LMFDB - Embedded newform 8042.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, 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("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.38233 q^{3} +1.00000 q^{4} +3.47698 q^{5} -3.38233 q^{6} +4.68177 q^{7} +1.00000 q^{8} +8.44012 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.38233 q^{3} +1.00000 q^{4} +3.47698 q^{5} -3.38233 q^{6} +4.68177 q^{7} +1.00000 q^{8} +8.44012 q^{9} +3.47698 q^{10} -5.69261 q^{11} -3.38233 q^{12} +3.67478 q^{13} +4.68177 q^{14} -11.7603 q^{15} +1.00000 q^{16} -1.00450 q^{17} +8.44012 q^{18} -3.25024 q^{19} +3.47698 q^{20} -15.8353 q^{21} -5.69261 q^{22} -6.38575 q^{23} -3.38233 q^{24} +7.08936 q^{25} +3.67478 q^{26} -18.4003 q^{27} +4.68177 q^{28} -4.06627 q^{29} -11.7603 q^{30} +2.26611 q^{31} +1.00000 q^{32} +19.2543 q^{33} -1.00450 q^{34} +16.2784 q^{35} +8.44012 q^{36} +7.00605 q^{37} -3.25024 q^{38} -12.4293 q^{39} +3.47698 q^{40} +0.301868 q^{41} -15.8353 q^{42} -9.35541 q^{43} -5.69261 q^{44} +29.3461 q^{45} -6.38575 q^{46} +7.89073 q^{47} -3.38233 q^{48} +14.9190 q^{49} +7.08936 q^{50} +3.39755 q^{51} +3.67478 q^{52} +2.12174 q^{53} -18.4003 q^{54} -19.7931 q^{55} +4.68177 q^{56} +10.9934 q^{57} -4.06627 q^{58} -1.58863 q^{59} -11.7603 q^{60} +2.97928 q^{61} +2.26611 q^{62} +39.5147 q^{63} +1.00000 q^{64} +12.7771 q^{65} +19.2543 q^{66} -6.46535 q^{67} -1.00450 q^{68} +21.5987 q^{69} +16.2784 q^{70} +14.6890 q^{71} +8.44012 q^{72} +12.5542 q^{73} +7.00605 q^{74} -23.9785 q^{75} -3.25024 q^{76} -26.6515 q^{77} -12.4293 q^{78} +8.43802 q^{79} +3.47698 q^{80} +36.9153 q^{81} +0.301868 q^{82} +14.9638 q^{83} -15.8353 q^{84} -3.49263 q^{85} -9.35541 q^{86} +13.7534 q^{87} -5.69261 q^{88} +13.8092 q^{89} +29.3461 q^{90} +17.2045 q^{91} -6.38575 q^{92} -7.66471 q^{93} +7.89073 q^{94} -11.3010 q^{95} -3.38233 q^{96} +0.158623 q^{97} +14.9190 q^{98} -48.0464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) $ 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.38233	−1.95279	−0.976393	−	0.216001i	$-0.930699\pi$
$3$	−3.38233	−1.95279	−0.976393	+	0.216001i	$0.930699\pi$
$4$	1.00000	0.500000
$5$	3.47698	1.55495	0.777475	−	0.628914i	$-0.216500\pi$
$5$	3.47698	1.55495	0.777475	+	0.628914i	$0.216500\pi$
$6$	−3.38233	−1.38083
$7$	4.68177	1.76954	0.884771	−	0.466025i	$-0.154314\pi$
$7$	4.68177	1.76954	0.884771	+	0.466025i	$0.154314\pi$
$8$	1.00000	0.353553
$9$	8.44012	2.81337
$10$	3.47698	1.09952
$11$	−5.69261	−1.71639	−0.858194	−	0.513326i	$-0.828413\pi$
$11$	−5.69261	−1.71639	−0.858194	+	0.513326i	$0.828413\pi$
$12$	−3.38233	−0.976393
$13$	3.67478	1.01920	0.509601	−	0.860411i	$-0.329793\pi$
$13$	3.67478	1.01920	0.509601	+	0.860411i	$0.329793\pi$
$14$	4.68177	1.25126
$15$	−11.7603	−3.03649
$16$	1.00000	0.250000
$17$	−1.00450	−0.243628	−0.121814	−	0.992553i	$-0.538871\pi$
$17$	−1.00450	−0.243628	−0.121814	+	0.992553i	$0.538871\pi$
$18$	8.44012	1.98936
$19$	−3.25024	−0.745657	−0.372829	−	0.927900i	$-0.621612\pi$
$19$	−3.25024	−0.745657	−0.372829	+	0.927900i	$0.621612\pi$
$20$	3.47698	0.777475
$21$	−15.8353	−3.45554
$22$	−5.69261	−1.21367
$23$	−6.38575	−1.33152	−0.665761	−	0.746165i	$-0.731893\pi$
$23$	−6.38575	−1.33152	−0.665761	+	0.746165i	$0.731893\pi$
$24$	−3.38233	−0.690414
$25$	7.08936	1.41787
$26$	3.67478	0.720685
$27$	−18.4003	−3.54113
$28$	4.68177	0.884771
$29$	−4.06627	−0.755087	−0.377543	−	0.925992i	$-0.623231\pi$
$29$	−4.06627	−0.755087	−0.377543	+	0.925992i	$0.623231\pi$
$30$	−11.7603	−2.14712
$31$	2.26611	0.407005	0.203503	−	0.979074i	$-0.434767\pi$
$31$	2.26611	0.407005	0.203503	+	0.979074i	$0.434767\pi$
$32$	1.00000	0.176777
$33$	19.2543	3.35174
$34$	−1.00450	−0.172271
$35$	16.2784	2.75155
$36$	8.44012	1.40669
$37$	7.00605	1.15179	0.575894	−	0.817524i	$-0.304654\pi$
$37$	7.00605	1.15179	0.575894	+	0.817524i	$0.304654\pi$
$38$	−3.25024	−0.527259
$39$	−12.4293	−1.99028
$40$	3.47698	0.549758
$41$	0.301868	0.0471438	0.0235719	−	0.999722i	$-0.492496\pi$
$41$	0.301868	0.0471438	0.0235719	+	0.999722i	$0.492496\pi$
$42$	−15.8353	−2.44344
$43$	−9.35541	−1.42669	−0.713343	−	0.700815i	$-0.752820\pi$
$43$	−9.35541	−1.42669	−0.713343	+	0.700815i	$0.752820\pi$
$44$	−5.69261	−0.858194
$45$	29.3461	4.37466
$46$	−6.38575	−0.941528
$47$	7.89073	1.15098	0.575491	−	0.817808i	$-0.304811\pi$
$47$	7.89073	1.15098	0.575491	+	0.817808i	$0.304811\pi$
$48$	−3.38233	−0.488197
$49$	14.9190	2.13128
$50$	7.08936	1.00259
$51$	3.39755	0.475752
$52$	3.67478	0.509601
$53$	2.12174	0.291444	0.145722	−	0.989326i	$-0.453450\pi$
$53$	2.12174	0.291444	0.145722	+	0.989326i	$0.453450\pi$
$54$	−18.4003	−2.50396
$55$	−19.7931	−2.66890
$56$	4.68177	0.625628
$57$	10.9934	1.45611
$58$	−4.06627	−0.533927
$59$	−1.58863	−0.206822	−0.103411	−	0.994639i	$-0.532976\pi$
$59$	−1.58863	−0.206822	−0.103411	+	0.994639i	$0.532976\pi$
$60$	−11.7603	−1.51824
$61$	2.97928	0.381457	0.190729	−	0.981643i	$-0.438915\pi$
$61$	2.97928	0.381457	0.190729	+	0.981643i	$0.438915\pi$
$62$	2.26611	0.287796
$63$	39.5147	4.97839
$64$	1.00000	0.125000
$65$	12.7771	1.58481
$66$	19.2543	2.37004
$67$	−6.46535	−0.789868	−0.394934	−	0.918709i	$-0.629233\pi$
$67$	−6.46535	−0.789868	−0.394934	+	0.918709i	$0.629233\pi$
$68$	−1.00450	−0.121814
$69$	21.5987	2.60018
$70$	16.2784	1.94564
$71$	14.6890	1.74327	0.871633	−	0.490159i	$-0.163061\pi$
$71$	14.6890	1.74327	0.871633	+	0.490159i	$0.163061\pi$
$72$	8.44012	0.994678
$73$	12.5542	1.46936	0.734679	−	0.678414i	$-0.237333\pi$
$73$	12.5542	1.46936	0.734679	+	0.678414i	$0.237333\pi$
$74$	7.00605	0.814437
$75$	−23.9785	−2.76880
$76$	−3.25024	−0.372829
$77$	−26.6515	−3.03722
$78$	−12.4293	−1.40734
$79$	8.43802	0.949351	0.474676	−	0.880161i	$-0.342565\pi$
$79$	8.43802	0.949351	0.474676	+	0.880161i	$0.342565\pi$
$80$	3.47698	0.388738
$81$	36.9153	4.10170
$82$	0.301868	0.0333357
$83$	14.9638	1.64249	0.821243	−	0.570578i	$-0.193281\pi$
$83$	14.9638	1.64249	0.821243	+	0.570578i	$0.193281\pi$
$84$	−15.8353	−1.72777
$85$	−3.49263	−0.378829
$86$	−9.35541	−1.00882
$87$	13.7534	1.47452
$88$	−5.69261	−0.606835
$89$	13.8092	1.46377	0.731885	−	0.681428i	$-0.238641\pi$
$89$	13.8092	1.46377	0.731885	+	0.681428i	$0.238641\pi$
$90$	29.3461	3.09335
$91$	17.2045	1.80352
$92$	−6.38575	−0.665761
$93$	−7.66471	−0.794794
$94$	7.89073	0.813867
$95$	−11.3010	−1.15946
$96$	−3.38233	−0.345207
$97$	0.158623	0.0161057	0.00805285	−	0.999968i	$-0.497437\pi$
$97$	0.158623	0.0161057	0.00805285	+	0.999968i	$0.497437\pi$
$98$	14.9190	1.50704
$99$	−48.0464	−4.82884
$100$	7.08936	0.708936
$101$	1.26838	0.126208	0.0631042	−	0.998007i	$-0.479900\pi$
$101$	1.26838	0.126208	0.0631042	+	0.998007i	$0.479900\pi$
$102$	3.39755	0.336408
$103$	7.55086	0.744008	0.372004	−	0.928231i	$-0.378671\pi$
$103$	7.55086	0.744008	0.372004	+	0.928231i	$0.378671\pi$
$104$	3.67478	0.360342
$105$	−55.0588	−5.37319
$106$	2.12174	0.206082
$107$	12.8085	1.23825	0.619124	−	0.785293i	$-0.287488\pi$
$107$	12.8085	1.23825	0.619124	+	0.785293i	$0.287488\pi$
$108$	−18.4003	−1.77057
$109$	−18.2709	−1.75004	−0.875018	−	0.484090i	$-0.839151\pi$
$109$	−18.2709	−1.75004	−0.875018	+	0.484090i	$0.839151\pi$
$110$	−19.7931	−1.88720
$111$	−23.6968	−2.24920
$112$	4.68177	0.442386
$113$	−19.4174	−1.82663	−0.913317	−	0.407249i	$-0.866488\pi$
$113$	−19.4174	−1.82663	−0.913317	+	0.407249i	$0.866488\pi$
$114$	10.9934	1.02962
$115$	−22.2031	−2.07045
$116$	−4.06627	−0.377543
$117$	31.0156	2.86740
$118$	−1.58863	−0.146245
$119$	−4.70285	−0.431109
$120$	−11.7603	−1.07356
$121$	21.4059	1.94599
$122$	2.97928	0.269731
$123$	−1.02101	−0.0920618
$124$	2.26611	0.203503
$125$	7.26464	0.649769
$126$	39.5147	3.52025
$127$	7.02246	0.623143	0.311571	−	0.950223i	$-0.399145\pi$
$127$	7.02246	0.623143	0.311571	+	0.950223i	$0.399145\pi$
$128$	1.00000	0.0883883
$129$	31.6430	2.78601
$130$	12.7771	1.12063
$131$	2.78671	0.243476	0.121738	−	0.992562i	$-0.461153\pi$
$131$	2.78671	0.243476	0.121738	+	0.992562i	$0.461153\pi$
$132$	19.2543	1.67587
$133$	−15.2169	−1.31947
$134$	−6.46535	−0.558521
$135$	−63.9773	−5.50629
$136$	−1.00450	−0.0861353
$137$	10.5090	0.897844	0.448922	−	0.893571i	$-0.351808\pi$
$137$	10.5090	0.897844	0.448922	+	0.893571i	$0.351808\pi$
$138$	21.5987	1.83860
$139$	−7.47768	−0.634248	−0.317124	−	0.948384i	$-0.602717\pi$
$139$	−7.47768	−0.634248	−0.317124	+	0.948384i	$0.602717\pi$
$140$	16.2784	1.37578
$141$	−26.6890	−2.24762
$142$	14.6890	1.23268
$143$	−20.9191	−1.74935
$144$	8.44012	0.703344
$145$	−14.1383	−1.17412
$146$	12.5542	1.03899
$147$	−50.4608	−4.16194
$148$	7.00605	0.575894
$149$	10.9544	0.897421	0.448710	−	0.893677i	$-0.351883\pi$
$149$	10.9544	0.897421	0.448710	+	0.893677i	$0.351883\pi$
$150$	−23.9785	−1.95784
$151$	18.6781	1.52000	0.760001	−	0.649922i	$-0.225198\pi$
$151$	18.6781	1.52000	0.760001	+	0.649922i	$0.225198\pi$
$152$	−3.25024	−0.263630
$153$	−8.47812	−0.685415
$154$	−26.6515	−2.14764
$155$	7.87920	0.632873
$156$	−12.4293	−0.995142
$157$	3.64140	0.290615	0.145308	−	0.989387i	$-0.453583\pi$
$157$	3.64140	0.290615	0.145308	+	0.989387i	$0.453583\pi$
$158$	8.43802	0.671293
$159$	−7.17643	−0.569128
$160$	3.47698	0.274879
$161$	−29.8966	−2.35618
$162$	36.9153	2.90034
$163$	6.76777	0.530093	0.265046	−	0.964236i	$-0.414613\pi$
$163$	6.76777	0.530093	0.265046	+	0.964236i	$0.414613\pi$
$164$	0.301868	0.0235719
$165$	66.9466	5.21179
$166$	14.9638	1.16141
$167$	10.0864	0.780507	0.390253	−	0.920707i	$-0.372387\pi$
$167$	10.0864	0.780507	0.390253	+	0.920707i	$0.372387\pi$
$168$	−15.8353	−1.22172
$169$	0.504042	0.0387725
$170$	−3.49263	−0.267872
$171$	−27.4325	−2.09781
$172$	−9.35541	−0.713343
$173$	3.24728	0.246886	0.123443	−	0.992352i	$-0.460606\pi$
$173$	3.24728	0.246886	0.123443	+	0.992352i	$0.460606\pi$
$174$	13.7534	1.04265
$175$	33.1907	2.50898
$176$	−5.69261	−0.429097
$177$	5.37326	0.403879
$178$	13.8092	1.03504
$179$	−17.5316	−1.31037	−0.655186	−	0.755467i	$-0.727410\pi$
$179$	−17.5316	−1.31037	−0.655186	+	0.755467i	$0.727410\pi$
$180$	29.3461	2.18733
$181$	15.2097	1.13052	0.565262	−	0.824911i	$-0.308775\pi$
$181$	15.2097	1.13052	0.565262	+	0.824911i	$0.308775\pi$
$182$	17.2045	1.27528
$183$	−10.0769	−0.744904
$184$	−6.38575	−0.470764
$185$	24.3599	1.79097
$186$	−7.66471	−0.562004
$187$	5.71824	0.418159
$188$	7.89073	0.575491
$189$	−86.1458	−6.26619
$190$	−11.3010	−0.819862
$191$	20.5394	1.48618	0.743089	−	0.669192i	$-0.233360\pi$
$191$	20.5394	1.48618	0.743089	+	0.669192i	$0.233360\pi$
$192$	−3.38233	−0.244098
$193$	−16.5583	−1.19190	−0.595948	−	0.803023i	$-0.703224\pi$
$193$	−16.5583	−1.19190	−0.595948	+	0.803023i	$0.703224\pi$
$194$	0.158623	0.0113884
$195$	−43.2164	−3.09479
$196$	14.9190	1.06564
$197$	−22.8892	−1.63079	−0.815394	−	0.578907i	$-0.803479\pi$
$197$	−22.8892	−1.63079	−0.815394	+	0.578907i	$0.803479\pi$
$198$	−48.0464	−3.41451
$199$	3.83250	0.271678	0.135839	−	0.990731i	$-0.456627\pi$
$199$	3.83250	0.271678	0.135839	+	0.990731i	$0.456627\pi$
$200$	7.08936	0.501293
$201$	21.8679	1.54244
$202$	1.26838	0.0892428
$203$	−19.0373	−1.33616
$204$	3.39755	0.237876
$205$	1.04959	0.0733063
$206$	7.55086	0.526093
$207$	−53.8965	−3.74607
$208$	3.67478	0.254800
$209$	18.5024	1.27984
$210$	−55.0588	−3.79942
$211$	0.100033	0.00688653	0.00344326	−	0.999994i	$-0.498904\pi$
$211$	0.100033	0.00688653	0.00344326	+	0.999994i	$0.498904\pi$
$212$	2.12174	0.145722
$213$	−49.6830	−3.40423
$214$	12.8085	0.875573
$215$	−32.5285	−2.21843
$216$	−18.4003	−1.25198
$217$	10.6094	0.720213
$218$	−18.2709	−1.23746
$219$	−42.4624	−2.86934
$220$	−19.7931	−1.33445
$221$	−3.69133	−0.248306
$222$	−23.6968	−1.59042
$223$	−10.4478	−0.699637	−0.349819	−	0.936817i	$-0.613757\pi$
$223$	−10.4478	−0.699637	−0.349819	+	0.936817i	$0.613757\pi$
$224$	4.68177	0.312814
$225$	59.8350	3.98900
$226$	−19.4174	−1.29163
$227$	15.7818	1.04747	0.523737	−	0.851880i	$-0.324537\pi$
$227$	15.7818	1.04747	0.523737	+	0.851880i	$0.324537\pi$
$228$	10.9934	0.728055
$229$	18.0276	1.19130	0.595650	−	0.803244i	$-0.296895\pi$
$229$	18.0276	1.19130	0.595650	+	0.803244i	$0.296895\pi$
$230$	−22.2031	−1.46403
$231$	90.1441	5.93105
$232$	−4.06627	−0.266963
$233$	−16.1454	−1.05772	−0.528859	−	0.848710i	$-0.677380\pi$
$233$	−16.1454	−1.05772	−0.528859	+	0.848710i	$0.677380\pi$
$234$	31.0156	2.02756
$235$	27.4359	1.78972
$236$	−1.58863	−0.103411
$237$	−28.5401	−1.85388
$238$	−4.70285	−0.304840
$239$	15.3673	0.994030	0.497015	−	0.867742i	$-0.334429\pi$
$239$	15.3673	0.994030	0.497015	+	0.867742i	$0.334429\pi$
$240$	−11.7603	−0.759122
$241$	−16.3007	−1.05002	−0.525009	−	0.851097i	$-0.675938\pi$
$241$	−16.3007	−1.05002	−0.525009	+	0.851097i	$0.675938\pi$
$242$	21.4059	1.37602
$243$	−69.6588	−4.46862
$244$	2.97928	0.190729
$245$	51.8729	3.31404
$246$	−1.02101	−0.0650975
$247$	−11.9439	−0.759975
$248$	2.26611	0.143898
$249$	−50.6123	−3.20743
$250$	7.26464	0.459456
$251$	−15.7430	−0.993687	−0.496843	−	0.867840i	$-0.665508\pi$
$251$	−15.7430	−0.993687	−0.496843	+	0.867840i	$0.665508\pi$
$252$	39.5147	2.48919
$253$	36.3516	2.28541
$254$	7.02246	0.440629
$255$	11.8132	0.739772
$256$	1.00000	0.0625000
$257$	24.0294	1.49891	0.749457	−	0.662053i	$-0.230315\pi$
$257$	24.0294	1.49891	0.749457	+	0.662053i	$0.230315\pi$
$258$	31.6430	1.97001
$259$	32.8007	2.03814
$260$	12.7771	0.792404
$261$	−34.3198	−2.12434
$262$	2.78671	0.172164
$263$	−25.3051	−1.56038	−0.780191	−	0.625541i	$-0.784878\pi$
$263$	−25.3051	−1.56038	−0.780191	+	0.625541i	$0.784878\pi$
$264$	19.2543	1.18502
$265$	7.37725	0.453181
$266$	−15.2169	−0.933008
$267$	−46.7071	−2.85843
$268$	−6.46535	−0.394934
$269$	−4.34371	−0.264841	−0.132420	−	0.991194i	$-0.542275\pi$
$269$	−4.34371	−0.264841	−0.132420	+	0.991194i	$0.542275\pi$
$270$	−63.9773	−3.89353
$271$	−0.480775	−0.0292050	−0.0146025	−	0.999893i	$-0.504648\pi$
$271$	−0.480775	−0.0292050	−0.0146025	+	0.999893i	$0.504648\pi$
$272$	−1.00450	−0.0609069
$273$	−58.1912	−3.52189
$274$	10.5090	0.634871
$275$	−40.3570	−2.43362
$276$	21.5987	1.30009
$277$	23.7047	1.42428	0.712138	−	0.702040i	$-0.247727\pi$
$277$	23.7047	1.42428	0.712138	+	0.702040i	$0.247727\pi$
$278$	−7.47768	−0.448481
$279$	19.1262	1.14506
$280$	16.2784	0.972820
$281$	8.08186	0.482124	0.241062	−	0.970510i	$-0.422504\pi$
$281$	8.08186	0.482124	0.241062	+	0.970510i	$0.422504\pi$
$282$	−26.6890	−1.58931
$283$	9.52695	0.566318	0.283159	−	0.959073i	$-0.408618\pi$
$283$	9.52695	0.566318	0.283159	+	0.959073i	$0.408618\pi$
$284$	14.6890	0.871633
$285$	38.2237	2.26418
$286$	−20.9191	−1.23697
$287$	1.41328	0.0834230
$288$	8.44012	0.497339
$289$	−15.9910	−0.940646
$290$	−14.1383	−0.830230
$291$	−0.536514	−0.0314510
$292$	12.5542	0.734679
$293$	−22.4118	−1.30931	−0.654657	−	0.755926i	$-0.727187\pi$
$293$	−22.4118	−1.30931	−0.654657	+	0.755926i	$0.727187\pi$
$294$	−50.4608	−2.94294
$295$	−5.52362	−0.321598
$296$	7.00605	0.407219
$297$	104.746	6.07796
$298$	10.9544	0.634572
$299$	−23.4663	−1.35709
$300$	−23.9785	−1.38440
$301$	−43.7999	−2.52458
$302$	18.6781	1.07480
$303$	−4.29007	−0.246458
$304$	−3.25024	−0.186414
$305$	10.3589	0.593147
$306$	−8.47812	−0.484662
$307$	13.7412	0.784251	0.392126	−	0.919912i	$-0.371740\pi$
$307$	13.7412	0.784251	0.392126	+	0.919912i	$0.371740\pi$
$308$	−26.6515	−1.51861
$309$	−25.5395	−1.45289
$310$	7.87920	0.447509
$311$	2.09532	0.118814	0.0594072	−	0.998234i	$-0.481079\pi$
$311$	2.09532	0.118814	0.0594072	+	0.998234i	$0.481079\pi$
$312$	−12.4293	−0.703672
$313$	−22.0807	−1.24808	−0.624038	−	0.781394i	$-0.714509\pi$
$313$	−22.0807	−1.24808	−0.624038	+	0.781394i	$0.714509\pi$
$314$	3.64140	0.205496
$315$	137.392	7.74115
$316$	8.43802	0.474676
$317$	8.87209	0.498306	0.249153	−	0.968464i	$-0.419848\pi$
$317$	8.87209	0.498306	0.249153	+	0.968464i	$0.419848\pi$
$318$	−7.17643	−0.402434
$319$	23.1477	1.29602
$320$	3.47698	0.194369
$321$	−43.3226	−2.41803
$322$	−29.8966	−1.66607
$323$	3.26488	0.181663
$324$	36.9153	2.05085
$325$	26.0519	1.44510
$326$	6.76777	0.374832
$327$	61.7982	3.41745
$328$	0.301868	0.0166679
$329$	36.9426	2.03671
$330$	66.9466	3.68529
$331$	33.1778	1.82361	0.911807	−	0.410618i	$-0.134687\pi$
$331$	33.1778	1.82361	0.911807	+	0.410618i	$0.134687\pi$
$332$	14.9638	0.821243
$333$	59.1320	3.24041
$334$	10.0864	0.551902
$335$	−22.4799	−1.22821
$336$	−15.8353	−0.863885
$337$	15.3951	0.838624	0.419312	−	0.907842i	$-0.362271\pi$
$337$	15.3951	0.838624	0.419312	+	0.907842i	$0.362271\pi$
$338$	0.504042	0.0274163
$339$	65.6759	3.56703
$340$	−3.49263	−0.189414
$341$	−12.9001	−0.698578
$342$	−27.4325	−1.48338
$343$	37.0748	2.00185
$344$	−9.35541	−0.504410
$345$	75.0981	4.04315
$346$	3.24728	0.174575
$347$	−1.09237	−0.0586414	−0.0293207	−	0.999570i	$-0.509334\pi$
$347$	−1.09237	−0.0586414	−0.0293207	+	0.999570i	$0.509334\pi$
$348$	13.7534	0.737262
$349$	22.3637	1.19710	0.598551	−	0.801085i	$-0.295744\pi$
$349$	22.3637	1.19710	0.598551	+	0.801085i	$0.295744\pi$
$350$	33.1907	1.77412
$351$	−67.6170	−3.60913
$352$	−5.69261	−0.303417
$353$	−26.5731	−1.41434	−0.707172	−	0.707042i	$-0.750029\pi$
$353$	−26.5731	−1.41434	−0.707172	+	0.707042i	$0.750029\pi$
$354$	5.37326	0.285586
$355$	51.0734	2.71069
$356$	13.8092	0.731885
$357$	15.9066	0.841864
$358$	−17.5316	−0.926574
$359$	−1.26143	−0.0665757	−0.0332879	−	0.999446i	$-0.510598\pi$
$359$	−1.26143	−0.0665757	−0.0332879	+	0.999446i	$0.510598\pi$
$360$	29.3461	1.54668
$361$	−8.43591	−0.443995
$362$	15.2097	0.799402
$363$	−72.4016	−3.80010
$364$	17.2045	0.901761
$365$	43.6507	2.28478
$366$	−10.0769	−0.526727
$367$	−20.9583	−1.09401	−0.547007	−	0.837128i	$-0.684233\pi$
$367$	−20.9583	−1.09401	−0.547007	+	0.837128i	$0.684233\pi$
$368$	−6.38575	−0.332880
$369$	2.54780	0.132633
$370$	24.3599	1.26641
$371$	9.93352	0.515723
$372$	−7.66471	−0.397397
$373$	16.9066	0.875389	0.437695	−	0.899124i	$-0.355795\pi$
$373$	16.9066	0.875389	0.437695	+	0.899124i	$0.355795\pi$
$374$	5.71824	0.295683
$375$	−24.5714	−1.26886
$376$	7.89073	0.406933
$377$	−14.9427	−0.769586
$378$	−86.1458	−4.43086
$379$	28.3677	1.45715	0.728574	−	0.684967i	$-0.240183\pi$
$379$	28.3677	1.45715	0.728574	+	0.684967i	$0.240183\pi$
$380$	−11.3010	−0.579730
$381$	−23.7523	−1.21686
$382$	20.5394	1.05089
$383$	12.6778	0.647807	0.323904	−	0.946090i	$-0.395005\pi$
$383$	12.6778	0.647807	0.323904	+	0.946090i	$0.395005\pi$
$384$	−3.38233	−0.172604
$385$	−92.6667	−4.72273
$386$	−16.5583	−0.842798
$387$	−78.9608	−4.01380
$388$	0.158623	0.00805285
$389$	−22.2958	−1.13044	−0.565221	−	0.824939i	$-0.691209\pi$
$389$	−22.2958	−1.13044	−0.565221	+	0.824939i	$0.691209\pi$
$390$	−43.2164	−2.18835
$391$	6.41450	0.324395
$392$	14.9190	0.753522
$393$	−9.42556	−0.475457
$394$	−22.8892	−1.15314
$395$	29.3388	1.47619
$396$	−48.0464	−2.41442
$397$	−11.2354	−0.563890	−0.281945	−	0.959431i	$-0.590980\pi$
$397$	−11.2354	−0.563890	−0.281945	+	0.959431i	$0.590980\pi$
$398$	3.83250	0.192106
$399$	51.4685	2.57665
$400$	7.08936	0.354468
$401$	−36.0589	−1.80070	−0.900349	−	0.435169i	$-0.856689\pi$
$401$	−36.0589	−1.80070	−0.900349	+	0.435169i	$0.856689\pi$
$402$	21.8679	1.09067
$403$	8.32746	0.414820
$404$	1.26838	0.0631042
$405$	128.354	6.37794
$406$	−19.0373	−0.944807
$407$	−39.8828	−1.97692
$408$	3.39755	0.168204
$409$	−9.82954	−0.486039	−0.243020	−	0.970021i	$-0.578138\pi$
$409$	−9.82954	−0.486039	−0.243020	+	0.970021i	$0.578138\pi$
$410$	1.04959	0.0518354
$411$	−35.5448	−1.75330
$412$	7.55086	0.372004
$413$	−7.43760	−0.365980
$414$	−53.8965	−2.64887
$415$	52.0286	2.55399
$416$	3.67478	0.180171
$417$	25.2919	1.23855
$418$	18.5024	0.904981
$419$	−10.3496	−0.505611	−0.252806	−	0.967517i	$-0.581353\pi$
$419$	−10.3496	−0.505611	−0.252806	+	0.967517i	$0.581353\pi$
$420$	−55.0588	−2.68660
$421$	17.3393	0.845066	0.422533	−	0.906348i	$-0.361141\pi$
$421$	17.3393	0.845066	0.422533	+	0.906348i	$0.361141\pi$
$422$	0.100033	0.00486951
$423$	66.5987	3.23814
$424$	2.12174	0.103041
$425$	−7.12127	−0.345432
$426$	−49.6830	−2.40715
$427$	13.9483	0.675005
$428$	12.8085	0.619124
$429$	70.7553	3.41610
$430$	−32.5285	−1.56866
$431$	23.5467	1.13421	0.567103	−	0.823647i	$-0.308064\pi$
$431$	23.5467	1.13421	0.567103	+	0.823647i	$0.308064\pi$
$432$	−18.4003	−0.885283
$433$	−16.7975	−0.807237	−0.403619	−	0.914927i	$-0.632248\pi$
$433$	−16.7975	−0.807237	−0.403619	+	0.914927i	$0.632248\pi$
$434$	10.6094	0.509267
$435$	47.8204	2.29281
$436$	−18.2709	−0.875018
$437$	20.7553	0.992859
$438$	−42.4624	−2.02893
$439$	−3.52072	−0.168035	−0.0840174	−	0.996464i	$-0.526775\pi$
$439$	−3.52072	−0.168035	−0.0840174	+	0.996464i	$0.526775\pi$
$440$	−19.7931	−0.943598
$441$	125.918	5.99610
$442$	−3.69133	−0.175579
$443$	−22.4606	−1.06714	−0.533569	−	0.845757i	$-0.679149\pi$
$443$	−22.4606	−1.06714	−0.533569	+	0.845757i	$0.679149\pi$
$444$	−23.6968	−1.12460
$445$	48.0142	2.27609
$446$	−10.4478	−0.494718
$447$	−37.0514	−1.75247
$448$	4.68177	0.221193
$449$	−35.1092	−1.65691	−0.828453	−	0.560059i	$-0.810779\pi$
$449$	−35.1092	−1.65691	−0.828453	+	0.560059i	$0.810779\pi$
$450$	59.8350	2.82065
$451$	−1.71842	−0.0809171
$452$	−19.4174	−0.913317
$453$	−63.1754	−2.96824
$454$	15.7818	0.740676
$455$	59.8196	2.80439
$456$	10.9934	0.514812
$457$	−15.4078	−0.720748	−0.360374	−	0.932808i	$-0.617351\pi$
$457$	−15.4078	−0.720748	−0.360374	+	0.932808i	$0.617351\pi$
$458$	18.0276	0.842376
$459$	18.4831	0.862718
$460$	−22.2031	−1.03522
$461$	7.94254	0.369921	0.184961	−	0.982746i	$-0.440784\pi$
$461$	7.94254	0.369921	0.184961	+	0.982746i	$0.440784\pi$
$462$	90.1441	4.19388
$463$	38.9312	1.80929	0.904643	−	0.426170i	$-0.140138\pi$
$463$	38.9312	1.80929	0.904643	+	0.426170i	$0.140138\pi$
$464$	−4.06627	−0.188772
$465$	−26.6500	−1.23587
$466$	−16.1454	−0.747920
$467$	−8.30887	−0.384489	−0.192244	−	0.981347i	$-0.561577\pi$
$467$	−8.30887	−0.384489	−0.192244	+	0.981347i	$0.561577\pi$
$468$	31.0156	1.43370
$469$	−30.2693	−1.39771
$470$	27.4359	1.26552
$471$	−12.3164	−0.567509
$472$	−1.58863	−0.0731226
$473$	53.2567	2.44875
$474$	−28.5401	−1.31089
$475$	−23.0421	−1.05725
$476$	−4.70285	−0.215555
$477$	17.9078	0.819941
$478$	15.3673	0.702886
$479$	−13.3229	−0.608738	−0.304369	−	0.952554i	$-0.598446\pi$
$479$	−13.3229	−0.608738	−0.304369	+	0.952554i	$0.598446\pi$
$480$	−11.7603	−0.536780
$481$	25.7457	1.17390
$482$	−16.3007	−0.742474
$483$	101.120	4.60112
$484$	21.4059	0.972994
$485$	0.551527	0.0250436
$486$	−69.6588	−3.15979
$487$	22.5367	1.02123	0.510617	−	0.859808i	$-0.329417\pi$
$487$	22.5367	1.02123	0.510617	+	0.859808i	$0.329417\pi$
$488$	2.97928	0.134865
$489$	−22.8908	−1.03516
$490$	51.8729	2.34338
$491$	−13.5134	−0.609852	−0.304926	−	0.952376i	$-0.598632\pi$
$491$	−13.5134	−0.609852	−0.304926	+	0.952376i	$0.598632\pi$
$492$	−1.02101	−0.0460309
$493$	4.08457	0.183960
$494$	−11.9439	−0.537384
$495$	−167.056	−7.50861
$496$	2.26611	0.101751
$497$	68.7706	3.08478
$498$	−50.6123	−2.26799
$499$	29.8928	1.33818	0.669092	−	0.743179i	$-0.266683\pi$
$499$	29.8928	1.33818	0.669092	+	0.743179i	$0.266683\pi$
$500$	7.26464	0.324884
$501$	−34.1154	−1.52416
$502$	−15.7430	−0.702643
$503$	−5.91228	−0.263615	−0.131808	−	0.991275i	$-0.542078\pi$
$503$	−5.91228	−0.263615	−0.131808	+	0.991275i	$0.542078\pi$
$504$	39.5147	1.76013
$505$	4.41012	0.196248
$506$	36.3516	1.61603
$507$	−1.70483	−0.0757143
$508$	7.02246	0.311571
$509$	−22.9962	−1.01929	−0.509644	−	0.860386i	$-0.670223\pi$
$509$	−22.9962	−1.01929	−0.509644	+	0.860386i	$0.670223\pi$
$510$	11.8132	0.523097
$511$	58.7759	2.60009
$512$	1.00000	0.0441942
$513$	59.8054	2.64047
$514$	24.0294	1.05989
$515$	26.2541	1.15690
$516$	31.6430	1.39301
$517$	−44.9189	−1.97553
$518$	32.8007	1.44118
$519$	−10.9833	−0.482115
$520$	12.7771	0.560314
$521$	28.8951	1.26592	0.632959	−	0.774185i	$-0.281840\pi$
$521$	28.8951	1.26592	0.632959	+	0.774185i	$0.281840\pi$
$522$	−34.3198	−1.50214
$523$	−29.9496	−1.30960	−0.654801	−	0.755801i	$-0.727248\pi$
$523$	−29.9496	−1.30960	−0.654801	+	0.755801i	$0.727248\pi$
$524$	2.78671	0.121738
$525$	−112.262	−4.89951
$526$	−25.3051	−1.10336
$527$	−2.27631	−0.0991576
$528$	19.2543	0.837935
$529$	17.7778	0.772949
$530$	7.37725	0.320447
$531$	−13.4082	−0.581868
$532$	−15.2169	−0.659736
$533$	1.10930	0.0480491
$534$	−46.7071	−2.02122
$535$	44.5349	1.92541
$536$	−6.46535	−0.279261
$537$	59.2976	2.55888
$538$	−4.34371	−0.187271
$539$	−84.9280	−3.65811
$540$	−63.9773	−2.75314
$541$	1.99306	0.0856884	0.0428442	−	0.999082i	$-0.486358\pi$
$541$	1.99306	0.0856884	0.0428442	+	0.999082i	$0.486358\pi$
$542$	−0.480775	−0.0206510
$543$	−51.4440	−2.20767
$544$	−1.00450	−0.0430677
$545$	−63.5275	−2.72122
$546$	−58.1912	−2.49035
$547$	15.9512	0.682023	0.341012	−	0.940059i	$-0.389230\pi$
$547$	15.9512	0.682023	0.341012	+	0.940059i	$0.389230\pi$
$548$	10.5090	0.448922
$549$	25.1455	1.07318
$550$	−40.3570	−1.72083
$551$	13.2164	0.563036
$552$	21.5987	0.919301
$553$	39.5049	1.67992
$554$	23.7047	1.00712
$555$	−82.3930	−3.49739
$556$	−7.47768	−0.317124
$557$	14.7120	0.623366	0.311683	−	0.950186i	$-0.399107\pi$
$557$	14.7120	0.623366	0.311683	+	0.950186i	$0.399107\pi$
$558$	19.1262	0.809678
$559$	−34.3791	−1.45408
$560$	16.2784	0.687888
$561$	−19.3410	−0.816576
$562$	8.08186	0.340913
$563$	−14.3944	−0.606651	−0.303326	−	0.952887i	$-0.598097\pi$
$563$	−14.3944	−0.606651	−0.303326	+	0.952887i	$0.598097\pi$
$564$	−26.6890	−1.12381
$565$	−67.5138	−2.84033
$566$	9.52695	0.400448
$567$	172.829	7.25814
$568$	14.6890	0.616338
$569$	−21.1521	−0.886741	−0.443371	−	0.896338i	$-0.646217\pi$
$569$	−21.1521	−0.886741	−0.443371	+	0.896338i	$0.646217\pi$
$570$	38.2237	1.60102
$571$	−28.7550	−1.20336	−0.601679	−	0.798738i	$-0.705501\pi$
$571$	−28.7550	−1.20336	−0.601679	+	0.798738i	$0.705501\pi$
$572$	−20.9191	−0.874673
$573$	−69.4709	−2.90219
$574$	1.41328	0.0589890
$575$	−45.2709	−1.88793
$576$	8.44012	0.351672
$577$	−10.9799	−0.457100	−0.228550	−	0.973532i	$-0.573398\pi$
$577$	−10.9799	−0.457100	−0.228550	+	0.973532i	$0.573398\pi$
$578$	−15.9910	−0.665137
$579$	56.0057	2.32752
$580$	−14.1383	−0.587061
$581$	70.0569	2.90645
$582$	−0.536514	−0.0222392
$583$	−12.0783	−0.500231
$584$	12.5542	0.519497
$585$	107.841	4.45866
$586$	−22.4118	−0.925824
$587$	−37.0175	−1.52788	−0.763938	−	0.645290i	$-0.776737\pi$
$587$	−37.0175	−1.52788	−0.763938	+	0.645290i	$0.776737\pi$
$588$	−50.4608	−2.08097
$589$	−7.36541	−0.303486
$590$	−5.52362	−0.227404
$591$	77.4187	3.18458
$592$	7.00605	0.287947
$593$	−36.5388	−1.50047	−0.750234	−	0.661172i	$-0.770059\pi$
$593$	−36.5388	−1.50047	−0.750234	+	0.661172i	$0.770059\pi$
$594$	104.746	4.29777
$595$	−16.3517	−0.670354
$596$	10.9544	0.448710
$597$	−12.9627	−0.530530
$598$	−23.4663	−0.959607
$599$	−15.5607	−0.635795	−0.317897	−	0.948125i	$-0.602977\pi$
$599$	−15.5607	−0.635795	−0.317897	+	0.948125i	$0.602977\pi$
$600$	−23.9785	−0.978918
$601$	−27.1354	−1.10687	−0.553437	−	0.832891i	$-0.686684\pi$
$601$	−27.1354	−1.10687	−0.553437	+	0.832891i	$0.686684\pi$
$602$	−43.7999	−1.78515
$603$	−54.5684	−2.22220
$604$	18.6781	0.760001
$605$	74.4276	3.02591
$606$	−4.29007	−0.174272
$607$	−11.3002	−0.458660	−0.229330	−	0.973349i	$-0.573653\pi$
$607$	−11.3002	−0.458660	−0.229330	+	0.973349i	$0.573653\pi$
$608$	−3.25024	−0.131815
$609$	64.3904	2.60923
$610$	10.3589	0.419418
$611$	28.9967	1.17308
$612$	−8.47812	−0.342708
$613$	−9.94181	−0.401546	−0.200773	−	0.979638i	$-0.564345\pi$
$613$	−9.94181	−0.401546	−0.200773	+	0.979638i	$0.564345\pi$
$614$	13.7412	0.554550
$615$	−3.55004	−0.143152
$616$	−26.6515	−1.07382
$617$	−22.8911	−0.921563	−0.460781	−	0.887514i	$-0.652431\pi$
$617$	−22.8911	−0.921563	−0.460781	+	0.887514i	$0.652431\pi$
$618$	−25.5395	−1.02735
$619$	−2.00763	−0.0806935	−0.0403467	−	0.999186i	$-0.512846\pi$
$619$	−2.00763	−0.0806935	−0.0403467	+	0.999186i	$0.512846\pi$
$620$	7.87920	0.316436
$621$	117.500	4.71509
$622$	2.09532	0.0840145
$623$	64.6514	2.59020
$624$	−12.4293	−0.497571
$625$	−10.1878	−0.407513
$626$	−22.0807	−0.882523
$627$	−62.5811	−2.49925
$628$	3.64140	0.145308
$629$	−7.03760	−0.280607
$630$	137.392	5.47382
$631$	−16.4967	−0.656725	−0.328363	−	0.944552i	$-0.606497\pi$
$631$	−16.4967	−0.656725	−0.328363	+	0.944552i	$0.606497\pi$
$632$	8.43802	0.335646
$633$	−0.338343	−0.0134479
$634$	8.87209	0.352356
$635$	24.4169	0.968956
$636$	−7.17643	−0.284564
$637$	54.8240	2.17221
$638$	23.1477	0.916426
$639$	123.977	4.90446
$640$	3.47698	0.137440
$641$	10.1649	0.401488	0.200744	−	0.979644i	$-0.435664\pi$
$641$	10.1649	0.401488	0.200744	+	0.979644i	$0.435664\pi$
$642$	−43.3226	−1.70981
$643$	23.2791	0.918039	0.459020	−	0.888426i	$-0.348201\pi$
$643$	23.2791	0.918039	0.459020	+	0.888426i	$0.348201\pi$
$644$	−29.8966	−1.17809
$645$	110.022	4.33211
$646$	3.26488	0.128455
$647$	−14.1730	−0.557199	−0.278600	−	0.960407i	$-0.589870\pi$
$647$	−14.1730	−0.557199	−0.278600	+	0.960407i	$0.589870\pi$
$648$	36.9153	1.45017
$649$	9.04345	0.354987
$650$	26.0519	1.02184
$651$	−35.8844	−1.40642
$652$	6.76777	0.265046
$653$	26.1100	1.02176	0.510881	−	0.859652i	$-0.329319\pi$
$653$	26.1100	1.02176	0.510881	+	0.859652i	$0.329319\pi$
$654$	61.7982	2.41650
$655$	9.68932	0.378593
$656$	0.301868	0.0117860
$657$	105.959	4.13386
$658$	36.9426	1.44017
$659$	−34.1508	−1.33033	−0.665163	−	0.746699i	$-0.731638\pi$
$659$	−34.1508	−1.33033	−0.665163	+	0.746699i	$0.731638\pi$
$660$	66.9466	2.60589
$661$	35.8326	1.39373	0.696863	−	0.717204i	$-0.254578\pi$
$661$	35.8326	1.39373	0.696863	+	0.717204i	$0.254578\pi$
$662$	33.1778	1.28949
$663$	12.4853	0.484888
$664$	14.9638	0.580707
$665$	−52.9088	−2.05171
$666$	59.1320	2.29132
$667$	25.9662	1.00541
$668$	10.0864	0.390253
$669$	35.3379	1.36624
$670$	−22.4799	−0.868473
$671$	−16.9599	−0.654728
$672$	−15.8353	−0.610859
$673$	−40.0405	−1.54345	−0.771723	−	0.635959i	$-0.780605\pi$
$673$	−40.0405	−1.54345	−0.771723	+	0.635959i	$0.780605\pi$
$674$	15.3951	0.592997
$675$	−130.446	−5.02087
$676$	0.504042	0.0193862
$677$	−16.6749	−0.640870	−0.320435	−	0.947270i	$-0.603829\pi$
$677$	−16.6749	−0.640870	−0.320435	+	0.947270i	$0.603829\pi$
$678$	65.6759	2.52227
$679$	0.742635	0.0284997
$680$	−3.49263	−0.133936
$681$	−53.3791	−2.04549
$682$	−12.9001	−0.493970
$683$	12.7911	0.489437	0.244718	−	0.969594i	$-0.421304\pi$
$683$	12.7911	0.489437	0.244718	+	0.969594i	$0.421304\pi$
$684$	−27.4325	−1.04891
$685$	36.5395	1.39610
$686$	37.0748	1.41552
$687$	−60.9753	−2.32635
$688$	−9.35541	−0.356672
$689$	7.79695	0.297040
$690$	75.0981	2.85894
$691$	−36.5919	−1.39202	−0.696011	−	0.718031i	$-0.745044\pi$
$691$	−36.5919	−1.39202	−0.696011	+	0.718031i	$0.745044\pi$
$692$	3.24728	0.123443
$693$	−224.942	−8.54484
$694$	−1.09237	−0.0414657
$695$	−25.9997	−0.986225
$696$	13.7534	0.521323
$697$	−0.303227	−0.0114855
$698$	22.3637	0.846478
$699$	54.6089	2.06550
$700$	33.1907	1.25449
$701$	−34.5333	−1.30431	−0.652153	−	0.758088i	$-0.726134\pi$
$701$	−34.5333	−1.30431	−0.652153	+	0.758088i	$0.726134\pi$
$702$	−67.6170	−2.55204
$703$	−22.7714	−0.858839
$704$	−5.69261	−0.214548
$705$	−92.7970	−3.49494
$706$	−26.5731	−1.00009
$707$	5.93826	0.223331
$708$	5.37326	0.201940
$709$	28.1681	1.05787	0.528937	−	0.848661i	$-0.322591\pi$
$709$	28.1681	1.05787	0.528937	+	0.848661i	$0.322591\pi$
$710$	51.0734	1.91675
$711$	71.2179	2.67088
$712$	13.8092	0.517521
$713$	−14.4708	−0.541936
$714$	15.9066	0.595288
$715$	−72.7353	−2.72015
$716$	−17.5316	−0.655186
$717$	−51.9773	−1.94113
$718$	−1.26143	−0.0470762
$719$	7.64477	0.285102	0.142551	−	0.989787i	$-0.454470\pi$
$719$	7.64477	0.285102	0.142551	+	0.989787i	$0.454470\pi$
$720$	29.3461	1.09366
$721$	35.3514	1.31655
$722$	−8.43591	−0.313952
$723$	55.1341	2.05046
$724$	15.2097	0.565262
$725$	−28.8272	−1.07062
$726$	−72.4016	−2.68707
$727$	−2.57741	−0.0955908	−0.0477954	−	0.998857i	$-0.515220\pi$
$727$	−2.57741	−0.0955908	−0.0477954	+	0.998857i	$0.515220\pi$
$728$	17.2045	0.637641
$729$	124.863	4.62455
$730$	43.6507	1.61558
$731$	9.39752	0.347580
$732$	−10.0769	−0.372452
$733$	−19.6205	−0.724699	−0.362349	−	0.932042i	$-0.618025\pi$
$733$	−19.6205	−0.724699	−0.362349	+	0.932042i	$0.618025\pi$
$734$	−20.9583	−0.773584
$735$	−175.451	−6.47161
$736$	−6.38575	−0.235382
$737$	36.8047	1.35572
$738$	2.54780	0.0937859
$739$	−5.04600	−0.185620	−0.0928101	−	0.995684i	$-0.529585\pi$
$739$	−5.04600	−0.185620	−0.0928101	+	0.995684i	$0.529585\pi$
$740$	24.3599	0.895487
$741$	40.3983	1.48407
$742$	9.93352	0.364671
$743$	−42.1974	−1.54807	−0.774036	−	0.633142i	$-0.781765\pi$
$743$	−42.1974	−1.54807	−0.774036	+	0.633142i	$0.781765\pi$
$744$	−7.66471	−0.281002
$745$	38.0882	1.39544
$746$	16.9066	0.618994
$747$	126.296	4.62093
$748$	5.71824	0.209080
$749$	59.9666	2.19113
$750$	−24.5714	−0.897219
$751$	30.9834	1.13060	0.565300	−	0.824886i	$-0.308761\pi$
$751$	30.9834	1.13060	0.565300	+	0.824886i	$0.308761\pi$
$752$	7.89073	0.287745
$753$	53.2478	1.94046
$754$	−14.9427	−0.544179
$755$	64.9433	2.36353
$756$	−86.1458	−3.13309
$757$	6.23611	0.226655	0.113328	−	0.993558i	$-0.463849\pi$
$757$	6.23611	0.226655	0.113328	+	0.993558i	$0.463849\pi$
$758$	28.3677	1.03036
$759$	−122.953	−4.46291
$760$	−11.3010	−0.409931
$761$	16.8723	0.611622	0.305811	−	0.952092i	$-0.401072\pi$
$761$	16.8723	0.611622	0.305811	+	0.952092i	$0.401072\pi$
$762$	−23.7523	−0.860453
$763$	−85.5403	−3.09677
$764$	20.5394	0.743089
$765$	−29.4782	−1.06579
$766$	12.6778	0.458069
$767$	−5.83787	−0.210793
$768$	−3.38233	−0.122049
$769$	−38.7051	−1.39574	−0.697871	−	0.716224i	$-0.745869\pi$
$769$	−38.7051	−1.39574	−0.697871	+	0.716224i	$0.745869\pi$
$770$	−92.6667	−3.33947
$771$	−81.2753	−2.92706
$772$	−16.5583	−0.595948
$773$	22.2156	0.799038	0.399519	−	0.916725i	$-0.369177\pi$
$773$	22.2156	0.799038	0.399519	+	0.916725i	$0.369177\pi$
$774$	−78.9608	−2.83819
$775$	16.0652	0.577081
$776$	0.158623	0.00569422
$777$	−110.943	−3.98005
$778$	−22.2958	−0.799344
$779$	−0.981144	−0.0351531
$780$	−43.2164	−1.54740
$781$	−83.6189	−2.99212
$782$	6.41450	0.229382
$783$	74.8204	2.67386
$784$	14.9190	0.532821
$785$	12.6610	0.451892
$786$	−9.42556	−0.336199
$787$	3.81386	0.135950	0.0679748	−	0.997687i	$-0.478346\pi$
$787$	3.81386	0.135950	0.0679748	+	0.997687i	$0.478346\pi$
$788$	−22.8892	−0.815394
$789$	85.5902	3.04709
$790$	29.3388	1.04383
$791$	−90.9078	−3.23231
$792$	−48.0464	−1.70725
$793$	10.9482	0.388782
$794$	−11.2354	−0.398730
$795$	−24.9523	−0.884965
$796$	3.83250	0.135839
$797$	21.5616	0.763750	0.381875	−	0.924214i	$-0.375278\pi$
$797$	21.5616	0.763750	0.381875	+	0.924214i	$0.375278\pi$
$798$	51.4685	1.82197
$799$	−7.92625	−0.280411
$800$	7.08936	0.250647
$801$	116.551	4.11813
$802$	−36.0589	−1.27329
$803$	−71.4663	−2.52199
$804$	21.8679	0.771222
$805$	−103.950	−3.66375
$806$	8.32746	0.293322
$807$	14.6918	0.517178
$808$	1.26838	0.0446214
$809$	−28.7825	−1.01194	−0.505970	−	0.862551i	$-0.668865\pi$
$809$	−28.7825	−1.01194	−0.505970	+	0.862551i	$0.668865\pi$
$810$	128.354	4.50989
$811$	−37.0935	−1.30253	−0.651264	−	0.758851i	$-0.725761\pi$
$811$	−37.0935	−1.30253	−0.651264	+	0.758851i	$0.725761\pi$
$812$	−19.0373	−0.668079
$813$	1.62614	0.0570311
$814$	−39.8828	−1.39789
$815$	23.5314	0.824268
$816$	3.39755	0.118938
$817$	30.4074	1.06382
$818$	−9.82954	−0.343682
$819$	145.208	5.07398
$820$	1.04959	0.0366532
$821$	−14.2017	−0.495642	−0.247821	−	0.968806i	$-0.579714\pi$
$821$	−14.2017	−0.495642	−0.247821	+	0.968806i	$0.579714\pi$
$822$	−35.5448	−1.23977
$823$	−32.1382	−1.12027	−0.560134	−	0.828402i	$-0.689250\pi$
$823$	−32.1382	−1.12027	−0.560134	+	0.828402i	$0.689250\pi$
$824$	7.55086	0.263047
$825$	136.500	4.75233
$826$	−7.43760	−0.258787
$827$	11.9042	0.413949	0.206975	−	0.978346i	$-0.433638\pi$
$827$	11.9042	0.413949	0.206975	+	0.978346i	$0.433638\pi$
$828$	−53.8965	−1.87303
$829$	38.6922	1.34383	0.671917	−	0.740626i	$-0.265471\pi$
$829$	38.6922	1.34383	0.671917	+	0.740626i	$0.265471\pi$
$830$	52.0286	1.80594
$831$	−80.1769	−2.78131
$832$	3.67478	0.127400
$833$	−14.9861	−0.519239
$834$	25.2919	0.875788
$835$	35.0701	1.21365
$836$	18.5024	0.639919
$837$	−41.6970	−1.44126
$838$	−10.3496	−0.357521
$839$	−19.2927	−0.666057	−0.333029	−	0.942917i	$-0.608071\pi$
$839$	−19.2927	−0.666057	−0.333029	+	0.942917i	$0.608071\pi$
$840$	−55.0588	−1.89971
$841$	−12.4655	−0.429844
$842$	17.3393	0.597552
$843$	−27.3355	−0.941484
$844$	0.100033	0.00344326
$845$	1.75254	0.0602893
$846$	66.5987	2.28971
$847$	100.217	3.44351
$848$	2.12174	0.0728610
$849$	−32.2232	−1.10590
$850$	−7.12127	−0.244258
$851$	−44.7389	−1.53363
$852$	−49.6830	−1.70211
$853$	31.0434	1.06291	0.531453	−	0.847088i	$-0.321646\pi$
$853$	31.0434	1.06291	0.531453	+	0.847088i	$0.321646\pi$
$854$	13.9483	0.477300
$855$	−95.3820	−3.26200
$856$	12.8085	0.437787
$857$	15.1444	0.517323	0.258661	−	0.965968i	$-0.416719\pi$
$857$	15.1444	0.517323	0.258661	+	0.965968i	$0.416719\pi$
$858$	70.7553	2.41555
$859$	12.5493	0.428177	0.214089	−	0.976814i	$-0.431322\pi$
$859$	12.5493	0.428177	0.214089	+	0.976814i	$0.431322\pi$
$860$	−32.5285	−1.10921
$861$	−4.78016	−0.162907
$862$	23.5467	0.802004
$863$	−7.76247	−0.264238	−0.132119	−	0.991234i	$-0.542178\pi$
$863$	−7.76247	−0.264238	−0.132119	+	0.991234i	$0.542178\pi$
$864$	−18.4003	−0.625990
$865$	11.2907	0.383895
$866$	−16.7975	−0.570803
$867$	54.0867	1.83688
$868$	10.6094	0.360106
$869$	−48.0344	−1.62946
$870$	47.8204	1.62126
$871$	−23.7588	−0.805035
$872$	−18.2709	−0.618731
$873$	1.33880	0.0453114
$874$	20.7553	0.702057
$875$	34.0114	1.14979
$876$	−42.4624	−1.43467
$877$	1.17301	0.0396097	0.0198048	−	0.999804i	$-0.493696\pi$
$877$	1.17301	0.0396097	0.0198048	+	0.999804i	$0.493696\pi$
$878$	−3.52072	−0.118819
$879$	75.8041	2.55681
$880$	−19.7931	−0.667225
$881$	8.24857	0.277901	0.138951	−	0.990299i	$-0.455627\pi$
$881$	8.24857	0.277901	0.138951	+	0.990299i	$0.455627\pi$
$882$	125.918	4.23988
$883$	−25.3891	−0.854413	−0.427206	−	0.904154i	$-0.640502\pi$
$883$	−25.3891	−0.854413	−0.427206	+	0.904154i	$0.640502\pi$
$884$	−3.69133	−0.124153
$885$	18.6827	0.628012
$886$	−22.4606	−0.754580
$887$	−50.2826	−1.68832	−0.844162	−	0.536089i	$-0.819901\pi$
$887$	−50.2826	−1.68832	−0.844162	+	0.536089i	$0.819901\pi$
$888$	−23.6968	−0.795211
$889$	32.8776	1.10268
$890$	48.0142	1.60944
$891$	−210.145	−7.04011
$892$	−10.4478	−0.349819
$893$	−25.6468	−0.858237
$894$	−37.0514	−1.23918
$895$	−60.9569	−2.03756
$896$	4.68177	0.156407
$897$	79.3705	2.65011
$898$	−35.1092	−1.17161
$899$	−9.21460	−0.307324
$900$	59.8350	1.99450
$901$	−2.13130	−0.0710038
$902$	−1.71842	−0.0572170
$903$	148.145	4.92997
$904$	−19.4174	−0.645813
$905$	52.8836	1.75791
$906$	−63.1754	−2.09886
$907$	−32.4944	−1.07896	−0.539479	−	0.841999i	$-0.681379\pi$
$907$	−32.4944	−1.07896	−0.539479	+	0.841999i	$0.681379\pi$
$908$	15.7818	0.523737
$909$	10.7053	0.355072
$910$	59.8196	1.98300
$911$	13.9176	0.461109	0.230555	−	0.973059i	$-0.425946\pi$
$911$	13.9176	0.461109	0.230555	+	0.973059i	$0.425946\pi$
$912$	10.9934	0.364027
$913$	−85.1829	−2.81914
$914$	−15.4078	−0.509646
$915$	−35.0371	−1.15829
$916$	18.0276	0.595650
$917$	13.0467	0.430841
$918$	18.4831	0.610033
$919$	28.7673	0.948947	0.474473	−	0.880270i	$-0.342639\pi$
$919$	28.7673	0.948947	0.474473	+	0.880270i	$0.342639\pi$
$920$	−22.2031	−0.732015
$921$	−46.4772	−1.53148
$922$	7.94254	0.261574
$923$	53.9790	1.77674
$924$	90.1441	2.96552
$925$	49.6684	1.63309
$926$	38.9312	1.27936
$927$	63.7302	2.09317
$928$	−4.06627	−0.133482
$929$	28.2547	0.927005	0.463503	−	0.886096i	$-0.346592\pi$
$929$	28.2547	0.927005	0.463503	+	0.886096i	$0.346592\pi$
$930$	−26.6500	−0.873889
$931$	−48.4903	−1.58921
$932$	−16.1454	−0.528859
$933$	−7.08704	−0.232019
$934$	−8.30887	−0.271875
$935$	19.8822	0.650217
$936$	31.0156	1.01378
$937$	−22.4072	−0.732010	−0.366005	−	0.930613i	$-0.619275\pi$
$937$	−22.4072	−0.732010	−0.366005	+	0.930613i	$0.619275\pi$
$938$	−30.2693	−0.988327
$939$	74.6841	2.43722
$940$	27.4359	0.894859
$941$	−6.04794	−0.197157	−0.0985786	−	0.995129i	$-0.531430\pi$
$941$	−6.04794	−0.197157	−0.0985786	+	0.995129i	$0.531430\pi$
$942$	−12.3164	−0.401290
$943$	−1.92765	−0.0627730
$944$	−1.58863	−0.0517055
$945$	−299.527	−9.74361
$946$	53.2567	1.73153
$947$	17.3006	0.562193	0.281097	−	0.959679i	$-0.409302\pi$
$947$	17.3006	0.562193	0.281097	+	0.959679i	$0.409302\pi$
$948$	−28.5401	−0.926940
$949$	46.1340	1.49757
$950$	−23.0421	−0.747586
$951$	−30.0083	−0.973086
$952$	−4.70285	−0.152420
$953$	−17.9136	−0.580278	−0.290139	−	0.956984i	$-0.593702\pi$
$953$	−17.9136	−0.580278	−0.290139	+	0.956984i	$0.593702\pi$
$954$	17.9078	0.579786
$955$	71.4150	2.31093
$956$	15.3673	0.497015
$957$	−78.2930	−2.53085
$958$	−13.3229	−0.430443
$959$	49.2007	1.58877
$960$	−11.7603	−0.379561
$961$	−25.8648	−0.834347
$962$	25.7457	0.830076
$963$	108.106	3.48365
$964$	−16.3007	−0.525009
$965$	−57.5730	−1.85334
$966$	101.120	3.25349
$967$	20.8407	0.670193	0.335096	−	0.942184i	$-0.391231\pi$
$967$	20.8407	0.670193	0.335096	+	0.942184i	$0.391231\pi$
$968$	21.4059	0.688010
$969$	−11.0429	−0.354748
$970$	0.551527	0.0177085
$971$	−6.84040	−0.219519	−0.109759	−	0.993958i	$-0.535008\pi$
$971$	−6.84040	−0.219519	−0.109759	+	0.993958i	$0.535008\pi$
$972$	−69.6588	−2.23431
$973$	−35.0088	−1.12233
$974$	22.5367	0.722122
$975$	−88.1158	−2.82197
$976$	2.97928	0.0953643
$977$	4.44231	0.142122	0.0710610	−	0.997472i	$-0.477362\pi$
$977$	4.44231	0.142122	0.0710610	+	0.997472i	$0.477362\pi$
$978$	−22.8908	−0.731967
$979$	−78.6103	−2.51240
$980$	51.8729	1.65702
$981$	−154.209	−4.92351
$982$	−13.5134	−0.431231
$983$	−33.6414	−1.07299	−0.536497	−	0.843902i	$-0.680253\pi$
$983$	−33.6414	−1.07299	−0.536497	+	0.843902i	$0.680253\pi$
$984$	−1.02101	−0.0325488
$985$	−79.5851	−2.53579
$986$	4.08457	0.130079
$987$	−124.952	−3.97726
$988$	−11.9439	−0.379988
$989$	59.7413	1.89966
$990$	−167.056	−5.30939
$991$	−1.23214	−0.0391402	−0.0195701	−	0.999808i	$-0.506230\pi$
$991$	−1.23214	−0.0391402	−0.0195701	+	0.999808i	$0.506230\pi$
$992$	2.26611	0.0719490
$993$	−112.218	−3.56113
$994$	68.7706	2.18127
$995$	13.3255	0.422446
$996$	−50.6123	−1.60371
$997$	−35.2219	−1.11549	−0.557744	−	0.830013i	$-0.688333\pi$
$997$	−35.2219	−1.11549	−0.557744	+	0.830013i	$0.688333\pi$
$998$	29.8928	0.946240
$999$	−128.913	−4.07864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.d.1.2	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.d.1.2	✓	101	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.38233 q^{3} +1.00000 q^{4} +3.47698 q^{5} -3.38233 q^{6} +4.68177 q^{7} +1.00000 q^{8} +8.44012 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.38233 q^{3} +1.00000 q^{4} +3.47698 q^{5} -3.38233 q^{6} +4.68177 q^{7} +1.00000 q^{8} +8.44012 q^{9} +3.47698 q^{10} -5.69261 q^{11} -3.38233 q^{12} +3.67478 q^{13} +4.68177 q^{14} -11.7603 q^{15} +1.00000 q^{16} -1.00450 q^{17} +8.44012 q^{18} -3.25024 q^{19} +3.47698 q^{20} -15.8353 q^{21} -5.69261 q^{22} -6.38575 q^{23} -3.38233 q^{24} +7.08936 q^{25} +3.67478 q^{26} -18.4003 q^{27} +4.68177 q^{28} -4.06627 q^{29} -11.7603 q^{30} +2.26611 q^{31} +1.00000 q^{32} +19.2543 q^{33} -1.00450 q^{34} +16.2784 q^{35} +8.44012 q^{36} +7.00605 q^{37} -3.25024 q^{38} -12.4293 q^{39} +3.47698 q^{40} +0.301868 q^{41} -15.8353 q^{42} -9.35541 q^{43} -5.69261 q^{44} +29.3461 q^{45} -6.38575 q^{46} +7.89073 q^{47} -3.38233 q^{48} +14.9190 q^{49} +7.08936 q^{50} +3.39755 q^{51} +3.67478 q^{52} +2.12174 q^{53} -18.4003 q^{54} -19.7931 q^{55} +4.68177 q^{56} +10.9934 q^{57} -4.06627 q^{58} -1.58863 q^{59} -11.7603 q^{60} +2.97928 q^{61} +2.26611 q^{62} +39.5147 q^{63} +1.00000 q^{64} +12.7771 q^{65} +19.2543 q^{66} -6.46535 q^{67} -1.00450 q^{68} +21.5987 q^{69} +16.2784 q^{70} +14.6890 q^{71} +8.44012 q^{72} +12.5542 q^{73} +7.00605 q^{74} -23.9785 q^{75} -3.25024 q^{76} -26.6515 q^{77} -12.4293 q^{78} +8.43802 q^{79} +3.47698 q^{80} +36.9153 q^{81} +0.301868 q^{82} +14.9638 q^{83} -15.8353 q^{84} -3.49263 q^{85} -9.35541 q^{86} +13.7534 q^{87} -5.69261 q^{88} +13.8092 q^{89} +29.3461 q^{90} +17.2045 q^{91} -6.38575 q^{92} -7.66471 q^{93} +7.89073 q^{94} -11.3010 q^{95} -3.38233 q^{96} +0.158623 q^{97} +14.9190 q^{98} -48.0464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9}+O(q^{10}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9	\( 101 q + 101 q^{2} + 10 q^{3} + 101 q^{4} + 19 q^{5} + 10 q^{6} + 42 q^{7} + 101 q^{8} + 147 q^{9} + 19 q^{10} + 4 q^{11} + 10 q^{12} + 58 q^{13} + 42 q^{14} + 27 q^{15} + 101 q^{16} + 34 q^{17} + 147 q^{18} + 36 q^{19} + 19 q^{20} + 45 q^{21} + 4 q^{22} + 47 q^{23} + 10 q^{24} + 174 q^{25} + 58 q^{26} + 31 q^{27} + 42 q^{28} + 62 q^{29} + 27 q^{30} + 47 q^{31} + 101 q^{32} + 55 q^{33} + 34 q^{34} + 16 q^{35} + 147 q^{36} + 90 q^{37} + 36 q^{38} + 50 q^{39} + 19 q^{40} + 54 q^{41} + 45 q^{42} + 65 q^{43} + 4 q^{44} + 47 q^{45} + 47 q^{46} + 54 q^{47} + 10 q^{48} + 189 q^{49} + 174 q^{50} + 36 q^{51} + 58 q^{52} + 94 q^{53} + 31 q^{54} + 68 q^{55} + 42 q^{56} + 79 q^{57} + 62 q^{58} - 6 q^{59} + 27 q^{60} + 58 q^{61} + 47 q^{62} + 117 q^{63} + 101 q^{64} + 89 q^{65} + 55 q^{66} + 127 q^{67} + 34 q^{68} + 45 q^{69} + 16 q^{70} + 87 q^{71} + 147 q^{72} + 83 q^{73} + 90 q^{74} - 4 q^{75} + 36 q^{76} + 53 q^{77} + 50 q^{78} + 74 q^{79} + 19 q^{80} + 241 q^{81} + 54 q^{82} + 11 q^{83} + 45 q^{84} + 120 q^{85} + 65 q^{86} + 37 q^{87} + 4 q^{88} + 89 q^{89} + 47 q^{90} + 31 q^{91} + 47 q^{92} + 123 q^{93} + 54 q^{94} + 61 q^{95} + 10 q^{96} + 85 q^{97} + 189 q^{98} - 55 q^{99}+O(q^{100}) \) 101 * q + 101 * q^2 + 10 * q^3 + 101 * q^4 + 19 * q^5 + 10 * q^6 + 42 * q^7 + 101 * q^8 + 147 * q^9 + 19 * q^10 + 4 * q^11 + 10 * q^12 + 58 * q^13 + 42 * q^14 + 27 * q^15 + 101 * q^16 + 34 * q^17 + 147 * q^18 + 36 * q^19 + 19 * q^20 + 45 * q^21 + 4 * q^22 + 47 * q^23 + 10 * q^24 + 174 * q^25 + 58 * q^26 + 31 * q^27 + 42 * q^28 + 62 * q^29 + 27 * q^30 + 47 * q^31 + 101 * q^32 + 55 * q^33 + 34 * q^34 + 16 * q^35 + 147 * q^36 + 90 * q^37 + 36 * q^38 + 50 * q^39 + 19 * q^40 + 54 * q^41 + 45 * q^42 + 65 * q^43 + 4 * q^44 + 47 * q^45 + 47 * q^46 + 54 * q^47 + 10 * q^48 + 189 * q^49 + 174 * q^50 + 36 * q^51 + 58 * q^52 + 94 * q^53 + 31 * q^54 + 68 * q^55 + 42 * q^56 + 79 * q^57 + 62 * q^58 - 6 * q^59 + 27 * q^60 + 58 * q^61 + 47 * q^62 + 117 * q^63 + 101 * q^64 + 89 * q^65 + 55 * q^66 + 127 * q^67 + 34 * q^68 + 45 * q^69 + 16 * q^70 + 87 * q^71 + 147 * q^72 + 83 * q^73 + 90 * q^74 - 4 * q^75 + 36 * q^76 + 53 * q^77 + 50 * q^78 + 74 * q^79 + 19 * q^80 + 241 * q^81 + 54 * q^82 + 11 * q^83 + 45 * q^84 + 120 * q^85 + 65 * q^86 + 37 * q^87 + 4 * q^88 + 89 * q^89 + 47 * q^90 + 31 * q^91 + 47 * q^92 + 123 * q^93 + 54 * q^94 + 61 * q^95 + 10 * q^96 + 85 * q^97 + 189 * q^98 - 55 * q^99

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