LMFDB - Embedded newform 6033.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66273 q^{2} -1.00000 q^{3} +5.09011 q^{4} +2.84840 q^{5} +2.66273 q^{6} -4.34717 q^{7} -8.22811 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.66273 q^{2} -1.00000 q^{3} +5.09011 q^{4} +2.84840 q^{5} +2.66273 q^{6} -4.34717 q^{7} -8.22811 q^{8} +1.00000 q^{9} -7.58450 q^{10} +3.55348 q^{11} -5.09011 q^{12} -1.07202 q^{13} +11.5753 q^{14} -2.84840 q^{15} +11.7290 q^{16} +5.75976 q^{17} -2.66273 q^{18} -6.98319 q^{19} +14.4987 q^{20} +4.34717 q^{21} -9.46194 q^{22} -0.571276 q^{23} +8.22811 q^{24} +3.11337 q^{25} +2.85449 q^{26} -1.00000 q^{27} -22.1276 q^{28} +0.0642876 q^{29} +7.58450 q^{30} +9.53436 q^{31} -14.7749 q^{32} -3.55348 q^{33} -15.3367 q^{34} -12.3825 q^{35} +5.09011 q^{36} -3.41148 q^{37} +18.5943 q^{38} +1.07202 q^{39} -23.4369 q^{40} -10.5578 q^{41} -11.5753 q^{42} -5.17657 q^{43} +18.0876 q^{44} +2.84840 q^{45} +1.52115 q^{46} -0.744927 q^{47} -11.7290 q^{48} +11.8979 q^{49} -8.29004 q^{50} -5.75976 q^{51} -5.45669 q^{52} +0.366222 q^{53} +2.66273 q^{54} +10.1217 q^{55} +35.7690 q^{56} +6.98319 q^{57} -0.171180 q^{58} -14.7819 q^{59} -14.4987 q^{60} +6.75425 q^{61} -25.3874 q^{62} -4.34717 q^{63} +15.8834 q^{64} -3.05354 q^{65} +9.46194 q^{66} +9.17911 q^{67} +29.3178 q^{68} +0.571276 q^{69} +32.9711 q^{70} +14.8569 q^{71} -8.22811 q^{72} -3.15258 q^{73} +9.08385 q^{74} -3.11337 q^{75} -35.5452 q^{76} -15.4476 q^{77} -2.85449 q^{78} +8.99966 q^{79} +33.4088 q^{80} +1.00000 q^{81} +28.1124 q^{82} -15.2839 q^{83} +22.1276 q^{84} +16.4061 q^{85} +13.7838 q^{86} -0.0642876 q^{87} -29.2384 q^{88} +14.4848 q^{89} -7.58450 q^{90} +4.66025 q^{91} -2.90786 q^{92} -9.53436 q^{93} +1.98354 q^{94} -19.8909 q^{95} +14.7749 q^{96} +12.9227 q^{97} -31.6809 q^{98} +3.55348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) $ 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * 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 $

$2$	−2.66273	−1.88283	−0.941416	−	0.337248i	$-0.890504\pi$
$2$	−2.66273	−1.88283	−0.941416	+	0.337248i	$0.890504\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.09011	2.54505
$5$	2.84840	1.27384	0.636921	−	0.770929i	$-0.280208\pi$
$5$	2.84840	1.27384	0.636921	+	0.770929i	$0.280208\pi$
$6$	2.66273	1.08705
$7$	−4.34717	−1.64308	−0.821539	−	0.570153i	$-0.806884\pi$
$7$	−4.34717	−1.64308	−0.821539	+	0.570153i	$0.806884\pi$
$8$	−8.22811	−2.90908
$9$	1.00000	0.333333
$10$	−7.58450	−2.39843
$11$	3.55348	1.07141	0.535707	−	0.844404i	$-0.320045\pi$
$11$	3.55348	1.07141	0.535707	+	0.844404i	$0.320045\pi$
$12$	−5.09011	−1.46939
$13$	−1.07202	−0.297325	−0.148662	−	0.988888i	$-0.547497\pi$
$13$	−1.07202	−0.297325	−0.148662	+	0.988888i	$0.547497\pi$
$14$	11.5753	3.09364
$15$	−2.84840	−0.735453
$16$	11.7290	2.93225
$17$	5.75976	1.39695	0.698473	−	0.715636i	$-0.253863\pi$
$17$	5.75976	1.39695	0.698473	+	0.715636i	$0.253863\pi$
$18$	−2.66273	−0.627610
$19$	−6.98319	−1.60205	−0.801027	−	0.598628i	$-0.795713\pi$
$19$	−6.98319	−1.60205	−0.801027	+	0.598628i	$0.795713\pi$
$20$	14.4987	3.24200
$21$	4.34717	0.948631
$22$	−9.46194	−2.01729
$23$	−0.571276	−0.119119	−0.0595597	−	0.998225i	$-0.518970\pi$
$23$	−0.571276	−0.119119	−0.0595597	+	0.998225i	$0.518970\pi$
$24$	8.22811	1.67956
$25$	3.11337	0.622673
$26$	2.85449	0.559812
$27$	−1.00000	−0.192450
$28$	−22.1276	−4.18172
$29$	0.0642876	0.0119379	0.00596895	−	0.999982i	$-0.498100\pi$
$29$	0.0642876	0.0119379	0.00596895	+	0.999982i	$0.498100\pi$
$30$	7.58450	1.38473
$31$	9.53436	1.71242	0.856211	−	0.516627i	$-0.172812\pi$
$31$	9.53436	1.71242	0.856211	+	0.516627i	$0.172812\pi$
$32$	−14.7749	−2.61185
$33$	−3.55348	−0.618581
$34$	−15.3367	−2.63021
$35$	−12.3825	−2.09302
$36$	5.09011	0.848351
$37$	−3.41148	−0.560845	−0.280422	−	0.959877i	$-0.590475\pi$
$37$	−3.41148	−0.560845	−0.280422	+	0.959877i	$0.590475\pi$
$38$	18.5943	3.01640
$39$	1.07202	0.171660
$40$	−23.4369	−3.70570
$41$	−10.5578	−1.64885	−0.824423	−	0.565975i	$-0.808500\pi$
$41$	−10.5578	−1.64885	−0.824423	+	0.565975i	$0.808500\pi$
$42$	−11.5753	−1.78611
$43$	−5.17657	−0.789419	−0.394710	−	0.918806i	$-0.629155\pi$
$43$	−5.17657	−0.789419	−0.394710	+	0.918806i	$0.629155\pi$
$44$	18.0876	2.72681
$45$	2.84840	0.424614
$46$	1.52115	0.224282
$47$	−0.744927	−0.108659	−0.0543294	−	0.998523i	$-0.517302\pi$
$47$	−0.744927	−0.108659	−0.0543294	+	0.998523i	$0.517302\pi$
$48$	−11.7290	−1.69293
$49$	11.8979	1.69970
$50$	−8.29004	−1.17239
$51$	−5.75976	−0.806527
$52$	−5.45669	−0.756707
$53$	0.366222	0.0503045	0.0251522	−	0.999684i	$-0.491993\pi$
$53$	0.366222	0.0503045	0.0251522	+	0.999684i	$0.491993\pi$
$54$	2.66273	0.362351
$55$	10.1217	1.36481
$56$	35.7690	4.77984
$57$	6.98319	0.924946
$58$	−0.171180	−0.0224771
$59$	−14.7819	−1.92444	−0.962222	−	0.272264i	$-0.912227\pi$
$59$	−14.7819	−1.92444	−0.962222	+	0.272264i	$0.912227\pi$
$60$	−14.4987	−1.87177
$61$	6.75425	0.864793	0.432397	−	0.901684i	$-0.357668\pi$
$61$	6.75425	0.864793	0.432397	+	0.901684i	$0.357668\pi$
$62$	−25.3874	−3.22420
$63$	−4.34717	−0.547692
$64$	15.8834	1.98543
$65$	−3.05354	−0.378745
$66$	9.46194	1.16468
$67$	9.17911	1.12141	0.560703	−	0.828017i	$-0.310531\pi$
$67$	9.17911	1.12141	0.560703	+	0.828017i	$0.310531\pi$
$68$	29.3178	3.55530
$69$	0.571276	0.0687736
$70$	32.9711	3.94080
$71$	14.8569	1.76319	0.881593	−	0.472010i	$-0.156471\pi$
$71$	14.8569	1.76319	0.881593	+	0.472010i	$0.156471\pi$
$72$	−8.22811	−0.969692
$73$	−3.15258	−0.368981	−0.184491	−	0.982834i	$-0.559063\pi$
$73$	−3.15258	−0.368981	−0.184491	+	0.982834i	$0.559063\pi$
$74$	9.08385	1.05598
$75$	−3.11337	−0.359501
$76$	−35.5452	−4.07732
$77$	−15.4476	−1.76042
$78$	−2.85449	−0.323208
$79$	8.99966	1.01254	0.506270	−	0.862375i	$-0.331024\pi$
$79$	8.99966	1.01254	0.506270	+	0.862375i	$0.331024\pi$
$80$	33.4088	3.73522
$81$	1.00000	0.111111
$82$	28.1124	3.10450
$83$	−15.2839	−1.67763	−0.838814	−	0.544418i	$-0.816751\pi$
$83$	−15.2839	−1.67763	−0.838814	+	0.544418i	$0.816751\pi$
$84$	22.1276	2.41432
$85$	16.4061	1.77949
$86$	13.7838	1.48634
$87$	−0.0642876	−0.00689235
$88$	−29.2384	−3.11682
$89$	14.4848	1.53538	0.767690	−	0.640821i	$-0.221406\pi$
$89$	14.4848	1.53538	0.767690	+	0.640821i	$0.221406\pi$
$90$	−7.58450	−0.799477
$91$	4.66025	0.488527
$92$	−2.90786	−0.303165
$93$	−9.53436	−0.988667
$94$	1.98354	0.204586
$95$	−19.8909	−2.04076
$96$	14.7749	1.50795
$97$	12.9227	1.31211	0.656053	−	0.754715i	$-0.272225\pi$
$97$	12.9227	1.31211	0.656053	+	0.754715i	$0.272225\pi$
$98$	−31.6809	−3.20025
$99$	3.55348	0.357138
$100$	15.8474	1.58474
$101$	−13.5987	−1.35312	−0.676561	−	0.736386i	$-0.736531\pi$
$101$	−13.5987	−1.35312	−0.676561	+	0.736386i	$0.736531\pi$
$102$	15.3367	1.51856
$103$	−15.9711	−1.57368	−0.786839	−	0.617159i	$-0.788284\pi$
$103$	−15.9711	−1.57368	−0.786839	+	0.617159i	$0.788284\pi$
$104$	8.82069	0.864940
$105$	12.3825	1.20841
$106$	−0.975149	−0.0947149
$107$	4.29758	0.415462	0.207731	−	0.978186i	$-0.433392\pi$
$107$	4.29758	0.415462	0.207731	+	0.978186i	$0.433392\pi$
$108$	−5.09011	−0.489796
$109$	9.13779	0.875242	0.437621	−	0.899160i	$-0.355821\pi$
$109$	9.13779	0.875242	0.437621	+	0.899160i	$0.355821\pi$
$110$	−26.9514	−2.56971
$111$	3.41148	0.323804
$112$	−50.9879	−4.81791
$113$	−11.2608	−1.05933	−0.529665	−	0.848207i	$-0.677682\pi$
$113$	−11.2608	−1.05933	−0.529665	+	0.848207i	$0.677682\pi$
$114$	−18.5943	−1.74152
$115$	−1.62722	−0.151739
$116$	0.327231	0.0303826
$117$	−1.07202	−0.0991082
$118$	39.3603	3.62341
$119$	−25.0387	−2.29529
$120$	23.4369	2.13949
$121$	1.62720	0.147927
$122$	−17.9847	−1.62826
$123$	10.5578	0.951961
$124$	48.5309	4.35821
$125$	−5.37388	−0.480655
$126$	11.5753	1.03121
$127$	−16.6991	−1.48181	−0.740904	−	0.671611i	$-0.765602\pi$
$127$	−16.6991	−1.48181	−0.740904	+	0.671611i	$0.765602\pi$
$128$	−12.7435	−1.12637
$129$	5.17657	0.455771
$130$	8.13073	0.713112
$131$	−2.92465	−0.255528	−0.127764	−	0.991805i	$-0.540780\pi$
$131$	−2.92465	−0.255528	−0.127764	+	0.991805i	$0.540780\pi$
$132$	−18.0876	−1.57432
$133$	30.3571	2.63230
$134$	−24.4414	−2.11142
$135$	−2.84840	−0.245151
$136$	−47.3919	−4.06382
$137$	−15.5218	−1.32612	−0.663058	−	0.748568i	$-0.730742\pi$
$137$	−15.5218	−1.32612	−0.663058	+	0.748568i	$0.730742\pi$
$138$	−1.52115	−0.129489
$139$	−12.0592	−1.02285	−0.511426	−	0.859327i	$-0.670883\pi$
$139$	−12.0592	−1.02285	−0.511426	+	0.859327i	$0.670883\pi$
$140$	−63.0281	−5.32685
$141$	0.744927	0.0627342
$142$	−39.5598	−3.31978
$143$	−3.80940	−0.318558
$144$	11.7290	0.977416
$145$	0.183117	0.0152070
$146$	8.39444	0.694729
$147$	−11.8979	−0.981323
$148$	−17.3648	−1.42738
$149$	9.34083	0.765230	0.382615	−	0.923908i	$-0.375023\pi$
$149$	9.34083	0.765230	0.382615	+	0.923908i	$0.375023\pi$
$150$	8.29004	0.676879
$151$	−9.96130	−0.810639	−0.405319	−	0.914175i	$-0.632840\pi$
$151$	−9.96130	−0.810639	−0.405319	+	0.914175i	$0.632840\pi$
$152$	57.4585	4.66050
$153$	5.75976	0.465649
$154$	41.1327	3.31457
$155$	27.1576	2.18135
$156$	5.45669	0.436885
$157$	−4.36088	−0.348036	−0.174018	−	0.984742i	$-0.555675\pi$
$157$	−4.36088	−0.348036	−0.174018	+	0.984742i	$0.555675\pi$
$158$	−23.9636	−1.90644
$159$	−0.366222	−0.0290433
$160$	−42.0847	−3.32708
$161$	2.48344	0.195722
$162$	−2.66273	−0.209203
$163$	−8.69569	−0.681099	−0.340550	−	0.940227i	$-0.610613\pi$
$163$	−8.69569	−0.681099	−0.340550	+	0.940227i	$0.610613\pi$
$164$	−53.7401	−4.19640
$165$	−10.1217	−0.787974
$166$	40.6969	3.15869
$167$	4.72478	0.365614	0.182807	−	0.983149i	$-0.441482\pi$
$167$	4.72478	0.365614	0.182807	+	0.983149i	$0.441482\pi$
$168$	−35.7690	−2.75964
$169$	−11.8508	−0.911598
$170$	−43.6849	−3.35048
$171$	−6.98319	−0.534018
$172$	−26.3493	−2.00911
$173$	−1.46806	−0.111615	−0.0558074	−	0.998442i	$-0.517773\pi$
$173$	−1.46806	−0.111615	−0.0558074	+	0.998442i	$0.517773\pi$
$174$	0.171180	0.0129771
$175$	−13.5343	−1.02310
$176$	41.6787	3.14165
$177$	14.7819	1.11108
$178$	−38.5689	−2.89086
$179$	−0.213200	−0.0159353	−0.00796765	−	0.999968i	$-0.502536\pi$
$179$	−0.213200	−0.0159353	−0.00796765	+	0.999968i	$0.502536\pi$
$180$	14.4987	1.08067
$181$	21.5929	1.60498	0.802492	−	0.596663i	$-0.203507\pi$
$181$	21.5929	1.60498	0.802492	+	0.596663i	$0.203507\pi$
$182$	−12.4090	−0.919815
$183$	−6.75425	−0.499289
$184$	4.70053	0.346527
$185$	−9.71726	−0.714427
$186$	25.3874	1.86149
$187$	20.4672	1.49671
$188$	−3.79176	−0.276543
$189$	4.34717	0.316210
$190$	52.9640	3.84241
$191$	−4.50375	−0.325880	−0.162940	−	0.986636i	$-0.552098\pi$
$191$	−4.50375	−0.325880	−0.162940	+	0.986636i	$0.552098\pi$
$192$	−15.8834	−1.14629
$193$	5.15069	0.370755	0.185377	−	0.982667i	$-0.440649\pi$
$193$	5.15069	0.370755	0.185377	+	0.982667i	$0.440649\pi$
$194$	−34.4097	−2.47047
$195$	3.05354	0.218668
$196$	60.5617	4.32583
$197$	25.2582	1.79957	0.899786	−	0.436332i	$-0.143723\pi$
$197$	25.2582	1.79957	0.899786	+	0.436332i	$0.143723\pi$
$198$	−9.46194	−0.672430
$199$	1.70860	0.121119	0.0605596	−	0.998165i	$-0.480711\pi$
$199$	1.70860	0.121119	0.0605596	+	0.998165i	$0.480711\pi$
$200$	−25.6171	−1.81140
$201$	−9.17911	−0.647444
$202$	36.2097	2.54770
$203$	−0.279469	−0.0196149
$204$	−29.3178	−2.05266
$205$	−30.0727	−2.10037
$206$	42.5266	2.96297
$207$	−0.571276	−0.0397065
$208$	−12.5737	−0.871829
$209$	−24.8146	−1.71646
$210$	−32.9711	−2.27522
$211$	9.46783	0.651792	0.325896	−	0.945406i	$-0.394334\pi$
$211$	9.46783	0.651792	0.325896	+	0.945406i	$0.394334\pi$
$212$	1.86411	0.128028
$213$	−14.8569	−1.01798
$214$	−11.4433	−0.782246
$215$	−14.7449	−1.00560
$216$	8.22811	0.559852
$217$	−41.4475	−2.81364
$218$	−24.3314	−1.64793
$219$	3.15258	0.213031
$220$	51.5206	3.47352
$221$	−6.17457	−0.415347
$222$	−9.08385	−0.609668
$223$	6.04974	0.405120	0.202560	−	0.979270i	$-0.435074\pi$
$223$	6.04974	0.405120	0.202560	+	0.979270i	$0.435074\pi$
$224$	64.2289	4.29147
$225$	3.11337	0.207558
$226$	29.9845	1.99454
$227$	13.6981	0.909178	0.454589	−	0.890701i	$-0.349786\pi$
$227$	13.6981	0.909178	0.454589	+	0.890701i	$0.349786\pi$
$228$	35.5452	2.35404
$229$	−11.1291	−0.735434	−0.367717	−	0.929938i	$-0.619860\pi$
$229$	−11.1291	−0.735434	−0.367717	+	0.929938i	$0.619860\pi$
$230$	4.33285	0.285699
$231$	15.4476	1.01638
$232$	−0.528965	−0.0347283
$233$	−3.47264	−0.227500	−0.113750	−	0.993509i	$-0.536286\pi$
$233$	−3.47264	−0.227500	−0.113750	+	0.993509i	$0.536286\pi$
$234$	2.85449	0.186604
$235$	−2.12185	−0.138414
$236$	−75.2417	−4.89782
$237$	−8.99966	−0.584591
$238$	66.6711	4.32165
$239$	−23.6765	−1.53150	−0.765752	−	0.643136i	$-0.777633\pi$
$239$	−23.6765	−1.53150	−0.765752	+	0.643136i	$0.777633\pi$
$240$	−33.4088	−2.15653
$241$	−4.45549	−0.287003	−0.143502	−	0.989650i	$-0.545836\pi$
$241$	−4.45549	−0.287003	−0.143502	+	0.989650i	$0.545836\pi$
$242$	−4.33279	−0.278522
$243$	−1.00000	−0.0641500
$244$	34.3799	2.20095
$245$	33.8900	2.16515
$246$	−28.1124	−1.79238
$247$	7.48612	0.476330
$248$	−78.4498	−4.98157
$249$	15.2839	0.968579
$250$	14.3092	0.904992
$251$	26.9526	1.70123	0.850617	−	0.525786i	$-0.176229\pi$
$251$	26.9526	1.70123	0.850617	+	0.525786i	$0.176229\pi$
$252$	−22.1276	−1.39391
$253$	−2.03002	−0.127626
$254$	44.4652	2.78999
$255$	−16.4061	−1.02739
$256$	2.16551	0.135345
$257$	16.0368	1.00035	0.500175	−	0.865925i	$-0.333269\pi$
$257$	16.0368	1.00035	0.500175	+	0.865925i	$0.333269\pi$
$258$	−13.7838	−0.858141
$259$	14.8303	0.921511
$260$	−15.5428	−0.963926
$261$	0.0642876	0.00397930
$262$	7.78755	0.481116
$263$	−22.0628	−1.36045	−0.680225	−	0.733003i	$-0.738118\pi$
$263$	−22.0628	−1.36045	−0.680225	+	0.733003i	$0.738118\pi$
$264$	29.2384	1.79950
$265$	1.04315	0.0640800
$266$	−80.8328	−4.95617
$267$	−14.4848	−0.886453
$268$	46.7226	2.85404
$269$	−15.8904	−0.968856	−0.484428	−	0.874831i	$-0.660972\pi$
$269$	−15.8904	−0.968856	−0.484428	+	0.874831i	$0.660972\pi$
$270$	7.58450	0.461578
$271$	24.6598	1.49797	0.748987	−	0.662585i	$-0.230541\pi$
$271$	24.6598	1.49797	0.748987	+	0.662585i	$0.230541\pi$
$272$	67.5561	4.09619
$273$	−4.66025	−0.282051
$274$	41.3303	2.49685
$275$	11.0633	0.667141
$276$	2.90786	0.175033
$277$	−13.1663	−0.791084	−0.395542	−	0.918448i	$-0.629443\pi$
$277$	−13.1663	−0.791084	−0.395542	+	0.918448i	$0.629443\pi$
$278$	32.1105	1.92586
$279$	9.53436	0.570807
$280$	101.884	6.08876
$281$	8.93464	0.532996	0.266498	−	0.963835i	$-0.414133\pi$
$281$	8.93464	0.532996	0.266498	+	0.963835i	$0.414133\pi$
$282$	−1.98354	−0.118118
$283$	−17.4049	−1.03461	−0.517306	−	0.855800i	$-0.673065\pi$
$283$	−17.4049	−1.03461	−0.517306	+	0.855800i	$0.673065\pi$
$284$	75.6231	4.48741
$285$	19.8909	1.17824
$286$	10.1434	0.599790
$287$	45.8964	2.70918
$288$	−14.7749	−0.870617
$289$	16.1748	0.951460
$290$	−0.487589	−0.0286322
$291$	−12.9227	−0.757545
$292$	−16.0470	−0.939077
$293$	15.8313	0.924875	0.462438	−	0.886652i	$-0.346975\pi$
$293$	15.8313	0.924875	0.462438	+	0.886652i	$0.346975\pi$
$294$	31.6809	1.84767
$295$	−42.1048	−2.45144
$296$	28.0701	1.63154
$297$	−3.55348	−0.206194
$298$	−24.8721	−1.44080
$299$	0.612419	0.0354171
$300$	−15.8474	−0.914948
$301$	22.5034	1.29708
$302$	26.5242	1.52630
$303$	13.5987	0.781226
$304$	−81.9058	−4.69762
$305$	19.2388	1.10161
$306$	−15.3367	−0.876738
$307$	4.36223	0.248966	0.124483	−	0.992222i	$-0.460273\pi$
$307$	4.36223	0.248966	0.124483	+	0.992222i	$0.460273\pi$
$308$	−78.6299	−4.48035
$309$	15.9711	0.908563
$310$	−72.3134	−4.10712
$311$	−23.8792	−1.35407	−0.677033	−	0.735952i	$-0.736735\pi$
$311$	−23.8792	−1.35407	−0.677033	+	0.735952i	$0.736735\pi$
$312$	−8.82069	−0.499373
$313$	−12.6256	−0.713643	−0.356821	−	0.934173i	$-0.616139\pi$
$313$	−12.6256	−0.713643	−0.356821	+	0.934173i	$0.616139\pi$
$314$	11.6118	0.655294
$315$	−12.3825	−0.697673
$316$	45.8092	2.57697
$317$	−4.26965	−0.239807	−0.119904	−	0.992786i	$-0.538259\pi$
$317$	−4.26965	−0.239807	−0.119904	+	0.992786i	$0.538259\pi$
$318$	0.975149	0.0546836
$319$	0.228444	0.0127904
$320$	45.2423	2.52912
$321$	−4.29758	−0.239867
$322$	−6.61271	−0.368512
$323$	−40.2215	−2.23798
$324$	5.09011	0.282784
$325$	−3.33759	−0.185136
$326$	23.1542	1.28239
$327$	−9.13779	−0.505321
$328$	86.8704	4.79662
$329$	3.23833	0.178535
$330$	26.9514	1.48362
$331$	−22.5246	−1.23806	−0.619032	−	0.785366i	$-0.712475\pi$
$331$	−22.5246	−1.23806	−0.619032	+	0.785366i	$0.712475\pi$
$332$	−77.7968	−4.26965
$333$	−3.41148	−0.186948
$334$	−12.5808	−0.688390
$335$	26.1457	1.42849
$336$	50.9879	2.78162
$337$	15.1700	0.826364	0.413182	−	0.910649i	$-0.364417\pi$
$337$	15.1700	0.826364	0.413182	+	0.910649i	$0.364417\pi$
$338$	31.5554	1.71639
$339$	11.2608	0.611605
$340$	83.5087	4.52890
$341$	33.8801	1.83471
$342$	18.5943	1.00547
$343$	−21.2921	−1.14966
$344$	42.5934	2.29648
$345$	1.62722	0.0876067
$346$	3.90905	0.210152
$347$	−29.2609	−1.57081	−0.785405	−	0.618983i	$-0.787545\pi$
$347$	−29.2609	−1.57081	−0.785405	+	0.618983i	$0.787545\pi$
$348$	−0.327231	−0.0175414
$349$	27.5906	1.47689	0.738444	−	0.674315i	$-0.235561\pi$
$349$	27.5906	1.47689	0.738444	+	0.674315i	$0.235561\pi$
$350$	36.0382	1.92633
$351$	1.07202	0.0572202
$352$	−52.5021	−2.79837
$353$	4.68553	0.249386	0.124693	−	0.992195i	$-0.460205\pi$
$353$	4.68553	0.249386	0.124693	+	0.992195i	$0.460205\pi$
$354$	−39.3603	−2.09197
$355$	42.3183	2.24602
$356$	73.7290	3.90763
$357$	25.0387	1.32519
$358$	0.567693	0.0300035
$359$	18.6699	0.985360	0.492680	−	0.870211i	$-0.336017\pi$
$359$	18.6699	0.985360	0.492680	+	0.870211i	$0.336017\pi$
$360$	−23.4369	−1.23523
$361$	29.7650	1.56658
$362$	−57.4958	−3.02191
$363$	−1.62720	−0.0854059
$364$	23.7212	1.24333
$365$	−8.97979	−0.470024
$366$	17.9847	0.940076
$367$	−27.0627	−1.41266	−0.706331	−	0.707882i	$-0.749651\pi$
$367$	−27.0627	−1.41266	−0.706331	+	0.707882i	$0.749651\pi$
$368$	−6.70049	−0.349287
$369$	−10.5578	−0.549615
$370$	25.8744	1.34515
$371$	−1.59203	−0.0826541
$372$	−48.5309	−2.51621
$373$	−1.88573	−0.0976396	−0.0488198	−	0.998808i	$-0.515546\pi$
$373$	−1.88573	−0.0976396	−0.0488198	+	0.998808i	$0.515546\pi$
$374$	−54.4985	−2.81805
$375$	5.37388	0.277506
$376$	6.12934	0.316097
$377$	−0.0689175	−0.00354943
$378$	−11.5753	−0.595371
$379$	−2.56741	−0.131879	−0.0659396	−	0.997824i	$-0.521004\pi$
$379$	−2.56741	−0.131879	−0.0659396	+	0.997824i	$0.521004\pi$
$380$	−101.247	−5.19385
$381$	16.6991	0.855522
$382$	11.9923	0.613577
$383$	−1.29569	−0.0662066	−0.0331033	−	0.999452i	$-0.510539\pi$
$383$	−1.29569	−0.0662066	−0.0331033	+	0.999452i	$0.510539\pi$
$384$	12.7435	0.650312
$385$	−44.0008	−2.24249
$386$	−13.7149	−0.698069
$387$	−5.17657	−0.263140
$388$	65.7782	3.33938
$389$	10.5606	0.535444	0.267722	−	0.963496i	$-0.413729\pi$
$389$	10.5606	0.535444	0.267722	+	0.963496i	$0.413729\pi$
$390$	−8.13073	−0.411716
$391$	−3.29041	−0.166403
$392$	−97.8974	−4.94456
$393$	2.92465	0.147529
$394$	−67.2556	−3.38829
$395$	25.6346	1.28982
$396$	18.0876	0.908935
$397$	12.1149	0.608028	0.304014	−	0.952668i	$-0.401673\pi$
$397$	12.1149	0.608028	0.304014	+	0.952668i	$0.401673\pi$
$398$	−4.54952	−0.228047
$399$	−30.3571	−1.51976
$400$	36.5166	1.82583
$401$	−31.2137	−1.55874	−0.779368	−	0.626567i	$-0.784460\pi$
$401$	−31.2137	−1.55874	−0.779368	+	0.626567i	$0.784460\pi$
$402$	24.4414	1.21903
$403$	−10.2210	−0.509145
$404$	−69.2189	−3.44377
$405$	2.84840	0.141538
$406$	0.744150	0.0369315
$407$	−12.1226	−0.600897
$408$	47.3919	2.34625
$409$	−11.1938	−0.553497	−0.276749	−	0.960942i	$-0.589257\pi$
$409$	−11.1938	−0.553497	−0.276749	+	0.960942i	$0.589257\pi$
$410$	80.0753	3.95464
$411$	15.5218	0.765634
$412$	−81.2945	−4.00509
$413$	64.2597	3.16201
$414$	1.52115	0.0747606
$415$	−43.5347	−2.13703
$416$	15.8389	0.776567
$417$	12.0592	0.590544
$418$	66.0745	3.23181
$419$	−15.0676	−0.736098	−0.368049	−	0.929806i	$-0.619974\pi$
$419$	−15.0676	−0.736098	−0.368049	+	0.929806i	$0.619974\pi$
$420$	63.0281	3.07546
$421$	19.2395	0.937674	0.468837	−	0.883285i	$-0.344673\pi$
$421$	19.2395	0.937674	0.468837	+	0.883285i	$0.344673\pi$
$422$	−25.2102	−1.22722
$423$	−0.744927	−0.0362196
$424$	−3.01332	−0.146340
$425$	17.9322	0.869841
$426$	39.5598	1.91668
$427$	−29.3619	−1.42092
$428$	21.8751	1.05737
$429$	3.80940	0.183919
$430$	39.2617	1.89337
$431$	−29.6723	−1.42926	−0.714632	−	0.699501i	$-0.753406\pi$
$431$	−29.6723	−1.42926	−0.714632	+	0.699501i	$0.753406\pi$
$432$	−11.7290	−0.564311
$433$	20.0090	0.961571	0.480786	−	0.876838i	$-0.340351\pi$
$433$	20.0090	0.961571	0.480786	+	0.876838i	$0.340351\pi$
$434$	110.363	5.29761
$435$	−0.183117	−0.00877977
$436$	46.5124	2.22754
$437$	3.98933	0.190836
$438$	−8.39444	−0.401102
$439$	12.9581	0.618454	0.309227	−	0.950988i	$-0.399930\pi$
$439$	12.9581	0.618454	0.309227	+	0.950988i	$0.399930\pi$
$440$	−83.2826	−3.97034
$441$	11.8979	0.566567
$442$	16.4412	0.782028
$443$	37.2783	1.77115	0.885573	−	0.464500i	$-0.153766\pi$
$443$	37.2783	1.77115	0.885573	+	0.464500i	$0.153766\pi$
$444$	17.3648	0.824098
$445$	41.2583	1.95583
$446$	−16.1088	−0.762774
$447$	−9.34083	−0.441806
$448$	−69.0479	−3.26221
$449$	−11.8595	−0.559686	−0.279843	−	0.960046i	$-0.590282\pi$
$449$	−11.8595	−0.559686	−0.279843	+	0.960046i	$0.590282\pi$
$450$	−8.29004	−0.390796
$451$	−37.5168	−1.76660
$452$	−57.3189	−2.69605
$453$	9.96130	0.468023
$454$	−36.4744	−1.71183
$455$	13.2743	0.622307
$456$	−57.4585	−2.69074
$457$	−2.80704	−0.131308	−0.0656540	−	0.997842i	$-0.520913\pi$
$457$	−2.80704	−0.131308	−0.0656540	+	0.997842i	$0.520913\pi$
$458$	29.6338	1.38470
$459$	−5.75976	−0.268842
$460$	−8.28274	−0.386185
$461$	−35.8506	−1.66973	−0.834865	−	0.550454i	$-0.814455\pi$
$461$	−35.8506	−1.66973	−0.834865	+	0.550454i	$0.814455\pi$
$462$	−41.1327	−1.91367
$463$	−21.3696	−0.993129	−0.496565	−	0.868000i	$-0.665405\pi$
$463$	−21.3696	−0.993129	−0.496565	+	0.868000i	$0.665405\pi$
$464$	0.754028	0.0350049
$465$	−27.1576	−1.25941
$466$	9.24669	0.428345
$467$	−30.4371	−1.40846	−0.704231	−	0.709971i	$-0.748708\pi$
$467$	−30.4371	−1.40846	−0.704231	+	0.709971i	$0.748708\pi$
$468$	−5.45669	−0.252236
$469$	−39.9032	−1.84256
$470$	5.64990	0.260611
$471$	4.36088	0.200939
$472$	121.627	5.59836
$473$	−18.3948	−0.845795
$474$	23.9636	1.10069
$475$	−21.7412	−0.997556
$476$	−127.450	−5.84164
$477$	0.366222	0.0167682
$478$	63.0439	2.88356
$479$	15.2948	0.698836	0.349418	−	0.936967i	$-0.386379\pi$
$479$	15.2948	0.698836	0.349418	+	0.936967i	$0.386379\pi$
$480$	42.0847	1.92089
$481$	3.65718	0.166753
$482$	11.8638	0.540379
$483$	−2.48344	−0.113000
$484$	8.28263	0.376483
$485$	36.8091	1.67142
$486$	2.66273	0.120784
$487$	1.59200	0.0721403	0.0360701	−	0.999349i	$-0.488516\pi$
$487$	1.59200	0.0721403	0.0360701	+	0.999349i	$0.488516\pi$
$488$	−55.5747	−2.51575
$489$	8.69569	0.393233
$490$	−90.2397	−4.07662
$491$	−33.6236	−1.51741	−0.758707	−	0.651432i	$-0.774168\pi$
$491$	−33.6236	−1.51741	−0.758707	+	0.651432i	$0.774168\pi$
$492$	53.7401	2.42279
$493$	0.370281	0.0166766
$494$	−19.9335	−0.896849
$495$	10.1217	0.454937
$496$	111.828	5.02124
$497$	−64.5854	−2.89705
$498$	−40.6969	−1.82367
$499$	−26.6448	−1.19278	−0.596392	−	0.802693i	$-0.703400\pi$
$499$	−26.6448	−1.19278	−0.596392	+	0.802693i	$0.703400\pi$
$500$	−27.3536	−1.22329
$501$	−4.72478	−0.211087
$502$	−71.7674	−3.20314
$503$	−0.984019	−0.0438753	−0.0219376	−	0.999759i	$-0.506984\pi$
$503$	−0.984019	−0.0438753	−0.0219376	+	0.999759i	$0.506984\pi$
$504$	35.7690	1.59328
$505$	−38.7345	−1.72366
$506$	5.40538	0.240298
$507$	11.8508	0.526311
$508$	−85.0003	−3.77128
$509$	35.0687	1.55439	0.777196	−	0.629258i	$-0.216641\pi$
$509$	35.0687	1.55439	0.777196	+	0.629258i	$0.216641\pi$
$510$	43.6849	1.93440
$511$	13.7048	0.606264
$512$	19.7207	0.871542
$513$	6.98319	0.308315
$514$	−42.7016	−1.88349
$515$	−45.4920	−2.00462
$516$	26.3493	1.15996
$517$	−2.64708	−0.116419
$518$	−39.4891	−1.73505
$519$	1.46806	0.0644409
$520$	25.1248	1.10180
$521$	8.00295	0.350616	0.175308	−	0.984514i	$-0.443908\pi$
$521$	8.00295	0.350616	0.175308	+	0.984514i	$0.443908\pi$
$522$	−0.171180	−0.00749235
$523$	−18.6681	−0.816299	−0.408150	−	0.912915i	$-0.633826\pi$
$523$	−18.6681	−0.816299	−0.408150	+	0.912915i	$0.633826\pi$
$524$	−14.8868	−0.650333
$525$	13.5343	0.590687
$526$	58.7472	2.56150
$527$	54.9156	2.39216
$528$	−41.6787	−1.81383
$529$	−22.6736	−0.985811
$530$	−2.77761	−0.120652
$531$	−14.7819	−0.641482
$532$	154.521	6.69934
$533$	11.3181	0.490242
$534$	38.5689	1.66904
$535$	12.2412	0.529233
$536$	−75.5267	−3.26226
$537$	0.213200	0.00920026
$538$	42.3118	1.82419
$539$	42.2790	1.82108
$540$	−14.4987	−0.623923
$541$	22.6246	0.972709	0.486354	−	0.873762i	$-0.338326\pi$
$541$	22.6246	0.972709	0.486354	+	0.873762i	$0.338326\pi$
$542$	−65.6622	−2.82043
$543$	−21.5929	−0.926638
$544$	−85.0996	−3.64861
$545$	26.0281	1.11492
$546$	12.4090	0.531055
$547$	20.4780	0.875576	0.437788	−	0.899078i	$-0.355762\pi$
$547$	20.4780	0.875576	0.437788	+	0.899078i	$0.355762\pi$
$548$	−79.0076	−3.37504
$549$	6.75425	0.288264
$550$	−29.4585	−1.25611
$551$	−0.448933	−0.0191252
$552$	−4.70053	−0.200068
$553$	−39.1231	−1.66368
$554$	35.0582	1.48948
$555$	9.71726	0.412475
$556$	−61.3829	−2.60321
$557$	16.0952	0.681975	0.340988	−	0.940068i	$-0.389239\pi$
$557$	16.0952	0.681975	0.340988	+	0.940068i	$0.389239\pi$
$558$	−25.3874	−1.07473
$559$	5.54938	0.234714
$560$	−145.234	−6.13725
$561$	−20.4672	−0.864125
$562$	−23.7905	−1.00354
$563$	−26.7744	−1.12841	−0.564203	−	0.825636i	$-0.690816\pi$
$563$	−26.7744	−1.12841	−0.564203	+	0.825636i	$0.690816\pi$
$564$	3.79176	0.159662
$565$	−32.0753	−1.34942
$566$	46.3444	1.94800
$567$	−4.34717	−0.182564
$568$	−122.244	−5.12924
$569$	12.7692	0.535312	0.267656	−	0.963514i	$-0.413751\pi$
$569$	12.7692	0.535312	0.267656	+	0.963514i	$0.413751\pi$
$570$	−52.9640	−2.21842
$571$	−9.60557	−0.401981	−0.200990	−	0.979593i	$-0.564416\pi$
$571$	−9.60557	−0.401981	−0.200990	+	0.979593i	$0.564416\pi$
$572$	−19.3902	−0.810747
$573$	4.50375	0.188147
$574$	−122.210	−5.10093
$575$	−1.77859	−0.0741724
$576$	15.8834	0.661809
$577$	20.3959	0.849094	0.424547	−	0.905406i	$-0.360433\pi$
$577$	20.3959	0.849094	0.424547	+	0.905406i	$0.360433\pi$
$578$	−43.0691	−1.79144
$579$	−5.15069	−0.214055
$580$	0.932083	0.0387026
$581$	66.4418	2.75647
$582$	34.4097	1.42633
$583$	1.30136	0.0538969
$584$	25.9397	1.07339
$585$	−3.05354	−0.126248
$586$	−42.1545	−1.74138
$587$	9.75027	0.402437	0.201218	−	0.979546i	$-0.435510\pi$
$587$	9.75027	0.402437	0.201218	+	0.979546i	$0.435510\pi$
$588$	−60.5617	−2.49752
$589$	−66.5803	−2.74339
$590$	112.114	4.61565
$591$	−25.2582	−1.03898
$592$	−40.0133	−1.64453
$593$	5.31689	0.218338	0.109169	−	0.994023i	$-0.465181\pi$
$593$	5.31689	0.218338	0.109169	+	0.994023i	$0.465181\pi$
$594$	9.46194	0.388228
$595$	−71.3201	−2.92384
$596$	47.5458	1.94755
$597$	−1.70860	−0.0699282
$598$	−1.63070	−0.0666845
$599$	−36.2611	−1.48159	−0.740795	−	0.671732i	$-0.765551\pi$
$599$	−36.2611	−1.48159	−0.740795	+	0.671732i	$0.765551\pi$
$600$	25.6171	1.04581
$601$	−32.1155	−1.31002	−0.655009	−	0.755621i	$-0.727335\pi$
$601$	−32.1155	−1.31002	−0.655009	+	0.755621i	$0.727335\pi$
$602$	−59.9205	−2.44218
$603$	9.17911	0.373802
$604$	−50.7041	−2.06312
$605$	4.63491	0.188436
$606$	−36.2097	−1.47092
$607$	25.1101	1.01919	0.509594	−	0.860415i	$-0.329795\pi$
$607$	25.1101	1.01919	0.509594	+	0.860415i	$0.329795\pi$
$608$	103.176	4.18433
$609$	0.279469	0.0113247
$610$	−51.2276	−2.07415
$611$	0.798576	0.0323069
$612$	29.3178	1.18510
$613$	9.84069	0.397462	0.198731	−	0.980054i	$-0.436318\pi$
$613$	9.84069	0.397462	0.198731	+	0.980054i	$0.436318\pi$
$614$	−11.6154	−0.468761
$615$	30.0727	1.21265
$616$	127.104	5.12118
$617$	−30.9276	−1.24510	−0.622549	−	0.782581i	$-0.713903\pi$
$617$	−30.9276	−1.24510	−0.622549	+	0.782581i	$0.713903\pi$
$618$	−42.5266	−1.71067
$619$	34.7103	1.39513	0.697563	−	0.716523i	$-0.254268\pi$
$619$	34.7103	1.39513	0.697563	+	0.716523i	$0.254268\pi$
$620$	138.235	5.55167
$621$	0.571276	0.0229245
$622$	63.5838	2.54948
$623$	−62.9677	−2.52275
$624$	12.5737	0.503351
$625$	−30.8738	−1.23495
$626$	33.6186	1.34367
$627$	24.8146	0.991000
$628$	−22.1974	−0.885772
$629$	−19.6493	−0.783470
$630$	32.9711	1.31360
$631$	−35.8378	−1.42668	−0.713340	−	0.700818i	$-0.752819\pi$
$631$	−35.8378	−1.42668	−0.713340	+	0.700818i	$0.752819\pi$
$632$	−74.0502	−2.94556
$633$	−9.46783	−0.376312
$634$	11.3689	0.451517
$635$	−47.5657	−1.88759
$636$	−1.86411	−0.0739168
$637$	−12.7548	−0.505363
$638$	−0.608285	−0.0240822
$639$	14.8569	0.587729
$640$	−36.2984	−1.43482
$641$	−2.41675	−0.0954559	−0.0477280	−	0.998860i	$-0.515198\pi$
$641$	−2.41675	−0.0954559	−0.0477280	+	0.998860i	$0.515198\pi$
$642$	11.4433	0.451630
$643$	37.6211	1.48363	0.741815	−	0.670604i	$-0.233965\pi$
$643$	37.6211	1.48363	0.741815	+	0.670604i	$0.233965\pi$
$644$	12.6410	0.498124
$645$	14.7449	0.580581
$646$	107.099	4.21375
$647$	−28.1648	−1.10727	−0.553637	−	0.832758i	$-0.686761\pi$
$647$	−28.1648	−1.10727	−0.553637	+	0.832758i	$0.686761\pi$
$648$	−8.22811	−0.323231
$649$	−52.5273	−2.06188
$650$	8.88708	0.348580
$651$	41.4475	1.62446
$652$	−44.2620	−1.73343
$653$	−36.5444	−1.43009	−0.715046	−	0.699077i	$-0.753594\pi$
$653$	−36.5444	−1.43009	−0.715046	+	0.699077i	$0.753594\pi$
$654$	24.3314	0.951435
$655$	−8.33057	−0.325502
$656$	−123.832	−4.83482
$657$	−3.15258	−0.122994
$658$	−8.62278	−0.336151
$659$	−14.0601	−0.547703	−0.273852	−	0.961772i	$-0.588298\pi$
$659$	−14.0601	−0.547703	−0.273852	+	0.961772i	$0.588298\pi$
$660$	−51.5206	−2.00544
$661$	28.6753	1.11534	0.557669	−	0.830063i	$-0.311696\pi$
$661$	28.6753	1.11534	0.557669	+	0.830063i	$0.311696\pi$
$662$	59.9769	2.33107
$663$	6.17457	0.239800
$664$	125.758	4.88035
$665$	86.4692	3.35313
$666$	9.08385	0.351992
$667$	−0.0367260	−0.00142204
$668$	24.0496	0.930508
$669$	−6.04974	−0.233896
$670$	−69.6189	−2.68961
$671$	24.0011	0.926551
$672$	−64.2289	−2.47768
$673$	−33.6452	−1.29693	−0.648464	−	0.761245i	$-0.724588\pi$
$673$	−33.6452	−1.29693	−0.648464	+	0.761245i	$0.724588\pi$
$674$	−40.3936	−1.55590
$675$	−3.11337	−0.119834
$676$	−60.3217	−2.32007
$677$	−35.2352	−1.35420	−0.677100	−	0.735891i	$-0.736763\pi$
$677$	−35.2352	−1.35420	−0.677100	+	0.735891i	$0.736763\pi$
$678$	−29.9845	−1.15155
$679$	−56.1774	−2.15589
$680$	−134.991	−5.17667
$681$	−13.6981	−0.524914
$682$	−90.2135	−3.45445
$683$	−13.6994	−0.524194	−0.262097	−	0.965042i	$-0.584414\pi$
$683$	−13.6994	−0.524194	−0.262097	+	0.965042i	$0.584414\pi$
$684$	−35.5452	−1.35911
$685$	−44.2122	−1.68926
$686$	56.6950	2.16462
$687$	11.1291	0.424603
$688$	−60.7159	−2.31477
$689$	−0.392597	−0.0149568
$690$	−4.33285	−0.164949
$691$	21.9000	0.833116	0.416558	−	0.909109i	$-0.363236\pi$
$691$	21.9000	0.833116	0.416558	+	0.909109i	$0.363236\pi$
$692$	−7.47261	−0.284066
$693$	−15.4476	−0.586805
$694$	77.9138	2.95757
$695$	−34.3495	−1.30295
$696$	0.528965	0.0200504
$697$	−60.8101	−2.30335
$698$	−73.4661	−2.78073
$699$	3.47264	0.131347
$700$	−68.8913	−2.60385
$701$	−41.7855	−1.57821	−0.789107	−	0.614255i	$-0.789457\pi$
$701$	−41.7855	−1.57821	−0.789107	+	0.614255i	$0.789457\pi$
$702$	−2.85449	−0.107736
$703$	23.8231	0.898504
$704$	56.4413	2.12721
$705$	2.12185	0.0799134
$706$	−12.4763	−0.469551
$707$	59.1160	2.22329
$708$	75.2417	2.82776
$709$	−30.0636	−1.12906	−0.564531	−	0.825412i	$-0.690943\pi$
$709$	−30.0636	−1.12906	−0.564531	+	0.825412i	$0.690943\pi$
$710$	−112.682	−4.22888
$711$	8.99966	0.337514
$712$	−119.182	−4.46654
$713$	−5.44676	−0.203983
$714$	−66.6711	−2.49510
$715$	−10.8507	−0.405792
$716$	−1.08521	−0.0405562
$717$	23.6765	0.884214
$718$	−49.7128	−1.85527
$719$	−8.02946	−0.299448	−0.149724	−	0.988728i	$-0.547839\pi$
$719$	−8.02946	−0.299448	−0.149724	+	0.988728i	$0.547839\pi$
$720$	33.4088	1.24507
$721$	69.4291	2.58567
$722$	−79.2560	−2.94960
$723$	4.45549	0.165702
$724$	109.910	4.08477
$725$	0.200151	0.00743341
$726$	4.33279	0.160805
$727$	−23.1851	−0.859888	−0.429944	−	0.902856i	$-0.641467\pi$
$727$	−23.1851	−0.859888	−0.429944	+	0.902856i	$0.641467\pi$
$728$	−38.3451	−1.42116
$729$	1.00000	0.0370370
$730$	23.9107	0.884975
$731$	−29.8158	−1.10278
$732$	−34.3799	−1.27072
$733$	−51.1621	−1.88972	−0.944858	−	0.327480i	$-0.893801\pi$
$733$	−51.1621	−1.88972	−0.944858	+	0.327480i	$0.893801\pi$
$734$	72.0606	2.65980
$735$	−33.8900	−1.25005
$736$	8.44053	0.311122
$737$	32.6177	1.20149
$738$	28.1124	1.03483
$739$	2.75596	0.101380	0.0506898	−	0.998714i	$-0.483858\pi$
$739$	2.75596	0.101380	0.0506898	+	0.998714i	$0.483858\pi$
$740$	−49.4619	−1.81826
$741$	−7.48612	−0.275009
$742$	4.23914	0.155624
$743$	−50.7610	−1.86224	−0.931120	−	0.364714i	$-0.881167\pi$
$743$	−50.7610	−1.86224	−0.931120	+	0.364714i	$0.881167\pi$
$744$	78.4498	2.87611
$745$	26.6064	0.974783
$746$	5.02119	0.183839
$747$	−15.2839	−0.559209
$748$	104.180	3.80920
$749$	−18.6823	−0.682637
$750$	−14.3092	−0.522497
$751$	−15.9996	−0.583833	−0.291916	−	0.956444i	$-0.594293\pi$
$751$	−15.9996	−0.583833	−0.291916	+	0.956444i	$0.594293\pi$
$752$	−8.73724	−0.318614
$753$	−26.9526	−0.982207
$754$	0.183508	0.00668298
$755$	−28.3737	−1.03263
$756$	22.1276	0.804772
$757$	−2.92654	−0.106367	−0.0531835	−	0.998585i	$-0.516937\pi$
$757$	−2.92654	−0.106367	−0.0531835	+	0.998585i	$0.516937\pi$
$758$	6.83632	0.248306
$759$	2.03002	0.0736850
$760$	163.665	5.93674
$761$	−52.6167	−1.90736	−0.953678	−	0.300830i	$-0.902736\pi$
$761$	−52.6167	−1.90736	−0.953678	+	0.300830i	$0.902736\pi$
$762$	−44.4652	−1.61080
$763$	−39.7236	−1.43809
$764$	−22.9246	−0.829382
$765$	16.4061	0.593163
$766$	3.45006	0.124656
$767$	15.8465	0.572185
$768$	−2.16551	−0.0781413
$769$	30.7416	1.10857	0.554285	−	0.832327i	$-0.312992\pi$
$769$	30.7416	1.10857	0.554285	+	0.832327i	$0.312992\pi$
$770$	117.162	4.22223
$771$	−16.0368	−0.577552
$772$	26.2176	0.943592
$773$	24.1381	0.868187	0.434093	−	0.900868i	$-0.357069\pi$
$773$	24.1381	0.868187	0.434093	+	0.900868i	$0.357069\pi$
$774$	13.7838	0.495448
$775$	29.6840	1.06628
$776$	−106.330	−3.81702
$777$	−14.8303	−0.532035
$778$	−28.1200	−1.00815
$779$	73.7269	2.64154
$780$	15.5428	0.556523
$781$	52.7936	1.88910
$782$	8.76147	0.313310
$783$	−0.0642876	−0.00229745
$784$	139.551	4.98395
$785$	−12.4215	−0.443343
$786$	−7.78755	−0.277773
$787$	35.3685	1.26075	0.630375	−	0.776291i	$-0.282901\pi$
$787$	35.3685	1.26075	0.630375	+	0.776291i	$0.282901\pi$
$788$	128.567	4.58001
$789$	22.0628	0.785456
$790$	−68.2579	−2.42851
$791$	48.9528	1.74056
$792$	−29.2384	−1.03894
$793$	−7.24069	−0.257124
$794$	−32.2586	−1.14481
$795$	−1.04315	−0.0369966
$796$	8.69694	0.308255
$797$	11.8540	0.419892	0.209946	−	0.977713i	$-0.432671\pi$
$797$	11.8540	0.419892	0.209946	+	0.977713i	$0.432671\pi$
$798$	80.8328	2.86145
$799$	−4.29060	−0.151791
$800$	−45.9995	−1.62633
$801$	14.4848	0.511794
$802$	83.1134	2.93484
$803$	−11.2026	−0.395331
$804$	−46.7226	−1.64778
$805$	7.07382	0.249319
$806$	27.2158	0.958634
$807$	15.8904	0.559369
$808$	111.892	3.93634
$809$	32.1451	1.13016	0.565080	−	0.825036i	$-0.308845\pi$
$809$	32.1451	1.13016	0.565080	+	0.825036i	$0.308845\pi$
$810$	−7.58450	−0.266492
$811$	−29.1785	−1.02460	−0.512298	−	0.858808i	$-0.671206\pi$
$811$	−29.1785	−1.02460	−0.512298	+	0.858808i	$0.671206\pi$
$812$	−1.42253	−0.0499210
$813$	−24.6598	−0.864856
$814$	32.2792	1.13139
$815$	−24.7688	−0.867613
$816$	−67.5561	−2.36494
$817$	36.1490	1.26469
$818$	29.8060	1.04214
$819$	4.66025	0.162842
$820$	−153.073	−5.34555
$821$	19.9017	0.694574	0.347287	−	0.937759i	$-0.387103\pi$
$821$	19.9017	0.694574	0.347287	+	0.937759i	$0.387103\pi$
$822$	−41.3303	−1.44156
$823$	−29.3478	−1.02300	−0.511501	−	0.859283i	$-0.670910\pi$
$823$	−29.3478	−1.02300	−0.511501	+	0.859283i	$0.670910\pi$
$824$	131.412	4.57795
$825$	−11.0633	−0.385174
$826$	−171.106	−5.95353
$827$	−9.77351	−0.339858	−0.169929	−	0.985456i	$-0.554354\pi$
$827$	−9.77351	−0.339858	−0.169929	+	0.985456i	$0.554354\pi$
$828$	−2.90786	−0.101055
$829$	−16.2649	−0.564903	−0.282452	−	0.959282i	$-0.591148\pi$
$829$	−16.2649	−0.564903	−0.282452	+	0.959282i	$0.591148\pi$
$830$	115.921	4.02367
$831$	13.1663	0.456733
$832$	−17.0273	−0.590316
$833$	68.5291	2.37439
$834$	−32.1105	−1.11189
$835$	13.4580	0.465735
$836$	−126.309	−4.36849
$837$	−9.53436	−0.329556
$838$	40.1208	1.38595
$839$	16.8224	0.580773	0.290386	−	0.956909i	$-0.406216\pi$
$839$	16.8224	0.580773	0.290386	+	0.956909i	$0.406216\pi$
$840$	−101.884	−3.51535
$841$	−28.9959	−0.999857
$842$	−51.2294	−1.76548
$843$	−8.93464	−0.307725
$844$	48.1923	1.65885
$845$	−33.7557	−1.16123
$846$	1.98354	0.0681954
$847$	−7.07372	−0.243056
$848$	4.29541	0.147505
$849$	17.4049	0.597334
$850$	−47.7486	−1.63776
$851$	1.94890	0.0668075
$852$	−75.6231	−2.59080
$853$	25.4459	0.871252	0.435626	−	0.900128i	$-0.356527\pi$
$853$	25.4459	0.871252	0.435626	+	0.900128i	$0.356527\pi$
$854$	78.1827	2.67536
$855$	−19.8909	−0.680255
$856$	−35.3609	−1.20861
$857$	−29.4112	−1.00467	−0.502334	−	0.864674i	$-0.667525\pi$
$857$	−29.4112	−1.00467	−0.502334	+	0.864674i	$0.667525\pi$
$858$	−10.1434	−0.346289
$859$	−13.9406	−0.475647	−0.237824	−	0.971308i	$-0.576434\pi$
$859$	−13.9406	−0.475647	−0.237824	+	0.971308i	$0.576434\pi$
$860$	−75.0532	−2.55929
$861$	−45.8964	−1.56415
$862$	79.0091	2.69106
$863$	22.0492	0.750562	0.375281	−	0.926911i	$-0.377546\pi$
$863$	22.0492	0.750562	0.375281	+	0.926911i	$0.377546\pi$
$864$	14.7749	0.502651
$865$	−4.18163	−0.142180
$866$	−53.2785	−1.81048
$867$	−16.1748	−0.549325
$868$	−210.972	−7.16087
$869$	31.9801	1.08485
$870$	0.487589	0.0165308
$871$	−9.84018	−0.333422
$872$	−75.1868	−2.54615
$873$	12.9227	0.437369
$874$	−10.6225	−0.359311
$875$	23.3612	0.789753
$876$	16.0470	0.542176
$877$	−1.94973	−0.0658377	−0.0329188	−	0.999458i	$-0.510480\pi$
$877$	−1.94973	−0.0658377	−0.0329188	+	0.999458i	$0.510480\pi$
$878$	−34.5037	−1.16444
$879$	−15.8313	−0.533977
$880$	118.717	4.00197
$881$	−52.1959	−1.75852	−0.879262	−	0.476338i	$-0.841964\pi$
$881$	−52.1959	−1.75852	−0.879262	+	0.476338i	$0.841964\pi$
$882$	−31.6809	−1.06675
$883$	50.3914	1.69581	0.847903	−	0.530151i	$-0.177865\pi$
$883$	50.3914	1.69581	0.847903	+	0.530151i	$0.177865\pi$
$884$	−31.4292	−1.05708
$885$	42.1048	1.41534
$886$	−99.2619	−3.33477
$887$	−9.21536	−0.309422	−0.154711	−	0.987960i	$-0.549445\pi$
$887$	−9.21536	−0.309422	−0.154711	+	0.987960i	$0.549445\pi$
$888$	−28.0701	−0.941970
$889$	72.5940	2.43472
$890$	−109.860	−3.68250
$891$	3.55348	0.119046
$892$	30.7938	1.03105
$893$	5.20197	0.174077
$894$	24.8721	0.831846
$895$	−0.607278	−0.0202991
$896$	55.3980	1.85072
$897$	−0.612419	−0.0204481
$898$	31.5787	1.05379
$899$	0.612941	0.0204427
$900$	15.8474	0.528246
$901$	2.10935	0.0702727
$902$	99.8968	3.32620
$903$	−22.5034	−0.748868
$904$	92.6554	3.08167
$905$	61.5050	2.04450
$906$	−26.5242	−0.881208
$907$	7.43189	0.246772	0.123386	−	0.992359i	$-0.460625\pi$
$907$	7.43189	0.246772	0.123386	+	0.992359i	$0.460625\pi$
$908$	69.7250	2.31391
$909$	−13.5987	−0.451041
$910$	−35.3457	−1.17170
$911$	−11.1195	−0.368406	−0.184203	−	0.982888i	$-0.558970\pi$
$911$	−11.1195	−0.368406	−0.184203	+	0.982888i	$0.558970\pi$
$912$	81.9058	2.71217
$913$	−54.3111	−1.79743
$914$	7.47439	0.247231
$915$	−19.2388	−0.636015
$916$	−56.6485	−1.87172
$917$	12.7140	0.419852
$918$	15.3367	0.506185
$919$	17.2501	0.569029	0.284515	−	0.958672i	$-0.408168\pi$
$919$	17.2501	0.569029	0.284515	+	0.958672i	$0.408168\pi$
$920$	13.3890	0.441421
$921$	−4.36223	−0.143740
$922$	95.4604	3.14382
$923$	−15.9269	−0.524239
$924$	78.6299	2.58673
$925$	−10.6212	−0.349223
$926$	56.9014	1.86990
$927$	−15.9711	−0.524559
$928$	−0.949840	−0.0311800
$929$	−54.0161	−1.77221	−0.886106	−	0.463482i	$-0.846600\pi$
$929$	−54.0161	−1.77221	−0.886106	+	0.463482i	$0.846600\pi$
$930$	72.3134	2.37125
$931$	−83.0854	−2.72302
$932$	−17.6761	−0.579001
$933$	23.8792	0.781771
$934$	81.0457	2.65190
$935$	58.2986	1.90657
$936$	8.82069	0.288313
$937$	18.3359	0.599006	0.299503	−	0.954095i	$-0.403179\pi$
$937$	18.3359	0.599006	0.299503	+	0.954095i	$0.403179\pi$
$938$	106.251	3.46922
$939$	12.6256	0.412022
$940$	−10.8004	−0.352272
$941$	−37.6921	−1.22873	−0.614363	−	0.789023i	$-0.710587\pi$
$941$	−37.6921	−1.22873	−0.614363	+	0.789023i	$0.710587\pi$
$942$	−11.6118	−0.378334
$943$	6.03140	0.196409
$944$	−173.377	−5.64295
$945$	12.3825	0.402802
$946$	48.9804	1.59249
$947$	−3.85674	−0.125327	−0.0626636	−	0.998035i	$-0.519960\pi$
$947$	−3.85674	−0.125327	−0.0626636	+	0.998035i	$0.519960\pi$
$948$	−45.8092	−1.48782
$949$	3.37962	0.109707
$950$	57.8910	1.87823
$951$	4.26965	0.138453
$952$	206.021	6.67718
$953$	−44.7465	−1.44948	−0.724741	−	0.689021i	$-0.758041\pi$
$953$	−44.7465	−1.44948	−0.724741	+	0.689021i	$0.758041\pi$
$954$	−0.975149	−0.0315716
$955$	−12.8285	−0.415119
$956$	−120.516	−3.89776
$957$	−0.228444	−0.00738456
$958$	−40.7258	−1.31579
$959$	67.4759	2.17891
$960$	−45.2423	−1.46019
$961$	59.9040	1.93239
$962$	−9.73806	−0.313968
$963$	4.29758	0.138487
$964$	−22.6789	−0.730439
$965$	14.6712	0.472283
$966$	6.61271	0.212761
$967$	−7.80984	−0.251147	−0.125574	−	0.992084i	$-0.540077\pi$
$967$	−7.80984	−0.251147	−0.125574	+	0.992084i	$0.540077\pi$
$968$	−13.3888	−0.430332
$969$	40.2215	1.29210
$970$	−98.0126	−3.14699
$971$	−27.6428	−0.887100	−0.443550	−	0.896250i	$-0.646281\pi$
$971$	−27.6428	−0.887100	−0.443550	+	0.896250i	$0.646281\pi$
$972$	−5.09011	−0.163265
$973$	52.4236	1.68062
$974$	−4.23905	−0.135828
$975$	3.33759	0.106888
$976$	79.2205	2.53579
$977$	−10.2098	−0.326639	−0.163319	−	0.986573i	$-0.552220\pi$
$977$	−10.2098	−0.326639	−0.163319	+	0.986573i	$0.552220\pi$
$978$	−23.1542	−0.740391
$979$	51.4712	1.64503
$980$	172.504	5.51043
$981$	9.13779	0.291747
$982$	89.5305	2.85703
$983$	−3.67559	−0.117233	−0.0586166	−	0.998281i	$-0.518669\pi$
$983$	−3.67559	−0.117233	−0.0586166	+	0.998281i	$0.518669\pi$
$984$	−86.8704	−2.76933
$985$	71.9454	2.29237
$986$	−0.985956	−0.0313993
$987$	−3.23833	−0.103077
$988$	38.1051	1.21229
$989$	2.95725	0.0940351
$990$	−26.9514	−0.856570
$991$	3.63244	0.115388	0.0576941	−	0.998334i	$-0.481625\pi$
$991$	3.63244	0.115388	0.0576941	+	0.998334i	$0.481625\pi$
$992$	−140.869	−4.47259
$993$	22.5246	0.714797
$994$	171.973	5.45466
$995$	4.86676	0.154287
$996$	77.7968	2.46509
$997$	25.7046	0.814072	0.407036	−	0.913412i	$-0.366562\pi$
$997$	25.7046	0.814072	0.407036	+	0.913412i	$0.366562\pi$
$998$	70.9478	2.24581
$999$	3.41148	0.107935

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.d.1.4	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.d.1.4	✓	84	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66273 q^{2} -1.00000 q^{3} +5.09011 q^{4} +2.84840 q^{5} +2.66273 q^{6} -4.34717 q^{7} -8.22811 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.66273 q^{2} -1.00000 q^{3} +5.09011 q^{4} +2.84840 q^{5} +2.66273 q^{6} -4.34717 q^{7} -8.22811 q^{8} +1.00000 q^{9} -7.58450 q^{10} +3.55348 q^{11} -5.09011 q^{12} -1.07202 q^{13} +11.5753 q^{14} -2.84840 q^{15} +11.7290 q^{16} +5.75976 q^{17} -2.66273 q^{18} -6.98319 q^{19} +14.4987 q^{20} +4.34717 q^{21} -9.46194 q^{22} -0.571276 q^{23} +8.22811 q^{24} +3.11337 q^{25} +2.85449 q^{26} -1.00000 q^{27} -22.1276 q^{28} +0.0642876 q^{29} +7.58450 q^{30} +9.53436 q^{31} -14.7749 q^{32} -3.55348 q^{33} -15.3367 q^{34} -12.3825 q^{35} +5.09011 q^{36} -3.41148 q^{37} +18.5943 q^{38} +1.07202 q^{39} -23.4369 q^{40} -10.5578 q^{41} -11.5753 q^{42} -5.17657 q^{43} +18.0876 q^{44} +2.84840 q^{45} +1.52115 q^{46} -0.744927 q^{47} -11.7290 q^{48} +11.8979 q^{49} -8.29004 q^{50} -5.75976 q^{51} -5.45669 q^{52} +0.366222 q^{53} +2.66273 q^{54} +10.1217 q^{55} +35.7690 q^{56} +6.98319 q^{57} -0.171180 q^{58} -14.7819 q^{59} -14.4987 q^{60} +6.75425 q^{61} -25.3874 q^{62} -4.34717 q^{63} +15.8834 q^{64} -3.05354 q^{65} +9.46194 q^{66} +9.17911 q^{67} +29.3178 q^{68} +0.571276 q^{69} +32.9711 q^{70} +14.8569 q^{71} -8.22811 q^{72} -3.15258 q^{73} +9.08385 q^{74} -3.11337 q^{75} -35.5452 q^{76} -15.4476 q^{77} -2.85449 q^{78} +8.99966 q^{79} +33.4088 q^{80} +1.00000 q^{81} +28.1124 q^{82} -15.2839 q^{83} +22.1276 q^{84} +16.4061 q^{85} +13.7838 q^{86} -0.0642876 q^{87} -29.2384 q^{88} +14.4848 q^{89} -7.58450 q^{90} +4.66025 q^{91} -2.90786 q^{92} -9.53436 q^{93} +1.98354 q^{94} -19.8909 q^{95} +14.7749 q^{96} +12.9227 q^{97} -31.6809 q^{98} +3.55348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9}+O(q^{10}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9	\( 84 q - 13 q^{2} - 84 q^{3} + 81 q^{4} - 10 q^{5} + 13 q^{6} - 32 q^{7} - 39 q^{8} + 84 q^{9} + 13 q^{10} - 20 q^{11} - 81 q^{12} + 7 q^{13} - 9 q^{14} + 10 q^{15} + 83 q^{16} - 39 q^{17} - 13 q^{18} + 13 q^{19} - 26 q^{20} + 32 q^{21} - 21 q^{22} - 93 q^{23} + 39 q^{24} + 66 q^{25} - 34 q^{26} - 84 q^{27} - 59 q^{28} - 39 q^{29} - 13 q^{30} + 8 q^{31} - 96 q^{32} + 20 q^{33} - 69 q^{35} + 81 q^{36} + 6 q^{37} - 59 q^{38} - 7 q^{39} + 28 q^{40} - 23 q^{41} + 9 q^{42} - 74 q^{43} - 43 q^{44} - 10 q^{45} - 6 q^{46} - 77 q^{47} - 83 q^{48} + 100 q^{49} - 74 q^{50} + 39 q^{51} - 44 q^{52} - 66 q^{53} + 13 q^{54} - 60 q^{55} - 31 q^{56} - 13 q^{57} - 39 q^{58} - 36 q^{59} + 26 q^{60} + 104 q^{61} - 53 q^{62} - 32 q^{63} + 85 q^{64} - 47 q^{65} + 21 q^{66} - 65 q^{67} - 118 q^{68} + 93 q^{69} - 3 q^{70} - 68 q^{71} - 39 q^{72} + 8 q^{73} - 30 q^{74} - 66 q^{75} + 71 q^{76} - 83 q^{77} + 34 q^{78} - 24 q^{79} - 67 q^{80} + 84 q^{81} - 9 q^{82} - 95 q^{83} + 59 q^{84} + 24 q^{85} - 32 q^{86} + 39 q^{87} - 65 q^{88} - 44 q^{89} + 13 q^{90} + 8 q^{91} - 184 q^{92} - 8 q^{93} + 61 q^{94} - 153 q^{95} + 96 q^{96} + 19 q^{97} - 67 q^{98} - 20 q^{99}+O(q^{100}) \) 84 * q - 13 * q^2 - 84 * q^3 + 81 * q^4 - 10 * q^5 + 13 * q^6 - 32 * q^7 - 39 * q^8 + 84 * q^9 + 13 * q^10 - 20 * q^11 - 81 * q^12 + 7 * q^13 - 9 * q^14 + 10 * q^15 + 83 * q^16 - 39 * q^17 - 13 * q^18 + 13 * q^19 - 26 * q^20 + 32 * q^21 - 21 * q^22 - 93 * q^23 + 39 * q^24 + 66 * q^25 - 34 * q^26 - 84 * q^27 - 59 * q^28 - 39 * q^29 - 13 * q^30 + 8 * q^31 - 96 * q^32 + 20 * q^33 - 69 * q^35 + 81 * q^36 + 6 * q^37 - 59 * q^38 - 7 * q^39 + 28 * q^40 - 23 * q^41 + 9 * q^42 - 74 * q^43 - 43 * q^44 - 10 * q^45 - 6 * q^46 - 77 * q^47 - 83 * q^48 + 100 * q^49 - 74 * q^50 + 39 * q^51 - 44 * q^52 - 66 * q^53 + 13 * q^54 - 60 * q^55 - 31 * q^56 - 13 * q^57 - 39 * q^58 - 36 * q^59 + 26 * q^60 + 104 * q^61 - 53 * q^62 - 32 * q^63 + 85 * q^64 - 47 * q^65 + 21 * q^66 - 65 * q^67 - 118 * q^68 + 93 * q^69 - 3 * q^70 - 68 * q^71 - 39 * q^72 + 8 * q^73 - 30 * q^74 - 66 * q^75 + 71 * q^76 - 83 * q^77 + 34 * q^78 - 24 * q^79 - 67 * q^80 + 84 * q^81 - 9 * q^82 - 95 * q^83 + 59 * q^84 + 24 * q^85 - 32 * q^86 + 39 * q^87 - 65 * q^88 - 44 * q^89 + 13 * q^90 + 8 * q^91 - 184 * q^92 - 8 * q^93 + 61 * q^94 - 153 * q^95 + 96 * q^96 + 19 * q^97 - 67 * q^98 - 20 * q^99

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