LMFDB - Embedded newform 4017.2.a.j.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} -9.62067 q^{10} +0.122675 q^{11} -5.03939 q^{12} +1.00000 q^{13} +4.50300 q^{14} -3.62608 q^{15} +11.3167 q^{16} +1.64880 q^{17} -2.65319 q^{18} +2.48476 q^{19} +18.2733 q^{20} +1.69720 q^{21} -0.325481 q^{22} +7.71361 q^{23} +8.06407 q^{24} +8.14847 q^{25} -2.65319 q^{26} -1.00000 q^{27} -8.55288 q^{28} -8.37984 q^{29} +9.62067 q^{30} -5.04198 q^{31} -13.8971 q^{32} -0.122675 q^{33} -4.37458 q^{34} -6.15420 q^{35} +5.03939 q^{36} +7.37109 q^{37} -6.59252 q^{38} -1.00000 q^{39} -29.2410 q^{40} -5.29852 q^{41} -4.50300 q^{42} +5.82960 q^{43} +0.618209 q^{44} +3.62608 q^{45} -20.4656 q^{46} +11.9749 q^{47} -11.3167 q^{48} -4.11950 q^{49} -21.6194 q^{50} -1.64880 q^{51} +5.03939 q^{52} -3.27337 q^{53} +2.65319 q^{54} +0.444831 q^{55} +13.6864 q^{56} -2.48476 q^{57} +22.2333 q^{58} +9.14392 q^{59} -18.2733 q^{60} -11.7962 q^{61} +13.3773 q^{62} -1.69720 q^{63} +14.2383 q^{64} +3.62608 q^{65} +0.325481 q^{66} -12.8241 q^{67} +8.30897 q^{68} -7.71361 q^{69} +16.3282 q^{70} +12.5788 q^{71} -8.06407 q^{72} -6.39645 q^{73} -19.5569 q^{74} -8.14847 q^{75} +12.5217 q^{76} -0.208205 q^{77} +2.65319 q^{78} +9.16008 q^{79} +41.0352 q^{80} +1.00000 q^{81} +14.0579 q^{82} +16.7645 q^{83} +8.55288 q^{84} +5.97870 q^{85} -15.4670 q^{86} +8.37984 q^{87} -0.989263 q^{88} +1.34263 q^{89} -9.62067 q^{90} -1.69720 q^{91} +38.8719 q^{92} +5.04198 q^{93} -31.7716 q^{94} +9.00994 q^{95} +13.8971 q^{96} +8.30957 q^{97} +10.9298 q^{98} +0.122675 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.65319	−1.87609	−0.938043	−	0.346520i	$-0.887363\pi$
$2$	−2.65319	−1.87609	−0.938043	+	0.346520i	$0.887363\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.03939	2.51970
$5$	3.62608	1.62163	0.810817	−	0.585300i	$-0.199023\pi$
$5$	3.62608	1.62163	0.810817	+	0.585300i	$0.199023\pi$
$6$	2.65319	1.08316
$7$	−1.69720	−0.641483	−0.320741	−	0.947167i	$-0.603932\pi$
$7$	−1.69720	−0.641483	−0.320741	+	0.947167i	$0.603932\pi$
$8$	−8.06407	−2.85108
$9$	1.00000	0.333333
$10$	−9.62067	−3.04232
$11$	0.122675	0.0369880	0.0184940	−	0.999829i	$-0.494113\pi$
$11$	0.122675	0.0369880	0.0184940	+	0.999829i	$0.494113\pi$
$12$	−5.03939	−1.45475
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.50300	1.20348
$15$	−3.62608	−0.936250
$16$	11.3167	2.82917
$17$	1.64880	0.399894	0.199947	−	0.979807i	$-0.435923\pi$
$17$	1.64880	0.399894	0.199947	+	0.979807i	$0.435923\pi$
$18$	−2.65319	−0.625362
$19$	2.48476	0.570043	0.285021	−	0.958521i	$-0.407999\pi$
$19$	2.48476	0.570043	0.285021	+	0.958521i	$0.407999\pi$
$20$	18.2733	4.08602
$21$	1.69720	0.370360
$22$	−0.325481	−0.0693927
$23$	7.71361	1.60840	0.804200	−	0.594359i	$-0.202594\pi$
$23$	7.71361	1.60840	0.804200	+	0.594359i	$0.202594\pi$
$24$	8.06407	1.64607
$25$	8.14847	1.62969
$26$	−2.65319	−0.520332
$27$	−1.00000	−0.192450
$28$	−8.55288	−1.61634
$29$	−8.37984	−1.55610	−0.778049	−	0.628204i	$-0.783790\pi$
$29$	−8.37984	−1.55610	−0.778049	+	0.628204i	$0.783790\pi$
$30$	9.62067	1.75649
$31$	−5.04198	−0.905567	−0.452783	−	0.891621i	$-0.649569\pi$
$31$	−5.04198	−0.905567	−0.452783	+	0.891621i	$0.649569\pi$
$32$	−13.8971	−2.45669
$33$	−0.122675	−0.0213550
$34$	−4.37458	−0.750235
$35$	−6.15420	−1.04025
$36$	5.03939	0.839899
$37$	7.37109	1.21180	0.605900	−	0.795541i	$-0.292813\pi$
$37$	7.37109	1.21180	0.605900	+	0.795541i	$0.292813\pi$
$38$	−6.59252	−1.06945
$39$	−1.00000	−0.160128
$40$	−29.2410	−4.62341
$41$	−5.29852	−0.827489	−0.413745	−	0.910393i	$-0.635779\pi$
$41$	−5.29852	−0.827489	−0.413745	+	0.910393i	$0.635779\pi$
$42$	−4.50300	−0.694827
$43$	5.82960	0.889006	0.444503	−	0.895777i	$-0.353380\pi$
$43$	5.82960	0.889006	0.444503	+	0.895777i	$0.353380\pi$
$44$	0.618209	0.0931986
$45$	3.62608	0.540544
$46$	−20.4656	−3.01749
$47$	11.9749	1.74672	0.873359	−	0.487077i	$-0.161937\pi$
$47$	11.9749	1.74672	0.873359	+	0.487077i	$0.161937\pi$
$48$	−11.3167	−1.63342
$49$	−4.11950	−0.588500
$50$	−21.6194	−3.05745
$51$	−1.64880	−0.230879
$52$	5.03939	0.698838
$53$	−3.27337	−0.449633	−0.224816	−	0.974401i	$-0.572178\pi$
$53$	−3.27337	−0.449633	−0.224816	+	0.974401i	$0.572178\pi$
$54$	2.65319	0.361053
$55$	0.444831	0.0599810
$56$	13.6864	1.82892
$57$	−2.48476	−0.329114
$58$	22.2333	2.91937
$59$	9.14392	1.19044	0.595218	−	0.803564i	$-0.297066\pi$
$59$	9.14392	1.19044	0.595218	+	0.803564i	$0.297066\pi$
$60$	−18.2733	−2.35907
$61$	−11.7962	−1.51035	−0.755177	−	0.655521i	$-0.772449\pi$
$61$	−11.7962	−1.51035	−0.755177	+	0.655521i	$0.772449\pi$
$62$	13.3773	1.69892
$63$	−1.69720	−0.213828
$64$	14.2383	1.77979
$65$	3.62608	0.449760
$66$	0.325481	0.0400639
$67$	−12.8241	−1.56672	−0.783359	−	0.621569i	$-0.786495\pi$
$67$	−12.8241	−1.56672	−0.783359	+	0.621569i	$0.786495\pi$
$68$	8.30897	1.00761
$69$	−7.71361	−0.928610
$70$	16.3282	1.95160
$71$	12.5788	1.49283	0.746413	−	0.665483i	$-0.231775\pi$
$71$	12.5788	1.49283	0.746413	+	0.665483i	$0.231775\pi$
$72$	−8.06407	−0.950360
$73$	−6.39645	−0.748648	−0.374324	−	0.927298i	$-0.622125\pi$
$73$	−6.39645	−0.748648	−0.374324	+	0.927298i	$0.622125\pi$
$74$	−19.5569	−2.27344
$75$	−8.14847	−0.940905
$76$	12.5217	1.43633
$77$	−0.208205	−0.0237272
$78$	2.65319	0.300414
$79$	9.16008	1.03059	0.515295	−	0.857013i	$-0.327682\pi$
$79$	9.16008	1.03059	0.515295	+	0.857013i	$0.327682\pi$
$80$	41.0352	4.58788
$81$	1.00000	0.111111
$82$	14.0579	1.55244
$83$	16.7645	1.84014	0.920071	−	0.391753i	$-0.128131\pi$
$83$	16.7645	1.84014	0.920071	+	0.391753i	$0.128131\pi$
$84$	8.55288	0.933195
$85$	5.97870	0.648481
$86$	−15.4670	−1.66785
$87$	8.37984	0.898413
$88$	−0.989263	−0.105456
$89$	1.34263	0.142319	0.0711595	−	0.997465i	$-0.477330\pi$
$89$	1.34263	0.142319	0.0711595	+	0.997465i	$0.477330\pi$
$90$	−9.62067	−1.01411
$91$	−1.69720	−0.177915
$92$	38.8719	4.05268
$93$	5.04198	0.522829
$94$	−31.7716	−3.27699
$95$	9.00994	0.924400
$96$	13.8971	1.41837
$97$	8.30957	0.843709	0.421854	−	0.906664i	$-0.361379\pi$
$97$	8.30957	0.843709	0.421854	+	0.906664i	$0.361379\pi$
$98$	10.9298	1.10408
$99$	0.122675	0.0123293
$100$	41.0634	4.10634
$101$	13.7971	1.37286	0.686430	−	0.727196i	$-0.259177\pi$
$101$	13.7971	1.37286	0.686430	+	0.727196i	$0.259177\pi$
$102$	4.37458	0.433148
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−8.06407	−0.790747
$105$	6.15420	0.600589
$106$	8.68487	0.843549
$107$	−18.8039	−1.81784	−0.908919	−	0.416972i	$-0.863091\pi$
$107$	−18.8039	−1.81784	−0.908919	+	0.416972i	$0.863091\pi$
$108$	−5.03939	−0.484916
$109$	3.01954	0.289220	0.144610	−	0.989489i	$-0.453807\pi$
$109$	3.01954	0.289220	0.144610	+	0.989489i	$0.453807\pi$
$110$	−1.18022	−0.112530
$111$	−7.37109	−0.699633
$112$	−19.2067	−1.81486
$113$	16.5599	1.55782	0.778911	−	0.627134i	$-0.215772\pi$
$113$	16.5599	1.55782	0.778911	+	0.627134i	$0.215772\pi$
$114$	6.59252	0.617446
$115$	27.9702	2.60823
$116$	−42.2293	−3.92089
$117$	1.00000	0.0924500
$118$	−24.2605	−2.23336
$119$	−2.79836	−0.256525
$120$	29.2410	2.66932
$121$	−10.9850	−0.998632
$122$	31.2976	2.83355
$123$	5.29852	0.477751
$124$	−25.4085	−2.28175
$125$	11.4166	1.02113
$126$	4.50300	0.401159
$127$	8.09714	0.718505	0.359252	−	0.933240i	$-0.383032\pi$
$127$	8.09714	0.718505	0.359252	+	0.933240i	$0.383032\pi$
$128$	−9.98254	−0.882341
$129$	−5.82960	−0.513268
$130$	−9.62067	−0.843788
$131$	−6.12661	−0.535284	−0.267642	−	0.963518i	$-0.586244\pi$
$131$	−6.12661	−0.535284	−0.267642	+	0.963518i	$0.586244\pi$
$132$	−0.618209	−0.0538082
$133$	−4.21714	−0.365673
$134$	34.0248	2.93930
$135$	−3.62608	−0.312083
$136$	−13.2961	−1.14013
$137$	16.4654	1.40673	0.703366	−	0.710828i	$-0.251680\pi$
$137$	16.4654	1.40673	0.703366	+	0.710828i	$0.251680\pi$
$138$	20.4656	1.74215
$139$	6.84474	0.580563	0.290282	−	0.956941i	$-0.406251\pi$
$139$	6.84474	0.580563	0.290282	+	0.956941i	$0.406251\pi$
$140$	−31.0134	−2.62111
$141$	−11.9749	−1.00847
$142$	−33.3738	−2.80067
$143$	0.122675	0.0102586
$144$	11.3167	0.943057
$145$	−30.3860	−2.52342
$146$	16.9710	1.40453
$147$	4.11950	0.339771
$148$	37.1458	3.05337
$149$	−9.62736	−0.788704	−0.394352	−	0.918959i	$-0.629031\pi$
$149$	−9.62736	−0.788704	−0.394352	+	0.918959i	$0.629031\pi$
$150$	21.6194	1.76522
$151$	−22.5090	−1.83175	−0.915877	−	0.401458i	$-0.868504\pi$
$151$	−22.5090	−1.83175	−0.915877	+	0.401458i	$0.868504\pi$
$152$	−20.0373	−1.62524
$153$	1.64880	0.133298
$154$	0.552407	0.0445142
$155$	−18.2826	−1.46850
$156$	−5.03939	−0.403474
$157$	−13.9794	−1.11568	−0.557840	−	0.829948i	$-0.688370\pi$
$157$	−13.9794	−1.11568	−0.557840	+	0.829948i	$0.688370\pi$
$158$	−24.3034	−1.93347
$159$	3.27337	0.259596
$160$	−50.3921	−3.98385
$161$	−13.0916	−1.03176
$162$	−2.65319	−0.208454
$163$	12.7910	1.00187	0.500936	−	0.865485i	$-0.332989\pi$
$163$	12.7910	1.00187	0.500936	+	0.865485i	$0.332989\pi$
$164$	−26.7013	−2.08502
$165$	−0.444831	−0.0346301
$166$	−44.4793	−3.45226
$167$	6.86951	0.531579	0.265789	−	0.964031i	$-0.414367\pi$
$167$	6.86951	0.531579	0.265789	+	0.964031i	$0.414367\pi$
$168$	−13.6864	−1.05593
$169$	1.00000	0.0769231
$170$	−15.8626	−1.21661
$171$	2.48476	0.190014
$172$	29.3776	2.24002
$173$	−0.853628	−0.0649002	−0.0324501	−	0.999473i	$-0.510331\pi$
$173$	−0.853628	−0.0649002	−0.0324501	+	0.999473i	$0.510331\pi$
$174$	−22.2333	−1.68550
$175$	−13.8296	−1.04542
$176$	1.38828	0.104645
$177$	−9.14392	−0.687299
$178$	−3.56226	−0.267003
$179$	0.172575	0.0128989	0.00644943	−	0.999979i	$-0.497947\pi$
$179$	0.172575	0.0128989	0.00644943	+	0.999979i	$0.497947\pi$
$180$	18.2733	1.36201
$181$	−16.3527	−1.21548	−0.607742	−	0.794135i	$-0.707924\pi$
$181$	−16.3527	−1.21548	−0.607742	+	0.794135i	$0.707924\pi$
$182$	4.50300	0.333784
$183$	11.7962	0.872003
$184$	−62.2031	−4.58567
$185$	26.7282	1.96509
$186$	−13.3773	−0.980872
$187$	0.202268	0.0147913
$188$	60.3462	4.40120
$189$	1.69720	0.123453
$190$	−23.9050	−1.73425
$191$	4.28492	0.310046	0.155023	−	0.987911i	$-0.450455\pi$
$191$	4.28492	0.310046	0.155023	+	0.987911i	$0.450455\pi$
$192$	−14.2383	−1.02756
$193$	−22.8864	−1.64740	−0.823698	−	0.567029i	$-0.808093\pi$
$193$	−22.8864	−1.64740	−0.823698	+	0.567029i	$0.808093\pi$
$194$	−22.0468	−1.58287
$195$	−3.62608	−0.259669
$196$	−20.7598	−1.48284
$197$	1.55653	0.110898	0.0554492	−	0.998462i	$-0.482341\pi$
$197$	1.55653	0.110898	0.0554492	+	0.998462i	$0.482341\pi$
$198$	−0.325481	−0.0231309
$199$	6.78405	0.480908	0.240454	−	0.970660i	$-0.422704\pi$
$199$	6.78405	0.480908	0.240454	+	0.970660i	$0.422704\pi$
$200$	−65.7099	−4.64639
$201$	12.8241	0.904545
$202$	−36.6062	−2.57560
$203$	14.2223	0.998209
$204$	−8.30897	−0.581744
$205$	−19.2129	−1.34188
$206$	2.65319	0.184856
$207$	7.71361	0.536133
$208$	11.3167	0.784671
$209$	0.304819	0.0210848
$210$	−16.3282	−1.12676
$211$	16.6781	1.14817	0.574083	−	0.818797i	$-0.305359\pi$
$211$	16.6781	1.14817	0.574083	+	0.818797i	$0.305359\pi$
$212$	−16.4958	−1.13294
$213$	−12.5788	−0.861883
$214$	49.8901	3.41042
$215$	21.1386	1.44164
$216$	8.06407	0.548690
$217$	8.55727	0.580905
$218$	−8.01141	−0.542601
$219$	6.39645	0.432232
$220$	2.24168	0.151134
$221$	1.64880	0.110911
$222$	19.5569	1.31257
$223$	3.87678	0.259608	0.129804	−	0.991540i	$-0.458565\pi$
$223$	3.87678	0.259608	0.129804	+	0.991540i	$0.458565\pi$
$224$	23.5863	1.57592
$225$	8.14847	0.543232
$226$	−43.9364	−2.92261
$227$	−29.7814	−1.97666	−0.988332	−	0.152315i	$-0.951327\pi$
$227$	−29.7814	−1.97666	−0.988332	+	0.152315i	$0.951327\pi$
$228$	−12.5217	−0.829268
$229$	−15.9711	−1.05540	−0.527701	−	0.849430i	$-0.676946\pi$
$229$	−15.9711	−1.05540	−0.527701	+	0.849430i	$0.676946\pi$
$230$	−74.2101	−4.89327
$231$	0.208205	0.0136989
$232$	67.5756	4.43656
$233$	14.3408	0.939497	0.469748	−	0.882800i	$-0.344345\pi$
$233$	14.3408	0.939497	0.469748	+	0.882800i	$0.344345\pi$
$234$	−2.65319	−0.173444
$235$	43.4219	2.83254
$236$	46.0798	2.99954
$237$	−9.16008	−0.595011
$238$	7.42456	0.481263
$239$	−3.34738	−0.216524	−0.108262	−	0.994122i	$-0.534529\pi$
$239$	−3.34738	−0.216524	−0.108262	+	0.994122i	$0.534529\pi$
$240$	−41.0352	−2.64881
$241$	7.97897	0.513971	0.256985	−	0.966415i	$-0.417271\pi$
$241$	7.97897	0.513971	0.256985	+	0.966415i	$0.417271\pi$
$242$	29.1451	1.87352
$243$	−1.00000	−0.0641500
$244$	−59.4459	−3.80563
$245$	−14.9376	−0.954331
$246$	−14.0579	−0.896302
$247$	2.48476	0.158101
$248$	40.6589	2.58184
$249$	−16.7645	−1.06241
$250$	−30.2904	−1.91574
$251$	16.3350	1.03105	0.515527	−	0.856873i	$-0.327596\pi$
$251$	16.3350	1.03105	0.515527	+	0.856873i	$0.327596\pi$
$252$	−8.55288	−0.538780
$253$	0.946270	0.0594915
$254$	−21.4832	−1.34798
$255$	−5.97870	−0.374401
$256$	−1.99103	−0.124439
$257$	5.39908	0.336786	0.168393	−	0.985720i	$-0.446142\pi$
$257$	5.39908	0.336786	0.168393	+	0.985720i	$0.446142\pi$
$258$	15.4670	0.962934
$259$	−12.5102	−0.777348
$260$	18.2733	1.13326
$261$	−8.37984	−0.518699
$262$	16.2550	1.00424
$263$	4.35020	0.268245	0.134123	−	0.990965i	$-0.457178\pi$
$263$	4.35020	0.268245	0.134123	+	0.990965i	$0.457178\pi$
$264$	0.989263	0.0608849
$265$	−11.8695	−0.729139
$266$	11.1889	0.686033
$267$	−1.34263	−0.0821679
$268$	−64.6259	−3.94765
$269$	−2.42763	−0.148015	−0.0740076	−	0.997258i	$-0.523579\pi$
$269$	−2.42763	−0.148015	−0.0740076	+	0.997258i	$0.523579\pi$
$270$	9.62067	0.585495
$271$	18.5705	1.12808	0.564038	−	0.825749i	$-0.309247\pi$
$271$	18.5705	1.12808	0.564038	+	0.825749i	$0.309247\pi$
$272$	18.6590	1.13137
$273$	1.69720	0.102719
$274$	−43.6857	−2.63915
$275$	0.999617	0.0602792
$276$	−38.8719	−2.33981
$277$	4.53094	0.272238	0.136119	−	0.990693i	$-0.456537\pi$
$277$	4.53094	0.272238	0.136119	+	0.990693i	$0.456537\pi$
$278$	−18.1604	−1.08919
$279$	−5.04198	−0.301856
$280$	49.6279	2.96583
$281$	18.8843	1.12655	0.563273	−	0.826271i	$-0.309542\pi$
$281$	18.8843	1.12655	0.563273	+	0.826271i	$0.309542\pi$
$282$	31.7716	1.89197
$283$	9.24039	0.549284	0.274642	−	0.961547i	$-0.411441\pi$
$283$	9.24039	0.549284	0.274642	+	0.961547i	$0.411441\pi$
$284$	63.3894	3.76147
$285$	−9.00994	−0.533703
$286$	−0.325481	−0.0192461
$287$	8.99266	0.530820
$288$	−13.8971	−0.818896
$289$	−14.2814	−0.840085
$290$	80.6197	4.73415
$291$	−8.30957	−0.487115
$292$	−32.2342	−1.88637
$293$	−4.77518	−0.278969	−0.139484	−	0.990224i	$-0.544545\pi$
$293$	−4.77518	−0.278969	−0.139484	+	0.990224i	$0.544545\pi$
$294$	−10.9298	−0.637439
$295$	33.1566	1.93045
$296$	−59.4410	−3.45494
$297$	−0.122675	−0.00711835
$298$	25.5432	1.47968
$299$	7.71361	0.446090
$300$	−41.0634	−2.37079
$301$	−9.89402	−0.570282
$302$	59.7205	3.43653
$303$	−13.7971	−0.792621
$304$	28.1192	1.61275
$305$	−42.7742	−2.44924
$306$	−4.37458	−0.250078
$307$	24.1332	1.37735	0.688677	−	0.725068i	$-0.258192\pi$
$307$	24.1332	1.37735	0.688677	+	0.725068i	$0.258192\pi$
$308$	−1.04923	−0.0597853
$309$	1.00000	0.0568880
$310$	48.5072	2.75503
$311$	−1.20829	−0.0685157	−0.0342578	−	0.999413i	$-0.510907\pi$
$311$	−1.20829	−0.0685157	−0.0342578	+	0.999413i	$0.510907\pi$
$312$	8.06407	0.456538
$313$	8.52454	0.481835	0.240918	−	0.970546i	$-0.422552\pi$
$313$	8.52454	0.481835	0.240918	+	0.970546i	$0.422552\pi$
$314$	37.0900	2.09311
$315$	−6.15420	−0.346750
$316$	46.1612	2.59677
$317$	6.81411	0.382718	0.191359	−	0.981520i	$-0.438710\pi$
$317$	6.81411	0.382718	0.191359	+	0.981520i	$0.438710\pi$
$318$	−8.68487	−0.487023
$319$	−1.02800	−0.0575570
$320$	51.6292	2.88616
$321$	18.8039	1.04953
$322$	34.7344	1.93567
$323$	4.09688	0.227957
$324$	5.03939	0.279966
$325$	8.14847	0.451996
$326$	−33.9370	−1.87960
$327$	−3.01954	−0.166981
$328$	42.7276	2.35924
$329$	−20.3238	−1.12049
$330$	1.18022	0.0649689
$331$	8.88374	0.488295	0.244147	−	0.969738i	$-0.421492\pi$
$331$	8.88374	0.488295	0.244147	+	0.969738i	$0.421492\pi$
$332$	84.4828	4.63660
$333$	7.37109	0.403933
$334$	−18.2261	−0.997287
$335$	−46.5014	−2.54064
$336$	19.2067	1.04781
$337$	14.4415	0.786678	0.393339	−	0.919394i	$-0.371320\pi$
$337$	14.4415	0.786678	0.393339	+	0.919394i	$0.371320\pi$
$338$	−2.65319	−0.144314
$339$	−16.5599	−0.899409
$340$	30.1290	1.63398
$341$	−0.618527	−0.0334951
$342$	−6.59252	−0.356483
$343$	18.8721	1.01900
$344$	−47.0103	−2.53463
$345$	−27.9702	−1.50586
$346$	2.26483	0.121758
$347$	−19.1942	−1.03040	−0.515200	−	0.857070i	$-0.672282\pi$
$347$	−19.1942	−1.03040	−0.515200	+	0.857070i	$0.672282\pi$
$348$	42.2293	2.26373
$349$	22.0422	1.17989	0.589947	−	0.807442i	$-0.299149\pi$
$349$	22.0422	1.17989	0.589947	+	0.807442i	$0.299149\pi$
$350$	36.6925	1.96130
$351$	−1.00000	−0.0533761
$352$	−1.70484	−0.0908681
$353$	−28.7933	−1.53251	−0.766256	−	0.642536i	$-0.777882\pi$
$353$	−28.7933	−1.53251	−0.766256	+	0.642536i	$0.777882\pi$
$354$	24.2605	1.28943
$355$	45.6117	2.42082
$356$	6.76606	0.358601
$357$	2.79836	0.148105
$358$	−0.457873	−0.0241994
$359$	10.1538	0.535897	0.267949	−	0.963433i	$-0.413654\pi$
$359$	10.1538	0.535897	0.267949	+	0.963433i	$0.413654\pi$
$360$	−29.2410	−1.54114
$361$	−12.8260	−0.675051
$362$	43.3866	2.28035
$363$	10.9850	0.576560
$364$	−8.55288	−0.448292
$365$	−23.1941	−1.21403
$366$	−31.2976	−1.63595
$367$	−18.3419	−0.957441	−0.478721	−	0.877967i	$-0.658899\pi$
$367$	−18.3419	−0.957441	−0.478721	+	0.877967i	$0.658899\pi$
$368$	87.2925	4.55044
$369$	−5.29852	−0.275830
$370$	−70.9148	−3.68668
$371$	5.55558	0.288432
$372$	25.4085	1.31737
$373$	−6.57033	−0.340199	−0.170099	−	0.985427i	$-0.554409\pi$
$373$	−6.57033	−0.340199	−0.170099	+	0.985427i	$0.554409\pi$
$374$	−0.536654	−0.0277497
$375$	−11.4166	−0.589552
$376$	−96.5664	−4.98003
$377$	−8.37984	−0.431584
$378$	−4.50300	−0.231609
$379$	25.3617	1.30274	0.651371	−	0.758759i	$-0.274194\pi$
$379$	25.3617	1.30274	0.651371	+	0.758759i	$0.274194\pi$
$380$	45.4046	2.32921
$381$	−8.09714	−0.414829
$382$	−11.3687	−0.581673
$383$	7.27999	0.371990	0.185995	−	0.982551i	$-0.440449\pi$
$383$	7.27999	0.371990	0.185995	+	0.982551i	$0.440449\pi$
$384$	9.98254	0.509420
$385$	−0.754969	−0.0384768
$386$	60.7217	3.09066
$387$	5.82960	0.296335
$388$	41.8752	2.12589
$389$	−7.67944	−0.389363	−0.194681	−	0.980867i	$-0.562367\pi$
$389$	−7.67944	−0.389363	−0.194681	+	0.980867i	$0.562367\pi$
$390$	9.62067	0.487161
$391$	12.7182	0.643189
$392$	33.2199	1.67786
$393$	6.12661	0.309046
$394$	−4.12977	−0.208055
$395$	33.2152	1.67124
$396$	0.618209	0.0310662
$397$	16.4485	0.825527	0.412764	−	0.910838i	$-0.364564\pi$
$397$	16.4485	0.825527	0.412764	+	0.910838i	$0.364564\pi$
$398$	−17.9993	−0.902225
$399$	4.21714	0.211121
$400$	92.2137	4.61069
$401$	9.58200	0.478502	0.239251	−	0.970958i	$-0.423098\pi$
$401$	9.58200	0.478502	0.239251	+	0.970958i	$0.423098\pi$
$402$	−34.0248	−1.69700
$403$	−5.04198	−0.251159
$404$	69.5288	3.45919
$405$	3.62608	0.180181
$406$	−37.7344	−1.87273
$407$	0.904251	0.0448221
$408$	13.2961	0.658254
$409$	−6.85379	−0.338898	−0.169449	−	0.985539i	$-0.554199\pi$
$409$	−6.85379	−0.338898	−0.169449	+	0.985539i	$0.554199\pi$
$410$	50.9753	2.51749
$411$	−16.4654	−0.812177
$412$	−5.03939	−0.248273
$413$	−15.5191	−0.763645
$414$	−20.4656	−1.00583
$415$	60.7894	2.98403
$416$	−13.8971	−0.681363
$417$	−6.84474	−0.335188
$418$	−0.808741	−0.0395568
$419$	−39.3855	−1.92411	−0.962053	−	0.272863i	$-0.912029\pi$
$419$	−39.3855	−1.92411	−0.962053	+	0.272863i	$0.912029\pi$
$420$	31.0134	1.51330
$421$	−15.5708	−0.758877	−0.379438	−	0.925217i	$-0.623883\pi$
$421$	−15.5708	−0.758877	−0.379438	+	0.925217i	$0.623883\pi$
$422$	−44.2500	−2.15406
$423$	11.9749	0.582239
$424$	26.3967	1.28194
$425$	13.4352	0.651705
$426$	33.3738	1.61697
$427$	20.0206	0.968866
$428$	−94.7601	−4.58040
$429$	−0.122675	−0.00592282
$430$	−56.0847	−2.70464
$431$	−17.8741	−0.860967	−0.430484	−	0.902598i	$-0.641657\pi$
$431$	−17.8741	−0.860967	−0.430484	+	0.902598i	$0.641657\pi$
$432$	−11.3167	−0.544474
$433$	−7.56596	−0.363597	−0.181798	−	0.983336i	$-0.558192\pi$
$433$	−7.56596	−0.363597	−0.181798	+	0.983336i	$0.558192\pi$
$434$	−22.7040	−1.08983
$435$	30.3860	1.45690
$436$	15.2167	0.728746
$437$	19.1665	0.916856
$438$	−16.9710	−0.810905
$439$	−9.55373	−0.455975	−0.227987	−	0.973664i	$-0.573215\pi$
$439$	−9.55373	−0.455975	−0.227987	+	0.973664i	$0.573215\pi$
$440$	−3.58715	−0.171011
$441$	−4.11950	−0.196167
$442$	−4.37458	−0.208078
$443$	−28.4283	−1.35067	−0.675335	−	0.737511i	$-0.736001\pi$
$443$	−28.4283	−1.35067	−0.675335	+	0.737511i	$0.736001\pi$
$444$	−37.1458	−1.76286
$445$	4.86850	0.230789
$446$	−10.2858	−0.487047
$447$	9.62736	0.455358
$448$	−24.1653	−1.14170
$449$	23.9759	1.13149	0.565747	−	0.824579i	$-0.308588\pi$
$449$	23.9759	1.13149	0.565747	+	0.824579i	$0.308588\pi$
$450$	−21.6194	−1.01915
$451$	−0.649998	−0.0306072
$452$	83.4517	3.92524
$453$	22.5090	1.05756
$454$	79.0157	3.70839
$455$	−6.15420	−0.288513
$456$	20.0373	0.938331
$457$	30.9830	1.44933	0.724663	−	0.689103i	$-0.241995\pi$
$457$	30.9830	1.44933	0.724663	+	0.689103i	$0.241995\pi$
$458$	42.3744	1.98002
$459$	−1.64880	−0.0769596
$460$	140.953	6.57196
$461$	15.9537	0.743038	0.371519	−	0.928425i	$-0.378837\pi$
$461$	15.9537	0.743038	0.371519	+	0.928425i	$0.378837\pi$
$462$	−0.552407	−0.0257003
$463$	−26.9533	−1.25263	−0.626314	−	0.779571i	$-0.715437\pi$
$463$	−26.9533	−1.25263	−0.626314	+	0.779571i	$0.715437\pi$
$464$	−94.8320	−4.40247
$465$	18.2826	0.847837
$466$	−38.0488	−1.76258
$467$	−25.1178	−1.16231	−0.581156	−	0.813792i	$-0.697399\pi$
$467$	−25.1178	−1.16231	−0.581156	+	0.813792i	$0.697399\pi$
$468$	5.03939	0.232946
$469$	21.7652	1.00502
$470$	−115.206	−5.31408
$471$	13.9794	0.644138
$472$	−73.7372	−3.39403
$473$	0.715149	0.0328826
$474$	24.3034	1.11629
$475$	20.2470	0.928996
$476$	−14.1020	−0.646365
$477$	−3.27337	−0.149878
$478$	8.88123	0.406218
$479$	40.4928	1.85017	0.925083	−	0.379766i	$-0.123995\pi$
$479$	40.4928	1.85017	0.925083	+	0.379766i	$0.123995\pi$
$480$	50.3921	2.30008
$481$	7.37109	0.336093
$482$	−21.1697	−0.964253
$483$	13.0916	0.595687
$484$	−55.3575	−2.51625
$485$	30.1312	1.36819
$486$	2.65319	0.120351
$487$	30.3711	1.37624	0.688122	−	0.725595i	$-0.258435\pi$
$487$	30.3711	1.37624	0.688122	+	0.725595i	$0.258435\pi$
$488$	95.1257	4.30614
$489$	−12.7910	−0.578431
$490$	39.6323	1.79041
$491$	1.93259	0.0872166	0.0436083	−	0.999049i	$-0.486115\pi$
$491$	1.93259	0.0872166	0.0436083	+	0.999049i	$0.486115\pi$
$492$	26.7013	1.20379
$493$	−13.8167	−0.622274
$494$	−6.59252	−0.296612
$495$	0.444831	0.0199937
$496$	−57.0585	−2.56200
$497$	−21.3487	−0.957622
$498$	44.4793	1.99316
$499$	−17.8437	−0.798794	−0.399397	−	0.916778i	$-0.630780\pi$
$499$	−17.8437	−0.798794	−0.399397	+	0.916778i	$0.630780\pi$
$500$	57.5329	2.57295
$501$	−6.86951	−0.306907
$502$	−43.3397	−1.93435
$503$	38.1058	1.69905	0.849526	−	0.527547i	$-0.176888\pi$
$503$	38.1058	1.69905	0.849526	+	0.527547i	$0.176888\pi$
$504$	13.6864	0.609639
$505$	50.0293	2.22627
$506$	−2.51063	−0.111611
$507$	−1.00000	−0.0444116
$508$	40.8047	1.81041
$509$	31.1794	1.38200	0.691001	−	0.722854i	$-0.257170\pi$
$509$	31.1794	1.38200	0.691001	+	0.722854i	$0.257170\pi$
$510$	15.8626	0.702408
$511$	10.8561	0.480245
$512$	25.2477	1.11580
$513$	−2.48476	−0.109705
$514$	−14.3248	−0.631839
$515$	−3.62608	−0.159784
$516$	−29.3776	−1.29328
$517$	1.46902	0.0646076
$518$	33.1920	1.45837
$519$	0.853628	0.0374701
$520$	−29.2410	−1.28230
$521$	−3.67012	−0.160791	−0.0803954	−	0.996763i	$-0.525618\pi$
$521$	−3.67012	−0.160791	−0.0803954	+	0.996763i	$0.525618\pi$
$522$	22.2333	0.973124
$523$	14.4506	0.631880	0.315940	−	0.948779i	$-0.397680\pi$
$523$	14.4506	0.631880	0.315940	+	0.948779i	$0.397680\pi$
$524$	−30.8744	−1.34875
$525$	13.8296	0.603574
$526$	−11.5419	−0.503251
$527$	−8.31324	−0.362130
$528$	−1.38828	−0.0604171
$529$	36.4998	1.58695
$530$	31.4921	1.36793
$531$	9.14392	0.396812
$532$	−21.2518	−0.921384
$533$	−5.29852	−0.229504
$534$	3.56226	0.154154
$535$	−68.1844	−2.94787
$536$	103.415	4.46684
$537$	−0.172575	−0.00744716
$538$	6.44095	0.277689
$539$	−0.505361	−0.0217674
$540$	−18.2733	−0.786356
$541$	2.64398	0.113674	0.0568368	−	0.998383i	$-0.481899\pi$
$541$	2.64398	0.113674	0.0568368	+	0.998383i	$0.481899\pi$
$542$	−49.2709	−2.11637
$543$	16.3527	0.701760
$544$	−22.9136	−0.982415
$545$	10.9491	0.469009
$546$	−4.50300	−0.192710
$547$	−5.19347	−0.222057	−0.111028	−	0.993817i	$-0.535414\pi$
$547$	−5.19347	−0.222057	−0.111028	+	0.993817i	$0.535414\pi$
$548$	82.9755	3.54454
$549$	−11.7962	−0.503451
$550$	−2.65217	−0.113089
$551$	−20.8219	−0.887042
$552$	62.2031	2.64754
$553$	−15.5465	−0.661106
$554$	−12.0214	−0.510742
$555$	−26.7282	−1.13455
$556$	34.4933	1.46284
$557$	7.83612	0.332027	0.166013	−	0.986123i	$-0.446910\pi$
$557$	7.83612	0.332027	0.166013	+	0.986123i	$0.446910\pi$
$558$	13.3773	0.566307
$559$	5.82960	0.246566
$560$	−69.6452	−2.94305
$561$	−0.202268	−0.00853975
$562$	−50.1037	−2.11350
$563$	7.13649	0.300767	0.150384	−	0.988628i	$-0.451949\pi$
$563$	7.13649	0.300767	0.150384	+	0.988628i	$0.451949\pi$
$564$	−60.3462	−2.54103
$565$	60.0475	2.52622
$566$	−24.5165	−1.03050
$567$	−1.69720	−0.0712759
$568$	−101.436	−4.25616
$569$	3.09009	0.129543	0.0647717	−	0.997900i	$-0.479368\pi$
$569$	3.09009	0.129543	0.0647717	+	0.997900i	$0.479368\pi$
$570$	23.9050	1.00127
$571$	6.74506	0.282272	0.141136	−	0.989990i	$-0.454925\pi$
$571$	6.74506	0.282272	0.141136	+	0.989990i	$0.454925\pi$
$572$	0.618209	0.0258486
$573$	−4.28492	−0.179005
$574$	−23.8592	−0.995864
$575$	62.8542	2.62120
$576$	14.2383	0.593262
$577$	−12.9125	−0.537556	−0.268778	−	0.963202i	$-0.586620\pi$
$577$	−12.9125	−0.537556	−0.268778	+	0.963202i	$0.586620\pi$
$578$	37.8913	1.57607
$579$	22.8864	0.951124
$580$	−153.127	−6.35825
$581$	−28.4527	−1.18042
$582$	22.0468	0.913870
$583$	−0.401563	−0.0166310
$584$	51.5815	2.13446
$585$	3.62608	0.149920
$586$	12.6694	0.523369
$587$	5.58930	0.230695	0.115348	−	0.993325i	$-0.463202\pi$
$587$	5.58930	0.230695	0.115348	+	0.993325i	$0.463202\pi$
$588$	20.7598	0.856119
$589$	−12.5281	−0.516212
$590$	−87.9706	−3.62169
$591$	−1.55653	−0.0640272
$592$	83.4163	3.42839
$593$	28.2176	1.15876	0.579379	−	0.815058i	$-0.303295\pi$
$593$	28.2176	1.15876	0.579379	+	0.815058i	$0.303295\pi$
$594$	0.325481	0.0133546
$595$	−10.1471	−0.415989
$596$	−48.5160	−1.98729
$597$	−6.78405	−0.277653
$598$	−20.4656	−0.836902
$599$	11.1988	0.457569	0.228784	−	0.973477i	$-0.426525\pi$
$599$	11.1988	0.457569	0.228784	+	0.973477i	$0.426525\pi$
$600$	65.7099	2.68259
$601$	−17.5761	−0.716943	−0.358471	−	0.933541i	$-0.616702\pi$
$601$	−17.5761	−0.716943	−0.358471	+	0.933541i	$0.616702\pi$
$602$	26.2507	1.06990
$603$	−12.8241	−0.522240
$604$	−113.432	−4.61547
$605$	−39.8323	−1.61941
$606$	36.6062	1.48702
$607$	−5.50321	−0.223368	−0.111684	−	0.993744i	$-0.535625\pi$
$607$	−5.50321	−0.223368	−0.111684	+	0.993744i	$0.535625\pi$
$608$	−34.5310	−1.40042
$609$	−14.2223	−0.576317
$610$	113.488	4.59498
$611$	11.9749	0.484452
$612$	8.30897	0.335870
$613$	28.5464	1.15298	0.576490	−	0.817104i	$-0.304422\pi$
$613$	28.5464	1.15298	0.576490	+	0.817104i	$0.304422\pi$
$614$	−64.0298	−2.58403
$615$	19.2129	0.774737
$616$	1.67898	0.0676481
$617$	47.1027	1.89628	0.948141	−	0.317849i	$-0.102961\pi$
$617$	47.1027	1.89628	0.948141	+	0.317849i	$0.102961\pi$
$618$	−2.65319	−0.106727
$619$	−6.48009	−0.260457	−0.130228	−	0.991484i	$-0.541571\pi$
$619$	−6.48009	−0.260457	−0.130228	+	0.991484i	$0.541571\pi$
$620$	−92.1334	−3.70017
$621$	−7.71361	−0.309537
$622$	3.20581	0.128541
$623$	−2.27872	−0.0912952
$624$	−11.3167	−0.453030
$625$	0.655265	0.0262106
$626$	−22.6172	−0.903964
$627$	−0.304819	−0.0121733
$628$	−70.4478	−2.81117
$629$	12.1535	0.484591
$630$	16.3282	0.650532
$631$	12.6135	0.502137	0.251068	−	0.967969i	$-0.419218\pi$
$631$	12.6135	0.502137	0.251068	+	0.967969i	$0.419218\pi$
$632$	−73.8675	−2.93829
$633$	−16.6781	−0.662894
$634$	−18.0791	−0.718012
$635$	29.3609	1.16515
$636$	16.4958	0.654102
$637$	−4.11950	−0.163221
$638$	2.72748	0.107982
$639$	12.5788	0.497608
$640$	−36.1975	−1.43083
$641$	−12.2027	−0.481977	−0.240988	−	0.970528i	$-0.577472\pi$
$641$	−12.2027	−0.481977	−0.240988	+	0.970528i	$0.577472\pi$
$642$	−49.8901	−1.96901
$643$	−6.29470	−0.248239	−0.124119	−	0.992267i	$-0.539611\pi$
$643$	−6.29470	−0.248239	−0.124119	+	0.992267i	$0.539611\pi$
$644$	−65.9736	−2.59972
$645$	−21.1386	−0.832332
$646$	−10.8698	−0.427666
$647$	−22.2602	−0.875139	−0.437569	−	0.899185i	$-0.644161\pi$
$647$	−22.2602	−0.875139	−0.437569	+	0.899185i	$0.644161\pi$
$648$	−8.06407	−0.316787
$649$	1.12173	0.0440319
$650$	−21.6194	−0.847983
$651$	−8.55727	−0.335386
$652$	64.4590	2.52441
$653$	15.1065	0.591164	0.295582	−	0.955317i	$-0.404487\pi$
$653$	15.1065	0.591164	0.295582	+	0.955317i	$0.404487\pi$
$654$	8.01141	0.313271
$655$	−22.2156	−0.868035
$656$	−59.9617	−2.34111
$657$	−6.39645	−0.249549
$658$	53.9229	2.10213
$659$	38.2470	1.48989	0.744945	−	0.667126i	$-0.232476\pi$
$659$	38.2470	1.48989	0.744945	+	0.667126i	$0.232476\pi$
$660$	−2.24168	−0.0872572
$661$	−48.5155	−1.88704	−0.943518	−	0.331323i	$-0.892505\pi$
$661$	−48.5155	−1.88704	−0.943518	+	0.331323i	$0.892505\pi$
$662$	−23.5702	−0.916082
$663$	−1.64880	−0.0640343
$664$	−135.190	−5.24639
$665$	−15.2917	−0.592987
$666$	−19.5569	−0.757813
$667$	−64.6388	−2.50283
$668$	34.6182	1.33942
$669$	−3.87678	−0.149885
$670$	123.377	4.76646
$671$	−1.44711	−0.0558650
$672$	−23.5863	−0.909860
$673$	−34.6677	−1.33634	−0.668170	−	0.744008i	$-0.732922\pi$
$673$	−34.6677	−1.33634	−0.668170	+	0.744008i	$0.732922\pi$
$674$	−38.3159	−1.47587
$675$	−8.14847	−0.313635
$676$	5.03939	0.193823
$677$	−19.4973	−0.749340	−0.374670	−	0.927158i	$-0.622244\pi$
$677$	−19.4973	−0.749340	−0.374670	+	0.927158i	$0.622244\pi$
$678$	43.9364	1.68737
$679$	−14.1030	−0.541225
$680$	−48.2127	−1.84887
$681$	29.7814	1.14123
$682$	1.64107	0.0628397
$683$	40.3459	1.54379	0.771896	−	0.635748i	$-0.219308\pi$
$683$	40.3459	1.54379	0.771896	+	0.635748i	$0.219308\pi$
$684$	12.5217	0.478778
$685$	59.7048	2.28120
$686$	−50.0711	−1.91172
$687$	15.9711	0.609337
$688$	65.9718	2.51515
$689$	−3.27337	−0.124706
$690$	74.2101	2.82513
$691$	30.3413	1.15424	0.577118	−	0.816660i	$-0.304177\pi$
$691$	30.3413	1.15424	0.577118	+	0.816660i	$0.304177\pi$
$692$	−4.30177	−0.163529
$693$	−0.208205	−0.00790906
$694$	50.9258	1.93312
$695$	24.8196	0.941461
$696$	−67.5756	−2.56145
$697$	−8.73622	−0.330908
$698$	−58.4821	−2.21358
$699$	−14.3408	−0.542419
$700$	−69.6929	−2.63414
$701$	−12.8526	−0.485438	−0.242719	−	0.970097i	$-0.578039\pi$
$701$	−12.8526	−0.485438	−0.242719	+	0.970097i	$0.578039\pi$
$702$	2.65319	0.100138
$703$	18.3154	0.690777
$704$	1.74669	0.0658307
$705$	−43.4219	−1.63537
$706$	76.3939	2.87512
$707$	−23.4164	−0.880666
$708$	−46.0798	−1.73178
$709$	38.8701	1.45980	0.729899	−	0.683555i	$-0.239567\pi$
$709$	38.8701	1.45980	0.729899	+	0.683555i	$0.239567\pi$
$710$	−121.016	−4.54166
$711$	9.16008	0.343530
$712$	−10.8271	−0.405763
$713$	−38.8919	−1.45651
$714$	−7.42456	−0.277857
$715$	0.444831	0.0166357
$716$	0.869673	0.0325012
$717$	3.34738	0.125010
$718$	−26.9399	−1.00539
$719$	−19.6238	−0.731843	−0.365922	−	0.930646i	$-0.619246\pi$
$719$	−19.6238	−0.731843	−0.365922	+	0.930646i	$0.619246\pi$
$720$	41.0352	1.52929
$721$	1.69720	0.0632072
$722$	34.0297	1.26645
$723$	−7.97897	−0.296741
$724$	−82.4075	−3.06265
$725$	−68.2829	−2.53596
$726$	−29.1451	−1.08168
$727$	10.9018	0.404326	0.202163	−	0.979352i	$-0.435203\pi$
$727$	10.9018	0.404326	0.202163	+	0.979352i	$0.435203\pi$
$728$	13.6864	0.507251
$729$	1.00000	0.0370370
$730$	61.5382	2.27763
$731$	9.61187	0.355508
$732$	59.4459	2.19718
$733$	42.8070	1.58111	0.790555	−	0.612391i	$-0.209792\pi$
$733$	42.8070	1.58111	0.790555	+	0.612391i	$0.209792\pi$
$734$	48.6645	1.79624
$735$	14.9376	0.550983
$736$	−107.197	−3.95134
$737$	−1.57321	−0.0579498
$738$	14.0579	0.517480
$739$	−33.2915	−1.22465	−0.612323	−	0.790608i	$-0.709765\pi$
$739$	−33.2915	−1.22465	−0.612323	+	0.790608i	$0.709765\pi$
$740$	134.694	4.95144
$741$	−2.48476	−0.0912799
$742$	−14.7400	−0.541122
$743$	−15.8368	−0.580994	−0.290497	−	0.956876i	$-0.593821\pi$
$743$	−15.8368	−0.580994	−0.290497	+	0.956876i	$0.593821\pi$
$744$	−40.6589	−1.49063
$745$	−34.9096	−1.27899
$746$	17.4323	0.638242
$747$	16.7645	0.613380
$748$	1.01931	0.0372695
$749$	31.9140	1.16611
$750$	30.2904	1.10605
$751$	49.7107	1.81397	0.906985	−	0.421163i	$-0.138378\pi$
$751$	49.7107	1.81397	0.906985	+	0.421163i	$0.138378\pi$
$752$	135.516	4.94176
$753$	−16.3350	−0.595280
$754$	22.2333	0.809688
$755$	−81.6194	−2.97043
$756$	8.55288	0.311065
$757$	47.0953	1.71171	0.855854	−	0.517217i	$-0.173032\pi$
$757$	47.0953	1.71171	0.855854	+	0.517217i	$0.173032\pi$
$758$	−67.2893	−2.44406
$759$	−0.946270	−0.0343474
$760$	−72.6568	−2.63554
$761$	−34.7500	−1.25969	−0.629843	−	0.776722i	$-0.716881\pi$
$761$	−34.7500	−1.25969	−0.629843	+	0.776722i	$0.716881\pi$
$762$	21.4832	0.778255
$763$	−5.12478	−0.185530
$764$	21.5934	0.781222
$765$	5.97870	0.216160
$766$	−19.3152	−0.697885
$767$	9.14392	0.330168
$768$	1.99103	0.0718450
$769$	22.6587	0.817093	0.408546	−	0.912738i	$-0.366036\pi$
$769$	22.6587	0.817093	0.408546	+	0.912738i	$0.366036\pi$
$770$	2.00307	0.0721857
$771$	−5.39908	−0.194443
$772$	−115.333	−4.15094
$773$	−2.52607	−0.0908564	−0.0454282	−	0.998968i	$-0.514465\pi$
$773$	−2.52607	−0.0908564	−0.0454282	+	0.998968i	$0.514465\pi$
$774$	−15.4670	−0.555950
$775$	−41.0845	−1.47580
$776$	−67.0089	−2.40548
$777$	12.5102	0.448802
$778$	20.3750	0.730478
$779$	−13.1655	−0.471704
$780$	−18.2733	−0.654287
$781$	1.54311	0.0552167
$782$	−33.7438	−1.20668
$783$	8.37984	0.299471
$784$	−46.6191	−1.66497
$785$	−50.6906	−1.80922
$786$	−16.2550	−0.579798
$787$	−20.2595	−0.722173	−0.361087	−	0.932532i	$-0.617594\pi$
$787$	−20.2595	−0.722173	−0.361087	+	0.932532i	$0.617594\pi$
$788$	7.84398	0.279430
$789$	−4.35020	−0.154871
$790$	−88.1261	−3.13539
$791$	−28.1055	−0.999316
$792$	−0.989263	−0.0351519
$793$	−11.7962	−0.418897
$794$	−43.6410	−1.54876
$795$	11.8695	0.420969
$796$	34.1875	1.21174
$797$	−0.0330833	−0.00117187	−0.000585935	−	1.00000i	$-0.500187\pi$
$797$	−0.0330833	−0.00117187	−0.000585935		1.00000i	$0.500187\pi$
$798$	−11.1889	−0.396081
$799$	19.7443	0.698502
$800$	−113.240	−4.00365
$801$	1.34263	0.0474397
$802$	−25.4228	−0.897711
$803$	−0.784688	−0.0276910
$804$	64.6259	2.27918
$805$	−47.4711	−1.67314
$806$	13.3773	0.471196
$807$	2.42763	0.0854566
$808$	−111.261	−3.91413
$809$	−4.39339	−0.154463	−0.0772316	−	0.997013i	$-0.524608\pi$
$809$	−4.39339	−0.154463	−0.0772316	+	0.997013i	$0.524608\pi$
$810$	−9.62067	−0.338036
$811$	−32.8133	−1.15223	−0.576116	−	0.817368i	$-0.695432\pi$
$811$	−32.8133	−1.15223	−0.576116	+	0.817368i	$0.695432\pi$
$812$	71.6717	2.51518
$813$	−18.5705	−0.651295
$814$	−2.39915	−0.0840900
$815$	46.3813	1.62467
$816$	−18.6590	−0.653196
$817$	14.4851	0.506771
$818$	18.1844	0.635802
$819$	−1.69720	−0.0593051
$820$	−96.8211	−3.38114
$821$	−25.2885	−0.882575	−0.441287	−	0.897366i	$-0.645478\pi$
$821$	−25.2885	−0.882575	−0.441287	+	0.897366i	$0.645478\pi$
$822$	43.6857	1.52371
$823$	−31.6894	−1.10462	−0.552312	−	0.833638i	$-0.686254\pi$
$823$	−31.6894	−1.10462	−0.552312	+	0.833638i	$0.686254\pi$
$824$	8.06407	0.280925
$825$	−0.999617	−0.0348022
$826$	41.1750	1.43266
$827$	−42.8039	−1.48844	−0.744218	−	0.667936i	$-0.767178\pi$
$827$	−42.8039	−1.48844	−0.744218	+	0.667936i	$0.767178\pi$
$828$	38.8719	1.35089
$829$	−26.7030	−0.927435	−0.463717	−	0.885983i	$-0.653485\pi$
$829$	−26.7030	−0.927435	−0.463717	+	0.885983i	$0.653485\pi$
$830$	−161.286	−5.59830
$831$	−4.53094	−0.157177
$832$	14.2383	0.493624
$833$	−6.79225	−0.235337
$834$	18.1604	0.628842
$835$	24.9094	0.862026
$836$	1.53610	0.0531272
$837$	5.04198	0.174276
$838$	104.497	3.60979
$839$	10.0561	0.347174	0.173587	−	0.984818i	$-0.444464\pi$
$839$	10.0561	0.347174	0.173587	+	0.984818i	$0.444464\pi$
$840$	−49.6279	−1.71233
$841$	41.2217	1.42144
$842$	41.3123	1.42372
$843$	−18.8843	−0.650412
$844$	84.0473	2.89303
$845$	3.62608	0.124741
$846$	−31.7716	−1.09233
$847$	18.6437	0.640605
$848$	−37.0438	−1.27209
$849$	−9.24039	−0.317129
$850$	−35.6462	−1.22265
$851$	56.8577	1.94906
$852$	−63.3894	−2.17168
$853$	19.2631	0.659558	0.329779	−	0.944058i	$-0.393026\pi$
$853$	19.2631	0.659558	0.329779	+	0.944058i	$0.393026\pi$
$854$	−53.1184	−1.81768
$855$	9.00994	0.308133
$856$	151.636	5.18280
$857$	36.0152	1.23026	0.615128	−	0.788427i	$-0.289104\pi$
$857$	36.0152	1.23026	0.615128	+	0.788427i	$0.289104\pi$
$858$	0.325481	0.0111117
$859$	53.6352	1.83001	0.915004	−	0.403445i	$-0.132187\pi$
$859$	53.6352	1.83001	0.915004	+	0.403445i	$0.132187\pi$
$860$	106.526	3.63250
$861$	−8.99266	−0.306469
$862$	47.4234	1.61525
$863$	−0.00516474	−0.000175810 0	−8.79049e−5	−	1.00000i	$-0.500028\pi$
$863$	−0.00516474	−0.000175810 0	−8.79049e−5		1.00000i	$0.500028\pi$
$864$	13.8971	0.472790
$865$	−3.09533	−0.105244
$866$	20.0739	0.682139
$867$	14.2814	0.485023
$868$	43.1234	1.46370
$869$	1.12372	0.0381195
$870$	−80.6197	−2.73326
$871$	−12.8241	−0.434530
$872$	−24.3498	−0.824589
$873$	8.30957	0.281236
$874$	−50.8522	−1.72010
$875$	−19.3763	−0.655040
$876$	32.2342	1.08909
$877$	−34.8877	−1.17807	−0.589037	−	0.808106i	$-0.700493\pi$
$877$	−34.8877	−1.17807	−0.589037	+	0.808106i	$0.700493\pi$
$878$	25.3478	0.855448
$879$	4.77518	0.161063
$880$	5.03402	0.169697
$881$	−47.3217	−1.59431	−0.797155	−	0.603775i	$-0.793662\pi$
$881$	−47.3217	−1.59431	−0.797155	+	0.603775i	$0.793662\pi$
$882$	10.9298	0.368025
$883$	44.3753	1.49335	0.746673	−	0.665191i	$-0.231650\pi$
$883$	44.3753	1.49335	0.746673	+	0.665191i	$0.231650\pi$
$884$	8.30897	0.279461
$885$	−33.1566	−1.11455
$886$	75.4256	2.53397
$887$	−2.29556	−0.0770774	−0.0385387	−	0.999257i	$-0.512270\pi$
$887$	−2.29556	−0.0770774	−0.0385387	+	0.999257i	$0.512270\pi$
$888$	59.4410	1.99471
$889$	−13.7425	−0.460908
$890$	−12.9170	−0.432980
$891$	0.122675	0.00410978
$892$	19.5366	0.654134
$893$	29.7547	0.995704
$894$	−25.5432	−0.854291
$895$	0.625771	0.0209172
$896$	16.9424	0.566006
$897$	−7.71361	−0.257550
$898$	−63.6125	−2.12278
$899$	42.2510	1.40915
$900$	41.0634	1.36878
$901$	−5.39715	−0.179805
$902$	1.72456	0.0574217
$903$	9.89402	0.329252
$904$	−133.540	−4.44147
$905$	−59.2961	−1.97107
$906$	−59.7205	−1.98408
$907$	57.9664	1.92474	0.962371	−	0.271740i	$-0.0875990\pi$
$907$	57.9664	1.92474	0.962371	+	0.271740i	$0.0875990\pi$
$908$	−150.080	−4.98059
$909$	13.7971	0.457620
$910$	16.3282	0.541276
$911$	44.9297	1.48859	0.744294	−	0.667852i	$-0.232786\pi$
$911$	44.9297	1.48859	0.744294	+	0.667852i	$0.232786\pi$
$912$	−28.1192	−0.931121
$913$	2.05659	0.0680632
$914$	−82.2038	−2.71906
$915$	42.7742	1.41407
$916$	−80.4848	−2.65929
$917$	10.3981	0.343376
$918$	4.37458	0.144383
$919$	43.1119	1.42213	0.711064	−	0.703127i	$-0.248213\pi$
$919$	43.1119	1.42213	0.711064	+	0.703127i	$0.248213\pi$
$920$	−225.554	−7.43628
$921$	−24.1332	−0.795215
$922$	−42.3281	−1.39400
$923$	12.5788	0.414035
$924$	1.04923	0.0345170
$925$	60.0631	1.97486
$926$	71.5122	2.35004
$927$	−1.00000	−0.0328443
$928$	116.456	3.82285
$929$	57.7847	1.89585	0.947927	−	0.318486i	$-0.103175\pi$
$929$	57.7847	1.89585	0.947927	+	0.318486i	$0.103175\pi$
$930$	−48.5072	−1.59061
$931$	−10.2360	−0.335470
$932$	72.2689	2.36725
$933$	1.20829	0.0395575
$934$	66.6421	2.18060
$935$	0.733439	0.0239860
$936$	−8.06407	−0.263582
$937$	16.0601	0.524662	0.262331	−	0.964978i	$-0.415509\pi$
$937$	16.0601	0.524662	0.262331	+	0.964978i	$0.415509\pi$
$938$	−57.7471	−1.88551
$939$	−8.52454	−0.278188
$940$	218.820	7.13713
$941$	46.5017	1.51591	0.757956	−	0.652306i	$-0.226198\pi$
$941$	46.5017	1.51591	0.757956	+	0.652306i	$0.226198\pi$
$942$	−37.0900	−1.20846
$943$	−40.8707	−1.33093
$944$	103.479	3.36795
$945$	6.15420	0.200196
$946$	−1.89742	−0.0616905
$947$	39.3923	1.28008	0.640039	−	0.768343i	$-0.278918\pi$
$947$	39.3923	1.28008	0.640039	+	0.768343i	$0.278918\pi$
$948$	−46.1612	−1.49925
$949$	−6.39645	−0.207638
$950$	−53.7190	−1.74288
$951$	−6.81411	−0.220963
$952$	22.5661	0.731373
$953$	−20.8160	−0.674297	−0.337149	−	0.941451i	$-0.609463\pi$
$953$	−20.8160	−0.674297	−0.337149	+	0.941451i	$0.609463\pi$
$954$	8.68487	0.281183
$955$	15.5375	0.502781
$956$	−16.8688	−0.545575
$957$	1.02800	0.0332305
$958$	−107.435	−3.47107
$959$	−27.9451	−0.902394
$960$	−51.6292	−1.66632
$961$	−5.57842	−0.179949
$962$	−19.5569	−0.630538
$963$	−18.8039	−0.605946
$964$	40.2092	1.29505
$965$	−82.9878	−2.67147
$966$	−34.7344	−1.11756
$967$	9.03615	0.290583	0.145291	−	0.989389i	$-0.453588\pi$
$967$	9.03615	0.290583	0.145291	+	0.989389i	$0.453588\pi$
$968$	88.5834	2.84718
$969$	−4.09688	−0.131611
$970$	−79.9436	−2.56683
$971$	−17.4820	−0.561025	−0.280513	−	0.959850i	$-0.590504\pi$
$971$	−17.4820	−0.561025	−0.280513	+	0.959850i	$0.590504\pi$
$972$	−5.03939	−0.161639
$973$	−11.6169	−0.372421
$974$	−80.5801	−2.58195
$975$	−8.14847	−0.260960
$976$	−133.494	−4.27305
$977$	−11.9914	−0.383640	−0.191820	−	0.981430i	$-0.561439\pi$
$977$	−11.9914	−0.383640	−0.191820	+	0.981430i	$0.561439\pi$
$978$	33.9370	1.08519
$979$	0.164708	0.00526410
$980$	−75.2766	−2.40462
$981$	3.01954	0.0964066
$982$	−5.12752	−0.163626
$983$	8.38753	0.267521	0.133760	−	0.991014i	$-0.457295\pi$
$983$	8.38753	0.267521	0.133760	+	0.991014i	$0.457295\pi$
$984$	−42.7276	−1.36211
$985$	5.64412	0.179837
$986$	36.6583	1.16744
$987$	20.3238	0.646915
$988$	12.5217	0.398367
$989$	44.9673	1.42988
$990$	−1.18022	−0.0375098
$991$	1.02483	0.0325548	0.0162774	−	0.999868i	$-0.494819\pi$
$991$	1.02483	0.0325548	0.0162774	+	0.999868i	$0.494819\pi$
$992$	70.0691	2.22470
$993$	−8.88374	−0.281917
$994$	56.6422	1.79658
$995$	24.5995	0.779857
$996$	−84.4828	−2.67694
$997$	−1.09020	−0.0345270	−0.0172635	−	0.999851i	$-0.505495\pi$
$997$	−1.09020	−0.0345270	−0.0172635	+	0.999851i	$0.505495\pi$
$998$	47.3426	1.49860
$999$	−7.37109	−0.233211

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.j.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65319 q^{2} -1.00000 q^{3} +5.03939 q^{4} +3.62608 q^{5} +2.65319 q^{6} -1.69720 q^{7} -8.06407 q^{8} +1.00000 q^{9} -9.62067 q^{10} +0.122675 q^{11} -5.03939 q^{12} +1.00000 q^{13} +4.50300 q^{14} -3.62608 q^{15} +11.3167 q^{16} +1.64880 q^{17} -2.65319 q^{18} +2.48476 q^{19} +18.2733 q^{20} +1.69720 q^{21} -0.325481 q^{22} +7.71361 q^{23} +8.06407 q^{24} +8.14847 q^{25} -2.65319 q^{26} -1.00000 q^{27} -8.55288 q^{28} -8.37984 q^{29} +9.62067 q^{30} -5.04198 q^{31} -13.8971 q^{32} -0.122675 q^{33} -4.37458 q^{34} -6.15420 q^{35} +5.03939 q^{36} +7.37109 q^{37} -6.59252 q^{38} -1.00000 q^{39} -29.2410 q^{40} -5.29852 q^{41} -4.50300 q^{42} +5.82960 q^{43} +0.618209 q^{44} +3.62608 q^{45} -20.4656 q^{46} +11.9749 q^{47} -11.3167 q^{48} -4.11950 q^{49} -21.6194 q^{50} -1.64880 q^{51} +5.03939 q^{52} -3.27337 q^{53} +2.65319 q^{54} +0.444831 q^{55} +13.6864 q^{56} -2.48476 q^{57} +22.2333 q^{58} +9.14392 q^{59} -18.2733 q^{60} -11.7962 q^{61} +13.3773 q^{62} -1.69720 q^{63} +14.2383 q^{64} +3.62608 q^{65} +0.325481 q^{66} -12.8241 q^{67} +8.30897 q^{68} -7.71361 q^{69} +16.3282 q^{70} +12.5788 q^{71} -8.06407 q^{72} -6.39645 q^{73} -19.5569 q^{74} -8.14847 q^{75} +12.5217 q^{76} -0.208205 q^{77} +2.65319 q^{78} +9.16008 q^{79} +41.0352 q^{80} +1.00000 q^{81} +14.0579 q^{82} +16.7645 q^{83} +8.55288 q^{84} +5.97870 q^{85} -15.4670 q^{86} +8.37984 q^{87} -0.989263 q^{88} +1.34263 q^{89} -9.62067 q^{90} -1.69720 q^{91} +38.8719 q^{92} +5.04198 q^{93} -31.7716 q^{94} +9.00994 q^{95} +13.8971 q^{96} +8.30957 q^{97} +10.9298 q^{98} +0.122675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} - 25 q^{3} + 28 q^{4} + 7 q^{5} - 6 q^{6} + 17 q^{7} + 21 q^{8} + 25 q^{9}+O(q^{10}) \) 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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