LMFDB - Embedded newform 4006.2.a.i.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, 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("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.20020 q^{3} +1.00000 q^{4} +4.05453 q^{5} -1.20020 q^{6} -4.32579 q^{7} +1.00000 q^{8} -1.55952 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.20020 q^{3} +1.00000 q^{4} +4.05453 q^{5} -1.20020 q^{6} -4.32579 q^{7} +1.00000 q^{8} -1.55952 q^{9} +4.05453 q^{10} +4.06000 q^{11} -1.20020 q^{12} -4.67846 q^{13} -4.32579 q^{14} -4.86625 q^{15} +1.00000 q^{16} -2.89792 q^{17} -1.55952 q^{18} +2.38824 q^{19} +4.05453 q^{20} +5.19182 q^{21} +4.06000 q^{22} +7.66290 q^{23} -1.20020 q^{24} +11.4392 q^{25} -4.67846 q^{26} +5.47234 q^{27} -4.32579 q^{28} +3.27018 q^{29} -4.86625 q^{30} -7.34526 q^{31} +1.00000 q^{32} -4.87282 q^{33} -2.89792 q^{34} -17.5390 q^{35} -1.55952 q^{36} -5.59945 q^{37} +2.38824 q^{38} +5.61510 q^{39} +4.05453 q^{40} +7.92174 q^{41} +5.19182 q^{42} -2.51117 q^{43} +4.06000 q^{44} -6.32310 q^{45} +7.66290 q^{46} +4.99508 q^{47} -1.20020 q^{48} +11.7125 q^{49} +11.4392 q^{50} +3.47808 q^{51} -4.67846 q^{52} +4.51253 q^{53} +5.47234 q^{54} +16.4614 q^{55} -4.32579 q^{56} -2.86637 q^{57} +3.27018 q^{58} +10.3709 q^{59} -4.86625 q^{60} +10.0742 q^{61} -7.34526 q^{62} +6.74615 q^{63} +1.00000 q^{64} -18.9690 q^{65} -4.87282 q^{66} +8.86550 q^{67} -2.89792 q^{68} -9.19702 q^{69} -17.5390 q^{70} +15.7852 q^{71} -1.55952 q^{72} -7.80660 q^{73} -5.59945 q^{74} -13.7293 q^{75} +2.38824 q^{76} -17.5627 q^{77} +5.61510 q^{78} +7.77550 q^{79} +4.05453 q^{80} -1.88936 q^{81} +7.92174 q^{82} -5.06171 q^{83} +5.19182 q^{84} -11.7497 q^{85} -2.51117 q^{86} -3.92488 q^{87} +4.06000 q^{88} +13.3990 q^{89} -6.32310 q^{90} +20.2381 q^{91} +7.66290 q^{92} +8.81579 q^{93} +4.99508 q^{94} +9.68318 q^{95} -1.20020 q^{96} -6.23389 q^{97} +11.7125 q^{98} -6.33164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) $ 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * 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
$3$	−1.20020	−0.692937	−0.346468	−	0.938062i	$-0.612619\pi$
$3$	−1.20020	−0.692937	−0.346468	+	0.938062i	$0.612619\pi$
$4$	1.00000	0.500000
$5$	4.05453	1.81324	0.906619	−	0.421949i	$-0.138654\pi$
$5$	4.05453	1.81324	0.906619	+	0.421949i	$0.138654\pi$
$6$	−1.20020	−0.489980
$7$	−4.32579	−1.63500	−0.817498	−	0.575932i	$-0.804639\pi$
$7$	−4.32579	−1.63500	−0.817498	+	0.575932i	$0.804639\pi$
$8$	1.00000	0.353553
$9$	−1.55952	−0.519839
$10$	4.05453	1.28215
$11$	4.06000	1.22414	0.612068	−	0.790805i	$-0.290338\pi$
$11$	4.06000	1.22414	0.612068	+	0.790805i	$0.290338\pi$
$12$	−1.20020	−0.346468
$13$	−4.67846	−1.29757	−0.648786	−	0.760971i	$-0.724723\pi$
$13$	−4.67846	−1.29757	−0.648786	+	0.760971i	$0.724723\pi$
$14$	−4.32579	−1.15612
$15$	−4.86625	−1.25646
$16$	1.00000	0.250000
$17$	−2.89792	−0.702848	−0.351424	−	0.936216i	$-0.614302\pi$
$17$	−2.89792	−0.702848	−0.351424	+	0.936216i	$0.614302\pi$
$18$	−1.55952	−0.367582
$19$	2.38824	0.547900	0.273950	−	0.961744i	$-0.411670\pi$
$19$	2.38824	0.547900	0.273950	+	0.961744i	$0.411670\pi$
$20$	4.05453	0.906619
$21$	5.19182	1.13295
$22$	4.06000	0.865595
$23$	7.66290	1.59782	0.798912	−	0.601448i	$-0.205409\pi$
$23$	7.66290	1.59782	0.798912	+	0.601448i	$0.205409\pi$
$24$	−1.20020	−0.244990
$25$	11.4392	2.28784
$26$	−4.67846	−0.917522
$27$	5.47234	1.05315
$28$	−4.32579	−0.817498
$29$	3.27018	0.607258	0.303629	−	0.952790i	$-0.401802\pi$
$29$	3.27018	0.607258	0.303629	+	0.952790i	$0.401802\pi$
$30$	−4.86625	−0.888451
$31$	−7.34526	−1.31925	−0.659623	−	0.751596i	$-0.729284\pi$
$31$	−7.34526	−1.31925	−0.659623	+	0.751596i	$0.729284\pi$
$32$	1.00000	0.176777
$33$	−4.87282	−0.848248
$34$	−2.89792	−0.496989
$35$	−17.5390	−2.96464
$36$	−1.55952	−0.259919
$37$	−5.59945	−0.920544	−0.460272	−	0.887778i	$-0.652248\pi$
$37$	−5.59945	−0.920544	−0.460272	+	0.887778i	$0.652248\pi$
$38$	2.38824	0.387424
$39$	5.61510	0.899135
$40$	4.05453	0.641077
$41$	7.92174	1.23717	0.618584	−	0.785719i	$-0.287707\pi$
$41$	7.92174	1.23717	0.618584	+	0.785719i	$0.287707\pi$
$42$	5.19182	0.801115
$43$	−2.51117	−0.382950	−0.191475	−	0.981498i	$-0.561327\pi$
$43$	−2.51117	−0.382950	−0.191475	+	0.981498i	$0.561327\pi$
$44$	4.06000	0.612068
$45$	−6.32310	−0.942592
$46$	7.66290	1.12983
$47$	4.99508	0.728608	0.364304	−	0.931280i	$-0.381307\pi$
$47$	4.99508	0.728608	0.364304	+	0.931280i	$0.381307\pi$
$48$	−1.20020	−0.173234
$49$	11.7125	1.67321
$50$	11.4392	1.61774
$51$	3.47808	0.487029
$52$	−4.67846	−0.648786
$53$	4.51253	0.619843	0.309922	−	0.950762i	$-0.399697\pi$
$53$	4.51253	0.619843	0.309922	+	0.950762i	$0.399697\pi$
$54$	5.47234	0.744691
$55$	16.4614	2.21965
$56$	−4.32579	−0.578058
$57$	−2.86637	−0.379660
$58$	3.27018	0.429396
$59$	10.3709	1.35018	0.675089	−	0.737736i	$-0.264105\pi$
$59$	10.3709	1.35018	0.675089	+	0.737736i	$0.264105\pi$
$60$	−4.86625	−0.628230
$61$	10.0742	1.28987	0.644937	−	0.764235i	$-0.276883\pi$
$61$	10.0742	1.28987	0.644937	+	0.764235i	$0.276883\pi$
$62$	−7.34526	−0.932848
$63$	6.74615	0.849935
$64$	1.00000	0.125000
$65$	−18.9690	−2.35281
$66$	−4.87282	−0.599802
$67$	8.86550	1.08309	0.541547	−	0.840671i	$-0.317839\pi$
$67$	8.86550	1.08309	0.541547	+	0.840671i	$0.317839\pi$
$68$	−2.89792	−0.351424
$69$	−9.19702	−1.10719
$70$	−17.5390	−2.09632
$71$	15.7852	1.87336	0.936681	−	0.350183i	$-0.113881\pi$
$71$	15.7852	1.87336	0.936681	+	0.350183i	$0.113881\pi$
$72$	−1.55952	−0.183791
$73$	−7.80660	−0.913693	−0.456847	−	0.889545i	$-0.651021\pi$
$73$	−7.80660	−0.913693	−0.456847	+	0.889545i	$0.651021\pi$
$74$	−5.59945	−0.650923
$75$	−13.7293	−1.58532
$76$	2.38824	0.273950
$77$	−17.5627	−2.00146
$78$	5.61510	0.635785
$79$	7.77550	0.874812	0.437406	−	0.899264i	$-0.355897\pi$
$79$	7.77550	0.874812	0.437406	+	0.899264i	$0.355897\pi$
$80$	4.05453	0.453310
$81$	−1.88936	−0.209929
$82$	7.92174	0.874810
$83$	−5.06171	−0.555595	−0.277797	−	0.960640i	$-0.589604\pi$
$83$	−5.06171	−0.555595	−0.277797	+	0.960640i	$0.589604\pi$
$84$	5.19182	0.566474
$85$	−11.7497	−1.27443
$86$	−2.51117	−0.270786
$87$	−3.92488	−0.420791
$88$	4.06000	0.432797
$89$	13.3990	1.42029	0.710143	−	0.704057i	$-0.248630\pi$
$89$	13.3990	1.42029	0.710143	+	0.704057i	$0.248630\pi$
$90$	−6.32310	−0.666513
$91$	20.2381	2.12153
$92$	7.66290	0.798912
$93$	8.81579	0.914154
$94$	4.99508	0.515204
$95$	9.68318	0.993474
$96$	−1.20020	−0.122495
$97$	−6.23389	−0.632956	−0.316478	−	0.948600i	$-0.602500\pi$
$97$	−6.23389	−0.632956	−0.316478	+	0.948600i	$0.602500\pi$
$98$	11.7125	1.18314
$99$	−6.33164	−0.636353
$100$	11.4392	1.14392
$101$	0.00520235	0.000517653 0	0.000258827	−	1.00000i	$-0.499918\pi$
$101$	0.00520235	0.000517653 0	0.000258827		1.00000i	$0.499918\pi$
$102$	3.47808	0.344382
$103$	3.26154	0.321369	0.160684	−	0.987006i	$-0.448630\pi$
$103$	3.26154	0.321369	0.160684	+	0.987006i	$0.448630\pi$
$104$	−4.67846	−0.458761
$105$	21.0504	2.05431
$106$	4.51253	0.438295
$107$	−10.8841	−1.05220	−0.526102	−	0.850421i	$-0.676347\pi$
$107$	−10.8841	−1.05220	−0.526102	+	0.850421i	$0.676347\pi$
$108$	5.47234	0.526576
$109$	−7.63468	−0.731270	−0.365635	−	0.930758i	$-0.619148\pi$
$109$	−7.63468	−0.731270	−0.365635	+	0.930758i	$0.619148\pi$
$110$	16.4614	1.56953
$111$	6.72047	0.637878
$112$	−4.32579	−0.408749
$113$	−6.35923	−0.598226	−0.299113	−	0.954218i	$-0.596691\pi$
$113$	−6.35923	−0.598226	−0.299113	+	0.954218i	$0.596691\pi$
$114$	−2.86637	−0.268460
$115$	31.0694	2.89724
$116$	3.27018	0.303629
$117$	7.29614	0.674529
$118$	10.3709	0.954720
$119$	12.5358	1.14915
$120$	−4.86625	−0.444226
$121$	5.48359	0.498508
$122$	10.0742	0.912079
$123$	−9.50768	−0.857279
$124$	−7.34526	−0.659623
$125$	26.1078	2.33515
$126$	6.74615	0.600994
$127$	−7.10820	−0.630751	−0.315375	−	0.948967i	$-0.602130\pi$
$127$	−7.10820	−0.630751	−0.315375	+	0.948967i	$0.602130\pi$
$128$	1.00000	0.0883883
$129$	3.01391	0.265360
$130$	−18.9690	−1.66369
$131$	0.618726	0.0540584	0.0270292	−	0.999635i	$-0.491395\pi$
$131$	0.618726	0.0540584	0.0270292	+	0.999635i	$0.491395\pi$
$132$	−4.87282	−0.424124
$133$	−10.3310	−0.895814
$134$	8.86550	0.765863
$135$	22.1877	1.90962
$136$	−2.89792	−0.248494
$137$	−20.9326	−1.78839	−0.894196	−	0.447677i	$-0.852252\pi$
$137$	−20.9326	−1.78839	−0.894196	+	0.447677i	$0.852252\pi$
$138$	−9.19702	−0.782902
$139$	20.2000	1.71334	0.856671	−	0.515863i	$-0.172529\pi$
$139$	20.2000	1.71334	0.856671	+	0.515863i	$0.172529\pi$
$140$	−17.5390	−1.48232
$141$	−5.99511	−0.504879
$142$	15.7852	1.32467
$143$	−18.9946	−1.58840
$144$	−1.55952	−0.129960
$145$	13.2590	1.10110
$146$	−7.80660	−0.646079
$147$	−14.0573	−1.15943
$148$	−5.59945	−0.460272
$149$	−12.3570	−1.01232	−0.506162	−	0.862439i	$-0.668936\pi$
$149$	−12.3570	−1.01232	−0.506162	+	0.862439i	$0.668936\pi$
$150$	−13.7293	−1.12099
$151$	−13.3642	−1.08757	−0.543783	−	0.839226i	$-0.683008\pi$
$151$	−13.3642	−1.08757	−0.543783	+	0.839226i	$0.683008\pi$
$152$	2.38824	0.193712
$153$	4.51935	0.365368
$154$	−17.5627	−1.41524
$155$	−29.7815	−2.39211
$156$	5.61510	0.449568
$157$	10.8129	0.862964	0.431482	−	0.902122i	$-0.357991\pi$
$157$	10.8129	0.862964	0.431482	+	0.902122i	$0.357991\pi$
$158$	7.77550	0.618586
$159$	−5.41594	−0.429512
$160$	4.05453	0.320538
$161$	−33.1481	−2.61244
$162$	−1.88936	−0.148442
$163$	9.74636	0.763394	0.381697	−	0.924288i	$-0.375340\pi$
$163$	9.74636	0.763394	0.381697	+	0.924288i	$0.375340\pi$
$164$	7.92174	0.618584
$165$	−19.7570	−1.53808
$166$	−5.06171	−0.392865
$167$	12.4386	0.962531	0.481265	−	0.876575i	$-0.340177\pi$
$167$	12.4386	0.962531	0.481265	+	0.876575i	$0.340177\pi$
$168$	5.19182	0.400558
$169$	8.88802	0.683694
$170$	−11.7497	−0.901159
$171$	−3.72450	−0.284820
$172$	−2.51117	−0.191475
$173$	−15.7589	−1.19812	−0.599062	−	0.800703i	$-0.704460\pi$
$173$	−15.7589	−1.19812	−0.599062	+	0.800703i	$0.704460\pi$
$174$	−3.92488	−0.297544
$175$	−49.4835	−3.74060
$176$	4.06000	0.306034
$177$	−12.4472	−0.935588
$178$	13.3990	1.00429
$179$	4.30398	0.321694	0.160847	−	0.986979i	$-0.448577\pi$
$179$	4.30398	0.321694	0.160847	+	0.986979i	$0.448577\pi$
$180$	−6.32310	−0.471296
$181$	−11.0691	−0.822759	−0.411379	−	0.911464i	$-0.634953\pi$
$181$	−11.0691	−0.822759	−0.411379	+	0.911464i	$0.634953\pi$
$182$	20.2381	1.50015
$183$	−12.0911	−0.893801
$184$	7.66290	0.564916
$185$	−22.7031	−1.66917
$186$	8.81579	0.646405
$187$	−11.7655	−0.860381
$188$	4.99508	0.364304
$189$	−23.6722	−1.72190
$190$	9.68318	0.702492
$191$	8.39431	0.607391	0.303695	−	0.952769i	$-0.401780\pi$
$191$	8.39431	0.607391	0.303695	+	0.952769i	$0.401780\pi$
$192$	−1.20020	−0.0866171
$193$	−5.99750	−0.431709	−0.215855	−	0.976426i	$-0.569254\pi$
$193$	−5.99750	−0.431709	−0.215855	+	0.976426i	$0.569254\pi$
$194$	−6.23389	−0.447567
$195$	22.7666	1.63035
$196$	11.7125	0.836606
$197$	−4.83348	−0.344371	−0.172186	−	0.985065i	$-0.555083\pi$
$197$	−4.83348	−0.344371	−0.172186	+	0.985065i	$0.555083\pi$
$198$	−6.33164	−0.449970
$199$	12.9404	0.917319	0.458659	−	0.888612i	$-0.348330\pi$
$199$	12.9404	0.917319	0.458659	+	0.888612i	$0.348330\pi$
$200$	11.4392	0.808872
$201$	−10.6404	−0.750515
$202$	0.00520235	0.000366036 0
$203$	−14.1461	−0.992864
$204$	3.47808	0.243515
$205$	32.1189	2.24328
$206$	3.26154	0.227242
$207$	−11.9504	−0.830611
$208$	−4.67846	−0.324393
$209$	9.69625	0.670704
$210$	21.0504	1.45261
$211$	−15.1882	−1.04560	−0.522799	−	0.852456i	$-0.675112\pi$
$211$	−15.1882	−1.04560	−0.522799	+	0.852456i	$0.675112\pi$
$212$	4.51253	0.309922
$213$	−18.9455	−1.29812
$214$	−10.8841	−0.744021
$215$	−10.1816	−0.694379
$216$	5.47234	0.372345
$217$	31.7741	2.15696
$218$	−7.63468	−0.517086
$219$	9.36949	0.633132
$220$	16.4614	1.10983
$221$	13.5578	0.911996
$222$	6.72047	0.451048
$223$	25.5339	1.70988	0.854940	−	0.518727i	$-0.173594\pi$
$223$	25.5339	1.70988	0.854940	+	0.518727i	$0.173594\pi$
$224$	−4.32579	−0.289029
$225$	−17.8396	−1.18931
$226$	−6.35923	−0.423009
$227$	19.6387	1.30347	0.651734	−	0.758448i	$-0.274042\pi$
$227$	19.6387	1.30347	0.651734	+	0.758448i	$0.274042\pi$
$228$	−2.86637	−0.189830
$229$	−1.60634	−0.106150	−0.0530751	−	0.998591i	$-0.516902\pi$
$229$	−1.60634	−0.106150	−0.0530751	+	0.998591i	$0.516902\pi$
$230$	31.0694	2.04866
$231$	21.0788	1.38688
$232$	3.27018	0.214698
$233$	24.7069	1.61860	0.809301	−	0.587394i	$-0.199846\pi$
$233$	24.7069	1.61860	0.809301	+	0.587394i	$0.199846\pi$
$234$	7.29614	0.476964
$235$	20.2527	1.32114
$236$	10.3709	0.675089
$237$	−9.33217	−0.606189
$238$	12.5358	0.812574
$239$	−16.9234	−1.09469	−0.547343	−	0.836908i	$-0.684361\pi$
$239$	−16.9234	−1.09469	−0.547343	+	0.836908i	$0.684361\pi$
$240$	−4.86625	−0.314115
$241$	3.39470	0.218672	0.109336	−	0.994005i	$-0.465128\pi$
$241$	3.39470	0.218672	0.109336	+	0.994005i	$0.465128\pi$
$242$	5.48359	0.352498
$243$	−14.1494	−0.907685
$244$	10.0742	0.644937
$245$	47.4886	3.03393
$246$	−9.50768	−0.606188
$247$	−11.1733	−0.710940
$248$	−7.34526	−0.466424
$249$	6.07507	0.384992
$250$	26.1078	1.65120
$251$	−12.5610	−0.792841	−0.396420	−	0.918069i	$-0.629748\pi$
$251$	−12.5610	−0.792841	−0.396420	+	0.918069i	$0.629748\pi$
$252$	6.74615	0.424967
$253$	31.1114	1.95595
$254$	−7.10820	−0.446008
$255$	14.1020	0.883100
$256$	1.00000	0.0625000
$257$	6.50115	0.405530	0.202765	−	0.979227i	$-0.435007\pi$
$257$	6.50115	0.405530	0.202765	+	0.979227i	$0.435007\pi$
$258$	3.01391	0.187638
$259$	24.2221	1.50509
$260$	−18.9690	−1.17640
$261$	−5.09991	−0.315676
$262$	0.618726	0.0382250
$263$	−11.6844	−0.720492	−0.360246	−	0.932857i	$-0.617307\pi$
$263$	−11.6844	−0.720492	−0.360246	+	0.932857i	$0.617307\pi$
$264$	−4.87282	−0.299901
$265$	18.2962	1.12392
$266$	−10.3310	−0.633436
$267$	−16.0814	−0.984168
$268$	8.86550	0.541547
$269$	32.4880	1.98083	0.990415	−	0.138120i	$-0.0441060\pi$
$269$	32.4880	1.98083	0.990415	+	0.138120i	$0.0441060\pi$
$270$	22.1877	1.35030
$271$	−24.9649	−1.51651	−0.758256	−	0.651957i	$-0.773948\pi$
$271$	−24.9649	−1.51651	−0.758256	+	0.651957i	$0.773948\pi$
$272$	−2.89792	−0.175712
$273$	−24.2898	−1.47008
$274$	−20.9326	−1.26458
$275$	46.4430	2.80062
$276$	−9.19702	−0.553596
$277$	5.96542	0.358427	0.179214	−	0.983810i	$-0.442645\pi$
$277$	5.96542	0.358427	0.179214	+	0.983810i	$0.442645\pi$
$278$	20.2000	1.21152
$279$	11.4551	0.685796
$280$	−17.5390	−1.04816
$281$	−10.6083	−0.632837	−0.316419	−	0.948620i	$-0.602480\pi$
$281$	−10.6083	−0.632837	−0.316419	+	0.948620i	$0.602480\pi$
$282$	−5.99511	−0.357003
$283$	7.56886	0.449922	0.224961	−	0.974368i	$-0.427775\pi$
$283$	7.56886	0.449922	0.224961	+	0.974368i	$0.427775\pi$
$284$	15.7852	0.936681
$285$	−11.6218	−0.688414
$286$	−18.9946	−1.12317
$287$	−34.2678	−2.02276
$288$	−1.55952	−0.0918954
$289$	−8.60208	−0.506005
$290$	13.2590	0.778598
$291$	7.48192	0.438598
$292$	−7.80660	−0.456847
$293$	30.1558	1.76172	0.880861	−	0.473374i	$-0.156964\pi$
$293$	30.1558	1.76172	0.880861	+	0.473374i	$0.156964\pi$
$294$	−14.0573	−0.819840
$295$	42.0491	2.44820
$296$	−5.59945	−0.325461
$297$	22.2177	1.28920
$298$	−12.3570	−0.715821
$299$	−35.8506	−2.07329
$300$	−13.7293	−0.792662
$301$	10.8628	0.626121
$302$	−13.3642	−0.769025
$303$	−0.00624387	−0.000358701 0
$304$	2.38824	0.136975
$305$	40.8463	2.33885
$306$	4.51935	0.258354
$307$	−3.00650	−0.171590	−0.0857950	−	0.996313i	$-0.527343\pi$
$307$	−3.00650	−0.171590	−0.0857950	+	0.996313i	$0.527343\pi$
$308$	−17.5627	−1.00073
$309$	−3.91450	−0.222688
$310$	−29.7815	−1.69148
$311$	−4.54511	−0.257729	−0.128865	−	0.991662i	$-0.541133\pi$
$311$	−4.54511	−0.257729	−0.128865	+	0.991662i	$0.541133\pi$
$312$	5.61510	0.317892
$313$	−23.2896	−1.31641	−0.658204	−	0.752839i	$-0.728684\pi$
$313$	−23.2896	−1.31641	−0.658204	+	0.752839i	$0.728684\pi$
$314$	10.8129	0.610208
$315$	27.3524	1.54113
$316$	7.77550	0.437406
$317$	−29.3430	−1.64807	−0.824034	−	0.566540i	$-0.808282\pi$
$317$	−29.3430	−1.64807	−0.824034	+	0.566540i	$0.808282\pi$
$318$	−5.41594	−0.303711
$319$	13.2769	0.743366
$320$	4.05453	0.226655
$321$	13.0631	0.729111
$322$	−33.1481	−1.84727
$323$	−6.92092	−0.385090
$324$	−1.88936	−0.104964
$325$	−53.5178	−2.96863
$326$	9.74636	0.539801
$327$	9.16315	0.506724
$328$	7.92174	0.437405
$329$	−21.6077	−1.19127
$330$	−19.7570	−1.08758
$331$	22.7737	1.25176	0.625879	−	0.779920i	$-0.284740\pi$
$331$	22.7737	1.25176	0.625879	+	0.779920i	$0.284740\pi$
$332$	−5.06171	−0.277797
$333$	8.73243	0.478534
$334$	12.4386	0.680612
$335$	35.9454	1.96391
$336$	5.19182	0.283237
$337$	29.4003	1.60153	0.800767	−	0.598976i	$-0.204426\pi$
$337$	29.4003	1.60153	0.800767	+	0.598976i	$0.204426\pi$
$338$	8.88802	0.483445
$339$	7.63235	0.414532
$340$	−11.7497	−0.637216
$341$	−29.8217	−1.61494
$342$	−3.72450	−0.201398
$343$	−20.3852	−1.10070
$344$	−2.51117	−0.135393
$345$	−37.2896	−2.00760
$346$	−15.7589	−0.847202
$347$	20.2567	1.08744	0.543719	−	0.839267i	$-0.317016\pi$
$347$	20.2567	1.08744	0.543719	+	0.839267i	$0.317016\pi$
$348$	−3.92488	−0.210396
$349$	27.7374	1.48475	0.742375	−	0.669984i	$-0.233699\pi$
$349$	27.7374	1.48475	0.742375	+	0.669984i	$0.233699\pi$
$350$	−49.4835	−2.64500
$351$	−25.6021	−1.36654
$352$	4.06000	0.216399
$353$	0.802764	0.0427268	0.0213634	−	0.999772i	$-0.493199\pi$
$353$	0.802764	0.0427268	0.0213634	+	0.999772i	$0.493199\pi$
$354$	−12.4472	−0.661560
$355$	64.0016	3.39685
$356$	13.3990	0.710143
$357$	−15.0455	−0.796290
$358$	4.30398	0.227472
$359$	−8.25664	−0.435769	−0.217884	−	0.975975i	$-0.569916\pi$
$359$	−8.25664	−0.435769	−0.217884	+	0.975975i	$0.569916\pi$
$360$	−6.32310	−0.333257
$361$	−13.2963	−0.699806
$362$	−11.0691	−0.581778
$363$	−6.58141	−0.345434
$364$	20.2381	1.06076
$365$	−31.6521	−1.65674
$366$	−12.0911	−0.632013
$367$	32.9664	1.72083	0.860415	−	0.509593i	$-0.170204\pi$
$367$	32.9664	1.72083	0.860415	+	0.509593i	$0.170204\pi$
$368$	7.66290	0.399456
$369$	−12.3541	−0.643128
$370$	−22.7031	−1.18028
$371$	−19.5203	−1.01344
$372$	8.81579	0.457077
$373$	−26.0452	−1.34857	−0.674286	−	0.738470i	$-0.735548\pi$
$373$	−26.0452	−1.34857	−0.674286	+	0.738470i	$0.735548\pi$
$374$	−11.7655	−0.608381
$375$	−31.3346	−1.61811
$376$	4.99508	0.257602
$377$	−15.2994	−0.787961
$378$	−23.6722	−1.21757
$379$	5.35349	0.274990	0.137495	−	0.990502i	$-0.456095\pi$
$379$	5.35349	0.274990	0.137495	+	0.990502i	$0.456095\pi$
$380$	9.68318	0.496737
$381$	8.53127	0.437070
$382$	8.39431	0.429490
$383$	13.0186	0.665219	0.332609	−	0.943065i	$-0.392071\pi$
$383$	13.0186	0.665219	0.332609	+	0.943065i	$0.392071\pi$
$384$	−1.20020	−0.0612475
$385$	−71.2085	−3.62912
$386$	−5.99750	−0.305265
$387$	3.91621	0.199072
$388$	−6.23389	−0.316478
$389$	−27.7624	−1.40761	−0.703805	−	0.710393i	$-0.748517\pi$
$389$	−27.7624	−1.40761	−0.703805	+	0.710393i	$0.748517\pi$
$390$	22.7666	1.15283
$391$	−22.2064	−1.12303
$392$	11.7125	0.591570
$393$	−0.742596	−0.0374590
$394$	−4.83348	−0.243507
$395$	31.5260	1.58624
$396$	−6.33164	−0.318177
$397$	−15.7568	−0.790812	−0.395406	−	0.918506i	$-0.629396\pi$
$397$	−15.7568	−0.790812	−0.395406	+	0.918506i	$0.629396\pi$
$398$	12.9404	0.648642
$399$	12.3993	0.620742
$400$	11.4392	0.571959
$401$	−8.79126	−0.439015	−0.219507	−	0.975611i	$-0.570445\pi$
$401$	−8.79126	−0.439015	−0.219507	+	0.975611i	$0.570445\pi$
$402$	−10.6404	−0.530694
$403$	34.3645	1.71182
$404$	0.00520235	0.000258827 0
$405$	−7.66044	−0.380651
$406$	−14.1461	−0.702061
$407$	−22.7338	−1.12687
$408$	3.47808	0.172191
$409$	−1.86275	−0.0921070	−0.0460535	−	0.998939i	$-0.514664\pi$
$409$	−1.86275	−0.0921070	−0.0460535	+	0.998939i	$0.514664\pi$
$410$	32.1189	1.58624
$411$	25.1233	1.23924
$412$	3.26154	0.160684
$413$	−44.8624	−2.20754
$414$	−11.9504	−0.587331
$415$	−20.5228	−1.00743
$416$	−4.67846	−0.229381
$417$	−24.2441	−1.18724
$418$	9.69625	0.474259
$419$	−6.62634	−0.323718	−0.161859	−	0.986814i	$-0.551749\pi$
$419$	−6.62634	−0.323718	−0.161859	+	0.986814i	$0.551749\pi$
$420$	21.0504	1.02715
$421$	9.11898	0.444432	0.222216	−	0.974997i	$-0.428671\pi$
$421$	9.11898	0.444432	0.222216	+	0.974997i	$0.428671\pi$
$422$	−15.1882	−0.739349
$423$	−7.78992	−0.378759
$424$	4.51253	0.219148
$425$	−33.1498	−1.60800
$426$	−18.9455	−0.917910
$427$	−43.5791	−2.10894
$428$	−10.8841	−0.526102
$429$	22.7973	1.10066
$430$	−10.1816	−0.491000
$431$	−30.8344	−1.48524	−0.742621	−	0.669712i	$-0.766417\pi$
$431$	−30.8344	−1.48524	−0.742621	+	0.669712i	$0.766417\pi$
$432$	5.47234	0.263288
$433$	20.7544	0.997394	0.498697	−	0.866777i	$-0.333812\pi$
$433$	20.7544	0.997394	0.498697	+	0.866777i	$0.333812\pi$
$434$	31.7741	1.52520
$435$	−15.9135	−0.762995
$436$	−7.63468	−0.365635
$437$	18.3008	0.875448
$438$	9.36949	0.447692
$439$	−15.1321	−0.722217	−0.361108	−	0.932524i	$-0.617602\pi$
$439$	−15.1321	−0.722217	−0.361108	+	0.932524i	$0.617602\pi$
$440$	16.4614	0.784765
$441$	−18.2658	−0.869801
$442$	13.5578	0.644879
$443$	3.02720	0.143827	0.0719133	−	0.997411i	$-0.477090\pi$
$443$	3.02720	0.143827	0.0719133	+	0.997411i	$0.477090\pi$
$444$	6.72047	0.318939
$445$	54.3264	2.57532
$446$	25.5339	1.20907
$447$	14.8309	0.701476
$448$	−4.32579	−0.204374
$449$	−33.5603	−1.58381	−0.791904	−	0.610646i	$-0.790910\pi$
$449$	−33.5603	−1.58381	−0.791904	+	0.610646i	$0.790910\pi$
$450$	−17.8396	−0.840966
$451$	32.1623	1.51446
$452$	−6.35923	−0.299113
$453$	16.0398	0.753614
$454$	19.6387	0.921691
$455$	82.0557	3.84683
$456$	−2.86637	−0.134230
$457$	−20.2745	−0.948403	−0.474201	−	0.880416i	$-0.657263\pi$
$457$	−20.2745	−0.948403	−0.474201	+	0.880416i	$0.657263\pi$
$458$	−1.60634	−0.0750596
$459$	−15.8584	−0.740206
$460$	31.0694	1.44862
$461$	13.5023	0.628867	0.314434	−	0.949279i	$-0.398185\pi$
$461$	13.5023	0.628867	0.314434	+	0.949279i	$0.398185\pi$
$462$	21.0788	0.980674
$463$	13.1152	0.609513	0.304757	−	0.952430i	$-0.401425\pi$
$463$	13.1152	0.609513	0.304757	+	0.952430i	$0.401425\pi$
$464$	3.27018	0.151814
$465$	35.7438	1.65758
$466$	24.7069	1.14452
$467$	2.12649	0.0984024	0.0492012	−	0.998789i	$-0.484332\pi$
$467$	2.12649	0.0984024	0.0492012	+	0.998789i	$0.484332\pi$
$468$	7.29614	0.337264
$469$	−38.3503	−1.77085
$470$	20.2527	0.934187
$471$	−12.9777	−0.597979
$472$	10.3709	0.477360
$473$	−10.1953	−0.468782
$474$	−9.33217	−0.428641
$475$	27.3195	1.25351
$476$	12.5358	0.574577
$477$	−7.03736	−0.322219
$478$	−16.9234	−0.774060
$479$	−33.8468	−1.54650	−0.773250	−	0.634102i	$-0.781370\pi$
$479$	−33.8468	−1.54650	−0.773250	+	0.634102i	$0.781370\pi$
$480$	−4.86625	−0.222113
$481$	26.1968	1.19447
$482$	3.39470	0.154624
$483$	39.7844	1.81025
$484$	5.48359	0.249254
$485$	−25.2755	−1.14770
$486$	−14.1494	−0.641830
$487$	−13.8312	−0.626753	−0.313377	−	0.949629i	$-0.601460\pi$
$487$	−13.8312	−0.626753	−0.313377	+	0.949629i	$0.601460\pi$
$488$	10.0742	0.456040
$489$	−11.6976	−0.528983
$490$	47.4886	2.14531
$491$	6.95907	0.314059	0.157029	−	0.987594i	$-0.449808\pi$
$491$	6.95907	0.314059	0.157029	+	0.987594i	$0.449808\pi$
$492$	−9.50768	−0.428639
$493$	−9.47672	−0.426810
$494$	−11.1733	−0.502710
$495$	−25.6718	−1.15386
$496$	−7.34526	−0.329812
$497$	−68.2836	−3.06294
$498$	6.07507	0.272230
$499$	38.4157	1.71972	0.859862	−	0.510527i	$-0.170550\pi$
$499$	38.4157	1.71972	0.859862	+	0.510527i	$0.170550\pi$
$500$	26.1078	1.16758
$501$	−14.9289	−0.666973
$502$	−12.5610	−0.560623
$503$	−32.1438	−1.43322	−0.716611	−	0.697473i	$-0.754308\pi$
$503$	−32.1438	−1.43322	−0.716611	+	0.697473i	$0.754308\pi$
$504$	6.74615	0.300497
$505$	0.0210931	0.000938629 0
$506$	31.1114	1.38307
$507$	−10.6674	−0.473757
$508$	−7.10820	−0.315375
$509$	14.4196	0.639136	0.319568	−	0.947563i	$-0.396462\pi$
$509$	14.4196	0.639136	0.319568	+	0.947563i	$0.396462\pi$
$510$	14.1020	0.624446
$511$	33.7697	1.49389
$512$	1.00000	0.0441942
$513$	13.0693	0.577022
$514$	6.50115	0.286753
$515$	13.2240	0.582718
$516$	3.01391	0.132680
$517$	20.2800	0.891915
$518$	24.2221	1.06426
$519$	18.9138	0.830224
$520$	−18.9690	−0.831844
$521$	16.9836	0.744064	0.372032	−	0.928220i	$-0.378661\pi$
$521$	16.9836	0.744064	0.372032	+	0.928220i	$0.378661\pi$
$522$	−5.09991	−0.223217
$523$	39.6938	1.73569	0.867844	−	0.496836i	$-0.165505\pi$
$523$	39.6938	1.73569	0.867844	+	0.496836i	$0.165505\pi$
$524$	0.618726	0.0270292
$525$	59.3902	2.59200
$526$	−11.6844	−0.509465
$527$	21.2859	0.927230
$528$	−4.87282	−0.212062
$529$	35.7200	1.55304
$530$	18.2962	0.794734
$531$	−16.1736	−0.701875
$532$	−10.3310	−0.447907
$533$	−37.0616	−1.60532
$534$	−16.0814	−0.695912
$535$	−44.1298	−1.90790
$536$	8.86550	0.382931
$537$	−5.16564	−0.222914
$538$	32.4880	1.40066
$539$	47.5527	2.04824
$540$	22.1877	0.954808
$541$	−28.9169	−1.24323	−0.621617	−	0.783321i	$-0.713524\pi$
$541$	−28.9169	−1.24323	−0.621617	+	0.783321i	$0.713524\pi$
$542$	−24.9649	−1.07234
$543$	13.2851	0.570120
$544$	−2.89792	−0.124247
$545$	−30.9550	−1.32597
$546$	−24.2898	−1.03951
$547$	−8.37147	−0.357938	−0.178969	−	0.983855i	$-0.557276\pi$
$547$	−8.37147	−0.357938	−0.178969	+	0.983855i	$0.557276\pi$
$548$	−20.9326	−0.894196
$549$	−15.7110	−0.670527
$550$	46.4430	1.98034
$551$	7.80999	0.332717
$552$	−9.19702	−0.391451
$553$	−33.6352	−1.43031
$554$	5.96542	0.253446
$555$	27.2483	1.15663
$556$	20.2000	0.856671
$557$	−34.7901	−1.47410	−0.737051	−	0.675837i	$-0.763782\pi$
$557$	−34.7901	−1.47410	−0.737051	+	0.675837i	$0.763782\pi$
$558$	11.4551	0.484931
$559$	11.7484	0.496905
$560$	−17.5390	−0.741160
$561$	14.1210	0.596190
$562$	−10.6083	−0.447484
$563$	−3.33619	−0.140604	−0.0703019	−	0.997526i	$-0.522396\pi$
$563$	−3.33619	−0.140604	−0.0703019	+	0.997526i	$0.522396\pi$
$564$	−5.99511	−0.252440
$565$	−25.7836	−1.08473
$566$	7.56886	0.318143
$567$	8.17296	0.343232
$568$	15.7852	0.662334
$569$	−10.1040	−0.423580	−0.211790	−	0.977315i	$-0.567929\pi$
$569$	−10.1040	−0.423580	−0.211790	+	0.977315i	$0.567929\pi$
$570$	−11.6218	−0.486782
$571$	2.72558	0.114062	0.0570310	−	0.998372i	$-0.481837\pi$
$571$	2.72558	0.114062	0.0570310	+	0.998372i	$0.481837\pi$
$572$	−18.9946	−0.794202
$573$	−10.0749	−0.420883
$574$	−34.2678	−1.43031
$575$	87.6572	3.65556
$576$	−1.55952	−0.0649799
$577$	−33.1004	−1.37799	−0.688993	−	0.724768i	$-0.741947\pi$
$577$	−33.1004	−1.37799	−0.688993	+	0.724768i	$0.741947\pi$
$578$	−8.60208	−0.357799
$579$	7.19820	0.299147
$580$	13.2590	0.550552
$581$	21.8959	0.908395
$582$	7.48192	0.310136
$583$	18.3208	0.758772
$584$	−7.80660	−0.323039
$585$	29.5824	1.22308
$586$	30.1558	1.24573
$587$	10.9828	0.453309	0.226655	−	0.973975i	$-0.427221\pi$
$587$	10.9828	0.453309	0.226655	+	0.973975i	$0.427221\pi$
$588$	−14.0573	−0.579715
$589$	−17.5422	−0.722815
$590$	42.0491	1.73114
$591$	5.80115	0.238627
$592$	−5.59945	−0.230136
$593$	14.8769	0.610922	0.305461	−	0.952205i	$-0.401189\pi$
$593$	14.8769	0.610922	0.305461	+	0.952205i	$0.401189\pi$
$594$	22.2177	0.911603
$595$	50.8267	2.08369
$596$	−12.3570	−0.506162
$597$	−15.5311	−0.635644
$598$	−35.8506	−1.46604
$599$	−28.2826	−1.15560	−0.577798	−	0.816180i	$-0.696088\pi$
$599$	−28.2826	−1.15560	−0.577798	+	0.816180i	$0.696088\pi$
$600$	−13.7293	−0.560497
$601$	−32.6460	−1.33166	−0.665828	−	0.746105i	$-0.731922\pi$
$601$	−32.6460	−1.33166	−0.665828	+	0.746105i	$0.731922\pi$
$602$	10.8628	0.442735
$603$	−13.8259	−0.563034
$604$	−13.3642	−0.543783
$605$	22.2333	0.903914
$606$	−0.00624387	−0.000253640 0
$607$	−35.7859	−1.45250	−0.726252	−	0.687429i	$-0.758739\pi$
$607$	−35.7859	−1.45250	−0.726252	+	0.687429i	$0.758739\pi$
$608$	2.38824	0.0968560
$609$	16.9782	0.687992
$610$	40.8463	1.65382
$611$	−23.3693	−0.945421
$612$	4.51935	0.182684
$613$	0.465796	0.0188133	0.00940667	−	0.999956i	$-0.497006\pi$
$613$	0.465796	0.0188133	0.00940667	+	0.999956i	$0.497006\pi$
$614$	−3.00650	−0.121332
$615$	−38.5491	−1.55445
$616$	−17.5627	−0.707622
$617$	−24.8388	−0.999971	−0.499986	−	0.866034i	$-0.666661\pi$
$617$	−24.8388	−0.999971	−0.499986	+	0.866034i	$0.666661\pi$
$618$	−3.91450	−0.157464
$619$	−27.8948	−1.12119	−0.560593	−	0.828092i	$-0.689427\pi$
$619$	−27.8948	−1.12119	−0.560593	+	0.828092i	$0.689427\pi$
$620$	−29.7815	−1.19605
$621$	41.9340	1.68275
$622$	−4.54511	−0.182242
$623$	−57.9611	−2.32216
$624$	5.61510	0.224784
$625$	48.6589	1.94636
$626$	−23.2896	−0.930841
$627$	−11.6375	−0.464755
$628$	10.8129	0.431482
$629$	16.2267	0.647002
$630$	27.3524	1.08975
$631$	13.6465	0.543259	0.271629	−	0.962402i	$-0.412438\pi$
$631$	13.6465	0.543259	0.271629	+	0.962402i	$0.412438\pi$
$632$	7.77550	0.309293
$633$	18.2289	0.724533
$634$	−29.3430	−1.16536
$635$	−28.8204	−1.14370
$636$	−5.41594	−0.214756
$637$	−54.7964	−2.17111
$638$	13.2769	0.525639
$639$	−24.6173	−0.973847
$640$	4.05453	0.160269
$641$	13.7437	0.542845	0.271422	−	0.962460i	$-0.412506\pi$
$641$	13.7437	0.542845	0.271422	+	0.962460i	$0.412506\pi$
$642$	13.0631	0.515559
$643$	34.8583	1.37468	0.687339	−	0.726337i	$-0.258779\pi$
$643$	34.8583	1.37468	0.687339	+	0.726337i	$0.258779\pi$
$644$	−33.1481	−1.30622
$645$	12.2200	0.481161
$646$	−6.92092	−0.272300
$647$	−41.0980	−1.61573	−0.807864	−	0.589369i	$-0.799377\pi$
$647$	−41.0980	−1.61573	−0.807864	+	0.589369i	$0.799377\pi$
$648$	−1.88936	−0.0742209
$649$	42.1059	1.65280
$650$	−53.5178	−2.09914
$651$	−38.1353	−1.49464
$652$	9.74636	0.381697
$653$	36.3021	1.42061	0.710305	−	0.703894i	$-0.248557\pi$
$653$	36.3021	1.42061	0.710305	+	0.703894i	$0.248557\pi$
$654$	9.16315	0.358308
$655$	2.50864	0.0980208
$656$	7.92174	0.309292
$657$	12.1745	0.474973
$658$	−21.6077	−0.842356
$659$	−31.6609	−1.23333	−0.616666	−	0.787225i	$-0.711517\pi$
$659$	−31.6609	−1.23333	−0.616666	+	0.787225i	$0.711517\pi$
$660$	−19.7570	−0.769038
$661$	−2.02090	−0.0786040	−0.0393020	−	0.999227i	$-0.512513\pi$
$661$	−2.02090	−0.0786040	−0.0393020	+	0.999227i	$0.512513\pi$
$662$	22.7737	0.885126
$663$	−16.2721	−0.631955
$664$	−5.06171	−0.196432
$665$	−41.8874	−1.62433
$666$	8.73243	0.338375
$667$	25.0591	0.970292
$668$	12.4386	0.481265
$669$	−30.6459	−1.18484
$670$	35.9454	1.38869
$671$	40.9014	1.57898
$672$	5.19182	0.200279
$673$	8.93396	0.344379	0.172189	−	0.985064i	$-0.444916\pi$
$673$	8.93396	0.344379	0.172189	+	0.985064i	$0.444916\pi$
$674$	29.4003	1.13246
$675$	62.5990	2.40944
$676$	8.88802	0.341847
$677$	−17.2637	−0.663498	−0.331749	−	0.943368i	$-0.607639\pi$
$677$	−17.2637	−0.663498	−0.331749	+	0.943368i	$0.607639\pi$
$678$	7.63235	0.293119
$679$	26.9665	1.03488
$680$	−11.7497	−0.450580
$681$	−23.5704	−0.903220
$682$	−29.8217	−1.14193
$683$	28.5946	1.09414	0.547071	−	0.837086i	$-0.315743\pi$
$683$	28.5946	1.09414	0.547071	+	0.837086i	$0.315743\pi$
$684$	−3.72450	−0.142410
$685$	−84.8717	−3.24278
$686$	−20.3852	−0.778311
$687$	1.92794	0.0735554
$688$	−2.51117	−0.0957374
$689$	−21.1117	−0.804291
$690$	−37.2896	−1.41959
$691$	−40.1101	−1.52586	−0.762929	−	0.646482i	$-0.776240\pi$
$691$	−40.1101	−1.52586	−0.762929	+	0.646482i	$0.776240\pi$
$692$	−15.7589	−0.599062
$693$	27.3893	1.04044
$694$	20.2567	0.768935
$695$	81.9014	3.10670
$696$	−3.92488	−0.148772
$697$	−22.9565	−0.869541
$698$	27.7374	1.04988
$699$	−29.6532	−1.12159
$700$	−49.4835	−1.87030
$701$	23.5957	0.891197	0.445599	−	0.895233i	$-0.352991\pi$
$701$	23.5957	0.891197	0.445599	+	0.895233i	$0.352991\pi$
$702$	−25.6021	−0.966290
$703$	−13.3728	−0.504366
$704$	4.06000	0.153017
$705$	−24.3073	−0.915466
$706$	0.802764	0.0302124
$707$	−0.0225043	−0.000846361 0
$708$	−12.4472	−0.467794
$709$	−13.0403	−0.489737	−0.244869	−	0.969556i	$-0.578745\pi$
$709$	−13.0403	−0.489737	−0.244869	+	0.969556i	$0.578745\pi$
$710$	64.0016	2.40194
$711$	−12.1260	−0.454762
$712$	13.3990	0.502147
$713$	−56.2859	−2.10793
$714$	−15.0455	−0.563062
$715$	−77.0139	−2.88016
$716$	4.30398	0.160847
$717$	20.3115	0.758548
$718$	−8.25664	−0.308135
$719$	−4.04715	−0.150933	−0.0754667	−	0.997148i	$-0.524045\pi$
$719$	−4.04715	−0.150933	−0.0754667	+	0.997148i	$0.524045\pi$
$720$	−6.32310	−0.235648
$721$	−14.1087	−0.525436
$722$	−13.2963	−0.494837
$723$	−4.07432	−0.151526
$724$	−11.0691	−0.411379
$725$	37.4082	1.38931
$726$	−6.58141	−0.244259
$727$	29.5444	1.09574	0.547871	−	0.836563i	$-0.315439\pi$
$727$	29.5444	1.09574	0.547871	+	0.836563i	$0.315439\pi$
$728$	20.2381	0.750073
$729$	22.6502	0.838896
$730$	−31.6521	−1.17150
$731$	7.27716	0.269155
$732$	−12.0911	−0.446901
$733$	−47.7133	−1.76233	−0.881166	−	0.472808i	$-0.843240\pi$
$733$	−47.7133	−1.76233	−0.881166	+	0.472808i	$0.843240\pi$
$734$	32.9664	1.21681
$735$	−56.9958	−2.10232
$736$	7.66290	0.282458
$737$	35.9939	1.32585
$738$	−12.3541	−0.454760
$739$	50.3620	1.85260	0.926299	−	0.376790i	$-0.122972\pi$
$739$	50.3620	1.85260	0.926299	+	0.376790i	$0.122972\pi$
$740$	−22.7031	−0.834583
$741$	13.4102	0.492636
$742$	−19.5203	−0.716611
$743$	27.8706	1.02247	0.511236	−	0.859440i	$-0.329188\pi$
$743$	27.8706	1.02247	0.511236	+	0.859440i	$0.329188\pi$
$744$	8.81579	0.323202
$745$	−50.1017	−1.83558
$746$	−26.0452	−0.953584
$747$	7.89382	0.288820
$748$	−11.7655	−0.430191
$749$	47.0823	1.72035
$750$	−31.3346	−1.14418
$751$	−35.2140	−1.28498	−0.642488	−	0.766296i	$-0.722098\pi$
$751$	−35.2140	−1.28498	−0.642488	+	0.766296i	$0.722098\pi$
$752$	4.99508	0.182152
$753$	15.0757	0.549388
$754$	−15.2994	−0.557173
$755$	−54.1856	−1.97202
$756$	−23.6722	−0.860950
$757$	41.7062	1.51584	0.757919	−	0.652348i	$-0.226216\pi$
$757$	41.7062	1.51584	0.757919	+	0.652348i	$0.226216\pi$
$758$	5.35349	0.194447
$759$	−37.3399	−1.35535
$760$	9.68318	0.351246
$761$	20.8597	0.756162	0.378081	−	0.925773i	$-0.376584\pi$
$761$	20.8597	0.756162	0.378081	+	0.925773i	$0.376584\pi$
$762$	8.53127	0.309055
$763$	33.0260	1.19562
$764$	8.39431	0.303695
$765$	18.3238	0.662499
$766$	13.0186	0.470381
$767$	−48.5200	−1.75195
$768$	−1.20020	−0.0433085
$769$	35.3375	1.27430	0.637151	−	0.770739i	$-0.280113\pi$
$769$	35.3375	1.27430	0.637151	+	0.770739i	$0.280113\pi$
$770$	−71.2085	−2.56617
$771$	−7.80269	−0.281007
$772$	−5.99750	−0.215855
$773$	−38.6450	−1.38997	−0.694983	−	0.719027i	$-0.744588\pi$
$773$	−38.6450	−1.38997	−0.694983	+	0.719027i	$0.744588\pi$
$774$	3.91621	0.140765
$775$	−84.0237	−3.01822
$776$	−6.23389	−0.223784
$777$	−29.0713	−1.04293
$778$	−27.7624	−0.995331
$779$	18.9190	0.677844
$780$	22.7666	0.815174
$781$	64.0880	2.29325
$782$	−22.2064	−0.794101
$783$	17.8956	0.639535
$784$	11.7125	0.418303
$785$	43.8412	1.56476
$786$	−0.742596	−0.0264875
$787$	43.8384	1.56267	0.781334	−	0.624113i	$-0.214539\pi$
$787$	43.8384	1.56267	0.781334	+	0.624113i	$0.214539\pi$
$788$	−4.83348	−0.172186
$789$	14.0236	0.499255
$790$	31.5260	1.12164
$791$	27.5087	0.978096
$792$	−6.33164	−0.224985
$793$	−47.1320	−1.67371
$794$	−15.7568	−0.559189
$795$	−21.9591	−0.778808
$796$	12.9404	0.458659
$797$	30.1008	1.06623	0.533113	−	0.846044i	$-0.321022\pi$
$797$	30.1008	1.06623	0.533113	+	0.846044i	$0.321022\pi$
$798$	12.3993	0.438931
$799$	−14.4753	−0.512101
$800$	11.4392	0.404436
$801$	−20.8959	−0.738320
$802$	−8.79126	−0.310430
$803$	−31.6948	−1.11848
$804$	−10.6404	−0.375258
$805$	−134.400	−4.73697
$806$	34.3645	1.21044
$807$	−38.9922	−1.37259
$808$	0.00520235	0.000183018 0
$809$	24.7759	0.871075	0.435537	−	0.900171i	$-0.356558\pi$
$809$	24.7759	0.871075	0.435537	+	0.900171i	$0.356558\pi$
$810$	−7.66044	−0.269161
$811$	−12.2988	−0.431869	−0.215934	−	0.976408i	$-0.569280\pi$
$811$	−12.2988	−0.431869	−0.215934	+	0.976408i	$0.569280\pi$
$812$	−14.1461	−0.496432
$813$	29.9629	1.05085
$814$	−22.7338	−0.796818
$815$	39.5169	1.38422
$816$	3.47808	0.121757
$817$	−5.99728	−0.209818
$818$	−1.86275	−0.0651295
$819$	−31.5616	−1.10285
$820$	32.1189	1.12164
$821$	15.0202	0.524208	0.262104	−	0.965040i	$-0.415584\pi$
$821$	15.0202	0.524208	0.262104	+	0.965040i	$0.415584\pi$
$822$	25.1233	0.876276
$823$	−49.4291	−1.72299	−0.861495	−	0.507767i	$-0.830471\pi$
$823$	−49.4291	−1.72299	−0.861495	+	0.507767i	$0.830471\pi$
$824$	3.26154	0.113621
$825$	−55.7410	−1.94065
$826$	−44.8624	−1.56096
$827$	11.7837	0.409760	0.204880	−	0.978787i	$-0.434320\pi$
$827$	11.7837	0.409760	0.204880	+	0.978787i	$0.434320\pi$
$828$	−11.9504	−0.415306
$829$	−10.4146	−0.361712	−0.180856	−	0.983510i	$-0.557887\pi$
$829$	−10.4146	−0.361712	−0.180856	+	0.983510i	$0.557887\pi$
$830$	−20.5228	−0.712358
$831$	−7.15970	−0.248367
$832$	−4.67846	−0.162197
$833$	−33.9418	−1.17601
$834$	−24.2441	−0.839504
$835$	50.4328	1.74530
$836$	9.69625	0.335352
$837$	−40.1957	−1.38937
$838$	−6.62634	−0.228903
$839$	33.9234	1.17117	0.585583	−	0.810613i	$-0.300866\pi$
$839$	33.9234	1.17117	0.585583	+	0.810613i	$0.300866\pi$
$840$	21.0504	0.726307
$841$	−18.3059	−0.631238
$842$	9.11898	0.314261
$843$	12.7321	0.438516
$844$	−15.1882	−0.522799
$845$	36.0367	1.23970
$846$	−7.78992	−0.267823
$847$	−23.7209	−0.815058
$848$	4.51253	0.154961
$849$	−9.08415	−0.311767
$850$	−33.1498	−1.13703
$851$	−42.9080	−1.47087
$852$	−18.9455	−0.649061
$853$	11.0682	0.378968	0.189484	−	0.981884i	$-0.439319\pi$
$853$	11.0682	0.378968	0.189484	+	0.981884i	$0.439319\pi$
$854$	−43.5791	−1.49125
$855$	−15.1011	−0.516446
$856$	−10.8841	−0.372010
$857$	−46.9498	−1.60377	−0.801887	−	0.597476i	$-0.796170\pi$
$857$	−46.9498	−1.60377	−0.801887	+	0.597476i	$0.796170\pi$
$858$	22.7973	0.778287
$859$	−50.7885	−1.73288	−0.866440	−	0.499281i	$-0.833597\pi$
$859$	−50.7885	−1.73288	−0.866440	+	0.499281i	$0.833597\pi$
$860$	−10.1816	−0.347190
$861$	41.1283	1.40165
$862$	−30.8344	−1.05022
$863$	−35.7078	−1.21551	−0.607753	−	0.794126i	$-0.707929\pi$
$863$	−35.7078	−1.21551	−0.607753	+	0.794126i	$0.707929\pi$
$864$	5.47234	0.186173
$865$	−63.8947	−2.17249
$866$	20.7544	0.705264
$867$	10.3242	0.350629
$868$	31.7741	1.07848
$869$	31.5685	1.07089
$870$	−15.9135	−0.539519
$871$	−41.4769	−1.40539
$872$	−7.63468	−0.258543
$873$	9.72186	0.329035
$874$	18.3008	0.619035
$875$	−112.937	−3.81797
$876$	9.36949	0.316566
$877$	−7.96512	−0.268963	−0.134481	−	0.990916i	$-0.542937\pi$
$877$	−7.96512	−0.268963	−0.134481	+	0.990916i	$0.542937\pi$
$878$	−15.1321	−0.510684
$879$	−36.1931	−1.22076
$880$	16.4614	0.554913
$881$	−53.1167	−1.78955	−0.894774	−	0.446519i	$-0.852663\pi$
$881$	−53.1167	−1.78955	−0.894774	+	0.446519i	$0.852663\pi$
$882$	−18.2658	−0.615042
$883$	31.1473	1.04819	0.524095	−	0.851660i	$-0.324404\pi$
$883$	31.1473	1.04819	0.524095	+	0.851660i	$0.324404\pi$
$884$	13.5578	0.455998
$885$	−50.4674	−1.69644
$886$	3.02720	0.101701
$887$	13.5937	0.456432	0.228216	−	0.973610i	$-0.426711\pi$
$887$	13.5937	0.456432	0.228216	+	0.973610i	$0.426711\pi$
$888$	6.72047	0.225524
$889$	30.7486	1.03128
$890$	54.3264	1.82103
$891$	−7.67078	−0.256981
$892$	25.5339	0.854940
$893$	11.9295	0.399204
$894$	14.8309	0.496018
$895$	17.4506	0.583309
$896$	−4.32579	−0.144515
$897$	43.0279	1.43666
$898$	−33.5603	−1.11992
$899$	−24.0203	−0.801123
$900$	−17.8396	−0.594653
$901$	−13.0769	−0.435655
$902$	32.1623	1.07089
$903$	−13.0375	−0.433862
$904$	−6.35923	−0.211505
$905$	−44.8799	−1.49186
$906$	16.0398	0.532885
$907$	16.3354	0.542409	0.271205	−	0.962522i	$-0.412578\pi$
$907$	16.3354	0.542409	0.271205	+	0.962522i	$0.412578\pi$
$908$	19.6387	0.651734
$909$	−0.00811315	−0.000269096 0
$910$	82.0557	2.72012
$911$	−15.6857	−0.519690	−0.259845	−	0.965650i	$-0.583671\pi$
$911$	−15.6857	−0.519690	−0.259845	+	0.965650i	$0.583671\pi$
$912$	−2.86637	−0.0949150
$913$	−20.5505	−0.680123
$914$	−20.2745	−0.670622
$915$	−49.0238	−1.62068
$916$	−1.60634	−0.0530751
$917$	−2.67648	−0.0883852
$918$	−15.8584	−0.523404
$919$	18.2020	0.600428	0.300214	−	0.953872i	$-0.402942\pi$
$919$	18.2020	0.600428	0.300214	+	0.953872i	$0.402942\pi$
$920$	31.0694	1.02433
$921$	3.60840	0.118901
$922$	13.5023	0.444676
$923$	−73.8506	−2.43082
$924$	21.0788	0.693441
$925$	−64.0531	−2.10605
$926$	13.1152	0.430991
$927$	−5.08642	−0.167060
$928$	3.27018	0.107349
$929$	−15.6768	−0.514340	−0.257170	−	0.966366i	$-0.582790\pi$
$929$	−15.6768	−0.514340	−0.257170	+	0.966366i	$0.582790\pi$
$930$	35.7438	1.17209
$931$	27.9722	0.916753
$932$	24.7069	0.809301
$933$	5.45504	0.178590
$934$	2.12649	0.0695810
$935$	−47.7037	−1.56008
$936$	7.29614	0.238482
$937$	56.7356	1.85347	0.926736	−	0.375713i	$-0.122602\pi$
$937$	56.7356	1.85347	0.926736	+	0.375713i	$0.122602\pi$
$938$	−38.3503	−1.25218
$939$	27.9523	0.912187
$940$	20.2527	0.660570
$941$	47.1637	1.53749	0.768747	−	0.639553i	$-0.220881\pi$
$941$	47.1637	1.53749	0.768747	+	0.639553i	$0.220881\pi$
$942$	−12.9777	−0.422835
$943$	60.7035	1.97678
$944$	10.3709	0.337545
$945$	−95.9795	−3.12221
$946$	−10.1953	−0.331479
$947$	−28.0752	−0.912320	−0.456160	−	0.889898i	$-0.650776\pi$
$947$	−28.0752	−0.912320	−0.456160	+	0.889898i	$0.650776\pi$
$948$	−9.33217	−0.303095
$949$	36.5229	1.18558
$950$	27.3195	0.886362
$951$	35.2175	1.14201
$952$	12.5358	0.406287
$953$	31.9751	1.03577	0.517887	−	0.855449i	$-0.326719\pi$
$953$	31.9751	1.03577	0.517887	+	0.855449i	$0.326719\pi$
$954$	−7.03736	−0.227843
$955$	34.0349	1.10134
$956$	−16.9234	−0.547343
$957$	−15.9350	−0.515105
$958$	−33.8468	−1.09354
$959$	90.5500	2.92401
$960$	−4.86625	−0.157057
$961$	22.9528	0.740412
$962$	26.1968	0.844619
$963$	16.9739	0.546977
$964$	3.39470	0.109336
$965$	−24.3170	−0.782792
$966$	39.7844	1.28004
$967$	−47.7182	−1.53451	−0.767256	−	0.641340i	$-0.778379\pi$
$967$	−47.7182	−1.53451	−0.767256	+	0.641340i	$0.778379\pi$
$968$	5.48359	0.176249
$969$	8.30650	0.266843
$970$	−25.2755	−0.811546
$971$	−6.16109	−0.197719	−0.0988594	−	0.995101i	$-0.531519\pi$
$971$	−6.16109	−0.197719	−0.0988594	+	0.995101i	$0.531519\pi$
$972$	−14.1494	−0.453842
$973$	−87.3810	−2.80131
$974$	−13.8312	−0.443181
$975$	64.2321	2.05707
$976$	10.0742	0.322469
$977$	−18.2433	−0.583656	−0.291828	−	0.956471i	$-0.594263\pi$
$977$	−18.2433	−0.583656	−0.291828	+	0.956471i	$0.594263\pi$
$978$	−11.6976	−0.374048
$979$	54.3997	1.73862
$980$	47.4886	1.51697
$981$	11.9064	0.380142
$982$	6.95907	0.222073
$983$	−56.3766	−1.79814	−0.899068	−	0.437810i	$-0.855754\pi$
$983$	−56.3766	−1.79814	−0.899068	+	0.437810i	$0.855754\pi$
$984$	−9.50768	−0.303094
$985$	−19.5975	−0.624427
$986$	−9.47672	−0.301800
$987$	25.9336	0.825475
$988$	−11.1733	−0.355470
$989$	−19.2428	−0.611887
$990$	−25.6718	−0.815903
$991$	−1.14825	−0.0364753	−0.0182376	−	0.999834i	$-0.505806\pi$
$991$	−1.14825	−0.0364753	−0.0182376	+	0.999834i	$0.505806\pi$
$992$	−7.34526	−0.233212
$993$	−27.3331	−0.867389
$994$	−68.2836	−2.16583
$995$	52.4671	1.66332
$996$	6.07507	0.192496
$997$	−33.4142	−1.05824	−0.529120	−	0.848547i	$-0.677478\pi$
$997$	−33.4142	−1.05824	−0.529120	+	0.848547i	$0.677478\pi$
$998$	38.4157	1.21603
$999$	−30.6421	−0.969472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.i.1.13	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.i.1.13	✓	46	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.20020 q^{3} +1.00000 q^{4} +4.05453 q^{5} -1.20020 q^{6} -4.32579 q^{7} +1.00000 q^{8} -1.55952 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.20020 q^{3} +1.00000 q^{4} +4.05453 q^{5} -1.20020 q^{6} -4.32579 q^{7} +1.00000 q^{8} -1.55952 q^{9} +4.05453 q^{10} +4.06000 q^{11} -1.20020 q^{12} -4.67846 q^{13} -4.32579 q^{14} -4.86625 q^{15} +1.00000 q^{16} -2.89792 q^{17} -1.55952 q^{18} +2.38824 q^{19} +4.05453 q^{20} +5.19182 q^{21} +4.06000 q^{22} +7.66290 q^{23} -1.20020 q^{24} +11.4392 q^{25} -4.67846 q^{26} +5.47234 q^{27} -4.32579 q^{28} +3.27018 q^{29} -4.86625 q^{30} -7.34526 q^{31} +1.00000 q^{32} -4.87282 q^{33} -2.89792 q^{34} -17.5390 q^{35} -1.55952 q^{36} -5.59945 q^{37} +2.38824 q^{38} +5.61510 q^{39} +4.05453 q^{40} +7.92174 q^{41} +5.19182 q^{42} -2.51117 q^{43} +4.06000 q^{44} -6.32310 q^{45} +7.66290 q^{46} +4.99508 q^{47} -1.20020 q^{48} +11.7125 q^{49} +11.4392 q^{50} +3.47808 q^{51} -4.67846 q^{52} +4.51253 q^{53} +5.47234 q^{54} +16.4614 q^{55} -4.32579 q^{56} -2.86637 q^{57} +3.27018 q^{58} +10.3709 q^{59} -4.86625 q^{60} +10.0742 q^{61} -7.34526 q^{62} +6.74615 q^{63} +1.00000 q^{64} -18.9690 q^{65} -4.87282 q^{66} +8.86550 q^{67} -2.89792 q^{68} -9.19702 q^{69} -17.5390 q^{70} +15.7852 q^{71} -1.55952 q^{72} -7.80660 q^{73} -5.59945 q^{74} -13.7293 q^{75} +2.38824 q^{76} -17.5627 q^{77} +5.61510 q^{78} +7.77550 q^{79} +4.05453 q^{80} -1.88936 q^{81} +7.92174 q^{82} -5.06171 q^{83} +5.19182 q^{84} -11.7497 q^{85} -2.51117 q^{86} -3.92488 q^{87} +4.06000 q^{88} +13.3990 q^{89} -6.32310 q^{90} +20.2381 q^{91} +7.66290 q^{92} +8.81579 q^{93} +4.99508 q^{94} +9.68318 q^{95} -1.20020 q^{96} -6.23389 q^{97} +11.7125 q^{98} -6.33164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9	\( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 46 * q + 46 * q^2 + 21 * q^3 + 46 * q^4 + 23 * q^5 + 21 * q^6 + 26 * q^7 + 46 * q^8 + 59 * q^9 + 23 * q^10 + 39 * q^11 + 21 * q^12 + 8 * q^13 + 26 * q^14 + 14 * q^15 + 46 * q^16 + 36 * q^17 + 59 * q^18 + 37 * q^19 + 23 * q^20 + 20 * q^21 + 39 * q^22 + 38 * q^23 + 21 * q^24 + 57 * q^25 + 8 * q^26 + 63 * q^27 + 26 * q^28 + 23 * q^29 + 14 * q^30 + 44 * q^31 + 46 * q^32 + 25 * q^33 + 36 * q^34 + 26 * q^35 + 59 * q^36 + 9 * q^37 + 37 * q^38 - 2 * q^39 + 23 * q^40 + 50 * q^41 + 20 * q^42 + 46 * q^43 + 39 * q^44 + 30 * q^45 + 38 * q^46 + 57 * q^47 + 21 * q^48 + 62 * q^49 + 57 * q^50 + 5 * q^51 + 8 * q^52 + 21 * q^53 + 63 * q^54 + 40 * q^55 + 26 * q^56 + 3 * q^57 + 23 * q^58 + 68 * q^59 + 14 * q^60 - q^61 + 44 * q^62 + 40 * q^63 + 46 * q^64 + 18 * q^65 + 25 * q^66 + 42 * q^67 + 36 * q^68 - 7 * q^69 + 26 * q^70 + 67 * q^71 + 59 * q^72 + 48 * q^73 + 9 * q^74 + 71 * q^75 + 37 * q^76 - 5 * q^77 - 2 * q^78 + 40 * q^79 + 23 * q^80 + 82 * q^81 + 50 * q^82 + 48 * q^83 + 20 * q^84 - 68 * q^85 + 46 * q^86 + 18 * q^87 + 39 * q^88 + 90 * q^89 + 30 * q^90 + 9 * q^91 + 38 * q^92 - 42 * q^93 + 57 * q^94 + 6 * q^95 + 21 * q^96 + 46 * q^97 + 62 * q^98 + 61 * q^99

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