LMFDB - Embedded newform 6046.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, 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("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$0$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.23522 q^{3} +1.00000 q^{4} -0.854459 q^{5} -1.23522 q^{6} +4.26002 q^{7} +1.00000 q^{8} -1.47423 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.23522 q^{3} +1.00000 q^{4} -0.854459 q^{5} -1.23522 q^{6} +4.26002 q^{7} +1.00000 q^{8} -1.47423 q^{9} -0.854459 q^{10} +4.13667 q^{11} -1.23522 q^{12} -5.17948 q^{13} +4.26002 q^{14} +1.05544 q^{15} +1.00000 q^{16} +4.83037 q^{17} -1.47423 q^{18} -5.48399 q^{19} -0.854459 q^{20} -5.26207 q^{21} +4.13667 q^{22} +5.47930 q^{23} -1.23522 q^{24} -4.26990 q^{25} -5.17948 q^{26} +5.52666 q^{27} +4.26002 q^{28} -0.234899 q^{29} +1.05544 q^{30} +4.50440 q^{31} +1.00000 q^{32} -5.10970 q^{33} +4.83037 q^{34} -3.64001 q^{35} -1.47423 q^{36} +10.9315 q^{37} -5.48399 q^{38} +6.39780 q^{39} -0.854459 q^{40} -10.0024 q^{41} -5.26207 q^{42} +0.532706 q^{43} +4.13667 q^{44} +1.25967 q^{45} +5.47930 q^{46} -8.38175 q^{47} -1.23522 q^{48} +11.1478 q^{49} -4.26990 q^{50} -5.96657 q^{51} -5.17948 q^{52} +13.1414 q^{53} +5.52666 q^{54} -3.53461 q^{55} +4.26002 q^{56} +6.77394 q^{57} -0.234899 q^{58} -4.07580 q^{59} +1.05544 q^{60} +7.14272 q^{61} +4.50440 q^{62} -6.28026 q^{63} +1.00000 q^{64} +4.42565 q^{65} -5.10970 q^{66} +11.0582 q^{67} +4.83037 q^{68} -6.76814 q^{69} -3.64001 q^{70} +1.35717 q^{71} -1.47423 q^{72} +1.42244 q^{73} +10.9315 q^{74} +5.27427 q^{75} -5.48399 q^{76} +17.6223 q^{77} +6.39780 q^{78} +5.33037 q^{79} -0.854459 q^{80} -2.40396 q^{81} -10.0024 q^{82} -10.4134 q^{83} -5.26207 q^{84} -4.12735 q^{85} +0.532706 q^{86} +0.290152 q^{87} +4.13667 q^{88} -12.5980 q^{89} +1.25967 q^{90} -22.0647 q^{91} +5.47930 q^{92} -5.56393 q^{93} -8.38175 q^{94} +4.68585 q^{95} -1.23522 q^{96} +14.3998 q^{97} +11.1478 q^{98} -6.09840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * 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
$3$	−1.23522	−0.713155	−0.356577	−	0.934266i	$-0.616056\pi$
$3$	−1.23522	−0.713155	−0.356577	+	0.934266i	$0.616056\pi$
$4$	1.00000	0.500000
$5$	−0.854459	−0.382125	−0.191063	−	0.981578i	$-0.561193\pi$
$5$	−0.854459	−0.382125	−0.191063	+	0.981578i	$0.561193\pi$
$6$	−1.23522	−0.504277
$7$	4.26002	1.61014	0.805069	−	0.593181i	$-0.202128\pi$
$7$	4.26002	1.61014	0.805069	+	0.593181i	$0.202128\pi$
$8$	1.00000	0.353553
$9$	−1.47423	−0.491410
$10$	−0.854459	−0.270204
$11$	4.13667	1.24725	0.623626	−	0.781723i	$-0.285659\pi$
$11$	4.13667	1.24725	0.623626	+	0.781723i	$0.285659\pi$
$12$	−1.23522	−0.356577
$13$	−5.17948	−1.43653	−0.718264	−	0.695771i	$-0.755063\pi$
$13$	−5.17948	−1.43653	−0.718264	+	0.695771i	$0.755063\pi$
$14$	4.26002	1.13854
$15$	1.05544	0.272515
$16$	1.00000	0.250000
$17$	4.83037	1.17154	0.585768	−	0.810478i	$-0.300793\pi$
$17$	4.83037	1.17154	0.585768	+	0.810478i	$0.300793\pi$
$18$	−1.47423	−0.347479
$19$	−5.48399	−1.25811	−0.629057	−	0.777359i	$-0.716559\pi$
$19$	−5.48399	−1.25811	−0.629057	+	0.777359i	$0.716559\pi$
$20$	−0.854459	−0.191063
$21$	−5.26207	−1.14828
$22$	4.13667	0.881941
$23$	5.47930	1.14251	0.571256	−	0.820772i	$-0.306456\pi$
$23$	5.47930	1.14251	0.571256	+	0.820772i	$0.306456\pi$
$24$	−1.23522	−0.252138
$25$	−4.26990	−0.853980
$26$	−5.17948	−1.01578
$27$	5.52666	1.06361
$28$	4.26002	0.805069
$29$	−0.234899	−0.0436196	−0.0218098	−	0.999762i	$-0.506943\pi$
$29$	−0.234899	−0.0436196	−0.0218098	+	0.999762i	$0.506943\pi$
$30$	1.05544	0.192697
$31$	4.50440	0.809015	0.404507	−	0.914535i	$-0.367443\pi$
$31$	4.50440	0.809015	0.404507	+	0.914535i	$0.367443\pi$
$32$	1.00000	0.176777
$33$	−5.10970	−0.889485
$34$	4.83037	0.828402
$35$	−3.64001	−0.615275
$36$	−1.47423	−0.245705
$37$	10.9315	1.79714	0.898568	−	0.438835i	$-0.144609\pi$
$37$	10.9315	1.79714	0.898568	+	0.438835i	$0.144609\pi$
$38$	−5.48399	−0.889621
$39$	6.39780	1.02447
$40$	−0.854459	−0.135102
$41$	−10.0024	−1.56211	−0.781055	−	0.624462i	$-0.785318\pi$
$41$	−10.0024	−1.56211	−0.781055	+	0.624462i	$0.785318\pi$
$42$	−5.26207	−0.811955
$43$	0.532706	0.0812369	0.0406185	−	0.999175i	$-0.487067\pi$
$43$	0.532706	0.0812369	0.0406185	+	0.999175i	$0.487067\pi$
$44$	4.13667	0.623626
$45$	1.25967	0.187780
$46$	5.47930	0.807879
$47$	−8.38175	−1.22260	−0.611302	−	0.791397i	$-0.709354\pi$
$47$	−8.38175	−1.22260	−0.611302	+	0.791397i	$0.709354\pi$
$48$	−1.23522	−0.178289
$49$	11.1478	1.59254
$50$	−4.26990	−0.603855
$51$	−5.96657	−0.835487
$52$	−5.17948	−0.718264
$53$	13.1414	1.80511	0.902554	−	0.430578i	$-0.141690\pi$
$53$	13.1414	1.80511	0.902554	+	0.430578i	$0.141690\pi$
$54$	5.52666	0.752083
$55$	−3.53461	−0.476607
$56$	4.26002	0.569270
$57$	6.77394	0.897231
$58$	−0.234899	−0.0308437
$59$	−4.07580	−0.530625	−0.265312	−	0.964163i	$-0.585475\pi$
$59$	−4.07580	−0.530625	−0.265312	+	0.964163i	$0.585475\pi$
$60$	1.05544	0.136257
$61$	7.14272	0.914531	0.457266	−	0.889330i	$-0.348829\pi$
$61$	7.14272	0.914531	0.457266	+	0.889330i	$0.348829\pi$
$62$	4.50440	0.572060
$63$	−6.28026	−0.791238
$64$	1.00000	0.125000
$65$	4.42565	0.548934
$66$	−5.10970	−0.628961
$67$	11.0582	1.35097	0.675485	−	0.737374i	$-0.263934\pi$
$67$	11.0582	1.35097	0.675485	+	0.737374i	$0.263934\pi$
$68$	4.83037	0.585768
$69$	−6.76814	−0.814789
$70$	−3.64001	−0.435065
$71$	1.35717	0.161067	0.0805334	−	0.996752i	$-0.474338\pi$
$71$	1.35717	0.161067	0.0805334	+	0.996752i	$0.474338\pi$
$72$	−1.47423	−0.173740
$73$	1.42244	0.166484	0.0832418	−	0.996529i	$-0.473473\pi$
$73$	1.42244	0.166484	0.0832418	+	0.996529i	$0.473473\pi$
$74$	10.9315	1.27077
$75$	5.27427	0.609020
$76$	−5.48399	−0.629057
$77$	17.6223	2.00825
$78$	6.39780	0.724408
$79$	5.33037	0.599714	0.299857	−	0.953984i	$-0.403061\pi$
$79$	5.33037	0.599714	0.299857	+	0.953984i	$0.403061\pi$
$80$	−0.854459	−0.0955314
$81$	−2.40396	−0.267106
$82$	−10.0024	−1.10458
$83$	−10.4134	−1.14302	−0.571509	−	0.820596i	$-0.693642\pi$
$83$	−10.4134	−1.14302	−0.571509	+	0.820596i	$0.693642\pi$
$84$	−5.26207	−0.574139
$85$	−4.12735	−0.447674
$86$	0.532706	0.0574432
$87$	0.290152	0.0311075
$88$	4.13667	0.440970
$89$	−12.5980	−1.33539	−0.667693	−	0.744437i	$-0.732718\pi$
$89$	−12.5980	−1.33539	−0.667693	+	0.744437i	$0.732718\pi$
$90$	1.25967	0.132781
$91$	−22.0647	−2.31301
$92$	5.47930	0.571256
$93$	−5.56393	−0.576953
$94$	−8.38175	−0.864512
$95$	4.68585	0.480758
$96$	−1.23522	−0.126069
$97$	14.3998	1.46207	0.731037	−	0.682338i	$-0.239037\pi$
$97$	14.3998	1.46207	0.731037	+	0.682338i	$0.239037\pi$
$98$	11.1478	1.12610
$99$	−6.09840	−0.612913
$100$	−4.26990	−0.426990
$101$	3.61824	0.360029	0.180014	−	0.983664i	$-0.442386\pi$
$101$	3.61824	0.360029	0.180014	+	0.983664i	$0.442386\pi$
$102$	−5.96657	−0.590779
$103$	−18.8516	−1.85751	−0.928753	−	0.370699i	$-0.879118\pi$
$103$	−18.8516	−1.85751	−0.928753	+	0.370699i	$0.879118\pi$
$104$	−5.17948	−0.507889
$105$	4.49622	0.438786
$106$	13.1414	1.27640
$107$	−12.0843	−1.16824	−0.584118	−	0.811669i	$-0.698560\pi$
$107$	−12.0843	−1.16824	−0.584118	+	0.811669i	$0.698560\pi$
$108$	5.52666	0.531803
$109$	5.46055	0.523025	0.261513	−	0.965200i	$-0.415779\pi$
$109$	5.46055	0.523025	0.261513	+	0.965200i	$0.415779\pi$
$110$	−3.53461	−0.337012
$111$	−13.5029	−1.28164
$112$	4.26002	0.402534
$113$	11.9461	1.12380	0.561899	−	0.827206i	$-0.310071\pi$
$113$	11.9461	1.12380	0.561899	+	0.827206i	$0.310071\pi$
$114$	6.77394	0.634438
$115$	−4.68183	−0.436583
$116$	−0.234899	−0.0218098
$117$	7.63574	0.705924
$118$	−4.07580	−0.375208
$119$	20.5775	1.88634
$120$	1.05544	0.0963485
$121$	6.11204	0.555640
$122$	7.14272	0.646671
$123$	12.3552	1.11403
$124$	4.50440	0.404507
$125$	7.92075	0.708453
$126$	−6.28026	−0.559490
$127$	−7.58526	−0.673083	−0.336541	−	0.941669i	$-0.609257\pi$
$127$	−7.58526	−0.673083	−0.336541	+	0.941669i	$0.609257\pi$
$128$	1.00000	0.0883883
$129$	−0.658010	−0.0579345
$130$	4.42565	0.388155
$131$	17.2996	1.51147	0.755737	−	0.654875i	$-0.227279\pi$
$131$	17.2996	1.51147	0.755737	+	0.654875i	$0.227279\pi$
$132$	−5.10970	−0.444742
$133$	−23.3620	−2.02574
$134$	11.0582	0.955280
$135$	−4.72230	−0.406431
$136$	4.83037	0.414201
$137$	15.9139	1.35962	0.679810	−	0.733388i	$-0.262062\pi$
$137$	15.9139	1.35962	0.679810	+	0.733388i	$0.262062\pi$
$138$	−6.76814	−0.576143
$139$	−7.55284	−0.640623	−0.320312	−	0.947312i	$-0.603788\pi$
$139$	−7.55284	−0.640623	−0.320312	+	0.947312i	$0.603788\pi$
$140$	−3.64001	−0.307637
$141$	10.3533	0.871906
$142$	1.35717	0.113891
$143$	−21.4258	−1.79171
$144$	−1.47423	−0.122853
$145$	0.200711	0.0166681
$146$	1.42244	0.117722
$147$	−13.7700	−1.13573
$148$	10.9315	0.898568
$149$	−15.8375	−1.29746	−0.648730	−	0.761019i	$-0.724699\pi$
$149$	−15.8375	−1.29746	−0.648730	+	0.761019i	$0.724699\pi$
$150$	5.27427	0.430642
$151$	9.74842	0.793315	0.396657	−	0.917967i	$-0.370170\pi$
$151$	9.74842	0.793315	0.396657	+	0.917967i	$0.370170\pi$
$152$	−5.48399	−0.444811
$153$	−7.12108	−0.575705
$154$	17.6223	1.42005
$155$	−3.84883	−0.309145
$156$	6.39780	0.512234
$157$	15.4521	1.23321	0.616606	−	0.787272i	$-0.288507\pi$
$157$	15.4521	1.23321	0.616606	+	0.787272i	$0.288507\pi$
$158$	5.33037	0.424062
$159$	−16.2325	−1.28732
$160$	−0.854459	−0.0675509
$161$	23.3419	1.83960
$162$	−2.40396	−0.188873
$163$	21.3935	1.67567	0.837834	−	0.545925i	$-0.183822\pi$
$163$	21.3935	1.67567	0.837834	+	0.545925i	$0.183822\pi$
$164$	−10.0024	−0.781055
$165$	4.36603	0.339895
$166$	−10.4134	−0.808235
$167$	4.86303	0.376312	0.188156	−	0.982139i	$-0.439749\pi$
$167$	4.86303	0.376312	0.188156	+	0.982139i	$0.439749\pi$
$168$	−5.26207	−0.405978
$169$	13.8270	1.06361
$170$	−4.12735	−0.316553
$171$	8.08467	0.618250
$172$	0.532706	0.0406185
$173$	−5.94847	−0.452254	−0.226127	−	0.974098i	$-0.572606\pi$
$173$	−5.94847	−0.452254	−0.226127	+	0.974098i	$0.572606\pi$
$174$	0.290152	0.0219963
$175$	−18.1899	−1.37503
$176$	4.13667	0.311813
$177$	5.03452	0.378418
$178$	−12.5980	−0.944260
$179$	16.3176	1.21964	0.609818	−	0.792541i	$-0.291242\pi$
$179$	16.3176	1.21964	0.609818	+	0.792541i	$0.291242\pi$
$180$	1.25967	0.0938901
$181$	3.57147	0.265465	0.132733	−	0.991152i	$-0.457625\pi$
$181$	3.57147	0.265465	0.132733	+	0.991152i	$0.457625\pi$
$182$	−22.0647	−1.63554
$183$	−8.82283	−0.652202
$184$	5.47930	0.403939
$185$	−9.34055	−0.686731
$186$	−5.56393	−0.407967
$187$	19.9816	1.46120
$188$	−8.38175	−0.611302
$189$	23.5437	1.71255
$190$	4.68585	0.339947
$191$	−26.8152	−1.94028	−0.970140	−	0.242548i	$-0.922017\pi$
$191$	−26.8152	−1.94028	−0.970140	+	0.242548i	$0.922017\pi$
$192$	−1.23522	−0.0891444
$193$	2.84229	0.204592	0.102296	−	0.994754i	$-0.467381\pi$
$193$	2.84229	0.204592	0.102296	+	0.994754i	$0.467381\pi$
$194$	14.3998	1.03384
$195$	−5.46665	−0.391475
$196$	11.1478	0.796272
$197$	3.30483	0.235460	0.117730	−	0.993046i	$-0.462438\pi$
$197$	3.30483	0.235460	0.117730	+	0.993046i	$0.462438\pi$
$198$	−6.09840	−0.433395
$199$	−19.7286	−1.39852	−0.699261	−	0.714867i	$-0.746487\pi$
$199$	−19.7286	−1.39852	−0.699261	+	0.714867i	$0.746487\pi$
$200$	−4.26990	−0.301928
$201$	−13.6593	−0.963451
$202$	3.61824	0.254579
$203$	−1.00067	−0.0702335
$204$	−5.96657	−0.417744
$205$	8.54663	0.596922
$206$	−18.8516	−1.31346
$207$	−8.07775	−0.561442
$208$	−5.17948	−0.359132
$209$	−22.6855	−1.56919
$210$	4.49622	0.310269
$211$	9.19328	0.632891	0.316446	−	0.948611i	$-0.397511\pi$
$211$	9.19328	0.632891	0.316446	+	0.948611i	$0.397511\pi$
$212$	13.1414	0.902554
$213$	−1.67641	−0.114866
$214$	−12.0843	−0.826068
$215$	−0.455175	−0.0310427
$216$	5.52666	0.376042
$217$	19.1889	1.30263
$218$	5.46055	0.369835
$219$	−1.75702	−0.118729
$220$	−3.53461	−0.238304
$221$	−25.0188	−1.68295
$222$	−13.5029	−0.906253
$223$	−3.80568	−0.254847	−0.127424	−	0.991848i	$-0.540671\pi$
$223$	−3.80568	−0.254847	−0.127424	+	0.991848i	$0.540671\pi$
$224$	4.26002	0.284635
$225$	6.29482	0.419654
$226$	11.9461	0.794646
$227$	24.4865	1.62522	0.812612	−	0.582806i	$-0.198045\pi$
$227$	24.4865	1.62522	0.812612	+	0.582806i	$0.198045\pi$
$228$	6.77394	0.448615
$229$	−22.4241	−1.48183	−0.740913	−	0.671601i	$-0.765607\pi$
$229$	−22.4241	−1.48183	−0.740913	+	0.671601i	$0.765607\pi$
$230$	−4.68183	−0.308711
$231$	−21.7674	−1.43219
$232$	−0.234899	−0.0154218
$233$	21.9133	1.43558	0.717792	−	0.696257i	$-0.245153\pi$
$233$	21.9133	1.43558	0.717792	+	0.696257i	$0.245153\pi$
$234$	7.63574	0.499164
$235$	7.16186	0.467188
$236$	−4.07580	−0.265312
$237$	−6.58419	−0.427689
$238$	20.5775	1.33384
$239$	10.1851	0.658819	0.329410	−	0.944187i	$-0.393150\pi$
$239$	10.1851	0.658819	0.329410	+	0.944187i	$0.393150\pi$
$240$	1.05544	0.0681287
$241$	−22.3443	−1.43932	−0.719661	−	0.694326i	$-0.755703\pi$
$241$	−22.3443	−1.43932	−0.719661	+	0.694326i	$0.755703\pi$
$242$	6.11204	0.392897
$243$	−13.6106	−0.873118
$244$	7.14272	0.457266
$245$	−9.52534	−0.608552
$246$	12.3552	0.787736
$247$	28.4042	1.80732
$248$	4.50440	0.286030
$249$	12.8628	0.815148
$250$	7.92075	0.500952
$251$	19.6752	1.24189	0.620944	−	0.783855i	$-0.286749\pi$
$251$	19.6752	1.24189	0.620944	+	0.783855i	$0.286749\pi$
$252$	−6.28026	−0.395619
$253$	22.6660	1.42500
$254$	−7.58526	−0.475941
$255$	5.09819	0.319261
$256$	1.00000	0.0625000
$257$	20.3163	1.26729	0.633647	−	0.773622i	$-0.281557\pi$
$257$	20.3163	1.26729	0.633647	+	0.773622i	$0.281557\pi$
$258$	−0.658010	−0.0409659
$259$	46.5687	2.89364
$260$	4.42565	0.274467
$261$	0.346295	0.0214351
$262$	17.2996	1.06877
$263$	0.436136	0.0268933	0.0134466	−	0.999910i	$-0.495720\pi$
$263$	0.436136	0.0268933	0.0134466	+	0.999910i	$0.495720\pi$
$264$	−5.10970	−0.314480
$265$	−11.2288	−0.689777
$266$	−23.3620	−1.43241
$267$	15.5613	0.952337
$268$	11.0582	0.675485
$269$	11.1140	0.677630	0.338815	−	0.940853i	$-0.389974\pi$
$269$	11.1140	0.677630	0.338815	+	0.940853i	$0.389974\pi$
$270$	−4.72230	−0.287390
$271$	6.01786	0.365559	0.182779	−	0.983154i	$-0.441491\pi$
$271$	6.01786	0.365559	0.182779	+	0.983154i	$0.441491\pi$
$272$	4.83037	0.292884
$273$	27.2548	1.64953
$274$	15.9139	0.961397
$275$	−17.6632	−1.06513
$276$	−6.76814	−0.407394
$277$	1.48783	0.0893950	0.0446975	−	0.999001i	$-0.485768\pi$
$277$	1.48783	0.0893950	0.0446975	+	0.999001i	$0.485768\pi$
$278$	−7.55284	−0.452989
$279$	−6.64053	−0.397558
$280$	−3.64001	−0.217532
$281$	−19.2209	−1.14662	−0.573311	−	0.819338i	$-0.694341\pi$
$281$	−19.2209	−1.14662	−0.573311	+	0.819338i	$0.694341\pi$
$282$	10.3533	0.616531
$283$	30.6142	1.81982	0.909912	−	0.414801i	$-0.136149\pi$
$283$	30.6142	1.81982	0.909912	+	0.414801i	$0.136149\pi$
$284$	1.35717	0.0805334
$285$	−5.78805	−0.342855
$286$	−21.4258	−1.26693
$287$	−42.6104	−2.51521
$288$	−1.47423	−0.0868698
$289$	6.33248	0.372499
$290$	0.200711	0.0117862
$291$	−17.7869	−1.04269
$292$	1.42244	0.0832418
$293$	4.46791	0.261018	0.130509	−	0.991447i	$-0.458339\pi$
$293$	4.46791	0.261018	0.130509	+	0.991447i	$0.458339\pi$
$294$	−13.7700	−0.803083
$295$	3.48261	0.202765
$296$	10.9315	0.635383
$297$	22.8620	1.32659
$298$	−15.8375	−0.917442
$299$	−28.3799	−1.64125
$300$	5.27427	0.304510
$301$	2.26934	0.130803
$302$	9.74842	0.560958
$303$	−4.46933	−0.256756
$304$	−5.48399	−0.314529
$305$	−6.10316	−0.349466
$306$	−7.12108	−0.407085
$307$	24.5752	1.40258	0.701291	−	0.712875i	$-0.252607\pi$
$307$	24.5752	1.40258	0.701291	+	0.712875i	$0.252607\pi$
$308$	17.6223	1.00412
$309$	23.2859	1.32469
$310$	−3.84883	−0.218599
$311$	11.2027	0.635248	0.317624	−	0.948217i	$-0.397115\pi$
$311$	11.2027	0.635248	0.317624	+	0.948217i	$0.397115\pi$
$312$	6.39780	0.362204
$313$	−16.8358	−0.951618	−0.475809	−	0.879549i	$-0.657845\pi$
$313$	−16.8358	−0.951618	−0.475809	+	0.879549i	$0.657845\pi$
$314$	15.4521	0.872013
$315$	5.36622	0.302352
$316$	5.33037	0.299857
$317$	−11.3663	−0.638394	−0.319197	−	0.947688i	$-0.603413\pi$
$317$	−11.3663	−0.638394	−0.319197	+	0.947688i	$0.603413\pi$
$318$	−16.2325	−0.910273
$319$	−0.971698	−0.0544046
$320$	−0.854459	−0.0477657
$321$	14.9268	0.833133
$322$	23.3419	1.30080
$323$	−26.4897	−1.47393
$324$	−2.40396	−0.133553
$325$	22.1158	1.22677
$326$	21.3935	1.18488
$327$	−6.74498	−0.372998
$328$	−10.0024	−0.552290
$329$	−35.7065	−1.96856
$330$	4.36603	0.240342
$331$	0.225515	0.0123954	0.00619772	−	0.999981i	$-0.498027\pi$
$331$	0.225515	0.0123954	0.00619772	+	0.999981i	$0.498027\pi$
$332$	−10.4134	−0.571509
$333$	−16.1156	−0.883130
$334$	4.86303	0.266093
$335$	−9.44875	−0.516240
$336$	−5.26207	−0.287069
$337$	5.20286	0.283418	0.141709	−	0.989908i	$-0.454740\pi$
$337$	5.20286	0.283418	0.141709	+	0.989908i	$0.454740\pi$
$338$	13.8270	0.752088
$339$	−14.7561	−0.801442
$340$	−4.12735	−0.223837
$341$	18.6332	1.00905
$342$	8.08467	0.437169
$343$	17.6698	0.954078
$344$	0.532706	0.0287216
$345$	5.78310	0.311351
$346$	−5.94847	−0.319792
$347$	12.7275	0.683246	0.341623	−	0.939837i	$-0.389023\pi$
$347$	12.7275	0.683246	0.341623	+	0.939837i	$0.389023\pi$
$348$	0.290152	0.0155538
$349$	11.6419	0.623176	0.311588	−	0.950217i	$-0.399139\pi$
$349$	11.6419	0.623176	0.311588	+	0.950217i	$0.399139\pi$
$350$	−18.1899	−0.972290
$351$	−28.6252	−1.52790
$352$	4.13667	0.220485
$353$	27.8187	1.48064	0.740321	−	0.672253i	$-0.234673\pi$
$353$	27.8187	1.48064	0.740321	+	0.672253i	$0.234673\pi$
$354$	5.03452	0.267582
$355$	−1.15965	−0.0615478
$356$	−12.5980	−0.667693
$357$	−25.4177	−1.34525
$358$	16.3176	0.862413
$359$	−10.9962	−0.580360	−0.290180	−	0.956972i	$-0.593715\pi$
$359$	−10.9962	−0.580360	−0.290180	+	0.956972i	$0.593715\pi$
$360$	1.25967	0.0663904
$361$	11.0742	0.582852
$362$	3.57147	0.187712
$363$	−7.54971	−0.396257
$364$	−22.0647	−1.15650
$365$	−1.21541	−0.0636176
$366$	−8.82283	−0.461177
$367$	34.3535	1.79324	0.896620	−	0.442802i	$-0.146015\pi$
$367$	34.3535	1.79324	0.896620	+	0.442802i	$0.146015\pi$
$368$	5.47930	0.285628
$369$	14.7458	0.767637
$370$	−9.34055	−0.485592
$371$	55.9826	2.90647
$372$	−5.56393	−0.288476
$373$	−6.24331	−0.323266	−0.161633	−	0.986851i	$-0.551676\pi$
$373$	−6.24331	−0.323266	−0.161633	+	0.986851i	$0.551676\pi$
$374$	19.9816	1.03323
$375$	−9.78387	−0.505237
$376$	−8.38175	−0.432256
$377$	1.21665	0.0626607
$378$	23.5437	1.21096
$379$	−5.31542	−0.273035	−0.136517	−	0.990638i	$-0.543591\pi$
$379$	−5.31542	−0.273035	−0.136517	+	0.990638i	$0.543591\pi$
$380$	4.68585	0.240379
$381$	9.36947	0.480012
$382$	−26.8152	−1.37198
$383$	12.4634	0.636852	0.318426	−	0.947948i	$-0.396846\pi$
$383$	12.4634	0.636852	0.318426	+	0.947948i	$0.396846\pi$
$384$	−1.23522	−0.0630346
$385$	−15.0575	−0.767403
$386$	2.84229	0.144669
$387$	−0.785332	−0.0399206
$388$	14.3998	0.731037
$389$	5.93900	0.301119	0.150560	−	0.988601i	$-0.451892\pi$
$389$	5.93900	0.301119	0.150560	+	0.988601i	$0.451892\pi$
$390$	−5.46665	−0.276815
$391$	26.4670	1.33850
$392$	11.1478	0.563049
$393$	−21.3688	−1.07792
$394$	3.30483	0.166495
$395$	−4.55458	−0.229166
$396$	−6.09840	−0.306456
$397$	2.92461	0.146782	0.0733909	−	0.997303i	$-0.476618\pi$
$397$	2.92461	0.146782	0.0733909	+	0.997303i	$0.476618\pi$
$398$	−19.7286	−0.988904
$399$	28.8572	1.44467
$400$	−4.26990	−0.213495
$401$	−23.4525	−1.17116	−0.585580	−	0.810614i	$-0.699133\pi$
$401$	−23.4525	−1.17116	−0.585580	+	0.810614i	$0.699133\pi$
$402$	−13.6593	−0.681263
$403$	−23.3305	−1.16217
$404$	3.61824	0.180014
$405$	2.05408	0.102068
$406$	−1.00067	−0.0496626
$407$	45.2202	2.24148
$408$	−5.96657	−0.295389
$409$	−11.9837	−0.592556	−0.296278	−	0.955102i	$-0.595745\pi$
$409$	−11.9837	−0.592556	−0.296278	+	0.955102i	$0.595745\pi$
$410$	8.54663	0.422088
$411$	−19.6572	−0.969620
$412$	−18.8516	−0.928753
$413$	−17.3630	−0.854379
$414$	−8.07775	−0.397000
$415$	8.89780	0.436776
$416$	−5.17948	−0.253945
$417$	9.32942	0.456864
$418$	−22.6855	−1.10958
$419$	2.73152	0.133443	0.0667217	−	0.997772i	$-0.478746\pi$
$419$	2.73152	0.133443	0.0667217	+	0.997772i	$0.478746\pi$
$420$	4.49622	0.219393
$421$	−8.19491	−0.399396	−0.199698	−	0.979858i	$-0.563996\pi$
$421$	−8.19491	−0.399396	−0.199698	+	0.979858i	$0.563996\pi$
$422$	9.19328	0.447522
$423$	12.3566	0.600800
$424$	13.1414	0.638202
$425$	−20.6252	−1.00047
$426$	−1.67641	−0.0812223
$427$	30.4281	1.47252
$428$	−12.0843	−0.584118
$429$	26.4656	1.27777
$430$	−0.455175	−0.0219505
$431$	36.2587	1.74652	0.873260	−	0.487254i	$-0.162002\pi$
$431$	36.2587	1.74652	0.873260	+	0.487254i	$0.162002\pi$
$432$	5.52666	0.265902
$433$	40.2075	1.93225	0.966125	−	0.258076i	$-0.0830884\pi$
$433$	40.2075	1.93225	0.966125	+	0.258076i	$0.0830884\pi$
$434$	19.1889	0.921095
$435$	−0.247922	−0.0118870
$436$	5.46055	0.261513
$437$	−30.0484	−1.43741
$438$	−1.75702	−0.0839538
$439$	10.2002	0.486829	0.243415	−	0.969922i	$-0.421732\pi$
$439$	10.2002	0.486829	0.243415	+	0.969922i	$0.421732\pi$
$440$	−3.53461	−0.168506
$441$	−16.4344	−0.782592
$442$	−25.0188	−1.19002
$443$	−25.7627	−1.22402	−0.612010	−	0.790850i	$-0.709639\pi$
$443$	−25.7627	−1.22402	−0.612010	+	0.790850i	$0.709639\pi$
$444$	−13.5029	−0.640818
$445$	10.7645	0.510285
$446$	−3.80568	−0.180204
$447$	19.5628	0.925289
$448$	4.26002	0.201267
$449$	−31.9705	−1.50878	−0.754390	−	0.656427i	$-0.772067\pi$
$449$	−31.9705	−1.50878	−0.754390	+	0.656427i	$0.772067\pi$
$450$	6.29482	0.296740
$451$	−41.3766	−1.94835
$452$	11.9461	0.561899
$453$	−12.0414	−0.565756
$454$	24.4865	1.14921
$455$	18.8534	0.883860
$456$	6.77394	0.317219
$457$	−40.4230	−1.89091	−0.945453	−	0.325758i	$-0.894381\pi$
$457$	−40.4230	−1.89091	−0.945453	+	0.325758i	$0.894381\pi$
$458$	−22.4241	−1.04781
$459$	26.6958	1.24605
$460$	−4.68183	−0.218292
$461$	−14.1015	−0.656773	−0.328387	−	0.944543i	$-0.606505\pi$
$461$	−14.1015	−0.656773	−0.328387	+	0.944543i	$0.606505\pi$
$462$	−21.7674	−1.01271
$463$	−23.5190	−1.09302	−0.546509	−	0.837453i	$-0.684044\pi$
$463$	−23.5190	−1.09302	−0.546509	+	0.837453i	$0.684044\pi$
$464$	−0.234899	−0.0109049
$465$	4.75415	0.220468
$466$	21.9133	1.01511
$467$	−4.79873	−0.222059	−0.111029	−	0.993817i	$-0.535415\pi$
$467$	−4.79873	−0.222059	−0.111029	+	0.993817i	$0.535415\pi$
$468$	7.63574	0.352962
$469$	47.1081	2.17525
$470$	7.16186	0.330352
$471$	−19.0868	−0.879472
$472$	−4.07580	−0.187604
$473$	2.20363	0.101323
$474$	−6.58419	−0.302422
$475$	23.4161	1.07440
$476$	20.5775	0.943168
$477$	−19.3734	−0.887048
$478$	10.1851	0.465855
$479$	−15.0147	−0.686038	−0.343019	−	0.939328i	$-0.611450\pi$
$479$	−15.0147	−0.686038	−0.343019	+	0.939328i	$0.611450\pi$
$480$	1.05544	0.0481742
$481$	−56.6197	−2.58164
$482$	−22.3443	−1.01775
$483$	−28.8325	−1.31192
$484$	6.11204	0.277820
$485$	−12.3040	−0.558696
$486$	−13.6106	−0.617388
$487$	−18.8463	−0.854006	−0.427003	−	0.904250i	$-0.640431\pi$
$487$	−18.8463	−0.854006	−0.427003	+	0.904250i	$0.640431\pi$
$488$	7.14272	0.323336
$489$	−26.4257	−1.19501
$490$	−9.52534	−0.430311
$491$	21.4284	0.967048	0.483524	−	0.875331i	$-0.339357\pi$
$491$	21.4284	0.967048	0.483524	+	0.875331i	$0.339357\pi$
$492$	12.3552	0.557013
$493$	−1.13465	−0.0511019
$494$	28.4042	1.27797
$495$	5.21083	0.234209
$496$	4.50440	0.202254
$497$	5.78159	0.259340
$498$	12.8628	0.576397
$499$	6.31315	0.282616	0.141308	−	0.989966i	$-0.454869\pi$
$499$	6.31315	0.282616	0.141308	+	0.989966i	$0.454869\pi$
$500$	7.92075	0.354227
$501$	−6.00691	−0.268369
$502$	19.6752	0.878148
$503$	−28.8976	−1.28848	−0.644240	−	0.764823i	$-0.722826\pi$
$503$	−28.8976	−1.28848	−0.644240	+	0.764823i	$0.722826\pi$
$504$	−6.28026	−0.279745
$505$	−3.09164	−0.137576
$506$	22.6660	1.00763
$507$	−17.0794	−0.758521
$508$	−7.58526	−0.336541
$509$	18.4253	0.816686	0.408343	−	0.912829i	$-0.366107\pi$
$509$	18.4253	0.816686	0.408343	+	0.912829i	$0.366107\pi$
$510$	5.09819	0.225752
$511$	6.05961	0.268062
$512$	1.00000	0.0441942
$513$	−30.3082	−1.33814
$514$	20.3163	0.896112
$515$	16.1079	0.709801
$516$	−0.658010	−0.0289673
$517$	−34.6725	−1.52490
$518$	46.5687	2.04611
$519$	7.34768	0.322527
$520$	4.42565	0.194077
$521$	43.2425	1.89449	0.947245	−	0.320510i	$-0.103854\pi$
$521$	43.2425	1.89449	0.947245	+	0.320510i	$0.103854\pi$
$522$	0.346295	0.0151569
$523$	−19.5626	−0.855414	−0.427707	−	0.903918i	$-0.640678\pi$
$523$	−19.5626	−0.855414	−0.427707	+	0.903918i	$0.640678\pi$
$524$	17.2996	0.755737
$525$	22.4685	0.980606
$526$	0.436136	0.0190164
$527$	21.7579	0.947791
$528$	−5.10970	−0.222371
$529$	7.02272	0.305335
$530$	−11.2288	−0.487746
$531$	6.00867	0.260754
$532$	−23.3620	−1.01287
$533$	51.8071	2.24402
$534$	15.5613	0.673404
$535$	10.3256	0.446413
$536$	11.0582	0.477640
$537$	−20.1559	−0.869790
$538$	11.1140	0.479157
$539$	46.1148	1.98631
$540$	−4.72230	−0.203216
$541$	−19.7120	−0.847486	−0.423743	−	0.905782i	$-0.639284\pi$
$541$	−19.7120	−0.847486	−0.423743	+	0.905782i	$0.639284\pi$
$542$	6.01786	0.258489
$543$	−4.41155	−0.189318
$544$	4.83037	0.207100
$545$	−4.66581	−0.199861
$546$	27.2548	1.16640
$547$	−22.9734	−0.982272	−0.491136	−	0.871083i	$-0.663418\pi$
$547$	−22.9734	−0.982272	−0.491136	+	0.871083i	$0.663418\pi$
$548$	15.9139	0.679810
$549$	−10.5300	−0.449410
$550$	−17.6632	−0.753160
$551$	1.28818	0.0548784
$552$	−6.76814	−0.288071
$553$	22.7075	0.965622
$554$	1.48783	0.0632118
$555$	11.5376	0.489746
$556$	−7.55284	−0.320312
$557$	0.518772	0.0219811	0.0109905	−	0.999940i	$-0.496502\pi$
$557$	0.518772	0.0219811	0.0109905	+	0.999940i	$0.496502\pi$
$558$	−6.64053	−0.281116
$559$	−2.75914	−0.116699
$560$	−3.64001	−0.153819
$561$	−24.6817	−1.04206
$562$	−19.2209	−0.810784
$563$	−0.353280	−0.0148890	−0.00744449	−	0.999972i	$-0.502370\pi$
$563$	−0.353280	−0.0148890	−0.00744449	+	0.999972i	$0.502370\pi$
$564$	10.3533	0.435953
$565$	−10.2075	−0.429432
$566$	30.6142	1.28681
$567$	−10.2409	−0.430078
$568$	1.35717	0.0569457
$569$	8.87309	0.371979	0.185990	−	0.982552i	$-0.440451\pi$
$569$	8.87309	0.371979	0.185990	+	0.982552i	$0.440451\pi$
$570$	−5.78805	−0.242435
$571$	−39.6933	−1.66111	−0.830557	−	0.556933i	$-0.811978\pi$
$571$	−39.6933	−1.66111	−0.830557	+	0.556933i	$0.811978\pi$
$572$	−21.4258	−0.895857
$573$	33.1227	1.38372
$574$	−42.6104	−1.77852
$575$	−23.3961	−0.975683
$576$	−1.47423	−0.0614263
$577$	15.4902	0.644864	0.322432	−	0.946593i	$-0.395500\pi$
$577$	15.4902	0.644864	0.322432	+	0.946593i	$0.395500\pi$
$578$	6.33248	0.263396
$579$	−3.51085	−0.145906
$580$	0.200711	0.00833407
$581$	−44.3613	−1.84042
$582$	−17.7869	−0.737290
$583$	54.3615	2.25142
$584$	1.42244	0.0588608
$585$	−6.52442	−0.269752
$586$	4.46791	0.184568
$587$	22.8380	0.942626	0.471313	−	0.881966i	$-0.343780\pi$
$587$	22.8380	0.942626	0.471313	+	0.881966i	$0.343780\pi$
$588$	−13.7700	−0.567865
$589$	−24.7021	−1.01783
$590$	3.48261	0.143377
$591$	−4.08220	−0.167919
$592$	10.9315	0.449284
$593$	14.5350	0.596882	0.298441	−	0.954428i	$-0.403533\pi$
$593$	14.5350	0.596882	0.298441	+	0.954428i	$0.403533\pi$
$594$	22.8620	0.938038
$595$	−17.5826	−0.720817
$596$	−15.8375	−0.648730
$597$	24.3691	0.997363
$598$	−28.3799	−1.16054
$599$	16.7339	0.683728	0.341864	−	0.939749i	$-0.388942\pi$
$599$	16.7339	0.683728	0.341864	+	0.939749i	$0.388942\pi$
$600$	5.27427	0.215321
$601$	−39.1849	−1.59838	−0.799192	−	0.601076i	$-0.794739\pi$
$601$	−39.1849	−1.59838	−0.799192	+	0.601076i	$0.794739\pi$
$602$	2.26934	0.0924915
$603$	−16.3023	−0.663880
$604$	9.74842	0.396657
$605$	−5.22248	−0.212324
$606$	−4.46933	−0.181554
$607$	0.117311	0.00476152	0.00238076	−	0.999997i	$-0.499242\pi$
$607$	0.117311	0.00476152	0.00238076	+	0.999997i	$0.499242\pi$
$608$	−5.48399	−0.222405
$609$	1.23605	0.0500874
$610$	−6.10316	−0.247110
$611$	43.4131	1.75631
$612$	−7.12108	−0.287853
$613$	1.07806	0.0435425	0.0217713	−	0.999763i	$-0.493069\pi$
$613$	1.07806	0.0435425	0.0217713	+	0.999763i	$0.493069\pi$
$614$	24.5752	0.991775
$615$	−10.5570	−0.425698
$616$	17.6223	0.710023
$617$	3.70215	0.149043	0.0745215	−	0.997219i	$-0.476257\pi$
$617$	3.70215	0.149043	0.0745215	+	0.997219i	$0.476257\pi$
$618$	23.2859	0.936697
$619$	15.2567	0.613220	0.306610	−	0.951835i	$-0.400805\pi$
$619$	15.2567	0.613220	0.306610	+	0.951835i	$0.400805\pi$
$620$	−3.84883	−0.154573
$621$	30.2822	1.21518
$622$	11.2027	0.449188
$623$	−53.6678	−2.15015
$624$	6.39780	0.256117
$625$	14.5816	0.583262
$626$	−16.8358	−0.672895
$627$	28.0216	1.11907
$628$	15.4521	0.616606
$629$	52.8034	2.10541
$630$	5.36622	0.213795
$631$	−41.3159	−1.64476	−0.822381	−	0.568938i	$-0.807355\pi$
$631$	−41.3159	−1.64476	−0.822381	+	0.568938i	$0.807355\pi$
$632$	5.33037	0.212031
$633$	−11.3557	−0.451350
$634$	−11.3663	−0.451413
$635$	6.48129	0.257202
$636$	−16.2325	−0.643661
$637$	−57.7398	−2.28773
$638$	−0.971698	−0.0384699
$639$	−2.00079	−0.0791499
$640$	−0.854459	−0.0337754
$641$	−4.38392	−0.173154	−0.0865772	−	0.996245i	$-0.527593\pi$
$641$	−4.38392	−0.173154	−0.0865772	+	0.996245i	$0.527593\pi$
$642$	14.9268	0.589114
$643$	21.2825	0.839299	0.419649	−	0.907686i	$-0.362153\pi$
$643$	21.2825	0.839299	0.419649	+	0.907686i	$0.362153\pi$
$644$	23.3419	0.919802
$645$	0.562242	0.0221383
$646$	−26.4897	−1.04222
$647$	−22.2220	−0.873638	−0.436819	−	0.899549i	$-0.643895\pi$
$647$	−22.2220	−0.873638	−0.436819	+	0.899549i	$0.643895\pi$
$648$	−2.40396	−0.0944363
$649$	−16.8603	−0.661823
$650$	22.1158	0.867455
$651$	−23.7025	−0.928974
$652$	21.3935	0.837834
$653$	23.1357	0.905370	0.452685	−	0.891670i	$-0.350466\pi$
$653$	23.1357	0.905370	0.452685	+	0.891670i	$0.350466\pi$
$654$	−6.74498	−0.263750
$655$	−14.7818	−0.577573
$656$	−10.0024	−0.390528
$657$	−2.09700	−0.0818117
$658$	−35.7065	−1.39198
$659$	−4.93560	−0.192264	−0.0961318	−	0.995369i	$-0.530647\pi$
$659$	−4.93560	−0.192264	−0.0961318	+	0.995369i	$0.530647\pi$
$660$	4.36603	0.169947
$661$	26.2394	1.02060	0.510298	−	0.859998i	$-0.329535\pi$
$661$	26.2394	1.02060	0.510298	+	0.859998i	$0.329535\pi$
$662$	0.225515	0.00876490
$663$	30.9037	1.20020
$664$	−10.4134	−0.404118
$665$	19.9618	0.774086
$666$	−16.1156	−0.624467
$667$	−1.28708	−0.0498359
$668$	4.86303	0.188156
$669$	4.70086	0.181746
$670$	−9.44875	−0.365037
$671$	29.5471	1.14065
$672$	−5.26207	−0.202989
$673$	18.0680	0.696471	0.348235	−	0.937407i	$-0.386781\pi$
$673$	18.0680	0.696471	0.348235	+	0.937407i	$0.386781\pi$
$674$	5.20286	0.200407
$675$	−23.5983	−0.908299
$676$	13.8270	0.531807
$677$	−15.7670	−0.605974	−0.302987	−	0.952995i	$-0.597984\pi$
$677$	−15.7670	−0.605974	−0.302987	+	0.952995i	$0.597984\pi$
$678$	−14.7561	−0.566705
$679$	61.3433	2.35414
$680$	−4.12735	−0.158277
$681$	−30.2462	−1.15904
$682$	18.6332	0.713503
$683$	−8.15502	−0.312043	−0.156021	−	0.987754i	$-0.549867\pi$
$683$	−8.15502	−0.312043	−0.156021	+	0.987754i	$0.549867\pi$
$684$	8.08467	0.309125
$685$	−13.5978	−0.519546
$686$	17.6698	0.674635
$687$	27.6987	1.05677
$688$	0.532706	0.0203092
$689$	−68.0655	−2.59309
$690$	5.78310	0.220159
$691$	−39.7123	−1.51073	−0.755364	−	0.655305i	$-0.772540\pi$
$691$	−39.7123	−1.51073	−0.755364	+	0.655305i	$0.772540\pi$
$692$	−5.94847	−0.226127
$693$	−25.9793	−0.986874
$694$	12.7275	0.483128
$695$	6.45358	0.244798
$696$	0.290152	0.0109982
$697$	−48.3152	−1.83007
$698$	11.6419	0.440652
$699$	−27.0677	−1.02379
$700$	−18.1899	−0.687513
$701$	−19.8010	−0.747874	−0.373937	−	0.927454i	$-0.621992\pi$
$701$	−19.8010	−0.747874	−0.373937	+	0.927454i	$0.621992\pi$
$702$	−28.6252	−1.08039
$703$	−59.9485	−2.26100
$704$	4.13667	0.155907
$705$	−8.84648	−0.333178
$706$	27.8187	1.04697
$707$	15.4138	0.579696
$708$	5.03452	0.189209
$709$	38.9917	1.46436	0.732181	−	0.681110i	$-0.238502\pi$
$709$	38.9917	1.46436	0.732181	+	0.681110i	$0.238502\pi$
$710$	−1.15965	−0.0435208
$711$	−7.85819	−0.294705
$712$	−12.5980	−0.472130
$713$	24.6810	0.924310
$714$	−25.4177	−0.951235
$715$	18.3074	0.684660
$716$	16.3176	0.609818
$717$	−12.5808	−0.469840
$718$	−10.9962	−0.410376
$719$	−16.2314	−0.605329	−0.302664	−	0.953097i	$-0.597876\pi$
$719$	−16.2314	−0.605329	−0.302664	+	0.953097i	$0.597876\pi$
$720$	1.25967	0.0469451
$721$	−80.3084	−2.99084
$722$	11.0742	0.412139
$723$	27.6001	1.02646
$724$	3.57147	0.132733
$725$	1.00299	0.0372502
$726$	−7.54971	−0.280196
$727$	−26.2416	−0.973246	−0.486623	−	0.873612i	$-0.661771\pi$
$727$	−26.2416	−0.973246	−0.486623	+	0.873612i	$0.661771\pi$
$728$	−22.0647	−0.817772
$729$	24.0239	0.889775
$730$	−1.21541	−0.0449845
$731$	2.57317	0.0951721
$732$	−8.82283	−0.326101
$733$	−6.13633	−0.226651	−0.113325	−	0.993558i	$-0.536150\pi$
$733$	−6.13633	−0.226651	−0.113325	+	0.993558i	$0.536150\pi$
$734$	34.3535	1.26801
$735$	11.7659	0.433992
$736$	5.47930	0.201970
$737$	45.7440	1.68500
$738$	14.7458	0.542801
$739$	−20.9880	−0.772057	−0.386029	−	0.922487i	$-0.626153\pi$
$739$	−20.9880	−0.772057	−0.386029	+	0.922487i	$0.626153\pi$
$740$	−9.34055	−0.343366
$741$	−35.0855	−1.28890
$742$	55.9826	2.05519
$743$	−39.1312	−1.43559	−0.717793	−	0.696257i	$-0.754848\pi$
$743$	−39.1312	−1.43559	−0.717793	+	0.696257i	$0.754848\pi$
$744$	−5.56393	−0.203984
$745$	13.5325	0.495792
$746$	−6.24331	−0.228584
$747$	15.3517	0.561690
$748$	19.9816	0.730601
$749$	−51.4795	−1.88102
$750$	−9.78387	−0.357256
$751$	−4.66159	−0.170104	−0.0850518	−	0.996377i	$-0.527106\pi$
$751$	−4.66159	−0.170104	−0.0850518	+	0.996377i	$0.527106\pi$
$752$	−8.38175	−0.305651
$753$	−24.3032	−0.885659
$754$	1.21665	0.0443078
$755$	−8.32962	−0.303146
$756$	23.5437	0.856277
$757$	−24.9501	−0.906826	−0.453413	−	0.891300i	$-0.649794\pi$
$757$	−24.9501	−0.906826	−0.453413	+	0.891300i	$0.649794\pi$
$758$	−5.31542	−0.193065
$759$	−27.9976	−1.01625
$760$	4.68585	0.169973
$761$	−44.1557	−1.60064	−0.800322	−	0.599570i	$-0.795338\pi$
$761$	−44.1557	−1.60064	−0.800322	+	0.599570i	$0.795338\pi$
$762$	9.36947	0.339420
$763$	23.2621	0.842143
$764$	−26.8152	−0.970140
$765$	6.08467	0.219992
$766$	12.4634	0.450322
$767$	21.1105	0.762257
$768$	−1.23522	−0.0445722
$769$	−16.7529	−0.604126	−0.302063	−	0.953288i	$-0.597675\pi$
$769$	−16.7529	−0.604126	−0.302063	+	0.953288i	$0.597675\pi$
$770$	−15.0575	−0.542636
$771$	−25.0951	−0.903777
$772$	2.84229	0.102296
$773$	48.6881	1.75119	0.875594	−	0.483047i	$-0.160470\pi$
$773$	48.6881	1.75119	0.875594	+	0.483047i	$0.160470\pi$
$774$	−0.785332	−0.0282282
$775$	−19.2334	−0.690883
$776$	14.3998	0.516921
$777$	−57.5226	−2.06361
$778$	5.93900	0.212924
$779$	54.8530	1.96531
$780$	−5.46665	−0.195738
$781$	5.61418	0.200891
$782$	26.4670	0.946460
$783$	−1.29820	−0.0463940
$784$	11.1478	0.398136
$785$	−13.2032	−0.471242
$786$	−21.3688	−0.762201
$787$	−29.4526	−1.04987	−0.524936	−	0.851142i	$-0.675911\pi$
$787$	−29.4526	−1.04987	−0.524936	+	0.851142i	$0.675911\pi$
$788$	3.30483	0.117730
$789$	−0.538724	−0.0191791
$790$	−4.55458	−0.162045
$791$	50.8909	1.80947
$792$	−6.09840	−0.216697
$793$	−36.9955	−1.31375
$794$	2.92461	0.103790
$795$	13.8700	0.491918
$796$	−19.7286	−0.699261
$797$	−48.8905	−1.73179	−0.865895	−	0.500226i	$-0.833250\pi$
$797$	−48.8905	−1.73179	−0.865895	+	0.500226i	$0.833250\pi$
$798$	28.8572	1.02153
$799$	−40.4870	−1.43233
$800$	−4.26990	−0.150964
$801$	18.5723	0.656222
$802$	−23.4525	−0.828136
$803$	5.88415	0.207647
$804$	−13.6593	−0.481726
$805$	−19.9447	−0.702959
$806$	−23.3305	−0.821780
$807$	−13.7282	−0.483255
$808$	3.61824	0.127289
$809$	−25.4715	−0.895530	−0.447765	−	0.894151i	$-0.647780\pi$
$809$	−25.4715	−0.895530	−0.447765	+	0.894151i	$0.647780\pi$
$810$	2.05408	0.0721730
$811$	−20.3193	−0.713509	−0.356754	−	0.934198i	$-0.616117\pi$
$811$	−20.3193	−0.713509	−0.356754	+	0.934198i	$0.616117\pi$
$812$	−1.00067	−0.0351168
$813$	−7.43338	−0.260700
$814$	45.2202	1.58497
$815$	−18.2799	−0.640315
$816$	−5.96657	−0.208872
$817$	−2.92136	−0.102205
$818$	−11.9837	−0.419000
$819$	32.5284	1.13664
$820$	8.54663	0.298461
$821$	1.40103	0.0488963	0.0244482	−	0.999701i	$-0.492217\pi$
$821$	1.40103	0.0488963	0.0244482	+	0.999701i	$0.492217\pi$
$822$	−19.6572	−0.685625
$823$	−19.1980	−0.669199	−0.334599	−	0.942360i	$-0.608601\pi$
$823$	−19.1980	−0.669199	−0.334599	+	0.942360i	$0.608601\pi$
$824$	−18.8516	−0.656728
$825$	21.8179	0.759602
$826$	−17.3630	−0.604137
$827$	31.1865	1.08446	0.542230	−	0.840230i	$-0.317580\pi$
$827$	31.1865	1.08446	0.542230	+	0.840230i	$0.317580\pi$
$828$	−8.07775	−0.280721
$829$	0.913746	0.0317357	0.0158678	−	0.999874i	$-0.494949\pi$
$829$	0.913746	0.0317357	0.0158678	+	0.999874i	$0.494949\pi$
$830$	8.89780	0.308847
$831$	−1.83780	−0.0637525
$832$	−5.17948	−0.179566
$833$	53.8481	1.86572
$834$	9.32942	0.323051
$835$	−4.15526	−0.143799
$836$	−22.6855	−0.784593
$837$	24.8943	0.860473
$838$	2.73152	0.0943588
$839$	−44.3494	−1.53111	−0.765555	−	0.643370i	$-0.777536\pi$
$839$	−44.3494	−1.53111	−0.765555	+	0.643370i	$0.777536\pi$
$840$	4.49622	0.155134
$841$	−28.9448	−0.998097
$842$	−8.19491	−0.282415
$843$	23.7420	0.817719
$844$	9.19328	0.316446
$845$	−11.8146	−0.406434
$846$	12.3566	0.424830
$847$	26.0374	0.894657
$848$	13.1414	0.451277
$849$	−37.8153	−1.29782
$850$	−20.6252	−0.707439
$851$	59.8972	2.05325
$852$	−1.67641	−0.0574328
$853$	−0.860760	−0.0294719	−0.0147359	−	0.999891i	$-0.504691\pi$
$853$	−0.860760	−0.0294719	−0.0147359	+	0.999891i	$0.504691\pi$
$854$	30.4281	1.04123
$855$	−6.90801	−0.236249
$856$	−12.0843	−0.413034
$857$	39.9539	1.36480	0.682400	−	0.730979i	$-0.260936\pi$
$857$	39.9539	1.36480	0.682400	+	0.730979i	$0.260936\pi$
$858$	26.4656	0.903520
$859$	−54.1409	−1.84726	−0.923632	−	0.383280i	$-0.874794\pi$
$859$	−54.1409	−1.84726	−0.923632	+	0.383280i	$0.874794\pi$
$860$	−0.455175	−0.0155214
$861$	52.6333	1.79374
$862$	36.2587	1.23498
$863$	−3.54337	−0.120618	−0.0603088	−	0.998180i	$-0.519209\pi$
$863$	−3.54337	−0.120618	−0.0603088	+	0.998180i	$0.519209\pi$
$864$	5.52666	0.188021
$865$	5.08272	0.172818
$866$	40.2075	1.36631
$867$	−7.82201	−0.265649
$868$	19.1889	0.651313
$869$	22.0500	0.747995
$870$	−0.247922	−0.00840536
$871$	−57.2755	−1.94071
$872$	5.46055	0.184917
$873$	−21.2286	−0.718478
$874$	−30.0484	−1.01640
$875$	33.7426	1.14071
$876$	−1.75702	−0.0593643
$877$	47.7642	1.61288	0.806441	−	0.591315i	$-0.201391\pi$
$877$	47.7642	1.61288	0.806441	+	0.591315i	$0.201391\pi$
$878$	10.2002	0.344240
$879$	−5.51885	−0.186146
$880$	−3.53461	−0.119152
$881$	−19.7026	−0.663796	−0.331898	−	0.943315i	$-0.607689\pi$
$881$	−19.7026	−0.663796	−0.331898	+	0.943315i	$0.607689\pi$
$882$	−16.4344	−0.553376
$883$	−31.8984	−1.07347	−0.536733	−	0.843752i	$-0.680342\pi$
$883$	−31.8984	−1.07347	−0.536733	+	0.843752i	$0.680342\pi$
$884$	−25.0188	−0.841473
$885$	−4.30179	−0.144603
$886$	−25.7627	−0.865513
$887$	−44.7006	−1.50090	−0.750449	−	0.660928i	$-0.770163\pi$
$887$	−44.7006	−1.50090	−0.750449	+	0.660928i	$0.770163\pi$
$888$	−13.5029	−0.453127
$889$	−32.3134	−1.08376
$890$	10.7645	0.360826
$891$	−9.94437	−0.333149
$892$	−3.80568	−0.127424
$893$	45.9655	1.53818
$894$	19.5628	0.654278
$895$	−13.9427	−0.466054
$896$	4.26002	0.142317
$897$	35.0554	1.17047
$898$	−31.9705	−1.06687
$899$	−1.05808	−0.0352889
$900$	6.29482	0.209827
$901$	63.4777	2.11475
$902$	−41.3766	−1.37769
$903$	−2.80314	−0.0932826
$904$	11.9461	0.397323
$905$	−3.05167	−0.101441
$906$	−12.0414	−0.400050
$907$	10.4889	0.348278	0.174139	−	0.984721i	$-0.444286\pi$
$907$	10.4889	0.348278	0.174139	+	0.984721i	$0.444286\pi$
$908$	24.4865	0.812612
$909$	−5.33412	−0.176922
$910$	18.8534	0.624983
$911$	19.4195	0.643398	0.321699	−	0.946842i	$-0.395746\pi$
$911$	19.4195	0.643398	0.321699	+	0.946842i	$0.395746\pi$
$912$	6.77394	0.224308
$913$	−43.0767	−1.42563
$914$	−40.4230	−1.33707
$915$	7.53874	0.249223
$916$	−22.4241	−0.740913
$917$	73.6968	2.43368
$918$	26.6958	0.881093
$919$	−48.8721	−1.61214	−0.806071	−	0.591819i	$-0.798410\pi$
$919$	−48.8721	−1.61214	−0.806071	+	0.591819i	$0.798410\pi$
$920$	−4.68183	−0.154355
$921$	−30.3558	−1.00026
$922$	−14.1015	−0.464409
$923$	−7.02945	−0.231377
$924$	−21.7674	−0.716096
$925$	−46.6766	−1.53472
$926$	−23.5190	−0.772881
$927$	27.7916	0.912797
$928$	−0.234899	−0.00771092
$929$	−14.8347	−0.486711	−0.243356	−	0.969937i	$-0.578248\pi$
$929$	−14.8347	−0.486711	−0.243356	+	0.969937i	$0.578248\pi$
$930$	4.75415	0.155895
$931$	−61.1345	−2.00360
$932$	21.9133	0.717792
$933$	−13.8378	−0.453030
$934$	−4.79873	−0.157019
$935$	−17.0735	−0.558363
$936$	7.63574	0.249582
$937$	−6.63311	−0.216694	−0.108347	−	0.994113i	$-0.534556\pi$
$937$	−6.63311	−0.216694	−0.108347	+	0.994113i	$0.534556\pi$
$938$	47.1081	1.53813
$939$	20.7960	0.678651
$940$	7.16186	0.233594
$941$	12.9627	0.422573	0.211287	−	0.977424i	$-0.432235\pi$
$941$	12.9627	0.422573	0.211287	+	0.977424i	$0.432235\pi$
$942$	−19.0868	−0.621880
$943$	−54.8061	−1.78473
$944$	−4.07580	−0.132656
$945$	−20.1171	−0.654410
$946$	2.20363	0.0716462
$947$	−17.0567	−0.554268	−0.277134	−	0.960831i	$-0.589385\pi$
$947$	−17.0567	−0.554268	−0.277134	+	0.960831i	$0.589385\pi$
$948$	−6.58419	−0.213844
$949$	−7.36748	−0.239158
$950$	23.4161	0.759719
$951$	14.0399	0.455274
$952$	20.5775	0.666921
$953$	−29.2582	−0.947767	−0.473883	−	0.880588i	$-0.657148\pi$
$953$	−29.2582	−0.947767	−0.473883	+	0.880588i	$0.657148\pi$
$954$	−19.3734	−0.627237
$955$	22.9125	0.741430
$956$	10.1851	0.329410
$957$	1.20026	0.0387989
$958$	−15.0147	−0.485102
$959$	67.7938	2.18918
$960$	1.05544	0.0340643
$961$	−10.7103	−0.345495
$962$	−56.6197	−1.82549
$963$	17.8151	0.574083
$964$	−22.3443	−0.719661
$965$	−2.42862	−0.0781799
$966$	−28.8325	−0.927669
$967$	−53.1316	−1.70860	−0.854299	−	0.519782i	$-0.826013\pi$
$967$	−53.1316	−1.70860	−0.854299	+	0.519782i	$0.826013\pi$
$968$	6.11204	0.196448
$969$	32.7207	1.05114
$970$	−12.3040	−0.395057
$971$	−13.4644	−0.432093	−0.216047	−	0.976383i	$-0.569316\pi$
$971$	−13.4644	−0.432093	−0.216047	+	0.976383i	$0.569316\pi$
$972$	−13.6106	−0.436559
$973$	−32.1753	−1.03149
$974$	−18.8463	−0.603873
$975$	−27.3180	−0.874875
$976$	7.14272	0.228633
$977$	19.1461	0.612538	0.306269	−	0.951945i	$-0.400919\pi$
$977$	19.1461	0.612538	0.306269	+	0.951945i	$0.400919\pi$
$978$	−26.4257	−0.845000
$979$	−52.1138	−1.66556
$980$	−9.52534	−0.304276
$981$	−8.05010	−0.257020
$982$	21.4284	0.683806
$983$	−6.97697	−0.222531	−0.111265	−	0.993791i	$-0.535490\pi$
$983$	−6.97697	−0.222531	−0.111265	+	0.993791i	$0.535490\pi$
$984$	12.3552	0.393868
$985$	−2.82384	−0.0899751
$986$	−1.13465	−0.0361345
$987$	44.1054	1.40389
$988$	28.4042	0.903659
$989$	2.91886	0.0928142
$990$	5.21083	0.165611
$991$	12.5442	0.398481	0.199240	−	0.979951i	$-0.436153\pi$
$991$	12.5442	0.398481	0.199240	+	0.979951i	$0.436153\pi$
$992$	4.50440	0.143015
$993$	−0.278561	−0.00883987
$994$	5.78159	0.183381
$995$	16.8572	0.534411
$996$	12.8628	0.407574
$997$	−37.9490	−1.20186	−0.600929	−	0.799302i	$-0.705203\pi$
$997$	−37.9490	−1.20186	−0.600929	+	0.799302i	$0.705203\pi$
$998$	6.31315	0.199839
$999$	60.4150	1.91144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.f.1.20	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.f.1.20	✓	67	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.23522 q^{3} +1.00000 q^{4} -0.854459 q^{5} -1.23522 q^{6} +4.26002 q^{7} +1.00000 q^{8} -1.47423 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.23522 q^{3} +1.00000 q^{4} -0.854459 q^{5} -1.23522 q^{6} +4.26002 q^{7} +1.00000 q^{8} -1.47423 q^{9} -0.854459 q^{10} +4.13667 q^{11} -1.23522 q^{12} -5.17948 q^{13} +4.26002 q^{14} +1.05544 q^{15} +1.00000 q^{16} +4.83037 q^{17} -1.47423 q^{18} -5.48399 q^{19} -0.854459 q^{20} -5.26207 q^{21} +4.13667 q^{22} +5.47930 q^{23} -1.23522 q^{24} -4.26990 q^{25} -5.17948 q^{26} +5.52666 q^{27} +4.26002 q^{28} -0.234899 q^{29} +1.05544 q^{30} +4.50440 q^{31} +1.00000 q^{32} -5.10970 q^{33} +4.83037 q^{34} -3.64001 q^{35} -1.47423 q^{36} +10.9315 q^{37} -5.48399 q^{38} +6.39780 q^{39} -0.854459 q^{40} -10.0024 q^{41} -5.26207 q^{42} +0.532706 q^{43} +4.13667 q^{44} +1.25967 q^{45} +5.47930 q^{46} -8.38175 q^{47} -1.23522 q^{48} +11.1478 q^{49} -4.26990 q^{50} -5.96657 q^{51} -5.17948 q^{52} +13.1414 q^{53} +5.52666 q^{54} -3.53461 q^{55} +4.26002 q^{56} +6.77394 q^{57} -0.234899 q^{58} -4.07580 q^{59} +1.05544 q^{60} +7.14272 q^{61} +4.50440 q^{62} -6.28026 q^{63} +1.00000 q^{64} +4.42565 q^{65} -5.10970 q^{66} +11.0582 q^{67} +4.83037 q^{68} -6.76814 q^{69} -3.64001 q^{70} +1.35717 q^{71} -1.47423 q^{72} +1.42244 q^{73} +10.9315 q^{74} +5.27427 q^{75} -5.48399 q^{76} +17.6223 q^{77} +6.39780 q^{78} +5.33037 q^{79} -0.854459 q^{80} -2.40396 q^{81} -10.0024 q^{82} -10.4134 q^{83} -5.26207 q^{84} -4.12735 q^{85} +0.532706 q^{86} +0.290152 q^{87} +4.13667 q^{88} -12.5980 q^{89} +1.25967 q^{90} -22.0647 q^{91} +5.47930 q^{92} -5.56393 q^{93} -8.38175 q^{94} +4.68585 q^{95} -1.23522 q^{96} +14.3998 q^{97} +11.1478 q^{98} -6.09840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9	\( 67 q + 67 q^{2} + 21 q^{3} + 67 q^{4} + 21 q^{5} + 21 q^{6} + 38 q^{7} + 67 q^{8} + 90 q^{9} + 21 q^{10} + 56 q^{11} + 21 q^{12} + 33 q^{13} + 38 q^{14} + 25 q^{15} + 67 q^{16} + 30 q^{17} + 90 q^{18} + 36 q^{19} + 21 q^{20} + 20 q^{21} + 56 q^{22} + 65 q^{23} + 21 q^{24} + 72 q^{25} + 33 q^{26} + 57 q^{27} + 38 q^{28} + 84 q^{29} + 25 q^{30} + 52 q^{31} + 67 q^{32} - 9 q^{33} + 30 q^{34} + 30 q^{35} + 90 q^{36} + 52 q^{37} + 36 q^{38} + 41 q^{39} + 21 q^{40} + 46 q^{41} + 20 q^{42} + 61 q^{43} + 56 q^{44} + 23 q^{45} + 65 q^{46} + 51 q^{47} + 21 q^{48} + 81 q^{49} + 72 q^{50} + 33 q^{51} + 33 q^{52} + 72 q^{53} + 57 q^{54} + 14 q^{55} + 38 q^{56} - 26 q^{57} + 84 q^{58} + 71 q^{59} + 25 q^{60} + 42 q^{61} + 52 q^{62} + 63 q^{63} + 67 q^{64} - 2 q^{65} - 9 q^{66} + 70 q^{67} + 30 q^{68} + 21 q^{69} + 30 q^{70} + 104 q^{71} + 90 q^{72} - 31 q^{73} + 52 q^{74} + 69 q^{75} + 36 q^{76} + 48 q^{77} + 41 q^{78} + 79 q^{79} + 21 q^{80} + 123 q^{81} + 46 q^{82} + 41 q^{83} + 20 q^{84} + 6 q^{85} + 61 q^{86} + 19 q^{87} + 56 q^{88} + 58 q^{89} + 23 q^{90} + 31 q^{91} + 65 q^{92} + 13 q^{93} + 51 q^{94} + 77 q^{95} + 21 q^{96} - 8 q^{97} + 81 q^{98} + 129 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 + 21 * q^3 + 67 * q^4 + 21 * q^5 + 21 * q^6 + 38 * q^7 + 67 * q^8 + 90 * q^9 + 21 * q^10 + 56 * q^11 + 21 * q^12 + 33 * q^13 + 38 * q^14 + 25 * q^15 + 67 * q^16 + 30 * q^17 + 90 * q^18 + 36 * q^19 + 21 * q^20 + 20 * q^21 + 56 * q^22 + 65 * q^23 + 21 * q^24 + 72 * q^25 + 33 * q^26 + 57 * q^27 + 38 * q^28 + 84 * q^29 + 25 * q^30 + 52 * q^31 + 67 * q^32 - 9 * q^33 + 30 * q^34 + 30 * q^35 + 90 * q^36 + 52 * q^37 + 36 * q^38 + 41 * q^39 + 21 * q^40 + 46 * q^41 + 20 * q^42 + 61 * q^43 + 56 * q^44 + 23 * q^45 + 65 * q^46 + 51 * q^47 + 21 * q^48 + 81 * q^49 + 72 * q^50 + 33 * q^51 + 33 * q^52 + 72 * q^53 + 57 * q^54 + 14 * q^55 + 38 * q^56 - 26 * q^57 + 84 * q^58 + 71 * q^59 + 25 * q^60 + 42 * q^61 + 52 * q^62 + 63 * q^63 + 67 * q^64 - 2 * q^65 - 9 * q^66 + 70 * q^67 + 30 * q^68 + 21 * q^69 + 30 * q^70 + 104 * q^71 + 90 * q^72 - 31 * q^73 + 52 * q^74 + 69 * q^75 + 36 * q^76 + 48 * q^77 + 41 * q^78 + 79 * q^79 + 21 * q^80 + 123 * q^81 + 46 * q^82 + 41 * q^83 + 20 * q^84 + 6 * q^85 + 61 * q^86 + 19 * q^87 + 56 * q^88 + 58 * q^89 + 23 * q^90 + 31 * q^91 + 65 * q^92 + 13 * q^93 + 51 * q^94 + 77 * q^95 + 21 * q^96 - 8 * q^97 + 81 * q^98 + 129 * q^99

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