LMFDB - Embedded newform 4017.2.a.i.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.883592 q^{2} -1.00000 q^{3} -1.21927 q^{4} +3.49819 q^{5} -0.883592 q^{6} -3.21070 q^{7} -2.84452 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.883592 q^{2} -1.00000 q^{3} -1.21927 q^{4} +3.49819 q^{5} -0.883592 q^{6} -3.21070 q^{7} -2.84452 q^{8} +1.00000 q^{9} +3.09097 q^{10} -2.18808 q^{11} +1.21927 q^{12} -1.00000 q^{13} -2.83694 q^{14} -3.49819 q^{15} -0.0748627 q^{16} +3.52232 q^{17} +0.883592 q^{18} -0.250455 q^{19} -4.26522 q^{20} +3.21070 q^{21} -1.93337 q^{22} +1.88124 q^{23} +2.84452 q^{24} +7.23735 q^{25} -0.883592 q^{26} -1.00000 q^{27} +3.91469 q^{28} +6.65346 q^{29} -3.09097 q^{30} +8.75503 q^{31} +5.62289 q^{32} +2.18808 q^{33} +3.11230 q^{34} -11.2316 q^{35} -1.21927 q^{36} -4.14980 q^{37} -0.221300 q^{38} +1.00000 q^{39} -9.95067 q^{40} -7.71856 q^{41} +2.83694 q^{42} -6.78136 q^{43} +2.66785 q^{44} +3.49819 q^{45} +1.66225 q^{46} -4.33689 q^{47} +0.0748627 q^{48} +3.30856 q^{49} +6.39486 q^{50} -3.52232 q^{51} +1.21927 q^{52} -1.48476 q^{53} -0.883592 q^{54} -7.65432 q^{55} +9.13288 q^{56} +0.250455 q^{57} +5.87894 q^{58} -9.06390 q^{59} +4.26522 q^{60} -3.32729 q^{61} +7.73588 q^{62} -3.21070 q^{63} +5.11806 q^{64} -3.49819 q^{65} +1.93337 q^{66} -15.8488 q^{67} -4.29465 q^{68} -1.88124 q^{69} -9.92418 q^{70} -10.7615 q^{71} -2.84452 q^{72} -12.4062 q^{73} -3.66673 q^{74} -7.23735 q^{75} +0.305372 q^{76} +7.02525 q^{77} +0.883592 q^{78} -8.80691 q^{79} -0.261884 q^{80} +1.00000 q^{81} -6.82006 q^{82} +8.17582 q^{83} -3.91469 q^{84} +12.3218 q^{85} -5.99196 q^{86} -6.65346 q^{87} +6.22402 q^{88} +13.3814 q^{89} +3.09097 q^{90} +3.21070 q^{91} -2.29373 q^{92} -8.75503 q^{93} -3.83204 q^{94} -0.876141 q^{95} -5.62289 q^{96} -10.9384 q^{97} +2.92342 q^{98} -2.18808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	0.883592	0.624794	0.312397	−	0.949952i	$-0.398868\pi$
$2$	0.883592	0.624794	0.312397	+	0.949952i	$0.398868\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.21927	−0.609633
$5$	3.49819	1.56444	0.782220	−	0.623003i	$-0.214088\pi$
$5$	3.49819	1.56444	0.782220	+	0.623003i	$0.214088\pi$
$6$	−0.883592	−0.360725
$7$	−3.21070	−1.21353	−0.606764	−	0.794882i	$-0.707533\pi$
$7$	−3.21070	−1.21353	−0.606764	+	0.794882i	$0.707533\pi$
$8$	−2.84452	−1.00569
$9$	1.00000	0.333333
$10$	3.09097	0.977452
$11$	−2.18808	−0.659730	−0.329865	−	0.944028i	$-0.607003\pi$
$11$	−2.18808	−0.659730	−0.329865	+	0.944028i	$0.607003\pi$
$12$	1.21927	0.351971
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.83694	−0.758205
$15$	−3.49819	−0.903229
$16$	−0.0748627	−0.0187157
$17$	3.52232	0.854289	0.427144	−	0.904183i	$-0.359520\pi$
$17$	3.52232	0.854289	0.427144	+	0.904183i	$0.359520\pi$
$18$	0.883592	0.208265
$19$	−0.250455	−0.0574584	−0.0287292	−	0.999587i	$-0.509146\pi$
$19$	−0.250455	−0.0574584	−0.0287292	+	0.999587i	$0.509146\pi$
$20$	−4.26522	−0.953733
$21$	3.21070	0.700631
$22$	−1.93337	−0.412195
$23$	1.88124	0.392265	0.196133	−	0.980577i	$-0.437162\pi$
$23$	1.88124	0.392265	0.196133	+	0.980577i	$0.437162\pi$
$24$	2.84452	0.580635
$25$	7.23735	1.44747
$26$	−0.883592	−0.173287
$27$	−1.00000	−0.192450
$28$	3.91469	0.739807
$29$	6.65346	1.23552	0.617758	−	0.786368i	$-0.288041\pi$
$29$	6.65346	1.23552	0.617758	+	0.786368i	$0.288041\pi$
$30$	−3.09097	−0.564332
$31$	8.75503	1.57245	0.786225	−	0.617940i	$-0.212033\pi$
$31$	8.75503	1.57245	0.786225	+	0.617940i	$0.212033\pi$
$32$	5.62289	0.993995
$33$	2.18808	0.380895
$34$	3.11230	0.533755
$35$	−11.2316	−1.89849
$36$	−1.21927	−0.203211
$37$	−4.14980	−0.682222	−0.341111	−	0.940023i	$-0.610803\pi$
$37$	−4.14980	−0.682222	−0.341111	+	0.940023i	$0.610803\pi$
$38$	−0.221300	−0.0358997
$39$	1.00000	0.160128
$40$	−9.95067	−1.57334
$41$	−7.71856	−1.20544	−0.602718	−	0.797954i	$-0.705916\pi$
$41$	−7.71856	−1.20544	−0.602718	+	0.797954i	$0.705916\pi$
$42$	2.83694	0.437750
$43$	−6.78136	−1.03415	−0.517074	−	0.855941i	$-0.672979\pi$
$43$	−6.78136	−1.03415	−0.517074	+	0.855941i	$0.672979\pi$
$44$	2.66785	0.402193
$45$	3.49819	0.521480
$46$	1.66225	0.245085
$47$	−4.33689	−0.632600	−0.316300	−	0.948659i	$-0.602441\pi$
$47$	−4.33689	−0.632600	−0.316300	+	0.948659i	$0.602441\pi$
$48$	0.0748627	0.0108055
$49$	3.30856	0.472652
$50$	6.39486	0.904370
$51$	−3.52232	−0.493224
$52$	1.21927	0.169082
$53$	−1.48476	−0.203947	−0.101974	−	0.994787i	$-0.532516\pi$
$53$	−1.48476	−0.203947	−0.101974	+	0.994787i	$0.532516\pi$
$54$	−0.883592	−0.120242
$55$	−7.65432	−1.03211
$56$	9.13288	1.22043
$57$	0.250455	0.0331736
$58$	5.87894	0.771943
$59$	−9.06390	−1.18002	−0.590009	−	0.807396i	$-0.700876\pi$
$59$	−9.06390	−1.18002	−0.590009	+	0.807396i	$0.700876\pi$
$60$	4.26522	0.550638
$61$	−3.32729	−0.426016	−0.213008	−	0.977050i	$-0.568326\pi$
$61$	−3.32729	−0.426016	−0.213008	+	0.977050i	$0.568326\pi$
$62$	7.73588	0.982457
$63$	−3.21070	−0.404510
$64$	5.11806	0.639758
$65$	−3.49819	−0.433897
$66$	1.93337	0.237981
$67$	−15.8488	−1.93624	−0.968119	−	0.250492i	$-0.919407\pi$
$67$	−15.8488	−1.93624	−0.968119	+	0.250492i	$0.919407\pi$
$68$	−4.29465	−0.520802
$69$	−1.88124	−0.226474
$70$	−9.92418	−1.18617
$71$	−10.7615	−1.27716	−0.638579	−	0.769556i	$-0.720478\pi$
$71$	−10.7615	−1.27716	−0.638579	+	0.769556i	$0.720478\pi$
$72$	−2.84452	−0.335230
$73$	−12.4062	−1.45204	−0.726020	−	0.687674i	$-0.758632\pi$
$73$	−12.4062	−1.45204	−0.726020	+	0.687674i	$0.758632\pi$
$74$	−3.66673	−0.426248
$75$	−7.23735	−0.835697
$76$	0.305372	0.0350285
$77$	7.02525	0.800601
$78$	0.883592	0.100047
$79$	−8.80691	−0.990855	−0.495427	−	0.868649i	$-0.664989\pi$
$79$	−8.80691	−0.990855	−0.495427	+	0.868649i	$0.664989\pi$
$80$	−0.261884	−0.0292795
$81$	1.00000	0.111111
$82$	−6.82006	−0.753149
$83$	8.17582	0.897413	0.448707	−	0.893679i	$-0.351885\pi$
$83$	8.17582	0.897413	0.448707	+	0.893679i	$0.351885\pi$
$84$	−3.91469	−0.427128
$85$	12.3218	1.33648
$86$	−5.99196	−0.646130
$87$	−6.65346	−0.713325
$88$	6.22402	0.663483
$89$	13.3814	1.41843	0.709213	−	0.704994i	$-0.249050\pi$
$89$	13.3814	1.41843	0.709213	+	0.704994i	$0.249050\pi$
$90$	3.09097	0.325817
$91$	3.21070	0.336572
$92$	−2.29373	−0.239138
$93$	−8.75503	−0.907855
$94$	−3.83204	−0.395245
$95$	−0.876141	−0.0898902
$96$	−5.62289	−0.573883
$97$	−10.9384	−1.11062	−0.555311	−	0.831643i	$-0.687401\pi$
$97$	−10.9384	−1.11062	−0.555311	+	0.831643i	$0.687401\pi$
$98$	2.92342	0.295310
$99$	−2.18808	−0.219910
$100$	−8.82425	−0.882425
$101$	7.85878	0.781978	0.390989	−	0.920395i	$-0.372133\pi$
$101$	7.85878	0.781978	0.390989	+	0.920395i	$0.372133\pi$
$102$	−3.11230	−0.308163
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.84452	0.278928
$105$	11.2316	1.09609
$106$	−1.31192	−0.127425
$107$	−11.1684	−1.07969	−0.539843	−	0.841766i	$-0.681516\pi$
$107$	−11.1684	−1.07969	−0.539843	+	0.841766i	$0.681516\pi$
$108$	1.21927	0.117324
$109$	−6.25147	−0.598782	−0.299391	−	0.954130i	$-0.596784\pi$
$109$	−6.25147	−0.598782	−0.299391	+	0.954130i	$0.596784\pi$
$110$	−6.76329	−0.644855
$111$	4.14980	0.393881
$112$	0.240361	0.0227120
$113$	1.01044	0.0950545	0.0475273	−	0.998870i	$-0.484866\pi$
$113$	1.01044	0.0950545	0.0475273	+	0.998870i	$0.484866\pi$
$114$	0.221300	0.0207267
$115$	6.58093	0.613675
$116$	−8.11233	−0.753211
$117$	−1.00000	−0.0924500
$118$	−8.00879	−0.737269
$119$	−11.3091	−1.03670
$120$	9.95067	0.908367
$121$	−6.21232	−0.564756
$122$	−2.93997	−0.266172
$123$	7.71856	0.695959
$124$	−10.6747	−0.958617
$125$	7.82667	0.700039
$126$	−2.83694	−0.252735
$127$	1.58898	0.140999	0.0704996	−	0.997512i	$-0.477541\pi$
$127$	1.58898	0.140999	0.0704996	+	0.997512i	$0.477541\pi$
$128$	−6.72349	−0.594278
$129$	6.78136	0.597066
$130$	−3.09097	−0.271096
$131$	8.61767	0.752930	0.376465	−	0.926431i	$-0.377140\pi$
$131$	8.61767	0.752930	0.376465	+	0.926431i	$0.377140\pi$
$132$	−2.66785	−0.232206
$133$	0.804136	0.0697274
$134$	−14.0039	−1.20975
$135$	−3.49819	−0.301076
$136$	−10.0193	−0.859149
$137$	14.2004	1.21322	0.606610	−	0.795000i	$-0.292529\pi$
$137$	14.2004	1.21322	0.606610	+	0.795000i	$0.292529\pi$
$138$	−1.66225	−0.141500
$139$	−17.4027	−1.47608	−0.738039	−	0.674758i	$-0.764248\pi$
$139$	−17.4027	−1.47608	−0.738039	+	0.674758i	$0.764248\pi$
$140$	13.6943	1.15738
$141$	4.33689	0.365232
$142$	−9.50880	−0.797961
$143$	2.18808	0.182976
$144$	−0.0748627	−0.00623856
$145$	23.2751	1.93289
$146$	−10.9620	−0.907225
$147$	−3.30856	−0.272886
$148$	5.05970	0.415905
$149$	11.3364	0.928714	0.464357	−	0.885648i	$-0.346285\pi$
$149$	11.3364	0.928714	0.464357	+	0.885648i	$0.346285\pi$
$150$	−6.39486	−0.522138
$151$	20.3849	1.65890	0.829450	−	0.558581i	$-0.188654\pi$
$151$	20.3849	1.65890	0.829450	+	0.558581i	$0.188654\pi$
$152$	0.712425	0.0577853
$153$	3.52232	0.284763
$154$	6.20745	0.500211
$155$	30.6268	2.46000
$156$	−1.21927	−0.0976193
$157$	−20.9053	−1.66842	−0.834212	−	0.551444i	$-0.814077\pi$
$157$	−20.9053	−1.66842	−0.834212	+	0.551444i	$0.814077\pi$
$158$	−7.78172	−0.619080
$159$	1.48476	0.117749
$160$	19.6699	1.55504
$161$	−6.04008	−0.476025
$162$	0.883592	0.0694216
$163$	−1.35978	−0.106506	−0.0532531	−	0.998581i	$-0.516959\pi$
$163$	−1.35978	−0.106506	−0.0532531	+	0.998581i	$0.516959\pi$
$164$	9.41097	0.734873
$165$	7.65432	0.595888
$166$	7.22409	0.560698
$167$	12.6892	0.981921	0.490961	−	0.871182i	$-0.336646\pi$
$167$	12.6892	0.981921	0.490961	+	0.871182i	$0.336646\pi$
$168$	−9.13288	−0.704617
$169$	1.00000	0.0769231
$170$	10.8874	0.835026
$171$	−0.250455	−0.0191528
$172$	8.26828	0.630450
$173$	−18.1153	−1.37728	−0.688642	−	0.725101i	$-0.741793\pi$
$173$	−18.1153	−1.37728	−0.688642	+	0.725101i	$0.741793\pi$
$174$	−5.87894	−0.445681
$175$	−23.2369	−1.75655
$176$	0.163805	0.0123473
$177$	9.06390	0.681284
$178$	11.8237	0.886224
$179$	−12.1806	−0.910423	−0.455211	−	0.890383i	$-0.650436\pi$
$179$	−12.1806	−0.910423	−0.455211	+	0.890383i	$0.650436\pi$
$180$	−4.26522	−0.317911
$181$	18.3456	1.36362	0.681810	−	0.731530i	$-0.261193\pi$
$181$	18.3456	1.36362	0.681810	+	0.731530i	$0.261193\pi$
$182$	2.83694	0.210288
$183$	3.32729	0.245960
$184$	−5.35121	−0.394497
$185$	−14.5168	−1.06730
$186$	−7.73588	−0.567222
$187$	−7.70712	−0.563600
$188$	5.28782	0.385654
$189$	3.21070	0.233544
$190$	−0.774151	−0.0561628
$191$	−16.2576	−1.17636	−0.588180	−	0.808730i	$-0.700155\pi$
$191$	−16.2576	−1.17636	−0.588180	+	0.808730i	$0.700155\pi$
$192$	−5.11806	−0.369364
$193$	−21.8194	−1.57060	−0.785299	−	0.619117i	$-0.787491\pi$
$193$	−21.8194	−1.57060	−0.785299	+	0.619117i	$0.787491\pi$
$194$	−9.66504	−0.693909
$195$	3.49819	0.250511
$196$	−4.03402	−0.288144
$197$	14.6958	1.04703	0.523517	−	0.852015i	$-0.324620\pi$
$197$	14.6958	1.04703	0.523517	+	0.852015i	$0.324620\pi$
$198$	−1.93337	−0.137398
$199$	−17.8690	−1.26670	−0.633351	−	0.773864i	$-0.718321\pi$
$199$	−17.8690	−1.26670	−0.633351	+	0.773864i	$0.718321\pi$
$200$	−20.5868	−1.45570
$201$	15.8488	1.11789
$202$	6.94396	0.488575
$203$	−21.3622	−1.49933
$204$	4.29465	0.300685
$205$	−27.0010	−1.88583
$206$	−0.883592	−0.0615628
$207$	1.88124	0.130755
$208$	0.0748627	0.00519079
$209$	0.548016	0.0379070
$210$	9.92418	0.684833
$211$	2.30666	0.158797	0.0793984	−	0.996843i	$-0.474700\pi$
$211$	2.30666	0.158797	0.0793984	+	0.996843i	$0.474700\pi$
$212$	1.81031	0.124333
$213$	10.7615	0.737368
$214$	−9.86827	−0.674581
$215$	−23.7225	−1.61786
$216$	2.84452	0.193545
$217$	−28.1097	−1.90821
$218$	−5.52375	−0.374116
$219$	12.4062	0.838335
$220$	9.33264	0.629206
$221$	−3.52232	−0.236937
$222$	3.66673	0.246095
$223$	−12.9019	−0.863975	−0.431988	−	0.901880i	$-0.642188\pi$
$223$	−12.9019	−0.863975	−0.431988	+	0.901880i	$0.642188\pi$
$224$	−18.0534	−1.20624
$225$	7.23735	0.482490
$226$	0.892820	0.0593895
$227$	−3.59829	−0.238827	−0.119413	−	0.992845i	$-0.538101\pi$
$227$	−3.59829	−0.238827	−0.119413	+	0.992845i	$0.538101\pi$
$228$	−0.305372	−0.0202237
$229$	16.3904	1.08311	0.541555	−	0.840665i	$-0.317836\pi$
$229$	16.3904	1.08311	0.541555	+	0.840665i	$0.317836\pi$
$230$	5.81486	0.383421
$231$	−7.02525	−0.462227
$232$	−18.9259	−1.24254
$233$	−14.2811	−0.935583	−0.467792	−	0.883839i	$-0.654950\pi$
$233$	−14.2811	−0.935583	−0.467792	+	0.883839i	$0.654950\pi$
$234$	−0.883592	−0.0577622
$235$	−15.1713	−0.989665
$236$	11.0513	0.719378
$237$	8.80691	0.572070
$238$	−9.99264	−0.647726
$239$	−1.89979	−0.122887	−0.0614436	−	0.998111i	$-0.519570\pi$
$239$	−1.89979	−0.122887	−0.0614436	+	0.998111i	$0.519570\pi$
$240$	0.261884	0.0169045
$241$	−21.8916	−1.41016	−0.705080	−	0.709127i	$-0.749089\pi$
$241$	−21.8916	−1.41016	−0.705080	+	0.709127i	$0.749089\pi$
$242$	−5.48915	−0.352856
$243$	−1.00000	−0.0641500
$244$	4.05685	0.259713
$245$	11.5740	0.739435
$246$	6.82006	0.434831
$247$	0.250455	0.0159361
$248$	−24.9038	−1.58140
$249$	−8.17582	−0.518122
$250$	6.91559	0.437380
$251$	13.4409	0.848384	0.424192	−	0.905572i	$-0.360558\pi$
$251$	13.4409	0.848384	0.424192	+	0.905572i	$0.360558\pi$
$252$	3.91469	0.246602
$253$	−4.11630	−0.258789
$254$	1.40401	0.0880954
$255$	−12.3218	−0.771619
$256$	−16.1770	−1.01106
$257$	4.69096	0.292614	0.146307	−	0.989239i	$-0.453261\pi$
$257$	4.69096	0.292614	0.146307	+	0.989239i	$0.453261\pi$
$258$	5.99196	0.373043
$259$	13.3237	0.827896
$260$	4.26522	0.264518
$261$	6.65346	0.411839
$262$	7.61451	0.470426
$263$	21.2756	1.31191	0.655954	−	0.754801i	$-0.272267\pi$
$263$	21.2756	1.31191	0.655954	+	0.754801i	$0.272267\pi$
$264$	−6.22402	−0.383062
$265$	−5.19397	−0.319063
$266$	0.710528	0.0435653
$267$	−13.3814	−0.818929
$268$	19.3239	1.18039
$269$	0.599818	0.0365716	0.0182858	−	0.999833i	$-0.494179\pi$
$269$	0.599818	0.0365716	0.0182858	+	0.999833i	$0.494179\pi$
$270$	−3.09097	−0.188111
$271$	5.26222	0.319657	0.159829	−	0.987145i	$-0.448906\pi$
$271$	5.26222	0.319657	0.159829	+	0.987145i	$0.448906\pi$
$272$	−0.263691	−0.0159886
$273$	−3.21070	−0.194320
$274$	12.5473	0.758012
$275$	−15.8359	−0.954939
$276$	2.29373	0.138066
$277$	10.7649	0.646798	0.323399	−	0.946263i	$-0.395174\pi$
$277$	10.7649	0.646798	0.323399	+	0.946263i	$0.395174\pi$
$278$	−15.3769	−0.922245
$279$	8.75503	0.524150
$280$	31.9486	1.90929
$281$	−8.51770	−0.508124	−0.254062	−	0.967188i	$-0.581767\pi$
$281$	−8.51770	−0.508124	−0.254062	+	0.967188i	$0.581767\pi$
$282$	3.83204	0.228195
$283$	−31.1839	−1.85369	−0.926846	−	0.375441i	$-0.877491\pi$
$283$	−31.1839	−1.85369	−0.926846	+	0.375441i	$0.877491\pi$
$284$	13.1212	0.778597
$285$	0.876141	0.0518981
$286$	1.93337	0.114322
$287$	24.7819	1.46283
$288$	5.62289	0.331332
$289$	−4.59324	−0.270190
$290$	20.5657	1.20766
$291$	10.9384	0.641218
$292$	15.1265	0.885210
$293$	20.6371	1.20563	0.602817	−	0.797880i	$-0.294045\pi$
$293$	20.6371	1.20563	0.602817	+	0.797880i	$0.294045\pi$
$294$	−2.92342	−0.170497
$295$	−31.7073	−1.84607
$296$	11.8042	0.686103
$297$	2.18808	0.126965
$298$	10.0168	0.580255
$299$	−1.88124	−0.108795
$300$	8.82425	0.509468
$301$	21.7729	1.25497
$302$	18.0119	1.03647
$303$	−7.85878	−0.451475
$304$	0.0187498	0.00107537
$305$	−11.6395	−0.666476
$306$	3.11230	0.177918
$307$	31.2833	1.78543	0.892716	−	0.450619i	$-0.148797\pi$
$307$	31.2833	1.78543	0.892716	+	0.450619i	$0.148797\pi$
$308$	−8.56564	−0.488073
$309$	1.00000	0.0568880
$310$	27.0616	1.53699
$311$	−16.9223	−0.959573	−0.479786	−	0.877385i	$-0.659286\pi$
$311$	−16.9223	−0.959573	−0.479786	+	0.877385i	$0.659286\pi$
$312$	−2.84452	−0.161039
$313$	−19.3125	−1.09161	−0.545805	−	0.837912i	$-0.683776\pi$
$313$	−19.3125	−1.09161	−0.545805	+	0.837912i	$0.683776\pi$
$314$	−18.4718	−1.04242
$315$	−11.2316	−0.632831
$316$	10.7380	0.604057
$317$	5.34451	0.300177	0.150089	−	0.988673i	$-0.452044\pi$
$317$	5.34451	0.300177	0.150089	+	0.988673i	$0.452044\pi$
$318$	1.31192	0.0735689
$319$	−14.5583	−0.815107
$320$	17.9040	1.00086
$321$	11.1684	0.623357
$322$	−5.33697	−0.297418
$323$	−0.882185	−0.0490861
$324$	−1.21927	−0.0677369
$325$	−7.23735	−0.401456
$326$	−1.20149	−0.0665445
$327$	6.25147	0.345707
$328$	21.9556	1.21229
$329$	13.9244	0.767679
$330$	6.76329	0.372307
$331$	9.20608	0.506012	0.253006	−	0.967465i	$-0.418581\pi$
$331$	9.20608	0.506012	0.253006	+	0.967465i	$0.418581\pi$
$332$	−9.96850	−0.547092
$333$	−4.14980	−0.227407
$334$	11.2121	0.613498
$335$	−55.4421	−3.02912
$336$	−0.240361	−0.0131128
$337$	−1.07512	−0.0585657	−0.0292828	−	0.999571i	$-0.509322\pi$
$337$	−1.07512	−0.0585657	−0.0292828	+	0.999571i	$0.509322\pi$
$338$	0.883592	0.0480611
$339$	−1.01044	−0.0548798
$340$	−15.0235	−0.814763
$341$	−19.1567	−1.03739
$342$	−0.221300	−0.0119666
$343$	11.8521	0.639952
$344$	19.2897	1.04003
$345$	−6.58093	−0.354306
$346$	−16.0066	−0.860519
$347$	−8.82176	−0.473577	−0.236789	−	0.971561i	$-0.576095\pi$
$347$	−8.82176	−0.473577	−0.236789	+	0.971561i	$0.576095\pi$
$348$	8.11233	0.434866
$349$	18.9218	1.01286	0.506430	−	0.862281i	$-0.330965\pi$
$349$	18.9218	1.01286	0.506430	+	0.862281i	$0.330965\pi$
$350$	−20.5320	−1.09748
$351$	1.00000	0.0533761
$352$	−12.3033	−0.655769
$353$	29.9001	1.59142	0.795710	−	0.605678i	$-0.207098\pi$
$353$	29.9001	1.59142	0.795710	+	0.605678i	$0.207098\pi$
$354$	8.00879	0.425662
$355$	−37.6459	−1.99804
$356$	−16.3155	−0.864719
$357$	11.3091	0.598541
$358$	−10.7627	−0.568826
$359$	15.5015	0.818136	0.409068	−	0.912504i	$-0.365854\pi$
$359$	15.5015	0.818136	0.409068	+	0.912504i	$0.365854\pi$
$360$	−9.95067	−0.524446
$361$	−18.9373	−0.996699
$362$	16.2100	0.851981
$363$	6.21232	0.326062
$364$	−3.91469	−0.205185
$365$	−43.3994	−2.27163
$366$	2.93997	0.153675
$367$	−23.8409	−1.24448	−0.622242	−	0.782825i	$-0.713778\pi$
$367$	−23.8409	−1.24448	−0.622242	+	0.782825i	$0.713778\pi$
$368$	−0.140835	−0.00734151
$369$	−7.71856	−0.401812
$370$	−12.8269	−0.666840
$371$	4.76711	0.247496
$372$	10.6747	0.553458
$373$	3.20012	0.165696	0.0828481	−	0.996562i	$-0.473598\pi$
$373$	3.20012	0.165696	0.0828481	+	0.996562i	$0.473598\pi$
$374$	−6.80995	−0.352134
$375$	−7.82667	−0.404168
$376$	12.3364	0.636199
$377$	−6.65346	−0.342670
$378$	2.83694	0.145917
$379$	30.0076	1.54139	0.770694	−	0.637205i	$-0.219910\pi$
$379$	30.0076	1.54139	0.770694	+	0.637205i	$0.219910\pi$
$380$	1.06825	0.0548000
$381$	−1.58898	−0.0814059
$382$	−14.3651	−0.734983
$383$	19.5400	0.998448	0.499224	−	0.866473i	$-0.333619\pi$
$383$	19.5400	0.998448	0.499224	+	0.866473i	$0.333619\pi$
$384$	6.72349	0.343107
$385$	24.5757	1.25249
$386$	−19.2795	−0.981300
$387$	−6.78136	−0.344716
$388$	13.3367	0.677071
$389$	28.7168	1.45600	0.728001	−	0.685577i	$-0.240450\pi$
$389$	28.7168	1.45600	0.728001	+	0.685577i	$0.240450\pi$
$390$	3.09097	0.156518
$391$	6.62633	0.335108
$392$	−9.41126	−0.475341
$393$	−8.61767	−0.434704
$394$	12.9851	0.654180
$395$	−30.8083	−1.55013
$396$	2.66785	0.134064
$397$	13.2239	0.663691	0.331845	−	0.943334i	$-0.392329\pi$
$397$	13.2239	0.663691	0.331845	+	0.943334i	$0.392329\pi$
$398$	−15.7889	−0.791428
$399$	−0.804136	−0.0402572
$400$	−0.541807	−0.0270904
$401$	5.85698	0.292484	0.146242	−	0.989249i	$-0.453282\pi$
$401$	5.85698	0.292484	0.146242	+	0.989249i	$0.453282\pi$
$402$	14.0039	0.698449
$403$	−8.75503	−0.436119
$404$	−9.58194	−0.476719
$405$	3.49819	0.173827
$406$	−18.8755	−0.936775
$407$	9.08008	0.450083
$408$	10.0193	0.496030
$409$	−35.2245	−1.74174	−0.870868	−	0.491516i	$-0.836443\pi$
$409$	−35.2245	−1.74174	−0.870868	+	0.491516i	$0.836443\pi$
$410$	−23.8579	−1.17826
$411$	−14.2004	−0.700453
$412$	1.21927	0.0600689
$413$	29.1014	1.43199
$414$	1.66225	0.0816950
$415$	28.6006	1.40395
$416$	−5.62289	−0.275685
$417$	17.4027	0.852214
$418$	0.484222	0.0236841
$419$	−29.6305	−1.44755	−0.723773	−	0.690039i	$-0.757594\pi$
$419$	−29.6305	−1.44755	−0.723773	+	0.690039i	$0.757594\pi$
$420$	−13.6943	−0.668215
$421$	−18.0860	−0.881456	−0.440728	−	0.897641i	$-0.645280\pi$
$421$	−18.0860	−0.881456	−0.440728	+	0.897641i	$0.645280\pi$
$422$	2.03814	0.0992152
$423$	−4.33689	−0.210867
$424$	4.22342	0.205107
$425$	25.4923	1.23656
$426$	9.50880	0.460703
$427$	10.6829	0.516983
$428$	13.6172	0.658212
$429$	−2.18808	−0.105641
$430$	−20.9610	−1.01083
$431$	27.1891	1.30965	0.654825	−	0.755780i	$-0.272742\pi$
$431$	27.1891	1.30965	0.654825	+	0.755780i	$0.272742\pi$
$432$	0.0748627	0.00360183
$433$	33.5085	1.61032	0.805159	−	0.593059i	$-0.202080\pi$
$433$	33.5085	1.61032	0.805159	+	0.593059i	$0.202080\pi$
$434$	−24.8375	−1.19224
$435$	−23.2751	−1.11595
$436$	7.62220	0.365037
$437$	−0.471166	−0.0225389
$438$	10.9620	0.523787
$439$	1.27300	0.0607571	0.0303786	−	0.999538i	$-0.490329\pi$
$439$	1.27300	0.0607571	0.0303786	+	0.999538i	$0.490329\pi$
$440$	21.7728	1.03798
$441$	3.30856	0.157551
$442$	−3.11230	−0.148037
$443$	−9.53315	−0.452933	−0.226467	−	0.974019i	$-0.572717\pi$
$443$	−9.53315	−0.452933	−0.226467	+	0.974019i	$0.572717\pi$
$444$	−5.05970	−0.240123
$445$	46.8107	2.21904
$446$	−11.4000	−0.539806
$447$	−11.3364	−0.536193
$448$	−16.4325	−0.776365
$449$	1.88076	0.0887583	0.0443792	−	0.999015i	$-0.485869\pi$
$449$	1.88076	0.0887583	0.0443792	+	0.999015i	$0.485869\pi$
$450$	6.39486	0.301457
$451$	16.8888	0.795263
$452$	−1.23200	−0.0579483
$453$	−20.3849	−0.957767
$454$	−3.17942	−0.149218
$455$	11.2316	0.526547
$456$	−0.712425	−0.0333623
$457$	−20.8672	−0.976126	−0.488063	−	0.872809i	$-0.662296\pi$
$457$	−20.8672	−0.976126	−0.488063	+	0.872809i	$0.662296\pi$
$458$	14.4825	0.676721
$459$	−3.52232	−0.164408
$460$	−8.02390	−0.374116
$461$	−6.50537	−0.302985	−0.151493	−	0.988458i	$-0.548408\pi$
$461$	−6.50537	−0.302985	−0.151493	+	0.988458i	$0.548408\pi$
$462$	−6.20745	−0.288797
$463$	−23.3509	−1.08521	−0.542603	−	0.839989i	$-0.682561\pi$
$463$	−23.3509	−1.08521	−0.542603	+	0.839989i	$0.682561\pi$
$464$	−0.498096	−0.0231235
$465$	−30.6268	−1.42028
$466$	−12.6186	−0.584547
$467$	−30.7515	−1.42301	−0.711505	−	0.702681i	$-0.751986\pi$
$467$	−30.7515	−1.42301	−0.711505	+	0.702681i	$0.751986\pi$
$468$	1.21927	0.0563605
$469$	50.8856	2.34968
$470$	−13.4052	−0.618336
$471$	20.9053	0.963265
$472$	25.7824	1.18673
$473$	14.8381	0.682259
$474$	7.78172	0.357426
$475$	−1.81263	−0.0831693
$476$	13.7888	0.632009
$477$	−1.48476	−0.0679824
$478$	−1.67864	−0.0767791
$479$	−8.71799	−0.398335	−0.199168	−	0.979965i	$-0.563824\pi$
$479$	−8.71799	−0.398335	−0.199168	+	0.979965i	$0.563824\pi$
$480$	−19.6699	−0.897806
$481$	4.14980	0.189214
$482$	−19.3432	−0.881060
$483$	6.04008	0.274833
$484$	7.57446	0.344294
$485$	−38.2645	−1.73750
$486$	−0.883592	−0.0400806
$487$	−5.72147	−0.259264	−0.129632	−	0.991562i	$-0.541380\pi$
$487$	−5.72147	−0.259264	−0.129632	+	0.991562i	$0.541380\pi$
$488$	9.46453	0.428439
$489$	1.35978	0.0614914
$490$	10.2267	0.461995
$491$	−6.36864	−0.287413	−0.143706	−	0.989620i	$-0.545902\pi$
$491$	−6.36864	−0.287413	−0.143706	+	0.989620i	$0.545902\pi$
$492$	−9.41097	−0.424279
$493$	23.4356	1.05549
$494$	0.221300	0.00995678
$495$	−7.65432	−0.344036
$496$	−0.655425	−0.0294295
$497$	34.5520	1.54987
$498$	−7.22409	−0.323719
$499$	−15.0942	−0.675709	−0.337854	−	0.941198i	$-0.609701\pi$
$499$	−15.0942	−0.675709	−0.337854	+	0.941198i	$0.609701\pi$
$500$	−9.54279	−0.426766
$501$	−12.6892	−0.566912
$502$	11.8763	0.530065
$503$	−36.0280	−1.60641	−0.803205	−	0.595702i	$-0.796874\pi$
$503$	−36.0280	−1.60641	−0.803205	+	0.595702i	$0.796874\pi$
$504$	9.13288	0.406811
$505$	27.4915	1.22336
$506$	−3.63713	−0.161690
$507$	−1.00000	−0.0444116
$508$	−1.93739	−0.0859577
$509$	−2.39534	−0.106171	−0.0530857	−	0.998590i	$-0.516906\pi$
$509$	−2.39534	−0.106171	−0.0530857	+	0.998590i	$0.516906\pi$
$510$	−10.8874	−0.482103
$511$	39.8326	1.76209
$512$	−0.846841	−0.0374254
$513$	0.250455	0.0110579
$514$	4.14489	0.182823
$515$	−3.49819	−0.154149
$516$	−8.26828	−0.363991
$517$	9.48945	0.417346
$518$	11.7727	0.517265
$519$	18.1153	0.795175
$520$	9.95067	0.436366
$521$	−35.7686	−1.56705	−0.783526	−	0.621359i	$-0.786581\pi$
$521$	−35.7686	−1.56705	−0.783526	+	0.621359i	$0.786581\pi$
$522$	5.87894	0.257314
$523$	−27.5892	−1.20639	−0.603197	−	0.797593i	$-0.706107\pi$
$523$	−27.5892	−1.20639	−0.603197	+	0.797593i	$0.706107\pi$
$524$	−10.5072	−0.459010
$525$	23.2369	1.01414
$526$	18.7989	0.819672
$527$	30.8381	1.34333
$528$	−0.163805	−0.00712871
$529$	−19.4609	−0.846128
$530$	−4.58935	−0.199349
$531$	−9.06390	−0.393340
$532$	−0.980455	−0.0425081
$533$	7.71856	0.334328
$534$	−11.8237	−0.511662
$535$	−39.0691	−1.68910
$536$	45.0821	1.94725
$537$	12.1806	0.525633
$538$	0.529995	0.0228497
$539$	−7.23939	−0.311823
$540$	4.26522	0.183546
$541$	16.5445	0.711303	0.355651	−	0.934619i	$-0.384259\pi$
$541$	16.5445	0.711303	0.355651	+	0.934619i	$0.384259\pi$
$542$	4.64966	0.199720
$543$	−18.3456	−0.787286
$544$	19.8056	0.849159
$545$	−21.8689	−0.936759
$546$	−2.83694	−0.121410
$547$	42.5345	1.81864	0.909322	−	0.416093i	$-0.136601\pi$
$547$	42.5345	1.81864	0.909322	+	0.416093i	$0.136601\pi$
$548$	−17.3140	−0.739618
$549$	−3.32729	−0.142005
$550$	−13.9925	−0.596640
$551$	−1.66639	−0.0709908
$552$	5.35121	0.227763
$553$	28.2763	1.20243
$554$	9.51174	0.404115
$555$	14.5168	0.616203
$556$	21.2185	0.899865
$557$	−34.7917	−1.47417	−0.737086	−	0.675799i	$-0.763799\pi$
$557$	−34.7917	−1.47417	−0.737086	+	0.675799i	$0.763799\pi$
$558$	7.73588	0.327486
$559$	6.78136	0.286821
$560$	0.840830	0.0355316
$561$	7.70712	0.325395
$562$	−7.52618	−0.317473
$563$	−36.5956	−1.54232	−0.771160	−	0.636641i	$-0.780323\pi$
$563$	−36.5956	−1.54232	−0.771160	+	0.636641i	$0.780323\pi$
$564$	−5.28782	−0.222657
$565$	3.53473	0.148707
$566$	−27.5539	−1.15818
$567$	−3.21070	−0.134837
$568$	30.6114	1.28442
$569$	7.29939	0.306006	0.153003	−	0.988226i	$-0.451106\pi$
$569$	7.29939	0.306006	0.153003	+	0.988226i	$0.451106\pi$
$570$	0.774151	0.0324256
$571$	28.6564	1.19923	0.599617	−	0.800287i	$-0.295319\pi$
$571$	28.6564	1.19923	0.599617	+	0.800287i	$0.295319\pi$
$572$	−2.66785	−0.111548
$573$	16.2576	0.679172
$574$	21.8971	0.913968
$575$	13.6152	0.567792
$576$	5.11806	0.213253
$577$	27.9136	1.16206	0.581030	−	0.813882i	$-0.302650\pi$
$577$	27.9136	1.16206	0.581030	+	0.813882i	$0.302650\pi$
$578$	−4.05855	−0.168813
$579$	21.8194	0.906785
$580$	−28.3785	−1.17835
$581$	−26.2501	−1.08904
$582$	9.66504	0.400629
$583$	3.24877	0.134550
$584$	35.2897	1.46030
$585$	−3.49819	−0.144632
$586$	18.2348	0.753272
$587$	19.7840	0.816575	0.408287	−	0.912853i	$-0.366126\pi$
$587$	19.7840	0.816575	0.408287	+	0.912853i	$0.366126\pi$
$588$	4.03402	0.166360
$589$	−2.19275	−0.0903505
$590$	−28.0163	−1.15341
$591$	−14.6958	−0.604505
$592$	0.310665	0.0127683
$593$	22.4383	0.921429	0.460714	−	0.887548i	$-0.347593\pi$
$593$	22.4383	0.921429	0.460714	+	0.887548i	$0.347593\pi$
$594$	1.93337	0.0793270
$595$	−39.5614	−1.62186
$596$	−13.8221	−0.566174
$597$	17.8690	0.731331
$598$	−1.66225	−0.0679743
$599$	−7.95038	−0.324844	−0.162422	−	0.986721i	$-0.551931\pi$
$599$	−7.95038	−0.324844	−0.162422	+	0.986721i	$0.551931\pi$
$600$	20.5868	0.840451
$601$	10.0398	0.409533	0.204767	−	0.978811i	$-0.434356\pi$
$601$	10.0398	0.409533	0.204767	+	0.978811i	$0.434356\pi$
$602$	19.2384	0.784097
$603$	−15.8488	−0.645412
$604$	−24.8546	−1.01132
$605$	−21.7319	−0.883527
$606$	−6.94396	−0.282079
$607$	−8.93409	−0.362624	−0.181312	−	0.983426i	$-0.558034\pi$
$607$	−8.93409	−0.362624	−0.181312	+	0.983426i	$0.558034\pi$
$608$	−1.40828	−0.0571134
$609$	21.3622	0.865641
$610$	−10.2846	−0.416410
$611$	4.33689	0.175452
$612$	−4.29465	−0.173601
$613$	−22.2590	−0.899031	−0.449516	−	0.893272i	$-0.648403\pi$
$613$	−22.2590	−0.899031	−0.449516	+	0.893272i	$0.648403\pi$
$614$	27.6417	1.11553
$615$	27.0010	1.08879
$616$	−19.9834	−0.805156
$617$	−14.8835	−0.599186	−0.299593	−	0.954067i	$-0.596851\pi$
$617$	−14.8835	−0.599186	−0.299593	+	0.954067i	$0.596851\pi$
$618$	0.883592	0.0355433
$619$	31.1056	1.25024	0.625119	−	0.780529i	$-0.285050\pi$
$619$	31.1056	1.25024	0.625119	+	0.780529i	$0.285050\pi$
$620$	−37.3422	−1.49970
$621$	−1.88124	−0.0754915
$622$	−14.9524	−0.599535
$623$	−42.9636	−1.72130
$624$	−0.0748627	−0.00299691
$625$	−8.80753	−0.352301
$626$	−17.0644	−0.682031
$627$	−0.548016	−0.0218856
$628$	25.4891	1.01713
$629$	−14.6169	−0.582815
$630$	−9.92418	−0.395389
$631$	19.0440	0.758129	0.379065	−	0.925370i	$-0.376246\pi$
$631$	19.0440	0.758129	0.379065	+	0.925370i	$0.376246\pi$
$632$	25.0514	0.996491
$633$	−2.30666	−0.0916813
$634$	4.72236	0.187549
$635$	5.55856	0.220585
$636$	−1.81031	−0.0717836
$637$	−3.30856	−0.131090
$638$	−12.8636	−0.509274
$639$	−10.7615	−0.425720
$640$	−23.5201	−0.929712
$641$	−10.4272	−0.411851	−0.205926	−	0.978568i	$-0.566021\pi$
$641$	−10.4272	−0.411851	−0.205926	+	0.978568i	$0.566021\pi$
$642$	9.86827	0.389470
$643$	3.78607	0.149308	0.0746541	−	0.997209i	$-0.476215\pi$
$643$	3.78607	0.149308	0.0746541	+	0.997209i	$0.476215\pi$
$644$	7.36446	0.290200
$645$	23.7225	0.934073
$646$	−0.779492	−0.0306687
$647$	−3.45629	−0.135881	−0.0679403	−	0.997689i	$-0.521643\pi$
$647$	−3.45629	−0.135881	−0.0679403	+	0.997689i	$0.521643\pi$
$648$	−2.84452	−0.111743
$649$	19.8325	0.778494
$650$	−6.39486	−0.250827
$651$	28.1097	1.10171
$652$	1.65793	0.0649297
$653$	−27.8735	−1.09078	−0.545388	−	0.838184i	$-0.683618\pi$
$653$	−27.8735	−1.09078	−0.545388	+	0.838184i	$0.683618\pi$
$654$	5.52375	0.215996
$655$	30.1463	1.17791
$656$	0.577832	0.0225606
$657$	−12.4062	−0.484013
$658$	12.3035	0.479641
$659$	−12.2018	−0.475313	−0.237657	−	0.971349i	$-0.576379\pi$
$659$	−12.2018	−0.475313	−0.237657	+	0.971349i	$0.576379\pi$
$660$	−9.33264	−0.363272
$661$	−26.1968	−1.01894	−0.509470	−	0.860489i	$-0.670158\pi$
$661$	−26.1968	−1.01894	−0.509470	+	0.860489i	$0.670158\pi$
$662$	8.13442	0.316153
$663$	3.52232	0.136796
$664$	−23.2563	−0.902518
$665$	2.81302	0.109084
$666$	−3.66673	−0.142083
$667$	12.5167	0.484650
$668$	−15.4715	−0.598611
$669$	12.9019	0.498816
$670$	−48.9882	−1.89258
$671$	7.28037	0.281056
$672$	18.0534	0.696424
$673$	48.3654	1.86435	0.932174	−	0.362011i	$-0.117910\pi$
$673$	48.3654	1.86435	0.932174	+	0.362011i	$0.117910\pi$
$674$	−0.949970	−0.0365915
$675$	−7.23735	−0.278566
$676$	−1.21927	−0.0468948
$677$	13.0917	0.503153	0.251577	−	0.967837i	$-0.419051\pi$
$677$	13.0917	0.503153	0.251577	+	0.967837i	$0.419051\pi$
$678$	−0.892820	−0.0342885
$679$	35.1197	1.34777
$680$	−35.0495	−1.34409
$681$	3.59829	0.137887
$682$	−16.9267	−0.648157
$683$	−27.5870	−1.05559	−0.527793	−	0.849373i	$-0.676980\pi$
$683$	−27.5870	−1.05559	−0.527793	+	0.849373i	$0.676980\pi$
$684$	0.305372	0.0116762
$685$	49.6756	1.89801
$686$	10.4724	0.399838
$687$	−16.3904	−0.625334
$688$	0.507671	0.0193548
$689$	1.48476	0.0565648
$690$	−5.81486	−0.221368
$691$	−22.1164	−0.841348	−0.420674	−	0.907212i	$-0.638206\pi$
$691$	−22.1164	−0.841348	−0.420674	+	0.907212i	$0.638206\pi$
$692$	22.0874	0.839637
$693$	7.02525	0.266867
$694$	−7.79484	−0.295888
$695$	−60.8780	−2.30923
$696$	18.9259	0.717383
$697$	−27.1873	−1.02979
$698$	16.7191	0.632829
$699$	14.2811	0.540159
$700$	28.3320	1.07085
$701$	14.9690	0.565371	0.282686	−	0.959213i	$-0.408775\pi$
$701$	14.9690	0.565371	0.282686	+	0.959213i	$0.408775\pi$
$702$	0.883592	0.0333490
$703$	1.03934	0.0391994
$704$	−11.1987	−0.422068
$705$	15.1713	0.571383
$706$	26.4194	0.994309
$707$	−25.2322	−0.948953
$708$	−11.0513	−0.415333
$709$	25.9078	0.972989	0.486495	−	0.873684i	$-0.338275\pi$
$709$	25.9078	0.972989	0.486495	+	0.873684i	$0.338275\pi$
$710$	−33.2636	−1.24836
$711$	−8.80691	−0.330285
$712$	−38.0636	−1.42650
$713$	16.4703	0.616818
$714$	9.99264	0.373965
$715$	7.65432	0.286255
$716$	14.8514	0.555023
$717$	1.89979	0.0709489
$718$	13.6970	0.511166
$719$	−3.61959	−0.134988	−0.0674940	−	0.997720i	$-0.521500\pi$
$719$	−3.61959	−0.134988	−0.0674940	+	0.997720i	$0.521500\pi$
$720$	−0.261884	−0.00975984
$721$	3.21070	0.119573
$722$	−16.7328	−0.622731
$723$	21.8916	0.814157
$724$	−22.3682	−0.831307
$725$	48.1534	1.78837
$726$	5.48915	0.203722
$727$	10.6075	0.393409	0.196704	−	0.980463i	$-0.436976\pi$
$727$	10.6075	0.393409	0.196704	+	0.980463i	$0.436976\pi$
$728$	−9.13288	−0.338487
$729$	1.00000	0.0370370
$730$	−38.3473	−1.41930
$731$	−23.8862	−0.883461
$732$	−4.05685	−0.149945
$733$	−5.85899	−0.216407	−0.108203	−	0.994129i	$-0.534510\pi$
$733$	−5.85899	−0.216407	−0.108203	+	0.994129i	$0.534510\pi$
$734$	−21.0656	−0.777546
$735$	−11.5740	−0.426913
$736$	10.5780	0.389910
$737$	34.6784	1.27739
$738$	−6.82006	−0.251050
$739$	17.2533	0.634672	0.317336	−	0.948313i	$-0.397212\pi$
$739$	17.2533	0.634672	0.317336	+	0.948313i	$0.397212\pi$
$740$	17.6998	0.650658
$741$	−0.250455	−0.00920071
$742$	4.21218	0.154634
$743$	42.6980	1.56644	0.783219	−	0.621746i	$-0.213576\pi$
$743$	42.6980	1.56644	0.783219	+	0.621746i	$0.213576\pi$
$744$	24.9038	0.913019
$745$	39.6569	1.45292
$746$	2.82760	0.103526
$747$	8.17582	0.299138
$748$	9.39702	0.343589
$749$	35.8582	1.31023
$750$	−6.91559	−0.252522
$751$	22.7947	0.831792	0.415896	−	0.909412i	$-0.363468\pi$
$751$	22.7947	0.831792	0.415896	+	0.909412i	$0.363468\pi$
$752$	0.324671	0.0118395
$753$	−13.4409	−0.489815
$754$	−5.87894	−0.214098
$755$	71.3103	2.59525
$756$	−3.91469	−0.142376
$757$	47.4652	1.72515	0.862576	−	0.505927i	$-0.168850\pi$
$757$	47.4652	1.72515	0.862576	+	0.505927i	$0.168850\pi$
$758$	26.5145	0.963050
$759$	4.11630	0.149412
$760$	2.49220	0.0904015
$761$	−21.8743	−0.792944	−0.396472	−	0.918047i	$-0.629766\pi$
$761$	−21.8743	−0.792944	−0.396472	+	0.918047i	$0.629766\pi$
$762$	−1.40401	−0.0508619
$763$	20.0716	0.726640
$764$	19.8223	0.717147
$765$	12.3218	0.445494
$766$	17.2654	0.623824
$767$	9.06390	0.327278
$768$	16.1770	0.583735
$769$	−37.9828	−1.36969	−0.684847	−	0.728687i	$-0.740131\pi$
$769$	−37.9828	−1.36969	−0.684847	+	0.728687i	$0.740131\pi$
$770$	21.7149	0.782550
$771$	−4.69096	−0.168941
$772$	26.6037	0.957487
$773$	−3.06838	−0.110362	−0.0551810	−	0.998476i	$-0.517574\pi$
$773$	−3.06838	−0.110362	−0.0551810	+	0.998476i	$0.517574\pi$
$774$	−5.99196	−0.215377
$775$	63.3632	2.27607
$776$	31.1143	1.11694
$777$	−13.3237	−0.477986
$778$	25.3740	0.909701
$779$	1.93315	0.0692624
$780$	−4.26522	−0.152719
$781$	23.5471	0.842580
$782$	5.85497	0.209373
$783$	−6.65346	−0.237775
$784$	−0.247688	−0.00884600
$785$	−73.1307	−2.61015
$786$	−7.61451	−0.271600
$787$	12.8243	0.457136	0.228568	−	0.973528i	$-0.426596\pi$
$787$	12.8243	0.457136	0.228568	+	0.973528i	$0.426596\pi$
$788$	−17.9181	−0.638306
$789$	−21.2756	−0.757430
$790$	−27.2219	−0.968513
$791$	−3.24423	−0.115351
$792$	6.22402	0.221161
$793$	3.32729	0.118156
$794$	11.6846	0.414670
$795$	5.19397	0.184211
$796$	21.7871	0.772223
$797$	13.0388	0.461858	0.230929	−	0.972971i	$-0.425823\pi$
$797$	13.0388	0.461858	0.230929	+	0.972971i	$0.425823\pi$
$798$	−0.710528	−0.0251524
$799$	−15.2759	−0.540423
$800$	40.6948	1.43878
$801$	13.3814	0.472809
$802$	5.17518	0.182742
$803$	27.1458	0.957954
$804$	−19.3239	−0.681500
$805$	−21.1294	−0.744712
$806$	−7.73588	−0.272485
$807$	−0.599818	−0.0211146
$808$	−22.3544	−0.786427
$809$	39.6784	1.39502	0.697510	−	0.716575i	$-0.254291\pi$
$809$	39.6784	1.39502	0.697510	+	0.716575i	$0.254291\pi$
$810$	3.09097	0.108606
$811$	39.4041	1.38366	0.691832	−	0.722059i	$-0.256804\pi$
$811$	39.4041	1.38366	0.691832	+	0.722059i	$0.256804\pi$
$812$	26.0462	0.914043
$813$	−5.26222	−0.184554
$814$	8.02308	0.281209
$815$	−4.75677	−0.166623
$816$	0.263691	0.00923102
$817$	1.69843	0.0594205
$818$	−31.1240	−1.08823
$819$	3.21070	0.112191
$820$	32.9214	1.14966
$821$	−16.1334	−0.563059	−0.281529	−	0.959553i	$-0.590842\pi$
$821$	−16.1334	−0.563059	−0.281529	+	0.959553i	$0.590842\pi$
$822$	−12.5473	−0.437639
$823$	0.850556	0.0296485	0.0148243	−	0.999890i	$-0.495281\pi$
$823$	0.850556	0.0296485	0.0148243	+	0.999890i	$0.495281\pi$
$824$	2.84452	0.0990934
$825$	15.8359	0.551334
$826$	25.7138	0.894697
$827$	30.8939	1.07429	0.537143	−	0.843491i	$-0.319503\pi$
$827$	30.8939	1.07429	0.537143	+	0.843491i	$0.319503\pi$
$828$	−2.29373	−0.0797126
$829$	18.3507	0.637347	0.318673	−	0.947865i	$-0.396763\pi$
$829$	18.3507	0.637347	0.318673	+	0.947865i	$0.396763\pi$
$830$	25.2713	0.877178
$831$	−10.7649	−0.373429
$832$	−5.11806	−0.177437
$833$	11.6538	0.403781
$834$	15.3769	0.532458
$835$	44.3893	1.53616
$836$	−0.668177	−0.0231094
$837$	−8.75503	−0.302618
$838$	−26.1813	−0.904417
$839$	−47.3700	−1.63540	−0.817698	−	0.575648i	$-0.804750\pi$
$839$	−47.3700	−1.63540	−0.817698	+	0.575648i	$0.804750\pi$
$840$	−31.9486	−1.10233
$841$	15.2685	0.526499
$842$	−15.9806	−0.550728
$843$	8.51770	0.293365
$844$	−2.81242	−0.0968077
$845$	3.49819	0.120341
$846$	−3.83204	−0.131748
$847$	19.9459	0.685348
$848$	0.111153	0.00381701
$849$	31.1839	1.07023
$850$	22.5248	0.772593
$851$	−7.80676	−0.267612
$852$	−13.1212	−0.449523
$853$	−23.1684	−0.793270	−0.396635	−	0.917976i	$-0.629822\pi$
$853$	−23.1684	−0.793270	−0.396635	+	0.917976i	$0.629822\pi$
$854$	9.43934	0.323008
$855$	−0.876141	−0.0299634
$856$	31.7686	1.08583
$857$	5.46845	0.186799	0.0933994	−	0.995629i	$-0.470227\pi$
$857$	5.46845	0.186799	0.0933994	+	0.995629i	$0.470227\pi$
$858$	−1.93337	−0.0660041
$859$	−37.7017	−1.28637	−0.643183	−	0.765713i	$-0.722386\pi$
$859$	−37.7017	−1.28637	−0.643183	+	0.765713i	$0.722386\pi$
$860$	28.9240	0.986301
$861$	−24.7819	−0.844566
$862$	24.0240	0.818262
$863$	−38.4258	−1.30803	−0.654014	−	0.756482i	$-0.726916\pi$
$863$	−38.4258	−1.30803	−0.654014	+	0.756482i	$0.726916\pi$
$864$	−5.62289	−0.191294
$865$	−63.3710	−2.15468
$866$	29.6079	1.00612
$867$	4.59324	0.155995
$868$	34.2732	1.16331
$869$	19.2702	0.653697
$870$	−20.5657	−0.697241
$871$	15.8488	0.537016
$872$	17.7824	0.602189
$873$	−10.9384	−0.370207
$874$	−0.416319	−0.0140822
$875$	−25.1291	−0.849517
$876$	−15.1265	−0.511076
$877$	−29.9942	−1.01283	−0.506416	−	0.862289i	$-0.669030\pi$
$877$	−29.9942	−1.01283	−0.506416	+	0.862289i	$0.669030\pi$
$878$	1.12482	0.0379607
$879$	−20.6371	−0.696073
$880$	0.573023	0.0193166
$881$	−19.4865	−0.656518	−0.328259	−	0.944588i	$-0.606462\pi$
$881$	−19.4865	−0.656518	−0.328259	+	0.944588i	$0.606462\pi$
$882$	2.92342	0.0984367
$883$	−38.3852	−1.29176	−0.645882	−	0.763437i	$-0.723510\pi$
$883$	−38.3852	−1.29176	−0.645882	+	0.763437i	$0.723510\pi$
$884$	4.29465	0.144445
$885$	31.7073	1.06583
$886$	−8.42341	−0.282990
$887$	1.24169	0.0416920	0.0208460	−	0.999783i	$-0.493364\pi$
$887$	1.24169	0.0416920	0.0208460	+	0.999783i	$0.493364\pi$
$888$	−11.8042	−0.396122
$889$	−5.10173	−0.171107
$890$	41.3616	1.38644
$891$	−2.18808	−0.0733034
$892$	15.7308	0.526707
$893$	1.08620	0.0363482
$894$	−10.0168	−0.335010
$895$	−42.6102	−1.42430
$896$	21.5871	0.721174
$897$	1.88124	0.0628127
$898$	1.66182	0.0554557
$899$	58.2512	1.94279
$900$	−8.82425	−0.294142
$901$	−5.22980	−0.174230
$902$	14.9228	0.496875
$903$	−21.7729	−0.724556
$904$	−2.87422	−0.0955953
$905$	64.1765	2.13330
$906$	−18.0119	−0.598407
$907$	−16.8992	−0.561130	−0.280565	−	0.959835i	$-0.590522\pi$
$907$	−16.8992	−0.561130	−0.280565	+	0.959835i	$0.590522\pi$
$908$	4.38727	0.145597
$909$	7.85878	0.260659
$910$	9.92418	0.328983
$911$	40.3887	1.33814	0.669069	−	0.743200i	$-0.266693\pi$
$911$	40.3887	1.33814	0.669069	+	0.743200i	$0.266693\pi$
$912$	−0.0187498	−0.000620867 0
$913$	−17.8893	−0.592051
$914$	−18.4381	−0.609877
$915$	11.6395	0.384790
$916$	−19.9843	−0.660299
$917$	−27.6687	−0.913702
$918$	−3.11230	−0.102721
$919$	−14.8927	−0.491265	−0.245633	−	0.969363i	$-0.578996\pi$
$919$	−14.8927	−0.491265	−0.245633	+	0.969363i	$0.578996\pi$
$920$	−18.7196	−0.617166
$921$	−31.2833	−1.03082
$922$	−5.74809	−0.189303
$923$	10.7615	0.354220
$924$	8.56564	0.281789
$925$	−30.0335	−0.987496
$926$	−20.6326	−0.678031
$927$	−1.00000	−0.0328443
$928$	37.4116	1.22810
$929$	18.7737	0.615944	0.307972	−	0.951395i	$-0.400350\pi$
$929$	18.7737	0.615944	0.307972	+	0.951395i	$0.400350\pi$
$930$	−27.0616	−0.887384
$931$	−0.828648	−0.0271578
$932$	17.4124	0.570362
$933$	16.9223	0.554010
$934$	−27.1718	−0.889088
$935$	−26.9610	−0.881718
$936$	2.84452	0.0929759
$937$	24.3704	0.796145	0.398073	−	0.917354i	$-0.369679\pi$
$937$	24.3704	0.796145	0.398073	+	0.917354i	$0.369679\pi$
$938$	44.9621	1.46807
$939$	19.3125	0.630241
$940$	18.4978	0.603332
$941$	19.1162	0.623169	0.311584	−	0.950218i	$-0.399140\pi$
$941$	19.1162	0.623169	0.311584	+	0.950218i	$0.399140\pi$
$942$	18.4718	0.601842
$943$	−14.5204	−0.472851
$944$	0.678548	0.0220848
$945$	11.2316	0.365365
$946$	13.1109	0.426271
$947$	26.0502	0.846518	0.423259	−	0.906009i	$-0.360886\pi$
$947$	26.0502	0.846518	0.423259	+	0.906009i	$0.360886\pi$
$948$	−10.7380	−0.348753
$949$	12.4062	0.402723
$950$	−1.60163	−0.0519637
$951$	−5.34451	−0.173307
$952$	32.1689	1.04260
$953$	−25.0042	−0.809965	−0.404982	−	0.914324i	$-0.632722\pi$
$953$	−25.0042	−0.809965	−0.404982	+	0.914324i	$0.632722\pi$
$954$	−1.31192	−0.0424750
$955$	−56.8723	−1.84034
$956$	2.31635	0.0749160
$957$	14.5583	0.470602
$958$	−7.70315	−0.248878
$959$	−45.5931	−1.47228
$960$	−17.9040	−0.577848
$961$	45.6506	1.47260
$962$	3.66673	0.118220
$963$	−11.1684	−0.359895
$964$	26.6916	0.859680
$965$	−76.3286	−2.45710
$966$	5.33697	0.171714
$967$	28.9927	0.932341	0.466170	−	0.884695i	$-0.345633\pi$
$967$	28.9927	0.932341	0.466170	+	0.884695i	$0.345633\pi$
$968$	17.6710	0.567969
$969$	0.882185	0.0283399
$970$	−33.8102	−1.08558
$971$	17.0828	0.548212	0.274106	−	0.961700i	$-0.411618\pi$
$971$	17.0828	0.548212	0.274106	+	0.961700i	$0.411618\pi$
$972$	1.21927	0.0391079
$973$	55.8748	1.79126
$974$	−5.05544	−0.161987
$975$	7.23735	0.231781
$976$	0.249090	0.00797318
$977$	49.9703	1.59869	0.799346	−	0.600871i	$-0.205179\pi$
$977$	49.9703	1.59869	0.799346	+	0.600871i	$0.205179\pi$
$978$	1.20149	0.0384195
$979$	−29.2796	−0.935778
$980$	−14.1118	−0.450784
$981$	−6.25147	−0.199594
$982$	−5.62728	−0.179574
$983$	−54.6374	−1.74266	−0.871332	−	0.490694i	$-0.836743\pi$
$983$	−54.6374	−1.74266	−0.871332	+	0.490694i	$0.836743\pi$
$984$	−21.9556	−0.699918
$985$	51.4088	1.63802
$986$	20.7075	0.659462
$987$	−13.9244	−0.443219
$988$	−0.305372	−0.00971516
$989$	−12.7574	−0.405661
$990$	−6.76329	−0.214952
$991$	13.5615	0.430796	0.215398	−	0.976526i	$-0.430895\pi$
$991$	13.5615	0.430796	0.215398	+	0.976526i	$0.430895\pi$
$992$	49.2286	1.56301
$993$	−9.20608	−0.292146
$994$	30.5299	0.968349
$995$	−62.5093	−1.98168
$996$	9.96850	0.315864
$997$	−18.7549	−0.593973	−0.296987	−	0.954882i	$-0.595982\pi$
$997$	−18.7549	−0.593973	−0.296987	+	0.954882i	$0.595982\pi$
$998$	−13.3371	−0.422179
$999$	4.14980	0.131294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.17	✓	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)

\(f(q)\)	\(=\)	\(q+0.883592 q^{2} -1.00000 q^{3} -1.21927 q^{4} +3.49819 q^{5} -0.883592 q^{6} -3.21070 q^{7} -2.84452 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.883592 q^{2} -1.00000 q^{3} -1.21927 q^{4} +3.49819 q^{5} -0.883592 q^{6} -3.21070 q^{7} -2.84452 q^{8} +1.00000 q^{9} +3.09097 q^{10} -2.18808 q^{11} +1.21927 q^{12} -1.00000 q^{13} -2.83694 q^{14} -3.49819 q^{15} -0.0748627 q^{16} +3.52232 q^{17} +0.883592 q^{18} -0.250455 q^{19} -4.26522 q^{20} +3.21070 q^{21} -1.93337 q^{22} +1.88124 q^{23} +2.84452 q^{24} +7.23735 q^{25} -0.883592 q^{26} -1.00000 q^{27} +3.91469 q^{28} +6.65346 q^{29} -3.09097 q^{30} +8.75503 q^{31} +5.62289 q^{32} +2.18808 q^{33} +3.11230 q^{34} -11.2316 q^{35} -1.21927 q^{36} -4.14980 q^{37} -0.221300 q^{38} +1.00000 q^{39} -9.95067 q^{40} -7.71856 q^{41} +2.83694 q^{42} -6.78136 q^{43} +2.66785 q^{44} +3.49819 q^{45} +1.66225 q^{46} -4.33689 q^{47} +0.0748627 q^{48} +3.30856 q^{49} +6.39486 q^{50} -3.52232 q^{51} +1.21927 q^{52} -1.48476 q^{53} -0.883592 q^{54} -7.65432 q^{55} +9.13288 q^{56} +0.250455 q^{57} +5.87894 q^{58} -9.06390 q^{59} +4.26522 q^{60} -3.32729 q^{61} +7.73588 q^{62} -3.21070 q^{63} +5.11806 q^{64} -3.49819 q^{65} +1.93337 q^{66} -15.8488 q^{67} -4.29465 q^{68} -1.88124 q^{69} -9.92418 q^{70} -10.7615 q^{71} -2.84452 q^{72} -12.4062 q^{73} -3.66673 q^{74} -7.23735 q^{75} +0.305372 q^{76} +7.02525 q^{77} +0.883592 q^{78} -8.80691 q^{79} -0.261884 q^{80} +1.00000 q^{81} -6.82006 q^{82} +8.17582 q^{83} -3.91469 q^{84} +12.3218 q^{85} -5.99196 q^{86} -6.65346 q^{87} +6.22402 q^{88} +13.3814 q^{89} +3.09097 q^{90} +3.21070 q^{91} -2.29373 q^{92} -8.75503 q^{93} -3.83204 q^{94} -0.876141 q^{95} -5.62289 q^{96} -10.9384 q^{97} +2.92342 q^{98} -2.18808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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