LMFDB - Embedded newform 6034.2.a.p.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.32317 q^{3} +1.00000 q^{4} -0.695345 q^{5} +1.32317 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.24923 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.32317 q^{3} +1.00000 q^{4} -0.695345 q^{5} +1.32317 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.24923 q^{9} +0.695345 q^{10} +1.13495 q^{11} -1.32317 q^{12} +4.90471 q^{13} -1.00000 q^{14} +0.920056 q^{15} +1.00000 q^{16} +6.41111 q^{17} +1.24923 q^{18} -6.05821 q^{19} -0.695345 q^{20} -1.32317 q^{21} -1.13495 q^{22} -4.13283 q^{23} +1.32317 q^{24} -4.51650 q^{25} -4.90471 q^{26} +5.62244 q^{27} +1.00000 q^{28} -1.46114 q^{29} -0.920056 q^{30} +6.04617 q^{31} -1.00000 q^{32} -1.50173 q^{33} -6.41111 q^{34} -0.695345 q^{35} -1.24923 q^{36} +5.19637 q^{37} +6.05821 q^{38} -6.48974 q^{39} +0.695345 q^{40} +1.30926 q^{41} +1.32317 q^{42} +6.76344 q^{43} +1.13495 q^{44} +0.868647 q^{45} +4.13283 q^{46} -2.14552 q^{47} -1.32317 q^{48} +1.00000 q^{49} +4.51650 q^{50} -8.48297 q^{51} +4.90471 q^{52} +3.09745 q^{53} -5.62244 q^{54} -0.789182 q^{55} -1.00000 q^{56} +8.01602 q^{57} +1.46114 q^{58} +10.3038 q^{59} +0.920056 q^{60} -6.64283 q^{61} -6.04617 q^{62} -1.24923 q^{63} +1.00000 q^{64} -3.41046 q^{65} +1.50173 q^{66} -2.82175 q^{67} +6.41111 q^{68} +5.46842 q^{69} +0.695345 q^{70} +5.36288 q^{71} +1.24923 q^{72} -11.3723 q^{73} -5.19637 q^{74} +5.97607 q^{75} -6.05821 q^{76} +1.13495 q^{77} +6.48974 q^{78} -6.21873 q^{79} -0.695345 q^{80} -3.69172 q^{81} -1.30926 q^{82} +13.2288 q^{83} -1.32317 q^{84} -4.45794 q^{85} -6.76344 q^{86} +1.93333 q^{87} -1.13495 q^{88} -5.53228 q^{89} -0.868647 q^{90} +4.90471 q^{91} -4.13283 q^{92} -8.00008 q^{93} +2.14552 q^{94} +4.21255 q^{95} +1.32317 q^{96} -10.7699 q^{97} -1.00000 q^{98} -1.41782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.32317	−0.763930	−0.381965	−	0.924177i	$-0.624753\pi$
$3$	−1.32317	−0.763930	−0.381965	+	0.924177i	$0.624753\pi$
$4$	1.00000	0.500000
$5$	−0.695345	−0.310968	−0.155484	−	0.987838i	$-0.549694\pi$
$5$	−0.695345	−0.310968	−0.155484	+	0.987838i	$0.549694\pi$
$6$	1.32317	0.540180
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−1.24923	−0.416411
$10$	0.695345	0.219887
$11$	1.13495	0.342201	0.171100	−	0.985254i	$-0.445268\pi$
$11$	1.13495	0.342201	0.171100	+	0.985254i	$0.445268\pi$
$12$	−1.32317	−0.381965
$13$	4.90471	1.36032	0.680160	−	0.733063i	$-0.261910\pi$
$13$	4.90471	1.36032	0.680160	+	0.733063i	$0.261910\pi$
$14$	−1.00000	−0.267261
$15$	0.920056	0.237558
$16$	1.00000	0.250000
$17$	6.41111	1.55492	0.777462	−	0.628930i	$-0.216507\pi$
$17$	6.41111	1.55492	0.777462	+	0.628930i	$0.216507\pi$
$18$	1.24923	0.294447
$19$	−6.05821	−1.38985	−0.694924	−	0.719083i	$-0.744562\pi$
$19$	−6.05821	−1.38985	−0.694924	+	0.719083i	$0.744562\pi$
$20$	−0.695345	−0.155484
$21$	−1.32317	−0.288738
$22$	−1.13495	−0.241972
$23$	−4.13283	−0.861754	−0.430877	−	0.902411i	$-0.641796\pi$
$23$	−4.13283	−0.861754	−0.430877	+	0.902411i	$0.641796\pi$
$24$	1.32317	0.270090
$25$	−4.51650	−0.903299
$26$	−4.90471	−0.961892
$27$	5.62244	1.08204
$28$	1.00000	0.188982
$29$	−1.46114	−0.271327	−0.135663	−	0.990755i	$-0.543317\pi$
$29$	−1.46114	−0.271327	−0.135663	+	0.990755i	$0.543317\pi$
$30$	−0.920056	−0.167979
$31$	6.04617	1.08592	0.542962	−	0.839757i	$-0.317303\pi$
$31$	6.04617	1.08592	0.542962	+	0.839757i	$0.317303\pi$
$32$	−1.00000	−0.176777
$33$	−1.50173	−0.261417
$34$	−6.41111	−1.09950
$35$	−0.695345	−0.117535
$36$	−1.24923	−0.208205
$37$	5.19637	0.854279	0.427139	−	0.904186i	$-0.359521\pi$
$37$	5.19637	0.854279	0.427139	+	0.904186i	$0.359521\pi$
$38$	6.05821	0.982771
$39$	−6.48974	−1.03919
$40$	0.695345	0.109944
$41$	1.30926	0.204472	0.102236	−	0.994760i	$-0.467400\pi$
$41$	1.30926	0.204472	0.102236	+	0.994760i	$0.467400\pi$
$42$	1.32317	0.204169
$43$	6.76344	1.03141	0.515707	−	0.856765i	$-0.327529\pi$
$43$	6.76344	1.03141	0.515707	+	0.856765i	$0.327529\pi$
$44$	1.13495	0.171100
$45$	0.868647	0.129490
$46$	4.13283	0.609352
$47$	−2.14552	−0.312956	−0.156478	−	0.987681i	$-0.550014\pi$
$47$	−2.14552	−0.312956	−0.156478	+	0.987681i	$0.550014\pi$
$48$	−1.32317	−0.190983
$49$	1.00000	0.142857
$50$	4.51650	0.638729
$51$	−8.48297	−1.18785
$52$	4.90471	0.680160
$53$	3.09745	0.425467	0.212734	−	0.977110i	$-0.431763\pi$
$53$	3.09745	0.425467	0.212734	+	0.977110i	$0.431763\pi$
$54$	−5.62244	−0.765117
$55$	−0.789182	−0.106413
$56$	−1.00000	−0.133631
$57$	8.01602	1.06175
$58$	1.46114	0.191857
$59$	10.3038	1.34144	0.670722	−	0.741709i	$-0.265984\pi$
$59$	10.3038	1.34144	0.670722	+	0.741709i	$0.265984\pi$
$60$	0.920056	0.118779
$61$	−6.64283	−0.850527	−0.425264	−	0.905070i	$-0.639819\pi$
$61$	−6.64283	−0.850527	−0.425264	+	0.905070i	$0.639819\pi$
$62$	−6.04617	−0.767864
$63$	−1.24923	−0.157388
$64$	1.00000	0.125000
$65$	−3.41046	−0.423016
$66$	1.50173	0.184850
$67$	−2.82175	−0.344732	−0.172366	−	0.985033i	$-0.555141\pi$
$67$	−2.82175	−0.344732	−0.172366	+	0.985033i	$0.555141\pi$
$68$	6.41111	0.777462
$69$	5.46842	0.658320
$70$	0.695345	0.0831096
$71$	5.36288	0.636457	0.318228	−	0.948014i	$-0.396912\pi$
$71$	5.36288	0.636457	0.318228	+	0.948014i	$0.396912\pi$
$72$	1.24923	0.147223
$73$	−11.3723	−1.33103	−0.665516	−	0.746384i	$-0.731788\pi$
$73$	−11.3723	−1.33103	−0.665516	+	0.746384i	$0.731788\pi$
$74$	−5.19637	−0.604066
$75$	5.97607	0.690057
$76$	−6.05821	−0.694924
$77$	1.13495	0.129340
$78$	6.48974	0.734818
$79$	−6.21873	−0.699662	−0.349831	−	0.936813i	$-0.613761\pi$
$79$	−6.21873	−0.699662	−0.349831	+	0.936813i	$0.613761\pi$
$80$	−0.695345	−0.0777419
$81$	−3.69172	−0.410191
$82$	−1.30926	−0.144583
$83$	13.2288	1.45205	0.726023	−	0.687670i	$-0.241367\pi$
$83$	13.2288	1.45205	0.726023	+	0.687670i	$0.241367\pi$
$84$	−1.32317	−0.144369
$85$	−4.45794	−0.483531
$86$	−6.76344	−0.729320
$87$	1.93333	0.207275
$88$	−1.13495	−0.120986
$89$	−5.53228	−0.586420	−0.293210	−	0.956048i	$-0.594724\pi$
$89$	−5.53228	−0.586420	−0.293210	+	0.956048i	$0.594724\pi$
$90$	−0.868647	−0.0915635
$91$	4.90471	0.514153
$92$	−4.13283	−0.430877
$93$	−8.00008	−0.829570
$94$	2.14552	0.221294
$95$	4.21255	0.432198
$96$	1.32317	0.135045
$97$	−10.7699	−1.09352	−0.546760	−	0.837289i	$-0.684139\pi$
$97$	−10.7699	−1.09352	−0.546760	+	0.837289i	$0.684139\pi$
$98$	−1.00000	−0.101015
$99$	−1.41782	−0.142496
$100$	−4.51650	−0.451650
$101$	−4.34520	−0.432363	−0.216182	−	0.976353i	$-0.569360\pi$
$101$	−4.34520	−0.432363	−0.216182	+	0.976353i	$0.569360\pi$
$102$	8.48297	0.839939
$103$	10.3239	1.01724	0.508621	−	0.860990i	$-0.330155\pi$
$103$	10.3239	1.01724	0.508621	+	0.860990i	$0.330155\pi$
$104$	−4.90471	−0.480946
$105$	0.920056	0.0897883
$106$	−3.09745	−0.300851
$107$	1.81820	0.175772	0.0878859	−	0.996131i	$-0.471989\pi$
$107$	1.81820	0.175772	0.0878859	+	0.996131i	$0.471989\pi$
$108$	5.62244	0.541019
$109$	−11.4588	−1.09755	−0.548775	−	0.835970i	$-0.684906\pi$
$109$	−11.4588	−1.09755	−0.548775	+	0.835970i	$0.684906\pi$
$110$	0.789182	0.0752456
$111$	−6.87566	−0.652609
$112$	1.00000	0.0944911
$113$	−1.81942	−0.171157	−0.0855783	−	0.996331i	$-0.527274\pi$
$113$	−1.81942	−0.171157	−0.0855783	+	0.996331i	$0.527274\pi$
$114$	−8.01602	−0.750769
$115$	2.87374	0.267978
$116$	−1.46114	−0.135663
$117$	−6.12712	−0.566452
$118$	−10.3038	−0.948545
$119$	6.41111	0.587706
$120$	−0.920056	−0.0839893
$121$	−9.71189	−0.882899
$122$	6.64283	0.601414
$123$	−1.73237	−0.156202
$124$	6.04617	0.542962
$125$	6.61725	0.591864
$126$	1.24923	0.111290
$127$	7.70094	0.683348	0.341674	−	0.939819i	$-0.389006\pi$
$127$	7.70094	0.683348	0.341674	+	0.939819i	$0.389006\pi$
$128$	−1.00000	−0.0883883
$129$	−8.94915	−0.787929
$130$	3.41046	0.299117
$131$	−9.31152	−0.813551	−0.406776	−	0.913528i	$-0.633347\pi$
$131$	−9.31152	−0.813551	−0.406776	+	0.913528i	$0.633347\pi$
$132$	−1.50173	−0.130709
$133$	−6.05821	−0.525313
$134$	2.82175	0.243762
$135$	−3.90953	−0.336479
$136$	−6.41111	−0.549749
$137$	19.6913	1.68234	0.841172	−	0.540768i	$-0.181866\pi$
$137$	19.6913	1.68234	0.841172	+	0.540768i	$0.181866\pi$
$138$	−5.46842	−0.465502
$139$	−2.25874	−0.191584	−0.0957921	−	0.995401i	$-0.530538\pi$
$139$	−2.25874	−0.191584	−0.0957921	+	0.995401i	$0.530538\pi$
$140$	−0.695345	−0.0587674
$141$	2.83888	0.239077
$142$	−5.36288	−0.450043
$143$	5.56660	0.465503
$144$	−1.24923	−0.104103
$145$	1.01599	0.0843738
$146$	11.3723	0.941181
$147$	−1.32317	−0.109133
$148$	5.19637	0.427139
$149$	−7.96319	−0.652370	−0.326185	−	0.945306i	$-0.605763\pi$
$149$	−7.96319	−0.652370	−0.326185	+	0.945306i	$0.605763\pi$
$150$	−5.97607	−0.487944
$151$	−17.2498	−1.40377	−0.701884	−	0.712291i	$-0.747658\pi$
$151$	−17.2498	−1.40377	−0.701884	+	0.712291i	$0.747658\pi$
$152$	6.05821	0.491386
$153$	−8.00897	−0.647487
$154$	−1.13495	−0.0914570
$155$	−4.20417	−0.337687
$156$	−6.48974	−0.519595
$157$	13.9844	1.11608	0.558038	−	0.829815i	$-0.311554\pi$
$157$	13.9844	1.11608	0.558038	+	0.829815i	$0.311554\pi$
$158$	6.21873	0.494736
$159$	−4.09844	−0.325027
$160$	0.695345	0.0549718
$161$	−4.13283	−0.325712
$162$	3.69172	0.290049
$163$	3.42218	0.268046	0.134023	−	0.990978i	$-0.457210\pi$
$163$	3.42218	0.268046	0.134023	+	0.990978i	$0.457210\pi$
$164$	1.30926	0.102236
$165$	1.04422	0.0812923
$166$	−13.2288	−1.02675
$167$	5.58991	0.432560	0.216280	−	0.976331i	$-0.430608\pi$
$167$	5.58991	0.432560	0.216280	+	0.976331i	$0.430608\pi$
$168$	1.32317	0.102084
$169$	11.0561	0.850472
$170$	4.45794	0.341908
$171$	7.56811	0.578748
$172$	6.76344	0.515707
$173$	−1.38604	−0.105379	−0.0526894	−	0.998611i	$-0.516779\pi$
$173$	−1.38604	−0.105379	−0.0526894	+	0.998611i	$0.516779\pi$
$174$	−1.93333	−0.146565
$175$	−4.51650	−0.341415
$176$	1.13495	0.0855502
$177$	−13.6337	−1.02477
$178$	5.53228	0.414662
$179$	14.8286	1.10834	0.554172	−	0.832402i	$-0.313035\pi$
$179$	14.8286	1.10834	0.554172	+	0.832402i	$0.313035\pi$
$180$	0.868647	0.0647451
$181$	10.3335	0.768086	0.384043	−	0.923315i	$-0.374531\pi$
$181$	10.3335	0.768086	0.384043	+	0.923315i	$0.374531\pi$
$182$	−4.90471	−0.363561
$183$	8.78957	0.649743
$184$	4.13283	0.304676
$185$	−3.61327	−0.265653
$186$	8.00008	0.586595
$187$	7.27630	0.532096
$188$	−2.14552	−0.156478
$189$	5.62244	0.408972
$190$	−4.21255	−0.305610
$191$	6.85280	0.495851	0.247926	−	0.968779i	$-0.420251\pi$
$191$	6.85280	0.495851	0.247926	+	0.968779i	$0.420251\pi$
$192$	−1.32317	−0.0954913
$193$	−13.9762	−1.00603	−0.503015	−	0.864277i	$-0.667776\pi$
$193$	−13.9762	−1.00603	−0.503015	+	0.864277i	$0.667776\pi$
$194$	10.7699	0.773235
$195$	4.51261	0.323154
$196$	1.00000	0.0714286
$197$	−8.53047	−0.607771	−0.303885	−	0.952709i	$-0.598284\pi$
$197$	−8.53047	−0.607771	−0.303885	+	0.952709i	$0.598284\pi$
$198$	1.41782	0.100760
$199$	−7.00891	−0.496848	−0.248424	−	0.968651i	$-0.579913\pi$
$199$	−7.00891	−0.496848	−0.248424	+	0.968651i	$0.579913\pi$
$200$	4.51650	0.319364
$201$	3.73365	0.263351
$202$	4.34520	0.305727
$203$	−1.46114	−0.102552
$204$	−8.48297	−0.593926
$205$	−0.910386	−0.0635841
$206$	−10.3239	−0.719299
$207$	5.16286	0.358844
$208$	4.90471	0.340080
$209$	−6.87577	−0.475607
$210$	−0.920056	−0.0634899
$211$	−16.8481	−1.15987	−0.579934	−	0.814663i	$-0.696922\pi$
$211$	−16.8481	−1.15987	−0.579934	+	0.814663i	$0.696922\pi$
$212$	3.09745	0.212734
$213$	−7.09598	−0.486208
$214$	−1.81820	−0.124289
$215$	−4.70292	−0.320737
$216$	−5.62244	−0.382559
$217$	6.04617	0.410441
$218$	11.4588	0.776085
$219$	15.0475	1.01681
$220$	−0.789182	−0.0532067
$221$	31.4446	2.11519
$222$	6.87566	0.461464
$223$	27.3848	1.83382	0.916912	−	0.399089i	$-0.130674\pi$
$223$	27.3848	1.83382	0.916912	+	0.399089i	$0.130674\pi$
$224$	−1.00000	−0.0668153
$225$	5.64215	0.376144
$226$	1.81942	0.121026
$227$	−15.6285	−1.03730	−0.518651	−	0.854986i	$-0.673566\pi$
$227$	−15.6285	−1.03730	−0.518651	+	0.854986i	$0.673566\pi$
$228$	8.01602	0.530874
$229$	21.4318	1.41625	0.708126	−	0.706086i	$-0.249541\pi$
$229$	21.4318	1.41625	0.708126	+	0.706086i	$0.249541\pi$
$230$	−2.87374	−0.189489
$231$	−1.50173	−0.0988065
$232$	1.46114	0.0959284
$233$	−2.81098	−0.184154	−0.0920769	−	0.995752i	$-0.529351\pi$
$233$	−2.81098	−0.184154	−0.0920769	+	0.995752i	$0.529351\pi$
$234$	6.12712	0.400542
$235$	1.49188	0.0973194
$236$	10.3038	0.670722
$237$	8.22841	0.534493
$238$	−6.41111	−0.415571
$239$	−18.4783	−1.19526	−0.597632	−	0.801770i	$-0.703892\pi$
$239$	−18.4783	−1.19526	−0.597632	+	0.801770i	$0.703892\pi$
$240$	0.920056	0.0593894
$241$	17.5178	1.12842	0.564211	−	0.825631i	$-0.309181\pi$
$241$	17.5178	1.12842	0.564211	+	0.825631i	$0.309181\pi$
$242$	9.71189	0.624304
$243$	−11.9826	−0.768681
$244$	−6.64283	−0.425264
$245$	−0.695345	−0.0444240
$246$	1.73237	0.110452
$247$	−29.7137	−1.89064
$248$	−6.04617	−0.383932
$249$	−17.5039	−1.10926
$250$	−6.61725	−0.418511
$251$	23.1934	1.46396	0.731978	−	0.681328i	$-0.238597\pi$
$251$	23.1934	1.46396	0.731978	+	0.681328i	$0.238597\pi$
$252$	−1.24923	−0.0786942
$253$	−4.69056	−0.294893
$254$	−7.70094	−0.483200
$255$	5.89859	0.369384
$256$	1.00000	0.0625000
$257$	22.0930	1.37813	0.689063	−	0.724701i	$-0.258022\pi$
$257$	22.0930	1.37813	0.689063	+	0.724701i	$0.258022\pi$
$258$	8.94915	0.557150
$259$	5.19637	0.322887
$260$	−3.41046	−0.211508
$261$	1.82530	0.112983
$262$	9.31152	0.575268
$263$	13.9840	0.862290	0.431145	−	0.902283i	$-0.358110\pi$
$263$	13.9840	0.862290	0.431145	+	0.902283i	$0.358110\pi$
$264$	1.50173	0.0924250
$265$	−2.15380	−0.132307
$266$	6.05821	0.371453
$267$	7.32012	0.447984
$268$	−2.82175	−0.172366
$269$	−14.9843	−0.913609	−0.456804	−	0.889567i	$-0.651006\pi$
$269$	−14.9843	−0.913609	−0.456804	+	0.889567i	$0.651006\pi$
$270$	3.90953	0.237927
$271$	18.9388	1.15045	0.575227	−	0.817994i	$-0.304914\pi$
$271$	18.9388	1.15045	0.575227	+	0.817994i	$0.304914\pi$
$272$	6.41111	0.388731
$273$	−6.48974	−0.392777
$274$	−19.6913	−1.18960
$275$	−5.12600	−0.309110
$276$	5.46842	0.329160
$277$	22.5320	1.35381	0.676907	−	0.736068i	$-0.263320\pi$
$277$	22.5320	1.35381	0.676907	+	0.736068i	$0.263320\pi$
$278$	2.25874	0.135470
$279$	−7.55307	−0.452191
$280$	0.695345	0.0415548
$281$	22.2379	1.32660	0.663301	−	0.748353i	$-0.269155\pi$
$281$	22.2379	1.32660	0.663301	+	0.748353i	$0.269155\pi$
$282$	−2.83888	−0.169053
$283$	−28.7407	−1.70846	−0.854230	−	0.519895i	$-0.825971\pi$
$283$	−28.7407	−1.70846	−0.854230	+	0.519895i	$0.825971\pi$
$284$	5.36288	0.318228
$285$	−5.57390	−0.330169
$286$	−5.56660	−0.329160
$287$	1.30926	0.0772831
$288$	1.24923	0.0736117
$289$	24.1024	1.41779
$290$	−1.01599	−0.0596613
$291$	14.2504	0.835373
$292$	−11.3723	−0.665516
$293$	−29.9113	−1.74743	−0.873717	−	0.486435i	$-0.838297\pi$
$293$	−29.9113	−1.74743	−0.873717	+	0.486435i	$0.838297\pi$
$294$	1.32317	0.0771686
$295$	−7.16472	−0.417146
$296$	−5.19637	−0.302033
$297$	6.38119	0.370274
$298$	7.96319	0.461295
$299$	−20.2703	−1.17226
$300$	5.97607	0.345029
$301$	6.76344	0.389838
$302$	17.2498	0.992614
$303$	5.74942	0.330295
$304$	−6.05821	−0.347462
$305$	4.61906	0.264486
$306$	8.00897	0.457842
$307$	−0.657251	−0.0375113	−0.0187556	−	0.999824i	$-0.505970\pi$
$307$	−0.657251	−0.0375113	−0.0187556	+	0.999824i	$0.505970\pi$
$308$	1.13495	0.0646698
$309$	−13.6602	−0.777102
$310$	4.20417	0.238781
$311$	13.7185	0.777904	0.388952	−	0.921258i	$-0.372837\pi$
$311$	13.7185	0.777904	0.388952	+	0.921258i	$0.372837\pi$
$312$	6.48974	0.367409
$313$	−4.14358	−0.234209	−0.117105	−	0.993120i	$-0.537361\pi$
$313$	−4.14358	−0.234209	−0.117105	+	0.993120i	$0.537361\pi$
$314$	−13.9844	−0.789185
$315$	0.868647	0.0489427
$316$	−6.21873	−0.349831
$317$	8.34865	0.468907	0.234454	−	0.972127i	$-0.424670\pi$
$317$	8.34865	0.468907	0.234454	+	0.972127i	$0.424670\pi$
$318$	4.09844	0.229829
$319$	−1.65832	−0.0928481
$320$	−0.695345	−0.0388710
$321$	−2.40578	−0.134277
$322$	4.13283	0.230313
$323$	−38.8399	−2.16111
$324$	−3.69172	−0.205096
$325$	−22.1521	−1.22878
$326$	−3.42218	−0.189537
$327$	15.1618	0.838451
$328$	−1.30926	−0.0722917
$329$	−2.14552	−0.118286
$330$	−1.04422	−0.0574824
$331$	8.68271	0.477245	0.238623	−	0.971112i	$-0.423304\pi$
$331$	8.68271	0.477245	0.238623	+	0.971112i	$0.423304\pi$
$332$	13.2288	0.726023
$333$	−6.49148	−0.355731
$334$	−5.58991	−0.305866
$335$	1.96209	0.107200
$336$	−1.32317	−0.0721846
$337$	−12.4703	−0.679298	−0.339649	−	0.940552i	$-0.610308\pi$
$337$	−12.4703	−0.679298	−0.339649	+	0.940552i	$0.610308\pi$
$338$	−11.0561	−0.601375
$339$	2.40740	0.130752
$340$	−4.45794	−0.241765
$341$	6.86211	0.371604
$342$	−7.56811	−0.409237
$343$	1.00000	0.0539949
$344$	−6.76344	−0.364660
$345$	−3.80243	−0.204716
$346$	1.38604	0.0745141
$347$	24.1693	1.29748	0.648738	−	0.761011i	$-0.275297\pi$
$347$	24.1693	1.29748	0.648738	+	0.761011i	$0.275297\pi$
$348$	1.93333	0.103637
$349$	16.0881	0.861179	0.430589	−	0.902548i	$-0.358306\pi$
$349$	16.0881	0.861179	0.430589	+	0.902548i	$0.358306\pi$
$350$	4.51650	0.241417
$351$	27.5764	1.47192
$352$	−1.13495	−0.0604931
$353$	2.67849	0.142562	0.0712808	−	0.997456i	$-0.477291\pi$
$353$	2.67849	0.142562	0.0712808	+	0.997456i	$0.477291\pi$
$354$	13.6337	0.724622
$355$	−3.72905	−0.197917
$356$	−5.53228	−0.293210
$357$	−8.48297	−0.448966
$358$	−14.8286	−0.783717
$359$	27.3126	1.44151	0.720753	−	0.693192i	$-0.243796\pi$
$359$	27.3126	1.44151	0.720753	+	0.693192i	$0.243796\pi$
$360$	−0.868647	−0.0457817
$361$	17.7019	0.931679
$362$	−10.3335	−0.543119
$363$	12.8504	0.674473
$364$	4.90471	0.257076
$365$	7.90769	0.413908
$366$	−8.78957	−0.459438
$367$	−0.144410	−0.00753814	−0.00376907	−	0.999993i	$-0.501200\pi$
$367$	−0.144410	−0.00753814	−0.00376907	+	0.999993i	$0.501200\pi$
$368$	−4.13283	−0.215439
$369$	−1.63557	−0.0851443
$370$	3.61327	0.187845
$371$	3.09745	0.160812
$372$	−8.00008	−0.414785
$373$	−19.1519	−0.991648	−0.495824	−	0.868423i	$-0.665134\pi$
$373$	−19.1519	−0.991648	−0.495824	+	0.868423i	$0.665134\pi$
$374$	−7.27630	−0.376249
$375$	−8.75571	−0.452143
$376$	2.14552	0.110647
$377$	−7.16645	−0.369091
$378$	−5.62244	−0.289187
$379$	8.06830	0.414441	0.207220	−	0.978294i	$-0.433558\pi$
$379$	8.06830	0.414441	0.207220	+	0.978294i	$0.433558\pi$
$380$	4.21255	0.216099
$381$	−10.1896	−0.522030
$382$	−6.85280	−0.350620
$383$	−16.1179	−0.823584	−0.411792	−	0.911278i	$-0.635097\pi$
$383$	−16.1179	−0.823584	−0.411792	+	0.911278i	$0.635097\pi$
$384$	1.32317	0.0675225
$385$	−0.789182	−0.0402205
$386$	13.9762	0.711371
$387$	−8.44911	−0.429492
$388$	−10.7699	−0.546760
$389$	9.19895	0.466405	0.233203	−	0.972428i	$-0.425079\pi$
$389$	9.19895	0.466405	0.233203	+	0.972428i	$0.425079\pi$
$390$	−4.51261	−0.228505
$391$	−26.4960	−1.33996
$392$	−1.00000	−0.0505076
$393$	12.3207	0.621496
$394$	8.53047	0.429759
$395$	4.32416	0.217572
$396$	−1.41782	−0.0712480
$397$	0.178207	0.00894397	0.00447198	−	0.999990i	$-0.498577\pi$
$397$	0.178207	0.00894397	0.00447198	+	0.999990i	$0.498577\pi$
$398$	7.00891	0.351325
$399$	8.01602	0.401303
$400$	−4.51650	−0.225825
$401$	16.9720	0.847543	0.423772	−	0.905769i	$-0.360706\pi$
$401$	16.9720	0.847543	0.423772	+	0.905769i	$0.360706\pi$
$402$	−3.73365	−0.186217
$403$	29.6547	1.47720
$404$	−4.34520	−0.216182
$405$	2.56702	0.127556
$406$	1.46114	0.0725151
$407$	5.89763	0.292335
$408$	8.48297	0.419969
$409$	0.0283946	0.00140402	0.000702012	−	1.00000i	$-0.499777\pi$
$409$	0.0283946	0.00140402	0.000702012		1.00000i	$0.499777\pi$
$410$	0.910386	0.0449608
$411$	−26.0549	−1.28519
$412$	10.3239	0.508621
$413$	10.3038	0.507018
$414$	−5.16286	−0.253741
$415$	−9.19856	−0.451539
$416$	−4.90471	−0.240473
$417$	2.98869	0.146357
$418$	6.87577	0.336305
$419$	−9.39792	−0.459118	−0.229559	−	0.973295i	$-0.573728\pi$
$419$	−9.39792	−0.459118	−0.229559	+	0.973295i	$0.573728\pi$
$420$	0.920056	0.0448942
$421$	−8.32166	−0.405573	−0.202786	−	0.979223i	$-0.565000\pi$
$421$	−8.32166	−0.405573	−0.202786	+	0.979223i	$0.565000\pi$
$422$	16.8481	0.820151
$423$	2.68026	0.130318
$424$	−3.09745	−0.150425
$425$	−28.9558	−1.40456
$426$	7.09598	0.343801
$427$	−6.64283	−0.321469
$428$	1.81820	0.0878859
$429$	−7.36554	−0.355611
$430$	4.70292	0.226795
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.62244	0.270510
$433$	−0.907871	−0.0436295	−0.0218147	−	0.999762i	$-0.506944\pi$
$433$	−0.907871	−0.0436295	−0.0218147	+	0.999762i	$0.506944\pi$
$434$	−6.04617	−0.290225
$435$	−1.34433	−0.0644557
$436$	−11.4588	−0.548775
$437$	25.0375	1.19771
$438$	−15.0475	−0.718997
$439$	−32.5358	−1.55285	−0.776425	−	0.630210i	$-0.782969\pi$
$439$	−32.5358	−1.55285	−0.776425	+	0.630210i	$0.782969\pi$
$440$	0.789182	0.0376228
$441$	−1.24923	−0.0594873
$442$	−31.4446	−1.49567
$443$	25.9572	1.23326	0.616631	−	0.787253i	$-0.288497\pi$
$443$	25.9572	1.23326	0.616631	+	0.787253i	$0.288497\pi$
$444$	−6.87566	−0.326305
$445$	3.84684	0.182358
$446$	−27.3848	−1.29671
$447$	10.5366	0.498365
$448$	1.00000	0.0472456
$449$	20.8620	0.984537	0.492268	−	0.870443i	$-0.336168\pi$
$449$	20.8620	0.984537	0.492268	+	0.870443i	$0.336168\pi$
$450$	−5.64215	−0.265974
$451$	1.48594	0.0699704
$452$	−1.81942	−0.0855783
$453$	22.8243	1.07238
$454$	15.6285	0.733484
$455$	−3.41046	−0.159885
$456$	−8.01602	−0.375384
$457$	32.0069	1.49722	0.748610	−	0.663010i	$-0.230721\pi$
$457$	32.0069	1.49722	0.748610	+	0.663010i	$0.230721\pi$
$458$	−21.4318	−1.00144
$459$	36.0461	1.68249
$460$	2.87374	0.133989
$461$	−9.39383	−0.437514	−0.218757	−	0.975779i	$-0.570200\pi$
$461$	−9.39383	−0.437514	−0.218757	+	0.975779i	$0.570200\pi$
$462$	1.50173	0.0698667
$463$	2.96839	0.137953	0.0689764	−	0.997618i	$-0.478027\pi$
$463$	2.96839	0.137953	0.0689764	+	0.997618i	$0.478027\pi$
$464$	−1.46114	−0.0678316
$465$	5.56282	0.257970
$466$	2.81098	0.130216
$467$	21.8484	1.01102	0.505512	−	0.862820i	$-0.331304\pi$
$467$	21.8484	1.01102	0.505512	+	0.862820i	$0.331304\pi$
$468$	−6.12712	−0.283226
$469$	−2.82175	−0.130296
$470$	−1.49188	−0.0688152
$471$	−18.5037	−0.852604
$472$	−10.3038	−0.474272
$473$	7.67617	0.352951
$474$	−8.22841	−0.377943
$475$	27.3619	1.25545
$476$	6.41111	0.293853
$477$	−3.86943	−0.177169
$478$	18.4783	0.845179
$479$	42.0654	1.92202	0.961009	−	0.276519i	$-0.0891808\pi$
$479$	42.0654	1.92202	0.961009	+	0.276519i	$0.0891808\pi$
$480$	−0.920056	−0.0419946
$481$	25.4867	1.16209
$482$	−17.5178	−0.797915
$483$	5.46842	0.248822
$484$	−9.71189	−0.441449
$485$	7.48881	0.340049
$486$	11.9826	0.543540
$487$	13.9934	0.634100	0.317050	−	0.948409i	$-0.397308\pi$
$487$	13.9934	0.634100	0.317050	+	0.948409i	$0.397308\pi$
$488$	6.64283	0.300707
$489$	−4.52811	−0.204768
$490$	0.695345	0.0314125
$491$	16.5057	0.744894	0.372447	−	0.928054i	$-0.378519\pi$
$491$	16.5057	0.744894	0.372447	+	0.928054i	$0.378519\pi$
$492$	−1.73237	−0.0781011
$493$	−9.36752	−0.421892
$494$	29.7137	1.33688
$495$	0.985872	0.0443117
$496$	6.04617	0.271481
$497$	5.36288	0.240558
$498$	17.5039	0.784366
$499$	9.04228	0.404788	0.202394	−	0.979304i	$-0.435128\pi$
$499$	9.04228	0.404788	0.202394	+	0.979304i	$0.435128\pi$
$500$	6.61725	0.295932
$501$	−7.39638	−0.330446
$502$	−23.1934	−1.03517
$503$	24.4697	1.09105	0.545524	−	0.838095i	$-0.316331\pi$
$503$	24.4697	1.09105	0.545524	+	0.838095i	$0.316331\pi$
$504$	1.24923	0.0556452
$505$	3.02141	0.134451
$506$	4.69056	0.208521
$507$	−14.6291	−0.649701
$508$	7.70094	0.341674
$509$	−18.1707	−0.805403	−0.402701	−	0.915331i	$-0.631929\pi$
$509$	−18.1707	−0.805403	−0.402701	+	0.915331i	$0.631929\pi$
$510$	−5.89859	−0.261194
$511$	−11.3723	−0.503082
$512$	−1.00000	−0.0441942
$513$	−34.0619	−1.50387
$514$	−22.0930	−0.974482
$515$	−7.17866	−0.316330
$516$	−8.94915	−0.393964
$517$	−2.43506	−0.107094
$518$	−5.19637	−0.228316
$519$	1.83396	0.0805021
$520$	3.41046	0.149559
$521$	−23.6148	−1.03458	−0.517292	−	0.855809i	$-0.673060\pi$
$521$	−23.6148	−1.03458	−0.517292	+	0.855809i	$0.673060\pi$
$522$	−1.82530	−0.0798913
$523$	19.8115	0.866297	0.433149	−	0.901323i	$-0.357403\pi$
$523$	19.8115	0.866297	0.433149	+	0.901323i	$0.357403\pi$
$524$	−9.31152	−0.406776
$525$	5.97607	0.260817
$526$	−13.9840	−0.609731
$527$	38.7627	1.68853
$528$	−1.50173	−0.0653543
$529$	−5.91973	−0.257380
$530$	2.15380	0.0935549
$531$	−12.8719	−0.558592
$532$	−6.05821	−0.262657
$533$	6.42153	0.278147
$534$	−7.32012	−0.316773
$535$	−1.26427	−0.0546593
$536$	2.82175	0.121881
$537$	−19.6207	−0.846697
$538$	14.9843	0.646019
$539$	1.13495	0.0488858
$540$	−3.90953	−0.168240
$541$	14.9666	0.643466	0.321733	−	0.946830i	$-0.395735\pi$
$541$	14.9666	0.643466	0.321733	+	0.946830i	$0.395735\pi$
$542$	−18.9388	−0.813493
$543$	−13.6730	−0.586764
$544$	−6.41111	−0.274874
$545$	7.96779	0.341302
$546$	6.48974	0.277735
$547$	20.8275	0.890518	0.445259	−	0.895402i	$-0.353112\pi$
$547$	20.8275	0.890518	0.445259	+	0.895402i	$0.353112\pi$
$548$	19.6913	0.841172
$549$	8.29844	0.354169
$550$	5.12600	0.218573
$551$	8.85188	0.377103
$552$	−5.46842	−0.232751
$553$	−6.21873	−0.264447
$554$	−22.5320	−0.957291
$555$	4.78096	0.202940
$556$	−2.25874	−0.0957921
$557$	−2.87376	−0.121765	−0.0608825	−	0.998145i	$-0.519392\pi$
$557$	−2.87376	−0.121765	−0.0608825	+	0.998145i	$0.519392\pi$
$558$	7.55307	0.319747
$559$	33.1727	1.40305
$560$	−0.695345	−0.0293837
$561$	−9.62775	−0.406484
$562$	−22.2379	−0.938050
$563$	31.1729	1.31378	0.656891	−	0.753986i	$-0.271871\pi$
$563$	31.1729	1.31378	0.656891	+	0.753986i	$0.271871\pi$
$564$	2.83888	0.119538
$565$	1.26512	0.0532242
$566$	28.7407	1.20806
$567$	−3.69172	−0.155038
$568$	−5.36288	−0.225021
$569$	8.90729	0.373413	0.186706	−	0.982416i	$-0.440219\pi$
$569$	8.90729	0.373413	0.186706	+	0.982416i	$0.440219\pi$
$570$	5.57390	0.233465
$571$	29.2583	1.22442	0.612210	−	0.790695i	$-0.290281\pi$
$571$	29.2583	1.22442	0.612210	+	0.790695i	$0.290281\pi$
$572$	5.56660	0.232751
$573$	−9.06739	−0.378796
$574$	−1.30926	−0.0546474
$575$	18.6659	0.778422
$576$	−1.24923	−0.0520513
$577$	−2.67614	−0.111409	−0.0557047	−	0.998447i	$-0.517741\pi$
$577$	−2.67614	−0.111409	−0.0557047	+	0.998447i	$0.517741\pi$
$578$	−24.1024	−1.00253
$579$	18.4929	0.768537
$580$	1.01599	0.0421869
$581$	13.2288	0.548822
$582$	−14.2504	−0.590698
$583$	3.51545	0.145595
$584$	11.3723	0.470591
$585$	4.26046	0.176148
$586$	29.9113	1.23562
$587$	13.6828	0.564750	0.282375	−	0.959304i	$-0.408878\pi$
$587$	13.6828	0.564750	0.282375	+	0.959304i	$0.408878\pi$
$588$	−1.32317	−0.0545664
$589$	−36.6290	−1.50927
$590$	7.16472	0.294967
$591$	11.2872	0.464294
$592$	5.19637	0.213570
$593$	38.2903	1.57239	0.786196	−	0.617977i	$-0.212047\pi$
$593$	38.2903	1.57239	0.786196	+	0.617977i	$0.212047\pi$
$594$	−6.38119	−0.261824
$595$	−4.45794	−0.182758
$596$	−7.96319	−0.326185
$597$	9.27395	0.379558
$598$	20.2703	0.828914
$599$	33.6758	1.37595	0.687977	−	0.725732i	$-0.258499\pi$
$599$	33.6758	1.37595	0.687977	+	0.725732i	$0.258499\pi$
$600$	−5.97607	−0.243972
$601$	−1.99255	−0.0812778	−0.0406389	−	0.999174i	$-0.512939\pi$
$601$	−1.99255	−0.0812778	−0.0406389	+	0.999174i	$0.512939\pi$
$602$	−6.76344	−0.275657
$603$	3.52502	0.143550
$604$	−17.2498	−0.701884
$605$	6.75311	0.274553
$606$	−5.74942	−0.233554
$607$	25.3367	1.02838	0.514192	−	0.857675i	$-0.328092\pi$
$607$	25.3367	1.02838	0.514192	+	0.857675i	$0.328092\pi$
$608$	6.05821	0.245693
$609$	1.93333	0.0783424
$610$	−4.61906	−0.187020
$611$	−10.5232	−0.425721
$612$	−8.00897	−0.323743
$613$	−2.22627	−0.0899180	−0.0449590	−	0.998989i	$-0.514316\pi$
$613$	−2.22627	−0.0899180	−0.0449590	+	0.998989i	$0.514316\pi$
$614$	0.657251	0.0265245
$615$	1.20459	0.0485738
$616$	−1.13495	−0.0457285
$617$	16.0268	0.645214	0.322607	−	0.946533i	$-0.395441\pi$
$617$	16.0268	0.645214	0.322607	+	0.946533i	$0.395441\pi$
$618$	13.6602	0.549494
$619$	−40.1733	−1.61470	−0.807351	−	0.590071i	$-0.799100\pi$
$619$	−40.1733	−1.61470	−0.807351	+	0.590071i	$0.799100\pi$
$620$	−4.20417	−0.168844
$621$	−23.2366	−0.932451
$622$	−13.7185	−0.550062
$623$	−5.53228	−0.221646
$624$	−6.48974	−0.259797
$625$	17.9812	0.719248
$626$	4.14358	0.165611
$627$	9.09779	0.363331
$628$	13.9844	0.558038
$629$	33.3145	1.32834
$630$	−0.868647	−0.0346077
$631$	42.3514	1.68598	0.842992	−	0.537926i	$-0.180792\pi$
$631$	42.3514	1.68598	0.842992	+	0.537926i	$0.180792\pi$
$632$	6.21873	0.247368
$633$	22.2928	0.886058
$634$	−8.34865	−0.331567
$635$	−5.35481	−0.212499
$636$	−4.09844	−0.162514
$637$	4.90471	0.194332
$638$	1.65832	0.0656535
$639$	−6.69948	−0.265027
$640$	0.695345	0.0274859
$641$	17.5336	0.692534	0.346267	−	0.938136i	$-0.387449\pi$
$641$	17.5336	0.692534	0.346267	+	0.938136i	$0.387449\pi$
$642$	2.40578	0.0949484
$643$	−31.8893	−1.25759	−0.628795	−	0.777571i	$-0.716452\pi$
$643$	−31.8893	−1.25759	−0.628795	+	0.777571i	$0.716452\pi$
$644$	−4.13283	−0.162856
$645$	6.22275	0.245020
$646$	38.8399	1.52813
$647$	−36.5754	−1.43793	−0.718963	−	0.695048i	$-0.755383\pi$
$647$	−36.5754	−1.43793	−0.718963	+	0.695048i	$0.755383\pi$
$648$	3.69172	0.145025
$649$	11.6943	0.459043
$650$	22.1521	0.868876
$651$	−8.00008	−0.313548
$652$	3.42218	0.134023
$653$	33.5268	1.31200	0.656002	−	0.754759i	$-0.272246\pi$
$653$	33.5268	1.31200	0.656002	+	0.754759i	$0.272246\pi$
$654$	−15.1618	−0.592874
$655$	6.47472	0.252988
$656$	1.30926	0.0511180
$657$	14.2067	0.554256
$658$	2.14552	0.0836411
$659$	17.5175	0.682386	0.341193	−	0.939993i	$-0.389169\pi$
$659$	17.5175	0.682386	0.341193	+	0.939993i	$0.389169\pi$
$660$	1.04422	0.0406462
$661$	−2.69790	−0.104936	−0.0524681	−	0.998623i	$-0.516709\pi$
$661$	−2.69790	−0.104936	−0.0524681	+	0.998623i	$0.516709\pi$
$662$	−8.68271	−0.337463
$663$	−41.6065	−1.61586
$664$	−13.2288	−0.513376
$665$	4.21255	0.163355
$666$	6.49148	0.251540
$667$	6.03863	0.233817
$668$	5.58991	0.216280
$669$	−36.2347	−1.40091
$670$	−1.96209	−0.0758022
$671$	−7.53929	−0.291051
$672$	1.32317	0.0510422
$673$	−2.16033	−0.0832747	−0.0416374	−	0.999133i	$-0.513257\pi$
$673$	−2.16033	−0.0832747	−0.0416374	+	0.999133i	$0.513257\pi$
$674$	12.4703	0.480336
$675$	−25.3937	−0.977405
$676$	11.0561	0.425236
$677$	18.0612	0.694147	0.347073	−	0.937838i	$-0.387176\pi$
$677$	18.0612	0.694147	0.347073	+	0.937838i	$0.387176\pi$
$678$	−2.40740	−0.0924555
$679$	−10.7699	−0.413312
$680$	4.45794	0.170954
$681$	20.6791	0.792427
$682$	−6.86211	−0.262764
$683$	−12.2143	−0.467367	−0.233683	−	0.972313i	$-0.575078\pi$
$683$	−12.2143	−0.467367	−0.233683	+	0.972313i	$0.575078\pi$
$684$	7.56811	0.289374
$685$	−13.6923	−0.523155
$686$	−1.00000	−0.0381802
$687$	−28.3578	−1.08192
$688$	6.76344	0.257854
$689$	15.1921	0.578772
$690$	3.80243	0.144756
$691$	51.8004	1.97058	0.985290	−	0.170891i	$-0.0546645\pi$
$691$	51.8004	1.97058	0.985290	+	0.170891i	$0.0546645\pi$
$692$	−1.38604	−0.0526894
$693$	−1.41782	−0.0538584
$694$	−24.1693	−0.917455
$695$	1.57061	0.0595765
$696$	−1.93333	−0.0732826
$697$	8.39381	0.317938
$698$	−16.0881	−0.608945
$699$	3.71940	0.140681
$700$	−4.51650	−0.170707
$701$	3.92723	0.148329	0.0741646	−	0.997246i	$-0.476371\pi$
$701$	3.92723	0.148329	0.0741646	+	0.997246i	$0.476371\pi$
$702$	−27.5764	−1.04080
$703$	−31.4807	−1.18732
$704$	1.13495	0.0427751
$705$	−1.97400	−0.0743452
$706$	−2.67849	−0.100806
$707$	−4.34520	−0.163418
$708$	−13.6337	−0.512385
$709$	19.5059	0.732558	0.366279	−	0.930505i	$-0.380632\pi$
$709$	19.5059	0.732558	0.366279	+	0.930505i	$0.380632\pi$
$710$	3.72905	0.139949
$711$	7.76864	0.291347
$712$	5.53228	0.207331
$713$	−24.9878	−0.935800
$714$	8.48297	0.317467
$715$	−3.87071	−0.144756
$716$	14.8286	0.554172
$717$	24.4499	0.913098
$718$	−27.3126	−1.01930
$719$	−5.25728	−0.196063	−0.0980317	−	0.995183i	$-0.531255\pi$
$719$	−5.25728	−0.196063	−0.0980317	+	0.995183i	$0.531255\pi$
$720$	0.868647	0.0323726
$721$	10.3239	0.384481
$722$	−17.7019	−0.658797
$723$	−23.1790	−0.862035
$724$	10.3335	0.384043
$725$	6.59922	0.245089
$726$	−12.8504	−0.476924
$727$	−17.7819	−0.659494	−0.329747	−	0.944069i	$-0.606964\pi$
$727$	−17.7819	−0.659494	−0.329747	+	0.944069i	$0.606964\pi$
$728$	−4.90471	−0.181780
$729$	26.9301	0.997410
$730$	−7.90769	−0.292677
$731$	43.3612	1.60377
$732$	8.78957	0.324872
$733$	−27.9798	−1.03346	−0.516728	−	0.856150i	$-0.672850\pi$
$733$	−27.9798	−1.03346	−0.516728	+	0.856150i	$0.672850\pi$
$734$	0.144410	0.00533027
$735$	0.920056	0.0339368
$736$	4.13283	0.152338
$737$	−3.20255	−0.117967
$738$	1.63557	0.0602061
$739$	−0.691726	−0.0254455	−0.0127228	−	0.999919i	$-0.504050\pi$
$739$	−0.691726	−0.0254455	−0.0127228	+	0.999919i	$0.504050\pi$
$740$	−3.61327	−0.132827
$741$	39.3162	1.44432
$742$	−3.09745	−0.113711
$743$	5.18354	0.190166	0.0950829	−	0.995469i	$-0.469688\pi$
$743$	5.18354	0.190166	0.0950829	+	0.995469i	$0.469688\pi$
$744$	8.00008	0.293297
$745$	5.53716	0.202866
$746$	19.1519	0.701201
$747$	−16.5258	−0.604648
$748$	7.27630	0.266048
$749$	1.81820	0.0664355
$750$	8.75571	0.319713
$751$	−39.5859	−1.44451	−0.722256	−	0.691626i	$-0.756895\pi$
$751$	−39.5859	−1.44451	−0.722256	+	0.691626i	$0.756895\pi$
$752$	−2.14552	−0.0782391
$753$	−30.6887	−1.11836
$754$	7.16645	0.260987
$755$	11.9946	0.436527
$756$	5.62244	0.204486
$757$	7.37110	0.267907	0.133954	−	0.990988i	$-0.457233\pi$
$757$	7.37110	0.267907	0.133954	+	0.990988i	$0.457233\pi$
$758$	−8.06830	−0.293054
$759$	6.20638	0.225277
$760$	−4.21255	−0.152805
$761$	23.5935	0.855265	0.427633	−	0.903953i	$-0.359348\pi$
$761$	23.5935	0.855265	0.427633	+	0.903953i	$0.359348\pi$
$762$	10.1896	0.369131
$763$	−11.4588	−0.414835
$764$	6.85280	0.247926
$765$	5.56900	0.201348
$766$	16.1179	0.582362
$767$	50.5373	1.82479
$768$	−1.32317	−0.0477456
$769$	−6.13963	−0.221401	−0.110700	−	0.993854i	$-0.535309\pi$
$769$	−6.13963	−0.221401	−0.110700	+	0.993854i	$0.535309\pi$
$770$	0.789182	0.0284402
$771$	−29.2328	−1.05279
$772$	−13.9762	−0.503015
$773$	−8.25669	−0.296973	−0.148486	−	0.988914i	$-0.547440\pi$
$773$	−8.25669	−0.296973	−0.148486	+	0.988914i	$0.547440\pi$
$774$	8.44911	0.303697
$775$	−27.3075	−0.980914
$776$	10.7699	0.386618
$777$	−6.87566	−0.246663
$778$	−9.19895	−0.329798
$779$	−7.93177	−0.284185
$780$	4.51261	0.161577
$781$	6.08661	0.217796
$782$	26.4960	0.947496
$783$	−8.21516	−0.293586
$784$	1.00000	0.0357143
$785$	−9.72398	−0.347064
$786$	−12.3207	−0.439464
$787$	14.2724	0.508755	0.254377	−	0.967105i	$-0.418129\pi$
$787$	14.2724	0.508755	0.254377	+	0.967105i	$0.418129\pi$
$788$	−8.53047	−0.303885
$789$	−18.5031	−0.658729
$790$	−4.32416	−0.153847
$791$	−1.81942	−0.0646912
$792$	1.41782	0.0503800
$793$	−32.5811	−1.15699
$794$	−0.178207	−0.00632434
$795$	2.84983	0.101073
$796$	−7.00891	−0.248424
$797$	3.68742	0.130615	0.0653076	−	0.997865i	$-0.479197\pi$
$797$	3.68742	0.130615	0.0653076	+	0.997865i	$0.479197\pi$
$798$	−8.01602	−0.283764
$799$	−13.7552	−0.486623
$800$	4.51650	0.159682
$801$	6.91110	0.244192
$802$	−16.9720	−0.599304
$803$	−12.9070	−0.455480
$804$	3.73365	0.131676
$805$	2.87374	0.101286
$806$	−29.6547	−1.04454
$807$	19.8267	0.697933
$808$	4.34520	0.152864
$809$	−6.97544	−0.245243	−0.122622	−	0.992453i	$-0.539130\pi$
$809$	−6.97544	−0.245243	−0.122622	+	0.992453i	$0.539130\pi$
$810$	−2.56702	−0.0901959
$811$	−39.6741	−1.39315	−0.696573	−	0.717486i	$-0.745293\pi$
$811$	−39.6741	−1.39315	−0.696573	+	0.717486i	$0.745293\pi$
$812$	−1.46114	−0.0512759
$813$	−25.0592	−0.878866
$814$	−5.89763	−0.206712
$815$	−2.37959	−0.0833535
$816$	−8.48297	−0.296963
$817$	−40.9743	−1.43351
$818$	−0.0283946	−0.000992795 0
$819$	−6.12712	−0.214099
$820$	−0.910386	−0.0317921
$821$	−28.6846	−1.00110	−0.500551	−	0.865707i	$-0.666869\pi$
$821$	−28.6846	−1.00110	−0.500551	+	0.865707i	$0.666869\pi$
$822$	26.0549	0.908769
$823$	43.4755	1.51546	0.757730	−	0.652569i	$-0.226309\pi$
$823$	43.4755	1.51546	0.757730	+	0.652569i	$0.226309\pi$
$824$	−10.3239	−0.359650
$825$	6.78255	0.236138
$826$	−10.3038	−0.358516
$827$	−31.9070	−1.10952	−0.554758	−	0.832012i	$-0.687189\pi$
$827$	−31.9070	−1.10952	−0.554758	+	0.832012i	$0.687189\pi$
$828$	5.16286	0.179422
$829$	−42.3901	−1.47227	−0.736134	−	0.676835i	$-0.763351\pi$
$829$	−42.3901	−1.47227	−0.736134	+	0.676835i	$0.763351\pi$
$830$	9.19856	0.319287
$831$	−29.8135	−1.03422
$832$	4.90471	0.170040
$833$	6.41111	0.222132
$834$	−2.98869	−0.103490
$835$	−3.88691	−0.134512
$836$	−6.87577	−0.237804
$837$	33.9942	1.17501
$838$	9.39792	0.324646
$839$	−21.0542	−0.726870	−0.363435	−	0.931620i	$-0.618396\pi$
$839$	−21.0542	−0.726870	−0.363435	+	0.931620i	$0.618396\pi$
$840$	−0.920056	−0.0317450
$841$	−26.8651	−0.926382
$842$	8.32166	0.286783
$843$	−29.4244	−1.01343
$844$	−16.8481	−0.579934
$845$	−7.68783	−0.264469
$846$	−2.68026	−0.0921491
$847$	−9.71189	−0.333704
$848$	3.09745	0.106367
$849$	38.0288	1.30514
$850$	28.9558	0.993175
$851$	−21.4757	−0.736178
$852$	−7.09598	−0.243104
$853$	−27.6074	−0.945259	−0.472629	−	0.881261i	$-0.656695\pi$
$853$	−27.6074	−0.945259	−0.472629	+	0.881261i	$0.656695\pi$
$854$	6.64283	0.227313
$855$	−5.26245	−0.179972
$856$	−1.81820	−0.0621447
$857$	21.8293	0.745674	0.372837	−	0.927897i	$-0.378385\pi$
$857$	21.8293	0.745674	0.372837	+	0.927897i	$0.378385\pi$
$858$	7.36554	0.251455
$859$	9.90608	0.337991	0.168996	−	0.985617i	$-0.445948\pi$
$859$	9.90608	0.337991	0.168996	+	0.985617i	$0.445948\pi$
$860$	−4.70292	−0.160368
$861$	−1.73237	−0.0590389
$862$	1.00000	0.0340601
$863$	21.2956	0.724911	0.362456	−	0.932001i	$-0.381938\pi$
$863$	21.2956	0.724911	0.362456	+	0.932001i	$0.381938\pi$
$864$	−5.62244	−0.191279
$865$	0.963778	0.0327694
$866$	0.907871	0.0308507
$867$	−31.8915	−1.08309
$868$	6.04617	0.205220
$869$	−7.05795	−0.239425
$870$	1.34433	0.0455770
$871$	−13.8399	−0.468946
$872$	11.4588	0.388042
$873$	13.4541	0.455353
$874$	−25.0375	−0.846907
$875$	6.61725	0.223704
$876$	15.0475	0.508407
$877$	−45.5853	−1.53931	−0.769653	−	0.638463i	$-0.779571\pi$
$877$	−45.5853	−1.53931	−0.769653	+	0.638463i	$0.779571\pi$
$878$	32.5358	1.09803
$879$	39.5775	1.33492
$880$	−0.789182	−0.0266033
$881$	10.6678	0.359407	0.179704	−	0.983721i	$-0.442486\pi$
$881$	10.6678	0.359407	0.179704	+	0.983721i	$0.442486\pi$
$882$	1.24923	0.0420638
$883$	−51.3320	−1.72746	−0.863729	−	0.503956i	$-0.831877\pi$
$883$	−51.3320	−1.72746	−0.863729	+	0.503956i	$0.831877\pi$
$884$	31.4446	1.05760
$885$	9.48011	0.318670
$886$	−25.9572	−0.872048
$887$	−6.87988	−0.231004	−0.115502	−	0.993307i	$-0.536848\pi$
$887$	−6.87988	−0.231004	−0.115502	+	0.993307i	$0.536848\pi$
$888$	6.87566	0.230732
$889$	7.70094	0.258281
$890$	−3.84684	−0.128946
$891$	−4.18992	−0.140368
$892$	27.3848	0.916912
$893$	12.9980	0.434962
$894$	−10.5366	−0.352397
$895$	−10.3110	−0.344659
$896$	−1.00000	−0.0334077
$897$	26.8210	0.895526
$898$	−20.8620	−0.696173
$899$	−8.83429	−0.294640
$900$	5.64215	0.188072
$901$	19.8581	0.661569
$902$	−1.48594	−0.0494766
$903$	−8.94915	−0.297809
$904$	1.81942	0.0605130
$905$	−7.18538	−0.238850
$906$	−22.8243	−0.758288
$907$	29.8987	0.992771	0.496386	−	0.868102i	$-0.334660\pi$
$907$	29.8987	0.992771	0.496386	+	0.868102i	$0.334660\pi$
$908$	−15.6285	−0.518651
$909$	5.42816	0.180041
$910$	3.41046	0.113056
$911$	39.8478	1.32022	0.660108	−	0.751170i	$-0.270510\pi$
$911$	39.8478	1.32022	0.660108	+	0.751170i	$0.270510\pi$
$912$	8.01602	0.265437
$913$	15.0140	0.496891
$914$	−32.0069	−1.05870
$915$	−6.11178	−0.202049
$916$	21.4318	0.708126
$917$	−9.31152	−0.307493
$918$	−36.0461	−1.18970
$919$	−18.9097	−0.623772	−0.311886	−	0.950119i	$-0.600961\pi$
$919$	−18.9097	−0.623772	−0.311886	+	0.950119i	$0.600961\pi$
$920$	−2.87374	−0.0947444
$921$	0.869652	0.0286560
$922$	9.39383	0.309369
$923$	26.3033	0.865785
$924$	−1.50173	−0.0494032
$925$	−23.4694	−0.771669
$926$	−2.96839	−0.0975474
$927$	−12.8969	−0.423591
$928$	1.46114	0.0479642
$929$	−47.9467	−1.57308	−0.786540	−	0.617539i	$-0.788130\pi$
$929$	−47.9467	−1.57308	−0.786540	+	0.617539i	$0.788130\pi$
$930$	−5.56282	−0.182412
$931$	−6.05821	−0.198550
$932$	−2.81098	−0.0920769
$933$	−18.1518	−0.594265
$934$	−21.8484	−0.714902
$935$	−5.05954	−0.165465
$936$	6.12712	0.200271
$937$	7.54504	0.246486	0.123243	−	0.992377i	$-0.460671\pi$
$937$	7.54504	0.246486	0.123243	+	0.992377i	$0.460671\pi$
$938$	2.82175	0.0921335
$939$	5.48265	0.178919
$940$	1.49188	0.0486597
$941$	−44.1632	−1.43968	−0.719840	−	0.694140i	$-0.755785\pi$
$941$	−44.1632	−1.43968	−0.719840	+	0.694140i	$0.755785\pi$
$942$	18.5037	0.602882
$943$	−5.41094	−0.176205
$944$	10.3038	0.335361
$945$	−3.90953	−0.127177
$946$	−7.67617	−0.249574
$947$	−54.7561	−1.77933	−0.889667	−	0.456610i	$-0.849064\pi$
$947$	−54.7561	−1.77933	−0.889667	+	0.456610i	$0.849064\pi$
$948$	8.22841	0.267246
$949$	−55.7779	−1.81063
$950$	−27.3619	−0.887737
$951$	−11.0467	−0.358212
$952$	−6.41111	−0.207785
$953$	−19.8218	−0.642090	−0.321045	−	0.947064i	$-0.604034\pi$
$953$	−19.8218	−0.642090	−0.321045	+	0.947064i	$0.604034\pi$
$954$	3.86943	0.125278
$955$	−4.76506	−0.154194
$956$	−18.4783	−0.597632
$957$	2.19423	0.0709295
$958$	−42.0654	−1.35907
$959$	19.6913	0.635866
$960$	0.920056	0.0296947
$961$	5.55617	0.179231
$962$	−25.4867	−0.821724
$963$	−2.27135	−0.0731932
$964$	17.5178	0.564211
$965$	9.71830	0.312843
$966$	−5.46842	−0.175943
$967$	10.1234	0.325546	0.162773	−	0.986664i	$-0.447956\pi$
$967$	10.1234	0.325546	0.162773	+	0.986664i	$0.447956\pi$
$968$	9.71189	0.312152
$969$	51.3916	1.65094
$970$	−7.48881	−0.240451
$971$	−12.0419	−0.386444	−0.193222	−	0.981155i	$-0.561894\pi$
$971$	−12.0419	−0.386444	−0.193222	+	0.981155i	$0.561894\pi$
$972$	−11.9826	−0.384341
$973$	−2.25874	−0.0724120
$974$	−13.9934	−0.448377
$975$	29.3109	0.938699
$976$	−6.64283	−0.212632
$977$	−1.18584	−0.0379383	−0.0189692	−	0.999820i	$-0.506038\pi$
$977$	−1.18584	−0.0379383	−0.0189692	+	0.999820i	$0.506038\pi$
$978$	4.52811	0.144793
$979$	−6.27887	−0.200673
$980$	−0.695345	−0.0222120
$981$	14.3146	0.457031
$982$	−16.5057	−0.526719
$983$	−4.24559	−0.135413	−0.0677066	−	0.997705i	$-0.521568\pi$
$983$	−4.24559	−0.135413	−0.0677066	+	0.997705i	$0.521568\pi$
$984$	1.73237	0.0552258
$985$	5.93162	0.188997
$986$	9.36752	0.298323
$987$	2.83888	0.0903626
$988$	−29.7137	−0.945320
$989$	−27.9521	−0.888826
$990$	−0.985872	−0.0313331
$991$	45.6160	1.44904	0.724520	−	0.689254i	$-0.242062\pi$
$991$	45.6160	1.44904	0.724520	+	0.689254i	$0.242062\pi$
$992$	−6.04617	−0.191966
$993$	−11.4887	−0.364582
$994$	−5.36288	−0.170100
$995$	4.87361	0.154504
$996$	−17.5039	−0.554631
$997$	−60.6577	−1.92105	−0.960524	−	0.278197i	$-0.910263\pi$
$997$	−60.6577	−1.92105	−0.960524	+	0.278197i	$0.910263\pi$
$998$	−9.04228	−0.286228
$999$	29.2163	0.924363

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.8	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.8	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.32317 q^{3} +1.00000 q^{4} -0.695345 q^{5} +1.32317 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.24923 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.32317 q^{3} +1.00000 q^{4} -0.695345 q^{5} +1.32317 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.24923 q^{9} +0.695345 q^{10} +1.13495 q^{11} -1.32317 q^{12} +4.90471 q^{13} -1.00000 q^{14} +0.920056 q^{15} +1.00000 q^{16} +6.41111 q^{17} +1.24923 q^{18} -6.05821 q^{19} -0.695345 q^{20} -1.32317 q^{21} -1.13495 q^{22} -4.13283 q^{23} +1.32317 q^{24} -4.51650 q^{25} -4.90471 q^{26} +5.62244 q^{27} +1.00000 q^{28} -1.46114 q^{29} -0.920056 q^{30} +6.04617 q^{31} -1.00000 q^{32} -1.50173 q^{33} -6.41111 q^{34} -0.695345 q^{35} -1.24923 q^{36} +5.19637 q^{37} +6.05821 q^{38} -6.48974 q^{39} +0.695345 q^{40} +1.30926 q^{41} +1.32317 q^{42} +6.76344 q^{43} +1.13495 q^{44} +0.868647 q^{45} +4.13283 q^{46} -2.14552 q^{47} -1.32317 q^{48} +1.00000 q^{49} +4.51650 q^{50} -8.48297 q^{51} +4.90471 q^{52} +3.09745 q^{53} -5.62244 q^{54} -0.789182 q^{55} -1.00000 q^{56} +8.01602 q^{57} +1.46114 q^{58} +10.3038 q^{59} +0.920056 q^{60} -6.64283 q^{61} -6.04617 q^{62} -1.24923 q^{63} +1.00000 q^{64} -3.41046 q^{65} +1.50173 q^{66} -2.82175 q^{67} +6.41111 q^{68} +5.46842 q^{69} +0.695345 q^{70} +5.36288 q^{71} +1.24923 q^{72} -11.3723 q^{73} -5.19637 q^{74} +5.97607 q^{75} -6.05821 q^{76} +1.13495 q^{77} +6.48974 q^{78} -6.21873 q^{79} -0.695345 q^{80} -3.69172 q^{81} -1.30926 q^{82} +13.2288 q^{83} -1.32317 q^{84} -4.45794 q^{85} -6.76344 q^{86} +1.93333 q^{87} -1.13495 q^{88} -5.53228 q^{89} -0.868647 q^{90} +4.90471 q^{91} -4.13283 q^{92} -8.00008 q^{93} +2.14552 q^{94} +4.21255 q^{95} +1.32317 q^{96} -10.7699 q^{97} -1.00000 q^{98} -1.41782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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