LMFDB - Embedded newform 6046.2.a.e.1.9

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:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.44881 q^{3} +1.00000 q^{4} +2.87933 q^{5} -2.44881 q^{6} -3.14262 q^{7} +1.00000 q^{8} +2.99666 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.44881 q^{3} +1.00000 q^{4} +2.87933 q^{5} -2.44881 q^{6} -3.14262 q^{7} +1.00000 q^{8} +2.99666 q^{9} +2.87933 q^{10} -3.58337 q^{11} -2.44881 q^{12} -2.44736 q^{13} -3.14262 q^{14} -7.05093 q^{15} +1.00000 q^{16} -0.485959 q^{17} +2.99666 q^{18} -1.70933 q^{19} +2.87933 q^{20} +7.69566 q^{21} -3.58337 q^{22} +6.28484 q^{23} -2.44881 q^{24} +3.29054 q^{25} -2.44736 q^{26} +0.00818672 q^{27} -3.14262 q^{28} +5.84498 q^{29} -7.05093 q^{30} +8.31794 q^{31} +1.00000 q^{32} +8.77498 q^{33} -0.485959 q^{34} -9.04863 q^{35} +2.99666 q^{36} +6.89647 q^{37} -1.70933 q^{38} +5.99312 q^{39} +2.87933 q^{40} -0.133244 q^{41} +7.69566 q^{42} +3.40114 q^{43} -3.58337 q^{44} +8.62837 q^{45} +6.28484 q^{46} -7.79529 q^{47} -2.44881 q^{48} +2.87604 q^{49} +3.29054 q^{50} +1.19002 q^{51} -2.44736 q^{52} -10.3214 q^{53} +0.00818672 q^{54} -10.3177 q^{55} -3.14262 q^{56} +4.18583 q^{57} +5.84498 q^{58} -12.2561 q^{59} -7.05093 q^{60} +11.8468 q^{61} +8.31794 q^{62} -9.41735 q^{63} +1.00000 q^{64} -7.04676 q^{65} +8.77498 q^{66} -3.32337 q^{67} -0.485959 q^{68} -15.3904 q^{69} -9.04863 q^{70} -13.8090 q^{71} +2.99666 q^{72} -0.396742 q^{73} +6.89647 q^{74} -8.05791 q^{75} -1.70933 q^{76} +11.2612 q^{77} +5.99312 q^{78} -12.4145 q^{79} +2.87933 q^{80} -9.01002 q^{81} -0.133244 q^{82} +1.89872 q^{83} +7.69566 q^{84} -1.39924 q^{85} +3.40114 q^{86} -14.3132 q^{87} -3.58337 q^{88} -9.24598 q^{89} +8.62837 q^{90} +7.69112 q^{91} +6.28484 q^{92} -20.3690 q^{93} -7.79529 q^{94} -4.92174 q^{95} -2.44881 q^{96} +8.08104 q^{97} +2.87604 q^{98} -10.7381 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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
$3$	−2.44881	−1.41382	−0.706910	−	0.707304i	$-0.749911\pi$
$3$	−2.44881	−1.41382	−0.706910	+	0.707304i	$0.749911\pi$
$4$	1.00000	0.500000
$5$	2.87933	1.28768	0.643838	−	0.765162i	$-0.277341\pi$
$5$	2.87933	1.28768	0.643838	+	0.765162i	$0.277341\pi$
$6$	−2.44881	−0.999721
$7$	−3.14262	−1.18780	−0.593899	−	0.804540i	$-0.702412\pi$
$7$	−3.14262	−1.18780	−0.593899	+	0.804540i	$0.702412\pi$
$8$	1.00000	0.353553
$9$	2.99666	0.998886
$10$	2.87933	0.910524
$11$	−3.58337	−1.08043	−0.540213	−	0.841528i	$-0.681656\pi$
$11$	−3.58337	−1.08043	−0.540213	+	0.841528i	$0.681656\pi$
$12$	−2.44881	−0.706910
$13$	−2.44736	−0.678776	−0.339388	−	0.940647i	$-0.610220\pi$
$13$	−2.44736	−0.678776	−0.339388	+	0.940647i	$0.610220\pi$
$14$	−3.14262	−0.839900
$15$	−7.05093	−1.82054
$16$	1.00000	0.250000
$17$	−0.485959	−0.117862	−0.0589312	−	0.998262i	$-0.518769\pi$
$17$	−0.485959	−0.117862	−0.0589312	+	0.998262i	$0.518769\pi$
$18$	2.99666	0.706319
$19$	−1.70933	−0.392148	−0.196074	−	0.980589i	$-0.562819\pi$
$19$	−1.70933	−0.392148	−0.196074	+	0.980589i	$0.562819\pi$
$20$	2.87933	0.643838
$21$	7.69566	1.67933
$22$	−3.58337	−0.763977
$23$	6.28484	1.31048	0.655239	−	0.755421i	$-0.272568\pi$
$23$	6.28484	1.31048	0.655239	+	0.755421i	$0.272568\pi$
$24$	−2.44881	−0.499861
$25$	3.29054	0.658109
$26$	−2.44736	−0.479967
$27$	0.00818672	0.00157554
$28$	−3.14262	−0.593899
$29$	5.84498	1.08539	0.542693	−	0.839931i	$-0.317405\pi$
$29$	5.84498	1.08539	0.542693	+	0.839931i	$0.317405\pi$
$30$	−7.05093	−1.28732
$31$	8.31794	1.49395	0.746973	−	0.664854i	$-0.231506\pi$
$31$	8.31794	1.49395	0.746973	+	0.664854i	$0.231506\pi$
$32$	1.00000	0.176777
$33$	8.77498	1.52753
$34$	−0.485959	−0.0833413
$35$	−9.04863	−1.52950
$36$	2.99666	0.499443
$37$	6.89647	1.13377	0.566886	−	0.823796i	$-0.308148\pi$
$37$	6.89647	1.13377	0.566886	+	0.823796i	$0.308148\pi$
$38$	−1.70933	−0.277291
$39$	5.99312	0.959666
$40$	2.87933	0.455262
$41$	−0.133244	−0.0208092	−0.0104046	−	0.999946i	$-0.503312\pi$
$41$	−0.133244	−0.0208092	−0.0104046	+	0.999946i	$0.503312\pi$
$42$	7.69566	1.18747
$43$	3.40114	0.518670	0.259335	−	0.965787i	$-0.416497\pi$
$43$	3.40114	0.518670	0.259335	+	0.965787i	$0.416497\pi$
$44$	−3.58337	−0.540213
$45$	8.62837	1.28624
$46$	6.28484	0.926648
$47$	−7.79529	−1.13706	−0.568530	−	0.822663i	$-0.692488\pi$
$47$	−7.79529	−1.13706	−0.568530	+	0.822663i	$0.692488\pi$
$48$	−2.44881	−0.353455
$49$	2.87604	0.410864
$50$	3.29054	0.465353
$51$	1.19002	0.166636
$52$	−2.44736	−0.339388
$53$	−10.3214	−1.41776	−0.708879	−	0.705331i	$-0.750799\pi$
$53$	−10.3214	−1.41776	−0.708879	+	0.705331i	$0.750799\pi$
$54$	0.00818672	0.00111407
$55$	−10.3177	−1.39124
$56$	−3.14262	−0.419950
$57$	4.18583	0.554427
$58$	5.84498	0.767484
$59$	−12.2561	−1.59561	−0.797804	−	0.602916i	$-0.794005\pi$
$59$	−12.2561	−1.59561	−0.797804	+	0.602916i	$0.794005\pi$
$60$	−7.05093	−0.910271
$61$	11.8468	1.51682	0.758411	−	0.651777i	$-0.225976\pi$
$61$	11.8468	1.51682	0.758411	+	0.651777i	$0.225976\pi$
$62$	8.31794	1.05638
$63$	−9.41735	−1.18647
$64$	1.00000	0.125000
$65$	−7.04676	−0.874043
$66$	8.77498	1.08012
$67$	−3.32337	−0.406014	−0.203007	−	0.979177i	$-0.565071\pi$
$67$	−3.32337	−0.406014	−0.203007	+	0.979177i	$0.565071\pi$
$68$	−0.485959	−0.0589312
$69$	−15.3904	−1.85278
$70$	−9.04863	−1.08152
$71$	−13.8090	−1.63883	−0.819413	−	0.573203i	$-0.805701\pi$
$71$	−13.8090	−1.63883	−0.819413	+	0.573203i	$0.805701\pi$
$72$	2.99666	0.353159
$73$	−0.396742	−0.0464352	−0.0232176	−	0.999730i	$-0.507391\pi$
$73$	−0.396742	−0.0464352	−0.0232176	+	0.999730i	$0.507391\pi$
$74$	6.89647	0.801698
$75$	−8.05791	−0.930447
$76$	−1.70933	−0.196074
$77$	11.2612	1.28333
$78$	5.99312	0.678587
$79$	−12.4145	−1.39674	−0.698370	−	0.715737i	$-0.746091\pi$
$79$	−12.4145	−1.39674	−0.698370	+	0.715737i	$0.746091\pi$
$80$	2.87933	0.321919
$81$	−9.01002	−1.00111
$82$	−0.133244	−0.0147143
$83$	1.89872	0.208412	0.104206	−	0.994556i	$-0.466770\pi$
$83$	1.89872	0.208412	0.104206	+	0.994556i	$0.466770\pi$
$84$	7.69566	0.839666
$85$	−1.39924	−0.151769
$86$	3.40114	0.366755
$87$	−14.3132	−1.53454
$88$	−3.58337	−0.381988
$89$	−9.24598	−0.980072	−0.490036	−	0.871702i	$-0.663016\pi$
$89$	−9.24598	−0.980072	−0.490036	+	0.871702i	$0.663016\pi$
$90$	8.62837	0.909510
$91$	7.69112	0.806248
$92$	6.28484	0.655239
$93$	−20.3690	−2.11217
$94$	−7.79529	−0.804022
$95$	−4.92174	−0.504960
$96$	−2.44881	−0.249930
$97$	8.08104	0.820505	0.410253	−	0.911972i	$-0.365440\pi$
$97$	8.08104	0.820505	0.410253	+	0.911972i	$0.365440\pi$
$98$	2.87604	0.290524
$99$	−10.7381	−1.07922
$100$	3.29054	0.329054
$101$	−6.11390	−0.608356	−0.304178	−	0.952615i	$-0.598382\pi$
$101$	−6.11390	−0.608356	−0.304178	+	0.952615i	$0.598382\pi$
$102$	1.19002	0.117830
$103$	−18.7681	−1.84928	−0.924638	−	0.380847i	$-0.875632\pi$
$103$	−18.7681	−1.84928	−0.924638	+	0.380847i	$0.875632\pi$
$104$	−2.44736	−0.239983
$105$	22.1584	2.16243
$106$	−10.3214	−1.00251
$107$	−11.9793	−1.15808	−0.579042	−	0.815298i	$-0.696573\pi$
$107$	−11.9793	−1.15808	−0.579042	+	0.815298i	$0.696573\pi$
$108$	0.00818672	0.000787768 0
$109$	−3.08904	−0.295876	−0.147938	−	0.988997i	$-0.547264\pi$
$109$	−3.08904	−0.295876	−0.147938	+	0.988997i	$0.547264\pi$
$110$	−10.3177	−0.983754
$111$	−16.8881	−1.60295
$112$	−3.14262	−0.296949
$113$	16.3673	1.53970	0.769852	−	0.638222i	$-0.220330\pi$
$113$	16.3673	1.53970	0.769852	+	0.638222i	$0.220330\pi$
$114$	4.18583	0.392039
$115$	18.0961	1.68747
$116$	5.84498	0.542693
$117$	−7.33390	−0.678019
$118$	−12.2561	−1.12827
$119$	1.52718	0.139997
$120$	−7.05093	−0.643659
$121$	1.84052	0.167320
$122$	11.8468	1.07255
$123$	0.326288	0.0294204
$124$	8.31794	0.746973
$125$	−4.92209	−0.440245
$126$	−9.41735	−0.838964
$127$	−10.3216	−0.915895	−0.457948	−	0.888979i	$-0.651415\pi$
$127$	−10.3216	−0.915895	−0.457948	+	0.888979i	$0.651415\pi$
$128$	1.00000	0.0883883
$129$	−8.32875	−0.733305
$130$	−7.04676	−0.618042
$131$	11.8612	1.03632	0.518158	−	0.855285i	$-0.326618\pi$
$131$	11.8612	1.03632	0.518158	+	0.855285i	$0.326618\pi$
$132$	8.77498	0.763764
$133$	5.37178	0.465793
$134$	−3.32337	−0.287095
$135$	0.0235723	0.00202878
$136$	−0.485959	−0.0416707
$137$	−1.10912	−0.0947589	−0.0473795	−	0.998877i	$-0.515087\pi$
$137$	−1.10912	−0.0947589	−0.0473795	+	0.998877i	$0.515087\pi$
$138$	−15.3904	−1.31011
$139$	−1.19293	−0.101183	−0.0505915	−	0.998719i	$-0.516111\pi$
$139$	−1.19293	−0.101183	−0.0505915	+	0.998719i	$0.516111\pi$
$140$	−9.04863	−0.764749
$141$	19.0892	1.60760
$142$	−13.8090	−1.15883
$143$	8.76979	0.733367
$144$	2.99666	0.249721
$145$	16.8296	1.39763
$146$	−0.396742	−0.0328346
$147$	−7.04288	−0.580887
$148$	6.89647	0.566886
$149$	−20.0727	−1.64442	−0.822209	−	0.569186i	$-0.807259\pi$
$149$	−20.0727	−1.64442	−0.822209	+	0.569186i	$0.807259\pi$
$150$	−8.05791	−0.657926
$151$	−8.77777	−0.714325	−0.357162	−	0.934042i	$-0.616256\pi$
$151$	−8.77777	−0.714325	−0.357162	+	0.934042i	$0.616256\pi$
$152$	−1.70933	−0.138645
$153$	−1.45625	−0.117731
$154$	11.2612	0.907450
$155$	23.9501	1.92372
$156$	5.99312	0.479833
$157$	4.93727	0.394037	0.197019	−	0.980400i	$-0.436874\pi$
$157$	4.93727	0.394037	0.197019	+	0.980400i	$0.436874\pi$
$158$	−12.4145	−0.987645
$159$	25.2752	2.00445
$160$	2.87933	0.227631
$161$	−19.7508	−1.55658
$162$	−9.01002	−0.707894
$163$	2.93231	0.229677	0.114838	−	0.993384i	$-0.463365\pi$
$163$	2.93231	0.229677	0.114838	+	0.993384i	$0.463365\pi$
$164$	−0.133244	−0.0104046
$165$	25.2661	1.96696
$166$	1.89872	0.147369
$167$	14.6497	1.13362	0.566812	−	0.823847i	$-0.308176\pi$
$167$	14.6497	1.13362	0.566812	+	0.823847i	$0.308176\pi$
$168$	7.69566	0.593733
$169$	−7.01042	−0.539263
$170$	−1.39924	−0.107317
$171$	−5.12229	−0.391711
$172$	3.40114	0.259335
$173$	−11.9772	−0.910608	−0.455304	−	0.890336i	$-0.650469\pi$
$173$	−11.9772	−0.910608	−0.455304	+	0.890336i	$0.650469\pi$
$174$	−14.3132	−1.08508
$175$	−10.3409	−0.781700
$176$	−3.58337	−0.270106
$177$	30.0128	2.25590
$178$	−9.24598	−0.693015
$179$	−13.4935	−1.00855	−0.504274	−	0.863544i	$-0.668240\pi$
$179$	−13.4935	−1.00855	−0.504274	+	0.863544i	$0.668240\pi$
$180$	8.62837	0.643120
$181$	−3.92575	−0.291799	−0.145899	−	0.989299i	$-0.546608\pi$
$181$	−3.92575	−0.291799	−0.145899	+	0.989299i	$0.546608\pi$
$182$	7.69112	0.570104
$183$	−29.0104	−2.14451
$184$	6.28484	0.463324
$185$	19.8572	1.45993
$186$	−20.3690	−1.49353
$187$	1.74137	0.127342
$188$	−7.79529	−0.568530
$189$	−0.0257277	−0.00187142
$190$	−4.92174	−0.357060
$191$	21.5097	1.55639	0.778194	−	0.628024i	$-0.216136\pi$
$191$	21.5097	1.55639	0.778194	+	0.628024i	$0.216136\pi$
$192$	−2.44881	−0.176727
$193$	−9.74815	−0.701687	−0.350844	−	0.936434i	$-0.614105\pi$
$193$	−9.74815	−0.701687	−0.350844	+	0.936434i	$0.614105\pi$
$194$	8.08104	0.580185
$195$	17.2562	1.23574
$196$	2.87604	0.205432
$197$	−19.4759	−1.38760	−0.693801	−	0.720167i	$-0.744065\pi$
$197$	−19.4759	−1.38760	−0.693801	+	0.720167i	$0.744065\pi$
$198$	−10.7381	−0.763125
$199$	−2.37529	−0.168380	−0.0841900	−	0.996450i	$-0.526830\pi$
$199$	−2.37529	−0.168380	−0.0841900	+	0.996450i	$0.526830\pi$
$200$	3.29054	0.232677
$201$	8.13829	0.574031
$202$	−6.11390	−0.430173
$203$	−18.3685	−1.28922
$204$	1.19002	0.0833181
$205$	−0.383653	−0.0267955
$206$	−18.7681	−1.30764
$207$	18.8335	1.30902
$208$	−2.44736	−0.169694
$209$	6.12517	0.423687
$210$	22.1584	1.52907
$211$	−23.3913	−1.61032	−0.805162	−	0.593055i	$-0.797921\pi$
$211$	−23.3913	−1.61032	−0.805162	+	0.593055i	$0.797921\pi$
$212$	−10.3214	−0.708879
$213$	33.8156	2.31701
$214$	−11.9793	−0.818888
$215$	9.79302	0.667878
$216$	0.00818672	0.000557036 0
$217$	−26.1401	−1.77451
$218$	−3.08904	−0.209216
$219$	0.971546	0.0656510
$220$	−10.3177	−0.695619
$221$	1.18932	0.0800022
$222$	−16.8881	−1.13346
$223$	−12.5669	−0.841545	−0.420772	−	0.907166i	$-0.638241\pi$
$223$	−12.5669	−0.841545	−0.420772	+	0.907166i	$0.638241\pi$
$224$	−3.14262	−0.209975
$225$	9.86063	0.657376
$226$	16.3673	1.08874
$227$	−12.9012	−0.856280	−0.428140	−	0.903712i	$-0.640831\pi$
$227$	−12.9012	−0.856280	−0.428140	+	0.903712i	$0.640831\pi$
$228$	4.18583	0.277213
$229$	14.2920	0.944439	0.472219	−	0.881481i	$-0.343453\pi$
$229$	14.2920	0.944439	0.472219	+	0.881481i	$0.343453\pi$
$230$	18.0961	1.19322
$231$	−27.5764	−1.81439
$232$	5.84498	0.383742
$233$	21.9100	1.43537	0.717687	−	0.696366i	$-0.245201\pi$
$233$	21.9100	1.43537	0.717687	+	0.696366i	$0.245201\pi$
$234$	−7.33390	−0.479432
$235$	−22.4452	−1.46416
$236$	−12.2561	−0.797804
$237$	30.4007	1.97474
$238$	1.52718	0.0989926
$239$	22.6295	1.46378	0.731890	−	0.681422i	$-0.238638\pi$
$239$	22.6295	1.46378	0.731890	+	0.681422i	$0.238638\pi$
$240$	−7.05093	−0.455135
$241$	9.79992	0.631268	0.315634	−	0.948881i	$-0.397783\pi$
$241$	9.79992	0.631268	0.315634	+	0.948881i	$0.397783\pi$
$242$	1.84052	0.118313
$243$	22.0392	1.41382
$244$	11.8468	0.758411
$245$	8.28108	0.529059
$246$	0.326288	0.0208034
$247$	4.18336	0.266181
$248$	8.31794	0.528190
$249$	−4.64961	−0.294657
$250$	−4.92209	−0.311300
$251$	−25.4567	−1.60681	−0.803406	−	0.595432i	$-0.796981\pi$
$251$	−25.4567	−1.60681	−0.803406	+	0.595432i	$0.796981\pi$
$252$	−9.41735	−0.593237
$253$	−22.5209	−1.41588
$254$	−10.3216	−0.647636
$255$	3.42646	0.214573
$256$	1.00000	0.0625000
$257$	−7.42569	−0.463202	−0.231601	−	0.972811i	$-0.574396\pi$
$257$	−7.42569	−0.463202	−0.231601	+	0.972811i	$0.574396\pi$
$258$	−8.32875	−0.518525
$259$	−21.6730	−1.34669
$260$	−7.04676	−0.437022
$261$	17.5154	1.08418
$262$	11.8612	0.732785
$263$	10.1421	0.625388	0.312694	−	0.949854i	$-0.398768\pi$
$263$	10.1421	0.625388	0.312694	+	0.949854i	$0.398768\pi$
$264$	8.77498	0.540062
$265$	−29.7188	−1.82561
$266$	5.37178	0.329365
$267$	22.6416	1.38564
$268$	−3.32337	−0.203007
$269$	0.384096	0.0234187	0.0117094	−	0.999931i	$-0.496273\pi$
$269$	0.384096	0.0234187	0.0117094	+	0.999931i	$0.496273\pi$
$270$	0.0235723	0.00143456
$271$	−9.22397	−0.560316	−0.280158	−	0.959954i	$-0.590387\pi$
$271$	−9.22397	−0.560316	−0.280158	+	0.959954i	$0.590387\pi$
$272$	−0.485959	−0.0294656
$273$	−18.8341	−1.13989
$274$	−1.10912	−0.0670047
$275$	−11.7912	−0.711038
$276$	−15.3904	−0.926390
$277$	15.3135	0.920096	0.460048	−	0.887894i	$-0.347832\pi$
$277$	15.3135	0.920096	0.460048	+	0.887894i	$0.347832\pi$
$278$	−1.19293	−0.0715472
$279$	24.9260	1.49228
$280$	−9.04863	−0.540759
$281$	11.6450	0.694684	0.347342	−	0.937739i	$-0.387084\pi$
$281$	11.6450	0.694684	0.347342	+	0.937739i	$0.387084\pi$
$282$	19.0892	1.13674
$283$	28.2293	1.67806	0.839029	−	0.544086i	$-0.183123\pi$
$283$	28.2293	1.67806	0.839029	+	0.544086i	$0.183123\pi$
$284$	−13.8090	−0.819413
$285$	12.0524	0.713922
$286$	8.76979	0.518569
$287$	0.418734	0.0247171
$288$	2.99666	0.176580
$289$	−16.7638	−0.986108
$290$	16.8296	0.988270
$291$	−19.7889	−1.16005
$292$	−0.396742	−0.0232176
$293$	8.49844	0.496484	0.248242	−	0.968698i	$-0.420147\pi$
$293$	8.49844	0.496484	0.248242	+	0.968698i	$0.420147\pi$
$294$	−7.04288	−0.410749
$295$	−35.2894	−2.05463
$296$	6.89647	0.400849
$297$	−0.0293360	−0.00170225
$298$	−20.0727	−1.16278
$299$	−15.3813	−0.889521
$300$	−8.05791	−0.465224
$301$	−10.6885	−0.616075
$302$	−8.77777	−0.505104
$303$	14.9718	0.860106
$304$	−1.70933	−0.0980370
$305$	34.1107	1.95317
$306$	−1.45625	−0.0832485
$307$	−17.6193	−1.00559	−0.502793	−	0.864407i	$-0.667694\pi$
$307$	−17.6193	−1.00559	−0.502793	+	0.864407i	$0.667694\pi$
$308$	11.2612	0.641664
$309$	45.9595	2.61454
$310$	23.9501	1.36027
$311$	13.7349	0.778833	0.389416	−	0.921062i	$-0.372677\pi$
$311$	13.7349	0.778833	0.389416	+	0.921062i	$0.372677\pi$
$312$	5.99312	0.339293
$313$	−23.1094	−1.30622	−0.653110	−	0.757263i	$-0.726536\pi$
$313$	−23.1094	−1.30622	−0.653110	+	0.757263i	$0.726536\pi$
$314$	4.93727	0.278626
$315$	−27.1157	−1.52779
$316$	−12.4145	−0.698370
$317$	31.7713	1.78445	0.892226	−	0.451590i	$-0.149143\pi$
$317$	31.7713	1.78445	0.892226	+	0.451590i	$0.149143\pi$
$318$	25.2752	1.41736
$319$	−20.9447	−1.17268
$320$	2.87933	0.160959
$321$	29.3350	1.63732
$322$	−19.7508	−1.10067
$323$	0.830667	0.0462195
$324$	−9.01002	−0.500557
$325$	−8.05315	−0.446708
$326$	2.93231	0.162406
$327$	7.56446	0.418315
$328$	−0.133244	−0.00735716
$329$	24.4976	1.35060
$330$	25.2661	1.39085
$331$	9.12619	0.501621	0.250810	−	0.968036i	$-0.419303\pi$
$331$	9.12619	0.501621	0.250810	+	0.968036i	$0.419303\pi$
$332$	1.89872	0.104206
$333$	20.6663	1.13251
$334$	14.6497	0.801594
$335$	−9.56908	−0.522815
$336$	7.69566	0.419833
$337$	2.44560	0.133220	0.0666101	−	0.997779i	$-0.478782\pi$
$337$	2.44560	0.133220	0.0666101	+	0.997779i	$0.478782\pi$
$338$	−7.01042	−0.381317
$339$	−40.0803	−2.17686
$340$	−1.39924	−0.0758843
$341$	−29.8062	−1.61410
$342$	−5.12229	−0.276982
$343$	12.9600	0.699775
$344$	3.40114	0.183377
$345$	−44.3139	−2.38578
$346$	−11.9772	−0.643897
$347$	−19.9586	−1.07144	−0.535718	−	0.844397i	$-0.679959\pi$
$347$	−19.9586	−1.07144	−0.535718	+	0.844397i	$0.679959\pi$
$348$	−14.3132	−0.767270
$349$	−12.3000	−0.658405	−0.329203	−	0.944259i	$-0.606780\pi$
$349$	−12.3000	−0.658405	−0.329203	+	0.944259i	$0.606780\pi$
$350$	−10.3409	−0.552746
$351$	−0.0200359	−0.00106944
$352$	−3.58337	−0.190994
$353$	−23.8380	−1.26877	−0.634385	−	0.773018i	$-0.718746\pi$
$353$	−23.8380	−1.26877	−0.634385	+	0.773018i	$0.718746\pi$
$354$	30.0128	1.59516
$355$	−39.7607	−2.11028
$356$	−9.24598	−0.490036
$357$	−3.73978	−0.197930
$358$	−13.4935	−0.713151
$359$	−17.3091	−0.913537	−0.456769	−	0.889585i	$-0.650993\pi$
$359$	−17.3091	−0.913537	−0.456769	+	0.889585i	$0.650993\pi$
$360$	8.62837	0.454755
$361$	−16.0782	−0.846220
$362$	−3.92575	−0.206333
$363$	−4.50708	−0.236561
$364$	7.69112	0.403124
$365$	−1.14235	−0.0597935
$366$	−29.0104	−1.51640
$367$	−17.4035	−0.908453	−0.454227	−	0.890886i	$-0.650084\pi$
$367$	−17.4035	−0.908453	−0.454227	+	0.890886i	$0.650084\pi$
$368$	6.28484	0.327620
$369$	−0.399286	−0.0207860
$370$	19.8572	1.03233
$371$	32.4363	1.68401
$372$	−20.3690	−1.05608
$373$	−9.64782	−0.499545	−0.249773	−	0.968305i	$-0.580356\pi$
$373$	−9.64782	−0.499545	−0.249773	+	0.968305i	$0.580356\pi$
$374$	1.74137	0.0900441
$375$	12.0532	0.622427
$376$	−7.79529	−0.402011
$377$	−14.3048	−0.736734
$378$	−0.0257277	−0.00132329
$379$	19.2178	0.987153	0.493576	−	0.869702i	$-0.335689\pi$
$379$	19.2178	0.987153	0.493576	+	0.869702i	$0.335689\pi$
$380$	−4.92174	−0.252480
$381$	25.2757	1.29491
$382$	21.5097	1.10053
$383$	11.8519	0.605602	0.302801	−	0.953054i	$-0.402078\pi$
$383$	11.8519	0.605602	0.302801	+	0.953054i	$0.402078\pi$
$384$	−2.44881	−0.124965
$385$	32.4246	1.65251
$386$	−9.74815	−0.496168
$387$	10.1921	0.518092
$388$	8.08104	0.410253
$389$	−0.831830	−0.0421754	−0.0210877	−	0.999778i	$-0.506713\pi$
$389$	−0.831830	−0.0421754	−0.0210877	+	0.999778i	$0.506713\pi$
$390$	17.2562	0.873800
$391$	−3.05417	−0.154456
$392$	2.87604	0.145262
$393$	−29.0457	−1.46516
$394$	−19.4759	−0.981183
$395$	−35.7454	−1.79855
$396$	−10.7381	−0.539611
$397$	19.3691	0.972106	0.486053	−	0.873929i	$-0.338436\pi$
$397$	19.3691	0.972106	0.486053	+	0.873929i	$0.338436\pi$
$398$	−2.37529	−0.119063
$399$	−13.1545	−0.658547
$400$	3.29054	0.164527
$401$	−31.8319	−1.58961	−0.794805	−	0.606864i	$-0.792427\pi$
$401$	−31.8319	−1.58961	−0.794805	+	0.606864i	$0.792427\pi$
$402$	8.13829	0.405901
$403$	−20.3570	−1.01405
$404$	−6.11390	−0.304178
$405$	−25.9428	−1.28911
$406$	−18.3685	−0.911615
$407$	−24.7126	−1.22496
$408$	1.19002	0.0589148
$409$	35.5846	1.75955	0.879773	−	0.475394i	$-0.157694\pi$
$409$	35.5846	1.75955	0.879773	+	0.475394i	$0.157694\pi$
$410$	−0.383653	−0.0189473
$411$	2.71603	0.133972
$412$	−18.7681	−0.924638
$413$	38.5162	1.89526
$414$	18.8335	0.925616
$415$	5.46705	0.268367
$416$	−2.44736	−0.119992
$417$	2.92126	0.143054
$418$	6.12517	0.299592
$419$	−32.5011	−1.58778	−0.793892	−	0.608059i	$-0.791949\pi$
$419$	−32.5011	−1.58778	−0.793892	+	0.608059i	$0.791949\pi$
$420$	22.1584	1.08122
$421$	−29.8065	−1.45268	−0.726339	−	0.687337i	$-0.758780\pi$
$421$	−29.8065	−1.45268	−0.726339	+	0.687337i	$0.758780\pi$
$422$	−23.3913	−1.13867
$423$	−23.3598	−1.13579
$424$	−10.3214	−0.501253
$425$	−1.59907	−0.0775663
$426$	33.8156	1.63837
$427$	−37.2298	−1.80168
$428$	−11.9793	−0.579042
$429$	−21.4755	−1.03685
$430$	9.79302	0.472261
$431$	−36.9293	−1.77882	−0.889410	−	0.457110i	$-0.848884\pi$
$431$	−36.9293	−1.77882	−0.889410	+	0.457110i	$0.848884\pi$
$432$	0.00818672	0.000393884 0
$433$	5.93862	0.285392	0.142696	−	0.989767i	$-0.454423\pi$
$433$	5.93862	0.285392	0.142696	+	0.989767i	$0.454423\pi$
$434$	−26.1401	−1.25476
$435$	−41.2125	−1.97599
$436$	−3.08904	−0.147938
$437$	−10.7429	−0.513902
$438$	0.971546	0.0464222
$439$	33.4671	1.59730	0.798649	−	0.601796i	$-0.205548\pi$
$439$	33.4671	1.59730	0.798649	+	0.601796i	$0.205548\pi$
$440$	−10.3177	−0.491877
$441$	8.61852	0.410406
$442$	1.18932	0.0565701
$443$	13.5506	0.643809	0.321904	−	0.946772i	$-0.395677\pi$
$443$	13.5506	0.643809	0.321904	+	0.946772i	$0.395677\pi$
$444$	−16.8881	−0.801475
$445$	−26.6222	−1.26201
$446$	−12.5669	−0.595062
$447$	49.1541	2.32491
$448$	−3.14262	−0.148475
$449$	7.87634	0.371708	0.185854	−	0.982577i	$-0.440495\pi$
$449$	7.87634	0.371708	0.185854	+	0.982577i	$0.440495\pi$
$450$	9.86063	0.464835
$451$	0.477461	0.0224828
$452$	16.3673	0.769852
$453$	21.4951	1.00993
$454$	−12.9012	−0.605481
$455$	22.1453	1.03819
$456$	4.18583	0.196019
$457$	15.4315	0.721857	0.360929	−	0.932593i	$-0.382460\pi$
$457$	15.4315	0.721857	0.360929	+	0.932593i	$0.382460\pi$
$458$	14.2920	0.667819
$459$	−0.00397841	−0.000185696 0
$460$	18.0961	0.843736
$461$	5.42936	0.252871	0.126435	−	0.991975i	$-0.459646\pi$
$461$	5.42936	0.252871	0.126435	+	0.991975i	$0.459646\pi$
$462$	−27.5764	−1.28297
$463$	35.6688	1.65767	0.828834	−	0.559495i	$-0.189005\pi$
$463$	35.6688	1.65767	0.828834	+	0.559495i	$0.189005\pi$
$464$	5.84498	0.271346
$465$	−58.6492	−2.71979
$466$	21.9100	1.01496
$467$	−6.75140	−0.312418	−0.156209	−	0.987724i	$-0.549927\pi$
$467$	−6.75140	−0.312418	−0.156209	+	0.987724i	$0.549927\pi$
$468$	−7.33390	−0.339010
$469$	10.4441	0.482263
$470$	−22.4452	−1.03532
$471$	−12.0904	−0.557097
$472$	−12.2561	−0.564133
$473$	−12.1876	−0.560384
$474$	30.4007	1.39635
$475$	−5.62464	−0.258076
$476$	1.52718	0.0699984
$477$	−30.9298	−1.41618
$478$	22.6295	1.03505
$479$	−0.150715	−0.00688636	−0.00344318	−	0.999994i	$-0.501096\pi$
$479$	−0.150715	−0.00688636	−0.00344318	+	0.999994i	$0.501096\pi$
$480$	−7.05093	−0.321829
$481$	−16.8781	−0.769577
$482$	9.79992	0.446374
$483$	48.3660	2.20073
$484$	1.84052	0.0836601
$485$	23.2680	1.05655
$486$	22.0392	0.999720
$487$	−29.0724	−1.31740	−0.658698	−	0.752407i	$-0.728892\pi$
$487$	−29.0724	−1.31740	−0.658698	+	0.752407i	$0.728892\pi$
$488$	11.8468	0.536277
$489$	−7.18067	−0.324721
$490$	8.28108	0.374101
$491$	−12.1907	−0.550157	−0.275079	−	0.961422i	$-0.588704\pi$
$491$	−12.1907	−0.550157	−0.275079	+	0.961422i	$0.588704\pi$
$492$	0.326288	0.0147102
$493$	−2.84042	−0.127926
$494$	4.18336	0.188218
$495$	−30.9186	−1.38969
$496$	8.31794	0.373486
$497$	43.3964	1.94659
$498$	−4.64961	−0.208354
$499$	−37.7053	−1.68792	−0.843960	−	0.536406i	$-0.819782\pi$
$499$	−37.7053	−1.68792	−0.843960	+	0.536406i	$0.819782\pi$
$500$	−4.92209	−0.220122
$501$	−35.8742	−1.60274
$502$	−25.4567	−1.13619
$503$	1.90186	0.0847997	0.0423999	−	0.999101i	$-0.486500\pi$
$503$	1.90186	0.0847997	0.0423999	+	0.999101i	$0.486500\pi$
$504$	−9.41735	−0.419482
$505$	−17.6040	−0.783366
$506$	−22.5209	−1.00118
$507$	17.1672	0.762421
$508$	−10.3216	−0.457948
$509$	6.34495	0.281235	0.140617	−	0.990064i	$-0.455091\pi$
$509$	6.34495	0.281235	0.140617	+	0.990064i	$0.455091\pi$
$510$	3.42646	0.151726
$511$	1.24681	0.0551556
$512$	1.00000	0.0441942
$513$	−0.0139938	−0.000617843 0
$514$	−7.42569	−0.327533
$515$	−54.0396	−2.38127
$516$	−8.32875	−0.366653
$517$	27.9334	1.22851
$518$	−21.6730	−0.952255
$519$	29.3298	1.28744
$520$	−7.04676	−0.309021
$521$	17.0393	0.746507	0.373254	−	0.927729i	$-0.378242\pi$
$521$	17.0393	0.746507	0.373254	+	0.927729i	$0.378242\pi$
$522$	17.5154	0.766628
$523$	5.20687	0.227680	0.113840	−	0.993499i	$-0.463685\pi$
$523$	5.20687	0.227680	0.113840	+	0.993499i	$0.463685\pi$
$524$	11.8612	0.518158
$525$	25.3229	1.10518
$526$	10.1421	0.442216
$527$	−4.04218	−0.176080
$528$	8.77498	0.381882
$529$	16.4992	0.717355
$530$	−29.7188	−1.29090
$531$	−36.7273	−1.59383
$532$	5.37178	0.232896
$533$	0.326096	0.0141248
$534$	22.6416	0.979799
$535$	−34.4924	−1.49124
$536$	−3.32337	−0.143548
$537$	33.0429	1.42590
$538$	0.384096	0.0165595
$539$	−10.3059	−0.443908
$540$	0.0235723	0.00101439
$541$	−21.5657	−0.927183	−0.463592	−	0.886049i	$-0.653440\pi$
$541$	−21.5657	−0.927183	−0.463592	+	0.886049i	$0.653440\pi$
$542$	−9.22397	−0.396204
$543$	9.61341	0.412551
$544$	−0.485959	−0.0208353
$545$	−8.89436	−0.380993
$546$	−18.8341	−0.806024
$547$	19.5179	0.834526	0.417263	−	0.908786i	$-0.362989\pi$
$547$	19.5179	0.834526	0.417263	+	0.908786i	$0.362989\pi$
$548$	−1.10912	−0.0473795
$549$	35.5007	1.51513
$550$	−11.7912	−0.502780
$551$	−9.99103	−0.425632
$552$	−15.3904	−0.655057
$553$	39.0140	1.65905
$554$	15.3135	0.650606
$555$	−48.6265	−2.06408
$556$	−1.19293	−0.0505915
$557$	39.8651	1.68914	0.844569	−	0.535447i	$-0.179857\pi$
$557$	39.8651	1.68914	0.844569	+	0.535447i	$0.179857\pi$
$558$	24.9260	1.05520
$559$	−8.32383	−0.352060
$560$	−9.04863	−0.382375
$561$	−4.26428	−0.180038
$562$	11.6450	0.491216
$563$	33.1303	1.39628	0.698138	−	0.715963i	$-0.254012\pi$
$563$	33.1303	1.39628	0.698138	+	0.715963i	$0.254012\pi$
$564$	19.0892	0.803798
$565$	47.1268	1.98264
$566$	28.2293	1.18657
$567$	28.3150	1.18912
$568$	−13.8090	−0.579413
$569$	6.31591	0.264777	0.132388	−	0.991198i	$-0.457735\pi$
$569$	6.31591	0.264777	0.132388	+	0.991198i	$0.457735\pi$
$570$	12.0524	0.504819
$571$	32.5756	1.36325	0.681624	−	0.731703i	$-0.261274\pi$
$571$	32.5756	1.36325	0.681624	+	0.731703i	$0.261274\pi$
$572$	8.76979	0.366683
$573$	−52.6731	−2.20045
$574$	0.418734	0.0174776
$575$	20.6805	0.862438
$576$	2.99666	0.124861
$577$	−15.4153	−0.641748	−0.320874	−	0.947122i	$-0.603977\pi$
$577$	−15.4153	−0.641748	−0.320874	+	0.947122i	$0.603977\pi$
$578$	−16.7638	−0.697284
$579$	23.8713	0.992059
$580$	16.8296	0.698813
$581$	−5.96696	−0.247551
$582$	−19.7889	−0.820277
$583$	36.9855	1.53178
$584$	−0.396742	−0.0164173
$585$	−21.1167	−0.873069
$586$	8.49844	0.351067
$587$	−3.74564	−0.154599	−0.0772995	−	0.997008i	$-0.524630\pi$
$587$	−3.74564	−0.154599	−0.0772995	+	0.997008i	$0.524630\pi$
$588$	−7.04288	−0.290443
$589$	−14.2181	−0.585848
$590$	−35.2894	−1.45284
$591$	47.6928	1.96182
$592$	6.89647	0.283443
$593$	−30.6555	−1.25887	−0.629434	−	0.777054i	$-0.716713\pi$
$593$	−30.6555	−1.25887	−0.629434	+	0.777054i	$0.716713\pi$
$594$	−0.0293360	−0.00120367
$595$	4.39727	0.180270
$596$	−20.0727	−0.822209
$597$	5.81663	0.238059
$598$	−15.3813	−0.628987
$599$	24.2752	0.991857	0.495929	−	0.868363i	$-0.334828\pi$
$599$	24.2752	0.991857	0.495929	+	0.868363i	$0.334828\pi$
$600$	−8.05791	−0.328963
$601$	−32.7233	−1.33481	−0.667406	−	0.744694i	$-0.732595\pi$
$601$	−32.7233	−1.33481	−0.667406	+	0.744694i	$0.732595\pi$
$602$	−10.6885	−0.435631
$603$	−9.95900	−0.405562
$604$	−8.77777	−0.357162
$605$	5.29947	0.215454
$606$	14.9718	0.608187
$607$	−6.93012	−0.281285	−0.140642	−	0.990060i	$-0.544917\pi$
$607$	−6.93012	−0.281285	−0.140642	+	0.990060i	$0.544917\pi$
$608$	−1.70933	−0.0693226
$609$	44.9810	1.82272
$610$	34.1107	1.38110
$611$	19.0779	0.771808
$612$	−1.45625	−0.0588655
$613$	32.3542	1.30677	0.653387	−	0.757024i	$-0.273348\pi$
$613$	32.3542	1.30677	0.653387	+	0.757024i	$0.273348\pi$
$614$	−17.6193	−0.711057
$615$	0.939492	0.0378840
$616$	11.2612	0.453725
$617$	27.3309	1.10030	0.550150	−	0.835066i	$-0.314571\pi$
$617$	27.3309	1.10030	0.550150	+	0.835066i	$0.314571\pi$
$618$	45.9595	1.84876
$619$	22.0584	0.886601	0.443300	−	0.896373i	$-0.353808\pi$
$619$	22.0584	0.886601	0.443300	+	0.896373i	$0.353808\pi$
$620$	23.9501	0.961859
$621$	0.0514522	0.00206471
$622$	13.7349	0.550718
$623$	29.0566	1.16413
$624$	5.99312	0.239917
$625$	−30.6250	−1.22500
$626$	−23.1094	−0.923636
$627$	−14.9994	−0.599017
$628$	4.93727	0.197019
$629$	−3.35140	−0.133629
$630$	−27.1157	−1.08031
$631$	−5.62806	−0.224050	−0.112025	−	0.993705i	$-0.535734\pi$
$631$	−5.62806	−0.224050	−0.112025	+	0.993705i	$0.535734\pi$
$632$	−12.4145	−0.493822
$633$	57.2808	2.27671
$634$	31.7713	1.26180
$635$	−29.7193	−1.17938
$636$	25.2752	1.00223
$637$	−7.03872	−0.278884
$638$	−20.9447	−0.829209
$639$	−41.3808	−1.63700
$640$	2.87933	0.113816
$641$	−12.0548	−0.476134	−0.238067	−	0.971249i	$-0.576514\pi$
$641$	−12.0548	−0.476134	−0.238067	+	0.971249i	$0.576514\pi$
$642$	29.3350	1.15776
$643$	−15.8632	−0.625582	−0.312791	−	0.949822i	$-0.601264\pi$
$643$	−15.8632	−0.625582	−0.312791	+	0.949822i	$0.601264\pi$
$644$	−19.7508	−0.778292
$645$	−23.9812	−0.944260
$646$	0.830667	0.0326821
$647$	18.1598	0.713934	0.356967	−	0.934117i	$-0.383811\pi$
$647$	18.1598	0.713934	0.356967	+	0.934117i	$0.383811\pi$
$648$	−9.01002	−0.353947
$649$	43.9181	1.72394
$650$	−8.05315	−0.315871
$651$	64.0121	2.50883
$652$	2.93231	0.114838
$653$	−8.69811	−0.340383	−0.170192	−	0.985411i	$-0.554439\pi$
$653$	−8.69811	−0.340383	−0.170192	+	0.985411i	$0.554439\pi$
$654$	7.56446	0.295794
$655$	34.1522	1.33444
$656$	−0.133244	−0.00520229
$657$	−1.18890	−0.0463834
$658$	24.4976	0.955016
$659$	−40.5063	−1.57790	−0.788950	−	0.614458i	$-0.789375\pi$
$659$	−40.5063	−1.57790	−0.788950	+	0.614458i	$0.789375\pi$
$660$	25.2661	0.983480
$661$	45.8004	1.78143	0.890714	−	0.454565i	$-0.150205\pi$
$661$	45.8004	1.78143	0.890714	+	0.454565i	$0.150205\pi$
$662$	9.12619	0.354700
$663$	−2.91241	−0.113109
$664$	1.89872	0.0736847
$665$	15.4671	0.599790
$666$	20.6663	0.800805
$667$	36.7348	1.42238
$668$	14.6497	0.566812
$669$	30.7740	1.18979
$670$	−9.56908	−0.369686
$671$	−42.4513	−1.63881
$672$	7.69566	0.296867
$673$	−27.2223	−1.04934	−0.524671	−	0.851305i	$-0.675812\pi$
$673$	−27.2223	−1.04934	−0.524671	+	0.851305i	$0.675812\pi$
$674$	2.44560	0.0942009
$675$	0.0269388	0.00103687
$676$	−7.01042	−0.269632
$677$	28.0462	1.07790	0.538952	−	0.842336i	$-0.318820\pi$
$677$	28.0462	1.07790	0.538952	+	0.842336i	$0.318820\pi$
$678$	−40.0803	−1.53928
$679$	−25.3956	−0.974595
$680$	−1.39924	−0.0536583
$681$	31.5925	1.21063
$682$	−29.8062	−1.14134
$683$	−1.34359	−0.0514112	−0.0257056	−	0.999670i	$-0.508183\pi$
$683$	−1.34359	−0.0514112	−0.0257056	+	0.999670i	$0.508183\pi$
$684$	−5.12229	−0.195856
$685$	−3.19354	−0.122019
$686$	12.9600	0.494816
$687$	−34.9982	−1.33527
$688$	3.40114	0.129667
$689$	25.2603	0.962339
$690$	−44.3139	−1.68700
$691$	12.7226	0.483991	0.241996	−	0.970277i	$-0.422198\pi$
$691$	12.7226	0.483991	0.241996	+	0.970277i	$0.422198\pi$
$692$	−11.9772	−0.455304
$693$	33.7458	1.28190
$694$	−19.9586	−0.757620
$695$	−3.43484	−0.130291
$696$	−14.3132	−0.542542
$697$	0.0647510	0.00245262
$698$	−12.3000	−0.465563
$699$	−53.6535	−2.02936
$700$	−10.3409	−0.390850
$701$	−39.9746	−1.50982	−0.754910	−	0.655828i	$-0.772320\pi$
$701$	−39.9746	−1.50982	−0.754910	+	0.655828i	$0.772320\pi$
$702$	−0.0200359	−0.000756205 0
$703$	−11.7884	−0.444607
$704$	−3.58337	−0.135053
$705$	54.9640	2.07006
$706$	−23.8380	−0.897155
$707$	19.2137	0.722604
$708$	30.0128	1.12795
$709$	36.5380	1.37221	0.686106	−	0.727502i	$-0.259319\pi$
$709$	36.5380	1.37221	0.686106	+	0.727502i	$0.259319\pi$
$710$	−39.7607	−1.49219
$711$	−37.2020	−1.39518
$712$	−9.24598	−0.346508
$713$	52.2769	1.95778
$714$	−3.73978	−0.139958
$715$	25.2511	0.944339
$716$	−13.4935	−0.504274
$717$	−55.4153	−2.06952
$718$	−17.3091	−0.645969
$719$	−14.8536	−0.553945	−0.276972	−	0.960878i	$-0.589331\pi$
$719$	−14.8536	−0.553945	−0.276972	+	0.960878i	$0.589331\pi$
$720$	8.62837	0.321560
$721$	58.9810	2.19657
$722$	−16.0782	−0.598368
$723$	−23.9981	−0.892499
$724$	−3.92575	−0.145899
$725$	19.2332	0.714302
$726$	−4.50708	−0.167274
$727$	28.0932	1.04192	0.520959	−	0.853582i	$-0.325574\pi$
$727$	28.0932	1.04192	0.520959	+	0.853582i	$0.325574\pi$
$728$	7.69112	0.285052
$729$	−26.9398	−0.997770
$730$	−1.14235	−0.0422804
$731$	−1.65282	−0.0611317
$732$	−29.0104	−1.07226
$733$	−26.1129	−0.964501	−0.482250	−	0.876033i	$-0.660180\pi$
$733$	−26.1129	−0.964501	−0.482250	+	0.876033i	$0.660180\pi$
$734$	−17.4035	−0.642373
$735$	−20.2788	−0.747994
$736$	6.28484	0.231662
$737$	11.9089	0.438668
$738$	−0.399286	−0.0146979
$739$	2.40948	0.0886342	0.0443171	−	0.999018i	$-0.485889\pi$
$739$	2.40948	0.0886342	0.0443171	+	0.999018i	$0.485889\pi$
$740$	19.8572	0.729966
$741$	−10.2442	−0.376331
$742$	32.4363	1.19077
$743$	9.25783	0.339637	0.169818	−	0.985475i	$-0.445682\pi$
$743$	9.25783	0.339637	0.169818	+	0.985475i	$0.445682\pi$
$744$	−20.3690	−0.746765
$745$	−57.7959	−2.11748
$746$	−9.64782	−0.353232
$747$	5.68982	0.208180
$748$	1.74137	0.0636708
$749$	37.6464	1.37557
$750$	12.0532	0.440122
$751$	−43.7889	−1.59788	−0.798940	−	0.601411i	$-0.794605\pi$
$751$	−43.7889	−1.59788	−0.798940	+	0.601411i	$0.794605\pi$
$752$	−7.79529	−0.284265
$753$	62.3385	2.27174
$754$	−14.3048	−0.520949
$755$	−25.2741	−0.919819
$756$	−0.0257277	−0.000935709 0
$757$	−51.5182	−1.87246	−0.936231	−	0.351386i	$-0.885710\pi$
$757$	−51.5182	−1.87246	−0.936231	+	0.351386i	$0.885710\pi$
$758$	19.2178	0.698022
$759$	55.1493	2.00179
$760$	−4.92174	−0.178530
$761$	13.4157	0.486317	0.243159	−	0.969987i	$-0.421816\pi$
$761$	13.4157	0.486317	0.243159	+	0.969987i	$0.421816\pi$
$762$	25.2757	0.915640
$763$	9.70766	0.351441
$764$	21.5097	0.778194
$765$	−4.19303	−0.151599
$766$	11.8519	0.428225
$767$	29.9951	1.08306
$768$	−2.44881	−0.0883637
$769$	−6.93637	−0.250132	−0.125066	−	0.992148i	$-0.539914\pi$
$769$	−6.93637	−0.250132	−0.125066	+	0.992148i	$0.539914\pi$
$770$	32.4246	1.16850
$771$	18.1841	0.654884
$772$	−9.74815	−0.350844
$773$	−11.8596	−0.426561	−0.213280	−	0.976991i	$-0.568415\pi$
$773$	−11.8596	−0.426561	−0.213280	+	0.976991i	$0.568415\pi$
$774$	10.1921	0.366346
$775$	27.3706	0.983179
$776$	8.08104	0.290092
$777$	53.0729	1.90398
$778$	−0.831830	−0.0298225
$779$	0.227758	0.00816028
$780$	17.2562	0.617870
$781$	49.4827	1.77063
$782$	−3.05417	−0.109217
$783$	0.0478513	0.00171006
$784$	2.87604	0.102716
$785$	14.2160	0.507392
$786$	−29.0457	−1.03603
$787$	23.4528	0.836001	0.418001	−	0.908447i	$-0.362731\pi$
$787$	23.4528	0.836001	0.418001	+	0.908447i	$0.362731\pi$
$788$	−19.4759	−0.693801
$789$	−24.8360	−0.884186
$790$	−35.7454	−1.27177
$791$	−51.4361	−1.82886
$792$	−10.7381	−0.381563
$793$	−28.9933	−1.02958
$794$	19.3691	0.687383
$795$	72.7756	2.58109
$796$	−2.37529	−0.0841900
$797$	−31.2693	−1.10762	−0.553808	−	0.832645i	$-0.686826\pi$
$797$	−31.2693	−1.10762	−0.553808	+	0.832645i	$0.686826\pi$
$798$	−13.1545	−0.465663
$799$	3.78819	0.134017
$800$	3.29054	0.116338
$801$	−27.7070	−0.978980
$802$	−31.8319	−1.12402
$803$	1.42167	0.0501698
$804$	8.13829	0.287015
$805$	−56.8692	−2.00438
$806$	−20.3570	−0.717045
$807$	−0.940576	−0.0331098
$808$	−6.11390	−0.215086
$809$	43.3858	1.52536	0.762681	−	0.646775i	$-0.223883\pi$
$809$	43.3858	1.52536	0.762681	+	0.646775i	$0.223883\pi$
$810$	−25.9428	−0.911538
$811$	6.99831	0.245744	0.122872	−	0.992423i	$-0.460790\pi$
$811$	6.99831	0.245744	0.122872	+	0.992423i	$0.460790\pi$
$812$	−18.3685	−0.644609
$813$	22.5877	0.792186
$814$	−24.7126	−0.866175
$815$	8.44310	0.295749
$816$	1.19002	0.0416591
$817$	−5.81369	−0.203395
$818$	35.5846	1.24419
$819$	23.0476	0.805350
$820$	−0.383653	−0.0133977
$821$	−33.5593	−1.17123	−0.585613	−	0.810590i	$-0.699146\pi$
$821$	−33.5593	−1.17123	−0.585613	+	0.810590i	$0.699146\pi$
$822$	2.71603	0.0947325
$823$	18.1419	0.632387	0.316194	−	0.948695i	$-0.397595\pi$
$823$	18.1419	0.632387	0.316194	+	0.948695i	$0.397595\pi$
$824$	−18.7681	−0.653818
$825$	28.8745	1.00528
$826$	38.5162	1.34015
$827$	−41.2866	−1.43568	−0.717839	−	0.696210i	$-0.754868\pi$
$827$	−41.2866	−1.43568	−0.717839	+	0.696210i	$0.754868\pi$
$828$	18.8335	0.654509
$829$	−29.5190	−1.02524	−0.512619	−	0.858616i	$-0.671325\pi$
$829$	−29.5190	−1.02524	−0.512619	+	0.858616i	$0.671325\pi$
$830$	5.46705	0.189764
$831$	−37.4997	−1.30085
$832$	−2.44736	−0.0848470
$833$	−1.39764	−0.0484254
$834$	2.92126	0.101155
$835$	42.1812	1.45974
$836$	6.12517	0.211843
$837$	0.0680967	0.00235377
$838$	−32.5011	−1.12273
$839$	−0.262035	−0.00904644	−0.00452322	−	0.999990i	$-0.501440\pi$
$839$	−0.262035	−0.00904644	−0.00452322	+	0.999990i	$0.501440\pi$
$840$	22.1584	0.764536
$841$	5.16381	0.178063
$842$	−29.8065	−1.02720
$843$	−28.5164	−0.982157
$844$	−23.3913	−0.805162
$845$	−20.1853	−0.694396
$846$	−23.3598	−0.803126
$847$	−5.78406	−0.198743
$848$	−10.3214	−0.354439
$849$	−69.1282	−2.37247
$850$	−1.59907	−0.0548477
$851$	43.3432	1.48578
$852$	33.8156	1.15850
$853$	−13.8837	−0.475367	−0.237684	−	0.971343i	$-0.576388\pi$
$853$	−13.8837	−0.475367	−0.237684	+	0.971343i	$0.576388\pi$
$854$	−37.2298	−1.27398
$855$	−14.7488	−0.504397
$856$	−11.9793	−0.409444
$857$	−19.6350	−0.670718	−0.335359	−	0.942090i	$-0.608858\pi$
$857$	−19.6350	−0.670718	−0.335359	+	0.942090i	$0.608858\pi$
$858$	−21.4755	−0.733163
$859$	34.4969	1.17702	0.588509	−	0.808491i	$-0.299715\pi$
$859$	34.4969	1.17702	0.588509	+	0.808491i	$0.299715\pi$
$860$	9.79302	0.333939
$861$	−1.02540	−0.0349455
$862$	−36.9293	−1.25782
$863$	34.0025	1.15746	0.578729	−	0.815520i	$-0.303549\pi$
$863$	34.0025	1.15746	0.578729	+	0.815520i	$0.303549\pi$
$864$	0.00818672	0.000278518 0
$865$	−34.4863	−1.17257
$866$	5.93862	0.201803
$867$	41.0514	1.39418
$868$	−26.1401	−0.887253
$869$	44.4857	1.50907
$870$	−41.2125	−1.39724
$871$	8.13348	0.275593
$872$	−3.08904	−0.104608
$873$	24.2161	0.819591
$874$	−10.7429	−0.363383
$875$	15.4682	0.522922
$876$	0.971546	0.0328255
$877$	−1.05388	−0.0355870	−0.0177935	−	0.999842i	$-0.505664\pi$
$877$	−1.05388	−0.0355870	−0.0177935	+	0.999842i	$0.505664\pi$
$878$	33.4671	1.12946
$879$	−20.8110	−0.701939
$880$	−10.3177	−0.347810
$881$	−23.0539	−0.776706	−0.388353	−	0.921511i	$-0.626956\pi$
$881$	−23.0539	−0.776706	−0.388353	+	0.921511i	$0.626956\pi$
$882$	8.61852	0.290201
$883$	−47.2837	−1.59122	−0.795612	−	0.605806i	$-0.792851\pi$
$883$	−47.2837	−1.59122	−0.795612	+	0.605806i	$0.792851\pi$
$884$	1.18932	0.0400011
$885$	86.4169	2.90487
$886$	13.5506	0.455241
$887$	37.4219	1.25650	0.628252	−	0.778010i	$-0.283771\pi$
$887$	37.4219	1.25650	0.628252	+	0.778010i	$0.283771\pi$
$888$	−16.8881	−0.566728
$889$	32.4369	1.08790
$890$	−26.6222	−0.892379
$891$	32.2862	1.08163
$892$	−12.5669	−0.420772
$893$	13.3247	0.445896
$894$	49.1541	1.64396
$895$	−38.8521	−1.29868
$896$	−3.14262	−0.104987
$897$	37.6657	1.25762
$898$	7.87634	0.262837
$899$	48.6182	1.62151
$900$	9.86063	0.328688
$901$	5.01579	0.167100
$902$	0.477461	0.0158977
$903$	26.1741	0.871018
$904$	16.3673	0.544368
$905$	−11.3035	−0.375742
$906$	21.4951	0.714126
$907$	−27.7373	−0.921001	−0.460500	−	0.887659i	$-0.652330\pi$
$907$	−27.7373	−0.921001	−0.460500	+	0.887659i	$0.652330\pi$
$908$	−12.9012	−0.428140
$909$	−18.3213	−0.607678
$910$	22.1453	0.734109
$911$	36.6037	1.21273	0.606367	−	0.795185i	$-0.292626\pi$
$911$	36.6037	1.21273	0.606367	+	0.795185i	$0.292626\pi$
$912$	4.18583	0.138607
$913$	−6.80382	−0.225174
$914$	15.4315	0.510430
$915$	−83.5306	−2.76144
$916$	14.2920	0.472219
$917$	−37.2751	−1.23093
$918$	−0.00397841	−0.000131307 0
$919$	−1.93409	−0.0637996	−0.0318998	−	0.999491i	$-0.510156\pi$
$919$	−1.93409	−0.0637996	−0.0318998	+	0.999491i	$0.510156\pi$
$920$	18.0961	0.596611
$921$	43.1463	1.42172
$922$	5.42936	0.178807
$923$	33.7956	1.11240
$924$	−27.5764	−0.907197
$925$	22.6931	0.746146
$926$	35.6688	1.17215
$927$	−56.2416	−1.84722
$928$	5.84498	0.191871
$929$	−46.5848	−1.52840	−0.764199	−	0.644981i	$-0.776865\pi$
$929$	−46.5848	−1.52840	−0.764199	+	0.644981i	$0.776865\pi$
$930$	−58.6492	−1.92318
$931$	−4.91612	−0.161119
$932$	21.9100	0.717687
$933$	−33.6340	−1.10113
$934$	−6.75140	−0.220913
$935$	5.01398	0.163975
$936$	−7.33390	−0.239716
$937$	−20.6247	−0.673779	−0.336889	−	0.941544i	$-0.609375\pi$
$937$	−20.6247	−0.673779	−0.336889	+	0.941544i	$0.609375\pi$
$938$	10.4441	0.341011
$939$	56.5904	1.84676
$940$	−22.4452	−0.732082
$941$	13.3231	0.434321	0.217160	−	0.976136i	$-0.430321\pi$
$941$	13.3231	0.434321	0.217160	+	0.976136i	$0.430321\pi$
$942$	−12.0904	−0.393927
$943$	−0.837415	−0.0272700
$944$	−12.2561	−0.398902
$945$	−0.0740787	−0.00240978
$946$	−12.1876	−0.396251
$947$	−48.2110	−1.56665	−0.783323	−	0.621615i	$-0.786477\pi$
$947$	−48.2110	−1.56665	−0.783323	+	0.621615i	$0.786477\pi$
$948$	30.4007	0.987369
$949$	0.970972	0.0315191
$950$	−5.62464	−0.182487
$951$	−77.8017	−2.52289
$952$	1.52718	0.0494963
$953$	−34.7386	−1.12529	−0.562647	−	0.826697i	$-0.690217\pi$
$953$	−34.7386	−1.12529	−0.562647	+	0.826697i	$0.690217\pi$
$954$	−30.9298	−1.00139
$955$	61.9336	2.00412
$956$	22.6295	0.731890
$957$	51.2896	1.65796
$958$	−0.150715	−0.00486939
$959$	3.48556	0.112554
$960$	−7.05093	−0.227568
$961$	38.1881	1.23187
$962$	−16.8781	−0.544173
$963$	−35.8979	−1.15679
$964$	9.79992	0.315634
$965$	−28.0682	−0.903546
$966$	48.3660	1.55615
$967$	−18.9220	−0.608491	−0.304246	−	0.952594i	$-0.598404\pi$
$967$	−18.9220	−0.608491	−0.304246	+	0.952594i	$0.598404\pi$
$968$	1.84052	0.0591566
$969$	−2.03414	−0.0653461
$970$	23.2680	0.747090
$971$	−57.6709	−1.85075	−0.925374	−	0.379056i	$-0.876249\pi$
$971$	−57.6709	−1.85075	−0.925374	+	0.379056i	$0.876249\pi$
$972$	22.0392	0.706909
$973$	3.74892	0.120185
$974$	−29.0724	−0.931540
$975$	19.7206	0.631565
$976$	11.8468	0.379205
$977$	−13.7527	−0.439988	−0.219994	−	0.975501i	$-0.570604\pi$
$977$	−13.7527	−0.439988	−0.219994	+	0.975501i	$0.570604\pi$
$978$	−7.18067	−0.229613
$979$	33.1317	1.05889
$980$	8.28108	0.264530
$981$	−9.25678	−0.295546
$982$	−12.1907	−0.389020
$983$	17.3874	0.554573	0.277287	−	0.960787i	$-0.410565\pi$
$983$	17.3874	0.554573	0.277287	+	0.960787i	$0.410565\pi$
$984$	0.326288	0.0104017
$985$	−56.0776	−1.78678
$986$	−2.84042	−0.0904575
$987$	−59.9899	−1.90950
$988$	4.18336	0.133090
$989$	21.3756	0.679706
$990$	−30.9186	−0.982658
$991$	−5.48961	−0.174383	−0.0871916	−	0.996192i	$-0.527789\pi$
$991$	−5.48961	−0.174383	−0.0871916	+	0.996192i	$0.527789\pi$
$992$	8.31794	0.264095
$993$	−22.3483	−0.709201
$994$	43.3964	1.37645
$995$	−6.83925	−0.216819
$996$	−4.64961	−0.147328
$997$	−33.0473	−1.04662	−0.523310	−	0.852142i	$-0.675303\pi$
$997$	−33.0473	−1.04662	−0.523310	+	0.852142i	$0.675303\pi$
$998$	−37.7053	−1.19354
$999$	0.0564595	0.00178630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.9	✓	56	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.44881 q^{3} +1.00000 q^{4} +2.87933 q^{5} -2.44881 q^{6} -3.14262 q^{7} +1.00000 q^{8} +2.99666 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.44881 q^{3} +1.00000 q^{4} +2.87933 q^{5} -2.44881 q^{6} -3.14262 q^{7} +1.00000 q^{8} +2.99666 q^{9} +2.87933 q^{10} -3.58337 q^{11} -2.44881 q^{12} -2.44736 q^{13} -3.14262 q^{14} -7.05093 q^{15} +1.00000 q^{16} -0.485959 q^{17} +2.99666 q^{18} -1.70933 q^{19} +2.87933 q^{20} +7.69566 q^{21} -3.58337 q^{22} +6.28484 q^{23} -2.44881 q^{24} +3.29054 q^{25} -2.44736 q^{26} +0.00818672 q^{27} -3.14262 q^{28} +5.84498 q^{29} -7.05093 q^{30} +8.31794 q^{31} +1.00000 q^{32} +8.77498 q^{33} -0.485959 q^{34} -9.04863 q^{35} +2.99666 q^{36} +6.89647 q^{37} -1.70933 q^{38} +5.99312 q^{39} +2.87933 q^{40} -0.133244 q^{41} +7.69566 q^{42} +3.40114 q^{43} -3.58337 q^{44} +8.62837 q^{45} +6.28484 q^{46} -7.79529 q^{47} -2.44881 q^{48} +2.87604 q^{49} +3.29054 q^{50} +1.19002 q^{51} -2.44736 q^{52} -10.3214 q^{53} +0.00818672 q^{54} -10.3177 q^{55} -3.14262 q^{56} +4.18583 q^{57} +5.84498 q^{58} -12.2561 q^{59} -7.05093 q^{60} +11.8468 q^{61} +8.31794 q^{62} -9.41735 q^{63} +1.00000 q^{64} -7.04676 q^{65} +8.77498 q^{66} -3.32337 q^{67} -0.485959 q^{68} -15.3904 q^{69} -9.04863 q^{70} -13.8090 q^{71} +2.99666 q^{72} -0.396742 q^{73} +6.89647 q^{74} -8.05791 q^{75} -1.70933 q^{76} +11.2612 q^{77} +5.99312 q^{78} -12.4145 q^{79} +2.87933 q^{80} -9.01002 q^{81} -0.133244 q^{82} +1.89872 q^{83} +7.69566 q^{84} -1.39924 q^{85} +3.40114 q^{86} -14.3132 q^{87} -3.58337 q^{88} -9.24598 q^{89} +8.62837 q^{90} +7.69112 q^{91} +6.28484 q^{92} -20.3690 q^{93} -7.79529 q^{94} -4.92174 q^{95} -2.44881 q^{96} +8.08104 q^{97} +2.87604 q^{98} -10.7381 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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