LMFDB - Embedded newform 6034.2.a.m.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.63595 q^{3} +1.00000 q^{4} -2.93756 q^{5} -1.63595 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.323656 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.63595 q^{3} +1.00000 q^{4} -2.93756 q^{5} -1.63595 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.323656 q^{9} -2.93756 q^{10} -6.21010 q^{11} -1.63595 q^{12} +3.27734 q^{13} +1.00000 q^{14} +4.80572 q^{15} +1.00000 q^{16} +6.10676 q^{17} -0.323656 q^{18} -7.03050 q^{19} -2.93756 q^{20} -1.63595 q^{21} -6.21010 q^{22} +5.94631 q^{23} -1.63595 q^{24} +3.62928 q^{25} +3.27734 q^{26} +5.43735 q^{27} +1.00000 q^{28} +7.76943 q^{29} +4.80572 q^{30} +3.70949 q^{31} +1.00000 q^{32} +10.1594 q^{33} +6.10676 q^{34} -2.93756 q^{35} -0.323656 q^{36} -4.52131 q^{37} -7.03050 q^{38} -5.36158 q^{39} -2.93756 q^{40} -1.19439 q^{41} -1.63595 q^{42} +2.16930 q^{43} -6.21010 q^{44} +0.950761 q^{45} +5.94631 q^{46} +5.87374 q^{47} -1.63595 q^{48} +1.00000 q^{49} +3.62928 q^{50} -9.99037 q^{51} +3.27734 q^{52} -9.30165 q^{53} +5.43735 q^{54} +18.2426 q^{55} +1.00000 q^{56} +11.5016 q^{57} +7.76943 q^{58} -2.79654 q^{59} +4.80572 q^{60} -1.33493 q^{61} +3.70949 q^{62} -0.323656 q^{63} +1.00000 q^{64} -9.62740 q^{65} +10.1594 q^{66} +7.06366 q^{67} +6.10676 q^{68} -9.72788 q^{69} -2.93756 q^{70} -5.97215 q^{71} -0.323656 q^{72} -15.4990 q^{73} -4.52131 q^{74} -5.93733 q^{75} -7.03050 q^{76} -6.21010 q^{77} -5.36158 q^{78} +1.88349 q^{79} -2.93756 q^{80} -7.92428 q^{81} -1.19439 q^{82} -2.47075 q^{83} -1.63595 q^{84} -17.9390 q^{85} +2.16930 q^{86} -12.7104 q^{87} -6.21010 q^{88} +2.26844 q^{89} +0.950761 q^{90} +3.27734 q^{91} +5.94631 q^{92} -6.06855 q^{93} +5.87374 q^{94} +20.6525 q^{95} -1.63595 q^{96} +6.97793 q^{97} +1.00000 q^{98} +2.00994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.63595	−0.944518	−0.472259	−	0.881460i	$-0.656561\pi$
$3$	−1.63595	−0.944518	−0.472259	+	0.881460i	$0.656561\pi$
$4$	1.00000	0.500000
$5$	−2.93756	−1.31372	−0.656859	−	0.754013i	$-0.728115\pi$
$5$	−2.93756	−1.31372	−0.656859	+	0.754013i	$0.728115\pi$
$6$	−1.63595	−0.667875
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−0.323656	−0.107885
$10$	−2.93756	−0.928939
$11$	−6.21010	−1.87242	−0.936208	−	0.351448i	$-0.885690\pi$
$11$	−6.21010	−1.87242	−0.936208	+	0.351448i	$0.885690\pi$
$12$	−1.63595	−0.472259
$13$	3.27734	0.908972	0.454486	−	0.890754i	$-0.349823\pi$
$13$	3.27734	0.908972	0.454486	+	0.890754i	$0.349823\pi$
$14$	1.00000	0.267261
$15$	4.80572	1.24083
$16$	1.00000	0.250000
$17$	6.10676	1.48111	0.740553	−	0.671997i	$-0.234563\pi$
$17$	6.10676	1.48111	0.740553	+	0.671997i	$0.234563\pi$
$18$	−0.323656	−0.0762865
$19$	−7.03050	−1.61291	−0.806454	−	0.591297i	$-0.798616\pi$
$19$	−7.03050	−1.61291	−0.806454	+	0.591297i	$0.798616\pi$
$20$	−2.93756	−0.656859
$21$	−1.63595	−0.356994
$22$	−6.21010	−1.32400
$23$	5.94631	1.23989	0.619945	−	0.784645i	$-0.287155\pi$
$23$	5.94631	1.23989	0.619945	+	0.784645i	$0.287155\pi$
$24$	−1.63595	−0.333938
$25$	3.62928	0.725855
$26$	3.27734	0.642740
$27$	5.43735	1.04642
$28$	1.00000	0.188982
$29$	7.76943	1.44275	0.721373	−	0.692546i	$-0.243511\pi$
$29$	7.76943	1.44275	0.721373	+	0.692546i	$0.243511\pi$
$30$	4.80572	0.877400
$31$	3.70949	0.666243	0.333122	−	0.942884i	$-0.391898\pi$
$31$	3.70949	0.666243	0.333122	+	0.942884i	$0.391898\pi$
$32$	1.00000	0.176777
$33$	10.1594	1.76853
$34$	6.10676	1.04730
$35$	−2.93756	−0.496539
$36$	−0.323656	−0.0539427
$37$	−4.52131	−0.743299	−0.371650	−	0.928373i	$-0.621208\pi$
$37$	−4.52131	−0.743299	−0.371650	+	0.928373i	$0.621208\pi$
$38$	−7.03050	−1.14050
$39$	−5.36158	−0.858540
$40$	−2.93756	−0.464469
$41$	−1.19439	−0.186532	−0.0932659	−	0.995641i	$-0.529731\pi$
$41$	−1.19439	−0.186532	−0.0932659	+	0.995641i	$0.529731\pi$
$42$	−1.63595	−0.252433
$43$	2.16930	0.330814	0.165407	−	0.986225i	$-0.447106\pi$
$43$	2.16930	0.330814	0.165407	+	0.986225i	$0.447106\pi$
$44$	−6.21010	−0.936208
$45$	0.950761	0.141731
$46$	5.94631	0.876735
$47$	5.87374	0.856774	0.428387	−	0.903595i	$-0.359082\pi$
$47$	5.87374	0.856774	0.428387	+	0.903595i	$0.359082\pi$
$48$	−1.63595	−0.236130
$49$	1.00000	0.142857
$50$	3.62928	0.513257
$51$	−9.99037	−1.39893
$52$	3.27734	0.454486
$53$	−9.30165	−1.27768	−0.638840	−	0.769339i	$-0.720585\pi$
$53$	−9.30165	−1.27768	−0.638840	+	0.769339i	$0.720585\pi$
$54$	5.43735	0.739929
$55$	18.2426	2.45983
$56$	1.00000	0.133631
$57$	11.5016	1.52342
$58$	7.76943	1.02018
$59$	−2.79654	−0.364079	−0.182039	−	0.983291i	$-0.558270\pi$
$59$	−2.79654	−0.364079	−0.182039	+	0.983291i	$0.558270\pi$
$60$	4.80572	0.620415
$61$	−1.33493	−0.170920	−0.0854602	−	0.996342i	$-0.527236\pi$
$61$	−1.33493	−0.170920	−0.0854602	+	0.996342i	$0.527236\pi$
$62$	3.70949	0.471105
$63$	−0.323656	−0.0407769
$64$	1.00000	0.125000
$65$	−9.62740	−1.19413
$66$	10.1594	1.25054
$67$	7.06366	0.862963	0.431482	−	0.902122i	$-0.357991\pi$
$67$	7.06366	0.862963	0.431482	+	0.902122i	$0.357991\pi$
$68$	6.10676	0.740553
$69$	−9.72788	−1.17110
$70$	−2.93756	−0.351106
$71$	−5.97215	−0.708764	−0.354382	−	0.935101i	$-0.615309\pi$
$71$	−5.97215	−0.708764	−0.354382	+	0.935101i	$0.615309\pi$
$72$	−0.323656	−0.0381433
$73$	−15.4990	−1.81402	−0.907009	−	0.421111i	$-0.861640\pi$
$73$	−15.4990	−1.81402	−0.907009	+	0.421111i	$0.861640\pi$
$74$	−4.52131	−0.525592
$75$	−5.93733	−0.685583
$76$	−7.03050	−0.806454
$77$	−6.21010	−0.707706
$78$	−5.36158	−0.607080
$79$	1.88349	0.211909	0.105955	−	0.994371i	$-0.466210\pi$
$79$	1.88349	0.211909	0.105955	+	0.994371i	$0.466210\pi$
$80$	−2.93756	−0.328430
$81$	−7.92428	−0.880475
$82$	−1.19439	−0.131898
$83$	−2.47075	−0.271200	−0.135600	−	0.990764i	$-0.543296\pi$
$83$	−2.47075	−0.271200	−0.135600	+	0.990764i	$0.543296\pi$
$84$	−1.63595	−0.178497
$85$	−17.9390	−1.94576
$86$	2.16930	0.233921
$87$	−12.7104	−1.36270
$88$	−6.21010	−0.661999
$89$	2.26844	0.240454	0.120227	−	0.992746i	$-0.461638\pi$
$89$	2.26844	0.240454	0.120227	+	0.992746i	$0.461638\pi$
$90$	0.950761	0.100219
$91$	3.27734	0.343559
$92$	5.94631	0.619945
$93$	−6.06855	−0.629279
$94$	5.87374	0.605831
$95$	20.6525	2.11891
$96$	−1.63595	−0.166969
$97$	6.97793	0.708501	0.354251	−	0.935151i	$-0.384736\pi$
$97$	6.97793	0.708501	0.354251	+	0.935151i	$0.384736\pi$
$98$	1.00000	0.101015
$99$	2.00994	0.202006
$100$	3.62928	0.362928
$101$	−16.0841	−1.60043	−0.800214	−	0.599714i	$-0.795281\pi$
$101$	−16.0841	−1.60043	−0.800214	+	0.599714i	$0.795281\pi$
$102$	−9.99037	−0.989195
$103$	11.7167	1.15448	0.577242	−	0.816573i	$-0.304129\pi$
$103$	11.7167	1.15448	0.577242	+	0.816573i	$0.304129\pi$
$104$	3.27734	0.321370
$105$	4.80572	0.468990
$106$	−9.30165	−0.903456
$107$	−8.40246	−0.812296	−0.406148	−	0.913807i	$-0.633128\pi$
$107$	−8.40246	−0.812296	−0.406148	+	0.913807i	$0.633128\pi$
$108$	5.43735	0.523209
$109$	−8.48767	−0.812971	−0.406486	−	0.913657i	$-0.633246\pi$
$109$	−8.48767	−0.812971	−0.406486	+	0.913657i	$0.633246\pi$
$110$	18.2426	1.73936
$111$	7.39666	0.702059
$112$	1.00000	0.0944911
$113$	−17.4821	−1.64458	−0.822288	−	0.569071i	$-0.807303\pi$
$113$	−17.4821	−1.64458	−0.822288	+	0.569071i	$0.807303\pi$
$114$	11.5016	1.07722
$115$	−17.4676	−1.62887
$116$	7.76943	0.721373
$117$	−1.06073	−0.0980648
$118$	−2.79654	−0.257442
$119$	6.10676	0.559806
$120$	4.80572	0.438700
$121$	27.5653	2.50594
$122$	−1.33493	−0.120859
$123$	1.95396	0.176183
$124$	3.70949	0.333122
$125$	4.02659	0.360149
$126$	−0.323656	−0.0288336
$127$	−13.3187	−1.18185	−0.590924	−	0.806727i	$-0.701237\pi$
$127$	−13.3187	−1.18185	−0.590924	+	0.806727i	$0.701237\pi$
$128$	1.00000	0.0883883
$129$	−3.54887	−0.312460
$130$	−9.62740	−0.844379
$131$	13.2797	1.16026	0.580128	−	0.814526i	$-0.303003\pi$
$131$	13.2797	1.16026	0.580128	+	0.814526i	$0.303003\pi$
$132$	10.1594	0.884265
$133$	−7.03050	−0.609622
$134$	7.06366	0.610207
$135$	−15.9725	−1.37470
$136$	6.10676	0.523650
$137$	−16.3431	−1.39629	−0.698144	−	0.715958i	$-0.745990\pi$
$137$	−16.3431	−1.39629	−0.698144	+	0.715958i	$0.745990\pi$
$138$	−9.72788	−0.828092
$139$	4.78152	0.405563	0.202781	−	0.979224i	$-0.435002\pi$
$139$	4.78152	0.405563	0.202781	+	0.979224i	$0.435002\pi$
$140$	−2.93756	−0.248269
$141$	−9.60917	−0.809238
$142$	−5.97215	−0.501172
$143$	−20.3526	−1.70197
$144$	−0.323656	−0.0269714
$145$	−22.8232	−1.89536
$146$	−15.4990	−1.28270
$147$	−1.63595	−0.134931
$148$	−4.52131	−0.371650
$149$	−22.6790	−1.85794	−0.928970	−	0.370156i	$-0.879304\pi$
$149$	−22.6790	−1.85794	−0.928970	+	0.370156i	$0.879304\pi$
$150$	−5.93733	−0.484781
$151$	5.86309	0.477131	0.238566	−	0.971126i	$-0.423323\pi$
$151$	5.86309	0.477131	0.238566	+	0.971126i	$0.423323\pi$
$152$	−7.03050	−0.570249
$153$	−1.97649	−0.159790
$154$	−6.21010	−0.500424
$155$	−10.8969	−0.875256
$156$	−5.36158	−0.429270
$157$	−3.20728	−0.255969	−0.127984	−	0.991776i	$-0.540851\pi$
$157$	−3.20728	−0.255969	−0.127984	+	0.991776i	$0.540851\pi$
$158$	1.88349	0.149843
$159$	15.2171	1.20679
$160$	−2.93756	−0.232235
$161$	5.94631	0.468634
$162$	−7.92428	−0.622590
$163$	−11.0458	−0.865173	−0.432587	−	0.901592i	$-0.642399\pi$
$163$	−11.0458	−0.865173	−0.432587	+	0.901592i	$0.642399\pi$
$164$	−1.19439	−0.0932659
$165$	−29.8440	−2.32335
$166$	−2.47075	−0.191767
$167$	25.7311	1.99113	0.995564	−	0.0940838i	$-0.0299922\pi$
$167$	25.7311	1.99113	0.995564	+	0.0940838i	$0.0299922\pi$
$168$	−1.63595	−0.126217
$169$	−2.25902	−0.173770
$170$	−17.9390	−1.37586
$171$	2.27547	0.174009
$172$	2.16930	0.165407
$173$	−7.50228	−0.570387	−0.285194	−	0.958470i	$-0.592058\pi$
$173$	−7.50228	−0.570387	−0.285194	+	0.958470i	$0.592058\pi$
$174$	−12.7104	−0.963575
$175$	3.62928	0.274347
$176$	−6.21010	−0.468104
$177$	4.57501	0.343879
$178$	2.26844	0.170027
$179$	16.9974	1.27045	0.635223	−	0.772329i	$-0.280908\pi$
$179$	16.9974	1.27045	0.635223	+	0.772329i	$0.280908\pi$
$180$	0.950761	0.0708655
$181$	20.2914	1.50825	0.754125	−	0.656731i	$-0.228061\pi$
$181$	20.2914	1.50825	0.754125	+	0.656731i	$0.228061\pi$
$182$	3.27734	0.242933
$183$	2.18389	0.161437
$184$	5.94631	0.438367
$185$	13.2816	0.976485
$186$	−6.06855	−0.444967
$187$	−37.9236	−2.77325
$188$	5.87374	0.428387
$189$	5.43735	0.395509
$190$	20.6525	1.49829
$191$	−19.5592	−1.41526	−0.707629	−	0.706585i	$-0.750235\pi$
$191$	−19.5592	−1.41526	−0.707629	+	0.706585i	$0.750235\pi$
$192$	−1.63595	−0.118065
$193$	−2.71073	−0.195123	−0.0975614	−	0.995230i	$-0.531104\pi$
$193$	−2.71073	−0.195123	−0.0975614	+	0.995230i	$0.531104\pi$
$194$	6.97793	0.500986
$195$	15.7500	1.12788
$196$	1.00000	0.0714286
$197$	−12.5860	−0.896714	−0.448357	−	0.893855i	$-0.647991\pi$
$197$	−12.5860	−0.896714	−0.448357	+	0.893855i	$0.647991\pi$
$198$	2.00994	0.142840
$199$	2.58337	0.183130	0.0915652	−	0.995799i	$-0.470813\pi$
$199$	2.58337	0.183130	0.0915652	+	0.995799i	$0.470813\pi$
$200$	3.62928	0.256629
$201$	−11.5558	−0.815084
$202$	−16.0841	−1.13167
$203$	7.76943	0.545307
$204$	−9.99037	−0.699466
$205$	3.50858	0.245050
$206$	11.7167	0.816343
$207$	−1.92456	−0.133766
$208$	3.27734	0.227243
$209$	43.6601	3.02003
$210$	4.80572	0.331626
$211$	24.8190	1.70861	0.854306	−	0.519770i	$-0.173982\pi$
$211$	24.8190	1.70861	0.854306	+	0.519770i	$0.173982\pi$
$212$	−9.30165	−0.638840
$213$	9.77016	0.669441
$214$	−8.40246	−0.574380
$215$	−6.37244	−0.434597
$216$	5.43735	0.369965
$217$	3.70949	0.251816
$218$	−8.48767	−0.574858
$219$	25.3556	1.71337
$220$	18.2426	1.22991
$221$	20.0140	1.34628
$222$	7.39666	0.496431
$223$	−5.67162	−0.379800	−0.189900	−	0.981803i	$-0.560816\pi$
$223$	−5.67162	−0.379800	−0.189900	+	0.981803i	$0.560816\pi$
$224$	1.00000	0.0668153
$225$	−1.17464	−0.0783092
$226$	−17.4821	−1.16289
$227$	−12.9015	−0.856304	−0.428152	−	0.903707i	$-0.640835\pi$
$227$	−12.9015	−0.856304	−0.428152	+	0.903707i	$0.640835\pi$
$228$	11.5016	0.761710
$229$	8.38132	0.553853	0.276927	−	0.960891i	$-0.410684\pi$
$229$	8.38132	0.553853	0.276927	+	0.960891i	$0.410684\pi$
$230$	−17.4676	−1.15178
$231$	10.1594	0.668441
$232$	7.76943	0.510088
$233$	−8.33989	−0.546365	−0.273182	−	0.961962i	$-0.588076\pi$
$233$	−8.33989	−0.546365	−0.273182	+	0.961962i	$0.588076\pi$
$234$	−1.06073	−0.0693423
$235$	−17.2545	−1.12556
$236$	−2.79654	−0.182039
$237$	−3.08131	−0.200152
$238$	6.10676	0.395842
$239$	−18.9551	−1.22610	−0.613051	−	0.790043i	$-0.710058\pi$
$239$	−18.9551	−1.22610	−0.613051	+	0.790043i	$0.710058\pi$
$240$	4.80572	0.310208
$241$	−21.1120	−1.35994	−0.679972	−	0.733238i	$-0.738008\pi$
$241$	−21.1120	−1.35994	−0.679972	+	0.733238i	$0.738008\pi$
$242$	27.5653	1.77197
$243$	−3.34829	−0.214793
$244$	−1.33493	−0.0854602
$245$	−2.93756	−0.187674
$246$	1.95396	0.124580
$247$	−23.0414	−1.46609
$248$	3.70949	0.235553
$249$	4.04203	0.256153
$250$	4.02659	0.254664
$251$	−17.1416	−1.08197	−0.540984	−	0.841033i	$-0.681948\pi$
$251$	−17.1416	−1.08197	−0.540984	+	0.841033i	$0.681948\pi$
$252$	−0.323656	−0.0203884
$253$	−36.9271	−2.32159
$254$	−13.3187	−0.835692
$255$	29.3474	1.83780
$256$	1.00000	0.0625000
$257$	11.6509	0.726765	0.363383	−	0.931640i	$-0.381622\pi$
$257$	11.6509	0.726765	0.363383	+	0.931640i	$0.381622\pi$
$258$	−3.54887	−0.220943
$259$	−4.52131	−0.280941
$260$	−9.62740	−0.597066
$261$	−2.51463	−0.155651
$262$	13.2797	0.820424
$263$	−9.12150	−0.562456	−0.281228	−	0.959641i	$-0.590742\pi$
$263$	−9.12150	−0.562456	−0.281228	+	0.959641i	$0.590742\pi$
$264$	10.1594	0.625270
$265$	27.3242	1.67851
$266$	−7.03050	−0.431068
$267$	−3.71106	−0.227113
$268$	7.06366	0.431482
$269$	−15.7995	−0.963310	−0.481655	−	0.876361i	$-0.659964\pi$
$269$	−15.7995	−0.963310	−0.481655	+	0.876361i	$0.659964\pi$
$270$	−15.9725	−0.972058
$271$	17.1114	1.03945	0.519723	−	0.854335i	$-0.326035\pi$
$271$	17.1114	1.03945	0.519723	+	0.854335i	$0.326035\pi$
$272$	6.10676	0.370277
$273$	−5.36158	−0.324498
$274$	−16.3431	−0.987324
$275$	−22.5382	−1.35910
$276$	−9.72788	−0.585549
$277$	−29.8622	−1.79425	−0.897124	−	0.441779i	$-0.854347\pi$
$277$	−29.8622	−1.79425	−0.897124	+	0.441779i	$0.854347\pi$
$278$	4.78152	0.286776
$279$	−1.20060	−0.0718780
$280$	−2.93756	−0.175553
$281$	23.3677	1.39400	0.697000	−	0.717071i	$-0.254518\pi$
$281$	23.3677	1.39400	0.697000	+	0.717071i	$0.254518\pi$
$282$	−9.60917	−0.572218
$283$	−19.7398	−1.17341	−0.586704	−	0.809801i	$-0.699575\pi$
$283$	−19.7398	−1.17341	−0.586704	+	0.809801i	$0.699575\pi$
$284$	−5.97215	−0.354382
$285$	−33.7866	−2.00135
$286$	−20.3526	−1.20348
$287$	−1.19439	−0.0705024
$288$	−0.323656	−0.0190716
$289$	20.2925	1.19368
$290$	−22.8232	−1.34022
$291$	−11.4156	−0.669192
$292$	−15.4990	−0.907009
$293$	14.7202	0.859962	0.429981	−	0.902838i	$-0.358520\pi$
$293$	14.7202	0.859962	0.429981	+	0.902838i	$0.358520\pi$
$294$	−1.63595	−0.0954107
$295$	8.21502	0.478297
$296$	−4.52131	−0.262796
$297$	−33.7665	−1.95933
$298$	−22.6790	−1.31376
$299$	19.4881	1.12703
$300$	−5.93733	−0.342792
$301$	2.16930	0.125036
$302$	5.86309	0.337383
$303$	26.3128	1.51163
$304$	−7.03050	−0.403227
$305$	3.92145	0.224541
$306$	−1.97649	−0.112989
$307$	−5.59937	−0.319573	−0.159786	−	0.987152i	$-0.551081\pi$
$307$	−5.59937	−0.319573	−0.159786	+	0.987152i	$0.551081\pi$
$308$	−6.21010	−0.353853
$309$	−19.1680	−1.09043
$310$	−10.8969	−0.618900
$311$	22.2514	1.26176	0.630880	−	0.775881i	$-0.282694\pi$
$311$	22.2514	1.26176	0.630880	+	0.775881i	$0.282694\pi$
$312$	−5.36158	−0.303540
$313$	7.19614	0.406750	0.203375	−	0.979101i	$-0.434809\pi$
$313$	7.19614	0.406750	0.203375	+	0.979101i	$0.434809\pi$
$314$	−3.20728	−0.180997
$315$	0.950761	0.0535693
$316$	1.88349	0.105955
$317$	−17.3651	−0.975320	−0.487660	−	0.873034i	$-0.662149\pi$
$317$	−17.3651	−0.975320	−0.487660	+	0.873034i	$0.662149\pi$
$318$	15.2171	0.853331
$319$	−48.2489	−2.70142
$320$	−2.93756	−0.164215
$321$	13.7460	0.767229
$322$	5.94631	0.331375
$323$	−42.9336	−2.38889
$324$	−7.92428	−0.440238
$325$	11.8944	0.659782
$326$	−11.0458	−0.611770
$327$	13.8854	0.767866
$328$	−1.19439	−0.0659489
$329$	5.87374	0.323830
$330$	−29.8440	−1.64286
$331$	10.3669	0.569816	0.284908	−	0.958555i	$-0.408037\pi$
$331$	10.3669	0.569816	0.284908	+	0.958555i	$0.408037\pi$
$332$	−2.47075	−0.135600
$333$	1.46335	0.0801912
$334$	25.7311	1.40794
$335$	−20.7499	−1.13369
$336$	−1.63595	−0.0892486
$337$	−5.72591	−0.311910	−0.155955	−	0.987764i	$-0.549846\pi$
$337$	−5.72591	−0.311910	−0.155955	+	0.987764i	$0.549846\pi$
$338$	−2.25902	−0.122874
$339$	28.5999	1.55333
$340$	−17.9390	−0.972878
$341$	−23.0363	−1.24748
$342$	2.27547	0.123043
$343$	1.00000	0.0539949
$344$	2.16930	0.116961
$345$	28.5763	1.53849
$346$	−7.50228	−0.403325
$347$	6.93954	0.372534	0.186267	−	0.982499i	$-0.440361\pi$
$347$	6.93954	0.372534	0.186267	+	0.982499i	$0.440361\pi$
$348$	−12.7104	−0.681350
$349$	−30.1464	−1.61370	−0.806851	−	0.590755i	$-0.798830\pi$
$349$	−30.1464	−1.61370	−0.806851	+	0.590755i	$0.798830\pi$
$350$	3.62928	0.193993
$351$	17.8201	0.951164
$352$	−6.21010	−0.330999
$353$	−17.9597	−0.955900	−0.477950	−	0.878387i	$-0.658620\pi$
$353$	−17.9597	−0.955900	−0.477950	+	0.878387i	$0.658620\pi$
$354$	4.57501	0.243159
$355$	17.5436	0.931116
$356$	2.26844	0.120227
$357$	−9.99037	−0.528747
$358$	16.9974	0.898341
$359$	−31.5638	−1.66587	−0.832936	−	0.553370i	$-0.813342\pi$
$359$	−31.5638	−1.66587	−0.832936	+	0.553370i	$0.813342\pi$
$360$	0.950761	0.0501095
$361$	30.4280	1.60147
$362$	20.2914	1.06649
$363$	−45.0956	−2.36690
$364$	3.27734	0.171780
$365$	45.5292	2.38311
$366$	2.18389	0.114154
$367$	−12.0724	−0.630177	−0.315088	−	0.949062i	$-0.602034\pi$
$367$	−12.0724	−0.630177	−0.315088	+	0.949062i	$0.602034\pi$
$368$	5.94631	0.309973
$369$	0.386571	0.0201241
$370$	13.2816	0.690479
$371$	−9.30165	−0.482918
$372$	−6.06855	−0.314640
$373$	−0.363651	−0.0188291	−0.00941457	−	0.999956i	$-0.502997\pi$
$373$	−0.363651	−0.0188291	−0.00941457	+	0.999956i	$0.502997\pi$
$374$	−37.9236	−1.96098
$375$	−6.58731	−0.340167
$376$	5.87374	0.302915
$377$	25.4631	1.31142
$378$	5.43735	0.279667
$379$	17.1296	0.879889	0.439944	−	0.898025i	$-0.354998\pi$
$379$	17.1296	0.879889	0.439944	+	0.898025i	$0.354998\pi$
$380$	20.6525	1.05945
$381$	21.7888	1.11628
$382$	−19.5592	−1.00074
$383$	3.43910	0.175730	0.0878648	−	0.996132i	$-0.471996\pi$
$383$	3.43910	0.175730	0.0878648	+	0.996132i	$0.471996\pi$
$384$	−1.63595	−0.0834844
$385$	18.2426	0.929727
$386$	−2.71073	−0.137973
$387$	−0.702106	−0.0356901
$388$	6.97793	0.354251
$389$	−1.92498	−0.0976002	−0.0488001	−	0.998809i	$-0.515540\pi$
$389$	−1.92498	−0.0976002	−0.0488001	+	0.998809i	$0.515540\pi$
$390$	15.7500	0.797531
$391$	36.3127	1.83641
$392$	1.00000	0.0505076
$393$	−21.7250	−1.09588
$394$	−12.5860	−0.634073
$395$	−5.53288	−0.278389
$396$	2.00994	0.101003
$397$	33.3409	1.67333	0.836666	−	0.547713i	$-0.184501\pi$
$397$	33.3409	1.67333	0.836666	+	0.547713i	$0.184501\pi$
$398$	2.58337	0.129493
$399$	11.5016	0.575799
$400$	3.62928	0.181464
$401$	−17.9446	−0.896109	−0.448055	−	0.894006i	$-0.647883\pi$
$401$	−17.9446	−0.896109	−0.448055	+	0.894006i	$0.647883\pi$
$402$	−11.5558	−0.576352
$403$	12.1573	0.605596
$404$	−16.0841	−0.800214
$405$	23.2781	1.15670
$406$	7.76943	0.385590
$407$	28.0778	1.39176
$408$	−9.99037	−0.494597
$409$	10.9192	0.539920	0.269960	−	0.962872i	$-0.412990\pi$
$409$	10.9192	0.539920	0.269960	+	0.962872i	$0.412990\pi$
$410$	3.50858	0.173277
$411$	26.7366	1.31882
$412$	11.7167	0.577242
$413$	−2.79654	−0.137609
$414$	−1.92456	−0.0945870
$415$	7.25797	0.356280
$416$	3.27734	0.160685
$417$	−7.82234	−0.383061
$418$	43.6601	2.13549
$419$	−29.5347	−1.44287	−0.721433	−	0.692485i	$-0.756516\pi$
$419$	−29.5347	−1.44287	−0.721433	+	0.692485i	$0.756516\pi$
$420$	4.80572	0.234495
$421$	19.0214	0.927046	0.463523	−	0.886085i	$-0.346585\pi$
$421$	19.0214	0.927046	0.463523	+	0.886085i	$0.346585\pi$
$422$	24.8190	1.20817
$423$	−1.90108	−0.0924334
$424$	−9.30165	−0.451728
$425$	22.1631	1.07507
$426$	9.77016	0.473366
$427$	−1.33493	−0.0646019
$428$	−8.40246	−0.406148
$429$	33.2960	1.60754
$430$	−6.37244	−0.307306
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.43735	0.261604
$433$	−11.0574	−0.531385	−0.265692	−	0.964058i	$-0.585601\pi$
$433$	−11.0574	−0.531385	−0.265692	+	0.964058i	$0.585601\pi$
$434$	3.70949	0.178061
$435$	37.3377	1.79020
$436$	−8.48767	−0.406486
$437$	−41.8055	−1.99983
$438$	25.3556	1.21154
$439$	−14.4215	−0.688299	−0.344149	−	0.938915i	$-0.611833\pi$
$439$	−14.4215	−0.688299	−0.344149	+	0.938915i	$0.611833\pi$
$440$	18.2426	0.869680
$441$	−0.323656	−0.0154122
$442$	20.0140	0.951967
$443$	1.23456	0.0586558	0.0293279	−	0.999570i	$-0.490663\pi$
$443$	1.23456	0.0586558	0.0293279	+	0.999570i	$0.490663\pi$
$444$	7.39666	0.351030
$445$	−6.66369	−0.315889
$446$	−5.67162	−0.268559
$447$	37.1018	1.75486
$448$	1.00000	0.0472456
$449$	−25.9042	−1.22250	−0.611248	−	0.791439i	$-0.709332\pi$
$449$	−25.9042	−1.22250	−0.611248	+	0.791439i	$0.709332\pi$
$450$	−1.17464	−0.0553730
$451$	7.41726	0.349265
$452$	−17.4821	−0.822288
$453$	−9.59174	−0.450659
$454$	−12.9015	−0.605498
$455$	−9.62740	−0.451340
$456$	11.5016	0.538611
$457$	38.1282	1.78356	0.891782	−	0.452466i	$-0.149456\pi$
$457$	38.1282	1.78356	0.891782	+	0.452466i	$0.149456\pi$
$458$	8.38132	0.391633
$459$	33.2046	1.54986
$460$	−17.4676	−0.814433
$461$	10.6781	0.497328	0.248664	−	0.968590i	$-0.420009\pi$
$461$	10.6781	0.497328	0.248664	+	0.968590i	$0.420009\pi$
$462$	10.1594	0.472660
$463$	6.63721	0.308457	0.154229	−	0.988035i	$-0.450711\pi$
$463$	6.63721	0.308457	0.154229	+	0.988035i	$0.450711\pi$
$464$	7.76943	0.360687
$465$	17.8267	0.826695
$466$	−8.33989	−0.386338
$467$	−31.7007	−1.46694	−0.733468	−	0.679724i	$-0.762099\pi$
$467$	−31.7007	−1.46694	−0.733468	+	0.679724i	$0.762099\pi$
$468$	−1.06073	−0.0490324
$469$	7.06366	0.326169
$470$	−17.2545	−0.795890
$471$	5.24696	0.241767
$472$	−2.79654	−0.128721
$473$	−13.4715	−0.619422
$474$	−3.08131	−0.141529
$475$	−25.5156	−1.17074
$476$	6.10676	0.279903
$477$	3.01054	0.137843
$478$	−18.9551	−0.866985
$479$	2.15357	0.0983993	0.0491997	−	0.998789i	$-0.484333\pi$
$479$	2.15357	0.0983993	0.0491997	+	0.998789i	$0.484333\pi$
$480$	4.80572	0.219350
$481$	−14.8179	−0.675638
$482$	−21.1120	−0.961625
$483$	−9.72788	−0.442634
$484$	27.5653	1.25297
$485$	−20.4981	−0.930771
$486$	−3.34829	−0.151882
$487$	−33.5130	−1.51862	−0.759309	−	0.650730i	$-0.774463\pi$
$487$	−33.5130	−1.51862	−0.759309	+	0.650730i	$0.774463\pi$
$488$	−1.33493	−0.0604295
$489$	18.0704	0.817172
$490$	−2.93756	−0.132706
$491$	−25.6028	−1.15544	−0.577718	−	0.816236i	$-0.696057\pi$
$491$	−25.6028	−1.15544	−0.577718	+	0.816236i	$0.696057\pi$
$492$	1.95396	0.0880913
$493$	47.4460	2.13686
$494$	−23.0414	−1.03668
$495$	−5.90432	−0.265379
$496$	3.70949	0.166561
$497$	−5.97215	−0.267888
$498$	4.04203	0.181127
$499$	−12.6027	−0.564172	−0.282086	−	0.959389i	$-0.591026\pi$
$499$	−12.6027	−0.564172	−0.282086	+	0.959389i	$0.591026\pi$
$500$	4.02659	0.180075
$501$	−42.0948	−1.88066
$502$	−17.1416	−0.765068
$503$	−24.3396	−1.08525	−0.542624	−	0.839976i	$-0.682569\pi$
$503$	−24.3396	−1.08525	−0.542624	+	0.839976i	$0.682569\pi$
$504$	−0.323656	−0.0144168
$505$	47.2481	2.10251
$506$	−36.9271	−1.64161
$507$	3.69564	0.164129
$508$	−13.3187	−0.590924
$509$	−37.6344	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$509$	−37.6344	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$510$	29.3474	1.29952
$511$	−15.4990	−0.685635
$512$	1.00000	0.0441942
$513$	−38.2273	−1.68778
$514$	11.6509	0.513901
$515$	−34.4186	−1.51667
$516$	−3.54887	−0.156230
$517$	−36.4765	−1.60424
$518$	−4.52131	−0.198655
$519$	12.2734	0.538741
$520$	−9.62740	−0.422190
$521$	4.56698	0.200083	0.100041	−	0.994983i	$-0.468102\pi$
$521$	4.56698	0.200083	0.100041	+	0.994983i	$0.468102\pi$
$522$	−2.51463	−0.110062
$523$	27.7051	1.21146	0.605729	−	0.795671i	$-0.292881\pi$
$523$	27.7051	1.21146	0.605729	+	0.795671i	$0.292881\pi$
$524$	13.2797	0.580128
$525$	−5.93733	−0.259126
$526$	−9.12150	−0.397716
$527$	22.6529	0.986778
$528$	10.1594	0.442132
$529$	12.3585	0.537328
$530$	27.3242	1.18689
$531$	0.905118	0.0392788
$532$	−7.03050	−0.304811
$533$	−3.91441	−0.169552
$534$	−3.71106	−0.160593
$535$	24.6827	1.06713
$536$	7.06366	0.305104
$537$	−27.8070	−1.19996
$538$	−15.7995	−0.681163
$539$	−6.21010	−0.267488
$540$	−15.9725	−0.687349
$541$	−18.5988	−0.799626	−0.399813	−	0.916597i	$-0.630925\pi$
$541$	−18.5988	−0.799626	−0.399813	+	0.916597i	$0.630925\pi$
$542$	17.1114	0.734999
$543$	−33.1958	−1.42457
$544$	6.10676	0.261825
$545$	24.9331	1.06802
$546$	−5.36158	−0.229455
$547$	10.5904	0.452815	0.226407	−	0.974033i	$-0.427302\pi$
$547$	10.5904	0.452815	0.226407	+	0.974033i	$0.427302\pi$
$548$	−16.3431	−0.698144
$549$	0.432059	0.0184398
$550$	−22.5382	−0.961030
$551$	−54.6230	−2.32702
$552$	−9.72788	−0.414046
$553$	1.88349	0.0800943
$554$	−29.8622	−1.26872
$555$	−21.7281	−0.922308
$556$	4.78152	0.202781
$557$	32.4424	1.37463	0.687315	−	0.726359i	$-0.258789\pi$
$557$	32.4424	1.37463	0.687315	+	0.726359i	$0.258789\pi$
$558$	−1.20060	−0.0508254
$559$	7.10953	0.300701
$560$	−2.93756	−0.124135
$561$	62.0412	2.61938
$562$	23.3677	0.985706
$563$	27.2271	1.14748	0.573742	−	0.819036i	$-0.305491\pi$
$563$	27.2271	1.14748	0.573742	+	0.819036i	$0.305491\pi$
$564$	−9.60917	−0.404619
$565$	51.3547	2.16051
$566$	−19.7398	−0.829725
$567$	−7.92428	−0.332788
$568$	−5.97215	−0.250586
$569$	−15.3809	−0.644800	−0.322400	−	0.946604i	$-0.604490\pi$
$569$	−15.3809	−0.644800	−0.322400	+	0.946604i	$0.604490\pi$
$570$	−33.7866	−1.41516
$571$	15.1498	0.634001	0.317001	−	0.948425i	$-0.397324\pi$
$571$	15.1498	0.634001	0.317001	+	0.948425i	$0.397324\pi$
$572$	−20.3526	−0.850986
$573$	31.9980	1.33674
$574$	−1.19439	−0.0498527
$575$	21.5808	0.899981
$576$	−0.323656	−0.0134857
$577$	32.3604	1.34718	0.673591	−	0.739104i	$-0.264751\pi$
$577$	32.3604	1.34718	0.673591	+	0.739104i	$0.264751\pi$
$578$	20.2925	0.844057
$579$	4.43463	0.184297
$580$	−22.8232	−0.947681
$581$	−2.47075	−0.102504
$582$	−11.4156	−0.473190
$583$	57.7642	2.39235
$584$	−15.4990	−0.641352
$585$	3.11597	0.128830
$586$	14.7202	0.608085
$587$	−6.93619	−0.286287	−0.143144	−	0.989702i	$-0.545721\pi$
$587$	−6.93619	−0.286287	−0.143144	+	0.989702i	$0.545721\pi$
$588$	−1.63595	−0.0674656
$589$	−26.0796	−1.07459
$590$	8.21502	0.338207
$591$	20.5901	0.846963
$592$	−4.52131	−0.185825
$593$	−38.0499	−1.56252	−0.781262	−	0.624203i	$-0.785424\pi$
$593$	−38.0499	−1.56252	−0.781262	+	0.624203i	$0.785424\pi$
$594$	−33.7665	−1.38545
$595$	−17.9390	−0.735427
$596$	−22.6790	−0.928970
$597$	−4.22628	−0.172970
$598$	19.4881	0.796927
$599$	29.8164	1.21827	0.609133	−	0.793068i	$-0.291518\pi$
$599$	29.8164	1.21827	0.609133	+	0.793068i	$0.291518\pi$
$600$	−5.93733	−0.242390
$601$	−13.9086	−0.567343	−0.283671	−	0.958922i	$-0.591552\pi$
$601$	−13.9086	−0.567343	−0.283671	+	0.958922i	$0.591552\pi$
$602$	2.16930	0.0884139
$603$	−2.28620	−0.0931012
$604$	5.86309	0.238566
$605$	−80.9749	−3.29210
$606$	26.3128	1.06889
$607$	0.385720	0.0156559	0.00782794	−	0.999969i	$-0.497508\pi$
$607$	0.385720	0.0156559	0.00782794	+	0.999969i	$0.497508\pi$
$608$	−7.03050	−0.285125
$609$	−12.7104	−0.515052
$610$	3.92145	0.158775
$611$	19.2503	0.778783
$612$	−1.97649	−0.0798950
$613$	6.29793	0.254371	0.127186	−	0.991879i	$-0.459406\pi$
$613$	6.29793	0.254371	0.127186	+	0.991879i	$0.459406\pi$
$614$	−5.59937	−0.225972
$615$	−5.73988	−0.231454
$616$	−6.21010	−0.250212
$617$	−13.1448	−0.529192	−0.264596	−	0.964359i	$-0.585239\pi$
$617$	−13.1448	−0.529192	−0.264596	+	0.964359i	$0.585239\pi$
$618$	−19.1680	−0.771051
$619$	18.5320	0.744863	0.372431	−	0.928060i	$-0.378524\pi$
$619$	18.5320	0.744863	0.372431	+	0.928060i	$0.378524\pi$
$620$	−10.8969	−0.437628
$621$	32.3321	1.29744
$622$	22.2514	0.892199
$623$	2.26844	0.0908832
$624$	−5.36158	−0.214635
$625$	−29.9747	−1.19899
$626$	7.19614	0.287616
$627$	−71.4259	−2.85248
$628$	−3.20728	−0.127984
$629$	−27.6106	−1.10091
$630$	0.950761	0.0378792
$631$	−31.9605	−1.27233	−0.636164	−	0.771554i	$-0.719480\pi$
$631$	−31.9605	−1.27233	−0.636164	+	0.771554i	$0.719480\pi$
$632$	1.88349	0.0749213
$633$	−40.6028	−1.61382
$634$	−17.3651	−0.689656
$635$	39.1246	1.55261
$636$	15.2171	0.603396
$637$	3.27734	0.129853
$638$	−48.2489	−1.91019
$639$	1.93293	0.0764653
$640$	−2.93756	−0.116117
$641$	−9.99174	−0.394650	−0.197325	−	0.980338i	$-0.563225\pi$
$641$	−9.99174	−0.394650	−0.197325	+	0.980338i	$0.563225\pi$
$642$	13.7460	0.542513
$643$	44.5056	1.75513	0.877564	−	0.479459i	$-0.159167\pi$
$643$	44.5056	1.75513	0.877564	+	0.479459i	$0.159167\pi$
$644$	5.94631	0.234317
$645$	10.4250	0.410485
$646$	−42.9336	−1.68920
$647$	21.8411	0.858664	0.429332	−	0.903147i	$-0.358749\pi$
$647$	21.8411	0.858664	0.429332	+	0.903147i	$0.358749\pi$
$648$	−7.92428	−0.311295
$649$	17.3668	0.681706
$650$	11.8944	0.466536
$651$	−6.06855	−0.237845
$652$	−11.0458	−0.432587
$653$	−46.9729	−1.83819	−0.919095	−	0.394036i	$-0.871079\pi$
$653$	−46.9729	−1.83819	−0.919095	+	0.394036i	$0.871079\pi$
$654$	13.8854	0.542963
$655$	−39.0100	−1.52425
$656$	−1.19439	−0.0466329
$657$	5.01634	0.195706
$658$	5.87374	0.228982
$659$	3.29916	0.128517	0.0642584	−	0.997933i	$-0.479532\pi$
$659$	3.29916	0.128517	0.0642584	+	0.997933i	$0.479532\pi$
$660$	−29.8440	−1.16167
$661$	−35.0096	−1.36171	−0.680857	−	0.732416i	$-0.738392\pi$
$661$	−35.0096	−1.36171	−0.680857	+	0.732416i	$0.738392\pi$
$662$	10.3669	0.402921
$663$	−32.7419	−1.27159
$664$	−2.47075	−0.0958835
$665$	20.6525	0.800871
$666$	1.46335	0.0567037
$667$	46.1994	1.78885
$668$	25.7311	0.995564
$669$	9.27851	0.358728
$670$	−20.7499	−0.801640
$671$	8.29006	0.320034
$672$	−1.63595	−0.0631083
$673$	16.7988	0.647545	0.323772	−	0.946135i	$-0.395049\pi$
$673$	16.7988	0.647545	0.323772	+	0.946135i	$0.395049\pi$
$674$	−5.72591	−0.220554
$675$	19.7336	0.759548
$676$	−2.25902	−0.0868852
$677$	−43.0232	−1.65352	−0.826759	−	0.562557i	$-0.809818\pi$
$677$	−43.0232	−1.65352	−0.826759	+	0.562557i	$0.809818\pi$
$678$	28.5999	1.09837
$679$	6.97793	0.267788
$680$	−17.9390	−0.687929
$681$	21.1063	0.808795
$682$	−23.0363	−0.882105
$683$	33.7434	1.29116	0.645578	−	0.763694i	$-0.276617\pi$
$683$	33.7434	1.29116	0.645578	+	0.763694i	$0.276617\pi$
$684$	2.27547	0.0870047
$685$	48.0090	1.83433
$686$	1.00000	0.0381802
$687$	−13.7114	−0.523124
$688$	2.16930	0.0827036
$689$	−30.4847	−1.16138
$690$	28.5763	1.08788
$691$	−7.05390	−0.268343	−0.134172	−	0.990958i	$-0.542837\pi$
$691$	−7.05390	−0.268343	−0.134172	+	0.990958i	$0.542837\pi$
$692$	−7.50228	−0.285194
$693$	2.00994	0.0763512
$694$	6.93954	0.263421
$695$	−14.0460	−0.532795
$696$	−12.7104	−0.481787
$697$	−7.29383	−0.276273
$698$	−30.1464	−1.14106
$699$	13.6437	0.516051
$700$	3.62928	0.137174
$701$	−23.7707	−0.897805	−0.448903	−	0.893581i	$-0.648185\pi$
$701$	−23.7707	−0.897805	−0.448903	+	0.893581i	$0.648185\pi$
$702$	17.8201	0.672575
$703$	31.7871	1.19887
$704$	−6.21010	−0.234052
$705$	28.2275	1.06311
$706$	−17.9597	−0.675923
$707$	−16.0841	−0.604905
$708$	4.57501	0.171939
$709$	−14.7343	−0.553357	−0.276679	−	0.960962i	$-0.589234\pi$
$709$	−14.7343	−0.553357	−0.276679	+	0.960962i	$0.589234\pi$
$710$	17.5436	0.658399
$711$	−0.609604	−0.0228620
$712$	2.26844	0.0850134
$713$	22.0577	0.826069
$714$	−9.99037	−0.373880
$715$	59.7871	2.23591
$716$	16.9974	0.635223
$717$	31.0096	1.15808
$718$	−31.5638	−1.17795
$719$	2.99759	0.111791	0.0558955	−	0.998437i	$-0.482199\pi$
$719$	2.99759	0.111791	0.0558955	+	0.998437i	$0.482199\pi$
$720$	0.950761	0.0354328
$721$	11.7167	0.436354
$722$	30.4280	1.13241
$723$	34.5382	1.28449
$724$	20.2914	0.754125
$725$	28.1974	1.04722
$726$	−45.0956	−1.67365
$727$	12.4636	0.462250	0.231125	−	0.972924i	$-0.425759\pi$
$727$	12.4636	0.462250	0.231125	+	0.972924i	$0.425759\pi$
$728$	3.27734	0.121466
$729$	29.2505	1.08335
$730$	45.5292	1.68511
$731$	13.2474	0.489972
$732$	2.18389	0.0807187
$733$	−41.5525	−1.53478	−0.767389	−	0.641182i	$-0.778445\pi$
$733$	−41.5525	−1.53478	−0.767389	+	0.641182i	$0.778445\pi$
$734$	−12.0724	−0.445602
$735$	4.80572	0.177262
$736$	5.94631	0.219184
$737$	−43.8660	−1.61583
$738$	0.386571	0.0142299
$739$	−10.5402	−0.387729	−0.193864	−	0.981028i	$-0.562102\pi$
$739$	−10.5402	−0.387729	−0.193864	+	0.981028i	$0.562102\pi$
$740$	13.2816	0.488243
$741$	37.6946	1.38475
$742$	−9.30165	−0.341474
$743$	−21.7611	−0.798337	−0.399169	−	0.916878i	$-0.630701\pi$
$743$	−21.7611	−0.798337	−0.399169	+	0.916878i	$0.630701\pi$
$744$	−6.06855	−0.222484
$745$	66.6211	2.44081
$746$	−0.363651	−0.0133142
$747$	0.799673	0.0292585
$748$	−37.9236	−1.38662
$749$	−8.40246	−0.307019
$750$	−6.58731	−0.240535
$751$	4.84657	0.176854	0.0884270	−	0.996083i	$-0.471816\pi$
$751$	4.84657	0.176854	0.0884270	+	0.996083i	$0.471816\pi$
$752$	5.87374	0.214193
$753$	28.0429	1.02194
$754$	25.4631	0.927311
$755$	−17.2232	−0.626816
$756$	5.43735	0.197754
$757$	5.23272	0.190186	0.0950932	−	0.995468i	$-0.469685\pi$
$757$	5.23272	0.190186	0.0950932	+	0.995468i	$0.469685\pi$
$758$	17.1296	0.622175
$759$	60.4111	2.19278
$760$	20.6525	0.749147
$761$	7.97844	0.289218	0.144609	−	0.989489i	$-0.453808\pi$
$761$	7.97844	0.289218	0.144609	+	0.989489i	$0.453808\pi$
$762$	21.7888	0.789327
$763$	−8.48767	−0.307274
$764$	−19.5592	−0.707629
$765$	5.80607	0.209919
$766$	3.43910	0.124260
$767$	−9.16523	−0.330937
$768$	−1.63595	−0.0590324
$769$	−17.3331	−0.625046	−0.312523	−	0.949910i	$-0.601174\pi$
$769$	−17.3331	−0.625046	−0.312523	+	0.949910i	$0.601174\pi$
$770$	18.2426	0.657416
$771$	−19.0604	−0.686443
$772$	−2.71073	−0.0975614
$773$	6.02408	0.216671	0.108336	−	0.994114i	$-0.465448\pi$
$773$	6.02408	0.216671	0.108336	+	0.994114i	$0.465448\pi$
$774$	−0.702106	−0.0252367
$775$	13.4627	0.483596
$776$	6.97793	0.250493
$777$	7.39666	0.265354
$778$	−1.92498	−0.0690138
$779$	8.39714	0.300859
$780$	15.7500	0.563940
$781$	37.0877	1.32710
$782$	36.3127	1.29854
$783$	42.2451	1.50972
$784$	1.00000	0.0357143
$785$	9.42158	0.336271
$786$	−21.7250	−0.774906
$787$	−25.8064	−0.919900	−0.459950	−	0.887945i	$-0.652133\pi$
$787$	−25.8064	−0.919900	−0.459950	+	0.887945i	$0.652133\pi$
$788$	−12.5860	−0.448357
$789$	14.9223	0.531250
$790$	−5.53288	−0.196851
$791$	−17.4821	−0.621591
$792$	2.00994	0.0714200
$793$	−4.37503	−0.155362
$794$	33.3409	1.18322
$795$	−44.7011	−1.58538
$796$	2.58337	0.0915652
$797$	25.7325	0.911493	0.455746	−	0.890110i	$-0.349372\pi$
$797$	25.7325	0.911493	0.455746	+	0.890110i	$0.349372\pi$
$798$	11.5016	0.407151
$799$	35.8695	1.26897
$800$	3.62928	0.128314
$801$	−0.734195	−0.0259415
$802$	−17.9446	−0.633645
$803$	96.2502	3.39660
$804$	−11.5558	−0.407542
$805$	−17.4676	−0.615654
$806$	12.1573	0.428221
$807$	25.8472	0.909864
$808$	−16.0841	−0.565837
$809$	30.1116	1.05867	0.529334	−	0.848413i	$-0.322442\pi$
$809$	30.1116	1.05867	0.529334	+	0.848413i	$0.322442\pi$
$810$	23.2781	0.817908
$811$	14.5245	0.510023	0.255011	−	0.966938i	$-0.417921\pi$
$811$	14.5245	0.510023	0.255011	+	0.966938i	$0.417921\pi$
$812$	7.76943	0.272653
$813$	−27.9935	−0.981776
$814$	28.0778	0.984126
$815$	32.4477	1.13659
$816$	−9.99037	−0.349733
$817$	−15.2512	−0.533573
$818$	10.9192	0.381781
$819$	−1.06073	−0.0370650
$820$	3.50858	0.122525
$821$	36.3814	1.26972	0.634860	−	0.772627i	$-0.281058\pi$
$821$	36.3814	1.26972	0.634860	+	0.772627i	$0.281058\pi$
$822$	26.7366	0.932546
$823$	17.4889	0.609626	0.304813	−	0.952412i	$-0.401406\pi$
$823$	17.4889	0.609626	0.304813	+	0.952412i	$0.401406\pi$
$824$	11.7167	0.408172
$825$	36.8714	1.28370
$826$	−2.79654	−0.0973041
$827$	20.6333	0.717490	0.358745	−	0.933436i	$-0.383205\pi$
$827$	20.6333	0.717490	0.358745	+	0.933436i	$0.383205\pi$
$828$	−1.92456	−0.0668831
$829$	15.0105	0.521338	0.260669	−	0.965428i	$-0.416057\pi$
$829$	15.0105	0.521338	0.260669	+	0.965428i	$0.416057\pi$
$830$	7.25797	0.251928
$831$	48.8532	1.69470
$832$	3.27734	0.113621
$833$	6.10676	0.211587
$834$	−7.82234	−0.270865
$835$	−75.5866	−2.61578
$836$	43.6601	1.51002
$837$	20.1698	0.697169
$838$	−29.5347	−1.02026
$839$	−47.9273	−1.65463	−0.827317	−	0.561736i	$-0.810134\pi$
$839$	−47.9273	−1.65463	−0.827317	+	0.561736i	$0.810134\pi$
$840$	4.80572	0.165813
$841$	31.3640	1.08152
$842$	19.0214	0.655521
$843$	−38.2284	−1.31666
$844$	24.8190	0.854306
$845$	6.63600	0.228285
$846$	−1.90108	−0.0653603
$847$	27.5653	0.947156
$848$	−9.30165	−0.319420
$849$	32.2934	1.10831
$850$	22.1631	0.760188
$851$	−26.8851	−0.921609
$852$	9.77016	0.334720
$853$	53.4930	1.83156	0.915782	−	0.401675i	$-0.131572\pi$
$853$	53.4930	1.83156	0.915782	+	0.401675i	$0.131572\pi$
$854$	−1.33493	−0.0456804
$855$	−6.68433	−0.228599
$856$	−8.40246	−0.287190
$857$	22.9023	0.782326	0.391163	−	0.920321i	$-0.372073\pi$
$857$	22.9023	0.782326	0.391163	+	0.920321i	$0.372073\pi$
$858$	33.2960	1.13671
$859$	−12.2509	−0.417995	−0.208998	−	0.977916i	$-0.567020\pi$
$859$	−12.2509	−0.417995	−0.208998	+	0.977916i	$0.567020\pi$
$860$	−6.37244	−0.217298
$861$	1.95396	0.0665908
$862$	−1.00000	−0.0340601
$863$	−50.6813	−1.72521	−0.862606	−	0.505877i	$-0.831169\pi$
$863$	−50.6813	−1.72521	−0.862606	+	0.505877i	$0.831169\pi$
$864$	5.43735	0.184982
$865$	22.0384	0.749328
$866$	−11.0574	−0.375746
$867$	−33.1976	−1.12745
$868$	3.70949	0.125908
$869$	−11.6967	−0.396782
$870$	37.3377	1.26587
$871$	23.1500	0.784409
$872$	−8.48767	−0.287429
$873$	−2.25845	−0.0764370
$874$	−41.8055	−1.41409
$875$	4.02659	0.136124
$876$	25.3556	0.856687
$877$	23.1701	0.782398	0.391199	−	0.920306i	$-0.372060\pi$
$877$	23.1701	0.782398	0.391199	+	0.920306i	$0.372060\pi$
$878$	−14.4215	−0.486701
$879$	−24.0815	−0.812250
$880$	18.2426	0.614956
$881$	18.1991	0.613142	0.306571	−	0.951848i	$-0.400818\pi$
$881$	18.1991	0.613142	0.306571	+	0.951848i	$0.400818\pi$
$882$	−0.323656	−0.0108981
$883$	−51.3989	−1.72971	−0.864855	−	0.502022i	$-0.832589\pi$
$883$	−51.3989	−1.72971	−0.864855	+	0.502022i	$0.832589\pi$
$884$	20.0140	0.673142
$885$	−13.4394	−0.451760
$886$	1.23456	0.0414759
$887$	8.14619	0.273522	0.136761	−	0.990604i	$-0.456331\pi$
$887$	8.14619	0.273522	0.136761	+	0.990604i	$0.456331\pi$
$888$	7.39666	0.248216
$889$	−13.3187	−0.446696
$890$	−6.66369	−0.223367
$891$	49.2105	1.64862
$892$	−5.67162	−0.189900
$893$	−41.2954	−1.38190
$894$	37.1018	1.24087
$895$	−49.9310	−1.66901
$896$	1.00000	0.0334077
$897$	−31.8816	−1.06450
$898$	−25.9042	−0.864435
$899$	28.8206	0.961221
$900$	−1.17464	−0.0391546
$901$	−56.8030	−1.89238
$902$	7.41726	0.246968
$903$	−3.54887	−0.118099
$904$	−17.4821	−0.581446
$905$	−59.6073	−1.98141
$906$	−9.59174	−0.318664
$907$	39.2628	1.30370	0.651850	−	0.758348i	$-0.273993\pi$
$907$	39.2628	1.30370	0.651850	+	0.758348i	$0.273993\pi$
$908$	−12.9015	−0.428152
$909$	5.20572	0.172663
$910$	−9.62740	−0.319145
$911$	3.64212	0.120669	0.0603344	−	0.998178i	$-0.480783\pi$
$911$	3.64212	0.120669	0.0603344	+	0.998178i	$0.480783\pi$
$912$	11.5016	0.380855
$913$	15.3436	0.507798
$914$	38.1282	1.26117
$915$	−6.41530	−0.212083
$916$	8.38132	0.276927
$917$	13.2797	0.438535
$918$	33.2046	1.09591
$919$	−7.53437	−0.248536	−0.124268	−	0.992249i	$-0.539658\pi$
$919$	−7.53437	−0.248536	−0.124268	+	0.992249i	$0.539658\pi$
$920$	−17.4676	−0.575891
$921$	9.16031	0.301842
$922$	10.6781	0.351664
$923$	−19.5728	−0.644247
$924$	10.1594	0.334221
$925$	−16.4091	−0.539527
$926$	6.63721	0.218112
$927$	−3.79219	−0.124552
$928$	7.76943	0.255044
$929$	37.1059	1.21740	0.608702	−	0.793399i	$-0.291691\pi$
$929$	37.1059	1.21740	0.608702	+	0.793399i	$0.291691\pi$
$930$	17.8267	0.584562
$931$	−7.03050	−0.230415
$932$	−8.33989	−0.273182
$933$	−36.4022	−1.19175
$934$	−31.7007	−1.03728
$935$	111.403	3.64326
$936$	−1.06073	−0.0346712
$937$	45.0119	1.47048	0.735238	−	0.677809i	$-0.237070\pi$
$937$	45.0119	1.47048	0.735238	+	0.677809i	$0.237070\pi$
$938$	7.06366	0.230637
$939$	−11.7726	−0.384183
$940$	−17.2545	−0.562780
$941$	22.4243	0.731013	0.365506	−	0.930809i	$-0.380896\pi$
$941$	22.4243	0.731013	0.365506	+	0.930809i	$0.380896\pi$
$942$	5.24696	0.170955
$943$	−7.10218	−0.231279
$944$	−2.79654	−0.0910197
$945$	−15.9725	−0.519587
$946$	−13.4715	−0.437997
$947$	23.7861	0.772943	0.386472	−	0.922301i	$-0.373694\pi$
$947$	23.7861	0.772943	0.386472	+	0.922301i	$0.373694\pi$
$948$	−3.08131	−0.100076
$949$	−50.7955	−1.64889
$950$	−25.5156	−0.827836
$951$	28.4085	0.921208
$952$	6.10676	0.197921
$953$	−31.7441	−1.02829	−0.514146	−	0.857703i	$-0.671891\pi$
$953$	−31.7441	−1.02829	−0.514146	+	0.857703i	$0.671891\pi$
$954$	3.01054	0.0974698
$955$	57.4565	1.85925
$956$	−18.9551	−0.613051
$957$	78.9330	2.55154
$958$	2.15357	0.0695788
$959$	−16.3431	−0.527747
$960$	4.80572	0.155104
$961$	−17.2397	−0.556120
$962$	−14.8179	−0.477748
$963$	2.71951	0.0876350
$964$	−21.1120	−0.679972
$965$	7.96295	0.256336
$966$	−9.72788	−0.312989
$967$	12.1112	0.389469	0.194735	−	0.980856i	$-0.437615\pi$
$967$	12.1112	0.389469	0.194735	+	0.980856i	$0.437615\pi$
$968$	27.5653	0.885983
$969$	70.2374	2.25635
$970$	−20.4981	−0.658154
$971$	−22.3899	−0.718527	−0.359263	−	0.933236i	$-0.616972\pi$
$971$	−22.3899	−0.718527	−0.359263	+	0.933236i	$0.616972\pi$
$972$	−3.34829	−0.107397
$973$	4.78152	0.153288
$974$	−33.5130	−1.07383
$975$	−19.4587	−0.623176
$976$	−1.33493	−0.0427301
$977$	−23.9520	−0.766292	−0.383146	−	0.923688i	$-0.625159\pi$
$977$	−23.9520	−0.766292	−0.383146	+	0.923688i	$0.625159\pi$
$978$	18.0704	0.577828
$979$	−14.0872	−0.450230
$980$	−2.93756	−0.0938370
$981$	2.74709	0.0877078
$982$	−25.6028	−0.817017
$983$	18.6302	0.594210	0.297105	−	0.954845i	$-0.403979\pi$
$983$	18.6302	0.594210	0.297105	+	0.954845i	$0.403979\pi$
$984$	1.95396	0.0622900
$985$	36.9721	1.17803
$986$	47.4460	1.51099
$987$	−9.60917	−0.305863
$988$	−23.0414	−0.733044
$989$	12.8993	0.410174
$990$	−5.90432	−0.187652
$991$	60.6691	1.92722	0.963609	−	0.267317i	$-0.0861369\pi$
$991$	60.6691	1.92722	0.963609	+	0.267317i	$0.0861369\pi$
$992$	3.70949	0.117776
$993$	−16.9598	−0.538202
$994$	−5.97215	−0.189425
$995$	−7.58882	−0.240582
$996$	4.04203	0.128076
$997$	−10.9499	−0.346787	−0.173393	−	0.984853i	$-0.555473\pi$
$997$	−10.9499	−0.346787	−0.173393	+	0.984853i	$0.555473\pi$
$998$	−12.6027	−0.398930
$999$	−24.5839	−0.777801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.6	✓	21	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.63595 q^{3} +1.00000 q^{4} -2.93756 q^{5} -1.63595 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.323656 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.63595 q^{3} +1.00000 q^{4} -2.93756 q^{5} -1.63595 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.323656 q^{9} -2.93756 q^{10} -6.21010 q^{11} -1.63595 q^{12} +3.27734 q^{13} +1.00000 q^{14} +4.80572 q^{15} +1.00000 q^{16} +6.10676 q^{17} -0.323656 q^{18} -7.03050 q^{19} -2.93756 q^{20} -1.63595 q^{21} -6.21010 q^{22} +5.94631 q^{23} -1.63595 q^{24} +3.62928 q^{25} +3.27734 q^{26} +5.43735 q^{27} +1.00000 q^{28} +7.76943 q^{29} +4.80572 q^{30} +3.70949 q^{31} +1.00000 q^{32} +10.1594 q^{33} +6.10676 q^{34} -2.93756 q^{35} -0.323656 q^{36} -4.52131 q^{37} -7.03050 q^{38} -5.36158 q^{39} -2.93756 q^{40} -1.19439 q^{41} -1.63595 q^{42} +2.16930 q^{43} -6.21010 q^{44} +0.950761 q^{45} +5.94631 q^{46} +5.87374 q^{47} -1.63595 q^{48} +1.00000 q^{49} +3.62928 q^{50} -9.99037 q^{51} +3.27734 q^{52} -9.30165 q^{53} +5.43735 q^{54} +18.2426 q^{55} +1.00000 q^{56} +11.5016 q^{57} +7.76943 q^{58} -2.79654 q^{59} +4.80572 q^{60} -1.33493 q^{61} +3.70949 q^{62} -0.323656 q^{63} +1.00000 q^{64} -9.62740 q^{65} +10.1594 q^{66} +7.06366 q^{67} +6.10676 q^{68} -9.72788 q^{69} -2.93756 q^{70} -5.97215 q^{71} -0.323656 q^{72} -15.4990 q^{73} -4.52131 q^{74} -5.93733 q^{75} -7.03050 q^{76} -6.21010 q^{77} -5.36158 q^{78} +1.88349 q^{79} -2.93756 q^{80} -7.92428 q^{81} -1.19439 q^{82} -2.47075 q^{83} -1.63595 q^{84} -17.9390 q^{85} +2.16930 q^{86} -12.7104 q^{87} -6.21010 q^{88} +2.26844 q^{89} +0.950761 q^{90} +3.27734 q^{91} +5.94631 q^{92} -6.06855 q^{93} +5.87374 q^{94} +20.6525 q^{95} -1.63595 q^{96} +6.97793 q^{97} +1.00000 q^{98} +2.00994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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