LMFDB - Embedded newform 4029.2.a.k.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46449 q^{2} +1.00000 q^{3} +4.07369 q^{4} +0.00469045 q^{5} +2.46449 q^{6} +4.87243 q^{7} +5.11058 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.46449 q^{2} +1.00000 q^{3} +4.07369 q^{4} +0.00469045 q^{5} +2.46449 q^{6} +4.87243 q^{7} +5.11058 q^{8} +1.00000 q^{9} +0.0115595 q^{10} -2.31839 q^{11} +4.07369 q^{12} -4.34750 q^{13} +12.0080 q^{14} +0.00469045 q^{15} +4.44756 q^{16} +1.00000 q^{17} +2.46449 q^{18} +6.19689 q^{19} +0.0191074 q^{20} +4.87243 q^{21} -5.71365 q^{22} +0.574459 q^{23} +5.11058 q^{24} -4.99998 q^{25} -10.7144 q^{26} +1.00000 q^{27} +19.8488 q^{28} +1.99576 q^{29} +0.0115595 q^{30} -1.79911 q^{31} +0.739803 q^{32} -2.31839 q^{33} +2.46449 q^{34} +0.0228539 q^{35} +4.07369 q^{36} +4.56763 q^{37} +15.2722 q^{38} -4.34750 q^{39} +0.0239709 q^{40} +4.02994 q^{41} +12.0080 q^{42} -4.88385 q^{43} -9.44441 q^{44} +0.00469045 q^{45} +1.41575 q^{46} +12.1785 q^{47} +4.44756 q^{48} +16.7405 q^{49} -12.3224 q^{50} +1.00000 q^{51} -17.7104 q^{52} +9.71702 q^{53} +2.46449 q^{54} -0.0108743 q^{55} +24.9009 q^{56} +6.19689 q^{57} +4.91852 q^{58} -3.03708 q^{59} +0.0191074 q^{60} -13.4619 q^{61} -4.43387 q^{62} +4.87243 q^{63} -7.07189 q^{64} -0.0203917 q^{65} -5.71365 q^{66} +5.89516 q^{67} +4.07369 q^{68} +0.574459 q^{69} +0.0563230 q^{70} -13.1393 q^{71} +5.11058 q^{72} -10.7622 q^{73} +11.2569 q^{74} -4.99998 q^{75} +25.2442 q^{76} -11.2962 q^{77} -10.7144 q^{78} +1.00000 q^{79} +0.0208611 q^{80} +1.00000 q^{81} +9.93172 q^{82} -0.853080 q^{83} +19.8488 q^{84} +0.00469045 q^{85} -12.0362 q^{86} +1.99576 q^{87} -11.8483 q^{88} -15.1784 q^{89} +0.0115595 q^{90} -21.1829 q^{91} +2.34017 q^{92} -1.79911 q^{93} +30.0137 q^{94} +0.0290662 q^{95} +0.739803 q^{96} -1.53244 q^{97} +41.2568 q^{98} -2.31839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.46449	1.74265	0.871327	−	0.490702i	$-0.163260\pi$
$2$	2.46449	1.74265	0.871327	+	0.490702i	$0.163260\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.07369	2.03684
$5$	0.00469045	0.00209763	0.00104882	−	0.999999i	$-0.499666\pi$
$5$	0.00469045	0.00209763	0.00104882	+	0.999999i	$0.499666\pi$
$6$	2.46449	1.00612
$7$	4.87243	1.84160	0.920802	−	0.390030i	$-0.127535\pi$
$7$	4.87243	1.84160	0.920802	+	0.390030i	$0.127535\pi$
$8$	5.11058	1.80686
$9$	1.00000	0.333333
$10$	0.0115595	0.00365545
$11$	−2.31839	−0.699022	−0.349511	−	0.936932i	$-0.613652\pi$
$11$	−2.31839	−0.699022	−0.349511	+	0.936932i	$0.613652\pi$
$12$	4.07369	1.17597
$13$	−4.34750	−1.20578	−0.602890	−	0.797824i	$-0.705984\pi$
$13$	−4.34750	−1.20578	−0.602890	+	0.797824i	$0.705984\pi$
$14$	12.0080	3.20928
$15$	0.00469045	0.00121107
$16$	4.44756	1.11189
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.46449	0.580885
$19$	6.19689	1.42166	0.710832	−	0.703361i	$-0.248318\pi$
$19$	6.19689	1.42166	0.710832	+	0.703361i	$0.248318\pi$
$20$	0.0191074	0.00427255
$21$	4.87243	1.06325
$22$	−5.71365	−1.21815
$23$	0.574459	0.119783	0.0598915	−	0.998205i	$-0.480925\pi$
$23$	0.574459	0.119783	0.0598915	+	0.998205i	$0.480925\pi$
$24$	5.11058	1.04319
$25$	−4.99998	−0.999996
$26$	−10.7144	−2.10126
$27$	1.00000	0.192450
$28$	19.8488	3.75106
$29$	1.99576	0.370603	0.185301	−	0.982682i	$-0.440674\pi$
$29$	1.99576	0.370603	0.185301	+	0.982682i	$0.440674\pi$
$30$	0.0115595	0.00211047
$31$	−1.79911	−0.323129	−0.161564	−	0.986862i	$-0.551654\pi$
$31$	−1.79911	−0.323129	−0.161564	+	0.986862i	$0.551654\pi$
$32$	0.739803	0.130780
$33$	−2.31839	−0.403580
$34$	2.46449	0.422656
$35$	0.0228539	0.00386301
$36$	4.07369	0.678948
$37$	4.56763	0.750914	0.375457	−	0.926840i	$-0.377486\pi$
$37$	4.56763	0.750914	0.375457	+	0.926840i	$0.377486\pi$
$38$	15.2722	2.47747
$39$	−4.34750	−0.696157
$40$	0.0239709	0.00379013
$41$	4.02994	0.629371	0.314685	−	0.949196i	$-0.398101\pi$
$41$	4.02994	0.629371	0.314685	+	0.949196i	$0.398101\pi$
$42$	12.0080	1.85288
$43$	−4.88385	−0.744780	−0.372390	−	0.928076i	$-0.621462\pi$
$43$	−4.88385	−0.744780	−0.372390	+	0.928076i	$0.621462\pi$
$44$	−9.44441	−1.42380
$45$	0.00469045	0.000699210 0
$46$	1.41575	0.208740
$47$	12.1785	1.77641	0.888206	−	0.459445i	$-0.151952\pi$
$47$	12.1785	1.77641	0.888206	+	0.459445i	$0.151952\pi$
$48$	4.44756	0.641950
$49$	16.7405	2.39151
$50$	−12.3224	−1.74265
$51$	1.00000	0.140028
$52$	−17.7104	−2.45599
$53$	9.71702	1.33474	0.667368	−	0.744728i	$-0.267421\pi$
$53$	9.71702	1.33474	0.667368	+	0.744728i	$0.267421\pi$
$54$	2.46449	0.335374
$55$	−0.0108743	−0.00146629
$56$	24.9009	3.32752
$57$	6.19689	0.820799
$58$	4.91852	0.645833
$59$	−3.03708	−0.395394	−0.197697	−	0.980263i	$-0.563346\pi$
$59$	−3.03708	−0.395394	−0.197697	+	0.980263i	$0.563346\pi$
$60$	0.0191074	0.00246676
$61$	−13.4619	−1.72362	−0.861808	−	0.507235i	$-0.830668\pi$
$61$	−13.4619	−1.72362	−0.861808	+	0.507235i	$0.830668\pi$
$62$	−4.43387	−0.563102
$63$	4.87243	0.613868
$64$	−7.07189	−0.883987
$65$	−0.0203917	−0.00252928
$66$	−5.71365	−0.703301
$67$	5.89516	0.720209	0.360104	−	0.932912i	$-0.382741\pi$
$67$	5.89516	0.720209	0.360104	+	0.932912i	$0.382741\pi$
$68$	4.07369	0.494007
$69$	0.574459	0.0691568
$70$	0.0563230	0.00673189
$71$	−13.1393	−1.55934	−0.779672	−	0.626188i	$-0.784614\pi$
$71$	−13.1393	−1.55934	−0.779672	+	0.626188i	$0.784614\pi$
$72$	5.11058	0.602287
$73$	−10.7622	−1.25961	−0.629807	−	0.776751i	$-0.716866\pi$
$73$	−10.7622	−1.25961	−0.629807	+	0.776751i	$0.716866\pi$
$74$	11.2569	1.30858
$75$	−4.99998	−0.577348
$76$	25.2442	2.89571
$77$	−11.2962	−1.28732
$78$	−10.7144	−1.21316
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.0208611	0.00233234
$81$	1.00000	0.111111
$82$	9.93172	1.09678
$83$	−0.853080	−0.0936377	−0.0468189	−	0.998903i	$-0.514908\pi$
$83$	−0.853080	−0.0936377	−0.0468189	+	0.998903i	$0.514908\pi$
$84$	19.8488	2.16568
$85$	0.00469045	0.000508750 0
$86$	−12.0362	−1.29789
$87$	1.99576	0.213968
$88$	−11.8483	−1.26304
$89$	−15.1784	−1.60890	−0.804452	−	0.594018i	$-0.797541\pi$
$89$	−15.1784	−1.60890	−0.804452	+	0.594018i	$0.797541\pi$
$90$	0.0115595	0.00121848
$91$	−21.1829	−2.22057
$92$	2.34017	0.243979
$93$	−1.79911	−0.186559
$94$	30.0137	3.09567
$95$	0.0290662	0.00298213
$96$	0.739803	0.0755058
$97$	−1.53244	−0.155596	−0.0777980	−	0.996969i	$-0.524789\pi$
$97$	−1.53244	−0.155596	−0.0777980	+	0.996969i	$0.524789\pi$
$98$	41.2568	4.16757
$99$	−2.31839	−0.233007
$100$	−20.3684	−2.03684
$101$	−8.33395	−0.829259	−0.414630	−	0.909990i	$-0.636089\pi$
$101$	−8.33395	−0.829259	−0.414630	+	0.909990i	$0.636089\pi$
$102$	2.46449	0.244020
$103$	−13.5205	−1.33221	−0.666105	−	0.745858i	$-0.732040\pi$
$103$	−13.5205	−1.33221	−0.666105	+	0.745858i	$0.732040\pi$
$104$	−22.2182	−2.17868
$105$	0.0228539	0.00223031
$106$	23.9475	2.32598
$107$	−5.37067	−0.519202	−0.259601	−	0.965716i	$-0.583591\pi$
$107$	−5.37067	−0.519202	−0.259601	+	0.965716i	$0.583591\pi$
$108$	4.07369	0.391991
$109$	−12.2697	−1.17523	−0.587614	−	0.809141i	$-0.699933\pi$
$109$	−12.2697	−1.17523	−0.587614	+	0.809141i	$0.699933\pi$
$110$	−0.0267996	−0.00255524
$111$	4.56763	0.433541
$112$	21.6704	2.04766
$113$	11.5772	1.08909	0.544546	−	0.838731i	$-0.316702\pi$
$113$	11.5772	1.08909	0.544546	+	0.838731i	$0.316702\pi$
$114$	15.2722	1.43037
$115$	0.00269447	0.000251261 0
$116$	8.13010	0.754860
$117$	−4.34750	−0.401927
$118$	−7.48483	−0.689034
$119$	4.87243	0.446655
$120$	0.0239709	0.00218823
$121$	−5.62505	−0.511368
$122$	−33.1766	−3.00367
$123$	4.02994	0.363367
$124$	−7.32899	−0.658163
$125$	−0.0469044	−0.00419525
$126$	12.0080	1.06976
$127$	13.2277	1.17377	0.586883	−	0.809672i	$-0.300355\pi$
$127$	13.2277	1.17377	0.586883	+	0.809672i	$0.300355\pi$
$128$	−18.9082	−1.67126
$129$	−4.88385	−0.429999
$130$	−0.0502551	−0.00440766
$131$	2.87664	0.251333	0.125667	−	0.992073i	$-0.459893\pi$
$131$	2.87664	0.251333	0.125667	+	0.992073i	$0.459893\pi$
$132$	−9.44441	−0.822031
$133$	30.1939	2.61814
$134$	14.5285	1.25508
$135$	0.00469045	0.000403689 0
$136$	5.11058	0.438228
$137$	3.21352	0.274549	0.137275	−	0.990533i	$-0.456166\pi$
$137$	3.21352	0.274549	0.137275	+	0.990533i	$0.456166\pi$
$138$	1.41575	0.120516
$139$	7.14597	0.606113	0.303057	−	0.952973i	$-0.401993\pi$
$139$	7.14597	0.606113	0.303057	+	0.952973i	$0.401993\pi$
$140$	0.0930995	0.00786834
$141$	12.1785	1.02561
$142$	−32.3815	−2.71740
$143$	10.0792	0.842867
$144$	4.44756	0.370630
$145$	0.00936099	0.000777388 0
$146$	−26.5232	−2.19507
$147$	16.7405	1.38074
$148$	18.6071	1.52950
$149$	−0.599309	−0.0490973	−0.0245487	−	0.999699i	$-0.507815\pi$
$149$	−0.599309	−0.0490973	−0.0245487	+	0.999699i	$0.507815\pi$
$150$	−12.3224	−1.00612
$151$	−14.6686	−1.19371	−0.596856	−	0.802348i	$-0.703584\pi$
$151$	−14.6686	−1.19371	−0.596856	+	0.802348i	$0.703584\pi$
$152$	31.6697	2.56875
$153$	1.00000	0.0808452
$154$	−27.8393	−2.24336
$155$	−0.00843861	−0.000677805 0
$156$	−17.7104	−1.41796
$157$	13.4542	1.07376	0.536879	−	0.843659i	$-0.319603\pi$
$157$	13.4542	1.07376	0.536879	+	0.843659i	$0.319603\pi$
$158$	2.46449	0.196064
$159$	9.71702	0.770610
$160$	0.00347001	0.000274328 0
$161$	2.79901	0.220593
$162$	2.46449	0.193628
$163$	−17.3814	−1.36141	−0.680706	−	0.732556i	$-0.738327\pi$
$163$	−17.3814	−1.36141	−0.680706	+	0.732556i	$0.738327\pi$
$164$	16.4167	1.28193
$165$	−0.0108743	−0.000846563 0
$166$	−2.10240	−0.163178
$167$	−1.84431	−0.142717	−0.0713587	−	0.997451i	$-0.522733\pi$
$167$	−1.84431	−0.142717	−0.0713587	+	0.997451i	$0.522733\pi$
$168$	24.9009	1.92115
$169$	5.90077	0.453905
$170$	0.0115595	0.000886576 0
$171$	6.19689	0.473888
$172$	−19.8953	−1.51700
$173$	20.7273	1.57587	0.787935	−	0.615758i	$-0.211150\pi$
$173$	20.7273	1.57587	0.787935	+	0.615758i	$0.211150\pi$
$174$	4.91852	0.372872
$175$	−24.3620	−1.84160
$176$	−10.3112	−0.777236
$177$	−3.03708	−0.228281
$178$	−37.4069	−2.80376
$179$	17.0441	1.27394	0.636968	−	0.770890i	$-0.280188\pi$
$179$	17.0441	1.27394	0.636968	+	0.770890i	$0.280188\pi$
$180$	0.0191074	0.00142418
$181$	−10.4119	−0.773910	−0.386955	−	0.922099i	$-0.626473\pi$
$181$	−10.4119	−0.773910	−0.386955	+	0.922099i	$0.626473\pi$
$182$	−52.2049	−3.86969
$183$	−13.4619	−0.995130
$184$	2.93582	0.216431
$185$	0.0214242	0.00157514
$186$	−4.43387	−0.325107
$187$	−2.31839	−0.169538
$188$	49.6113	3.61828
$189$	4.87243	0.354417
$190$	0.0716332	0.00519682
$191$	4.27815	0.309556	0.154778	−	0.987949i	$-0.450534\pi$
$191$	4.27815	0.309556	0.154778	+	0.987949i	$0.450534\pi$
$192$	−7.07189	−0.510370
$193$	−2.32125	−0.167087	−0.0835436	−	0.996504i	$-0.526624\pi$
$193$	−2.32125	−0.167087	−0.0835436	+	0.996504i	$0.526624\pi$
$194$	−3.77669	−0.271150
$195$	−0.0203917	−0.00146028
$196$	68.1958	4.87113
$197$	17.8022	1.26836	0.634178	−	0.773187i	$-0.281339\pi$
$197$	17.8022	1.26836	0.634178	+	0.773187i	$0.281339\pi$
$198$	−5.71365	−0.406051
$199$	3.49045	0.247432	0.123716	−	0.992318i	$-0.460519\pi$
$199$	3.49045	0.247432	0.123716	+	0.992318i	$0.460519\pi$
$200$	−25.5528	−1.80685
$201$	5.89516	0.415813
$202$	−20.5389	−1.44511
$203$	9.72418	0.682504
$204$	4.07369	0.285215
$205$	0.0189022	0.00132019
$206$	−33.3210	−2.32158
$207$	0.574459	0.0399277
$208$	−19.3358	−1.34070
$209$	−14.3668	−0.993775
$210$	0.0563230	0.00388666
$211$	−7.86388	−0.541372	−0.270686	−	0.962668i	$-0.587250\pi$
$211$	−7.86388	−0.541372	−0.270686	+	0.962668i	$0.587250\pi$
$212$	39.5841	2.71865
$213$	−13.1393	−0.900288
$214$	−13.2359	−0.904790
$215$	−0.0229074	−0.00156227
$216$	5.11058	0.347731
$217$	−8.76601	−0.595075
$218$	−30.2386	−2.04802
$219$	−10.7622	−0.727239
$220$	−0.0442985	−0.00298660
$221$	−4.34750	−0.292445
$222$	11.2569	0.755511
$223$	−14.6473	−0.980857	−0.490428	−	0.871481i	$-0.663160\pi$
$223$	−14.6473	−0.980857	−0.490428	+	0.871481i	$0.663160\pi$
$224$	3.60464	0.240845
$225$	−4.99998	−0.333332
$226$	28.5319	1.89791
$227$	20.3316	1.34945	0.674727	−	0.738068i	$-0.264262\pi$
$227$	20.3316	1.34945	0.674727	+	0.738068i	$0.264262\pi$
$228$	25.2442	1.67184
$229$	5.74085	0.379366	0.189683	−	0.981845i	$-0.439254\pi$
$229$	5.74085	0.379366	0.189683	+	0.981845i	$0.439254\pi$
$230$	0.00664048	0.000437861 0
$231$	−11.2962	−0.743236
$232$	10.1995	0.669628
$233$	20.9789	1.37437	0.687185	−	0.726482i	$-0.258846\pi$
$233$	20.9789	1.37437	0.687185	+	0.726482i	$0.258846\pi$
$234$	−10.7144	−0.700419
$235$	0.0571225	0.00372626
$236$	−12.3721	−0.805355
$237$	1.00000	0.0649570
$238$	12.0080	0.778365
$239$	−3.07209	−0.198717	−0.0993586	−	0.995052i	$-0.531679\pi$
$239$	−3.07209	−0.198717	−0.0993586	+	0.995052i	$0.531679\pi$
$240$	0.0208611	0.00134658
$241$	−18.5259	−1.19336	−0.596678	−	0.802481i	$-0.703513\pi$
$241$	−18.5259	−1.19336	−0.596678	+	0.802481i	$0.703513\pi$
$242$	−13.8629	−0.891138
$243$	1.00000	0.0641500
$244$	−54.8395	−3.51074
$245$	0.0785206	0.00501650
$246$	9.93172	0.633224
$247$	−26.9410	−1.71421
$248$	−9.19446	−0.583849
$249$	−0.853080	−0.0540618
$250$	−0.115595	−0.00731088
$251$	−13.5742	−0.856795	−0.428398	−	0.903590i	$-0.640922\pi$
$251$	−13.5742	−0.856795	−0.428398	+	0.903590i	$0.640922\pi$
$252$	19.8488	1.25035
$253$	−1.33182	−0.0837310
$254$	32.5994	2.04547
$255$	0.00469045	0.000293727 0
$256$	−32.4552	−2.02845
$257$	−22.5898	−1.40912	−0.704558	−	0.709646i	$-0.748855\pi$
$257$	−22.5898	−1.40912	−0.704558	+	0.709646i	$0.748855\pi$
$258$	−12.0362	−0.749340
$259$	22.2555	1.38289
$260$	−0.0830695	−0.00515175
$261$	1.99576	0.123534
$262$	7.08943	0.437987
$263$	−10.6322	−0.655609	−0.327805	−	0.944746i	$-0.606309\pi$
$263$	−10.6322	−0.655609	−0.327805	+	0.944746i	$0.606309\pi$
$264$	−11.8483	−0.729214
$265$	0.0455772	0.00279978
$266$	74.4125	4.56252
$267$	−15.1784	−0.928901
$268$	24.0151	1.46695
$269$	26.7970	1.63384	0.816920	−	0.576751i	$-0.195680\pi$
$269$	26.7970	1.63384	0.816920	+	0.576751i	$0.195680\pi$
$270$	0.0115595	0.000703491 0
$271$	−20.2916	−1.23263	−0.616313	−	0.787501i	$-0.711374\pi$
$271$	−20.2916	−1.23263	−0.616313	+	0.787501i	$0.711374\pi$
$272$	4.44756	0.269673
$273$	−21.1829	−1.28205
$274$	7.91967	0.478445
$275$	11.5919	0.699019
$276$	2.34017	0.140862
$277$	0.556509	0.0334374	0.0167187	−	0.999860i	$-0.494678\pi$
$277$	0.556509	0.0334374	0.0167187	+	0.999860i	$0.494678\pi$
$278$	17.6111	1.05625
$279$	−1.79911	−0.107710
$280$	0.116796	0.00697992
$281$	−20.7701	−1.23904	−0.619520	−	0.784981i	$-0.712673\pi$
$281$	−20.7701	−1.23904	−0.619520	+	0.784981i	$0.712673\pi$
$282$	30.0137	1.78729
$283$	−15.0583	−0.895121	−0.447561	−	0.894254i	$-0.647707\pi$
$283$	−15.0583	−0.895121	−0.447561	+	0.894254i	$0.647707\pi$
$284$	−53.5253	−3.17614
$285$	0.0290662	0.00172173
$286$	24.8401	1.46883
$287$	19.6356	1.15905
$288$	0.739803	0.0435933
$289$	1.00000	0.0588235
$290$	0.0230700	0.00135472
$291$	−1.53244	−0.0898334
$292$	−43.8417	−2.56564
$293$	9.35642	0.546608	0.273304	−	0.961928i	$-0.411883\pi$
$293$	9.35642	0.546608	0.273304	+	0.961928i	$0.411883\pi$
$294$	41.2568	2.40615
$295$	−0.0142452	−0.000829390 0
$296$	23.3432	1.35680
$297$	−2.31839	−0.134527
$298$	−1.47699	−0.0855597
$299$	−2.49746	−0.144432
$300$	−20.3684	−1.17597
$301$	−23.7962	−1.37159
$302$	−36.1505	−2.08023
$303$	−8.33395	−0.478773
$304$	27.5611	1.58074
$305$	−0.0631422	−0.00361551
$306$	2.46449	0.140885
$307$	4.40847	0.251605	0.125802	−	0.992055i	$-0.459849\pi$
$307$	4.40847	0.251605	0.125802	+	0.992055i	$0.459849\pi$
$308$	−46.0172	−2.62207
$309$	−13.5205	−0.769152
$310$	−0.0207968	−0.00118118
$311$	−8.37756	−0.475048	−0.237524	−	0.971382i	$-0.576336\pi$
$311$	−8.37756	−0.475048	−0.237524	+	0.971382i	$0.576336\pi$
$312$	−22.2182	−1.25786
$313$	28.8881	1.63285	0.816427	−	0.577449i	$-0.195952\pi$
$313$	28.8881	1.63285	0.816427	+	0.577449i	$0.195952\pi$
$314$	33.1576	1.87119
$315$	0.0228539	0.00128767
$316$	4.07369	0.229163
$317$	−8.45405	−0.474827	−0.237413	−	0.971409i	$-0.576300\pi$
$317$	−8.45405	−0.474827	−0.237413	+	0.971409i	$0.576300\pi$
$318$	23.9475	1.34291
$319$	−4.62695	−0.259060
$320$	−0.0331703	−0.00185428
$321$	−5.37067	−0.299762
$322$	6.89812	0.384417
$323$	6.19689	0.344804
$324$	4.07369	0.226316
$325$	21.7374	1.20577
$326$	−42.8361	−2.37247
$327$	−12.2697	−0.678518
$328$	20.5953	1.13719
$329$	59.3387	3.27145
$330$	−0.0267996	−0.00147527
$331$	−27.1285	−1.49112	−0.745559	−	0.666439i	$-0.767818\pi$
$331$	−27.1285	−1.49112	−0.745559	+	0.666439i	$0.767818\pi$
$332$	−3.47518	−0.190725
$333$	4.56763	0.250305
$334$	−4.54529	−0.248707
$335$	0.0276509	0.00151073
$336$	21.6704	1.18222
$337$	10.1262	0.551608	0.275804	−	0.961214i	$-0.411056\pi$
$337$	10.1262	0.551608	0.275804	+	0.961214i	$0.411056\pi$
$338$	14.5424	0.791000
$339$	11.5772	0.628788
$340$	0.0191074	0.00103625
$341$	4.17103	0.225874
$342$	15.2722	0.825824
$343$	47.4601	2.56261
$344$	−24.9593	−1.34571
$345$	0.00269447	0.000145065 0
$346$	51.0822	2.74620
$347$	−11.5569	−0.620408	−0.310204	−	0.950670i	$-0.600397\pi$
$347$	−11.5569	−0.620408	−0.310204	+	0.950670i	$0.600397\pi$
$348$	8.13010	0.435819
$349$	19.1305	1.02403	0.512017	−	0.858975i	$-0.328899\pi$
$349$	19.1305	1.02403	0.512017	+	0.858975i	$0.328899\pi$
$350$	−60.0399	−3.20927
$351$	−4.34750	−0.232052
$352$	−1.71515	−0.0914181
$353$	13.5766	0.722609	0.361305	−	0.932448i	$-0.382331\pi$
$353$	13.5766	0.722609	0.361305	+	0.932448i	$0.382331\pi$
$354$	−7.48483	−0.397814
$355$	−0.0616290	−0.00327093
$356$	−61.8319	−3.27709
$357$	4.87243	0.257876
$358$	42.0050	2.22003
$359$	15.2719	0.806022	0.403011	−	0.915195i	$-0.367964\pi$
$359$	15.2719	0.806022	0.403011	+	0.915195i	$0.367964\pi$
$360$	0.0239709	0.00126338
$361$	19.4015	1.02113
$362$	−25.6600	−1.34866
$363$	−5.62505	−0.295239
$364$	−86.2925	−4.52295
$365$	−0.0504793	−0.00264221
$366$	−33.1766	−1.73417
$367$	−13.3619	−0.697484	−0.348742	−	0.937219i	$-0.613391\pi$
$367$	−13.3619	−0.697484	−0.348742	+	0.937219i	$0.613391\pi$
$368$	2.55494	0.133186
$369$	4.02994	0.209790
$370$	0.0527997	0.00274493
$371$	47.3455	2.45805
$372$	−7.32899	−0.379991
$373$	37.5063	1.94200	0.971002	−	0.239072i	$-0.0768431\pi$
$373$	37.5063	1.94200	0.971002	+	0.239072i	$0.0768431\pi$
$374$	−5.71365	−0.295446
$375$	−0.0469044	−0.00242213
$376$	62.2390	3.20973
$377$	−8.67656	−0.446866
$378$	12.0080	0.617626
$379$	−6.90564	−0.354719	−0.177359	−	0.984146i	$-0.556756\pi$
$379$	−6.90564	−0.354719	−0.177359	+	0.984146i	$0.556756\pi$
$380$	0.118407	0.00607413
$381$	13.2277	0.677674
$382$	10.5434	0.539450
$383$	−20.2535	−1.03490	−0.517452	−	0.855712i	$-0.673119\pi$
$383$	−20.2535	−1.03490	−0.517452	+	0.855712i	$0.673119\pi$
$384$	−18.9082	−0.964904
$385$	−0.0529842	−0.00270033
$386$	−5.72069	−0.291175
$387$	−4.88385	−0.248260
$388$	−6.24270	−0.316925
$389$	−23.7702	−1.20519	−0.602597	−	0.798045i	$-0.705867\pi$
$389$	−23.7702	−1.20519	−0.602597	+	0.798045i	$0.705867\pi$
$390$	−0.0502551	−0.00254477
$391$	0.574459	0.0290517
$392$	85.5538	4.32112
$393$	2.87664	0.145107
$394$	43.8733	2.21031
$395$	0.00469045	0.000236002 0
$396$	−9.44441	−0.474600
$397$	24.2034	1.21473	0.607366	−	0.794422i	$-0.292226\pi$
$397$	24.2034	1.21473	0.607366	+	0.794422i	$0.292226\pi$
$398$	8.60217	0.431188
$399$	30.1939	1.51159
$400$	−22.2377	−1.11189
$401$	29.5509	1.47570	0.737850	−	0.674964i	$-0.235841\pi$
$401$	29.5509	1.47570	0.737850	+	0.674964i	$0.235841\pi$
$402$	14.5285	0.724618
$403$	7.82161	0.389622
$404$	−33.9499	−1.68907
$405$	0.00469045	0.000233070 0
$406$	23.9651	1.18937
$407$	−10.5896	−0.524906
$408$	5.11058	0.253011
$409$	16.4127	0.811554	0.405777	−	0.913972i	$-0.367001\pi$
$409$	16.4127	0.811554	0.405777	+	0.913972i	$0.367001\pi$
$410$	0.0465842	0.00230063
$411$	3.21352	0.158511
$412$	−55.0781	−2.71350
$413$	−14.7979	−0.728158
$414$	1.41575	0.0695802
$415$	−0.00400133	−0.000196417 0
$416$	−3.21630	−0.157692
$417$	7.14597	0.349940
$418$	−35.4069	−1.73181
$419$	−15.4331	−0.753956	−0.376978	−	0.926222i	$-0.623037\pi$
$419$	−15.4331	−0.753956	−0.376978	+	0.926222i	$0.623037\pi$
$420$	0.0930995	0.00454279
$421$	−3.36617	−0.164057	−0.0820285	−	0.996630i	$-0.526140\pi$
$421$	−3.36617	−0.164057	−0.0820285	+	0.996630i	$0.526140\pi$
$422$	−19.3804	−0.943424
$423$	12.1785	0.592137
$424$	49.6596	2.41168
$425$	−4.99998	−0.242535
$426$	−32.3815	−1.56889
$427$	−65.5920	−3.17422
$428$	−21.8784	−1.05753
$429$	10.0792	0.486629
$430$	−0.0564550	−0.00272250
$431$	−28.0944	−1.35326	−0.676629	−	0.736324i	$-0.736560\pi$
$431$	−28.0944	−1.35326	−0.676629	+	0.736324i	$0.736560\pi$
$432$	4.44756	0.213983
$433$	−33.6473	−1.61699	−0.808493	−	0.588506i	$-0.799716\pi$
$433$	−33.6473	−1.61699	−0.808493	+	0.588506i	$0.799716\pi$
$434$	−21.6037	−1.03701
$435$	0.00936099	0.000448825 0
$436$	−49.9831	−2.39376
$437$	3.55986	0.170291
$438$	−26.5232	−1.26733
$439$	17.5546	0.837836	0.418918	−	0.908024i	$-0.362410\pi$
$439$	17.5546	0.837836	0.418918	+	0.908024i	$0.362410\pi$
$440$	−0.0555739	−0.00264938
$441$	16.7405	0.797169
$442$	−10.7144	−0.509630
$443$	4.96762	0.236019	0.118009	−	0.993012i	$-0.462349\pi$
$443$	4.96762	0.236019	0.118009	+	0.993012i	$0.462349\pi$
$444$	18.6071	0.883055
$445$	−0.0711933	−0.00337489
$446$	−36.0981	−1.70929
$447$	−0.599309	−0.0283464
$448$	−34.4573	−1.62795
$449$	−9.96414	−0.470237	−0.235118	−	0.971967i	$-0.575548\pi$
$449$	−9.96414	−0.470237	−0.235118	+	0.971967i	$0.575548\pi$
$450$	−12.3224	−0.580882
$451$	−9.34298	−0.439944
$452$	47.1620	2.21831
$453$	−14.6686	−0.689190
$454$	50.1068	2.35163
$455$	−0.0993572	−0.00465794
$456$	31.6697	1.48307
$457$	−1.69516	−0.0792961	−0.0396481	−	0.999214i	$-0.512624\pi$
$457$	−1.69516	−0.0792961	−0.0396481	+	0.999214i	$0.512624\pi$
$458$	14.1482	0.661104
$459$	1.00000	0.0466760
$460$	0.0109764	0.000511779 0
$461$	−11.4957	−0.535408	−0.267704	−	0.963501i	$-0.586265\pi$
$461$	−11.4957	−0.535408	−0.267704	+	0.963501i	$0.586265\pi$
$462$	−27.8393	−1.29520
$463$	−35.1967	−1.63573	−0.817864	−	0.575412i	$-0.804842\pi$
$463$	−35.1967	−1.63573	−0.817864	+	0.575412i	$0.804842\pi$
$464$	8.87626	0.412070
$465$	−0.00843861	−0.000391331 0
$466$	51.7021	2.39505
$467$	39.5430	1.82983	0.914917	−	0.403642i	$-0.132256\pi$
$467$	39.5430	1.82983	0.914917	+	0.403642i	$0.132256\pi$
$468$	−17.7104	−0.818662
$469$	28.7238	1.32634
$470$	0.140777	0.00649358
$471$	13.4542	0.619935
$472$	−15.5212	−0.714421
$473$	11.3227	0.520618
$474$	2.46449	0.113198
$475$	−30.9843	−1.42166
$476$	19.8488	0.909766
$477$	9.71702	0.444912
$478$	−7.57113	−0.346295
$479$	−10.2472	−0.468205	−0.234103	−	0.972212i	$-0.575215\pi$
$479$	−10.2472	−0.468205	−0.234103	+	0.972212i	$0.575215\pi$
$480$	0.00347001	0.000158383 0
$481$	−19.8578	−0.905437
$482$	−45.6567	−2.07961
$483$	2.79901	0.127359
$484$	−22.9147	−1.04158
$485$	−0.00718784	−0.000326383 0
$486$	2.46449	0.111791
$487$	9.42217	0.426959	0.213480	−	0.976948i	$-0.431520\pi$
$487$	9.42217	0.426959	0.213480	+	0.976948i	$0.431520\pi$
$488$	−68.7979	−3.11433
$489$	−17.3814	−0.786012
$490$	0.193513	0.00874202
$491$	28.9128	1.30481	0.652407	−	0.757869i	$-0.273759\pi$
$491$	28.9128	1.30481	0.652407	+	0.757869i	$0.273759\pi$
$492$	16.4167	0.740123
$493$	1.99576	0.0898844
$494$	−66.3957	−2.98728
$495$	−0.0108743	−0.000488763 0
$496$	−8.00163	−0.359284
$497$	−64.0201	−2.87169
$498$	−2.10240	−0.0942110
$499$	13.8542	0.620198	0.310099	−	0.950704i	$-0.399638\pi$
$499$	13.8542	0.620198	0.310099	+	0.950704i	$0.399638\pi$
$500$	−0.191074	−0.00854508
$501$	−1.84431	−0.0823979
$502$	−33.4534	−1.49310
$503$	32.3998	1.44464	0.722318	−	0.691561i	$-0.243077\pi$
$503$	32.3998	1.44464	0.722318	+	0.691561i	$0.243077\pi$
$504$	24.9009	1.10917
$505$	−0.0390899	−0.00173948
$506$	−3.28226	−0.145914
$507$	5.90077	0.262062
$508$	53.8854	2.39078
$509$	13.3442	0.591470	0.295735	−	0.955270i	$-0.404435\pi$
$509$	13.3442	0.591470	0.295735	+	0.955270i	$0.404435\pi$
$510$	0.0115595	0.000511865 0
$511$	−52.4378	−2.31971
$512$	−42.1689	−1.86362
$513$	6.19689	0.273600
$514$	−55.6723	−2.45560
$515$	−0.0634169	−0.00279448
$516$	−19.8953	−0.875841
$517$	−28.2345	−1.24175
$518$	54.8483	2.40989
$519$	20.7273	0.909829
$520$	−0.104213	−0.00457006
$521$	−3.90541	−0.171099	−0.0855497	−	0.996334i	$-0.527265\pi$
$521$	−3.90541	−0.171099	−0.0855497	+	0.996334i	$0.527265\pi$
$522$	4.91852	0.215278
$523$	17.4139	0.761455	0.380727	−	0.924687i	$-0.375674\pi$
$523$	17.4139	0.761455	0.380727	+	0.924687i	$0.375674\pi$
$524$	11.7185	0.511926
$525$	−24.3620	−1.06325
$526$	−26.2029	−1.14250
$527$	−1.79911	−0.0783703
$528$	−10.3112	−0.448737
$529$	−22.6700	−0.985652
$530$	0.112324	0.00487905
$531$	−3.03708	−0.131798
$532$	123.001	5.33275
$533$	−17.5202	−0.758882
$534$	−37.4069	−1.61875
$535$	−0.0251908	−0.00108909
$536$	30.1277	1.30132
$537$	17.0441	0.735508
$538$	66.0407	2.84722
$539$	−38.8112	−1.67172
$540$	0.0191074	0.000822252 0
$541$	19.6275	0.843852	0.421926	−	0.906630i	$-0.361354\pi$
$541$	19.6275	0.843852	0.421926	+	0.906630i	$0.361354\pi$
$542$	−50.0083	−2.14804
$543$	−10.4119	−0.446817
$544$	0.739803	0.0317188
$545$	−0.0575506	−0.00246520
$546$	−52.2049	−2.23416
$547$	−12.7324	−0.544396	−0.272198	−	0.962241i	$-0.587751\pi$
$547$	−12.7324	−0.544396	−0.272198	+	0.962241i	$0.587751\pi$
$548$	13.0909	0.559214
$549$	−13.4619	−0.574539
$550$	28.5681	1.21815
$551$	12.3675	0.526873
$552$	2.93582	0.124957
$553$	4.87243	0.207197
$554$	1.37151	0.0582698
$555$	0.0214242	0.000909408 0
$556$	29.1104	1.23456
$557$	−39.9966	−1.69471	−0.847355	−	0.531027i	$-0.821806\pi$
$557$	−39.9966	−1.69471	−0.847355	+	0.531027i	$0.821806\pi$
$558$	−4.43387	−0.187701
$559$	21.2325	0.898041
$560$	0.101644	0.00429524
$561$	−2.31839	−0.0978826
$562$	−51.1876	−2.15922
$563$	2.73533	0.115281	0.0576403	−	0.998337i	$-0.481642\pi$
$563$	2.73533	0.115281	0.0576403	+	0.998337i	$0.481642\pi$
$564$	49.6113	2.08901
$565$	0.0543023	0.00228451
$566$	−37.1109	−1.55989
$567$	4.87243	0.204623
$568$	−67.1492	−2.81752
$569$	−27.1394	−1.13774	−0.568872	−	0.822426i	$-0.692620\pi$
$569$	−27.1394	−1.13774	−0.568872	+	0.822426i	$0.692620\pi$
$570$	0.0716332	0.00300039
$571$	20.8022	0.870547	0.435273	−	0.900298i	$-0.356652\pi$
$571$	20.8022	0.870547	0.435273	+	0.900298i	$0.356652\pi$
$572$	41.0596	1.71679
$573$	4.27815	0.178722
$574$	48.3916	2.01983
$575$	−2.87228	−0.119783
$576$	−7.07189	−0.294662
$577$	−21.7502	−0.905473	−0.452737	−	0.891644i	$-0.649552\pi$
$577$	−21.7502	−0.905473	−0.452737	+	0.891644i	$0.649552\pi$
$578$	2.46449	0.102509
$579$	−2.32125	−0.0964679
$580$	0.0381338	0.00158342
$581$	−4.15657	−0.172444
$582$	−3.77669	−0.156549
$583$	−22.5279	−0.933009
$584$	−55.0008	−2.27595
$585$	−0.0203917	−0.000843094 0
$586$	23.0588	0.952549
$587$	44.0516	1.81821	0.909103	−	0.416571i	$-0.136768\pi$
$587$	44.0516	1.81821	0.909103	+	0.416571i	$0.136768\pi$
$588$	68.1958	2.81235
$589$	−11.1489	−0.459381
$590$	−0.0351072	−0.00144534
$591$	17.8022	0.732286
$592$	20.3148	0.834935
$593$	21.8644	0.897863	0.448932	−	0.893566i	$-0.351805\pi$
$593$	21.8644	0.897863	0.448932	+	0.893566i	$0.351805\pi$
$594$	−5.71365	−0.234434
$595$	0.0228539	0.000936917 0
$596$	−2.44140	−0.100004
$597$	3.49045	0.142855
$598$	−6.15496	−0.251695
$599$	−19.2247	−0.785500	−0.392750	−	0.919645i	$-0.628476\pi$
$599$	−19.2247	−0.785500	−0.392750	+	0.919645i	$0.628476\pi$
$600$	−25.5528	−1.04319
$601$	23.0922	0.941952	0.470976	−	0.882146i	$-0.343902\pi$
$601$	23.0922	0.941952	0.470976	+	0.882146i	$0.343902\pi$
$602$	−58.6454	−2.39021
$603$	5.89516	0.240070
$604$	−59.7552	−2.43141
$605$	−0.0263840	−0.00107266
$606$	−20.5389	−0.834336
$607$	20.1637	0.818418	0.409209	−	0.912441i	$-0.365805\pi$
$607$	20.1637	0.818418	0.409209	+	0.912441i	$0.365805\pi$
$608$	4.58448	0.185925
$609$	9.72418	0.394044
$610$	−0.155613	−0.00630058
$611$	−52.9459	−2.14196
$612$	4.07369	0.164669
$613$	−39.8885	−1.61108	−0.805541	−	0.592541i	$-0.798125\pi$
$613$	−39.8885	−1.61108	−0.805541	+	0.592541i	$0.798125\pi$
$614$	10.8646	0.438460
$615$	0.0189022	0.000762211 0
$616$	−57.7301	−2.32601
$617$	−1.74104	−0.0700916	−0.0350458	−	0.999386i	$-0.511158\pi$
$617$	−1.74104	−0.0700916	−0.0350458	+	0.999386i	$0.511158\pi$
$618$	−33.3210	−1.34037
$619$	−29.6985	−1.19368	−0.596841	−	0.802360i	$-0.703578\pi$
$619$	−29.6985	−1.19368	−0.596841	+	0.802360i	$0.703578\pi$
$620$	−0.0343763	−0.00138058
$621$	0.574459	0.0230523
$622$	−20.6464	−0.827845
$623$	−73.9555	−2.96296
$624$	−19.3358	−0.774051
$625$	24.9997	0.999987
$626$	71.1944	2.84550
$627$	−14.3668	−0.573756
$628$	54.8081	2.18708
$629$	4.56763	0.182123
$630$	0.0563230	0.00224396
$631$	−6.83828	−0.272228	−0.136114	−	0.990693i	$-0.543461\pi$
$631$	−6.83828	−0.272228	−0.136114	+	0.990693i	$0.543461\pi$
$632$	5.11058	0.203288
$633$	−7.86388	−0.312561
$634$	−20.8349	−0.827459
$635$	0.0620436	0.00246213
$636$	39.5841	1.56961
$637$	−72.7795	−2.88363
$638$	−11.4031	−0.451451
$639$	−13.1393	−0.519781
$640$	−0.0886878	−0.00350569
$641$	43.3382	1.71176	0.855878	−	0.517177i	$-0.173017\pi$
$641$	43.3382	1.71176	0.855878	+	0.517177i	$0.173017\pi$
$642$	−13.2359	−0.522381
$643$	36.7903	1.45087	0.725434	−	0.688291i	$-0.241639\pi$
$643$	36.7903	1.45087	0.725434	+	0.688291i	$0.241639\pi$
$644$	11.4023	0.449314
$645$	−0.0229074	−0.000901979 0
$646$	15.2722	0.600875
$647$	−31.8190	−1.25093	−0.625466	−	0.780251i	$-0.715091\pi$
$647$	−31.8190	−1.25093	−0.625466	+	0.780251i	$0.715091\pi$
$648$	5.11058	0.200762
$649$	7.04114	0.276389
$650$	53.5715	2.10125
$651$	−8.76601	−0.343567
$652$	−70.8062	−2.77299
$653$	−11.0253	−0.431452	−0.215726	−	0.976454i	$-0.569212\pi$
$653$	−11.0253	−0.431452	−0.215726	+	0.976454i	$0.569212\pi$
$654$	−30.2386	−1.18242
$655$	0.0134927	0.000527204 0
$656$	17.9234	0.699791
$657$	−10.7622	−0.419872
$658$	146.239	5.70100
$659$	9.08388	0.353858	0.176929	−	0.984224i	$-0.443384\pi$
$659$	9.08388	0.353858	0.176929	+	0.984224i	$0.443384\pi$
$660$	−0.0442985	−0.00172432
$661$	46.8443	1.82203	0.911016	−	0.412371i	$-0.135299\pi$
$661$	46.8443	1.82203	0.911016	+	0.412371i	$0.135299\pi$
$662$	−66.8579	−2.59850
$663$	−4.34750	−0.168843
$664$	−4.35973	−0.169190
$665$	0.141623	0.00549190
$666$	11.2569	0.436195
$667$	1.14648	0.0443920
$668$	−7.51316	−0.290693
$669$	−14.6473	−0.566298
$670$	0.0681454	0.00263268
$671$	31.2099	1.20485
$672$	3.60464	0.139052
$673$	7.39559	0.285079	0.142539	−	0.989789i	$-0.454473\pi$
$673$	7.39559	0.285079	0.142539	+	0.989789i	$0.454473\pi$
$674$	24.9558	0.961261
$675$	−4.99998	−0.192449
$676$	24.0379	0.924534
$677$	−0.796413	−0.0306086	−0.0153043	−	0.999883i	$-0.504872\pi$
$677$	−0.796413	−0.0306086	−0.0153043	+	0.999883i	$0.504872\pi$
$678$	28.5319	1.09576
$679$	−7.46672	−0.286546
$680$	0.0239709	0.000919241 0
$681$	20.3316	0.779107
$682$	10.2795	0.393621
$683$	−42.4294	−1.62351	−0.811757	−	0.583995i	$-0.801489\pi$
$683$	−42.4294	−1.62351	−0.811757	+	0.583995i	$0.801489\pi$
$684$	25.2442	0.965237
$685$	0.0150728	0.000575903 0
$686$	116.965	4.46574
$687$	5.74085	0.219027
$688$	−21.7212	−0.828114
$689$	−42.2448	−1.60940
$690$	0.00664048	0.000252799 0
$691$	17.0161	0.647323	0.323662	−	0.946173i	$-0.395086\pi$
$691$	17.0161	0.647323	0.323662	+	0.946173i	$0.395086\pi$
$692$	84.4367	3.20980
$693$	−11.2962	−0.429107
$694$	−28.4819	−1.08116
$695$	0.0335178	0.00127140
$696$	10.1995	0.386610
$697$	4.02994	0.152645
$698$	47.1469	1.78454
$699$	20.9789	0.793493
$700$	−99.2433	−3.75105
$701$	−1.37198	−0.0518189	−0.0259094	−	0.999664i	$-0.508248\pi$
$701$	−1.37198	−0.0518189	−0.0259094	+	0.999664i	$0.508248\pi$
$702$	−10.7144	−0.404387
$703$	28.3051	1.06755
$704$	16.3954	0.617926
$705$	0.0571225	0.00215136
$706$	33.4593	1.25926
$707$	−40.6066	−1.52717
$708$	−12.3721	−0.464972
$709$	10.6157	0.398682	0.199341	−	0.979930i	$-0.436120\pi$
$709$	10.6157	0.398682	0.199341	+	0.979930i	$0.436120\pi$
$710$	−0.151884	−0.00570010
$711$	1.00000	0.0375029
$712$	−77.5702	−2.90707
$713$	−1.03351	−0.0387054
$714$	12.0080	0.449389
$715$	0.0472760	0.00176802
$716$	69.4324	2.59481
$717$	−3.07209	−0.114729
$718$	37.6375	1.40462
$719$	34.1568	1.27383	0.636916	−	0.770933i	$-0.280210\pi$
$719$	34.1568	1.27383	0.636916	+	0.770933i	$0.280210\pi$
$720$	0.0208611	0.000777446 0
$721$	−65.8774	−2.45340
$722$	47.8147	1.77948
$723$	−18.5259	−0.688984
$724$	−42.4148	−1.57633
$725$	−9.97874	−0.370601
$726$	−13.8629	−0.514499
$727$	31.1913	1.15682	0.578410	−	0.815746i	$-0.303673\pi$
$727$	31.1913	1.15682	0.578410	+	0.815746i	$0.303673\pi$
$728$	−108.257	−4.01226
$729$	1.00000	0.0370370
$730$	−0.124406	−0.00460445
$731$	−4.88385	−0.180636
$732$	−54.8395	−2.02692
$733$	−25.2181	−0.931451	−0.465725	−	0.884929i	$-0.654207\pi$
$733$	−25.2181	−0.931451	−0.465725	+	0.884929i	$0.654207\pi$
$734$	−32.9301	−1.21547
$735$	0.0785206	0.00289628
$736$	0.424987	0.0156652
$737$	−13.6673	−0.503442
$738$	9.93172	0.365592
$739$	10.4933	0.386003	0.193002	−	0.981198i	$-0.438178\pi$
$739$	10.4933	0.386003	0.193002	+	0.981198i	$0.438178\pi$
$740$	0.0872757	0.00320832
$741$	−26.9410	−0.989702
$742$	116.682	4.28354
$743$	26.2129	0.961658	0.480829	−	0.876814i	$-0.340336\pi$
$743$	26.2129	0.961658	0.480829	+	0.876814i	$0.340336\pi$
$744$	−9.19446	−0.337085
$745$	−0.00281103	−0.000102988 0
$746$	92.4338	3.38424
$747$	−0.853080	−0.0312126
$748$	−9.44441	−0.345322
$749$	−26.1682	−0.956165
$750$	−0.115595	−0.00422094
$751$	16.6831	0.608777	0.304388	−	0.952548i	$-0.401548\pi$
$751$	16.6831	0.608777	0.304388	+	0.952548i	$0.401548\pi$
$752$	54.1645	1.97518
$753$	−13.5742	−0.494671
$754$	−21.3833	−0.778732
$755$	−0.0688022	−0.00250397
$756$	19.8488	0.721892
$757$	−6.25230	−0.227244	−0.113622	−	0.993524i	$-0.536245\pi$
$757$	−6.25230	−0.227244	−0.113622	+	0.993524i	$0.536245\pi$
$758$	−17.0188	−0.618152
$759$	−1.33182	−0.0483421
$760$	0.148545	0.00538829
$761$	29.1015	1.05493	0.527464	−	0.849577i	$-0.323143\pi$
$761$	29.1015	1.05493	0.527464	+	0.849577i	$0.323143\pi$
$762$	32.5994	1.18095
$763$	−59.7834	−2.16431
$764$	17.4279	0.630518
$765$	0.00469045	0.000169583 0
$766$	−49.9143	−1.80348
$767$	13.2037	0.476758
$768$	−32.4552	−1.17112
$769$	33.7930	1.21861	0.609304	−	0.792937i	$-0.291449\pi$
$769$	33.7930	1.21861	0.609304	+	0.792937i	$0.291449\pi$
$770$	−0.130579	−0.00470574
$771$	−22.5898	−0.813553
$772$	−9.45605	−0.340331
$773$	−45.4509	−1.63475	−0.817377	−	0.576103i	$-0.804573\pi$
$773$	−45.4509	−1.63475	−0.817377	+	0.576103i	$0.804573\pi$
$774$	−12.0362	−0.432631
$775$	8.99549	0.323127
$776$	−7.83167	−0.281141
$777$	22.2555	0.798410
$778$	−58.5812	−2.10024
$779$	24.9731	0.894754
$780$	−0.0830695	−0.00297437
$781$	30.4620	1.09002
$782$	1.41575	0.0506270
$783$	1.99576	0.0713226
$784$	74.4546	2.65909
$785$	0.0631060	0.00225235
$786$	7.08943	0.252872
$787$	30.6595	1.09289	0.546447	−	0.837494i	$-0.315980\pi$
$787$	30.6595	1.09289	0.546447	+	0.837494i	$0.315980\pi$
$788$	72.5207	2.58344
$789$	−10.6322	−0.378516
$790$	0.0115595	0.000411270 0
$791$	56.4091	2.00568
$792$	−11.8483	−0.421012
$793$	58.5255	2.07830
$794$	59.6489	2.11686
$795$	0.0455772	0.00161646
$796$	14.2190	0.503980
$797$	1.71924	0.0608987	0.0304494	−	0.999536i	$-0.490306\pi$
$797$	1.71924	0.0608987	0.0304494	+	0.999536i	$0.490306\pi$
$798$	74.4125	2.63417
$799$	12.1785	0.430843
$800$	−3.69900	−0.130779
$801$	−15.1784	−0.536301
$802$	72.8277	2.57164
$803$	24.9509	0.880498
$804$	24.0151	0.846946
$805$	0.0131286	0.000462723 0
$806$	19.2762	0.678977
$807$	26.7970	0.943298
$808$	−42.5913	−1.49836
$809$	−28.7813	−1.01190	−0.505948	−	0.862564i	$-0.668857\pi$
$809$	−28.7813	−1.01190	−0.505948	+	0.862564i	$0.668857\pi$
$810$	0.0115595	0.000406161 0
$811$	−39.3609	−1.38215	−0.691073	−	0.722785i	$-0.742862\pi$
$811$	−39.3609	−1.38215	−0.691073	+	0.722785i	$0.742862\pi$
$812$	39.6133	1.39015
$813$	−20.2916	−0.711657
$814$	−26.0978	−0.914729
$815$	−0.0815263	−0.00285574
$816$	4.44756	0.155696
$817$	−30.2647	−1.05883
$818$	40.4488	1.41426
$819$	−21.1829	−0.740190
$820$	0.0770017	0.00268902
$821$	15.5312	0.542041	0.271020	−	0.962574i	$-0.412639\pi$
$821$	15.5312	0.542041	0.271020	+	0.962574i	$0.412639\pi$
$822$	7.91967	0.276230
$823$	5.64955	0.196931	0.0984655	−	0.995140i	$-0.468607\pi$
$823$	5.64955	0.196931	0.0984655	+	0.995140i	$0.468607\pi$
$824$	−69.0973	−2.40712
$825$	11.5919	0.403579
$826$	−36.4693	−1.26893
$827$	2.29977	0.0799707	0.0399854	−	0.999200i	$-0.487269\pi$
$827$	2.29977	0.0799707	0.0399854	+	0.999200i	$0.487269\pi$
$828$	2.34017	0.0813265
$829$	22.7140	0.788888	0.394444	−	0.918920i	$-0.370937\pi$
$829$	22.7140	0.788888	0.394444	+	0.918920i	$0.370937\pi$
$830$	−0.00986121	−0.000342288 0
$831$	0.556509	0.0193051
$832$	30.7451	1.06589
$833$	16.7405	0.580026
$834$	17.6111	0.609824
$835$	−0.00865066	−0.000299368 0
$836$	−58.5260	−2.02416
$837$	−1.79911	−0.0621862
$838$	−38.0347	−1.31389
$839$	9.17634	0.316802	0.158401	−	0.987375i	$-0.449366\pi$
$839$	9.17634	0.316802	0.158401	+	0.987375i	$0.449366\pi$
$840$	0.116796	0.00402986
$841$	−25.0170	−0.862653
$842$	−8.29587	−0.285895
$843$	−20.7701	−0.715360
$844$	−32.0350	−1.10269
$845$	0.0276772	0.000952125 0
$846$	30.0137	1.03189
$847$	−27.4077	−0.941738
$848$	43.2171	1.48408
$849$	−15.0583	−0.516798
$850$	−12.3224	−0.422654
$851$	2.62392	0.0899468
$852$	−53.5253	−1.83375
$853$	−15.8093	−0.541301	−0.270651	−	0.962678i	$-0.587239\pi$
$853$	−15.8093	−0.541301	−0.270651	+	0.962678i	$0.587239\pi$
$854$	−161.650	−5.53157
$855$	0.0290662	0.000994043 0
$856$	−27.4472	−0.938127
$857$	13.8763	0.474004	0.237002	−	0.971509i	$-0.423835\pi$
$857$	13.8763	0.474004	0.237002	+	0.971509i	$0.423835\pi$
$858$	24.8401	0.848027
$859$	33.4242	1.14042	0.570210	−	0.821499i	$-0.306862\pi$
$859$	33.4242	1.14042	0.570210	+	0.821499i	$0.306862\pi$
$860$	−0.0933177	−0.00318211
$861$	19.6356	0.669179
$862$	−69.2381	−2.35826
$863$	43.4046	1.47751	0.738755	−	0.673974i	$-0.235414\pi$
$863$	43.4046	1.47751	0.738755	+	0.673974i	$0.235414\pi$
$864$	0.739803	0.0251686
$865$	0.0972205	0.00330560
$866$	−82.9233	−2.81785
$867$	1.00000	0.0339618
$868$	−35.7100	−1.21208
$869$	−2.31839	−0.0786461
$870$	0.0230700	0.000782147 0
$871$	−25.6292	−0.868413
$872$	−62.7055	−2.12348
$873$	−1.53244	−0.0518654
$874$	8.77323	0.296759
$875$	−0.228538	−0.00772600
$876$	−43.8417	−1.48127
$877$	34.9877	1.18145	0.590725	−	0.806873i	$-0.298842\pi$
$877$	34.9877	1.18145	0.590725	+	0.806873i	$0.298842\pi$
$878$	43.2631	1.46006
$879$	9.35642	0.315584
$880$	−0.0483641	−0.00163035
$881$	−42.9770	−1.44793	−0.723965	−	0.689836i	$-0.757682\pi$
$881$	−42.9770	−1.44793	−0.723965	+	0.689836i	$0.757682\pi$
$882$	41.2568	1.38919
$883$	−37.8527	−1.27384	−0.636922	−	0.770928i	$-0.719793\pi$
$883$	−37.8527	−1.27384	−0.636922	+	0.770928i	$0.719793\pi$
$884$	−17.7104	−0.595664
$885$	−0.0142452	−0.000478848 0
$886$	12.2426	0.411299
$887$	15.6210	0.524503	0.262251	−	0.965000i	$-0.415535\pi$
$887$	15.6210	0.524503	0.262251	+	0.965000i	$0.415535\pi$
$888$	23.3432	0.783348
$889$	64.4508	2.16161
$890$	−0.175455	−0.00588126
$891$	−2.31839	−0.0776691
$892$	−59.6686	−1.99785
$893$	75.4687	2.52546
$894$	−1.47699	−0.0493979
$895$	0.0799445	0.00267225
$896$	−92.1287	−3.07781
$897$	−2.49746	−0.0833879
$898$	−24.5565	−0.819460
$899$	−3.59058	−0.119752
$900$	−20.3684	−0.678945
$901$	9.71702	0.323721
$902$	−23.0256	−0.766670
$903$	−23.7962	−0.791888
$904$	59.1662	1.96784
$905$	−0.0488364	−0.00162338
$906$	−36.1505	−1.20102
$907$	−31.6271	−1.05016	−0.525081	−	0.851053i	$-0.675965\pi$
$907$	−31.6271	−1.05016	−0.525081	+	0.851053i	$0.675965\pi$
$908$	82.8245	2.74863
$909$	−8.33395	−0.276420
$910$	−0.244864	−0.00811717
$911$	7.47287	0.247587	0.123794	−	0.992308i	$-0.460494\pi$
$911$	7.47287	0.247587	0.123794	+	0.992308i	$0.460494\pi$
$912$	27.5611	0.912638
$913$	1.97778	0.0654548
$914$	−4.17769	−0.138186
$915$	−0.0631422	−0.00208742
$916$	23.3864	0.772710
$917$	14.0162	0.462856
$918$	2.46449	0.0813401
$919$	−34.3518	−1.13316	−0.566580	−	0.824007i	$-0.691734\pi$
$919$	−34.3518	−1.13316	−0.566580	+	0.824007i	$0.691734\pi$
$920$	0.0137703	0.000453993 0
$921$	4.40847	0.145264
$922$	−28.3310	−0.933030
$923$	57.1230	1.88023
$924$	−46.0172	−1.51386
$925$	−22.8381	−0.750911
$926$	−86.7417	−2.85051
$927$	−13.5205	−0.444070
$928$	1.47647	0.0484674
$929$	37.9505	1.24512	0.622558	−	0.782574i	$-0.286094\pi$
$929$	37.9505	1.24512	0.622558	+	0.782574i	$0.286094\pi$
$930$	−0.0207968	−0.000681955 0
$931$	103.739	3.39992
$932$	85.4613	2.79938
$933$	−8.37756	−0.274269
$934$	97.4533	3.18877
$935$	−0.0108743	−0.000355628 0
$936$	−22.2182	−0.726226
$937$	48.6516	1.58938	0.794690	−	0.607016i	$-0.207634\pi$
$937$	48.6516	1.58938	0.794690	+	0.607016i	$0.207634\pi$
$938$	70.7893	2.31135
$939$	28.8881	0.942728
$940$	0.232699	0.00758981
$941$	35.5293	1.15822	0.579111	−	0.815249i	$-0.303400\pi$
$941$	35.5293	1.15822	0.579111	+	0.815249i	$0.303400\pi$
$942$	33.1576	1.08033
$943$	2.31504	0.0753879
$944$	−13.5076	−0.439634
$945$	0.0228539	0.000743436 0
$946$	27.9046	0.907256
$947$	37.7498	1.22670	0.613352	−	0.789810i	$-0.289821\pi$
$947$	37.7498	1.22670	0.613352	+	0.789810i	$0.289821\pi$
$948$	4.07369	0.132307
$949$	46.7885	1.51882
$950$	−76.3604	−2.47746
$951$	−8.45405	−0.274141
$952$	24.9009	0.807043
$953$	−26.7928	−0.867905	−0.433952	−	0.900936i	$-0.642881\pi$
$953$	−26.7928	−0.867905	−0.433952	+	0.900936i	$0.642881\pi$
$954$	23.9475	0.775328
$955$	0.0200664	0.000649335 0
$956$	−12.5148	−0.404756
$957$	−4.62695	−0.149568
$958$	−25.2540	−0.815920
$959$	15.6576	0.505611
$960$	−0.0331703	−0.00107057
$961$	−27.7632	−0.895588
$962$	−48.9392	−1.57786
$963$	−5.37067	−0.173067
$964$	−75.4686	−2.43068
$965$	−0.0108877	−0.000350487 0
$966$	6.89812	0.221943
$967$	−2.97124	−0.0955487	−0.0477743	−	0.998858i	$-0.515213\pi$
$967$	−2.97124	−0.0955487	−0.0477743	+	0.998858i	$0.515213\pi$
$968$	−28.7473	−0.923972
$969$	6.19689	0.199073
$970$	−0.0177143	−0.000568773 0
$971$	25.6232	0.822288	0.411144	−	0.911570i	$-0.365129\pi$
$971$	25.6232	0.822288	0.411144	+	0.911570i	$0.365129\pi$
$972$	4.07369	0.130664
$973$	34.8182	1.11622
$974$	23.2208	0.744043
$975$	21.7374	0.696154
$976$	−59.8725	−1.91647
$977$	−47.1999	−1.51006	−0.755029	−	0.655691i	$-0.772377\pi$
$977$	−47.1999	−1.51006	−0.755029	+	0.655691i	$0.772377\pi$
$978$	−42.8361	−1.36975
$979$	35.1894	1.12466
$980$	0.319869	0.0102178
$981$	−12.2697	−0.391743
$982$	71.2551	2.27384
$983$	15.0359	0.479569	0.239785	−	0.970826i	$-0.422923\pi$
$983$	15.0359	0.479569	0.239785	+	0.970826i	$0.422923\pi$
$984$	20.5953	0.656554
$985$	0.0835004	0.00266054
$986$	4.91852	0.156637
$987$	59.3387	1.88877
$988$	−109.749	−3.49159
$989$	−2.80557	−0.0892120
$990$	−0.0267996	−0.000851746 0
$991$	−58.0672	−1.84456	−0.922282	−	0.386518i	$-0.873678\pi$
$991$	−58.0672	−1.84456	−0.922282	+	0.386518i	$0.873678\pi$
$992$	−1.33098	−0.0422588
$993$	−27.1285	−0.860898
$994$	−157.777	−5.00437
$995$	0.0163718	0.000519020 0
$996$	−3.47518	−0.110115
$997$	30.6228	0.969835	0.484917	−	0.874560i	$-0.338850\pi$
$997$	30.6228	0.969835	0.484917	+	0.874560i	$0.338850\pi$
$998$	34.1434	1.08079
$999$	4.56763	0.144514

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.28	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.28	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46449 q^{2} +1.00000 q^{3} +4.07369 q^{4} +0.00469045 q^{5} +2.46449 q^{6} +4.87243 q^{7} +5.11058 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.46449 q^{2} +1.00000 q^{3} +4.07369 q^{4} +0.00469045 q^{5} +2.46449 q^{6} +4.87243 q^{7} +5.11058 q^{8} +1.00000 q^{9} +0.0115595 q^{10} -2.31839 q^{11} +4.07369 q^{12} -4.34750 q^{13} +12.0080 q^{14} +0.00469045 q^{15} +4.44756 q^{16} +1.00000 q^{17} +2.46449 q^{18} +6.19689 q^{19} +0.0191074 q^{20} +4.87243 q^{21} -5.71365 q^{22} +0.574459 q^{23} +5.11058 q^{24} -4.99998 q^{25} -10.7144 q^{26} +1.00000 q^{27} +19.8488 q^{28} +1.99576 q^{29} +0.0115595 q^{30} -1.79911 q^{31} +0.739803 q^{32} -2.31839 q^{33} +2.46449 q^{34} +0.0228539 q^{35} +4.07369 q^{36} +4.56763 q^{37} +15.2722 q^{38} -4.34750 q^{39} +0.0239709 q^{40} +4.02994 q^{41} +12.0080 q^{42} -4.88385 q^{43} -9.44441 q^{44} +0.00469045 q^{45} +1.41575 q^{46} +12.1785 q^{47} +4.44756 q^{48} +16.7405 q^{49} -12.3224 q^{50} +1.00000 q^{51} -17.7104 q^{52} +9.71702 q^{53} +2.46449 q^{54} -0.0108743 q^{55} +24.9009 q^{56} +6.19689 q^{57} +4.91852 q^{58} -3.03708 q^{59} +0.0191074 q^{60} -13.4619 q^{61} -4.43387 q^{62} +4.87243 q^{63} -7.07189 q^{64} -0.0203917 q^{65} -5.71365 q^{66} +5.89516 q^{67} +4.07369 q^{68} +0.574459 q^{69} +0.0563230 q^{70} -13.1393 q^{71} +5.11058 q^{72} -10.7622 q^{73} +11.2569 q^{74} -4.99998 q^{75} +25.2442 q^{76} -11.2962 q^{77} -10.7144 q^{78} +1.00000 q^{79} +0.0208611 q^{80} +1.00000 q^{81} +9.93172 q^{82} -0.853080 q^{83} +19.8488 q^{84} +0.00469045 q^{85} -12.0362 q^{86} +1.99576 q^{87} -11.8483 q^{88} -15.1784 q^{89} +0.0115595 q^{90} -21.1829 q^{91} +2.34017 q^{92} -1.79911 q^{93} +30.0137 q^{94} +0.0290662 q^{95} +0.739803 q^{96} -1.53244 q^{97} +41.2568 q^{98} -2.31839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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