LMFDB - Embedded newform 4011.2.a.m.1.15

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			1.15
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)

$f(q)$	$=$	$q+0.336232 q^{2} +1.00000 q^{3} -1.88695 q^{4} +4.17128 q^{5} +0.336232 q^{6} -1.00000 q^{7} -1.30692 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.336232 q^{2} +1.00000 q^{3} -1.88695 q^{4} +4.17128 q^{5} +0.336232 q^{6} -1.00000 q^{7} -1.30692 q^{8} +1.00000 q^{9} +1.40252 q^{10} -5.19867 q^{11} -1.88695 q^{12} -0.719458 q^{13} -0.336232 q^{14} +4.17128 q^{15} +3.33447 q^{16} +4.70641 q^{17} +0.336232 q^{18} -6.93509 q^{19} -7.87100 q^{20} -1.00000 q^{21} -1.74796 q^{22} +1.38621 q^{23} -1.30692 q^{24} +12.3996 q^{25} -0.241905 q^{26} +1.00000 q^{27} +1.88695 q^{28} +7.28390 q^{29} +1.40252 q^{30} +2.48273 q^{31} +3.73499 q^{32} -5.19867 q^{33} +1.58245 q^{34} -4.17128 q^{35} -1.88695 q^{36} +6.10322 q^{37} -2.33180 q^{38} -0.719458 q^{39} -5.45152 q^{40} -6.82507 q^{41} -0.336232 q^{42} -1.71068 q^{43} +9.80962 q^{44} +4.17128 q^{45} +0.466088 q^{46} +3.46042 q^{47} +3.33447 q^{48} +1.00000 q^{49} +4.16914 q^{50} +4.70641 q^{51} +1.35758 q^{52} +6.93370 q^{53} +0.336232 q^{54} -21.6851 q^{55} +1.30692 q^{56} -6.93509 q^{57} +2.44908 q^{58} +9.78274 q^{59} -7.87100 q^{60} +0.455540 q^{61} +0.834774 q^{62} -1.00000 q^{63} -5.41312 q^{64} -3.00106 q^{65} -1.74796 q^{66} +12.6532 q^{67} -8.88076 q^{68} +1.38621 q^{69} -1.40252 q^{70} +15.1859 q^{71} -1.30692 q^{72} +7.63566 q^{73} +2.05210 q^{74} +12.3996 q^{75} +13.0862 q^{76} +5.19867 q^{77} -0.241905 q^{78} +12.2700 q^{79} +13.9090 q^{80} +1.00000 q^{81} -2.29480 q^{82} +2.53129 q^{83} +1.88695 q^{84} +19.6318 q^{85} -0.575185 q^{86} +7.28390 q^{87} +6.79422 q^{88} -1.80820 q^{89} +1.40252 q^{90} +0.719458 q^{91} -2.61571 q^{92} +2.48273 q^{93} +1.16350 q^{94} -28.9282 q^{95} +3.73499 q^{96} +10.5131 q^{97} +0.336232 q^{98} -5.19867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.336232	0.237752	0.118876	−	0.992909i	$-0.462071\pi$
$2$	0.336232	0.237752	0.118876	+	0.992909i	$0.462071\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.88695	−0.943474
$5$	4.17128	1.86545	0.932727	−	0.360582i	$-0.117422\pi$
$5$	4.17128	1.86545	0.932727	+	0.360582i	$0.117422\pi$
$6$	0.336232	0.137266
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.30692	−0.462064
$9$	1.00000	0.333333
$10$	1.40252	0.443515
$11$	−5.19867	−1.56746	−0.783729	−	0.621103i	$-0.786685\pi$
$11$	−5.19867	−1.56746	−0.783729	+	0.621103i	$0.786685\pi$
$12$	−1.88695	−0.544715
$13$	−0.719458	−0.199542	−0.0997709	−	0.995010i	$-0.531811\pi$
$13$	−0.719458	−0.199542	−0.0997709	+	0.995010i	$0.531811\pi$
$14$	−0.336232	−0.0898617
$15$	4.17128	1.07702
$16$	3.33447	0.833617
$17$	4.70641	1.14147	0.570737	−	0.821133i	$-0.306658\pi$
$17$	4.70641	1.14147	0.570737	+	0.821133i	$0.306658\pi$
$18$	0.336232	0.0792506
$19$	−6.93509	−1.59102	−0.795510	−	0.605941i	$-0.792797\pi$
$19$	−6.93509	−1.59102	−0.795510	+	0.605941i	$0.792797\pi$
$20$	−7.87100	−1.76001
$21$	−1.00000	−0.218218
$22$	−1.74796	−0.372666
$23$	1.38621	0.289045	0.144522	−	0.989502i	$-0.453835\pi$
$23$	1.38621	0.289045	0.144522	+	0.989502i	$0.453835\pi$
$24$	−1.30692	−0.266773
$25$	12.3996	2.47992
$26$	−0.241905	−0.0474414
$27$	1.00000	0.192450
$28$	1.88695	0.356600
$29$	7.28390	1.35259	0.676293	−	0.736632i	$-0.263585\pi$
$29$	7.28390	1.35259	0.676293	+	0.736632i	$0.263585\pi$
$30$	1.40252	0.256064
$31$	2.48273	0.445912	0.222956	−	0.974829i	$-0.428429\pi$
$31$	2.48273	0.445912	0.222956	+	0.974829i	$0.428429\pi$
$32$	3.73499	0.660258
$33$	−5.19867	−0.904972
$34$	1.58245	0.271387
$35$	−4.17128	−0.705076
$36$	−1.88695	−0.314491
$37$	6.10322	1.00336	0.501682	−	0.865052i	$-0.332715\pi$
$37$	6.10322	1.00336	0.501682	+	0.865052i	$0.332715\pi$
$38$	−2.33180	−0.378268
$39$	−0.719458	−0.115205
$40$	−5.45152	−0.861960
$41$	−6.82507	−1.06590	−0.532948	−	0.846148i	$-0.678916\pi$
$41$	−6.82507	−1.06590	−0.532948	+	0.846148i	$0.678916\pi$
$42$	−0.336232	−0.0518817
$43$	−1.71068	−0.260876	−0.130438	−	0.991456i	$-0.541638\pi$
$43$	−1.71068	−0.260876	−0.130438	+	0.991456i	$0.541638\pi$
$44$	9.80962	1.47886
$45$	4.17128	0.621818
$46$	0.466088	0.0687209
$47$	3.46042	0.504755	0.252377	−	0.967629i	$-0.418788\pi$
$47$	3.46042	0.504755	0.252377	+	0.967629i	$0.418788\pi$
$48$	3.33447	0.481289
$49$	1.00000	0.142857
$50$	4.16914	0.589606
$51$	4.70641	0.659030
$52$	1.35758	0.188262
$53$	6.93370	0.952417	0.476208	−	0.879333i	$-0.342011\pi$
$53$	6.93370	0.952417	0.476208	+	0.879333i	$0.342011\pi$
$54$	0.336232	0.0457554
$55$	−21.6851	−2.92402
$56$	1.30692	0.174644
$57$	−6.93509	−0.918575
$58$	2.44908	0.321580
$59$	9.78274	1.27360	0.636802	−	0.771027i	$-0.280257\pi$
$59$	9.78274	1.27360	0.636802	+	0.771027i	$0.280257\pi$
$60$	−7.87100	−1.01614
$61$	0.455540	0.0583259	0.0291630	−	0.999575i	$-0.490716\pi$
$61$	0.455540	0.0583259	0.0291630	+	0.999575i	$0.490716\pi$
$62$	0.834774	0.106016
$63$	−1.00000	−0.125988
$64$	−5.41312	−0.676640
$65$	−3.00106	−0.372236
$66$	−1.74796	−0.215159
$67$	12.6532	1.54584	0.772920	−	0.634503i	$-0.218795\pi$
$67$	12.6532	1.54584	0.772920	+	0.634503i	$0.218795\pi$
$68$	−8.88076	−1.07695
$69$	1.38621	0.166880
$70$	−1.40252	−0.167633
$71$	15.1859	1.80224	0.901119	−	0.433571i	$-0.142747\pi$
$71$	15.1859	1.80224	0.901119	+	0.433571i	$0.142747\pi$
$72$	−1.30692	−0.154021
$73$	7.63566	0.893686	0.446843	−	0.894612i	$-0.352548\pi$
$73$	7.63566	0.893686	0.446843	+	0.894612i	$0.352548\pi$
$74$	2.05210	0.238551
$75$	12.3996	1.43178
$76$	13.0862	1.50109
$77$	5.19867	0.592443
$78$	−0.241905	−0.0273903
$79$	12.2700	1.38049	0.690243	−	0.723578i	$-0.257504\pi$
$79$	12.2700	1.38049	0.690243	+	0.723578i	$0.257504\pi$
$80$	13.9090	1.55508
$81$	1.00000	0.111111
$82$	−2.29480	−0.253419
$83$	2.53129	0.277845	0.138922	−	0.990303i	$-0.455636\pi$
$83$	2.53129	0.277845	0.138922	+	0.990303i	$0.455636\pi$
$84$	1.88695	0.205883
$85$	19.6318	2.12937
$86$	−0.575185	−0.0620238
$87$	7.28390	0.780916
$88$	6.79422	0.724266
$89$	−1.80820	−0.191668	−0.0958341	−	0.995397i	$-0.530552\pi$
$89$	−1.80820	−0.191668	−0.0958341	+	0.995397i	$0.530552\pi$
$90$	1.40252	0.147838
$91$	0.719458	0.0754197
$92$	−2.61571	−0.272706
$93$	2.48273	0.257447
$94$	1.16350	0.120006
$95$	−28.9282	−2.96797
$96$	3.73499	0.381200
$97$	10.5131	1.06744	0.533722	−	0.845660i	$-0.320793\pi$
$97$	10.5131	1.06744	0.533722	+	0.845660i	$0.320793\pi$
$98$	0.336232	0.0339645
$99$	−5.19867	−0.522486
$100$	−23.3974	−2.33974
$101$	−16.9446	−1.68605	−0.843025	−	0.537874i	$-0.819228\pi$
$101$	−16.9446	−1.68605	−0.843025	+	0.537874i	$0.819228\pi$
$102$	1.58245	0.156686
$103$	−0.0591281	−0.00582607	−0.00291303	−	0.999996i	$-0.500927\pi$
$103$	−0.0591281	−0.00582607	−0.00291303	+	0.999996i	$0.500927\pi$
$104$	0.940271	0.0922012
$105$	−4.17128	−0.407076
$106$	2.33133	0.226439
$107$	−16.3534	−1.58094	−0.790472	−	0.612498i	$-0.790165\pi$
$107$	−16.3534	−1.58094	−0.790472	+	0.612498i	$0.790165\pi$
$108$	−1.88695	−0.181572
$109$	−1.48435	−0.142175	−0.0710876	−	0.997470i	$-0.522647\pi$
$109$	−1.48435	−0.142175	−0.0710876	+	0.997470i	$0.522647\pi$
$110$	−7.29123	−0.695191
$111$	6.10322	0.579292
$112$	−3.33447	−0.315078
$113$	0.601285	0.0565641	0.0282821	−	0.999600i	$-0.490996\pi$
$113$	0.601285	0.0565641	0.0282821	+	0.999600i	$0.490996\pi$
$114$	−2.33180	−0.218393
$115$	5.78228	0.539200
$116$	−13.7443	−1.27613
$117$	−0.719458	−0.0665139
$118$	3.28927	0.302802
$119$	−4.70641	−0.431436
$120$	−5.45152	−0.497653
$121$	16.0262	1.45692
$122$	0.153167	0.0138671
$123$	−6.82507	−0.615396
$124$	−4.68479	−0.420706
$125$	30.8659	2.76073
$126$	−0.336232	−0.0299539
$127$	4.22758	0.375138	0.187569	−	0.982251i	$-0.439939\pi$
$127$	4.22758	0.375138	0.187569	+	0.982251i	$0.439939\pi$
$128$	−9.29003	−0.821131
$129$	−1.71068	−0.150617
$130$	−1.00905	−0.0884998
$131$	−14.9785	−1.30868	−0.654338	−	0.756202i	$-0.727052\pi$
$131$	−14.9785	−1.30868	−0.654338	+	0.756202i	$0.727052\pi$
$132$	9.80962	0.853818
$133$	6.93509	0.601349
$134$	4.25442	0.367526
$135$	4.17128	0.359007
$136$	−6.15089	−0.527434
$137$	−10.6671	−0.911348	−0.455674	−	0.890147i	$-0.650602\pi$
$137$	−10.6671	−0.911348	−0.455674	+	0.890147i	$0.650602\pi$
$138$	0.466088	0.0396761
$139$	5.03743	0.427269	0.213634	−	0.976914i	$-0.431470\pi$
$139$	5.03743	0.427269	0.213634	+	0.976914i	$0.431470\pi$
$140$	7.87100	0.665221
$141$	3.46042	0.291420
$142$	5.10599	0.428485
$143$	3.74022	0.312773
$144$	3.33447	0.277872
$145$	30.3832	2.52319
$146$	2.56735	0.212475
$147$	1.00000	0.0824786
$148$	−11.5165	−0.946647
$149$	−5.27313	−0.431991	−0.215996	−	0.976394i	$-0.569300\pi$
$149$	−5.27313	−0.431991	−0.215996	+	0.976394i	$0.569300\pi$
$150$	4.16914	0.340409
$151$	−18.6093	−1.51440	−0.757200	−	0.653183i	$-0.773433\pi$
$151$	−18.6093	−1.51440	−0.757200	+	0.653183i	$0.773433\pi$
$152$	9.06358	0.735153
$153$	4.70641	0.380491
$154$	1.74796	0.140854
$155$	10.3562	0.831829
$156$	1.35758	0.108693
$157$	−4.11707	−0.328578	−0.164289	−	0.986412i	$-0.552533\pi$
$157$	−4.11707	−0.328578	−0.164289	+	0.986412i	$0.552533\pi$
$158$	4.12557	0.328213
$159$	6.93370	0.549878
$160$	15.5797	1.23168
$161$	−1.38621	−0.109249
$162$	0.336232	0.0264169
$163$	8.44230	0.661252	0.330626	−	0.943762i	$-0.392740\pi$
$163$	8.44230	0.661252	0.330626	+	0.943762i	$0.392740\pi$
$164$	12.8785	1.00565
$165$	−21.6851	−1.68818
$166$	0.851099	0.0660581
$167$	−12.3266	−0.953861	−0.476930	−	0.878941i	$-0.658251\pi$
$167$	−12.3266	−0.953861	−0.476930	+	0.878941i	$0.658251\pi$
$168$	1.30692	0.100831
$169$	−12.4824	−0.960183
$170$	6.60083	0.506261
$171$	−6.93509	−0.530340
$172$	3.22796	0.246130
$173$	−12.4310	−0.945111	−0.472555	−	0.881301i	$-0.656668\pi$
$173$	−12.4310	−0.945111	−0.472555	+	0.881301i	$0.656668\pi$
$174$	2.44908	0.185664
$175$	−12.3996	−0.937322
$176$	−17.3348	−1.30666
$177$	9.78274	0.735315
$178$	−0.607973	−0.0455695
$179$	−8.69554	−0.649935	−0.324968	−	0.945725i	$-0.605353\pi$
$179$	−8.69554	−0.649935	−0.324968	+	0.945725i	$0.605353\pi$
$180$	−7.87100	−0.586669
$181$	12.6116	0.937409	0.468705	−	0.883355i	$-0.344721\pi$
$181$	12.6116	0.937409	0.468705	+	0.883355i	$0.344721\pi$
$182$	0.241905	0.0179312
$183$	0.455540	0.0336745
$184$	−1.81166	−0.133557
$185$	25.4583	1.87173
$186$	0.834774	0.0612086
$187$	−24.4671	−1.78921
$188$	−6.52964	−0.476223
$189$	−1.00000	−0.0727393
$190$	−9.72659	−0.705641
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−5.41312	−0.390658
$193$	18.7307	1.34827	0.674133	−	0.738610i	$-0.264517\pi$
$193$	18.7307	1.34827	0.674133	+	0.738610i	$0.264517\pi$
$194$	3.53484	0.253787
$195$	−3.00106	−0.214911
$196$	−1.88695	−0.134782
$197$	7.39601	0.526944	0.263472	−	0.964667i	$-0.415132\pi$
$197$	7.39601	0.526944	0.263472	+	0.964667i	$0.415132\pi$
$198$	−1.74796	−0.124222
$199$	−12.0815	−0.856433	−0.428216	−	0.903676i	$-0.640858\pi$
$199$	−12.0815	−0.856433	−0.428216	+	0.903676i	$0.640858\pi$
$200$	−16.2052	−1.14588
$201$	12.6532	0.892491
$202$	−5.69731	−0.400861
$203$	−7.28390	−0.511230
$204$	−8.88076	−0.621778
$205$	−28.4693	−1.98838
$206$	−0.0198808	−0.00138516
$207$	1.38621	0.0963483
$208$	−2.39901	−0.166342
$209$	36.0532	2.49386
$210$	−1.40252	−0.0967830
$211$	−17.5210	−1.20619	−0.603097	−	0.797668i	$-0.706067\pi$
$211$	−17.5210	−1.20619	−0.603097	+	0.797668i	$0.706067\pi$
$212$	−13.0835	−0.898580
$213$	15.1859	1.04052
$214$	−5.49854	−0.375872
$215$	−7.13573	−0.486653
$216$	−1.30692	−0.0889243
$217$	−2.48273	−0.168539
$218$	−0.499086	−0.0338024
$219$	7.63566	0.515970
$220$	40.9187	2.75874
$221$	−3.38607	−0.227772
$222$	2.05210	0.137728
$223$	−10.3620	−0.693894	−0.346947	−	0.937885i	$-0.612782\pi$
$223$	−10.3620	−0.693894	−0.346947	+	0.937885i	$0.612782\pi$
$224$	−3.73499	−0.249554
$225$	12.3996	0.826641
$226$	0.202171	0.0134482
$227$	23.3687	1.55104	0.775519	−	0.631324i	$-0.217488\pi$
$227$	23.3687	1.55104	0.775519	+	0.631324i	$0.217488\pi$
$228$	13.0862	0.866652
$229$	−9.68164	−0.639781	−0.319890	−	0.947455i	$-0.603646\pi$
$229$	−9.68164	−0.639781	−0.319890	+	0.947455i	$0.603646\pi$
$230$	1.94419	0.128196
$231$	5.19867	0.342047
$232$	−9.51944	−0.624982
$233$	0.494159	0.0323734	0.0161867	−	0.999869i	$-0.494847\pi$
$233$	0.494159	0.0323734	0.0161867	+	0.999869i	$0.494847\pi$
$234$	−0.241905	−0.0158138
$235$	14.4344	0.941597
$236$	−18.4595	−1.20161
$237$	12.2700	0.797024
$238$	−1.58245	−0.102575
$239$	20.7646	1.34315	0.671577	−	0.740935i	$-0.265617\pi$
$239$	20.7646	1.34315	0.671577	+	0.740935i	$0.265617\pi$
$240$	13.9090	0.897823
$241$	10.0005	0.644190	0.322095	−	0.946707i	$-0.395613\pi$
$241$	10.0005	0.644190	0.322095	+	0.946707i	$0.395613\pi$
$242$	5.38850	0.346386
$243$	1.00000	0.0641500
$244$	−0.859580	−0.0550290
$245$	4.17128	0.266494
$246$	−2.29480	−0.146311
$247$	4.98951	0.317475
$248$	−3.24472	−0.206040
$249$	2.53129	0.160414
$250$	10.3781	0.656368
$251$	7.56787	0.477680	0.238840	−	0.971059i	$-0.423233\pi$
$251$	7.56787	0.477680	0.238840	+	0.971059i	$0.423233\pi$
$252$	1.88695	0.118867
$253$	−7.20645	−0.453066
$254$	1.42145	0.0891896
$255$	19.6318	1.22939
$256$	7.70263	0.481415
$257$	4.54855	0.283731	0.141865	−	0.989886i	$-0.454690\pi$
$257$	4.54855	0.283731	0.141865	+	0.989886i	$0.454690\pi$
$258$	−0.575185	−0.0358094
$259$	−6.10322	−0.379236
$260$	5.66285	0.351195
$261$	7.28390	0.450862
$262$	−5.03624	−0.311140
$263$	−4.99420	−0.307955	−0.153978	−	0.988074i	$-0.549208\pi$
$263$	−4.99420	−0.307955	−0.153978	+	0.988074i	$0.549208\pi$
$264$	6.79422	0.418155
$265$	28.9224	1.77669
$266$	2.33180	0.142972
$267$	−1.80820	−0.110660
$268$	−23.8760	−1.45846
$269$	−21.5844	−1.31602	−0.658011	−	0.753008i	$-0.728602\pi$
$269$	−21.5844	−1.31602	−0.658011	+	0.753008i	$0.728602\pi$
$270$	1.40252	0.0853545
$271$	−28.4172	−1.72622	−0.863112	−	0.505013i	$-0.831488\pi$
$271$	−28.4172	−1.72622	−0.863112	+	0.505013i	$0.831488\pi$
$272$	15.6934	0.951552
$273$	0.719458	0.0435436
$274$	−3.58660	−0.216675
$275$	−64.4615	−3.88717
$276$	−2.61571	−0.157447
$277$	7.02589	0.422145	0.211072	−	0.977470i	$-0.432304\pi$
$277$	7.02589	0.422145	0.211072	+	0.977470i	$0.432304\pi$
$278$	1.69374	0.101584
$279$	2.48273	0.148637
$280$	5.45152	0.325790
$281$	6.47751	0.386416	0.193208	−	0.981158i	$-0.438111\pi$
$281$	6.47751	0.386416	0.193208	+	0.981158i	$0.438111\pi$
$282$	1.16350	0.0692857
$283$	12.1452	0.721957	0.360978	−	0.932574i	$-0.382443\pi$
$283$	12.1452	0.721957	0.360978	+	0.932574i	$0.382443\pi$
$284$	−28.6551	−1.70037
$285$	−28.9282	−1.71356
$286$	1.25758	0.0743624
$287$	6.82507	0.402871
$288$	3.73499	0.220086
$289$	5.15034	0.302961
$290$	10.2158	0.599893
$291$	10.5131	0.616289
$292$	−14.4081	−0.843169
$293$	−0.525304	−0.0306886	−0.0153443	−	0.999882i	$-0.504884\pi$
$293$	−0.525304	−0.0306886	−0.0153443	+	0.999882i	$0.504884\pi$
$294$	0.336232	0.0196094
$295$	40.8066	2.37585
$296$	−7.97639	−0.463618
$297$	−5.19867	−0.301657
$298$	−1.77299	−0.102707
$299$	−0.997321	−0.0576765
$300$	−23.3974	−1.35085
$301$	1.71068	0.0986019
$302$	−6.25703	−0.360051
$303$	−16.9446	−0.973442
$304$	−23.1249	−1.32630
$305$	1.90019	0.108804
$306$	1.58245	0.0904624
$307$	−16.2048	−0.924858	−0.462429	−	0.886656i	$-0.653022\pi$
$307$	−16.2048	−0.924858	−0.462429	+	0.886656i	$0.653022\pi$
$308$	−9.80962	−0.558955
$309$	−0.0591281	−0.00336368
$310$	3.48208	0.197769
$311$	7.90878	0.448466	0.224233	−	0.974536i	$-0.428012\pi$
$311$	7.90878	0.448466	0.224233	+	0.974536i	$0.428012\pi$
$312$	0.940271	0.0532324
$313$	21.7995	1.23218	0.616089	−	0.787676i	$-0.288716\pi$
$313$	21.7995	1.23218	0.616089	+	0.787676i	$0.288716\pi$
$314$	−1.38429	−0.0781201
$315$	−4.17128	−0.235025
$316$	−23.1529	−1.30245
$317$	16.6694	0.936249	0.468125	−	0.883662i	$-0.344930\pi$
$317$	16.6694	0.936249	0.468125	+	0.883662i	$0.344930\pi$
$318$	2.33133	0.130734
$319$	−37.8666	−2.12012
$320$	−22.5797	−1.26224
$321$	−16.3534	−0.912759
$322$	−0.466088	−0.0259741
$323$	−32.6394	−1.81611
$324$	−1.88695	−0.104830
$325$	−8.92100	−0.494848
$326$	2.83857	0.157214
$327$	−1.48435	−0.0820848
$328$	8.91979	0.492513
$329$	−3.46042	−0.190779
$330$	−7.29123	−0.401369
$331$	8.62256	0.473939	0.236969	−	0.971517i	$-0.423846\pi$
$331$	8.62256	0.473939	0.236969	+	0.971517i	$0.423846\pi$
$332$	−4.77641	−0.262139
$333$	6.10322	0.334454
$334$	−4.14459	−0.226782
$335$	52.7803	2.88370
$336$	−3.33447	−0.181910
$337$	11.5945	0.631593	0.315797	−	0.948827i	$-0.397728\pi$
$337$	11.5945	0.631593	0.315797	+	0.948827i	$0.397728\pi$
$338$	−4.19697	−0.228285
$339$	0.601285	0.0326573
$340$	−37.0442	−2.00900
$341$	−12.9069	−0.698948
$342$	−2.33180	−0.126089
$343$	−1.00000	−0.0539949
$344$	2.23571	0.120542
$345$	5.78228	0.311307
$346$	−4.17969	−0.224702
$347$	20.0203	1.07475	0.537373	−	0.843345i	$-0.319417\pi$
$347$	20.0203	1.07475	0.537373	+	0.843345i	$0.319417\pi$
$348$	−13.7443	−0.736774
$349$	27.7327	1.48450	0.742248	−	0.670125i	$-0.233759\pi$
$349$	27.7327	1.48450	0.742248	+	0.670125i	$0.233759\pi$
$350$	−4.16914	−0.222850
$351$	−0.719458	−0.0384018
$352$	−19.4170	−1.03493
$353$	36.4101	1.93792	0.968958	−	0.247226i	$-0.0795191\pi$
$353$	36.4101	1.93792	0.968958	+	0.247226i	$0.0795191\pi$
$354$	3.28927	0.174823
$355$	63.3448	3.36199
$356$	3.41197	0.180834
$357$	−4.70641	−0.249090
$358$	−2.92372	−0.154523
$359$	−32.7778	−1.72995	−0.864974	−	0.501816i	$-0.832665\pi$
$359$	−32.7778	−1.72995	−0.864974	+	0.501816i	$0.832665\pi$
$360$	−5.45152	−0.287320
$361$	29.0955	1.53134
$362$	4.24040	0.222871
$363$	16.0262	0.841155
$364$	−1.35758	−0.0711565
$365$	31.8505	1.66713
$366$	0.153167	0.00800617
$367$	−27.7979	−1.45104	−0.725520	−	0.688201i	$-0.758401\pi$
$367$	−27.7979	−1.45104	−0.725520	+	0.688201i	$0.758401\pi$
$368$	4.62228	0.240953
$369$	−6.82507	−0.355299
$370$	8.55988	0.445007
$371$	−6.93370	−0.359980
$372$	−4.68479	−0.242895
$373$	32.5396	1.68484	0.842419	−	0.538823i	$-0.181131\pi$
$373$	32.5396	1.68484	0.842419	+	0.538823i	$0.181131\pi$
$374$	−8.22661	−0.425388
$375$	30.8659	1.59391
$376$	−4.52248	−0.233229
$377$	−5.24046	−0.269898
$378$	−0.336232	−0.0172939
$379$	18.0584	0.927597	0.463798	−	0.885941i	$-0.346486\pi$
$379$	18.0584	0.927597	0.463798	+	0.885941i	$0.346486\pi$
$380$	54.5861	2.80021
$381$	4.22758	0.216586
$382$	−0.336232	−0.0172031
$383$	19.4848	0.995625	0.497812	−	0.867285i	$-0.334137\pi$
$383$	19.4848	0.995625	0.497812	+	0.867285i	$0.334137\pi$
$384$	−9.29003	−0.474080
$385$	21.6851	1.10518
$386$	6.29786	0.320553
$387$	−1.71068	−0.0869587
$388$	−19.8377	−1.00711
$389$	5.20012	0.263657	0.131828	−	0.991273i	$-0.457915\pi$
$389$	5.20012	0.263657	0.131828	+	0.991273i	$0.457915\pi$
$390$	−1.00905	−0.0510954
$391$	6.52408	0.329937
$392$	−1.30692	−0.0660092
$393$	−14.9785	−0.755564
$394$	2.48677	0.125282
$395$	51.1818	2.57523
$396$	9.80962	0.492952
$397$	2.54338	0.127648	0.0638242	−	0.997961i	$-0.479670\pi$
$397$	2.54338	0.127648	0.0638242	+	0.997961i	$0.479670\pi$
$398$	−4.06217	−0.203618
$399$	6.93509	0.347189
$400$	41.3461	2.06731
$401$	−39.1330	−1.95421	−0.977104	−	0.212764i	$-0.931753\pi$
$401$	−39.1330	−1.95421	−0.977104	+	0.212764i	$0.931753\pi$
$402$	4.25442	0.212191
$403$	−1.78622	−0.0889781
$404$	31.9736	1.59074
$405$	4.17128	0.207273
$406$	−2.44908	−0.121546
$407$	−31.7286	−1.57273
$408$	−6.15089	−0.304514
$409$	−28.4812	−1.40831	−0.704153	−	0.710048i	$-0.748673\pi$
$409$	−28.4812	−1.40831	−0.704153	+	0.710048i	$0.748673\pi$
$410$	−9.57228	−0.472741
$411$	−10.6671	−0.526167
$412$	0.111572	0.00549674
$413$	−9.78274	−0.481377
$414$	0.466088	0.0229070
$415$	10.5587	0.518307
$416$	−2.68717	−0.131749
$417$	5.03743	0.246684
$418$	12.1222	0.592919
$419$	37.6656	1.84009	0.920043	−	0.391817i	$-0.128153\pi$
$419$	37.6656	1.84009	0.920043	+	0.391817i	$0.128153\pi$
$420$	7.87100	0.384065
$421$	−21.4233	−1.04411	−0.522054	−	0.852913i	$-0.674834\pi$
$421$	−21.4233	−1.04411	−0.522054	+	0.852913i	$0.674834\pi$
$422$	−5.89111	−0.286775
$423$	3.46042	0.168252
$424$	−9.06176	−0.440078
$425$	58.3577	2.83076
$426$	5.10599	0.247386
$427$	−0.455540	−0.0220451
$428$	30.8580	1.49158
$429$	3.74022	0.180580
$430$	−2.39926	−0.115703
$431$	−16.6181	−0.800466	−0.400233	−	0.916413i	$-0.631071\pi$
$431$	−16.6181	−0.800466	−0.400233	+	0.916413i	$0.631071\pi$
$432$	3.33447	0.160430
$433$	−33.6117	−1.61527	−0.807637	−	0.589679i	$-0.799254\pi$
$433$	−33.6117	−1.61527	−0.807637	+	0.589679i	$0.799254\pi$
$434$	−0.834774	−0.0400704
$435$	30.3832	1.45676
$436$	2.80089	0.134139
$437$	−9.61350	−0.459876
$438$	2.56735	0.122673
$439$	−24.0405	−1.14739	−0.573695	−	0.819069i	$-0.694491\pi$
$439$	−24.0405	−1.14739	−0.573695	+	0.819069i	$0.694491\pi$
$440$	28.3406	1.35109
$441$	1.00000	0.0476190
$442$	−1.13850	−0.0541531
$443$	10.3565	0.492051	0.246026	−	0.969263i	$-0.420875\pi$
$443$	10.3565	0.492051	0.246026	+	0.969263i	$0.420875\pi$
$444$	−11.5165	−0.546547
$445$	−7.54250	−0.357549
$446$	−3.48405	−0.164974
$447$	−5.27313	−0.249410
$448$	5.41312	0.255746
$449$	−3.79478	−0.179087	−0.0895434	−	0.995983i	$-0.528541\pi$
$449$	−3.79478	−0.179087	−0.0895434	+	0.995983i	$0.528541\pi$
$450$	4.16914	0.196535
$451$	35.4813	1.67075
$452$	−1.13459	−0.0533668
$453$	−18.6093	−0.874340
$454$	7.85732	0.368762
$455$	3.00106	0.140692
$456$	9.06358	0.424441
$457$	−11.5001	−0.537950	−0.268975	−	0.963147i	$-0.586685\pi$
$457$	−11.5001	−0.537950	−0.268975	+	0.963147i	$0.586685\pi$
$458$	−3.25528	−0.152109
$459$	4.70641	0.219677
$460$	−10.9109	−0.508721
$461$	19.0482	0.887164	0.443582	−	0.896234i	$-0.353707\pi$
$461$	19.0482	0.887164	0.443582	+	0.896234i	$0.353707\pi$
$462$	1.74796	0.0813224
$463$	8.19808	0.380997	0.190499	−	0.981687i	$-0.438990\pi$
$463$	8.19808	0.380997	0.190499	+	0.981687i	$0.438990\pi$
$464$	24.2879	1.12754
$465$	10.3562	0.480256
$466$	0.166152	0.00769684
$467$	−15.7481	−0.728736	−0.364368	−	0.931255i	$-0.618715\pi$
$467$	−15.7481	−0.728736	−0.364368	+	0.931255i	$0.618715\pi$
$468$	1.35758	0.0627542
$469$	−12.6532	−0.584273
$470$	4.85331	0.223866
$471$	−4.11707	−0.189705
$472$	−12.7852	−0.588487
$473$	8.89326	0.408912
$474$	4.12557	0.189494
$475$	−85.9924	−3.94560
$476$	8.88076	0.407049
$477$	6.93370	0.317472
$478$	6.98173	0.319337
$479$	−33.3999	−1.52608	−0.763039	−	0.646352i	$-0.776294\pi$
$479$	−33.3999	−1.52608	−0.763039	+	0.646352i	$0.776294\pi$
$480$	15.5797	0.711112
$481$	−4.39101	−0.200213
$482$	3.36249	0.153157
$483$	−1.38621	−0.0630748
$484$	−30.2405	−1.37457
$485$	43.8532	1.99127
$486$	0.336232	0.0152518
$487$	23.0479	1.04440	0.522200	−	0.852823i	$-0.325111\pi$
$487$	23.0479	1.04440	0.522200	+	0.852823i	$0.325111\pi$
$488$	−0.595352	−0.0269503
$489$	8.44230	0.381774
$490$	1.40252	0.0633593
$491$	−27.9009	−1.25915	−0.629575	−	0.776940i	$-0.716771\pi$
$491$	−27.9009	−1.25915	−0.629575	+	0.776940i	$0.716771\pi$
$492$	12.8785	0.580610
$493$	34.2811	1.54394
$494$	1.67763	0.0754802
$495$	−21.6851	−0.974674
$496$	8.27860	0.371720
$497$	−15.1859	−0.681182
$498$	0.851099	0.0381387
$499$	−20.8154	−0.931826	−0.465913	−	0.884831i	$-0.654274\pi$
$499$	−20.8154	−0.931826	−0.465913	+	0.884831i	$0.654274\pi$
$500$	−58.2423	−2.60467
$501$	−12.3266	−0.550712
$502$	2.54456	0.113569
$503$	30.9777	1.38123	0.690614	−	0.723223i	$-0.257340\pi$
$503$	30.9777	1.38123	0.690614	+	0.723223i	$0.257340\pi$
$504$	1.30692	0.0582146
$505$	−70.6807	−3.14525
$506$	−2.42304	−0.107717
$507$	−12.4824	−0.554362
$508$	−7.97723	−0.353933
$509$	2.38553	0.105737	0.0528685	−	0.998601i	$-0.483164\pi$
$509$	2.38553	0.105737	0.0528685	+	0.998601i	$0.483164\pi$
$510$	6.60083	0.292290
$511$	−7.63566	−0.337782
$512$	21.1699	0.935588
$513$	−6.93509	−0.306192
$514$	1.52937	0.0674575
$515$	−0.246640	−0.0108683
$516$	3.22796	0.142103
$517$	−17.9896	−0.791181
$518$	−2.05210	−0.0901640
$519$	−12.4310	−0.545660
$520$	3.92214	0.171997
$521$	−10.5743	−0.463269	−0.231634	−	0.972803i	$-0.574407\pi$
$521$	−10.5743	−0.463269	−0.231634	+	0.972803i	$0.574407\pi$
$522$	2.44908	0.107193
$523$	−18.3669	−0.803131	−0.401565	−	0.915830i	$-0.631534\pi$
$523$	−18.3669	−0.803131	−0.401565	+	0.915830i	$0.631534\pi$
$524$	28.2636	1.23470
$525$	−12.3996	−0.541163
$526$	−1.67921	−0.0732170
$527$	11.6848	0.508997
$528$	−17.3348	−0.754401
$529$	−21.0784	−0.916453
$530$	9.72464	0.422411
$531$	9.78274	0.424535
$532$	−13.0862	−0.567357
$533$	4.91035	0.212691
$534$	−0.607973	−0.0263096
$535$	−68.2147	−2.94918
$536$	−16.5367	−0.714278
$537$	−8.69554	−0.375240
$538$	−7.25735	−0.312887
$539$	−5.19867	−0.223923
$540$	−7.87100	−0.338714
$541$	−38.7671	−1.66673	−0.833365	−	0.552724i	$-0.813589\pi$
$541$	−38.7671	−1.66673	−0.833365	+	0.552724i	$0.813589\pi$
$542$	−9.55477	−0.410413
$543$	12.6116	0.541213
$544$	17.5784	0.753667
$545$	−6.19165	−0.265221
$546$	0.241905	0.0103526
$547$	35.6905	1.52601	0.763007	−	0.646390i	$-0.223722\pi$
$547$	35.6905	1.52601	0.763007	+	0.646390i	$0.223722\pi$
$548$	20.1282	0.859833
$549$	0.455540	0.0194420
$550$	−21.6740	−0.924182
$551$	−50.5145	−2.15199
$552$	−1.81166	−0.0771094
$553$	−12.2700	−0.521775
$554$	2.36233	0.100366
$555$	25.4583	1.08064
$556$	−9.50536	−0.403117
$557$	−19.5467	−0.828218	−0.414109	−	0.910227i	$-0.635907\pi$
$557$	−19.5467	−0.828218	−0.414109	+	0.910227i	$0.635907\pi$
$558$	0.834774	0.0353388
$559$	1.23076	0.0520557
$560$	−13.9090	−0.587763
$561$	−24.4671	−1.03300
$562$	2.17795	0.0918711
$563$	28.6922	1.20923	0.604617	−	0.796516i	$-0.293326\pi$
$563$	28.6922	1.20923	0.604617	+	0.796516i	$0.293326\pi$
$564$	−6.52964	−0.274947
$565$	2.50813	0.105518
$566$	4.08360	0.171647
$567$	−1.00000	−0.0419961
$568$	−19.8467	−0.832750
$569$	−32.7312	−1.37216	−0.686082	−	0.727524i	$-0.740671\pi$
$569$	−32.7312	−1.37216	−0.686082	+	0.727524i	$0.740671\pi$
$570$	−9.72659	−0.407402
$571$	25.1039	1.05056	0.525282	−	0.850928i	$-0.323960\pi$
$571$	25.1039	1.05056	0.525282	+	0.850928i	$0.323960\pi$
$572$	−7.05761	−0.295093
$573$	−1.00000	−0.0417756
$574$	2.29480	0.0957833
$575$	17.1885	0.716809
$576$	−5.41312	−0.225547
$577$	−32.6650	−1.35986	−0.679932	−	0.733275i	$-0.737991\pi$
$577$	−32.6650	−1.35986	−0.679932	+	0.733275i	$0.737991\pi$
$578$	1.73171	0.0720295
$579$	18.7307	0.778422
$580$	−57.3316	−2.38056
$581$	−2.53129	−0.105015
$582$	3.53484	0.146524
$583$	−36.0460	−1.49287
$584$	−9.97916	−0.412940
$585$	−3.00106	−0.124079
$586$	−0.176624	−0.00729627
$587$	−29.8891	−1.23365	−0.616827	−	0.787099i	$-0.711582\pi$
$587$	−29.8891	−1.23365	−0.616827	+	0.787099i	$0.711582\pi$
$588$	−1.88695	−0.0778164
$589$	−17.2180	−0.709454
$590$	13.7205	0.564863
$591$	7.39601	0.304231
$592$	20.3510	0.836421
$593$	47.8742	1.96596	0.982978	−	0.183723i	$-0.0588148\pi$
$593$	47.8742	1.96596	0.982978	+	0.183723i	$0.0588148\pi$
$594$	−1.74796	−0.0717196
$595$	−19.6318	−0.804825
$596$	9.95012	0.407573
$597$	−12.0815	−0.494462
$598$	−0.335331	−0.0137127
$599$	41.4398	1.69318	0.846592	−	0.532243i	$-0.178651\pi$
$599$	41.4398	1.69318	0.846592	+	0.532243i	$0.178651\pi$
$600$	−16.2052	−0.661576
$601$	−25.4309	−1.03735	−0.518674	−	0.854972i	$-0.673574\pi$
$601$	−25.4309	−1.03735	−0.518674	+	0.854972i	$0.673574\pi$
$602$	0.575185	0.0234428
$603$	12.6532	0.515280
$604$	35.1147	1.42880
$605$	66.8497	2.71783
$606$	−5.69731	−0.231437
$607$	−20.1081	−0.816165	−0.408082	−	0.912945i	$-0.633802\pi$
$607$	−20.1081	−0.816165	−0.408082	+	0.912945i	$0.633802\pi$
$608$	−25.9025	−1.05048
$609$	−7.28390	−0.295159
$610$	0.638903	0.0258684
$611$	−2.48963	−0.100720
$612$	−8.88076	−0.358983
$613$	−1.75230	−0.0707747	−0.0353873	−	0.999374i	$-0.511266\pi$
$613$	−1.75230	−0.0707747	−0.0353873	+	0.999374i	$0.511266\pi$
$614$	−5.44857	−0.219887
$615$	−28.4693	−1.14799
$616$	−6.79422	−0.273747
$617$	−30.2076	−1.21611	−0.608057	−	0.793893i	$-0.708051\pi$
$617$	−30.2076	−1.21611	−0.608057	+	0.793893i	$0.708051\pi$
$618$	−0.0198808	−0.000799721 0
$619$	3.85133	0.154798	0.0773990	−	0.997000i	$-0.475338\pi$
$619$	3.85133	0.154798	0.0773990	+	0.997000i	$0.475338\pi$
$620$	−19.5416	−0.784809
$621$	1.38621	0.0556267
$622$	2.65918	0.106624
$623$	1.80820	0.0724438
$624$	−2.39901	−0.0960373
$625$	66.7523	2.67009
$626$	7.32967	0.292953
$627$	36.0532	1.43983
$628$	7.76871	0.310005
$629$	28.7243	1.14531
$630$	−1.40252	−0.0558777
$631$	15.2998	0.609074	0.304537	−	0.952501i	$-0.401498\pi$
$631$	15.2998	0.609074	0.304537	+	0.952501i	$0.401498\pi$
$632$	−16.0359	−0.637873
$633$	−17.5210	−0.696396
$634$	5.60480	0.222595
$635$	17.6345	0.699802
$636$	−13.0835	−0.518796
$637$	−0.719458	−0.0285060
$638$	−12.7320	−0.504063
$639$	15.1859	0.600746
$640$	−38.7514	−1.53178
$641$	−5.95689	−0.235283	−0.117641	−	0.993056i	$-0.537533\pi$
$641$	−5.95689	−0.235283	−0.117641	+	0.993056i	$0.537533\pi$
$642$	−5.49854	−0.217010
$643$	17.9210	0.706736	0.353368	−	0.935484i	$-0.385036\pi$
$643$	17.9210	0.706736	0.353368	+	0.935484i	$0.385036\pi$
$644$	2.61571	0.103073
$645$	−7.13573	−0.280969
$646$	−10.9744	−0.431782
$647$	−39.1921	−1.54080	−0.770400	−	0.637561i	$-0.779943\pi$
$647$	−39.1921	−1.54080	−0.770400	+	0.637561i	$0.779943\pi$
$648$	−1.30692	−0.0513405
$649$	−50.8572	−1.99632
$650$	−2.99952	−0.117651
$651$	−2.48273	−0.0973060
$652$	−15.9302	−0.623874
$653$	0.122476	0.00479285	0.00239643	−	0.999997i	$-0.499237\pi$
$653$	0.122476	0.00479285	0.00239643	+	0.999997i	$0.499237\pi$
$654$	−0.499086	−0.0195158
$655$	−62.4795	−2.44127
$656$	−22.7580	−0.888550
$657$	7.63566	0.297895
$658$	−1.16350	−0.0453581
$659$	−29.6283	−1.15416	−0.577078	−	0.816689i	$-0.695807\pi$
$659$	−29.6283	−1.15416	−0.577078	+	0.816689i	$0.695807\pi$
$660$	40.9187	1.59276
$661$	32.6260	1.26900	0.634502	−	0.772921i	$-0.281205\pi$
$661$	32.6260	1.26900	0.634502	+	0.772921i	$0.281205\pi$
$662$	2.89918	0.112680
$663$	−3.38607	−0.131504
$664$	−3.30818	−0.128382
$665$	28.9282	1.12179
$666$	2.05210	0.0795171
$667$	10.0970	0.390958
$668$	23.2596	0.899943
$669$	−10.3620	−0.400620
$670$	17.7464	0.685604
$671$	−2.36820	−0.0914234
$672$	−3.73499	−0.144080
$673$	20.4501	0.788294	0.394147	−	0.919047i	$-0.371040\pi$
$673$	20.4501	0.788294	0.394147	+	0.919047i	$0.371040\pi$
$674$	3.89844	0.150162
$675$	12.3996	0.477261
$676$	23.5536	0.905908
$677$	4.45439	0.171196	0.0855980	−	0.996330i	$-0.472720\pi$
$677$	4.45439	0.171196	0.0855980	+	0.996330i	$0.472720\pi$
$678$	0.202171	0.00776433
$679$	−10.5131	−0.403456
$680$	−25.6571	−0.983905
$681$	23.3687	0.895492
$682$	−4.33971	−0.166176
$683$	−17.5879	−0.672981	−0.336490	−	0.941687i	$-0.609240\pi$
$683$	−17.5879	−0.672981	−0.336490	+	0.941687i	$0.609240\pi$
$684$	13.0862	0.500362
$685$	−44.4953	−1.70008
$686$	−0.336232	−0.0128374
$687$	−9.68164	−0.369378
$688$	−5.70421	−0.217471
$689$	−4.98850	−0.190047
$690$	1.94419	0.0740139
$691$	19.8762	0.756125	0.378062	−	0.925780i	$-0.376591\pi$
$691$	19.8762	0.756125	0.378062	+	0.925780i	$0.376591\pi$
$692$	23.4566	0.891687
$693$	5.19867	0.197481
$694$	6.73146	0.255523
$695$	21.0125	0.797051
$696$	−9.51944	−0.360834
$697$	−32.1216	−1.21669
$698$	9.32461	0.352942
$699$	0.494159	0.0186908
$700$	23.3974	0.884339
$701$	2.97007	0.112178	0.0560889	−	0.998426i	$-0.482137\pi$
$701$	2.97007	0.112178	0.0560889	+	0.998426i	$0.482137\pi$
$702$	−0.241905	−0.00913010
$703$	−42.3264	−1.59637
$704$	28.1410	1.06060
$705$	14.4344	0.543631
$706$	12.2422	0.460743
$707$	16.9446	0.637267
$708$	−18.4595	−0.693751
$709$	34.9105	1.31109	0.655546	−	0.755155i	$-0.272438\pi$
$709$	34.9105	1.31109	0.655546	+	0.755155i	$0.272438\pi$
$710$	21.2985	0.799320
$711$	12.2700	0.460162
$712$	2.36316	0.0885631
$713$	3.44159	0.128889
$714$	−1.58245	−0.0592216
$715$	15.6015	0.583464
$716$	16.4080	0.613197
$717$	20.7646	0.775470
$718$	−11.0210	−0.411298
$719$	−21.1567	−0.789012	−0.394506	−	0.918893i	$-0.629084\pi$
$719$	−21.1567	−0.789012	−0.394506	+	0.918893i	$0.629084\pi$
$720$	13.9090	0.518359
$721$	0.0591281	0.00220205
$722$	9.78283	0.364079
$723$	10.0005	0.371923
$724$	−23.7973	−0.884421
$725$	90.3175	3.35431
$726$	5.38850	0.199986
$727$	−38.8351	−1.44031	−0.720157	−	0.693811i	$-0.755930\pi$
$727$	−38.8351	−1.44031	−0.720157	+	0.693811i	$0.755930\pi$
$728$	−0.940271	−0.0348488
$729$	1.00000	0.0370370
$730$	10.7091	0.396363
$731$	−8.05117	−0.297783
$732$	−0.859580	−0.0317710
$733$	−24.5101	−0.905302	−0.452651	−	0.891688i	$-0.649522\pi$
$733$	−24.5101	−0.905302	−0.452651	+	0.891688i	$0.649522\pi$
$734$	−9.34655	−0.344988
$735$	4.17128	0.153860
$736$	5.17748	0.190844
$737$	−65.7801	−2.42304
$738$	−2.29480	−0.0844729
$739$	−46.1626	−1.69812	−0.849060	−	0.528297i	$-0.822831\pi$
$739$	−46.1626	−1.69812	−0.849060	+	0.528297i	$0.822831\pi$
$740$	−48.0384	−1.76593
$741$	4.98951	0.183294
$742$	−2.33133	−0.0855858
$743$	23.6807	0.868760	0.434380	−	0.900730i	$-0.356968\pi$
$743$	23.6807	0.868760	0.434380	+	0.900730i	$0.356968\pi$
$744$	−3.24472	−0.118957
$745$	−21.9957	−0.805860
$746$	10.9409	0.400573
$747$	2.53129	0.0926149
$748$	46.1681	1.68807
$749$	16.3534	0.597541
$750$	10.3781	0.378954
$751$	31.7838	1.15981	0.579904	−	0.814684i	$-0.303090\pi$
$751$	31.7838	1.15981	0.579904	+	0.814684i	$0.303090\pi$
$752$	11.5387	0.420772
$753$	7.56787	0.275789
$754$	−1.76201	−0.0641686
$755$	−77.6245	−2.82505
$756$	1.88695	0.0686276
$757$	−33.3192	−1.21101	−0.605503	−	0.795843i	$-0.707028\pi$
$757$	−33.3192	−1.21101	−0.605503	+	0.795843i	$0.707028\pi$
$758$	6.07180	0.220538
$759$	−7.20645	−0.261578
$760$	37.8068	1.37140
$761$	10.1487	0.367891	0.183946	−	0.982936i	$-0.441113\pi$
$761$	10.1487	0.367891	0.183946	+	0.982936i	$0.441113\pi$
$762$	1.42145	0.0514936
$763$	1.48435	0.0537371
$764$	1.88695	0.0682674
$765$	19.6318	0.709789
$766$	6.55139	0.236712
$767$	−7.03827	−0.254137
$768$	7.70263	0.277945
$769$	−17.3594	−0.625997	−0.312999	−	0.949754i	$-0.601334\pi$
$769$	−17.3594	−0.625997	−0.312999	+	0.949754i	$0.601334\pi$
$770$	7.29123	0.262758
$771$	4.54855	0.163812
$772$	−35.3439	−1.27205
$773$	−27.3930	−0.985257	−0.492629	−	0.870240i	$-0.663964\pi$
$773$	−27.3930	−0.985257	−0.492629	+	0.870240i	$0.663964\pi$
$774$	−0.575185	−0.0206746
$775$	30.7849	1.10583
$776$	−13.7397	−0.493228
$777$	−6.10322	−0.218952
$778$	1.74845	0.0626848
$779$	47.3325	1.69586
$780$	5.66285	0.202763
$781$	−78.9466	−2.82493
$782$	2.19360	0.0784431
$783$	7.28390	0.260305
$784$	3.33447	0.119088
$785$	−17.1735	−0.612948
$786$	−5.03624	−0.179637
$787$	0.248230	0.00884845	0.00442423	−	0.999990i	$-0.498592\pi$
$787$	0.248230	0.00884845	0.00442423	+	0.999990i	$0.498592\pi$
$788$	−13.9559	−0.497158
$789$	−4.99420	−0.177798
$790$	17.2089	0.612266
$791$	−0.601285	−0.0213792
$792$	6.79422	0.241422
$793$	−0.327742	−0.0116385
$794$	0.855165	0.0303487
$795$	28.9224	1.02577
$796$	22.7971	0.808022
$797$	40.1090	1.42073	0.710366	−	0.703832i	$-0.248529\pi$
$797$	40.1090	1.42073	0.710366	+	0.703832i	$0.248529\pi$
$798$	2.33180	0.0825448
$799$	16.2862	0.576164
$800$	46.3124	1.63739
$801$	−1.80820	−0.0638894
$802$	−13.1577	−0.464616
$803$	−39.6952	−1.40081
$804$	−23.8760	−0.842042
$805$	−5.78228	−0.203799
$806$	−0.600585	−0.0211547
$807$	−21.5844	−0.759806
$808$	22.1452	0.779064
$809$	20.5620	0.722923	0.361461	−	0.932387i	$-0.382278\pi$
$809$	20.5620	0.722923	0.361461	+	0.932387i	$0.382278\pi$
$810$	1.40252	0.0492795
$811$	29.9622	1.05211	0.526057	−	0.850449i	$-0.323670\pi$
$811$	29.9622	1.05211	0.526057	+	0.850449i	$0.323670\pi$
$812$	13.7443	0.482332
$813$	−28.4172	−0.996636
$814$	−10.6682	−0.373919
$815$	35.2152	1.23354
$816$	15.6934	0.549379
$817$	11.8637	0.415059
$818$	−9.57630	−0.334827
$819$	0.719458	0.0251399
$820$	53.7201	1.87599
$821$	51.0848	1.78287	0.891436	−	0.453146i	$-0.149698\pi$
$821$	51.0848	1.78287	0.891436	+	0.453146i	$0.149698\pi$
$822$	−3.58660	−0.125097
$823$	11.5314	0.401958	0.200979	−	0.979596i	$-0.435588\pi$
$823$	11.5314	0.401958	0.200979	+	0.979596i	$0.435588\pi$
$824$	0.0772755	0.00269202
$825$	−64.4615	−2.24426
$826$	−3.28927	−0.114448
$827$	19.6089	0.681867	0.340934	−	0.940087i	$-0.389257\pi$
$827$	19.6089	0.681867	0.340934	+	0.940087i	$0.389257\pi$
$828$	−2.61571	−0.0909021
$829$	11.0713	0.384523	0.192262	−	0.981344i	$-0.438418\pi$
$829$	11.0713	0.384523	0.192262	+	0.981344i	$0.438418\pi$
$830$	3.55017	0.123228
$831$	7.02589	0.243725
$832$	3.89451	0.135018
$833$	4.70641	0.163068
$834$	1.69374	0.0586495
$835$	−51.4177	−1.77938
$836$	−68.0306	−2.35289
$837$	2.48273	0.0858158
$838$	12.6644	0.437484
$839$	−1.74995	−0.0604149	−0.0302075	−	0.999544i	$-0.509617\pi$
$839$	−1.74995	−0.0604149	−0.0302075	+	0.999544i	$0.509617\pi$
$840$	5.45152	0.188095
$841$	24.0552	0.829490
$842$	−7.20319	−0.248238
$843$	6.47751	0.223097
$844$	33.0612	1.13801
$845$	−52.0676	−1.79118
$846$	1.16350	0.0400021
$847$	−16.0262	−0.550665
$848$	23.1202	0.793951
$849$	12.1452	0.416822
$850$	19.6217	0.673019
$851$	8.46035	0.290017
$852$	−28.6551	−0.981706
$853$	−23.6017	−0.808106	−0.404053	−	0.914735i	$-0.632399\pi$
$853$	−23.6017	−0.808106	−0.404053	+	0.914735i	$0.632399\pi$
$854$	−0.153167	−0.00524127
$855$	−28.9282	−0.989325
$856$	21.3725	0.730498
$857$	55.0238	1.87958	0.939788	−	0.341757i	$-0.111022\pi$
$857$	55.0238	1.87958	0.939788	+	0.341757i	$0.111022\pi$
$858$	1.25758	0.0429332
$859$	−45.5941	−1.55565	−0.777826	−	0.628480i	$-0.783678\pi$
$859$	−45.5941	−1.55565	−0.777826	+	0.628480i	$0.783678\pi$
$860$	13.4648	0.459144
$861$	6.82507	0.232598
$862$	−5.58754	−0.190312
$863$	23.9237	0.814372	0.407186	−	0.913345i	$-0.366510\pi$
$863$	23.9237	0.814372	0.407186	+	0.913345i	$0.366510\pi$
$864$	3.73499	0.127067
$865$	−51.8532	−1.76306
$866$	−11.3013	−0.384034
$867$	5.15034	0.174915
$868$	4.68479	0.159012
$869$	−63.7878	−2.16385
$870$	10.2158	0.346348
$871$	−9.10348	−0.308460
$872$	1.93992	0.0656941
$873$	10.5131	0.355815
$874$	−3.23236	−0.109336
$875$	−30.8659	−1.04346
$876$	−14.4081	−0.486804
$877$	21.4238	0.723431	0.361716	−	0.932288i	$-0.382191\pi$
$877$	21.4238	0.723431	0.361716	+	0.932288i	$0.382191\pi$
$878$	−8.08318	−0.272794
$879$	−0.525304	−0.0177181
$880$	−72.3084	−2.43752
$881$	25.6688	0.864805	0.432402	−	0.901681i	$-0.357666\pi$
$881$	25.6688	0.864805	0.432402	+	0.901681i	$0.357666\pi$
$882$	0.336232	0.0113215
$883$	25.0183	0.841934	0.420967	−	0.907076i	$-0.361691\pi$
$883$	25.0183	0.841934	0.420967	+	0.907076i	$0.361691\pi$
$884$	6.38934	0.214897
$885$	40.8066	1.37170
$886$	3.48218	0.116986
$887$	−22.2293	−0.746388	−0.373194	−	0.927753i	$-0.621737\pi$
$887$	−22.2293	−0.746388	−0.373194	+	0.927753i	$0.621737\pi$
$888$	−7.97639	−0.267670
$889$	−4.22758	−0.141789
$890$	−2.53603	−0.0850078
$891$	−5.19867	−0.174162
$892$	19.5526	0.654671
$893$	−23.9984	−0.803074
$894$	−1.77299	−0.0592977
$895$	−36.2716	−1.21242
$896$	9.29003	0.310358
$897$	−0.997321	−0.0332996
$898$	−1.27593	−0.0425782
$899$	18.0840	0.603134
$900$	−23.3974	−0.779914
$901$	32.6329	1.08716
$902$	11.9299	0.397223
$903$	1.71068	0.0569278
$904$	−0.785829	−0.0261363
$905$	52.6064	1.74869
$906$	−6.25703	−0.207876
$907$	−19.0231	−0.631650	−0.315825	−	0.948817i	$-0.602281\pi$
$907$	−19.0231	−0.631650	−0.315825	+	0.948817i	$0.602281\pi$
$908$	−44.0956	−1.46336
$909$	−16.9446	−0.562017
$910$	1.00905	0.0334498
$911$	−32.6553	−1.08192	−0.540960	−	0.841049i	$-0.681939\pi$
$911$	−32.6553	−1.08192	−0.540960	+	0.841049i	$0.681939\pi$
$912$	−23.1249	−0.765740
$913$	−13.1593	−0.435510
$914$	−3.86668	−0.127898
$915$	1.90019	0.0628182
$916$	18.2688	0.603617
$917$	14.9785	0.494633
$918$	1.58245	0.0522285
$919$	−53.7138	−1.77186	−0.885928	−	0.463823i	$-0.846477\pi$
$919$	−53.7138	−1.77186	−0.885928	+	0.463823i	$0.846477\pi$
$920$	−7.55695	−0.249145
$921$	−16.2048	−0.533967
$922$	6.40462	0.210925
$923$	−10.9256	−0.359622
$924$	−9.80962	−0.322713
$925$	75.6775	2.48826
$926$	2.75646	0.0905827
$927$	−0.0591281	−0.00194202
$928$	27.2053	0.893057
$929$	23.8466	0.782381	0.391191	−	0.920310i	$-0.372063\pi$
$929$	23.8466	0.782381	0.391191	+	0.920310i	$0.372063\pi$
$930$	3.48208	0.114182
$931$	−6.93509	−0.227288
$932$	−0.932452	−0.0305435
$933$	7.90878	0.258922
$934$	−5.29502	−0.173258
$935$	−102.059	−3.33769
$936$	0.940271	0.0307337
$937$	−37.7338	−1.23271	−0.616355	−	0.787469i	$-0.711391\pi$
$937$	−37.7338	−1.23271	−0.616355	+	0.787469i	$0.711391\pi$
$938$	−4.25442	−0.138912
$939$	21.7995	0.711398
$940$	−27.2370	−0.888372
$941$	11.6680	0.380367	0.190184	−	0.981749i	$-0.439092\pi$
$941$	11.6680	0.380367	0.190184	+	0.981749i	$0.439092\pi$
$942$	−1.38429	−0.0451027
$943$	−9.46098	−0.308092
$944$	32.6202	1.06170
$945$	−4.17128	−0.135692
$946$	2.99020	0.0972196
$947$	49.2836	1.60150	0.800750	−	0.598998i	$-0.204434\pi$
$947$	49.2836	1.60150	0.800750	+	0.598998i	$0.204434\pi$
$948$	−23.1529	−0.751971
$949$	−5.49353	−0.178328
$950$	−28.9134	−0.938074
$951$	16.6694	0.540544
$952$	6.15089	0.199351
$953$	58.5661	1.89714	0.948572	−	0.316563i	$-0.102529\pi$
$953$	58.5661	1.89714	0.948572	+	0.316563i	$0.102529\pi$
$954$	2.33133	0.0754796
$955$	−4.17128	−0.134980
$956$	−39.1818	−1.26723
$957$	−37.8666	−1.22405
$958$	−11.2301	−0.362828
$959$	10.6671	0.344457
$960$	−22.5797	−0.728755
$961$	−24.8360	−0.801163
$962$	−1.47640	−0.0476010
$963$	−16.3534	−0.526981
$964$	−18.8705	−0.607777
$965$	78.1311	2.51513
$966$	−0.466088	−0.0149961
$967$	−6.81225	−0.219067	−0.109534	−	0.993983i	$-0.534936\pi$
$967$	−6.81225	−0.219067	−0.109534	+	0.993983i	$0.534936\pi$
$968$	−20.9448	−0.673193
$969$	−32.6394	−1.04853
$970$	14.7448	0.473428
$971$	−53.0248	−1.70165	−0.850824	−	0.525451i	$-0.823897\pi$
$971$	−53.0248	−1.70165	−0.850824	+	0.525451i	$0.823897\pi$
$972$	−1.88695	−0.0605239
$973$	−5.03743	−0.161492
$974$	7.74944	0.248308
$975$	−8.92100	−0.285701
$976$	1.51898	0.0486215
$977$	−23.0423	−0.737188	−0.368594	−	0.929590i	$-0.620161\pi$
$977$	−23.0423	−0.737188	−0.368594	+	0.929590i	$0.620161\pi$
$978$	2.83857	0.0907674
$979$	9.40021	0.300432
$980$	−7.87100	−0.251430
$981$	−1.48435	−0.0473917
$982$	−9.38117	−0.299365
$983$	41.4956	1.32351	0.661753	−	0.749722i	$-0.269813\pi$
$983$	41.4956	1.32351	0.661753	+	0.749722i	$0.269813\pi$
$984$	8.91979	0.284352
$985$	30.8509	0.982990
$986$	11.5264	0.367075
$987$	−3.46042	−0.110146
$988$	−9.41494	−0.299529
$989$	−2.37136	−0.0754049
$990$	−7.29123	−0.231730
$991$	−56.4055	−1.79178	−0.895889	−	0.444277i	$-0.853460\pi$
$991$	−56.4055	−1.79178	−0.895889	+	0.444277i	$0.853460\pi$
$992$	9.27297	0.294417
$993$	8.62256	0.273629
$994$	−5.10599	−0.161952
$995$	−50.3952	−1.59764
$996$	−4.77641	−0.151346
$997$	19.8387	0.628298	0.314149	−	0.949374i	$-0.398281\pi$
$997$	19.8387	0.628298	0.314149	+	0.949374i	$0.398281\pi$
$998$	−6.99880	−0.221543
$999$	6.10322	0.193097

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.15	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+0.336232 q^{2} +1.00000 q^{3} -1.88695 q^{4} +4.17128 q^{5} +0.336232 q^{6} -1.00000 q^{7} -1.30692 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.336232 q^{2} +1.00000 q^{3} -1.88695 q^{4} +4.17128 q^{5} +0.336232 q^{6} -1.00000 q^{7} -1.30692 q^{8} +1.00000 q^{9} +1.40252 q^{10} -5.19867 q^{11} -1.88695 q^{12} -0.719458 q^{13} -0.336232 q^{14} +4.17128 q^{15} +3.33447 q^{16} +4.70641 q^{17} +0.336232 q^{18} -6.93509 q^{19} -7.87100 q^{20} -1.00000 q^{21} -1.74796 q^{22} +1.38621 q^{23} -1.30692 q^{24} +12.3996 q^{25} -0.241905 q^{26} +1.00000 q^{27} +1.88695 q^{28} +7.28390 q^{29} +1.40252 q^{30} +2.48273 q^{31} +3.73499 q^{32} -5.19867 q^{33} +1.58245 q^{34} -4.17128 q^{35} -1.88695 q^{36} +6.10322 q^{37} -2.33180 q^{38} -0.719458 q^{39} -5.45152 q^{40} -6.82507 q^{41} -0.336232 q^{42} -1.71068 q^{43} +9.80962 q^{44} +4.17128 q^{45} +0.466088 q^{46} +3.46042 q^{47} +3.33447 q^{48} +1.00000 q^{49} +4.16914 q^{50} +4.70641 q^{51} +1.35758 q^{52} +6.93370 q^{53} +0.336232 q^{54} -21.6851 q^{55} +1.30692 q^{56} -6.93509 q^{57} +2.44908 q^{58} +9.78274 q^{59} -7.87100 q^{60} +0.455540 q^{61} +0.834774 q^{62} -1.00000 q^{63} -5.41312 q^{64} -3.00106 q^{65} -1.74796 q^{66} +12.6532 q^{67} -8.88076 q^{68} +1.38621 q^{69} -1.40252 q^{70} +15.1859 q^{71} -1.30692 q^{72} +7.63566 q^{73} +2.05210 q^{74} +12.3996 q^{75} +13.0862 q^{76} +5.19867 q^{77} -0.241905 q^{78} +12.2700 q^{79} +13.9090 q^{80} +1.00000 q^{81} -2.29480 q^{82} +2.53129 q^{83} +1.88695 q^{84} +19.6318 q^{85} -0.575185 q^{86} +7.28390 q^{87} +6.79422 q^{88} -1.80820 q^{89} +1.40252 q^{90} +0.719458 q^{91} -2.61571 q^{92} +2.48273 q^{93} +1.16350 q^{94} -28.9282 q^{95} +3.73499 q^{96} +10.5131 q^{97} +0.336232 q^{98} -5.19867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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