LMFDB - Embedded newform 8015.2.a.o.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$73$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45229 q^{2} -0.606235 q^{3} +4.01370 q^{4} +1.00000 q^{5} +1.48666 q^{6} +1.00000 q^{7} -4.93818 q^{8} -2.63248 q^{9} +O(q^{10})$	\(q-2.45229 q^{2} -0.606235 q^{3} +4.01370 q^{4} +1.00000 q^{5} +1.48666 q^{6} +1.00000 q^{7} -4.93818 q^{8} -2.63248 q^{9} -2.45229 q^{10} +5.04944 q^{11} -2.43325 q^{12} -1.39131 q^{13} -2.45229 q^{14} -0.606235 q^{15} +4.08241 q^{16} -6.65987 q^{17} +6.45559 q^{18} -6.66692 q^{19} +4.01370 q^{20} -0.606235 q^{21} -12.3827 q^{22} -1.14707 q^{23} +2.99370 q^{24} +1.00000 q^{25} +3.41189 q^{26} +3.41461 q^{27} +4.01370 q^{28} +9.49639 q^{29} +1.48666 q^{30} -4.73569 q^{31} -0.134881 q^{32} -3.06115 q^{33} +16.3319 q^{34} +1.00000 q^{35} -10.5660 q^{36} -11.8594 q^{37} +16.3492 q^{38} +0.843460 q^{39} -4.93818 q^{40} -10.5331 q^{41} +1.48666 q^{42} -11.8417 q^{43} +20.2669 q^{44} -2.63248 q^{45} +2.81293 q^{46} +3.37218 q^{47} -2.47490 q^{48} +1.00000 q^{49} -2.45229 q^{50} +4.03745 q^{51} -5.58430 q^{52} -6.05085 q^{53} -8.37359 q^{54} +5.04944 q^{55} -4.93818 q^{56} +4.04173 q^{57} -23.2879 q^{58} +0.108771 q^{59} -2.43325 q^{60} +4.10974 q^{61} +11.6133 q^{62} -2.63248 q^{63} -7.83405 q^{64} -1.39131 q^{65} +7.50681 q^{66} +8.29932 q^{67} -26.7308 q^{68} +0.695392 q^{69} -2.45229 q^{70} +1.69802 q^{71} +12.9996 q^{72} +3.25604 q^{73} +29.0826 q^{74} -0.606235 q^{75} -26.7591 q^{76} +5.04944 q^{77} -2.06841 q^{78} -0.0139514 q^{79} +4.08241 q^{80} +5.82738 q^{81} +25.8301 q^{82} -7.26835 q^{83} -2.43325 q^{84} -6.65987 q^{85} +29.0392 q^{86} -5.75705 q^{87} -24.9350 q^{88} -6.33177 q^{89} +6.45559 q^{90} -1.39131 q^{91} -4.60399 q^{92} +2.87094 q^{93} -8.26954 q^{94} -6.66692 q^{95} +0.0817695 q^{96} +13.2082 q^{97} -2.45229 q^{98} -13.2925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) $ 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * 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 $

$2$	−2.45229	−1.73403	−0.867014	−	0.498284i	$-0.833964\pi$
$2$	−2.45229	−1.73403	−0.867014	+	0.498284i	$0.833964\pi$
$3$	−0.606235	−0.350010	−0.175005	−	0.984568i	$-0.555994\pi$
$3$	−0.606235	−0.350010	−0.175005	+	0.984568i	$0.555994\pi$
$4$	4.01370	2.00685
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.48666	0.606927
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.93818	−1.74591
$9$	−2.63248	−0.877493
$10$	−2.45229	−0.775481
$11$	5.04944	1.52246	0.761231	−	0.648481i	$-0.224595\pi$
$11$	5.04944	1.52246	0.761231	+	0.648481i	$0.224595\pi$
$12$	−2.43325	−0.702419
$13$	−1.39131	−0.385880	−0.192940	−	0.981211i	$-0.561802\pi$
$13$	−1.39131	−0.385880	−0.192940	+	0.981211i	$0.561802\pi$
$14$	−2.45229	−0.655401
$15$	−0.606235	−0.156529
$16$	4.08241	1.02060
$17$	−6.65987	−1.61526	−0.807628	−	0.589692i	$-0.799249\pi$
$17$	−6.65987	−1.61526	−0.807628	+	0.589692i	$0.799249\pi$
$18$	6.45559	1.52160
$19$	−6.66692	−1.52950	−0.764749	−	0.644329i	$-0.777137\pi$
$19$	−6.66692	−1.52950	−0.764749	+	0.644329i	$0.777137\pi$
$20$	4.01370	0.897491
$21$	−0.606235	−0.132291
$22$	−12.3827	−2.63999
$23$	−1.14707	−0.239180	−0.119590	−	0.992823i	$-0.538158\pi$
$23$	−1.14707	−0.239180	−0.119590	+	0.992823i	$0.538158\pi$
$24$	2.99370	0.611086
$25$	1.00000	0.200000
$26$	3.41189	0.669126
$27$	3.41461	0.657142
$28$	4.01370	0.758519
$29$	9.49639	1.76343	0.881717	−	0.471778i	$-0.156388\pi$
$29$	9.49639	1.76343	0.881717	+	0.471778i	$0.156388\pi$
$30$	1.48666	0.271426
$31$	−4.73569	−0.850555	−0.425278	−	0.905063i	$-0.639824\pi$
$31$	−4.73569	−0.850555	−0.425278	+	0.905063i	$0.639824\pi$
$32$	−0.134881	−0.0238438
$33$	−3.06115	−0.532877
$34$	16.3319	2.80090
$35$	1.00000	0.169031
$36$	−10.5660	−1.76100
$37$	−11.8594	−1.94967	−0.974835	−	0.222927i	$-0.928439\pi$
$37$	−11.8594	−1.94967	−0.974835	+	0.222927i	$0.928439\pi$
$38$	16.3492	2.65219
$39$	0.843460	0.135062
$40$	−4.93818	−0.780794
$41$	−10.5331	−1.64499	−0.822495	−	0.568772i	$-0.807419\pi$
$41$	−10.5331	−1.64499	−0.822495	+	0.568772i	$0.807419\pi$
$42$	1.48666	0.229397
$43$	−11.8417	−1.80584	−0.902921	−	0.429806i	$-0.858582\pi$
$43$	−11.8417	−1.80584	−0.902921	+	0.429806i	$0.858582\pi$
$44$	20.2669	3.05536
$45$	−2.63248	−0.392427
$46$	2.81293	0.414745
$47$	3.37218	0.491882	0.245941	−	0.969285i	$-0.420903\pi$
$47$	3.37218	0.491882	0.245941	+	0.969285i	$0.420903\pi$
$48$	−2.47490	−0.357221
$49$	1.00000	0.142857
$50$	−2.45229	−0.346806
$51$	4.03745	0.565356
$52$	−5.58430	−0.774403
$53$	−6.05085	−0.831147	−0.415574	−	0.909559i	$-0.636419\pi$
$53$	−6.05085	−0.831147	−0.415574	+	0.909559i	$0.636419\pi$
$54$	−8.37359	−1.13950
$55$	5.04944	0.680866
$56$	−4.93818	−0.659892
$57$	4.04173	0.535340
$58$	−23.2879	−3.05784
$59$	0.108771	0.0141608	0.00708042	−	0.999975i	$-0.497746\pi$
$59$	0.108771	0.0141608	0.00708042	+	0.999975i	$0.497746\pi$
$60$	−2.43325	−0.314131
$61$	4.10974	0.526199	0.263099	−	0.964769i	$-0.415255\pi$
$61$	4.10974	0.526199	0.263099	+	0.964769i	$0.415255\pi$
$62$	11.6133	1.47489
$63$	−2.63248	−0.331661
$64$	−7.83405	−0.979257
$65$	−1.39131	−0.172571
$66$	7.50681	0.924024
$67$	8.29932	1.01392	0.506962	−	0.861969i	$-0.330769\pi$
$67$	8.29932	1.01392	0.506962	+	0.861969i	$0.330769\pi$
$68$	−26.7308	−3.24158
$69$	0.695392	0.0837154
$70$	−2.45229	−0.293104
$71$	1.69802	0.201518	0.100759	−	0.994911i	$-0.467873\pi$
$71$	1.69802	0.201518	0.100759	+	0.994911i	$0.467873\pi$
$72$	12.9996	1.53202
$73$	3.25604	0.381091	0.190545	−	0.981678i	$-0.438974\pi$
$73$	3.25604	0.381091	0.190545	+	0.981678i	$0.438974\pi$
$74$	29.0826	3.38078
$75$	−0.606235	−0.0700020
$76$	−26.7591	−3.06947
$77$	5.04944	0.575437
$78$	−2.06841	−0.234201
$79$	−0.0139514	−0.00156965	−0.000784826	−	1.00000i	$-0.500250\pi$
$79$	−0.0139514	−0.00156965	−0.000784826		1.00000i	$0.500250\pi$
$80$	4.08241	0.456427
$81$	5.82738	0.647487
$82$	25.8301	2.85246
$83$	−7.26835	−0.797805	−0.398902	−	0.916993i	$-0.630609\pi$
$83$	−7.26835	−0.797805	−0.398902	+	0.916993i	$0.630609\pi$
$84$	−2.43325	−0.265489
$85$	−6.65987	−0.722365
$86$	29.0392	3.13138
$87$	−5.75705	−0.617220
$88$	−24.9350	−2.65808
$89$	−6.33177	−0.671166	−0.335583	−	0.942011i	$-0.608933\pi$
$89$	−6.33177	−0.671166	−0.335583	+	0.942011i	$0.608933\pi$
$90$	6.45559	0.680479
$91$	−1.39131	−0.145849
$92$	−4.60399	−0.479999
$93$	2.87094	0.297703
$94$	−8.26954	−0.852938
$95$	−6.66692	−0.684012
$96$	0.0817695	0.00834557
$97$	13.2082	1.34109	0.670546	−	0.741868i	$-0.266060\pi$
$97$	13.2082	1.34109	0.670546	+	0.741868i	$0.266060\pi$
$98$	−2.45229	−0.247718
$99$	−13.2925	−1.33595
$100$	4.01370	0.401370
$101$	−1.08672	−0.108133	−0.0540663	−	0.998537i	$-0.517218\pi$
$101$	−1.08672	−0.108133	−0.0540663	+	0.998537i	$0.517218\pi$
$102$	−9.90098	−0.980343
$103$	−0.288267	−0.0284038	−0.0142019	−	0.999899i	$-0.504521\pi$
$103$	−0.288267	−0.0284038	−0.0142019	+	0.999899i	$0.504521\pi$
$104$	6.87053	0.673711
$105$	−0.606235	−0.0591625
$106$	14.8384	1.44123
$107$	−8.71677	−0.842682	−0.421341	−	0.906902i	$-0.638440\pi$
$107$	−8.71677	−0.842682	−0.421341	+	0.906902i	$0.638440\pi$
$108$	13.7052	1.31879
$109$	20.1401	1.92907	0.964537	−	0.263947i	$-0.0850244\pi$
$109$	20.1401	1.92907	0.964537	+	0.263947i	$0.0850244\pi$
$110$	−12.3827	−1.18064
$111$	7.18958	0.682404
$112$	4.08241	0.385751
$113$	−3.24352	−0.305125	−0.152562	−	0.988294i	$-0.548753\pi$
$113$	−3.24352	−0.305125	−0.152562	+	0.988294i	$0.548753\pi$
$114$	−9.91146	−0.928294
$115$	−1.14707	−0.106965
$116$	38.1157	3.53895
$117$	3.66259	0.338607
$118$	−0.266739	−0.0245553
$119$	−6.65987	−0.610510
$120$	2.99370	0.273286
$121$	14.4968	1.31789
$122$	−10.0783	−0.912443
$123$	6.38553	0.575763
$124$	−19.0077	−1.70694
$125$	1.00000	0.0894427
$126$	6.45559	0.575110
$127$	15.4489	1.37087	0.685435	−	0.728134i	$-0.259612\pi$
$127$	15.4489	1.37087	0.685435	+	0.728134i	$0.259612\pi$
$128$	19.4811	1.72190
$129$	7.17886	0.632063
$130$	3.41189	0.299242
$131$	13.1552	1.14938	0.574689	−	0.818372i	$-0.305123\pi$
$131$	13.1552	1.14938	0.574689	+	0.818372i	$0.305123\pi$
$132$	−12.2865	−1.06941
$133$	−6.66692	−0.578096
$134$	−20.3523	−1.75817
$135$	3.41461	0.293883
$136$	32.8876	2.82009
$137$	−1.65241	−0.141175	−0.0705874	−	0.997506i	$-0.522487\pi$
$137$	−1.65241	−0.141175	−0.0705874	+	0.997506i	$0.522487\pi$
$138$	−1.70530	−0.145165
$139$	12.2670	1.04048	0.520238	−	0.854021i	$-0.325843\pi$
$139$	12.2670	1.04048	0.520238	+	0.854021i	$0.325843\pi$
$140$	4.01370	0.339220
$141$	−2.04433	−0.172164
$142$	−4.16404	−0.349439
$143$	−7.02532	−0.587487
$144$	−10.7469	−0.895571
$145$	9.49639	0.788632
$146$	−7.98474	−0.660822
$147$	−0.606235	−0.0500015
$148$	−47.6000	−3.91270
$149$	4.37339	0.358282	0.179141	−	0.983823i	$-0.442668\pi$
$149$	4.37339	0.358282	0.179141	+	0.983823i	$0.442668\pi$
$150$	1.48666	0.121385
$151$	4.35302	0.354244	0.177122	−	0.984189i	$-0.443321\pi$
$151$	4.35302	0.354244	0.177122	+	0.984189i	$0.443321\pi$
$152$	32.9224	2.67036
$153$	17.5320	1.41738
$154$	−12.3827	−0.997823
$155$	−4.73569	−0.380380
$156$	3.38540	0.271049
$157$	10.1697	0.811627	0.405814	−	0.913956i	$-0.366988\pi$
$157$	10.1697	0.811627	0.405814	+	0.913956i	$0.366988\pi$
$158$	0.0342128	0.00272182
$159$	3.66824	0.290910
$160$	−0.134881	−0.0106633
$161$	−1.14707	−0.0904015
$162$	−14.2904	−1.12276
$163$	10.1505	0.795048	0.397524	−	0.917592i	$-0.369870\pi$
$163$	10.1505	0.795048	0.397524	+	0.917592i	$0.369870\pi$
$164$	−42.2767	−3.30125
$165$	−3.06115	−0.238310
$166$	17.8241	1.38342
$167$	20.5414	1.58954	0.794771	−	0.606910i	$-0.207591\pi$
$167$	20.5414	1.58954	0.794771	+	0.606910i	$0.207591\pi$
$168$	2.99370	0.230969
$169$	−11.0643	−0.851097
$170$	16.3319	1.25260
$171$	17.5505	1.34212
$172$	−47.5291	−3.62406
$173$	−14.9399	−1.13586	−0.567928	−	0.823078i	$-0.692255\pi$
$173$	−14.9399	−1.13586	−0.567928	+	0.823078i	$0.692255\pi$
$174$	14.1179	1.07028
$175$	1.00000	0.0755929
$176$	20.6139	1.55383
$177$	−0.0659411	−0.00495644
$178$	15.5273	1.16382
$179$	5.38002	0.402121	0.201061	−	0.979579i	$-0.435561\pi$
$179$	5.38002	0.402121	0.201061	+	0.979579i	$0.435561\pi$
$180$	−10.5660	−0.787542
$181$	−1.22139	−0.0907849	−0.0453924	−	0.998969i	$-0.514454\pi$
$181$	−1.22139	−0.0907849	−0.0453924	+	0.998969i	$0.514454\pi$
$182$	3.41189	0.252906
$183$	−2.49147	−0.184175
$184$	5.66442	0.417586
$185$	−11.8594	−0.871919
$186$	−7.04037	−0.516225
$187$	−33.6286	−2.45917
$188$	13.5349	0.987135
$189$	3.41461	0.248376
$190$	16.3492	1.18610
$191$	10.7797	0.779989	0.389994	−	0.920817i	$-0.372477\pi$
$191$	10.7797	0.779989	0.389994	+	0.920817i	$0.372477\pi$
$192$	4.74928	0.342750
$193$	14.0840	1.01379	0.506893	−	0.862009i	$-0.330794\pi$
$193$	14.0840	1.01379	0.506893	+	0.862009i	$0.330794\pi$
$194$	−32.3903	−2.32549
$195$	0.843460	0.0604015
$196$	4.01370	0.286693
$197$	12.3608	0.880668	0.440334	−	0.897834i	$-0.354860\pi$
$197$	12.3608	0.880668	0.440334	+	0.897834i	$0.354860\pi$
$198$	32.5971	2.31657
$199$	6.97276	0.494286	0.247143	−	0.968979i	$-0.420508\pi$
$199$	6.97276	0.494286	0.247143	+	0.968979i	$0.420508\pi$
$200$	−4.93818	−0.349182
$201$	−5.03134	−0.354884
$202$	2.66495	0.187505
$203$	9.49639	0.666516
$204$	16.2051	1.13459
$205$	−10.5331	−0.735662
$206$	0.706913	0.0492530
$207$	3.01963	0.209879
$208$	−5.67989	−0.393830
$209$	−33.6642	−2.32860
$210$	1.48666	0.102589
$211$	21.7045	1.49420	0.747101	−	0.664710i	$-0.231445\pi$
$211$	21.7045	1.49420	0.747101	+	0.664710i	$0.231445\pi$
$212$	−24.2863	−1.66799
$213$	−1.02940	−0.0705335
$214$	21.3760	1.46123
$215$	−11.8417	−0.807597
$216$	−16.8619	−1.14731
$217$	−4.73569	−0.321480
$218$	−49.3893	−3.34507
$219$	−1.97393	−0.133386
$220$	20.2669	1.36640
$221$	9.26594	0.623295
$222$	−17.6309	−1.18331
$223$	15.7664	1.05579	0.527896	−	0.849309i	$-0.322981\pi$
$223$	15.7664	1.05579	0.527896	+	0.849309i	$0.322981\pi$
$224$	−0.134881	−0.00901210
$225$	−2.63248	−0.175499
$226$	7.95404	0.529095
$227$	−18.3470	−1.21774	−0.608868	−	0.793272i	$-0.708376\pi$
$227$	−18.3470	−1.21774	−0.608868	+	0.793272i	$0.708376\pi$
$228$	16.2223	1.07435
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	2.81293	0.185479
$231$	−3.06115	−0.201409
$232$	−46.8948	−3.07880
$233$	−29.6141	−1.94009	−0.970043	−	0.242933i	$-0.921890\pi$
$233$	−29.6141	−1.94009	−0.970043	+	0.242933i	$0.921890\pi$
$234$	−8.98172	−0.587153
$235$	3.37218	0.219976
$236$	0.436576	0.0284187
$237$	0.00845782	0.000549394 0
$238$	16.3319	1.05864
$239$	27.7677	1.79614	0.898070	−	0.439852i	$-0.144969\pi$
$239$	27.7677	1.79614	0.898070	+	0.439852i	$0.144969\pi$
$240$	−2.47490	−0.159754
$241$	1.90839	0.122930	0.0614651	−	0.998109i	$-0.480423\pi$
$241$	1.90839	0.122930	0.0614651	+	0.998109i	$0.480423\pi$
$242$	−35.5503	−2.28526
$243$	−13.7766	−0.883769
$244$	16.4953	1.05600
$245$	1.00000	0.0638877
$246$	−15.6591	−0.998390
$247$	9.27575	0.590202
$248$	23.3857	1.48499
$249$	4.40633	0.279240
$250$	−2.45229	−0.155096
$251$	4.89931	0.309242	0.154621	−	0.987974i	$-0.450584\pi$
$251$	4.89931	0.309242	0.154621	+	0.987974i	$0.450584\pi$
$252$	−10.5660	−0.665595
$253$	−5.79204	−0.364142
$254$	−37.8852	−2.37713
$255$	4.03745	0.252835
$256$	−32.1051	−2.00657
$257$	−7.38046	−0.460381	−0.230190	−	0.973146i	$-0.573935\pi$
$257$	−7.38046	−0.460381	−0.230190	+	0.973146i	$0.573935\pi$
$258$	−17.6046	−1.09601
$259$	−11.8594	−0.736906
$260$	−5.58430	−0.346324
$261$	−24.9990	−1.54740
$262$	−32.2604	−1.99305
$263$	4.95790	0.305717	0.152859	−	0.988248i	$-0.451152\pi$
$263$	4.95790	0.305717	0.152859	+	0.988248i	$0.451152\pi$
$264$	15.1165	0.930355
$265$	−6.05085	−0.371700
$266$	16.3492	1.00243
$267$	3.83854	0.234915
$268$	33.3110	2.03479
$269$	22.9390	1.39862	0.699308	−	0.714821i	$-0.253492\pi$
$269$	22.9390	1.39862	0.699308	+	0.714821i	$0.253492\pi$
$270$	−8.37359	−0.509601
$271$	4.40394	0.267520	0.133760	−	0.991014i	$-0.457295\pi$
$271$	4.40394	0.267520	0.133760	+	0.991014i	$0.457295\pi$
$272$	−27.1883	−1.64853
$273$	0.843460	0.0510485
$274$	4.05218	0.244801
$275$	5.04944	0.304493
$276$	2.79110	0.168004
$277$	21.8650	1.31374	0.656871	−	0.754003i	$-0.271880\pi$
$277$	21.8650	1.31374	0.656871	+	0.754003i	$0.271880\pi$
$278$	−30.0823	−1.80421
$279$	12.4666	0.746356
$280$	−4.93818	−0.295112
$281$	−16.6067	−0.990673	−0.495337	−	0.868701i	$-0.664955\pi$
$281$	−16.6067	−0.990673	−0.495337	+	0.868701i	$0.664955\pi$
$282$	5.01329	0.298537
$283$	5.91393	0.351547	0.175773	−	0.984431i	$-0.443757\pi$
$283$	5.91393	0.351547	0.175773	+	0.984431i	$0.443757\pi$
$284$	6.81537	0.404418
$285$	4.04173	0.239411
$286$	17.2281	1.01872
$287$	−10.5331	−0.621748
$288$	0.355071	0.0209227
$289$	27.3539	1.60905
$290$	−23.2879	−1.36751
$291$	−8.00729	−0.469396
$292$	13.0688	0.764793
$293$	−27.9263	−1.63147	−0.815736	−	0.578425i	$-0.803668\pi$
$293$	−27.9263	−1.63147	−0.815736	+	0.578425i	$0.803668\pi$
$294$	1.48666	0.0867039
$295$	0.108771	0.00633292
$296$	58.5637	3.40395
$297$	17.2418	1.00047
$298$	−10.7248	−0.621271
$299$	1.59592	0.0922946
$300$	−2.43325	−0.140484
$301$	−11.8417	−0.682544
$302$	−10.6748	−0.614268
$303$	0.658808	0.0378475
$304$	−27.2171	−1.56101
$305$	4.10974	0.235323
$306$	−42.9934	−2.45777
$307$	6.70850	0.382874	0.191437	−	0.981505i	$-0.438685\pi$
$307$	6.70850	0.382874	0.191437	+	0.981505i	$0.438685\pi$
$308$	20.2669	1.15482
$309$	0.174758	0.00994162
$310$	11.6133	0.659589
$311$	9.66850	0.548250	0.274125	−	0.961694i	$-0.411612\pi$
$311$	9.66850	0.548250	0.274125	+	0.961694i	$0.411612\pi$
$312$	−4.16516	−0.235806
$313$	5.14987	0.291088	0.145544	−	0.989352i	$-0.453507\pi$
$313$	5.14987	0.291088	0.145544	+	0.989352i	$0.453507\pi$
$314$	−24.9389	−1.40738
$315$	−2.63248	−0.148323
$316$	−0.0559967	−0.00315006
$317$	17.4078	0.977718	0.488859	−	0.872363i	$-0.337413\pi$
$317$	17.4078	0.977718	0.488859	+	0.872363i	$0.337413\pi$
$318$	−8.99556	−0.504446
$319$	47.9514	2.68476
$320$	−7.83405	−0.437937
$321$	5.28441	0.294947
$322$	2.81293	0.156759
$323$	44.4009	2.47053
$324$	23.3894	1.29941
$325$	−1.39131	−0.0771759
$326$	−24.8919	−1.37864
$327$	−12.2097	−0.675196
$328$	52.0142	2.87200
$329$	3.37218	0.185914
$330$	7.50681	0.413236
$331$	16.4678	0.905153	0.452576	−	0.891726i	$-0.350505\pi$
$331$	16.4678	0.905153	0.452576	+	0.891726i	$0.350505\pi$
$332$	−29.1730	−1.60108
$333$	31.2196	1.71082
$334$	−50.3734	−2.75631
$335$	8.29932	0.453440
$336$	−2.47490	−0.135017
$337$	−22.4012	−1.22027	−0.610136	−	0.792297i	$-0.708885\pi$
$337$	−22.4012	−1.22027	−0.610136	+	0.792297i	$0.708885\pi$
$338$	27.1327	1.47583
$339$	1.96634	0.106797
$340$	−26.7308	−1.44968
$341$	−23.9126	−1.29494
$342$	−43.0389	−2.32728
$343$	1.00000	0.0539949
$344$	58.4764	3.15284
$345$	0.695392	0.0374387
$346$	36.6368	1.96961
$347$	1.69967	0.0912428	0.0456214	−	0.998959i	$-0.485473\pi$
$347$	1.69967	0.0912428	0.0456214	+	0.998959i	$0.485473\pi$
$348$	−23.1071	−1.23867
$349$	−28.8420	−1.54388	−0.771938	−	0.635698i	$-0.780712\pi$
$349$	−28.8420	−1.54388	−0.771938	+	0.635698i	$0.780712\pi$
$350$	−2.45229	−0.131080
$351$	−4.75077	−0.253578
$352$	−0.681072	−0.0363013
$353$	−22.3869	−1.19154	−0.595768	−	0.803157i	$-0.703152\pi$
$353$	−22.3869	−1.19154	−0.595768	+	0.803157i	$0.703152\pi$
$354$	0.161706	0.00859460
$355$	1.69802	0.0901218
$356$	−25.4138	−1.34693
$357$	4.03745	0.213685
$358$	−13.1933	−0.697289
$359$	−17.2787	−0.911934	−0.455967	−	0.889997i	$-0.650707\pi$
$359$	−17.2787	−0.911934	−0.455967	+	0.889997i	$0.650707\pi$
$360$	12.9996	0.685141
$361$	25.4479	1.33936
$362$	2.99519	0.157423
$363$	−8.78848	−0.461276
$364$	−5.58430	−0.292697
$365$	3.25604	0.170429
$366$	6.10980	0.319364
$367$	−2.17323	−0.113441	−0.0567207	−	0.998390i	$-0.518064\pi$
$367$	−2.17323	−0.113441	−0.0567207	+	0.998390i	$0.518064\pi$
$368$	−4.68280	−0.244108
$369$	27.7281	1.44347
$370$	29.0826	1.51193
$371$	−6.05085	−0.314144
$372$	11.5231	0.597446
$373$	−25.6929	−1.33033	−0.665164	−	0.746697i	$-0.731638\pi$
$373$	−25.6929	−1.33033	−0.665164	+	0.746697i	$0.731638\pi$
$374$	82.4670	4.26426
$375$	−0.606235	−0.0313059
$376$	−16.6524	−0.858782
$377$	−13.2124	−0.680473
$378$	−8.37359	−0.430691
$379$	5.82768	0.299348	0.149674	−	0.988735i	$-0.452178\pi$
$379$	5.82768	0.299348	0.149674	+	0.988735i	$0.452178\pi$
$380$	−26.7591	−1.37271
$381$	−9.36568	−0.479818
$382$	−26.4348	−1.35252
$383$	4.11775	0.210407	0.105204	−	0.994451i	$-0.466451\pi$
$383$	4.11775	0.210407	0.105204	+	0.994451i	$0.466451\pi$
$384$	−11.8101	−0.602683
$385$	5.04944	0.257343
$386$	−34.5379	−1.75793
$387$	31.1730	1.58461
$388$	53.0139	2.69137
$389$	−7.40823	−0.375612	−0.187806	−	0.982206i	$-0.560138\pi$
$389$	−7.40823	−0.375612	−0.187806	+	0.982206i	$0.560138\pi$
$390$	−2.06841	−0.104738
$391$	7.63932	0.386337
$392$	−4.93818	−0.249416
$393$	−7.97517	−0.402294
$394$	−30.3121	−1.52710
$395$	−0.0139514	−0.000701970 0
$396$	−53.3523	−2.68105
$397$	−26.3480	−1.32237	−0.661184	−	0.750224i	$-0.729946\pi$
$397$	−26.3480	−1.32237	−0.661184	+	0.750224i	$0.729946\pi$
$398$	−17.0992	−0.857105
$399$	4.04173	0.202339
$400$	4.08241	0.204120
$401$	9.90306	0.494535	0.247268	−	0.968947i	$-0.420467\pi$
$401$	9.90306	0.494535	0.247268	+	0.968947i	$0.420467\pi$
$402$	12.3383	0.615378
$403$	6.58881	0.328212
$404$	−4.36177	−0.217006
$405$	5.82738	0.289565
$406$	−23.2879	−1.15576
$407$	−59.8832	−2.96830
$408$	−19.9376	−0.987060
$409$	−0.360205	−0.0178110	−0.00890550	−	0.999960i	$-0.502835\pi$
$409$	−0.360205	−0.0178110	−0.00890550	+	0.999960i	$0.502835\pi$
$410$	25.8301	1.27566
$411$	1.00175	0.0494126
$412$	−1.15702	−0.0570022
$413$	0.108771	0.00535229
$414$	−7.40499	−0.363935
$415$	−7.26835	−0.356789
$416$	0.187661	0.00920083
$417$	−7.43671	−0.364177
$418$	82.5543	4.03786
$419$	−30.4597	−1.48805	−0.744026	−	0.668151i	$-0.767086\pi$
$419$	−30.4597	−1.48805	−0.744026	+	0.668151i	$0.767086\pi$
$420$	−2.43325	−0.118730
$421$	37.9627	1.85019	0.925095	−	0.379737i	$-0.123985\pi$
$421$	37.9627	1.85019	0.925095	+	0.379737i	$0.123985\pi$
$422$	−53.2257	−2.59099
$423$	−8.87718	−0.431623
$424$	29.8801	1.45111
$425$	−6.65987	−0.323051
$426$	2.52439	0.122307
$427$	4.10974	0.198884
$428$	−34.9865	−1.69114
$429$	4.25900	0.205626
$430$	29.0392	1.40040
$431$	−16.8774	−0.812954	−0.406477	−	0.913661i	$-0.633243\pi$
$431$	−16.8774	−0.812954	−0.406477	+	0.913661i	$0.633243\pi$
$432$	13.9398	0.670680
$433$	−16.0736	−0.772449	−0.386225	−	0.922405i	$-0.626221\pi$
$433$	−16.0736	−0.772449	−0.386225	+	0.922405i	$0.626221\pi$
$434$	11.6133	0.557455
$435$	−5.75705	−0.276029
$436$	80.8365	3.87137
$437$	7.64741	0.365825
$438$	4.84063	0.231294
$439$	10.7997	0.515442	0.257721	−	0.966219i	$-0.417029\pi$
$439$	10.7997	0.515442	0.257721	+	0.966219i	$0.417029\pi$
$440$	−24.9350	−1.18873
$441$	−2.63248	−0.125356
$442$	−22.7227	−1.08081
$443$	−3.29996	−0.156786	−0.0783928	−	0.996923i	$-0.524979\pi$
$443$	−3.29996	−0.156786	−0.0783928	+	0.996923i	$0.524979\pi$
$444$	28.8568	1.36948
$445$	−6.33177	−0.300155
$446$	−38.6636	−1.83077
$447$	−2.65130	−0.125402
$448$	−7.83405	−0.370124
$449$	3.46166	0.163366	0.0816829	−	0.996658i	$-0.473971\pi$
$449$	3.46166	0.163366	0.0816829	+	0.996658i	$0.473971\pi$
$450$	6.45559	0.304319
$451$	−53.1861	−2.50444
$452$	−13.0185	−0.612341
$453$	−2.63895	−0.123989
$454$	44.9922	2.11159
$455$	−1.39131	−0.0652255
$456$	−19.9588	−0.934654
$457$	20.4128	0.954872	0.477436	−	0.878667i	$-0.341566\pi$
$457$	20.4128	0.954872	0.477436	+	0.878667i	$0.341566\pi$
$458$	−2.45229	−0.114588
$459$	−22.7409	−1.06145
$460$	−4.60399	−0.214662
$461$	−19.3873	−0.902958	−0.451479	−	0.892282i	$-0.649103\pi$
$461$	−19.3873	−0.902958	−0.451479	+	0.892282i	$0.649103\pi$
$462$	7.50681	0.349248
$463$	−6.58349	−0.305961	−0.152980	−	0.988229i	$-0.548887\pi$
$463$	−6.58349	−0.305961	−0.152980	+	0.988229i	$0.548887\pi$
$464$	38.7681	1.79977
$465$	2.87094	0.133137
$466$	72.6223	3.36416
$467$	31.2273	1.44503	0.722513	−	0.691357i	$-0.242987\pi$
$467$	31.2273	1.44503	0.722513	+	0.691357i	$0.242987\pi$
$468$	14.7006	0.679533
$469$	8.29932	0.383227
$470$	−8.26954	−0.381445
$471$	−6.16521	−0.284078
$472$	−0.537133	−0.0247235
$473$	−59.7939	−2.74933
$474$	−0.0207410	−0.000952665 0
$475$	−6.66692	−0.305899
$476$	−26.7308	−1.22520
$477$	15.9287	0.729326
$478$	−68.0942	−3.11456
$479$	−35.9928	−1.64455	−0.822275	−	0.569090i	$-0.807296\pi$
$479$	−35.9928	−1.64455	−0.822275	+	0.569090i	$0.807296\pi$
$480$	0.0817695	0.00373225
$481$	16.5001	0.752338
$482$	−4.67992	−0.213164
$483$	0.695392	0.0316414
$484$	58.1859	2.64481
$485$	13.2082	0.599755
$486$	33.7841	1.53248
$487$	21.4172	0.970504	0.485252	−	0.874374i	$-0.338728\pi$
$487$	21.4172	0.970504	0.485252	+	0.874374i	$0.338728\pi$
$488$	−20.2946	−0.918695
$489$	−6.15359	−0.278275
$490$	−2.45229	−0.110783
$491$	35.8008	1.61567	0.807834	−	0.589409i	$-0.200639\pi$
$491$	35.8008	1.61567	0.807834	+	0.589409i	$0.200639\pi$
$492$	25.6296	1.15547
$493$	−63.2447	−2.84840
$494$	−22.7468	−1.02343
$495$	−13.2925	−0.597455
$496$	−19.3330	−0.868079
$497$	1.69802	0.0761668
$498$	−10.8056	−0.484209
$499$	1.20292	0.0538502	0.0269251	−	0.999637i	$-0.491428\pi$
$499$	1.20292	0.0538502	0.0269251	+	0.999637i	$0.491428\pi$
$500$	4.01370	0.179498
$501$	−12.4529	−0.556356
$502$	−12.0145	−0.536234
$503$	−30.3581	−1.35360	−0.676800	−	0.736167i	$-0.736634\pi$
$503$	−30.3581	−1.35360	−0.676800	+	0.736167i	$0.736634\pi$
$504$	12.9996	0.579050
$505$	−1.08672	−0.0483584
$506$	14.2037	0.631433
$507$	6.70755	0.297893
$508$	62.0074	2.75113
$509$	43.8861	1.94522	0.972609	−	0.232448i	$-0.0746736\pi$
$509$	43.8861	1.94522	0.972609	+	0.232448i	$0.0746736\pi$
$510$	−9.90098	−0.438423
$511$	3.25604	0.144039
$512$	39.7687	1.75754
$513$	−22.7649	−1.00510
$514$	18.0990	0.798313
$515$	−0.288267	−0.0127026
$516$	28.8138	1.26846
$517$	17.0276	0.748872
$518$	29.0826	1.27782
$519$	9.05707	0.397561
$520$	6.87053	0.301293
$521$	−2.35308	−0.103091	−0.0515453	−	0.998671i	$-0.516415\pi$
$521$	−2.35308	−0.103091	−0.0515453	+	0.998671i	$0.516415\pi$
$522$	61.3048	2.68324
$523$	−23.5856	−1.03133	−0.515663	−	0.856791i	$-0.672454\pi$
$523$	−23.5856	−1.03133	−0.515663	+	0.856791i	$0.672454\pi$
$524$	52.8012	2.30663
$525$	−0.606235	−0.0264583
$526$	−12.1582	−0.530122
$527$	31.5391	1.37387
$528$	−12.4969	−0.543856
$529$	−21.6842	−0.942793
$530$	14.8384	0.644539
$531$	−0.286339	−0.0124260
$532$	−26.7591	−1.16015
$533$	14.6548	0.634768
$534$	−9.41320	−0.407349
$535$	−8.71677	−0.376859
$536$	−40.9835	−1.77022
$537$	−3.26156	−0.140747
$538$	−56.2530	−2.42524
$539$	5.04944	0.217495
$540$	13.7052	0.589779
$541$	−4.12872	−0.177508	−0.0887538	−	0.996054i	$-0.528288\pi$
$541$	−4.12872	−0.177508	−0.0887538	+	0.996054i	$0.528288\pi$
$542$	−10.7997	−0.463888
$543$	0.740447	0.0317756
$544$	0.898289	0.0385138
$545$	20.1401	0.862708
$546$	−2.06841	−0.0885196
$547$	−33.5719	−1.43543	−0.717716	−	0.696336i	$-0.754812\pi$
$547$	−33.5719	−1.43543	−0.717716	+	0.696336i	$0.754812\pi$
$548$	−6.63228	−0.283317
$549$	−10.8188	−0.461735
$550$	−12.3827	−0.527998
$551$	−63.3117	−2.69717
$552$	−3.43397	−0.146159
$553$	−0.0139514	−0.000593273 0
$554$	−53.6192	−2.27806
$555$	7.18958	0.305180
$556$	49.2362	2.08808
$557$	2.60286	0.110287	0.0551433	−	0.998478i	$-0.482438\pi$
$557$	2.60286	0.110287	0.0551433	+	0.998478i	$0.482438\pi$
$558$	−30.5717	−1.29420
$559$	16.4755	0.696838
$560$	4.08241	0.172513
$561$	20.3869	0.860734
$562$	40.7244	1.71785
$563$	45.4377	1.91497	0.957486	−	0.288481i	$-0.0931502\pi$
$563$	45.4377	1.91497	0.957486	+	0.288481i	$0.0931502\pi$
$564$	−8.20534	−0.345507
$565$	−3.24352	−0.136456
$566$	−14.5026	−0.609592
$567$	5.82738	0.244727
$568$	−8.38514	−0.351833
$569$	−24.2023	−1.01461	−0.507307	−	0.861766i	$-0.669359\pi$
$569$	−24.2023	−1.01461	−0.507307	+	0.861766i	$0.669359\pi$
$570$	−9.91146	−0.415146
$571$	10.8421	0.453726	0.226863	−	0.973927i	$-0.427153\pi$
$571$	10.8421	0.453726	0.226863	+	0.973927i	$0.427153\pi$
$572$	−28.1976	−1.17900
$573$	−6.53501	−0.273004
$574$	25.8301	1.07813
$575$	−1.14707	−0.0478360
$576$	20.6230	0.859291
$577$	−3.06883	−0.127757	−0.0638785	−	0.997958i	$-0.520347\pi$
$577$	−3.06883	−0.127757	−0.0638785	+	0.997958i	$0.520347\pi$
$578$	−67.0796	−2.79014
$579$	−8.53820	−0.354835
$580$	38.1157	1.58267
$581$	−7.26835	−0.301542
$582$	19.6362	0.813945
$583$	−30.5534	−1.26539
$584$	−16.0789	−0.665350
$585$	3.66259	0.151429
$586$	68.4832	2.82902
$587$	15.9153	0.656896	0.328448	−	0.944522i	$-0.393474\pi$
$587$	15.9153	0.656896	0.328448	+	0.944522i	$0.393474\pi$
$588$	−2.43325	−0.100346
$589$	31.5725	1.30092
$590$	−0.266739	−0.0109815
$591$	−7.49354	−0.308243
$592$	−48.4148	−1.98984
$593$	−40.7339	−1.67274	−0.836371	−	0.548164i	$-0.815327\pi$
$593$	−40.7339	−1.67274	−0.836371	+	0.548164i	$0.815327\pi$
$594$	−42.2819	−1.73485
$595$	−6.65987	−0.273028
$596$	17.5535	0.719019
$597$	−4.22713	−0.173005
$598$	−3.91366	−0.160041
$599$	17.2080	0.703100	0.351550	−	0.936169i	$-0.385655\pi$
$599$	17.2080	0.703100	0.351550	+	0.936169i	$0.385655\pi$
$600$	2.99370	0.122217
$601$	36.6027	1.49305	0.746527	−	0.665355i	$-0.231720\pi$
$601$	36.6027	1.49305	0.746527	+	0.665355i	$0.231720\pi$
$602$	29.0392	1.18355
$603$	−21.8478	−0.889711
$604$	17.4717	0.710915
$605$	14.4968	0.589379
$606$	−1.61559	−0.0656287
$607$	−0.0515657	−0.00209299	−0.00104649	−	0.999999i	$-0.500333\pi$
$607$	−0.0515657	−0.00209299	−0.00104649	+	0.999999i	$0.500333\pi$
$608$	0.899240	0.0364690
$609$	−5.75705	−0.233287
$610$	−10.0783	−0.408057
$611$	−4.69174	−0.189807
$612$	70.3682	2.84446
$613$	24.2578	0.979764	0.489882	−	0.871789i	$-0.337040\pi$
$613$	24.2578	0.979764	0.489882	+	0.871789i	$0.337040\pi$
$614$	−16.4512	−0.663915
$615$	6.38553	0.257489
$616$	−24.9350	−1.00466
$617$	18.7288	0.753995	0.376998	−	0.926214i	$-0.376957\pi$
$617$	18.7288	0.753995	0.376998	+	0.926214i	$0.376957\pi$
$618$	−0.428556	−0.0172390
$619$	10.0979	0.405868	0.202934	−	0.979192i	$-0.434952\pi$
$619$	10.0979	0.405868	0.202934	+	0.979192i	$0.434952\pi$
$620$	−19.0077	−0.763366
$621$	−3.91678	−0.157175
$622$	−23.7099	−0.950681
$623$	−6.33177	−0.253677
$624$	3.44335	0.137844
$625$	1.00000	0.0400000
$626$	−12.6290	−0.504755
$627$	20.4084	0.815034
$628$	40.8180	1.62882
$629$	78.9820	3.14922
$630$	6.45559	0.257197
$631$	−43.8337	−1.74499	−0.872496	−	0.488622i	$-0.837500\pi$
$631$	−43.8337	−1.74499	−0.872496	+	0.488622i	$0.837500\pi$
$632$	0.0688943	0.00274047
$633$	−13.1581	−0.522986
$634$	−42.6888	−1.69539
$635$	15.4489	0.613072
$636$	14.7232	0.583813
$637$	−1.39131	−0.0551257
$638$	−117.591	−4.65545
$639$	−4.47001	−0.176831
$640$	19.4811	0.770058
$641$	−19.0977	−0.754314	−0.377157	−	0.926149i	$-0.623098\pi$
$641$	−19.0977	−0.754314	−0.377157	+	0.926149i	$0.623098\pi$
$642$	−12.9589	−0.511447
$643$	−45.7091	−1.80259	−0.901295	−	0.433207i	$-0.857382\pi$
$643$	−45.7091	−1.80259	−0.901295	+	0.433207i	$0.857382\pi$
$644$	−4.60399	−0.181422
$645$	7.17886	0.282667
$646$	−108.884	−4.28397
$647$	14.0455	0.552184	0.276092	−	0.961131i	$-0.410961\pi$
$647$	14.0455	0.552184	0.276092	+	0.961131i	$0.410961\pi$
$648$	−28.7766	−1.13045
$649$	0.549235	0.0215593
$650$	3.41189	0.133825
$651$	2.87094	0.112521
$652$	40.7411	1.59554
$653$	8.67998	0.339674	0.169837	−	0.985472i	$-0.445676\pi$
$653$	8.67998	0.339674	0.169837	+	0.985472i	$0.445676\pi$
$654$	29.9416	1.17081
$655$	13.1552	0.514018
$656$	−43.0003	−1.67888
$657$	−8.57146	−0.334405
$658$	−8.26954	−0.322380
$659$	−28.6406	−1.11568	−0.557840	−	0.829949i	$-0.688370\pi$
$659$	−28.6406	−1.11568	−0.557840	+	0.829949i	$0.688370\pi$
$660$	−12.2865	−0.478253
$661$	−9.52741	−0.370573	−0.185287	−	0.982685i	$-0.559321\pi$
$661$	−9.52741	−0.370573	−0.185287	+	0.982685i	$0.559321\pi$
$662$	−40.3838	−1.56956
$663$	−5.61734	−0.218159
$664$	35.8924	1.39289
$665$	−6.66692	−0.258532
$666$	−76.5593	−2.96661
$667$	−10.8930	−0.421778
$668$	82.4471	3.18997
$669$	−9.55812	−0.369538
$670$	−20.3523	−0.786278
$671$	20.7519	0.801117
$672$	0.0817695	0.00315433
$673$	−7.22078	−0.278340	−0.139170	−	0.990268i	$-0.544444\pi$
$673$	−7.22078	−0.278340	−0.139170	+	0.990268i	$0.544444\pi$
$674$	54.9342	2.11599
$675$	3.41461	0.131428
$676$	−44.4087	−1.70803
$677$	49.3841	1.89799	0.948993	−	0.315298i	$-0.102104\pi$
$677$	49.3841	1.89799	0.948993	+	0.315298i	$0.102104\pi$
$678$	−4.82202	−0.185189
$679$	13.2082	0.506885
$680$	32.8876	1.26118
$681$	11.1226	0.426220
$682$	58.6405	2.24546
$683$	13.5094	0.516922	0.258461	−	0.966022i	$-0.416785\pi$
$683$	13.5094	0.516922	0.258461	+	0.966022i	$0.416785\pi$
$684$	70.4426	2.69344
$685$	−1.65241	−0.0631353
$686$	−2.45229	−0.0936287
$687$	−0.606235	−0.0231293
$688$	−48.3427	−1.84305
$689$	8.41859	0.320723
$690$	−1.70530	−0.0649197
$691$	−18.2661	−0.694875	−0.347438	−	0.937703i	$-0.612948\pi$
$691$	−18.2661	−0.694875	−0.347438	+	0.937703i	$0.612948\pi$
$692$	−59.9642	−2.27950
$693$	−13.2925	−0.504942
$694$	−4.16807	−0.158218
$695$	12.2670	0.465315
$696$	28.4293	1.07761
$697$	70.1490	2.65708
$698$	70.7288	2.67712
$699$	17.9531	0.679050
$700$	4.01370	0.151704
$701$	31.1300	1.17577	0.587883	−	0.808946i	$-0.299962\pi$
$701$	31.1300	1.17577	0.587883	+	0.808946i	$0.299962\pi$
$702$	11.6503	0.439710
$703$	79.0656	2.98202
$704$	−39.5576	−1.49088
$705$	−2.04433	−0.0769940
$706$	54.8991	2.06616
$707$	−1.08672	−0.0408703
$708$	−0.264668	−0.00994684
$709$	13.3267	0.500493	0.250247	−	0.968182i	$-0.419488\pi$
$709$	13.3267	0.500493	0.250247	+	0.968182i	$0.419488\pi$
$710$	−4.16404	−0.156274
$711$	0.0367267	0.00137736
$712$	31.2674	1.17179
$713$	5.43215	0.203436
$714$	−9.90098	−0.370535
$715$	−7.02532	−0.262732
$716$	21.5938	0.806998
$717$	−16.8337	−0.628667
$718$	42.3723	1.58132
$719$	−8.61330	−0.321222	−0.160611	−	0.987018i	$-0.551346\pi$
$719$	−8.61330	−0.321222	−0.160611	+	0.987018i	$0.551346\pi$
$720$	−10.7469	−0.400512
$721$	−0.288267	−0.0107356
$722$	−62.4055	−2.32249
$723$	−1.15693	−0.0430268
$724$	−4.90228	−0.182192
$725$	9.49639	0.352687
$726$	21.5519	0.799865
$727$	−48.3122	−1.79180	−0.895901	−	0.444254i	$-0.853469\pi$
$727$	−48.3122	−1.79180	−0.895901	+	0.444254i	$0.853469\pi$
$728$	6.87053	0.254639
$729$	−9.13028	−0.338159
$730$	−7.98474	−0.295529
$731$	78.8642	2.91690
$732$	−10.0000	−0.369612
$733$	−15.5274	−0.573517	−0.286759	−	0.958003i	$-0.592578\pi$
$733$	−15.5274	−0.573517	−0.286759	+	0.958003i	$0.592578\pi$
$734$	5.32937	0.196711
$735$	−0.606235	−0.0223613
$736$	0.154717	0.00570295
$737$	41.9069	1.54366
$738$	−67.9972	−2.50301
$739$	−3.08674	−0.113548	−0.0567739	−	0.998387i	$-0.518081\pi$
$739$	−3.08674	−0.113548	−0.0567739	+	0.998387i	$0.518081\pi$
$740$	−47.6000	−1.74981
$741$	−5.62329	−0.206577
$742$	14.8384	0.544735
$743$	26.7627	0.981830	0.490915	−	0.871207i	$-0.336663\pi$
$743$	26.7627	0.981830	0.490915	+	0.871207i	$0.336663\pi$
$744$	−14.1772	−0.519762
$745$	4.37339	0.160229
$746$	63.0063	2.30682
$747$	19.1338	0.700068
$748$	−134.975	−4.93519
$749$	−8.71677	−0.318504
$750$	1.48666	0.0542852
$751$	5.15152	0.187982	0.0939908	−	0.995573i	$-0.470038\pi$
$751$	5.15152	0.187982	0.0939908	+	0.995573i	$0.470038\pi$
$752$	13.7666	0.502016
$753$	−2.97014	−0.108238
$754$	32.4006	1.17996
$755$	4.35302	0.158423
$756$	13.7052	0.498454
$757$	28.4071	1.03247	0.516237	−	0.856446i	$-0.327333\pi$
$757$	28.4071	1.03247	0.516237	+	0.856446i	$0.327333\pi$
$758$	−14.2911	−0.519077
$759$	3.51134	0.127454
$760$	32.9224	1.19422
$761$	21.7933	0.790008	0.395004	−	0.918679i	$-0.370743\pi$
$761$	21.7933	0.790008	0.395004	+	0.918679i	$0.370743\pi$
$762$	22.9673	0.832018
$763$	20.1401	0.729122
$764$	43.2664	1.56532
$765$	17.5320	0.633870
$766$	−10.0979	−0.364852
$767$	−0.151335	−0.00546438
$768$	19.4632	0.702319
$769$	43.4568	1.56709	0.783546	−	0.621334i	$-0.213409\pi$
$769$	43.4568	1.56709	0.783546	+	0.621334i	$0.213409\pi$
$770$	−12.3827	−0.446240
$771$	4.47430	0.161138
$772$	56.5288	2.03452
$773$	30.1461	1.08428	0.542141	−	0.840288i	$-0.317614\pi$
$773$	30.1461	1.08428	0.542141	+	0.840288i	$0.317614\pi$
$774$	−76.4451	−2.74776
$775$	−4.73569	−0.170111
$776$	−65.2245	−2.34142
$777$	7.18958	0.257925
$778$	18.1671	0.651322
$779$	70.2232	2.51601
$780$	3.38540	0.121217
$781$	8.57407	0.306804
$782$	−18.7338	−0.669919
$783$	32.4264	1.15883
$784$	4.08241	0.145800
$785$	10.1697	0.362971
$786$	19.5574	0.697589
$787$	−10.0072	−0.356718	−0.178359	−	0.983965i	$-0.557079\pi$
$787$	−10.0072	−0.356718	−0.178359	+	0.983965i	$0.557079\pi$
$788$	49.6125	1.76737
$789$	−3.00566	−0.107004
$790$	0.0342128	0.00121724
$791$	−3.24352	−0.115326
$792$	65.6409	2.33245
$793$	−5.71792	−0.203049
$794$	64.6128	2.29302
$795$	3.66824	0.130099
$796$	27.9866	0.991958
$797$	−21.0562	−0.745849	−0.372925	−	0.927862i	$-0.621645\pi$
$797$	−21.0562	−0.745849	−0.372925	+	0.927862i	$0.621645\pi$
$798$	−9.91146	−0.350862
$799$	−22.4583	−0.794516
$800$	−0.134881	−0.00476876
$801$	16.6682	0.588943
$802$	−24.2851	−0.857538
$803$	16.4412	0.580197
$804$	−20.1943	−0.712199
$805$	−1.14707	−0.0404288
$806$	−16.1576	−0.569128
$807$	−13.9064	−0.489530
$808$	5.36641	0.188790
$809$	−10.5996	−0.372662	−0.186331	−	0.982487i	$-0.559660\pi$
$809$	−10.5996	−0.372662	−0.186331	+	0.982487i	$0.559660\pi$
$810$	−14.2904	−0.502113
$811$	−51.6397	−1.81332	−0.906658	−	0.421867i	$-0.861375\pi$
$811$	−51.6397	−1.81332	−0.906658	+	0.421867i	$0.861375\pi$
$812$	38.1157	1.33760
$813$	−2.66983	−0.0936349
$814$	146.851	5.14711
$815$	10.1505	0.355556
$816$	16.4825	0.577004
$817$	78.9477	2.76203
$818$	0.883326	0.0308848
$819$	3.66259	0.127981
$820$	−42.2767	−1.47636
$821$	−19.5459	−0.682156	−0.341078	−	0.940035i	$-0.610792\pi$
$821$	−19.5459	−0.682156	−0.341078	+	0.940035i	$0.610792\pi$
$822$	−2.45657	−0.0856828
$823$	49.4909	1.72514	0.862571	−	0.505935i	$-0.168853\pi$
$823$	49.4909	1.72514	0.862571	+	0.505935i	$0.168853\pi$
$824$	1.42351	0.0495904
$825$	−3.06115	−0.106575
$826$	−0.266739	−0.00928103
$827$	−21.5757	−0.750260	−0.375130	−	0.926972i	$-0.622402\pi$
$827$	−21.5757	−0.750260	−0.375130	+	0.926972i	$0.622402\pi$
$828$	12.1199	0.421195
$829$	2.38657	0.0828891	0.0414446	−	0.999141i	$-0.486804\pi$
$829$	2.38657	0.0828891	0.0414446	+	0.999141i	$0.486804\pi$
$830$	17.8241	0.618682
$831$	−13.2553	−0.459823
$832$	10.8996	0.377875
$833$	−6.65987	−0.230751
$834$	18.2369	0.631494
$835$	20.5414	0.710864
$836$	−135.118	−4.67316
$837$	−16.1705	−0.558935
$838$	74.6958	2.58032
$839$	0.159376	0.00550228	0.00275114	−	0.999996i	$-0.499124\pi$
$839$	0.159376	0.00550228	0.00275114	+	0.999996i	$0.499124\pi$
$840$	2.99370	0.103292
$841$	61.1814	2.10970
$842$	−93.0954	−3.20828
$843$	10.0676	0.346746
$844$	87.1156	2.99864
$845$	−11.0643	−0.380622
$846$	21.7694	0.748447
$847$	14.4968	0.498116
$848$	−24.7020	−0.848271
$849$	−3.58523	−0.123045
$850$	16.3319	0.560180
$851$	13.6035	0.466322
$852$	−4.13172	−0.141550
$853$	49.9721	1.71101	0.855507	−	0.517792i	$-0.173246\pi$
$853$	49.9721	1.71101	0.855507	+	0.517792i	$0.173246\pi$
$854$	−10.0783	−0.344871
$855$	17.5505	0.600216
$856$	43.0449	1.47125
$857$	−16.2952	−0.556635	−0.278317	−	0.960489i	$-0.589777\pi$
$857$	−16.2952	−0.556635	−0.278317	+	0.960489i	$0.589777\pi$
$858$	−10.4443	−0.356562
$859$	15.3363	0.523269	0.261634	−	0.965167i	$-0.415739\pi$
$859$	15.3363	0.523269	0.261634	+	0.965167i	$0.415739\pi$
$860$	−47.5291	−1.62073
$861$	6.38553	0.217618
$862$	41.3881	1.40968
$863$	39.0749	1.33013	0.665063	−	0.746787i	$-0.268405\pi$
$863$	39.0749	1.33013	0.665063	+	0.746787i	$0.268405\pi$
$864$	−0.460565	−0.0156687
$865$	−14.9399	−0.507971
$866$	39.4171	1.33945
$867$	−16.5829	−0.563185
$868$	−19.0077	−0.645162
$869$	−0.0704466	−0.00238974
$870$	14.1179	0.478642
$871$	−11.5469	−0.391252
$872$	−99.4555	−3.36799
$873$	−34.7704	−1.17680
$874$	−18.7536	−0.634351
$875$	1.00000	0.0338062
$876$	−7.92276	−0.267685
$877$	10.2588	0.346415	0.173207	−	0.984885i	$-0.444587\pi$
$877$	10.2588	0.346415	0.173207	+	0.984885i	$0.444587\pi$
$878$	−26.4840	−0.893790
$879$	16.9299	0.571031
$880$	20.6139	0.694893
$881$	20.1470	0.678769	0.339385	−	0.940648i	$-0.389781\pi$
$881$	20.1470	0.678769	0.339385	+	0.940648i	$0.389781\pi$
$882$	6.45559	0.217371
$883$	−9.36703	−0.315226	−0.157613	−	0.987501i	$-0.550380\pi$
$883$	−9.36703	−0.315226	−0.157613	+	0.987501i	$0.550380\pi$
$884$	37.1907	1.25086
$885$	−0.0659411	−0.00221659
$886$	8.09243	0.271871
$887$	6.99983	0.235031	0.117516	−	0.993071i	$-0.462507\pi$
$887$	6.99983	0.235031	0.117516	+	0.993071i	$0.462507\pi$
$888$	−35.5034	−1.19142
$889$	15.4489	0.518140
$890$	15.5273	0.520476
$891$	29.4250	0.985774
$892$	63.2815	2.11882
$893$	−22.4820	−0.752333
$894$	6.50175	0.217451
$895$	5.38002	0.179834
$896$	19.4811	0.650818
$897$	−0.967505	−0.0323041
$898$	−8.48898	−0.283281
$899$	−44.9720	−1.49990
$900$	−10.5660	−0.352200
$901$	40.2979	1.34252
$902$	130.428	4.34276
$903$	7.17886	0.238897
$904$	16.0171	0.532720
$905$	−1.22139	−0.0406002
$906$	6.47147	0.215000
$907$	27.4399	0.911128	0.455564	−	0.890203i	$-0.349438\pi$
$907$	27.4399	0.911128	0.455564	+	0.890203i	$0.349438\pi$
$908$	−73.6396	−2.44381
$909$	2.86077	0.0948857
$910$	3.41189	0.113103
$911$	35.5161	1.17670	0.588351	−	0.808606i	$-0.299777\pi$
$911$	35.5161	1.17670	0.588351	+	0.808606i	$0.299777\pi$
$912$	16.5000	0.546369
$913$	−36.7011	−1.21463
$914$	−50.0581	−1.65577
$915$	−2.49147	−0.0823655
$916$	4.01370	0.132616
$917$	13.1552	0.434424
$918$	55.7671	1.84059
$919$	−35.8371	−1.18216	−0.591078	−	0.806615i	$-0.701297\pi$
$919$	−35.8371	−1.18216	−0.591078	+	0.806615i	$0.701297\pi$
$920$	5.66442	0.186750
$921$	−4.06693	−0.134010
$922$	47.5433	1.56575
$923$	−2.36248	−0.0777618
$924$	−12.2865	−0.404197
$925$	−11.8594	−0.389934
$926$	16.1446	0.530544
$927$	0.758857	0.0249241
$928$	−1.28088	−0.0420470
$929$	47.7820	1.56768	0.783839	−	0.620965i	$-0.213259\pi$
$929$	47.7820	1.56768	0.783839	+	0.620965i	$0.213259\pi$
$930$	−7.04037	−0.230863
$931$	−6.66692	−0.218500
$932$	−118.862	−3.89347
$933$	−5.86139	−0.191893
$934$	−76.5782	−2.50572
$935$	−33.6286	−1.09977
$936$	−18.0865	−0.591176
$937$	4.25143	0.138888	0.0694442	−	0.997586i	$-0.477877\pi$
$937$	4.25143	0.138888	0.0694442	+	0.997586i	$0.477877\pi$
$938$	−20.3523	−0.664526
$939$	−3.12204	−0.101884
$940$	13.5349	0.441460
$941$	49.7282	1.62109	0.810547	−	0.585673i	$-0.199170\pi$
$941$	49.7282	1.62109	0.810547	+	0.585673i	$0.199170\pi$
$942$	15.1188	0.492599
$943$	12.0821	0.393449
$944$	0.444050	0.0144526
$945$	3.41461	0.111077
$946$	146.632	4.76741
$947$	45.1972	1.46871	0.734356	−	0.678764i	$-0.237484\pi$
$947$	45.1972	1.46871	0.734356	+	0.678764i	$0.237484\pi$
$948$	0.0339472	0.00110255
$949$	−4.53016	−0.147055
$950$	16.3492	0.530438
$951$	−10.5532	−0.342211
$952$	32.8876	1.06589
$953$	57.5079	1.86286	0.931432	−	0.363917i	$-0.118561\pi$
$953$	57.5079	1.86286	0.931432	+	0.363917i	$0.118561\pi$
$954$	−39.0618	−1.26467
$955$	10.7797	0.348822
$956$	111.451	3.60459
$957$	−29.0698	−0.939695
$958$	88.2645	2.85170
$959$	−1.65241	−0.0533590
$960$	4.74928	0.153282
$961$	−8.57323	−0.276556
$962$	−40.4628	−1.30457
$963$	22.9467	0.739447
$964$	7.65971	0.246703
$965$	14.0840	0.453379
$966$	−1.70530	−0.0548671
$967$	10.9290	0.351453	0.175727	−	0.984439i	$-0.443773\pi$
$967$	10.9290	0.351453	0.175727	+	0.984439i	$0.443773\pi$
$968$	−71.5878	−2.30092
$969$	−26.9174	−0.864711
$970$	−32.3903	−1.03999
$971$	−46.3539	−1.48757	−0.743785	−	0.668419i	$-0.766971\pi$
$971$	−46.3539	−1.48757	−0.743785	+	0.668419i	$0.766971\pi$
$972$	−55.2951	−1.77359
$973$	12.2670	0.393263
$974$	−52.5210	−1.68288
$975$	0.843460	0.0270124
$976$	16.7776	0.537039
$977$	−56.9548	−1.82215	−0.911073	−	0.412245i	$-0.864745\pi$
$977$	−56.9548	−1.82215	−0.911073	+	0.412245i	$0.864745\pi$
$978$	15.0904	0.482536
$979$	−31.9719	−1.02182
$980$	4.01370	0.128213
$981$	−53.0185	−1.69275
$982$	−87.7939	−2.80161
$983$	31.5326	1.00573	0.502867	−	0.864364i	$-0.332279\pi$
$983$	31.5326	1.00573	0.502867	+	0.864364i	$0.332279\pi$
$984$	−31.5328	−1.00523
$985$	12.3608	0.393847
$986$	155.094	4.93920
$987$	−2.04433	−0.0650718
$988$	37.2301	1.18445
$989$	13.5832	0.431921
$990$	32.5971	1.03600
$991$	−44.0787	−1.40020	−0.700102	−	0.714043i	$-0.746862\pi$
$991$	−44.0787	−1.40020	−0.700102	+	0.714043i	$0.746862\pi$
$992$	0.638754	0.0202805
$993$	−9.98337	−0.316813
$994$	−4.16404	−0.132075
$995$	6.97276	0.221051
$996$	17.6857	0.560393
$997$	45.1813	1.43091	0.715453	−	0.698661i	$-0.246221\pi$
$997$	45.1813	1.43091	0.715453	+	0.698661i	$0.246221\pi$
$998$	−2.94991	−0.0933777
$999$	−40.4951	−1.28121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.o.1.8	✓	73

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.o.1.8	✓	73	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45229 q^{2} -0.606235 q^{3} +4.01370 q^{4} +1.00000 q^{5} +1.48666 q^{6} +1.00000 q^{7} -4.93818 q^{8} -2.63248 q^{9} +O(q^{10})\)	\(q-2.45229 q^{2} -0.606235 q^{3} +4.01370 q^{4} +1.00000 q^{5} +1.48666 q^{6} +1.00000 q^{7} -4.93818 q^{8} -2.63248 q^{9} -2.45229 q^{10} +5.04944 q^{11} -2.43325 q^{12} -1.39131 q^{13} -2.45229 q^{14} -0.606235 q^{15} +4.08241 q^{16} -6.65987 q^{17} +6.45559 q^{18} -6.66692 q^{19} +4.01370 q^{20} -0.606235 q^{21} -12.3827 q^{22} -1.14707 q^{23} +2.99370 q^{24} +1.00000 q^{25} +3.41189 q^{26} +3.41461 q^{27} +4.01370 q^{28} +9.49639 q^{29} +1.48666 q^{30} -4.73569 q^{31} -0.134881 q^{32} -3.06115 q^{33} +16.3319 q^{34} +1.00000 q^{35} -10.5660 q^{36} -11.8594 q^{37} +16.3492 q^{38} +0.843460 q^{39} -4.93818 q^{40} -10.5331 q^{41} +1.48666 q^{42} -11.8417 q^{43} +20.2669 q^{44} -2.63248 q^{45} +2.81293 q^{46} +3.37218 q^{47} -2.47490 q^{48} +1.00000 q^{49} -2.45229 q^{50} +4.03745 q^{51} -5.58430 q^{52} -6.05085 q^{53} -8.37359 q^{54} +5.04944 q^{55} -4.93818 q^{56} +4.04173 q^{57} -23.2879 q^{58} +0.108771 q^{59} -2.43325 q^{60} +4.10974 q^{61} +11.6133 q^{62} -2.63248 q^{63} -7.83405 q^{64} -1.39131 q^{65} +7.50681 q^{66} +8.29932 q^{67} -26.7308 q^{68} +0.695392 q^{69} -2.45229 q^{70} +1.69802 q^{71} +12.9996 q^{72} +3.25604 q^{73} +29.0826 q^{74} -0.606235 q^{75} -26.7591 q^{76} +5.04944 q^{77} -2.06841 q^{78} -0.0139514 q^{79} +4.08241 q^{80} +5.82738 q^{81} +25.8301 q^{82} -7.26835 q^{83} -2.43325 q^{84} -6.65987 q^{85} +29.0392 q^{86} -5.75705 q^{87} -24.9350 q^{88} -6.33177 q^{89} +6.45559 q^{90} -1.39131 q^{91} -4.60399 q^{92} +2.87094 q^{93} -8.26954 q^{94} -6.66692 q^{95} +0.0817695 q^{96} +13.2082 q^{97} -2.45229 q^{98} -13.2925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9}+O(q^{10}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9	\( 73 q + 7 q^{2} + 14 q^{3} + 95 q^{4} + 73 q^{5} - q^{6} + 73 q^{7} + 18 q^{8} + 111 q^{9} + 7 q^{10} + 27 q^{11} + 21 q^{12} + 21 q^{13} + 7 q^{14} + 14 q^{15} + 135 q^{16} + 23 q^{17} + 41 q^{18} + 26 q^{19} + 95 q^{20} + 14 q^{21} + 48 q^{22} + 16 q^{23} - q^{24} + 73 q^{25} + 7 q^{26} + 44 q^{27} + 95 q^{28} + 66 q^{29} - q^{30} + 23 q^{31} + 3 q^{32} + 77 q^{33} + 29 q^{34} + 73 q^{35} + 142 q^{36} + 66 q^{37} - 12 q^{38} + 53 q^{39} + 18 q^{40} + 50 q^{41} - q^{42} + 43 q^{43} + 37 q^{44} + 111 q^{45} + 65 q^{46} + 28 q^{47} - 20 q^{48} + 73 q^{49} + 7 q^{50} + 71 q^{51} + 29 q^{52} - 7 q^{53} - 16 q^{54} + 27 q^{55} + 18 q^{56} + 33 q^{57} + 48 q^{58} + 16 q^{59} + 21 q^{60} + 42 q^{61} - 3 q^{62} + 111 q^{63} + 216 q^{64} + 21 q^{65} - 53 q^{66} + 48 q^{67} + 13 q^{68} + 73 q^{69} + 7 q^{70} + 68 q^{71} + 18 q^{72} + 65 q^{73} + 4 q^{74} + 14 q^{75} + 37 q^{76} + 27 q^{77} + 60 q^{78} + 116 q^{79} + 135 q^{80} + 177 q^{81} + 20 q^{82} + 40 q^{83} + 21 q^{84} + 23 q^{85} + 35 q^{86} - 14 q^{87} + 47 q^{88} + 59 q^{89} + 41 q^{90} + 21 q^{91} + 3 q^{92} + 37 q^{93} - 11 q^{94} + 26 q^{95} - 23 q^{96} + 70 q^{97} + 7 q^{98} + 49 q^{99}+O(q^{100}) \) 73 * q + 7 * q^2 + 14 * q^3 + 95 * q^4 + 73 * q^5 - q^6 + 73 * q^7 + 18 * q^8 + 111 * q^9 + 7 * q^10 + 27 * q^11 + 21 * q^12 + 21 * q^13 + 7 * q^14 + 14 * q^15 + 135 * q^16 + 23 * q^17 + 41 * q^18 + 26 * q^19 + 95 * q^20 + 14 * q^21 + 48 * q^22 + 16 * q^23 - q^24 + 73 * q^25 + 7 * q^26 + 44 * q^27 + 95 * q^28 + 66 * q^29 - q^30 + 23 * q^31 + 3 * q^32 + 77 * q^33 + 29 * q^34 + 73 * q^35 + 142 * q^36 + 66 * q^37 - 12 * q^38 + 53 * q^39 + 18 * q^40 + 50 * q^41 - q^42 + 43 * q^43 + 37 * q^44 + 111 * q^45 + 65 * q^46 + 28 * q^47 - 20 * q^48 + 73 * q^49 + 7 * q^50 + 71 * q^51 + 29 * q^52 - 7 * q^53 - 16 * q^54 + 27 * q^55 + 18 * q^56 + 33 * q^57 + 48 * q^58 + 16 * q^59 + 21 * q^60 + 42 * q^61 - 3 * q^62 + 111 * q^63 + 216 * q^64 + 21 * q^65 - 53 * q^66 + 48 * q^67 + 13 * q^68 + 73 * q^69 + 7 * q^70 + 68 * q^71 + 18 * q^72 + 65 * q^73 + 4 * q^74 + 14 * q^75 + 37 * q^76 + 27 * q^77 + 60 * q^78 + 116 * q^79 + 135 * q^80 + 177 * q^81 + 20 * q^82 + 40 * q^83 + 21 * q^84 + 23 * q^85 + 35 * q^86 - 14 * q^87 + 47 * q^88 + 59 * q^89 + 41 * q^90 + 21 * q^91 + 3 * q^92 + 37 * q^93 - 11 * q^94 + 26 * q^95 - 23 * q^96 + 70 * q^97 + 7 * q^98 + 49 * q^99

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