LMFDB - Embedded newform 6026.2.a.m.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.356133 q^{3} +1.00000 q^{4} +3.98743 q^{5} -0.356133 q^{6} +1.62862 q^{7} +1.00000 q^{8} -2.87317 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.356133 q^{3} +1.00000 q^{4} +3.98743 q^{5} -0.356133 q^{6} +1.62862 q^{7} +1.00000 q^{8} -2.87317 q^{9} +3.98743 q^{10} +2.63756 q^{11} -0.356133 q^{12} +6.02374 q^{13} +1.62862 q^{14} -1.42006 q^{15} +1.00000 q^{16} -0.903922 q^{17} -2.87317 q^{18} +4.65419 q^{19} +3.98743 q^{20} -0.580006 q^{21} +2.63756 q^{22} +1.00000 q^{23} -0.356133 q^{24} +10.8996 q^{25} +6.02374 q^{26} +2.09163 q^{27} +1.62862 q^{28} +0.600851 q^{29} -1.42006 q^{30} -1.99192 q^{31} +1.00000 q^{32} -0.939322 q^{33} -0.903922 q^{34} +6.49403 q^{35} -2.87317 q^{36} -8.50454 q^{37} +4.65419 q^{38} -2.14525 q^{39} +3.98743 q^{40} -2.47178 q^{41} -0.580006 q^{42} +4.11077 q^{43} +2.63756 q^{44} -11.4566 q^{45} +1.00000 q^{46} -2.46140 q^{47} -0.356133 q^{48} -4.34759 q^{49} +10.8996 q^{50} +0.321916 q^{51} +6.02374 q^{52} -7.94078 q^{53} +2.09163 q^{54} +10.5171 q^{55} +1.62862 q^{56} -1.65751 q^{57} +0.600851 q^{58} +0.448619 q^{59} -1.42006 q^{60} -0.851838 q^{61} -1.99192 q^{62} -4.67931 q^{63} +1.00000 q^{64} +24.0193 q^{65} -0.939322 q^{66} -7.36349 q^{67} -0.903922 q^{68} -0.356133 q^{69} +6.49403 q^{70} -2.42936 q^{71} -2.87317 q^{72} +7.80010 q^{73} -8.50454 q^{74} -3.88171 q^{75} +4.65419 q^{76} +4.29560 q^{77} -2.14525 q^{78} -9.01101 q^{79} +3.98743 q^{80} +7.87461 q^{81} -2.47178 q^{82} -13.4154 q^{83} -0.580006 q^{84} -3.60433 q^{85} +4.11077 q^{86} -0.213982 q^{87} +2.63756 q^{88} +2.73259 q^{89} -11.4566 q^{90} +9.81040 q^{91} +1.00000 q^{92} +0.709389 q^{93} -2.46140 q^{94} +18.5583 q^{95} -0.356133 q^{96} -17.5738 q^{97} -4.34759 q^{98} -7.57816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.356133	−0.205613	−0.102807	−	0.994701i	$-0.532782\pi$
$3$	−0.356133	−0.205613	−0.102807	+	0.994701i	$0.532782\pi$
$4$	1.00000	0.500000
$5$	3.98743	1.78324	0.891618	−	0.452789i	$-0.149571\pi$
$5$	3.98743	1.78324	0.891618	+	0.452789i	$0.149571\pi$
$6$	−0.356133	−0.145390
$7$	1.62862	0.615562	0.307781	−	0.951457i	$-0.400414\pi$
$7$	1.62862	0.615562	0.307781	+	0.951457i	$0.400414\pi$
$8$	1.00000	0.353553
$9$	−2.87317	−0.957723
$10$	3.98743	1.26094
$11$	2.63756	0.795255	0.397627	−	0.917547i	$-0.369834\pi$
$11$	2.63756	0.795255	0.397627	+	0.917547i	$0.369834\pi$
$12$	−0.356133	−0.102807
$13$	6.02374	1.67068	0.835342	−	0.549730i	$-0.185270\pi$
$13$	6.02374	1.67068	0.835342	+	0.549730i	$0.185270\pi$
$14$	1.62862	0.435268
$15$	−1.42006	−0.366657
$16$	1.00000	0.250000
$17$	−0.903922	−0.219233	−0.109617	−	0.993974i	$-0.534962\pi$
$17$	−0.903922	−0.219233	−0.109617	+	0.993974i	$0.534962\pi$
$18$	−2.87317	−0.677213
$19$	4.65419	1.06775	0.533873	−	0.845565i	$-0.320736\pi$
$19$	4.65419	1.06775	0.533873	+	0.845565i	$0.320736\pi$
$20$	3.98743	0.891618
$21$	−0.580006	−0.126568
$22$	2.63756	0.562330
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.356133	−0.0726952
$25$	10.8996	2.17993
$26$	6.02374	1.18135
$27$	2.09163	0.402534
$28$	1.62862	0.307781
$29$	0.600851	0.111575	0.0557876	−	0.998443i	$-0.482233\pi$
$29$	0.600851	0.111575	0.0557876	+	0.998443i	$0.482233\pi$
$30$	−1.42006	−0.259265
$31$	−1.99192	−0.357760	−0.178880	−	0.983871i	$-0.557247\pi$
$31$	−1.99192	−0.357760	−0.178880	+	0.983871i	$0.557247\pi$
$32$	1.00000	0.176777
$33$	−0.939322	−0.163515
$34$	−0.903922	−0.155021
$35$	6.49403	1.09769
$36$	−2.87317	−0.478862
$37$	−8.50454	−1.39814	−0.699069	−	0.715054i	$-0.746402\pi$
$37$	−8.50454	−1.39814	−0.699069	+	0.715054i	$0.746402\pi$
$38$	4.65419	0.755010
$39$	−2.14525	−0.343515
$40$	3.98743	0.630469
$41$	−2.47178	−0.386027	−0.193013	−	0.981196i	$-0.561826\pi$
$41$	−2.47178	−0.386027	−0.193013	+	0.981196i	$0.561826\pi$
$42$	−0.580006	−0.0894968
$43$	4.11077	0.626887	0.313444	−	0.949607i	$-0.398517\pi$
$43$	4.11077	0.626887	0.313444	+	0.949607i	$0.398517\pi$
$44$	2.63756	0.397627
$45$	−11.4566	−1.70785
$46$	1.00000	0.147442
$47$	−2.46140	−0.359032	−0.179516	−	0.983755i	$-0.557453\pi$
$47$	−2.46140	−0.359032	−0.179516	+	0.983755i	$0.557453\pi$
$48$	−0.356133	−0.0514033
$49$	−4.34759	−0.621084
$50$	10.8996	1.54144
$51$	0.321916	0.0450773
$52$	6.02374	0.835342
$53$	−7.94078	−1.09075	−0.545375	−	0.838192i	$-0.683613\pi$
$53$	−7.94078	−1.09075	−0.545375	+	0.838192i	$0.683613\pi$
$54$	2.09163	0.284634
$55$	10.5171	1.41813
$56$	1.62862	0.217634
$57$	−1.65751	−0.219543
$58$	0.600851	0.0788955
$59$	0.448619	0.0584053	0.0292026	−	0.999574i	$-0.490703\pi$
$59$	0.448619	0.0584053	0.0292026	+	0.999574i	$0.490703\pi$
$60$	−1.42006	−0.183328
$61$	−0.851838	−0.109067	−0.0545333	−	0.998512i	$-0.517367\pi$
$61$	−0.851838	−0.109067	−0.0545333	+	0.998512i	$0.517367\pi$
$62$	−1.99192	−0.252975
$63$	−4.67931	−0.589538
$64$	1.00000	0.125000
$65$	24.0193	2.97922
$66$	−0.939322	−0.115623
$67$	−7.36349	−0.899594	−0.449797	−	0.893131i	$-0.648504\pi$
$67$	−7.36349	−0.899594	−0.449797	+	0.893131i	$0.648504\pi$
$68$	−0.903922	−0.109617
$69$	−0.356133	−0.0428733
$70$	6.49403	0.776185
$71$	−2.42936	−0.288312	−0.144156	−	0.989555i	$-0.546047\pi$
$71$	−2.42936	−0.288312	−0.144156	+	0.989555i	$0.546047\pi$
$72$	−2.87317	−0.338606
$73$	7.80010	0.912932	0.456466	−	0.889741i	$-0.349115\pi$
$73$	7.80010	0.912932	0.456466	+	0.889741i	$0.349115\pi$
$74$	−8.50454	−0.988633
$75$	−3.88171	−0.448222
$76$	4.65419	0.533873
$77$	4.29560	0.489529
$78$	−2.14525	−0.242902
$79$	−9.01101	−1.01382	−0.506909	−	0.862000i	$-0.669212\pi$
$79$	−9.01101	−1.01382	−0.506909	+	0.862000i	$0.669212\pi$
$80$	3.98743	0.445809
$81$	7.87461	0.874957
$82$	−2.47178	−0.272962
$83$	−13.4154	−1.47253	−0.736264	−	0.676695i	$-0.763412\pi$
$83$	−13.4154	−1.47253	−0.736264	+	0.676695i	$0.763412\pi$
$84$	−0.580006	−0.0632838
$85$	−3.60433	−0.390945
$86$	4.11077	0.443276
$87$	−0.213982	−0.0229413
$88$	2.63756	0.281165
$89$	2.73259	0.289654	0.144827	−	0.989457i	$-0.453737\pi$
$89$	2.73259	0.289654	0.144827	+	0.989457i	$0.453737\pi$
$90$	−11.4566	−1.20763
$91$	9.81040	1.02841
$92$	1.00000	0.104257
$93$	0.709389	0.0735602
$94$	−2.46140	−0.253874
$95$	18.5583	1.90404
$96$	−0.356133	−0.0363476
$97$	−17.5738	−1.78435	−0.892173	−	0.451694i	$-0.850820\pi$
$97$	−17.5738	−1.78435	−0.892173	+	0.451694i	$0.850820\pi$
$98$	−4.34759	−0.439173
$99$	−7.57816	−0.761634
$100$	10.8996	1.08996
$101$	−6.92774	−0.689336	−0.344668	−	0.938725i	$-0.612008\pi$
$101$	−6.92774	−0.689336	−0.344668	+	0.938725i	$0.612008\pi$
$102$	0.321916	0.0318745
$103$	7.26549	0.715890	0.357945	−	0.933743i	$-0.383478\pi$
$103$	7.26549	0.715890	0.357945	+	0.933743i	$0.383478\pi$
$104$	6.02374	0.590676
$105$	−2.31274	−0.225700
$106$	−7.94078	−0.771277
$107$	−6.78136	−0.655579	−0.327789	−	0.944751i	$-0.606304\pi$
$107$	−6.78136	−0.655579	−0.327789	+	0.944751i	$0.606304\pi$
$108$	2.09163	0.201267
$109$	11.4733	1.09895	0.549474	−	0.835511i	$-0.314828\pi$
$109$	11.4733	1.09895	0.549474	+	0.835511i	$0.314828\pi$
$110$	10.5171	1.00277
$111$	3.02874	0.287476
$112$	1.62862	0.153890
$113$	3.58170	0.336938	0.168469	−	0.985707i	$-0.446118\pi$
$113$	3.58170	0.336938	0.168469	+	0.985707i	$0.446118\pi$
$114$	−1.65751	−0.155240
$115$	3.98743	0.371830
$116$	0.600851	0.0557876
$117$	−17.3072	−1.60005
$118$	0.448619	0.0412988
$119$	−1.47215	−0.134952
$120$	−1.42006	−0.129633
$121$	−4.04327	−0.367570
$122$	−0.851838	−0.0771218
$123$	0.880280	0.0793722
$124$	−1.99192	−0.178880
$125$	23.5244	2.10409
$126$	−4.67931	−0.416866
$127$	16.0544	1.42460	0.712298	−	0.701877i	$-0.247654\pi$
$127$	16.0544	1.42460	0.712298	+	0.701877i	$0.247654\pi$
$128$	1.00000	0.0883883
$129$	−1.46398	−0.128896
$130$	24.0193	2.10663
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.939322	−0.0817575
$133$	7.57993	0.657263
$134$	−7.36349	−0.636109
$135$	8.34023	0.717812
$136$	−0.903922	−0.0775107
$137$	−15.7066	−1.34190	−0.670951	−	0.741501i	$-0.734114\pi$
$137$	−15.7066	−1.34190	−0.670951	+	0.741501i	$0.734114\pi$
$138$	−0.356133	−0.0303160
$139$	2.49471	0.211599	0.105799	−	0.994387i	$-0.466260\pi$
$139$	2.49471	0.211599	0.105799	+	0.994387i	$0.466260\pi$
$140$	6.49403	0.548846
$141$	0.876585	0.0738218
$142$	−2.42936	−0.203867
$143$	15.8880	1.32862
$144$	−2.87317	−0.239431
$145$	2.39585	0.198965
$146$	7.80010	0.645541
$147$	1.54832	0.127703
$148$	−8.50454	−0.699069
$149$	5.80283	0.475386	0.237693	−	0.971340i	$-0.423609\pi$
$149$	5.80283	0.475386	0.237693	+	0.971340i	$0.423609\pi$
$150$	−3.88171	−0.316941
$151$	6.20578	0.505019	0.252509	−	0.967594i	$-0.418744\pi$
$151$	6.20578	0.505019	0.252509	+	0.967594i	$0.418744\pi$
$152$	4.65419	0.377505
$153$	2.59712	0.209965
$154$	4.29560	0.346149
$155$	−7.94267	−0.637971
$156$	−2.14525	−0.171757
$157$	20.3960	1.62778	0.813891	−	0.581018i	$-0.197345\pi$
$157$	20.3960	1.62778	0.813891	+	0.581018i	$0.197345\pi$
$158$	−9.01101	−0.716877
$159$	2.82797	0.224273
$160$	3.98743	0.315234
$161$	1.62862	0.128353
$162$	7.87461	0.618688
$163$	−23.5667	−1.84589	−0.922945	−	0.384933i	$-0.874225\pi$
$163$	−23.5667	−1.84589	−0.922945	+	0.384933i	$0.874225\pi$
$164$	−2.47178	−0.193013
$165$	−3.74548	−0.291586
$166$	−13.4154	−1.04123
$167$	−15.6592	−1.21175	−0.605874	−	0.795560i	$-0.707177\pi$
$167$	−15.6592	−1.21175	−0.605874	+	0.795560i	$0.707177\pi$
$168$	−0.580006	−0.0447484
$169$	23.2854	1.79119
$170$	−3.60433	−0.276440
$171$	−13.3723	−1.02260
$172$	4.11077	0.313444
$173$	5.53072	0.420493	0.210247	−	0.977648i	$-0.432573\pi$
$173$	5.53072	0.420493	0.210247	+	0.977648i	$0.432573\pi$
$174$	−0.213982	−0.0162220
$175$	17.7514	1.34188
$176$	2.63756	0.198814
$177$	−0.159768	−0.0120089
$178$	2.73259	0.204817
$179$	10.3086	0.770499	0.385250	−	0.922812i	$-0.374115\pi$
$179$	10.3086	0.770499	0.385250	+	0.922812i	$0.374115\pi$
$180$	−11.4566	−0.853923
$181$	17.8886	1.32965	0.664825	−	0.746999i	$-0.268506\pi$
$181$	17.8886	1.32965	0.664825	+	0.746999i	$0.268506\pi$
$182$	9.81040	0.727195
$183$	0.303367	0.0224255
$184$	1.00000	0.0737210
$185$	−33.9113	−2.49321
$186$	0.709389	0.0520149
$187$	−2.38415	−0.174346
$188$	−2.46140	−0.179516
$189$	3.40647	0.247784
$190$	18.5583	1.34636
$191$	−6.73032	−0.486989	−0.243494	−	0.969902i	$-0.578294\pi$
$191$	−6.73032	−0.486989	−0.243494	+	0.969902i	$0.578294\pi$
$192$	−0.356133	−0.0257017
$193$	15.3659	1.10607	0.553033	−	0.833160i	$-0.313470\pi$
$193$	15.3659	1.10607	0.553033	+	0.833160i	$0.313470\pi$
$194$	−17.5738	−1.26172
$195$	−8.55404	−0.612568
$196$	−4.34759	−0.310542
$197$	−6.71751	−0.478603	−0.239302	−	0.970945i	$-0.576918\pi$
$197$	−6.71751	−0.478603	−0.239302	+	0.970945i	$0.576918\pi$
$198$	−7.57816	−0.538557
$199$	−24.9475	−1.76848	−0.884240	−	0.467033i	$-0.845323\pi$
$199$	−24.9475	−1.76848	−0.884240	+	0.467033i	$0.845323\pi$
$200$	10.8996	0.770721
$201$	2.62238	0.184968
$202$	−6.92774	−0.487434
$203$	0.978559	0.0686814
$204$	0.321916	0.0225386
$205$	−9.85605	−0.688376
$206$	7.26549	0.506210
$207$	−2.87317	−0.199699
$208$	6.02374	0.417671
$209$	12.2757	0.849130
$210$	−2.31274	−0.159594
$211$	−12.6457	−0.870569	−0.435285	−	0.900293i	$-0.643352\pi$
$211$	−12.6457	−0.870569	−0.435285	+	0.900293i	$0.643352\pi$
$212$	−7.94078	−0.545375
$213$	0.865173	0.0592807
$214$	−6.78136	−0.463564
$215$	16.3914	1.11789
$216$	2.09163	0.142317
$217$	−3.24409	−0.220224
$218$	11.4733	0.777073
$219$	−2.77787	−0.187711
$220$	10.5171	0.709063
$221$	−5.44499	−0.366270
$222$	3.02874	0.203276
$223$	1.76553	0.118228	0.0591142	−	0.998251i	$-0.481172\pi$
$223$	1.76553	0.118228	0.0591142	+	0.998251i	$0.481172\pi$
$224$	1.62862	0.108817
$225$	−31.3165	−2.08777
$226$	3.58170	0.238251
$227$	−15.8665	−1.05310	−0.526550	−	0.850144i	$-0.676515\pi$
$227$	−15.8665	−1.05310	−0.526550	+	0.850144i	$0.676515\pi$
$228$	−1.65751	−0.109771
$229$	18.2596	1.20663	0.603313	−	0.797504i	$-0.293847\pi$
$229$	18.2596	1.20663	0.603313	+	0.797504i	$0.293847\pi$
$230$	3.98743	0.262924
$231$	−1.52980	−0.100654
$232$	0.600851	0.0394478
$233$	8.19423	0.536822	0.268411	−	0.963304i	$-0.413501\pi$
$233$	8.19423	0.536822	0.268411	+	0.963304i	$0.413501\pi$
$234$	−17.3072	−1.13141
$235$	−9.81468	−0.640239
$236$	0.448619	0.0292026
$237$	3.20911	0.208454
$238$	−1.47215	−0.0954253
$239$	−26.7327	−1.72920	−0.864599	−	0.502463i	$-0.832427\pi$
$239$	−26.7327	−1.72920	−0.864599	+	0.502463i	$0.832427\pi$
$240$	−1.42006	−0.0916642
$241$	−2.27803	−0.146741	−0.0733704	−	0.997305i	$-0.523376\pi$
$241$	−2.27803	−0.146741	−0.0733704	+	0.997305i	$0.523376\pi$
$242$	−4.04327	−0.259911
$243$	−9.07929	−0.582436
$244$	−0.851838	−0.0545333
$245$	−17.3357	−1.10754
$246$	0.880280	0.0561246
$247$	28.0356	1.78387
$248$	−1.99192	−0.126487
$249$	4.77765	0.302771
$250$	23.5244	1.48781
$251$	22.9009	1.44549	0.722745	−	0.691115i	$-0.242880\pi$
$251$	22.9009	1.44549	0.722745	+	0.691115i	$0.242880\pi$
$252$	−4.67931	−0.294769
$253$	2.63756	0.165822
$254$	16.0544	1.00734
$255$	1.28362	0.0803834
$256$	1.00000	0.0625000
$257$	7.76988	0.484672	0.242336	−	0.970192i	$-0.422086\pi$
$257$	7.76988	0.484672	0.242336	+	0.970192i	$0.422086\pi$
$258$	−1.46398	−0.0911434
$259$	−13.8507	−0.860640
$260$	24.0193	1.48961
$261$	−1.72635	−0.106858
$262$	1.00000	0.0617802
$263$	−17.4664	−1.07702	−0.538512	−	0.842618i	$-0.681013\pi$
$263$	−17.4664	−1.07702	−0.538512	+	0.842618i	$0.681013\pi$
$264$	−0.939322	−0.0578113
$265$	−31.6634	−1.94506
$266$	7.57993	0.464755
$267$	−0.973165	−0.0595568
$268$	−7.36349	−0.449797
$269$	22.0852	1.34656	0.673280	−	0.739387i	$-0.264885\pi$
$269$	22.0852	1.34656	0.673280	+	0.739387i	$0.264885\pi$
$270$	8.34023	0.507570
$271$	−17.6021	−1.06925	−0.534626	−	0.845089i	$-0.679548\pi$
$271$	−17.6021	−1.06925	−0.534626	+	0.845089i	$0.679548\pi$
$272$	−0.903922	−0.0548083
$273$	−3.49380	−0.211455
$274$	−15.7066	−0.948868
$275$	28.7485	1.73360
$276$	−0.356133	−0.0214367
$277$	−7.21963	−0.433785	−0.216893	−	0.976195i	$-0.569592\pi$
$277$	−7.21963	−0.433785	−0.216893	+	0.976195i	$0.569592\pi$
$278$	2.49471	0.149623
$279$	5.72314	0.342635
$280$	6.49403	0.388092
$281$	−30.1280	−1.79729	−0.898643	−	0.438681i	$-0.855446\pi$
$281$	−30.1280	−1.79729	−0.898643	+	0.438681i	$0.855446\pi$
$282$	0.876585	0.0521999
$283$	−4.52611	−0.269049	−0.134525	−	0.990910i	$-0.542951\pi$
$283$	−4.52611	−0.269049	−0.134525	+	0.990910i	$0.542951\pi$
$284$	−2.42936	−0.144156
$285$	−6.60921	−0.391496
$286$	15.8880	0.939476
$287$	−4.02559	−0.237623
$288$	−2.87317	−0.169303
$289$	−16.1829	−0.951937
$290$	2.39585	0.140689
$291$	6.25859	0.366885
$292$	7.80010	0.456466
$293$	5.09926	0.297902	0.148951	−	0.988845i	$-0.452410\pi$
$293$	5.09926	0.297902	0.148951	+	0.988845i	$0.452410\pi$
$294$	1.54832	0.0902997
$295$	1.78884	0.104150
$296$	−8.50454	−0.494316
$297$	5.51680	0.320117
$298$	5.80283	0.336149
$299$	6.02374	0.348362
$300$	−3.88171	−0.224111
$301$	6.69490	0.385888
$302$	6.20578	0.357102
$303$	2.46719	0.141736
$304$	4.65419	0.266936
$305$	−3.39665	−0.194492
$306$	2.59712	0.148468
$307$	32.2551	1.84090	0.920448	−	0.390866i	$-0.127824\pi$
$307$	32.2551	1.84090	0.920448	+	0.390866i	$0.127824\pi$
$308$	4.29560	0.244764
$309$	−2.58748	−0.147196
$310$	−7.94267	−0.451113
$311$	−13.9931	−0.793474	−0.396737	−	0.917932i	$-0.629858\pi$
$311$	−13.9931	−0.793474	−0.396737	+	0.917932i	$0.629858\pi$
$312$	−2.14525	−0.121451
$313$	23.9492	1.35369	0.676846	−	0.736125i	$-0.263346\pi$
$313$	23.9492	1.35369	0.676846	+	0.736125i	$0.263346\pi$
$314$	20.3960	1.15102
$315$	−18.6584	−1.05128
$316$	−9.01101	−0.506909
$317$	27.2287	1.52932	0.764658	−	0.644437i	$-0.222908\pi$
$317$	27.2287	1.52932	0.764658	+	0.644437i	$0.222908\pi$
$318$	2.82797	0.158585
$319$	1.58478	0.0887307
$320$	3.98743	0.222904
$321$	2.41506	0.134796
$322$	1.62862	0.0907596
$323$	−4.20703	−0.234085
$324$	7.87461	0.437478
$325$	65.6566	3.64197
$326$	−23.5667	−1.30524
$327$	−4.08603	−0.225958
$328$	−2.47178	−0.136481
$329$	−4.00870	−0.221007
$330$	−3.74548	−0.206182
$331$	−14.4666	−0.795154	−0.397577	−	0.917569i	$-0.630149\pi$
$331$	−14.4666	−0.795154	−0.397577	+	0.917569i	$0.630149\pi$
$332$	−13.4154	−0.736264
$333$	24.4350	1.33903
$334$	−15.6592	−0.856835
$335$	−29.3614	−1.60419
$336$	−0.580006	−0.0316419
$337$	−2.21502	−0.120660	−0.0603298	−	0.998178i	$-0.519215\pi$
$337$	−2.21502	−0.120660	−0.0603298	+	0.998178i	$0.519215\pi$
$338$	23.2854	1.26656
$339$	−1.27556	−0.0692790
$340$	−3.60433	−0.195472
$341$	−5.25383	−0.284511
$342$	−13.3723	−0.723090
$343$	−18.4809	−0.997877
$344$	4.11077	0.221638
$345$	−1.42006	−0.0764532
$346$	5.53072	0.297333
$347$	3.34343	0.179485	0.0897424	−	0.995965i	$-0.471396\pi$
$347$	3.34343	0.179485	0.0897424	+	0.995965i	$0.471396\pi$
$348$	−0.213982	−0.0114707
$349$	−13.0699	−0.699615	−0.349807	−	0.936822i	$-0.613753\pi$
$349$	−13.0699	−0.699615	−0.349807	+	0.936822i	$0.613753\pi$
$350$	17.7514	0.948852
$351$	12.5994	0.672507
$352$	2.63756	0.140583
$353$	14.9610	0.796293	0.398146	−	0.917322i	$-0.369654\pi$
$353$	14.9610	0.796293	0.398146	+	0.917322i	$0.369654\pi$
$354$	−0.159768	−0.00849157
$355$	−9.68691	−0.514128
$356$	2.73259	0.144827
$357$	0.524280	0.0277479
$358$	10.3086	0.544825
$359$	29.1747	1.53978	0.769892	−	0.638174i	$-0.220310\pi$
$359$	29.1747	1.53978	0.769892	+	0.638174i	$0.220310\pi$
$360$	−11.4566	−0.603815
$361$	2.66152	0.140080
$362$	17.8886	0.940204
$363$	1.43994	0.0755772
$364$	9.81040	0.514205
$365$	31.1024	1.62797
$366$	0.303367	0.0158573
$367$	19.1833	1.00136	0.500679	−	0.865633i	$-0.333084\pi$
$367$	19.1833	1.00136	0.500679	+	0.865633i	$0.333084\pi$
$368$	1.00000	0.0521286
$369$	7.10183	0.369707
$370$	−33.9113	−1.76296
$371$	−12.9325	−0.671424
$372$	0.709389	0.0367801
$373$	15.4698	0.800997	0.400498	−	0.916298i	$-0.368837\pi$
$373$	15.4698	0.800997	0.400498	+	0.916298i	$0.368837\pi$
$374$	−2.38415	−0.123282
$375$	−8.37781	−0.432628
$376$	−2.46140	−0.126937
$377$	3.61937	0.186407
$378$	3.40647	0.175210
$379$	1.78065	0.0914660	0.0457330	−	0.998954i	$-0.485438\pi$
$379$	1.78065	0.0914660	0.0457330	+	0.998954i	$0.485438\pi$
$380$	18.5583	0.952020
$381$	−5.71749	−0.292916
$382$	−6.73032	−0.344353
$383$	−20.8028	−1.06298	−0.531488	−	0.847066i	$-0.678367\pi$
$383$	−20.8028	−1.06298	−0.531488	+	0.847066i	$0.678367\pi$
$384$	−0.356133	−0.0181738
$385$	17.1284	0.872944
$386$	15.3659	0.782106
$387$	−11.8110	−0.600384
$388$	−17.5738	−0.892173
$389$	−19.3336	−0.980252	−0.490126	−	0.871652i	$-0.663049\pi$
$389$	−19.3336	−0.980252	−0.490126	+	0.871652i	$0.663049\pi$
$390$	−8.55404	−0.433151
$391$	−0.903922	−0.0457133
$392$	−4.34759	−0.219586
$393$	−0.356133	−0.0179645
$394$	−6.71751	−0.338423
$395$	−35.9308	−1.80787
$396$	−7.57816	−0.380817
$397$	7.08834	0.355754	0.177877	−	0.984053i	$-0.443077\pi$
$397$	7.08834	0.355754	0.177877	+	0.984053i	$0.443077\pi$
$398$	−24.9475	−1.25050
$399$	−2.69946	−0.135142
$400$	10.8996	0.544982
$401$	26.1554	1.30614	0.653068	−	0.757299i	$-0.273482\pi$
$401$	26.1554	1.30614	0.653068	+	0.757299i	$0.273482\pi$
$402$	2.62238	0.130792
$403$	−11.9988	−0.597704
$404$	−6.92774	−0.344668
$405$	31.3995	1.56025
$406$	0.978559	0.0485651
$407$	−22.4313	−1.11188
$408$	0.321916	0.0159372
$409$	−2.12579	−0.105114	−0.0525568	−	0.998618i	$-0.516737\pi$
$409$	−2.12579	−0.105114	−0.0525568	+	0.998618i	$0.516737\pi$
$410$	−9.85605	−0.486755
$411$	5.59362	0.275913
$412$	7.26549	0.357945
$413$	0.730632	0.0359520
$414$	−2.87317	−0.141209
$415$	−53.4929	−2.62586
$416$	6.02374	0.295338
$417$	−0.888448	−0.0435075
$418$	12.2757	0.600425
$419$	31.3199	1.53008	0.765038	−	0.643985i	$-0.222720\pi$
$419$	31.3199	1.53008	0.765038	+	0.643985i	$0.222720\pi$
$420$	−2.31274	−0.112850
$421$	36.7597	1.79156	0.895779	−	0.444501i	$-0.146619\pi$
$421$	36.7597	1.79156	0.895779	+	0.444501i	$0.146619\pi$
$422$	−12.6457	−0.615585
$423$	7.07203	0.343854
$424$	−7.94078	−0.385639
$425$	−9.85243	−0.477913
$426$	0.865173	0.0419178
$427$	−1.38732	−0.0671373
$428$	−6.78136	−0.327789
$429$	−5.65823	−0.273182
$430$	16.3914	0.790466
$431$	−8.51657	−0.410229	−0.205114	−	0.978738i	$-0.565757\pi$
$431$	−8.51657	−0.410229	−0.205114	+	0.978738i	$0.565757\pi$
$432$	2.09163	0.100633
$433$	7.66978	0.368586	0.184293	−	0.982871i	$-0.441000\pi$
$433$	7.66978	0.368586	0.184293	+	0.982871i	$0.441000\pi$
$434$	−3.24409	−0.155722
$435$	−0.853241	−0.0409098
$436$	11.4733	0.549474
$437$	4.65419	0.222640
$438$	−2.77787	−0.132732
$439$	22.2224	1.06062	0.530308	−	0.847805i	$-0.322076\pi$
$439$	22.2224	1.06062	0.530308	+	0.847805i	$0.322076\pi$
$440$	10.5171	0.501383
$441$	12.4914	0.594826
$442$	−5.44499	−0.258992
$443$	5.14025	0.244221	0.122110	−	0.992517i	$-0.461034\pi$
$443$	5.14025	0.244221	0.122110	+	0.992517i	$0.461034\pi$
$444$	3.02874	0.143738
$445$	10.8960	0.516522
$446$	1.76553	0.0836001
$447$	−2.06658	−0.0977457
$448$	1.62862	0.0769452
$449$	−31.1194	−1.46862	−0.734308	−	0.678817i	$-0.762493\pi$
$449$	−31.1194	−1.46862	−0.734308	+	0.678817i	$0.762493\pi$
$450$	−31.3165	−1.47627
$451$	−6.51946	−0.306990
$452$	3.58170	0.168469
$453$	−2.21008	−0.103839
$454$	−15.8665	−0.744654
$455$	39.1183	1.83390
$456$	−1.65751	−0.0776200
$457$	−25.8230	−1.20795	−0.603974	−	0.797004i	$-0.706417\pi$
$457$	−25.8230	−1.20795	−0.603974	+	0.797004i	$0.706417\pi$
$458$	18.2596	0.853214
$459$	−1.89067	−0.0882488
$460$	3.98743	0.185915
$461$	28.5801	1.33111	0.665555	−	0.746349i	$-0.268195\pi$
$461$	28.5801	1.33111	0.665555	+	0.746349i	$0.268195\pi$
$462$	−1.52980	−0.0711728
$463$	−23.7078	−1.10180	−0.550898	−	0.834573i	$-0.685715\pi$
$463$	−23.7078	−1.10180	−0.550898	+	0.834573i	$0.685715\pi$
$464$	0.600851	0.0278938
$465$	2.82864	0.131175
$466$	8.19423	0.379590
$467$	−8.67639	−0.401496	−0.200748	−	0.979643i	$-0.564337\pi$
$467$	−8.67639	−0.401496	−0.200748	+	0.979643i	$0.564337\pi$
$468$	−17.3072	−0.800027
$469$	−11.9924	−0.553755
$470$	−9.81468	−0.452717
$471$	−7.26370	−0.334693
$472$	0.448619	0.0206494
$473$	10.8424	0.498535
$474$	3.20911	0.147399
$475$	50.7290	2.32761
$476$	−1.47215	−0.0674758
$477$	22.8152	1.04464
$478$	−26.7327	−1.22273
$479$	23.3400	1.06643	0.533217	−	0.845979i	$-0.320983\pi$
$479$	23.3400	1.06643	0.533217	+	0.845979i	$0.320983\pi$
$480$	−1.42006	−0.0648164
$481$	−51.2291	−2.33585
$482$	−2.27803	−0.103761
$483$	−0.580006	−0.0263912
$484$	−4.04327	−0.183785
$485$	−70.0743	−3.18191
$486$	−9.07929	−0.411845
$487$	17.2369	0.781078	0.390539	−	0.920586i	$-0.372289\pi$
$487$	17.2369	0.781078	0.390539	+	0.920586i	$0.372289\pi$
$488$	−0.851838	−0.0385609
$489$	8.39288	0.379539
$490$	−17.3357	−0.783148
$491$	8.05765	0.363637	0.181818	−	0.983332i	$-0.441802\pi$
$491$	8.05765	0.363637	0.181818	+	0.983332i	$0.441802\pi$
$492$	0.880280	0.0396861
$493$	−0.543122	−0.0244610
$494$	28.0356	1.26138
$495$	−30.2174	−1.35817
$496$	−1.99192	−0.0894401
$497$	−3.95651	−0.177474
$498$	4.77765	0.214091
$499$	7.26520	0.325235	0.162618	−	0.986689i	$-0.448006\pi$
$499$	7.26520	0.325235	0.162618	+	0.986689i	$0.448006\pi$
$500$	23.5244	1.05204
$501$	5.57676	0.249151
$502$	22.9009	1.02212
$503$	−25.6197	−1.14233	−0.571163	−	0.820836i	$-0.693508\pi$
$503$	−25.6197	−1.14233	−0.571163	+	0.820836i	$0.693508\pi$
$504$	−4.67931	−0.208433
$505$	−27.6239	−1.22925
$506$	2.63756	0.117254
$507$	−8.29270	−0.368292
$508$	16.0544	0.712298
$509$	−32.2430	−1.42915	−0.714573	−	0.699561i	$-0.753379\pi$
$509$	−32.2430	−1.42915	−0.714573	+	0.699561i	$0.753379\pi$
$510$	1.28362	0.0568396
$511$	12.7034	0.561966
$512$	1.00000	0.0441942
$513$	9.73484	0.429803
$514$	7.76988	0.342715
$515$	28.9707	1.27660
$516$	−1.46398	−0.0644481
$517$	−6.49210	−0.285522
$518$	−13.8507	−0.608565
$519$	−1.96967	−0.0864589
$520$	24.0193	1.05331
$521$	−22.1429	−0.970099	−0.485050	−	0.874487i	$-0.661198\pi$
$521$	−22.1429	−0.970099	−0.485050	+	0.874487i	$0.661198\pi$
$522$	−1.72635	−0.0755601
$523$	30.2651	1.32340	0.661701	−	0.749768i	$-0.269835\pi$
$523$	30.2651	1.32340	0.661701	+	0.749768i	$0.269835\pi$
$524$	1.00000	0.0436852
$525$	−6.32185	−0.275908
$526$	−17.4664	−0.761570
$527$	1.80055	0.0784330
$528$	−0.939322	−0.0408787
$529$	1.00000	0.0434783
$530$	−31.6634	−1.37537
$531$	−1.28896	−0.0559361
$532$	7.57993	0.328632
$533$	−14.8893	−0.644929
$534$	−0.973165	−0.0421130
$535$	−27.0402	−1.16905
$536$	−7.36349	−0.318054
$537$	−3.67122	−0.158425
$538$	22.0852	0.952162
$539$	−11.4670	−0.493920
$540$	8.34023	0.358906
$541$	−17.7863	−0.764692	−0.382346	−	0.924019i	$-0.624884\pi$
$541$	−17.7863	−0.764692	−0.382346	+	0.924019i	$0.624884\pi$
$542$	−17.6021	−0.756076
$543$	−6.37071	−0.273393
$544$	−0.903922	−0.0387554
$545$	45.7492	1.95968
$546$	−3.49380	−0.149521
$547$	21.9878	0.940132	0.470066	−	0.882631i	$-0.344230\pi$
$547$	21.9878	0.940132	0.470066	+	0.882631i	$0.344230\pi$
$548$	−15.7066	−0.670951
$549$	2.44747	0.104456
$550$	28.7485	1.22584
$551$	2.79647	0.119134
$552$	−0.356133	−0.0151580
$553$	−14.6755	−0.624067
$554$	−7.21963	−0.306732
$555$	12.0769	0.512637
$556$	2.49471	0.105799
$557$	7.94034	0.336443	0.168221	−	0.985749i	$-0.446198\pi$
$557$	7.94034	0.336443	0.168221	+	0.985749i	$0.446198\pi$
$558$	5.72314	0.242280
$559$	24.7622	1.04733
$560$	6.49403	0.274423
$561$	0.849074	0.0358479
$562$	−30.1280	−1.27087
$563$	16.9856	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$563$	16.9856	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$564$	0.876585	0.0369109
$565$	14.2818	0.600840
$566$	−4.52611	−0.190247
$567$	12.8248	0.538590
$568$	−2.42936	−0.101934
$569$	−16.6522	−0.698095	−0.349047	−	0.937105i	$-0.613495\pi$
$569$	−16.6522	−0.698095	−0.349047	+	0.937105i	$0.613495\pi$
$570$	−6.60921	−0.276829
$571$	−18.4473	−0.771997	−0.385999	−	0.922499i	$-0.626143\pi$
$571$	−18.4473	−0.771997	−0.385999	+	0.922499i	$0.626143\pi$
$572$	15.8880	0.664310
$573$	2.39689	0.100131
$574$	−4.02559	−0.168025
$575$	10.8996	0.454546
$576$	−2.87317	−0.119715
$577$	−23.4320	−0.975486	−0.487743	−	0.872987i	$-0.662180\pi$
$577$	−23.4320	−0.975486	−0.487743	+	0.872987i	$0.662180\pi$
$578$	−16.1829	−0.673121
$579$	−5.47231	−0.227422
$580$	2.39585	0.0994824
$581$	−21.8486	−0.906431
$582$	6.25859	0.259427
$583$	−20.9443	−0.867425
$584$	7.80010	0.322770
$585$	−69.0114	−2.85327
$586$	5.09926	0.210648
$587$	25.1646	1.03865	0.519327	−	0.854575i	$-0.326183\pi$
$587$	25.1646	1.03865	0.519327	+	0.854575i	$0.326183\pi$
$588$	1.54832	0.0638515
$589$	−9.27080	−0.381997
$590$	1.78884	0.0736454
$591$	2.39232	0.0984071
$592$	−8.50454	−0.349534
$593$	3.86558	0.158740	0.0793701	−	0.996845i	$-0.474709\pi$
$593$	3.86558	0.158740	0.0793701	+	0.996845i	$0.474709\pi$
$594$	5.51680	0.226357
$595$	−5.87010	−0.240651
$596$	5.80283	0.237693
$597$	8.88461	0.363623
$598$	6.02374	0.246329
$599$	−25.1988	−1.02960	−0.514798	−	0.857311i	$-0.672133\pi$
$599$	−25.1988	−1.02960	−0.514798	+	0.857311i	$0.672133\pi$
$600$	−3.88171	−0.158470
$601$	20.8167	0.849132	0.424566	−	0.905397i	$-0.360427\pi$
$601$	20.8167	0.849132	0.424566	+	0.905397i	$0.360427\pi$
$602$	6.69490	0.272864
$603$	21.1566	0.861562
$604$	6.20578	0.252509
$605$	−16.1223	−0.655463
$606$	2.46719	0.100223
$607$	−39.2398	−1.59270	−0.796348	−	0.604839i	$-0.793238\pi$
$607$	−39.2398	−1.59270	−0.796348	+	0.604839i	$0.793238\pi$
$608$	4.65419	0.188752
$609$	−0.348497	−0.0141218
$610$	−3.39665	−0.137526
$611$	−14.8268	−0.599830
$612$	2.59712	0.104982
$613$	−10.3096	−0.416400	−0.208200	−	0.978086i	$-0.566761\pi$
$613$	−10.3096	−0.416400	−0.208200	+	0.978086i	$0.566761\pi$
$614$	32.2551	1.30171
$615$	3.51006	0.141539
$616$	4.29560	0.173074
$617$	45.8235	1.84478	0.922391	−	0.386256i	$-0.126232\pi$
$617$	45.8235	1.84478	0.922391	+	0.386256i	$0.126232\pi$
$618$	−2.58748	−0.104084
$619$	−2.27063	−0.0912641	−0.0456321	−	0.998958i	$-0.514530\pi$
$619$	−2.27063	−0.0912641	−0.0456321	+	0.998958i	$0.514530\pi$
$620$	−7.94267	−0.318985
$621$	2.09163	0.0839341
$622$	−13.9931	−0.561071
$623$	4.45037	0.178300
$624$	−2.14525	−0.0858787
$625$	39.3039	1.57216
$626$	23.9492	0.957204
$627$	−4.37179	−0.174592
$628$	20.3960	0.813891
$629$	7.68745	0.306519
$630$	−18.6584	−0.743370
$631$	−27.8448	−1.10848	−0.554241	−	0.832356i	$-0.686992\pi$
$631$	−27.8448	−1.10848	−0.554241	+	0.832356i	$0.686992\pi$
$632$	−9.01101	−0.358439
$633$	4.50356	0.179000
$634$	27.2287	1.08139
$635$	64.0158	2.54039
$636$	2.82797	0.112136
$637$	−26.1887	−1.03763
$638$	1.58478	0.0627421
$639$	6.97996	0.276123
$640$	3.98743	0.157617
$641$	39.6095	1.56448	0.782241	−	0.622976i	$-0.214076\pi$
$641$	39.6095	1.56448	0.782241	+	0.622976i	$0.214076\pi$
$642$	2.41506	0.0953149
$643$	19.0760	0.752285	0.376143	−	0.926562i	$-0.377250\pi$
$643$	19.0760	0.752285	0.376143	+	0.926562i	$0.377250\pi$
$644$	1.62862	0.0641767
$645$	−5.83753	−0.229852
$646$	−4.20703	−0.165523
$647$	20.6089	0.810220	0.405110	−	0.914268i	$-0.367233\pi$
$647$	20.6089	0.810220	0.405110	+	0.914268i	$0.367233\pi$
$648$	7.87461	0.309344
$649$	1.18326	0.0464471
$650$	65.6566	2.57526
$651$	1.15533	0.0452809
$652$	−23.5667	−0.922945
$653$	35.7773	1.40007	0.700036	−	0.714107i	$-0.253167\pi$
$653$	35.7773	1.40007	0.700036	+	0.714107i	$0.253167\pi$
$654$	−4.08603	−0.159776
$655$	3.98743	0.155802
$656$	−2.47178	−0.0965067
$657$	−22.4110	−0.874337
$658$	−4.00870	−0.156275
$659$	1.51431	0.0589890	0.0294945	−	0.999565i	$-0.490610\pi$
$659$	1.51431	0.0589890	0.0294945	+	0.999565i	$0.490610\pi$
$660$	−3.74548	−0.145793
$661$	−0.479930	−0.0186671	−0.00933355	−	0.999956i	$-0.502971\pi$
$661$	−0.479930	−0.0186671	−0.00933355	+	0.999956i	$0.502971\pi$
$662$	−14.4666	−0.562259
$663$	1.93914	0.0753099
$664$	−13.4154	−0.520617
$665$	30.2245	1.17205
$666$	24.4350	0.946837
$667$	0.600851	0.0232650
$668$	−15.6592	−0.605874
$669$	−0.628762	−0.0243093
$670$	−29.3614	−1.13433
$671$	−2.24678	−0.0867358
$672$	−0.580006	−0.0223742
$673$	−7.46533	−0.287767	−0.143884	−	0.989595i	$-0.545959\pi$
$673$	−7.46533	−0.287767	−0.143884	+	0.989595i	$0.545959\pi$
$674$	−2.21502	−0.0853193
$675$	22.7980	0.877494
$676$	23.2854	0.895593
$677$	−3.43831	−0.132145	−0.0660725	−	0.997815i	$-0.521047\pi$
$677$	−3.43831	−0.132145	−0.0660725	+	0.997815i	$0.521047\pi$
$678$	−1.27556	−0.0489876
$679$	−28.6211	−1.09838
$680$	−3.60433	−0.138220
$681$	5.65059	0.216531
$682$	−5.25383	−0.201179
$683$	3.75209	0.143570	0.0717848	−	0.997420i	$-0.477131\pi$
$683$	3.75209	0.143570	0.0717848	+	0.997420i	$0.477131\pi$
$684$	−13.3723	−0.511302
$685$	−62.6289	−2.39293
$686$	−18.4809	−0.705606
$687$	−6.50283	−0.248098
$688$	4.11077	0.156722
$689$	−47.8332	−1.82230
$690$	−1.42006	−0.0540606
$691$	−26.7176	−1.01639	−0.508193	−	0.861243i	$-0.669686\pi$
$691$	−26.7176	−1.01639	−0.508193	+	0.861243i	$0.669686\pi$
$692$	5.53072	0.210247
$693$	−12.3420	−0.468833
$694$	3.34343	0.126915
$695$	9.94750	0.377330
$696$	−0.213982	−0.00811098
$697$	2.23429	0.0846299
$698$	−13.0699	−0.494702
$699$	−2.91823	−0.110378
$700$	17.7514	0.670940
$701$	10.4023	0.392891	0.196446	−	0.980515i	$-0.437060\pi$
$701$	10.4023	0.392891	0.196446	+	0.980515i	$0.437060\pi$
$702$	12.5994	0.475534
$703$	−39.5818	−1.49286
$704$	2.63756	0.0994069
$705$	3.49533	0.131642
$706$	14.9610	0.563064
$707$	−11.2827	−0.424329
$708$	−0.159768	−0.00600445
$709$	−10.0465	−0.377305	−0.188652	−	0.982044i	$-0.560412\pi$
$709$	−10.0465	−0.377305	−0.188652	+	0.982044i	$0.560412\pi$
$710$	−9.68691	−0.363543
$711$	25.8902	0.970957
$712$	2.73259	0.102408
$713$	−1.99192	−0.0745982
$714$	0.524280	0.0196207
$715$	63.3523	2.36924
$716$	10.3086	0.385250
$717$	9.52040	0.355546
$718$	29.1747	1.08879
$719$	26.3785	0.983751	0.491875	−	0.870666i	$-0.336312\pi$
$719$	26.3785	0.983751	0.491875	+	0.870666i	$0.336312\pi$
$720$	−11.4566	−0.426961
$721$	11.8327	0.440674
$722$	2.66152	0.0990514
$723$	0.811280	0.0301718
$724$	17.8886	0.664825
$725$	6.54905	0.243226
$726$	1.43994	0.0534411
$727$	7.44940	0.276283	0.138141	−	0.990413i	$-0.455887\pi$
$727$	7.44940	0.276283	0.138141	+	0.990413i	$0.455887\pi$
$728$	9.81040	0.363598
$729$	−20.3904	−0.755200
$730$	31.1024	1.15115
$731$	−3.71582	−0.137435
$732$	0.303367	0.0112128
$733$	37.7518	1.39440	0.697198	−	0.716879i	$-0.254430\pi$
$733$	37.7518	1.39440	0.697198	+	0.716879i	$0.254430\pi$
$734$	19.1833	0.708067
$735$	6.17381	0.227724
$736$	1.00000	0.0368605
$737$	−19.4217	−0.715406
$738$	7.10183	0.261422
$739$	27.7660	1.02139	0.510694	−	0.859762i	$-0.329388\pi$
$739$	27.7660	1.02139	0.510694	+	0.859762i	$0.329388\pi$
$740$	−33.9113	−1.24660
$741$	−9.98440	−0.366786
$742$	−12.9325	−0.474769
$743$	−32.8990	−1.20695	−0.603474	−	0.797383i	$-0.706217\pi$
$743$	−32.8990	−1.20695	−0.603474	+	0.797383i	$0.706217\pi$
$744$	0.709389	0.0260075
$745$	23.1384	0.847726
$746$	15.4698	0.566390
$747$	38.5446	1.41027
$748$	−2.38415	−0.0871732
$749$	−11.0443	−0.403549
$750$	−8.37781	−0.305914
$751$	−43.6924	−1.59436	−0.797179	−	0.603743i	$-0.793675\pi$
$751$	−43.6924	−1.59436	−0.797179	+	0.603743i	$0.793675\pi$
$752$	−2.46140	−0.0897581
$753$	−8.15574	−0.297212
$754$	3.61937	0.131810
$755$	24.7451	0.900567
$756$	3.40647	0.123892
$757$	−13.6533	−0.496238	−0.248119	−	0.968730i	$-0.579812\pi$
$757$	−13.6533	−0.496238	−0.248119	+	0.968730i	$0.579812\pi$
$758$	1.78065	0.0646762
$759$	−0.939322	−0.0340952
$760$	18.5583	0.673180
$761$	26.4704	0.959552	0.479776	−	0.877391i	$-0.340718\pi$
$761$	26.4704	0.959552	0.479776	+	0.877391i	$0.340718\pi$
$762$	−5.71749	−0.207123
$763$	18.6858	0.676470
$764$	−6.73032	−0.243494
$765$	10.3559	0.374417
$766$	−20.8028	−0.751637
$767$	2.70237	0.0975768
$768$	−0.356133	−0.0128508
$769$	41.3592	1.49145	0.745726	−	0.666253i	$-0.232103\pi$
$769$	41.3592	1.49145	0.745726	+	0.666253i	$0.232103\pi$
$770$	17.1284	0.617265
$771$	−2.76711	−0.0996549
$772$	15.3659	0.553033
$773$	−7.11640	−0.255959	−0.127980	−	0.991777i	$-0.540849\pi$
$773$	−7.11640	−0.255959	−0.127980	+	0.991777i	$0.540849\pi$
$774$	−11.8110	−0.424536
$775$	−21.7113	−0.779891
$776$	−17.5738	−0.630862
$777$	4.93268	0.176959
$778$	−19.3336	−0.693143
$779$	−11.5041	−0.412178
$780$	−8.55404	−0.306284
$781$	−6.40758	−0.229281
$782$	−0.903922	−0.0323242
$783$	1.25676	0.0449128
$784$	−4.34759	−0.155271
$785$	81.3279	2.90272
$786$	−0.356133	−0.0127028
$787$	36.8498	1.31355	0.656777	−	0.754085i	$-0.271919\pi$
$787$	36.8498	1.31355	0.656777	+	0.754085i	$0.271919\pi$
$788$	−6.71751	−0.239302
$789$	6.22035	0.221450
$790$	−35.9308	−1.27836
$791$	5.83325	0.207406
$792$	−7.57816	−0.269278
$793$	−5.13125	−0.182216
$794$	7.08834	0.251556
$795$	11.2764	0.399931
$796$	−24.9475	−0.884240
$797$	40.0403	1.41830	0.709151	−	0.705057i	$-0.249079\pi$
$797$	40.0403	1.41830	0.709151	+	0.705057i	$0.249079\pi$
$798$	−2.69946	−0.0955598
$799$	2.22492	0.0787119
$800$	10.8996	0.385360
$801$	−7.85120	−0.277409
$802$	26.1554	0.923578
$803$	20.5732	0.726014
$804$	2.62238	0.0924842
$805$	6.49403	0.228884
$806$	−11.9988	−0.422641
$807$	−7.86527	−0.276871
$808$	−6.92774	−0.243717
$809$	0.469088	0.0164923	0.00824613	−	0.999966i	$-0.497375\pi$
$809$	0.469088	0.0164923	0.00824613	+	0.999966i	$0.497375\pi$
$810$	31.3995	1.10327
$811$	−1.53831	−0.0540175	−0.0270088	−	0.999635i	$-0.508598\pi$
$811$	−1.53831	−0.0540175	−0.0270088	+	0.999635i	$0.508598\pi$
$812$	0.978559	0.0343407
$813$	6.26869	0.219852
$814$	−22.4313	−0.786215
$815$	−93.9708	−3.29165
$816$	0.321916	0.0112693
$817$	19.1323	0.669356
$818$	−2.12579	−0.0743265
$819$	−28.1869	−0.984932
$820$	−9.85605	−0.344188
$821$	10.3973	0.362869	0.181434	−	0.983403i	$-0.441926\pi$
$821$	10.3973	0.362869	0.181434	+	0.983403i	$0.441926\pi$
$822$	5.59362	0.195100
$823$	−50.9485	−1.77595	−0.887977	−	0.459889i	$-0.847889\pi$
$823$	−50.9485	−1.77595	−0.887977	+	0.459889i	$0.847889\pi$
$824$	7.26549	0.253105
$825$	−10.2383	−0.356451
$826$	0.730632	0.0254219
$827$	−54.7277	−1.90307	−0.951534	−	0.307545i	$-0.900493\pi$
$827$	−54.7277	−1.90307	−0.951534	+	0.307545i	$0.900493\pi$
$828$	−2.87317	−0.0998495
$829$	−14.7256	−0.511440	−0.255720	−	0.966751i	$-0.582313\pi$
$829$	−14.7256	−0.511440	−0.255720	+	0.966751i	$0.582313\pi$
$830$	−53.4929	−1.85676
$831$	2.57114	0.0891920
$832$	6.02374	0.208836
$833$	3.92988	0.136162
$834$	−0.888448	−0.0307644
$835$	−62.4402	−2.16083
$836$	12.2757	0.424565
$837$	−4.16636	−0.144011
$838$	31.3199	1.08193
$839$	−14.9398	−0.515781	−0.257890	−	0.966174i	$-0.583027\pi$
$839$	−14.9398	−0.515781	−0.257890	+	0.966174i	$0.583027\pi$
$840$	−2.31274	−0.0797969
$841$	−28.6390	−0.987551
$842$	36.7597	1.26682
$843$	10.7296	0.369546
$844$	−12.6457	−0.435285
$845$	92.8491	3.19411
$846$	7.07203	0.243141
$847$	−6.58496	−0.226262
$848$	−7.94078	−0.272688
$849$	1.61190	0.0553201
$850$	−9.85243	−0.337935
$851$	−8.50454	−0.291532
$852$	0.865173	0.0296403
$853$	21.0559	0.720941	0.360471	−	0.932771i	$-0.382616\pi$
$853$	21.0559	0.720941	0.360471	+	0.932771i	$0.382616\pi$
$854$	−1.38732	−0.0474732
$855$	−53.3211	−1.82354
$856$	−6.78136	−0.231782
$857$	−38.2780	−1.30755	−0.653777	−	0.756688i	$-0.726816\pi$
$857$	−38.2780	−1.30755	−0.653777	+	0.756688i	$0.726816\pi$
$858$	−5.65823	−0.193169
$859$	20.1644	0.688001	0.344000	−	0.938969i	$-0.388218\pi$
$859$	20.1644	0.688001	0.344000	+	0.938969i	$0.388218\pi$
$860$	16.3914	0.558944
$861$	1.43364	0.0488585
$862$	−8.51657	−0.290076
$863$	30.7917	1.04816	0.524081	−	0.851668i	$-0.324409\pi$
$863$	30.7917	1.04816	0.524081	+	0.851668i	$0.324409\pi$
$864$	2.09163	0.0711586
$865$	22.0534	0.749838
$866$	7.66978	0.260630
$867$	5.76327	0.195731
$868$	−3.24409	−0.110112
$869$	−23.7671	−0.806243
$870$	−0.853241	−0.0289276
$871$	−44.3557	−1.50294
$872$	11.4733	0.388536
$873$	50.4924	1.70891
$874$	4.65419	0.157430
$875$	38.3124	1.29520
$876$	−2.77787	−0.0938555
$877$	−38.7939	−1.30998	−0.654989	−	0.755639i	$-0.727327\pi$
$877$	−38.7939	−1.30998	−0.654989	+	0.755639i	$0.727327\pi$
$878$	22.2224	0.749969
$879$	−1.81601	−0.0612526
$880$	10.5171	0.354532
$881$	−51.3127	−1.72877	−0.864384	−	0.502832i	$-0.832291\pi$
$881$	−51.3127	−1.72877	−0.864384	+	0.502832i	$0.832291\pi$
$882$	12.4914	0.420606
$883$	0.924109	0.0310988	0.0155494	−	0.999879i	$-0.495050\pi$
$883$	0.924109	0.0310988	0.0155494	+	0.999879i	$0.495050\pi$
$884$	−5.44499	−0.183135
$885$	−0.637064	−0.0214147
$886$	5.14025	0.172690
$887$	−53.4556	−1.79487	−0.897433	−	0.441152i	$-0.854570\pi$
$887$	−53.4556	−1.79487	−0.897433	+	0.441152i	$0.854570\pi$
$888$	3.02874	0.101638
$889$	26.1466	0.876927
$890$	10.8960	0.365236
$891$	20.7698	0.695814
$892$	1.76553	0.0591142
$893$	−11.4558	−0.383355
$894$	−2.06658	−0.0691167
$895$	41.1048	1.37398
$896$	1.62862	0.0544085
$897$	−2.14525	−0.0716278
$898$	−31.1194	−1.03847
$899$	−1.19685	−0.0399172
$900$	−31.3165	−1.04388
$901$	7.17785	0.239129
$902$	−6.51946	−0.217074
$903$	−2.38427	−0.0793436
$904$	3.58170	0.119126
$905$	71.3296	2.37108
$906$	−2.21008	−0.0734249
$907$	−38.1384	−1.26637	−0.633183	−	0.774002i	$-0.718252\pi$
$907$	−38.1384	−1.26637	−0.633183	+	0.774002i	$0.718252\pi$
$908$	−15.8665	−0.526550
$909$	19.9046	0.660193
$910$	39.1183	1.29676
$911$	11.4726	0.380104	0.190052	−	0.981774i	$-0.439134\pi$
$911$	11.4726	0.380104	0.190052	+	0.981774i	$0.439134\pi$
$912$	−1.65751	−0.0548856
$913$	−35.3838	−1.17103
$914$	−25.8230	−0.854148
$915$	1.20966	0.0399900
$916$	18.2596	0.603313
$917$	1.62862	0.0537819
$918$	−1.89067	−0.0624014
$919$	−32.4042	−1.06892	−0.534458	−	0.845195i	$-0.679484\pi$
$919$	−32.4042	−1.06892	−0.534458	+	0.845195i	$0.679484\pi$
$920$	3.98743	0.131462
$921$	−11.4871	−0.378512
$922$	28.5801	0.941237
$923$	−14.6338	−0.481678
$924$	−1.52980	−0.0503268
$925$	−92.6964	−3.04784
$926$	−23.7078	−0.779087
$927$	−20.8750	−0.685624
$928$	0.600851	0.0197239
$929$	29.8766	0.980218	0.490109	−	0.871661i	$-0.336957\pi$
$929$	29.8766	0.980218	0.490109	+	0.871661i	$0.336957\pi$
$930$	2.82864	0.0927549
$931$	−20.2345	−0.663159
$932$	8.19423	0.268411
$933$	4.98339	0.163149
$934$	−8.67639	−0.283900
$935$	−9.50665	−0.310901
$936$	−17.3072	−0.565704
$937$	14.6010	0.476994	0.238497	−	0.971143i	$-0.423345\pi$
$937$	14.6010	0.476994	0.238497	+	0.971143i	$0.423345\pi$
$938$	−11.9924	−0.391564
$939$	−8.52911	−0.278337
$940$	−9.81468	−0.320120
$941$	−57.7814	−1.88362	−0.941810	−	0.336146i	$-0.890876\pi$
$941$	−57.7814	−1.88362	−0.941810	+	0.336146i	$0.890876\pi$
$942$	−7.26370	−0.236664
$943$	−2.47178	−0.0804921
$944$	0.448619	0.0146013
$945$	13.5831	0.441858
$946$	10.8424	0.352518
$947$	−13.2508	−0.430595	−0.215297	−	0.976549i	$-0.569072\pi$
$947$	−13.2508	−0.430595	−0.215297	+	0.976549i	$0.569072\pi$
$948$	3.20911	0.104227
$949$	46.9858	1.52522
$950$	50.7290	1.64587
$951$	−9.69702	−0.314447
$952$	−1.47215	−0.0477126
$953$	−1.40575	−0.0455367	−0.0227684	−	0.999741i	$-0.507248\pi$
$953$	−1.40575	−0.0455367	−0.0227684	+	0.999741i	$0.507248\pi$
$954$	22.8152	0.738670
$955$	−26.8367	−0.868415
$956$	−26.7327	−0.864599
$957$	−0.564392	−0.0182442
$958$	23.3400	0.754082
$959$	−25.5801	−0.826024
$960$	−1.42006	−0.0458321
$961$	−27.0322	−0.872008
$962$	−51.2291	−1.65169
$963$	19.4840	0.627863
$964$	−2.27803	−0.0733704
$965$	61.2707	1.97237
$966$	−0.580006	−0.0186614
$967$	−29.2152	−0.939499	−0.469750	−	0.882800i	$-0.655656\pi$
$967$	−29.2152	−0.939499	−0.469750	+	0.882800i	$0.655656\pi$
$968$	−4.04327	−0.129955
$969$	1.49826	0.0481311
$970$	−70.0743	−2.24995
$971$	19.9095	0.638928	0.319464	−	0.947598i	$-0.396497\pi$
$971$	19.9095	0.638928	0.319464	+	0.947598i	$0.396497\pi$
$972$	−9.07929	−0.291218
$973$	4.06295	0.130252
$974$	17.2369	0.552306
$975$	−23.3824	−0.748837
$976$	−0.851838	−0.0272667
$977$	7.35722	0.235378	0.117689	−	0.993050i	$-0.462451\pi$
$977$	7.35722	0.235378	0.117689	+	0.993050i	$0.462451\pi$
$978$	8.39288	0.268375
$979$	7.20739	0.230349
$980$	−17.3357	−0.553769
$981$	−32.9649	−1.05249
$982$	8.05765	0.257130
$983$	−60.0553	−1.91547	−0.957734	−	0.287656i	$-0.907124\pi$
$983$	−60.0553	−1.91547	−0.957734	+	0.287656i	$0.907124\pi$
$984$	0.880280	0.0280623
$985$	−26.7856	−0.853462
$986$	−0.543122	−0.0172965
$987$	1.42763	0.0454419
$988$	28.0356	0.891933
$989$	4.11077	0.130715
$990$	−30.2174	−0.960373
$991$	27.2780	0.866514	0.433257	−	0.901270i	$-0.357364\pi$
$991$	27.2780	0.866514	0.433257	+	0.901270i	$0.357364\pi$
$992$	−1.99192	−0.0632437
$993$	5.15201	0.163494
$994$	−3.95651	−0.125493
$995$	−99.4764	−3.15361
$996$	4.77765	0.151385
$997$	−38.0810	−1.20604	−0.603019	−	0.797727i	$-0.706036\pi$
$997$	−38.0810	−1.20604	−0.603019	+	0.797727i	$0.706036\pi$
$998$	7.26520	0.229976
$999$	−17.7883	−0.562798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.18	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.18	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.356133 q^{3} +1.00000 q^{4} +3.98743 q^{5} -0.356133 q^{6} +1.62862 q^{7} +1.00000 q^{8} -2.87317 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.356133 q^{3} +1.00000 q^{4} +3.98743 q^{5} -0.356133 q^{6} +1.62862 q^{7} +1.00000 q^{8} -2.87317 q^{9} +3.98743 q^{10} +2.63756 q^{11} -0.356133 q^{12} +6.02374 q^{13} +1.62862 q^{14} -1.42006 q^{15} +1.00000 q^{16} -0.903922 q^{17} -2.87317 q^{18} +4.65419 q^{19} +3.98743 q^{20} -0.580006 q^{21} +2.63756 q^{22} +1.00000 q^{23} -0.356133 q^{24} +10.8996 q^{25} +6.02374 q^{26} +2.09163 q^{27} +1.62862 q^{28} +0.600851 q^{29} -1.42006 q^{30} -1.99192 q^{31} +1.00000 q^{32} -0.939322 q^{33} -0.903922 q^{34} +6.49403 q^{35} -2.87317 q^{36} -8.50454 q^{37} +4.65419 q^{38} -2.14525 q^{39} +3.98743 q^{40} -2.47178 q^{41} -0.580006 q^{42} +4.11077 q^{43} +2.63756 q^{44} -11.4566 q^{45} +1.00000 q^{46} -2.46140 q^{47} -0.356133 q^{48} -4.34759 q^{49} +10.8996 q^{50} +0.321916 q^{51} +6.02374 q^{52} -7.94078 q^{53} +2.09163 q^{54} +10.5171 q^{55} +1.62862 q^{56} -1.65751 q^{57} +0.600851 q^{58} +0.448619 q^{59} -1.42006 q^{60} -0.851838 q^{61} -1.99192 q^{62} -4.67931 q^{63} +1.00000 q^{64} +24.0193 q^{65} -0.939322 q^{66} -7.36349 q^{67} -0.903922 q^{68} -0.356133 q^{69} +6.49403 q^{70} -2.42936 q^{71} -2.87317 q^{72} +7.80010 q^{73} -8.50454 q^{74} -3.88171 q^{75} +4.65419 q^{76} +4.29560 q^{77} -2.14525 q^{78} -9.01101 q^{79} +3.98743 q^{80} +7.87461 q^{81} -2.47178 q^{82} -13.4154 q^{83} -0.580006 q^{84} -3.60433 q^{85} +4.11077 q^{86} -0.213982 q^{87} +2.63756 q^{88} +2.73259 q^{89} -11.4566 q^{90} +9.81040 q^{91} +1.00000 q^{92} +0.709389 q^{93} -2.46140 q^{94} +18.5583 q^{95} -0.356133 q^{96} -17.5738 q^{97} -4.34759 q^{98} -7.57816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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