LMFDB - Embedded newform 8005.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, 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("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$0$
Dimension:	$137$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80769 q^{2} +1.97654 q^{3} +5.88311 q^{4} -1.00000 q^{5} -5.54949 q^{6} -3.00934 q^{7} -10.9026 q^{8} +0.906693 q^{9} +O(q^{10})$	\(q-2.80769 q^{2} +1.97654 q^{3} +5.88311 q^{4} -1.00000 q^{5} -5.54949 q^{6} -3.00934 q^{7} -10.9026 q^{8} +0.906693 q^{9} +2.80769 q^{10} -1.33147 q^{11} +11.6282 q^{12} -6.55973 q^{13} +8.44929 q^{14} -1.97654 q^{15} +18.8448 q^{16} -4.87340 q^{17} -2.54571 q^{18} -4.63083 q^{19} -5.88311 q^{20} -5.94807 q^{21} +3.73835 q^{22} -3.97947 q^{23} -21.5493 q^{24} +1.00000 q^{25} +18.4177 q^{26} -4.13750 q^{27} -17.7043 q^{28} +6.57281 q^{29} +5.54949 q^{30} -7.94317 q^{31} -31.1051 q^{32} -2.63169 q^{33} +13.6830 q^{34} +3.00934 q^{35} +5.33417 q^{36} -3.39915 q^{37} +13.0019 q^{38} -12.9655 q^{39} +10.9026 q^{40} -12.0714 q^{41} +16.7003 q^{42} -3.52259 q^{43} -7.83318 q^{44} -0.906693 q^{45} +11.1731 q^{46} -1.96349 q^{47} +37.2474 q^{48} +2.05612 q^{49} -2.80769 q^{50} -9.63245 q^{51} -38.5916 q^{52} +5.26572 q^{53} +11.6168 q^{54} +1.33147 q^{55} +32.8095 q^{56} -9.15300 q^{57} -18.4544 q^{58} +7.65543 q^{59} -11.6282 q^{60} +3.42596 q^{61} +22.3019 q^{62} -2.72855 q^{63} +49.6439 q^{64} +6.55973 q^{65} +7.38898 q^{66} -14.6675 q^{67} -28.6708 q^{68} -7.86557 q^{69} -8.44929 q^{70} +6.65278 q^{71} -9.88527 q^{72} +2.09239 q^{73} +9.54375 q^{74} +1.97654 q^{75} -27.2437 q^{76} +4.00684 q^{77} +36.4032 q^{78} -7.20958 q^{79} -18.8448 q^{80} -10.8980 q^{81} +33.8927 q^{82} +12.6205 q^{83} -34.9931 q^{84} +4.87340 q^{85} +9.89034 q^{86} +12.9914 q^{87} +14.5164 q^{88} +4.56538 q^{89} +2.54571 q^{90} +19.7405 q^{91} -23.4117 q^{92} -15.7000 q^{93} +5.51288 q^{94} +4.63083 q^{95} -61.4804 q^{96} +5.38502 q^{97} -5.77295 q^{98} -1.20723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) $ 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * 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 $

$2$	−2.80769	−1.98534	−0.992668	−	0.120876i	$-0.961430\pi$
$2$	−2.80769	−1.98534	−0.992668	+	0.120876i	$0.961430\pi$
$3$	1.97654	1.14115	0.570577	−	0.821244i	$-0.306720\pi$
$3$	1.97654	1.14115	0.570577	+	0.821244i	$0.306720\pi$
$4$	5.88311	2.94156
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−5.54949	−2.26557
$7$	−3.00934	−1.13742	−0.568712	−	0.822537i	$-0.692558\pi$
$7$	−3.00934	−1.13742	−0.568712	+	0.822537i	$0.692558\pi$
$8$	−10.9026	−3.85464
$9$	0.906693	0.302231
$10$	2.80769	0.887869
$11$	−1.33147	−0.401453	−0.200726	−	0.979647i	$-0.564330\pi$
$11$	−1.33147	−0.401453	−0.200726	+	0.979647i	$0.564330\pi$
$12$	11.6282	3.35677
$13$	−6.55973	−1.81934	−0.909671	−	0.415330i	$-0.863666\pi$
$13$	−6.55973	−1.81934	−0.909671	+	0.415330i	$0.863666\pi$
$14$	8.44929	2.25817
$15$	−1.97654	−0.510339
$16$	18.8448	4.71119
$17$	−4.87340	−1.18197	−0.590987	−	0.806681i	$-0.701261\pi$
$17$	−4.87340	−1.18197	−0.590987	+	0.806681i	$0.701261\pi$
$18$	−2.54571	−0.600030
$19$	−4.63083	−1.06238	−0.531192	−	0.847251i	$-0.678256\pi$
$19$	−4.63083	−1.06238	−0.531192	+	0.847251i	$0.678256\pi$
$20$	−5.88311	−1.31550
$21$	−5.94807	−1.29797
$22$	3.73835	0.797019
$23$	−3.97947	−0.829777	−0.414889	−	0.909872i	$-0.636179\pi$
$23$	−3.97947	−0.829777	−0.414889	+	0.909872i	$0.636179\pi$
$24$	−21.5493	−4.39873
$25$	1.00000	0.200000
$26$	18.4177	3.61200
$27$	−4.13750	−0.796262
$28$	−17.7043	−3.34579
$29$	6.57281	1.22054	0.610271	−	0.792193i	$-0.291061\pi$
$29$	6.57281	1.22054	0.610271	+	0.792193i	$0.291061\pi$
$30$	5.54949	1.01319
$31$	−7.94317	−1.42663	−0.713317	−	0.700841i	$-0.752808\pi$
$31$	−7.94317	−1.42663	−0.713317	+	0.700841i	$0.752808\pi$
$32$	−31.1051	−5.49866
$33$	−2.63169	−0.458119
$34$	13.6830	2.34661
$35$	3.00934	0.508671
$36$	5.33417	0.889029
$37$	−3.39915	−0.558817	−0.279408	−	0.960172i	$-0.590138\pi$
$37$	−3.39915	−0.558817	−0.279408	+	0.960172i	$0.590138\pi$
$38$	13.0019	2.10919
$39$	−12.9655	−2.07615
$40$	10.9026	1.72385
$41$	−12.0714	−1.88523	−0.942616	−	0.333878i	$-0.891643\pi$
$41$	−12.0714	−1.88523	−0.942616	+	0.333878i	$0.891643\pi$
$42$	16.7003	2.57691
$43$	−3.52259	−0.537190	−0.268595	−	0.963253i	$-0.586559\pi$
$43$	−3.52259	−0.537190	−0.268595	+	0.963253i	$0.586559\pi$
$44$	−7.83318	−1.18090
$45$	−0.906693	−0.135162
$46$	11.1731	1.64739
$47$	−1.96349	−0.286405	−0.143202	−	0.989693i	$-0.545740\pi$
$47$	−1.96349	−0.286405	−0.143202	+	0.989693i	$0.545740\pi$
$48$	37.2474	5.37620
$49$	2.05612	0.293732
$50$	−2.80769	−0.397067
$51$	−9.63245	−1.34881
$52$	−38.5916	−5.35170
$53$	5.26572	0.723302	0.361651	−	0.932314i	$-0.382213\pi$
$53$	5.26572	0.723302	0.361651	+	0.932314i	$0.382213\pi$
$54$	11.6168	1.58085
$55$	1.33147	0.179535
$56$	32.8095	4.38436
$57$	−9.15300	−1.21234
$58$	−18.4544	−2.42318
$59$	7.65543	0.996652	0.498326	−	0.866990i	$-0.333948\pi$
$59$	7.65543	0.996652	0.498326	+	0.866990i	$0.333948\pi$
$60$	−11.6282	−1.50119
$61$	3.42596	0.438649	0.219324	−	0.975652i	$-0.429615\pi$
$61$	3.42596	0.438649	0.219324	+	0.975652i	$0.429615\pi$
$62$	22.3019	2.83235
$63$	−2.72855	−0.343764
$64$	49.6439	6.20549
$65$	6.55973	0.813634
$66$	7.38898	0.909520
$67$	−14.6675	−1.79192	−0.895959	−	0.444138i	$-0.853510\pi$
$67$	−14.6675	−1.79192	−0.895959	+	0.444138i	$0.853510\pi$
$68$	−28.6708	−3.47684
$69$	−7.86557	−0.946903
$70$	−8.44929	−1.00988
$71$	6.65278	0.789539	0.394770	−	0.918780i	$-0.370824\pi$
$71$	6.65278	0.789539	0.394770	+	0.918780i	$0.370824\pi$
$72$	−9.88527	−1.16499
$73$	2.09239	0.244896	0.122448	−	0.992475i	$-0.460926\pi$
$73$	2.09239	0.244896	0.122448	+	0.992475i	$0.460926\pi$
$74$	9.54375	1.10944
$75$	1.97654	0.228231
$76$	−27.2437	−3.12506
$77$	4.00684	0.456622
$78$	36.4032	4.12185
$79$	−7.20958	−0.811141	−0.405570	−	0.914064i	$-0.632927\pi$
$79$	−7.20958	−0.811141	−0.405570	+	0.914064i	$0.632927\pi$
$80$	−18.8448	−2.10691
$81$	−10.8980	−1.21089
$82$	33.8927	3.74282
$83$	12.6205	1.38528	0.692639	−	0.721285i	$-0.256448\pi$
$83$	12.6205	1.38528	0.692639	+	0.721285i	$0.256448\pi$
$84$	−34.9931	−3.81806
$85$	4.87340	0.528594
$86$	9.89034	1.06650
$87$	12.9914	1.39282
$88$	14.5164	1.54746
$89$	4.56538	0.483929	0.241965	−	0.970285i	$-0.422208\pi$
$89$	4.56538	0.483929	0.241965	+	0.970285i	$0.422208\pi$
$90$	2.54571	0.268341
$91$	19.7405	2.06936
$92$	−23.4117	−2.44084
$93$	−15.7000	−1.62801
$94$	5.51288	0.568610
$95$	4.63083	0.475113
$96$	−61.4804	−6.27482
$97$	5.38502	0.546766	0.273383	−	0.961905i	$-0.411857\pi$
$97$	5.38502	0.546766	0.273383	+	0.961905i	$0.411857\pi$
$98$	−5.77295	−0.583156
$99$	−1.20723	−0.121331
$100$	5.88311	0.588311
$101$	−12.8732	−1.28093	−0.640465	−	0.767988i	$-0.721258\pi$
$101$	−12.8732	−1.28093	−0.640465	+	0.767988i	$0.721258\pi$
$102$	27.0449	2.67784
$103$	−2.99442	−0.295049	−0.147525	−	0.989058i	$-0.547131\pi$
$103$	−2.99442	−0.295049	−0.147525	+	0.989058i	$0.547131\pi$
$104$	71.5179	7.01291
$105$	5.94807	0.580472
$106$	−14.7845	−1.43600
$107$	−1.76422	−0.170554	−0.0852770	−	0.996357i	$-0.527178\pi$
$107$	−1.76422	−0.170554	−0.0852770	+	0.996357i	$0.527178\pi$
$108$	−24.3414	−2.34225
$109$	13.7816	1.32004	0.660018	−	0.751250i	$-0.270549\pi$
$109$	13.7816	1.32004	0.660018	+	0.751250i	$0.270549\pi$
$110$	−3.73835	−0.356438
$111$	−6.71854	−0.637696
$112$	−56.7103	−5.35862
$113$	−5.19290	−0.488507	−0.244253	−	0.969711i	$-0.578543\pi$
$113$	−5.19290	−0.488507	−0.244253	+	0.969711i	$0.578543\pi$
$114$	25.6988	2.40691
$115$	3.97947	0.371088
$116$	38.6686	3.59029
$117$	−5.94766	−0.549861
$118$	−21.4940	−1.97869
$119$	14.6657	1.34440
$120$	21.5493	1.96717
$121$	−9.22719	−0.838836
$122$	−9.61902	−0.870865
$123$	−23.8595	−2.15134
$124$	−46.7305	−4.19653
$125$	−1.00000	−0.0894427
$126$	7.66090	0.682488
$127$	−11.1183	−0.986588	−0.493294	−	0.869863i	$-0.664207\pi$
$127$	−11.1183	−0.986588	−0.493294	+	0.869863i	$0.664207\pi$
$128$	−77.1744	−6.82132
$129$	−6.96253	−0.613016
$130$	−18.4177	−1.61534
$131$	7.65813	0.669094	0.334547	−	0.942379i	$-0.391417\pi$
$131$	7.65813	0.669094	0.334547	+	0.942379i	$0.391417\pi$
$132$	−15.4826	−1.34758
$133$	13.9357	1.20838
$134$	41.1817	3.55756
$135$	4.13750	0.356099
$136$	53.1326	4.55608
$137$	−8.24956	−0.704808	−0.352404	−	0.935848i	$-0.614636\pi$
$137$	−8.24956	−0.704808	−0.352404	+	0.935848i	$0.614636\pi$
$138$	22.0841	1.87992
$139$	−14.3152	−1.21420	−0.607100	−	0.794626i	$-0.707667\pi$
$139$	−14.3152	−1.21420	−0.607100	+	0.794626i	$0.707667\pi$
$140$	17.7043	1.49628
$141$	−3.88091	−0.326832
$142$	−18.6789	−1.56750
$143$	8.73407	0.730380
$144$	17.0864	1.42387
$145$	−6.57281	−0.545843
$146$	−5.87478	−0.486200
$147$	4.06400	0.335193
$148$	−19.9976	−1.64379
$149$	−13.9244	−1.14073	−0.570366	−	0.821390i	$-0.693199\pi$
$149$	−13.9244	−1.14073	−0.570366	+	0.821390i	$0.693199\pi$
$150$	−5.54949	−0.453114
$151$	−10.0685	−0.819364	−0.409682	−	0.912228i	$-0.634360\pi$
$151$	−10.0685	−0.819364	−0.409682	+	0.912228i	$0.634360\pi$
$152$	50.4879	4.09511
$153$	−4.41867	−0.357229
$154$	−11.2500	−0.906547
$155$	7.94317	0.638011
$156$	−76.2777	−6.10710
$157$	−3.03013	−0.241831	−0.120915	−	0.992663i	$-0.538583\pi$
$157$	−3.03013	−0.241831	−0.120915	+	0.992663i	$0.538583\pi$
$158$	20.2422	1.61039
$159$	10.4079	0.825398
$160$	31.1051	2.45908
$161$	11.9756	0.943808
$162$	30.5981	2.40402
$163$	−4.35952	−0.341464	−0.170732	−	0.985318i	$-0.554613\pi$
$163$	−4.35952	−0.341464	−0.170732	+	0.985318i	$0.554613\pi$
$164$	−71.0173	−5.54552
$165$	2.63169	0.204877
$166$	−35.4344	−2.75024
$167$	19.1535	1.48214	0.741072	−	0.671426i	$-0.234318\pi$
$167$	19.1535	1.48214	0.741072	+	0.671426i	$0.234318\pi$
$168$	64.8492	5.00322
$169$	30.0301	2.31000
$170$	−13.6830	−1.04944
$171$	−4.19874	−0.321085
$172$	−20.7238	−1.58017
$173$	−4.39320	−0.334009	−0.167005	−	0.985956i	$-0.553409\pi$
$173$	−4.39320	−0.334009	−0.167005	+	0.985956i	$0.553409\pi$
$174$	−36.4758	−2.76522
$175$	−3.00934	−0.227485
$176$	−25.0912	−1.89132
$177$	15.1312	1.13733
$178$	−12.8182	−0.960761
$179$	15.8332	1.18343	0.591714	−	0.806148i	$-0.298452\pi$
$179$	15.8332	1.18343	0.591714	+	0.806148i	$0.298452\pi$
$180$	−5.33417	−0.397586
$181$	−18.9978	−1.41210	−0.706048	−	0.708164i	$-0.749524\pi$
$181$	−18.9978	−1.41210	−0.706048	+	0.708164i	$0.749524\pi$
$182$	−55.4250	−4.10838
$183$	6.77153	0.500566
$184$	43.3864	3.19849
$185$	3.39915	0.249910
$186$	44.0806	3.23214
$187$	6.48878	0.474506
$188$	−11.5515	−0.842476
$189$	12.4511	0.905687
$190$	−13.0019	−0.943259
$191$	−23.4130	−1.69411	−0.847053	−	0.531508i	$-0.821626\pi$
$191$	−23.4130	−1.69411	−0.847053	+	0.531508i	$0.821626\pi$
$192$	98.1230	7.08142
$193$	0.594783	0.0428134	0.0214067	−	0.999771i	$-0.493186\pi$
$193$	0.594783	0.0428134	0.0214067	+	0.999771i	$0.493186\pi$
$194$	−15.1195	−1.08551
$195$	12.9655	0.928482
$196$	12.0964	0.864029
$197$	−4.45450	−0.317370	−0.158685	−	0.987329i	$-0.550725\pi$
$197$	−4.45450	−0.317370	−0.158685	+	0.987329i	$0.550725\pi$
$198$	3.38953	0.240884
$199$	17.2044	1.21959	0.609795	−	0.792559i	$-0.291252\pi$
$199$	17.2044	1.21959	0.609795	+	0.792559i	$0.291252\pi$
$200$	−10.9026	−0.770928
$201$	−28.9908	−2.04485
$202$	36.1439	2.54307
$203$	−19.7798	−1.38827
$204$	−56.6688	−3.96761
$205$	12.0714	0.843102
$206$	8.40741	0.585772
$207$	−3.60816	−0.250784
$208$	−123.617	−8.57127
$209$	6.16580	0.426498
$210$	−16.7003	−1.15243
$211$	14.4849	0.997182	0.498591	−	0.866837i	$-0.333851\pi$
$211$	14.4849	0.997182	0.498591	+	0.866837i	$0.333851\pi$
$212$	30.9788	2.12763
$213$	13.1494	0.900985
$214$	4.95339	0.338607
$215$	3.52259	0.240239
$216$	45.1093	3.06930
$217$	23.9037	1.62269
$218$	−38.6944	−2.62071
$219$	4.13568	0.279464
$220$	7.83318	0.528113
$221$	31.9682	2.15041
$222$	18.8636	1.26604
$223$	−12.0876	−0.809447	−0.404724	−	0.914439i	$-0.632632\pi$
$223$	−12.0876	−0.809447	−0.404724	+	0.914439i	$0.632632\pi$
$224$	93.6059	6.25431
$225$	0.906693	0.0604462
$226$	14.5800	0.969850
$227$	28.1890	1.87097	0.935484	−	0.353369i	$-0.114964\pi$
$227$	28.1890	1.87097	0.935484	+	0.353369i	$0.114964\pi$
$228$	−53.8481	−3.56618
$229$	−1.84807	−0.122124	−0.0610619	−	0.998134i	$-0.519449\pi$
$229$	−1.84807	−0.122124	−0.0610619	+	0.998134i	$0.519449\pi$
$230$	−11.1731	−0.736733
$231$	7.91966	0.521076
$232$	−71.6605	−4.70475
$233$	2.71977	0.178178	0.0890890	−	0.996024i	$-0.471604\pi$
$233$	2.71977	0.178178	0.0890890	+	0.996024i	$0.471604\pi$
$234$	16.6992	1.09166
$235$	1.96349	0.128084
$236$	45.0377	2.93171
$237$	−14.2500	−0.925636
$238$	−41.1767	−2.66909
$239$	−20.7496	−1.34218	−0.671089	−	0.741377i	$-0.734173\pi$
$239$	−20.7496	−1.34218	−0.671089	+	0.741377i	$0.734173\pi$
$240$	−37.2474	−2.40431
$241$	−4.08203	−0.262947	−0.131473	−	0.991320i	$-0.541971\pi$
$241$	−4.08203	−0.262947	−0.131473	+	0.991320i	$0.541971\pi$
$242$	25.9071	1.66537
$243$	−9.12777	−0.585547
$244$	20.1553	1.29031
$245$	−2.05612	−0.131361
$246$	66.9900	4.27113
$247$	30.3770	1.93284
$248$	86.6009	5.49916
$249$	24.9448	1.58081
$250$	2.80769	0.177574
$251$	22.1018	1.39505	0.697525	−	0.716560i	$-0.254284\pi$
$251$	22.1018	1.39505	0.697525	+	0.716560i	$0.254284\pi$
$252$	−16.0523	−1.01120
$253$	5.29854	0.333116
$254$	31.2167	1.95871
$255$	9.63245	0.603207
$256$	117.394	7.33711
$257$	20.0768	1.25236	0.626180	−	0.779679i	$-0.284618\pi$
$257$	20.0768	1.25236	0.626180	+	0.779679i	$0.284618\pi$
$258$	19.5486	1.21704
$259$	10.2292	0.635611
$260$	38.5916	2.39335
$261$	5.95952	0.368885
$262$	−21.5016	−1.32838
$263$	30.1922	1.86173	0.930865	−	0.365364i	$-0.119056\pi$
$263$	30.1922	1.86173	0.930865	+	0.365364i	$0.119056\pi$
$264$	28.6922	1.76588
$265$	−5.26572	−0.323470
$266$	−39.1272	−2.39904
$267$	9.02363	0.552237
$268$	−86.2904	−5.27102
$269$	0.579934	0.0353592	0.0176796	−	0.999844i	$-0.494372\pi$
$269$	0.579934	0.0353592	0.0176796	+	0.999844i	$0.494372\pi$
$270$	−11.6168	−0.706976
$271$	−15.8003	−0.959801	−0.479901	−	0.877323i	$-0.659327\pi$
$271$	−15.8003	−0.959801	−0.479901	+	0.877323i	$0.659327\pi$
$272$	−91.8381	−5.56850
$273$	39.0177	2.36146
$274$	23.1622	1.39928
$275$	−1.33147	−0.0802906
$276$	−46.2740	−2.78537
$277$	−11.8620	−0.712720	−0.356360	−	0.934349i	$-0.615982\pi$
$277$	−11.8620	−0.712720	−0.356360	+	0.934349i	$0.615982\pi$
$278$	40.1926	2.41059
$279$	−7.20201	−0.431173
$280$	−32.8095	−1.96074
$281$	−27.4609	−1.63818	−0.819089	−	0.573667i	$-0.805521\pi$
$281$	−27.4609	−1.63818	−0.819089	+	0.573667i	$0.805521\pi$
$282$	10.8964	0.648871
$283$	−12.4114	−0.737780	−0.368890	−	0.929473i	$-0.620262\pi$
$283$	−12.4114	−0.737780	−0.368890	+	0.929473i	$0.620262\pi$
$284$	39.1390	2.32247
$285$	9.15300	0.542177
$286$	−24.5226	−1.45005
$287$	36.3269	2.14431
$288$	−28.2028	−1.66186
$289$	6.75002	0.397060
$290$	18.4544	1.08368
$291$	10.6437	0.623944
$292$	12.3098	0.720375
$293$	−30.8859	−1.80438	−0.902188	−	0.431343i	$-0.858040\pi$
$293$	−30.8859	−1.80438	−0.902188	+	0.431343i	$0.858040\pi$
$294$	−11.4104	−0.665471
$295$	−7.65543	−0.445716
$296$	37.0595	2.15404
$297$	5.50895	0.319662
$298$	39.0954	2.26474
$299$	26.1043	1.50965
$300$	11.6282	0.671353
$301$	10.6007	0.611013
$302$	28.2692	1.62671
$303$	−25.4443	−1.46174
$304$	−87.2669	−5.00510
$305$	−3.42596	−0.196170
$306$	12.4063	0.709219
$307$	4.22609	0.241196	0.120598	−	0.992701i	$-0.461519\pi$
$307$	4.22609	0.241196	0.120598	+	0.992701i	$0.461519\pi$
$308$	23.5727	1.34318
$309$	−5.91859	−0.336697
$310$	−22.3019	−1.26666
$311$	24.9773	1.41633	0.708167	−	0.706045i	$-0.249523\pi$
$311$	24.9773	1.41633	0.708167	+	0.706045i	$0.249523\pi$
$312$	141.358	8.00280
$313$	30.0205	1.69686	0.848428	−	0.529310i	$-0.177549\pi$
$313$	30.0205	1.69686	0.848428	+	0.529310i	$0.177549\pi$
$314$	8.50765	0.480115
$315$	2.72855	0.153736
$316$	−42.4147	−2.38602
$317$	−6.90294	−0.387708	−0.193854	−	0.981030i	$-0.562099\pi$
$317$	−6.90294	−0.387708	−0.193854	+	0.981030i	$0.562099\pi$
$318$	−29.2221	−1.63869
$319$	−8.75150	−0.489990
$320$	−49.6439	−2.77518
$321$	−3.48705	−0.194628
$322$	−33.6237	−1.87377
$323$	22.5679	1.25571
$324$	−64.1141	−3.56189
$325$	−6.55973	−0.363868
$326$	12.2402	0.677920
$327$	27.2398	1.50636
$328$	131.609	7.26689
$329$	5.90882	0.325764
$330$	−7.38898	−0.406750
$331$	−8.26881	−0.454495	−0.227247	−	0.973837i	$-0.572973\pi$
$331$	−8.26881	−0.454495	−0.227247	+	0.973837i	$0.572973\pi$
$332$	74.2477	4.07487
$333$	−3.08198	−0.168892
$334$	−53.7771	−2.94255
$335$	14.6675	0.801370
$336$	−112.090	−6.11501
$337$	3.28599	0.178999	0.0894996	−	0.995987i	$-0.471473\pi$
$337$	3.28599	0.178999	0.0894996	+	0.995987i	$0.471473\pi$
$338$	−84.3150	−4.58613
$339$	−10.2640	−0.557461
$340$	28.6708	1.55489
$341$	10.5761	0.572727
$342$	11.7887	0.637462
$343$	14.8778	0.803326
$344$	38.4053	2.07067
$345$	7.86557	0.423468
$346$	12.3347	0.663120
$347$	9.40556	0.504917	0.252458	−	0.967608i	$-0.418761\pi$
$347$	9.40556	0.504917	0.252458	+	0.967608i	$0.418761\pi$
$348$	76.4299	4.09707
$349$	−24.8094	−1.32802	−0.664009	−	0.747724i	$-0.731146\pi$
$349$	−24.8094	−1.32802	−0.664009	+	0.747724i	$0.731146\pi$
$350$	8.44929	0.451633
$351$	27.1409	1.44867
$352$	41.4155	2.20745
$353$	0.745724	0.0396909	0.0198454	−	0.999803i	$-0.493683\pi$
$353$	0.745724	0.0396909	0.0198454	+	0.999803i	$0.493683\pi$
$354$	−42.4838	−2.25799
$355$	−6.65278	−0.353093
$356$	26.8586	1.42350
$357$	28.9873	1.53417
$358$	−44.4546	−2.34950
$359$	−23.3535	−1.23255	−0.616274	−	0.787532i	$-0.711359\pi$
$359$	−23.3535	−1.23255	−0.616274	+	0.787532i	$0.711359\pi$
$360$	9.88527	0.521000
$361$	2.44457	0.128662
$362$	53.3399	2.80349
$363$	−18.2379	−0.957240
$364$	116.135	6.08714
$365$	−2.09239	−0.109521
$366$	−19.0123	−0.993791
$367$	−5.69874	−0.297472	−0.148736	−	0.988877i	$-0.547520\pi$
$367$	−5.69874	−0.297472	−0.148736	+	0.988877i	$0.547520\pi$
$368$	−74.9922	−3.90924
$369$	−10.9450	−0.569775
$370$	−9.54375	−0.496156
$371$	−15.8463	−0.822700
$372$	−92.3646	−4.78888
$373$	17.5308	0.907709	0.453855	−	0.891076i	$-0.350049\pi$
$373$	17.5308	0.907709	0.453855	+	0.891076i	$0.350049\pi$
$374$	−18.2185	−0.942054
$375$	−1.97654	−0.102068
$376$	21.4071	1.10399
$377$	−43.1159	−2.22058
$378$	−34.9589	−1.79809
$379$	−28.0835	−1.44255	−0.721275	−	0.692648i	$-0.756444\pi$
$379$	−28.0835	−1.44255	−0.721275	+	0.692648i	$0.756444\pi$
$380$	27.2437	1.39757
$381$	−21.9757	−1.12585
$382$	65.7365	3.36337
$383$	−27.0118	−1.38024	−0.690120	−	0.723695i	$-0.742442\pi$
$383$	−27.0118	−1.38024	−0.690120	+	0.723695i	$0.742442\pi$
$384$	−152.538	−7.78417
$385$	−4.00684	−0.204208
$386$	−1.66997	−0.0849990
$387$	−3.19391	−0.162355
$388$	31.6807	1.60834
$389$	−5.42659	−0.275139	−0.137570	−	0.990492i	$-0.543929\pi$
$389$	−5.42659	−0.275139	−0.137570	+	0.990492i	$0.543929\pi$
$390$	−36.4032	−1.84335
$391$	19.3936	0.980774
$392$	−22.4170	−1.13223
$393$	15.1366	0.763539
$394$	12.5068	0.630086
$395$	7.20958	0.362753
$396$	−7.10228	−0.356903
$397$	−11.9664	−0.600575	−0.300288	−	0.953849i	$-0.597083\pi$
$397$	−11.9664	−0.600575	−0.300288	+	0.953849i	$0.597083\pi$
$398$	−48.3047	−2.42130
$399$	27.5445	1.37895
$400$	18.8448	0.942239
$401$	15.4498	0.771526	0.385763	−	0.922598i	$-0.373938\pi$
$401$	15.4498	0.771526	0.385763	+	0.922598i	$0.373938\pi$
$402$	81.3971	4.05972
$403$	52.1050	2.59554
$404$	−75.7344	−3.76793
$405$	10.8980	0.541525
$406$	55.5356	2.75619
$407$	4.52586	0.224339
$408$	105.018	5.19918
$409$	−35.4403	−1.75241	−0.876205	−	0.481939i	$-0.839933\pi$
$409$	−35.4403	−1.75241	−0.876205	+	0.481939i	$0.839933\pi$
$410$	−33.8927	−1.67384
$411$	−16.3056	−0.804294
$412$	−17.6165	−0.867904
$413$	−23.0378	−1.13361
$414$	10.1306	0.497891
$415$	−12.6205	−0.619515
$416$	204.041	10.0039
$417$	−28.2945	−1.38559
$418$	−17.3117	−0.846740
$419$	5.28017	0.257953	0.128977	−	0.991648i	$-0.458831\pi$
$419$	5.28017	0.257953	0.128977	+	0.991648i	$0.458831\pi$
$420$	34.9931	1.70749
$421$	9.79106	0.477187	0.238593	−	0.971120i	$-0.423314\pi$
$421$	9.79106	0.477187	0.238593	+	0.971120i	$0.423314\pi$
$422$	−40.6691	−1.97974
$423$	−1.78028	−0.0865604
$424$	−57.4098	−2.78807
$425$	−4.87340	−0.236395
$426$	−36.9195	−1.78876
$427$	−10.3099	−0.498930
$428$	−10.3791	−0.501694
$429$	17.2632	0.833476
$430$	−9.89034	−0.476954
$431$	−14.4298	−0.695061	−0.347531	−	0.937669i	$-0.612980\pi$
$431$	−14.4298	−0.695061	−0.347531	+	0.937669i	$0.612980\pi$
$432$	−77.9702	−3.75134
$433$	15.1030	0.725802	0.362901	−	0.931828i	$-0.381786\pi$
$433$	15.1030	0.725802	0.362901	+	0.931828i	$0.381786\pi$
$434$	−67.1141	−3.22158
$435$	−12.9914	−0.622890
$436$	81.0785	3.88296
$437$	18.4282	0.881543
$438$	−11.6117	−0.554829
$439$	22.1110	1.05530	0.527651	−	0.849461i	$-0.323073\pi$
$439$	22.1110	1.05530	0.527651	+	0.849461i	$0.323073\pi$
$440$	−14.5164	−0.692043
$441$	1.86427	0.0887748
$442$	−89.7567	−4.26929
$443$	−27.4424	−1.30383	−0.651914	−	0.758293i	$-0.726034\pi$
$443$	−27.4424	−1.30383	−0.651914	+	0.758293i	$0.726034\pi$
$444$	−39.5259	−1.87582
$445$	−4.56538	−0.216420
$446$	33.9383	1.60702
$447$	−27.5221	−1.30175
$448$	−149.395	−7.05827
$449$	6.04935	0.285487	0.142743	−	0.989760i	$-0.454408\pi$
$449$	6.04935	0.285487	0.142743	+	0.989760i	$0.454408\pi$
$450$	−2.54571	−0.120006
$451$	16.0727	0.756832
$452$	−30.5504	−1.43697
$453$	−19.9008	−0.935020
$454$	−79.1458	−3.71450
$455$	−19.7405	−0.925447
$456$	99.7911	4.67315
$457$	−29.4860	−1.37930	−0.689649	−	0.724144i	$-0.742235\pi$
$457$	−29.4860	−1.37930	−0.689649	+	0.724144i	$0.742235\pi$
$458$	5.18880	0.242457
$459$	20.1637	0.941160
$460$	23.4117	1.09157
$461$	13.6552	0.635988	0.317994	−	0.948093i	$-0.396991\pi$
$461$	13.6552	0.635988	0.317994	+	0.948093i	$0.396991\pi$
$462$	−22.2359	−1.03451
$463$	42.7486	1.98670	0.993348	−	0.115147i	$-0.0367340\pi$
$463$	42.7486	1.98670	0.993348	+	0.115147i	$0.0367340\pi$
$464$	123.863	5.75021
$465$	15.7000	0.728068
$466$	−7.63626	−0.353743
$467$	−12.2708	−0.567825	−0.283913	−	0.958850i	$-0.591633\pi$
$467$	−12.2708	−0.567825	−0.283913	+	0.958850i	$0.591633\pi$
$468$	−34.9907	−1.61745
$469$	44.1394	2.03817
$470$	−5.51288	−0.254290
$471$	−5.98916	−0.275966
$472$	−83.4638	−3.84173
$473$	4.69022	0.215656
$474$	40.0095	1.83770
$475$	−4.63083	−0.212477
$476$	86.2800	3.95464
$477$	4.77438	0.218604
$478$	58.2583	2.66467
$479$	28.0182	1.28018	0.640092	−	0.768298i	$-0.278896\pi$
$479$	28.0182	1.28018	0.640092	+	0.768298i	$0.278896\pi$
$480$	61.4804	2.80618
$481$	22.2975	1.01668
$482$	11.4611	0.522038
$483$	23.6702	1.07703
$484$	−54.2846	−2.46748
$485$	−5.38502	−0.244521
$486$	25.6279	1.16251
$487$	−34.8961	−1.58129	−0.790646	−	0.612274i	$-0.790255\pi$
$487$	−34.8961	−1.58129	−0.790646	+	0.612274i	$0.790255\pi$
$488$	−37.3517	−1.69083
$489$	−8.61674	−0.389662
$490$	5.77295	0.260795
$491$	−14.5498	−0.656623	−0.328312	−	0.944570i	$-0.606480\pi$
$491$	−14.5498	−0.656623	−0.328312	+	0.944570i	$0.606480\pi$
$492$	−140.368	−6.32828
$493$	−32.0320	−1.44265
$494$	−85.2891	−3.83734
$495$	1.20723	0.0542611
$496$	−149.687	−6.72115
$497$	−20.0205	−0.898040
$498$	−70.0373	−3.13845
$499$	−38.8572	−1.73949	−0.869744	−	0.493503i	$-0.835716\pi$
$499$	−38.8572	−1.73949	−0.869744	+	0.493503i	$0.835716\pi$
$500$	−5.88311	−0.263101
$501$	37.8576	1.69135
$502$	−62.0548	−2.76964
$503$	−0.916550	−0.0408670	−0.0204335	−	0.999791i	$-0.506505\pi$
$503$	−0.916550	−0.0408670	−0.0204335	+	0.999791i	$0.506505\pi$
$504$	29.7481	1.32509
$505$	12.8732	0.572849
$506$	−14.8766	−0.661348
$507$	59.3555	2.63607
$508$	−65.4101	−2.90210
$509$	−39.6794	−1.75876	−0.879380	−	0.476121i	$-0.842042\pi$
$509$	−39.6794	−1.75876	−0.879380	+	0.476121i	$0.842042\pi$
$510$	−27.0449	−1.19757
$511$	−6.29671	−0.278550
$512$	−175.256	−7.74531
$513$	19.1600	0.845936
$514$	−56.3695	−2.48635
$515$	2.99442	0.131950
$516$	−40.9613	−1.80322
$517$	2.61433	0.114978
$518$	−28.7204	−1.26190
$519$	−8.68332	−0.381156
$520$	−71.5179	−3.13627
$521$	31.1525	1.36481	0.682407	−	0.730972i	$-0.260933\pi$
$521$	31.1525	1.36481	0.682407	+	0.730972i	$0.260933\pi$
$522$	−16.7325	−0.732361
$523$	−37.9005	−1.65727	−0.828636	−	0.559788i	$-0.810883\pi$
$523$	−37.9005	−1.65727	−0.828636	+	0.559788i	$0.810883\pi$
$524$	45.0536	1.96818
$525$	−5.94807	−0.259595
$526$	−84.7702	−3.69616
$527$	38.7102	1.68624
$528$	−49.5937	−2.15829
$529$	−7.16381	−0.311470
$530$	14.7845	0.642197
$531$	6.94112	0.301219
$532$	81.9855	3.55452
$533$	79.1850	3.42988
$534$	−25.3355	−1.09638
$535$	1.76422	0.0762741
$536$	159.913	6.90719
$537$	31.2949	1.35047
$538$	−1.62827	−0.0701999
$539$	−2.73766	−0.117920
$540$	24.3414	1.04749
$541$	27.7276	1.19210	0.596051	−	0.802947i	$-0.296736\pi$
$541$	27.7276	1.19210	0.596051	+	0.802947i	$0.296736\pi$
$542$	44.3624	1.90553
$543$	−37.5499	−1.61142
$544$	151.588	6.49927
$545$	−13.7816	−0.590338
$546$	−109.550	−4.68829
$547$	−37.5324	−1.60477	−0.802386	−	0.596806i	$-0.796436\pi$
$547$	−37.5324	−1.60477	−0.802386	+	0.596806i	$0.796436\pi$
$548$	−48.5331	−2.07323
$549$	3.10629	0.132573
$550$	3.73835	0.159404
$551$	−30.4376	−1.29668
$552$	85.7548	3.64997
$553$	21.6961	0.922610
$554$	33.3049	1.41499
$555$	6.71854	0.285186
$556$	−84.2179	−3.57163
$557$	7.96272	0.337391	0.168696	−	0.985668i	$-0.446045\pi$
$557$	7.96272	0.337391	0.168696	+	0.985668i	$0.446045\pi$
$558$	20.2210	0.856023
$559$	23.1072	0.977332
$560$	56.7103	2.39645
$561$	12.8253	0.541485
$562$	77.1015	3.25233
$563$	−43.2764	−1.82388	−0.911942	−	0.410318i	$-0.865418\pi$
$563$	−43.2764	−1.82388	−0.911942	+	0.410318i	$0.865418\pi$
$564$	−22.8319	−0.961394
$565$	5.19290	0.218467
$566$	34.8473	1.46474
$567$	32.7957	1.37729
$568$	−72.5323	−3.04339
$569$	−20.0949	−0.842421	−0.421211	−	0.906963i	$-0.638395\pi$
$569$	−20.0949	−0.842421	−0.421211	+	0.906963i	$0.638395\pi$
$570$	−25.6988	−1.07640
$571$	12.0754	0.505338	0.252669	−	0.967553i	$-0.418692\pi$
$571$	12.0754	0.505338	0.252669	+	0.967553i	$0.418692\pi$
$572$	51.3835	2.14845
$573$	−46.2767	−1.93324
$574$	−101.995	−4.25717
$575$	−3.97947	−0.165955
$576$	45.0118	1.87549
$577$	31.8654	1.32657	0.663287	−	0.748365i	$-0.269161\pi$
$577$	31.8654	1.32657	0.663287	+	0.748365i	$0.269161\pi$
$578$	−18.9520	−0.788298
$579$	1.17561	0.0488567
$580$	−38.6686	−1.60563
$581$	−37.9793	−1.57565
$582$	−29.8841	−1.23874
$583$	−7.01113	−0.290372
$584$	−22.8124	−0.943985
$585$	5.94766	0.245905
$586$	86.7181	3.58229
$587$	−8.21949	−0.339255	−0.169627	−	0.985508i	$-0.554256\pi$
$587$	−8.21949	−0.339255	−0.169627	+	0.985508i	$0.554256\pi$
$588$	23.9090	0.985989
$589$	36.7834	1.51564
$590$	21.4940	0.884896
$591$	−8.80448	−0.362168
$592$	−64.0562	−2.63269
$593$	10.6629	0.437874	0.218937	−	0.975739i	$-0.429741\pi$
$593$	10.6629	0.437874	0.218937	+	0.975739i	$0.429741\pi$
$594$	−15.4674	−0.634635
$595$	−14.6657	−0.601236
$596$	−81.9189	−3.35553
$597$	34.0052	1.39174
$598$	−73.2926	−2.99716
$599$	26.5005	1.08278	0.541391	−	0.840771i	$-0.317898\pi$
$599$	26.5005	1.08278	0.541391	+	0.840771i	$0.317898\pi$
$600$	−21.5493	−0.879747
$601$	43.3696	1.76908	0.884542	−	0.466461i	$-0.154471\pi$
$601$	43.3696	1.76908	0.884542	+	0.466461i	$0.154471\pi$
$602$	−29.7634	−1.21306
$603$	−13.2989	−0.541573
$604$	−59.2342	−2.41020
$605$	9.22719	0.375139
$606$	71.4397	2.90204
$607$	−13.6133	−0.552546	−0.276273	−	0.961079i	$-0.589099\pi$
$607$	−13.6133	−0.552546	−0.276273	+	0.961079i	$0.589099\pi$
$608$	144.043	5.84169
$609$	−39.0955	−1.58423
$610$	9.61902	0.389463
$611$	12.8800	0.521069
$612$	−25.9956	−1.05081
$613$	−10.7402	−0.433792	−0.216896	−	0.976195i	$-0.569593\pi$
$613$	−10.7402	−0.433792	−0.216896	+	0.976195i	$0.569593\pi$
$614$	−11.8655	−0.478854
$615$	23.8595	0.962108
$616$	−43.6848	−1.76011
$617$	2.90879	0.117104	0.0585518	−	0.998284i	$-0.481352\pi$
$617$	2.90879	0.117104	0.0585518	+	0.998284i	$0.481352\pi$
$618$	16.6175	0.668456
$619$	−13.4395	−0.540180	−0.270090	−	0.962835i	$-0.587053\pi$
$619$	−13.4395	−0.540180	−0.270090	+	0.962835i	$0.587053\pi$
$620$	46.7305	1.87674
$621$	16.4650	0.660720
$622$	−70.1285	−2.81190
$623$	−13.7388	−0.550432
$624$	−244.333	−9.78114
$625$	1.00000	0.0400000
$626$	−84.2881	−3.36883
$627$	12.1869	0.486699
$628$	−17.8266	−0.711358
$629$	16.5654	0.660506
$630$	−7.66090	−0.305218
$631$	−3.87684	−0.154335	−0.0771673	−	0.997018i	$-0.524588\pi$
$631$	−3.87684	−0.154335	−0.0771673	+	0.997018i	$0.524588\pi$
$632$	78.6029	3.12665
$633$	28.6299	1.13794
$634$	19.3813	0.769730
$635$	11.1183	0.441216
$636$	61.2307	2.42795
$637$	−13.4876	−0.534399
$638$	24.5715	0.972794
$639$	6.03202	0.238623
$640$	77.1744	3.05059
$641$	−18.7334	−0.739924	−0.369962	−	0.929047i	$-0.620629\pi$
$641$	−18.7334	−0.739924	−0.369962	+	0.929047i	$0.620629\pi$
$642$	9.79055	0.386402
$643$	−19.2915	−0.760784	−0.380392	−	0.924825i	$-0.624211\pi$
$643$	−19.2915	−0.760784	−0.380392	+	0.924825i	$0.624211\pi$
$644$	70.4537	2.77626
$645$	6.96253	0.274149
$646$	−63.3636	−2.49301
$647$	0.247467	0.00972894	0.00486447	−	0.999988i	$-0.498452\pi$
$647$	0.247467	0.00972894	0.00486447	+	0.999988i	$0.498452\pi$
$648$	118.816	4.66753
$649$	−10.1930	−0.400109
$650$	18.4177	0.722401
$651$	47.2465	1.85174
$652$	−25.6475	−1.00443
$653$	−14.1349	−0.553140	−0.276570	−	0.960994i	$-0.589198\pi$
$653$	−14.1349	−0.553140	−0.276570	+	0.960994i	$0.589198\pi$
$654$	−76.4808	−2.99063
$655$	−7.65813	−0.299228
$656$	−227.482	−8.88170
$657$	1.89715	0.0740151
$658$	−16.5901	−0.646750
$659$	−39.7801	−1.54961	−0.774806	−	0.632199i	$-0.782152\pi$
$659$	−39.7801	−1.54961	−0.774806	+	0.632199i	$0.782152\pi$
$660$	15.4826	0.602658
$661$	−20.8603	−0.811371	−0.405685	−	0.914013i	$-0.632967\pi$
$661$	−20.8603	−0.811371	−0.405685	+	0.914013i	$0.632967\pi$
$662$	23.2162	0.902325
$663$	63.1863	2.45395
$664$	−137.596	−5.33974
$665$	−13.9357	−0.540405
$666$	8.65325	0.335307
$667$	−26.1563	−1.01278
$668$	112.682	4.35981
$669$	−23.8916	−0.923703
$670$	−41.1817	−1.59099
$671$	−4.56155	−0.176097
$672$	185.015	7.13712
$673$	−20.9650	−0.808142	−0.404071	−	0.914728i	$-0.632405\pi$
$673$	−20.9650	−0.808142	−0.404071	+	0.914728i	$0.632405\pi$
$674$	−9.22603	−0.355373
$675$	−4.13750	−0.159252
$676$	176.670	6.79501
$677$	9.45989	0.363573	0.181787	−	0.983338i	$-0.441812\pi$
$677$	9.45989	0.363573	0.181787	+	0.983338i	$0.441812\pi$
$678$	28.8180	1.10675
$679$	−16.2054	−0.621904
$680$	−53.1326	−2.03754
$681$	55.7165	2.13506
$682$	−29.6943	−1.13705
$683$	9.65608	0.369480	0.184740	−	0.982787i	$-0.440856\pi$
$683$	9.65608	0.369480	0.184740	+	0.982787i	$0.440856\pi$
$684$	−24.7016	−0.944491
$685$	8.24956	0.315200
$686$	−41.7722	−1.59487
$687$	−3.65277	−0.139362
$688$	−66.3824	−2.53081
$689$	−34.5417	−1.31593
$690$	−22.0841	−0.840726
$691$	31.4091	1.19486	0.597429	−	0.801922i	$-0.296189\pi$
$691$	31.4091	1.19486	0.597429	+	0.801922i	$0.296189\pi$
$692$	−25.8457	−0.982506
$693$	3.63297	0.138005
$694$	−26.4079	−1.00243
$695$	14.3152	0.543006
$696$	−141.640	−5.36884
$697$	58.8286	2.22829
$698$	69.6571	2.63656
$699$	5.37572	0.203328
$700$	−17.7043	−0.669159
$701$	−49.3559	−1.86415	−0.932073	−	0.362272i	$-0.882001\pi$
$701$	−49.3559	−1.86415	−0.932073	+	0.362272i	$0.882001\pi$
$702$	−76.2031	−2.87610
$703$	15.7409	0.593679
$704$	−66.0993	−2.49121
$705$	3.88091	0.146164
$706$	−2.09376	−0.0787997
$707$	38.7398	1.45696
$708$	89.0187	3.34553
$709$	27.7285	1.04136	0.520682	−	0.853751i	$-0.325678\pi$
$709$	27.7285	1.04136	0.520682	+	0.853751i	$0.325678\pi$
$710$	18.6789	0.701007
$711$	−6.53687	−0.245152
$712$	−49.7743	−1.86537
$713$	31.6096	1.18379
$714$	−81.3873	−3.04584
$715$	−8.73407	−0.326636
$716$	93.1484	3.48112
$717$	−41.0123	−1.53163
$718$	65.5692	2.44702
$719$	18.0405	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$719$	18.0405	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$720$	−17.0864	−0.636773
$721$	9.01124	0.335596
$722$	−6.86360	−0.255437
$723$	−8.06828	−0.300063
$724$	−111.766	−4.15376
$725$	6.57281	0.244108
$726$	51.2063	1.90044
$727$	−4.45449	−0.165208	−0.0826040	−	0.996582i	$-0.526324\pi$
$727$	−4.45449	−0.165208	−0.0826040	+	0.996582i	$0.526324\pi$
$728$	−215.222	−7.97664
$729$	14.6526	0.542689
$730$	5.87478	0.217435
$731$	17.1670	0.634944
$732$	39.8376	1.47244
$733$	−28.6515	−1.05827	−0.529133	−	0.848539i	$-0.677483\pi$
$733$	−28.6515	−1.05827	−0.529133	+	0.848539i	$0.677483\pi$
$734$	16.0003	0.590581
$735$	−4.06400	−0.149903
$736$	123.782	4.56266
$737$	19.5293	0.719370
$738$	30.7302	1.13120
$739$	−3.13700	−0.115397	−0.0576983	−	0.998334i	$-0.518376\pi$
$739$	−3.13700	−0.115397	−0.0576983	+	0.998334i	$0.518376\pi$
$740$	19.9976	0.735126
$741$	60.0412	2.20567
$742$	44.4915	1.63334
$743$	−38.0381	−1.39548	−0.697742	−	0.716349i	$-0.745812\pi$
$743$	−38.0381	−1.39548	−0.697742	+	0.716349i	$0.745812\pi$
$744$	171.170	6.27539
$745$	13.9244	0.510151
$746$	−49.2210	−1.80211
$747$	11.4429	0.418673
$748$	38.1742	1.39579
$749$	5.30915	0.193992
$750$	5.54949	0.202639
$751$	−19.8792	−0.725401	−0.362700	−	0.931906i	$-0.618145\pi$
$751$	−19.8792	−0.725401	−0.362700	+	0.931906i	$0.618145\pi$
$752$	−37.0016	−1.34931
$753$	43.6849	1.59197
$754$	121.056	4.40860
$755$	10.0685	0.366431
$756$	73.2514	2.66413
$757$	1.76161	0.0640269	0.0320135	−	0.999487i	$-0.489808\pi$
$757$	1.76161	0.0640269	0.0320135	+	0.999487i	$0.489808\pi$
$758$	78.8496	2.86395
$759$	10.4728	0.380137
$760$	−50.4879	−1.83139
$761$	−18.7381	−0.679256	−0.339628	−	0.940560i	$-0.610301\pi$
$761$	−18.7381	−0.679256	−0.339628	+	0.940560i	$0.610301\pi$
$762$	61.7009	2.23519
$763$	−41.4734	−1.50144
$764$	−137.741	−4.98331
$765$	4.41867	0.159758
$766$	75.8408	2.74024
$767$	−50.2175	−1.81325
$768$	232.033	8.37277
$769$	−42.0795	−1.51743	−0.758713	−	0.651425i	$-0.774171\pi$
$769$	−42.0795	−1.51743	−0.758713	+	0.651425i	$0.774171\pi$
$770$	11.2500	0.405420
$771$	39.6826	1.42913
$772$	3.49918	0.125938
$773$	−4.72947	−0.170107	−0.0850535	−	0.996376i	$-0.527106\pi$
$773$	−4.72947	−0.170107	−0.0850535	+	0.996376i	$0.527106\pi$
$774$	8.96749	0.322330
$775$	−7.94317	−0.285327
$776$	−58.7105	−2.10759
$777$	20.2184	0.725330
$778$	15.2362	0.546243
$779$	55.9005	2.00284
$780$	76.2777	2.73118
$781$	−8.85796	−0.316963
$782$	−54.4510	−1.94717
$783$	−27.1950	−0.971870
$784$	38.7472	1.38383
$785$	3.03013	0.108150
$786$	−42.4988	−1.51588
$787$	9.06089	0.322986	0.161493	−	0.986874i	$-0.448369\pi$
$787$	9.06089	0.322986	0.161493	+	0.986874i	$0.448369\pi$
$788$	−26.2063	−0.933562
$789$	59.6759	2.12452
$790$	−20.2422	−0.720187
$791$	15.6272	0.555639
$792$	13.1619	0.467689
$793$	−22.4734	−0.798052
$794$	33.5979	1.19234
$795$	−10.4079	−0.369129
$796$	101.216	3.58749
$797$	6.98328	0.247361	0.123680	−	0.992322i	$-0.460530\pi$
$797$	6.98328	0.247361	0.123680	+	0.992322i	$0.460530\pi$
$798$	−77.3363	−2.73767
$799$	9.56889	0.338523
$800$	−31.1051	−1.09973
$801$	4.13939	0.146258
$802$	−43.3782	−1.53174
$803$	−2.78595	−0.0983141
$804$	−170.556	−6.01505
$805$	−11.9756	−0.422084
$806$	−146.295	−5.15301
$807$	1.14626	0.0403503
$808$	140.351	4.93752
$809$	13.5034	0.474753	0.237377	−	0.971418i	$-0.423712\pi$
$809$	13.5034	0.474753	0.237377	+	0.971418i	$0.423712\pi$
$810$	−30.5981	−1.07511
$811$	−6.39682	−0.224623	−0.112311	−	0.993673i	$-0.535825\pi$
$811$	−6.39682	−0.224623	−0.112311	+	0.993673i	$0.535825\pi$
$812$	−116.367	−4.08368
$813$	−31.2299	−1.09528
$814$	−12.7072	−0.445387
$815$	4.35952	0.152707
$816$	−181.521	−6.35452
$817$	16.3125	0.570703
$818$	99.5053	3.47912
$819$	17.8985	0.625425
$820$	71.0173	2.48003
$821$	20.0522	0.699826	0.349913	−	0.936782i	$-0.386211\pi$
$821$	20.0522	0.699826	0.349913	+	0.936782i	$0.386211\pi$
$822$	45.7809	1.59679
$823$	16.9171	0.589694	0.294847	−	0.955544i	$-0.404731\pi$
$823$	16.9171	0.589694	0.294847	+	0.955544i	$0.404731\pi$
$824$	32.6469	1.13731
$825$	−2.63169	−0.0916239
$826$	64.6829	2.25061
$827$	54.4660	1.89397	0.946985	−	0.321279i	$-0.104113\pi$
$827$	54.4660	1.89397	0.946985	+	0.321279i	$0.104113\pi$
$828$	−21.2272	−0.737696
$829$	−39.8983	−1.38572	−0.692862	−	0.721070i	$-0.743651\pi$
$829$	−39.8983	−1.38572	−0.692862	+	0.721070i	$0.743651\pi$
$830$	35.4344	1.22994
$831$	−23.4457	−0.813323
$832$	−325.651	−11.2899
$833$	−10.0203	−0.347183
$834$	79.4421	2.75086
$835$	−19.1535	−0.662835
$836$	36.2741	1.25457
$837$	32.8648	1.13597
$838$	−14.8251	−0.512124
$839$	−1.65193	−0.0570308	−0.0285154	−	0.999593i	$-0.509078\pi$
$839$	−1.65193	−0.0570308	−0.0285154	+	0.999593i	$0.509078\pi$
$840$	−64.8492	−2.23751
$841$	14.2019	0.489721
$842$	−27.4902	−0.947376
$843$	−54.2774	−1.86941
$844$	85.2163	2.93327
$845$	−30.0301	−1.03307
$846$	4.99848	0.171851
$847$	27.7678	0.954111
$848$	99.2312	3.40761
$849$	−24.5315	−0.841920
$850$	13.6830	0.469323
$851$	13.5268	0.463693
$852$	77.3597	2.65030
$853$	−6.85277	−0.234635	−0.117317	−	0.993094i	$-0.537429\pi$
$853$	−6.85277	−0.234635	−0.117317	+	0.993094i	$0.537429\pi$
$854$	28.9469	0.990542
$855$	4.19874	0.143594
$856$	19.2346	0.657424
$857$	25.3297	0.865244	0.432622	−	0.901575i	$-0.357588\pi$
$857$	25.3297	0.865244	0.432622	+	0.901575i	$0.357588\pi$
$858$	−48.4697	−1.65473
$859$	−31.8775	−1.08765	−0.543824	−	0.839199i	$-0.683024\pi$
$859$	−31.8775	−1.08765	−0.543824	+	0.839199i	$0.683024\pi$
$860$	20.7238	0.706676
$861$	71.8014	2.44698
$862$	40.5145	1.37993
$863$	−13.2036	−0.449457	−0.224728	−	0.974421i	$-0.572149\pi$
$863$	−13.2036	−0.449457	−0.224728	+	0.974421i	$0.572149\pi$
$864$	128.697	4.37837
$865$	4.39320	0.149373
$866$	−42.4044	−1.44096
$867$	13.3417	0.453107
$868$	140.628	4.77323
$869$	9.59933	0.325635
$870$	36.4758	1.23665
$871$	96.2147	3.26011
$872$	−150.255	−5.08826
$873$	4.88256	0.165250
$874$	−51.7408	−1.75016
$875$	3.00934	0.101734
$876$	24.3307	0.822058
$877$	34.8750	1.17765	0.588823	−	0.808262i	$-0.299591\pi$
$877$	34.8750	1.17765	0.588823	+	0.808262i	$0.299591\pi$
$878$	−62.0809	−2.09513
$879$	−61.0472	−2.05907
$880$	25.0912	0.845825
$881$	−3.69809	−0.124592	−0.0622959	−	0.998058i	$-0.519842\pi$
$881$	−3.69809	−0.124592	−0.0622959	+	0.998058i	$0.519842\pi$
$882$	−5.23429	−0.176248
$883$	8.21518	0.276463	0.138231	−	0.990400i	$-0.455858\pi$
$883$	8.21518	0.276463	0.138231	+	0.990400i	$0.455858\pi$
$884$	188.072	6.32556
$885$	−15.1312	−0.508630
$886$	77.0497	2.58854
$887$	42.4698	1.42599	0.712997	−	0.701167i	$-0.247337\pi$
$887$	42.4698	1.42599	0.712997	+	0.701167i	$0.247337\pi$
$888$	73.2493	2.45809
$889$	33.4587	1.12217
$890$	12.8182	0.429666
$891$	14.5103	0.486114
$892$	−71.1128	−2.38103
$893$	9.09260	0.304272
$894$	77.2735	2.58441
$895$	−15.8332	−0.529245
$896$	232.244	7.75873
$897$	51.5960	1.72274
$898$	−16.9847	−0.566787
$899$	−52.2090	−1.74127
$900$	5.33417	0.177806
$901$	−25.6619	−0.854923
$902$	−45.1270	−1.50257
$903$	20.9526	0.697259
$904$	56.6159	1.88302
$905$	18.9978	0.631509
$906$	55.8752	1.85633
$907$	26.8555	0.891723	0.445861	−	0.895102i	$-0.352897\pi$
$907$	26.8555	0.891723	0.445861	+	0.895102i	$0.352897\pi$
$908$	165.839	5.50356
$909$	−11.6720	−0.387136
$910$	55.4250	1.83732
$911$	47.5964	1.57694	0.788469	−	0.615075i	$-0.210874\pi$
$911$	47.5964	1.57694	0.788469	+	0.615075i	$0.210874\pi$
$912$	−172.486	−5.71159
$913$	−16.8038	−0.556124
$914$	82.7875	2.73837
$915$	−6.77153	−0.223860
$916$	−10.8724	−0.359234
$917$	−23.0459	−0.761043
$918$	−56.6133	−1.86852
$919$	23.0210	0.759392	0.379696	−	0.925111i	$-0.376029\pi$
$919$	23.0210	0.759392	0.379696	+	0.925111i	$0.376029\pi$
$920$	−43.3864	−1.43041
$921$	8.35302	0.275241
$922$	−38.3396	−1.26265
$923$	−43.6404	−1.43644
$924$	46.5923	1.53277
$925$	−3.39915	−0.111763
$926$	−120.025	−3.94426
$927$	−2.71502	−0.0891730
$928$	−204.448	−6.71134
$929$	1.76698	0.0579728	0.0289864	−	0.999580i	$-0.490772\pi$
$929$	1.76698	0.0579728	0.0289864	+	0.999580i	$0.490772\pi$
$930$	−44.0806	−1.44546
$931$	−9.52156	−0.312056
$932$	16.0007	0.524120
$933$	49.3685	1.61625
$934$	34.4526	1.12732
$935$	−6.48878	−0.212206
$936$	64.8447	2.11952
$937$	−12.3948	−0.404919	−0.202460	−	0.979291i	$-0.564894\pi$
$937$	−12.3948	−0.404919	−0.202460	+	0.979291i	$0.564894\pi$
$938$	−123.930	−4.04645
$939$	59.3365	1.93637
$940$	11.5515	0.376767
$941$	−31.7966	−1.03654	−0.518269	−	0.855218i	$-0.673423\pi$
$941$	−31.7966	−1.03654	−0.518269	+	0.855218i	$0.673423\pi$
$942$	16.8157	0.547884
$943$	48.0377	1.56432
$944$	144.265	4.69542
$945$	−12.4511	−0.405035
$946$	−13.1687	−0.428150
$947$	−12.6568	−0.411289	−0.205645	−	0.978627i	$-0.565929\pi$
$947$	−12.6568	−0.411289	−0.205645	+	0.978627i	$0.565929\pi$
$948$	−83.8342	−2.72281
$949$	−13.7255	−0.445549
$950$	13.0019	0.421838
$951$	−13.6439	−0.442434
$952$	−159.894	−5.18219
$953$	36.2391	1.17390	0.586950	−	0.809623i	$-0.300329\pi$
$953$	36.2391	1.17390	0.586950	+	0.809623i	$0.300329\pi$
$954$	−13.4050	−0.434002
$955$	23.4130	0.757628
$956$	−122.072	−3.94809
$957$	−17.2976	−0.559153
$958$	−78.6664	−2.54159
$959$	24.8257	0.801665
$960$	−98.1230	−3.16691
$961$	32.0939	1.03529
$962$	−62.6044	−2.01845
$963$	−1.59961	−0.0515467
$964$	−24.0151	−0.773473
$965$	−0.594783	−0.0191467
$966$	−66.4584	−2.13826
$967$	−46.1396	−1.48375	−0.741875	−	0.670538i	$-0.766063\pi$
$967$	−46.1396	−1.48375	−0.741875	+	0.670538i	$0.766063\pi$
$968$	100.600	3.23341
$969$	44.6062	1.43296
$970$	15.1195	0.485457
$971$	−16.8905	−0.542042	−0.271021	−	0.962573i	$-0.587361\pi$
$971$	−16.8905	−0.542042	−0.271021	+	0.962573i	$0.587361\pi$
$972$	−53.6997	−1.72242
$973$	43.0793	1.38106
$974$	97.9772	3.13939
$975$	−12.9655	−0.415230
$976$	64.5614	2.06656
$977$	37.1563	1.18874	0.594368	−	0.804193i	$-0.297402\pi$
$977$	37.1563	1.18874	0.594368	+	0.804193i	$0.297402\pi$
$978$	24.1931	0.773611
$979$	−6.07866	−0.194275
$980$	−12.0964	−0.386405
$981$	12.4956	0.398955
$982$	40.8513	1.30362
$983$	−36.8032	−1.17384	−0.586920	−	0.809645i	$-0.699660\pi$
$983$	−36.8032	−1.17384	−0.586920	+	0.809645i	$0.699660\pi$
$984$	260.130	8.29264
$985$	4.45450	0.141932
$986$	89.9357	2.86414
$987$	11.6790	0.371746
$988$	178.711	5.68556
$989$	14.0180	0.445748
$990$	−3.38953	−0.107726
$991$	−10.3333	−0.328247	−0.164123	−	0.986440i	$-0.552480\pi$
$991$	−10.3333	−0.328247	−0.164123	+	0.986440i	$0.552480\pi$
$992$	247.073	7.84458
$993$	−16.3436	−0.518648
$994$	56.2112	1.78291
$995$	−17.2044	−0.545418
$996$	146.753	4.65005
$997$	−2.89975	−0.0918360	−0.0459180	−	0.998945i	$-0.514621\pi$
$997$	−2.89975	−0.0918360	−0.0459180	+	0.998945i	$0.514621\pi$
$998$	109.099	3.45347
$999$	14.0640	0.444964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.g.1.1	✓	137

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.g.1.1	✓	137	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80769 q^{2} +1.97654 q^{3} +5.88311 q^{4} -1.00000 q^{5} -5.54949 q^{6} -3.00934 q^{7} -10.9026 q^{8} +0.906693 q^{9} +O(q^{10})\)	\(q-2.80769 q^{2} +1.97654 q^{3} +5.88311 q^{4} -1.00000 q^{5} -5.54949 q^{6} -3.00934 q^{7} -10.9026 q^{8} +0.906693 q^{9} +2.80769 q^{10} -1.33147 q^{11} +11.6282 q^{12} -6.55973 q^{13} +8.44929 q^{14} -1.97654 q^{15} +18.8448 q^{16} -4.87340 q^{17} -2.54571 q^{18} -4.63083 q^{19} -5.88311 q^{20} -5.94807 q^{21} +3.73835 q^{22} -3.97947 q^{23} -21.5493 q^{24} +1.00000 q^{25} +18.4177 q^{26} -4.13750 q^{27} -17.7043 q^{28} +6.57281 q^{29} +5.54949 q^{30} -7.94317 q^{31} -31.1051 q^{32} -2.63169 q^{33} +13.6830 q^{34} +3.00934 q^{35} +5.33417 q^{36} -3.39915 q^{37} +13.0019 q^{38} -12.9655 q^{39} +10.9026 q^{40} -12.0714 q^{41} +16.7003 q^{42} -3.52259 q^{43} -7.83318 q^{44} -0.906693 q^{45} +11.1731 q^{46} -1.96349 q^{47} +37.2474 q^{48} +2.05612 q^{49} -2.80769 q^{50} -9.63245 q^{51} -38.5916 q^{52} +5.26572 q^{53} +11.6168 q^{54} +1.33147 q^{55} +32.8095 q^{56} -9.15300 q^{57} -18.4544 q^{58} +7.65543 q^{59} -11.6282 q^{60} +3.42596 q^{61} +22.3019 q^{62} -2.72855 q^{63} +49.6439 q^{64} +6.55973 q^{65} +7.38898 q^{66} -14.6675 q^{67} -28.6708 q^{68} -7.86557 q^{69} -8.44929 q^{70} +6.65278 q^{71} -9.88527 q^{72} +2.09239 q^{73} +9.54375 q^{74} +1.97654 q^{75} -27.2437 q^{76} +4.00684 q^{77} +36.4032 q^{78} -7.20958 q^{79} -18.8448 q^{80} -10.8980 q^{81} +33.8927 q^{82} +12.6205 q^{83} -34.9931 q^{84} +4.87340 q^{85} +9.89034 q^{86} +12.9914 q^{87} +14.5164 q^{88} +4.56538 q^{89} +2.54571 q^{90} +19.7405 q^{91} -23.4117 q^{92} -15.7000 q^{93} +5.51288 q^{94} +4.63083 q^{95} -61.4804 q^{96} +5.38502 q^{97} -5.77295 q^{98} -1.20723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9}+O(q^{10}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9	\( 137 q + 4 q^{2} + 20 q^{3} + 152 q^{4} - 137 q^{5} + 14 q^{6} - 30 q^{7} + 24 q^{8} + 163 q^{9} - 4 q^{10} + 51 q^{11} + 32 q^{12} - 6 q^{13} + 49 q^{14} - 20 q^{15} + 170 q^{16} + 46 q^{17} + 4 q^{18} + 47 q^{19} - 152 q^{20} + 28 q^{21} - 19 q^{22} + 29 q^{23} + 39 q^{24} + 137 q^{25} + 67 q^{26} + 77 q^{27} - 58 q^{28} + 27 q^{29} - 14 q^{30} + 23 q^{31} + 42 q^{32} + 40 q^{33} + 38 q^{34} + 30 q^{35} + 222 q^{36} - 56 q^{37} + 87 q^{38} + 44 q^{39} - 24 q^{40} + 66 q^{41} + 34 q^{42} + 15 q^{43} + 87 q^{44} - 163 q^{45} + 37 q^{46} + 52 q^{47} + 56 q^{48} + 195 q^{49} + 4 q^{50} + 106 q^{51} - 31 q^{52} + 45 q^{53} + 83 q^{54} - 51 q^{55} + 148 q^{56} + 4 q^{57} - 101 q^{58} + 239 q^{59} - 32 q^{60} + 46 q^{61} + 63 q^{62} - 59 q^{63} + 200 q^{64} + 6 q^{65} + 108 q^{66} - 18 q^{67} + 152 q^{68} + 63 q^{69} - 49 q^{70} + 110 q^{71} + 6 q^{72} - 19 q^{73} + 81 q^{74} + 20 q^{75} + 94 q^{76} + 43 q^{77} - 3 q^{78} + 40 q^{79} - 170 q^{80} + 229 q^{81} + 3 q^{82} + 235 q^{83} + 94 q^{84} - 46 q^{85} + 110 q^{86} + 31 q^{87} - 105 q^{88} + 150 q^{89} - 4 q^{90} + 110 q^{91} + 76 q^{92} + 11 q^{93} + 56 q^{94} - 47 q^{95} + 146 q^{96} + 17 q^{97} + 75 q^{98} + 125 q^{99}+O(q^{100}) \) 137 * q + 4 * q^2 + 20 * q^3 + 152 * q^4 - 137 * q^5 + 14 * q^6 - 30 * q^7 + 24 * q^8 + 163 * q^9 - 4 * q^10 + 51 * q^11 + 32 * q^12 - 6 * q^13 + 49 * q^14 - 20 * q^15 + 170 * q^16 + 46 * q^17 + 4 * q^18 + 47 * q^19 - 152 * q^20 + 28 * q^21 - 19 * q^22 + 29 * q^23 + 39 * q^24 + 137 * q^25 + 67 * q^26 + 77 * q^27 - 58 * q^28 + 27 * q^29 - 14 * q^30 + 23 * q^31 + 42 * q^32 + 40 * q^33 + 38 * q^34 + 30 * q^35 + 222 * q^36 - 56 * q^37 + 87 * q^38 + 44 * q^39 - 24 * q^40 + 66 * q^41 + 34 * q^42 + 15 * q^43 + 87 * q^44 - 163 * q^45 + 37 * q^46 + 52 * q^47 + 56 * q^48 + 195 * q^49 + 4 * q^50 + 106 * q^51 - 31 * q^52 + 45 * q^53 + 83 * q^54 - 51 * q^55 + 148 * q^56 + 4 * q^57 - 101 * q^58 + 239 * q^59 - 32 * q^60 + 46 * q^61 + 63 * q^62 - 59 * q^63 + 200 * q^64 + 6 * q^65 + 108 * q^66 - 18 * q^67 + 152 * q^68 + 63 * q^69 - 49 * q^70 + 110 * q^71 + 6 * q^72 - 19 * q^73 + 81 * q^74 + 20 * q^75 + 94 * q^76 + 43 * q^77 - 3 * q^78 + 40 * q^79 - 170 * q^80 + 229 * q^81 + 3 * q^82 + 235 * q^83 + 94 * q^84 - 46 * q^85 + 110 * q^86 + 31 * q^87 - 105 * q^88 + 150 * q^89 - 4 * q^90 + 110 * q^91 + 76 * q^92 + 11 * q^93 + 56 * q^94 - 47 * q^95 + 146 * q^96 + 17 * q^97 + 75 * q^98 + 125 * q^99

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