LMFDB - Embedded newform 6017.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58511 q^{2} -2.87890 q^{3} +4.68281 q^{4} -1.51557 q^{5} +7.44229 q^{6} +0.161489 q^{7} -6.93538 q^{8} +5.28808 q^{9} +O(q^{10})$	\(q-2.58511 q^{2} -2.87890 q^{3} +4.68281 q^{4} -1.51557 q^{5} +7.44229 q^{6} +0.161489 q^{7} -6.93538 q^{8} +5.28808 q^{9} +3.91792 q^{10} +1.00000 q^{11} -13.4814 q^{12} -6.99617 q^{13} -0.417469 q^{14} +4.36317 q^{15} +8.56312 q^{16} -4.66254 q^{17} -13.6703 q^{18} +4.03748 q^{19} -7.09712 q^{20} -0.464912 q^{21} -2.58511 q^{22} +4.97780 q^{23} +19.9663 q^{24} -2.70305 q^{25} +18.0859 q^{26} -6.58715 q^{27} +0.756225 q^{28} -1.95167 q^{29} -11.2793 q^{30} -0.546934 q^{31} -8.26588 q^{32} -2.87890 q^{33} +12.0532 q^{34} -0.244748 q^{35} +24.7631 q^{36} -3.94217 q^{37} -10.4373 q^{38} +20.1413 q^{39} +10.5110 q^{40} +4.07011 q^{41} +1.20185 q^{42} +5.47625 q^{43} +4.68281 q^{44} -8.01444 q^{45} -12.8682 q^{46} -2.72261 q^{47} -24.6524 q^{48} -6.97392 q^{49} +6.98770 q^{50} +13.4230 q^{51} -32.7618 q^{52} +13.7242 q^{53} +17.0285 q^{54} -1.51557 q^{55} -1.11999 q^{56} -11.6235 q^{57} +5.04528 q^{58} -0.114947 q^{59} +20.4319 q^{60} -2.36507 q^{61} +1.41389 q^{62} +0.853969 q^{63} +4.24200 q^{64} +10.6032 q^{65} +7.44229 q^{66} +4.13899 q^{67} -21.8338 q^{68} -14.3306 q^{69} +0.632702 q^{70} +5.67318 q^{71} -36.6748 q^{72} -14.8910 q^{73} +10.1909 q^{74} +7.78183 q^{75} +18.9068 q^{76} +0.161489 q^{77} -52.0675 q^{78} -7.56851 q^{79} -12.9780 q^{80} +3.09954 q^{81} -10.5217 q^{82} -9.11300 q^{83} -2.17710 q^{84} +7.06640 q^{85} -14.1567 q^{86} +5.61865 q^{87} -6.93538 q^{88} +10.4253 q^{89} +20.7182 q^{90} -1.12981 q^{91} +23.3101 q^{92} +1.57457 q^{93} +7.03827 q^{94} -6.11907 q^{95} +23.7967 q^{96} -6.91061 q^{97} +18.0284 q^{98} +5.28808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.58511	−1.82795	−0.913976	−	0.405769i	$-0.867004\pi$
$2$	−2.58511	−1.82795	−0.913976	+	0.405769i	$0.867004\pi$
$3$	−2.87890	−1.66214	−0.831068	−	0.556172i	$-0.812270\pi$
$3$	−2.87890	−1.66214	−0.831068	+	0.556172i	$0.812270\pi$
$4$	4.68281	2.34141
$5$	−1.51557	−0.677783	−0.338891	−	0.940826i	$-0.610052\pi$
$5$	−1.51557	−0.677783	−0.338891	+	0.940826i	$0.610052\pi$
$6$	7.44229	3.03830
$7$	0.161489	0.0610373	0.0305186	−	0.999534i	$-0.490284\pi$
$7$	0.161489	0.0610373	0.0305186	+	0.999534i	$0.490284\pi$
$8$	−6.93538	−2.45203
$9$	5.28808	1.76269
$10$	3.91792	1.23895
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−13.4814	−3.89173
$13$	−6.99617	−1.94039	−0.970194	−	0.242329i	$-0.922089\pi$
$13$	−6.99617	−1.94039	−0.970194	+	0.242329i	$0.922089\pi$
$14$	−0.417469	−0.111573
$15$	4.36317	1.12657
$16$	8.56312	2.14078
$17$	−4.66254	−1.13083	−0.565417	−	0.824805i	$-0.691285\pi$
$17$	−4.66254	−1.13083	−0.565417	+	0.824805i	$0.691285\pi$
$18$	−13.6703	−3.22212
$19$	4.03748	0.926261	0.463131	−	0.886290i	$-0.346726\pi$
$19$	4.03748	0.926261	0.463131	+	0.886290i	$0.346726\pi$
$20$	−7.09712	−1.58696
$21$	−0.464912	−0.101452
$22$	−2.58511	−0.551148
$23$	4.97780	1.03794	0.518972	−	0.854792i	$-0.326315\pi$
$23$	4.97780	1.03794	0.518972	+	0.854792i	$0.326315\pi$
$24$	19.9663	4.07560
$25$	−2.70305	−0.540611
$26$	18.0859	3.54694
$27$	−6.58715	−1.26770
$28$	0.756225	0.142913
$29$	−1.95167	−0.362415	−0.181208	−	0.983445i	$-0.558001\pi$
$29$	−1.95167	−0.362415	−0.181208	+	0.983445i	$0.558001\pi$
$30$	−11.2793	−2.05931
$31$	−0.546934	−0.0982323	−0.0491162	−	0.998793i	$-0.515640\pi$
$31$	−0.546934	−0.0982323	−0.0491162	+	0.998793i	$0.515640\pi$
$32$	−8.26588	−1.46121
$33$	−2.87890	−0.501153
$34$	12.0532	2.06711
$35$	−0.244748	−0.0413700
$36$	24.7631	4.12718
$37$	−3.94217	−0.648088	−0.324044	−	0.946042i	$-0.605043\pi$
$37$	−3.94217	−0.648088	−0.324044	+	0.946042i	$0.605043\pi$
$38$	−10.4373	−1.69316
$39$	20.1413	3.22519
$40$	10.5110	1.66194
$41$	4.07011	0.635644	0.317822	−	0.948150i	$-0.397048\pi$
$41$	4.07011	0.635644	0.317822	+	0.948150i	$0.397048\pi$
$42$	1.20185	0.185450
$43$	5.47625	0.835120	0.417560	−	0.908649i	$-0.362885\pi$
$43$	5.47625	0.835120	0.417560	+	0.908649i	$0.362885\pi$
$44$	4.68281	0.705961
$45$	−8.01444	−1.19472
$46$	−12.8682	−1.89731
$47$	−2.72261	−0.397134	−0.198567	−	0.980087i	$-0.563629\pi$
$47$	−2.72261	−0.397134	−0.198567	+	0.980087i	$0.563629\pi$
$48$	−24.6524	−3.55826
$49$	−6.97392	−0.996274
$50$	6.98770	0.988210
$51$	13.4230	1.87960
$52$	−32.7618	−4.54324
$53$	13.7242	1.88516	0.942581	−	0.333978i	$-0.108391\pi$
$53$	13.7242	1.88516	0.942581	+	0.333978i	$0.108391\pi$
$54$	17.0285	2.31729
$55$	−1.51557	−0.204359
$56$	−1.11999	−0.149665
$57$	−11.6235	−1.53957
$58$	5.04528	0.662477
$59$	−0.114947	−0.0149648	−0.00748240	−	0.999972i	$-0.502382\pi$
$59$	−0.114947	−0.0149648	−0.00748240	+	0.999972i	$0.502382\pi$
$60$	20.4319	2.63775
$61$	−2.36507	−0.302816	−0.151408	−	0.988471i	$-0.548381\pi$
$61$	−2.36507	−0.302816	−0.151408	+	0.988471i	$0.548381\pi$
$62$	1.41389	0.179564
$63$	0.853969	0.107590
$64$	4.24200	0.530250
$65$	10.6032	1.31516
$66$	7.44229	0.916083
$67$	4.13899	0.505658	0.252829	−	0.967511i	$-0.418639\pi$
$67$	4.13899	0.505658	0.252829	+	0.967511i	$0.418639\pi$
$68$	−21.8338	−2.64774
$69$	−14.3306	−1.72520
$70$	0.632702	0.0756224
$71$	5.67318	0.673282	0.336641	−	0.941633i	$-0.390709\pi$
$71$	5.67318	0.673282	0.336641	+	0.941633i	$0.390709\pi$
$72$	−36.6748	−4.32217
$73$	−14.8910	−1.74286	−0.871430	−	0.490520i	$-0.836807\pi$
$73$	−14.8910	−1.74286	−0.871430	+	0.490520i	$0.836807\pi$
$74$	10.1909	1.18467
$75$	7.78183	0.898568
$76$	18.9068	2.16875
$77$	0.161489	0.0184034
$78$	−52.0675	−5.89549
$79$	−7.56851	−0.851524	−0.425762	−	0.904835i	$-0.639994\pi$
$79$	−7.56851	−0.851524	−0.425762	+	0.904835i	$0.639994\pi$
$80$	−12.9780	−1.45098
$81$	3.09954	0.344393
$82$	−10.5217	−1.16193
$83$	−9.11300	−1.00028	−0.500141	−	0.865944i	$-0.666719\pi$
$83$	−9.11300	−1.00028	−0.500141	+	0.865944i	$0.666719\pi$
$84$	−2.17710	−0.237541
$85$	7.06640	0.766459
$86$	−14.1567	−1.52656
$87$	5.61865	0.602383
$88$	−6.93538	−0.739314
$89$	10.4253	1.10508	0.552542	−	0.833485i	$-0.313658\pi$
$89$	10.4253	1.10508	0.552542	+	0.833485i	$0.313658\pi$
$90$	20.7182	2.18389
$91$	−1.12981	−0.118436
$92$	23.3101	2.43025
$93$	1.57457	0.163275
$94$	7.03827	0.725942
$95$	−6.11907	−0.627804
$96$	23.7967	2.42874
$97$	−6.91061	−0.701667	−0.350833	−	0.936438i	$-0.614102\pi$
$97$	−6.91061	−0.701667	−0.350833	+	0.936438i	$0.614102\pi$
$98$	18.0284	1.82114
$99$	5.28808	0.531472
$100$	−12.6579	−1.26579
$101$	−5.03261	−0.500763	−0.250382	−	0.968147i	$-0.580556\pi$
$101$	−5.03261	−0.500763	−0.250382	+	0.968147i	$0.580556\pi$
$102$	−34.7000	−3.43581
$103$	2.72640	0.268641	0.134320	−	0.990938i	$-0.457115\pi$
$103$	2.72640	0.268641	0.134320	+	0.990938i	$0.457115\pi$
$104$	48.5211	4.75788
$105$	0.704606	0.0687625
$106$	−35.4786	−3.44598
$107$	13.6287	1.31753	0.658766	−	0.752348i	$-0.271079\pi$
$107$	13.6287	1.31753	0.658766	+	0.752348i	$0.271079\pi$
$108$	−30.8464	−2.96820
$109$	−15.2555	−1.46122	−0.730608	−	0.682797i	$-0.760763\pi$
$109$	−15.2555	−1.46122	−0.730608	+	0.682797i	$0.760763\pi$
$110$	3.91792	0.373559
$111$	11.3491	1.07721
$112$	1.38285	0.130667
$113$	5.26182	0.494990	0.247495	−	0.968889i	$-0.420393\pi$
$113$	5.26182	0.494990	0.247495	+	0.968889i	$0.420393\pi$
$114$	30.0481	2.81426
$115$	−7.54419	−0.703500
$116$	−9.13929	−0.848562
$117$	−36.9963	−3.42031
$118$	0.297151	0.0273549
$119$	−0.752952	−0.0690230
$120$	−30.2603	−2.76237
$121$	1.00000	0.0909091
$122$	6.11397	0.553533
$123$	−11.7175	−1.05653
$124$	−2.56119	−0.230002
$125$	11.6745	1.04420
$126$	−2.20761	−0.196669
$127$	0.925858	0.0821566	0.0410783	−	0.999156i	$-0.486921\pi$
$127$	0.925858	0.0821566	0.0410783	+	0.999156i	$0.486921\pi$
$128$	5.56571	0.491944
$129$	−15.7656	−1.38808
$130$	−27.4104	−2.40405
$131$	10.4749	0.915192	0.457596	−	0.889160i	$-0.348711\pi$
$131$	10.4749	0.915192	0.457596	+	0.889160i	$0.348711\pi$
$132$	−13.4814	−1.17340
$133$	0.652010	0.0565365
$134$	−10.6997	−0.924318
$135$	9.98328	0.859224
$136$	32.3365	2.77283
$137$	−3.09197	−0.264165	−0.132082	−	0.991239i	$-0.542166\pi$
$137$	−3.09197	−0.264165	−0.132082	+	0.991239i	$0.542166\pi$
$138$	37.0462	3.15358
$139$	14.6916	1.24612	0.623061	−	0.782173i	$-0.285889\pi$
$139$	14.6916	1.24612	0.623061	+	0.782173i	$0.285889\pi$
$140$	−1.14611	−0.0968640
$141$	7.83814	0.660090
$142$	−14.6658	−1.23073
$143$	−6.99617	−0.585049
$144$	45.2824	3.77354
$145$	2.95788	0.245639
$146$	38.4949	3.18586
$147$	20.0772	1.65594
$148$	−18.4604	−1.51744
$149$	8.05954	0.660263	0.330132	−	0.943935i	$-0.392907\pi$
$149$	8.05954	0.660263	0.330132	+	0.943935i	$0.392907\pi$
$150$	−20.1169	−1.64254
$151$	7.99433	0.650570	0.325285	−	0.945616i	$-0.394540\pi$
$151$	7.99433	0.650570	0.325285	+	0.945616i	$0.394540\pi$
$152$	−28.0014	−2.27122
$153$	−24.6559	−1.99331
$154$	−0.417469	−0.0336406
$155$	0.828916	0.0665801
$156$	94.3179	7.55148
$157$	−9.44993	−0.754187	−0.377093	−	0.926175i	$-0.623076\pi$
$157$	−9.44993	−0.754187	−0.377093	+	0.926175i	$0.623076\pi$
$158$	19.5655	1.55654
$159$	−39.5106	−3.13339
$160$	12.5275	0.990386
$161$	0.803862	0.0633532
$162$	−8.01266	−0.629534
$163$	8.41794	0.659344	0.329672	−	0.944096i	$-0.393062\pi$
$163$	8.41794	0.659344	0.329672	+	0.944096i	$0.393062\pi$
$164$	19.0596	1.48830
$165$	4.36317	0.339672
$166$	23.5582	1.82847
$167$	−19.7872	−1.53118	−0.765590	−	0.643329i	$-0.777553\pi$
$167$	−19.7872	−1.53118	−0.765590	+	0.643329i	$0.777553\pi$
$168$	3.22434	0.248764
$169$	35.9464	2.76511
$170$	−18.2675	−1.40105
$171$	21.3505	1.63271
$172$	25.6442	1.95536
$173$	−7.68459	−0.584249	−0.292124	−	0.956380i	$-0.594362\pi$
$173$	−7.68459	−0.584249	−0.292124	+	0.956380i	$0.594362\pi$
$174$	−14.5249	−1.10113
$175$	−0.436515	−0.0329974
$176$	8.56312	0.645469
$177$	0.330921	0.0248735
$178$	−26.9507	−2.02004
$179$	10.5445	0.788135	0.394067	−	0.919082i	$-0.371068\pi$
$179$	10.5445	0.788135	0.394067	+	0.919082i	$0.371068\pi$
$180$	−37.5301	−2.79733
$181$	15.0626	1.11959	0.559796	−	0.828630i	$-0.310879\pi$
$181$	15.0626	1.11959	0.559796	+	0.828630i	$0.310879\pi$
$182$	2.92068	0.216495
$183$	6.80880	0.503321
$184$	−34.5229	−2.54506
$185$	5.97462	0.439263
$186$	−4.07044	−0.298459
$187$	−4.66254	−0.340959
$188$	−12.7495	−0.929852
$189$	−1.06376	−0.0773769
$190$	15.8185	1.14759
$191$	−11.1598	−0.807496	−0.403748	−	0.914870i	$-0.632293\pi$
$191$	−11.1598	−0.807496	−0.403748	+	0.914870i	$0.632293\pi$
$192$	−12.2123	−0.881347
$193$	−2.87338	−0.206830	−0.103415	−	0.994638i	$-0.532977\pi$
$193$	−2.87338	−0.206830	−0.103415	+	0.994638i	$0.532977\pi$
$194$	17.8647	1.28261
$195$	−30.5255	−2.18598
$196$	−32.6576	−2.33268
$197$	1.34645	0.0959306	0.0479653	−	0.998849i	$-0.484726\pi$
$197$	1.34645	0.0959306	0.0479653	+	0.998849i	$0.484726\pi$
$198$	−13.6703	−0.971505
$199$	−9.04600	−0.641254	−0.320627	−	0.947206i	$-0.603894\pi$
$199$	−9.04600	−0.641254	−0.320627	+	0.947206i	$0.603894\pi$
$200$	18.7467	1.32559
$201$	−11.9157	−0.840471
$202$	13.0099	0.915371
$203$	−0.315174	−0.0221208
$204$	62.8575	4.40090
$205$	−6.16853	−0.430829
$206$	−7.04807	−0.491062
$207$	26.3230	1.82957
$208$	−59.9090	−4.15394
$209$	4.03748	0.279278
$210$	−1.82149	−0.125695
$211$	9.37452	0.645369	0.322684	−	0.946507i	$-0.395415\pi$
$211$	9.37452	0.645369	0.322684	+	0.946507i	$0.395415\pi$
$212$	64.2678	4.41393
$213$	−16.3325	−1.11909
$214$	−35.2316	−2.40838
$215$	−8.29962	−0.566030
$216$	45.6844	3.10843
$217$	−0.0883242	−0.00599583
$218$	39.4373	2.67103
$219$	42.8697	2.89687
$220$	−7.09712	−0.478488
$221$	32.6200	2.19426
$222$	−29.3387	−1.96909
$223$	20.9816	1.40503	0.702515	−	0.711668i	$-0.252060\pi$
$223$	20.9816	1.40503	0.702515	+	0.711668i	$0.252060\pi$
$224$	−1.33485	−0.0891886
$225$	−14.2940	−0.952931
$226$	−13.6024	−0.904818
$227$	3.20659	0.212829	0.106415	−	0.994322i	$-0.466063\pi$
$227$	3.20659	0.212829	0.106415	+	0.994322i	$0.466063\pi$
$228$	−54.4307	−3.60476
$229$	12.1614	0.803651	0.401825	−	0.915716i	$-0.368376\pi$
$229$	12.1614	0.803651	0.401825	+	0.915716i	$0.368376\pi$
$230$	19.5026	1.28596
$231$	−0.464912	−0.0305890
$232$	13.5355	0.888652
$233$	12.3003	0.805817	0.402909	−	0.915240i	$-0.367999\pi$
$233$	12.3003	0.805817	0.402909	+	0.915240i	$0.367999\pi$
$234$	95.6396	6.25216
$235$	4.12631	0.269171
$236$	−0.538274	−0.0350387
$237$	21.7890	1.41535
$238$	1.94647	0.126171
$239$	18.9956	1.22872	0.614360	−	0.789026i	$-0.289414\pi$
$239$	18.9956	1.22872	0.614360	+	0.789026i	$0.289414\pi$
$240$	37.3624	2.41173
$241$	22.0061	1.41754	0.708769	−	0.705440i	$-0.249251\pi$
$241$	22.0061	1.41754	0.708769	+	0.705440i	$0.249251\pi$
$242$	−2.58511	−0.166177
$243$	10.8382	0.695271
$244$	−11.0752	−0.709016
$245$	10.5695	0.675257
$246$	30.2909	1.93128
$247$	−28.2469	−1.79731
$248$	3.79320	0.240868
$249$	26.2354	1.66260
$250$	−30.1799	−1.90875
$251$	−19.7167	−1.24451	−0.622253	−	0.782816i	$-0.713783\pi$
$251$	−19.7167	−1.24451	−0.622253	+	0.782816i	$0.713783\pi$
$252$	3.99898	0.251912
$253$	4.97780	0.312952
$254$	−2.39345	−0.150178
$255$	−20.3435	−1.27396
$256$	−22.8720	−1.42950
$257$	3.09154	0.192845	0.0964225	−	0.995340i	$-0.469260\pi$
$257$	3.09154	0.192845	0.0964225	+	0.995340i	$0.469260\pi$
$258$	40.7558	2.53735
$259$	−0.636618	−0.0395575
$260$	49.6527	3.07933
$261$	−10.3206	−0.638827
$262$	−27.0787	−1.67293
$263$	21.5974	1.33175	0.665876	−	0.746062i	$-0.268058\pi$
$263$	21.5974	1.33175	0.665876	+	0.746062i	$0.268058\pi$
$264$	19.9663	1.22884
$265$	−20.7999	−1.27773
$266$	−1.68552	−0.103346
$267$	−30.0135	−1.83680
$268$	19.3821	1.18395
$269$	13.3903	0.816419	0.408210	−	0.912888i	$-0.366153\pi$
$269$	13.3903	0.816419	0.408210	+	0.912888i	$0.366153\pi$
$270$	−25.8079	−1.57062
$271$	−6.57861	−0.399622	−0.199811	−	0.979834i	$-0.564033\pi$
$271$	−6.57861	−0.399622	−0.199811	+	0.979834i	$0.564033\pi$
$272$	−39.9259	−2.42086
$273$	3.25261	0.196857
$274$	7.99308	0.482880
$275$	−2.70305	−0.163000
$276$	−67.1075	−4.03940
$277$	−22.2248	−1.33536	−0.667678	−	0.744450i	$-0.732712\pi$
$277$	−22.2248	−1.33536	−0.667678	+	0.744450i	$0.732712\pi$
$278$	−37.9794	−2.27785
$279$	−2.89223	−0.173153
$280$	1.69742	0.101440
$281$	−10.1465	−0.605288	−0.302644	−	0.953104i	$-0.597869\pi$
$281$	−10.1465	−0.605288	−0.302644	+	0.953104i	$0.597869\pi$
$282$	−20.2625	−1.20661
$283$	2.43092	0.144503	0.0722515	−	0.997386i	$-0.476982\pi$
$283$	2.43092	0.144503	0.0722515	+	0.997386i	$0.476982\pi$
$284$	26.5664	1.57643
$285$	17.6162	1.04349
$286$	18.0859	1.06944
$287$	0.657280	0.0387980
$288$	−43.7106	−2.57567
$289$	4.73932	0.278784
$290$	−7.64646	−0.449016
$291$	19.8950	1.16626
$292$	−69.7318	−4.08074
$293$	8.83366	0.516068	0.258034	−	0.966136i	$-0.416925\pi$
$293$	8.83366	0.516068	0.258034	+	0.966136i	$0.416925\pi$
$294$	−51.9019	−3.02698
$295$	0.174210	0.0101429
$296$	27.3404	1.58913
$297$	−6.58715	−0.382225
$298$	−20.8348	−1.20693
$299$	−34.8255	−2.01401
$300$	36.4409	2.10391
$301$	0.884356	0.0509735
$302$	−20.6663	−1.18921
$303$	14.4884	0.832336
$304$	34.5734	1.98292
$305$	3.58442	0.205243
$306$	63.7383	3.64368
$307$	20.7216	1.18265	0.591323	−	0.806434i	$-0.298606\pi$
$307$	20.7216	1.18265	0.591323	+	0.806434i	$0.298606\pi$
$308$	0.756225	0.0430899
$309$	−7.84905	−0.446517
$310$	−2.14284	−0.121705
$311$	3.17697	0.180149	0.0900747	−	0.995935i	$-0.471289\pi$
$311$	3.17697	0.180149	0.0900747	+	0.995935i	$0.471289\pi$
$312$	−139.687	−7.90825
$313$	32.6979	1.84819	0.924096	−	0.382160i	$-0.124820\pi$
$313$	32.6979	1.84819	0.924096	+	0.382160i	$0.124820\pi$
$314$	24.4291	1.37862
$315$	−1.29425	−0.0729226
$316$	−35.4419	−1.99376
$317$	1.74848	0.0982045	0.0491022	−	0.998794i	$-0.484364\pi$
$317$	1.74848	0.0982045	0.0491022	+	0.998794i	$0.484364\pi$
$318$	102.139	5.72769
$319$	−1.95167	−0.109272
$320$	−6.42904	−0.359394
$321$	−39.2356	−2.18992
$322$	−2.07808	−0.115807
$323$	−18.8249	−1.04745
$324$	14.5146	0.806364
$325$	18.9110	1.04899
$326$	−21.7613	−1.20525
$327$	43.9192	2.42874
$328$	−28.2278	−1.55862
$329$	−0.439674	−0.0242400
$330$	−11.2793	−0.620905
$331$	13.6593	0.750782	0.375391	−	0.926866i	$-0.377508\pi$
$331$	13.6593	0.750782	0.375391	+	0.926866i	$0.377508\pi$
$332$	−42.6745	−2.34207
$333$	−20.8465	−1.14238
$334$	51.1522	2.79892
$335$	−6.27291	−0.342726
$336$	−3.98110	−0.217187
$337$	29.2215	1.59180	0.795898	−	0.605431i	$-0.206999\pi$
$337$	29.2215	1.59180	0.795898	+	0.605431i	$0.206999\pi$
$338$	−92.9255	−5.05448
$339$	−15.1483	−0.822741
$340$	33.0907	1.79459
$341$	−0.546934	−0.0296182
$342$	−55.1935	−2.98452
$343$	−2.25664	−0.121847
$344$	−37.9799	−2.04774
$345$	21.7190	1.16931
$346$	19.8655	1.06798
$347$	5.25371	0.282034	0.141017	−	0.990007i	$-0.454963\pi$
$347$	5.25371	0.282034	0.141017	+	0.990007i	$0.454963\pi$
$348$	26.3111	1.41042
$349$	−29.1507	−1.56040	−0.780200	−	0.625531i	$-0.784882\pi$
$349$	−29.1507	−1.56040	−0.780200	+	0.625531i	$0.784882\pi$
$350$	1.12844	0.0603177
$351$	46.0848	2.45983
$352$	−8.26588	−0.440573
$353$	−11.8078	−0.628467	−0.314234	−	0.949346i	$-0.601748\pi$
$353$	−11.8078	−0.628467	−0.314234	+	0.949346i	$0.601748\pi$
$354$	−0.855467	−0.0454676
$355$	−8.59809	−0.456339
$356$	48.8199	2.58745
$357$	2.16768	0.114726
$358$	−27.2588	−1.44067
$359$	−37.5797	−1.98338	−0.991689	−	0.128656i	$-0.958934\pi$
$359$	−37.5797	−1.98338	−0.991689	+	0.128656i	$0.958934\pi$
$360$	55.5832	2.92949
$361$	−2.69877	−0.142040
$362$	−38.9385	−2.04656
$363$	−2.87890	−0.151103
$364$	−5.29068	−0.277307
$365$	22.5683	1.18128
$366$	−17.6015	−0.920047
$367$	21.8766	1.14195	0.570975	−	0.820967i	$-0.306565\pi$
$367$	21.8766	1.14195	0.570975	+	0.820967i	$0.306565\pi$
$368$	42.6255	2.22201
$369$	21.5231	1.12045
$370$	−15.4451	−0.802951
$371$	2.21631	0.115065
$372$	7.37342	0.382294
$373$	−16.3409	−0.846100	−0.423050	−	0.906106i	$-0.639041\pi$
$373$	−16.3409	−0.846100	−0.423050	+	0.906106i	$0.639041\pi$
$374$	12.0532	0.623257
$375$	−33.6097	−1.73560
$376$	18.8824	0.973783
$377$	13.6542	0.703226
$378$	2.74993	0.141441
$379$	23.9542	1.23044	0.615222	−	0.788354i	$-0.289066\pi$
$379$	23.9542	1.23044	0.615222	+	0.788354i	$0.289066\pi$
$380$	−28.6545	−1.46994
$381$	−2.66545	−0.136555
$382$	28.8494	1.47606
$383$	9.53268	0.487097	0.243549	−	0.969889i	$-0.421688\pi$
$383$	9.53268	0.487097	0.243549	+	0.969889i	$0.421688\pi$
$384$	−16.0231	−0.817677
$385$	−0.244748	−0.0124735
$386$	7.42801	0.378076
$387$	28.9588	1.47206
$388$	−32.3611	−1.64289
$389$	17.4434	0.884417	0.442209	−	0.896912i	$-0.354195\pi$
$389$	17.4434	0.884417	0.442209	+	0.896912i	$0.354195\pi$
$390$	78.9119	3.99586
$391$	−23.2092	−1.17374
$392$	48.3668	2.44289
$393$	−30.1561	−1.52117
$394$	−3.48073	−0.175357
$395$	11.4706	0.577148
$396$	24.7631	1.24439
$397$	−21.0785	−1.05790	−0.528950	−	0.848653i	$-0.677414\pi$
$397$	−21.0785	−1.05790	−0.528950	+	0.848653i	$0.677414\pi$
$398$	23.3849	1.17218
$399$	−1.87707	−0.0939712
$400$	−23.1466	−1.15733
$401$	−8.79432	−0.439167	−0.219584	−	0.975594i	$-0.570470\pi$
$401$	−8.79432	−0.439167	−0.219584	+	0.975594i	$0.570470\pi$
$402$	30.8035	1.53634
$403$	3.82645	0.190609
$404$	−23.5668	−1.17249
$405$	−4.69756	−0.233424
$406$	0.814759	0.0404358
$407$	−3.94217	−0.195406
$408$	−93.0937	−4.60882
$409$	−22.7627	−1.12554	−0.562772	−	0.826612i	$-0.690265\pi$
$409$	−22.7627	−1.12554	−0.562772	+	0.826612i	$0.690265\pi$
$410$	15.9463	0.787534
$411$	8.90147	0.439077
$412$	12.7672	0.628997
$413$	−0.0185627	−0.000913411 0
$414$	−68.0479	−3.34437
$415$	13.8114	0.677974
$416$	57.8295	2.83532
$417$	−42.2956	−2.07122
$418$	−10.4373	−0.510507
$419$	−7.39567	−0.361302	−0.180651	−	0.983547i	$-0.557820\pi$
$419$	−7.39567	−0.361302	−0.180651	+	0.983547i	$0.557820\pi$
$420$	3.29954	0.161001
$421$	14.3276	0.698285	0.349143	−	0.937070i	$-0.386473\pi$
$421$	14.3276	0.698285	0.349143	+	0.937070i	$0.386473\pi$
$422$	−24.2342	−1.17970
$423$	−14.3974	−0.700025
$424$	−95.1824	−4.62247
$425$	12.6031	0.611341
$426$	42.2214	2.04564
$427$	−0.381934	−0.0184831
$428$	63.8205	3.08488
$429$	20.1413	0.972431
$430$	21.4555	1.03467
$431$	8.81640	0.424671	0.212336	−	0.977197i	$-0.431893\pi$
$431$	8.81640	0.424671	0.212336	+	0.977197i	$0.431893\pi$
$432$	−56.4066	−2.71386
$433$	−13.3556	−0.641829	−0.320915	−	0.947108i	$-0.603990\pi$
$433$	−13.3556	−0.641829	−0.320915	+	0.947108i	$0.603990\pi$
$434$	0.228328	0.0109601
$435$	−8.51545	−0.408285
$436$	−71.4388	−3.42130
$437$	20.0978	0.961406
$438$	−110.823	−5.29534
$439$	1.22712	0.0585675	0.0292837	−	0.999571i	$-0.490677\pi$
$439$	1.22712	0.0585675	0.0292837	+	0.999571i	$0.490677\pi$
$440$	10.5110	0.501094
$441$	−36.8786	−1.75613
$442$	−84.3263	−4.01099
$443$	−34.7240	−1.64979	−0.824894	−	0.565288i	$-0.808765\pi$
$443$	−34.7240	−1.64979	−0.824894	+	0.565288i	$0.808765\pi$
$444$	53.1458	2.52219
$445$	−15.8003	−0.749006
$446$	−54.2398	−2.56833
$447$	−23.2026	−1.09745
$448$	0.685038	0.0323650
$449$	−11.6811	−0.551266	−0.275633	−	0.961263i	$-0.588887\pi$
$449$	−11.6811	−0.551266	−0.275633	+	0.961263i	$0.588887\pi$
$450$	36.9515	1.74191
$451$	4.07011	0.191654
$452$	24.6401	1.15897
$453$	−23.0149	−1.08133
$454$	−8.28941	−0.389041
$455$	1.71230	0.0802739
$456$	80.6134	3.77507
$457$	−2.17391	−0.101691	−0.0508456	−	0.998707i	$-0.516192\pi$
$457$	−2.17391	−0.101691	−0.0508456	+	0.998707i	$0.516192\pi$
$458$	−31.4387	−1.46903
$459$	30.7129	1.43356
$460$	−35.3281	−1.64718
$461$	1.29809	0.0604579	0.0302290	−	0.999543i	$-0.490376\pi$
$461$	1.29809	0.0604579	0.0302290	+	0.999543i	$0.490376\pi$
$462$	1.20185	0.0559152
$463$	−2.86111	−0.132967	−0.0664834	−	0.997788i	$-0.521178\pi$
$463$	−2.86111	−0.132967	−0.0664834	+	0.997788i	$0.521178\pi$
$464$	−16.7123	−0.775851
$465$	−2.38637	−0.110665
$466$	−31.7976	−1.47299
$467$	0.427463	0.0197806	0.00989032	−	0.999951i	$-0.496852\pi$
$467$	0.427463	0.0197806	0.00989032	+	0.999951i	$0.496852\pi$
$468$	−173.247	−8.00833
$469$	0.668403	0.0308640
$470$	−10.6670	−0.492031
$471$	27.2054	1.25356
$472$	0.797200	0.0366941
$473$	5.47625	0.251798
$474$	−56.3271	−2.58719
$475$	−10.9135	−0.500747
$476$	−3.52593	−0.161611
$477$	72.5746	3.32296
$478$	−49.1057	−2.24604
$479$	14.1486	0.646468	0.323234	−	0.946319i	$-0.395230\pi$
$479$	14.1486	0.646468	0.323234	+	0.946319i	$0.395230\pi$
$480$	−36.0654	−1.64615
$481$	27.5801	1.25754
$482$	−56.8883	−2.59119
$483$	−2.31424	−0.105302
$484$	4.68281	0.212855
$485$	10.4735	0.475577
$486$	−28.0180	−1.27092
$487$	−17.3031	−0.784076	−0.392038	−	0.919949i	$-0.628230\pi$
$487$	−17.3031	−0.784076	−0.392038	+	0.919949i	$0.628230\pi$
$488$	16.4027	0.742513
$489$	−24.2344	−1.09592
$490$	−27.3232	−1.23434
$491$	8.70093	0.392667	0.196334	−	0.980537i	$-0.437096\pi$
$491$	8.70093	0.392667	0.196334	+	0.980537i	$0.437096\pi$
$492$	−54.8706	−2.47376
$493$	9.09973	0.409831
$494$	73.0214	3.28539
$495$	−8.01444	−0.360222
$496$	−4.68346	−0.210294
$497$	0.916159	0.0410953
$498$	−67.8216	−3.03916
$499$	−16.8790	−0.755606	−0.377803	−	0.925886i	$-0.623320\pi$
$499$	−16.8790	−0.755606	−0.377803	+	0.925886i	$0.623320\pi$
$500$	54.6695	2.44490
$501$	56.9654	2.54503
$502$	50.9699	2.27490
$503$	−31.8644	−1.42076	−0.710382	−	0.703816i	$-0.751478\pi$
$503$	−31.8644	−1.42076	−0.710382	+	0.703816i	$0.751478\pi$
$504$	−5.92260	−0.263814
$505$	7.62726	0.339409
$506$	−12.8682	−0.572060
$507$	−103.486	−4.59598
$508$	4.33562	0.192362
$509$	19.5984	0.868684	0.434342	−	0.900748i	$-0.356981\pi$
$509$	19.5984	0.868684	0.434342	+	0.900748i	$0.356981\pi$
$510$	52.5902	2.32873
$511$	−2.40474	−0.106379
$512$	47.9953	2.12111
$513$	−26.5955	−1.17422
$514$	−7.99198	−0.352511
$515$	−4.13205	−0.182080
$516$	−73.8273	−3.25006
$517$	−2.72261	−0.119740
$518$	1.64573	0.0723093
$519$	22.1232	0.971100
$520$	−73.5370	−3.22481
$521$	−43.8426	−1.92078	−0.960389	−	0.278662i	$-0.910109\pi$
$521$	−43.8426	−1.92078	−0.960389	+	0.278662i	$0.910109\pi$
$522$	26.6798	1.16774
$523$	−9.32950	−0.407950	−0.203975	−	0.978976i	$-0.565386\pi$
$523$	−9.32950	−0.407950	−0.203975	+	0.978976i	$0.565386\pi$
$524$	49.0518	2.14284
$525$	1.25668	0.0548462
$526$	−55.8317	−2.43438
$527$	2.55011	0.111084
$528$	−24.6524	−1.07286
$529$	1.77849	0.0773258
$530$	53.7702	2.33563
$531$	−0.607848	−0.0263783
$532$	3.05324	0.132375
$533$	−28.4752	−1.23340
$534$	77.5884	3.35758
$535$	−20.6552	−0.893000
$536$	−28.7054	−1.23989
$537$	−30.3567	−1.30999
$538$	−34.6154	−1.49237
$539$	−6.97392	−0.300388
$540$	46.7498	2.01179
$541$	5.07859	0.218345	0.109173	−	0.994023i	$-0.465180\pi$
$541$	5.07859	0.218345	0.109173	+	0.994023i	$0.465180\pi$
$542$	17.0065	0.730490
$543$	−43.3637	−1.86091
$544$	38.5400	1.65239
$545$	23.1208	0.990386
$546$	−8.40836	−0.359845
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−14.4791	−0.618517
$549$	−12.5067	−0.533772
$550$	6.98770	0.297957
$551$	−7.87981	−0.335691
$552$	99.3881	4.23024
$553$	−1.22223	−0.0519747
$554$	57.4535	2.44097
$555$	−17.2003	−0.730114
$556$	68.7979	2.91768
$557$	38.7081	1.64012	0.820058	−	0.572280i	$-0.193941\pi$
$557$	38.7081	1.64012	0.820058	+	0.572280i	$0.193941\pi$
$558$	7.47675	0.316516
$559$	−38.3128	−1.62046
$560$	−2.09581	−0.0885641
$561$	13.4230	0.566720
$562$	26.2298	1.10644
$563$	13.0177	0.548632	0.274316	−	0.961640i	$-0.411549\pi$
$563$	13.0177	0.548632	0.274316	+	0.961640i	$0.411549\pi$
$564$	36.7045	1.54554
$565$	−7.97464	−0.335496
$566$	−6.28420	−0.264144
$567$	0.500543	0.0210208
$568$	−39.3456	−1.65091
$569$	−1.88665	−0.0790925	−0.0395462	−	0.999218i	$-0.512591\pi$
$569$	−1.88665	−0.0790925	−0.0395462	+	0.999218i	$0.512591\pi$
$570$	−45.5399	−1.90746
$571$	−0.986817	−0.0412970	−0.0206485	−	0.999787i	$-0.506573\pi$
$571$	−0.986817	−0.0412970	−0.0206485	+	0.999787i	$0.506573\pi$
$572$	−32.7618	−1.36984
$573$	32.1280	1.34217
$574$	−1.69914	−0.0709209
$575$	−13.4553	−0.561123
$576$	22.4320	0.934667
$577$	15.2056	0.633019	0.316510	−	0.948589i	$-0.397489\pi$
$577$	15.2056	0.633019	0.316510	+	0.948589i	$0.397489\pi$
$578$	−12.2517	−0.509603
$579$	8.27217	0.343780
$580$	13.8512	0.575140
$581$	−1.47165	−0.0610545
$582$	−51.4308	−2.13188
$583$	13.7242	0.568398
$584$	103.275	4.27354
$585$	56.0704	2.31823
$586$	−22.8360	−0.943347
$587$	−14.1367	−0.583484	−0.291742	−	0.956497i	$-0.594235\pi$
$587$	−14.1367	−0.583484	−0.291742	+	0.956497i	$0.594235\pi$
$588$	94.0180	3.87724
$589$	−2.20824	−0.0909888
$590$	−0.450352	−0.0185407
$591$	−3.87630	−0.159450
$592$	−33.7572	−1.38741
$593$	33.4461	1.37347	0.686733	−	0.726910i	$-0.259044\pi$
$593$	33.4461	1.37347	0.686733	+	0.726910i	$0.259044\pi$
$594$	17.0285	0.698690
$595$	1.14115	0.0467826
$596$	37.7413	1.54595
$597$	26.0425	1.06585
$598$	90.0280	3.68152
$599$	31.4078	1.28329	0.641645	−	0.767002i	$-0.278252\pi$
$599$	31.4078	1.28329	0.641645	+	0.767002i	$0.278252\pi$
$600$	−53.9699	−2.20331
$601$	−34.3757	−1.40222	−0.701108	−	0.713055i	$-0.747311\pi$
$601$	−34.3757	−1.40222	−0.701108	+	0.713055i	$0.747311\pi$
$602$	−2.28616	−0.0931770
$603$	21.8873	0.891319
$604$	37.4360	1.52325
$605$	−1.51557	−0.0616166
$606$	−37.4541	−1.52147
$607$	−17.9097	−0.726931	−0.363466	−	0.931608i	$-0.618407\pi$
$607$	−17.9097	−0.726931	−0.363466	+	0.931608i	$0.618407\pi$
$608$	−33.3733	−1.35347
$609$	0.907354	0.0367678
$610$	−9.26614	−0.375175
$611$	19.0479	0.770594
$612$	−115.459	−4.66715
$613$	16.8330	0.679879	0.339939	−	0.940447i	$-0.389593\pi$
$613$	16.8330	0.679879	0.339939	+	0.940447i	$0.389593\pi$
$614$	−53.5678	−2.16182
$615$	17.7586	0.716096
$616$	−1.11999	−0.0451257
$617$	41.4502	1.66872	0.834360	−	0.551219i	$-0.185837\pi$
$617$	41.4502	1.66872	0.834360	+	0.551219i	$0.185837\pi$
$618$	20.2907	0.816211
$619$	−26.6160	−1.06979	−0.534894	−	0.844919i	$-0.679649\pi$
$619$	−26.6160	−1.06979	−0.534894	+	0.844919i	$0.679649\pi$
$620$	3.88166	0.155891
$621$	−32.7895	−1.31580
$622$	−8.21283	−0.329305
$623$	1.68358	0.0674513
$624$	172.472	6.90442
$625$	−4.17823	−0.167129
$626$	−84.5277	−3.37841
$627$	−11.6235	−0.464198
$628$	−44.2523	−1.76586
$629$	18.3805	0.732879
$630$	3.34578	0.133299
$631$	−44.0330	−1.75293	−0.876463	−	0.481468i	$-0.840104\pi$
$631$	−44.0330	−1.75293	−0.876463	+	0.481468i	$0.840104\pi$
$632$	52.4905	2.08796
$633$	−26.9883	−1.07269
$634$	−4.52002	−0.179513
$635$	−1.40320	−0.0556843
$636$	−185.021	−7.33655
$637$	48.7907	1.93316
$638$	5.04528	0.199744
$639$	30.0002	1.18679
$640$	−8.43521	−0.333431
$641$	−20.5714	−0.812521	−0.406260	−	0.913757i	$-0.633167\pi$
$641$	−20.5714	−0.812521	−0.406260	+	0.913757i	$0.633167\pi$
$642$	101.428	4.00306
$643$	43.0152	1.69635	0.848177	−	0.529713i	$-0.177700\pi$
$643$	43.0152	1.69635	0.848177	+	0.529713i	$0.177700\pi$
$644$	3.76434	0.148336
$645$	23.8938	0.940818
$646$	48.6646	1.91468
$647$	−7.20143	−0.283117	−0.141559	−	0.989930i	$-0.545211\pi$
$647$	−7.20143	−0.283117	−0.141559	+	0.989930i	$0.545211\pi$
$648$	−21.4965	−0.844461
$649$	−0.114947	−0.00451206
$650$	−48.8872	−1.91751
$651$	0.254277	0.00996589
$652$	39.4196	1.54379
$653$	0.250362	0.00979742	0.00489871	−	0.999988i	$-0.498441\pi$
$653$	0.250362	0.00979742	0.00489871	+	0.999988i	$0.498441\pi$
$654$	−113.536	−4.43961
$655$	−15.8754	−0.620301
$656$	34.8528	1.36077
$657$	−78.7448	−3.07213
$658$	1.13661	0.0443095
$659$	−5.67795	−0.221182	−0.110591	−	0.993866i	$-0.535274\pi$
$659$	−5.67795	−0.221182	−0.110591	+	0.993866i	$0.535274\pi$
$660$	20.4319	0.795311
$661$	−24.6075	−0.957122	−0.478561	−	0.878054i	$-0.658841\pi$
$661$	−24.6075	−0.957122	−0.478561	+	0.878054i	$0.658841\pi$
$662$	−35.3108	−1.37239
$663$	−93.9097	−3.64715
$664$	63.2021	2.45272
$665$	−0.988166	−0.0383194
$666$	53.8905	2.08822
$667$	−9.71500	−0.376166
$668$	−92.6598	−3.58512
$669$	−60.4039	−2.33535
$670$	16.2162	0.626486
$671$	−2.36507	−0.0913025
$672$	3.84291	0.148243
$673$	−27.7457	−1.06952	−0.534758	−	0.845005i	$-0.679597\pi$
$673$	−27.7457	−1.06952	−0.534758	+	0.845005i	$0.679597\pi$
$674$	−75.5409	−2.90973
$675$	17.8054	0.685331
$676$	168.330	6.47424
$677$	47.0005	1.80638	0.903188	−	0.429245i	$-0.141220\pi$
$677$	47.0005	1.80638	0.903188	+	0.429245i	$0.141220\pi$
$678$	39.1600	1.50393
$679$	−1.11599	−0.0428278
$680$	−49.0082	−1.87938
$681$	−9.23147	−0.353751
$682$	1.41389	0.0541406
$683$	16.5936	0.634937	0.317469	−	0.948269i	$-0.397167\pi$
$683$	16.5936	0.634937	0.317469	+	0.948269i	$0.397167\pi$
$684$	99.9804	3.82285
$685$	4.68608	0.179046
$686$	5.83368	0.222731
$687$	−35.0116	−1.33578
$688$	46.8938	1.78781
$689$	−96.0167	−3.65795
$690$	−56.1461	−2.13744
$691$	38.5825	1.46775	0.733874	−	0.679285i	$-0.237710\pi$
$691$	38.5825	1.46775	0.733874	+	0.679285i	$0.237710\pi$
$692$	−35.9855	−1.36796
$693$	0.853969	0.0324396
$694$	−13.5814	−0.515544
$695$	−22.2661	−0.844600
$696$	−38.9675	−1.47706
$697$	−18.9771	−0.718808
$698$	75.3578	2.85233
$699$	−35.4113	−1.33938
$700$	−2.04412	−0.0772604
$701$	−2.14089	−0.0808603	−0.0404302	−	0.999182i	$-0.512873\pi$
$701$	−2.14089	−0.0808603	−0.0404302	+	0.999182i	$0.512873\pi$
$702$	−119.135	−4.49645
$703$	−15.9164	−0.600299
$704$	4.24200	0.159876
$705$	−11.8792	−0.447398
$706$	30.5246	1.14881
$707$	−0.812714	−0.0305652
$708$	1.54964	0.0582390
$709$	25.9461	0.974428	0.487214	−	0.873283i	$-0.338013\pi$
$709$	25.9461	0.974428	0.487214	+	0.873283i	$0.338013\pi$
$710$	22.2270	0.834166
$711$	−40.0229	−1.50098
$712$	−72.3037	−2.70969
$713$	−2.72253	−0.101960
$714$	−5.60369	−0.209713
$715$	10.6032	0.396536
$716$	49.3781	1.84534
$717$	−54.6864	−2.04230
$718$	97.1477	3.62552
$719$	1.93803	0.0722765	0.0361382	−	0.999347i	$-0.488494\pi$
$719$	1.93803	0.0722765	0.0361382	+	0.999347i	$0.488494\pi$
$720$	−68.6286	−2.55764
$721$	0.440286	0.0163971
$722$	6.97663	0.259643
$723$	−63.3535	−2.35614
$724$	70.5352	2.62142
$725$	5.27546	0.195926
$726$	7.44229	0.276209
$727$	−36.5797	−1.35667	−0.678333	−	0.734754i	$-0.737297\pi$
$727$	−36.5797	−1.35667	−0.678333	+	0.734754i	$0.737297\pi$
$728$	7.83565	0.290408
$729$	−40.5007	−1.50003
$730$	−58.3417	−2.15932
$731$	−25.5332	−0.944381
$732$	31.8844	1.17848
$733$	−14.3156	−0.528761	−0.264380	−	0.964419i	$-0.585167\pi$
$733$	−14.3156	−0.528761	−0.264380	+	0.964419i	$0.585167\pi$
$734$	−56.5536	−2.08743
$735$	−30.4284	−1.12237
$736$	−41.1459	−1.51666
$737$	4.13899	0.152461
$738$	−55.6396	−2.04812
$739$	32.2885	1.18775	0.593876	−	0.804557i	$-0.297597\pi$
$739$	32.2885	1.18775	0.593876	+	0.804557i	$0.297597\pi$
$740$	27.9780	1.02849
$741$	81.3200	2.98737
$742$	−5.72942	−0.210334
$743$	−43.3774	−1.59136	−0.795682	−	0.605715i	$-0.792887\pi$
$743$	−43.3774	−1.59136	−0.795682	+	0.605715i	$0.792887\pi$
$744$	−10.9202	−0.400356
$745$	−12.2148	−0.447515
$746$	42.2431	1.54663
$747$	−48.1903	−1.76319
$748$	−21.8338	−0.798324
$749$	2.20088	0.0804186
$750$	86.8850	3.17259
$751$	5.03165	0.183607	0.0918037	−	0.995777i	$-0.470737\pi$
$751$	5.03165	0.183607	0.0918037	+	0.995777i	$0.470737\pi$
$752$	−23.3141	−0.850176
$753$	56.7624	2.06854
$754$	−35.2976	−1.28546
$755$	−12.1160	−0.440945
$756$	−4.98137	−0.181171
$757$	−43.1143	−1.56702	−0.783509	−	0.621381i	$-0.786572\pi$
$757$	−43.1143	−1.56702	−0.783509	+	0.621381i	$0.786572\pi$
$758$	−61.9243	−2.24919
$759$	−14.3306	−0.520168
$760$	42.4381	1.53939
$761$	−15.4426	−0.559793	−0.279896	−	0.960030i	$-0.590300\pi$
$761$	−15.4426	−0.559793	−0.279896	+	0.960030i	$0.590300\pi$
$762$	6.89050	0.249617
$763$	−2.46361	−0.0891886
$764$	−52.2594	−1.89068
$765$	37.3677	1.35103
$766$	−24.6431	−0.890390
$767$	0.804187	0.0290375
$768$	65.8462	2.37602
$769$	−52.1705	−1.88132	−0.940658	−	0.339356i	$-0.889791\pi$
$769$	−52.1705	−1.88132	−0.940658	+	0.339356i	$0.889791\pi$
$770$	0.632702	0.0228010
$771$	−8.90024	−0.320534
$772$	−13.4555	−0.484274
$773$	−37.7145	−1.35650	−0.678249	−	0.734833i	$-0.737261\pi$
$773$	−37.7145	−1.35650	−0.678249	+	0.734833i	$0.737261\pi$
$774$	−74.8619	−2.69085
$775$	1.47839	0.0531054
$776$	47.9277	1.72051
$777$	1.83276	0.0657500
$778$	−45.0933	−1.61667
$779$	16.4330	0.588773
$780$	−142.945	−5.11826
$781$	5.67318	0.203002
$782$	59.9985	2.14554
$783$	12.8559	0.459433
$784$	−59.7185	−2.13280
$785$	14.3220	0.511175
$786$	77.9569	2.78063
$787$	−51.9526	−1.85191	−0.925955	−	0.377633i	$-0.876738\pi$
$787$	−51.9526	−1.85191	−0.925955	+	0.377633i	$0.876738\pi$
$788$	6.30518	0.224613
$789$	−62.1768	−2.21355
$790$	−29.6528	−1.05500
$791$	0.849729	0.0302129
$792$	−36.6748	−1.30318
$793$	16.5464	0.587581
$794$	54.4904	1.93379
$795$	59.8810	2.12376
$796$	−42.3607	−1.50144
$797$	−21.6111	−0.765506	−0.382753	−	0.923851i	$-0.625024\pi$
$797$	−21.6111	−0.765506	−0.382753	+	0.923851i	$0.625024\pi$
$798$	4.85245	0.171775
$799$	12.6943	0.449092
$800$	22.3431	0.789948
$801$	55.1300	1.94792
$802$	22.7343	0.802777
$803$	−14.8910	−0.525492
$804$	−55.7992	−1.96789
$805$	−1.21831	−0.0429397
$806$	−9.89180	−0.348424
$807$	−38.5493	−1.35700
$808$	34.9031	1.22789
$809$	−40.3141	−1.41737	−0.708684	−	0.705526i	$-0.750711\pi$
$809$	−40.3141	−1.41737	−0.708684	+	0.705526i	$0.750711\pi$
$810$	12.1437	0.426687
$811$	−49.2849	−1.73063	−0.865313	−	0.501232i	$-0.832880\pi$
$811$	−49.2849	−1.73063	−0.865313	+	0.501232i	$0.832880\pi$
$812$	−1.47590	−0.0517939
$813$	18.9392	0.664226
$814$	10.1909	0.357192
$815$	−12.7580	−0.446892
$816$	114.943	4.02380
$817$	22.1102	0.773539
$818$	58.8442	2.05744
$819$	−5.97451	−0.208766
$820$	−28.8861	−1.00875
$821$	−6.67849	−0.233081	−0.116540	−	0.993186i	$-0.537180\pi$
$821$	−6.67849	−0.233081	−0.116540	+	0.993186i	$0.537180\pi$
$822$	−23.0113	−0.802612
$823$	−54.4162	−1.89683	−0.948415	−	0.317033i	$-0.897313\pi$
$823$	−54.4162	−1.89683	−0.948415	+	0.317033i	$0.897313\pi$
$824$	−18.9086	−0.658714
$825$	7.78183	0.270928
$826$	0.0479867	0.00166967
$827$	3.10943	0.108125	0.0540627	−	0.998538i	$-0.482783\pi$
$827$	3.10943	0.108125	0.0540627	+	0.998538i	$0.482783\pi$
$828$	123.266	4.28378
$829$	19.2971	0.670216	0.335108	−	0.942180i	$-0.391227\pi$
$829$	19.2971	0.670216	0.335108	+	0.942180i	$0.391227\pi$
$830$	−35.7040	−1.23930
$831$	63.9829	2.21954
$832$	−29.6777	−1.02889
$833$	32.5162	1.12662
$834$	109.339	3.78610
$835$	29.9889	1.03781
$836$	18.9068	0.653904
$837$	3.60274	0.124529
$838$	19.1186	0.660443
$839$	−14.9063	−0.514622	−0.257311	−	0.966329i	$-0.582837\pi$
$839$	−14.9063	−0.514622	−0.257311	+	0.966329i	$0.582837\pi$
$840$	−4.88671	−0.168608
$841$	−25.1910	−0.868655
$842$	−37.0385	−1.27643
$843$	29.2107	1.00607
$844$	43.8991	1.51107
$845$	−54.4792	−1.87414
$846$	37.2189	1.27961
$847$	0.161489	0.00554884
$848$	117.522	4.03572
$849$	−6.99837	−0.240183
$850$	−32.5805	−1.11750
$851$	−19.6233	−0.672678
$852$	−76.4822	−2.62024
$853$	−46.4502	−1.59043	−0.795213	−	0.606330i	$-0.792641\pi$
$853$	−46.4502	−1.59043	−0.795213	+	0.606330i	$0.792641\pi$
$854$	0.987342	0.0337862
$855$	−32.3581	−1.10662
$856$	−94.5199	−3.23062
$857$	49.7322	1.69882	0.849409	−	0.527734i	$-0.176958\pi$
$857$	49.7322	1.69882	0.849409	+	0.527734i	$0.176958\pi$
$858$	−52.0675	−1.77756
$859$	17.6664	0.602770	0.301385	−	0.953502i	$-0.402551\pi$
$859$	17.6664	0.602770	0.301385	+	0.953502i	$0.402551\pi$
$860$	−38.8656	−1.32531
$861$	−1.89225	−0.0644875
$862$	−22.7914	−0.776278
$863$	26.3017	0.895320	0.447660	−	0.894204i	$-0.352257\pi$
$863$	26.3017	0.895320	0.447660	+	0.894204i	$0.352257\pi$
$864$	54.4486	1.85238
$865$	11.6465	0.395994
$866$	34.5258	1.17323
$867$	−13.6440	−0.463376
$868$	−0.413606	−0.0140387
$869$	−7.56851	−0.256744
$870$	22.0134	0.746325
$871$	−28.9570	−0.981172
$872$	105.803	3.58294
$873$	−36.5439	−1.23682
$874$	−51.9550	−1.75740
$875$	1.88531	0.0637351
$876$	200.751	6.78275
$877$	41.9397	1.41620	0.708102	−	0.706111i	$-0.249552\pi$
$877$	41.9397	1.41620	0.708102	+	0.706111i	$0.249552\pi$
$878$	−3.17226	−0.107059
$879$	−25.4313	−0.857775
$880$	−12.9780	−0.437488
$881$	54.7979	1.84619	0.923094	−	0.384574i	$-0.125652\pi$
$881$	54.7979	1.84619	0.923094	+	0.384574i	$0.125652\pi$
$882$	95.3355	3.21011
$883$	−32.4485	−1.09198	−0.545990	−	0.837792i	$-0.683846\pi$
$883$	−32.4485	−1.09198	−0.545990	+	0.837792i	$0.683846\pi$
$884$	152.753	5.13765
$885$	−0.501533	−0.0168588
$886$	89.7655	3.01573
$887$	−2.47299	−0.0830347	−0.0415174	−	0.999138i	$-0.513219\pi$
$887$	−2.47299	−0.0830347	−0.0415174	+	0.999138i	$0.513219\pi$
$888$	−78.7104	−2.64135
$889$	0.149516	0.00501461
$890$	40.8456	1.36915
$891$	3.09954	0.103838
$892$	98.2529	3.28975
$893$	−10.9925	−0.367850
$894$	59.9815	2.00608
$895$	−15.9809	−0.534184
$896$	0.898803	0.0300269
$897$	100.259	3.34756
$898$	30.1970	1.00769
$899$	1.06743	0.0356009
$900$	−66.9360	−2.23120
$901$	−63.9896	−2.13180
$902$	−10.5217	−0.350334
$903$	−2.54598	−0.0847248
$904$	−36.4927	−1.21373
$905$	−22.8284	−0.758840
$906$	59.4961	1.97663
$907$	49.8744	1.65605	0.828026	−	0.560690i	$-0.189464\pi$
$907$	49.8744	1.65605	0.828026	+	0.560690i	$0.189464\pi$
$908$	15.0159	0.498319
$909$	−26.6128	−0.882692
$910$	−4.42649	−0.146737
$911$	−49.5070	−1.64024	−0.820120	−	0.572192i	$-0.806093\pi$
$911$	−49.5070	−1.64024	−0.820120	+	0.572192i	$0.806093\pi$
$912$	−99.5335	−3.29588
$913$	−9.11300	−0.301596
$914$	5.61980	0.185887
$915$	−10.3192	−0.341142
$916$	56.9498	1.88167
$917$	1.69158	0.0558609
$918$	−79.3963	−2.62047
$919$	−44.3554	−1.46315	−0.731574	−	0.681762i	$-0.761214\pi$
$919$	−44.3554	−1.46315	−0.731574	+	0.681762i	$0.761214\pi$
$920$	52.3218	1.72500
$921$	−59.6556	−1.96572
$922$	−3.35570	−0.110514
$923$	−39.6905	−1.30643
$924$	−2.17710	−0.0716213
$925$	10.6559	0.350363
$926$	7.39629	0.243057
$927$	14.4174	0.473531
$928$	16.1322	0.529566
$929$	−10.8535	−0.356091	−0.178046	−	0.984022i	$-0.556977\pi$
$929$	−10.8535	−0.356091	−0.178046	+	0.984022i	$0.556977\pi$
$930$	6.16903	0.202291
$931$	−28.1571	−0.922810
$932$	57.5999	1.88675
$933$	−9.14619	−0.299433
$934$	−1.10504	−0.0361581
$935$	7.06640	0.231096
$936$	256.583	8.38669
$937$	38.0257	1.24225	0.621123	−	0.783713i	$-0.286677\pi$
$937$	38.0257	1.24225	0.621123	+	0.783713i	$0.286677\pi$
$938$	−1.72790	−0.0564178
$939$	−94.1340	−3.07195
$940$	19.3227	0.630238
$941$	−24.8764	−0.810947	−0.405474	−	0.914107i	$-0.632893\pi$
$941$	−24.8764	−0.810947	−0.405474	+	0.914107i	$0.632893\pi$
$942$	−70.3291	−2.29145
$943$	20.2602	0.659763
$944$	−0.984303	−0.0320363
$945$	1.61219	0.0524447
$946$	−14.1567	−0.460275
$947$	−40.0294	−1.30078	−0.650391	−	0.759600i	$-0.725395\pi$
$947$	−40.0294	−1.30078	−0.650391	+	0.759600i	$0.725395\pi$
$948$	102.034	3.31391
$949$	104.180	3.38183
$950$	28.2127	0.915341
$951$	−5.03371	−0.163229
$952$	5.22201	0.169246
$953$	17.9403	0.581144	0.290572	−	0.956853i	$-0.406154\pi$
$953$	17.9403	0.581144	0.290572	+	0.956853i	$0.406154\pi$
$954$	−187.614	−6.07421
$955$	16.9135	0.547307
$956$	88.9527	2.87694
$957$	5.61865	0.181625
$958$	−36.5758	−1.18171
$959$	−0.499320	−0.0161239
$960$	18.5086	0.597361
$961$	−30.7009	−0.990350
$962$	−71.2976	−2.29873
$963$	72.0694	2.32240
$964$	103.051	3.31903
$965$	4.35480	0.140186
$966$	5.98258	0.192486
$967$	51.1550	1.64503	0.822516	−	0.568742i	$-0.192570\pi$
$967$	51.1550	1.64503	0.822516	+	0.568742i	$0.192570\pi$
$968$	−6.93538	−0.222912
$969$	54.1951	1.74100
$970$	−27.0752	−0.869332
$971$	−16.8976	−0.542269	−0.271134	−	0.962542i	$-0.587399\pi$
$971$	−16.8976	−0.542269	−0.271134	+	0.962542i	$0.587399\pi$
$972$	50.7533	1.62791
$973$	2.37253	0.0760599
$974$	44.7304	1.43325
$975$	−54.4430	−1.74357
$976$	−20.2524	−0.648263
$977$	27.2904	0.873098	0.436549	−	0.899681i	$-0.356201\pi$
$977$	27.2904	0.873098	0.436549	+	0.899681i	$0.356201\pi$
$978$	62.6487	2.00329
$979$	10.4253	0.333195
$980$	49.4948	1.58105
$981$	−80.6725	−2.57567
$982$	−22.4929	−0.717777
$983$	5.15037	0.164271	0.0821356	−	0.996621i	$-0.473826\pi$
$983$	5.15037	0.164271	0.0821356	+	0.996621i	$0.473826\pi$
$984$	81.2650	2.59063
$985$	−2.04064	−0.0650201
$986$	−23.5238	−0.749152
$987$	1.26578	0.0402901
$988$	−132.275	−4.20823
$989$	27.2597	0.866807
$990$	20.7182	0.658469
$991$	3.83886	0.121946	0.0609728	−	0.998139i	$-0.480580\pi$
$991$	3.83886	0.121946	0.0609728	+	0.998139i	$0.480580\pi$
$992$	4.52089	0.143538
$993$	−39.3238	−1.24790
$994$	−2.36837	−0.0751203
$995$	13.7098	0.434631
$996$	122.856	3.89283
$997$	36.0307	1.14110	0.570551	−	0.821262i	$-0.306730\pi$
$997$	36.0307	1.14110	0.570551	+	0.821262i	$0.306730\pi$
$998$	43.6340	1.38121
$999$	25.9676	0.821580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.7	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.7	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58511 q^{2} -2.87890 q^{3} +4.68281 q^{4} -1.51557 q^{5} +7.44229 q^{6} +0.161489 q^{7} -6.93538 q^{8} +5.28808 q^{9} +O(q^{10})\)	\(q-2.58511 q^{2} -2.87890 q^{3} +4.68281 q^{4} -1.51557 q^{5} +7.44229 q^{6} +0.161489 q^{7} -6.93538 q^{8} +5.28808 q^{9} +3.91792 q^{10} +1.00000 q^{11} -13.4814 q^{12} -6.99617 q^{13} -0.417469 q^{14} +4.36317 q^{15} +8.56312 q^{16} -4.66254 q^{17} -13.6703 q^{18} +4.03748 q^{19} -7.09712 q^{20} -0.464912 q^{21} -2.58511 q^{22} +4.97780 q^{23} +19.9663 q^{24} -2.70305 q^{25} +18.0859 q^{26} -6.58715 q^{27} +0.756225 q^{28} -1.95167 q^{29} -11.2793 q^{30} -0.546934 q^{31} -8.26588 q^{32} -2.87890 q^{33} +12.0532 q^{34} -0.244748 q^{35} +24.7631 q^{36} -3.94217 q^{37} -10.4373 q^{38} +20.1413 q^{39} +10.5110 q^{40} +4.07011 q^{41} +1.20185 q^{42} +5.47625 q^{43} +4.68281 q^{44} -8.01444 q^{45} -12.8682 q^{46} -2.72261 q^{47} -24.6524 q^{48} -6.97392 q^{49} +6.98770 q^{50} +13.4230 q^{51} -32.7618 q^{52} +13.7242 q^{53} +17.0285 q^{54} -1.51557 q^{55} -1.11999 q^{56} -11.6235 q^{57} +5.04528 q^{58} -0.114947 q^{59} +20.4319 q^{60} -2.36507 q^{61} +1.41389 q^{62} +0.853969 q^{63} +4.24200 q^{64} +10.6032 q^{65} +7.44229 q^{66} +4.13899 q^{67} -21.8338 q^{68} -14.3306 q^{69} +0.632702 q^{70} +5.67318 q^{71} -36.6748 q^{72} -14.8910 q^{73} +10.1909 q^{74} +7.78183 q^{75} +18.9068 q^{76} +0.161489 q^{77} -52.0675 q^{78} -7.56851 q^{79} -12.9780 q^{80} +3.09954 q^{81} -10.5217 q^{82} -9.11300 q^{83} -2.17710 q^{84} +7.06640 q^{85} -14.1567 q^{86} +5.61865 q^{87} -6.93538 q^{88} +10.4253 q^{89} +20.7182 q^{90} -1.12981 q^{91} +23.3101 q^{92} +1.57457 q^{93} +7.03827 q^{94} -6.11907 q^{95} +23.7967 q^{96} -6.91061 q^{97} +18.0284 q^{98} +5.28808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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