LMFDB - Embedded newform 4017.2.a.k.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.262075 q^{2} +1.00000 q^{3} -1.93132 q^{4} +0.855445 q^{5} +0.262075 q^{6} +3.34709 q^{7} -1.03030 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.262075 q^{2} +1.00000 q^{3} -1.93132 q^{4} +0.855445 q^{5} +0.262075 q^{6} +3.34709 q^{7} -1.03030 q^{8} +1.00000 q^{9} +0.224191 q^{10} +5.09536 q^{11} -1.93132 q^{12} +1.00000 q^{13} +0.877189 q^{14} +0.855445 q^{15} +3.59262 q^{16} -1.83355 q^{17} +0.262075 q^{18} +6.03069 q^{19} -1.65214 q^{20} +3.34709 q^{21} +1.33537 q^{22} +3.14824 q^{23} -1.03030 q^{24} -4.26821 q^{25} +0.262075 q^{26} +1.00000 q^{27} -6.46430 q^{28} +5.61481 q^{29} +0.224191 q^{30} +1.52041 q^{31} +3.00213 q^{32} +5.09536 q^{33} -0.480526 q^{34} +2.86326 q^{35} -1.93132 q^{36} +0.765297 q^{37} +1.58049 q^{38} +1.00000 q^{39} -0.881365 q^{40} -8.75808 q^{41} +0.877189 q^{42} -6.89527 q^{43} -9.84075 q^{44} +0.855445 q^{45} +0.825075 q^{46} -7.42547 q^{47} +3.59262 q^{48} +4.20304 q^{49} -1.11859 q^{50} -1.83355 q^{51} -1.93132 q^{52} -10.3182 q^{53} +0.262075 q^{54} +4.35880 q^{55} -3.44851 q^{56} +6.03069 q^{57} +1.47150 q^{58} +3.09365 q^{59} -1.65214 q^{60} +12.7832 q^{61} +0.398462 q^{62} +3.34709 q^{63} -6.39845 q^{64} +0.855445 q^{65} +1.33537 q^{66} -14.5491 q^{67} +3.54116 q^{68} +3.14824 q^{69} +0.750387 q^{70} +6.30495 q^{71} -1.03030 q^{72} +14.0822 q^{73} +0.200565 q^{74} -4.26821 q^{75} -11.6472 q^{76} +17.0546 q^{77} +0.262075 q^{78} -6.70838 q^{79} +3.07329 q^{80} +1.00000 q^{81} -2.29527 q^{82} +15.4576 q^{83} -6.46430 q^{84} -1.56850 q^{85} -1.80708 q^{86} +5.61481 q^{87} -5.24974 q^{88} -8.13554 q^{89} +0.224191 q^{90} +3.34709 q^{91} -6.08025 q^{92} +1.52041 q^{93} -1.94603 q^{94} +5.15892 q^{95} +3.00213 q^{96} +2.06414 q^{97} +1.10151 q^{98} +5.09536 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	0.262075	0.185315	0.0926574	−	0.995698i	$-0.470464\pi$
$2$	0.262075	0.185315	0.0926574	+	0.995698i	$0.470464\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.93132	−0.965658
$5$	0.855445	0.382567	0.191283	−	0.981535i	$-0.438735\pi$
$5$	0.855445	0.382567	0.191283	+	0.981535i	$0.438735\pi$
$6$	0.262075	0.106992
$7$	3.34709	1.26508	0.632541	−	0.774527i	$-0.282012\pi$
$7$	3.34709	1.26508	0.632541	+	0.774527i	$0.282012\pi$
$8$	−1.03030	−0.364266
$9$	1.00000	0.333333
$10$	0.224191	0.0708953
$11$	5.09536	1.53631	0.768154	−	0.640265i	$-0.221175\pi$
$11$	5.09536	1.53631	0.768154	+	0.640265i	$0.221175\pi$
$12$	−1.93132	−0.557523
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.877189	0.234439
$15$	0.855445	0.220875
$16$	3.59262	0.898155
$17$	−1.83355	−0.444700	−0.222350	−	0.974967i	$-0.571373\pi$
$17$	−1.83355	−0.444700	−0.222350	+	0.974967i	$0.571373\pi$
$18$	0.262075	0.0617716
$19$	6.03069	1.38353	0.691767	−	0.722121i	$-0.256832\pi$
$19$	6.03069	1.38353	0.691767	+	0.722121i	$0.256832\pi$
$20$	−1.65214	−0.369429
$21$	3.34709	0.730396
$22$	1.33537	0.284701
$23$	3.14824	0.656454	0.328227	−	0.944599i	$-0.393549\pi$
$23$	3.14824	0.656454	0.328227	+	0.944599i	$0.393549\pi$
$24$	−1.03030	−0.210309
$25$	−4.26821	−0.853643
$26$	0.262075	0.0513971
$27$	1.00000	0.192450
$28$	−6.46430	−1.22164
$29$	5.61481	1.04264	0.521322	−	0.853360i	$-0.325439\pi$
$29$	5.61481	1.04264	0.521322	+	0.853360i	$0.325439\pi$
$30$	0.224191	0.0409314
$31$	1.52041	0.273074	0.136537	−	0.990635i	$-0.456403\pi$
$31$	1.52041	0.273074	0.136537	+	0.990635i	$0.456403\pi$
$32$	3.00213	0.530707
$33$	5.09536	0.886988
$34$	−0.480526	−0.0824096
$35$	2.86326	0.483979
$36$	−1.93132	−0.321886
$37$	0.765297	0.125814	0.0629070	−	0.998019i	$-0.479963\pi$
$37$	0.765297	0.125814	0.0629070	+	0.998019i	$0.479963\pi$
$38$	1.58049	0.256390
$39$	1.00000	0.160128
$40$	−0.881365	−0.139356
$41$	−8.75808	−1.36778	−0.683891	−	0.729584i	$-0.739714\pi$
$41$	−8.75808	−1.36778	−0.683891	+	0.729584i	$0.739714\pi$
$42$	0.877189	0.135353
$43$	−6.89527	−1.05152	−0.525760	−	0.850633i	$-0.676219\pi$
$43$	−6.89527	−1.05152	−0.525760	+	0.850633i	$0.676219\pi$
$44$	−9.84075	−1.48355
$45$	0.855445	0.127522
$46$	0.825075	0.121651
$47$	−7.42547	−1.08312	−0.541558	−	0.840663i	$-0.682165\pi$
$47$	−7.42547	−1.08312	−0.541558	+	0.840663i	$0.682165\pi$
$48$	3.59262	0.518550
$49$	4.20304	0.600434
$50$	−1.11859	−0.158193
$51$	−1.83355	−0.256748
$52$	−1.93132	−0.267825
$53$	−10.3182	−1.41731	−0.708656	−	0.705554i	$-0.750698\pi$
$53$	−10.3182	−1.41731	−0.708656	+	0.705554i	$0.750698\pi$
$54$	0.262075	0.0356639
$55$	4.35880	0.587740
$56$	−3.44851	−0.460826
$57$	6.03069	0.798784
$58$	1.47150	0.193218
$59$	3.09365	0.402759	0.201379	−	0.979513i	$-0.435458\pi$
$59$	3.09365	0.402759	0.201379	+	0.979513i	$0.435458\pi$
$60$	−1.65214	−0.213290
$61$	12.7832	1.63671	0.818357	−	0.574710i	$-0.194885\pi$
$61$	12.7832	1.63671	0.818357	+	0.574710i	$0.194885\pi$
$62$	0.398462	0.0506047
$63$	3.34709	0.421694
$64$	−6.39845	−0.799807
$65$	0.855445	0.106105
$66$	1.33537	0.164372
$67$	−14.5491	−1.77746	−0.888728	−	0.458435i	$-0.848410\pi$
$67$	−14.5491	−1.77746	−0.888728	+	0.458435i	$0.848410\pi$
$68$	3.54116	0.429429
$69$	3.14824	0.379004
$70$	0.750387	0.0896884
$71$	6.30495	0.748260	0.374130	−	0.927376i	$-0.377941\pi$
$71$	6.30495	0.748260	0.374130	+	0.927376i	$0.377941\pi$
$72$	−1.03030	−0.121422
$73$	14.0822	1.64819	0.824096	−	0.566450i	$-0.191684\pi$
$73$	14.0822	1.64819	0.824096	+	0.566450i	$0.191684\pi$
$74$	0.200565	0.0233152
$75$	−4.26821	−0.492851
$76$	−11.6472	−1.33602
$77$	17.0546	1.94356
$78$	0.262075	0.0296741
$79$	−6.70838	−0.754752	−0.377376	−	0.926060i	$-0.623173\pi$
$79$	−6.70838	−0.754752	−0.377376	+	0.926060i	$0.623173\pi$
$80$	3.07329	0.343604
$81$	1.00000	0.111111
$82$	−2.29527	−0.253470
$83$	15.4576	1.69670	0.848348	−	0.529439i	$-0.177597\pi$
$83$	15.4576	1.69670	0.848348	+	0.529439i	$0.177597\pi$
$84$	−6.46430	−0.705313
$85$	−1.56850	−0.170128
$86$	−1.80708	−0.194862
$87$	5.61481	0.601971
$88$	−5.24974	−0.559624
$89$	−8.13554	−0.862366	−0.431183	−	0.902265i	$-0.641904\pi$
$89$	−8.13554	−0.862366	−0.431183	+	0.902265i	$0.641904\pi$
$90$	0.224191	0.0236318
$91$	3.34709	0.350871
$92$	−6.08025	−0.633910
$93$	1.52041	0.157659
$94$	−1.94603	−0.200718
$95$	5.15892	0.529294
$96$	3.00213	0.306404
$97$	2.06414	0.209581	0.104791	−	0.994494i	$-0.466583\pi$
$97$	2.06414	0.209581	0.104791	+	0.994494i	$0.466583\pi$
$98$	1.10151	0.111269
$99$	5.09536	0.512103
$100$	8.24327	0.824327
$101$	−2.07101	−0.206073	−0.103036	−	0.994678i	$-0.532856\pi$
$101$	−2.07101	−0.206073	−0.103036	+	0.994678i	$0.532856\pi$
$102$	−0.480526	−0.0475792
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.03030	−0.101029
$105$	2.86326	0.279425
$106$	−2.70414	−0.262649
$107$	2.01394	0.194695	0.0973475	−	0.995250i	$-0.468964\pi$
$107$	2.01394	0.194695	0.0973475	+	0.995250i	$0.468964\pi$
$108$	−1.93132	−0.185841
$109$	7.53220	0.721454	0.360727	−	0.932671i	$-0.382529\pi$
$109$	7.53220	0.721454	0.360727	+	0.932671i	$0.382529\pi$
$110$	1.14233	0.108917
$111$	0.765297	0.0726388
$112$	12.0248	1.13624
$113$	−3.07933	−0.289679	−0.144839	−	0.989455i	$-0.546267\pi$
$113$	−3.07933	−0.289679	−0.144839	+	0.989455i	$0.546267\pi$
$114$	1.58049	0.148027
$115$	2.69315	0.251137
$116$	−10.8440	−1.00684
$117$	1.00000	0.0924500
$118$	0.810768	0.0746372
$119$	−6.13705	−0.562583
$120$	−0.881365	−0.0804572
$121$	14.9627	1.36024
$122$	3.35014	0.303308
$123$	−8.75808	−0.789689
$124$	−2.93640	−0.263696
$125$	−7.92845	−0.709142
$126$	0.877189	0.0781462
$127$	−20.4457	−1.81427	−0.907133	−	0.420844i	$-0.861734\pi$
$127$	−20.4457	−1.81427	−0.907133	+	0.420844i	$0.861734\pi$
$128$	−7.68114	−0.678923
$129$	−6.89527	−0.607095
$130$	0.224191	0.0196628
$131$	10.0844	0.881076	0.440538	−	0.897734i	$-0.354788\pi$
$131$	10.0844	0.881076	0.440538	+	0.897734i	$0.354788\pi$
$132$	−9.84075	−0.856527
$133$	20.1853	1.75029
$134$	−3.81295	−0.329389
$135$	0.855445	0.0736250
$136$	1.88910	0.161989
$137$	4.50855	0.385191	0.192596	−	0.981278i	$-0.438309\pi$
$137$	4.50855	0.385191	0.192596	+	0.981278i	$0.438309\pi$
$138$	0.825075	0.0702350
$139$	15.5972	1.32294	0.661470	−	0.749972i	$-0.269933\pi$
$139$	15.5972	1.32294	0.661470	+	0.749972i	$0.269933\pi$
$140$	−5.52985	−0.467358
$141$	−7.42547	−0.625337
$142$	1.65237	0.138664
$143$	5.09536	0.426095
$144$	3.59262	0.299385
$145$	4.80317	0.398881
$146$	3.69058	0.305435
$147$	4.20304	0.346661
$148$	−1.47803	−0.121493
$149$	−15.9286	−1.30492	−0.652460	−	0.757823i	$-0.726263\pi$
$149$	−15.9286	−1.30492	−0.652460	+	0.757823i	$0.726263\pi$
$150$	−1.11859	−0.0913326
$151$	−12.1926	−0.992222	−0.496111	−	0.868259i	$-0.665239\pi$
$151$	−12.1926	−0.992222	−0.496111	+	0.868259i	$0.665239\pi$
$152$	−6.21341	−0.503974
$153$	−1.83355	−0.148233
$154$	4.46959	0.360170
$155$	1.30063	0.104469
$156$	−1.93132	−0.154629
$157$	21.0714	1.68168	0.840841	−	0.541282i	$-0.182061\pi$
$157$	21.0714	1.68168	0.840841	+	0.541282i	$0.182061\pi$
$158$	−1.75810	−0.139867
$159$	−10.3182	−0.818285
$160$	2.56816	0.203031
$161$	10.5375	0.830468
$162$	0.262075	0.0205905
$163$	−13.2587	−1.03850	−0.519252	−	0.854621i	$-0.673789\pi$
$163$	−13.2587	−1.03850	−0.519252	+	0.854621i	$0.673789\pi$
$164$	16.9146	1.32081
$165$	4.35880	0.339332
$166$	4.05106	0.314423
$167$	14.8542	1.14945	0.574727	−	0.818345i	$-0.305108\pi$
$167$	14.8542	1.14945	0.574727	+	0.818345i	$0.305108\pi$
$168$	−3.44851	−0.266058
$169$	1.00000	0.0769231
$170$	−0.411064	−0.0315272
$171$	6.03069	0.461178
$172$	13.3170	1.01541
$173$	−5.53696	−0.420968	−0.210484	−	0.977597i	$-0.567504\pi$
$173$	−5.53696	−0.420968	−0.210484	+	0.977597i	$0.567504\pi$
$174$	1.47150	0.111554
$175$	−14.2861	−1.07993
$176$	18.3057	1.37984
$177$	3.09365	0.232533
$178$	−2.13212	−0.159809
$179$	−7.62197	−0.569693	−0.284847	−	0.958573i	$-0.591943\pi$
$179$	−7.62197	−0.569693	−0.284847	+	0.958573i	$0.591943\pi$
$180$	−1.65214	−0.123143
$181$	9.60409	0.713867	0.356933	−	0.934130i	$-0.383822\pi$
$181$	9.60409	0.713867	0.356933	+	0.934130i	$0.383822\pi$
$182$	0.877189	0.0650216
$183$	12.7832	0.944958
$184$	−3.24363	−0.239124
$185$	0.654670	0.0481323
$186$	0.398462	0.0292167
$187$	−9.34258	−0.683197
$188$	14.3409	1.04592
$189$	3.34709	0.243465
$190$	1.35202	0.0980861
$191$	−17.9491	−1.29875	−0.649376	−	0.760468i	$-0.724970\pi$
$191$	−17.9491	−1.29875	−0.649376	+	0.760468i	$0.724970\pi$
$192$	−6.39845	−0.461769
$193$	4.40571	0.317130	0.158565	−	0.987349i	$-0.449313\pi$
$193$	4.40571	0.317130	0.158565	+	0.987349i	$0.449313\pi$
$194$	0.540958	0.0388385
$195$	0.855445	0.0612597
$196$	−8.11740	−0.579815
$197$	23.3654	1.66472	0.832358	−	0.554238i	$-0.186990\pi$
$197$	23.3654	1.66472	0.832358	+	0.554238i	$0.186990\pi$
$198$	1.33537	0.0949003
$199$	10.8936	0.772227	0.386114	−	0.922451i	$-0.373817\pi$
$199$	10.8936	0.772227	0.386114	+	0.922451i	$0.373817\pi$
$200$	4.39754	0.310953
$201$	−14.5491	−1.02621
$202$	−0.542759	−0.0381884
$203$	18.7933	1.31903
$204$	3.54116	0.247931
$205$	−7.49206	−0.523268
$206$	0.262075	0.0182596
$207$	3.14824	0.218818
$208$	3.59262	0.249103
$209$	30.7285	2.12553
$210$	0.750387	0.0517816
$211$	5.11984	0.352464	0.176232	−	0.984349i	$-0.443609\pi$
$211$	5.11984	0.352464	0.176232	+	0.984349i	$0.443609\pi$
$212$	19.9277	1.36864
$213$	6.30495	0.432008
$214$	0.527803	0.0360799
$215$	−5.89853	−0.402276
$216$	−1.03030	−0.0701030
$217$	5.08897	0.345462
$218$	1.97400	0.133696
$219$	14.0822	0.951584
$220$	−8.41822	−0.567556
$221$	−1.83355	−0.123338
$222$	0.200565	0.0134610
$223$	−23.0389	−1.54280	−0.771398	−	0.636353i	$-0.780442\pi$
$223$	−23.0389	−1.54280	−0.771398	+	0.636353i	$0.780442\pi$
$224$	10.0484	0.671389
$225$	−4.26821	−0.284548
$226$	−0.807014	−0.0536817
$227$	−15.0748	−1.00055	−0.500274	−	0.865867i	$-0.666767\pi$
$227$	−15.0748	−1.00055	−0.500274	+	0.865867i	$0.666767\pi$
$228$	−11.6472	−0.771352
$229$	−26.1378	−1.72724	−0.863619	−	0.504145i	$-0.831808\pi$
$229$	−26.1378	−1.72724	−0.863619	+	0.504145i	$0.831808\pi$
$230$	0.705806	0.0465395
$231$	17.0546	1.12211
$232$	−5.78494	−0.379800
$233$	1.30433	0.0854497	0.0427248	−	0.999087i	$-0.486396\pi$
$233$	1.30433	0.0854497	0.0427248	+	0.999087i	$0.486396\pi$
$234$	0.262075	0.0171324
$235$	−6.35208	−0.414364
$236$	−5.97482	−0.388927
$237$	−6.70838	−0.435756
$238$	−1.60837	−0.104255
$239$	−28.7072	−1.85691	−0.928456	−	0.371443i	$-0.878863\pi$
$239$	−28.7072	−1.85691	−0.928456	+	0.371443i	$0.878863\pi$
$240$	3.07329	0.198380
$241$	−15.4658	−0.996238	−0.498119	−	0.867109i	$-0.665976\pi$
$241$	−15.4658	−0.996238	−0.498119	+	0.867109i	$0.665976\pi$
$242$	3.92134	0.252073
$243$	1.00000	0.0641500
$244$	−24.6883	−1.58051
$245$	3.59547	0.229706
$246$	−2.29527	−0.146341
$247$	6.03069	0.383723
$248$	−1.56648	−0.0994716
$249$	15.4576	0.979588
$250$	−2.07785	−0.131415
$251$	−8.89152	−0.561227	−0.280614	−	0.959821i	$-0.590538\pi$
$251$	−8.89152	−0.561227	−0.280614	+	0.959821i	$0.590538\pi$
$252$	−6.46430	−0.407213
$253$	16.0414	1.00852
$254$	−5.35831	−0.336210
$255$	−1.56850	−0.0982232
$256$	10.7839	0.673992
$257$	27.5838	1.72063	0.860315	−	0.509763i	$-0.170267\pi$
$257$	27.5838	1.72063	0.860315	+	0.509763i	$0.170267\pi$
$258$	−1.80708	−0.112504
$259$	2.56152	0.159165
$260$	−1.65214	−0.102461
$261$	5.61481	0.347548
$262$	2.64286	0.163277
$263$	30.8116	1.89992	0.949962	−	0.312365i	$-0.101121\pi$
$263$	30.8116	1.89992	0.949962	+	0.312365i	$0.101121\pi$
$264$	−5.24974	−0.323099
$265$	−8.82664	−0.542216
$266$	5.29005	0.324354
$267$	−8.13554	−0.497887
$268$	28.0989	1.71642
$269$	1.60340	0.0977611	0.0488806	−	0.998805i	$-0.484435\pi$
$269$	1.60340	0.0977611	0.0488806	+	0.998805i	$0.484435\pi$
$270$	0.224191	0.0136438
$271$	−1.29306	−0.0785476	−0.0392738	−	0.999228i	$-0.512504\pi$
$271$	−1.29306	−0.0785476	−0.0392738	+	0.999228i	$0.512504\pi$
$272$	−6.58723	−0.399410
$273$	3.34709	0.202575
$274$	1.18158	0.0713816
$275$	−21.7481	−1.31146
$276$	−6.08025	−0.365988
$277$	8.81030	0.529360	0.264680	−	0.964336i	$-0.414734\pi$
$277$	8.81030	0.529360	0.264680	+	0.964336i	$0.414734\pi$
$278$	4.08764	0.245161
$279$	1.52041	0.0910247
$280$	−2.95001	−0.176297
$281$	−5.83315	−0.347977	−0.173988	−	0.984748i	$-0.555666\pi$
$281$	−5.83315	−0.347977	−0.173988	+	0.984748i	$0.555666\pi$
$282$	−1.94603	−0.115884
$283$	26.4325	1.57125	0.785623	−	0.618705i	$-0.212342\pi$
$283$	26.4325	1.57125	0.785623	+	0.618705i	$0.212342\pi$
$284$	−12.1769	−0.722564
$285$	5.15892	0.305588
$286$	1.33537	0.0789618
$287$	−29.3141	−1.73036
$288$	3.00213	0.176902
$289$	−13.6381	−0.802242
$290$	1.25879	0.0739186
$291$	2.06414	0.121002
$292$	−27.1971	−1.59159
$293$	33.0347	1.92991	0.964953	−	0.262424i	$-0.0845219\pi$
$293$	33.0347	1.92991	0.964953	+	0.262424i	$0.0845219\pi$
$294$	1.10151	0.0642414
$295$	2.64645	0.154082
$296$	−0.788485	−0.0458298
$297$	5.09536	0.295663
$298$	−4.17448	−0.241821
$299$	3.14824	0.182067
$300$	8.24327	0.475926
$301$	−23.0791	−1.33026
$302$	−3.19538	−0.183874
$303$	−2.07101	−0.118976
$304$	21.6660	1.24263
$305$	10.9353	0.626153
$306$	−0.480526	−0.0274699
$307$	9.21710	0.526048	0.263024	−	0.964789i	$-0.415280\pi$
$307$	9.21710	0.526048	0.263024	+	0.964789i	$0.415280\pi$
$308$	−32.9379	−1.87681
$309$	1.00000	0.0568880
$310$	0.340862	0.0193597
$311$	8.00126	0.453710	0.226855	−	0.973929i	$-0.427156\pi$
$311$	8.00126	0.453710	0.226855	+	0.973929i	$0.427156\pi$
$312$	−1.03030	−0.0583292
$313$	16.2506	0.918537	0.459268	−	0.888298i	$-0.348112\pi$
$313$	16.2506	0.918537	0.459268	+	0.888298i	$0.348112\pi$
$314$	5.52229	0.311641
$315$	2.86326	0.161326
$316$	12.9560	0.728832
$317$	−16.0050	−0.898931	−0.449466	−	0.893298i	$-0.648386\pi$
$317$	−16.0050	−0.898931	−0.449466	+	0.893298i	$0.648386\pi$
$318$	−2.70414	−0.151640
$319$	28.6095	1.60182
$320$	−5.47353	−0.305979
$321$	2.01394	0.112407
$322$	2.76160	0.153898
$323$	−11.0575	−0.615258
$324$	−1.93132	−0.107295
$325$	−4.26821	−0.236758
$326$	−3.47478	−0.192450
$327$	7.53220	0.416532
$328$	9.02344	0.498236
$329$	−24.8537	−1.37023
$330$	1.14233	0.0628833
$331$	24.2650	1.33373	0.666864	−	0.745180i	$-0.267636\pi$
$331$	24.2650	1.33373	0.666864	+	0.745180i	$0.267636\pi$
$332$	−29.8536	−1.63843
$333$	0.765297	0.0419380
$334$	3.89292	0.213011
$335$	−12.4460	−0.679996
$336$	12.0248	0.656008
$337$	31.4399	1.71264	0.856319	−	0.516447i	$-0.172746\pi$
$337$	31.4399	1.71264	0.856319	+	0.516447i	$0.172746\pi$
$338$	0.262075	0.0142550
$339$	−3.07933	−0.167246
$340$	3.02927	0.164285
$341$	7.74705	0.419526
$342$	1.58049	0.0854632
$343$	−9.36169	−0.505483
$344$	7.10419	0.383032
$345$	2.69315	0.144994
$346$	−1.45110	−0.0780115
$347$	4.66230	0.250285	0.125143	−	0.992139i	$-0.460061\pi$
$347$	4.66230	0.250285	0.125143	+	0.992139i	$0.460061\pi$
$348$	−10.8440	−0.581299
$349$	20.0706	1.07435	0.537177	−	0.843470i	$-0.319491\pi$
$349$	20.0706	1.07435	0.537177	+	0.843470i	$0.319491\pi$
$350$	−3.74403	−0.200127
$351$	1.00000	0.0533761
$352$	15.2969	0.815330
$353$	7.72697	0.411265	0.205632	−	0.978629i	$-0.434075\pi$
$353$	7.72697	0.411265	0.205632	+	0.978629i	$0.434075\pi$
$354$	0.810768	0.0430918
$355$	5.39354	0.286259
$356$	15.7123	0.832751
$357$	−6.13705	−0.324807
$358$	−1.99753	−0.105573
$359$	−11.7627	−0.620811	−0.310405	−	0.950604i	$-0.600465\pi$
$359$	−11.7627	−0.620811	−0.310405	+	0.950604i	$0.600465\pi$
$360$	−0.881365	−0.0464520
$361$	17.3692	0.914167
$362$	2.51699	0.132290
$363$	14.9627	0.785337
$364$	−6.46430	−0.338821
$365$	12.0465	0.630543
$366$	3.35014	0.175115
$367$	−19.2724	−1.00601	−0.503005	−	0.864284i	$-0.667772\pi$
$367$	−19.2724	−1.00601	−0.503005	+	0.864284i	$0.667772\pi$
$368$	11.3104	0.589597
$369$	−8.75808	−0.455927
$370$	0.171572	0.00891963
$371$	−34.5359	−1.79302
$372$	−2.93640	−0.152245
$373$	22.7656	1.17876	0.589380	−	0.807856i	$-0.299372\pi$
$373$	22.7656	1.17876	0.589380	+	0.807856i	$0.299372\pi$
$374$	−2.44845	−0.126607
$375$	−7.92845	−0.409423
$376$	7.65046	0.394542
$377$	5.61481	0.289178
$378$	0.877189	0.0451177
$379$	17.0097	0.873728	0.436864	−	0.899528i	$-0.356089\pi$
$379$	17.0097	0.873728	0.436864	+	0.899528i	$0.356089\pi$
$380$	−9.96351	−0.511117
$381$	−20.4457	−1.04747
$382$	−4.70401	−0.240678
$383$	−8.60239	−0.439561	−0.219781	−	0.975549i	$-0.570534\pi$
$383$	−8.60239	−0.439561	−0.219781	+	0.975549i	$0.570534\pi$
$384$	−7.68114	−0.391977
$385$	14.5893	0.743540
$386$	1.15462	0.0587688
$387$	−6.89527	−0.350506
$388$	−3.98650	−0.202384
$389$	−28.2356	−1.43160	−0.715800	−	0.698305i	$-0.753938\pi$
$389$	−28.2356	−1.43160	−0.715800	+	0.698305i	$0.753938\pi$
$390$	0.224191	0.0113523
$391$	−5.77245	−0.291925
$392$	−4.33039	−0.218718
$393$	10.0844	0.508689
$394$	6.12349	0.308497
$395$	−5.73865	−0.288743
$396$	−9.84075	−0.494516
$397$	−8.16709	−0.409895	−0.204947	−	0.978773i	$-0.565702\pi$
$397$	−8.16709	−0.409895	−0.204947	+	0.978773i	$0.565702\pi$
$398$	2.85494	0.143105
$399$	20.1853	1.01053
$400$	−15.3341	−0.766703
$401$	−15.4970	−0.773882	−0.386941	−	0.922105i	$-0.626468\pi$
$401$	−15.4970	−0.773882	−0.386941	+	0.922105i	$0.626468\pi$
$402$	−3.81295	−0.190173
$403$	1.52041	0.0757372
$404$	3.99977	0.198996
$405$	0.855445	0.0425074
$406$	4.92525	0.244436
$407$	3.89946	0.193289
$408$	1.88910	0.0935245
$409$	−12.4386	−0.615048	−0.307524	−	0.951540i	$-0.599500\pi$
$409$	−12.4386	−0.615048	−0.307524	+	0.951540i	$0.599500\pi$
$410$	−1.96348	−0.0969694
$411$	4.50855	0.222390
$412$	−1.93132	−0.0951491
$413$	10.3547	0.509523
$414$	0.825075	0.0405502
$415$	13.2232	0.649100
$416$	3.00213	0.147192
$417$	15.5972	0.763800
$418$	8.05317	0.393893
$419$	−26.1898	−1.27945	−0.639727	−	0.768602i	$-0.720953\pi$
$419$	−26.1898	−1.27945	−0.639727	+	0.768602i	$0.720953\pi$
$420$	−5.52985	−0.269829
$421$	−4.37446	−0.213198	−0.106599	−	0.994302i	$-0.533996\pi$
$421$	−4.37446	−0.213198	−0.106599	+	0.994302i	$0.533996\pi$
$422$	1.34178	0.0653168
$423$	−7.42547	−0.361039
$424$	10.6308	0.516278
$425$	7.82597	0.379615
$426$	1.65237	0.0800576
$427$	42.7864	2.07058
$428$	−3.88956	−0.188009
$429$	5.09536	0.246006
$430$	−1.54586	−0.0745478
$431$	−16.2109	−0.780850	−0.390425	−	0.920635i	$-0.627672\pi$
$431$	−16.2109	−0.780850	−0.390425	+	0.920635i	$0.627672\pi$
$432$	3.59262	0.172850
$433$	0.716266	0.0344215	0.0172108	−	0.999852i	$-0.494521\pi$
$433$	0.716266	0.0344215	0.0172108	+	0.999852i	$0.494521\pi$
$434$	1.33369	0.0640192
$435$	4.80317	0.230294
$436$	−14.5471	−0.696678
$437$	18.9861	0.908226
$438$	3.69058	0.176343
$439$	−25.6674	−1.22504	−0.612520	−	0.790455i	$-0.709844\pi$
$439$	−25.6674	−1.22504	−0.612520	+	0.790455i	$0.709844\pi$
$440$	−4.49087	−0.214094
$441$	4.20304	0.200145
$442$	−0.480526	−0.0228563
$443$	−8.38261	−0.398270	−0.199135	−	0.979972i	$-0.563813\pi$
$443$	−8.38261	−0.398270	−0.199135	+	0.979972i	$0.563813\pi$
$444$	−1.47803	−0.0701442
$445$	−6.95951	−0.329913
$446$	−6.03790	−0.285903
$447$	−15.9286	−0.753396
$448$	−21.4162	−1.01182
$449$	−36.2255	−1.70959	−0.854795	−	0.518966i	$-0.826317\pi$
$449$	−36.2255	−1.70959	−0.854795	+	0.518966i	$0.826317\pi$
$450$	−1.11859	−0.0527309
$451$	−44.6255	−2.10134
$452$	5.94715	0.279731
$453$	−12.1926	−0.572860
$454$	−3.95072	−0.185416
$455$	2.86326	0.134232
$456$	−6.21341	−0.290970
$457$	−33.5419	−1.56903	−0.784513	−	0.620113i	$-0.787087\pi$
$457$	−33.5419	−1.56903	−0.784513	+	0.620113i	$0.787087\pi$
$458$	−6.85007	−0.320083
$459$	−1.83355	−0.0855826
$460$	−5.20132	−0.242513
$461$	5.36594	0.249917	0.124958	−	0.992162i	$-0.460120\pi$
$461$	5.36594	0.249917	0.124958	+	0.992162i	$0.460120\pi$
$462$	4.46959	0.207944
$463$	5.48436	0.254880	0.127440	−	0.991846i	$-0.459324\pi$
$463$	5.48436	0.254880	0.127440	+	0.991846i	$0.459324\pi$
$464$	20.1719	0.936456
$465$	1.30063	0.0603153
$466$	0.341833	0.0158351
$467$	−38.9262	−1.80129	−0.900645	−	0.434556i	$-0.856905\pi$
$467$	−38.9262	−1.80129	−0.900645	+	0.434556i	$0.856905\pi$
$468$	−1.93132	−0.0892751
$469$	−48.6972	−2.24863
$470$	−1.66472	−0.0767878
$471$	21.0714	0.970920
$472$	−3.18738	−0.146711
$473$	−35.1339	−1.61546
$474$	−1.75810	−0.0807521
$475$	−25.7403	−1.18104
$476$	11.8526	0.543263
$477$	−10.3182	−0.472437
$478$	−7.52342	−0.344113
$479$	−9.97027	−0.455553	−0.227777	−	0.973713i	$-0.573146\pi$
$479$	−9.97027	−0.455553	−0.227777	+	0.973713i	$0.573146\pi$
$480$	2.56816	0.117220
$481$	0.765297	0.0348945
$482$	−4.05319	−0.184618
$483$	10.5375	0.479471
$484$	−28.8977	−1.31353
$485$	1.76576	0.0801788
$486$	0.262075	0.0118880
$487$	−6.64730	−0.301218	−0.150609	−	0.988593i	$-0.548123\pi$
$487$	−6.64730	−0.301218	−0.150609	+	0.988593i	$0.548123\pi$
$488$	−13.1705	−0.596199
$489$	−13.2587	−0.599580
$490$	0.942283	0.0425680
$491$	7.32496	0.330571	0.165285	−	0.986246i	$-0.447145\pi$
$491$	7.32496	0.330571	0.165285	+	0.986246i	$0.447145\pi$
$492$	16.9146	0.762570
$493$	−10.2950	−0.463665
$494$	1.58049	0.0711097
$495$	4.35880	0.195913
$496$	5.46226	0.245263
$497$	21.1033	0.946611
$498$	4.05106	0.181532
$499$	28.0055	1.25370	0.626848	−	0.779141i	$-0.284344\pi$
$499$	28.0055	1.25370	0.626848	+	0.779141i	$0.284344\pi$
$500$	15.3123	0.684789
$501$	14.8542	0.663637
$502$	−2.33024	−0.104004
$503$	3.51453	0.156705	0.0783525	−	0.996926i	$-0.475034\pi$
$503$	3.51453	0.156705	0.0783525	+	0.996926i	$0.475034\pi$
$504$	−3.44851	−0.153609
$505$	−1.77163	−0.0788367
$506$	4.20405	0.186893
$507$	1.00000	0.0444116
$508$	39.4872	1.75196
$509$	−26.4400	−1.17193	−0.585966	−	0.810336i	$-0.699285\pi$
$509$	−26.4400	−1.17193	−0.585966	+	0.810336i	$0.699285\pi$
$510$	−0.411064	−0.0182022
$511$	47.1343	2.08510
$512$	18.1885	0.803824
$513$	6.03069	0.266261
$514$	7.22902	0.318858
$515$	0.855445	0.0376954
$516$	13.3170	0.586246
$517$	−37.8354	−1.66400
$518$	0.671310	0.0294957
$519$	−5.53696	−0.243046
$520$	−0.881365	−0.0386504
$521$	−11.5544	−0.506209	−0.253104	−	0.967439i	$-0.581452\pi$
$521$	−11.5544	−0.506209	−0.253104	+	0.967439i	$0.581452\pi$
$522$	1.47150	0.0644059
$523$	42.4247	1.85510	0.927550	−	0.373698i	$-0.121910\pi$
$523$	42.4247	1.85510	0.927550	+	0.373698i	$0.121910\pi$
$524$	−19.4761	−0.850818
$525$	−14.2861	−0.623497
$526$	8.07494	0.352084
$527$	−2.78775	−0.121436
$528$	18.3057	0.796652
$529$	−13.0886	−0.569069
$530$	−2.31324	−0.100481
$531$	3.09365	0.134253
$532$	−38.9842	−1.69018
$533$	−8.75808	−0.379355
$534$	−2.13212	−0.0922659
$535$	1.72282	0.0744838
$536$	14.9899	0.647466
$537$	−7.62197	−0.328912
$538$	0.420211	0.0181166
$539$	21.4160	0.922452
$540$	−1.65214	−0.0710966
$541$	16.6199	0.714547	0.357274	−	0.934000i	$-0.383706\pi$
$541$	16.6199	0.714547	0.357274	+	0.934000i	$0.383706\pi$
$542$	−0.338878	−0.0145560
$543$	9.60409	0.412151
$544$	−5.50455	−0.236006
$545$	6.44338	0.276004
$546$	0.877189	0.0375402
$547$	17.9327	0.766746	0.383373	−	0.923594i	$-0.374762\pi$
$547$	17.9327	0.766746	0.383373	+	0.923594i	$0.374762\pi$
$548$	−8.70743	−0.371963
$549$	12.7832	0.545572
$550$	−5.69962	−0.243033
$551$	33.8612	1.44253
$552$	−3.24363	−0.138058
$553$	−22.4536	−0.954823
$554$	2.30896	0.0980982
$555$	0.654670	0.0277892
$556$	−30.1232	−1.27751
$557$	−18.7795	−0.795714	−0.397857	−	0.917447i	$-0.630246\pi$
$557$	−18.7795	−0.795714	−0.397857	+	0.917447i	$0.630246\pi$
$558$	0.398462	0.0168682
$559$	−6.89527	−0.291639
$560$	10.2866	0.434688
$561$	−9.34258	−0.394444
$562$	−1.52872	−0.0644853
$563$	9.41542	0.396812	0.198406	−	0.980120i	$-0.436423\pi$
$563$	9.41542	0.396812	0.198406	+	0.980120i	$0.436423\pi$
$564$	14.3409	0.603862
$565$	−2.63419	−0.110821
$566$	6.92728	0.291175
$567$	3.34709	0.140565
$568$	−6.49599	−0.272566
$569$	−7.34025	−0.307719	−0.153860	−	0.988093i	$-0.549170\pi$
$569$	−7.34025	−0.307719	−0.153860	+	0.988093i	$0.549170\pi$
$570$	1.35202	0.0566300
$571$	−8.86087	−0.370816	−0.185408	−	0.982662i	$-0.559361\pi$
$571$	−8.86087	−0.370816	−0.185408	+	0.982662i	$0.559361\pi$
$572$	−9.84075	−0.411462
$573$	−17.9491	−0.749835
$574$	−7.68249	−0.320661
$575$	−13.4374	−0.560377
$576$	−6.39845	−0.266602
$577$	16.2005	0.674436	0.337218	−	0.941427i	$-0.390514\pi$
$577$	16.2005	0.674436	0.337218	+	0.941427i	$0.390514\pi$
$578$	−3.57420	−0.148667
$579$	4.40571	0.183095
$580$	−9.27643	−0.385183
$581$	51.7382	2.14646
$582$	0.540958	0.0224234
$583$	−52.5748	−2.17743
$584$	−14.5088	−0.600380
$585$	0.855445	0.0353683
$586$	8.65755	0.357640
$587$	−15.1408	−0.624928	−0.312464	−	0.949930i	$-0.601154\pi$
$587$	−15.1408	−0.624928	−0.312464	+	0.949930i	$0.601154\pi$
$588$	−8.11740	−0.334756
$589$	9.16913	0.377808
$590$	0.693567	0.0285537
$591$	23.3654	0.961125
$592$	2.74942	0.113000
$593$	−3.68631	−0.151378	−0.0756892	−	0.997131i	$-0.524116\pi$
$593$	−3.68631	−0.151378	−0.0756892	+	0.997131i	$0.524116\pi$
$594$	1.33537	0.0547907
$595$	−5.24991	−0.215225
$596$	30.7631	1.26011
$597$	10.8936	0.445846
$598$	0.825075	0.0337398
$599$	−44.9975	−1.83855	−0.919275	−	0.393616i	$-0.871224\pi$
$599$	−44.9975	−1.83855	−0.919275	+	0.393616i	$0.871224\pi$
$600$	4.39754	0.179529
$601$	−34.3828	−1.40250	−0.701252	−	0.712914i	$-0.747375\pi$
$601$	−34.3828	−1.40250	−0.701252	+	0.712914i	$0.747375\pi$
$602$	−6.04846	−0.246517
$603$	−14.5491	−0.592485
$604$	23.5478	0.958148
$605$	12.7997	0.520384
$606$	−0.542759	−0.0220481
$607$	9.59898	0.389611	0.194805	−	0.980842i	$-0.437592\pi$
$607$	9.59898	0.389611	0.194805	+	0.980842i	$0.437592\pi$
$608$	18.1049	0.734252
$609$	18.7933	0.761543
$610$	2.86586	0.116035
$611$	−7.42547	−0.300402
$612$	3.54116	0.143143
$613$	37.3119	1.50701	0.753506	−	0.657441i	$-0.228361\pi$
$613$	37.3119	1.50701	0.753506	+	0.657441i	$0.228361\pi$
$614$	2.41557	0.0974845
$615$	−7.49206	−0.302109
$616$	−17.5714	−0.707971
$617$	−7.48985	−0.301530	−0.150765	−	0.988570i	$-0.548174\pi$
$617$	−7.48985	−0.301530	−0.150765	+	0.988570i	$0.548174\pi$
$618$	0.262075	0.0105422
$619$	20.6709	0.830832	0.415416	−	0.909631i	$-0.363636\pi$
$619$	20.6709	0.830832	0.415416	+	0.909631i	$0.363636\pi$
$620$	−2.51193	−0.100881
$621$	3.14824	0.126335
$622$	2.09693	0.0840791
$623$	−27.2304	−1.09096
$624$	3.59262	0.143820
$625$	14.5587	0.582349
$626$	4.25887	0.170219
$627$	30.7285	1.22718
$628$	−40.6956	−1.62393
$629$	−1.40321	−0.0559496
$630$	0.750387	0.0298961
$631$	1.02339	0.0407404	0.0203702	−	0.999793i	$-0.493516\pi$
$631$	1.02339	0.0407404	0.0203702	+	0.999793i	$0.493516\pi$
$632$	6.91164	0.274930
$633$	5.11984	0.203495
$634$	−4.19451	−0.166585
$635$	−17.4902	−0.694078
$636$	19.9277	0.790184
$637$	4.20304	0.166531
$638$	7.49783	0.296842
$639$	6.30495	0.249420
$640$	−6.57079	−0.259733
$641$	−18.8292	−0.743710	−0.371855	−	0.928291i	$-0.621278\pi$
$641$	−18.8292	−0.743710	−0.371855	+	0.928291i	$0.621278\pi$
$642$	0.527803	0.0208307
$643$	−1.32383	−0.0522069	−0.0261035	−	0.999659i	$-0.508310\pi$
$643$	−1.32383	−0.0522069	−0.0261035	+	0.999659i	$0.508310\pi$
$644$	−20.3512	−0.801949
$645$	−5.89853	−0.232254
$646$	−2.89790	−0.114017
$647$	−36.0850	−1.41865	−0.709324	−	0.704883i	$-0.751000\pi$
$647$	−36.0850	−1.41865	−0.709324	+	0.704883i	$0.751000\pi$
$648$	−1.03030	−0.0404740
$649$	15.7632	0.618762
$650$	−1.11859	−0.0438748
$651$	5.08897	0.199452
$652$	25.6068	1.00284
$653$	−17.5735	−0.687705	−0.343853	−	0.939024i	$-0.611732\pi$
$653$	−17.5735	−0.687705	−0.343853	+	0.939024i	$0.611732\pi$
$654$	1.97400	0.0771895
$655$	8.62663	0.337070
$656$	−31.4644	−1.22848
$657$	14.0822	0.549397
$658$	−6.51354	−0.253924
$659$	−14.2479	−0.555021	−0.277510	−	0.960723i	$-0.589509\pi$
$659$	−14.2479	−0.555021	−0.277510	+	0.960723i	$0.589509\pi$
$660$	−8.41822	−0.327679
$661$	44.9847	1.74970	0.874850	−	0.484393i	$-0.160960\pi$
$661$	44.9847	1.74970	0.874850	+	0.484393i	$0.160960\pi$
$662$	6.35926	0.247160
$663$	−1.83355	−0.0712091
$664$	−15.9260	−0.618048
$665$	17.2674	0.669601
$666$	0.200565	0.00777174
$667$	17.6768	0.684448
$668$	−28.6882	−1.10998
$669$	−23.0389	−0.890734
$670$	−3.26177	−0.126013
$671$	65.1347	2.51450
$672$	10.0484	0.387626
$673$	−33.3966	−1.28735	−0.643673	−	0.765301i	$-0.722590\pi$
$673$	−33.3966	−1.28735	−0.643673	+	0.765301i	$0.722590\pi$
$674$	8.23960	0.317377
$675$	−4.26821	−0.164284
$676$	−1.93132	−0.0742814
$677$	−37.0480	−1.42387	−0.711935	−	0.702245i	$-0.752181\pi$
$677$	−37.0480	−1.42387	−0.711935	+	0.702245i	$0.752181\pi$
$678$	−0.807014	−0.0309932
$679$	6.90886	0.265138
$680$	1.61602	0.0619717
$681$	−15.0748	−0.577666
$682$	2.03031	0.0777444
$683$	33.0497	1.26461	0.632306	−	0.774719i	$-0.282109\pi$
$683$	33.0497	1.26461	0.632306	+	0.774719i	$0.282109\pi$
$684$	−11.6472	−0.445340
$685$	3.85681	0.147361
$686$	−2.45346	−0.0936736
$687$	−26.1378	−0.997221
$688$	−24.7721	−0.944427
$689$	−10.3182	−0.393092
$690$	0.705806	0.0268696
$691$	−40.4577	−1.53908	−0.769542	−	0.638596i	$-0.779516\pi$
$691$	−40.4577	−1.53908	−0.769542	+	0.638596i	$0.779516\pi$
$692$	10.6936	0.406511
$693$	17.0546	0.647852
$694$	1.22187	0.0463816
$695$	13.3426	0.506113
$696$	−5.78494	−0.219278
$697$	16.0583	0.608253
$698$	5.26000	0.199094
$699$	1.30433	0.0493344
$700$	27.5910	1.04284
$701$	−3.74432	−0.141421	−0.0707106	−	0.997497i	$-0.522527\pi$
$701$	−3.74432	−0.141421	−0.0707106	+	0.997497i	$0.522527\pi$
$702$	0.262075	0.00989138
$703$	4.61527	0.174068
$704$	−32.6024	−1.22875
$705$	−6.35208	−0.239233
$706$	2.02504	0.0762135
$707$	−6.93186	−0.260699
$708$	−5.97482	−0.224547
$709$	−22.9787	−0.862982	−0.431491	−	0.902117i	$-0.642012\pi$
$709$	−22.9787	−0.862982	−0.431491	+	0.902117i	$0.642012\pi$
$710$	1.41351	0.0530481
$711$	−6.70838	−0.251584
$712$	8.38204	0.314130
$713$	4.78663	0.179261
$714$	−1.60837	−0.0601916
$715$	4.35880	0.163010
$716$	14.7204	0.550129
$717$	−28.7072	−1.07209
$718$	−3.08270	−0.115045
$719$	28.8780	1.07697	0.538483	−	0.842636i	$-0.318997\pi$
$719$	28.8780	1.07697	0.538483	+	0.842636i	$0.318997\pi$
$720$	3.07329	0.114535
$721$	3.34709	0.124652
$722$	4.55202	0.169409
$723$	−15.4658	−0.575178
$724$	−18.5485	−0.689351
$725$	−23.9652	−0.890046
$726$	3.92134	0.145535
$727$	−50.1223	−1.85893	−0.929466	−	0.368908i	$-0.879732\pi$
$727$	−50.1223	−1.85893	−0.929466	+	0.368908i	$0.879732\pi$
$728$	−3.44851	−0.127810
$729$	1.00000	0.0370370
$730$	3.15709	0.116849
$731$	12.6428	0.467611
$732$	−24.6883	−0.912506
$733$	−1.36705	−0.0504930	−0.0252465	−	0.999681i	$-0.508037\pi$
$733$	−1.36705	−0.0504930	−0.0252465	+	0.999681i	$0.508037\pi$
$734$	−5.05080	−0.186429
$735$	3.59547	0.132621
$736$	9.45144	0.348385
$737$	−74.1329	−2.73072
$738$	−2.29527	−0.0844901
$739$	32.2726	1.18716	0.593582	−	0.804773i	$-0.297713\pi$
$739$	32.2726	1.18716	0.593582	+	0.804773i	$0.297713\pi$
$740$	−1.26437	−0.0464793
$741$	6.03069	0.221543
$742$	−9.05100	−0.332273
$743$	48.1354	1.76592	0.882958	−	0.469453i	$-0.155549\pi$
$743$	48.1354	1.76592	0.882958	+	0.469453i	$0.155549\pi$
$744$	−1.56648	−0.0574300
$745$	−13.6260	−0.499219
$746$	5.96630	0.218442
$747$	15.4576	0.565565
$748$	18.0435	0.659735
$749$	6.74085	0.246305
$750$	−2.07785	−0.0758722
$751$	−15.2949	−0.558119	−0.279059	−	0.960274i	$-0.590023\pi$
$751$	−15.2949	−0.558119	−0.279059	+	0.960274i	$0.590023\pi$
$752$	−26.6769	−0.972806
$753$	−8.89152	−0.324025
$754$	1.47150	0.0535889
$755$	−10.4301	−0.379591
$756$	−6.46430	−0.235104
$757$	17.7186	0.643992	0.321996	−	0.946741i	$-0.395646\pi$
$757$	17.7186	0.643992	0.321996	+	0.946741i	$0.395646\pi$
$758$	4.45781	0.161915
$759$	16.0414	0.582266
$760$	−5.31523	−0.192804
$761$	−4.24097	−0.153735	−0.0768676	−	0.997041i	$-0.524492\pi$
$761$	−4.24097	−0.153735	−0.0768676	+	0.997041i	$0.524492\pi$
$762$	−5.35831	−0.194111
$763$	25.2110	0.912699
$764$	34.6654	1.25415
$765$	−1.56850	−0.0567092
$766$	−2.25447	−0.0814573
$767$	3.09365	0.111705
$768$	10.7839	0.389129
$769$	−12.9145	−0.465710	−0.232855	−	0.972512i	$-0.574807\pi$
$769$	−12.9145	−0.465710	−0.232855	+	0.972512i	$0.574807\pi$
$770$	3.82349	0.137789
$771$	27.5838	0.993406
$772$	−8.50881	−0.306239
$773$	−52.1150	−1.87445	−0.937224	−	0.348729i	$-0.886613\pi$
$773$	−52.1150	−1.87445	−0.937224	+	0.348729i	$0.886613\pi$
$774$	−1.80708	−0.0649541
$775$	−6.48945	−0.233108
$776$	−2.12668	−0.0763433
$777$	2.56152	0.0918941
$778$	−7.39984	−0.265297
$779$	−52.8172	−1.89237
$780$	−1.65214	−0.0591559
$781$	32.1260	1.14956
$782$	−1.51281	−0.0540981
$783$	5.61481	0.200657
$784$	15.0999	0.539283
$785$	18.0254	0.643356
$786$	2.64286	0.0942677
$787$	−44.1855	−1.57504	−0.787522	−	0.616286i	$-0.788636\pi$
$787$	−44.1855	−1.57504	−0.787522	+	0.616286i	$0.788636\pi$
$788$	−45.1260	−1.60755
$789$	30.8116	1.09692
$790$	−1.50396	−0.0535084
$791$	−10.3068	−0.366467
$792$	−5.24974	−0.186541
$793$	12.7832	0.453943
$794$	−2.14039	−0.0759596
$795$	−8.82664	−0.313049
$796$	−21.0390	−0.745708
$797$	−10.2108	−0.361685	−0.180843	−	0.983512i	$-0.557882\pi$
$797$	−10.2108	−0.361685	−0.180843	+	0.983512i	$0.557882\pi$
$798$	5.29005	0.187266
$799$	13.6149	0.481662
$800$	−12.8137	−0.453034
$801$	−8.13554	−0.287455
$802$	−4.06137	−0.143412
$803$	71.7536	2.53213
$804$	28.0989	0.990973
$805$	9.01422	0.317710
$806$	0.398462	0.0140352
$807$	1.60340	0.0564424
$808$	2.13376	0.0750653
$809$	15.2992	0.537891	0.268946	−	0.963155i	$-0.413325\pi$
$809$	15.2992	0.537891	0.268946	+	0.963155i	$0.413325\pi$
$810$	0.224191	0.00787726
$811$	19.2496	0.675945	0.337972	−	0.941156i	$-0.390259\pi$
$811$	19.2496	0.675945	0.337972	+	0.941156i	$0.390259\pi$
$812$	−36.2958	−1.27373
$813$	−1.29306	−0.0453495
$814$	1.02195	0.0358194
$815$	−11.3421	−0.397297
$816$	−6.58723	−0.230599
$817$	−41.5832	−1.45481
$818$	−3.25984	−0.113978
$819$	3.34709	0.116957
$820$	14.4695	0.505298
$821$	27.0498	0.944044	0.472022	−	0.881587i	$-0.343524\pi$
$821$	27.0498	0.944044	0.472022	+	0.881587i	$0.343524\pi$
$822$	1.18158	0.0412122
$823$	18.9352	0.660041	0.330020	−	0.943974i	$-0.392944\pi$
$823$	18.9352	0.660041	0.330020	+	0.943974i	$0.392944\pi$
$824$	−1.03030	−0.0358922
$825$	−21.7481	−0.757171
$826$	2.71372	0.0944222
$827$	−21.7795	−0.757346	−0.378673	−	0.925530i	$-0.623620\pi$
$827$	−21.7795	−0.757346	−0.378673	+	0.925530i	$0.623620\pi$
$828$	−6.08025	−0.211303
$829$	53.1843	1.84717	0.923583	−	0.383398i	$-0.125246\pi$
$829$	53.1843	1.84717	0.923583	+	0.383398i	$0.125246\pi$
$830$	3.46546	0.120288
$831$	8.81030	0.305626
$832$	−6.39845	−0.221826
$833$	−7.70647	−0.267013
$834$	4.08764	0.141543
$835$	12.7070	0.439743
$836$	−59.3465	−2.05254
$837$	1.52041	0.0525532
$838$	−6.86368	−0.237102
$839$	−56.0888	−1.93640	−0.968199	−	0.250180i	$-0.919510\pi$
$839$	−56.0888	−1.93640	−0.968199	+	0.250180i	$0.919510\pi$
$840$	−2.95001	−0.101785
$841$	2.52614	0.0871081
$842$	−1.14644	−0.0395088
$843$	−5.83315	−0.200905
$844$	−9.88802	−0.340360
$845$	0.855445	0.0294282
$846$	−1.94603	−0.0669058
$847$	50.0815	1.72082
$848$	−37.0693	−1.27297
$849$	26.4325	0.907160
$850$	2.05099	0.0703484
$851$	2.40934	0.0825911
$852$	−12.1769	−0.417172
$853$	32.0354	1.09687	0.548435	−	0.836193i	$-0.315224\pi$
$853$	32.0354	1.09687	0.548435	+	0.836193i	$0.315224\pi$
$854$	11.2132	0.383709
$855$	5.15892	0.176431
$856$	−2.07496	−0.0709207
$857$	42.2904	1.44461	0.722305	−	0.691574i	$-0.243082\pi$
$857$	42.2904	1.44461	0.722305	+	0.691574i	$0.243082\pi$
$858$	1.33537	0.0455886
$859$	−16.6265	−0.567290	−0.283645	−	0.958929i	$-0.591544\pi$
$859$	−16.6265	−0.567290	−0.283645	+	0.958929i	$0.591544\pi$
$860$	11.3919	0.388461
$861$	−29.3141	−0.999023
$862$	−4.24846	−0.144703
$863$	24.1084	0.820659	0.410329	−	0.911937i	$-0.365414\pi$
$863$	24.1084	0.820659	0.410329	+	0.911937i	$0.365414\pi$
$864$	3.00213	0.102135
$865$	−4.73657	−0.161048
$866$	0.187715	0.00637883
$867$	−13.6381	−0.463174
$868$	−9.82841	−0.333598
$869$	−34.1816	−1.15953
$870$	1.25879	0.0426769
$871$	−14.5491	−0.492978
$872$	−7.76042	−0.262801
$873$	2.06414	0.0698604
$874$	4.97577	0.168308
$875$	−26.5373	−0.897123
$876$	−27.1971	−0.918905
$877$	23.0547	0.778502	0.389251	−	0.921132i	$-0.372734\pi$
$877$	23.0547	0.778502	0.389251	+	0.921132i	$0.372734\pi$
$878$	−6.72679	−0.227018
$879$	33.0347	1.11423
$880$	15.6595	0.527882
$881$	28.6370	0.964804	0.482402	−	0.875950i	$-0.339764\pi$
$881$	28.6370	0.964804	0.482402	+	0.875950i	$0.339764\pi$
$882$	1.10151	0.0370898
$883$	34.1875	1.15050	0.575250	−	0.817978i	$-0.304905\pi$
$883$	34.1875	1.15050	0.575250	+	0.817978i	$0.304905\pi$
$884$	3.54116	0.119102
$885$	2.64645	0.0889594
$886$	−2.19687	−0.0738053
$887$	16.5290	0.554988	0.277494	−	0.960727i	$-0.410496\pi$
$887$	16.5290	0.554988	0.277494	+	0.960727i	$0.410496\pi$
$888$	−0.788485	−0.0264598
$889$	−68.4338	−2.29520
$890$	−1.82391	−0.0611377
$891$	5.09536	0.170701
$892$	44.4953	1.48981
$893$	−44.7807	−1.49853
$894$	−4.17448	−0.139616
$895$	−6.52018	−0.217946
$896$	−25.7095	−0.858894
$897$	3.14824	0.105117
$898$	−9.49380	−0.316812
$899$	8.53684	0.284719
$900$	8.24327	0.274776
$901$	18.9189	0.630279
$902$	−11.6952	−0.389409
$903$	−23.0791	−0.768025
$904$	3.17263	0.105520
$905$	8.21578	0.273102
$906$	−3.19538	−0.106159
$907$	23.8917	0.793312	0.396656	−	0.917967i	$-0.370171\pi$
$907$	23.8917	0.793312	0.396656	+	0.917967i	$0.370171\pi$
$908$	29.1142	0.966187
$909$	−2.07101	−0.0686910
$910$	0.750387	0.0248751
$911$	10.4812	0.347257	0.173629	−	0.984811i	$-0.444451\pi$
$911$	10.4812	0.347257	0.173629	+	0.984811i	$0.444451\pi$
$912$	21.6660	0.717431
$913$	78.7622	2.60665
$914$	−8.79050	−0.290764
$915$	10.9353	0.361509
$916$	50.4805	1.66792
$917$	33.7534	1.11463
$918$	−0.480526	−0.0158597
$919$	−27.9604	−0.922327	−0.461164	−	0.887315i	$-0.652568\pi$
$919$	−27.9604	−0.922327	−0.461164	+	0.887315i	$0.652568\pi$
$920$	−2.77475	−0.0914807
$921$	9.21710	0.303714
$922$	1.40628	0.0463133
$923$	6.30495	0.207530
$924$	−32.9379	−1.08358
$925$	−3.26645	−0.107400
$926$	1.43731	0.0472330
$927$	1.00000	0.0328443
$928$	16.8564	0.553339
$929$	−4.03266	−0.132307	−0.0661536	−	0.997809i	$-0.521073\pi$
$929$	−4.03266	−0.132307	−0.0661536	+	0.997809i	$0.521073\pi$
$930$	0.340862	0.0111773
$931$	25.3472	0.830722
$932$	−2.51908	−0.0825152
$933$	8.00126	0.261949
$934$	−10.2016	−0.333806
$935$	−7.99206	−0.261368
$936$	−1.03030	−0.0336764
$937$	0.965594	0.0315446	0.0157723	−	0.999876i	$-0.494979\pi$
$937$	0.965594	0.0315446	0.0157723	+	0.999876i	$0.494979\pi$
$938$	−12.7623	−0.416705
$939$	16.2506	0.530317
$940$	12.2679	0.400134
$941$	−20.7923	−0.677809	−0.338905	−	0.940821i	$-0.610056\pi$
$941$	−20.7923	−0.677809	−0.338905	+	0.940821i	$0.610056\pi$
$942$	5.52229	0.179926
$943$	−27.5725	−0.897886
$944$	11.1143	0.361740
$945$	2.86326	0.0931417
$946$	−9.20771	−0.299368
$947$	13.7810	0.447822	0.223911	−	0.974610i	$-0.428118\pi$
$947$	13.7810	0.447822	0.223911	+	0.974610i	$0.428118\pi$
$948$	12.9560	0.420791
$949$	14.0822	0.457126
$950$	−6.74587	−0.218865
$951$	−16.0050	−0.518998
$952$	6.32300	0.204930
$953$	−30.1962	−0.978150	−0.489075	−	0.872242i	$-0.662666\pi$
$953$	−30.1962	−0.978150	−0.489075	+	0.872242i	$0.662666\pi$
$954$	−2.70414	−0.0875497
$955$	−15.3545	−0.496859
$956$	55.4426	1.79314
$957$	28.6095	0.924813
$958$	−2.61296	−0.0844208
$959$	15.0905	0.487299
$960$	−5.47353	−0.176657
$961$	−28.6883	−0.925430
$962$	0.200565	0.00646648
$963$	2.01394	0.0648983
$964$	29.8693	0.962026
$965$	3.76884	0.121323
$966$	2.76160	0.0888531
$967$	38.1056	1.22539	0.612697	−	0.790318i	$-0.290084\pi$
$967$	38.1056	1.22539	0.612697	+	0.790318i	$0.290084\pi$
$968$	−15.4160	−0.495490
$969$	−11.0575	−0.355220
$970$	0.462760	0.0148583
$971$	−52.9908	−1.70056	−0.850278	−	0.526333i	$-0.823566\pi$
$971$	−52.9908	−1.70056	−0.850278	+	0.526333i	$0.823566\pi$
$972$	−1.93132	−0.0619470
$973$	52.2054	1.67363
$974$	−1.74209	−0.0558201
$975$	−4.26821	−0.136692
$976$	45.9250	1.47002
$977$	−6.77026	−0.216600	−0.108300	−	0.994118i	$-0.534541\pi$
$977$	−6.77026	−0.216600	−0.108300	+	0.994118i	$0.534541\pi$
$978$	−3.47478	−0.111111
$979$	−41.4535	−1.32486
$980$	−6.94399	−0.221818
$981$	7.53220	0.240485
$982$	1.91969	0.0612597
$983$	−7.09416	−0.226269	−0.113134	−	0.993580i	$-0.536089\pi$
$983$	−7.09416	−0.226269	−0.113134	+	0.993580i	$0.536089\pi$
$984$	9.02344	0.287657
$985$	19.9878	0.636865
$986$	−2.69807	−0.0859239
$987$	−24.8537	−0.791103
$988$	−11.6472	−0.370546
$989$	−21.7080	−0.690274
$990$	1.14233	0.0363057
$991$	11.5462	0.366777	0.183389	−	0.983040i	$-0.441293\pi$
$991$	11.5462	0.366777	0.183389	+	0.983040i	$0.441293\pi$
$992$	4.56448	0.144922
$993$	24.2650	0.770028
$994$	5.53064	0.175421
$995$	9.31888	0.295428
$996$	−29.8536	−0.945947
$997$	39.2608	1.24340	0.621700	−	0.783255i	$-0.286442\pi$
$997$	39.2608	1.24340	0.621700	+	0.783255i	$0.286442\pi$
$998$	7.33953	0.232329
$999$	0.765297	0.0242129

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.17	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.17	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.262075 q^{2} +1.00000 q^{3} -1.93132 q^{4} +0.855445 q^{5} +0.262075 q^{6} +3.34709 q^{7} -1.03030 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.262075 q^{2} +1.00000 q^{3} -1.93132 q^{4} +0.855445 q^{5} +0.262075 q^{6} +3.34709 q^{7} -1.03030 q^{8} +1.00000 q^{9} +0.224191 q^{10} +5.09536 q^{11} -1.93132 q^{12} +1.00000 q^{13} +0.877189 q^{14} +0.855445 q^{15} +3.59262 q^{16} -1.83355 q^{17} +0.262075 q^{18} +6.03069 q^{19} -1.65214 q^{20} +3.34709 q^{21} +1.33537 q^{22} +3.14824 q^{23} -1.03030 q^{24} -4.26821 q^{25} +0.262075 q^{26} +1.00000 q^{27} -6.46430 q^{28} +5.61481 q^{29} +0.224191 q^{30} +1.52041 q^{31} +3.00213 q^{32} +5.09536 q^{33} -0.480526 q^{34} +2.86326 q^{35} -1.93132 q^{36} +0.765297 q^{37} +1.58049 q^{38} +1.00000 q^{39} -0.881365 q^{40} -8.75808 q^{41} +0.877189 q^{42} -6.89527 q^{43} -9.84075 q^{44} +0.855445 q^{45} +0.825075 q^{46} -7.42547 q^{47} +3.59262 q^{48} +4.20304 q^{49} -1.11859 q^{50} -1.83355 q^{51} -1.93132 q^{52} -10.3182 q^{53} +0.262075 q^{54} +4.35880 q^{55} -3.44851 q^{56} +6.03069 q^{57} +1.47150 q^{58} +3.09365 q^{59} -1.65214 q^{60} +12.7832 q^{61} +0.398462 q^{62} +3.34709 q^{63} -6.39845 q^{64} +0.855445 q^{65} +1.33537 q^{66} -14.5491 q^{67} +3.54116 q^{68} +3.14824 q^{69} +0.750387 q^{70} +6.30495 q^{71} -1.03030 q^{72} +14.0822 q^{73} +0.200565 q^{74} -4.26821 q^{75} -11.6472 q^{76} +17.0546 q^{77} +0.262075 q^{78} -6.70838 q^{79} +3.07329 q^{80} +1.00000 q^{81} -2.29527 q^{82} +15.4576 q^{83} -6.46430 q^{84} -1.56850 q^{85} -1.80708 q^{86} +5.61481 q^{87} -5.24974 q^{88} -8.13554 q^{89} +0.224191 q^{90} +3.34709 q^{91} -6.08025 q^{92} +1.52041 q^{93} -1.94603 q^{94} +5.15892 q^{95} +3.00213 q^{96} +2.06414 q^{97} +1.10151 q^{98} +5.09536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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