LMFDB - Embedded newform 4011.2.a.m.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.22787 q^{2} +1.00000 q^{3} -0.492335 q^{4} +2.78453 q^{5} +1.22787 q^{6} -1.00000 q^{7} -3.06026 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.22787 q^{2} +1.00000 q^{3} -0.492335 q^{4} +2.78453 q^{5} +1.22787 q^{6} -1.00000 q^{7} -3.06026 q^{8} +1.00000 q^{9} +3.41904 q^{10} +0.773136 q^{11} -0.492335 q^{12} +4.48510 q^{13} -1.22787 q^{14} +2.78453 q^{15} -2.77294 q^{16} -0.115905 q^{17} +1.22787 q^{18} +3.33600 q^{19} -1.37092 q^{20} -1.00000 q^{21} +0.949311 q^{22} -1.55225 q^{23} -3.06026 q^{24} +2.75360 q^{25} +5.50712 q^{26} +1.00000 q^{27} +0.492335 q^{28} +6.92156 q^{29} +3.41904 q^{30} -3.61860 q^{31} +2.71572 q^{32} +0.773136 q^{33} -0.142316 q^{34} -2.78453 q^{35} -0.492335 q^{36} +4.37091 q^{37} +4.09617 q^{38} +4.48510 q^{39} -8.52139 q^{40} +9.83729 q^{41} -1.22787 q^{42} -5.70971 q^{43} -0.380642 q^{44} +2.78453 q^{45} -1.90596 q^{46} -6.40849 q^{47} -2.77294 q^{48} +1.00000 q^{49} +3.38106 q^{50} -0.115905 q^{51} -2.20817 q^{52} -6.08444 q^{53} +1.22787 q^{54} +2.15282 q^{55} +3.06026 q^{56} +3.33600 q^{57} +8.49877 q^{58} -2.05700 q^{59} -1.37092 q^{60} +6.27331 q^{61} -4.44317 q^{62} -1.00000 q^{63} +8.88043 q^{64} +12.4889 q^{65} +0.949311 q^{66} -7.09947 q^{67} +0.0570641 q^{68} -1.55225 q^{69} -3.41904 q^{70} +5.03630 q^{71} -3.06026 q^{72} +16.7401 q^{73} +5.36690 q^{74} +2.75360 q^{75} -1.64243 q^{76} -0.773136 q^{77} +5.50712 q^{78} -11.2996 q^{79} -7.72132 q^{80} +1.00000 q^{81} +12.0789 q^{82} +17.8695 q^{83} +0.492335 q^{84} -0.322741 q^{85} -7.01078 q^{86} +6.92156 q^{87} -2.36600 q^{88} +3.27246 q^{89} +3.41904 q^{90} -4.48510 q^{91} +0.764229 q^{92} -3.61860 q^{93} -7.86879 q^{94} +9.28918 q^{95} +2.71572 q^{96} +8.04130 q^{97} +1.22787 q^{98} +0.773136 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.22787	0.868235	0.434118	−	0.900856i	$-0.357060\pi$
$2$	1.22787	0.868235	0.434118	+	0.900856i	$0.357060\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.492335	−0.246168
$5$	2.78453	1.24528	0.622640	−	0.782509i	$-0.286060\pi$
$5$	2.78453	1.24528	0.622640	+	0.782509i	$0.286060\pi$
$6$	1.22787	0.501276
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.06026	−1.08197
$9$	1.00000	0.333333
$10$	3.41904	1.08120
$11$	0.773136	0.233109	0.116555	−	0.993184i	$-0.462815\pi$
$11$	0.773136	0.233109	0.116555	+	0.993184i	$0.462815\pi$
$12$	−0.492335	−0.142125
$13$	4.48510	1.24394	0.621972	−	0.783040i	$-0.286332\pi$
$13$	4.48510	1.24394	0.621972	+	0.783040i	$0.286332\pi$
$14$	−1.22787	−0.328162
$15$	2.78453	0.718962
$16$	−2.77294	−0.693234
$17$	−0.115905	−0.0281111	−0.0140555	−	0.999901i	$-0.504474\pi$
$17$	−0.115905	−0.0281111	−0.0140555	+	0.999901i	$0.504474\pi$
$18$	1.22787	0.289412
$19$	3.33600	0.765330	0.382665	−	0.923887i	$-0.375006\pi$
$19$	3.33600	0.765330	0.382665	+	0.923887i	$0.375006\pi$
$20$	−1.37092	−0.306547
$21$	−1.00000	−0.218218
$22$	0.949311	0.202394
$23$	−1.55225	−0.323667	−0.161834	−	0.986818i	$-0.551741\pi$
$23$	−1.55225	−0.323667	−0.161834	+	0.986818i	$0.551741\pi$
$24$	−3.06026	−0.624674
$25$	2.75360	0.550720
$26$	5.50712	1.08004
$27$	1.00000	0.192450
$28$	0.492335	0.0930426
$29$	6.92156	1.28530	0.642651	−	0.766159i	$-0.277835\pi$
$29$	6.92156	1.28530	0.642651	+	0.766159i	$0.277835\pi$
$30$	3.41904	0.624228
$31$	−3.61860	−0.649919	−0.324959	−	0.945728i	$-0.605351\pi$
$31$	−3.61860	−0.649919	−0.324959	+	0.945728i	$0.605351\pi$
$32$	2.71572	0.480076
$33$	0.773136	0.134586
$34$	−0.142316	−0.0244070
$35$	−2.78453	−0.470671
$36$	−0.492335	−0.0820559
$37$	4.37091	0.718572	0.359286	−	0.933227i	$-0.383020\pi$
$37$	4.37091	0.718572	0.359286	+	0.933227i	$0.383020\pi$
$38$	4.09617	0.664486
$39$	4.48510	0.718191
$40$	−8.52139	−1.34735
$41$	9.83729	1.53633	0.768163	−	0.640254i	$-0.221171\pi$
$41$	9.83729	1.53633	0.768163	+	0.640254i	$0.221171\pi$
$42$	−1.22787	−0.189464
$43$	−5.70971	−0.870722	−0.435361	−	0.900256i	$-0.643379\pi$
$43$	−5.70971	−0.870722	−0.435361	+	0.900256i	$0.643379\pi$
$44$	−0.380642	−0.0573840
$45$	2.78453	0.415093
$46$	−1.90596	−0.281019
$47$	−6.40849	−0.934774	−0.467387	−	0.884053i	$-0.654805\pi$
$47$	−6.40849	−0.934774	−0.467387	+	0.884053i	$0.654805\pi$
$48$	−2.77294	−0.400239
$49$	1.00000	0.142857
$50$	3.38106	0.478155
$51$	−0.115905	−0.0162299
$52$	−2.20817	−0.306219
$53$	−6.08444	−0.835762	−0.417881	−	0.908502i	$-0.637227\pi$
$53$	−6.08444	−0.835762	−0.417881	+	0.908502i	$0.637227\pi$
$54$	1.22787	0.167092
$55$	2.15282	0.290286
$56$	3.06026	0.408945
$57$	3.33600	0.441863
$58$	8.49877	1.11594
$59$	−2.05700	−0.267799	−0.133900	−	0.990995i	$-0.542750\pi$
$59$	−2.05700	−0.267799	−0.133900	+	0.990995i	$0.542750\pi$
$60$	−1.37092	−0.176985
$61$	6.27331	0.803216	0.401608	−	0.915812i	$-0.368452\pi$
$61$	6.27331	0.803216	0.401608	+	0.915812i	$0.368452\pi$
$62$	−4.44317	−0.564283
$63$	−1.00000	−0.125988
$64$	8.88043	1.11005
$65$	12.4889	1.54906
$66$	0.949311	0.116852
$67$	−7.09947	−0.867338	−0.433669	−	0.901072i	$-0.642781\pi$
$67$	−7.09947	−0.867338	−0.433669	+	0.901072i	$0.642781\pi$
$68$	0.0570641	0.00692004
$69$	−1.55225	−0.186869
$70$	−3.41904	−0.408653
$71$	5.03630	0.597698	0.298849	−	0.954300i	$-0.403397\pi$
$71$	5.03630	0.597698	0.298849	+	0.954300i	$0.403397\pi$
$72$	−3.06026	−0.360656
$73$	16.7401	1.95928	0.979641	−	0.200759i	$-0.0643408\pi$
$73$	16.7401	1.95928	0.979641	+	0.200759i	$0.0643408\pi$
$74$	5.36690	0.623890
$75$	2.75360	0.317958
$76$	−1.64243	−0.188399
$77$	−0.773136	−0.0881071
$78$	5.50712	0.623559
$79$	−11.2996	−1.27130	−0.635650	−	0.771977i	$-0.719268\pi$
$79$	−11.2996	−1.27130	−0.635650	+	0.771977i	$0.719268\pi$
$80$	−7.72132	−0.863270
$81$	1.00000	0.111111
$82$	12.0789	1.33389
$83$	17.8695	1.96143	0.980715	−	0.195446i	$-0.0626153\pi$
$83$	17.8695	1.96143	0.980715	+	0.195446i	$0.0626153\pi$
$84$	0.492335	0.0537182
$85$	−0.322741	−0.0350062
$86$	−7.01078	−0.755992
$87$	6.92156	0.742069
$88$	−2.36600	−0.252217
$89$	3.27246	0.346880	0.173440	−	0.984844i	$-0.444512\pi$
$89$	3.27246	0.346880	0.173440	+	0.984844i	$0.444512\pi$
$90$	3.41904	0.360398
$91$	−4.48510	−0.470166
$92$	0.764229	0.0796764
$93$	−3.61860	−0.375231
$94$	−7.86879	−0.811604
$95$	9.28918	0.953049
$96$	2.71572	0.277172
$97$	8.04130	0.816470	0.408235	−	0.912877i	$-0.366144\pi$
$97$	8.04130	0.816470	0.408235	+	0.912877i	$0.366144\pi$
$98$	1.22787	0.124034
$99$	0.773136	0.0777031
$100$	−1.35569	−0.135569
$101$	16.4384	1.63568	0.817842	−	0.575443i	$-0.195171\pi$
$101$	16.4384	1.63568	0.817842	+	0.575443i	$0.195171\pi$
$102$	−0.142316	−0.0140914
$103$	−0.723603	−0.0712987	−0.0356493	−	0.999364i	$-0.511350\pi$
$103$	−0.723603	−0.0712987	−0.0356493	+	0.999364i	$0.511350\pi$
$104$	−13.7256	−1.34591
$105$	−2.78453	−0.271742
$106$	−7.47090	−0.725638
$107$	−13.4712	−1.30231	−0.651153	−	0.758947i	$-0.725714\pi$
$107$	−13.4712	−1.30231	−0.651153	+	0.758947i	$0.725714\pi$
$108$	−0.492335	−0.0473750
$109$	15.9125	1.52415	0.762073	−	0.647491i	$-0.224182\pi$
$109$	15.9125	1.52415	0.762073	+	0.647491i	$0.224182\pi$
$110$	2.64338	0.252037
$111$	4.37091	0.414868
$112$	2.77294	0.262018
$113$	−12.4907	−1.17502	−0.587511	−	0.809216i	$-0.699892\pi$
$113$	−12.4907	−1.17502	−0.587511	+	0.809216i	$0.699892\pi$
$114$	4.09617	0.383641
$115$	−4.32229	−0.403056
$116$	−3.40773	−0.316399
$117$	4.48510	0.414648
$118$	−2.52573	−0.232513
$119$	0.115905	0.0106250
$120$	−8.52139	−0.777893
$121$	−10.4023	−0.945660
$122$	7.70281	0.697380
$123$	9.83729	0.886999
$124$	1.78156	0.159989
$125$	−6.25517	−0.559479
$126$	−1.22787	−0.109387
$127$	−13.5717	−1.20429	−0.602146	−	0.798386i	$-0.705687\pi$
$127$	−13.5717	−1.20429	−0.602146	+	0.798386i	$0.705687\pi$
$128$	5.47256	0.483711
$129$	−5.70971	−0.502712
$130$	15.3347	1.34495
$131$	7.47912	0.653454	0.326727	−	0.945119i	$-0.394054\pi$
$131$	7.47912	0.653454	0.326727	+	0.945119i	$0.394054\pi$
$132$	−0.380642	−0.0331307
$133$	−3.33600	−0.289268
$134$	−8.71722	−0.753053
$135$	2.78453	0.239654
$136$	0.354700	0.0304153
$137$	−3.40820	−0.291182	−0.145591	−	0.989345i	$-0.546508\pi$
$137$	−3.40820	−0.291182	−0.145591	+	0.989345i	$0.546508\pi$
$138$	−1.90596	−0.162246
$139$	6.06876	0.514745	0.257373	−	0.966312i	$-0.417143\pi$
$139$	6.06876	0.514745	0.257373	+	0.966312i	$0.417143\pi$
$140$	1.37092	0.115864
$141$	−6.40849	−0.539692
$142$	6.18392	0.518943
$143$	3.46759	0.289975
$144$	−2.77294	−0.231078
$145$	19.2733	1.60056
$146$	20.5547	1.70112
$147$	1.00000	0.0824786
$148$	−2.15195	−0.176889
$149$	2.01504	0.165078	0.0825392	−	0.996588i	$-0.473697\pi$
$149$	2.01504	0.165078	0.0825392	+	0.996588i	$0.473697\pi$
$150$	3.38106	0.276063
$151$	9.42282	0.766818	0.383409	−	0.923579i	$-0.374750\pi$
$151$	9.42282	0.766818	0.383409	+	0.923579i	$0.374750\pi$
$152$	−10.2090	−0.828061
$153$	−0.115905	−0.00937036
$154$	−0.949311	−0.0764977
$155$	−10.0761	−0.809330
$156$	−2.20817	−0.176795
$157$	15.0837	1.20381	0.601903	−	0.798569i	$-0.294409\pi$
$157$	15.0837	1.20381	0.601903	+	0.798569i	$0.294409\pi$
$158$	−13.8744	−1.10379
$159$	−6.08444	−0.482528
$160$	7.56201	0.597829
$161$	1.55225	0.122335
$162$	1.22787	0.0964706
$163$	−3.02821	−0.237188	−0.118594	−	0.992943i	$-0.537839\pi$
$163$	−3.02821	−0.237188	−0.118594	+	0.992943i	$0.537839\pi$
$164$	−4.84324	−0.378194
$165$	2.15282	0.167597
$166$	21.9414	1.70298
$167$	−3.64207	−0.281831	−0.140916	−	0.990022i	$-0.545005\pi$
$167$	−3.64207	−0.281831	−0.140916	+	0.990022i	$0.545005\pi$
$168$	3.06026	0.236104
$169$	7.11613	0.547395
$170$	−0.396284	−0.0303936
$171$	3.33600	0.255110
$172$	2.81109	0.214344
$173$	−21.7730	−1.65537	−0.827685	−	0.561193i	$-0.810342\pi$
$173$	−21.7730	−1.65537	−0.827685	+	0.561193i	$0.810342\pi$
$174$	8.49877	0.644290
$175$	−2.75360	−0.208153
$176$	−2.14386	−0.161599
$177$	−2.05700	−0.154614
$178$	4.01815	0.301173
$179$	−13.3551	−0.998208	−0.499104	−	0.866542i	$-0.666337\pi$
$179$	−13.3551	−0.998208	−0.499104	+	0.866542i	$0.666337\pi$
$180$	−1.37092	−0.102182
$181$	−14.4209	−1.07190	−0.535949	−	0.844250i	$-0.680046\pi$
$181$	−14.4209	−1.07190	−0.535949	+	0.844250i	$0.680046\pi$
$182$	−5.50712	−0.408215
$183$	6.27331	0.463737
$184$	4.75030	0.350197
$185$	12.1709	0.894823
$186$	−4.44317	−0.325789
$187$	−0.0896104	−0.00655296
$188$	3.15512	0.230111
$189$	−1.00000	−0.0727393
$190$	11.4059	0.827471
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	8.88043	0.640890
$193$	−13.2009	−0.950225	−0.475113	−	0.879925i	$-0.657593\pi$
$193$	−13.2009	−0.950225	−0.475113	+	0.879925i	$0.657593\pi$
$194$	9.87367	0.708888
$195$	12.4889	0.894348
$196$	−0.492335	−0.0351668
$197$	19.0990	1.36075	0.680374	−	0.732865i	$-0.261817\pi$
$197$	19.0990	1.36075	0.680374	+	0.732865i	$0.261817\pi$
$198$	0.949311	0.0674646
$199$	12.7380	0.902970	0.451485	−	0.892279i	$-0.350894\pi$
$199$	12.7380	0.902970	0.451485	+	0.892279i	$0.350894\pi$
$200$	−8.42674	−0.595861
$201$	−7.09947	−0.500758
$202$	20.1842	1.42016
$203$	−6.92156	−0.485798
$204$	0.0570641	0.00399529
$205$	27.3922	1.91316
$206$	−0.888490	−0.0619040
$207$	−1.55225	−0.107889
$208$	−12.4369	−0.862344
$209$	2.57918	0.178406
$210$	−3.41904	−0.235936
$211$	18.2217	1.25443	0.627216	−	0.778846i	$-0.284194\pi$
$211$	18.2217	1.25443	0.627216	+	0.778846i	$0.284194\pi$
$212$	2.99558	0.205738
$213$	5.03630	0.345081
$214$	−16.5408	−1.13071
$215$	−15.8988	−1.08429
$216$	−3.06026	−0.208225
$217$	3.61860	0.245646
$218$	19.5385	1.32332
$219$	16.7401	1.13119
$220$	−1.05991	−0.0714591
$221$	−0.519846	−0.0349686
$222$	5.36690	0.360203
$223$	4.50000	0.301343	0.150671	−	0.988584i	$-0.451856\pi$
$223$	4.50000	0.301343	0.150671	+	0.988584i	$0.451856\pi$
$224$	−2.71572	−0.181452
$225$	2.75360	0.183573
$226$	−15.3369	−1.02020
$227$	−20.2673	−1.34519	−0.672593	−	0.740012i	$-0.734820\pi$
$227$	−20.2673	−1.34519	−0.672593	+	0.740012i	$0.734820\pi$
$228$	−1.64243	−0.108772
$229$	2.69001	0.177761	0.0888805	−	0.996042i	$-0.471671\pi$
$229$	2.69001	0.177761	0.0888805	+	0.996042i	$0.471671\pi$
$230$	−5.30721	−0.349947
$231$	−0.773136	−0.0508686
$232$	−21.1818	−1.39065
$233$	−19.6415	−1.28675	−0.643377	−	0.765549i	$-0.722467\pi$
$233$	−19.6415	−1.28675	−0.643377	+	0.765549i	$0.722467\pi$
$234$	5.50712	0.360012
$235$	−17.8446	−1.16405
$236$	1.01274	0.0659235
$237$	−11.2996	−0.733985
$238$	0.142316	0.00922500
$239$	8.55891	0.553630	0.276815	−	0.960923i	$-0.410721\pi$
$239$	8.55891	0.553630	0.276815	+	0.960923i	$0.410721\pi$
$240$	−7.72132	−0.498409
$241$	−10.7786	−0.694309	−0.347154	−	0.937808i	$-0.612852\pi$
$241$	−10.7786	−0.694309	−0.347154	+	0.937808i	$0.612852\pi$
$242$	−12.7726	−0.821055
$243$	1.00000	0.0641500
$244$	−3.08857	−0.197726
$245$	2.78453	0.177897
$246$	12.0789	0.770123
$247$	14.9623	0.952027
$248$	11.0739	0.703191
$249$	17.8695	1.13243
$250$	−7.68053	−0.485759
$251$	18.7621	1.18425	0.592125	−	0.805846i	$-0.298289\pi$
$251$	18.7621	1.18425	0.592125	+	0.805846i	$0.298289\pi$
$252$	0.492335	0.0310142
$253$	−1.20010	−0.0754498
$254$	−16.6643	−1.04561
$255$	−0.322741	−0.0202108
$256$	−11.0413	−0.690078
$257$	−29.0455	−1.81181	−0.905906	−	0.423479i	$-0.860809\pi$
$257$	−29.0455	−1.81181	−0.905906	+	0.423479i	$0.860809\pi$
$258$	−7.01078	−0.436472
$259$	−4.37091	−0.271595
$260$	−6.14872	−0.381328
$261$	6.92156	0.428434
$262$	9.18339	0.567351
$263$	−9.54708	−0.588698	−0.294349	−	0.955698i	$-0.595103\pi$
$263$	−9.54708	−0.588698	−0.294349	+	0.955698i	$0.595103\pi$
$264$	−2.36600	−0.145617
$265$	−16.9423	−1.04076
$266$	−4.09617	−0.251152
$267$	3.27246	0.200271
$268$	3.49532	0.213510
$269$	19.9076	1.21379	0.606893	−	0.794784i	$-0.292416\pi$
$269$	19.9076	1.21379	0.606893	+	0.794784i	$0.292416\pi$
$270$	3.41904	0.208076
$271$	−15.8835	−0.964851	−0.482426	−	0.875937i	$-0.660244\pi$
$271$	−15.8835	−0.964851	−0.482426	+	0.875937i	$0.660244\pi$
$272$	0.321397	0.0194876
$273$	−4.48510	−0.271451
$274$	−4.18483	−0.252815
$275$	2.12891	0.128378
$276$	0.764229	0.0460012
$277$	2.06702	0.124195	0.0620976	−	0.998070i	$-0.480221\pi$
$277$	2.06702	0.124195	0.0620976	+	0.998070i	$0.480221\pi$
$278$	7.45164	0.446920
$279$	−3.61860	−0.216640
$280$	8.52139	0.509251
$281$	−15.5226	−0.926003	−0.463001	−	0.886358i	$-0.653227\pi$
$281$	−15.5226	−0.926003	−0.463001	+	0.886358i	$0.653227\pi$
$282$	−7.86879	−0.468580
$283$	26.0592	1.54906	0.774528	−	0.632539i	$-0.217987\pi$
$283$	26.0592	1.54906	0.774528	+	0.632539i	$0.217987\pi$
$284$	−2.47955	−0.147134
$285$	9.28918	0.550243
$286$	4.25776	0.251766
$287$	−9.83729	−0.580677
$288$	2.71572	0.160025
$289$	−16.9866	−0.999210
$290$	23.6651	1.38966
$291$	8.04130	0.471389
$292$	−8.24174	−0.482312
$293$	−24.8388	−1.45110	−0.725549	−	0.688170i	$-0.758414\pi$
$293$	−24.8388	−1.45110	−0.725549	+	0.688170i	$0.758414\pi$
$294$	1.22787	0.0716108
$295$	−5.72779	−0.333485
$296$	−13.3761	−0.777471
$297$	0.773136	0.0448619
$298$	2.47421	0.143327
$299$	−6.96201	−0.402623
$300$	−1.35569	−0.0782710
$301$	5.70971	0.329102
$302$	11.5700	0.665779
$303$	16.4384	0.944362
$304$	−9.25050	−0.530553
$305$	17.4682	1.00023
$306$	−0.142316	−0.00813568
$307$	−33.5454	−1.91453	−0.957267	−	0.289205i	$-0.906609\pi$
$307$	−33.5454	−1.91453	−0.957267	+	0.289205i	$0.906609\pi$
$308$	0.380642	0.0216891
$309$	−0.723603	−0.0411643
$310$	−12.3721	−0.702689
$311$	7.05071	0.399809	0.199905	−	0.979815i	$-0.435937\pi$
$311$	7.05071	0.399809	0.199905	+	0.979815i	$0.435937\pi$
$312$	−13.7256	−0.777059
$313$	−8.63644	−0.488160	−0.244080	−	0.969755i	$-0.578486\pi$
$313$	−8.63644	−0.488160	−0.244080	+	0.969755i	$0.578486\pi$
$314$	18.5208	1.04519
$315$	−2.78453	−0.156890
$316$	5.56317	0.312953
$317$	−11.0980	−0.623326	−0.311663	−	0.950193i	$-0.600886\pi$
$317$	−11.0980	−0.623326	−0.311663	+	0.950193i	$0.600886\pi$
$318$	−7.47090	−0.418947
$319$	5.35131	0.299616
$320$	24.7278	1.38233
$321$	−13.4712	−0.751886
$322$	1.90596	0.106215
$323$	−0.386659	−0.0215143
$324$	−0.492335	−0.0273520
$325$	12.3502	0.685064
$326$	−3.71825	−0.205935
$327$	15.9125	0.879966
$328$	−30.1047	−1.66225
$329$	6.40849	0.353311
$330$	2.64338	0.145513
$331$	−12.7241	−0.699379	−0.349690	−	0.936866i	$-0.613713\pi$
$331$	−12.7241	−0.699379	−0.349690	+	0.936866i	$0.613713\pi$
$332$	−8.79777	−0.482840
$333$	4.37091	0.239524
$334$	−4.47198	−0.244696
$335$	−19.7687	−1.08008
$336$	2.77294	0.151276
$337$	14.3837	0.783530	0.391765	−	0.920065i	$-0.371865\pi$
$337$	14.3837	0.783530	0.391765	+	0.920065i	$0.371865\pi$
$338$	8.73769	0.475267
$339$	−12.4907	−0.678399
$340$	0.158897	0.00861738
$341$	−2.79767	−0.151502
$342$	4.09617	0.221495
$343$	−1.00000	−0.0539949
$344$	17.4732	0.942093
$345$	−4.32229	−0.232704
$346$	−26.7344	−1.43725
$347$	30.1074	1.61625	0.808125	−	0.589010i	$-0.200482\pi$
$347$	30.1074	1.61625	0.808125	+	0.589010i	$0.200482\pi$
$348$	−3.40773	−0.182673
$349$	−19.0572	−1.02011	−0.510055	−	0.860142i	$-0.670375\pi$
$349$	−19.0572	−1.02011	−0.510055	+	0.860142i	$0.670375\pi$
$350$	−3.38106	−0.180725
$351$	4.48510	0.239397
$352$	2.09962	0.111910
$353$	18.2597	0.971863	0.485932	−	0.873997i	$-0.338480\pi$
$353$	18.2597	0.971863	0.485932	+	0.873997i	$0.338480\pi$
$354$	−2.52573	−0.134241
$355$	14.0237	0.744301
$356$	−1.61115	−0.0853906
$357$	0.115905	0.00613434
$358$	−16.3983	−0.866679
$359$	−5.55700	−0.293287	−0.146644	−	0.989189i	$-0.546847\pi$
$359$	−5.55700	−0.293287	−0.146644	+	0.989189i	$0.546847\pi$
$360$	−8.52139	−0.449117
$361$	−7.87113	−0.414270
$362$	−17.7070	−0.930660
$363$	−10.4023	−0.545977
$364$	2.20817	0.115740
$365$	46.6133	2.43985
$366$	7.70281	0.402633
$367$	30.0644	1.56935	0.784675	−	0.619907i	$-0.212830\pi$
$367$	30.0644	1.56935	0.784675	+	0.619907i	$0.212830\pi$
$368$	4.30430	0.224377
$369$	9.83729	0.512109
$370$	14.9443	0.776917
$371$	6.08444	0.315888
$372$	1.78156	0.0923697
$373$	−16.1667	−0.837078	−0.418539	−	0.908199i	$-0.637458\pi$
$373$	−16.1667	−0.837078	−0.418539	+	0.908199i	$0.637458\pi$
$374$	−0.110030	−0.00568951
$375$	−6.25517	−0.323015
$376$	19.6117	1.01139
$377$	31.0439	1.59884
$378$	−1.22787	−0.0631548
$379$	−8.68994	−0.446372	−0.223186	−	0.974776i	$-0.571646\pi$
$379$	−8.68994	−0.446372	−0.223186	+	0.974776i	$0.571646\pi$
$380$	−4.57339	−0.234610
$381$	−13.5717	−0.695298
$382$	−1.22787	−0.0628233
$383$	−31.6714	−1.61833	−0.809166	−	0.587580i	$-0.800081\pi$
$383$	−31.6714	−1.61833	−0.809166	+	0.587580i	$0.800081\pi$
$384$	5.47256	0.279271
$385$	−2.15282	−0.109718
$386$	−16.2090	−0.825019
$387$	−5.70971	−0.290241
$388$	−3.95901	−0.200988
$389$	−25.0173	−1.26843	−0.634214	−	0.773158i	$-0.718676\pi$
$389$	−25.0173	−1.26843	−0.634214	+	0.773158i	$0.718676\pi$
$390$	15.3347	0.776505
$391$	0.179914	0.00909864
$392$	−3.06026	−0.154567
$393$	7.47912	0.377272
$394$	23.4511	1.18145
$395$	−31.4640	−1.58312
$396$	−0.380642	−0.0191280
$397$	−26.5901	−1.33452	−0.667260	−	0.744824i	$-0.732533\pi$
$397$	−26.5901	−1.33452	−0.667260	+	0.744824i	$0.732533\pi$
$398$	15.6406	0.783990
$399$	−3.33600	−0.167009
$400$	−7.63556	−0.381778
$401$	−38.1575	−1.90549	−0.952747	−	0.303764i	$-0.901757\pi$
$401$	−38.1575	−1.90549	−0.952747	+	0.303764i	$0.901757\pi$
$402$	−8.71722	−0.434776
$403$	−16.2298	−0.808462
$404$	−8.09321	−0.402652
$405$	2.78453	0.138364
$406$	−8.49877	−0.421787
$407$	3.37931	0.167506
$408$	0.354700	0.0175603
$409$	17.8130	0.880797	0.440398	−	0.897803i	$-0.354837\pi$
$409$	17.8130	0.880797	0.440398	+	0.897803i	$0.354837\pi$
$410$	33.6341	1.66107
$411$	−3.40820	−0.168114
$412$	0.356255	0.0175514
$413$	2.05700	0.101219
$414$	−1.90596	−0.0936731
$415$	49.7580	2.44253
$416$	12.1803	0.597188
$417$	6.06876	0.297188
$418$	3.16690	0.154898
$419$	14.3316	0.700145	0.350072	−	0.936723i	$-0.386157\pi$
$419$	14.3316	0.700145	0.350072	+	0.936723i	$0.386157\pi$
$420$	1.37092	0.0668941
$421$	−34.2218	−1.66787	−0.833935	−	0.551862i	$-0.813917\pi$
$421$	−34.2218	−1.66787	−0.833935	+	0.551862i	$0.813917\pi$
$422$	22.3738	1.08914
$423$	−6.40849	−0.311591
$424$	18.6200	0.904267
$425$	−0.319156	−0.0154813
$426$	6.18392	0.299612
$427$	−6.27331	−0.303587
$428$	6.63232	0.320585
$429$	3.46759	0.167417
$430$	−19.5217	−0.941421
$431$	−19.0880	−0.919438	−0.459719	−	0.888064i	$-0.652050\pi$
$431$	−19.0880	−0.919438	−0.459719	+	0.888064i	$0.652050\pi$
$432$	−2.77294	−0.133413
$433$	−13.8705	−0.666575	−0.333288	−	0.942825i	$-0.608158\pi$
$433$	−13.8705	−0.666575	−0.333288	+	0.942825i	$0.608158\pi$
$434$	4.44317	0.213279
$435$	19.2733	0.924083
$436$	−7.83431	−0.375195
$437$	−5.17831	−0.247712
$438$	20.5547	0.982140
$439$	−8.71320	−0.415858	−0.207929	−	0.978144i	$-0.566672\pi$
$439$	−8.71320	−0.415858	−0.207929	+	0.978144i	$0.566672\pi$
$440$	−6.58820	−0.314080
$441$	1.00000	0.0476190
$442$	−0.638303	−0.0303610
$443$	19.9084	0.945875	0.472938	−	0.881096i	$-0.343194\pi$
$443$	19.9084	0.945875	0.472938	+	0.881096i	$0.343194\pi$
$444$	−2.15195	−0.102127
$445$	9.11225	0.431962
$446$	5.52542	0.261636
$447$	2.01504	0.0953081
$448$	−8.88043	−0.419561
$449$	13.0863	0.617582	0.308791	−	0.951130i	$-0.400076\pi$
$449$	13.0863	0.617582	0.308791	+	0.951130i	$0.400076\pi$
$450$	3.38106	0.159385
$451$	7.60557	0.358132
$452$	6.14959	0.289252
$453$	9.42282	0.442723
$454$	−24.8856	−1.16794
$455$	−12.4889	−0.585488
$456$	−10.2090	−0.478081
$457$	26.2561	1.22821	0.614104	−	0.789225i	$-0.289518\pi$
$457$	26.2561	1.22821	0.614104	+	0.789225i	$0.289518\pi$
$458$	3.30299	0.154338
$459$	−0.115905	−0.00540998
$460$	2.12802	0.0992193
$461$	25.6314	1.19377	0.596887	−	0.802326i	$-0.296404\pi$
$461$	25.6314	1.19377	0.596887	+	0.802326i	$0.296404\pi$
$462$	−0.949311	−0.0441659
$463$	9.48207	0.440669	0.220335	−	0.975424i	$-0.429285\pi$
$463$	9.48207	0.440669	0.220335	+	0.975424i	$0.429285\pi$
$464$	−19.1930	−0.891014
$465$	−10.0761	−0.467267
$466$	−24.1171	−1.11721
$467$	−32.3127	−1.49525	−0.747627	−	0.664119i	$-0.768807\pi$
$467$	−32.3127	−1.49525	−0.747627	+	0.664119i	$0.768807\pi$
$468$	−2.20817	−0.102073
$469$	7.09947	0.327823
$470$	−21.9109	−1.01067
$471$	15.0837	0.695018
$472$	6.29497	0.289750
$473$	−4.41438	−0.202974
$474$	−13.8744	−0.637272
$475$	9.18600	0.421483
$476$	−0.0570641	−0.00261553
$477$	−6.08444	−0.278587
$478$	10.5092	0.480681
$479$	28.1603	1.28668	0.643339	−	0.765581i	$-0.277548\pi$
$479$	28.1603	1.28668	0.643339	+	0.765581i	$0.277548\pi$
$480$	7.56201	0.345157
$481$	19.6040	0.893863
$482$	−13.2347	−0.602823
$483$	1.55225	0.0706300
$484$	5.12140	0.232791
$485$	22.3912	1.01673
$486$	1.22787	0.0556973
$487$	−21.1664	−0.959139	−0.479570	−	0.877504i	$-0.659207\pi$
$487$	−21.1664	−0.959139	−0.479570	+	0.877504i	$0.659207\pi$
$488$	−19.1980	−0.869052
$489$	−3.02821	−0.136941
$490$	3.41904	0.154456
$491$	−12.7210	−0.574089	−0.287044	−	0.957917i	$-0.592673\pi$
$491$	−12.7210	−0.574089	−0.287044	+	0.957917i	$0.592673\pi$
$492$	−4.84324	−0.218350
$493$	−0.802243	−0.0361312
$494$	18.3717	0.826583
$495$	2.15282	0.0967621
$496$	10.0341	0.450546
$497$	−5.03630	−0.225909
$498$	21.9414	0.983217
$499$	−11.5683	−0.517870	−0.258935	−	0.965895i	$-0.583372\pi$
$499$	−11.5683	−0.517870	−0.258935	+	0.965895i	$0.583372\pi$
$500$	3.07964	0.137726
$501$	−3.64207	−0.162715
$502$	23.0374	1.02821
$503$	35.3201	1.57484	0.787422	−	0.616415i	$-0.211416\pi$
$503$	35.3201	1.57484	0.787422	+	0.616415i	$0.211416\pi$
$504$	3.06026	0.136315
$505$	45.7732	2.03688
$506$	−1.47357	−0.0655082
$507$	7.11613	0.316039
$508$	6.68181	0.296457
$509$	−8.12153	−0.359980	−0.179990	−	0.983668i	$-0.557607\pi$
$509$	−8.12153	−0.359980	−0.179990	+	0.983668i	$0.557607\pi$
$510$	−0.396284	−0.0175477
$511$	−16.7401	−0.740539
$512$	−24.5024	−1.08286
$513$	3.33600	0.147288
$514$	−35.6642	−1.57308
$515$	−2.01489	−0.0887868
$516$	2.81109	0.123751
$517$	−4.95464	−0.217905
$518$	−5.36690	−0.235808
$519$	−21.7730	−0.955728
$520$	−38.2193	−1.67603
$521$	13.9082	0.609330	0.304665	−	0.952460i	$-0.401455\pi$
$521$	13.9082	0.609330	0.304665	+	0.952460i	$0.401455\pi$
$522$	8.49877	0.371981
$523$	32.6758	1.42881	0.714406	−	0.699731i	$-0.246697\pi$
$523$	32.6758	1.42881	0.714406	+	0.699731i	$0.246697\pi$
$524$	−3.68223	−0.160859
$525$	−2.75360	−0.120177
$526$	−11.7226	−0.511128
$527$	0.419413	0.0182699
$528$	−2.14386	−0.0932994
$529$	−20.5905	−0.895240
$530$	−20.8029	−0.903622
$531$	−2.05700	−0.0892664
$532$	1.64243	0.0712083
$533$	44.1212	1.91110
$534$	4.01815	0.173883
$535$	−37.5108	−1.62173
$536$	21.7262	0.938431
$537$	−13.3551	−0.576316
$538$	24.4439	1.05385
$539$	0.773136	0.0333013
$540$	−1.37092	−0.0589951
$541$	0.497745	0.0213997	0.0106999	−	0.999943i	$-0.496594\pi$
$541$	0.497745	0.0213997	0.0106999	+	0.999943i	$0.496594\pi$
$542$	−19.5028	−0.837718
$543$	−14.4209	−0.618861
$544$	−0.314766	−0.0134955
$545$	44.3089	1.89799
$546$	−5.50712	−0.235683
$547$	−19.7410	−0.844065	−0.422033	−	0.906581i	$-0.638683\pi$
$547$	−19.7410	−0.844065	−0.422033	+	0.906581i	$0.638683\pi$
$548$	1.67798	0.0716796
$549$	6.27331	0.267739
$550$	2.61402	0.111462
$551$	23.0903	0.983679
$552$	4.75030	0.202186
$553$	11.2996	0.480506
$554$	2.53803	0.107831
$555$	12.1709	0.516626
$556$	−2.98786	−0.126714
$557$	−2.19384	−0.0929561	−0.0464781	−	0.998919i	$-0.514800\pi$
$557$	−2.19384	−0.0929561	−0.0464781	+	0.998919i	$0.514800\pi$
$558$	−4.44317	−0.188094
$559$	−25.6086	−1.08313
$560$	7.72132	0.326285
$561$	−0.0896104	−0.00378335
$562$	−19.0598	−0.803988
$563$	22.5371	0.949825	0.474913	−	0.880033i	$-0.342480\pi$
$563$	22.5371	0.949825	0.474913	+	0.880033i	$0.342480\pi$
$564$	3.15512	0.132855
$565$	−34.7806	−1.46323
$566$	31.9973	1.34495
$567$	−1.00000	−0.0419961
$568$	−15.4124	−0.646690
$569$	43.3873	1.81889	0.909445	−	0.415824i	$-0.136507\pi$
$569$	43.3873	1.81889	0.909445	+	0.415824i	$0.136507\pi$
$570$	11.4059	0.477741
$571$	−15.6736	−0.655921	−0.327960	−	0.944691i	$-0.606361\pi$
$571$	−15.6736	−0.655921	−0.327960	+	0.944691i	$0.606361\pi$
$572$	−1.70722	−0.0713824
$573$	−1.00000	−0.0417756
$574$	−12.0789	−0.504164
$575$	−4.27428	−0.178250
$576$	8.88043	0.370018
$577$	−11.1553	−0.464400	−0.232200	−	0.972668i	$-0.574592\pi$
$577$	−11.1553	−0.464400	−0.232200	+	0.972668i	$0.574592\pi$
$578$	−20.8573	−0.867549
$579$	−13.2009	−0.548613
$580$	−9.48891	−0.394006
$581$	−17.8695	−0.741351
$582$	9.87367	0.409277
$583$	−4.70410	−0.194824
$584$	−51.2291	−2.11988
$585$	12.4889	0.516352
$586$	−30.4988	−1.25990
$587$	−8.33304	−0.343942	−0.171971	−	0.985102i	$-0.555013\pi$
$587$	−8.33304	−0.343942	−0.171971	+	0.985102i	$0.555013\pi$
$588$	−0.492335	−0.0203036
$589$	−12.0716	−0.497402
$590$	−7.03298	−0.289543
$591$	19.0990	0.785628
$592$	−12.1202	−0.498139
$593$	−35.1001	−1.44139	−0.720694	−	0.693253i	$-0.756177\pi$
$593$	−35.1001	−1.44139	−0.720694	+	0.693253i	$0.756177\pi$
$594$	0.949311	0.0389507
$595$	0.322741	0.0132311
$596$	−0.992075	−0.0406370
$597$	12.7380	0.521330
$598$	−8.54844	−0.349572
$599$	27.7601	1.13425	0.567124	−	0.823632i	$-0.308056\pi$
$599$	27.7601	1.13425	0.567124	+	0.823632i	$0.308056\pi$
$600$	−8.42674	−0.344020
$601$	34.0666	1.38961	0.694804	−	0.719200i	$-0.255491\pi$
$601$	34.0666	1.38961	0.694804	+	0.719200i	$0.255491\pi$
$602$	7.01078	0.285738
$603$	−7.09947	−0.289113
$604$	−4.63919	−0.188766
$605$	−28.9654	−1.17761
$606$	20.1842	0.819928
$607$	−22.8043	−0.925597	−0.462799	−	0.886463i	$-0.653155\pi$
$607$	−22.8043	−0.925597	−0.462799	+	0.886463i	$0.653155\pi$
$608$	9.05964	0.367417
$609$	−6.92156	−0.280476
$610$	21.4487	0.868433
$611$	−28.7427	−1.16281
$612$	0.0570641	0.00230668
$613$	4.76784	0.192571	0.0962857	−	0.995354i	$-0.469304\pi$
$613$	4.76784	0.192571	0.0962857	+	0.995354i	$0.469304\pi$
$614$	−41.1893	−1.66227
$615$	27.3922	1.10456
$616$	2.36600	0.0953289
$617$	33.8794	1.36393	0.681967	−	0.731383i	$-0.261125\pi$
$617$	33.8794	1.36393	0.681967	+	0.731383i	$0.261125\pi$
$618$	−0.888490	−0.0357403
$619$	−14.4140	−0.579347	−0.289673	−	0.957126i	$-0.593547\pi$
$619$	−14.4140	−0.579347	−0.289673	+	0.957126i	$0.593547\pi$
$620$	4.96081	0.199231
$621$	−1.55225	−0.0622898
$622$	8.65736	0.347129
$623$	−3.27246	−0.131108
$624$	−12.4369	−0.497874
$625$	−31.1857	−1.24743
$626$	−10.6044	−0.423838
$627$	2.57918	0.103003
$628$	−7.42621	−0.296338
$629$	−0.506610	−0.0201999
$630$	−3.41904	−0.136218
$631$	1.66082	0.0661164	0.0330582	−	0.999453i	$-0.489475\pi$
$631$	1.66082	0.0661164	0.0330582	+	0.999453i	$0.489475\pi$
$632$	34.5796	1.37550
$633$	18.2217	0.724246
$634$	−13.6269	−0.541193
$635$	−37.7907	−1.49968
$636$	2.99558	0.118783
$637$	4.48510	0.177706
$638$	6.57071	0.260137
$639$	5.03630	0.199233
$640$	15.2385	0.602355
$641$	36.1786	1.42897	0.714485	−	0.699651i	$-0.246661\pi$
$641$	36.1786	1.42897	0.714485	+	0.699651i	$0.246661\pi$
$642$	−16.5408	−0.652814
$643$	−29.4889	−1.16293	−0.581464	−	0.813572i	$-0.697520\pi$
$643$	−29.4889	−1.16293	−0.581464	+	0.813572i	$0.697520\pi$
$644$	−0.764229	−0.0301148
$645$	−15.8988	−0.626017
$646$	−0.474767	−0.0186794
$647$	−38.9714	−1.53212	−0.766062	−	0.642766i	$-0.777787\pi$
$647$	−38.9714	−1.53212	−0.766062	+	0.642766i	$0.777787\pi$
$648$	−3.06026	−0.120219
$649$	−1.59034	−0.0624265
$650$	15.1644	0.594797
$651$	3.61860	0.141824
$652$	1.49090	0.0583880
$653$	43.3141	1.69501	0.847506	−	0.530785i	$-0.178103\pi$
$653$	43.3141	1.69501	0.847506	+	0.530785i	$0.178103\pi$
$654$	19.5385	0.764017
$655$	20.8258	0.813732
$656$	−27.2782	−1.06503
$657$	16.7401	0.653094
$658$	7.86879	0.306757
$659$	20.0367	0.780519	0.390260	−	0.920705i	$-0.372385\pi$
$659$	20.0367	0.780519	0.390260	+	0.920705i	$0.372385\pi$
$660$	−1.05991	−0.0412569
$661$	−3.50900	−0.136484	−0.0682422	−	0.997669i	$-0.521739\pi$
$661$	−3.50900	−0.136484	−0.0682422	+	0.997669i	$0.521739\pi$
$662$	−15.6235	−0.607226
$663$	−0.519846	−0.0201891
$664$	−54.6853	−2.12220
$665$	−9.28918	−0.360219
$666$	5.36690	0.207963
$667$	−10.7440	−0.416010
$668$	1.79312	0.0693778
$669$	4.50000	0.173980
$670$	−24.2734	−0.937761
$671$	4.85013	0.187237
$672$	−2.71572	−0.104761
$673$	−13.1563	−0.507139	−0.253570	−	0.967317i	$-0.581605\pi$
$673$	−13.1563	−0.507139	−0.253570	+	0.967317i	$0.581605\pi$
$674$	17.6613	0.680288
$675$	2.75360	0.105986
$676$	−3.50352	−0.134751
$677$	6.41092	0.246392	0.123196	−	0.992382i	$-0.460686\pi$
$677$	6.41092	0.246392	0.123196	+	0.992382i	$0.460686\pi$
$678$	−15.3369	−0.589010
$679$	−8.04130	−0.308597
$680$	0.987672	0.0378755
$681$	−20.2673	−0.776644
$682$	−3.43517	−0.131540
$683$	0.645441	0.0246971	0.0123486	−	0.999924i	$-0.496069\pi$
$683$	0.645441	0.0246971	0.0123486	+	0.999924i	$0.496069\pi$
$684$	−1.64243	−0.0627998
$685$	−9.49023	−0.362603
$686$	−1.22787	−0.0468803
$687$	2.69001	0.102630
$688$	15.8327	0.603614
$689$	−27.2893	−1.03964
$690$	−5.30721	−0.202042
$691$	25.2349	0.959981	0.479990	−	0.877274i	$-0.340640\pi$
$691$	25.2349	0.959981	0.479990	+	0.877274i	$0.340640\pi$
$692$	10.7196	0.407498
$693$	−0.773136	−0.0293690
$694$	36.9680	1.40329
$695$	16.8986	0.641001
$696$	−21.1818	−0.802894
$697$	−1.14019	−0.0431878
$698$	−23.3998	−0.885696
$699$	−19.6415	−0.742908
$700$	1.35569	0.0512404
$701$	−35.1630	−1.32809	−0.664044	−	0.747693i	$-0.731161\pi$
$701$	−35.1630	−1.32809	−0.664044	+	0.747693i	$0.731161\pi$
$702$	5.50712	0.207853
$703$	14.5813	0.549945
$704$	6.86578	0.258764
$705$	−17.8446	−0.672067
$706$	22.4205	0.843806
$707$	−16.4384	−0.618230
$708$	1.01274	0.0380609
$709$	−30.3756	−1.14078	−0.570389	−	0.821375i	$-0.693208\pi$
$709$	−30.3756	−1.14078	−0.570389	+	0.821375i	$0.693208\pi$
$710$	17.2193	0.646229
$711$	−11.2996	−0.423767
$712$	−10.0146	−0.375312
$713$	5.61698	0.210357
$714$	0.142316	0.00532605
$715$	9.65562	0.361100
$716$	6.57519	0.245726
$717$	8.55891	0.319638
$718$	−6.82327	−0.254642
$719$	−13.9590	−0.520582	−0.260291	−	0.965530i	$-0.583818\pi$
$719$	−13.9590	−0.520582	−0.260291	+	0.965530i	$0.583818\pi$
$720$	−7.72132	−0.287757
$721$	0.723603	0.0269484
$722$	−9.66473	−0.359684
$723$	−10.7786	−0.400859
$724$	7.09992	0.263867
$725$	19.0592	0.707841
$726$	−12.7726	−0.474037
$727$	−13.9023	−0.515606	−0.257803	−	0.966197i	$-0.582999\pi$
$727$	−13.9023	−0.515606	−0.257803	+	0.966197i	$0.582999\pi$
$728$	13.7256	0.508704
$729$	1.00000	0.0370370
$730$	57.2351	2.11837
$731$	0.661784	0.0244770
$732$	−3.08857	−0.114157
$733$	−51.4290	−1.89957	−0.949786	−	0.312901i	$-0.898699\pi$
$733$	−51.4290	−1.89957	−0.949786	+	0.312901i	$0.898699\pi$
$734$	36.9152	1.36257
$735$	2.78453	0.102709
$736$	−4.21549	−0.155385
$737$	−5.48886	−0.202185
$738$	12.0789	0.444631
$739$	−16.6035	−0.610771	−0.305385	−	0.952229i	$-0.598785\pi$
$739$	−16.6035	−0.610771	−0.305385	+	0.952229i	$0.598785\pi$
$740$	−5.99217	−0.220276
$741$	14.9623	0.549653
$742$	7.47090	0.274265
$743$	19.7719	0.725361	0.362680	−	0.931914i	$-0.381862\pi$
$743$	19.7719	0.725361	0.362680	+	0.931914i	$0.381862\pi$
$744$	11.0739	0.405987
$745$	5.61093	0.205569
$746$	−19.8506	−0.726781
$747$	17.8695	0.653810
$748$	0.0441183	0.00161313
$749$	13.4712	0.492225
$750$	−7.68053	−0.280453
$751$	−24.1852	−0.882530	−0.441265	−	0.897377i	$-0.645470\pi$
$751$	−24.1852	−0.882530	−0.441265	+	0.897377i	$0.645470\pi$
$752$	17.7703	0.648017
$753$	18.7621	0.683728
$754$	38.1179	1.38817
$755$	26.2381	0.954903
$756$	0.492335	0.0179061
$757$	17.3330	0.629979	0.314989	−	0.949095i	$-0.397999\pi$
$757$	17.3330	0.629979	0.314989	+	0.949095i	$0.397999\pi$
$758$	−10.6701	−0.387556
$759$	−1.20010	−0.0435610
$760$	−28.4273	−1.03117
$761$	10.6315	0.385391	0.192696	−	0.981259i	$-0.438277\pi$
$761$	10.6315	0.385391	0.192696	+	0.981259i	$0.438277\pi$
$762$	−16.6643	−0.603682
$763$	−15.9125	−0.576073
$764$	0.492335	0.0178121
$765$	−0.322741	−0.0116687
$766$	−38.8884	−1.40509
$767$	−9.22587	−0.333127
$768$	−11.0413	−0.398417
$769$	−1.79657	−0.0647858	−0.0323929	−	0.999475i	$-0.510313\pi$
$769$	−1.79657	−0.0647858	−0.0323929	+	0.999475i	$0.510313\pi$
$770$	−2.64338	−0.0952609
$771$	−29.0455	−1.04605
$772$	6.49929	0.233915
$773$	−10.5659	−0.380031	−0.190015	−	0.981781i	$-0.560854\pi$
$773$	−10.5659	−0.380031	−0.190015	+	0.981781i	$0.560854\pi$
$774$	−7.01078	−0.251997
$775$	−9.96417	−0.357923
$776$	−24.6085	−0.883393
$777$	−4.37091	−0.156805
$778$	−30.7180	−1.10129
$779$	32.8172	1.17580
$780$	−6.14872	−0.220160
$781$	3.89374	0.139329
$782$	0.220911	0.00789976
$783$	6.92156	0.247356
$784$	−2.77294	−0.0990334
$785$	42.0009	1.49908
$786$	9.18339	0.327561
$787$	32.5239	1.15935	0.579676	−	0.814847i	$-0.303179\pi$
$787$	32.5239	1.15935	0.579676	+	0.814847i	$0.303179\pi$
$788$	−9.40311	−0.334972
$789$	−9.54708	−0.339885
$790$	−38.6336	−1.37452
$791$	12.4907	0.444117
$792$	−2.36600	−0.0840722
$793$	28.1364	0.999155
$794$	−32.6492	−1.15868
$795$	−16.9423	−0.600881
$796$	−6.27134	−0.222282
$797$	−26.3847	−0.934596	−0.467298	−	0.884100i	$-0.654772\pi$
$797$	−26.3847	−0.934596	−0.467298	+	0.884100i	$0.654772\pi$
$798$	−4.09617	−0.145003
$799$	0.742776	0.0262775
$800$	7.47801	0.264388
$801$	3.27246	0.115627
$802$	−46.8524	−1.65442
$803$	12.9424	0.456727
$804$	3.49532	0.123270
$805$	4.32229	0.152341
$806$	−19.9280	−0.701935
$807$	19.9076	0.700779
$808$	−50.3059	−1.76975
$809$	−15.4311	−0.542529	−0.271264	−	0.962505i	$-0.587442\pi$
$809$	−15.4311	−0.542529	−0.271264	+	0.962505i	$0.587442\pi$
$810$	3.41904	0.120133
$811$	−53.4501	−1.87689	−0.938444	−	0.345431i	$-0.887733\pi$
$811$	−53.4501	−1.87689	−0.938444	+	0.345431i	$0.887733\pi$
$812$	3.40773	0.119588
$813$	−15.8835	−0.557057
$814$	4.14935	0.145435
$815$	−8.43215	−0.295365
$816$	0.321397	0.0112512
$817$	−19.0476	−0.666390
$818$	21.8721	0.764739
$819$	−4.48510	−0.156722
$820$	−13.4862	−0.470957
$821$	2.56847	0.0896402	0.0448201	−	0.998995i	$-0.485729\pi$
$821$	2.56847	0.0896402	0.0448201	+	0.998995i	$0.485729\pi$
$822$	−4.18483	−0.145963
$823$	14.2080	0.495258	0.247629	−	0.968855i	$-0.420349\pi$
$823$	14.2080	0.495258	0.247629	+	0.968855i	$0.420349\pi$
$824$	2.21441	0.0771428
$825$	2.12891	0.0741191
$826$	2.52573	0.0878815
$827$	−33.7567	−1.17383	−0.586917	−	0.809647i	$-0.699659\pi$
$827$	−33.7567	−1.17383	−0.586917	+	0.809647i	$0.699659\pi$
$828$	0.764229	0.0265588
$829$	27.3031	0.948275	0.474138	−	0.880451i	$-0.342760\pi$
$829$	27.3031	0.948275	0.474138	+	0.880451i	$0.342760\pi$
$830$	61.0964	2.12069
$831$	2.06702	0.0717042
$832$	39.8296	1.38084
$833$	−0.115905	−0.00401587
$834$	7.45164	0.258029
$835$	−10.1414	−0.350959
$836$	−1.26982	−0.0439177
$837$	−3.61860	−0.125077
$838$	17.5973	0.607890
$839$	5.89426	0.203492	0.101746	−	0.994810i	$-0.467557\pi$
$839$	5.89426	0.203492	0.101746	+	0.994810i	$0.467557\pi$
$840$	8.52139	0.294016
$841$	18.9080	0.651999
$842$	−42.0200	−1.44810
$843$	−15.5226	−0.534628
$844$	−8.97117	−0.308800
$845$	19.8151	0.681659
$846$	−7.86879	−0.270535
$847$	10.4023	0.357426
$848$	16.8718	0.579379
$849$	26.0592	0.894348
$850$	−0.391882	−0.0134414
$851$	−6.78475	−0.232578
$852$	−2.47955	−0.0849479
$853$	−30.5397	−1.04566	−0.522829	−	0.852437i	$-0.675123\pi$
$853$	−30.5397	−1.04566	−0.522829	+	0.852437i	$0.675123\pi$
$854$	−7.70281	−0.263585
$855$	9.28918	0.317683
$856$	41.2253	1.40905
$857$	−29.6665	−1.01339	−0.506695	−	0.862125i	$-0.669133\pi$
$857$	−29.6665	−1.01339	−0.506695	+	0.862125i	$0.669133\pi$
$858$	4.25776	0.145357
$859$	−44.2061	−1.50829	−0.754146	−	0.656707i	$-0.771949\pi$
$859$	−44.2061	−1.50829	−0.754146	+	0.656707i	$0.771949\pi$
$860$	7.82756	0.266918
$861$	−9.83729	−0.335254
$862$	−23.4376	−0.798288
$863$	−58.7154	−1.99869	−0.999347	−	0.0361332i	$-0.988496\pi$
$863$	−58.7154	−1.99869	−0.999347	+	0.0361332i	$0.988496\pi$
$864$	2.71572	0.0923908
$865$	−60.6275	−2.06140
$866$	−17.0312	−0.578744
$867$	−16.9866	−0.576894
$868$	−1.78156	−0.0604702
$869$	−8.73610	−0.296352
$870$	23.6651	0.802321
$871$	−31.8418	−1.07892
$872$	−48.6966	−1.64907
$873$	8.04130	0.272157
$874$	−6.35829	−0.215072
$875$	6.25517	0.211463
$876$	−8.24174	−0.278463
$877$	16.1514	0.545394	0.272697	−	0.962100i	$-0.412084\pi$
$877$	16.1514	0.545394	0.272697	+	0.962100i	$0.412084\pi$
$878$	−10.6987	−0.361063
$879$	−24.8388	−0.837792
$880$	−5.96963	−0.201236
$881$	43.0980	1.45201	0.726005	−	0.687689i	$-0.241375\pi$
$881$	43.0980	1.45201	0.726005	+	0.687689i	$0.241375\pi$
$882$	1.22787	0.0413445
$883$	30.4715	1.02545	0.512724	−	0.858554i	$-0.328637\pi$
$883$	30.4715	1.02545	0.512724	+	0.858554i	$0.328637\pi$
$884$	0.255938	0.00860814
$885$	−5.72779	−0.192537
$886$	24.4449	0.821242
$887$	−11.2723	−0.378487	−0.189244	−	0.981930i	$-0.560604\pi$
$887$	−11.2723	−0.378487	−0.189244	+	0.981930i	$0.560604\pi$
$888$	−13.3761	−0.448873
$889$	13.5717	0.455179
$890$	11.1887	0.375045
$891$	0.773136	0.0259010
$892$	−2.21551	−0.0741808
$893$	−21.3787	−0.715411
$894$	2.47421	0.0827498
$895$	−37.1877	−1.24305
$896$	−5.47256	−0.182826
$897$	−6.96201	−0.232455
$898$	16.0683	0.536207
$899$	−25.0463	−0.835342
$900$	−1.35569	−0.0451898
$901$	0.705217	0.0234942
$902$	9.33865	0.310943
$903$	5.70971	0.190007
$904$	38.2247	1.27133
$905$	−40.1554	−1.33481
$906$	11.5700	0.384387
$907$	−15.3933	−0.511125	−0.255563	−	0.966793i	$-0.582261\pi$
$907$	−15.3933	−0.511125	−0.255563	+	0.966793i	$0.582261\pi$
$908$	9.97830	0.331141
$909$	16.4384	0.545228
$910$	−15.3347	−0.508342
$911$	−8.97744	−0.297436	−0.148718	−	0.988880i	$-0.547515\pi$
$911$	−8.97744	−0.297436	−0.148718	+	0.988880i	$0.547515\pi$
$912$	−9.25050	−0.306315
$913$	13.8155	0.457228
$914$	32.2391	1.06637
$915$	17.4682	0.577482
$916$	−1.32439	−0.0437590
$917$	−7.47912	−0.246982
$918$	−0.142316	−0.00469714
$919$	35.3769	1.16698	0.583489	−	0.812121i	$-0.301687\pi$
$919$	35.3769	1.16698	0.583489	+	0.812121i	$0.301687\pi$
$920$	13.2274	0.436093
$921$	−33.5454	−1.10536
$922$	31.4720	1.03648
$923$	22.5883	0.743503
$924$	0.380642	0.0125222
$925$	12.0357	0.395732
$926$	11.6427	0.382604
$927$	−0.723603	−0.0237662
$928$	18.7970	0.617043
$929$	36.1341	1.18552	0.592761	−	0.805379i	$-0.298038\pi$
$929$	36.1341	1.18552	0.592761	+	0.805379i	$0.298038\pi$
$930$	−12.3721	−0.405698
$931$	3.33600	0.109333
$932$	9.67018	0.316757
$933$	7.05071	0.230830
$934$	−39.6758	−1.29823
$935$	−0.249523	−0.00816026
$936$	−13.7256	−0.448635
$937$	−4.20976	−0.137527	−0.0687634	−	0.997633i	$-0.521905\pi$
$937$	−4.20976	−0.137527	−0.0687634	+	0.997633i	$0.521905\pi$
$938$	8.71722	0.284627
$939$	−8.63644	−0.281839
$940$	8.78553	0.286553
$941$	−34.5683	−1.12689	−0.563447	−	0.826152i	$-0.690525\pi$
$941$	−34.5683	−1.12689	−0.563447	+	0.826152i	$0.690525\pi$
$942$	18.5208	0.603439
$943$	−15.2700	−0.497258
$944$	5.70394	0.185647
$945$	−2.78453	−0.0905807
$946$	−5.42029	−0.176229
$947$	−32.8053	−1.06603	−0.533015	−	0.846106i	$-0.678941\pi$
$947$	−32.8053	−1.06603	−0.533015	+	0.846106i	$0.678941\pi$
$948$	5.56317	0.180683
$949$	75.0811	2.43723
$950$	11.2792	0.365946
$951$	−11.0980	−0.359877
$952$	−0.354700	−0.0114959
$953$	−20.7877	−0.673378	−0.336689	−	0.941616i	$-0.609307\pi$
$953$	−20.7877	−0.673378	−0.336689	+	0.941616i	$0.609307\pi$
$954$	−7.47090	−0.241879
$955$	−2.78453	−0.0901052
$956$	−4.21385	−0.136286
$957$	5.35131	0.172983
$958$	34.5772	1.11714
$959$	3.40820	0.110056
$960$	24.7278	0.798086
$961$	−17.9058	−0.577605
$962$	24.0711	0.776084
$963$	−13.4712	−0.434102
$964$	5.30667	0.170916
$965$	−36.7584	−1.18330
$966$	1.90596	0.0613234
$967$	−21.9427	−0.705631	−0.352815	−	0.935693i	$-0.614776\pi$
$967$	−21.9427	−0.705631	−0.352815	+	0.935693i	$0.614776\pi$
$968$	31.8337	1.02317
$969$	−0.386659	−0.0124213
$970$	27.4935	0.882763
$971$	45.7948	1.46962	0.734812	−	0.678271i	$-0.237270\pi$
$971$	45.7948	1.46962	0.734812	+	0.678271i	$0.237270\pi$
$972$	−0.492335	−0.0157917
$973$	−6.06876	−0.194555
$974$	−25.9895	−0.832759
$975$	12.3502	0.395522
$976$	−17.3955	−0.556816
$977$	−35.3323	−1.13038	−0.565191	−	0.824960i	$-0.691197\pi$
$977$	−35.3323	−1.13038	−0.565191	+	0.824960i	$0.691197\pi$
$978$	−3.71825	−0.118897
$979$	2.53006	0.0808610
$980$	−1.37092	−0.0437925
$981$	15.9125	0.508049
$982$	−15.6197	−0.498444
$983$	23.9507	0.763909	0.381955	−	0.924181i	$-0.375251\pi$
$983$	23.9507	0.763909	0.381955	+	0.924181i	$0.375251\pi$
$984$	−30.1047	−0.959703
$985$	53.1817	1.69451
$986$	−0.985051	−0.0313704
$987$	6.40849	0.203984
$988$	−7.36646	−0.234358
$989$	8.86291	0.281824
$990$	2.64338	0.0840122
$991$	−35.5826	−1.13032	−0.565159	−	0.824982i	$-0.691185\pi$
$991$	−35.5826	−1.13032	−0.565159	+	0.824982i	$0.691185\pi$
$992$	−9.82710	−0.312011
$993$	−12.7241	−0.403787
$994$	−6.18392	−0.196142
$995$	35.4692	1.12445
$996$	−8.79777	−0.278768
$997$	−52.7072	−1.66925	−0.834627	−	0.550816i	$-0.814317\pi$
$997$	−52.7072	−1.66925	−0.834627	+	0.550816i	$0.814317\pi$
$998$	−14.2044	−0.449633
$999$	4.37091	0.138289

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.20	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.22787 q^{2} +1.00000 q^{3} -0.492335 q^{4} +2.78453 q^{5} +1.22787 q^{6} -1.00000 q^{7} -3.06026 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.22787 q^{2} +1.00000 q^{3} -0.492335 q^{4} +2.78453 q^{5} +1.22787 q^{6} -1.00000 q^{7} -3.06026 q^{8} +1.00000 q^{9} +3.41904 q^{10} +0.773136 q^{11} -0.492335 q^{12} +4.48510 q^{13} -1.22787 q^{14} +2.78453 q^{15} -2.77294 q^{16} -0.115905 q^{17} +1.22787 q^{18} +3.33600 q^{19} -1.37092 q^{20} -1.00000 q^{21} +0.949311 q^{22} -1.55225 q^{23} -3.06026 q^{24} +2.75360 q^{25} +5.50712 q^{26} +1.00000 q^{27} +0.492335 q^{28} +6.92156 q^{29} +3.41904 q^{30} -3.61860 q^{31} +2.71572 q^{32} +0.773136 q^{33} -0.142316 q^{34} -2.78453 q^{35} -0.492335 q^{36} +4.37091 q^{37} +4.09617 q^{38} +4.48510 q^{39} -8.52139 q^{40} +9.83729 q^{41} -1.22787 q^{42} -5.70971 q^{43} -0.380642 q^{44} +2.78453 q^{45} -1.90596 q^{46} -6.40849 q^{47} -2.77294 q^{48} +1.00000 q^{49} +3.38106 q^{50} -0.115905 q^{51} -2.20817 q^{52} -6.08444 q^{53} +1.22787 q^{54} +2.15282 q^{55} +3.06026 q^{56} +3.33600 q^{57} +8.49877 q^{58} -2.05700 q^{59} -1.37092 q^{60} +6.27331 q^{61} -4.44317 q^{62} -1.00000 q^{63} +8.88043 q^{64} +12.4889 q^{65} +0.949311 q^{66} -7.09947 q^{67} +0.0570641 q^{68} -1.55225 q^{69} -3.41904 q^{70} +5.03630 q^{71} -3.06026 q^{72} +16.7401 q^{73} +5.36690 q^{74} +2.75360 q^{75} -1.64243 q^{76} -0.773136 q^{77} +5.50712 q^{78} -11.2996 q^{79} -7.72132 q^{80} +1.00000 q^{81} +12.0789 q^{82} +17.8695 q^{83} +0.492335 q^{84} -0.322741 q^{85} -7.01078 q^{86} +6.92156 q^{87} -2.36600 q^{88} +3.27246 q^{89} +3.41904 q^{90} -4.48510 q^{91} +0.764229 q^{92} -3.61860 q^{93} -7.86879 q^{94} +9.28918 q^{95} +2.71572 q^{96} +8.04130 q^{97} +1.22787 q^{98} +0.773136 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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