LMFDB - Embedded newform 4011.2.a.m.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.18058 q^{2} +1.00000 q^{3} -0.606227 q^{4} +0.961582 q^{5} +1.18058 q^{6} -1.00000 q^{7} -3.07686 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.18058 q^{2} +1.00000 q^{3} -0.606227 q^{4} +0.961582 q^{5} +1.18058 q^{6} -1.00000 q^{7} -3.07686 q^{8} +1.00000 q^{9} +1.13523 q^{10} +3.15289 q^{11} -0.606227 q^{12} -4.59478 q^{13} -1.18058 q^{14} +0.961582 q^{15} -2.42003 q^{16} +6.22259 q^{17} +1.18058 q^{18} +3.21365 q^{19} -0.582937 q^{20} -1.00000 q^{21} +3.72225 q^{22} +0.430954 q^{23} -3.07686 q^{24} -4.07536 q^{25} -5.42451 q^{26} +1.00000 q^{27} +0.606227 q^{28} +0.690340 q^{29} +1.13523 q^{30} +5.00614 q^{31} +3.29668 q^{32} +3.15289 q^{33} +7.34628 q^{34} -0.961582 q^{35} -0.606227 q^{36} +9.34586 q^{37} +3.79398 q^{38} -4.59478 q^{39} -2.95866 q^{40} -6.97492 q^{41} -1.18058 q^{42} -0.172100 q^{43} -1.91137 q^{44} +0.961582 q^{45} +0.508776 q^{46} +0.252698 q^{47} -2.42003 q^{48} +1.00000 q^{49} -4.81130 q^{50} +6.22259 q^{51} +2.78548 q^{52} -2.60045 q^{53} +1.18058 q^{54} +3.03176 q^{55} +3.07686 q^{56} +3.21365 q^{57} +0.815003 q^{58} +11.4050 q^{59} -0.582937 q^{60} +10.9994 q^{61} +5.91016 q^{62} -1.00000 q^{63} +8.73207 q^{64} -4.41825 q^{65} +3.72225 q^{66} +4.54673 q^{67} -3.77230 q^{68} +0.430954 q^{69} -1.13523 q^{70} -6.63312 q^{71} -3.07686 q^{72} -0.951859 q^{73} +11.0336 q^{74} -4.07536 q^{75} -1.94820 q^{76} -3.15289 q^{77} -5.42451 q^{78} +10.3719 q^{79} -2.32706 q^{80} +1.00000 q^{81} -8.23446 q^{82} -5.68146 q^{83} +0.606227 q^{84} +5.98353 q^{85} -0.203178 q^{86} +0.690340 q^{87} -9.70103 q^{88} +6.78915 q^{89} +1.13523 q^{90} +4.59478 q^{91} -0.261256 q^{92} +5.00614 q^{93} +0.298330 q^{94} +3.09019 q^{95} +3.29668 q^{96} -10.2964 q^{97} +1.18058 q^{98} +3.15289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.18058	0.834797	0.417399	−	0.908723i	$-0.362942\pi$
$2$	1.18058	0.834797	0.417399	+	0.908723i	$0.362942\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.606227	−0.303114
$5$	0.961582	0.430032	0.215016	−	0.976610i	$-0.431020\pi$
$5$	0.961582	0.430032	0.215016	+	0.976610i	$0.431020\pi$
$6$	1.18058	0.481970
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.07686	−1.08784
$9$	1.00000	0.333333
$10$	1.13523	0.358990
$11$	3.15289	0.950633	0.475317	−	0.879815i	$-0.342334\pi$
$11$	3.15289	0.950633	0.475317	+	0.879815i	$0.342334\pi$
$12$	−0.606227	−0.175003
$13$	−4.59478	−1.27436	−0.637181	−	0.770714i	$-0.719900\pi$
$13$	−4.59478	−1.27436	−0.637181	+	0.770714i	$0.719900\pi$
$14$	−1.18058	−0.315524
$15$	0.961582	0.248279
$16$	−2.42003	−0.605009
$17$	6.22259	1.50920	0.754600	−	0.656185i	$-0.227831\pi$
$17$	6.22259	1.50920	0.754600	+	0.656185i	$0.227831\pi$
$18$	1.18058	0.278266
$19$	3.21365	0.737263	0.368631	−	0.929576i	$-0.379826\pi$
$19$	3.21365	0.737263	0.368631	+	0.929576i	$0.379826\pi$
$20$	−0.582937	−0.130349
$21$	−1.00000	−0.218218
$22$	3.72225	0.793586
$23$	0.430954	0.0898601	0.0449300	−	0.998990i	$-0.485694\pi$
$23$	0.430954	0.0898601	0.0449300	+	0.998990i	$0.485694\pi$
$24$	−3.07686	−0.628062
$25$	−4.07536	−0.815072
$26$	−5.42451	−1.06383
$27$	1.00000	0.192450
$28$	0.606227	0.114566
$29$	0.690340	0.128193	0.0640965	−	0.997944i	$-0.479583\pi$
$29$	0.690340	0.128193	0.0640965	+	0.997944i	$0.479583\pi$
$30$	1.13523	0.207263
$31$	5.00614	0.899129	0.449565	−	0.893248i	$-0.351579\pi$
$31$	5.00614	0.899129	0.449565	+	0.893248i	$0.351579\pi$
$32$	3.29668	0.582776
$33$	3.15289	0.548848
$34$	7.34628	1.25988
$35$	−0.961582	−0.162537
$36$	−0.606227	−0.101038
$37$	9.34586	1.53645	0.768225	−	0.640180i	$-0.221140\pi$
$37$	9.34586	1.53645	0.768225	+	0.640180i	$0.221140\pi$
$38$	3.79398	0.615465
$39$	−4.59478	−0.735753
$40$	−2.95866	−0.467805
$41$	−6.97492	−1.08930	−0.544650	−	0.838664i	$-0.683337\pi$
$41$	−6.97492	−1.08930	−0.544650	+	0.838664i	$0.683337\pi$
$42$	−1.18058	−0.182168
$43$	−0.172100	−0.0262450	−0.0131225	−	0.999914i	$-0.504177\pi$
$43$	−0.172100	−0.0262450	−0.0131225	+	0.999914i	$0.504177\pi$
$44$	−1.91137	−0.288150
$45$	0.961582	0.143344
$46$	0.508776	0.0750150
$47$	0.252698	0.0368597	0.0184299	−	0.999830i	$-0.494133\pi$
$47$	0.252698	0.0368597	0.0184299	+	0.999830i	$0.494133\pi$
$48$	−2.42003	−0.349302
$49$	1.00000	0.142857
$50$	−4.81130	−0.680420
$51$	6.22259	0.871337
$52$	2.78548	0.386276
$53$	−2.60045	−0.357200	−0.178600	−	0.983922i	$-0.557157\pi$
$53$	−2.60045	−0.357200	−0.178600	+	0.983922i	$0.557157\pi$
$54$	1.18058	0.160657
$55$	3.03176	0.408803
$56$	3.07686	0.411163
$57$	3.21365	0.425659
$58$	0.815003	0.107015
$59$	11.4050	1.48480	0.742402	−	0.669955i	$-0.233687\pi$
$59$	11.4050	1.48480	0.742402	+	0.669955i	$0.233687\pi$
$60$	−0.582937	−0.0752568
$61$	10.9994	1.40832	0.704162	−	0.710040i	$-0.251323\pi$
$61$	10.9994	1.40832	0.704162	+	0.710040i	$0.251323\pi$
$62$	5.91016	0.750591
$63$	−1.00000	−0.125988
$64$	8.73207	1.09151
$65$	−4.41825	−0.548017
$66$	3.72225	0.458177
$67$	4.54673	0.555472	0.277736	−	0.960657i	$-0.410416\pi$
$67$	4.54673	0.555472	0.277736	+	0.960657i	$0.410416\pi$
$68$	−3.77230	−0.457459
$69$	0.430954	0.0518807
$70$	−1.13523	−0.135685
$71$	−6.63312	−0.787206	−0.393603	−	0.919280i	$-0.628772\pi$
$71$	−6.63312	−0.787206	−0.393603	+	0.919280i	$0.628772\pi$
$72$	−3.07686	−0.362612
$73$	−0.951859	−0.111407	−0.0557033	−	0.998447i	$-0.517740\pi$
$73$	−0.951859	−0.111407	−0.0557033	+	0.998447i	$0.517740\pi$
$74$	11.0336	1.28262
$75$	−4.07536	−0.470582
$76$	−1.94820	−0.223474
$77$	−3.15289	−0.359306
$78$	−5.42451	−0.614205
$79$	10.3719	1.16693	0.583466	−	0.812138i	$-0.301696\pi$
$79$	10.3719	1.16693	0.583466	+	0.812138i	$0.301696\pi$
$80$	−2.32706	−0.260173
$81$	1.00000	0.111111
$82$	−8.23446	−0.909344
$83$	−5.68146	−0.623621	−0.311811	−	0.950144i	$-0.600935\pi$
$83$	−5.68146	−0.623621	−0.311811	+	0.950144i	$0.600935\pi$
$84$	0.606227	0.0661448
$85$	5.98353	0.649005
$86$	−0.203178	−0.0219092
$87$	0.690340	0.0740122
$88$	−9.70103	−1.03413
$89$	6.78915	0.719649	0.359824	−	0.933020i	$-0.382837\pi$
$89$	6.78915	0.719649	0.359824	+	0.933020i	$0.382837\pi$
$90$	1.13523	0.119663
$91$	4.59478	0.481664
$92$	−0.261256	−0.0272378
$93$	5.00614	0.519113
$94$	0.298330	0.0307704
$95$	3.09019	0.317047
$96$	3.29668	0.336466
$97$	−10.2964	−1.04544	−0.522719	−	0.852505i	$-0.675082\pi$
$97$	−10.2964	−1.04544	−0.522719	+	0.852505i	$0.675082\pi$
$98$	1.18058	0.119257
$99$	3.15289	0.316878
$100$	2.47059	0.247059
$101$	4.11763	0.409719	0.204860	−	0.978791i	$-0.434326\pi$
$101$	4.11763	0.409719	0.204860	+	0.978791i	$0.434326\pi$
$102$	7.34628	0.727390
$103$	16.0897	1.58536	0.792682	−	0.609635i	$-0.208684\pi$
$103$	16.0897	1.58536	0.792682	+	0.609635i	$0.208684\pi$
$104$	14.1375	1.38630
$105$	−0.961582	−0.0938408
$106$	−3.07005	−0.298189
$107$	2.36427	0.228563	0.114281	−	0.993448i	$-0.463543\pi$
$107$	2.36427	0.228563	0.114281	+	0.993448i	$0.463543\pi$
$108$	−0.606227	−0.0583342
$109$	13.8090	1.32267	0.661333	−	0.750093i	$-0.269991\pi$
$109$	13.8090	1.32267	0.661333	+	0.750093i	$0.269991\pi$
$110$	3.57925	0.341268
$111$	9.34586	0.887070
$112$	2.42003	0.228672
$113$	0.737324	0.0693616	0.0346808	−	0.999398i	$-0.488959\pi$
$113$	0.737324	0.0693616	0.0346808	+	0.999398i	$0.488959\pi$
$114$	3.79398	0.355339
$115$	0.414397	0.0386427
$116$	−0.418503	−0.0388570
$117$	−4.59478	−0.424787
$118$	13.4645	1.23951
$119$	−6.22259	−0.570424
$120$	−2.95866	−0.270087
$121$	−1.05926	−0.0962963
$122$	12.9856	1.17566
$123$	−6.97492	−0.628907
$124$	−3.03486	−0.272538
$125$	−8.72670	−0.780540
$126$	−1.18058	−0.105175
$127$	3.82137	0.339092	0.169546	−	0.985522i	$-0.445770\pi$
$127$	3.82137	0.339092	0.169546	+	0.985522i	$0.445770\pi$
$128$	3.71556	0.328412
$129$	−0.172100	−0.0151526
$130$	−5.21611	−0.457483
$131$	−0.762411	−0.0666122	−0.0333061	−	0.999445i	$-0.510604\pi$
$131$	−0.762411	−0.0666122	−0.0333061	+	0.999445i	$0.510604\pi$
$132$	−1.91137	−0.166363
$133$	−3.21365	−0.278659
$134$	5.36779	0.463706
$135$	0.961582	0.0827598
$136$	−19.1461	−1.64176
$137$	10.5749	0.903474	0.451737	−	0.892151i	$-0.350804\pi$
$137$	10.5749	0.903474	0.451737	+	0.892151i	$0.350804\pi$
$138$	0.508776	0.0433099
$139$	−9.36955	−0.794715	−0.397357	−	0.917664i	$-0.630073\pi$
$139$	−9.36955	−0.794715	−0.397357	+	0.917664i	$0.630073\pi$
$140$	0.582937	0.0492672
$141$	0.252698	0.0212810
$142$	−7.83094	−0.657158
$143$	−14.4868	−1.21145
$144$	−2.42003	−0.201670
$145$	0.663818	0.0551271
$146$	−1.12375	−0.0930020
$147$	1.00000	0.0824786
$148$	−5.66571	−0.465719
$149$	−9.54870	−0.782260	−0.391130	−	0.920335i	$-0.627916\pi$
$149$	−9.54870	−0.782260	−0.391130	+	0.920335i	$0.627916\pi$
$150$	−4.81130	−0.392841
$151$	2.34953	0.191202	0.0956010	−	0.995420i	$-0.469523\pi$
$151$	2.34953	0.191202	0.0956010	+	0.995420i	$0.469523\pi$
$152$	−9.88797	−0.802021
$153$	6.22259	0.503067
$154$	−3.72225	−0.299947
$155$	4.81381	0.386655
$156$	2.78548	0.223017
$157$	12.6897	1.01275	0.506375	−	0.862313i	$-0.330985\pi$
$157$	12.6897	1.01275	0.506375	+	0.862313i	$0.330985\pi$
$158$	12.2449	0.974152
$159$	−2.60045	−0.206229
$160$	3.17003	0.250613
$161$	−0.430954	−0.0339639
$162$	1.18058	0.0927553
$163$	−7.60963	−0.596032	−0.298016	−	0.954561i	$-0.596325\pi$
$163$	−7.60963	−0.596032	−0.298016	+	0.954561i	$0.596325\pi$
$164$	4.22839	0.330181
$165$	3.03176	0.236023
$166$	−6.70743	−0.520597
$167$	7.07583	0.547544	0.273772	−	0.961795i	$-0.411729\pi$
$167$	7.07583	0.547544	0.273772	+	0.961795i	$0.411729\pi$
$168$	3.07686	0.237385
$169$	8.11198	0.623998
$170$	7.06405	0.541788
$171$	3.21365	0.245754
$172$	0.104332	0.00795521
$173$	10.6999	0.813496	0.406748	−	0.913541i	$-0.366663\pi$
$173$	10.6999	0.813496	0.406748	+	0.913541i	$0.366663\pi$
$174$	0.815003	0.0617852
$175$	4.07536	0.308068
$176$	−7.63011	−0.575141
$177$	11.4050	0.857252
$178$	8.01515	0.600761
$179$	14.3393	1.07177	0.535883	−	0.844292i	$-0.319979\pi$
$179$	14.3393	1.07177	0.535883	+	0.844292i	$0.319979\pi$
$180$	−0.582937	−0.0434495
$181$	−12.4081	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$181$	−12.4081	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$182$	5.42451	0.402091
$183$	10.9994	0.813096
$184$	−1.32599	−0.0977530
$185$	8.98681	0.660723
$186$	5.91016	0.433354
$187$	19.6192	1.43470
$188$	−0.153192	−0.0111727
$189$	−1.00000	−0.0727393
$190$	3.64822	0.264670
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	8.73207	0.630183
$193$	−14.6447	−1.05415	−0.527075	−	0.849819i	$-0.676711\pi$
$193$	−14.6447	−1.05415	−0.527075	+	0.849819i	$0.676711\pi$
$194$	−12.1557	−0.872729
$195$	−4.41825	−0.316398
$196$	−0.606227	−0.0433019
$197$	−21.1487	−1.50678	−0.753390	−	0.657574i	$-0.771583\pi$
$197$	−21.1487	−1.50678	−0.753390	+	0.657574i	$0.771583\pi$
$198$	3.72225	0.264529
$199$	10.9426	0.775698	0.387849	−	0.921723i	$-0.373218\pi$
$199$	10.9426	0.775698	0.387849	+	0.921723i	$0.373218\pi$
$200$	12.5393	0.886665
$201$	4.54673	0.320702
$202$	4.86119	0.342032
$203$	−0.690340	−0.0484524
$204$	−3.77230	−0.264114
$205$	−6.70696	−0.468434
$206$	18.9952	1.32346
$207$	0.430954	0.0299534
$208$	11.1195	0.771000
$209$	10.1323	0.700866
$210$	−1.13523	−0.0783380
$211$	−20.2707	−1.39549	−0.697746	−	0.716345i	$-0.745814\pi$
$211$	−20.2707	−1.39549	−0.697746	+	0.716345i	$0.745814\pi$
$212$	1.57646	0.108272
$213$	−6.63312	−0.454494
$214$	2.79122	0.190804
$215$	−0.165488	−0.0112862
$216$	−3.07686	−0.209354
$217$	−5.00614	−0.339839
$218$	16.3027	1.10416
$219$	−0.951859	−0.0643206
$220$	−1.83794	−0.123914
$221$	−28.5914	−1.92327
$222$	11.0336	0.740524
$223$	−7.57937	−0.507552	−0.253776	−	0.967263i	$-0.581673\pi$
$223$	−7.57937	−0.507552	−0.253776	+	0.967263i	$0.581673\pi$
$224$	−3.29668	−0.220269
$225$	−4.07536	−0.271691
$226$	0.870472	0.0579029
$227$	−9.18389	−0.609556	−0.304778	−	0.952423i	$-0.598582\pi$
$227$	−9.18389	−0.609556	−0.304778	+	0.952423i	$0.598582\pi$
$228$	−1.94820	−0.129023
$229$	−19.3917	−1.28144	−0.640719	−	0.767775i	$-0.721364\pi$
$229$	−19.3917	−1.28144	−0.640719	+	0.767775i	$0.721364\pi$
$230$	0.489230	0.0322589
$231$	−3.15289	−0.207445
$232$	−2.12408	−0.139453
$233$	0.417554	0.0273549	0.0136774	−	0.999906i	$-0.495646\pi$
$233$	0.417554	0.0273549	0.0136774	+	0.999906i	$0.495646\pi$
$234$	−5.42451	−0.354611
$235$	0.242989	0.0158509
$236$	−6.91402	−0.450064
$237$	10.3719	0.673728
$238$	−7.34628	−0.476188
$239$	1.96307	0.126981	0.0634903	−	0.997982i	$-0.479777\pi$
$239$	1.96307	0.126981	0.0634903	+	0.997982i	$0.479777\pi$
$240$	−2.32706	−0.150211
$241$	25.2173	1.62439	0.812196	−	0.583385i	$-0.198272\pi$
$241$	25.2173	1.62439	0.812196	+	0.583385i	$0.198272\pi$
$242$	−1.25054	−0.0803879
$243$	1.00000	0.0641500
$244$	−6.66811	−0.426882
$245$	0.961582	0.0614332
$246$	−8.23446	−0.525010
$247$	−14.7660	−0.939539
$248$	−15.4032	−0.978105
$249$	−5.68146	−0.360048
$250$	−10.3026	−0.651592
$251$	−18.3504	−1.15827	−0.579135	−	0.815232i	$-0.696609\pi$
$251$	−18.3504	−1.15827	−0.579135	+	0.815232i	$0.696609\pi$
$252$	0.606227	0.0381887
$253$	1.35875	0.0854240
$254$	4.51144	0.283073
$255$	5.98353	0.374703
$256$	−13.0776	−0.817351
$257$	−5.25253	−0.327644	−0.163822	−	0.986490i	$-0.552382\pi$
$257$	−5.25253	−0.327644	−0.163822	+	0.986490i	$0.552382\pi$
$258$	−0.203178	−0.0126493
$259$	−9.34586	−0.580724
$260$	2.67846	0.166111
$261$	0.690340	0.0427310
$262$	−0.900088	−0.0556076
$263$	27.4023	1.68970	0.844849	−	0.535005i	$-0.179690\pi$
$263$	27.4023	1.68970	0.844849	+	0.535005i	$0.179690\pi$
$264$	−9.70103	−0.597057
$265$	−2.50055	−0.153607
$266$	−3.79398	−0.232624
$267$	6.78915	0.415490
$268$	−2.75635	−0.168371
$269$	−5.64077	−0.343924	−0.171962	−	0.985104i	$-0.555011\pi$
$269$	−5.64077	−0.343924	−0.171962	+	0.985104i	$0.555011\pi$
$270$	1.13523	0.0690876
$271$	13.4218	0.815317	0.407659	−	0.913134i	$-0.366345\pi$
$271$	13.4218	0.815317	0.407659	+	0.913134i	$0.366345\pi$
$272$	−15.0589	−0.913079
$273$	4.59478	0.278089
$274$	12.4845	0.754218
$275$	−12.8492	−0.774835
$276$	−0.261256	−0.0157258
$277$	−11.4264	−0.686546	−0.343273	−	0.939236i	$-0.611536\pi$
$277$	−11.4264	−0.686546	−0.343273	+	0.939236i	$0.611536\pi$
$278$	−11.0615	−0.663426
$279$	5.00614	0.299710
$280$	2.95866	0.176813
$281$	−7.66601	−0.457316	−0.228658	−	0.973507i	$-0.573434\pi$
$281$	−7.66601	−0.457316	−0.228658	+	0.973507i	$0.573434\pi$
$282$	0.298330	0.0177653
$283$	−11.6113	−0.690218	−0.345109	−	0.938563i	$-0.612158\pi$
$283$	−11.6113	−0.690218	−0.345109	+	0.938563i	$0.612158\pi$
$284$	4.02118	0.238613
$285$	3.09019	0.183047
$286$	−17.1029	−1.01132
$287$	6.97492	0.411717
$288$	3.29668	0.194259
$289$	21.7206	1.27768
$290$	0.783692	0.0460200
$291$	−10.2964	−0.603584
$292$	0.577043	0.0337689
$293$	25.9862	1.51813	0.759065	−	0.651015i	$-0.225656\pi$
$293$	25.9862	1.51813	0.759065	+	0.651015i	$0.225656\pi$
$294$	1.18058	0.0688529
$295$	10.9668	0.638514
$296$	−28.7559	−1.67141
$297$	3.15289	0.182949
$298$	−11.2730	−0.653029
$299$	−1.98014	−0.114514
$300$	2.47059	0.142640
$301$	0.172100	0.00991967
$302$	2.77381	0.159615
$303$	4.11763	0.236551
$304$	−7.77715	−0.446050
$305$	10.5768	0.605625
$306$	7.34628	0.419959
$307$	−3.05629	−0.174432	−0.0872159	−	0.996189i	$-0.527797\pi$
$307$	−3.05629	−0.174432	−0.0872159	+	0.996189i	$0.527797\pi$
$308$	1.91137	0.108910
$309$	16.0897	0.915311
$310$	5.68310	0.322778
$311$	−28.3547	−1.60785	−0.803925	−	0.594731i	$-0.797258\pi$
$311$	−28.3547	−1.60785	−0.803925	+	0.594731i	$0.797258\pi$
$312$	14.1375	0.800378
$313$	−17.1124	−0.967248	−0.483624	−	0.875276i	$-0.660680\pi$
$313$	−17.1124	−0.967248	−0.483624	+	0.875276i	$0.660680\pi$
$314$	14.9813	0.845442
$315$	−0.961582	−0.0541790
$316$	−6.28774	−0.353713
$317$	−0.665530	−0.0373799	−0.0186899	−	0.999825i	$-0.505950\pi$
$317$	−0.665530	−0.0373799	−0.0186899	+	0.999825i	$0.505950\pi$
$318$	−3.07005	−0.172160
$319$	2.17657	0.121864
$320$	8.39660	0.469384
$321$	2.36427	0.131961
$322$	−0.508776	−0.0283530
$323$	19.9973	1.11268
$324$	−0.606227	−0.0336793
$325$	18.7254	1.03870
$326$	−8.98379	−0.497566
$327$	13.8090	0.763641
$328$	21.4609	1.18498
$329$	−0.252698	−0.0139317
$330$	3.57925	0.197031
$331$	−1.49730	−0.0822991	−0.0411495	−	0.999153i	$-0.513102\pi$
$331$	−1.49730	−0.0822991	−0.0411495	+	0.999153i	$0.513102\pi$
$332$	3.44425	0.189028
$333$	9.34586	0.512150
$334$	8.35360	0.457089
$335$	4.37206	0.238871
$336$	2.42003	0.132024
$337$	6.61620	0.360407	0.180204	−	0.983629i	$-0.442324\pi$
$337$	6.61620	0.360407	0.180204	+	0.983629i	$0.442324\pi$
$338$	9.57685	0.520912
$339$	0.737324	0.0400460
$340$	−3.62738	−0.196722
$341$	15.7838	0.854742
$342$	3.79398	0.205155
$343$	−1.00000	−0.0539949
$344$	0.529528	0.0285502
$345$	0.414397	0.0223104
$346$	12.6321	0.679104
$347$	−25.1786	−1.35166	−0.675829	−	0.737058i	$-0.736214\pi$
$347$	−25.1786	−1.35166	−0.675829	+	0.737058i	$0.736214\pi$
$348$	−0.418503	−0.0224341
$349$	−19.9657	−1.06874	−0.534370	−	0.845251i	$-0.679451\pi$
$349$	−19.9657	−1.06874	−0.534370	+	0.845251i	$0.679451\pi$
$350$	4.81130	0.257175
$351$	−4.59478	−0.245251
$352$	10.3941	0.554006
$353$	18.5358	0.986563	0.493282	−	0.869870i	$-0.335797\pi$
$353$	18.5358	0.986563	0.493282	+	0.869870i	$0.335797\pi$
$354$	13.4645	0.715631
$355$	−6.37829	−0.338524
$356$	−4.11577	−0.218135
$357$	−6.22259	−0.329334
$358$	16.9287	0.894708
$359$	−15.6750	−0.827294	−0.413647	−	0.910437i	$-0.635745\pi$
$359$	−15.6750	−0.827294	−0.413647	+	0.910437i	$0.635745\pi$
$360$	−2.95866	−0.155935
$361$	−8.67243	−0.456444
$362$	−14.6488	−0.769924
$363$	−1.05926	−0.0555967
$364$	−2.78548	−0.145999
$365$	−0.915290	−0.0479085
$366$	12.9856	0.678770
$367$	11.3301	0.591428	0.295714	−	0.955277i	$-0.404442\pi$
$367$	11.3301	0.591428	0.295714	+	0.955277i	$0.404442\pi$
$368$	−1.04292	−0.0543661
$369$	−6.97492	−0.363100
$370$	10.6097	0.551570
$371$	2.60045	0.135009
$372$	−3.03486	−0.157350
$373$	−5.94763	−0.307957	−0.153978	−	0.988074i	$-0.549209\pi$
$373$	−5.94763	−0.307957	−0.153978	+	0.988074i	$0.549209\pi$
$374$	23.1620	1.19768
$375$	−8.72670	−0.450645
$376$	−0.777516	−0.0400973
$377$	−3.17196	−0.163364
$378$	−1.18058	−0.0607226
$379$	36.6915	1.88471	0.942357	−	0.334609i	$-0.108604\pi$
$379$	36.6915	1.88471	0.942357	+	0.334609i	$0.108604\pi$
$380$	−1.87336	−0.0961012
$381$	3.82137	0.195775
$382$	−1.18058	−0.0604038
$383$	−21.2504	−1.08585	−0.542923	−	0.839783i	$-0.682682\pi$
$383$	−21.2504	−1.08585	−0.542923	+	0.839783i	$0.682682\pi$
$384$	3.71556	0.189609
$385$	−3.03176	−0.154513
$386$	−17.2893	−0.880002
$387$	−0.172100	−0.00874833
$388$	6.24194	0.316886
$389$	−25.3655	−1.28608	−0.643041	−	0.765832i	$-0.722327\pi$
$389$	−25.3655	−1.28608	−0.643041	+	0.765832i	$0.722327\pi$
$390$	−5.21611	−0.264128
$391$	2.68165	0.135617
$392$	−3.07686	−0.155405
$393$	−0.762411	−0.0384585
$394$	−24.9677	−1.25786
$395$	9.97345	0.501819
$396$	−1.91137	−0.0960499
$397$	−17.1383	−0.860145	−0.430072	−	0.902794i	$-0.641512\pi$
$397$	−17.1383	−0.860145	−0.430072	+	0.902794i	$0.641512\pi$
$398$	12.9186	0.647551
$399$	−3.21365	−0.160884
$400$	9.86251	0.493126
$401$	10.1525	0.506993	0.253497	−	0.967336i	$-0.418419\pi$
$401$	10.1525	0.506993	0.253497	+	0.967336i	$0.418419\pi$
$402$	5.36779	0.267721
$403$	−23.0021	−1.14582
$404$	−2.49622	−0.124191
$405$	0.961582	0.0477814
$406$	−0.815003	−0.0404479
$407$	29.4665	1.46060
$408$	−19.1461	−0.947871
$409$	4.54025	0.224501	0.112250	−	0.993680i	$-0.464194\pi$
$409$	4.54025	0.224501	0.112250	+	0.993680i	$0.464194\pi$
$410$	−7.91811	−0.391048
$411$	10.5749	0.521621
$412$	−9.75401	−0.480545
$413$	−11.4050	−0.561203
$414$	0.508776	0.0250050
$415$	−5.46319	−0.268177
$416$	−15.1475	−0.742668
$417$	−9.36955	−0.458829
$418$	11.9620	0.585081
$419$	0.721687	0.0352567	0.0176284	−	0.999845i	$-0.494388\pi$
$419$	0.721687	0.0352567	0.0176284	+	0.999845i	$0.494388\pi$
$420$	0.582937	0.0284444
$421$	28.7884	1.40306	0.701530	−	0.712640i	$-0.252501\pi$
$421$	28.7884	1.40306	0.701530	+	0.712640i	$0.252501\pi$
$422$	−23.9312	−1.16495
$423$	0.252698	0.0122866
$424$	8.00124	0.388574
$425$	−25.3593	−1.23011
$426$	−7.83094	−0.379410
$427$	−10.9994	−0.532296
$428$	−1.43329	−0.0692805
$429$	−14.4868	−0.699431
$430$	−0.195372	−0.00942168
$431$	1.99043	0.0958756	0.0479378	−	0.998850i	$-0.484735\pi$
$431$	1.99043	0.0958756	0.0479378	+	0.998850i	$0.484735\pi$
$432$	−2.42003	−0.116434
$433$	−17.6397	−0.847709	−0.423855	−	0.905730i	$-0.639323\pi$
$433$	−17.6397	−0.847709	−0.423855	+	0.905730i	$0.639323\pi$
$434$	−5.91016	−0.283697
$435$	0.663818	0.0318277
$436$	−8.37141	−0.400918
$437$	1.38494	0.0662505
$438$	−1.12375	−0.0536947
$439$	24.6063	1.17440	0.587198	−	0.809444i	$-0.300231\pi$
$439$	24.6063	1.17440	0.587198	+	0.809444i	$0.300231\pi$
$440$	−9.32833	−0.444711
$441$	1.00000	0.0476190
$442$	−33.7545	−1.60554
$443$	1.94606	0.0924599	0.0462299	−	0.998931i	$-0.485279\pi$
$443$	1.94606	0.0924599	0.0462299	+	0.998931i	$0.485279\pi$
$444$	−5.66571	−0.268883
$445$	6.52833	0.309472
$446$	−8.94807	−0.423703
$447$	−9.54870	−0.451638
$448$	−8.73207	−0.412551
$449$	−17.8497	−0.842378	−0.421189	−	0.906973i	$-0.638387\pi$
$449$	−17.8497	−0.842378	−0.421189	+	0.906973i	$0.638387\pi$
$450$	−4.81130	−0.226807
$451$	−21.9912	−1.03552
$452$	−0.446986	−0.0210245
$453$	2.34953	0.110391
$454$	−10.8423	−0.508856
$455$	4.41825	0.207131
$456$	−9.88797	−0.463047
$457$	−0.231363	−0.0108227	−0.00541135	−	0.999985i	$-0.501722\pi$
$457$	−0.231363	−0.0108227	−0.00541135	+	0.999985i	$0.501722\pi$
$458$	−22.8935	−1.06974
$459$	6.22259	0.290446
$460$	−0.251219	−0.0117131
$461$	23.3128	1.08579	0.542893	−	0.839802i	$-0.317329\pi$
$461$	23.3128	1.08579	0.542893	+	0.839802i	$0.317329\pi$
$462$	−3.72225	−0.173175
$463$	16.5938	0.771180	0.385590	−	0.922670i	$-0.373998\pi$
$463$	16.5938	0.771180	0.385590	+	0.922670i	$0.373998\pi$
$464$	−1.67065	−0.0775578
$465$	4.81381	0.223235
$466$	0.492957	0.0228358
$467$	−0.0592315	−0.00274091	−0.00137045	−	0.999999i	$-0.500436\pi$
$467$	−0.0592315	−0.00274091	−0.00137045	+	0.999999i	$0.500436\pi$
$468$	2.78548	0.128759
$469$	−4.54673	−0.209949
$470$	0.286869	0.0132323
$471$	12.6897	0.584712
$472$	−35.0916	−1.61522
$473$	−0.542613	−0.0249494
$474$	12.2449	0.562427
$475$	−13.0968	−0.600922
$476$	3.77230	0.172903
$477$	−2.60045	−0.119067
$478$	2.31757	0.106003
$479$	−28.0795	−1.28298	−0.641492	−	0.767129i	$-0.721684\pi$
$479$	−28.0795	−1.28298	−0.641492	+	0.767129i	$0.721684\pi$
$480$	3.17003	0.144691
$481$	−42.9421	−1.95799
$482$	29.7711	1.35604
$483$	−0.430954	−0.0196091
$484$	0.642152	0.0291887
$485$	−9.90080	−0.449572
$486$	1.18058	0.0535523
$487$	−9.00723	−0.408157	−0.204078	−	0.978955i	$-0.565420\pi$
$487$	−9.00723	−0.408157	−0.204078	+	0.978955i	$0.565420\pi$
$488$	−33.8435	−1.53202
$489$	−7.60963	−0.344120
$490$	1.13523	0.0512843
$491$	34.0376	1.53610	0.768048	−	0.640393i	$-0.221228\pi$
$491$	34.0376	1.53610	0.768048	+	0.640393i	$0.221228\pi$
$492$	4.22839	0.190630
$493$	4.29571	0.193469
$494$	−17.4325	−0.784325
$495$	3.03176	0.136268
$496$	−12.1150	−0.543981
$497$	6.63312	0.297536
$498$	−6.70743	−0.300567
$499$	16.8826	0.755769	0.377885	−	0.925853i	$-0.376652\pi$
$499$	16.8826	0.755769	0.377885	+	0.925853i	$0.376652\pi$
$500$	5.29036	0.236592
$501$	7.07583	0.316125
$502$	−21.6642	−0.966920
$503$	−11.0860	−0.494300	−0.247150	−	0.968977i	$-0.579494\pi$
$503$	−11.0860	−0.494300	−0.247150	+	0.968977i	$0.579494\pi$
$504$	3.07686	0.137054
$505$	3.95943	0.176192
$506$	1.60412	0.0713117
$507$	8.11198	0.360266
$508$	−2.31662	−0.102783
$509$	20.5264	0.909815	0.454907	−	0.890539i	$-0.349672\pi$
$509$	20.5264	0.909815	0.454907	+	0.890539i	$0.349672\pi$
$510$	7.06405	0.312801
$511$	0.951859	0.0421077
$512$	−22.8703	−1.01073
$513$	3.21365	0.141886
$514$	−6.20104	−0.273516
$515$	15.4716	0.681758
$516$	0.104332	0.00459294
$517$	0.796728	0.0350401
$518$	−11.0336	−0.484786
$519$	10.6999	0.469672
$520$	13.5944	0.596152
$521$	−15.6281	−0.684681	−0.342340	−	0.939576i	$-0.611220\pi$
$521$	−15.6281	−0.684681	−0.342340	+	0.939576i	$0.611220\pi$
$522$	0.815003	0.0356717
$523$	−40.7504	−1.78189	−0.890945	−	0.454111i	$-0.849957\pi$
$523$	−40.7504	−1.78189	−0.890945	+	0.454111i	$0.849957\pi$
$524$	0.462194	0.0201910
$525$	4.07536	0.177863
$526$	32.3507	1.41056
$527$	31.1512	1.35697
$528$	−7.63011	−0.332058
$529$	−22.8143	−0.991925
$530$	−2.95210	−0.128231
$531$	11.4050	0.494935
$532$	1.94820	0.0844653
$533$	32.0482	1.38816
$534$	8.01515	0.346850
$535$	2.27344	0.0982894
$536$	−13.9897	−0.604262
$537$	14.3393	0.618785
$538$	−6.65938	−0.287106
$539$	3.15289	0.135805
$540$	−0.582937	−0.0250856
$541$	20.5273	0.882538	0.441269	−	0.897375i	$-0.354528\pi$
$541$	20.5273	0.882538	0.441269	+	0.897375i	$0.354528\pi$
$542$	15.8455	0.680625
$543$	−12.4081	−0.532483
$544$	20.5139	0.879526
$545$	13.2785	0.568789
$546$	5.42451	0.232148
$547$	−24.1724	−1.03354	−0.516769	−	0.856125i	$-0.672865\pi$
$547$	−24.1724	−1.03354	−0.516769	+	0.856125i	$0.672865\pi$
$548$	−6.41079	−0.273855
$549$	10.9994	0.469441
$550$	−15.1695	−0.646830
$551$	2.21851	0.0945119
$552$	−1.32599	−0.0564377
$553$	−10.3719	−0.441059
$554$	−13.4898	−0.573127
$555$	8.98681	0.381469
$556$	5.68008	0.240889
$557$	−21.6720	−0.918274	−0.459137	−	0.888366i	$-0.651841\pi$
$557$	−21.6720	−0.918274	−0.459137	+	0.888366i	$0.651841\pi$
$558$	5.91016	0.250197
$559$	0.790761	0.0334456
$560$	2.32706	0.0983363
$561$	19.6192	0.828322
$562$	−9.05035	−0.381766
$563$	−21.4041	−0.902077	−0.451038	−	0.892505i	$-0.648946\pi$
$563$	−21.4041	−0.902077	−0.451038	+	0.892505i	$0.648946\pi$
$564$	−0.153192	−0.00645055
$565$	0.708998	0.0298278
$566$	−13.7080	−0.576192
$567$	−1.00000	−0.0419961
$568$	20.4092	0.856351
$569$	38.7146	1.62300	0.811500	−	0.584353i	$-0.198652\pi$
$569$	38.7146	1.62300	0.811500	+	0.584353i	$0.198652\pi$
$570$	3.64822	0.152807
$571$	−19.6612	−0.822797	−0.411399	−	0.911455i	$-0.634960\pi$
$571$	−19.6612	−0.822797	−0.411399	+	0.911455i	$0.634960\pi$
$572$	8.78232	0.367207
$573$	−1.00000	−0.0417756
$574$	8.23446	0.343700
$575$	−1.75629	−0.0732425
$576$	8.73207	0.363836
$577$	0.826745	0.0344178	0.0172089	−	0.999852i	$-0.494522\pi$
$577$	0.826745	0.0344178	0.0172089	+	0.999852i	$0.494522\pi$
$578$	25.6430	1.06661
$579$	−14.6447	−0.608614
$580$	−0.402425	−0.0167098
$581$	5.68146	0.235707
$582$	−12.1557	−0.503870
$583$	−8.19895	−0.339566
$584$	2.92874	0.121192
$585$	−4.41825	−0.182672
$586$	30.6788	1.26733
$587$	21.1966	0.874877	0.437438	−	0.899248i	$-0.355886\pi$
$587$	21.1966	0.874877	0.437438	+	0.899248i	$0.355886\pi$
$588$	−0.606227	−0.0250004
$589$	16.0880	0.662894
$590$	12.9472	0.533029
$591$	−21.1487	−0.869940
$592$	−22.6173	−0.929566
$593$	−9.93068	−0.407804	−0.203902	−	0.978991i	$-0.565362\pi$
$593$	−9.93068	−0.407804	−0.203902	+	0.978991i	$0.565362\pi$
$594$	3.72225	0.152726
$595$	−5.98353	−0.245301
$596$	5.78868	0.237114
$597$	10.9426	0.447850
$598$	−2.33771	−0.0955962
$599$	−6.55520	−0.267838	−0.133919	−	0.990992i	$-0.542756\pi$
$599$	−6.55520	−0.267838	−0.133919	+	0.990992i	$0.542756\pi$
$600$	12.5393	0.511916
$601$	−22.8028	−0.930144	−0.465072	−	0.885273i	$-0.653972\pi$
$601$	−22.8028	−0.930144	−0.465072	+	0.885273i	$0.653972\pi$
$602$	0.203178	0.00828092
$603$	4.54673	0.185157
$604$	−1.42435	−0.0579559
$605$	−1.01856	−0.0414105
$606$	4.86119	0.197472
$607$	−35.2723	−1.43166	−0.715829	−	0.698276i	$-0.753951\pi$
$607$	−35.2723	−1.43166	−0.715829	+	0.698276i	$0.753951\pi$
$608$	10.5944	0.429659
$609$	−0.690340	−0.0279740
$610$	12.4867	0.505574
$611$	−1.16109	−0.0469726
$612$	−3.77230	−0.152486
$613$	31.7362	1.28181	0.640907	−	0.767619i	$-0.278559\pi$
$613$	31.7362	1.28181	0.640907	+	0.767619i	$0.278559\pi$
$614$	−3.60820	−0.145615
$615$	−6.70696	−0.270451
$616$	9.70103	0.390865
$617$	1.38227	0.0556480	0.0278240	−	0.999613i	$-0.491142\pi$
$617$	1.38227	0.0556480	0.0278240	+	0.999613i	$0.491142\pi$
$618$	18.9952	0.764099
$619$	−19.5496	−0.785763	−0.392882	−	0.919589i	$-0.628522\pi$
$619$	−19.5496	−0.785763	−0.392882	+	0.919589i	$0.628522\pi$
$620$	−2.91826	−0.117200
$621$	0.430954	0.0172936
$622$	−33.4751	−1.34223
$623$	−6.78915	−0.272002
$624$	11.1195	0.445137
$625$	11.9854	0.479415
$626$	−20.2025	−0.807456
$627$	10.1323	0.404645
$628$	−7.69286	−0.306979
$629$	58.1555	2.31881
$630$	−1.13523	−0.0452285
$631$	20.7961	0.827881	0.413940	−	0.910304i	$-0.364152\pi$
$631$	20.7961	0.827881	0.413940	+	0.910304i	$0.364152\pi$
$632$	−31.9130	−1.26943
$633$	−20.2707	−0.805688
$634$	−0.785713	−0.0312046
$635$	3.67456	0.145821
$636$	1.57646	0.0625109
$637$	−4.59478	−0.182052
$638$	2.56962	0.101732
$639$	−6.63312	−0.262402
$640$	3.57281	0.141228
$641$	18.3639	0.725332	0.362666	−	0.931919i	$-0.381867\pi$
$641$	18.3639	0.725332	0.362666	+	0.931919i	$0.381867\pi$
$642$	2.79122	0.110160
$643$	22.8842	0.902466	0.451233	−	0.892406i	$-0.350984\pi$
$643$	22.8842	0.902466	0.451233	+	0.892406i	$0.350984\pi$
$644$	0.261256	0.0102949
$645$	−0.165488	−0.00651609
$646$	23.6084	0.928860
$647$	16.6862	0.656004	0.328002	−	0.944677i	$-0.393625\pi$
$647$	16.6862	0.656004	0.328002	+	0.944677i	$0.393625\pi$
$648$	−3.07686	−0.120871
$649$	35.9587	1.41150
$650$	22.1068	0.867101
$651$	−5.00614	−0.196206
$652$	4.61317	0.180666
$653$	0.311562	0.0121924	0.00609618	−	0.999981i	$-0.498060\pi$
$653$	0.311562	0.0121924	0.00609618	+	0.999981i	$0.498060\pi$
$654$	16.3027	0.637485
$655$	−0.733120	−0.0286454
$656$	16.8795	0.659036
$657$	−0.951859	−0.0371355
$658$	−0.298330	−0.0116301
$659$	−11.4908	−0.447620	−0.223810	−	0.974633i	$-0.571849\pi$
$659$	−11.4908	−0.447620	−0.223810	+	0.974633i	$0.571849\pi$
$660$	−1.83794	−0.0715416
$661$	−32.4502	−1.26217	−0.631083	−	0.775716i	$-0.717389\pi$
$661$	−32.4502	−1.26217	−0.631083	+	0.775716i	$0.717389\pi$
$662$	−1.76769	−0.0687030
$663$	−28.5914	−1.11040
$664$	17.4811	0.678397
$665$	−3.09019	−0.119832
$666$	11.0336	0.427541
$667$	0.297505	0.0115194
$668$	−4.28956	−0.165968
$669$	−7.57937	−0.293035
$670$	5.16157	0.199409
$671$	34.6798	1.33880
$672$	−3.29668	−0.127172
$673$	−33.4628	−1.28990	−0.644949	−	0.764226i	$-0.723121\pi$
$673$	−33.4628	−1.28990	−0.644949	+	0.764226i	$0.723121\pi$
$674$	7.81096	0.300867
$675$	−4.07536	−0.156861
$676$	−4.91770	−0.189142
$677$	−10.7714	−0.413977	−0.206989	−	0.978343i	$-0.566366\pi$
$677$	−10.7714	−0.413977	−0.206989	+	0.978343i	$0.566366\pi$
$678$	0.870472	0.0334303
$679$	10.2964	0.395138
$680$	−18.4105	−0.706011
$681$	−9.18389	−0.351927
$682$	18.6341	0.713537
$683$	−31.1096	−1.19038	−0.595188	−	0.803586i	$-0.702923\pi$
$683$	−31.1096	−1.19038	−0.595188	+	0.803586i	$0.702923\pi$
$684$	−1.94820	−0.0744914
$685$	10.1686	0.388523
$686$	−1.18058	−0.0450748
$687$	−19.3917	−0.739839
$688$	0.416488	0.0158784
$689$	11.9485	0.455202
$690$	0.489230	0.0186247
$691$	−1.11168	−0.0422904	−0.0211452	−	0.999776i	$-0.506731\pi$
$691$	−1.11168	−0.0422904	−0.0211452	+	0.999776i	$0.506731\pi$
$692$	−6.48655	−0.246582
$693$	−3.15289	−0.119769
$694$	−29.7254	−1.12836
$695$	−9.00959	−0.341753
$696$	−2.12408	−0.0805132
$697$	−43.4021	−1.64397
$698$	−23.5711	−0.892180
$699$	0.417554	0.0157933
$700$	−2.47059	−0.0933797
$701$	43.3441	1.63708	0.818542	−	0.574446i	$-0.194783\pi$
$701$	43.3441	1.63708	0.818542	+	0.574446i	$0.194783\pi$
$702$	−5.42451	−0.204735
$703$	30.0344	1.13277
$704$	27.5313	1.03762
$705$	0.242989	0.00915151
$706$	21.8831	0.823580
$707$	−4.11763	−0.154859
$708$	−6.91402	−0.259845
$709$	24.9350	0.936452	0.468226	−	0.883609i	$-0.344893\pi$
$709$	24.9350	0.936452	0.468226	+	0.883609i	$0.344893\pi$
$710$	−7.53009	−0.282599
$711$	10.3719	0.388977
$712$	−20.8893	−0.782860
$713$	2.15742	0.0807958
$714$	−7.34628	−0.274928
$715$	−13.9303	−0.520963
$716$	−8.69285	−0.324867
$717$	1.96307	0.0733123
$718$	−18.5056	−0.690623
$719$	26.9446	1.00486	0.502432	−	0.864617i	$-0.332439\pi$
$719$	26.9446	1.00486	0.502432	+	0.864617i	$0.332439\pi$
$720$	−2.32706	−0.0867244
$721$	−16.0897	−0.599212
$722$	−10.2385	−0.381038
$723$	25.2173	0.937843
$724$	7.52214	0.279558
$725$	−2.81339	−0.104487
$726$	−1.25054	−0.0464120
$727$	−31.2600	−1.15937	−0.579685	−	0.814841i	$-0.696824\pi$
$727$	−31.2600	−1.15937	−0.579685	+	0.814841i	$0.696824\pi$
$728$	−14.1375	−0.523971
$729$	1.00000	0.0370370
$730$	−1.08057	−0.0399939
$731$	−1.07091	−0.0396089
$732$	−6.66811	−0.246460
$733$	−21.0970	−0.779236	−0.389618	−	0.920977i	$-0.627393\pi$
$733$	−21.0970	−0.779236	−0.389618	+	0.920977i	$0.627393\pi$
$734$	13.3761	0.493723
$735$	0.961582	0.0354685
$736$	1.42072	0.0523683
$737$	14.3354	0.528050
$738$	−8.23446	−0.303115
$739$	−18.4925	−0.680257	−0.340128	−	0.940379i	$-0.610471\pi$
$739$	−18.4925	−0.680257	−0.340128	+	0.940379i	$0.610471\pi$
$740$	−5.44805	−0.200274
$741$	−14.7660	−0.542443
$742$	3.07005	0.112705
$743$	−16.5353	−0.606622	−0.303311	−	0.952892i	$-0.598092\pi$
$743$	−16.5353	−0.606622	−0.303311	+	0.952892i	$0.598092\pi$
$744$	−15.4032	−0.564709
$745$	−9.18186	−0.336397
$746$	−7.02166	−0.257081
$747$	−5.68146	−0.207874
$748$	−11.8937	−0.434876
$749$	−2.36427	−0.0863886
$750$	−10.3026	−0.376197
$751$	22.5696	0.823577	0.411789	−	0.911279i	$-0.364904\pi$
$751$	22.5696	0.823577	0.411789	+	0.911279i	$0.364904\pi$
$752$	−0.611537	−0.0223004
$753$	−18.3504	−0.668727
$754$	−3.74476	−0.136376
$755$	2.25927	0.0822231
$756$	0.606227	0.0220483
$757$	5.46931	0.198785	0.0993927	−	0.995048i	$-0.468310\pi$
$757$	5.46931	0.198785	0.0993927	+	0.995048i	$0.468310\pi$
$758$	43.3173	1.57335
$759$	1.35875	0.0493196
$760$	−9.50809	−0.344895
$761$	−40.7618	−1.47761	−0.738806	−	0.673918i	$-0.764610\pi$
$761$	−40.7618	−1.47761	−0.738806	+	0.673918i	$0.764610\pi$
$762$	4.51144	0.163432
$763$	−13.8090	−0.499920
$764$	0.606227	0.0219325
$765$	5.98353	0.216335
$766$	−25.0878	−0.906461
$767$	−52.4034	−1.89218
$768$	−13.0776	−0.471898
$769$	−52.6129	−1.89727	−0.948635	−	0.316372i	$-0.897535\pi$
$769$	−52.6129	−1.89727	−0.948635	+	0.316372i	$0.897535\pi$
$770$	−3.57925	−0.128987
$771$	−5.25253	−0.189165
$772$	8.87803	0.319527
$773$	48.7378	1.75298	0.876488	−	0.481423i	$-0.159880\pi$
$773$	48.7378	1.75298	0.876488	+	0.481423i	$0.159880\pi$
$774$	−0.203178	−0.00730308
$775$	−20.4018	−0.732855
$776$	31.6805	1.13726
$777$	−9.34586	−0.335281
$778$	−29.9460	−1.07362
$779$	−22.4150	−0.803100
$780$	2.67846	0.0959044
$781$	−20.9135	−0.748345
$782$	3.16591	0.113213
$783$	0.690340	0.0246707
$784$	−2.42003	−0.0864298
$785$	12.2022	0.435516
$786$	−0.900088	−0.0321051
$787$	−50.6128	−1.80415	−0.902075	−	0.431579i	$-0.857957\pi$
$787$	−50.6128	−1.80415	−0.902075	+	0.431579i	$0.857957\pi$
$788$	12.8209	0.456726
$789$	27.4023	0.975548
$790$	11.7745	0.418917
$791$	−0.737324	−0.0262162
$792$	−9.70103	−0.344711
$793$	−50.5396	−1.79471
$794$	−20.2331	−0.718046
$795$	−2.50055	−0.0886853
$796$	−6.63368	−0.235125
$797$	−13.5147	−0.478715	−0.239357	−	0.970932i	$-0.576937\pi$
$797$	−13.5147	−0.478715	−0.239357	+	0.970932i	$0.576937\pi$
$798$	−3.79398	−0.134305
$799$	1.57243	0.0556287
$800$	−13.4352	−0.475005
$801$	6.78915	0.239883
$802$	11.9859	0.423237
$803$	−3.00111	−0.105907
$804$	−2.75635	−0.0972091
$805$	−0.414397	−0.0146056
$806$	−27.1559	−0.956524
$807$	−5.64077	−0.198564
$808$	−12.6694	−0.445707
$809$	51.1158	1.79713	0.898567	−	0.438835i	$-0.144609\pi$
$809$	51.1158	1.79713	0.898567	+	0.438835i	$0.144609\pi$
$810$	1.13523	0.0398878
$811$	−5.42536	−0.190510	−0.0952551	−	0.995453i	$-0.530367\pi$
$811$	−5.42536	−0.190510	−0.0952551	+	0.995453i	$0.530367\pi$
$812$	0.418503	0.0146866
$813$	13.4218	0.470724
$814$	34.7876	1.21931
$815$	−7.31728	−0.256313
$816$	−15.0589	−0.527166
$817$	−0.553069	−0.0193494
$818$	5.36013	0.187413
$819$	4.59478	0.160555
$820$	4.06594	0.141989
$821$	31.2722	1.09141	0.545704	−	0.837978i	$-0.316262\pi$
$821$	31.2722	1.09141	0.545704	+	0.837978i	$0.316262\pi$
$822$	12.4845	0.435448
$823$	27.2215	0.948880	0.474440	−	0.880288i	$-0.342651\pi$
$823$	27.2215	0.948880	0.474440	+	0.880288i	$0.342651\pi$
$824$	−49.5058	−1.72462
$825$	−12.8492	−0.447351
$826$	−13.4645	−0.468491
$827$	−36.2858	−1.26178	−0.630891	−	0.775872i	$-0.717310\pi$
$827$	−36.2858	−1.26178	−0.630891	+	0.775872i	$0.717310\pi$
$828$	−0.261256	−0.00907927
$829$	16.1802	0.561961	0.280981	−	0.959713i	$-0.409340\pi$
$829$	16.1802	0.561961	0.280981	+	0.959713i	$0.409340\pi$
$830$	−6.44974	−0.223874
$831$	−11.4264	−0.396377
$832$	−40.1219	−1.39098
$833$	6.22259	0.215600
$834$	−11.0615	−0.383029
$835$	6.80399	0.235462
$836$	−6.14248	−0.212442
$837$	5.00614	0.173038
$838$	0.852010	0.0294322
$839$	17.7516	0.612854	0.306427	−	0.951894i	$-0.400866\pi$
$839$	17.7516	0.612854	0.306427	+	0.951894i	$0.400866\pi$
$840$	2.95866	0.102083
$841$	−28.5234	−0.983567
$842$	33.9870	1.17127
$843$	−7.66601	−0.264032
$844$	12.2886	0.422993
$845$	7.80033	0.268339
$846$	0.298330	0.0102568
$847$	1.05926	0.0363966
$848$	6.29318	0.216109
$849$	−11.6113	−0.398497
$850$	−29.9387	−1.02689
$851$	4.02763	0.138066
$852$	4.02118	0.137763
$853$	9.64737	0.330320	0.165160	−	0.986267i	$-0.447186\pi$
$853$	9.64737	0.330320	0.165160	+	0.986267i	$0.447186\pi$
$854$	−12.9856	−0.444359
$855$	3.09019	0.105682
$856$	−7.27454	−0.248639
$857$	38.6340	1.31971	0.659856	−	0.751392i	$-0.270617\pi$
$857$	38.6340	1.31971	0.659856	+	0.751392i	$0.270617\pi$
$858$	−17.1029	−0.583883
$859$	−33.9671	−1.15894	−0.579471	−	0.814993i	$-0.696741\pi$
$859$	−33.9671	−1.15894	−0.579471	+	0.814993i	$0.696741\pi$
$860$	0.100323	0.00342100
$861$	6.97492	0.237705
$862$	2.34986	0.0800367
$863$	34.0535	1.15920	0.579598	−	0.814903i	$-0.303210\pi$
$863$	34.0535	1.15920	0.579598	+	0.814903i	$0.303210\pi$
$864$	3.29668	0.112155
$865$	10.2888	0.349829
$866$	−20.8251	−0.707665
$867$	21.7206	0.737672
$868$	3.03486	0.103010
$869$	32.7016	1.10932
$870$	0.783692	0.0265696
$871$	−20.8912	−0.707872
$872$	−42.4885	−1.43884
$873$	−10.2964	−0.348479
$874$	1.63503	0.0553057
$875$	8.72670	0.295016
$876$	0.577043	0.0194965
$877$	13.6078	0.459503	0.229752	−	0.973249i	$-0.426209\pi$
$877$	13.6078	0.459503	0.229752	+	0.973249i	$0.426209\pi$
$878$	29.0498	0.980382
$879$	25.9862	0.876493
$880$	−7.33698	−0.247329
$881$	10.5563	0.355651	0.177825	−	0.984062i	$-0.443094\pi$
$881$	10.5563	0.355651	0.177825	+	0.984062i	$0.443094\pi$
$882$	1.18058	0.0397523
$883$	−4.40583	−0.148268	−0.0741340	−	0.997248i	$-0.523619\pi$
$883$	−4.40583	−0.148268	−0.0741340	+	0.997248i	$0.523619\pi$
$884$	17.3329	0.582968
$885$	10.9668	0.368646
$886$	2.29748	0.0771853
$887$	−42.2158	−1.41747	−0.708733	−	0.705476i	$-0.750733\pi$
$887$	−42.2158	−1.41747	−0.708733	+	0.705476i	$0.750733\pi$
$888$	−28.7559	−0.964986
$889$	−3.82137	−0.128165
$890$	7.70722	0.258347
$891$	3.15289	0.105626
$892$	4.59482	0.153846
$893$	0.812082	0.0271753
$894$	−11.2730	−0.377026
$895$	13.7884	0.460894
$896$	−3.71556	−0.124128
$897$	−1.98014	−0.0661148
$898$	−21.0730	−0.703214
$899$	3.45594	0.115262
$900$	2.47059	0.0823531
$901$	−16.1816	−0.539086
$902$	−25.9624	−0.864453
$903$	0.172100	0.00572713
$904$	−2.26865	−0.0754541
$905$	−11.9314	−0.396614
$906$	2.77381	0.0921537
$907$	2.34162	0.0777522	0.0388761	−	0.999244i	$-0.487622\pi$
$907$	2.34162	0.0777522	0.0388761	+	0.999244i	$0.487622\pi$
$908$	5.56752	0.184765
$909$	4.11763	0.136573
$910$	5.21611	0.172912
$911$	40.7983	1.35171	0.675853	−	0.737036i	$-0.263775\pi$
$911$	40.7983	1.35171	0.675853	+	0.737036i	$0.263775\pi$
$912$	−7.77715	−0.257527
$913$	−17.9130	−0.592835
$914$	−0.273143	−0.00903476
$915$	10.5768	0.349657
$916$	11.7558	0.388421
$917$	0.762411	0.0251770
$918$	7.34628	0.242463
$919$	20.1038	0.663165	0.331582	−	0.943426i	$-0.392418\pi$
$919$	20.1038	0.663165	0.331582	+	0.943426i	$0.392418\pi$
$920$	−1.27504	−0.0420370
$921$	−3.05629	−0.100708
$922$	27.5227	0.906411
$923$	30.4777	1.00319
$924$	1.91137	0.0628794
$925$	−38.0878	−1.25232
$926$	19.5903	0.643779
$927$	16.0897	0.528455
$928$	2.27583	0.0747078
$929$	−33.6552	−1.10419	−0.552096	−	0.833781i	$-0.686172\pi$
$929$	−33.6552	−1.10419	−0.552096	+	0.833781i	$0.686172\pi$
$930$	5.68310	0.186356
$931$	3.21365	0.105323
$932$	−0.253133	−0.00829163
$933$	−28.3547	−0.928292
$934$	−0.0699276	−0.00228810
$935$	18.8654	0.616966
$936$	14.1375	0.462099
$937$	46.2013	1.50933	0.754666	−	0.656109i	$-0.227799\pi$
$937$	46.2013	1.50933	0.754666	+	0.656109i	$0.227799\pi$
$938$	−5.36779	−0.175265
$939$	−17.1124	−0.558441
$940$	−0.147307	−0.00480461
$941$	−24.2911	−0.791866	−0.395933	−	0.918279i	$-0.629579\pi$
$941$	−24.2911	−0.791866	−0.395933	+	0.918279i	$0.629579\pi$
$942$	14.9813	0.488116
$943$	−3.00587	−0.0978846
$944$	−27.6005	−0.898319
$945$	−0.961582	−0.0312803
$946$	−0.640599	−0.0208277
$947$	−3.30199	−0.107300	−0.0536501	−	0.998560i	$-0.517086\pi$
$947$	−3.30199	−0.107300	−0.0536501	+	0.998560i	$0.517086\pi$
$948$	−6.28774	−0.204216
$949$	4.37358	0.141972
$950$	−15.4618	−0.501648
$951$	−0.665530	−0.0215813
$952$	19.1461	0.620528
$953$	30.2116	0.978651	0.489325	−	0.872101i	$-0.337243\pi$
$953$	30.2116	0.978651	0.489325	+	0.872101i	$0.337243\pi$
$954$	−3.07005	−0.0993964
$955$	−0.961582	−0.0311161
$956$	−1.19007	−0.0384895
$957$	2.17657	0.0703585
$958$	−33.1501	−1.07103
$959$	−10.5749	−0.341481
$960$	8.39660	0.270999
$961$	−5.93856	−0.191566
$962$	−50.6967	−1.63453
$963$	2.36427	0.0761876
$964$	−15.2874	−0.492375
$965$	−14.0821	−0.453319
$966$	−0.508776	−0.0163696
$967$	−45.0742	−1.44949	−0.724744	−	0.689018i	$-0.758042\pi$
$967$	−45.0742	−1.44949	−0.724744	+	0.689018i	$0.758042\pi$
$968$	3.25920	0.104755
$969$	19.9973	0.642404
$970$	−11.6887	−0.375302
$971$	24.4625	0.785040	0.392520	−	0.919743i	$-0.371603\pi$
$971$	24.4625	0.785040	0.392520	+	0.919743i	$0.371603\pi$
$972$	−0.606227	−0.0194447
$973$	9.36955	0.300374
$974$	−10.6338	−0.340728
$975$	18.7254	0.599692
$976$	−26.6188	−0.852048
$977$	9.60464	0.307280	0.153640	−	0.988127i	$-0.450900\pi$
$977$	9.60464	0.307280	0.153640	+	0.988127i	$0.450900\pi$
$978$	−8.98379	−0.287270
$979$	21.4055	0.684122
$980$	−0.582937	−0.0186212
$981$	13.8090	0.440888
$982$	40.1842	1.28233
$983$	−16.5962	−0.529336	−0.264668	−	0.964340i	$-0.585262\pi$
$983$	−16.5962	−0.529336	−0.264668	+	0.964340i	$0.585262\pi$
$984$	21.4609	0.684148
$985$	−20.3362	−0.647965
$986$	5.07143	0.161507
$987$	−0.252698	−0.00804345
$988$	8.95156	0.284787
$989$	−0.0741671	−0.00235838
$990$	3.57925	0.113756
$991$	−24.4002	−0.775097	−0.387549	−	0.921849i	$-0.626678\pi$
$991$	−24.4002	−0.775097	−0.387549	+	0.921849i	$0.626678\pi$
$992$	16.5036	0.523991
$993$	−1.49730	−0.0475154
$994$	7.83094	0.248382
$995$	10.5222	0.333575
$996$	3.44425	0.109135
$997$	24.2622	0.768393	0.384196	−	0.923251i	$-0.374479\pi$
$997$	24.2622	0.768393	0.384196	+	0.923251i	$0.374479\pi$
$998$	19.9313	0.630914
$999$	9.34586	0.295690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.19	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.19	✓	29	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.18058 q^{2} +1.00000 q^{3} -0.606227 q^{4} +0.961582 q^{5} +1.18058 q^{6} -1.00000 q^{7} -3.07686 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.18058 q^{2} +1.00000 q^{3} -0.606227 q^{4} +0.961582 q^{5} +1.18058 q^{6} -1.00000 q^{7} -3.07686 q^{8} +1.00000 q^{9} +1.13523 q^{10} +3.15289 q^{11} -0.606227 q^{12} -4.59478 q^{13} -1.18058 q^{14} +0.961582 q^{15} -2.42003 q^{16} +6.22259 q^{17} +1.18058 q^{18} +3.21365 q^{19} -0.582937 q^{20} -1.00000 q^{21} +3.72225 q^{22} +0.430954 q^{23} -3.07686 q^{24} -4.07536 q^{25} -5.42451 q^{26} +1.00000 q^{27} +0.606227 q^{28} +0.690340 q^{29} +1.13523 q^{30} +5.00614 q^{31} +3.29668 q^{32} +3.15289 q^{33} +7.34628 q^{34} -0.961582 q^{35} -0.606227 q^{36} +9.34586 q^{37} +3.79398 q^{38} -4.59478 q^{39} -2.95866 q^{40} -6.97492 q^{41} -1.18058 q^{42} -0.172100 q^{43} -1.91137 q^{44} +0.961582 q^{45} +0.508776 q^{46} +0.252698 q^{47} -2.42003 q^{48} +1.00000 q^{49} -4.81130 q^{50} +6.22259 q^{51} +2.78548 q^{52} -2.60045 q^{53} +1.18058 q^{54} +3.03176 q^{55} +3.07686 q^{56} +3.21365 q^{57} +0.815003 q^{58} +11.4050 q^{59} -0.582937 q^{60} +10.9994 q^{61} +5.91016 q^{62} -1.00000 q^{63} +8.73207 q^{64} -4.41825 q^{65} +3.72225 q^{66} +4.54673 q^{67} -3.77230 q^{68} +0.430954 q^{69} -1.13523 q^{70} -6.63312 q^{71} -3.07686 q^{72} -0.951859 q^{73} +11.0336 q^{74} -4.07536 q^{75} -1.94820 q^{76} -3.15289 q^{77} -5.42451 q^{78} +10.3719 q^{79} -2.32706 q^{80} +1.00000 q^{81} -8.23446 q^{82} -5.68146 q^{83} +0.606227 q^{84} +5.98353 q^{85} -0.203178 q^{86} +0.690340 q^{87} -9.70103 q^{88} +6.78915 q^{89} +1.13523 q^{90} +4.59478 q^{91} -0.261256 q^{92} +5.00614 q^{93} +0.298330 q^{94} +3.09019 q^{95} +3.29668 q^{96} -10.2964 q^{97} +1.18058 q^{98} +3.15289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more