LMFDB - Embedded newform 4006.2.a.h.1.12

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:	$42$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.69783 q^{3} +1.00000 q^{4} +2.46315 q^{5} +1.69783 q^{6} -3.98093 q^{7} -1.00000 q^{8} -0.117367 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.69783 q^{3} +1.00000 q^{4} +2.46315 q^{5} +1.69783 q^{6} -3.98093 q^{7} -1.00000 q^{8} -0.117367 q^{9} -2.46315 q^{10} -3.98953 q^{11} -1.69783 q^{12} +6.75369 q^{13} +3.98093 q^{14} -4.18202 q^{15} +1.00000 q^{16} +1.91590 q^{17} +0.117367 q^{18} +6.53145 q^{19} +2.46315 q^{20} +6.75895 q^{21} +3.98953 q^{22} +3.45914 q^{23} +1.69783 q^{24} +1.06711 q^{25} -6.75369 q^{26} +5.29276 q^{27} -3.98093 q^{28} -1.06413 q^{29} +4.18202 q^{30} -10.6557 q^{31} -1.00000 q^{32} +6.77355 q^{33} -1.91590 q^{34} -9.80563 q^{35} -0.117367 q^{36} +1.48999 q^{37} -6.53145 q^{38} -11.4666 q^{39} -2.46315 q^{40} -0.603470 q^{41} -6.75895 q^{42} -12.5763 q^{43} -3.98953 q^{44} -0.289092 q^{45} -3.45914 q^{46} +4.82901 q^{47} -1.69783 q^{48} +8.84780 q^{49} -1.06711 q^{50} -3.25288 q^{51} +6.75369 q^{52} -12.1441 q^{53} -5.29276 q^{54} -9.82681 q^{55} +3.98093 q^{56} -11.0893 q^{57} +1.06413 q^{58} -5.34100 q^{59} -4.18202 q^{60} +11.0084 q^{61} +10.6557 q^{62} +0.467228 q^{63} +1.00000 q^{64} +16.6353 q^{65} -6.77355 q^{66} +3.80142 q^{67} +1.91590 q^{68} -5.87304 q^{69} +9.80563 q^{70} +10.7649 q^{71} +0.117367 q^{72} -7.23149 q^{73} -1.48999 q^{74} -1.81177 q^{75} +6.53145 q^{76} +15.8820 q^{77} +11.4666 q^{78} -17.6866 q^{79} +2.46315 q^{80} -8.63413 q^{81} +0.603470 q^{82} +2.26007 q^{83} +6.75895 q^{84} +4.71915 q^{85} +12.5763 q^{86} +1.80671 q^{87} +3.98953 q^{88} +14.6525 q^{89} +0.289092 q^{90} -26.8859 q^{91} +3.45914 q^{92} +18.0915 q^{93} -4.82901 q^{94} +16.0879 q^{95} +1.69783 q^{96} -5.72593 q^{97} -8.84780 q^{98} +0.468238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) $ 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * 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
$3$	−1.69783	−0.980244	−0.490122	−	0.871654i	$-0.663048\pi$
$3$	−1.69783	−0.980244	−0.490122	+	0.871654i	$0.663048\pi$
$4$	1.00000	0.500000
$5$	2.46315	1.10155	0.550777	−	0.834652i	$-0.314331\pi$
$5$	2.46315	1.10155	0.550777	+	0.834652i	$0.314331\pi$
$6$	1.69783	0.693137
$7$	−3.98093	−1.50465	−0.752325	−	0.658792i	$-0.771068\pi$
$7$	−3.98093	−1.50465	−0.752325	+	0.658792i	$0.771068\pi$
$8$	−1.00000	−0.353553
$9$	−0.117367	−0.0391222
$10$	−2.46315	−0.778916
$11$	−3.98953	−1.20289	−0.601444	−	0.798915i	$-0.705408\pi$
$11$	−3.98953	−1.20289	−0.601444	+	0.798915i	$0.705408\pi$
$12$	−1.69783	−0.490122
$13$	6.75369	1.87314	0.936568	−	0.350486i	$-0.113984\pi$
$13$	6.75369	1.87314	0.936568	+	0.350486i	$0.113984\pi$
$14$	3.98093	1.06395
$15$	−4.18202	−1.07979
$16$	1.00000	0.250000
$17$	1.91590	0.464674	0.232337	−	0.972635i	$-0.425363\pi$
$17$	1.91590	0.464674	0.232337	+	0.972635i	$0.425363\pi$
$18$	0.117367	0.0276636
$19$	6.53145	1.49842	0.749208	−	0.662334i	$-0.230434\pi$
$19$	6.53145	1.49842	0.749208	+	0.662334i	$0.230434\pi$
$20$	2.46315	0.550777
$21$	6.75895	1.47492
$22$	3.98953	0.850571
$23$	3.45914	0.721281	0.360641	−	0.932705i	$-0.382558\pi$
$23$	3.45914	0.721281	0.360641	+	0.932705i	$0.382558\pi$
$24$	1.69783	0.346569
$25$	1.06711	0.213422
$26$	−6.75369	−1.32451
$27$	5.29276	1.01859
$28$	−3.98093	−0.752325
$29$	−1.06413	−0.197603	−0.0988017	−	0.995107i	$-0.531501\pi$
$29$	−1.06413	−0.197603	−0.0988017	+	0.995107i	$0.531501\pi$
$30$	4.18202	0.763528
$31$	−10.6557	−1.91381	−0.956907	−	0.290395i	$-0.906213\pi$
$31$	−10.6557	−1.91381	−0.956907	+	0.290395i	$0.906213\pi$
$32$	−1.00000	−0.176777
$33$	6.77355	1.17912
$34$	−1.91590	−0.328574
$35$	−9.80563	−1.65745
$36$	−0.117367	−0.0195611
$37$	1.48999	0.244953	0.122476	−	0.992471i	$-0.460916\pi$
$37$	1.48999	0.244953	0.122476	+	0.992471i	$0.460916\pi$
$38$	−6.53145	−1.05954
$39$	−11.4666	−1.83613
$40$	−2.46315	−0.389458
$41$	−0.603470	−0.0942461	−0.0471231	−	0.998889i	$-0.515005\pi$
$41$	−0.603470	−0.0942461	−0.0471231	+	0.998889i	$0.515005\pi$
$42$	−6.75895	−1.04293
$43$	−12.5763	−1.91787	−0.958933	−	0.283633i	$-0.908460\pi$
$43$	−12.5763	−1.91787	−0.958933	+	0.283633i	$0.908460\pi$
$44$	−3.98953	−0.601444
$45$	−0.289092	−0.0430952
$46$	−3.45914	−0.510023
$47$	4.82901	0.704383	0.352192	−	0.935928i	$-0.385437\pi$
$47$	4.82901	0.704383	0.352192	+	0.935928i	$0.385437\pi$
$48$	−1.69783	−0.245061
$49$	8.84780	1.26397
$50$	−1.06711	−0.150912
$51$	−3.25288	−0.455494
$52$	6.75369	0.936568
$53$	−12.1441	−1.66812	−0.834061	−	0.551673i	$-0.813990\pi$
$53$	−12.1441	−1.66812	−0.834061	+	0.551673i	$0.813990\pi$
$54$	−5.29276	−0.720254
$55$	−9.82681	−1.32505
$56$	3.98093	0.531974
$57$	−11.0893	−1.46881
$58$	1.06413	0.139727
$59$	−5.34100	−0.695339	−0.347669	−	0.937617i	$-0.613027\pi$
$59$	−5.34100	−0.695339	−0.347669	+	0.937617i	$0.613027\pi$
$60$	−4.18202	−0.539896
$61$	11.0084	1.40949	0.704743	−	0.709463i	$-0.251062\pi$
$61$	11.0084	1.40949	0.704743	+	0.709463i	$0.251062\pi$
$62$	10.6557	1.35327
$63$	0.467228	0.0588652
$64$	1.00000	0.125000
$65$	16.6353	2.06336
$66$	−6.77355	−0.833767
$67$	3.80142	0.464417	0.232209	−	0.972666i	$-0.425405\pi$
$67$	3.80142	0.464417	0.232209	+	0.972666i	$0.425405\pi$
$68$	1.91590	0.232337
$69$	−5.87304	−0.707031
$70$	9.80563	1.17200
$71$	10.7649	1.27755	0.638777	−	0.769392i	$-0.279441\pi$
$71$	10.7649	1.27755	0.638777	+	0.769392i	$0.279441\pi$
$72$	0.117367	0.0138318
$73$	−7.23149	−0.846382	−0.423191	−	0.906040i	$-0.639090\pi$
$73$	−7.23149	−0.846382	−0.423191	+	0.906040i	$0.639090\pi$
$74$	−1.48999	−0.173208
$75$	−1.81177	−0.209205
$76$	6.53145	0.749208
$77$	15.8820	1.80993
$78$	11.4666	1.29834
$79$	−17.6866	−1.98990	−0.994951	−	0.100364i	$-0.967999\pi$
$79$	−17.6866	−1.98990	−0.994951	+	0.100364i	$0.967999\pi$
$80$	2.46315	0.275389
$81$	−8.63413	−0.959347
$82$	0.603470	0.0666421
$83$	2.26007	0.248075	0.124037	−	0.992278i	$-0.460416\pi$
$83$	2.26007	0.248075	0.124037	+	0.992278i	$0.460416\pi$
$84$	6.75895	0.737462
$85$	4.71915	0.511864
$86$	12.5763	1.35614
$87$	1.80671	0.193700
$88$	3.98953	0.425285
$89$	14.6525	1.55316	0.776581	−	0.630018i	$-0.216952\pi$
$89$	14.6525	1.55316	0.776581	+	0.630018i	$0.216952\pi$
$90$	0.289092	0.0304729
$91$	−26.8859	−2.81841
$92$	3.45914	0.360641
$93$	18.0915	1.87600
$94$	−4.82901	−0.498074
$95$	16.0879	1.65059
$96$	1.69783	0.173284
$97$	−5.72593	−0.581380	−0.290690	−	0.956817i	$-0.593885\pi$
$97$	−5.72593	−0.581380	−0.290690	+	0.956817i	$0.593885\pi$
$98$	−8.84780	−0.893762
$99$	0.468238	0.0470596
$100$	1.06711	0.106711
$101$	−7.93699	−0.789760	−0.394880	−	0.918733i	$-0.629214\pi$
$101$	−7.93699	−0.789760	−0.394880	+	0.918733i	$0.629214\pi$
$102$	3.25288	0.322083
$103$	13.0916	1.28996	0.644978	−	0.764201i	$-0.276866\pi$
$103$	13.0916	1.28996	0.644978	+	0.764201i	$0.276866\pi$
$104$	−6.75369	−0.662253
$105$	16.6483	1.62471
$106$	12.1441	1.17954
$107$	5.21830	0.504472	0.252236	−	0.967666i	$-0.418834\pi$
$107$	5.21830	0.504472	0.252236	+	0.967666i	$0.418834\pi$
$108$	5.29276	0.509297
$109$	15.9785	1.53046	0.765231	−	0.643756i	$-0.222625\pi$
$109$	15.9785	1.53046	0.765231	+	0.643756i	$0.222625\pi$
$110$	9.82681	0.936950
$111$	−2.52975	−0.240113
$112$	−3.98093	−0.376162
$113$	11.7415	1.10455	0.552273	−	0.833663i	$-0.313761\pi$
$113$	11.7415	1.10455	0.552273	+	0.833663i	$0.313761\pi$
$114$	11.0893	1.03861
$115$	8.52039	0.794530
$116$	−1.06413	−0.0988017
$117$	−0.792657	−0.0732812
$118$	5.34100	0.491679
$119$	−7.62706	−0.699171
$120$	4.18202	0.381764
$121$	4.91635	0.446941
$122$	−11.0084	−0.996657
$123$	1.02459	0.0923842
$124$	−10.6557	−0.956907
$125$	−9.68730	−0.866459
$126$	−0.467228	−0.0416240
$127$	−6.48146	−0.575136	−0.287568	−	0.957760i	$-0.592847\pi$
$127$	−6.48146	−0.575136	−0.287568	+	0.957760i	$0.592847\pi$
$128$	−1.00000	−0.0883883
$129$	21.3524	1.87998
$130$	−16.6353	−1.45902
$131$	20.4335	1.78528	0.892640	−	0.450770i	$-0.148851\pi$
$131$	20.4335	1.78528	0.892640	+	0.450770i	$0.148851\pi$
$132$	6.77355	0.589562
$133$	−26.0012	−2.25459
$134$	−3.80142	−0.328393
$135$	13.0369	1.12204
$136$	−1.91590	−0.164287
$137$	−22.0274	−1.88193	−0.940963	−	0.338508i	$-0.890078\pi$
$137$	−22.0274	−1.88193	−0.940963	+	0.338508i	$0.890078\pi$
$138$	5.87304	0.499947
$139$	−0.965611	−0.0819020	−0.0409510	−	0.999161i	$-0.513039\pi$
$139$	−0.965611	−0.0819020	−0.0409510	+	0.999161i	$0.513039\pi$
$140$	−9.80563	−0.828727
$141$	−8.19884	−0.690467
$142$	−10.7649	−0.903367
$143$	−26.9440	−2.25317
$144$	−0.117367	−0.00978055
$145$	−2.62111	−0.217671
$146$	7.23149	0.598483
$147$	−15.0221	−1.23900
$148$	1.48999	0.122476
$149$	1.81437	0.148639	0.0743194	−	0.997234i	$-0.476322\pi$
$149$	1.81437	0.148639	0.0743194	+	0.997234i	$0.476322\pi$
$150$	1.81177	0.147930
$151$	9.97557	0.811800	0.405900	−	0.913918i	$-0.366958\pi$
$151$	9.97557	0.811800	0.405900	+	0.913918i	$0.366958\pi$
$152$	−6.53145	−0.529770
$153$	−0.224863	−0.0181791
$154$	−15.8820	−1.27981
$155$	−26.2465	−2.10817
$156$	−11.4666	−0.918065
$157$	−0.592157	−0.0472593	−0.0236297	−	0.999721i	$-0.507522\pi$
$157$	−0.592157	−0.0472593	−0.0236297	+	0.999721i	$0.507522\pi$
$158$	17.6866	1.40707
$159$	20.6186	1.63517
$160$	−2.46315	−0.194729
$161$	−13.7706	−1.08528
$162$	8.63413	0.678361
$163$	12.5394	0.982164	0.491082	−	0.871113i	$-0.336602\pi$
$163$	12.5394	0.982164	0.491082	+	0.871113i	$0.336602\pi$
$164$	−0.603470	−0.0471231
$165$	16.6843	1.29887
$166$	−2.26007	−0.175415
$167$	6.53570	0.505747	0.252874	−	0.967499i	$-0.418624\pi$
$167$	6.53570	0.505747	0.252874	+	0.967499i	$0.418624\pi$
$168$	−6.75895	−0.521464
$169$	32.6123	2.50864
$170$	−4.71915	−0.361942
$171$	−0.766574	−0.0586214
$172$	−12.5763	−0.958933
$173$	−4.43015	−0.336818	−0.168409	−	0.985717i	$-0.553863\pi$
$173$	−4.43015	−0.336818	−0.168409	+	0.985717i	$0.553863\pi$
$174$	−1.80671	−0.136966
$175$	−4.24808	−0.321125
$176$	−3.98953	−0.300722
$177$	9.06812	0.681601
$178$	−14.6525	−1.09825
$179$	−1.75763	−0.131372	−0.0656858	−	0.997840i	$-0.520924\pi$
$179$	−1.75763	−0.131372	−0.0656858	+	0.997840i	$0.520924\pi$
$180$	−0.289092	−0.0215476
$181$	19.6765	1.46255	0.731273	−	0.682085i	$-0.238927\pi$
$181$	19.6765	1.46255	0.731273	+	0.682085i	$0.238927\pi$
$182$	26.8859	1.99292
$183$	−18.6905	−1.38164
$184$	−3.45914	−0.255011
$185$	3.67006	0.269829
$186$	−18.0915	−1.32654
$187$	−7.64354	−0.558951
$188$	4.82901	0.352192
$189$	−21.0701	−1.53263
$190$	−16.0879	−1.16714
$191$	16.3247	1.18121	0.590606	−	0.806960i	$-0.298889\pi$
$191$	16.3247	1.18121	0.590606	+	0.806960i	$0.298889\pi$
$192$	−1.69783	−0.122530
$193$	7.13118	0.513313	0.256657	−	0.966503i	$-0.417379\pi$
$193$	7.13118	0.513313	0.256657	+	0.966503i	$0.417379\pi$
$194$	5.72593	0.411098
$195$	−28.2440	−2.02260
$196$	8.84780	0.631985
$197$	24.2658	1.72887	0.864433	−	0.502749i	$-0.167678\pi$
$197$	24.2658	1.72887	0.864433	+	0.502749i	$0.167678\pi$
$198$	−0.468238	−0.0332762
$199$	0.881972	0.0625213	0.0312607	−	0.999511i	$-0.490048\pi$
$199$	0.881972	0.0625213	0.0312607	+	0.999511i	$0.490048\pi$
$200$	−1.06711	−0.0754560
$201$	−6.45417	−0.455242
$202$	7.93699	0.558445
$203$	4.23621	0.297324
$204$	−3.25288	−0.227747
$205$	−1.48644	−0.103817
$206$	−13.0916	−0.912137
$207$	−0.405988	−0.0282181
$208$	6.75369	0.468284
$209$	−26.0574	−1.80243
$210$	−16.6483	−1.14884
$211$	5.95141	0.409712	0.204856	−	0.978792i	$-0.434327\pi$
$211$	5.95141	0.409712	0.204856	+	0.978792i	$0.434327\pi$
$212$	−12.1441	−0.834061
$213$	−18.2769	−1.25231
$214$	−5.21830	−0.356716
$215$	−30.9773	−2.11263
$216$	−5.29276	−0.360127
$217$	42.4194	2.87962
$218$	−15.9785	−1.08220
$219$	12.2779	0.829661
$220$	−9.82681	−0.662523
$221$	12.9394	0.870397
$222$	2.52975	0.169786
$223$	−5.59203	−0.374470	−0.187235	−	0.982315i	$-0.559953\pi$
$223$	−5.59203	−0.374470	−0.187235	+	0.982315i	$0.559953\pi$
$224$	3.98093	0.265987
$225$	−0.125243	−0.00834953
$226$	−11.7415	−0.781032
$227$	−7.30445	−0.484813	−0.242407	−	0.970175i	$-0.577937\pi$
$227$	−7.30445	−0.484813	−0.242407	+	0.970175i	$0.577937\pi$
$228$	−11.0893	−0.734407
$229$	−3.75994	−0.248464	−0.124232	−	0.992253i	$-0.539647\pi$
$229$	−3.75994	−0.248464	−0.124232	+	0.992253i	$0.539647\pi$
$230$	−8.52039	−0.561818
$231$	−26.9650	−1.77417
$232$	1.06413	0.0698634
$233$	11.5502	0.756679	0.378340	−	0.925667i	$-0.376495\pi$
$233$	11.5502	0.756679	0.378340	+	0.925667i	$0.376495\pi$
$234$	0.792657	0.0518176
$235$	11.8946	0.775916
$236$	−5.34100	−0.347669
$237$	30.0289	1.95059
$238$	7.62706	0.494389
$239$	20.0023	1.29384	0.646921	−	0.762557i	$-0.276057\pi$
$239$	20.0023	1.29384	0.646921	+	0.762557i	$0.276057\pi$
$240$	−4.18202	−0.269948
$241$	24.0863	1.55153	0.775766	−	0.631021i	$-0.217364\pi$
$241$	24.0863	1.55153	0.775766	+	0.631021i	$0.217364\pi$
$242$	−4.91635	−0.316035
$243$	−1.21900	−0.0781989
$244$	11.0084	0.704743
$245$	21.7934	1.39233
$246$	−1.02459	−0.0653255
$247$	44.1113	2.80674
$248$	10.6557	0.676635
$249$	−3.83722	−0.243174
$250$	9.68730	0.612679
$251$	−14.6827	−0.926764	−0.463382	−	0.886159i	$-0.653364\pi$
$251$	−14.6827	−0.926764	−0.463382	+	0.886159i	$0.653364\pi$
$252$	0.467228	0.0294326
$253$	−13.8004	−0.867621
$254$	6.48146	0.406683
$255$	−8.01232	−0.501751
$256$	1.00000	0.0625000
$257$	8.49582	0.529954	0.264977	−	0.964255i	$-0.414636\pi$
$257$	8.49582	0.529954	0.264977	+	0.964255i	$0.414636\pi$
$258$	−21.3524	−1.32934
$259$	−5.93154	−0.368568
$260$	16.6353	1.03168
$261$	0.124893	0.00773068
$262$	−20.4335	−1.26238
$263$	−4.62030	−0.284900	−0.142450	−	0.989802i	$-0.545498\pi$
$263$	−4.62030	−0.284900	−0.142450	+	0.989802i	$0.545498\pi$
$264$	−6.77355	−0.416883
$265$	−29.9128	−1.83753
$266$	26.0012	1.59424
$267$	−24.8775	−1.52248
$268$	3.80142	0.232209
$269$	−8.06828	−0.491932	−0.245966	−	0.969279i	$-0.579105\pi$
$269$	−8.06828	−0.491932	−0.245966	+	0.969279i	$0.579105\pi$
$270$	−13.0369	−0.793399
$271$	22.0096	1.33699	0.668495	−	0.743717i	$-0.266939\pi$
$271$	22.0096	1.33699	0.668495	+	0.743717i	$0.266939\pi$
$272$	1.91590	0.116168
$273$	45.6478	2.76273
$274$	22.0274	1.33072
$275$	−4.25726	−0.256723
$276$	−5.87304	−0.353516
$277$	14.8208	0.890497	0.445248	−	0.895407i	$-0.353115\pi$
$277$	14.8208	0.890497	0.445248	+	0.895407i	$0.353115\pi$
$278$	0.965611	0.0579135
$279$	1.25062	0.0748726
$280$	9.80563	0.585998
$281$	8.45712	0.504509	0.252255	−	0.967661i	$-0.418828\pi$
$281$	8.45712	0.504509	0.252255	+	0.967661i	$0.418828\pi$
$282$	8.19884	0.488234
$283$	−19.5523	−1.16226	−0.581131	−	0.813810i	$-0.697389\pi$
$283$	−19.5523	−1.16226	−0.581131	+	0.813810i	$0.697389\pi$
$284$	10.7649	0.638777
$285$	−27.3146	−1.61798
$286$	26.9440	1.59323
$287$	2.40237	0.141807
$288$	0.117367	0.00691589
$289$	−13.3293	−0.784078
$290$	2.62111	0.153917
$291$	9.72166	0.569894
$292$	−7.23149	−0.423191
$293$	−20.9179	−1.22204	−0.611019	−	0.791616i	$-0.709240\pi$
$293$	−20.9179	−1.22204	−0.611019	+	0.791616i	$0.709240\pi$
$294$	15.0221	0.876105
$295$	−13.1557	−0.765953
$296$	−1.48999	−0.0866038
$297$	−21.1156	−1.22525
$298$	−1.81437	−0.105103
$299$	23.3620	1.35106
$300$	−1.81177	−0.104603
$301$	50.0653	2.88572
$302$	−9.97557	−0.574029
$303$	13.4757	0.774157
$304$	6.53145	0.374604
$305$	27.1154	1.55262
$306$	0.224863	0.0128545
$307$	−2.27950	−0.130098	−0.0650491	−	0.997882i	$-0.520720\pi$
$307$	−2.27950	−0.130098	−0.0650491	+	0.997882i	$0.520720\pi$
$308$	15.8820	0.904963
$309$	−22.2274	−1.26447
$310$	26.2465	1.49070
$311$	13.4107	0.760451	0.380225	−	0.924894i	$-0.375846\pi$
$311$	13.4107	0.760451	0.380225	+	0.924894i	$0.375846\pi$
$312$	11.4666	0.649170
$313$	27.2997	1.54307	0.771535	−	0.636187i	$-0.219489\pi$
$313$	27.2997	1.54307	0.771535	+	0.636187i	$0.219489\pi$
$314$	0.592157	0.0334174
$315$	1.15085	0.0648432
$316$	−17.6866	−0.994951
$317$	−27.9168	−1.56797	−0.783983	−	0.620783i	$-0.786815\pi$
$317$	−27.9168	−1.56797	−0.783983	+	0.620783i	$0.786815\pi$
$318$	−20.6186	−1.15624
$319$	4.24537	0.237695
$320$	2.46315	0.137694
$321$	−8.85979	−0.494505
$322$	13.7706	0.767406
$323$	12.5136	0.696275
$324$	−8.63413	−0.479674
$325$	7.20692	0.399768
$326$	−12.5394	−0.694495
$327$	−27.1288	−1.50023
$328$	0.603470	0.0333210
$329$	−19.2239	−1.05985
$330$	−16.6843	−0.918439
$331$	−16.4377	−0.903499	−0.451750	−	0.892145i	$-0.649200\pi$
$331$	−16.4377	−0.903499	−0.451750	+	0.892145i	$0.649200\pi$
$332$	2.26007	0.124037
$333$	−0.174875	−0.00958308
$334$	−6.53570	−0.357617
$335$	9.36347	0.511581
$336$	6.75895	0.368731
$337$	19.6220	1.06888	0.534438	−	0.845208i	$-0.320523\pi$
$337$	19.6220	1.06888	0.534438	+	0.845208i	$0.320523\pi$
$338$	−32.6123	−1.77387
$339$	−19.9351	−1.08272
$340$	4.71915	0.255932
$341$	42.5111	2.30210
$342$	0.766574	0.0414516
$343$	−7.35594	−0.397183
$344$	12.5763	0.678068
$345$	−14.4662	−0.778833
$346$	4.43015	0.238167
$347$	24.7420	1.32822	0.664109	−	0.747636i	$-0.268811\pi$
$347$	24.7420	1.32822	0.664109	+	0.747636i	$0.268811\pi$
$348$	1.80671	0.0968498
$349$	3.77052	0.201831	0.100916	−	0.994895i	$-0.467823\pi$
$349$	3.77052	0.201831	0.100916	+	0.994895i	$0.467823\pi$
$350$	4.24808	0.227070
$351$	35.7457	1.90796
$352$	3.98953	0.212643
$353$	13.3716	0.711701	0.355850	−	0.934543i	$-0.384191\pi$
$353$	13.3716	0.711701	0.355850	+	0.934543i	$0.384191\pi$
$354$	−9.06812	−0.481965
$355$	26.5155	1.40730
$356$	14.6525	0.776581
$357$	12.9495	0.685358
$358$	1.75763	0.0928938
$359$	10.7367	0.566659	0.283329	−	0.959023i	$-0.408561\pi$
$359$	10.7367	0.566659	0.283329	+	0.959023i	$0.408561\pi$
$360$	0.289092	0.0152365
$361$	23.6598	1.24525
$362$	−19.6765	−1.03418
$363$	−8.34713	−0.438111
$364$	−26.8859	−1.40921
$365$	−17.8123	−0.932336
$366$	18.6905	0.976967
$367$	−27.7822	−1.45022	−0.725109	−	0.688634i	$-0.758211\pi$
$367$	−27.7822	−1.45022	−0.725109	+	0.688634i	$0.758211\pi$
$368$	3.45914	0.180320
$369$	0.0708272	0.00368712
$370$	−3.67006	−0.190798
$371$	48.3448	2.50994
$372$	18.0915	0.938002
$373$	9.91960	0.513617	0.256809	−	0.966462i	$-0.417329\pi$
$373$	9.91960	0.513617	0.256809	+	0.966462i	$0.417329\pi$
$374$	7.64354	0.395238
$375$	16.4474	0.849341
$376$	−4.82901	−0.249037
$377$	−7.18678	−0.370138
$378$	21.0701	1.08373
$379$	−27.0463	−1.38927	−0.694637	−	0.719360i	$-0.744435\pi$
$379$	−27.0463	−1.38927	−0.694637	+	0.719360i	$0.744435\pi$
$380$	16.0879	0.825294
$381$	11.0044	0.563774
$382$	−16.3247	−0.835243
$383$	−3.63690	−0.185837	−0.0929183	−	0.995674i	$-0.529620\pi$
$383$	−3.63690	−0.185837	−0.0929183	+	0.995674i	$0.529620\pi$
$384$	1.69783	0.0866421
$385$	39.1198	1.99373
$386$	−7.13118	−0.362967
$387$	1.47604	0.0750311
$388$	−5.72593	−0.290690
$389$	31.5684	1.60058	0.800291	−	0.599612i	$-0.204679\pi$
$389$	31.5684	1.60058	0.800291	+	0.599612i	$0.204679\pi$
$390$	28.2440	1.43019
$391$	6.62737	0.335161
$392$	−8.84780	−0.446881
$393$	−34.6926	−1.75001
$394$	−24.2658	−1.22249
$395$	−43.5648	−2.19198
$396$	0.468238	0.0235298
$397$	−18.3245	−0.919678	−0.459839	−	0.888002i	$-0.652093\pi$
$397$	−18.3245	−0.919678	−0.459839	+	0.888002i	$0.652093\pi$
$398$	−0.881972	−0.0442093
$399$	44.1457	2.21005
$400$	1.06711	0.0533554
$401$	11.8360	0.591061	0.295531	−	0.955333i	$-0.404504\pi$
$401$	11.8360	0.591061	0.295531	+	0.955333i	$0.404504\pi$
$402$	6.45417	0.321905
$403$	−71.9650	−3.58483
$404$	−7.93699	−0.394880
$405$	−21.2671	−1.05677
$406$	−4.23621	−0.210240
$407$	−5.94435	−0.294651
$408$	3.25288	0.161041
$409$	−29.1431	−1.44103	−0.720516	−	0.693439i	$-0.756095\pi$
$409$	−29.1431	−1.44103	−0.720516	+	0.693439i	$0.756095\pi$
$410$	1.48644	0.0734099
$411$	37.3988	1.84475
$412$	13.0916	0.644978
$413$	21.2621	1.04624
$414$	0.405988	0.0199532
$415$	5.56689	0.273268
$416$	−6.75369	−0.331127
$417$	1.63944	0.0802840
$418$	26.0574	1.27451
$419$	28.0234	1.36903	0.684516	−	0.728998i	$-0.260014\pi$
$419$	28.0234	1.36903	0.684516	+	0.728998i	$0.260014\pi$
$420$	16.6483	0.812354
$421$	−10.5323	−0.513313	−0.256656	−	0.966503i	$-0.582621\pi$
$421$	−10.5323	−0.513313	−0.256656	+	0.966503i	$0.582621\pi$
$422$	−5.95141	−0.289710
$423$	−0.566764	−0.0275570
$424$	12.1441	0.589770
$425$	2.04447	0.0991715
$426$	18.2769	0.885520
$427$	−43.8238	−2.12078
$428$	5.21830	0.252236
$429$	45.7464	2.20866
$430$	30.9773	1.49386
$431$	18.2901	0.881004	0.440502	−	0.897752i	$-0.354800\pi$
$431$	18.2901	0.881004	0.440502	+	0.897752i	$0.354800\pi$
$432$	5.29276	0.254648
$433$	12.6636	0.608573	0.304286	−	0.952581i	$-0.401582\pi$
$433$	12.6636	0.608573	0.304286	+	0.952581i	$0.401582\pi$
$434$	−42.4194	−2.03620
$435$	4.45020	0.213371
$436$	15.9785	0.765231
$437$	22.5932	1.08078
$438$	−12.2779	−0.586659
$439$	−21.4195	−1.02230	−0.511148	−	0.859492i	$-0.670780\pi$
$439$	−21.4195	−1.02230	−0.511148	+	0.859492i	$0.670780\pi$
$440$	9.82681	0.468475
$441$	−1.03844	−0.0494493
$442$	−12.9394	−0.615464
$443$	−21.9810	−1.04435	−0.522175	−	0.852838i	$-0.674879\pi$
$443$	−21.9810	−1.04435	−0.522175	+	0.852838i	$0.674879\pi$
$444$	−2.52975	−0.120057
$445$	36.0913	1.71089
$446$	5.59203	0.264790
$447$	−3.08049	−0.145702
$448$	−3.98093	−0.188081
$449$	37.8922	1.78824	0.894122	−	0.447823i	$-0.147800\pi$
$449$	37.8922	1.78824	0.894122	+	0.447823i	$0.147800\pi$
$450$	0.125243	0.00590401
$451$	2.40756	0.113368
$452$	11.7415	0.552273
$453$	−16.9368	−0.795762
$454$	7.30445	0.342815
$455$	−66.2241	−3.10463
$456$	11.0893	0.519304
$457$	−12.8727	−0.602160	−0.301080	−	0.953599i	$-0.597347\pi$
$457$	−12.8727	−0.602160	−0.301080	+	0.953599i	$0.597347\pi$
$458$	3.75994	0.175690
$459$	10.1404	0.473314
$460$	8.52039	0.397265
$461$	−22.2698	−1.03721	−0.518605	−	0.855014i	$-0.673548\pi$
$461$	−22.2698	−1.03721	−0.518605	+	0.855014i	$0.673548\pi$
$462$	26.9650	1.25453
$463$	12.4289	0.577621	0.288811	−	0.957386i	$-0.406740\pi$
$463$	12.4289	0.577621	0.288811	+	0.957386i	$0.406740\pi$
$464$	−1.06413	−0.0494009
$465$	44.5621	2.06652
$466$	−11.5502	−0.535053
$467$	9.26186	0.428588	0.214294	−	0.976769i	$-0.431255\pi$
$467$	9.26186	0.428588	0.214294	+	0.976769i	$0.431255\pi$
$468$	−0.792657	−0.0366406
$469$	−15.1332	−0.698785
$470$	−11.8946	−0.548656
$471$	1.00538	0.0463256
$472$	5.34100	0.245839
$473$	50.1735	2.30698
$474$	−30.0289	−1.37927
$475$	6.96976	0.319795
$476$	−7.62706	−0.349586
$477$	1.42531	0.0652606
$478$	−20.0023	−0.914884
$479$	3.79251	0.173284	0.0866420	−	0.996240i	$-0.472386\pi$
$479$	3.79251	0.173284	0.0866420	+	0.996240i	$0.472386\pi$
$480$	4.18202	0.190882
$481$	10.0629	0.458829
$482$	−24.0863	−1.09710
$483$	23.3802	1.06383
$484$	4.91635	0.223470
$485$	−14.1038	−0.640422
$486$	1.21900	0.0552950
$487$	18.3907	0.833361	0.416680	−	0.909053i	$-0.363193\pi$
$487$	18.3907	0.833361	0.416680	+	0.909053i	$0.363193\pi$
$488$	−11.0084	−0.498328
$489$	−21.2899	−0.962760
$490$	−21.7934	−0.984528
$491$	36.5400	1.64903	0.824514	−	0.565842i	$-0.191449\pi$
$491$	36.5400	1.64903	0.824514	+	0.565842i	$0.191449\pi$
$492$	1.02459	0.0461921
$493$	−2.03876	−0.0918212
$494$	−44.1113	−1.98466
$495$	1.15334	0.0518387
$496$	−10.6557	−0.478453
$497$	−42.8541	−1.92227
$498$	3.83722	0.171950
$499$	−17.5884	−0.787367	−0.393684	−	0.919246i	$-0.628799\pi$
$499$	−17.5884	−0.787367	−0.393684	+	0.919246i	$0.628799\pi$
$500$	−9.68730	−0.433229
$501$	−11.0965	−0.495756
$502$	14.6827	0.655321
$503$	15.8240	0.705556	0.352778	−	0.935707i	$-0.385237\pi$
$503$	15.8240	0.705556	0.352778	+	0.935707i	$0.385237\pi$
$504$	−0.467228	−0.0208120
$505$	−19.5500	−0.869963
$506$	13.8004	0.613501
$507$	−55.3702	−2.45908
$508$	−6.48146	−0.287568
$509$	22.5750	1.00062	0.500309	−	0.865847i	$-0.333220\pi$
$509$	22.5750	1.00062	0.500309	+	0.865847i	$0.333220\pi$
$510$	8.01232	0.354792
$511$	28.7881	1.27351
$512$	−1.00000	−0.0441942
$513$	34.5694	1.52628
$514$	−8.49582	−0.374734
$515$	32.2467	1.42096
$516$	21.3524	0.939988
$517$	−19.2655	−0.847294
$518$	5.93154	0.260617
$519$	7.52166	0.330164
$520$	−16.6353	−0.729508
$521$	14.0314	0.614727	0.307363	−	0.951592i	$-0.400553\pi$
$521$	14.0314	0.614727	0.307363	+	0.951592i	$0.400553\pi$
$522$	−0.124893	−0.00546642
$523$	−15.3511	−0.671255	−0.335627	−	0.941995i	$-0.608948\pi$
$523$	−15.3511	−0.671255	−0.335627	+	0.941995i	$0.608948\pi$
$524$	20.4335	0.892640
$525$	7.21253	0.314781
$526$	4.62030	0.201455
$527$	−20.4152	−0.889299
$528$	6.77355	0.294781
$529$	−11.0343	−0.479753
$530$	29.9128	1.29933
$531$	0.626855	0.0272032
$532$	−26.0012	−1.12730
$533$	−4.07564	−0.176536
$534$	24.8775	1.07655
$535$	12.8535	0.555703
$536$	−3.80142	−0.164196
$537$	2.98416	0.128776
$538$	8.06828	0.347848
$539$	−35.2985	−1.52042
$540$	13.0369	0.561018
$541$	16.5084	0.709750	0.354875	−	0.934914i	$-0.384523\pi$
$541$	16.5084	0.709750	0.354875	+	0.934914i	$0.384523\pi$
$542$	−22.0096	−0.945395
$543$	−33.4075	−1.43365
$544$	−1.91590	−0.0821435
$545$	39.3574	1.68589
$546$	−45.6478	−1.95355
$547$	−2.66263	−0.113846	−0.0569230	−	0.998379i	$-0.518129\pi$
$547$	−2.66263	−0.113846	−0.0569230	+	0.998379i	$0.518129\pi$
$548$	−22.0274	−0.940963
$549$	−1.29202	−0.0551422
$550$	4.25726	0.181530
$551$	−6.95029	−0.296092
$552$	5.87304	0.249973
$553$	70.4092	2.99410
$554$	−14.8208	−0.629676
$555$	−6.23115	−0.264498
$556$	−0.965611	−0.0409510
$557$	−21.2882	−0.902012	−0.451006	−	0.892521i	$-0.648935\pi$
$557$	−21.2882	−0.902012	−0.451006	+	0.892521i	$0.648935\pi$
$558$	−1.25062	−0.0529429
$559$	−84.9363	−3.59242
$560$	−9.80563	−0.414363
$561$	12.9774	0.547908
$562$	−8.45712	−0.356742
$563$	8.53844	0.359853	0.179926	−	0.983680i	$-0.442414\pi$
$563$	8.53844	0.359853	0.179926	+	0.983680i	$0.442414\pi$
$564$	−8.19884	−0.345234
$565$	28.9211	1.21672
$566$	19.5523	0.821843
$567$	34.3718	1.44348
$568$	−10.7649	−0.451684
$569$	3.98763	0.167170	0.0835850	−	0.996501i	$-0.473363\pi$
$569$	3.98763	0.167170	0.0835850	+	0.996501i	$0.473363\pi$
$570$	27.3146	1.14408
$571$	33.0029	1.38113	0.690564	−	0.723271i	$-0.257362\pi$
$571$	33.0029	1.38113	0.690564	+	0.723271i	$0.257362\pi$
$572$	−26.9440	−1.12659
$573$	−27.7166	−1.15788
$574$	−2.40237	−0.100273
$575$	3.69128	0.153937
$576$	−0.117367	−0.00489027
$577$	2.47988	0.103239	0.0516194	−	0.998667i	$-0.483562\pi$
$577$	2.47988	0.103239	0.0516194	+	0.998667i	$0.483562\pi$
$578$	13.3293	0.554427
$579$	−12.1075	−0.503172
$580$	−2.62111	−0.108835
$581$	−8.99718	−0.373266
$582$	−9.72166	−0.402976
$583$	48.4493	2.00656
$584$	7.23149	0.299241
$585$	−1.95243	−0.0807232
$586$	20.9179	0.864112
$587$	7.32228	0.302223	0.151111	−	0.988517i	$-0.451715\pi$
$587$	7.32228	0.302223	0.151111	+	0.988517i	$0.451715\pi$
$588$	−15.0221	−0.619500
$589$	−69.5969	−2.86769
$590$	13.1557	0.541611
$591$	−41.1992	−1.69471
$592$	1.48999	0.0612381
$593$	−0.274635	−0.0112779	−0.00563895	−	0.999984i	$-0.501795\pi$
$593$	−0.274635	−0.0112779	−0.00563895	+	0.999984i	$0.501795\pi$
$594$	21.1156	0.866385
$595$	−18.7866	−0.770175
$596$	1.81437	0.0743194
$597$	−1.49744	−0.0612862
$598$	−23.3620	−0.955342
$599$	35.4471	1.44833	0.724164	−	0.689628i	$-0.242226\pi$
$599$	35.4471	1.44833	0.724164	+	0.689628i	$0.242226\pi$
$600$	1.81177	0.0739652
$601$	−13.5504	−0.552734	−0.276367	−	0.961052i	$-0.589131\pi$
$601$	−13.5504	−0.552734	−0.276367	+	0.961052i	$0.589131\pi$
$602$	−50.0653	−2.04051
$603$	−0.446160	−0.0181690
$604$	9.97557	0.405900
$605$	12.1097	0.492330
$606$	−13.4757	−0.547412
$607$	−8.79649	−0.357039	−0.178519	−	0.983936i	$-0.557131\pi$
$607$	−8.79649	−0.357039	−0.178519	+	0.983936i	$0.557131\pi$
$608$	−6.53145	−0.264885
$609$	−7.19238	−0.291450
$610$	−27.1154	−1.09787
$611$	32.6136	1.31941
$612$	−0.224863	−0.00908953
$613$	−21.0736	−0.851154	−0.425577	−	0.904922i	$-0.639929\pi$
$613$	−21.0736	−0.851154	−0.425577	+	0.904922i	$0.639929\pi$
$614$	2.27950	0.0919933
$615$	2.52372	0.101766
$616$	−15.8820	−0.639905
$617$	−4.01342	−0.161574	−0.0807871	−	0.996731i	$-0.525743\pi$
$617$	−4.01342	−0.161574	−0.0807871	+	0.996731i	$0.525743\pi$
$618$	22.2274	0.894117
$619$	36.1476	1.45289	0.726447	−	0.687223i	$-0.241170\pi$
$619$	36.1476	1.45289	0.726447	+	0.687223i	$0.241170\pi$
$620$	−26.2465	−1.05408
$621$	18.3084	0.734692
$622$	−13.4107	−0.537720
$623$	−58.3305	−2.33696
$624$	−11.4666	−0.459032
$625$	−29.1968	−1.16787
$626$	−27.2997	−1.09112
$627$	44.2411	1.76682
$628$	−0.592157	−0.0236297
$629$	2.85467	0.113823
$630$	−1.15085	−0.0458511
$631$	26.0139	1.03560	0.517799	−	0.855502i	$-0.326752\pi$
$631$	26.0139	1.03560	0.517799	+	0.855502i	$0.326752\pi$
$632$	17.6866	0.703536
$633$	−10.1045	−0.401618
$634$	27.9168	1.10872
$635$	−15.9648	−0.633544
$636$	20.6186	0.817583
$637$	59.7552	2.36759
$638$	−4.24537	−0.168076
$639$	−1.26344	−0.0499807
$640$	−2.46315	−0.0973646
$641$	−0.336331	−0.0132843	−0.00664214	−	0.999978i	$-0.502114\pi$
$641$	−0.336331	−0.0132843	−0.00664214	+	0.999978i	$0.502114\pi$
$642$	8.85979	0.349668
$643$	13.8805	0.547394	0.273697	−	0.961816i	$-0.411754\pi$
$643$	13.8805	0.547394	0.273697	+	0.961816i	$0.411754\pi$
$644$	−13.7706	−0.542638
$645$	52.5942	2.07090
$646$	−12.5136	−0.492341
$647$	25.7639	1.01288	0.506442	−	0.862274i	$-0.330960\pi$
$647$	25.7639	1.01288	0.506442	+	0.862274i	$0.330960\pi$
$648$	8.63413	0.339180
$649$	21.3081	0.836415
$650$	−7.20692	−0.282679
$651$	−72.0211	−2.82273
$652$	12.5394	0.491082
$653$	−26.8150	−1.04935	−0.524677	−	0.851302i	$-0.675814\pi$
$653$	−26.8150	−1.04935	−0.524677	+	0.851302i	$0.675814\pi$
$654$	27.1288	1.06082
$655$	50.3307	1.96658
$656$	−0.603470	−0.0235615
$657$	0.848736	0.0331123
$658$	19.2239	0.749427
$659$	22.5001	0.876480	0.438240	−	0.898858i	$-0.355602\pi$
$659$	22.5001	0.876480	0.438240	+	0.898858i	$0.355602\pi$
$660$	16.6843	0.649434
$661$	−37.6136	−1.46300	−0.731499	−	0.681842i	$-0.761179\pi$
$661$	−37.6136	−1.46300	−0.731499	+	0.681842i	$0.761179\pi$
$662$	16.4377	0.638870
$663$	−21.9689	−0.853201
$664$	−2.26007	−0.0877077
$665$	−64.0449	−2.48356
$666$	0.174875	0.00677626
$667$	−3.68097	−0.142528
$668$	6.53570	0.252874
$669$	9.49433	0.367072
$670$	−9.36347	−0.361742
$671$	−43.9185	−1.69545
$672$	−6.75895	−0.260732
$673$	−3.03351	−0.116933	−0.0584667	−	0.998289i	$-0.518621\pi$
$673$	−3.03351	−0.116933	−0.0584667	+	0.998289i	$0.518621\pi$
$674$	−19.6220	−0.755810
$675$	5.64795	0.217390
$676$	32.6123	1.25432
$677$	11.8638	0.455965	0.227982	−	0.973665i	$-0.426787\pi$
$677$	11.8638	0.455965	0.227982	+	0.973665i	$0.426787\pi$
$678$	19.9351	0.765602
$679$	22.7945	0.874773
$680$	−4.71915	−0.180971
$681$	12.4017	0.475235
$682$	−42.5111	−1.62783
$683$	−7.56106	−0.289316	−0.144658	−	0.989482i	$-0.546208\pi$
$683$	−7.56106	−0.289316	−0.144658	+	0.989482i	$0.546208\pi$
$684$	−0.766574	−0.0293107
$685$	−54.2568	−2.07304
$686$	7.35594	0.280851
$687$	6.38375	0.243555
$688$	−12.5763	−0.479466
$689$	−82.0175	−3.12462
$690$	14.4662	0.550718
$691$	−0.418561	−0.0159228	−0.00796140	−	0.999968i	$-0.502534\pi$
$691$	−0.418561	−0.0159228	−0.00796140	+	0.999968i	$0.502534\pi$
$692$	−4.43015	−0.168409
$693$	−1.86402	−0.0708083
$694$	−24.7420	−0.939192
$695$	−2.37844	−0.0902195
$696$	−1.80671	−0.0684831
$697$	−1.15619	−0.0437937
$698$	−3.77052	−0.142716
$699$	−19.6103	−0.741730
$700$	−4.24808	−0.160562
$701$	−27.8393	−1.05147	−0.525737	−	0.850647i	$-0.676210\pi$
$701$	−27.8393	−1.05147	−0.525737	+	0.850647i	$0.676210\pi$
$702$	−35.7457	−1.34913
$703$	9.73178	0.367041
$704$	−3.98953	−0.150361
$705$	−20.1950	−0.760587
$706$	−13.3716	−0.503248
$707$	31.5966	1.18831
$708$	9.06812	0.340801
$709$	−27.0029	−1.01412	−0.507058	−	0.861912i	$-0.669267\pi$
$709$	−27.0029	−1.01412	−0.507058	+	0.861912i	$0.669267\pi$
$710$	−26.5155	−0.995108
$711$	2.07582	0.0778493
$712$	−14.6525	−0.549125
$713$	−36.8595	−1.38040
$714$	−12.9495	−0.484622
$715$	−66.3672	−2.48199
$716$	−1.75763	−0.0656858
$717$	−33.9605	−1.26828
$718$	−10.7367	−0.400688
$719$	−7.36593	−0.274703	−0.137351	−	0.990522i	$-0.543859\pi$
$719$	−7.36593	−0.274703	−0.137351	+	0.990522i	$0.543859\pi$
$720$	−0.289092	−0.0107738
$721$	−52.1169	−1.94093
$722$	−23.6598	−0.880527
$723$	−40.8944	−1.52088
$724$	19.6765	0.731273
$725$	−1.13554	−0.0421729
$726$	8.34713	0.309791
$727$	0.566129	0.0209966	0.0104983	−	0.999945i	$-0.496658\pi$
$727$	0.566129	0.0209966	0.0104983	+	0.999945i	$0.496658\pi$
$728$	26.8859	0.996459
$729$	27.9720	1.03600
$730$	17.8123	0.659261
$731$	−24.0949	−0.891182
$732$	−18.6905	−0.690820
$733$	−35.4599	−1.30974	−0.654872	−	0.755740i	$-0.727277\pi$
$733$	−35.4599	−1.30974	−0.654872	+	0.755740i	$0.727277\pi$
$734$	27.7822	1.02546
$735$	−37.0016	−1.36483
$736$	−3.45914	−0.127506
$737$	−15.1659	−0.558642
$738$	−0.0708272	−0.00260718
$739$	30.1882	1.11049	0.555245	−	0.831687i	$-0.312624\pi$
$739$	30.1882	1.11049	0.555245	+	0.831687i	$0.312624\pi$
$740$	3.67006	0.134914
$741$	−74.8937	−2.75129
$742$	−48.3448	−1.77479
$743$	−18.9808	−0.696339	−0.348169	−	0.937432i	$-0.613197\pi$
$743$	−18.9808	−0.696339	−0.348169	+	0.937432i	$0.613197\pi$
$744$	−18.0915	−0.663268
$745$	4.46906	0.163734
$746$	−9.91960	−0.363182
$747$	−0.265257	−0.00970523
$748$	−7.64354	−0.279475
$749$	−20.7737	−0.759054
$750$	−16.4474	−0.600575
$751$	5.60261	0.204442	0.102221	−	0.994762i	$-0.467405\pi$
$751$	5.60261	0.204442	0.102221	+	0.994762i	$0.467405\pi$
$752$	4.82901	0.176096
$753$	24.9288	0.908455
$754$	7.18678	0.261727
$755$	24.5713	0.894242
$756$	−21.0701	−0.766313
$757$	16.5044	0.599862	0.299931	−	0.953961i	$-0.403036\pi$
$757$	16.5044	0.599862	0.299931	+	0.953961i	$0.403036\pi$
$758$	27.0463	0.982365
$759$	23.4307	0.850480
$760$	−16.0879	−0.583571
$761$	−2.51575	−0.0911960	−0.0455980	−	0.998960i	$-0.514519\pi$
$761$	−2.51575	−0.0911960	−0.0455980	+	0.998960i	$0.514519\pi$
$762$	−11.0044	−0.398648
$763$	−63.6092	−2.30281
$764$	16.3247	0.590606
$765$	−0.553870	−0.0200252
$766$	3.63690	0.131406
$767$	−36.0714	−1.30246
$768$	−1.69783	−0.0612652
$769$	−50.1847	−1.80971	−0.904853	−	0.425724i	$-0.860019\pi$
$769$	−50.1847	−1.80971	−0.904853	+	0.425724i	$0.860019\pi$
$770$	−39.1198	−1.40978
$771$	−14.4245	−0.519485
$772$	7.13118	0.256657
$773$	−5.36307	−0.192896	−0.0964481	−	0.995338i	$-0.530748\pi$
$773$	−5.36307	−0.192896	−0.0964481	+	0.995338i	$0.530748\pi$
$774$	−1.47604	−0.0530550
$775$	−11.3708	−0.408449
$776$	5.72593	0.205549
$777$	10.0708	0.361286
$778$	−31.5684	−1.13178
$779$	−3.94153	−0.141220
$780$	−28.2440	−1.01130
$781$	−42.9467	−1.53676
$782$	−6.62737	−0.236994
$783$	−5.63218	−0.201278
$784$	8.84780	0.315993
$785$	−1.45857	−0.0520587
$786$	34.6926	1.23744
$787$	−1.58955	−0.0566615	−0.0283307	−	0.999599i	$-0.509019\pi$
$787$	−1.58955	−0.0566615	−0.0283307	+	0.999599i	$0.509019\pi$
$788$	24.2658	0.864433
$789$	7.84449	0.279271
$790$	43.5648	1.54997
$791$	−46.7420	−1.66196
$792$	−0.468238	−0.0166381
$793$	74.3475	2.64016
$794$	18.3245	0.650311
$795$	50.7868	1.80122
$796$	0.881972	0.0312607
$797$	53.2182	1.88508	0.942542	−	0.334087i	$-0.108428\pi$
$797$	53.2182	1.88508	0.942542	+	0.334087i	$0.108428\pi$
$798$	−44.1457	−1.56274
$799$	9.25189	0.327308
$800$	−1.06711	−0.0377280
$801$	−1.71971	−0.0607631
$802$	−11.8360	−0.417944
$803$	28.8503	1.01810
$804$	−6.45417	−0.227621
$805$	−33.9191	−1.19549
$806$	71.9650	2.53486
$807$	13.6986	0.482213
$808$	7.93699	0.279222
$809$	16.6068	0.583866	0.291933	−	0.956439i	$-0.405702\pi$
$809$	16.6068	0.583866	0.291933	+	0.956439i	$0.405702\pi$
$810$	21.2671	0.747251
$811$	50.3541	1.76817	0.884086	−	0.467323i	$-0.154782\pi$
$811$	50.3541	1.76817	0.884086	+	0.467323i	$0.154782\pi$
$812$	4.23621	0.148662
$813$	−37.3687	−1.31058
$814$	5.94435	0.208349
$815$	30.8865	1.08191
$816$	−3.25288	−0.113873
$817$	−82.1413	−2.87376
$818$	29.1431	1.01896
$819$	3.15551	0.110263
$820$	−1.48644	−0.0519086
$821$	−54.6330	−1.90670	−0.953352	−	0.301862i	$-0.902392\pi$
$821$	−54.6330	−1.90670	−0.953352	+	0.301862i	$0.902392\pi$
$822$	−37.3988	−1.30443
$823$	0.192147	0.00669783	0.00334891	−	0.999994i	$-0.498934\pi$
$823$	0.192147	0.00669783	0.00334891	+	0.999994i	$0.498934\pi$
$824$	−13.0916	−0.456069
$825$	7.22811	0.251651
$826$	−21.2621	−0.739804
$827$	−19.0413	−0.662130	−0.331065	−	0.943608i	$-0.607408\pi$
$827$	−19.0413	−0.662130	−0.331065	+	0.943608i	$0.607408\pi$
$828$	−0.405988	−0.0141091
$829$	21.4559	0.745192	0.372596	−	0.927994i	$-0.378468\pi$
$829$	21.4559	0.745192	0.372596	+	0.927994i	$0.378468\pi$
$830$	−5.56689	−0.193230
$831$	−25.1633	−0.872904
$832$	6.75369	0.234142
$833$	16.9515	0.587334
$834$	−1.63944	−0.0567693
$835$	16.0984	0.557108
$836$	−26.0574	−0.901214
$837$	−56.3979	−1.94940
$838$	−28.0234	−0.968052
$839$	44.7817	1.54604	0.773019	−	0.634383i	$-0.218746\pi$
$839$	44.7817	1.54604	0.773019	+	0.634383i	$0.218746\pi$
$840$	−16.6483	−0.574421
$841$	−27.8676	−0.960953
$842$	10.5323	0.362967
$843$	−14.3588	−0.494542
$844$	5.95141	0.204856
$845$	80.3289	2.76340
$846$	0.566764	0.0194858
$847$	−19.5716	−0.672489
$848$	−12.1441	−0.417030
$849$	33.1964	1.13930
$850$	−2.04447	−0.0701248
$851$	5.15408	0.176680
$852$	−18.2769	−0.626157
$853$	17.9716	0.615334	0.307667	−	0.951494i	$-0.400452\pi$
$853$	17.9716	0.615334	0.307667	+	0.951494i	$0.400452\pi$
$854$	43.8238	1.49962
$855$	−1.88819	−0.0645746
$856$	−5.21830	−0.178358
$857$	41.7576	1.42641	0.713206	−	0.700955i	$-0.247243\pi$
$857$	41.7576	1.42641	0.713206	+	0.700955i	$0.247243\pi$
$858$	−45.7464	−1.56176
$859$	40.4811	1.38120	0.690598	−	0.723239i	$-0.257347\pi$
$859$	40.4811	1.38120	0.690598	+	0.723239i	$0.257347\pi$
$860$	−30.9773	−1.05632
$861$	−4.07882	−0.139006
$862$	−18.2901	−0.622964
$863$	39.6841	1.35086	0.675432	−	0.737422i	$-0.263957\pi$
$863$	39.6841	1.35086	0.675432	+	0.737422i	$0.263957\pi$
$864$	−5.29276	−0.180064
$865$	−10.9121	−0.371024
$866$	−12.6636	−0.430326
$867$	22.6310	0.768588
$868$	42.4194	1.43981
$869$	70.5613	2.39363
$870$	−4.45020	−0.150876
$871$	25.6736	0.869917
$872$	−15.9785	−0.541100
$873$	0.672033	0.0227449
$874$	−22.5932	−0.764227
$875$	38.5645	1.30372
$876$	12.2779	0.414831
$877$	−6.73459	−0.227411	−0.113705	−	0.993515i	$-0.536272\pi$
$877$	−6.73459	−0.227411	−0.113705	+	0.993515i	$0.536272\pi$
$878$	21.4195	0.722873
$879$	35.5151	1.19790
$880$	−9.82681	−0.331262
$881$	55.7390	1.87790	0.938948	−	0.344060i	$-0.111802\pi$
$881$	55.7390	1.87790	0.938948	+	0.344060i	$0.111802\pi$
$882$	1.03844	0.0349659
$883$	−12.1450	−0.408712	−0.204356	−	0.978897i	$-0.565510\pi$
$883$	−12.1450	−0.408712	−0.204356	+	0.978897i	$0.565510\pi$
$884$	12.9394	0.435199
$885$	22.3361	0.750821
$886$	21.9810	0.738467
$887$	−25.4134	−0.853300	−0.426650	−	0.904417i	$-0.640306\pi$
$887$	−25.4134	−0.853300	−0.426650	+	0.904417i	$0.640306\pi$
$888$	2.52975	0.0848928
$889$	25.8022	0.865379
$890$	−36.0913	−1.20978
$891$	34.4461	1.15399
$892$	−5.59203	−0.187235
$893$	31.5404	1.05546
$894$	3.08049	0.103027
$895$	−4.32931	−0.144713
$896$	3.98093	0.132994
$897$	−39.6647	−1.32437
$898$	−37.8922	−1.26448
$899$	11.3390	0.378176
$900$	−0.125243	−0.00417476
$901$	−23.2669	−0.775132
$902$	−2.40756	−0.0801630
$903$	−85.0025	−2.82870
$904$	−11.7415	−0.390516
$905$	48.4663	1.61107
$906$	16.9368	0.562689
$907$	−26.9550	−0.895025	−0.447512	−	0.894278i	$-0.647690\pi$
$907$	−26.9550	−0.895025	−0.447512	+	0.894278i	$0.647690\pi$
$908$	−7.30445	−0.242407
$909$	0.931537	0.0308971
$910$	66.2241	2.19531
$911$	−29.3595	−0.972723	−0.486362	−	0.873758i	$-0.661676\pi$
$911$	−29.3595	−0.972723	−0.486362	+	0.873758i	$0.661676\pi$
$912$	−11.0893	−0.367203
$913$	−9.01661	−0.298406
$914$	12.8727	0.425791
$915$	−46.0374	−1.52195
$916$	−3.75994	−0.124232
$917$	−81.3442	−2.68622
$918$	−10.1404	−0.334683
$919$	−56.3560	−1.85901	−0.929507	−	0.368805i	$-0.879767\pi$
$919$	−56.3560	−1.85901	−0.929507	+	0.368805i	$0.879767\pi$
$920$	−8.52039	−0.280909
$921$	3.87021	0.127528
$922$	22.2698	0.733418
$923$	72.7025	2.39303
$924$	−26.9650	−0.887084
$925$	1.58998	0.0522782
$926$	−12.4289	−0.408440
$927$	−1.53652	−0.0504659
$928$	1.06413	0.0349317
$929$	−20.3537	−0.667782	−0.333891	−	0.942612i	$-0.608362\pi$
$929$	−20.3537	−0.667782	−0.333891	+	0.942612i	$0.608362\pi$
$930$	−44.5621	−1.46125
$931$	57.7889	1.89395
$932$	11.5502	0.378340
$933$	−22.7691	−0.745427
$934$	−9.26186	−0.303057
$935$	−18.8272	−0.615715
$936$	0.792657	0.0259088
$937$	−18.1948	−0.594398	−0.297199	−	0.954816i	$-0.596053\pi$
$937$	−18.1948	−0.594398	−0.297199	+	0.954816i	$0.596053\pi$
$938$	15.1332	0.494116
$939$	−46.3503	−1.51258
$940$	11.8946	0.387958
$941$	−3.79437	−0.123693	−0.0618465	−	0.998086i	$-0.519699\pi$
$941$	−3.79437	−0.123693	−0.0618465	+	0.998086i	$0.519699\pi$
$942$	−1.00538	−0.0327572
$943$	−2.08749	−0.0679780
$944$	−5.34100	−0.173835
$945$	−51.8989	−1.68827
$946$	−50.1735	−1.63128
$947$	−7.74180	−0.251575	−0.125787	−	0.992057i	$-0.540146\pi$
$947$	−7.74180	−0.251575	−0.125787	+	0.992057i	$0.540146\pi$
$948$	30.0289	0.975294
$949$	−48.8392	−1.58539
$950$	−6.96976	−0.226129
$951$	47.3981	1.53699
$952$	7.62706	0.247194
$953$	−30.3253	−0.982334	−0.491167	−	0.871065i	$-0.663430\pi$
$953$	−30.3253	−0.982334	−0.491167	+	0.871065i	$0.663430\pi$
$954$	−1.42531	−0.0461462
$955$	40.2101	1.30117
$956$	20.0023	0.646921
$957$	−7.20792	−0.232999
$958$	−3.79251	−0.122530
$959$	87.6895	2.83164
$960$	−4.18202	−0.134974
$961$	82.5432	2.66268
$962$	−10.0629	−0.324441
$963$	−0.612454	−0.0197361
$964$	24.0863	0.775766
$965$	17.5652	0.565442
$966$	−23.3802	−0.752245
$967$	8.99225	0.289171	0.144586	−	0.989492i	$-0.453815\pi$
$967$	8.99225	0.289171	0.144586	+	0.989492i	$0.453815\pi$
$968$	−4.91635	−0.158017
$969$	−21.2460	−0.682519
$970$	14.1038	0.452846
$971$	4.52062	0.145074	0.0725369	−	0.997366i	$-0.476890\pi$
$971$	4.52062	0.145074	0.0725369	+	0.997366i	$0.476890\pi$
$972$	−1.21900	−0.0390994
$973$	3.84403	0.123234
$974$	−18.3907	−0.589275
$975$	−12.2361	−0.391870
$976$	11.0084	0.352371
$977$	13.3385	0.426736	0.213368	−	0.976972i	$-0.431557\pi$
$977$	13.3385	0.426736	0.213368	+	0.976972i	$0.431557\pi$
$978$	21.2899	0.680774
$979$	−58.4566	−1.86828
$980$	21.7934	0.696166
$981$	−1.87534	−0.0598750
$982$	−36.5400	−1.16604
$983$	−45.5265	−1.45207	−0.726036	−	0.687657i	$-0.758639\pi$
$983$	−45.5265	−1.45207	−0.726036	+	0.687657i	$0.758639\pi$
$984$	−1.02459	−0.0326627
$985$	59.7703	1.90444
$986$	2.03876	0.0649274
$987$	32.6390	1.03891
$988$	44.1113	1.40337
$989$	−43.5032	−1.38332
$990$	−1.15334	−0.0366555
$991$	−20.6003	−0.654390	−0.327195	−	0.944957i	$-0.606103\pi$
$991$	−20.6003	−0.654390	−0.327195	+	0.944957i	$0.606103\pi$
$992$	10.6557	0.338318
$993$	27.9085	0.885649
$994$	42.8541	1.35925
$995$	2.17243	0.0688706
$996$	−3.83722	−0.121587
$997$	6.81887	0.215956	0.107978	−	0.994153i	$-0.465562\pi$
$997$	6.81887	0.215956	0.107978	+	0.994153i	$0.465562\pi$
$998$	17.5884	0.556753
$999$	7.88616	0.249507

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.h.1.12	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.h.1.12	✓	42	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.69783 q^{3} +1.00000 q^{4} +2.46315 q^{5} +1.69783 q^{6} -3.98093 q^{7} -1.00000 q^{8} -0.117367 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.69783 q^{3} +1.00000 q^{4} +2.46315 q^{5} +1.69783 q^{6} -3.98093 q^{7} -1.00000 q^{8} -0.117367 q^{9} -2.46315 q^{10} -3.98953 q^{11} -1.69783 q^{12} +6.75369 q^{13} +3.98093 q^{14} -4.18202 q^{15} +1.00000 q^{16} +1.91590 q^{17} +0.117367 q^{18} +6.53145 q^{19} +2.46315 q^{20} +6.75895 q^{21} +3.98953 q^{22} +3.45914 q^{23} +1.69783 q^{24} +1.06711 q^{25} -6.75369 q^{26} +5.29276 q^{27} -3.98093 q^{28} -1.06413 q^{29} +4.18202 q^{30} -10.6557 q^{31} -1.00000 q^{32} +6.77355 q^{33} -1.91590 q^{34} -9.80563 q^{35} -0.117367 q^{36} +1.48999 q^{37} -6.53145 q^{38} -11.4666 q^{39} -2.46315 q^{40} -0.603470 q^{41} -6.75895 q^{42} -12.5763 q^{43} -3.98953 q^{44} -0.289092 q^{45} -3.45914 q^{46} +4.82901 q^{47} -1.69783 q^{48} +8.84780 q^{49} -1.06711 q^{50} -3.25288 q^{51} +6.75369 q^{52} -12.1441 q^{53} -5.29276 q^{54} -9.82681 q^{55} +3.98093 q^{56} -11.0893 q^{57} +1.06413 q^{58} -5.34100 q^{59} -4.18202 q^{60} +11.0084 q^{61} +10.6557 q^{62} +0.467228 q^{63} +1.00000 q^{64} +16.6353 q^{65} -6.77355 q^{66} +3.80142 q^{67} +1.91590 q^{68} -5.87304 q^{69} +9.80563 q^{70} +10.7649 q^{71} +0.117367 q^{72} -7.23149 q^{73} -1.48999 q^{74} -1.81177 q^{75} +6.53145 q^{76} +15.8820 q^{77} +11.4666 q^{78} -17.6866 q^{79} +2.46315 q^{80} -8.63413 q^{81} +0.603470 q^{82} +2.26007 q^{83} +6.75895 q^{84} +4.71915 q^{85} +12.5763 q^{86} +1.80671 q^{87} +3.98953 q^{88} +14.6525 q^{89} +0.289092 q^{90} -26.8859 q^{91} +3.45914 q^{92} +18.0915 q^{93} -4.82901 q^{94} +16.0879 q^{95} +1.69783 q^{96} -5.72593 q^{97} -8.84780 q^{98} +0.468238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9}+O(q^{10}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9	\( 42 q - 42 q^{2} + 42 q^{4} + 27 q^{5} - 10 q^{7} - 42 q^{8} + 56 q^{9} - 27 q^{10} + 23 q^{11} + 15 q^{13} + 10 q^{14} + 6 q^{15} + 42 q^{16} + 14 q^{17} - 56 q^{18} - 4 q^{19} + 27 q^{20} + 26 q^{21} - 23 q^{22} + 12 q^{23} + 45 q^{25} - 15 q^{26} - 3 q^{27} - 10 q^{28} + 41 q^{29} - 6 q^{30} + 18 q^{31} - 42 q^{32} + 25 q^{33} - 14 q^{34} + 8 q^{35} + 56 q^{36} + 33 q^{37} + 4 q^{38} + 10 q^{39} - 27 q^{40} + 84 q^{41} - 26 q^{42} - 36 q^{43} + 23 q^{44} + 66 q^{45} - 12 q^{46} + 28 q^{47} + 58 q^{49} - 45 q^{50} + 17 q^{51} + 15 q^{52} + 68 q^{53} + 3 q^{54} - 28 q^{55} + 10 q^{56} - 9 q^{57} - 41 q^{58} + 59 q^{59} + 6 q^{60} + 41 q^{61} - 18 q^{62} - 28 q^{63} + 42 q^{64} + 44 q^{65} - 25 q^{66} + 14 q^{68} + 67 q^{69} - 8 q^{70} + 69 q^{71} - 56 q^{72} - 27 q^{73} - 33 q^{74} + 14 q^{75} - 4 q^{76} + 43 q^{77} - 10 q^{78} - 19 q^{79} + 27 q^{80} + 74 q^{81} - 84 q^{82} + 20 q^{83} + 26 q^{84} + 16 q^{85} + 36 q^{86} - 28 q^{87} - 23 q^{88} + 123 q^{89} - 66 q^{90} - 9 q^{91} + 12 q^{92} + 48 q^{93} - 28 q^{94} + 28 q^{95} + 10 q^{97} - 58 q^{98} + 75 q^{99}+O(q^{100}) \) 42 * q - 42 * q^2 + 42 * q^4 + 27 * q^5 - 10 * q^7 - 42 * q^8 + 56 * q^9 - 27 * q^10 + 23 * q^11 + 15 * q^13 + 10 * q^14 + 6 * q^15 + 42 * q^16 + 14 * q^17 - 56 * q^18 - 4 * q^19 + 27 * q^20 + 26 * q^21 - 23 * q^22 + 12 * q^23 + 45 * q^25 - 15 * q^26 - 3 * q^27 - 10 * q^28 + 41 * q^29 - 6 * q^30 + 18 * q^31 - 42 * q^32 + 25 * q^33 - 14 * q^34 + 8 * q^35 + 56 * q^36 + 33 * q^37 + 4 * q^38 + 10 * q^39 - 27 * q^40 + 84 * q^41 - 26 * q^42 - 36 * q^43 + 23 * q^44 + 66 * q^45 - 12 * q^46 + 28 * q^47 + 58 * q^49 - 45 * q^50 + 17 * q^51 + 15 * q^52 + 68 * q^53 + 3 * q^54 - 28 * q^55 + 10 * q^56 - 9 * q^57 - 41 * q^58 + 59 * q^59 + 6 * q^60 + 41 * q^61 - 18 * q^62 - 28 * q^63 + 42 * q^64 + 44 * q^65 - 25 * q^66 + 14 * q^68 + 67 * q^69 - 8 * q^70 + 69 * q^71 - 56 * q^72 - 27 * q^73 - 33 * q^74 + 14 * q^75 - 4 * q^76 + 43 * q^77 - 10 * q^78 - 19 * q^79 + 27 * q^80 + 74 * q^81 - 84 * q^82 + 20 * q^83 + 26 * q^84 + 16 * q^85 + 36 * q^86 - 28 * q^87 - 23 * q^88 + 123 * q^89 - 66 * q^90 - 9 * q^91 + 12 * q^92 + 48 * q^93 - 28 * q^94 + 28 * q^95 + 10 * q^97 - 58 * q^98 + 75 * q^99

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