LMFDB - Embedded newform 4017.2.a.j.1.23

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			1.23
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)

$f(q)$	$=$	$q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +1.93520 q^{10} -1.53272 q^{11} -4.59383 q^{12} +1.00000 q^{13} +10.3372 q^{14} -0.753628 q^{15} +7.91560 q^{16} +4.91511 q^{17} +2.56785 q^{18} -0.0697656 q^{19} +3.46204 q^{20} -4.02564 q^{21} -3.93579 q^{22} +6.24416 q^{23} -6.66055 q^{24} -4.43205 q^{25} +2.56785 q^{26} -1.00000 q^{27} +18.4931 q^{28} -1.50409 q^{29} -1.93520 q^{30} -5.24621 q^{31} +7.00494 q^{32} +1.53272 q^{33} +12.6213 q^{34} +3.03383 q^{35} +4.59383 q^{36} -9.76561 q^{37} -0.179147 q^{38} -1.00000 q^{39} +5.01957 q^{40} +0.427756 q^{41} -10.3372 q^{42} +8.14611 q^{43} -7.04105 q^{44} +0.753628 q^{45} +16.0340 q^{46} -4.93673 q^{47} -7.91560 q^{48} +9.20579 q^{49} -11.3808 q^{50} -4.91511 q^{51} +4.59383 q^{52} -0.860257 q^{53} -2.56785 q^{54} -1.15510 q^{55} +26.8130 q^{56} +0.0697656 q^{57} -3.86226 q^{58} -9.54775 q^{59} -3.46204 q^{60} +8.58629 q^{61} -13.4714 q^{62} +4.02564 q^{63} +2.15640 q^{64} +0.753628 q^{65} +3.93579 q^{66} +8.96869 q^{67} +22.5792 q^{68} -6.24416 q^{69} +7.79042 q^{70} +6.17201 q^{71} +6.66055 q^{72} -0.238197 q^{73} -25.0766 q^{74} +4.43205 q^{75} -0.320491 q^{76} -6.17018 q^{77} -2.56785 q^{78} -8.45410 q^{79} +5.96542 q^{80} +1.00000 q^{81} +1.09841 q^{82} -15.3727 q^{83} -18.4931 q^{84} +3.70417 q^{85} +20.9180 q^{86} +1.50409 q^{87} -10.2088 q^{88} +3.54954 q^{89} +1.93520 q^{90} +4.02564 q^{91} +28.6846 q^{92} +5.24621 q^{93} -12.6768 q^{94} -0.0525773 q^{95} -7.00494 q^{96} +9.72261 q^{97} +23.6390 q^{98} -1.53272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.56785	1.81574	0.907870	−	0.419251i	$-0.137707\pi$
$2$	2.56785	1.81574	0.907870	+	0.419251i	$0.137707\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.59383	2.29691
$5$	0.753628	0.337032	0.168516	−	0.985699i	$-0.446102\pi$
$5$	0.753628	0.337032	0.168516	+	0.985699i	$0.446102\pi$
$6$	−2.56785	−1.04832
$7$	4.02564	1.52155	0.760775	−	0.649016i	$-0.224819\pi$
$7$	4.02564	1.52155	0.760775	+	0.649016i	$0.224819\pi$
$8$	6.66055	2.35486
$9$	1.00000	0.333333
$10$	1.93520	0.611964
$11$	−1.53272	−0.462133	−0.231066	−	0.972938i	$-0.574221\pi$
$11$	−1.53272	−0.462133	−0.231066	+	0.972938i	$0.574221\pi$
$12$	−4.59383	−1.32612
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	10.3372	2.76274
$15$	−0.753628	−0.194586
$16$	7.91560	1.97890
$17$	4.91511	1.19209	0.596045	−	0.802951i	$-0.296738\pi$
$17$	4.91511	1.19209	0.596045	+	0.802951i	$0.296738\pi$
$18$	2.56785	0.605247
$19$	−0.0697656	−0.0160053	−0.00800267	−	0.999968i	$-0.502547\pi$
$19$	−0.0697656	−0.0160053	−0.00800267	+	0.999968i	$0.502547\pi$
$20$	3.46204	0.774135
$21$	−4.02564	−0.878467
$22$	−3.93579	−0.839113
$23$	6.24416	1.30200	0.650998	−	0.759079i	$-0.274351\pi$
$23$	6.24416	1.30200	0.650998	+	0.759079i	$0.274351\pi$
$24$	−6.66055	−1.35958
$25$	−4.43205	−0.886409
$26$	2.56785	0.503596
$27$	−1.00000	−0.192450
$28$	18.4931	3.49487
$29$	−1.50409	−0.279302	−0.139651	−	0.990201i	$-0.544598\pi$
$29$	−1.50409	−0.279302	−0.139651	+	0.990201i	$0.544598\pi$
$30$	−1.93520	−0.353317
$31$	−5.24621	−0.942246	−0.471123	−	0.882067i	$-0.656151\pi$
$31$	−5.24621	−0.942246	−0.471123	+	0.882067i	$0.656151\pi$
$32$	7.00494	1.23831
$33$	1.53272	0.266812
$34$	12.6213	2.16453
$35$	3.03383	0.512812
$36$	4.59383	0.765638
$37$	−9.76561	−1.60546	−0.802728	−	0.596345i	$-0.796619\pi$
$37$	−9.76561	−1.60546	−0.802728	+	0.596345i	$0.796619\pi$
$38$	−0.179147	−0.0290615
$39$	−1.00000	−0.160128
$40$	5.01957	0.793664
$41$	0.427756	0.0668043	0.0334022	−	0.999442i	$-0.489366\pi$
$41$	0.427756	0.0668043	0.0334022	+	0.999442i	$0.489366\pi$
$42$	−10.3372	−1.59507
$43$	8.14611	1.24227	0.621135	−	0.783703i	$-0.286672\pi$
$43$	8.14611	1.24227	0.621135	+	0.783703i	$0.286672\pi$
$44$	−7.04105	−1.06148
$45$	0.753628	0.112344
$46$	16.0340	2.36409
$47$	−4.93673	−0.720096	−0.360048	−	0.932934i	$-0.617240\pi$
$47$	−4.93673	−0.720096	−0.360048	+	0.932934i	$0.617240\pi$
$48$	−7.91560	−1.14252
$49$	9.20579	1.31511
$50$	−11.3808	−1.60949
$51$	−4.91511	−0.688254
$52$	4.59383	0.637049
$53$	−0.860257	−0.118165	−0.0590827	−	0.998253i	$-0.518818\pi$
$53$	−0.860257	−0.118165	−0.0590827	+	0.998253i	$0.518818\pi$
$54$	−2.56785	−0.349439
$55$	−1.15510	−0.155754
$56$	26.8130	3.58304
$57$	0.0697656	0.00924068
$58$	−3.86226	−0.507139
$59$	−9.54775	−1.24301	−0.621505	−	0.783410i	$-0.713479\pi$
$59$	−9.54775	−1.24301	−0.621505	+	0.783410i	$0.713479\pi$
$60$	−3.46204	−0.446947
$61$	8.58629	1.09936	0.549681	−	0.835375i	$-0.314749\pi$
$61$	8.58629	1.09936	0.549681	+	0.835375i	$0.314749\pi$
$62$	−13.4714	−1.71088
$63$	4.02564	0.507183
$64$	2.15640	0.269551
$65$	0.753628	0.0934760
$66$	3.93579	0.484462
$67$	8.96869	1.09570	0.547850	−	0.836577i	$-0.315446\pi$
$67$	8.96869	1.09570	0.547850	+	0.836577i	$0.315446\pi$
$68$	22.5792	2.73813
$69$	−6.24416	−0.751708
$70$	7.79042	0.931133
$71$	6.17201	0.732483	0.366242	−	0.930520i	$-0.380644\pi$
$71$	6.17201	0.732483	0.366242	+	0.930520i	$0.380644\pi$
$72$	6.66055	0.784953
$73$	−0.238197	−0.0278788	−0.0139394	−	0.999903i	$-0.504437\pi$
$73$	−0.238197	−0.0278788	−0.0139394	+	0.999903i	$0.504437\pi$
$74$	−25.0766	−2.91509
$75$	4.43205	0.511769
$76$	−0.320491	−0.0367629
$77$	−6.17018	−0.703157
$78$	−2.56785	−0.290751
$79$	−8.45410	−0.951161	−0.475580	−	0.879672i	$-0.657762\pi$
$79$	−8.45410	−0.951161	−0.475580	+	0.879672i	$0.657762\pi$
$80$	5.96542	0.666954
$81$	1.00000	0.111111
$82$	1.09841	0.121299
$83$	−15.3727	−1.68737	−0.843686	−	0.536838i	$-0.819619\pi$
$83$	−15.3727	−1.68737	−0.843686	+	0.536838i	$0.819619\pi$
$84$	−18.4931	−2.01776
$85$	3.70417	0.401773
$86$	20.9180	2.25564
$87$	1.50409	0.161255
$88$	−10.2088	−1.08826
$89$	3.54954	0.376250	0.188125	−	0.982145i	$-0.439759\pi$
$89$	3.54954	0.376250	0.188125	+	0.982145i	$0.439759\pi$
$90$	1.93520	0.203988
$91$	4.02564	0.422002
$92$	28.6846	2.99057
$93$	5.24621	0.544006
$94$	−12.6768	−1.30751
$95$	−0.0525773	−0.00539432
$96$	−7.00494	−0.714939
$97$	9.72261	0.987181	0.493591	−	0.869694i	$-0.335684\pi$
$97$	9.72261	0.987181	0.493591	+	0.869694i	$0.335684\pi$
$98$	23.6390	2.38790
$99$	−1.53272	−0.154044
$100$	−20.3601	−2.03601
$101$	6.78390	0.675024	0.337512	−	0.941321i	$-0.390415\pi$
$101$	6.78390	0.675024	0.337512	+	0.941321i	$0.390415\pi$
$102$	−12.6213	−1.24969
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	6.66055	0.653121
$105$	−3.03383	−0.296072
$106$	−2.20901	−0.214558
$107$	9.45117	0.913679	0.456839	−	0.889549i	$-0.348981\pi$
$107$	9.45117	0.913679	0.456839	+	0.889549i	$0.348981\pi$
$108$	−4.59383	−0.442041
$109$	−0.157687	−0.0151036	−0.00755182	−	0.999971i	$-0.502404\pi$
$109$	−0.157687	−0.0151036	−0.00755182	+	0.999971i	$0.502404\pi$
$110$	−2.96612	−0.282808
$111$	9.76561	0.926910
$112$	31.8654	3.01100
$113$	−11.9407	−1.12328	−0.561642	−	0.827381i	$-0.689830\pi$
$113$	−11.9407	−1.12328	−0.561642	+	0.827381i	$0.689830\pi$
$114$	0.179147	0.0167787
$115$	4.70577	0.438815
$116$	−6.90951	−0.641532
$117$	1.00000	0.0924500
$118$	−24.5171	−2.25699
$119$	19.7865	1.81382
$120$	−5.01957	−0.458222
$121$	−8.65077	−0.786434
$122$	22.0483	1.99616
$123$	−0.427756	−0.0385695
$124$	−24.1002	−2.16426
$125$	−7.10825	−0.635781
$126$	10.3372	0.920913
$127$	−22.1645	−1.96678	−0.983390	−	0.181506i	$-0.941903\pi$
$127$	−22.1645	−1.96678	−0.983390	+	0.181506i	$0.941903\pi$
$128$	−8.47258	−0.748877
$129$	−8.14611	−0.717225
$130$	1.93520	0.169728
$131$	−12.9047	−1.12749	−0.563746	−	0.825948i	$-0.690640\pi$
$131$	−12.9047	−1.12749	−0.563746	+	0.825948i	$0.690640\pi$
$132$	7.04105	0.612845
$133$	−0.280851	−0.0243529
$134$	23.0302	1.98951
$135$	−0.753628	−0.0648619
$136$	32.7374	2.80721
$137$	7.45335	0.636783	0.318391	−	0.947959i	$-0.396857\pi$
$137$	7.45335	0.636783	0.318391	+	0.947959i	$0.396857\pi$
$138$	−16.0340	−1.36491
$139$	5.95099	0.504757	0.252378	−	0.967629i	$-0.418787\pi$
$139$	5.95099	0.504757	0.252378	+	0.967629i	$0.418787\pi$
$140$	13.9369	1.17788
$141$	4.93673	0.415748
$142$	15.8488	1.33000
$143$	−1.53272	−0.128172
$144$	7.91560	0.659634
$145$	−1.13352	−0.0941337
$146$	−0.611652	−0.0506207
$147$	−9.20579	−0.759281
$148$	−44.8615	−3.68759
$149$	3.38143	0.277017	0.138509	−	0.990361i	$-0.455769\pi$
$149$	3.38143	0.277017	0.138509	+	0.990361i	$0.455769\pi$
$150$	11.3808	0.929239
$151$	7.38300	0.600820	0.300410	−	0.953810i	$-0.402876\pi$
$151$	7.38300	0.600820	0.300410	+	0.953810i	$0.402876\pi$
$152$	−0.464677	−0.0376903
$153$	4.91511	0.397363
$154$	−15.8441	−1.27675
$155$	−3.95369	−0.317568
$156$	−4.59383	−0.367801
$157$	21.4048	1.70829	0.854144	−	0.520036i	$-0.174082\pi$
$157$	21.4048	1.70829	0.854144	+	0.520036i	$0.174082\pi$
$158$	−21.7088	−1.72706
$159$	0.860257	0.0682228
$160$	5.27912	0.417351
$161$	25.1367	1.98105
$162$	2.56785	0.201749
$163$	13.7063	1.07356	0.536780	−	0.843722i	$-0.319640\pi$
$163$	13.7063	1.07356	0.536780	+	0.843722i	$0.319640\pi$
$164$	1.96504	0.153444
$165$	1.15510	0.0899244
$166$	−39.4747	−3.06383
$167$	15.9327	1.23291	0.616453	−	0.787391i	$-0.288569\pi$
$167$	15.9327	1.23291	0.616453	+	0.787391i	$0.288569\pi$
$168$	−26.8130	−2.06867
$169$	1.00000	0.0769231
$170$	9.51172	0.729516
$171$	−0.0697656	−0.00533511
$172$	37.4218	2.85339
$173$	−19.6800	−1.49625	−0.748123	−	0.663560i	$-0.769045\pi$
$173$	−19.6800	−1.49625	−0.748123	+	0.663560i	$0.769045\pi$
$174$	3.86226	0.292797
$175$	−17.8418	−1.34872
$176$	−12.1324	−0.914514
$177$	9.54775	0.717653
$178$	9.11466	0.683173
$179$	13.0526	0.975596	0.487798	−	0.872956i	$-0.337800\pi$
$179$	13.0526	0.975596	0.487798	+	0.872956i	$0.337800\pi$
$180$	3.46204	0.258045
$181$	−4.70882	−0.350004	−0.175002	−	0.984568i	$-0.555993\pi$
$181$	−4.70882	−0.350004	−0.175002	+	0.984568i	$0.555993\pi$
$182$	10.3372	0.766246
$183$	−8.58629	−0.634717
$184$	41.5895	3.06602
$185$	−7.35963	−0.541091
$186$	13.4714	0.987774
$187$	−7.53349	−0.550904
$188$	−22.6785	−1.65400
$189$	−4.02564	−0.292822
$190$	−0.135010	−0.00979468
$191$	20.7789	1.50351	0.751755	−	0.659443i	$-0.229208\pi$
$191$	20.7789	1.50351	0.751755	+	0.659443i	$0.229208\pi$
$192$	−2.15640	−0.155625
$193$	−13.9816	−1.00641	−0.503207	−	0.864166i	$-0.667847\pi$
$193$	−13.9816	−1.00641	−0.503207	+	0.864166i	$0.667847\pi$
$194$	24.9662	1.79247
$195$	−0.753628	−0.0539684
$196$	42.2898	3.02070
$197$	24.4098	1.73912	0.869562	−	0.493824i	$-0.164401\pi$
$197$	24.4098	1.73912	0.869562	+	0.493824i	$0.164401\pi$
$198$	−3.93579	−0.279704
$199$	−9.54847	−0.676873	−0.338437	−	0.940989i	$-0.609898\pi$
$199$	−9.54847	−0.676873	−0.338437	+	0.940989i	$0.609898\pi$
$200$	−29.5199	−2.08737
$201$	−8.96869	−0.632603
$202$	17.4200	1.22567
$203$	−6.05491	−0.424971
$204$	−22.5792	−1.58086
$205$	0.322369	0.0225152
$206$	−2.56785	−0.178910
$207$	6.24416	0.433999
$208$	7.91560	0.548848
$209$	0.106931	0.00739658
$210$	−7.79042	−0.537590
$211$	−8.76259	−0.603241	−0.301621	−	0.953428i	$-0.597528\pi$
$211$	−8.76259	−0.603241	−0.301621	+	0.953428i	$0.597528\pi$
$212$	−3.95187	−0.271416
$213$	−6.17201	−0.422899
$214$	24.2691	1.65900
$215$	6.13914	0.418686
$216$	−6.66055	−0.453193
$217$	−21.1193	−1.43367
$218$	−0.404915	−0.0274243
$219$	0.238197	0.0160958
$220$	−5.30633	−0.357753
$221$	4.91511	0.330626
$222$	25.0766	1.68303
$223$	−10.3977	−0.696281	−0.348141	−	0.937442i	$-0.613187\pi$
$223$	−10.3977	−0.696281	−0.348141	+	0.937442i	$0.613187\pi$
$224$	28.1994	1.88415
$225$	−4.43205	−0.295470
$226$	−30.6618	−2.03959
$227$	−13.9555	−0.926259	−0.463129	−	0.886291i	$-0.653273\pi$
$227$	−13.9555	−0.926259	−0.463129	+	0.886291i	$0.653273\pi$
$228$	0.320491	0.0212251
$229$	−20.1645	−1.33250	−0.666252	−	0.745726i	$-0.732103\pi$
$229$	−20.1645	−1.33250	−0.666252	+	0.745726i	$0.732103\pi$
$230$	12.0837	0.796774
$231$	6.17018	0.405968
$232$	−10.0180	−0.657716
$233$	−11.2654	−0.738018	−0.369009	−	0.929426i	$-0.620303\pi$
$233$	−11.2654	−0.738018	−0.369009	+	0.929426i	$0.620303\pi$
$234$	2.56785	0.167865
$235$	−3.72046	−0.242696
$236$	−43.8607	−2.85509
$237$	8.45410	0.549153
$238$	50.8086	3.29343
$239$	21.3460	1.38076	0.690379	−	0.723448i	$-0.257444\pi$
$239$	21.3460	1.38076	0.690379	+	0.723448i	$0.257444\pi$
$240$	−5.96542	−0.385066
$241$	−9.34196	−0.601769	−0.300884	−	0.953661i	$-0.597282\pi$
$241$	−9.34196	−0.601769	−0.300884	+	0.953661i	$0.597282\pi$
$242$	−22.2138	−1.42796
$243$	−1.00000	−0.0641500
$244$	39.4440	2.52514
$245$	6.93774	0.443236
$246$	−1.09841	−0.0700322
$247$	−0.0697656	−0.00443908
$248$	−34.9426	−2.21886
$249$	15.3727	0.974204
$250$	−18.2529	−1.15441
$251$	−25.1478	−1.58732	−0.793658	−	0.608364i	$-0.791826\pi$
$251$	−25.1478	−1.58732	−0.793658	+	0.608364i	$0.791826\pi$
$252$	18.4931	1.16496
$253$	−9.57054	−0.601695
$254$	−56.9150	−3.57116
$255$	−3.70417	−0.231964
$256$	−26.0691	−1.62932
$257$	−7.81426	−0.487440	−0.243720	−	0.969846i	$-0.578368\pi$
$257$	−7.81426	−0.487440	−0.243720	+	0.969846i	$0.578368\pi$
$258$	−20.9180	−1.30230
$259$	−39.3128	−2.44278
$260$	3.46204	0.214706
$261$	−1.50409	−0.0931006
$262$	−33.1374	−2.04723
$263$	19.9147	1.22799	0.613996	−	0.789309i	$-0.289561\pi$
$263$	19.9147	1.22799	0.613996	+	0.789309i	$0.289561\pi$
$264$	10.2088	0.628306
$265$	−0.648313	−0.0398256
$266$	−0.721183	−0.0442186
$267$	−3.54954	−0.217228
$268$	41.2006	2.51673
$269$	−19.9305	−1.21518	−0.607591	−	0.794250i	$-0.707864\pi$
$269$	−19.9305	−1.21518	−0.607591	+	0.794250i	$0.707864\pi$
$270$	−1.93520	−0.117772
$271$	1.68019	0.102064	0.0510322	−	0.998697i	$-0.483749\pi$
$271$	1.68019	0.102064	0.0510322	+	0.998697i	$0.483749\pi$
$272$	38.9061	2.35903
$273$	−4.02564	−0.243643
$274$	19.1390	1.15623
$275$	6.79309	0.409638
$276$	−28.6846	−1.72661
$277$	−15.6127	−0.938075	−0.469038	−	0.883178i	$-0.655399\pi$
$277$	−15.6127	−0.938075	−0.469038	+	0.883178i	$0.655399\pi$
$278$	15.2812	0.916507
$279$	−5.24621	−0.314082
$280$	20.2070	1.20760
$281$	9.76451	0.582502	0.291251	−	0.956647i	$-0.405929\pi$
$281$	9.76451	0.582502	0.291251	+	0.956647i	$0.405929\pi$
$282$	12.6768	0.754890
$283$	−2.35538	−0.140013	−0.0700065	−	0.997547i	$-0.522302\pi$
$283$	−2.35538	−0.140013	−0.0700065	+	0.997547i	$0.522302\pi$
$284$	28.3532	1.68245
$285$	0.0525773	0.00311441
$286$	−3.93579	−0.232728
$287$	1.72199	0.101646
$288$	7.00494	0.412770
$289$	7.15834	0.421079
$290$	−2.91070	−0.170922
$291$	−9.72261	−0.569949
$292$	−1.09423	−0.0640352
$293$	12.9252	0.755101	0.377550	−	0.925989i	$-0.376767\pi$
$293$	12.9252	0.755101	0.377550	+	0.925989i	$0.376767\pi$
$294$	−23.6390	−1.37866
$295$	−7.19545	−0.418935
$296$	−65.0443	−3.78062
$297$	1.53272	0.0889374
$298$	8.68299	0.502992
$299$	6.24416	0.361109
$300$	20.3601	1.17549
$301$	32.7933	1.89018
$302$	18.9584	1.09093
$303$	−6.78390	−0.389725
$304$	−0.552237	−0.0316730
$305$	6.47087	0.370521
$306$	12.6213	0.721509
$307$	−7.02986	−0.401215	−0.200608	−	0.979672i	$-0.564292\pi$
$307$	−7.02986	−0.401215	−0.200608	+	0.979672i	$0.564292\pi$
$308$	−28.3448	−1.61509
$309$	1.00000	0.0568880
$310$	−10.1525	−0.576621
$311$	14.5830	0.826927	0.413464	−	0.910521i	$-0.364319\pi$
$311$	14.5830	0.826927	0.413464	+	0.910521i	$0.364319\pi$
$312$	−6.66055	−0.377079
$313$	29.5782	1.67186	0.835929	−	0.548837i	$-0.184929\pi$
$313$	29.5782	1.67186	0.835929	+	0.548837i	$0.184929\pi$
$314$	54.9642	3.10181
$315$	3.03383	0.170937
$316$	−38.8367	−2.18473
$317$	3.96422	0.222653	0.111326	−	0.993784i	$-0.464490\pi$
$317$	3.96422	0.222653	0.111326	+	0.993784i	$0.464490\pi$
$318$	2.20901	0.123875
$319$	2.30534	0.129074
$320$	1.62513	0.0908473
$321$	−9.45117	−0.527513
$322$	64.5472	3.59708
$323$	−0.342906	−0.0190798
$324$	4.59383	0.255213
$325$	−4.43205	−0.245846
$326$	35.1957	1.94931
$327$	0.157687	0.00872009
$328$	2.84909	0.157315
$329$	−19.8735	−1.09566
$330$	2.96612	0.163279
$331$	17.6719	0.971337	0.485668	−	0.874143i	$-0.338576\pi$
$331$	17.6719	0.971337	0.485668	+	0.874143i	$0.338576\pi$
$332$	−70.6195	−3.87575
$333$	−9.76561	−0.535152
$334$	40.9126	2.23864
$335$	6.75905	0.369286
$336$	−31.8654	−1.73840
$337$	−8.21093	−0.447278	−0.223639	−	0.974672i	$-0.571794\pi$
$337$	−8.21093	−0.447278	−0.223639	+	0.974672i	$0.571794\pi$
$338$	2.56785	0.139672
$339$	11.9407	0.648528
$340$	17.0163	0.922838
$341$	8.04097	0.435443
$342$	−0.179147	−0.00968718
$343$	8.87972	0.479460
$344$	54.2576	2.92537
$345$	−4.70577	−0.253350
$346$	−50.5353	−2.71679
$347$	−14.7394	−0.791250	−0.395625	−	0.918412i	$-0.629472\pi$
$347$	−14.7394	−0.791250	−0.395625	+	0.918412i	$0.629472\pi$
$348$	6.90951	0.370389
$349$	−15.4725	−0.828226	−0.414113	−	0.910226i	$-0.635908\pi$
$349$	−15.4725	−0.828226	−0.414113	+	0.910226i	$0.635908\pi$
$350$	−45.8150	−2.44892
$351$	−1.00000	−0.0533761
$352$	−10.7366	−0.572264
$353$	−20.9194	−1.11343	−0.556713	−	0.830705i	$-0.687938\pi$
$353$	−20.9194	−1.11343	−0.556713	+	0.830705i	$0.687938\pi$
$354$	24.5171	1.30307
$355$	4.65140	0.246871
$356$	16.3060	0.864215
$357$	−19.7865	−1.04721
$358$	33.5170	1.77143
$359$	−0.351935	−0.0185744	−0.00928721	−	0.999957i	$-0.502956\pi$
$359$	−0.351935	−0.0185744	−0.00928721	+	0.999957i	$0.502956\pi$
$360$	5.01957	0.264555
$361$	−18.9951	−0.999744
$362$	−12.0915	−0.635516
$363$	8.65077	0.454048
$364$	18.4931	0.969302
$365$	−0.179512	−0.00939606
$366$	−22.0483	−1.15248
$367$	−29.1509	−1.52166	−0.760832	−	0.648949i	$-0.775209\pi$
$367$	−29.1509	−1.52166	−0.760832	+	0.648949i	$0.775209\pi$
$368$	49.4263	2.57652
$369$	0.427756	0.0222681
$370$	−18.8984	−0.982481
$371$	−3.46309	−0.179795
$372$	24.1002	1.24954
$373$	−16.9152	−0.875836	−0.437918	−	0.899015i	$-0.644284\pi$
$373$	−16.9152	−0.875836	−0.437918	+	0.899015i	$0.644284\pi$
$374$	−19.3448	−1.00030
$375$	7.10825	0.367068
$376$	−32.8814	−1.69573
$377$	−1.50409	−0.0774643
$378$	−10.3372	−0.531689
$379$	−0.978175	−0.0502455	−0.0251227	−	0.999684i	$-0.507998\pi$
$379$	−0.978175	−0.0502455	−0.0251227	+	0.999684i	$0.507998\pi$
$380$	−0.241531	−0.0123903
$381$	22.1645	1.13552
$382$	53.3570	2.72998
$383$	11.0540	0.564831	0.282416	−	0.959292i	$-0.408864\pi$
$383$	11.0540	0.564831	0.282416	+	0.959292i	$0.408864\pi$
$384$	8.47258	0.432364
$385$	−4.65002	−0.236987
$386$	−35.9025	−1.82739
$387$	8.14611	0.414090
$388$	44.6640	2.26747
$389$	−4.64305	−0.235412	−0.117706	−	0.993048i	$-0.537554\pi$
$389$	−4.64305	−0.235412	−0.117706	+	0.993048i	$0.537554\pi$
$390$	−1.93520	−0.0979926
$391$	30.6907	1.55210
$392$	61.3156	3.09691
$393$	12.9047	0.650958
$394$	62.6805	3.15780
$395$	−6.37124	−0.320572
$396$	−7.04105	−0.353826
$397$	−26.8473	−1.34743	−0.673714	−	0.738992i	$-0.735302\pi$
$397$	−26.8473	−1.34743	−0.673714	+	0.738992i	$0.735302\pi$
$398$	−24.5190	−1.22903
$399$	0.280851	0.0140602
$400$	−35.0823	−1.75412
$401$	35.5655	1.77606	0.888029	−	0.459787i	$-0.152074\pi$
$401$	35.5655	1.77606	0.888029	+	0.459787i	$0.152074\pi$
$402$	−23.0302	−1.14864
$403$	−5.24621	−0.261332
$404$	31.1641	1.55047
$405$	0.753628	0.0374481
$406$	−15.5481	−0.771638
$407$	14.9679	0.741933
$408$	−32.7374	−1.62074
$409$	18.6967	0.924494	0.462247	−	0.886751i	$-0.347043\pi$
$409$	18.6967	0.924494	0.462247	+	0.886751i	$0.347043\pi$
$410$	0.827794	0.0408818
$411$	−7.45335	−0.367647
$412$	−4.59383	−0.226322
$413$	−38.4358	−1.89130
$414$	16.0340	0.788029
$415$	−11.5853	−0.568699
$416$	7.00494	0.343446
$417$	−5.95099	−0.291421
$418$	0.274583	0.0134303
$419$	−7.06660	−0.345226	−0.172613	−	0.984990i	$-0.555221\pi$
$419$	−7.06660	−0.345226	−0.172613	+	0.984990i	$0.555221\pi$
$420$	−13.9369	−0.680052
$421$	−5.73356	−0.279437	−0.139718	−	0.990191i	$-0.544620\pi$
$421$	−5.73356	−0.279437	−0.139718	+	0.990191i	$0.544620\pi$
$422$	−22.5010	−1.09533
$423$	−4.93673	−0.240032
$424$	−5.72979	−0.278263
$425$	−21.7840	−1.05668
$426$	−15.8488	−0.767875
$427$	34.5653	1.67273
$428$	43.4170	2.09864
$429$	1.53272	0.0740004
$430$	15.7643	0.760224
$431$	28.0805	1.35259	0.676296	−	0.736630i	$-0.263584\pi$
$431$	28.0805	1.35259	0.676296	+	0.736630i	$0.263584\pi$
$432$	−7.91560	−0.380840
$433$	1.14762	0.0551512	0.0275756	−	0.999620i	$-0.491221\pi$
$433$	1.14762	0.0551512	0.0275756	+	0.999620i	$0.491221\pi$
$434$	−54.2312	−2.60318
$435$	1.13352	0.0543481
$436$	−0.724385	−0.0346917
$437$	−0.435627	−0.0208389
$438$	0.611652	0.0292259
$439$	−17.7511	−0.847212	−0.423606	−	0.905847i	$-0.639236\pi$
$439$	−17.7511	−0.847212	−0.423606	+	0.905847i	$0.639236\pi$
$440$	−7.69360	−0.366778
$441$	9.20579	0.438371
$442$	12.6213	0.600332
$443$	9.73512	0.462530	0.231265	−	0.972891i	$-0.425714\pi$
$443$	9.73512	0.462530	0.231265	+	0.972891i	$0.425714\pi$
$444$	44.8615	2.12903
$445$	2.67503	0.126809
$446$	−26.6997	−1.26427
$447$	−3.38143	−0.159936
$448$	8.68091	0.410135
$449$	26.9762	1.27308	0.636542	−	0.771242i	$-0.280364\pi$
$449$	26.9762	1.27308	0.636542	+	0.771242i	$0.280364\pi$
$450$	−11.3808	−0.536496
$451$	−0.655631	−0.0308724
$452$	−54.8534	−2.58009
$453$	−7.38300	−0.346884
$454$	−35.8355	−1.68185
$455$	3.03383	0.142228
$456$	0.464677	0.0217605
$457$	−15.2298	−0.712421	−0.356210	−	0.934406i	$-0.615931\pi$
$457$	−15.2298	−0.712421	−0.356210	+	0.934406i	$0.615931\pi$
$458$	−51.7792	−2.41948
$459$	−4.91511	−0.229418
$460$	21.6175	1.00792
$461$	−26.2141	−1.22091	−0.610457	−	0.792049i	$-0.709014\pi$
$461$	−26.2141	−1.22091	−0.610457	+	0.792049i	$0.709014\pi$
$462$	15.8441	0.737133
$463$	−38.6214	−1.79489	−0.897445	−	0.441127i	$-0.854579\pi$
$463$	−38.6214	−1.79489	−0.897445	+	0.441127i	$0.854579\pi$
$464$	−11.9057	−0.552710
$465$	3.95369	0.183348
$466$	−28.9277	−1.34005
$467$	3.88345	0.179705	0.0898523	−	0.995955i	$-0.471360\pi$
$467$	3.88345	0.179705	0.0898523	+	0.995955i	$0.471360\pi$
$468$	4.59383	0.212350
$469$	36.1047	1.66716
$470$	−9.55356	−0.440673
$471$	−21.4048	−0.986281
$472$	−63.5932	−2.92712
$473$	−12.4857	−0.574094
$474$	21.7088	0.997119
$475$	0.309204	0.0141873
$476$	90.8957	4.16620
$477$	−0.860257	−0.0393885
$478$	54.8132	2.50710
$479$	41.5638	1.89910	0.949550	−	0.313616i	$-0.101540\pi$
$479$	41.5638	1.89910	0.949550	+	0.313616i	$0.101540\pi$
$480$	−5.27912	−0.240958
$481$	−9.76561	−0.445273
$482$	−23.9887	−1.09266
$483$	−25.1367	−1.14376
$484$	−39.7401	−1.80637
$485$	7.32723	0.332712
$486$	−2.56785	−0.116480
$487$	32.8306	1.48770	0.743848	−	0.668349i	$-0.232999\pi$
$487$	32.8306	1.48770	0.743848	+	0.668349i	$0.232999\pi$
$488$	57.1894	2.58884
$489$	−13.7063	−0.619820
$490$	17.8150	0.804801
$491$	−4.04624	−0.182604	−0.0913022	−	0.995823i	$-0.529103\pi$
$491$	−4.04624	−0.182604	−0.0913022	+	0.995823i	$0.529103\pi$
$492$	−1.96504	−0.0885908
$493$	−7.39275	−0.332953
$494$	−0.179147	−0.00806022
$495$	−1.15510	−0.0519179
$496$	−41.5269	−1.86461
$497$	24.8463	1.11451
$498$	39.4747	1.76890
$499$	−29.9618	−1.34127	−0.670636	−	0.741786i	$-0.733979\pi$
$499$	−29.9618	−1.34127	−0.670636	+	0.741786i	$0.733979\pi$
$500$	−32.6541	−1.46033
$501$	−15.9327	−0.711819
$502$	−64.5757	−2.88215
$503$	5.69578	0.253962	0.126981	−	0.991905i	$-0.459471\pi$
$503$	5.69578	0.253962	0.126981	+	0.991905i	$0.459471\pi$
$504$	26.8130	1.19435
$505$	5.11254	0.227505
$506$	−24.5757	−1.09252
$507$	−1.00000	−0.0444116
$508$	−101.820	−4.51752
$509$	11.1028	0.492124	0.246062	−	0.969254i	$-0.420863\pi$
$509$	11.1028	0.492124	0.246062	+	0.969254i	$0.420863\pi$
$510$	−9.51172	−0.421186
$511$	−0.958894	−0.0424190
$512$	−49.9962	−2.20954
$513$	0.0697656	0.00308023
$514$	−20.0658	−0.885065
$515$	−0.753628	−0.0332088
$516$	−37.4218	−1.64740
$517$	7.56663	0.332780
$518$	−100.949	−4.43546
$519$	19.6800	0.863858
$520$	5.01957	0.220123
$521$	−18.9692	−0.831055	−0.415527	−	0.909581i	$-0.636403\pi$
$521$	−18.9692	−0.831055	−0.415527	+	0.909581i	$0.636403\pi$
$522$	−3.86226	−0.169046
$523$	−20.5439	−0.898321	−0.449161	−	0.893451i	$-0.648277\pi$
$523$	−20.5439	−0.898321	−0.449161	+	0.893451i	$0.648277\pi$
$524$	−59.2821	−2.58975
$525$	17.8418	0.778681
$526$	51.1379	2.22972
$527$	−25.7857	−1.12324
$528$	12.1324	0.527995
$529$	15.9895	0.695195
$530$	−1.66477	−0.0723129
$531$	−9.54775	−0.414337
$532$	−1.29018	−0.0559365
$533$	0.427756	0.0185282
$534$	−9.11466	−0.394430
$535$	7.12266	0.307939
$536$	59.7364	2.58022
$537$	−13.0526	−0.563261
$538$	−51.1784	−2.20646
$539$	−14.1099	−0.607756
$540$	−3.46204	−0.148982
$541$	−20.8922	−0.898225	−0.449112	−	0.893475i	$-0.648260\pi$
$541$	−20.8922	−0.898225	−0.449112	+	0.893475i	$0.648260\pi$
$542$	4.31447	0.185322
$543$	4.70882	0.202075
$544$	34.4301	1.47618
$545$	−0.118837	−0.00509041
$546$	−10.3372	−0.442392
$547$	−29.6638	−1.26833	−0.634166	−	0.773197i	$-0.718657\pi$
$547$	−29.6638	−1.26833	−0.634166	+	0.773197i	$0.718657\pi$
$548$	34.2394	1.46264
$549$	8.58629	0.366454
$550$	17.4436	0.743797
$551$	0.104933	0.00447032
$552$	−41.5895	−1.77017
$553$	−34.0332	−1.44724
$554$	−40.0910	−1.70330
$555$	7.35963	0.312399
$556$	27.3378	1.15938
$557$	−8.79439	−0.372630	−0.186315	−	0.982490i	$-0.559655\pi$
$557$	−8.79439	−0.372630	−0.186315	+	0.982490i	$0.559655\pi$
$558$	−13.4714	−0.570292
$559$	8.14611	0.344544
$560$	24.0146	1.01480
$561$	7.53349	0.318064
$562$	25.0737	1.05767
$563$	9.31467	0.392567	0.196283	−	0.980547i	$-0.437113\pi$
$563$	9.31467	0.392567	0.196283	+	0.980547i	$0.437113\pi$
$564$	22.6785	0.954937
$565$	−8.99881	−0.378583
$566$	−6.04826	−0.254227
$567$	4.02564	0.169061
$568$	41.1090	1.72489
$569$	−8.26466	−0.346472	−0.173236	−	0.984880i	$-0.555422\pi$
$569$	−8.26466	−0.346472	−0.173236	+	0.984880i	$0.555422\pi$
$570$	0.135010	0.00565496
$571$	36.8776	1.54328	0.771640	−	0.636059i	$-0.219437\pi$
$571$	36.8776	1.54328	0.771640	+	0.636059i	$0.219437\pi$
$572$	−7.04105	−0.294401
$573$	−20.7789	−0.868051
$574$	4.42181	0.184563
$575$	−27.6744	−1.15410
$576$	2.15640	0.0898502
$577$	−1.41656	−0.0589723	−0.0294862	−	0.999565i	$-0.509387\pi$
$577$	−1.41656	−0.0589723	−0.0294862	+	0.999565i	$0.509387\pi$
$578$	18.3815	0.764570
$579$	13.9816	0.581053
$580$	−5.20720	−0.216217
$581$	−61.8849	−2.56742
$582$	−24.9662	−1.03488
$583$	1.31853	0.0546081
$584$	−1.58652	−0.0656507
$585$	0.753628	0.0311587
$586$	33.1900	1.37107
$587$	−12.2617	−0.506093	−0.253046	−	0.967454i	$-0.581432\pi$
$587$	−12.2617	−0.506093	−0.253046	+	0.967454i	$0.581432\pi$
$588$	−42.2898	−1.74400
$589$	0.366005	0.0150810
$590$	−18.4768	−0.760677
$591$	−24.4098	−1.00408
$592$	−77.3007	−3.17704
$593$	−42.0989	−1.72880	−0.864398	−	0.502809i	$-0.832300\pi$
$593$	−42.0989	−1.72880	−0.864398	+	0.502809i	$0.832300\pi$
$594$	3.93579	0.161487
$595$	14.9116	0.611318
$596$	15.5337	0.636285
$597$	9.54847	0.390793
$598$	16.0340	0.655680
$599$	−12.5514	−0.512837	−0.256419	−	0.966566i	$-0.582543\pi$
$599$	−12.5514	−0.512837	−0.256419	+	0.966566i	$0.582543\pi$
$600$	29.5199	1.20514
$601$	−37.6749	−1.53679	−0.768395	−	0.639976i	$-0.778944\pi$
$601$	−37.6749	−1.53679	−0.768395	+	0.639976i	$0.778944\pi$
$602$	84.2082	3.43207
$603$	8.96869	0.365233
$604$	33.9162	1.38003
$605$	−6.51946	−0.265054
$606$	−17.4200	−0.707640
$607$	17.4729	0.709202	0.354601	−	0.935018i	$-0.384617\pi$
$607$	17.4729	0.709202	0.354601	+	0.935018i	$0.384617\pi$
$608$	−0.488704	−0.0198196
$609$	6.05491	0.245357
$610$	16.6162	0.672770
$611$	−4.93673	−0.199719
$612$	22.5792	0.912710
$613$	−35.6028	−1.43798	−0.718992	−	0.695019i	$-0.755396\pi$
$613$	−35.6028	−1.43798	−0.718992	+	0.695019i	$0.755396\pi$
$614$	−18.0516	−0.728503
$615$	−0.322369	−0.0129992
$616$	−41.0968	−1.65584
$617$	27.1997	1.09502	0.547510	−	0.836799i	$-0.315576\pi$
$617$	27.1997	1.09502	0.547510	+	0.836799i	$0.315576\pi$
$618$	2.56785	0.103294
$619$	12.4081	0.498725	0.249362	−	0.968410i	$-0.419779\pi$
$619$	12.4081	0.498725	0.249362	+	0.968410i	$0.419779\pi$
$620$	−18.1626	−0.729426
$621$	−6.24416	−0.250569
$622$	37.4469	1.50149
$623$	14.2892	0.572483
$624$	−7.91560	−0.316878
$625$	16.8033	0.672130
$626$	75.9522	3.03566
$627$	−0.106931	−0.00427042
$628$	98.3299	3.92379
$629$	−47.9991	−1.91385
$630$	7.79042	0.310378
$631$	34.9182	1.39007	0.695036	−	0.718975i	$-0.255388\pi$
$631$	34.9182	1.39007	0.695036	+	0.718975i	$0.255388\pi$
$632$	−56.3090	−2.23985
$633$	8.76259	0.348282
$634$	10.1795	0.404279
$635$	−16.7038	−0.662869
$636$	3.95187	0.156702
$637$	9.20579	0.364747
$638$	5.91976	0.234366
$639$	6.17201	0.244161
$640$	−6.38517	−0.252396
$641$	20.8605	0.823941	0.411971	−	0.911197i	$-0.364841\pi$
$641$	20.8605	0.823941	0.411971	+	0.911197i	$0.364841\pi$
$642$	−24.2691	−0.957826
$643$	−8.84522	−0.348821	−0.174411	−	0.984673i	$-0.555802\pi$
$643$	−8.84522	−0.348821	−0.174411	+	0.984673i	$0.555802\pi$
$644$	115.474	4.55031
$645$	−6.13914	−0.241728
$646$	−0.880529	−0.0346440
$647$	−8.15864	−0.320749	−0.160375	−	0.987056i	$-0.551270\pi$
$647$	−8.15864	−0.320749	−0.160375	+	0.987056i	$0.551270\pi$
$648$	6.66055	0.261651
$649$	14.6340	0.574436
$650$	−11.3808	−0.446392
$651$	21.1193	0.827732
$652$	62.9644	2.46588
$653$	−16.9131	−0.661862	−0.330931	−	0.943655i	$-0.607363\pi$
$653$	−16.9131	−0.661862	−0.330931	+	0.943655i	$0.607363\pi$
$654$	0.404915	0.0158334
$655$	−9.72536	−0.380001
$656$	3.38595	0.132199
$657$	−0.238197	−0.00929293
$658$	−51.0321	−1.98944
$659$	22.7068	0.884530	0.442265	−	0.896884i	$-0.354175\pi$
$659$	22.7068	0.884530	0.442265	+	0.896884i	$0.354175\pi$
$660$	5.30633	0.206549
$661$	1.32046	0.0513598	0.0256799	−	0.999670i	$-0.491825\pi$
$661$	1.32046	0.0513598	0.0256799	+	0.999670i	$0.491825\pi$
$662$	45.3788	1.76370
$663$	−4.91511	−0.190887
$664$	−102.391	−3.97352
$665$	−0.211657	−0.00820772
$666$	−25.0766	−0.971697
$667$	−9.39174	−0.363650
$668$	73.1919	2.83188
$669$	10.3977	0.401998
$670$	17.3562	0.670528
$671$	−13.1604	−0.508051
$672$	−28.1994	−1.08782
$673$	14.1709	0.546246	0.273123	−	0.961979i	$-0.411943\pi$
$673$	14.1709	0.546246	0.273123	+	0.961979i	$0.411943\pi$
$674$	−21.0844	−0.812140
$675$	4.43205	0.170590
$676$	4.59383	0.176686
$677$	−33.5126	−1.28799	−0.643997	−	0.765028i	$-0.722725\pi$
$677$	−33.5126	−1.28799	−0.643997	+	0.765028i	$0.722725\pi$
$678$	30.6618	1.17756
$679$	39.1397	1.50205
$680$	24.6718	0.946119
$681$	13.9555	0.534776
$682$	20.6480	0.790651
$683$	−16.9612	−0.649004	−0.324502	−	0.945885i	$-0.605197\pi$
$683$	−16.9612	−0.649004	−0.324502	+	0.945885i	$0.605197\pi$
$684$	−0.320491	−0.0122543
$685$	5.61705	0.214616
$686$	22.8017	0.870575
$687$	20.1645	0.769322
$688$	64.4814	2.45833
$689$	−0.860257	−0.0327732
$690$	−12.0837	−0.460018
$691$	−3.56530	−0.135631	−0.0678153	−	0.997698i	$-0.521603\pi$
$691$	−3.56530	−0.135631	−0.0678153	+	0.997698i	$0.521603\pi$
$692$	−90.4067	−3.43675
$693$	−6.17018	−0.234386
$694$	−37.8484	−1.43670
$695$	4.48483	0.170119
$696$	10.0180	0.379733
$697$	2.10247	0.0796368
$698$	−39.7311	−1.50384
$699$	11.2654	0.426095
$700$	−81.9623	−3.09788
$701$	10.1457	0.383199	0.191600	−	0.981473i	$-0.438632\pi$
$701$	10.1457	0.383199	0.191600	+	0.981473i	$0.438632\pi$
$702$	−2.56785	−0.0969171
$703$	0.681304	0.0256959
$704$	−3.30516	−0.124568
$705$	3.72046	0.140121
$706$	−53.7177	−2.02169
$707$	27.3096	1.02708
$708$	43.8607	1.64839
$709$	26.9164	1.01087	0.505434	−	0.862866i	$-0.331333\pi$
$709$	26.9164	1.01087	0.505434	+	0.862866i	$0.331333\pi$
$710$	11.9441	0.448253
$711$	−8.45410	−0.317054
$712$	23.6419	0.886017
$713$	−32.7581	−1.22680
$714$	−50.8086	−1.90147
$715$	−1.15510	−0.0431983
$716$	59.9613	2.24086
$717$	−21.3460	−0.797181
$718$	−0.903715	−0.0337263
$719$	34.8774	1.30071	0.650355	−	0.759631i	$-0.274620\pi$
$719$	34.8774	1.30071	0.650355	+	0.759631i	$0.274620\pi$
$720$	5.96542	0.222318
$721$	−4.02564	−0.149923
$722$	−48.7766	−1.81528
$723$	9.34196	0.347431
$724$	−21.6315	−0.803929
$725$	6.66618	0.247576
$726$	22.2138	0.824433
$727$	1.83373	0.0680094	0.0340047	−	0.999422i	$-0.489174\pi$
$727$	1.83373	0.0680094	0.0340047	+	0.999422i	$0.489174\pi$
$728$	26.8130	0.993755
$729$	1.00000	0.0370370
$730$	−0.460958	−0.0170608
$731$	40.0391	1.48090
$732$	−39.4440	−1.45789
$733$	−37.1021	−1.37040	−0.685199	−	0.728356i	$-0.740285\pi$
$733$	−37.1021	−1.37040	−0.685199	+	0.728356i	$0.740285\pi$
$734$	−74.8549	−2.76295
$735$	−6.93774	−0.255902
$736$	43.7400	1.61228
$737$	−13.7465	−0.506359
$738$	1.09841	0.0404331
$739$	−10.6811	−0.392912	−0.196456	−	0.980513i	$-0.562943\pi$
$739$	−10.6811	−0.392912	−0.196456	+	0.980513i	$0.562943\pi$
$740$	−33.8089	−1.24284
$741$	0.0697656	0.00256290
$742$	−8.89267	−0.326460
$743$	25.5886	0.938755	0.469377	−	0.882998i	$-0.344478\pi$
$743$	25.5886	0.938755	0.469377	+	0.882998i	$0.344478\pi$
$744$	34.9426	1.28106
$745$	2.54834	0.0933639
$746$	−43.4356	−1.59029
$747$	−15.3727	−0.562457
$748$	−34.6076	−1.26538
$749$	38.0470	1.39021
$750$	18.2529	0.666501
$751$	−27.1942	−0.992329	−0.496165	−	0.868228i	$-0.665259\pi$
$751$	−27.1942	−0.992329	−0.496165	+	0.868228i	$0.665259\pi$
$752$	−39.0772	−1.42500
$753$	25.1478	0.916437
$754$	−3.86226	−0.140655
$755$	5.56403	0.202496
$756$	−18.4931	−0.672588
$757$	36.5157	1.32719	0.663593	−	0.748094i	$-0.269031\pi$
$757$	36.5157	1.32719	0.663593	+	0.748094i	$0.269031\pi$
$758$	−2.51180	−0.0912328
$759$	9.57054	0.347389
$760$	−0.350194	−0.0127029
$761$	19.3220	0.700421	0.350211	−	0.936671i	$-0.386110\pi$
$761$	19.3220	0.700421	0.350211	+	0.936671i	$0.386110\pi$
$762$	56.9150	2.06181
$763$	−0.634789	−0.0229809
$764$	95.4548	3.45343
$765$	3.70417	0.133924
$766$	28.3849	1.02559
$767$	−9.54775	−0.344749
$768$	26.0691	0.940687
$769$	29.2293	1.05404	0.527018	−	0.849854i	$-0.323310\pi$
$769$	29.2293	1.05404	0.527018	+	0.849854i	$0.323310\pi$
$770$	−11.9405	−0.430307
$771$	7.81426	0.281424
$772$	−64.2288	−2.31165
$773$	2.57526	0.0926257	0.0463129	−	0.998927i	$-0.485253\pi$
$773$	2.57526	0.0926257	0.0463129	+	0.998927i	$0.485253\pi$
$774$	20.9180	0.751880
$775$	23.2514	0.835216
$776$	64.7579	2.32467
$777$	39.3128	1.41034
$778$	−11.9226	−0.427447
$779$	−0.0298427	−0.00106923
$780$	−3.46204	−0.123961
$781$	−9.45997	−0.338504
$782$	78.8091	2.81821
$783$	1.50409	0.0537516
$784$	72.8694	2.60248
$785$	16.1312	0.575749
$786$	33.1374	1.18197
$787$	13.2448	0.472126	0.236063	−	0.971738i	$-0.424143\pi$
$787$	13.2448	0.472126	0.236063	+	0.971738i	$0.424143\pi$
$788$	112.134	3.99462
$789$	−19.9147	−0.708982
$790$	−16.3604	−0.582076
$791$	−48.0688	−1.70913
$792$	−10.2088	−0.362752
$793$	8.58629	0.304908
$794$	−68.9398	−2.44658
$795$	0.648313	0.0229933
$796$	−43.8640	−1.55472
$797$	1.15649	0.0409651	0.0204826	−	0.999790i	$-0.493480\pi$
$797$	1.15649	0.0409651	0.0204826	+	0.999790i	$0.493480\pi$
$798$	0.721183	0.0255296
$799$	−24.2646	−0.858420
$800$	−31.0462	−1.09765
$801$	3.54954	0.125417
$802$	91.3268	3.22486
$803$	0.365089	0.0128837
$804$	−41.2006	−1.45303
$805$	18.9437	0.667679
$806$	−13.4714	−0.474511
$807$	19.9305	0.701586
$808$	45.1845	1.58959
$809$	−34.3868	−1.20897	−0.604487	−	0.796615i	$-0.706622\pi$
$809$	−34.3868	−1.20897	−0.604487	+	0.796615i	$0.706622\pi$
$810$	1.93520	0.0679960
$811$	−36.8430	−1.29373	−0.646866	−	0.762604i	$-0.723921\pi$
$811$	−36.8430	−1.29373	−0.646866	+	0.762604i	$0.723921\pi$
$812$	−27.8152	−0.976123
$813$	−1.68019	−0.0589269
$814$	38.4354	1.34716
$815$	10.3294	0.361825
$816$	−38.9061	−1.36199
$817$	−0.568319	−0.0198830
$818$	48.0103	1.67864
$819$	4.02564	0.140667
$820$	1.48091	0.0517155
$821$	29.8368	1.04131	0.520656	−	0.853767i	$-0.325688\pi$
$821$	29.8368	1.04131	0.520656	+	0.853767i	$0.325688\pi$
$822$	−19.1390	−0.667551
$823$	−7.22794	−0.251950	−0.125975	−	0.992033i	$-0.540206\pi$
$823$	−7.22794	−0.251950	−0.125975	+	0.992033i	$0.540206\pi$
$824$	−6.66055	−0.232031
$825$	−6.79309	−0.236505
$826$	−98.6972	−3.43411
$827$	23.2046	0.806902	0.403451	−	0.915001i	$-0.367811\pi$
$827$	23.2046	0.806902	0.403451	+	0.915001i	$0.367811\pi$
$828$	28.6846	0.996858
$829$	17.2545	0.599275	0.299638	−	0.954053i	$-0.403134\pi$
$829$	17.2545	0.599275	0.299638	+	0.954053i	$0.403134\pi$
$830$	−29.7492	−1.03261
$831$	15.6127	0.541598
$832$	2.15640	0.0747599
$833$	45.2475	1.56773
$834$	−15.2812	−0.529146
$835$	12.0073	0.415530
$836$	0.491223	0.0169893
$837$	5.24621	0.181335
$838$	−18.1459	−0.626841
$839$	−14.9565	−0.516355	−0.258178	−	0.966097i	$-0.583122\pi$
$839$	−14.9565	−0.516355	−0.258178	+	0.966097i	$0.583122\pi$
$840$	−20.2070	−0.697208
$841$	−26.7377	−0.921991
$842$	−14.7229	−0.507385
$843$	−9.76451	−0.336307
$844$	−40.2538	−1.38559
$845$	0.753628	0.0259256
$846$	−12.6768	−0.435836
$847$	−34.8249	−1.19660
$848$	−6.80945	−0.233838
$849$	2.35538	0.0808366
$850$	−55.9380	−1.91866
$851$	−60.9780	−2.09030
$852$	−28.3532	−0.971363
$853$	−0.583746	−0.0199871	−0.00999355	−	0.999950i	$-0.503181\pi$
$853$	−0.583746	−0.0199871	−0.00999355	+	0.999950i	$0.503181\pi$
$854$	88.7584	3.03725
$855$	−0.0525773	−0.00179811
$856$	62.9500	2.15159
$857$	29.3409	1.00227	0.501133	−	0.865370i	$-0.332917\pi$
$857$	29.3409	1.00227	0.501133	+	0.865370i	$0.332917\pi$
$858$	3.93579	0.134366
$859$	33.5962	1.14629	0.573144	−	0.819455i	$-0.305724\pi$
$859$	33.5962	1.14629	0.573144	+	0.819455i	$0.305724\pi$
$860$	28.2021	0.961685
$861$	−1.72199	−0.0586854
$862$	72.1065	2.45596
$863$	45.7565	1.55757	0.778786	−	0.627290i	$-0.215836\pi$
$863$	45.7565	1.55757	0.778786	+	0.627290i	$0.215836\pi$
$864$	−7.00494	−0.238313
$865$	−14.8314	−0.504283
$866$	2.94691	0.100140
$867$	−7.15834	−0.243110
$868$	−97.0187	−3.29303
$869$	12.9578	0.439562
$870$	2.91070	0.0986821
$871$	8.96869	0.303892
$872$	−1.05028	−0.0355669
$873$	9.72261	0.329060
$874$	−1.11862	−0.0378380
$875$	−28.6153	−0.967372
$876$	1.09423	0.0369707
$877$	−54.6191	−1.84436	−0.922178	−	0.386766i	$-0.873592\pi$
$877$	−54.6191	−1.84436	−0.922178	+	0.386766i	$0.873592\pi$
$878$	−45.5820	−1.53832
$879$	−12.9252	−0.435958
$880$	−9.14331	−0.308221
$881$	1.34888	0.0454451	0.0227225	−	0.999742i	$-0.492767\pi$
$881$	1.34888	0.0454451	0.0227225	+	0.999742i	$0.492767\pi$
$882$	23.6390	0.795968
$883$	−32.7093	−1.10075	−0.550377	−	0.834916i	$-0.685516\pi$
$883$	−32.7093	−1.10075	−0.550377	+	0.834916i	$0.685516\pi$
$884$	22.5792	0.759420
$885$	7.19545	0.241872
$886$	24.9983	0.839834
$887$	−58.2866	−1.95707	−0.978537	−	0.206072i	$-0.933932\pi$
$887$	−58.2866	−1.95707	−0.978537	+	0.206072i	$0.933932\pi$
$888$	65.0443	2.18274
$889$	−89.2263	−2.99255
$890$	6.86906	0.230251
$891$	−1.53272	−0.0513481
$892$	−47.7652	−1.59930
$893$	0.344414	0.0115254
$894$	−8.68299	−0.290403
$895$	9.83679	0.328808
$896$	−34.1076	−1.13945
$897$	−6.24416	−0.208486
$898$	69.2707	2.31159
$899$	7.89074	0.263171
$900$	−20.3601	−0.678669
$901$	−4.22826	−0.140864
$902$	−1.68356	−0.0560564
$903$	−32.7933	−1.09129
$904$	−79.5314	−2.64517
$905$	−3.54870	−0.117963
$906$	−18.9584	−0.629851
$907$	36.4308	1.20966	0.604832	−	0.796353i	$-0.293240\pi$
$907$	36.4308	1.20966	0.604832	+	0.796353i	$0.293240\pi$
$908$	−64.1091	−2.12754
$909$	6.78390	0.225008
$910$	7.79042	0.258250
$911$	−39.2112	−1.29913	−0.649563	−	0.760308i	$-0.725048\pi$
$911$	−39.2112	−1.29913	−0.649563	+	0.760308i	$0.725048\pi$
$912$	0.552237	0.0182864
$913$	23.5620	0.779789
$914$	−39.1078	−1.29357
$915$	−6.47087	−0.213920
$916$	−92.6320	−3.06065
$917$	−51.9498	−1.71553
$918$	−12.6213	−0.416563
$919$	−33.8709	−1.11730	−0.558650	−	0.829404i	$-0.688680\pi$
$919$	−33.8709	−1.11730	−0.558650	+	0.829404i	$0.688680\pi$
$920$	31.3430	1.03335
$921$	7.02986	0.231642
$922$	−67.3138	−2.21686
$923$	6.17201	0.203154
$924$	28.3448	0.932474
$925$	43.2816	1.42309
$926$	−99.1738	−3.25905
$927$	−1.00000	−0.0328443
$928$	−10.5360	−0.345862
$929$	7.69768	0.252553	0.126276	−	0.991995i	$-0.459697\pi$
$929$	7.69768	0.252553	0.126276	+	0.991995i	$0.459697\pi$
$930$	10.1525	0.332912
$931$	−0.642248	−0.0210488
$932$	−51.7511	−1.69516
$933$	−14.5830	−0.477427
$934$	9.97210	0.326297
$935$	−5.67745	−0.185672
$936$	6.66055	0.217707
$937$	59.7890	1.95322	0.976611	−	0.215013i	$-0.0689794\pi$
$937$	59.7890	1.95322	0.976611	+	0.215013i	$0.0689794\pi$
$938$	92.7114	3.02713
$939$	−29.5782	−0.965248
$940$	−17.0911	−0.557452
$941$	−22.5376	−0.734705	−0.367353	−	0.930082i	$-0.619736\pi$
$941$	−22.5376	−0.734705	−0.367353	+	0.930082i	$0.619736\pi$
$942$	−54.9642	−1.79083
$943$	2.67098	0.0869790
$944$	−75.5762	−2.45980
$945$	−3.03383	−0.0986906
$946$	−32.0614	−1.04241
$947$	−11.6363	−0.378130	−0.189065	−	0.981965i	$-0.560546\pi$
$947$	−11.6363	−0.378130	−0.189065	+	0.981965i	$0.560546\pi$
$948$	38.8367	1.26136
$949$	−0.238197	−0.00773219
$950$	0.793989	0.0257604
$951$	−3.96422	−0.128549
$952$	131.789	4.27130
$953$	−19.1906	−0.621644	−0.310822	−	0.950468i	$-0.600604\pi$
$953$	−19.1906	−0.621644	−0.310822	+	0.950468i	$0.600604\pi$
$954$	−2.20901	−0.0715192
$955$	15.6596	0.506731
$956$	98.0599	3.17148
$957$	−2.30534	−0.0745211
$958$	106.729	3.44827
$959$	30.0045	0.968896
$960$	−1.62513	−0.0524507
$961$	−3.47732	−0.112172
$962$	−25.0766	−0.808501
$963$	9.45117	0.304560
$964$	−42.9154	−1.38221
$965$	−10.5369	−0.339194
$966$	−64.5472	−2.07677
$967$	60.8434	1.95659	0.978296	−	0.207210i	$-0.0664383\pi$
$967$	60.8434	1.95659	0.978296	+	0.207210i	$0.0664383\pi$
$968$	−57.6189	−1.85194
$969$	0.342906	0.0110157
$970$	18.8152	0.604119
$971$	4.53003	0.145375	0.0726877	−	0.997355i	$-0.476842\pi$
$971$	4.53003	0.145375	0.0726877	+	0.997355i	$0.476842\pi$
$972$	−4.59383	−0.147347
$973$	23.9566	0.768012
$974$	84.3039	2.70127
$975$	4.43205	0.141939
$976$	67.9657	2.17553
$977$	−29.2598	−0.936105	−0.468052	−	0.883701i	$-0.655044\pi$
$977$	−29.2598	−0.936105	−0.468052	+	0.883701i	$0.655044\pi$
$978$	−35.1957	−1.12543
$979$	−5.44045	−0.173877
$980$	31.8708	1.01807
$981$	−0.157687	−0.00503454
$982$	−10.3901	−0.331562
$983$	26.5529	0.846907	0.423453	−	0.905918i	$-0.360818\pi$
$983$	26.5529	0.846907	0.423453	+	0.905918i	$0.360818\pi$
$984$	−2.84909	−0.0908258
$985$	18.3959	0.586141
$986$	−18.9834	−0.604556
$987$	19.8735	0.632581
$988$	−0.320491	−0.0101962
$989$	50.8656	1.61743
$990$	−2.96612	−0.0942694
$991$	23.8623	0.758010	0.379005	−	0.925395i	$-0.376266\pi$
$991$	23.8623	0.758010	0.379005	+	0.925395i	$0.376266\pi$
$992$	−36.7494	−1.16679
$993$	−17.6719	−0.560802
$994$	63.8015	2.02366
$995$	−7.19599	−0.228128
$996$	70.6195	2.23766
$997$	−2.34842	−0.0743753	−0.0371876	−	0.999308i	$-0.511840\pi$
$997$	−2.34842	−0.0743753	−0.0371876	+	0.999308i	$0.511840\pi$
$998$	−76.9371	−2.43540
$999$	9.76561	0.308970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.j.1.23	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.23	✓	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)

\(f(q)\)	\(=\)	\(q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +1.93520 q^{10} -1.53272 q^{11} -4.59383 q^{12} +1.00000 q^{13} +10.3372 q^{14} -0.753628 q^{15} +7.91560 q^{16} +4.91511 q^{17} +2.56785 q^{18} -0.0697656 q^{19} +3.46204 q^{20} -4.02564 q^{21} -3.93579 q^{22} +6.24416 q^{23} -6.66055 q^{24} -4.43205 q^{25} +2.56785 q^{26} -1.00000 q^{27} +18.4931 q^{28} -1.50409 q^{29} -1.93520 q^{30} -5.24621 q^{31} +7.00494 q^{32} +1.53272 q^{33} +12.6213 q^{34} +3.03383 q^{35} +4.59383 q^{36} -9.76561 q^{37} -0.179147 q^{38} -1.00000 q^{39} +5.01957 q^{40} +0.427756 q^{41} -10.3372 q^{42} +8.14611 q^{43} -7.04105 q^{44} +0.753628 q^{45} +16.0340 q^{46} -4.93673 q^{47} -7.91560 q^{48} +9.20579 q^{49} -11.3808 q^{50} -4.91511 q^{51} +4.59383 q^{52} -0.860257 q^{53} -2.56785 q^{54} -1.15510 q^{55} +26.8130 q^{56} +0.0697656 q^{57} -3.86226 q^{58} -9.54775 q^{59} -3.46204 q^{60} +8.58629 q^{61} -13.4714 q^{62} +4.02564 q^{63} +2.15640 q^{64} +0.753628 q^{65} +3.93579 q^{66} +8.96869 q^{67} +22.5792 q^{68} -6.24416 q^{69} +7.79042 q^{70} +6.17201 q^{71} +6.66055 q^{72} -0.238197 q^{73} -25.0766 q^{74} +4.43205 q^{75} -0.320491 q^{76} -6.17018 q^{77} -2.56785 q^{78} -8.45410 q^{79} +5.96542 q^{80} +1.00000 q^{81} +1.09841 q^{82} -15.3727 q^{83} -18.4931 q^{84} +3.70417 q^{85} +20.9180 q^{86} +1.50409 q^{87} -10.2088 q^{88} +3.54954 q^{89} +1.93520 q^{90} +4.02564 q^{91} +28.6846 q^{92} +5.24621 q^{93} -12.6768 q^{94} -0.0525773 q^{95} -7.00494 q^{96} +9.72261 q^{97} +23.6390 q^{98} -1.53272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 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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