0.972046	+	0.234792i	$0.924559\pi$
$524$	0.298646	0.0130464
$525$	7.97721	0.348154
$526$	−5.44562	−0.237440
$527$	3.76664	0.164077
$528$	−9.14308	−0.397901
$529$	54.4910	2.36917
$530$	0.763530	0.0331656
$531$	57.2447	2.48421
$532$	−1.00947	−0.0437661
$533$	−9.45011	−0.409330
$534$	17.8323	0.771677
$535$	−0.615218	−0.0265982
$536$	−28.2982	−1.22230
$537$	24.7718	1.06898
$538$	−22.5800	−0.973493
$539$	6.63083	0.285610
$540$	−0.149488	−0.00643293
$541$	−9.71132	−0.417522	−0.208761	−	0.977967i	$-0.566943\pi$
$541$	−9.71132	−0.417522	−0.208761	+	0.977967i	$0.566943\pi$
$542$	−17.5498	−0.753828
$543$	57.6140	2.47245
$544$	1.38293	0.0592927
$545$	−0.146056	−0.00625635
$546$	−3.17458	−0.135859
$547$	23.1955	0.991768	0.495884	−	0.868389i	$-0.334844\pi$
$547$	23.1955	0.991768	0.495884	+	0.868389i	$0.334844\pi$
$548$	0.761319	0.0325219
$549$	35.2328	1.50370
$550$	−6.55685	−0.279585
$551$	−16.9888	−0.723745
$552$	69.4404	2.95558
$553$	−3.88423	−0.165174
$554$	39.5248	1.67925
$555$	0.572674	0.0243087
$556$	0.521640	0.0221225
$557$	−18.1890	−0.770691	−0.385346	−	0.922772i	$-0.625918\pi$
$557$	−18.1890	−0.770691	−0.385346	+	0.922772i	$0.625918\pi$
$558$	20.1185	0.851682
$559$	−1.48759	−0.0629183
$560$	0.464856	0.0196438
$561$	−2.65196	−0.111966
$562$	11.0527	0.466229
$563$	1.33469	0.0562503	0.0281251	−	0.999604i	$-0.491046\pi$
$563$	1.33469	0.0562503	0.0281251	+	0.999604i	$0.491046\pi$
$564$	0.269294	0.0113393
$565$	4.28739	0.180372
$566$	6.75262	0.283834
$567$	−2.93738	−0.123359
$568$	29.9996	1.25875
$569$	−12.2024	−0.511552	−0.255776	−	0.966736i	$-0.582331\pi$
$569$	−12.2024	−0.511552	−0.255776	+	0.966736i	$0.582331\pi$
$570$	−5.26561	−0.220552
$571$	46.3848	1.94114	0.970572	−	0.240811i	$-0.0774133\pi$
$571$	46.3848	1.94114	0.970572	+	0.240811i	$0.0774133\pi$
$572$	−0.365836	−0.0152964
$573$	−22.8656	−0.955225
$574$	−5.11199	−0.213371
$575$	43.5810	1.81745
$576$	35.1947	1.46645
$577$	13.6218	0.567083	0.283542	−	0.958960i	$-0.408491\pi$
$577$	13.6218	0.567083	0.283542	+	0.958960i	$0.408491\pi$
$578$	−1.32441	−0.0550884
$579$	7.67545	0.318981
$580$	−0.137236	−0.00569842
$581$	−5.03201	−0.208763
$582$	17.9057	0.742213
$583$	−2.59789	−0.107594
$584$	13.0961	0.541921
$585$	1.33131	0.0550430
$586$	31.3633	1.29561
$587$	13.8124	0.570099	0.285049	−	0.958513i	$-0.407990\pi$
$587$	13.8124	0.570099	0.285049	+	0.958513i	$0.407990\pi$
$588$	−4.32453	−0.178341
$589$	−25.4467	−1.04851
$590$	4.17179	0.171750
$591$	−2.87701	−0.118344
$592$	−3.35495	−0.137888
$593$	44.3255	1.82023	0.910114	−	0.414357i	$-0.135994\pi$
$593$	44.3255	1.82023	0.910114	+	0.414357i	$0.135994\pi$
$594$	−3.62782	−0.148851
$595$	0.134832	0.00552757
$596$	−3.03174	−0.124185
$597$	−33.4203	−1.36780
$598$	−17.3433	−0.709221
$599$	−3.29965	−0.134820	−0.0674099	−	0.997725i	$-0.521474\pi$
$599$	−3.29965	−0.134820	−0.0674099	+	0.997725i	$0.521474\pi$
$600$	39.0533	1.59434
$601$	−13.4276	−0.547725	−0.273862	−	0.961769i	$-0.588301\pi$
$601$	−13.4276	−0.547725	−0.273862	+	0.961769i	$0.588301\pi$
$602$	−0.804705	−0.0327973
$603$	−38.3669	−1.56242
$604$	2.94563	0.119856
$605$	−0.221912	−0.00902200
$606$	−48.8569	−1.98467
$607$	17.1251	0.695088	0.347544	−	0.937664i	$-0.387016\pi$
$607$	17.1251	0.695088	0.347544	+	0.937664i	$0.387016\pi$
$608$	−9.34282	−0.378901
$609$	4.05195	0.164193
$610$	2.56765	0.103961
$611$	−0.614241	−0.0248495
$612$	0.991792	0.0400908
$613$	3.32542	0.134313	0.0671563	−	0.997742i	$-0.478607\pi$
$613$	3.32542	0.134313	0.0671563	+	0.997742i	$0.478607\pi$
$614$	13.5616	0.547303
$615$	3.73853	0.150752
$616$	−1.80731	−0.0728185
$617$	22.5574	0.908127	0.454064	−	0.890969i	$-0.349974\pi$
$617$	22.5574	0.908127	0.454064	+	0.890969i	$0.349974\pi$
$618$	−25.5338	−1.02712
$619$	17.5797	0.706588	0.353294	−	0.935512i	$-0.385062\pi$
$619$	17.5797	0.706588	0.353294	+	0.935512i	$0.385062\pi$
$620$	−0.205560	−0.00825549
$621$	24.1128	0.967612
$622$	−18.9497	−0.759815
$623$	3.08481	0.123590
$624$	−13.6011	−0.544481
$625$	24.2638	0.970550
$626$	−7.27992	−0.290964
$627$	17.9161	0.715501
$628$	−4.54264	−0.181271
$629$	−0.973107	−0.0388003
$630$	0.720167	0.0286921
$631$	27.8359	1.10813	0.554064	−	0.832474i	$-0.313076\pi$
$631$	27.8359	1.10813	0.554064	+	0.832474i	$0.313076\pi$
$632$	−19.0157	−0.756402
$633$	23.9254	0.950950
$634$	−14.3771	−0.570988
$635$	4.15368	0.164834
$636$	1.69431	0.0671837
$637$	9.86395	0.390824
$638$	−3.33049	−0.131855
$639$	40.6736	1.60902
$640$	1.95109	0.0771236
$641$	−41.8906	−1.65458	−0.827289	−	0.561776i	$-0.810118\pi$
$641$	−41.8906	−1.65458	−0.827289	+	0.561776i	$0.810118\pi$
$642$	9.73732	0.384301
$643$	−22.9581	−0.905381	−0.452690	−	0.891668i	$-0.649536\pi$
$643$	−22.9581	−0.905381	−0.452690	+	0.891668i	$0.649536\pi$
$644$	1.31535	0.0518322
$645$	0.588501	0.0231722
$646$	8.94749	0.352034
$647$	11.4772	0.451214	0.225607	−	0.974218i	$-0.427564\pi$
$647$	11.4772	0.451214	0.225607	+	0.974218i	$0.427564\pi$
$648$	−14.3803	−0.564911
$649$	−14.1945	−0.557181
$650$	−9.75390	−0.382579
$651$	6.06923	0.237872
$652$	−3.23179	−0.126567
$653$	25.6404	1.00339	0.501694	−	0.865045i	$-0.332710\pi$
$653$	25.6404	1.00339	0.501694	+	0.865045i	$0.332710\pi$
$654$	2.31169	0.0903943
$655$	0.269484	0.0105296
$656$	−21.9018	−0.855121
$657$	17.7558	0.692719
$658$	−0.332271	−0.0129533
$659$	−25.3650	−0.988078	−0.494039	−	0.869440i	$-0.664480\pi$
$659$	−25.3650	−0.988078	−0.494039	+	0.869440i	$0.664480\pi$
$660$	0.144728	0.00563352
$661$	34.5778	1.34492	0.672460	−	0.740133i	$-0.265238\pi$
$661$	34.5778	1.34492	0.672460	+	0.740133i	$0.265238\pi$
$662$	31.6067	1.22843
$663$	−3.94502	−0.153212
$664$	−24.6347	−0.956013
$665$	−0.910899	−0.0353231
$666$	−5.19758	−0.201402
$667$	22.1365	0.857131
$668$	−4.26187	−0.164897
$669$	−3.72776	−0.144124
$670$	−2.79605	−0.108021
$671$	−8.73637	−0.337264
$672$	2.22833	0.0859598
$673$	26.8062	1.03330	0.516652	−	0.856196i	$-0.327178\pi$
$673$	26.8062	1.03330	0.516652	+	0.856196i	$0.327178\pi$
$674$	6.82930	0.263055
$675$	13.5610	0.521964
$676$	2.65282	0.102032
$677$	−16.3280	−0.627535	−0.313767	−	0.949500i	$-0.601591\pi$
$677$	−16.3280	−0.627535	−0.313767	+	0.949500i	$0.601591\pi$
$678$	−67.8584	−2.60609
$679$	3.09750	0.118871
$680$	0.660085	0.0253131
$681$	−46.0200	−1.76349
$682$	−4.98859	−0.191023
$683$	22.0680	0.844409	0.422204	−	0.906501i	$-0.361256\pi$
$683$	22.0680	0.844409	0.422204	+	0.906501i	$0.361256\pi$
$684$	−6.70036	−0.256195
$685$	0.686978	0.0262481
$686$	10.9688	0.418790
$687$	15.4061	0.587780
$688$	−3.44767	−0.131441
$689$	−3.86460	−0.147229
$690$	6.86115	0.261200
$691$	45.0804	1.71494	0.857469	−	0.514536i	$-0.172036\pi$
$691$	45.0804	1.71494	0.857469	+	0.514536i	$0.172036\pi$
$692$	3.65830	0.139068
$693$	−2.45035	−0.0930813
$694$	1.69726	0.0644270
$695$	0.470703	0.0178548
$696$	19.8368	0.751910
$697$	−6.35263	−0.240623
$698$	15.3397	0.580618
$699$	10.0538	0.380270
$700$	0.739755	0.0279601
$701$	39.6187	1.49638	0.748188	−	0.663487i	$-0.230924\pi$
$701$	39.6187	1.49638	0.748188	+	0.663487i	$0.230924\pi$
$702$	−5.39670	−0.203685
$703$	6.57412	0.247948
$704$	−8.72691	−0.328908
$705$	0.242998	0.00915185
$706$	39.3678	1.48163
$707$	−8.45176	−0.317861
$708$	9.25741	0.347915
$709$	17.3911	0.653138	0.326569	−	0.945173i	$-0.394107\pi$
$709$	17.3911	0.653138	0.326569	+	0.945173i	$0.394107\pi$
$710$	2.96415	0.111243
$711$	−25.7815	−0.966882
$712$	15.1020	0.565972
$713$	33.1573	1.24175
$714$	−2.13404	−0.0798646
$715$	−0.330113	−0.0123455
$716$	2.29718	0.0858497
$717$	43.0607	1.60813
$718$	34.1433	1.27422
$719$	28.5754	1.06568	0.532842	−	0.846215i	$-0.321124\pi$
$719$	28.5754	1.06568	0.532842	+	0.846215i	$0.321124\pi$
$720$	3.08548	0.114989
$721$	−4.41710	−0.164501
$722$	−35.2837	−1.31312
$723$	−26.2733	−0.977113
$724$	5.34275	0.198562
$725$	12.4496	0.462367
$726$	3.51229	0.130353
$727$	15.8264	0.586969	0.293484	−	0.955964i	$-0.405185\pi$
$727$	15.8264	0.586969	0.293484	+	0.955964i	$0.405185\pi$
$728$	−2.68853	−0.0996435
$729$	−41.2895	−1.52924
$730$	1.29398	0.0478924
$731$	−1.00000	−0.0369863
$732$	5.69773	0.210594
$733$	−37.5904	−1.38843	−0.694217	−	0.719766i	$-0.744249\pi$
$733$	−37.5904	−1.38843	−0.694217	+	0.719766i	$0.744249\pi$
$734$	30.1979	1.11462
$735$	−3.90225	−0.143937
$736$	12.1738	0.448732
$737$	9.51349	0.350434
$738$	−33.9308	−1.24901
$739$	−14.2827	−0.525399	−0.262700	−	0.964878i	$-0.584613\pi$
$739$	−14.2827	−0.525399	−0.262700	+	0.964878i	$0.584613\pi$
$740$	0.0531062	0.00195222
$741$	26.6518	0.979079
$742$	−2.09054	−0.0767461
$743$	−9.41091	−0.345253	−0.172626	−	0.984987i	$-0.555225\pi$
$743$	−9.41091	−0.345253	−0.172626	+	0.984987i	$0.555225\pi$
$744$	29.7126	1.08932
$745$	−2.73570	−0.100228
$746$	−44.9593	−1.64608
$747$	−33.3999	−1.22204
$748$	−0.245926	−0.00899194
$749$	1.68446	0.0615489
$750$	7.75581	0.283202
$751$	0.975349	0.0355910	0.0177955	−	0.999842i	$-0.494335\pi$
$751$	0.975349	0.0355910	0.0177955	+	0.999842i	$0.494335\pi$
$752$	−1.42358	−0.0519126
$753$	−5.82310	−0.212205
$754$	−4.95440	−0.180429
$755$	2.65799	0.0967343
$756$	0.409296	0.0148860
$757$	14.2244	0.516993	0.258497	−	0.966012i	$-0.416773\pi$
$757$	14.2244	0.516993	0.258497	+	0.966012i	$0.416773\pi$
$758$	−0.257950	−0.00936915
$759$	−23.3449	−0.847367
$760$	−4.45941	−0.161760
$761$	−27.9445	−1.01299	−0.506493	−	0.862244i	$-0.669058\pi$
$761$	−27.9445	−1.01299	−0.506493	+	0.862244i	$0.669058\pi$
$762$	−65.7421	−2.38158
$763$	0.399900	0.0144774
$764$	−2.12041	−0.0767138
$765$	0.894946	0.0323568
$766$	28.2547	1.02088
$767$	−21.1155	−0.762437
$768$	15.4061	0.555919
$769$	−9.80483	−0.353571	−0.176786	−	0.984249i	$-0.556570\pi$
$769$	−9.80483	−0.353571	−0.176786	+	0.984249i	$0.556570\pi$
$770$	−0.178573	−0.00643534
$771$	−16.8896	−0.608263
$772$	0.711773	0.0256173
$773$	−7.77533	−0.279659	−0.139830	−	0.990176i	$-0.544655\pi$
$773$	−7.77533	−0.279659	−0.139830	+	0.990176i	$0.544655\pi$
$774$	−5.34122	−0.191986
$775$	18.6477	0.669846
$776$	15.1642	0.544362
$777$	−1.56798	−0.0562509
$778$	48.3554	1.73362
$779$	42.9172	1.53767
$780$	0.215295	0.00770880
$781$	−10.0855	−0.360886
$782$	−11.6587	−0.416914
$783$	6.88820	0.246164
$784$	22.8609	0.816461
$785$	−4.09907	−0.146302
$786$	−4.26524	−0.152136
$787$	−43.3203	−1.54420	−0.772101	−	0.635500i	$-0.780794\pi$
$787$	−43.3203	−1.54420	−0.772101	+	0.635500i	$0.780794\pi$
$788$	−0.266795	−0.00950418
$789$	−10.9041	−0.388197
$790$	−1.87887	−0.0668471
$791$	−11.7388	−0.417385
$792$	−11.9960	−0.426259
$793$	−12.9961	−0.461506
$794$	−9.37983	−0.332878
$795$	1.52886	0.0542232
$796$	−3.09918	−0.109848
$797$	−41.3934	−1.46623	−0.733114	−	0.680105i	$-0.761934\pi$
$797$	−41.3934	−1.46623	−0.733114	+	0.680105i	$0.761934\pi$
$798$	14.4172	0.510363
$799$	−0.412911	−0.0146077
$800$	6.84655	0.242062
$801$	20.4754	0.723462
$802$	−3.13763	−0.110793
$803$	−4.40274	−0.155369
$804$	−6.20456	−0.218818
$805$	1.18691	0.0418332
$806$	−7.42097	−0.261393
$807$	−45.2134	−1.59159
$808$	−41.3765	−1.45562
$809$	18.6689	0.656363	0.328182	−	0.944615i	$-0.393564\pi$
$809$	18.6689	0.656363	0.328182	+	0.944615i	$0.393564\pi$
$810$	−1.42086	−0.0499241
$811$	11.3466	0.398434	0.199217	−	0.979955i	$-0.436160\pi$
$811$	11.3466	0.398434	0.199217	+	0.979955i	$0.436160\pi$
$812$	0.375752	0.0131863
$813$	−35.1410	−1.23245
$814$	1.28880	0.0451723
$815$	−2.91622	−0.102151
$816$	−9.14308	−0.320072
$817$	6.75581	0.236356
$818$	−19.4665	−0.680632
$819$	−3.64512	−0.127371
$820$	0.346688	0.0121069
$821$	−35.8882	−1.25251	−0.626254	−	0.779619i	$-0.715413\pi$
$821$	−35.8882	−1.25251	−0.626254	+	0.779619i	$0.715413\pi$
$822$	−10.8731	−0.379243
$823$	−21.1212	−0.736238	−0.368119	−	0.929779i	$-0.619998\pi$
$823$	−21.1212	−0.736238	−0.368119	+	0.929779i	$0.619998\pi$
$824$	−21.6244	−0.753321
$825$	−13.1292	−0.457100
$826$	−11.4223	−0.397434
$827$	22.5313	0.783489	0.391745	−	0.920074i	$-0.371872\pi$
$827$	22.5313	0.783489	0.391745	+	0.920074i	$0.371872\pi$
$828$	8.73064	0.303411
$829$	−10.0861	−0.350305	−0.175153	−	0.984541i	$-0.556042\pi$
$829$	−10.0861	−0.350305	−0.175153	+	0.984541i	$0.556042\pi$
$830$	−2.43407	−0.0844878
$831$	79.1431	2.74544
$832$	−12.9821	−0.450072
$833$	6.63083	0.229745
$834$	−7.45002	−0.257973
$835$	−3.84571	−0.133086
$836$	1.66143	0.0574617
$837$	10.3175	0.356626
$838$	28.6618	0.990105
$839$	47.8923	1.65343	0.826713	−	0.562625i	$-0.190208\pi$
$839$	47.8923	1.65343	0.826713	+	0.562625i	$0.190208\pi$
$840$	1.06360	0.0366978
$841$	−22.6763	−0.781943
$842$	41.0432	1.41444
$843$	22.1315	0.762249
$844$	2.21869	0.0763704
$845$	2.39378	0.0823485
$846$	−2.20545	−0.0758248
$847$	0.607593	0.0208771
$848$	−8.95668	−0.307574
$849$	13.5212	0.464047
$850$	−6.55685	−0.224898
$851$	−8.56616	−0.293644
$852$	6.57759	0.225345
$853$	23.6547	0.809921	0.404961	−	0.914334i	$-0.367285\pi$
$853$	23.6547	0.809921	0.404961	+	0.914334i	$0.367285\pi$
$854$	−7.03019	−0.240568
$855$	−6.04608	−0.206772
$856$	8.24647	0.281858
$857$	34.3460	1.17324	0.586618	−	0.809864i	$-0.300459\pi$
$857$	34.3460	1.17324	0.586618	+	0.809864i	$0.300459\pi$
$858$	5.22485	0.178373
$859$	55.2048	1.88356	0.941782	−	0.336225i	$-0.109150\pi$
$859$	55.2048	1.88356	0.941782	+	0.336225i	$0.109150\pi$
$860$	0.0545738	0.00186095
$861$	−10.2361	−0.348844
$862$	−4.93876	−0.168215
$863$	1.91987	0.0653530	0.0326765	−	0.999466i	$-0.489597\pi$
$863$	1.91987	0.0653530	0.0326765	+	0.999466i	$0.489597\pi$
$864$	3.78810	0.128874
$865$	3.30107	0.112240
$866$	39.1831	1.33150
$867$	−2.65196	−0.0900653
$868$	0.562822	0.0191034
$869$	6.39281	0.216861
$870$	1.96000	0.0664501
$871$	14.1522	0.479528
$872$	1.95776	0.0662980
$873$	20.5596	0.695839
$874$	78.7638	2.66423
$875$	1.34168	0.0453571
$876$	2.87140	0.0970158
$877$	−11.6106	−0.392062	−0.196031	−	0.980598i	$-0.562805\pi$
$877$	−11.6106	−0.392062	−0.196031	+	0.980598i	$0.562805\pi$
$878$	−15.4327	−0.520827
$879$	62.8007	2.11822
$880$	−0.765078	−0.0257908
$881$	−24.5496	−0.827098	−0.413549	−	0.910482i	$-0.635711\pi$
$881$	−24.5496	−0.827098	−0.413549	+	0.910482i	$0.635711\pi$
$882$	35.4167	1.19254
$883$	−45.5835	−1.53401	−0.767004	−	0.641642i	$-0.778253\pi$
$883$	−45.5835	−1.53401	−0.767004	+	0.641642i	$0.778253\pi$
$884$	−0.365836	−0.0123044
$885$	8.35345	0.280798
$886$	1.30228	0.0437511
$887$	43.5361	1.46180	0.730900	−	0.682484i	$-0.239100\pi$
$887$	43.5361	1.46180	0.730900	+	0.682484i	$0.239100\pi$
$888$	−7.67621	−0.257597
$889$	−11.3727	−0.381430
$890$	1.49217	0.0500178
$891$	4.83446	0.161961
$892$	−0.345689	−0.0115745
$893$	2.78954	0.0933485
$894$	43.2991	1.44814
$895$	2.07287	0.0692883
$896$	−5.34207	−0.178466
$897$	−34.7276	−1.15952
$898$	−55.9896	−1.86840
$899$	9.47193	0.315907
$900$	4.91012	0.163671
$901$	−2.59789	−0.0865484
$902$	8.41352	0.280140
$903$	−1.61131	−0.0536211
$904$	−57.4688	−1.91138
$905$	4.82105	0.160257
$906$	−42.0692	−1.39766
$907$	−47.9673	−1.59273	−0.796363	−	0.604818i	$-0.793246\pi$
$907$	−47.9673	−1.59273	−0.796363	+	0.604818i	$0.793246\pi$
$908$	−4.26760	−0.141625
$909$	−56.0985	−1.86067
$910$	−0.265644	−0.00880601
$911$	16.7608	0.555310	0.277655	−	0.960681i	$-0.410443\pi$
$911$	16.7608	0.555310	0.277655	+	0.960681i	$0.410443\pi$
$912$	61.7689	2.04537
$913$	8.28187	0.274090
$914$	37.2756	1.23297
$915$	5.14136	0.169968
$916$	1.42866	0.0472044
$917$	−0.737846	−0.0243658
$918$	−3.62782	−0.119736
$919$	29.3596	0.968485	0.484243	−	0.874934i	$-0.339095\pi$
$919$	29.3596	0.968485	0.484243	+	0.874934i	$0.339095\pi$
$920$	5.81066	0.191572
$921$	27.1553	0.894799
$922$	−24.8604	−0.818735
$923$	−15.0030	−0.493830
$924$	−0.396263	−0.0130361
$925$	−4.81761	−0.158402
$926$	−45.2910	−1.48835
$927$	−29.3184	−0.962944
$928$	3.47764	0.114159
$929$	12.0144	0.394180	0.197090	−	0.980385i	$-0.436851\pi$
$929$	12.0144	0.394180	0.197090	+	0.980385i	$0.436851\pi$
$930$	2.93579	0.0962685
$931$	−44.7966	−1.46815
$932$	0.932326	0.0305394
$933$	−37.9443	−1.24224
$934$	−36.7458	−1.20236
$935$	−0.221912	−0.00725729
$936$	−17.8451	−0.583285
$937$	−17.6752	−0.577423	−0.288711	−	0.957416i	$-0.593227\pi$
$937$	−17.6752	−0.577423	−0.288711	+	0.957416i	$0.593227\pi$
$938$	7.65555	0.249963
$939$	−14.5770	−0.475704
$940$	0.0225341	0.000734982 0
$941$	31.9618	1.04193	0.520963	−	0.853579i	$-0.325573\pi$
$941$	31.9618	1.04193	0.520963	+	0.853579i	$0.325573\pi$
$942$	64.8777	2.11383
$943$	−55.9216	−1.82106
$944$	−48.9378	−1.59279
$945$	0.369330	0.0120143
$946$	1.32441	0.0430604
$947$	8.30269	0.269801	0.134901	−	0.990859i	$-0.456928\pi$
$947$	8.30269	0.269801	0.134901	+	0.990859i	$0.456928\pi$
$948$	−4.16930	−0.135413
$949$	−6.54947	−0.212605
$950$	44.2968	1.43718
$951$	−28.7882	−0.933522
$952$	−1.80731	−0.0585752
$953$	15.6031	0.505433	0.252716	−	0.967540i	$-0.418676\pi$
$953$	15.6031	0.505433	0.252716	+	0.967540i	$0.418676\pi$
$954$	−13.8759	−0.449250
$955$	−1.91336	−0.0619149
$956$	3.99318	0.129149
$957$	−6.66885	−0.215573
$958$	−36.7037	−1.18584
$959$	−1.88094	−0.0607388
$960$	5.13580	0.165757
$961$	−16.8124	−0.542336
$962$	1.91720	0.0618130
$963$	11.1806	0.360290
$964$	−2.43641	−0.0784716
$965$	0.642270	0.0206754
$966$	−18.7858	−0.604422
$967$	26.8859	0.864591	0.432295	−	0.901732i	$-0.357704\pi$
$967$	26.8859	0.864591	0.432295	+	0.901732i	$0.357704\pi$
$968$	2.97454	0.0956052
$969$	17.9161	0.575549
$970$	1.49832	0.0481080
$971$	36.7760	1.18020	0.590100	−	0.807330i	$-0.299088\pi$
$971$	36.7760	1.18020	0.590100	+	0.807330i	$0.299088\pi$
$972$	−5.17388	−0.165952
$973$	−1.28878	−0.0413164
$974$	−24.2955	−0.778478
$975$	−19.5309	−0.625488
$976$	−30.1201	−0.964121
$977$	−32.2282	−1.03107	−0.515536	−	0.856868i	$-0.672407\pi$
$977$	−32.2282	−1.03107	−0.515536	+	0.856868i	$0.672407\pi$
$978$	46.1562	1.47591
$979$	−5.07709	−0.162265
$980$	−0.361870	−0.0115595
$981$	2.65433	0.0847464
$982$	−12.9569	−0.413471
$983$	−3.13152	−0.0998798	−0.0499399	−	0.998752i	$-0.515903\pi$
$983$	−3.13152	−0.0998798	−0.0499399	+	0.998752i	$0.515903\pi$
$984$	−50.1118	−1.59751
$985$	−0.240743	−0.00767072
$986$	−3.33049	−0.106064
$987$	−0.665327	−0.0211776
$988$	2.47152	0.0786295
$989$	−8.80290	−0.279916
$990$	−1.18528	−0.0376707
$991$	−10.2243	−0.324785	−0.162393	−	0.986726i	$-0.551921\pi$
$991$	−10.2243	−0.324785	−0.162393	+	0.986726i	$0.551921\pi$
$992$	5.20900	0.165386
$993$	63.2882	2.00839
$994$	−8.11582	−0.257418
$995$	−2.79656	−0.0886568
$996$	−5.40132	−0.171147
$997$	−54.2279	−1.71741	−0.858707	−	0.512466i	$-0.828732\pi$
$997$	−54.2279	−1.71741	−0.858707	+	0.512466i	$0.828732\pi$
$998$	−39.8840	−1.26251
$999$	−2.66552	−0.0843333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.18	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.18	✓	66	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.32441 q^{2} -2.65196 q^{3} -0.245926 q^{4} -0.221912 q^{5} +3.51229 q^{6} +0.607593 q^{7} +2.97454 q^{8} +4.03289 q^{9} +O(q^{10})\)	\(q-1.32441 q^{2} -2.65196 q^{3} -0.245926 q^{4} -0.221912 q^{5} +3.51229 q^{6} +0.607593 q^{7} +2.97454 q^{8} +4.03289 q^{9} +0.293903 q^{10} -1.00000 q^{11} +0.652185 q^{12} -1.48759 q^{13} -0.804705 q^{14} +0.588501 q^{15} -3.44767 q^{16} -1.00000 q^{17} -5.34122 q^{18} +6.75581 q^{19} +0.0545738 q^{20} -1.61131 q^{21} +1.32441 q^{22} -8.80290 q^{23} -7.88835 q^{24} -4.95076 q^{25} +1.97018 q^{26} -2.73919 q^{27} -0.149423 q^{28} -2.51469 q^{29} -0.779420 q^{30} -3.76664 q^{31} -1.38293 q^{32} +2.65196 q^{33} +1.32441 q^{34} -0.134832 q^{35} -0.991792 q^{36} +0.973107 q^{37} -8.94749 q^{38} +3.94502 q^{39} -0.660085 q^{40} +6.35263 q^{41} +2.13404 q^{42} +1.00000 q^{43} +0.245926 q^{44} -0.894946 q^{45} +11.6587 q^{46} +0.412911 q^{47} +9.14308 q^{48} -6.63083 q^{49} +6.55685 q^{50} +2.65196 q^{51} +0.365836 q^{52} +2.59789 q^{53} +3.62782 q^{54} +0.221912 q^{55} +1.80731 q^{56} -17.9161 q^{57} +3.33049 q^{58} +14.1945 q^{59} -0.144728 q^{60} +8.73637 q^{61} +4.98859 q^{62} +2.45035 q^{63} +8.72691 q^{64} +0.330113 q^{65} -3.51229 q^{66} -9.51349 q^{67} +0.245926 q^{68} +23.3449 q^{69} +0.178573 q^{70} +10.0855 q^{71} +11.9960 q^{72} +4.40274 q^{73} -1.28880 q^{74} +13.1292 q^{75} -1.66143 q^{76} -0.607593 q^{77} -5.22485 q^{78} -6.39281 q^{79} +0.765078 q^{80} -4.83446 q^{81} -8.41352 q^{82} -8.28187 q^{83} +0.396263 q^{84} +0.221912 q^{85} -1.32441 q^{86} +6.66885 q^{87} -2.97454 q^{88} +5.07709 q^{89} +1.18528 q^{90} -0.903848 q^{91} +2.16486 q^{92} +9.98898 q^{93} -0.546865 q^{94} -1.49919 q^{95} +3.66748 q^{96} +5.09799 q^{97} +8.78197 q^{98} -4.03289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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