LMFDB - Embedded newform 8017.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$0$
Dimension:	$340$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61686 q^{2} +2.24685 q^{3} +4.84797 q^{4} +1.56834 q^{5} -5.87971 q^{6} +3.28305 q^{7} -7.45273 q^{8} +2.04835 q^{9} +O(q^{10})$	\(q-2.61686 q^{2} +2.24685 q^{3} +4.84797 q^{4} +1.56834 q^{5} -5.87971 q^{6} +3.28305 q^{7} -7.45273 q^{8} +2.04835 q^{9} -4.10414 q^{10} +1.73334 q^{11} +10.8927 q^{12} +6.68251 q^{13} -8.59129 q^{14} +3.52384 q^{15} +9.80684 q^{16} +6.95839 q^{17} -5.36025 q^{18} -4.98322 q^{19} +7.60328 q^{20} +7.37654 q^{21} -4.53591 q^{22} +6.77874 q^{23} -16.7452 q^{24} -2.54030 q^{25} -17.4872 q^{26} -2.13822 q^{27} +15.9161 q^{28} -4.31025 q^{29} -9.22140 q^{30} +7.21594 q^{31} -10.7577 q^{32} +3.89456 q^{33} -18.2091 q^{34} +5.14895 q^{35} +9.93033 q^{36} -8.98380 q^{37} +13.0404 q^{38} +15.0146 q^{39} -11.6884 q^{40} -6.33270 q^{41} -19.3034 q^{42} -7.43569 q^{43} +8.40317 q^{44} +3.21252 q^{45} -17.7390 q^{46} +9.90073 q^{47} +22.0345 q^{48} +3.77843 q^{49} +6.64761 q^{50} +15.6345 q^{51} +32.3966 q^{52} -2.03247 q^{53} +5.59542 q^{54} +2.71847 q^{55} -24.4677 q^{56} -11.1966 q^{57} +11.2793 q^{58} +14.5868 q^{59} +17.0834 q^{60} +12.2205 q^{61} -18.8831 q^{62} +6.72484 q^{63} +8.53769 q^{64} +10.4805 q^{65} -10.1915 q^{66} -11.3481 q^{67} +33.7340 q^{68} +15.2308 q^{69} -13.4741 q^{70} -5.71984 q^{71} -15.2658 q^{72} +1.26939 q^{73} +23.5094 q^{74} -5.70768 q^{75} -24.1585 q^{76} +5.69064 q^{77} -39.2912 q^{78} +13.7338 q^{79} +15.3805 q^{80} -10.9493 q^{81} +16.5718 q^{82} -11.8795 q^{83} +35.7612 q^{84} +10.9132 q^{85} +19.4582 q^{86} -9.68451 q^{87} -12.9181 q^{88} -9.90347 q^{89} -8.40671 q^{90} +21.9390 q^{91} +32.8631 q^{92} +16.2132 q^{93} -25.9088 q^{94} -7.81540 q^{95} -24.1709 q^{96} +16.7253 q^{97} -9.88762 q^{98} +3.55049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) $ 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * 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 $

$2$	−2.61686	−1.85040	−0.925200	−	0.379479i	$-0.876103\pi$
$2$	−2.61686	−1.85040	−0.925200	+	0.379479i	$0.876103\pi$
$3$	2.24685	1.29722	0.648611	−	0.761120i	$-0.275350\pi$
$3$	2.24685	1.29722	0.648611	+	0.761120i	$0.275350\pi$
$4$	4.84797	2.42398
$5$	1.56834	0.701385	0.350692	−	0.936491i	$-0.385946\pi$
$5$	1.56834	0.701385	0.350692	+	0.936491i	$0.385946\pi$
$6$	−5.87971	−2.40038
$7$	3.28305	1.24088	0.620438	−	0.784255i	$-0.286955\pi$
$7$	3.28305	1.24088	0.620438	+	0.784255i	$0.286955\pi$
$8$	−7.45273	−2.63494
$9$	2.04835	0.682783
$10$	−4.10414	−1.29784
$11$	1.73334	0.522622	0.261311	−	0.965255i	$-0.415845\pi$
$11$	1.73334	0.522622	0.261311	+	0.965255i	$0.415845\pi$
$12$	10.8927	3.14444
$13$	6.68251	1.85340	0.926698	−	0.375807i	$-0.122634\pi$
$13$	6.68251	1.85340	0.926698	+	0.375807i	$0.122634\pi$
$14$	−8.59129	−2.29612
$15$	3.52384	0.909851
$16$	9.80684	2.45171
$17$	6.95839	1.68766	0.843829	−	0.536612i	$-0.180296\pi$
$17$	6.95839	1.68766	0.843829	+	0.536612i	$0.180296\pi$
$18$	−5.36025	−1.26342
$19$	−4.98322	−1.14323	−0.571614	−	0.820523i	$-0.693683\pi$
$19$	−4.98322	−1.14323	−0.571614	+	0.820523i	$0.693683\pi$
$20$	7.60328	1.70014
$21$	7.37654	1.60969
$22$	−4.53591	−0.967059
$23$	6.77874	1.41346	0.706732	−	0.707481i	$-0.250169\pi$
$23$	6.77874	1.41346	0.706732	+	0.707481i	$0.250169\pi$
$24$	−16.7452	−3.41810
$25$	−2.54030	−0.508060
$26$	−17.4872	−3.42953
$27$	−2.13822	−0.411500
$28$	15.9161	3.00786
$29$	−4.31025	−0.800394	−0.400197	−	0.916429i	$-0.631058\pi$
$29$	−4.31025	−0.800394	−0.400197	+	0.916429i	$0.631058\pi$
$30$	−9.22140	−1.68359
$31$	7.21594	1.29602	0.648011	−	0.761631i	$-0.275601\pi$
$31$	7.21594	1.29602	0.648011	+	0.761631i	$0.275601\pi$
$32$	−10.7577	−1.90171
$33$	3.89456	0.677956
$34$	−18.2091	−3.12284
$35$	5.14895	0.870332
$36$	9.93033	1.65506
$37$	−8.98380	−1.47693	−0.738464	−	0.674293i	$-0.764448\pi$
$37$	−8.98380	−1.47693	−0.738464	+	0.674293i	$0.764448\pi$
$38$	13.0404	2.11543
$39$	15.0146	2.40426
$40$	−11.6884	−1.84811
$41$	−6.33270	−0.989001	−0.494501	−	0.869177i	$-0.664649\pi$
$41$	−6.33270	−0.989001	−0.494501	+	0.869177i	$0.664649\pi$
$42$	−19.3034	−2.97858
$43$	−7.43569	−1.13393	−0.566966	−	0.823741i	$-0.691883\pi$
$43$	−7.43569	−1.13393	−0.566966	+	0.823741i	$0.691883\pi$
$44$	8.40317	1.26683
$45$	3.21252	0.478894
$46$	−17.7390	−2.61547
$47$	9.90073	1.44417	0.722085	−	0.691805i	$-0.243184\pi$
$47$	9.90073	1.44417	0.722085	+	0.691805i	$0.243184\pi$
$48$	22.0345	3.18041
$49$	3.77843	0.539775
$50$	6.64761	0.940114
$51$	15.6345	2.18927
$52$	32.3966	4.49260
$53$	−2.03247	−0.279182	−0.139591	−	0.990209i	$-0.544579\pi$
$53$	−2.03247	−0.279182	−0.139591	+	0.990209i	$0.544579\pi$
$54$	5.59542	0.761440
$55$	2.71847	0.366559
$56$	−24.4677	−3.26963
$57$	−11.1966	−1.48302
$58$	11.2793	1.48105
$59$	14.5868	1.89905	0.949523	−	0.313698i	$-0.101568\pi$
$59$	14.5868	1.89905	0.949523	+	0.313698i	$0.101568\pi$
$60$	17.0834	2.20546
$61$	12.2205	1.56467	0.782335	−	0.622858i	$-0.214028\pi$
$61$	12.2205	1.56467	0.782335	+	0.622858i	$0.214028\pi$
$62$	−18.8831	−2.39816
$63$	6.72484	0.847250
$64$	8.53769	1.06721
$65$	10.4805	1.29994
$66$	−10.1915	−1.25449
$67$	−11.3481	−1.38639	−0.693195	−	0.720750i	$-0.743798\pi$
$67$	−11.3481	−1.38639	−0.693195	+	0.720750i	$0.743798\pi$
$68$	33.7340	4.09085
$69$	15.2308	1.83358
$70$	−13.4741	−1.61046
$71$	−5.71984	−0.678820	−0.339410	−	0.940639i	$-0.610227\pi$
$71$	−5.71984	−0.678820	−0.339410	+	0.940639i	$0.610227\pi$
$72$	−15.2658	−1.79909
$73$	1.26939	0.148571	0.0742856	−	0.997237i	$-0.476332\pi$
$73$	1.26939	0.148571	0.0742856	+	0.997237i	$0.476332\pi$
$74$	23.5094	2.73291
$75$	−5.70768	−0.659066
$76$	−24.1585	−2.77117
$77$	5.69064	0.648509
$78$	−39.2912	−4.44885
$79$	13.7338	1.54517	0.772584	−	0.634912i	$-0.218964\pi$
$79$	13.7338	1.54517	0.772584	+	0.634912i	$0.218964\pi$
$80$	15.3805	1.71959
$81$	−10.9493	−1.21659
$82$	16.5718	1.83005
$83$	−11.8795	−1.30394	−0.651972	−	0.758243i	$-0.726058\pi$
$83$	−11.8795	−1.30394	−0.651972	+	0.758243i	$0.726058\pi$
$84$	35.7612	3.90187
$85$	10.9132	1.18370
$86$	19.4582	2.09823
$87$	−9.68451	−1.03829
$88$	−12.9181	−1.37708
$89$	−9.90347	−1.04977	−0.524883	−	0.851174i	$-0.675891\pi$
$89$	−9.90347	−1.04977	−0.524883	+	0.851174i	$0.675891\pi$
$90$	−8.40671	−0.886146
$91$	21.9390	2.29984
$92$	32.8631	3.42621
$93$	16.2132	1.68123
$94$	−25.9088	−2.67229
$95$	−7.81540	−0.801843
$96$	−24.1709	−2.46694
$97$	16.7253	1.69820	0.849099	−	0.528234i	$-0.177146\pi$
$97$	16.7253	1.69820	0.849099	+	0.528234i	$0.177146\pi$
$98$	−9.88762	−0.998801
$99$	3.55049	0.356837
$100$	−12.3153	−1.23153
$101$	6.89576	0.686154	0.343077	−	0.939307i	$-0.388531\pi$
$101$	6.89576	0.686154	0.343077	+	0.939307i	$0.388531\pi$
$102$	−40.9133	−4.05102
$103$	−10.6226	−1.04668	−0.523340	−	0.852124i	$-0.675314\pi$
$103$	−10.6226	−1.04668	−0.523340	+	0.852124i	$0.675314\pi$
$104$	−49.8030	−4.88359
$105$	11.5689	1.12901
$106$	5.31870	0.516598
$107$	9.68630	0.936410	0.468205	−	0.883620i	$-0.344901\pi$
$107$	9.68630	0.936410	0.468205	+	0.883620i	$0.344901\pi$
$108$	−10.3660	−0.997469
$109$	−6.38287	−0.611368	−0.305684	−	0.952133i	$-0.598885\pi$
$109$	−6.38287	−0.611368	−0.305684	+	0.952133i	$0.598885\pi$
$110$	−7.11387	−0.678281
$111$	−20.1853	−1.91590
$112$	32.1964	3.04227
$113$	15.3065	1.43992	0.719958	−	0.694018i	$-0.244161\pi$
$113$	15.3065	1.43992	0.719958	+	0.694018i	$0.244161\pi$
$114$	29.2998	2.74418
$115$	10.6314	0.991382
$116$	−20.8960	−1.94014
$117$	13.6881	1.26547
$118$	−38.1718	−3.51400
$119$	22.8448	2.09418
$120$	−26.2622	−2.39740
$121$	−7.99553	−0.726867
$122$	−31.9793	−2.89527
$123$	−14.2286	−1.28295
$124$	34.9826	3.14153
$125$	−11.8258	−1.05773
$126$	−17.5980	−1.56775
$127$	−21.4228	−1.90096	−0.950481	−	0.310782i	$-0.899409\pi$
$127$	−21.4228	−1.90096	−0.950481	+	0.310782i	$0.899409\pi$
$128$	−0.826582	−0.0730602
$129$	−16.7069	−1.47096
$130$	−27.4260	−2.40542
$131$	−6.78438	−0.592754	−0.296377	−	0.955071i	$-0.595779\pi$
$131$	−6.78438	−0.592754	−0.296377	+	0.955071i	$0.595779\pi$
$132$	18.8807	1.64335
$133$	−16.3602	−1.41861
$134$	29.6964	2.56538
$135$	−3.35346	−0.288620
$136$	−51.8590	−4.44688
$137$	2.24189	0.191538	0.0957688	−	0.995404i	$-0.469469\pi$
$137$	2.24189	0.191538	0.0957688	+	0.995404i	$0.469469\pi$
$138$	−39.8570	−3.39285
$139$	10.7871	0.914954	0.457477	−	0.889221i	$-0.348753\pi$
$139$	10.7871	0.914954	0.457477	+	0.889221i	$0.348753\pi$
$140$	24.9620	2.10967
$141$	22.2455	1.87341
$142$	14.9680	1.25609
$143$	11.5831	0.968625
$144$	20.0878	1.67399
$145$	−6.75996	−0.561384
$146$	−3.32183	−0.274916
$147$	8.48957	0.700208
$148$	−43.5531	−3.58005
$149$	12.7540	1.04485	0.522423	−	0.852686i	$-0.325028\pi$
$149$	12.7540	1.04485	0.522423	+	0.852686i	$0.325028\pi$
$150$	14.9362	1.21954
$151$	−11.3818	−0.926235	−0.463118	−	0.886297i	$-0.653269\pi$
$151$	−11.3818	−0.926235	−0.463118	+	0.886297i	$0.653269\pi$
$152$	37.1386	3.01234
$153$	14.2532	1.15230
$154$	−14.8916	−1.20000
$155$	11.3171	0.909009
$156$	72.7904	5.82790
$157$	−2.33671	−0.186490	−0.0932448	−	0.995643i	$-0.529724\pi$
$157$	−2.33671	−0.186490	−0.0932448	+	0.995643i	$0.529724\pi$
$158$	−35.9393	−2.85918
$159$	−4.56667	−0.362160
$160$	−16.8717	−1.33383
$161$	22.2549	1.75393
$162$	28.6528	2.25118
$163$	−13.3023	−1.04192	−0.520959	−	0.853581i	$-0.674426\pi$
$163$	−13.3023	−1.04192	−0.520959	+	0.853581i	$0.674426\pi$
$164$	−30.7007	−2.39732
$165$	6.10801	0.475508
$166$	31.0870	2.41282
$167$	−6.09803	−0.471880	−0.235940	−	0.971768i	$-0.575817\pi$
$167$	−6.09803	−0.471880	−0.235940	+	0.971768i	$0.575817\pi$
$168$	−54.9754	−4.24144
$169$	31.6560	2.43508
$170$	−28.5582	−2.19031
$171$	−10.2074	−0.780577
$172$	−36.0480	−2.74863
$173$	2.75073	0.209134	0.104567	−	0.994518i	$-0.466654\pi$
$173$	2.75073	0.209134	0.104567	+	0.994518i	$0.466654\pi$
$174$	25.3430	1.92125
$175$	−8.33993	−0.630439
$176$	16.9986	1.28132
$177$	32.7745	2.46348
$178$	25.9160	1.94249
$179$	6.26798	0.468491	0.234245	−	0.972177i	$-0.424738\pi$
$179$	6.26798	0.468491	0.234245	+	0.972177i	$0.424738\pi$
$180$	15.5742	1.16083
$181$	−1.35918	−0.101027	−0.0505135	−	0.998723i	$-0.516086\pi$
$181$	−1.35918	−0.101027	−0.0505135	+	0.998723i	$0.516086\pi$
$182$	−57.4114	−4.25562
$183$	27.4576	2.02972
$184$	−50.5201	−3.72439
$185$	−14.0897	−1.03589
$186$	−42.4276	−3.11094
$187$	12.0613	0.882007
$188$	47.9984	3.50064
$189$	−7.01988	−0.510621
$190$	20.4518	1.48373
$191$	−3.28852	−0.237949	−0.118974	−	0.992897i	$-0.537961\pi$
$191$	−3.28852	−0.237949	−0.118974	+	0.992897i	$0.537961\pi$
$192$	19.1829	1.38441
$193$	−7.60369	−0.547326	−0.273663	−	0.961826i	$-0.588235\pi$
$193$	−7.60369	−0.547326	−0.273663	+	0.961826i	$0.588235\pi$
$194$	−43.7678	−3.14235
$195$	23.5481	1.68631
$196$	18.3177	1.30841
$197$	−18.1539	−1.29341	−0.646706	−	0.762740i	$-0.723854\pi$
$197$	−18.1539	−1.29341	−0.646706	+	0.762740i	$0.723854\pi$
$198$	−9.29113	−0.660292
$199$	−8.09842	−0.574082	−0.287041	−	0.957918i	$-0.592672\pi$
$199$	−8.09842	−0.574082	−0.287041	+	0.957918i	$0.592672\pi$
$200$	18.9322	1.33871
$201$	−25.4975	−1.79846
$202$	−18.0453	−1.26966
$203$	−14.1508	−0.993190
$204$	75.7955	5.30674
$205$	−9.93185	−0.693670
$206$	27.7980	1.93678
$207$	13.8852	0.965090
$208$	65.5344	4.54399
$209$	−8.63761	−0.597476
$210$	−30.2743	−2.08913
$211$	−3.06950	−0.211313	−0.105656	−	0.994403i	$-0.533694\pi$
$211$	−3.06950	−0.211313	−0.105656	+	0.994403i	$0.533694\pi$
$212$	−9.85336	−0.676731
$213$	−12.8516	−0.880580
$214$	−25.3477	−1.73273
$215$	−11.6617	−0.795322
$216$	15.9356	1.08428
$217$	23.6903	1.60820
$218$	16.7031	1.13128
$219$	2.85214	0.192730
$220$	13.1791	0.888532
$221$	46.4996	3.12790
$222$	52.8221	3.54519
$223$	−14.3424	−0.960435	−0.480217	−	0.877149i	$-0.659442\pi$
$223$	−14.3424	−0.960435	−0.480217	+	0.877149i	$0.659442\pi$
$224$	−35.3180	−2.35979
$225$	−5.20342	−0.346895
$226$	−40.0550	−2.66442
$227$	28.0044	1.85872	0.929360	−	0.369176i	$-0.120360\pi$
$227$	28.0044	1.85872	0.929360	+	0.369176i	$0.120360\pi$
$228$	−54.2805	−3.59482
$229$	1.26358	0.0834998	0.0417499	−	0.999128i	$-0.486707\pi$
$229$	1.26358	0.0834998	0.0417499	+	0.999128i	$0.486707\pi$
$230$	−27.8209	−1.83445
$231$	12.7860	0.841260
$232$	32.1232	2.10899
$233$	−4.93410	−0.323244	−0.161622	−	0.986853i	$-0.551673\pi$
$233$	−4.93410	−0.323244	−0.161622	+	0.986853i	$0.551673\pi$
$234$	−35.8199	−2.34162
$235$	15.5277	1.01292
$236$	70.7165	4.60325
$237$	30.8577	2.00443
$238$	−59.7816	−3.87506
$239$	12.7478	0.824585	0.412292	−	0.911052i	$-0.364728\pi$
$239$	12.7478	0.824585	0.412292	+	0.911052i	$0.364728\pi$
$240$	34.5577	2.23069
$241$	2.65350	0.170927	0.0854636	−	0.996341i	$-0.472763\pi$
$241$	2.65350	0.170927	0.0854636	+	0.996341i	$0.472763\pi$
$242$	20.9232	1.34499
$243$	−18.1868	−1.16669
$244$	59.2444	3.79273
$245$	5.92587	0.378590
$246$	37.2344	2.37398
$247$	−33.3004	−2.11885
$248$	−53.7785	−3.41494
$249$	−26.6915	−1.69151
$250$	30.9464	1.95722
$251$	1.22746	0.0774769	0.0387384	−	0.999249i	$-0.487666\pi$
$251$	1.22746	0.0774769	0.0387384	+	0.999249i	$0.487666\pi$
$252$	32.6018	2.05372
$253$	11.7499	0.738707
$254$	56.0604	3.51754
$255$	24.5202	1.53552
$256$	−14.9123	−0.932020
$257$	22.2652	1.38887	0.694434	−	0.719557i	$-0.255655\pi$
$257$	22.2652	1.38887	0.694434	+	0.719557i	$0.255655\pi$
$258$	43.7197	2.72187
$259$	−29.4943	−1.83268
$260$	50.8090	3.15104
$261$	−8.82891	−0.546496
$262$	17.7538	1.09683
$263$	−14.4925	−0.893645	−0.446822	−	0.894623i	$-0.647444\pi$
$263$	−14.4925	−0.893645	−0.446822	+	0.894623i	$0.647444\pi$
$264$	−29.0251	−1.78637
$265$	−3.18762	−0.195814
$266$	42.8123	2.62499
$267$	−22.2517	−1.36178
$268$	−55.0152	−3.36059
$269$	−24.4000	−1.48770	−0.743848	−	0.668348i	$-0.767002\pi$
$269$	−24.4000	−1.48770	−0.743848	+	0.668348i	$0.767002\pi$
$270$	8.77554	0.534062
$271$	4.30082	0.261256	0.130628	−	0.991431i	$-0.458301\pi$
$271$	4.30082	0.261256	0.130628	+	0.991431i	$0.458301\pi$
$272$	68.2398	4.13765
$273$	49.2938	2.98340
$274$	−5.86672	−0.354421
$275$	−4.40320	−0.265523
$276$	73.8385	4.44456
$277$	−7.69220	−0.462179	−0.231090	−	0.972932i	$-0.574229\pi$
$277$	−7.69220	−0.462179	−0.231090	+	0.972932i	$0.574229\pi$
$278$	−28.2285	−1.69303
$279$	14.7808	0.884902
$280$	−38.3738	−2.29327
$281$	−10.9331	−0.652216	−0.326108	−	0.945333i	$-0.605737\pi$
$281$	−10.9331	−0.652216	−0.326108	+	0.945333i	$0.605737\pi$
$282$	−58.2133	−3.46655
$283$	27.2019	1.61699	0.808494	−	0.588505i	$-0.200283\pi$
$283$	27.2019	1.61699	0.808494	+	0.588505i	$0.200283\pi$
$284$	−27.7296	−1.64545
$285$	−17.5601	−1.04017
$286$	−30.3113	−1.79234
$287$	−20.7906	−1.22723
$288$	−22.0355	−1.29845
$289$	31.4192	1.84819
$290$	17.6899	1.03879
$291$	37.5793	2.20294
$292$	6.15398	0.360134
$293$	16.3010	0.952315	0.476158	−	0.879360i	$-0.342029\pi$
$293$	16.3010	0.952315	0.476158	+	0.879360i	$0.342029\pi$
$294$	−22.2160	−1.29567
$295$	22.8772	1.33196
$296$	66.9538	3.89161
$297$	−3.70626	−0.215059
$298$	−33.3754	−1.93338
$299$	45.2990	2.61971
$300$	−27.6706	−1.59756
$301$	−24.4117	−1.40707
$302$	29.7845	1.71391
$303$	15.4938	0.890093
$304$	−48.8696	−2.80286
$305$	19.1659	1.09744
$306$	−37.2987	−2.13223
$307$	−3.30787	−0.188790	−0.0943951	−	0.995535i	$-0.530092\pi$
$307$	−3.30787	−0.188790	−0.0943951	+	0.995535i	$0.530092\pi$
$308$	27.5880	1.57197
$309$	−23.8675	−1.35778
$310$	−29.6152	−1.68203
$311$	20.8706	1.18346	0.591731	−	0.806136i	$-0.298445\pi$
$311$	20.8706	1.18346	0.591731	+	0.806136i	$0.298445\pi$
$312$	−111.900	−6.33509
$313$	−6.57454	−0.371615	−0.185808	−	0.982586i	$-0.559490\pi$
$313$	−6.57454	−0.371615	−0.185808	+	0.982586i	$0.559490\pi$
$314$	6.11484	0.345080
$315$	10.5469	0.594248
$316$	66.5808	3.74546
$317$	−5.07027	−0.284775	−0.142387	−	0.989811i	$-0.545478\pi$
$317$	−5.07027	−0.284775	−0.142387	+	0.989811i	$0.545478\pi$
$318$	11.9503	0.670142
$319$	−7.47113	−0.418303
$320$	13.3900	0.748525
$321$	21.7637	1.21473
$322$	−58.2381	−3.24548
$323$	−34.6752	−1.92938
$324$	−53.0819	−2.94899
$325$	−16.9756	−0.941636
$326$	34.8104	1.92797
$327$	−14.3414	−0.793080
$328$	47.1959	2.60596
$329$	32.5046	1.79204
$330$	−15.9838	−0.879880
$331$	−7.92026	−0.435337	−0.217668	−	0.976023i	$-0.569845\pi$
$331$	−7.92026	−0.435337	−0.217668	+	0.976023i	$0.569845\pi$
$332$	−57.5914	−3.16074
$333$	−18.4020	−1.00842
$334$	15.9577	0.873167
$335$	−17.7977	−0.972393
$336$	72.3405	3.94650
$337$	−5.75868	−0.313695	−0.156848	−	0.987623i	$-0.550133\pi$
$337$	−5.75868	−0.313695	−0.156848	+	0.987623i	$0.550133\pi$
$338$	−82.8394	−4.50587
$339$	34.3915	1.86789
$340$	52.9066	2.86926
$341$	12.5077	0.677329
$342$	26.7113	1.44438
$343$	−10.5766	−0.571082
$344$	55.4162	2.98784
$345$	23.8872	1.28604
$346$	−7.19827	−0.386982
$347$	−13.4587	−0.722501	−0.361251	−	0.932469i	$-0.617650\pi$
$347$	−13.4587	−0.722501	−0.361251	+	0.932469i	$0.617650\pi$
$348$	−46.9502	−2.51679
$349$	11.9418	0.639230	0.319615	−	0.947547i	$-0.396446\pi$
$349$	11.9418	0.639230	0.319615	+	0.947547i	$0.396446\pi$
$350$	21.8244	1.16657
$351$	−14.2887	−0.762673
$352$	−18.6467	−0.993874
$353$	4.48493	0.238709	0.119354	−	0.992852i	$-0.461918\pi$
$353$	4.48493	0.238709	0.119354	+	0.992852i	$0.461918\pi$
$354$	−85.7663	−4.55843
$355$	−8.97067	−0.476114
$356$	−48.0117	−2.54462
$357$	51.3288	2.71661
$358$	−16.4024	−0.866896
$359$	−28.0876	−1.48241	−0.741203	−	0.671281i	$-0.765744\pi$
$359$	−28.0876	−1.48241	−0.741203	+	0.671281i	$0.765744\pi$
$360$	−23.9420	−1.26186
$361$	5.83245	0.306971
$362$	3.55679	0.186941
$363$	−17.9648	−0.942907
$364$	106.360	5.57476
$365$	1.99085	0.104206
$366$	−71.8527	−3.75580
$367$	−25.7215	−1.34265	−0.671326	−	0.741162i	$-0.734275\pi$
$367$	−25.7215	−1.34265	−0.671326	+	0.741162i	$0.734275\pi$
$368$	66.4780	3.46540
$369$	−12.9716	−0.675274
$370$	36.8708	1.91682
$371$	−6.67271	−0.346430
$372$	78.6009	4.07526
$373$	−34.9350	−1.80887	−0.904434	−	0.426614i	$-0.859706\pi$
$373$	−34.9350	−1.80887	−0.904434	+	0.426614i	$0.859706\pi$
$374$	−31.5626	−1.63207
$375$	−26.5708	−1.37211
$376$	−73.7875	−3.80530
$377$	−28.8033	−1.48345
$378$	18.3701	0.944853
$379$	−20.2307	−1.03918	−0.519590	−	0.854416i	$-0.673915\pi$
$379$	−20.2307	−1.03918	−0.519590	+	0.854416i	$0.673915\pi$
$380$	−37.8888	−1.94365
$381$	−48.1338	−2.46597
$382$	8.60560	0.440301
$383$	−14.3219	−0.731816	−0.365908	−	0.930651i	$-0.619242\pi$
$383$	−14.3219	−0.731816	−0.365908	+	0.930651i	$0.619242\pi$
$384$	−1.85721	−0.0947752
$385$	8.92489	0.454854
$386$	19.8978	1.01277
$387$	−15.2309	−0.774230
$388$	81.0837	4.11640
$389$	1.75543	0.0890038	0.0445019	−	0.999009i	$-0.485830\pi$
$389$	1.75543	0.0890038	0.0445019	+	0.999009i	$0.485830\pi$
$390$	−61.6221	−3.12036
$391$	47.1691	2.38544
$392$	−28.1596	−1.42228
$393$	−15.2435	−0.768933
$394$	47.5062	2.39333
$395$	21.5393	1.08376
$396$	17.2126	0.864968
$397$	20.4703	1.02737	0.513687	−	0.857978i	$-0.328279\pi$
$397$	20.4703	1.02737	0.513687	+	0.857978i	$0.328279\pi$
$398$	21.1924	1.06228
$399$	−36.7589	−1.84025
$400$	−24.9123	−1.24561
$401$	12.3754	0.617998	0.308999	−	0.951062i	$-0.400006\pi$
$401$	12.3754	0.617998	0.308999	+	0.951062i	$0.400006\pi$
$402$	66.7234	3.32786
$403$	48.2206	2.40204
$404$	33.4304	1.66323
$405$	−17.1723	−0.853298
$406$	37.0306	1.83780
$407$	−15.5720	−0.771874
$408$	−116.520	−5.76858
$409$	−13.9783	−0.691180	−0.345590	−	0.938386i	$-0.612321\pi$
$409$	−13.9783	−0.691180	−0.345590	+	0.938386i	$0.612321\pi$
$410$	25.9903	1.28357
$411$	5.03720	0.248467
$412$	−51.4982	−2.53713
$413$	47.8894	2.35648
$414$	−36.3357	−1.78580
$415$	−18.6311	−0.914567
$416$	−71.8884	−3.52462
$417$	24.2371	1.18690
$418$	22.6034	1.10557
$419$	−12.1349	−0.592831	−0.296415	−	0.955059i	$-0.595791\pi$
$419$	−12.1349	−0.592831	−0.296415	+	0.955059i	$0.595791\pi$
$420$	56.0858	2.73671
$421$	−14.6338	−0.713209	−0.356604	−	0.934255i	$-0.616066\pi$
$421$	−14.6338	−0.713209	−0.356604	+	0.934255i	$0.616066\pi$
$422$	8.03245	0.391014
$423$	20.2802	0.986055
$424$	15.1475	0.735626
$425$	−17.6764	−0.857431
$426$	33.6310	1.62943
$427$	40.1204	1.94156
$428$	46.9589	2.26984
$429$	26.0255	1.25652
$430$	30.5171	1.47167
$431$	8.99824	0.433430	0.216715	−	0.976235i	$-0.430466\pi$
$431$	8.99824	0.433430	0.216715	+	0.976235i	$0.430466\pi$
$432$	−20.9692	−1.00888
$433$	−13.3603	−0.642056	−0.321028	−	0.947070i	$-0.604028\pi$
$433$	−13.3603	−0.642056	−0.321028	+	0.947070i	$0.604028\pi$
$434$	−61.9943	−2.97582
$435$	−15.1886	−0.728239
$436$	−30.9439	−1.48195
$437$	−33.7799	−1.61591
$438$	−7.46366	−0.356627
$439$	15.0100	0.716390	0.358195	−	0.933647i	$-0.383392\pi$
$439$	15.0100	0.716390	0.358195	+	0.933647i	$0.383392\pi$
$440$	−20.2601	−0.965860
$441$	7.73954	0.368550
$442$	−121.683	−5.78787
$443$	21.0027	0.997867	0.498933	−	0.866640i	$-0.333725\pi$
$443$	21.0027	0.997867	0.498933	+	0.866640i	$0.333725\pi$
$444$	−97.8575	−4.64411
$445$	−15.5321	−0.736290
$446$	37.5320	1.77719
$447$	28.6563	1.35540
$448$	28.0297	1.32428
$449$	−7.76417	−0.366414	−0.183207	−	0.983074i	$-0.558648\pi$
$449$	−7.76417	−0.366414	−0.183207	+	0.983074i	$0.558648\pi$
$450$	13.6166	0.641894
$451$	−10.9767	−0.516873
$452$	74.2055	3.49033
$453$	−25.5732	−1.20153
$454$	−73.2837	−3.43938
$455$	34.4080	1.61307
$456$	83.4450	3.90767
$457$	19.8929	0.930552	0.465276	−	0.885166i	$-0.345955\pi$
$457$	19.8929	0.930552	0.465276	+	0.885166i	$0.345955\pi$
$458$	−3.30662	−0.154508
$459$	−14.8786	−0.694471
$460$	51.5406	2.40309
$461$	10.9952	0.512098	0.256049	−	0.966664i	$-0.417579\pi$
$461$	10.9952	0.512098	0.256049	+	0.966664i	$0.417579\pi$
$462$	−33.4593	−1.55667
$463$	−42.3513	−1.96823	−0.984116	−	0.177525i	$-0.943191\pi$
$463$	−42.3513	−1.96823	−0.984116	+	0.177525i	$0.943191\pi$
$464$	−42.2700	−1.96233
$465$	25.4278	1.17919
$466$	12.9119	0.598131
$467$	−21.3066	−0.985952	−0.492976	−	0.870043i	$-0.664091\pi$
$467$	−21.3066	−0.985952	−0.492976	+	0.870043i	$0.664091\pi$
$468$	66.3596	3.06747
$469$	−37.2564	−1.72034
$470$	−40.6340	−1.87430
$471$	−5.25024	−0.241918
$472$	−108.712	−5.00387
$473$	−12.8886	−0.592617
$474$	−80.7504	−3.70899
$475$	12.6589	0.580828
$476$	110.751	5.07625
$477$	−4.16322	−0.190621
$478$	−33.3592	−1.52581
$479$	15.9238	0.727575	0.363788	−	0.931482i	$-0.381483\pi$
$479$	15.9238	0.727575	0.363788	+	0.931482i	$0.381483\pi$
$480$	−37.9083	−1.73027
$481$	−60.0344	−2.73733
$482$	−6.94385	−0.316284
$483$	50.0036	2.27524
$484$	−38.7621	−1.76191
$485$	26.2310	1.19109
$486$	47.5925	2.15884
$487$	−2.74381	−0.124334	−0.0621669	−	0.998066i	$-0.519801\pi$
$487$	−2.74381	−0.124334	−0.0621669	+	0.998066i	$0.519801\pi$
$488$	−91.0759	−4.12281
$489$	−29.8884	−1.35160
$490$	−15.5072	−0.700544
$491$	15.1156	0.682155	0.341078	−	0.940035i	$-0.389208\pi$
$491$	15.1156	0.682155	0.341078	+	0.940035i	$0.389208\pi$
$492$	−68.9800	−3.10986
$493$	−29.9924	−1.35079
$494$	87.1426	3.92073
$495$	5.56838	0.250280
$496$	70.7656	3.17747
$497$	−18.7785	−0.842332
$498$	69.8480	3.12996
$499$	30.1386	1.34919	0.674594	−	0.738189i	$-0.264319\pi$
$499$	30.1386	1.34919	0.674594	+	0.738189i	$0.264319\pi$
$500$	−57.3310	−2.56392
$501$	−13.7014	−0.612133
$502$	−3.21210	−0.143363
$503$	39.7587	1.77275	0.886377	−	0.462963i	$-0.153214\pi$
$503$	39.7587	1.77275	0.886377	+	0.462963i	$0.153214\pi$
$504$	−50.1184	−2.23245
$505$	10.8149	0.481258
$506$	−30.7477	−1.36690
$507$	71.1264	3.15883
$508$	−103.857	−4.60790
$509$	7.15060	0.316945	0.158472	−	0.987363i	$-0.449343\pi$
$509$	7.15060	0.316945	0.158472	+	0.987363i	$0.449343\pi$
$510$	−64.1661	−2.84132
$511$	4.16748	0.184359
$512$	40.6767	1.79767
$513$	10.6552	0.470439
$514$	−58.2650	−2.56996
$515$	−16.6600	−0.734125
$516$	−80.9945	−3.56558
$517$	17.1613	0.754754
$518$	77.1824	3.39120
$519$	6.18048	0.271293
$520$	−78.1082	−3.42527
$521$	−22.0393	−0.965559	−0.482780	−	0.875742i	$-0.660373\pi$
$521$	−22.0393	−0.965559	−0.482780	+	0.875742i	$0.660373\pi$
$522$	23.1040	1.01124
$523$	−4.07944	−0.178382	−0.0891908	−	0.996015i	$-0.528428\pi$
$523$	−4.07944	−0.178382	−0.0891908	+	0.996015i	$0.528428\pi$
$524$	−32.8905	−1.43683
$525$	−18.7386	−0.817819
$526$	37.9248	1.65360
$527$	50.2113	2.18724
$528$	38.1933	1.66215
$529$	22.9513	0.997881
$530$	8.34155	0.362334
$531$	29.8790	1.29664
$532$	−79.3135	−3.43868
$533$	−42.3183	−1.83301
$534$	58.2295	2.51984
$535$	15.1915	0.656784
$536$	84.5743	3.65305
$537$	14.0832	0.607736
$538$	63.8515	2.75284
$539$	6.54930	0.282098
$540$	−16.2575	−0.699610
$541$	−23.1618	−0.995802	−0.497901	−	0.867234i	$-0.665896\pi$
$541$	−23.1618	−0.995802	−0.497901	+	0.867234i	$0.665896\pi$
$542$	−11.2546	−0.483428
$543$	−3.05388	−0.131054
$544$	−74.8562	−3.20943
$545$	−10.0105	−0.428804
$546$	−128.995	−5.52048
$547$	−41.8882	−1.79101	−0.895506	−	0.445050i	$-0.853186\pi$
$547$	−41.8882	−1.79101	−0.895506	+	0.445050i	$0.853186\pi$
$548$	10.8686	0.464284
$549$	25.0318	1.06833
$550$	11.5226	0.491324
$551$	21.4789	0.915033
$552$	−113.511	−4.83136
$553$	45.0886	1.91736
$554$	20.1294	0.855217
$555$	−31.6575	−1.34378
$556$	52.2957	2.21783
$557$	−2.42264	−0.102650	−0.0513252	−	0.998682i	$-0.516345\pi$
$557$	−2.42264	−0.102650	−0.0513252	+	0.998682i	$0.516345\pi$
$558$	−38.6792	−1.63742
$559$	−49.6891	−2.10162
$560$	50.4950	2.13380
$561$	27.0999	1.14416
$562$	28.6105	1.20686
$563$	29.2393	1.23229	0.616144	−	0.787634i	$-0.288694\pi$
$563$	29.2393	1.23229	0.616144	+	0.787634i	$0.288694\pi$
$564$	107.845	4.54111
$565$	24.0059	1.00994
$566$	−71.1837	−2.99207
$567$	−35.9472	−1.50964
$568$	42.6284	1.78865
$569$	−23.9316	−1.00326	−0.501632	−	0.865081i	$-0.667267\pi$
$569$	−23.9316	−1.00326	−0.501632	+	0.865081i	$0.667267\pi$
$570$	45.9522	1.92473
$571$	31.1137	1.30207	0.651035	−	0.759048i	$-0.274335\pi$
$571$	31.1137	1.30207	0.651035	+	0.759048i	$0.274335\pi$
$572$	56.1543	2.34793
$573$	−7.38882	−0.308672
$574$	54.4061	2.27087
$575$	−17.2200	−0.718124
$576$	17.4882	0.728674
$577$	8.84647	0.368283	0.184142	−	0.982900i	$-0.441049\pi$
$577$	8.84647	0.368283	0.184142	+	0.982900i	$0.441049\pi$
$578$	−82.2197	−3.41989
$579$	−17.0844	−0.710002
$580$	−32.7720	−1.36079
$581$	−39.0010	−1.61803
$582$	−98.3399	−4.07632
$583$	−3.52297	−0.145906
$584$	−9.46045	−0.391476
$585$	21.4677	0.887580
$586$	−42.6575	−1.76217
$587$	−34.6306	−1.42936	−0.714679	−	0.699452i	$-0.753427\pi$
$587$	−34.6306	−1.42936	−0.714679	+	0.699452i	$0.753427\pi$
$588$	41.1572	1.69729
$589$	−35.9586	−1.48165
$590$	−59.8664	−2.46466
$591$	−40.7891	−1.67784
$592$	−88.1027	−3.62100
$593$	6.29810	0.258632	0.129316	−	0.991603i	$-0.458722\pi$
$593$	6.29810	0.258632	0.129316	+	0.991603i	$0.458722\pi$
$594$	9.69876	0.397945
$595$	35.8284	1.46882
$596$	61.8308	2.53269
$597$	−18.1960	−0.744711
$598$	−118.541	−4.84751
$599$	16.0909	0.657457	0.328729	−	0.944424i	$-0.393380\pi$
$599$	16.0909	0.657457	0.328729	+	0.944424i	$0.393380\pi$
$600$	42.5378	1.73660
$601$	4.91420	0.200455	0.100227	−	0.994965i	$-0.468043\pi$
$601$	4.91420	0.200455	0.100227	+	0.994965i	$0.468043\pi$
$602$	63.8822	2.60364
$603$	−23.2449	−0.946604
$604$	−55.1784	−2.24518
$605$	−12.5397	−0.509813
$606$	−40.5450	−1.64703
$607$	11.1392	0.452128	0.226064	−	0.974112i	$-0.427414\pi$
$607$	11.1392	0.452128	0.226064	+	0.974112i	$0.427414\pi$
$608$	53.6079	2.17409
$609$	−31.7947	−1.28839
$610$	−50.1545	−2.03070
$611$	66.1617	2.67662
$612$	69.0991	2.79317
$613$	−21.7169	−0.877139	−0.438570	−	0.898697i	$-0.644515\pi$
$613$	−21.7169	−0.877139	−0.438570	+	0.898697i	$0.644515\pi$
$614$	8.65624	0.349337
$615$	−22.3154	−0.899844
$616$	−42.4109	−1.70878
$617$	−20.3301	−0.818460	−0.409230	−	0.912431i	$-0.634203\pi$
$617$	−20.3301	−0.818460	−0.409230	+	0.912431i	$0.634203\pi$
$618$	62.4580	2.51243
$619$	−40.2070	−1.61606	−0.808028	−	0.589144i	$-0.799465\pi$
$619$	−40.2070	−1.61606	−0.808028	+	0.589144i	$0.799465\pi$
$620$	54.8648	2.20342
$621$	−14.4944	−0.581641
$622$	−54.6154	−2.18988
$623$	−32.5136	−1.30263
$624$	147.246	5.89456
$625$	−5.84540	−0.233816
$626$	17.2047	0.687637
$627$	−19.4074	−0.775058
$628$	−11.3283	−0.452048
$629$	−62.5128	−2.49255
$630$	−27.5997	−1.09960
$631$	−15.9732	−0.635882	−0.317941	−	0.948111i	$-0.602991\pi$
$631$	−15.9732	−0.635882	−0.317941	+	0.948111i	$0.602991\pi$
$632$	−102.354	−4.07142
$633$	−6.89671	−0.274120
$634$	13.2682	0.526948
$635$	−33.5982	−1.33331
$636$	−22.1390	−0.877870
$637$	25.2494	1.00042
$638$	19.5509	0.774028
$639$	−11.7162	−0.463487
$640$	−1.29636	−0.0512433
$641$	−27.0640	−1.06896	−0.534482	−	0.845180i	$-0.679493\pi$
$641$	−27.0640	−1.06896	−0.534482	+	0.845180i	$0.679493\pi$
$642$	−56.9526	−2.24774
$643$	21.7123	0.856250	0.428125	−	0.903720i	$-0.359174\pi$
$643$	21.7123	0.856250	0.428125	+	0.903720i	$0.359174\pi$
$644$	107.891	4.25151
$645$	−26.2022	−1.03171
$646$	90.7401	3.57012
$647$	−22.8408	−0.897965	−0.448982	−	0.893541i	$-0.648213\pi$
$647$	−22.8408	−0.897965	−0.448982	+	0.893541i	$0.648213\pi$
$648$	81.6023	3.20564
$649$	25.2840	0.992482
$650$	44.4227	1.74240
$651$	53.2286	2.08620
$652$	−64.4892	−2.52559
$653$	−28.7863	−1.12650	−0.563248	−	0.826288i	$-0.690448\pi$
$653$	−28.7863	−1.12650	−0.563248	+	0.826288i	$0.690448\pi$
$654$	37.5294	1.46752
$655$	−10.6402	−0.415749
$656$	−62.1038	−2.42474
$657$	2.60016	0.101442
$658$	−85.0600	−3.31599
$659$	8.84395	0.344511	0.172256	−	0.985052i	$-0.444894\pi$
$659$	8.84395	0.344511	0.172256	+	0.985052i	$0.444894\pi$
$660$	29.6114	1.15262
$661$	−36.4821	−1.41899	−0.709495	−	0.704710i	$-0.751077\pi$
$661$	−36.4821	−1.41899	−0.709495	+	0.704710i	$0.751077\pi$
$662$	20.7262	0.805547
$663$	104.478	4.05758
$664$	88.5348	3.43582
$665$	−25.6584	−0.994988
$666$	48.1554	1.86598
$667$	−29.2181	−1.13133
$668$	−29.5630	−1.14383
$669$	−32.2252	−1.24590
$670$	46.5742	1.79932
$671$	21.1822	0.817731
$672$	−79.3544	−3.06116
$673$	31.7154	1.22254	0.611269	−	0.791423i	$-0.290659\pi$
$673$	31.7154	1.22254	0.611269	+	0.791423i	$0.290659\pi$
$674$	15.0697	0.580462
$675$	5.43171	0.209067
$676$	153.467	5.90258
$677$	23.2533	0.893696	0.446848	−	0.894610i	$-0.352547\pi$
$677$	23.2533	0.893696	0.446848	+	0.894610i	$0.352547\pi$
$678$	−89.9978	−3.45635
$679$	54.9100	2.10725
$680$	−81.3328	−3.11897
$681$	62.9218	2.41117
$682$	−32.7309	−1.25333
$683$	−5.84245	−0.223555	−0.111777	−	0.993733i	$-0.535654\pi$
$683$	−5.84245	−0.223555	−0.111777	+	0.993733i	$0.535654\pi$
$684$	−49.4850	−1.89211
$685$	3.51606	0.134342
$686$	27.6775	1.05673
$687$	2.83908	0.108318
$688$	−72.9206	−2.78007
$689$	−13.5820	−0.517434
$690$	−62.5094	−2.37969
$691$	11.0683	0.421057	0.210529	−	0.977588i	$-0.432481\pi$
$691$	11.0683	0.421057	0.210529	+	0.977588i	$0.432481\pi$
$692$	13.3354	0.506937
$693$	11.6564	0.442791
$694$	35.2196	1.33692
$695$	16.9180	0.641735
$696$	72.1760	2.73583
$697$	−44.0654	−1.66910
$698$	−31.2501	−1.18283
$699$	−11.0862	−0.419319
$700$	−40.4317	−1.52817
$701$	18.1424	0.685228	0.342614	−	0.939476i	$-0.388688\pi$
$701$	18.1424	0.685228	0.342614	+	0.939476i	$0.388688\pi$
$702$	37.3915	1.41125
$703$	44.7682	1.68847
$704$	14.7987	0.557747
$705$	34.8886	1.31398
$706$	−11.7364	−0.441706
$707$	22.6391	0.851432
$708$	158.890	5.97144
$709$	45.4042	1.70519	0.852595	−	0.522572i	$-0.175027\pi$
$709$	45.4042	1.70519	0.852595	+	0.522572i	$0.175027\pi$
$710$	23.4750	0.881001
$711$	28.1315	1.05502
$712$	73.8079	2.76607
$713$	48.9150	1.83188
$714$	−134.320	−5.02682
$715$	18.1662	0.679379
$716$	30.3870	1.13561
$717$	28.6424	1.06967
$718$	73.5013	2.74304
$719$	39.4660	1.47184	0.735918	−	0.677071i	$-0.236751\pi$
$719$	39.4660	1.47184	0.735918	+	0.677071i	$0.236751\pi$
$720$	31.5047	1.17411
$721$	−34.8747	−1.29880
$722$	−15.2627	−0.568019
$723$	5.96203	0.221730
$724$	−6.58926	−0.244888
$725$	10.9493	0.406648
$726$	47.0114	1.74476
$727$	−47.7849	−1.77224	−0.886121	−	0.463453i	$-0.846610\pi$
$727$	−47.7849	−1.77224	−0.886121	+	0.463453i	$0.846610\pi$
$728$	−163.506	−6.05993
$729$	−8.01524	−0.296861
$730$	−5.20977	−0.192822
$731$	−51.7404	−1.91369
$732$	133.114	4.92002
$733$	22.4642	0.829732	0.414866	−	0.909882i	$-0.363828\pi$
$733$	22.4642	0.829732	0.414866	+	0.909882i	$0.363828\pi$
$734$	67.3096	2.48444
$735$	13.3146	0.491115
$736$	−72.9235	−2.68800
$737$	−19.6701	−0.724558
$738$	33.9448	1.24953
$739$	0.963426	0.0354402	0.0177201	−	0.999843i	$-0.494359\pi$
$739$	0.963426	0.0354402	0.0177201	+	0.999843i	$0.494359\pi$
$740$	−68.3063	−2.51099
$741$	−74.8212	−2.74862
$742$	17.4616	0.641034
$743$	−15.1344	−0.555228	−0.277614	−	0.960693i	$-0.589544\pi$
$743$	−15.1344	−0.555228	−0.277614	+	0.960693i	$0.589544\pi$
$744$	−120.832	−4.42993
$745$	20.0026	0.732839
$746$	91.4202	3.34713
$747$	−24.3334	−0.890312
$748$	58.4726	2.13797
$749$	31.8006	1.16197
$750$	69.5321	2.53895
$751$	−13.0828	−0.477398	−0.238699	−	0.971094i	$-0.576721\pi$
$751$	−13.0828	−0.477398	−0.238699	+	0.971094i	$0.576721\pi$
$752$	97.0948	3.54068
$753$	2.75793	0.100505
$754$	75.3743	2.74497
$755$	−17.8505	−0.649647
$756$	−34.0321	−1.23774
$757$	43.4816	1.58037	0.790183	−	0.612870i	$-0.209985\pi$
$757$	43.4816	1.58037	0.790183	+	0.612870i	$0.209985\pi$
$758$	52.9409	1.92290
$759$	26.4002	0.958266
$760$	58.2461	2.11281
$761$	−41.8035	−1.51538	−0.757689	−	0.652616i	$-0.773671\pi$
$761$	−41.8035	−1.51538	−0.757689	+	0.652616i	$0.773671\pi$
$762$	125.959	4.56303
$763$	−20.9553	−0.758633
$764$	−15.9426	−0.576784
$765$	22.3540	0.808209
$766$	37.4785	1.35415
$767$	97.4768	3.51968
$768$	−33.5058	−1.20904
$769$	8.58526	0.309592	0.154796	−	0.987946i	$-0.450528\pi$
$769$	8.58526	0.309592	0.154796	+	0.987946i	$0.450528\pi$
$770$	−23.3552	−0.841663
$771$	50.0267	1.80167
$772$	−36.8624	−1.32671
$773$	−48.3930	−1.74058	−0.870288	−	0.492544i	$-0.836067\pi$
$773$	−48.3930	−1.74058	−0.870288	+	0.492544i	$0.836067\pi$
$774$	39.8571	1.43264
$775$	−18.3306	−0.658456
$776$	−124.649	−4.47465
$777$	−66.2693	−2.37740
$778$	−4.59371	−0.164693
$779$	31.5572	1.13065
$780$	114.160	4.08760
$781$	−9.91442	−0.354766
$782$	−123.435	−4.41403
$783$	9.21626	0.329362
$784$	37.0544	1.32337
$785$	−3.66476	−0.130801
$786$	39.8902	1.42284
$787$	−0.357306	−0.0127366	−0.00636829	−	0.999980i	$-0.502027\pi$
$787$	−0.357306	−0.0127366	−0.00636829	+	0.999980i	$0.502027\pi$
$788$	−88.0095	−3.13521
$789$	−32.5625	−1.15926
$790$	−56.3652	−2.00539
$791$	50.2521	1.78676
$792$	−26.4608	−0.940245
$793$	81.6634	2.89995
$794$	−53.5679	−1.90105
$795$	−7.16210	−0.254014
$796$	−39.2609	−1.39156
$797$	2.47019	0.0874986	0.0437493	−	0.999043i	$-0.486070\pi$
$797$	2.47019	0.0874986	0.0437493	+	0.999043i	$0.486070\pi$
$798$	96.1929	3.40519
$799$	68.8931	2.43726
$800$	27.3277	0.966181
$801$	−20.2858	−0.716763
$802$	−32.3847	−1.14354
$803$	2.20029	0.0776465
$804$	−123.611	−4.35942
$805$	34.9034	1.23018
$806$	−126.187	−4.44474
$807$	−54.8233	−1.92987
$808$	−51.3923	−1.80797
$809$	−25.5981	−0.899980	−0.449990	−	0.893034i	$-0.648573\pi$
$809$	−25.5981	−0.899980	−0.449990	+	0.893034i	$0.648573\pi$
$810$	44.9375	1.57894
$811$	−20.9045	−0.734055	−0.367027	−	0.930210i	$-0.619624\pi$
$811$	−20.9045	−0.734055	−0.367027	+	0.930210i	$0.619624\pi$
$812$	−68.6025	−2.40748
$813$	9.66330	0.338907
$814$	40.7497	1.42828
$815$	−20.8626	−0.730786
$816$	153.325	5.36745
$817$	37.0536	1.29634
$818$	36.5792	1.27896
$819$	44.9388	1.57029
$820$	−48.1493	−1.68145
$821$	−21.5309	−0.751433	−0.375717	−	0.926735i	$-0.622603\pi$
$821$	−21.5309	−0.751433	−0.375717	+	0.926735i	$0.622603\pi$
$822$	−13.1817	−0.459763
$823$	26.8583	0.936221	0.468111	−	0.883670i	$-0.344935\pi$
$823$	26.8583	0.936221	0.468111	+	0.883670i	$0.344935\pi$
$824$	79.1677	2.75794
$825$	−9.89334	−0.344442
$826$	−125.320	−4.36044
$827$	12.7348	0.442831	0.221415	−	0.975180i	$-0.428932\pi$
$827$	12.7348	0.442831	0.221415	+	0.975180i	$0.428932\pi$
$828$	67.3151	2.33936
$829$	2.69982	0.0937685	0.0468842	−	0.998900i	$-0.485071\pi$
$829$	2.69982	0.0937685	0.0468842	+	0.998900i	$0.485071\pi$
$830$	48.7551	1.69232
$831$	−17.2832	−0.599549
$832$	57.0532	1.97796
$833$	26.2918	0.910956
$834$	−63.4253	−2.19624
$835$	−9.56381	−0.330969
$836$	−41.8748	−1.44827
$837$	−15.4293	−0.533313
$838$	31.7555	1.09697
$839$	25.0654	0.865355	0.432677	−	0.901549i	$-0.357569\pi$
$839$	25.0654	0.865355	0.432677	+	0.901549i	$0.357569\pi$
$840$	−86.2203	−2.97488
$841$	−10.4217	−0.359370
$842$	38.2947	1.31972
$843$	−24.5651	−0.846068
$844$	−14.8808	−0.512219
$845$	49.6475	1.70793
$846$	−53.0704	−1.82460
$847$	−26.2497	−0.901952
$848$	−19.9321	−0.684472
$849$	61.1188	2.09759
$850$	46.2567	1.58659
$851$	−60.8988	−2.08758
$852$	−62.3043	−2.13451
$853$	15.4667	0.529568	0.264784	−	0.964308i	$-0.414699\pi$
$853$	15.4667	0.529568	0.264784	+	0.964308i	$0.414699\pi$
$854$	−104.990	−3.59267
$855$	−16.0087	−0.547485
$856$	−72.1894	−2.46738
$857$	9.96114	0.340266	0.170133	−	0.985421i	$-0.445580\pi$
$857$	9.96114	0.340266	0.170133	+	0.985421i	$0.445580\pi$
$858$	−68.1050	−2.32507
$859$	−1.50557	−0.0513694	−0.0256847	−	0.999670i	$-0.508177\pi$
$859$	−1.50557	−0.0513694	−0.0256847	+	0.999670i	$0.508177\pi$
$860$	−56.5356	−1.92785
$861$	−46.7134	−1.59199
$862$	−23.5472	−0.802019
$863$	−24.1132	−0.820822	−0.410411	−	0.911901i	$-0.634615\pi$
$863$	−24.1132	−0.820822	−0.410411	+	0.911901i	$0.634615\pi$
$864$	23.0023	0.782553
$865$	4.31409	0.146683
$866$	34.9621	1.18806
$867$	70.5944	2.39751
$868$	114.850	3.89826
$869$	23.8053	0.807538
$870$	39.7466	1.34753
$871$	−75.8338	−2.56953
$872$	47.5698	1.61092
$873$	34.2593	1.15950
$874$	88.3974	2.99009
$875$	−38.8246	−1.31251
$876$	13.8271	0.467174
$877$	42.3668	1.43062	0.715312	−	0.698805i	$-0.246285\pi$
$877$	42.3668	1.43062	0.715312	+	0.698805i	$0.246285\pi$
$878$	−39.2792	−1.32561
$879$	36.6260	1.23536
$880$	26.6596	0.898696
$881$	14.7491	0.496911	0.248456	−	0.968643i	$-0.420077\pi$
$881$	14.7491	0.496911	0.248456	+	0.968643i	$0.420077\pi$
$882$	−20.2533	−0.681965
$883$	8.31343	0.279769	0.139885	−	0.990168i	$-0.455327\pi$
$883$	8.31343	0.279769	0.139885	+	0.990168i	$0.455327\pi$
$884$	225.428	7.58197
$885$	51.4017	1.72785
$886$	−54.9611	−1.84645
$887$	8.20030	0.275339	0.137670	−	0.990478i	$-0.456039\pi$
$887$	8.20030	0.275339	0.137670	+	0.990478i	$0.456039\pi$
$888$	150.435	5.04828
$889$	−70.3320	−2.35886
$890$	40.6452	1.36243
$891$	−18.9789	−0.635816
$892$	−69.5312	−2.32808
$893$	−49.3375	−1.65102
$894$	−74.9896	−2.50803
$895$	9.83035	0.328592
$896$	−2.71371	−0.0906587
$897$	101.780	3.39834
$898$	20.3177	0.678012
$899$	−31.1025	−1.03733
$900$	−25.2260	−0.840867
$901$	−14.1427	−0.471163
$902$	28.7246	0.956423
$903$	−54.8496	−1.82528
$904$	−114.075	−3.79409
$905$	−2.13166	−0.0708588
$906$	66.9214	2.22332
$907$	2.37459	0.0788471	0.0394235	−	0.999223i	$-0.487448\pi$
$907$	2.37459	0.0788471	0.0394235	+	0.999223i	$0.487448\pi$
$908$	135.765	4.50550
$909$	14.1249	0.468494
$910$	−90.0409	−2.98483
$911$	14.5220	0.481137	0.240568	−	0.970632i	$-0.422666\pi$
$911$	14.5220	0.481137	0.240568	+	0.970632i	$0.422666\pi$
$912$	−109.803	−3.63594
$913$	−20.5912	−0.681470
$914$	−52.0571	−1.72189
$915$	43.0630	1.42362
$916$	6.12580	0.202402
$917$	−22.2735	−0.735535
$918$	38.9351	1.28505
$919$	56.3333	1.85827	0.929133	−	0.369747i	$-0.120556\pi$
$919$	56.3333	1.85827	0.929133	+	0.369747i	$0.120556\pi$
$920$	−79.2329	−2.61223
$921$	−7.43230	−0.244903
$922$	−28.7729	−0.947586
$923$	−38.2229	−1.25812
$924$	61.9863	2.03920
$925$	22.8215	0.750367
$926$	110.828	3.64202
$927$	−21.7589	−0.714656
$928$	46.3683	1.52212
$929$	54.8114	1.79830	0.899151	−	0.437638i	$-0.144185\pi$
$929$	54.8114	1.79830	0.899151	+	0.437638i	$0.144185\pi$
$930$	−66.5411	−2.18197
$931$	−18.8287	−0.617086
$932$	−23.9204	−0.783538
$933$	46.8931	1.53521
$934$	55.7564	1.82441
$935$	18.9162	0.618626
$936$	−102.014	−3.33443
$937$	9.64147	0.314973	0.157487	−	0.987521i	$-0.449661\pi$
$937$	9.64147	0.314973	0.157487	+	0.987521i	$0.449661\pi$
$938$	97.4948	3.18332
$939$	−14.7720	−0.482067
$940$	75.2780	2.45530
$941$	−49.8669	−1.62561	−0.812807	−	0.582533i	$-0.802061\pi$
$941$	−49.8669	−1.62561	−0.812807	+	0.582533i	$0.802061\pi$
$942$	13.7392	0.447646
$943$	−42.9277	−1.39792
$944$	143.051	4.65591
$945$	−11.0096	−0.358142
$946$	33.7276	1.09658
$947$	18.2974	0.594584	0.297292	−	0.954787i	$-0.403916\pi$
$947$	18.2974	0.594584	0.297292	+	0.954787i	$0.403916\pi$
$948$	149.597	4.85869
$949$	8.48274	0.275361
$950$	−33.1265	−1.07476
$951$	−11.3922	−0.369416
$952$	−170.256	−5.51803
$953$	14.0821	0.456163	0.228082	−	0.973642i	$-0.426755\pi$
$953$	14.0821	0.456163	0.228082	+	0.973642i	$0.426755\pi$
$954$	10.8946	0.352724
$955$	−5.15753	−0.166894
$956$	61.8008	1.99878
$957$	−16.7865	−0.542632
$958$	−41.6703	−1.34631
$959$	7.36024	0.237675
$960$	30.0854	0.971003
$961$	21.0698	0.679671
$962$	157.102	5.06516
$963$	19.8409	0.639365
$964$	12.8641	0.414325
$965$	−11.9252	−0.383886
$966$	−130.852	−4.21011
$967$	7.34217	0.236108	0.118054	−	0.993007i	$-0.462334\pi$
$967$	7.34217	0.236108	0.118054	+	0.993007i	$0.462334\pi$
$968$	59.5886	1.91525
$969$	−77.9100	−2.50283
$970$	−68.6430	−2.20399
$971$	21.3757	0.685979	0.342990	−	0.939339i	$-0.388560\pi$
$971$	21.3757	0.685979	0.342990	+	0.939339i	$0.388560\pi$
$972$	−88.1692	−2.82803
$973$	35.4148	1.13535
$974$	7.18017	0.230067
$975$	−38.1416	−1.22151
$976$	119.844	3.83612
$977$	4.84193	0.154907	0.0774535	−	0.996996i	$-0.475321\pi$
$977$	4.84193	0.154907	0.0774535	+	0.996996i	$0.475321\pi$
$978$	78.2138	2.50100
$979$	−17.1661	−0.548630
$980$	28.7284	0.917696
$981$	−13.0744	−0.417432
$982$	−39.5553	−1.26226
$983$	18.2234	0.581235	0.290617	−	0.956839i	$-0.406139\pi$
$983$	18.2234	0.581235	0.290617	+	0.956839i	$0.406139\pi$
$984$	106.042	3.38050
$985$	−28.4715	−0.907179
$986$	78.4860	2.49950
$987$	73.0331	2.32467
$988$	−161.439	−5.13607
$989$	−50.4046	−1.60277
$990$	−14.5717	−0.463119
$991$	13.3017	0.422544	0.211272	−	0.977427i	$-0.432239\pi$
$991$	13.3017	0.422544	0.211272	+	0.977427i	$0.432239\pi$
$992$	−77.6268	−2.46465
$993$	−17.7957	−0.564728
$994$	49.1408	1.55865
$995$	−12.7011	−0.402652
$996$	−129.399	−4.10018
$997$	17.5760	0.556636	0.278318	−	0.960489i	$-0.410223\pi$
$997$	17.5760	0.556636	0.278318	+	0.960489i	$0.410223\pi$
$998$	−78.8685	−2.49654
$999$	19.2093	0.607756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.b.1.14	✓	340

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.b.1.14	✓	340	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61686 q^{2} +2.24685 q^{3} +4.84797 q^{4} +1.56834 q^{5} -5.87971 q^{6} +3.28305 q^{7} -7.45273 q^{8} +2.04835 q^{9} +O(q^{10})\)	\(q-2.61686 q^{2} +2.24685 q^{3} +4.84797 q^{4} +1.56834 q^{5} -5.87971 q^{6} +3.28305 q^{7} -7.45273 q^{8} +2.04835 q^{9} -4.10414 q^{10} +1.73334 q^{11} +10.8927 q^{12} +6.68251 q^{13} -8.59129 q^{14} +3.52384 q^{15} +9.80684 q^{16} +6.95839 q^{17} -5.36025 q^{18} -4.98322 q^{19} +7.60328 q^{20} +7.37654 q^{21} -4.53591 q^{22} +6.77874 q^{23} -16.7452 q^{24} -2.54030 q^{25} -17.4872 q^{26} -2.13822 q^{27} +15.9161 q^{28} -4.31025 q^{29} -9.22140 q^{30} +7.21594 q^{31} -10.7577 q^{32} +3.89456 q^{33} -18.2091 q^{34} +5.14895 q^{35} +9.93033 q^{36} -8.98380 q^{37} +13.0404 q^{38} +15.0146 q^{39} -11.6884 q^{40} -6.33270 q^{41} -19.3034 q^{42} -7.43569 q^{43} +8.40317 q^{44} +3.21252 q^{45} -17.7390 q^{46} +9.90073 q^{47} +22.0345 q^{48} +3.77843 q^{49} +6.64761 q^{50} +15.6345 q^{51} +32.3966 q^{52} -2.03247 q^{53} +5.59542 q^{54} +2.71847 q^{55} -24.4677 q^{56} -11.1966 q^{57} +11.2793 q^{58} +14.5868 q^{59} +17.0834 q^{60} +12.2205 q^{61} -18.8831 q^{62} +6.72484 q^{63} +8.53769 q^{64} +10.4805 q^{65} -10.1915 q^{66} -11.3481 q^{67} +33.7340 q^{68} +15.2308 q^{69} -13.4741 q^{70} -5.71984 q^{71} -15.2658 q^{72} +1.26939 q^{73} +23.5094 q^{74} -5.70768 q^{75} -24.1585 q^{76} +5.69064 q^{77} -39.2912 q^{78} +13.7338 q^{79} +15.3805 q^{80} -10.9493 q^{81} +16.5718 q^{82} -11.8795 q^{83} +35.7612 q^{84} +10.9132 q^{85} +19.4582 q^{86} -9.68451 q^{87} -12.9181 q^{88} -9.90347 q^{89} -8.40671 q^{90} +21.9390 q^{91} +32.8631 q^{92} +16.2132 q^{93} -25.9088 q^{94} -7.81540 q^{95} -24.1709 q^{96} +16.7253 q^{97} -9.88762 q^{98} +3.55049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9}+O(q^{10}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9	\( 340 q + 20 q^{2} + 44 q^{3} + 350 q^{4} + 53 q^{5} + 34 q^{6} + 81 q^{7} + 54 q^{8} + 360 q^{9} + 36 q^{10} + 70 q^{11} + 92 q^{12} + 45 q^{13} + 44 q^{14} + 71 q^{15} + 362 q^{16} + 162 q^{17} + 41 q^{18} + 49 q^{19} + 147 q^{20} + 41 q^{21} + 32 q^{22} + 244 q^{23} + 85 q^{24} + 355 q^{25} + 83 q^{26} + 155 q^{27} + 129 q^{28} + 91 q^{29} + 51 q^{30} + 65 q^{31} + 113 q^{32} + 73 q^{33} + 26 q^{34} + 200 q^{35} + 380 q^{36} + 28 q^{37} + 171 q^{38} + 117 q^{39} + 95 q^{40} + 115 q^{41} + 42 q^{42} + 98 q^{43} + 139 q^{44} + 127 q^{45} + 29 q^{46} + 312 q^{47} + 168 q^{48} + 365 q^{49} + 64 q^{50} + 72 q^{51} + 100 q^{52} + 154 q^{53} + 89 q^{54} + 161 q^{55} + 89 q^{56} + 82 q^{57} + 29 q^{58} + 149 q^{59} + 93 q^{60} + 70 q^{61} + 257 q^{62} + 376 q^{63} + 346 q^{64} + 125 q^{65} + 48 q^{66} + 65 q^{67} + 464 q^{68} + 58 q^{69} - 54 q^{70} + 216 q^{71} + 90 q^{72} + 93 q^{73} + 147 q^{74} + 162 q^{75} + 64 q^{76} + 190 q^{77} + 12 q^{78} + 139 q^{79} + 274 q^{80} + 376 q^{81} + 59 q^{82} + 402 q^{83} + 10 q^{84} + 32 q^{85} + 53 q^{86} + 364 q^{87} + 42 q^{88} + 114 q^{89} + 126 q^{90} + 43 q^{91} + 422 q^{92} + 47 q^{93} + 2 q^{94} + 347 q^{95} + 146 q^{96} + 47 q^{97} + 96 q^{98} + 129 q^{99}+O(q^{100}) \) 340 * q + 20 * q^2 + 44 * q^3 + 350 * q^4 + 53 * q^5 + 34 * q^6 + 81 * q^7 + 54 * q^8 + 360 * q^9 + 36 * q^10 + 70 * q^11 + 92 * q^12 + 45 * q^13 + 44 * q^14 + 71 * q^15 + 362 * q^16 + 162 * q^17 + 41 * q^18 + 49 * q^19 + 147 * q^20 + 41 * q^21 + 32 * q^22 + 244 * q^23 + 85 * q^24 + 355 * q^25 + 83 * q^26 + 155 * q^27 + 129 * q^28 + 91 * q^29 + 51 * q^30 + 65 * q^31 + 113 * q^32 + 73 * q^33 + 26 * q^34 + 200 * q^35 + 380 * q^36 + 28 * q^37 + 171 * q^38 + 117 * q^39 + 95 * q^40 + 115 * q^41 + 42 * q^42 + 98 * q^43 + 139 * q^44 + 127 * q^45 + 29 * q^46 + 312 * q^47 + 168 * q^48 + 365 * q^49 + 64 * q^50 + 72 * q^51 + 100 * q^52 + 154 * q^53 + 89 * q^54 + 161 * q^55 + 89 * q^56 + 82 * q^57 + 29 * q^58 + 149 * q^59 + 93 * q^60 + 70 * q^61 + 257 * q^62 + 376 * q^63 + 346 * q^64 + 125 * q^65 + 48 * q^66 + 65 * q^67 + 464 * q^68 + 58 * q^69 - 54 * q^70 + 216 * q^71 + 90 * q^72 + 93 * q^73 + 147 * q^74 + 162 * q^75 + 64 * q^76 + 190 * q^77 + 12 * q^78 + 139 * q^79 + 274 * q^80 + 376 * q^81 + 59 * q^82 + 402 * q^83 + 10 * q^84 + 32 * q^85 + 53 * q^86 + 364 * q^87 + 42 * q^88 + 114 * q^89 + 126 * q^90 + 43 * q^91 + 422 * q^92 + 47 * q^93 + 2 * q^94 + 347 * q^95 + 146 * q^96 + 47 * q^97 + 96 * q^98 + 129 * q^99

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