LMFDB - Embedded newform 6009.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31785 q^{2} -1.00000 q^{3} +3.37244 q^{4} -1.66098 q^{5} +2.31785 q^{6} +0.0321142 q^{7} -3.18111 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31785 q^{2} -1.00000 q^{3} +3.37244 q^{4} -1.66098 q^{5} +2.31785 q^{6} +0.0321142 q^{7} -3.18111 q^{8} +1.00000 q^{9} +3.84991 q^{10} -2.63307 q^{11} -3.37244 q^{12} -0.489035 q^{13} -0.0744361 q^{14} +1.66098 q^{15} +0.628467 q^{16} -3.94565 q^{17} -2.31785 q^{18} +4.36967 q^{19} -5.60156 q^{20} -0.0321142 q^{21} +6.10307 q^{22} -8.82183 q^{23} +3.18111 q^{24} -2.24113 q^{25} +1.13351 q^{26} -1.00000 q^{27} +0.108303 q^{28} -0.245430 q^{29} -3.84991 q^{30} +2.91018 q^{31} +4.90553 q^{32} +2.63307 q^{33} +9.14543 q^{34} -0.0533412 q^{35} +3.37244 q^{36} -5.90247 q^{37} -10.1282 q^{38} +0.489035 q^{39} +5.28377 q^{40} +1.47670 q^{41} +0.0744361 q^{42} -10.2051 q^{43} -8.87987 q^{44} -1.66098 q^{45} +20.4477 q^{46} +3.09780 q^{47} -0.628467 q^{48} -6.99897 q^{49} +5.19462 q^{50} +3.94565 q^{51} -1.64924 q^{52} -9.77325 q^{53} +2.31785 q^{54} +4.37349 q^{55} -0.102159 q^{56} -4.36967 q^{57} +0.568871 q^{58} -5.23506 q^{59} +5.60156 q^{60} +10.9023 q^{61} -6.74536 q^{62} +0.0321142 q^{63} -12.6272 q^{64} +0.812279 q^{65} -6.10307 q^{66} +13.0273 q^{67} -13.3065 q^{68} +8.82183 q^{69} +0.123637 q^{70} -6.36889 q^{71} -3.18111 q^{72} -5.84496 q^{73} +13.6810 q^{74} +2.24113 q^{75} +14.7364 q^{76} -0.0845591 q^{77} -1.13351 q^{78} +3.39770 q^{79} -1.04387 q^{80} +1.00000 q^{81} -3.42278 q^{82} -6.61912 q^{83} -0.108303 q^{84} +6.55366 q^{85} +23.6538 q^{86} +0.245430 q^{87} +8.37609 q^{88} +7.43806 q^{89} +3.84991 q^{90} -0.0157050 q^{91} -29.7511 q^{92} -2.91018 q^{93} -7.18024 q^{94} -7.25795 q^{95} -4.90553 q^{96} +14.1363 q^{97} +16.2226 q^{98} -2.63307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * 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 $

$2$	−2.31785	−1.63897	−0.819485	−	0.573101i	$-0.805740\pi$
$2$	−2.31785	−1.63897	−0.819485	+	0.573101i	$0.805740\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.37244	1.68622
$5$	−1.66098	−0.742814	−0.371407	−	0.928470i	$-0.621125\pi$
$5$	−1.66098	−0.742814	−0.371407	+	0.928470i	$0.621125\pi$
$6$	2.31785	0.946259
$7$	0.0321142	0.0121380	0.00606902	−	0.999982i	$-0.498068\pi$
$7$	0.0321142	0.0121380	0.00606902	+	0.999982i	$0.498068\pi$
$8$	−3.18111	−1.12469
$9$	1.00000	0.333333
$10$	3.84991	1.21745
$11$	−2.63307	−0.793901	−0.396950	−	0.917840i	$-0.629932\pi$
$11$	−2.63307	−0.793901	−0.396950	+	0.917840i	$0.629932\pi$
$12$	−3.37244	−0.973539
$13$	−0.489035	−0.135634	−0.0678170	−	0.997698i	$-0.521603\pi$
$13$	−0.489035	−0.135634	−0.0678170	+	0.997698i	$0.521603\pi$
$14$	−0.0744361	−0.0198939
$15$	1.66098	0.428864
$16$	0.628467	0.157117
$17$	−3.94565	−0.956960	−0.478480	−	0.878098i	$-0.658812\pi$
$17$	−3.94565	−0.956960	−0.478480	+	0.878098i	$0.658812\pi$
$18$	−2.31785	−0.546323
$19$	4.36967	1.00247	0.501235	−	0.865311i	$-0.332879\pi$
$19$	4.36967	1.00247	0.501235	+	0.865311i	$0.332879\pi$
$20$	−5.60156	−1.25255
$21$	−0.0321142	−0.00700790
$22$	6.10307	1.30118
$23$	−8.82183	−1.83948	−0.919739	−	0.392531i	$-0.871600\pi$
$23$	−8.82183	−1.83948	−0.919739	+	0.392531i	$0.871600\pi$
$24$	3.18111	0.649342
$25$	−2.24113	−0.448227
$26$	1.13351	0.222300
$27$	−1.00000	−0.192450
$28$	0.108303	0.0204674
$29$	−0.245430	−0.0455752	−0.0227876	−	0.999740i	$-0.507254\pi$
$29$	−0.245430	−0.0455752	−0.0227876	+	0.999740i	$0.507254\pi$
$30$	−3.84991	−0.702895
$31$	2.91018	0.522684	0.261342	−	0.965246i	$-0.415835\pi$
$31$	2.91018	0.522684	0.261342	+	0.965246i	$0.415835\pi$
$32$	4.90553	0.867183
$33$	2.63307	0.458359
$34$	9.14543	1.56843
$35$	−0.0533412	−0.00901631
$36$	3.37244	0.562073
$37$	−5.90247	−0.970359	−0.485180	−	0.874414i	$-0.661246\pi$
$37$	−5.90247	−0.970359	−0.485180	+	0.874414i	$0.661246\pi$
$38$	−10.1282	−1.64302
$39$	0.489035	0.0783083
$40$	5.28377	0.835438
$41$	1.47670	0.230623	0.115311	−	0.993329i	$-0.463213\pi$
$41$	1.47670	0.230623	0.115311	+	0.993329i	$0.463213\pi$
$42$	0.0744361	0.0114857
$43$	−10.2051	−1.55626	−0.778128	−	0.628106i	$-0.783831\pi$
$43$	−10.2051	−1.55626	−0.778128	+	0.628106i	$0.783831\pi$
$44$	−8.87987	−1.33869
$45$	−1.66098	−0.247605
$46$	20.4477	3.01485
$47$	3.09780	0.451860	0.225930	−	0.974144i	$-0.427458\pi$
$47$	3.09780	0.451860	0.225930	+	0.974144i	$0.427458\pi$
$48$	−0.628467	−0.0907115
$49$	−6.99897	−0.999853
$50$	5.19462	0.734630
$51$	3.94565	0.552501
$52$	−1.64924	−0.228709
$53$	−9.77325	−1.34246	−0.671230	−	0.741249i	$-0.734234\pi$
$53$	−9.77325	−1.34246	−0.671230	+	0.741249i	$0.734234\pi$
$54$	2.31785	0.315420
$55$	4.37349	0.589721
$56$	−0.102159	−0.0136516
$57$	−4.36967	−0.578777
$58$	0.568871	0.0746964
$59$	−5.23506	−0.681546	−0.340773	−	0.940146i	$-0.610689\pi$
$59$	−5.23506	−0.681546	−0.340773	+	0.940146i	$0.610689\pi$
$60$	5.60156	0.723159
$61$	10.9023	1.39589	0.697947	−	0.716149i	$-0.254097\pi$
$61$	10.9023	1.39589	0.697947	+	0.716149i	$0.254097\pi$
$62$	−6.74536	−0.856662
$63$	0.0321142	0.00404601
$64$	−12.6272	−1.57840
$65$	0.812279	0.100751
$66$	−6.10307	−0.751236
$67$	13.0273	1.59154	0.795771	−	0.605598i	$-0.207066\pi$
$67$	13.0273	1.59154	0.795771	+	0.605598i	$0.207066\pi$
$68$	−13.3065	−1.61365
$69$	8.82183	1.06202
$70$	0.123637	0.0147775
$71$	−6.36889	−0.755848	−0.377924	−	0.925837i	$-0.623362\pi$
$71$	−6.36889	−0.755848	−0.377924	+	0.925837i	$0.623362\pi$
$72$	−3.18111	−0.374898
$73$	−5.84496	−0.684101	−0.342050	−	0.939682i	$-0.611121\pi$
$73$	−5.84496	−0.684101	−0.342050	+	0.939682i	$0.611121\pi$
$74$	13.6810	1.59039
$75$	2.24113	0.258784
$76$	14.7364	1.69039
$77$	−0.0845591	−0.00963640
$78$	−1.13351	−0.128345
$79$	3.39770	0.382271	0.191135	−	0.981564i	$-0.438783\pi$
$79$	3.39770	0.382271	0.191135	+	0.981564i	$0.438783\pi$
$80$	−1.04387	−0.116709
$81$	1.00000	0.111111
$82$	−3.42278	−0.377983
$83$	−6.61912	−0.726543	−0.363271	−	0.931683i	$-0.618340\pi$
$83$	−6.61912	−0.726543	−0.363271	+	0.931683i	$0.618340\pi$
$84$	−0.108303	−0.0118169
$85$	6.55366	0.710844
$86$	23.6538	2.55066
$87$	0.245430	0.0263129
$88$	8.37609	0.892894
$89$	7.43806	0.788433	0.394217	−	0.919018i	$-0.371016\pi$
$89$	7.43806	0.788433	0.394217	+	0.919018i	$0.371016\pi$
$90$	3.84991	0.405817
$91$	−0.0157050	−0.00164633
$92$	−29.7511	−3.10176
$93$	−2.91018	−0.301771
$94$	−7.18024	−0.740585
$95$	−7.25795	−0.744650
$96$	−4.90553	−0.500668
$97$	14.1363	1.43532	0.717660	−	0.696394i	$-0.245213\pi$
$97$	14.1363	1.43532	0.717660	+	0.696394i	$0.245213\pi$
$98$	16.2226	1.63873
$99$	−2.63307	−0.264634
$100$	−7.55809	−0.755809
$101$	7.82640	0.778756	0.389378	−	0.921078i	$-0.372690\pi$
$101$	7.82640	0.778756	0.389378	+	0.921078i	$0.372690\pi$
$102$	−9.14543	−0.905533
$103$	−7.59252	−0.748114	−0.374057	−	0.927406i	$-0.622034\pi$
$103$	−7.59252	−0.748114	−0.374057	+	0.927406i	$0.622034\pi$
$104$	1.55568	0.152547
$105$	0.0533412	0.00520557
$106$	22.6530	2.20025
$107$	−17.8745	−1.72799	−0.863996	−	0.503498i	$-0.832046\pi$
$107$	−17.8745	−1.72799	−0.863996	+	0.503498i	$0.832046\pi$
$108$	−3.37244	−0.324513
$109$	−9.31592	−0.892303	−0.446151	−	0.894957i	$-0.647206\pi$
$109$	−9.31592	−0.892303	−0.446151	+	0.894957i	$0.647206\pi$
$110$	−10.1371	−0.966534
$111$	5.90247	0.560237
$112$	0.0201828	0.00190709
$113$	−16.0796	−1.51264	−0.756321	−	0.654200i	$-0.773005\pi$
$113$	−16.0796	−1.51264	−0.756321	+	0.654200i	$0.773005\pi$
$114$	10.1282	0.948597
$115$	14.6529	1.36639
$116$	−0.827698	−0.0768498
$117$	−0.489035	−0.0452113
$118$	12.1341	1.11703
$119$	−0.126712	−0.0116156
$120$	−5.28377	−0.482340
$121$	−4.06694	−0.369721
$122$	−25.2699	−2.28783
$123$	−1.47670	−0.133150
$124$	9.81440	0.881359
$125$	12.0274	1.07576
$126$	−0.0744361	−0.00663129
$127$	1.74038	0.154434	0.0772169	−	0.997014i	$-0.475397\pi$
$127$	1.74038	0.154434	0.0772169	+	0.997014i	$0.475397\pi$
$128$	19.4570	1.71977
$129$	10.2051	0.898505
$130$	−1.88274	−0.165128
$131$	0.826430	0.0722056	0.0361028	−	0.999348i	$-0.488506\pi$
$131$	0.826430	0.0722056	0.0361028	+	0.999348i	$0.488506\pi$
$132$	8.87987	0.772894
$133$	0.140329	0.0121680
$134$	−30.1954	−2.60849
$135$	1.66098	0.142955
$136$	12.5515	1.07629
$137$	18.5760	1.58706	0.793528	−	0.608534i	$-0.208242\pi$
$137$	18.5760	1.58706	0.793528	+	0.608534i	$0.208242\pi$
$138$	−20.4477	−1.74062
$139$	1.19856	0.101660	0.0508302	−	0.998707i	$-0.483813\pi$
$139$	1.19856	0.101660	0.0508302	+	0.998707i	$0.483813\pi$
$140$	−0.179890	−0.0152035
$141$	−3.09780	−0.260882
$142$	14.7621	1.23881
$143$	1.28766	0.107680
$144$	0.628467	0.0523723
$145$	0.407655	0.0338539
$146$	13.5478	1.12122
$147$	6.99897	0.577265
$148$	−19.9057	−1.63624
$149$	2.41891	0.198165	0.0990823	−	0.995079i	$-0.468409\pi$
$149$	2.41891	0.198165	0.0990823	+	0.995079i	$0.468409\pi$
$150$	−5.19462	−0.424139
$151$	−15.6758	−1.27568	−0.637840	−	0.770169i	$-0.720172\pi$
$151$	−15.6758	−1.27568	−0.637840	+	0.770169i	$0.720172\pi$
$152$	−13.9004	−1.12747
$153$	−3.94565	−0.318987
$154$	0.195995	0.0157938
$155$	−4.83376	−0.388257
$156$	1.64924	0.132045
$157$	−20.5443	−1.63962	−0.819809	−	0.572637i	$-0.805920\pi$
$157$	−20.5443	−1.63962	−0.819809	+	0.572637i	$0.805920\pi$
$158$	−7.87536	−0.626530
$159$	9.77325	0.775069
$160$	−8.14800	−0.644156
$161$	−0.283306	−0.0223277
$162$	−2.31785	−0.182108
$163$	16.1513	1.26507	0.632535	−	0.774532i	$-0.282015\pi$
$163$	16.1513	1.26507	0.632535	+	0.774532i	$0.282015\pi$
$164$	4.98010	0.388880
$165$	−4.37349	−0.340476
$166$	15.3421	1.19078
$167$	3.01699	0.233462	0.116731	−	0.993164i	$-0.462758\pi$
$167$	3.01699	0.233462	0.116731	+	0.993164i	$0.462758\pi$
$168$	0.102159	0.00788173
$169$	−12.7608	−0.981603
$170$	−15.1904	−1.16505
$171$	4.36967	0.334157
$172$	−34.4159	−2.62419
$173$	−22.6750	−1.72395	−0.861975	−	0.506951i	$-0.830773\pi$
$173$	−22.6750	−1.72395	−0.861975	+	0.506951i	$0.830773\pi$
$174$	−0.568871	−0.0431260
$175$	−0.0719723	−0.00544060
$176$	−1.65480	−0.124735
$177$	5.23506	0.393491
$178$	−17.2403	−1.29222
$179$	−9.62452	−0.719370	−0.359685	−	0.933074i	$-0.617116\pi$
$179$	−9.62452	−0.719370	−0.359685	+	0.933074i	$0.617116\pi$
$180$	−5.60156	−0.417516
$181$	16.4574	1.22327	0.611636	−	0.791139i	$-0.290512\pi$
$181$	16.4574	1.22327	0.611636	+	0.791139i	$0.290512\pi$
$182$	0.0364019	0.00269829
$183$	−10.9023	−0.805920
$184$	28.0632	2.06885
$185$	9.80390	0.720797
$186$	6.74536	0.494594
$187$	10.3892	0.759732
$188$	10.4471	0.761935
$189$	−0.0321142	−0.00233597
$190$	16.8228	1.22046
$191$	−15.6560	−1.13283	−0.566414	−	0.824121i	$-0.691670\pi$
$191$	−15.6560	−1.13283	−0.566414	+	0.824121i	$0.691670\pi$
$192$	12.6272	0.911291
$193$	−2.72183	−0.195922	−0.0979608	−	0.995190i	$-0.531232\pi$
$193$	−2.72183	−0.195922	−0.0979608	+	0.995190i	$0.531232\pi$
$194$	−32.7658	−2.35244
$195$	−0.812279	−0.0581685
$196$	−23.6036	−1.68597
$197$	22.8531	1.62822	0.814108	−	0.580714i	$-0.197226\pi$
$197$	22.8531	1.62822	0.814108	+	0.580714i	$0.197226\pi$
$198$	6.10307	0.433726
$199$	−14.7278	−1.04402	−0.522012	−	0.852938i	$-0.674818\pi$
$199$	−14.7278	−1.04402	−0.522012	+	0.852938i	$0.674818\pi$
$200$	7.12930	0.504118
$201$	−13.0273	−0.918877
$202$	−18.1404	−1.27636
$203$	−0.00788180	−0.000553194 0
$204$	13.3065	0.931639
$205$	−2.45278	−0.171310
$206$	17.5983	1.22614
$207$	−8.82183	−0.613159
$208$	−0.307343	−0.0213104
$209$	−11.5056	−0.795862
$210$	−0.123637	−0.00853177
$211$	−10.7980	−0.743363	−0.371682	−	0.928360i	$-0.621219\pi$
$211$	−10.7980	−0.743363	−0.371682	+	0.928360i	$0.621219\pi$
$212$	−32.9597	−2.26368
$213$	6.36889	0.436389
$214$	41.4304	2.83213
$215$	16.9504	1.15601
$216$	3.18111	0.216447
$217$	0.0934582	0.00634435
$218$	21.5929	1.46246
$219$	5.84496	0.394966
$220$	14.7493	0.994399
$221$	1.92956	0.129796
$222$	−13.6810	−0.918212
$223$	26.5980	1.78113	0.890567	−	0.454853i	$-0.150308\pi$
$223$	26.5980	1.78113	0.890567	+	0.454853i	$0.150308\pi$
$224$	0.157537	0.0105259
$225$	−2.24113	−0.149409
$226$	37.2702	2.47917
$227$	8.29116	0.550304	0.275152	−	0.961401i	$-0.411272\pi$
$227$	8.29116	0.550304	0.275152	+	0.961401i	$0.411272\pi$
$228$	−14.7364	−0.975945
$229$	−7.96481	−0.526330	−0.263165	−	0.964751i	$-0.584766\pi$
$229$	−7.96481	−0.526330	−0.263165	+	0.964751i	$0.584766\pi$
$230$	−33.9633	−2.23947
$231$	0.0845591	0.00556358
$232$	0.780741	0.0512581
$233$	2.75629	0.180571	0.0902853	−	0.995916i	$-0.471222\pi$
$233$	2.75629	0.180571	0.0902853	+	0.995916i	$0.471222\pi$
$234$	1.13351	0.0741000
$235$	−5.14539	−0.335648
$236$	−17.6549	−1.14924
$237$	−3.39770	−0.220704
$238$	0.293699	0.0190376
$239$	−17.2782	−1.11763	−0.558816	−	0.829292i	$-0.688744\pi$
$239$	−17.2782	−1.11763	−0.558816	+	0.829292i	$0.688744\pi$
$240$	1.04387	0.0673818
$241$	−2.73131	−0.175939	−0.0879697	−	0.996123i	$-0.528038\pi$
$241$	−2.73131	−0.175939	−0.0879697	+	0.996123i	$0.528038\pi$
$242$	9.42656	0.605962
$243$	−1.00000	−0.0641500
$244$	36.7673	2.35378
$245$	11.6252	0.742705
$246$	3.42278	0.218229
$247$	−2.13692	−0.135969
$248$	−9.25760	−0.587858
$249$	6.61912	0.419470
$250$	−27.8777	−1.76314
$251$	9.01164	0.568810	0.284405	−	0.958704i	$-0.408204\pi$
$251$	9.01164	0.568810	0.284405	+	0.958704i	$0.408204\pi$
$252$	0.108303	0.00682247
$253$	23.2285	1.46036
$254$	−4.03395	−0.253112
$255$	−6.55366	−0.410406
$256$	−19.8440	−1.24025
$257$	−0.215275	−0.0134285	−0.00671423	−	0.999977i	$-0.502137\pi$
$257$	−0.215275	−0.0134285	−0.00671423	+	0.999977i	$0.502137\pi$
$258$	−23.6538	−1.47262
$259$	−0.189553	−0.0117783
$260$	2.73936	0.169888
$261$	−0.245430	−0.0151917
$262$	−1.91554	−0.118343
$263$	−10.3087	−0.635660	−0.317830	−	0.948148i	$-0.602954\pi$
$263$	−10.3087	−0.635660	−0.317830	+	0.948148i	$0.602954\pi$
$264$	−8.37609	−0.515513
$265$	16.2332	0.997198
$266$	−0.325261	−0.0199430
$267$	−7.43806	−0.455202
$268$	43.9339	2.68369
$269$	12.1502	0.740809	0.370405	−	0.928870i	$-0.379219\pi$
$269$	12.1502	0.740809	0.370405	+	0.928870i	$0.379219\pi$
$270$	−3.84991	−0.234298
$271$	12.9952	0.789399	0.394700	−	0.918810i	$-0.370849\pi$
$271$	12.9952	0.789399	0.394700	+	0.918810i	$0.370849\pi$
$272$	−2.47971	−0.150355
$273$	0.0157050	0.000950510 0
$274$	−43.0564	−2.60114
$275$	5.90107	0.355848
$276$	29.7511	1.79080
$277$	−10.9581	−0.658411	−0.329205	−	0.944258i	$-0.606781\pi$
$277$	−10.9581	−0.658411	−0.329205	+	0.944258i	$0.606781\pi$
$278$	−2.77808	−0.166618
$279$	2.91018	0.174228
$280$	0.169684	0.0101406
$281$	−26.3205	−1.57015	−0.785076	−	0.619400i	$-0.787376\pi$
$281$	−26.3205	−1.57015	−0.785076	+	0.619400i	$0.787376\pi$
$282$	7.18024	0.427577
$283$	−12.3744	−0.735581	−0.367790	−	0.929909i	$-0.619886\pi$
$283$	−12.3744	−0.735581	−0.367790	+	0.929909i	$0.619886\pi$
$284$	−21.4787	−1.27453
$285$	7.25795	0.429924
$286$	−2.98462	−0.176484
$287$	0.0474232	0.00279931
$288$	4.90553	0.289061
$289$	−1.43186	−0.0842268
$290$	−0.944885	−0.0554855
$291$	−14.1363	−0.828682
$292$	−19.7118	−1.15354
$293$	−16.7891	−0.980830	−0.490415	−	0.871489i	$-0.663155\pi$
$293$	−16.7891	−0.980830	−0.490415	+	0.871489i	$0.663155\pi$
$294$	−16.2226	−0.946120
$295$	8.69534	0.506262
$296$	18.7764	1.09136
$297$	2.63307	0.152786
$298$	−5.60667	−0.324786
$299$	4.31418	0.249496
$300$	7.55809	0.436367
$301$	−0.327728	−0.0188899
$302$	36.3342	2.09080
$303$	−7.82640	−0.449615
$304$	2.74619	0.157505
$305$	−18.1085	−1.03689
$306$	9.14543	0.522810
$307$	−27.5098	−1.57007	−0.785033	−	0.619454i	$-0.787354\pi$
$307$	−27.5098	−1.57007	−0.785033	+	0.619454i	$0.787354\pi$
$308$	−0.285170	−0.0162491
$309$	7.59252	0.431924
$310$	11.2039	0.636341
$311$	24.3603	1.38135	0.690674	−	0.723166i	$-0.257314\pi$
$311$	24.3603	1.38135	0.690674	+	0.723166i	$0.257314\pi$
$312$	−1.55568	−0.0880728
$313$	−12.1214	−0.685144	−0.342572	−	0.939492i	$-0.611298\pi$
$313$	−12.1214	−0.685144	−0.342572	+	0.939492i	$0.611298\pi$
$314$	47.6188	2.68728
$315$	−0.0533412	−0.00300544
$316$	11.4585	0.644592
$317$	0.915693	0.0514305	0.0257152	−	0.999669i	$-0.491814\pi$
$317$	0.915693	0.0514305	0.0257152	+	0.999669i	$0.491814\pi$
$318$	−22.6530	−1.27031
$319$	0.646235	0.0361822
$320$	20.9736	1.17246
$321$	17.8745	0.997657
$322$	0.656662	0.0365943
$323$	−17.2412	−0.959325
$324$	3.37244	0.187358
$325$	1.09599	0.0607948
$326$	−37.4364	−2.07341
$327$	9.31592	0.515171
$328$	−4.69756	−0.259379
$329$	0.0994834	0.00548470
$330$	10.1371	0.558029
$331$	10.7630	0.591589	0.295795	−	0.955252i	$-0.404416\pi$
$331$	10.7630	0.591589	0.295795	+	0.955252i	$0.404416\pi$
$332$	−22.3226	−1.22511
$333$	−5.90247	−0.323453
$334$	−6.99295	−0.382637
$335$	−21.6382	−1.18222
$336$	−0.0201828	−0.00110106
$337$	−7.86368	−0.428362	−0.214181	−	0.976794i	$-0.568708\pi$
$337$	−7.86368	−0.428362	−0.214181	+	0.976794i	$0.568708\pi$
$338$	29.5778	1.60882
$339$	16.0796	0.873325
$340$	22.1018	1.19864
$341$	−7.66271	−0.414959
$342$	−10.1282	−0.547673
$343$	−0.449566	−0.0242743
$344$	32.4634	1.75031
$345$	−14.6529	−0.788886
$346$	52.5574	2.82550
$347$	−11.0762	−0.594600	−0.297300	−	0.954784i	$-0.596086\pi$
$347$	−11.0762	−0.594600	−0.297300	+	0.954784i	$0.596086\pi$
$348$	0.827698	0.0443693
$349$	24.5692	1.31516	0.657578	−	0.753386i	$-0.271581\pi$
$349$	24.5692	1.31516	0.657578	+	0.753386i	$0.271581\pi$
$350$	0.166821	0.00891697
$351$	0.489035	0.0261028
$352$	−12.9166	−0.688457
$353$	21.0154	1.11853	0.559267	−	0.828987i	$-0.311083\pi$
$353$	21.0154	1.11853	0.559267	+	0.828987i	$0.311083\pi$
$354$	−12.1341	−0.644919
$355$	10.5786	0.561454
$356$	25.0844	1.32947
$357$	0.126712	0.00670628
$358$	22.3082	1.17903
$359$	−2.33352	−0.123159	−0.0615793	−	0.998102i	$-0.519614\pi$
$359$	−2.33352	−0.123159	−0.0615793	+	0.998102i	$0.519614\pi$
$360$	5.28377	0.278479
$361$	0.0940081	0.00494780
$362$	−38.1459	−2.00490
$363$	4.06694	0.213459
$364$	−0.0529641	−0.00277608
$365$	9.70838	0.508160
$366$	25.2699	1.32088
$367$	−8.40293	−0.438629	−0.219315	−	0.975654i	$-0.570382\pi$
$367$	−8.40293	−0.438629	−0.219315	+	0.975654i	$0.570382\pi$
$368$	−5.54423	−0.289013
$369$	1.47670	0.0768742
$370$	−22.7240	−1.18136
$371$	−0.313860	−0.0162948
$372$	−9.81440	−0.508853
$373$	10.5758	0.547596	0.273798	−	0.961787i	$-0.411720\pi$
$373$	10.5758	0.547596	0.273798	+	0.961787i	$0.411720\pi$
$374$	−24.0806	−1.24518
$375$	−12.0274	−0.621092
$376$	−9.85444	−0.508204
$377$	0.120024	0.00618155
$378$	0.0744361	0.00382858
$379$	5.01251	0.257475	0.128738	−	0.991679i	$-0.458907\pi$
$379$	5.01251	0.257475	0.128738	+	0.991679i	$0.458907\pi$
$380$	−24.4770	−1.25564
$381$	−1.74038	−0.0891624
$382$	36.2883	1.85667
$383$	−13.5276	−0.691226	−0.345613	−	0.938377i	$-0.612329\pi$
$383$	−13.5276	−0.691226	−0.345613	+	0.938377i	$0.612329\pi$
$384$	−19.4570	−0.992910
$385$	0.140451	0.00715806
$386$	6.30880	0.321109
$387$	−10.2051	−0.518752
$388$	47.6737	2.42026
$389$	−23.5786	−1.19548	−0.597741	−	0.801689i	$-0.703935\pi$
$389$	−23.5786	−1.19548	−0.597741	+	0.801689i	$0.703935\pi$
$390$	1.88274	0.0953364
$391$	34.8078	1.76031
$392$	22.2645	1.12453
$393$	−0.826430	−0.0416879
$394$	−52.9701	−2.66859
$395$	−5.64352	−0.283956
$396$	−8.87987	−0.446230
$397$	−34.4447	−1.72873	−0.864366	−	0.502864i	$-0.832280\pi$
$397$	−34.4447	−1.72873	−0.864366	+	0.502864i	$0.832280\pi$
$398$	34.1368	1.71112
$399$	−0.140329	−0.00702522
$400$	−1.40848	−0.0704240
$401$	−16.8172	−0.839813	−0.419907	−	0.907567i	$-0.637937\pi$
$401$	−16.8172	−0.839813	−0.419907	+	0.907567i	$0.637937\pi$
$402$	30.1954	1.50601
$403$	−1.42318	−0.0708936
$404$	26.3941	1.31315
$405$	−1.66098	−0.0825349
$406$	0.0182689	0.000906668 0
$407$	15.5416	0.770369
$408$	−12.5515	−0.621394
$409$	27.1025	1.34013	0.670067	−	0.742300i	$-0.266265\pi$
$409$	27.1025	1.34013	0.670067	+	0.742300i	$0.266265\pi$
$410$	5.68519	0.280771
$411$	−18.5760	−0.916287
$412$	−25.6053	−1.26148
$413$	−0.168120	−0.00827264
$414$	20.4477	1.00495
$415$	10.9942	0.539687
$416$	−2.39898	−0.117619
$417$	−1.19856	−0.0586937
$418$	26.6684	1.30439
$419$	−2.49599	−0.121937	−0.0609687	−	0.998140i	$-0.519419\pi$
$419$	−2.49599	−0.121937	−0.0609687	+	0.998140i	$0.519419\pi$
$420$	0.179890	0.00877773
$421$	−7.06194	−0.344178	−0.172089	−	0.985081i	$-0.555052\pi$
$421$	−7.06194	−0.344178	−0.172089	+	0.985081i	$0.555052\pi$
$422$	25.0281	1.21835
$423$	3.09780	0.150620
$424$	31.0898	1.50985
$425$	8.84273	0.428935
$426$	−14.7621	−0.715228
$427$	0.350118	0.0169434
$428$	−60.2806	−2.91377
$429$	−1.28766	−0.0621690
$430$	−39.2886	−1.89466
$431$	−12.0930	−0.582497	−0.291248	−	0.956647i	$-0.594071\pi$
$431$	−12.0930	−0.582497	−0.291248	+	0.956647i	$0.594071\pi$
$432$	−0.628467	−0.0302372
$433$	33.7492	1.62188	0.810942	−	0.585127i	$-0.198955\pi$
$433$	33.7492	1.62188	0.810942	+	0.585127i	$0.198955\pi$
$434$	−0.216622	−0.0103982
$435$	−0.407655	−0.0195456
$436$	−31.4174	−1.50462
$437$	−38.5485	−1.84402
$438$	−13.5478	−0.647337
$439$	37.5920	1.79417	0.897085	−	0.441859i	$-0.145681\pi$
$439$	37.5920	1.79417	0.897085	+	0.441859i	$0.145681\pi$
$440$	−13.9125	−0.663255
$441$	−6.99897	−0.333284
$442$	−4.47244	−0.212732
$443$	16.9558	0.805595	0.402797	−	0.915289i	$-0.368038\pi$
$443$	16.9558	0.805595	0.402797	+	0.915289i	$0.368038\pi$
$444$	19.9057	0.944683
$445$	−12.3545	−0.585660
$446$	−61.6502	−2.91922
$447$	−2.41891	−0.114410
$448$	−0.405514	−0.0191587
$449$	5.93777	0.280221	0.140110	−	0.990136i	$-0.455254\pi$
$449$	5.93777	0.280221	0.140110	+	0.990136i	$0.455254\pi$
$450$	5.19462	0.244877
$451$	−3.88827	−0.183091
$452$	−54.2275	−2.55065
$453$	15.6758	0.736515
$454$	−19.2177	−0.901931
$455$	0.0260857	0.00122292
$456$	13.9004	0.650946
$457$	14.9745	0.700479	0.350240	−	0.936660i	$-0.386100\pi$
$457$	14.9745	0.700479	0.350240	+	0.936660i	$0.386100\pi$
$458$	18.4613	0.862638
$459$	3.94565	0.184167
$460$	49.4160	2.30403
$461$	0.432535	0.0201452	0.0100726	−	0.999949i	$-0.496794\pi$
$461$	0.432535	0.0201452	0.0100726	+	0.999949i	$0.496794\pi$
$462$	−0.195995	−0.00911853
$463$	11.3883	0.529261	0.264630	−	0.964350i	$-0.414750\pi$
$463$	11.3883	0.529261	0.264630	+	0.964350i	$0.414750\pi$
$464$	−0.154245	−0.00716064
$465$	4.83376	0.224160
$466$	−6.38868	−0.295950
$467$	38.4152	1.77764	0.888822	−	0.458253i	$-0.151525\pi$
$467$	38.4152	1.77764	0.888822	+	0.458253i	$0.151525\pi$
$468$	−1.64924	−0.0762362
$469$	0.418363	0.0193182
$470$	11.9263	0.550117
$471$	20.5443	0.946634
$472$	16.6533	0.766530
$473$	26.8706	1.23551
$474$	7.87536	0.361727
$475$	−9.79302	−0.449334
$476$	−0.427327	−0.0195865
$477$	−9.77325	−0.447486
$478$	40.0482	1.83176
$479$	−12.1783	−0.556442	−0.278221	−	0.960517i	$-0.589745\pi$
$479$	−12.1783	−0.556442	−0.278221	+	0.960517i	$0.589745\pi$
$480$	8.14800	0.371904
$481$	2.88651	0.131614
$482$	6.33078	0.288359
$483$	0.283306	0.0128909
$484$	−13.7155	−0.623432
$485$	−23.4801	−1.06618
$486$	2.31785	0.105140
$487$	25.6789	1.16362	0.581812	−	0.813324i	$-0.302344\pi$
$487$	25.6789	1.16362	0.581812	+	0.813324i	$0.302344\pi$
$488$	−34.6814	−1.56995
$489$	−16.1513	−0.730388
$490$	−26.9454	−1.21727
$491$	29.8392	1.34663	0.673313	−	0.739358i	$-0.264871\pi$
$491$	29.8392	1.34663	0.673313	+	0.739358i	$0.264871\pi$
$492$	−4.98010	−0.224520
$493$	0.968381	0.0436137
$494$	4.95307	0.222849
$495$	4.37349	0.196574
$496$	1.82895	0.0821224
$497$	−0.204532	−0.00917451
$498$	−15.3421	−0.687498
$499$	13.6546	0.611264	0.305632	−	0.952150i	$-0.401132\pi$
$499$	13.6546	0.611264	0.305632	+	0.952150i	$0.401132\pi$
$500$	40.5617	1.81397
$501$	−3.01699	−0.134789
$502$	−20.8877	−0.932262
$503$	42.0742	1.87600	0.937998	−	0.346641i	$-0.112678\pi$
$503$	42.0742	1.87600	0.937998	+	0.346641i	$0.112678\pi$
$504$	−0.102159	−0.00455052
$505$	−12.9995	−0.578471
$506$	−53.8402	−2.39349
$507$	12.7608	0.566729
$508$	5.86933	0.260409
$509$	−16.7064	−0.740500	−0.370250	−	0.928932i	$-0.620728\pi$
$509$	−16.7064	−0.740500	−0.370250	+	0.928932i	$0.620728\pi$
$510$	15.1904	0.672643
$511$	−0.187706	−0.00830364
$512$	7.08141	0.312957
$513$	−4.36967	−0.192926
$514$	0.498975	0.0220088
$515$	12.6111	0.555710
$516$	34.4159	1.51508
$517$	−8.15672	−0.358732
$518$	0.439356	0.0193042
$519$	22.6750	0.995323
$520$	−2.58395	−0.113314
$521$	3.62257	0.158708	0.0793538	−	0.996847i	$-0.474714\pi$
$521$	3.62257	0.158708	0.0793538	+	0.996847i	$0.474714\pi$
$522$	0.568871	0.0248988
$523$	15.3826	0.672636	0.336318	−	0.941749i	$-0.390818\pi$
$523$	15.3826	0.672636	0.336318	+	0.941749i	$0.390818\pi$
$524$	2.78709	0.121754
$525$	0.0719723	0.00314113
$526$	23.8940	1.04183
$527$	−11.4825	−0.500187
$528$	1.65480	0.0720159
$529$	54.8246	2.38368
$530$	−37.6262	−1.63438
$531$	−5.23506	−0.227182
$532$	0.473250	0.0205180
$533$	−0.722161	−0.0312803
$534$	17.2403	0.746062
$535$	29.6892	1.28358
$536$	−41.4414	−1.78999
$537$	9.62452	0.415329
$538$	−28.1623	−1.21416
$539$	18.4288	0.793784
$540$	5.60156	0.241053
$541$	4.08607	0.175674	0.0878370	−	0.996135i	$-0.472005\pi$
$541$	4.08607	0.175674	0.0878370	+	0.996135i	$0.472005\pi$
$542$	−30.1208	−1.29380
$543$	−16.4574	−0.706256
$544$	−19.3555	−0.829860
$545$	15.4736	0.662815
$546$	−0.0364019	−0.00155786
$547$	4.79968	0.205220	0.102610	−	0.994722i	$-0.467281\pi$
$547$	4.79968	0.205220	0.102610	+	0.994722i	$0.467281\pi$
$548$	62.6465	2.67612
$549$	10.9023	0.465298
$550$	−13.6778	−0.583223
$551$	−1.07245	−0.0456878
$552$	−28.0632	−1.19445
$553$	0.109114	0.00464002
$554$	25.3993	1.07911
$555$	−9.80390	−0.416152
$556$	4.04207	0.171422
$557$	10.9759	0.465066	0.232533	−	0.972589i	$-0.425299\pi$
$557$	10.9759	0.465066	0.232533	+	0.972589i	$0.425299\pi$
$558$	−6.74536	−0.285554
$559$	4.99063	0.211081
$560$	−0.0335232	−0.00141661
$561$	−10.3892	−0.438631
$562$	61.0071	2.57343
$563$	−27.5142	−1.15959	−0.579794	−	0.814763i	$-0.696867\pi$
$563$	−27.5142	−1.15959	−0.579794	+	0.814763i	$0.696867\pi$
$564$	−10.4471	−0.439904
$565$	26.7080	1.12361
$566$	28.6820	1.20559
$567$	0.0321142	0.00134867
$568$	20.2601	0.850096
$569$	−32.4936	−1.36220	−0.681101	−	0.732189i	$-0.738499\pi$
$569$	−32.4936	−1.36220	−0.681101	+	0.732189i	$0.738499\pi$
$570$	−16.8228	−0.704632
$571$	−18.5897	−0.777956	−0.388978	−	0.921247i	$-0.627172\pi$
$571$	−18.5897	−0.777956	−0.388978	+	0.921247i	$0.627172\pi$
$572$	4.34257	0.181572
$573$	15.6560	0.654039
$574$	−0.109920	−0.00458798
$575$	19.7709	0.824503
$576$	−12.6272	−0.526134
$577$	15.4937	0.645013	0.322507	−	0.946567i	$-0.395475\pi$
$577$	15.4937	0.645013	0.322507	+	0.946567i	$0.395475\pi$
$578$	3.31883	0.138045
$579$	2.72183	0.113115
$580$	1.37479	0.0570852
$581$	−0.212568	−0.00881881
$582$	32.7658	1.35818
$583$	25.7337	1.06578
$584$	18.5935	0.769403
$585$	0.812279	0.0335836
$586$	38.9147	1.60755
$587$	0.0148692	0.000613720 0	0.000306860	−	1.00000i	$-0.499902\pi$
$587$	0.0148692	0.000613720 0	0.000306860		1.00000i	$0.499902\pi$
$588$	23.6036	0.973396
$589$	12.7165	0.523975
$590$	−20.1545	−0.829748
$591$	−22.8531	−0.940051
$592$	−3.70951	−0.152460
$593$	−3.82088	−0.156905	−0.0784523	−	0.996918i	$-0.524998\pi$
$593$	−3.82088	−0.156905	−0.0784523	+	0.996918i	$0.524998\pi$
$594$	−6.10307	−0.250412
$595$	0.210466	0.00862825
$596$	8.15762	0.334149
$597$	14.7278	0.602767
$598$	−9.99964	−0.408916
$599$	42.4501	1.73446	0.867232	−	0.497904i	$-0.165897\pi$
$599$	42.4501	1.73446	0.867232	+	0.497904i	$0.165897\pi$
$600$	−7.12930	−0.291052
$601$	20.2229	0.824911	0.412456	−	0.910978i	$-0.364671\pi$
$601$	20.2229	0.824911	0.412456	+	0.910978i	$0.364671\pi$
$602$	0.759624	0.0309600
$603$	13.0273	0.530514
$604$	−52.8658	−2.15108
$605$	6.75511	0.274634
$606$	18.1404	0.736905
$607$	−42.0773	−1.70786	−0.853931	−	0.520385i	$-0.825788\pi$
$607$	−42.0773	−1.70786	−0.853931	+	0.520385i	$0.825788\pi$
$608$	21.4355	0.869326
$609$	0.00788180	0.000319387 0
$610$	41.9728	1.69943
$611$	−1.51493	−0.0612876
$612$	−13.3065	−0.537882
$613$	−43.0664	−1.73944	−0.869719	−	0.493548i	$-0.835700\pi$
$613$	−43.0664	−1.73944	−0.869719	+	0.493548i	$0.835700\pi$
$614$	63.7636	2.57329
$615$	2.45278	0.0989057
$616$	0.268992	0.0108380
$617$	5.31469	0.213961	0.106981	−	0.994261i	$-0.465882\pi$
$617$	5.31469	0.213961	0.106981	+	0.994261i	$0.465882\pi$
$618$	−17.5983	−0.707909
$619$	34.3076	1.37894	0.689470	−	0.724314i	$-0.257844\pi$
$619$	34.3076	1.37894	0.689470	+	0.724314i	$0.257844\pi$
$620$	−16.3016	−0.654686
$621$	8.82183	0.354008
$622$	−56.4637	−2.26399
$623$	0.238868	0.00957004
$624$	0.307343	0.0123036
$625$	−8.77164	−0.350866
$626$	28.0957	1.12293
$627$	11.5056	0.459491
$628$	−69.2846	−2.76476
$629$	23.2891	0.928596
$630$	0.123637	0.00492582
$631$	19.9010	0.792247	0.396124	−	0.918197i	$-0.370355\pi$
$631$	19.9010	0.792247	0.396124	+	0.918197i	$0.370355\pi$
$632$	−10.8084	−0.429937
$633$	10.7980	0.429181
$634$	−2.12244	−0.0842929
$635$	−2.89074	−0.114716
$636$	32.9597	1.30694
$637$	3.42274	0.135614
$638$	−1.49788	−0.0593015
$639$	−6.36889	−0.251949
$640$	−32.3177	−1.27747
$641$	13.1719	0.520260	0.260130	−	0.965574i	$-0.416235\pi$
$641$	13.1719	0.520260	0.260130	+	0.965574i	$0.416235\pi$
$642$	−41.4304	−1.63513
$643$	−34.0014	−1.34088	−0.670442	−	0.741962i	$-0.733895\pi$
$643$	−34.0014	−1.34088	−0.670442	+	0.741962i	$0.733895\pi$
$644$	−0.955433	−0.0376493
$645$	−16.9504	−0.667422
$646$	39.9625	1.57230
$647$	−1.97376	−0.0775967	−0.0387983	−	0.999247i	$-0.512353\pi$
$647$	−1.97376	−0.0775967	−0.0387983	+	0.999247i	$0.512353\pi$
$648$	−3.18111	−0.124966
$649$	13.7843	0.541080
$650$	−2.54035	−0.0996408
$651$	−0.0934582	−0.00366291
$652$	54.4694	2.13319
$653$	22.4524	0.878629	0.439315	−	0.898333i	$-0.355221\pi$
$653$	22.4524	0.878629	0.439315	+	0.898333i	$0.355221\pi$
$654$	−21.5929	−0.844350
$655$	−1.37269	−0.0536353
$656$	0.928061	0.0362347
$657$	−5.84496	−0.228034
$658$	−0.230588	−0.00898925
$659$	44.3455	1.72746	0.863728	−	0.503958i	$-0.168124\pi$
$659$	44.3455	1.72746	0.863728	+	0.503958i	$0.168124\pi$
$660$	−14.7493	−0.574116
$661$	5.76557	0.224255	0.112127	−	0.993694i	$-0.464234\pi$
$661$	5.76557	0.224255	0.112127	+	0.993694i	$0.464234\pi$
$662$	−24.9471	−0.969596
$663$	−1.92956	−0.0749380
$664$	21.0562	0.817138
$665$	−0.233083	−0.00903859
$666$	13.6810	0.530130
$667$	2.16514	0.0838346
$668$	10.1746	0.393668
$669$	−26.5980	−1.02834
$670$	50.1541	1.93762
$671$	−28.7065	−1.10820
$672$	−0.157537	−0.00607713
$673$	−15.8853	−0.612334	−0.306167	−	0.951978i	$-0.599047\pi$
$673$	−15.8853	−0.612334	−0.306167	+	0.951978i	$0.599047\pi$
$674$	18.2269	0.702072
$675$	2.24113	0.0862613
$676$	−43.0352	−1.65520
$677$	42.5280	1.63448	0.817241	−	0.576296i	$-0.195502\pi$
$677$	42.5280	1.63448	0.817241	+	0.576296i	$0.195502\pi$
$678$	−37.2702	−1.43135
$679$	0.453975	0.0174220
$680$	−20.8479	−0.799481
$681$	−8.29116	−0.317718
$682$	17.7610	0.680105
$683$	−1.01500	−0.0388379	−0.0194189	−	0.999811i	$-0.506182\pi$
$683$	−1.01500	−0.0388379	−0.0194189	+	0.999811i	$0.506182\pi$
$684$	14.7364	0.563462
$685$	−30.8544	−1.17889
$686$	1.04203	0.0397848
$687$	7.96481	0.303877
$688$	−6.41354	−0.244514
$689$	4.77946	0.182083
$690$	33.9633	1.29296
$691$	34.3658	1.30734	0.653669	−	0.756781i	$-0.273229\pi$
$691$	34.3658	1.30734	0.653669	+	0.756781i	$0.273229\pi$
$692$	−76.4701	−2.90696
$693$	−0.0845591	−0.00321213
$694$	25.6729	0.974532
$695$	−1.99079	−0.0755149
$696$	−0.780741	−0.0295939
$697$	−5.82656	−0.220697
$698$	−56.9477	−2.15550
$699$	−2.75629	−0.104253
$700$	−0.242722	−0.00917404
$701$	22.9069	0.865182	0.432591	−	0.901590i	$-0.357599\pi$
$701$	22.9069	0.865182	0.432591	+	0.901590i	$0.357599\pi$
$702$	−1.13351	−0.0427816
$703$	−25.7918	−0.972757
$704$	33.2484	1.25310
$705$	5.14539	0.193787
$706$	−48.7105	−1.83324
$707$	0.251339	0.00945258
$708$	17.6549	0.663512
$709$	4.86016	0.182527	0.0912636	−	0.995827i	$-0.470909\pi$
$709$	4.86016	0.182527	0.0912636	+	0.995827i	$0.470909\pi$
$710$	−24.5197	−0.920207
$711$	3.39770	0.127424
$712$	−23.6613	−0.886745
$713$	−25.6731	−0.961465
$714$	−0.293699	−0.0109914
$715$	−2.13879	−0.0799862
$716$	−32.4581	−1.21302
$717$	17.2782	0.645265
$718$	5.40876	0.201853
$719$	−25.1898	−0.939421	−0.469711	−	0.882820i	$-0.655642\pi$
$719$	−25.1898	−0.939421	−0.469711	+	0.882820i	$0.655642\pi$
$720$	−1.04387	−0.0389029
$721$	−0.243828	−0.00908063
$722$	−0.217897	−0.00810928
$723$	2.73131	0.101579
$724$	55.5017	2.06270
$725$	0.550042	0.0204280
$726$	−9.42656	−0.349852
$727$	47.9486	1.77832	0.889158	−	0.457600i	$-0.151291\pi$
$727$	47.9486	1.77832	0.889158	+	0.457600i	$0.151291\pi$
$728$	0.0499593	0.00185162
$729$	1.00000	0.0370370
$730$	−22.5026	−0.832858
$731$	40.2656	1.48928
$732$	−36.7673	−1.35896
$733$	−42.1175	−1.55565	−0.777823	−	0.628483i	$-0.783676\pi$
$733$	−42.1175	−1.55565	−0.777823	+	0.628483i	$0.783676\pi$
$734$	19.4767	0.718900
$735$	−11.6252	−0.428801
$736$	−43.2757	−1.59516
$737$	−34.3019	−1.26353
$738$	−3.42278	−0.125994
$739$	35.2627	1.29716	0.648580	−	0.761147i	$-0.275363\pi$
$739$	35.2627	1.29716	0.648580	+	0.761147i	$0.275363\pi$
$740$	33.0630	1.21542
$741$	2.13692	0.0785018
$742$	0.727482	0.0267067
$743$	14.2085	0.521261	0.260631	−	0.965439i	$-0.416070\pi$
$743$	14.2085	0.521261	0.260631	+	0.965439i	$0.416070\pi$
$744$	9.25760	0.339400
$745$	−4.01776	−0.147199
$746$	−24.5132	−0.897494
$747$	−6.61912	−0.242181
$748$	35.0369	1.28107
$749$	−0.574026	−0.0209744
$750$	27.8777	1.01795
$751$	31.1321	1.13603	0.568013	−	0.823020i	$-0.307712\pi$
$751$	31.1321	1.13603	0.568013	+	0.823020i	$0.307712\pi$
$752$	1.94686	0.0709948
$753$	−9.01164	−0.328402
$754$	−0.278198	−0.0101314
$755$	26.0373	0.947594
$756$	−0.108303	−0.00393895
$757$	44.5299	1.61847	0.809234	−	0.587486i	$-0.199882\pi$
$757$	44.5299	1.61847	0.809234	+	0.587486i	$0.199882\pi$
$758$	−11.6183	−0.421994
$759$	−23.2285	−0.843141
$760$	23.0883	0.837502
$761$	53.1291	1.92593	0.962963	−	0.269632i	$-0.0869020\pi$
$761$	53.1291	1.92593	0.962963	+	0.269632i	$0.0869020\pi$
$762$	4.03395	0.146134
$763$	−0.299174	−0.0108308
$764$	−52.7989	−1.91020
$765$	6.55366	0.236948
$766$	31.3549	1.13290
$767$	2.56013	0.0924408
$768$	19.8440	0.716057
$769$	−14.5293	−0.523939	−0.261970	−	0.965076i	$-0.584372\pi$
$769$	−14.5293	−0.523939	−0.261970	+	0.965076i	$0.584372\pi$
$770$	−0.325545	−0.0117318
$771$	0.215275	0.00775293
$772$	−9.17921	−0.330367
$773$	−3.59661	−0.129361	−0.0646806	−	0.997906i	$-0.520603\pi$
$773$	−3.59661	−0.129361	−0.0646806	+	0.997906i	$0.520603\pi$
$774$	23.6538	0.850219
$775$	−6.52210	−0.234281
$776$	−44.9690	−1.61429
$777$	0.189553	0.00680018
$778$	54.6517	1.95936
$779$	6.45271	0.231192
$780$	−2.73936	−0.0980849
$781$	16.7697	0.600068
$782$	−80.6794	−2.88509
$783$	0.245430	0.00877096
$784$	−4.39862	−0.157094
$785$	34.1238	1.21793
$786$	1.91554	0.0683252
$787$	−42.5639	−1.51724	−0.758619	−	0.651535i	$-0.774125\pi$
$787$	−42.5639	−1.51724	−0.758619	+	0.651535i	$0.774125\pi$
$788$	77.0707	2.74553
$789$	10.3087	0.366998
$790$	13.0808	0.465395
$791$	−0.516384	−0.0183605
$792$	8.37609	0.297631
$793$	−5.33160	−0.189331
$794$	79.8378	2.83334
$795$	−16.2332	−0.575732
$796$	−49.6685	−1.76045
$797$	−3.85925	−0.136702	−0.0683509	−	0.997661i	$-0.521774\pi$
$797$	−3.85925	−0.136702	−0.0683509	+	0.997661i	$0.521774\pi$
$798$	0.325261	0.0115141
$799$	−12.2228	−0.432412
$800$	−10.9939	−0.388695
$801$	7.43806	0.262811
$802$	38.9799	1.37643
$803$	15.3902	0.543108
$804$	−43.9339	−1.54943
$805$	0.470567	0.0165853
$806$	3.29872	0.116192
$807$	−12.1502	−0.427706
$808$	−24.8967	−0.875862
$809$	−15.8379	−0.556829	−0.278415	−	0.960461i	$-0.589809\pi$
$809$	−15.8379	−0.556829	−0.278415	+	0.960461i	$0.589809\pi$
$810$	3.84991	0.135272
$811$	27.1562	0.953582	0.476791	−	0.879017i	$-0.341800\pi$
$811$	27.1562	0.953582	0.476791	+	0.879017i	$0.341800\pi$
$812$	−0.0265809	−0.000932807 0
$813$	−12.9952	−0.455760
$814$	−36.0232	−1.26261
$815$	−26.8271	−0.939712
$816$	2.47971	0.0868073
$817$	−44.5927	−1.56010
$818$	−62.8197	−2.19644
$819$	−0.0157050	−0.000548777 0
$820$	−8.27186	−0.288866
$821$	−12.2104	−0.426145	−0.213073	−	0.977036i	$-0.568347\pi$
$821$	−12.2104	−0.426145	−0.213073	+	0.977036i	$0.568347\pi$
$822$	43.0564	1.50177
$823$	−52.5650	−1.83230	−0.916150	−	0.400835i	$-0.868720\pi$
$823$	−52.5650	−1.83230	−0.916150	+	0.400835i	$0.868720\pi$
$824$	24.1527	0.841398
$825$	−5.90107	−0.205449
$826$	0.389677	0.0135586
$827$	−23.5728	−0.819706	−0.409853	−	0.912152i	$-0.634420\pi$
$827$	−23.5728	−0.819706	−0.409853	+	0.912152i	$0.634420\pi$
$828$	−29.7511	−1.03392
$829$	−33.3279	−1.15753	−0.578763	−	0.815496i	$-0.696464\pi$
$829$	−33.3279	−1.15753	−0.578763	+	0.815496i	$0.696464\pi$
$830$	−25.4830	−0.884529
$831$	10.9581	0.380134
$832$	6.17516	0.214085
$833$	27.6155	0.956819
$834$	2.77808	0.0961972
$835$	−5.01118	−0.173419
$836$	−38.8021	−1.34200
$837$	−2.91018	−0.100590
$838$	5.78535	0.199851
$839$	49.2549	1.70047	0.850234	−	0.526405i	$-0.176460\pi$
$839$	49.2549	1.70047	0.850234	+	0.526405i	$0.176460\pi$
$840$	−0.169684	−0.00585466
$841$	−28.9398	−0.997923
$842$	16.3685	0.564097
$843$	26.3205	0.906527
$844$	−36.4155	−1.25347
$845$	21.1955	0.729149
$846$	−7.18024	−0.246862
$847$	−0.130607	−0.00448769
$848$	−6.14217	−0.210923
$849$	12.3744	0.424688
$850$	−20.4961	−0.703012
$851$	52.0705	1.78495
$852$	21.4787	0.735847
$853$	28.4566	0.974334	0.487167	−	0.873309i	$-0.338030\pi$
$853$	28.4566	0.974334	0.487167	+	0.873309i	$0.338030\pi$
$854$	−0.811523	−0.0277697
$855$	−7.25795	−0.248217
$856$	56.8608	1.94346
$857$	−5.33638	−0.182287	−0.0911436	−	0.995838i	$-0.529052\pi$
$857$	−5.33638	−0.182287	−0.0911436	+	0.995838i	$0.529052\pi$
$858$	2.98462	0.101893
$859$	3.44767	0.117633	0.0588165	−	0.998269i	$-0.481267\pi$
$859$	3.44767	0.117633	0.0588165	+	0.998269i	$0.481267\pi$
$860$	57.1643	1.94929
$861$	−0.0474232	−0.00161618
$862$	28.0297	0.954694
$863$	44.0933	1.50095	0.750477	−	0.660896i	$-0.229824\pi$
$863$	44.0933	1.50095	0.750477	+	0.660896i	$0.229824\pi$
$864$	−4.90553	−0.166889
$865$	37.6628	1.28057
$866$	−78.2257	−2.65822
$867$	1.43186	0.0486283
$868$	0.315182	0.0106980
$869$	−8.94638	−0.303485
$870$	0.944885	0.0320346
$871$	−6.37082	−0.215867
$872$	29.6350	1.00357
$873$	14.1363	0.478440
$874$	89.3496	3.02230
$875$	0.386251	0.0130577
$876$	19.7118	0.665999
$877$	−29.3753	−0.991933	−0.495966	−	0.868342i	$-0.665186\pi$
$877$	−29.3753	−0.991933	−0.495966	+	0.868342i	$0.665186\pi$
$878$	−87.1328	−2.94059
$879$	16.7891	0.566283
$880$	2.74859	0.0926551
$881$	35.4125	1.19308	0.596538	−	0.802585i	$-0.296543\pi$
$881$	35.4125	1.19308	0.596538	+	0.802585i	$0.296543\pi$
$882$	16.2226	0.546243
$883$	−40.8273	−1.37395	−0.686974	−	0.726682i	$-0.741061\pi$
$883$	−40.8273	−1.37395	−0.686974	+	0.726682i	$0.741061\pi$
$884$	6.50733	0.218865
$885$	−8.69534	−0.292291
$886$	−39.3011	−1.32035
$887$	55.7682	1.87251	0.936257	−	0.351316i	$-0.114266\pi$
$887$	55.7682	1.87251	0.936257	+	0.351316i	$0.114266\pi$
$888$	−18.7764	−0.630095
$889$	0.0558910	0.00187452
$890$	28.6359	0.959878
$891$	−2.63307	−0.0882112
$892$	89.7001	3.00338
$893$	13.5363	0.452977
$894$	5.60667	0.187515
$895$	15.9862	0.534358
$896$	0.624846	0.0208746
$897$	−4.31418	−0.144046
$898$	−13.7629	−0.459273
$899$	−0.714246	−0.0238214
$900$	−7.55809	−0.251936
$901$	38.5618	1.28468
$902$	9.01243	0.300081
$903$	0.327728	0.0109061
$904$	51.1510	1.70126
$905$	−27.3355	−0.908664
$906$	−36.3342	−1.20712
$907$	−26.0103	−0.863658	−0.431829	−	0.901955i	$-0.642132\pi$
$907$	−26.0103	−0.863658	−0.431829	+	0.901955i	$0.642132\pi$
$908$	27.9614	0.927933
$909$	7.82640	0.259585
$910$	−0.0604629	−0.00200432
$911$	−23.3641	−0.774086	−0.387043	−	0.922062i	$-0.626503\pi$
$911$	−23.3641	−0.774086	−0.387043	+	0.922062i	$0.626503\pi$
$912$	−2.74619	−0.0909356
$913$	17.4286	0.576803
$914$	−34.7088	−1.14806
$915$	18.1085	0.598649
$916$	−26.8608	−0.887507
$917$	0.0265402	0.000876434 0
$918$	−9.14543	−0.301844
$919$	−33.0468	−1.09011	−0.545056	−	0.838399i	$-0.683492\pi$
$919$	−33.0468	−1.09011	−0.545056	+	0.838399i	$0.683492\pi$
$920$	−46.6125	−1.53677
$921$	27.5098	0.906478
$922$	−1.00255	−0.0330173
$923$	3.11461	0.102519
$924$	0.285170	0.00938141
$925$	13.2282	0.434941
$926$	−26.3965	−0.867442
$927$	−7.59252	−0.249371
$928$	−1.20396	−0.0395221
$929$	48.2634	1.58347	0.791736	−	0.610863i	$-0.209178\pi$
$929$	48.2634	1.58347	0.791736	+	0.610863i	$0.209178\pi$
$930$	−11.2039	−0.367392
$931$	−30.5832	−1.00232
$932$	9.29543	0.304482
$933$	−24.3603	−0.797522
$934$	−89.0408	−2.91350
$935$	−17.2562	−0.564340
$936$	1.55568	0.0508488
$937$	21.0533	0.687781	0.343890	−	0.939010i	$-0.388255\pi$
$937$	21.0533	0.687781	0.343890	+	0.939010i	$0.388255\pi$
$938$	−0.969703	−0.0316619
$939$	12.1214	0.395568
$940$	−17.3525	−0.565976
$941$	34.8923	1.13746	0.568728	−	0.822526i	$-0.307436\pi$
$941$	34.8923	1.13746	0.568728	+	0.822526i	$0.307436\pi$
$942$	−47.6188	−1.55150
$943$	−13.0272	−0.424225
$944$	−3.29006	−0.107082
$945$	0.0533412	0.00173519
$946$	−62.2822	−2.02497
$947$	−28.0437	−0.911298	−0.455649	−	0.890159i	$-0.650593\pi$
$947$	−28.0437	−0.911298	−0.455649	+	0.890159i	$0.650593\pi$
$948$	−11.4585	−0.372156
$949$	2.85839	0.0927873
$950$	22.6988	0.736445
$951$	−0.915693	−0.0296934
$952$	0.403083	0.0130640
$953$	55.5878	1.80066	0.900332	−	0.435204i	$-0.143324\pi$
$953$	55.5878	1.80066	0.900332	+	0.435204i	$0.143324\pi$
$954$	22.6530	0.733416
$955$	26.0043	0.841481
$956$	−58.2696	−1.88457
$957$	−0.646235	−0.0208898
$958$	28.2276	0.911992
$959$	0.596554	0.0192637
$960$	−20.9736	−0.676920
$961$	−22.5309	−0.726802
$962$	−6.69051	−0.215711
$963$	−17.8745	−0.575998
$964$	−9.21119	−0.296672
$965$	4.52091	0.145533
$966$	−0.656662	−0.0211277
$967$	−5.52301	−0.177608	−0.0888040	−	0.996049i	$-0.528304\pi$
$967$	−5.52301	−0.177608	−0.0888040	+	0.996049i	$0.528304\pi$
$968$	12.9374	0.415823
$969$	17.2412	0.553866
$970$	54.4234	1.74743
$971$	55.6000	1.78429	0.892144	−	0.451751i	$-0.149200\pi$
$971$	55.6000	1.78429	0.892144	+	0.451751i	$0.149200\pi$
$972$	−3.37244	−0.108171
$973$	0.0384908	0.00123396
$974$	−59.5200	−1.90714
$975$	−1.09599	−0.0350999
$976$	6.85173	0.219318
$977$	−26.8193	−0.858027	−0.429013	−	0.903298i	$-0.641139\pi$
$977$	−26.8193	−0.858027	−0.429013	+	0.903298i	$0.641139\pi$
$978$	37.4364	1.19708
$979$	−19.5850	−0.625938
$980$	39.2052	1.25236
$981$	−9.31592	−0.297434
$982$	−69.1629	−2.20708
$983$	21.9376	0.699702	0.349851	−	0.936805i	$-0.386232\pi$
$983$	21.9376	0.699702	0.349851	+	0.936805i	$0.386232\pi$
$984$	4.69756	0.149753
$985$	−37.9586	−1.20946
$986$	−2.24456	−0.0714815
$987$	−0.0994834	−0.00316659
$988$	−7.20664	−0.229274
$989$	90.0272	2.86270
$990$	−10.1371	−0.322178
$991$	−53.4225	−1.69702	−0.848511	−	0.529178i	$-0.822500\pi$
$991$	−53.4225	−1.69702	−0.848511	+	0.529178i	$0.822500\pi$
$992$	14.2760	0.453262
$993$	−10.7630	−0.341554
$994$	0.474075	0.0150367
$995$	24.4626	0.775515
$996$	22.3226	0.707318
$997$	31.2590	0.989981	0.494991	−	0.868898i	$-0.335171\pi$
$997$	31.2590	0.989981	0.494991	+	0.868898i	$0.335171\pi$
$998$	−31.6494	−1.00184
$999$	5.90247	0.186746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.12	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.12	✓	93	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31785 q^{2} -1.00000 q^{3} +3.37244 q^{4} -1.66098 q^{5} +2.31785 q^{6} +0.0321142 q^{7} -3.18111 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31785 q^{2} -1.00000 q^{3} +3.37244 q^{4} -1.66098 q^{5} +2.31785 q^{6} +0.0321142 q^{7} -3.18111 q^{8} +1.00000 q^{9} +3.84991 q^{10} -2.63307 q^{11} -3.37244 q^{12} -0.489035 q^{13} -0.0744361 q^{14} +1.66098 q^{15} +0.628467 q^{16} -3.94565 q^{17} -2.31785 q^{18} +4.36967 q^{19} -5.60156 q^{20} -0.0321142 q^{21} +6.10307 q^{22} -8.82183 q^{23} +3.18111 q^{24} -2.24113 q^{25} +1.13351 q^{26} -1.00000 q^{27} +0.108303 q^{28} -0.245430 q^{29} -3.84991 q^{30} +2.91018 q^{31} +4.90553 q^{32} +2.63307 q^{33} +9.14543 q^{34} -0.0533412 q^{35} +3.37244 q^{36} -5.90247 q^{37} -10.1282 q^{38} +0.489035 q^{39} +5.28377 q^{40} +1.47670 q^{41} +0.0744361 q^{42} -10.2051 q^{43} -8.87987 q^{44} -1.66098 q^{45} +20.4477 q^{46} +3.09780 q^{47} -0.628467 q^{48} -6.99897 q^{49} +5.19462 q^{50} +3.94565 q^{51} -1.64924 q^{52} -9.77325 q^{53} +2.31785 q^{54} +4.37349 q^{55} -0.102159 q^{56} -4.36967 q^{57} +0.568871 q^{58} -5.23506 q^{59} +5.60156 q^{60} +10.9023 q^{61} -6.74536 q^{62} +0.0321142 q^{63} -12.6272 q^{64} +0.812279 q^{65} -6.10307 q^{66} +13.0273 q^{67} -13.3065 q^{68} +8.82183 q^{69} +0.123637 q^{70} -6.36889 q^{71} -3.18111 q^{72} -5.84496 q^{73} +13.6810 q^{74} +2.24113 q^{75} +14.7364 q^{76} -0.0845591 q^{77} -1.13351 q^{78} +3.39770 q^{79} -1.04387 q^{80} +1.00000 q^{81} -3.42278 q^{82} -6.61912 q^{83} -0.108303 q^{84} +6.55366 q^{85} +23.6538 q^{86} +0.245430 q^{87} +8.37609 q^{88} +7.43806 q^{89} +3.84991 q^{90} -0.0157050 q^{91} -29.7511 q^{92} -2.91018 q^{93} -7.18024 q^{94} -7.25795 q^{95} -4.90553 q^{96} +14.1363 q^{97} +16.2226 q^{98} -2.63307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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