LMFDB - Embedded newform 4017.2.a.g.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.16909 q^{2} -1.00000 q^{3} +2.70494 q^{4} +0.657691 q^{5} +2.16909 q^{6} -0.817989 q^{7} -1.52908 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16909 q^{2} -1.00000 q^{3} +2.70494 q^{4} +0.657691 q^{5} +2.16909 q^{6} -0.817989 q^{7} -1.52908 q^{8} +1.00000 q^{9} -1.42659 q^{10} +0.238154 q^{11} -2.70494 q^{12} -1.00000 q^{13} +1.77429 q^{14} -0.657691 q^{15} -2.09317 q^{16} -7.29215 q^{17} -2.16909 q^{18} -7.89148 q^{19} +1.77902 q^{20} +0.817989 q^{21} -0.516577 q^{22} -4.80968 q^{23} +1.52908 q^{24} -4.56744 q^{25} +2.16909 q^{26} -1.00000 q^{27} -2.21261 q^{28} -5.74601 q^{29} +1.42659 q^{30} -2.15879 q^{31} +7.59843 q^{32} -0.238154 q^{33} +15.8173 q^{34} -0.537984 q^{35} +2.70494 q^{36} +8.40747 q^{37} +17.1173 q^{38} +1.00000 q^{39} -1.00567 q^{40} -1.39322 q^{41} -1.77429 q^{42} -2.47981 q^{43} +0.644193 q^{44} +0.657691 q^{45} +10.4326 q^{46} +1.14963 q^{47} +2.09317 q^{48} -6.33089 q^{49} +9.90719 q^{50} +7.29215 q^{51} -2.70494 q^{52} +7.78793 q^{53} +2.16909 q^{54} +0.156632 q^{55} +1.25077 q^{56} +7.89148 q^{57} +12.4636 q^{58} +13.4644 q^{59} -1.77902 q^{60} -8.43426 q^{61} +4.68262 q^{62} -0.817989 q^{63} -12.2953 q^{64} -0.657691 q^{65} +0.516577 q^{66} -6.19072 q^{67} -19.7249 q^{68} +4.80968 q^{69} +1.16694 q^{70} -0.371575 q^{71} -1.52908 q^{72} +8.08329 q^{73} -18.2366 q^{74} +4.56744 q^{75} -21.3460 q^{76} -0.194808 q^{77} -2.16909 q^{78} +8.84351 q^{79} -1.37666 q^{80} +1.00000 q^{81} +3.02202 q^{82} -6.90175 q^{83} +2.21261 q^{84} -4.79598 q^{85} +5.37892 q^{86} +5.74601 q^{87} -0.364158 q^{88} +2.55828 q^{89} -1.42659 q^{90} +0.817989 q^{91} -13.0099 q^{92} +2.15879 q^{93} -2.49366 q^{94} -5.19015 q^{95} -7.59843 q^{96} -5.02301 q^{97} +13.7323 q^{98} +0.238154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.16909	−1.53378	−0.766888	−	0.641780i	$-0.778196\pi$
$2$	−2.16909	−1.53378	−0.766888	+	0.641780i	$0.778196\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.70494	1.35247
$5$	0.657691	0.294128	0.147064	−	0.989127i	$-0.453018\pi$
$5$	0.657691	0.294128	0.147064	+	0.989127i	$0.453018\pi$
$6$	2.16909	0.885527
$7$	−0.817989	−0.309171	−0.154585	−	0.987979i	$-0.549404\pi$
$7$	−0.817989	−0.309171	−0.154585	+	0.987979i	$0.549404\pi$
$8$	−1.52908	−0.540613
$9$	1.00000	0.333333
$10$	−1.42659	−0.451127
$11$	0.238154	0.0718062	0.0359031	−	0.999355i	$-0.488569\pi$
$11$	0.238154	0.0718062	0.0359031	+	0.999355i	$0.488569\pi$
$12$	−2.70494	−0.780850
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.77429	0.474199
$15$	−0.657691	−0.169815
$16$	−2.09317	−0.523292
$17$	−7.29215	−1.76861	−0.884303	−	0.466913i	$-0.845366\pi$
$17$	−7.29215	−1.76861	−0.884303	+	0.466913i	$0.845366\pi$
$18$	−2.16909	−0.511259
$19$	−7.89148	−1.81043	−0.905215	−	0.424954i	$-0.860290\pi$
$19$	−7.89148	−1.81043	−0.905215	+	0.424954i	$0.860290\pi$
$20$	1.77902	0.397800
$21$	0.817989	0.178500
$22$	−0.516577	−0.110135
$23$	−4.80968	−1.00289	−0.501444	−	0.865190i	$-0.667198\pi$
$23$	−4.80968	−1.00289	−0.501444	+	0.865190i	$0.667198\pi$
$24$	1.52908	0.312123
$25$	−4.56744	−0.913489
$26$	2.16909	0.425393
$27$	−1.00000	−0.192450
$28$	−2.21261	−0.418145
$29$	−5.74601	−1.06701	−0.533504	−	0.845798i	$-0.679125\pi$
$29$	−5.74601	−1.06701	−0.533504	+	0.845798i	$0.679125\pi$
$30$	1.42659	0.260458
$31$	−2.15879	−0.387731	−0.193865	−	0.981028i	$-0.562103\pi$
$31$	−2.15879	−0.387731	−0.193865	+	0.981028i	$0.562103\pi$
$32$	7.59843	1.34323
$33$	−0.238154	−0.0414573
$34$	15.8173	2.71265
$35$	−0.537984	−0.0909359
$36$	2.70494	0.450824
$37$	8.40747	1.38218	0.691090	−	0.722769i	$-0.257131\pi$
$37$	8.40747	1.38218	0.691090	+	0.722769i	$0.257131\pi$
$38$	17.1173	2.77680
$39$	1.00000	0.160128
$40$	−1.00567	−0.159010
$41$	−1.39322	−0.217584	−0.108792	−	0.994065i	$-0.534698\pi$
$41$	−1.39322	−0.217584	−0.108792	+	0.994065i	$0.534698\pi$
$42$	−1.77429	−0.273779
$43$	−2.47981	−0.378167	−0.189084	−	0.981961i	$-0.560552\pi$
$43$	−2.47981	−0.378167	−0.189084	+	0.981961i	$0.560552\pi$
$44$	0.644193	0.0971158
$45$	0.657691	0.0980428
$46$	10.4326	1.53821
$47$	1.14963	0.167691	0.0838457	−	0.996479i	$-0.473280\pi$
$47$	1.14963	0.167691	0.0838457	+	0.996479i	$0.473280\pi$
$48$	2.09317	0.302123
$49$	−6.33089	−0.904413
$50$	9.90719	1.40109
$51$	7.29215	1.02111
$52$	−2.70494	−0.375108
$53$	7.78793	1.06975	0.534877	−	0.844930i	$-0.320358\pi$
$53$	7.78793	1.06975	0.534877	+	0.844930i	$0.320358\pi$
$54$	2.16909	0.295176
$55$	0.156632	0.0211202
$56$	1.25077	0.167142
$57$	7.89148	1.04525
$58$	12.4636	1.63655
$59$	13.4644	1.75291	0.876456	−	0.481481i	$-0.159901\pi$
$59$	13.4644	1.75291	0.876456	+	0.481481i	$0.159901\pi$
$60$	−1.77902	−0.229670
$61$	−8.43426	−1.07990	−0.539948	−	0.841698i	$-0.681556\pi$
$61$	−8.43426	−1.07990	−0.539948	+	0.841698i	$0.681556\pi$
$62$	4.68262	0.594693
$63$	−0.817989	−0.103057
$64$	−12.2953	−1.53692
$65$	−0.657691	−0.0815765
$66$	0.516577	0.0635863
$67$	−6.19072	−0.756317	−0.378159	−	0.925741i	$-0.623443\pi$
$67$	−6.19072	−0.756317	−0.378159	+	0.925741i	$0.623443\pi$
$68$	−19.7249	−2.39199
$69$	4.80968	0.579018
$70$	1.16694	0.139475
$71$	−0.371575	−0.0440979	−0.0220489	−	0.999757i	$-0.507019\pi$
$71$	−0.371575	−0.0440979	−0.0220489	+	0.999757i	$0.507019\pi$
$72$	−1.52908	−0.180204
$73$	8.08329	0.946078	0.473039	−	0.881042i	$-0.343157\pi$
$73$	8.08329	0.946078	0.473039	+	0.881042i	$0.343157\pi$
$74$	−18.2366	−2.11996
$75$	4.56744	0.527403
$76$	−21.3460	−2.44855
$77$	−0.194808	−0.0222004
$78$	−2.16909	−0.245601
$79$	8.84351	0.994973	0.497486	−	0.867472i	$-0.334256\pi$
$79$	8.84351	0.994973	0.497486	+	0.867472i	$0.334256\pi$
$80$	−1.37666	−0.153915
$81$	1.00000	0.111111
$82$	3.02202	0.333726
$83$	−6.90175	−0.757565	−0.378783	−	0.925486i	$-0.623657\pi$
$83$	−6.90175	−0.757565	−0.378783	+	0.925486i	$0.623657\pi$
$84$	2.21261	0.241416
$85$	−4.79598	−0.520197
$86$	5.37892	0.580024
$87$	5.74601	0.616037
$88$	−0.364158	−0.0388193
$89$	2.55828	0.271177	0.135589	−	0.990765i	$-0.456707\pi$
$89$	2.55828	0.271177	0.135589	+	0.990765i	$0.456707\pi$
$90$	−1.42659	−0.150376
$91$	0.817989	0.0857486
$92$	−13.0099	−1.35638
$93$	2.15879	0.223857
$94$	−2.49366	−0.257201
$95$	−5.19015	−0.532499
$96$	−7.59843	−0.775512
$97$	−5.02301	−0.510009	−0.255005	−	0.966940i	$-0.582077\pi$
$97$	−5.02301	−0.510009	−0.255005	+	0.966940i	$0.582077\pi$
$98$	13.7323	1.38717
$99$	0.238154	0.0239354
$100$	−12.3547	−1.23547
$101$	12.8758	1.28119	0.640595	−	0.767879i	$-0.278688\pi$
$101$	12.8758	1.28119	0.640595	+	0.767879i	$0.278688\pi$
$102$	−15.8173	−1.56615
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.52908	0.149939
$105$	0.537984	0.0525019
$106$	−16.8927	−1.64077
$107$	16.8978	1.63357	0.816785	−	0.576942i	$-0.195754\pi$
$107$	16.8978	1.63357	0.816785	+	0.576942i	$0.195754\pi$
$108$	−2.70494	−0.260283
$109$	−13.6929	−1.31154	−0.655769	−	0.754962i	$-0.727656\pi$
$109$	−13.6929	−1.31154	−0.655769	+	0.754962i	$0.727656\pi$
$110$	−0.339748	−0.0323937
$111$	−8.40747	−0.798002
$112$	1.71219	0.161787
$113$	−0.108996	−0.0102534	−0.00512672	−	0.999987i	$-0.501632\pi$
$113$	−0.108996	−0.0102534	−0.00512672	+	0.999987i	$0.501632\pi$
$114$	−17.1173	−1.60318
$115$	−3.16329	−0.294978
$116$	−15.5426	−1.44310
$117$	−1.00000	−0.0924500
$118$	−29.2054	−2.68858
$119$	5.96490	0.546802
$120$	1.00567	0.0918042
$121$	−10.9433	−0.994844
$122$	18.2947	1.65632
$123$	1.39322	0.125622
$124$	−5.83942	−0.524395
$125$	−6.29242	−0.562811
$126$	1.77429	0.158066
$127$	14.7728	1.31087	0.655437	−	0.755250i	$-0.272485\pi$
$127$	14.7728	1.31087	0.655437	+	0.755250i	$0.272485\pi$
$128$	11.4728	1.01406
$129$	2.47981	0.218335
$130$	1.42659	0.125120
$131$	20.3381	1.77695	0.888474	−	0.458927i	$-0.151766\pi$
$131$	20.3381	1.77695	0.888474	+	0.458927i	$0.151766\pi$
$132$	−0.644193	−0.0560698
$133$	6.45515	0.559732
$134$	13.4282	1.16002
$135$	−0.657691	−0.0566050
$136$	11.1503	0.956132
$137$	11.7362	1.00269	0.501346	−	0.865247i	$-0.332838\pi$
$137$	11.7362	1.00269	0.501346	+	0.865247i	$0.332838\pi$
$138$	−10.4326	−0.888084
$139$	3.79541	0.321923	0.160961	−	0.986961i	$-0.448541\pi$
$139$	3.79541	0.321923	0.160961	+	0.986961i	$0.448541\pi$
$140$	−1.45522	−0.122988
$141$	−1.14963	−0.0968166
$142$	0.805979	0.0676363
$143$	−0.238154	−0.0199154
$144$	−2.09317	−0.174431
$145$	−3.77910	−0.313837
$146$	−17.5334	−1.45107
$147$	6.33089	0.522163
$148$	22.7417	1.86936
$149$	−23.5247	−1.92722	−0.963608	−	0.267320i	$-0.913862\pi$
$149$	−23.5247	−1.92722	−0.963608	+	0.267320i	$0.913862\pi$
$150$	−9.90719	−0.808918
$151$	16.0263	1.30420	0.652101	−	0.758132i	$-0.273888\pi$
$151$	16.0263	1.30420	0.652101	+	0.758132i	$0.273888\pi$
$152$	12.0667	0.978742
$153$	−7.29215	−0.589535
$154$	0.422555	0.0340504
$155$	−1.41982	−0.114043
$156$	2.70494	0.216569
$157$	−0.863139	−0.0688860	−0.0344430	−	0.999407i	$-0.510966\pi$
$157$	−0.863139	−0.0688860	−0.0344430	+	0.999407i	$0.510966\pi$
$158$	−19.1824	−1.52607
$159$	−7.78793	−0.617623
$160$	4.99742	0.395081
$161$	3.93427	0.310064
$162$	−2.16909	−0.170420
$163$	−14.4469	−1.13157	−0.565784	−	0.824553i	$-0.691427\pi$
$163$	−14.4469	−1.13157	−0.565784	+	0.824553i	$0.691427\pi$
$164$	−3.76858	−0.294277
$165$	−0.156632	−0.0121938
$166$	14.9705	1.16194
$167$	−11.8995	−0.920809	−0.460404	−	0.887709i	$-0.652296\pi$
$167$	−11.8995	−0.920809	−0.460404	+	0.887709i	$0.652296\pi$
$168$	−1.25077	−0.0964994
$169$	1.00000	0.0769231
$170$	10.4029	0.797867
$171$	−7.89148	−0.603477
$172$	−6.70774	−0.511460
$173$	14.5559	1.10666	0.553330	−	0.832962i	$-0.313357\pi$
$173$	14.5559	1.10666	0.553330	+	0.832962i	$0.313357\pi$
$174$	−12.4636	−0.944863
$175$	3.73612	0.282424
$176$	−0.498496	−0.0375756
$177$	−13.4644	−1.01204
$178$	−5.54914	−0.415926
$179$	17.0632	1.27536	0.637682	−	0.770300i	$-0.279894\pi$
$179$	17.0632	1.27536	0.637682	+	0.770300i	$0.279894\pi$
$180$	1.77902	0.132600
$181$	−7.32882	−0.544747	−0.272373	−	0.962192i	$-0.587809\pi$
$181$	−7.32882	−0.544747	−0.272373	+	0.962192i	$0.587809\pi$
$182$	−1.77429	−0.131519
$183$	8.43426	0.623479
$184$	7.35441	0.542175
$185$	5.52952	0.406538
$186$	−4.68262	−0.343346
$187$	−1.73666	−0.126997
$188$	3.10969	0.226798
$189$	0.817989	0.0595000
$190$	11.2579	0.816734
$191$	−5.51876	−0.399323	−0.199662	−	0.979865i	$-0.563984\pi$
$191$	−5.51876	−0.399323	−0.199662	+	0.979865i	$0.563984\pi$
$192$	12.2953	0.887340
$193$	−19.3330	−1.39162	−0.695808	−	0.718228i	$-0.744954\pi$
$193$	−19.3330	−1.39162	−0.695808	+	0.718228i	$0.744954\pi$
$194$	10.8954	0.782241
$195$	0.657691	0.0470982
$196$	−17.1247	−1.22319
$197$	22.0917	1.57397	0.786984	−	0.616973i	$-0.211641\pi$
$197$	22.0917	1.57397	0.786984	+	0.616973i	$0.211641\pi$
$198$	−0.516577	−0.0367115
$199$	−8.06339	−0.571598	−0.285799	−	0.958290i	$-0.592259\pi$
$199$	−8.06339	−0.571598	−0.285799	+	0.958290i	$0.592259\pi$
$200$	6.98401	0.493844
$201$	6.19072	0.436660
$202$	−27.9287	−1.96506
$203$	4.70017	0.329888
$204$	19.7249	1.38102
$205$	−0.916308	−0.0639977
$206$	−2.16909	−0.151128
$207$	−4.80968	−0.334296
$208$	2.09317	0.145135
$209$	−1.87939	−0.130000
$210$	−1.16694	−0.0805262
$211$	−1.19761	−0.0824470	−0.0412235	−	0.999150i	$-0.513126\pi$
$211$	−1.19761	−0.0824470	−0.0412235	+	0.999150i	$0.513126\pi$
$212$	21.0659	1.44681
$213$	0.371575	0.0254599
$214$	−36.6528	−2.50553
$215$	−1.63095	−0.111230
$216$	1.52908	0.104041
$217$	1.76587	0.119875
$218$	29.7010	2.01161
$219$	−8.08329	−0.546218
$220$	0.423680	0.0285645
$221$	7.29215	0.490523
$222$	18.2366	1.22396
$223$	24.1619	1.61800	0.809000	−	0.587809i	$-0.200009\pi$
$223$	24.1619	1.61800	0.809000	+	0.587809i	$0.200009\pi$
$224$	−6.21544	−0.415286
$225$	−4.56744	−0.304496
$226$	0.236421	0.0157265
$227$	10.4516	0.693697	0.346848	−	0.937921i	$-0.387252\pi$
$227$	10.4516	0.693697	0.346848	+	0.937921i	$0.387252\pi$
$228$	21.3460	1.41367
$229$	−0.805614	−0.0532365	−0.0266182	−	0.999646i	$-0.508474\pi$
$229$	−0.805614	−0.0532365	−0.0266182	+	0.999646i	$0.508474\pi$
$230$	6.86145	0.452430
$231$	0.194808	0.0128174
$232$	8.78613	0.576838
$233$	23.0362	1.50915	0.754577	−	0.656212i	$-0.227842\pi$
$233$	23.0362	1.50915	0.754577	+	0.656212i	$0.227842\pi$
$234$	2.16909	0.141798
$235$	0.756104	0.0493228
$236$	36.4204	2.37076
$237$	−8.84351	−0.574448
$238$	−12.9384	−0.838672
$239$	−21.6824	−1.40252	−0.701260	−	0.712906i	$-0.747379\pi$
$239$	−21.6824	−1.40252	−0.701260	+	0.712906i	$0.747379\pi$
$240$	1.37666	0.0888629
$241$	−23.6104	−1.52088	−0.760441	−	0.649407i	$-0.775017\pi$
$241$	−23.6104	−1.52088	−0.760441	+	0.649407i	$0.775017\pi$
$242$	23.7369	1.52587
$243$	−1.00000	−0.0641500
$244$	−22.8142	−1.46053
$245$	−4.16377	−0.266014
$246$	−3.02202	−0.192677
$247$	7.89148	0.502123
$248$	3.30098	0.209612
$249$	6.90175	0.437380
$250$	13.6488	0.863227
$251$	−10.0395	−0.633690	−0.316845	−	0.948477i	$-0.602624\pi$
$251$	−10.0395	−0.633690	−0.316845	+	0.948477i	$0.602624\pi$
$252$	−2.21261	−0.139382
$253$	−1.14545	−0.0720136
$254$	−32.0435	−2.01059
$255$	4.79598	0.300336
$256$	−0.294848	−0.0184280
$257$	22.1641	1.38256	0.691278	−	0.722589i	$-0.257048\pi$
$257$	22.1641	1.38256	0.691278	+	0.722589i	$0.257048\pi$
$258$	−5.37892	−0.334877
$259$	−6.87722	−0.427330
$260$	−1.77902	−0.110330
$261$	−5.74601	−0.355669
$262$	−44.1151	−2.72544
$263$	−26.5442	−1.63679	−0.818393	−	0.574660i	$-0.805134\pi$
$263$	−26.5442	−1.63679	−0.818393	+	0.574660i	$0.805134\pi$
$264$	0.364158	0.0224124
$265$	5.12205	0.314645
$266$	−14.0018	−0.858504
$267$	−2.55828	−0.156564
$268$	−16.7456	−1.02290
$269$	3.68548	0.224708	0.112354	−	0.993668i	$-0.464161\pi$
$269$	3.68548	0.224708	0.112354	+	0.993668i	$0.464161\pi$
$270$	1.42659	0.0868195
$271$	−11.7128	−0.711503	−0.355751	−	0.934581i	$-0.615775\pi$
$271$	−11.7128	−0.711503	−0.355751	+	0.934581i	$0.615775\pi$
$272$	15.2637	0.925498
$273$	−0.817989	−0.0495070
$274$	−25.4569	−1.53791
$275$	−1.08776	−0.0655941
$276$	13.0099	0.783105
$277$	−25.9954	−1.56191	−0.780955	−	0.624587i	$-0.785267\pi$
$277$	−25.9954	−1.56191	−0.780955	+	0.624587i	$0.785267\pi$
$278$	−8.23258	−0.493757
$279$	−2.15879	−0.129244
$280$	0.822623	0.0491611
$281$	−10.7280	−0.639981	−0.319991	−	0.947421i	$-0.603680\pi$
$281$	−10.7280	−0.639981	−0.319991	+	0.947421i	$0.603680\pi$
$282$	2.49366	0.148495
$283$	−24.1473	−1.43541	−0.717704	−	0.696349i	$-0.754807\pi$
$283$	−24.1473	−1.43541	−0.717704	+	0.696349i	$0.754807\pi$
$284$	−1.00509	−0.0596411
$285$	5.19015	0.307438
$286$	0.516577	0.0305459
$287$	1.13964	0.0672707
$288$	7.59843	0.447742
$289$	36.1755	2.12797
$290$	8.19720	0.481356
$291$	5.02301	0.294454
$292$	21.8648	1.27954
$293$	8.87597	0.518540	0.259270	−	0.965805i	$-0.416518\pi$
$293$	8.87597	0.518540	0.259270	+	0.965805i	$0.416518\pi$
$294$	−13.7323	−0.800882
$295$	8.85540	0.515581
$296$	−12.8557	−0.747225
$297$	−0.238154	−0.0138191
$298$	51.0271	2.95592
$299$	4.80968	0.278151
$300$	12.3547	0.713297
$301$	2.02846	0.116918
$302$	−34.7625	−2.00035
$303$	−12.8758	−0.739695
$304$	16.5182	0.947383
$305$	−5.54714	−0.317628
$306$	15.8173	0.904216
$307$	27.1043	1.54692	0.773462	−	0.633843i	$-0.218523\pi$
$307$	27.1043	1.54692	0.773462	+	0.633843i	$0.218523\pi$
$308$	−0.526943	−0.0300254
$309$	−1.00000	−0.0568880
$310$	3.07971	0.174916
$311$	−18.8025	−1.06619	−0.533095	−	0.846055i	$-0.678971\pi$
$311$	−18.8025	−1.06619	−0.533095	+	0.846055i	$0.678971\pi$
$312$	−1.52908	−0.0865674
$313$	15.8992	0.898677	0.449339	−	0.893362i	$-0.351660\pi$
$313$	15.8992	0.898677	0.449339	+	0.893362i	$0.351660\pi$
$314$	1.87222	0.105656
$315$	−0.537984	−0.0303120
$316$	23.9212	1.34567
$317$	8.36182	0.469647	0.234823	−	0.972038i	$-0.424549\pi$
$317$	8.36182	0.469647	0.234823	+	0.972038i	$0.424549\pi$
$318$	16.8927	0.947296
$319$	−1.36844	−0.0766177
$320$	−8.08653	−0.452051
$321$	−16.8978	−0.943142
$322$	−8.53378	−0.475569
$323$	57.5459	3.20194
$324$	2.70494	0.150275
$325$	4.56744	0.253356
$326$	31.3366	1.73557
$327$	13.6929	0.757217
$328$	2.13035	0.117629
$329$	−0.940388	−0.0518453
$330$	0.339748	0.0187025
$331$	18.7500	1.03059	0.515296	−	0.857012i	$-0.327682\pi$
$331$	18.7500	1.03059	0.515296	+	0.857012i	$0.327682\pi$
$332$	−18.6688	−1.02459
$333$	8.40747	0.460727
$334$	25.8110	1.41232
$335$	−4.07158	−0.222454
$336$	−1.71219	−0.0934076
$337$	1.03357	0.0563020	0.0281510	−	0.999604i	$-0.491038\pi$
$337$	1.03357	0.0563020	0.0281510	+	0.999604i	$0.491038\pi$
$338$	−2.16909	−0.117983
$339$	0.108996	0.00591983
$340$	−12.9729	−0.703552
$341$	−0.514126	−0.0278415
$342$	17.1173	0.925598
$343$	10.9045	0.588789
$344$	3.79184	0.204442
$345$	3.16329	0.170306
$346$	−31.5729	−1.69737
$347$	16.4728	0.884306	0.442153	−	0.896940i	$-0.354215\pi$
$347$	16.4728	0.884306	0.442153	+	0.896940i	$0.354215\pi$
$348$	15.5426	0.833172
$349$	−11.1249	−0.595504	−0.297752	−	0.954643i	$-0.596237\pi$
$349$	−11.1249	−0.595504	−0.297752	+	0.954643i	$0.596237\pi$
$350$	−8.10397	−0.433176
$351$	1.00000	0.0533761
$352$	1.80960	0.0964519
$353$	−26.2649	−1.39794	−0.698970	−	0.715151i	$-0.746358\pi$
$353$	−26.2649	−1.39794	−0.698970	+	0.715151i	$0.746358\pi$
$354$	29.2054	1.55225
$355$	−0.244382	−0.0129704
$356$	6.92001	0.366760
$357$	−5.96490	−0.315696
$358$	−37.0116	−1.95612
$359$	0.467444	0.0246708	0.0123354	−	0.999924i	$-0.496073\pi$
$359$	0.467444	0.0246708	0.0123354	+	0.999924i	$0.496073\pi$
$360$	−1.00567	−0.0530032
$361$	43.2755	2.27766
$362$	15.8968	0.835520
$363$	10.9433	0.574373
$364$	2.21261	0.115973
$365$	5.31631	0.278268
$366$	−18.2947	−0.956277
$367$	11.5547	0.603149	0.301575	−	0.953443i	$-0.402488\pi$
$367$	11.5547	0.603149	0.301575	+	0.953443i	$0.402488\pi$
$368$	10.0675	0.524803
$369$	−1.39322	−0.0725281
$370$	−11.9940	−0.623539
$371$	−6.37044	−0.330737
$372$	5.83942	0.302760
$373$	7.22235	0.373959	0.186979	−	0.982364i	$-0.440130\pi$
$373$	7.22235	0.373959	0.186979	+	0.982364i	$0.440130\pi$
$374$	3.76696	0.194785
$375$	6.29242	0.324939
$376$	−1.75789	−0.0906561
$377$	5.74601	0.295935
$378$	−1.77429	−0.0912597
$379$	25.1674	1.29276	0.646381	−	0.763015i	$-0.276282\pi$
$379$	25.1674	1.29276	0.646381	+	0.763015i	$0.276282\pi$
$380$	−14.0391	−0.720189
$381$	−14.7728	−0.756833
$382$	11.9707	0.612473
$383$	26.1690	1.33717	0.668586	−	0.743635i	$-0.266900\pi$
$383$	26.1690	1.33717	0.668586	+	0.743635i	$0.266900\pi$
$384$	−11.4728	−0.585469
$385$	−0.128123	−0.00652976
$386$	41.9349	2.13443
$387$	−2.47981	−0.126056
$388$	−13.5870	−0.689773
$389$	9.12007	0.462406	0.231203	−	0.972906i	$-0.425734\pi$
$389$	9.12007	0.462406	0.231203	+	0.972906i	$0.425734\pi$
$390$	−1.42659	−0.0722382
$391$	35.0729	1.77371
$392$	9.68047	0.488938
$393$	−20.3381	−1.02592
$394$	−47.9188	−2.41412
$395$	5.81630	0.292650
$396$	0.644193	0.0323719
$397$	18.6034	0.933680	0.466840	−	0.884342i	$-0.345392\pi$
$397$	18.6034	0.933680	0.466840	+	0.884342i	$0.345392\pi$
$398$	17.4902	0.876705
$399$	−6.45515	−0.323162
$400$	9.56042	0.478021
$401$	−10.2523	−0.511976	−0.255988	−	0.966680i	$-0.582401\pi$
$401$	−10.2523	−0.511976	−0.255988	+	0.966680i	$0.582401\pi$
$402$	−13.4282	−0.669739
$403$	2.15879	0.107537
$404$	34.8283	1.73277
$405$	0.657691	0.0326809
$406$	−10.1951	−0.505974
$407$	2.00227	0.0992490
$408$	−11.1503	−0.552023
$409$	−12.4065	−0.613464	−0.306732	−	0.951796i	$-0.599236\pi$
$409$	−12.4065	−0.613464	−0.306732	+	0.951796i	$0.599236\pi$
$410$	1.98755	0.0981582
$411$	−11.7362	−0.578904
$412$	2.70494	0.133263
$413$	−11.0137	−0.541950
$414$	10.4326	0.512736
$415$	−4.53922	−0.222821
$416$	−7.59843	−0.372544
$417$	−3.79541	−0.185862
$418$	4.07656	0.199391
$419$	−6.33041	−0.309261	−0.154630	−	0.987972i	$-0.549419\pi$
$419$	−6.33041	−0.309261	−0.154630	+	0.987972i	$0.549419\pi$
$420$	1.45522	0.0710073
$421$	−30.1479	−1.46932	−0.734660	−	0.678436i	$-0.762658\pi$
$421$	−30.1479	−1.46932	−0.734660	+	0.678436i	$0.762658\pi$
$422$	2.59773	0.126455
$423$	1.14963	0.0558971
$424$	−11.9084	−0.578323
$425$	33.3065	1.61560
$426$	−0.805979	−0.0390498
$427$	6.89914	0.333873
$428$	45.7075	2.20936
$429$	0.238154	0.0114982
$430$	3.53767	0.170601
$431$	−6.15515	−0.296483	−0.148242	−	0.988951i	$-0.547361\pi$
$431$	−6.15515	−0.296483	−0.148242	+	0.988951i	$0.547361\pi$
$432$	2.09317	0.100708
$433$	−14.4862	−0.696162	−0.348081	−	0.937464i	$-0.613167\pi$
$433$	−14.4862	−0.696162	−0.348081	+	0.937464i	$0.613167\pi$
$434$	−3.83033	−0.183862
$435$	3.77910	0.181194
$436$	−37.0384	−1.77382
$437$	37.9555	1.81566
$438$	17.5334	0.837777
$439$	7.54567	0.360135	0.180068	−	0.983654i	$-0.442368\pi$
$439$	7.54567	0.360135	0.180068	+	0.983654i	$0.442368\pi$
$440$	−0.239503	−0.0114179
$441$	−6.33089	−0.301471
$442$	−15.8173	−0.752353
$443$	2.56260	0.121753	0.0608764	−	0.998145i	$-0.480610\pi$
$443$	2.56260	0.121753	0.0608764	+	0.998145i	$0.480610\pi$
$444$	−22.7417	−1.07928
$445$	1.68256	0.0797609
$446$	−52.4093	−2.48165
$447$	23.5247	1.11268
$448$	10.0575	0.475170
$449$	−1.69568	−0.0800239	−0.0400120	−	0.999199i	$-0.512740\pi$
$449$	−1.69568	−0.0800239	−0.0400120	+	0.999199i	$0.512740\pi$
$450$	9.90719	0.467029
$451$	−0.331801	−0.0156239
$452$	−0.294827	−0.0138675
$453$	−16.0263	−0.752981
$454$	−22.6704	−1.06398
$455$	0.537984	0.0252211
$456$	−12.0667	−0.565077
$457$	−3.30251	−0.154485	−0.0772425	−	0.997012i	$-0.524612\pi$
$457$	−3.30251	−0.154485	−0.0772425	+	0.997012i	$0.524612\pi$
$458$	1.74745	0.0816529
$459$	7.29215	0.340368
$460$	−8.55651	−0.398949
$461$	−20.6391	−0.961261	−0.480630	−	0.876923i	$-0.659592\pi$
$461$	−20.6391	−0.961261	−0.480630	+	0.876923i	$0.659592\pi$
$462$	−0.422555	−0.0196590
$463$	36.3687	1.69020	0.845099	−	0.534610i	$-0.179542\pi$
$463$	36.3687	1.69020	0.845099	+	0.534610i	$0.179542\pi$
$464$	12.0274	0.558356
$465$	1.41982	0.0658425
$466$	−49.9676	−2.31470
$467$	7.69542	0.356101	0.178051	−	0.984021i	$-0.443021\pi$
$467$	7.69542	0.356101	0.178051	+	0.984021i	$0.443021\pi$
$468$	−2.70494	−0.125036
$469$	5.06394	0.233831
$470$	−1.64006	−0.0756501
$471$	0.863139	0.0397713
$472$	−20.5882	−0.947647
$473$	−0.590576	−0.0271547
$474$	19.1824	0.881075
$475$	36.0439	1.65381
$476$	16.1347	0.739534
$477$	7.78793	0.356585
$478$	47.0311	2.15115
$479$	−38.2453	−1.74747	−0.873737	−	0.486398i	$-0.838310\pi$
$479$	−38.2453	−1.74747	−0.873737	+	0.486398i	$0.838310\pi$
$480$	−4.99742	−0.228100
$481$	−8.40747	−0.383348
$482$	51.2131	2.33269
$483$	−3.93427	−0.179015
$484$	−29.6010	−1.34550
$485$	−3.30359	−0.150008
$486$	2.16909	0.0983918
$487$	1.27542	0.0577950	0.0288975	−	0.999582i	$-0.490800\pi$
$487$	1.27542	0.0577950	0.0288975	+	0.999582i	$0.490800\pi$
$488$	12.8967	0.583806
$489$	14.4469	0.653311
$490$	9.03159	0.408005
$491$	−25.4856	−1.15015	−0.575076	−	0.818100i	$-0.695027\pi$
$491$	−25.4856	−1.15015	−0.575076	+	0.818100i	$0.695027\pi$
$492$	3.76858	0.169901
$493$	41.9008	1.88712
$494$	−17.1173	−0.770144
$495$	0.156632	0.00704008
$496$	4.51872	0.202896
$497$	0.303945	0.0136338
$498$	−14.9705	−0.670844
$499$	11.9003	0.532732	0.266366	−	0.963872i	$-0.414177\pi$
$499$	11.9003	0.532732	0.266366	+	0.963872i	$0.414177\pi$
$500$	−17.0206	−0.761186
$501$	11.8995	0.531629
$502$	21.7767	0.971940
$503$	−13.2869	−0.592435	−0.296218	−	0.955120i	$-0.595725\pi$
$503$	−13.2869	−0.592435	−0.296218	+	0.955120i	$0.595725\pi$
$504$	1.25077	0.0557139
$505$	8.46829	0.376834
$506$	2.48457	0.110453
$507$	−1.00000	−0.0444116
$508$	39.9596	1.77292
$509$	12.0674	0.534877	0.267438	−	0.963575i	$-0.413823\pi$
$509$	12.0674	0.534877	0.267438	+	0.963575i	$0.413823\pi$
$510$	−10.4029	−0.460648
$511$	−6.61205	−0.292500
$512$	−22.3061	−0.985798
$513$	7.89148	0.348417
$514$	−48.0758	−2.12053
$515$	0.657691	0.0289813
$516$	6.70774	0.295292
$517$	0.273790	0.0120413
$518$	14.9173	0.655429
$519$	−14.5559	−0.638931
$520$	1.00567	0.0441013
$521$	27.8216	1.21889	0.609443	−	0.792830i	$-0.291393\pi$
$521$	27.8216	1.21889	0.609443	+	0.792830i	$0.291393\pi$
$522$	12.4636	0.545517
$523$	−35.5681	−1.55529	−0.777643	−	0.628707i	$-0.783585\pi$
$523$	−35.5681	−1.55529	−0.777643	+	0.628707i	$0.783585\pi$
$524$	55.0134	2.40327
$525$	−3.73612	−0.163058
$526$	57.5767	2.51046
$527$	15.7423	0.685743
$528$	0.498496	0.0216943
$529$	0.133061	0.00578527
$530$	−11.1102	−0.482595
$531$	13.4644	0.584304
$532$	17.4608	0.757022
$533$	1.39322	0.0603470
$534$	5.54914	0.240135
$535$	11.1135	0.480479
$536$	9.46614	0.408875
$537$	−17.0632	−0.736331
$538$	−7.99413	−0.344651
$539$	−1.50773	−0.0649424
$540$	−1.77902	−0.0765567
$541$	37.1358	1.59659	0.798296	−	0.602265i	$-0.205735\pi$
$541$	37.1358	1.59659	0.798296	+	0.602265i	$0.205735\pi$
$542$	25.4061	1.09129
$543$	7.32882	0.314510
$544$	−55.4089	−2.37564
$545$	−9.00567	−0.385761
$546$	1.77429	0.0759326
$547$	8.78364	0.375561	0.187781	−	0.982211i	$-0.439871\pi$
$547$	8.78364	0.375561	0.187781	+	0.982211i	$0.439871\pi$
$548$	31.7458	1.35611
$549$	−8.43426	−0.359966
$550$	2.35944	0.100607
$551$	45.3445	1.93174
$552$	−7.35441	−0.313025
$553$	−7.23390	−0.307617
$554$	56.3862	2.39562
$555$	−5.52952	−0.234715
$556$	10.2664	0.435391
$557$	−17.7240	−0.750989	−0.375494	−	0.926825i	$-0.622527\pi$
$557$	−17.7240	−0.750989	−0.375494	+	0.926825i	$0.622527\pi$
$558$	4.68262	0.198231
$559$	2.47981	0.104885
$560$	1.12609	0.0475860
$561$	1.73666	0.0733217
$562$	23.2701	0.981589
$563$	−0.463456	−0.0195324	−0.00976618	−	0.999952i	$-0.503109\pi$
$563$	−0.463456	−0.0195324	−0.00976618	+	0.999952i	$0.503109\pi$
$564$	−3.10969	−0.130942
$565$	−0.0716854	−0.00301583
$566$	52.3776	2.20159
$567$	−0.817989	−0.0343523
$568$	0.568170	0.0238399
$569$	17.7168	0.742728	0.371364	−	0.928487i	$-0.378890\pi$
$569$	17.7168	0.742728	0.371364	+	0.928487i	$0.378890\pi$
$570$	−11.2579	−0.471542
$571$	21.1115	0.883487	0.441744	−	0.897141i	$-0.354360\pi$
$571$	21.1115	0.883487	0.441744	+	0.897141i	$0.354360\pi$
$572$	−0.644193	−0.0269351
$573$	5.51876	0.230549
$574$	−2.47198	−0.103178
$575$	21.9680	0.916127
$576$	−12.2953	−0.512306
$577$	−30.0648	−1.25161	−0.625806	−	0.779979i	$-0.715230\pi$
$577$	−30.0648	−1.25161	−0.625806	+	0.779979i	$0.715230\pi$
$578$	−78.4678	−3.26383
$579$	19.3330	0.803450
$580$	−10.2222	−0.424456
$581$	5.64556	0.234217
$582$	−10.8954	−0.451627
$583$	1.85473	0.0768150
$584$	−12.3600	−0.511462
$585$	−0.657691	−0.0271922
$586$	−19.2528	−0.795324
$587$	14.5128	0.599008	0.299504	−	0.954095i	$-0.403179\pi$
$587$	14.5128	0.599008	0.299504	+	0.954095i	$0.403179\pi$
$588$	17.1247	0.706211
$589$	17.0361	0.701960
$590$	−19.2081	−0.790787
$591$	−22.0917	−0.908731
$592$	−17.5983	−0.723284
$593$	−2.44406	−0.100366	−0.0501828	−	0.998740i	$-0.515980\pi$
$593$	−2.44406	−0.100366	−0.0501828	+	0.998740i	$0.515980\pi$
$594$	0.516577	0.0211954
$595$	3.92306	0.160830
$596$	−63.6329	−2.60650
$597$	8.06339	0.330013
$598$	−10.4326	−0.426622
$599$	4.65973	0.190391	0.0951957	−	0.995459i	$-0.469652\pi$
$599$	4.65973	0.190391	0.0951957	+	0.995459i	$0.469652\pi$
$600$	−6.98401	−0.285121
$601$	−5.06110	−0.206447	−0.103223	−	0.994658i	$-0.532916\pi$
$601$	−5.06110	−0.206447	−0.103223	+	0.994658i	$0.532916\pi$
$602$	−4.39990	−0.179327
$603$	−6.19072	−0.252106
$604$	43.3502	1.76390
$605$	−7.19730	−0.292612
$606$	27.9287	1.13453
$607$	−39.1391	−1.58861	−0.794304	−	0.607521i	$-0.792164\pi$
$607$	−39.1391	−1.58861	−0.794304	+	0.607521i	$0.792164\pi$
$608$	−59.9629	−2.43182
$609$	−4.70017	−0.190461
$610$	12.0322	0.487171
$611$	−1.14963	−0.0465092
$612$	−19.7249	−0.797330
$613$	−13.2376	−0.534663	−0.267332	−	0.963605i	$-0.586142\pi$
$613$	−13.2376	−0.534663	−0.267332	+	0.963605i	$0.586142\pi$
$614$	−58.7916	−2.37264
$615$	0.916308	0.0369491
$616$	0.297877	0.0120018
$617$	28.0649	1.12985	0.564926	−	0.825142i	$-0.308905\pi$
$617$	28.0649	1.12985	0.564926	+	0.825142i	$0.308905\pi$
$618$	2.16909	0.0872535
$619$	0.223259	0.00897355	0.00448678	−	0.999990i	$-0.498572\pi$
$619$	0.223259	0.00897355	0.00448678	+	0.999990i	$0.498572\pi$
$620$	−3.84053	−0.154239
$621$	4.80968	0.193006
$622$	40.7842	1.63530
$623$	−2.09265	−0.0838401
$624$	−2.09317	−0.0837938
$625$	18.6987	0.747950
$626$	−34.4868	−1.37837
$627$	1.87939	0.0750555
$628$	−2.33474	−0.0931663
$629$	−61.3086	−2.44453
$630$	1.16694	0.0464918
$631$	11.5577	0.460103	0.230052	−	0.973178i	$-0.426111\pi$
$631$	11.5577	0.460103	0.230052	+	0.973178i	$0.426111\pi$
$632$	−13.5225	−0.537895
$633$	1.19761	0.0476008
$634$	−18.1375	−0.720333
$635$	9.71593	0.385565
$636$	−21.0659	−0.835318
$637$	6.33089	0.250839
$638$	2.96826	0.117514
$639$	−0.371575	−0.0146993
$640$	7.54556	0.298264
$641$	−7.18149	−0.283652	−0.141826	−	0.989892i	$-0.545297\pi$
$641$	−7.18149	−0.283652	−0.141826	+	0.989892i	$0.545297\pi$
$642$	36.6528	1.44657
$643$	−23.1494	−0.912924	−0.456462	−	0.889743i	$-0.650884\pi$
$643$	−23.1494	−0.912924	−0.456462	+	0.889743i	$0.650884\pi$
$644$	10.6420	0.419353
$645$	1.63095	0.0642185
$646$	−124.822	−4.91106
$647$	24.5092	0.963554	0.481777	−	0.876294i	$-0.339991\pi$
$647$	24.5092	0.963554	0.481777	+	0.876294i	$0.339991\pi$
$648$	−1.52908	−0.0600681
$649$	3.20660	0.125870
$650$	−9.90719	−0.388592
$651$	−1.76587	−0.0692099
$652$	−39.0780	−1.53041
$653$	15.5668	0.609176	0.304588	−	0.952484i	$-0.401481\pi$
$653$	15.5668	0.609176	0.304588	+	0.952484i	$0.401481\pi$
$654$	−29.7010	−1.16140
$655$	13.3762	0.522651
$656$	2.91624	0.113860
$657$	8.08329	0.315359
$658$	2.03978	0.0795191
$659$	23.5138	0.915969	0.457985	−	0.888960i	$-0.348571\pi$
$659$	23.5138	0.915969	0.457985	+	0.888960i	$0.348571\pi$
$660$	−0.423680	−0.0164917
$661$	−39.3348	−1.52995	−0.764974	−	0.644062i	$-0.777248\pi$
$661$	−39.3348	−1.52995	−0.764974	+	0.644062i	$0.777248\pi$
$662$	−40.6704	−1.58070
$663$	−7.29215	−0.283204
$664$	10.5534	0.409550
$665$	4.24549	0.164633
$666$	−18.2366	−0.706652
$667$	27.6365	1.07009
$668$	−32.1874	−1.24537
$669$	−24.1619	−0.934153
$670$	8.83162	0.341195
$671$	−2.00865	−0.0775432
$672$	6.21544	0.239766
$673$	−1.44560	−0.0557238	−0.0278619	−	0.999612i	$-0.508870\pi$
$673$	−1.44560	−0.0557238	−0.0278619	+	0.999612i	$0.508870\pi$
$674$	−2.24190	−0.0863547
$675$	4.56744	0.175801
$676$	2.70494	0.104036
$677$	5.85083	0.224866	0.112433	−	0.993659i	$-0.464136\pi$
$677$	5.85083	0.224866	0.112433	+	0.993659i	$0.464136\pi$
$678$	−0.236421	−0.00907970
$679$	4.10877	0.157680
$680$	7.33346	0.281225
$681$	−10.4516	−0.400506
$682$	1.11518	0.0427026
$683$	−35.0806	−1.34232	−0.671161	−	0.741312i	$-0.734204\pi$
$683$	−35.0806	−1.34232	−0.671161	+	0.741312i	$0.734204\pi$
$684$	−21.3460	−0.816185
$685$	7.71880	0.294920
$686$	−23.6529	−0.903071
$687$	0.805614	0.0307361
$688$	5.19065	0.197892
$689$	−7.78793	−0.296697
$690$	−6.86145	−0.261211
$691$	48.5538	1.84707	0.923536	−	0.383511i	$-0.125285\pi$
$691$	48.5538	1.84707	0.923536	+	0.383511i	$0.125285\pi$
$692$	39.3728	1.49673
$693$	−0.194808	−0.00740013
$694$	−35.7309	−1.35633
$695$	2.49621	0.0946865
$696$	−8.78613	−0.333038
$697$	10.1596	0.384821
$698$	24.1310	0.913370
$699$	−23.0362	−0.871310
$700$	10.1060	0.381971
$701$	−27.4011	−1.03493	−0.517463	−	0.855706i	$-0.673124\pi$
$701$	−27.4011	−1.03493	−0.517463	+	0.855706i	$0.673124\pi$
$702$	−2.16909	−0.0818670
$703$	−66.3474	−2.50234
$704$	−2.92819	−0.110360
$705$	−0.756104	−0.0284765
$706$	56.9709	2.14413
$707$	−10.5323	−0.396107
$708$	−36.4204	−1.36876
$709$	−4.60770	−0.173046	−0.0865229	−	0.996250i	$-0.527576\pi$
$709$	−4.60770	−0.173046	−0.0865229	+	0.996250i	$0.527576\pi$
$710$	0.530085	0.0198937
$711$	8.84351	0.331658
$712$	−3.91183	−0.146602
$713$	10.3831	0.388851
$714$	12.9384	0.484207
$715$	−0.156632	−0.00585770
$716$	46.1550	1.72489
$717$	21.6824	0.809745
$718$	−1.01393	−0.0378394
$719$	−0.447795	−0.0166999	−0.00834997	−	0.999965i	$-0.502658\pi$
$719$	−0.447795	−0.0166999	−0.00834997	+	0.999965i	$0.502658\pi$
$720$	−1.37666	−0.0513050
$721$	−0.817989	−0.0304635
$722$	−93.8683	−3.49342
$723$	23.6104	0.878081
$724$	−19.8240	−0.736754
$725$	26.2446	0.974699
$726$	−23.7369	−0.880961
$727$	−11.1260	−0.412642	−0.206321	−	0.978484i	$-0.566149\pi$
$727$	−11.1260	−0.412642	−0.206321	+	0.978484i	$0.566149\pi$
$728$	−1.25077	−0.0463568
$729$	1.00000	0.0370370
$730$	−11.5315	−0.426801
$731$	18.0831	0.668829
$732$	22.8142	0.843237
$733$	−7.99825	−0.295422	−0.147711	−	0.989031i	$-0.547191\pi$
$733$	−7.99825	−0.295422	−0.147711	+	0.989031i	$0.547191\pi$
$734$	−25.0631	−0.925096
$735$	4.16377	0.153583
$736$	−36.5461	−1.34711
$737$	−1.47435	−0.0543082
$738$	3.02202	0.111242
$739$	12.4849	0.459263	0.229631	−	0.973278i	$-0.426248\pi$
$739$	12.4849	0.459263	0.229631	+	0.973278i	$0.426248\pi$
$740$	14.9570	0.549832
$741$	−7.89148	−0.289901
$742$	13.8181	0.507277
$743$	−43.1830	−1.58423	−0.792115	−	0.610372i	$-0.791020\pi$
$743$	−43.1830	−1.58423	−0.792115	+	0.610372i	$0.791020\pi$
$744$	−3.30098	−0.121020
$745$	−15.4720	−0.566849
$746$	−15.6659	−0.573570
$747$	−6.90175	−0.252522
$748$	−4.69756	−0.171760
$749$	−13.8222	−0.505052
$750$	−13.6488	−0.498384
$751$	−19.6031	−0.715326	−0.357663	−	0.933851i	$-0.616426\pi$
$751$	−19.6031	−0.715326	−0.357663	+	0.933851i	$0.616426\pi$
$752$	−2.40638	−0.0877515
$753$	10.0395	0.365861
$754$	−12.4636	−0.453898
$755$	10.5404	0.383603
$756$	2.21261	0.0804720
$757$	−23.9359	−0.869966	−0.434983	−	0.900439i	$-0.643246\pi$
$757$	−23.9359	−0.869966	−0.434983	+	0.900439i	$0.643246\pi$
$758$	−54.5903	−1.98281
$759$	1.14545	0.0415771
$760$	7.93619	0.287876
$761$	−21.5372	−0.780724	−0.390362	−	0.920661i	$-0.627650\pi$
$761$	−21.5372	−0.780724	−0.390362	+	0.920661i	$0.627650\pi$
$762$	32.0435	1.16081
$763$	11.2006	0.405489
$764$	−14.9279	−0.540074
$765$	−4.79598	−0.173399
$766$	−56.7628	−2.05092
$767$	−13.4644	−0.486170
$768$	0.294848	0.0106394
$769$	−1.79926	−0.0648831	−0.0324415	−	0.999474i	$-0.510328\pi$
$769$	−1.79926	−0.0648831	−0.0324415	+	0.999474i	$0.510328\pi$
$770$	0.277910	0.0100152
$771$	−22.1641	−0.798219
$772$	−52.2946	−1.88212
$773$	−11.3973	−0.409934	−0.204967	−	0.978769i	$-0.565709\pi$
$773$	−11.3973	−0.409934	−0.204967	+	0.978769i	$0.565709\pi$
$774$	5.37892	0.193341
$775$	9.86017	0.354188
$776$	7.68061	0.275718
$777$	6.87722	0.246719
$778$	−19.7822	−0.709227
$779$	10.9946	0.393921
$780$	1.77902	0.0636990
$781$	−0.0884922	−0.00316650
$782$	−76.0763	−2.72048
$783$	5.74601	0.205346
$784$	13.2516	0.473272
$785$	−0.567678	−0.0202613
$786$	44.1151	1.57353
$787$	22.0149	0.784747	0.392374	−	0.919806i	$-0.371654\pi$
$787$	22.0149	0.784747	0.392374	+	0.919806i	$0.371654\pi$
$788$	59.7568	2.12875
$789$	26.5442	0.944998
$790$	−12.6161	−0.448859
$791$	0.0891573	0.00317007
$792$	−0.364158	−0.0129398
$793$	8.43426	0.299509
$794$	−40.3525	−1.43206
$795$	−5.12205	−0.181660
$796$	−21.8110	−0.773071
$797$	3.41659	0.121022	0.0605109	−	0.998168i	$-0.480727\pi$
$797$	3.41659	0.121022	0.0605109	+	0.998168i	$0.480727\pi$
$798$	14.0018	0.495658
$799$	−8.38330	−0.296580
$800$	−34.7054	−1.22702
$801$	2.55828	0.0903924
$802$	22.2381	0.785256
$803$	1.92507	0.0679342
$804$	16.7456	0.590570
$805$	2.58753	0.0911986
$806$	−4.68262	−0.164938
$807$	−3.68548	−0.129735
$808$	−19.6882	−0.692628
$809$	38.7625	1.36282	0.681408	−	0.731904i	$-0.261368\pi$
$809$	38.7625	1.36282	0.681408	+	0.731904i	$0.261368\pi$
$810$	−1.42659	−0.0501252
$811$	25.1545	0.883293	0.441647	−	0.897189i	$-0.354395\pi$
$811$	25.1545	0.883293	0.441647	+	0.897189i	$0.354395\pi$
$812$	12.7137	0.446164
$813$	11.7128	0.410786
$814$	−4.34311	−0.152226
$815$	−9.50160	−0.332826
$816$	−15.2637	−0.534336
$817$	19.5694	0.684645
$818$	26.9109	0.940917
$819$	0.817989	0.0285829
$820$	−2.47856	−0.0865551
$821$	−27.1541	−0.947685	−0.473842	−	0.880610i	$-0.657133\pi$
$821$	−27.1541	−0.947685	−0.473842	+	0.880610i	$0.657133\pi$
$822$	25.4569	0.887910
$823$	28.8709	1.00638	0.503188	−	0.864177i	$-0.332160\pi$
$823$	28.8709	1.00638	0.503188	+	0.864177i	$0.332160\pi$
$824$	−1.52908	−0.0532682
$825$	1.08776	0.0378708
$826$	23.8897	0.831230
$827$	−46.9272	−1.63182	−0.815909	−	0.578180i	$-0.803763\pi$
$827$	−46.9272	−1.63182	−0.815909	+	0.578180i	$0.803763\pi$
$828$	−13.0099	−0.452126
$829$	−52.6047	−1.82704	−0.913519	−	0.406797i	$-0.866646\pi$
$829$	−52.6047	−1.82704	−0.913519	+	0.406797i	$0.866646\pi$
$830$	9.84596	0.341758
$831$	25.9954	0.901769
$832$	12.2953	0.426264
$833$	46.1658	1.59955
$834$	8.23258	0.285071
$835$	−7.82617	−0.270836
$836$	−5.08364	−0.175821
$837$	2.15879	0.0746188
$838$	13.7312	0.474337
$839$	−7.13558	−0.246348	−0.123174	−	0.992385i	$-0.539307\pi$
$839$	−7.13558	−0.246348	−0.123174	+	0.992385i	$0.539307\pi$
$840$	−0.822623	−0.0283832
$841$	4.01663	0.138504
$842$	65.3935	2.25361
$843$	10.7280	0.369493
$844$	−3.23947	−0.111507
$845$	0.657691	0.0226253
$846$	−2.49366	−0.0857337
$847$	8.95149	0.307577
$848$	−16.3014	−0.559794
$849$	24.1473	0.828733
$850$	−72.2447	−2.47797
$851$	−40.4373	−1.38617
$852$	1.00509	0.0344338
$853$	21.9247	0.750686	0.375343	−	0.926886i	$-0.377525\pi$
$853$	21.9247	0.750686	0.375343	+	0.926886i	$0.377525\pi$
$854$	−14.9648	−0.512086
$855$	−5.19015	−0.177500
$856$	−25.8381	−0.883129
$857$	7.82737	0.267378	0.133689	−	0.991023i	$-0.457318\pi$
$857$	7.82737	0.267378	0.133689	+	0.991023i	$0.457318\pi$
$858$	−0.516577	−0.0176357
$859$	57.0504	1.94653	0.973266	−	0.229679i	$-0.0737675\pi$
$859$	57.0504	1.94653	0.973266	+	0.229679i	$0.0737675\pi$
$860$	−4.41162	−0.150435
$861$	−1.13964	−0.0388388
$862$	13.3511	0.454739
$863$	−22.6724	−0.771777	−0.385888	−	0.922545i	$-0.626105\pi$
$863$	−22.6724	−0.771777	−0.385888	+	0.922545i	$0.626105\pi$
$864$	−7.59843	−0.258504
$865$	9.57325	0.325500
$866$	31.4218	1.06776
$867$	−36.1755	−1.22858
$868$	4.77658	0.162128
$869$	2.10612	0.0714452
$870$	−8.19720	−0.277911
$871$	6.19072	0.209765
$872$	20.9375	0.709035
$873$	−5.02301	−0.170003
$874$	−82.3289	−2.78482
$875$	5.14713	0.174005
$876$	−21.8648	−0.738745
$877$	17.4965	0.590815	0.295408	−	0.955371i	$-0.404545\pi$
$877$	17.4965	0.590815	0.295408	+	0.955371i	$0.404545\pi$
$878$	−16.3672	−0.552367
$879$	−8.87597	−0.299379
$880$	−0.327857	−0.0110520
$881$	−40.5860	−1.36738	−0.683688	−	0.729774i	$-0.739625\pi$
$881$	−40.5860	−1.36738	−0.683688	+	0.729774i	$0.739625\pi$
$882$	13.7323	0.462389
$883$	29.8928	1.00597	0.502987	−	0.864294i	$-0.332234\pi$
$883$	29.8928	1.00597	0.502987	+	0.864294i	$0.332234\pi$
$884$	19.7249	0.663419
$885$	−8.85540	−0.297671
$886$	−5.55850	−0.186742
$887$	53.0589	1.78154	0.890772	−	0.454451i	$-0.150165\pi$
$887$	53.0589	1.78154	0.890772	+	0.454451i	$0.150165\pi$
$888$	12.8557	0.431410
$889$	−12.0840	−0.405284
$890$	−3.64962	−0.122335
$891$	0.238154	0.00797846
$892$	65.3565	2.18830
$893$	−9.07231	−0.303593
$894$	−51.0271	−1.70660
$895$	11.2223	0.375120
$896$	−9.38463	−0.313519
$897$	−4.80968	−0.160591
$898$	3.67807	0.122739
$899$	12.4045	0.413712
$900$	−12.3547	−0.411822
$901$	−56.7908	−1.89197
$902$	0.719705	0.0239636
$903$	−2.02846	−0.0675028
$904$	0.166664	0.00554315
$905$	−4.82010	−0.160225
$906$	34.7625	1.15491
$907$	−46.3636	−1.53948	−0.769739	−	0.638358i	$-0.779614\pi$
$907$	−46.3636	−1.53948	−0.769739	+	0.638358i	$0.779614\pi$
$908$	28.2710	0.938205
$909$	12.8758	0.427063
$910$	−1.16694	−0.0386835
$911$	22.9717	0.761086	0.380543	−	0.924763i	$-0.375737\pi$
$911$	22.9717	0.761086	0.380543	+	0.924763i	$0.375737\pi$
$912$	−16.5182	−0.546972
$913$	−1.64368	−0.0543978
$914$	7.16344	0.236945
$915$	5.54714	0.183383
$916$	−2.17914	−0.0720009
$917$	−16.6363	−0.549381
$918$	−15.8173	−0.522049
$919$	−58.3269	−1.92403	−0.962014	−	0.273001i	$-0.911984\pi$
$919$	−58.3269	−1.92403	−0.962014	+	0.273001i	$0.911984\pi$
$920$	4.83693	0.159469
$921$	−27.1043	−0.893117
$922$	44.7681	1.47436
$923$	0.371575	0.0122305
$924$	0.526943	0.0173352
$925$	−38.4007	−1.26261
$926$	−78.8869	−2.59239
$927$	1.00000	0.0328443
$928$	−43.6607	−1.43323
$929$	−56.9248	−1.86764	−0.933821	−	0.357741i	$-0.883547\pi$
$929$	−56.9248	−1.86764	−0.933821	+	0.357741i	$0.883547\pi$
$930$	−3.07971	−0.100988
$931$	49.9601	1.63738
$932$	62.3117	2.04109
$933$	18.8025	0.615565
$934$	−16.6920	−0.546180
$935$	−1.14218	−0.0373534
$936$	1.52908	0.0499797
$937$	32.6146	1.06547	0.532737	−	0.846281i	$-0.321164\pi$
$937$	32.6146	1.06547	0.532737	+	0.846281i	$0.321164\pi$
$938$	−10.9841	−0.358645
$939$	−15.8992	−0.518851
$940$	2.04522	0.0667077
$941$	28.6806	0.934961	0.467480	−	0.884003i	$-0.345162\pi$
$941$	28.6806	0.934961	0.467480	+	0.884003i	$0.345162\pi$
$942$	−1.87222	−0.0610003
$943$	6.70095	0.218213
$944$	−28.1832	−0.917285
$945$	0.537984	0.0175006
$946$	1.28101	0.0416493
$947$	22.9610	0.746134	0.373067	−	0.927804i	$-0.378306\pi$
$947$	22.9610	0.746134	0.373067	+	0.927804i	$0.378306\pi$
$948$	−23.9212	−0.776924
$949$	−8.08329	−0.262395
$950$	−78.1824	−2.53657
$951$	−8.36182	−0.271151
$952$	−9.12084	−0.295608
$953$	45.7437	1.48178	0.740892	−	0.671624i	$-0.234403\pi$
$953$	45.7437	1.48178	0.740892	+	0.671624i	$0.234403\pi$
$954$	−16.8927	−0.546922
$955$	−3.62964	−0.117452
$956$	−58.6497	−1.89687
$957$	1.36844	0.0442352
$958$	82.9575	2.68024
$959$	−9.60009	−0.310003
$960$	8.08653	0.260992
$961$	−26.3396	−0.849665
$962$	18.2366	0.587970
$963$	16.8978	0.544523
$964$	−63.8649	−2.05695
$965$	−12.7151	−0.409314
$966$	8.53378	0.274570
$967$	40.6691	1.30783	0.653914	−	0.756569i	$-0.273126\pi$
$967$	40.6691	1.30783	0.653914	+	0.756569i	$0.273126\pi$
$968$	16.7332	0.537826
$969$	−57.5459	−1.84864
$970$	7.16577	0.230079
$971$	26.4735	0.849576	0.424788	−	0.905293i	$-0.360349\pi$
$971$	26.4735	0.849576	0.424788	+	0.905293i	$0.360349\pi$
$972$	−2.70494	−0.0867611
$973$	−3.10461	−0.0995291
$974$	−2.76651	−0.0886446
$975$	−4.56744	−0.146275
$976$	17.6543	0.565101
$977$	25.4988	0.815778	0.407889	−	0.913032i	$-0.366265\pi$
$977$	25.4988	0.815778	0.407889	+	0.913032i	$0.366265\pi$
$978$	−31.3366	−1.00203
$979$	0.609265	0.0194722
$980$	−11.2628	−0.359776
$981$	−13.6929	−0.437179
$982$	55.2806	1.76408
$983$	−54.9073	−1.75127	−0.875635	−	0.482973i	$-0.839557\pi$
$983$	−54.9073	−1.75127	−0.875635	+	0.482973i	$0.839557\pi$
$984$	−2.13035	−0.0679131
$985$	14.5295	0.462949
$986$	−90.8865	−2.89441
$987$	0.940388	0.0299329
$988$	21.3460	0.679107
$989$	11.9271	0.379259
$990$	−0.339748	−0.0107979
$991$	46.7883	1.48628	0.743140	−	0.669136i	$-0.233336\pi$
$991$	46.7883	1.48628	0.743140	+	0.669136i	$0.233336\pi$
$992$	−16.4035	−0.520810
$993$	−18.7500	−0.595013
$994$	−0.659283	−0.0209112
$995$	−5.30322	−0.168123
$996$	18.6688	0.591545
$997$	1.98899	0.0629918	0.0314959	−	0.999504i	$-0.489973\pi$
$997$	1.98899	0.0629918	0.0314959	+	0.999504i	$0.489973\pi$
$998$	−25.8128	−0.817091
$999$	−8.40747	−0.266001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.16909 q^{2} -1.00000 q^{3} +2.70494 q^{4} +0.657691 q^{5} +2.16909 q^{6} -0.817989 q^{7} -1.52908 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16909 q^{2} -1.00000 q^{3} +2.70494 q^{4} +0.657691 q^{5} +2.16909 q^{6} -0.817989 q^{7} -1.52908 q^{8} +1.00000 q^{9} -1.42659 q^{10} +0.238154 q^{11} -2.70494 q^{12} -1.00000 q^{13} +1.77429 q^{14} -0.657691 q^{15} -2.09317 q^{16} -7.29215 q^{17} -2.16909 q^{18} -7.89148 q^{19} +1.77902 q^{20} +0.817989 q^{21} -0.516577 q^{22} -4.80968 q^{23} +1.52908 q^{24} -4.56744 q^{25} +2.16909 q^{26} -1.00000 q^{27} -2.21261 q^{28} -5.74601 q^{29} +1.42659 q^{30} -2.15879 q^{31} +7.59843 q^{32} -0.238154 q^{33} +15.8173 q^{34} -0.537984 q^{35} +2.70494 q^{36} +8.40747 q^{37} +17.1173 q^{38} +1.00000 q^{39} -1.00567 q^{40} -1.39322 q^{41} -1.77429 q^{42} -2.47981 q^{43} +0.644193 q^{44} +0.657691 q^{45} +10.4326 q^{46} +1.14963 q^{47} +2.09317 q^{48} -6.33089 q^{49} +9.90719 q^{50} +7.29215 q^{51} -2.70494 q^{52} +7.78793 q^{53} +2.16909 q^{54} +0.156632 q^{55} +1.25077 q^{56} +7.89148 q^{57} +12.4636 q^{58} +13.4644 q^{59} -1.77902 q^{60} -8.43426 q^{61} +4.68262 q^{62} -0.817989 q^{63} -12.2953 q^{64} -0.657691 q^{65} +0.516577 q^{66} -6.19072 q^{67} -19.7249 q^{68} +4.80968 q^{69} +1.16694 q^{70} -0.371575 q^{71} -1.52908 q^{72} +8.08329 q^{73} -18.2366 q^{74} +4.56744 q^{75} -21.3460 q^{76} -0.194808 q^{77} -2.16909 q^{78} +8.84351 q^{79} -1.37666 q^{80} +1.00000 q^{81} +3.02202 q^{82} -6.90175 q^{83} +2.21261 q^{84} -4.79598 q^{85} +5.37892 q^{86} +5.74601 q^{87} -0.364158 q^{88} +2.55828 q^{89} -1.42659 q^{90} +0.817989 q^{91} -13.0099 q^{92} +2.15879 q^{93} -2.49366 q^{94} -5.19015 q^{95} -7.59843 q^{96} -5.02301 q^{97} +13.7323 q^{98} +0.238154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 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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