LMFDB - Embedded newform 667.4.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.01219 q^{2} +7.50590 q^{3} +8.09767 q^{4} -10.1837 q^{5} -30.1151 q^{6} +25.8615 q^{7} -0.391885 q^{8} +29.3385 q^{9} +O(q^{10})$	\(q-4.01219 q^{2} +7.50590 q^{3} +8.09767 q^{4} -10.1837 q^{5} -30.1151 q^{6} +25.8615 q^{7} -0.391885 q^{8} +29.3385 q^{9} +40.8590 q^{10} -2.06961 q^{11} +60.7803 q^{12} +0.124778 q^{13} -103.761 q^{14} -76.4379 q^{15} -63.2091 q^{16} -86.9902 q^{17} -117.712 q^{18} -135.821 q^{19} -82.4644 q^{20} +194.114 q^{21} +8.30367 q^{22} +23.0000 q^{23} -2.94145 q^{24} -21.2919 q^{25} -0.500635 q^{26} +17.5524 q^{27} +209.418 q^{28} -29.0000 q^{29} +306.684 q^{30} +144.108 q^{31} +256.742 q^{32} -15.5343 q^{33} +349.021 q^{34} -263.367 q^{35} +237.573 q^{36} -202.455 q^{37} +544.940 q^{38} +0.936574 q^{39} +3.99085 q^{40} -309.384 q^{41} -778.822 q^{42} +105.868 q^{43} -16.7590 q^{44} -298.775 q^{45} -92.2804 q^{46} +81.2378 q^{47} -474.441 q^{48} +325.819 q^{49} +85.4271 q^{50} -652.939 q^{51} +1.01042 q^{52} -235.630 q^{53} -70.4235 q^{54} +21.0763 q^{55} -10.1348 q^{56} -1019.46 q^{57} +116.354 q^{58} -445.950 q^{59} -618.969 q^{60} +583.248 q^{61} -578.188 q^{62} +758.738 q^{63} -524.425 q^{64} -1.27071 q^{65} +62.3265 q^{66} +476.901 q^{67} -704.418 q^{68} +172.636 q^{69} +1056.68 q^{70} -679.251 q^{71} -11.4973 q^{72} -116.630 q^{73} +812.289 q^{74} -159.815 q^{75} -1099.83 q^{76} -53.5233 q^{77} -3.75772 q^{78} +589.196 q^{79} +643.703 q^{80} -660.393 q^{81} +1241.31 q^{82} +187.265 q^{83} +1571.87 q^{84} +885.884 q^{85} -424.761 q^{86} -217.671 q^{87} +0.811050 q^{88} -1399.65 q^{89} +1198.74 q^{90} +3.22696 q^{91} +186.246 q^{92} +1081.66 q^{93} -325.942 q^{94} +1383.16 q^{95} +1927.08 q^{96} +1038.93 q^{97} -1307.25 q^{98} -60.7192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * 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 $

$2$	−4.01219	−1.41852	−0.709262	−	0.704945i	$-0.750972\pi$
$2$	−4.01219	−1.41852	−0.709262	+	0.704945i	$0.750972\pi$
$3$	7.50590	1.44451	0.722255	−	0.691627i	$-0.243106\pi$
$3$	7.50590	1.44451	0.722255	+	0.691627i	$0.243106\pi$
$4$	8.09767	1.01221
$5$	−10.1837	−0.910859	−0.455430	−	0.890272i	$-0.650514\pi$
$5$	−10.1837	−0.910859	−0.455430	+	0.890272i	$0.650514\pi$
$6$	−30.1151	−2.04907
$7$	25.8615	1.39639	0.698196	−	0.715907i	$-0.253987\pi$
$7$	25.8615	1.39639	0.698196	+	0.715907i	$0.253987\pi$
$8$	−0.391885	−0.0173190
$9$	29.3385	1.08661
$10$	40.8590	1.29208
$11$	−2.06961	−0.0567283	−0.0283641	−	0.999598i	$-0.509030\pi$
$11$	−2.06961	−0.0567283	−0.0283641	+	0.999598i	$0.509030\pi$
$12$	60.7803	1.46215
$13$	0.124778	0.00266210	0.00133105	−	0.999999i	$-0.499576\pi$
$13$	0.124778	0.00266210	0.00133105	+	0.999999i	$0.499576\pi$
$14$	−103.761	−1.98081
$15$	−76.4379	−1.31575
$16$	−63.2091	−0.987642
$17$	−86.9902	−1.24107	−0.620536	−	0.784178i	$-0.713085\pi$
$17$	−86.9902	−1.24107	−0.620536	+	0.784178i	$0.713085\pi$
$18$	−117.712	−1.54138
$19$	−135.821	−1.63997	−0.819986	−	0.572384i	$-0.806019\pi$
$19$	−135.821	−1.63997	−0.819986	+	0.572384i	$0.806019\pi$
$20$	−82.4644	−0.921980
$21$	194.114	2.01710
$22$	8.30367	0.0804704
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−2.94145	−0.0250175
$25$	−21.2919	−0.170335
$26$	−0.500635	−0.00377625
$27$	17.5524	0.125110
$28$	209.418	1.41344
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	306.684	1.86642
$31$	144.108	0.834920	0.417460	−	0.908695i	$-0.362920\pi$
$31$	144.108	0.834920	0.417460	+	0.908695i	$0.362920\pi$
$32$	256.742	1.41831
$33$	−15.5343	−0.0819446
$34$	349.021	1.76049
$35$	−263.367	−1.27192
$36$	237.573	1.09988
$37$	−202.455	−0.899553	−0.449776	−	0.893141i	$-0.648496\pi$
$37$	−202.455	−0.899553	−0.449776	+	0.893141i	$0.648496\pi$
$38$	544.940	2.32634
$39$	0.936574	0.00384543
$40$	3.99085	0.0157752
$41$	−309.384	−1.17848	−0.589240	−	0.807958i	$-0.700573\pi$
$41$	−309.384	−1.17848	−0.589240	+	0.807958i	$0.700573\pi$
$42$	−778.822	−2.86131
$43$	105.868	0.375457	0.187729	−	0.982221i	$-0.439887\pi$
$43$	105.868	0.375457	0.187729	+	0.982221i	$0.439887\pi$
$44$	−16.7590	−0.0574209
$45$	−298.775	−0.989749
$46$	−92.2804	−0.295783
$47$	81.2378	0.252122	0.126061	−	0.992022i	$-0.459766\pi$
$47$	81.2378	0.252122	0.126061	+	0.992022i	$0.459766\pi$
$48$	−474.441	−1.42666
$49$	325.819	0.949909
$50$	85.4271	0.241624
$51$	−652.939	−1.79274
$52$	1.01042	0.00269460
$53$	−235.630	−0.610684	−0.305342	−	0.952243i	$-0.598771\pi$
$53$	−235.630	−0.610684	−0.305342	+	0.952243i	$0.598771\pi$
$54$	−70.4235	−0.177471
$55$	21.0763	0.0516715
$56$	−10.1348	−0.0241842
$57$	−1019.46	−2.36896
$58$	116.354	0.263413
$59$	−445.950	−0.984030	−0.492015	−	0.870587i	$-0.663739\pi$
$59$	−445.950	−0.984030	−0.492015	+	0.870587i	$0.663739\pi$
$60$	−618.969	−1.33181
$61$	583.248	1.22422	0.612109	−	0.790773i	$-0.290321\pi$
$61$	583.248	1.22422	0.612109	+	0.790773i	$0.290321\pi$
$62$	−578.188	−1.18435
$63$	758.738	1.51733
$64$	−524.425	−1.02427
$65$	−1.27071	−0.00242480
$66$	62.3265	0.116240
$67$	476.901	0.869594	0.434797	−	0.900529i	$-0.356820\pi$
$67$	476.901	0.869594	0.434797	+	0.900529i	$0.356820\pi$
$68$	−704.418	−1.25622
$69$	172.636	0.301201
$70$	1056.68	1.80424
$71$	−679.251	−1.13538	−0.567692	−	0.823241i	$-0.692164\pi$
$71$	−679.251	−1.13538	−0.567692	+	0.823241i	$0.692164\pi$
$72$	−11.4973	−0.0188191
$73$	−116.630	−0.186994	−0.0934969	−	0.995620i	$-0.529805\pi$
$73$	−116.630	−0.186994	−0.0934969	+	0.995620i	$0.529805\pi$
$74$	812.289	1.27604
$75$	−159.815	−0.246051
$76$	−1099.83	−1.65999
$77$	−53.5233	−0.0792149
$78$	−3.75772	−0.00545484
$79$	589.196	0.839110	0.419555	−	0.907730i	$-0.362186\pi$
$79$	589.196	0.839110	0.419555	+	0.907730i	$0.362186\pi$
$80$	643.703	0.899603
$81$	−660.393	−0.905888
$82$	1241.31	1.67170
$83$	187.265	0.247651	0.123826	−	0.992304i	$-0.460484\pi$
$83$	187.265	0.247651	0.123826	+	0.992304i	$0.460484\pi$
$84$	1571.87	2.04173
$85$	885.884	1.13044
$86$	−424.761	−0.532595
$87$	−217.671	−0.268239
$88$	0.811050	0.000982480 0
$89$	−1399.65	−1.66699	−0.833496	−	0.552526i	$-0.813664\pi$
$89$	−1399.65	−1.66699	−0.833496	+	0.552526i	$0.813664\pi$
$90$	1198.74	1.40398
$91$	3.22696	0.00371734
$92$	186.246	0.211060
$93$	1081.66	1.20605
$94$	−325.942	−0.357642
$95$	1383.16	1.49378
$96$	1927.08	2.04877
$97$	1038.93	1.08750	0.543751	−	0.839247i	$-0.317004\pi$
$97$	1038.93	1.08750	0.543751	+	0.839247i	$0.317004\pi$
$98$	−1307.25	−1.34747
$99$	−60.7192	−0.0616415
$100$	−172.415	−0.172415
$101$	406.638	0.400614	0.200307	−	0.979733i	$-0.435806\pi$
$101$	406.638	0.400614	0.200307	+	0.979733i	$0.435806\pi$
$102$	2619.72	2.54305
$103$	1681.17	1.60826	0.804131	−	0.594452i	$-0.202631\pi$
$103$	1681.17	1.60826	0.804131	+	0.594452i	$0.202631\pi$
$104$	−0.0488989	−4.61051e−5 0
$105$	−1976.80	−1.83730
$106$	945.392	0.866270
$107$	−1353.68	−1.22304	−0.611519	−	0.791230i	$-0.709441\pi$
$107$	−1353.68	−1.22304	−0.611519	+	0.791230i	$0.709441\pi$
$108$	142.134	0.126637
$109$	−2165.93	−1.90329	−0.951645	−	0.307201i	$-0.900608\pi$
$109$	−2165.93	−1.90329	−0.951645	+	0.307201i	$0.900608\pi$
$110$	−84.5623	−0.0732972
$111$	−1519.61	−1.29941
$112$	−1634.68	−1.37913
$113$	−2186.95	−1.82063	−0.910316	−	0.413915i	$-0.864161\pi$
$113$	−2186.95	−1.82063	−0.910316	+	0.413915i	$0.864161\pi$
$114$	4090.26	3.36042
$115$	−234.226	−0.189927
$116$	−234.833	−0.187963
$117$	3.66081	0.00289267
$118$	1789.24	1.39587
$119$	−2249.70	−1.73302
$120$	29.9549	0.0227875
$121$	−1326.72	−0.996782
$122$	−2340.10	−1.73658
$123$	−2322.20	−1.70233
$124$	1166.94	0.845114
$125$	1489.80	1.06601
$126$	−3044.20	−2.15237
$127$	683.021	0.477231	0.238615	−	0.971114i	$-0.423306\pi$
$127$	683.021	0.477231	0.238615	+	0.971114i	$0.423306\pi$
$128$	50.1576	0.0346355
$129$	794.631	0.542352
$130$	5.09833	0.00343964
$131$	−1290.38	−0.860619	−0.430310	−	0.902681i	$-0.641596\pi$
$131$	−1290.38	−0.860619	−0.430310	+	0.902681i	$0.641596\pi$
$132$	−125.792	−0.0829451
$133$	−3512.54	−2.29004
$134$	−1913.42	−1.23354
$135$	−178.749	−0.113957
$136$	34.0902	0.0214942
$137$	2941.04	1.83409	0.917043	−	0.398789i	$-0.130570\pi$
$137$	2941.04	1.83409	0.917043	+	0.398789i	$0.130570\pi$
$138$	−692.647	−0.427261
$139$	−755.894	−0.461252	−0.230626	−	0.973042i	$-0.574077\pi$
$139$	−755.894	−0.461252	−0.230626	+	0.973042i	$0.574077\pi$
$140$	−2132.66	−1.28745
$141$	609.763	0.364194
$142$	2725.29	1.61057
$143$	−0.258243	−0.000151016 0
$144$	−1854.46	−1.07318
$145$	295.328	0.169142
$146$	467.943	0.265255
$147$	2445.56	1.37215
$148$	−1639.42	−0.910535
$149$	−1141.73	−0.627748	−0.313874	−	0.949465i	$-0.601627\pi$
$149$	−1141.73	−0.627748	−0.313874	+	0.949465i	$0.601627\pi$
$150$	641.207	0.349029
$151$	901.229	0.485702	0.242851	−	0.970064i	$-0.421917\pi$
$151$	901.229	0.485702	0.242851	+	0.970064i	$0.421917\pi$
$152$	53.2262	0.0284027
$153$	−2552.16	−1.34856
$154$	214.746	0.112368
$155$	−1467.55	−0.760495
$156$	7.58407	0.00389238
$157$	−711.939	−0.361904	−0.180952	−	0.983492i	$-0.557918\pi$
$157$	−711.939	−0.361904	−0.180952	+	0.983492i	$0.557918\pi$
$158$	−2363.97	−1.19030
$159$	−1768.61	−0.882140
$160$	−2614.59	−1.29188
$161$	594.815	0.291168
$162$	2649.62	1.28502
$163$	70.3478	0.0338041	0.0169020	−	0.999857i	$-0.494620\pi$
$163$	70.3478	0.0338041	0.0169020	+	0.999857i	$0.494620\pi$
$164$	−2505.29	−1.19287
$165$	158.197	0.0746400
$166$	−751.344	−0.351299
$167$	−75.9514	−0.0351934	−0.0175967	−	0.999845i	$-0.505601\pi$
$167$	−75.9514	−0.0351934	−0.0175967	+	0.999845i	$0.505601\pi$
$168$	−76.0704	−0.0349343
$169$	−2196.98	−0.999993
$170$	−3554.33	−1.60356
$171$	−3984.78	−1.78201
$172$	857.281	0.380041
$173$	−1056.12	−0.464136	−0.232068	−	0.972700i	$-0.574549\pi$
$173$	−1056.12	−0.464136	−0.232068	+	0.972700i	$0.574549\pi$
$174$	873.338	0.380503
$175$	−550.640	−0.237854
$176$	130.818	0.0560272
$177$	−3347.25	−1.42144
$178$	5615.65	2.36467
$179$	−846.384	−0.353417	−0.176709	−	0.984263i	$-0.556545\pi$
$179$	−846.384	−0.353417	−0.176709	+	0.984263i	$0.556545\pi$
$180$	−2419.38	−1.00183
$181$	3032.56	1.24535	0.622676	−	0.782480i	$-0.286045\pi$
$181$	3032.56	1.24535	0.622676	+	0.782480i	$0.286045\pi$
$182$	−12.9472	−0.00527313
$183$	4377.80	1.76840
$184$	−9.01336	−0.00361127
$185$	2061.75	0.819366
$186$	−4339.82	−1.71081
$187$	180.036	0.0704039
$188$	657.837	0.255201
$189$	453.932	0.174702
$190$	−5549.51	−2.11897
$191$	−2094.53	−0.793482	−0.396741	−	0.917931i	$-0.629859\pi$
$191$	−2094.53	−0.793482	−0.396741	+	0.917931i	$0.629859\pi$
$192$	−3936.28	−1.47957
$193$	2280.26	0.850449	0.425224	−	0.905088i	$-0.360195\pi$
$193$	2280.26	0.850449	0.425224	+	0.905088i	$0.360195\pi$
$194$	−4168.40	−1.54265
$195$	−9.53781	−0.00350265
$196$	2638.37	0.961506
$197$	−1271.30	−0.459778	−0.229889	−	0.973217i	$-0.573836\pi$
$197$	−1271.30	−0.459778	−0.229889	+	0.973217i	$0.573836\pi$
$198$	243.617	0.0874400
$199$	−3069.47	−1.09341	−0.546705	−	0.837325i	$-0.684118\pi$
$199$	−3069.47	−1.09341	−0.546705	+	0.837325i	$0.684118\pi$
$200$	8.34397	0.00295004
$201$	3579.57	1.25614
$202$	−1631.51	−0.568280
$203$	−749.984	−0.259303
$204$	−5287.29	−1.81463
$205$	3150.68	1.07343
$206$	−6745.19	−2.28136
$207$	674.785	0.226574
$208$	−7.88713	−0.00262920
$209$	281.097	0.0930328
$210$	7931.31	2.60625
$211$	−3229.46	−1.05367	−0.526836	−	0.849967i	$-0.676622\pi$
$211$	−3229.46	−1.05367	−0.526836	+	0.849967i	$0.676622\pi$
$212$	−1908.05	−0.618140
$213$	−5098.39	−1.64007
$214$	5431.21	1.73491
$215$	−1078.13	−0.341989
$216$	−6.87852	−0.00216678
$217$	3726.85	1.16588
$218$	8690.13	2.69986
$219$	−875.415	−0.270115
$220$	170.669	0.0523024
$221$	−10.8545	−0.00330386
$222$	6096.96	1.84325
$223$	−4294.83	−1.28970	−0.644850	−	0.764309i	$-0.723080\pi$
$223$	−4294.83	−1.28970	−0.644850	+	0.764309i	$0.723080\pi$
$224$	6639.74	1.98052
$225$	−624.671	−0.185088
$226$	8774.48	2.58261
$227$	4051.86	1.18472	0.592359	−	0.805674i	$-0.298197\pi$
$227$	4051.86	1.18472	0.592359	+	0.805674i	$0.298197\pi$
$228$	−8255.24	−2.39788
$229$	1370.49	0.395478	0.197739	−	0.980255i	$-0.436640\pi$
$229$	1370.49	0.395478	0.197739	+	0.980255i	$0.436640\pi$
$230$	939.757	0.269416
$231$	−401.740	−0.114427
$232$	11.3647	0.00321607
$233$	−706.920	−0.198764	−0.0993818	−	0.995049i	$-0.531687\pi$
$233$	−706.920	−0.198764	−0.0993818	+	0.995049i	$0.531687\pi$
$234$	−14.6879	−0.00410332
$235$	−827.303	−0.229648
$236$	−3611.16	−0.996044
$237$	4422.44	1.21210
$238$	9026.22	2.45833
$239$	−6612.76	−1.78972	−0.894862	−	0.446342i	$-0.852726\pi$
$239$	−6612.76	−1.78972	−0.894862	+	0.446342i	$0.852726\pi$
$240$	4831.57	1.29949
$241$	2036.44	0.544310	0.272155	−	0.962253i	$-0.412264\pi$
$241$	2036.44	0.544310	0.272155	+	0.962253i	$0.412264\pi$
$242$	5323.04	1.41396
$243$	−5430.75	−1.43367
$244$	4722.95	1.23916
$245$	−3318.05	−0.865233
$246$	9317.13	2.41479
$247$	−16.9475	−0.00436577
$248$	−56.4737	−0.0144600
$249$	1405.59	0.357734
$250$	−5977.34	−1.51216
$251$	32.9198	0.00827841	0.00413921	−	0.999991i	$-0.498682\pi$
$251$	32.9198	0.00827841	0.00413921	+	0.999991i	$0.498682\pi$
$252$	6144.01	1.53586
$253$	−47.6011	−0.0118287
$254$	−2740.41	−0.676963
$255$	6649.35	1.63294
$256$	3994.16	0.975136
$257$	6075.62	1.47466	0.737328	−	0.675535i	$-0.236087\pi$
$257$	6075.62	1.47466	0.737328	+	0.675535i	$0.236087\pi$
$258$	−3188.21	−0.769339
$259$	−5235.80	−1.25613
$260$	−10.2898	−0.00245441
$261$	−850.816	−0.201778
$262$	5177.25	1.22081
$263$	3119.49	0.731392	0.365696	−	0.930734i	$-0.380831\pi$
$263$	3119.49	0.731392	0.365696	+	0.930734i	$0.380831\pi$
$264$	6.08766	0.00141920
$265$	2399.59	0.556248
$266$	14093.0	3.24848
$267$	−10505.6	−2.40799
$268$	3861.79	0.880211
$269$	1497.56	0.339433	0.169717	−	0.985493i	$-0.445715\pi$
$269$	1497.56	0.339433	0.169717	+	0.985493i	$0.445715\pi$
$270$	717.174	0.161651
$271$	−5432.10	−1.21763	−0.608813	−	0.793314i	$-0.708354\pi$
$271$	−5432.10	−1.21763	−0.608813	+	0.793314i	$0.708354\pi$
$272$	5498.57	1.22573
$273$	24.2212	0.00536973
$274$	−11800.0	−2.60169
$275$	44.0659	0.00966281
$276$	1397.95	0.304879
$277$	−259.366	−0.0562591	−0.0281295	−	0.999604i	$-0.508955\pi$
$277$	−259.366	−0.0562591	−0.0281295	+	0.999604i	$0.508955\pi$
$278$	3032.79	0.654297
$279$	4227.90	0.907233
$280$	103.209	0.0220284
$281$	2698.40	0.572857	0.286429	−	0.958102i	$-0.407532\pi$
$281$	2698.40	0.572857	0.286429	+	0.958102i	$0.407532\pi$
$282$	−2446.48	−0.516617
$283$	3727.16	0.782886	0.391443	−	0.920202i	$-0.371976\pi$
$283$	3727.16	0.782886	0.391443	+	0.920202i	$0.371976\pi$
$284$	−5500.35	−1.14925
$285$	10381.9	2.15779
$286$	1.03612	0.000214220 0
$287$	−8001.14	−1.64562
$288$	7532.42	1.54115
$289$	2654.29	0.540259
$290$	−1184.91	−0.239932
$291$	7798.12	1.57091
$292$	−944.435	−0.189277
$293$	2112.75	0.421257	0.210629	−	0.977566i	$-0.432449\pi$
$293$	2112.75	0.421257	0.210629	+	0.977566i	$0.432449\pi$
$294$	−9812.06	−1.94643
$295$	4541.43	0.896313
$296$	79.3393	0.0155794
$297$	−36.3266	−0.00709725
$298$	4580.86	0.890476
$299$	2.86991	0.000555087 0
$300$	−1294.13	−0.249055
$301$	2737.90	0.524285
$302$	−3615.90	−0.688979
$303$	3052.18	0.578691
$304$	8585.12	1.61970
$305$	−5939.64	−1.11509
$306$	10239.8	1.91297
$307$	10.6887	0.00198708	0.000993540	−	1.00000i	$-0.499684\pi$
$307$	10.6887	0.00198708	0.000993540		1.00000i	$0.499684\pi$
$308$	−433.414	−0.0801820
$309$	12618.7	2.32315
$310$	5888.10	1.07878
$311$	6968.17	1.27051	0.635255	−	0.772302i	$-0.280895\pi$
$311$	6968.17	1.27051	0.635255	+	0.772302i	$0.280895\pi$
$312$	−0.367030	−6.65993e−5 0
$313$	3945.79	0.712553	0.356276	−	0.934381i	$-0.384046\pi$
$313$	3945.79	0.712553	0.356276	+	0.934381i	$0.384046\pi$
$314$	2856.43	0.513369
$315$	−7726.77	−1.38208
$316$	4771.12	0.849355
$317$	316.843	0.0561377	0.0280689	−	0.999606i	$-0.491064\pi$
$317$	316.843	0.0561377	0.0280689	+	0.999606i	$0.491064\pi$
$318$	7096.02	1.25134
$319$	60.0187	0.0105342
$320$	5340.60	0.932964
$321$	−10160.6	−1.76669
$322$	−2386.51	−0.413028
$323$	11815.1	2.03532
$324$	−5347.64	−0.916948
$325$	−2.65677	−0.000453449 0
$326$	−282.249	−0.0479519
$327$	−16257.3	−2.74932
$328$	121.243	0.0204101
$329$	2100.93	0.352062
$330$	−634.716	−0.105879
$331$	4152.75	0.689594	0.344797	−	0.938677i	$-0.387948\pi$
$331$	4152.75	0.689594	0.344797	+	0.938677i	$0.387948\pi$
$332$	1516.41	0.250675
$333$	−5939.73	−0.977463
$334$	304.731	0.0499226
$335$	−4856.63	−0.792078
$336$	−12269.8	−1.99217
$337$	−7757.13	−1.25388	−0.626941	−	0.779067i	$-0.715693\pi$
$337$	−7757.13	−1.25388	−0.626941	+	0.779067i	$0.715693\pi$
$338$	8814.72	1.41851
$339$	−16415.1	−2.62992
$340$	7173.60	1.14424
$341$	−298.247	−0.0473636
$342$	15987.7	2.52782
$343$	−444.335	−0.0699470
$344$	−41.4880	−0.00650256
$345$	−1758.07	−0.274352
$346$	4237.36	0.658388
$347$	−5667.69	−0.876823	−0.438411	−	0.898774i	$-0.644459\pi$
$347$	−5667.69	−0.876823	−0.438411	+	0.898774i	$0.644459\pi$
$348$	−1762.63	−0.271514
$349$	−7169.42	−1.09963	−0.549814	−	0.835287i	$-0.685301\pi$
$349$	−7169.42	−1.09963	−0.549814	+	0.835287i	$0.685301\pi$
$350$	2209.27	0.337402
$351$	2.19016	0.000333055 0
$352$	−531.356	−0.0804584
$353$	1884.50	0.284142	0.142071	−	0.989856i	$-0.454624\pi$
$353$	1884.50	0.284142	0.142071	+	0.989856i	$0.454624\pi$
$354$	13429.8	2.01635
$355$	6917.30	1.03418
$356$	−11333.9	−1.68734
$357$	−16886.0	−2.50337
$358$	3395.85	0.501331
$359$	−344.194	−0.0506013	−0.0253007	−	0.999680i	$-0.508054\pi$
$359$	−344.194	−0.0506013	−0.0253007	+	0.999680i	$0.508054\pi$
$360$	117.085	0.0171415
$361$	11588.3	1.68951
$362$	−12167.2	−1.76656
$363$	−9958.20	−1.43986
$364$	26.1309	0.00376272
$365$	1187.73	0.170325
$366$	−17564.6	−2.50851
$367$	−10951.1	−1.55760	−0.778802	−	0.627269i	$-0.784173\pi$
$367$	−10951.1	−1.55760	−0.778802	+	0.627269i	$0.784173\pi$
$368$	−1453.81	−0.205938
$369$	−9076.86	−1.28055
$370$	−8272.13	−1.16229
$371$	−6093.75	−0.852754
$372$	8758.92	1.22078
$373$	13258.2	1.84044	0.920221	−	0.391400i	$-0.128009\pi$
$373$	13258.2	1.84044	0.920221	+	0.391400i	$0.128009\pi$
$374$	−722.338	−0.0998696
$375$	11182.2	1.53986
$376$	−31.8359	−0.00436652
$377$	−3.61858	−0.000494340 0
$378$	−1821.26	−0.247819
$379$	−10420.1	−1.41225	−0.706126	−	0.708086i	$-0.749559\pi$
$379$	−10420.1	−1.41225	−0.706126	+	0.708086i	$0.749559\pi$
$380$	11200.4	1.51202
$381$	5126.69	0.689365
$382$	8403.66	1.12557
$383$	12325.2	1.64436	0.822179	−	0.569230i	$-0.192758\pi$
$383$	12325.2	1.64436	0.822179	+	0.569230i	$0.192758\pi$
$384$	376.478	0.0500314
$385$	545.066	0.0721536
$386$	−9148.83	−1.20638
$387$	3106.00	0.407976
$388$	8412.94	1.10078
$389$	−6149.05	−0.801464	−0.400732	−	0.916195i	$-0.631244\pi$
$389$	−6149.05	−0.801464	−0.400732	+	0.916195i	$0.631244\pi$
$390$	38.2675	0.00496859
$391$	−2000.77	−0.258781
$392$	−127.684	−0.0164515
$393$	−9685.47	−1.24317
$394$	5100.69	0.652206
$395$	−6000.21	−0.764312
$396$	−491.685	−0.0623941
$397$	12498.8	1.58009	0.790044	−	0.613051i	$-0.210058\pi$
$397$	12498.8	1.58009	0.790044	+	0.613051i	$0.210058\pi$
$398$	12315.3	1.55103
$399$	−26364.7	−3.30799
$400$	1345.84	0.168230
$401$	3411.97	0.424902	0.212451	−	0.977172i	$-0.431855\pi$
$401$	3411.97	0.424902	0.212451	+	0.977172i	$0.431855\pi$
$402$	−14361.9	−1.78186
$403$	17.9816	0.00222264
$404$	3292.82	0.405505
$405$	6725.25	0.825137
$406$	3009.08	0.367828
$407$	419.004	0.0510301
$408$	255.877	0.0310486
$409$	12657.3	1.53022	0.765112	−	0.643897i	$-0.222684\pi$
$409$	12657.3	1.53022	0.765112	+	0.643897i	$0.222684\pi$
$410$	−12641.1	−1.52268
$411$	22075.1	2.64936
$412$	13613.6	1.62790
$413$	−11532.9	−1.37409
$414$	−2707.37	−0.321400
$415$	−1907.06	−0.225575
$416$	32.0359	0.00377569
$417$	−5673.66	−0.666284
$418$	−1127.81	−0.131969
$419$	−13183.4	−1.53712	−0.768558	−	0.639780i	$-0.779026\pi$
$419$	−13183.4	−1.53712	−0.768558	+	0.639780i	$0.779026\pi$
$420$	−16007.5	−1.85973
$421$	−1494.89	−0.173056	−0.0865281	−	0.996249i	$-0.527577\pi$
$421$	−1494.89	−0.173056	−0.0865281	+	0.996249i	$0.527577\pi$
$422$	12957.2	1.49466
$423$	2383.39	0.273959
$424$	92.3399	0.0105765
$425$	1852.18	0.211398
$426$	20455.7	2.32648
$427$	15083.7	1.70949
$428$	−10961.6	−1.23797
$429$	−1.93834	−0.000218145 0
$430$	4325.65	0.485119
$431$	10100.9	1.12887	0.564436	−	0.825477i	$-0.309094\pi$
$431$	10100.9	1.12887	0.564436	+	0.825477i	$0.309094\pi$
$432$	−1109.47	−0.123563
$433$	1571.61	0.174427	0.0872135	−	0.996190i	$-0.472204\pi$
$433$	1571.61	0.174427	0.0872135	+	0.996190i	$0.472204\pi$
$434$	−14952.8	−1.65382
$435$	2216.70	0.244328
$436$	−17539.0	−1.92653
$437$	−3123.88	−0.341958
$438$	3512.33	0.383164
$439$	−7203.61	−0.783165	−0.391582	−	0.920143i	$-0.628072\pi$
$439$	−7203.61	−0.783165	−0.391582	+	0.920143i	$0.628072\pi$
$440$	−8.25951	−0.000894901 0
$441$	9559.03	1.03218
$442$	43.5503	0.00468660
$443$	−3739.68	−0.401078	−0.200539	−	0.979686i	$-0.564269\pi$
$443$	−3739.68	−0.401078	−0.200539	+	0.979686i	$0.564269\pi$
$444$	−12305.3	−1.31528
$445$	14253.6	1.51840
$446$	17231.7	1.82947
$447$	−8569.74	−0.906789
$448$	−13562.4	−1.43028
$449$	2993.33	0.314619	0.157309	−	0.987549i	$-0.449718\pi$
$449$	2993.33	0.314619	0.157309	+	0.987549i	$0.449718\pi$
$450$	2506.30	0.262551
$451$	640.304	0.0668531
$452$	−17709.2	−1.84286
$453$	6764.53	0.701601
$454$	−16256.8	−1.68055
$455$	−32.8625	−0.00338597
$456$	399.511	0.0410281
$457$	−18402.0	−1.88361	−0.941805	−	0.336161i	$-0.890871\pi$
$457$	−18402.0	−1.88361	−0.941805	+	0.336161i	$0.890871\pi$
$458$	−5498.66	−0.560994
$459$	−1526.89	−0.155270
$460$	−1896.68	−0.192246
$461$	8826.75	0.891763	0.445881	−	0.895092i	$-0.352890\pi$
$461$	8826.75	0.891763	0.445881	+	0.895092i	$0.352890\pi$
$462$	1611.86	0.162317
$463$	−5896.30	−0.591845	−0.295923	−	0.955212i	$-0.595627\pi$
$463$	−5896.30	−0.591845	−0.295923	+	0.955212i	$0.595627\pi$
$464$	1833.06	0.183400
$465$	−11015.3	−1.09854
$466$	2836.30	0.281951
$467$	18644.6	1.84747	0.923736	−	0.383030i	$-0.125119\pi$
$467$	18644.6	1.84747	0.923736	+	0.383030i	$0.125119\pi$
$468$	29.6441	0.00292798
$469$	12333.4	1.21429
$470$	3319.30	0.325761
$471$	−5343.74	−0.522774
$472$	174.761	0.0170425
$473$	−219.105	−0.0212990
$474$	−17743.7	−1.71940
$475$	2891.88	0.279345
$476$	−18217.3	−1.75418
$477$	−6913.03	−0.663576
$478$	26531.7	2.53877
$479$	14222.4	1.35665	0.678326	−	0.734761i	$-0.262706\pi$
$479$	14222.4	1.35665	0.678326	+	0.734761i	$0.262706\pi$
$480$	−19624.8	−1.86614
$481$	−25.2621	−0.00239470
$482$	−8170.60	−0.772117
$483$	4464.62	0.420595
$484$	−10743.3	−1.00895
$485$	−10580.2	−0.990561
$486$	21789.2	2.03370
$487$	15622.8	1.45367	0.726833	−	0.686814i	$-0.240991\pi$
$487$	15622.8	1.45367	0.726833	+	0.686814i	$0.240991\pi$
$488$	−228.566	−0.0212023
$489$	528.023	0.0488304
$490$	13312.6	1.22735
$491$	−4309.27	−0.396079	−0.198039	−	0.980194i	$-0.563457\pi$
$491$	−4309.27	−0.396079	−0.198039	+	0.980194i	$0.563457\pi$
$492$	−18804.5	−1.72311
$493$	2522.72	0.230461
$494$	67.9967	0.00619295
$495$	618.348	0.0561468
$496$	−9108.92	−0.824602
$497$	−17566.5	−1.58544
$498$	−5639.51	−0.507455
$499$	7225.44	0.648207	0.324103	−	0.946022i	$-0.394937\pi$
$499$	7225.44	0.648207	0.324103	+	0.946022i	$0.394937\pi$
$500$	12063.9	1.07903
$501$	−570.083	−0.0508372
$502$	−132.081	−0.0117431
$503$	−1339.42	−0.118731	−0.0593654	−	0.998236i	$-0.518908\pi$
$503$	−1339.42	−0.118731	−0.0593654	+	0.998236i	$0.518908\pi$
$504$	−297.338	−0.0262788
$505$	−4141.09	−0.364903
$506$	190.984	0.0167792
$507$	−16490.3	−1.44450
$508$	5530.88	0.483057
$509$	−10347.2	−0.901043	−0.450521	−	0.892766i	$-0.648762\pi$
$509$	−10347.2	−0.901043	−0.450521	+	0.892766i	$0.648762\pi$
$510$	−26678.5	−2.31636
$511$	−3016.24	−0.261117
$512$	−16426.6	−1.41789
$513$	−2383.98	−0.205176
$514$	−24376.5	−2.09183
$515$	−17120.6	−1.46490
$516$	6434.67	0.548974
$517$	−168.131	−0.0143025
$518$	21007.0	1.78185
$519$	−7927.14	−0.670449
$520$	0.497972	4.19952e−5 0
$521$	−7597.93	−0.638909	−0.319454	−	0.947602i	$-0.603500\pi$
$521$	−7597.93	−0.638909	−0.319454	+	0.947602i	$0.603500\pi$
$522$	3413.64	0.286228
$523$	8447.65	0.706290	0.353145	−	0.935569i	$-0.385112\pi$
$523$	8447.65	0.706290	0.353145	+	0.935569i	$0.385112\pi$
$524$	−10449.1	−0.871127
$525$	−4133.05	−0.343583
$526$	−12516.0	−1.03750
$527$	−12536.0	−1.03620
$528$	981.908	0.0809319
$529$	529.000	0.0434783
$530$	−9627.61	−0.789050
$531$	−13083.5	−1.06926
$532$	−28443.4	−2.31800
$533$	−38.6045	−0.00313723
$534$	42150.5	3.41579
$535$	13785.5	1.11402
$536$	−186.891	−0.0150605
$537$	−6352.87	−0.510515
$538$	−6008.48	−0.481494
$539$	−674.318	−0.0538867
$540$	−1447.45	−0.115349
$541$	4333.83	0.344410	0.172205	−	0.985061i	$-0.444911\pi$
$541$	4333.83	0.344410	0.172205	+	0.985061i	$0.444911\pi$
$542$	21794.6	1.72723
$543$	22762.1	1.79892
$544$	−22334.0	−1.76023
$545$	22057.2	1.73363
$546$	−97.1803	−0.00761709
$547$	−1272.54	−0.0994699	−0.0497349	−	0.998762i	$-0.515838\pi$
$547$	−1272.54	−0.0994699	−0.0497349	+	0.998762i	$0.515838\pi$
$548$	23815.5	1.85648
$549$	17111.6	1.33025
$550$	−176.801	−0.0137069
$551$	3938.81	0.304535
$552$	−67.6534	−0.00521652
$553$	15237.5	1.17173
$554$	1040.62	0.0798049
$555$	15475.3	1.18358
$556$	−6120.98	−0.466884
$557$	9374.75	0.713143	0.356572	−	0.934268i	$-0.383946\pi$
$557$	9374.75	0.713143	0.356572	+	0.934268i	$0.383946\pi$
$558$	−16963.2	−1.28693
$559$	13.2100	0.000999505 0
$560$	16647.2	1.25620
$561$	1351.33	0.101699
$562$	−10826.5	−0.812612
$563$	−8266.82	−0.618837	−0.309418	−	0.950926i	$-0.600134\pi$
$563$	−8266.82	−0.618837	−0.309418	+	0.950926i	$0.600134\pi$
$564$	4937.66	0.368640
$565$	22271.3	1.65834
$566$	−14954.1	−1.11054
$567$	−17078.8	−1.26497
$568$	266.189	0.0196638
$569$	3640.34	0.268209	0.134105	−	0.990967i	$-0.457184\pi$
$569$	3640.34	0.268209	0.134105	+	0.990967i	$0.457184\pi$
$570$	−41654.1	−3.06087
$571$	−1734.41	−0.127115	−0.0635576	−	0.997978i	$-0.520245\pi$
$571$	−1734.41	−0.127115	−0.0635576	+	0.997978i	$0.520245\pi$
$572$	−2.09117	−0.000152860 0
$573$	−15721.3	−1.14619
$574$	32102.1	2.33435
$575$	−489.713	−0.0355173
$576$	−15385.8	−1.11298
$577$	−9384.14	−0.677065	−0.338533	−	0.940955i	$-0.609931\pi$
$577$	−9384.14	−0.677065	−0.338533	+	0.940955i	$0.609931\pi$
$578$	−10649.5	−0.766371
$579$	17115.4	1.22848
$580$	2391.47	0.171207
$581$	4842.97	0.345818
$582$	−31287.6	−2.22837
$583$	487.662	0.0346431
$584$	45.7057	0.00323856
$585$	−37.2807	−0.00263481
$586$	−8476.77	−0.597563
$587$	3978.39	0.279737	0.139869	−	0.990170i	$-0.455332\pi$
$587$	3978.39	0.279737	0.139869	+	0.990170i	$0.455332\pi$
$588$	19803.4	1.38891
$589$	−19572.9	−1.36925
$590$	−18221.1	−1.27144
$591$	−9542.23	−0.664154
$592$	12797.0	0.888436
$593$	2509.87	0.173808	0.0869038	−	0.996217i	$-0.472303\pi$
$593$	2509.87	0.173808	0.0869038	+	0.996217i	$0.472303\pi$
$594$	145.749	0.0100676
$595$	22910.3	1.57854
$596$	−9245.39	−0.635413
$597$	−23039.1	−1.57944
$598$	−11.5146	−0.000787404 0
$599$	−598.942	−0.0408549	−0.0204275	−	0.999791i	$-0.506503\pi$
$599$	−598.942	−0.0408549	−0.0204275	+	0.999791i	$0.506503\pi$
$600$	62.6290	0.00426136
$601$	21126.3	1.43388	0.716939	−	0.697136i	$-0.245542\pi$
$601$	21126.3	1.43388	0.716939	+	0.697136i	$0.245542\pi$
$602$	−10985.0	−0.743711
$603$	13991.6	0.944910
$604$	7297.86	0.491632
$605$	13510.9	0.907928
$606$	−12245.9	−0.820886
$607$	17806.5	1.19068	0.595340	−	0.803474i	$-0.297017\pi$
$607$	17806.5	1.19068	0.595340	+	0.803474i	$0.297017\pi$
$608$	−34870.9	−2.32599
$609$	−5629.30	−0.374566
$610$	23831.0	1.58178
$611$	10.1367	0.000671176 0
$612$	−20666.6	−1.36503
$613$	23520.2	1.54971	0.774854	−	0.632141i	$-0.217823\pi$
$613$	23520.2	1.54971	0.774854	+	0.632141i	$0.217823\pi$
$614$	−42.8849	−0.00281872
$615$	23648.7	1.55058
$616$	20.9750	0.00137193
$617$	30529.4	1.99201	0.996003	−	0.0893202i	$-0.0284695\pi$
$617$	30529.4	1.99201	0.996003	+	0.0893202i	$0.0284695\pi$
$618$	−50628.7	−3.29544
$619$	−14028.1	−0.910883	−0.455442	−	0.890266i	$-0.650519\pi$
$619$	−14028.1	−0.910883	−0.455442	+	0.890266i	$0.650519\pi$
$620$	−11883.8	−0.769780
$621$	403.705	0.0260872
$622$	−27957.6	−1.80225
$623$	−36197.0	−2.32777
$624$	−59.2000	−0.00379791
$625$	−12510.2	−0.800651
$626$	−15831.2	−1.01077
$627$	2109.88	0.134387
$628$	−5765.05	−0.366322
$629$	17611.6	1.11641
$630$	31001.3	1.96051
$631$	−19497.8	−1.23010	−0.615051	−	0.788487i	$-0.710865\pi$
$631$	−19497.8	−1.23010	−0.615051	+	0.788487i	$0.710865\pi$
$632$	−230.897	−0.0145326
$633$	−24240.0	−1.52204
$634$	−1271.23	−0.0796327
$635$	−6955.69	−0.434690
$636$	−14321.7	−0.892910
$637$	40.6552	0.00252875
$638$	−240.807	−0.0149430
$639$	−19928.2	−1.23372
$640$	−510.791	−0.0315481
$641$	15119.1	0.931618	0.465809	−	0.884885i	$-0.345763\pi$
$641$	15119.1	0.931618	0.465809	+	0.884885i	$0.345763\pi$
$642$	40766.1	2.50609
$643$	−9451.74	−0.579689	−0.289845	−	0.957074i	$-0.593604\pi$
$643$	−9451.74	−0.579689	−0.289845	+	0.957074i	$0.593604\pi$
$644$	4816.62	0.294723
$645$	−8092.30	−0.494006
$646$	−47404.4	−2.88715
$647$	−18178.5	−1.10459	−0.552297	−	0.833647i	$-0.686249\pi$
$647$	−18178.5	−1.10459	−0.552297	+	0.833647i	$0.686249\pi$
$648$	258.798	0.0156891
$649$	922.943	0.0558223
$650$	10.6595	0.000643228 0
$651$	27973.3	1.68412
$652$	569.654	0.0342168
$653$	5885.31	0.352695	0.176348	−	0.984328i	$-0.443572\pi$
$653$	5885.31	0.352695	0.176348	+	0.984328i	$0.443572\pi$
$654$	65227.2	3.89998
$655$	13140.9	0.783903
$656$	19555.9	1.16392
$657$	−3421.76	−0.203189
$658$	−8429.35	−0.499408
$659$	−3645.29	−0.215479	−0.107739	−	0.994179i	$-0.534361\pi$
$659$	−3645.29	−0.215479	−0.107739	+	0.994179i	$0.534361\pi$
$660$	1281.03	0.0755513
$661$	−28317.2	−1.66628	−0.833140	−	0.553062i	$-0.813459\pi$
$661$	−28317.2	−1.66628	−0.833140	+	0.553062i	$0.813459\pi$
$662$	−16661.6	−0.978205
$663$	−81.4728	−0.00477246
$664$	−73.3865	−0.00428908
$665$	35770.7	2.08591
$666$	23831.3	1.38655
$667$	−667.000	−0.0387202
$668$	−615.030	−0.0356231
$669$	−32236.6	−1.86299
$670$	19485.7	1.12358
$671$	−1207.10	−0.0694478
$672$	49837.2	2.86088
$673$	1052.65	0.0602922	0.0301461	−	0.999546i	$-0.490403\pi$
$673$	1052.65	0.0602922	0.0301461	+	0.999546i	$0.490403\pi$
$674$	31123.1	1.77866
$675$	−373.723	−0.0213105
$676$	−17790.5	−1.01220
$677$	−9452.38	−0.536609	−0.268305	−	0.963334i	$-0.586463\pi$
$677$	−9452.38	−0.536609	−0.268305	+	0.963334i	$0.586463\pi$
$678$	65860.3	3.73060
$679$	26868.4	1.51858
$680$	−347.165	−0.0195782
$681$	30412.8	1.71134
$682$	1196.62	0.0671864
$683$	−22891.4	−1.28245	−0.641227	−	0.767351i	$-0.721574\pi$
$683$	−22891.4	−1.28245	−0.641227	+	0.767351i	$0.721574\pi$
$684$	−32267.4	−1.80377
$685$	−29950.7	−1.67059
$686$	1782.76	0.0992215
$687$	10286.7	0.571271
$688$	−6691.79	−0.370817
$689$	−29.4016	−0.00162570
$690$	7053.72	0.389175
$691$	−11319.7	−0.623188	−0.311594	−	0.950215i	$-0.600863\pi$
$691$	−11319.7	−0.623188	−0.311594	+	0.950215i	$0.600863\pi$
$692$	−8552.13	−0.469802
$693$	−1570.29	−0.0860757
$694$	22739.9	1.24379
$695$	7697.81	0.420136
$696$	85.3021	0.00464564
$697$	26913.4	1.46258
$698$	28765.1	1.55985
$699$	−5306.07	−0.287116
$700$	−4458.91	−0.240758
$701$	−359.539	−0.0193717	−0.00968587	−	0.999953i	$-0.503083\pi$
$701$	−359.539	−0.0193717	−0.00968587	+	0.999953i	$0.503083\pi$
$702$	−8.78734	−0.000472446 0
$703$	27497.7	1.47524
$704$	1085.36	0.0581049
$705$	−6209.65	−0.331729
$706$	−7560.99	−0.403062
$707$	10516.3	0.559413
$708$	−27105.0	−1.43880
$709$	318.223	0.0168563	0.00842815	−	0.999964i	$-0.497317\pi$
$709$	318.223	0.0168563	0.00842815	+	0.999964i	$0.497317\pi$
$710$	−27753.5	−1.46700
$711$	17286.1	0.911786
$712$	548.501	0.0288707
$713$	3314.48	0.174093
$714$	67749.9	3.55109
$715$	2.62987	0.000137555 0
$716$	−6853.74	−0.357732
$717$	−49634.7	−2.58528
$718$	1380.97	0.0717792
$719$	23555.6	1.22180	0.610901	−	0.791707i	$-0.290807\pi$
$719$	23555.6	1.22180	0.610901	+	0.791707i	$0.290807\pi$
$720$	18885.3	0.977518
$721$	43477.7	2.24576
$722$	−46494.6	−2.39661
$723$	15285.3	0.786262
$724$	24556.7	1.26056
$725$	617.464	0.0316304
$726$	39954.2	2.04248
$727$	1912.95	0.0975894	0.0487947	−	0.998809i	$-0.484462\pi$
$727$	1912.95	0.0975894	0.0487947	+	0.998809i	$0.484462\pi$
$728$	−1.26460	−6.43807e−5 0
$729$	−22932.1	−1.16507
$730$	−4765.40	−0.241610
$731$	−9209.44	−0.465969
$732$	35450.0	1.78999
$733$	2485.68	0.125254	0.0626268	−	0.998037i	$-0.480052\pi$
$733$	2485.68	0.125254	0.0626268	+	0.998037i	$0.480052\pi$
$734$	43937.8	2.20950
$735$	−24904.9	−1.24984
$736$	5905.06	0.295739
$737$	−987.000	−0.0493306
$738$	36418.1	1.81649
$739$	−14675.4	−0.730507	−0.365253	−	0.930908i	$-0.619018\pi$
$739$	−14675.4	−0.730507	−0.365253	+	0.930908i	$0.619018\pi$
$740$	16695.4	0.829370
$741$	−127.206	−0.00630640
$742$	24449.3	1.20965
$743$	14789.5	0.730247	0.365124	−	0.930959i	$-0.381027\pi$
$743$	14789.5	0.730247	0.365124	+	0.930959i	$0.381027\pi$
$744$	−423.886	−0.0208877
$745$	11627.1	0.571791
$746$	−53194.5	−2.61071
$747$	5494.08	0.269100
$748$	1457.87	0.0712635
$749$	−35008.2	−1.70784
$750$	−44865.3	−2.18433
$751$	11518.7	0.559684	0.279842	−	0.960046i	$-0.409718\pi$
$751$	11518.7	0.559684	0.279842	+	0.960046i	$0.409718\pi$
$752$	−5134.97	−0.249007
$753$	247.093	0.0119583
$754$	14.5184	0.000701233 0
$755$	−9177.86	−0.442406
$756$	3675.79	0.176835
$757$	29347.0	1.40903	0.704515	−	0.709689i	$-0.251164\pi$
$757$	29347.0	1.40903	0.704515	+	0.709689i	$0.251164\pi$
$758$	41807.3	2.00331
$759$	−357.289	−0.0170866
$760$	−542.041	−0.0258709
$761$	22782.9	1.08525	0.542627	−	0.839974i	$-0.317430\pi$
$761$	22782.9	1.08525	0.542627	+	0.839974i	$0.317430\pi$
$762$	−20569.2	−0.977880
$763$	−56014.3	−2.65774
$764$	−16960.8	−0.803170
$765$	25990.5	1.22835
$766$	−49451.1	−2.33256
$767$	−55.6450	−0.00261959
$768$	29979.7	1.40859
$769$	1003.80	0.0470713	0.0235356	−	0.999723i	$-0.492508\pi$
$769$	1003.80	0.0470713	0.0235356	+	0.999723i	$0.492508\pi$
$770$	−2186.91	−0.102352
$771$	45603.0	2.13016
$772$	18464.8	0.860832
$773$	−34247.7	−1.59354	−0.796768	−	0.604285i	$-0.793459\pi$
$773$	−34247.7	−1.59354	−0.796768	+	0.604285i	$0.793459\pi$
$774$	−12461.8	−0.578723
$775$	−3068.33	−0.142216
$776$	−407.143	−0.0188345
$777$	−39299.4	−1.81449
$778$	24671.2	1.13690
$779$	42020.8	1.93267
$780$	−77.2341	−0.00354541
$781$	1405.79	0.0644084
$782$	8027.49	0.367087
$783$	−509.019	−0.0232323
$784$	−20594.7	−0.938169
$785$	7250.19	0.329644
$786$	38859.9	1.76347
$787$	−22221.1	−1.00648	−0.503239	−	0.864148i	$-0.667858\pi$
$787$	−22221.1	−1.00648	−0.503239	+	0.864148i	$0.667858\pi$
$788$	−10294.6	−0.465391
$789$	23414.6	1.05650
$790$	24074.0	1.08419
$791$	−56558.0	−2.54231
$792$	23.7950	0.00106757
$793$	72.7768	0.00325899
$794$	−50147.4	−2.24139
$795$	18011.1	0.803505
$796$	−24855.5	−1.10676
$797$	−40017.3	−1.77853	−0.889264	−	0.457394i	$-0.848783\pi$
$797$	−40017.3	−1.77853	−0.889264	+	0.457394i	$0.848783\pi$
$798$	105780.	4.69246
$799$	−7066.89	−0.312902
$800$	−5466.52	−0.241588
$801$	−41063.5	−1.81137
$802$	−13689.5	−0.602733
$803$	241.379	0.0106078
$804$	28986.2	1.27147
$805$	−6057.43	−0.265213
$806$	−72.1454	−0.00315287
$807$	11240.5	0.490315
$808$	−159.355	−0.00693825
$809$	22723.4	0.987532	0.493766	−	0.869595i	$-0.335620\pi$
$809$	22723.4	0.987532	0.493766	+	0.869595i	$0.335620\pi$
$810$	−26983.0	−1.17048
$811$	21978.8	0.951639	0.475819	−	0.879543i	$-0.342152\pi$
$811$	21978.8	0.951639	0.475819	+	0.879543i	$0.342152\pi$
$812$	−6073.13	−0.262469
$813$	−40772.8	−1.75887
$814$	−1681.12	−0.0723874
$815$	−716.402	−0.0307908
$816$	41271.7	1.77059
$817$	−14379.0	−0.615739
$818$	−50783.4	−2.17066
$819$	94.6742	0.00403930
$820$	25513.2	1.08653
$821$	−11753.3	−0.499625	−0.249812	−	0.968294i	$-0.580369\pi$
$821$	−11753.3	−0.499625	−0.249812	+	0.968294i	$0.580369\pi$
$822$	−88569.6	−3.75817
$823$	−17183.9	−0.727817	−0.363908	−	0.931435i	$-0.618558\pi$
$823$	−17183.9	−0.727817	−0.363908	+	0.931435i	$0.618558\pi$
$824$	−658.827	−0.0278536
$825$	330.754	0.0139580
$826$	46272.4	1.94918
$827$	−21528.1	−0.905208	−0.452604	−	0.891712i	$-0.649505\pi$
$827$	−21528.1	−0.905208	−0.452604	+	0.891712i	$0.649505\pi$
$828$	5464.19	0.229340
$829$	−22252.0	−0.932262	−0.466131	−	0.884716i	$-0.654352\pi$
$829$	−22252.0	−0.932262	−0.466131	+	0.884716i	$0.654352\pi$
$830$	7651.48	0.319984
$831$	−1946.77	−0.0812669
$832$	−65.4370	−0.00272670
$833$	−28343.0	−1.17890
$834$	22763.8	0.945139
$835$	773.468	0.0320562
$836$	2276.23	0.0941686
$837$	2529.44	0.104457
$838$	52894.4	2.18044
$839$	−31496.9	−1.29606	−0.648030	−	0.761615i	$-0.724407\pi$
$839$	−31496.9	−1.29606	−0.648030	+	0.761615i	$0.724407\pi$
$840$	774.680	0.0318202
$841$	841.000	0.0344828
$842$	5997.80	0.245484
$843$	20253.9	0.827498
$844$	−26151.1	−1.06654
$845$	22373.5	0.910853
$846$	−9562.63	−0.388617
$847$	−34310.9	−1.39190
$848$	14894.0	0.603137
$849$	27975.7	1.13089
$850$	−7431.32	−0.299873
$851$	−4656.47	−0.187570
$852$	−41285.1	−1.66010
$853$	−27497.1	−1.10373	−0.551866	−	0.833933i	$-0.686084\pi$
$853$	−27497.1	−1.10373	−0.551866	+	0.833933i	$0.686084\pi$
$854$	−60518.6	−2.42495
$855$	40579.9	1.62316
$856$	530.487	0.0211818
$857$	−43763.2	−1.74437	−0.872184	−	0.489178i	$-0.837297\pi$
$857$	−43763.2	−1.74437	−0.872184	+	0.489178i	$0.837297\pi$
$858$	7.77701	0.000309444 0
$859$	−39640.7	−1.57453	−0.787266	−	0.616614i	$-0.788504\pi$
$859$	−39640.7	−1.57453	−0.787266	+	0.616614i	$0.788504\pi$
$860$	−8730.31	−0.346164
$861$	−60055.7	−2.37711
$862$	−40526.8	−1.60133
$863$	−36653.9	−1.44579	−0.722893	−	0.690960i	$-0.757188\pi$
$863$	−36653.9	−1.44579	−0.722893	+	0.690960i	$0.757188\pi$
$864$	4506.44	0.177444
$865$	10755.3	0.422762
$866$	−6305.61	−0.247429
$867$	19922.9	0.780410
$868$	30178.8	1.18011
$869$	−1219.41	−0.0476013
$870$	−8893.82	−0.346585
$871$	59.5070	0.00231495
$872$	848.796	0.0329632
$873$	30480.7	1.18169
$874$	12533.6	0.485075
$875$	38528.4	1.48857
$876$	−7088.83	−0.273412
$877$	23677.4	0.911662	0.455831	−	0.890066i	$-0.349342\pi$
$877$	23677.4	0.911662	0.455831	+	0.890066i	$0.349342\pi$
$878$	28902.2	1.11094
$879$	15858.1	0.608510
$880$	−1332.22	−0.0510329
$881$	24098.9	0.921579	0.460790	−	0.887509i	$-0.347566\pi$
$881$	24098.9	0.921579	0.460790	+	0.887509i	$0.347566\pi$
$882$	−38352.6	−1.46417
$883$	−7641.81	−0.291243	−0.145621	−	0.989340i	$-0.546518\pi$
$883$	−7641.81	−0.291243	−0.145621	+	0.989340i	$0.546518\pi$
$884$	−87.8962	−0.00334420
$885$	34087.5	1.29473
$886$	15004.3	0.568939
$887$	−32190.0	−1.21853	−0.609265	−	0.792967i	$-0.708535\pi$
$887$	−32190.0	−1.21853	−0.609265	+	0.792967i	$0.708535\pi$
$888$	595.512	0.0225046
$889$	17664.0	0.666401
$890$	−57188.2	−2.15388
$891$	1366.76	0.0513895
$892$	−34778.2	−1.30545
$893$	−11033.8	−0.413474
$894$	34383.4	1.28630
$895$	8619.34	0.321914
$896$	1297.15	0.0483647
$897$	21.5412	0.000801828 0
$898$	−12009.8	−0.446294
$899$	−4179.13	−0.155041
$900$	−5058.38	−0.187348
$901$	20497.5	0.757903
$902$	−2569.02	−0.0948327
$903$	20550.4	0.757335
$904$	857.035	0.0315316
$905$	−30882.8	−1.13434
$906$	−27140.6	−0.995238
$907$	−4953.70	−0.181350	−0.0906752	−	0.995881i	$-0.528903\pi$
$907$	−4953.70	−0.181350	−0.0906752	+	0.995881i	$0.528903\pi$
$908$	32810.6	1.19918
$909$	11930.1	0.435311
$910$	131.851	0.00480308
$911$	28587.7	1.03968	0.519842	−	0.854262i	$-0.325991\pi$
$911$	28587.7	1.03968	0.519842	+	0.854262i	$0.325991\pi$
$912$	64439.0	2.33968
$913$	−387.566	−0.0140488
$914$	73832.3	2.67194
$915$	−44582.3	−1.61076
$916$	11097.8	0.400306
$917$	−33371.2	−1.20176
$918$	6126.16	0.220254
$919$	30049.3	1.07860	0.539300	−	0.842114i	$-0.318689\pi$
$919$	30049.3	1.07860	0.539300	+	0.842114i	$0.318689\pi$
$920$	91.7895	0.00328936
$921$	80.2279	0.00287036
$922$	−35414.6	−1.26499
$923$	−84.7559	−0.00302251
$924$	−3253.16	−0.115824
$925$	4310.65	0.153225
$926$	23657.1	0.839547
$927$	49323.1	1.74755
$928$	−7445.52	−0.263374
$929$	15047.2	0.531413	0.265706	−	0.964054i	$-0.414395\pi$
$929$	15047.2	0.531413	0.265706	+	0.964054i	$0.414395\pi$
$930$	44195.5	1.55831
$931$	−44253.0	−1.55782
$932$	−5724.41	−0.201190
$933$	52302.4	1.83527
$934$	−74805.7	−2.62068
$935$	−1833.43	−0.0641280
$936$	−1.43462	−5.00982e−5 0
$937$	−45834.2	−1.59801	−0.799006	−	0.601324i	$-0.794640\pi$
$937$	−45834.2	−1.59801	−0.799006	+	0.601324i	$0.794640\pi$
$938$	−49483.9	−1.72250
$939$	29616.7	1.02929
$940$	−6699.23	−0.232452
$941$	−16093.5	−0.557528	−0.278764	−	0.960360i	$-0.589925\pi$
$941$	−16093.5	−0.557528	−0.278764	+	0.960360i	$0.589925\pi$
$942$	21440.1	0.741567
$943$	−7115.83	−0.245730
$944$	28188.1	0.971869
$945$	−4622.71	−0.159129
$946$	879.090	0.0302132
$947$	17780.7	0.610133	0.305066	−	0.952331i	$-0.401321\pi$
$947$	17780.7	0.610133	0.305066	+	0.952331i	$0.401321\pi$
$948$	35811.5	1.22690
$949$	−14.5530	−0.000497797 0
$950$	−11602.8	−0.396257
$951$	2378.19	0.0810915
$952$	881.624	0.0300143
$953$	−42244.5	−1.43592	−0.717960	−	0.696084i	$-0.754924\pi$
$953$	−42244.5	−1.43592	−0.717960	+	0.696084i	$0.754924\pi$
$954$	27736.4	0.941298
$955$	21330.1	0.722750
$956$	−53548.0	−1.81158
$957$	450.494	0.0152167
$958$	−57062.8	−1.92444
$959$	76059.7	2.56110
$960$	40086.0	1.34768
$961$	−9023.93	−0.302908
$962$	101.356	0.00339694
$963$	−39714.9	−1.32897
$964$	16490.4	0.550956
$965$	−23221.5	−0.774639
$966$	−17912.9	−0.596624
$967$	5413.56	0.180029	0.0900147	−	0.995940i	$-0.471309\pi$
$967$	5413.56	0.180029	0.0900147	+	0.995940i	$0.471309\pi$
$968$	519.921	0.0172633
$969$	88682.8	2.94004
$970$	42449.8	1.40513
$971$	−29069.3	−0.960739	−0.480370	−	0.877066i	$-0.659497\pi$
$971$	−29069.3	−0.960739	−0.480370	+	0.877066i	$0.659497\pi$
$972$	−43976.5	−1.45118
$973$	−19548.6	−0.644089
$974$	−62681.6	−2.06206
$975$	−19.9414	−0.000655012 0
$976$	−36866.6	−1.20909
$977$	53235.7	1.74325	0.871627	−	0.490169i	$-0.163065\pi$
$977$	53235.7	1.74325	0.871627	+	0.490169i	$0.163065\pi$
$978$	−2118.53	−0.0692670
$979$	2896.72	0.0945656
$980$	−26868.5	−0.875797
$981$	−63545.1	−2.06813
$982$	17289.6	0.561847
$983$	59678.3	1.93636	0.968180	−	0.250254i	$-0.0805143\pi$
$983$	59678.3	1.93636	0.968180	+	0.250254i	$0.0805143\pi$
$984$	910.038	0.0294827
$985$	12946.5	0.418793
$986$	−10121.6	−0.326915
$987$	15769.4	0.508557
$988$	−137.236	−0.00441907
$989$	2434.96	0.0782882
$990$	−2480.93	−0.0796455
$991$	−9000.25	−0.288499	−0.144249	−	0.989541i	$-0.546077\pi$
$991$	−9000.25	−0.288499	−0.144249	+	0.989541i	$0.546077\pi$
$992$	36998.5	1.18418
$993$	31170.1	0.996126
$994$	70480.0	2.24899
$995$	31258.6	0.995944
$996$	11382.0	0.362102
$997$	−4417.52	−0.140325	−0.0701627	−	0.997536i	$-0.522352\pi$
$997$	−4417.52	−0.140325	−0.0701627	+	0.997536i	$0.522352\pi$
$998$	−28989.9	−0.919497
$999$	−3553.58	−0.112543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.6	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.6	✓	35	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-4.01219 q^{2} +7.50590 q^{3} +8.09767 q^{4} -10.1837 q^{5} -30.1151 q^{6} +25.8615 q^{7} -0.391885 q^{8} +29.3385 q^{9} +O(q^{10})\)	\(q-4.01219 q^{2} +7.50590 q^{3} +8.09767 q^{4} -10.1837 q^{5} -30.1151 q^{6} +25.8615 q^{7} -0.391885 q^{8} +29.3385 q^{9} +40.8590 q^{10} -2.06961 q^{11} +60.7803 q^{12} +0.124778 q^{13} -103.761 q^{14} -76.4379 q^{15} -63.2091 q^{16} -86.9902 q^{17} -117.712 q^{18} -135.821 q^{19} -82.4644 q^{20} +194.114 q^{21} +8.30367 q^{22} +23.0000 q^{23} -2.94145 q^{24} -21.2919 q^{25} -0.500635 q^{26} +17.5524 q^{27} +209.418 q^{28} -29.0000 q^{29} +306.684 q^{30} +144.108 q^{31} +256.742 q^{32} -15.5343 q^{33} +349.021 q^{34} -263.367 q^{35} +237.573 q^{36} -202.455 q^{37} +544.940 q^{38} +0.936574 q^{39} +3.99085 q^{40} -309.384 q^{41} -778.822 q^{42} +105.868 q^{43} -16.7590 q^{44} -298.775 q^{45} -92.2804 q^{46} +81.2378 q^{47} -474.441 q^{48} +325.819 q^{49} +85.4271 q^{50} -652.939 q^{51} +1.01042 q^{52} -235.630 q^{53} -70.4235 q^{54} +21.0763 q^{55} -10.1348 q^{56} -1019.46 q^{57} +116.354 q^{58} -445.950 q^{59} -618.969 q^{60} +583.248 q^{61} -578.188 q^{62} +758.738 q^{63} -524.425 q^{64} -1.27071 q^{65} +62.3265 q^{66} +476.901 q^{67} -704.418 q^{68} +172.636 q^{69} +1056.68 q^{70} -679.251 q^{71} -11.4973 q^{72} -116.630 q^{73} +812.289 q^{74} -159.815 q^{75} -1099.83 q^{76} -53.5233 q^{77} -3.75772 q^{78} +589.196 q^{79} +643.703 q^{80} -660.393 q^{81} +1241.31 q^{82} +187.265 q^{83} +1571.87 q^{84} +885.884 q^{85} -424.761 q^{86} -217.671 q^{87} +0.811050 q^{88} -1399.65 q^{89} +1198.74 q^{90} +3.22696 q^{91} +186.246 q^{92} +1081.66 q^{93} -325.942 q^{94} +1383.16 q^{95} +1927.08 q^{96} +1038.93 q^{97} -1307.25 q^{98} -60.7192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * q^99

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