LMFDB - Embedded newform 4011.2.a.m.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.359948 q^{2} +1.00000 q^{3} -1.87044 q^{4} -1.76526 q^{5} -0.359948 q^{6} -1.00000 q^{7} +1.39316 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.359948 q^{2} +1.00000 q^{3} -1.87044 q^{4} -1.76526 q^{5} -0.359948 q^{6} -1.00000 q^{7} +1.39316 q^{8} +1.00000 q^{9} +0.635404 q^{10} -4.93492 q^{11} -1.87044 q^{12} -4.06932 q^{13} +0.359948 q^{14} -1.76526 q^{15} +3.23941 q^{16} -3.23344 q^{17} -0.359948 q^{18} -1.79330 q^{19} +3.30181 q^{20} -1.00000 q^{21} +1.77632 q^{22} -5.43193 q^{23} +1.39316 q^{24} -1.88384 q^{25} +1.46474 q^{26} +1.00000 q^{27} +1.87044 q^{28} +9.41891 q^{29} +0.635404 q^{30} -9.32721 q^{31} -3.95233 q^{32} -4.93492 q^{33} +1.16387 q^{34} +1.76526 q^{35} -1.87044 q^{36} +2.56184 q^{37} +0.645496 q^{38} -4.06932 q^{39} -2.45929 q^{40} +3.91699 q^{41} +0.359948 q^{42} +7.54816 q^{43} +9.23046 q^{44} -1.76526 q^{45} +1.95521 q^{46} +3.41548 q^{47} +3.23941 q^{48} +1.00000 q^{49} +0.678087 q^{50} -3.23344 q^{51} +7.61141 q^{52} -13.6269 q^{53} -0.359948 q^{54} +8.71144 q^{55} -1.39316 q^{56} -1.79330 q^{57} -3.39032 q^{58} -1.37250 q^{59} +3.30181 q^{60} -6.83109 q^{61} +3.35731 q^{62} -1.00000 q^{63} -5.05618 q^{64} +7.18342 q^{65} +1.77632 q^{66} +3.86423 q^{67} +6.04795 q^{68} -5.43193 q^{69} -0.635404 q^{70} +14.1207 q^{71} +1.39316 q^{72} -3.93079 q^{73} -0.922130 q^{74} -1.88384 q^{75} +3.35426 q^{76} +4.93492 q^{77} +1.46474 q^{78} +3.31275 q^{79} -5.71841 q^{80} +1.00000 q^{81} -1.40991 q^{82} -11.9354 q^{83} +1.87044 q^{84} +5.70787 q^{85} -2.71695 q^{86} +9.41891 q^{87} -6.87512 q^{88} +14.5498 q^{89} +0.635404 q^{90} +4.06932 q^{91} +10.1601 q^{92} -9.32721 q^{93} -1.22939 q^{94} +3.16565 q^{95} -3.95233 q^{96} -6.36208 q^{97} -0.359948 q^{98} -4.93492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * 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 $

$2$	−0.359948	−0.254522	−0.127261	−	0.991869i	$-0.540619\pi$
$2$	−0.359948	−0.254522	−0.127261	+	0.991869i	$0.540619\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.87044	−0.935219
$5$	−1.76526	−0.789450	−0.394725	−	0.918799i	$-0.629160\pi$
$5$	−1.76526	−0.789450	−0.394725	+	0.918799i	$0.629160\pi$
$6$	−0.359948	−0.146948
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.39316	0.492555
$9$	1.00000	0.333333
$10$	0.635404	0.200932
$11$	−4.93492	−1.48793	−0.743967	−	0.668216i	$-0.767058\pi$
$11$	−4.93492	−1.48793	−0.743967	+	0.668216i	$0.767058\pi$
$12$	−1.87044	−0.539949
$13$	−4.06932	−1.12863	−0.564313	−	0.825561i	$-0.690859\pi$
$13$	−4.06932	−1.12863	−0.564313	+	0.825561i	$0.690859\pi$
$14$	0.359948	0.0962002
$15$	−1.76526	−0.455789
$16$	3.23941	0.809852
$17$	−3.23344	−0.784224	−0.392112	−	0.919917i	$-0.628256\pi$
$17$	−3.23344	−0.784224	−0.392112	+	0.919917i	$0.628256\pi$
$18$	−0.359948	−0.0848406
$19$	−1.79330	−0.411412	−0.205706	−	0.978614i	$-0.565949\pi$
$19$	−1.79330	−0.411412	−0.205706	+	0.978614i	$0.565949\pi$
$20$	3.30181	0.738308
$21$	−1.00000	−0.218218
$22$	1.77632	0.378712
$23$	−5.43193	−1.13264	−0.566318	−	0.824187i	$-0.691632\pi$
$23$	−5.43193	−1.13264	−0.566318	+	0.824187i	$0.691632\pi$
$24$	1.39316	0.284377
$25$	−1.88384	−0.376769
$26$	1.46474	0.287260
$27$	1.00000	0.192450
$28$	1.87044	0.353479
$29$	9.41891	1.74905	0.874524	−	0.484983i	$-0.161174\pi$
$29$	9.41891	1.74905	0.874524	+	0.484983i	$0.161174\pi$
$30$	0.635404	0.116008
$31$	−9.32721	−1.67522	−0.837608	−	0.546272i	$-0.816047\pi$
$31$	−9.32721	−1.67522	−0.837608	+	0.546272i	$0.816047\pi$
$32$	−3.95233	−0.698681
$33$	−4.93492	−0.859060
$34$	1.16387	0.199602
$35$	1.76526	0.298384
$36$	−1.87044	−0.311740
$37$	2.56184	0.421164	0.210582	−	0.977576i	$-0.432464\pi$
$37$	2.56184	0.421164	0.210582	+	0.977576i	$0.432464\pi$
$38$	0.645496	0.104713
$39$	−4.06932	−0.651613
$40$	−2.45929	−0.388848
$41$	3.91699	0.611731	0.305865	−	0.952075i	$-0.401054\pi$
$41$	3.91699	0.611731	0.305865	+	0.952075i	$0.401054\pi$
$42$	0.359948	0.0555412
$43$	7.54816	1.15108	0.575542	−	0.817772i	$-0.304791\pi$
$43$	7.54816	1.15108	0.575542	+	0.817772i	$0.304791\pi$
$44$	9.23046	1.39154
$45$	−1.76526	−0.263150
$46$	1.95521	0.288280
$47$	3.41548	0.498198	0.249099	−	0.968478i	$-0.419865\pi$
$47$	3.41548	0.498198	0.249099	+	0.968478i	$0.419865\pi$
$48$	3.23941	0.467569
$49$	1.00000	0.142857
$50$	0.678087	0.0958959
$51$	−3.23344	−0.452772
$52$	7.61141	1.05551
$53$	−13.6269	−1.87180	−0.935901	−	0.352263i	$-0.885412\pi$
$53$	−13.6269	−1.87180	−0.935901	+	0.352263i	$0.885412\pi$
$54$	−0.359948	−0.0489828
$55$	8.71144	1.17465
$56$	−1.39316	−0.186168
$57$	−1.79330	−0.237529
$58$	−3.39032	−0.445171
$59$	−1.37250	−0.178685	−0.0893423	−	0.996001i	$-0.528477\pi$
$59$	−1.37250	−0.178685	−0.0893423	+	0.996001i	$0.528477\pi$
$60$	3.30181	0.426262
$61$	−6.83109	−0.874631	−0.437315	−	0.899308i	$-0.644071\pi$
$61$	−6.83109	−0.874631	−0.437315	+	0.899308i	$0.644071\pi$
$62$	3.35731	0.426379
$63$	−1.00000	−0.125988
$64$	−5.05618	−0.632023
$65$	7.18342	0.890994
$66$	1.77632	0.218649
$67$	3.86423	0.472091	0.236046	−	0.971742i	$-0.424149\pi$
$67$	3.86423	0.472091	0.236046	+	0.971742i	$0.424149\pi$
$68$	6.04795	0.733421
$69$	−5.43193	−0.653927
$70$	−0.635404	−0.0759453
$71$	14.1207	1.67582	0.837910	−	0.545809i	$-0.183777\pi$
$71$	14.1207	1.67582	0.837910	+	0.545809i	$0.183777\pi$
$72$	1.39316	0.164185
$73$	−3.93079	−0.460064	−0.230032	−	0.973183i	$-0.573883\pi$
$73$	−3.93079	−0.460064	−0.230032	+	0.973183i	$0.573883\pi$
$74$	−0.922130	−0.107195
$75$	−1.88384	−0.217528
$76$	3.35426	0.384760
$77$	4.93492	0.562387
$78$	1.46474	0.165850
$79$	3.31275	0.372714	0.186357	−	0.982482i	$-0.440332\pi$
$79$	3.31275	0.372714	0.186357	+	0.982482i	$0.440332\pi$
$80$	−5.71841	−0.639338
$81$	1.00000	0.111111
$82$	−1.40991	−0.155699
$83$	−11.9354	−1.31008	−0.655041	−	0.755594i	$-0.727349\pi$
$83$	−11.9354	−1.31008	−0.655041	+	0.755594i	$0.727349\pi$
$84$	1.87044	0.204081
$85$	5.70787	0.619106
$86$	−2.71695	−0.292976
$87$	9.41891	1.00981
$88$	−6.87512	−0.732890
$89$	14.5498	1.54227	0.771137	−	0.636669i	$-0.219688\pi$
$89$	14.5498	1.54227	0.771137	+	0.636669i	$0.219688\pi$
$90$	0.635404	0.0669774
$91$	4.06932	0.426581
$92$	10.1601	1.05926
$93$	−9.32721	−0.967187
$94$	−1.22939	−0.126802
$95$	3.16565	0.324789
$96$	−3.95233	−0.403383
$97$	−6.36208	−0.645971	−0.322986	−	0.946404i	$-0.604687\pi$
$97$	−6.36208	−0.645971	−0.322986	+	0.946404i	$0.604687\pi$
$98$	−0.359948	−0.0363603
$99$	−4.93492	−0.495978
$100$	3.52361	0.352361
$101$	14.2867	1.42158	0.710791	−	0.703404i	$-0.248337\pi$
$101$	14.2867	1.42158	0.710791	+	0.703404i	$0.248337\pi$
$102$	1.16387	0.115240
$103$	−9.73850	−0.959563	−0.479781	−	0.877388i	$-0.659284\pi$
$103$	−9.73850	−0.959563	−0.479781	+	0.877388i	$0.659284\pi$
$104$	−5.66920	−0.555911
$105$	1.76526	0.172272
$106$	4.90499	0.476414
$107$	5.20271	0.502965	0.251482	−	0.967862i	$-0.419082\pi$
$107$	5.20271	0.502965	0.251482	+	0.967862i	$0.419082\pi$
$108$	−1.87044	−0.179983
$109$	12.6343	1.21015	0.605073	−	0.796170i	$-0.293144\pi$
$109$	12.6343	1.21015	0.605073	+	0.796170i	$0.293144\pi$
$110$	−3.13567	−0.298974
$111$	2.56184	0.243159
$112$	−3.23941	−0.306095
$113$	−13.9271	−1.31015	−0.655074	−	0.755565i	$-0.727363\pi$
$113$	−13.9271	−1.31015	−0.655074	+	0.755565i	$0.727363\pi$
$114$	0.645496	0.0604562
$115$	9.58879	0.894159
$116$	−17.6175	−1.63574
$117$	−4.06932	−0.376209
$118$	0.494030	0.0454791
$119$	3.23344	0.296409
$120$	−2.45929	−0.224501
$121$	13.3535	1.21395
$122$	2.45884	0.222613
$123$	3.91699	0.353183
$124$	17.4460	1.56669
$125$	12.1518	1.08689
$126$	0.359948	0.0320667
$127$	−5.01056	−0.444615	−0.222307	−	0.974977i	$-0.571359\pi$
$127$	−5.01056	−0.444615	−0.222307	+	0.974977i	$0.571359\pi$
$128$	9.72463	0.859544
$129$	7.54816	0.664579
$130$	−2.58566	−0.226777
$131$	−19.3577	−1.69129	−0.845646	−	0.533744i	$-0.820785\pi$
$131$	−19.3577	−1.69129	−0.845646	+	0.533744i	$0.820785\pi$
$132$	9.23046	0.803409
$133$	1.79330	0.155499
$134$	−1.39092	−0.120157
$135$	−1.76526	−0.151930
$136$	−4.50469	−0.386274
$137$	3.17607	0.271350	0.135675	−	0.990753i	$-0.456680\pi$
$137$	3.17607	0.271350	0.135675	+	0.990753i	$0.456680\pi$
$138$	1.95521	0.166439
$139$	−13.2073	−1.12023	−0.560115	−	0.828415i	$-0.689243\pi$
$139$	−13.2073	−1.12023	−0.560115	+	0.828415i	$0.689243\pi$
$140$	−3.30181	−0.279054
$141$	3.41548	0.287635
$142$	−5.08273	−0.426533
$143$	20.0818	1.67932
$144$	3.23941	0.269951
$145$	−16.6269	−1.38079
$146$	1.41488	0.117096
$147$	1.00000	0.0824786
$148$	−4.79176	−0.393880
$149$	14.5141	1.18904	0.594519	−	0.804082i	$-0.297343\pi$
$149$	14.5141	1.18904	0.594519	+	0.804082i	$0.297343\pi$
$150$	0.678087	0.0553655
$151$	−10.8133	−0.879976	−0.439988	−	0.898004i	$-0.645017\pi$
$151$	−10.8133	−0.879976	−0.439988	+	0.898004i	$0.645017\pi$
$152$	−2.49835	−0.202643
$153$	−3.23344	−0.261408
$154$	−1.77632	−0.143140
$155$	16.4650	1.32250
$156$	7.61141	0.609400
$157$	5.63741	0.449914	0.224957	−	0.974369i	$-0.427776\pi$
$157$	5.63741	0.449914	0.224957	+	0.974369i	$0.427776\pi$
$158$	−1.19242	−0.0948638
$159$	−13.6269	−1.08069
$160$	6.97691	0.551573
$161$	5.43193	0.428096
$162$	−0.359948	−0.0282802
$163$	15.6089	1.22259	0.611293	−	0.791404i	$-0.290650\pi$
$163$	15.6089	1.22259	0.611293	+	0.791404i	$0.290650\pi$
$164$	−7.32648	−0.572102
$165$	8.71144	0.678185
$166$	4.29613	0.333444
$167$	0.256590	0.0198555	0.00992777	−	0.999951i	$-0.496840\pi$
$167$	0.256590	0.0198555	0.00992777	+	0.999951i	$0.496840\pi$
$168$	−1.39316	−0.107484
$169$	3.55937	0.273798
$170$	−2.05454	−0.157576
$171$	−1.79330	−0.137137
$172$	−14.1184	−1.07652
$173$	26.1110	1.98518	0.992591	−	0.121501i	$-0.0387706\pi$
$173$	26.1110	1.98518	0.992591	+	0.121501i	$0.0387706\pi$
$174$	−3.39032	−0.257019
$175$	1.88384	0.142405
$176$	−15.9862	−1.20501
$177$	−1.37250	−0.103164
$178$	−5.23717	−0.392543
$179$	−11.6278	−0.869101	−0.434550	−	0.900648i	$-0.643093\pi$
$179$	−11.6278	−0.869101	−0.434550	+	0.900648i	$0.643093\pi$
$180$	3.30181	0.246103
$181$	−10.1262	−0.752675	−0.376338	−	0.926483i	$-0.622817\pi$
$181$	−10.1262	−0.752675	−0.376338	+	0.926483i	$0.622817\pi$
$182$	−1.46474	−0.108574
$183$	−6.83109	−0.504968
$184$	−7.56753	−0.557886
$185$	−4.52232	−0.332488
$186$	3.35731	0.246170
$187$	15.9568	1.16687
$188$	−6.38843	−0.465924
$189$	−1.00000	−0.0727393
$190$	−1.13947	−0.0826658
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−5.05618	−0.364899
$193$	20.8696	1.50223	0.751113	−	0.660174i	$-0.229518\pi$
$193$	20.8696	1.50223	0.751113	+	0.660174i	$0.229518\pi$
$194$	2.29002	0.164414
$195$	7.18342	0.514416
$196$	−1.87044	−0.133603
$197$	−25.8950	−1.84494	−0.922472	−	0.386064i	$-0.873834\pi$
$197$	−25.8950	−1.84494	−0.922472	+	0.386064i	$0.873834\pi$
$198$	1.77632	0.126237
$199$	17.7997	1.26179	0.630893	−	0.775870i	$-0.282689\pi$
$199$	17.7997	1.26179	0.630893	+	0.775870i	$0.282689\pi$
$200$	−2.62449	−0.185580
$201$	3.86423	0.272562
$202$	−5.14248	−0.361823
$203$	−9.41891	−0.661078
$204$	6.04795	0.423441
$205$	−6.91451	−0.482931
$206$	3.50536	0.244230
$207$	−5.43193	−0.377545
$208$	−13.1822	−0.914021
$209$	8.84980	0.612154
$210$	−0.635404	−0.0438470
$211$	23.2589	1.60121	0.800605	−	0.599193i	$-0.204512\pi$
$211$	23.2589	1.60121	0.800605	+	0.599193i	$0.204512\pi$
$212$	25.4883	1.75054
$213$	14.1207	0.967535
$214$	−1.87271	−0.128016
$215$	−13.3245	−0.908723
$216$	1.39316	0.0947923
$217$	9.32721	0.633172
$218$	−4.54770	−0.308009
$219$	−3.93079	−0.265618
$220$	−16.2942	−1.09855
$221$	13.1579	0.885096
$222$	−0.922130	−0.0618893
$223$	0.292895	0.0196137	0.00980685	−	0.999952i	$-0.496878\pi$
$223$	0.292895	0.0196137	0.00980685	+	0.999952i	$0.496878\pi$
$224$	3.95233	0.264076
$225$	−1.88384	−0.125590
$226$	5.01302	0.333461
$227$	−9.09536	−0.603680	−0.301840	−	0.953359i	$-0.597601\pi$
$227$	−9.09536	−0.603680	−0.301840	+	0.953359i	$0.597601\pi$
$228$	3.35426	0.222141
$229$	−18.2248	−1.20433	−0.602165	−	0.798371i	$-0.705695\pi$
$229$	−18.2248	−1.20433	−0.602165	+	0.798371i	$0.705695\pi$
$230$	−3.45147	−0.227583
$231$	4.93492	0.324694
$232$	13.1220	0.861503
$233$	−0.516964	−0.0338674	−0.0169337	−	0.999857i	$-0.505390\pi$
$233$	−0.516964	−0.0338674	−0.0169337	+	0.999857i	$0.505390\pi$
$234$	1.46474	0.0957534
$235$	−6.02922	−0.393303
$236$	2.56718	0.167109
$237$	3.31275	0.215186
$238$	−1.16387	−0.0754426
$239$	−4.88313	−0.315863	−0.157932	−	0.987450i	$-0.550483\pi$
$239$	−4.88313	−0.315863	−0.157932	+	0.987450i	$0.550483\pi$
$240$	−5.71841	−0.369122
$241$	29.4304	1.89578	0.947889	−	0.318601i	$-0.103213\pi$
$241$	29.4304	1.89578	0.947889	+	0.318601i	$0.103213\pi$
$242$	−4.80655	−0.308977
$243$	1.00000	0.0641500
$244$	12.7771	0.817971
$245$	−1.76526	−0.112779
$246$	−1.40991	−0.0898927
$247$	7.29752	0.464330
$248$	−12.9943	−0.825137
$249$	−11.9354	−0.756376
$250$	−4.37402	−0.276637
$251$	28.4887	1.79819	0.899095	−	0.437754i	$-0.144226\pi$
$251$	28.4887	1.79819	0.899095	+	0.437754i	$0.144226\pi$
$252$	1.87044	0.117826
$253$	26.8061	1.68529
$254$	1.80354	0.113164
$255$	5.70787	0.357441
$256$	6.61200	0.413250
$257$	0.712800	0.0444632	0.0222316	−	0.999753i	$-0.492923\pi$
$257$	0.712800	0.0444632	0.0222316	+	0.999753i	$0.492923\pi$
$258$	−2.71695	−0.169150
$259$	−2.56184	−0.159185
$260$	−13.4361	−0.833274
$261$	9.41891	0.583016
$262$	6.96778	0.430471
$263$	25.2203	1.55515	0.777576	−	0.628789i	$-0.216449\pi$
$263$	25.2203	1.55515	0.777576	+	0.628789i	$0.216449\pi$
$264$	−6.87512	−0.423134
$265$	24.0551	1.47769
$266$	−0.645496	−0.0395779
$267$	14.5498	0.890432
$268$	−7.22780	−0.441508
$269$	30.6316	1.86764	0.933821	−	0.357742i	$-0.116453\pi$
$269$	30.6316	1.86764	0.933821	+	0.357742i	$0.116453\pi$
$270$	0.635404	0.0386694
$271$	6.82404	0.414531	0.207265	−	0.978285i	$-0.433544\pi$
$271$	6.82404	0.414531	0.207265	+	0.978285i	$0.433544\pi$
$272$	−10.4744	−0.635106
$273$	4.06932	0.246286
$274$	−1.14322	−0.0690646
$275$	9.29662	0.560608
$276$	10.1601	0.611565
$277$	−14.7033	−0.883434	−0.441717	−	0.897154i	$-0.645630\pi$
$277$	−14.7033	−0.883434	−0.441717	+	0.897154i	$0.645630\pi$
$278$	4.75395	0.285123
$279$	−9.32721	−0.558405
$280$	2.45929	0.146971
$281$	16.4164	0.979323	0.489661	−	0.871913i	$-0.337120\pi$
$281$	16.4164	0.979323	0.489661	+	0.871913i	$0.337120\pi$
$282$	−1.22939	−0.0732094
$283$	−9.14058	−0.543351	−0.271676	−	0.962389i	$-0.587578\pi$
$283$	−9.14058	−0.543351	−0.271676	+	0.962389i	$0.587578\pi$
$284$	−26.4119	−1.56726
$285$	3.16565	0.187517
$286$	−7.22840	−0.427424
$287$	−3.91699	−0.231212
$288$	−3.95233	−0.232894
$289$	−6.54487	−0.384992
$290$	5.98481	0.351440
$291$	−6.36208	−0.372952
$292$	7.35230	0.430261
$293$	13.0388	0.761733	0.380867	−	0.924630i	$-0.375626\pi$
$293$	13.0388	0.761733	0.380867	+	0.924630i	$0.375626\pi$
$294$	−0.359948	−0.0209926
$295$	2.42283	0.141063
$296$	3.56905	0.207447
$297$	−4.93492	−0.286353
$298$	−5.22431	−0.302636
$299$	22.1043	1.27832
$300$	3.52361	0.203436
$301$	−7.54816	−0.435069
$302$	3.89224	0.223973
$303$	14.2867	0.820750
$304$	−5.80924	−0.333183
$305$	12.0587	0.690477
$306$	1.16387	0.0665341
$307$	−28.3673	−1.61900	−0.809502	−	0.587117i	$-0.800263\pi$
$307$	−28.3673	−1.61900	−0.809502	+	0.587117i	$0.800263\pi$
$308$	−9.23046	−0.525954
$309$	−9.73850	−0.554004
$310$	−5.92654	−0.336605
$311$	6.18735	0.350852	0.175426	−	0.984493i	$-0.443870\pi$
$311$	6.18735	0.350852	0.175426	+	0.984493i	$0.443870\pi$
$312$	−5.66920	−0.320955
$313$	−1.42917	−0.0807813	−0.0403906	−	0.999184i	$-0.512860\pi$
$313$	−1.42917	−0.0807813	−0.0403906	+	0.999184i	$0.512860\pi$
$314$	−2.02917	−0.114513
$315$	1.76526	0.0994613
$316$	−6.19629	−0.348569
$317$	1.75562	0.0986055	0.0493027	−	0.998784i	$-0.484300\pi$
$317$	1.75562	0.0986055	0.0493027	+	0.998784i	$0.484300\pi$
$318$	4.90499	0.275058
$319$	−46.4816	−2.60247
$320$	8.92550	0.498950
$321$	5.20271	0.290387
$322$	−1.95521	−0.108960
$323$	5.79853	0.322639
$324$	−1.87044	−0.103913
$325$	7.66597	0.425231
$326$	−5.61841	−0.311175
$327$	12.6343	0.698679
$328$	5.45698	0.301311
$329$	−3.41548	−0.188301
$330$	−3.13567	−0.172613
$331$	−16.2764	−0.894632	−0.447316	−	0.894376i	$-0.647620\pi$
$331$	−16.2764	−0.894632	−0.447316	+	0.894376i	$0.647620\pi$
$332$	22.3244	1.22521
$333$	2.56184	0.140388
$334$	−0.0923591	−0.00505367
$335$	−6.82139	−0.372692
$336$	−3.23941	−0.176724
$337$	32.9646	1.79570	0.897849	−	0.440303i	$-0.145129\pi$
$337$	32.9646	1.79570	0.897849	+	0.440303i	$0.145129\pi$
$338$	−1.28119	−0.0696875
$339$	−13.9271	−0.756414
$340$	−10.6762	−0.578999
$341$	46.0290	2.49261
$342$	0.645496	0.0349044
$343$	−1.00000	−0.0539949
$344$	10.5158	0.566973
$345$	9.58879	0.516243
$346$	−9.39861	−0.505272
$347$	−9.51387	−0.510731	−0.255366	−	0.966845i	$-0.582196\pi$
$347$	−9.51387	−0.510731	−0.255366	+	0.966845i	$0.582196\pi$
$348$	−17.6175	−0.944396
$349$	−22.2192	−1.18937	−0.594684	−	0.803960i	$-0.702723\pi$
$349$	−22.2192	−1.18937	−0.594684	+	0.803960i	$0.702723\pi$
$350$	−0.678087	−0.0362452
$351$	−4.06932	−0.217204
$352$	19.5045	1.03959
$353$	−15.2026	−0.809152	−0.404576	−	0.914504i	$-0.632581\pi$
$353$	−15.2026	−0.809152	−0.404576	+	0.914504i	$0.632581\pi$
$354$	0.494030	0.0262574
$355$	−24.9268	−1.32298
$356$	−27.2145	−1.44236
$357$	3.23344	0.171132
$358$	4.18540	0.221205
$359$	31.5110	1.66309	0.831543	−	0.555461i	$-0.187458\pi$
$359$	31.5110	1.66309	0.831543	+	0.555461i	$0.187458\pi$
$360$	−2.45929	−0.129616
$361$	−15.7841	−0.830741
$362$	3.64491	0.191572
$363$	13.3535	0.700874
$364$	−7.61141	−0.398946
$365$	6.93888	0.363198
$366$	2.45884	0.128526
$367$	−28.6339	−1.49468	−0.747338	−	0.664444i	$-0.768668\pi$
$367$	−28.6339	−1.49468	−0.747338	+	0.664444i	$0.768668\pi$
$368$	−17.5962	−0.917268
$369$	3.91699	0.203910
$370$	1.62780	0.0846254
$371$	13.6269	0.707475
$372$	17.4460	0.904531
$373$	−31.9419	−1.65389	−0.826944	−	0.562284i	$-0.809923\pi$
$373$	−31.9419	−1.65389	−0.826944	+	0.562284i	$0.809923\pi$
$374$	−5.74361	−0.296995
$375$	12.1518	0.627516
$376$	4.75829	0.245390
$377$	−38.3286	−1.97402
$378$	0.359948	0.0185137
$379$	−27.6188	−1.41868	−0.709341	−	0.704866i	$-0.751007\pi$
$379$	−27.6188	−1.41868	−0.709341	+	0.704866i	$0.751007\pi$
$380$	−5.92115	−0.303749
$381$	−5.01056	−0.256699
$382$	0.359948	0.0184166
$383$	−16.0806	−0.821678	−0.410839	−	0.911708i	$-0.634764\pi$
$383$	−16.0806	−0.821678	−0.410839	+	0.911708i	$0.634764\pi$
$384$	9.72463	0.496258
$385$	−8.71144	−0.443976
$386$	−7.51197	−0.382349
$387$	7.54816	0.383695
$388$	11.8999	0.604124
$389$	−5.33269	−0.270378	−0.135189	−	0.990820i	$-0.543164\pi$
$389$	−5.33269	−0.270378	−0.135189	+	0.990820i	$0.543164\pi$
$390$	−2.58566	−0.130930
$391$	17.5638	0.888240
$392$	1.39316	0.0703651
$393$	−19.3577	−0.976468
$394$	9.32087	0.469579
$395$	−5.84788	−0.294239
$396$	9.23046	0.463848
$397$	−19.1402	−0.960621	−0.480311	−	0.877098i	$-0.659476\pi$
$397$	−19.1402	−0.960621	−0.480311	+	0.877098i	$0.659476\pi$
$398$	−6.40696	−0.321152
$399$	1.79330	0.0897773
$400$	−6.10254	−0.305127
$401$	−5.17782	−0.258568	−0.129284	−	0.991608i	$-0.541268\pi$
$401$	−5.17782	−0.258568	−0.129284	+	0.991608i	$0.541268\pi$
$402$	−1.39092	−0.0693730
$403$	37.9554	1.89069
$404$	−26.7224	−1.32949
$405$	−1.76526	−0.0877167
$406$	3.39032	0.168259
$407$	−12.6425	−0.626664
$408$	−4.50469	−0.223015
$409$	−24.8267	−1.22760	−0.613800	−	0.789462i	$-0.710360\pi$
$409$	−24.8267	−1.22760	−0.613800	+	0.789462i	$0.710360\pi$
$410$	2.48887	0.122916
$411$	3.17607	0.156664
$412$	18.2152	0.897401
$413$	1.37250	0.0675364
$414$	1.95521	0.0960935
$415$	21.0691	1.03424
$416$	16.0833	0.788549
$417$	−13.2073	−0.646765
$418$	−3.18547	−0.155806
$419$	30.6593	1.49781	0.748903	−	0.662680i	$-0.230581\pi$
$419$	30.6593	1.49781	0.748903	+	0.662680i	$0.230581\pi$
$420$	−3.30181	−0.161112
$421$	5.38438	0.262418	0.131209	−	0.991355i	$-0.458114\pi$
$421$	5.38438	0.262418	0.131209	+	0.991355i	$0.458114\pi$
$422$	−8.37200	−0.407543
$423$	3.41548	0.166066
$424$	−18.9844	−0.921966
$425$	6.09130	0.295471
$426$	−5.08273	−0.246259
$427$	6.83109	0.330579
$428$	−9.73134	−0.470382
$429$	20.0818	0.969557
$430$	4.79613	0.231290
$431$	18.7375	0.902556	0.451278	−	0.892383i	$-0.350968\pi$
$431$	18.7375	0.902556	0.451278	+	0.892383i	$0.350968\pi$
$432$	3.23941	0.155856
$433$	10.7117	0.514774	0.257387	−	0.966308i	$-0.417139\pi$
$433$	10.7117	0.514774	0.257387	+	0.966308i	$0.417139\pi$
$434$	−3.35731	−0.161156
$435$	−16.6269	−0.797197
$436$	−23.6317	−1.13175
$437$	9.74108	0.465979
$438$	1.41488	0.0676057
$439$	26.0505	1.24332	0.621661	−	0.783286i	$-0.286458\pi$
$439$	26.0505	1.24332	0.621661	+	0.783286i	$0.286458\pi$
$440$	12.1364	0.578580
$441$	1.00000	0.0476190
$442$	−4.73617	−0.225276
$443$	15.1310	0.718896	0.359448	−	0.933165i	$-0.382965\pi$
$443$	15.1310	0.718896	0.359448	+	0.933165i	$0.382965\pi$
$444$	−4.79176	−0.227407
$445$	−25.6842	−1.21755
$446$	−0.105427	−0.00499212
$447$	14.5141	0.686491
$448$	5.05618	0.238882
$449$	−6.29001	−0.296844	−0.148422	−	0.988924i	$-0.547419\pi$
$449$	−6.29001	−0.296844	−0.148422	+	0.988924i	$0.547419\pi$
$450$	0.678087	0.0319653
$451$	−19.3300	−0.910215
$452$	26.0497	1.22527
$453$	−10.8133	−0.508055
$454$	3.27386	0.153650
$455$	−7.18342	−0.336764
$456$	−2.49835	−0.116996
$457$	−7.95233	−0.371994	−0.185997	−	0.982550i	$-0.559551\pi$
$457$	−7.95233	−0.371994	−0.185997	+	0.982550i	$0.559551\pi$
$458$	6.56000	0.306529
$459$	−3.23344	−0.150924
$460$	−17.9352	−0.836234
$461$	30.4285	1.41719	0.708597	−	0.705613i	$-0.249328\pi$
$461$	30.4285	1.41719	0.708597	+	0.705613i	$0.249328\pi$
$462$	−1.77632	−0.0826417
$463$	30.3858	1.41215	0.706073	−	0.708139i	$-0.250465\pi$
$463$	30.3858	1.41215	0.706073	+	0.708139i	$0.250465\pi$
$464$	30.5117	1.41647
$465$	16.4650	0.763545
$466$	0.186080	0.00862000
$467$	−18.8756	−0.873458	−0.436729	−	0.899593i	$-0.643863\pi$
$467$	−18.8756	−0.873458	−0.436729	+	0.899593i	$0.643863\pi$
$468$	7.61141	0.351837
$469$	−3.86423	−0.178434
$470$	2.17021	0.100104
$471$	5.63741	0.259758
$472$	−1.91211	−0.0880121
$473$	−37.2496	−1.71274
$474$	−1.19242	−0.0547696
$475$	3.37830	0.155007
$476$	−6.04795	−0.277207
$477$	−13.6269	−0.623934
$478$	1.75767	0.0803942
$479$	−35.2700	−1.61153	−0.805764	−	0.592237i	$-0.798245\pi$
$479$	−35.2700	−1.61153	−0.805764	+	0.592237i	$0.798245\pi$
$480$	6.97691	0.318451
$481$	−10.4249	−0.475337
$482$	−10.5934	−0.482517
$483$	5.43193	0.247161
$484$	−24.9768	−1.13531
$485$	11.2307	0.509962
$486$	−0.359948	−0.0163276
$487$	−14.8665	−0.673666	−0.336833	−	0.941564i	$-0.609356\pi$
$487$	−14.8665	−0.673666	−0.336833	+	0.941564i	$0.609356\pi$
$488$	−9.51678	−0.430804
$489$	15.6089	0.705861
$490$	0.635404	0.0287046
$491$	−7.26692	−0.327952	−0.163976	−	0.986464i	$-0.552432\pi$
$491$	−7.26692	−0.327952	−0.163976	+	0.986464i	$0.552432\pi$
$492$	−7.32648	−0.330303
$493$	−30.4555	−1.37165
$494$	−2.62673	−0.118182
$495$	8.71144	0.391550
$496$	−30.2147	−1.35668
$497$	−14.1207	−0.633400
$498$	4.29613	0.192514
$499$	−17.8891	−0.800824	−0.400412	−	0.916335i	$-0.631133\pi$
$499$	−17.8891	−0.800824	−0.400412	+	0.916335i	$0.631133\pi$
$500$	−22.7292	−1.01648
$501$	0.256590	0.0114636
$502$	−10.2545	−0.457679
$503$	15.8911	0.708549	0.354275	−	0.935141i	$-0.384728\pi$
$503$	15.8911	0.708549	0.354275	+	0.935141i	$0.384728\pi$
$504$	−1.39316	−0.0620562
$505$	−25.2198	−1.12227
$506$	−9.64882	−0.428943
$507$	3.55937	0.158077
$508$	9.37193	0.415812
$509$	12.9163	0.572507	0.286254	−	0.958154i	$-0.407590\pi$
$509$	12.9163	0.572507	0.286254	+	0.958154i	$0.407590\pi$
$510$	−2.05454	−0.0909765
$511$	3.93079	0.173888
$512$	−21.8292	−0.964726
$513$	−1.79330	−0.0791762
$514$	−0.256571	−0.0113169
$515$	17.1910	0.757527
$516$	−14.1184	−0.621526
$517$	−16.8551	−0.741287
$518$	0.922130	0.0405161
$519$	26.1110	1.14615
$520$	10.0076	0.438864
$521$	−31.5390	−1.38175	−0.690873	−	0.722976i	$-0.742774\pi$
$521$	−31.5390	−1.38175	−0.690873	+	0.722976i	$0.742774\pi$
$522$	−3.39032	−0.148390
$523$	−1.84062	−0.0804845	−0.0402423	−	0.999190i	$-0.512813\pi$
$523$	−1.84062	−0.0804845	−0.0402423	+	0.999190i	$0.512813\pi$
$524$	36.2074	1.58173
$525$	1.88384	0.0822177
$526$	−9.07802	−0.395820
$527$	30.1590	1.31375
$528$	−15.9862	−0.695712
$529$	6.50584	0.282863
$530$	−8.65860	−0.376105
$531$	−1.37250	−0.0595615
$532$	−3.35426	−0.145425
$533$	−15.9395	−0.690415
$534$	−5.23717	−0.226635
$535$	−9.18415	−0.397065
$536$	5.38348	0.232531
$537$	−11.6278	−0.501775
$538$	−11.0258	−0.475356
$539$	−4.93492	−0.212562
$540$	3.30181	0.142087
$541$	5.57678	0.239765	0.119882	−	0.992788i	$-0.461748\pi$
$541$	5.57678	0.239765	0.119882	+	0.992788i	$0.461748\pi$
$542$	−2.45630	−0.105507
$543$	−10.1262	−0.434557
$544$	12.7796	0.547922
$545$	−22.3029	−0.955350
$546$	−1.46474	−0.0626853
$547$	−24.3206	−1.03987	−0.519936	−	0.854205i	$-0.674044\pi$
$547$	−24.3206	−1.03987	−0.519936	+	0.854205i	$0.674044\pi$
$548$	−5.94065	−0.253772
$549$	−6.83109	−0.291544
$550$	−3.34630	−0.142687
$551$	−16.8909	−0.719578
$552$	−7.56753	−0.322095
$553$	−3.31275	−0.140873
$554$	5.29242	0.224853
$555$	−4.52232	−0.191962
$556$	24.7034	1.04766
$557$	−8.01901	−0.339776	−0.169888	−	0.985463i	$-0.554341\pi$
$557$	−8.01901	−0.339776	−0.169888	+	0.985463i	$0.554341\pi$
$558$	3.35731	0.142126
$559$	−30.7159	−1.29914
$560$	5.71841	0.241647
$561$	15.9568	0.673695
$562$	−5.90907	−0.249259
$563$	−20.8473	−0.878610	−0.439305	−	0.898338i	$-0.644775\pi$
$563$	−20.8473	−0.878610	−0.439305	+	0.898338i	$0.644775\pi$
$564$	−6.38843	−0.269002
$565$	24.5849	1.03430
$566$	3.29014	0.138295
$567$	−1.00000	−0.0419961
$568$	19.6724	0.825434
$569$	10.6470	0.446345	0.223172	−	0.974779i	$-0.428359\pi$
$569$	10.6470	0.446345	0.223172	+	0.974779i	$0.428359\pi$
$570$	−1.13947	−0.0477271
$571$	−31.3399	−1.31154	−0.655768	−	0.754962i	$-0.727655\pi$
$571$	−31.3399	−1.31154	−0.655768	+	0.754962i	$0.727655\pi$
$572$	−37.5617	−1.57053
$573$	−1.00000	−0.0417756
$574$	1.40991	0.0588486
$575$	10.2329	0.426742
$576$	−5.05618	−0.210674
$577$	−27.9076	−1.16181	−0.580904	−	0.813972i	$-0.697301\pi$
$577$	−27.9076	−1.16181	−0.580904	+	0.813972i	$0.697301\pi$
$578$	2.35581	0.0979889
$579$	20.8696	0.867310
$580$	31.0995	1.29134
$581$	11.9354	0.495164
$582$	2.29002	0.0949244
$583$	67.2478	2.78512
$584$	−5.47621	−0.226607
$585$	7.18342	0.296998
$586$	−4.69328	−0.193878
$587$	−10.3272	−0.426248	−0.213124	−	0.977025i	$-0.568364\pi$
$587$	−10.3272	−0.426248	−0.213124	+	0.977025i	$0.568364\pi$
$588$	−1.87044	−0.0771355
$589$	16.7265	0.689203
$590$	−0.872093	−0.0359035
$591$	−25.8950	−1.06518
$592$	8.29885	0.341081
$593$	−3.46512	−0.142295	−0.0711477	−	0.997466i	$-0.522666\pi$
$593$	−3.46512	−0.142295	−0.0711477	+	0.997466i	$0.522666\pi$
$594$	1.77632	0.0728832
$595$	−5.70787	−0.234000
$596$	−27.1476	−1.11201
$597$	17.7997	0.728492
$598$	−7.95639	−0.325361
$599$	0.593768	0.0242607	0.0121303	−	0.999926i	$-0.496139\pi$
$599$	0.593768	0.0242607	0.0121303	+	0.999926i	$0.496139\pi$
$600$	−2.62449	−0.107144
$601$	5.75822	0.234883	0.117441	−	0.993080i	$-0.462531\pi$
$601$	5.75822	0.234883	0.117441	+	0.993080i	$0.462531\pi$
$602$	2.71695	0.110735
$603$	3.86423	0.157364
$604$	20.2257	0.822970
$605$	−23.5724	−0.958353
$606$	−5.14248	−0.208899
$607$	39.6997	1.61136	0.805681	−	0.592350i	$-0.201800\pi$
$607$	39.6997	1.61136	0.805681	+	0.592350i	$0.201800\pi$
$608$	7.08773	0.287445
$609$	−9.41891	−0.381673
$610$	−4.34050	−0.175742
$611$	−13.8987	−0.562280
$612$	6.04795	0.244474
$613$	−15.4365	−0.623474	−0.311737	−	0.950168i	$-0.600911\pi$
$613$	−15.4365	−0.623474	−0.311737	+	0.950168i	$0.600911\pi$
$614$	10.2107	0.412072
$615$	−6.91451	−0.278820
$616$	6.87512	0.277007
$617$	38.2898	1.54149	0.770745	−	0.637143i	$-0.219884\pi$
$617$	38.2898	1.54149	0.770745	+	0.637143i	$0.219884\pi$
$618$	3.50536	0.141006
$619$	−9.37357	−0.376755	−0.188378	−	0.982097i	$-0.560323\pi$
$619$	−9.37357	−0.376755	−0.188378	+	0.982097i	$0.560323\pi$
$620$	−30.7967	−1.23683
$621$	−5.43193	−0.217976
$622$	−2.22713	−0.0892996
$623$	−14.5498	−0.582925
$624$	−13.1822	−0.527710
$625$	−12.0319	−0.481276
$626$	0.514426	0.0205606
$627$	8.84980	0.353427
$628$	−10.5444	−0.420768
$629$	−8.28356	−0.330287
$630$	−0.635404	−0.0253151
$631$	−8.15339	−0.324581	−0.162291	−	0.986743i	$-0.551888\pi$
$631$	−8.15339	−0.324581	−0.162291	+	0.986743i	$0.551888\pi$
$632$	4.61518	0.183582
$633$	23.2589	0.924459
$634$	−0.631932	−0.0250972
$635$	8.84495	0.351001
$636$	25.4883	1.01068
$637$	−4.06932	−0.161232
$638$	16.7310	0.662385
$639$	14.1207	0.558607
$640$	−17.1665	−0.678567
$641$	3.74766	0.148024	0.0740118	−	0.997257i	$-0.476420\pi$
$641$	3.74766	0.148024	0.0740118	+	0.997257i	$0.476420\pi$
$642$	−1.87271	−0.0739098
$643$	27.5663	1.08711	0.543555	−	0.839373i	$-0.317078\pi$
$643$	27.5663	1.08711	0.543555	+	0.839373i	$0.317078\pi$
$644$	−10.1601	−0.400363
$645$	−13.3245	−0.524652
$646$	−2.08717	−0.0821187
$647$	18.0860	0.711033	0.355517	−	0.934670i	$-0.384305\pi$
$647$	18.0860	0.711033	0.355517	+	0.934670i	$0.384305\pi$
$648$	1.39316	0.0547284
$649$	6.77319	0.265871
$650$	−2.75935	−0.108231
$651$	9.32721	0.365562
$652$	−29.1956	−1.14339
$653$	−10.6515	−0.416826	−0.208413	−	0.978041i	$-0.566830\pi$
$653$	−10.6515	−0.416826	−0.208413	+	0.978041i	$0.566830\pi$
$654$	−4.54770	−0.177829
$655$	34.1715	1.33519
$656$	12.6887	0.495411
$657$	−3.93079	−0.153355
$658$	1.22939	0.0479268
$659$	46.1103	1.79620	0.898101	−	0.439789i	$-0.144947\pi$
$659$	46.1103	1.79620	0.898101	+	0.439789i	$0.144947\pi$
$660$	−16.2942	−0.634251
$661$	43.3783	1.68722	0.843609	−	0.536958i	$-0.180426\pi$
$661$	43.3783	1.68722	0.843609	+	0.536958i	$0.180426\pi$
$662$	5.85867	0.227703
$663$	13.1579	0.511011
$664$	−16.6279	−0.645288
$665$	−3.16565	−0.122759
$666$	−0.922130	−0.0357318
$667$	−51.1628	−1.98103
$668$	−0.479936	−0.0185693
$669$	0.292895	0.0113240
$670$	2.45535	0.0948583
$671$	33.7109	1.30139
$672$	3.95233	0.152465
$673$	−31.5806	−1.21734	−0.608671	−	0.793423i	$-0.708297\pi$
$673$	−31.5806	−1.21734	−0.608671	+	0.793423i	$0.708297\pi$
$674$	−11.8656	−0.457045
$675$	−1.88384	−0.0725092
$676$	−6.65758	−0.256061
$677$	38.3194	1.47273	0.736367	−	0.676583i	$-0.236540\pi$
$677$	38.3194	1.47273	0.736367	+	0.676583i	$0.236540\pi$
$678$	5.01302	0.192524
$679$	6.36208	0.244154
$680$	7.95197	0.304944
$681$	−9.09536	−0.348535
$682$	−16.5681	−0.634424
$683$	17.1842	0.657535	0.328767	−	0.944411i	$-0.393367\pi$
$683$	17.1842	0.657535	0.328767	+	0.944411i	$0.393367\pi$
$684$	3.35426	0.128253
$685$	−5.60661	−0.214217
$686$	0.359948	0.0137429
$687$	−18.2248	−0.695321
$688$	24.4516	0.932208
$689$	55.4523	2.11256
$690$	−3.45147	−0.131395
$691$	0.698571	0.0265749	0.0132875	−	0.999912i	$-0.495770\pi$
$691$	0.698571	0.0265749	0.0132875	+	0.999912i	$0.495770\pi$
$692$	−48.8390	−1.85658
$693$	4.93492	0.187462
$694$	3.42450	0.129992
$695$	23.3144	0.884365
$696$	13.1220	0.497389
$697$	−12.6653	−0.479734
$698$	7.99777	0.302720
$699$	−0.516964	−0.0195534
$700$	−3.52361	−0.133180
$701$	28.5917	1.07990	0.539948	−	0.841699i	$-0.318444\pi$
$701$	28.5917	1.07990	0.539948	+	0.841699i	$0.318444\pi$
$702$	1.46474	0.0552832
$703$	−4.59415	−0.173272
$704$	24.9519	0.940409
$705$	−6.02922	−0.227073
$706$	5.47214	0.205947
$707$	−14.2867	−0.537307
$708$	2.56718	0.0964805
$709$	−5.35640	−0.201164	−0.100582	−	0.994929i	$-0.532070\pi$
$709$	−5.35640	−0.201164	−0.100582	+	0.994929i	$0.532070\pi$
$710$	8.97235	0.336726
$711$	3.31275	0.124238
$712$	20.2701	0.759656
$713$	50.6647	1.89741
$714$	−1.16387	−0.0435568
$715$	−35.4496	−1.32574
$716$	21.7490	0.812799
$717$	−4.88313	−0.182364
$718$	−11.3423	−0.423292
$719$	−1.62117	−0.0604595	−0.0302297	−	0.999543i	$-0.509624\pi$
$719$	−1.62117	−0.0604595	−0.0302297	+	0.999543i	$0.509624\pi$
$720$	−5.71841	−0.213113
$721$	9.73850	0.362681
$722$	5.68145	0.211442
$723$	29.4304	1.09453
$724$	18.9404	0.703916
$725$	−17.7438	−0.658987
$726$	−4.80655	−0.178388
$727$	2.78199	0.103178	0.0515891	−	0.998668i	$-0.483571\pi$
$727$	2.78199	0.103178	0.0515891	+	0.998668i	$0.483571\pi$
$728$	5.66920	0.210115
$729$	1.00000	0.0370370
$730$	−2.49764	−0.0924418
$731$	−24.4065	−0.902708
$732$	12.7771	0.472256
$733$	51.6399	1.90736	0.953682	−	0.300818i	$-0.0972597\pi$
$733$	51.6399	1.90736	0.953682	+	0.300818i	$0.0972597\pi$
$734$	10.3067	0.380428
$735$	−1.76526	−0.0651127
$736$	21.4688	0.791350
$737$	−19.0697	−0.702441
$738$	−1.40991	−0.0518996
$739$	25.2045	0.927162	0.463581	−	0.886055i	$-0.346564\pi$
$739$	25.2045	0.927162	0.463581	+	0.886055i	$0.346564\pi$
$740$	8.45872	0.310949
$741$	7.29752	0.268081
$742$	−4.90499	−0.180068
$743$	−50.9858	−1.87049	−0.935244	−	0.354003i	$-0.884820\pi$
$743$	−50.9858	−1.87049	−0.935244	+	0.354003i	$0.884820\pi$
$744$	−12.9943	−0.476393
$745$	−25.6211	−0.938685
$746$	11.4974	0.420951
$747$	−11.9354	−0.436694
$748$	−29.8461	−1.09128
$749$	−5.20271	−0.190103
$750$	−4.37402	−0.159717
$751$	−50.4661	−1.84153	−0.920767	−	0.390114i	$-0.872436\pi$
$751$	−50.4661	−1.84153	−0.920767	+	0.390114i	$0.872436\pi$
$752$	11.0641	0.403467
$753$	28.4887	1.03819
$754$	13.7963	0.502431
$755$	19.0884	0.694697
$756$	1.87044	0.0680271
$757$	−41.1800	−1.49671	−0.748356	−	0.663297i	$-0.769157\pi$
$757$	−41.1800	−1.49671	−0.748356	+	0.663297i	$0.769157\pi$
$758$	9.94133	0.361085
$759$	26.8061	0.973001
$760$	4.41025	0.159976
$761$	4.19897	0.152212	0.0761062	−	0.997100i	$-0.475751\pi$
$761$	4.19897	0.152212	0.0761062	+	0.997100i	$0.475751\pi$
$762$	1.80354	0.0653354
$763$	−12.6343	−0.457393
$764$	1.87044	0.0676700
$765$	5.70787	0.206369
$766$	5.78817	0.209135
$767$	5.58515	0.201668
$768$	6.61200	0.238590
$769$	1.45938	0.0526265	0.0263132	−	0.999654i	$-0.491623\pi$
$769$	1.45938	0.0526265	0.0263132	+	0.999654i	$0.491623\pi$
$770$	3.13567	0.113002
$771$	0.712800	0.0256709
$772$	−39.0352	−1.40491
$773$	−28.3602	−1.02004	−0.510022	−	0.860161i	$-0.670363\pi$
$773$	−28.3602	−1.02004	−0.510022	+	0.860161i	$0.670363\pi$
$774$	−2.71695	−0.0976587
$775$	17.5710	0.631169
$776$	−8.86338	−0.318177
$777$	−2.56184	−0.0919055
$778$	1.91949	0.0688172
$779$	−7.02434	−0.251673
$780$	−13.4361	−0.481091
$781$	−69.6846	−2.49351
$782$	−6.32206	−0.226077
$783$	9.41891	0.336604
$784$	3.23941	0.115693
$785$	−9.95151	−0.355185
$786$	6.96778	0.248533
$787$	37.4855	1.33621	0.668107	−	0.744065i	$-0.267105\pi$
$787$	37.4855	1.33621	0.668107	+	0.744065i	$0.267105\pi$
$788$	48.4350	1.72543
$789$	25.2203	0.897868
$790$	2.10493	0.0748902
$791$	13.9271	0.495189
$792$	−6.87512	−0.244297
$793$	27.7979	0.987132
$794$	6.88950	0.244499
$795$	24.0551	0.853147
$796$	−33.2932	−1.18005
$797$	10.0819	0.357118	0.178559	−	0.983929i	$-0.442856\pi$
$797$	10.0819	0.357118	0.178559	+	0.983929i	$0.442856\pi$
$798$	−0.645496	−0.0228503
$799$	−11.0437	−0.390699
$800$	7.44558	0.263241
$801$	14.5498	0.514091
$802$	1.86375	0.0658112
$803$	19.3982	0.684546
$804$	−7.22780	−0.254905
$805$	−9.58879	−0.337960
$806$	−13.6620	−0.481223
$807$	30.6316	1.07828
$808$	19.9036	0.700208
$809$	−23.1867	−0.815202	−0.407601	−	0.913160i	$-0.633635\pi$
$809$	−23.1867	−0.815202	−0.407601	+	0.913160i	$0.633635\pi$
$810$	0.635404	0.0223258
$811$	−34.4874	−1.21102	−0.605509	−	0.795838i	$-0.707030\pi$
$811$	−34.4874	−1.21102	−0.605509	+	0.795838i	$0.707030\pi$
$812$	17.6175	0.618252
$813$	6.82404	0.239330
$814$	4.55064	0.159500
$815$	−27.5539	−0.965171
$816$	−10.4744	−0.366679
$817$	−13.5361	−0.473569
$818$	8.93632	0.312451
$819$	4.06932	0.142194
$820$	12.9332	0.451646
$821$	−56.0014	−1.95446	−0.977230	−	0.212181i	$-0.931943\pi$
$821$	−56.0014	−1.95446	−0.977230	+	0.212181i	$0.931943\pi$
$822$	−1.14322	−0.0398745
$823$	35.7142	1.24492	0.622460	−	0.782652i	$-0.286133\pi$
$823$	35.7142	1.24492	0.622460	+	0.782652i	$0.286133\pi$
$824$	−13.5673	−0.472638
$825$	9.29662	0.323667
$826$	−0.494030	−0.0171895
$827$	36.6221	1.27347	0.636737	−	0.771081i	$-0.280284\pi$
$827$	36.6221	1.27347	0.636737	+	0.771081i	$0.280284\pi$
$828$	10.1601	0.353087
$829$	−11.7089	−0.406667	−0.203334	−	0.979110i	$-0.565178\pi$
$829$	−11.7089	−0.406667	−0.203334	+	0.979110i	$0.565178\pi$
$830$	−7.58380	−0.263238
$831$	−14.7033	−0.510051
$832$	20.5752	0.713318
$833$	−3.23344	−0.112032
$834$	4.75395	0.164616
$835$	−0.452949	−0.0156749
$836$	−16.5530	−0.572497
$837$	−9.32721	−0.322396
$838$	−11.0358	−0.381224
$839$	3.40321	0.117492	0.0587459	−	0.998273i	$-0.481290\pi$
$839$	3.40321	0.117492	0.0587459	+	0.998273i	$0.481290\pi$
$840$	2.45929	0.0848536
$841$	59.7158	2.05917
$842$	−1.93810	−0.0667912
$843$	16.4164	0.565412
$844$	−43.5043	−1.49748
$845$	−6.28323	−0.216150
$846$	−1.22939	−0.0422675
$847$	−13.3535	−0.458830
$848$	−44.1432	−1.51588
$849$	−9.14058	−0.313704
$850$	−2.19255	−0.0752039
$851$	−13.9157	−0.477025
$852$	−26.4119	−0.904857
$853$	20.8882	0.715197	0.357599	−	0.933875i	$-0.383596\pi$
$853$	20.8882	0.715197	0.357599	+	0.933875i	$0.383596\pi$
$854$	−2.45884	−0.0841397
$855$	3.16565	0.108263
$856$	7.24819	0.247738
$857$	20.2434	0.691501	0.345751	−	0.938326i	$-0.387624\pi$
$857$	20.2434	0.691501	0.345751	+	0.938326i	$0.387624\pi$
$858$	−7.22840	−0.246774
$859$	−46.3409	−1.58113	−0.790565	−	0.612378i	$-0.790213\pi$
$859$	−46.3409	−1.58113	−0.790565	+	0.612378i	$0.790213\pi$
$860$	24.9226	0.849855
$861$	−3.91699	−0.133491
$862$	−6.74455	−0.229720
$863$	31.8850	1.08538	0.542689	−	0.839934i	$-0.317406\pi$
$863$	31.8850	1.08538	0.542689	+	0.839934i	$0.317406\pi$
$864$	−3.95233	−0.134461
$865$	−46.0928	−1.56720
$866$	−3.85568	−0.131021
$867$	−6.54487	−0.222275
$868$	−17.4460	−0.592154
$869$	−16.3482	−0.554574
$870$	5.98481	0.202904
$871$	−15.7248	−0.532814
$872$	17.6016	0.596065
$873$	−6.36208	−0.215324
$874$	−3.50629	−0.118602
$875$	−12.1518	−0.410806
$876$	7.35230	0.248411
$877$	42.1512	1.42335	0.711673	−	0.702511i	$-0.247938\pi$
$877$	42.1512	1.42335	0.711673	+	0.702511i	$0.247938\pi$
$878$	−9.37683	−0.316453
$879$	13.0388	0.439787
$880$	28.2199	0.951293
$881$	−54.6879	−1.84248	−0.921242	−	0.388990i	$-0.872824\pi$
$881$	−54.6879	−1.84248	−0.921242	+	0.388990i	$0.872824\pi$
$882$	−0.359948	−0.0121201
$883$	−7.50017	−0.252401	−0.126200	−	0.992005i	$-0.540278\pi$
$883$	−7.50017	−0.252401	−0.126200	+	0.992005i	$0.540278\pi$
$884$	−24.6110	−0.827759
$885$	2.42283	0.0814425
$886$	−5.44638	−0.182975
$887$	−18.6639	−0.626674	−0.313337	−	0.949642i	$-0.601447\pi$
$887$	−18.6639	−0.626674	−0.313337	+	0.949642i	$0.601447\pi$
$888$	3.56905	0.119769
$889$	5.01056	0.168049
$890$	9.24499	0.309893
$891$	−4.93492	−0.165326
$892$	−0.547842	−0.0183431
$893$	−6.12498	−0.204965
$894$	−5.22431	−0.174727
$895$	20.5261	0.686111
$896$	−9.72463	−0.324877
$897$	22.1043	0.738040
$898$	2.26408	0.0755533
$899$	−87.8521	−2.93003
$900$	3.52361	0.117454
$901$	44.0618	1.46791
$902$	6.95781	0.231670
$903$	−7.54816	−0.251187
$904$	−19.4026	−0.645320
$905$	17.8754	0.594199
$906$	3.89224	0.129311
$907$	17.1696	0.570108	0.285054	−	0.958511i	$-0.407988\pi$
$907$	17.1696	0.570108	0.285054	+	0.958511i	$0.407988\pi$
$908$	17.0123	0.564573
$909$	14.2867	0.473860
$910$	2.58566	0.0857138
$911$	−35.6103	−1.17982	−0.589911	−	0.807468i	$-0.700837\pi$
$911$	−35.6103	−1.17982	−0.589911	+	0.807468i	$0.700837\pi$
$912$	−5.80924	−0.192363
$913$	58.9003	1.94932
$914$	2.86243	0.0946806
$915$	12.0587	0.398647
$916$	34.0884	1.12631
$917$	19.3577	0.639249
$918$	1.16387	0.0384135
$919$	−28.9317	−0.954369	−0.477184	−	0.878803i	$-0.658343\pi$
$919$	−28.9317	−0.954369	−0.477184	+	0.878803i	$0.658343\pi$
$920$	13.3587	0.440423
$921$	−28.3673	−0.934733
$922$	−10.9527	−0.360707
$923$	−57.4617	−1.89137
$924$	−9.23046	−0.303660
$925$	−4.82611	−0.158681
$926$	−10.9373	−0.359422
$927$	−9.73850	−0.319854
$928$	−37.2267	−1.22203
$929$	−45.6150	−1.49658	−0.748289	−	0.663373i	$-0.769124\pi$
$929$	−45.6150	−1.49658	−0.748289	+	0.663373i	$0.769124\pi$
$930$	−5.92654	−0.194339
$931$	−1.79330	−0.0587731
$932$	0.966948	0.0316734
$933$	6.18735	0.202565
$934$	6.79424	0.222314
$935$	−28.1679	−0.921189
$936$	−5.66920	−0.185304
$937$	−33.1182	−1.08192	−0.540962	−	0.841047i	$-0.681940\pi$
$937$	−33.1182	−1.08192	−0.540962	+	0.841047i	$0.681940\pi$
$938$	1.39092	0.0454153
$939$	−1.42917	−0.0466391
$940$	11.2773	0.367824
$941$	−6.12506	−0.199671	−0.0998356	−	0.995004i	$-0.531832\pi$
$941$	−6.12506	−0.199671	−0.0998356	+	0.995004i	$0.531832\pi$
$942$	−2.02917	−0.0661141
$943$	−21.2768	−0.692868
$944$	−4.44610	−0.144708
$945$	1.76526	0.0574240
$946$	13.4079	0.435929
$947$	−9.36072	−0.304183	−0.152091	−	0.988366i	$-0.548601\pi$
$947$	−9.36072	−0.304183	−0.152091	+	0.988366i	$0.548601\pi$
$948$	−6.19629	−0.201246
$949$	15.9957	0.519241
$950$	−1.21601	−0.0394527
$951$	1.75562	0.0569299
$952$	4.50469	0.145998
$953$	−4.12594	−0.133652	−0.0668261	−	0.997765i	$-0.521287\pi$
$953$	−4.12594	−0.133652	−0.0668261	+	0.997765i	$0.521287\pi$
$954$	4.90499	0.158805
$955$	1.76526	0.0571226
$956$	9.13359	0.295401
$957$	−46.4816	−1.50254
$958$	12.6954	0.410169
$959$	−3.17607	−0.102561
$960$	8.92550	0.288069
$961$	55.9968	1.80635
$962$	3.75244	0.120984
$963$	5.20271	0.167655
$964$	−55.0477	−1.77297
$965$	−36.8403	−1.18593
$966$	−1.95521	−0.0629080
$967$	−46.5239	−1.49611	−0.748053	−	0.663638i	$-0.769011\pi$
$967$	−46.5239	−1.49611	−0.748053	+	0.663638i	$0.769011\pi$
$968$	18.6035	0.597938
$969$	5.79853	0.186276
$970$	−4.04249	−0.129796
$971$	−29.5039	−0.946824	−0.473412	−	0.880841i	$-0.656978\pi$
$971$	−29.5039	−0.946824	−0.473412	+	0.880841i	$0.656978\pi$
$972$	−1.87044	−0.0599943
$973$	13.2073	0.423407
$974$	5.35117	0.171463
$975$	7.66597	0.245507
$976$	−22.1287	−0.708322
$977$	56.7752	1.81640	0.908200	−	0.418536i	$-0.137457\pi$
$977$	56.7752	1.81640	0.908200	+	0.418536i	$0.137457\pi$
$978$	−5.61841	−0.179657
$979$	−71.8021	−2.29480
$980$	3.30181	0.105473
$981$	12.6343	0.403382
$982$	2.61572	0.0834709
$983$	44.5700	1.42156	0.710782	−	0.703412i	$-0.248341\pi$
$983$	44.5700	1.42156	0.710782	+	0.703412i	$0.248341\pi$
$984$	5.45698	0.173962
$985$	45.7115	1.45649
$986$	10.9624	0.349114
$987$	−3.41548	−0.108716
$988$	−13.6495	−0.434250
$989$	−41.0011	−1.30376
$990$	−3.13567	−0.0996580
$991$	−25.5903	−0.812903	−0.406452	−	0.913672i	$-0.633234\pi$
$991$	−25.5903	−0.812903	−0.406452	+	0.913672i	$0.633234\pi$
$992$	36.8643	1.17044
$993$	−16.2764	−0.516516
$994$	5.08273	0.161214
$995$	−31.4211	−0.996116
$996$	22.3244	0.707377
$997$	−33.0428	−1.04648	−0.523238	−	0.852186i	$-0.675276\pi$
$997$	−33.0428	−1.04648	−0.523238	+	0.852186i	$0.675276\pi$
$998$	6.43913	0.203827
$999$	2.56184	0.0810530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.12	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.12	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.359948 q^{2} +1.00000 q^{3} -1.87044 q^{4} -1.76526 q^{5} -0.359948 q^{6} -1.00000 q^{7} +1.39316 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.359948 q^{2} +1.00000 q^{3} -1.87044 q^{4} -1.76526 q^{5} -0.359948 q^{6} -1.00000 q^{7} +1.39316 q^{8} +1.00000 q^{9} +0.635404 q^{10} -4.93492 q^{11} -1.87044 q^{12} -4.06932 q^{13} +0.359948 q^{14} -1.76526 q^{15} +3.23941 q^{16} -3.23344 q^{17} -0.359948 q^{18} -1.79330 q^{19} +3.30181 q^{20} -1.00000 q^{21} +1.77632 q^{22} -5.43193 q^{23} +1.39316 q^{24} -1.88384 q^{25} +1.46474 q^{26} +1.00000 q^{27} +1.87044 q^{28} +9.41891 q^{29} +0.635404 q^{30} -9.32721 q^{31} -3.95233 q^{32} -4.93492 q^{33} +1.16387 q^{34} +1.76526 q^{35} -1.87044 q^{36} +2.56184 q^{37} +0.645496 q^{38} -4.06932 q^{39} -2.45929 q^{40} +3.91699 q^{41} +0.359948 q^{42} +7.54816 q^{43} +9.23046 q^{44} -1.76526 q^{45} +1.95521 q^{46} +3.41548 q^{47} +3.23941 q^{48} +1.00000 q^{49} +0.678087 q^{50} -3.23344 q^{51} +7.61141 q^{52} -13.6269 q^{53} -0.359948 q^{54} +8.71144 q^{55} -1.39316 q^{56} -1.79330 q^{57} -3.39032 q^{58} -1.37250 q^{59} +3.30181 q^{60} -6.83109 q^{61} +3.35731 q^{62} -1.00000 q^{63} -5.05618 q^{64} +7.18342 q^{65} +1.77632 q^{66} +3.86423 q^{67} +6.04795 q^{68} -5.43193 q^{69} -0.635404 q^{70} +14.1207 q^{71} +1.39316 q^{72} -3.93079 q^{73} -0.922130 q^{74} -1.88384 q^{75} +3.35426 q^{76} +4.93492 q^{77} +1.46474 q^{78} +3.31275 q^{79} -5.71841 q^{80} +1.00000 q^{81} -1.40991 q^{82} -11.9354 q^{83} +1.87044 q^{84} +5.70787 q^{85} -2.71695 q^{86} +9.41891 q^{87} -6.87512 q^{88} +14.5498 q^{89} +0.635404 q^{90} +4.06932 q^{91} +10.1601 q^{92} -9.32721 q^{93} -1.22939 q^{94} +3.16565 q^{95} -3.95233 q^{96} -6.36208 q^{97} -0.359948 q^{98} -4.93492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

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