LMFDB - Embedded newform 4006.2.a.g.1.18

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:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +4.09209 q^{10} +4.23375 q^{11} -0.712075 q^{12} -0.870599 q^{13} -2.33011 q^{14} +2.91388 q^{15} +1.00000 q^{16} -6.84125 q^{17} +2.49295 q^{18} +1.01005 q^{19} -4.09209 q^{20} -1.65921 q^{21} -4.23375 q^{22} -2.53327 q^{23} +0.712075 q^{24} +11.7452 q^{25} +0.870599 q^{26} +3.91139 q^{27} +2.33011 q^{28} +0.501652 q^{29} -2.91388 q^{30} +5.40493 q^{31} -1.00000 q^{32} -3.01475 q^{33} +6.84125 q^{34} -9.53500 q^{35} -2.49295 q^{36} +7.79791 q^{37} -1.01005 q^{38} +0.619932 q^{39} +4.09209 q^{40} -6.82665 q^{41} +1.65921 q^{42} +0.979903 q^{43} +4.23375 q^{44} +10.2014 q^{45} +2.53327 q^{46} +0.948587 q^{47} -0.712075 q^{48} -1.57061 q^{49} -11.7452 q^{50} +4.87148 q^{51} -0.870599 q^{52} +12.3207 q^{53} -3.91139 q^{54} -17.3249 q^{55} -2.33011 q^{56} -0.719229 q^{57} -0.501652 q^{58} -8.74441 q^{59} +2.91388 q^{60} -3.12405 q^{61} -5.40493 q^{62} -5.80883 q^{63} +1.00000 q^{64} +3.56257 q^{65} +3.01475 q^{66} -2.12825 q^{67} -6.84125 q^{68} +1.80388 q^{69} +9.53500 q^{70} -0.135202 q^{71} +2.49295 q^{72} -5.71895 q^{73} -7.79791 q^{74} -8.36347 q^{75} +1.01005 q^{76} +9.86509 q^{77} -0.619932 q^{78} +15.1609 q^{79} -4.09209 q^{80} +4.69364 q^{81} +6.82665 q^{82} -6.20844 q^{83} -1.65921 q^{84} +27.9950 q^{85} -0.979903 q^{86} -0.357214 q^{87} -4.23375 q^{88} +3.24155 q^{89} -10.2014 q^{90} -2.02859 q^{91} -2.53327 q^{92} -3.84872 q^{93} -0.948587 q^{94} -4.13320 q^{95} +0.712075 q^{96} +18.9534 q^{97} +1.57061 q^{98} -10.5545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * 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
$3$	−0.712075	−0.411117	−0.205558	−	0.978645i	$-0.565901\pi$
$3$	−0.712075	−0.411117	−0.205558	+	0.978645i	$0.565901\pi$
$4$	1.00000	0.500000
$5$	−4.09209	−1.83004	−0.915019	−	0.403410i	$-0.867825\pi$
$5$	−4.09209	−1.83004	−0.915019	+	0.403410i	$0.867825\pi$
$6$	0.712075	0.290703
$7$	2.33011	0.880697	0.440348	−	0.897827i	$-0.354855\pi$
$7$	2.33011	0.880697	0.440348	+	0.897827i	$0.354855\pi$
$8$	−1.00000	−0.353553
$9$	−2.49295	−0.830983
$10$	4.09209	1.29403
$11$	4.23375	1.27652	0.638262	−	0.769819i	$-0.279654\pi$
$11$	4.23375	1.27652	0.638262	+	0.769819i	$0.279654\pi$
$12$	−0.712075	−0.205558
$13$	−0.870599	−0.241461	−0.120730	−	0.992685i	$-0.538524\pi$
$13$	−0.870599	−0.241461	−0.120730	+	0.992685i	$0.538524\pi$
$14$	−2.33011	−0.622747
$15$	2.91388	0.752359
$16$	1.00000	0.250000
$17$	−6.84125	−1.65925	−0.829623	−	0.558324i	$-0.811445\pi$
$17$	−6.84125	−1.65925	−0.829623	+	0.558324i	$0.811445\pi$
$18$	2.49295	0.587594
$19$	1.01005	0.231721	0.115860	−	0.993266i	$-0.463037\pi$
$19$	1.01005	0.231721	0.115860	+	0.993266i	$0.463037\pi$
$20$	−4.09209	−0.915019
$21$	−1.65921	−0.362069
$22$	−4.23375	−0.902639
$23$	−2.53327	−0.528223	−0.264111	−	0.964492i	$-0.585079\pi$
$23$	−2.53327	−0.528223	−0.264111	+	0.964492i	$0.585079\pi$
$24$	0.712075	0.145352
$25$	11.7452	2.34904
$26$	0.870599	0.170739
$27$	3.91139	0.752748
$28$	2.33011	0.440348
$29$	0.501652	0.0931545	0.0465772	−	0.998915i	$-0.485169\pi$
$29$	0.501652	0.0931545	0.0465772	+	0.998915i	$0.485169\pi$
$30$	−2.91388	−0.531998
$31$	5.40493	0.970754	0.485377	−	0.874305i	$-0.338682\pi$
$31$	5.40493	0.970754	0.485377	+	0.874305i	$0.338682\pi$
$32$	−1.00000	−0.176777
$33$	−3.01475	−0.524801
$34$	6.84125	1.17326
$35$	−9.53500	−1.61171
$36$	−2.49295	−0.415492
$37$	7.79791	1.28197	0.640984	−	0.767554i	$-0.278526\pi$
$37$	7.79791	1.28197	0.640984	+	0.767554i	$0.278526\pi$
$38$	−1.01005	−0.163851
$39$	0.619932	0.0992686
$40$	4.09209	0.647016
$41$	−6.82665	−1.06614	−0.533072	−	0.846070i	$-0.678962\pi$
$41$	−6.82665	−1.06614	−0.533072	+	0.846070i	$0.678962\pi$
$42$	1.65921	0.256022
$43$	0.979903	0.149434	0.0747169	−	0.997205i	$-0.476195\pi$
$43$	0.979903	0.149434	0.0747169	+	0.997205i	$0.476195\pi$
$44$	4.23375	0.638262
$45$	10.2014	1.52073
$46$	2.53327	0.373510
$47$	0.948587	0.138366	0.0691828	−	0.997604i	$-0.477961\pi$
$47$	0.948587	0.138366	0.0691828	+	0.997604i	$0.477961\pi$
$48$	−0.712075	−0.102779
$49$	−1.57061	−0.224373
$50$	−11.7452	−1.66102
$51$	4.87148	0.682144
$52$	−0.870599	−0.120730
$53$	12.3207	1.69238	0.846192	−	0.532878i	$-0.178890\pi$
$53$	12.3207	1.69238	0.846192	+	0.532878i	$0.178890\pi$
$54$	−3.91139	−0.532273
$55$	−17.3249	−2.33609
$56$	−2.33011	−0.311373
$57$	−0.719229	−0.0952642
$58$	−0.501652	−0.0658702
$59$	−8.74441	−1.13842	−0.569212	−	0.822191i	$-0.692752\pi$
$59$	−8.74441	−1.13842	−0.569212	+	0.822191i	$0.692752\pi$
$60$	2.91388	0.376180
$61$	−3.12405	−0.399994	−0.199997	−	0.979797i	$-0.564093\pi$
$61$	−3.12405	−0.399994	−0.199997	+	0.979797i	$0.564093\pi$
$62$	−5.40493	−0.686427
$63$	−5.80883	−0.731844
$64$	1.00000	0.125000
$65$	3.56257	0.441883
$66$	3.01475	0.371090
$67$	−2.12825	−0.260007	−0.130003	−	0.991514i	$-0.541499\pi$
$67$	−2.12825	−0.260007	−0.130003	+	0.991514i	$0.541499\pi$
$68$	−6.84125	−0.829623
$69$	1.80388	0.217161
$70$	9.53500	1.13965
$71$	−0.135202	−0.0160455	−0.00802275	−	0.999968i	$-0.502554\pi$
$71$	−0.135202	−0.0160455	−0.00802275	+	0.999968i	$0.502554\pi$
$72$	2.49295	0.293797
$73$	−5.71895	−0.669352	−0.334676	−	0.942333i	$-0.608627\pi$
$73$	−5.71895	−0.669352	−0.334676	+	0.942333i	$0.608627\pi$
$74$	−7.79791	−0.906488
$75$	−8.36347	−0.965730
$76$	1.01005	0.115860
$77$	9.86509	1.12423
$78$	−0.619932	−0.0701935
$79$	15.1609	1.70573	0.852867	−	0.522128i	$-0.174862\pi$
$79$	15.1609	1.70573	0.852867	+	0.522128i	$0.174862\pi$
$80$	−4.09209	−0.457510
$81$	4.69364	0.521516
$82$	6.82665	0.753877
$83$	−6.20844	−0.681465	−0.340732	−	0.940160i	$-0.610675\pi$
$83$	−6.20844	−0.681465	−0.340732	+	0.940160i	$0.610675\pi$
$84$	−1.65921	−0.181035
$85$	27.9950	3.03648
$86$	−0.979903	−0.105666
$87$	−0.357214	−0.0382974
$88$	−4.23375	−0.451320
$89$	3.24155	0.343603	0.171802	−	0.985132i	$-0.445041\pi$
$89$	3.24155	0.343603	0.171802	+	0.985132i	$0.445041\pi$
$90$	−10.2014	−1.07532
$91$	−2.02859	−0.212654
$92$	−2.53327	−0.264111
$93$	−3.84872	−0.399093
$94$	−0.948587	−0.0978392
$95$	−4.13320	−0.424058
$96$	0.712075	0.0726758
$97$	18.9534	1.92443	0.962213	−	0.272297i	$-0.0877834\pi$
$97$	18.9534	1.92443	0.962213	+	0.272297i	$0.0877834\pi$
$98$	1.57061	0.158656
$99$	−10.5545	−1.06077
$100$	11.7452	1.17452
$101$	0.897568	0.0893114	0.0446557	−	0.999002i	$-0.485781\pi$
$101$	0.897568	0.0893114	0.0446557	+	0.999002i	$0.485781\pi$
$102$	−4.87148	−0.482349
$103$	1.99610	0.196681	0.0983406	−	0.995153i	$-0.468647\pi$
$103$	1.99610	0.196681	0.0983406	+	0.995153i	$0.468647\pi$
$104$	0.870599	0.0853693
$105$	6.78964	0.662601
$106$	−12.3207	−1.19670
$107$	0.418296	0.0404382	0.0202191	−	0.999796i	$-0.493564\pi$
$107$	0.418296	0.0404382	0.0202191	+	0.999796i	$0.493564\pi$
$108$	3.91139	0.376374
$109$	−11.0518	−1.05857	−0.529285	−	0.848444i	$-0.677540\pi$
$109$	−11.0518	−1.05857	−0.529285	+	0.848444i	$0.677540\pi$
$110$	17.3249	1.65186
$111$	−5.55269	−0.527038
$112$	2.33011	0.220174
$113$	8.73234	0.821469	0.410735	−	0.911755i	$-0.365272\pi$
$113$	8.73234	0.821469	0.410735	+	0.911755i	$0.365272\pi$
$114$	0.719229	0.0673620
$115$	10.3664	0.966668
$116$	0.501652	0.0465772
$117$	2.17036	0.200650
$118$	8.74441	0.804988
$119$	−15.9408	−1.46129
$120$	−2.91388	−0.265999
$121$	6.92467	0.629515
$122$	3.12405	0.282838
$123$	4.86109	0.438309
$124$	5.40493	0.485377
$125$	−27.6020	−2.46880
$126$	5.80883	0.517492
$127$	−2.79511	−0.248026	−0.124013	−	0.992281i	$-0.539576\pi$
$127$	−2.79511	−0.248026	−0.124013	+	0.992281i	$0.539576\pi$
$128$	−1.00000	−0.0883883
$129$	−0.697765	−0.0614348
$130$	−3.56257	−0.312458
$131$	7.27881	0.635953	0.317976	−	0.948099i	$-0.396997\pi$
$131$	7.27881	0.635953	0.317976	+	0.948099i	$0.396997\pi$
$132$	−3.01475	−0.262400
$133$	2.35352	0.204076
$134$	2.12825	0.183853
$135$	−16.0058	−1.37756
$136$	6.84125	0.586632
$137$	0.158074	0.0135052	0.00675259	−	0.999977i	$-0.497851\pi$
$137$	0.158074	0.0135052	0.00675259	+	0.999977i	$0.497851\pi$
$138$	−1.80388	−0.153556
$139$	−16.6942	−1.41598	−0.707990	−	0.706223i	$-0.750398\pi$
$139$	−16.6942	−1.41598	−0.707990	+	0.706223i	$0.750398\pi$
$140$	−9.53500	−0.805855
$141$	−0.675465	−0.0568844
$142$	0.135202	0.0113459
$143$	−3.68590	−0.308231
$144$	−2.49295	−0.207746
$145$	−2.05281	−0.170476
$146$	5.71895	0.473303
$147$	1.11839	0.0922435
$148$	7.79791	0.640984
$149$	11.6457	0.954055	0.477028	−	0.878888i	$-0.341714\pi$
$149$	11.6457	0.954055	0.477028	+	0.878888i	$0.341714\pi$
$150$	8.36347	0.682874
$151$	−22.1165	−1.79981	−0.899907	−	0.436081i	$-0.856366\pi$
$151$	−22.1165	−1.79981	−0.899907	+	0.436081i	$0.856366\pi$
$152$	−1.01005	−0.0819256
$153$	17.0549	1.37881
$154$	−9.86509	−0.794952
$155$	−22.1175	−1.77652
$156$	0.619932	0.0496343
$157$	−12.3994	−0.989580	−0.494790	−	0.869013i	$-0.664755\pi$
$157$	−12.3994	−0.989580	−0.494790	+	0.869013i	$0.664755\pi$
$158$	−15.1609	−1.20614
$159$	−8.77329	−0.695767
$160$	4.09209	0.323508
$161$	−5.90278	−0.465204
$162$	−4.69364	−0.368767
$163$	2.20063	0.172367	0.0861833	−	0.996279i	$-0.472533\pi$
$163$	2.20063	0.172367	0.0861833	+	0.996279i	$0.472533\pi$
$164$	−6.82665	−0.533072
$165$	12.3366	0.960405
$166$	6.20844	0.481868
$167$	12.5024	0.967467	0.483734	−	0.875215i	$-0.339280\pi$
$167$	12.5024	0.967467	0.483734	+	0.875215i	$0.339280\pi$
$168$	1.65921	0.128011
$169$	−12.2421	−0.941697
$170$	−27.9950	−2.14712
$171$	−2.51800	−0.192556
$172$	0.979903	0.0747169
$173$	13.1085	0.996620	0.498310	−	0.866999i	$-0.333954\pi$
$173$	13.1085	0.996620	0.498310	+	0.866999i	$0.333954\pi$
$174$	0.357214	0.0270803
$175$	27.3676	2.06879
$176$	4.23375	0.319131
$177$	6.22667	0.468025
$178$	−3.24155	−0.242964
$179$	−7.80940	−0.583702	−0.291851	−	0.956464i	$-0.594271\pi$
$179$	−7.80940	−0.583702	−0.291851	+	0.956464i	$0.594271\pi$
$180$	10.2014	0.760366
$181$	−15.6233	−1.16127	−0.580636	−	0.814163i	$-0.697196\pi$
$181$	−15.6233	−1.16127	−0.580636	+	0.814163i	$0.697196\pi$
$182$	2.02859	0.150369
$183$	2.22456	0.164444
$184$	2.53327	0.186755
$185$	−31.9097	−2.34605
$186$	3.84872	0.282202
$187$	−28.9642	−2.11807
$188$	0.948587	0.0691828
$189$	9.11395	0.662943
$190$	4.13320	0.299854
$191$	−25.5535	−1.84898	−0.924492	−	0.381202i	$-0.875510\pi$
$191$	−25.5535	−1.84898	−0.924492	+	0.381202i	$0.875510\pi$
$192$	−0.712075	−0.0513896
$193$	−14.3261	−1.03122	−0.515608	−	0.856825i	$-0.672434\pi$
$193$	−14.3261	−1.03122	−0.515608	+	0.856825i	$0.672434\pi$
$194$	−18.9534	−1.36077
$195$	−2.53682	−0.181665
$196$	−1.57061	−0.112186
$197$	8.07366	0.575225	0.287612	−	0.957747i	$-0.407139\pi$
$197$	8.07366	0.575225	0.287612	+	0.957747i	$0.407139\pi$
$198$	10.5545	0.750078
$199$	9.45893	0.670526	0.335263	−	0.942125i	$-0.391175\pi$
$199$	9.45893	0.670526	0.335263	+	0.942125i	$0.391175\pi$
$200$	−11.7452	−0.830512
$201$	1.51547	0.106893
$202$	−0.897568	−0.0631527
$203$	1.16890	0.0820409
$204$	4.87148	0.341072
$205$	27.9353	1.95108
$206$	−1.99610	−0.139075
$207$	6.31531	0.438944
$208$	−0.870599	−0.0603652
$209$	4.27629	0.295797
$210$	−6.78964	−0.468529
$211$	−13.9975	−0.963625	−0.481812	−	0.876274i	$-0.660021\pi$
$211$	−13.9975	−0.963625	−0.481812	+	0.876274i	$0.660021\pi$
$212$	12.3207	0.846192
$213$	0.0962739	0.00659658
$214$	−0.418296	−0.0285941
$215$	−4.00985	−0.273470
$216$	−3.91139	−0.266136
$217$	12.5941	0.854940
$218$	11.0518	0.748522
$219$	4.07232	0.275182
$220$	−17.3249	−1.16804
$221$	5.95599	0.400643
$222$	5.55269	0.372672
$223$	−7.35326	−0.492410	−0.246205	−	0.969218i	$-0.579184\pi$
$223$	−7.35326	−0.492410	−0.246205	+	0.969218i	$0.579184\pi$
$224$	−2.33011	−0.155687
$225$	−29.2802	−1.95201
$226$	−8.73234	−0.580867
$227$	−0.904122	−0.0600087	−0.0300043	−	0.999550i	$-0.509552\pi$
$227$	−0.904122	−0.0600087	−0.0300043	+	0.999550i	$0.509552\pi$
$228$	−0.719229	−0.0476321
$229$	−10.6473	−0.703592	−0.351796	−	0.936077i	$-0.614429\pi$
$229$	−10.6473	−0.703592	−0.351796	+	0.936077i	$0.614429\pi$
$230$	−10.3664	−0.683538
$231$	−7.02468	−0.462190
$232$	−0.501652	−0.0329351
$233$	−20.9772	−1.37426	−0.687130	−	0.726535i	$-0.741130\pi$
$233$	−20.9772	−1.37426	−0.687130	+	0.726535i	$0.741130\pi$
$234$	−2.17036	−0.141881
$235$	−3.88170	−0.253214
$236$	−8.74441	−0.569212
$237$	−10.7957	−0.701256
$238$	15.9408	1.03329
$239$	12.1770	0.787663	0.393831	−	0.919183i	$-0.371149\pi$
$239$	12.1770	0.787663	0.393831	+	0.919183i	$0.371149\pi$
$240$	2.91388	0.188090
$241$	−0.973327	−0.0626975	−0.0313488	−	0.999509i	$-0.509980\pi$
$241$	−0.973327	−0.0626975	−0.0313488	+	0.999509i	$0.509980\pi$
$242$	−6.92467	−0.445135
$243$	−15.0764	−0.967152
$244$	−3.12405	−0.199997
$245$	6.42708	0.410611
$246$	−4.86109	−0.309932
$247$	−0.879346	−0.0559515
$248$	−5.40493	−0.343214
$249$	4.42087	0.280162
$250$	27.6020	1.74570
$251$	−22.6555	−1.43000	−0.715000	−	0.699124i	$-0.753573\pi$
$251$	−22.6555	−1.43000	−0.715000	+	0.699124i	$0.753573\pi$
$252$	−5.80883	−0.365922
$253$	−10.7252	−0.674289
$254$	2.79511	0.175381
$255$	−19.9345	−1.24835
$256$	1.00000	0.0625000
$257$	1.66655	0.103957	0.0519784	−	0.998648i	$-0.483447\pi$
$257$	1.66655	0.103957	0.0519784	+	0.998648i	$0.483447\pi$
$258$	0.697765	0.0434409
$259$	18.1699	1.12903
$260$	3.56257	0.220941
$261$	−1.25059	−0.0774098
$262$	−7.27881	−0.449687
$263$	−21.7022	−1.33821	−0.669106	−	0.743167i	$-0.733323\pi$
$263$	−21.7022	−1.33821	−0.669106	+	0.743167i	$0.733323\pi$
$264$	3.01475	0.185545
$265$	−50.4176	−3.09713
$266$	−2.35352	−0.144303
$267$	−2.30822	−0.141261
$268$	−2.12825	−0.130003
$269$	−21.5484	−1.31383	−0.656915	−	0.753965i	$-0.728139\pi$
$269$	−21.5484	−1.31383	−0.656915	+	0.753965i	$0.728139\pi$
$270$	16.0058	0.974080
$271$	4.49788	0.273227	0.136613	−	0.990624i	$-0.456378\pi$
$271$	4.49788	0.273227	0.136613	+	0.990624i	$0.456378\pi$
$272$	−6.84125	−0.414812
$273$	1.44451	0.0874255
$274$	−0.158074	−0.00954961
$275$	49.7263	2.99861
$276$	1.80388	0.108581
$277$	−12.9141	−0.775935	−0.387968	−	0.921673i	$-0.626823\pi$
$277$	−12.9141	−0.775935	−0.387968	+	0.921673i	$0.626823\pi$
$278$	16.6942	1.00125
$279$	−13.4742	−0.806681
$280$	9.53500	0.569825
$281$	−3.82996	−0.228476	−0.114238	−	0.993453i	$-0.536443\pi$
$281$	−3.82996	−0.228476	−0.114238	+	0.993453i	$0.536443\pi$
$282$	0.675465	0.0402233
$283$	−11.6200	−0.690735	−0.345367	−	0.938468i	$-0.612246\pi$
$283$	−11.6200	−0.690735	−0.345367	+	0.938468i	$0.612246\pi$
$284$	−0.135202	−0.00802275
$285$	2.94315	0.174337
$286$	3.68590	0.217952
$287$	−15.9068	−0.938949
$288$	2.49295	0.146898
$289$	29.8027	1.75310
$290$	2.05281	0.120545
$291$	−13.4962	−0.791164
$292$	−5.71895	−0.334676
$293$	−18.8463	−1.10101	−0.550507	−	0.834831i	$-0.685565\pi$
$293$	−18.8463	−1.10101	−0.550507	+	0.834831i	$0.685565\pi$
$294$	−1.11839	−0.0652260
$295$	35.7829	2.08336
$296$	−7.79791	−0.453244
$297$	16.5599	0.960901
$298$	−11.6457	−0.674619
$299$	2.20546	0.127545
$300$	−8.36347	−0.482865
$301$	2.28328	0.131606
$302$	22.1165	1.27266
$303$	−0.639136	−0.0367174
$304$	1.01005	0.0579302
$305$	12.7839	0.732004
$306$	−17.0549	−0.974963
$307$	0.510129	0.0291146	0.0145573	−	0.999894i	$-0.495366\pi$
$307$	0.510129	0.0291146	0.0145573	+	0.999894i	$0.495366\pi$
$308$	9.86509	0.562116
$309$	−1.42137	−0.0808590
$310$	22.1175	1.25619
$311$	−14.9458	−0.847498	−0.423749	−	0.905780i	$-0.639286\pi$
$311$	−14.9458	−0.847498	−0.423749	+	0.905780i	$0.639286\pi$
$312$	−0.619932	−0.0350967
$313$	7.64337	0.432029	0.216014	−	0.976390i	$-0.430694\pi$
$313$	7.64337	0.432029	0.216014	+	0.976390i	$0.430694\pi$
$314$	12.3994	0.699739
$315$	23.7703	1.33930
$316$	15.1609	0.852867
$317$	29.8745	1.67792	0.838959	−	0.544194i	$-0.183164\pi$
$317$	29.8745	1.67792	0.838959	+	0.544194i	$0.183164\pi$
$318$	8.77329	0.491982
$319$	2.12387	0.118914
$320$	−4.09209	−0.228755
$321$	−0.297858	−0.0166248
$322$	5.90278	0.328949
$323$	−6.90998	−0.384482
$324$	4.69364	0.260758
$325$	−10.2254	−0.567201
$326$	−2.20063	−0.121882
$327$	7.86970	0.435196
$328$	6.82665	0.376939
$329$	2.21031	0.121858
$330$	−12.3366	−0.679109
$331$	18.3774	1.01011	0.505055	−	0.863087i	$-0.331472\pi$
$331$	18.3774	1.01011	0.505055	+	0.863087i	$0.331472\pi$
$332$	−6.20844	−0.340732
$333$	−19.4398	−1.06529
$334$	−12.5024	−0.684103
$335$	8.70899	0.475823
$336$	−1.65921	−0.0905173
$337$	8.21174	0.447322	0.223661	−	0.974667i	$-0.428199\pi$
$337$	8.21174	0.447322	0.223661	+	0.974667i	$0.428199\pi$
$338$	12.2421	0.665880
$339$	−6.21808	−0.337720
$340$	27.9950	1.51824
$341$	22.8831	1.23919
$342$	2.51800	0.136158
$343$	−19.9704	−1.07830
$344$	−0.979903	−0.0528329
$345$	−7.38163	−0.397413
$346$	−13.1085	−0.704717
$347$	20.4850	1.09969	0.549847	−	0.835266i	$-0.314686\pi$
$347$	20.4850	1.09969	0.549847	+	0.835266i	$0.314686\pi$
$348$	−0.357214	−0.0191487
$349$	−32.6783	−1.74923	−0.874615	−	0.484819i	$-0.838886\pi$
$349$	−32.6783	−1.74923	−0.874615	+	0.484819i	$0.838886\pi$
$350$	−27.3676	−1.46286
$351$	−3.40525	−0.181759
$352$	−4.23375	−0.225660
$353$	14.5838	0.776219	0.388110	−	0.921613i	$-0.373128\pi$
$353$	14.5838	0.776219	0.388110	+	0.921613i	$0.373128\pi$
$354$	−6.22667	−0.330944
$355$	0.553258	0.0293639
$356$	3.24155	0.171802
$357$	11.3511	0.600762
$358$	7.80940	0.412740
$359$	−13.0576	−0.689156	−0.344578	−	0.938758i	$-0.611978\pi$
$359$	−13.0576	−0.689156	−0.344578	+	0.938758i	$0.611978\pi$
$360$	−10.2014	−0.537660
$361$	−17.9798	−0.946306
$362$	15.6233	0.821144
$363$	−4.93088	−0.258804
$364$	−2.02859	−0.106327
$365$	23.4024	1.22494
$366$	−2.22456	−0.116280
$367$	−2.70482	−0.141190	−0.0705952	−	0.997505i	$-0.522490\pi$
$367$	−2.70482	−0.141190	−0.0705952	+	0.997505i	$0.522490\pi$
$368$	−2.53327	−0.132056
$369$	17.0185	0.885947
$370$	31.9097	1.65891
$371$	28.7086	1.49048
$372$	−3.84872	−0.199547
$373$	−11.4842	−0.594630	−0.297315	−	0.954779i	$-0.596091\pi$
$373$	−11.4842	−0.594630	−0.297315	+	0.954779i	$0.596091\pi$
$374$	28.9642	1.49770
$375$	19.6547	1.01496
$376$	−0.948587	−0.0489196
$377$	−0.436738	−0.0224932
$378$	−9.11395	−0.468771
$379$	−4.40530	−0.226285	−0.113143	−	0.993579i	$-0.536092\pi$
$379$	−4.40530	−0.226285	−0.113143	+	0.993579i	$0.536092\pi$
$380$	−4.13320	−0.212029
$381$	1.99033	0.101968
$382$	25.5535	1.30743
$383$	−19.4014	−0.991366	−0.495683	−	0.868504i	$-0.665082\pi$
$383$	−19.4014	−0.991366	−0.495683	+	0.868504i	$0.665082\pi$
$384$	0.712075	0.0363379
$385$	−40.3688	−2.05739
$386$	14.3261	0.729180
$387$	−2.44285	−0.124177
$388$	18.9534	0.962213
$389$	−21.2228	−1.07604	−0.538020	−	0.842932i	$-0.680828\pi$
$389$	−21.2228	−1.07604	−0.538020	+	0.842932i	$0.680828\pi$
$390$	2.53682	0.128457
$391$	17.3307	0.876452
$392$	1.57061	0.0793278
$393$	−5.18306	−0.261451
$394$	−8.07366	−0.406745
$395$	−62.0398	−3.12156
$396$	−10.5545	−0.530385
$397$	−8.02549	−0.402788	−0.201394	−	0.979510i	$-0.564547\pi$
$397$	−8.02549	−0.402788	−0.201394	+	0.979510i	$0.564547\pi$
$398$	−9.45893	−0.474134
$399$	−1.67588	−0.0838989
$400$	11.7452	0.587260
$401$	19.9104	0.994280	0.497140	−	0.867670i	$-0.334384\pi$
$401$	19.9104	0.994280	0.497140	+	0.867670i	$0.334384\pi$
$402$	−1.51547	−0.0755849
$403$	−4.70553	−0.234399
$404$	0.897568	0.0446557
$405$	−19.2068	−0.954394
$406$	−1.16890	−0.0580116
$407$	33.0144	1.63646
$408$	−4.87148	−0.241174
$409$	33.2530	1.64425	0.822127	−	0.569304i	$-0.192787\pi$
$409$	33.2530	1.64425	0.822127	+	0.569304i	$0.192787\pi$
$410$	−27.9353	−1.37962
$411$	−0.112561	−0.00555221
$412$	1.99610	0.0983406
$413$	−20.3754	−1.00261
$414$	−6.31531	−0.310380
$415$	25.4055	1.24711
$416$	0.870599	0.0426846
$417$	11.8875	0.582133
$418$	−4.27629	−0.209160
$419$	−33.4842	−1.63581	−0.817904	−	0.575355i	$-0.804864\pi$
$419$	−33.4842	−1.63581	−0.817904	+	0.575355i	$0.804864\pi$
$420$	6.78964	0.331300
$421$	26.8544	1.30880	0.654402	−	0.756147i	$-0.272920\pi$
$421$	26.8544	1.30880	0.654402	+	0.756147i	$0.272920\pi$
$422$	13.9975	0.681386
$423$	−2.36478	−0.114979
$424$	−12.3207	−0.598348
$425$	−80.3519	−3.89764
$426$	−0.0962739	−0.00466448
$427$	−7.27937	−0.352273
$428$	0.418296	0.0202191
$429$	2.62464	0.126719
$430$	4.00985	0.193372
$431$	19.1591	0.922863	0.461431	−	0.887176i	$-0.347336\pi$
$431$	19.1591	0.922863	0.461431	+	0.887176i	$0.347336\pi$
$432$	3.91139	0.188187
$433$	−36.0575	−1.73281	−0.866407	−	0.499338i	$-0.833577\pi$
$433$	−36.0575	−1.73281	−0.866407	+	0.499338i	$0.833577\pi$
$434$	−12.5941	−0.604534
$435$	1.46175	0.0700856
$436$	−11.0518	−0.529285
$437$	−2.55872	−0.122400
$438$	−4.07232	−0.194583
$439$	−12.0904	−0.577042	−0.288521	−	0.957474i	$-0.593164\pi$
$439$	−12.0904	−0.577042	−0.288521	+	0.957474i	$0.593164\pi$
$440$	17.3249	0.825932
$441$	3.91545	0.186450
$442$	−5.95599	−0.283297
$443$	−10.2782	−0.488332	−0.244166	−	0.969733i	$-0.578514\pi$
$443$	−10.2782	−0.488332	−0.244166	+	0.969733i	$0.578514\pi$
$444$	−5.55269	−0.263519
$445$	−13.2647	−0.628807
$446$	7.35326	0.348187
$447$	−8.29263	−0.392228
$448$	2.33011	0.110087
$449$	3.17411	0.149795	0.0748977	−	0.997191i	$-0.476137\pi$
$449$	3.17411	0.149795	0.0748977	+	0.997191i	$0.476137\pi$
$450$	29.2802	1.38028
$451$	−28.9024	−1.36096
$452$	8.73234	0.410735
$453$	15.7486	0.739934
$454$	0.904122	0.0424325
$455$	8.30117	0.389165
$456$	0.719229	0.0336810
$457$	28.7951	1.34698	0.673489	−	0.739197i	$-0.264795\pi$
$457$	28.7951	1.34698	0.673489	+	0.739197i	$0.264795\pi$
$458$	10.6473	0.497515
$459$	−26.7588	−1.24899
$460$	10.3664	0.483334
$461$	−35.9244	−1.67317	−0.836583	−	0.547840i	$-0.815450\pi$
$461$	−35.9244	−1.67317	−0.836583	+	0.547840i	$0.815450\pi$
$462$	7.02468	0.326818
$463$	−0.718497	−0.0333914	−0.0166957	−	0.999861i	$-0.505315\pi$
$463$	−0.718497	−0.0333914	−0.0166957	+	0.999861i	$0.505315\pi$
$464$	0.501652	0.0232886
$465$	15.7493	0.730356
$466$	20.9772	0.971748
$467$	1.47721	0.0683572	0.0341786	−	0.999416i	$-0.489119\pi$
$467$	1.47721	0.0683572	0.0341786	+	0.999416i	$0.489119\pi$
$468$	2.17036	0.100325
$469$	−4.95904	−0.228987
$470$	3.88170	0.179050
$471$	8.82930	0.406833
$472$	8.74441	0.402494
$473$	4.14867	0.190756
$474$	10.7957	0.495863
$475$	11.8632	0.544321
$476$	−15.9408	−0.730647
$477$	−30.7150	−1.40634
$478$	−12.1770	−0.556962
$479$	28.7909	1.31549	0.657745	−	0.753240i	$-0.271510\pi$
$479$	28.7909	1.31549	0.657745	+	0.753240i	$0.271510\pi$
$480$	−2.91388	−0.133000
$481$	−6.78885	−0.309545
$482$	0.973327	0.0443338
$483$	4.20322	0.191253
$484$	6.92467	0.314758
$485$	−77.5590	−3.52177
$486$	15.0764	0.683879
$487$	−35.3461	−1.60169	−0.800843	−	0.598875i	$-0.795615\pi$
$487$	−35.3461	−1.60169	−0.800843	+	0.598875i	$0.795615\pi$
$488$	3.12405	0.141419
$489$	−1.56701	−0.0708628
$490$	−6.42708	−0.290346
$491$	−1.60442	−0.0724064	−0.0362032	−	0.999344i	$-0.511526\pi$
$491$	−1.60442	−0.0724064	−0.0362032	+	0.999344i	$0.511526\pi$
$492$	4.86109	0.219155
$493$	−3.43193	−0.154566
$494$	0.879346	0.0395637
$495$	43.1901	1.94125
$496$	5.40493	0.242689
$497$	−0.315034	−0.0141312
$498$	−4.42087	−0.198104
$499$	−1.55989	−0.0698301	−0.0349151	−	0.999390i	$-0.511116\pi$
$499$	−1.55989	−0.0698301	−0.0349151	+	0.999390i	$0.511116\pi$
$500$	−27.6020	−1.23440
$501$	−8.90267	−0.397742
$502$	22.6555	1.01116
$503$	−8.95983	−0.399499	−0.199749	−	0.979847i	$-0.564013\pi$
$503$	−8.95983	−0.399499	−0.199749	+	0.979847i	$0.564013\pi$
$504$	5.80883	0.258746
$505$	−3.67293	−0.163443
$506$	10.7252	0.476795
$507$	8.71726	0.387147
$508$	−2.79511	−0.124013
$509$	−9.01585	−0.399621	−0.199810	−	0.979835i	$-0.564033\pi$
$509$	−9.01585	−0.399621	−0.199810	+	0.979835i	$0.564033\pi$
$510$	19.9345	0.882716
$511$	−13.3257	−0.589496
$512$	−1.00000	−0.0441942
$513$	3.95069	0.174427
$514$	−1.66655	−0.0735086
$515$	−8.16821	−0.359934
$516$	−0.697765	−0.0307174
$517$	4.01608	0.176627
$518$	−18.1699	−0.798341
$519$	−9.33423	−0.409727
$520$	−3.56257	−0.156229
$521$	−29.7055	−1.30142	−0.650710	−	0.759326i	$-0.725529\pi$
$521$	−29.7055	−1.30142	−0.650710	+	0.759326i	$0.725529\pi$
$522$	1.25059	0.0547370
$523$	25.0384	1.09485	0.547426	−	0.836854i	$-0.315608\pi$
$523$	25.0384	1.09485	0.547426	+	0.836854i	$0.315608\pi$
$524$	7.27881	0.317976
$525$	−19.4878	−0.850515
$526$	21.7022	0.946259
$527$	−36.9765	−1.61072
$528$	−3.01475	−0.131200
$529$	−16.5826	−0.720981
$530$	50.4176	2.19000
$531$	21.7994	0.946012
$532$	2.35352	0.102038
$533$	5.94328	0.257432
$534$	2.30822	0.0998866
$535$	−1.71170	−0.0740034
$536$	2.12825	0.0919263
$537$	5.56088	0.239970
$538$	21.5484	0.929018
$539$	−6.64958	−0.286418
$540$	−16.0058	−0.688779
$541$	−28.7667	−1.23678	−0.618388	−	0.785873i	$-0.712214\pi$
$541$	−28.7667	−1.23678	−0.618388	+	0.785873i	$0.712214\pi$
$542$	−4.49788	−0.193200
$543$	11.1250	0.477419
$544$	6.84125	0.293316
$545$	45.2249	1.93722
$546$	−1.44451	−0.0618192
$547$	27.9399	1.19462	0.597312	−	0.802009i	$-0.296235\pi$
$547$	27.9399	1.19462	0.597312	+	0.802009i	$0.296235\pi$
$548$	0.158074	0.00675259
$549$	7.78810	0.332388
$550$	−49.7263	−2.12034
$551$	0.506692	0.0215858
$552$	−1.80388	−0.0767781
$553$	35.3265	1.50223
$554$	12.9141	0.548669
$555$	22.7221	0.964501
$556$	−16.6942	−0.707990
$557$	2.60449	0.110356	0.0551778	−	0.998477i	$-0.482427\pi$
$557$	2.60449	0.110356	0.0551778	+	0.998477i	$0.482427\pi$
$558$	13.4742	0.570409
$559$	−0.853103	−0.0360824
$560$	−9.53500	−0.402927
$561$	20.6247	0.870773
$562$	3.82996	0.161557
$563$	6.06500	0.255609	0.127805	−	0.991799i	$-0.459207\pi$
$563$	6.06500	0.255609	0.127805	+	0.991799i	$0.459207\pi$
$564$	−0.675465	−0.0284422
$565$	−35.7335	−1.50332
$566$	11.6200	0.488423
$567$	10.9367	0.459297
$568$	0.135202	0.00567294
$569$	25.3277	1.06179	0.530896	−	0.847437i	$-0.321855\pi$
$569$	25.3277	1.06179	0.530896	+	0.847437i	$0.321855\pi$
$570$	−2.94315	−0.123275
$571$	46.1410	1.93094	0.965471	−	0.260511i	$-0.0838911\pi$
$571$	46.1410	1.93094	0.965471	+	0.260511i	$0.0838911\pi$
$572$	−3.68590	−0.154115
$573$	18.1960	0.760148
$574$	15.9068	0.663937
$575$	−29.7537	−1.24082
$576$	−2.49295	−0.103873
$577$	31.7310	1.32098	0.660489	−	0.750836i	$-0.270349\pi$
$577$	31.7310	1.32098	0.660489	+	0.750836i	$0.270349\pi$
$578$	−29.8027	−1.23963
$579$	10.2013	0.423950
$580$	−2.05281	−0.0852381
$581$	−14.4663	−0.600164
$582$	13.4962	0.559437
$583$	52.1630	2.16037
$584$	5.71895	0.236652
$585$	−8.88131	−0.367197
$586$	18.8463	0.778534
$587$	−7.93999	−0.327718	−0.163859	−	0.986484i	$-0.552394\pi$
$587$	−7.93999	−0.327718	−0.163859	+	0.986484i	$0.552394\pi$
$588$	1.11839	0.0461217
$589$	5.45923	0.224944
$590$	−35.7829	−1.47316
$591$	−5.74905	−0.236484
$592$	7.79791	0.320492
$593$	16.7180	0.686524	0.343262	−	0.939240i	$-0.388468\pi$
$593$	16.7180	0.686524	0.343262	+	0.939240i	$0.388468\pi$
$594$	−16.5599	−0.679460
$595$	65.2313	2.67422
$596$	11.6457	0.477028
$597$	−6.73547	−0.275664
$598$	−2.20546	−0.0901880
$599$	−24.2998	−0.992862	−0.496431	−	0.868076i	$-0.665356\pi$
$599$	−24.2998	−0.992862	−0.496431	+	0.868076i	$0.665356\pi$
$600$	8.36347	0.341437
$601$	20.9753	0.855602	0.427801	−	0.903873i	$-0.359288\pi$
$601$	20.9753	0.855602	0.427801	+	0.903873i	$0.359288\pi$
$602$	−2.28328	−0.0930595
$603$	5.30561	0.216061
$604$	−22.1165	−0.899907
$605$	−28.3364	−1.15204
$606$	0.639136	0.0259631
$607$	19.3213	0.784229	0.392115	−	0.919916i	$-0.371744\pi$
$607$	19.3213	0.784229	0.392115	+	0.919916i	$0.371744\pi$
$608$	−1.01005	−0.0409628
$609$	−0.832346	−0.0337284
$610$	−12.7839	−0.517605
$611$	−0.825839	−0.0334099
$612$	17.0549	0.689403
$613$	−17.4799	−0.706007	−0.353003	−	0.935622i	$-0.614840\pi$
$613$	−17.4799	−0.706007	−0.353003	+	0.935622i	$0.614840\pi$
$614$	−0.510129	−0.0205871
$615$	−19.8920	−0.802123
$616$	−9.86509	−0.397476
$617$	−9.31507	−0.375011	−0.187505	−	0.982264i	$-0.560040\pi$
$617$	−9.31507	−0.375011	−0.187505	+	0.982264i	$0.560040\pi$
$618$	1.42137	0.0571759
$619$	29.7035	1.19388	0.596942	−	0.802284i	$-0.296382\pi$
$619$	29.7035	1.19388	0.596942	+	0.802284i	$0.296382\pi$
$620$	−22.1175	−0.888259
$621$	−9.90860	−0.397618
$622$	14.9458	0.599272
$623$	7.55314	0.302610
$624$	0.619932	0.0248171
$625$	54.2238	2.16895
$626$	−7.64337	−0.305490
$627$	−3.04504	−0.121607
$628$	−12.3994	−0.494790
$629$	−53.3474	−2.12710
$630$	−23.7703	−0.947030
$631$	38.6855	1.54004	0.770022	−	0.638017i	$-0.220245\pi$
$631$	38.6855	1.54004	0.770022	+	0.638017i	$0.220245\pi$
$632$	−15.1609	−0.603068
$633$	9.96724	0.396162
$634$	−29.8745	−1.18647
$635$	11.4378	0.453897
$636$	−8.77329	−0.347884
$637$	1.36737	0.0541773
$638$	−2.12387	−0.0840849
$639$	0.337051	0.0133335
$640$	4.09209	0.161754
$641$	−32.8284	−1.29665	−0.648323	−	0.761366i	$-0.724529\pi$
$641$	−32.8284	−1.29665	−0.648323	+	0.761366i	$0.724529\pi$
$642$	0.297858	0.0117555
$643$	3.14040	0.123845	0.0619227	−	0.998081i	$-0.480277\pi$
$643$	3.14040	0.123845	0.0619227	+	0.998081i	$0.480277\pi$
$644$	−5.90278	−0.232602
$645$	2.85532	0.112428
$646$	6.90998	0.271870
$647$	−30.3503	−1.19319	−0.596597	−	0.802541i	$-0.703481\pi$
$647$	−30.3503	−1.19319	−0.596597	+	0.802541i	$0.703481\pi$
$648$	−4.69364	−0.184384
$649$	−37.0217	−1.45323
$650$	10.2254	0.401072
$651$	−8.96791	−0.351480
$652$	2.20063	0.0861833
$653$	−19.0354	−0.744912	−0.372456	−	0.928050i	$-0.621484\pi$
$653$	−19.0354	−0.744912	−0.372456	+	0.928050i	$0.621484\pi$
$654$	−7.86970	−0.307730
$655$	−29.7856	−1.16382
$656$	−6.82665	−0.266536
$657$	14.2570	0.556220
$658$	−2.21031	−0.0861667
$659$	12.5844	0.490218	0.245109	−	0.969495i	$-0.421176\pi$
$659$	12.5844	0.490218	0.245109	+	0.969495i	$0.421176\pi$
$660$	12.3366	0.480203
$661$	−15.8137	−0.615081	−0.307541	−	0.951535i	$-0.599506\pi$
$661$	−15.8137	−0.615081	−0.307541	+	0.951535i	$0.599506\pi$
$662$	−18.3774	−0.714256
$663$	−4.24111	−0.164711
$664$	6.20844	0.240934
$665$	−9.63080	−0.373466
$666$	19.4398	0.753276
$667$	−1.27082	−0.0492063
$668$	12.5024	0.483734
$669$	5.23607	0.202438
$670$	−8.70899	−0.336457
$671$	−13.2265	−0.510602
$672$	1.65921	0.0640054
$673$	50.3738	1.94177	0.970883	−	0.239553i	$-0.0770010\pi$
$673$	50.3738	1.94177	0.970883	+	0.239553i	$0.0770010\pi$
$674$	−8.21174	−0.316304
$675$	45.9401	1.76824
$676$	−12.2421	−0.470848
$677$	20.9677	0.805855	0.402927	−	0.915232i	$-0.367993\pi$
$677$	20.9677	0.805855	0.402927	+	0.915232i	$0.367993\pi$
$678$	6.21808	0.238804
$679$	44.1634	1.69484
$680$	−27.9950	−1.07356
$681$	0.643803	0.0246706
$682$	−22.8831	−0.876241
$683$	−35.5051	−1.35857	−0.679283	−	0.733876i	$-0.737709\pi$
$683$	−35.5051	−1.35857	−0.679283	+	0.733876i	$0.737709\pi$
$684$	−2.51800	−0.0962780
$685$	−0.646854	−0.0247150
$686$	19.9704	0.762474
$687$	7.58166	0.289258
$688$	0.979903	0.0373585
$689$	−10.7264	−0.408644
$690$	7.38163	0.281014
$691$	16.6656	0.633989	0.316995	−	0.948427i	$-0.397326\pi$
$691$	16.6656	0.633989	0.316995	+	0.948427i	$0.397326\pi$
$692$	13.1085	0.498310
$693$	−24.5932	−0.934217
$694$	−20.4850	−0.777601
$695$	68.3140	2.59130
$696$	0.357214	0.0135402
$697$	46.7028	1.76899
$698$	32.6783	1.23689
$699$	14.9373	0.564981
$700$	27.3676	1.03440
$701$	16.9774	0.641226	0.320613	−	0.947210i	$-0.396111\pi$
$701$	16.9774	0.641226	0.320613	+	0.947210i	$0.396111\pi$
$702$	3.40525	0.128523
$703$	7.87625	0.297058
$704$	4.23375	0.159566
$705$	2.76406	0.104101
$706$	−14.5838	−0.548870
$707$	2.09143	0.0786563
$708$	6.22667	0.234013
$709$	−35.1698	−1.32083	−0.660415	−	0.750901i	$-0.729619\pi$
$709$	−35.1698	−1.32083	−0.660415	+	0.750901i	$0.729619\pi$
$710$	−0.553258	−0.0207634
$711$	−37.7953	−1.41744
$712$	−3.24155	−0.121482
$713$	−13.6921	−0.512775
$714$	−11.3511	−0.424803
$715$	15.0830	0.564074
$716$	−7.80940	−0.291851
$717$	−8.67091	−0.323821
$718$	13.0576	0.487307
$719$	−22.2923	−0.831362	−0.415681	−	0.909510i	$-0.636457\pi$
$719$	−22.2923	−0.831362	−0.415681	+	0.909510i	$0.636457\pi$
$720$	10.2014	0.380183
$721$	4.65112	0.173217
$722$	17.9798	0.669139
$723$	0.693082	0.0257760
$724$	−15.6233	−0.580636
$725$	5.89201	0.218824
$726$	4.93088	0.183002
$727$	−27.3474	−1.01426	−0.507129	−	0.861870i	$-0.669293\pi$
$727$	−27.3474	−1.01426	−0.507129	+	0.861870i	$0.669293\pi$
$728$	2.02859	0.0751845
$729$	−3.34540	−0.123904
$730$	−23.4024	−0.866163
$731$	−6.70376	−0.247948
$732$	2.22456	0.0822221
$733$	20.8307	0.769398	0.384699	−	0.923042i	$-0.374305\pi$
$733$	20.8307	0.769398	0.384699	+	0.923042i	$0.374305\pi$
$734$	2.70482	0.0998368
$735$	−4.57656	−0.168809
$736$	2.53327	0.0933775
$737$	−9.01048	−0.331905
$738$	−17.0185	−0.626459
$739$	−44.5756	−1.63974	−0.819870	−	0.572550i	$-0.805954\pi$
$739$	−44.5756	−1.63974	−0.819870	+	0.572550i	$0.805954\pi$
$740$	−31.9097	−1.17303
$741$	0.626160	0.0230026
$742$	−28.7086	−1.05393
$743$	−25.3011	−0.928208	−0.464104	−	0.885781i	$-0.653624\pi$
$743$	−25.3011	−0.928208	−0.464104	+	0.885781i	$0.653624\pi$
$744$	3.84872	0.141101
$745$	−47.6554	−1.74596
$746$	11.4842	0.420467
$747$	15.4773	0.566286
$748$	−28.9642	−1.05903
$749$	0.974673	0.0356138
$750$	−19.6547	−0.717688
$751$	34.0226	1.24150	0.620751	−	0.784008i	$-0.286828\pi$
$751$	34.0226	1.24150	0.620751	+	0.784008i	$0.286828\pi$
$752$	0.948587	0.0345914
$753$	16.1324	0.587897
$754$	0.436738	0.0159051
$755$	90.5027	3.29373
$756$	9.11395	0.331471
$757$	−30.7475	−1.11754	−0.558768	−	0.829324i	$-0.688726\pi$
$757$	−30.7475	−1.11754	−0.558768	+	0.829324i	$0.688726\pi$
$758$	4.40530	0.160008
$759$	7.63717	0.277212
$760$	4.13320	0.149927
$761$	−1.63233	−0.0591720	−0.0295860	−	0.999562i	$-0.509419\pi$
$761$	−1.63233	−0.0591720	−0.0295860	+	0.999562i	$0.509419\pi$
$762$	−1.99033	−0.0721019
$763$	−25.7518	−0.932279
$764$	−25.5535	−0.924492
$765$	−69.7901	−2.52327
$766$	19.4014	0.701002
$767$	7.61287	0.274885
$768$	−0.712075	−0.0256948
$769$	35.8161	1.29156	0.645781	−	0.763523i	$-0.276532\pi$
$769$	35.8161	1.29156	0.645781	+	0.763523i	$0.276532\pi$
$770$	40.3688	1.45479
$771$	−1.18671	−0.0427384
$772$	−14.3261	−0.515608
$773$	−38.5684	−1.38721	−0.693604	−	0.720357i	$-0.743978\pi$
$773$	−38.5684	−1.38721	−0.693604	+	0.720357i	$0.743978\pi$
$774$	2.44285	0.0878064
$775$	63.4820	2.28034
$776$	−18.9534	−0.680387
$777$	−12.9384	−0.464161
$778$	21.2228	0.760875
$779$	−6.89524	−0.247047
$780$	−2.53682	−0.0908327
$781$	−0.572411	−0.0204825
$782$	−17.3307	−0.619745
$783$	1.96216	0.0701218
$784$	−1.57061	−0.0560932
$785$	50.7395	1.81097
$786$	5.18306	0.184874
$787$	−5.94577	−0.211944	−0.105972	−	0.994369i	$-0.533795\pi$
$787$	−5.94577	−0.211944	−0.105972	+	0.994369i	$0.533795\pi$
$788$	8.07366	0.287612
$789$	15.4536	0.550161
$790$	62.0398	2.20728
$791$	20.3473	0.723465
$792$	10.5545	0.375039
$793$	2.71980	0.0965828
$794$	8.02549	0.284814
$795$	35.9011	1.27328
$796$	9.45893	0.335263
$797$	50.6289	1.79337	0.896684	−	0.442672i	$-0.145969\pi$
$797$	50.6289	1.79337	0.896684	+	0.442672i	$0.145969\pi$
$798$	1.67588	0.0593255
$799$	−6.48952	−0.229583
$800$	−11.7452	−0.415256
$801$	−8.08101	−0.285528
$802$	−19.9104	−0.703062
$803$	−24.2126	−0.854444
$804$	1.51547	0.0534466
$805$	24.1547	0.851342
$806$	4.70553	0.165745
$807$	15.3441	0.540137
$808$	−0.897568	−0.0315763
$809$	−19.7695	−0.695058	−0.347529	−	0.937669i	$-0.612979\pi$
$809$	−19.7695	−0.695058	−0.347529	+	0.937669i	$0.612979\pi$
$810$	19.2068	0.674859
$811$	45.8141	1.60875	0.804376	−	0.594120i	$-0.202500\pi$
$811$	45.8141	1.60875	0.804376	+	0.594120i	$0.202500\pi$
$812$	1.16890	0.0410204
$813$	−3.20283	−0.112328
$814$	−33.0144	−1.15715
$815$	−9.00518	−0.315438
$816$	4.87148	0.170536
$817$	0.989749	0.0346269
$818$	−33.2530	−1.16266
$819$	5.05717	0.176712
$820$	27.9353	0.975542
$821$	7.56824	0.264133	0.132067	−	0.991241i	$-0.457839\pi$
$821$	7.56824	0.264133	0.132067	+	0.991241i	$0.457839\pi$
$822$	0.112561	0.00392600
$823$	41.6560	1.45204	0.726018	−	0.687676i	$-0.241369\pi$
$823$	41.6560	1.45204	0.726018	+	0.687676i	$0.241369\pi$
$824$	−1.99610	−0.0695373
$825$	−35.4089	−1.23278
$826$	20.3754	0.708950
$827$	−54.2004	−1.88473	−0.942366	−	0.334582i	$-0.891405\pi$
$827$	−54.2004	−1.88473	−0.942366	+	0.334582i	$0.891405\pi$
$828$	6.31531	0.219472
$829$	−8.66757	−0.301037	−0.150519	−	0.988607i	$-0.548094\pi$
$829$	−8.66757	−0.301037	−0.150519	+	0.988607i	$0.548094\pi$
$830$	−25.4055	−0.881838
$831$	9.19583	0.319000
$832$	−0.870599	−0.0301826
$833$	10.7449	0.372290
$834$	−11.8875	−0.411630
$835$	−51.1611	−1.77050
$836$	4.27629	0.147899
$837$	21.1408	0.730733
$838$	33.4842	1.15669
$839$	43.6592	1.50728	0.753642	−	0.657285i	$-0.228295\pi$
$839$	43.6592	1.50728	0.753642	+	0.657285i	$0.228295\pi$
$840$	−6.78964	−0.234265
$841$	−28.7483	−0.991322
$842$	−26.8544	−0.925464
$843$	2.72722	0.0939303
$844$	−13.9975	−0.481812
$845$	50.0956	1.72334
$846$	2.36478	0.0813027
$847$	16.1352	0.554412
$848$	12.3207	0.423096
$849$	8.27428	0.283973
$850$	80.3519	2.75605
$851$	−19.7542	−0.677165
$852$	0.0962739	0.00329829
$853$	−45.6881	−1.56433	−0.782166	−	0.623070i	$-0.785885\pi$
$853$	−45.6881	−1.56433	−0.782166	+	0.623070i	$0.785885\pi$
$854$	7.27937	0.249095
$855$	10.3039	0.352385
$856$	−0.418296	−0.0142971
$857$	12.5219	0.427740	0.213870	−	0.976862i	$-0.431393\pi$
$857$	12.5219	0.427740	0.213870	+	0.976862i	$0.431393\pi$
$858$	−2.62464	−0.0896037
$859$	−49.8697	−1.70153	−0.850766	−	0.525544i	$-0.823862\pi$
$859$	−49.8697	−1.70153	−0.850766	+	0.525544i	$0.823862\pi$
$860$	−4.00985	−0.136735
$861$	11.3268	0.386018
$862$	−19.1591	−0.652562
$863$	−18.7104	−0.636909	−0.318455	−	0.947938i	$-0.603164\pi$
$863$	−18.7104	−0.636909	−0.318455	+	0.947938i	$0.603164\pi$
$864$	−3.91139	−0.133068
$865$	−53.6411	−1.82385
$866$	36.0575	1.22529
$867$	−21.2217	−0.720728
$868$	12.5941	0.427470
$869$	64.1875	2.17741
$870$	−1.46175	−0.0495580
$871$	1.85285	0.0627815
$872$	11.0518	0.374261
$873$	−47.2499	−1.59917
$874$	2.55872	0.0865500
$875$	−64.3156	−2.17426
$876$	4.07232	0.137591
$877$	52.2040	1.76280	0.881402	−	0.472366i	$-0.156600\pi$
$877$	52.2040	1.76280	0.881402	+	0.472366i	$0.156600\pi$
$878$	12.0904	0.408031
$879$	13.4200	0.452645
$880$	−17.3249	−0.584022
$881$	−15.6956	−0.528799	−0.264400	−	0.964413i	$-0.585174\pi$
$881$	−15.6956	−0.528799	−0.264400	+	0.964413i	$0.585174\pi$
$882$	−3.91545	−0.131840
$883$	−15.0775	−0.507399	−0.253700	−	0.967283i	$-0.581647\pi$
$883$	−15.0775	−0.507399	−0.253700	+	0.967283i	$0.581647\pi$
$884$	5.95599	0.200321
$885$	−25.4801	−0.856504
$886$	10.2782	0.345303
$887$	43.1336	1.44829	0.724143	−	0.689650i	$-0.242236\pi$
$887$	43.1336	1.44829	0.724143	+	0.689650i	$0.242236\pi$
$888$	5.55269	0.186336
$889$	−6.51290	−0.218436
$890$	13.2647	0.444634
$891$	19.8717	0.665728
$892$	−7.35326	−0.246205
$893$	0.958117	0.0320622
$894$	8.29263	0.277347
$895$	31.9568	1.06820
$896$	−2.33011	−0.0778433
$897$	−1.57045	−0.0524359
$898$	−3.17411	−0.105921
$899$	2.71140	0.0904301
$900$	−29.2802	−0.976007
$901$	−84.2893	−2.80808
$902$	28.9024	0.962343
$903$	−1.62587	−0.0541054
$904$	−8.73234	−0.290433
$905$	63.9321	2.12517
$906$	−15.7486	−0.523212
$907$	29.9261	0.993678	0.496839	−	0.867843i	$-0.334494\pi$
$907$	29.9261	0.993678	0.496839	+	0.867843i	$0.334494\pi$
$908$	−0.904122	−0.0300043
$909$	−2.23759	−0.0742163
$910$	−8.30117	−0.275181
$911$	−16.1721	−0.535806	−0.267903	−	0.963446i	$-0.586331\pi$
$911$	−16.1721	−0.535806	−0.267903	+	0.963446i	$0.586331\pi$
$912$	−0.719229	−0.0238161
$913$	−26.2850	−0.869907
$914$	−28.7951	−0.952457
$915$	−9.10310	−0.300939
$916$	−10.6473	−0.351796
$917$	16.9604	0.560082
$918$	26.7588	0.883172
$919$	5.63291	0.185812	0.0929062	−	0.995675i	$-0.470384\pi$
$919$	5.63291	0.185812	0.0929062	+	0.995675i	$0.470384\pi$
$920$	−10.3664	−0.341769
$921$	−0.363250	−0.0119695
$922$	35.9244	1.18311
$923$	0.117707	0.00387436
$924$	−7.02468	−0.231095
$925$	91.5880	3.01140
$926$	0.718497	0.0236113
$927$	−4.97617	−0.163439
$928$	−0.501652	−0.0164675
$929$	−3.76229	−0.123437	−0.0617184	−	0.998094i	$-0.519658\pi$
$929$	−3.76229	−0.123437	−0.0617184	+	0.998094i	$0.519658\pi$
$930$	−15.7493	−0.516440
$931$	−1.58639	−0.0519918
$932$	−20.9772	−0.687130
$933$	10.6425	0.348421
$934$	−1.47721	−0.0483358
$935$	118.524	3.87615
$936$	−2.17036	−0.0709404
$937$	15.2741	0.498983	0.249491	−	0.968377i	$-0.419737\pi$
$937$	15.2741	0.498983	0.249491	+	0.968377i	$0.419737\pi$
$938$	4.95904	0.161918
$939$	−5.44265	−0.177614
$940$	−3.88170	−0.126607
$941$	6.98732	0.227780	0.113890	−	0.993493i	$-0.463669\pi$
$941$	6.98732	0.227780	0.113890	+	0.993493i	$0.463669\pi$
$942$	−8.82930	−0.287674
$943$	17.2937	0.563161
$944$	−8.74441	−0.284606
$945$	−37.2951	−1.21321
$946$	−4.14867	−0.134885
$947$	−45.3630	−1.47410	−0.737049	−	0.675839i	$-0.763781\pi$
$947$	−45.3630	−1.47410	−0.737049	+	0.675839i	$0.763781\pi$
$948$	−10.7957	−0.350628
$949$	4.97891	0.161622
$950$	−11.8632	−0.384893
$951$	−21.2729	−0.689820
$952$	15.9408	0.516645
$953$	45.1998	1.46417	0.732083	−	0.681215i	$-0.238548\pi$
$953$	45.1998	1.46417	0.732083	+	0.681215i	$0.238548\pi$
$954$	30.7150	0.994434
$955$	104.567	3.38371
$956$	12.1770	0.393831
$957$	−1.51236	−0.0488875
$958$	−28.7909	−0.930192
$959$	0.368329	0.0118940
$960$	2.91388	0.0940449
$961$	−1.78671	−0.0576358
$962$	6.78885	0.218881
$963$	−1.04279	−0.0336034
$964$	−0.973327	−0.0313488
$965$	58.6237	1.88716
$966$	−4.20322	−0.135236
$967$	−28.0220	−0.901126	−0.450563	−	0.892745i	$-0.648777\pi$
$967$	−28.0220	−0.901126	−0.450563	+	0.892745i	$0.648777\pi$
$968$	−6.92467	−0.222567
$969$	4.92042	0.158067
$970$	77.5590	2.49027
$971$	36.0791	1.15783	0.578917	−	0.815386i	$-0.303475\pi$
$971$	36.0791	1.15783	0.578917	+	0.815386i	$0.303475\pi$
$972$	−15.0764	−0.483576
$973$	−38.8991	−1.24705
$974$	35.3461	1.13256
$975$	7.28123	0.233186
$976$	−3.12405	−0.0999985
$977$	56.6369	1.81197	0.905987	−	0.423306i	$-0.139130\pi$
$977$	56.6369	1.81197	0.905987	+	0.423306i	$0.139130\pi$
$978$	1.56701	0.0501076
$979$	13.7239	0.438618
$980$	6.42708	0.205306
$981$	27.5515	0.879653
$982$	1.60442	0.0511990
$983$	28.1008	0.896275	0.448137	−	0.893965i	$-0.352088\pi$
$983$	28.1008	0.896275	0.448137	+	0.893965i	$0.352088\pi$
$984$	−4.86109	−0.154966
$985$	−33.0382	−1.05268
$986$	3.43193	0.109295
$987$	−1.57390	−0.0500979
$988$	−0.879346	−0.0279757
$989$	−2.48236	−0.0789344
$990$	−43.1901	−1.37267
$991$	−37.2309	−1.18268	−0.591339	−	0.806423i	$-0.701401\pi$
$991$	−37.2309	−1.18268	−0.591339	+	0.806423i	$0.701401\pi$
$992$	−5.40493	−0.171607
$993$	−13.0861	−0.415273
$994$	0.315034	0.00999229
$995$	−38.7068	−1.22709
$996$	4.42087	0.140081
$997$	−10.8662	−0.344137	−0.172069	−	0.985085i	$-0.555045\pi$
$997$	−10.8662	−0.344137	−0.172069	+	0.985085i	$0.555045\pi$
$998$	1.55989	0.0493774
$999$	30.5007	0.964998

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.18	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.18	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.712075 q^{3} +1.00000 q^{4} -4.09209 q^{5} +0.712075 q^{6} +2.33011 q^{7} -1.00000 q^{8} -2.49295 q^{9} +4.09209 q^{10} +4.23375 q^{11} -0.712075 q^{12} -0.870599 q^{13} -2.33011 q^{14} +2.91388 q^{15} +1.00000 q^{16} -6.84125 q^{17} +2.49295 q^{18} +1.01005 q^{19} -4.09209 q^{20} -1.65921 q^{21} -4.23375 q^{22} -2.53327 q^{23} +0.712075 q^{24} +11.7452 q^{25} +0.870599 q^{26} +3.91139 q^{27} +2.33011 q^{28} +0.501652 q^{29} -2.91388 q^{30} +5.40493 q^{31} -1.00000 q^{32} -3.01475 q^{33} +6.84125 q^{34} -9.53500 q^{35} -2.49295 q^{36} +7.79791 q^{37} -1.01005 q^{38} +0.619932 q^{39} +4.09209 q^{40} -6.82665 q^{41} +1.65921 q^{42} +0.979903 q^{43} +4.23375 q^{44} +10.2014 q^{45} +2.53327 q^{46} +0.948587 q^{47} -0.712075 q^{48} -1.57061 q^{49} -11.7452 q^{50} +4.87148 q^{51} -0.870599 q^{52} +12.3207 q^{53} -3.91139 q^{54} -17.3249 q^{55} -2.33011 q^{56} -0.719229 q^{57} -0.501652 q^{58} -8.74441 q^{59} +2.91388 q^{60} -3.12405 q^{61} -5.40493 q^{62} -5.80883 q^{63} +1.00000 q^{64} +3.56257 q^{65} +3.01475 q^{66} -2.12825 q^{67} -6.84125 q^{68} +1.80388 q^{69} +9.53500 q^{70} -0.135202 q^{71} +2.49295 q^{72} -5.71895 q^{73} -7.79791 q^{74} -8.36347 q^{75} +1.01005 q^{76} +9.86509 q^{77} -0.619932 q^{78} +15.1609 q^{79} -4.09209 q^{80} +4.69364 q^{81} +6.82665 q^{82} -6.20844 q^{83} -1.65921 q^{84} +27.9950 q^{85} -0.979903 q^{86} -0.357214 q^{87} -4.23375 q^{88} +3.24155 q^{89} -10.2014 q^{90} -2.02859 q^{91} -2.53327 q^{92} -3.84872 q^{93} -0.948587 q^{94} -4.13320 q^{95} +0.712075 q^{96} +18.9534 q^{97} +1.57061 q^{98} -10.5545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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