LMFDB - Embedded newform 4334.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.745887 q^{3} +1.00000 q^{4} +2.52923 q^{5} -0.745887 q^{6} +4.14909 q^{7} -1.00000 q^{8} -2.44365 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.745887 q^{3} +1.00000 q^{4} +2.52923 q^{5} -0.745887 q^{6} +4.14909 q^{7} -1.00000 q^{8} -2.44365 q^{9} -2.52923 q^{10} -1.00000 q^{11} +0.745887 q^{12} +0.317859 q^{13} -4.14909 q^{14} +1.88652 q^{15} +1.00000 q^{16} -0.311689 q^{17} +2.44365 q^{18} +4.80394 q^{19} +2.52923 q^{20} +3.09475 q^{21} +1.00000 q^{22} +4.58185 q^{23} -0.745887 q^{24} +1.39702 q^{25} -0.317859 q^{26} -4.06035 q^{27} +4.14909 q^{28} -10.0133 q^{29} -1.88652 q^{30} +7.30004 q^{31} -1.00000 q^{32} -0.745887 q^{33} +0.311689 q^{34} +10.4940 q^{35} -2.44365 q^{36} -5.00260 q^{37} -4.80394 q^{38} +0.237087 q^{39} -2.52923 q^{40} +8.13597 q^{41} -3.09475 q^{42} +0.409434 q^{43} -1.00000 q^{44} -6.18057 q^{45} -4.58185 q^{46} +2.81913 q^{47} +0.745887 q^{48} +10.2149 q^{49} -1.39702 q^{50} -0.232485 q^{51} +0.317859 q^{52} -5.22869 q^{53} +4.06035 q^{54} -2.52923 q^{55} -4.14909 q^{56} +3.58319 q^{57} +10.0133 q^{58} +12.7788 q^{59} +1.88652 q^{60} -3.43337 q^{61} -7.30004 q^{62} -10.1389 q^{63} +1.00000 q^{64} +0.803939 q^{65} +0.745887 q^{66} +7.85187 q^{67} -0.311689 q^{68} +3.41754 q^{69} -10.4940 q^{70} -8.35679 q^{71} +2.44365 q^{72} +7.35181 q^{73} +5.00260 q^{74} +1.04202 q^{75} +4.80394 q^{76} -4.14909 q^{77} -0.237087 q^{78} +8.91050 q^{79} +2.52923 q^{80} +4.30240 q^{81} -8.13597 q^{82} +13.1921 q^{83} +3.09475 q^{84} -0.788334 q^{85} -0.409434 q^{86} -7.46876 q^{87} +1.00000 q^{88} +2.11177 q^{89} +6.18057 q^{90} +1.31882 q^{91} +4.58185 q^{92} +5.44500 q^{93} -2.81913 q^{94} +12.1503 q^{95} -0.745887 q^{96} +6.62590 q^{97} -10.2149 q^{98} +2.44365 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.745887	0.430638	0.215319	−	0.976544i	$-0.430921\pi$
$3$	0.745887	0.430638	0.215319	+	0.976544i	$0.430921\pi$
$4$	1.00000	0.500000
$5$	2.52923	1.13111	0.565554	−	0.824711i	$-0.308662\pi$
$5$	2.52923	1.13111	0.565554	+	0.824711i	$0.308662\pi$
$6$	−0.745887	−0.304507
$7$	4.14909	1.56821	0.784103	−	0.620630i	$-0.213123\pi$
$7$	4.14909	1.56821	0.784103	+	0.620630i	$0.213123\pi$
$8$	−1.00000	−0.353553
$9$	−2.44365	−0.814551
$10$	−2.52923	−0.799814
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.745887	0.215319
$13$	0.317859	0.0881581	0.0440791	−	0.999028i	$-0.485965\pi$
$13$	0.317859	0.0881581	0.0440791	+	0.999028i	$0.485965\pi$
$14$	−4.14909	−1.10889
$15$	1.88652	0.487098
$16$	1.00000	0.250000
$17$	−0.311689	−0.0755957	−0.0377978	−	0.999285i	$-0.512034\pi$
$17$	−0.311689	−0.0755957	−0.0377978	+	0.999285i	$0.512034\pi$
$18$	2.44365	0.575975
$19$	4.80394	1.10210	0.551049	−	0.834473i	$-0.314228\pi$
$19$	4.80394	1.10210	0.551049	+	0.834473i	$0.314228\pi$
$20$	2.52923	0.565554
$21$	3.09475	0.675329
$22$	1.00000	0.213201
$23$	4.58185	0.955382	0.477691	−	0.878528i	$-0.341474\pi$
$23$	4.58185	0.955382	0.477691	+	0.878528i	$0.341474\pi$
$24$	−0.745887	−0.152253
$25$	1.39702	0.279405
$26$	−0.317859	−0.0623372
$27$	−4.06035	−0.781414
$28$	4.14909	0.784103
$29$	−10.0133	−1.85942	−0.929708	−	0.368297i	$-0.879941\pi$
$29$	−10.0133	−1.85942	−0.929708	+	0.368297i	$0.879941\pi$
$30$	−1.88652	−0.344430
$31$	7.30004	1.31113	0.655563	−	0.755140i	$-0.272431\pi$
$31$	7.30004	1.31113	0.655563	+	0.755140i	$0.272431\pi$
$32$	−1.00000	−0.176777
$33$	−0.745887	−0.129842
$34$	0.311689	0.0534542
$35$	10.4940	1.77381
$36$	−2.44365	−0.407276
$37$	−5.00260	−0.822423	−0.411211	−	0.911540i	$-0.634894\pi$
$37$	−5.00260	−0.822423	−0.411211	+	0.911540i	$0.634894\pi$
$38$	−4.80394	−0.779301
$39$	0.237087	0.0379642
$40$	−2.52923	−0.399907
$41$	8.13597	1.27062	0.635312	−	0.772255i	$-0.280871\pi$
$41$	8.13597	1.27062	0.635312	+	0.772255i	$0.280871\pi$
$42$	−3.09475	−0.477530
$43$	0.409434	0.0624381	0.0312191	−	0.999513i	$-0.490061\pi$
$43$	0.409434	0.0624381	0.0312191	+	0.999513i	$0.490061\pi$
$44$	−1.00000	−0.150756
$45$	−6.18057	−0.921345
$46$	−4.58185	−0.675557
$47$	2.81913	0.411213	0.205606	−	0.978635i	$-0.434083\pi$
$47$	2.81913	0.411213	0.205606	+	0.978635i	$0.434083\pi$
$48$	0.745887	0.107659
$49$	10.2149	1.45927
$50$	−1.39702	−0.197569
$51$	−0.232485	−0.0325543
$52$	0.317859	0.0440791
$53$	−5.22869	−0.718216	−0.359108	−	0.933296i	$-0.616919\pi$
$53$	−5.22869	−0.718216	−0.359108	+	0.933296i	$0.616919\pi$
$54$	4.06035	0.552543
$55$	−2.52923	−0.341042
$56$	−4.14909	−0.554445
$57$	3.58319	0.474605
$58$	10.0133	1.31481
$59$	12.7788	1.66365	0.831826	−	0.555036i	$-0.187295\pi$
$59$	12.7788	1.66365	0.831826	+	0.555036i	$0.187295\pi$
$60$	1.88652	0.243549
$61$	−3.43337	−0.439597	−0.219799	−	0.975545i	$-0.570540\pi$
$61$	−3.43337	−0.439597	−0.219799	+	0.975545i	$0.570540\pi$
$62$	−7.30004	−0.927106
$63$	−10.1389	−1.27738
$64$	1.00000	0.125000
$65$	0.803939	0.0997163
$66$	0.745887	0.0918123
$67$	7.85187	0.959258	0.479629	−	0.877471i	$-0.340771\pi$
$67$	7.85187	0.959258	0.479629	+	0.877471i	$0.340771\pi$
$68$	−0.311689	−0.0377978
$69$	3.41754	0.411424
$70$	−10.4940	−1.25427
$71$	−8.35679	−0.991769	−0.495885	−	0.868388i	$-0.665156\pi$
$71$	−8.35679	−0.991769	−0.495885	+	0.868388i	$0.665156\pi$
$72$	2.44365	0.287987
$73$	7.35181	0.860464	0.430232	−	0.902718i	$-0.358432\pi$
$73$	7.35181	0.860464	0.430232	+	0.902718i	$0.358432\pi$
$74$	5.00260	0.581541
$75$	1.04202	0.120322
$76$	4.80394	0.551049
$77$	−4.14909	−0.472832
$78$	−0.237087	−0.0268448
$79$	8.91050	1.00251	0.501255	−	0.865300i	$-0.332872\pi$
$79$	8.91050	1.00251	0.501255	+	0.865300i	$0.332872\pi$
$80$	2.52923	0.282777
$81$	4.30240	0.478045
$82$	−8.13597	−0.898467
$83$	13.1921	1.44802	0.724011	−	0.689789i	$-0.242297\pi$
$83$	13.1921	1.44802	0.724011	+	0.689789i	$0.242297\pi$
$84$	3.09475	0.337665
$85$	−0.788334	−0.0855068
$86$	−0.409434	−0.0441504
$87$	−7.46876	−0.800735
$88$	1.00000	0.106600
$89$	2.11177	0.223847	0.111923	−	0.993717i	$-0.464299\pi$
$89$	2.11177	0.223847	0.111923	+	0.993717i	$0.464299\pi$
$90$	6.18057	0.651489
$91$	1.31882	0.138250
$92$	4.58185	0.477691
$93$	5.44500	0.564621
$94$	−2.81913	−0.290771
$95$	12.1503	1.24659
$96$	−0.745887	−0.0761267
$97$	6.62590	0.672758	0.336379	−	0.941727i	$-0.390798\pi$
$97$	6.62590	0.672758	0.336379	+	0.941727i	$0.390798\pi$
$98$	−10.2149	−1.03186
$99$	2.44365	0.245596
$100$	1.39702	0.139702
$101$	−4.66384	−0.464069	−0.232035	−	0.972708i	$-0.574538\pi$
$101$	−4.66384	−0.464069	−0.232035	+	0.972708i	$0.574538\pi$
$102$	0.232485	0.0230194
$103$	3.51258	0.346105	0.173053	−	0.984913i	$-0.444637\pi$
$103$	3.51258	0.346105	0.173053	+	0.984913i	$0.444637\pi$
$104$	−0.317859	−0.0311686
$105$	7.82734	0.763870
$106$	5.22869	0.507855
$107$	3.33603	0.322507	0.161253	−	0.986913i	$-0.448446\pi$
$107$	3.33603	0.322507	0.161253	+	0.986913i	$0.448446\pi$
$108$	−4.06035	−0.390707
$109$	1.48472	0.142211	0.0711053	−	0.997469i	$-0.477347\pi$
$109$	1.48472	0.142211	0.0711053	+	0.997469i	$0.477347\pi$
$110$	2.52923	0.241153
$111$	−3.73137	−0.354166
$112$	4.14909	0.392052
$113$	−6.46755	−0.608416	−0.304208	−	0.952606i	$-0.598392\pi$
$113$	−6.46755	−0.608416	−0.304208	+	0.952606i	$0.598392\pi$
$114$	−3.58319	−0.335597
$115$	11.5886	1.08064
$116$	−10.0133	−0.929708
$117$	−0.776736	−0.0718093
$118$	−12.7788	−1.17638
$119$	−1.29322	−0.118550
$120$	−1.88652	−0.172215
$121$	1.00000	0.0909091
$122$	3.43337	0.310842
$123$	6.06851	0.547179
$124$	7.30004	0.655563
$125$	−9.11277	−0.815071
$126$	10.1389	0.903247
$127$	12.0883	1.07267	0.536333	−	0.844007i	$-0.319809\pi$
$127$	12.0883	1.07267	0.536333	+	0.844007i	$0.319809\pi$
$128$	−1.00000	−0.0883883
$129$	0.305391	0.0268882
$130$	−0.803939	−0.0705101
$131$	−18.4235	−1.60967	−0.804835	−	0.593499i	$-0.797746\pi$
$131$	−18.4235	−1.60967	−0.804835	+	0.593499i	$0.797746\pi$
$132$	−0.745887	−0.0649211
$133$	19.9319	1.72832
$134$	−7.85187	−0.678298
$135$	−10.2696	−0.883864
$136$	0.311689	0.0267271
$137$	9.37094	0.800613	0.400307	−	0.916381i	$-0.368904\pi$
$137$	9.37094	0.800613	0.400307	+	0.916381i	$0.368904\pi$
$138$	−3.41754	−0.290920
$139$	21.3938	1.81460	0.907298	−	0.420489i	$-0.138141\pi$
$139$	21.3938	1.81460	0.907298	+	0.420489i	$0.138141\pi$
$140$	10.4940	0.886905
$141$	2.10275	0.177084
$142$	8.35679	0.701287
$143$	−0.317859	−0.0265807
$144$	−2.44365	−0.203638
$145$	−25.3259	−2.10320
$146$	−7.35181	−0.608440
$147$	7.61916	0.628418
$148$	−5.00260	−0.411211
$149$	−8.04174	−0.658805	−0.329402	−	0.944190i	$-0.606847\pi$
$149$	−8.04174	−0.658805	−0.329402	+	0.944190i	$0.606847\pi$
$150$	−1.04202	−0.0850807
$151$	−4.14584	−0.337384	−0.168692	−	0.985669i	$-0.553954\pi$
$151$	−4.14584	−0.337384	−0.168692	+	0.985669i	$0.553954\pi$
$152$	−4.80394	−0.389651
$153$	0.761659	0.0615765
$154$	4.14909	0.334343
$155$	18.4635	1.48303
$156$	0.237087	0.0189821
$157$	−7.67435	−0.612480	−0.306240	−	0.951954i	$-0.599071\pi$
$157$	−7.67435	−0.612480	−0.306240	+	0.951954i	$0.599071\pi$
$158$	−8.91050	−0.708881
$159$	−3.90001	−0.309291
$160$	−2.52923	−0.199953
$161$	19.0105	1.49824
$162$	−4.30240	−0.338029
$163$	−10.1607	−0.795844	−0.397922	−	0.917419i	$-0.630268\pi$
$163$	−10.1607	−0.795844	−0.397922	+	0.917419i	$0.630268\pi$
$164$	8.13597	0.635312
$165$	−1.88652	−0.146866
$166$	−13.1921	−1.02391
$167$	−4.36856	−0.338049	−0.169025	−	0.985612i	$-0.554062\pi$
$167$	−4.36856	−0.338049	−0.169025	+	0.985612i	$0.554062\pi$
$168$	−3.09475	−0.238765
$169$	−12.8990	−0.992228
$170$	0.788334	0.0604625
$171$	−11.7392	−0.897715
$172$	0.409434	0.0312191
$173$	4.84819	0.368601	0.184301	−	0.982870i	$-0.440998\pi$
$173$	4.84819	0.368601	0.184301	+	0.982870i	$0.440998\pi$
$174$	7.46876	0.566205
$175$	5.79637	0.438164
$176$	−1.00000	−0.0753778
$177$	9.53151	0.716432
$178$	−2.11177	−0.158284
$179$	−19.9947	−1.49447	−0.747235	−	0.664560i	$-0.768619\pi$
$179$	−19.9947	−1.49447	−0.747235	+	0.664560i	$0.768619\pi$
$180$	−6.18057	−0.460673
$181$	−7.52251	−0.559144	−0.279572	−	0.960125i	$-0.590192\pi$
$181$	−7.52251	−0.559144	−0.279572	+	0.960125i	$0.590192\pi$
$182$	−1.31882	−0.0977576
$183$	−2.56090	−0.189307
$184$	−4.58185	−0.337779
$185$	−12.6528	−0.930249
$186$	−5.44500	−0.399247
$187$	0.311689	0.0227929
$188$	2.81913	0.205606
$189$	−16.8467	−1.22542
$190$	−12.1503	−0.881474
$191$	10.0596	0.727888	0.363944	−	0.931421i	$-0.381430\pi$
$191$	10.0596	0.727888	0.363944	+	0.931421i	$0.381430\pi$
$192$	0.745887	0.0538297
$193$	−9.24558	−0.665511	−0.332756	−	0.943013i	$-0.607978\pi$
$193$	−9.24558	−0.665511	−0.332756	+	0.943013i	$0.607978\pi$
$194$	−6.62590	−0.475712
$195$	0.599647	0.0429416
$196$	10.2149	0.729636
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−2.44365	−0.173663
$199$	21.1414	1.49867	0.749337	−	0.662189i	$-0.230372\pi$
$199$	21.1414	1.49867	0.749337	+	0.662189i	$0.230372\pi$
$200$	−1.39702	−0.0987845
$201$	5.85660	0.413093
$202$	4.66384	0.328146
$203$	−41.5459	−2.91595
$204$	−0.232485	−0.0162772
$205$	20.5778	1.43721
$206$	−3.51258	−0.244733
$207$	−11.1965	−0.778208
$208$	0.317859	0.0220395
$209$	−4.80394	−0.332295
$210$	−7.82734	−0.540138
$211$	−12.6604	−0.871581	−0.435790	−	0.900048i	$-0.643531\pi$
$211$	−12.6604	−0.871581	−0.435790	+	0.900048i	$0.643531\pi$
$212$	−5.22869	−0.359108
$213$	−6.23322	−0.427093
$214$	−3.33603	−0.228047
$215$	1.03555	0.0706243
$216$	4.06035	0.276272
$217$	30.2885	2.05612
$218$	−1.48472	−0.100558
$219$	5.48361	0.370548
$220$	−2.52923	−0.170521
$221$	−0.0990730	−0.00666437
$222$	3.73137	0.250433
$223$	−24.9986	−1.67403	−0.837014	−	0.547181i	$-0.815701\pi$
$223$	−24.9986	−1.67403	−0.837014	+	0.547181i	$0.815701\pi$
$224$	−4.14909	−0.277222
$225$	−3.41384	−0.227589
$226$	6.46755	0.430215
$227$	−14.1599	−0.939827	−0.469914	−	0.882712i	$-0.655715\pi$
$227$	−14.1599	−0.939827	−0.469914	+	0.882712i	$0.655715\pi$
$228$	3.58319	0.237303
$229$	−20.9822	−1.38654	−0.693271	−	0.720677i	$-0.743831\pi$
$229$	−20.9822	−1.38654	−0.693271	+	0.720677i	$0.743831\pi$
$230$	−11.5886	−0.764128
$231$	−3.09475	−0.203619
$232$	10.0133	0.657403
$233$	−5.28649	−0.346329	−0.173165	−	0.984893i	$-0.555399\pi$
$233$	−5.28649	−0.346329	−0.173165	+	0.984893i	$0.555399\pi$
$234$	0.776736	0.0507768
$235$	7.13024	0.465126
$236$	12.7788	0.831826
$237$	6.64622	0.431718
$238$	1.29322	0.0838272
$239$	6.17671	0.399538	0.199769	−	0.979843i	$-0.435981\pi$
$239$	6.17671	0.399538	0.199769	+	0.979843i	$0.435981\pi$
$240$	1.88652	0.121774
$241$	25.5607	1.64651	0.823254	−	0.567673i	$-0.192156\pi$
$241$	25.5607	1.64651	0.823254	+	0.567673i	$0.192156\pi$
$242$	−1.00000	−0.0642824
$243$	15.3901	0.987278
$244$	−3.43337	−0.219799
$245$	25.8359	1.65059
$246$	−6.06851	−0.386914
$247$	1.52697	0.0971589
$248$	−7.30004	−0.463553
$249$	9.83981	0.623573
$250$	9.11277	0.576342
$251$	−20.9869	−1.32468	−0.662339	−	0.749204i	$-0.730436\pi$
$251$	−20.9869	−1.32468	−0.662339	+	0.749204i	$0.730436\pi$
$252$	−10.1389	−0.638692
$253$	−4.58185	−0.288059
$254$	−12.0883	−0.758489
$255$	−0.588008	−0.0368225
$256$	1.00000	0.0625000
$257$	−9.00211	−0.561536	−0.280768	−	0.959776i	$-0.590589\pi$
$257$	−9.00211	−0.561536	−0.280768	+	0.959776i	$0.590589\pi$
$258$	−0.305391	−0.0190128
$259$	−20.7562	−1.28973
$260$	0.803939	0.0498582
$261$	24.4689	1.51459
$262$	18.4235	1.13821
$263$	21.1198	1.30230	0.651152	−	0.758948i	$-0.274286\pi$
$263$	21.1198	1.30230	0.651152	+	0.758948i	$0.274286\pi$
$264$	0.745887	0.0459061
$265$	−13.2246	−0.812380
$266$	−19.9319	−1.22211
$267$	1.57514	0.0963969
$268$	7.85187	0.479629
$269$	6.83640	0.416823	0.208411	−	0.978041i	$-0.433171\pi$
$269$	6.83640	0.416823	0.208411	+	0.978041i	$0.433171\pi$
$270$	10.2696	0.624986
$271$	1.02728	0.0624026	0.0312013	−	0.999513i	$-0.490067\pi$
$271$	1.02728	0.0624026	0.0312013	+	0.999513i	$0.490067\pi$
$272$	−0.311689	−0.0188989
$273$	0.983692	0.0595358
$274$	−9.37094	−0.566119
$275$	−1.39702	−0.0842437
$276$	3.41754	0.205712
$277$	−12.8779	−0.773756	−0.386878	−	0.922131i	$-0.626447\pi$
$277$	−12.8779	−0.773756	−0.386878	+	0.922131i	$0.626447\pi$
$278$	−21.3938	−1.28311
$279$	−17.8388	−1.06798
$280$	−10.4940	−0.627137
$281$	25.5286	1.52291	0.761454	−	0.648219i	$-0.224486\pi$
$281$	25.5286	1.52291	0.761454	+	0.648219i	$0.224486\pi$
$282$	−2.10275	−0.125217
$283$	−18.4746	−1.09820	−0.549099	−	0.835757i	$-0.685029\pi$
$283$	−18.4746	−1.09820	−0.549099	+	0.835757i	$0.685029\pi$
$284$	−8.35679	−0.495885
$285$	9.06273	0.536830
$286$	0.317859	0.0187954
$287$	33.7568	1.99260
$288$	2.44365	0.143994
$289$	−16.9029	−0.994285
$290$	25.3259	1.48719
$291$	4.94217	0.289715
$292$	7.35181	0.430232
$293$	−11.0154	−0.643527	−0.321763	−	0.946820i	$-0.604276\pi$
$293$	−11.0154	−0.643527	−0.321763	+	0.946820i	$0.604276\pi$
$294$	−7.61916	−0.444359
$295$	32.3205	1.88177
$296$	5.00260	0.290770
$297$	4.06035	0.235605
$298$	8.04174	0.465845
$299$	1.45638	0.0842247
$300$	1.04202	0.0601611
$301$	1.69878	0.0979159
$302$	4.14584	0.238567
$303$	−3.47869	−0.199846
$304$	4.80394	0.275525
$305$	−8.68378	−0.497232
$306$	−0.761659	−0.0435412
$307$	20.3130	1.15932	0.579662	−	0.814857i	$-0.303185\pi$
$307$	20.3130	1.15932	0.579662	+	0.814857i	$0.303185\pi$
$308$	−4.14909	−0.236416
$309$	2.61999	0.149046
$310$	−18.4635	−1.04866
$311$	−3.94348	−0.223614	−0.111807	−	0.993730i	$-0.535664\pi$
$311$	−3.94348	−0.223614	−0.111807	+	0.993730i	$0.535664\pi$
$312$	−0.237087	−0.0134224
$313$	31.8387	1.79963	0.899816	−	0.436270i	$-0.143701\pi$
$313$	31.8387	1.79963	0.899816	+	0.436270i	$0.143701\pi$
$314$	7.67435	0.433089
$315$	−25.6437	−1.44486
$316$	8.91050	0.501255
$317$	−12.3696	−0.694748	−0.347374	−	0.937727i	$-0.612927\pi$
$317$	−12.3696	−0.694748	−0.347374	+	0.937727i	$0.612927\pi$
$318$	3.90001	0.218702
$319$	10.0133	0.560635
$320$	2.52923	0.141388
$321$	2.48830	0.138884
$322$	−19.0105	−1.05941
$323$	−1.49733	−0.0833139
$324$	4.30240	0.239022
$325$	0.444056	0.0246318
$326$	10.1607	0.562746
$327$	1.10743	0.0612412
$328$	−8.13597	−0.449234
$329$	11.6968	0.644866
$330$	1.88652	0.103850
$331$	−9.97836	−0.548460	−0.274230	−	0.961664i	$-0.588423\pi$
$331$	−9.97836	−0.548460	−0.274230	+	0.961664i	$0.588423\pi$
$332$	13.1921	0.724011
$333$	12.2246	0.669905
$334$	4.36856	0.239037
$335$	19.8592	1.08502
$336$	3.09475	0.168832
$337$	24.9340	1.35824	0.679120	−	0.734027i	$-0.262362\pi$
$337$	24.9340	1.35824	0.679120	+	0.734027i	$0.262362\pi$
$338$	12.8990	0.701611
$339$	−4.82406	−0.262007
$340$	−0.788334	−0.0427534
$341$	−7.30004	−0.395319
$342$	11.7392	0.634781
$343$	13.3389	0.720235
$344$	−0.409434	−0.0220752
$345$	8.64376	0.465365
$346$	−4.84819	−0.260640
$347$	26.1869	1.40579	0.702893	−	0.711296i	$-0.251891\pi$
$347$	26.1869	1.40579	0.702893	+	0.711296i	$0.251891\pi$
$348$	−7.46876	−0.400368
$349$	3.61000	0.193239	0.0966194	−	0.995321i	$-0.469197\pi$
$349$	3.61000	0.193239	0.0966194	+	0.995321i	$0.469197\pi$
$350$	−5.79637	−0.309829
$351$	−1.29062	−0.0688880
$352$	1.00000	0.0533002
$353$	6.70926	0.357098	0.178549	−	0.983931i	$-0.442860\pi$
$353$	6.70926	0.357098	0.178549	+	0.983931i	$0.442860\pi$
$354$	−9.53151	−0.506594
$355$	−21.1363	−1.12180
$356$	2.11177	0.111923
$357$	−0.964598	−0.0510520
$358$	19.9947	1.05675
$359$	2.74786	0.145027	0.0725133	−	0.997367i	$-0.476898\pi$
$359$	2.74786	0.145027	0.0725133	+	0.997367i	$0.476898\pi$
$360$	6.18057	0.325745
$361$	4.07780	0.214621
$362$	7.52251	0.395374
$363$	0.745887	0.0391489
$364$	1.31882	0.0691251
$365$	18.5944	0.973277
$366$	2.56090	0.133860
$367$	12.2241	0.638093	0.319046	−	0.947739i	$-0.396637\pi$
$367$	12.2241	0.638093	0.319046	+	0.947739i	$0.396637\pi$
$368$	4.58185	0.238846
$369$	−19.8815	−1.03499
$370$	12.6528	0.657785
$371$	−21.6943	−1.12631
$372$	5.44500	0.282310
$373$	−6.20727	−0.321400	−0.160700	−	0.987003i	$-0.551375\pi$
$373$	−6.20727	−0.321400	−0.160700	+	0.987003i	$0.551375\pi$
$374$	−0.311689	−0.0161170
$375$	−6.79709	−0.351000
$376$	−2.81913	−0.145386
$377$	−3.18280	−0.163923
$378$	16.8467	0.866502
$379$	13.0376	0.669698	0.334849	−	0.942272i	$-0.391315\pi$
$379$	13.0376	0.669698	0.334849	+	0.942272i	$0.391315\pi$
$380$	12.1503	0.623296
$381$	9.01652	0.461930
$382$	−10.0596	−0.514695
$383$	11.8955	0.607831	0.303915	−	0.952699i	$-0.401706\pi$
$383$	11.8955	0.607831	0.303915	+	0.952699i	$0.401706\pi$
$384$	−0.745887	−0.0380634
$385$	−10.4940	−0.534824
$386$	9.24558	0.470587
$387$	−1.00052	−0.0508590
$388$	6.62590	0.336379
$389$	15.1673	0.769011	0.384505	−	0.923123i	$-0.374372\pi$
$389$	15.1673	0.769011	0.384505	+	0.923123i	$0.374372\pi$
$390$	−0.599647	−0.0303643
$391$	−1.42811	−0.0722227
$392$	−10.2149	−0.515931
$393$	−13.7419	−0.693185
$394$	−1.00000	−0.0503793
$395$	22.5367	1.13395
$396$	2.44365	0.122798
$397$	8.39856	0.421512	0.210756	−	0.977539i	$-0.432408\pi$
$397$	8.39856	0.421512	0.210756	+	0.977539i	$0.432408\pi$
$398$	−21.1414	−1.05972
$399$	14.8670	0.744279
$400$	1.39702	0.0698512
$401$	−20.0113	−0.999317	−0.499658	−	0.866223i	$-0.666541\pi$
$401$	−20.0113	−0.999317	−0.499658	+	0.866223i	$0.666541\pi$
$402$	−5.85660	−0.292101
$403$	2.32038	0.115586
$404$	−4.66384	−0.232035
$405$	10.8818	0.540720
$406$	41.5459	2.06189
$407$	5.00260	0.247970
$408$	0.232485	0.0115097
$409$	−27.7637	−1.37282	−0.686412	−	0.727213i	$-0.740815\pi$
$409$	−27.7637	−1.37282	−0.686412	+	0.727213i	$0.740815\pi$
$410$	−20.5778	−1.01626
$411$	6.98966	0.344774
$412$	3.51258	0.173053
$413$	53.0202	2.60895
$414$	11.1965	0.550276
$415$	33.3659	1.63787
$416$	−0.317859	−0.0155843
$417$	15.9573	0.781434
$418$	4.80394	0.234968
$419$	−0.722133	−0.0352785	−0.0176393	−	0.999844i	$-0.505615\pi$
$419$	−0.722133	−0.0352785	−0.0176393	+	0.999844i	$0.505615\pi$
$420$	7.82734	0.381935
$421$	1.35091	0.0658391	0.0329195	−	0.999458i	$-0.489519\pi$
$421$	1.35091	0.0658391	0.0329195	+	0.999458i	$0.489519\pi$
$422$	12.6604	0.616301
$423$	−6.88898	−0.334954
$424$	5.22869	0.253928
$425$	−0.435437	−0.0211218
$426$	6.23322	0.302001
$427$	−14.2453	−0.689380
$428$	3.33603	0.161253
$429$	−0.237087	−0.0114466
$430$	−1.03555	−0.0499389
$431$	−29.3471	−1.41360	−0.706799	−	0.707414i	$-0.749862\pi$
$431$	−29.3471	−1.41360	−0.706799	+	0.707414i	$0.749862\pi$
$432$	−4.06035	−0.195354
$433$	−31.9548	−1.53565	−0.767826	−	0.640658i	$-0.778661\pi$
$433$	−31.9548	−1.53565	−0.767826	+	0.640658i	$0.778661\pi$
$434$	−30.2885	−1.45389
$435$	−18.8902	−0.905718
$436$	1.48472	0.0711053
$437$	22.0109	1.05293
$438$	−5.48361	−0.262017
$439$	−31.9091	−1.52294	−0.761470	−	0.648200i	$-0.775522\pi$
$439$	−31.9091	−1.52294	−0.761470	+	0.648200i	$0.775522\pi$
$440$	2.52923	0.120576
$441$	−24.9617	−1.18865
$442$	0.0990730	0.00471242
$443$	−17.8680	−0.848936	−0.424468	−	0.905443i	$-0.639539\pi$
$443$	−17.8680	−0.848936	−0.424468	+	0.905443i	$0.639539\pi$
$444$	−3.73137	−0.177083
$445$	5.34115	0.253195
$446$	24.9986	1.18372
$447$	−5.99822	−0.283706
$448$	4.14909	0.196026
$449$	−4.45013	−0.210015	−0.105007	−	0.994471i	$-0.533487\pi$
$449$	−4.45013	−0.210015	−0.105007	+	0.994471i	$0.533487\pi$
$450$	3.41384	0.160930
$451$	−8.13597	−0.383108
$452$	−6.46755	−0.304208
$453$	−3.09233	−0.145290
$454$	14.1599	0.664558
$455$	3.33561	0.156376
$456$	−3.58319	−0.167798
$457$	11.8197	0.552901	0.276451	−	0.961028i	$-0.410842\pi$
$457$	11.8197	0.552901	0.276451	+	0.961028i	$0.410842\pi$
$458$	20.9822	0.980434
$459$	1.26557	0.0590715
$460$	11.5886	0.540320
$461$	−5.43794	−0.253270	−0.126635	−	0.991949i	$-0.540418\pi$
$461$	−5.43794	−0.253270	−0.126635	+	0.991949i	$0.540418\pi$
$462$	3.09475	0.143981
$463$	−6.00682	−0.279161	−0.139580	−	0.990211i	$-0.544575\pi$
$463$	−6.00682	−0.279161	−0.139580	+	0.990211i	$0.544575\pi$
$464$	−10.0133	−0.464854
$465$	13.7717	0.638647
$466$	5.28649	0.244892
$467$	−11.7319	−0.542887	−0.271444	−	0.962454i	$-0.587501\pi$
$467$	−11.7319	−0.542887	−0.271444	+	0.962454i	$0.587501\pi$
$468$	−0.776736	−0.0359047
$469$	32.5781	1.50432
$470$	−7.13024	−0.328894
$471$	−5.72420	−0.263757
$472$	−12.7788	−0.588190
$473$	−0.409434	−0.0188258
$474$	−6.64622	−0.305271
$475$	6.71121	0.307932
$476$	−1.29322	−0.0592748
$477$	12.7771	0.585024
$478$	−6.17671	−0.282516
$479$	13.6436	0.623390	0.311695	−	0.950182i	$-0.399103\pi$
$479$	13.6436	0.623390	0.311695	+	0.950182i	$0.399103\pi$
$480$	−1.88652	−0.0861075
$481$	−1.59012	−0.0725033
$482$	−25.5607	−1.16426
$483$	14.1797	0.645197
$484$	1.00000	0.0454545
$485$	16.7584	0.760961
$486$	−15.3901	−0.698111
$487$	24.4240	1.10676	0.553379	−	0.832930i	$-0.313338\pi$
$487$	24.4240	1.10676	0.553379	+	0.832930i	$0.313338\pi$
$488$	3.43337	0.155421
$489$	−7.57869	−0.342720
$490$	−25.8359	−1.16715
$491$	12.7825	0.576866	0.288433	−	0.957500i	$-0.406866\pi$
$491$	12.7825	0.576866	0.288433	+	0.957500i	$0.406866\pi$
$492$	6.06851	0.273590
$493$	3.12102	0.140564
$494$	−1.52697	−0.0687017
$495$	6.18057	0.277796
$496$	7.30004	0.327782
$497$	−34.6731	−1.55530
$498$	−9.83981	−0.440932
$499$	−38.0200	−1.70201	−0.851003	−	0.525160i	$-0.824005\pi$
$499$	−38.0200	−1.70201	−0.851003	+	0.525160i	$0.824005\pi$
$500$	−9.11277	−0.407535
$501$	−3.25845	−0.145577
$502$	20.9869	0.936689
$503$	−9.24474	−0.412203	−0.206101	−	0.978531i	$-0.566078\pi$
$503$	−9.24474	−0.412203	−0.206101	+	0.978531i	$0.566078\pi$
$504$	10.1389	0.451624
$505$	−11.7959	−0.524912
$506$	4.58185	0.203688
$507$	−9.62117	−0.427291
$508$	12.0883	0.536333
$509$	−37.0856	−1.64379	−0.821895	−	0.569638i	$-0.807083\pi$
$509$	−37.0856	−1.64379	−0.821895	+	0.569638i	$0.807083\pi$
$510$	0.588008	0.0260374
$511$	30.5033	1.34939
$512$	−1.00000	−0.0441942
$513$	−19.5057	−0.861196
$514$	9.00211	0.397066
$515$	8.88415	0.391482
$516$	0.305391	0.0134441
$517$	−2.81913	−0.123985
$518$	20.7562	0.911976
$519$	3.61620	0.158734
$520$	−0.803939	−0.0352551
$521$	−40.7889	−1.78699	−0.893497	−	0.449070i	$-0.851755\pi$
$521$	−40.7889	−1.78699	−0.893497	+	0.449070i	$0.851755\pi$
$522$	−24.4689	−1.07098
$523$	26.1794	1.14475	0.572373	−	0.819994i	$-0.306023\pi$
$523$	26.1794	1.14475	0.572373	+	0.819994i	$0.306023\pi$
$524$	−18.4235	−0.804835
$525$	4.32344	0.188690
$526$	−21.1198	−0.920868
$527$	−2.27534	−0.0991155
$528$	−0.745887	−0.0324605
$529$	−2.00663	−0.0872450
$530$	13.2246	0.574439
$531$	−31.2269	−1.35513
$532$	19.9319	0.864159
$533$	2.58609	0.112016
$534$	−1.57514	−0.0681629
$535$	8.43761	0.364790
$536$	−7.85187	−0.339149
$537$	−14.9137	−0.643575
$538$	−6.83640	−0.294738
$539$	−10.2149	−0.439987
$540$	−10.2696	−0.441932
$541$	−11.7229	−0.504006	−0.252003	−	0.967726i	$-0.581089\pi$
$541$	−11.7229	−0.504006	−0.252003	+	0.967726i	$0.581089\pi$
$542$	−1.02728	−0.0441253
$543$	−5.61094	−0.240788
$544$	0.311689	0.0133635
$545$	3.75521	0.160855
$546$	−0.983692	−0.0420981
$547$	28.4573	1.21675	0.608373	−	0.793651i	$-0.291822\pi$
$547$	28.4573	1.21675	0.608373	+	0.793651i	$0.291822\pi$
$548$	9.37094	0.400307
$549$	8.38996	0.358075
$550$	1.39702	0.0595693
$551$	−48.1031	−2.04926
$552$	−3.41754	−0.145460
$553$	36.9704	1.57214
$554$	12.8779	0.547128
$555$	−9.43752	−0.400600
$556$	21.3938	0.907298
$557$	10.2899	0.435998	0.217999	−	0.975949i	$-0.430047\pi$
$557$	10.2899	0.435998	0.217999	+	0.975949i	$0.430047\pi$
$558$	17.8388	0.755175
$559$	0.130142	0.00550443
$560$	10.4940	0.443453
$561$	0.232485	0.00981551
$562$	−25.5286	−1.07686
$563$	−4.05369	−0.170842	−0.0854212	−	0.996345i	$-0.527224\pi$
$563$	−4.05369	−0.170842	−0.0854212	+	0.996345i	$0.527224\pi$
$564$	2.10275	0.0885418
$565$	−16.3580	−0.688184
$566$	18.4746	0.776544
$567$	17.8510	0.749673
$568$	8.35679	0.350643
$569$	36.4567	1.52834	0.764172	−	0.645012i	$-0.223148\pi$
$569$	36.4567	1.52834	0.764172	+	0.645012i	$0.223148\pi$
$570$	−9.06273	−0.379596
$571$	31.5222	1.31916	0.659582	−	0.751633i	$-0.270733\pi$
$571$	31.5222	1.31916	0.659582	+	0.751633i	$0.270733\pi$
$572$	−0.317859	−0.0132903
$573$	7.50333	0.313456
$574$	−33.7568	−1.40898
$575$	6.40096	0.266938
$576$	−2.44365	−0.101819
$577$	28.3924	1.18199	0.590995	−	0.806675i	$-0.298735\pi$
$577$	28.3924	1.18199	0.590995	+	0.806675i	$0.298735\pi$
$578$	16.9029	0.703066
$579$	−6.89615	−0.286594
$580$	−25.3259	−1.05160
$581$	54.7351	2.27080
$582$	−4.94217	−0.204859
$583$	5.22869	0.216550
$584$	−7.35181	−0.304220
$585$	−1.96455	−0.0812241
$586$	11.0154	0.455042
$587$	13.9373	0.575253	0.287627	−	0.957743i	$-0.407134\pi$
$587$	13.9373	0.575253	0.287627	+	0.957743i	$0.407134\pi$
$588$	7.61916	0.314209
$589$	35.0689	1.44499
$590$	−32.3205	−1.33061
$591$	0.745887	0.0306817
$592$	−5.00260	−0.205606
$593$	−11.9072	−0.488971	−0.244485	−	0.969653i	$-0.578619\pi$
$593$	−11.9072	−0.488971	−0.244485	+	0.969653i	$0.578619\pi$
$594$	−4.06035	−0.166598
$595$	−3.27087	−0.134092
$596$	−8.04174	−0.329402
$597$	15.7691	0.645386
$598$	−1.45638	−0.0595559
$599$	−5.55938	−0.227150	−0.113575	−	0.993529i	$-0.536230\pi$
$599$	−5.55938	−0.227150	−0.113575	+	0.993529i	$0.536230\pi$
$600$	−1.04202	−0.0425403
$601$	−10.6098	−0.432782	−0.216391	−	0.976307i	$-0.569429\pi$
$601$	−10.6098	−0.432782	−0.216391	+	0.976307i	$0.569429\pi$
$602$	−1.69878	−0.0692370
$603$	−19.1872	−0.781365
$604$	−4.14584	−0.168692
$605$	2.52923	0.102828
$606$	3.47869	0.141312
$607$	27.8601	1.13080	0.565402	−	0.824815i	$-0.308721\pi$
$607$	27.8601	1.13080	0.565402	+	0.824815i	$0.308721\pi$
$608$	−4.80394	−0.194825
$609$	−30.9885	−1.25572
$610$	8.68378	0.351596
$611$	0.896085	0.0362517
$612$	0.761659	0.0307883
$613$	−8.80586	−0.355665	−0.177833	−	0.984061i	$-0.556909\pi$
$613$	−8.80586	−0.355665	−0.177833	+	0.984061i	$0.556909\pi$
$614$	−20.3130	−0.819766
$615$	15.3487	0.618919
$616$	4.14909	0.167171
$617$	20.2841	0.816608	0.408304	−	0.912846i	$-0.366120\pi$
$617$	20.2841	0.816608	0.408304	+	0.912846i	$0.366120\pi$
$618$	−2.61999	−0.105391
$619$	13.0742	0.525498	0.262749	−	0.964864i	$-0.415371\pi$
$619$	13.0742	0.525498	0.262749	+	0.964864i	$0.415371\pi$
$620$	18.4635	0.741513
$621$	−18.6039	−0.746549
$622$	3.94348	0.158119
$623$	8.76190	0.351038
$624$	0.237087	0.00949106
$625$	−30.0334	−1.20134
$626$	−31.8387	−1.27253
$627$	−3.58319	−0.143099
$628$	−7.67435	−0.306240
$629$	1.55926	0.0621716
$630$	25.6437	1.02167
$631$	14.5562	0.579475	0.289737	−	0.957106i	$-0.406432\pi$
$631$	14.5562	0.579475	0.289737	+	0.957106i	$0.406432\pi$
$632$	−8.91050	−0.354441
$633$	−9.44326	−0.375336
$634$	12.3696	0.491261
$635$	30.5742	1.21330
$636$	−3.90001	−0.154645
$637$	3.24690	0.128647
$638$	−10.0133	−0.396429
$639$	20.4211	0.807847
$640$	−2.52923	−0.0999767
$641$	−13.9284	−0.550140	−0.275070	−	0.961424i	$-0.588701\pi$
$641$	−13.9284	−0.550140	−0.275070	+	0.961424i	$0.588701\pi$
$642$	−2.48830	−0.0982055
$643$	−42.1934	−1.66395	−0.831973	−	0.554817i	$-0.812788\pi$
$643$	−42.1934	−1.66395	−0.831973	+	0.554817i	$0.812788\pi$
$644$	19.0105	0.749118
$645$	0.772406	0.0304135
$646$	1.49733	0.0589118
$647$	−1.15339	−0.0453444	−0.0226722	−	0.999743i	$-0.507217\pi$
$647$	−1.15339	−0.0453444	−0.0226722	+	0.999743i	$0.507217\pi$
$648$	−4.30240	−0.169014
$649$	−12.7788	−0.501610
$650$	−0.444056	−0.0174173
$651$	22.5918	0.885442
$652$	−10.1607	−0.397922
$653$	2.21963	0.0868607	0.0434303	−	0.999056i	$-0.486171\pi$
$653$	2.21963	0.0868607	0.0434303	+	0.999056i	$0.486171\pi$
$654$	−1.10743	−0.0433041
$655$	−46.5974	−1.82071
$656$	8.13597	0.317656
$657$	−17.9653	−0.700892
$658$	−11.6968	−0.455989
$659$	26.0634	1.01528	0.507642	−	0.861568i	$-0.330517\pi$
$659$	26.0634	1.01528	0.507642	+	0.861568i	$0.330517\pi$
$660$	−1.88652	−0.0734328
$661$	22.0573	0.857928	0.428964	−	0.903321i	$-0.358879\pi$
$661$	22.0573	0.857928	0.428964	+	0.903321i	$0.358879\pi$
$662$	9.97836	0.387820
$663$	−0.0738972	−0.00286993
$664$	−13.1921	−0.511953
$665$	50.4125	1.95491
$666$	−12.2246	−0.473695
$667$	−45.8793	−1.77645
$668$	−4.36856	−0.169025
$669$	−18.6461	−0.720900
$670$	−19.8592	−0.767228
$671$	3.43337	0.132544
$672$	−3.09475	−0.119382
$673$	4.89902	0.188843	0.0944216	−	0.995532i	$-0.469900\pi$
$673$	4.89902	0.188843	0.0944216	+	0.995532i	$0.469900\pi$
$674$	−24.9340	−0.960420
$675$	−5.67240	−0.218331
$676$	−12.8990	−0.496114
$677$	−36.5904	−1.40628	−0.703142	−	0.711049i	$-0.748220\pi$
$677$	−36.5904	−1.40628	−0.703142	+	0.711049i	$0.748220\pi$
$678$	4.82406	0.185267
$679$	27.4914	1.05502
$680$	0.788334	0.0302312
$681$	−10.5617	−0.404725
$682$	7.30004	0.279533
$683$	−9.76472	−0.373637	−0.186818	−	0.982394i	$-0.559818\pi$
$683$	−9.76472	−0.373637	−0.186818	+	0.982394i	$0.559818\pi$
$684$	−11.7392	−0.448858
$685$	23.7013	0.905580
$686$	−13.3389	−0.509283
$687$	−15.6503	−0.597098
$688$	0.409434	0.0156095
$689$	−1.66198	−0.0633166
$690$	−8.64376	−0.329062
$691$	26.4368	1.00570	0.502851	−	0.864373i	$-0.332284\pi$
$691$	26.4368	1.00570	0.502851	+	0.864373i	$0.332284\pi$
$692$	4.84819	0.184301
$693$	10.1389	0.385146
$694$	−26.1869	−0.994041
$695$	54.1098	2.05250
$696$	7.46876	0.283103
$697$	−2.53589	−0.0960537
$698$	−3.61000	−0.136640
$699$	−3.94312	−0.149143
$700$	5.79637	0.219082
$701$	23.4937	0.887344	0.443672	−	0.896189i	$-0.353676\pi$
$701$	23.4937	0.887344	0.443672	+	0.896189i	$0.353676\pi$
$702$	1.29062	0.0487112
$703$	−24.0322	−0.906391
$704$	−1.00000	−0.0376889
$705$	5.31835	0.200301
$706$	−6.70926	−0.252506
$707$	−19.3507	−0.727756
$708$	9.53151	0.358216
$709$	−15.9199	−0.597884	−0.298942	−	0.954271i	$-0.596634\pi$
$709$	−15.9199	−0.597884	−0.298942	+	0.954271i	$0.596634\pi$
$710$	21.1363	0.793231
$711$	−21.7742	−0.816595
$712$	−2.11177	−0.0791418
$713$	33.4477	1.25263
$714$	0.964598	0.0360992
$715$	−0.803939	−0.0300656
$716$	−19.9947	−0.747235
$717$	4.60713	0.172056
$718$	−2.74786	−0.102549
$719$	−17.6884	−0.659665	−0.329833	−	0.944039i	$-0.606992\pi$
$719$	−17.6884	−0.659665	−0.329833	+	0.944039i	$0.606992\pi$
$720$	−6.18057	−0.230336
$721$	14.5740	0.542764
$722$	−4.07780	−0.151760
$723$	19.0654	0.709049
$724$	−7.52251	−0.279572
$725$	−13.9888	−0.519530
$726$	−0.745887	−0.0276824
$727$	−33.2277	−1.23235	−0.616174	−	0.787610i	$-0.711318\pi$
$727$	−33.2277	−1.23235	−0.616174	+	0.787610i	$0.711318\pi$
$728$	−1.31882	−0.0488788
$729$	−1.42790	−0.0528851
$730$	−18.5944	−0.688211
$731$	−0.127616	−0.00472005
$732$	−2.56090	−0.0946536
$733$	36.0336	1.33093	0.665465	−	0.746429i	$-0.268233\pi$
$733$	36.0336	1.33093	0.665465	+	0.746429i	$0.268233\pi$
$734$	−12.2241	−0.451200
$735$	19.2706	0.710809
$736$	−4.58185	−0.168889
$737$	−7.85187	−0.289227
$738$	19.8815	0.731848
$739$	1.95891	0.0720598	0.0360299	−	0.999351i	$-0.488529\pi$
$739$	1.95891	0.0720598	0.0360299	+	0.999351i	$0.488529\pi$
$740$	−12.6528	−0.465124
$741$	1.13895	0.0418403
$742$	21.6943	0.796422
$743$	−51.3350	−1.88330	−0.941649	−	0.336596i	$-0.890724\pi$
$743$	−51.3350	−1.88330	−0.941649	+	0.336596i	$0.890724\pi$
$744$	−5.44500	−0.199624
$745$	−20.3394	−0.745179
$746$	6.20727	0.227264
$747$	−32.2369	−1.17949
$748$	0.311689	0.0113965
$749$	13.8415	0.505757
$750$	6.79709	0.248195
$751$	−9.76300	−0.356257	−0.178128	−	0.984007i	$-0.557004\pi$
$751$	−9.76300	−0.356257	−0.178128	+	0.984007i	$0.557004\pi$
$752$	2.81913	0.102803
$753$	−15.6538	−0.570457
$754$	3.18280	0.115911
$755$	−10.4858	−0.381618
$756$	−16.8467	−0.612710
$757$	−28.3692	−1.03110	−0.515548	−	0.856861i	$-0.672412\pi$
$757$	−28.3692	−1.03110	−0.515548	+	0.856861i	$0.672412\pi$
$758$	−13.0376	−0.473548
$759$	−3.41754	−0.124049
$760$	−12.1503	−0.440737
$761$	−6.56741	−0.238068	−0.119034	−	0.992890i	$-0.537980\pi$
$761$	−6.56741	−0.238068	−0.119034	+	0.992890i	$0.537980\pi$
$762$	−9.01652	−0.326634
$763$	6.16024	0.223016
$764$	10.0596	0.363944
$765$	1.92641	0.0696497
$766$	−11.8955	−0.429801
$767$	4.06184	0.146665
$768$	0.745887	0.0269149
$769$	38.0922	1.37364	0.686819	−	0.726828i	$-0.259006\pi$
$769$	38.0922	1.37364	0.686819	+	0.726828i	$0.259006\pi$
$770$	10.4940	0.378178
$771$	−6.71455	−0.241819
$772$	−9.24558	−0.332756
$773$	−40.1457	−1.44394	−0.721971	−	0.691923i	$-0.756764\pi$
$773$	−40.1457	−1.44394	−0.721971	+	0.691923i	$0.756764\pi$
$774$	1.00052	0.0359628
$775$	10.1983	0.366335
$776$	−6.62590	−0.237856
$777$	−15.4818	−0.555406
$778$	−15.1673	−0.543773
$779$	39.0847	1.40035
$780$	0.599647	0.0214708
$781$	8.35679	0.299030
$782$	1.42811	0.0510692
$783$	40.6573	1.45297
$784$	10.2149	0.364818
$785$	−19.4102	−0.692781
$786$	13.7419	0.490156
$787$	−41.7276	−1.48743	−0.743714	−	0.668498i	$-0.766938\pi$
$787$	−41.7276	−1.48743	−0.743714	+	0.668498i	$0.766938\pi$
$788$	1.00000	0.0356235
$789$	15.7530	0.560821
$790$	−22.5367	−0.801821
$791$	−26.8344	−0.954123
$792$	−2.44365	−0.0868314
$793$	−1.09133	−0.0387541
$794$	−8.39856	−0.298054
$795$	−9.86404	−0.349841
$796$	21.1414	0.749337
$797$	23.9097	0.846924	0.423462	−	0.905914i	$-0.360815\pi$
$797$	23.9097	0.846924	0.423462	+	0.905914i	$0.360815\pi$
$798$	−14.8670	−0.526285
$799$	−0.878692	−0.0310859
$800$	−1.39702	−0.0493922
$801$	−5.16042	−0.182335
$802$	20.0113	0.706624
$803$	−7.35181	−0.259440
$804$	5.85660	0.206546
$805$	48.0820	1.69467
$806$	−2.32038	−0.0817320
$807$	5.09918	0.179500
$808$	4.66384	0.164073
$809$	−29.2326	−1.02776	−0.513881	−	0.857862i	$-0.671793\pi$
$809$	−29.2326	−1.02776	−0.513881	+	0.857862i	$0.671793\pi$
$810$	−10.8818	−0.382347
$811$	−23.1953	−0.814498	−0.407249	−	0.913317i	$-0.633512\pi$
$811$	−23.1953	−0.814498	−0.407249	+	0.913317i	$0.633512\pi$
$812$	−41.5459	−1.45797
$813$	0.766232	0.0268729
$814$	−5.00260	−0.175341
$815$	−25.6987	−0.900185
$816$	−0.232485	−0.00813859
$817$	1.96690	0.0688130
$818$	27.7637	0.970733
$819$	−3.22275	−0.112612
$820$	20.5778	0.718607
$821$	23.6970	0.827030	0.413515	−	0.910497i	$-0.364301\pi$
$821$	23.6970	0.827030	0.413515	+	0.910497i	$0.364301\pi$
$822$	−6.98966	−0.243792
$823$	−30.8749	−1.07623	−0.538116	−	0.842871i	$-0.680864\pi$
$823$	−30.8749	−1.07623	−0.538116	+	0.842871i	$0.680864\pi$
$824$	−3.51258	−0.122367
$825$	−1.04202	−0.0362785
$826$	−53.0202	−1.84481
$827$	2.36696	0.0823074	0.0411537	−	0.999153i	$-0.486897\pi$
$827$	2.36696	0.0823074	0.0411537	+	0.999153i	$0.486897\pi$
$828$	−11.1965	−0.389104
$829$	30.0787	1.04468	0.522339	−	0.852738i	$-0.325060\pi$
$829$	30.0787	1.04468	0.522339	+	0.852738i	$0.325060\pi$
$830$	−33.3659	−1.15815
$831$	−9.60543	−0.333209
$832$	0.317859	0.0110198
$833$	−3.18387	−0.110315
$834$	−15.9573	−0.552557
$835$	−11.0491	−0.382370
$836$	−4.80394	−0.166148
$837$	−29.6407	−1.02453
$838$	0.722133	0.0249457
$839$	4.76419	0.164478	0.0822390	−	0.996613i	$-0.473793\pi$
$839$	4.76419	0.164478	0.0822390	+	0.996613i	$0.473793\pi$
$840$	−7.82734	−0.270069
$841$	71.2655	2.45743
$842$	−1.35091	−0.0465553
$843$	19.0414	0.655822
$844$	−12.6604	−0.435790
$845$	−32.6245	−1.12232
$846$	6.88898	0.236848
$847$	4.14909	0.142564
$848$	−5.22869	−0.179554
$849$	−13.7799	−0.472926
$850$	0.435437	0.0149354
$851$	−22.9212	−0.785728
$852$	−6.23322	−0.213547
$853$	−21.9395	−0.751193	−0.375596	−	0.926783i	$-0.622562\pi$
$853$	−21.9395	−0.751193	−0.375596	+	0.926783i	$0.622562\pi$
$854$	14.2453	0.487465
$855$	−29.6911	−1.01541
$856$	−3.33603	−0.114023
$857$	−39.3098	−1.34280	−0.671399	−	0.741096i	$-0.734306\pi$
$857$	−39.3098	−1.34280	−0.671399	+	0.741096i	$0.734306\pi$
$858$	0.237087	0.00809400
$859$	−29.7051	−1.01353	−0.506763	−	0.862085i	$-0.669158\pi$
$859$	−29.7051	−1.01353	−0.506763	+	0.862085i	$0.669158\pi$
$860$	1.03555	0.0353121
$861$	25.1788	0.858090
$862$	29.3471	0.999565
$863$	3.55687	0.121077	0.0605386	−	0.998166i	$-0.480718\pi$
$863$	3.55687	0.121077	0.0605386	+	0.998166i	$0.480718\pi$
$864$	4.06035	0.138136
$865$	12.2622	0.416927
$866$	31.9548	1.08587
$867$	−12.6076	−0.428177
$868$	30.2885	1.02806
$869$	−8.91050	−0.302268
$870$	18.8902	0.640439
$871$	2.49578	0.0845664
$872$	−1.48472	−0.0502790
$873$	−16.1914	−0.547996
$874$	−22.0109	−0.744531
$875$	−37.8097	−1.27820
$876$	5.48361	0.185274
$877$	34.6168	1.16893	0.584464	−	0.811420i	$-0.301305\pi$
$877$	34.6168	1.16893	0.584464	+	0.811420i	$0.301305\pi$
$878$	31.9091	1.07688
$879$	−8.21624	−0.277127
$880$	−2.52923	−0.0852605
$881$	−42.4329	−1.42960	−0.714801	−	0.699328i	$-0.753483\pi$
$881$	−42.4329	−1.42960	−0.714801	+	0.699328i	$0.753483\pi$
$882$	24.9617	0.840504
$883$	45.6159	1.53510	0.767549	−	0.640990i	$-0.221476\pi$
$883$	45.6159	1.53510	0.767549	+	0.640990i	$0.221476\pi$
$884$	−0.0990730	−0.00333219
$885$	24.1074	0.810362
$886$	17.8680	0.600289
$887$	19.9158	0.668707	0.334353	−	0.942448i	$-0.391482\pi$
$887$	19.9158	0.668707	0.334353	+	0.942448i	$0.391482\pi$
$888$	3.73137	0.125217
$889$	50.1555	1.68216
$890$	−5.34115	−0.179036
$891$	−4.30240	−0.144136
$892$	−24.9986	−0.837014
$893$	13.5429	0.453197
$894$	5.99822	0.200611
$895$	−50.5711	−1.69041
$896$	−4.14909	−0.138611
$897$	1.08630	0.0362703
$898$	4.45013	0.148503
$899$	−73.0973	−2.43793
$900$	−3.41384	−0.113795
$901$	1.62972	0.0542940
$902$	8.13597	0.270898
$903$	1.26710	0.0421663
$904$	6.46755	0.215108
$905$	−19.0262	−0.632452
$906$	3.09233	0.102736
$907$	−9.23655	−0.306695	−0.153347	−	0.988172i	$-0.549005\pi$
$907$	−9.23655	−0.306695	−0.153347	+	0.988172i	$0.549005\pi$
$908$	−14.1599	−0.469914
$909$	11.3968	0.378008
$910$	−3.33561	−0.110574
$911$	11.8103	0.391291	0.195646	−	0.980675i	$-0.437320\pi$
$911$	11.8103	0.391291	0.195646	+	0.980675i	$0.437320\pi$
$912$	3.58319	0.118651
$913$	−13.1921	−0.436595
$914$	−11.8197	−0.390960
$915$	−6.47712	−0.214127
$916$	−20.9822	−0.693271
$917$	−76.4407	−2.52430
$918$	−1.26557	−0.0417699
$919$	16.2361	0.535580	0.267790	−	0.963477i	$-0.413707\pi$
$919$	16.2361	0.535580	0.267790	+	0.963477i	$0.413707\pi$
$920$	−11.5886	−0.382064
$921$	15.1512	0.499249
$922$	5.43794	0.179089
$923$	−2.65628	−0.0874325
$924$	−3.09475	−0.101810
$925$	−6.98875	−0.229789
$926$	6.00682	0.197396
$927$	−8.58354	−0.281920
$928$	10.0133	0.328701
$929$	−11.3906	−0.373714	−0.186857	−	0.982387i	$-0.559830\pi$
$929$	−11.3906	−0.373714	−0.186857	+	0.982387i	$0.559830\pi$
$930$	−13.7717	−0.451591
$931$	49.0718	1.60826
$932$	−5.28649	−0.173165
$933$	−2.94139	−0.0962968
$934$	11.7319	0.383879
$935$	0.788334	0.0257813
$936$	0.776736	0.0253884
$937$	26.3538	0.860943	0.430471	−	0.902604i	$-0.358347\pi$
$937$	26.3538	0.860943	0.430471	+	0.902604i	$0.358347\pi$
$938$	−32.5781	−1.06371
$939$	23.7481	0.774989
$940$	7.13024	0.232563
$941$	3.59600	0.117226	0.0586131	−	0.998281i	$-0.481332\pi$
$941$	3.59600	0.117226	0.0586131	+	0.998281i	$0.481332\pi$
$942$	5.72420	0.186504
$943$	37.2778	1.21393
$944$	12.7788	0.415913
$945$	−42.6093	−1.38608
$946$	0.409434	0.0133119
$947$	−23.3123	−0.757549	−0.378775	−	0.925489i	$-0.623654\pi$
$947$	−23.3123	−0.757549	−0.378775	+	0.925489i	$0.623654\pi$
$948$	6.64622	0.215859
$949$	2.33684	0.0758569
$950$	−6.71121	−0.217740
$951$	−9.22634	−0.299185
$952$	1.29322	0.0419136
$953$	−38.9957	−1.26319	−0.631597	−	0.775297i	$-0.717600\pi$
$953$	−38.9957	−1.26319	−0.631597	+	0.775297i	$0.717600\pi$
$954$	−12.7771	−0.413674
$955$	25.4431	0.823320
$956$	6.17671	0.199769
$957$	7.46876	0.241431
$958$	−13.6436	−0.440803
$959$	38.8808	1.25553
$960$	1.88652	0.0608872
$961$	22.2906	0.719052
$962$	1.59012	0.0512675
$963$	−8.15211	−0.262698
$964$	25.5607	0.823254
$965$	−23.3842	−0.752765
$966$	−14.1797	−0.456223
$967$	−26.3961	−0.848840	−0.424420	−	0.905465i	$-0.639522\pi$
$967$	−26.3961	−0.848840	−0.424420	+	0.905465i	$0.639522\pi$
$968$	−1.00000	−0.0321412
$969$	−1.11684	−0.0358781
$970$	−16.7584	−0.538081
$971$	21.0786	0.676444	0.338222	−	0.941066i	$-0.390175\pi$
$971$	21.0786	0.676444	0.338222	+	0.941066i	$0.390175\pi$
$972$	15.3901	0.493639
$973$	88.7646	2.84566
$974$	−24.4240	−0.782596
$975$	0.331215	0.0106074
$976$	−3.43337	−0.109899
$977$	−43.4907	−1.39139	−0.695696	−	0.718336i	$-0.744904\pi$
$977$	−43.4907	−1.39139	−0.695696	+	0.718336i	$0.744904\pi$
$978$	7.57869	0.242340
$979$	−2.11177	−0.0674923
$980$	25.8359	0.825297
$981$	−3.62814	−0.115838
$982$	−12.7825	−0.407906
$983$	43.9676	1.40235	0.701174	−	0.712990i	$-0.252659\pi$
$983$	43.9676	1.40235	0.701174	+	0.712990i	$0.252659\pi$
$984$	−6.06851	−0.193457
$985$	2.52923	0.0805881
$986$	−3.12102	−0.0993936
$987$	8.72450	0.277704
$988$	1.52697	0.0485795
$989$	1.87597	0.0596523
$990$	−6.18057	−0.196431
$991$	−40.2786	−1.27949	−0.639746	−	0.768586i	$-0.720961\pi$
$991$	−40.2786	−1.27949	−0.639746	+	0.768586i	$0.720961\pi$
$992$	−7.30004	−0.231777
$993$	−7.44272	−0.236188
$994$	34.6731	1.09976
$995$	53.4715	1.69516
$996$	9.83981	0.311786
$997$	9.33280	0.295573	0.147786	−	0.989019i	$-0.452785\pi$
$997$	9.33280	0.295573	0.147786	+	0.989019i	$0.452785\pi$
$998$	38.0200	1.20350
$999$	20.3123	0.642653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.e.1.16	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.e.1.16	✓	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.745887 q^{3} +1.00000 q^{4} +2.52923 q^{5} -0.745887 q^{6} +4.14909 q^{7} -1.00000 q^{8} -2.44365 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.745887 q^{3} +1.00000 q^{4} +2.52923 q^{5} -0.745887 q^{6} +4.14909 q^{7} -1.00000 q^{8} -2.44365 q^{9} -2.52923 q^{10} -1.00000 q^{11} +0.745887 q^{12} +0.317859 q^{13} -4.14909 q^{14} +1.88652 q^{15} +1.00000 q^{16} -0.311689 q^{17} +2.44365 q^{18} +4.80394 q^{19} +2.52923 q^{20} +3.09475 q^{21} +1.00000 q^{22} +4.58185 q^{23} -0.745887 q^{24} +1.39702 q^{25} -0.317859 q^{26} -4.06035 q^{27} +4.14909 q^{28} -10.0133 q^{29} -1.88652 q^{30} +7.30004 q^{31} -1.00000 q^{32} -0.745887 q^{33} +0.311689 q^{34} +10.4940 q^{35} -2.44365 q^{36} -5.00260 q^{37} -4.80394 q^{38} +0.237087 q^{39} -2.52923 q^{40} +8.13597 q^{41} -3.09475 q^{42} +0.409434 q^{43} -1.00000 q^{44} -6.18057 q^{45} -4.58185 q^{46} +2.81913 q^{47} +0.745887 q^{48} +10.2149 q^{49} -1.39702 q^{50} -0.232485 q^{51} +0.317859 q^{52} -5.22869 q^{53} +4.06035 q^{54} -2.52923 q^{55} -4.14909 q^{56} +3.58319 q^{57} +10.0133 q^{58} +12.7788 q^{59} +1.88652 q^{60} -3.43337 q^{61} -7.30004 q^{62} -10.1389 q^{63} +1.00000 q^{64} +0.803939 q^{65} +0.745887 q^{66} +7.85187 q^{67} -0.311689 q^{68} +3.41754 q^{69} -10.4940 q^{70} -8.35679 q^{71} +2.44365 q^{72} +7.35181 q^{73} +5.00260 q^{74} +1.04202 q^{75} +4.80394 q^{76} -4.14909 q^{77} -0.237087 q^{78} +8.91050 q^{79} +2.52923 q^{80} +4.30240 q^{81} -8.13597 q^{82} +13.1921 q^{83} +3.09475 q^{84} -0.788334 q^{85} -0.409434 q^{86} -7.46876 q^{87} +1.00000 q^{88} +2.11177 q^{89} +6.18057 q^{90} +1.31882 q^{91} +4.58185 q^{92} +5.44500 q^{93} -2.81913 q^{94} +12.1503 q^{95} -0.745887 q^{96} +6.62590 q^{97} -10.2149 q^{98} +2.44365 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * q^99

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