LMFDB - Embedded newform 4029.2.a.i.1.14

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:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-0.0249015 q^{2} -1.00000 q^{3} -1.99938 q^{4} -2.90996 q^{5} +0.0249015 q^{6} +1.03650 q^{7} +0.0995904 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0249015 q^{2} -1.00000 q^{3} -1.99938 q^{4} -2.90996 q^{5} +0.0249015 q^{6} +1.03650 q^{7} +0.0995904 q^{8} +1.00000 q^{9} +0.0724622 q^{10} +4.05947 q^{11} +1.99938 q^{12} +6.69820 q^{13} -0.0258104 q^{14} +2.90996 q^{15} +3.99628 q^{16} +1.00000 q^{17} -0.0249015 q^{18} -2.37172 q^{19} +5.81811 q^{20} -1.03650 q^{21} -0.101087 q^{22} -2.49486 q^{23} -0.0995904 q^{24} +3.46786 q^{25} -0.166795 q^{26} -1.00000 q^{27} -2.07236 q^{28} -7.67100 q^{29} -0.0724622 q^{30} -0.454287 q^{31} -0.298694 q^{32} -4.05947 q^{33} -0.0249015 q^{34} -3.01618 q^{35} -1.99938 q^{36} +10.2673 q^{37} +0.0590594 q^{38} -6.69820 q^{39} -0.289804 q^{40} -5.84895 q^{41} +0.0258104 q^{42} -1.58782 q^{43} -8.11642 q^{44} -2.90996 q^{45} +0.0621257 q^{46} +6.87468 q^{47} -3.99628 q^{48} -5.92566 q^{49} -0.0863549 q^{50} -1.00000 q^{51} -13.3922 q^{52} +1.80583 q^{53} +0.0249015 q^{54} -11.8129 q^{55} +0.103226 q^{56} +2.37172 q^{57} +0.191019 q^{58} -2.48371 q^{59} -5.81811 q^{60} +1.40468 q^{61} +0.0113124 q^{62} +1.03650 q^{63} -7.98512 q^{64} -19.4915 q^{65} +0.101087 q^{66} +3.20204 q^{67} -1.99938 q^{68} +2.49486 q^{69} +0.0751072 q^{70} +14.7181 q^{71} +0.0995904 q^{72} +7.25379 q^{73} -0.255670 q^{74} -3.46786 q^{75} +4.74198 q^{76} +4.20765 q^{77} +0.166795 q^{78} -1.00000 q^{79} -11.6290 q^{80} +1.00000 q^{81} +0.145647 q^{82} -9.84725 q^{83} +2.07236 q^{84} -2.90996 q^{85} +0.0395390 q^{86} +7.67100 q^{87} +0.404284 q^{88} -0.599972 q^{89} +0.0724622 q^{90} +6.94269 q^{91} +4.98818 q^{92} +0.454287 q^{93} -0.171190 q^{94} +6.90162 q^{95} +0.298694 q^{96} +13.3306 q^{97} +0.147558 q^{98} +4.05947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−0.0249015	−0.0176080	−0.00880400	−	0.999961i	$-0.502802\pi$
$2$	−0.0249015	−0.0176080	−0.00880400	+	0.999961i	$0.502802\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99938	−0.999690
$5$	−2.90996	−1.30137	−0.650687	−	0.759346i	$-0.725519\pi$
$5$	−2.90996	−1.30137	−0.650687	+	0.759346i	$0.725519\pi$
$6$	0.0249015	0.0101660
$7$	1.03650	0.391761	0.195880	−	0.980628i	$-0.437244\pi$
$7$	1.03650	0.391761	0.195880	+	0.980628i	$0.437244\pi$
$8$	0.0995904	0.0352105
$9$	1.00000	0.333333
$10$	0.0724622	0.0229146
$11$	4.05947	1.22398	0.611988	−	0.790867i	$-0.290370\pi$
$11$	4.05947	1.22398	0.611988	+	0.790867i	$0.290370\pi$
$12$	1.99938	0.577171
$13$	6.69820	1.85775	0.928873	−	0.370399i	$-0.120779\pi$
$13$	6.69820	1.85775	0.928873	+	0.370399i	$0.120779\pi$
$14$	−0.0258104	−0.00689812
$15$	2.90996	0.751348
$16$	3.99628	0.999070
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0249015	−0.00586933
$19$	−2.37172	−0.544111	−0.272055	−	0.962282i	$-0.587703\pi$
$19$	−2.37172	−0.544111	−0.272055	+	0.962282i	$0.587703\pi$
$20$	5.81811	1.30097
$21$	−1.03650	−0.226183
$22$	−0.101087	−0.0215518
$23$	−2.49486	−0.520215	−0.260107	−	0.965580i	$-0.583758\pi$
$23$	−2.49486	−0.520215	−0.260107	+	0.965580i	$0.583758\pi$
$24$	−0.0995904	−0.0203288
$25$	3.46786	0.693573
$26$	−0.166795	−0.0327112
$27$	−1.00000	−0.192450
$28$	−2.07236	−0.391639
$29$	−7.67100	−1.42447	−0.712235	−	0.701941i	$-0.752317\pi$
$29$	−7.67100	−1.42447	−0.712235	+	0.701941i	$0.752317\pi$
$30$	−0.0724622	−0.0132297
$31$	−0.454287	−0.0815923	−0.0407962	−	0.999167i	$-0.512989\pi$
$31$	−0.454287	−0.0815923	−0.0407962	+	0.999167i	$0.512989\pi$
$32$	−0.298694	−0.0528021
$33$	−4.05947	−0.706663
$34$	−0.0249015	−0.00427057
$35$	−3.01618	−0.509827
$36$	−1.99938	−0.333230
$37$	10.2673	1.68793	0.843965	−	0.536398i	$-0.180215\pi$
$37$	10.2673	1.68793	0.843965	+	0.536398i	$0.180215\pi$
$38$	0.0590594	0.00958069
$39$	−6.69820	−1.07257
$40$	−0.289804	−0.0458220
$41$	−5.84895	−0.913453	−0.456726	−	0.889607i	$-0.650978\pi$
$41$	−5.84895	−0.913453	−0.456726	+	0.889607i	$0.650978\pi$
$42$	0.0258104	0.00398263
$43$	−1.58782	−0.242140	−0.121070	−	0.992644i	$-0.538633\pi$
$43$	−1.58782	−0.242140	−0.121070	+	0.992644i	$0.538633\pi$
$44$	−8.11642	−1.22360
$45$	−2.90996	−0.433791
$46$	0.0621257	0.00915994
$47$	6.87468	1.00278	0.501388	−	0.865223i	$-0.332823\pi$
$47$	6.87468	1.00278	0.501388	+	0.865223i	$0.332823\pi$
$48$	−3.99628	−0.576813
$49$	−5.92566	−0.846524
$50$	−0.0863549	−0.0122124
$51$	−1.00000	−0.140028
$52$	−13.3922	−1.85717
$53$	1.80583	0.248050	0.124025	−	0.992279i	$-0.460420\pi$
$53$	1.80583	0.248050	0.124025	+	0.992279i	$0.460420\pi$
$54$	0.0249015	0.00338866
$55$	−11.8129	−1.59285
$56$	0.103226	0.0137941
$57$	2.37172	0.314142
$58$	0.191019	0.0250821
$59$	−2.48371	−0.323351	−0.161676	−	0.986844i	$-0.551690\pi$
$59$	−2.48371	−0.323351	−0.161676	+	0.986844i	$0.551690\pi$
$60$	−5.81811	−0.751115
$61$	1.40468	0.179851	0.0899256	−	0.995948i	$-0.471337\pi$
$61$	1.40468	0.179851	0.0899256	+	0.995948i	$0.471337\pi$
$62$	0.0113124	0.00143668
$63$	1.03650	0.130587
$64$	−7.98512	−0.998140
$65$	−19.4915	−2.41762
$66$	0.101087	0.0124429
$67$	3.20204	0.391192	0.195596	−	0.980685i	$-0.437336\pi$
$67$	3.20204	0.391192	0.195596	+	0.980685i	$0.437336\pi$
$68$	−1.99938	−0.242460
$69$	2.49486	0.300346
$70$	0.0751072	0.00897703
$71$	14.7181	1.74672	0.873359	−	0.487077i	$-0.161937\pi$
$71$	14.7181	1.74672	0.873359	+	0.487077i	$0.161937\pi$
$72$	0.0995904	0.0117368
$73$	7.25379	0.848992	0.424496	−	0.905430i	$-0.360451\pi$
$73$	7.25379	0.848992	0.424496	+	0.905430i	$0.360451\pi$
$74$	−0.255670	−0.0297211
$75$	−3.46786	−0.400434
$76$	4.74198	0.543942
$77$	4.20765	0.479506
$78$	0.166795	0.0188858
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−11.6290	−1.30016
$81$	1.00000	0.111111
$82$	0.145647	0.0160841
$83$	−9.84725	−1.08088	−0.540438	−	0.841384i	$-0.681741\pi$
$83$	−9.84725	−1.08088	−0.540438	+	0.841384i	$0.681741\pi$
$84$	2.07236	0.226113
$85$	−2.90996	−0.315629
$86$	0.0395390	0.00426360
$87$	7.67100	0.822418
$88$	0.404284	0.0430968
$89$	−0.599972	−0.0635969	−0.0317984	−	0.999494i	$-0.510123\pi$
$89$	−0.599972	−0.0635969	−0.0317984	+	0.999494i	$0.510123\pi$
$90$	0.0724622	0.00763819
$91$	6.94269	0.727792
$92$	4.98818	0.520054
$93$	0.454287	0.0471073
$94$	−0.171190	−0.0176569
$95$	6.90162	0.708091
$96$	0.298694	0.0304853
$97$	13.3306	1.35352	0.676760	−	0.736204i	$-0.263383\pi$
$97$	13.3306	1.35352	0.676760	+	0.736204i	$0.263383\pi$
$98$	0.147558	0.0149056
$99$	4.05947	0.407992
$100$	−6.93358	−0.693358
$101$	−14.3950	−1.43235	−0.716177	−	0.697919i	$-0.754109\pi$
$101$	−14.3950	−1.43235	−0.716177	+	0.697919i	$0.754109\pi$
$102$	0.0249015	0.00246561
$103$	−7.12108	−0.701661	−0.350831	−	0.936439i	$-0.614101\pi$
$103$	−7.12108	−0.701661	−0.350831	+	0.936439i	$0.614101\pi$
$104$	0.667076	0.0654122
$105$	3.01618	0.294349
$106$	−0.0449678	−0.00436766
$107$	−7.01460	−0.678127	−0.339063	−	0.940764i	$-0.610110\pi$
$107$	−7.01460	−0.678127	−0.339063	+	0.940764i	$0.610110\pi$
$108$	1.99938	0.192390
$109$	−16.8916	−1.61793	−0.808963	−	0.587859i	$-0.799971\pi$
$109$	−16.8916	−1.61793	−0.808963	+	0.587859i	$0.799971\pi$
$110$	0.294158	0.0280469
$111$	−10.2673	−0.974527
$112$	4.14215	0.391396
$113$	1.95424	0.183839	0.0919195	−	0.995766i	$-0.470700\pi$
$113$	1.95424	0.183839	0.0919195	+	0.995766i	$0.470700\pi$
$114$	−0.0590594	−0.00553142
$115$	7.25995	0.676994
$116$	15.3372	1.42403
$117$	6.69820	0.619248
$118$	0.0618479	0.00569356
$119$	1.03650	0.0950159
$120$	0.289804	0.0264554
$121$	5.47929	0.498117
$122$	−0.0349786	−0.00316682
$123$	5.84895	0.527382
$124$	0.908292	0.0815670
$125$	4.45846	0.398776
$126$	−0.0258104	−0.00229937
$127$	4.50956	0.400159	0.200079	−	0.979780i	$-0.435880\pi$
$127$	4.50956	0.400159	0.200079	+	0.979780i	$0.435880\pi$
$128$	0.796229	0.0703774
$129$	1.58782	0.139800
$130$	0.485366	0.0425694
$131$	15.6563	1.36789	0.683947	−	0.729531i	$-0.260262\pi$
$131$	15.6563	1.36789	0.683947	+	0.729531i	$0.260262\pi$
$132$	8.11642	0.706444
$133$	−2.45829	−0.213161
$134$	−0.0797355	−0.00688810
$135$	2.90996	0.250449
$136$	0.0995904	0.00853981
$137$	17.6749	1.51007	0.755035	−	0.655685i	$-0.227620\pi$
$137$	17.6749	1.51007	0.755035	+	0.655685i	$0.227620\pi$
$138$	−0.0621257	−0.00528849
$139$	9.47484	0.803646	0.401823	−	0.915717i	$-0.368377\pi$
$139$	9.47484	0.803646	0.401823	+	0.915717i	$0.368377\pi$
$140$	6.03048	0.509669
$141$	−6.87468	−0.578953
$142$	−0.366502	−0.0307562
$143$	27.1911	2.27384
$144$	3.99628	0.333023
$145$	22.3223	1.85377
$146$	−0.180630	−0.0149491
$147$	5.92566	0.488741
$148$	−20.5282	−1.68741
$149$	−13.0514	−1.06921	−0.534605	−	0.845102i	$-0.679540\pi$
$149$	−13.0514	−1.06921	−0.534605	+	0.845102i	$0.679540\pi$
$150$	0.0863549	0.00705085
$151$	−3.44925	−0.280696	−0.140348	−	0.990102i	$-0.544822\pi$
$151$	−3.44925	−0.280696	−0.140348	+	0.990102i	$0.544822\pi$
$152$	−0.236201	−0.0191584
$153$	1.00000	0.0808452
$154$	−0.104777	−0.00844313
$155$	1.32196	0.106182
$156$	13.3922	1.07224
$157$	14.7117	1.17412	0.587059	−	0.809544i	$-0.300286\pi$
$157$	14.7117	1.17412	0.587059	+	0.809544i	$0.300286\pi$
$158$	0.0249015	0.00198105
$159$	−1.80583	−0.143212
$160$	0.869187	0.0687153
$161$	−2.58593	−0.203800
$162$	−0.0249015	−0.00195644
$163$	17.8773	1.40026	0.700130	−	0.714015i	$-0.253125\pi$
$163$	17.8773	1.40026	0.700130	+	0.714015i	$0.253125\pi$
$164$	11.6943	0.913170
$165$	11.8129	0.919632
$166$	0.245211	0.0190320
$167$	−6.74066	−0.521608	−0.260804	−	0.965392i	$-0.583988\pi$
$167$	−6.74066	−0.521608	−0.260804	+	0.965392i	$0.583988\pi$
$168$	−0.103226	−0.00796403
$169$	31.8658	2.45122
$170$	0.0724622	0.00555760
$171$	−2.37172	−0.181370
$172$	3.17466	0.242065
$173$	16.2491	1.23539	0.617696	−	0.786417i	$-0.288066\pi$
$173$	16.2491	1.23539	0.617696	+	0.786417i	$0.288066\pi$
$174$	−0.191019	−0.0144811
$175$	3.59444	0.271714
$176$	16.2228	1.22284
$177$	2.48371	0.186687
$178$	0.0149402	0.00111981
$179$	−1.08719	−0.0812601	−0.0406301	−	0.999174i	$-0.512937\pi$
$179$	−1.08719	−0.0812601	−0.0406301	+	0.999174i	$0.512937\pi$
$180$	5.81811	0.433657
$181$	4.37465	0.325166	0.162583	−	0.986695i	$-0.448018\pi$
$181$	4.37465	0.325166	0.162583	+	0.986695i	$0.448018\pi$
$182$	−0.172883	−0.0128149
$183$	−1.40468	−0.103837
$184$	−0.248464	−0.0183170
$185$	−29.8774	−2.19663
$186$	−0.0113124	−0.000829466 0
$187$	4.05947	0.296858
$188$	−13.7451	−1.00246
$189$	−1.03650	−0.0753944
$190$	−0.171860	−0.0124681
$191$	−11.9948	−0.867910	−0.433955	−	0.900935i	$-0.642882\pi$
$191$	−11.9948	−0.867910	−0.433955	+	0.900935i	$0.642882\pi$
$192$	7.98512	0.576277
$193$	−10.9214	−0.786137	−0.393068	−	0.919509i	$-0.628586\pi$
$193$	−10.9214	−0.786137	−0.393068	+	0.919509i	$0.628586\pi$
$194$	−0.331952	−0.0238328
$195$	19.4915	1.39581
$196$	11.8477	0.846261
$197$	−5.70152	−0.406216	−0.203108	−	0.979156i	$-0.565104\pi$
$197$	−5.70152	−0.406216	−0.203108	+	0.979156i	$0.565104\pi$
$198$	−0.101087	−0.00718392
$199$	−1.95029	−0.138252	−0.0691261	−	0.997608i	$-0.522021\pi$
$199$	−1.95029	−0.138252	−0.0691261	+	0.997608i	$0.522021\pi$
$200$	0.345366	0.0244211
$201$	−3.20204	−0.225855
$202$	0.358456	0.0252209
$203$	−7.95101	−0.558051
$204$	1.99938	0.139985
$205$	17.0202	1.18874
$206$	0.177325	0.0123548
$207$	−2.49486	−0.173405
$208$	26.7679	1.85602
$209$	−9.62794	−0.665978
$210$	−0.0751072	−0.00518289
$211$	5.78953	0.398568	0.199284	−	0.979942i	$-0.436138\pi$
$211$	5.78953	0.398568	0.199284	+	0.979942i	$0.436138\pi$
$212$	−3.61054	−0.247973
$213$	−14.7181	−1.00847
$214$	0.174674	0.0119405
$215$	4.62049	0.315115
$216$	−0.0995904	−0.00677627
$217$	−0.470869	−0.0319647
$218$	0.420627	0.0284884
$219$	−7.25379	−0.490166
$220$	23.6185	1.59236
$221$	6.69820	0.450569
$222$	0.255670	0.0171595
$223$	7.88540	0.528045	0.264023	−	0.964516i	$-0.414951\pi$
$223$	7.88540	0.528045	0.264023	+	0.964516i	$0.414951\pi$
$224$	−0.309597	−0.0206858
$225$	3.46786	0.231191
$226$	−0.0486633	−0.00323704
$227$	28.7601	1.90887	0.954437	−	0.298411i	$-0.0964566\pi$
$227$	28.7601	1.90887	0.954437	+	0.298411i	$0.0964566\pi$
$228$	−4.74198	−0.314045
$229$	−15.2133	−1.00532	−0.502661	−	0.864484i	$-0.667645\pi$
$229$	−15.2133	−1.00532	−0.502661	+	0.864484i	$0.667645\pi$
$230$	−0.180783	−0.0119205
$231$	−4.20765	−0.276843
$232$	−0.763958	−0.0501563
$233$	−21.5995	−1.41503	−0.707515	−	0.706699i	$-0.750184\pi$
$233$	−21.5995	−1.41503	−0.707515	+	0.706699i	$0.750184\pi$
$234$	−0.166795	−0.0109037
$235$	−20.0050	−1.30499
$236$	4.96587	0.323251
$237$	1.00000	0.0649570
$238$	−0.0258104	−0.00167304
$239$	6.00418	0.388378	0.194189	−	0.980964i	$-0.437792\pi$
$239$	6.00418	0.388378	0.194189	+	0.980964i	$0.437792\pi$
$240$	11.6290	0.750649
$241$	19.8263	1.27713	0.638563	−	0.769570i	$-0.279529\pi$
$241$	19.8263	1.27713	0.638563	+	0.769570i	$0.279529\pi$
$242$	−0.136442	−0.00877084
$243$	−1.00000	−0.0641500
$244$	−2.80849	−0.179795
$245$	17.2434	1.10164
$246$	−0.145647	−0.00928614
$247$	−15.8863	−1.01082
$248$	−0.0452426	−0.00287291
$249$	9.84725	0.624044
$250$	−0.111022	−0.00702165
$251$	−17.9762	−1.13465	−0.567323	−	0.823495i	$-0.692021\pi$
$251$	−17.9762	−1.13465	−0.567323	+	0.823495i	$0.692021\pi$
$252$	−2.07236	−0.130546
$253$	−10.1278	−0.636731
$254$	−0.112295	−0.00704599
$255$	2.90996	0.182229
$256$	15.9504	0.996901
$257$	−16.0635	−1.00202	−0.501008	−	0.865443i	$-0.667037\pi$
$257$	−16.0635	−1.00202	−0.501008	+	0.865443i	$0.667037\pi$
$258$	−0.0395390	−0.00246159
$259$	10.6420	0.661265
$260$	38.9709	2.41687
$261$	−7.67100	−0.474823
$262$	−0.389864	−0.0240859
$263$	3.72190	0.229502	0.114751	−	0.993394i	$-0.463393\pi$
$263$	3.72190	0.229502	0.114751	+	0.993394i	$0.463393\pi$
$264$	−0.404284	−0.0248820
$265$	−5.25490	−0.322806
$266$	0.0612151	0.00375334
$267$	0.599972	0.0367177
$268$	−6.40210	−0.391070
$269$	20.6003	1.25602	0.628011	−	0.778204i	$-0.283869\pi$
$269$	20.6003	1.25602	0.628011	+	0.778204i	$0.283869\pi$
$270$	−0.0724622	−0.00440991
$271$	−19.0404	−1.15662	−0.578310	−	0.815817i	$-0.696288\pi$
$271$	−19.0404	−1.15662	−0.578310	+	0.815817i	$0.696288\pi$
$272$	3.99628	0.242310
$273$	−6.94269	−0.420191
$274$	−0.440131	−0.0265893
$275$	14.0777	0.848916
$276$	−4.98818	−0.300253
$277$	29.1165	1.74944	0.874719	−	0.484630i	$-0.161046\pi$
$277$	29.1165	1.74944	0.874719	+	0.484630i	$0.161046\pi$
$278$	−0.235937	−0.0141506
$279$	−0.454287	−0.0271974
$280$	−0.300382	−0.0179513
$281$	−16.3363	−0.974540	−0.487270	−	0.873251i	$-0.662007\pi$
$281$	−16.3363	−0.974540	−0.487270	+	0.873251i	$0.662007\pi$
$282$	0.171190	0.0101942
$283$	−10.1049	−0.600675	−0.300337	−	0.953833i	$-0.597099\pi$
$283$	−10.1049	−0.600675	−0.300337	+	0.953833i	$0.597099\pi$
$284$	−29.4271	−1.74618
$285$	−6.90162	−0.408817
$286$	−0.677099	−0.0400377
$287$	−6.06245	−0.357855
$288$	−0.298694	−0.0176007
$289$	1.00000	0.0588235
$290$	−0.555858	−0.0326411
$291$	−13.3306	−0.781455
$292$	−14.5031	−0.848729
$293$	21.0739	1.23115	0.615575	−	0.788079i	$-0.288924\pi$
$293$	21.0739	1.23115	0.615575	+	0.788079i	$0.288924\pi$
$294$	−0.147558	−0.00860574
$295$	7.22749	0.420800
$296$	1.02252	0.0594329
$297$	−4.05947	−0.235554
$298$	0.324998	0.0188267
$299$	−16.7111	−0.966427
$300$	6.93358	0.400310
$301$	−1.64578	−0.0948610
$302$	0.0858914	0.00494249
$303$	14.3950	0.826969
$304$	−9.47807	−0.543604
$305$	−4.08757	−0.234054
$306$	−0.0249015	−0.00142352
$307$	8.58631	0.490047	0.245023	−	0.969517i	$-0.421204\pi$
$307$	8.58631	0.490047	0.245023	+	0.969517i	$0.421204\pi$
$308$	−8.41268	−0.479357
$309$	7.12108	0.405104
$310$	−0.0329186	−0.00186965
$311$	23.2305	1.31728	0.658640	−	0.752458i	$-0.271132\pi$
$311$	23.2305	1.31728	0.658640	+	0.752458i	$0.271132\pi$
$312$	−0.667076	−0.0377657
$313$	−0.840580	−0.0475124	−0.0237562	−	0.999718i	$-0.507563\pi$
$313$	−0.840580	−0.0475124	−0.0237562	+	0.999718i	$0.507563\pi$
$314$	−0.366342	−0.0206739
$315$	−3.01618	−0.169942
$316$	1.99938	0.112474
$317$	−10.4981	−0.589633	−0.294816	−	0.955554i	$-0.595258\pi$
$317$	−10.4981	−0.589633	−0.294816	+	0.955554i	$0.595258\pi$
$318$	0.0449678	0.00252167
$319$	−31.1402	−1.74352
$320$	23.2364	1.29895
$321$	7.01460	0.391517
$322$	0.0643934	0.00358851
$323$	−2.37172	−0.131966
$324$	−1.99938	−0.111077
$325$	23.2284	1.28848
$326$	−0.445172	−0.0246558
$327$	16.8916	0.934110
$328$	−0.582500	−0.0321632
$329$	7.12562	0.392848
$330$	−0.294158	−0.0161929
$331$	15.1743	0.834057	0.417028	−	0.908893i	$-0.363072\pi$
$331$	15.1743	0.834057	0.417028	+	0.908893i	$0.363072\pi$
$332$	19.6884	1.08054
$333$	10.2673	0.562643
$334$	0.167852	0.00918447
$335$	−9.31781	−0.509087
$336$	−4.14215	−0.225973
$337$	−21.4378	−1.16779	−0.583896	−	0.811828i	$-0.698473\pi$
$337$	−21.4378	−1.16779	−0.583896	+	0.811828i	$0.698473\pi$
$338$	−0.793506	−0.0431610
$339$	−1.95424	−0.106140
$340$	5.81811	0.315532
$341$	−1.84416	−0.0998670
$342$	0.0590594	0.00319356
$343$	−13.3975	−0.723395
$344$	−0.158132	−0.00852589
$345$	−7.25995	−0.390863
$346$	−0.404625	−0.0217528
$347$	1.82011	0.0977087	0.0488543	−	0.998806i	$-0.484443\pi$
$347$	1.82011	0.0977087	0.0488543	+	0.998806i	$0.484443\pi$
$348$	−15.3372	−0.822163
$349$	28.4929	1.52519	0.762596	−	0.646875i	$-0.223925\pi$
$349$	28.4929	1.52519	0.762596	+	0.646875i	$0.223925\pi$
$350$	−0.0895069	−0.00478435
$351$	−6.69820	−0.357523
$352$	−1.21254	−0.0646286
$353$	19.7289	1.05007	0.525033	−	0.851082i	$-0.324053\pi$
$353$	19.7289	1.05007	0.525033	+	0.851082i	$0.324053\pi$
$354$	−0.0618479	−0.00328718
$355$	−42.8291	−2.27313
$356$	1.19957	0.0635772
$357$	−1.03650	−0.0548575
$358$	0.0270725	0.00143083
$359$	31.8040	1.67855	0.839275	−	0.543707i	$-0.182980\pi$
$359$	31.8040	1.67855	0.839275	+	0.543707i	$0.182980\pi$
$360$	−0.289804	−0.0152740
$361$	−13.3749	−0.703944
$362$	−0.108935	−0.00572551
$363$	−5.47929	−0.287588
$364$	−13.8811	−0.727566
$365$	−21.1082	−1.10486
$366$	0.0349786	0.00182836
$367$	21.3839	1.11623	0.558116	−	0.829763i	$-0.311524\pi$
$367$	21.3839	1.11623	0.558116	+	0.829763i	$0.311524\pi$
$368$	−9.97017	−0.519731
$369$	−5.84895	−0.304484
$370$	0.743990	0.0386782
$371$	1.87175	0.0971763
$372$	−0.908292	−0.0470927
$373$	0.592442	0.0306755	0.0153377	−	0.999882i	$-0.495118\pi$
$373$	0.592442	0.0306755	0.0153377	+	0.999882i	$0.495118\pi$
$374$	−0.101087	−0.00522707
$375$	−4.45846	−0.230234
$376$	0.684652	0.0353083
$377$	−51.3819	−2.64630
$378$	0.0258104	0.00132754
$379$	4.65407	0.239064	0.119532	−	0.992830i	$-0.461861\pi$
$379$	4.65407	0.239064	0.119532	+	0.992830i	$0.461861\pi$
$380$	−13.7990	−0.707871
$381$	−4.50956	−0.231032
$382$	0.298687	0.0152822
$383$	−11.3668	−0.580816	−0.290408	−	0.956903i	$-0.593791\pi$
$383$	−11.3668	−0.580816	−0.290408	+	0.956903i	$0.593791\pi$
$384$	−0.796229	−0.0406324
$385$	−12.2441	−0.624016
$386$	0.271958	0.0138423
$387$	−1.58782	−0.0807134
$388$	−26.6530	−1.35310
$389$	5.76029	0.292058	0.146029	−	0.989280i	$-0.453351\pi$
$389$	5.76029	0.292058	0.146029	+	0.989280i	$0.453351\pi$
$390$	−0.485366	−0.0245775
$391$	−2.49486	−0.126171
$392$	−0.590139	−0.0298065
$393$	−15.6563	−0.789754
$394$	0.141976	0.00715266
$395$	2.90996	0.146416
$396$	−8.11642	−0.407865
$397$	−6.66107	−0.334310	−0.167155	−	0.985931i	$-0.553458\pi$
$397$	−6.66107	−0.334310	−0.167155	+	0.985931i	$0.553458\pi$
$398$	0.0485650	0.00243434
$399$	2.45829	0.123069
$400$	13.8586	0.692928
$401$	9.11153	0.455008	0.227504	−	0.973777i	$-0.426943\pi$
$401$	9.11153	0.455008	0.227504	+	0.973777i	$0.426943\pi$
$402$	0.0797355	0.00397685
$403$	−3.04290	−0.151578
$404$	28.7810	1.43191
$405$	−2.90996	−0.144597
$406$	0.197992	0.00982616
$407$	41.6797	2.06599
$408$	−0.0995904	−0.00493046
$409$	−1.26878	−0.0627371	−0.0313685	−	0.999508i	$-0.509987\pi$
$409$	−1.26878	−0.0627371	−0.0313685	+	0.999508i	$0.509987\pi$
$410$	−0.423828	−0.0209314
$411$	−17.6749	−0.871839
$412$	14.2378	0.701444
$413$	−2.57437	−0.126676
$414$	0.0621257	0.00305331
$415$	28.6551	1.40662
$416$	−2.00071	−0.0980929
$417$	−9.47484	−0.463985
$418$	0.239750	0.0117265
$419$	−34.1927	−1.67042	−0.835211	−	0.549930i	$-0.814655\pi$
$419$	−34.1927	−1.67042	−0.835211	+	0.549930i	$0.814655\pi$
$420$	−6.03048	−0.294257
$421$	27.5166	1.34107	0.670537	−	0.741876i	$-0.266064\pi$
$421$	27.5166	1.34107	0.670537	+	0.741876i	$0.266064\pi$
$422$	−0.144168	−0.00701798
$423$	6.87468	0.334259
$424$	0.179844	0.00873397
$425$	3.46786	0.168216
$426$	0.366502	0.0177571
$427$	1.45596	0.0704586
$428$	14.0248	0.677917
$429$	−27.1911	−1.31280
$430$	−0.115057	−0.00554854
$431$	−19.5047	−0.939509	−0.469755	−	0.882797i	$-0.655658\pi$
$431$	−19.5047	−0.939509	−0.469755	+	0.882797i	$0.655658\pi$
$432$	−3.99628	−0.192271
$433$	33.4931	1.60957	0.804787	−	0.593563i	$-0.202279\pi$
$433$	33.4931	1.60957	0.804787	+	0.593563i	$0.202279\pi$
$434$	0.0117253	0.000562834 0
$435$	−22.3223	−1.07027
$436$	33.7728	1.61742
$437$	5.91712	0.283054
$438$	0.180630	0.00863084
$439$	13.7822	0.657787	0.328894	−	0.944367i	$-0.393324\pi$
$439$	13.7822	0.657787	0.328894	+	0.944367i	$0.393324\pi$
$440$	−1.17645	−0.0560851
$441$	−5.92566	−0.282175
$442$	−0.166795	−0.00793362
$443$	15.1791	0.721181	0.360591	−	0.932724i	$-0.382575\pi$
$443$	15.1791	0.721181	0.360591	+	0.932724i	$0.382575\pi$
$444$	20.5282	0.974225
$445$	1.74589	0.0827633
$446$	−0.196358	−0.00929782
$447$	13.0514	0.617309
$448$	−8.27659	−0.391032
$449$	14.0812	0.664531	0.332266	−	0.943186i	$-0.392187\pi$
$449$	14.0812	0.664531	0.332266	+	0.943186i	$0.392187\pi$
$450$	−0.0863549	−0.00407081
$451$	−23.7436	−1.11804
$452$	−3.90726	−0.183782
$453$	3.44925	0.162060
$454$	−0.716169	−0.0336115
$455$	−20.2029	−0.947129
$456$	0.236201	0.0110611
$457$	−2.50520	−0.117188	−0.0585941	−	0.998282i	$-0.518662\pi$
$457$	−2.50520	−0.117188	−0.0585941	+	0.998282i	$0.518662\pi$
$458$	0.378833	0.0177017
$459$	−1.00000	−0.0466760
$460$	−14.5154	−0.676784
$461$	−22.4385	−1.04507	−0.522533	−	0.852619i	$-0.675013\pi$
$461$	−22.4385	−1.04507	−0.522533	+	0.852619i	$0.675013\pi$
$462$	0.104777	0.00487465
$463$	16.9464	0.787565	0.393783	−	0.919204i	$-0.371166\pi$
$463$	16.9464	0.787565	0.393783	+	0.919204i	$0.371166\pi$
$464$	−30.6555	−1.42314
$465$	−1.32196	−0.0613042
$466$	0.537859	0.0249158
$467$	−30.6212	−1.41698	−0.708491	−	0.705720i	$-0.750624\pi$
$467$	−30.6212	−1.41698	−0.708491	+	0.705720i	$0.750624\pi$
$468$	−13.3922	−0.619056
$469$	3.31892	0.153254
$470$	0.498155	0.0229782
$471$	−14.7117	−0.677877
$472$	−0.247353	−0.0113854
$473$	−6.44571	−0.296374
$474$	−0.0249015	−0.00114376
$475$	−8.22481	−0.377380
$476$	−2.07236	−0.0949865
$477$	1.80583	0.0826833
$478$	−0.149513	−0.00683856
$479$	30.7471	1.40487	0.702435	−	0.711748i	$-0.252096\pi$
$479$	30.7471	1.40487	0.702435	+	0.711748i	$0.252096\pi$
$480$	−0.869187	−0.0396728
$481$	68.7722	3.13574
$482$	−0.493705	−0.0224876
$483$	2.58593	0.117664
$484$	−10.9552	−0.497963
$485$	−38.7916	−1.76144
$486$	0.0249015	0.00112955
$487$	−31.0665	−1.40776	−0.703878	−	0.710321i	$-0.748550\pi$
$487$	−31.0665	−1.40776	−0.703878	+	0.710321i	$0.748550\pi$
$488$	0.139893	0.00633265
$489$	−17.8773	−0.808441
$490$	−0.429387	−0.0193977
$491$	−28.2663	−1.27564	−0.637820	−	0.770186i	$-0.720164\pi$
$491$	−28.2663	−1.27564	−0.637820	+	0.770186i	$0.720164\pi$
$492$	−11.6943	−0.527219
$493$	−7.67100	−0.345485
$494$	0.395591	0.0177985
$495$	−11.8129	−0.530950
$496$	−1.81546	−0.0815164
$497$	15.2553	0.684296
$498$	−0.245211	−0.0109882
$499$	0.937707	0.0419775	0.0209888	−	0.999780i	$-0.493319\pi$
$499$	0.937707	0.0419775	0.0209888	+	0.999780i	$0.493319\pi$
$500$	−8.91415	−0.398653
$501$	6.74066	0.301150
$502$	0.447633	0.0199788
$503$	20.1017	0.896290	0.448145	−	0.893961i	$-0.352085\pi$
$503$	20.1017	0.896290	0.448145	+	0.893961i	$0.352085\pi$
$504$	0.103226	0.00459803
$505$	41.8888	1.86403
$506$	0.252198	0.0112115
$507$	−31.8658	−1.41521
$508$	−9.01633	−0.400035
$509$	18.1330	0.803731	0.401865	−	0.915699i	$-0.368362\pi$
$509$	18.1330	0.803731	0.401865	+	0.915699i	$0.368362\pi$
$510$	−0.0724622	−0.00320868
$511$	7.51857	0.332602
$512$	−1.98965	−0.0879308
$513$	2.37172	0.104714
$514$	0.400006	0.0176435
$515$	20.7221	0.913123
$516$	−3.17466	−0.139756
$517$	27.9076	1.22737
$518$	−0.265003	−0.0116435
$519$	−16.2491	−0.713254
$520$	−1.94116	−0.0851257
$521$	3.94710	0.172926	0.0864628	−	0.996255i	$-0.472444\pi$
$521$	3.94710	0.172926	0.0864628	+	0.996255i	$0.472444\pi$
$522$	0.191019	0.00836068
$523$	−5.97457	−0.261250	−0.130625	−	0.991432i	$-0.541698\pi$
$523$	−5.97457	−0.261250	−0.130625	+	0.991432i	$0.541698\pi$
$524$	−31.3028	−1.36747
$525$	−3.59444	−0.156874
$526$	−0.0926808	−0.00404107
$527$	−0.454287	−0.0197890
$528$	−16.2228	−0.706006
$529$	−16.7757	−0.729376
$530$	0.130855	0.00568396
$531$	−2.48371	−0.107784
$532$	4.91506	0.213095
$533$	−39.1774	−1.69696
$534$	−0.0149402	−0.000646525 0
$535$	20.4122	0.882496
$536$	0.318893	0.0137741
$537$	1.08719	0.0469155
$538$	−0.512977	−0.0221160
$539$	−24.0551	−1.03612
$540$	−5.81811	−0.250372
$541$	−1.93628	−0.0832472	−0.0416236	−	0.999133i	$-0.513253\pi$
$541$	−1.93628	−0.0832472	−0.0416236	+	0.999133i	$0.513253\pi$
$542$	0.474133	0.0203658
$543$	−4.37465	−0.187734
$544$	−0.298694	−0.0128064
$545$	49.1540	2.10553
$546$	0.172883	0.00739871
$547$	24.3218	1.03993	0.519963	−	0.854189i	$-0.325946\pi$
$547$	24.3218	1.03993	0.519963	+	0.854189i	$0.325946\pi$
$548$	−35.3389	−1.50960
$549$	1.40468	0.0599504
$550$	−0.350555	−0.0149477
$551$	18.1935	0.775069
$552$	0.248464	0.0105754
$553$	−1.03650	−0.0440765
$554$	−0.725043	−0.0308041
$555$	29.8774	1.26822
$556$	−18.9438	−0.803396
$557$	41.0624	1.73987	0.869935	−	0.493167i	$-0.164161\pi$
$557$	41.0624	1.73987	0.869935	+	0.493167i	$0.164161\pi$
$558$	0.0113124	0.000478892 0
$559$	−10.6355	−0.449835
$560$	−12.0535	−0.509353
$561$	−4.05947	−0.171391
$562$	0.406797	0.0171597
$563$	−15.3225	−0.645768	−0.322884	−	0.946439i	$-0.604652\pi$
$563$	−15.3225	−0.645768	−0.322884	+	0.946439i	$0.604652\pi$
$564$	13.7451	0.578773
$565$	−5.68675	−0.239243
$566$	0.251627	0.0105767
$567$	1.03650	0.0435290
$568$	1.46578	0.0615029
$569$	−3.75501	−0.157418	−0.0787092	−	0.996898i	$-0.525080\pi$
$569$	−3.75501	−0.157418	−0.0787092	+	0.996898i	$0.525080\pi$
$570$	0.171860	0.00719844
$571$	36.2678	1.51776	0.758880	−	0.651230i	$-0.225747\pi$
$571$	36.2678	1.51776	0.758880	+	0.651230i	$0.225747\pi$
$572$	−54.3654	−2.27313
$573$	11.9948	0.501088
$574$	0.150964	0.00630111
$575$	−8.65184	−0.360807
$576$	−7.98512	−0.332713
$577$	23.0277	0.958655	0.479327	−	0.877636i	$-0.340881\pi$
$577$	23.0277	0.958655	0.479327	+	0.877636i	$0.340881\pi$
$578$	−0.0249015	−0.00103576
$579$	10.9214	0.453876
$580$	−44.6308	−1.85319
$581$	−10.2067	−0.423445
$582$	0.331952	0.0137599
$583$	7.33072	0.303607
$584$	0.722408	0.0298935
$585$	−19.4915	−0.805873
$586$	−0.524770	−0.0216781
$587$	−24.0357	−0.992061	−0.496031	−	0.868305i	$-0.665210\pi$
$587$	−24.0357	−0.992061	−0.496031	+	0.868305i	$0.665210\pi$
$588$	−11.8477	−0.488589
$589$	1.07744	0.0443952
$590$	−0.179975	−0.00740945
$591$	5.70152	0.234529
$592$	41.0309	1.68636
$593$	−11.4794	−0.471401	−0.235701	−	0.971826i	$-0.575738\pi$
$593$	−11.4794	−0.471401	−0.235701	+	0.971826i	$0.575738\pi$
$594$	0.101087	0.00414764
$595$	−3.01618	−0.123651
$596$	26.0947	1.06888
$597$	1.95029	0.0798200
$598$	0.416130	0.0170168
$599$	−13.9284	−0.569101	−0.284550	−	0.958661i	$-0.591844\pi$
$599$	−13.9284	−0.569101	−0.284550	+	0.958661i	$0.591844\pi$
$600$	−0.345366	−0.0140995
$601$	−22.4015	−0.913778	−0.456889	−	0.889524i	$-0.651036\pi$
$601$	−22.4015	−0.913778	−0.456889	+	0.889524i	$0.651036\pi$
$602$	0.0409823	0.00167031
$603$	3.20204	0.130397
$604$	6.89636	0.280609
$605$	−15.9445	−0.648236
$606$	−0.358456	−0.0145613
$607$	11.9455	0.484851	0.242426	−	0.970170i	$-0.422057\pi$
$607$	11.9455	0.484851	0.242426	+	0.970170i	$0.422057\pi$
$608$	0.708419	0.0287302
$609$	7.95101	0.322191
$610$	0.101786	0.00412121
$611$	46.0480	1.86290
$612$	−1.99938	−0.0808201
$613$	5.83048	0.235491	0.117745	−	0.993044i	$-0.462433\pi$
$613$	5.83048	0.235491	0.117745	+	0.993044i	$0.462433\pi$
$614$	−0.213812	−0.00862874
$615$	−17.0202	−0.686321
$616$	0.419041	0.0168836
$617$	16.5988	0.668243	0.334122	−	0.942530i	$-0.391560\pi$
$617$	16.5988	0.668243	0.334122	+	0.942530i	$0.391560\pi$
$618$	−0.177325	−0.00713307
$619$	19.1636	0.770252	0.385126	−	0.922864i	$-0.374158\pi$
$619$	19.1636	0.770252	0.385126	+	0.922864i	$0.374158\pi$
$620$	−2.64309	−0.106149
$621$	2.49486	0.100115
$622$	−0.578473	−0.0231947
$623$	−0.621872	−0.0249148
$624$	−26.7679	−1.07157
$625$	−30.3132	−1.21253
$626$	0.0209317	0.000836597 0
$627$	9.62794	0.384503
$628$	−29.4142	−1.17375
$629$	10.2673	0.409383
$630$	0.0751072	0.00299234
$631$	14.0695	0.560097	0.280049	−	0.959986i	$-0.409649\pi$
$631$	14.0695	0.560097	0.280049	+	0.959986i	$0.409649\pi$
$632$	−0.0995904	−0.00396149
$633$	−5.78953	−0.230113
$634$	0.261418	0.0103822
$635$	−13.1226	−0.520756
$636$	3.61054	0.143167
$637$	−39.6913	−1.57263
$638$	0.775437	0.0306998
$639$	14.7181	0.582239
$640$	−2.31699	−0.0915873
$641$	−19.5953	−0.773969	−0.386984	−	0.922086i	$-0.626483\pi$
$641$	−19.5953	−0.773969	−0.386984	+	0.922086i	$0.626483\pi$
$642$	−0.174674	−0.00689382
$643$	−0.112533	−0.00443787	−0.00221893	−	0.999998i	$-0.500706\pi$
$643$	−0.112533	−0.00443787	−0.00221893	+	0.999998i	$0.500706\pi$
$644$	5.17026	0.203737
$645$	−4.62049	−0.181932
$646$	0.0590594	0.00232366
$647$	29.8596	1.17390	0.586952	−	0.809622i	$-0.300328\pi$
$647$	29.8596	1.17390	0.586952	+	0.809622i	$0.300328\pi$
$648$	0.0995904	0.00391228
$649$	−10.0825	−0.395774
$650$	−0.578422	−0.0226876
$651$	0.470869	0.0184548
$652$	−35.7436	−1.39983
$653$	−45.1570	−1.76713	−0.883564	−	0.468310i	$-0.844863\pi$
$653$	−45.1570	−1.76713	−0.883564	+	0.468310i	$0.844863\pi$
$654$	−0.420627	−0.0164478
$655$	−45.5591	−1.78014
$656$	−23.3741	−0.912603
$657$	7.25379	0.282997
$658$	−0.177438	−0.00691727
$659$	13.1908	0.513839	0.256920	−	0.966433i	$-0.417292\pi$
$659$	13.1908	0.513839	0.256920	+	0.966433i	$0.417292\pi$
$660$	−23.6185	−0.919347
$661$	31.5931	1.22883	0.614415	−	0.788983i	$-0.289392\pi$
$661$	31.5931	1.22883	0.614415	+	0.788983i	$0.289392\pi$
$662$	−0.377863	−0.0146861
$663$	−6.69820	−0.260136
$664$	−0.980691	−0.0380582
$665$	7.15354	0.277402
$666$	−0.255670	−0.00990702
$667$	19.1381	0.741030
$668$	13.4771	0.521446
$669$	−7.88540	−0.304867
$670$	0.232027	0.00896399
$671$	5.70227	0.220134
$672$	0.309597	0.0119430
$673$	14.9067	0.574612	0.287306	−	0.957839i	$-0.407240\pi$
$673$	14.9067	0.574612	0.287306	+	0.957839i	$0.407240\pi$
$674$	0.533833	0.0205625
$675$	−3.46786	−0.133478
$676$	−63.7119	−2.45046
$677$	−20.7961	−0.799258	−0.399629	−	0.916677i	$-0.630861\pi$
$677$	−20.7961	−0.799258	−0.399629	+	0.916677i	$0.630861\pi$
$678$	0.0486633	0.00186890
$679$	13.8172	0.530256
$680$	−0.289804	−0.0111135
$681$	−28.7601	−1.10209
$682$	0.0459224	0.00175846
$683$	29.0283	1.11074	0.555369	−	0.831604i	$-0.312577\pi$
$683$	29.0283	1.11074	0.555369	+	0.831604i	$0.312577\pi$
$684$	4.74198	0.181314
$685$	−51.4333	−1.96516
$686$	0.333617	0.0127375
$687$	15.2133	0.580422
$688$	−6.34537	−0.241915
$689$	12.0958	0.460814
$690$	0.180783	0.00688231
$691$	13.0362	0.495920	0.247960	−	0.968770i	$-0.420240\pi$
$691$	13.0362	0.495920	0.247960	+	0.968770i	$0.420240\pi$
$692$	−32.4880	−1.23501
$693$	4.20765	0.159835
$694$	−0.0453234	−0.00172045
$695$	−27.5714	−1.04584
$696$	0.763958	0.0289578
$697$	−5.84895	−0.221545
$698$	−0.709516	−0.0268556
$699$	21.5995	0.816968
$700$	−7.18666	−0.271630
$701$	−5.41336	−0.204460	−0.102230	−	0.994761i	$-0.532598\pi$
$701$	−5.41336	−0.204460	−0.102230	+	0.994761i	$0.532598\pi$
$702$	0.166795	0.00629527
$703$	−24.3511	−0.918420
$704$	−32.4154	−1.22170
$705$	20.0050	0.753434
$706$	−0.491280	−0.0184896
$707$	−14.9204	−0.561140
$708$	−4.96587	−0.186629
$709$	31.0716	1.16692	0.583458	−	0.812143i	$-0.301699\pi$
$709$	31.0716	1.16692	0.583458	+	0.812143i	$0.301699\pi$
$710$	1.06651	0.0400253
$711$	−1.00000	−0.0375029
$712$	−0.0597514	−0.00223928
$713$	1.13338	0.0424455
$714$	0.0258104	0.000965930 0
$715$	−79.1250	−2.95911
$716$	2.17370	0.0812349
$717$	−6.00418	−0.224230
$718$	−0.791966	−0.0295559
$719$	−11.9949	−0.447333	−0.223666	−	0.974666i	$-0.571803\pi$
$719$	−11.9949	−0.447333	−0.223666	+	0.974666i	$0.571803\pi$
$720$	−11.6290	−0.433388
$721$	−7.38101	−0.274883
$722$	0.333055	0.0123950
$723$	−19.8263	−0.737349
$724$	−8.74660	−0.325065
$725$	−26.6020	−0.987973
$726$	0.136442	0.00506385
$727$	−14.6161	−0.542082	−0.271041	−	0.962568i	$-0.587368\pi$
$727$	−14.6161	−0.542082	−0.271041	+	0.962568i	$0.587368\pi$
$728$	0.691425	0.0256259
$729$	1.00000	0.0370370
$730$	0.525626	0.0194543
$731$	−1.58782	−0.0587276
$732$	2.80849	0.103805
$733$	−11.5118	−0.425197	−0.212598	−	0.977140i	$-0.568193\pi$
$733$	−11.5118	−0.425197	−0.212598	+	0.977140i	$0.568193\pi$
$734$	−0.532491	−0.0196546
$735$	−17.2434	−0.636034
$736$	0.745201	0.0274685
$737$	12.9986	0.478809
$738$	0.145647	0.00536136
$739$	34.5469	1.27083	0.635414	−	0.772171i	$-0.280829\pi$
$739$	34.5469	1.27083	0.635414	+	0.772171i	$0.280829\pi$
$740$	59.7362	2.19595
$741$	15.8863	0.583596
$742$	−0.0466092	−0.00171108
$743$	26.3839	0.967932	0.483966	−	0.875087i	$-0.339196\pi$
$743$	26.3839	0.967932	0.483966	+	0.875087i	$0.339196\pi$
$744$	0.0452426	0.00165867
$745$	37.9790	1.39144
$746$	−0.0147527	−0.000540134 0
$747$	−9.84725	−0.360292
$748$	−8.11642	−0.296766
$749$	−7.27064	−0.265663
$750$	0.111022	0.00405395
$751$	5.23686	0.191096	0.0955479	−	0.995425i	$-0.469540\pi$
$751$	5.23686	0.191096	0.0955479	+	0.995425i	$0.469540\pi$
$752$	27.4732	1.00184
$753$	17.9762	0.655088
$754$	1.27948	0.0465961
$755$	10.0372	0.365290
$756$	2.07236	0.0753710
$757$	41.2112	1.49785	0.748923	−	0.662657i	$-0.230571\pi$
$757$	41.2112	1.49785	0.748923	+	0.662657i	$0.230571\pi$
$758$	−0.115893	−0.00420943
$759$	10.1278	0.367617
$760$	0.687335	0.0249323
$761$	36.5213	1.32390	0.661949	−	0.749549i	$-0.269730\pi$
$761$	36.5213	1.32390	0.661949	+	0.749549i	$0.269730\pi$
$762$	0.112295	0.00406801
$763$	−17.5082	−0.633840
$764$	23.9821	0.867641
$765$	−2.90996	−0.105210
$766$	0.283050	0.0102270
$767$	−16.6364	−0.600704
$768$	−15.9504	−0.575561
$769$	44.6267	1.60928	0.804640	−	0.593762i	$-0.202358\pi$
$769$	44.6267	1.60928	0.804640	+	0.593762i	$0.202358\pi$
$770$	0.304895	0.0109877
$771$	16.0635	0.578514
$772$	21.8360	0.785893
$773$	10.9673	0.394468	0.197234	−	0.980356i	$-0.436804\pi$
$773$	10.9673	0.394468	0.197234	+	0.980356i	$0.436804\pi$
$774$	0.0395390	0.00142120
$775$	−1.57540	−0.0565902
$776$	1.32760	0.0476582
$777$	−10.6420	−0.381781
$778$	−0.143440	−0.00514256
$779$	13.8721	0.497019
$780$	−38.9709	−1.39538
$781$	59.7477	2.13794
$782$	0.0621257	0.00222161
$783$	7.67100	0.274139
$784$	−23.6806	−0.845736
$785$	−42.8103	−1.52797
$786$	0.389864	0.0139060
$787$	35.9296	1.28075	0.640376	−	0.768061i	$-0.278778\pi$
$787$	35.9296	1.28075	0.640376	+	0.768061i	$0.278778\pi$
$788$	11.3995	0.406090
$789$	−3.72190	−0.132503
$790$	−0.0724622	−0.00257809
$791$	2.02557	0.0720209
$792$	0.404284	0.0143656
$793$	9.40884	0.334118
$794$	0.165870	0.00588652
$795$	5.25490	0.186372
$796$	3.89937	0.138209
$797$	−8.19016	−0.290110	−0.145055	−	0.989424i	$-0.546336\pi$
$797$	−8.19016	−0.290110	−0.145055	+	0.989424i	$0.546336\pi$
$798$	−0.0612151	−0.00216699
$799$	6.87468	0.243209
$800$	−1.03583	−0.0366221
$801$	−0.599972	−0.0211990
$802$	−0.226890	−0.00801178
$803$	29.4466	1.03915
$804$	6.40210	0.225785
$805$	7.52495	0.265220
$806$	0.0757727	0.00266898
$807$	−20.6003	−0.725165
$808$	−1.43360	−0.0504339
$809$	7.68925	0.270340	0.135170	−	0.990822i	$-0.456842\pi$
$809$	7.68925	0.270340	0.135170	+	0.990822i	$0.456842\pi$
$810$	0.0724622	0.00254606
$811$	31.1649	1.09435	0.547174	−	0.837019i	$-0.315704\pi$
$811$	31.1649	1.09435	0.547174	+	0.837019i	$0.315704\pi$
$812$	15.8971	0.557878
$813$	19.0404	0.667775
$814$	−1.03789	−0.0363779
$815$	−52.0223	−1.82226
$816$	−3.99628	−0.139898
$817$	3.76587	0.131751
$818$	0.0315945	0.00110467
$819$	6.94269	0.242597
$820$	−34.0299	−1.18837
$821$	38.0210	1.32694	0.663471	−	0.748202i	$-0.269083\pi$
$821$	38.0210	1.32694	0.663471	+	0.748202i	$0.269083\pi$
$822$	0.440131	0.0153513
$823$	−24.5663	−0.856328	−0.428164	−	0.903701i	$-0.640839\pi$
$823$	−24.5663	−0.856328	−0.428164	+	0.903701i	$0.640839\pi$
$824$	−0.709192	−0.0247059
$825$	−14.0777	−0.490122
$826$	0.0641055	0.00223051
$827$	3.37100	0.117221	0.0586106	−	0.998281i	$-0.481333\pi$
$827$	3.37100	0.117221	0.0586106	+	0.998281i	$0.481333\pi$
$828$	4.98818	0.173351
$829$	18.2048	0.632279	0.316140	−	0.948713i	$-0.397613\pi$
$829$	18.2048	0.632279	0.316140	+	0.948713i	$0.397613\pi$
$830$	−0.713553	−0.0247678
$831$	−29.1165	−1.01004
$832$	−53.4859	−1.85429
$833$	−5.92566	−0.205312
$834$	0.235937	0.00816985
$835$	19.6150	0.678807
$836$	19.2499	0.665772
$837$	0.454287	0.0157024
$838$	0.851448	0.0294128
$839$	−2.94275	−0.101595	−0.0507975	−	0.998709i	$-0.516176\pi$
$839$	−2.94275	−0.101595	−0.0507975	+	0.998709i	$0.516176\pi$
$840$	0.300382	0.0103642
$841$	29.8443	1.02911
$842$	−0.685202	−0.0236136
$843$	16.3363	0.562651
$844$	−11.5755	−0.398444
$845$	−92.7283	−3.18995
$846$	−0.171190	−0.00588562
$847$	5.67929	0.195143
$848$	7.21661	0.247819
$849$	10.1049	0.346800
$850$	−0.0863549	−0.00296195
$851$	−25.6155	−0.878086
$852$	29.4271	1.00816
$853$	−28.0009	−0.958732	−0.479366	−	0.877615i	$-0.659133\pi$
$853$	−28.0009	−0.958732	−0.479366	+	0.877615i	$0.659133\pi$
$854$	−0.0362554	−0.00124063
$855$	6.90162	0.236030
$856$	−0.698587	−0.0238772
$857$	29.4641	1.00648	0.503238	−	0.864148i	$-0.332142\pi$
$857$	29.4641	1.00648	0.503238	+	0.864148i	$0.332142\pi$
$858$	0.677099	0.0231158
$859$	−35.5262	−1.21214	−0.606070	−	0.795412i	$-0.707255\pi$
$859$	−35.5262	−1.21214	−0.606070	+	0.795412i	$0.707255\pi$
$860$	−9.23812	−0.315017
$861$	6.06245	0.206608
$862$	0.485696	0.0165429
$863$	−46.0515	−1.56761	−0.783806	−	0.621006i	$-0.786724\pi$
$863$	−46.0515	−1.56761	−0.783806	+	0.621006i	$0.786724\pi$
$864$	0.298694	0.0101618
$865$	−47.2841	−1.60771
$866$	−0.834027	−0.0283414
$867$	−1.00000	−0.0339618
$868$	0.941446	0.0319548
$869$	−4.05947	−0.137708
$870$	0.555858	0.0188454
$871$	21.4479	0.726735
$872$	−1.68225	−0.0569680
$873$	13.3306	0.451173
$874$	−0.147345	−0.00498402
$875$	4.62120	0.156225
$876$	14.5031	0.490014
$877$	31.1831	1.05298	0.526489	−	0.850182i	$-0.323508\pi$
$877$	31.1831	1.05298	0.526489	+	0.850182i	$0.323508\pi$
$878$	−0.343196	−0.0115823
$879$	−21.0739	−0.710804
$880$	−47.2076	−1.59137
$881$	−11.2004	−0.377350	−0.188675	−	0.982040i	$-0.560419\pi$
$881$	−11.2004	−0.377350	−0.188675	+	0.982040i	$0.560419\pi$
$882$	0.147558	0.00496853
$883$	44.6392	1.50223	0.751115	−	0.660171i	$-0.229516\pi$
$883$	44.6392	1.50223	0.751115	+	0.660171i	$0.229516\pi$
$884$	−13.3922	−0.450430
$885$	−7.22749	−0.242949
$886$	−0.377982	−0.0126986
$887$	9.77983	0.328374	0.164187	−	0.986429i	$-0.447500\pi$
$887$	9.77983	0.328374	0.164187	+	0.986429i	$0.447500\pi$
$888$	−1.02252	−0.0343136
$889$	4.67417	0.156767
$890$	−0.0434753	−0.00145730
$891$	4.05947	0.135997
$892$	−15.7659	−0.527882
$893$	−16.3048	−0.545621
$894$	−0.324998	−0.0108696
$895$	3.16367	0.105750
$896$	0.825293	0.0275711
$897$	16.7111	0.557967
$898$	−0.350642	−0.0117011
$899$	3.48484	0.116226
$900$	−6.93358	−0.231119
$901$	1.80583	0.0601610
$902$	0.591251	0.0196865
$903$	1.64578	0.0547680
$904$	0.194623	0.00647307
$905$	−12.7301	−0.423162
$906$	−0.0858914	−0.00285355
$907$	25.4805	0.846067	0.423034	−	0.906114i	$-0.360965\pi$
$907$	25.4805	0.846067	0.423034	+	0.906114i	$0.360965\pi$
$908$	−57.5024	−1.90828
$909$	−14.3950	−0.477451
$910$	0.503083	0.0166770
$911$	−7.35297	−0.243615	−0.121807	−	0.992554i	$-0.538869\pi$
$911$	−7.35297	−0.243615	−0.121807	+	0.992554i	$0.538869\pi$
$912$	9.47807	0.313850
$913$	−39.9746	−1.32297
$914$	0.0623831	0.00206345
$915$	4.08757	0.135131
$916$	30.4171	1.00501
$917$	16.2277	0.535887
$918$	0.0249015	0.000821871 0
$919$	25.5347	0.842311	0.421156	−	0.906988i	$-0.361625\pi$
$919$	25.5347	0.842311	0.421156	+	0.906988i	$0.361625\pi$
$920$	0.723021	0.0238373
$921$	−8.58631	−0.282929
$922$	0.558752	0.0184015
$923$	98.5848	3.24496
$924$	8.41268	0.276757
$925$	35.6055	1.17070
$926$	−0.421990	−0.0138674
$927$	−7.12108	−0.233887
$928$	2.29128	0.0752150
$929$	35.0182	1.14891	0.574455	−	0.818536i	$-0.305214\pi$
$929$	35.0182	1.14891	0.574455	+	0.818536i	$0.305214\pi$
$930$	0.0329186	0.00107944
$931$	14.0540	0.460602
$932$	43.1856	1.41459
$933$	−23.2305	−0.760532
$934$	0.762514	0.0249502
$935$	−11.8129	−0.386323
$936$	0.667076	0.0218041
$937$	−35.6506	−1.16466	−0.582328	−	0.812954i	$-0.697858\pi$
$937$	−35.6506	−1.16466	−0.582328	+	0.812954i	$0.697858\pi$
$938$	−0.0826460	−0.00269849
$939$	0.840580	0.0274313
$940$	39.9977	1.30458
$941$	22.5578	0.735363	0.367682	−	0.929952i	$-0.380152\pi$
$941$	22.5578	0.735363	0.367682	+	0.929952i	$0.380152\pi$
$942$	0.366342	0.0119361
$943$	14.5923	0.475192
$944$	−9.92559	−0.323050
$945$	3.01618	0.0981162
$946$	0.160507	0.00521855
$947$	−28.5068	−0.926345	−0.463173	−	0.886268i	$-0.653289\pi$
$947$	−28.5068	−0.926345	−0.463173	+	0.886268i	$0.653289\pi$
$948$	−1.99938	−0.0649368
$949$	48.5873	1.57721
$950$	0.204810	0.00664491
$951$	10.4981	0.340425
$952$	0.103226	0.00334556
$953$	−40.0213	−1.29642	−0.648208	−	0.761463i	$-0.724481\pi$
$953$	−40.0213	−1.29642	−0.648208	+	0.761463i	$0.724481\pi$
$954$	−0.0449678	−0.00145589
$955$	34.9042	1.12947
$956$	−12.0046	−0.388258
$957$	31.1402	1.00662
$958$	−0.765647	−0.0247369
$959$	18.3201	0.591586
$960$	−23.2364	−0.749951
$961$	−30.7936	−0.993343
$962$	−1.71253	−0.0552142
$963$	−7.01460	−0.226042
$964$	−39.6404	−1.27673
$965$	31.7807	1.02306
$966$	−0.0643934	−0.00207182
$967$	36.4423	1.17190	0.585952	−	0.810345i	$-0.300721\pi$
$967$	36.4423	1.17190	0.585952	+	0.810345i	$0.300721\pi$
$968$	0.545685	0.0175390
$969$	2.37172	0.0761907
$970$	0.965967	0.0310153
$971$	−26.6339	−0.854723	−0.427362	−	0.904081i	$-0.640557\pi$
$971$	−26.6339	−0.854723	−0.427362	+	0.904081i	$0.640557\pi$
$972$	1.99938	0.0641301
$973$	9.82069	0.314837
$974$	0.773600	0.0247877
$975$	−23.2284	−0.743905
$976$	5.61350	0.179684
$977$	2.87541	0.0919924	0.0459962	−	0.998942i	$-0.485354\pi$
$977$	2.87541	0.0919924	0.0459962	+	0.998942i	$0.485354\pi$
$978$	0.445172	0.0142350
$979$	−2.43557	−0.0778410
$980$	−34.4762	−1.10130
$981$	−16.8916	−0.539309
$982$	0.703872	0.0224615
$983$	11.6727	0.372300	0.186150	−	0.982521i	$-0.440399\pi$
$983$	11.6727	0.372300	0.186150	+	0.982521i	$0.440399\pi$
$984$	0.582500	0.0185694
$985$	16.5912	0.528639
$986$	0.191019	0.00608329
$987$	−7.12562	−0.226811
$988$	31.7627	1.01051
$989$	3.96139	0.125965
$990$	0.294158	0.00934896
$991$	−38.5042	−1.22313	−0.611564	−	0.791195i	$-0.709459\pi$
$991$	−38.5042	−1.22313	−0.611564	+	0.791195i	$0.709459\pi$
$992$	0.135693	0.00430825
$993$	−15.1743	−0.481543
$994$	−0.379880	−0.0120491
$995$	5.67526	0.179918
$996$	−19.6884	−0.623850
$997$	−27.2273	−0.862298	−0.431149	−	0.902281i	$-0.641892\pi$
$997$	−27.2273	−0.862298	−0.431149	+	0.902281i	$0.641892\pi$
$998$	−0.0233503	−0.000739140 0
$999$	−10.2673	−0.324842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.14	✓	25	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)

\(f(q)\)	\(=\)	\(q-0.0249015 q^{2} -1.00000 q^{3} -1.99938 q^{4} -2.90996 q^{5} +0.0249015 q^{6} +1.03650 q^{7} +0.0995904 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0249015 q^{2} -1.00000 q^{3} -1.99938 q^{4} -2.90996 q^{5} +0.0249015 q^{6} +1.03650 q^{7} +0.0995904 q^{8} +1.00000 q^{9} +0.0724622 q^{10} +4.05947 q^{11} +1.99938 q^{12} +6.69820 q^{13} -0.0258104 q^{14} +2.90996 q^{15} +3.99628 q^{16} +1.00000 q^{17} -0.0249015 q^{18} -2.37172 q^{19} +5.81811 q^{20} -1.03650 q^{21} -0.101087 q^{22} -2.49486 q^{23} -0.0995904 q^{24} +3.46786 q^{25} -0.166795 q^{26} -1.00000 q^{27} -2.07236 q^{28} -7.67100 q^{29} -0.0724622 q^{30} -0.454287 q^{31} -0.298694 q^{32} -4.05947 q^{33} -0.0249015 q^{34} -3.01618 q^{35} -1.99938 q^{36} +10.2673 q^{37} +0.0590594 q^{38} -6.69820 q^{39} -0.289804 q^{40} -5.84895 q^{41} +0.0258104 q^{42} -1.58782 q^{43} -8.11642 q^{44} -2.90996 q^{45} +0.0621257 q^{46} +6.87468 q^{47} -3.99628 q^{48} -5.92566 q^{49} -0.0863549 q^{50} -1.00000 q^{51} -13.3922 q^{52} +1.80583 q^{53} +0.0249015 q^{54} -11.8129 q^{55} +0.103226 q^{56} +2.37172 q^{57} +0.191019 q^{58} -2.48371 q^{59} -5.81811 q^{60} +1.40468 q^{61} +0.0113124 q^{62} +1.03650 q^{63} -7.98512 q^{64} -19.4915 q^{65} +0.101087 q^{66} +3.20204 q^{67} -1.99938 q^{68} +2.49486 q^{69} +0.0751072 q^{70} +14.7181 q^{71} +0.0995904 q^{72} +7.25379 q^{73} -0.255670 q^{74} -3.46786 q^{75} +4.74198 q^{76} +4.20765 q^{77} +0.166795 q^{78} -1.00000 q^{79} -11.6290 q^{80} +1.00000 q^{81} +0.145647 q^{82} -9.84725 q^{83} +2.07236 q^{84} -2.90996 q^{85} +0.0395390 q^{86} +7.67100 q^{87} +0.404284 q^{88} -0.599972 q^{89} +0.0724622 q^{90} +6.94269 q^{91} +4.98818 q^{92} +0.454287 q^{93} -0.171190 q^{94} +6.90162 q^{95} +0.298694 q^{96} +13.3306 q^{97} +0.147558 q^{98} +4.05947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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