LMFDB - Embedded newform 8041.2.a.e.1.1

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			1.1
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67289 q^{2} -2.02637 q^{3} +5.14435 q^{4} +2.69749 q^{5} +5.41626 q^{6} +1.58680 q^{7} -8.40451 q^{8} +1.10617 q^{9} +O(q^{10})$	\(q-2.67289 q^{2} -2.02637 q^{3} +5.14435 q^{4} +2.69749 q^{5} +5.41626 q^{6} +1.58680 q^{7} -8.40451 q^{8} +1.10617 q^{9} -7.21011 q^{10} -1.00000 q^{11} -10.4244 q^{12} -1.72415 q^{13} -4.24134 q^{14} -5.46612 q^{15} +12.1756 q^{16} -1.00000 q^{17} -2.95667 q^{18} +4.98962 q^{19} +13.8769 q^{20} -3.21544 q^{21} +2.67289 q^{22} +3.51030 q^{23} +17.0306 q^{24} +2.27648 q^{25} +4.60848 q^{26} +3.83760 q^{27} +8.16305 q^{28} +9.51708 q^{29} +14.6103 q^{30} -1.70297 q^{31} -15.7351 q^{32} +2.02637 q^{33} +2.67289 q^{34} +4.28038 q^{35} +5.69053 q^{36} +8.93708 q^{37} -13.3367 q^{38} +3.49377 q^{39} -22.6711 q^{40} +1.59605 q^{41} +8.59452 q^{42} +1.00000 q^{43} -5.14435 q^{44} +2.98389 q^{45} -9.38265 q^{46} +4.50324 q^{47} -24.6723 q^{48} -4.48207 q^{49} -6.08477 q^{50} +2.02637 q^{51} -8.86965 q^{52} +9.53128 q^{53} -10.2575 q^{54} -2.69749 q^{55} -13.3363 q^{56} -10.1108 q^{57} -25.4381 q^{58} +1.97582 q^{59} -28.1196 q^{60} +14.7269 q^{61} +4.55186 q^{62} +1.75527 q^{63} +17.7071 q^{64} -4.65090 q^{65} -5.41626 q^{66} -12.0177 q^{67} -5.14435 q^{68} -7.11316 q^{69} -11.4410 q^{70} +2.79281 q^{71} -9.29681 q^{72} -15.7919 q^{73} -23.8878 q^{74} -4.61298 q^{75} +25.6684 q^{76} -1.58680 q^{77} -9.33847 q^{78} +9.93150 q^{79} +32.8437 q^{80} -11.0949 q^{81} -4.26606 q^{82} +6.77975 q^{83} -16.5414 q^{84} -2.69749 q^{85} -2.67289 q^{86} -19.2851 q^{87} +8.40451 q^{88} -7.88940 q^{89} -7.97561 q^{90} -2.73589 q^{91} +18.0582 q^{92} +3.45085 q^{93} -12.0367 q^{94} +13.4595 q^{95} +31.8852 q^{96} -16.8285 q^{97} +11.9801 q^{98} -1.10617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.67289	−1.89002	−0.945010	−	0.327042i	$-0.893948\pi$
$2$	−2.67289	−1.89002	−0.945010	+	0.327042i	$0.893948\pi$
$3$	−2.02637	−1.16992	−0.584962	−	0.811061i	$-0.698891\pi$
$3$	−2.02637	−1.16992	−0.584962	+	0.811061i	$0.698891\pi$
$4$	5.14435	2.57218
$5$	2.69749	1.20636	0.603178	−	0.797607i	$-0.293901\pi$
$5$	2.69749	1.20636	0.603178	+	0.797607i	$0.293901\pi$
$6$	5.41626	2.21118
$7$	1.58680	0.599754	0.299877	−	0.953978i	$-0.403054\pi$
$7$	1.58680	0.599754	0.299877	+	0.953978i	$0.403054\pi$
$8$	−8.40451	−2.97144
$9$	1.10617	0.368723
$10$	−7.21011	−2.28004
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−10.4244	−3.00925
$13$	−1.72415	−0.478194	−0.239097	−	0.970996i	$-0.576851\pi$
$13$	−1.72415	−0.478194	−0.239097	+	0.970996i	$0.576851\pi$
$14$	−4.24134	−1.13355
$15$	−5.46612	−1.41135
$16$	12.1756	3.04391
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.95667	−0.696894
$19$	4.98962	1.14470	0.572349	−	0.820010i	$-0.306032\pi$
$19$	4.98962	1.14470	0.572349	+	0.820010i	$0.306032\pi$
$20$	13.8769	3.10296
$21$	−3.21544	−0.701667
$22$	2.67289	0.569862
$23$	3.51030	0.731948	0.365974	−	0.930625i	$-0.380736\pi$
$23$	3.51030	0.731948	0.365974	+	0.930625i	$0.380736\pi$
$24$	17.0306	3.47636
$25$	2.27648	0.455295
$26$	4.60848	0.903797
$27$	3.83760	0.738546
$28$	8.16305	1.54267
$29$	9.51708	1.76728	0.883638	−	0.468170i	$-0.155087\pi$
$29$	9.51708	1.76728	0.883638	+	0.468170i	$0.155087\pi$
$30$	14.6103	2.66747
$31$	−1.70297	−0.305863	−0.152931	−	0.988237i	$-0.548871\pi$
$31$	−1.70297	−0.305863	−0.152931	+	0.988237i	$0.548871\pi$
$32$	−15.7351	−2.78161
$33$	2.02637	0.352746
$34$	2.67289	0.458397
$35$	4.28038	0.723517
$36$	5.69053	0.948421
$37$	8.93708	1.46925	0.734623	−	0.678475i	$-0.237359\pi$
$37$	8.93708	1.46925	0.734623	+	0.678475i	$0.237359\pi$
$38$	−13.3367	−2.16350
$39$	3.49377	0.559451
$40$	−22.6711	−3.58462
$41$	1.59605	0.249261	0.124630	−	0.992203i	$-0.460226\pi$
$41$	1.59605	0.249261	0.124630	+	0.992203i	$0.460226\pi$
$42$	8.59452	1.32616
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−5.14435	−0.775540
$45$	2.98389	0.444812
$46$	−9.38265	−1.38340
$47$	4.50324	0.656865	0.328432	−	0.944527i	$-0.393480\pi$
$47$	4.50324	0.656865	0.328432	+	0.944527i	$0.393480\pi$
$48$	−24.6723	−3.56114
$49$	−4.48207	−0.640295
$50$	−6.08477	−0.860517
$51$	2.02637	0.283748
$52$	−8.86965	−1.23000
$53$	9.53128	1.30922	0.654611	−	0.755966i	$-0.272832\pi$
$53$	9.53128	1.30922	0.654611	+	0.755966i	$0.272832\pi$
$54$	−10.2575	−1.39587
$55$	−2.69749	−0.363730
$56$	−13.3363	−1.78213
$57$	−10.1108	−1.33921
$58$	−25.4381	−3.34019
$59$	1.97582	0.257230	0.128615	−	0.991695i	$-0.458947\pi$
$59$	1.97582	0.257230	0.128615	+	0.991695i	$0.458947\pi$
$60$	−28.1196	−3.63023
$61$	14.7269	1.88559	0.942793	−	0.333378i	$-0.108188\pi$
$61$	14.7269	1.88559	0.942793	+	0.333378i	$0.108188\pi$
$62$	4.55186	0.578087
$63$	1.75527	0.221143
$64$	17.7071	2.21338
$65$	−4.65090	−0.576873
$66$	−5.41626	−0.666696
$67$	−12.0177	−1.46819	−0.734097	−	0.679045i	$-0.762394\pi$
$67$	−12.0177	−1.46819	−0.734097	+	0.679045i	$0.762394\pi$
$68$	−5.14435	−0.623844
$69$	−7.11316	−0.856324
$70$	−11.4410	−1.36746
$71$	2.79281	0.331445	0.165723	−	0.986172i	$-0.447004\pi$
$71$	2.79281	0.331445	0.165723	+	0.986172i	$0.447004\pi$
$72$	−9.29681	−1.09564
$73$	−15.7919	−1.84830	−0.924150	−	0.382030i	$-0.875225\pi$
$73$	−15.7919	−1.84830	−0.924150	+	0.382030i	$0.875225\pi$
$74$	−23.8878	−2.77691
$75$	−4.61298	−0.532661
$76$	25.6684	2.94436
$77$	−1.58680	−0.180833
$78$	−9.33847	−1.05737
$79$	9.93150	1.11738	0.558690	−	0.829376i	$-0.311304\pi$
$79$	9.93150	1.11738	0.558690	+	0.829376i	$0.311304\pi$
$80$	32.8437	3.67204
$81$	−11.0949	−1.23277
$82$	−4.26606	−0.471108
$83$	6.77975	0.744174	0.372087	−	0.928198i	$-0.378642\pi$
$83$	6.77975	0.744174	0.372087	+	0.928198i	$0.378642\pi$
$84$	−16.5414	−1.80481
$85$	−2.69749	−0.292584
$86$	−2.67289	−0.288225
$87$	−19.2851	−2.06758
$88$	8.40451	0.895924
$89$	−7.88940	−0.836274	−0.418137	−	0.908384i	$-0.637317\pi$
$89$	−7.88940	−0.836274	−0.418137	+	0.908384i	$0.637317\pi$
$90$	−7.97561	−0.840703
$91$	−2.73589	−0.286799
$92$	18.0582	1.88270
$93$	3.45085	0.357837
$94$	−12.0367	−1.24149
$95$	13.4595	1.38091
$96$	31.8852	3.25427
$97$	−16.8285	−1.70868	−0.854339	−	0.519716i	$-0.826038\pi$
$97$	−16.8285	−1.70868	−0.854339	+	0.519716i	$0.826038\pi$
$98$	11.9801	1.21017
$99$	−1.10617	−0.111174
$100$	11.7110	1.17110
$101$	−2.40168	−0.238976	−0.119488	−	0.992836i	$-0.538125\pi$
$101$	−2.40168	−0.238976	−0.119488	+	0.992836i	$0.538125\pi$
$102$	−5.41626	−0.536290
$103$	−7.14065	−0.703590	−0.351795	−	0.936077i	$-0.614429\pi$
$103$	−7.14065	−0.703590	−0.351795	+	0.936077i	$0.614429\pi$
$104$	14.4907	1.42093
$105$	−8.67363	−0.846460
$106$	−25.4761	−2.47446
$107$	14.2487	1.37747	0.688736	−	0.725012i	$-0.258166\pi$
$107$	14.2487	1.37747	0.688736	+	0.725012i	$0.258166\pi$
$108$	19.7419	1.89967
$109$	18.3748	1.75999	0.879995	−	0.474984i	$-0.157546\pi$
$109$	18.3748	1.75999	0.879995	+	0.474984i	$0.157546\pi$
$110$	7.21011	0.687457
$111$	−18.1098	−1.71891
$112$	19.3203	1.82560
$113$	−5.17993	−0.487286	−0.243643	−	0.969865i	$-0.578343\pi$
$113$	−5.17993	−0.487286	−0.243643	+	0.969865i	$0.578343\pi$
$114$	27.0251	2.53113
$115$	9.46902	0.882990
$116$	48.9592	4.54574
$117$	−1.90721	−0.176321
$118$	−5.28116	−0.486170
$119$	−1.58680	−0.145462
$120$	45.9400	4.19373
$121$	1.00000	0.0909091
$122$	−39.3634	−3.56380
$123$	−3.23418	−0.291616
$124$	−8.76069	−0.786733
$125$	−7.34669	−0.657108
$126$	−4.69165	−0.417965
$127$	−1.27338	−0.112994	−0.0564969	−	0.998403i	$-0.517993\pi$
$127$	−1.27338	−0.112994	−0.0564969	+	0.998403i	$0.517993\pi$
$128$	−15.8588	−1.40173
$129$	−2.02637	−0.178412
$130$	12.4313	1.09030
$131$	−7.83625	−0.684656	−0.342328	−	0.939580i	$-0.611215\pi$
$131$	−7.83625	−0.684656	−0.342328	+	0.939580i	$0.611215\pi$
$132$	10.4244	0.907323
$133$	7.91753	0.686537
$134$	32.1220	2.77491
$135$	10.3519	0.890950
$136$	8.40451	0.720681
$137$	7.13611	0.609679	0.304840	−	0.952404i	$-0.401397\pi$
$137$	7.13611	0.609679	0.304840	+	0.952404i	$0.401397\pi$
$138$	19.0127	1.61847
$139$	−15.5919	−1.32249	−0.661245	−	0.750170i	$-0.729972\pi$
$139$	−15.5919	−1.32249	−0.661245	+	0.750170i	$0.729972\pi$
$140$	22.0198	1.86101
$141$	−9.12522	−0.768482
$142$	−7.46487	−0.626438
$143$	1.72415	0.144181
$144$	13.4683	1.12236
$145$	25.6723	2.13196
$146$	42.2100	3.49332
$147$	9.08232	0.749097
$148$	45.9755	3.77916
$149$	17.2195	1.41068	0.705339	−	0.708870i	$-0.250795\pi$
$149$	17.2195	1.41068	0.705339	+	0.708870i	$0.250795\pi$
$150$	12.3300	1.00674
$151$	16.5511	1.34691	0.673455	−	0.739228i	$-0.264809\pi$
$151$	16.5511	1.34691	0.673455	+	0.739228i	$0.264809\pi$
$152$	−41.9353	−3.40140
$153$	−1.10617	−0.0894285
$154$	4.24134	0.341777
$155$	−4.59376	−0.368980
$156$	17.9732	1.43901
$157$	10.3151	0.823235	0.411618	−	0.911357i	$-0.364964\pi$
$157$	10.3151	0.823235	0.411618	+	0.911357i	$0.364964\pi$
$158$	−26.5458	−2.11187
$159$	−19.3139	−1.53169
$160$	−42.4455	−3.35561
$161$	5.57014	0.438989
$162$	29.6555	2.32995
$163$	−11.1523	−0.873514	−0.436757	−	0.899579i	$-0.643873\pi$
$163$	−11.1523	−0.873514	−0.436757	+	0.899579i	$0.643873\pi$
$164$	8.21062	0.641142
$165$	5.46612	0.425537
$166$	−18.1215	−1.40650
$167$	5.50045	0.425638	0.212819	−	0.977092i	$-0.431736\pi$
$167$	5.50045	0.425638	0.212819	+	0.977092i	$0.431736\pi$
$168$	27.0242	2.08496
$169$	−10.0273	−0.771330
$170$	7.21011	0.552990
$171$	5.51937	0.422077
$172$	5.14435	0.392253
$173$	7.85324	0.597071	0.298535	−	0.954399i	$-0.403502\pi$
$173$	7.85324	0.597071	0.298535	+	0.954399i	$0.403502\pi$
$174$	51.5470	3.90777
$175$	3.61231	0.273065
$176$	−12.1756	−0.917773
$177$	−4.00374	−0.300940
$178$	21.0875	1.58058
$179$	19.6748	1.47056	0.735281	−	0.677762i	$-0.237050\pi$
$179$	19.6748	1.47056	0.735281	+	0.677762i	$0.237050\pi$
$180$	15.3502	1.14413
$181$	−14.2573	−1.05973	−0.529867	−	0.848081i	$-0.677758\pi$
$181$	−14.2573	−1.05973	−0.529867	+	0.848081i	$0.677758\pi$
$182$	7.31273	0.542056
$183$	−29.8421	−2.20599
$184$	−29.5024	−2.17494
$185$	24.1077	1.77243
$186$	−9.22375	−0.676318
$187$	1.00000	0.0731272
$188$	23.1662	1.68957
$189$	6.08950	0.442946
$190$	−35.9757	−2.60995
$191$	11.4662	0.829662	0.414831	−	0.909898i	$-0.363841\pi$
$191$	11.4662	0.829662	0.414831	+	0.909898i	$0.363841\pi$
$192$	−35.8811	−2.58949
$193$	13.4618	0.969002	0.484501	−	0.874791i	$-0.339001\pi$
$193$	13.4618	0.969002	0.484501	+	0.874791i	$0.339001\pi$
$194$	44.9808	3.22944
$195$	9.42443	0.674898
$196$	−23.0573	−1.64695
$197$	−23.3613	−1.66442	−0.832210	−	0.554460i	$-0.812925\pi$
$197$	−23.3613	−1.66442	−0.832210	+	0.554460i	$0.812925\pi$
$198$	2.95667	0.210122
$199$	−5.38952	−0.382053	−0.191027	−	0.981585i	$-0.561182\pi$
$199$	−5.38952	−0.382053	−0.191027	+	0.981585i	$0.561182\pi$
$200$	−19.1327	−1.35288
$201$	24.3523	1.71768
$202$	6.41944	0.451670
$203$	15.1017	1.05993
$204$	10.4244	0.729850
$205$	4.30533	0.300697
$206$	19.0862	1.32980
$207$	3.88299	0.269886
$208$	−20.9927	−1.45558
$209$	−4.98962	−0.345139
$210$	23.1837	1.59983
$211$	−8.84811	−0.609129	−0.304564	−	0.952492i	$-0.598511\pi$
$211$	−8.84811	−0.609129	−0.304564	+	0.952492i	$0.598511\pi$
$212$	49.0323	3.36755
$213$	−5.65926	−0.387766
$214$	−38.0852	−2.60345
$215$	2.69749	0.183968
$216$	−32.2531	−2.19455
$217$	−2.70228	−0.183442
$218$	−49.1139	−3.32641
$219$	32.0002	2.16237
$220$	−13.8769	−0.935577
$221$	1.72415	0.115979
$222$	48.4056	3.24877
$223$	−27.8659	−1.86604	−0.933018	−	0.359829i	$-0.882835\pi$
$223$	−27.8659	−1.86604	−0.933018	+	0.359829i	$0.882835\pi$
$224$	−24.9685	−1.66828
$225$	2.51817	0.167878
$226$	13.8454	0.920981
$227$	−9.42952	−0.625859	−0.312930	−	0.949776i	$-0.601310\pi$
$227$	−9.42952	−0.625859	−0.312930	+	0.949776i	$0.601310\pi$
$228$	−52.0136	−3.44468
$229$	29.2915	1.93564	0.967820	−	0.251644i	$-0.0809713\pi$
$229$	29.2915	1.93564	0.967820	+	0.251644i	$0.0809713\pi$
$230$	−25.3097	−1.66887
$231$	3.21544	0.211560
$232$	−79.9863	−5.25136
$233$	−16.6075	−1.08799	−0.543996	−	0.839088i	$-0.683089\pi$
$233$	−16.6075	−1.08799	−0.543996	+	0.839088i	$0.683089\pi$
$234$	5.09776	0.333251
$235$	12.1475	0.792413
$236$	10.1643	0.661641
$237$	−20.1249	−1.30725
$238$	4.24134	0.274925
$239$	7.83388	0.506732	0.253366	−	0.967371i	$-0.418462\pi$
$239$	7.83388	0.506732	0.253366	+	0.967371i	$0.418462\pi$
$240$	−66.5535	−4.29601
$241$	6.26109	0.403312	0.201656	−	0.979456i	$-0.435368\pi$
$241$	6.26109	0.403312	0.201656	+	0.979456i	$0.435368\pi$
$242$	−2.67289	−0.171820
$243$	10.9696	0.703698
$244$	75.7603	4.85006
$245$	−12.0904	−0.772424
$246$	8.64461	0.551160
$247$	−8.60288	−0.547388
$248$	14.3127	0.908854
$249$	−13.7383	−0.870627
$250$	19.6369	1.24195
$251$	25.1219	1.58568	0.792840	−	0.609429i	$-0.208601\pi$
$251$	25.1219	1.58568	0.792840	+	0.609429i	$0.208601\pi$
$252$	9.02972	0.568819
$253$	−3.51030	−0.220691
$254$	3.40360	0.213561
$255$	5.46612	0.342302
$256$	6.97468	0.435918
$257$	−11.2238	−0.700121	−0.350061	−	0.936727i	$-0.613839\pi$
$257$	−11.2238	−0.700121	−0.350061	+	0.936727i	$0.613839\pi$
$258$	5.41626	0.337202
$259$	14.1813	0.881186
$260$	−23.9258	−1.48382
$261$	10.5275	0.651636
$262$	20.9455	1.29401
$263$	−29.1498	−1.79745	−0.898727	−	0.438509i	$-0.855507\pi$
$263$	−29.1498	−1.79745	−0.898727	+	0.438509i	$0.855507\pi$
$264$	−17.0306	−1.04816
$265$	25.7106	1.57939
$266$	−21.1627	−1.29757
$267$	15.9868	0.978378
$268$	−61.8232	−3.77645
$269$	−16.7061	−1.01859	−0.509296	−	0.860592i	$-0.670094\pi$
$269$	−16.7061	−1.01859	−0.509296	+	0.860592i	$0.670094\pi$
$270$	−27.6695	−1.68391
$271$	−17.4927	−1.06261	−0.531303	−	0.847182i	$-0.678297\pi$
$271$	−17.4927	−1.06261	−0.531303	+	0.847182i	$0.678297\pi$
$272$	−12.1756	−0.738257
$273$	5.54392	0.335533
$274$	−19.0741	−1.15231
$275$	−2.27648	−0.137277
$276$	−36.5926	−2.20262
$277$	−12.4667	−0.749050	−0.374525	−	0.927217i	$-0.622194\pi$
$277$	−12.4667	−0.749050	−0.374525	+	0.927217i	$0.622194\pi$
$278$	41.6755	2.49953
$279$	−1.88378	−0.112779
$280$	−35.9745	−2.14989
$281$	−10.5775	−0.631002	−0.315501	−	0.948925i	$-0.602173\pi$
$281$	−10.5775	−0.631002	−0.315501	+	0.948925i	$0.602173\pi$
$282$	24.3907	1.45245
$283$	6.55935	0.389913	0.194956	−	0.980812i	$-0.437543\pi$
$283$	6.55935	0.389913	0.194956	+	0.980812i	$0.437543\pi$
$284$	14.3672	0.852535
$285$	−27.2739	−1.61556
$286$	−4.60848	−0.272505
$287$	2.53261	0.149495
$288$	−17.4057	−1.02564
$289$	1.00000	0.0588235
$290$	−68.6192	−4.02946
$291$	34.1008	1.99902
$292$	−81.2390	−4.75415
$293$	5.12231	0.299248	0.149624	−	0.988743i	$-0.452194\pi$
$293$	5.12231	0.299248	0.149624	+	0.988743i	$0.452194\pi$
$294$	−24.2761	−1.41581
$295$	5.32977	0.310311
$296$	−75.1117	−4.36578
$297$	−3.83760	−0.222680
$298$	−46.0259	−2.66621
$299$	−6.05230	−0.350014
$300$	−23.7308	−1.37010
$301$	1.58680	0.0914616
$302$	−44.2393	−2.54569
$303$	4.86670	0.279584
$304$	60.7518	3.48436
$305$	39.7257	2.27469
$306$	2.95667	0.169022
$307$	19.8754	1.13435	0.567175	−	0.823597i	$-0.308036\pi$
$307$	19.8754	1.13435	0.567175	+	0.823597i	$0.308036\pi$
$308$	−8.16305	−0.465133
$309$	14.4696	0.823147
$310$	12.2786	0.697379
$311$	−16.3796	−0.928802	−0.464401	−	0.885625i	$-0.653730\pi$
$311$	−16.3796	−0.928802	−0.464401	+	0.885625i	$0.653730\pi$
$312$	−29.3634	−1.66238
$313$	−0.0376923	−0.00213050	−0.00106525	−	0.999999i	$-0.500339\pi$
$313$	−0.0376923	−0.00213050	−0.00106525	+	0.999999i	$0.500339\pi$
$314$	−27.5712	−1.55593
$315$	4.73483	0.266777
$316$	51.0911	2.87410
$317$	20.5915	1.15654	0.578268	−	0.815847i	$-0.303729\pi$
$317$	20.5915	1.15654	0.578268	+	0.815847i	$0.303729\pi$
$318$	51.6239	2.89493
$319$	−9.51708	−0.532854
$320$	47.7647	2.67013
$321$	−28.8731	−1.61154
$322$	−14.8884	−0.829698
$323$	−4.98962	−0.277630
$324$	−57.0760	−3.17089
$325$	−3.92500	−0.217720
$326$	29.8088	1.65096
$327$	−37.2342	−2.05905
$328$	−13.4140	−0.740664
$329$	7.14574	0.393957
$330$	−14.6103	−0.804273
$331$	32.2929	1.77498	0.887489	−	0.460829i	$-0.152448\pi$
$331$	32.2929	1.77498	0.887489	+	0.460829i	$0.152448\pi$
$332$	34.8774	1.91415
$333$	9.88593	0.541745
$334$	−14.7021	−0.804464
$335$	−32.4176	−1.77116
$336$	−39.1500	−2.13581
$337$	−8.51279	−0.463721	−0.231861	−	0.972749i	$-0.574481\pi$
$337$	−8.51279	−0.463721	−0.231861	+	0.972749i	$0.574481\pi$
$338$	26.8019	1.45783
$339$	10.4964	0.570088
$340$	−13.8769	−0.752578
$341$	1.70297	0.0922212
$342$	−14.7527	−0.797733
$343$	−18.2197	−0.983773
$344$	−8.40451	−0.453141
$345$	−19.1877	−1.03303
$346$	−20.9909	−1.12848
$347$	20.1820	1.08343	0.541713	−	0.840563i	$-0.317776\pi$
$347$	20.1820	1.08343	0.541713	+	0.840563i	$0.317776\pi$
$348$	−99.2093	−5.31818
$349$	−12.4005	−0.663785	−0.331893	−	0.943317i	$-0.607687\pi$
$349$	−12.4005	−0.663785	−0.331893	+	0.943317i	$0.607687\pi$
$350$	−9.65531	−0.516098
$351$	−6.61661	−0.353169
$352$	15.7351	0.838686
$353$	−32.5099	−1.73033	−0.865164	−	0.501488i	$-0.832786\pi$
$353$	−32.5099	−1.73033	−0.865164	+	0.501488i	$0.832786\pi$
$354$	10.7016	0.568782
$355$	7.53358	0.399841
$356$	−40.5858	−2.15104
$357$	3.21544	0.170179
$358$	−52.5886	−2.77939
$359$	36.1862	1.90983	0.954916	−	0.296875i	$-0.0959443\pi$
$359$	36.1862	1.90983	0.954916	+	0.296875i	$0.0959443\pi$
$360$	−25.0781	−1.32173
$361$	5.89632	0.310333
$362$	38.1081	2.00292
$363$	−2.02637	−0.106357
$364$	−14.0744	−0.737697
$365$	−42.5985	−2.22971
$366$	79.7648	4.16937
$367$	−12.8027	−0.668297	−0.334148	−	0.942521i	$-0.608449\pi$
$367$	−12.8027	−0.668297	−0.334148	+	0.942521i	$0.608449\pi$
$368$	42.7402	2.22798
$369$	1.76550	0.0919082
$370$	−64.4373	−3.34994
$371$	15.1242	0.785211
$372$	17.7524	0.920418
$373$	−24.4609	−1.26654	−0.633269	−	0.773932i	$-0.718287\pi$
$373$	−24.4609	−1.26654	−0.633269	+	0.773932i	$0.718287\pi$
$374$	−2.67289	−0.138212
$375$	14.8871	0.768767
$376$	−37.8475	−1.95184
$377$	−16.4089	−0.845102
$378$	−16.2766	−0.837176
$379$	7.63578	0.392224	0.196112	−	0.980582i	$-0.437168\pi$
$379$	7.63578	0.392224	0.196112	+	0.980582i	$0.437168\pi$
$380$	69.2403	3.55195
$381$	2.58033	0.132194
$382$	−30.6478	−1.56808
$383$	29.8785	1.52672	0.763361	−	0.645972i	$-0.223548\pi$
$383$	29.8785	1.52672	0.763361	+	0.645972i	$0.223548\pi$
$384$	32.1358	1.63992
$385$	−4.28038	−0.218148
$386$	−35.9819	−1.83143
$387$	1.10617	0.0562298
$388$	−86.5718	−4.39502
$389$	20.3460	1.03158	0.515791	−	0.856715i	$-0.327498\pi$
$389$	20.3460	1.03158	0.515791	+	0.856715i	$0.327498\pi$
$390$	−25.1905	−1.27557
$391$	−3.51030	−0.177524
$392$	37.6696	1.90260
$393$	15.8791	0.800996
$394$	62.4421	3.14579
$395$	26.7902	1.34796
$396$	−5.69053	−0.285960
$397$	−11.1623	−0.560219	−0.280109	−	0.959968i	$-0.590371\pi$
$397$	−11.1623	−0.560219	−0.280109	+	0.959968i	$0.590371\pi$
$398$	14.4056	0.722088
$399$	−16.0438	−0.803196
$400$	27.7175	1.38588
$401$	−20.5989	−1.02866	−0.514330	−	0.857592i	$-0.671959\pi$
$401$	−20.5989	−1.02866	−0.514330	+	0.857592i	$0.671959\pi$
$402$	−65.0909	−3.24644
$403$	2.93619	0.146262
$404$	−12.3551	−0.614689
$405$	−29.9284	−1.48716
$406$	−40.3652	−2.00329
$407$	−8.93708	−0.442994
$408$	−17.0306	−0.843142
$409$	4.10088	0.202776	0.101388	−	0.994847i	$-0.467672\pi$
$409$	4.10088	0.202776	0.101388	+	0.994847i	$0.467672\pi$
$410$	−11.5077	−0.568324
$411$	−14.4604	−0.713279
$412$	−36.7340	−1.80976
$413$	3.13523	0.154275
$414$	−10.3788	−0.510091
$415$	18.2883	0.897739
$416$	27.1298	1.33015
$417$	31.5950	1.54721
$418$	13.3367	0.652320
$419$	29.5158	1.44194	0.720970	−	0.692966i	$-0.243696\pi$
$419$	29.5158	1.44194	0.720970	+	0.692966i	$0.243696\pi$
$420$	−44.6202	−2.17724
$421$	−19.0309	−0.927507	−0.463754	−	0.885964i	$-0.653498\pi$
$421$	−19.0309	−0.927507	−0.463754	+	0.885964i	$0.653498\pi$
$422$	23.6500	1.15127
$423$	4.98135	0.242201
$424$	−80.1057	−3.89028
$425$	−2.27648	−0.110425
$426$	15.1266	0.732885
$427$	23.3686	1.13089
$428$	73.3002	3.54310
$429$	−3.49377	−0.168681
$430$	−7.21011	−0.347702
$431$	14.5017	0.698524	0.349262	−	0.937025i	$-0.386432\pi$
$431$	14.5017	0.698524	0.349262	+	0.937025i	$0.386432\pi$
$432$	46.7252	2.24807
$433$	0.822093	0.0395073	0.0197536	−	0.999805i	$-0.493712\pi$
$433$	0.822093	0.0395073	0.0197536	+	0.999805i	$0.493712\pi$
$434$	7.22289	0.346710
$435$	−52.0215	−2.49424
$436$	94.5266	4.52700
$437$	17.5151	0.837860
$438$	−85.5330	−4.08693
$439$	4.88117	0.232966	0.116483	−	0.993193i	$-0.462838\pi$
$439$	4.88117	0.232966	0.116483	+	0.993193i	$0.462838\pi$
$440$	22.6711	1.08080
$441$	−4.95793	−0.236092
$442$	−4.60848	−0.219203
$443$	−7.11880	−0.338225	−0.169112	−	0.985597i	$-0.554090\pi$
$443$	−7.11880	−0.338225	−0.169112	+	0.985597i	$0.554090\pi$
$444$	−93.1632	−4.42133
$445$	−21.2816	−1.00884
$446$	74.4824	3.52685
$447$	−34.8931	−1.65039
$448$	28.0976	1.32749
$449$	20.6274	0.973469	0.486734	−	0.873550i	$-0.338188\pi$
$449$	20.6274	0.973469	0.486734	+	0.873550i	$0.338188\pi$
$450$	−6.73079	−0.317293
$451$	−1.59605	−0.0751549
$452$	−26.6474	−1.25339
$453$	−33.5386	−1.57578
$454$	25.2041	1.18289
$455$	−7.38004	−0.345982
$456$	84.9764	3.97938
$457$	28.2003	1.31916	0.659578	−	0.751636i	$-0.270735\pi$
$457$	28.2003	1.31916	0.659578	+	0.751636i	$0.270735\pi$
$458$	−78.2931	−3.65840
$459$	−3.83760	−0.179124
$460$	48.7119	2.27121
$461$	−0.646917	−0.0301299	−0.0150650	−	0.999887i	$-0.504796\pi$
$461$	−0.646917	−0.0301299	−0.0150650	+	0.999887i	$0.504796\pi$
$462$	−8.59452	−0.399853
$463$	25.3046	1.17601	0.588003	−	0.808859i	$-0.299914\pi$
$463$	25.3046	1.17601	0.588003	+	0.808859i	$0.299914\pi$
$464$	115.876	5.37943
$465$	9.30865	0.431678
$466$	44.3900	2.05633
$467$	−17.2508	−0.798271	−0.399135	−	0.916892i	$-0.630690\pi$
$467$	−17.2508	−0.798271	−0.399135	+	0.916892i	$0.630690\pi$
$468$	−9.81134	−0.453530
$469$	−19.0696	−0.880555
$470$	−32.4689	−1.49768
$471$	−20.9022	−0.963123
$472$	−16.6058	−0.764344
$473$	−1.00000	−0.0459800
$474$	53.7916	2.47073
$475$	11.3588	0.521175
$476$	−8.16305	−0.374153
$477$	10.5432	0.482741
$478$	−20.9391	−0.957733
$479$	−41.0746	−1.87675	−0.938373	−	0.345624i	$-0.887667\pi$
$479$	−41.0746	−1.87675	−0.938373	+	0.345624i	$0.887667\pi$
$480$	86.0102	3.92581
$481$	−15.4089	−0.702585
$482$	−16.7352	−0.762268
$483$	−11.2872	−0.513584
$484$	5.14435	0.233834
$485$	−45.3949	−2.06127
$486$	−29.3204	−1.33000
$487$	17.6893	0.801578	0.400789	−	0.916170i	$-0.368736\pi$
$487$	17.6893	0.801578	0.400789	+	0.916170i	$0.368736\pi$
$488$	−123.772	−5.60291
$489$	22.5986	1.02195
$490$	32.3162	1.45990
$491$	25.6505	1.15759	0.578795	−	0.815473i	$-0.303523\pi$
$491$	25.6505	1.15759	0.578795	+	0.815473i	$0.303523\pi$
$492$	−16.6378	−0.750088
$493$	−9.51708	−0.428628
$494$	22.9946	1.03457
$495$	−2.98389	−0.134116
$496$	−20.7348	−0.931019
$497$	4.43163	0.198786
$498$	36.7209	1.64550
$499$	25.8304	1.15633	0.578164	−	0.815921i	$-0.303769\pi$
$499$	25.8304	1.15633	0.578164	+	0.815921i	$0.303769\pi$
$500$	−37.7940	−1.69020
$501$	−11.1459	−0.497964
$502$	−67.1481	−2.99697
$503$	22.1968	0.989705	0.494853	−	0.868977i	$-0.335222\pi$
$503$	22.1968	0.989705	0.494853	+	0.868977i	$0.335222\pi$
$504$	−14.7522	−0.657114
$505$	−6.47853	−0.288291
$506$	9.38265	0.417110
$507$	20.3190	0.902398
$508$	−6.55069	−0.290640
$509$	−36.6263	−1.62343	−0.811716	−	0.584052i	$-0.801466\pi$
$509$	−36.6263	−1.62343	−0.811716	+	0.584052i	$0.801466\pi$
$510$	−14.6103	−0.646957
$511$	−25.0585	−1.10852
$512$	13.0750	0.577839
$513$	19.1482	0.845412
$514$	30.0000	1.32324
$515$	−19.2619	−0.848780
$516$	−10.4244	−0.458906
$517$	−4.50324	−0.198052
$518$	−37.9052	−1.66546
$519$	−15.9136	−0.698528
$520$	39.0885	1.71414
$521$	−6.54038	−0.286539	−0.143270	−	0.989684i	$-0.545762\pi$
$521$	−6.54038	−0.286539	−0.143270	+	0.989684i	$0.545762\pi$
$522$	−28.1389	−1.23161
$523$	−23.6554	−1.03438	−0.517190	−	0.855871i	$-0.673022\pi$
$523$	−23.6554	−1.03438	−0.517190	+	0.855871i	$0.673022\pi$
$524$	−40.3124	−1.76106
$525$	−7.31987	−0.319465
$526$	77.9143	3.39722
$527$	1.70297	0.0741827
$528$	24.6723	1.07373
$529$	−10.6778	−0.464252
$530$	−68.7216	−2.98508
$531$	2.18559	0.0948467
$532$	40.7305	1.76589
$533$	−2.75183	−0.119195
$534$	−42.7311	−1.84915
$535$	38.4357	1.66172
$536$	101.003	4.36265
$537$	−39.8684	−1.72045
$538$	44.6537	1.92516
$539$	4.48207	0.193056
$540$	53.2538	2.29168
$541$	30.3638	1.30544	0.652721	−	0.757599i	$-0.273628\pi$
$541$	30.3638	1.30544	0.652721	+	0.757599i	$0.273628\pi$
$542$	46.7561	2.00835
$543$	28.8905	1.23981
$544$	15.7351	0.674639
$545$	49.5660	2.12317
$546$	−14.8183	−0.634164
$547$	9.24979	0.395492	0.197746	−	0.980253i	$-0.436638\pi$
$547$	9.24979	0.395492	0.197746	+	0.980253i	$0.436638\pi$
$548$	36.7107	1.56820
$549$	16.2905	0.695260
$550$	6.08477	0.259456
$551$	47.4866	2.02300
$552$	59.7826	2.54452
$553$	15.7593	0.670153
$554$	33.3221	1.41572
$555$	−48.8511	−2.07361
$556$	−80.2104	−3.40168
$557$	21.1359	0.895555	0.447777	−	0.894145i	$-0.352216\pi$
$557$	21.1359	0.895555	0.447777	+	0.894145i	$0.352216\pi$
$558$	5.03513	0.213154
$559$	−1.72415	−0.0729240
$560$	52.1164	2.20232
$561$	−2.02637	−0.0855534
$562$	28.2726	1.19261
$563$	25.2799	1.06542	0.532710	−	0.846298i	$-0.321173\pi$
$563$	25.2799	1.06542	0.532710	+	0.846298i	$0.321173\pi$
$564$	−46.9433	−1.97667
$565$	−13.9728	−0.587841
$566$	−17.5324	−0.736943
$567$	−17.6054	−0.739356
$568$	−23.4722	−0.984871
$569$	30.1681	1.26471	0.632357	−	0.774677i	$-0.282088\pi$
$569$	30.1681	1.26471	0.632357	+	0.774677i	$0.282088\pi$
$570$	72.9001	3.05345
$571$	−29.9988	−1.25541	−0.627706	−	0.778451i	$-0.716006\pi$
$571$	−29.9988	−1.25541	−0.627706	+	0.778451i	$0.716006\pi$
$572$	8.86965	0.370859
$573$	−23.2347	−0.970642
$574$	−6.76938	−0.282549
$575$	7.99112	0.333253
$576$	19.5870	0.816126
$577$	1.84670	0.0768790	0.0384395	−	0.999261i	$-0.487761\pi$
$577$	1.84670	0.0768790	0.0384395	+	0.999261i	$0.487761\pi$
$578$	−2.67289	−0.111178
$579$	−27.2786	−1.13366
$580$	132.067	5.48379
$581$	10.7581	0.446321
$582$	−91.1477	−3.77820
$583$	−9.53128	−0.394745
$584$	132.723	5.49212
$585$	−5.14468	−0.212706
$586$	−13.6914	−0.565586
$587$	−22.4847	−0.928041	−0.464021	−	0.885824i	$-0.653594\pi$
$587$	−22.4847	−0.928041	−0.464021	+	0.885824i	$0.653594\pi$
$588$	46.7226	1.92681
$589$	−8.49719	−0.350121
$590$	−14.2459	−0.586494
$591$	47.3385	1.94725
$592$	108.815	4.47225
$593$	8.19437	0.336502	0.168251	−	0.985744i	$-0.446188\pi$
$593$	8.19437	0.336502	0.168251	+	0.985744i	$0.446188\pi$
$594$	10.2575	0.420870
$595$	−4.28038	−0.175479
$596$	88.5833	3.62851
$597$	10.9212	0.446973
$598$	16.1771	0.661533
$599$	41.3201	1.68829	0.844146	−	0.536113i	$-0.180108\pi$
$599$	41.3201	1.68829	0.844146	+	0.536113i	$0.180108\pi$
$600$	38.7698	1.58277
$601$	34.5408	1.40895	0.704474	−	0.709730i	$-0.251183\pi$
$601$	34.5408	1.40895	0.704474	+	0.709730i	$0.251183\pi$
$602$	−4.24134	−0.172864
$603$	−13.2936	−0.541357
$604$	85.1447	3.46449
$605$	2.69749	0.109669
$606$	−13.0081	−0.528420
$607$	−1.41164	−0.0572966	−0.0286483	−	0.999590i	$-0.509120\pi$
$607$	−1.41164	−0.0572966	−0.0286483	+	0.999590i	$0.509120\pi$
$608$	−78.5124	−3.18410
$609$	−30.6016	−1.24004
$610$	−106.183	−4.29921
$611$	−7.76428	−0.314109
$612$	−5.69053	−0.230026
$613$	2.82077	0.113930	0.0569649	−	0.998376i	$-0.481858\pi$
$613$	2.82077	0.113930	0.0569649	+	0.998376i	$0.481858\pi$
$614$	−53.1249	−2.14395
$615$	−8.72418	−0.351793
$616$	13.3363	0.537334
$617$	−32.5815	−1.31168	−0.655842	−	0.754899i	$-0.727686\pi$
$617$	−32.5815	−1.31168	−0.655842	+	0.754899i	$0.727686\pi$
$618$	−38.6757	−1.55576
$619$	9.82932	0.395074	0.197537	−	0.980295i	$-0.436706\pi$
$619$	9.82932	0.395074	0.197537	+	0.980295i	$0.436706\pi$
$620$	−23.6319	−0.949080
$621$	13.4711	0.540578
$622$	43.7809	1.75545
$623$	−12.5189	−0.501559
$624$	42.5389	1.70292
$625$	−31.2000	−1.24800
$626$	0.100747	0.00402668
$627$	10.1108	0.403787
$628$	53.0645	2.11750
$629$	−8.93708	−0.356345
$630$	−12.6557	−0.504215
$631$	−36.8405	−1.46660	−0.733298	−	0.679907i	$-0.762020\pi$
$631$	−36.8405	−1.46660	−0.733298	+	0.679907i	$0.762020\pi$
$632$	−83.4693	−3.32023
$633$	17.9295	0.712635
$634$	−55.0389	−2.18587
$635$	−3.43492	−0.136311
$636$	−99.3574	−3.93978
$637$	7.72778	0.306186
$638$	25.4381	1.00710
$639$	3.08932	0.122212
$640$	−42.7790	−1.69099
$641$	−49.4081	−1.95150	−0.975752	−	0.218879i	$-0.929760\pi$
$641$	−49.4081	−1.95150	−0.975752	+	0.218879i	$0.929760\pi$
$642$	77.1746	3.04584
$643$	−1.60401	−0.0632562	−0.0316281	−	0.999500i	$-0.510069\pi$
$643$	−1.60401	−0.0632562	−0.0316281	+	0.999500i	$0.510069\pi$
$644$	28.6548	1.12916
$645$	−5.46612	−0.215228
$646$	13.3367	0.524726
$647$	−8.16234	−0.320895	−0.160447	−	0.987044i	$-0.551294\pi$
$647$	−8.16234	−0.320895	−0.160447	+	0.987044i	$0.551294\pi$
$648$	93.2472	3.66309
$649$	−1.97582	−0.0775578
$650$	10.4911	0.411494
$651$	5.47581	0.214614
$652$	−57.3712	−2.24683
$653$	−32.9887	−1.29095	−0.645474	−	0.763782i	$-0.723340\pi$
$653$	−32.9887	−1.29095	−0.645474	+	0.763782i	$0.723340\pi$
$654$	99.5229	3.89165
$655$	−21.1382	−0.825939
$656$	19.4329	0.758727
$657$	−17.4685	−0.681511
$658$	−19.0998	−0.744587
$659$	9.00347	0.350725	0.175363	−	0.984504i	$-0.443890\pi$
$659$	9.00347	0.350725	0.175363	+	0.984504i	$0.443890\pi$
$660$	28.1196	1.09455
$661$	0.231764	0.00901459	0.00450729	−	0.999990i	$-0.498565\pi$
$661$	0.231764	0.00901459	0.00450729	+	0.999990i	$0.498565\pi$
$662$	−86.3154	−3.35474
$663$	−3.49377	−0.135687
$664$	−56.9804	−2.21127
$665$	21.3575	0.828208
$666$	−26.4240	−1.02391
$667$	33.4078	1.29356
$668$	28.2962	1.09481
$669$	56.4665	2.18312
$670$	86.6488	3.34754
$671$	−14.7269	−0.568526
$672$	50.5954	1.95176
$673$	11.9038	0.458859	0.229429	−	0.973325i	$-0.426314\pi$
$673$	11.9038	0.458859	0.229429	+	0.973325i	$0.426314\pi$
$674$	22.7538	0.876443
$675$	8.73620	0.336256
$676$	−51.5839	−1.98400
$677$	2.67367	0.102757	0.0513787	−	0.998679i	$-0.483638\pi$
$677$	2.67367	0.102757	0.0513787	+	0.998679i	$0.483638\pi$
$678$	−28.0558	−1.07748
$679$	−26.7035	−1.02479
$680$	22.6711	0.869397
$681$	19.1077	0.732208
$682$	−4.55186	−0.174300
$683$	25.7682	0.985992	0.492996	−	0.870032i	$-0.335902\pi$
$683$	25.7682	0.985992	0.492996	+	0.870032i	$0.335902\pi$
$684$	28.3936	1.08566
$685$	19.2496	0.735490
$686$	48.6994	1.85935
$687$	−59.3555	−2.26455
$688$	12.1756	0.464192
$689$	−16.4334	−0.626063
$690$	51.2867	1.95245
$691$	14.1210	0.537188	0.268594	−	0.963253i	$-0.413441\pi$
$691$	14.1210	0.537188	0.268594	+	0.963253i	$0.413441\pi$
$692$	40.3998	1.53577
$693$	−1.75527	−0.0666772
$694$	−53.9443	−2.04770
$695$	−42.0591	−1.59539
$696$	162.082	6.14369
$697$	−1.59605	−0.0604546
$698$	33.1453	1.25457
$699$	33.6529	1.27287
$700$	18.5830	0.702371
$701$	2.58458	0.0976184	0.0488092	−	0.998808i	$-0.484457\pi$
$701$	2.58458	0.0976184	0.0488092	+	0.998808i	$0.484457\pi$
$702$	17.6855	0.667496
$703$	44.5926	1.68184
$704$	−17.7071	−0.667360
$705$	−24.6152	−0.927063
$706$	86.8955	3.27036
$707$	−3.81099	−0.143327
$708$	−20.5967	−0.774070
$709$	−6.93169	−0.260325	−0.130162	−	0.991493i	$-0.541550\pi$
$709$	−6.93169	−0.260325	−0.130162	+	0.991493i	$0.541550\pi$
$710$	−20.1365	−0.755708
$711$	10.9859	0.412004
$712$	66.3065	2.48494
$713$	−5.97795	−0.223876
$714$	−8.59452	−0.321642
$715$	4.65090	0.173934
$716$	101.214	3.78254
$717$	−15.8743	−0.592838
$718$	−96.7217	−3.60962
$719$	27.4803	1.02484	0.512421	−	0.858734i	$-0.328749\pi$
$719$	27.4803	1.02484	0.512421	+	0.858734i	$0.328749\pi$
$720$	36.3307	1.35397
$721$	−11.3308	−0.421981
$722$	−15.7602	−0.586535
$723$	−12.6873	−0.471845
$724$	−73.3443	−2.72582
$725$	21.6654	0.804632
$726$	5.41626	0.201016
$727$	−38.2106	−1.41715	−0.708576	−	0.705635i	$-0.750662\pi$
$727$	−38.2106	−1.41715	−0.708576	+	0.705635i	$0.750662\pi$
$728$	22.9938	0.852206
$729$	11.0563	0.409493
$730$	113.861	4.21419
$731$	−1.00000	−0.0369863
$732$	−153.518	−5.67420
$733$	3.64082	0.134477	0.0672384	−	0.997737i	$-0.478581\pi$
$733$	3.64082	0.134477	0.0672384	+	0.997737i	$0.478581\pi$
$734$	34.2203	1.26309
$735$	24.4995	0.903678
$736$	−55.2351	−2.03599
$737$	12.0177	0.442677
$738$	−4.71899	−0.173708
$739$	−30.7193	−1.13003	−0.565015	−	0.825081i	$-0.691129\pi$
$739$	−30.7193	−1.13003	−0.565015	+	0.825081i	$0.691129\pi$
$740$	124.019	4.55901
$741$	17.4326	0.640403
$742$	−40.4254	−1.48406
$743$	−8.50003	−0.311836	−0.155918	−	0.987770i	$-0.549834\pi$
$743$	−8.50003	−0.311836	−0.155918	+	0.987770i	$0.549834\pi$
$744$	−29.0027	−1.06329
$745$	46.4496	1.70178
$746$	65.3814	2.39378
$747$	7.49955	0.274394
$748$	5.14435	0.188096
$749$	22.6098	0.826144
$750$	−39.7916	−1.45298
$751$	−3.82946	−0.139739	−0.0698696	−	0.997556i	$-0.522258\pi$
$751$	−3.82946	−0.139739	−0.0698696	+	0.997556i	$0.522258\pi$
$752$	54.8298	1.99944
$753$	−50.9062	−1.85513
$754$	43.8592	1.59726
$755$	44.6465	1.62485
$756$	31.3265	1.13933
$757$	−29.9562	−1.08878	−0.544388	−	0.838833i	$-0.683238\pi$
$757$	−29.9562	−1.08878	−0.544388	+	0.838833i	$0.683238\pi$
$758$	−20.4096	−0.741311
$759$	7.11316	0.258191
$760$	−113.120	−4.10330
$761$	−48.2164	−1.74784	−0.873922	−	0.486067i	$-0.838431\pi$
$761$	−48.2164	−1.74784	−0.873922	+	0.486067i	$0.838431\pi$
$762$	−6.89694	−0.249850
$763$	29.1572	1.05556
$764$	58.9859	2.13404
$765$	−2.98389	−0.107883
$766$	−79.8621	−2.88553
$767$	−3.40662	−0.123006
$768$	−14.1333	−0.509991
$769$	21.4770	0.774479	0.387240	−	0.921979i	$-0.373429\pi$
$769$	21.4770	0.774479	0.387240	+	0.921979i	$0.373429\pi$
$770$	11.4410	0.412305
$771$	22.7435	0.819089
$772$	69.2522	2.49244
$773$	19.2498	0.692368	0.346184	−	0.938167i	$-0.387477\pi$
$773$	19.2498	0.692368	0.346184	+	0.938167i	$0.387477\pi$
$774$	−2.95667	−0.106275
$775$	−3.87678	−0.139258
$776$	141.435	5.07724
$777$	−28.7366	−1.03092
$778$	−54.3825	−1.94971
$779$	7.96367	0.285328
$780$	48.4826	1.73595
$781$	−2.79281	−0.0999345
$782$	9.38265	0.335523
$783$	36.5227	1.30522
$784$	−54.5720	−1.94900
$785$	27.8249	0.993115
$786$	−42.4432	−1.51390
$787$	−13.6741	−0.487428	−0.243714	−	0.969847i	$-0.578366\pi$
$787$	−13.6741	−0.487428	−0.243714	+	0.969847i	$0.578366\pi$
$788$	−120.179	−4.28118
$789$	59.0682	2.10288
$790$	−71.6072	−2.54767
$791$	−8.21950	−0.292252
$792$	9.29681	0.330348
$793$	−25.3915	−0.901677
$794$	29.8356	1.05882
$795$	−52.0991	−1.84777
$796$	−27.7256	−0.982708
$797$	6.68734	0.236878	0.118439	−	0.992961i	$-0.462211\pi$
$797$	6.68734	0.236878	0.118439	+	0.992961i	$0.462211\pi$
$798$	42.8834	1.51806
$799$	−4.50324	−0.159313
$800$	−35.8207	−1.26645
$801$	−8.72701	−0.308354
$802$	55.0586	1.94419
$803$	15.7919	0.557283
$804$	125.277	4.41816
$805$	15.0254	0.529577
$806$	−7.84811	−0.276438
$807$	33.8528	1.19168
$808$	20.1850	0.710105
$809$	44.7238	1.57241	0.786203	−	0.617969i	$-0.212044\pi$
$809$	44.7238	1.57241	0.786203	+	0.617969i	$0.212044\pi$
$810$	79.9954	2.81075
$811$	−52.7349	−1.85177	−0.925886	−	0.377802i	$-0.876680\pi$
$811$	−52.7349	−1.85177	−0.925886	+	0.377802i	$0.876680\pi$
$812$	77.6884	2.72633
$813$	35.4467	1.24317
$814$	23.8878	0.837268
$815$	−30.0832	−1.05377
$816$	24.6723	0.863704
$817$	4.98962	0.174565
$818$	−10.9612	−0.383250
$819$	−3.02636	−0.105749
$820$	22.1481	0.773446
$821$	14.5997	0.509532	0.254766	−	0.967003i	$-0.418002\pi$
$821$	14.5997	0.509532	0.254766	+	0.967003i	$0.418002\pi$
$822$	38.6511	1.34811
$823$	25.9821	0.905678	0.452839	−	0.891592i	$-0.350411\pi$
$823$	25.9821	0.905678	0.452839	+	0.891592i	$0.350411\pi$
$824$	60.0137	2.09068
$825$	4.61298	0.160603
$826$	−8.38014	−0.291582
$827$	50.8118	1.76690	0.883449	−	0.468527i	$-0.155215\pi$
$827$	50.8118	1.76690	0.883449	+	0.468527i	$0.155215\pi$
$828$	19.9755	0.694195
$829$	23.0219	0.799585	0.399793	−	0.916606i	$-0.369082\pi$
$829$	23.0219	0.799585	0.399793	+	0.916606i	$0.369082\pi$
$830$	−48.8827	−1.69674
$831$	25.2621	0.876332
$832$	−30.5297	−1.05843
$833$	4.48207	0.155294
$834$	−84.4500	−2.92427
$835$	14.8374	0.513471
$836$	−25.6684	−0.887759
$837$	−6.53533	−0.225894
$838$	−78.8925	−2.72530
$839$	−37.7366	−1.30281	−0.651405	−	0.758730i	$-0.725820\pi$
$839$	−37.7366	−1.30281	−0.651405	+	0.758730i	$0.725820\pi$
$840$	72.8976	2.51521
$841$	61.5747	2.12327
$842$	50.8674	1.75301
$843$	21.4339	0.738224
$844$	−45.5178	−1.56679
$845$	−27.0486	−0.930499
$846$	−13.3146	−0.457766
$847$	1.58680	0.0545231
$848$	116.049	3.98515
$849$	−13.2917	−0.456169
$850$	6.08477	0.208706
$851$	31.3718	1.07541
$852$	−29.1132	−0.997402
$853$	40.1540	1.37485	0.687424	−	0.726256i	$-0.258741\pi$
$853$	40.1540	1.37485	0.687424	+	0.726256i	$0.258741\pi$
$854$	−62.4618	−2.13740
$855$	14.8885	0.509175
$856$	−119.753	−4.09308
$857$	−32.3746	−1.10590	−0.552948	−	0.833216i	$-0.686497\pi$
$857$	−32.3746	−1.10590	−0.552948	+	0.833216i	$0.686497\pi$
$858$	9.33847	0.318810
$859$	−54.5811	−1.86228	−0.931142	−	0.364656i	$-0.881187\pi$
$859$	−54.5811	−1.86228	−0.931142	+	0.364656i	$0.881187\pi$
$860$	13.8769	0.473197
$861$	−5.13199	−0.174898
$862$	−38.7616	−1.32022
$863$	26.3378	0.896549	0.448274	−	0.893896i	$-0.352039\pi$
$863$	26.3378	0.896549	0.448274	+	0.893896i	$0.352039\pi$
$864$	−60.3852	−2.05435
$865$	21.1841	0.720280
$866$	−2.19737	−0.0746695
$867$	−2.02637	−0.0688191
$868$	−13.9015	−0.471846
$869$	−9.93150	−0.336903
$870$	139.048	4.71416
$871$	20.7203	0.702082
$872$	−154.431	−5.22971
$873$	−18.6152	−0.630029
$874$	−46.8159	−1.58357
$875$	−11.6577	−0.394103
$876$	164.620	5.56200
$877$	49.0414	1.65601	0.828005	−	0.560721i	$-0.189476\pi$
$877$	49.0414	1.65601	0.828005	+	0.560721i	$0.189476\pi$
$878$	−13.0468	−0.440310
$879$	−10.3797	−0.350098
$880$	−32.8437	−1.10716
$881$	−23.6651	−0.797297	−0.398648	−	0.917104i	$-0.630521\pi$
$881$	−23.6651	−0.797297	−0.398648	+	0.917104i	$0.630521\pi$
$882$	13.2520	0.446218
$883$	48.1971	1.62196	0.810980	−	0.585073i	$-0.198934\pi$
$883$	48.1971	1.62196	0.810980	+	0.585073i	$0.198934\pi$
$884$	8.86965	0.298319
$885$	−10.8001	−0.363040
$886$	19.0278	0.639251
$887$	26.2990	0.883033	0.441517	−	0.897253i	$-0.354441\pi$
$887$	26.2990	0.883033	0.441517	+	0.897253i	$0.354441\pi$
$888$	152.204	5.10763
$889$	−2.02059	−0.0677685
$890$	56.8834	1.90674
$891$	11.0949	0.371693
$892$	−143.352	−4.79977
$893$	22.4695	0.751912
$894$	93.2655	3.11927
$895$	53.0726	1.77402
$896$	−25.1647	−0.840694
$897$	12.2642	0.409489
$898$	−55.1349	−1.83988
$899$	−16.2073	−0.540544
$900$	12.9543	0.431811
$901$	−9.53128	−0.317533
$902$	4.26606	0.142044
$903$	−3.21544	−0.107003
$904$	43.5347	1.44794
$905$	−38.4589	−1.27842
$906$	89.6452	2.97826
$907$	−4.41424	−0.146573	−0.0732863	−	0.997311i	$-0.523349\pi$
$907$	−4.41424	−0.146573	−0.0732863	+	0.997311i	$0.523349\pi$
$908$	−48.5088	−1.60982
$909$	−2.65667	−0.0881162
$910$	19.7260	0.653912
$911$	−12.8322	−0.425151	−0.212576	−	0.977145i	$-0.568185\pi$
$911$	−12.8322	−0.425151	−0.212576	+	0.977145i	$0.568185\pi$
$912$	−123.106	−4.07643
$913$	−6.77975	−0.224377
$914$	−75.3764	−2.49323
$915$	−80.4990	−2.66121
$916$	150.686	4.97880
$917$	−12.4346	−0.410625
$918$	10.2575	0.338547
$919$	−43.0138	−1.41889	−0.709447	−	0.704759i	$-0.751055\pi$
$919$	−43.0138	−1.41889	−0.709447	+	0.704759i	$0.751055\pi$
$920$	−79.5824	−2.62376
$921$	−40.2750	−1.32710
$922$	1.72914	0.0569462
$923$	−4.81523	−0.158495
$924$	16.5414	0.544171
$925$	20.3450	0.668941
$926$	−67.6365	−2.22267
$927$	−7.89878	−0.259430
$928$	−149.753	−4.91587
$929$	12.8079	0.420214	0.210107	−	0.977678i	$-0.432619\pi$
$929$	12.8079	0.420214	0.210107	+	0.977678i	$0.432619\pi$
$930$	−24.8810	−0.815881
$931$	−22.3638	−0.732945
$932$	−85.4347	−2.79851
$933$	33.1911	1.08663
$934$	46.1094	1.50875
$935$	2.69749	0.0882175
$936$	16.0291	0.523929
$937$	45.1598	1.47531	0.737653	−	0.675179i	$-0.235934\pi$
$937$	45.1598	1.47531	0.737653	+	0.675179i	$0.235934\pi$
$938$	50.9711	1.66427
$939$	0.0763785	0.00249252
$940$	62.4908	2.03823
$941$	−42.8911	−1.39821	−0.699104	−	0.715020i	$-0.746418\pi$
$941$	−42.8911	−1.39821	−0.699104	+	0.715020i	$0.746418\pi$
$942$	55.8693	1.82032
$943$	5.60261	0.182446
$944$	24.0569	0.782985
$945$	16.4264	0.534350
$946$	2.67289	0.0869032
$947$	10.7143	0.348167	0.174083	−	0.984731i	$-0.444304\pi$
$947$	10.7143	0.348167	0.174083	+	0.984731i	$0.444304\pi$
$948$	−103.529	−3.36248
$949$	27.2276	0.883847
$950$	−30.3607	−0.985032
$951$	−41.7260	−1.35306
$952$	13.3363	0.432231
$953$	19.2573	0.623807	0.311903	−	0.950114i	$-0.399033\pi$
$953$	19.2573	0.623807	0.311903	+	0.950114i	$0.399033\pi$
$954$	−28.1809	−0.912390
$955$	30.9299	1.00087
$956$	40.3002	1.30340
$957$	19.2851	0.623399
$958$	109.788	3.54709
$959$	11.3236	0.365657
$960$	−96.7890	−3.12385
$961$	−28.0999	−0.906448
$962$	41.1863	1.32790
$963$	15.7615	0.507906
$964$	32.2093	1.03739
$965$	36.3131	1.16896
$966$	30.1694	0.970684
$967$	14.5805	0.468877	0.234439	−	0.972131i	$-0.424675\pi$
$967$	14.5805	0.468877	0.234439	+	0.972131i	$0.424675\pi$
$968$	−8.40451	−0.270131
$969$	10.1108	0.324806
$970$	121.336	3.89585
$971$	−1.41246	−0.0453280	−0.0226640	−	0.999743i	$-0.507215\pi$
$971$	−1.41246	−0.0453280	−0.0226640	+	0.999743i	$0.507215\pi$
$972$	56.4313	1.81003
$973$	−24.7413	−0.793169
$974$	−47.2816	−1.51500
$975$	7.95349	0.254715
$976$	179.309	5.73956
$977$	47.5732	1.52200	0.761001	−	0.648750i	$-0.224708\pi$
$977$	47.5732	1.52200	0.761001	+	0.648750i	$0.224708\pi$
$978$	−60.4037	−1.93150
$979$	7.88940	0.252146
$980$	−62.1970	−1.98681
$981$	20.3257	0.648949
$982$	−68.5610	−2.18787
$983$	32.9076	1.04959	0.524794	−	0.851229i	$-0.324142\pi$
$983$	32.9076	1.04959	0.524794	+	0.851229i	$0.324142\pi$
$984$	27.1817	0.866521
$985$	−63.0169	−2.00788
$986$	25.4381	0.810114
$987$	−14.4799	−0.460900
$988$	−44.2562	−1.40798
$989$	3.51030	0.111621
$990$	7.97561	0.253481
$991$	−32.0033	−1.01662	−0.508309	−	0.861175i	$-0.669729\pi$
$991$	−32.0033	−1.01662	−0.508309	+	0.861175i	$0.669729\pi$
$992$	26.7965	0.850791
$993$	−65.4373	−2.07659
$994$	−11.8453	−0.375709
$995$	−14.5382	−0.460892
$996$	−70.6745	−2.23941
$997$	−27.2361	−0.862574	−0.431287	−	0.902215i	$-0.641940\pi$
$997$	−27.2361	−0.862574	−0.431287	+	0.902215i	$0.641940\pi$
$998$	−69.0419	−2.18548
$999$	34.2969	1.08511

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.67289 q^{2} -2.02637 q^{3} +5.14435 q^{4} +2.69749 q^{5} +5.41626 q^{6} +1.58680 q^{7} -8.40451 q^{8} +1.10617 q^{9} +O(q^{10})\)	\(q-2.67289 q^{2} -2.02637 q^{3} +5.14435 q^{4} +2.69749 q^{5} +5.41626 q^{6} +1.58680 q^{7} -8.40451 q^{8} +1.10617 q^{9} -7.21011 q^{10} -1.00000 q^{11} -10.4244 q^{12} -1.72415 q^{13} -4.24134 q^{14} -5.46612 q^{15} +12.1756 q^{16} -1.00000 q^{17} -2.95667 q^{18} +4.98962 q^{19} +13.8769 q^{20} -3.21544 q^{21} +2.67289 q^{22} +3.51030 q^{23} +17.0306 q^{24} +2.27648 q^{25} +4.60848 q^{26} +3.83760 q^{27} +8.16305 q^{28} +9.51708 q^{29} +14.6103 q^{30} -1.70297 q^{31} -15.7351 q^{32} +2.02637 q^{33} +2.67289 q^{34} +4.28038 q^{35} +5.69053 q^{36} +8.93708 q^{37} -13.3367 q^{38} +3.49377 q^{39} -22.6711 q^{40} +1.59605 q^{41} +8.59452 q^{42} +1.00000 q^{43} -5.14435 q^{44} +2.98389 q^{45} -9.38265 q^{46} +4.50324 q^{47} -24.6723 q^{48} -4.48207 q^{49} -6.08477 q^{50} +2.02637 q^{51} -8.86965 q^{52} +9.53128 q^{53} -10.2575 q^{54} -2.69749 q^{55} -13.3363 q^{56} -10.1108 q^{57} -25.4381 q^{58} +1.97582 q^{59} -28.1196 q^{60} +14.7269 q^{61} +4.55186 q^{62} +1.75527 q^{63} +17.7071 q^{64} -4.65090 q^{65} -5.41626 q^{66} -12.0177 q^{67} -5.14435 q^{68} -7.11316 q^{69} -11.4410 q^{70} +2.79281 q^{71} -9.29681 q^{72} -15.7919 q^{73} -23.8878 q^{74} -4.61298 q^{75} +25.6684 q^{76} -1.58680 q^{77} -9.33847 q^{78} +9.93150 q^{79} +32.8437 q^{80} -11.0949 q^{81} -4.26606 q^{82} +6.77975 q^{83} -16.5414 q^{84} -2.69749 q^{85} -2.67289 q^{86} -19.2851 q^{87} +8.40451 q^{88} -7.88940 q^{89} -7.97561 q^{90} -2.73589 q^{91} +18.0582 q^{92} +3.45085 q^{93} -12.0367 q^{94} +13.4595 q^{95} +31.8852 q^{96} -16.8285 q^{97} +11.9801 q^{98} -1.10617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 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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