LMFDB - Embedded newform 4007.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74088 q^{2} +3.29634 q^{3} +5.51241 q^{4} -3.80383 q^{5} -9.03487 q^{6} -0.926403 q^{7} -9.62710 q^{8} +7.86587 q^{9} +O(q^{10})$	\(q-2.74088 q^{2} +3.29634 q^{3} +5.51241 q^{4} -3.80383 q^{5} -9.03487 q^{6} -0.926403 q^{7} -9.62710 q^{8} +7.86587 q^{9} +10.4258 q^{10} -4.12512 q^{11} +18.1708 q^{12} +0.363653 q^{13} +2.53916 q^{14} -12.5387 q^{15} +15.3619 q^{16} +3.51722 q^{17} -21.5594 q^{18} +4.30590 q^{19} -20.9683 q^{20} -3.05374 q^{21} +11.3065 q^{22} -8.25212 q^{23} -31.7342 q^{24} +9.46915 q^{25} -0.996729 q^{26} +16.0396 q^{27} -5.10671 q^{28} -1.67265 q^{29} +34.3672 q^{30} -3.99121 q^{31} -22.8508 q^{32} -13.5978 q^{33} -9.64028 q^{34} +3.52388 q^{35} +43.3600 q^{36} -1.40804 q^{37} -11.8020 q^{38} +1.19872 q^{39} +36.6199 q^{40} +10.1549 q^{41} +8.36993 q^{42} +3.20843 q^{43} -22.7394 q^{44} -29.9205 q^{45} +22.6181 q^{46} +2.70024 q^{47} +50.6380 q^{48} -6.14178 q^{49} -25.9538 q^{50} +11.5940 q^{51} +2.00461 q^{52} +7.94525 q^{53} -43.9626 q^{54} +15.6913 q^{55} +8.91857 q^{56} +14.1937 q^{57} +4.58454 q^{58} +2.03892 q^{59} -69.1187 q^{60} -5.95545 q^{61} +10.9394 q^{62} -7.28697 q^{63} +31.9076 q^{64} -1.38328 q^{65} +37.2700 q^{66} +11.9686 q^{67} +19.3884 q^{68} -27.2018 q^{69} -9.65853 q^{70} +6.69338 q^{71} -75.7256 q^{72} -10.9491 q^{73} +3.85927 q^{74} +31.2136 q^{75} +23.7359 q^{76} +3.82152 q^{77} -3.28556 q^{78} -13.5818 q^{79} -58.4340 q^{80} +29.2744 q^{81} -27.8333 q^{82} -12.3014 q^{83} -16.8335 q^{84} -13.3789 q^{85} -8.79392 q^{86} -5.51364 q^{87} +39.7130 q^{88} -12.1410 q^{89} +82.0084 q^{90} -0.336889 q^{91} -45.4891 q^{92} -13.1564 q^{93} -7.40104 q^{94} -16.3789 q^{95} -75.3242 q^{96} +5.22820 q^{97} +16.8339 q^{98} -32.4477 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.74088	−1.93809	−0.969047	−	0.246877i	$-0.920596\pi$
$2$	−2.74088	−1.93809	−0.969047	+	0.246877i	$0.920596\pi$
$3$	3.29634	1.90314	0.951572	−	0.307426i	$-0.0994675\pi$
$3$	3.29634	1.90314	0.951572	+	0.307426i	$0.0994675\pi$
$4$	5.51241	2.75621
$5$	−3.80383	−1.70113	−0.850563	−	0.525873i	$-0.823739\pi$
$5$	−3.80383	−1.70113	−0.850563	+	0.525873i	$0.823739\pi$
$6$	−9.03487	−3.68847
$7$	−0.926403	−0.350147	−0.175074	−	0.984555i	$-0.556016\pi$
$7$	−0.926403	−0.350147	−0.175074	+	0.984555i	$0.556016\pi$
$8$	−9.62710	−3.40369
$9$	7.86587	2.62196
$10$	10.4258	3.29694
$11$	−4.12512	−1.24377	−0.621886	−	0.783108i	$-0.713633\pi$
$11$	−4.12512	−1.24377	−0.621886	+	0.783108i	$0.713633\pi$
$12$	18.1708	5.24546
$13$	0.363653	0.100859	0.0504296	−	0.998728i	$-0.483941\pi$
$13$	0.363653	0.100859	0.0504296	+	0.998728i	$0.483941\pi$
$14$	2.53916	0.678618
$15$	−12.5387	−3.23749
$16$	15.3619	3.84047
$17$	3.51722	0.853052	0.426526	−	0.904475i	$-0.359737\pi$
$17$	3.51722	0.853052	0.426526	+	0.904475i	$0.359737\pi$
$18$	−21.5594	−5.08160
$19$	4.30590	0.987842	0.493921	−	0.869507i	$-0.335563\pi$
$19$	4.30590	0.987842	0.493921	+	0.869507i	$0.335563\pi$
$20$	−20.9683	−4.68866
$21$	−3.05374	−0.666381
$22$	11.3065	2.41055
$23$	−8.25212	−1.72069	−0.860343	−	0.509715i	$-0.829751\pi$
$23$	−8.25212	−1.72069	−0.860343	+	0.509715i	$0.829751\pi$
$24$	−31.7342	−6.47772
$25$	9.46915	1.89383
$26$	−0.996729	−0.195475
$27$	16.0396	3.08682
$28$	−5.10671	−0.965078
$29$	−1.67265	−0.310604	−0.155302	−	0.987867i	$-0.549635\pi$
$29$	−1.67265	−0.310604	−0.155302	+	0.987867i	$0.549635\pi$
$30$	34.3672	6.27456
$31$	−3.99121	−0.716843	−0.358421	−	0.933560i	$-0.616685\pi$
$31$	−3.99121	−0.716843	−0.358421	+	0.933560i	$0.616685\pi$
$32$	−22.8508	−4.03950
$33$	−13.5978	−2.36708
$34$	−9.64028	−1.65330
$35$	3.52388	0.595645
$36$	43.3600	7.22666
$37$	−1.40804	−0.231480	−0.115740	−	0.993280i	$-0.536924\pi$
$37$	−1.40804	−0.231480	−0.115740	+	0.993280i	$0.536924\pi$
$38$	−11.8020	−1.91453
$39$	1.19872	0.191950
$40$	36.6199	5.79011
$41$	10.1549	1.58593	0.792965	−	0.609268i	$-0.208537\pi$
$41$	10.1549	1.58593	0.792965	+	0.609268i	$0.208537\pi$
$42$	8.36993	1.29151
$43$	3.20843	0.489281	0.244640	−	0.969614i	$-0.421330\pi$
$43$	3.20843	0.489281	0.244640	+	0.969614i	$0.421330\pi$
$44$	−22.7394	−3.42809
$45$	−29.9205	−4.46028
$46$	22.6181	3.33485
$47$	2.70024	0.393871	0.196936	−	0.980416i	$-0.436901\pi$
$47$	2.70024	0.393871	0.196936	+	0.980416i	$0.436901\pi$
$48$	50.6380	7.30897
$49$	−6.14178	−0.877397
$50$	−25.9538	−3.67042
$51$	11.5940	1.62348
$52$	2.00461	0.277989
$53$	7.94525	1.09136	0.545682	−	0.837992i	$-0.316271\pi$
$53$	7.94525	1.09136	0.545682	+	0.837992i	$0.316271\pi$
$54$	−43.9626	−5.98255
$55$	15.6913	2.11581
$56$	8.91857	1.19179
$57$	14.1937	1.88001
$58$	4.58454	0.601980
$59$	2.03892	0.265445	0.132722	−	0.991153i	$-0.457628\pi$
$59$	2.03892	0.265445	0.132722	+	0.991153i	$0.457628\pi$
$60$	−69.1187	−8.92319
$61$	−5.95545	−0.762518	−0.381259	−	0.924468i	$-0.624509\pi$
$61$	−5.95545	−0.762518	−0.381259	+	0.924468i	$0.624509\pi$
$62$	10.9394	1.38931
$63$	−7.28697	−0.918072
$64$	31.9076	3.98845
$65$	−1.38328	−0.171574
$66$	37.2700	4.58762
$67$	11.9686	1.46220	0.731098	−	0.682272i	$-0.239008\pi$
$67$	11.9686	1.46220	0.731098	+	0.682272i	$0.239008\pi$
$68$	19.3884	2.35119
$69$	−27.2018	−3.27471
$70$	−9.65853	−1.15442
$71$	6.69338	0.794359	0.397179	−	0.917741i	$-0.369989\pi$
$71$	6.69338	0.794359	0.397179	+	0.917741i	$0.369989\pi$
$72$	−75.7256	−8.92434
$73$	−10.9491	−1.28150	−0.640748	−	0.767751i	$-0.721376\pi$
$73$	−10.9491	−1.28150	−0.640748	+	0.767751i	$0.721376\pi$
$74$	3.85927	0.448631
$75$	31.2136	3.60423
$76$	23.7359	2.72270
$77$	3.82152	0.435503
$78$	−3.28556	−0.372016
$79$	−13.5818	−1.52808	−0.764038	−	0.645171i	$-0.776786\pi$
$79$	−13.5818	−1.52808	−0.764038	+	0.645171i	$0.776786\pi$
$80$	−58.4340	−6.53312
$81$	29.2744	3.25271
$82$	−27.8333	−3.07368
$83$	−12.3014	−1.35025	−0.675127	−	0.737701i	$-0.735911\pi$
$83$	−12.3014	−1.35025	−0.675127	+	0.737701i	$0.735911\pi$
$84$	−16.8335	−1.83668
$85$	−13.3789	−1.45115
$86$	−8.79392	−0.948272
$87$	−5.51364	−0.591124
$88$	39.7130	4.23342
$89$	−12.1410	−1.28695	−0.643474	−	0.765468i	$-0.722508\pi$
$89$	−12.1410	−1.28695	−0.643474	+	0.765468i	$0.722508\pi$
$90$	82.0084	8.64444
$91$	−0.336889	−0.0353156
$92$	−45.4891	−4.74257
$93$	−13.1564	−1.36426
$94$	−7.40104	−0.763359
$95$	−16.3789	−1.68044
$96$	−75.3242	−7.68775
$97$	5.22820	0.530843	0.265421	−	0.964132i	$-0.414489\pi$
$97$	5.22820	0.530843	0.265421	+	0.964132i	$0.414489\pi$
$98$	16.8339	1.70048
$99$	−32.4477	−3.26112
$100$	52.1979	5.21979
$101$	3.91790	0.389845	0.194923	−	0.980819i	$-0.437554\pi$
$101$	3.91790	0.389845	0.194923	+	0.980819i	$0.437554\pi$
$102$	−31.7777	−3.14646
$103$	1.06884	0.105316	0.0526580	−	0.998613i	$-0.483231\pi$
$103$	1.06884	0.105316	0.0526580	+	0.998613i	$0.483231\pi$
$104$	−3.50092	−0.343294
$105$	11.6159	1.13360
$106$	−21.7770	−2.11517
$107$	19.9076	1.92454	0.962271	−	0.272093i	$-0.0877158\pi$
$107$	19.9076	1.92454	0.962271	+	0.272093i	$0.0877158\pi$
$108$	88.4169	8.50792
$109$	17.3705	1.66379	0.831895	−	0.554933i	$-0.187256\pi$
$109$	17.3705	1.66379	0.831895	+	0.554933i	$0.187256\pi$
$110$	−43.0079	−4.10064
$111$	−4.64138	−0.440541
$112$	−14.2313	−1.34473
$113$	9.20258	0.865706	0.432853	−	0.901465i	$-0.357507\pi$
$113$	9.20258	0.865706	0.432853	+	0.901465i	$0.357507\pi$
$114$	−38.9033	−3.64363
$115$	31.3897	2.92710
$116$	−9.22036	−0.856089
$117$	2.86045	0.264449
$118$	−5.58843	−0.514457
$119$	−3.25837	−0.298694
$120$	120.712	11.0194
$121$	6.01664	0.546967
$122$	16.3232	1.47783
$123$	33.4740	3.01825
$124$	−22.0012	−1.97577
$125$	−16.9999	−1.52052
$126$	19.9727	1.77931
$127$	14.1687	1.25727	0.628636	−	0.777700i	$-0.283614\pi$
$127$	14.1687	1.25727	0.628636	+	0.777700i	$0.283614\pi$
$128$	−41.7532	−3.69050
$129$	10.5761	0.931172
$130$	3.79139	0.332527
$131$	−12.4991	−1.09205	−0.546025	−	0.837769i	$-0.683860\pi$
$131$	−12.4991	−1.09205	−0.546025	+	0.837769i	$0.683860\pi$
$132$	−74.9568	−6.52415
$133$	−3.98900	−0.345890
$134$	−32.8045	−2.83387
$135$	−61.0119	−5.25107
$136$	−33.8607	−2.90353
$137$	6.70127	0.572528	0.286264	−	0.958151i	$-0.407587\pi$
$137$	6.70127	0.572528	0.286264	+	0.958151i	$0.407587\pi$
$138$	74.5569	6.34670
$139$	16.4452	1.39486	0.697430	−	0.716653i	$-0.254327\pi$
$139$	16.4452	1.39486	0.697430	+	0.716653i	$0.254327\pi$
$140$	19.4251	1.64172
$141$	8.90093	0.749594
$142$	−18.3458	−1.53954
$143$	−1.50011	−0.125446
$144$	120.835	10.0696
$145$	6.36250	0.528377
$146$	30.0102	2.48366
$147$	−20.2454	−1.66981
$148$	−7.76170	−0.638008
$149$	23.9051	1.95838	0.979190	−	0.202945i	$-0.0650513\pi$
$149$	23.9051	1.95838	0.979190	+	0.202945i	$0.0650513\pi$
$150$	−85.5526	−6.98534
$151$	5.55055	0.451698	0.225849	−	0.974162i	$-0.427484\pi$
$151$	5.55055	0.451698	0.225849	+	0.974162i	$0.427484\pi$
$152$	−41.4534	−3.36231
$153$	27.6660	2.23667
$154$	−10.4743	−0.844046
$155$	15.1819	1.21944
$156$	6.60787	0.529053
$157$	−0.943906	−0.0753319	−0.0376660	−	0.999290i	$-0.511992\pi$
$157$	−0.943906	−0.0753319	−0.0376660	+	0.999290i	$0.511992\pi$
$158$	37.2262	2.96155
$159$	26.1903	2.07702
$160$	86.9208	6.87170
$161$	7.64479	0.602494
$162$	−80.2375	−6.30405
$163$	5.29969	0.415104	0.207552	−	0.978224i	$-0.433450\pi$
$163$	5.29969	0.415104	0.207552	+	0.978224i	$0.433450\pi$
$164$	55.9780	4.37115
$165$	51.7238	4.02670
$166$	33.7167	2.61692
$167$	7.26499	0.562182	0.281091	−	0.959681i	$-0.409304\pi$
$167$	7.26499	0.562182	0.281091	+	0.959681i	$0.409304\pi$
$168$	29.3987	2.26816
$169$	−12.8678	−0.989827
$170$	36.6700	2.81246
$171$	33.8697	2.59008
$172$	17.6862	1.34856
$173$	13.9900	1.06364	0.531819	−	0.846858i	$-0.321509\pi$
$173$	13.9900	1.06364	0.531819	+	0.846858i	$0.321509\pi$
$174$	15.1122	1.14565
$175$	−8.77225	−0.663120
$176$	−63.3697	−4.77667
$177$	6.72098	0.505180
$178$	33.2771	2.49423
$179$	−8.06027	−0.602453	−0.301226	−	0.953553i	$-0.597396\pi$
$179$	−8.06027	−0.602453	−0.301226	+	0.953553i	$0.597396\pi$
$180$	−164.934	−12.2935
$181$	−20.3489	−1.51252	−0.756259	−	0.654272i	$-0.772975\pi$
$181$	−20.3489	−1.51252	−0.756259	+	0.654272i	$0.772975\pi$
$182$	0.923372	0.0684449
$183$	−19.6312	−1.45118
$184$	79.4440	5.85669
$185$	5.35595	0.393777
$186$	36.0601	2.64405
$187$	−14.5090	−1.06100
$188$	14.8849	1.08559
$189$	−14.8591	−1.08084
$190$	44.8927	3.25686
$191$	3.59672	0.260250	0.130125	−	0.991498i	$-0.458462\pi$
$191$	3.59672	0.260250	0.130125	+	0.991498i	$0.458462\pi$
$192$	105.178	7.59060
$193$	18.0307	1.29788	0.648939	−	0.760840i	$-0.275213\pi$
$193$	18.0307	1.29788	0.648939	+	0.760840i	$0.275213\pi$
$194$	−14.3299	−1.02882
$195$	−4.55975	−0.326530
$196$	−33.8560	−2.41829
$197$	20.8210	1.48344	0.741718	−	0.670711i	$-0.234011\pi$
$197$	20.8210	1.48344	0.741718	+	0.670711i	$0.234011\pi$
$198$	88.9352	6.32035
$199$	15.6749	1.11117	0.555583	−	0.831461i	$-0.312495\pi$
$199$	15.6749	1.11117	0.555583	+	0.831461i	$0.312495\pi$
$200$	−91.1605	−6.44602
$201$	39.4526	2.78277
$202$	−10.7385	−0.755557
$203$	1.54955	0.108757
$204$	63.9108	4.47465
$205$	−38.6276	−2.69787
$206$	−2.92956	−0.204112
$207$	−64.9101	−4.51157
$208$	5.58639	0.387347
$209$	−17.7624	−1.22865
$210$	−31.8378	−2.19702
$211$	2.11160	0.145369	0.0726844	−	0.997355i	$-0.476843\pi$
$211$	2.11160	0.145369	0.0726844	+	0.997355i	$0.476843\pi$
$212$	43.7975	3.00803
$213$	22.0637	1.51178
$214$	−54.5644	−3.72994
$215$	−12.2043	−0.832329
$216$	−154.415	−10.5066
$217$	3.69747	0.251001
$218$	−47.6104	−3.22458
$219$	−36.0920	−2.43887
$220$	86.4968	5.83162
$221$	1.27905	0.0860382
$222$	12.7215	0.853809
$223$	−23.6607	−1.58444	−0.792220	−	0.610236i	$-0.791075\pi$
$223$	−23.6607	−1.58444	−0.792220	+	0.610236i	$0.791075\pi$
$224$	21.1691	1.41442
$225$	74.4832	4.96554
$226$	−25.2231	−1.67782
$227$	8.08842	0.536847	0.268423	−	0.963301i	$-0.413497\pi$
$227$	8.08842	0.536847	0.268423	+	0.963301i	$0.413497\pi$
$228$	78.2417	5.18169
$229$	−0.695733	−0.0459754	−0.0229877	−	0.999736i	$-0.507318\pi$
$229$	−0.695733	−0.0459754	−0.0229877	+	0.999736i	$0.507318\pi$
$230$	−86.0353	−5.67300
$231$	12.5971	0.828825
$232$	16.1028	1.05720
$233$	18.8130	1.23248	0.616242	−	0.787557i	$-0.288654\pi$
$233$	18.8130	1.23248	0.616242	+	0.787557i	$0.288654\pi$
$234$	−7.84014	−0.512526
$235$	−10.2713	−0.670025
$236$	11.2394	0.731621
$237$	−44.7704	−2.90815
$238$	8.93078	0.578897
$239$	−1.12568	−0.0728144	−0.0364072	−	0.999337i	$-0.511591\pi$
$239$	−1.12568	−0.0728144	−0.0364072	+	0.999337i	$0.511591\pi$
$240$	−192.619	−12.4335
$241$	24.2677	1.56322	0.781611	−	0.623766i	$-0.214398\pi$
$241$	24.2677	1.56322	0.781611	+	0.623766i	$0.214398\pi$
$242$	−16.4909	−1.06007
$243$	48.3795	3.10355
$244$	−32.8289	−2.10166
$245$	23.3623	1.49256
$246$	−91.7482	−5.84965
$247$	1.56585	0.0996330
$248$	38.4238	2.43991
$249$	−40.5496	−2.56973
$250$	46.5947	2.94691
$251$	5.08718	0.321100	0.160550	−	0.987028i	$-0.448673\pi$
$251$	5.08718	0.321100	0.160550	+	0.987028i	$0.448673\pi$
$252$	−40.1688	−2.53040
$253$	34.0410	2.14014
$254$	−38.8348	−2.43671
$255$	−44.1016	−2.76175
$256$	50.6253	3.16408
$257$	15.5151	0.967806	0.483903	−	0.875122i	$-0.339219\pi$
$257$	15.5151	0.967806	0.483903	+	0.875122i	$0.339219\pi$
$258$	−28.9878	−1.80470
$259$	1.30441	0.0810522
$260$	−7.62519	−0.472894
$261$	−13.1569	−0.814391
$262$	34.2585	2.11649
$263$	−5.98648	−0.369142	−0.184571	−	0.982819i	$-0.559090\pi$
$263$	−5.98648	−0.369142	−0.184571	+	0.982819i	$0.559090\pi$
$264$	130.908	8.05680
$265$	−30.2224	−1.85655
$266$	10.9334	0.670368
$267$	−40.0210	−2.44925
$268$	65.9758	4.03012
$269$	15.0838	0.919676	0.459838	−	0.888003i	$-0.347907\pi$
$269$	15.0838	0.919676	0.459838	+	0.888003i	$0.347907\pi$
$270$	167.226	10.1771
$271$	13.9580	0.847890	0.423945	−	0.905688i	$-0.360645\pi$
$271$	13.9580	0.847890	0.423945	+	0.905688i	$0.360645\pi$
$272$	54.0312	3.27612
$273$	−1.11050	−0.0672106
$274$	−18.3674	−1.10961
$275$	−39.0614	−2.35549
$276$	−149.948	−9.02579
$277$	7.64144	0.459130	0.229565	−	0.973293i	$-0.426270\pi$
$277$	7.64144	0.459130	0.229565	+	0.973293i	$0.426270\pi$
$278$	−45.0742	−2.70337
$279$	−31.3944	−1.87953
$280$	−33.9248	−2.02739
$281$	−7.30984	−0.436069	−0.218034	−	0.975941i	$-0.569964\pi$
$281$	−7.30984	−0.436069	−0.218034	+	0.975941i	$0.569964\pi$
$282$	−24.3964	−1.45278
$283$	−2.85939	−0.169973	−0.0849866	−	0.996382i	$-0.527085\pi$
$283$	−2.85939	−0.169973	−0.0849866	+	0.996382i	$0.527085\pi$
$284$	36.8967	2.18942
$285$	−53.9906	−3.19813
$286$	4.11163	0.243126
$287$	−9.40753	−0.555309
$288$	−179.742	−10.5914
$289$	−4.62913	−0.272302
$290$	−17.4388	−1.02404
$291$	17.2339	1.01027
$292$	−60.3560	−3.53207
$293$	−22.0448	−1.28787	−0.643936	−	0.765080i	$-0.722700\pi$
$293$	−22.0448	−1.28787	−0.643936	+	0.765080i	$0.722700\pi$
$294$	55.4902	3.23625
$295$	−7.75571	−0.451555
$296$	13.5553	0.787888
$297$	−66.1653	−3.83930
$298$	−65.5209	−3.79552
$299$	−3.00091	−0.173547
$300$	172.062	9.93401
$301$	−2.97230	−0.171320
$302$	−15.2134	−0.875432
$303$	12.9147	0.741932
$304$	66.1468	3.79378
$305$	22.6536	1.29714
$306$	−75.8293	−4.33487
$307$	−12.9660	−0.740006	−0.370003	−	0.929031i	$-0.620643\pi$
$307$	−12.9660	−0.740006	−0.370003	+	0.929031i	$0.620643\pi$
$308$	21.0658	1.20034
$309$	3.52327	0.200432
$310$	−41.6118	−2.36339
$311$	12.0436	0.682932	0.341466	−	0.939894i	$-0.389077\pi$
$311$	12.0436	0.682932	0.341466	+	0.939894i	$0.389077\pi$
$312$	−11.5402	−0.653338
$313$	0.760696	0.0429971	0.0214985	−	0.999769i	$-0.493156\pi$
$313$	0.760696	0.0429971	0.0214985	+	0.999769i	$0.493156\pi$
$314$	2.58713	0.146000
$315$	27.7184	1.56176
$316$	−74.8687	−4.21169
$317$	2.42984	0.136473	0.0682367	−	0.997669i	$-0.478263\pi$
$317$	2.42984	0.136473	0.0682367	+	0.997669i	$0.478263\pi$
$318$	−71.7844	−4.02547
$319$	6.89991	0.386321
$320$	−121.371	−6.78486
$321$	65.6223	3.66268
$322$	−20.9534	−1.16769
$323$	15.1448	0.842681
$324$	161.372	8.96513
$325$	3.44349	0.191010
$326$	−14.5258	−0.804510
$327$	57.2590	3.16643
$328$	−97.7622	−5.39802
$329$	−2.50151	−0.137913
$330$	−141.769	−7.80411
$331$	−35.1690	−1.93306	−0.966531	−	0.256552i	$-0.917414\pi$
$331$	−35.1690	−1.93306	−0.966531	+	0.256552i	$0.917414\pi$
$332$	−67.8104	−3.72158
$333$	−11.0755	−0.606932
$334$	−19.9125	−1.08956
$335$	−45.5265	−2.48738
$336$	−46.9112	−2.55922
$337$	7.19695	0.392043	0.196022	−	0.980600i	$-0.437198\pi$
$337$	7.19695	0.392043	0.196022	+	0.980600i	$0.437198\pi$
$338$	35.2690	1.91838
$339$	30.3348	1.64756
$340$	−73.7502	−3.99967
$341$	16.4642	0.891589
$342$	−92.8327	−5.01982
$343$	12.1746	0.657365
$344$	−30.8879	−1.66536
$345$	103.471	5.57070
$346$	−38.3448	−2.06143
$347$	30.2373	1.62323	0.811613	−	0.584196i	$-0.198590\pi$
$347$	30.2373	1.62323	0.811613	+	0.584196i	$0.198590\pi$
$348$	−30.3935	−1.62926
$349$	23.9020	1.27945	0.639723	−	0.768605i	$-0.279049\pi$
$349$	23.9020	1.27945	0.639723	+	0.768605i	$0.279049\pi$
$350$	24.0437	1.28519
$351$	5.83284	0.311334
$352$	94.2626	5.02421
$353$	34.0574	1.81269	0.906345	−	0.422538i	$-0.138861\pi$
$353$	34.0574	1.81269	0.906345	+	0.422538i	$0.138861\pi$
$354$	−18.4214	−0.979086
$355$	−25.4605	−1.35130
$356$	−66.9265	−3.54710
$357$	−10.7407	−0.568458
$358$	22.0922	1.16761
$359$	−22.2334	−1.17343	−0.586716	−	0.809793i	$-0.699580\pi$
$359$	−22.2334	−1.17343	−0.586716	+	0.809793i	$0.699580\pi$
$360$	288.047	15.1814
$361$	−0.459193	−0.0241680
$362$	55.7738	2.93140
$363$	19.8329	1.04096
$364$	−1.85707	−0.0973370
$365$	41.6486	2.17999
$366$	53.8068	2.81253
$367$	7.01089	0.365965	0.182983	−	0.983116i	$-0.441425\pi$
$367$	7.01089	0.365965	0.182983	+	0.983116i	$0.441425\pi$
$368$	−126.768	−6.60824
$369$	79.8772	4.15824
$370$	−14.6800	−0.763177
$371$	−7.36050	−0.382138
$372$	−72.5235	−3.76017
$373$	−16.2762	−0.842748	−0.421374	−	0.906887i	$-0.638452\pi$
$373$	−16.2762	−0.842748	−0.421374	+	0.906887i	$0.638452\pi$
$374$	39.7674	2.05632
$375$	−56.0375	−2.89377
$376$	−25.9955	−1.34062
$377$	−0.608266	−0.0313273
$378$	40.7270	2.09477
$379$	16.1436	0.829243	0.414621	−	0.909994i	$-0.363914\pi$
$379$	16.1436	0.829243	0.414621	+	0.909994i	$0.363914\pi$
$380$	−90.2875	−4.63165
$381$	46.7050	2.39277
$382$	−9.85817	−0.504388
$383$	0.660144	0.0337318	0.0168659	−	0.999858i	$-0.494631\pi$
$383$	0.660144	0.0337318	0.0168659	+	0.999858i	$0.494631\pi$
$384$	−137.633	−7.02355
$385$	−14.5364	−0.740846
$386$	−49.4200	−2.51541
$387$	25.2371	1.28287
$388$	28.8200	1.46311
$389$	2.46240	0.124849	0.0624244	−	0.998050i	$-0.480117\pi$
$389$	2.46240	0.124849	0.0624244	+	0.998050i	$0.480117\pi$
$390$	12.4977	0.632847
$391$	−29.0246	−1.46784
$392$	59.1275	2.98639
$393$	−41.2013	−2.07833
$394$	−57.0679	−2.87504
$395$	51.6631	2.59945
$396$	−178.865	−8.98831
$397$	−11.5899	−0.581679	−0.290839	−	0.956772i	$-0.593935\pi$
$397$	−11.5899	−0.581679	−0.290839	+	0.956772i	$0.593935\pi$
$398$	−42.9631	−2.15354
$399$	−13.1491	−0.658279
$400$	145.464	7.27320
$401$	−12.1748	−0.607982	−0.303991	−	0.952675i	$-0.598319\pi$
$401$	−12.1748	−0.607982	−0.303991	+	0.952675i	$0.598319\pi$
$402$	−108.135	−5.39327
$403$	−1.45142	−0.0723002
$404$	21.5971	1.07449
$405$	−111.355	−5.53326
$406$	−4.24713	−0.210782
$407$	5.80834	0.287909
$408$	−111.616	−5.52583
$409$	−23.7274	−1.17325	−0.586623	−	0.809860i	$-0.699543\pi$
$409$	−23.7274	−1.17325	−0.586623	+	0.809860i	$0.699543\pi$
$410$	105.873	5.22872
$411$	22.0897	1.08960
$412$	5.89190	0.290273
$413$	−1.88886	−0.0929448
$414$	177.911	8.74384
$415$	46.7925	2.29695
$416$	−8.30978	−0.407420
$417$	54.2089	2.65462
$418$	48.6845	2.38124
$419$	−2.21723	−0.108319	−0.0541593	−	0.998532i	$-0.517248\pi$
$419$	−2.21723	−0.108319	−0.0541593	+	0.998532i	$0.517248\pi$
$420$	64.0318	3.12443
$421$	0.336481	0.0163991	0.00819953	−	0.999966i	$-0.497390\pi$
$421$	0.336481	0.0163991	0.00819953	+	0.999966i	$0.497390\pi$
$422$	−5.78765	−0.281738
$423$	21.2398	1.03271
$424$	−76.4897	−3.71467
$425$	33.3051	1.61554
$426$	−60.4739	−2.92997
$427$	5.51715	0.266993
$428$	109.739	5.30444
$429$	−4.94489	−0.238741
$430$	33.4506	1.61313
$431$	7.59705	0.365937	0.182968	−	0.983119i	$-0.441429\pi$
$431$	7.59705	0.365937	0.182968	+	0.983119i	$0.441429\pi$
$432$	246.398	11.8548
$433$	−4.63873	−0.222923	−0.111462	−	0.993769i	$-0.535553\pi$
$433$	−4.63873	−0.222923	−0.111462	+	0.993769i	$0.535553\pi$
$434$	−10.1343	−0.486463
$435$	20.9730	1.00558
$436$	95.7533	4.58575
$437$	−35.5328	−1.69977
$438$	98.9238	4.72676
$439$	−21.9471	−1.04748	−0.523738	−	0.851879i	$-0.675463\pi$
$439$	−21.9471	−1.04748	−0.523738	+	0.851879i	$0.675463\pi$
$440$	−151.062	−7.20158
$441$	−48.3105	−2.30050
$442$	−3.50572	−0.166750
$443$	−32.0968	−1.52497	−0.762484	−	0.647007i	$-0.776020\pi$
$443$	−32.0968	−1.52497	−0.762484	+	0.647007i	$0.776020\pi$
$444$	−25.5852	−1.21422
$445$	46.1825	2.18926
$446$	64.8512	3.07079
$447$	78.7993	3.72708
$448$	−29.5593	−1.39655
$449$	20.1809	0.952397	0.476198	−	0.879338i	$-0.342014\pi$
$449$	20.1809	0.952397	0.476198	+	0.879338i	$0.342014\pi$
$450$	−204.149	−9.62369
$451$	−41.8902	−1.97253
$452$	50.7284	2.38606
$453$	18.2965	0.859646
$454$	−22.1694	−1.04046
$455$	1.28147	0.0600762
$456$	−136.644	−6.39896
$457$	31.7317	1.48435	0.742173	−	0.670208i	$-0.233795\pi$
$457$	31.7317	1.48435	0.742173	+	0.670208i	$0.233795\pi$
$458$	1.90692	0.0891046
$459$	56.4148	2.63322
$460$	173.033	8.06771
$461$	20.7241	0.965219	0.482610	−	0.875836i	$-0.339689\pi$
$461$	20.7241	0.965219	0.482610	+	0.875836i	$0.339689\pi$
$462$	−34.5270	−1.60634
$463$	15.1130	0.702358	0.351179	−	0.936308i	$-0.385781\pi$
$463$	15.1130	0.702358	0.351179	+	0.936308i	$0.385781\pi$
$464$	−25.6951	−1.19287
$465$	50.0448	2.32077
$466$	−51.5643	−2.38867
$467$	−30.8926	−1.42954	−0.714771	−	0.699359i	$-0.753469\pi$
$467$	−30.8926	−1.42954	−0.714771	+	0.699359i	$0.753469\pi$
$468$	15.7680	0.728875
$469$	−11.0877	−0.511984
$470$	28.1523	1.29857
$471$	−3.11144	−0.143368
$472$	−19.6289	−0.903493
$473$	−13.2352	−0.608554
$474$	122.710	5.63627
$475$	40.7733	1.87081
$476$	−17.9615	−0.823262
$477$	62.4964	2.86151
$478$	3.08536	0.141121
$479$	4.51585	0.206334	0.103167	−	0.994664i	$-0.467102\pi$
$479$	4.51585	0.206334	0.103167	+	0.994664i	$0.467102\pi$
$480$	286.521	13.0778
$481$	−0.512038	−0.0233469
$482$	−66.5149	−3.02967
$483$	25.1998	1.14663
$484$	33.1662	1.50756
$485$	−19.8872	−0.903031
$486$	−132.602	−6.01497
$487$	−1.11428	−0.0504929	−0.0252465	−	0.999681i	$-0.508037\pi$
$487$	−1.11428	−0.0504929	−0.0252465	+	0.999681i	$0.508037\pi$
$488$	57.3337	2.59538
$489$	17.4696	0.790002
$490$	−64.0332	−2.89273
$491$	−3.64169	−0.164347	−0.0821736	−	0.996618i	$-0.526186\pi$
$491$	−3.64169	−0.164347	−0.0821736	+	0.996618i	$0.526186\pi$
$492$	184.523	8.31893
$493$	−5.88310	−0.264962
$494$	−4.29182	−0.193098
$495$	123.426	5.54757
$496$	−61.3125	−2.75301
$497$	−6.20077	−0.278143
$498$	111.142	4.98038
$499$	16.4949	0.738414	0.369207	−	0.929347i	$-0.379629\pi$
$499$	16.4949	0.738414	0.369207	+	0.929347i	$0.379629\pi$
$500$	−93.7105	−4.19086
$501$	23.9479	1.06991
$502$	−13.9433	−0.622322
$503$	3.32336	0.148181	0.0740907	−	0.997252i	$-0.476395\pi$
$503$	3.32336	0.148181	0.0740907	+	0.997252i	$0.476395\pi$
$504$	70.1524	3.12483
$505$	−14.9030	−0.663176
$506$	−93.3023	−4.14779
$507$	−42.4165	−1.88378
$508$	78.1039	3.46530
$509$	14.9074	0.660759	0.330380	−	0.943848i	$-0.392823\pi$
$509$	14.9074	0.660759	0.330380	+	0.943848i	$0.392823\pi$
$510$	120.877	5.35252
$511$	10.1433	0.448712
$512$	−55.2513	−2.44179
$513$	69.0649	3.04929
$514$	−42.5250	−1.87570
$515$	−4.06570	−0.179156
$516$	58.2998	2.56650
$517$	−11.1388	−0.489886
$518$	−3.57524	−0.157087
$519$	46.1158	2.02426
$520$	13.3169	0.583986
$521$	−22.8853	−1.00262	−0.501311	−	0.865267i	$-0.667149\pi$
$521$	−22.8853	−1.00262	−0.501311	+	0.865267i	$0.667149\pi$
$522$	36.0614	1.57837
$523$	−36.9377	−1.61517	−0.807587	−	0.589748i	$-0.799227\pi$
$523$	−36.9377	−1.61517	−0.807587	+	0.589748i	$0.799227\pi$
$524$	−68.9001	−3.00992
$525$	−28.9163	−1.26201
$526$	16.4082	0.715432
$527$	−14.0380	−0.611504
$528$	−208.888	−9.09069
$529$	45.0975	1.96076
$530$	82.8360	3.59817
$531$	16.0379	0.695985
$532$	−21.9890	−0.953345
$533$	3.69286	0.159956
$534$	109.693	4.74687
$535$	−75.7253	−3.27389
$536$	−115.223	−4.97687
$537$	−26.5694	−1.14655
$538$	−41.3429	−1.78242
$539$	25.3356	1.09128
$540$	−336.323	−14.4730
$541$	9.52330	0.409439	0.204719	−	0.978821i	$-0.434372\pi$
$541$	9.52330	0.409439	0.204719	+	0.978821i	$0.434372\pi$
$542$	−38.2573	−1.64329
$543$	−67.0768	−2.87854
$544$	−80.3716	−3.44590
$545$	−66.0744	−2.83032
$546$	3.04375	0.130260
$547$	17.0452	0.728801	0.364401	−	0.931242i	$-0.381274\pi$
$547$	17.0452	0.728801	0.364401	+	0.931242i	$0.381274\pi$
$548$	36.9402	1.57801
$549$	−46.8448	−1.99929
$550$	107.063	4.56516
$551$	−7.20229	−0.306828
$552$	261.875	11.1461
$553$	12.5823	0.535052
$554$	−20.9443	−0.889837
$555$	17.6551	0.749415
$556$	90.6525	3.84452
$557$	20.2653	0.858668	0.429334	−	0.903146i	$-0.358748\pi$
$557$	20.2653	0.858668	0.429334	+	0.903146i	$0.358748\pi$
$558$	86.0482	3.64271
$559$	1.16676	0.0493485
$560$	54.1335	2.28756
$561$	−47.8266	−2.01924
$562$	20.0354	0.845142
$563$	−12.0776	−0.509012	−0.254506	−	0.967071i	$-0.581913\pi$
$563$	−12.0776	−0.509012	−0.254506	+	0.967071i	$0.581913\pi$
$564$	49.0656	2.06604
$565$	−35.0051	−1.47267
$566$	7.83725	0.329424
$567$	−27.1198	−1.13893
$568$	−64.4379	−2.70375
$569$	−41.6092	−1.74435	−0.872174	−	0.489196i	$-0.837290\pi$
$569$	−41.6092	−1.74435	−0.872174	+	0.489196i	$0.837290\pi$
$570$	147.982	6.19827
$571$	−10.1796	−0.426005	−0.213002	−	0.977052i	$-0.568324\pi$
$571$	−10.1796	−0.426005	−0.213002	+	0.977052i	$0.568324\pi$
$572$	−8.26925	−0.345755
$573$	11.8560	0.495293
$574$	25.7849	1.07624
$575$	−78.1406	−3.25869
$576$	250.981	10.4576
$577$	−9.13505	−0.380297	−0.190148	−	0.981755i	$-0.560897\pi$
$577$	−9.13505	−0.380297	−0.190148	+	0.981755i	$0.560897\pi$
$578$	12.6879	0.527747
$579$	59.4354	2.47005
$580$	35.0727	1.45632
$581$	11.3961	0.472788
$582$	−47.2361	−1.95800
$583$	−32.7751	−1.35741
$584$	105.408	4.36182
$585$	−10.8807	−0.449860
$586$	60.4221	2.49602
$587$	−24.4799	−1.01039	−0.505197	−	0.863004i	$-0.668580\pi$
$587$	−24.4799	−1.01039	−0.505197	+	0.863004i	$0.668580\pi$
$588$	−111.601	−4.60235
$589$	−17.1858	−0.708128
$590$	21.2575	0.875156
$591$	68.6332	2.82319
$592$	−21.6302	−0.888994
$593$	−34.6267	−1.42195	−0.710975	−	0.703218i	$-0.751746\pi$
$593$	−34.6267	−1.42195	−0.710975	+	0.703218i	$0.751746\pi$
$594$	181.351	7.44092
$595$	12.3943	0.508116
$596$	131.775	5.39770
$597$	51.6699	2.11471
$598$	8.22513	0.336350
$599$	−30.9201	−1.26336	−0.631680	−	0.775229i	$-0.717634\pi$
$599$	−30.9201	−1.26336	−0.631680	+	0.775229i	$0.717634\pi$
$600$	−300.496	−12.2677
$601$	−16.6780	−0.680310	−0.340155	−	0.940369i	$-0.610479\pi$
$601$	−16.6780	−0.680310	−0.340155	+	0.940369i	$0.610479\pi$
$602$	8.14671	0.332035
$603$	94.1435	3.83382
$604$	30.5970	1.24497
$605$	−22.8863	−0.930460
$606$	−35.3977	−1.43793
$607$	22.8578	0.927770	0.463885	−	0.885895i	$-0.346455\pi$
$607$	22.8578	0.927770	0.463885	+	0.885895i	$0.346455\pi$
$608$	−98.3936	−3.99039
$609$	5.10785	0.206981
$610$	−62.0906	−2.51398
$611$	0.981952	0.0397255
$612$	152.507	6.16472
$613$	−17.1414	−0.692337	−0.346168	−	0.938172i	$-0.612517\pi$
$613$	−17.1414	−0.692337	−0.346168	+	0.938172i	$0.612517\pi$
$614$	35.5381	1.43420
$615$	−127.330	−5.13443
$616$	−36.7902	−1.48232
$617$	−27.0766	−1.09006	−0.545031	−	0.838416i	$-0.683482\pi$
$617$	−27.0766	−1.09006	−0.545031	+	0.838416i	$0.683482\pi$
$618$	−9.65685	−0.388455
$619$	16.4701	0.661989	0.330994	−	0.943633i	$-0.392616\pi$
$619$	16.4701	0.661989	0.330994	+	0.943633i	$0.392616\pi$
$620$	83.6890	3.36103
$621$	−132.361	−5.31145
$622$	−33.0102	−1.32359
$623$	11.2475	0.450621
$624$	18.4147	0.737177
$625$	17.3191	0.692763
$626$	−2.08498	−0.0833324
$627$	−58.5509	−2.33830
$628$	−5.20320	−0.207630
$629$	−4.95239	−0.197465
$630$	−75.9728	−3.02683
$631$	−0.922713	−0.0367326	−0.0183663	−	0.999831i	$-0.505847\pi$
$631$	−0.922713	−0.0367326	−0.0183663	+	0.999831i	$0.505847\pi$
$632$	130.754	5.20110
$633$	6.96057	0.276658
$634$	−6.65990	−0.264498
$635$	−53.8955	−2.13878
$636$	144.372	5.72471
$637$	−2.23348	−0.0884935
$638$	−18.9118	−0.748725
$639$	52.6493	2.08278
$640$	158.822	6.27801
$641$	−34.9495	−1.38042	−0.690212	−	0.723608i	$-0.742483\pi$
$641$	−34.9495	−1.38042	−0.690212	+	0.723608i	$0.742483\pi$
$642$	−179.863	−7.09862
$643$	33.9647	1.33944	0.669718	−	0.742615i	$-0.266415\pi$
$643$	33.9647	1.33944	0.669718	+	0.742615i	$0.266415\pi$
$644$	42.1412	1.66060
$645$	−40.2297	−1.58404
$646$	−41.5101	−1.63319
$647$	39.3444	1.54679	0.773393	−	0.633926i	$-0.218558\pi$
$647$	39.3444	1.54679	0.773393	+	0.633926i	$0.218558\pi$
$648$	−281.827	−11.0712
$649$	−8.41080	−0.330153
$650$	−9.43817	−0.370196
$651$	12.1881	0.477690
$652$	29.2141	1.14411
$653$	−20.2605	−0.792853	−0.396426	−	0.918067i	$-0.629750\pi$
$653$	−20.2605	−0.792853	−0.396426	+	0.918067i	$0.629750\pi$
$654$	−156.940	−6.13684
$655$	47.5444	1.85771
$656$	155.998	6.09071
$657$	−86.1243	−3.36003
$658$	6.85635	0.267288
$659$	−13.0840	−0.509680	−0.254840	−	0.966983i	$-0.582023\pi$
$659$	−13.0840	−0.509680	−0.254840	+	0.966983i	$0.582023\pi$
$660$	285.123	11.0984
$661$	19.8142	0.770684	0.385342	−	0.922774i	$-0.374083\pi$
$661$	19.8142	0.770684	0.385342	+	0.922774i	$0.374083\pi$
$662$	96.3939	3.74645
$663$	4.21618	0.163743
$664$	118.427	4.59585
$665$	15.1735	0.588403
$666$	30.3565	1.17629
$667$	13.8029	0.534452
$668$	40.0477	1.54949
$669$	−77.9939	−3.01542
$670$	124.783	4.82078
$671$	24.5670	0.948398
$672$	69.7806	2.69184
$673$	46.9123	1.80834	0.904168	−	0.427177i	$-0.140492\pi$
$673$	46.9123	1.80834	0.904168	+	0.427177i	$0.140492\pi$
$674$	−19.7260	−0.759816
$675$	151.881	5.84591
$676$	−70.9324	−2.72817
$677$	−42.7348	−1.64243	−0.821215	−	0.570618i	$-0.806704\pi$
$677$	−42.7348	−1.64243	−0.821215	+	0.570618i	$0.806704\pi$
$678$	−83.1441	−3.19313
$679$	−4.84341	−0.185873
$680$	128.800	4.93927
$681$	26.6622	1.02170
$682$	−45.1265	−1.72798
$683$	−15.1272	−0.578825	−0.289413	−	0.957204i	$-0.593460\pi$
$683$	−15.1272	−0.578825	−0.289413	+	0.957204i	$0.593460\pi$
$684$	186.704	7.13880
$685$	−25.4905	−0.973943
$686$	−33.3690	−1.27404
$687$	−2.29338	−0.0874977
$688$	49.2875	1.87907
$689$	2.88932	0.110074
$690$	−283.602	−10.7965
$691$	−0.414150	−0.0157550	−0.00787751	−	0.999969i	$-0.502508\pi$
$691$	−0.414150	−0.0157550	−0.00787751	+	0.999969i	$0.502508\pi$
$692$	77.1186	2.93161
$693$	30.0596	1.14187
$694$	−82.8769	−3.14596
$695$	−62.5547	−2.37283
$696$	53.0804	2.01201
$697$	35.7171	1.35288
$698$	−65.5126	−2.47969
$699$	62.0142	2.34559
$700$	−48.3563	−1.82769
$701$	5.61804	0.212190	0.106095	−	0.994356i	$-0.466165\pi$
$701$	5.61804	0.212190	0.106095	+	0.994356i	$0.466165\pi$
$702$	−15.9871	−0.603395
$703$	−6.06289	−0.228666
$704$	−131.623	−4.96073
$705$	−33.8577	−1.27515
$706$	−93.3471	−3.51316
$707$	−3.62955	−0.136503
$708$	37.0488	1.39238
$709$	51.9864	1.95239	0.976196	−	0.216890i	$-0.0695914\pi$
$709$	51.9864	1.95239	0.976196	+	0.216890i	$0.0695914\pi$
$710$	69.7842	2.61895
$711$	−106.833	−4.00655
$712$	116.883	4.38038
$713$	32.9360	1.23346
$714$	29.4389	1.10172
$715$	5.70618	0.213399
$716$	−44.4315	−1.66048
$717$	−3.71064	−0.138576
$718$	60.9390	2.27422
$719$	27.5554	1.02764	0.513822	−	0.857897i	$-0.328229\pi$
$719$	27.5554	1.02764	0.513822	+	0.857897i	$0.328229\pi$
$720$	−459.635	−17.1296
$721$	−0.990178	−0.0368761
$722$	1.25859	0.0468399
$723$	79.9948	2.97504
$724$	−112.171	−4.16882
$725$	−15.8386	−0.588232
$726$	−54.3596	−2.01747
$727$	−38.7874	−1.43855	−0.719273	−	0.694727i	$-0.755525\pi$
$727$	−38.7874	−1.43855	−0.719273	+	0.694727i	$0.755525\pi$
$728$	3.24327	0.120203
$729$	71.6525	2.65380
$730$	−114.154	−4.22502
$731$	11.2848	0.417382
$732$	−108.215	−3.99976
$733$	5.82002	0.214967	0.107484	−	0.994207i	$-0.465721\pi$
$733$	5.82002	0.214967	0.107484	+	0.994207i	$0.465721\pi$
$734$	−19.2160	−0.709275
$735$	77.0102	2.84056
$736$	188.568	6.95071
$737$	−49.3719	−1.81864
$738$	−218.934	−8.05906
$739$	−6.93806	−0.255221	−0.127610	−	0.991824i	$-0.540731\pi$
$739$	−6.93806	−0.255221	−0.127610	+	0.991824i	$0.540731\pi$
$740$	29.5242	1.08533
$741$	5.16159	0.189616
$742$	20.1742	0.740620
$743$	−1.38137	−0.0506775	−0.0253387	−	0.999679i	$-0.508066\pi$
$743$	−1.38137	−0.0506775	−0.0253387	+	0.999679i	$0.508066\pi$
$744$	126.658	4.64351
$745$	−90.9309	−3.33145
$746$	44.6110	1.63332
$747$	−96.7613	−3.54031
$748$	−79.9795	−2.92434
$749$	−18.4425	−0.673873
$750$	153.592	5.60839
$751$	32.2694	1.17753	0.588763	−	0.808306i	$-0.299615\pi$
$751$	32.2694	1.17753	0.588763	+	0.808306i	$0.299615\pi$
$752$	41.4808	1.51265
$753$	16.7691	0.611099
$754$	1.66718	0.0607152
$755$	−21.1134	−0.768395
$756$	−81.9096	−2.97902
$757$	−14.1879	−0.515667	−0.257833	−	0.966189i	$-0.583009\pi$
$757$	−14.1879	−0.515667	−0.257833	+	0.966189i	$0.583009\pi$
$758$	−44.2477	−1.60715
$759$	112.211	4.07300
$760$	157.682	5.71972
$761$	16.7034	0.605497	0.302749	−	0.953070i	$-0.402096\pi$
$761$	16.7034	0.605497	0.302749	+	0.953070i	$0.402096\pi$
$762$	−128.013	−4.63741
$763$	−16.0921	−0.582571
$764$	19.8266	0.717302
$765$	−105.237	−3.80485
$766$	−1.80938	−0.0653754
$767$	0.741459	0.0267725
$768$	166.878	6.02170
$769$	0.805128	0.0290336	0.0145168	−	0.999895i	$-0.495379\pi$
$769$	0.805128	0.0290336	0.0145168	+	0.999895i	$0.495379\pi$
$770$	39.8426	1.43583
$771$	51.1431	1.84187
$772$	99.3927	3.57722
$773$	13.2915	0.478061	0.239031	−	0.971012i	$-0.423170\pi$
$773$	13.2915	0.478061	0.239031	+	0.971012i	$0.423170\pi$
$774$	−69.1718	−2.48633
$775$	−37.7934	−1.35758
$776$	−50.3324	−1.80683
$777$	4.29979	0.154254
$778$	−6.74915	−0.241969
$779$	43.7260	1.56665
$780$	−25.1352	−0.899986
$781$	−27.6110	−0.988001
$782$	79.5528	2.84480
$783$	−26.8287	−0.958779
$784$	−94.3493	−3.36962
$785$	3.59046	0.128149
$786$	112.928	4.02799
$787$	12.0456	0.429379	0.214689	−	0.976682i	$-0.431126\pi$
$787$	12.0456	0.429379	0.214689	+	0.976682i	$0.431126\pi$
$788$	114.774	4.08866
$789$	−19.7335	−0.702530
$790$	−141.602	−5.03798
$791$	−8.52529	−0.303124
$792$	312.377	11.0998
$793$	−2.16572	−0.0769069
$794$	31.7664	1.12735
$795$	−99.6235	−3.53328
$796$	86.4067	3.06260
$797$	6.90981	0.244758	0.122379	−	0.992483i	$-0.460948\pi$
$797$	6.90981	0.244758	0.122379	+	0.992483i	$0.460948\pi$
$798$	36.0401	1.27581
$799$	9.49737	0.335993
$800$	−216.378	−7.65012
$801$	−95.4999	−3.37432
$802$	33.3697	1.17833
$803$	45.1664	1.59389
$804$	217.479	7.66989
$805$	−29.0795	−1.02492
$806$	3.97816	0.140125
$807$	49.7214	1.75028
$808$	−37.7180	−1.32691
$809$	43.3207	1.52307	0.761537	−	0.648121i	$-0.224445\pi$
$809$	43.3207	1.52307	0.761537	+	0.648121i	$0.224445\pi$
$810$	305.210	10.7240
$811$	−7.73391	−0.271574	−0.135787	−	0.990738i	$-0.543356\pi$
$811$	−7.73391	−0.271574	−0.135787	+	0.990738i	$0.543356\pi$
$812$	8.54177	0.299757
$813$	46.0104	1.61366
$814$	−15.9200	−0.557994
$815$	−20.1591	−0.706144
$816$	178.105	6.23493
$817$	13.8152	0.483332
$818$	65.0340	2.27386
$819$	−2.64993	−0.0925960
$820$	−212.931	−7.43588
$821$	10.8829	0.379815	0.189908	−	0.981802i	$-0.439181\pi$
$821$	10.8829	0.379815	0.189908	+	0.981802i	$0.439181\pi$
$822$	−60.5452	−2.11175
$823$	36.9251	1.28713	0.643564	−	0.765392i	$-0.277455\pi$
$823$	36.9251	1.28713	0.643564	+	0.765392i	$0.277455\pi$
$824$	−10.2898	−0.358464
$825$	−128.760	−4.48284
$826$	5.17714	0.180136
$827$	−11.6838	−0.406284	−0.203142	−	0.979149i	$-0.565115\pi$
$827$	−11.6838	−0.406284	−0.203142	+	0.979149i	$0.565115\pi$
$828$	−357.812	−12.4348
$829$	−22.4927	−0.781204	−0.390602	−	0.920560i	$-0.627733\pi$
$829$	−22.4927	−0.781204	−0.390602	+	0.920560i	$0.627733\pi$
$830$	−128.253	−4.45171
$831$	25.1888	0.873790
$832$	11.6033	0.402272
$833$	−21.6020	−0.748465
$834$	−148.580	−5.14490
$835$	−27.6348	−0.956343
$836$	−97.9136	−3.38641
$837$	−64.0174	−2.21277
$838$	6.07715	0.209932
$839$	5.79594	0.200098	0.100049	−	0.994983i	$-0.468100\pi$
$839$	5.79594	0.200098	0.100049	+	0.994983i	$0.468100\pi$
$840$	−111.828	−3.85842
$841$	−26.2022	−0.903525
$842$	−0.922253	−0.0317829
$843$	−24.0957	−0.829902
$844$	11.6400	0.400667
$845$	48.9468	1.68382
$846$	−58.2157	−2.00150
$847$	−5.57383	−0.191519
$848$	122.054	4.19135
$849$	−9.42554	−0.323484
$850$	−91.2853	−3.13106
$851$	11.6193	0.398305
$852$	121.624	4.16678
$853$	23.1385	0.792249	0.396124	−	0.918197i	$-0.370355\pi$
$853$	23.1385	0.792249	0.396124	+	0.918197i	$0.370355\pi$
$854$	−15.1218	−0.517458
$855$	−128.835	−4.40605
$856$	−191.653	−6.55055
$857$	5.90230	0.201619	0.100809	−	0.994906i	$-0.467857\pi$
$857$	5.90230	0.201619	0.100809	+	0.994906i	$0.467857\pi$
$858$	13.5533	0.462703
$859$	−35.9226	−1.22566	−0.612832	−	0.790213i	$-0.709970\pi$
$859$	−35.9226	−1.22566	−0.612832	+	0.790213i	$0.709970\pi$
$860$	−67.2753	−2.29407
$861$	−31.0104	−1.05683
$862$	−20.8226	−0.709220
$863$	38.5994	1.31394	0.656969	−	0.753917i	$-0.271838\pi$
$863$	38.5994	1.31394	0.656969	+	0.753917i	$0.271838\pi$
$864$	−366.518	−12.4692
$865$	−53.2156	−1.80938
$866$	12.7142	0.432046
$867$	−15.2592	−0.518230
$868$	20.3820	0.691810
$869$	56.0268	1.90058
$870$	−57.4844	−1.94890
$871$	4.35242	0.147476
$872$	−167.227	−5.66303
$873$	41.1243	1.39185
$874$	97.3912	3.29431
$875$	15.7488	0.532405
$876$	−198.954	−6.72203
$877$	42.8441	1.44674	0.723372	−	0.690459i	$-0.242591\pi$
$877$	42.8441	1.44674	0.723372	+	0.690459i	$0.242591\pi$
$878$	60.1543	2.03011
$879$	−72.6672	−2.45101
$880$	241.048	8.12571
$881$	−45.6989	−1.53963	−0.769817	−	0.638265i	$-0.779653\pi$
$881$	−45.6989	−1.53963	−0.769817	+	0.638265i	$0.779653\pi$
$882$	132.413	4.45858
$883$	34.1457	1.14909	0.574547	−	0.818472i	$-0.305178\pi$
$883$	34.1457	1.14909	0.574547	+	0.818472i	$0.305178\pi$
$884$	7.05065	0.237139
$885$	−25.5655	−0.859374
$886$	87.9736	2.95553
$887$	24.8202	0.833380	0.416690	−	0.909049i	$-0.363190\pi$
$887$	24.8202	0.833380	0.416690	+	0.909049i	$0.363190\pi$
$888$	44.6831	1.49947
$889$	−13.1260	−0.440230
$890$	−126.581	−4.24299
$891$	−120.760	−4.04562
$892$	−130.428	−4.36704
$893$	11.6270	0.389083
$894$	−215.979	−7.22343
$895$	30.6599	1.02485
$896$	38.6803	1.29222
$897$	−9.89202	−0.330285
$898$	−55.3135	−1.84583
$899$	6.67592	0.222654
$900$	410.582	13.6861
$901$	27.9452	0.930991
$902$	114.816	3.82295
$903$	−9.79771	−0.326047
$904$	−88.5941	−2.94660
$905$	77.4037	2.57299
$906$	−50.1486	−1.66607
$907$	−0.0316358	−0.00105045	−0.000525224	−	1.00000i	$-0.500167\pi$
$907$	−0.0316358	−0.00105045	−0.000525224		1.00000i	$0.500167\pi$
$908$	44.5867	1.47966
$909$	30.8177	1.02216
$910$	−3.51235	−0.116433
$911$	6.52524	0.216191	0.108095	−	0.994141i	$-0.465525\pi$
$911$	6.52524	0.216191	0.108095	+	0.994141i	$0.465525\pi$
$912$	218.042	7.22011
$913$	50.7448	1.67941
$914$	−86.9727	−2.87680
$915$	74.6739	2.46864
$916$	−3.83517	−0.126718
$917$	11.5792	0.382378
$918$	−154.626	−5.10342
$919$	−34.0214	−1.12226	−0.561131	−	0.827727i	$-0.689634\pi$
$919$	−34.0214	−1.12226	−0.561131	+	0.827727i	$0.689634\pi$
$920$	−302.192	−9.96297
$921$	−42.7402	−1.40834
$922$	−56.8023	−1.87069
$923$	2.43407	0.0801184
$924$	69.4402	2.28441
$925$	−13.3329	−0.438385
$926$	−41.4228	−1.36124
$927$	8.40737	0.276134
$928$	38.2216	1.25468
$929$	−51.9541	−1.70456	−0.852279	−	0.523087i	$-0.824780\pi$
$929$	−51.9541	−1.70456	−0.852279	+	0.523087i	$0.824780\pi$
$930$	−137.167	−4.49787
$931$	−26.4459	−0.866730
$932$	103.705	3.39698
$933$	39.7000	1.29972
$934$	84.6730	2.77058
$935$	55.1898	1.80490
$936$	−27.5378	−0.900102
$937$	38.2071	1.24817	0.624086	−	0.781356i	$-0.285472\pi$
$937$	38.2071	1.24817	0.624086	+	0.781356i	$0.285472\pi$
$938$	30.3901	0.992273
$939$	2.50752	0.0818297
$940$	−56.6196	−1.84673
$941$	−14.7943	−0.482281	−0.241140	−	0.970490i	$-0.577521\pi$
$941$	−14.7943	−0.482281	−0.241140	+	0.970490i	$0.577521\pi$
$942$	8.52807	0.277860
$943$	−83.7995	−2.72889
$944$	31.3216	1.01943
$945$	56.5216	1.83865
$946$	36.2760	1.17943
$947$	−52.9709	−1.72132	−0.860661	−	0.509178i	$-0.829949\pi$
$947$	−52.9709	−1.72132	−0.860661	+	0.509178i	$0.829949\pi$
$948$	−246.793	−8.01546
$949$	−3.98167	−0.129251
$950$	−111.755	−3.62580
$951$	8.00959	0.259729
$952$	31.3686	1.01666
$953$	30.6257	0.992063	0.496031	−	0.868305i	$-0.334790\pi$
$953$	30.6257	0.992063	0.496031	+	0.868305i	$0.334790\pi$
$954$	−171.295	−5.54588
$955$	−13.6813	−0.442717
$956$	−6.20523	−0.200692
$957$	22.7445	0.735224
$958$	−12.3774	−0.399895
$959$	−6.20808	−0.200469
$960$	−400.082	−12.9126
$961$	−15.0702	−0.486136
$962$	1.40343	0.0452485
$963$	156.591	5.04607
$964$	133.774	4.30856
$965$	−68.5858	−2.20786
$966$	−69.0697	−2.22228
$967$	−31.0491	−0.998471	−0.499235	−	0.866466i	$-0.666386\pi$
$967$	−31.0491	−0.998471	−0.499235	+	0.866466i	$0.666386\pi$
$968$	−57.9228	−1.86171
$969$	49.9225	1.60374
$970$	54.5084	1.75016
$971$	0.991268	0.0318113	0.0159057	−	0.999873i	$-0.494937\pi$
$971$	0.991268	0.0318113	0.0159057	+	0.999873i	$0.494937\pi$
$972$	266.688	8.55402
$973$	−15.2348	−0.488407
$974$	3.05411	0.0978600
$975$	11.3509	0.363520
$976$	−91.4870	−2.92843
$977$	−36.3428	−1.16271	−0.581355	−	0.813650i	$-0.697477\pi$
$977$	−36.3428	−1.16271	−0.581355	+	0.813650i	$0.697477\pi$
$978$	−47.8820	−1.53110
$979$	50.0833	1.60067
$980$	128.783	4.11381
$981$	136.634	4.36239
$982$	9.98143	0.318520
$983$	4.47385	0.142693	0.0713467	−	0.997452i	$-0.477270\pi$
$983$	4.47385	0.142693	0.0713467	+	0.997452i	$0.477270\pi$
$984$	−322.258	−10.2732
$985$	−79.1997	−2.52351
$986$	16.1249	0.513520
$987$	−8.24585	−0.262468
$988$	8.63164	0.274609
$989$	−26.4763	−0.841899
$990$	−338.295	−10.7517
$991$	−54.0946	−1.71837	−0.859186	−	0.511663i	$-0.829030\pi$
$991$	−54.0946	−1.71837	−0.859186	+	0.511663i	$0.829030\pi$
$992$	91.2026	2.89568
$993$	−115.929	−3.67889
$994$	16.9956	0.539066
$995$	−59.6248	−1.89023
$996$	−223.526	−7.08271
$997$	22.3045	0.706391	0.353195	−	0.935550i	$-0.385095\pi$
$997$	22.3045	0.706391	0.353195	+	0.935550i	$0.385095\pi$
$998$	−45.2106	−1.43111
$999$	−22.5844	−0.714538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.4	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.4	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.74088 q^{2} +3.29634 q^{3} +5.51241 q^{4} -3.80383 q^{5} -9.03487 q^{6} -0.926403 q^{7} -9.62710 q^{8} +7.86587 q^{9} +O(q^{10})\)	\(q-2.74088 q^{2} +3.29634 q^{3} +5.51241 q^{4} -3.80383 q^{5} -9.03487 q^{6} -0.926403 q^{7} -9.62710 q^{8} +7.86587 q^{9} +10.4258 q^{10} -4.12512 q^{11} +18.1708 q^{12} +0.363653 q^{13} +2.53916 q^{14} -12.5387 q^{15} +15.3619 q^{16} +3.51722 q^{17} -21.5594 q^{18} +4.30590 q^{19} -20.9683 q^{20} -3.05374 q^{21} +11.3065 q^{22} -8.25212 q^{23} -31.7342 q^{24} +9.46915 q^{25} -0.996729 q^{26} +16.0396 q^{27} -5.10671 q^{28} -1.67265 q^{29} +34.3672 q^{30} -3.99121 q^{31} -22.8508 q^{32} -13.5978 q^{33} -9.64028 q^{34} +3.52388 q^{35} +43.3600 q^{36} -1.40804 q^{37} -11.8020 q^{38} +1.19872 q^{39} +36.6199 q^{40} +10.1549 q^{41} +8.36993 q^{42} +3.20843 q^{43} -22.7394 q^{44} -29.9205 q^{45} +22.6181 q^{46} +2.70024 q^{47} +50.6380 q^{48} -6.14178 q^{49} -25.9538 q^{50} +11.5940 q^{51} +2.00461 q^{52} +7.94525 q^{53} -43.9626 q^{54} +15.6913 q^{55} +8.91857 q^{56} +14.1937 q^{57} +4.58454 q^{58} +2.03892 q^{59} -69.1187 q^{60} -5.95545 q^{61} +10.9394 q^{62} -7.28697 q^{63} +31.9076 q^{64} -1.38328 q^{65} +37.2700 q^{66} +11.9686 q^{67} +19.3884 q^{68} -27.2018 q^{69} -9.65853 q^{70} +6.69338 q^{71} -75.7256 q^{72} -10.9491 q^{73} +3.85927 q^{74} +31.2136 q^{75} +23.7359 q^{76} +3.82152 q^{77} -3.28556 q^{78} -13.5818 q^{79} -58.4340 q^{80} +29.2744 q^{81} -27.8333 q^{82} -12.3014 q^{83} -16.8335 q^{84} -13.3789 q^{85} -8.79392 q^{86} -5.51364 q^{87} +39.7130 q^{88} -12.1410 q^{89} +82.0084 q^{90} -0.336889 q^{91} -45.4891 q^{92} -13.1564 q^{93} -7.40104 q^{94} -16.3789 q^{95} -75.3242 q^{96} +5.22820 q^{97} +16.8339 q^{98} -32.4477 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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