LMFDB - Embedded newform 4017.2.a.g.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.29414 q^{2} -1.00000 q^{3} +3.26307 q^{4} -3.12687 q^{5} +2.29414 q^{6} -2.80124 q^{7} -2.89765 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.29414 q^{2} -1.00000 q^{3} +3.26307 q^{4} -3.12687 q^{5} +2.29414 q^{6} -2.80124 q^{7} -2.89765 q^{8} +1.00000 q^{9} +7.17346 q^{10} +0.416671 q^{11} -3.26307 q^{12} -1.00000 q^{13} +6.42644 q^{14} +3.12687 q^{15} +0.121475 q^{16} +6.72425 q^{17} -2.29414 q^{18} -0.991424 q^{19} -10.2032 q^{20} +2.80124 q^{21} -0.955900 q^{22} +5.08704 q^{23} +2.89765 q^{24} +4.77729 q^{25} +2.29414 q^{26} -1.00000 q^{27} -9.14065 q^{28} -2.63056 q^{29} -7.17346 q^{30} +1.49809 q^{31} +5.51662 q^{32} -0.416671 q^{33} -15.4264 q^{34} +8.75912 q^{35} +3.26307 q^{36} -2.62448 q^{37} +2.27446 q^{38} +1.00000 q^{39} +9.06057 q^{40} +0.0147872 q^{41} -6.42644 q^{42} -5.30095 q^{43} +1.35962 q^{44} -3.12687 q^{45} -11.6704 q^{46} -5.68597 q^{47} -0.121475 q^{48} +0.846973 q^{49} -10.9598 q^{50} -6.72425 q^{51} -3.26307 q^{52} +7.63444 q^{53} +2.29414 q^{54} -1.30287 q^{55} +8.11703 q^{56} +0.991424 q^{57} +6.03487 q^{58} -6.67863 q^{59} +10.2032 q^{60} -10.9725 q^{61} -3.43683 q^{62} -2.80124 q^{63} -12.8988 q^{64} +3.12687 q^{65} +0.955900 q^{66} +3.12186 q^{67} +21.9417 q^{68} -5.08704 q^{69} -20.0946 q^{70} +12.5943 q^{71} -2.89765 q^{72} -4.28406 q^{73} +6.02092 q^{74} -4.77729 q^{75} -3.23508 q^{76} -1.16720 q^{77} -2.29414 q^{78} -1.69703 q^{79} -0.379837 q^{80} +1.00000 q^{81} -0.0339238 q^{82} -11.1302 q^{83} +9.14065 q^{84} -21.0258 q^{85} +12.1611 q^{86} +2.63056 q^{87} -1.20737 q^{88} -16.6424 q^{89} +7.17346 q^{90} +2.80124 q^{91} +16.5994 q^{92} -1.49809 q^{93} +13.0444 q^{94} +3.10005 q^{95} -5.51662 q^{96} -6.49117 q^{97} -1.94307 q^{98} +0.416671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.29414	−1.62220	−0.811100	−	0.584907i	$-0.801131\pi$
$2$	−2.29414	−1.62220	−0.811100	+	0.584907i	$0.801131\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.26307	1.63153
$5$	−3.12687	−1.39838	−0.699189	−	0.714937i	$-0.746455\pi$
$5$	−3.12687	−1.39838	−0.699189	+	0.714937i	$0.746455\pi$
$6$	2.29414	0.936578
$7$	−2.80124	−1.05877	−0.529386	−	0.848381i	$-0.677577\pi$
$7$	−2.80124	−1.05877	−0.529386	+	0.848381i	$0.677577\pi$
$8$	−2.89765	−1.02447
$9$	1.00000	0.333333
$10$	7.17346	2.26845
$11$	0.416671	0.125631	0.0628155	−	0.998025i	$-0.479992\pi$
$11$	0.416671	0.125631	0.0628155	+	0.998025i	$0.479992\pi$
$12$	−3.26307	−0.941967
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	6.42644	1.71754
$15$	3.12687	0.807353
$16$	0.121475	0.0303688
$17$	6.72425	1.63087	0.815436	−	0.578848i	$-0.196497\pi$
$17$	6.72425	1.63087	0.815436	+	0.578848i	$0.196497\pi$
$18$	−2.29414	−0.540733
$19$	−0.991424	−0.227448	−0.113724	−	0.993512i	$-0.536278\pi$
$19$	−0.991424	−0.227448	−0.113724	+	0.993512i	$0.536278\pi$
$20$	−10.2032	−2.28150
$21$	2.80124	0.611282
$22$	−0.955900	−0.203799
$23$	5.08704	1.06072	0.530361	−	0.847772i	$-0.322056\pi$
$23$	5.08704	1.06072	0.530361	+	0.847772i	$0.322056\pi$
$24$	2.89765	0.591481
$25$	4.77729	0.955459
$26$	2.29414	0.449917
$27$	−1.00000	−0.192450
$28$	−9.14065	−1.72742
$29$	−2.63056	−0.488483	−0.244242	−	0.969714i	$-0.578539\pi$
$29$	−2.63056	−0.488483	−0.244242	+	0.969714i	$0.578539\pi$
$30$	−7.17346	−1.30969
$31$	1.49809	0.269065	0.134533	−	0.990909i	$-0.457047\pi$
$31$	1.49809	0.269065	0.134533	+	0.990909i	$0.457047\pi$
$32$	5.51662	0.975210
$33$	−0.416671	−0.0725330
$34$	−15.4264	−2.64560
$35$	8.75912	1.48056
$36$	3.26307	0.543845
$37$	−2.62448	−0.431462	−0.215731	−	0.976453i	$-0.569213\pi$
$37$	−2.62448	−0.431462	−0.215731	+	0.976453i	$0.569213\pi$
$38$	2.27446	0.368967
$39$	1.00000	0.160128
$40$	9.06057	1.43260
$41$	0.0147872	0.00230937	0.00115468	−	0.999999i	$-0.499632\pi$
$41$	0.0147872	0.00230937	0.00115468	+	0.999999i	$0.499632\pi$
$42$	−6.42644	−0.991621
$43$	−5.30095	−0.808387	−0.404193	−	0.914674i	$-0.632448\pi$
$43$	−5.30095	−0.808387	−0.404193	+	0.914674i	$0.632448\pi$
$44$	1.35962	0.204971
$45$	−3.12687	−0.466126
$46$	−11.6704	−1.72070
$47$	−5.68597	−0.829385	−0.414692	−	0.909962i	$-0.636111\pi$
$47$	−5.68597	−0.829385	−0.414692	+	0.909962i	$0.636111\pi$
$48$	−0.121475	−0.0175335
$49$	0.846973	0.120996
$50$	−10.9598	−1.54995
$51$	−6.72425	−0.941584
$52$	−3.26307	−0.452506
$53$	7.63444	1.04867	0.524336	−	0.851512i	$-0.324314\pi$
$53$	7.63444	1.04867	0.524336	+	0.851512i	$0.324314\pi$
$54$	2.29414	0.312193
$55$	−1.30287	−0.175679
$56$	8.11703	1.08468
$57$	0.991424	0.131317
$58$	6.03487	0.792418
$59$	−6.67863	−0.869483	−0.434742	−	0.900555i	$-0.643160\pi$
$59$	−6.67863	−0.869483	−0.434742	+	0.900555i	$0.643160\pi$
$60$	10.2032	1.31722
$61$	−10.9725	−1.40489	−0.702444	−	0.711739i	$-0.747908\pi$
$61$	−10.9725	−1.40489	−0.702444	+	0.711739i	$0.747908\pi$
$62$	−3.43683	−0.436477
$63$	−2.80124	−0.352924
$64$	−12.8988	−1.61235
$65$	3.12687	0.387840
$66$	0.955900	0.117663
$67$	3.12186	0.381396	0.190698	−	0.981649i	$-0.438925\pi$
$67$	3.12186	0.381396	0.190698	+	0.981649i	$0.438925\pi$
$68$	21.9417	2.66082
$69$	−5.08704	−0.612408
$70$	−20.0946	−2.40177
$71$	12.5943	1.49467	0.747335	−	0.664448i	$-0.231333\pi$
$71$	12.5943	1.49467	0.747335	+	0.664448i	$0.231333\pi$
$72$	−2.89765	−0.341491
$73$	−4.28406	−0.501412	−0.250706	−	0.968063i	$-0.580663\pi$
$73$	−4.28406	−0.501412	−0.250706	+	0.968063i	$0.580663\pi$
$74$	6.02092	0.699917
$75$	−4.77729	−0.551634
$76$	−3.23508	−0.371090
$77$	−1.16720	−0.133014
$78$	−2.29414	−0.259760
$79$	−1.69703	−0.190931	−0.0954655	−	0.995433i	$-0.530434\pi$
$79$	−1.69703	−0.190931	−0.0954655	+	0.995433i	$0.530434\pi$
$80$	−0.379837	−0.0424671
$81$	1.00000	0.111111
$82$	−0.0339238	−0.00374626
$83$	−11.1302	−1.22170	−0.610848	−	0.791748i	$-0.709171\pi$
$83$	−11.1302	−1.22170	−0.610848	+	0.791748i	$0.709171\pi$
$84$	9.14065	0.997327
$85$	−21.0258	−2.28057
$86$	12.1611	1.31137
$87$	2.63056	0.282026
$88$	−1.20737	−0.128706
$89$	−16.6424	−1.76409	−0.882044	−	0.471167i	$-0.843833\pi$
$89$	−16.6424	−1.76409	−0.882044	+	0.471167i	$0.843833\pi$
$90$	7.17346	0.756149
$91$	2.80124	0.293650
$92$	16.5994	1.73060
$93$	−1.49809	−0.155345
$94$	13.0444	1.34543
$95$	3.10005	0.318058
$96$	−5.51662	−0.563038
$97$	−6.49117	−0.659079	−0.329539	−	0.944142i	$-0.606893\pi$
$97$	−6.49117	−0.659079	−0.329539	+	0.944142i	$0.606893\pi$
$98$	−1.94307	−0.196280
$99$	0.416671	0.0418770
$100$	15.5886	1.55886
$101$	7.09486	0.705965	0.352983	−	0.935630i	$-0.385167\pi$
$101$	7.09486	0.705965	0.352983	+	0.935630i	$0.385167\pi$
$102$	15.4264	1.52744
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.89765	0.284138
$105$	−8.75912	−0.854802
$106$	−17.5145	−1.70116
$107$	−3.84268	−0.371486	−0.185743	−	0.982598i	$-0.559469\pi$
$107$	−3.84268	−0.371486	−0.185743	+	0.982598i	$0.559469\pi$
$108$	−3.26307	−0.313989
$109$	2.42641	0.232408	0.116204	−	0.993225i	$-0.462927\pi$
$109$	2.42641	0.232408	0.116204	+	0.993225i	$0.462927\pi$
$110$	2.98897	0.284987
$111$	2.62448	0.249105
$112$	−0.340282	−0.0321537
$113$	−3.10357	−0.291959	−0.145980	−	0.989288i	$-0.546633\pi$
$113$	−3.10357	−0.291959	−0.145980	+	0.989288i	$0.546633\pi$
$114$	−2.27446	−0.213023
$115$	−15.9065	−1.48329
$116$	−8.58370	−0.796977
$117$	−1.00000	−0.0924500
$118$	15.3217	1.41048
$119$	−18.8363	−1.72672
$120$	−9.06057	−0.827113
$121$	−10.8264	−0.984217
$122$	25.1725	2.27901
$123$	−0.0147872	−0.00133332
$124$	4.88837	0.438989
$125$	0.696373	0.0622855
$126$	6.42644	0.572513
$127$	20.9663	1.86046	0.930230	−	0.366977i	$-0.119607\pi$
$127$	20.9663	1.86046	0.930230	+	0.366977i	$0.119607\pi$
$128$	18.5585	1.64035
$129$	5.30095	0.466722
$130$	−7.17346	−0.629154
$131$	−2.72196	−0.237819	−0.118909	−	0.992905i	$-0.537940\pi$
$131$	−2.72196	−0.237819	−0.118909	+	0.992905i	$0.537940\pi$
$132$	−1.35962	−0.118340
$133$	2.77722	0.240816
$134$	−7.16198	−0.618701
$135$	3.12687	0.269118
$136$	−19.4845	−1.67079
$137$	14.7375	1.25911	0.629554	−	0.776957i	$-0.283238\pi$
$137$	14.7375	1.25911	0.629554	+	0.776957i	$0.283238\pi$
$138$	11.6704	0.993449
$139$	−0.286154	−0.0242713	−0.0121356	−	0.999926i	$-0.503863\pi$
$139$	−0.286154	−0.0242713	−0.0121356	+	0.999926i	$0.503863\pi$
$140$	28.5816	2.41559
$141$	5.68597	0.478845
$142$	−28.8931	−2.42465
$143$	−0.416671	−0.0348437
$144$	0.121475	0.0101229
$145$	8.22542	0.683084
$146$	9.82823	0.813390
$147$	−0.846973	−0.0698571
$148$	−8.56385	−0.703944
$149$	−2.87834	−0.235803	−0.117901	−	0.993025i	$-0.537617\pi$
$149$	−2.87834	−0.235803	−0.117901	+	0.993025i	$0.537617\pi$
$150$	10.9598	0.894861
$151$	−23.1559	−1.88440	−0.942201	−	0.335047i	$-0.891248\pi$
$151$	−23.1559	−1.88440	−0.942201	+	0.335047i	$0.891248\pi$
$152$	2.87280	0.233015
$153$	6.72425	0.543624
$154$	2.67771	0.215776
$155$	−4.68433	−0.376254
$156$	3.26307	0.261255
$157$	3.63217	0.289878	0.144939	−	0.989441i	$-0.453701\pi$
$157$	3.63217	0.289878	0.144939	+	0.989441i	$0.453701\pi$
$158$	3.89322	0.309728
$159$	−7.63444	−0.605451
$160$	−17.2497	−1.36371
$161$	−14.2501	−1.12306
$162$	−2.29414	−0.180244
$163$	−10.8690	−0.851326	−0.425663	−	0.904882i	$-0.639959\pi$
$163$	−10.8690	−0.851326	−0.425663	+	0.904882i	$0.639959\pi$
$164$	0.0482516	0.00376781
$165$	1.30287	0.101429
$166$	25.5342	1.98184
$167$	11.3788	0.880519	0.440259	−	0.897871i	$-0.354887\pi$
$167$	11.3788	0.880519	0.440259	+	0.897871i	$0.354887\pi$
$168$	−8.11703	−0.626242
$169$	1.00000	0.0769231
$170$	48.2362	3.69955
$171$	−0.991424	−0.0758161
$172$	−17.2974	−1.31891
$173$	−5.10026	−0.387766	−0.193883	−	0.981025i	$-0.562108\pi$
$173$	−5.10026	−0.387766	−0.193883	+	0.981025i	$0.562108\pi$
$174$	−6.03487	−0.457502
$175$	−13.3824	−1.01161
$176$	0.0506152	0.00381527
$177$	6.67863	0.501996
$178$	38.1799	2.86170
$179$	25.3688	1.89615	0.948076	−	0.318044i	$-0.103026\pi$
$179$	25.3688	1.89615	0.948076	+	0.318044i	$0.103026\pi$
$180$	−10.2032	−0.760500
$181$	6.34124	0.471340	0.235670	−	0.971833i	$-0.424272\pi$
$181$	6.34124	0.471340	0.235670	+	0.971833i	$0.424272\pi$
$182$	−6.42644	−0.476360
$183$	10.9725	0.811112
$184$	−14.7405	−1.08668
$185$	8.20640	0.603346
$186$	3.43683	0.252000
$187$	2.80180	0.204888
$188$	−18.5537	−1.35317
$189$	2.80124	0.203761
$190$	−7.11194	−0.515955
$191$	9.42686	0.682104	0.341052	−	0.940045i	$-0.389217\pi$
$191$	9.42686	0.682104	0.341052	+	0.940045i	$0.389217\pi$
$192$	12.8988	0.930894
$193$	10.1340	0.729464	0.364732	−	0.931113i	$-0.381161\pi$
$193$	10.1340	0.729464	0.364732	+	0.931113i	$0.381161\pi$
$194$	14.8916	1.06916
$195$	−3.12687	−0.223920
$196$	2.76373	0.197409
$197$	−25.4106	−1.81043	−0.905216	−	0.424951i	$-0.860291\pi$
$197$	−25.4106	−1.81043	−0.905216	+	0.424951i	$0.860291\pi$
$198$	−0.955900	−0.0679328
$199$	−2.66862	−0.189174	−0.0945868	−	0.995517i	$-0.530153\pi$
$199$	−2.66862	−0.189174	−0.0945868	+	0.995517i	$0.530153\pi$
$200$	−13.8429	−0.978843
$201$	−3.12186	−0.220199
$202$	−16.2766	−1.14522
$203$	7.36885	0.517192
$204$	−21.9417	−1.53623
$205$	−0.0462375	−0.00322937
$206$	−2.29414	−0.159840
$207$	5.08704	0.353574
$208$	−0.121475	−0.00842280
$209$	−0.413097	−0.0285745
$210$	20.0946	1.38666
$211$	−4.92676	−0.339172	−0.169586	−	0.985515i	$-0.554243\pi$
$211$	−4.92676	−0.339172	−0.169586	+	0.985515i	$0.554243\pi$
$212$	24.9117	1.71094
$213$	−12.5943	−0.862948
$214$	8.81564	0.602625
$215$	16.5754	1.13043
$216$	2.89765	0.197160
$217$	−4.19652	−0.284878
$218$	−5.56652	−0.377012
$219$	4.28406	0.289490
$220$	−4.25136	−0.286627
$221$	−6.72425	−0.452322
$222$	−6.02092	−0.404098
$223$	5.57403	0.373265	0.186632	−	0.982430i	$-0.440243\pi$
$223$	5.57403	0.373265	0.186632	+	0.982430i	$0.440243\pi$
$224$	−15.4534	−1.03252
$225$	4.77729	0.318486
$226$	7.12002	0.473616
$227$	8.28893	0.550155	0.275078	−	0.961422i	$-0.411296\pi$
$227$	8.28893	0.550155	0.275078	+	0.961422i	$0.411296\pi$
$228$	3.23508	0.214249
$229$	−16.8664	−1.11457	−0.557283	−	0.830323i	$-0.688156\pi$
$229$	−16.8664	−1.11457	−0.557283	+	0.830323i	$0.688156\pi$
$230$	36.4917	2.40619
$231$	1.16720	0.0767959
$232$	7.62245	0.500438
$233$	−13.2380	−0.867249	−0.433625	−	0.901094i	$-0.642766\pi$
$233$	−13.2380	−0.867249	−0.433625	+	0.901094i	$0.642766\pi$
$234$	2.29414	0.149972
$235$	17.7793	1.15979
$236$	−21.7928	−1.41859
$237$	1.69703	0.110234
$238$	43.2130	2.80108
$239$	−13.1763	−0.852304	−0.426152	−	0.904651i	$-0.640131\pi$
$239$	−13.1763	−0.852304	−0.426152	+	0.904651i	$0.640131\pi$
$240$	0.379837	0.0245184
$241$	−5.63098	−0.362723	−0.181362	−	0.983416i	$-0.558050\pi$
$241$	−5.63098	−0.362723	−0.181362	+	0.983416i	$0.558050\pi$
$242$	24.8372	1.59660
$243$	−1.00000	−0.0641500
$244$	−35.8041	−2.29212
$245$	−2.64837	−0.169198
$246$	0.0339238	0.00216290
$247$	0.991424	0.0630828
$248$	−4.34094	−0.275650
$249$	11.1302	0.705347
$250$	−1.59758	−0.101040
$251$	−23.6282	−1.49140	−0.745698	−	0.666284i	$-0.767884\pi$
$251$	−23.6282	−1.49140	−0.745698	+	0.666284i	$0.767884\pi$
$252$	−9.14065	−0.575807
$253$	2.11962	0.133259
$254$	−48.0996	−3.01804
$255$	21.0258	1.31669
$256$	−16.7780	−1.04863
$257$	−12.7923	−0.797962	−0.398981	−	0.916959i	$-0.630636\pi$
$257$	−12.7923	−0.797962	−0.398981	+	0.916959i	$0.630636\pi$
$258$	−12.1611	−0.757117
$259$	7.35181	0.456819
$260$	10.2032	0.632774
$261$	−2.63056	−0.162828
$262$	6.24455	0.385789
$263$	4.60401	0.283896	0.141948	−	0.989874i	$-0.454663\pi$
$263$	4.60401	0.283896	0.141948	+	0.989874i	$0.454663\pi$
$264$	1.20737	0.0743082
$265$	−23.8719	−1.46644
$266$	−6.37133	−0.390651
$267$	16.6424	1.01850
$268$	10.1868	0.622261
$269$	−13.7601	−0.838969	−0.419484	−	0.907763i	$-0.637789\pi$
$269$	−13.7601	−0.838969	−0.419484	+	0.907763i	$0.637789\pi$
$270$	−7.17346	−0.436563
$271$	9.20576	0.559210	0.279605	−	0.960115i	$-0.409796\pi$
$271$	9.20576	0.559210	0.279605	+	0.960115i	$0.409796\pi$
$272$	0.816831	0.0495277
$273$	−2.80124	−0.169539
$274$	−33.8098	−2.04252
$275$	1.99056	0.120035
$276$	−16.5994	−0.999165
$277$	−5.92366	−0.355918	−0.177959	−	0.984038i	$-0.556949\pi$
$277$	−5.92366	−0.355918	−0.177959	+	0.984038i	$0.556949\pi$
$278$	0.656478	0.0393729
$279$	1.49809	0.0896883
$280$	−25.3809	−1.51680
$281$	−7.54883	−0.450325	−0.225163	−	0.974321i	$-0.572291\pi$
$281$	−7.54883	−0.450325	−0.225163	+	0.974321i	$0.572291\pi$
$282$	−13.0444	−0.776783
$283$	7.05192	0.419193	0.209597	−	0.977788i	$-0.432785\pi$
$283$	7.05192	0.419193	0.209597	+	0.977788i	$0.432785\pi$
$284$	41.0961	2.43860
$285$	−3.10005	−0.183631
$286$	0.955900	0.0565235
$287$	−0.0414225	−0.00244509
$288$	5.51662	0.325070
$289$	28.2156	1.65974
$290$	−18.8702	−1.10810
$291$	6.49117	0.380519
$292$	−13.9792	−0.818070
$293$	7.38295	0.431316	0.215658	−	0.976469i	$-0.430810\pi$
$293$	7.38295	0.431316	0.215658	+	0.976469i	$0.430810\pi$
$294$	1.94307	0.113322
$295$	20.8832	1.21587
$296$	7.60483	0.442022
$297$	−0.416671	−0.0241777
$298$	6.60330	0.382519
$299$	−5.08704	−0.294191
$300$	−15.5886	−0.900010
$301$	14.8493	0.855897
$302$	53.1229	3.05688
$303$	−7.09486	−0.407589
$304$	−0.120434	−0.00690734
$305$	34.3096	1.96456
$306$	−15.4264	−0.881867
$307$	16.3416	0.932667	0.466333	−	0.884609i	$-0.345575\pi$
$307$	16.3416	0.932667	0.466333	+	0.884609i	$0.345575\pi$
$308$	−3.80864	−0.217017
$309$	−1.00000	−0.0568880
$310$	10.7465	0.610360
$311$	1.10282	0.0625355	0.0312677	−	0.999511i	$-0.490046\pi$
$311$	1.10282	0.0625355	0.0312677	+	0.999511i	$0.490046\pi$
$312$	−2.89765	−0.164047
$313$	−8.86829	−0.501266	−0.250633	−	0.968082i	$-0.580639\pi$
$313$	−8.86829	−0.501266	−0.250633	+	0.968082i	$0.580639\pi$
$314$	−8.33269	−0.470241
$315$	8.75912	0.493520
$316$	−5.53753	−0.311510
$317$	24.9172	1.39949	0.699745	−	0.714393i	$-0.253297\pi$
$317$	24.9172	1.39949	0.699745	+	0.714393i	$0.253297\pi$
$318$	17.5145	0.982163
$319$	−1.09608	−0.0613686
$320$	40.3329	2.25468
$321$	3.84268	0.214478
$322$	32.6916	1.82183
$323$	−6.66659	−0.370939
$324$	3.26307	0.181282
$325$	−4.77729	−0.264997
$326$	24.9350	1.38102
$327$	−2.42641	−0.134181
$328$	−0.0428481	−0.00236589
$329$	15.9278	0.878128
$330$	−2.98897	−0.164537
$331$	−13.1957	−0.725302	−0.362651	−	0.931925i	$-0.618128\pi$
$331$	−13.1957	−0.725302	−0.362651	+	0.931925i	$0.618128\pi$
$332$	−36.3185	−1.99324
$333$	−2.62448	−0.143821
$334$	−26.1046	−1.42838
$335$	−9.76164	−0.533336
$336$	0.340282	0.0185639
$337$	29.4928	1.60658	0.803288	−	0.595591i	$-0.203082\pi$
$337$	29.4928	1.60658	0.803288	+	0.595591i	$0.203082\pi$
$338$	−2.29414	−0.124785
$339$	3.10357	0.168563
$340$	−68.6088	−3.72083
$341$	0.624210	0.0338029
$342$	2.27446	0.122989
$343$	17.2361	0.930664
$344$	15.3603	0.828172
$345$	15.9065	0.856378
$346$	11.7007	0.629034
$347$	−9.88153	−0.530468	−0.265234	−	0.964184i	$-0.585449\pi$
$347$	−9.88153	−0.530468	−0.265234	+	0.964184i	$0.585449\pi$
$348$	8.58370	0.460135
$349$	−4.17812	−0.223650	−0.111825	−	0.993728i	$-0.535670\pi$
$349$	−4.17812	−0.223650	−0.111825	+	0.993728i	$0.535670\pi$
$350$	30.7010	1.64104
$351$	1.00000	0.0533761
$352$	2.29861	0.122517
$353$	29.3261	1.56087	0.780435	−	0.625236i	$-0.214997\pi$
$353$	29.3261	1.56087	0.780435	+	0.625236i	$0.214997\pi$
$354$	−15.3217	−0.814339
$355$	−39.3807	−2.09011
$356$	−54.3052	−2.87817
$357$	18.8363	0.996922
$358$	−58.1995	−3.07594
$359$	36.8632	1.94557	0.972784	−	0.231714i	$-0.0744334\pi$
$359$	36.8632	1.94557	0.972784	+	0.231714i	$0.0744334\pi$
$360$	9.06057	0.477534
$361$	−18.0171	−0.948267
$362$	−14.5477	−0.764608
$363$	10.8264	0.568238
$364$	9.14065	0.479100
$365$	13.3957	0.701163
$366$	−25.1725	−1.31579
$367$	27.4706	1.43396	0.716978	−	0.697096i	$-0.245525\pi$
$367$	27.4706	1.43396	0.716978	+	0.697096i	$0.245525\pi$
$368$	0.617951	0.0322129
$369$	0.0147872	0.000769790 0
$370$	−18.8266	−0.978749
$371$	−21.3859	−1.11030
$372$	−4.88837	−0.253450
$373$	28.6163	1.48169	0.740847	−	0.671674i	$-0.234424\pi$
$373$	28.6163	1.48169	0.740847	+	0.671674i	$0.234424\pi$
$374$	−6.42771	−0.332369
$375$	−0.696373	−0.0359605
$376$	16.4760	0.849683
$377$	2.63056	0.135481
$378$	−6.42644	−0.330540
$379$	−17.9011	−0.919516	−0.459758	−	0.888044i	$-0.652064\pi$
$379$	−17.9011	−0.919516	−0.459758	+	0.888044i	$0.652064\pi$
$380$	10.1157	0.518923
$381$	−20.9663	−1.07414
$382$	−21.6265	−1.10651
$383$	0.420043	0.0214632	0.0107316	−	0.999942i	$-0.496584\pi$
$383$	0.420043	0.0214632	0.0107316	+	0.999942i	$0.496584\pi$
$384$	−18.5585	−0.947058
$385$	3.64967	0.186004
$386$	−23.2489	−1.18334
$387$	−5.30095	−0.269462
$388$	−21.1811	−1.07531
$389$	9.81529	0.497655	0.248827	−	0.968548i	$-0.419955\pi$
$389$	9.81529	0.497655	0.248827	+	0.968548i	$0.419955\pi$
$390$	7.17346	0.363242
$391$	34.2066	1.72990
$392$	−2.45423	−0.123957
$393$	2.72196	0.137305
$394$	58.2955	2.93688
$395$	5.30639	0.266993
$396$	1.35962	0.0683237
$397$	−14.4178	−0.723608	−0.361804	−	0.932254i	$-0.617839\pi$
$397$	−14.4178	−0.723608	−0.361804	+	0.932254i	$0.617839\pi$
$398$	6.12219	0.306877
$399$	−2.77722	−0.139035
$400$	0.580324	0.0290162
$401$	12.3763	0.618042	0.309021	−	0.951055i	$-0.399999\pi$
$401$	12.3763	0.618042	0.309021	+	0.951055i	$0.399999\pi$
$402$	7.16198	0.357207
$403$	−1.49809	−0.0746252
$404$	23.1510	1.15181
$405$	−3.12687	−0.155375
$406$	−16.9052	−0.838989
$407$	−1.09354	−0.0542049
$408$	19.4845	0.964629
$409$	19.7320	0.975684	0.487842	−	0.872932i	$-0.337784\pi$
$409$	19.7320	0.975684	0.487842	+	0.872932i	$0.337784\pi$
$410$	0.106075	0.00523868
$411$	−14.7375	−0.726946
$412$	3.26307	0.160760
$413$	18.7085	0.920584
$414$	−11.6704	−0.573568
$415$	34.8026	1.70839
$416$	−5.51662	−0.270475
$417$	0.286154	0.0140130
$418$	0.947702	0.0463536
$419$	−15.8642	−0.775016	−0.387508	−	0.921866i	$-0.626664\pi$
$419$	−15.8642	−0.775016	−0.387508	+	0.921866i	$0.626664\pi$
$420$	−28.5816	−1.39464
$421$	2.27529	0.110891	0.0554453	−	0.998462i	$-0.482342\pi$
$421$	2.27529	0.110891	0.0554453	+	0.998462i	$0.482342\pi$
$422$	11.3027	0.550206
$423$	−5.68597	−0.276462
$424$	−22.1220	−1.07434
$425$	32.1237	1.55823
$426$	28.8931	1.39987
$427$	30.7367	1.48745
$428$	−12.5389	−0.606092
$429$	0.416671	0.0201170
$430$	−38.0261	−1.83378
$431$	−21.4395	−1.03270	−0.516352	−	0.856376i	$-0.672711\pi$
$431$	−21.4395	−1.03270	−0.516352	+	0.856376i	$0.672711\pi$
$432$	−0.121475	−0.00584449
$433$	11.7448	0.564418	0.282209	−	0.959353i	$-0.408933\pi$
$433$	11.7448	0.564418	0.282209	+	0.959353i	$0.408933\pi$
$434$	9.62739	0.462130
$435$	−8.22542	−0.394379
$436$	7.91754	0.379182
$437$	−5.04342	−0.241259
$438$	−9.82823	−0.469611
$439$	5.52865	0.263868	0.131934	−	0.991258i	$-0.457881\pi$
$439$	5.52865	0.263868	0.131934	+	0.991258i	$0.457881\pi$
$440$	3.77527	0.179979
$441$	0.846973	0.0403320
$442$	15.4264	0.733757
$443$	8.05159	0.382543	0.191271	−	0.981537i	$-0.438739\pi$
$443$	8.05159	0.382543	0.191271	+	0.981537i	$0.438739\pi$
$444$	8.56385	0.406423
$445$	52.0385	2.46686
$446$	−12.7876	−0.605510
$447$	2.87834	0.136141
$448$	36.1328	1.70711
$449$	−11.0525	−0.521600	−0.260800	−	0.965393i	$-0.583986\pi$
$449$	−11.0525	−0.521600	−0.260800	+	0.965393i	$0.583986\pi$
$450$	−10.9598	−0.516648
$451$	0.00616138	0.000290128 0
$452$	−10.1272	−0.476341
$453$	23.1559	1.08796
$454$	−19.0159	−0.892462
$455$	−8.75912	−0.410634
$456$	−2.87280	−0.134531
$457$	7.69106	0.359773	0.179886	−	0.983687i	$-0.442427\pi$
$457$	7.69106	0.359773	0.179886	+	0.983687i	$0.442427\pi$
$458$	38.6939	1.80805
$459$	−6.72425	−0.313861
$460$	−51.9040	−2.42004
$461$	−0.331613	−0.0154447	−0.00772237	−	0.999970i	$-0.502458\pi$
$461$	−0.331613	−0.0154447	−0.00772237	+	0.999970i	$0.502458\pi$
$462$	−2.67771	−0.124578
$463$	14.3859	0.668571	0.334286	−	0.942472i	$-0.391505\pi$
$463$	14.3859	0.668571	0.334286	+	0.942472i	$0.391505\pi$
$464$	−0.319549	−0.0148347
$465$	4.68433	0.217231
$466$	30.3698	1.40685
$467$	18.2041	0.842386	0.421193	−	0.906971i	$-0.361611\pi$
$467$	18.2041	0.842386	0.421193	+	0.906971i	$0.361611\pi$
$468$	−3.26307	−0.150835
$469$	−8.74510	−0.403811
$470$	−40.7881	−1.88142
$471$	−3.63217	−0.167361
$472$	19.3523	0.890763
$473$	−2.20875	−0.101558
$474$	−3.89322	−0.178822
$475$	−4.73632	−0.217317
$476$	−61.4641	−2.81720
$477$	7.63444	0.349557
$478$	30.2283	1.38261
$479$	26.1759	1.19601	0.598003	−	0.801494i	$-0.295961\pi$
$479$	26.1759	1.19601	0.598003	+	0.801494i	$0.295961\pi$
$480$	17.2497	0.787339
$481$	2.62448	0.119666
$482$	12.9182	0.588410
$483$	14.2501	0.648400
$484$	−35.3272	−1.60578
$485$	20.2970	0.921640
$486$	2.29414	0.104064
$487$	4.10655	0.186086	0.0930428	−	0.995662i	$-0.470341\pi$
$487$	4.10655	0.186086	0.0930428	+	0.995662i	$0.470341\pi$
$488$	31.7946	1.43927
$489$	10.8690	0.491513
$490$	6.07573	0.274473
$491$	−7.72399	−0.348579	−0.174289	−	0.984694i	$-0.555763\pi$
$491$	−7.72399	−0.348579	−0.174289	+	0.984694i	$0.555763\pi$
$492$	−0.0482516	−0.00217535
$493$	−17.6886	−0.796653
$494$	−2.27446	−0.102333
$495$	−1.30287	−0.0585598
$496$	0.181981	0.00817119
$497$	−35.2797	−1.58251
$498$	−25.5342	−1.14421
$499$	31.2412	1.39855	0.699275	−	0.714853i	$-0.253506\pi$
$499$	31.2412	1.39855	0.699275	+	0.714853i	$0.253506\pi$
$500$	2.27231	0.101621
$501$	−11.3788	−0.508368
$502$	54.2063	2.41934
$503$	26.3735	1.17594	0.587968	−	0.808884i	$-0.299928\pi$
$503$	26.3735	1.17594	0.587968	+	0.808884i	$0.299928\pi$
$504$	8.11703	0.361561
$505$	−22.1847	−0.987206
$506$	−4.86270	−0.216174
$507$	−1.00000	−0.0444116
$508$	68.4145	3.03540
$509$	40.0295	1.77428	0.887138	−	0.461504i	$-0.152690\pi$
$509$	40.0295	1.77428	0.887138	+	0.461504i	$0.152690\pi$
$510$	−48.2362	−2.13593
$511$	12.0007	0.530880
$512$	1.37412	0.0607281
$513$	0.991424	0.0437724
$514$	29.3473	1.29445
$515$	−3.12687	−0.137786
$516$	17.2974	0.761473
$517$	−2.36918	−0.104196
$518$	−16.8661	−0.741052
$519$	5.10026	0.223877
$520$	−9.06057	−0.397332
$521$	14.2424	0.623971	0.311985	−	0.950087i	$-0.399006\pi$
$521$	14.2424	0.623971	0.311985	+	0.950087i	$0.399006\pi$
$522$	6.03487	0.264139
$523$	−13.5386	−0.592001	−0.296000	−	0.955188i	$-0.595653\pi$
$523$	−13.5386	−0.592001	−0.296000	+	0.955188i	$0.595653\pi$
$524$	−8.88193	−0.388009
$525$	13.3824	0.584054
$526$	−10.5622	−0.460536
$527$	10.0735	0.438810
$528$	−0.0506152	−0.00220274
$529$	2.87802	0.125131
$530$	54.7654	2.37886
$531$	−6.67863	−0.289828
$532$	9.06226	0.392899
$533$	−0.0147872	−0.000640504 0
$534$	−38.1799	−1.65221
$535$	12.0156	0.519478
$536$	−9.04607	−0.390731
$537$	−25.3688	−1.09474
$538$	31.5676	1.36098
$539$	0.352909	0.0152009
$540$	10.2032	0.439075
$541$	−32.2193	−1.38521	−0.692607	−	0.721315i	$-0.743538\pi$
$541$	−32.2193	−1.38521	−0.692607	+	0.721315i	$0.743538\pi$
$542$	−21.1193	−0.907151
$543$	−6.34124	−0.272128
$544$	37.0952	1.59044
$545$	−7.58706	−0.324994
$546$	6.42644	0.275026
$547$	23.6233	1.01006	0.505030	−	0.863102i	$-0.331481\pi$
$547$	23.6233	1.01006	0.505030	+	0.863102i	$0.331481\pi$
$548$	48.0894	2.05428
$549$	−10.9725	−0.468296
$550$	−4.56661	−0.194721
$551$	2.60800	0.111105
$552$	14.7405	0.627397
$553$	4.75380	0.202152
$554$	13.5897	0.577371
$555$	−8.20640	−0.348342
$556$	−0.933741	−0.0395994
$557$	11.5090	0.487653	0.243827	−	0.969819i	$-0.421597\pi$
$557$	11.5090	0.487653	0.243827	+	0.969819i	$0.421597\pi$
$558$	−3.43683	−0.145492
$559$	5.30095	0.224206
$560$	1.06402	0.0449629
$561$	−2.80180	−0.118292
$562$	17.3181	0.730518
$563$	−32.2011	−1.35711	−0.678557	−	0.734548i	$-0.737394\pi$
$563$	−32.2011	−1.35711	−0.678557	+	0.734548i	$0.737394\pi$
$564$	18.5537	0.781252
$565$	9.70445	0.408269
$566$	−16.1781	−0.680015
$567$	−2.80124	−0.117641
$568$	−36.4939	−1.53125
$569$	2.04598	0.0857720	0.0428860	−	0.999080i	$-0.486345\pi$
$569$	2.04598	0.0857720	0.0428860	+	0.999080i	$0.486345\pi$
$570$	7.11194	0.297887
$571$	33.7208	1.41117	0.705586	−	0.708625i	$-0.250684\pi$
$571$	33.7208	1.41117	0.705586	+	0.708625i	$0.250684\pi$
$572$	−1.35962	−0.0568488
$573$	−9.42686	−0.393813
$574$	0.0950289	0.00396643
$575$	24.3023	1.01348
$576$	−12.8988	−0.537452
$577$	7.99663	0.332904	0.166452	−	0.986050i	$-0.446769\pi$
$577$	7.99663	0.332904	0.166452	+	0.986050i	$0.446769\pi$
$578$	−64.7305	−2.69243
$579$	−10.1340	−0.421156
$580$	26.8401	1.11447
$581$	31.1784	1.29350
$582$	−14.8916	−0.617278
$583$	3.18105	0.131746
$584$	12.4137	0.513683
$585$	3.12687	0.129280
$586$	−16.9375	−0.699682
$587$	−3.76126	−0.155244	−0.0776218	−	0.996983i	$-0.524733\pi$
$587$	−3.76126	−0.155244	−0.0776218	+	0.996983i	$0.524733\pi$
$588$	−2.76373	−0.113974
$589$	−1.48524	−0.0611984
$590$	−47.9089	−1.97238
$591$	25.4106	1.04525
$592$	−0.318810	−0.0131030
$593$	−4.18560	−0.171882	−0.0859410	−	0.996300i	$-0.527390\pi$
$593$	−4.18560	−0.171882	−0.0859410	+	0.996300i	$0.527390\pi$
$594$	0.955900	0.0392210
$595$	58.8985	2.41460
$596$	−9.39221	−0.384720
$597$	2.66862	0.109219
$598$	11.6704	0.477237
$599$	9.76944	0.399169	0.199584	−	0.979881i	$-0.436041\pi$
$599$	9.76944	0.399169	0.199584	+	0.979881i	$0.436041\pi$
$600$	13.8429	0.565135
$601$	−5.16256	−0.210585	−0.105293	−	0.994441i	$-0.533578\pi$
$601$	−5.16256	−0.210585	−0.105293	+	0.994441i	$0.533578\pi$
$602$	−34.0662	−1.38844
$603$	3.12186	0.127132
$604$	−75.5594	−3.07447
$605$	33.8527	1.37631
$606$	16.2766	0.661191
$607$	7.44519	0.302191	0.151096	−	0.988519i	$-0.451720\pi$
$607$	7.44519	0.302191	0.151096	+	0.988519i	$0.451720\pi$
$608$	−5.46931	−0.221810
$609$	−7.36885	−0.298601
$610$	−78.7110	−3.18692
$611$	5.68597	0.230030
$612$	21.9417	0.886940
$613$	−36.8658	−1.48899	−0.744497	−	0.667626i	$-0.767311\pi$
$613$	−36.8658	−1.48899	−0.744497	+	0.667626i	$0.767311\pi$
$614$	−37.4900	−1.51297
$615$	0.0462375	0.00186448
$616$	3.38213	0.136270
$617$	18.2512	0.734768	0.367384	−	0.930069i	$-0.380254\pi$
$617$	18.2512	0.734768	0.367384	+	0.930069i	$0.380254\pi$
$618$	2.29414	0.0922838
$619$	44.9976	1.80860	0.904302	−	0.426893i	$-0.140392\pi$
$619$	44.9976	1.80860	0.904302	+	0.426893i	$0.140392\pi$
$620$	−15.2853	−0.613872
$621$	−5.08704	−0.204136
$622$	−2.53003	−0.101445
$623$	46.6194	1.86777
$624$	0.121475	0.00486291
$625$	−26.0639	−1.04256
$626$	20.3451	0.813153
$627$	0.413097	0.0164975
$628$	11.8520	0.472946
$629$	−17.6477	−0.703659
$630$	−20.0946	−0.800589
$631$	14.3262	0.570316	0.285158	−	0.958481i	$-0.407954\pi$
$631$	14.3262	0.570316	0.285158	+	0.958481i	$0.407954\pi$
$632$	4.91740	0.195604
$633$	4.92676	0.195821
$634$	−57.1635	−2.27025
$635$	−65.5589	−2.60162
$636$	−24.9117	−0.987814
$637$	−0.846973	−0.0335583
$638$	2.51455	0.0995521
$639$	12.5943	0.498223
$640$	−58.0299	−2.29383
$641$	−44.7597	−1.76790	−0.883951	−	0.467580i	$-0.845126\pi$
$641$	−44.7597	−1.76790	−0.883951	+	0.467580i	$0.845126\pi$
$642$	−8.81564	−0.347926
$643$	−2.78715	−0.109914	−0.0549572	−	0.998489i	$-0.517502\pi$
$643$	−2.78715	−0.109914	−0.0549572	+	0.998489i	$0.517502\pi$
$644$	−46.4989	−1.83231
$645$	−16.5754	−0.652654
$646$	15.2941	0.601737
$647$	−29.5041	−1.15993	−0.579963	−	0.814643i	$-0.696933\pi$
$647$	−29.5041	−1.15993	−0.579963	+	0.814643i	$0.696933\pi$
$648$	−2.89765	−0.113830
$649$	−2.78279	−0.109234
$650$	10.9598	0.429878
$651$	4.19652	0.164475
$652$	−35.4663	−1.38897
$653$	15.8744	0.621214	0.310607	−	0.950538i	$-0.399468\pi$
$653$	15.8744	0.621214	0.310607	+	0.950538i	$0.399468\pi$
$654$	5.56652	0.217668
$655$	8.51120	0.332560
$656$	0.00179628	7.01329e−5 0
$657$	−4.28406	−0.167137
$658$	−36.5406	−1.42450
$659$	−25.3849	−0.988854	−0.494427	−	0.869219i	$-0.664622\pi$
$659$	−25.3849	−0.988854	−0.494427	+	0.869219i	$0.664622\pi$
$660$	4.25136	0.165484
$661$	−40.1548	−1.56184	−0.780921	−	0.624630i	$-0.785250\pi$
$661$	−40.1548	−1.56184	−0.780921	+	0.624630i	$0.785250\pi$
$662$	30.2728	1.17658
$663$	6.72425	0.261148
$664$	32.2514	1.25160
$665$	−8.68400	−0.336751
$666$	6.02092	0.233306
$667$	−13.3818	−0.518145
$668$	37.1298	1.43660
$669$	−5.57403	−0.215505
$670$	22.3946	0.865177
$671$	−4.57193	−0.176497
$672$	15.4534	0.596128
$673$	−17.2197	−0.663770	−0.331885	−	0.943320i	$-0.607685\pi$
$673$	−17.2197	−0.663770	−0.331885	+	0.943320i	$0.607685\pi$
$674$	−67.6606	−2.60619
$675$	−4.77729	−0.183878
$676$	3.26307	0.125503
$677$	31.0166	1.19206	0.596032	−	0.802961i	$-0.296743\pi$
$677$	31.0166	1.19206	0.596032	+	0.802961i	$0.296743\pi$
$678$	−7.12002	−0.273443
$679$	18.1834	0.697813
$680$	60.9256	2.33639
$681$	−8.28893	−0.317632
$682$	−1.43202	−0.0548351
$683$	33.1191	1.26727	0.633634	−	0.773633i	$-0.281562\pi$
$683$	33.1191	1.26727	0.633634	+	0.773633i	$0.281562\pi$
$684$	−3.23508	−0.123697
$685$	−46.0821	−1.76071
$686$	−39.5421	−1.50972
$687$	16.8664	0.643495
$688$	−0.643935	−0.0245498
$689$	−7.63444	−0.290849
$690$	−36.4917	−1.38922
$691$	−22.3007	−0.848360	−0.424180	−	0.905578i	$-0.639438\pi$
$691$	−22.3007	−0.848360	−0.424180	+	0.905578i	$0.639438\pi$
$692$	−16.6425	−0.632653
$693$	−1.16720	−0.0443381
$694$	22.6696	0.860526
$695$	0.894767	0.0339404
$696$	−7.62245	−0.288928
$697$	0.0994328	0.00376628
$698$	9.58518	0.362804
$699$	13.2380	0.500707
$700$	−43.6676	−1.65048
$701$	46.0740	1.74019	0.870096	−	0.492883i	$-0.164057\pi$
$701$	46.0740	1.74019	0.870096	+	0.492883i	$0.164057\pi$
$702$	−2.29414	−0.0865866
$703$	2.60197	0.0981352
$704$	−5.37457	−0.202562
$705$	−17.7793	−0.669606
$706$	−67.2781	−2.53205
$707$	−19.8744	−0.747455
$708$	21.7928	0.819024
$709$	−16.8540	−0.632964	−0.316482	−	0.948599i	$-0.602502\pi$
$709$	−16.8540	−0.632964	−0.316482	+	0.948599i	$0.602502\pi$
$710$	90.3448	3.39058
$711$	−1.69703	−0.0636436
$712$	48.2238	1.80726
$713$	7.62085	0.285403
$714$	−43.2130	−1.61721
$715$	1.30287	0.0487247
$716$	82.7801	3.09364
$717$	13.1763	0.492078
$718$	−84.5694	−3.15610
$719$	12.4235	0.463320	0.231660	−	0.972797i	$-0.425584\pi$
$719$	12.4235	0.463320	0.231660	+	0.972797i	$0.425584\pi$
$720$	−0.379837	−0.0141557
$721$	−2.80124	−0.104324
$722$	41.3337	1.53828
$723$	5.63098	0.209418
$724$	20.6919	0.769008
$725$	−12.5670	−0.466725
$726$	−24.8372	−0.921796
$727$	15.4411	0.572677	0.286338	−	0.958129i	$-0.407562\pi$
$727$	15.4411	0.572677	0.286338	+	0.958129i	$0.407562\pi$
$728$	−8.11703	−0.300837
$729$	1.00000	0.0370370
$730$	−30.7316	−1.13743
$731$	−35.6449	−1.31837
$732$	35.8041	1.32336
$733$	23.6049	0.871867	0.435933	−	0.899979i	$-0.356418\pi$
$733$	23.6049	0.871867	0.435933	+	0.899979i	$0.356418\pi$
$734$	−63.0214	−2.32616
$735$	2.64837	0.0976866
$736$	28.0633	1.03443
$737$	1.30079	0.0479151
$738$	−0.0339238	−0.00124875
$739$	−21.4218	−0.788013	−0.394007	−	0.919108i	$-0.628911\pi$
$739$	−21.4218	−0.788013	−0.394007	+	0.919108i	$0.628911\pi$
$740$	26.7780	0.984380
$741$	−0.991424	−0.0364209
$742$	49.0623	1.80113
$743$	−34.4359	−1.26333	−0.631666	−	0.775241i	$-0.717628\pi$
$743$	−34.4359	−1.26333	−0.631666	+	0.775241i	$0.717628\pi$
$744$	4.34094	0.159147
$745$	9.00018	0.329741
$746$	−65.6496	−2.40360
$747$	−11.1302	−0.407232
$748$	9.14246	0.334281
$749$	10.7643	0.393319
$750$	1.59758	0.0583352
$751$	−1.42706	−0.0520743	−0.0260371	−	0.999661i	$-0.508289\pi$
$751$	−1.42706	−0.0520743	−0.0260371	+	0.999661i	$0.508289\pi$
$752$	−0.690706	−0.0251875
$753$	23.6282	0.861058
$754$	−6.03487	−0.219777
$755$	72.4055	2.63511
$756$	9.14065	0.332442
$757$	37.9486	1.37927	0.689633	−	0.724159i	$-0.257772\pi$
$757$	37.9486	1.37927	0.689633	+	0.724159i	$0.257772\pi$
$758$	41.0675	1.49164
$759$	−2.11962	−0.0769374
$760$	−8.98287	−0.325843
$761$	31.8145	1.15328	0.576638	−	0.817000i	$-0.304364\pi$
$761$	31.8145	1.15328	0.576638	+	0.817000i	$0.304364\pi$
$762$	48.0996	1.74247
$763$	−6.79697	−0.246067
$764$	30.7605	1.11288
$765$	−21.0258	−0.760191
$766$	−0.963636	−0.0348176
$767$	6.67863	0.241151
$768$	16.7780	0.605424
$769$	−8.73395	−0.314954	−0.157477	−	0.987523i	$-0.550336\pi$
$769$	−8.73395	−0.314954	−0.157477	+	0.987523i	$0.550336\pi$
$770$	−8.37284	−0.301736
$771$	12.7923	0.460704
$772$	33.0681	1.19015
$773$	−6.20228	−0.223081	−0.111540	−	0.993760i	$-0.535578\pi$
$773$	−6.20228	−0.223081	−0.111540	+	0.993760i	$0.535578\pi$
$774$	12.1611	0.437122
$775$	7.15682	0.257081
$776$	18.8091	0.675209
$777$	−7.35181	−0.263745
$778$	−22.5176	−0.807296
$779$	−0.0146604	−0.000525262 0
$780$	−10.2032	−0.365332
$781$	5.24768	0.187777
$782$	−78.4746	−2.80625
$783$	2.63056	0.0940086
$784$	0.102886	0.00367451
$785$	−11.3573	−0.405359
$786$	−6.24455	−0.222736
$787$	−1.43209	−0.0510486	−0.0255243	−	0.999674i	$-0.508126\pi$
$787$	−1.43209	−0.0510486	−0.0255243	+	0.999674i	$0.508126\pi$
$788$	−82.9166	−2.95378
$789$	−4.60401	−0.163907
$790$	−12.1736	−0.433117
$791$	8.69386	0.309118
$792$	−1.20737	−0.0429019
$793$	10.9725	0.389646
$794$	33.0764	1.17384
$795$	23.8719	0.846649
$796$	−8.70789	−0.308643
$797$	−25.3268	−0.897120	−0.448560	−	0.893753i	$-0.648063\pi$
$797$	−25.3268	−0.897120	−0.448560	+	0.893753i	$0.648063\pi$
$798$	6.37133	0.225543
$799$	−38.2339	−1.35262
$800$	26.3545	0.931773
$801$	−16.6424	−0.588029
$802$	−28.3929	−1.00259
$803$	−1.78504	−0.0629928
$804$	−10.1868	−0.359262
$805$	44.5580	1.57046
$806$	3.43683	0.121057
$807$	13.7601	0.484379
$808$	−20.5584	−0.723243
$809$	−21.1538	−0.743727	−0.371863	−	0.928287i	$-0.621281\pi$
$809$	−21.1538	−0.743727	−0.371863	+	0.928287i	$0.621281\pi$
$810$	7.17346	0.252050
$811$	−27.7029	−0.972781	−0.486390	−	0.873742i	$-0.661687\pi$
$811$	−27.7029	−0.972781	−0.486390	+	0.873742i	$0.661687\pi$
$812$	24.0451	0.843816
$813$	−9.20576	−0.322860
$814$	2.50874	0.0879313
$815$	33.9859	1.19047
$816$	−0.816831	−0.0285948
$817$	5.25549	0.183866
$818$	−45.2679	−1.58276
$819$	2.80124	0.0978834
$820$	−0.150876	−0.00526883
$821$	19.0200	0.663802	0.331901	−	0.943314i	$-0.392310\pi$
$821$	19.0200	0.663802	0.331901	+	0.943314i	$0.392310\pi$
$822$	33.8098	1.17925
$823$	−0.532213	−0.0185518	−0.00927589	−	0.999957i	$-0.502953\pi$
$823$	−0.532213	−0.0185518	−0.00927589	+	0.999957i	$0.502953\pi$
$824$	−2.89765	−0.100944
$825$	−1.99056	−0.0693023
$826$	−42.9198	−1.49337
$827$	10.9199	0.379722	0.189861	−	0.981811i	$-0.439196\pi$
$827$	10.9199	0.379722	0.189861	+	0.981811i	$0.439196\pi$
$828$	16.5994	0.576868
$829$	−44.9752	−1.56205	−0.781026	−	0.624498i	$-0.785303\pi$
$829$	−44.9752	−1.56205	−0.781026	+	0.624498i	$0.785303\pi$
$830$	−79.8419	−2.77135
$831$	5.92366	0.205490
$832$	12.8988	0.447187
$833$	5.69526	0.197329
$834$	−0.656478	−0.0227320
$835$	−35.5800	−1.23130
$836$	−1.34796	−0.0466203
$837$	−1.49809	−0.0517816
$838$	36.3946	1.25723
$839$	16.4348	0.567394	0.283697	−	0.958914i	$-0.408439\pi$
$839$	16.4348	0.567394	0.283697	+	0.958914i	$0.408439\pi$
$840$	25.3809	0.875723
$841$	−22.0801	−0.761384
$842$	−5.21982	−0.179887
$843$	7.54883	0.259996
$844$	−16.0764	−0.553371
$845$	−3.12687	−0.107567
$846$	13.0444	0.448476
$847$	30.3274	1.04206
$848$	0.927397	0.0318469
$849$	−7.05192	−0.242021
$850$	−73.6963	−2.52776
$851$	−13.3508	−0.457661
$852$	−41.0961	−1.40793
$853$	0.435655	0.0149165	0.00745826	−	0.999972i	$-0.497626\pi$
$853$	0.435655	0.0149165	0.00745826	+	0.999972i	$0.497626\pi$
$854$	−70.5143	−2.41295
$855$	3.10005	0.106019
$856$	11.1348	0.380578
$857$	32.4275	1.10770	0.553852	−	0.832615i	$-0.313157\pi$
$857$	32.4275	1.10770	0.553852	+	0.832615i	$0.313157\pi$
$858$	−0.955900	−0.0326339
$859$	−45.8431	−1.56415	−0.782073	−	0.623187i	$-0.785837\pi$
$859$	−45.8431	−1.56415	−0.782073	+	0.623187i	$0.785837\pi$
$860$	54.0865	1.84433
$861$	0.0414225	0.00141168
$862$	49.1852	1.67525
$863$	1.29482	0.0440763	0.0220382	−	0.999757i	$-0.492984\pi$
$863$	1.29482	0.0440763	0.0220382	+	0.999757i	$0.492984\pi$
$864$	−5.51662	−0.187679
$865$	15.9478	0.542243
$866$	−26.9441	−0.915598
$867$	−28.2156	−0.958252
$868$	−13.6935	−0.464789
$869$	−0.707103	−0.0239868
$870$	18.8702	0.639761
$871$	−3.12186	−0.105780
$872$	−7.03089	−0.238096
$873$	−6.49117	−0.219693
$874$	11.5703	0.391371
$875$	−1.95071	−0.0659461
$876$	13.9792	0.472313
$877$	49.6760	1.67744	0.838719	−	0.544564i	$-0.183305\pi$
$877$	49.6760	1.67744	0.838719	+	0.544564i	$0.183305\pi$
$878$	−12.6835	−0.428047
$879$	−7.38295	−0.249021
$880$	−0.158267	−0.00533518
$881$	8.94971	0.301523	0.150762	−	0.988570i	$-0.451827\pi$
$881$	8.94971	0.301523	0.150762	+	0.988570i	$0.451827\pi$
$882$	−1.94307	−0.0654266
$883$	7.74546	0.260656	0.130328	−	0.991471i	$-0.458397\pi$
$883$	7.74546	0.260656	0.130328	+	0.991471i	$0.458397\pi$
$884$	−21.9417	−0.737979
$885$	−20.8832	−0.701980
$886$	−18.4715	−0.620561
$887$	−6.17030	−0.207178	−0.103589	−	0.994620i	$-0.533033\pi$
$887$	−6.17030	−0.207178	−0.103589	+	0.994620i	$0.533033\pi$
$888$	−7.60483	−0.255201
$889$	−58.7318	−1.96980
$890$	−119.383	−4.00174
$891$	0.416671	0.0139590
$892$	18.1884	0.608994
$893$	5.63721	0.188642
$894$	−6.60330	−0.220847
$895$	−79.3248	−2.65154
$896$	−51.9868	−1.73676
$897$	5.08704	0.169851
$898$	25.3560	0.846140
$899$	−3.94082	−0.131434
$900$	15.5886	0.519621
$901$	51.3359	1.71025
$902$	−0.0141351	−0.000470646 0
$903$	−14.8493	−0.494152
$904$	8.99306	0.299105
$905$	−19.8282	−0.659112
$906$	−53.1229	−1.76489
$907$	19.7579	0.656050	0.328025	−	0.944669i	$-0.393617\pi$
$907$	19.7579	0.656050	0.328025	+	0.944669i	$0.393617\pi$
$908$	27.0473	0.897597
$909$	7.09486	0.235322
$910$	20.0946	0.666130
$911$	1.00609	0.0333333	0.0166667	−	0.999861i	$-0.494695\pi$
$911$	1.00609	0.0333333	0.0166667	+	0.999861i	$0.494695\pi$
$912$	0.120434	0.00398796
$913$	−4.63762	−0.153483
$914$	−17.6444	−0.583623
$915$	−34.3096	−1.13424
$916$	−55.0364	−1.81845
$917$	7.62487	0.251795
$918$	15.4264	0.509146
$919$	−48.3843	−1.59605	−0.798025	−	0.602624i	$-0.794122\pi$
$919$	−48.3843	−1.59605	−0.798025	+	0.602624i	$0.794122\pi$
$920$	46.0915	1.51959
$921$	−16.3416	−0.538476
$922$	0.760765	0.0250545
$923$	−12.5943	−0.414547
$924$	3.80864	0.125295
$925$	−12.5379	−0.412244
$926$	−33.0033	−1.08456
$927$	1.00000	0.0328443
$928$	−14.5118	−0.476374
$929$	−24.7925	−0.813414	−0.406707	−	0.913559i	$-0.633323\pi$
$929$	−24.7925	−0.813414	−0.406707	+	0.913559i	$0.633323\pi$
$930$	−10.7465	−0.352392
$931$	−0.839709	−0.0275204
$932$	−43.1964	−1.41495
$933$	−1.10282	−0.0361049
$934$	−41.7628	−1.36652
$935$	−8.76085	−0.286510
$936$	2.89765	0.0947127
$937$	−15.3896	−0.502755	−0.251378	−	0.967889i	$-0.580884\pi$
$937$	−15.3896	−0.502755	−0.251378	+	0.967889i	$0.580884\pi$
$938$	20.0625	0.655063
$939$	8.86829	0.289406
$940$	58.0150	1.89224
$941$	−30.3324	−0.988810	−0.494405	−	0.869232i	$-0.664614\pi$
$941$	−30.3324	−0.988810	−0.494405	+	0.869232i	$0.664614\pi$
$942$	8.33269	0.271494
$943$	0.0752230	0.00244960
$944$	−0.811289	−0.0264052
$945$	−8.75912	−0.284934
$946$	5.06717	0.164748
$947$	19.0004	0.617429	0.308715	−	0.951155i	$-0.400101\pi$
$947$	19.0004	0.617429	0.308715	+	0.951155i	$0.400101\pi$
$948$	5.53753	0.179851
$949$	4.28406	0.139067
$950$	10.8658	0.352532
$951$	−24.9172	−0.807996
$952$	54.5810	1.76898
$953$	−35.9064	−1.16312	−0.581561	−	0.813503i	$-0.697558\pi$
$953$	−35.9064	−1.16312	−0.581561	+	0.813503i	$0.697558\pi$
$954$	−17.5145	−0.567052
$955$	−29.4765	−0.953838
$956$	−42.9952	−1.39056
$957$	1.09608	0.0354312
$958$	−60.0510	−1.94016
$959$	−41.2833	−1.33311
$960$	−40.3329	−1.30174
$961$	−28.7557	−0.927604
$962$	−6.02092	−0.194122
$963$	−3.84268	−0.123829
$964$	−18.3743	−0.591795
$965$	−31.6878	−1.02007
$966$	−32.6916	−1.05183
$967$	−11.4759	−0.369040	−0.184520	−	0.982829i	$-0.559073\pi$
$967$	−11.4759	−0.369040	−0.184520	+	0.982829i	$0.559073\pi$
$968$	31.3711	1.00830
$969$	6.66659	0.214162
$970$	−46.5642	−1.49509
$971$	25.9907	0.834082	0.417041	−	0.908888i	$-0.363067\pi$
$971$	25.9907	0.834082	0.417041	+	0.908888i	$0.363067\pi$
$972$	−3.26307	−0.104663
$973$	0.801589	0.0256977
$974$	−9.42099	−0.301868
$975$	4.77729	0.152996
$976$	−1.33289	−0.0426648
$977$	−40.9136	−1.30894	−0.654471	−	0.756087i	$-0.727109\pi$
$977$	−40.9136	−1.30894	−0.654471	+	0.756087i	$0.727109\pi$
$978$	−24.9350	−0.797333
$979$	−6.93439	−0.221624
$980$	−8.64181	−0.276053
$981$	2.42641	0.0774693
$982$	17.7199	0.565464
$983$	−49.8271	−1.58924	−0.794619	−	0.607109i	$-0.792329\pi$
$983$	−49.8271	−1.58924	−0.794619	+	0.607109i	$0.792329\pi$
$984$	0.0428481	0.00136595
$985$	79.4556	2.53167
$986$	40.5800	1.29233
$987$	−15.9278	−0.506988
$988$	3.23508	0.102922
$989$	−26.9662	−0.857474
$990$	2.98897	0.0949957
$991$	24.4823	0.777706	0.388853	−	0.921300i	$-0.372871\pi$
$991$	24.4823	0.777706	0.388853	+	0.921300i	$0.372871\pi$
$992$	8.26440	0.262395
$993$	13.1957	0.418753
$994$	80.9366	2.56715
$995$	8.34442	0.264536
$996$	36.3185	1.15080
$997$	−46.5926	−1.47560	−0.737801	−	0.675018i	$-0.764136\pi$
$997$	−46.5926	−1.47560	−0.737801	+	0.675018i	$0.764136\pi$
$998$	−71.6717	−2.26873
$999$	2.62448	0.0830349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-2.29414 q^{2} -1.00000 q^{3} +3.26307 q^{4} -3.12687 q^{5} +2.29414 q^{6} -2.80124 q^{7} -2.89765 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.29414 q^{2} -1.00000 q^{3} +3.26307 q^{4} -3.12687 q^{5} +2.29414 q^{6} -2.80124 q^{7} -2.89765 q^{8} +1.00000 q^{9} +7.17346 q^{10} +0.416671 q^{11} -3.26307 q^{12} -1.00000 q^{13} +6.42644 q^{14} +3.12687 q^{15} +0.121475 q^{16} +6.72425 q^{17} -2.29414 q^{18} -0.991424 q^{19} -10.2032 q^{20} +2.80124 q^{21} -0.955900 q^{22} +5.08704 q^{23} +2.89765 q^{24} +4.77729 q^{25} +2.29414 q^{26} -1.00000 q^{27} -9.14065 q^{28} -2.63056 q^{29} -7.17346 q^{30} +1.49809 q^{31} +5.51662 q^{32} -0.416671 q^{33} -15.4264 q^{34} +8.75912 q^{35} +3.26307 q^{36} -2.62448 q^{37} +2.27446 q^{38} +1.00000 q^{39} +9.06057 q^{40} +0.0147872 q^{41} -6.42644 q^{42} -5.30095 q^{43} +1.35962 q^{44} -3.12687 q^{45} -11.6704 q^{46} -5.68597 q^{47} -0.121475 q^{48} +0.846973 q^{49} -10.9598 q^{50} -6.72425 q^{51} -3.26307 q^{52} +7.63444 q^{53} +2.29414 q^{54} -1.30287 q^{55} +8.11703 q^{56} +0.991424 q^{57} +6.03487 q^{58} -6.67863 q^{59} +10.2032 q^{60} -10.9725 q^{61} -3.43683 q^{62} -2.80124 q^{63} -12.8988 q^{64} +3.12687 q^{65} +0.955900 q^{66} +3.12186 q^{67} +21.9417 q^{68} -5.08704 q^{69} -20.0946 q^{70} +12.5943 q^{71} -2.89765 q^{72} -4.28406 q^{73} +6.02092 q^{74} -4.77729 q^{75} -3.23508 q^{76} -1.16720 q^{77} -2.29414 q^{78} -1.69703 q^{79} -0.379837 q^{80} +1.00000 q^{81} -0.0339238 q^{82} -11.1302 q^{83} +9.14065 q^{84} -21.0258 q^{85} +12.1611 q^{86} +2.63056 q^{87} -1.20737 q^{88} -16.6424 q^{89} +7.17346 q^{90} +2.80124 q^{91} +16.5994 q^{92} -1.49809 q^{93} +13.0444 q^{94} +3.10005 q^{95} -5.51662 q^{96} -6.49117 q^{97} -1.94307 q^{98} +0.416671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 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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