LMFDB - Embedded newform 8041.2.a.e.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88145 q^{2} -3.19345 q^{3} +1.53984 q^{4} +2.05646 q^{5} +6.00831 q^{6} -0.224588 q^{7} +0.865759 q^{8} +7.19812 q^{9} +O(q^{10})$	\(q-1.88145 q^{2} -3.19345 q^{3} +1.53984 q^{4} +2.05646 q^{5} +6.00831 q^{6} -0.224588 q^{7} +0.865759 q^{8} +7.19812 q^{9} -3.86912 q^{10} -1.00000 q^{11} -4.91742 q^{12} +3.19762 q^{13} +0.422550 q^{14} -6.56720 q^{15} -4.70857 q^{16} -1.00000 q^{17} -13.5429 q^{18} +1.82274 q^{19} +3.16663 q^{20} +0.717210 q^{21} +1.88145 q^{22} +6.91974 q^{23} -2.76476 q^{24} -0.770972 q^{25} -6.01615 q^{26} -13.4065 q^{27} -0.345830 q^{28} +0.0484324 q^{29} +12.3558 q^{30} +5.73190 q^{31} +7.12741 q^{32} +3.19345 q^{33} +1.88145 q^{34} -0.461856 q^{35} +11.0840 q^{36} -3.02065 q^{37} -3.42939 q^{38} -10.2114 q^{39} +1.78040 q^{40} -9.96611 q^{41} -1.34939 q^{42} +1.00000 q^{43} -1.53984 q^{44} +14.8027 q^{45} -13.0191 q^{46} -2.99854 q^{47} +15.0366 q^{48} -6.94956 q^{49} +1.45054 q^{50} +3.19345 q^{51} +4.92383 q^{52} -5.38877 q^{53} +25.2236 q^{54} -2.05646 q^{55} -0.194439 q^{56} -5.82083 q^{57} -0.0911231 q^{58} +8.27973 q^{59} -10.1125 q^{60} +14.0151 q^{61} -10.7843 q^{62} -1.61661 q^{63} -3.99270 q^{64} +6.57577 q^{65} -6.00831 q^{66} -3.77977 q^{67} -1.53984 q^{68} -22.0978 q^{69} +0.868957 q^{70} +8.06955 q^{71} +6.23184 q^{72} -4.90586 q^{73} +5.68319 q^{74} +2.46206 q^{75} +2.80673 q^{76} +0.224588 q^{77} +19.2123 q^{78} +4.00486 q^{79} -9.68298 q^{80} +21.2186 q^{81} +18.7507 q^{82} +13.1567 q^{83} +1.10439 q^{84} -2.05646 q^{85} -1.88145 q^{86} -0.154667 q^{87} -0.865759 q^{88} +9.79517 q^{89} -27.8504 q^{90} -0.718146 q^{91} +10.6553 q^{92} -18.3045 q^{93} +5.64159 q^{94} +3.74839 q^{95} -22.7610 q^{96} +10.8483 q^{97} +13.0752 q^{98} -7.19812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.88145	−1.33038	−0.665192	−	0.746672i	$-0.731650\pi$
$2$	−1.88145	−1.33038	−0.665192	+	0.746672i	$0.731650\pi$
$3$	−3.19345	−1.84374	−0.921870	−	0.387500i	$-0.873339\pi$
$3$	−3.19345	−1.84374	−0.921870	+	0.387500i	$0.873339\pi$
$4$	1.53984	0.769922
$5$	2.05646	0.919677	0.459838	−	0.888003i	$-0.347907\pi$
$5$	2.05646	0.919677	0.459838	+	0.888003i	$0.347907\pi$
$6$	6.00831	2.45288
$7$	−0.224588	−0.0848862	−0.0424431	−	0.999099i	$-0.513514\pi$
$7$	−0.224588	−0.0848862	−0.0424431	+	0.999099i	$0.513514\pi$
$8$	0.865759	0.306092
$9$	7.19812	2.39937
$10$	−3.86912	−1.22352
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.91742	−1.41954
$13$	3.19762	0.886859	0.443430	−	0.896309i	$-0.353762\pi$
$13$	3.19762	0.886859	0.443430	+	0.896309i	$0.353762\pi$
$14$	0.422550	0.112931
$15$	−6.56720	−1.69564
$16$	−4.70857	−1.17714
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−13.5429	−3.19209
$19$	1.82274	0.418165	0.209083	−	0.977898i	$-0.432952\pi$
$19$	1.82274	0.418165	0.209083	+	0.977898i	$0.432952\pi$
$20$	3.16663	0.708080
$21$	0.717210	0.156508
$22$	1.88145	0.401126
$23$	6.91974	1.44287	0.721433	−	0.692485i	$-0.243484\pi$
$23$	6.91974	1.44287	0.721433	+	0.692485i	$0.243484\pi$
$24$	−2.76476	−0.564354
$25$	−0.770972	−0.154194
$26$	−6.01615	−1.17986
$27$	−13.4065	−2.58008
$28$	−0.345830	−0.0653557
$29$	0.0484324	0.00899368	0.00449684	−	0.999990i	$-0.498569\pi$
$29$	0.0484324	0.00899368	0.00449684	+	0.999990i	$0.498569\pi$
$30$	12.3558	2.25586
$31$	5.73190	1.02948	0.514740	−	0.857346i	$-0.327889\pi$
$31$	5.73190	1.02948	0.514740	+	0.857346i	$0.327889\pi$
$32$	7.12741	1.25996
$33$	3.19345	0.555908
$34$	1.88145	0.322666
$35$	−0.461856	−0.0780679
$36$	11.0840	1.84733
$37$	−3.02065	−0.496591	−0.248296	−	0.968684i	$-0.579870\pi$
$37$	−3.02065	−0.496591	−0.248296	+	0.968684i	$0.579870\pi$
$38$	−3.42939	−0.556320
$39$	−10.2114	−1.63514
$40$	1.78040	0.281506
$41$	−9.96611	−1.55645	−0.778223	−	0.627989i	$-0.783878\pi$
$41$	−9.96611	−1.55645	−0.778223	+	0.627989i	$0.783878\pi$
$42$	−1.34939	−0.208216
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.53984	−0.232140
$45$	14.8027	2.20665
$46$	−13.0191	−1.91957
$47$	−2.99854	−0.437381	−0.218691	−	0.975794i	$-0.570179\pi$
$47$	−2.99854	−0.437381	−0.218691	+	0.975794i	$0.570179\pi$
$48$	15.0366	2.17034
$49$	−6.94956	−0.992794
$50$	1.45054	0.205138
$51$	3.19345	0.447172
$52$	4.92383	0.682813
$53$	−5.38877	−0.740205	−0.370102	−	0.928991i	$-0.620677\pi$
$53$	−5.38877	−0.740205	−0.370102	+	0.928991i	$0.620677\pi$
$54$	25.2236	3.43250
$55$	−2.05646	−0.277293
$56$	−0.194439	−0.0259830
$57$	−5.82083	−0.770987
$58$	−0.0911231	−0.0119650
$59$	8.27973	1.07793	0.538965	−	0.842328i	$-0.318816\pi$
$59$	8.27973	1.07793	0.538965	+	0.842328i	$0.318816\pi$
$60$	−10.1125	−1.30551
$61$	14.0151	1.79445	0.897226	−	0.441572i	$-0.145579\pi$
$61$	14.0151	1.79445	0.897226	+	0.441572i	$0.145579\pi$
$62$	−10.7843	−1.36960
$63$	−1.61661	−0.203674
$64$	−3.99270	−0.499088
$65$	6.57577	0.815624
$66$	−6.00831	−0.739572
$67$	−3.77977	−0.461772	−0.230886	−	0.972981i	$-0.574163\pi$
$67$	−3.77977	−0.461772	−0.230886	+	0.972981i	$0.574163\pi$
$68$	−1.53984	−0.186734
$69$	−22.0978	−2.66027
$70$	0.868957	0.103860
$71$	8.06955	0.957679	0.478840	−	0.877902i	$-0.341058\pi$
$71$	8.06955	0.957679	0.478840	+	0.877902i	$0.341058\pi$
$72$	6.23184	0.734429
$73$	−4.90586	−0.574187	−0.287094	−	0.957903i	$-0.592689\pi$
$73$	−4.90586	−0.574187	−0.287094	+	0.957903i	$0.592689\pi$
$74$	5.68319	0.660657
$75$	2.46206	0.284294
$76$	2.80673	0.321955
$77$	0.224588	0.0255941
$78$	19.2123	2.17536
$79$	4.00486	0.450582	0.225291	−	0.974292i	$-0.427667\pi$
$79$	4.00486	0.450582	0.225291	+	0.974292i	$0.427667\pi$
$80$	−9.68298	−1.08259
$81$	21.2186	2.35762
$82$	18.7507	2.07067
$83$	13.1567	1.44413	0.722066	−	0.691824i	$-0.243193\pi$
$83$	13.1567	1.44413	0.722066	+	0.691824i	$0.243193\pi$
$84$	1.10439	0.120499
$85$	−2.05646	−0.223054
$86$	−1.88145	−0.202882
$87$	−0.154667	−0.0165820
$88$	−0.865759	−0.0922902
$89$	9.79517	1.03829	0.519143	−	0.854687i	$-0.326251\pi$
$89$	9.79517	1.03829	0.519143	+	0.854687i	$0.326251\pi$
$90$	−27.8504	−2.93569
$91$	−0.718146	−0.0752821
$92$	10.6553	1.11089
$93$	−18.3045	−1.89809
$94$	5.64159	0.581885
$95$	3.74839	0.384577
$96$	−22.7610	−2.32304
$97$	10.8483	1.10148	0.550740	−	0.834677i	$-0.314345\pi$
$97$	10.8483	1.10148	0.550740	+	0.834677i	$0.314345\pi$
$98$	13.0752	1.32080
$99$	−7.19812	−0.723439
$100$	−1.18718	−0.118718
$101$	2.68860	0.267526	0.133763	−	0.991013i	$-0.457294\pi$
$101$	2.68860	0.267526	0.133763	+	0.991013i	$0.457294\pi$
$102$	−6.00831	−0.594911
$103$	12.9445	1.27546	0.637729	−	0.770261i	$-0.279874\pi$
$103$	12.9445	1.27546	0.637729	+	0.770261i	$0.279874\pi$
$104$	2.76837	0.271461
$105$	1.47491	0.143937
$106$	10.1387	0.984757
$107$	−4.38544	−0.423957	−0.211978	−	0.977274i	$-0.567991\pi$
$107$	−4.38544	−0.423957	−0.211978	+	0.977274i	$0.567991\pi$
$108$	−20.6439	−1.98646
$109$	−15.0990	−1.44622	−0.723110	−	0.690733i	$-0.757288\pi$
$109$	−15.0990	−1.44622	−0.723110	+	0.690733i	$0.757288\pi$
$110$	3.86912	0.368906
$111$	9.64629	0.915585
$112$	1.05749	0.0999231
$113$	11.9611	1.12521	0.562605	−	0.826726i	$-0.309799\pi$
$113$	11.9611	1.12521	0.562605	+	0.826726i	$0.309799\pi$
$114$	10.9516	1.02571
$115$	14.2302	1.32697
$116$	0.0745784	0.00692443
$117$	23.0168	2.12791
$118$	−15.5779	−1.43406
$119$	0.224588	0.0205879
$120$	−5.68562	−0.519023
$121$	1.00000	0.0909091
$122$	−26.3687	−2.38731
$123$	31.8263	2.86968
$124$	8.82623	0.792619
$125$	−11.8678	−1.06149
$126$	3.04157	0.270964
$127$	6.26338	0.555785	0.277893	−	0.960612i	$-0.410364\pi$
$127$	6.26338	0.555785	0.277893	+	0.960612i	$0.410364\pi$
$128$	−6.74275	−0.595981
$129$	−3.19345	−0.281168
$130$	−12.3720	−1.08509
$131$	17.4480	1.52444	0.762220	−	0.647318i	$-0.224109\pi$
$131$	17.4480	1.52444	0.762220	+	0.647318i	$0.224109\pi$
$132$	4.91742	0.428006
$133$	−0.409365	−0.0354964
$134$	7.11144	0.614335
$135$	−27.5699	−2.37284
$136$	−0.865759	−0.0742382
$137$	−14.9461	−1.27693	−0.638464	−	0.769651i	$-0.720430\pi$
$137$	−14.9461	−1.27693	−0.638464	+	0.769651i	$0.720430\pi$
$138$	41.5759	3.53918
$139$	10.5525	0.895048	0.447524	−	0.894272i	$-0.352306\pi$
$139$	10.5525	0.895048	0.447524	+	0.894272i	$0.352306\pi$
$140$	−0.711186	−0.0601062
$141$	9.57567	0.806417
$142$	−15.1824	−1.27408
$143$	−3.19762	−0.267398
$144$	−33.8929	−2.82440
$145$	0.0995994	0.00827128
$146$	9.23011	0.763890
$147$	22.1931	1.83045
$148$	−4.65133	−0.382337
$149$	−5.34934	−0.438235	−0.219117	−	0.975698i	$-0.570318\pi$
$149$	−5.34934	−0.438235	−0.219117	+	0.975698i	$0.570318\pi$
$150$	−4.63223	−0.378220
$151$	13.2884	1.08140	0.540698	−	0.841217i	$-0.318160\pi$
$151$	13.2884	1.08140	0.540698	+	0.841217i	$0.318160\pi$
$152$	1.57805	0.127997
$153$	−7.19812	−0.581934
$154$	−0.422550	−0.0340500
$155$	11.7874	0.946789
$156$	−15.7240	−1.25893
$157$	−8.12874	−0.648744	−0.324372	−	0.945930i	$-0.605153\pi$
$157$	−8.12874	−0.648744	−0.324372	+	0.945930i	$0.605153\pi$
$158$	−7.53493	−0.599447
$159$	17.2088	1.36474
$160$	14.6572	1.15876
$161$	−1.55409	−0.122479
$162$	−39.9217	−3.13655
$163$	−0.917037	−0.0718279	−0.0359140	−	0.999355i	$-0.511434\pi$
$163$	−0.917037	−0.0718279	−0.0359140	+	0.999355i	$0.511434\pi$
$164$	−15.3463	−1.19834
$165$	6.56720	0.511256
$166$	−24.7536	−1.92125
$167$	1.85038	0.143186	0.0715932	−	0.997434i	$-0.477192\pi$
$167$	1.85038	0.143186	0.0715932	+	0.997434i	$0.477192\pi$
$168$	0.620931	0.0479058
$169$	−2.77524	−0.213480
$170$	3.86912	0.296748
$171$	13.1203	1.00333
$172$	1.53984	0.117412
$173$	−7.81181	−0.593921	−0.296961	−	0.954890i	$-0.595973\pi$
$173$	−7.81181	−0.593921	−0.296961	+	0.954890i	$0.595973\pi$
$174$	0.290997	0.0220604
$175$	0.173151	0.0130890
$176$	4.70857	0.354922
$177$	−26.4409	−1.98742
$178$	−18.4291	−1.38132
$179$	−21.4142	−1.60057	−0.800285	−	0.599620i	$-0.795318\pi$
$179$	−21.4142	−1.60057	−0.800285	+	0.599620i	$0.795318\pi$
$180$	22.7938	1.69895
$181$	19.9586	1.48351	0.741757	−	0.670669i	$-0.233993\pi$
$181$	19.9586	1.48351	0.741757	+	0.670669i	$0.233993\pi$
$182$	1.35115	0.100154
$183$	−44.7566	−3.30850
$184$	5.99083	0.441650
$185$	−6.21184	−0.456704
$186$	34.4390	2.52519
$187$	1.00000	0.0731272
$188$	−4.61728	−0.336750
$189$	3.01094	0.219013
$190$	−7.05240	−0.511635
$191$	13.9965	1.01275	0.506375	−	0.862314i	$-0.330985\pi$
$191$	13.9965	1.01275	0.506375	+	0.862314i	$0.330985\pi$
$192$	12.7505	0.920188
$193$	−7.82166	−0.563015	−0.281508	−	0.959559i	$-0.590834\pi$
$193$	−7.82166	−0.563015	−0.281508	+	0.959559i	$0.590834\pi$
$194$	−20.4106	−1.46539
$195$	−20.9994	−1.50380
$196$	−10.7012	−0.764374
$197$	11.7610	0.837939	0.418969	−	0.908000i	$-0.362391\pi$
$197$	11.7610	0.837939	0.418969	+	0.908000i	$0.362391\pi$
$198$	13.5429	0.962451
$199$	−7.51580	−0.532781	−0.266390	−	0.963865i	$-0.585831\pi$
$199$	−7.51580	−0.532781	−0.266390	+	0.963865i	$0.585831\pi$
$200$	−0.667476	−0.0471976
$201$	12.0705	0.851388
$202$	−5.05847	−0.355913
$203$	−0.0108773	−0.000763439 0
$204$	4.91742	0.344288
$205$	−20.4949	−1.43143
$206$	−24.3544	−1.69685
$207$	49.8091	3.46197
$208$	−15.0562	−1.04396
$209$	−1.82274	−0.126082
$210$	−2.77497	−0.191491
$211$	−1.49084	−0.102634	−0.0513168	−	0.998682i	$-0.516342\pi$
$211$	−1.49084	−0.102634	−0.0513168	+	0.998682i	$0.516342\pi$
$212$	−8.29787	−0.569900
$213$	−25.7697	−1.76571
$214$	8.25098	0.564025
$215$	2.05646	0.140249
$216$	−11.6068	−0.789743
$217$	−1.28731	−0.0873886
$218$	28.4079	1.92403
$219$	15.6666	1.05865
$220$	−3.16663	−0.213494
$221$	−3.19762	−0.215095
$222$	−18.1490	−1.21808
$223$	−10.9703	−0.734627	−0.367314	−	0.930097i	$-0.619722\pi$
$223$	−10.9703	−0.734627	−0.367314	+	0.930097i	$0.619722\pi$
$224$	−1.60073	−0.106953
$225$	−5.54955	−0.369970
$226$	−22.5043	−1.49696
$227$	−11.0791	−0.735344	−0.367672	−	0.929955i	$-0.619845\pi$
$227$	−11.0791	−0.735344	−0.367672	+	0.929955i	$0.619845\pi$
$228$	−8.96317	−0.593600
$229$	2.52024	0.166542	0.0832710	−	0.996527i	$-0.473463\pi$
$229$	2.52024	0.166542	0.0832710	+	0.996527i	$0.473463\pi$
$230$	−26.7733	−1.76538
$231$	−0.717210	−0.0471889
$232$	0.0419308	0.00275289
$233$	−12.9142	−0.846039	−0.423020	−	0.906120i	$-0.639030\pi$
$233$	−12.9142	−0.846039	−0.423020	+	0.906120i	$0.639030\pi$
$234$	−43.3050	−2.83094
$235$	−6.16637	−0.402250
$236$	12.7495	0.829922
$237$	−12.7893	−0.830756
$238$	−0.422550	−0.0273898
$239$	10.0760	0.651761	0.325880	−	0.945411i	$-0.394339\pi$
$239$	10.0760	0.651761	0.325880	+	0.945411i	$0.394339\pi$
$240$	30.9221	1.99601
$241$	−19.5848	−1.26157	−0.630783	−	0.775960i	$-0.717266\pi$
$241$	−19.5848	−1.26157	−0.630783	+	0.775960i	$0.717266\pi$
$242$	−1.88145	−0.120944
$243$	−27.5411	−1.76676
$244$	21.5811	1.38159
$245$	−14.2915	−0.913050
$246$	−59.8795	−3.81778
$247$	5.82842	0.370854
$248$	4.96244	0.315116
$249$	−42.0152	−2.66260
$250$	22.3286	1.41218
$251$	−3.69703	−0.233354	−0.116677	−	0.993170i	$-0.537224\pi$
$251$	−3.69703	−0.233354	−0.116677	+	0.993170i	$0.537224\pi$
$252$	−2.48933	−0.156813
$253$	−6.91974	−0.435040
$254$	−11.7842	−0.739408
$255$	6.56720	0.411254
$256$	20.6715	1.29197
$257$	−5.73019	−0.357439	−0.178720	−	0.983900i	$-0.557196\pi$
$257$	−5.73019	−0.357439	−0.178720	+	0.983900i	$0.557196\pi$
$258$	6.00831	0.374061
$259$	0.678400	0.0421537
$260$	10.1257	0.627967
$261$	0.348623	0.0215792
$262$	−32.8275	−2.02809
$263$	−23.8744	−1.47216	−0.736080	−	0.676894i	$-0.763325\pi$
$263$	−23.8744	−1.47216	−0.736080	+	0.676894i	$0.763325\pi$
$264$	2.76476	0.170159
$265$	−11.0818	−0.680749
$266$	0.770198	0.0472239
$267$	−31.2804	−1.91433
$268$	−5.82026	−0.355529
$269$	−16.9683	−1.03458	−0.517289	−	0.855811i	$-0.673059\pi$
$269$	−16.9683	−1.03458	−0.517289	+	0.855811i	$0.673059\pi$
$270$	51.8714	3.15679
$271$	13.2233	0.803259	0.401630	−	0.915802i	$-0.368444\pi$
$271$	13.2233	0.803259	0.401630	+	0.915802i	$0.368444\pi$
$272$	4.70857	0.285499
$273$	2.29336	0.138801
$274$	28.1202	1.69881
$275$	0.770972	0.0464913
$276$	−34.0272	−2.04820
$277$	−9.16772	−0.550835	−0.275417	−	0.961325i	$-0.588816\pi$
$277$	−9.16772	−0.550835	−0.275417	+	0.961325i	$0.588816\pi$
$278$	−19.8539	−1.19076
$279$	41.2589	2.47011
$280$	−0.399856	−0.0238960
$281$	0.264409	0.0157733	0.00788665	−	0.999969i	$-0.497490\pi$
$281$	0.264409	0.0157733	0.00788665	+	0.999969i	$0.497490\pi$
$282$	−18.0161	−1.07284
$283$	−4.25492	−0.252929	−0.126464	−	0.991971i	$-0.540363\pi$
$283$	−4.25492	−0.252929	−0.126464	+	0.991971i	$0.540363\pi$
$284$	12.4258	0.737338
$285$	−11.9703	−0.709059
$286$	6.01615	0.355742
$287$	2.23827	0.132121
$288$	51.3039	3.02311
$289$	1.00000	0.0588235
$290$	−0.187391	−0.0110040
$291$	−34.6436	−2.03084
$292$	−7.55426	−0.442079
$293$	17.0529	0.996239	0.498120	−	0.867108i	$-0.334024\pi$
$293$	17.0529	0.996239	0.498120	+	0.867108i	$0.334024\pi$
$294$	−41.7551	−2.43521
$295$	17.0269	0.991347
$296$	−2.61515	−0.152003
$297$	13.4065	0.777924
$298$	10.0645	0.583021
$299$	22.1267	1.27962
$300$	3.79119	0.218884
$301$	−0.224588	−0.0129450
$302$	−25.0014	−1.43867
$303$	−8.58592	−0.493248
$304$	−8.58249	−0.492240
$305$	28.8215	1.65032
$306$	13.5429	0.774196
$307$	−14.5819	−0.832233	−0.416117	−	0.909311i	$-0.636609\pi$
$307$	−14.5819	−0.832233	−0.416117	+	0.909311i	$0.636609\pi$
$308$	0.345830	0.0197055
$309$	−41.3376	−2.35161
$310$	−22.1774	−1.25959
$311$	21.1687	1.20037	0.600184	−	0.799862i	$-0.295094\pi$
$311$	21.1687	1.20037	0.600184	+	0.799862i	$0.295094\pi$
$312$	−8.84064	−0.500503
$313$	−25.1673	−1.42254	−0.711270	−	0.702919i	$-0.751880\pi$
$313$	−25.1673	−1.42254	−0.711270	+	0.702919i	$0.751880\pi$
$314$	15.2938	0.863079
$315$	−3.32449	−0.187314
$316$	6.16686	0.346913
$317$	29.7929	1.67333	0.836667	−	0.547712i	$-0.184501\pi$
$317$	29.7929	1.67333	0.836667	+	0.547712i	$0.184501\pi$
$318$	−32.3774	−1.81563
$319$	−0.0484324	−0.00271170
$320$	−8.21083	−0.458999
$321$	14.0047	0.781666
$322$	2.92394	0.162945
$323$	−1.82274	−0.101420
$324$	32.6734	1.81519
$325$	−2.46527	−0.136749
$326$	1.72536	0.0955587
$327$	48.2179	2.66645
$328$	−8.62825	−0.476415
$329$	0.673434	0.0371276
$330$	−12.3558	−0.680167
$331$	11.7684	0.646850	0.323425	−	0.946254i	$-0.395166\pi$
$331$	11.7684	0.646850	0.323425	+	0.946254i	$0.395166\pi$
$332$	20.2592	1.11187
$333$	−21.7430	−1.19151
$334$	−3.48139	−0.190493
$335$	−7.77295	−0.424681
$336$	−3.37703	−0.184232
$337$	13.9090	0.757671	0.378836	−	0.925464i	$-0.376325\pi$
$337$	13.9090	0.757671	0.378836	+	0.925464i	$0.376325\pi$
$338$	5.22148	0.284011
$339$	−38.1973	−2.07459
$340$	−3.16663	−0.171735
$341$	−5.73190	−0.310400
$342$	−24.6852	−1.33482
$343$	3.13290	0.169161
$344$	0.865759	0.0466786
$345$	−45.4433	−2.44659
$346$	14.6975	0.790143
$347$	−14.9241	−0.801167	−0.400584	−	0.916260i	$-0.631193\pi$
$347$	−14.9241	−0.801167	−0.400584	+	0.916260i	$0.631193\pi$
$348$	−0.238162	−0.0127668
$349$	−8.12724	−0.435041	−0.217520	−	0.976056i	$-0.569797\pi$
$349$	−8.12724	−0.435041	−0.217520	+	0.976056i	$0.569797\pi$
$350$	−0.325774	−0.0174134
$351$	−42.8689	−2.28817
$352$	−7.12741	−0.379892
$353$	0.303954	0.0161778	0.00808892	−	0.999967i	$-0.497425\pi$
$353$	0.303954	0.0161778	0.00808892	+	0.999967i	$0.497425\pi$
$354$	49.7472	2.64403
$355$	16.5947	0.880755
$356$	15.0830	0.799399
$357$	−0.717210	−0.0379588
$358$	40.2896	2.12937
$359$	−9.06149	−0.478247	−0.239124	−	0.970989i	$-0.576860\pi$
$359$	−9.06149	−0.478247	−0.239124	+	0.970989i	$0.576860\pi$
$360$	12.8155	0.675438
$361$	−15.6776	−0.825138
$362$	−37.5511	−1.97364
$363$	−3.19345	−0.167613
$364$	−1.10583	−0.0579614
$365$	−10.0887	−0.528067
$366$	84.2071	4.40158
$367$	9.99877	0.521932	0.260966	−	0.965348i	$-0.415959\pi$
$367$	9.99877	0.521932	0.260966	+	0.965348i	$0.415959\pi$
$368$	−32.5821	−1.69846
$369$	−71.7373	−3.73449
$370$	11.6873	0.607591
$371$	1.21025	0.0628331
$372$	−28.1861	−1.46138
$373$	25.3541	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$373$	25.3541	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$374$	−1.88145	−0.0972873
$375$	37.8991	1.95710
$376$	−2.59601	−0.133879
$377$	0.154868	0.00797613
$378$	−5.66492	−0.291372
$379$	−5.72263	−0.293952	−0.146976	−	0.989140i	$-0.546954\pi$
$379$	−5.72263	−0.293952	−0.146976	+	0.989140i	$0.546954\pi$
$380$	5.77194	0.296094
$381$	−20.0018	−1.02472
$382$	−26.3336	−1.34735
$383$	3.24068	0.165591	0.0827954	−	0.996567i	$-0.473615\pi$
$383$	3.24068	0.165591	0.0827954	+	0.996567i	$0.473615\pi$
$384$	21.5326	1.09883
$385$	0.461856	0.0235383
$386$	14.7160	0.749027
$387$	7.19812	0.365901
$388$	16.7047	0.848054
$389$	−8.46496	−0.429190	−0.214595	−	0.976703i	$-0.568843\pi$
$389$	−8.46496	−0.429190	−0.214595	+	0.976703i	$0.568843\pi$
$390$	39.5093	2.00063
$391$	−6.91974	−0.349946
$392$	−6.01664	−0.303886
$393$	−55.7194	−2.81067
$394$	−22.1278	−1.11478
$395$	8.23583	0.414390
$396$	−11.0840	−0.556991
$397$	13.6282	0.683978	0.341989	−	0.939704i	$-0.388899\pi$
$397$	13.6282	0.683978	0.341989	+	0.939704i	$0.388899\pi$
$398$	14.1406	0.708803
$399$	1.30729	0.0654462
$400$	3.63017	0.181509
$401$	14.1848	0.708357	0.354179	−	0.935178i	$-0.384760\pi$
$401$	14.1848	0.708357	0.354179	+	0.935178i	$0.384760\pi$
$402$	−22.7100	−1.13267
$403$	18.3284	0.913004
$404$	4.14003	0.205974
$405$	43.6352	2.16825
$406$	0.0204651	0.00101567
$407$	3.02065	0.149728
$408$	2.76476	0.136876
$409$	30.1168	1.48918	0.744589	−	0.667523i	$-0.232645\pi$
$409$	30.1168	1.48918	0.744589	+	0.667523i	$0.232645\pi$
$410$	38.5601	1.90435
$411$	47.7295	2.35432
$412$	19.9325	0.982004
$413$	−1.85953	−0.0915013
$414$	−93.7133	−4.60576
$415$	27.0562	1.32813
$416$	22.7907	1.11741
$417$	−33.6988	−1.65024
$418$	3.42939	0.167737
$419$	20.7472	1.01357	0.506784	−	0.862073i	$-0.330834\pi$
$419$	20.7472	1.01357	0.506784	+	0.862073i	$0.330834\pi$
$420$	2.27114	0.110820
$421$	4.13437	0.201497	0.100749	−	0.994912i	$-0.467876\pi$
$421$	4.13437	0.201497	0.100749	+	0.994912i	$0.467876\pi$
$422$	2.80493	0.136542
$423$	−21.5838	−1.04944
$424$	−4.66538	−0.226571
$425$	0.770972	0.0373976
$426$	48.4843	2.34907
$427$	−3.14762	−0.152324
$428$	−6.75290	−0.326414
$429$	10.2114	0.493013
$430$	−3.86912	−0.186586
$431$	−9.56074	−0.460525	−0.230262	−	0.973129i	$-0.573958\pi$
$431$	−9.56074	−0.460525	−0.230262	+	0.973129i	$0.573958\pi$
$432$	63.1254	3.03712
$433$	−6.12027	−0.294122	−0.147061	−	0.989127i	$-0.546981\pi$
$433$	−6.12027	−0.294122	−0.147061	+	0.989127i	$0.546981\pi$
$434$	2.42201	0.116260
$435$	−0.318066	−0.0152501
$436$	−23.2501	−1.11348
$437$	12.6129	0.603356
$438$	−29.4759	−1.40841
$439$	−12.4016	−0.591898	−0.295949	−	0.955204i	$-0.595636\pi$
$439$	−12.4016	−0.591898	−0.295949	+	0.955204i	$0.595636\pi$
$440$	−1.78040	−0.0848772
$441$	−50.0238	−2.38209
$442$	6.01615	0.286159
$443$	6.87673	0.326723	0.163362	−	0.986566i	$-0.447766\pi$
$443$	6.87673	0.326723	0.163362	+	0.986566i	$0.447766\pi$
$444$	14.8538	0.704929
$445$	20.1434	0.954888
$446$	20.6401	0.977337
$447$	17.0828	0.807991
$448$	0.896712	0.0423656
$449$	23.7616	1.12138	0.560689	−	0.828026i	$-0.310536\pi$
$449$	23.7616	1.12138	0.560689	+	0.828026i	$0.310536\pi$
$450$	10.4412	0.492202
$451$	9.96611	0.469286
$452$	18.4183	0.866324
$453$	−42.4359	−1.99381
$454$	20.8447	0.978291
$455$	−1.47684	−0.0692352
$456$	−5.03943	−0.235993
$457$	40.1504	1.87816	0.939079	−	0.343702i	$-0.111681\pi$
$457$	40.1504	1.87816	0.939079	+	0.343702i	$0.111681\pi$
$458$	−4.74169	−0.221565
$459$	13.4065	0.625762
$460$	21.9122	1.02166
$461$	35.8357	1.66904	0.834518	−	0.550980i	$-0.185746\pi$
$461$	35.8357	1.66904	0.834518	+	0.550980i	$0.185746\pi$
$462$	1.34939	0.0627794
$463$	−2.80524	−0.130370	−0.0651852	−	0.997873i	$-0.520764\pi$
$463$	−2.80524	−0.130370	−0.0651852	+	0.997873i	$0.520764\pi$
$464$	−0.228047	−0.0105868
$465$	−37.6426	−1.74563
$466$	24.2974	1.12556
$467$	0.515125	0.0238371	0.0119186	−	0.999929i	$-0.496206\pi$
$467$	0.515125	0.0238371	0.0119186	+	0.999929i	$0.496206\pi$
$468$	35.4424	1.63832
$469$	0.848890	0.0391981
$470$	11.6017	0.535146
$471$	25.9587	1.19611
$472$	7.16825	0.329946
$473$	−1.00000	−0.0459800
$474$	24.0624	1.10522
$475$	−1.40528	−0.0644787
$476$	0.345830	0.0158511
$477$	−38.7890	−1.77603
$478$	−18.9574	−0.867092
$479$	14.1525	0.646646	0.323323	−	0.946289i	$-0.395200\pi$
$479$	14.1525	0.646646	0.323323	+	0.946289i	$0.395200\pi$
$480$	−46.8071	−2.13644
$481$	−9.65887	−0.440407
$482$	36.8477	1.67837
$483$	4.96290	0.225820
$484$	1.53984	0.0699929
$485$	22.3092	1.01301
$486$	51.8171	2.35047
$487$	−26.6315	−1.20679	−0.603393	−	0.797444i	$-0.706185\pi$
$487$	−26.6315	−1.20679	−0.603393	+	0.797444i	$0.706185\pi$
$488$	12.1337	0.549267
$489$	2.92851	0.132432
$490$	26.8887	1.21471
$491$	−25.1250	−1.13388	−0.566939	−	0.823760i	$-0.691872\pi$
$491$	−25.1250	−1.13388	−0.566939	+	0.823760i	$0.691872\pi$
$492$	49.0075	2.20943
$493$	−0.0484324	−0.00218129
$494$	−10.9659	−0.493378
$495$	−14.8027	−0.665330
$496$	−26.9890	−1.21184
$497$	−1.81232	−0.0812937
$498$	79.0493	3.54228
$499$	−23.5541	−1.05443	−0.527213	−	0.849733i	$-0.676763\pi$
$499$	−23.5541	−1.05443	−0.527213	+	0.849733i	$0.676763\pi$
$500$	−18.2745	−0.817261
$501$	−5.90909	−0.263999
$502$	6.95577	0.310451
$503$	21.9862	0.980318	0.490159	−	0.871633i	$-0.336939\pi$
$503$	21.9862	0.980318	0.490159	+	0.871633i	$0.336939\pi$
$504$	−1.39959	−0.0623429
$505$	5.52901	0.246038
$506$	13.0191	0.578771
$507$	8.86261	0.393602
$508$	9.64463	0.427911
$509$	−7.19750	−0.319024	−0.159512	−	0.987196i	$-0.550992\pi$
$509$	−7.19750	−0.319024	−0.159512	+	0.987196i	$0.550992\pi$
$510$	−12.3558	−0.547126
$511$	1.10180	0.0487406
$512$	−25.4069	−1.12284
$513$	−24.4366	−1.07890
$514$	10.7811	0.475532
$515$	26.6198	1.17301
$516$	−4.91742	−0.216477
$517$	2.99854	0.131875
$518$	−1.27637	−0.0560807
$519$	24.9466	1.09504
$520$	5.69303	0.249656
$521$	29.1764	1.27824	0.639121	−	0.769106i	$-0.279298\pi$
$521$	29.1764	1.27824	0.639121	+	0.769106i	$0.279298\pi$
$522$	−0.655915	−0.0287086
$523$	−27.9806	−1.22351	−0.611753	−	0.791049i	$-0.709535\pi$
$523$	−27.9806	−1.22351	−0.611753	+	0.791049i	$0.709535\pi$
$524$	26.8672	1.17370
$525$	−0.552948	−0.0241326
$526$	44.9185	1.95854
$527$	−5.73190	−0.249685
$528$	−15.0366	−0.654383
$529$	24.8828	1.08186
$530$	20.8498	0.905658
$531$	59.5986	2.58636
$532$	−0.630358	−0.0273295
$533$	−31.8678	−1.38035
$534$	58.8524	2.54679
$535$	−9.01849	−0.389903
$536$	−3.27237	−0.141345
$537$	68.3851	2.95103
$538$	31.9250	1.37639
$539$	6.94956	0.299339
$540$	−42.4534	−1.82690
$541$	−0.302921	−0.0130236	−0.00651181	−	0.999979i	$-0.502073\pi$
$541$	−0.302921	−0.0130236	−0.00651181	+	0.999979i	$0.502073\pi$
$542$	−24.8790	−1.06864
$543$	−63.7369	−2.73521
$544$	−7.12741	−0.305585
$545$	−31.0505	−1.33006
$546$	−4.31484	−0.184658
$547$	−0.747107	−0.0319440	−0.0159720	−	0.999872i	$-0.505084\pi$
$547$	−0.747107	−0.0319440	−0.0159720	+	0.999872i	$0.505084\pi$
$548$	−23.0146	−0.983136
$549$	100.883	4.30556
$550$	−1.45054	−0.0618513
$551$	0.0882797	0.00376084
$552$	−19.1314	−0.814287
$553$	−0.899442	−0.0382482
$554$	17.2486	0.732822
$555$	19.8372	0.842042
$556$	16.2491	0.689117
$557$	−29.5863	−1.25361	−0.626806	−	0.779175i	$-0.715638\pi$
$557$	−29.5863	−1.25361	−0.626806	+	0.779175i	$0.715638\pi$
$558$	−77.6265	−3.28619
$559$	3.19762	0.135245
$560$	2.17468	0.0918970
$561$	−3.19345	−0.134828
$562$	−0.497471	−0.0209846
$563$	13.6151	0.573810	0.286905	−	0.957959i	$-0.407374\pi$
$563$	13.6151	0.573810	0.286905	+	0.957959i	$0.407374\pi$
$564$	14.7450	0.620878
$565$	24.5976	1.03483
$566$	8.00540	0.336492
$567$	−4.76544	−0.200130
$568$	6.98628	0.293138
$569$	17.4530	0.731670	0.365835	−	0.930680i	$-0.380783\pi$
$569$	17.4530	0.731670	0.365835	+	0.930680i	$0.380783\pi$
$570$	22.5215	0.943321
$571$	36.6753	1.53481	0.767407	−	0.641161i	$-0.221547\pi$
$571$	36.6753	1.53481	0.767407	+	0.641161i	$0.221547\pi$
$572$	−4.92383	−0.205876
$573$	−44.6971	−1.86725
$574$	−4.21118	−0.175771
$575$	−5.33492	−0.222482
$576$	−28.7400	−1.19750
$577$	−31.9286	−1.32920	−0.664602	−	0.747197i	$-0.731399\pi$
$577$	−31.9286	−1.32920	−0.664602	+	0.747197i	$0.731399\pi$
$578$	−1.88145	−0.0782579
$579$	24.9781	1.03805
$580$	0.153367	0.00636824
$581$	−2.95483	−0.122587
$582$	65.1801	2.70180
$583$	5.38877	0.223180
$584$	−4.24729	−0.175754
$585$	47.3332	1.95699
$586$	−32.0841	−1.32538
$587$	−19.6692	−0.811833	−0.405917	−	0.913910i	$-0.633048\pi$
$587$	−19.6692	−0.811833	−0.405917	+	0.913910i	$0.633048\pi$
$588$	34.1739	1.40931
$589$	10.4478	0.430492
$590$	−32.0353	−1.31887
$591$	−37.5583	−1.54494
$592$	14.2229	0.584559
$593$	−32.5239	−1.33560	−0.667798	−	0.744343i	$-0.732763\pi$
$593$	−32.5239	−1.33560	−0.667798	+	0.744343i	$0.732763\pi$
$594$	−25.2236	−1.03494
$595$	0.461856	0.0189342
$596$	−8.23715	−0.337407
$597$	24.0013	0.982309
$598$	−41.6302	−1.70238
$599$	−28.0031	−1.14418	−0.572088	−	0.820193i	$-0.693866\pi$
$599$	−28.0031	−1.14418	−0.572088	+	0.820193i	$0.693866\pi$
$600$	2.13155	0.0870202
$601$	39.8251	1.62450	0.812249	−	0.583311i	$-0.198243\pi$
$601$	39.8251	1.62450	0.812249	+	0.583311i	$0.198243\pi$
$602$	0.422550	0.0172219
$603$	−27.2073	−1.10796
$604$	20.4621	0.832590
$605$	2.05646	0.0836070
$606$	16.1540	0.656210
$607$	−40.7473	−1.65388	−0.826942	−	0.562288i	$-0.809921\pi$
$607$	−40.7473	−1.65388	−0.826942	+	0.562288i	$0.809921\pi$
$608$	12.9914	0.526871
$609$	0.0347362	0.00140758
$610$	−54.2262	−2.19555
$611$	−9.58817	−0.387896
$612$	−11.0840	−0.448044
$613$	−24.7612	−1.00010	−0.500048	−	0.865998i	$-0.666684\pi$
$613$	−24.7612	−1.00010	−0.500048	+	0.865998i	$0.666684\pi$
$614$	27.4351	1.10719
$615$	65.4495	2.63918
$616$	0.194439	0.00783416
$617$	−25.5432	−1.02833	−0.514166	−	0.857691i	$-0.671898\pi$
$617$	−25.5432	−1.02833	−0.514166	+	0.857691i	$0.671898\pi$
$618$	77.7745	3.12855
$619$	22.4382	0.901866	0.450933	−	0.892558i	$-0.351091\pi$
$619$	22.4382	0.901866	0.450933	+	0.892558i	$0.351091\pi$
$620$	18.1508	0.728954
$621$	−92.7695	−3.72271
$622$	−39.8278	−1.59695
$623$	−2.19987	−0.0881361
$624$	48.0812	1.92479
$625$	−20.5507	−0.822030
$626$	47.3510	1.89253
$627$	5.82083	0.232461
$628$	−12.5170	−0.499482
$629$	3.02065	0.120441
$630$	6.25486	0.249200
$631$	−6.55532	−0.260963	−0.130482	−	0.991451i	$-0.541652\pi$
$631$	−6.55532	−0.260963	−0.130482	+	0.991451i	$0.541652\pi$
$632$	3.46724	0.137920
$633$	4.76092	0.189230
$634$	−56.0537	−2.22618
$635$	12.8804	0.511143
$636$	26.4988	1.05075
$637$	−22.2220	−0.880469
$638$	0.0911231	0.00360760
$639$	58.0856	2.29783
$640$	−13.8662	−0.548110
$641$	−21.7794	−0.860236	−0.430118	−	0.902773i	$-0.641528\pi$
$641$	−21.7794	−0.860236	−0.430118	+	0.902773i	$0.641528\pi$
$642$	−26.3491	−1.03992
$643$	−3.82520	−0.150851	−0.0754257	−	0.997151i	$-0.524032\pi$
$643$	−3.82520	−0.150851	−0.0754257	+	0.997151i	$0.524032\pi$
$644$	−2.39305	−0.0942995
$645$	−6.56720	−0.258583
$646$	3.42939	0.134927
$647$	38.6315	1.51876	0.759381	−	0.650646i	$-0.225502\pi$
$647$	38.6315	1.51876	0.759381	+	0.650646i	$0.225502\pi$
$648$	18.3702	0.721650
$649$	−8.27973	−0.325008
$650$	4.63828	0.181928
$651$	4.11097	0.161122
$652$	−1.41209	−0.0553019
$653$	11.5302	0.451211	0.225606	−	0.974219i	$-0.427564\pi$
$653$	11.5302	0.451211	0.225606	+	0.974219i	$0.427564\pi$
$654$	−90.7194	−3.54741
$655$	35.8811	1.40199
$656$	46.9261	1.83216
$657$	−35.3130	−1.37769
$658$	−1.26703	−0.0493940
$659$	20.8984	0.814086	0.407043	−	0.913409i	$-0.366560\pi$
$659$	20.8984	0.814086	0.407043	+	0.913409i	$0.366560\pi$
$660$	10.1125	0.393627
$661$	−5.39044	−0.209664	−0.104832	−	0.994490i	$-0.533430\pi$
$661$	−5.39044	−0.209664	−0.104832	+	0.994490i	$0.533430\pi$
$662$	−22.1416	−0.860560
$663$	10.2114	0.396579
$664$	11.3905	0.442037
$665$	−0.841843	−0.0326453
$666$	40.9083	1.58516
$667$	0.335140	0.0129767
$668$	2.84929	0.110242
$669$	35.0332	1.35446
$670$	14.6244	0.564989
$671$	−14.0151	−0.541047
$672$	5.11184	0.197194
$673$	−17.3841	−0.670109	−0.335055	−	0.942199i	$-0.608755\pi$
$673$	−17.3841	−0.670109	−0.335055	+	0.942199i	$0.608755\pi$
$674$	−26.1690	−1.00799
$675$	10.3360	0.397834
$676$	−4.27344	−0.164363
$677$	4.51013	0.173338	0.0866692	−	0.996237i	$-0.472378\pi$
$677$	4.51013	0.173338	0.0866692	+	0.996237i	$0.472378\pi$
$678$	71.8662	2.76001
$679$	−2.43640	−0.0935005
$680$	−1.78040	−0.0682752
$681$	35.3805	1.35578
$682$	10.7843	0.412951
$683$	24.1911	0.925647	0.462824	−	0.886450i	$-0.346836\pi$
$683$	24.1911	0.925647	0.462824	+	0.886450i	$0.346836\pi$
$684$	20.2032	0.772490
$685$	−30.7360	−1.17436
$686$	−5.89439	−0.225049
$687$	−8.04825	−0.307060
$688$	−4.70857	−0.179512
$689$	−17.2312	−0.656457
$690$	85.4992	3.25490
$691$	−47.0841	−1.79116	−0.895581	−	0.444898i	$-0.853240\pi$
$691$	−47.0841	−1.79116	−0.895581	+	0.444898i	$0.853240\pi$
$692$	−12.0290	−0.457273
$693$	1.61661	0.0614099
$694$	28.0789	1.06586
$695$	21.7007	0.823155
$696$	−0.133904	−0.00507562
$697$	9.96611	0.377493
$698$	15.2910	0.578772
$699$	41.2410	1.55988
$700$	0.266625	0.0100775
$701$	42.9287	1.62140	0.810698	−	0.585464i	$-0.199088\pi$
$701$	42.9287	1.62140	0.810698	+	0.585464i	$0.199088\pi$
$702$	80.6555	3.04415
$703$	−5.50585	−0.207657
$704$	3.99270	0.150481
$705$	19.6920	0.741643
$706$	−0.571873	−0.0215227
$707$	−0.603828	−0.0227093
$708$	−40.7149	−1.53016
$709$	25.9780	0.975624	0.487812	−	0.872949i	$-0.337795\pi$
$709$	25.9780	0.975624	0.487812	+	0.872949i	$0.337795\pi$
$710$	−31.2221	−1.17174
$711$	28.8275	1.08111
$712$	8.48026	0.317811
$713$	39.6633	1.48540
$714$	1.34939	0.0504997
$715$	−6.57577	−0.245920
$716$	−32.9745	−1.23231
$717$	−32.1771	−1.20168
$718$	17.0487	0.636253
$719$	−5.42362	−0.202267	−0.101133	−	0.994873i	$-0.532247\pi$
$719$	−5.42362	−0.202267	−0.101133	+	0.994873i	$0.532247\pi$
$720$	−69.6993	−2.59754
$721$	−2.90717	−0.108269
$722$	29.4966	1.09775
$723$	62.5430	2.32600
$724$	30.7332	1.14219
$725$	−0.0373400	−0.00138677
$726$	6.00831	0.222989
$727$	−49.3222	−1.82926	−0.914630	−	0.404291i	$-0.867518\pi$
$727$	−49.3222	−1.82926	−0.914630	+	0.404291i	$0.867518\pi$
$728$	−0.621741	−0.0230433
$729$	24.2953	0.899825
$730$	18.9814	0.702532
$731$	−1.00000	−0.0369863
$732$	−68.9181	−2.54729
$733$	−17.8535	−0.659433	−0.329716	−	0.944080i	$-0.606953\pi$
$733$	−17.8535	−0.659433	−0.329716	+	0.944080i	$0.606953\pi$
$734$	−18.8122	−0.694370
$735$	45.6392	1.68343
$736$	49.3198	1.81795
$737$	3.77977	0.139230
$738$	134.970	4.96831
$739$	36.5220	1.34348	0.671741	−	0.740786i	$-0.265547\pi$
$739$	36.5220	1.34348	0.671741	+	0.740786i	$0.265547\pi$
$740$	−9.56527	−0.351626
$741$	−18.6128	−0.683757
$742$	−2.27702	−0.0835922
$743$	17.1740	0.630052	0.315026	−	0.949083i	$-0.397987\pi$
$743$	17.1740	0.630052	0.315026	+	0.949083i	$0.397987\pi$
$744$	−15.8473	−0.580991
$745$	−11.0007	−0.403034
$746$	−47.7024	−1.74651
$747$	94.7033	3.46501
$748$	1.53984	0.0563023
$749$	0.984917	0.0359881
$750$	−71.3052	−2.60370
$751$	17.6172	0.642859	0.321430	−	0.946933i	$-0.395837\pi$
$751$	17.6172	0.642859	0.321430	+	0.946933i	$0.395837\pi$
$752$	14.1188	0.514860
$753$	11.8063	0.430245
$754$	−0.291377	−0.0106113
$755$	27.3271	0.994534
$756$	4.63637	0.168623
$757$	−1.19972	−0.0436044	−0.0218022	−	0.999762i	$-0.506940\pi$
$757$	−1.19972	−0.0436044	−0.0218022	+	0.999762i	$0.506940\pi$
$758$	10.7668	0.391069
$759$	22.0978	0.802101
$760$	3.24520	0.117716
$761$	43.3079	1.56991	0.784954	−	0.619553i	$-0.212686\pi$
$761$	43.3079	1.56991	0.784954	+	0.619553i	$0.212686\pi$
$762$	37.6323	1.36328
$763$	3.39105	0.122764
$764$	21.5524	0.779738
$765$	−14.8027	−0.535191
$766$	−6.09716	−0.220299
$767$	26.4754	0.955972
$768$	−66.0135	−2.38206
$769$	−0.0683532	−0.00246488	−0.00123244	−	0.999999i	$-0.500392\pi$
$769$	−0.0683532	−0.00246488	−0.00123244	+	0.999999i	$0.500392\pi$
$770$	−0.868957	−0.0313150
$771$	18.2991	0.659025
$772$	−12.0441	−0.433478
$773$	12.5804	0.452486	0.226243	−	0.974071i	$-0.427356\pi$
$773$	12.5804	0.452486	0.226243	+	0.974071i	$0.427356\pi$
$774$	−13.5429	−0.486789
$775$	−4.41913	−0.158740
$776$	9.39204	0.337154
$777$	−2.16644	−0.0777205
$778$	15.9264	0.570988
$779$	−18.1656	−0.650851
$780$	−32.3358	−1.15781
$781$	−8.06955	−0.288751
$782$	13.0191	0.465563
$783$	−0.649309	−0.0232044
$784$	32.7225	1.16866
$785$	−16.7164	−0.596635
$786$	104.833	3.73927
$787$	9.23475	0.329183	0.164592	−	0.986362i	$-0.447369\pi$
$787$	9.23475	0.329183	0.164592	+	0.986362i	$0.447369\pi$
$788$	18.1102	0.645148
$789$	76.2418	2.71428
$790$	−15.4953	−0.551298
$791$	−2.68633	−0.0955148
$792$	−6.23184	−0.221439
$793$	44.8150	1.59143
$794$	−25.6407	−0.909953
$795$	35.3892	1.25512
$796$	−11.5732	−0.410200
$797$	−18.0001	−0.637598	−0.318799	−	0.947822i	$-0.603279\pi$
$797$	−18.0001	−0.637598	−0.318799	+	0.947822i	$0.603279\pi$
$798$	−2.45959	−0.0870686
$799$	2.99854	0.106081
$800$	−5.49503	−0.194279
$801$	70.5068	2.49124
$802$	−26.6880	−0.942387
$803$	4.90586	0.173124
$804$	18.5867	0.655502
$805$	−3.19592	−0.112641
$806$	−34.4840	−1.21465
$807$	54.1876	1.90749
$808$	2.32768	0.0818876
$809$	25.5892	0.899668	0.449834	−	0.893112i	$-0.351483\pi$
$809$	25.5892	0.899668	0.449834	+	0.893112i	$0.351483\pi$
$810$	−82.0974	−2.88461
$811$	−19.5555	−0.686685	−0.343342	−	0.939210i	$-0.611559\pi$
$811$	−19.5555	−0.686685	−0.343342	+	0.939210i	$0.611559\pi$
$812$	−0.0167494	−0.000587788 0
$813$	−42.2280	−1.48100
$814$	−5.68319	−0.199196
$815$	−1.88585	−0.0660585
$816$	−15.0366	−0.526386
$817$	1.82274	0.0637696
$818$	−56.6631	−1.98118
$819$	−5.16930	−0.180630
$820$	−31.5590	−1.10209
$821$	2.33451	0.0814751	0.0407376	−	0.999170i	$-0.487029\pi$
$821$	2.33451	0.0814751	0.0407376	+	0.999170i	$0.487029\pi$
$822$	−89.8006	−3.13215
$823$	46.7360	1.62912	0.814558	−	0.580082i	$-0.196980\pi$
$823$	46.7360	1.62912	0.814558	+	0.580082i	$0.196980\pi$
$824$	11.2068	0.390408
$825$	−2.46206	−0.0857179
$826$	3.49860	0.121732
$827$	26.0140	0.904597	0.452299	−	0.891867i	$-0.350604\pi$
$827$	26.0140	0.904597	0.452299	+	0.891867i	$0.350604\pi$
$828$	76.6983	2.66545
$829$	−15.9989	−0.555666	−0.277833	−	0.960629i	$-0.589616\pi$
$829$	−15.9989	−0.555666	−0.277833	+	0.960629i	$0.589616\pi$
$830$	−50.9047	−1.76693
$831$	29.2767	1.01560
$832$	−12.7671	−0.442621
$833$	6.94956	0.240788
$834$	63.4024	2.19545
$835$	3.80523	0.131685
$836$	−2.80673	−0.0970729
$837$	−76.8447	−2.65614
$838$	−39.0348	−1.34843
$839$	11.2620	0.388808	0.194404	−	0.980922i	$-0.437723\pi$
$839$	11.2620	0.388808	0.194404	+	0.980922i	$0.437723\pi$
$840$	1.27692	0.0440579
$841$	−28.9977	−0.999919
$842$	−7.77861	−0.268069
$843$	−0.844376	−0.0290819
$844$	−2.29566	−0.0790199
$845$	−5.70718	−0.196333
$846$	40.6088	1.39616
$847$	−0.224588	−0.00771693
$848$	25.3734	0.871326
$849$	13.5879	0.466334
$850$	−1.45054	−0.0497532
$851$	−20.9021	−0.716515
$852$	−39.6813	−1.35946
$853$	−44.5988	−1.52703	−0.763517	−	0.645788i	$-0.776529\pi$
$853$	−44.5988	−1.52703	−0.763517	+	0.645788i	$0.776529\pi$
$854$	5.92208	0.202650
$855$	26.9814	0.922744
$856$	−3.79674	−0.129770
$857$	−11.1183	−0.379795	−0.189898	−	0.981804i	$-0.560816\pi$
$857$	−11.1183	−0.379795	−0.189898	+	0.981804i	$0.560816\pi$
$858$	−19.2123	−0.655896
$859$	−42.4005	−1.44669	−0.723343	−	0.690488i	$-0.757396\pi$
$859$	−42.4005	−1.44669	−0.723343	+	0.690488i	$0.757396\pi$
$860$	3.16663	0.107981
$861$	−7.14779	−0.243596
$862$	17.9880	0.612675
$863$	−15.6022	−0.531105	−0.265553	−	0.964096i	$-0.585554\pi$
$863$	−15.6022	−0.531105	−0.265553	+	0.964096i	$0.585554\pi$
$864$	−95.5536	−3.25080
$865$	−16.0647	−0.546216
$866$	11.5150	0.391295
$867$	−3.19345	−0.108455
$868$	−1.98226	−0.0672824
$869$	−4.00486	−0.135856
$870$	0.598424	0.0202885
$871$	−12.0863	−0.409527
$872$	−13.0721	−0.442677
$873$	78.0876	2.64286
$874$	−23.7305	−0.802695
$875$	2.66536	0.0901055
$876$	24.1241	0.815079
$877$	−14.2194	−0.480154	−0.240077	−	0.970754i	$-0.577173\pi$
$877$	−14.2194	−0.480154	−0.240077	+	0.970754i	$0.577173\pi$
$878$	23.3330	0.787452
$879$	−54.4575	−1.83681
$880$	9.68298	0.326413
$881$	57.4922	1.93696	0.968481	−	0.249086i	$-0.0801302\pi$
$881$	57.4922	1.93696	0.968481	+	0.249086i	$0.0801302\pi$
$882$	94.1171	3.16909
$883$	−44.9958	−1.51423	−0.757115	−	0.653282i	$-0.773392\pi$
$883$	−44.9958	−1.51423	−0.757115	+	0.653282i	$0.773392\pi$
$884$	−4.92383	−0.165606
$885$	−54.3747	−1.82779
$886$	−12.9382	−0.434668
$887$	−58.2678	−1.95644	−0.978221	−	0.207566i	$-0.933446\pi$
$887$	−58.2678	−1.95644	−0.978221	+	0.207566i	$0.933446\pi$
$888$	8.35136	0.280253
$889$	−1.40668	−0.0471785
$890$	−37.8987	−1.27037
$891$	−21.2186	−0.710850
$892$	−16.8926	−0.565606
$893$	−5.46555	−0.182898
$894$	−32.1405	−1.07494
$895$	−44.0374	−1.47201
$896$	1.51434	0.0505905
$897$	−70.6604	−2.35928
$898$	−44.7062	−1.49186
$899$	0.277610	0.00925881
$900$	−8.54544	−0.284848
$901$	5.38877	0.179526
$902$	−18.7507	−0.624330
$903$	0.717210	0.0238672
$904$	10.3555	0.344418
$905$	41.0442	1.36435
$906$	79.8408	2.65253
$907$	31.9973	1.06245	0.531226	−	0.847230i	$-0.321731\pi$
$907$	31.9973	1.06245	0.531226	+	0.847230i	$0.321731\pi$
$908$	−17.0601	−0.566158
$909$	19.3529	0.641895
$910$	2.77859	0.0921094
$911$	44.1100	1.46143	0.730715	−	0.682683i	$-0.239187\pi$
$911$	44.1100	1.46143	0.730715	+	0.682683i	$0.239187\pi$
$912$	27.4078	0.907562
$913$	−13.1567	−0.435422
$914$	−75.5409	−2.49867
$915$	−92.0401	−3.04275
$916$	3.88077	0.128224
$917$	−3.91861	−0.129404
$918$	−25.2236	−0.832504
$919$	−15.6666	−0.516792	−0.258396	−	0.966039i	$-0.583194\pi$
$919$	−15.6666	−0.516792	−0.258396	+	0.966039i	$0.583194\pi$
$920$	12.3199	0.406175
$921$	46.5666	1.53442
$922$	−67.4231	−2.22046
$923$	25.8033	0.849327
$924$	−1.10439	−0.0363318
$925$	2.32883	0.0765716
$926$	5.27791	0.173443
$927$	93.1761	3.06030
$928$	0.345198	0.0113317
$929$	−47.5655	−1.56057	−0.780286	−	0.625422i	$-0.784927\pi$
$929$	−47.5655	−1.56057	−0.780286	+	0.625422i	$0.784927\pi$
$930$	70.8225	2.32236
$931$	−12.6672	−0.415152
$932$	−19.8859	−0.651384
$933$	−67.6013	−2.21317
$934$	−0.969180	−0.0317125
$935$	2.05646	0.0672534
$936$	19.9270	0.651336
$937$	−14.3048	−0.467317	−0.233658	−	0.972319i	$-0.575070\pi$
$937$	−14.3048	−0.467317	−0.233658	+	0.972319i	$0.575070\pi$
$938$	−1.59714	−0.0521485
$939$	80.3706	2.62279
$940$	−9.49525	−0.309701
$941$	29.1544	0.950407	0.475203	−	0.879876i	$-0.342374\pi$
$941$	29.1544	0.950407	0.475203	+	0.879876i	$0.342374\pi$
$942$	−48.8400	−1.59129
$943$	−68.9629	−2.24574
$944$	−38.9857	−1.26888
$945$	6.19187	0.201421
$946$	1.88145	0.0611711
$947$	−10.0697	−0.327222	−0.163611	−	0.986525i	$-0.552314\pi$
$947$	−10.0697	−0.327222	−0.163611	+	0.986525i	$0.552314\pi$
$948$	−19.6936	−0.639617
$949$	−15.6871	−0.509223
$950$	2.64396	0.0857814
$951$	−95.1421	−3.08519
$952$	0.194439	0.00630180
$953$	−32.7792	−1.06182	−0.530911	−	0.847428i	$-0.678150\pi$
$953$	−32.7792	−1.06182	−0.530911	+	0.847428i	$0.678150\pi$
$954$	72.9795	2.36280
$955$	28.7832	0.931402
$956$	15.5154	0.501805
$957$	0.154667	0.00499966
$958$	−26.6272	−0.860287
$959$	3.35670	0.108394
$960$	26.2209	0.846275
$961$	1.85468	0.0598284
$962$	18.1727	0.585910
$963$	−31.5670	−1.01723
$964$	−30.1575	−0.971307
$965$	−16.0849	−0.517792
$966$	−9.33744	−0.300427
$967$	−23.2972	−0.749189	−0.374594	−	0.927189i	$-0.622218\pi$
$967$	−23.2972	−0.749189	−0.374594	+	0.927189i	$0.622218\pi$
$968$	0.865759	0.0278265
$969$	5.82083	0.186992
$970$	−41.9735	−1.34769
$971$	57.0618	1.83120	0.915600	−	0.402090i	$-0.131716\pi$
$971$	57.0618	1.83120	0.915600	+	0.402090i	$0.131716\pi$
$972$	−42.4090	−1.36027
$973$	−2.36995	−0.0759772
$974$	50.1057	1.60549
$975$	7.87272	0.252129
$976$	−65.9911	−2.11232
$977$	48.5812	1.55425	0.777125	−	0.629347i	$-0.216677\pi$
$977$	48.5812	1.55425	0.777125	+	0.629347i	$0.216677\pi$
$978$	−5.50984	−0.176185
$979$	−9.79517	−0.313055
$980$	−22.0067	−0.702977
$981$	−108.684	−3.47002
$982$	47.2714	1.50849
$983$	58.5863	1.86861	0.934307	−	0.356470i	$-0.116020\pi$
$983$	58.5863	1.86861	0.934307	+	0.356470i	$0.116020\pi$
$984$	27.5539	0.878386
$985$	24.1861	0.770633
$986$	0.0911231	0.00290195
$987$	−2.15058	−0.0684537
$988$	8.97486	0.285528
$989$	6.91974	0.220035
$990$	27.8504	0.885144
$991$	17.1124	0.543594	0.271797	−	0.962355i	$-0.412382\pi$
$991$	17.1124	0.543594	0.271797	+	0.962355i	$0.412382\pi$
$992$	40.8536	1.29710
$993$	−37.5818	−1.19262
$994$	3.40979	0.108152
$995$	−15.4559	−0.489986
$996$	−64.6968	−2.05000
$997$	49.6007	1.57087	0.785435	−	0.618944i	$-0.212439\pi$
$997$	49.6007	1.57087	0.785435	+	0.618944i	$0.212439\pi$
$998$	44.3158	1.40279
$999$	40.4963	1.28125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.12	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.12	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88145 q^{2} -3.19345 q^{3} +1.53984 q^{4} +2.05646 q^{5} +6.00831 q^{6} -0.224588 q^{7} +0.865759 q^{8} +7.19812 q^{9} +O(q^{10})\)	\(q-1.88145 q^{2} -3.19345 q^{3} +1.53984 q^{4} +2.05646 q^{5} +6.00831 q^{6} -0.224588 q^{7} +0.865759 q^{8} +7.19812 q^{9} -3.86912 q^{10} -1.00000 q^{11} -4.91742 q^{12} +3.19762 q^{13} +0.422550 q^{14} -6.56720 q^{15} -4.70857 q^{16} -1.00000 q^{17} -13.5429 q^{18} +1.82274 q^{19} +3.16663 q^{20} +0.717210 q^{21} +1.88145 q^{22} +6.91974 q^{23} -2.76476 q^{24} -0.770972 q^{25} -6.01615 q^{26} -13.4065 q^{27} -0.345830 q^{28} +0.0484324 q^{29} +12.3558 q^{30} +5.73190 q^{31} +7.12741 q^{32} +3.19345 q^{33} +1.88145 q^{34} -0.461856 q^{35} +11.0840 q^{36} -3.02065 q^{37} -3.42939 q^{38} -10.2114 q^{39} +1.78040 q^{40} -9.96611 q^{41} -1.34939 q^{42} +1.00000 q^{43} -1.53984 q^{44} +14.8027 q^{45} -13.0191 q^{46} -2.99854 q^{47} +15.0366 q^{48} -6.94956 q^{49} +1.45054 q^{50} +3.19345 q^{51} +4.92383 q^{52} -5.38877 q^{53} +25.2236 q^{54} -2.05646 q^{55} -0.194439 q^{56} -5.82083 q^{57} -0.0911231 q^{58} +8.27973 q^{59} -10.1125 q^{60} +14.0151 q^{61} -10.7843 q^{62} -1.61661 q^{63} -3.99270 q^{64} +6.57577 q^{65} -6.00831 q^{66} -3.77977 q^{67} -1.53984 q^{68} -22.0978 q^{69} +0.868957 q^{70} +8.06955 q^{71} +6.23184 q^{72} -4.90586 q^{73} +5.68319 q^{74} +2.46206 q^{75} +2.80673 q^{76} +0.224588 q^{77} +19.2123 q^{78} +4.00486 q^{79} -9.68298 q^{80} +21.2186 q^{81} +18.7507 q^{82} +13.1567 q^{83} +1.10439 q^{84} -2.05646 q^{85} -1.88145 q^{86} -0.154667 q^{87} -0.865759 q^{88} +9.79517 q^{89} -27.8504 q^{90} -0.718146 q^{91} +10.6553 q^{92} -18.3045 q^{93} +5.64159 q^{94} +3.74839 q^{95} -22.7610 q^{96} +10.8483 q^{97} +13.0752 q^{98} -7.19812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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