LMFDB - Embedded newform 4017.2.a.h.1.6

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

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.82913 q^{2} -1.00000 q^{3} +1.34571 q^{4} +4.14175 q^{5} +1.82913 q^{6} -1.02190 q^{7} +1.19679 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.82913 q^{2} -1.00000 q^{3} +1.34571 q^{4} +4.14175 q^{5} +1.82913 q^{6} -1.02190 q^{7} +1.19679 q^{8} +1.00000 q^{9} -7.57579 q^{10} +1.59753 q^{11} -1.34571 q^{12} +1.00000 q^{13} +1.86918 q^{14} -4.14175 q^{15} -4.88049 q^{16} +3.45756 q^{17} -1.82913 q^{18} -7.53668 q^{19} +5.57358 q^{20} +1.02190 q^{21} -2.92208 q^{22} +1.69984 q^{23} -1.19679 q^{24} +12.1541 q^{25} -1.82913 q^{26} -1.00000 q^{27} -1.37517 q^{28} -2.96226 q^{29} +7.57579 q^{30} -4.28445 q^{31} +6.53346 q^{32} -1.59753 q^{33} -6.32432 q^{34} -4.23244 q^{35} +1.34571 q^{36} -11.2450 q^{37} +13.7856 q^{38} -1.00000 q^{39} +4.95680 q^{40} +4.76592 q^{41} -1.86918 q^{42} -8.21080 q^{43} +2.14980 q^{44} +4.14175 q^{45} -3.10922 q^{46} -7.29003 q^{47} +4.88049 q^{48} -5.95573 q^{49} -22.2314 q^{50} -3.45756 q^{51} +1.34571 q^{52} +2.79430 q^{53} +1.82913 q^{54} +6.61656 q^{55} -1.22299 q^{56} +7.53668 q^{57} +5.41836 q^{58} -10.5699 q^{59} -5.57358 q^{60} -13.2753 q^{61} +7.83681 q^{62} -1.02190 q^{63} -2.18954 q^{64} +4.14175 q^{65} +2.92208 q^{66} -0.576673 q^{67} +4.65286 q^{68} -1.69984 q^{69} +7.74167 q^{70} -9.51719 q^{71} +1.19679 q^{72} -3.46214 q^{73} +20.5686 q^{74} -12.1541 q^{75} -10.1422 q^{76} -1.63251 q^{77} +1.82913 q^{78} -0.683655 q^{79} -20.2138 q^{80} +1.00000 q^{81} -8.71747 q^{82} -16.7514 q^{83} +1.37517 q^{84} +14.3204 q^{85} +15.0186 q^{86} +2.96226 q^{87} +1.91190 q^{88} +0.765114 q^{89} -7.57579 q^{90} -1.02190 q^{91} +2.28748 q^{92} +4.28445 q^{93} +13.3344 q^{94} -31.2151 q^{95} -6.53346 q^{96} +5.58569 q^{97} +10.8938 q^{98} +1.59753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.82913	−1.29339	−0.646694	−	0.762750i	$-0.723849\pi$
$2$	−1.82913	−1.29339	−0.646694	+	0.762750i	$0.723849\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.34571	0.672853
$5$	4.14175	1.85225	0.926124	−	0.377219i	$-0.123120\pi$
$5$	4.14175	1.85225	0.926124	+	0.377219i	$0.123120\pi$
$6$	1.82913	0.746738
$7$	−1.02190	−0.386240	−0.193120	−	0.981175i	$-0.561861\pi$
$7$	−1.02190	−0.386240	−0.193120	+	0.981175i	$0.561861\pi$
$8$	1.19679	0.423128
$9$	1.00000	0.333333
$10$	−7.57579	−2.39568
$11$	1.59753	0.481672	0.240836	−	0.970566i	$-0.422578\pi$
$11$	1.59753	0.481672	0.240836	+	0.970566i	$0.422578\pi$
$12$	−1.34571	−0.388472
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.86918	0.499559
$15$	−4.14175	−1.06940
$16$	−4.88049	−1.22012
$17$	3.45756	0.838582	0.419291	−	0.907852i	$-0.362279\pi$
$17$	3.45756	0.838582	0.419291	+	0.907852i	$0.362279\pi$
$18$	−1.82913	−0.431129
$19$	−7.53668	−1.72903	−0.864517	−	0.502604i	$-0.832375\pi$
$19$	−7.53668	−1.72903	−0.864517	+	0.502604i	$0.832375\pi$
$20$	5.57358	1.24629
$21$	1.02190	0.222996
$22$	−2.92208	−0.622989
$23$	1.69984	0.354440	0.177220	−	0.984171i	$-0.443290\pi$
$23$	1.69984	0.354440	0.177220	+	0.984171i	$0.443290\pi$
$24$	−1.19679	−0.244293
$25$	12.1541	2.43082
$26$	−1.82913	−0.358721
$27$	−1.00000	−0.192450
$28$	−1.37517	−0.259883
$29$	−2.96226	−0.550079	−0.275039	−	0.961433i	$-0.588691\pi$
$29$	−2.96226	−0.550079	−0.275039	+	0.961433i	$0.588691\pi$
$30$	7.57579	1.38314
$31$	−4.28445	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$31$	−4.28445	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$32$	6.53346	1.15496
$33$	−1.59753	−0.278094
$34$	−6.32432	−1.08461
$35$	−4.23244	−0.715413
$36$	1.34571	0.224284
$37$	−11.2450	−1.84867	−0.924334	−	0.381584i	$-0.875379\pi$
$37$	−11.2450	−1.84867	−0.924334	+	0.381584i	$0.875379\pi$
$38$	13.7856	2.23631
$39$	−1.00000	−0.160128
$40$	4.95680	0.783739
$41$	4.76592	0.744311	0.372156	−	0.928170i	$-0.378619\pi$
$41$	4.76592	0.744311	0.372156	+	0.928170i	$0.378619\pi$
$42$	−1.86918	−0.288420
$43$	−8.21080	−1.25213	−0.626067	−	0.779769i	$-0.715337\pi$
$43$	−8.21080	−1.25213	−0.626067	+	0.779769i	$0.715337\pi$
$44$	2.14980	0.324094
$45$	4.14175	0.617416
$46$	−3.10922	−0.458429
$47$	−7.29003	−1.06336	−0.531680	−	0.846945i	$-0.678439\pi$
$47$	−7.29003	−1.06336	−0.531680	+	0.846945i	$0.678439\pi$
$48$	4.88049	0.704438
$49$	−5.95573	−0.850818
$50$	−22.2314	−3.14400
$51$	−3.45756	−0.484156
$52$	1.34571	0.186616
$53$	2.79430	0.383827	0.191914	−	0.981412i	$-0.438531\pi$
$53$	2.79430	0.383827	0.191914	+	0.981412i	$0.438531\pi$
$54$	1.82913	0.248913
$55$	6.61656	0.892177
$56$	−1.22299	−0.163429
$57$	7.53668	0.998258
$58$	5.41836	0.711465
$59$	−10.5699	−1.37609	−0.688044	−	0.725669i	$-0.741530\pi$
$59$	−10.5699	−1.37609	−0.688044	+	0.725669i	$0.741530\pi$
$60$	−5.57358	−0.719546
$61$	−13.2753	−1.69973	−0.849863	−	0.527003i	$-0.823316\pi$
$61$	−13.2753	−1.69973	−0.849863	+	0.527003i	$0.823316\pi$
$62$	7.83681	0.995276
$63$	−1.02190	−0.128747
$64$	−2.18954	−0.273693
$65$	4.14175	0.513721
$66$	2.92208	0.359683
$67$	−0.576673	−0.0704518	−0.0352259	−	0.999379i	$-0.511215\pi$
$67$	−0.576673	−0.0704518	−0.0352259	+	0.999379i	$0.511215\pi$
$68$	4.65286	0.564242
$69$	−1.69984	−0.204636
$70$	7.74167	0.925307
$71$	−9.51719	−1.12948	−0.564741	−	0.825268i	$-0.691024\pi$
$71$	−9.51719	−1.12948	−0.564741	+	0.825268i	$0.691024\pi$
$72$	1.19679	0.141043
$73$	−3.46214	−0.405213	−0.202606	−	0.979260i	$-0.564941\pi$
$73$	−3.46214	−0.405213	−0.202606	+	0.979260i	$0.564941\pi$
$74$	20.5686	2.39105
$75$	−12.1541	−1.40344
$76$	−10.1422	−1.16338
$77$	−1.63251	−0.186041
$78$	1.82913	0.207108
$79$	−0.683655	−0.0769172	−0.0384586	−	0.999260i	$-0.512245\pi$
$79$	−0.683655	−0.0769172	−0.0384586	+	0.999260i	$0.512245\pi$
$80$	−20.2138	−2.25997
$81$	1.00000	0.111111
$82$	−8.71747	−0.962683
$83$	−16.7514	−1.83871	−0.919355	−	0.393429i	$-0.871289\pi$
$83$	−16.7514	−1.83871	−0.919355	+	0.393429i	$0.871289\pi$
$84$	1.37517	0.150043
$85$	14.3204	1.55326
$86$	15.0186	1.61950
$87$	2.96226	0.317588
$88$	1.91190	0.203809
$89$	0.765114	0.0811019	0.0405510	−	0.999177i	$-0.487089\pi$
$89$	0.765114	0.0811019	0.0405510	+	0.999177i	$0.487089\pi$
$90$	−7.57579	−0.798559
$91$	−1.02190	−0.107124
$92$	2.28748	0.238486
$93$	4.28445	0.444277
$94$	13.3344	1.37534
$95$	−31.2151	−3.20260
$96$	−6.53346	−0.666818
$97$	5.58569	0.567141	0.283570	−	0.958951i	$-0.408481\pi$
$97$	5.58569	0.567141	0.283570	+	0.958951i	$0.408481\pi$
$98$	10.8938	1.10044
$99$	1.59753	0.160557
$100$	16.3559	1.63559
$101$	−9.70026	−0.965212	−0.482606	−	0.875838i	$-0.660310\pi$
$101$	−9.70026	−0.965212	−0.482606	+	0.875838i	$0.660310\pi$
$102$	6.32432	0.626201
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.19679	0.117355
$105$	4.23244	0.413044
$106$	−5.11113	−0.496437
$107$	−0.974353	−0.0941943	−0.0470971	−	0.998890i	$-0.514997\pi$
$107$	−0.974353	−0.0941943	−0.0470971	+	0.998890i	$0.514997\pi$
$108$	−1.34571	−0.129491
$109$	0.398882	0.0382060	0.0191030	−	0.999818i	$-0.493919\pi$
$109$	0.398882	0.0382060	0.0191030	+	0.999818i	$0.493919\pi$
$110$	−12.1025	−1.15393
$111$	11.2450	1.06733
$112$	4.98735	0.471260
$113$	14.6607	1.37917	0.689583	−	0.724206i	$-0.257794\pi$
$113$	14.6607	1.37917	0.689583	+	0.724206i	$0.257794\pi$
$114$	−13.7856	−1.29114
$115$	7.04030	0.656512
$116$	−3.98634	−0.370122
$117$	1.00000	0.0924500
$118$	19.3337	1.77981
$119$	−3.53327	−0.323894
$120$	−4.95680	−0.452492
$121$	−8.44791	−0.767992
$122$	24.2822	2.19841
$123$	−4.76592	−0.429728
$124$	−5.76561	−0.517767
$125$	29.6306	2.65024
$126$	1.86918	0.166520
$127$	−16.2572	−1.44259	−0.721297	−	0.692626i	$-0.756454\pi$
$127$	−16.2572	−1.44259	−0.721297	+	0.692626i	$0.756454\pi$
$128$	−9.06196	−0.800971
$129$	8.21080	0.722920
$130$	−7.57579	−0.664441
$131$	16.8178	1.46938	0.734691	−	0.678402i	$-0.237327\pi$
$131$	16.8178	1.46938	0.734691	+	0.678402i	$0.237327\pi$
$132$	−2.14980	−0.187116
$133$	7.70171	0.667823
$134$	1.05481	0.0911215
$135$	−4.14175	−0.356465
$136$	4.13797	0.354828
$137$	−18.8582	−1.61117	−0.805584	−	0.592482i	$-0.798148\pi$
$137$	−18.8582	−1.61117	−0.805584	+	0.592482i	$0.798148\pi$
$138$	3.10922	0.264674
$139$	13.4863	1.14389	0.571946	−	0.820291i	$-0.306189\pi$
$139$	13.4863	1.14389	0.571946	+	0.820291i	$0.306189\pi$
$140$	−5.69562	−0.481368
$141$	7.29003	0.613931
$142$	17.4081	1.46086
$143$	1.59753	0.133592
$144$	−4.88049	−0.406707
$145$	−12.2690	−1.01888
$146$	6.33269	0.524097
$147$	5.95573	0.491220
$148$	−15.1325	−1.24388
$149$	20.8515	1.70822	0.854111	−	0.520092i	$-0.174102\pi$
$149$	20.8515	1.70822	0.854111	+	0.520092i	$0.174102\pi$
$150$	22.2314	1.81519
$151$	13.3764	1.08855	0.544277	−	0.838905i	$-0.316804\pi$
$151$	13.3764	1.08855	0.544277	+	0.838905i	$0.316804\pi$
$152$	−9.01981	−0.731603
$153$	3.45756	0.279527
$154$	2.98606	0.240624
$155$	−17.7451	−1.42532
$156$	−1.34571	−0.107743
$157$	−1.53712	−0.122675	−0.0613377	−	0.998117i	$-0.519537\pi$
$157$	−1.53712	−0.122675	−0.0613377	+	0.998117i	$0.519537\pi$
$158$	1.25049	0.0994837
$159$	−2.79430	−0.221603
$160$	27.0600	2.13928
$161$	−1.73706	−0.136899
$162$	−1.82913	−0.143710
$163$	8.48022	0.664222	0.332111	−	0.943240i	$-0.392239\pi$
$163$	8.48022	0.664222	0.332111	+	0.943240i	$0.392239\pi$
$164$	6.41352	0.500812
$165$	−6.61656	−0.515098
$166$	30.6405	2.37817
$167$	4.01532	0.310715	0.155357	−	0.987858i	$-0.450347\pi$
$167$	4.01532	0.310715	0.155357	+	0.987858i	$0.450347\pi$
$168$	1.22299	0.0943560
$169$	1.00000	0.0769231
$170$	−26.1938	−2.00897
$171$	−7.53668	−0.576345
$172$	−11.0493	−0.842502
$173$	11.9116	0.905618	0.452809	−	0.891607i	$-0.350422\pi$
$173$	11.9116	0.905618	0.452809	+	0.891607i	$0.350422\pi$
$174$	−5.41836	−0.410765
$175$	−12.4202	−0.938882
$176$	−7.79671	−0.587699
$177$	10.5699	0.794484
$178$	−1.39949	−0.104896
$179$	19.1224	1.42927	0.714637	−	0.699495i	$-0.246592\pi$
$179$	19.1224	1.42927	0.714637	+	0.699495i	$0.246592\pi$
$180$	5.57358	0.415430
$181$	−8.18135	−0.608115	−0.304057	−	0.952654i	$-0.598341\pi$
$181$	−8.18135	−0.608115	−0.304057	+	0.952654i	$0.598341\pi$
$182$	1.86918	0.138553
$183$	13.2753	0.981338
$184$	2.03434	0.149974
$185$	−46.5741	−3.42419
$186$	−7.83681	−0.574623
$187$	5.52355	0.403922
$188$	−9.81023	−0.715484
$189$	1.02190	0.0743320
$190$	57.0963	4.14220
$191$	−9.92924	−0.718455	−0.359227	−	0.933250i	$-0.616960\pi$
$191$	−9.92924	−0.718455	−0.359227	+	0.933250i	$0.616960\pi$
$192$	2.18954	0.158017
$193$	−26.5957	−1.91440	−0.957201	−	0.289423i	$-0.906536\pi$
$193$	−26.5957	−1.91440	−0.957201	+	0.289423i	$0.906536\pi$
$194$	−10.2169	−0.733533
$195$	−4.14175	−0.296597
$196$	−8.01465	−0.572475
$197$	−18.2754	−1.30207	−0.651034	−	0.759048i	$-0.725665\pi$
$197$	−18.2754	−1.30207	−0.651034	+	0.759048i	$0.725665\pi$
$198$	−2.92208	−0.207663
$199$	−20.1107	−1.42561	−0.712807	−	0.701361i	$-0.752576\pi$
$199$	−20.1107	−1.42561	−0.712807	+	0.701361i	$0.752576\pi$
$200$	14.5459	1.02855
$201$	0.576673	0.0406754
$202$	17.7430	1.24839
$203$	3.02713	0.212463
$204$	−4.65286	−0.325765
$205$	19.7392	1.37865
$206$	−1.82913	−0.127441
$207$	1.69984	0.118147
$208$	−4.88049	−0.338401
$209$	−12.0400	−0.832828
$210$	−7.74167	−0.534226
$211$	26.3352	1.81299	0.906494	−	0.422218i	$-0.138748\pi$
$211$	26.3352	1.81299	0.906494	+	0.422218i	$0.138748\pi$
$212$	3.76031	0.258259
$213$	9.51719	0.652107
$214$	1.78222	0.121830
$215$	−34.0071	−2.31926
$216$	−1.19679	−0.0814311
$217$	4.37827	0.297216
$218$	−0.729606	−0.0494152
$219$	3.46214	0.233950
$220$	8.90394	0.600303
$221$	3.45756	0.232581
$222$	−20.5686	−1.38047
$223$	25.9168	1.73552	0.867759	−	0.496985i	$-0.165560\pi$
$223$	25.9168	1.73552	0.867759	+	0.496985i	$0.165560\pi$
$224$	−6.67651	−0.446093
$225$	12.1541	0.810274
$226$	−26.8164	−1.78380
$227$	13.2906	0.882129	0.441065	−	0.897475i	$-0.354601\pi$
$227$	13.2906	0.882129	0.441065	+	0.897475i	$0.354601\pi$
$228$	10.1422	0.671681
$229$	18.6463	1.23218	0.616090	−	0.787676i	$-0.288716\pi$
$229$	18.6463	1.23218	0.616090	+	0.787676i	$0.288716\pi$
$230$	−12.8776	−0.849124
$231$	1.63251	0.107411
$232$	−3.54520	−0.232754
$233$	16.2962	1.06760	0.533801	−	0.845610i	$-0.320763\pi$
$233$	16.2962	1.06760	0.533801	+	0.845610i	$0.320763\pi$
$234$	−1.82913	−0.119574
$235$	−30.1935	−1.96961
$236$	−14.2240	−0.925904
$237$	0.683655	0.0444081
$238$	6.46280	0.418921
$239$	17.8139	1.15229	0.576144	−	0.817348i	$-0.304557\pi$
$239$	17.8139	1.15229	0.576144	+	0.817348i	$0.304557\pi$
$240$	20.2138	1.30479
$241$	18.7878	1.21023	0.605113	−	0.796139i	$-0.293128\pi$
$241$	18.7878	1.21023	0.605113	+	0.796139i	$0.293128\pi$
$242$	15.4523	0.993312
$243$	−1.00000	−0.0641500
$244$	−17.8646	−1.14367
$245$	−24.6672	−1.57593
$246$	8.71747	0.555805
$247$	−7.53668	−0.479548
$248$	−5.12758	−0.325602
$249$	16.7514	1.06158
$250$	−54.1981	−3.42779
$251$	−26.5616	−1.67655	−0.838276	−	0.545245i	$-0.816436\pi$
$251$	−26.5616	−1.67655	−0.838276	+	0.545245i	$0.816436\pi$
$252$	−1.37517	−0.0866276
$253$	2.71553	0.170724
$254$	29.7365	1.86583
$255$	−14.3204	−0.896776
$256$	20.9546	1.30966
$257$	0.394043	0.0245798	0.0122899	−	0.999924i	$-0.496088\pi$
$257$	0.394043	0.0245798	0.0122899	+	0.999924i	$0.496088\pi$
$258$	−15.0186	−0.935017
$259$	11.4912	0.714030
$260$	5.57358	0.345659
$261$	−2.96226	−0.183360
$262$	−30.7620	−1.90048
$263$	−31.9366	−1.96929	−0.984647	−	0.174555i	$-0.944151\pi$
$263$	−31.9366	−1.96929	−0.984647	+	0.174555i	$0.944151\pi$
$264$	−1.91190	−0.117669
$265$	11.5733	0.710943
$266$	−14.0874	−0.863754
$267$	−0.765114	−0.0468242
$268$	−0.776031	−0.0474037
$269$	−7.02757	−0.428478	−0.214239	−	0.976781i	$-0.568727\pi$
$269$	−7.02757	−0.428478	−0.214239	+	0.976781i	$0.568727\pi$
$270$	7.57579	0.461048
$271$	−27.4608	−1.66812	−0.834062	−	0.551670i	$-0.813991\pi$
$271$	−27.4608	−1.66812	−0.834062	+	0.551670i	$0.813991\pi$
$272$	−16.8746	−1.02317
$273$	1.02190	0.0618480
$274$	34.4941	2.08387
$275$	19.4165	1.17086
$276$	−2.28748	−0.137690
$277$	21.8507	1.31288	0.656440	−	0.754378i	$-0.272062\pi$
$277$	21.8507	1.31288	0.656440	+	0.754378i	$0.272062\pi$
$278$	−24.6681	−1.47950
$279$	−4.28445	−0.256503
$280$	−5.06534	−0.302712
$281$	21.5377	1.28483	0.642415	−	0.766357i	$-0.277932\pi$
$281$	21.5377	1.28483	0.642415	+	0.766357i	$0.277932\pi$
$282$	−13.3344	−0.794051
$283$	22.8700	1.35948	0.679739	−	0.733454i	$-0.262093\pi$
$283$	22.8700	1.35948	0.679739	+	0.733454i	$0.262093\pi$
$284$	−12.8073	−0.759975
$285$	31.2151	1.84902
$286$	−2.92208	−0.172786
$287$	−4.87027	−0.287483
$288$	6.53346	0.384988
$289$	−5.04526	−0.296780
$290$	22.4415	1.31781
$291$	−5.58569	−0.327439
$292$	−4.65902	−0.272648
$293$	−11.2855	−0.659308	−0.329654	−	0.944102i	$-0.606932\pi$
$293$	−11.2855	−0.659308	−0.329654	+	0.944102i	$0.606932\pi$
$294$	−10.8938	−0.635338
$295$	−43.7780	−2.54885
$296$	−13.4579	−0.782224
$297$	−1.59753	−0.0926979
$298$	−38.1400	−2.20939
$299$	1.69984	0.0983041
$300$	−16.3559	−0.944306
$301$	8.39058	0.483625
$302$	−24.4671	−1.40792
$303$	9.70026	0.557266
$304$	36.7827	2.10963
$305$	−54.9830	−3.14832
$306$	−6.32432	−0.361537
$307$	14.3801	0.820715	0.410357	−	0.911925i	$-0.365404\pi$
$307$	14.3801	0.820715	0.410357	+	0.911925i	$0.365404\pi$
$308$	−2.19687	−0.125178
$309$	−1.00000	−0.0568880
$310$	32.4581	1.84350
$311$	−3.69710	−0.209644	−0.104822	−	0.994491i	$-0.533427\pi$
$311$	−3.69710	−0.209644	−0.104822	+	0.994491i	$0.533427\pi$
$312$	−1.19679	−0.0677548
$313$	−20.3947	−1.15277	−0.576387	−	0.817177i	$-0.695538\pi$
$313$	−20.3947	−1.15277	−0.576387	+	0.817177i	$0.695538\pi$
$314$	2.81159	0.158667
$315$	−4.23244	−0.238471
$316$	−0.919998	−0.0517539
$317$	−3.12116	−0.175302	−0.0876508	−	0.996151i	$-0.527936\pi$
$317$	−3.12116	−0.175302	−0.0876508	+	0.996151i	$0.527936\pi$
$318$	5.11113	0.286618
$319$	−4.73230	−0.264958
$320$	−9.06855	−0.506947
$321$	0.974353	0.0543831
$322$	3.17730	0.177064
$323$	−26.0586	−1.44994
$324$	1.34571	0.0747614
$325$	12.1541	0.674189
$326$	−15.5114	−0.859097
$327$	−0.398882	−0.0220582
$328$	5.70379	0.314939
$329$	7.44965	0.410713
$330$	12.1025	0.666222
$331$	−4.84998	−0.266579	−0.133289	−	0.991077i	$-0.542554\pi$
$331$	−4.84998	−0.266579	−0.133289	+	0.991077i	$0.542554\pi$
$332$	−22.5425	−1.23718
$333$	−11.2450	−0.616223
$334$	−7.34453	−0.401875
$335$	−2.38844	−0.130494
$336$	−4.98735	−0.272082
$337$	−5.27618	−0.287412	−0.143706	−	0.989620i	$-0.545902\pi$
$337$	−5.27618	−0.287412	−0.143706	+	0.989620i	$0.545902\pi$
$338$	−1.82913	−0.0994914
$339$	−14.6607	−0.796262
$340$	19.2710	1.04512
$341$	−6.84452	−0.370652
$342$	13.7856	0.745437
$343$	13.2394	0.714861
$344$	−9.82659	−0.529814
$345$	−7.04030	−0.379037
$346$	−21.7877	−1.17132
$347$	−27.3062	−1.46587	−0.732937	−	0.680297i	$-0.761851\pi$
$347$	−27.3062	−1.46587	−0.732937	+	0.680297i	$0.761851\pi$
$348$	3.98634	0.213690
$349$	14.7898	0.791678	0.395839	−	0.918320i	$-0.370454\pi$
$349$	14.7898	0.791678	0.395839	+	0.918320i	$0.370454\pi$
$350$	22.7182	1.21434
$351$	−1.00000	−0.0533761
$352$	10.4374	0.556313
$353$	12.5155	0.666133	0.333067	−	0.942903i	$-0.391917\pi$
$353$	12.5155	0.666133	0.333067	+	0.942903i	$0.391917\pi$
$354$	−19.3337	−1.02758
$355$	−39.4178	−2.09208
$356$	1.02962	0.0545696
$357$	3.53327	0.187000
$358$	−34.9773	−1.84861
$359$	7.30189	0.385379	0.192690	−	0.981260i	$-0.438279\pi$
$359$	7.30189	0.385379	0.192690	+	0.981260i	$0.438279\pi$
$360$	4.95680	0.261246
$361$	37.8016	1.98956
$362$	14.9647	0.786528
$363$	8.44791	0.443400
$364$	−1.37517	−0.0720785
$365$	−14.3393	−0.750555
$366$	−24.2822	−1.26925
$367$	−17.3087	−0.903505	−0.451752	−	0.892143i	$-0.649201\pi$
$367$	−17.3087	−0.903505	−0.451752	+	0.892143i	$0.649201\pi$
$368$	−8.29603	−0.432461
$369$	4.76592	0.248104
$370$	85.1899	4.42881
$371$	−2.85549	−0.148250
$372$	5.76561	0.298933
$373$	−13.4695	−0.697423	−0.348711	−	0.937230i	$-0.613381\pi$
$373$	−13.4695	−0.697423	−0.348711	+	0.937230i	$0.613381\pi$
$374$	−10.1033	−0.522428
$375$	−29.6306	−1.53012
$376$	−8.72462	−0.449938
$377$	−2.96226	−0.152564
$378$	−1.86918	−0.0961401
$379$	6.17235	0.317053	0.158526	−	0.987355i	$-0.449326\pi$
$379$	6.17235	0.317053	0.158526	+	0.987355i	$0.449326\pi$
$380$	−42.0063	−2.15488
$381$	16.2572	0.832882
$382$	18.1618	0.929241
$383$	−25.1773	−1.28650	−0.643251	−	0.765656i	$-0.722415\pi$
$383$	−25.1773	−1.28650	−0.643251	+	0.765656i	$0.722415\pi$
$384$	9.06196	0.462441
$385$	−6.76144	−0.344595
$386$	48.6470	2.47607
$387$	−8.21080	−0.417378
$388$	7.51669	0.381602
$389$	−4.58070	−0.232251	−0.116125	−	0.993235i	$-0.537047\pi$
$389$	−4.58070	−0.232251	−0.116125	+	0.993235i	$0.537047\pi$
$390$	7.57579	0.383615
$391$	5.87729	0.297227
$392$	−7.12774	−0.360005
$393$	−16.8178	−0.848348
$394$	33.4280	1.68408
$395$	−2.83153	−0.142470
$396$	2.14980	0.108031
$397$	23.6569	1.18731	0.593653	−	0.804721i	$-0.297685\pi$
$397$	23.6569	1.18731	0.593653	+	0.804721i	$0.297685\pi$
$398$	36.7851	1.84387
$399$	−7.70171	−0.385568
$400$	−59.3180	−2.96590
$401$	−19.0798	−0.952798	−0.476399	−	0.879229i	$-0.658058\pi$
$401$	−19.0798	−0.952798	−0.476399	+	0.879229i	$0.658058\pi$
$402$	−1.05481	−0.0526090
$403$	−4.28445	−0.213424
$404$	−13.0537	−0.649446
$405$	4.14175	0.205805
$406$	−5.53700	−0.274797
$407$	−17.9642	−0.890452
$408$	−4.13797	−0.204860
$409$	11.2527	0.556412	0.278206	−	0.960521i	$-0.410260\pi$
$409$	11.2527	0.556412	0.278206	+	0.960521i	$0.410260\pi$
$410$	−36.1056	−1.78313
$411$	18.8582	0.930208
$412$	1.34571	0.0662981
$413$	10.8014	0.531500
$414$	−3.10922	−0.152810
$415$	−69.3804	−3.40575
$416$	6.53346	0.320329
$417$	−13.4863	−0.660427
$418$	22.0228	1.07717
$419$	−8.19804	−0.400500	−0.200250	−	0.979745i	$-0.564175\pi$
$419$	−8.19804	−0.400500	−0.200250	+	0.979745i	$0.564175\pi$
$420$	5.69562	0.277918
$421$	−28.6948	−1.39850	−0.699249	−	0.714879i	$-0.746482\pi$
$421$	−28.6948	−1.39850	−0.699249	+	0.714879i	$0.746482\pi$
$422$	−48.1704	−2.34490
$423$	−7.29003	−0.354453
$424$	3.34419	0.162408
$425$	42.0236	2.03845
$426$	−17.4081	−0.843428
$427$	13.5660	0.656503
$428$	−1.31119	−0.0633789
$429$	−1.59753	−0.0771293
$430$	62.2033	2.99971
$431$	29.1697	1.40506	0.702528	−	0.711656i	$-0.252055\pi$
$431$	29.1697	1.40506	0.702528	+	0.711656i	$0.252055\pi$
$432$	4.88049	0.234813
$433$	−6.23571	−0.299669	−0.149835	−	0.988711i	$-0.547874\pi$
$433$	−6.23571	−0.299669	−0.149835	+	0.988711i	$0.547874\pi$
$434$	−8.00840	−0.384416
$435$	12.2690	0.588252
$436$	0.536778	0.0257070
$437$	−12.8111	−0.612840
$438$	−6.33269	−0.302588
$439$	−22.7718	−1.08684	−0.543419	−	0.839461i	$-0.682871\pi$
$439$	−22.7718	−1.08684	−0.543419	+	0.839461i	$0.682871\pi$
$440$	7.91862	0.377505
$441$	−5.95573	−0.283606
$442$	−6.32432	−0.300817
$443$	21.6003	1.02626	0.513130	−	0.858311i	$-0.328486\pi$
$443$	21.6003	1.02626	0.513130	+	0.858311i	$0.328486\pi$
$444$	15.1325	0.718155
$445$	3.16891	0.150221
$446$	−47.4051	−2.24470
$447$	−20.8515	−0.986242
$448$	2.23749	0.105711
$449$	−4.62937	−0.218473	−0.109237	−	0.994016i	$-0.534841\pi$
$449$	−4.62937	−0.218473	−0.109237	+	0.994016i	$0.534841\pi$
$450$	−22.2314	−1.04800
$451$	7.61368	0.358514
$452$	19.7290	0.927976
$453$	−13.3764	−0.628477
$454$	−24.3102	−1.14094
$455$	−4.23244	−0.198420
$456$	9.01981	0.422391
$457$	−36.7853	−1.72074	−0.860372	−	0.509666i	$-0.829769\pi$
$457$	−36.7853	−1.72074	−0.860372	+	0.509666i	$0.829769\pi$
$458$	−34.1064	−1.59369
$459$	−3.45756	−0.161385
$460$	9.47417	0.441736
$461$	−21.1669	−0.985839	−0.492920	−	0.870075i	$-0.664070\pi$
$461$	−21.1669	−0.985839	−0.492920	+	0.870075i	$0.664070\pi$
$462$	−2.98606	−0.138924
$463$	−31.8152	−1.47858	−0.739289	−	0.673389i	$-0.764838\pi$
$463$	−31.8152	−1.47858	−0.739289	+	0.673389i	$0.764838\pi$
$464$	14.4573	0.671163
$465$	17.7451	0.822911
$466$	−29.8079	−1.38082
$467$	23.6384	1.09385	0.546926	−	0.837181i	$-0.315798\pi$
$467$	23.6384	1.09385	0.546926	+	0.837181i	$0.315798\pi$
$468$	1.34571	0.0622052
$469$	0.589300	0.0272113
$470$	55.2277	2.54747
$471$	1.53712	0.0708267
$472$	−12.6500	−0.582262
$473$	−13.1170	−0.603119
$474$	−1.25049	−0.0574370
$475$	−91.6017	−4.20298
$476$	−4.75474	−0.217933
$477$	2.79430	0.127942
$478$	−32.5840	−1.49036
$479$	26.7861	1.22389	0.611943	−	0.790902i	$-0.290388\pi$
$479$	26.7861	1.22389	0.611943	+	0.790902i	$0.290388\pi$
$480$	−27.0600	−1.23511
$481$	−11.2450	−0.512728
$482$	−34.3652	−1.56529
$483$	1.73706	0.0790388
$484$	−11.3684	−0.516745
$485$	23.1345	1.05048
$486$	1.82913	0.0829709
$487$	−35.2418	−1.59696	−0.798480	−	0.602021i	$-0.794362\pi$
$487$	−35.2418	−1.59696	−0.798480	+	0.602021i	$0.794362\pi$
$488$	−15.8877	−0.719203
$489$	−8.48022	−0.383489
$490$	45.1194	2.03828
$491$	26.2085	1.18277	0.591387	−	0.806388i	$-0.298581\pi$
$491$	26.2085	1.18277	0.591387	+	0.806388i	$0.298581\pi$
$492$	−6.41352	−0.289144
$493$	−10.2422	−0.461286
$494$	13.7856	0.620241
$495$	6.61656	0.297392
$496$	20.9102	0.938897
$497$	9.72558	0.436252
$498$	−30.6405	−1.37303
$499$	0.569631	0.0255002	0.0127501	−	0.999919i	$-0.495941\pi$
$499$	0.569631	0.0255002	0.0127501	+	0.999919i	$0.495941\pi$
$500$	39.8740	1.78322
$501$	−4.01532	−0.179391
$502$	48.5845	2.16843
$503$	13.6002	0.606405	0.303202	−	0.952926i	$-0.401944\pi$
$503$	13.6002	0.606405	0.303202	+	0.952926i	$0.401944\pi$
$504$	−1.22299	−0.0544764
$505$	−40.1761	−1.78781
$506$	−4.96706	−0.220813
$507$	−1.00000	−0.0444116
$508$	−21.8774	−0.970653
$509$	−24.9894	−1.10764	−0.553818	−	0.832638i	$-0.686829\pi$
$509$	−24.9894	−1.10764	−0.553818	+	0.832638i	$0.686829\pi$
$510$	26.1938	1.15988
$511$	3.53795	0.156510
$512$	−20.2046	−0.892927
$513$	7.53668	0.332753
$514$	−0.720755	−0.0317912
$515$	4.14175	0.182507
$516$	11.0493	0.486419
$517$	−11.6460	−0.512191
$518$	−21.0189	−0.923519
$519$	−11.9116	−0.522859
$520$	4.95680	0.217370
$521$	10.6524	0.466689	0.233345	−	0.972394i	$-0.425033\pi$
$521$	10.6524	0.466689	0.233345	+	0.972394i	$0.425033\pi$
$522$	5.41836	0.237155
$523$	24.3155	1.06324	0.531620	−	0.846983i	$-0.321583\pi$
$523$	24.3155	1.06324	0.531620	+	0.846983i	$0.321583\pi$
$524$	22.6318	0.988677
$525$	12.4202	0.542064
$526$	58.4161	2.54706
$527$	−14.8138	−0.645298
$528$	7.79671	0.339308
$529$	−20.1106	−0.874372
$530$	−21.1691	−0.919525
$531$	−10.5699	−0.458696
$532$	10.3642	0.449346
$533$	4.76592	0.206435
$534$	1.39949	0.0605619
$535$	−4.03553	−0.174471
$536$	−0.690155	−0.0298102
$537$	−19.1224	−0.825192
$538$	12.8543	0.554189
$539$	−9.51443	−0.409816
$540$	−5.57358	−0.239849
$541$	7.48790	0.321930	0.160965	−	0.986960i	$-0.448539\pi$
$541$	7.48790	0.321930	0.160965	+	0.986960i	$0.448539\pi$
$542$	50.2293	2.15753
$543$	8.18135	0.351095
$544$	22.5898	0.968531
$545$	1.65207	0.0707670
$546$	−1.86918	−0.0799934
$547$	−9.66706	−0.413334	−0.206667	−	0.978411i	$-0.566262\pi$
$547$	−9.66706	−0.413334	−0.206667	+	0.978411i	$0.566262\pi$
$548$	−25.3776	−1.08408
$549$	−13.2753	−0.566576
$550$	−35.5153	−1.51438
$551$	22.3257	0.951105
$552$	−2.03434	−0.0865874
$553$	0.698624	0.0297085
$554$	−39.9677	−1.69806
$555$	46.5741	1.97696
$556$	18.1486	0.769671
$557$	−40.1403	−1.70080	−0.850400	−	0.526136i	$-0.823640\pi$
$557$	−40.1403	−1.70080	−0.850400	+	0.526136i	$0.823640\pi$
$558$	7.83681	0.331759
$559$	−8.21080	−0.347280
$560$	20.6564	0.872891
$561$	−5.52355	−0.233204
$562$	−39.3952	−1.66179
$563$	23.1656	0.976312	0.488156	−	0.872756i	$-0.337670\pi$
$563$	23.1656	0.976312	0.488156	+	0.872756i	$0.337670\pi$
$564$	9.81023	0.413085
$565$	60.7212	2.55456
$566$	−41.8321	−1.75833
$567$	−1.02190	−0.0429156
$568$	−11.3901	−0.477916
$569$	14.1073	0.591410	0.295705	−	0.955279i	$-0.404445\pi$
$569$	14.1073	0.591410	0.295705	+	0.955279i	$0.404445\pi$
$570$	−57.0963	−2.39150
$571$	−1.71624	−0.0718222	−0.0359111	−	0.999355i	$-0.511433\pi$
$571$	−1.71624	−0.0718222	−0.0359111	+	0.999355i	$0.511433\pi$
$572$	2.14980	0.0898876
$573$	9.92924	0.414800
$574$	8.90835	0.371827
$575$	20.6600	0.861582
$576$	−2.18954	−0.0912310
$577$	−29.7711	−1.23939	−0.619694	−	0.784844i	$-0.712743\pi$
$577$	−29.7711	−1.23939	−0.619694	+	0.784844i	$0.712743\pi$
$578$	9.22842	0.383852
$579$	26.5957	1.10528
$580$	−16.5104	−0.685558
$581$	17.1182	0.710184
$582$	10.2169	0.423505
$583$	4.46397	0.184879
$584$	−4.14345	−0.171457
$585$	4.14175	0.171240
$586$	20.6427	0.852741
$587$	−26.7962	−1.10600	−0.553000	−	0.833181i	$-0.686517\pi$
$587$	−26.7962	−1.10600	−0.553000	+	0.833181i	$0.686517\pi$
$588$	8.01465	0.330519
$589$	32.2906	1.33051
$590$	80.0756	3.29666
$591$	18.2754	0.751750
$592$	54.8811	2.25560
$593$	−20.5306	−0.843090	−0.421545	−	0.906808i	$-0.638512\pi$
$593$	−20.5306	−0.843090	−0.421545	+	0.906808i	$0.638512\pi$
$594$	2.92208	0.119894
$595$	−14.6339	−0.599933
$596$	28.0600	1.14938
$597$	20.1107	0.823078
$598$	−3.10922	−0.127145
$599$	8.04495	0.328708	0.164354	−	0.986401i	$-0.447446\pi$
$599$	8.04495	0.328708	0.164354	+	0.986401i	$0.447446\pi$
$600$	−14.5459	−0.593834
$601$	28.6778	1.16979	0.584896	−	0.811108i	$-0.301135\pi$
$601$	28.6778	1.16979	0.584896	+	0.811108i	$0.301135\pi$
$602$	−15.3474	−0.625515
$603$	−0.576673	−0.0234839
$604$	18.0007	0.732437
$605$	−34.9892	−1.42251
$606$	−17.7430	−0.720761
$607$	−32.8793	−1.33453	−0.667265	−	0.744821i	$-0.732535\pi$
$607$	−32.8793	−1.33453	−0.667265	+	0.744821i	$0.732535\pi$
$608$	−49.2406	−1.99697
$609$	−3.02713	−0.122665
$610$	100.571	4.07199
$611$	−7.29003	−0.294923
$612$	4.65286	0.188081
$613$	30.8599	1.24642	0.623211	−	0.782054i	$-0.285828\pi$
$613$	30.8599	1.24642	0.623211	+	0.782054i	$0.285828\pi$
$614$	−26.3030	−1.06150
$615$	−19.7392	−0.795963
$616$	−1.95376	−0.0787194
$617$	10.3172	0.415354	0.207677	−	0.978197i	$-0.433410\pi$
$617$	10.3172	0.415354	0.207677	+	0.978197i	$0.433410\pi$
$618$	1.82913	0.0735783
$619$	29.2251	1.17465	0.587327	−	0.809349i	$-0.300180\pi$
$619$	29.2251	1.17465	0.587327	+	0.809349i	$0.300180\pi$
$620$	−23.8797	−0.959033
$621$	−1.69984	−0.0682121
$622$	6.76247	0.271150
$623$	−0.781867	−0.0313248
$624$	4.88049	0.195376
$625$	61.9520	2.47808
$626$	37.3044	1.49099
$627$	12.0400	0.480833
$628$	−2.06851	−0.0825425
$629$	−38.8803	−1.55026
$630$	7.74167	0.308436
$631$	36.3929	1.44878	0.724389	−	0.689391i	$-0.242122\pi$
$631$	36.3929	1.44878	0.724389	+	0.689391i	$0.242122\pi$
$632$	−0.818190	−0.0325458
$633$	−26.3352	−1.04673
$634$	5.70899	0.226733
$635$	−67.3333	−2.67204
$636$	−3.76031	−0.149106
$637$	−5.95573	−0.235975
$638$	8.65597	0.342693
$639$	−9.51719	−0.376494
$640$	−37.5324	−1.48360
$641$	35.1717	1.38920	0.694599	−	0.719397i	$-0.255582\pi$
$641$	35.1717	1.38920	0.694599	+	0.719397i	$0.255582\pi$
$642$	−1.78222	−0.0703384
$643$	44.3156	1.74764	0.873818	−	0.486254i	$-0.161637\pi$
$643$	44.3156	1.74764	0.873818	+	0.486254i	$0.161637\pi$
$644$	−2.33757	−0.0921130
$645$	34.0071	1.33903
$646$	47.6644	1.87533
$647$	29.3122	1.15238	0.576191	−	0.817315i	$-0.304539\pi$
$647$	29.3122	1.15238	0.576191	+	0.817315i	$0.304539\pi$
$648$	1.19679	0.0470143
$649$	−16.8857	−0.662823
$650$	−22.2314	−0.871988
$651$	−4.37827	−0.171598
$652$	11.4119	0.446923
$653$	3.64157	0.142505	0.0712527	−	0.997458i	$-0.477300\pi$
$653$	3.64157	0.142505	0.0712527	+	0.997458i	$0.477300\pi$
$654$	0.729606	0.0285299
$655$	69.6553	2.72166
$656$	−23.2600	−0.908150
$657$	−3.46214	−0.135071
$658$	−13.6264	−0.531211
$659$	27.1239	1.05660	0.528299	−	0.849058i	$-0.322830\pi$
$659$	27.1239	1.05660	0.528299	+	0.849058i	$0.322830\pi$
$660$	−8.90394	−0.346585
$661$	10.0594	0.391265	0.195632	−	0.980677i	$-0.437324\pi$
$661$	10.0594	0.391265	0.195632	+	0.980677i	$0.437324\pi$
$662$	8.87122	0.344790
$663$	−3.45756	−0.134281
$664$	−20.0479	−0.778011
$665$	31.8986	1.23697
$666$	20.5686	0.797015
$667$	−5.03537	−0.194970
$668$	5.40344	0.209065
$669$	−25.9168	−1.00200
$670$	4.36875	0.168780
$671$	−21.2076	−0.818711
$672$	6.67651	0.257552
$673$	8.47375	0.326639	0.163320	−	0.986573i	$-0.447780\pi$
$673$	8.47375	0.326639	0.163320	+	0.986573i	$0.447780\pi$
$674$	9.65079	0.371735
$675$	−12.1541	−0.467812
$676$	1.34571	0.0517579
$677$	25.8817	0.994714	0.497357	−	0.867546i	$-0.334304\pi$
$677$	25.8817	0.994714	0.497357	+	0.867546i	$0.334304\pi$
$678$	26.8164	1.02988
$679$	−5.70799	−0.219053
$680$	17.1384	0.657230
$681$	−13.2906	−0.509298
$682$	12.5195	0.479397
$683$	42.2245	1.61568	0.807838	−	0.589404i	$-0.200637\pi$
$683$	42.2245	1.61568	0.807838	+	0.589404i	$0.200637\pi$
$684$	−10.1422	−0.387795
$685$	−78.1062	−2.98428
$686$	−24.2166	−0.924593
$687$	−18.6463	−0.711399
$688$	40.0727	1.52776
$689$	2.79430	0.106454
$690$	12.8776	0.490242
$691$	2.03828	0.0775397	0.0387698	−	0.999248i	$-0.487656\pi$
$691$	2.03828	0.0775397	0.0387698	+	0.999248i	$0.487656\pi$
$692$	16.0294	0.609348
$693$	−1.63251	−0.0620138
$694$	49.9465	1.89594
$695$	55.8569	2.11877
$696$	3.54520	0.134381
$697$	16.4785	0.624166
$698$	−27.0524	−1.02395
$699$	−16.2962	−0.616380
$700$	−16.7140	−0.631729
$701$	−1.89514	−0.0715786	−0.0357893	−	0.999359i	$-0.511395\pi$
$701$	−1.89514	−0.0715786	−0.0357893	+	0.999359i	$0.511395\pi$
$702$	1.82913	0.0690359
$703$	84.7501	3.19641
$704$	−3.49785	−0.131830
$705$	30.1935	1.13715
$706$	−22.8924	−0.861569
$707$	9.91266	0.372804
$708$	14.2240	0.534571
$709$	23.6711	0.888988	0.444494	−	0.895782i	$-0.353384\pi$
$709$	23.6711	0.888988	0.444494	+	0.895782i	$0.353384\pi$
$710$	72.1002	2.70587
$711$	−0.683655	−0.0256391
$712$	0.915679	0.0343165
$713$	−7.28287	−0.272746
$714$	−6.46280	−0.241864
$715$	6.61656	0.247445
$716$	25.7331	0.961691
$717$	−17.8139	−0.665274
$718$	−13.3561	−0.498445
$719$	0.881167	0.0328620	0.0164310	−	0.999865i	$-0.494770\pi$
$719$	0.881167	0.0328620	0.0164310	+	0.999865i	$0.494770\pi$
$720$	−20.2138	−0.753323
$721$	−1.02190	−0.0380574
$722$	−69.1439	−2.57327
$723$	−18.7878	−0.698725
$724$	−11.0097	−0.409172
$725$	−36.0037	−1.33714
$726$	−15.4523	−0.573489
$727$	−20.9697	−0.777721	−0.388861	−	0.921297i	$-0.627131\pi$
$727$	−20.9697	−0.777721	−0.388861	+	0.921297i	$0.627131\pi$
$728$	−1.22299	−0.0453271
$729$	1.00000	0.0370370
$730$	26.2284	0.970758
$731$	−28.3893	−1.05002
$732$	17.8646	0.660296
$733$	−38.4787	−1.42124	−0.710622	−	0.703574i	$-0.751587\pi$
$733$	−38.4787	−1.42124	−0.710622	+	0.703574i	$0.751587\pi$
$734$	31.6597	1.16858
$735$	24.6672	0.909862
$736$	11.1058	0.409365
$737$	−0.921250	−0.0339347
$738$	−8.71747	−0.320894
$739$	−42.7618	−1.57302	−0.786508	−	0.617580i	$-0.788113\pi$
$739$	−42.7618	−1.57302	−0.786508	+	0.617580i	$0.788113\pi$
$740$	−62.6750	−2.30398
$741$	7.53668	0.276867
$742$	5.22305	0.191744
$743$	−9.66205	−0.354466	−0.177233	−	0.984169i	$-0.556715\pi$
$743$	−9.66205	−0.354466	−0.177233	+	0.984169i	$0.556715\pi$
$744$	5.12758	0.187986
$745$	86.3617	3.16405
$746$	24.6374	0.902038
$747$	−16.7514	−0.612903
$748$	7.43307	0.271780
$749$	0.995688	0.0363816
$750$	54.1981	1.97903
$751$	17.9750	0.655919	0.327959	−	0.944692i	$-0.393639\pi$
$751$	17.9750	0.655919	0.327959	+	0.944692i	$0.393639\pi$
$752$	35.5789	1.29743
$753$	26.5616	0.967958
$754$	5.41836	0.197325
$755$	55.4017	2.01627
$756$	1.37517	0.0500145
$757$	−15.7697	−0.573158	−0.286579	−	0.958057i	$-0.592518\pi$
$757$	−15.7697	−0.573158	−0.286579	+	0.958057i	$0.592518\pi$
$758$	−11.2900	−0.410072
$759$	−2.71553	−0.0985676
$760$	−37.3578	−1.35511
$761$	−36.7791	−1.33324	−0.666620	−	0.745397i	$-0.732260\pi$
$761$	−36.7791	−1.33324	−0.666620	+	0.745397i	$0.732260\pi$
$762$	−29.7365	−1.07724
$763$	−0.407616	−0.0147567
$764$	−13.3618	−0.483414
$765$	14.3204	0.517754
$766$	46.0525	1.66395
$767$	−10.5699	−0.381658
$768$	−20.9546	−0.756132
$769$	18.2632	0.658588	0.329294	−	0.944227i	$-0.393189\pi$
$769$	18.2632	0.658588	0.329294	+	0.944227i	$0.393189\pi$
$770$	12.3675	0.445695
$771$	−0.394043	−0.0141911
$772$	−35.7900	−1.28811
$773$	−9.56717	−0.344107	−0.172054	−	0.985088i	$-0.555040\pi$
$773$	−9.56717	−0.344107	−0.172054	+	0.985088i	$0.555040\pi$
$774$	15.0186	0.539832
$775$	−52.0737	−1.87054
$776$	6.68488	0.239973
$777$	−11.4912	−0.412246
$778$	8.37868	0.300390
$779$	−35.9192	−1.28694
$780$	−5.57358	−0.199566
$781$	−15.2040	−0.544040
$782$	−10.7503	−0.384430
$783$	2.96226	0.105863
$784$	29.0669	1.03810
$785$	−6.36637	−0.227225
$786$	30.7620	1.09724
$787$	−42.3926	−1.51113	−0.755566	−	0.655073i	$-0.772638\pi$
$787$	−42.3926	−1.51113	−0.755566	+	0.655073i	$0.772638\pi$
$788$	−24.5933	−0.876100
$789$	31.9366	1.13697
$790$	5.17923	0.184269
$791$	−14.9818	−0.532690
$792$	1.91190	0.0679364
$793$	−13.2753	−0.471419
$794$	−43.2715	−1.53565
$795$	−11.5733	−0.410463
$796$	−27.0631	−0.959228
$797$	40.5963	1.43799	0.718997	−	0.695013i	$-0.244601\pi$
$797$	40.5963	1.43799	0.718997	+	0.695013i	$0.244601\pi$
$798$	14.0874	0.498689
$799$	−25.2057	−0.891715
$800$	79.4084	2.80751
$801$	0.765114	0.0270340
$802$	34.8993	1.23234
$803$	−5.53086	−0.195180
$804$	0.776031	0.0273685
$805$	−7.19446	−0.253571
$806$	7.83681	0.276040
$807$	7.02757	0.247382
$808$	−11.6092	−0.408409
$809$	27.1416	0.954247	0.477123	−	0.878836i	$-0.341680\pi$
$809$	27.1416	0.954247	0.477123	+	0.878836i	$0.341680\pi$
$810$	−7.57579	−0.266186
$811$	−27.9134	−0.980171	−0.490086	−	0.871674i	$-0.663035\pi$
$811$	−27.9134	−0.980171	−0.490086	+	0.871674i	$0.663035\pi$
$812$	4.07362	0.142956
$813$	27.4608	0.963092
$814$	32.8588	1.15170
$815$	35.1230	1.23030
$816$	16.8746	0.590729
$817$	61.8822	2.16498
$818$	−20.5827	−0.719657
$819$	−1.02190	−0.0357079
$820$	26.5632	0.927628
$821$	34.8352	1.21576	0.607878	−	0.794030i	$-0.292021\pi$
$821$	34.8352	1.21576	0.607878	+	0.794030i	$0.292021\pi$
$822$	−34.4941	−1.20312
$823$	−5.71931	−0.199362	−0.0996812	−	0.995019i	$-0.531782\pi$
$823$	−5.71931	−0.199362	−0.0996812	+	0.995019i	$0.531782\pi$
$824$	1.19679	0.0416921
$825$	−19.4165	−0.675996
$826$	−19.7571	−0.687436
$827$	−27.0794	−0.941643	−0.470821	−	0.882229i	$-0.656042\pi$
$827$	−27.0794	−0.941643	−0.470821	+	0.882229i	$0.656042\pi$
$828$	2.28748	0.0794954
$829$	35.2267	1.22347	0.611737	−	0.791062i	$-0.290471\pi$
$829$	35.2267	1.22347	0.611737	+	0.791062i	$0.290471\pi$
$830$	126.905	4.40495
$831$	−21.8507	−0.757992
$832$	−2.18954	−0.0759088
$833$	−20.5923	−0.713481
$834$	24.6681	0.854188
$835$	16.6305	0.575521
$836$	−16.2024	−0.560370
$837$	4.28445	0.148092
$838$	14.9953	0.518002
$839$	17.7707	0.613512	0.306756	−	0.951788i	$-0.400756\pi$
$839$	17.7707	0.613512	0.306756	+	0.951788i	$0.400756\pi$
$840$	5.06534	0.174771
$841$	−20.2250	−0.697413
$842$	52.4864	1.80880
$843$	−21.5377	−0.741798
$844$	35.4394	1.21987
$845$	4.14175	0.142481
$846$	13.3344	0.458446
$847$	8.63289	0.296630
$848$	−13.6376	−0.468316
$849$	−22.8700	−0.784895
$850$	−76.8665	−2.63650
$851$	−19.1147	−0.655243
$852$	12.8073	0.438772
$853$	−28.0295	−0.959711	−0.479856	−	0.877347i	$-0.659311\pi$
$853$	−28.0295	−0.959711	−0.479856	+	0.877347i	$0.659311\pi$
$854$	−24.8139	−0.849113
$855$	−31.2151	−1.06753
$856$	−1.16609	−0.0398563
$857$	35.0171	1.19616	0.598081	−	0.801436i	$-0.295930\pi$
$857$	35.0171	1.19616	0.598081	+	0.801436i	$0.295930\pi$
$858$	2.92208	0.0997581
$859$	−12.2000	−0.416257	−0.208129	−	0.978101i	$-0.566737\pi$
$859$	−12.2000	−0.416257	−0.208129	+	0.978101i	$0.566737\pi$
$860$	−45.7635	−1.56052
$861$	4.87027	0.165978
$862$	−53.3551	−1.81728
$863$	−13.1417	−0.447349	−0.223675	−	0.974664i	$-0.571805\pi$
$863$	−13.1417	−0.447349	−0.223675	+	0.974664i	$0.571805\pi$
$864$	−6.53346	−0.222273
$865$	49.3347	1.67743
$866$	11.4059	0.387589
$867$	5.04526	0.171346
$868$	5.89186	0.199983
$869$	−1.09216	−0.0370489
$870$	−22.4415	−0.760838
$871$	−0.576673	−0.0195398
$872$	0.477377	0.0161660
$873$	5.58569	0.189047
$874$	23.4332	0.792639
$875$	−30.2794	−1.02363
$876$	4.65902	0.157414
$877$	−39.8016	−1.34400	−0.672001	−	0.740550i	$-0.734565\pi$
$877$	−39.8016	−1.34400	−0.672001	+	0.740550i	$0.734565\pi$
$878$	41.6525	1.40570
$879$	11.2855	0.380652
$880$	−32.2920	−1.08856
$881$	48.6071	1.63762	0.818808	−	0.574067i	$-0.194635\pi$
$881$	48.6071	1.63762	0.818808	+	0.574067i	$0.194635\pi$
$882$	10.8938	0.366813
$883$	−0.638144	−0.0214753	−0.0107376	−	0.999942i	$-0.503418\pi$
$883$	−0.638144	−0.0214753	−0.0107376	+	0.999942i	$0.503418\pi$
$884$	4.65286	0.156493
$885$	43.7780	1.47158
$886$	−39.5096	−1.32735
$887$	10.4421	0.350611	0.175305	−	0.984514i	$-0.443909\pi$
$887$	10.4421	0.350611	0.175305	+	0.984514i	$0.443909\pi$
$888$	13.4579	0.451617
$889$	16.6132	0.557188
$890$	−5.79635	−0.194294
$891$	1.59753	0.0535191
$892$	34.8764	1.16775
$893$	54.9426	1.83859
$894$	38.1400	1.27559
$895$	79.2002	2.64737
$896$	9.26038	0.309368
$897$	−1.69984	−0.0567559
$898$	8.46770	0.282571
$899$	12.6917	0.423291
$900$	16.3559	0.545195
$901$	9.66148	0.321870
$902$	−13.9264	−0.463698
$903$	−8.39058	−0.279221
$904$	17.5458	0.583565
$905$	−33.8851	−1.12638
$906$	24.4671	0.812865
$907$	18.4528	0.612717	0.306358	−	0.951916i	$-0.400889\pi$
$907$	18.4528	0.612717	0.306358	+	0.951916i	$0.400889\pi$
$908$	17.8853	0.593543
$909$	−9.70026	−0.321737
$910$	7.74167	0.256634
$911$	−0.334592	−0.0110855	−0.00554276	−	0.999985i	$-0.501764\pi$
$911$	−0.334592	−0.0110855	−0.00554276	+	0.999985i	$0.501764\pi$
$912$	−36.7827	−1.21800
$913$	−26.7609	−0.885656
$914$	67.2850	2.22559
$915$	54.9830	1.81768
$916$	25.0924	0.829075
$917$	−17.1861	−0.567534
$918$	6.32432	0.208734
$919$	−36.6380	−1.20858	−0.604288	−	0.796766i	$-0.706542\pi$
$919$	−36.6380	−1.20858	−0.604288	+	0.796766i	$0.706542\pi$
$920$	8.42575	0.277789
$921$	−14.3801	−0.473840
$922$	38.7169	1.27507
$923$	−9.51719	−0.313262
$924$	2.19687	0.0722718
$925$	−136.673	−4.49379
$926$	58.1940	1.91237
$927$	1.00000	0.0328443
$928$	−19.3538	−0.635320
$929$	−29.5899	−0.970814	−0.485407	−	0.874288i	$-0.661328\pi$
$929$	−29.5899	−0.970814	−0.485407	+	0.874288i	$0.661328\pi$
$930$	−32.4581	−1.06434
$931$	44.8864	1.47109
$932$	21.9299	0.718338
$933$	3.69710	0.121038
$934$	−43.2376	−1.41478
$935$	22.8772	0.748163
$936$	1.19679	0.0391182
$937$	−40.4855	−1.32260	−0.661302	−	0.750119i	$-0.729996\pi$
$937$	−40.4855	−1.32260	−0.661302	+	0.750119i	$0.729996\pi$
$938$	−1.07790	−0.0351948
$939$	20.3947	0.665555
$940$	−40.6315	−1.32525
$941$	24.0365	0.783569	0.391784	−	0.920057i	$-0.371858\pi$
$941$	24.0365	0.783569	0.391784	+	0.920057i	$0.371858\pi$
$942$	−2.81159	−0.0916064
$943$	8.10128	0.263814
$944$	51.5864	1.67899
$945$	4.23244	0.137681
$946$	23.9926	0.780066
$947$	−5.94681	−0.193245	−0.0966226	−	0.995321i	$-0.530804\pi$
$947$	−5.94681	−0.193245	−0.0966226	+	0.995321i	$0.530804\pi$
$948$	0.919998	0.0298801
$949$	−3.46214	−0.112386
$950$	167.551	5.43608
$951$	3.12116	0.101210
$952$	−4.22858	−0.137049
$953$	−55.8904	−1.81047	−0.905233	−	0.424915i	$-0.860304\pi$
$953$	−55.8904	−1.81047	−0.905233	+	0.424915i	$0.860304\pi$
$954$	−5.11113	−0.165479
$955$	−41.1245	−1.33076
$956$	23.9723	0.775320
$957$	4.73230	0.152973
$958$	−48.9951	−1.58296
$959$	19.2712	0.622298
$960$	9.06855	0.292686
$961$	−12.6435	−0.407854
$962$	20.5686	0.663157
$963$	−0.974353	−0.0313981
$964$	25.2828	0.814304
$965$	−110.153	−3.54595
$966$	−3.17730	−0.102228
$967$	−48.7723	−1.56841	−0.784206	−	0.620500i	$-0.786930\pi$
$967$	−48.7723	−1.56841	−0.784206	+	0.620500i	$0.786930\pi$
$968$	−10.1104	−0.324959
$969$	26.0586	0.837121
$970$	−42.3160	−1.35868
$971$	2.93653	0.0942379	0.0471189	−	0.998889i	$-0.484996\pi$
$971$	2.93653	0.0942379	0.0471189	+	0.998889i	$0.484996\pi$
$972$	−1.34571	−0.0431635
$973$	−13.7816	−0.441818
$974$	64.4618	2.06549
$975$	−12.1541	−0.389243
$976$	64.7899	2.07387
$977$	0.339721	0.0108686	0.00543431	−	0.999985i	$-0.498270\pi$
$977$	0.339721	0.0108686	0.00543431	+	0.999985i	$0.498270\pi$
$978$	15.5114	0.496000
$979$	1.22229	0.0390645
$980$	−33.1947	−1.06037
$981$	0.398882	0.0127353
$982$	−47.9387	−1.52979
$983$	6.78776	0.216496	0.108248	−	0.994124i	$-0.465476\pi$
$983$	6.78776	0.216496	0.108248	+	0.994124i	$0.465476\pi$
$984$	−5.70379	−0.181830
$985$	−75.6922	−2.41175
$986$	18.7343	0.596622
$987$	−7.44965	−0.237125
$988$	−10.1422	−0.322665
$989$	−13.9570	−0.443807
$990$	−12.1025	−0.384643
$991$	−16.1804	−0.513986	−0.256993	−	0.966413i	$-0.582732\pi$
$991$	−16.1804	−0.513986	−0.256993	+	0.966413i	$0.582732\pi$
$992$	−27.9923	−0.888756
$993$	4.84998	0.153909
$994$	−17.7893	−0.564243
$995$	−83.2937	−2.64059
$996$	22.5425	0.714287
$997$	13.8327	0.438085	0.219042	−	0.975715i	$-0.429707\pi$
$997$	13.8327	0.438085	0.219042	+	0.975715i	$0.429707\pi$
$998$	−1.04193	−0.0329817
$999$	11.2450	0.355776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.6	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.82913 q^{2} -1.00000 q^{3} +1.34571 q^{4} +4.14175 q^{5} +1.82913 q^{6} -1.02190 q^{7} +1.19679 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.82913 q^{2} -1.00000 q^{3} +1.34571 q^{4} +4.14175 q^{5} +1.82913 q^{6} -1.02190 q^{7} +1.19679 q^{8} +1.00000 q^{9} -7.57579 q^{10} +1.59753 q^{11} -1.34571 q^{12} +1.00000 q^{13} +1.86918 q^{14} -4.14175 q^{15} -4.88049 q^{16} +3.45756 q^{17} -1.82913 q^{18} -7.53668 q^{19} +5.57358 q^{20} +1.02190 q^{21} -2.92208 q^{22} +1.69984 q^{23} -1.19679 q^{24} +12.1541 q^{25} -1.82913 q^{26} -1.00000 q^{27} -1.37517 q^{28} -2.96226 q^{29} +7.57579 q^{30} -4.28445 q^{31} +6.53346 q^{32} -1.59753 q^{33} -6.32432 q^{34} -4.23244 q^{35} +1.34571 q^{36} -11.2450 q^{37} +13.7856 q^{38} -1.00000 q^{39} +4.95680 q^{40} +4.76592 q^{41} -1.86918 q^{42} -8.21080 q^{43} +2.14980 q^{44} +4.14175 q^{45} -3.10922 q^{46} -7.29003 q^{47} +4.88049 q^{48} -5.95573 q^{49} -22.2314 q^{50} -3.45756 q^{51} +1.34571 q^{52} +2.79430 q^{53} +1.82913 q^{54} +6.61656 q^{55} -1.22299 q^{56} +7.53668 q^{57} +5.41836 q^{58} -10.5699 q^{59} -5.57358 q^{60} -13.2753 q^{61} +7.83681 q^{62} -1.02190 q^{63} -2.18954 q^{64} +4.14175 q^{65} +2.92208 q^{66} -0.576673 q^{67} +4.65286 q^{68} -1.69984 q^{69} +7.74167 q^{70} -9.51719 q^{71} +1.19679 q^{72} -3.46214 q^{73} +20.5686 q^{74} -12.1541 q^{75} -10.1422 q^{76} -1.63251 q^{77} +1.82913 q^{78} -0.683655 q^{79} -20.2138 q^{80} +1.00000 q^{81} -8.71747 q^{82} -16.7514 q^{83} +1.37517 q^{84} +14.3204 q^{85} +15.0186 q^{86} +2.96226 q^{87} +1.91190 q^{88} +0.765114 q^{89} -7.57579 q^{90} -1.02190 q^{91} +2.28748 q^{92} +4.28445 q^{93} +13.3344 q^{94} -31.2151 q^{95} -6.53346 q^{96} +5.58569 q^{97} +10.8938 q^{98} +1.59753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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