LMFDB - Embedded newform 4034.2.a.c.1.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.927777 q^{3} +1.00000 q^{4} -3.45166 q^{5} -0.927777 q^{6} +0.589686 q^{7} -1.00000 q^{8} -2.13923 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.927777 q^{3} +1.00000 q^{4} -3.45166 q^{5} -0.927777 q^{6} +0.589686 q^{7} -1.00000 q^{8} -2.13923 q^{9} +3.45166 q^{10} -5.30168 q^{11} +0.927777 q^{12} +1.98898 q^{13} -0.589686 q^{14} -3.20237 q^{15} +1.00000 q^{16} +0.522791 q^{17} +2.13923 q^{18} +1.04791 q^{19} -3.45166 q^{20} +0.547097 q^{21} +5.30168 q^{22} -4.99430 q^{23} -0.927777 q^{24} +6.91394 q^{25} -1.98898 q^{26} -4.76806 q^{27} +0.589686 q^{28} +2.19585 q^{29} +3.20237 q^{30} +0.410576 q^{31} -1.00000 q^{32} -4.91878 q^{33} -0.522791 q^{34} -2.03539 q^{35} -2.13923 q^{36} -2.93689 q^{37} -1.04791 q^{38} +1.84533 q^{39} +3.45166 q^{40} -5.71116 q^{41} -0.547097 q^{42} +7.26593 q^{43} -5.30168 q^{44} +7.38389 q^{45} +4.99430 q^{46} -10.8346 q^{47} +0.927777 q^{48} -6.65227 q^{49} -6.91394 q^{50} +0.485033 q^{51} +1.98898 q^{52} +0.669315 q^{53} +4.76806 q^{54} +18.2996 q^{55} -0.589686 q^{56} +0.972223 q^{57} -2.19585 q^{58} +9.36509 q^{59} -3.20237 q^{60} -10.3129 q^{61} -0.410576 q^{62} -1.26147 q^{63} +1.00000 q^{64} -6.86529 q^{65} +4.91878 q^{66} -13.0153 q^{67} +0.522791 q^{68} -4.63359 q^{69} +2.03539 q^{70} +11.9500 q^{71} +2.13923 q^{72} +3.54953 q^{73} +2.93689 q^{74} +6.41459 q^{75} +1.04791 q^{76} -3.12633 q^{77} -1.84533 q^{78} +7.17793 q^{79} -3.45166 q^{80} +1.99400 q^{81} +5.71116 q^{82} -0.951994 q^{83} +0.547097 q^{84} -1.80450 q^{85} -7.26593 q^{86} +2.03726 q^{87} +5.30168 q^{88} +0.124806 q^{89} -7.38389 q^{90} +1.17287 q^{91} -4.99430 q^{92} +0.380923 q^{93} +10.8346 q^{94} -3.61701 q^{95} -0.927777 q^{96} +19.5848 q^{97} +6.65227 q^{98} +11.3415 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	0.927777	0.535652	0.267826	−	0.963467i	$-0.413695\pi$
$3$	0.927777	0.535652	0.267826	+	0.963467i	$0.413695\pi$
$4$	1.00000	0.500000
$5$	−3.45166	−1.54363	−0.771814	−	0.635848i	$-0.780650\pi$
$5$	−3.45166	−1.54363	−0.771814	+	0.635848i	$0.780650\pi$
$6$	−0.927777	−0.378763
$7$	0.589686	0.222880	0.111440	−	0.993771i	$-0.464454\pi$
$7$	0.589686	0.222880	0.111440	+	0.993771i	$0.464454\pi$
$8$	−1.00000	−0.353553
$9$	−2.13923	−0.713077
$10$	3.45166	1.09151
$11$	−5.30168	−1.59852	−0.799259	−	0.600987i	$-0.794774\pi$
$11$	−5.30168	−1.59852	−0.799259	+	0.600987i	$0.794774\pi$
$12$	0.927777	0.267826
$13$	1.98898	0.551644	0.275822	−	0.961209i	$-0.411050\pi$
$13$	1.98898	0.551644	0.275822	+	0.961209i	$0.411050\pi$
$14$	−0.589686	−0.157600
$15$	−3.20237	−0.826848
$16$	1.00000	0.250000
$17$	0.522791	0.126795	0.0633977	−	0.997988i	$-0.479806\pi$
$17$	0.522791	0.126795	0.0633977	+	0.997988i	$0.479806\pi$
$18$	2.13923	0.504221
$19$	1.04791	0.240406	0.120203	−	0.992749i	$-0.461645\pi$
$19$	1.04791	0.240406	0.120203	+	0.992749i	$0.461645\pi$
$20$	−3.45166	−0.771814
$21$	0.547097	0.119386
$22$	5.30168	1.13032
$23$	−4.99430	−1.04138	−0.520692	−	0.853745i	$-0.674326\pi$
$23$	−4.99430	−1.04138	−0.520692	+	0.853745i	$0.674326\pi$
$24$	−0.927777	−0.189382
$25$	6.91394	1.38279
$26$	−1.98898	−0.390072
$27$	−4.76806	−0.917613
$28$	0.589686	0.111440
$29$	2.19585	0.407759	0.203879	−	0.978996i	$-0.434645\pi$
$29$	2.19585	0.407759	0.203879	+	0.978996i	$0.434645\pi$
$30$	3.20237	0.584670
$31$	0.410576	0.0737416	0.0368708	−	0.999320i	$-0.488261\pi$
$31$	0.410576	0.0737416	0.0368708	+	0.999320i	$0.488261\pi$
$32$	−1.00000	−0.176777
$33$	−4.91878	−0.856249
$34$	−0.522791	−0.0896579
$35$	−2.03539	−0.344044
$36$	−2.13923	−0.356538
$37$	−2.93689	−0.482822	−0.241411	−	0.970423i	$-0.577610\pi$
$37$	−2.93689	−0.482822	−0.241411	+	0.970423i	$0.577610\pi$
$38$	−1.04791	−0.169993
$39$	1.84533	0.295489
$40$	3.45166	0.545755
$41$	−5.71116	−0.891933	−0.445967	−	0.895050i	$-0.647140\pi$
$41$	−5.71116	−0.891933	−0.445967	+	0.895050i	$0.647140\pi$
$42$	−0.547097	−0.0844189
$43$	7.26593	1.10804	0.554022	−	0.832502i	$-0.313092\pi$
$43$	7.26593	1.10804	0.554022	+	0.832502i	$0.313092\pi$
$44$	−5.30168	−0.799259
$45$	7.38389	1.10073
$46$	4.99430	0.736369
$47$	−10.8346	−1.58039	−0.790193	−	0.612858i	$-0.790020\pi$
$47$	−10.8346	−1.58039	−0.790193	+	0.612858i	$0.790020\pi$
$48$	0.927777	0.133913
$49$	−6.65227	−0.950324
$50$	−6.91394	−0.977779
$51$	0.485033	0.0679182
$52$	1.98898	0.275822
$53$	0.669315	0.0919374	0.0459687	−	0.998943i	$-0.485363\pi$
$53$	0.669315	0.0919374	0.0459687	+	0.998943i	$0.485363\pi$
$54$	4.76806	0.648850
$55$	18.2996	2.46752
$56$	−0.589686	−0.0788001
$57$	0.972223	0.128774
$58$	−2.19585	−0.288329
$59$	9.36509	1.21923	0.609616	−	0.792697i	$-0.291324\pi$
$59$	9.36509	1.21923	0.609616	+	0.792697i	$0.291324\pi$
$60$	−3.20237	−0.413424
$61$	−10.3129	−1.32043	−0.660216	−	0.751076i	$-0.729535\pi$
$61$	−10.3129	−1.32043	−0.660216	+	0.751076i	$0.729535\pi$
$62$	−0.410576	−0.0521432
$63$	−1.26147	−0.158931
$64$	1.00000	0.125000
$65$	−6.86529	−0.851534
$66$	4.91878	0.605460
$67$	−13.0153	−1.59007	−0.795034	−	0.606564i	$-0.792547\pi$
$67$	−13.0153	−1.59007	−0.795034	+	0.606564i	$0.792547\pi$
$68$	0.522791	0.0633977
$69$	−4.63359	−0.557819
$70$	2.03539	0.243276
$71$	11.9500	1.41821	0.709103	−	0.705105i	$-0.249100\pi$
$71$	11.9500	1.41821	0.709103	+	0.705105i	$0.249100\pi$
$72$	2.13923	0.252111
$73$	3.54953	0.415441	0.207721	−	0.978188i	$-0.433395\pi$
$73$	3.54953	0.415441	0.207721	+	0.978188i	$0.433395\pi$
$74$	2.93689	0.341407
$75$	6.41459	0.740694
$76$	1.04791	0.120203
$77$	−3.12633	−0.356278
$78$	−1.84533	−0.208943
$79$	7.17793	0.807580	0.403790	−	0.914852i	$-0.367693\pi$
$79$	7.17793	0.807580	0.403790	+	0.914852i	$0.367693\pi$
$80$	−3.45166	−0.385907
$81$	1.99400	0.221556
$82$	5.71116	0.630692
$83$	−0.951994	−0.104495	−0.0522475	−	0.998634i	$-0.516638\pi$
$83$	−0.951994	−0.104495	−0.0522475	+	0.998634i	$0.516638\pi$
$84$	0.547097	0.0596932
$85$	−1.80450	−0.195725
$86$	−7.26593	−0.783506
$87$	2.03726	0.218417
$88$	5.30168	0.565161
$89$	0.124806	0.0132294	0.00661469	−	0.999978i	$-0.497894\pi$
$89$	0.124806	0.0132294	0.00661469	+	0.999978i	$0.497894\pi$
$90$	−7.38389	−0.778331
$91$	1.17287	0.122951
$92$	−4.99430	−0.520692
$93$	0.380923	0.0394998
$94$	10.8346	1.11750
$95$	−3.61701	−0.371098
$96$	−0.927777	−0.0946908
$97$	19.5848	1.98854	0.994269	−	0.106908i	$-0.0340949\pi$
$97$	19.5848	1.98854	0.994269	+	0.106908i	$0.0340949\pi$
$98$	6.65227	0.671981
$99$	11.3415	1.13987
$100$	6.91394	0.691394
$101$	0.169471	0.0168630	0.00843152	−	0.999964i	$-0.497316\pi$
$101$	0.169471	0.0168630	0.00843152	+	0.999964i	$0.497316\pi$
$102$	−0.485033	−0.0480255
$103$	17.2295	1.69768	0.848838	−	0.528652i	$-0.177302\pi$
$103$	17.2295	1.69768	0.848838	+	0.528652i	$0.177302\pi$
$104$	−1.98898	−0.195036
$105$	−1.88839	−0.184288
$106$	−0.669315	−0.0650096
$107$	−6.75485	−0.653016	−0.326508	−	0.945194i	$-0.605872\pi$
$107$	−6.75485	−0.653016	−0.326508	+	0.945194i	$0.605872\pi$
$108$	−4.76806	−0.458807
$109$	−11.5270	−1.10409	−0.552043	−	0.833816i	$-0.686152\pi$
$109$	−11.5270	−1.10409	−0.552043	+	0.833816i	$0.686152\pi$
$110$	−18.2996	−1.74480
$111$	−2.72478	−0.258625
$112$	0.589686	0.0557201
$113$	2.81049	0.264388	0.132194	−	0.991224i	$-0.457798\pi$
$113$	2.81049	0.264388	0.132194	+	0.991224i	$0.457798\pi$
$114$	−0.972223	−0.0910570
$115$	17.2386	1.60751
$116$	2.19585	0.203879
$117$	−4.25489	−0.393365
$118$	−9.36509	−0.862127
$119$	0.308283	0.0282602
$120$	3.20237	0.292335
$121$	17.1078	1.55526
$122$	10.3129	0.933686
$123$	−5.29868	−0.477766
$124$	0.410576	0.0368708
$125$	−6.60628	−0.590883
$126$	1.26147	0.112381
$127$	11.6255	1.03160	0.515798	−	0.856710i	$-0.327495\pi$
$127$	11.6255	1.03160	0.515798	+	0.856710i	$0.327495\pi$
$128$	−1.00000	−0.0883883
$129$	6.74116	0.593526
$130$	6.86529	0.602125
$131$	3.96520	0.346441	0.173221	−	0.984883i	$-0.444583\pi$
$131$	3.96520	0.346441	0.173221	+	0.984883i	$0.444583\pi$
$132$	−4.91878	−0.428125
$133$	0.617936	0.0535818
$134$	13.0153	1.12435
$135$	16.4577	1.41645
$136$	−0.522791	−0.0448290
$137$	3.57336	0.305293	0.152646	−	0.988281i	$-0.451220\pi$
$137$	3.57336	0.305293	0.152646	+	0.988281i	$0.451220\pi$
$138$	4.63359	0.394438
$139$	9.68967	0.821867	0.410934	−	0.911665i	$-0.365203\pi$
$139$	9.68967	0.821867	0.410934	+	0.911665i	$0.365203\pi$
$140$	−2.03539	−0.172022
$141$	−10.0521	−0.846537
$142$	−11.9500	−1.00282
$143$	−10.5450	−0.881813
$144$	−2.13923	−0.178269
$145$	−7.57932	−0.629428
$146$	−3.54953	−0.293761
$147$	−6.17182	−0.509043
$148$	−2.93689	−0.241411
$149$	6.32358	0.518048	0.259024	−	0.965871i	$-0.416599\pi$
$149$	6.32358	0.518048	0.259024	+	0.965871i	$0.416599\pi$
$150$	−6.41459	−0.523749
$151$	2.61665	0.212940	0.106470	−	0.994316i	$-0.466045\pi$
$151$	2.61665	0.212940	0.106470	+	0.994316i	$0.466045\pi$
$152$	−1.04791	−0.0849964
$153$	−1.11837	−0.0904149
$154$	3.12633	0.251927
$155$	−1.41717	−0.113830
$156$	1.84533	0.147745
$157$	13.6224	1.08718	0.543592	−	0.839350i	$-0.317064\pi$
$157$	13.6224	1.08718	0.543592	+	0.839350i	$0.317064\pi$
$158$	−7.17793	−0.571045
$159$	0.620974	0.0492465
$160$	3.45166	0.272878
$161$	−2.94507	−0.232104
$162$	−1.99400	−0.156663
$163$	−9.51786	−0.745496	−0.372748	−	0.927933i	$-0.621584\pi$
$163$	−9.51786	−0.745496	−0.372748	+	0.927933i	$0.621584\pi$
$164$	−5.71116	−0.445967
$165$	16.9779	1.32173
$166$	0.951994	0.0738891
$167$	4.16223	0.322083	0.161042	−	0.986948i	$-0.448515\pi$
$167$	4.16223	0.322083	0.161042	+	0.986948i	$0.448515\pi$
$168$	−0.547097	−0.0422094
$169$	−9.04395	−0.695688
$170$	1.80450	0.138399
$171$	−2.24171	−0.171428
$172$	7.26593	0.554022
$173$	18.6998	1.42172	0.710859	−	0.703334i	$-0.248306\pi$
$173$	18.6998	1.42172	0.710859	+	0.703334i	$0.248306\pi$
$174$	−2.03726	−0.154444
$175$	4.07705	0.308196
$176$	−5.30168	−0.399629
$177$	8.68871	0.653084
$178$	−0.124806	−0.00935458
$179$	0.128325	0.00959147	0.00479573	−	0.999989i	$-0.498473\pi$
$179$	0.128325	0.00959147	0.00479573	+	0.999989i	$0.498473\pi$
$180$	7.38389	0.550363
$181$	−17.6258	−1.31012	−0.655058	−	0.755579i	$-0.727356\pi$
$181$	−17.6258	−1.31012	−0.655058	+	0.755579i	$0.727356\pi$
$182$	−1.17287	−0.0869393
$183$	−9.56806	−0.707292
$184$	4.99430	0.368185
$185$	10.1371	0.745298
$186$	−0.380923	−0.0279306
$187$	−2.77167	−0.202685
$188$	−10.8346	−0.790193
$189$	−2.81166	−0.204518
$190$	3.61701	0.262406
$191$	2.22507	0.161000	0.0805002	−	0.996755i	$-0.474348\pi$
$191$	2.22507	0.161000	0.0805002	+	0.996755i	$0.474348\pi$
$192$	0.927777	0.0669565
$193$	23.6676	1.70363	0.851817	−	0.523840i	$-0.175501\pi$
$193$	23.6676	1.70363	0.851817	+	0.523840i	$0.175501\pi$
$194$	−19.5848	−1.40611
$195$	−6.36945	−0.456126
$196$	−6.65227	−0.475162
$197$	15.5092	1.10498	0.552492	−	0.833518i	$-0.313677\pi$
$197$	15.5092	1.10498	0.552492	+	0.833518i	$0.313677\pi$
$198$	−11.3415	−0.806007
$199$	−8.66728	−0.614407	−0.307204	−	0.951644i	$-0.599393\pi$
$199$	−8.66728	−0.614407	−0.307204	+	0.951644i	$0.599393\pi$
$200$	−6.91394	−0.488890
$201$	−12.0753	−0.851724
$202$	−0.169471	−0.0119240
$203$	1.29486	0.0908814
$204$	0.485033	0.0339591
$205$	19.7130	1.37681
$206$	−17.2295	−1.20044
$207$	10.6840	0.742586
$208$	1.98898	0.137911
$209$	−5.55567	−0.384293
$210$	1.88839	0.130311
$211$	11.3147	0.778936	0.389468	−	0.921040i	$-0.372659\pi$
$211$	11.3147	0.778936	0.389468	+	0.921040i	$0.372659\pi$
$212$	0.669315	0.0459687
$213$	11.0869	0.759665
$214$	6.75485	0.461752
$215$	−25.0795	−1.71041
$216$	4.76806	0.324425
$217$	0.242111	0.0164356
$218$	11.5270	0.780707
$219$	3.29317	0.222532
$220$	18.2996	1.23376
$221$	1.03982	0.0699460
$222$	2.72478	0.182875
$223$	−12.5986	−0.843664	−0.421832	−	0.906674i	$-0.638613\pi$
$223$	−12.5986	−0.843664	−0.421832	+	0.906674i	$0.638613\pi$
$224$	−0.589686	−0.0394000
$225$	−14.7905	−0.986035
$226$	−2.81049	−0.186951
$227$	4.49511	0.298351	0.149176	−	0.988811i	$-0.452338\pi$
$227$	4.49511	0.298351	0.149176	+	0.988811i	$0.452338\pi$
$228$	0.972223	0.0643870
$229$	13.8588	0.915815	0.457908	−	0.889000i	$-0.348599\pi$
$229$	13.8588	0.915815	0.457908	+	0.889000i	$0.348599\pi$
$230$	−17.2386	−1.13668
$231$	−2.90053	−0.190841
$232$	−2.19585	−0.144164
$233$	9.81478	0.642987	0.321494	−	0.946912i	$-0.395815\pi$
$233$	9.81478	0.642987	0.321494	+	0.946912i	$0.395815\pi$
$234$	4.25489	0.278151
$235$	37.3973	2.43953
$236$	9.36509	0.609616
$237$	6.65951	0.432582
$238$	−0.308283	−0.0199830
$239$	−4.02400	−0.260291	−0.130145	−	0.991495i	$-0.541544\pi$
$239$	−4.02400	−0.260291	−0.130145	+	0.991495i	$0.541544\pi$
$240$	−3.20237	−0.206712
$241$	2.10613	0.135668	0.0678338	−	0.997697i	$-0.478391\pi$
$241$	2.10613	0.135668	0.0678338	+	0.997697i	$0.478391\pi$
$242$	−17.1078	−1.09973
$243$	16.1542	1.03629
$244$	−10.3129	−0.660216
$245$	22.9614	1.46695
$246$	5.29868	0.337832
$247$	2.08427	0.132619
$248$	−0.410576	−0.0260716
$249$	−0.883238	−0.0559729
$250$	6.60628	0.417818
$251$	0.325465	0.0205431	0.0102716	−	0.999947i	$-0.496730\pi$
$251$	0.325465	0.0205431	0.0102716	+	0.999947i	$0.496730\pi$
$252$	−1.26147	−0.0794654
$253$	26.4782	1.66467
$254$	−11.6255	−0.729449
$255$	−1.67417	−0.104841
$256$	1.00000	0.0625000
$257$	0.0484342	0.00302124	0.00151062	−	0.999999i	$-0.499519\pi$
$257$	0.0484342	0.00302124	0.00151062	+	0.999999i	$0.499519\pi$
$258$	−6.74116	−0.419686
$259$	−1.73184	−0.107612
$260$	−6.86529	−0.425767
$261$	−4.69743	−0.290763
$262$	−3.96520	−0.244971
$263$	8.59355	0.529901	0.264950	−	0.964262i	$-0.414644\pi$
$263$	8.59355	0.529901	0.264950	+	0.964262i	$0.414644\pi$
$264$	4.91878	0.302730
$265$	−2.31025	−0.141917
$266$	−0.617936	−0.0378881
$267$	0.115792	0.00708634
$268$	−13.0153	−0.795034
$269$	−16.8585	−1.02788	−0.513941	−	0.857825i	$-0.671815\pi$
$269$	−16.8585	−1.02788	−0.513941	+	0.857825i	$0.671815\pi$
$270$	−16.4577	−1.00158
$271$	−19.0763	−1.15880	−0.579401	−	0.815042i	$-0.696714\pi$
$271$	−19.0763	−1.15880	−0.579401	+	0.815042i	$0.696714\pi$
$272$	0.522791	0.0316989
$273$	1.08817	0.0658588
$274$	−3.57336	−0.215875
$275$	−36.6555	−2.21041
$276$	−4.63359	−0.278910
$277$	−18.0398	−1.08391	−0.541953	−	0.840409i	$-0.682315\pi$
$277$	−18.0398	−1.08391	−0.541953	+	0.840409i	$0.682315\pi$
$278$	−9.68967	−0.581148
$279$	−0.878317	−0.0525834
$280$	2.03539	0.121638
$281$	−0.733174	−0.0437375	−0.0218687	−	0.999761i	$-0.506962\pi$
$281$	−0.733174	−0.0437375	−0.0218687	+	0.999761i	$0.506962\pi$
$282$	10.0521	0.598592
$283$	29.4961	1.75336	0.876679	−	0.481075i	$-0.159754\pi$
$283$	29.4961	1.75336	0.876679	+	0.481075i	$0.159754\pi$
$284$	11.9500	0.709103
$285$	−3.35578	−0.198779
$286$	10.5450	0.623536
$287$	−3.36779	−0.198794
$288$	2.13923	0.126055
$289$	−16.7267	−0.983923
$290$	7.57932	0.445073
$291$	18.1703	1.06516
$292$	3.54953	0.207721
$293$	17.8156	1.04080	0.520400	−	0.853922i	$-0.325783\pi$
$293$	17.8156	1.04080	0.520400	+	0.853922i	$0.325783\pi$
$294$	6.17182	0.359948
$295$	−32.3251	−1.88204
$296$	2.93689	0.170703
$297$	25.2787	1.46682
$298$	−6.32358	−0.366315
$299$	−9.93357	−0.574473
$300$	6.41459	0.370347
$301$	4.28462	0.246961
$302$	−2.61665	−0.150571
$303$	0.157232	0.00903272
$304$	1.04791	0.0601015
$305$	35.5966	2.03825
$306$	1.11837	0.0639330
$307$	−33.3102	−1.90111	−0.950556	−	0.310553i	$-0.899486\pi$
$307$	−33.3102	−1.90111	−0.950556	+	0.310553i	$0.899486\pi$
$308$	−3.12633	−0.178139
$309$	15.9852	0.909364
$310$	1.41717	0.0804897
$311$	17.0259	0.965453	0.482726	−	0.875771i	$-0.339647\pi$
$311$	17.0259	0.965453	0.482726	+	0.875771i	$0.339647\pi$
$312$	−1.84533	−0.104471
$313$	−18.8173	−1.06362	−0.531809	−	0.846864i	$-0.678488\pi$
$313$	−18.8173	−1.06362	−0.531809	+	0.846864i	$0.678488\pi$
$314$	−13.6224	−0.768755
$315$	4.35418	0.245330
$316$	7.17793	0.403790
$317$	−13.9378	−0.782822	−0.391411	−	0.920216i	$-0.628013\pi$
$317$	−13.9378	−0.782822	−0.391411	+	0.920216i	$0.628013\pi$
$318$	−0.620974	−0.0348225
$319$	−11.6417	−0.651809
$320$	−3.45166	−0.192954
$321$	−6.26699	−0.349789
$322$	2.94507	0.164122
$323$	0.547836	0.0304824
$324$	1.99400	0.110778
$325$	13.7517	0.762808
$326$	9.51786	0.527145
$327$	−10.6945	−0.591406
$328$	5.71116	0.315346
$329$	−6.38900	−0.352237
$330$	−16.9779	−0.934605
$331$	2.15037	0.118195	0.0590976	−	0.998252i	$-0.481178\pi$
$331$	2.15037	0.118195	0.0590976	+	0.998252i	$0.481178\pi$
$332$	−0.951994	−0.0522475
$333$	6.28269	0.344289
$334$	−4.16223	−0.227747
$335$	44.9243	2.45448
$336$	0.547097	0.0298466
$337$	12.0123	0.654349	0.327175	−	0.944964i	$-0.393903\pi$
$337$	12.0123	0.654349	0.327175	+	0.944964i	$0.393903\pi$
$338$	9.04395	0.491926
$339$	2.60750	0.141620
$340$	−1.80450	−0.0978625
$341$	−2.17674	−0.117877
$342$	2.24171	0.121218
$343$	−8.05055	−0.434689
$344$	−7.26593	−0.391753
$345$	15.9936	0.861065
$346$	−18.6998	−1.00531
$347$	−1.87335	−0.100566	−0.0502832	−	0.998735i	$-0.516012\pi$
$347$	−1.87335	−0.100566	−0.0502832	+	0.998735i	$0.516012\pi$
$348$	2.03726	0.109208
$349$	15.3417	0.821223	0.410612	−	0.911810i	$-0.365315\pi$
$349$	15.3417	0.821223	0.410612	+	0.911810i	$0.365315\pi$
$350$	−4.07705	−0.217928
$351$	−9.48358	−0.506196
$352$	5.30168	0.282581
$353$	1.89989	0.101121	0.0505604	−	0.998721i	$-0.483899\pi$
$353$	1.89989	0.101121	0.0505604	+	0.998721i	$0.483899\pi$
$354$	−8.68871	−0.461800
$355$	−41.2474	−2.18918
$356$	0.124806	0.00661469
$357$	0.286017	0.0151376
$358$	−0.128325	−0.00678219
$359$	−28.9660	−1.52877	−0.764383	−	0.644763i	$-0.776956\pi$
$359$	−28.9660	−1.52877	−0.764383	+	0.644763i	$0.776956\pi$
$360$	−7.38389	−0.389165
$361$	−17.9019	−0.942205
$362$	17.6258	0.926392
$363$	15.8722	0.833077
$364$	1.17287	0.0614753
$365$	−12.2518	−0.641287
$366$	9.56806	0.500131
$367$	−30.1142	−1.57195	−0.785974	−	0.618259i	$-0.787838\pi$
$367$	−30.1142	−1.57195	−0.785974	+	0.618259i	$0.787838\pi$
$368$	−4.99430	−0.260346
$369$	12.2175	0.636017
$370$	−10.1371	−0.527005
$371$	0.394685	0.0204910
$372$	0.380923	0.0197499
$373$	30.8524	1.59748	0.798739	−	0.601678i	$-0.205501\pi$
$373$	30.8524	1.59748	0.798739	+	0.601678i	$0.205501\pi$
$374$	2.77167	0.143320
$375$	−6.12915	−0.316508
$376$	10.8346	0.558751
$377$	4.36750	0.224938
$378$	2.81166	0.144616
$379$	11.1536	0.572920	0.286460	−	0.958092i	$-0.407521\pi$
$379$	11.1536	0.572920	0.286460	+	0.958092i	$0.407521\pi$
$380$	−3.61701	−0.185549
$381$	10.7859	0.552577
$382$	−2.22507	−0.113844
$383$	−30.1266	−1.53940	−0.769700	−	0.638406i	$-0.779594\pi$
$383$	−30.1266	−1.53940	−0.769700	+	0.638406i	$0.779594\pi$
$384$	−0.927777	−0.0473454
$385$	10.7910	0.549961
$386$	−23.6676	−1.20465
$387$	−15.5435	−0.790121
$388$	19.5848	0.994269
$389$	7.90562	0.400831	0.200415	−	0.979711i	$-0.435771\pi$
$389$	7.90562	0.400831	0.200415	+	0.979711i	$0.435771\pi$
$390$	6.36945	0.322530
$391$	−2.61097	−0.132043
$392$	6.65227	0.335990
$393$	3.67882	0.185572
$394$	−15.5092	−0.781342
$395$	−24.7758	−1.24660
$396$	11.3415	0.569933
$397$	−14.9521	−0.750427	−0.375213	−	0.926938i	$-0.622431\pi$
$397$	−14.9521	−0.750427	−0.375213	+	0.926938i	$0.622431\pi$
$398$	8.66728	0.434452
$399$	0.573306	0.0287012
$400$	6.91394	0.345697
$401$	3.35271	0.167426	0.0837131	−	0.996490i	$-0.473322\pi$
$401$	3.35271	0.167426	0.0837131	+	0.996490i	$0.473322\pi$
$402$	12.0753	0.602260
$403$	0.816628	0.0406791
$404$	0.169471	0.00843152
$405$	−6.88260	−0.341999
$406$	−1.29486	−0.0642629
$407$	15.5705	0.771799
$408$	−0.485033	−0.0240127
$409$	0.220368	0.0108965	0.00544824	−	0.999985i	$-0.498266\pi$
$409$	0.220368	0.0108965	0.00544824	+	0.999985i	$0.498266\pi$
$410$	−19.7130	−0.973554
$411$	3.31528	0.163531
$412$	17.2295	0.848838
$413$	5.52246	0.271743
$414$	−10.6840	−0.525088
$415$	3.28596	0.161301
$416$	−1.98898	−0.0975179
$417$	8.98985	0.440235
$418$	5.55567	0.271736
$419$	3.39630	0.165920	0.0829602	−	0.996553i	$-0.473563\pi$
$419$	3.39630	0.165920	0.0829602	+	0.996553i	$0.473563\pi$
$420$	−1.88839	−0.0921440
$421$	12.9377	0.630545	0.315272	−	0.949001i	$-0.397904\pi$
$421$	12.9377	0.630545	0.315272	+	0.949001i	$0.397904\pi$
$422$	−11.3147	−0.550791
$423$	23.1777	1.12694
$424$	−0.669315	−0.0325048
$425$	3.61455	0.175331
$426$	−11.0869	−0.537164
$427$	−6.08137	−0.294298
$428$	−6.75485	−0.326508
$429$	−9.78336	−0.472345
$430$	25.0795	1.20944
$431$	24.6852	1.18905	0.594523	−	0.804079i	$-0.297341\pi$
$431$	24.6852	1.18905	0.594523	+	0.804079i	$0.297341\pi$
$432$	−4.76806	−0.229403
$433$	−25.6119	−1.23083	−0.615414	−	0.788204i	$-0.711011\pi$
$433$	−25.6119	−1.23083	−0.615414	+	0.788204i	$0.711011\pi$
$434$	−0.242111	−0.0116217
$435$	−7.03191	−0.337154
$436$	−11.5270	−0.552043
$437$	−5.23356	−0.250355
$438$	−3.29317	−0.157354
$439$	31.2649	1.49219	0.746097	−	0.665837i	$-0.231925\pi$
$439$	31.2649	1.49219	0.746097	+	0.665837i	$0.231925\pi$
$440$	−18.2996	−0.872399
$441$	14.2307	0.677654
$442$	−1.03982	−0.0494593
$443$	10.3556	0.492010	0.246005	−	0.969269i	$-0.420882\pi$
$443$	10.3556	0.492010	0.246005	+	0.969269i	$0.420882\pi$
$444$	−2.72478	−0.129312
$445$	−0.430787	−0.0204212
$446$	12.5986	0.596561
$447$	5.86687	0.277493
$448$	0.589686	0.0278600
$449$	6.78385	0.320149	0.160075	−	0.987105i	$-0.448826\pi$
$449$	6.78385	0.320149	0.160075	+	0.987105i	$0.448826\pi$
$450$	14.7905	0.697232
$451$	30.2788	1.42577
$452$	2.81049	0.132194
$453$	2.42767	0.114062
$454$	−4.49511	−0.210966
$455$	−4.04836	−0.189790
$456$	−0.972223	−0.0455285
$457$	36.6596	1.71486	0.857432	−	0.514597i	$-0.172058\pi$
$457$	36.6596	1.71486	0.857432	+	0.514597i	$0.172058\pi$
$458$	−13.8588	−0.647579
$459$	−2.49270	−0.116349
$460$	17.2386	0.803754
$461$	−2.20969	−0.102915	−0.0514577	−	0.998675i	$-0.516387\pi$
$461$	−2.20969	−0.102915	−0.0514577	+	0.998675i	$0.516387\pi$
$462$	2.90053	0.134945
$463$	−19.7784	−0.919182	−0.459591	−	0.888131i	$-0.652004\pi$
$463$	−19.7784	−0.919182	−0.459591	+	0.888131i	$0.652004\pi$
$464$	2.19585	0.101940
$465$	−1.31481	−0.0609731
$466$	−9.81478	−0.454661
$467$	−37.0844	−1.71606	−0.858030	−	0.513600i	$-0.828312\pi$
$467$	−37.0844	−1.71606	−0.858030	+	0.513600i	$0.828312\pi$
$468$	−4.25489	−0.196682
$469$	−7.67492	−0.354395
$470$	−37.3973	−1.72501
$471$	12.6385	0.582352
$472$	−9.36509	−0.431063
$473$	−38.5217	−1.77123
$474$	−6.65951	−0.305882
$475$	7.24516	0.332431
$476$	0.308283	0.0141301
$477$	−1.43182	−0.0655585
$478$	4.02400	0.184053
$479$	20.0291	0.915152	0.457576	−	0.889170i	$-0.348718\pi$
$479$	20.0291	0.915152	0.457576	+	0.889170i	$0.348718\pi$
$480$	3.20237	0.146167
$481$	−5.84143	−0.266346
$482$	−2.10613	−0.0959315
$483$	−2.73236	−0.124327
$484$	17.1078	0.777629
$485$	−67.6001	−3.06956
$486$	−16.1542	−0.732768
$487$	26.2778	1.19076	0.595380	−	0.803444i	$-0.297001\pi$
$487$	26.2778	1.19076	0.595380	+	0.803444i	$0.297001\pi$
$488$	10.3129	0.466843
$489$	−8.83044	−0.399326
$490$	−22.9614	−1.03729
$491$	6.65403	0.300292	0.150146	−	0.988664i	$-0.452026\pi$
$491$	6.65403	0.300292	0.150146	+	0.988664i	$0.452026\pi$
$492$	−5.29868	−0.238883
$493$	1.14797	0.0517020
$494$	−2.08427	−0.0937756
$495$	−39.1471	−1.75953
$496$	0.410576	0.0184354
$497$	7.04675	0.316090
$498$	0.883238	0.0395788
$499$	−15.6466	−0.700438	−0.350219	−	0.936668i	$-0.613893\pi$
$499$	−15.6466	−0.700438	−0.350219	+	0.936668i	$0.613893\pi$
$500$	−6.60628	−0.295442
$501$	3.86162	0.172524
$502$	−0.325465	−0.0145262
$503$	42.9990	1.91723	0.958615	−	0.284704i	$-0.0918954\pi$
$503$	42.9990	1.91723	0.958615	+	0.284704i	$0.0918954\pi$
$504$	1.26147	0.0561905
$505$	−0.584957	−0.0260303
$506$	−26.4782	−1.17710
$507$	−8.39076	−0.372647
$508$	11.6255	0.515798
$509$	−16.8836	−0.748350	−0.374175	−	0.927358i	$-0.622074\pi$
$509$	−16.8836	−0.748350	−0.374175	+	0.927358i	$0.622074\pi$
$510$	1.67417	0.0741335
$511$	2.09311	0.0925937
$512$	−1.00000	−0.0441942
$513$	−4.99648	−0.220600
$514$	−0.0484342	−0.00213634
$515$	−59.4705	−2.62058
$516$	6.74116	0.296763
$517$	57.4415	2.52627
$518$	1.73184	0.0760929
$519$	17.3492	0.761546
$520$	6.86529	0.301063
$521$	16.8958	0.740221	0.370110	−	0.928988i	$-0.379320\pi$
$521$	16.8958	0.740221	0.370110	+	0.928988i	$0.379320\pi$
$522$	4.69743	0.205601
$523$	2.48584	0.108698	0.0543492	−	0.998522i	$-0.482692\pi$
$523$	2.48584	0.108698	0.0543492	+	0.998522i	$0.482692\pi$
$524$	3.96520	0.173221
$525$	3.78260	0.165086
$526$	−8.59355	−0.374696
$527$	0.214645	0.00935010
$528$	−4.91878	−0.214062
$529$	1.94302	0.0844792
$530$	2.31025	0.100351
$531$	−20.0341	−0.869406
$532$	0.617936	0.0267909
$533$	−11.3594	−0.492030
$534$	−0.115792	−0.00501080
$535$	23.3154	1.00801
$536$	13.0153	0.562174
$537$	0.119057	0.00513769
$538$	16.8585	0.726823
$539$	35.2682	1.51911
$540$	16.4577	0.708227
$541$	−23.9580	−1.03004	−0.515018	−	0.857179i	$-0.672215\pi$
$541$	−23.9580	−1.03004	−0.515018	+	0.857179i	$0.672215\pi$
$542$	19.0763	0.819397
$543$	−16.3528	−0.701766
$544$	−0.522791	−0.0224145
$545$	39.7872	1.70430
$546$	−1.08817	−0.0465692
$547$	25.5457	1.09226	0.546128	−	0.837702i	$-0.316101\pi$
$547$	25.5457	1.09226	0.546128	+	0.837702i	$0.316101\pi$
$548$	3.57336	0.152646
$549$	22.0617	0.941569
$550$	36.6555	1.56300
$551$	2.30104	0.0980277
$552$	4.63359	0.197219
$553$	4.23272	0.179994
$554$	18.0398	0.766437
$555$	9.40501	0.399220
$556$	9.68967	0.410934
$557$	1.58932	0.0673417	0.0336708	−	0.999433i	$-0.489280\pi$
$557$	1.58932	0.0673417	0.0336708	+	0.999433i	$0.489280\pi$
$558$	0.878317	0.0371821
$559$	14.4518	0.611247
$560$	−2.03539	−0.0860111
$561$	−2.57149	−0.108568
$562$	0.733174	0.0309271
$563$	9.95545	0.419572	0.209786	−	0.977747i	$-0.432723\pi$
$563$	9.95545	0.419572	0.209786	+	0.977747i	$0.432723\pi$
$564$	−10.0521	−0.423269
$565$	−9.70084	−0.408118
$566$	−29.4961	−1.23981
$567$	1.17583	0.0493804
$568$	−11.9500	−0.501411
$569$	25.7774	1.08065	0.540323	−	0.841458i	$-0.318302\pi$
$569$	25.7774	1.08065	0.540323	+	0.841458i	$0.318302\pi$
$570$	3.35578	0.140558
$571$	−13.4098	−0.561184	−0.280592	−	0.959827i	$-0.590531\pi$
$571$	−13.4098	−0.561184	−0.280592	+	0.959827i	$0.590531\pi$
$572$	−10.5450	−0.440907
$573$	2.06437	0.0862401
$574$	3.36779	0.140569
$575$	−34.5303	−1.44001
$576$	−2.13923	−0.0891346
$577$	−31.5064	−1.31163	−0.655814	−	0.754922i	$-0.727675\pi$
$577$	−31.5064	−1.31163	−0.655814	+	0.754922i	$0.727675\pi$
$578$	16.7267	0.695739
$579$	21.9583	0.912555
$580$	−7.57932	−0.314714
$581$	−0.561378	−0.0232899
$582$	−18.1703	−0.753185
$583$	−3.54849	−0.146964
$584$	−3.54953	−0.146881
$585$	14.6864	0.607209
$586$	−17.8156	−0.735957
$587$	−19.1676	−0.791131	−0.395566	−	0.918438i	$-0.629451\pi$
$587$	−19.1676	−0.791131	−0.395566	+	0.918438i	$0.629451\pi$
$588$	−6.17182	−0.254522
$589$	0.430245	0.0177279
$590$	32.3251	1.33080
$591$	14.3891	0.591887
$592$	−2.93689	−0.120706
$593$	−36.4608	−1.49727	−0.748633	−	0.662985i	$-0.769289\pi$
$593$	−36.4608	−1.49727	−0.748633	+	0.662985i	$0.769289\pi$
$594$	−25.2787	−1.03720
$595$	−1.06409	−0.0436233
$596$	6.32358	0.259024
$597$	−8.04130	−0.329109
$598$	9.93357	0.406214
$599$	26.1193	1.06721	0.533604	−	0.845735i	$-0.320837\pi$
$599$	26.1193	1.06721	0.533604	+	0.845735i	$0.320837\pi$
$600$	−6.41459	−0.261875
$601$	13.7785	0.562037	0.281019	−	0.959702i	$-0.409328\pi$
$601$	13.7785	0.562037	0.281019	+	0.959702i	$0.409328\pi$
$602$	−4.28462	−0.174628
$603$	27.8427	1.13384
$604$	2.61665	0.106470
$605$	−59.0504	−2.40074
$606$	−0.157232	−0.00638710
$607$	41.5053	1.68465	0.842325	−	0.538971i	$-0.181187\pi$
$607$	41.5053	1.68465	0.842325	+	0.538971i	$0.181187\pi$
$608$	−1.04791	−0.0424982
$609$	1.20134	0.0486808
$610$	−35.5966	−1.44126
$611$	−21.5498	−0.871811
$612$	−1.11837	−0.0452075
$613$	9.13138	0.368813	0.184406	−	0.982850i	$-0.440964\pi$
$613$	9.13138	0.368813	0.184406	+	0.982850i	$0.440964\pi$
$614$	33.3102	1.34429
$615$	18.2892	0.737493
$616$	3.12633	0.125963
$617$	2.84178	0.114406	0.0572029	−	0.998363i	$-0.481782\pi$
$617$	2.84178	0.114406	0.0572029	+	0.998363i	$0.481782\pi$
$618$	−15.9852	−0.643018
$619$	−40.9486	−1.64586	−0.822932	−	0.568140i	$-0.807663\pi$
$619$	−40.9486	−1.64586	−0.822932	+	0.568140i	$0.807663\pi$
$620$	−1.41717	−0.0569148
$621$	23.8131	0.955587
$622$	−17.0259	−0.682678
$623$	0.0735962	0.00294857
$624$	1.84533	0.0738724
$625$	−11.7671	−0.470684
$626$	18.8173	0.752091
$627$	−5.15442	−0.205848
$628$	13.6224	0.543592
$629$	−1.53538	−0.0612196
$630$	−4.35418	−0.173475
$631$	20.8630	0.830545	0.415272	−	0.909697i	$-0.363686\pi$
$631$	20.8630	0.830545	0.415272	+	0.909697i	$0.363686\pi$
$632$	−7.17793	−0.285523
$633$	10.4975	0.417239
$634$	13.9378	0.553539
$635$	−40.1273	−1.59240
$636$	0.620974	0.0246232
$637$	−13.2312	−0.524241
$638$	11.6417	0.460899
$639$	−25.5638	−1.01129
$640$	3.45166	0.136439
$641$	−36.1975	−1.42971	−0.714857	−	0.699271i	$-0.753508\pi$
$641$	−36.1975	−1.42971	−0.714857	+	0.699271i	$0.753508\pi$
$642$	6.26699	0.247338
$643$	26.0150	1.02593	0.512965	−	0.858410i	$-0.328547\pi$
$643$	26.0150	1.02593	0.512965	+	0.858410i	$0.328547\pi$
$644$	−2.94507	−0.116052
$645$	−23.2682	−0.916184
$646$	−0.547836	−0.0215543
$647$	42.1836	1.65841	0.829204	−	0.558946i	$-0.188794\pi$
$647$	42.1836	1.65841	0.829204	+	0.558946i	$0.188794\pi$
$648$	−1.99400	−0.0783317
$649$	−49.6507	−1.94896
$650$	−13.7517	−0.539386
$651$	0.224625	0.00880374
$652$	−9.51786	−0.372748
$653$	−2.32598	−0.0910225	−0.0455112	−	0.998964i	$-0.514492\pi$
$653$	−2.32598	−0.0910225	−0.0455112	+	0.998964i	$0.514492\pi$
$654$	10.6945	0.418187
$655$	−13.6865	−0.534776
$656$	−5.71116	−0.222983
$657$	−7.59327	−0.296242
$658$	6.38900	0.249069
$659$	−38.4921	−1.49944	−0.749720	−	0.661755i	$-0.769812\pi$
$659$	−38.4921	−1.49944	−0.749720	+	0.661755i	$0.769812\pi$
$660$	16.9779	0.660865
$661$	−30.6182	−1.19091	−0.595454	−	0.803389i	$-0.703028\pi$
$661$	−30.6182	−1.19091	−0.595454	+	0.803389i	$0.703028\pi$
$662$	−2.15037	−0.0835766
$663$	0.964723	0.0374667
$664$	0.951994	0.0369445
$665$	−2.13290	−0.0827104
$666$	−6.28269	−0.243449
$667$	−10.9667	−0.424633
$668$	4.16223	0.161042
$669$	−11.6887	−0.451910
$670$	−44.9243	−1.73558
$671$	54.6757	2.11073
$672$	−0.547097	−0.0211047
$673$	14.4067	0.555339	0.277669	−	0.960677i	$-0.410438\pi$
$673$	14.4067	0.555339	0.277669	+	0.960677i	$0.410438\pi$
$674$	−12.0123	−0.462695
$675$	−32.9661	−1.26886
$676$	−9.04395	−0.347844
$677$	45.5222	1.74956	0.874779	−	0.484522i	$-0.161006\pi$
$677$	45.5222	1.74956	0.874779	+	0.484522i	$0.161006\pi$
$678$	−2.60750	−0.100141
$679$	11.5489	0.443206
$680$	1.80450	0.0691993
$681$	4.17046	0.159812
$682$	2.17674	0.0833518
$683$	−27.0972	−1.03685	−0.518424	−	0.855124i	$-0.673481\pi$
$683$	−27.0972	−1.03685	−0.518424	+	0.855124i	$0.673481\pi$
$684$	−2.24171	−0.0857140
$685$	−12.3340	−0.471259
$686$	8.05055	0.307371
$687$	12.8579	0.490558
$688$	7.26593	0.277011
$689$	1.33125	0.0507168
$690$	−15.9936	−0.608865
$691$	30.1163	1.14568	0.572839	−	0.819668i	$-0.305842\pi$
$691$	30.1163	1.14568	0.572839	+	0.819668i	$0.305842\pi$
$692$	18.6998	0.710859
$693$	6.68794	0.254054
$694$	1.87335	0.0711112
$695$	−33.4454	−1.26866
$696$	−2.03726	−0.0772220
$697$	−2.98574	−0.113093
$698$	−15.3417	−0.580692
$699$	9.10592	0.344418
$700$	4.07705	0.154098
$701$	39.4946	1.49169	0.745844	−	0.666120i	$-0.232046\pi$
$701$	39.4946	1.49169	0.745844	+	0.666120i	$0.232046\pi$
$702$	9.48358	0.357935
$703$	−3.07759	−0.116073
$704$	−5.30168	−0.199815
$705$	34.6963	1.30674
$706$	−1.89989	−0.0715031
$707$	0.0999349	0.00375844
$708$	8.68871	0.326542
$709$	37.7000	1.41585	0.707927	−	0.706285i	$-0.249630\pi$
$709$	37.7000	1.41585	0.707927	+	0.706285i	$0.249630\pi$
$710$	41.2474	1.54799
$711$	−15.3552	−0.575867
$712$	−0.124806	−0.00467729
$713$	−2.05054	−0.0767933
$714$	−0.286017	−0.0107039
$715$	36.3976	1.36119
$716$	0.128325	0.00479573
$717$	−3.73337	−0.139425
$718$	28.9660	1.08100
$719$	31.1201	1.16058	0.580292	−	0.814408i	$-0.302938\pi$
$719$	31.1201	1.16058	0.580292	+	0.814408i	$0.302938\pi$
$720$	7.38389	0.275181
$721$	10.1600	0.378379
$722$	17.9019	0.666239
$723$	1.95402	0.0726706
$724$	−17.6258	−0.655058
$725$	15.1820	0.563844
$726$	−15.8722	−0.589074
$727$	−30.1784	−1.11926	−0.559628	−	0.828744i	$-0.689056\pi$
$727$	−30.1784	−1.11926	−0.559628	+	0.828744i	$0.689056\pi$
$728$	−1.17287	−0.0434696
$729$	9.00545	0.333535
$730$	12.2518	0.453458
$731$	3.79857	0.140495
$732$	−9.56806	−0.353646
$733$	4.79965	0.177279	0.0886395	−	0.996064i	$-0.471748\pi$
$733$	4.79965	0.177279	0.0886395	+	0.996064i	$0.471748\pi$
$734$	30.1142	1.11154
$735$	21.3030	0.785774
$736$	4.99430	0.184092
$737$	69.0028	2.54175
$738$	−12.2175	−0.449732
$739$	−1.59539	−0.0586873	−0.0293437	−	0.999569i	$-0.509342\pi$
$739$	−1.59539	−0.0586873	−0.0293437	+	0.999569i	$0.509342\pi$
$740$	10.1371	0.372649
$741$	1.93373	0.0710375
$742$	−0.394685	−0.0144894
$743$	15.6287	0.573360	0.286680	−	0.958026i	$-0.407448\pi$
$743$	15.6287	0.573360	0.286680	+	0.958026i	$0.407448\pi$
$744$	−0.380923	−0.0139653
$745$	−21.8268	−0.799674
$746$	−30.8524	−1.12959
$747$	2.03654	0.0745129
$748$	−2.77167	−0.101342
$749$	−3.98324	−0.145544
$750$	6.12915	0.223805
$751$	−10.5907	−0.386461	−0.193231	−	0.981153i	$-0.561897\pi$
$751$	−10.5907	−0.386461	−0.193231	+	0.981153i	$0.561897\pi$
$752$	−10.8346	−0.395097
$753$	0.301958	0.0110040
$754$	−4.36750	−0.159055
$755$	−9.03178	−0.328700
$756$	−2.81166	−0.102259
$757$	30.8558	1.12147	0.560737	−	0.827994i	$-0.310518\pi$
$757$	30.8558	1.12147	0.560737	+	0.827994i	$0.310518\pi$
$758$	−11.1536	−0.405116
$759$	24.5658	0.891684
$760$	3.61701	0.131203
$761$	4.38843	0.159080	0.0795401	−	0.996832i	$-0.474655\pi$
$761$	4.38843	0.159080	0.0795401	+	0.996832i	$0.474655\pi$
$762$	−10.7859	−0.390731
$763$	−6.79731	−0.246079
$764$	2.22507	0.0805002
$765$	3.86023	0.139567
$766$	30.1266	1.08852
$767$	18.6270	0.672582
$768$	0.927777	0.0334783
$769$	4.89228	0.176420	0.0882100	−	0.996102i	$-0.471885\pi$
$769$	4.89228	0.176420	0.0882100	+	0.996102i	$0.471885\pi$
$770$	−10.7910	−0.388881
$771$	0.0449361	0.00161833
$772$	23.6676	0.851817
$773$	−15.0180	−0.540159	−0.270079	−	0.962838i	$-0.587050\pi$
$773$	−15.0180	−0.540159	−0.270079	+	0.962838i	$0.587050\pi$
$774$	15.5435	0.558700
$775$	2.83870	0.101969
$776$	−19.5848	−0.703054
$777$	−1.60676	−0.0576423
$778$	−7.90562	−0.283430
$779$	−5.98476	−0.214426
$780$	−6.36945	−0.228063
$781$	−63.3552	−2.26703
$782$	2.61097	0.0933683
$783$	−10.4699	−0.374165
$784$	−6.65227	−0.237581
$785$	−47.0198	−1.67821
$786$	−3.67882	−0.131219
$787$	−10.9200	−0.389256	−0.194628	−	0.980877i	$-0.562350\pi$
$787$	−10.9200	−0.389256	−0.194628	+	0.980877i	$0.562350\pi$
$788$	15.5092	0.552492
$789$	7.97289	0.283842
$790$	24.7758	0.881482
$791$	1.65731	0.0589270
$792$	−11.3415	−0.403003
$793$	−20.5122	−0.728408
$794$	14.9521	0.530632
$795$	−2.14339	−0.0760183
$796$	−8.66728	−0.307204
$797$	−30.9971	−1.09797	−0.548987	−	0.835831i	$-0.684986\pi$
$797$	−30.9971	−1.09797	−0.548987	+	0.835831i	$0.684986\pi$
$798$	−0.573306	−0.0202948
$799$	−5.66422	−0.200386
$800$	−6.91394	−0.244445
$801$	−0.266988	−0.00943357
$802$	−3.35271	−0.118388
$803$	−18.8185	−0.664090
$804$	−12.0753	−0.425862
$805$	10.1654	0.358282
$806$	−0.816628	−0.0287645
$807$	−15.6409	−0.550587
$808$	−0.169471	−0.00596198
$809$	3.98077	0.139957	0.0699783	−	0.997549i	$-0.477707\pi$
$809$	3.98077	0.139957	0.0699783	+	0.997549i	$0.477707\pi$
$810$	6.88260	0.241830
$811$	−39.1587	−1.37505	−0.687524	−	0.726162i	$-0.741302\pi$
$811$	−39.1587	−1.37505	−0.687524	+	0.726162i	$0.741302\pi$
$812$	1.29486	0.0454407
$813$	−17.6985	−0.620715
$814$	−15.5705	−0.545745
$815$	32.8524	1.15077
$816$	0.485033	0.0169796
$817$	7.61402	0.266381
$818$	−0.220368	−0.00770498
$819$	−2.50905	−0.0876733
$820$	19.7130	0.688407
$821$	−41.1159	−1.43496	−0.717478	−	0.696581i	$-0.754704\pi$
$821$	−41.1159	−1.43496	−0.717478	+	0.696581i	$0.754704\pi$
$822$	−3.31528	−0.115634
$823$	25.8231	0.900136	0.450068	−	0.892994i	$-0.351400\pi$
$823$	25.8231	0.900136	0.450068	+	0.892994i	$0.351400\pi$
$824$	−17.2295	−0.600219
$825$	−34.0081	−1.18401
$826$	−5.52246	−0.192151
$827$	35.1323	1.22167	0.610835	−	0.791758i	$-0.290834\pi$
$827$	35.1323	1.22167	0.610835	+	0.791758i	$0.290834\pi$
$828$	10.6840	0.371293
$829$	3.67637	0.127686	0.0638428	−	0.997960i	$-0.479664\pi$
$829$	3.67637	0.127686	0.0638428	+	0.997960i	$0.479664\pi$
$830$	−3.28596	−0.114057
$831$	−16.7369	−0.580596
$832$	1.98898	0.0689556
$833$	−3.47775	−0.120497
$834$	−8.98985	−0.311293
$835$	−14.3666	−0.497177
$836$	−5.55567	−0.192147
$837$	−1.95765	−0.0676663
$838$	−3.39630	−0.117323
$839$	−1.80741	−0.0623987	−0.0311994	−	0.999513i	$-0.509933\pi$
$839$	−1.80741	−0.0623987	−0.0311994	+	0.999513i	$0.509933\pi$
$840$	1.88839	0.0651557
$841$	−24.1783	−0.833733
$842$	−12.9377	−0.445863
$843$	−0.680221	−0.0234281
$844$	11.3147	0.389468
$845$	31.2166	1.07388
$846$	−23.1777	−0.796865
$847$	10.0882	0.346636
$848$	0.669315	0.0229844
$849$	27.3658	0.939190
$850$	−3.61455	−0.123978
$851$	14.6677	0.502803
$852$	11.0869	0.379832
$853$	−30.0222	−1.02794	−0.513970	−	0.857808i	$-0.671826\pi$
$853$	−30.0222	−1.02794	−0.513970	+	0.857808i	$0.671826\pi$
$854$	6.08137	0.208100
$855$	7.73763	0.264621
$856$	6.75485	0.230876
$857$	−28.2645	−0.965496	−0.482748	−	0.875759i	$-0.660361\pi$
$857$	−28.2645	−0.965496	−0.482748	+	0.875759i	$0.660361\pi$
$858$	9.78336	0.333998
$859$	−25.3082	−0.863505	−0.431753	−	0.901992i	$-0.642105\pi$
$859$	−25.3082	−0.863505	−0.431753	+	0.901992i	$0.642105\pi$
$860$	−25.0795	−0.855204
$861$	−3.12456	−0.106485
$862$	−24.6852	−0.840782
$863$	−20.3150	−0.691532	−0.345766	−	0.938321i	$-0.612381\pi$
$863$	−20.3150	−0.691532	−0.345766	+	0.938321i	$0.612381\pi$
$864$	4.76806	0.162213
$865$	−64.5453	−2.19461
$866$	25.6119	0.870327
$867$	−15.5186	−0.527040
$868$	0.242111	0.00821778
$869$	−38.0551	−1.29093
$870$	7.03191	0.238404
$871$	−25.8871	−0.877153
$872$	11.5270	0.390353
$873$	−41.8965	−1.41798
$874$	5.23356	0.177028
$875$	−3.89563	−0.131696
$876$	3.29317	0.111266
$877$	−12.9088	−0.435899	−0.217949	−	0.975960i	$-0.569937\pi$
$877$	−12.9088	−0.435899	−0.217949	+	0.975960i	$0.569937\pi$
$878$	−31.2649	−1.05514
$879$	16.5289	0.557507
$880$	18.2996	0.616879
$881$	24.7251	0.833011	0.416505	−	0.909133i	$-0.363255\pi$
$881$	24.7251	0.833011	0.416505	+	0.909133i	$0.363255\pi$
$882$	−14.2307	−0.479174
$883$	12.1409	0.408573	0.204287	−	0.978911i	$-0.434513\pi$
$883$	12.1409	0.408573	0.204287	+	0.978911i	$0.434513\pi$
$884$	1.03982	0.0349730
$885$	−29.9905	−1.00812
$886$	−10.3556	−0.347904
$887$	−20.9009	−0.701783	−0.350891	−	0.936416i	$-0.614121\pi$
$887$	−20.9009	−0.701783	−0.350891	+	0.936416i	$0.614121\pi$
$888$	2.72478	0.0914376
$889$	6.85540	0.229923
$890$	0.430787	0.0144400
$891$	−10.5716	−0.354160
$892$	−12.5986	−0.421832
$893$	−11.3536	−0.379935
$894$	−5.86687	−0.196218
$895$	−0.442934	−0.0148057
$896$	−0.589686	−0.0197000
$897$	−9.21614	−0.307718
$898$	−6.78385	−0.226380
$899$	0.901562	0.0300688
$900$	−14.7905	−0.493017
$901$	0.349912	0.0116572
$902$	−30.2788	−1.00817
$903$	3.97517	0.132285
$904$	−2.81049	−0.0934754
$905$	60.8383	2.02233
$906$	−2.42767	−0.0806538
$907$	5.44321	0.180739	0.0903694	−	0.995908i	$-0.471195\pi$
$907$	5.44321	0.180739	0.0903694	+	0.995908i	$0.471195\pi$
$908$	4.49511	0.149176
$909$	−0.362538	−0.0120246
$910$	4.04836	0.134202
$911$	45.5070	1.50772	0.753858	−	0.657037i	$-0.228191\pi$
$911$	45.5070	1.50772	0.753858	+	0.657037i	$0.228191\pi$
$912$	0.972223	0.0321935
$913$	5.04717	0.167037
$914$	−36.6596	−1.21259
$915$	33.0257	1.09180
$916$	13.8588	0.457908
$917$	2.33822	0.0772149
$918$	2.49270	0.0822713
$919$	−26.5150	−0.874649	−0.437324	−	0.899304i	$-0.644074\pi$
$919$	−26.5150	−0.874649	−0.437324	+	0.899304i	$0.644074\pi$
$920$	−17.2386	−0.568340
$921$	−30.9044	−1.01833
$922$	2.20969	0.0727721
$923$	23.7684	0.782345
$924$	−2.90053	−0.0954205
$925$	−20.3055	−0.667641
$926$	19.7784	0.649960
$927$	−36.8580	−1.21057
$928$	−2.19585	−0.0720822
$929$	26.7219	0.876716	0.438358	−	0.898800i	$-0.355560\pi$
$929$	26.7219	0.876716	0.438358	+	0.898800i	$0.355560\pi$
$930$	1.31481	0.0431145
$931$	−6.97096	−0.228464
$932$	9.81478	0.321494
$933$	15.7963	0.517147
$934$	37.0844	1.21344
$935$	9.56686	0.312870
$936$	4.25489	0.139075
$937$	−8.01622	−0.261878	−0.130939	−	0.991390i	$-0.541799\pi$
$937$	−8.01622	−0.261878	−0.130939	+	0.991390i	$0.541799\pi$
$938$	7.67492	0.250595
$939$	−17.4583	−0.569729
$940$	37.3973	1.21976
$941$	46.9218	1.52961	0.764804	−	0.644263i	$-0.222836\pi$
$941$	46.9218	1.52961	0.764804	+	0.644263i	$0.222836\pi$
$942$	−12.6385	−0.411785
$943$	28.5232	0.928845
$944$	9.36509	0.304808
$945$	9.70488	0.315700
$946$	38.5217	1.25245
$947$	−0.178004	−0.00578434	−0.00289217	−	0.999996i	$-0.500921\pi$
$947$	−0.178004	−0.00578434	−0.00289217	+	0.999996i	$0.500921\pi$
$948$	6.65951	0.216291
$949$	7.05996	0.229176
$950$	−7.24516	−0.235064
$951$	−12.9311	−0.419320
$952$	−0.308283	−0.00999149
$953$	−51.6272	−1.67237	−0.836184	−	0.548449i	$-0.815219\pi$
$953$	−51.6272	−1.67237	−0.836184	+	0.548449i	$0.815219\pi$
$954$	1.43182	0.0463568
$955$	−7.68018	−0.248525
$956$	−4.02400	−0.130145
$957$	−10.8009	−0.349143
$958$	−20.0291	−0.647110
$959$	2.10716	0.0680438
$960$	−3.20237	−0.103356
$961$	−30.8314	−0.994562
$962$	5.84143	0.188335
$963$	14.4502	0.465650
$964$	2.10613	0.0678338
$965$	−81.6926	−2.62978
$966$	2.73236	0.0879124
$967$	−43.6010	−1.40211	−0.701057	−	0.713105i	$-0.747288\pi$
$967$	−43.6010	−1.40211	−0.701057	+	0.713105i	$0.747288\pi$
$968$	−17.1078	−0.549867
$969$	0.508269	0.0163280
$970$	67.6001	2.17051
$971$	−9.30053	−0.298468	−0.149234	−	0.988802i	$-0.547681\pi$
$971$	−9.30053	−0.298468	−0.149234	+	0.988802i	$0.547681\pi$
$972$	16.1542	0.518145
$973$	5.71386	0.183178
$974$	−26.2778	−0.841995
$975$	12.7585	0.408599
$976$	−10.3129	−0.330108
$977$	−0.236247	−0.00755821	−0.00377910	−	0.999993i	$-0.501203\pi$
$977$	−0.236247	−0.00755821	−0.00377910	+	0.999993i	$0.501203\pi$
$978$	8.83044	0.282366
$979$	−0.661680	−0.0211474
$980$	22.9614	0.733474
$981$	24.6589	0.787298
$982$	−6.65403	−0.212339
$983$	−26.7852	−0.854316	−0.427158	−	0.904177i	$-0.640485\pi$
$983$	−26.7852	−0.854316	−0.427158	+	0.904177i	$0.640485\pi$
$984$	5.29868	0.168916
$985$	−53.5325	−1.70569
$986$	−1.14797	−0.0365588
$987$	−5.92757	−0.188676
$988$	2.08427	0.0663094
$989$	−36.2882	−1.15390
$990$	39.1471	1.24417
$991$	5.62965	0.178832	0.0894159	−	0.995994i	$-0.471500\pi$
$991$	5.62965	0.178832	0.0894159	+	0.995994i	$0.471500\pi$
$992$	−0.410576	−0.0130358
$993$	1.99507	0.0633115
$994$	−7.04675	−0.223509
$995$	29.9165	0.948417
$996$	−0.883238	−0.0279865
$997$	24.8974	0.788509	0.394254	−	0.919001i	$-0.371003\pi$
$997$	24.8974	0.788509	0.394254	+	0.919001i	$0.371003\pi$
$998$	15.6466	0.495284
$999$	14.0033	0.443044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.30	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.30	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.927777 q^{3} +1.00000 q^{4} -3.45166 q^{5} -0.927777 q^{6} +0.589686 q^{7} -1.00000 q^{8} -2.13923 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.927777 q^{3} +1.00000 q^{4} -3.45166 q^{5} -0.927777 q^{6} +0.589686 q^{7} -1.00000 q^{8} -2.13923 q^{9} +3.45166 q^{10} -5.30168 q^{11} +0.927777 q^{12} +1.98898 q^{13} -0.589686 q^{14} -3.20237 q^{15} +1.00000 q^{16} +0.522791 q^{17} +2.13923 q^{18} +1.04791 q^{19} -3.45166 q^{20} +0.547097 q^{21} +5.30168 q^{22} -4.99430 q^{23} -0.927777 q^{24} +6.91394 q^{25} -1.98898 q^{26} -4.76806 q^{27} +0.589686 q^{28} +2.19585 q^{29} +3.20237 q^{30} +0.410576 q^{31} -1.00000 q^{32} -4.91878 q^{33} -0.522791 q^{34} -2.03539 q^{35} -2.13923 q^{36} -2.93689 q^{37} -1.04791 q^{38} +1.84533 q^{39} +3.45166 q^{40} -5.71116 q^{41} -0.547097 q^{42} +7.26593 q^{43} -5.30168 q^{44} +7.38389 q^{45} +4.99430 q^{46} -10.8346 q^{47} +0.927777 q^{48} -6.65227 q^{49} -6.91394 q^{50} +0.485033 q^{51} +1.98898 q^{52} +0.669315 q^{53} +4.76806 q^{54} +18.2996 q^{55} -0.589686 q^{56} +0.972223 q^{57} -2.19585 q^{58} +9.36509 q^{59} -3.20237 q^{60} -10.3129 q^{61} -0.410576 q^{62} -1.26147 q^{63} +1.00000 q^{64} -6.86529 q^{65} +4.91878 q^{66} -13.0153 q^{67} +0.522791 q^{68} -4.63359 q^{69} +2.03539 q^{70} +11.9500 q^{71} +2.13923 q^{72} +3.54953 q^{73} +2.93689 q^{74} +6.41459 q^{75} +1.04791 q^{76} -3.12633 q^{77} -1.84533 q^{78} +7.17793 q^{79} -3.45166 q^{80} +1.99400 q^{81} +5.71116 q^{82} -0.951994 q^{83} +0.547097 q^{84} -1.80450 q^{85} -7.26593 q^{86} +2.03726 q^{87} +5.30168 q^{88} +0.124806 q^{89} -7.38389 q^{90} +1.17287 q^{91} -4.99430 q^{92} +0.380923 q^{93} +10.8346 q^{94} -3.61701 q^{95} -0.927777 q^{96} +19.5848 q^{97} +6.65227 q^{98} +11.3415 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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