LMFDB - Embedded newform 4017.2.a.j.1.9

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

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +3.45668 q^{10} +4.28895 q^{11} +1.26284 q^{12} +1.00000 q^{13} -1.45173 q^{14} +4.02605 q^{15} +0.120444 q^{16} +7.37326 q^{17} -0.858580 q^{18} +0.247701 q^{19} +5.08425 q^{20} -1.69085 q^{21} -3.68241 q^{22} +7.02793 q^{23} -2.80141 q^{24} +11.2091 q^{25} -0.858580 q^{26} -1.00000 q^{27} -2.13527 q^{28} -2.37570 q^{29} -3.45668 q^{30} +7.06841 q^{31} -5.70623 q^{32} -4.28895 q^{33} -6.33054 q^{34} -6.80743 q^{35} -1.26284 q^{36} -0.651425 q^{37} -0.212671 q^{38} -1.00000 q^{39} -11.2786 q^{40} +4.11006 q^{41} +1.45173 q^{42} -4.16005 q^{43} -5.41625 q^{44} -4.02605 q^{45} -6.03404 q^{46} +2.62615 q^{47} -0.120444 q^{48} -4.14104 q^{49} -9.62387 q^{50} -7.37326 q^{51} -1.26284 q^{52} -7.05625 q^{53} +0.858580 q^{54} -17.2675 q^{55} +4.73675 q^{56} -0.247701 q^{57} +2.03973 q^{58} -10.9647 q^{59} -5.08425 q^{60} +9.22303 q^{61} -6.06880 q^{62} +1.69085 q^{63} +4.65837 q^{64} -4.02605 q^{65} +3.68241 q^{66} +0.887929 q^{67} -9.31125 q^{68} -7.02793 q^{69} +5.84472 q^{70} +12.7885 q^{71} +2.80141 q^{72} +8.42670 q^{73} +0.559301 q^{74} -11.2091 q^{75} -0.312806 q^{76} +7.25195 q^{77} +0.858580 q^{78} +5.27331 q^{79} -0.484914 q^{80} +1.00000 q^{81} -3.52881 q^{82} +11.2899 q^{83} +2.13527 q^{84} -29.6851 q^{85} +3.57174 q^{86} +2.37570 q^{87} +12.0151 q^{88} +0.789688 q^{89} +3.45668 q^{90} +1.69085 q^{91} -8.87515 q^{92} -7.06841 q^{93} -2.25476 q^{94} -0.997255 q^{95} +5.70623 q^{96} -14.1860 q^{97} +3.55541 q^{98} +4.28895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * 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 $

$2$	−0.858580	−0.607108	−0.303554	−	0.952814i	$-0.598173\pi$
$2$	−0.858580	−0.607108	−0.303554	+	0.952814i	$0.598173\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.26284	−0.631420
$5$	−4.02605	−1.80050	−0.900251	−	0.435370i	$-0.856617\pi$
$5$	−4.02605	−1.80050	−0.900251	+	0.435370i	$0.856617\pi$
$6$	0.858580	0.350514
$7$	1.69085	0.639080	0.319540	−	0.947573i	$-0.396472\pi$
$7$	1.69085	0.639080	0.319540	+	0.947573i	$0.396472\pi$
$8$	2.80141	0.990448
$9$	1.00000	0.333333
$10$	3.45668	1.09310
$11$	4.28895	1.29317	0.646583	−	0.762843i	$-0.276197\pi$
$11$	4.28895	1.29317	0.646583	+	0.762843i	$0.276197\pi$
$12$	1.26284	0.364550
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.45173	−0.387991
$15$	4.02605	1.03952
$16$	0.120444	0.0301110
$17$	7.37326	1.78828	0.894139	−	0.447789i	$-0.147789\pi$
$17$	7.37326	1.78828	0.894139	+	0.447789i	$0.147789\pi$
$18$	−0.858580	−0.202369
$19$	0.247701	0.0568265	0.0284132	−	0.999596i	$-0.490955\pi$
$19$	0.247701	0.0568265	0.0284132	+	0.999596i	$0.490955\pi$
$20$	5.08425	1.13687
$21$	−1.69085	−0.368973
$22$	−3.68241	−0.785092
$23$	7.02793	1.46542	0.732712	−	0.680539i	$-0.238254\pi$
$23$	7.02793	1.46542	0.732712	+	0.680539i	$0.238254\pi$
$24$	−2.80141	−0.571835
$25$	11.2091	2.24181
$26$	−0.858580	−0.168381
$27$	−1.00000	−0.192450
$28$	−2.13527	−0.403528
$29$	−2.37570	−0.441157	−0.220579	−	0.975369i	$-0.570795\pi$
$29$	−2.37570	−0.441157	−0.220579	+	0.975369i	$0.570795\pi$
$30$	−3.45668	−0.631101
$31$	7.06841	1.26952	0.634762	−	0.772708i	$-0.281098\pi$
$31$	7.06841	1.26952	0.634762	+	0.772708i	$0.281098\pi$
$32$	−5.70623	−1.00873
$33$	−4.28895	−0.746610
$34$	−6.33054	−1.08568
$35$	−6.80743	−1.15067
$36$	−1.26284	−0.210473
$37$	−0.651425	−0.107094	−0.0535468	−	0.998565i	$-0.517053\pi$
$37$	−0.651425	−0.107094	−0.0535468	+	0.998565i	$0.517053\pi$
$38$	−0.212671	−0.0344998
$39$	−1.00000	−0.160128
$40$	−11.2786	−1.78330
$41$	4.11006	0.641883	0.320942	−	0.947099i	$-0.396001\pi$
$41$	4.11006	0.641883	0.320942	+	0.947099i	$0.396001\pi$
$42$	1.45173	0.224006
$43$	−4.16005	−0.634402	−0.317201	−	0.948358i	$-0.602743\pi$
$43$	−4.16005	−0.634402	−0.317201	+	0.948358i	$0.602743\pi$
$44$	−5.41625	−0.816531
$45$	−4.02605	−0.600168
$46$	−6.03404	−0.889671
$47$	2.62615	0.383064	0.191532	−	0.981486i	$-0.438654\pi$
$47$	2.62615	0.383064	0.191532	+	0.981486i	$0.438654\pi$
$48$	−0.120444	−0.0173846
$49$	−4.14104	−0.591577
$50$	−9.62387	−1.36102
$51$	−7.37326	−1.03246
$52$	−1.26284	−0.175124
$53$	−7.05625	−0.969250	−0.484625	−	0.874722i	$-0.661044\pi$
$53$	−7.05625	−0.969250	−0.484625	+	0.874722i	$0.661044\pi$
$54$	0.858580	0.116838
$55$	−17.2675	−2.32835
$56$	4.73675	0.632975
$57$	−0.247701	−0.0328088
$58$	2.03973	0.267830
$59$	−10.9647	−1.42749	−0.713744	−	0.700407i	$-0.753002\pi$
$59$	−10.9647	−1.42749	−0.713744	+	0.700407i	$0.753002\pi$
$60$	−5.08425	−0.656374
$61$	9.22303	1.18089	0.590444	−	0.807079i	$-0.298953\pi$
$61$	9.22303	1.18089	0.590444	+	0.807079i	$0.298953\pi$
$62$	−6.06880	−0.770738
$63$	1.69085	0.213027
$64$	4.65837	0.582296
$65$	−4.02605	−0.499370
$66$	3.68241	0.453273
$67$	0.887929	0.108478	0.0542389	−	0.998528i	$-0.482727\pi$
$67$	0.887929	0.108478	0.0542389	+	0.998528i	$0.482727\pi$
$68$	−9.31125	−1.12915
$69$	−7.02793	−0.846063
$70$	5.84472	0.698578
$71$	12.7885	1.51772	0.758859	−	0.651254i	$-0.225757\pi$
$71$	12.7885	1.51772	0.758859	+	0.651254i	$0.225757\pi$
$72$	2.80141	0.330149
$73$	8.42670	0.986271	0.493135	−	0.869953i	$-0.335851\pi$
$73$	8.42670	0.986271	0.493135	+	0.869953i	$0.335851\pi$
$74$	0.559301	0.0650174
$75$	−11.2091	−1.29431
$76$	−0.312806	−0.0358814
$77$	7.25195	0.826437
$78$	0.858580	0.0972151
$79$	5.27331	0.593294	0.296647	−	0.954987i	$-0.404132\pi$
$79$	5.27331	0.593294	0.296647	+	0.954987i	$0.404132\pi$
$80$	−0.484914	−0.0542150
$81$	1.00000	0.111111
$82$	−3.52881	−0.389692
$83$	11.2899	1.23923	0.619613	−	0.784907i	$-0.287289\pi$
$83$	11.2899	1.23923	0.619613	+	0.784907i	$0.287289\pi$
$84$	2.13527	0.232977
$85$	−29.6851	−3.21980
$86$	3.57174	0.385151
$87$	2.37570	0.254702
$88$	12.0151	1.28081
$89$	0.789688	0.0837067	0.0418534	−	0.999124i	$-0.486674\pi$
$89$	0.789688	0.0837067	0.0418534	+	0.999124i	$0.486674\pi$
$90$	3.45668	0.364367
$91$	1.69085	0.177249
$92$	−8.87515	−0.925298
$93$	−7.06841	−0.732960
$94$	−2.25476	−0.232561
$95$	−0.997255	−0.102316
$96$	5.70623	0.582390
$97$	−14.1860	−1.44037	−0.720183	−	0.693784i	$-0.755942\pi$
$97$	−14.1860	−1.44037	−0.720183	+	0.693784i	$0.755942\pi$
$98$	3.55541	0.359151
$99$	4.28895	0.431055
$100$	−14.1552	−1.41552
$101$	17.1694	1.70842	0.854211	−	0.519926i	$-0.174040\pi$
$101$	17.1694	1.70842	0.854211	+	0.519926i	$0.174040\pi$
$102$	6.33054	0.626816
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.80141	0.274701
$105$	6.80743	0.664337
$106$	6.05836	0.588440
$107$	0.920374	0.0889759	0.0444879	−	0.999010i	$-0.485834\pi$
$107$	0.920374	0.0889759	0.0444879	+	0.999010i	$0.485834\pi$
$108$	1.26284	0.121517
$109$	−11.6041	−1.11147	−0.555734	−	0.831360i	$-0.687563\pi$
$109$	−11.6041	−1.11147	−0.555734	+	0.831360i	$0.687563\pi$
$110$	14.8255	1.41356
$111$	0.651425	0.0618305
$112$	0.203653	0.0192434
$113$	13.8477	1.30268	0.651341	−	0.758785i	$-0.274207\pi$
$113$	13.8477	1.30268	0.651341	+	0.758785i	$0.274207\pi$
$114$	0.212671	0.0199185
$115$	−28.2948	−2.63850
$116$	3.00013	0.278556
$117$	1.00000	0.0924500
$118$	9.41411	0.866639
$119$	12.4671	1.14285
$120$	11.2786	1.02959
$121$	7.39508	0.672280
$122$	−7.91871	−0.716927
$123$	−4.11006	−0.370591
$124$	−8.92627	−0.801602
$125$	−24.9979	−2.23588
$126$	−1.45173	−0.129330
$127$	−15.9315	−1.41369	−0.706845	−	0.707369i	$-0.749882\pi$
$127$	−15.9315	−1.41369	−0.706845	+	0.707369i	$0.749882\pi$
$128$	7.41288	0.655212
$129$	4.16005	0.366272
$130$	3.45668	0.303171
$131$	−11.6337	−1.01644	−0.508219	−	0.861228i	$-0.669696\pi$
$131$	−11.6337	−1.01644	−0.508219	+	0.861228i	$0.669696\pi$
$132$	5.41625	0.471424
$133$	0.418824	0.0363167
$134$	−0.762358	−0.0658577
$135$	4.02605	0.346507
$136$	20.6555	1.77120
$137$	17.0824	1.45945	0.729723	−	0.683743i	$-0.239649\pi$
$137$	17.0824	1.45945	0.729723	+	0.683743i	$0.239649\pi$
$138$	6.03404	0.513652
$139$	−16.3737	−1.38880	−0.694401	−	0.719588i	$-0.744330\pi$
$139$	−16.3737	−1.38880	−0.694401	+	0.719588i	$0.744330\pi$
$140$	8.59669	0.726553
$141$	−2.62615	−0.221162
$142$	−10.9800	−0.921419
$143$	4.28895	0.358660
$144$	0.120444	0.0100370
$145$	9.56470	0.794305
$146$	−7.23500	−0.598773
$147$	4.14104	0.341547
$148$	0.822646	0.0676211
$149$	9.15789	0.750244	0.375122	−	0.926975i	$-0.377601\pi$
$149$	9.15789	0.750244	0.375122	+	0.926975i	$0.377601\pi$
$150$	9.62387	0.785786
$151$	10.1681	0.827472	0.413736	−	0.910397i	$-0.364224\pi$
$151$	10.1681	0.827472	0.413736	+	0.910397i	$0.364224\pi$
$152$	0.693912	0.0562837
$153$	7.37326	0.596093
$154$	−6.22638	−0.501736
$155$	−28.4577	−2.28578
$156$	1.26284	0.101108
$157$	−13.1766	−1.05161	−0.525805	−	0.850605i	$-0.676236\pi$
$157$	−13.1766	−1.05161	−0.525805	+	0.850605i	$0.676236\pi$
$158$	−4.52756	−0.360193
$159$	7.05625	0.559597
$160$	22.9736	1.81622
$161$	11.8831	0.936523
$162$	−0.858580	−0.0674564
$163$	10.3849	0.813407	0.406703	−	0.913560i	$-0.366678\pi$
$163$	10.3849	0.813407	0.406703	+	0.913560i	$0.366678\pi$
$164$	−5.19034	−0.405298
$165$	17.2675	1.34427
$166$	−9.69328	−0.752344
$167$	−7.95912	−0.615895	−0.307948	−	0.951403i	$-0.599642\pi$
$167$	−7.95912	−0.615895	−0.307948	+	0.951403i	$0.599642\pi$
$168$	−4.73675	−0.365449
$169$	1.00000	0.0769231
$170$	25.4870	1.95477
$171$	0.247701	0.0189422
$172$	5.25348	0.400574
$173$	17.3009	1.31536	0.657682	−	0.753296i	$-0.271537\pi$
$173$	17.3009	1.31536	0.657682	+	0.753296i	$0.271537\pi$
$174$	−2.03973	−0.154632
$175$	18.9528	1.43270
$176$	0.516579	0.0389386
$177$	10.9647	0.824161
$178$	−0.678010	−0.0508190
$179$	−7.70431	−0.575847	−0.287923	−	0.957653i	$-0.592965\pi$
$179$	−7.70431	−0.575847	−0.287923	+	0.957653i	$0.592965\pi$
$180$	5.08425	0.378958
$181$	−23.8049	−1.76940	−0.884702	−	0.466158i	$-0.845638\pi$
$181$	−23.8049	−1.76940	−0.884702	+	0.466158i	$0.845638\pi$
$182$	−1.45173	−0.107609
$183$	−9.22303	−0.681786
$184$	19.6881	1.45143
$185$	2.62267	0.192822
$186$	6.06880	0.444986
$187$	31.6235	2.31254
$188$	−3.31641	−0.241874
$189$	−1.69085	−0.122991
$190$	0.856224	0.0621170
$191$	8.97563	0.649454	0.324727	−	0.945808i	$-0.394728\pi$
$191$	8.97563	0.649454	0.324727	+	0.945808i	$0.394728\pi$
$192$	−4.65837	−0.336189
$193$	−26.9771	−1.94185	−0.970926	−	0.239379i	$-0.923056\pi$
$193$	−26.9771	−1.94185	−0.970926	+	0.239379i	$0.923056\pi$
$194$	12.1798	0.874457
$195$	4.02605	0.288311
$196$	5.22947	0.373533
$197$	−4.08743	−0.291217	−0.145609	−	0.989342i	$-0.546514\pi$
$197$	−4.08743	−0.291217	−0.145609	+	0.989342i	$0.546514\pi$
$198$	−3.68241	−0.261697
$199$	11.2881	0.800196	0.400098	−	0.916472i	$-0.368976\pi$
$199$	11.2881	0.800196	0.400098	+	0.916472i	$0.368976\pi$
$200$	31.4011	2.22040
$201$	−0.887929	−0.0626297
$202$	−14.7413	−1.03720
$203$	−4.01695	−0.281935
$204$	9.31125	0.651918
$205$	−16.5473	−1.15571
$206$	0.858580	0.0598201
$207$	7.02793	0.488475
$208$	0.120444	0.00835130
$209$	1.06238	0.0734861
$210$	−5.84472	−0.403324
$211$	−1.09307	−0.0752500	−0.0376250	−	0.999292i	$-0.511979\pi$
$211$	−1.09307	−0.0752500	−0.0376250	+	0.999292i	$0.511979\pi$
$212$	8.91091	0.612004
$213$	−12.7885	−0.876255
$214$	−0.790215	−0.0540180
$215$	16.7486	1.14224
$216$	−2.80141	−0.190612
$217$	11.9516	0.811327
$218$	9.96303	0.674781
$219$	−8.42670	−0.569424
$220$	21.8061	1.47017
$221$	7.37326	0.495979
$222$	−0.559301	−0.0375378
$223$	−5.33525	−0.357274	−0.178637	−	0.983915i	$-0.557169\pi$
$223$	−5.33525	−0.357274	−0.178637	+	0.983915i	$0.557169\pi$
$224$	−9.64836	−0.644658
$225$	11.2091	0.747270
$226$	−11.8894	−0.790869
$227$	−26.6015	−1.76561	−0.882803	−	0.469744i	$-0.844346\pi$
$227$	−26.6015	−1.76561	−0.882803	+	0.469744i	$0.844346\pi$
$228$	0.312806	0.0207161
$229$	22.1490	1.46365	0.731825	−	0.681492i	$-0.238669\pi$
$229$	22.1490	1.46365	0.731825	+	0.681492i	$0.238669\pi$
$230$	24.2933	1.60185
$231$	−7.25195	−0.477143
$232$	−6.65532	−0.436943
$233$	1.31800	0.0863453	0.0431727	−	0.999068i	$-0.486253\pi$
$233$	1.31800	0.0863453	0.0431727	+	0.999068i	$0.486253\pi$
$234$	−0.858580	−0.0561272
$235$	−10.5730	−0.689707
$236$	13.8467	0.901344
$237$	−5.27331	−0.342538
$238$	−10.7040	−0.693835
$239$	25.6984	1.66229	0.831145	−	0.556056i	$-0.187686\pi$
$239$	25.6984	1.66229	0.831145	+	0.556056i	$0.187686\pi$
$240$	0.484914	0.0313011
$241$	−10.5609	−0.680288	−0.340144	−	0.940373i	$-0.610476\pi$
$241$	−10.5609	−0.680288	−0.340144	+	0.940373i	$0.610476\pi$
$242$	−6.34927	−0.408146
$243$	−1.00000	−0.0641500
$244$	−11.6472	−0.745636
$245$	16.6720	1.06514
$246$	3.52881	0.224989
$247$	0.247701	0.0157608
$248$	19.8015	1.25740
$249$	−11.2899	−0.715468
$250$	21.4627	1.35742
$251$	−6.47131	−0.408466	−0.204233	−	0.978922i	$-0.565470\pi$
$251$	−6.47131	−0.408466	−0.204233	+	0.978922i	$0.565470\pi$
$252$	−2.13527	−0.134509
$253$	30.1424	1.89504
$254$	13.6784	0.858262
$255$	29.6851	1.85895
$256$	−15.6813	−0.980081
$257$	5.50697	0.343515	0.171758	−	0.985139i	$-0.445055\pi$
$257$	5.50697	0.343515	0.171758	+	0.985139i	$0.445055\pi$
$258$	−3.57174	−0.222367
$259$	−1.10146	−0.0684414
$260$	5.08425	0.315312
$261$	−2.37570	−0.147052
$262$	9.98844	0.617088
$263$	−15.9892	−0.985938	−0.492969	−	0.870047i	$-0.664088\pi$
$263$	−15.9892	−0.985938	−0.492969	+	0.870047i	$0.664088\pi$
$264$	−12.0151	−0.739478
$265$	28.4088	1.74514
$266$	−0.359594	−0.0220481
$267$	−0.789688	−0.0483281
$268$	−1.12131	−0.0684950
$269$	19.2576	1.17416	0.587078	−	0.809531i	$-0.300278\pi$
$269$	19.2576	1.17416	0.587078	+	0.809531i	$0.300278\pi$
$270$	−3.45668	−0.210367
$271$	−26.8710	−1.63230	−0.816148	−	0.577842i	$-0.803895\pi$
$271$	−26.8710	−1.63230	−0.816148	+	0.577842i	$0.803895\pi$
$272$	0.888066	0.0538469
$273$	−1.69085	−0.102335
$274$	−14.6666	−0.886041
$275$	48.0750	2.89903
$276$	8.87515	0.534221
$277$	−16.4553	−0.988701	−0.494351	−	0.869263i	$-0.664594\pi$
$277$	−16.4553	−0.988701	−0.494351	+	0.869263i	$0.664594\pi$
$278$	14.0582	0.843153
$279$	7.06841	0.423175
$280$	−19.0704	−1.13967
$281$	21.9700	1.31062	0.655309	−	0.755361i	$-0.272539\pi$
$281$	21.9700	1.31062	0.655309	+	0.755361i	$0.272539\pi$
$282$	2.25476	0.134269
$283$	25.8394	1.53599	0.767995	−	0.640456i	$-0.221255\pi$
$283$	25.8394	1.53599	0.767995	+	0.640456i	$0.221255\pi$
$284$	−16.1499	−0.958318
$285$	0.997255	0.0590723
$286$	−3.68241	−0.217745
$287$	6.94948	0.410215
$288$	−5.70623	−0.336243
$289$	37.3650	2.19794
$290$	−8.21206	−0.482229
$291$	14.1860	0.831595
$292$	−10.6416	−0.622751
$293$	25.4574	1.48724	0.743618	−	0.668605i	$-0.233108\pi$
$293$	25.4574	1.48724	0.743618	+	0.668605i	$0.233108\pi$
$294$	−3.55541	−0.207356
$295$	44.1446	2.57020
$296$	−1.82491	−0.106071
$297$	−4.28895	−0.248870
$298$	−7.86279	−0.455479
$299$	7.02793	0.406436
$300$	14.1552	0.817253
$301$	−7.03401	−0.405434
$302$	−8.73017	−0.502365
$303$	−17.1694	−0.986358
$304$	0.0298341	0.00171110
$305$	−37.1324	−2.12619
$306$	−6.33054	−0.361893
$307$	−3.73983	−0.213443	−0.106722	−	0.994289i	$-0.534035\pi$
$307$	−3.73983	−0.213443	−0.106722	+	0.994289i	$0.534035\pi$
$308$	−9.15805	−0.521829
$309$	1.00000	0.0568880
$310$	24.4333	1.38772
$311$	−0.567475	−0.0321786	−0.0160893	−	0.999871i	$-0.505122\pi$
$311$	−0.567475	−0.0321786	−0.0160893	+	0.999871i	$0.505122\pi$
$312$	−2.80141	−0.158599
$313$	−22.0903	−1.24862	−0.624309	−	0.781177i	$-0.714619\pi$
$313$	−22.0903	−1.24862	−0.624309	+	0.781177i	$0.714619\pi$
$314$	11.3132	0.638441
$315$	−6.80743	−0.383555
$316$	−6.65935	−0.374617
$317$	−7.86061	−0.441496	−0.220748	−	0.975331i	$-0.570850\pi$
$317$	−7.86061	−0.441496	−0.220748	+	0.975331i	$0.570850\pi$
$318$	−6.05836	−0.339736
$319$	−10.1893	−0.570490
$320$	−18.7548	−1.04843
$321$	−0.920374	−0.0513703
$322$	−10.2026	−0.568571
$323$	1.82636	0.101622
$324$	−1.26284	−0.0701578
$325$	11.2091	0.621766
$326$	−8.91625	−0.493826
$327$	11.6041	0.641706
$328$	11.5140	0.635752
$329$	4.44042	0.244808
$330$	−14.8255	−0.816119
$331$	16.5682	0.910672	0.455336	−	0.890320i	$-0.349519\pi$
$331$	16.5682	0.910672	0.455336	+	0.890320i	$0.349519\pi$
$332$	−14.2573	−0.782472
$333$	−0.651425	−0.0356979
$334$	6.83354	0.373915
$335$	−3.57484	−0.195315
$336$	−0.203653	−0.0111102
$337$	34.0486	1.85475	0.927374	−	0.374136i	$-0.122061\pi$
$337$	34.0486	1.85475	0.927374	+	0.374136i	$0.122061\pi$
$338$	−0.858580	−0.0467006
$339$	−13.8477	−0.752104
$340$	37.4875	2.03305
$341$	30.3160	1.64171
$342$	−0.212671	−0.0114999
$343$	−18.8378	−1.01714
$344$	−11.6540	−0.628342
$345$	28.2948	1.52334
$346$	−14.8542	−0.798567
$347$	−30.0388	−1.61256	−0.806282	−	0.591531i	$-0.798524\pi$
$347$	−30.0388	−1.61256	−0.806282	+	0.591531i	$0.798524\pi$
$348$	−3.00013	−0.160824
$349$	−18.5260	−0.991674	−0.495837	−	0.868416i	$-0.665139\pi$
$349$	−18.5260	−0.991674	−0.495837	+	0.868416i	$0.665139\pi$
$350$	−16.2725	−0.869801
$351$	−1.00000	−0.0533761
$352$	−24.4737	−1.30445
$353$	−2.36822	−0.126048	−0.0630239	−	0.998012i	$-0.520074\pi$
$353$	−2.36822	−0.126048	−0.0630239	+	0.998012i	$0.520074\pi$
$354$	−9.41411	−0.500354
$355$	−51.4872	−2.73266
$356$	−0.997249	−0.0528541
$357$	−12.4671	−0.659826
$358$	6.61477	0.349601
$359$	−26.0752	−1.37620	−0.688098	−	0.725618i	$-0.741554\pi$
$359$	−26.0752	−1.37620	−0.688098	+	0.725618i	$0.741554\pi$
$360$	−11.2786	−0.594435
$361$	−18.9386	−0.996771
$362$	20.4384	1.07422
$363$	−7.39508	−0.388141
$364$	−2.13527	−0.111918
$365$	−33.9263	−1.77578
$366$	7.91871	0.413918
$367$	14.3303	0.748034	0.374017	−	0.927422i	$-0.377980\pi$
$367$	14.3303	0.748034	0.374017	+	0.927422i	$0.377980\pi$
$368$	0.846473	0.0441254
$369$	4.11006	0.213961
$370$	−2.25177	−0.117064
$371$	−11.9310	−0.619428
$372$	8.92627	0.462805
$373$	17.3301	0.897319	0.448660	−	0.893703i	$-0.351902\pi$
$373$	17.3301	0.897319	0.448660	+	0.893703i	$0.351902\pi$
$374$	−27.1513	−1.40396
$375$	24.9979	1.29089
$376$	7.35693	0.379405
$377$	−2.37570	−0.122355
$378$	1.45173	0.0746688
$379$	16.5516	0.850197	0.425098	−	0.905147i	$-0.360240\pi$
$379$	16.5516	0.850197	0.425098	+	0.905147i	$0.360240\pi$
$380$	1.25937	0.0646045
$381$	15.9315	0.816194
$382$	−7.70630	−0.394289
$383$	−17.8751	−0.913373	−0.456686	−	0.889628i	$-0.650964\pi$
$383$	−17.8751	−0.913373	−0.456686	+	0.889628i	$0.650964\pi$
$384$	−7.41288	−0.378287
$385$	−29.1967	−1.48800
$386$	23.1620	1.17891
$387$	−4.16005	−0.211467
$388$	17.9146	0.909475
$389$	27.8469	1.41189	0.705947	−	0.708265i	$-0.250522\pi$
$389$	27.8469	1.41189	0.705947	+	0.708265i	$0.250522\pi$
$390$	−3.45668	−0.175036
$391$	51.8187	2.62059
$392$	−11.6007	−0.585926
$393$	11.6337	0.586841
$394$	3.50939	0.176800
$395$	−21.2306	−1.06823
$396$	−5.41625	−0.272177
$397$	6.50228	0.326340	0.163170	−	0.986598i	$-0.447828\pi$
$397$	6.50228	0.326340	0.163170	+	0.986598i	$0.447828\pi$
$398$	−9.69178	−0.485805
$399$	−0.418824	−0.0209674
$400$	1.35006	0.0675032
$401$	8.41748	0.420349	0.210175	−	0.977664i	$-0.432597\pi$
$401$	8.41748	0.420349	0.210175	+	0.977664i	$0.432597\pi$
$402$	0.762358	0.0380230
$403$	7.06841	0.352102
$404$	−21.6822	−1.07873
$405$	−4.02605	−0.200056
$406$	3.44888	0.171165
$407$	−2.79393	−0.138490
$408$	−20.6555	−1.02260
$409$	−0.352704	−0.0174401	−0.00872003	−	0.999962i	$-0.502776\pi$
$409$	−0.352704	−0.0174401	−0.00872003	+	0.999962i	$0.502776\pi$
$410$	14.2072	0.701642
$411$	−17.0824	−0.842611
$412$	1.26284	0.0622157
$413$	−18.5397	−0.912279
$414$	−6.03404	−0.296557
$415$	−45.4536	−2.23123
$416$	−5.70623	−0.279771
$417$	16.3737	0.801825
$418$	−0.912135	−0.0446140
$419$	−1.00026	−0.0488659	−0.0244330	−	0.999701i	$-0.507778\pi$
$419$	−1.00026	−0.0488659	−0.0244330	+	0.999701i	$0.507778\pi$
$420$	−8.59669	−0.419476
$421$	8.40125	0.409452	0.204726	−	0.978819i	$-0.434370\pi$
$421$	8.40125	0.409452	0.204726	+	0.978819i	$0.434370\pi$
$422$	0.938488	0.0456849
$423$	2.62615	0.127688
$424$	−19.7674	−0.959992
$425$	82.6472	4.00898
$426$	10.9800	0.531982
$427$	15.5947	0.754682
$428$	−1.16228	−0.0561812
$429$	−4.28895	−0.207072
$430$	−14.3800	−0.693465
$431$	−17.1273	−0.824995	−0.412498	−	0.910959i	$-0.635344\pi$
$431$	−17.1273	−0.824995	−0.412498	+	0.910959i	$0.635344\pi$
$432$	−0.120444	−0.00579487
$433$	−18.1040	−0.870023	−0.435012	−	0.900425i	$-0.643256\pi$
$433$	−18.1040	−0.870023	−0.435012	+	0.900425i	$0.643256\pi$
$434$	−10.2614	−0.492563
$435$	−9.56470	−0.458592
$436$	14.6541	0.701803
$437$	1.74082	0.0832749
$438$	7.23500	0.345702
$439$	−22.1621	−1.05774	−0.528870	−	0.848703i	$-0.677384\pi$
$439$	−22.1621	−1.05774	−0.528870	+	0.848703i	$0.677384\pi$
$440$	−48.3734	−2.30611
$441$	−4.14104	−0.197192
$442$	−6.33054	−0.301113
$443$	19.8336	0.942322	0.471161	−	0.882047i	$-0.343835\pi$
$443$	19.8336	0.942322	0.471161	+	0.882047i	$0.343835\pi$
$444$	−0.822646	−0.0390410
$445$	−3.17932	−0.150714
$446$	4.58074	0.216904
$447$	−9.15789	−0.433153
$448$	7.87659	0.372134
$449$	−29.2381	−1.37983	−0.689917	−	0.723889i	$-0.742353\pi$
$449$	−29.2381	−1.37983	−0.689917	+	0.723889i	$0.742353\pi$
$450$	−9.62387	−0.453674
$451$	17.6278	0.830062
$452$	−17.4874	−0.822540
$453$	−10.1681	−0.477741
$454$	22.8396	1.07191
$455$	−6.80743	−0.319137
$456$	−0.693912	−0.0324954
$457$	23.8289	1.11467	0.557334	−	0.830289i	$-0.311824\pi$
$457$	23.8289	1.11467	0.557334	+	0.830289i	$0.311824\pi$
$458$	−19.0167	−0.888594
$459$	−7.37326	−0.344154
$460$	35.7318	1.66600
$461$	−29.9464	−1.39474	−0.697371	−	0.716710i	$-0.745647\pi$
$461$	−29.9464	−1.39474	−0.697371	+	0.716710i	$0.745647\pi$
$462$	6.22638	0.289678
$463$	7.86033	0.365300	0.182650	−	0.983178i	$-0.441532\pi$
$463$	7.86033	0.365300	0.182650	+	0.983178i	$0.441532\pi$
$464$	−0.286140	−0.0132837
$465$	28.4577	1.31970
$466$	−1.13161	−0.0524209
$467$	8.61609	0.398705	0.199353	−	0.979928i	$-0.436116\pi$
$467$	8.61609	0.398705	0.199353	+	0.979928i	$0.436116\pi$
$468$	−1.26284	−0.0583748
$469$	1.50135	0.0693260
$470$	9.07778	0.418727
$471$	13.1766	0.607148
$472$	−30.7167	−1.41385
$473$	−17.8423	−0.820388
$474$	4.52756	0.207958
$475$	2.77649	0.127394
$476$	−15.7439	−0.721620
$477$	−7.05625	−0.323083
$478$	−22.0641	−1.00919
$479$	24.5756	1.12289	0.561444	−	0.827515i	$-0.310246\pi$
$479$	24.5756	1.12289	0.561444	+	0.827515i	$0.310246\pi$
$480$	−22.9736	−1.04859
$481$	−0.651425	−0.0297024
$482$	9.06739	0.413008
$483$	−11.8831	−0.540702
$484$	−9.33880	−0.424491
$485$	57.1133	2.59338
$486$	0.858580	0.0389460
$487$	−11.7752	−0.533586	−0.266793	−	0.963754i	$-0.585964\pi$
$487$	−11.7752	−0.533586	−0.266793	+	0.963754i	$0.585964\pi$
$488$	25.8375	1.16961
$489$	−10.3849	−0.469620
$490$	−14.3143	−0.646652
$491$	6.54793	0.295504	0.147752	−	0.989024i	$-0.452796\pi$
$491$	6.54793	0.295504	0.147752	+	0.989024i	$0.452796\pi$
$492$	5.19034	0.233999
$493$	−17.5167	−0.788912
$494$	−0.212671	−0.00956852
$495$	−17.2675	−0.776117
$496$	0.851349	0.0382267
$497$	21.6234	0.969944
$498$	9.69328	0.434366
$499$	−18.6088	−0.833044	−0.416522	−	0.909126i	$-0.636751\pi$
$499$	−18.6088	−0.833044	−0.416522	+	0.909126i	$0.636751\pi$
$500$	31.5684	1.41178
$501$	7.95912	0.355587
$502$	5.55614	0.247983
$503$	−30.9395	−1.37953	−0.689763	−	0.724035i	$-0.742285\pi$
$503$	−30.9395	−1.37953	−0.689763	+	0.724035i	$0.742285\pi$
$504$	4.73675	0.210992
$505$	−69.1250	−3.07602
$506$	−25.8797	−1.15049
$507$	−1.00000	−0.0444116
$508$	20.1189	0.892632
$509$	12.4774	0.553053	0.276526	−	0.961006i	$-0.410817\pi$
$509$	12.4774	0.553053	0.276526	+	0.961006i	$0.410817\pi$
$510$	−25.4870	−1.12858
$511$	14.2483	0.630306
$512$	−1.36211	−0.0601973
$513$	−0.247701	−0.0109363
$514$	−4.72818	−0.208551
$515$	4.02605	0.177409
$516$	−5.25348	−0.231272
$517$	11.2634	0.495365
$518$	0.945692	0.0415513
$519$	−17.3009	−0.759425
$520$	−11.2786	−0.494600
$521$	0.969709	0.0424837	0.0212419	−	0.999774i	$-0.493238\pi$
$521$	0.969709	0.0424837	0.0212419	+	0.999774i	$0.493238\pi$
$522$	2.03973	0.0892767
$523$	43.8263	1.91639	0.958195	−	0.286116i	$-0.0923643\pi$
$523$	43.8263	1.91639	0.958195	+	0.286116i	$0.0923643\pi$
$524$	14.6915	0.641799
$525$	−18.9528	−0.827167
$526$	13.7280	0.598571
$527$	52.1172	2.27026
$528$	−0.516579	−0.0224812
$529$	26.3918	1.14747
$530$	−24.3912	−1.05949
$531$	−10.9647	−0.475829
$532$	−0.528908	−0.0229311
$533$	4.11006	0.178026
$534$	0.678010	0.0293404
$535$	−3.70547	−0.160201
$536$	2.48745	0.107442
$537$	7.70431	0.332465
$538$	−16.5342	−0.712839
$539$	−17.7607	−0.765007
$540$	−5.08425	−0.218791
$541$	40.3867	1.73636	0.868179	−	0.496251i	$-0.165290\pi$
$541$	40.3867	1.73636	0.868179	+	0.496251i	$0.165290\pi$
$542$	23.0709	0.990980
$543$	23.8049	1.02157
$544$	−42.0735	−1.80389
$545$	46.7185	2.00120
$546$	1.45173	0.0621282
$547$	−16.7888	−0.717837	−0.358918	−	0.933369i	$-0.616854\pi$
$547$	−16.7888	−0.717837	−0.358918	+	0.933369i	$0.616854\pi$
$548$	−21.5723	−0.921523
$549$	9.22303	0.393629
$550$	−41.2763	−1.76003
$551$	−0.588464	−0.0250694
$552$	−19.6881	−0.837981
$553$	8.91636	0.379162
$554$	14.1282	0.600248
$555$	−2.62267	−0.111326
$556$	20.6774	0.876917
$557$	20.3733	0.863242	0.431621	−	0.902055i	$-0.357942\pi$
$557$	20.3733	0.863242	0.431621	+	0.902055i	$0.357942\pi$
$558$	−6.06880	−0.256913
$559$	−4.16005	−0.175952
$560$	−0.819915	−0.0346477
$561$	−31.6235	−1.33515
$562$	−18.8630	−0.795686
$563$	−37.6179	−1.58540	−0.792702	−	0.609609i	$-0.791326\pi$
$563$	−37.6179	−1.58540	−0.792702	+	0.609609i	$0.791326\pi$
$564$	3.31641	0.139646
$565$	−55.7515	−2.34548
$566$	−22.1852	−0.932512
$567$	1.69085	0.0710089
$568$	35.8259	1.50322
$569$	−24.7169	−1.03619	−0.518094	−	0.855324i	$-0.673358\pi$
$569$	−24.7169	−1.03619	−0.518094	+	0.855324i	$0.673358\pi$
$570$	−0.856224	−0.0358633
$571$	−38.4567	−1.60936	−0.804681	−	0.593708i	$-0.797663\pi$
$571$	−38.4567	−1.60936	−0.804681	+	0.593708i	$0.797663\pi$
$572$	−5.41625	−0.226465
$573$	−8.97563	−0.374962
$574$	−5.96668	−0.249045
$575$	78.7764	3.28520
$576$	4.65837	0.194099
$577$	−18.7365	−0.780013	−0.390006	−	0.920812i	$-0.627527\pi$
$577$	−18.7365	−0.780013	−0.390006	+	0.920812i	$0.627527\pi$
$578$	−32.0808	−1.33439
$579$	26.9771	1.12113
$580$	−12.0787	−0.501540
$581$	19.0895	0.791965
$582$	−12.1798	−0.504868
$583$	−30.2639	−1.25340
$584$	23.6066	0.976850
$585$	−4.02605	−0.166457
$586$	−21.8572	−0.902913
$587$	32.0935	1.32464	0.662321	−	0.749220i	$-0.269571\pi$
$587$	32.0935	1.32464	0.662321	+	0.749220i	$0.269571\pi$
$588$	−5.22947	−0.215660
$589$	1.75085	0.0721425
$590$	−37.9017	−1.56039
$591$	4.08743	0.168134
$592$	−0.0784604	−0.00322470
$593$	−26.4755	−1.08722	−0.543610	−	0.839338i	$-0.682943\pi$
$593$	−26.4755	−1.08722	−0.543610	+	0.839338i	$0.682943\pi$
$594$	3.68241	0.151091
$595$	−50.1929	−2.05771
$596$	−11.5650	−0.473719
$597$	−11.2881	−0.461993
$598$	−6.03404	−0.246750
$599$	−17.5489	−0.717030	−0.358515	−	0.933524i	$-0.616717\pi$
$599$	−17.5489	−0.717030	−0.358515	+	0.933524i	$0.616717\pi$
$600$	−31.4011	−1.28195
$601$	−19.2224	−0.784099	−0.392049	−	0.919944i	$-0.628234\pi$
$601$	−19.2224	−0.784099	−0.392049	+	0.919944i	$0.628234\pi$
$602$	6.03926	0.246142
$603$	0.887929	0.0361593
$604$	−12.8407	−0.522482
$605$	−29.7729	−1.21044
$606$	14.7413	0.598826
$607$	−3.15030	−0.127867	−0.0639334	−	0.997954i	$-0.520365\pi$
$607$	−3.15030	−0.127867	−0.0639334	+	0.997954i	$0.520365\pi$
$608$	−1.41344	−0.0573225
$609$	4.01695	0.162775
$610$	31.8811	1.29083
$611$	2.62615	0.106243
$612$	−9.31125	−0.376385
$613$	43.6922	1.76471	0.882356	−	0.470582i	$-0.155956\pi$
$613$	43.6922	1.76471	0.882356	+	0.470582i	$0.155956\pi$
$614$	3.21094	0.129583
$615$	16.5473	0.667251
$616$	20.3157	0.818543
$617$	26.2667	1.05746	0.528728	−	0.848791i	$-0.322669\pi$
$617$	26.2667	1.05746	0.528728	+	0.848791i	$0.322669\pi$
$618$	−0.858580	−0.0345372
$619$	7.58897	0.305027	0.152513	−	0.988301i	$-0.451263\pi$
$619$	7.58897	0.305027	0.152513	+	0.988301i	$0.451263\pi$
$620$	35.9376	1.44329
$621$	−7.02793	−0.282021
$622$	0.487223	0.0195359
$623$	1.33524	0.0534953
$624$	−0.120444	−0.00482163
$625$	44.5976	1.78390
$626$	18.9663	0.758046
$627$	−1.06238	−0.0424272
$628$	16.6400	0.664008
$629$	−4.80313	−0.191513
$630$	5.84472	0.232859
$631$	−37.7400	−1.50241	−0.751203	−	0.660072i	$-0.770526\pi$
$631$	−37.7400	−1.50241	−0.751203	+	0.660072i	$0.770526\pi$
$632$	14.7727	0.587627
$633$	1.09307	0.0434456
$634$	6.74897	0.268036
$635$	64.1409	2.54535
$636$	−8.91091	−0.353341
$637$	−4.14104	−0.164074
$638$	8.74831	0.346349
$639$	12.7885	0.505906
$640$	−29.8446	−1.17971
$641$	1.53065	0.0604570	0.0302285	−	0.999543i	$-0.490376\pi$
$641$	1.53065	0.0604570	0.0302285	+	0.999543i	$0.490376\pi$
$642$	0.790215	0.0311873
$643$	23.5441	0.928491	0.464245	−	0.885707i	$-0.346326\pi$
$643$	23.5441	0.928491	0.464245	+	0.885707i	$0.346326\pi$
$644$	−15.0065	−0.591339
$645$	−16.7486	−0.659474
$646$	−1.56808	−0.0616952
$647$	5.36402	0.210881	0.105441	−	0.994426i	$-0.466375\pi$
$647$	5.36402	0.210881	0.105441	+	0.994426i	$0.466375\pi$
$648$	2.80141	0.110050
$649$	−47.0272	−1.84598
$650$	−9.62387	−0.377479
$651$	−11.9516	−0.468420
$652$	−13.1144	−0.513601
$653$	−12.2900	−0.480943	−0.240471	−	0.970656i	$-0.577302\pi$
$653$	−12.2900	−0.480943	−0.240471	+	0.970656i	$0.577302\pi$
$654$	−9.96303	−0.389585
$655$	46.8377	1.83010
$656$	0.495032	0.0193278
$657$	8.42670	0.328757
$658$	−3.81246	−0.148625
$659$	16.7295	0.651690	0.325845	−	0.945423i	$-0.394351\pi$
$659$	16.7295	0.651690	0.325845	+	0.945423i	$0.394351\pi$
$660$	−21.8061	−0.848801
$661$	29.0830	1.13120	0.565598	−	0.824681i	$-0.308645\pi$
$661$	29.0830	1.13120	0.565598	+	0.824681i	$0.308645\pi$
$662$	−14.2252	−0.552876
$663$	−7.37326	−0.286354
$664$	31.6276	1.22739
$665$	−1.68621	−0.0653882
$666$	0.559301	0.0216725
$667$	−16.6963	−0.646483
$668$	10.0511	0.388889
$669$	5.33525	0.206272
$670$	3.06929	0.118577
$671$	39.5571	1.52708
$672$	9.64836	0.372194
$673$	31.3705	1.20924	0.604622	−	0.796512i	$-0.293324\pi$
$673$	31.3705	1.20924	0.604622	+	0.796512i	$0.293324\pi$
$674$	−29.2335	−1.12603
$675$	−11.2091	−0.431437
$676$	−1.26284	−0.0485708
$677$	−33.5598	−1.28981	−0.644904	−	0.764264i	$-0.723103\pi$
$677$	−33.5598	−1.28981	−0.644904	+	0.764264i	$0.723103\pi$
$678$	11.8894	0.456608
$679$	−23.9863	−0.920509
$680$	−83.1601	−3.18904
$681$	26.6015	1.01937
$682$	−26.0288	−0.996692
$683$	25.0836	0.959796	0.479898	−	0.877324i	$-0.340674\pi$
$683$	25.0836	0.959796	0.479898	+	0.877324i	$0.340674\pi$
$684$	−0.312806	−0.0119605
$685$	−68.7744	−2.62774
$686$	16.1738	0.617517
$687$	−22.1490	−0.845039
$688$	−0.501054	−0.0191025
$689$	−7.05625	−0.268822
$690$	−24.2933	−0.924831
$691$	7.08459	0.269510	0.134755	−	0.990879i	$-0.456975\pi$
$691$	7.08459	0.269510	0.134755	+	0.990879i	$0.456975\pi$
$692$	−21.8483	−0.830547
$693$	7.25195	0.275479
$694$	25.7907	0.979001
$695$	65.9214	2.50054
$696$	6.65532	0.252269
$697$	30.3045	1.14787
$698$	15.9061	0.602053
$699$	−1.31800	−0.0498515
$700$	−23.9343	−0.904633
$701$	−36.3878	−1.37435	−0.687174	−	0.726493i	$-0.741149\pi$
$701$	−36.3878	−1.37435	−0.687174	+	0.726493i	$0.741149\pi$
$702$	0.858580	0.0324050
$703$	−0.161359	−0.00608575
$704$	19.9795	0.753006
$705$	10.5730	0.398203
$706$	2.03331	0.0765246
$707$	29.0309	1.09182
$708$	−13.8467	−0.520391
$709$	−17.7402	−0.666248	−0.333124	−	0.942883i	$-0.608103\pi$
$709$	−17.7402	−0.666248	−0.333124	+	0.942883i	$0.608103\pi$
$710$	44.2059	1.65902
$711$	5.27331	0.197765
$712$	2.21224	0.0829071
$713$	49.6763	1.86039
$714$	10.7040	0.400586
$715$	−17.2675	−0.645768
$716$	9.72930	0.363601
$717$	−25.6984	−0.959723
$718$	22.3876	0.835499
$719$	41.9110	1.56302	0.781508	−	0.623896i	$-0.214451\pi$
$719$	41.9110	1.56302	0.781508	+	0.623896i	$0.214451\pi$
$720$	−0.484914	−0.0180717
$721$	−1.69085	−0.0629704
$722$	16.2603	0.605147
$723$	10.5609	0.392764
$724$	30.0618	1.11724
$725$	−26.6294	−0.988991
$726$	6.34927	0.235643
$727$	19.2054	0.712290	0.356145	−	0.934431i	$-0.384091\pi$
$727$	19.2054	0.712290	0.356145	+	0.934431i	$0.384091\pi$
$728$	4.73675	0.175556
$729$	1.00000	0.0370370
$730$	29.1284	1.07809
$731$	−30.6732	−1.13449
$732$	11.6472	0.430493
$733$	16.4943	0.609230	0.304615	−	0.952476i	$-0.401472\pi$
$733$	16.4943	0.609230	0.304615	+	0.952476i	$0.401472\pi$
$734$	−12.3037	−0.454137
$735$	−16.6720	−0.614956
$736$	−40.1030	−1.47822
$737$	3.80828	0.140280
$738$	−3.52881	−0.129897
$739$	26.2905	0.967112	0.483556	−	0.875313i	$-0.339345\pi$
$739$	26.2905	0.967112	0.483556	+	0.875313i	$0.339345\pi$
$740$	−3.31201	−0.121752
$741$	−0.247701	−0.00909952
$742$	10.2438	0.376060
$743$	34.7413	1.27453	0.637267	−	0.770643i	$-0.280065\pi$
$743$	34.7413	1.27453	0.637267	+	0.770643i	$0.280065\pi$
$744$	−19.8015	−0.725959
$745$	−36.8701	−1.35082
$746$	−14.8793	−0.544770
$747$	11.2899	0.413076
$748$	−39.9355	−1.46018
$749$	1.55621	0.0568627
$750$	−21.4627	−0.783708
$751$	8.01149	0.292343	0.146172	−	0.989259i	$-0.453305\pi$
$751$	8.01149	0.292343	0.146172	+	0.989259i	$0.453305\pi$
$752$	0.316305	0.0115345
$753$	6.47131	0.235828
$754$	2.03973	0.0742827
$755$	−40.9374	−1.48987
$756$	2.13527	0.0776590
$757$	41.7228	1.51644	0.758221	−	0.651998i	$-0.226069\pi$
$757$	41.7228	1.51644	0.758221	+	0.651998i	$0.226069\pi$
$758$	−14.2108	−0.516161
$759$	−30.1424	−1.09410
$760$	−2.79372	−0.101339
$761$	−33.7882	−1.22482	−0.612411	−	0.790540i	$-0.709800\pi$
$761$	−33.7882	−1.22482	−0.612411	+	0.790540i	$0.709800\pi$
$762$	−13.6784	−0.495518
$763$	−19.6207	−0.710317
$764$	−11.3348	−0.410078
$765$	−29.6851	−1.07327
$766$	15.3472	0.554516
$767$	−10.9647	−0.395914
$768$	15.6813	0.565850
$769$	−37.2396	−1.34289	−0.671447	−	0.741053i	$-0.734327\pi$
$769$	−37.2396	−1.34289	−0.671447	+	0.741053i	$0.734327\pi$
$770$	25.0677	0.903378
$771$	−5.50697	−0.198329
$772$	34.0677	1.22612
$773$	−17.3275	−0.623226	−0.311613	−	0.950209i	$-0.600869\pi$
$773$	−17.3275	−0.623226	−0.311613	+	0.950209i	$0.600869\pi$
$774$	3.57174	0.128384
$775$	79.2301	2.84603
$776$	−39.7407	−1.42661
$777$	1.10146	0.0395147
$778$	−23.9088	−0.857172
$779$	1.01806	0.0364759
$780$	−5.08425	−0.182045
$781$	54.8493	1.96266
$782$	−44.4905	−1.59098
$783$	2.37570	0.0849008
$784$	−0.498764	−0.0178130
$785$	53.0498	1.89343
$786$	−9.98844	−0.356276
$787$	22.0824	0.787152	0.393576	−	0.919292i	$-0.371238\pi$
$787$	22.0824	0.787152	0.393576	+	0.919292i	$0.371238\pi$
$788$	5.16177	0.183880
$789$	15.9892	0.569231
$790$	18.2282	0.648529
$791$	23.4143	0.832518
$792$	12.0151	0.426938
$793$	9.22303	0.327519
$794$	−5.58273	−0.198124
$795$	−28.4088	−1.00756
$796$	−14.2551	−0.505259
$797$	6.25171	0.221447	0.110723	−	0.993851i	$-0.464683\pi$
$797$	6.25171	0.221447	0.110723	+	0.993851i	$0.464683\pi$
$798$	0.359594	0.0127295
$799$	19.3633	0.685025
$800$	−63.9614	−2.26138
$801$	0.789688	0.0279022
$802$	−7.22709	−0.255197
$803$	36.1417	1.27541
$804$	1.12131	0.0395456
$805$	−47.8421	−1.68621
$806$	−6.06880	−0.213764
$807$	−19.2576	−0.677899
$808$	48.0986	1.69210
$809$	22.0125	0.773917	0.386958	−	0.922097i	$-0.373526\pi$
$809$	22.0125	0.773917	0.386958	+	0.922097i	$0.373526\pi$
$810$	3.45668	0.121456
$811$	19.6597	0.690345	0.345173	−	0.938539i	$-0.387820\pi$
$811$	19.6597	0.690345	0.345173	+	0.938539i	$0.387820\pi$
$812$	5.07277	0.178019
$813$	26.8710	0.942407
$814$	2.39881	0.0840783
$815$	−41.8100	−1.46454
$816$	−0.888066	−0.0310885
$817$	−1.03045	−0.0360508
$818$	0.302824	0.0105880
$819$	1.69085	0.0590830
$820$	20.8966	0.729740
$821$	49.6609	1.73318	0.866588	−	0.499024i	$-0.166308\pi$
$821$	49.6609	1.73318	0.866588	+	0.499024i	$0.166308\pi$
$822$	14.6666	0.511556
$823$	19.5452	0.681305	0.340652	−	0.940189i	$-0.389352\pi$
$823$	19.5452	0.681305	0.340652	+	0.940189i	$0.389352\pi$
$824$	−2.80141	−0.0975917
$825$	−48.0750	−1.67376
$826$	15.9178	0.553852
$827$	−46.5843	−1.61989	−0.809947	−	0.586503i	$-0.800504\pi$
$827$	−46.5843	−1.61989	−0.809947	+	0.586503i	$0.800504\pi$
$828$	−8.87515	−0.308433
$829$	8.03996	0.279239	0.139620	−	0.990205i	$-0.455412\pi$
$829$	8.03996	0.279239	0.139620	+	0.990205i	$0.455412\pi$
$830$	39.0256	1.35460
$831$	16.4553	0.570827
$832$	4.65837	0.161500
$833$	−30.5329	−1.05790
$834$	−14.0582	−0.486794
$835$	32.0438	1.10892
$836$	−1.34161	−0.0464006
$837$	−7.06841	−0.244320
$838$	0.858804	0.0296669
$839$	16.3575	0.564725	0.282362	−	0.959308i	$-0.408882\pi$
$839$	16.3575	0.564725	0.282362	+	0.959308i	$0.408882\pi$
$840$	19.0704	0.657991
$841$	−23.3560	−0.805380
$842$	−7.21315	−0.248582
$843$	−21.9700	−0.756685
$844$	1.38037	0.0475144
$845$	−4.02605	−0.138500
$846$	−2.25476	−0.0775204
$847$	12.5039	0.429640
$848$	−0.849884	−0.0291851
$849$	−25.8394	−0.886804
$850$	−70.9593	−2.43388
$851$	−4.57817	−0.156938
$852$	16.1499	0.553285
$853$	−21.7263	−0.743894	−0.371947	−	0.928254i	$-0.621310\pi$
$853$	−21.7263	−0.743894	−0.371947	+	0.928254i	$0.621310\pi$
$854$	−13.3893	−0.458173
$855$	−0.997255	−0.0341054
$856$	2.57834	0.0881260
$857$	−22.3367	−0.763008	−0.381504	−	0.924367i	$-0.624594\pi$
$857$	−22.3367	−0.763008	−0.381504	+	0.924367i	$0.624594\pi$
$858$	3.68241	0.125715
$859$	−34.4469	−1.17531	−0.587656	−	0.809111i	$-0.699949\pi$
$859$	−34.4469	−1.17531	−0.587656	+	0.809111i	$0.699949\pi$
$860$	−21.1508	−0.721235
$861$	−6.94948	−0.236837
$862$	14.7052	0.500861
$863$	19.1394	0.651511	0.325756	−	0.945454i	$-0.394381\pi$
$863$	19.1394	0.651511	0.325756	+	0.945454i	$0.394381\pi$
$864$	5.70623	0.194130
$865$	−69.6542	−2.36832
$866$	15.5437	0.528198
$867$	−37.3650	−1.26898
$868$	−15.0929	−0.512288
$869$	22.6170	0.767228
$870$	8.21206	0.278415
$871$	0.887929	0.0300863
$872$	−32.5078	−1.10085
$873$	−14.1860	−0.480122
$874$	−1.49464	−0.0505568
$875$	−42.2677	−1.42891
$876$	10.6416	0.359545
$877$	2.28537	0.0771714	0.0385857	−	0.999255i	$-0.487715\pi$
$877$	2.28537	0.0771714	0.0385857	+	0.999255i	$0.487715\pi$
$878$	19.0280	0.642162
$879$	−25.4574	−0.858656
$880$	−2.07977	−0.0701090
$881$	−1.52068	−0.0512331	−0.0256166	−	0.999672i	$-0.508155\pi$
$881$	−1.52068	−0.0512331	−0.0256166	+	0.999672i	$0.508155\pi$
$882$	3.55541	0.119717
$883$	46.3371	1.55937	0.779683	−	0.626174i	$-0.215380\pi$
$883$	46.3371	1.55937	0.779683	+	0.626174i	$0.215380\pi$
$884$	−9.31125	−0.313171
$885$	−44.1446	−1.48390
$886$	−17.0287	−0.572091
$887$	5.17208	0.173661	0.0868307	−	0.996223i	$-0.472326\pi$
$887$	5.17208	0.173661	0.0868307	+	0.996223i	$0.472326\pi$
$888$	1.82491	0.0612399
$889$	−26.9377	−0.903461
$890$	2.72970	0.0914998
$891$	4.28895	0.143685
$892$	6.73756	0.225590
$893$	0.650500	0.0217682
$894$	7.86279	0.262971
$895$	31.0179	1.03681
$896$	12.5340	0.418733
$897$	−7.02793	−0.234656
$898$	25.1033	0.837708
$899$	−16.7925	−0.560060
$900$	−14.1552	−0.471841
$901$	−52.0276	−1.73329
$902$	−15.1349	−0.503937
$903$	7.03401	0.234077
$904$	38.7931	1.29024
$905$	95.8396	3.18582
$906$	8.73017	0.290040
$907$	−41.4596	−1.37664	−0.688321	−	0.725406i	$-0.741652\pi$
$907$	−41.4596	−1.37664	−0.688321	+	0.725406i	$0.741652\pi$
$908$	33.5935	1.11484
$909$	17.1694	0.569474
$910$	5.84472	0.193751
$911$	30.3949	1.00703	0.503514	−	0.863987i	$-0.332040\pi$
$911$	30.3949	1.00703	0.503514	+	0.863987i	$0.332040\pi$
$912$	−0.0298341	−0.000987906 0
$913$	48.4218	1.60253
$914$	−20.4590	−0.676724
$915$	37.1324	1.22756
$916$	−27.9707	−0.924178
$917$	−19.6707	−0.649585
$918$	6.33054	0.208939
$919$	−37.5419	−1.23839	−0.619196	−	0.785236i	$-0.712541\pi$
$919$	−37.5419	−1.23839	−0.619196	+	0.785236i	$0.712541\pi$
$920$	−79.2652	−2.61330
$921$	3.73983	0.123231
$922$	25.7114	0.846759
$923$	12.7885	0.420939
$924$	9.15805	0.301278
$925$	−7.30186	−0.240084
$926$	−6.74872	−0.221777
$927$	−1.00000	−0.0328443
$928$	13.5563	0.445008
$929$	14.7922	0.485318	0.242659	−	0.970112i	$-0.421980\pi$
$929$	14.7922	0.485318	0.242659	+	0.970112i	$0.421980\pi$
$930$	−24.4333	−0.801198
$931$	−1.02574	−0.0336172
$932$	−1.66443	−0.0545202
$933$	0.567475	0.0185783
$934$	−7.39760	−0.242057
$935$	−127.318	−4.16374
$936$	2.80141	0.0915670
$937$	−46.8617	−1.53090	−0.765452	−	0.643493i	$-0.777485\pi$
$937$	−46.8617	−1.53090	−0.765452	+	0.643493i	$0.777485\pi$
$938$	−1.28903	−0.0420884
$939$	22.0903	0.720890
$940$	13.3520	0.435495
$941$	−10.6042	−0.345686	−0.172843	−	0.984949i	$-0.555295\pi$
$941$	−10.6042	−0.345686	−0.172843	+	0.984949i	$0.555295\pi$
$942$	−11.3132	−0.368604
$943$	28.8852	0.940631
$944$	−1.32064	−0.0429832
$945$	6.80743	0.221446
$946$	15.3190	0.498064
$947$	−11.6656	−0.379081	−0.189540	−	0.981873i	$-0.560700\pi$
$947$	−11.6656	−0.379081	−0.189540	+	0.981873i	$0.560700\pi$
$948$	6.65935	0.216285
$949$	8.42670	0.273542
$950$	−2.38384	−0.0773420
$951$	7.86061	0.254898
$952$	34.9253	1.13194
$953$	−38.4317	−1.24492	−0.622462	−	0.782650i	$-0.713868\pi$
$953$	−38.4317	−1.24492	−0.622462	+	0.782650i	$0.713868\pi$
$954$	6.05836	0.196147
$955$	−36.1363	−1.16934
$956$	−32.4529	−1.04960
$957$	10.1893	0.329372
$958$	−21.1001	−0.681714
$959$	28.8837	0.932703
$960$	18.7548	0.605309
$961$	18.9624	0.611690
$962$	0.559301	0.0180326
$963$	0.920374	0.0296586
$964$	13.3367	0.429547
$965$	108.611	3.49631
$966$	10.2026	0.328264
$967$	27.7616	0.892752	0.446376	−	0.894845i	$-0.352714\pi$
$967$	27.7616	0.892752	0.446376	+	0.894845i	$0.352714\pi$
$968$	20.7166	0.665858
$969$	−1.82636	−0.0586712
$970$	−49.0364	−1.57446
$971$	−29.9900	−0.962425	−0.481213	−	0.876604i	$-0.659804\pi$
$971$	−29.9900	−0.962425	−0.481213	+	0.876604i	$0.659804\pi$
$972$	1.26284	0.0405056
$973$	−27.6855	−0.887555
$974$	10.1100	0.323944
$975$	−11.2091	−0.358977
$976$	1.11086	0.0355578
$977$	39.5870	1.26650	0.633250	−	0.773948i	$-0.281721\pi$
$977$	39.5870	1.26650	0.633250	+	0.773948i	$0.281721\pi$
$978$	8.91625	0.285110
$979$	3.38693	0.108247
$980$	−21.0541	−0.672548
$981$	−11.6041	−0.370489
$982$	−5.62192	−0.179403
$983$	−8.39756	−0.267841	−0.133920	−	0.990992i	$-0.542757\pi$
$983$	−8.39756	−0.267841	−0.133920	+	0.990992i	$0.542757\pi$
$984$	−11.5140	−0.367051
$985$	16.4562	0.524338
$986$	15.0395	0.478955
$987$	−4.44042	−0.141340
$988$	−0.312806	−0.00995170
$989$	−29.2366	−0.929668
$990$	14.8255	0.471187
$991$	−33.1761	−1.05387	−0.526936	−	0.849905i	$-0.676659\pi$
$991$	−33.1761	−1.05387	−0.526936	+	0.849905i	$0.676659\pi$
$992$	−40.3340	−1.28060
$993$	−16.5682	−0.525777
$994$	−18.5655	−0.588861
$995$	−45.4466	−1.44075
$996$	14.2573	0.451761
$997$	21.9615	0.695527	0.347764	−	0.937582i	$-0.386941\pi$
$997$	21.9615	0.695527	0.347764	+	0.937582i	$0.386941\pi$
$998$	15.9771	0.505747
$999$	0.651425	0.0206102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.9	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.9	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.858580 q^{2} -1.00000 q^{3} -1.26284 q^{4} -4.02605 q^{5} +0.858580 q^{6} +1.69085 q^{7} +2.80141 q^{8} +1.00000 q^{9} +3.45668 q^{10} +4.28895 q^{11} +1.26284 q^{12} +1.00000 q^{13} -1.45173 q^{14} +4.02605 q^{15} +0.120444 q^{16} +7.37326 q^{17} -0.858580 q^{18} +0.247701 q^{19} +5.08425 q^{20} -1.69085 q^{21} -3.68241 q^{22} +7.02793 q^{23} -2.80141 q^{24} +11.2091 q^{25} -0.858580 q^{26} -1.00000 q^{27} -2.13527 q^{28} -2.37570 q^{29} -3.45668 q^{30} +7.06841 q^{31} -5.70623 q^{32} -4.28895 q^{33} -6.33054 q^{34} -6.80743 q^{35} -1.26284 q^{36} -0.651425 q^{37} -0.212671 q^{38} -1.00000 q^{39} -11.2786 q^{40} +4.11006 q^{41} +1.45173 q^{42} -4.16005 q^{43} -5.41625 q^{44} -4.02605 q^{45} -6.03404 q^{46} +2.62615 q^{47} -0.120444 q^{48} -4.14104 q^{49} -9.62387 q^{50} -7.37326 q^{51} -1.26284 q^{52} -7.05625 q^{53} +0.858580 q^{54} -17.2675 q^{55} +4.73675 q^{56} -0.247701 q^{57} +2.03973 q^{58} -10.9647 q^{59} -5.08425 q^{60} +9.22303 q^{61} -6.06880 q^{62} +1.69085 q^{63} +4.65837 q^{64} -4.02605 q^{65} +3.68241 q^{66} +0.887929 q^{67} -9.31125 q^{68} -7.02793 q^{69} +5.84472 q^{70} +12.7885 q^{71} +2.80141 q^{72} +8.42670 q^{73} +0.559301 q^{74} -11.2091 q^{75} -0.312806 q^{76} +7.25195 q^{77} +0.858580 q^{78} +5.27331 q^{79} -0.484914 q^{80} +1.00000 q^{81} -3.52881 q^{82} +11.2899 q^{83} +2.13527 q^{84} -29.6851 q^{85} +3.57174 q^{86} +2.37570 q^{87} +12.0151 q^{88} +0.789688 q^{89} +3.45668 q^{90} +1.69085 q^{91} -8.87515 q^{92} -7.06841 q^{93} -2.25476 q^{94} -0.997255 q^{95} +5.70623 q^{96} -14.1860 q^{97} +3.55541 q^{98} +4.28895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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