LMFDB - Embedded newform 4011.2.a.j.1.18

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:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.06777 q^{2} -1.00000 q^{3} -0.859868 q^{4} +0.128461 q^{5} -1.06777 q^{6} -1.00000 q^{7} -3.05368 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.06777 q^{2} -1.00000 q^{3} -0.859868 q^{4} +0.128461 q^{5} -1.06777 q^{6} -1.00000 q^{7} -3.05368 q^{8} +1.00000 q^{9} +0.137167 q^{10} -1.51575 q^{11} +0.859868 q^{12} +7.04485 q^{13} -1.06777 q^{14} -0.128461 q^{15} -1.54089 q^{16} +1.04325 q^{17} +1.06777 q^{18} -7.25668 q^{19} -0.110460 q^{20} +1.00000 q^{21} -1.61847 q^{22} -9.19329 q^{23} +3.05368 q^{24} -4.98350 q^{25} +7.52228 q^{26} -1.00000 q^{27} +0.859868 q^{28} +1.55389 q^{29} -0.137167 q^{30} +10.5741 q^{31} +4.46204 q^{32} +1.51575 q^{33} +1.11396 q^{34} -0.128461 q^{35} -0.859868 q^{36} +5.99077 q^{37} -7.74847 q^{38} -7.04485 q^{39} -0.392279 q^{40} -10.0260 q^{41} +1.06777 q^{42} +6.56147 q^{43} +1.30334 q^{44} +0.128461 q^{45} -9.81631 q^{46} +10.4612 q^{47} +1.54089 q^{48} +1.00000 q^{49} -5.32123 q^{50} -1.04325 q^{51} -6.05764 q^{52} -4.01481 q^{53} -1.06777 q^{54} -0.194715 q^{55} +3.05368 q^{56} +7.25668 q^{57} +1.65920 q^{58} +1.21193 q^{59} +0.110460 q^{60} -6.89374 q^{61} +11.2907 q^{62} -1.00000 q^{63} +7.84622 q^{64} +0.904989 q^{65} +1.61847 q^{66} +0.339720 q^{67} -0.897061 q^{68} +9.19329 q^{69} -0.137167 q^{70} -10.5622 q^{71} -3.05368 q^{72} +12.5039 q^{73} +6.39676 q^{74} +4.98350 q^{75} +6.23979 q^{76} +1.51575 q^{77} -7.52228 q^{78} -4.33935 q^{79} -0.197945 q^{80} +1.00000 q^{81} -10.7055 q^{82} +0.441096 q^{83} -0.859868 q^{84} +0.134018 q^{85} +7.00614 q^{86} -1.55389 q^{87} +4.62861 q^{88} +8.73936 q^{89} +0.137167 q^{90} -7.04485 q^{91} +7.90501 q^{92} -10.5741 q^{93} +11.1701 q^{94} -0.932202 q^{95} -4.46204 q^{96} +6.25738 q^{97} +1.06777 q^{98} -1.51575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	1.06777	0.755027	0.377514	−	0.926004i	$-0.376779\pi$
$2$	1.06777	0.755027	0.377514	+	0.926004i	$0.376779\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.859868	−0.429934
$5$	0.128461	0.0574496	0.0287248	−	0.999587i	$-0.490855\pi$
$5$	0.128461	0.0574496	0.0287248	+	0.999587i	$0.490855\pi$
$6$	−1.06777	−0.435915
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.05368	−1.07964
$9$	1.00000	0.333333
$10$	0.137167	0.0433760
$11$	−1.51575	−0.457015	−0.228508	−	0.973542i	$-0.573385\pi$
$11$	−1.51575	−0.457015	−0.228508	+	0.973542i	$0.573385\pi$
$12$	0.859868	0.248223
$13$	7.04485	1.95389	0.976945	−	0.213492i	$-0.0684838\pi$
$13$	7.04485	1.95389	0.976945	+	0.213492i	$0.0684838\pi$
$14$	−1.06777	−0.285373
$15$	−0.128461	−0.0331685
$16$	−1.54089	−0.385223
$17$	1.04325	0.253026	0.126513	−	0.991965i	$-0.459621\pi$
$17$	1.04325	0.253026	0.126513	+	0.991965i	$0.459621\pi$
$18$	1.06777	0.251676
$19$	−7.25668	−1.66480	−0.832399	−	0.554177i	$-0.813033\pi$
$19$	−7.25668	−1.66480	−0.832399	+	0.554177i	$0.813033\pi$
$20$	−0.110460	−0.0246995
$21$	1.00000	0.218218
$22$	−1.61847	−0.345059
$23$	−9.19329	−1.91693	−0.958467	−	0.285205i	$-0.907938\pi$
$23$	−9.19329	−1.91693	−0.958467	+	0.285205i	$0.907938\pi$
$24$	3.05368	0.623330
$25$	−4.98350	−0.996700
$26$	7.52228	1.47524
$27$	−1.00000	−0.192450
$28$	0.859868	0.162500
$29$	1.55389	0.288551	0.144275	−	0.989538i	$-0.453915\pi$
$29$	1.55389	0.288551	0.144275	+	0.989538i	$0.453915\pi$
$30$	−0.137167	−0.0250431
$31$	10.5741	1.89916	0.949582	−	0.313520i	$-0.101508\pi$
$31$	10.5741	1.89916	0.949582	+	0.313520i	$0.101508\pi$
$32$	4.46204	0.788785
$33$	1.51575	0.263858
$34$	1.11396	0.191042
$35$	−0.128461	−0.0217139
$36$	−0.859868	−0.143311
$37$	5.99077	0.984877	0.492438	−	0.870347i	$-0.336106\pi$
$37$	5.99077	0.984877	0.492438	+	0.870347i	$0.336106\pi$
$38$	−7.74847	−1.25697
$39$	−7.04485	−1.12808
$40$	−0.392279	−0.0620248
$41$	−10.0260	−1.56580	−0.782899	−	0.622149i	$-0.786260\pi$
$41$	−10.0260	−1.56580	−0.782899	+	0.622149i	$0.786260\pi$
$42$	1.06777	0.164760
$43$	6.56147	1.00061	0.500307	−	0.865848i	$-0.333220\pi$
$43$	6.56147	1.00061	0.500307	+	0.865848i	$0.333220\pi$
$44$	1.30334	0.196486
$45$	0.128461	0.0191499
$46$	−9.81631	−1.44734
$47$	10.4612	1.52592	0.762958	−	0.646448i	$-0.223746\pi$
$47$	10.4612	1.52592	0.762958	+	0.646448i	$0.223746\pi$
$48$	1.54089	0.222408
$49$	1.00000	0.142857
$50$	−5.32123	−0.752535
$51$	−1.04325	−0.146085
$52$	−6.05764	−0.840044
$53$	−4.01481	−0.551476	−0.275738	−	0.961233i	$-0.588922\pi$
$53$	−4.01481	−0.551476	−0.275738	+	0.961233i	$0.588922\pi$
$54$	−1.06777	−0.145305
$55$	−0.194715	−0.0262553
$56$	3.05368	0.408065
$57$	7.25668	0.961171
$58$	1.65920	0.217864
$59$	1.21193	0.157780	0.0788901	−	0.996883i	$-0.474862\pi$
$59$	1.21193	0.157780	0.0788901	+	0.996883i	$0.474862\pi$
$60$	0.110460	0.0142603
$61$	−6.89374	−0.882653	−0.441327	−	0.897346i	$-0.645492\pi$
$61$	−6.89374	−0.882653	−0.441327	+	0.897346i	$0.645492\pi$
$62$	11.2907	1.43392
$63$	−1.00000	−0.125988
$64$	7.84622	0.980777
$65$	0.904989	0.112250
$66$	1.61847	0.199220
$67$	0.339720	0.0415034	0.0207517	−	0.999785i	$-0.493394\pi$
$67$	0.339720	0.0415034	0.0207517	+	0.999785i	$0.493394\pi$
$68$	−0.897061	−0.108785
$69$	9.19329	1.10674
$70$	−0.137167	−0.0163946
$71$	−10.5622	−1.25350	−0.626752	−	0.779219i	$-0.715616\pi$
$71$	−10.5622	−1.25350	−0.626752	+	0.779219i	$0.715616\pi$
$72$	−3.05368	−0.359880
$73$	12.5039	1.46347	0.731734	−	0.681591i	$-0.238712\pi$
$73$	12.5039	1.46347	0.731734	+	0.681591i	$0.238712\pi$
$74$	6.39676	0.743609
$75$	4.98350	0.575445
$76$	6.23979	0.715753
$77$	1.51575	0.172736
$78$	−7.52228	−0.851730
$79$	−4.33935	−0.488215	−0.244107	−	0.969748i	$-0.578495\pi$
$79$	−4.33935	−0.488215	−0.244107	+	0.969748i	$0.578495\pi$
$80$	−0.197945	−0.0221309
$81$	1.00000	0.111111
$82$	−10.7055	−1.18222
$83$	0.441096	0.0484166	0.0242083	−	0.999707i	$-0.492294\pi$
$83$	0.441096	0.0484166	0.0242083	+	0.999707i	$0.492294\pi$
$84$	−0.859868	−0.0938193
$85$	0.134018	0.0145363
$86$	7.00614	0.755491
$87$	−1.55389	−0.166595
$88$	4.62861	0.493411
$89$	8.73936	0.926370	0.463185	−	0.886262i	$-0.346706\pi$
$89$	8.73936	0.926370	0.463185	+	0.886262i	$0.346706\pi$
$90$	0.137167	0.0144587
$91$	−7.04485	−0.738501
$92$	7.90501	0.824155
$93$	−10.5741	−1.09648
$94$	11.1701	1.15211
$95$	−0.932202	−0.0956419
$96$	−4.46204	−0.455405
$97$	6.25738	0.635341	0.317670	−	0.948201i	$-0.397099\pi$
$97$	6.25738	0.635341	0.317670	+	0.948201i	$0.397099\pi$
$98$	1.06777	0.107861
$99$	−1.51575	−0.152338
$100$	4.28515	0.428515
$101$	−1.60367	−0.159571	−0.0797853	−	0.996812i	$-0.525423\pi$
$101$	−1.60367	−0.159571	−0.0797853	+	0.996812i	$0.525423\pi$
$102$	−1.11396	−0.110298
$103$	13.7446	1.35430	0.677148	−	0.735847i	$-0.263216\pi$
$103$	13.7446	1.35430	0.677148	+	0.735847i	$0.263216\pi$
$104$	−21.5127	−2.10950
$105$	0.128461	0.0125365
$106$	−4.28689	−0.416380
$107$	7.45192	0.720404	0.360202	−	0.932874i	$-0.382708\pi$
$107$	7.45192	0.720404	0.360202	+	0.932874i	$0.382708\pi$
$108$	0.859868	0.0827408
$109$	6.04612	0.579114	0.289557	−	0.957161i	$-0.406492\pi$
$109$	6.04612	0.579114	0.289557	+	0.957161i	$0.406492\pi$
$110$	−0.207910	−0.0198235
$111$	−5.99077	−0.568619
$112$	1.54089	0.145601
$113$	17.3896	1.63587	0.817936	−	0.575309i	$-0.195118\pi$
$113$	17.3896	1.63587	0.817936	+	0.575309i	$0.195118\pi$
$114$	7.74847	0.725710
$115$	−1.18098	−0.110127
$116$	−1.33614	−0.124058
$117$	7.04485	0.651297
$118$	1.29406	0.119128
$119$	−1.04325	−0.0956350
$120$	0.392279	0.0358100
$121$	−8.70251	−0.791137
$122$	−7.36093	−0.666427
$123$	10.0260	0.904014
$124$	−9.09232	−0.816515
$125$	−1.28249	−0.114710
$126$	−1.06777	−0.0951245
$127$	5.35972	0.475598	0.237799	−	0.971314i	$-0.423574\pi$
$127$	5.35972	0.475598	0.237799	+	0.971314i	$0.423574\pi$
$128$	−0.546135	−0.0482719
$129$	−6.56147	−0.577705
$130$	0.966320	0.0847519
$131$	−2.24961	−0.196549	−0.0982745	−	0.995159i	$-0.531332\pi$
$131$	−2.24961	−0.196549	−0.0982745	+	0.995159i	$0.531332\pi$
$132$	−1.30334	−0.113441
$133$	7.25668	0.629234
$134$	0.362743	0.0313362
$135$	−0.128461	−0.0110562
$136$	−3.18577	−0.273177
$137$	15.2576	1.30355	0.651774	−	0.758413i	$-0.274025\pi$
$137$	15.2576	1.30355	0.651774	+	0.758413i	$0.274025\pi$
$138$	9.81631	0.835620
$139$	−4.47580	−0.379632	−0.189816	−	0.981820i	$-0.560789\pi$
$139$	−4.47580	−0.379632	−0.189816	+	0.981820i	$0.560789\pi$
$140$	0.110460	0.00933554
$141$	−10.4612	−0.880988
$142$	−11.2780	−0.946430
$143$	−10.6782	−0.892957
$144$	−1.54089	−0.128408
$145$	0.199615	0.0165771
$146$	13.3513	1.10496
$147$	−1.00000	−0.0824786
$148$	−5.15127	−0.423432
$149$	−7.55224	−0.618704	−0.309352	−	0.950948i	$-0.600112\pi$
$149$	−7.55224	−0.618704	−0.309352	+	0.950948i	$0.600112\pi$
$150$	5.32123	0.434476
$151$	5.54599	0.451326	0.225663	−	0.974205i	$-0.427545\pi$
$151$	5.54599	0.451326	0.225663	+	0.974205i	$0.427545\pi$
$152$	22.1596	1.79738
$153$	1.04325	0.0843421
$154$	1.61847	0.130420
$155$	1.35836	0.109106
$156$	6.05764	0.484999
$157$	10.5131	0.839034	0.419517	−	0.907748i	$-0.362199\pi$
$157$	10.5131	0.839034	0.419517	+	0.907748i	$0.362199\pi$
$158$	−4.63342	−0.368615
$159$	4.01481	0.318395
$160$	0.573199	0.0453154
$161$	9.19329	0.724533
$162$	1.06777	0.0838919
$163$	10.5954	0.829898	0.414949	−	0.909845i	$-0.363799\pi$
$163$	10.5954	0.829898	0.414949	+	0.909845i	$0.363799\pi$
$164$	8.62103	0.673190
$165$	0.194715	0.0151585
$166$	0.470989	0.0365558
$167$	−5.00369	−0.387197	−0.193599	−	0.981081i	$-0.562016\pi$
$167$	−5.00369	−0.387197	−0.193599	+	0.981081i	$0.562016\pi$
$168$	−3.05368	−0.235597
$169$	36.6299	2.81768
$170$	0.143100	0.0109753
$171$	−7.25668	−0.554933
$172$	−5.64200	−0.430198
$173$	18.6047	1.41449	0.707246	−	0.706968i	$-0.249937\pi$
$173$	18.6047	1.41449	0.707246	+	0.706968i	$0.249937\pi$
$174$	−1.65920	−0.125784
$175$	4.98350	0.376717
$176$	2.33560	0.176053
$177$	−1.21193	−0.0910944
$178$	9.33162	0.699435
$179$	1.46281	0.109336	0.0546678	−	0.998505i	$-0.482590\pi$
$179$	1.46281	0.109336	0.0546678	+	0.998505i	$0.482590\pi$
$180$	−0.110460	−0.00823317
$181$	19.8690	1.47685	0.738426	−	0.674335i	$-0.235570\pi$
$181$	19.8690	1.47685	0.738426	+	0.674335i	$0.235570\pi$
$182$	−7.52228	−0.557588
$183$	6.89374	0.509600
$184$	28.0734	2.06960
$185$	0.769581	0.0565807
$186$	−11.2907	−0.827874
$187$	−1.58131	−0.115637
$188$	−8.99521	−0.656043
$189$	1.00000	0.0727393
$190$	−0.995377	−0.0722122
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−7.84622	−0.566252
$193$	5.96573	0.429423	0.214711	−	0.976678i	$-0.431119\pi$
$193$	5.96573	0.429423	0.214711	+	0.976678i	$0.431119\pi$
$194$	6.68144	0.479700
$195$	−0.904989	−0.0648076
$196$	−0.859868	−0.0614191
$197$	26.2879	1.87294	0.936469	−	0.350751i	$-0.114074\pi$
$197$	26.2879	1.87294	0.936469	+	0.350751i	$0.114074\pi$
$198$	−1.61847	−0.115020
$199$	19.4694	1.38015	0.690076	−	0.723737i	$-0.257577\pi$
$199$	19.4694	1.38015	0.690076	+	0.723737i	$0.257577\pi$
$200$	15.2180	1.07608
$201$	−0.339720	−0.0239620
$202$	−1.71235	−0.120480
$203$	−1.55389	−0.109062
$204$	0.897061	0.0628068
$205$	−1.28795	−0.0899544
$206$	14.6761	1.02253
$207$	−9.19329	−0.638978
$208$	−10.8553	−0.752683
$209$	10.9993	0.760838
$210$	0.137167	0.00946542
$211$	1.82305	0.125504	0.0627521	−	0.998029i	$-0.480012\pi$
$211$	1.82305	0.125504	0.0627521	+	0.998029i	$0.480012\pi$
$212$	3.45220	0.237098
$213$	10.5622	0.723711
$214$	7.95693	0.543925
$215$	0.842894	0.0574849
$216$	3.05368	0.207777
$217$	−10.5741	−0.717816
$218$	6.45587	0.437246
$219$	−12.5039	−0.844933
$220$	0.167429	0.0112881
$221$	7.34957	0.494386
$222$	−6.39676	−0.429323
$223$	−24.8270	−1.66254	−0.831269	−	0.555870i	$-0.812385\pi$
$223$	−24.8270	−1.66254	−0.831269	+	0.555870i	$0.812385\pi$
$224$	−4.46204	−0.298133
$225$	−4.98350	−0.332233
$226$	18.5680	1.23513
$227$	−13.5084	−0.896585	−0.448293	−	0.893887i	$-0.647968\pi$
$227$	−13.5084	−0.896585	−0.448293	+	0.893887i	$0.647968\pi$
$228$	−6.23979	−0.413240
$229$	4.91620	0.324871	0.162436	−	0.986719i	$-0.448065\pi$
$229$	4.91620	0.324871	0.162436	+	0.986719i	$0.448065\pi$
$230$	−1.26102	−0.0831489
$231$	−1.51575	−0.0997289
$232$	−4.74510	−0.311531
$233$	−16.6341	−1.08973	−0.544867	−	0.838523i	$-0.683420\pi$
$233$	−16.6341	−1.08973	−0.544867	+	0.838523i	$0.683420\pi$
$234$	7.52228	0.491747
$235$	1.34385	0.0876632
$236$	−1.04210	−0.0678350
$237$	4.33935	0.281871
$238$	−1.11396	−0.0722070
$239$	20.1094	1.30077	0.650386	−	0.759604i	$-0.274607\pi$
$239$	20.1094	1.30077	0.650386	+	0.759604i	$0.274607\pi$
$240$	0.197945	0.0127773
$241$	−7.46987	−0.481177	−0.240588	−	0.970627i	$-0.577340\pi$
$241$	−7.46987	−0.481177	−0.240588	+	0.970627i	$0.577340\pi$
$242$	−9.29227	−0.597330
$243$	−1.00000	−0.0641500
$244$	5.92771	0.379483
$245$	0.128461	0.00820708
$246$	10.7055	0.682555
$247$	−51.1222	−3.25283
$248$	−32.2899	−2.05041
$249$	−0.441096	−0.0279533
$250$	−1.36941	−0.0866088
$251$	21.7383	1.37211	0.686056	−	0.727549i	$-0.259340\pi$
$251$	21.7383	1.37211	0.686056	+	0.727549i	$0.259340\pi$
$252$	0.859868	0.0541666
$253$	13.9347	0.876068
$254$	5.72295	0.359090
$255$	−0.134018	−0.00839251
$256$	−16.2756	−1.01722
$257$	−6.79778	−0.424034	−0.212017	−	0.977266i	$-0.568003\pi$
$257$	−6.79778	−0.424034	−0.212017	+	0.977266i	$0.568003\pi$
$258$	−7.00614	−0.436183
$259$	−5.99077	−0.372248
$260$	−0.778171	−0.0482601
$261$	1.55389	0.0961837
$262$	−2.40206	−0.148400
$263$	18.1244	1.11760	0.558800	−	0.829303i	$-0.311262\pi$
$263$	18.1244	1.11760	0.558800	+	0.829303i	$0.311262\pi$
$264$	−4.62861	−0.284871
$265$	−0.515747	−0.0316821
$266$	7.74847	0.475089
$267$	−8.73936	−0.534840
$268$	−0.292114	−0.0178437
$269$	4.16442	0.253909	0.126954	−	0.991909i	$-0.459480\pi$
$269$	4.16442	0.253909	0.126954	+	0.991909i	$0.459480\pi$
$270$	−0.137167	−0.00834771
$271$	−24.8609	−1.51019	−0.755095	−	0.655616i	$-0.772409\pi$
$271$	−24.8609	−1.51019	−0.755095	+	0.655616i	$0.772409\pi$
$272$	−1.60754	−0.0974715
$273$	7.04485	0.426374
$274$	16.2916	0.984214
$275$	7.55373	0.455507
$276$	−7.90501	−0.475826
$277$	−14.3708	−0.863460	−0.431730	−	0.902003i	$-0.642097\pi$
$277$	−14.3708	−0.863460	−0.431730	+	0.902003i	$0.642097\pi$
$278$	−4.77912	−0.286633
$279$	10.5741	0.633054
$280$	0.392279	0.0234432
$281$	−0.174308	−0.0103983	−0.00519917	−	0.999986i	$-0.501655\pi$
$281$	−0.174308	−0.0103983	−0.00519917	+	0.999986i	$0.501655\pi$
$282$	−11.1701	−0.665170
$283$	−9.51920	−0.565858	−0.282929	−	0.959141i	$-0.591306\pi$
$283$	−9.51920	−0.565858	−0.282929	+	0.959141i	$0.591306\pi$
$284$	9.08211	0.538924
$285$	0.932202	0.0552189
$286$	−11.4019	−0.674207
$287$	10.0260	0.591816
$288$	4.46204	0.262928
$289$	−15.9116	−0.935978
$290$	0.213143	0.0125162
$291$	−6.25738	−0.366814
$292$	−10.7517	−0.629194
$293$	4.23099	0.247177	0.123589	−	0.992334i	$-0.460560\pi$
$293$	4.23099	0.247177	0.123589	+	0.992334i	$0.460560\pi$
$294$	−1.06777	−0.0622736
$295$	0.155686	0.00906440
$296$	−18.2939	−1.06331
$297$	1.51575	0.0879526
$298$	−8.06406	−0.467138
$299$	−64.7653	−3.74548
$300$	−4.28515	−0.247403
$301$	−6.56147	−0.378197
$302$	5.92184	0.340764
$303$	1.60367	0.0921282
$304$	11.1818	0.641318
$305$	−0.885578	−0.0507081
$306$	1.11396	0.0636806
$307$	−10.3037	−0.588063	−0.294032	−	0.955796i	$-0.594997\pi$
$307$	−10.3037	−0.588063	−0.294032	+	0.955796i	$0.594997\pi$
$308$	−1.30334	−0.0742649
$309$	−13.7446	−0.781903
$310$	1.45042	0.0823781
$311$	4.08229	0.231486	0.115743	−	0.993279i	$-0.463075\pi$
$311$	4.08229	0.231486	0.115743	+	0.993279i	$0.463075\pi$
$312$	21.5127	1.21792
$313$	−19.0211	−1.07514	−0.537569	−	0.843220i	$-0.680657\pi$
$313$	−19.0211	−1.07514	−0.537569	+	0.843220i	$0.680657\pi$
$314$	11.2255	0.633493
$315$	−0.128461	−0.00723797
$316$	3.73127	0.209900
$317$	18.5160	1.03996	0.519981	−	0.854178i	$-0.325939\pi$
$317$	18.5160	1.03996	0.519981	+	0.854178i	$0.325939\pi$
$318$	4.28689	0.240397
$319$	−2.35531	−0.131872
$320$	1.00793	0.0563452
$321$	−7.45192	−0.415925
$322$	9.81631	0.547042
$323$	−7.57057	−0.421238
$324$	−0.859868	−0.0477704
$325$	−35.1080	−1.94744
$326$	11.3135	0.626596
$327$	−6.04612	−0.334351
$328$	30.6162	1.69050
$329$	−10.4612	−0.576742
$330$	0.207910	0.0114451
$331$	−8.36822	−0.459959	−0.229979	−	0.973195i	$-0.573866\pi$
$331$	−8.36822	−0.459959	−0.229979	+	0.973195i	$0.573866\pi$
$332$	−0.379284	−0.0208159
$333$	5.99077	0.328292
$334$	−5.34279	−0.292344
$335$	0.0436408	0.00238435
$336$	−1.54089	−0.0840625
$337$	29.6096	1.61294	0.806468	−	0.591278i	$-0.201376\pi$
$337$	29.6096	1.61294	0.806468	+	0.591278i	$0.201376\pi$
$338$	39.1123	2.12743
$339$	−17.3896	−0.944471
$340$	−0.115237	−0.00624963
$341$	−16.0277	−0.867946
$342$	−7.74847	−0.418989
$343$	−1.00000	−0.0539949
$344$	−20.0366	−1.08030
$345$	1.18098	0.0635818
$346$	19.8656	1.06798
$347$	−23.9668	−1.28661	−0.643304	−	0.765611i	$-0.722437\pi$
$347$	−23.9668	−1.28661	−0.643304	+	0.765611i	$0.722437\pi$
$348$	1.33614	0.0716248
$349$	13.6257	0.729365	0.364683	−	0.931132i	$-0.381178\pi$
$349$	13.6257	0.729365	0.364683	+	0.931132i	$0.381178\pi$
$350$	5.32123	0.284432
$351$	−7.04485	−0.376026
$352$	−6.76333	−0.360487
$353$	1.47075	0.0782799	0.0391400	−	0.999234i	$-0.487538\pi$
$353$	1.47075	0.0782799	0.0391400	+	0.999234i	$0.487538\pi$
$354$	−1.29406	−0.0687787
$355$	−1.35683	−0.0720133
$356$	−7.51470	−0.398278
$357$	1.04325	0.0552149
$358$	1.56195	0.0825514
$359$	3.90479	0.206087	0.103043	−	0.994677i	$-0.467142\pi$
$359$	3.90479	0.206087	0.103043	+	0.994677i	$0.467142\pi$
$360$	−0.392279	−0.0206749
$361$	33.6595	1.77155
$362$	21.2155	1.11506
$363$	8.70251	0.456763
$364$	6.05764	0.317507
$365$	1.60626	0.0840756
$366$	7.36093	0.384762
$367$	−9.86665	−0.515035	−0.257518	−	0.966274i	$-0.582905\pi$
$367$	−9.86665	−0.515035	−0.257518	+	0.966274i	$0.582905\pi$
$368$	14.1659	0.738446
$369$	−10.0260	−0.521933
$370$	0.821735	0.0427200
$371$	4.01481	0.208438
$372$	9.09232	0.471415
$373$	−20.9407	−1.08427	−0.542134	−	0.840292i	$-0.682383\pi$
$373$	−20.9407	−1.08427	−0.542134	+	0.840292i	$0.682383\pi$
$374$	−1.68848	−0.0873090
$375$	1.28249	0.0662276
$376$	−31.9450	−1.64744
$377$	10.9470	0.563797
$378$	1.06777	0.0549201
$379$	19.5048	1.00189	0.500946	−	0.865478i	$-0.332985\pi$
$379$	19.5048	1.00189	0.500946	+	0.865478i	$0.332985\pi$
$380$	0.801571	0.0411197
$381$	−5.35972	−0.274587
$382$	1.06777	0.0546318
$383$	−36.2428	−1.85192	−0.925960	−	0.377621i	$-0.876742\pi$
$383$	−36.2428	−1.85192	−0.925960	+	0.377621i	$0.876742\pi$
$384$	0.546135	0.0278698
$385$	0.194715	0.00992358
$386$	6.37002	0.324226
$387$	6.56147	0.333538
$388$	−5.38052	−0.273155
$389$	5.97904	0.303149	0.151575	−	0.988446i	$-0.451566\pi$
$389$	5.97904	0.303149	0.151575	+	0.988446i	$0.451566\pi$
$390$	−0.966320	−0.0489315
$391$	−9.59094	−0.485035
$392$	−3.05368	−0.154234
$393$	2.24961	0.113478
$394$	28.0695	1.41412
$395$	−0.557438	−0.0280477
$396$	1.30334	0.0654955
$397$	−36.4469	−1.82922	−0.914609	−	0.404339i	$-0.867502\pi$
$397$	−36.4469	−1.82922	−0.914609	+	0.404339i	$0.867502\pi$
$398$	20.7889	1.04205
$399$	−7.25668	−0.363289
$400$	7.67903	0.383951
$401$	0.903472	0.0451173	0.0225586	−	0.999746i	$-0.492819\pi$
$401$	0.903472	0.0451173	0.0225586	+	0.999746i	$0.492819\pi$
$402$	−0.362743	−0.0180920
$403$	74.4929	3.71075
$404$	1.37894	0.0686049
$405$	0.128461	0.00638329
$406$	−1.65920	−0.0823448
$407$	−9.08050	−0.450104
$408$	3.18577	0.157719
$409$	6.24855	0.308971	0.154485	−	0.987995i	$-0.450628\pi$
$409$	6.24855	0.308971	0.154485	+	0.987995i	$0.450628\pi$
$410$	−1.37523	−0.0679180
$411$	−15.2576	−0.752604
$412$	−11.8185	−0.582258
$413$	−1.21193	−0.0596353
$414$	−9.81631	−0.482446
$415$	0.0566637	0.00278151
$416$	31.4344	1.54120
$417$	4.47580	0.219181
$418$	11.7447	0.574453
$419$	−25.1864	−1.23043	−0.615217	−	0.788358i	$-0.710932\pi$
$419$	−25.1864	−1.23043	−0.615217	+	0.788358i	$0.710932\pi$
$420$	−0.110460	−0.00538988
$421$	−4.87527	−0.237606	−0.118803	−	0.992918i	$-0.537906\pi$
$421$	−4.87527	−0.237606	−0.118803	+	0.992918i	$0.537906\pi$
$422$	1.94660	0.0947591
$423$	10.4612	0.508639
$424$	12.2599	0.595395
$425$	−5.19906	−0.252191
$426$	11.2780	0.546422
$427$	6.89374	0.333612
$428$	−6.40766	−0.309726
$429$	10.6782	0.515549
$430$	0.900017	0.0434027
$431$	−24.1961	−1.16549	−0.582743	−	0.812657i	$-0.698020\pi$
$431$	−24.1961	−1.16549	−0.582743	+	0.812657i	$0.698020\pi$
$432$	1.54089	0.0741362
$433$	25.9415	1.24667	0.623333	−	0.781956i	$-0.285778\pi$
$433$	25.9415	1.24667	0.623333	+	0.781956i	$0.285778\pi$
$434$	−11.2907	−0.541971
$435$	−0.199615	−0.00957081
$436$	−5.19887	−0.248981
$437$	66.7128	3.19131
$438$	−13.3513	−0.637947
$439$	−33.3127	−1.58993	−0.794964	−	0.606657i	$-0.792510\pi$
$439$	−33.3127	−1.58993	−0.794964	+	0.606657i	$0.792510\pi$
$440$	0.594597	0.0283463
$441$	1.00000	0.0476190
$442$	7.84765	0.373275
$443$	15.5188	0.737320	0.368660	−	0.929564i	$-0.379817\pi$
$443$	15.5188	0.737320	0.368660	+	0.929564i	$0.379817\pi$
$444$	5.15127	0.244469
$445$	1.12267	0.0532196
$446$	−26.5095	−1.25526
$447$	7.55224	0.357209
$448$	−7.84622	−0.370699
$449$	35.7997	1.68949	0.844747	−	0.535166i	$-0.179751\pi$
$449$	35.7997	1.68949	0.844747	+	0.535166i	$0.179751\pi$
$450$	−5.32123	−0.250845
$451$	15.1969	0.715593
$452$	−14.9527	−0.703317
$453$	−5.54599	−0.260573
$454$	−14.4239	−0.676946
$455$	−0.904989	−0.0424266
$456$	−22.1596	−1.03772
$457$	28.5544	1.33572	0.667860	−	0.744287i	$-0.267210\pi$
$457$	28.5544	1.33572	0.667860	+	0.744287i	$0.267210\pi$
$458$	5.24937	0.245287
$459$	−1.04325	−0.0486949
$460$	1.01549	0.0473473
$461$	−4.08950	−0.190467	−0.0952335	−	0.995455i	$-0.530360\pi$
$461$	−4.08950	−0.190467	−0.0952335	+	0.995455i	$0.530360\pi$
$462$	−1.61847	−0.0752980
$463$	8.40617	0.390668	0.195334	−	0.980737i	$-0.437421\pi$
$463$	8.40617	0.390668	0.195334	+	0.980737i	$0.437421\pi$
$464$	−2.39438	−0.111156
$465$	−1.35836	−0.0629924
$466$	−17.7613	−0.822778
$467$	−28.9500	−1.33965	−0.669824	−	0.742520i	$-0.733630\pi$
$467$	−28.9500	−1.33965	−0.669824	+	0.742520i	$0.733630\pi$
$468$	−6.05764	−0.280015
$469$	−0.339720	−0.0156868
$470$	1.43492	0.0661881
$471$	−10.5131	−0.484416
$472$	−3.70085	−0.170346
$473$	−9.94554	−0.457296
$474$	4.63342	0.212820
$475$	36.1637	1.65930
$476$	0.897061	0.0411167
$477$	−4.01481	−0.183825
$478$	21.4723	0.982118
$479$	−18.5504	−0.847588	−0.423794	−	0.905759i	$-0.639302\pi$
$479$	−18.5504	−0.847588	−0.423794	+	0.905759i	$0.639302\pi$
$480$	−0.573199	−0.0261628
$481$	42.2041	1.92434
$482$	−7.97610	−0.363302
$483$	−9.19329	−0.418309
$484$	7.48301	0.340137
$485$	0.803830	0.0365001
$486$	−1.06777	−0.0484350
$487$	0.355405	0.0161049	0.00805247	−	0.999968i	$-0.497437\pi$
$487$	0.355405	0.0161049	0.00805247	+	0.999968i	$0.497437\pi$
$488$	21.0513	0.952947
$489$	−10.5954	−0.479142
$490$	0.137167	0.00619657
$491$	−22.7661	−1.02742	−0.513710	−	0.857964i	$-0.671729\pi$
$491$	−22.7661	−1.02742	−0.513710	+	0.857964i	$0.671729\pi$
$492$	−8.62103	−0.388666
$493$	1.62111	0.0730110
$494$	−54.5868	−2.45598
$495$	−0.194715	−0.00875178
$496$	−16.2935	−0.731601
$497$	10.5622	0.473780
$498$	−0.470989	−0.0211055
$499$	23.6611	1.05921	0.529607	−	0.848243i	$-0.322339\pi$
$499$	23.6611	1.05921	0.529607	+	0.848243i	$0.322339\pi$
$500$	1.10277	0.0493175
$501$	5.00369	0.223548
$502$	23.2115	1.03598
$503$	−26.7516	−1.19279	−0.596396	−	0.802690i	$-0.703401\pi$
$503$	−26.7516	−1.19279	−0.596396	+	0.802690i	$0.703401\pi$
$504$	3.05368	0.136022
$505$	−0.206009	−0.00916727
$506$	14.8791	0.661455
$507$	−36.6299	−1.62679
$508$	−4.60865	−0.204476
$509$	−42.5923	−1.88787	−0.943934	−	0.330133i	$-0.892906\pi$
$509$	−42.5923	−1.88787	−0.943934	+	0.330133i	$0.892906\pi$
$510$	−0.143100	−0.00633657
$511$	−12.5039	−0.553139
$512$	−16.2863	−0.719760
$513$	7.25668	0.320390
$514$	−7.25846	−0.320157
$515$	1.76565	0.0778037
$516$	5.64200	0.248375
$517$	−15.8565	−0.697367
$518$	−6.39676	−0.281058
$519$	−18.6047	−0.816657
$520$	−2.76355	−0.121190
$521$	−7.99725	−0.350366	−0.175183	−	0.984536i	$-0.556052\pi$
$521$	−7.99725	−0.350366	−0.175183	+	0.984536i	$0.556052\pi$
$522$	1.65920	0.0726213
$523$	19.7623	0.864143	0.432072	−	0.901839i	$-0.357783\pi$
$523$	19.7623	0.864143	0.432072	+	0.901839i	$0.357783\pi$
$524$	1.93436	0.0845031
$525$	−4.98350	−0.217498
$526$	19.3527	0.843818
$527$	11.0315	0.480538
$528$	−2.33560	−0.101644
$529$	61.5166	2.67463
$530$	−0.550699	−0.0239208
$531$	1.21193	0.0525934
$532$	−6.23979	−0.270529
$533$	−70.6316	−3.05940
$534$	−9.33162	−0.403819
$535$	0.957282	0.0413869
$536$	−1.03740	−0.0448087
$537$	−1.46281	−0.0631250
$538$	4.44664	0.191708
$539$	−1.51575	−0.0652879
$540$	0.110460	0.00475343
$541$	−35.7866	−1.53858	−0.769292	−	0.638897i	$-0.779391\pi$
$541$	−35.7866	−1.53858	−0.769292	+	0.638897i	$0.779391\pi$
$542$	−26.5457	−1.14023
$543$	−19.8690	−0.852660
$544$	4.65505	0.199583
$545$	0.776692	0.0332698
$546$	7.52228	0.321924
$547$	−20.8208	−0.890232	−0.445116	−	0.895473i	$-0.646837\pi$
$547$	−20.8208	−0.890232	−0.445116	+	0.895473i	$0.646837\pi$
$548$	−13.1195	−0.560439
$549$	−6.89374	−0.294218
$550$	8.06564	0.343920
$551$	−11.2761	−0.480379
$552$	−28.0734	−1.19488
$553$	4.33935	0.184528
$554$	−15.3447	−0.651936
$555$	−0.769581	−0.0326669
$556$	3.84860	0.163217
$557$	−0.997679	−0.0422730	−0.0211365	−	0.999777i	$-0.506728\pi$
$557$	−0.997679	−0.0422730	−0.0211365	+	0.999777i	$0.506728\pi$
$558$	11.2907	0.477973
$559$	46.2246	1.95509
$560$	0.197945	0.00836469
$561$	1.58131	0.0667630
$562$	−0.186121	−0.00785102
$563$	23.2175	0.978502	0.489251	−	0.872143i	$-0.337270\pi$
$563$	23.2175	0.978502	0.489251	+	0.872143i	$0.337270\pi$
$564$	8.99521	0.378767
$565$	2.23388	0.0939802
$566$	−10.1643	−0.427238
$567$	−1.00000	−0.0419961
$568$	32.2536	1.35333
$569$	−32.4320	−1.35962	−0.679810	−	0.733388i	$-0.737938\pi$
$569$	−32.4320	−1.35962	−0.679810	+	0.733388i	$0.737938\pi$
$570$	0.995377	0.0416918
$571$	−27.5318	−1.15217	−0.576084	−	0.817390i	$-0.695420\pi$
$571$	−27.5318	−1.15217	−0.576084	+	0.817390i	$0.695420\pi$
$572$	9.18186	0.383913
$573$	−1.00000	−0.0417756
$574$	10.7055	0.446837
$575$	45.8147	1.91061
$576$	7.84622	0.326926
$577$	19.2003	0.799319	0.399659	−	0.916664i	$-0.369128\pi$
$577$	19.2003	0.799319	0.399659	+	0.916664i	$0.369128\pi$
$578$	−16.9899	−0.706689
$579$	−5.96573	−0.247927
$580$	−0.171643	−0.00712707
$581$	−0.441096	−0.0182998
$582$	−6.68144	−0.276955
$583$	6.08544	0.252033
$584$	−38.1828	−1.58002
$585$	0.904989	0.0374167
$586$	4.51772	0.186625
$587$	18.3794	0.758599	0.379299	−	0.925274i	$-0.376165\pi$
$587$	18.3794	0.758599	0.379299	+	0.925274i	$0.376165\pi$
$588$	0.859868	0.0354604
$589$	−76.7329	−3.16172
$590$	0.166237	0.00684387
$591$	−26.2879	−1.08134
$592$	−9.23112	−0.379397
$593$	39.7380	1.63184	0.815922	−	0.578162i	$-0.196230\pi$
$593$	39.7380	1.63184	0.815922	+	0.578162i	$0.196230\pi$
$594$	1.61847	0.0664066
$595$	−0.134018	−0.00549419
$596$	6.49393	0.266002
$597$	−19.4694	−0.796831
$598$	−69.1545	−2.82794
$599$	0.788341	0.0322107	0.0161054	−	0.999870i	$-0.494873\pi$
$599$	0.788341	0.0322107	0.0161054	+	0.999870i	$0.494873\pi$
$600$	−15.2180	−0.621273
$601$	34.2857	1.39854	0.699271	−	0.714857i	$-0.253508\pi$
$601$	34.2857	1.39854	0.699271	+	0.714857i	$0.253508\pi$
$602$	−7.00614	−0.285549
$603$	0.339720	0.0138345
$604$	−4.76882	−0.194041
$605$	−1.11793	−0.0454505
$606$	1.71235	0.0695593
$607$	44.0476	1.78784	0.893918	−	0.448231i	$-0.147946\pi$
$607$	44.0476	1.78784	0.893918	+	0.448231i	$0.147946\pi$
$608$	−32.3796	−1.31317
$609$	1.55389	0.0629670
$610$	−0.945594	−0.0382860
$611$	73.6973	2.98147
$612$	−0.897061	−0.0362615
$613$	−22.2688	−0.899429	−0.449714	−	0.893172i	$-0.648474\pi$
$613$	−22.2688	−0.899429	−0.449714	+	0.893172i	$0.648474\pi$
$614$	−11.0020	−0.444004
$615$	1.28795	0.0519352
$616$	−4.62861	−0.186492
$617$	−1.31331	−0.0528720	−0.0264360	−	0.999651i	$-0.508416\pi$
$617$	−1.31331	−0.0528720	−0.0264360	+	0.999651i	$0.508416\pi$
$618$	−14.6761	−0.590358
$619$	28.7935	1.15731	0.578654	−	0.815573i	$-0.303578\pi$
$619$	28.7935	1.15731	0.578654	+	0.815573i	$0.303578\pi$
$620$	−1.16801	−0.0469084
$621$	9.19329	0.368914
$622$	4.35895	0.174778
$623$	−8.73936	−0.350135
$624$	10.8553	0.434562
$625$	24.7527	0.990110
$626$	−20.3102	−0.811758
$627$	−10.9993	−0.439270
$628$	−9.03985	−0.360729
$629$	6.24990	0.249200
$630$	−0.137167	−0.00546486
$631$	8.31158	0.330879	0.165439	−	0.986220i	$-0.447096\pi$
$631$	8.31158	0.330879	0.165439	+	0.986220i	$0.447096\pi$
$632$	13.2510	0.527096
$633$	−1.82305	−0.0724599
$634$	19.7708	0.785200
$635$	0.688516	0.0273229
$636$	−3.45220	−0.136889
$637$	7.04485	0.279127
$638$	−2.51493	−0.0995671
$639$	−10.5622	−0.417835
$640$	−0.0701571	−0.00277320
$641$	4.81868	0.190327	0.0951633	−	0.995462i	$-0.469663\pi$
$641$	4.81868	0.190327	0.0951633	+	0.995462i	$0.469663\pi$
$642$	−7.95693	−0.314035
$643$	−37.4391	−1.47646	−0.738228	−	0.674552i	$-0.764337\pi$
$643$	−37.4391	−1.47646	−0.738228	+	0.674552i	$0.764337\pi$
$644$	−7.90501	−0.311501
$645$	−0.842894	−0.0331889
$646$	−8.08362	−0.318046
$647$	8.99611	0.353674	0.176837	−	0.984240i	$-0.443414\pi$
$647$	8.99611	0.353674	0.176837	+	0.984240i	$0.443414\pi$
$648$	−3.05368	−0.119960
$649$	−1.83698	−0.0721079
$650$	−37.4872	−1.47037
$651$	10.5741	0.414431
$652$	−9.11067	−0.356801
$653$	34.1427	1.33611	0.668053	−	0.744113i	$-0.267128\pi$
$653$	34.1427	1.33611	0.668053	+	0.744113i	$0.267128\pi$
$654$	−6.45587	−0.252444
$655$	−0.288987	−0.0112917
$656$	15.4490	0.603181
$657$	12.5039	0.487822
$658$	−11.1701	−0.435456
$659$	23.0074	0.896240	0.448120	−	0.893973i	$-0.352094\pi$
$659$	23.0074	0.896240	0.448120	+	0.893973i	$0.352094\pi$
$660$	−0.167429	−0.00651716
$661$	38.4609	1.49596	0.747978	−	0.663724i	$-0.231025\pi$
$661$	38.4609	1.49596	0.747978	+	0.663724i	$0.231025\pi$
$662$	−8.93533	−0.347281
$663$	−7.34957	−0.285434
$664$	−1.34697	−0.0522724
$665$	0.932202	0.0361492
$666$	6.39676	0.247870
$667$	−14.2854	−0.553133
$668$	4.30251	0.166469
$669$	24.8270	0.959867
$670$	0.0465984	0.00180025
$671$	10.4492	0.403386
$672$	4.46204	0.172127
$673$	41.4499	1.59778	0.798888	−	0.601480i	$-0.205422\pi$
$673$	41.4499	1.59778	0.798888	+	0.601480i	$0.205422\pi$
$674$	31.6162	1.21781
$675$	4.98350	0.191815
$676$	−31.4969	−1.21142
$677$	−4.55651	−0.175121	−0.0875605	−	0.996159i	$-0.527907\pi$
$677$	−4.55651	−0.175121	−0.0875605	+	0.996159i	$0.527907\pi$
$678$	−18.5680	−0.713102
$679$	−6.25738	−0.240136
$680$	−0.409247	−0.0156939
$681$	13.5084	0.517644
$682$	−17.1138	−0.655323
$683$	−30.5044	−1.16722	−0.583609	−	0.812035i	$-0.698360\pi$
$683$	−30.5044	−1.16722	−0.583609	+	0.812035i	$0.698360\pi$
$684$	6.23979	0.238584
$685$	1.96001	0.0748882
$686$	−1.06777	−0.0407676
$687$	−4.91620	−0.187565
$688$	−10.1105	−0.385460
$689$	−28.2837	−1.07752
$690$	1.26102	0.0480060
$691$	23.0578	0.877160	0.438580	−	0.898692i	$-0.355482\pi$
$691$	23.0578	0.877160	0.438580	+	0.898692i	$0.355482\pi$
$692$	−15.9976	−0.608138
$693$	1.51575	0.0575785
$694$	−25.5911	−0.971423
$695$	−0.574966	−0.0218097
$696$	4.74510	0.179862
$697$	−10.4597	−0.396188
$698$	14.5491	0.550691
$699$	16.6341	0.629158
$700$	−4.28515	−0.161963
$701$	−21.7283	−0.820668	−0.410334	−	0.911935i	$-0.634588\pi$
$701$	−21.7283	−0.820668	−0.410334	+	0.911935i	$0.634588\pi$
$702$	−7.52228	−0.283910
$703$	−43.4731	−1.63962
$704$	−11.8929	−0.448230
$705$	−1.34385	−0.0506124
$706$	1.57042	0.0591035
$707$	1.60367	0.0603120
$708$	1.04210	0.0391646
$709$	−1.58655	−0.0595843	−0.0297922	−	0.999556i	$-0.509485\pi$
$709$	−1.58655	−0.0595843	−0.0297922	+	0.999556i	$0.509485\pi$
$710$	−1.44879	−0.0543720
$711$	−4.33935	−0.162738
$712$	−26.6872	−1.00015
$713$	−97.2107	−3.64057
$714$	1.11396	0.0416887
$715$	−1.37174	−0.0513000
$716$	−1.25782	−0.0470071
$717$	−20.1094	−0.751001
$718$	4.16941	0.155601
$719$	3.35816	0.125238	0.0626192	−	0.998037i	$-0.480055\pi$
$719$	3.35816	0.125238	0.0626192	+	0.998037i	$0.480055\pi$
$720$	−0.197945	−0.00737696
$721$	−13.7446	−0.511876
$722$	35.9406	1.33757
$723$	7.46987	0.277808
$724$	−17.0847	−0.634949
$725$	−7.74383	−0.287599
$726$	9.29227	0.344869
$727$	39.9952	1.48334	0.741670	−	0.670765i	$-0.234034\pi$
$727$	39.9952	1.48334	0.741670	+	0.670765i	$0.234034\pi$
$728$	21.5127	0.797314
$729$	1.00000	0.0370370
$730$	1.71512	0.0634793
$731$	6.84528	0.253182
$732$	−5.92771	−0.219094
$733$	−35.0104	−1.29314	−0.646569	−	0.762855i	$-0.723797\pi$
$733$	−35.0104	−1.29314	−0.646569	+	0.762855i	$0.723797\pi$
$734$	−10.5353	−0.388866
$735$	−0.128461	−0.00473836
$736$	−41.0209	−1.51205
$737$	−0.514930	−0.0189677
$738$	−10.7055	−0.394073
$739$	0.309244	0.0113757	0.00568787	−	0.999984i	$-0.498189\pi$
$739$	0.309244	0.0113757	0.00568787	+	0.999984i	$0.498189\pi$
$740$	−0.661738	−0.0243260
$741$	51.1222	1.87802
$742$	4.28689	0.157377
$743$	−13.2435	−0.485858	−0.242929	−	0.970044i	$-0.578108\pi$
$743$	−13.2435	−0.485858	−0.242929	+	0.970044i	$0.578108\pi$
$744$	32.2899	1.18381
$745$	−0.970170	−0.0355443
$746$	−22.3598	−0.818651
$747$	0.441096	0.0161389
$748$	1.35972	0.0497162
$749$	−7.45192	−0.272287
$750$	1.36941	0.0500036
$751$	46.6218	1.70125	0.850626	−	0.525771i	$-0.176223\pi$
$751$	46.6218	1.70125	0.850626	+	0.525771i	$0.176223\pi$
$752$	−16.1195	−0.587818
$753$	−21.7383	−0.792189
$754$	11.6888	0.425682
$755$	0.712444	0.0259285
$756$	−0.859868	−0.0312731
$757$	20.8535	0.757933	0.378967	−	0.925410i	$-0.376279\pi$
$757$	20.8535	0.757933	0.378967	+	0.925410i	$0.376279\pi$
$758$	20.8266	0.756456
$759$	−13.9347	−0.505798
$760$	2.84665	0.103259
$761$	−45.4104	−1.64613	−0.823063	−	0.567950i	$-0.807737\pi$
$761$	−45.4104	−1.64613	−0.823063	+	0.567950i	$0.807737\pi$
$762$	−5.72295	−0.207320
$763$	−6.04612	−0.218884
$764$	−0.859868	−0.0311089
$765$	0.134018	0.00484542
$766$	−38.6990	−1.39825
$767$	8.53788	0.308285
$768$	16.2756	0.587294
$769$	−18.7532	−0.676259	−0.338130	−	0.941100i	$-0.609794\pi$
$769$	−18.7532	−0.676259	−0.338130	+	0.941100i	$0.609794\pi$
$770$	0.207910	0.00749257
$771$	6.79778	0.244816
$772$	−5.12974	−0.184623
$773$	5.39098	0.193900	0.0969500	−	0.995289i	$-0.469091\pi$
$773$	5.39098	0.193900	0.0969500	+	0.995289i	$0.469091\pi$
$774$	7.00614	0.251830
$775$	−52.6960	−1.89290
$776$	−19.1080	−0.685939
$777$	5.99077	0.214918
$778$	6.38424	0.228886
$779$	72.7555	2.60674
$780$	0.778171	0.0278630
$781$	16.0097	0.572871
$782$	−10.2409	−0.366214
$783$	−1.55389	−0.0555317
$784$	−1.54089	−0.0550318
$785$	1.35052	0.0482021
$786$	2.40206	0.0856787
$787$	−6.20308	−0.221116	−0.110558	−	0.993870i	$-0.535264\pi$
$787$	−6.20308	−0.221116	−0.110558	+	0.993870i	$0.535264\pi$
$788$	−22.6041	−0.805239
$789$	−18.1244	−0.645246
$790$	−0.595215	−0.0211768
$791$	−17.3896	−0.618302
$792$	4.62861	0.164470
$793$	−48.5654	−1.72461
$794$	−38.9169	−1.38111
$795$	0.515747	0.0182917
$796$	−16.7411	−0.593374
$797$	30.9937	1.09785	0.548926	−	0.835871i	$-0.315037\pi$
$797$	30.9937	1.09785	0.548926	+	0.835871i	$0.315037\pi$
$798$	−7.74847	−0.274293
$799$	10.9136	0.386097
$800$	−22.2366	−0.786182
$801$	8.73936	0.308790
$802$	0.964700	0.0340648
$803$	−18.9527	−0.668827
$804$	0.292114	0.0103021
$805$	1.18098	0.0416241
$806$	79.5412	2.80172
$807$	−4.16442	−0.146594
$808$	4.89708	0.172279
$809$	−37.1364	−1.30565	−0.652824	−	0.757510i	$-0.726416\pi$
$809$	−37.1364	−1.30565	−0.652824	+	0.757510i	$0.726416\pi$
$810$	0.137167	0.00481955
$811$	34.4861	1.21097	0.605486	−	0.795856i	$-0.292979\pi$
$811$	34.4861	1.21097	0.605486	+	0.795856i	$0.292979\pi$
$812$	1.33614	0.0468895
$813$	24.8609	0.871908
$814$	−9.69588	−0.339840
$815$	1.36110	0.0476773
$816$	1.60754	0.0562752
$817$	−47.6145	−1.66582
$818$	6.67201	0.233281
$819$	−7.04485	−0.246167
$820$	1.10747	0.0386745
$821$	−56.2867	−1.96442	−0.982210	−	0.187786i	$-0.939869\pi$
$821$	−56.2867	−1.96442	−0.982210	+	0.187786i	$0.939869\pi$
$822$	−16.2916	−0.568236
$823$	16.8018	0.585676	0.292838	−	0.956162i	$-0.405400\pi$
$823$	16.8018	0.585676	0.292838	+	0.956162i	$0.405400\pi$
$824$	−41.9716	−1.46215
$825$	−7.55373	−0.262987
$826$	−1.29406	−0.0450263
$827$	15.6294	0.543486	0.271743	−	0.962370i	$-0.412400\pi$
$827$	15.6294	0.543486	0.271743	+	0.962370i	$0.412400\pi$
$828$	7.90501	0.274718
$829$	14.4150	0.500655	0.250327	−	0.968161i	$-0.419462\pi$
$829$	14.4150	0.500655	0.250327	+	0.968161i	$0.419462\pi$
$830$	0.0605038	0.00210012
$831$	14.3708	0.498519
$832$	55.2754	1.91633
$833$	1.04325	0.0361466
$834$	4.77912	0.165488
$835$	−0.642780	−0.0222443
$836$	−9.45795	−0.327110
$837$	−10.5741	−0.365494
$838$	−26.8932	−0.929012
$839$	17.3142	0.597754	0.298877	−	0.954292i	$-0.403388\pi$
$839$	17.3142	0.597754	0.298877	+	0.954292i	$0.403388\pi$
$840$	−0.392279	−0.0135349
$841$	−26.5854	−0.916738
$842$	−5.20567	−0.179399
$843$	0.174308	0.00600348
$844$	−1.56759	−0.0539585
$845$	4.70552	0.161875
$846$	11.1701	0.384036
$847$	8.70251	0.299022
$848$	6.18638	0.212441
$849$	9.51920	0.326698
$850$	−5.55139	−0.190411
$851$	−55.0749	−1.88794
$852$	−9.08211	−0.311148
$853$	−16.2812	−0.557457	−0.278729	−	0.960370i	$-0.589913\pi$
$853$	−16.2812	−0.557457	−0.278729	+	0.960370i	$0.589913\pi$
$854$	7.36093	0.251886
$855$	−0.932202	−0.0318806
$856$	−22.7558	−0.777776
$857$	4.12506	0.140909	0.0704547	−	0.997515i	$-0.477555\pi$
$857$	4.12506	0.140909	0.0704547	+	0.997515i	$0.477555\pi$
$858$	11.4019	0.389254
$859$	25.7604	0.878932	0.439466	−	0.898259i	$-0.355168\pi$
$859$	25.7604	0.878932	0.439466	+	0.898259i	$0.355168\pi$
$860$	−0.724778	−0.0247147
$861$	−10.0260	−0.341685
$862$	−25.8359	−0.879973
$863$	33.8826	1.15338	0.576689	−	0.816964i	$-0.304344\pi$
$863$	33.8826	1.15338	0.576689	+	0.816964i	$0.304344\pi$
$864$	−4.46204	−0.151802
$865$	2.38998	0.0812619
$866$	27.6995	0.941267
$867$	15.9116	0.540387
$868$	9.09232	0.308614
$869$	6.57736	0.223122
$870$	−0.213143	−0.00722622
$871$	2.39328	0.0810931
$872$	−18.4629	−0.625234
$873$	6.25738	0.211780
$874$	71.2339	2.40952
$875$	1.28249	0.0433561
$876$	10.7517	0.363265
$877$	−23.2260	−0.784288	−0.392144	−	0.919904i	$-0.628266\pi$
$877$	−23.2260	−0.784288	−0.392144	+	0.919904i	$0.628266\pi$
$878$	−35.5703	−1.20044
$879$	−4.23099	−0.142708
$880$	0.300034	0.0101142
$881$	−8.97778	−0.302469	−0.151235	−	0.988498i	$-0.548325\pi$
$881$	−8.97778	−0.302469	−0.151235	+	0.988498i	$0.548325\pi$
$882$	1.06777	0.0359537
$883$	5.55217	0.186845	0.0934227	−	0.995627i	$-0.470219\pi$
$883$	5.55217	0.186845	0.0934227	+	0.995627i	$0.470219\pi$
$884$	−6.31966	−0.212553
$885$	−0.155686	−0.00523333
$886$	16.5705	0.556697
$887$	−10.9145	−0.366473	−0.183236	−	0.983069i	$-0.558657\pi$
$887$	−10.9145	−0.366473	−0.183236	+	0.983069i	$0.558657\pi$
$888$	18.2939	0.613903
$889$	−5.35972	−0.179759
$890$	1.19875	0.0401822
$891$	−1.51575	−0.0507795
$892$	21.3479	0.714782
$893$	−75.9133	−2.54034
$894$	8.06406	0.269702
$895$	0.187914	0.00628129
$896$	0.546135	0.0182451
$897$	64.7653	2.16245
$898$	38.2259	1.27561
$899$	16.4310	0.548005
$900$	4.28515	0.142838
$901$	−4.18847	−0.139538
$902$	16.2268	0.540292
$903$	6.56147	0.218352
$904$	−53.1022	−1.76615
$905$	2.55239	0.0848445
$906$	−5.92184	−0.196740
$907$	21.3709	0.709610	0.354805	−	0.934940i	$-0.384547\pi$
$907$	21.3709	0.709610	0.354805	+	0.934940i	$0.384547\pi$
$908$	11.6155	0.385472
$909$	−1.60367	−0.0531902
$910$	−0.966320	−0.0320332
$911$	−29.7155	−0.984517	−0.492259	−	0.870449i	$-0.663829\pi$
$911$	−29.7155	−0.984517	−0.492259	+	0.870449i	$0.663829\pi$
$912$	−11.1818	−0.370265
$913$	−0.668591	−0.0221271
$914$	30.4896	1.00850
$915$	0.885578	0.0292763
$916$	−4.22728	−0.139673
$917$	2.24961	0.0742885
$918$	−1.11396	−0.0367660
$919$	0.923821	0.0304741	0.0152370	−	0.999884i	$-0.495150\pi$
$919$	0.923821	0.0304741	0.0152370	+	0.999884i	$0.495150\pi$
$920$	3.60634	0.118897
$921$	10.3037	0.339518
$922$	−4.36664	−0.143808
$923$	−74.4092	−2.44921
$924$	1.30334	0.0428768
$925$	−29.8550	−0.981626
$926$	8.97585	0.294965
$927$	13.7446	0.451432
$928$	6.93355	0.227605
$929$	−16.8451	−0.552668	−0.276334	−	0.961062i	$-0.589120\pi$
$929$	−16.8451	−0.552668	−0.276334	+	0.961062i	$0.589120\pi$
$930$	−1.45042	−0.0475610
$931$	−7.25668	−0.237828
$932$	14.3031	0.468513
$933$	−4.08229	−0.133648
$934$	−30.9120	−1.01147
$935$	−0.203137	−0.00664329
$936$	−21.5127	−0.703165
$937$	3.14907	0.102876	0.0514379	−	0.998676i	$-0.483620\pi$
$937$	3.14907	0.102876	0.0514379	+	0.998676i	$0.483620\pi$
$938$	−0.362743	−0.0118440
$939$	19.0211	0.620731
$940$	−1.15554	−0.0376894
$941$	28.6420	0.933702	0.466851	−	0.884336i	$-0.345388\pi$
$941$	28.6420	0.933702	0.466851	+	0.884336i	$0.345388\pi$
$942$	−11.2255	−0.365748
$943$	92.1719	3.00153
$944$	−1.86746	−0.0607805
$945$	0.128461	0.00417884
$946$	−10.6195	−0.345271
$947$	−2.25286	−0.0732081	−0.0366040	−	0.999330i	$-0.511654\pi$
$947$	−2.25286	−0.0732081	−0.0366040	+	0.999330i	$0.511654\pi$
$948$	−3.73127	−0.121186
$949$	88.0879	2.85945
$950$	38.6145	1.25282
$951$	−18.5160	−0.600423
$952$	3.18577	0.103251
$953$	−4.24276	−0.137436	−0.0687182	−	0.997636i	$-0.521891\pi$
$953$	−4.24276	−0.137436	−0.0687182	+	0.997636i	$0.521891\pi$
$954$	−4.28689	−0.138793
$955$	0.128461	0.00415691
$956$	−17.2915	−0.559246
$957$	2.35531	0.0761364
$958$	−19.8075	−0.639952
$959$	−15.2576	−0.492695
$960$	−1.00793	−0.0325309
$961$	80.8114	2.60682
$962$	45.0642	1.45293
$963$	7.45192	0.240135
$964$	6.42310	0.206874
$965$	0.766364	0.0246701
$966$	−9.81631	−0.315835
$967$	61.8980	1.99051	0.995253	−	0.0973218i	$-0.0310276\pi$
$967$	61.8980	1.99051	0.995253	+	0.0973218i	$0.0310276\pi$
$968$	26.5747	0.854142
$969$	7.57057	0.243202
$970$	0.858306	0.0275585
$971$	−38.3074	−1.22934	−0.614672	−	0.788783i	$-0.710712\pi$
$971$	−38.3074	−1.22934	−0.614672	+	0.788783i	$0.710712\pi$
$972$	0.859868	0.0275803
$973$	4.47580	0.143488
$974$	0.379491	0.0121597
$975$	35.1080	1.12436
$976$	10.6225	0.340018
$977$	56.1276	1.79568	0.897840	−	0.440322i	$-0.145136\pi$
$977$	56.1276	1.79568	0.897840	+	0.440322i	$0.145136\pi$
$978$	−11.3135	−0.361765
$979$	−13.2467	−0.423365
$980$	−0.110460	−0.00352850
$981$	6.04612	0.193038
$982$	−24.3089	−0.775729
$983$	−44.2839	−1.41244	−0.706218	−	0.707994i	$-0.749600\pi$
$983$	−44.2839	−1.41244	−0.706218	+	0.707994i	$0.749600\pi$
$984$	−30.6162	−0.976008
$985$	3.37698	0.107599
$986$	1.73097	0.0551253
$987$	10.4612	0.332982
$988$	43.9584	1.39850
$989$	−60.3215	−1.91811
$990$	−0.207910	−0.00660783
$991$	−35.2504	−1.11977	−0.559883	−	0.828571i	$-0.689154\pi$
$991$	−35.2504	−1.11977	−0.559883	+	0.828571i	$0.689154\pi$
$992$	47.1821	1.49803
$993$	8.36822	0.265557
$994$	11.2780	0.357717
$995$	2.50107	0.0792891
$996$	0.379284	0.0120181
$997$	−18.9158	−0.599068	−0.299534	−	0.954086i	$-0.596831\pi$
$997$	−18.9158	−0.599068	−0.299534	+	0.954086i	$0.596831\pi$
$998$	25.2646	0.799735
$999$	−5.99077	−0.189540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.18	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.18	✓	26	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)

\(f(q)\)	\(=\)	\(q+1.06777 q^{2} -1.00000 q^{3} -0.859868 q^{4} +0.128461 q^{5} -1.06777 q^{6} -1.00000 q^{7} -3.05368 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.06777 q^{2} -1.00000 q^{3} -0.859868 q^{4} +0.128461 q^{5} -1.06777 q^{6} -1.00000 q^{7} -3.05368 q^{8} +1.00000 q^{9} +0.137167 q^{10} -1.51575 q^{11} +0.859868 q^{12} +7.04485 q^{13} -1.06777 q^{14} -0.128461 q^{15} -1.54089 q^{16} +1.04325 q^{17} +1.06777 q^{18} -7.25668 q^{19} -0.110460 q^{20} +1.00000 q^{21} -1.61847 q^{22} -9.19329 q^{23} +3.05368 q^{24} -4.98350 q^{25} +7.52228 q^{26} -1.00000 q^{27} +0.859868 q^{28} +1.55389 q^{29} -0.137167 q^{30} +10.5741 q^{31} +4.46204 q^{32} +1.51575 q^{33} +1.11396 q^{34} -0.128461 q^{35} -0.859868 q^{36} +5.99077 q^{37} -7.74847 q^{38} -7.04485 q^{39} -0.392279 q^{40} -10.0260 q^{41} +1.06777 q^{42} +6.56147 q^{43} +1.30334 q^{44} +0.128461 q^{45} -9.81631 q^{46} +10.4612 q^{47} +1.54089 q^{48} +1.00000 q^{49} -5.32123 q^{50} -1.04325 q^{51} -6.05764 q^{52} -4.01481 q^{53} -1.06777 q^{54} -0.194715 q^{55} +3.05368 q^{56} +7.25668 q^{57} +1.65920 q^{58} +1.21193 q^{59} +0.110460 q^{60} -6.89374 q^{61} +11.2907 q^{62} -1.00000 q^{63} +7.84622 q^{64} +0.904989 q^{65} +1.61847 q^{66} +0.339720 q^{67} -0.897061 q^{68} +9.19329 q^{69} -0.137167 q^{70} -10.5622 q^{71} -3.05368 q^{72} +12.5039 q^{73} +6.39676 q^{74} +4.98350 q^{75} +6.23979 q^{76} +1.51575 q^{77} -7.52228 q^{78} -4.33935 q^{79} -0.197945 q^{80} +1.00000 q^{81} -10.7055 q^{82} +0.441096 q^{83} -0.859868 q^{84} +0.134018 q^{85} +7.00614 q^{86} -1.55389 q^{87} +4.62861 q^{88} +8.73936 q^{89} +0.137167 q^{90} -7.04485 q^{91} +7.90501 q^{92} -10.5741 q^{93} +11.1701 q^{94} -0.932202 q^{95} -4.46204 q^{96} +6.25738 q^{97} +1.06777 q^{98} -1.51575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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