LMFDB - Embedded newform 4011.2.a.m.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.24191 q^{2} +1.00000 q^{3} +3.02615 q^{4} -1.20404 q^{5} -2.24191 q^{6} -1.00000 q^{7} -2.30052 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.24191 q^{2} +1.00000 q^{3} +3.02615 q^{4} -1.20404 q^{5} -2.24191 q^{6} -1.00000 q^{7} -2.30052 q^{8} +1.00000 q^{9} +2.69935 q^{10} +3.48348 q^{11} +3.02615 q^{12} +3.78465 q^{13} +2.24191 q^{14} -1.20404 q^{15} -0.894732 q^{16} +3.70393 q^{17} -2.24191 q^{18} +6.98234 q^{19} -3.64360 q^{20} -1.00000 q^{21} -7.80963 q^{22} +3.91380 q^{23} -2.30052 q^{24} -3.55029 q^{25} -8.48483 q^{26} +1.00000 q^{27} -3.02615 q^{28} +8.03776 q^{29} +2.69935 q^{30} +4.13048 q^{31} +6.60695 q^{32} +3.48348 q^{33} -8.30386 q^{34} +1.20404 q^{35} +3.02615 q^{36} -6.15109 q^{37} -15.6538 q^{38} +3.78465 q^{39} +2.76992 q^{40} +11.3772 q^{41} +2.24191 q^{42} -9.34313 q^{43} +10.5415 q^{44} -1.20404 q^{45} -8.77437 q^{46} -5.42356 q^{47} -0.894732 q^{48} +1.00000 q^{49} +7.95941 q^{50} +3.70393 q^{51} +11.4529 q^{52} +5.74006 q^{53} -2.24191 q^{54} -4.19425 q^{55} +2.30052 q^{56} +6.98234 q^{57} -18.0199 q^{58} +1.34548 q^{59} -3.64360 q^{60} +3.12982 q^{61} -9.26016 q^{62} -1.00000 q^{63} -13.0227 q^{64} -4.55687 q^{65} -7.80963 q^{66} -5.24309 q^{67} +11.2086 q^{68} +3.91380 q^{69} -2.69935 q^{70} -9.77372 q^{71} -2.30052 q^{72} +5.34108 q^{73} +13.7902 q^{74} -3.55029 q^{75} +21.1296 q^{76} -3.48348 q^{77} -8.48483 q^{78} -9.87463 q^{79} +1.07729 q^{80} +1.00000 q^{81} -25.5065 q^{82} -11.6734 q^{83} -3.02615 q^{84} -4.45968 q^{85} +20.9464 q^{86} +8.03776 q^{87} -8.01383 q^{88} +3.17892 q^{89} +2.69935 q^{90} -3.78465 q^{91} +11.8437 q^{92} +4.13048 q^{93} +12.1591 q^{94} -8.40701 q^{95} +6.60695 q^{96} -15.6599 q^{97} -2.24191 q^{98} +3.48348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.24191	−1.58527	−0.792634	−	0.609698i	$-0.791291\pi$
$2$	−2.24191	−1.58527	−0.792634	+	0.609698i	$0.791291\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.02615	1.51307
$5$	−1.20404	−0.538463	−0.269231	−	0.963075i	$-0.586770\pi$
$5$	−1.20404	−0.538463	−0.269231	+	0.963075i	$0.586770\pi$
$6$	−2.24191	−0.915255
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.30052	−0.813358
$9$	1.00000	0.333333
$10$	2.69935	0.853608
$11$	3.48348	1.05031	0.525154	−	0.851007i	$-0.324008\pi$
$11$	3.48348	1.05031	0.525154	+	0.851007i	$0.324008\pi$
$12$	3.02615	0.873573
$13$	3.78465	1.04967	0.524836	−	0.851203i	$-0.324127\pi$
$13$	3.78465	1.04967	0.524836	+	0.851203i	$0.324127\pi$
$14$	2.24191	0.599175
$15$	−1.20404	−0.310882
$16$	−0.894732	−0.223683
$17$	3.70393	0.898334	0.449167	−	0.893448i	$-0.351721\pi$
$17$	3.70393	0.898334	0.449167	+	0.893448i	$0.351721\pi$
$18$	−2.24191	−0.528422
$19$	6.98234	1.60186	0.800929	−	0.598759i	$-0.204339\pi$
$19$	6.98234	1.60186	0.800929	+	0.598759i	$0.204339\pi$
$20$	−3.64360	−0.814734
$21$	−1.00000	−0.218218
$22$	−7.80963	−1.66502
$23$	3.91380	0.816084	0.408042	−	0.912963i	$-0.366212\pi$
$23$	3.91380	0.816084	0.408042	+	0.912963i	$0.366212\pi$
$24$	−2.30052	−0.469592
$25$	−3.55029	−0.710058
$26$	−8.48483	−1.66401
$27$	1.00000	0.192450
$28$	−3.02615	−0.571888
$29$	8.03776	1.49258	0.746288	−	0.665624i	$-0.231834\pi$
$29$	8.03776	1.49258	0.746288	+	0.665624i	$0.231834\pi$
$30$	2.69935	0.492831
$31$	4.13048	0.741857	0.370928	−	0.928661i	$-0.379040\pi$
$31$	4.13048	0.741857	0.370928	+	0.928661i	$0.379040\pi$
$32$	6.60695	1.16796
$33$	3.48348	0.606396
$34$	−8.30386	−1.42410
$35$	1.20404	0.203520
$36$	3.02615	0.504358
$37$	−6.15109	−1.01123	−0.505616	−	0.862758i	$-0.668735\pi$
$37$	−6.15109	−1.01123	−0.505616	+	0.862758i	$0.668735\pi$
$38$	−15.6538	−2.53937
$39$	3.78465	0.606029
$40$	2.76992	0.437963
$41$	11.3772	1.77681	0.888407	−	0.459056i	$-0.151812\pi$
$41$	11.3772	1.77681	0.888407	+	0.459056i	$0.151812\pi$
$42$	2.24191	0.345934
$43$	−9.34313	−1.42481	−0.712407	−	0.701766i	$-0.752395\pi$
$43$	−9.34313	−1.42481	−0.712407	+	0.701766i	$0.752395\pi$
$44$	10.5415	1.58919
$45$	−1.20404	−0.179488
$46$	−8.77437	−1.29371
$47$	−5.42356	−0.791108	−0.395554	−	0.918443i	$-0.629447\pi$
$47$	−5.42356	−0.791108	−0.395554	+	0.918443i	$0.629447\pi$
$48$	−0.894732	−0.129143
$49$	1.00000	0.142857
$50$	7.95941	1.12563
$51$	3.70393	0.518653
$52$	11.4529	1.58823
$53$	5.74006	0.788458	0.394229	−	0.919012i	$-0.371012\pi$
$53$	5.74006	0.788458	0.394229	+	0.919012i	$0.371012\pi$
$54$	−2.24191	−0.305085
$55$	−4.19425	−0.565552
$56$	2.30052	0.307420
$57$	6.98234	0.924833
$58$	−18.0199	−2.36613
$59$	1.34548	0.175167	0.0875833	−	0.996157i	$-0.472086\pi$
$59$	1.34548	0.175167	0.0875833	+	0.996157i	$0.472086\pi$
$60$	−3.64360	−0.470387
$61$	3.12982	0.400732	0.200366	−	0.979721i	$-0.435787\pi$
$61$	3.12982	0.400732	0.200366	+	0.979721i	$0.435787\pi$
$62$	−9.26016	−1.17604
$63$	−1.00000	−0.125988
$64$	−13.0227	−1.62784
$65$	−4.55687	−0.565210
$66$	−7.80963	−0.961300
$67$	−5.24309	−0.640546	−0.320273	−	0.947325i	$-0.603775\pi$
$67$	−5.24309	−0.640546	−0.320273	+	0.947325i	$0.603775\pi$
$68$	11.2086	1.35925
$69$	3.91380	0.471166
$70$	−2.69935	−0.322633
$71$	−9.77372	−1.15993	−0.579964	−	0.814642i	$-0.696933\pi$
$71$	−9.77372	−1.15993	−0.579964	+	0.814642i	$0.696933\pi$
$72$	−2.30052	−0.271119
$73$	5.34108	0.625126	0.312563	−	0.949897i	$-0.398812\pi$
$73$	5.34108	0.625126	0.312563	+	0.949897i	$0.398812\pi$
$74$	13.7902	1.60307
$75$	−3.55029	−0.409952
$76$	21.1296	2.42373
$77$	−3.48348	−0.396979
$78$	−8.48483	−0.960718
$79$	−9.87463	−1.11098	−0.555491	−	0.831522i	$-0.687470\pi$
$79$	−9.87463	−1.11098	−0.555491	+	0.831522i	$0.687470\pi$
$80$	1.07729	0.120445
$81$	1.00000	0.111111
$82$	−25.5065	−2.81673
$83$	−11.6734	−1.28132	−0.640659	−	0.767825i	$-0.721339\pi$
$83$	−11.6734	−1.28132	−0.640659	+	0.767825i	$0.721339\pi$
$84$	−3.02615	−0.330180
$85$	−4.45968	−0.483720
$86$	20.9464	2.25871
$87$	8.03776	0.861739
$88$	−8.01383	−0.854277
$89$	3.17892	0.336965	0.168483	−	0.985705i	$-0.446113\pi$
$89$	3.17892	0.336965	0.168483	+	0.985705i	$0.446113\pi$
$90$	2.69935	0.284536
$91$	−3.78465	−0.396739
$92$	11.8437	1.23479
$93$	4.13048	0.428311
$94$	12.1591	1.25412
$95$	−8.40701	−0.862541
$96$	6.60695	0.674319
$97$	−15.6599	−1.59002	−0.795010	−	0.606597i	$-0.792534\pi$
$97$	−15.6599	−1.59002	−0.795010	+	0.606597i	$0.792534\pi$
$98$	−2.24191	−0.226467
$99$	3.48348	0.350103
$100$	−10.7437	−1.07437
$101$	−7.53953	−0.750211	−0.375106	−	0.926982i	$-0.622394\pi$
$101$	−7.53953	−0.750211	−0.375106	+	0.926982i	$0.622394\pi$
$102$	−8.30386	−0.822204
$103$	8.05022	0.793212	0.396606	−	0.917989i	$-0.370188\pi$
$103$	8.05022	0.793212	0.396606	+	0.917989i	$0.370188\pi$
$104$	−8.70667	−0.853760
$105$	1.20404	0.117502
$106$	−12.8687	−1.24992
$107$	19.3415	1.86981	0.934907	−	0.354893i	$-0.115483\pi$
$107$	19.3415	1.86981	0.934907	+	0.354893i	$0.115483\pi$
$108$	3.02615	0.291191
$109$	14.6812	1.40620	0.703102	−	0.711089i	$-0.251798\pi$
$109$	14.6812	1.40620	0.703102	+	0.711089i	$0.251798\pi$
$110$	9.40311	0.896551
$111$	−6.15109	−0.583836
$112$	0.894732	0.0845443
$113$	−19.0832	−1.79519	−0.897597	−	0.440817i	$-0.854689\pi$
$113$	−19.0832	−1.79519	−0.897597	+	0.440817i	$0.854689\pi$
$114$	−15.6538	−1.46611
$115$	−4.71237	−0.439431
$116$	24.3234	2.25838
$117$	3.78465	0.349891
$118$	−3.01644	−0.277686
$119$	−3.70393	−0.339538
$120$	2.76992	0.252858
$121$	1.13462	0.103148
$122$	−7.01675	−0.635267
$123$	11.3772	1.02584
$124$	12.4994	1.12248
$125$	10.2949	0.920803
$126$	2.24191	0.199725
$127$	3.15585	0.280036	0.140018	−	0.990149i	$-0.455284\pi$
$127$	3.15585	0.280036	0.140018	+	0.990149i	$0.455284\pi$
$128$	15.9818	1.41260
$129$	−9.34313	−0.822617
$130$	10.2161	0.896009
$131$	7.62953	0.666595	0.333298	−	0.942822i	$-0.391839\pi$
$131$	7.62953	0.666595	0.333298	+	0.942822i	$0.391839\pi$
$132$	10.5415	0.917521
$133$	−6.98234	−0.605446
$134$	11.7545	1.01544
$135$	−1.20404	−0.103627
$136$	−8.52097	−0.730667
$137$	8.15512	0.696739	0.348369	−	0.937357i	$-0.386735\pi$
$137$	8.15512	0.696739	0.348369	+	0.937357i	$0.386735\pi$
$138$	−8.77437	−0.746924
$139$	−1.42536	−0.120898	−0.0604488	−	0.998171i	$-0.519253\pi$
$139$	−1.42536	−0.120898	−0.0604488	+	0.998171i	$0.519253\pi$
$140$	3.64360	0.307940
$141$	−5.42356	−0.456746
$142$	21.9118	1.83880
$143$	13.1837	1.10248
$144$	−0.894732	−0.0745610
$145$	−9.67779	−0.803697
$146$	−11.9742	−0.990992
$147$	1.00000	0.0824786
$148$	−18.6141	−1.53007
$149$	−4.93512	−0.404301	−0.202150	−	0.979354i	$-0.564793\pi$
$149$	−4.93512	−0.404301	−0.202150	+	0.979354i	$0.564793\pi$
$150$	7.95941	0.649884
$151$	15.3850	1.25202	0.626008	−	0.779816i	$-0.284688\pi$
$151$	15.3850	1.25202	0.626008	+	0.779816i	$0.284688\pi$
$152$	−16.0630	−1.30288
$153$	3.70393	0.299445
$154$	7.80963	0.629318
$155$	−4.97327	−0.399462
$156$	11.4529	0.916966
$157$	11.4028	0.910044	0.455022	−	0.890480i	$-0.349631\pi$
$157$	11.4028	0.910044	0.455022	+	0.890480i	$0.349631\pi$
$158$	22.1380	1.76120
$159$	5.74006	0.455217
$160$	−7.95504	−0.628901
$161$	−3.91380	−0.308451
$162$	−2.24191	−0.176141
$163$	−16.5861	−1.29912	−0.649560	−	0.760310i	$-0.725047\pi$
$163$	−16.5861	−1.29912	−0.649560	+	0.760310i	$0.725047\pi$
$164$	34.4290	2.68845
$165$	−4.19425	−0.326522
$166$	26.1706	2.03123
$167$	14.6374	1.13268	0.566339	−	0.824173i	$-0.308359\pi$
$167$	14.6374	1.13268	0.566339	+	0.824173i	$0.308359\pi$
$168$	2.30052	0.177489
$169$	1.32357	0.101813
$170$	9.99818	0.766825
$171$	6.98234	0.533953
$172$	−28.2737	−2.15585
$173$	8.48872	0.645386	0.322693	−	0.946504i	$-0.395412\pi$
$173$	8.48872	0.645386	0.322693	+	0.946504i	$0.395412\pi$
$174$	−18.0199	−1.36609
$175$	3.55029	0.268377
$176$	−3.11678	−0.234936
$177$	1.34548	0.101132
$178$	−7.12685	−0.534180
$179$	−21.9329	−1.63934	−0.819672	−	0.572833i	$-0.805844\pi$
$179$	−21.9329	−1.63934	−0.819672	+	0.572833i	$0.805844\pi$
$180$	−3.64360	−0.271578
$181$	10.8383	0.805601	0.402800	−	0.915288i	$-0.368037\pi$
$181$	10.8383	0.805601	0.402800	+	0.915288i	$0.368037\pi$
$182$	8.48483	0.628937
$183$	3.12982	0.231363
$184$	−9.00379	−0.663768
$185$	7.40616	0.544511
$186$	−9.26016	−0.678988
$187$	12.9025	0.943528
$188$	−16.4125	−1.19700
$189$	−1.00000	−0.0727393
$190$	18.8477	1.36736
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−13.0227	−0.939833
$193$	−0.363700	−0.0261797	−0.0130898	−	0.999914i	$-0.504167\pi$
$193$	−0.363700	−0.0261797	−0.0130898	+	0.999914i	$0.504167\pi$
$194$	35.1080	2.52061
$195$	−4.55687	−0.326324
$196$	3.02615	0.216153
$197$	−19.9462	−1.42110	−0.710552	−	0.703644i	$-0.751555\pi$
$197$	−19.9462	−1.42110	−0.710552	+	0.703644i	$0.751555\pi$
$198$	−7.80963	−0.555007
$199$	11.1531	0.790625	0.395313	−	0.918547i	$-0.370636\pi$
$199$	11.1531	0.790625	0.395313	+	0.918547i	$0.370636\pi$
$200$	8.16752	0.577531
$201$	−5.24309	−0.369819
$202$	16.9029	1.18929
$203$	−8.03776	−0.564140
$204$	11.2086	0.784761
$205$	−13.6986	−0.956749
$206$	−18.0478	−1.25745
$207$	3.91380	0.272028
$208$	−3.38625	−0.234794
$209$	24.3228	1.68245
$210$	−2.69935	−0.186273
$211$	−4.33910	−0.298716	−0.149358	−	0.988783i	$-0.547721\pi$
$211$	−4.33910	−0.298716	−0.149358	+	0.988783i	$0.547721\pi$
$212$	17.3703	1.19299
$213$	−9.77372	−0.669684
$214$	−43.3618	−2.96415
$215$	11.2495	0.767210
$216$	−2.30052	−0.156531
$217$	−4.13048	−0.280395
$218$	−32.9139	−2.22921
$219$	5.34108	0.360917
$220$	−12.6924	−0.855722
$221$	14.0181	0.942957
$222$	13.7902	0.925536
$223$	−4.94454	−0.331111	−0.165556	−	0.986200i	$-0.552942\pi$
$223$	−4.94454	−0.331111	−0.165556	+	0.986200i	$0.552942\pi$
$224$	−6.60695	−0.441446
$225$	−3.55029	−0.236686
$226$	42.7827	2.84586
$227$	27.0946	1.79833	0.899165	−	0.437610i	$-0.144175\pi$
$227$	27.0946	1.79833	0.899165	+	0.437610i	$0.144175\pi$
$228$	21.1296	1.39934
$229$	−14.5531	−0.961695	−0.480848	−	0.876804i	$-0.659671\pi$
$229$	−14.5531	−0.961695	−0.480848	+	0.876804i	$0.659671\pi$
$230$	10.5647	0.696615
$231$	−3.48348	−0.229196
$232$	−18.4911	−1.21400
$233$	8.11619	0.531709	0.265855	−	0.964013i	$-0.414346\pi$
$233$	8.11619	0.531709	0.265855	+	0.964013i	$0.414346\pi$
$234$	−8.48483	−0.554671
$235$	6.53019	0.425982
$236$	4.07162	0.265040
$237$	−9.87463	−0.641426
$238$	8.30386	0.538259
$239$	−1.89186	−0.122374	−0.0611870	−	0.998126i	$-0.519489\pi$
$239$	−1.89186	−0.122374	−0.0611870	+	0.998126i	$0.519489\pi$
$240$	1.07729	0.0695390
$241$	−8.61286	−0.554803	−0.277402	−	0.960754i	$-0.589473\pi$
$241$	−8.61286	−0.554803	−0.277402	+	0.960754i	$0.589473\pi$
$242$	−2.54372	−0.163517
$243$	1.00000	0.0641500
$244$	9.47128	0.606336
$245$	−1.20404	−0.0769233
$246$	−25.5065	−1.62624
$247$	26.4257	1.68143
$248$	−9.50228	−0.603395
$249$	−11.6734	−0.739770
$250$	−23.0802	−1.45972
$251$	−15.7496	−0.994107	−0.497054	−	0.867720i	$-0.665585\pi$
$251$	−15.7496	−0.994107	−0.497054	+	0.867720i	$0.665585\pi$
$252$	−3.02615	−0.190629
$253$	13.6336	0.857139
$254$	−7.07512	−0.443932
$255$	−4.45968	−0.279276
$256$	−9.78427	−0.611517
$257$	24.8268	1.54865	0.774327	−	0.632786i	$-0.218089\pi$
$257$	24.8268	1.54865	0.774327	+	0.632786i	$0.218089\pi$
$258$	20.9464	1.30407
$259$	6.15109	0.382210
$260$	−13.7897	−0.855204
$261$	8.03776	0.497525
$262$	−17.1047	−1.05673
$263$	26.0980	1.60927	0.804637	−	0.593767i	$-0.202360\pi$
$263$	26.0980	1.60927	0.804637	+	0.593767i	$0.202360\pi$
$264$	−8.01383	−0.493217
$265$	−6.91126	−0.424556
$266$	15.6538	0.959793
$267$	3.17892	0.194547
$268$	−15.8664	−0.969193
$269$	−21.2558	−1.29599	−0.647995	−	0.761644i	$-0.724392\pi$
$269$	−21.2558	−1.29599	−0.647995	+	0.761644i	$0.724392\pi$
$270$	2.69935	0.164277
$271$	−14.8459	−0.901821	−0.450911	−	0.892569i	$-0.648901\pi$
$271$	−14.8459	−0.901821	−0.450911	+	0.892569i	$0.648901\pi$
$272$	−3.31402	−0.200942
$273$	−3.78465	−0.229057
$274$	−18.2830	−1.10452
$275$	−12.3674	−0.745779
$276$	11.8437	0.712909
$277$	−17.8482	−1.07240	−0.536198	−	0.844092i	$-0.680140\pi$
$277$	−17.8482	−1.07240	−0.536198	+	0.844092i	$0.680140\pi$
$278$	3.19553	0.191655
$279$	4.13048	0.247286
$280$	−2.76992	−0.165535
$281$	−2.89496	−0.172699	−0.0863494	−	0.996265i	$-0.527520\pi$
$281$	−2.89496	−0.172699	−0.0863494	+	0.996265i	$0.527520\pi$
$282$	12.1591	0.724065
$283$	−25.7601	−1.53128	−0.765640	−	0.643269i	$-0.777578\pi$
$283$	−25.7601	−1.53128	−0.765640	+	0.643269i	$0.777578\pi$
$284$	−29.5767	−1.75505
$285$	−8.40701	−0.497988
$286$	−29.5567	−1.74773
$287$	−11.3772	−0.671573
$288$	6.60695	0.389318
$289$	−3.28093	−0.192996
$290$	21.6967	1.27407
$291$	−15.6599	−0.917998
$292$	16.1629	0.945861
$293$	−26.5108	−1.54878	−0.774390	−	0.632709i	$-0.781943\pi$
$293$	−26.5108	−1.54878	−0.774390	+	0.632709i	$0.781943\pi$
$294$	−2.24191	−0.130751
$295$	−1.62001	−0.0943207
$296$	14.1507	0.822494
$297$	3.48348	0.202132
$298$	11.0641	0.640925
$299$	14.8124	0.856621
$300$	−10.7437	−0.620287
$301$	9.34313	0.538529
$302$	−34.4918	−1.98478
$303$	−7.53953	−0.433135
$304$	−6.24732	−0.358309
$305$	−3.76842	−0.215779
$306$	−8.30386	−0.474700
$307$	8.26367	0.471632	0.235816	−	0.971798i	$-0.424224\pi$
$307$	8.26367	0.471632	0.235816	+	0.971798i	$0.424224\pi$
$308$	−10.5415	−0.600659
$309$	8.05022	0.457961
$310$	11.1496	0.633255
$311$	0.313790	0.0177934	0.00889671	−	0.999960i	$-0.497168\pi$
$311$	0.313790	0.0177934	0.00889671	+	0.999960i	$0.497168\pi$
$312$	−8.70667	−0.492918
$313$	−30.6173	−1.73059	−0.865297	−	0.501259i	$-0.832870\pi$
$313$	−30.6173	−1.73059	−0.865297	+	0.501259i	$0.832870\pi$
$314$	−25.5640	−1.44266
$315$	1.20404	0.0678400
$316$	−29.8821	−1.68100
$317$	19.4228	1.09089	0.545447	−	0.838145i	$-0.316360\pi$
$317$	19.4228	1.09089	0.545447	+	0.838145i	$0.316360\pi$
$318$	−12.8687	−0.721640
$319$	27.9994	1.56766
$320$	15.6799	0.876531
$321$	19.3415	1.07954
$322$	8.77437	0.488977
$323$	25.8621	1.43900
$324$	3.02615	0.168119
$325$	−13.4366	−0.745328
$326$	37.1844	2.05945
$327$	14.6812	0.811872
$328$	−26.1734	−1.44519
$329$	5.42356	0.299011
$330$	9.40311	0.517624
$331$	−7.14609	−0.392785	−0.196392	−	0.980525i	$-0.562923\pi$
$331$	−7.14609	−0.392785	−0.196392	+	0.980525i	$0.562923\pi$
$332$	−35.3253	−1.93873
$333$	−6.15109	−0.337078
$334$	−32.8157	−1.79560
$335$	6.31289	0.344910
$336$	0.894732	0.0488117
$337$	−9.81641	−0.534734	−0.267367	−	0.963595i	$-0.586154\pi$
$337$	−9.81641	−0.534734	−0.267367	+	0.963595i	$0.586154\pi$
$338$	−2.96732	−0.161401
$339$	−19.0832	−1.03646
$340$	−13.4956	−0.731903
$341$	14.3885	0.779178
$342$	−15.6538	−0.846458
$343$	−1.00000	−0.0539949
$344$	21.4941	1.15888
$345$	−4.71237	−0.253706
$346$	−19.0309	−1.02311
$347$	22.4398	1.20463	0.602317	−	0.798257i	$-0.294244\pi$
$347$	22.4398	1.20463	0.602317	+	0.798257i	$0.294244\pi$
$348$	24.3234	1.30387
$349$	18.1408	0.971052	0.485526	−	0.874222i	$-0.338628\pi$
$349$	18.1408	0.971052	0.485526	+	0.874222i	$0.338628\pi$
$350$	−7.95941	−0.425449
$351$	3.78465	0.202010
$352$	23.0152	1.22671
$353$	−8.72050	−0.464145	−0.232073	−	0.972698i	$-0.574551\pi$
$353$	−8.72050	−0.464145	−0.232073	+	0.972698i	$0.574551\pi$
$354$	−3.01644	−0.160322
$355$	11.7680	0.624578
$356$	9.61989	0.509853
$357$	−3.70393	−0.196033
$358$	49.1716	2.59880
$359$	33.8229	1.78510	0.892552	−	0.450944i	$-0.148913\pi$
$359$	33.8229	1.78510	0.892552	+	0.450944i	$0.148913\pi$
$360$	2.76992	0.145988
$361$	29.7530	1.56595
$362$	−24.2984	−1.27709
$363$	1.13462	0.0595523
$364$	−11.4529	−0.600295
$365$	−6.43087	−0.336607
$366$	−7.01675	−0.366772
$367$	2.21897	0.115829	0.0579145	−	0.998322i	$-0.481555\pi$
$367$	2.21897	0.115829	0.0579145	+	0.998322i	$0.481555\pi$
$368$	−3.50180	−0.182544
$369$	11.3772	0.592272
$370$	−16.6039	−0.863196
$371$	−5.74006	−0.298009
$372$	12.4994	0.648066
$373$	14.9552	0.774353	0.387176	−	0.922006i	$-0.373450\pi$
$373$	14.9552	0.774353	0.387176	+	0.922006i	$0.373450\pi$
$374$	−28.9263	−1.49574
$375$	10.2949	0.531626
$376$	12.4770	0.643454
$377$	30.4201	1.56672
$378$	2.24191	0.115311
$379$	−17.2744	−0.887326	−0.443663	−	0.896194i	$-0.646321\pi$
$379$	−17.2744	−0.887326	−0.443663	+	0.896194i	$0.646321\pi$
$380$	−25.4408	−1.30509
$381$	3.15585	0.161679
$382$	2.24191	0.114706
$383$	−16.5466	−0.845491	−0.422746	−	0.906248i	$-0.638934\pi$
$383$	−16.5466	−0.845491	−0.422746	+	0.906248i	$0.638934\pi$
$384$	15.9818	0.815568
$385$	4.19425	0.213759
$386$	0.815381	0.0415018
$387$	−9.34313	−0.474938
$388$	−47.3891	−2.40582
$389$	27.7619	1.40758	0.703792	−	0.710406i	$-0.251489\pi$
$389$	27.7619	1.40758	0.703792	+	0.710406i	$0.251489\pi$
$390$	10.2161	0.517311
$391$	14.4964	0.733116
$392$	−2.30052	−0.116194
$393$	7.62953	0.384859
$394$	44.7174	2.25283
$395$	11.8894	0.598223
$396$	10.5415	0.529731
$397$	9.44996	0.474280	0.237140	−	0.971476i	$-0.423790\pi$
$397$	9.44996	0.474280	0.237140	+	0.971476i	$0.423790\pi$
$398$	−25.0043	−1.25335
$399$	−6.98234	−0.349554
$400$	3.17656	0.158828
$401$	−9.59080	−0.478942	−0.239471	−	0.970904i	$-0.576974\pi$
$401$	−9.59080	−0.478942	−0.239471	+	0.970904i	$0.576974\pi$
$402$	11.7545	0.586263
$403$	15.6324	0.778707
$404$	−22.8157	−1.13512
$405$	−1.20404	−0.0598292
$406$	18.0199	0.894313
$407$	−21.4272	−1.06211
$408$	−8.52097	−0.421851
$409$	−6.71584	−0.332077	−0.166038	−	0.986119i	$-0.553098\pi$
$409$	−6.71584	−0.332077	−0.166038	+	0.986119i	$0.553098\pi$
$410$	30.7109	1.51670
$411$	8.15512	0.402262
$412$	24.3612	1.20019
$413$	−1.34548	−0.0662067
$414$	−8.77437	−0.431237
$415$	14.0552	0.689943
$416$	25.0050	1.22597
$417$	−1.42536	−0.0698002
$418$	−54.5295	−2.66713
$419$	27.7068	1.35357	0.676783	−	0.736183i	$-0.263374\pi$
$419$	27.7068	1.35357	0.676783	+	0.736183i	$0.263374\pi$
$420$	3.64360	0.177789
$421$	25.0634	1.22152	0.610758	−	0.791817i	$-0.290865\pi$
$421$	25.0634	1.22152	0.610758	+	0.791817i	$0.290865\pi$
$422$	9.72785	0.473544
$423$	−5.42356	−0.263703
$424$	−13.2051	−0.641299
$425$	−13.1500	−0.637869
$426$	21.9118	1.06163
$427$	−3.12982	−0.151462
$428$	58.5302	2.82916
$429$	13.1837	0.636517
$430$	−25.2203	−1.21623
$431$	−5.64021	−0.271679	−0.135840	−	0.990731i	$-0.543373\pi$
$431$	−5.64021	−0.271679	−0.135840	+	0.990731i	$0.543373\pi$
$432$	−0.894732	−0.0430478
$433$	29.4570	1.41561	0.707807	−	0.706406i	$-0.249685\pi$
$433$	29.4570	1.41561	0.707807	+	0.706406i	$0.249685\pi$
$434$	9.26016	0.444502
$435$	−9.67779	−0.464014
$436$	44.4275	2.12769
$437$	27.3275	1.30725
$438$	−11.9742	−0.572149
$439$	24.3111	1.16030	0.580152	−	0.814508i	$-0.302993\pi$
$439$	24.3111	1.16030	0.580152	+	0.814508i	$0.302993\pi$
$440$	9.64897	0.459996
$441$	1.00000	0.0476190
$442$	−31.4272	−1.49484
$443$	15.0832	0.716624	0.358312	−	0.933602i	$-0.383352\pi$
$443$	15.0832	0.716624	0.358312	+	0.933602i	$0.383352\pi$
$444$	−18.6141	−0.883386
$445$	−3.82755	−0.181443
$446$	11.0852	0.524900
$447$	−4.93512	−0.233423
$448$	13.0227	0.615265
$449$	32.6603	1.54133	0.770667	−	0.637239i	$-0.219923\pi$
$449$	32.6603	1.54133	0.770667	+	0.637239i	$0.219923\pi$
$450$	7.95941	0.375210
$451$	39.6321	1.86620
$452$	−57.7485	−2.71626
$453$	15.3850	0.722852
$454$	−60.7435	−2.85083
$455$	4.55687	0.213629
$456$	−16.0630	−0.752221
$457$	6.68108	0.312528	0.156264	−	0.987715i	$-0.450055\pi$
$457$	6.68108	0.312528	0.156264	+	0.987715i	$0.450055\pi$
$458$	32.6267	1.52454
$459$	3.70393	0.172884
$460$	−14.2603	−0.664891
$461$	37.4914	1.74615	0.873073	−	0.487589i	$-0.162123\pi$
$461$	37.4914	1.74615	0.873073	+	0.487589i	$0.162123\pi$
$462$	7.80963	0.363337
$463$	−31.2404	−1.45186	−0.725931	−	0.687767i	$-0.758591\pi$
$463$	−31.2404	−1.45186	−0.725931	+	0.687767i	$0.758591\pi$
$464$	−7.19165	−0.333864
$465$	−4.97327	−0.230630
$466$	−18.1957	−0.842902
$467$	−23.2059	−1.07384	−0.536922	−	0.843632i	$-0.680413\pi$
$467$	−23.2059	−1.07384	−0.536922	+	0.843632i	$0.680413\pi$
$468$	11.4529	0.529411
$469$	5.24309	0.242104
$470$	−14.6401	−0.675296
$471$	11.4028	0.525414
$472$	−3.09531	−0.142473
$473$	−32.5466	−1.49649
$474$	22.1380	1.01683
$475$	−24.7893	−1.13741
$476$	−11.2086	−0.513746
$477$	5.74006	0.262819
$478$	4.24136	0.193995
$479$	−11.7326	−0.536074	−0.268037	−	0.963409i	$-0.586375\pi$
$479$	−11.7326	−0.536074	−0.268037	+	0.963409i	$0.586375\pi$
$480$	−7.95504	−0.363096
$481$	−23.2797	−1.06146
$482$	19.3092	0.879511
$483$	−3.91380	−0.178084
$484$	3.43354	0.156070
$485$	18.8551	0.856167
$486$	−2.24191	−0.101695
$487$	40.5988	1.83971	0.919854	−	0.392262i	$-0.128307\pi$
$487$	40.5988	1.83971	0.919854	+	0.392262i	$0.128307\pi$
$488$	−7.20021	−0.325938
$489$	−16.5861	−0.750047
$490$	2.69935	0.121944
$491$	−39.8124	−1.79671	−0.898355	−	0.439270i	$-0.855237\pi$
$491$	−39.8124	−1.79671	−0.898355	+	0.439270i	$0.855237\pi$
$492$	34.4290	1.55218
$493$	29.7713	1.34083
$494$	−59.2440	−2.66551
$495$	−4.19425	−0.188517
$496$	−3.69568	−0.165941
$497$	9.77372	0.438411
$498$	26.1706	1.17273
$499$	8.09389	0.362332	0.181166	−	0.983453i	$-0.442013\pi$
$499$	8.09389	0.362332	0.181166	+	0.983453i	$0.442013\pi$
$500$	31.1538	1.39324
$501$	14.6374	0.653952
$502$	35.3092	1.57593
$503$	−35.6865	−1.59118	−0.795591	−	0.605835i	$-0.792839\pi$
$503$	−35.6865	−1.59118	−0.795591	+	0.605835i	$0.792839\pi$
$504$	2.30052	0.102473
$505$	9.07790	0.403961
$506$	−30.5653	−1.35880
$507$	1.32357	0.0587817
$508$	9.55006	0.423715
$509$	0.0532497	0.00236025	0.00118012	−	0.999999i	$-0.499624\pi$
$509$	0.0532497	0.00236025	0.00118012	+	0.999999i	$0.499624\pi$
$510$	9.99818	0.442727
$511$	−5.34108	−0.236275
$512$	−10.0282	−0.443186
$513$	6.98234	0.308278
$514$	−55.6594	−2.45503
$515$	−9.69279	−0.427115
$516$	−28.2737	−1.24468
$517$	−18.8929	−0.830907
$518$	−13.7902	−0.605905
$519$	8.48872	0.372614
$520$	10.4832	0.459718
$521$	−15.9384	−0.698275	−0.349138	−	0.937071i	$-0.613525\pi$
$521$	−15.9384	−0.698275	−0.349138	+	0.937071i	$0.613525\pi$
$522$	−18.0199	−0.788710
$523$	0.822676	0.0359731	0.0179866	−	0.999838i	$-0.494274\pi$
$523$	0.822676	0.0359731	0.0179866	+	0.999838i	$0.494274\pi$
$524$	23.0881	1.00861
$525$	3.55029	0.154947
$526$	−58.5094	−2.55113
$527$	15.2990	0.666435
$528$	−3.11678	−0.135640
$529$	−7.68217	−0.334008
$530$	15.4944	0.673034
$531$	1.34548	0.0583888
$532$	−21.1296	−0.916083
$533$	43.0586	1.86507
$534$	−7.12685	−0.308409
$535$	−23.2879	−1.00683
$536$	12.0619	0.520993
$537$	−21.9329	−0.946476
$538$	47.6536	2.05449
$539$	3.48348	0.150044
$540$	−3.64360	−0.156796
$541$	32.9885	1.41829	0.709144	−	0.705064i	$-0.249082\pi$
$541$	32.9885	1.41829	0.709144	+	0.705064i	$0.249082\pi$
$542$	33.2830	1.42963
$543$	10.8383	0.465114
$544$	24.4717	1.04921
$545$	−17.6767	−0.757189
$546$	8.48483	0.363117
$547$	−23.9188	−1.02269	−0.511347	−	0.859374i	$-0.670853\pi$
$547$	−23.9188	−1.02269	−0.511347	+	0.859374i	$0.670853\pi$
$548$	24.6786	1.05422
$549$	3.12982	0.133577
$550$	27.7265	1.18226
$551$	56.1224	2.39089
$552$	−9.00379	−0.383227
$553$	9.87463	0.419912
$554$	40.0141	1.70003
$555$	7.40616	0.314374
$556$	−4.31335	−0.182927
$557$	15.3900	0.652096	0.326048	−	0.945353i	$-0.394283\pi$
$557$	15.3900	0.652096	0.326048	+	0.945353i	$0.394283\pi$
$558$	−9.26016	−0.392014
$559$	−35.3605	−1.49559
$560$	−1.07729	−0.0455240
$561$	12.9025	0.544746
$562$	6.49023	0.273774
$563$	−1.58400	−0.0667576	−0.0333788	−	0.999443i	$-0.510627\pi$
$563$	−1.58400	−0.0667576	−0.0333788	+	0.999443i	$0.510627\pi$
$564$	−16.4125	−0.691091
$565$	22.9769	0.966645
$566$	57.7518	2.42749
$567$	−1.00000	−0.0419961
$568$	22.4847	0.943436
$569$	−7.73642	−0.324328	−0.162164	−	0.986764i	$-0.551847\pi$
$569$	−7.73642	−0.324328	−0.162164	+	0.986764i	$0.551847\pi$
$570$	18.8477	0.789445
$571$	15.8675	0.664032	0.332016	−	0.943274i	$-0.392271\pi$
$571$	15.8675	0.664032	0.332016	+	0.943274i	$0.392271\pi$
$572$	39.8959	1.66813
$573$	−1.00000	−0.0417756
$574$	25.5065	1.06462
$575$	−13.8951	−0.579466
$576$	−13.0227	−0.542613
$577$	−5.37823	−0.223899	−0.111949	−	0.993714i	$-0.535709\pi$
$577$	−5.37823	−0.223899	−0.111949	+	0.993714i	$0.535709\pi$
$578$	7.35553	0.305950
$579$	−0.363700	−0.0151148
$580$	−29.2864	−1.21605
$581$	11.6734	0.484293
$582$	35.1080	1.45527
$583$	19.9954	0.828124
$584$	−12.2873	−0.508451
$585$	−4.55687	−0.188403
$586$	59.4348	2.45523
$587$	−41.5419	−1.71462	−0.857308	−	0.514804i	$-0.827865\pi$
$587$	−41.5419	−1.71462	−0.857308	+	0.514804i	$0.827865\pi$
$588$	3.02615	0.124796
$589$	28.8404	1.18835
$590$	3.63191	0.149524
$591$	−19.9462	−0.820475
$592$	5.50358	0.226196
$593$	−28.9965	−1.19074	−0.595372	−	0.803450i	$-0.702995\pi$
$593$	−28.9965	−1.19074	−0.595372	+	0.803450i	$0.702995\pi$
$594$	−7.80963	−0.320433
$595$	4.45968	0.182829
$596$	−14.9344	−0.611737
$597$	11.1531	0.456468
$598$	−33.2079	−1.35797
$599$	16.2897	0.665581	0.332790	−	0.943001i	$-0.392010\pi$
$599$	16.2897	0.665581	0.332790	+	0.943001i	$0.392010\pi$
$600$	8.16752	0.333438
$601$	−0.713070	−0.0290867	−0.0145434	−	0.999894i	$-0.504629\pi$
$601$	−0.713070	−0.0290867	−0.0145434	+	0.999894i	$0.504629\pi$
$602$	−20.9464	−0.853713
$603$	−5.24309	−0.213515
$604$	46.5574	1.89439
$605$	−1.36613	−0.0555412
$606$	16.9029	0.686634
$607$	28.0452	1.13832	0.569160	−	0.822227i	$-0.307269\pi$
$607$	28.0452	1.13832	0.569160	+	0.822227i	$0.307269\pi$
$608$	46.1320	1.87090
$609$	−8.03776	−0.325707
$610$	8.44845	0.342068
$611$	−20.5263	−0.830405
$612$	11.2086	0.453082
$613$	−10.4533	−0.422204	−0.211102	−	0.977464i	$-0.567705\pi$
$613$	−10.4533	−0.422204	−0.211102	+	0.977464i	$0.567705\pi$
$614$	−18.5264	−0.747663
$615$	−13.6986	−0.552379
$616$	8.01383	0.322886
$617$	−12.9503	−0.521360	−0.260680	−	0.965425i	$-0.583947\pi$
$617$	−12.9503	−0.521360	−0.260680	+	0.965425i	$0.583947\pi$
$618$	−18.0478	−0.725991
$619$	10.0372	0.403428	0.201714	−	0.979444i	$-0.435349\pi$
$619$	10.0372	0.403428	0.201714	+	0.979444i	$0.435349\pi$
$620$	−15.0498	−0.604416
$621$	3.91380	0.157055
$622$	−0.703489	−0.0282073
$623$	−3.17892	−0.127361
$624$	−3.38625	−0.135558
$625$	5.35599	0.214239
$626$	68.6412	2.74346
$627$	24.3228	0.971360
$628$	34.5066	1.37696
$629$	−22.7832	−0.908425
$630$	−2.69935	−0.107544
$631$	31.1599	1.24045	0.620227	−	0.784422i	$-0.287040\pi$
$631$	31.1599	1.24045	0.620227	+	0.784422i	$0.287040\pi$
$632$	22.7168	0.903626
$633$	−4.33910	−0.172464
$634$	−43.5442	−1.72936
$635$	−3.79977	−0.150789
$636$	17.3703	0.688776
$637$	3.78465	0.149953
$638$	−62.7720	−2.48517
$639$	−9.77372	−0.386642
$640$	−19.2427	−0.760635
$641$	28.9842	1.14481	0.572403	−	0.819973i	$-0.306011\pi$
$641$	28.9842	1.14481	0.572403	+	0.819973i	$0.306011\pi$
$642$	−43.3618	−1.71136
$643$	5.24635	0.206896	0.103448	−	0.994635i	$-0.467012\pi$
$643$	5.24635	0.206896	0.103448	+	0.994635i	$0.467012\pi$
$644$	−11.8437	−0.466708
$645$	11.2495	0.442949
$646$	−57.9803	−2.28121
$647$	−38.5783	−1.51667	−0.758334	−	0.651866i	$-0.773986\pi$
$647$	−38.5783	−1.51667	−0.758334	+	0.651866i	$0.773986\pi$
$648$	−2.30052	−0.0903731
$649$	4.68695	0.183979
$650$	30.1236	1.18154
$651$	−4.13048	−0.161886
$652$	−50.1918	−1.96566
$653$	−14.1153	−0.552376	−0.276188	−	0.961104i	$-0.589071\pi$
$653$	−14.1153	−0.552376	−0.276188	+	0.961104i	$0.589071\pi$
$654$	−32.9139	−1.28703
$655$	−9.18626	−0.358937
$656$	−10.1795	−0.397443
$657$	5.34108	0.208375
$658$	−12.1591	−0.474012
$659$	−1.61937	−0.0630817	−0.0315409	−	0.999502i	$-0.510041\pi$
$659$	−1.61937	−0.0630817	−0.0315409	+	0.999502i	$0.510041\pi$
$660$	−12.6924	−0.494051
$661$	18.0663	0.702699	0.351350	−	0.936244i	$-0.385723\pi$
$661$	18.0663	0.702699	0.351350	+	0.936244i	$0.385723\pi$
$662$	16.0209	0.622669
$663$	14.0181	0.544416
$664$	26.8549	1.04217
$665$	8.40701	0.326010
$666$	13.7902	0.534358
$667$	31.4582	1.21807
$668$	44.2950	1.71382
$669$	−4.94454	−0.191167
$670$	−14.1529	−0.546775
$671$	10.9026	0.420892
$672$	−6.60695	−0.254869
$673$	27.9142	1.07601	0.538007	−	0.842941i	$-0.319177\pi$
$673$	27.9142	1.07601	0.538007	+	0.842941i	$0.319177\pi$
$674$	22.0075	0.847696
$675$	−3.55029	−0.136651
$676$	4.00531	0.154050
$677$	−25.2401	−0.970055	−0.485028	−	0.874499i	$-0.661190\pi$
$677$	−25.2401	−0.970055	−0.485028	+	0.874499i	$0.661190\pi$
$678$	42.7827	1.64306
$679$	15.6599	0.600971
$680$	10.2596	0.393437
$681$	27.0946	1.03827
$682$	−32.2576	−1.23521
$683$	18.4650	0.706545	0.353272	−	0.935521i	$-0.385069\pi$
$683$	18.4650	0.706545	0.353272	+	0.935521i	$0.385069\pi$
$684$	21.1296	0.807909
$685$	−9.81909	−0.375168
$686$	2.24191	0.0855964
$687$	−14.5531	−0.555235
$688$	8.35960	0.318707
$689$	21.7241	0.827623
$690$	10.5647	0.402191
$691$	6.65792	0.253279	0.126640	−	0.991949i	$-0.459581\pi$
$691$	6.65792	0.253279	0.126640	+	0.991949i	$0.459581\pi$
$692$	25.6881	0.976516
$693$	−3.48348	−0.132326
$694$	−50.3080	−1.90967
$695$	1.71619	0.0650989
$696$	−18.4911	−0.700902
$697$	42.1402	1.59617
$698$	−40.6699	−1.53938
$699$	8.11619	0.306983
$700$	10.7437	0.406073
$701$	−39.3784	−1.48730	−0.743650	−	0.668569i	$-0.766907\pi$
$701$	−39.3784	−1.48730	−0.743650	+	0.668569i	$0.766907\pi$
$702$	−8.48483	−0.320239
$703$	−42.9490	−1.61985
$704$	−45.3643	−1.70973
$705$	6.53019	0.245941
$706$	19.5506	0.735795
$707$	7.53953	0.283553
$708$	4.07162	0.153021
$709$	14.2938	0.536813	0.268407	−	0.963306i	$-0.413503\pi$
$709$	14.2938	0.536813	0.268407	+	0.963306i	$0.413503\pi$
$710$	−26.3826	−0.990123
$711$	−9.87463	−0.370327
$712$	−7.31319	−0.274073
$713$	16.1659	0.605417
$714$	8.30386	0.310764
$715$	−15.8738	−0.593645
$716$	−66.3723	−2.48045
$717$	−1.89186	−0.0706526
$718$	−75.8278	−2.82987
$719$	13.8039	0.514797	0.257398	−	0.966305i	$-0.417135\pi$
$719$	13.8039	0.514797	0.257398	+	0.966305i	$0.417135\pi$
$720$	1.07729	0.0401484
$721$	−8.05022	−0.299806
$722$	−66.7036	−2.48245
$723$	−8.61286	−0.320316
$724$	32.7981	1.21893
$725$	−28.5364	−1.05981
$726$	−2.54372	−0.0944064
$727$	−13.3120	−0.493715	−0.246858	−	0.969052i	$-0.579398\pi$
$727$	−13.3120	−0.493715	−0.246858	+	0.969052i	$0.579398\pi$
$728$	8.70667	0.322691
$729$	1.00000	0.0370370
$730$	14.4174	0.533612
$731$	−34.6063	−1.27996
$732$	9.47128	0.350068
$733$	−4.48646	−0.165711	−0.0828556	−	0.996562i	$-0.526404\pi$
$733$	−4.48646	−0.165711	−0.0828556	+	0.996562i	$0.526404\pi$
$734$	−4.97472	−0.183620
$735$	−1.20404	−0.0444117
$736$	25.8583	0.953149
$737$	−18.2642	−0.672771
$738$	−25.5065	−0.938909
$739$	0.966570	0.0355559	0.0177779	−	0.999842i	$-0.494341\pi$
$739$	0.966570	0.0355559	0.0177779	+	0.999842i	$0.494341\pi$
$740$	22.4121	0.823886
$741$	26.4257	0.970772
$742$	12.8687	0.472424
$743$	4.92768	0.180779	0.0903895	−	0.995906i	$-0.471189\pi$
$743$	4.92768	0.180779	0.0903895	+	0.995906i	$0.471189\pi$
$744$	−9.50228	−0.348370
$745$	5.94208	0.217701
$746$	−33.5282	−1.22756
$747$	−11.6734	−0.427106
$748$	39.0450	1.42763
$749$	−19.3415	−0.706723
$750$	−23.0802	−0.842769
$751$	−28.5188	−1.04067	−0.520333	−	0.853963i	$-0.674192\pi$
$751$	−28.5188	−1.04067	−0.520333	+	0.853963i	$0.674192\pi$
$752$	4.85264	0.176957
$753$	−15.7496	−0.573948
$754$	−68.1991	−2.48366
$755$	−18.5242	−0.674165
$756$	−3.02615	−0.110060
$757$	−24.1755	−0.878672	−0.439336	−	0.898323i	$-0.644786\pi$
$757$	−24.1755	−0.878672	−0.439336	+	0.898323i	$0.644786\pi$
$758$	38.7276	1.40665
$759$	13.6336	0.494870
$760$	19.3405	0.701555
$761$	16.0558	0.582023	0.291011	−	0.956720i	$-0.406008\pi$
$761$	16.0558	0.582023	0.291011	+	0.956720i	$0.406008\pi$
$762$	−7.07512	−0.256305
$763$	−14.6812	−0.531495
$764$	−3.02615	−0.109482
$765$	−4.45968	−0.161240
$766$	37.0959	1.34033
$767$	5.09217	0.183868
$768$	−9.78427	−0.353060
$769$	48.8293	1.76083	0.880414	−	0.474205i	$-0.157265\pi$
$769$	48.8293	1.76083	0.880414	+	0.474205i	$0.157265\pi$
$770$	−9.40311	−0.338865
$771$	24.8268	0.894116
$772$	−1.10061	−0.0396118
$773$	−17.3983	−0.625773	−0.312887	−	0.949790i	$-0.601296\pi$
$773$	−17.3983	−0.625773	−0.312887	+	0.949790i	$0.601296\pi$
$774$	20.9464	0.752904
$775$	−14.6644	−0.526761
$776$	36.0259	1.29325
$777$	6.15109	0.220669
$778$	−62.2396	−2.23140
$779$	79.4392	2.84621
$780$	−13.7897	−0.493752
$781$	−34.0466	−1.21828
$782$	−32.4996	−1.16218
$783$	8.03776	0.287246
$784$	−0.894732	−0.0319547
$785$	−13.7294	−0.490025
$786$	−17.1047	−0.610104
$787$	18.7514	0.668417	0.334208	−	0.942499i	$-0.391531\pi$
$787$	18.7514	0.668417	0.334208	+	0.942499i	$0.391531\pi$
$788$	−60.3600	−2.15024
$789$	26.0980	0.929115
$790$	−26.6550	−0.948343
$791$	19.0832	0.678520
$792$	−8.01383	−0.284759
$793$	11.8453	0.420637
$794$	−21.1859	−0.751860
$795$	−6.91126	−0.245117
$796$	33.7510	1.19627
$797$	5.39559	0.191122	0.0955608	−	0.995424i	$-0.469536\pi$
$797$	5.39559	0.191122	0.0955608	+	0.995424i	$0.469536\pi$
$798$	15.6538	0.554137
$799$	−20.0885	−0.710679
$800$	−23.4566	−0.829316
$801$	3.17892	0.112322
$802$	21.5017	0.759250
$803$	18.6055	0.656575
$804$	−15.8664	−0.559564
$805$	4.71237	0.166089
$806$	−35.0465	−1.23446
$807$	−21.2558	−0.748241
$808$	17.3449	0.610190
$809$	−14.3162	−0.503330	−0.251665	−	0.967814i	$-0.580978\pi$
$809$	−14.3162	−0.503330	−0.251665	+	0.967814i	$0.580978\pi$
$810$	2.69935	0.0948453
$811$	50.0702	1.75820	0.879102	−	0.476634i	$-0.158143\pi$
$811$	50.0702	1.75820	0.879102	+	0.476634i	$0.158143\pi$
$812$	−24.3234	−0.853586
$813$	−14.8459	−0.520667
$814$	48.0378	1.68372
$815$	19.9703	0.699528
$816$	−3.31402	−0.116014
$817$	−65.2369	−2.28235
$818$	15.0563	0.526431
$819$	−3.78465	−0.132246
$820$	−41.4538	−1.44763
$821$	−14.5302	−0.507109	−0.253554	−	0.967321i	$-0.581600\pi$
$821$	−14.5302	−0.507109	−0.253554	+	0.967321i	$0.581600\pi$
$822$	−18.2830	−0.637694
$823$	−10.3577	−0.361047	−0.180524	−	0.983571i	$-0.557779\pi$
$823$	−10.3577	−0.361047	−0.180524	+	0.983571i	$0.557779\pi$
$824$	−18.5197	−0.645165
$825$	−12.3674	−0.430576
$826$	3.01644	0.104955
$827$	6.80040	0.236473	0.118237	−	0.992985i	$-0.462276\pi$
$827$	6.80040	0.236473	0.118237	+	0.992985i	$0.462276\pi$
$828$	11.8437	0.411598
$829$	−17.0895	−0.593544	−0.296772	−	0.954948i	$-0.595910\pi$
$829$	−17.0895	−0.593544	−0.296772	+	0.954948i	$0.595910\pi$
$830$	−31.5104	−1.09374
$831$	−17.8482	−0.619148
$832$	−49.2864	−1.70870
$833$	3.70393	0.128333
$834$	3.19553	0.110652
$835$	−17.6240	−0.609905
$836$	73.6044	2.54566
$837$	4.13048	0.142770
$838$	−62.1161	−2.14576
$839$	43.6093	1.50556	0.752780	−	0.658272i	$-0.228712\pi$
$839$	43.6093	1.50556	0.752780	+	0.658272i	$0.228712\pi$
$840$	−2.76992	−0.0955714
$841$	35.6056	1.22778
$842$	−56.1899	−1.93643
$843$	−2.89496	−0.0997077
$844$	−13.1307	−0.451979
$845$	−1.59363	−0.0548225
$846$	12.1591	0.418039
$847$	−1.13462	−0.0389862
$848$	−5.13582	−0.176365
$849$	−25.7601	−0.884085
$850$	29.4811	1.01119
$851$	−24.0741	−0.825251
$852$	−29.5767	−1.01328
$853$	−38.9952	−1.33517	−0.667585	−	0.744534i	$-0.732672\pi$
$853$	−38.9952	−1.33517	−0.667585	+	0.744534i	$0.732672\pi$
$854$	7.01675	0.240108
$855$	−8.40701	−0.287514
$856$	−44.4956	−1.52083
$857$	−26.1287	−0.892540	−0.446270	−	0.894898i	$-0.647248\pi$
$857$	−26.1287	−0.892540	−0.446270	+	0.894898i	$0.647248\pi$
$858$	−29.5567	−1.00905
$859$	−53.4346	−1.82316	−0.911582	−	0.411118i	$-0.865138\pi$
$859$	−53.4346	−1.82316	−0.911582	+	0.411118i	$0.865138\pi$
$860$	34.0426	1.16084
$861$	−11.3772	−0.387733
$862$	12.6448	0.430684
$863$	17.4117	0.592702	0.296351	−	0.955079i	$-0.404230\pi$
$863$	17.4117	0.592702	0.296351	+	0.955079i	$0.404230\pi$
$864$	6.60695	0.224773
$865$	−10.2208	−0.347516
$866$	−66.0399	−2.24413
$867$	−3.28093	−0.111426
$868$	−12.4994	−0.424259
$869$	−34.3981	−1.16687
$870$	21.6967	0.735587
$871$	−19.8433	−0.672364
$872$	−33.7744	−1.14375
$873$	−15.6599	−0.530006
$874$	−61.2656	−2.07234
$875$	−10.2949	−0.348031
$876$	16.1629	0.546093
$877$	18.0988	0.611154	0.305577	−	0.952167i	$-0.401151\pi$
$877$	18.0988	0.611154	0.305577	+	0.952167i	$0.401151\pi$
$878$	−54.5032	−1.83939
$879$	−26.5108	−0.894188
$880$	3.75273	0.126504
$881$	−10.9182	−0.367842	−0.183921	−	0.982941i	$-0.558879\pi$
$881$	−10.9182	−0.367842	−0.183921	+	0.982941i	$0.558879\pi$
$882$	−2.24191	−0.0754889
$883$	−54.1923	−1.82372	−0.911858	−	0.410506i	$-0.865352\pi$
$883$	−54.1923	−1.82372	−0.911858	+	0.410506i	$0.865352\pi$
$884$	42.4207	1.42676
$885$	−1.62001	−0.0544561
$886$	−33.8151	−1.13604
$887$	25.5060	0.856407	0.428203	−	0.903682i	$-0.359147\pi$
$887$	25.5060	0.856407	0.428203	+	0.903682i	$0.359147\pi$
$888$	14.1507	0.474867
$889$	−3.15585	−0.105844
$890$	8.58101	0.287636
$891$	3.48348	0.116701
$892$	−14.9629	−0.500995
$893$	−37.8692	−1.26724
$894$	11.0641	0.370038
$895$	26.4081	0.882726
$896$	−15.9818	−0.533914
$897$	14.8124	0.494570
$898$	−73.2213	−2.44343
$899$	33.1998	1.10728
$900$	−10.7437	−0.358123
$901$	21.2608	0.708299
$902$	−88.8515	−2.95843
$903$	9.34313	0.310920
$904$	43.9013	1.46014
$905$	−13.0497	−0.433786
$906$	−34.4918	−1.14591
$907$	−31.9202	−1.05989	−0.529946	−	0.848031i	$-0.677788\pi$
$907$	−31.9202	−1.05989	−0.529946	+	0.848031i	$0.677788\pi$
$908$	81.9921	2.72100
$909$	−7.53953	−0.250070
$910$	−10.2161	−0.338660
$911$	6.20266	0.205503	0.102752	−	0.994707i	$-0.467235\pi$
$911$	6.20266	0.205503	0.102752	+	0.994707i	$0.467235\pi$
$912$	−6.24732	−0.206870
$913$	−40.6639	−1.34578
$914$	−14.9784	−0.495440
$915$	−3.76842	−0.124580
$916$	−44.0398	−1.45512
$917$	−7.62953	−0.251949
$918$	−8.30386	−0.274068
$919$	−35.6245	−1.17514	−0.587572	−	0.809172i	$-0.699916\pi$
$919$	−35.6245	−1.17514	−0.587572	+	0.809172i	$0.699916\pi$
$920$	10.8409	0.357415
$921$	8.26367	0.272297
$922$	−84.0521	−2.76811
$923$	−36.9901	−1.21754
$924$	−10.5415	−0.346790
$925$	21.8381	0.718034
$926$	70.0380	2.30159
$927$	8.05022	0.264404
$928$	53.1051	1.74326
$929$	4.68564	0.153731	0.0768654	−	0.997041i	$-0.475509\pi$
$929$	4.68564	0.153731	0.0768654	+	0.997041i	$0.475509\pi$
$930$	11.1496	0.365610
$931$	6.98234	0.228837
$932$	24.5608	0.804515
$933$	0.313790	0.0102730
$934$	52.0256	1.70233
$935$	−15.5352	−0.508055
$936$	−8.70667	−0.284587
$937$	1.16457	0.0380449	0.0190224	−	0.999819i	$-0.493945\pi$
$937$	1.16457	0.0380449	0.0190224	+	0.999819i	$0.493945\pi$
$938$	−11.7545	−0.383799
$939$	−30.6173	−0.999159
$940$	19.7613	0.644542
$941$	9.35854	0.305080	0.152540	−	0.988297i	$-0.451255\pi$
$941$	9.35854	0.305080	0.152540	+	0.988297i	$0.451255\pi$
$942$	−25.5640	−0.832922
$943$	44.5279	1.45003
$944$	−1.20384	−0.0391818
$945$	1.20404	0.0391674
$946$	72.9665	2.37234
$947$	−32.5280	−1.05702	−0.528509	−	0.848928i	$-0.677249\pi$
$947$	−32.5280	−1.05702	−0.528509	+	0.848928i	$0.677249\pi$
$948$	−29.8821	−0.970524
$949$	20.2141	0.656178
$950$	55.5753	1.80310
$951$	19.4228	0.629828
$952$	8.52097	0.276166
$953$	−25.5277	−0.826922	−0.413461	−	0.910522i	$-0.635680\pi$
$953$	−25.5277	−0.826922	−0.413461	+	0.910522i	$0.635680\pi$
$954$	−12.8687	−0.416639
$955$	1.20404	0.0389618
$956$	−5.72503	−0.185161
$957$	27.9994	0.905091
$958$	26.3033	0.849821
$959$	−8.15512	−0.263343
$960$	15.6799	0.506065
$961$	−13.9391	−0.449649
$962$	52.1910	1.68270
$963$	19.3415	0.623271
$964$	−26.0638	−0.839458
$965$	0.437909	0.0140968
$966$	8.77437	0.282311
$967$	24.8781	0.800027	0.400014	−	0.916509i	$-0.369005\pi$
$967$	24.8781	0.800027	0.400014	+	0.916509i	$0.369005\pi$
$968$	−2.61023	−0.0838960
$969$	25.8621	0.830809
$970$	−42.2714	−1.35725
$971$	−7.02888	−0.225568	−0.112784	−	0.993620i	$-0.535977\pi$
$971$	−7.02888	−0.225568	−0.112784	+	0.993620i	$0.535977\pi$
$972$	3.02615	0.0970637
$973$	1.42536	0.0456950
$974$	−91.0187	−2.91643
$975$	−13.4366	−0.430315
$976$	−2.80035	−0.0896369
$977$	59.4498	1.90197	0.950984	−	0.309241i	$-0.100075\pi$
$977$	59.4498	1.90197	0.950984	+	0.309241i	$0.100075\pi$
$978$	37.1844	1.18903
$979$	11.0737	0.353918
$980$	−3.64360	−0.116391
$981$	14.6812	0.468735
$982$	89.2558	2.84827
$983$	−41.6665	−1.32895	−0.664477	−	0.747309i	$-0.731346\pi$
$983$	−41.6665	−1.32895	−0.664477	+	0.747309i	$0.731346\pi$
$984$	−26.1734	−0.834379
$985$	24.0160	0.765212
$986$	−66.7445	−2.12558
$987$	5.42356	0.172634
$988$	79.9680	2.54412
$989$	−36.5671	−1.16277
$990$	9.40311	0.298850
$991$	−2.68235	−0.0852077	−0.0426038	−	0.999092i	$-0.513565\pi$
$991$	−2.68235	−0.0852077	−0.0426038	+	0.999092i	$0.513565\pi$
$992$	27.2899	0.866456
$993$	−7.14609	−0.226774
$994$	−21.9118	−0.694999
$995$	−13.4288	−0.425722
$996$	−35.3253	−1.11933
$997$	−23.7071	−0.750811	−0.375405	−	0.926861i	$-0.622497\pi$
$997$	−23.7071	−0.750811	−0.375405	+	0.926861i	$0.622497\pi$
$998$	−18.1457	−0.574393
$999$	−6.15109	−0.194612

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.4	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.24191 q^{2} +1.00000 q^{3} +3.02615 q^{4} -1.20404 q^{5} -2.24191 q^{6} -1.00000 q^{7} -2.30052 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.24191 q^{2} +1.00000 q^{3} +3.02615 q^{4} -1.20404 q^{5} -2.24191 q^{6} -1.00000 q^{7} -2.30052 q^{8} +1.00000 q^{9} +2.69935 q^{10} +3.48348 q^{11} +3.02615 q^{12} +3.78465 q^{13} +2.24191 q^{14} -1.20404 q^{15} -0.894732 q^{16} +3.70393 q^{17} -2.24191 q^{18} +6.98234 q^{19} -3.64360 q^{20} -1.00000 q^{21} -7.80963 q^{22} +3.91380 q^{23} -2.30052 q^{24} -3.55029 q^{25} -8.48483 q^{26} +1.00000 q^{27} -3.02615 q^{28} +8.03776 q^{29} +2.69935 q^{30} +4.13048 q^{31} +6.60695 q^{32} +3.48348 q^{33} -8.30386 q^{34} +1.20404 q^{35} +3.02615 q^{36} -6.15109 q^{37} -15.6538 q^{38} +3.78465 q^{39} +2.76992 q^{40} +11.3772 q^{41} +2.24191 q^{42} -9.34313 q^{43} +10.5415 q^{44} -1.20404 q^{45} -8.77437 q^{46} -5.42356 q^{47} -0.894732 q^{48} +1.00000 q^{49} +7.95941 q^{50} +3.70393 q^{51} +11.4529 q^{52} +5.74006 q^{53} -2.24191 q^{54} -4.19425 q^{55} +2.30052 q^{56} +6.98234 q^{57} -18.0199 q^{58} +1.34548 q^{59} -3.64360 q^{60} +3.12982 q^{61} -9.26016 q^{62} -1.00000 q^{63} -13.0227 q^{64} -4.55687 q^{65} -7.80963 q^{66} -5.24309 q^{67} +11.2086 q^{68} +3.91380 q^{69} -2.69935 q^{70} -9.77372 q^{71} -2.30052 q^{72} +5.34108 q^{73} +13.7902 q^{74} -3.55029 q^{75} +21.1296 q^{76} -3.48348 q^{77} -8.48483 q^{78} -9.87463 q^{79} +1.07729 q^{80} +1.00000 q^{81} -25.5065 q^{82} -11.6734 q^{83} -3.02615 q^{84} -4.45968 q^{85} +20.9464 q^{86} +8.03776 q^{87} -8.01383 q^{88} +3.17892 q^{89} +2.69935 q^{90} -3.78465 q^{91} +11.8437 q^{92} +4.13048 q^{93} +12.1591 q^{94} -8.40701 q^{95} +6.60695 q^{96} -15.6599 q^{97} -2.24191 q^{98} +3.48348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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