LMFDB - Embedded newform 6041.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57911 q^{2} -0.702301 q^{3} +4.65183 q^{4} +2.85376 q^{5} +1.81131 q^{6} -1.00000 q^{7} -6.83937 q^{8} -2.50677 q^{9} +O(q^{10})$	\(q-2.57911 q^{2} -0.702301 q^{3} +4.65183 q^{4} +2.85376 q^{5} +1.81131 q^{6} -1.00000 q^{7} -6.83937 q^{8} -2.50677 q^{9} -7.36016 q^{10} -1.97893 q^{11} -3.26698 q^{12} -7.14198 q^{13} +2.57911 q^{14} -2.00420 q^{15} +8.33586 q^{16} -5.11887 q^{17} +6.46525 q^{18} +3.64817 q^{19} +13.2752 q^{20} +0.702301 q^{21} +5.10388 q^{22} -5.22822 q^{23} +4.80330 q^{24} +3.14393 q^{25} +18.4200 q^{26} +3.86741 q^{27} -4.65183 q^{28} +0.754554 q^{29} +5.16905 q^{30} +6.35426 q^{31} -7.82039 q^{32} +1.38980 q^{33} +13.2022 q^{34} -2.85376 q^{35} -11.6611 q^{36} -3.96789 q^{37} -9.40905 q^{38} +5.01582 q^{39} -19.5179 q^{40} +1.19646 q^{41} -1.81131 q^{42} -9.11995 q^{43} -9.20564 q^{44} -7.15372 q^{45} +13.4842 q^{46} -6.63101 q^{47} -5.85428 q^{48} +1.00000 q^{49} -8.10855 q^{50} +3.59499 q^{51} -33.2233 q^{52} +4.49152 q^{53} -9.97450 q^{54} -5.64738 q^{55} +6.83937 q^{56} -2.56211 q^{57} -1.94608 q^{58} -11.5526 q^{59} -9.32318 q^{60} +8.16361 q^{61} -16.3884 q^{62} +2.50677 q^{63} +3.49796 q^{64} -20.3815 q^{65} -3.58446 q^{66} -8.89197 q^{67} -23.8121 q^{68} +3.67179 q^{69} +7.36016 q^{70} +8.82456 q^{71} +17.1448 q^{72} -2.50677 q^{73} +10.2336 q^{74} -2.20798 q^{75} +16.9707 q^{76} +1.97893 q^{77} -12.9364 q^{78} -0.729616 q^{79} +23.7885 q^{80} +4.80423 q^{81} -3.08582 q^{82} -15.3470 q^{83} +3.26698 q^{84} -14.6080 q^{85} +23.5214 q^{86} -0.529924 q^{87} +13.5346 q^{88} +16.2713 q^{89} +18.4503 q^{90} +7.14198 q^{91} -24.3208 q^{92} -4.46260 q^{93} +17.1021 q^{94} +10.4110 q^{95} +5.49227 q^{96} +0.326706 q^{97} -2.57911 q^{98} +4.96073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.57911	−1.82371	−0.911855	−	0.410513i	$-0.865349\pi$
$2$	−2.57911	−1.82371	−0.911855	+	0.410513i	$0.865349\pi$
$3$	−0.702301	−0.405474	−0.202737	−	0.979233i	$-0.564984\pi$
$3$	−0.702301	−0.405474	−0.202737	+	0.979233i	$0.564984\pi$
$4$	4.65183	2.32591
$5$	2.85376	1.27624	0.638119	−	0.769937i	$-0.279713\pi$
$5$	2.85376	1.27624	0.638119	+	0.769937i	$0.279713\pi$
$6$	1.81131	0.739466
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.83937	−2.41808
$9$	−2.50677	−0.835591
$10$	−7.36016	−2.32749
$11$	−1.97893	−0.596670	−0.298335	−	0.954461i	$-0.596431\pi$
$11$	−1.97893	−0.596670	−0.298335	+	0.954461i	$0.596431\pi$
$12$	−3.26698	−0.943097
$13$	−7.14198	−1.98083	−0.990414	−	0.138128i	$-0.955891\pi$
$13$	−7.14198	−1.98083	−0.990414	+	0.138128i	$0.955891\pi$
$14$	2.57911	0.689297
$15$	−2.00420	−0.517481
$16$	8.33586	2.08396
$17$	−5.11887	−1.24151	−0.620754	−	0.784005i	$-0.713174\pi$
$17$	−5.11887	−1.24151	−0.620754	+	0.784005i	$0.713174\pi$
$18$	6.46525	1.52388
$19$	3.64817	0.836948	0.418474	−	0.908229i	$-0.362565\pi$
$19$	3.64817	0.836948	0.418474	+	0.908229i	$0.362565\pi$
$20$	13.2752	2.96842
$21$	0.702301	0.153255
$22$	5.10388	1.08815
$23$	−5.22822	−1.09016	−0.545080	−	0.838384i	$-0.683501\pi$
$23$	−5.22822	−1.09016	−0.545080	+	0.838384i	$0.683501\pi$
$24$	4.80330	0.980469
$25$	3.14393	0.628786
$26$	18.4200	3.61246
$27$	3.86741	0.744284
$28$	−4.65183	−0.879113
$29$	0.754554	0.140117	0.0700586	−	0.997543i	$-0.477681\pi$
$29$	0.754554	0.140117	0.0700586	+	0.997543i	$0.477681\pi$
$30$	5.16905	0.943735
$31$	6.35426	1.14126	0.570629	−	0.821208i	$-0.306699\pi$
$31$	6.35426	1.14126	0.570629	+	0.821208i	$0.306699\pi$
$32$	−7.82039	−1.38246
$33$	1.38980	0.241934
$34$	13.2022	2.26415
$35$	−2.85376	−0.482373
$36$	−11.6611	−1.94351
$37$	−3.96789	−0.652317	−0.326158	−	0.945315i	$-0.605754\pi$
$37$	−3.96789	−0.652317	−0.326158	+	0.945315i	$0.605754\pi$
$38$	−9.40905	−1.52635
$39$	5.01582	0.803174
$40$	−19.5179	−3.08605
$41$	1.19646	0.186856	0.0934282	−	0.995626i	$-0.470217\pi$
$41$	1.19646	0.186856	0.0934282	+	0.995626i	$0.470217\pi$
$42$	−1.81131	−0.279492
$43$	−9.11995	−1.39078	−0.695390	−	0.718633i	$-0.744768\pi$
$43$	−9.11995	−1.39078	−0.695390	+	0.718633i	$0.744768\pi$
$44$	−9.20564	−1.38780
$45$	−7.15372	−1.06641
$46$	13.4842	1.98813
$47$	−6.63101	−0.967233	−0.483616	−	0.875280i	$-0.660677\pi$
$47$	−6.63101	−0.967233	−0.483616	+	0.875280i	$0.660677\pi$
$48$	−5.85428	−0.844993
$49$	1.00000	0.142857
$50$	−8.10855	−1.14672
$51$	3.59499	0.503399
$52$	−33.2233	−4.60724
$53$	4.49152	0.616957	0.308479	−	0.951231i	$-0.400180\pi$
$53$	4.49152	0.616957	0.308479	+	0.951231i	$0.400180\pi$
$54$	−9.97450	−1.35736
$55$	−5.64738	−0.761493
$56$	6.83937	0.913949
$57$	−2.56211	−0.339360
$58$	−1.94608	−0.255533
$59$	−11.5526	−1.50402	−0.752010	−	0.659152i	$-0.770915\pi$
$59$	−11.5526	−1.50402	−0.752010	+	0.659152i	$0.770915\pi$
$60$	−9.32318	−1.20362
$61$	8.16361	1.04524	0.522622	−	0.852565i	$-0.324954\pi$
$61$	8.16361	1.04524	0.522622	+	0.852565i	$0.324954\pi$
$62$	−16.3884	−2.08132
$63$	2.50677	0.315824
$64$	3.49796	0.437245
$65$	−20.3815	−2.52801
$66$	−3.58446	−0.441217
$67$	−8.89197	−1.08633	−0.543163	−	0.839627i	$-0.682774\pi$
$67$	−8.89197	−1.08633	−0.543163	+	0.839627i	$0.682774\pi$
$68$	−23.8121	−2.88764
$69$	3.67179	0.442031
$70$	7.36016	0.879708
$71$	8.82456	1.04728	0.523641	−	0.851939i	$-0.324573\pi$
$71$	8.82456	1.04728	0.523641	+	0.851939i	$0.324573\pi$
$72$	17.1448	2.02053
$73$	−2.50677	−0.293395	−0.146698	−	0.989181i	$-0.546864\pi$
$73$	−2.50677	−0.293395	−0.146698	+	0.989181i	$0.546864\pi$
$74$	10.2336	1.18964
$75$	−2.20798	−0.254956
$76$	16.9707	1.94667
$77$	1.97893	0.225520
$78$	−12.9364	−1.46476
$79$	−0.729616	−0.0820883	−0.0410441	−	0.999157i	$-0.513068\pi$
$79$	−0.729616	−0.0820883	−0.0410441	+	0.999157i	$0.513068\pi$
$80$	23.7885	2.65964
$81$	4.80423	0.533804
$82$	−3.08582	−0.340772
$83$	−15.3470	−1.68455	−0.842276	−	0.539047i	$-0.818785\pi$
$83$	−15.3470	−1.68455	−0.842276	+	0.539047i	$0.818785\pi$
$84$	3.26698	0.356457
$85$	−14.6080	−1.58446
$86$	23.5214	2.53638
$87$	−0.529924	−0.0568138
$88$	13.5346	1.44280
$89$	16.2713	1.72475	0.862375	−	0.506271i	$-0.168976\pi$
$89$	16.2713	1.72475	0.862375	+	0.506271i	$0.168976\pi$
$90$	18.4503	1.94483
$91$	7.14198	0.748683
$92$	−24.3208	−2.53562
$93$	−4.46260	−0.462750
$94$	17.1021	1.76395
$95$	10.4110	1.06815
$96$	5.49227	0.560552
$97$	0.326706	0.0331720	0.0165860	−	0.999862i	$-0.494720\pi$
$97$	0.326706	0.0331720	0.0165860	+	0.999862i	$0.494720\pi$
$98$	−2.57911	−0.260530
$99$	4.96073	0.498572
$100$	14.6250	1.46250
$101$	−6.42009	−0.638823	−0.319412	−	0.947616i	$-0.603485\pi$
$101$	−6.42009	−0.638823	−0.319412	+	0.947616i	$0.603485\pi$
$102$	−9.27188	−0.918053
$103$	5.51062	0.542978	0.271489	−	0.962442i	$-0.412484\pi$
$103$	5.51062	0.542978	0.271489	+	0.962442i	$0.412484\pi$
$104$	48.8466	4.78981
$105$	2.00420	0.195589
$106$	−11.5841	−1.12515
$107$	−3.11560	−0.301196	−0.150598	−	0.988595i	$-0.548120\pi$
$107$	−3.11560	−0.301196	−0.150598	+	0.988595i	$0.548120\pi$
$108$	17.9905	1.73114
$109$	−14.9632	−1.43321	−0.716605	−	0.697479i	$-0.754305\pi$
$109$	−14.9632	−1.43321	−0.716605	+	0.697479i	$0.754305\pi$
$110$	14.5652	1.38874
$111$	2.78665	0.264497
$112$	−8.33586	−0.787665
$113$	17.4620	1.64269	0.821345	−	0.570432i	$-0.193224\pi$
$113$	17.4620	1.64269	0.821345	+	0.570432i	$0.193224\pi$
$114$	6.60798	0.618894
$115$	−14.9201	−1.39130
$116$	3.51006	0.325901
$117$	17.9033	1.65516
$118$	29.7955	2.74289
$119$	5.11887	0.469246
$120$	13.7074	1.25131
$121$	−7.08384	−0.643985
$122$	−21.0549	−1.90622
$123$	−0.840278	−0.0757653
$124$	29.5589	2.65447
$125$	−5.29678	−0.473758
$126$	−6.46525	−0.575971
$127$	16.2617	1.44299	0.721496	−	0.692419i	$-0.243455\pi$
$127$	16.2617	1.44299	0.721496	+	0.692419i	$0.243455\pi$
$128$	6.61914	0.585055
$129$	6.40495	0.563924
$130$	52.5661	4.61036
$131$	−7.88436	−0.688860	−0.344430	−	0.938812i	$-0.611928\pi$
$131$	−7.88436	−0.688860	−0.344430	+	0.938812i	$0.611928\pi$
$132$	6.46513	0.562717
$133$	−3.64817	−0.316337
$134$	22.9334	1.98114
$135$	11.0367	0.949884
$136$	35.0099	3.00207
$137$	6.44146	0.550331	0.275165	−	0.961397i	$-0.411267\pi$
$137$	6.44146	0.550331	0.275165	+	0.961397i	$0.411267\pi$
$138$	−9.46996	−0.806136
$139$	−9.54134	−0.809286	−0.404643	−	0.914475i	$-0.632604\pi$
$139$	−9.54134	−0.809286	−0.404643	+	0.914475i	$0.632604\pi$
$140$	−13.2752	−1.12196
$141$	4.65697	0.392187
$142$	−22.7595	−1.90994
$143$	14.1335	1.18190
$144$	−20.8961	−1.74134
$145$	2.15331	0.178823
$146$	6.46525	0.535068
$147$	−0.702301	−0.0579248
$148$	−18.4579	−1.51723
$149$	−5.46916	−0.448051	−0.224025	−	0.974583i	$-0.571920\pi$
$149$	−5.46916	−0.448051	−0.224025	+	0.974583i	$0.571920\pi$
$150$	5.69464	0.464965
$151$	0.359774	0.0292780	0.0146390	−	0.999893i	$-0.495340\pi$
$151$	0.359774	0.0292780	0.0146390	+	0.999893i	$0.495340\pi$
$152$	−24.9512	−2.02381
$153$	12.8319	1.03739
$154$	−5.10388	−0.411283
$155$	18.1335	1.45652
$156$	23.3327	1.86811
$157$	−3.18121	−0.253889	−0.126944	−	0.991910i	$-0.540517\pi$
$157$	−3.18121	−0.253889	−0.126944	+	0.991910i	$0.540517\pi$
$158$	1.88176	0.149705
$159$	−3.15440	−0.250160
$160$	−22.3175	−1.76435
$161$	5.22822	0.412042
$162$	−12.3907	−0.973503
$163$	24.2953	1.90296	0.951479	−	0.307713i	$-0.0995637\pi$
$163$	24.2953	1.90296	0.951479	+	0.307713i	$0.0995637\pi$
$164$	5.56575	0.434612
$165$	3.96616	0.308765
$166$	39.5817	3.07213
$167$	−0.964636	−0.0746458	−0.0373229	−	0.999303i	$-0.511883\pi$
$167$	−0.964636	−0.0746458	−0.0373229	+	0.999303i	$0.511883\pi$
$168$	−4.80330	−0.370582
$169$	38.0079	2.92368
$170$	37.6757	2.88960
$171$	−9.14514	−0.699346
$172$	−42.4245	−3.23483
$173$	−9.56670	−0.727343	−0.363671	−	0.931527i	$-0.618477\pi$
$173$	−9.56670	−0.727343	−0.363671	+	0.931527i	$0.618477\pi$
$174$	1.36673	0.103612
$175$	−3.14393	−0.237659
$176$	−16.4961	−1.24344
$177$	8.11340	0.609840
$178$	−41.9654	−3.14544
$179$	−18.0273	−1.34742	−0.673712	−	0.738994i	$-0.735301\pi$
$179$	−18.0273	−1.34742	−0.673712	+	0.738994i	$0.735301\pi$
$180$	−33.2779	−2.48039
$181$	−19.5165	−1.45065	−0.725324	−	0.688407i	$-0.758310\pi$
$181$	−19.5165	−1.45065	−0.725324	+	0.688407i	$0.758310\pi$
$182$	−18.4200	−1.36538
$183$	−5.73331	−0.423819
$184$	35.7578	2.63610
$185$	−11.3234	−0.832512
$186$	11.5096	0.843921
$187$	10.1299	0.740770
$188$	−30.8463	−2.24970
$189$	−3.86741	−0.281313
$190$	−26.8511	−1.94799
$191$	2.81078	0.203381	0.101691	−	0.994816i	$-0.467575\pi$
$191$	2.81078	0.203381	0.101691	+	0.994816i	$0.467575\pi$
$192$	−2.45662	−0.177291
$193$	22.4358	1.61496	0.807481	−	0.589894i	$-0.200830\pi$
$193$	22.4358	1.61496	0.807481	+	0.589894i	$0.200830\pi$
$194$	−0.842613	−0.0604961
$195$	14.3139	1.02504
$196$	4.65183	0.332274
$197$	−9.18737	−0.654573	−0.327286	−	0.944925i	$-0.606134\pi$
$197$	−9.18737	−0.654573	−0.327286	+	0.944925i	$0.606134\pi$
$198$	−12.7943	−0.909250
$199$	15.2910	1.08395	0.541974	−	0.840395i	$-0.317677\pi$
$199$	15.2910	1.08395	0.541974	+	0.840395i	$0.317677\pi$
$200$	−21.5025	−1.52046
$201$	6.24484	0.440477
$202$	16.5581	1.16503
$203$	−0.754554	−0.0529593
$204$	16.7233	1.17086
$205$	3.41442	0.238473
$206$	−14.2125	−0.990234
$207$	13.1060	0.910928
$208$	−59.5345	−4.12798
$209$	−7.21947	−0.499381
$210$	−5.16905	−0.356698
$211$	6.64807	0.457672	0.228836	−	0.973465i	$-0.426508\pi$
$211$	6.64807	0.457672	0.228836	+	0.973465i	$0.426508\pi$
$212$	20.8938	1.43499
$213$	−6.19750	−0.424645
$214$	8.03548	0.549294
$215$	−26.0261	−1.77497
$216$	−26.4507	−1.79974
$217$	−6.35426	−0.431355
$218$	38.5917	2.61376
$219$	1.76051	0.118964
$220$	−26.2707	−1.77117
$221$	36.5589	2.45922
$222$	−7.18709	−0.482366
$223$	24.5677	1.64518	0.822589	−	0.568637i	$-0.192529\pi$
$223$	24.5677	1.64518	0.822589	+	0.568637i	$0.192529\pi$
$224$	7.82039	0.522522
$225$	−7.88111	−0.525408
$226$	−45.0366	−2.99579
$227$	20.5765	1.36571	0.682855	−	0.730554i	$-0.260738\pi$
$227$	20.5765	1.36571	0.682855	+	0.730554i	$0.260738\pi$
$228$	−11.9185	−0.789323
$229$	9.04452	0.597679	0.298839	−	0.954303i	$-0.403401\pi$
$229$	9.04452	0.597679	0.298839	+	0.954303i	$0.403401\pi$
$230$	38.4806	2.53733
$231$	−1.38980	−0.0914424
$232$	−5.16068	−0.338815
$233$	−3.83488	−0.251232	−0.125616	−	0.992079i	$-0.540091\pi$
$233$	−3.83488	−0.251232	−0.125616	+	0.992079i	$0.540091\pi$
$234$	−46.1747	−3.01854
$235$	−18.9233	−1.23442
$236$	−53.7407	−3.49822
$237$	0.512410	0.0332846
$238$	−13.2022	−0.855768
$239$	−21.1540	−1.36834	−0.684170	−	0.729323i	$-0.739835\pi$
$239$	−21.1540	−1.36834	−0.684170	+	0.729323i	$0.739835\pi$
$240$	−16.7067	−1.07841
$241$	15.4878	0.997655	0.498828	−	0.866701i	$-0.333764\pi$
$241$	15.4878	0.997655	0.498828	+	0.866701i	$0.333764\pi$
$242$	18.2700	1.17444
$243$	−14.9763	−0.960727
$244$	37.9757	2.43115
$245$	2.85376	0.182320
$246$	2.16717	0.138174
$247$	−26.0552	−1.65785
$248$	−43.4591	−2.75966
$249$	10.7782	0.683041
$250$	13.6610	0.863997
$251$	30.4162	1.91985	0.959926	−	0.280254i	$-0.0904185\pi$
$251$	30.4162	1.91985	0.959926	+	0.280254i	$0.0904185\pi$
$252$	11.6611	0.734579
$253$	10.3463	0.650465
$254$	−41.9407	−2.63160
$255$	10.2592	0.642457
$256$	−24.0674	−1.50422
$257$	−11.8360	−0.738307	−0.369154	−	0.929368i	$-0.620352\pi$
$257$	−11.8360	−0.738307	−0.369154	+	0.929368i	$0.620352\pi$
$258$	−16.5191	−1.02843
$259$	3.96789	0.246553
$260$	−94.8111	−5.87994
$261$	−1.89150	−0.117081
$262$	20.3347	1.25628
$263$	21.8629	1.34813	0.674063	−	0.738674i	$-0.264548\pi$
$263$	21.8629	1.34813	0.674063	+	0.738674i	$0.264548\pi$
$264$	−9.50538	−0.585016
$265$	12.8177	0.787385
$266$	9.40905	0.576906
$267$	−11.4273	−0.699340
$268$	−41.3639	−2.52670
$269$	−20.0055	−1.21976	−0.609879	−	0.792495i	$-0.708782\pi$
$269$	−20.0055	−1.21976	−0.609879	+	0.792495i	$0.708782\pi$
$270$	−28.4648	−1.73231
$271$	−5.18128	−0.314740	−0.157370	−	0.987540i	$-0.550302\pi$
$271$	−5.18128	−0.314740	−0.157370	+	0.987540i	$0.550302\pi$
$272$	−42.6702	−2.58726
$273$	−5.01582	−0.303571
$274$	−16.6133	−1.00364
$275$	−6.22161	−0.375177
$276$	17.0805	1.02813
$277$	2.56678	0.154223	0.0771113	−	0.997022i	$-0.475430\pi$
$277$	2.56678	0.154223	0.0771113	+	0.997022i	$0.475430\pi$
$278$	24.6082	1.47590
$279$	−15.9287	−0.953625
$280$	19.5179	1.16642
$281$	−21.8776	−1.30511	−0.652554	−	0.757742i	$-0.726302\pi$
$281$	−21.8776	−1.30511	−0.652554	+	0.757742i	$0.726302\pi$
$282$	−12.0108	−0.715235
$283$	13.7007	0.814421	0.407210	−	0.913334i	$-0.366502\pi$
$283$	13.7007	0.814421	0.407210	+	0.913334i	$0.366502\pi$
$284$	41.0503	2.43589
$285$	−7.31165	−0.433105
$286$	−36.4518	−2.15544
$287$	−1.19646	−0.0706251
$288$	19.6039	1.15517
$289$	9.20284	0.541344
$290$	−5.55364	−0.326121
$291$	−0.229446	−0.0134504
$292$	−11.6611	−0.682413
$293$	18.3029	1.06927	0.534633	−	0.845084i	$-0.320450\pi$
$293$	18.3029	1.06927	0.534633	+	0.845084i	$0.320450\pi$
$294$	1.81131	0.105638
$295$	−32.9683	−1.91949
$296$	27.1379	1.57736
$297$	−7.65333	−0.444091
$298$	14.1056	0.817114
$299$	37.3399	2.15942
$300$	−10.2712	−0.593006
$301$	9.11995	0.525665
$302$	−0.927899	−0.0533946
$303$	4.50884	0.259026
$304$	30.4106	1.74417
$305$	23.2970	1.33398
$306$	−33.0948	−1.89190
$307$	−24.5988	−1.40393	−0.701963	−	0.712213i	$-0.747693\pi$
$307$	−24.5988	−1.40393	−0.701963	+	0.712213i	$0.747693\pi$
$308$	9.20564	0.524540
$309$	−3.87012	−0.220163
$310$	−46.7684	−2.65626
$311$	4.93322	0.279737	0.139869	−	0.990170i	$-0.455332\pi$
$311$	4.93322	0.279737	0.139869	+	0.990170i	$0.455332\pi$
$312$	−34.3050	−1.94214
$313$	−24.3971	−1.37901	−0.689503	−	0.724282i	$-0.742171\pi$
$313$	−24.3971	−1.37901	−0.689503	+	0.724282i	$0.742171\pi$
$314$	8.20471	0.463019
$315$	7.15372	0.403067
$316$	−3.39405	−0.190930
$317$	−7.73515	−0.434449	−0.217225	−	0.976122i	$-0.569700\pi$
$317$	−7.73515	−0.434449	−0.217225	+	0.976122i	$0.569700\pi$
$318$	8.13555	0.456219
$319$	−1.49321	−0.0836037
$320$	9.98232	0.558029
$321$	2.18809	0.122127
$322$	−13.4842	−0.751444
$323$	−18.6745	−1.03908
$324$	22.3485	1.24158
$325$	−22.4539	−1.24552
$326$	−62.6605	−3.47044
$327$	10.5086	0.581129
$328$	−8.18306	−0.451834
$329$	6.63101	0.365580
$330$	−10.2292	−0.563098
$331$	7.96071	0.437560	0.218780	−	0.975774i	$-0.429792\pi$
$331$	7.96071	0.437560	0.218780	+	0.975774i	$0.429792\pi$
$332$	−71.3916	−3.91812
$333$	9.94660	0.545070
$334$	2.48791	0.136132
$335$	−25.3755	−1.38641
$336$	5.85428	0.319377
$337$	−2.42258	−0.131966	−0.0659832	−	0.997821i	$-0.521018\pi$
$337$	−2.42258	−0.131966	−0.0659832	+	0.997821i	$0.521018\pi$
$338$	−98.0266	−5.33195
$339$	−12.2636	−0.666067
$340$	−67.9540	−3.68532
$341$	−12.5746	−0.680954
$342$	23.5864	1.27540
$343$	−1.00000	−0.0539949
$344$	62.3747	3.36302
$345$	10.4784	0.564137
$346$	24.6736	1.32646
$347$	20.6857	1.11047	0.555234	−	0.831694i	$-0.312629\pi$
$347$	20.6857	1.11047	0.555234	+	0.831694i	$0.312629\pi$
$348$	−2.46512	−0.132144
$349$	17.9243	0.959464	0.479732	−	0.877415i	$-0.340734\pi$
$349$	17.9243	0.959464	0.479732	+	0.877415i	$0.340734\pi$
$350$	8.10855	0.433420
$351$	−27.6210	−1.47430
$352$	15.4760	0.824873
$353$	20.3836	1.08491	0.542455	−	0.840085i	$-0.317495\pi$
$353$	20.3836	1.08491	0.542455	+	0.840085i	$0.317495\pi$
$354$	−20.9254	−1.11217
$355$	25.1831	1.33658
$356$	75.6911	4.01162
$357$	−3.59499	−0.190267
$358$	46.4945	2.45731
$359$	17.2198	0.908827	0.454413	−	0.890791i	$-0.349849\pi$
$359$	17.2198	0.908827	0.454413	+	0.890791i	$0.349849\pi$
$360$	48.9270	2.57868
$361$	−5.69085	−0.299518
$362$	50.3352	2.64556
$363$	4.97499	0.261119
$364$	33.2233	1.74137
$365$	−7.15372	−0.374443
$366$	14.7869	0.772922
$367$	26.4688	1.38166	0.690829	−	0.723018i	$-0.257246\pi$
$367$	26.4688	1.38166	0.690829	+	0.723018i	$0.257246\pi$
$368$	−43.5817	−2.27186
$369$	−2.99926	−0.156135
$370$	29.2043	1.51826
$371$	−4.49152	−0.233188
$372$	−20.7593	−1.07632
$373$	−15.8383	−0.820076	−0.410038	−	0.912069i	$-0.634484\pi$
$373$	−15.8383	−0.820076	−0.410038	+	0.912069i	$0.634484\pi$
$374$	−26.1261	−1.35095
$375$	3.71993	0.192096
$376$	45.3520	2.33885
$377$	−5.38901	−0.277548
$378$	9.97450	0.513033
$379$	−5.69887	−0.292731	−0.146366	−	0.989231i	$-0.546758\pi$
$379$	−5.69887	−0.292731	−0.146366	+	0.989231i	$0.546758\pi$
$380$	48.4302	2.48441
$381$	−11.4206	−0.585095
$382$	−7.24933	−0.370908
$383$	−36.8762	−1.88429	−0.942144	−	0.335208i	$-0.891193\pi$
$383$	−36.8762	−1.88429	−0.942144	+	0.335208i	$0.891193\pi$
$384$	−4.64863	−0.237224
$385$	5.64738	0.287817
$386$	−57.8644	−2.94522
$387$	22.8617	1.16212
$388$	1.51978	0.0771553
$389$	−3.52289	−0.178618	−0.0893088	−	0.996004i	$-0.528466\pi$
$389$	−3.52289	−0.178618	−0.0893088	+	0.996004i	$0.528466\pi$
$390$	−36.9172	−1.86938
$391$	26.7626	1.35344
$392$	−6.83937	−0.345440
$393$	5.53719	0.279315
$394$	23.6953	1.19375
$395$	−2.08215	−0.104764
$396$	23.0765	1.15964
$397$	34.6121	1.73713	0.868566	−	0.495574i	$-0.165042\pi$
$397$	34.6121	1.73713	0.868566	+	0.495574i	$0.165042\pi$
$398$	−39.4372	−1.97681
$399$	2.56211	0.128266
$400$	26.2073	1.31037
$401$	−11.4982	−0.574193	−0.287096	−	0.957902i	$-0.592690\pi$
$401$	−11.4982	−0.574193	−0.287096	+	0.957902i	$0.592690\pi$
$402$	−16.1061	−0.803302
$403$	−45.3820	−2.26064
$404$	−29.8652	−1.48585
$405$	13.7101	0.681261
$406$	1.94608	0.0965824
$407$	7.85217	0.389218
$408$	−24.5875	−1.21726
$409$	30.0921	1.48796	0.743980	−	0.668201i	$-0.232936\pi$
$409$	30.0921	1.48796	0.743980	+	0.668201i	$0.232936\pi$
$410$	−8.80617	−0.434906
$411$	−4.52384	−0.223145
$412$	25.6345	1.26292
$413$	11.5526	0.568466
$414$	−33.8018	−1.66127
$415$	−43.7966	−2.14989
$416$	55.8531	2.73842
$417$	6.70089	0.328144
$418$	18.6198	0.910726
$419$	20.9083	1.02144	0.510720	−	0.859747i	$-0.329379\pi$
$419$	20.9083	1.02144	0.510720	+	0.859747i	$0.329379\pi$
$420$	9.32318	0.454924
$421$	−11.5637	−0.563580	−0.281790	−	0.959476i	$-0.590928\pi$
$421$	−11.5637	−0.563580	−0.281790	+	0.959476i	$0.590928\pi$
$422$	−17.1461	−0.834660
$423$	16.6224	0.808211
$424$	−30.7192	−1.49185
$425$	−16.0934	−0.780643
$426$	15.9840	0.774430
$427$	−8.16361	−0.395065
$428$	−14.4932	−0.700556
$429$	−9.92595	−0.479229
$430$	67.1243	3.23702
$431$	12.7477	0.614036	0.307018	−	0.951704i	$-0.400669\pi$
$431$	12.7477	0.614036	0.307018	+	0.951704i	$0.400669\pi$
$432$	32.2382	1.55106
$433$	−2.39545	−0.115118	−0.0575589	−	0.998342i	$-0.518332\pi$
$433$	−2.39545	−0.115118	−0.0575589	+	0.998342i	$0.518332\pi$
$434$	16.3884	0.786666
$435$	−1.51227	−0.0725080
$436$	−69.6060	−3.33353
$437$	−19.0735	−0.912407
$438$	−4.54055	−0.216956
$439$	−5.33724	−0.254733	−0.127366	−	0.991856i	$-0.540652\pi$
$439$	−5.33724	−0.254733	−0.127366	+	0.991856i	$0.540652\pi$
$440$	38.6245	1.84135
$441$	−2.50677	−0.119370
$442$	−94.2895	−4.48489
$443$	6.94928	0.330170	0.165085	−	0.986279i	$-0.447210\pi$
$443$	6.94928	0.330170	0.165085	+	0.986279i	$0.447210\pi$
$444$	12.9630	0.615198
$445$	46.4342	2.20119
$446$	−63.3630	−3.00033
$447$	3.84099	0.181673
$448$	−3.49796	−0.165263
$449$	−4.95283	−0.233738	−0.116869	−	0.993147i	$-0.537286\pi$
$449$	−4.95283	−0.233738	−0.116869	+	0.993147i	$0.537286\pi$
$450$	20.3263	0.958191
$451$	−2.36772	−0.111491
$452$	81.2304	3.82076
$453$	−0.252670	−0.0118715
$454$	−53.0691	−2.49066
$455$	20.3815	0.955498
$456$	17.5232	0.820601
$457$	22.1430	1.03580	0.517902	−	0.855440i	$-0.326713\pi$
$457$	22.1430	1.03580	0.517902	+	0.855440i	$0.326713\pi$
$458$	−23.3269	−1.08999
$459$	−19.7968	−0.924035
$460$	−69.4057	−3.23606
$461$	−27.2380	−1.26860	−0.634300	−	0.773087i	$-0.718712\pi$
$461$	−27.2380	−1.26860	−0.634300	+	0.773087i	$0.718712\pi$
$462$	3.58446	0.166764
$463$	26.6590	1.23895	0.619473	−	0.785018i	$-0.287346\pi$
$463$	26.6590	1.23895	0.619473	+	0.785018i	$0.287346\pi$
$464$	6.28986	0.291999
$465$	−12.7352	−0.590579
$466$	9.89060	0.458173
$467$	−4.45582	−0.206191	−0.103095	−	0.994671i	$-0.532875\pi$
$467$	−4.45582	−0.206191	−0.103095	+	0.994671i	$0.532875\pi$
$468$	83.2832	3.84977
$469$	8.89197	0.410593
$470$	48.8053	2.25122
$471$	2.23417	0.102945
$472$	79.0125	3.63684
$473$	18.0477	0.829836
$474$	−1.32156	−0.0607015
$475$	11.4696	0.526261
$476$	23.8121	1.09143
$477$	−11.2592	−0.515524
$478$	54.5586	2.49545
$479$	−0.501244	−0.0229024	−0.0114512	−	0.999934i	$-0.503645\pi$
$479$	−0.501244	−0.0229024	−0.0114512	+	0.999934i	$0.503645\pi$
$480$	15.6736	0.715398
$481$	28.3386	1.29213
$482$	−39.9447	−1.81943
$483$	−3.67179	−0.167072
$484$	−32.9528	−1.49786
$485$	0.932341	0.0423354
$486$	38.6255	1.75209
$487$	28.0471	1.27093	0.635467	−	0.772128i	$-0.280807\pi$
$487$	28.0471	1.27093	0.635467	+	0.772128i	$0.280807\pi$
$488$	−55.8340	−2.52748
$489$	−17.0626	−0.771599
$490$	−7.36016	−0.332498
$491$	−32.6318	−1.47265	−0.736327	−	0.676626i	$-0.763441\pi$
$491$	−32.6318	−1.47265	−0.736327	+	0.676626i	$0.763441\pi$
$492$	−3.90883	−0.176224
$493$	−3.86247	−0.173957
$494$	67.1992	3.02344
$495$	14.1567	0.636297
$496$	52.9682	2.37834
$497$	−8.82456	−0.395836
$498$	−27.7982	−1.24567
$499$	−2.31263	−0.103528	−0.0517639	−	0.998659i	$-0.516484\pi$
$499$	−2.31263	−0.103528	−0.0517639	+	0.998659i	$0.516484\pi$
$500$	−24.6397	−1.10192
$501$	0.677465	0.0302669
$502$	−78.4468	−3.50125
$503$	−1.85066	−0.0825169	−0.0412585	−	0.999149i	$-0.513137\pi$
$503$	−1.85066	−0.0825169	−0.0412585	+	0.999149i	$0.513137\pi$
$504$	−17.1448	−0.763688
$505$	−18.3214	−0.815291
$506$	−26.6842	−1.18626
$507$	−26.6930	−1.18548
$508$	75.6466	3.35628
$509$	−33.8825	−1.50181	−0.750907	−	0.660408i	$-0.770383\pi$
$509$	−33.8825	−1.50181	−0.750907	+	0.660408i	$0.770383\pi$
$510$	−26.4597	−1.17166
$511$	2.50677	0.110893
$512$	48.8344	2.15820
$513$	14.1090	0.622927
$514$	30.5263	1.34646
$515$	15.7260	0.692970
$516$	29.7947	1.31164
$517$	13.1223	0.577118
$518$	−10.2336	−0.449640
$519$	6.71870	0.294918
$520$	139.396	6.11294
$521$	1.70295	0.0746075	0.0373038	−	0.999304i	$-0.488123\pi$
$521$	1.70295	0.0746075	0.0373038	+	0.999304i	$0.488123\pi$
$522$	4.87838	0.213521
$523$	2.41244	0.105489	0.0527444	−	0.998608i	$-0.483203\pi$
$523$	2.41244	0.105489	0.0527444	+	0.998608i	$0.483203\pi$
$524$	−36.6767	−1.60223
$525$	2.20798	0.0963643
$526$	−56.3870	−2.45859
$527$	−32.5266	−1.41688
$528$	11.5852	0.504181
$529$	4.33433	0.188449
$530$	−33.0583	−1.43596
$531$	28.9597	1.25675
$532$	−16.9707	−0.735772
$533$	−8.54512	−0.370130
$534$	29.4723	1.27539
$535$	−8.89115	−0.384398
$536$	60.8155	2.62683
$537$	12.6606	0.546345
$538$	51.5965	2.22448
$539$	−1.97893	−0.0852385
$540$	51.3406	2.20935
$541$	15.1480	0.651265	0.325633	−	0.945496i	$-0.394423\pi$
$541$	15.1480	0.651265	0.325633	+	0.945496i	$0.394423\pi$
$542$	13.3631	0.573994
$543$	13.7064	0.588200
$544$	40.0316	1.71634
$545$	−42.7012	−1.82912
$546$	12.9364	0.553625
$547$	39.2258	1.67718	0.838588	−	0.544766i	$-0.183382\pi$
$547$	39.2258	1.67718	0.838588	+	0.544766i	$0.183382\pi$
$548$	29.9646	1.28002
$549$	−20.4643	−0.873396
$550$	16.0462	0.684214
$551$	2.75274	0.117271
$552$	−25.1127	−1.06887
$553$	0.729616	0.0310264
$554$	−6.62001	−0.281257
$555$	7.95243	0.337562
$556$	−44.3847	−1.88233
$557$	6.26985	0.265662	0.132831	−	0.991139i	$-0.457593\pi$
$557$	6.26985	0.265662	0.132831	+	0.991139i	$0.457593\pi$
$558$	41.0819	1.73913
$559$	65.1345	2.75490
$560$	−23.7885	−1.00525
$561$	−7.11423	−0.300363
$562$	56.4248	2.38014
$563$	6.18674	0.260740	0.130370	−	0.991465i	$-0.458383\pi$
$563$	6.18674	0.260740	0.130370	+	0.991465i	$0.458383\pi$
$564$	21.6634	0.912194
$565$	49.8324	2.09646
$566$	−35.3356	−1.48527
$567$	−4.80423	−0.201759
$568$	−60.3544	−2.53242
$569$	−11.4367	−0.479450	−0.239725	−	0.970841i	$-0.577057\pi$
$569$	−11.4367	−0.479450	−0.239725	+	0.970841i	$0.577057\pi$
$570$	18.8576	0.789857
$571$	26.0554	1.09038	0.545192	−	0.838311i	$-0.316457\pi$
$571$	26.0554	1.09038	0.545192	+	0.838311i	$0.316457\pi$
$572$	65.7465	2.74900
$573$	−1.97401	−0.0824657
$574$	3.08582	0.128800
$575$	−16.4372	−0.685477
$576$	−8.76859	−0.365358
$577$	15.0489	0.626494	0.313247	−	0.949672i	$-0.398583\pi$
$577$	15.0489	0.626494	0.313247	+	0.949672i	$0.398583\pi$
$578$	−23.7352	−0.987253
$579$	−15.7567	−0.654824
$580$	10.0168	0.415927
$581$	15.3470	0.636701
$582$	0.591768	0.0245296
$583$	−8.88839	−0.368120
$584$	17.1447	0.709455
$585$	51.0917	2.11238
$586$	−47.2052	−1.95003
$587$	−32.6892	−1.34923	−0.674614	−	0.738171i	$-0.735690\pi$
$587$	−32.6892	−1.34923	−0.674614	+	0.738171i	$0.735690\pi$
$588$	−3.26698	−0.134728
$589$	23.1814	0.955173
$590$	85.0290	3.50059
$591$	6.45230	0.265412
$592$	−33.0758	−1.35941
$593$	14.6502	0.601612	0.300806	−	0.953685i	$-0.402744\pi$
$593$	14.6502	0.601612	0.300806	+	0.953685i	$0.402744\pi$
$594$	19.7388	0.809894
$595$	14.6080	0.598870
$596$	−25.4416	−1.04213
$597$	−10.7389	−0.439512
$598$	−96.3038	−3.93815
$599$	−18.6924	−0.763750	−0.381875	−	0.924214i	$-0.624721\pi$
$599$	−18.6924	−0.763750	−0.381875	+	0.924214i	$0.624721\pi$
$600$	15.1012	0.616504
$601$	−1.57243	−0.0641406	−0.0320703	−	0.999486i	$-0.510210\pi$
$601$	−1.57243	−0.0641406	−0.0320703	+	0.999486i	$0.510210\pi$
$602$	−23.5214	−0.958660
$603$	22.2901	0.907725
$604$	1.67361	0.0680982
$605$	−20.2156	−0.821879
$606$	−11.6288	−0.472388
$607$	−35.1750	−1.42771	−0.713855	−	0.700294i	$-0.753052\pi$
$607$	−35.1750	−1.42771	−0.713855	+	0.700294i	$0.753052\pi$
$608$	−28.5301	−1.15705
$609$	0.529924	0.0214736
$610$	−60.0855	−2.43279
$611$	47.3586	1.91592
$612$	59.6916	2.41289
$613$	7.80726	0.315332	0.157666	−	0.987492i	$-0.449603\pi$
$613$	7.80726	0.315332	0.157666	+	0.987492i	$0.449603\pi$
$614$	63.4430	2.56035
$615$	−2.39795	−0.0966946
$616$	−13.5346	−0.545326
$617$	−42.1111	−1.69533	−0.847664	−	0.530533i	$-0.821992\pi$
$617$	−42.1111	−1.69533	−0.847664	+	0.530533i	$0.821992\pi$
$618$	9.98147	0.401514
$619$	32.1199	1.29101	0.645504	−	0.763757i	$-0.276647\pi$
$619$	32.1199	1.29101	0.645504	+	0.763757i	$0.276647\pi$
$620$	84.3540	3.38774
$621$	−20.2197	−0.811388
$622$	−12.7233	−0.510159
$623$	−16.2713	−0.651894
$624$	41.8112	1.67379
$625$	−30.8354	−1.23341
$626$	62.9230	2.51491
$627$	5.07024	0.202486
$628$	−14.7985	−0.590523
$629$	20.3111	0.809857
$630$	−18.4503	−0.735076
$631$	37.9489	1.51072	0.755362	−	0.655308i	$-0.227461\pi$
$631$	37.9489	1.51072	0.755362	+	0.655308i	$0.227461\pi$
$632$	4.99012	0.198496
$633$	−4.66894	−0.185574
$634$	19.9498	0.792309
$635$	46.4069	1.84160
$636$	−14.6737	−0.581851
$637$	−7.14198	−0.282976
$638$	3.85116	0.152469
$639$	−22.1212	−0.875100
$640$	18.8894	0.746670
$641$	21.2881	0.840828	0.420414	−	0.907332i	$-0.361885\pi$
$641$	21.2881	0.840828	0.420414	+	0.907332i	$0.361885\pi$
$642$	−5.64332	−0.222724
$643$	−1.18491	−0.0467283	−0.0233642	−	0.999727i	$-0.507438\pi$
$643$	−1.18491	−0.0467283	−0.0233642	+	0.999727i	$0.507438\pi$
$644$	24.3208	0.958374
$645$	18.2782	0.719702
$646$	48.1637	1.89498
$647$	−3.74589	−0.147266	−0.0736331	−	0.997285i	$-0.523459\pi$
$647$	−3.74589	−0.147266	−0.0736331	+	0.997285i	$0.523459\pi$
$648$	−32.8579	−1.29078
$649$	22.8618	0.897403
$650$	57.9111	2.27146
$651$	4.46260	0.174903
$652$	113.018	4.42612
$653$	13.0669	0.511348	0.255674	−	0.966763i	$-0.417703\pi$
$653$	13.0669	0.511348	0.255674	+	0.966763i	$0.417703\pi$
$654$	−27.1030	−1.05981
$655$	−22.5001	−0.879150
$656$	9.97356	0.389402
$657$	6.28391	0.245159
$658$	−17.1021	−0.666711
$659$	−9.59878	−0.373915	−0.186958	−	0.982368i	$-0.559863\pi$
$659$	−9.59878	−0.373915	−0.186958	+	0.982368i	$0.559863\pi$
$660$	18.4499	0.718162
$661$	51.0141	1.98422	0.992109	−	0.125382i	$-0.0400155\pi$
$661$	51.0141	1.98422	0.992109	+	0.125382i	$0.0400155\pi$
$662$	−20.5316	−0.797982
$663$	−25.6753	−0.997147
$664$	104.964	4.07339
$665$	−10.4110	−0.403721
$666$	−25.6534	−0.994050
$667$	−3.94498	−0.152750
$668$	−4.48732	−0.173620
$669$	−17.2539	−0.667076
$670$	65.4463	2.52841
$671$	−16.1552	−0.623665
$672$	−5.49227	−0.211869
$673$	21.0542	0.811579	0.405790	−	0.913967i	$-0.366997\pi$
$673$	21.0542	0.811579	0.405790	+	0.913967i	$0.366997\pi$
$674$	6.24811	0.240668
$675$	12.1589	0.467995
$676$	176.806	6.80024
$677$	−47.6835	−1.83263	−0.916313	−	0.400463i	$-0.868849\pi$
$677$	−47.6835	−1.83263	−0.916313	+	0.400463i	$0.868849\pi$
$678$	31.6292	1.21471
$679$	−0.326706	−0.0125378
$680$	99.9096	3.83136
$681$	−14.4509	−0.553759
$682$	32.4314	1.24186
$683$	41.3730	1.58309	0.791547	−	0.611108i	$-0.209276\pi$
$683$	41.3730	1.58309	0.791547	+	0.611108i	$0.209276\pi$
$684$	−42.5416	−1.62662
$685$	18.3824	0.702354
$686$	2.57911	0.0984710
$687$	−6.35198	−0.242343
$688$	−76.0226	−2.89834
$689$	−32.0783	−1.22209
$690$	−27.0249	−1.02882
$691$	25.3495	0.964342	0.482171	−	0.876077i	$-0.339848\pi$
$691$	25.3495	0.964342	0.482171	+	0.876077i	$0.339848\pi$
$692$	−44.5027	−1.69174
$693$	−4.96073	−0.188442
$694$	−53.3509	−2.02517
$695$	−27.2287	−1.03284
$696$	3.62435	0.137381
$697$	−6.12455	−0.231984
$698$	−46.2287	−1.74978
$699$	2.69324	0.101868
$700$	−14.6250	−0.552774
$701$	23.7885	0.898480	0.449240	−	0.893411i	$-0.351695\pi$
$701$	23.7885	0.898480	0.449240	+	0.893411i	$0.351695\pi$
$702$	71.2376	2.68869
$703$	−14.4755	−0.545955
$704$	−6.92221	−0.260891
$705$	13.2898	0.500525
$706$	−52.5717	−1.97856
$707$	6.42009	0.241452
$708$	37.7421	1.41844
$709$	1.15916	0.0435332	0.0217666	−	0.999763i	$-0.493071\pi$
$709$	1.15916	0.0435332	0.0217666	+	0.999763i	$0.493071\pi$
$710$	−64.9502	−2.43754
$711$	1.82898	0.0685922
$712$	−111.285	−4.17059
$713$	−33.2215	−1.24415
$714$	9.27188	0.346991
$715$	40.3335	1.50839
$716$	−83.8600	−3.13399
$717$	14.8565	0.554826
$718$	−44.4119	−1.65744
$719$	−12.7127	−0.474102	−0.237051	−	0.971497i	$-0.576181\pi$
$719$	−12.7127	−0.474102	−0.237051	+	0.971497i	$0.576181\pi$
$720$	−59.6324	−2.22237
$721$	−5.51062	−0.205226
$722$	14.6774	0.546235
$723$	−10.8771	−0.404523
$724$	−90.7874	−3.37409
$725$	2.37226	0.0881037
$726$	−12.8311	−0.476205
$727$	−8.84053	−0.327877	−0.163939	−	0.986471i	$-0.552420\pi$
$727$	−8.84053	−0.327877	−0.163939	+	0.986471i	$0.552420\pi$
$728$	−48.8466	−1.81038
$729$	−3.89487	−0.144254
$730$	18.4503	0.682874
$731$	46.6839	1.72666
$732$	−26.6704	−0.985766
$733$	−29.5053	−1.08980	−0.544902	−	0.838500i	$-0.683433\pi$
$733$	−29.5053	−1.08980	−0.544902	+	0.838500i	$0.683433\pi$
$734$	−68.2660	−2.51974
$735$	−2.00420	−0.0739259
$736$	40.8867	1.50711
$737$	17.5966	0.648178
$738$	7.73545	0.284746
$739$	−7.54771	−0.277647	−0.138823	−	0.990317i	$-0.544332\pi$
$739$	−7.54771	−0.277647	−0.138823	+	0.990317i	$0.544332\pi$
$740$	−52.6745	−1.93635
$741$	18.2986	0.672214
$742$	11.5841	0.425267
$743$	26.5187	0.972876	0.486438	−	0.873715i	$-0.338296\pi$
$743$	26.5187	0.972876	0.486438	+	0.873715i	$0.338296\pi$
$744$	30.5214	1.11897
$745$	−15.6076	−0.571820
$746$	40.8488	1.49558
$747$	38.4714	1.40760
$748$	47.1225	1.72297
$749$	3.11560	0.113841
$750$	−9.59413	−0.350328
$751$	−39.0669	−1.42557	−0.712786	−	0.701382i	$-0.752567\pi$
$751$	−39.0669	−1.42557	−0.712786	+	0.701382i	$0.752567\pi$
$752$	−55.2752	−2.01568
$753$	−21.3613	−0.778449
$754$	13.8989	0.506167
$755$	1.02671	0.0373658
$756$	−17.9905	−0.654310
$757$	36.8836	1.34056	0.670278	−	0.742110i	$-0.266175\pi$
$757$	36.8836	1.34056	0.670278	+	0.742110i	$0.266175\pi$
$758$	14.6980	0.533856
$759$	−7.26620	−0.263747
$760$	−71.2046	−2.58286
$761$	−13.5768	−0.492157	−0.246079	−	0.969250i	$-0.579142\pi$
$761$	−13.5768	−0.492157	−0.246079	+	0.969250i	$0.579142\pi$
$762$	29.4550	1.06704
$763$	14.9632	0.541703
$764$	13.0753	0.473047
$765$	36.6190	1.32396
$766$	95.1080	3.43639
$767$	82.5084	2.97921
$768$	16.9026	0.609920
$769$	10.0537	0.362545	0.181273	−	0.983433i	$-0.441978\pi$
$769$	10.0537	0.362545	0.181273	+	0.983433i	$0.441978\pi$
$770$	−14.5652	−0.524895
$771$	8.31241	0.299364
$772$	104.367	3.75626
$773$	−6.29833	−0.226535	−0.113268	−	0.993565i	$-0.536132\pi$
$773$	−6.29833	−0.226535	−0.113268	+	0.993565i	$0.536132\pi$
$774$	−58.9628	−2.11937
$775$	19.9773	0.717607
$776$	−2.23447	−0.0802127
$777$	−2.78665	−0.0999706
$778$	9.08594	0.325747
$779$	4.36491	0.156389
$780$	66.5859	2.38416
$781$	−17.4632	−0.624882
$782$	−69.0238	−2.46829
$783$	2.91817	0.104287
$784$	8.33586	0.297709
$785$	−9.07841	−0.324022
$786$	−14.2811	−0.509388
$787$	−24.6650	−0.879214	−0.439607	−	0.898190i	$-0.644882\pi$
$787$	−24.6650	−0.879214	−0.439607	+	0.898190i	$0.644882\pi$
$788$	−42.7381	−1.52248
$789$	−15.3543	−0.546629
$790$	5.37010	0.191059
$791$	−17.4620	−0.620878
$792$	−33.9283	−1.20559
$793$	−58.3043	−2.07045
$794$	−89.2685	−3.16802
$795$	−9.00188	−0.319264
$796$	71.1310	2.52117
$797$	−32.3902	−1.14732	−0.573659	−	0.819094i	$-0.694477\pi$
$797$	−32.3902	−1.14732	−0.573659	+	0.819094i	$0.694477\pi$
$798$	−6.60798	−0.233920
$799$	33.9433	1.20083
$800$	−24.5867	−0.869272
$801$	−40.7883	−1.44119
$802$	29.6552	1.04716
$803$	4.96072	0.175060
$804$	29.0499	1.02451
$805$	14.9201	0.525864
$806$	117.045	4.12274
$807$	14.0499	0.494579
$808$	43.9094	1.54473
$809$	−26.6157	−0.935759	−0.467880	−	0.883792i	$-0.654982\pi$
$809$	−26.6157	−0.935759	−0.467880	+	0.883792i	$0.654982\pi$
$810$	−35.3600	−1.24242
$811$	9.00612	0.316248	0.158124	−	0.987419i	$-0.449455\pi$
$811$	9.00612	0.316248	0.158124	+	0.987419i	$0.449455\pi$
$812$	−3.51006	−0.123179
$813$	3.63882	0.127619
$814$	−20.2516	−0.709820
$815$	69.3330	2.42863
$816$	29.9673	1.04907
$817$	−33.2711	−1.16401
$818$	−77.6111	−2.71361
$819$	−17.9033	−0.625593
$820$	15.8833	0.554669
$821$	22.6552	0.790671	0.395336	−	0.918537i	$-0.370628\pi$
$821$	22.6552	0.790671	0.395336	+	0.918537i	$0.370628\pi$
$822$	11.6675	0.406951
$823$	−13.5536	−0.472449	−0.236225	−	0.971698i	$-0.575910\pi$
$823$	−13.5536	−0.472449	−0.236225	+	0.971698i	$0.575910\pi$
$824$	−37.6892	−1.31297
$825$	4.36944	0.152124
$826$	−29.7955	−1.03672
$827$	−4.24046	−0.147455	−0.0737277	−	0.997278i	$-0.523490\pi$
$827$	−4.24046	−0.147455	−0.0737277	+	0.997278i	$0.523490\pi$
$828$	60.9668	2.11874
$829$	−2.35730	−0.0818724	−0.0409362	−	0.999162i	$-0.513034\pi$
$829$	−2.35730	−0.0818724	−0.0409362	+	0.999162i	$0.513034\pi$
$830$	112.956	3.92077
$831$	−1.80265	−0.0625332
$832$	−24.9824	−0.866107
$833$	−5.11887	−0.177358
$834$	−17.2824	−0.598440
$835$	−2.75284	−0.0952659
$836$	−33.5837	−1.16152
$837$	24.5745	0.849420
$838$	−53.9250	−1.86281
$839$	45.0555	1.55549	0.777743	−	0.628582i	$-0.216364\pi$
$839$	45.0555	1.55549	0.777743	+	0.628582i	$0.216364\pi$
$840$	−13.7074	−0.472952
$841$	−28.4306	−0.980367
$842$	29.8241	1.02781
$843$	15.3646	0.529187
$844$	30.9257	1.06451
$845$	108.465	3.73132
$846$	−42.8712	−1.47394
$847$	7.08384	0.243404
$848$	37.4407	1.28572
$849$	−9.62200	−0.330226
$850$	41.5066	1.42367
$851$	20.7450	0.711130
$852$	−28.8297	−0.987689
$853$	5.80463	0.198747	0.0993734	−	0.995050i	$-0.468316\pi$
$853$	5.80463	0.198747	0.0993734	+	0.995050i	$0.468316\pi$
$854$	21.0549	0.720483
$855$	−26.0980	−0.892533
$856$	21.3087	0.728317
$857$	37.9178	1.29525	0.647624	−	0.761960i	$-0.275763\pi$
$857$	37.9178	1.29525	0.647624	+	0.761960i	$0.275763\pi$
$858$	25.6002	0.873975
$859$	−33.8209	−1.15395	−0.576977	−	0.816760i	$-0.695768\pi$
$859$	−33.8209	−1.15395	−0.576977	+	0.816760i	$0.695768\pi$
$860$	−121.069	−4.12842
$861$	0.840278	0.0286366
$862$	−32.8778	−1.11982
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	−30.2447	−1.02894
$865$	−27.3010	−0.928263
$866$	6.17813	0.209941
$867$	−6.46316	−0.219501
$868$	−29.5589	−1.00329
$869$	1.44386	0.0489796
$870$	3.90033	0.132233
$871$	63.5062	2.15183
$872$	102.339	3.46562
$873$	−0.818979	−0.0277182
$874$	49.1926	1.66396
$875$	5.29678	0.179064
$876$	8.18958	0.276700
$877$	−31.9445	−1.07869	−0.539345	−	0.842085i	$-0.681328\pi$
$877$	−31.9445	−1.07869	−0.539345	+	0.842085i	$0.681328\pi$
$878$	13.7654	0.464559
$879$	−12.8541	−0.433559
$880$	−47.0758	−1.58692
$881$	−24.0360	−0.809792	−0.404896	−	0.914363i	$-0.632692\pi$
$881$	−24.0360	−0.809792	−0.404896	+	0.914363i	$0.632692\pi$
$882$	6.46525	0.217696
$883$	−32.3856	−1.08986	−0.544930	−	0.838481i	$-0.683444\pi$
$883$	−32.3856	−1.08986	−0.544930	+	0.838481i	$0.683444\pi$
$884$	170.066	5.71993
$885$	23.1537	0.778302
$886$	−17.9230	−0.602135
$887$	−30.0238	−1.00810	−0.504051	−	0.863674i	$-0.668157\pi$
$887$	−30.0238	−1.00810	−0.504051	+	0.863674i	$0.668157\pi$
$888$	−19.0589	−0.639576
$889$	−16.2617	−0.545399
$890$	−119.759	−4.01433
$891$	−9.50724	−0.318504
$892$	114.285	3.82654
$893$	−24.1911	−0.809523
$894$	−9.90636	−0.331318
$895$	−51.4455	−1.71964
$896$	−6.61914	−0.221130
$897$	−26.2238	−0.875588
$898$	12.7739	0.426271
$899$	4.79463	0.159910
$900$	−36.6616	−1.22205
$901$	−22.9915	−0.765958
$902$	6.10661	0.203328
$903$	−6.40495	−0.213143
$904$	−119.429	−3.97216
$905$	−55.6953	−1.85137
$906$	0.651664	0.0216501
$907$	−14.4923	−0.481208	−0.240604	−	0.970623i	$-0.577346\pi$
$907$	−14.4923	−0.481208	−0.240604	+	0.970623i	$0.577346\pi$
$908$	95.7184	3.17653
$909$	16.0937	0.533795
$910$	−52.5661	−1.74255
$911$	−32.1409	−1.06488	−0.532438	−	0.846469i	$-0.678724\pi$
$911$	−32.1409	−1.06488	−0.532438	+	0.846469i	$0.678724\pi$
$912$	−21.3574	−0.707215
$913$	30.3706	1.00512
$914$	−57.1092	−1.88901
$915$	−16.3615	−0.540894
$916$	42.0736	1.39015
$917$	7.88436	0.260365
$918$	51.0582	1.68517
$919$	32.2820	1.06488	0.532442	−	0.846467i	$-0.321274\pi$
$919$	32.2820	1.06488	0.532442	+	0.846467i	$0.321274\pi$
$920$	102.044	3.36429
$921$	17.2757	0.569255
$922$	70.2499	2.31356
$923$	−63.0248	−2.07449
$924$	−6.46513	−0.212687
$925$	−12.4748	−0.410167
$926$	−68.7565	−2.25948
$927$	−13.8139	−0.453708
$928$	−5.90091	−0.193707
$929$	−12.4750	−0.409293	−0.204646	−	0.978836i	$-0.565604\pi$
$929$	−12.4750	−0.409293	−0.204646	+	0.978836i	$0.565604\pi$
$930$	32.8455	1.07705
$931$	3.64817	0.119564
$932$	−17.8392	−0.584343
$933$	−3.46460	−0.113426
$934$	11.4921	0.376032
$935$	28.9082	0.945400
$936$	−122.447	−4.00232
$937$	−55.0594	−1.79871	−0.899357	−	0.437216i	$-0.855965\pi$
$937$	−55.0594	−1.79871	−0.899357	+	0.437216i	$0.855965\pi$
$938$	−22.9334	−0.748802
$939$	17.1341	0.559151
$940$	−88.0279	−2.87116
$941$	34.2155	1.11539	0.557697	−	0.830044i	$-0.311685\pi$
$941$	34.2155	1.11539	0.557697	+	0.830044i	$0.311685\pi$
$942$	−5.76218	−0.187742
$943$	−6.25538	−0.203703
$944$	−96.3008	−3.13432
$945$	−11.0367	−0.359022
$946$	−46.5472	−1.51338
$947$	24.9601	0.811094	0.405547	−	0.914074i	$-0.367081\pi$
$947$	24.9601	0.811094	0.405547	+	0.914074i	$0.367081\pi$
$948$	2.38364	0.0774172
$949$	17.9033	0.581166
$950$	−29.5814	−0.959746
$951$	5.43240	0.176158
$952$	−35.0099	−1.13468
$953$	49.2430	1.59514	0.797569	−	0.603228i	$-0.206119\pi$
$953$	49.2430	1.59514	0.797569	+	0.603228i	$0.206119\pi$
$954$	29.0388	0.940166
$955$	8.02129	0.259563
$956$	−98.4049	−3.18264
$957$	1.04868	0.0338991
$958$	1.29277	0.0417674
$959$	−6.44146	−0.208006
$960$	−7.01059	−0.226266
$961$	9.37657	0.302470
$962$	−73.0884	−2.35647
$963$	7.81009	0.251677
$964$	72.0465	2.32046
$965$	64.0262	2.06108
$966$	9.46996	0.304691
$967$	13.1133	0.421695	0.210847	−	0.977519i	$-0.432378\pi$
$967$	13.1133	0.421695	0.210847	+	0.977519i	$0.432378\pi$
$968$	48.4490	1.55721
$969$	13.1151	0.421319
$970$	−2.40461	−0.0772075
$971$	−39.7493	−1.27562	−0.637808	−	0.770196i	$-0.720158\pi$
$971$	−39.7493	−1.27562	−0.637808	+	0.770196i	$0.720158\pi$
$972$	−69.6670	−2.23457
$973$	9.54134	0.305881
$974$	−72.3366	−2.31782
$975$	15.7694	0.505024
$976$	68.0507	2.17825
$977$	3.27105	0.104650	0.0523251	−	0.998630i	$-0.483337\pi$
$977$	3.27105	0.104650	0.0523251	+	0.998630i	$0.483337\pi$
$978$	44.0065	1.40717
$979$	−32.1997	−1.02911
$980$	13.2752	0.424060
$981$	37.5092	1.19758
$982$	84.1612	2.68569
$983$	−24.1269	−0.769528	−0.384764	−	0.923015i	$-0.625717\pi$
$983$	−24.1269	−0.769528	−0.384764	+	0.923015i	$0.625717\pi$
$984$	5.74697	0.183207
$985$	−26.2185	−0.835391
$986$	9.96174	0.317246
$987$	−4.65697	−0.148233
$988$	−121.204	−3.85602
$989$	47.6811	1.51617
$990$	−36.5118	−1.16042
$991$	−11.0443	−0.350834	−0.175417	−	0.984494i	$-0.556127\pi$
$991$	−11.0443	−0.350834	−0.175417	+	0.984494i	$0.556127\pi$
$992$	−49.6928	−1.57775
$993$	−5.59081	−0.177419
$994$	22.7595	0.721889
$995$	43.6367	1.38338
$996$	50.1384	1.58870
$997$	−7.54477	−0.238945	−0.119473	−	0.992837i	$-0.538120\pi$
$997$	−7.54477	−0.238945	−0.119473	+	0.992837i	$0.538120\pi$
$998$	5.96455	0.188804
$999$	−15.3455	−0.485509

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.8	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.8	✓	112	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57911 q^{2} -0.702301 q^{3} +4.65183 q^{4} +2.85376 q^{5} +1.81131 q^{6} -1.00000 q^{7} -6.83937 q^{8} -2.50677 q^{9} +O(q^{10})\)	\(q-2.57911 q^{2} -0.702301 q^{3} +4.65183 q^{4} +2.85376 q^{5} +1.81131 q^{6} -1.00000 q^{7} -6.83937 q^{8} -2.50677 q^{9} -7.36016 q^{10} -1.97893 q^{11} -3.26698 q^{12} -7.14198 q^{13} +2.57911 q^{14} -2.00420 q^{15} +8.33586 q^{16} -5.11887 q^{17} +6.46525 q^{18} +3.64817 q^{19} +13.2752 q^{20} +0.702301 q^{21} +5.10388 q^{22} -5.22822 q^{23} +4.80330 q^{24} +3.14393 q^{25} +18.4200 q^{26} +3.86741 q^{27} -4.65183 q^{28} +0.754554 q^{29} +5.16905 q^{30} +6.35426 q^{31} -7.82039 q^{32} +1.38980 q^{33} +13.2022 q^{34} -2.85376 q^{35} -11.6611 q^{36} -3.96789 q^{37} -9.40905 q^{38} +5.01582 q^{39} -19.5179 q^{40} +1.19646 q^{41} -1.81131 q^{42} -9.11995 q^{43} -9.20564 q^{44} -7.15372 q^{45} +13.4842 q^{46} -6.63101 q^{47} -5.85428 q^{48} +1.00000 q^{49} -8.10855 q^{50} +3.59499 q^{51} -33.2233 q^{52} +4.49152 q^{53} -9.97450 q^{54} -5.64738 q^{55} +6.83937 q^{56} -2.56211 q^{57} -1.94608 q^{58} -11.5526 q^{59} -9.32318 q^{60} +8.16361 q^{61} -16.3884 q^{62} +2.50677 q^{63} +3.49796 q^{64} -20.3815 q^{65} -3.58446 q^{66} -8.89197 q^{67} -23.8121 q^{68} +3.67179 q^{69} +7.36016 q^{70} +8.82456 q^{71} +17.1448 q^{72} -2.50677 q^{73} +10.2336 q^{74} -2.20798 q^{75} +16.9707 q^{76} +1.97893 q^{77} -12.9364 q^{78} -0.729616 q^{79} +23.7885 q^{80} +4.80423 q^{81} -3.08582 q^{82} -15.3470 q^{83} +3.26698 q^{84} -14.6080 q^{85} +23.5214 q^{86} -0.529924 q^{87} +13.5346 q^{88} +16.2713 q^{89} +18.4503 q^{90} +7.14198 q^{91} -24.3208 q^{92} -4.46260 q^{93} +17.1021 q^{94} +10.4110 q^{95} +5.49227 q^{96} +0.326706 q^{97} -2.57911 q^{98} +4.96073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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