LMFDB - Embedded newform 4017.2.a.g.1.18

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:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.68466 q^{2} -1.00000 q^{3} +0.838074 q^{4} +0.142092 q^{5} -1.68466 q^{6} -0.0282508 q^{7} -1.95745 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.68466 q^{2} -1.00000 q^{3} +0.838074 q^{4} +0.142092 q^{5} -1.68466 q^{6} -0.0282508 q^{7} -1.95745 q^{8} +1.00000 q^{9} +0.239376 q^{10} +0.586754 q^{11} -0.838074 q^{12} -1.00000 q^{13} -0.0475929 q^{14} -0.142092 q^{15} -4.97378 q^{16} +6.55349 q^{17} +1.68466 q^{18} +3.66121 q^{19} +0.119083 q^{20} +0.0282508 q^{21} +0.988481 q^{22} -4.69081 q^{23} +1.95745 q^{24} -4.97981 q^{25} -1.68466 q^{26} -1.00000 q^{27} -0.0236762 q^{28} +0.00650070 q^{29} -0.239376 q^{30} +7.78308 q^{31} -4.46422 q^{32} -0.586754 q^{33} +11.0404 q^{34} -0.00401420 q^{35} +0.838074 q^{36} -0.640954 q^{37} +6.16788 q^{38} +1.00000 q^{39} -0.278137 q^{40} -0.302934 q^{41} +0.0475929 q^{42} +1.22963 q^{43} +0.491743 q^{44} +0.142092 q^{45} -7.90241 q^{46} +8.93051 q^{47} +4.97378 q^{48} -6.99920 q^{49} -8.38928 q^{50} -6.55349 q^{51} -0.838074 q^{52} -2.65803 q^{53} -1.68466 q^{54} +0.0833730 q^{55} +0.0552994 q^{56} -3.66121 q^{57} +0.0109515 q^{58} +1.29157 q^{59} -0.119083 q^{60} +14.7304 q^{61} +13.1118 q^{62} -0.0282508 q^{63} +2.42687 q^{64} -0.142092 q^{65} -0.988481 q^{66} -7.28937 q^{67} +5.49231 q^{68} +4.69081 q^{69} -0.00676256 q^{70} +2.54704 q^{71} -1.95745 q^{72} +14.6562 q^{73} -1.07979 q^{74} +4.97981 q^{75} +3.06836 q^{76} -0.0165763 q^{77} +1.68466 q^{78} +4.48957 q^{79} -0.706734 q^{80} +1.00000 q^{81} -0.510340 q^{82} +12.6859 q^{83} +0.0236762 q^{84} +0.931197 q^{85} +2.07150 q^{86} -0.00650070 q^{87} -1.14854 q^{88} +11.3549 q^{89} +0.239376 q^{90} +0.0282508 q^{91} -3.93124 q^{92} -7.78308 q^{93} +15.0449 q^{94} +0.520228 q^{95} +4.46422 q^{96} +12.8350 q^{97} -11.7913 q^{98} +0.586754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.68466	1.19123	0.595617	−	0.803269i	$-0.296908\pi$
$2$	1.68466	1.19123	0.595617	+	0.803269i	$0.296908\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.838074	0.419037
$5$	0.142092	0.0635454	0.0317727	−	0.999495i	$-0.489885\pi$
$5$	0.142092	0.0635454	0.0317727	+	0.999495i	$0.489885\pi$
$6$	−1.68466	−0.687759
$7$	−0.0282508	−0.0106778	−0.00533889	−	0.999986i	$-0.501699\pi$
$7$	−0.0282508	−0.0106778	−0.00533889	+	0.999986i	$0.501699\pi$
$8$	−1.95745	−0.692063
$9$	1.00000	0.333333
$10$	0.239376	0.0756974
$11$	0.586754	0.176913	0.0884565	−	0.996080i	$-0.471807\pi$
$11$	0.586754	0.176913	0.0884565	+	0.996080i	$0.471807\pi$
$12$	−0.838074	−0.241931
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.0475929	−0.0127197
$15$	−0.142092	−0.0366880
$16$	−4.97378	−1.24344
$17$	6.55349	1.58945	0.794727	−	0.606967i	$-0.207614\pi$
$17$	6.55349	1.58945	0.794727	+	0.606967i	$0.207614\pi$
$18$	1.68466	0.397078
$19$	3.66121	0.839938	0.419969	−	0.907538i	$-0.362041\pi$
$19$	3.66121	0.839938	0.419969	+	0.907538i	$0.362041\pi$
$20$	0.119083	0.0266279
$21$	0.0282508	0.00616482
$22$	0.988481	0.210745
$23$	−4.69081	−0.978101	−0.489050	−	0.872255i	$-0.662657\pi$
$23$	−4.69081	−0.978101	−0.489050	+	0.872255i	$0.662657\pi$
$24$	1.95745	0.399563
$25$	−4.97981	−0.995962
$26$	−1.68466	−0.330389
$27$	−1.00000	−0.192450
$28$	−0.0236762	−0.00447439
$29$	0.00650070	0.00120715	0.000603575	−	1.00000i	$-0.499808\pi$
$29$	0.00650070	0.00120715	0.000603575		1.00000i	$0.499808\pi$
$30$	−0.239376	−0.0437039
$31$	7.78308	1.39788	0.698941	−	0.715180i	$-0.253655\pi$
$31$	7.78308	1.39788	0.698941	+	0.715180i	$0.253655\pi$
$32$	−4.46422	−0.789171
$33$	−0.586754	−0.102141
$34$	11.0404	1.89341
$35$	−0.00401420	−0.000678524 0
$36$	0.838074	0.139679
$37$	−0.640954	−0.105372	−0.0526861	−	0.998611i	$-0.516778\pi$
$37$	−0.640954	−0.105372	−0.0526861	+	0.998611i	$0.516778\pi$
$38$	6.16788	1.00056
$39$	1.00000	0.160128
$40$	−0.278137	−0.0439774
$41$	−0.302934	−0.0473103	−0.0236552	−	0.999720i	$-0.507530\pi$
$41$	−0.302934	−0.0473103	−0.0236552	+	0.999720i	$0.507530\pi$
$42$	0.0475929	0.00734374
$43$	1.22963	0.187517	0.0937583	−	0.995595i	$-0.470112\pi$
$43$	1.22963	0.187517	0.0937583	+	0.995595i	$0.470112\pi$
$44$	0.491743	0.0741331
$45$	0.142092	0.0211818
$46$	−7.90241	−1.16515
$47$	8.93051	1.30265	0.651324	−	0.758800i	$-0.274214\pi$
$47$	8.93051	1.30265	0.651324	+	0.758800i	$0.274214\pi$
$48$	4.97378	0.717903
$49$	−6.99920	−0.999886
$50$	−8.38928	−1.18642
$51$	−6.55349	−0.917672
$52$	−0.838074	−0.116220
$53$	−2.65803	−0.365109	−0.182554	−	0.983196i	$-0.558437\pi$
$53$	−2.65803	−0.365109	−0.182554	+	0.983196i	$0.558437\pi$
$54$	−1.68466	−0.229253
$55$	0.0833730	0.0112420
$56$	0.0552994	0.00738969
$57$	−3.66121	−0.484939
$58$	0.0109515	0.00143800
$59$	1.29157	0.168148	0.0840738	−	0.996460i	$-0.473207\pi$
$59$	1.29157	0.168148	0.0840738	+	0.996460i	$0.473207\pi$
$60$	−0.119083	−0.0153736
$61$	14.7304	1.88603	0.943015	−	0.332750i	$-0.107977\pi$
$61$	14.7304	1.88603	0.943015	+	0.332750i	$0.107977\pi$
$62$	13.1118	1.66520
$63$	−0.0282508	−0.00355926
$64$	2.42687	0.303359
$65$	−0.142092	−0.0176243
$66$	−0.988481	−0.121674
$67$	−7.28937	−0.890539	−0.445269	−	0.895397i	$-0.646892\pi$
$67$	−7.28937	−0.890539	−0.445269	+	0.895397i	$0.646892\pi$
$68$	5.49231	0.666040
$69$	4.69081	0.564707
$70$	−0.00676256	−0.000808281 0
$71$	2.54704	0.302278	0.151139	−	0.988513i	$-0.451706\pi$
$71$	2.54704	0.302278	0.151139	+	0.988513i	$0.451706\pi$
$72$	−1.95745	−0.230688
$73$	14.6562	1.71538	0.857690	−	0.514167i	$-0.171899\pi$
$73$	14.6562	1.71538	0.857690	+	0.514167i	$0.171899\pi$
$74$	−1.07979	−0.125523
$75$	4.97981	0.575019
$76$	3.06836	0.351965
$77$	−0.0165763	−0.00188904
$78$	1.68466	0.190750
$79$	4.48957	0.505116	0.252558	−	0.967582i	$-0.418728\pi$
$79$	4.48957	0.505116	0.252558	+	0.967582i	$0.418728\pi$
$80$	−0.706734	−0.0790152
$81$	1.00000	0.111111
$82$	−0.510340	−0.0563576
$83$	12.6859	1.39246	0.696230	−	0.717819i	$-0.254859\pi$
$83$	12.6859	1.39246	0.696230	+	0.717819i	$0.254859\pi$
$84$	0.0236762	0.00258329
$85$	0.931197	0.101003
$86$	2.07150	0.223376
$87$	−0.00650070	−0.000696948 0
$88$	−1.14854	−0.122435
$89$	11.3549	1.20362	0.601808	−	0.798641i	$-0.294447\pi$
$89$	11.3549	1.20362	0.601808	+	0.798641i	$0.294447\pi$
$90$	0.239376	0.0252325
$91$	0.0282508	0.00296148
$92$	−3.93124	−0.409860
$93$	−7.78308	−0.807067
$94$	15.0449	1.55176
$95$	0.520228	0.0533742
$96$	4.46422	0.455628
$97$	12.8350	1.30320	0.651600	−	0.758562i	$-0.274098\pi$
$97$	12.8350	1.30320	0.651600	+	0.758562i	$0.274098\pi$
$98$	−11.7913	−1.19110
$99$	0.586754	0.0589710
$100$	−4.17345	−0.417345
$101$	−0.505084	−0.0502578	−0.0251289	−	0.999684i	$-0.508000\pi$
$101$	−0.505084	−0.0502578	−0.0251289	+	0.999684i	$0.508000\pi$
$102$	−11.0404	−1.09316
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.95745	0.191944
$105$	0.00401420	0.000391746 0
$106$	−4.47787	−0.434930
$107$	−13.1759	−1.27376	−0.636881	−	0.770962i	$-0.719776\pi$
$107$	−13.1759	−1.27376	−0.636881	+	0.770962i	$0.719776\pi$
$108$	−0.838074	−0.0806437
$109$	6.50034	0.622619	0.311310	−	0.950308i	$-0.399232\pi$
$109$	6.50034	0.622619	0.311310	+	0.950308i	$0.399232\pi$
$110$	0.140455	0.0133919
$111$	0.640954	0.0608366
$112$	0.140513	0.0132772
$113$	−7.47118	−0.702829	−0.351415	−	0.936220i	$-0.614299\pi$
$113$	−7.47118	−0.702829	−0.351415	+	0.936220i	$0.614299\pi$
$114$	−6.16788	−0.577675
$115$	−0.666525	−0.0621538
$116$	0.00544807	0.000505840 0
$117$	−1.00000	−0.0924500
$118$	2.17585	0.200303
$119$	−0.185141	−0.0169719
$120$	0.278137	0.0253904
$121$	−10.6557	−0.968702
$122$	24.8156	2.24670
$123$	0.302934	0.0273146
$124$	6.52279	0.585764
$125$	−1.41805	−0.126834
$126$	−0.0475929	−0.00423991
$127$	13.3167	1.18166	0.590832	−	0.806795i	$-0.298800\pi$
$127$	13.3167	1.18166	0.590832	+	0.806795i	$0.298800\pi$
$128$	13.0169	1.15054
$129$	−1.22963	−0.108263
$130$	−0.239376	−0.0209947
$131$	3.02499	0.264294	0.132147	−	0.991230i	$-0.457813\pi$
$131$	3.02499	0.264294	0.132147	+	0.991230i	$0.457813\pi$
$132$	−0.491743	−0.0428008
$133$	−0.103432	−0.00896868
$134$	−12.2801	−1.06084
$135$	−0.142092	−0.0122293
$136$	−12.8281	−1.10000
$137$	16.4223	1.40305	0.701525	−	0.712645i	$-0.252503\pi$
$137$	16.4223	1.40305	0.701525	+	0.712645i	$0.252503\pi$
$138$	7.90241	0.672698
$139$	5.83218	0.494679	0.247340	−	0.968929i	$-0.420444\pi$
$139$	5.83218	0.494679	0.247340	+	0.968929i	$0.420444\pi$
$140$	−0.00336420	−0.000284327 0
$141$	−8.93051	−0.752084
$142$	4.29090	0.360084
$143$	−0.586754	−0.0490669
$144$	−4.97378	−0.414482
$145$	0.000923697 0	7.67088e−5 0
$146$	24.6907	2.04342
$147$	6.99920	0.577284
$148$	−0.537166	−0.0441548
$149$	7.45999	0.611146	0.305573	−	0.952169i	$-0.401152\pi$
$149$	7.45999	0.611146	0.305573	+	0.952169i	$0.401152\pi$
$150$	8.38928	0.684982
$151$	−17.1198	−1.39319	−0.696596	−	0.717463i	$-0.745303\pi$
$151$	−17.1198	−1.39319	−0.696596	+	0.717463i	$0.745303\pi$
$152$	−7.16662	−0.581290
$153$	6.55349	0.529818
$154$	−0.0279253	−0.00225029
$155$	1.10591	0.0888290
$156$	0.838074	0.0670996
$157$	15.0487	1.20102	0.600508	−	0.799619i	$-0.294965\pi$
$157$	15.0487	1.20102	0.600508	+	0.799619i	$0.294965\pi$
$158$	7.56339	0.601711
$159$	2.65803	0.210796
$160$	−0.634330	−0.0501482
$161$	0.132519	0.0104439
$162$	1.68466	0.132359
$163$	17.9372	1.40495	0.702473	−	0.711710i	$-0.252079\pi$
$163$	17.9372	1.40495	0.702473	+	0.711710i	$0.252079\pi$
$164$	−0.253881	−0.0198248
$165$	−0.0833730	−0.00649058
$166$	21.3714	1.65874
$167$	10.4875	0.811547	0.405774	−	0.913974i	$-0.367002\pi$
$167$	10.4875	0.811547	0.405774	+	0.913974i	$0.367002\pi$
$168$	−0.0552994	−0.00426644
$169$	1.00000	0.0769231
$170$	1.56875	0.120318
$171$	3.66121	0.279979
$172$	1.03052	0.0785764
$173$	−17.6965	−1.34544	−0.672722	−	0.739896i	$-0.734875\pi$
$173$	−17.6965	−1.34544	−0.672722	+	0.739896i	$0.734875\pi$
$174$	−0.0109515	−0.000830228 0
$175$	0.140683	0.0106347
$176$	−2.91839	−0.219982
$177$	−1.29157	−0.0970800
$178$	19.1291	1.43379
$179$	−0.958504	−0.0716419	−0.0358210	−	0.999358i	$-0.511405\pi$
$179$	−0.958504	−0.0716419	−0.0358210	+	0.999358i	$0.511405\pi$
$180$	0.119083	0.00887596
$181$	−20.3295	−1.51108	−0.755539	−	0.655104i	$-0.772625\pi$
$181$	−20.3295	−1.51108	−0.755539	+	0.655104i	$0.772625\pi$
$182$	0.0475929	0.00352782
$183$	−14.7304	−1.08890
$184$	9.18201	0.676907
$185$	−0.0910743	−0.00669591
$186$	−13.1118	−0.961406
$187$	3.84529	0.281195
$188$	7.48442	0.545858
$189$	0.0282508	0.00205494
$190$	0.876406	0.0635812
$191$	21.8102	1.57813	0.789066	−	0.614308i	$-0.210565\pi$
$191$	21.8102	1.57813	0.789066	+	0.614308i	$0.210565\pi$
$192$	−2.42687	−0.175144
$193$	−15.7684	−1.13504	−0.567518	−	0.823361i	$-0.692096\pi$
$193$	−15.7684	−1.13504	−0.567518	+	0.823361i	$0.692096\pi$
$194$	21.6227	1.55242
$195$	0.142092	0.0101754
$196$	−5.86585	−0.418989
$197$	6.67212	0.475369	0.237684	−	0.971342i	$-0.423612\pi$
$197$	6.67212	0.475369	0.237684	+	0.971342i	$0.423612\pi$
$198$	0.988481	0.0702483
$199$	−19.1889	−1.36027	−0.680133	−	0.733089i	$-0.738078\pi$
$199$	−19.1889	−1.36027	−0.680133	+	0.733089i	$0.738078\pi$
$200$	9.74772	0.689268
$201$	7.28937	0.514153
$202$	−0.850895	−0.0598687
$203$	−0.000183650 0	−1.28897e−5 0
$204$	−5.49231	−0.384538
$205$	−0.0430444	−0.00300635
$206$	1.68466	0.117376
$207$	−4.69081	−0.326034
$208$	4.97378	0.344870
$209$	2.14823	0.148596
$210$	0.00676256	0.000466661 0
$211$	−23.6262	−1.62649	−0.813247	−	0.581919i	$-0.802302\pi$
$211$	−23.6262	−1.62649	−0.813247	+	0.581919i	$0.802302\pi$
$212$	−2.22763	−0.152994
$213$	−2.54704	−0.174520
$214$	−22.1969	−1.51735
$215$	0.174720	0.0119158
$216$	1.95745	0.133188
$217$	−0.219878	−0.0149263
$218$	10.9508	0.741685
$219$	−14.6562	−0.990375
$220$	0.0698727	0.00471082
$221$	−6.55349	−0.440835
$222$	1.07979	0.0724706
$223$	−6.66830	−0.446543	−0.223271	−	0.974756i	$-0.571674\pi$
$223$	−6.66830	−0.446543	−0.223271	+	0.974756i	$0.571674\pi$
$224$	0.126118	0.00842659
$225$	−4.97981	−0.331987
$226$	−12.5864	−0.837234
$227$	11.1630	0.740917	0.370458	−	0.928849i	$-0.379201\pi$
$227$	11.1630	0.740917	0.370458	+	0.928849i	$0.379201\pi$
$228$	−3.06836	−0.203207
$229$	16.1952	1.07021	0.535106	−	0.844785i	$-0.320272\pi$
$229$	16.1952	1.07021	0.535106	+	0.844785i	$0.320272\pi$
$230$	−1.12287	−0.0740397
$231$	0.0165763	0.00109064
$232$	−0.0127248	−0.000835423 0
$233$	15.5918	1.02145	0.510725	−	0.859744i	$-0.329377\pi$
$233$	15.5918	1.02145	0.510725	+	0.859744i	$0.329377\pi$
$234$	−1.68466	−0.110130
$235$	1.26895	0.0827773
$236$	1.08243	0.0704600
$237$	−4.48957	−0.291629
$238$	−0.311899	−0.0202174
$239$	5.31180	0.343592	0.171796	−	0.985133i	$-0.445043\pi$
$239$	5.31180	0.343592	0.171796	+	0.985133i	$0.445043\pi$
$240$	0.706734	0.0456195
$241$	−4.94367	−0.318450	−0.159225	−	0.987242i	$-0.550900\pi$
$241$	−4.94367	−0.318450	−0.159225	+	0.987242i	$0.550900\pi$
$242$	−17.9512	−1.15395
$243$	−1.00000	−0.0641500
$244$	12.3451	0.790316
$245$	−0.994530	−0.0635382
$246$	0.510340	0.0325381
$247$	−3.66121	−0.232957
$248$	−15.2350	−0.967422
$249$	−12.6859	−0.803937
$250$	−2.38893	−0.151089
$251$	−25.2234	−1.59209	−0.796043	−	0.605240i	$-0.793077\pi$
$251$	−25.2234	−1.59209	−0.796043	+	0.605240i	$0.793077\pi$
$252$	−0.0236762	−0.00149146
$253$	−2.75235	−0.173039
$254$	22.4341	1.40764
$255$	−0.931197	−0.0583138
$256$	17.0753	1.06720
$257$	−14.3253	−0.893587	−0.446794	−	0.894637i	$-0.647434\pi$
$257$	−14.3253	−0.893587	−0.446794	+	0.894637i	$0.647434\pi$
$258$	−2.07150	−0.128966
$259$	0.0181074	0.00112514
$260$	−0.119083	−0.00738524
$261$	0.00650070	0.000402383 0
$262$	5.09607	0.314836
$263$	20.2891	1.25108	0.625540	−	0.780192i	$-0.284879\pi$
$263$	20.2891	1.25108	0.625540	+	0.780192i	$0.284879\pi$
$264$	1.14854	0.0706878
$265$	−0.377684	−0.0232010
$266$	−0.174247	−0.0106838
$267$	−11.3549	−0.694908
$268$	−6.10903	−0.373169
$269$	−16.2409	−0.990226	−0.495113	−	0.868829i	$-0.664873\pi$
$269$	−16.2409	−0.990226	−0.495113	+	0.868829i	$0.664873\pi$
$270$	−0.239376	−0.0145680
$271$	−7.10595	−0.431656	−0.215828	−	0.976431i	$-0.569245\pi$
$271$	−7.10595	−0.431656	−0.215828	+	0.976431i	$0.569245\pi$
$272$	−32.5956	−1.97640
$273$	−0.0282508	−0.00170981
$274$	27.6659	1.67136
$275$	−2.92193	−0.176199
$276$	3.93124	0.236633
$277$	−15.2699	−0.917480	−0.458740	−	0.888571i	$-0.651699\pi$
$277$	−15.2699	−0.917480	−0.458740	+	0.888571i	$0.651699\pi$
$278$	9.82523	0.589278
$279$	7.78308	0.465961
$280$	0.00785760	0.000469581 0
$281$	7.92619	0.472837	0.236418	−	0.971651i	$-0.424026\pi$
$281$	7.92619	0.472837	0.236418	+	0.971651i	$0.424026\pi$
$282$	−15.0449	−0.895908
$283$	28.4973	1.69399	0.846994	−	0.531602i	$-0.178410\pi$
$283$	28.4973	1.69399	0.846994	+	0.531602i	$0.178410\pi$
$284$	2.13461	0.126666
$285$	−0.520228	−0.0308156
$286$	−0.988481	−0.0584501
$287$	0.00855811	0.000505169 0
$288$	−4.46422	−0.263057
$289$	25.9482	1.52637
$290$	0.00155611	9.13781e−5 0
$291$	−12.8350	−0.752403
$292$	12.2830	0.718807
$293$	−17.5130	−1.02312	−0.511561	−	0.859247i	$-0.670932\pi$
$293$	−17.5130	−1.02312	−0.511561	+	0.859247i	$0.670932\pi$
$294$	11.7913	0.687680
$295$	0.183521	0.0106850
$296$	1.25463	0.0729241
$297$	−0.586754	−0.0340469
$298$	12.5675	0.728018
$299$	4.69081	0.271276
$300$	4.17345	0.240954
$301$	−0.0347379	−0.00200226
$302$	−28.8411	−1.65962
$303$	0.505084	0.0290163
$304$	−18.2100	−1.04442
$305$	2.09307	0.119849
$306$	11.0404	0.631137
$307$	4.82523	0.275390	0.137695	−	0.990475i	$-0.456031\pi$
$307$	4.82523	0.275390	0.137695	+	0.990475i	$0.456031\pi$
$308$	−0.0138921	−0.000791577 0
$309$	−1.00000	−0.0568880
$310$	1.86308	0.105816
$311$	4.98530	0.282691	0.141345	−	0.989960i	$-0.454857\pi$
$311$	4.98530	0.282691	0.141345	+	0.989960i	$0.454857\pi$
$312$	−1.95745	−0.110819
$313$	−14.3500	−0.811112	−0.405556	−	0.914070i	$-0.632922\pi$
$313$	−14.3500	−0.811112	−0.405556	+	0.914070i	$0.632922\pi$
$314$	25.3519	1.43069
$315$	−0.00401420	−0.000226175 0
$316$	3.76259	0.211662
$317$	−15.7146	−0.882617	−0.441309	−	0.897355i	$-0.645486\pi$
$317$	−15.7146	−0.882617	−0.441309	+	0.897355i	$0.645486\pi$
$318$	4.47787	0.251107
$319$	0.00381431	0.000213561 0
$320$	0.344838	0.0192770
$321$	13.1759	0.735407
$322$	0.223249	0.0124412
$323$	23.9937	1.33504
$324$	0.838074	0.0465597
$325$	4.97981	0.276230
$326$	30.2180	1.67362
$327$	−6.50034	−0.359470
$328$	0.592977	0.0327417
$329$	−0.252294	−0.0139094
$330$	−0.140455	−0.00773180
$331$	21.6256	1.18865	0.594325	−	0.804225i	$-0.297419\pi$
$331$	21.6256	1.18865	0.594325	+	0.804225i	$0.297419\pi$
$332$	10.6317	0.583492
$333$	−0.640954	−0.0351240
$334$	17.6679	0.966742
$335$	−1.03576	−0.0565896
$336$	−0.140513	−0.00766562
$337$	−8.68434	−0.473066	−0.236533	−	0.971623i	$-0.576011\pi$
$337$	−8.68434	−0.473066	−0.236533	+	0.971623i	$0.576011\pi$
$338$	1.68466	0.0916333
$339$	7.47118	0.405779
$340$	0.780412	0.0423238
$341$	4.56675	0.247304
$342$	6.16788	0.333521
$343$	0.395488	0.0213543
$344$	−2.40693	−0.129773
$345$	0.666525	0.0358845
$346$	−29.8126	−1.60274
$347$	7.55514	0.405581	0.202791	−	0.979222i	$-0.434999\pi$
$347$	7.55514	0.405581	0.202791	+	0.979222i	$0.434999\pi$
$348$	−0.00544807	−0.000292047 0
$349$	5.54717	0.296933	0.148467	−	0.988917i	$-0.452566\pi$
$349$	5.54717	0.296933	0.148467	+	0.988917i	$0.452566\pi$
$350$	0.237003	0.0126684
$351$	1.00000	0.0533761
$352$	−2.61940	−0.139615
$353$	−21.6789	−1.15385	−0.576925	−	0.816797i	$-0.695748\pi$
$353$	−21.6789	−1.15385	−0.576925	+	0.816797i	$0.695748\pi$
$354$	−2.17585	−0.115645
$355$	0.361914	0.0192084
$356$	9.51623	0.504359
$357$	0.185141	0.00979870
$358$	−1.61475	−0.0853423
$359$	10.3919	0.548464	0.274232	−	0.961664i	$-0.411576\pi$
$359$	10.3919	0.548464	0.274232	+	0.961664i	$0.411576\pi$
$360$	−0.278137	−0.0146591
$361$	−5.59556	−0.294503
$362$	−34.2482	−1.80005
$363$	10.6557	0.559280
$364$	0.0236762	0.00124097
$365$	2.08253	0.109005
$366$	−24.8156	−1.29713
$367$	15.6046	0.814554	0.407277	−	0.913305i	$-0.366478\pi$
$367$	15.6046	0.814554	0.407277	+	0.913305i	$0.366478\pi$
$368$	23.3310	1.21621
$369$	−0.302934	−0.0157701
$370$	−0.153429	−0.00797640
$371$	0.0750914	0.00389855
$372$	−6.52279	−0.338191
$373$	23.1400	1.19814	0.599072	−	0.800695i	$-0.295536\pi$
$373$	23.1400	1.19814	0.599072	+	0.800695i	$0.295536\pi$
$374$	6.47800	0.334969
$375$	1.41805	0.0732278
$376$	−17.4810	−0.901514
$377$	−0.00650070	−0.000334803 0
$378$	0.0475929	0.00244791
$379$	−15.9063	−0.817050	−0.408525	−	0.912747i	$-0.633957\pi$
$379$	−15.9063	−0.817050	−0.408525	+	0.912747i	$0.633957\pi$
$380$	0.435989	0.0223658
$381$	−13.3167	−0.682234
$382$	36.7428	1.87992
$383$	−31.3890	−1.60390	−0.801951	−	0.597390i	$-0.796205\pi$
$383$	−31.3890	−1.60390	−0.801951	+	0.597390i	$0.796205\pi$
$384$	−13.0169	−0.664265
$385$	−0.00235535	−0.000120040 0
$386$	−26.5644	−1.35209
$387$	1.22963	0.0625055
$388$	10.7567	0.546089
$389$	−27.8195	−1.41051	−0.705253	−	0.708956i	$-0.749166\pi$
$389$	−27.8195	−1.41051	−0.705253	+	0.708956i	$0.749166\pi$
$390$	0.239376	0.0121213
$391$	−30.7412	−1.55465
$392$	13.7006	0.691984
$393$	−3.02499	−0.152590
$394$	11.2402	0.566275
$395$	0.637931	0.0320978
$396$	0.491743	0.0247110
$397$	−25.5056	−1.28009	−0.640044	−	0.768339i	$-0.721084\pi$
$397$	−25.5056	−1.28009	−0.640044	+	0.768339i	$0.721084\pi$
$398$	−32.3268	−1.62039
$399$	0.103432	0.00517807
$400$	24.7685	1.23842
$401$	−22.8663	−1.14189	−0.570945	−	0.820988i	$-0.693423\pi$
$401$	−22.8663	−1.14189	−0.570945	+	0.820988i	$0.693423\pi$
$402$	12.2801	0.612476
$403$	−7.78308	−0.387703
$404$	−0.423298	−0.0210599
$405$	0.142092	0.00706060
$406$	−0.000309387 0	−1.53546e−5 0
$407$	−0.376082	−0.0186417
$408$	12.8281	0.635086
$409$	−16.4951	−0.815628	−0.407814	−	0.913065i	$-0.633709\pi$
$409$	−16.4951	−0.815628	−0.407814	+	0.913065i	$0.633709\pi$
$410$	−0.0725151	−0.00358127
$411$	−16.4223	−0.810051
$412$	0.838074	0.0412889
$413$	−0.0364877	−0.00179544
$414$	−7.90241	−0.388382
$415$	1.80256	0.0884844
$416$	4.46422	0.218877
$417$	−5.83218	−0.285603
$418$	3.61903	0.177013
$419$	29.9683	1.46405	0.732023	−	0.681280i	$-0.238576\pi$
$419$	29.9683	1.46405	0.732023	+	0.681280i	$0.238576\pi$
$420$	0.00336420	0.000164156 0
$421$	−1.75273	−0.0854229	−0.0427115	−	0.999087i	$-0.513600\pi$
$421$	−1.75273	−0.0854229	−0.0427115	+	0.999087i	$0.513600\pi$
$422$	−39.8020	−1.93753
$423$	8.93051	0.434216
$424$	5.20296	0.252678
$425$	−32.6351	−1.58304
$426$	−4.29090	−0.207895
$427$	−0.416144	−0.0201386
$428$	−11.0424	−0.533753
$429$	0.586754	0.0283288
$430$	0.294344	0.0141945
$431$	−25.4794	−1.22730	−0.613650	−	0.789578i	$-0.710300\pi$
$431$	−25.4794	−1.22730	−0.613650	+	0.789578i	$0.710300\pi$
$432$	4.97378	0.239301
$433$	7.00329	0.336557	0.168278	−	0.985740i	$-0.446179\pi$
$433$	7.00329	0.336557	0.168278	+	0.985740i	$0.446179\pi$
$434$	−0.370419	−0.0177807
$435$	−0.000923697 0	−4.42879e−5 0
$436$	5.44776	0.260901
$437$	−17.1740	−0.821545
$438$	−24.6907	−1.17977
$439$	25.6196	1.22276	0.611380	−	0.791337i	$-0.290615\pi$
$439$	25.6196	1.22276	0.611380	+	0.791337i	$0.290615\pi$
$440$	−0.163198	−0.00778018
$441$	−6.99920	−0.333295
$442$	−11.0404	−0.525138
$443$	17.5323	0.832982	0.416491	−	0.909140i	$-0.363260\pi$
$443$	17.5323	0.832982	0.416491	+	0.909140i	$0.363260\pi$
$444$	0.537166	0.0254928
$445$	1.61344	0.0764842
$446$	−11.2338	−0.531937
$447$	−7.45999	−0.352845
$448$	−0.0685609	−0.00323920
$449$	−1.27998	−0.0604061	−0.0302031	−	0.999544i	$-0.509615\pi$
$449$	−1.27998	−0.0604061	−0.0302031	+	0.999544i	$0.509615\pi$
$450$	−8.38928	−0.395474
$451$	−0.177748	−0.00836981
$452$	−6.26140	−0.294511
$453$	17.1198	0.804360
$454$	18.8059	0.882605
$455$	0.00401420	0.000188189 0
$456$	7.16662	0.335608
$457$	−7.99043	−0.373777	−0.186888	−	0.982381i	$-0.559840\pi$
$457$	−7.99043	−0.373777	−0.186888	+	0.982381i	$0.559840\pi$
$458$	27.2835	1.27487
$459$	−6.55349	−0.305891
$460$	−0.558598	−0.0260447
$461$	13.0031	0.605616	0.302808	−	0.953052i	$-0.402076\pi$
$461$	13.0031	0.605616	0.302808	+	0.953052i	$0.402076\pi$
$462$	0.0279253	0.00129920
$463$	18.9290	0.879706	0.439853	−	0.898070i	$-0.355031\pi$
$463$	18.9290	0.879706	0.439853	+	0.898070i	$0.355031\pi$
$464$	−0.0323331	−0.00150102
$465$	−1.10591	−0.0512854
$466$	26.2668	1.21679
$467$	16.4782	0.762522	0.381261	−	0.924468i	$-0.375490\pi$
$467$	16.4782	0.762522	0.381261	+	0.924468i	$0.375490\pi$
$468$	−0.838074	−0.0387400
$469$	0.205930	0.00950898
$470$	2.13775	0.0986071
$471$	−15.0487	−0.693407
$472$	−2.52817	−0.116369
$473$	0.721490	0.0331741
$474$	−7.56339	−0.347398
$475$	−18.2321	−0.836547
$476$	−0.155162	−0.00711183
$477$	−2.65803	−0.121703
$478$	8.94856	0.409298
$479$	21.3733	0.976571	0.488286	−	0.872684i	$-0.337622\pi$
$479$	21.3733	0.976571	0.488286	+	0.872684i	$0.337622\pi$
$480$	0.634330	0.0289531
$481$	0.640954	0.0292250
$482$	−8.32840	−0.379348
$483$	−0.132519	−0.00602982
$484$	−8.93028	−0.405922
$485$	1.82375	0.0828124
$486$	−1.68466	−0.0764177
$487$	11.4819	0.520297	0.260148	−	0.965569i	$-0.416229\pi$
$487$	11.4819	0.520297	0.260148	+	0.965569i	$0.416229\pi$
$488$	−28.8339	−1.30525
$489$	−17.9372	−0.811146
$490$	−1.67544	−0.0756888
$491$	−7.93330	−0.358025	−0.179012	−	0.983847i	$-0.557290\pi$
$491$	−7.93330	−0.358025	−0.179012	+	0.983847i	$0.557290\pi$
$492$	0.253881	0.0114458
$493$	0.0426023	0.00191871
$494$	−6.16788	−0.277506
$495$	0.0833730	0.00374734
$496$	−38.7113	−1.73819
$497$	−0.0719559	−0.00322766
$498$	−21.3714	−0.957677
$499$	3.09047	0.138349	0.0691743	−	0.997605i	$-0.477964\pi$
$499$	3.09047	0.138349	0.0691743	+	0.997605i	$0.477964\pi$
$500$	−1.18843	−0.0531482
$501$	−10.4875	−0.468547
$502$	−42.4928	−1.89655
$503$	12.0249	0.536164	0.268082	−	0.963396i	$-0.413610\pi$
$503$	12.0249	0.536164	0.268082	+	0.963396i	$0.413610\pi$
$504$	0.0552994	0.00246323
$505$	−0.0717684	−0.00319365
$506$	−4.63677	−0.206130
$507$	−1.00000	−0.0444116
$508$	11.1604	0.495161
$509$	−14.5131	−0.643280	−0.321640	−	0.946862i	$-0.604234\pi$
$509$	−14.5131	−0.643280	−0.321640	+	0.946862i	$0.604234\pi$
$510$	−1.56875	−0.0694654
$511$	−0.414049	−0.0183165
$512$	2.73223	0.120748
$513$	−3.66121	−0.161646
$514$	−24.1332	−1.06447
$515$	0.142092	0.00626131
$516$	−1.03052	−0.0453661
$517$	5.24001	0.230456
$518$	0.0305048	0.00134031
$519$	17.6965	0.776792
$520$	0.278137	0.0121971
$521$	13.3602	0.585319	0.292660	−	0.956217i	$-0.405460\pi$
$521$	13.3602	0.585319	0.292660	+	0.956217i	$0.405460\pi$
$522$	0.0109515	0.000479332 0
$523$	−29.1101	−1.27289	−0.636447	−	0.771320i	$-0.719597\pi$
$523$	−29.1101	−1.27289	−0.636447	+	0.771320i	$0.719597\pi$
$524$	2.53516	0.110749
$525$	−0.140683	−0.00613993
$526$	34.1802	1.49033
$527$	51.0063	2.22187
$528$	2.91839	0.127006
$529$	−0.996328	−0.0433186
$530$	−0.636269	−0.0276378
$531$	1.29157	0.0560492
$532$	−0.0866836	−0.00375821
$533$	0.302934	0.0131215
$534$	−19.1291	−0.827797
$535$	−1.87219	−0.0809417
$536$	14.2686	0.616309
$537$	0.958504	0.0413625
$538$	−27.3604	−1.17959
$539$	−4.10681	−0.176893
$540$	−0.119083	−0.00512454
$541$	−33.9318	−1.45884	−0.729422	−	0.684064i	$-0.760211\pi$
$541$	−33.9318	−1.45884	−0.729422	+	0.684064i	$0.760211\pi$
$542$	−11.9711	−0.514203
$543$	20.3295	0.872421
$544$	−29.2562	−1.25435
$545$	0.923645	0.0395646
$546$	−0.0475929	−0.00203679
$547$	−17.3418	−0.741483	−0.370742	−	0.928736i	$-0.620896\pi$
$547$	−17.3418	−0.741483	−0.370742	+	0.928736i	$0.620896\pi$
$548$	13.7631	0.587930
$549$	14.7304	0.628677
$550$	−4.92245	−0.209894
$551$	0.0238004	0.00101393
$552$	−9.18201	−0.390812
$553$	−0.126834	−0.00539352
$554$	−25.7246	−1.09293
$555$	0.0910743	0.00386589
$556$	4.88780	0.207289
$557$	3.78785	0.160496	0.0802482	−	0.996775i	$-0.474429\pi$
$557$	3.78785	0.160496	0.0802482	+	0.996775i	$0.474429\pi$
$558$	13.1118	0.555068
$559$	−1.22963	−0.0520077
$560$	0.0199658	0.000843707 0
$561$	−3.84529	−0.162348
$562$	13.3529	0.563259
$563$	36.2147	1.52627	0.763134	−	0.646240i	$-0.223659\pi$
$563$	36.2147	1.52627	0.763134	+	0.646240i	$0.223659\pi$
$564$	−7.48442	−0.315151
$565$	−1.06159	−0.0446616
$566$	48.0082	2.01794
$567$	−0.0282508	−0.00118642
$568$	−4.98570	−0.209195
$569$	31.4563	1.31871	0.659357	−	0.751830i	$-0.270828\pi$
$569$	31.4563	1.31871	0.659357	+	0.751830i	$0.270828\pi$
$570$	−0.876406	−0.0367086
$571$	−16.1568	−0.676139	−0.338070	−	0.941121i	$-0.609774\pi$
$571$	−16.1568	−0.676139	−0.338070	+	0.941121i	$0.609774\pi$
$572$	−0.491743	−0.0205608
$573$	−21.8102	−0.911135
$574$	0.0144175	0.000601774 0
$575$	23.3593	0.974151
$576$	2.42687	0.101120
$577$	36.7587	1.53028	0.765142	−	0.643862i	$-0.222669\pi$
$577$	36.7587	1.53028	0.765142	+	0.643862i	$0.222669\pi$
$578$	43.7139	1.81826
$579$	15.7684	0.655313
$580$	0.000774126 0	3.21438e−5 0
$581$	−0.358387	−0.0148684
$582$	−21.6227	−0.896288
$583$	−1.55961	−0.0645925
$584$	−28.6888	−1.18715
$585$	−0.142092	−0.00587477
$586$	−29.5034	−1.21878
$587$	−6.23800	−0.257470	−0.128735	−	0.991679i	$-0.541092\pi$
$587$	−6.23800	−0.257470	−0.128735	+	0.991679i	$0.541092\pi$
$588$	5.86585	0.241904
$589$	28.4955	1.17413
$590$	0.309170	0.0127283
$591$	−6.67212	−0.274454
$592$	3.18796	0.131024
$593$	5.01409	0.205904	0.102952	−	0.994686i	$-0.467171\pi$
$593$	5.01409	0.205904	0.102952	+	0.994686i	$0.467171\pi$
$594$	−0.988481	−0.0405579
$595$	−0.0263070	−0.00107848
$596$	6.25202	0.256093
$597$	19.1889	0.785350
$598$	7.90241	0.323153
$599$	−42.1735	−1.72316	−0.861581	−	0.507620i	$-0.830525\pi$
$599$	−42.1735	−1.72316	−0.861581	+	0.507620i	$0.830525\pi$
$600$	−9.74772	−0.397949
$601$	−40.0148	−1.63224	−0.816118	−	0.577885i	$-0.803878\pi$
$601$	−40.0148	−1.63224	−0.816118	+	0.577885i	$0.803878\pi$
$602$	−0.0585216	−0.00238516
$603$	−7.28937	−0.296846
$604$	−14.3477	−0.583799
$605$	−1.51409	−0.0615565
$606$	0.850895	0.0345652
$607$	2.02257	0.0820938	0.0410469	−	0.999157i	$-0.486931\pi$
$607$	2.02257	0.0820938	0.0410469	+	0.999157i	$0.486931\pi$
$608$	−16.3444	−0.662855
$609$	0.000183650 0	7.44186e−6 0
$610$	3.52610	0.142768
$611$	−8.93051	−0.361290
$612$	5.49231	0.222013
$613$	−11.6557	−0.470771	−0.235385	−	0.971902i	$-0.575635\pi$
$613$	−11.6557	−0.470771	−0.235385	+	0.971902i	$0.575635\pi$
$614$	8.12886	0.328054
$615$	0.0430444	0.00173572
$616$	0.0324472	0.00130733
$617$	25.1049	1.01068	0.505342	−	0.862919i	$-0.331366\pi$
$617$	25.1049	1.01068	0.505342	+	0.862919i	$0.331366\pi$
$618$	−1.68466	−0.0677669
$619$	−28.3723	−1.14038	−0.570189	−	0.821514i	$-0.693130\pi$
$619$	−28.3723	−1.14038	−0.570189	+	0.821514i	$0.693130\pi$
$620$	0.926836	0.0372226
$621$	4.69081	0.188236
$622$	8.39853	0.336750
$623$	−0.320784	−0.0128519
$624$	−4.97378	−0.199111
$625$	24.6976	0.987902
$626$	−24.1749	−0.966224
$627$	−2.14823	−0.0857920
$628$	12.6119	0.503270
$629$	−4.20048	−0.167484
$630$	−0.00676256	−0.000269427 0
$631$	−1.96932	−0.0783974	−0.0391987	−	0.999231i	$-0.512481\pi$
$631$	−1.96932	−0.0783974	−0.0391987	+	0.999231i	$0.512481\pi$
$632$	−8.78810	−0.349572
$633$	23.6262	0.939056
$634$	−26.4737	−1.05140
$635$	1.89219	0.0750893
$636$	2.22763	0.0883311
$637$	6.99920	0.277318
$638$	0.00642582	0.000254401 0
$639$	2.54704	0.100759
$640$	1.84959	0.0731116
$641$	−22.1527	−0.874979	−0.437490	−	0.899223i	$-0.644132\pi$
$641$	−22.1527	−0.874979	−0.437490	+	0.899223i	$0.644132\pi$
$642$	22.1969	0.876041
$643$	−27.7645	−1.09493	−0.547463	−	0.836830i	$-0.684406\pi$
$643$	−27.7645	−1.09493	−0.547463	+	0.836830i	$0.684406\pi$
$644$	0.111061	0.00437640
$645$	−0.174720	−0.00687960
$646$	40.4212	1.59035
$647$	9.19631	0.361544	0.180772	−	0.983525i	$-0.442140\pi$
$647$	9.19631	0.361544	0.180772	+	0.983525i	$0.442140\pi$
$648$	−1.95745	−0.0768958
$649$	0.757832	0.0297475
$650$	8.38928	0.329055
$651$	0.219878	0.00861769
$652$	15.0327	0.588725
$653$	−8.25048	−0.322866	−0.161433	−	0.986884i	$-0.551612\pi$
$653$	−8.25048	−0.322866	−0.161433	+	0.986884i	$0.551612\pi$
$654$	−10.9508	−0.428212
$655$	0.429826	0.0167947
$656$	1.50673	0.0588278
$657$	14.6562	0.571793
$658$	−0.425029	−0.0165693
$659$	49.9584	1.94610	0.973051	−	0.230591i	$-0.0740658\pi$
$659$	49.9584	1.94610	0.973051	+	0.230591i	$0.0740658\pi$
$660$	−0.0698727	−0.00271979
$661$	24.5045	0.953115	0.476558	−	0.879143i	$-0.341884\pi$
$661$	24.5045	0.953115	0.476558	+	0.879143i	$0.341884\pi$
$662$	36.4317	1.41596
$663$	6.55349	0.254516
$664$	−24.8320	−0.963669
$665$	−0.0146968	−0.000569918 0
$666$	−1.07979	−0.0418409
$667$	−0.0304935	−0.00118071
$668$	8.78930	0.340068
$669$	6.66830	0.257812
$670$	−1.74490	−0.0674115
$671$	8.64311	0.333663
$672$	−0.126118	−0.00486510
$673$	−40.9284	−1.57767	−0.788836	−	0.614604i	$-0.789316\pi$
$673$	−40.9284	−1.57767	−0.788836	+	0.614604i	$0.789316\pi$
$674$	−14.6301	−0.563532
$675$	4.97981	0.191673
$676$	0.838074	0.0322336
$677$	15.5337	0.597009	0.298505	−	0.954408i	$-0.403512\pi$
$677$	15.5337	0.597009	0.298505	+	0.954408i	$0.403512\pi$
$678$	12.5864	0.483377
$679$	−0.362600	−0.0139153
$680$	−1.82277	−0.0699001
$681$	−11.1630	−0.427769
$682$	7.69342	0.294596
$683$	−5.73846	−0.219576	−0.109788	−	0.993955i	$-0.535017\pi$
$683$	−5.73846	−0.219576	−0.109788	+	0.993955i	$0.535017\pi$
$684$	3.06836	0.117322
$685$	2.33347	0.0891574
$686$	0.666262	0.0254380
$687$	−16.1952	−0.617887
$688$	−6.11590	−0.233167
$689$	2.65803	0.101263
$690$	1.12287	0.0427468
$691$	−2.72305	−0.103590	−0.0517948	−	0.998658i	$-0.516494\pi$
$691$	−2.72305	−0.103590	−0.0517948	+	0.998658i	$0.516494\pi$
$692$	−14.8310	−0.563790
$693$	−0.0165763	−0.000629680 0
$694$	12.7278	0.483142
$695$	0.828705	0.0314346
$696$	0.0127248	0.000482332 0
$697$	−1.98527	−0.0751976
$698$	9.34509	0.353717
$699$	−15.5918	−0.589735
$700$	0.117903	0.00445632
$701$	−34.5717	−1.30575	−0.652877	−	0.757464i	$-0.726438\pi$
$701$	−34.5717	−1.30575	−0.652877	+	0.757464i	$0.726438\pi$
$702$	1.68466	0.0635833
$703$	−2.34666	−0.0885061
$704$	1.42398	0.0536681
$705$	−1.26895	−0.0477915
$706$	−36.5215	−1.37450
$707$	0.0142690	0.000536642 0
$708$	−1.08243	−0.0406801
$709$	31.1283	1.16905	0.584524	−	0.811376i	$-0.301281\pi$
$709$	31.1283	1.16905	0.584524	+	0.811376i	$0.301281\pi$
$710$	0.609701	0.0228817
$711$	4.48957	0.168372
$712$	−22.2266	−0.832977
$713$	−36.5089	−1.36727
$714$	0.311899	0.0116725
$715$	−0.0833730	−0.00311797
$716$	−0.803297	−0.0300206
$717$	−5.31180	−0.198373
$718$	17.5068	0.653349
$719$	43.6260	1.62698	0.813488	−	0.581582i	$-0.197566\pi$
$719$	43.6260	1.62698	0.813488	+	0.581582i	$0.197566\pi$
$720$	−0.706734	−0.0263384
$721$	−0.0282508	−0.00105211
$722$	−9.42661	−0.350822
$723$	4.94367	0.183857
$724$	−17.0376	−0.633198
$725$	−0.0323723	−0.00120228
$726$	17.9512	0.666233
$727$	−42.1106	−1.56180	−0.780898	−	0.624659i	$-0.785238\pi$
$727$	−42.1106	−1.56180	−0.780898	+	0.624659i	$0.785238\pi$
$728$	−0.0552994	−0.00204953
$729$	1.00000	0.0370370
$730$	3.50835	0.129850
$731$	8.05836	0.298049
$732$	−12.3451	−0.456289
$733$	23.4756	0.867091	0.433545	−	0.901132i	$-0.357262\pi$
$733$	23.4756	0.867091	0.433545	+	0.901132i	$0.357262\pi$
$734$	26.2884	0.970324
$735$	0.994530	0.0366838
$736$	20.9408	0.771888
$737$	−4.27707	−0.157548
$738$	−0.510340	−0.0187859
$739$	−12.4311	−0.457285	−0.228643	−	0.973510i	$-0.573429\pi$
$739$	−12.4311	−0.457285	−0.228643	+	0.973510i	$0.573429\pi$
$740$	−0.0763270	−0.00280584
$741$	3.66121	0.134498
$742$	0.126503	0.00464408
$743$	−23.3700	−0.857361	−0.428680	−	0.903456i	$-0.641021\pi$
$743$	−23.3700	−0.857361	−0.428680	+	0.903456i	$0.641021\pi$
$744$	15.2350	0.558541
$745$	1.06000	0.0388355
$746$	38.9830	1.42727
$747$	12.6859	0.464153
$748$	3.22264	0.117831
$749$	0.372229	0.0136010
$750$	2.38893	0.0872314
$751$	−40.4480	−1.47597	−0.737985	−	0.674817i	$-0.764223\pi$
$751$	−40.4480	−1.47597	−0.737985	+	0.674817i	$0.764223\pi$
$752$	−44.4184	−1.61977
$753$	25.2234	0.919191
$754$	−0.0109515	−0.000398829 0
$755$	−2.43259	−0.0885310
$756$	0.0236762	0.000861096 0
$757$	−40.5615	−1.47423	−0.737116	−	0.675766i	$-0.763813\pi$
$757$	−40.5615	−1.47423	−0.737116	+	0.675766i	$0.763813\pi$
$758$	−26.7966	−0.973298
$759$	2.75235	0.0999040
$760$	−1.01832	−0.0369383
$761$	8.76699	0.317803	0.158902	−	0.987294i	$-0.449205\pi$
$761$	8.76699	0.317803	0.158902	+	0.987294i	$0.449205\pi$
$762$	−22.4341	−0.812700
$763$	−0.183639	−0.00664820
$764$	18.2786	0.661296
$765$	0.931197	0.0336675
$766$	−52.8797	−1.91062
$767$	−1.29157	−0.0466357
$768$	−17.0753	−0.616151
$769$	−13.2673	−0.478432	−0.239216	−	0.970966i	$-0.576890\pi$
$769$	−13.2673	−0.478432	−0.239216	+	0.970966i	$0.576890\pi$
$770$	−0.00396796	−0.000142995 0
$771$	14.3253	0.515913
$772$	−13.2151	−0.475622
$773$	15.8064	0.568517	0.284258	−	0.958748i	$-0.408253\pi$
$773$	15.8064	0.568517	0.284258	+	0.958748i	$0.408253\pi$
$774$	2.07150	0.0744587
$775$	−38.7582	−1.39224
$776$	−25.1239	−0.901897
$777$	−0.0181074	−0.000649600 0
$778$	−46.8664	−1.68024
$779$	−1.10910	−0.0397377
$780$	0.119083	0.00426387
$781$	1.49449	0.0534770
$782$	−51.7883	−1.85195
$783$	−0.00650070	−0.000232316 0
$784$	34.8125	1.24330
$785$	2.13830	0.0763190
$786$	−5.09607	−0.181771
$787$	−18.7987	−0.670101	−0.335050	−	0.942200i	$-0.608753\pi$
$787$	−18.7987	−0.670101	−0.335050	+	0.942200i	$0.608753\pi$
$788$	5.59173	0.199197
$789$	−20.2891	−0.722312
$790$	1.07470	0.0382360
$791$	0.211066	0.00750466
$792$	−1.14854	−0.0408116
$793$	−14.7304	−0.523091
$794$	−42.9681	−1.52488
$795$	0.377684	0.0133951
$796$	−16.0817	−0.570002
$797$	−6.78458	−0.240322	−0.120161	−	0.992754i	$-0.538341\pi$
$797$	−6.78458	−0.240322	−0.120161	+	0.992754i	$0.538341\pi$
$798$	0.174247	0.00616829
$799$	58.5260	2.07050
$800$	22.2310	0.785984
$801$	11.3549	0.401205
$802$	−38.5220	−1.36026
$803$	8.59960	0.303473
$804$	6.10903	0.215449
$805$	0.0188299	0.000663665 0
$806$	−13.1118	−0.461844
$807$	16.2409	0.571707
$808$	0.988677	0.0347815
$809$	16.2654	0.571862	0.285931	−	0.958250i	$-0.407697\pi$
$809$	16.2654	0.571862	0.285931	+	0.958250i	$0.407697\pi$
$810$	0.239376	0.00841082
$811$	39.1648	1.37526	0.687632	−	0.726060i	$-0.258650\pi$
$811$	39.1648	1.37526	0.687632	+	0.726060i	$0.258650\pi$
$812$	−0.000153912 0	−5.40125e−6 0
$813$	7.10595	0.249217
$814$	−0.633570	−0.0222066
$815$	2.54872	0.0892779
$816$	32.5956	1.14107
$817$	4.50192	0.157502
$818$	−27.7885	−0.971603
$819$	0.0282508	0.000987161 0
$820$	−0.0360744	−0.00125977
$821$	−34.6582	−1.20958	−0.604789	−	0.796386i	$-0.706743\pi$
$821$	−34.6582	−1.20958	−0.604789	+	0.796386i	$0.706743\pi$
$822$	−27.6659	−0.964960
$823$	46.7496	1.62959	0.814794	−	0.579751i	$-0.196850\pi$
$823$	46.7496	1.62959	0.814794	+	0.579751i	$0.196850\pi$
$824$	−1.95745	−0.0681910
$825$	2.92193	0.101728
$826$	−0.0614693	−0.00213879
$827$	−26.1562	−0.909539	−0.454769	−	0.890609i	$-0.650278\pi$
$827$	−26.1562	−0.909539	−0.454769	+	0.890609i	$0.650278\pi$
$828$	−3.93124	−0.136620
$829$	−35.2168	−1.22313	−0.611566	−	0.791194i	$-0.709460\pi$
$829$	−35.2168	−1.22313	−0.611566	+	0.791194i	$0.709460\pi$
$830$	3.03671	0.105406
$831$	15.2699	0.529707
$832$	−2.42687	−0.0841366
$833$	−45.8692	−1.58927
$834$	−9.82523	−0.340220
$835$	1.49019	0.0515701
$836$	1.80037	0.0622673
$837$	−7.78308	−0.269022
$838$	50.4863	1.74402
$839$	−55.3731	−1.91169	−0.955846	−	0.293868i	$-0.905057\pi$
$839$	−55.3731	−1.91169	−0.955846	+	0.293868i	$0.905057\pi$
$840$	−0.00785760	−0.000271113 0
$841$	−29.0000	−0.999999
$842$	−2.95276	−0.101759
$843$	−7.92619	−0.272992
$844$	−19.8005	−0.681561
$845$	0.142092	0.00488811
$846$	15.0449	0.517253
$847$	0.301032	0.0103436
$848$	13.2205	0.453992
$849$	−28.4973	−0.978025
$850$	−54.9790	−1.88577
$851$	3.00659	0.103065
$852$	−2.13461	−0.0731305
$853$	15.0393	0.514936	0.257468	−	0.966287i	$-0.417112\pi$
$853$	15.0393	0.514936	0.257468	+	0.966287i	$0.417112\pi$
$854$	−0.701061	−0.0239898
$855$	0.520228	0.0177914
$856$	25.7911	0.881523
$857$	13.1074	0.447742	0.223871	−	0.974619i	$-0.428131\pi$
$857$	13.1074	0.447742	0.223871	+	0.974619i	$0.428131\pi$
$858$	0.988481	0.0337462
$859$	−51.6671	−1.76286	−0.881429	−	0.472316i	$-0.843418\pi$
$859$	−51.6671	−1.76286	−0.881429	+	0.472316i	$0.843418\pi$
$860$	0.146428	0.00499317
$861$	−0.00855811	−0.000291660 0
$862$	−42.9241	−1.46200
$863$	−34.3501	−1.16929	−0.584645	−	0.811289i	$-0.698766\pi$
$863$	−34.3501	−1.16929	−0.584645	+	0.811289i	$0.698766\pi$
$864$	4.46422	0.151876
$865$	−2.51453	−0.0854967
$866$	11.7981	0.400917
$867$	−25.9482	−0.881248
$868$	−0.184274	−0.00625466
$869$	2.63427	0.0893616
$870$	−0.00155611	−5.27572e−5 0
$871$	7.28937	0.246991
$872$	−12.7241	−0.430892
$873$	12.8350	0.434400
$874$	−28.9323	−0.978651
$875$	0.0400610	0.00135431
$876$	−12.2830	−0.415004
$877$	31.6509	1.06878	0.534388	−	0.845239i	$-0.320542\pi$
$877$	31.6509	1.06878	0.534388	+	0.845239i	$0.320542\pi$
$878$	43.1604	1.45659
$879$	17.5130	0.590699
$880$	−0.414679	−0.0139788
$881$	26.2673	0.884968	0.442484	−	0.896776i	$-0.354097\pi$
$881$	26.2673	0.884968	0.442484	+	0.896776i	$0.354097\pi$
$882$	−11.7913	−0.397033
$883$	−48.1192	−1.61934	−0.809670	−	0.586886i	$-0.800354\pi$
$883$	−48.1192	−1.61934	−0.809670	+	0.586886i	$0.800354\pi$
$884$	−5.49231	−0.184726
$885$	−0.183521	−0.00616899
$886$	29.5359	0.992277
$887$	11.5132	0.386577	0.193288	−	0.981142i	$-0.438085\pi$
$887$	11.5132	0.386577	0.193288	+	0.981142i	$0.438085\pi$
$888$	−1.25463	−0.0421027
$889$	−0.376206	−0.0126176
$890$	2.71809	0.0911106
$891$	0.586754	0.0196570
$892$	−5.58853	−0.187118
$893$	32.6964	1.09414
$894$	−12.5675	−0.420321
$895$	−0.136196	−0.00455252
$896$	−0.367737	−0.0122852
$897$	−4.69081	−0.156621
$898$	−2.15633	−0.0719578
$899$	0.0505954	0.00168745
$900$	−4.17345	−0.139115
$901$	−17.4194	−0.580323
$902$	−0.299444	−0.00997040
$903$	0.0347379	0.00115601
$904$	14.6244	0.486402
$905$	−2.88865	−0.0960221
$906$	28.8411	0.958180
$907$	−7.88873	−0.261941	−0.130971	−	0.991386i	$-0.541809\pi$
$907$	−7.88873	−0.261941	−0.130971	+	0.991386i	$0.541809\pi$
$908$	9.35545	0.310472
$909$	−0.505084	−0.0167526
$910$	0.00676256	0.000224177 0
$911$	52.4612	1.73812	0.869059	−	0.494708i	$-0.164725\pi$
$911$	52.4612	1.73812	0.869059	+	0.494708i	$0.164725\pi$
$912$	18.2100	0.602995
$913$	7.44351	0.246344
$914$	−13.4612	−0.445255
$915$	−2.09307	−0.0691946
$916$	13.5728	0.448458
$917$	−0.0854582	−0.00282208
$918$	−11.0404	−0.364387
$919$	44.7476	1.47609	0.738043	−	0.674753i	$-0.235750\pi$
$919$	44.7476	1.47609	0.738043	+	0.674753i	$0.235750\pi$
$920$	1.30469	0.0430143
$921$	−4.82523	−0.158997
$922$	21.9058	0.721430
$923$	−2.54704	−0.0838369
$924$	0.0138921	0.000457017 0
$925$	3.19183	0.104947
$926$	31.8889	1.04794
$927$	1.00000	0.0328443
$928$	−0.0290206	−0.000952647 0
$929$	−24.3344	−0.798385	−0.399192	−	0.916867i	$-0.630709\pi$
$929$	−24.3344	−0.798385	−0.399192	+	0.916867i	$0.630709\pi$
$930$	−1.86308	−0.0610929
$931$	−25.6255	−0.839843
$932$	13.0671	0.428026
$933$	−4.98530	−0.163211
$934$	27.7602	0.908341
$935$	0.546384	0.0178687
$936$	1.95745	0.0639812
$937$	−7.79279	−0.254579	−0.127290	−	0.991866i	$-0.540628\pi$
$937$	−7.79279	−0.254579	−0.127290	+	0.991866i	$0.540628\pi$
$938$	0.346922	0.0113274
$939$	14.3500	0.468296
$940$	1.06348	0.0346868
$941$	41.3403	1.34765	0.673827	−	0.738889i	$-0.264649\pi$
$941$	41.3403	1.34765	0.673827	+	0.738889i	$0.264649\pi$
$942$	−25.3519	−0.826009
$943$	1.42100	0.0462743
$944$	−6.42396	−0.209082
$945$	0.00401420	0.000130582 0
$946$	1.21546	0.0395181
$947$	53.6228	1.74251	0.871253	−	0.490833i	$-0.163308\pi$
$947$	53.6228	1.74251	0.871253	+	0.490833i	$0.163308\pi$
$948$	−3.76259	−0.122203
$949$	−14.6562	−0.475761
$950$	−30.7149	−0.996522
$951$	15.7146	0.509579
$952$	0.362404	0.0117456
$953$	−0.0226393	−0.000733359 0	−0.000366680	−	1.00000i	$-0.500117\pi$
$953$	−0.0226393	−0.000733359 0	−0.000366680		1.00000i	$0.500117\pi$
$954$	−4.47787	−0.144977
$955$	3.09906	0.100283
$956$	4.45168	0.143978
$957$	−0.00381431	−0.000123299 0
$958$	36.0067	1.16332
$959$	−0.463942	−0.0149815
$960$	−0.344838	−0.0111296
$961$	29.5763	0.954073
$962$	1.07979	0.0348138
$963$	−13.1759	−0.424587
$964$	−4.14316	−0.133442
$965$	−2.24056	−0.0721263
$966$	−0.223249	−0.00718292
$967$	−33.6420	−1.08186	−0.540928	−	0.841069i	$-0.681927\pi$
$967$	−33.6420	−1.08186	−0.540928	+	0.841069i	$0.681927\pi$
$968$	20.8580	0.670402
$969$	−23.9937	−0.770788
$970$	3.07240	0.0986489
$971$	3.95541	0.126935	0.0634676	−	0.997984i	$-0.479784\pi$
$971$	3.95541	0.126935	0.0634676	+	0.997984i	$0.479784\pi$
$972$	−0.838074	−0.0268812
$973$	−0.164764	−0.00528208
$974$	19.3432	0.619795
$975$	−4.97981	−0.159482
$976$	−73.2656	−2.34517
$977$	52.1039	1.66695	0.833475	−	0.552557i	$-0.186348\pi$
$977$	52.1039	1.66695	0.833475	+	0.552557i	$0.186348\pi$
$978$	−30.2180	−0.966265
$979$	6.66253	0.212935
$980$	−0.833489	−0.0266248
$981$	6.50034	0.207540
$982$	−13.3649	−0.426491
$983$	−19.1705	−0.611445	−0.305723	−	0.952121i	$-0.598898\pi$
$983$	−19.1705	−0.611445	−0.305723	+	0.952121i	$0.598898\pi$
$984$	−0.592977	−0.0189034
$985$	0.948053	0.0302075
$986$	0.0717703	0.00228563
$987$	0.252294	0.00803059
$988$	−3.06836	−0.0976176
$989$	−5.76795	−0.183410
$990$	0.140455	0.00446395
$991$	−8.62282	−0.273913	−0.136956	−	0.990577i	$-0.543732\pi$
$991$	−8.62282	−0.273913	−0.136956	+	0.990577i	$0.543732\pi$
$992$	−34.7454	−1.10317
$993$	−21.6256	−0.686267
$994$	−0.121221	−0.00384490
$995$	−2.72659	−0.0864386
$996$	−10.6317	−0.336879
$997$	27.0833	0.857737	0.428869	−	0.903367i	$-0.358912\pi$
$997$	27.0833	0.857737	0.428869	+	0.903367i	$0.358912\pi$
$998$	5.20639	0.164805
$999$	0.640954	0.0202789

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.18	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.18	✓	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.68466 q^{2} -1.00000 q^{3} +0.838074 q^{4} +0.142092 q^{5} -1.68466 q^{6} -0.0282508 q^{7} -1.95745 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.68466 q^{2} -1.00000 q^{3} +0.838074 q^{4} +0.142092 q^{5} -1.68466 q^{6} -0.0282508 q^{7} -1.95745 q^{8} +1.00000 q^{9} +0.239376 q^{10} +0.586754 q^{11} -0.838074 q^{12} -1.00000 q^{13} -0.0475929 q^{14} -0.142092 q^{15} -4.97378 q^{16} +6.55349 q^{17} +1.68466 q^{18} +3.66121 q^{19} +0.119083 q^{20} +0.0282508 q^{21} +0.988481 q^{22} -4.69081 q^{23} +1.95745 q^{24} -4.97981 q^{25} -1.68466 q^{26} -1.00000 q^{27} -0.0236762 q^{28} +0.00650070 q^{29} -0.239376 q^{30} +7.78308 q^{31} -4.46422 q^{32} -0.586754 q^{33} +11.0404 q^{34} -0.00401420 q^{35} +0.838074 q^{36} -0.640954 q^{37} +6.16788 q^{38} +1.00000 q^{39} -0.278137 q^{40} -0.302934 q^{41} +0.0475929 q^{42} +1.22963 q^{43} +0.491743 q^{44} +0.142092 q^{45} -7.90241 q^{46} +8.93051 q^{47} +4.97378 q^{48} -6.99920 q^{49} -8.38928 q^{50} -6.55349 q^{51} -0.838074 q^{52} -2.65803 q^{53} -1.68466 q^{54} +0.0833730 q^{55} +0.0552994 q^{56} -3.66121 q^{57} +0.0109515 q^{58} +1.29157 q^{59} -0.119083 q^{60} +14.7304 q^{61} +13.1118 q^{62} -0.0282508 q^{63} +2.42687 q^{64} -0.142092 q^{65} -0.988481 q^{66} -7.28937 q^{67} +5.49231 q^{68} +4.69081 q^{69} -0.00676256 q^{70} +2.54704 q^{71} -1.95745 q^{72} +14.6562 q^{73} -1.07979 q^{74} +4.97981 q^{75} +3.06836 q^{76} -0.0165763 q^{77} +1.68466 q^{78} +4.48957 q^{79} -0.706734 q^{80} +1.00000 q^{81} -0.510340 q^{82} +12.6859 q^{83} +0.0236762 q^{84} +0.931197 q^{85} +2.07150 q^{86} -0.00650070 q^{87} -1.14854 q^{88} +11.3549 q^{89} +0.239376 q^{90} +0.0282508 q^{91} -3.93124 q^{92} -7.78308 q^{93} +15.0449 q^{94} +0.520228 q^{95} +4.46422 q^{96} +12.8350 q^{97} -11.7913 q^{98} +0.586754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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