LMFDB - Embedded newform 4017.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +3.54292 q^{10} +4.39855 q^{11} +0.295718 q^{12} +1.00000 q^{13} +3.83151 q^{14} -2.71388 q^{15} -3.32111 q^{16} +7.00308 q^{17} +1.30548 q^{18} +2.39267 q^{19} -0.802544 q^{20} -2.93494 q^{21} +5.74223 q^{22} -3.41270 q^{23} +2.99702 q^{24} +2.36516 q^{25} +1.30548 q^{26} -1.00000 q^{27} -0.867916 q^{28} +4.65913 q^{29} -3.54292 q^{30} -2.86740 q^{31} +1.65838 q^{32} -4.39855 q^{33} +9.14239 q^{34} +7.96509 q^{35} -0.295718 q^{36} +4.87509 q^{37} +3.12358 q^{38} -1.00000 q^{39} -8.13355 q^{40} -9.26951 q^{41} -3.83151 q^{42} -0.300510 q^{43} -1.30073 q^{44} +2.71388 q^{45} -4.45522 q^{46} -6.75031 q^{47} +3.32111 q^{48} +1.61389 q^{49} +3.08767 q^{50} -7.00308 q^{51} -0.295718 q^{52} -9.66362 q^{53} -1.30548 q^{54} +11.9372 q^{55} -8.79608 q^{56} -2.39267 q^{57} +6.08240 q^{58} +0.569872 q^{59} +0.802544 q^{60} -5.37556 q^{61} -3.74333 q^{62} +2.93494 q^{63} +8.80722 q^{64} +2.71388 q^{65} -5.74223 q^{66} +10.6429 q^{67} -2.07094 q^{68} +3.41270 q^{69} +10.3983 q^{70} +5.14090 q^{71} -2.99702 q^{72} -9.70296 q^{73} +6.36434 q^{74} -2.36516 q^{75} -0.707555 q^{76} +12.9095 q^{77} -1.30548 q^{78} +11.5440 q^{79} -9.01311 q^{80} +1.00000 q^{81} -12.1012 q^{82} +6.57810 q^{83} +0.867916 q^{84} +19.0055 q^{85} -0.392310 q^{86} -4.65913 q^{87} -13.1825 q^{88} +10.8369 q^{89} +3.54292 q^{90} +2.93494 q^{91} +1.00920 q^{92} +2.86740 q^{93} -8.81241 q^{94} +6.49342 q^{95} -1.65838 q^{96} +1.43594 q^{97} +2.10691 q^{98} +4.39855 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.30548	0.923115	0.461557	−	0.887110i	$-0.347291\pi$
$2$	1.30548	0.923115	0.461557	+	0.887110i	$0.347291\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.295718	−0.147859
$5$	2.71388	1.21369	0.606843	−	0.794822i	$-0.292436\pi$
$5$	2.71388	1.21369	0.606843	+	0.794822i	$0.292436\pi$
$6$	−1.30548	−0.532961
$7$	2.93494	1.10930	0.554652	−	0.832082i	$-0.312851\pi$
$7$	2.93494	1.10930	0.554652	+	0.832082i	$0.312851\pi$
$8$	−2.99702	−1.05961
$9$	1.00000	0.333333
$10$	3.54292	1.12037
$11$	4.39855	1.32621	0.663107	−	0.748525i	$-0.269237\pi$
$11$	4.39855	1.32621	0.663107	+	0.748525i	$0.269237\pi$
$12$	0.295718	0.0853665
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.83151	1.02402
$15$	−2.71388	−0.700721
$16$	−3.32111	−0.830279
$17$	7.00308	1.69850	0.849248	−	0.527994i	$-0.177056\pi$
$17$	7.00308	1.69850	0.849248	+	0.527994i	$0.177056\pi$
$18$	1.30548	0.307705
$19$	2.39267	0.548916	0.274458	−	0.961599i	$-0.411502\pi$
$19$	2.39267	0.548916	0.274458	+	0.961599i	$0.411502\pi$
$20$	−0.802544	−0.179454
$21$	−2.93494	−0.640457
$22$	5.74223	1.22425
$23$	−3.41270	−0.711598	−0.355799	−	0.934562i	$-0.615791\pi$
$23$	−3.41270	−0.711598	−0.355799	+	0.934562i	$0.615791\pi$
$24$	2.99702	0.611764
$25$	2.36516	0.473031
$26$	1.30548	0.256026
$27$	−1.00000	−0.192450
$28$	−0.867916	−0.164021
$29$	4.65913	0.865178	0.432589	−	0.901591i	$-0.357600\pi$
$29$	4.65913	0.865178	0.432589	+	0.901591i	$0.357600\pi$
$30$	−3.54292	−0.646846
$31$	−2.86740	−0.515000	−0.257500	−	0.966278i	$-0.582899\pi$
$31$	−2.86740	−0.515000	−0.257500	+	0.966278i	$0.582899\pi$
$32$	1.65838	0.293163
$33$	−4.39855	−0.765690
$34$	9.14239	1.56791
$35$	7.96509	1.34635
$36$	−0.295718	−0.0492864
$37$	4.87509	0.801460	0.400730	−	0.916196i	$-0.368757\pi$
$37$	4.87509	0.801460	0.400730	+	0.916196i	$0.368757\pi$
$38$	3.12358	0.506712
$39$	−1.00000	−0.160128
$40$	−8.13355	−1.28603
$41$	−9.26951	−1.44765	−0.723827	−	0.689981i	$-0.757619\pi$
$41$	−9.26951	−1.44765	−0.723827	+	0.689981i	$0.757619\pi$
$42$	−3.83151	−0.591216
$43$	−0.300510	−0.0458273	−0.0229136	−	0.999737i	$-0.507294\pi$
$43$	−0.300510	−0.0458273	−0.0229136	+	0.999737i	$0.507294\pi$
$44$	−1.30073	−0.196093
$45$	2.71388	0.404562
$46$	−4.45522	−0.656887
$47$	−6.75031	−0.984634	−0.492317	−	0.870416i	$-0.663850\pi$
$47$	−6.75031	−0.984634	−0.492317	+	0.870416i	$0.663850\pi$
$48$	3.32111	0.479362
$49$	1.61389	0.230556
$50$	3.08767	0.436662
$51$	−7.00308	−0.980627
$52$	−0.295718	−0.0410087
$53$	−9.66362	−1.32740	−0.663700	−	0.747999i	$-0.731015\pi$
$53$	−9.66362	−1.32740	−0.663700	+	0.747999i	$0.731015\pi$
$54$	−1.30548	−0.177654
$55$	11.9372	1.60961
$56$	−8.79608	−1.17543
$57$	−2.39267	−0.316917
$58$	6.08240	0.798659
$59$	0.569872	0.0741911	0.0370955	−	0.999312i	$-0.488189\pi$
$59$	0.569872	0.0741911	0.0370955	+	0.999312i	$0.488189\pi$
$60$	0.802544	0.103608
$61$	−5.37556	−0.688270	−0.344135	−	0.938920i	$-0.611828\pi$
$61$	−5.37556	−0.688270	−0.344135	+	0.938920i	$0.611828\pi$
$62$	−3.74333	−0.475404
$63$	2.93494	0.369768
$64$	8.80722	1.10090
$65$	2.71388	0.336616
$66$	−5.74223	−0.706820
$67$	10.6429	1.30023	0.650117	−	0.759834i	$-0.274720\pi$
$67$	10.6429	1.30023	0.650117	+	0.759834i	$0.274720\pi$
$68$	−2.07094	−0.251138
$69$	3.41270	0.410841
$70$	10.3983	1.24283
$71$	5.14090	0.610113	0.305056	−	0.952334i	$-0.401325\pi$
$71$	5.14090	0.610113	0.305056	+	0.952334i	$0.401325\pi$
$72$	−2.99702	−0.353202
$73$	−9.70296	−1.13565	−0.567823	−	0.823151i	$-0.692214\pi$
$73$	−9.70296	−1.13565	−0.567823	+	0.823151i	$0.692214\pi$
$74$	6.36434	0.739839
$75$	−2.36516	−0.273105
$76$	−0.707555	−0.0811622
$77$	12.9095	1.47117
$78$	−1.30548	−0.147817
$79$	11.5440	1.29880	0.649398	−	0.760449i	$-0.275021\pi$
$79$	11.5440	1.29880	0.649398	+	0.760449i	$0.275021\pi$
$80$	−9.01311	−1.00770
$81$	1.00000	0.111111
$82$	−12.1012	−1.33635
$83$	6.57810	0.722041	0.361020	−	0.932558i	$-0.382429\pi$
$83$	6.57810	0.722041	0.361020	+	0.932558i	$0.382429\pi$
$84$	0.867916	0.0946974
$85$	19.0055	2.06144
$86$	−0.392310	−0.0423038
$87$	−4.65913	−0.499511
$88$	−13.1825	−1.40526
$89$	10.8369	1.14871	0.574355	−	0.818606i	$-0.305253\pi$
$89$	10.8369	1.14871	0.574355	+	0.818606i	$0.305253\pi$
$90$	3.54292	0.373457
$91$	2.93494	0.307666
$92$	1.00920	0.105216
$93$	2.86740	0.297335
$94$	−8.81241	−0.908931
$95$	6.49342	0.666211
$96$	−1.65838	−0.169258
$97$	1.43594	0.145798	0.0728988	−	0.997339i	$-0.476775\pi$
$97$	1.43594	0.145798	0.0728988	+	0.997339i	$0.476775\pi$
$98$	2.10691	0.212830
$99$	4.39855	0.442071
$100$	−0.699420	−0.0699420
$101$	−1.63848	−0.163035	−0.0815175	−	0.996672i	$-0.525977\pi$
$101$	−1.63848	−0.163035	−0.0815175	+	0.996672i	$0.525977\pi$
$102$	−9.14239	−0.905232
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.99702	−0.293882
$105$	−7.96509	−0.777313
$106$	−12.6157	−1.22534
$107$	8.71561	0.842570	0.421285	−	0.906928i	$-0.361579\pi$
$107$	8.71561	0.842570	0.421285	+	0.906928i	$0.361579\pi$
$108$	0.295718	0.0284555
$109$	−2.63094	−0.251998	−0.125999	−	0.992030i	$-0.540214\pi$
$109$	−2.63094	−0.251998	−0.125999	+	0.992030i	$0.540214\pi$
$110$	15.5837	1.48585
$111$	−4.87509	−0.462723
$112$	−9.74728	−0.921032
$113$	3.01548	0.283673	0.141836	−	0.989890i	$-0.454699\pi$
$113$	3.01548	0.283673	0.141836	+	0.989890i	$0.454699\pi$
$114$	−3.12358	−0.292550
$115$	−9.26168	−0.863656
$116$	−1.37779	−0.127924
$117$	1.00000	0.0924500
$118$	0.743958	0.0684869
$119$	20.5536	1.88415
$120$	8.13355	0.742488
$121$	8.34727	0.758843
$122$	−7.01770	−0.635352
$123$	9.26951	0.835803
$124$	0.847941	0.0761474
$125$	−7.15065	−0.639574
$126$	3.83151	0.341338
$127$	−14.7603	−1.30977	−0.654883	−	0.755730i	$-0.727282\pi$
$127$	−14.7603	−1.30977	−0.654883	+	0.755730i	$0.727282\pi$
$128$	8.18089	0.723096
$129$	0.300510	0.0264584
$130$	3.54292	0.310735
$131$	−6.60429	−0.577019	−0.288510	−	0.957477i	$-0.593160\pi$
$131$	−6.60429	−0.577019	−0.288510	+	0.957477i	$0.593160\pi$
$132$	1.30073	0.113214
$133$	7.02235	0.608915
$134$	13.8941	1.20026
$135$	−2.71388	−0.233574
$136$	−20.9884	−1.79974
$137$	−10.9548	−0.935931	−0.467965	−	0.883747i	$-0.655013\pi$
$137$	−10.9548	−0.935931	−0.467965	+	0.883747i	$0.655013\pi$
$138$	4.45522	0.379254
$139$	−11.5276	−0.977755	−0.488878	−	0.872352i	$-0.662594\pi$
$139$	−11.5276	−0.977755	−0.488878	+	0.872352i	$0.662594\pi$
$140$	−2.35542	−0.199069
$141$	6.75031	0.568479
$142$	6.71135	0.563204
$143$	4.39855	0.367825
$144$	−3.32111	−0.276760
$145$	12.6443	1.05005
$146$	−12.6670	−1.04833
$147$	−1.61389	−0.133112
$148$	−1.44165	−0.118503
$149$	−9.95077	−0.815199	−0.407600	−	0.913161i	$-0.633634\pi$
$149$	−9.95077	−0.815199	−0.407600	+	0.913161i	$0.633634\pi$
$150$	−3.08767	−0.252107
$151$	6.14232	0.499855	0.249928	−	0.968265i	$-0.419593\pi$
$151$	6.14232	0.499855	0.249928	+	0.968265i	$0.419593\pi$
$152$	−7.17087	−0.581634
$153$	7.00308	0.566166
$154$	16.8531	1.35806
$155$	−7.78178	−0.625047
$156$	0.295718	0.0236764
$157$	5.17014	0.412622	0.206311	−	0.978486i	$-0.433854\pi$
$157$	5.17014	0.412622	0.206311	+	0.978486i	$0.433854\pi$
$158$	15.0704	1.19894
$159$	9.66362	0.766375
$160$	4.50065	0.355808
$161$	−10.0161	−0.789379
$162$	1.30548	0.102568
$163$	22.6872	1.77700	0.888501	−	0.458876i	$-0.151748\pi$
$163$	22.6872	1.77700	0.888501	+	0.458876i	$0.151748\pi$
$164$	2.74116	0.214049
$165$	−11.9372	−0.929306
$166$	8.58759	0.666526
$167$	−0.389107	−0.0301100	−0.0150550	−	0.999887i	$-0.504792\pi$
$167$	−0.389107	−0.0301100	−0.0150550	+	0.999887i	$0.504792\pi$
$168$	8.79608	0.678632
$169$	1.00000	0.0769231
$170$	24.8114	1.90295
$171$	2.39267	0.182972
$172$	0.0888661	0.00677598
$173$	10.8648	0.826037	0.413019	−	0.910723i	$-0.364474\pi$
$173$	10.8648	0.826037	0.413019	+	0.910723i	$0.364474\pi$
$174$	−6.08240	−0.461106
$175$	6.94160	0.524736
$176$	−14.6081	−1.10113
$177$	−0.569872	−0.0428342
$178$	14.1474	1.06039
$179$	−5.98118	−0.447054	−0.223527	−	0.974698i	$-0.571757\pi$
$179$	−5.98118	−0.447054	−0.223527	+	0.974698i	$0.571757\pi$
$180$	−0.802544	−0.0598181
$181$	0.290058	0.0215598	0.0107799	−	0.999942i	$-0.496569\pi$
$181$	0.290058	0.0215598	0.0107799	+	0.999942i	$0.496569\pi$
$182$	3.83151	0.284011
$183$	5.37556	0.397373
$184$	10.2279	0.754013
$185$	13.2304	0.972720
$186$	3.74333	0.274474
$187$	30.8034	2.25257
$188$	1.99619	0.145587
$189$	−2.93494	−0.213486
$190$	8.47704	0.614989
$191$	−18.2201	−1.31836	−0.659180	−	0.751985i	$-0.729096\pi$
$191$	−18.2201	−1.31836	−0.659180	+	0.751985i	$0.729096\pi$
$192$	−8.80722	−0.635606
$193$	−10.9122	−0.785478	−0.392739	−	0.919650i	$-0.628472\pi$
$193$	−10.9122	−0.785478	−0.392739	+	0.919650i	$0.628472\pi$
$194$	1.87459	0.134588
$195$	−2.71388	−0.194345
$196$	−0.477258	−0.0340898
$197$	0.764541	0.0544713	0.0272357	−	0.999629i	$-0.491330\pi$
$197$	0.764541	0.0544713	0.0272357	+	0.999629i	$0.491330\pi$
$198$	5.74223	0.408082
$199$	−6.88046	−0.487743	−0.243871	−	0.969808i	$-0.578418\pi$
$199$	−6.88046	−0.487743	−0.243871	+	0.969808i	$0.578418\pi$
$200$	−7.08842	−0.501227
$201$	−10.6429	−0.750690
$202$	−2.13901	−0.150500
$203$	13.6743	0.959746
$204$	2.07094	0.144995
$205$	−25.1564	−1.75700
$206$	−1.30548	−0.0909572
$207$	−3.41270	−0.237199
$208$	−3.32111	−0.230278
$209$	10.5243	0.727980
$210$	−10.3983	−0.717549
$211$	−0.915251	−0.0630085	−0.0315042	−	0.999504i	$-0.510030\pi$
$211$	−0.915251	−0.0630085	−0.0315042	+	0.999504i	$0.510030\pi$
$212$	2.85771	0.196268
$213$	−5.14090	−0.352249
$214$	11.3781	0.777789
$215$	−0.815548	−0.0556199
$216$	2.99702	0.203921
$217$	−8.41565	−0.571291
$218$	−3.43464	−0.232623
$219$	9.70296	0.655666
$220$	−3.53003	−0.237995
$221$	7.00308	0.471078
$222$	−6.36434	−0.427146
$223$	13.7316	0.919538	0.459769	−	0.888039i	$-0.347932\pi$
$223$	13.7316	0.919538	0.459769	+	0.888039i	$0.347932\pi$
$224$	4.86726	0.325207
$225$	2.36516	0.157677
$226$	3.93665	0.261862
$227$	21.4823	1.42583	0.712915	−	0.701251i	$-0.247375\pi$
$227$	21.4823	1.42583	0.712915	+	0.701251i	$0.247375\pi$
$228$	0.707555	0.0468590
$229$	16.1117	1.06469	0.532345	−	0.846528i	$-0.321311\pi$
$229$	16.1117	1.06469	0.532345	+	0.846528i	$0.321311\pi$
$230$	−12.0909	−0.797254
$231$	−12.9095	−0.849383
$232$	−13.9635	−0.916747
$233$	−6.44479	−0.422213	−0.211106	−	0.977463i	$-0.567707\pi$
$233$	−6.44479	−0.422213	−0.211106	+	0.977463i	$0.567707\pi$
$234$	1.30548	0.0853420
$235$	−18.3196	−1.19504
$236$	−0.168522	−0.0109698
$237$	−11.5440	−0.749860
$238$	26.8324	1.73929
$239$	4.50706	0.291537	0.145769	−	0.989319i	$-0.453434\pi$
$239$	4.50706	0.291537	0.145769	+	0.989319i	$0.453434\pi$
$240$	9.01311	0.581794
$241$	7.64725	0.492603	0.246301	−	0.969193i	$-0.420785\pi$
$241$	7.64725	0.492603	0.246301	+	0.969193i	$0.420785\pi$
$242$	10.8972	0.700499
$243$	−1.00000	−0.0641500
$244$	1.58965	0.101767
$245$	4.37992	0.279823
$246$	12.1012	0.771543
$247$	2.39267	0.152242
$248$	8.59364	0.545696
$249$	−6.57810	−0.416870
$250$	−9.33505	−0.590400
$251$	28.1674	1.77791	0.888955	−	0.457995i	$-0.151432\pi$
$251$	28.1674	1.77791	0.888955	+	0.457995i	$0.151432\pi$
$252$	−0.867916	−0.0546736
$253$	−15.0110	−0.943731
$254$	−19.2693	−1.20906
$255$	−19.0055	−1.19017
$256$	−6.93443	−0.433402
$257$	−1.66440	−0.103822	−0.0519112	−	0.998652i	$-0.516531\pi$
$257$	−1.66440	−0.103822	−0.0519112	+	0.998652i	$0.516531\pi$
$258$	0.392310	0.0244241
$259$	14.3081	0.889063
$260$	−0.802544	−0.0497717
$261$	4.65913	0.288393
$262$	−8.62177	−0.532655
$263$	−11.9122	−0.734539	−0.367269	−	0.930115i	$-0.619707\pi$
$263$	−11.9122	−0.734539	−0.367269	+	0.930115i	$0.619707\pi$
$264$	13.1825	0.811329
$265$	−26.2259	−1.61105
$266$	9.16754	0.562098
$267$	−10.8369	−0.663208
$268$	−3.14729	−0.192251
$269$	10.8140	0.659344	0.329672	−	0.944096i	$-0.393062\pi$
$269$	10.8140	0.659344	0.329672	+	0.944096i	$0.393062\pi$
$270$	−3.54292	−0.215615
$271$	31.2042	1.89552	0.947760	−	0.318983i	$-0.103341\pi$
$271$	31.2042	1.89552	0.947760	+	0.318983i	$0.103341\pi$
$272$	−23.2580	−1.41023
$273$	−2.93494	−0.177631
$274$	−14.3013	−0.863971
$275$	10.4033	0.627341
$276$	−1.00920	−0.0607466
$277$	20.6938	1.24337	0.621686	−	0.783267i	$-0.286448\pi$
$277$	20.6938	1.24337	0.621686	+	0.783267i	$0.286448\pi$
$278$	−15.0490	−0.902580
$279$	−2.86740	−0.171667
$280$	−23.8715	−1.42660
$281$	3.99731	0.238459	0.119230	−	0.992867i	$-0.461958\pi$
$281$	3.99731	0.238459	0.119230	+	0.992867i	$0.461958\pi$
$282$	8.81241	0.524771
$283$	14.0429	0.834766	0.417383	−	0.908731i	$-0.362947\pi$
$283$	14.0429	0.834766	0.417383	+	0.908731i	$0.362947\pi$
$284$	−1.52026	−0.0902107
$285$	−6.49342	−0.384637
$286$	5.74223	0.339545
$287$	−27.2055	−1.60589
$288$	1.65838	0.0977211
$289$	32.0431	1.88489
$290$	16.5069	0.969320
$291$	−1.43594	−0.0841763
$292$	2.86934	0.167916
$293$	−23.5561	−1.37616	−0.688080	−	0.725635i	$-0.741546\pi$
$293$	−23.5561	−1.37616	−0.688080	+	0.725635i	$0.741546\pi$
$294$	−2.10691	−0.122877
$295$	1.54657	0.0900446
$296$	−14.6107	−0.849231
$297$	−4.39855	−0.255230
$298$	−12.9906	−0.752522
$299$	−3.41270	−0.197362
$300$	0.699420	0.0403810
$301$	−0.881979	−0.0508364
$302$	8.01869	0.461424
$303$	1.63848	0.0941283
$304$	−7.94633	−0.455753
$305$	−14.5886	−0.835343
$306$	9.14239	0.522636
$307$	−28.8999	−1.64941	−0.824703	−	0.565566i	$-0.808658\pi$
$307$	−28.8999	−1.64941	−0.824703	+	0.565566i	$0.808658\pi$
$308$	−3.81757	−0.217527
$309$	1.00000	0.0568880
$310$	−10.1590	−0.576990
$311$	10.2465	0.581028	0.290514	−	0.956871i	$-0.406174\pi$
$311$	10.2465	0.581028	0.290514	+	0.956871i	$0.406174\pi$
$312$	2.99702	0.169673
$313$	2.36100	0.133452	0.0667258	−	0.997771i	$-0.478745\pi$
$313$	2.36100	0.133452	0.0667258	+	0.997771i	$0.478745\pi$
$314$	6.74952	0.380898
$315$	7.96509	0.448782
$316$	−3.41376	−0.192039
$317$	19.8278	1.11364	0.556820	−	0.830633i	$-0.312021\pi$
$317$	19.8278	1.11364	0.556820	+	0.830633i	$0.312021\pi$
$318$	12.6157	0.707452
$319$	20.4934	1.14741
$320$	23.9017	1.33615
$321$	−8.71561	−0.486458
$322$	−13.0758	−0.728687
$323$	16.7561	0.932332
$324$	−0.295718	−0.0164288
$325$	2.36516	0.131195
$326$	29.6178	1.64038
$327$	2.63094	0.145491
$328$	27.7809	1.53394
$329$	−19.8118	−1.09226
$330$	−15.5837	−0.857856
$331$	−16.4923	−0.906498	−0.453249	−	0.891384i	$-0.649735\pi$
$331$	−16.4923	−0.906498	−0.453249	+	0.891384i	$0.649735\pi$
$332$	−1.94526	−0.106760
$333$	4.87509	0.267153
$334$	−0.507973	−0.0277950
$335$	28.8835	1.57807
$336$	9.74728	0.531758
$337$	−8.15646	−0.444311	−0.222155	−	0.975011i	$-0.571309\pi$
$337$	−8.15646	−0.444311	−0.222155	+	0.975011i	$0.571309\pi$
$338$	1.30548	0.0710088
$339$	−3.01548	−0.163778
$340$	−5.62028	−0.304803
$341$	−12.6124	−0.682999
$342$	3.12358	0.168904
$343$	−15.8079	−0.853547
$344$	0.900633	0.0485589
$345$	9.26168	0.498632
$346$	14.1838	0.762527
$347$	−19.9683	−1.07195	−0.535977	−	0.844233i	$-0.680057\pi$
$347$	−19.9683	−1.07195	−0.535977	+	0.844233i	$0.680057\pi$
$348$	1.37779	0.0738572
$349$	18.2338	0.976035	0.488018	−	0.872834i	$-0.337720\pi$
$349$	18.2338	0.976035	0.488018	+	0.872834i	$0.337720\pi$
$350$	9.06213	0.484391
$351$	−1.00000	−0.0533761
$352$	7.29448	0.388797
$353$	−23.2179	−1.23576	−0.617881	−	0.786272i	$-0.712009\pi$
$353$	−23.2179	−1.23576	−0.617881	+	0.786272i	$0.712009\pi$
$354$	−0.743958	−0.0395409
$355$	13.9518	0.740485
$356$	−3.20467	−0.169847
$357$	−20.5536	−1.08781
$358$	−7.80832	−0.412682
$359$	15.4908	0.817573	0.408786	−	0.912630i	$-0.365952\pi$
$359$	15.4908	0.817573	0.408786	+	0.912630i	$0.365952\pi$
$360$	−8.13355	−0.428676
$361$	−13.2751	−0.698691
$362$	0.378665	0.0199022
$363$	−8.34727	−0.438118
$364$	−0.867916	−0.0454912
$365$	−26.3327	−1.37832
$366$	7.01770	0.366821
$367$	8.73335	0.455877	0.227939	−	0.973675i	$-0.426801\pi$
$367$	8.73335	0.455877	0.227939	+	0.973675i	$0.426801\pi$
$368$	11.3340	0.590825
$369$	−9.26951	−0.482551
$370$	17.2721	0.897932
$371$	−28.3622	−1.47249
$372$	−0.847941	−0.0439637
$373$	−5.97453	−0.309350	−0.154675	−	0.987965i	$-0.549433\pi$
$373$	−5.97453	−0.309350	−0.154675	+	0.987965i	$0.549433\pi$
$374$	40.2133	2.07938
$375$	7.15065	0.369258
$376$	20.2308	1.04332
$377$	4.65913	0.239957
$378$	−3.83151	−0.197072
$379$	−16.4914	−0.847106	−0.423553	−	0.905871i	$-0.639217\pi$
$379$	−16.4914	−0.847106	−0.423553	+	0.905871i	$0.639217\pi$
$380$	−1.92022	−0.0985053
$381$	14.7603	0.756194
$382$	−23.7860	−1.21700
$383$	−23.3867	−1.19500	−0.597502	−	0.801868i	$-0.703840\pi$
$383$	−23.3867	−1.19500	−0.597502	+	0.801868i	$0.703840\pi$
$384$	−8.18089	−0.417479
$385$	35.0349	1.78554
$386$	−14.2457	−0.725086
$387$	−0.300510	−0.0152758
$388$	−0.424634	−0.0215575
$389$	−21.5187	−1.09104	−0.545520	−	0.838098i	$-0.683668\pi$
$389$	−21.5187	−1.09104	−0.545520	+	0.838098i	$0.683668\pi$
$390$	−3.54292	−0.179403
$391$	−23.8994	−1.20865
$392$	−4.83687	−0.244299
$393$	6.60429	0.333142
$394$	0.998095	0.0502833
$395$	31.3289	1.57633
$396$	−1.30073	−0.0653642
$397$	−16.5792	−0.832086	−0.416043	−	0.909345i	$-0.636583\pi$
$397$	−16.5792	−0.832086	−0.416043	+	0.909345i	$0.636583\pi$
$398$	−8.98231	−0.450243
$399$	−7.02235	−0.351557
$400$	−7.85496	−0.392748
$401$	−2.97880	−0.148754	−0.0743772	−	0.997230i	$-0.523697\pi$
$401$	−2.97880	−0.148754	−0.0743772	+	0.997230i	$0.523697\pi$
$402$	−13.8941	−0.692973
$403$	−2.86740	−0.142835
$404$	0.484528	0.0241062
$405$	2.71388	0.134854
$406$	17.8515	0.885955
$407$	21.4433	1.06291
$408$	20.9884	1.03908
$409$	−14.9045	−0.736982	−0.368491	−	0.929631i	$-0.620125\pi$
$409$	−14.9045	−0.736982	−0.368491	+	0.929631i	$0.620125\pi$
$410$	−32.8412	−1.62191
$411$	10.9548	0.540360
$412$	0.295718	0.0145690
$413$	1.67254	0.0823005
$414$	−4.45522	−0.218962
$415$	17.8522	0.876330
$416$	1.65838	0.0813088
$417$	11.5276	0.564507
$418$	13.7393	0.672009
$419$	−22.9263	−1.12002	−0.560011	−	0.828485i	$-0.689203\pi$
$419$	−22.9263	−1.12002	−0.560011	+	0.828485i	$0.689203\pi$
$420$	2.35542	0.114933
$421$	−29.9384	−1.45911	−0.729553	−	0.683924i	$-0.760272\pi$
$421$	−29.9384	−1.45911	−0.729553	+	0.683924i	$0.760272\pi$
$422$	−1.19484	−0.0581641
$423$	−6.75031	−0.328211
$424$	28.9620	1.40652
$425$	16.5634	0.803442
$426$	−6.71135	−0.325166
$427$	−15.7770	−0.763501
$428$	−2.57736	−0.124582
$429$	−4.39855	−0.212364
$430$	−1.06468	−0.0513435
$431$	−15.0439	−0.724640	−0.362320	−	0.932054i	$-0.618015\pi$
$431$	−15.0439	−0.724640	−0.362320	+	0.932054i	$0.618015\pi$
$432$	3.32111	0.159787
$433$	−28.9634	−1.39189	−0.695947	−	0.718093i	$-0.745015\pi$
$433$	−28.9634	−1.39189	−0.695947	+	0.718093i	$0.745015\pi$
$434$	−10.9865	−0.527367
$435$	−12.6443	−0.606249
$436$	0.778016	0.0372602
$437$	−8.16547	−0.390607
$438$	12.6670	0.605255
$439$	−13.4199	−0.640495	−0.320247	−	0.947334i	$-0.603766\pi$
$439$	−13.4199	−0.640495	−0.320247	+	0.947334i	$0.603766\pi$
$440$	−35.7759	−1.70555
$441$	1.61389	0.0768521
$442$	9.14239	0.434859
$443$	15.1174	0.718249	0.359124	−	0.933290i	$-0.383075\pi$
$443$	15.1174	0.718249	0.359124	+	0.933290i	$0.383075\pi$
$444$	1.44165	0.0684178
$445$	29.4101	1.39417
$446$	17.9264	0.848839
$447$	9.95077	0.470655
$448$	25.8487	1.22124
$449$	−38.2449	−1.80489	−0.902444	−	0.430806i	$-0.858229\pi$
$449$	−38.2449	−1.80489	−0.902444	+	0.430806i	$0.858229\pi$
$450$	3.08767	0.145554
$451$	−40.7724	−1.91990
$452$	−0.891732	−0.0419436
$453$	−6.14232	−0.288591
$454$	28.0447	1.31620
$455$	7.96509	0.373409
$456$	7.17087	0.335807
$457$	−3.77691	−0.176676	−0.0883382	−	0.996091i	$-0.528156\pi$
$457$	−3.77691	−0.176676	−0.0883382	+	0.996091i	$0.528156\pi$
$458$	21.0335	0.982831
$459$	−7.00308	−0.326876
$460$	2.73885	0.127699
$461$	33.2233	1.54736	0.773681	−	0.633575i	$-0.218413\pi$
$461$	33.2233	1.54736	0.773681	+	0.633575i	$0.218413\pi$
$462$	−16.8531	−0.784078
$463$	1.48993	0.0692431	0.0346215	−	0.999400i	$-0.488977\pi$
$463$	1.48993	0.0692431	0.0346215	+	0.999400i	$0.488977\pi$
$464$	−15.4735	−0.718339
$465$	7.78178	0.360871
$466$	−8.41356	−0.389751
$467$	16.0707	0.743662	0.371831	−	0.928300i	$-0.378730\pi$
$467$	16.0707	0.743662	0.371831	+	0.928300i	$0.378730\pi$
$468$	−0.295718	−0.0136696
$469$	31.2362	1.44235
$470$	−23.9158	−1.10316
$471$	−5.17014	−0.238228
$472$	−1.70792	−0.0786133
$473$	−1.32181	−0.0607768
$474$	−15.0704	−0.692207
$475$	5.65904	0.259654
$476$	−6.07809	−0.278589
$477$	−9.66362	−0.442467
$478$	5.88388	0.269122
$479$	−21.5503	−0.984660	−0.492330	−	0.870409i	$-0.663855\pi$
$479$	−21.5503	−0.984660	−0.492330	+	0.870409i	$0.663855\pi$
$480$	−4.50065	−0.205426
$481$	4.87509	0.222285
$482$	9.98335	0.454729
$483$	10.0161	0.455748
$484$	−2.46844	−0.112202
$485$	3.89697	0.176952
$486$	−1.30548	−0.0592178
$487$	−26.7129	−1.21048	−0.605238	−	0.796045i	$-0.706922\pi$
$487$	−26.7129	−1.21048	−0.605238	+	0.796045i	$0.706922\pi$
$488$	16.1107	0.729295
$489$	−22.6872	−1.02595
$490$	5.71790	0.258308
$491$	−9.86244	−0.445086	−0.222543	−	0.974923i	$-0.571436\pi$
$491$	−9.86244	−0.445086	−0.222543	+	0.974923i	$0.571436\pi$
$492$	−2.74116	−0.123581
$493$	32.6282	1.46950
$494$	3.12358	0.140537
$495$	11.9372	0.536535
$496$	9.52295	0.427593
$497$	15.0883	0.676801
$498$	−8.58759	−0.384819
$499$	7.66767	0.343252	0.171626	−	0.985162i	$-0.445098\pi$
$499$	7.66767	0.343252	0.171626	+	0.985162i	$0.445098\pi$
$500$	2.11458	0.0945668
$501$	0.389107	0.0173840
$502$	36.7720	1.64121
$503$	22.8239	1.01767	0.508833	−	0.860865i	$-0.330077\pi$
$503$	22.8239	1.01767	0.508833	+	0.860865i	$0.330077\pi$
$504$	−8.79608	−0.391808
$505$	−4.44664	−0.197873
$506$	−19.5965	−0.871172
$507$	−1.00000	−0.0444116
$508$	4.36489	0.193661
$509$	−30.0134	−1.33032	−0.665160	−	0.746700i	$-0.731637\pi$
$509$	−30.0134	−1.33032	−0.665160	+	0.746700i	$0.731637\pi$
$510$	−24.8114	−1.09867
$511$	−28.4777	−1.25978
$512$	−25.4146	−1.12318
$513$	−2.39267	−0.105639
$514$	−2.17284	−0.0958399
$515$	−2.71388	−0.119588
$516$	−0.0888661	−0.00391211
$517$	−29.6916	−1.30584
$518$	18.6790	0.820707
$519$	−10.8648	−0.476913
$520$	−8.13355	−0.356680
$521$	40.9397	1.79360	0.896799	−	0.442437i	$-0.145886\pi$
$521$	40.9397	1.79360	0.896799	+	0.442437i	$0.145886\pi$
$522$	6.08240	0.266220
$523$	−19.7665	−0.864330	−0.432165	−	0.901795i	$-0.642250\pi$
$523$	−19.7665	−0.864330	−0.432165	+	0.901795i	$0.642250\pi$
$524$	1.95301	0.0853175
$525$	−6.94160	−0.302956
$526$	−15.5512	−0.678063
$527$	−20.0806	−0.874725
$528$	14.6081	0.635736
$529$	−11.3534	−0.493628
$530$	−34.2375	−1.48718
$531$	0.569872	0.0247304
$532$	−2.07664	−0.0900336
$533$	−9.26951	−0.401507
$534$	−14.1474	−0.612217
$535$	23.6531	1.02261
$536$	−31.8969	−1.37773
$537$	5.98118	0.258107
$538$	14.1175	0.608650
$539$	7.09880	0.305767
$540$	0.802544	0.0345360
$541$	40.1714	1.72710	0.863551	−	0.504262i	$-0.168235\pi$
$541$	40.1714	1.72710	0.863551	+	0.504262i	$0.168235\pi$
$542$	40.7365	1.74978
$543$	−0.290058	−0.0124476
$544$	11.6138	0.497937
$545$	−7.14006	−0.305846
$546$	−3.83151	−0.163974
$547$	−23.1366	−0.989250	−0.494625	−	0.869107i	$-0.664695\pi$
$547$	−23.1366	−0.989250	−0.494625	+	0.869107i	$0.664695\pi$
$548$	3.23953	0.138386
$549$	−5.37556	−0.229423
$550$	13.5813	0.579108
$551$	11.1477	0.474910
$552$	−10.2279	−0.435330
$553$	33.8808	1.44076
$554$	27.0154	1.14778
$555$	−13.2304	−0.561600
$556$	3.40891	0.144570
$557$	35.7886	1.51641	0.758206	−	0.652015i	$-0.226076\pi$
$557$	35.7886	1.51641	0.758206	+	0.652015i	$0.226076\pi$
$558$	−3.74333	−0.158468
$559$	−0.300510	−0.0127102
$560$	−26.4530	−1.11784
$561$	−30.8034	−1.30052
$562$	5.21841	0.220125
$563$	3.02856	0.127639	0.0638193	−	0.997961i	$-0.479672\pi$
$563$	3.02856	0.127639	0.0638193	+	0.997961i	$0.479672\pi$
$564$	−1.99619	−0.0840548
$565$	8.18366	0.344289
$566$	18.3328	0.770585
$567$	2.93494	0.123256
$568$	−15.4074	−0.646479
$569$	−27.7102	−1.16167	−0.580835	−	0.814021i	$-0.697274\pi$
$569$	−27.7102	−1.16167	−0.580835	+	0.814021i	$0.697274\pi$
$570$	−8.47704	−0.355064
$571$	37.2513	1.55892	0.779458	−	0.626454i	$-0.215494\pi$
$571$	37.2513	1.55892	0.779458	+	0.626454i	$0.215494\pi$
$572$	−1.30073	−0.0543863
$573$	18.2201	0.761155
$574$	−35.5163	−1.48242
$575$	−8.07158	−0.336608
$576$	8.80722	0.366967
$577$	−9.99418	−0.416063	−0.208032	−	0.978122i	$-0.566706\pi$
$577$	−9.99418	−0.416063	−0.208032	+	0.978122i	$0.566706\pi$
$578$	41.8317	1.73997
$579$	10.9122	0.453496
$580$	−3.73915	−0.155260
$581$	19.3064	0.800963
$582$	−1.87459	−0.0777044
$583$	−42.5059	−1.76042
$584$	29.0800	1.20334
$585$	2.71388	0.112205
$586$	−30.7520	−1.27035
$587$	20.0870	0.829079	0.414539	−	0.910031i	$-0.363943\pi$
$587$	20.0870	0.829079	0.414539	+	0.910031i	$0.363943\pi$
$588$	0.477258	0.0196818
$589$	−6.86073	−0.282691
$590$	2.01901	0.0831215
$591$	−0.764541	−0.0314490
$592$	−16.1907	−0.665435
$593$	23.5401	0.966677	0.483338	−	0.875434i	$-0.339424\pi$
$593$	23.5401	0.966677	0.483338	+	0.875434i	$0.339424\pi$
$594$	−5.74223	−0.235607
$595$	55.7802	2.28676
$596$	2.94262	0.120535
$597$	6.88046	0.281599
$598$	−4.45522	−0.182188
$599$	43.4911	1.77700	0.888498	−	0.458880i	$-0.151749\pi$
$599$	43.4911	1.77700	0.888498	+	0.458880i	$0.151749\pi$
$600$	7.08842	0.289383
$601$	−31.5728	−1.28788	−0.643940	−	0.765076i	$-0.722701\pi$
$601$	−31.5728	−1.28788	−0.643940	+	0.765076i	$0.722701\pi$
$602$	−1.15141	−0.0469278
$603$	10.6429	0.433411
$604$	−1.81640	−0.0739081
$605$	22.6535	0.920996
$606$	2.13901	0.0868912
$607$	−25.6016	−1.03914	−0.519569	−	0.854428i	$-0.673908\pi$
$607$	−25.6016	−1.03914	−0.519569	+	0.854428i	$0.673908\pi$
$608$	3.96796	0.160922
$609$	−13.6743	−0.554109
$610$	−19.0452	−0.771118
$611$	−6.75031	−0.273088
$612$	−2.07094	−0.0837127
$613$	−0.495486	−0.0200125	−0.0100062	−	0.999950i	$-0.503185\pi$
$613$	−0.495486	−0.0200125	−0.0100062	+	0.999950i	$0.503185\pi$
$614$	−37.7283	−1.52259
$615$	25.1564	1.01440
$616$	−38.6900	−1.55887
$617$	−20.3310	−0.818497	−0.409249	−	0.912423i	$-0.634209\pi$
$617$	−20.3310	−0.818497	−0.409249	+	0.912423i	$0.634209\pi$
$618$	1.30548	0.0525142
$619$	−28.8765	−1.16065	−0.580323	−	0.814386i	$-0.697074\pi$
$619$	−28.8765	−1.16065	−0.580323	+	0.814386i	$0.697074\pi$
$620$	2.30121	0.0924189
$621$	3.41270	0.136947
$622$	13.3767	0.536355
$623$	31.8057	1.27427
$624$	3.32111	0.132951
$625$	−31.2318	−1.24927
$626$	3.08224	0.123191
$627$	−10.5243	−0.420299
$628$	−1.52890	−0.0610099
$629$	34.1406	1.36128
$630$	10.3983	0.414277
$631$	−17.9091	−0.712951	−0.356475	−	0.934305i	$-0.616022\pi$
$631$	−17.9091	−0.712951	−0.356475	+	0.934305i	$0.616022\pi$
$632$	−34.5974	−1.37621
$633$	0.915251	0.0363780
$634$	25.8848	1.02802
$635$	−40.0578	−1.58964
$636$	−2.85771	−0.113315
$637$	1.61389	0.0639448
$638$	26.7538	1.05919
$639$	5.14090	0.203371
$640$	22.2020	0.877610
$641$	−17.2776	−0.682424	−0.341212	−	0.939986i	$-0.610837\pi$
$641$	−17.2776	−0.682424	−0.341212	+	0.939986i	$0.610837\pi$
$642$	−11.3781	−0.449057
$643$	−14.1199	−0.556835	−0.278418	−	0.960460i	$-0.589810\pi$
$643$	−14.1199	−0.556835	−0.278418	+	0.960460i	$0.589810\pi$
$644$	2.96194	0.116717
$645$	0.815548	0.0321122
$646$	21.8747	0.860649
$647$	16.5033	0.648812	0.324406	−	0.945918i	$-0.394836\pi$
$647$	16.5033	0.648812	0.324406	+	0.945918i	$0.394836\pi$
$648$	−2.99702	−0.117734
$649$	2.50661	0.0983932
$650$	3.08767	0.121108
$651$	8.41565	0.329835
$652$	−6.70903	−0.262746
$653$	−9.97625	−0.390401	−0.195200	−	0.980763i	$-0.562536\pi$
$653$	−9.97625	−0.390401	−0.195200	+	0.980763i	$0.562536\pi$
$654$	3.43464	0.134305
$655$	−17.9233	−0.700320
$656$	30.7851	1.20196
$657$	−9.70296	−0.378549
$658$	−25.8639	−1.00828
$659$	−31.9738	−1.24552	−0.622761	−	0.782412i	$-0.713989\pi$
$659$	−31.9738	−1.24552	−0.622761	+	0.782412i	$0.713989\pi$
$660$	3.53003	0.137406
$661$	−20.2815	−0.788858	−0.394429	−	0.918926i	$-0.629058\pi$
$661$	−20.2815	−0.788858	−0.394429	+	0.918926i	$0.629058\pi$
$662$	−21.5304	−0.836801
$663$	−7.00308	−0.271977
$664$	−19.7147	−0.765078
$665$	19.0578	0.739031
$666$	6.36434	0.246613
$667$	−15.9002	−0.615659
$668$	0.115066	0.00445204
$669$	−13.7316	−0.530895
$670$	37.7069	1.45674
$671$	−23.6447	−0.912793
$672$	−4.86726	−0.187758
$673$	2.75171	0.106071	0.0530353	−	0.998593i	$-0.483110\pi$
$673$	2.75171	0.106071	0.0530353	+	0.998593i	$0.483110\pi$
$674$	−10.6481	−0.410150
$675$	−2.36516	−0.0910349
$676$	−0.295718	−0.0113738
$677$	−9.28770	−0.356955	−0.178478	−	0.983944i	$-0.557117\pi$
$677$	−9.28770	−0.356955	−0.178478	+	0.983944i	$0.557117\pi$
$678$	−3.93665	−0.151186
$679$	4.21441	0.161734
$680$	−56.9599	−2.18431
$681$	−21.4823	−0.823203
$682$	−16.4652	−0.630487
$683$	38.3720	1.46826	0.734132	−	0.679007i	$-0.237589\pi$
$683$	38.3720	1.46826	0.734132	+	0.679007i	$0.237589\pi$
$684$	−0.707555	−0.0270541
$685$	−29.7300	−1.13592
$686$	−20.6369	−0.787922
$687$	−16.1117	−0.614699
$688$	0.998027	0.0380494
$689$	−9.66362	−0.368155
$690$	12.0909	0.460295
$691$	−29.4899	−1.12185	−0.560925	−	0.827866i	$-0.689554\pi$
$691$	−29.4899	−1.12185	−0.560925	+	0.827866i	$0.689554\pi$
$692$	−3.21293	−0.122137
$693$	12.9095	0.490392
$694$	−26.0682	−0.989536
$695$	−31.2845	−1.18669
$696$	13.9635	0.529284
$697$	−64.9151	−2.45884
$698$	23.8039	0.900993
$699$	6.44479	0.243765
$700$	−2.05276	−0.0775870
$701$	39.0937	1.47655	0.738275	−	0.674500i	$-0.235641\pi$
$701$	39.0937	1.47655	0.738275	+	0.674500i	$0.235641\pi$
$702$	−1.30548	−0.0492722
$703$	11.6645	0.439934
$704$	38.7390	1.46003
$705$	18.3196	0.689954
$706$	−30.3105	−1.14075
$707$	−4.80885	−0.180855
$708$	0.168522	0.00633343
$709$	−24.0930	−0.904831	−0.452415	−	0.891807i	$-0.649438\pi$
$709$	−24.0930	−0.904831	−0.452415	+	0.891807i	$0.649438\pi$
$710$	18.2138	0.683553
$711$	11.5440	0.432932
$712$	−32.4784	−1.21718
$713$	9.78557	0.366473
$714$	−26.8324	−1.00418
$715$	11.9372	0.446424
$716$	1.76874	0.0661010
$717$	−4.50706	−0.168319
$718$	20.2229	0.754713
$719$	−18.1502	−0.676889	−0.338445	−	0.940986i	$-0.609901\pi$
$719$	−18.1502	−0.676889	−0.338445	+	0.940986i	$0.609901\pi$
$720$	−9.01311	−0.335899
$721$	−2.93494	−0.109303
$722$	−17.3304	−0.644972
$723$	−7.64725	−0.284404
$724$	−0.0857754	−0.00318782
$725$	11.0196	0.409256
$726$	−10.8972	−0.404433
$727$	14.0622	0.521538	0.260769	−	0.965401i	$-0.416024\pi$
$727$	14.0622	0.521538	0.260769	+	0.965401i	$0.416024\pi$
$728$	−8.79608	−0.326004
$729$	1.00000	0.0370370
$730$	−34.3769	−1.27234
$731$	−2.10449	−0.0778375
$732$	−1.58965	−0.0587552
$733$	−47.5969	−1.75803	−0.879016	−	0.476793i	$-0.841799\pi$
$733$	−47.5969	−1.75803	−0.879016	+	0.476793i	$0.841799\pi$
$734$	11.4012	0.420827
$735$	−4.37992	−0.161556
$736$	−5.65957	−0.208614
$737$	46.8132	1.72439
$738$	−12.1012	−0.445450
$739$	−1.11770	−0.0411151	−0.0205576	−	0.999789i	$-0.506544\pi$
$739$	−1.11770	−0.0411151	−0.0205576	+	0.999789i	$0.506544\pi$
$740$	−3.91247	−0.143825
$741$	−2.39267	−0.0878969
$742$	−37.0263	−1.35928
$743$	18.8094	0.690050	0.345025	−	0.938594i	$-0.387871\pi$
$743$	18.8094	0.690050	0.345025	+	0.938594i	$0.387871\pi$
$744$	−8.59364	−0.315058
$745$	−27.0052	−0.989395
$746$	−7.79964	−0.285565
$747$	6.57810	0.240680
$748$	−9.10913	−0.333063
$749$	25.5798	0.934667
$750$	9.33505	0.340868
$751$	51.1722	1.86730	0.933650	−	0.358186i	$-0.116605\pi$
$751$	51.1722	1.86730	0.933650	+	0.358186i	$0.116605\pi$
$752$	22.4186	0.817521
$753$	−28.1674	−1.02648
$754$	6.08240	0.221508
$755$	16.6695	0.606667
$756$	0.867916	0.0315658
$757$	22.4845	0.817214	0.408607	−	0.912711i	$-0.366015\pi$
$757$	22.4845	0.817214	0.408607	+	0.912711i	$0.366015\pi$
$758$	−21.5292	−0.781976
$759$	15.0110	0.544863
$760$	−19.4609	−0.705921
$761$	−44.7519	−1.62226	−0.811128	−	0.584869i	$-0.801146\pi$
$761$	−44.7519	−1.62226	−0.811128	+	0.584869i	$0.801146\pi$
$762$	19.2693	0.698054
$763$	−7.72166	−0.279543
$764$	5.38801	0.194931
$765$	19.0055	0.687147
$766$	−30.5309	−1.10313
$767$	0.569872	0.0205769
$768$	6.93443	0.250225
$769$	−29.0791	−1.04862	−0.524310	−	0.851528i	$-0.675677\pi$
$769$	−29.0791	−1.04862	−0.524310	+	0.851528i	$0.675677\pi$
$770$	45.7374	1.64826
$771$	1.66440	0.0599418
$772$	3.22694	0.116140
$773$	−26.9175	−0.968155	−0.484078	−	0.875025i	$-0.660845\pi$
$773$	−26.9175	−0.968155	−0.484078	+	0.875025i	$0.660845\pi$
$774$	−0.392310	−0.0141013
$775$	−6.78184	−0.243611
$776$	−4.30354	−0.154488
$777$	−14.3081	−0.513301
$778$	−28.0922	−1.00715
$779$	−22.1789	−0.794640
$780$	0.802544	0.0287357
$781$	22.6125	0.809140
$782$	−31.2003	−1.11572
$783$	−4.65913	−0.166504
$784$	−5.35993	−0.191426
$785$	14.0312	0.500793
$786$	8.62177	0.307528
$787$	−46.6118	−1.66153	−0.830766	−	0.556621i	$-0.812097\pi$
$787$	−46.6118	−1.66153	−0.830766	+	0.556621i	$0.812097\pi$
$788$	−0.226089	−0.00805408
$789$	11.9122	0.424086
$790$	40.8993	1.45513
$791$	8.85026	0.314679
$792$	−13.1825	−0.468421
$793$	−5.37556	−0.190892
$794$	−21.6438	−0.768111
$795$	26.2259	0.930138
$796$	2.03468	0.0721172
$797$	9.07218	0.321353	0.160677	−	0.987007i	$-0.448632\pi$
$797$	9.07218	0.321353	0.160677	+	0.987007i	$0.448632\pi$
$798$	−9.16754	−0.324528
$799$	−47.2730	−1.67240
$800$	3.92233	0.138675
$801$	10.8369	0.382903
$802$	−3.88877	−0.137317
$803$	−42.6790	−1.50611
$804$	3.14729	0.110996
$805$	−27.1825	−0.958057
$806$	−3.74333	−0.131853
$807$	−10.8140	−0.380672
$808$	4.91056	0.172753
$809$	−27.5336	−0.968031	−0.484015	−	0.875059i	$-0.660822\pi$
$809$	−27.5336	−0.968031	−0.484015	+	0.875059i	$0.660822\pi$
$810$	3.54292	0.124486
$811$	−40.7488	−1.43088	−0.715442	−	0.698673i	$-0.753774\pi$
$811$	−40.7488	−1.43088	−0.715442	+	0.698673i	$0.753774\pi$
$812$	−4.04373	−0.141907
$813$	−31.2042	−1.09438
$814$	27.9939	0.981185
$815$	61.5705	2.15672
$816$	23.2580	0.814194
$817$	−0.719020	−0.0251553
$818$	−19.4576	−0.680319
$819$	2.93494	0.102555
$820$	7.43919	0.259788
$821$	−5.80191	−0.202488	−0.101244	−	0.994862i	$-0.532282\pi$
$821$	−5.80191	−0.202488	−0.101244	+	0.994862i	$0.532282\pi$
$822$	14.3013	0.498814
$823$	33.9771	1.18437	0.592183	−	0.805803i	$-0.298266\pi$
$823$	33.9771	1.18437	0.592183	+	0.805803i	$0.298266\pi$
$824$	2.99702	0.104406
$825$	−10.4033	−0.362195
$826$	2.18347	0.0759728
$827$	55.0980	1.91594	0.957972	−	0.286860i	$-0.0926116\pi$
$827$	55.0980	1.91594	0.957972	+	0.286860i	$0.0926116\pi$
$828$	1.00920	0.0350721
$829$	9.62395	0.334254	0.167127	−	0.985935i	$-0.446551\pi$
$829$	9.62395	0.334254	0.167127	+	0.985935i	$0.446551\pi$
$830$	23.3057	0.808953
$831$	−20.6938	−0.717861
$832$	8.80722	0.305335
$833$	11.3022	0.391599
$834$	15.0490	0.521105
$835$	−1.05599	−0.0365441
$836$	−3.11222	−0.107638
$837$	2.86740	0.0991117
$838$	−29.9298	−1.03391
$839$	42.8559	1.47955	0.739775	−	0.672854i	$-0.234932\pi$
$839$	42.8559	1.47955	0.739775	+	0.672854i	$0.234932\pi$
$840$	23.8715	0.823646
$841$	−7.29255	−0.251467
$842$	−39.0840	−1.34692
$843$	−3.99731	−0.137675
$844$	0.270656	0.00931637
$845$	2.71388	0.0933604
$846$	−8.81241	−0.302977
$847$	24.4988	0.841788
$848$	32.0940	1.10211
$849$	−14.0429	−0.481952
$850$	21.6232	0.741669
$851$	−16.6372	−0.570317
$852$	1.52026	0.0520832
$853$	42.6021	1.45867	0.729333	−	0.684158i	$-0.239830\pi$
$853$	42.6021	1.45867	0.729333	+	0.684158i	$0.239830\pi$
$854$	−20.5965	−0.704799
$855$	6.49342	0.222070
$856$	−26.1208	−0.892792
$857$	7.44858	0.254439	0.127219	−	0.991875i	$-0.459395\pi$
$857$	7.44858	0.254439	0.127219	+	0.991875i	$0.459395\pi$
$858$	−5.74223	−0.196036
$859$	35.1881	1.20060	0.600301	−	0.799774i	$-0.295047\pi$
$859$	35.1881	1.20060	0.600301	+	0.799774i	$0.295047\pi$
$860$	0.241172	0.00822390
$861$	27.2055	0.927160
$862$	−19.6395	−0.668926
$863$	15.4402	0.525590	0.262795	−	0.964852i	$-0.415356\pi$
$863$	15.4402	0.525590	0.262795	+	0.964852i	$0.415356\pi$
$864$	−1.65838	−0.0564193
$865$	29.4859	1.00255
$866$	−37.8112	−1.28488
$867$	−32.0431	−1.08824
$868$	2.48866	0.0844706
$869$	50.7767	1.72248
$870$	−16.5069	−0.559637
$871$	10.6429	0.360620
$872$	7.88497	0.267019
$873$	1.43594	0.0485992
$874$	−10.6599	−0.360575
$875$	−20.9868	−0.709482
$876$	−2.86934	−0.0969461
$877$	−31.8697	−1.07616	−0.538081	−	0.842893i	$-0.680851\pi$
$877$	−31.8697	−1.07616	−0.538081	+	0.842893i	$0.680851\pi$
$878$	−17.5194	−0.591250
$879$	23.5561	0.794527
$880$	−39.6447	−1.33642
$881$	36.4299	1.22735	0.613677	−	0.789557i	$-0.289690\pi$
$881$	36.4299	1.22735	0.613677	+	0.789557i	$0.289690\pi$
$882$	2.10691	0.0709433
$883$	−41.0163	−1.38031	−0.690154	−	0.723662i	$-0.742457\pi$
$883$	−41.0163	−1.38031	−0.690154	+	0.723662i	$0.742457\pi$
$884$	−2.07094	−0.0696532
$885$	−1.54657	−0.0519873
$886$	19.7355	0.663026
$887$	−17.5850	−0.590447	−0.295224	−	0.955428i	$-0.595394\pi$
$887$	−17.5850	−0.590447	−0.295224	+	0.955428i	$0.595394\pi$
$888$	14.6107	0.490304
$889$	−43.3207	−1.45293
$890$	38.3943	1.28698
$891$	4.39855	0.147357
$892$	−4.06069	−0.135962
$893$	−16.1513	−0.540481
$894$	12.9906	0.434469
$895$	−16.2322	−0.542583
$896$	24.0105	0.802133
$897$	3.41270	0.113947
$898$	−49.9280	−1.66612
$899$	−13.3596	−0.445566
$900$	−0.699420	−0.0233140
$901$	−67.6751	−2.25458
$902$	−53.2276	−1.77229
$903$	0.881979	0.0293504
$904$	−9.03745	−0.300581
$905$	0.787183	0.0261669
$906$	−8.01869	−0.266403
$907$	−47.5325	−1.57829	−0.789146	−	0.614206i	$-0.789476\pi$
$907$	−47.5325	−1.57829	−0.789146	+	0.614206i	$0.789476\pi$
$908$	−6.35270	−0.210822
$909$	−1.63848	−0.0543450
$910$	10.3983	0.344700
$911$	−37.5801	−1.24508	−0.622542	−	0.782586i	$-0.713900\pi$
$911$	−37.5801	−1.24508	−0.622542	+	0.782586i	$0.713900\pi$
$912$	7.94633	0.263129
$913$	28.9341	0.957580
$914$	−4.93069	−0.163093
$915$	14.5886	0.482286
$916$	−4.76452	−0.157424
$917$	−19.3832	−0.640090
$918$	−9.14239	−0.301744
$919$	25.2754	0.833759	0.416880	−	0.908962i	$-0.363124\pi$
$919$	25.2754	0.833759	0.416880	+	0.908962i	$0.363124\pi$
$920$	27.7574	0.915135
$921$	28.8999	0.952285
$922$	43.3724	1.42839
$923$	5.14090	0.169215
$924$	3.81757	0.125589
$925$	11.5304	0.379116
$926$	1.94508	0.0639193
$927$	−1.00000	−0.0328443
$928$	7.72661	0.253638
$929$	31.9541	1.04838	0.524190	−	0.851601i	$-0.324368\pi$
$929$	31.9541	1.04838	0.524190	+	0.851601i	$0.324368\pi$
$930$	10.1590	0.333126
$931$	3.86151	0.126556
$932$	1.90584	0.0624280
$933$	−10.2465	−0.335457
$934$	20.9800	0.686485
$935$	83.5969	2.73391
$936$	−2.99702	−0.0979606
$937$	34.6534	1.13208	0.566038	−	0.824379i	$-0.308476\pi$
$937$	34.6534	1.13208	0.566038	+	0.824379i	$0.308476\pi$
$938$	40.7783	1.33146
$939$	−2.36100	−0.0770483
$940$	5.41743	0.176697
$941$	−34.6906	−1.13088	−0.565440	−	0.824789i	$-0.691294\pi$
$941$	−34.6906	−1.13088	−0.565440	+	0.824789i	$0.691294\pi$
$942$	−6.74952	−0.219911
$943$	31.6341	1.03015
$944$	−1.89261	−0.0615993
$945$	−7.96509	−0.259104
$946$	−1.72560	−0.0561039
$947$	51.6451	1.67824	0.839121	−	0.543945i	$-0.183070\pi$
$947$	51.6451	1.67824	0.839121	+	0.543945i	$0.183070\pi$
$948$	3.41376	0.110874
$949$	−9.70296	−0.314972
$950$	7.38777	0.239691
$951$	−19.8278	−0.642960
$952$	−61.5996	−1.99646
$953$	23.9187	0.774803	0.387401	−	0.921911i	$-0.373373\pi$
$953$	23.9187	0.774803	0.387401	+	0.921911i	$0.373373\pi$
$954$	−12.6157	−0.408448
$955$	−49.4472	−1.60007
$956$	−1.33282	−0.0431064
$957$	−20.4934	−0.662458
$958$	−28.1336	−0.908954
$959$	−32.1517	−1.03823
$960$	−23.9017	−0.771426
$961$	−22.7780	−0.734775
$962$	6.36434	0.205195
$963$	8.71561	0.280857
$964$	−2.26143	−0.0728358
$965$	−29.6145	−0.953323
$966$	13.0758	0.420708
$967$	−38.9073	−1.25117	−0.625587	−	0.780154i	$-0.715140\pi$
$967$	−38.9073	−1.25117	−0.625587	+	0.780154i	$0.715140\pi$
$968$	−25.0169	−0.804074
$969$	−16.7561	−0.538282
$970$	5.08743	0.163347
$971$	60.3481	1.93666	0.968332	−	0.249667i	$-0.0803210\pi$
$971$	60.3481	1.93666	0.968332	+	0.249667i	$0.0803210\pi$
$972$	0.295718	0.00948516
$973$	−33.8328	−1.08463
$974$	−34.8732	−1.11741
$975$	−2.36516	−0.0757456
$976$	17.8529	0.571456
$977$	31.2124	0.998574	0.499287	−	0.866437i	$-0.333595\pi$
$977$	31.2124	0.998574	0.499287	+	0.866437i	$0.333595\pi$
$978$	−29.6178	−0.947071
$979$	47.6667	1.52343
$980$	−1.29522	−0.0413743
$981$	−2.63094	−0.0839994
$982$	−12.8752	−0.410865
$983$	−37.1045	−1.18345	−0.591725	−	0.806140i	$-0.701553\pi$
$983$	−37.1045	−1.18345	−0.591725	+	0.806140i	$0.701553\pi$
$984$	−27.7809	−0.885622
$985$	2.07488	0.0661110
$986$	42.5956	1.35652
$987$	19.8118	0.630616
$988$	−0.707555	−0.0225103
$989$	1.02555	0.0326106
$990$	15.5837	0.495284
$991$	50.8547	1.61545	0.807727	−	0.589557i	$-0.200698\pi$
$991$	50.8547	1.61545	0.807727	+	0.589557i	$0.200698\pi$
$992$	−4.75524	−0.150979
$993$	16.4923	0.523367
$994$	19.6974	0.624765
$995$	−18.6728	−0.591966
$996$	1.94526	0.0616381
$997$	41.2907	1.30769	0.653845	−	0.756629i	$-0.273155\pi$
$997$	41.2907	1.30769	0.653845	+	0.756629i	$0.273155\pi$
$998$	10.0100	0.316861
$999$	−4.87509	−0.154241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.16	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.30548 q^{2} -1.00000 q^{3} -0.295718 q^{4} +2.71388 q^{5} -1.30548 q^{6} +2.93494 q^{7} -2.99702 q^{8} +1.00000 q^{9} +3.54292 q^{10} +4.39855 q^{11} +0.295718 q^{12} +1.00000 q^{13} +3.83151 q^{14} -2.71388 q^{15} -3.32111 q^{16} +7.00308 q^{17} +1.30548 q^{18} +2.39267 q^{19} -0.802544 q^{20} -2.93494 q^{21} +5.74223 q^{22} -3.41270 q^{23} +2.99702 q^{24} +2.36516 q^{25} +1.30548 q^{26} -1.00000 q^{27} -0.867916 q^{28} +4.65913 q^{29} -3.54292 q^{30} -2.86740 q^{31} +1.65838 q^{32} -4.39855 q^{33} +9.14239 q^{34} +7.96509 q^{35} -0.295718 q^{36} +4.87509 q^{37} +3.12358 q^{38} -1.00000 q^{39} -8.13355 q^{40} -9.26951 q^{41} -3.83151 q^{42} -0.300510 q^{43} -1.30073 q^{44} +2.71388 q^{45} -4.45522 q^{46} -6.75031 q^{47} +3.32111 q^{48} +1.61389 q^{49} +3.08767 q^{50} -7.00308 q^{51} -0.295718 q^{52} -9.66362 q^{53} -1.30548 q^{54} +11.9372 q^{55} -8.79608 q^{56} -2.39267 q^{57} +6.08240 q^{58} +0.569872 q^{59} +0.802544 q^{60} -5.37556 q^{61} -3.74333 q^{62} +2.93494 q^{63} +8.80722 q^{64} +2.71388 q^{65} -5.74223 q^{66} +10.6429 q^{67} -2.07094 q^{68} +3.41270 q^{69} +10.3983 q^{70} +5.14090 q^{71} -2.99702 q^{72} -9.70296 q^{73} +6.36434 q^{74} -2.36516 q^{75} -0.707555 q^{76} +12.9095 q^{77} -1.30548 q^{78} +11.5440 q^{79} -9.01311 q^{80} +1.00000 q^{81} -12.1012 q^{82} +6.57810 q^{83} +0.867916 q^{84} +19.0055 q^{85} -0.392310 q^{86} -4.65913 q^{87} -13.1825 q^{88} +10.8369 q^{89} +3.54292 q^{90} +2.93494 q^{91} +1.00920 q^{92} +2.86740 q^{93} -8.81241 q^{94} +6.49342 q^{95} -1.65838 q^{96} +1.43594 q^{97} +2.10691 q^{98} +4.39855 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9} - 6 q^{10} + 21 q^{11} - 28 q^{12} + 25 q^{13} + 10 q^{14} - 7 q^{15} + 30 q^{16} + 14 q^{17} + 6 q^{18} + 12 q^{19} + 24 q^{20} - 17 q^{21} + 3 q^{22} + 41 q^{23} - 21 q^{24} + 30 q^{25} + 6 q^{26} - 25 q^{27} + 14 q^{28} + 22 q^{29} + 6 q^{30} + 14 q^{31} + 28 q^{32} - 21 q^{33} - 11 q^{34} + 14 q^{35} + 28 q^{36} - 6 q^{37} + 16 q^{38} - 25 q^{39} - 34 q^{40} + 33 q^{41} - 10 q^{42} + 35 q^{43} + 45 q^{44} + 7 q^{45} + 3 q^{46} + 48 q^{47} - 30 q^{48} - 4 q^{49} + 7 q^{50} - 14 q^{51} + 28 q^{52} + 18 q^{53} - 6 q^{54} + 10 q^{55} + 32 q^{56} - 12 q^{57} + 33 q^{58} + 46 q^{59} - 24 q^{60} - 19 q^{61} + 5 q^{62} + 17 q^{63} + 29 q^{64} + 7 q^{65} - 3 q^{66} + 16 q^{67} + 20 q^{68} - 41 q^{69} - 43 q^{70} + 60 q^{71} + 21 q^{72} - 14 q^{73} - 50 q^{74} - 30 q^{75} + 59 q^{77} - 6 q^{78} + 7 q^{79} + 32 q^{80} + 25 q^{81} + 18 q^{82} + 23 q^{83} - 14 q^{84} - 9 q^{85} - 9 q^{86} - 22 q^{87} + 23 q^{88} + 10 q^{89} - 6 q^{90} + 17 q^{91} + 69 q^{92} - 14 q^{93} - 30 q^{94} + 81 q^{95} - 28 q^{96} - 10 q^{97} + 55 q^{98} + 21 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 - 25 * q^3 + 28 * q^4 + 7 * q^5 - 6 * q^6 + 17 * q^7 + 21 * q^8 + 25 * q^9 - 6 * q^10 + 21 * q^11 - 28 * q^12 + 25 * q^13 + 10 * q^14 - 7 * q^15 + 30 * q^16 + 14 * q^17 + 6 * q^18 + 12 * q^19 + 24 * q^20 - 17 * q^21 + 3 * q^22 + 41 * q^23 - 21 * q^24 + 30 * q^25 + 6 * q^26 - 25 * q^27 + 14 * q^28 + 22 * q^29 + 6 * q^30 + 14 * q^31 + 28 * q^32 - 21 * q^33 - 11 * q^34 + 14 * q^35 + 28 * q^36 - 6 * q^37 + 16 * q^38 - 25 * q^39 - 34 * q^40 + 33 * q^41 - 10 * q^42 + 35 * q^43 + 45 * q^44 + 7 * q^45 + 3 * q^46 + 48 * q^47 - 30 * q^48 - 4 * q^49 + 7 * q^50 - 14 * q^51 + 28 * q^52 + 18 * q^53 - 6 * q^54 + 10 * q^55 + 32 * q^56 - 12 * q^57 + 33 * q^58 + 46 * q^59 - 24 * q^60 - 19 * q^61 + 5 * q^62 + 17 * q^63 + 29 * q^64 + 7 * q^65 - 3 * q^66 + 16 * q^67 + 20 * q^68 - 41 * q^69 - 43 * q^70 + 60 * q^71 + 21 * q^72 - 14 * q^73 - 50 * q^74 - 30 * q^75 + 59 * q^77 - 6 * q^78 + 7 * q^79 + 32 * q^80 + 25 * q^81 + 18 * q^82 + 23 * q^83 - 14 * q^84 - 9 * q^85 - 9 * q^86 - 22 * q^87 + 23 * q^88 + 10 * q^89 - 6 * q^90 + 17 * q^91 + 69 * q^92 - 14 * q^93 - 30 * q^94 + 81 * q^95 - 28 * q^96 - 10 * q^97 + 55 * q^98 + 21 * q^99

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