LMFDB - Embedded newform 6033.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.54830 q^{2} +1.00000 q^{3} +0.397234 q^{4} -0.789007 q^{5} -1.54830 q^{6} -3.51923 q^{7} +2.48156 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.54830 q^{2} +1.00000 q^{3} +0.397234 q^{4} -0.789007 q^{5} -1.54830 q^{6} -3.51923 q^{7} +2.48156 q^{8} +1.00000 q^{9} +1.22162 q^{10} +4.65036 q^{11} +0.397234 q^{12} +3.54892 q^{13} +5.44883 q^{14} -0.789007 q^{15} -4.63667 q^{16} -5.72569 q^{17} -1.54830 q^{18} +4.07055 q^{19} -0.313420 q^{20} -3.51923 q^{21} -7.20016 q^{22} -2.69629 q^{23} +2.48156 q^{24} -4.37747 q^{25} -5.49479 q^{26} +1.00000 q^{27} -1.39796 q^{28} +1.07041 q^{29} +1.22162 q^{30} -4.46909 q^{31} +2.21584 q^{32} +4.65036 q^{33} +8.86508 q^{34} +2.77670 q^{35} +0.397234 q^{36} -3.08195 q^{37} -6.30243 q^{38} +3.54892 q^{39} -1.95797 q^{40} +5.58219 q^{41} +5.44883 q^{42} +12.5064 q^{43} +1.84728 q^{44} -0.789007 q^{45} +4.17467 q^{46} -8.78775 q^{47} -4.63667 q^{48} +5.38501 q^{49} +6.77763 q^{50} -5.72569 q^{51} +1.40975 q^{52} -13.5683 q^{53} -1.54830 q^{54} -3.66917 q^{55} -8.73320 q^{56} +4.07055 q^{57} -1.65731 q^{58} +6.06053 q^{59} -0.313420 q^{60} -3.12771 q^{61} +6.91949 q^{62} -3.51923 q^{63} +5.84257 q^{64} -2.80012 q^{65} -7.20016 q^{66} +9.40820 q^{67} -2.27444 q^{68} -2.69629 q^{69} -4.29917 q^{70} -14.1739 q^{71} +2.48156 q^{72} -5.62338 q^{73} +4.77179 q^{74} -4.37747 q^{75} +1.61696 q^{76} -16.3657 q^{77} -5.49479 q^{78} +0.0167179 q^{79} +3.65837 q^{80} +1.00000 q^{81} -8.64291 q^{82} +10.3910 q^{83} -1.39796 q^{84} +4.51761 q^{85} -19.3637 q^{86} +1.07041 q^{87} +11.5402 q^{88} +2.83759 q^{89} +1.22162 q^{90} -12.4895 q^{91} -1.07106 q^{92} -4.46909 q^{93} +13.6061 q^{94} -3.21169 q^{95} +2.21584 q^{96} -5.91410 q^{97} -8.33762 q^{98} +4.65036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−1.54830	−1.09481	−0.547407	−	0.836867i	$-0.684385\pi$
$2$	−1.54830	−1.09481	−0.547407	+	0.836867i	$0.684385\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.397234	0.198617
$5$	−0.789007	−0.352855	−0.176427	−	0.984314i	$-0.556454\pi$
$5$	−0.789007	−0.352855	−0.176427	+	0.984314i	$0.556454\pi$
$6$	−1.54830	−0.632091
$7$	−3.51923	−1.33015	−0.665073	−	0.746778i	$-0.731600\pi$
$7$	−3.51923	−1.33015	−0.665073	+	0.746778i	$0.731600\pi$
$8$	2.48156	0.877365
$9$	1.00000	0.333333
$10$	1.22162	0.386310
$11$	4.65036	1.40214	0.701068	−	0.713094i	$-0.252707\pi$
$11$	4.65036	1.40214	0.701068	+	0.713094i	$0.252707\pi$
$12$	0.397234	0.114672
$13$	3.54892	0.984293	0.492146	−	0.870512i	$-0.336212\pi$
$13$	3.54892	0.984293	0.492146	+	0.870512i	$0.336212\pi$
$14$	5.44883	1.45626
$15$	−0.789007	−0.203721
$16$	−4.63667	−1.15917
$17$	−5.72569	−1.38868	−0.694341	−	0.719646i	$-0.744304\pi$
$17$	−5.72569	−1.38868	−0.694341	+	0.719646i	$0.744304\pi$
$18$	−1.54830	−0.364938
$19$	4.07055	0.933848	0.466924	−	0.884297i	$-0.345362\pi$
$19$	4.07055	0.933848	0.466924	+	0.884297i	$0.345362\pi$
$20$	−0.313420	−0.0700829
$21$	−3.51923	−0.767960
$22$	−7.20016	−1.53508
$23$	−2.69629	−0.562216	−0.281108	−	0.959676i	$-0.590702\pi$
$23$	−2.69629	−0.562216	−0.281108	+	0.959676i	$0.590702\pi$
$24$	2.48156	0.506547
$25$	−4.37747	−0.875493
$26$	−5.49479	−1.07762
$27$	1.00000	0.192450
$28$	−1.39796	−0.264189
$29$	1.07041	0.198769	0.0993847	−	0.995049i	$-0.468313\pi$
$29$	1.07041	0.198769	0.0993847	+	0.995049i	$0.468313\pi$
$30$	1.22162	0.223036
$31$	−4.46909	−0.802672	−0.401336	−	0.915931i	$-0.631454\pi$
$31$	−4.46909	−0.802672	−0.401336	+	0.915931i	$0.631454\pi$
$32$	2.21584	0.391708
$33$	4.65036	0.809524
$34$	8.86508	1.52035
$35$	2.77670	0.469348
$36$	0.397234	0.0662056
$37$	−3.08195	−0.506670	−0.253335	−	0.967379i	$-0.581528\pi$
$37$	−3.08195	−0.506670	−0.253335	+	0.967379i	$0.581528\pi$
$38$	−6.30243	−1.02239
$39$	3.54892	0.568282
$40$	−1.95797	−0.309583
$41$	5.58219	0.871792	0.435896	−	0.899997i	$-0.356432\pi$
$41$	5.58219	0.871792	0.435896	+	0.899997i	$0.356432\pi$
$42$	5.44883	0.840773
$43$	12.5064	1.90722	0.953608	−	0.301052i	$-0.0973377\pi$
$43$	12.5064	1.90722	0.953608	+	0.301052i	$0.0973377\pi$
$44$	1.84728	0.278488
$45$	−0.789007	−0.117618
$46$	4.17467	0.615522
$47$	−8.78775	−1.28182	−0.640912	−	0.767614i	$-0.721444\pi$
$47$	−8.78775	−1.28182	−0.640912	+	0.767614i	$0.721444\pi$
$48$	−4.63667	−0.669246
$49$	5.38501	0.769288
$50$	6.77763	0.958502
$51$	−5.72569	−0.801756
$52$	1.40975	0.195497
$53$	−13.5683	−1.86374	−0.931872	−	0.362788i	$-0.881825\pi$
$53$	−13.5683	−1.86374	−0.931872	+	0.362788i	$0.881825\pi$
$54$	−1.54830	−0.210697
$55$	−3.66917	−0.494751
$56$	−8.73320	−1.16702
$57$	4.07055	0.539157
$58$	−1.65731	−0.217615
$59$	6.06053	0.789014	0.394507	−	0.918893i	$-0.370915\pi$
$59$	6.06053	0.789014	0.394507	+	0.918893i	$0.370915\pi$
$60$	−0.313420	−0.0404624
$61$	−3.12771	−0.400462	−0.200231	−	0.979749i	$-0.564169\pi$
$61$	−3.12771	−0.400462	−0.200231	+	0.979749i	$0.564169\pi$
$62$	6.91949	0.878776
$63$	−3.51923	−0.443382
$64$	5.84257	0.730321
$65$	−2.80012	−0.347313
$66$	−7.20016	−0.886278
$67$	9.40820	1.14939	0.574697	−	0.818366i	$-0.305120\pi$
$67$	9.40820	1.14939	0.574697	+	0.818366i	$0.305120\pi$
$68$	−2.27444	−0.275816
$69$	−2.69629	−0.324596
$70$	−4.29917	−0.513849
$71$	−14.1739	−1.68213	−0.841067	−	0.540930i	$-0.818072\pi$
$71$	−14.1739	−1.68213	−0.841067	+	0.540930i	$0.818072\pi$
$72$	2.48156	0.292455
$73$	−5.62338	−0.658167	−0.329083	−	0.944301i	$-0.606740\pi$
$73$	−5.62338	−0.658167	−0.329083	+	0.944301i	$0.606740\pi$
$74$	4.77179	0.554709
$75$	−4.37747	−0.505466
$76$	1.61696	0.185478
$77$	−16.3657	−1.86505
$78$	−5.49479	−0.622163
$79$	0.0167179	0.00188091	0.000940457	−	1.00000i	$-0.499701\pi$
$79$	0.0167179	0.00188091	0.000940457		1.00000i	$0.499701\pi$
$80$	3.65837	0.409018
$81$	1.00000	0.111111
$82$	−8.64291	−0.954450
$83$	10.3910	1.14056	0.570280	−	0.821450i	$-0.306835\pi$
$83$	10.3910	1.14056	0.570280	+	0.821450i	$0.306835\pi$
$84$	−1.39796	−0.152530
$85$	4.51761	0.490003
$86$	−19.3637	−2.08805
$87$	1.07041	0.114760
$88$	11.5402	1.23019
$89$	2.83759	0.300784	0.150392	−	0.988626i	$-0.451946\pi$
$89$	2.83759	0.300784	0.150392	+	0.988626i	$0.451946\pi$
$90$	1.22162	0.128770
$91$	−12.4895	−1.30925
$92$	−1.07106	−0.111666
$93$	−4.46909	−0.463423
$94$	13.6061	1.40336
$95$	−3.21169	−0.329513
$96$	2.21584	0.226153
$97$	−5.91410	−0.600486	−0.300243	−	0.953863i	$-0.597068\pi$
$97$	−5.91410	−0.600486	−0.300243	+	0.953863i	$0.597068\pi$
$98$	−8.33762	−0.842227
$99$	4.65036	0.467379
$100$	−1.73888	−0.173888
$101$	14.7014	1.46285	0.731424	−	0.681923i	$-0.238856\pi$
$101$	14.7014	1.46285	0.731424	+	0.681923i	$0.238856\pi$
$102$	8.86508	0.877774
$103$	−15.2174	−1.49941	−0.749707	−	0.661770i	$-0.769805\pi$
$103$	−15.2174	−1.49941	−0.749707	+	0.661770i	$0.769805\pi$
$104$	8.80687	0.863584
$105$	2.77670	0.270978
$106$	21.0077	2.04045
$107$	10.1020	0.976595	0.488298	−	0.872677i	$-0.337618\pi$
$107$	10.1020	0.976595	0.488298	+	0.872677i	$0.337618\pi$
$108$	0.397234	0.0382238
$109$	−7.20056	−0.689688	−0.344844	−	0.938660i	$-0.612068\pi$
$109$	−7.20056	−0.689688	−0.344844	+	0.938660i	$0.612068\pi$
$110$	5.68098	0.541660
$111$	−3.08195	−0.292526
$112$	16.3175	1.54186
$113$	5.99403	0.563871	0.281936	−	0.959433i	$-0.409024\pi$
$113$	5.99403	0.563871	0.281936	+	0.959433i	$0.409024\pi$
$114$	−6.30243	−0.590277
$115$	2.12740	0.198381
$116$	0.425202	0.0394790
$117$	3.54892	0.328098
$118$	−9.38352	−0.863823
$119$	20.1500	1.84715
$120$	−1.95797	−0.178738
$121$	10.6259	0.965987
$122$	4.84264	0.438432
$123$	5.58219	0.503329
$124$	−1.77527	−0.159424
$125$	7.39889	0.661777
$126$	5.44883	0.485421
$127$	11.6027	1.02958	0.514789	−	0.857317i	$-0.327870\pi$
$127$	11.6027	1.02958	0.514789	+	0.857317i	$0.327870\pi$
$128$	−13.4777	−1.19127
$129$	12.5064	1.10113
$130$	4.33543	0.380243
$131$	7.52958	0.657862	0.328931	−	0.944354i	$-0.393312\pi$
$131$	7.52958	0.657862	0.328931	+	0.944354i	$0.393312\pi$
$132$	1.84728	0.160785
$133$	−14.3252	−1.24215
$134$	−14.5667	−1.25837
$135$	−0.789007	−0.0679069
$136$	−14.2087	−1.21838
$137$	2.79632	0.238906	0.119453	−	0.992840i	$-0.461886\pi$
$137$	2.79632	0.238906	0.119453	+	0.992840i	$0.461886\pi$
$138$	4.17467	0.355372
$139$	−3.23185	−0.274122	−0.137061	−	0.990563i	$-0.543766\pi$
$139$	−3.23185	−0.274122	−0.137061	+	0.990563i	$0.543766\pi$
$140$	1.10300	0.0932205
$141$	−8.78775	−0.740062
$142$	21.9455	1.84162
$143$	16.5038	1.38011
$144$	−4.63667	−0.386389
$145$	−0.844558	−0.0701368
$146$	8.70668	0.720570
$147$	5.38501	0.444148
$148$	−1.22426	−0.100633
$149$	−3.43088	−0.281068	−0.140534	−	0.990076i	$-0.544882\pi$
$149$	−3.43088	−0.281068	−0.140534	+	0.990076i	$0.544882\pi$
$150$	6.77763	0.553391
$151$	8.25801	0.672028	0.336014	−	0.941857i	$-0.390921\pi$
$151$	8.25801	0.672028	0.336014	+	0.941857i	$0.390921\pi$
$152$	10.1013	0.819326
$153$	−5.72569	−0.462894
$154$	25.3390	2.04188
$155$	3.52614	0.283227
$156$	1.40975	0.112870
$157$	−17.8134	−1.42166	−0.710832	−	0.703362i	$-0.751681\pi$
$157$	−17.8134	−1.42166	−0.710832	+	0.703362i	$0.751681\pi$
$158$	−0.0258844	−0.00205925
$159$	−13.5683	−1.07603
$160$	−1.74831	−0.138216
$161$	9.48889	0.747829
$162$	−1.54830	−0.121646
$163$	−12.3503	−0.967349	−0.483675	−	0.875248i	$-0.660698\pi$
$163$	−12.3503	−0.967349	−0.483675	+	0.875248i	$0.660698\pi$
$164$	2.21744	0.173153
$165$	−3.66917	−0.285644
$166$	−16.0884	−1.24870
$167$	−18.5073	−1.43214	−0.716069	−	0.698029i	$-0.754060\pi$
$167$	−18.5073	−1.43214	−0.716069	+	0.698029i	$0.754060\pi$
$168$	−8.73320	−0.673781
$169$	−0.405177	−0.0311675
$170$	−6.99461	−0.536462
$171$	4.07055	0.311283
$172$	4.96798	0.378805
$173$	0.314656	0.0239229	0.0119614	−	0.999928i	$-0.496192\pi$
$173$	0.314656	0.0239229	0.0119614	+	0.999928i	$0.496192\pi$
$174$	−1.65731	−0.125640
$175$	15.4053	1.16453
$176$	−21.5622	−1.62531
$177$	6.06053	0.455537
$178$	−4.39345	−0.329303
$179$	11.4677	0.857136	0.428568	−	0.903510i	$-0.359018\pi$
$179$	11.4677	0.857136	0.428568	+	0.903510i	$0.359018\pi$
$180$	−0.313420	−0.0233610
$181$	0.298730	0.0222044	0.0111022	−	0.999938i	$-0.496466\pi$
$181$	0.298730	0.0222044	0.0111022	+	0.999938i	$0.496466\pi$
$182$	19.3375	1.43339
$183$	−3.12771	−0.231207
$184$	−6.69102	−0.493269
$185$	2.43169	0.178781
$186$	6.91949	0.507362
$187$	−26.6265	−1.94712
$188$	−3.49079	−0.254592
$189$	−3.51923	−0.255987
$190$	4.97267	0.360755
$191$	−6.53909	−0.473152	−0.236576	−	0.971613i	$-0.576025\pi$
$191$	−6.53909	−0.473152	−0.236576	+	0.971613i	$0.576025\pi$
$192$	5.84257	0.421651
$193$	−11.7984	−0.849270	−0.424635	−	0.905365i	$-0.639598\pi$
$193$	−11.7984	−0.849270	−0.424635	+	0.905365i	$0.639598\pi$
$194$	9.15680	0.657420
$195$	−2.80012	−0.200521
$196$	2.13911	0.152794
$197$	23.0192	1.64005	0.820026	−	0.572326i	$-0.193959\pi$
$197$	23.0192	1.64005	0.820026	+	0.572326i	$0.193959\pi$
$198$	−7.20016	−0.511693
$199$	14.9680	1.06105	0.530526	−	0.847669i	$-0.321994\pi$
$199$	14.9680	1.06105	0.530526	+	0.847669i	$0.321994\pi$
$200$	−10.8630	−0.768127
$201$	9.40820	0.663603
$202$	−22.7623	−1.60155
$203$	−3.76701	−0.264392
$204$	−2.27444	−0.159242
$205$	−4.40439	−0.307616
$206$	23.5611	1.64158
$207$	−2.69629	−0.187405
$208$	−16.4552	−1.14096
$209$	18.9295	1.30938
$210$	−4.29917	−0.296671
$211$	−9.33432	−0.642601	−0.321301	−	0.946977i	$-0.604120\pi$
$211$	−9.33432	−0.642601	−0.321301	+	0.946977i	$0.604120\pi$
$212$	−5.38977	−0.370171
$213$	−14.1739	−0.971181
$214$	−15.6409	−1.06919
$215$	−9.86768	−0.672970
$216$	2.48156	0.168849
$217$	15.7278	1.06767
$218$	11.1486	0.755080
$219$	−5.62338	−0.379993
$220$	−1.45752	−0.0982659
$221$	−20.3200	−1.36687
$222$	4.77179	0.320262
$223$	−15.5391	−1.04057	−0.520286	−	0.853992i	$-0.674175\pi$
$223$	−15.5391	−1.04057	−0.520286	+	0.853992i	$0.674175\pi$
$224$	−7.79805	−0.521029
$225$	−4.37747	−0.291831
$226$	−9.28056	−0.617334
$227$	25.6877	1.70495	0.852475	−	0.522767i	$-0.175100\pi$
$227$	25.6877	1.70495	0.852475	+	0.522767i	$0.175100\pi$
$228$	1.61696	0.107086
$229$	−23.0209	−1.52126	−0.760632	−	0.649183i	$-0.775111\pi$
$229$	−23.0209	−1.52126	−0.760632	+	0.649183i	$0.775111\pi$
$230$	−3.29385	−0.217190
$231$	−16.3657	−1.07678
$232$	2.65628	0.174393
$233$	−27.2536	−1.78544	−0.892720	−	0.450612i	$-0.851206\pi$
$233$	−27.2536	−1.78544	−0.892720	+	0.450612i	$0.851206\pi$
$234$	−5.49479	−0.359206
$235$	6.93360	0.452298
$236$	2.40745	0.156711
$237$	0.0167179	0.00108595
$238$	−31.1983	−2.02229
$239$	−26.3952	−1.70736	−0.853682	−	0.520795i	$-0.825636\pi$
$239$	−26.3952	−1.70736	−0.853682	+	0.520795i	$0.825636\pi$
$240$	3.65837	0.236147
$241$	0.912332	0.0587685	0.0293842	−	0.999568i	$-0.490645\pi$
$241$	0.912332	0.0587685	0.0293842	+	0.999568i	$0.490645\pi$
$242$	−16.4520	−1.05758
$243$	1.00000	0.0641500
$244$	−1.24243	−0.0795386
$245$	−4.24882	−0.271447
$246$	−8.64291	−0.551052
$247$	14.4460	0.919180
$248$	−11.0903	−0.704236
$249$	10.3910	0.658503
$250$	−11.4557	−0.724522
$251$	−19.6769	−1.24200	−0.620998	−	0.783812i	$-0.713272\pi$
$251$	−19.6769	−1.24200	−0.620998	+	0.783812i	$0.713272\pi$
$252$	−1.39796	−0.0880631
$253$	−12.5387	−0.788304
$254$	−17.9645	−1.12720
$255$	4.51761	0.282904
$256$	9.18242	0.573901
$257$	−4.88713	−0.304851	−0.152426	−	0.988315i	$-0.548708\pi$
$257$	−4.88713	−0.304851	−0.152426	+	0.988315i	$0.548708\pi$
$258$	−19.3637	−1.20553
$259$	10.8461	0.673945
$260$	−1.11230	−0.0689821
$261$	1.07041	0.0662565
$262$	−11.6580	−0.720237
$263$	−11.5044	−0.709389	−0.354695	−	0.934982i	$-0.615415\pi$
$263$	−11.5044	−0.709389	−0.354695	+	0.934982i	$0.615415\pi$
$264$	11.5402	0.710248
$265$	10.7055	0.657631
$266$	22.1797	1.35993
$267$	2.83759	0.173658
$268$	3.73725	0.228289
$269$	30.7521	1.87499	0.937495	−	0.348000i	$-0.113139\pi$
$269$	30.7521	1.87499	0.937495	+	0.348000i	$0.113139\pi$
$270$	1.22162	0.0743455
$271$	−0.395685	−0.0240361	−0.0120181	−	0.999928i	$-0.503826\pi$
$271$	−0.395685	−0.0240361	−0.0120181	+	0.999928i	$0.503826\pi$
$272$	26.5481	1.60972
$273$	−12.4895	−0.755898
$274$	−4.32955	−0.261558
$275$	−20.3568	−1.22756
$276$	−1.07106	−0.0644702
$277$	−15.7106	−0.943957	−0.471979	−	0.881610i	$-0.656460\pi$
$277$	−15.7106	−0.943957	−0.471979	+	0.881610i	$0.656460\pi$
$278$	5.00387	0.300112
$279$	−4.46909	−0.267557
$280$	6.89056	0.411790
$281$	−13.7509	−0.820311	−0.410156	−	0.912016i	$-0.634526\pi$
$281$	−13.7509	−0.820311	−0.410156	+	0.912016i	$0.634526\pi$
$282$	13.6061	0.810230
$283$	−6.46534	−0.384325	−0.192162	−	0.981363i	$-0.561550\pi$
$283$	−6.46534	−0.384325	−0.192162	+	0.981363i	$0.561550\pi$
$284$	−5.63036	−0.334100
$285$	−3.21169	−0.190244
$286$	−25.5528	−1.51097
$287$	−19.6450	−1.15961
$288$	2.21584	0.130569
$289$	15.7835	0.928440
$290$	1.30763	0.0767867
$291$	−5.91410	−0.346691
$292$	−2.23380	−0.130723
$293$	−26.0736	−1.52324	−0.761619	−	0.648025i	$-0.775595\pi$
$293$	−26.0736	−1.52324	−0.761619	+	0.648025i	$0.775595\pi$
$294$	−8.33762	−0.486260
$295$	−4.78180	−0.278407
$296$	−7.64807	−0.444535
$297$	4.65036	0.269841
$298$	5.31203	0.307717
$299$	−9.56893	−0.553385
$300$	−1.73888	−0.100394
$301$	−44.0131	−2.53687
$302$	−12.7859	−0.735745
$303$	14.7014	0.844576
$304$	−18.8738	−1.08249
$305$	2.46779	0.141305
$306$	8.86508	0.506783
$307$	−11.2027	−0.639373	−0.319686	−	0.947523i	$-0.603578\pi$
$307$	−11.2027	−0.639373	−0.319686	+	0.947523i	$0.603578\pi$
$308$	−6.50101	−0.370430
$309$	−15.2174	−0.865687
$310$	−5.45953	−0.310080
$311$	19.9378	1.13057	0.565285	−	0.824895i	$-0.308766\pi$
$311$	19.9378	1.13057	0.565285	+	0.824895i	$0.308766\pi$
$312$	8.80687	0.498591
$313$	−30.1350	−1.70333	−0.851666	−	0.524085i	$-0.824407\pi$
$313$	−30.1350	−1.70333	−0.851666	+	0.524085i	$0.824407\pi$
$314$	27.5805	1.55646
$315$	2.77670	0.156449
$316$	0.00664093	0.000373581 0
$317$	11.0711	0.621816	0.310908	−	0.950440i	$-0.399367\pi$
$317$	11.0711	0.621816	0.310908	+	0.950440i	$0.399367\pi$
$318$	21.0077	1.17806
$319$	4.97778	0.278702
$320$	−4.60983	−0.257697
$321$	10.1020	0.563838
$322$	−14.6917	−0.818734
$323$	−23.3067	−1.29682
$324$	0.397234	0.0220685
$325$	−15.5353	−0.861742
$326$	19.1220	1.05907
$327$	−7.20056	−0.398192
$328$	13.8526	0.764880
$329$	30.9261	1.70501
$330$	5.68098	0.312727
$331$	−19.4192	−1.06738	−0.533689	−	0.845681i	$-0.679195\pi$
$331$	−19.4192	−1.06738	−0.533689	+	0.845681i	$0.679195\pi$
$332$	4.12766	0.226535
$333$	−3.08195	−0.168890
$334$	28.6549	1.56792
$335$	−7.42314	−0.405569
$336$	16.3175	0.890195
$337$	−8.21288	−0.447384	−0.223692	−	0.974660i	$-0.571811\pi$
$337$	−8.21288	−0.447384	−0.223692	+	0.974660i	$0.571811\pi$
$338$	0.627336	0.0341226
$339$	5.99403	0.325551
$340$	1.79455	0.0973230
$341$	−20.7829	−1.12546
$342$	−6.30243	−0.340796
$343$	5.68351	0.306881
$344$	31.0355	1.67332
$345$	2.12740	0.114535
$346$	−0.487182	−0.0261911
$347$	8.78538	0.471624	0.235812	−	0.971799i	$-0.424225\pi$
$347$	8.78538	0.471624	0.235812	+	0.971799i	$0.424225\pi$
$348$	0.425202	0.0227932
$349$	2.36555	0.126625	0.0633126	−	0.997994i	$-0.479833\pi$
$349$	2.36555	0.126625	0.0633126	+	0.997994i	$0.479833\pi$
$350$	−23.8521	−1.27495
$351$	3.54892	0.189427
$352$	10.3044	0.549228
$353$	−9.22383	−0.490935	−0.245467	−	0.969405i	$-0.578941\pi$
$353$	−9.22383	−0.490935	−0.245467	+	0.969405i	$0.578941\pi$
$354$	−9.38352	−0.498728
$355$	11.1833	0.593549
$356$	1.12719	0.0597409
$357$	20.1500	1.06645
$358$	−17.7554	−0.938404
$359$	33.7993	1.78386	0.891929	−	0.452176i	$-0.149352\pi$
$359$	33.7993	1.78386	0.891929	+	0.452176i	$0.149352\pi$
$360$	−1.95797	−0.103194
$361$	−2.43063	−0.127928
$362$	−0.462524	−0.0243097
$363$	10.6259	0.557713
$364$	−4.96124	−0.260040
$365$	4.43689	0.232237
$366$	4.84264	0.253129
$367$	−31.7657	−1.65816	−0.829079	−	0.559132i	$-0.811134\pi$
$367$	−31.7657	−1.65816	−0.829079	+	0.559132i	$0.811134\pi$
$368$	12.5018	0.651703
$369$	5.58219	0.290597
$370$	−3.76498	−0.195732
$371$	47.7499	2.47905
$372$	−1.77527	−0.0920436
$373$	13.3082	0.689070	0.344535	−	0.938773i	$-0.388037\pi$
$373$	13.3082	0.689070	0.344535	+	0.938773i	$0.388037\pi$
$374$	41.2258	2.13174
$375$	7.39889	0.382077
$376$	−21.8074	−1.12463
$377$	3.79878	0.195647
$378$	5.44883	0.280258
$379$	−1.39755	−0.0717872	−0.0358936	−	0.999356i	$-0.511428\pi$
$379$	−1.39755	−0.0717872	−0.0358936	+	0.999356i	$0.511428\pi$
$380$	−1.27579	−0.0654468
$381$	11.6027	0.594427
$382$	10.1245	0.518013
$383$	−16.8438	−0.860676	−0.430338	−	0.902668i	$-0.641606\pi$
$383$	−16.8438	−0.860676	−0.430338	+	0.902668i	$0.641606\pi$
$384$	−13.4777	−0.687782
$385$	12.9127	0.658091
$386$	18.2675	0.929792
$387$	12.5064	0.635739
$388$	−2.34928	−0.119267
$389$	−31.9507	−1.61996	−0.809981	−	0.586456i	$-0.800523\pi$
$389$	−31.9507	−1.61996	−0.809981	+	0.586456i	$0.800523\pi$
$390$	4.33543	0.219533
$391$	15.4381	0.780740
$392$	13.3633	0.674946
$393$	7.52958	0.379817
$394$	−35.6407	−1.79555
$395$	−0.0131906	−0.000663690 0
$396$	1.84728	0.0928294
$397$	12.9445	0.649667	0.324834	−	0.945771i	$-0.394692\pi$
$397$	12.9445	0.649667	0.324834	+	0.945771i	$0.394692\pi$
$398$	−23.1749	−1.16165
$399$	−14.3252	−0.717158
$400$	20.2969	1.01484
$401$	−10.3754	−0.518123	−0.259062	−	0.965861i	$-0.583413\pi$
$401$	−10.3754	−0.518123	−0.259062	+	0.965861i	$0.583413\pi$
$402$	−14.5667	−0.726522
$403$	−15.8604	−0.790064
$404$	5.83991	0.290546
$405$	−0.789007	−0.0392061
$406$	5.83246	0.289460
$407$	−14.3322	−0.710421
$408$	−14.2087	−0.703433
$409$	24.0552	1.18945	0.594726	−	0.803928i	$-0.297261\pi$
$409$	24.0552	1.18945	0.594726	+	0.803928i	$0.297261\pi$
$410$	6.81932	0.336782
$411$	2.79632	0.137932
$412$	−6.04486	−0.297809
$413$	−21.3284	−1.04950
$414$	4.17467	0.205174
$415$	−8.19858	−0.402452
$416$	7.86382	0.385555
$417$	−3.23185	−0.158264
$418$	−29.3086	−1.43353
$419$	−1.75968	−0.0859659	−0.0429829	−	0.999076i	$-0.513686\pi$
$419$	−1.75968	−0.0859659	−0.0429829	+	0.999076i	$0.513686\pi$
$420$	1.10300	0.0538209
$421$	−17.9508	−0.874871	−0.437435	−	0.899250i	$-0.644113\pi$
$421$	−17.9508	−0.874871	−0.437435	+	0.899250i	$0.644113\pi$
$422$	14.4523	0.703529
$423$	−8.78775	−0.427275
$424$	−33.6705	−1.63518
$425$	25.0640	1.21578
$426$	21.9455	1.06326
$427$	11.0071	0.532673
$428$	4.01285	0.193968
$429$	16.5038	0.796809
$430$	15.2781	0.736777
$431$	−17.4646	−0.841241	−0.420621	−	0.907237i	$-0.638188\pi$
$431$	−17.4646	−0.841241	−0.420621	+	0.907237i	$0.638188\pi$
$432$	−4.63667	−0.223082
$433$	10.2718	0.493631	0.246815	−	0.969063i	$-0.420616\pi$
$433$	10.2718	0.493631	0.246815	+	0.969063i	$0.420616\pi$
$434$	−24.3513	−1.16890
$435$	−0.844558	−0.0404935
$436$	−2.86030	−0.136984
$437$	−10.9754	−0.525024
$438$	8.70668	0.416021
$439$	4.48776	0.214189	0.107095	−	0.994249i	$-0.465845\pi$
$439$	4.48776	0.214189	0.107095	+	0.994249i	$0.465845\pi$
$440$	−9.10528	−0.434077
$441$	5.38501	0.256429
$442$	31.4614	1.49647
$443$	−12.2958	−0.584192	−0.292096	−	0.956389i	$-0.594353\pi$
$443$	−12.2958	−0.584192	−0.292096	+	0.956389i	$0.594353\pi$
$444$	−1.22426	−0.0581006
$445$	−2.23888	−0.106133
$446$	24.0591	1.13923
$447$	−3.43088	−0.162275
$448$	−20.5614	−0.971433
$449$	2.01543	0.0951140	0.0475570	−	0.998869i	$-0.484856\pi$
$449$	2.01543	0.0951140	0.0475570	+	0.998869i	$0.484856\pi$
$450$	6.77763	0.319501
$451$	25.9592	1.22237
$452$	2.38103	0.111994
$453$	8.25801	0.387995
$454$	−39.7722	−1.86660
$455$	9.85429	0.461976
$456$	10.1013	0.473038
$457$	−21.6588	−1.01315	−0.506577	−	0.862195i	$-0.669089\pi$
$457$	−21.6588	−1.01315	−0.506577	+	0.862195i	$0.669089\pi$
$458$	35.6433	1.66550
$459$	−5.72569	−0.267252
$460$	0.845074	0.0394018
$461$	3.80581	0.177254	0.0886272	−	0.996065i	$-0.471752\pi$
$461$	3.80581	0.177254	0.0886272	+	0.996065i	$0.471752\pi$
$462$	25.3390	1.17888
$463$	21.7702	1.01174	0.505872	−	0.862608i	$-0.331171\pi$
$463$	21.7702	1.01174	0.505872	+	0.862608i	$0.331171\pi$
$464$	−4.96312	−0.230407
$465$	3.52614	0.163521
$466$	42.1967	1.95472
$467$	1.76244	0.0815562	0.0407781	−	0.999168i	$-0.487016\pi$
$467$	1.76244	0.0815562	0.0407781	+	0.999168i	$0.487016\pi$
$468$	1.40975	0.0651657
$469$	−33.1097	−1.52886
$470$	−10.7353	−0.495182
$471$	−17.8134	−0.820798
$472$	15.0396	0.692253
$473$	58.1595	2.67418
$474$	−0.0258844	−0.00118891
$475$	−17.8187	−0.817578
$476$	8.00427	0.366875
$477$	−13.5683	−0.621248
$478$	40.8677	1.86925
$479$	−15.0209	−0.686322	−0.343161	−	0.939277i	$-0.611498\pi$
$479$	−15.0209	−0.686322	−0.343161	+	0.939277i	$0.611498\pi$
$480$	−1.74831	−0.0797991
$481$	−10.9376	−0.498712
$482$	−1.41256	−0.0643405
$483$	9.48889	0.431759
$484$	4.22095	0.191861
$485$	4.66627	0.211884
$486$	−1.54830	−0.0702323
$487$	−15.8812	−0.719646	−0.359823	−	0.933021i	$-0.617163\pi$
$487$	−15.8812	−0.719646	−0.359823	+	0.933021i	$0.617163\pi$
$488$	−7.76161	−0.351352
$489$	−12.3503	−0.558499
$490$	6.57844	0.297184
$491$	−6.64797	−0.300019	−0.150009	−	0.988685i	$-0.547930\pi$
$491$	−6.64797	−0.300019	−0.150009	+	0.988685i	$0.547930\pi$
$492$	2.21744	0.0999697
$493$	−6.12881	−0.276028
$494$	−22.3668	−1.00633
$495$	−3.66917	−0.164917
$496$	20.7217	0.930432
$497$	49.8814	2.23748
$498$	−16.0884	−0.720938
$499$	−32.4797	−1.45399	−0.726996	−	0.686642i	$-0.759084\pi$
$499$	−32.4797	−1.45399	−0.726996	+	0.686642i	$0.759084\pi$
$500$	2.93909	0.131440
$501$	−18.5073	−0.826845
$502$	30.4658	1.35975
$503$	35.0002	1.56058	0.780292	−	0.625416i	$-0.215071\pi$
$503$	35.0002	1.56058	0.780292	+	0.625416i	$0.215071\pi$
$504$	−8.73320	−0.389008
$505$	−11.5996	−0.516173
$506$	19.4137	0.863046
$507$	−0.405177	−0.0179945
$508$	4.60900	0.204491
$509$	−37.2716	−1.65203	−0.826017	−	0.563645i	$-0.809399\pi$
$509$	−37.2716	−1.65203	−0.826017	+	0.563645i	$0.809399\pi$
$510$	−6.99461	−0.309727
$511$	19.7900	0.875458
$512$	12.7383	0.562958
$513$	4.07055	0.179719
$514$	7.56675	0.333755
$515$	12.0066	0.529075
$516$	4.96798	0.218703
$517$	−40.8662	−1.79729
$518$	−16.7931	−0.737844
$519$	0.314656	0.0138119
$520$	−6.94868	−0.304720
$521$	−2.80171	−0.122745	−0.0613725	−	0.998115i	$-0.519548\pi$
$521$	−2.80171	−0.122745	−0.0613725	+	0.998115i	$0.519548\pi$
$522$	−1.65731	−0.0725385
$523$	−25.5219	−1.11600	−0.557998	−	0.829842i	$-0.688430\pi$
$523$	−25.5219	−1.11600	−0.557998	+	0.829842i	$0.688430\pi$
$524$	2.99100	0.130663
$525$	15.4053	0.672344
$526$	17.8122	0.776649
$527$	25.5886	1.11466
$528$	−21.5622	−0.938374
$529$	−15.7300	−0.683913
$530$	−16.5753	−0.719983
$531$	6.06053	0.263005
$532$	−5.69046	−0.246713
$533$	19.8107	0.858099
$534$	−4.39345	−0.190123
$535$	−7.97054	−0.344596
$536$	23.3470	1.00844
$537$	11.4677	0.494868
$538$	−47.6135	−2.05276
$539$	25.0423	1.07865
$540$	−0.313420	−0.0134875
$541$	6.21306	0.267120	0.133560	−	0.991041i	$-0.457359\pi$
$541$	6.21306	0.267120	0.133560	+	0.991041i	$0.457359\pi$
$542$	0.612639	0.0263151
$543$	0.298730	0.0128197
$544$	−12.6872	−0.543958
$545$	5.68129	0.243360
$546$	19.3375	0.827567
$547$	−34.2600	−1.46485	−0.732426	−	0.680847i	$-0.761612\pi$
$547$	−34.2600	−1.46485	−0.732426	+	0.680847i	$0.761612\pi$
$548$	1.11079	0.0474508
$549$	−3.12771	−0.133487
$550$	31.5184	1.34395
$551$	4.35714	0.185620
$552$	−6.69102	−0.284789
$553$	−0.0588343	−0.00250189
$554$	24.3247	1.03346
$555$	2.43169	0.103219
$556$	−1.28380	−0.0544453
$557$	11.3974	0.482925	0.241463	−	0.970410i	$-0.422373\pi$
$557$	11.3974	0.482925	0.241463	+	0.970410i	$0.422373\pi$
$558$	6.91949	0.292925
$559$	44.3844	1.87726
$560$	−12.8747	−0.544054
$561$	−26.6265	−1.12417
$562$	21.2906	0.898088
$563$	11.4570	0.482854	0.241427	−	0.970419i	$-0.422385\pi$
$563$	11.4570	0.482854	0.241427	+	0.970419i	$0.422385\pi$
$564$	−3.49079	−0.146989
$565$	−4.72934	−0.198965
$566$	10.0103	0.420764
$567$	−3.51923	−0.147794
$568$	−35.1735	−1.47585
$569$	28.6042	1.19915	0.599576	−	0.800318i	$-0.295336\pi$
$569$	28.6042	1.19915	0.599576	+	0.800318i	$0.295336\pi$
$570$	4.97267	0.208282
$571$	12.5031	0.523239	0.261619	−	0.965171i	$-0.415743\pi$
$571$	12.5031	0.523239	0.261619	+	0.965171i	$0.415743\pi$
$572$	6.55585	0.274114
$573$	−6.53909	−0.273174
$574$	30.4164	1.26956
$575$	11.8029	0.492217
$576$	5.84257	0.243440
$577$	−10.7436	−0.447263	−0.223631	−	0.974674i	$-0.571791\pi$
$577$	−10.7436	−0.447263	−0.223631	+	0.974674i	$0.571791\pi$
$578$	−24.4376	−1.01647
$579$	−11.7984	−0.490326
$580$	−0.335487	−0.0139303
$581$	−36.5684	−1.51711
$582$	9.15680	0.379562
$583$	−63.0973	−2.61322
$584$	−13.9548	−0.577453
$585$	−2.80012	−0.115771
$586$	40.3698	1.66766
$587$	0.374134	0.0154422	0.00772108	−	0.999970i	$-0.497542\pi$
$587$	0.374134	0.0154422	0.00772108	+	0.999970i	$0.497542\pi$
$588$	2.13911	0.0882154
$589$	−18.1916	−0.749574
$590$	7.40367	0.304804
$591$	23.0192	0.946885
$592$	14.2900	0.587316
$593$	15.3210	0.629157	0.314579	−	0.949231i	$-0.398137\pi$
$593$	15.3210	0.629157	0.314579	+	0.949231i	$0.398137\pi$
$594$	−7.20016	−0.295426
$595$	−15.8985	−0.651776
$596$	−1.36286	−0.0558249
$597$	14.9680	0.612599
$598$	14.8156	0.605854
$599$	4.18527	0.171006	0.0855028	−	0.996338i	$-0.472750\pi$
$599$	4.18527	0.171006	0.0855028	+	0.996338i	$0.472750\pi$
$600$	−10.8630	−0.443479
$601$	−9.39090	−0.383063	−0.191531	−	0.981486i	$-0.561345\pi$
$601$	−9.39090	−0.383063	−0.191531	+	0.981486i	$0.561345\pi$
$602$	68.1455	2.77741
$603$	9.40820	0.383131
$604$	3.28036	0.133476
$605$	−8.38388	−0.340853
$606$	−22.7623	−0.924653
$607$	−37.6361	−1.52760	−0.763801	−	0.645451i	$-0.776669\pi$
$607$	−37.6361	−1.52760	−0.763801	+	0.645451i	$0.776669\pi$
$608$	9.01967	0.365796
$609$	−3.76701	−0.152647
$610$	−3.82088	−0.154703
$611$	−31.1870	−1.26169
$612$	−2.27444	−0.0919386
$613$	7.95767	0.321407	0.160704	−	0.987003i	$-0.448624\pi$
$613$	7.95767	0.321407	0.160704	+	0.987003i	$0.448624\pi$
$614$	17.3452	0.699994
$615$	−4.40439	−0.177602
$616$	−40.6126	−1.63633
$617$	−41.1507	−1.65667	−0.828333	−	0.560235i	$-0.810711\pi$
$617$	−41.1507	−1.65667	−0.828333	+	0.560235i	$0.810711\pi$
$618$	23.5611	0.947766
$619$	9.48890	0.381391	0.190695	−	0.981649i	$-0.438926\pi$
$619$	9.48890	0.381391	0.190695	+	0.981649i	$0.438926\pi$
$620$	1.40070	0.0562536
$621$	−2.69629	−0.108199
$622$	−30.8698	−1.23776
$623$	−9.98616	−0.400087
$624$	−16.4552	−0.658734
$625$	16.0496	0.641982
$626$	46.6580	1.86483
$627$	18.9295	0.755972
$628$	−7.07608	−0.282366
$629$	17.6463	0.703604
$630$	−4.29917	−0.171283
$631$	18.3713	0.731348	0.365674	−	0.930743i	$-0.380839\pi$
$631$	18.3713	0.731348	0.365674	+	0.930743i	$0.380839\pi$
$632$	0.0414866	0.00165025
$633$	−9.33432	−0.371006
$634$	−17.1414	−0.680773
$635$	−9.15465	−0.363291
$636$	−5.38977	−0.213718
$637$	19.1110	0.757204
$638$	−7.70709	−0.305127
$639$	−14.1739	−0.560712
$640$	10.6340	0.420347
$641$	−3.18978	−0.125989	−0.0629944	−	0.998014i	$-0.520065\pi$
$641$	−3.18978	−0.125989	−0.0629944	+	0.998014i	$0.520065\pi$
$642$	−15.6409	−0.617297
$643$	−38.9402	−1.53565	−0.767825	−	0.640660i	$-0.778661\pi$
$643$	−38.9402	−1.53565	−0.767825	+	0.640660i	$0.778661\pi$
$644$	3.76931	0.148532
$645$	−9.86768	−0.388540
$646$	36.0857	1.41977
$647$	−44.2880	−1.74114	−0.870571	−	0.492042i	$-0.836251\pi$
$647$	−44.2880	−1.74114	−0.870571	+	0.492042i	$0.836251\pi$
$648$	2.48156	0.0974850
$649$	28.1836	1.10630
$650$	24.0533	0.943447
$651$	15.7278	0.616420
$652$	−4.90595	−0.192132
$653$	21.8799	0.856225	0.428112	−	0.903726i	$-0.359179\pi$
$653$	21.8799	0.856225	0.428112	+	0.903726i	$0.359179\pi$
$654$	11.1486	0.435946
$655$	−5.94089	−0.232130
$656$	−25.8828	−1.01055
$657$	−5.62338	−0.219389
$658$	−47.8830	−1.86667
$659$	16.3177	0.635646	0.317823	−	0.948150i	$-0.397048\pi$
$659$	16.3177	0.635646	0.317823	+	0.948150i	$0.397048\pi$
$660$	−1.45752	−0.0567338
$661$	35.5171	1.38146	0.690728	−	0.723114i	$-0.257290\pi$
$661$	35.5171	1.38146	0.690728	+	0.723114i	$0.257290\pi$
$662$	30.0668	1.16858
$663$	−20.3200	−0.789163
$664$	25.7859	1.00069
$665$	11.3027	0.438300
$666$	4.77179	0.184903
$667$	−2.88613	−0.111751
$668$	−7.35173	−0.284447
$669$	−15.5391	−0.600775
$670$	11.4932	0.444023
$671$	−14.5450	−0.561503
$672$	−7.79805	−0.300816
$673$	30.2851	1.16741	0.583703	−	0.811968i	$-0.301603\pi$
$673$	30.2851	1.16741	0.583703	+	0.811968i	$0.301603\pi$
$674$	12.7160	0.489802
$675$	−4.37747	−0.168489
$676$	−0.160950	−0.00619038
$677$	36.4477	1.40080	0.700400	−	0.713751i	$-0.253005\pi$
$677$	36.4477	1.40080	0.700400	+	0.713751i	$0.253005\pi$
$678$	−9.28056	−0.356418
$679$	20.8131	0.798734
$680$	11.2107	0.429912
$681$	25.6877	0.984354
$682$	32.1781	1.23216
$683$	−12.4563	−0.476626	−0.238313	−	0.971188i	$-0.576594\pi$
$683$	−12.4563	−0.476626	−0.238313	+	0.971188i	$0.576594\pi$
$684$	1.61696	0.0618260
$685$	−2.20632	−0.0842992
$686$	−8.79979	−0.335977
$687$	−23.0209	−0.878302
$688$	−57.9883	−2.21078
$689$	−48.1526	−1.83447
$690$	−3.29385	−0.125395
$691$	−22.0759	−0.839808	−0.419904	−	0.907569i	$-0.637936\pi$
$691$	−22.0759	−0.839808	−0.419904	+	0.907569i	$0.637936\pi$
$692$	0.124992	0.00475149
$693$	−16.3657	−0.621682
$694$	−13.6024	−0.516340
$695$	2.54995	0.0967253
$696$	2.65628	0.100686
$697$	−31.9619	−1.21064
$698$	−3.66259	−0.138631
$699$	−27.2536	−1.03082
$700$	6.11952	0.231296
$701$	−35.5432	−1.34245	−0.671224	−	0.741254i	$-0.734231\pi$
$701$	−35.5432	−1.34245	−0.671224	+	0.741254i	$0.734231\pi$
$702$	−5.49479	−0.207388
$703$	−12.5452	−0.473153
$704$	27.1700	1.02401
$705$	6.93360	0.261134
$706$	14.2813	0.537482
$707$	−51.7378	−1.94580
$708$	2.40745	0.0904774
$709$	−15.8310	−0.594545	−0.297273	−	0.954793i	$-0.596077\pi$
$709$	−15.8310	−0.594545	−0.297273	+	0.954793i	$0.596077\pi$
$710$	−17.3152	−0.649826
$711$	0.0167179	0.000626971 0
$712$	7.04167	0.263898
$713$	12.0500	0.451275
$714$	−31.1983	−1.16757
$715$	−13.0216	−0.486980
$716$	4.55536	0.170242
$717$	−26.3952	−0.985747
$718$	−52.3314	−1.95299
$719$	33.0178	1.23135	0.615677	−	0.787998i	$-0.288882\pi$
$719$	33.0178	1.23135	0.615677	+	0.787998i	$0.288882\pi$
$720$	3.65837	0.136339
$721$	53.5535	1.99444
$722$	3.76335	0.140057
$723$	0.912332	0.0339300
$724$	0.118666	0.00441017
$725$	−4.68567	−0.174021
$726$	−16.4520	−0.610592
$727$	−23.3869	−0.867371	−0.433685	−	0.901064i	$-0.642787\pi$
$727$	−23.3869	−0.867371	−0.433685	+	0.901064i	$0.642787\pi$
$728$	−30.9934	−1.14869
$729$	1.00000	0.0370370
$730$	−6.86964	−0.254257
$731$	−71.6080	−2.64852
$732$	−1.24243	−0.0459216
$733$	−38.1863	−1.41044	−0.705222	−	0.708987i	$-0.749152\pi$
$733$	−38.1863	−1.41044	−0.705222	+	0.708987i	$0.749152\pi$
$734$	49.1829	1.81537
$735$	−4.24882	−0.156720
$736$	−5.97454	−0.220225
$737$	43.7515	1.61161
$738$	−8.64291	−0.318150
$739$	19.0759	0.701720	0.350860	−	0.936428i	$-0.385889\pi$
$739$	19.0759	0.701720	0.350860	+	0.936428i	$0.385889\pi$
$740$	0.965948	0.0355089
$741$	14.4460	0.530689
$742$	−73.9312	−2.71410
$743$	−8.32783	−0.305518	−0.152759	−	0.988263i	$-0.548816\pi$
$743$	−8.32783	−0.305518	−0.152759	+	0.988263i	$0.548816\pi$
$744$	−11.0903	−0.406591
$745$	2.70699	0.0991763
$746$	−20.6050	−0.754404
$747$	10.3910	0.380187
$748$	−10.5769	−0.386732
$749$	−35.5512	−1.29901
$750$	−11.4557	−0.418303
$751$	−30.8942	−1.12735	−0.563673	−	0.825998i	$-0.690612\pi$
$751$	−30.8942	−1.12735	−0.563673	+	0.825998i	$0.690612\pi$
$752$	40.7459	1.48585
$753$	−19.6769	−0.717066
$754$	−5.88166	−0.214197
$755$	−6.51563	−0.237128
$756$	−1.39796	−0.0508433
$757$	30.1559	1.09604	0.548018	−	0.836466i	$-0.315382\pi$
$757$	30.1559	1.09604	0.548018	+	0.836466i	$0.315382\pi$
$758$	2.16382	0.0785937
$759$	−12.5387	−0.455127
$760$	−7.97002	−0.289103
$761$	13.8468	0.501945	0.250972	−	0.967994i	$-0.419250\pi$
$761$	13.8468	0.501945	0.250972	+	0.967994i	$0.419250\pi$
$762$	−17.9645	−0.650786
$763$	25.3405	0.917386
$764$	−2.59755	−0.0939760
$765$	4.51761	0.163334
$766$	26.0792	0.942280
$767$	21.5083	0.776620
$768$	9.18242	0.331342
$769$	3.07551	0.110906	0.0554529	−	0.998461i	$-0.482340\pi$
$769$	3.07551	0.110906	0.0554529	+	0.998461i	$0.482340\pi$
$770$	−19.9927	−0.720487
$771$	−4.88713	−0.176006
$772$	−4.68674	−0.168679
$773$	14.5767	0.524288	0.262144	−	0.965029i	$-0.415571\pi$
$773$	14.5767	0.524288	0.262144	+	0.965029i	$0.415571\pi$
$774$	−19.3637	−0.696015
$775$	19.5633	0.702734
$776$	−14.6762	−0.526845
$777$	10.8461	0.389102
$778$	49.4692	1.77356
$779$	22.7226	0.814121
$780$	−1.11230	−0.0398269
$781$	−65.9138	−2.35858
$782$	−23.9029	−0.854765
$783$	1.07041	0.0382532
$784$	−24.9685	−0.891734
$785$	14.0549	0.501641
$786$	−11.6580	−0.415829
$787$	−13.6551	−0.486751	−0.243375	−	0.969932i	$-0.578255\pi$
$787$	−13.6551	−0.486751	−0.243375	+	0.969932i	$0.578255\pi$
$788$	9.14402	0.325742
$789$	−11.5044	−0.409566
$790$	0.0204230	0.000726617 0
$791$	−21.0944	−0.750031
$792$	11.5402	0.410062
$793$	−11.1000	−0.394172
$794$	−20.0420	−0.711265
$795$	10.7055	0.379683
$796$	5.94579	0.210743
$797$	50.0234	1.77192	0.885960	−	0.463762i	$-0.153501\pi$
$797$	50.0234	1.77192	0.885960	+	0.463762i	$0.153501\pi$
$798$	22.1797	0.785154
$799$	50.3159	1.78005
$800$	−9.69975	−0.342938
$801$	2.83759	0.100261
$802$	16.0642	0.567248
$803$	−26.1507	−0.922840
$804$	3.73725	0.131803
$805$	−7.48681	−0.263875
$806$	24.5567	0.864973
$807$	30.7521	1.08253
$808$	36.4826	1.28345
$809$	17.9657	0.631642	0.315821	−	0.948819i	$-0.397720\pi$
$809$	17.9657	0.631642	0.315821	+	0.948819i	$0.397720\pi$
$810$	1.22162	0.0429234
$811$	46.2427	1.62380	0.811900	−	0.583797i	$-0.198434\pi$
$811$	46.2427	1.62380	0.811900	+	0.583797i	$0.198434\pi$
$812$	−1.49638	−0.0525128
$813$	−0.395685	−0.0138773
$814$	22.1906	0.777779
$815$	9.74447	0.341334
$816$	26.5481	0.929370
$817$	50.9081	1.78105
$818$	−37.2446	−1.30223
$819$	−12.4895	−0.436418
$820$	−1.74957	−0.0610977
$821$	−34.3283	−1.19807	−0.599034	−	0.800724i	$-0.704448\pi$
$821$	−34.3283	−1.19807	−0.599034	+	0.800724i	$0.704448\pi$
$822$	−4.32955	−0.151010
$823$	−16.2939	−0.567968	−0.283984	−	0.958829i	$-0.591656\pi$
$823$	−16.2939	−0.567968	−0.283984	+	0.958829i	$0.591656\pi$
$824$	−37.7629	−1.31553
$825$	−20.3568	−0.708733
$826$	33.0228	1.14901
$827$	1.74986	0.0608487	0.0304243	−	0.999537i	$-0.490314\pi$
$827$	1.74986	0.0608487	0.0304243	+	0.999537i	$0.490314\pi$
$828$	−1.07106	−0.0372219
$829$	−49.1043	−1.70546	−0.852732	−	0.522349i	$-0.825056\pi$
$829$	−49.1043	−1.70546	−0.852732	+	0.522349i	$0.825056\pi$
$830$	12.6939	0.440610
$831$	−15.7106	−0.544994
$832$	20.7348	0.718850
$833$	−30.8329	−1.06830
$834$	5.00387	0.173270
$835$	14.6024	0.505337
$836$	7.51945	0.260065
$837$	−4.46909	−0.154474
$838$	2.72451	0.0941166
$839$	14.0641	0.485545	0.242773	−	0.970083i	$-0.421943\pi$
$839$	14.0641	0.485545	0.242773	+	0.970083i	$0.421943\pi$
$840$	6.89056	0.237747
$841$	−27.8542	−0.960491
$842$	27.7933	0.957820
$843$	−13.7509	−0.473607
$844$	−3.70791	−0.127632
$845$	0.319688	0.0109976
$846$	13.6061	0.467786
$847$	−37.3949	−1.28490
$848$	62.9116	2.16039
$849$	−6.46534	−0.221890
$850$	−38.8066	−1.33106
$851$	8.30986	0.284858
$852$	−5.63036	−0.192893
$853$	−31.0932	−1.06461	−0.532306	−	0.846552i	$-0.678674\pi$
$853$	−31.0932	−1.06461	−0.532306	+	0.846552i	$0.678674\pi$
$854$	−17.0424	−0.583178
$855$	−3.21169	−0.109838
$856$	25.0687	0.856831
$857$	−3.16251	−0.108029	−0.0540147	−	0.998540i	$-0.517202\pi$
$857$	−3.16251	−0.108029	−0.0540147	+	0.998540i	$0.517202\pi$
$858$	−25.5528	−0.872357
$859$	−47.4574	−1.61923	−0.809613	−	0.586964i	$-0.800323\pi$
$859$	−47.4574	−1.61923	−0.809613	+	0.586964i	$0.800323\pi$
$860$	−3.91978	−0.133663
$861$	−19.6450	−0.669501
$862$	27.0405	0.921003
$863$	−10.6408	−0.362218	−0.181109	−	0.983463i	$-0.557969\pi$
$863$	−10.6408	−0.362218	−0.181109	+	0.983463i	$0.557969\pi$
$864$	2.21584	0.0753843
$865$	−0.248266	−0.00844130
$866$	−15.9038	−0.540434
$867$	15.7835	0.536035
$868$	6.24760	0.212057
$869$	0.0777444	0.00263730
$870$	1.30763	0.0443328
$871$	33.3889	1.13134
$872$	−17.8686	−0.605108
$873$	−5.91410	−0.200162
$874$	16.9932	0.574804
$875$	−26.0384	−0.880260
$876$	−2.23380	−0.0754730
$877$	2.92234	0.0986805	0.0493402	−	0.998782i	$-0.484288\pi$
$877$	2.92234	0.0986805	0.0493402	+	0.998782i	$0.484288\pi$
$878$	−6.94840	−0.234497
$879$	−26.0736	−0.879442
$880$	17.0127	0.573499
$881$	−14.6429	−0.493332	−0.246666	−	0.969101i	$-0.579335\pi$
$881$	−14.6429	−0.493332	−0.246666	+	0.969101i	$0.579335\pi$
$882$	−8.33762	−0.280742
$883$	52.1851	1.75617	0.878084	−	0.478506i	$-0.158822\pi$
$883$	52.1851	1.75617	0.878084	+	0.478506i	$0.158822\pi$
$884$	−8.07179	−0.271484
$885$	−4.78180	−0.160739
$886$	19.0376	0.639581
$887$	−23.8754	−0.801656	−0.400828	−	0.916153i	$-0.631278\pi$
$887$	−23.8754	−0.801656	−0.400828	+	0.916153i	$0.631278\pi$
$888$	−7.64807	−0.256652
$889$	−40.8328	−1.36949
$890$	3.46646	0.116196
$891$	4.65036	0.155793
$892$	−6.17264	−0.206675
$893$	−35.7710	−1.19703
$894$	5.31203	0.177661
$895$	−9.04810	−0.302444
$896$	47.4313	1.58457
$897$	−9.56893	−0.319497
$898$	−3.12049	−0.104132
$899$	−4.78374	−0.159547
$900$	−1.73888	−0.0579626
$901$	77.6876	2.58815
$902$	−40.1927	−1.33827
$903$	−44.0131	−1.46467
$904$	14.8746	0.494721
$905$	−0.235700	−0.00783494
$906$	−12.7859	−0.424783
$907$	24.2755	0.806056	0.403028	−	0.915188i	$-0.367958\pi$
$907$	24.2755	0.806056	0.403028	+	0.915188i	$0.367958\pi$
$908$	10.2040	0.338632
$909$	14.7014	0.487616
$910$	−15.2574	−0.505778
$911$	51.5427	1.70769	0.853843	−	0.520531i	$-0.174266\pi$
$911$	51.5427	1.70769	0.853843	+	0.520531i	$0.174266\pi$
$912$	−18.8738	−0.624974
$913$	48.3219	1.59922
$914$	33.5343	1.10921
$915$	2.46779	0.0815825
$916$	−9.14468	−0.302149
$917$	−26.4984	−0.875053
$918$	8.86508	0.292591
$919$	−34.4377	−1.13599	−0.567997	−	0.823030i	$-0.692282\pi$
$919$	−34.4377	−1.13599	−0.567997	+	0.823030i	$0.692282\pi$
$920$	5.27927	0.174052
$921$	−11.2027	−0.369142
$922$	−5.89254	−0.194061
$923$	−50.3021	−1.65571
$924$	−6.50101	−0.213868
$925$	13.4912	0.443586
$926$	−33.7067	−1.10767
$927$	−15.2174	−0.499804
$928$	2.37184	0.0778596
$929$	−13.2884	−0.435978	−0.217989	−	0.975951i	$-0.569950\pi$
$929$	−13.2884	−0.435978	−0.217989	+	0.975951i	$0.569950\pi$
$930$	−5.45953	−0.179025
$931$	21.9200	0.718398
$932$	−10.8260	−0.354619
$933$	19.9378	0.652735
$934$	−2.72879	−0.0892888
$935$	21.0085	0.687052
$936$	8.80687	0.287861
$937$	−39.5167	−1.29095	−0.645477	−	0.763780i	$-0.723341\pi$
$937$	−39.5167	−1.29095	−0.645477	+	0.763780i	$0.723341\pi$
$938$	51.2637	1.67382
$939$	−30.1350	−0.983419
$940$	2.75426	0.0898341
$941$	−39.0473	−1.27291	−0.636453	−	0.771316i	$-0.719599\pi$
$941$	−39.0473	−1.27291	−0.636453	+	0.771316i	$0.719599\pi$
$942$	27.5805	0.898621
$943$	−15.0512	−0.490135
$944$	−28.1007	−0.914599
$945$	2.77670	0.0903261
$946$	−90.0484	−2.92773
$947$	−54.5695	−1.77327	−0.886636	−	0.462468i	$-0.846964\pi$
$947$	−54.5695	−1.77327	−0.886636	+	0.462468i	$0.846964\pi$
$948$	0.00664093	0.000215687 0
$949$	−19.9569	−0.647829
$950$	27.5887	0.895095
$951$	11.0711	0.359006
$952$	50.0036	1.62063
$953$	−25.7852	−0.835265	−0.417632	−	0.908616i	$-0.637140\pi$
$953$	−25.7852	−0.835265	−0.417632	+	0.908616i	$0.637140\pi$
$954$	21.0077	0.680151
$955$	5.15939	0.166954
$956$	−10.4851	−0.339111
$957$	4.97778	0.160909
$958$	23.2569	0.751395
$959$	−9.84092	−0.317780
$960$	−4.60983	−0.148782
$961$	−11.0272	−0.355718
$962$	16.9347	0.545997
$963$	10.1020	0.325532
$964$	0.362409	0.0116724
$965$	9.30905	0.299669
$966$	−14.6917	−0.472696
$967$	−5.91207	−0.190119	−0.0950597	−	0.995472i	$-0.530304\pi$
$967$	−5.91207	−0.190119	−0.0950597	+	0.995472i	$0.530304\pi$
$968$	26.3687	0.847524
$969$	−23.3067	−0.748719
$970$	−7.22479	−0.231974
$971$	3.02413	0.0970489	0.0485244	−	0.998822i	$-0.484548\pi$
$971$	3.02413	0.0970489	0.0485244	+	0.998822i	$0.484548\pi$
$972$	0.397234	0.0127413
$973$	11.3736	0.364622
$974$	24.5889	0.787878
$975$	−15.5353	−0.497527
$976$	14.5022	0.464203
$977$	43.7029	1.39818	0.699090	−	0.715034i	$-0.253589\pi$
$977$	43.7029	1.39818	0.699090	+	0.715034i	$0.253589\pi$
$978$	19.1220	0.611453
$979$	13.1958	0.421741
$980$	−1.68777	−0.0539139
$981$	−7.20056	−0.229896
$982$	10.2931	0.328465
$983$	−8.84859	−0.282226	−0.141113	−	0.989993i	$-0.545068\pi$
$983$	−8.84859	−0.282226	−0.141113	+	0.989993i	$0.545068\pi$
$984$	13.8526	0.441604
$985$	−18.1623	−0.578700
$986$	9.48924	0.302199
$987$	30.9261	0.984390
$988$	5.73846	0.182565
$989$	−33.7211	−1.07227
$990$	5.68098	0.180553
$991$	38.8630	1.23452	0.617262	−	0.786757i	$-0.288242\pi$
$991$	38.8630	1.23452	0.617262	+	0.786757i	$0.288242\pi$
$992$	−9.90276	−0.314413
$993$	−19.4192	−0.616251
$994$	−77.2313	−2.44963
$995$	−11.8098	−0.374397
$996$	4.12766	0.130790
$997$	27.2781	0.863906	0.431953	−	0.901896i	$-0.357825\pi$
$997$	27.2781	0.863906	0.431953	+	0.901896i	$0.357825\pi$
$998$	50.2884	1.59185
$999$	−3.08195	−0.0975087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.19	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.19	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.54830 q^{2} +1.00000 q^{3} +0.397234 q^{4} -0.789007 q^{5} -1.54830 q^{6} -3.51923 q^{7} +2.48156 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.54830 q^{2} +1.00000 q^{3} +0.397234 q^{4} -0.789007 q^{5} -1.54830 q^{6} -3.51923 q^{7} +2.48156 q^{8} +1.00000 q^{9} +1.22162 q^{10} +4.65036 q^{11} +0.397234 q^{12} +3.54892 q^{13} +5.44883 q^{14} -0.789007 q^{15} -4.63667 q^{16} -5.72569 q^{17} -1.54830 q^{18} +4.07055 q^{19} -0.313420 q^{20} -3.51923 q^{21} -7.20016 q^{22} -2.69629 q^{23} +2.48156 q^{24} -4.37747 q^{25} -5.49479 q^{26} +1.00000 q^{27} -1.39796 q^{28} +1.07041 q^{29} +1.22162 q^{30} -4.46909 q^{31} +2.21584 q^{32} +4.65036 q^{33} +8.86508 q^{34} +2.77670 q^{35} +0.397234 q^{36} -3.08195 q^{37} -6.30243 q^{38} +3.54892 q^{39} -1.95797 q^{40} +5.58219 q^{41} +5.44883 q^{42} +12.5064 q^{43} +1.84728 q^{44} -0.789007 q^{45} +4.17467 q^{46} -8.78775 q^{47} -4.63667 q^{48} +5.38501 q^{49} +6.77763 q^{50} -5.72569 q^{51} +1.40975 q^{52} -13.5683 q^{53} -1.54830 q^{54} -3.66917 q^{55} -8.73320 q^{56} +4.07055 q^{57} -1.65731 q^{58} +6.06053 q^{59} -0.313420 q^{60} -3.12771 q^{61} +6.91949 q^{62} -3.51923 q^{63} +5.84257 q^{64} -2.80012 q^{65} -7.20016 q^{66} +9.40820 q^{67} -2.27444 q^{68} -2.69629 q^{69} -4.29917 q^{70} -14.1739 q^{71} +2.48156 q^{72} -5.62338 q^{73} +4.77179 q^{74} -4.37747 q^{75} +1.61696 q^{76} -16.3657 q^{77} -5.49479 q^{78} +0.0167179 q^{79} +3.65837 q^{80} +1.00000 q^{81} -8.64291 q^{82} +10.3910 q^{83} -1.39796 q^{84} +4.51761 q^{85} -19.3637 q^{86} +1.07041 q^{87} +11.5402 q^{88} +2.83759 q^{89} +1.22162 q^{90} -12.4895 q^{91} -1.07106 q^{92} -4.46909 q^{93} +13.6061 q^{94} -3.21169 q^{95} +2.21584 q^{96} -5.91410 q^{97} -8.33762 q^{98} +4.65036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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