LMFDB - Embedded newform 6034.2.a.p.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.90367 q^{3} +1.00000 q^{4} -3.72741 q^{5} +1.90367 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.623956 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.90367 q^{3} +1.00000 q^{4} -3.72741 q^{5} +1.90367 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.623956 q^{9} +3.72741 q^{10} +2.91306 q^{11} -1.90367 q^{12} +0.858424 q^{13} -1.00000 q^{14} +7.09576 q^{15} +1.00000 q^{16} +2.98075 q^{17} -0.623956 q^{18} -1.77524 q^{19} -3.72741 q^{20} -1.90367 q^{21} -2.91306 q^{22} +7.03281 q^{23} +1.90367 q^{24} +8.89359 q^{25} -0.858424 q^{26} +4.52320 q^{27} +1.00000 q^{28} +7.80533 q^{29} -7.09576 q^{30} +0.802592 q^{31} -1.00000 q^{32} -5.54550 q^{33} -2.98075 q^{34} -3.72741 q^{35} +0.623956 q^{36} +0.206301 q^{37} +1.77524 q^{38} -1.63416 q^{39} +3.72741 q^{40} +4.82573 q^{41} +1.90367 q^{42} +1.00633 q^{43} +2.91306 q^{44} -2.32574 q^{45} -7.03281 q^{46} -5.24240 q^{47} -1.90367 q^{48} +1.00000 q^{49} -8.89359 q^{50} -5.67436 q^{51} +0.858424 q^{52} -9.66754 q^{53} -4.52320 q^{54} -10.8582 q^{55} -1.00000 q^{56} +3.37946 q^{57} -7.80533 q^{58} -5.01202 q^{59} +7.09576 q^{60} -11.9098 q^{61} -0.802592 q^{62} +0.623956 q^{63} +1.00000 q^{64} -3.19970 q^{65} +5.54550 q^{66} +8.51127 q^{67} +2.98075 q^{68} -13.3881 q^{69} +3.72741 q^{70} +12.7885 q^{71} -0.623956 q^{72} -0.847830 q^{73} -0.206301 q^{74} -16.9305 q^{75} -1.77524 q^{76} +2.91306 q^{77} +1.63416 q^{78} +2.38319 q^{79} -3.72741 q^{80} -10.4825 q^{81} -4.82573 q^{82} -1.46787 q^{83} -1.90367 q^{84} -11.1105 q^{85} -1.00633 q^{86} -14.8588 q^{87} -2.91306 q^{88} +8.13689 q^{89} +2.32574 q^{90} +0.858424 q^{91} +7.03281 q^{92} -1.52787 q^{93} +5.24240 q^{94} +6.61704 q^{95} +1.90367 q^{96} +14.3308 q^{97} -1.00000 q^{98} +1.81762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.90367	−1.09908	−0.549542	−	0.835466i	$-0.685198\pi$
$3$	−1.90367	−1.09908	−0.549542	+	0.835466i	$0.685198\pi$
$4$	1.00000	0.500000
$5$	−3.72741	−1.66695	−0.833474	−	0.552558i	$-0.813652\pi$
$5$	−3.72741	−1.66695	−0.833474	+	0.552558i	$0.813652\pi$
$6$	1.90367	0.777170
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0.623956	0.207985
$10$	3.72741	1.17871
$11$	2.91306	0.878320	0.439160	−	0.898409i	$-0.355276\pi$
$11$	2.91306	0.878320	0.439160	+	0.898409i	$0.355276\pi$
$12$	−1.90367	−0.549542
$13$	0.858424	0.238084	0.119042	−	0.992889i	$-0.462018\pi$
$13$	0.858424	0.238084	0.119042	+	0.992889i	$0.462018\pi$
$14$	−1.00000	−0.267261
$15$	7.09576	1.83212
$16$	1.00000	0.250000
$17$	2.98075	0.722938	0.361469	−	0.932384i	$-0.382275\pi$
$17$	2.98075	0.722938	0.361469	+	0.932384i	$0.382275\pi$
$18$	−0.623956	−0.147068
$19$	−1.77524	−0.407267	−0.203634	−	0.979047i	$-0.565275\pi$
$19$	−1.77524	−0.407267	−0.203634	+	0.979047i	$0.565275\pi$
$20$	−3.72741	−0.833474
$21$	−1.90367	−0.415415
$22$	−2.91306	−0.621066
$23$	7.03281	1.46644	0.733221	−	0.679991i	$-0.238016\pi$
$23$	7.03281	1.46644	0.733221	+	0.679991i	$0.238016\pi$
$24$	1.90367	0.388585
$25$	8.89359	1.77872
$26$	−0.858424	−0.168351
$27$	4.52320	0.870491
$28$	1.00000	0.188982
$29$	7.80533	1.44941	0.724707	−	0.689057i	$-0.241975\pi$
$29$	7.80533	1.44941	0.724707	+	0.689057i	$0.241975\pi$
$30$	−7.09576	−1.29550
$31$	0.802592	0.144150	0.0720749	−	0.997399i	$-0.477038\pi$
$31$	0.802592	0.144150	0.0720749	+	0.997399i	$0.477038\pi$
$32$	−1.00000	−0.176777
$33$	−5.54550	−0.965347
$34$	−2.98075	−0.511194
$35$	−3.72741	−0.630047
$36$	0.623956	0.103993
$37$	0.206301	0.0339156	0.0169578	−	0.999856i	$-0.494602\pi$
$37$	0.206301	0.0339156	0.0169578	+	0.999856i	$0.494602\pi$
$38$	1.77524	0.287982
$39$	−1.63416	−0.261674
$40$	3.72741	0.589355
$41$	4.82573	0.753652	0.376826	−	0.926284i	$-0.377015\pi$
$41$	4.82573	0.753652	0.376826	+	0.926284i	$0.377015\pi$
$42$	1.90367	0.293742
$43$	1.00633	0.153464	0.0767318	−	0.997052i	$-0.475551\pi$
$43$	1.00633	0.153464	0.0767318	+	0.997052i	$0.475551\pi$
$44$	2.91306	0.439160
$45$	−2.32574	−0.346701
$46$	−7.03281	−1.03693
$47$	−5.24240	−0.764683	−0.382341	−	0.924021i	$-0.624882\pi$
$47$	−5.24240	−0.764683	−0.382341	+	0.924021i	$0.624882\pi$
$48$	−1.90367	−0.274771
$49$	1.00000	0.142857
$50$	−8.89359	−1.25774
$51$	−5.67436	−0.794569
$52$	0.858424	0.119042
$53$	−9.66754	−1.32794	−0.663969	−	0.747760i	$-0.731129\pi$
$53$	−9.66754	−1.32794	−0.663969	+	0.747760i	$0.731129\pi$
$54$	−4.52320	−0.615530
$55$	−10.8582	−1.46411
$56$	−1.00000	−0.133631
$57$	3.37946	0.447621
$58$	−7.80533	−1.02489
$59$	−5.01202	−0.652510	−0.326255	−	0.945282i	$-0.605787\pi$
$59$	−5.01202	−0.652510	−0.326255	+	0.945282i	$0.605787\pi$
$60$	7.09576	0.916058
$61$	−11.9098	−1.52490	−0.762450	−	0.647047i	$-0.776004\pi$
$61$	−11.9098	−1.52490	−0.762450	+	0.647047i	$0.776004\pi$
$62$	−0.802592	−0.101929
$63$	0.623956	0.0786110
$64$	1.00000	0.125000
$65$	−3.19970	−0.396874
$66$	5.54550	0.682604
$67$	8.51127	1.03982	0.519908	−	0.854222i	$-0.325966\pi$
$67$	8.51127	1.03982	0.519908	+	0.854222i	$0.325966\pi$
$68$	2.98075	0.361469
$69$	−13.3881	−1.61174
$70$	3.72741	0.445511
$71$	12.7885	1.51771	0.758857	−	0.651257i	$-0.225758\pi$
$71$	12.7885	1.51771	0.758857	+	0.651257i	$0.225758\pi$
$72$	−0.623956	−0.0735339
$73$	−0.847830	−0.0992310	−0.0496155	−	0.998768i	$-0.515800\pi$
$73$	−0.847830	−0.0992310	−0.0496155	+	0.998768i	$0.515800\pi$
$74$	−0.206301	−0.0239820
$75$	−16.9305	−1.95496
$76$	−1.77524	−0.203634
$77$	2.91306	0.331974
$78$	1.63416	0.185032
$79$	2.38319	0.268130	0.134065	−	0.990973i	$-0.457197\pi$
$79$	2.38319	0.268130	0.134065	+	0.990973i	$0.457197\pi$
$80$	−3.72741	−0.416737
$81$	−10.4825	−1.16473
$82$	−4.82573	−0.532912
$83$	−1.46787	−0.161120	−0.0805600	−	0.996750i	$-0.525671\pi$
$83$	−1.46787	−0.161120	−0.0805600	+	0.996750i	$0.525671\pi$
$84$	−1.90367	−0.207707
$85$	−11.1105	−1.20510
$86$	−1.00633	−0.108515
$87$	−14.8588	−1.59303
$88$	−2.91306	−0.310533
$89$	8.13689	0.862509	0.431254	−	0.902230i	$-0.358071\pi$
$89$	8.13689	0.862509	0.431254	+	0.902230i	$0.358071\pi$
$90$	2.32574	0.245154
$91$	0.858424	0.0899873
$92$	7.03281	0.733221
$93$	−1.52787	−0.158433
$94$	5.24240	0.540712
$95$	6.61704	0.678894
$96$	1.90367	0.194292
$97$	14.3308	1.45508	0.727538	−	0.686067i	$-0.240664\pi$
$97$	14.3308	1.45508	0.727538	+	0.686067i	$0.240664\pi$
$98$	−1.00000	−0.101015
$99$	1.81762	0.182678
$100$	8.89359	0.889359
$101$	14.4359	1.43643	0.718214	−	0.695823i	$-0.244960\pi$
$101$	14.4359	1.43643	0.718214	+	0.695823i	$0.244960\pi$
$102$	5.67436	0.561845
$103$	−9.76032	−0.961713	−0.480857	−	0.876799i	$-0.659674\pi$
$103$	−9.76032	−0.961713	−0.480857	+	0.876799i	$0.659674\pi$
$104$	−0.858424	−0.0841754
$105$	7.09576	0.692475
$106$	9.66754	0.938994
$107$	−7.84253	−0.758166	−0.379083	−	0.925363i	$-0.623761\pi$
$107$	−7.84253	−0.758166	−0.379083	+	0.925363i	$0.623761\pi$
$108$	4.52320	0.435245
$109$	−1.09655	−0.105031	−0.0525154	−	0.998620i	$-0.516724\pi$
$109$	−1.09655	−0.105031	−0.0525154	+	0.998620i	$0.516724\pi$
$110$	10.8582	1.03529
$111$	−0.392728	−0.0372761
$112$	1.00000	0.0944911
$113$	19.6638	1.84982	0.924909	−	0.380188i	$-0.124141\pi$
$113$	19.6638	1.84982	0.924909	+	0.380188i	$0.124141\pi$
$114$	−3.37946	−0.316516
$115$	−26.2142	−2.44448
$116$	7.80533	0.724707
$117$	0.535618	0.0495179
$118$	5.01202	0.461394
$119$	2.98075	0.273245
$120$	−7.09576	−0.647751
$121$	−2.51409	−0.228554
$122$	11.9098	1.07827
$123$	−9.18659	−0.828327
$124$	0.802592	0.0720749
$125$	−14.5130	−1.29808
$126$	−0.623956	−0.0555864
$127$	−19.8079	−1.75767	−0.878833	−	0.477130i	$-0.841677\pi$
$127$	−19.8079	−1.75767	−0.878833	+	0.477130i	$0.841677\pi$
$128$	−1.00000	−0.0883883
$129$	−1.91572	−0.168669
$130$	3.19970	0.280632
$131$	−14.2456	−1.24465	−0.622324	−	0.782760i	$-0.713811\pi$
$131$	−14.2456	−1.24465	−0.622324	+	0.782760i	$0.713811\pi$
$132$	−5.54550	−0.482674
$133$	−1.77524	−0.153933
$134$	−8.51127	−0.735262
$135$	−16.8598	−1.45106
$136$	−2.98075	−0.255597
$137$	−9.57973	−0.818452	−0.409226	−	0.912433i	$-0.634201\pi$
$137$	−9.57973	−0.818452	−0.409226	+	0.912433i	$0.634201\pi$
$138$	13.3881	1.13967
$139$	−7.95766	−0.674960	−0.337480	−	0.941333i	$-0.609575\pi$
$139$	−7.95766	−0.674960	−0.337480	+	0.941333i	$0.609575\pi$
$140$	−3.72741	−0.315024
$141$	9.97980	0.840451
$142$	−12.7885	−1.07319
$143$	2.50064	0.209114
$144$	0.623956	0.0519963
$145$	−29.0937	−2.41610
$146$	0.847830	0.0701669
$147$	−1.90367	−0.157012
$148$	0.206301	0.0169578
$149$	−4.14942	−0.339934	−0.169967	−	0.985450i	$-0.554366\pi$
$149$	−4.14942	−0.339934	−0.169967	+	0.985450i	$0.554366\pi$
$150$	16.9305	1.38237
$151$	14.6540	1.19253	0.596263	−	0.802789i	$-0.296652\pi$
$151$	14.6540	1.19253	0.596263	+	0.802789i	$0.296652\pi$
$152$	1.77524	0.143991
$153$	1.85985	0.150360
$154$	−2.91306	−0.234741
$155$	−2.99159	−0.240290
$156$	−1.63416	−0.130837
$157$	3.06225	0.244394	0.122197	−	0.992506i	$-0.461006\pi$
$157$	3.06225	0.244394	0.122197	+	0.992506i	$0.461006\pi$
$158$	−2.38319	−0.189597
$159$	18.4038	1.45952
$160$	3.72741	0.294678
$161$	7.03281	0.554263
$162$	10.4825	0.823587
$163$	0.739064	0.0578880	0.0289440	−	0.999581i	$-0.490786\pi$
$163$	0.739064	0.0578880	0.0289440	+	0.999581i	$0.490786\pi$
$164$	4.82573	0.376826
$165$	20.6704	1.60918
$166$	1.46787	0.113929
$167$	−11.7550	−0.909627	−0.454814	−	0.890587i	$-0.650294\pi$
$167$	−11.7550	−0.909627	−0.454814	+	0.890587i	$0.650294\pi$
$168$	1.90367	0.146871
$169$	−12.2631	−0.943316
$170$	11.1105	0.852135
$171$	−1.10767	−0.0847056
$172$	1.00633	0.0767318
$173$	−0.571790	−0.0434724	−0.0217362	−	0.999764i	$-0.506919\pi$
$173$	−0.571790	−0.0434724	−0.0217362	+	0.999764i	$0.506919\pi$
$174$	14.8588	1.12644
$175$	8.89359	0.672293
$176$	2.91306	0.219580
$177$	9.54123	0.717163
$178$	−8.13689	−0.609886
$179$	−15.1293	−1.13082	−0.565409	−	0.824811i	$-0.691282\pi$
$179$	−15.1293	−1.13082	−0.565409	+	0.824811i	$0.691282\pi$
$180$	−2.32574	−0.173350
$181$	6.97258	0.518267	0.259134	−	0.965841i	$-0.416563\pi$
$181$	6.97258	0.518267	0.259134	+	0.965841i	$0.416563\pi$
$182$	−0.858424	−0.0636306
$183$	22.6724	1.67599
$184$	−7.03281	−0.518465
$185$	−0.768967	−0.0565356
$186$	1.52787	0.112029
$187$	8.68309	0.634971
$188$	−5.24240	−0.382341
$189$	4.52320	0.329015
$190$	−6.61704	−0.480051
$191$	27.2529	1.97195	0.985976	−	0.166888i	$-0.0533719\pi$
$191$	27.2529	1.97195	0.985976	+	0.166888i	$0.0533719\pi$
$192$	−1.90367	−0.137385
$193$	−4.63269	−0.333468	−0.166734	−	0.986002i	$-0.553322\pi$
$193$	−4.63269	−0.333468	−0.166734	+	0.986002i	$0.553322\pi$
$194$	−14.3308	−1.02889
$195$	6.09117	0.436198
$196$	1.00000	0.0714286
$197$	14.2844	1.01772	0.508860	−	0.860849i	$-0.330067\pi$
$197$	14.2844	1.01772	0.508860	+	0.860849i	$0.330067\pi$
$198$	−1.81762	−0.129173
$199$	3.98333	0.282370	0.141185	−	0.989983i	$-0.454909\pi$
$199$	3.98333	0.282370	0.141185	+	0.989983i	$0.454909\pi$
$200$	−8.89359	−0.628872
$201$	−16.2026	−1.14285
$202$	−14.4359	−1.01571
$203$	7.80533	0.547827
$204$	−5.67436	−0.397285
$205$	−17.9875	−1.25630
$206$	9.76032	0.680034
$207$	4.38816	0.304998
$208$	0.858424	0.0595210
$209$	−5.17137	−0.357711
$210$	−7.09576	−0.489654
$211$	5.02415	0.345877	0.172938	−	0.984933i	$-0.444674\pi$
$211$	5.02415	0.345877	0.172938	+	0.984933i	$0.444674\pi$
$212$	−9.66754	−0.663969
$213$	−24.3450	−1.66809
$214$	7.84253	0.536104
$215$	−3.75100	−0.255816
$216$	−4.52320	−0.307765
$217$	0.802592	0.0544835
$218$	1.09655	0.0742680
$219$	1.61399	0.109063
$220$	−10.8582	−0.732057
$221$	2.55875	0.172120
$222$	0.392728	0.0263582
$223$	1.21846	0.0815941	0.0407970	−	0.999167i	$-0.487010\pi$
$223$	1.21846	0.0815941	0.0407970	+	0.999167i	$0.487010\pi$
$224$	−1.00000	−0.0668153
$225$	5.54921	0.369947
$226$	−19.6638	−1.30802
$227$	−11.2629	−0.747543	−0.373771	−	0.927521i	$-0.621936\pi$
$227$	−11.2629	−0.747543	−0.373771	+	0.927521i	$0.621936\pi$
$228$	3.37946	0.223811
$229$	−1.13912	−0.0752754	−0.0376377	−	0.999291i	$-0.511983\pi$
$229$	−1.13912	−0.0752754	−0.0376377	+	0.999291i	$0.511983\pi$
$230$	26.2142	1.72851
$231$	−5.54550	−0.364867
$232$	−7.80533	−0.512445
$233$	−17.3780	−1.13847	−0.569235	−	0.822175i	$-0.692761\pi$
$233$	−17.3780	−1.13847	−0.569235	+	0.822175i	$0.692761\pi$
$234$	−0.535618	−0.0350145
$235$	19.5406	1.27469
$236$	−5.01202	−0.326255
$237$	−4.53681	−0.294697
$238$	−2.98075	−0.193213
$239$	18.0333	1.16648	0.583239	−	0.812301i	$-0.301785\pi$
$239$	18.0333	1.16648	0.583239	+	0.812301i	$0.301785\pi$
$240$	7.09576	0.458029
$241$	−0.947127	−0.0610098	−0.0305049	−	0.999535i	$-0.509712\pi$
$241$	−0.947127	−0.0610098	−0.0305049	+	0.999535i	$0.509712\pi$
$242$	2.51409	0.161612
$243$	6.38569	0.409642
$244$	−11.9098	−0.762450
$245$	−3.72741	−0.238136
$246$	9.18659	0.585715
$247$	−1.52391	−0.0969639
$248$	−0.802592	−0.0509646
$249$	2.79434	0.177084
$250$	14.5130	0.917884
$251$	2.98951	0.188696	0.0943480	−	0.995539i	$-0.469923\pi$
$251$	2.98951	0.188696	0.0943480	+	0.995539i	$0.469923\pi$
$252$	0.623956	0.0393055
$253$	20.4870	1.28801
$254$	19.8079	1.24286
$255$	21.1507	1.32451
$256$	1.00000	0.0625000
$257$	12.3344	0.769401	0.384700	−	0.923042i	$-0.374305\pi$
$257$	12.3344	0.769401	0.384700	+	0.923042i	$0.374305\pi$
$258$	1.91572	0.119267
$259$	0.206301	0.0128189
$260$	−3.19970	−0.198437
$261$	4.87018	0.301457
$262$	14.2456	0.880099
$263$	20.4794	1.26282	0.631408	−	0.775451i	$-0.282477\pi$
$263$	20.4794	1.26282	0.631408	+	0.775451i	$0.282477\pi$
$264$	5.54550	0.341302
$265$	36.0349	2.21361
$266$	1.77524	0.108847
$267$	−15.4899	−0.947969
$268$	8.51127	0.519908
$269$	13.2997	0.810896	0.405448	−	0.914118i	$-0.367115\pi$
$269$	13.2997	0.810896	0.405448	+	0.914118i	$0.367115\pi$
$270$	16.8598	1.02606
$271$	−19.3315	−1.17430	−0.587152	−	0.809477i	$-0.699751\pi$
$271$	−19.3315	−1.17430	−0.587152	+	0.809477i	$0.699751\pi$
$272$	2.98075	0.180734
$273$	−1.63416	−0.0989036
$274$	9.57973	0.578733
$275$	25.9076	1.56228
$276$	−13.3881	−0.805871
$277$	15.0762	0.905838	0.452919	−	0.891552i	$-0.350383\pi$
$277$	15.0762	0.905838	0.452919	+	0.891552i	$0.350383\pi$
$278$	7.95766	0.477269
$279$	0.500782	0.0299810
$280$	3.72741	0.222755
$281$	−13.5077	−0.805803	−0.402901	−	0.915243i	$-0.631998\pi$
$281$	−13.5077	−0.805803	−0.402901	+	0.915243i	$0.631998\pi$
$282$	−9.97980	−0.594288
$283$	9.66089	0.574281	0.287140	−	0.957889i	$-0.407295\pi$
$283$	9.66089	0.574281	0.287140	+	0.957889i	$0.407295\pi$
$284$	12.7885	0.758857
$285$	−12.5967	−0.746161
$286$	−2.50064	−0.147866
$287$	4.82573	0.284854
$288$	−0.623956	−0.0367669
$289$	−8.11514	−0.477361
$290$	29.0937	1.70844
$291$	−27.2812	−1.59925
$292$	−0.847830	−0.0496155
$293$	−23.7302	−1.38633	−0.693167	−	0.720777i	$-0.743785\pi$
$293$	−23.7302	−1.38633	−0.693167	+	0.720777i	$0.743785\pi$
$294$	1.90367	0.111024
$295$	18.6819	1.08770
$296$	−0.206301	−0.0119910
$297$	13.1764	0.764570
$298$	4.14942	0.240369
$299$	6.03713	0.349136
$300$	−16.9305	−0.977481
$301$	1.00633	0.0580038
$302$	−14.6540	−0.843243
$303$	−27.4812	−1.57875
$304$	−1.77524	−0.101817
$305$	44.3929	2.54193
$306$	−1.85985	−0.106321
$307$	−19.0227	−1.08568	−0.542841	−	0.839835i	$-0.682651\pi$
$307$	−19.0227	−1.08568	−0.542841	+	0.839835i	$0.682651\pi$
$308$	2.91306	0.165987
$309$	18.5804	1.05700
$310$	2.99159	0.169911
$311$	31.3009	1.77491	0.887456	−	0.460892i	$-0.152470\pi$
$311$	31.3009	1.77491	0.887456	+	0.460892i	$0.152470\pi$
$312$	1.63416	0.0925158
$313$	24.9640	1.41105	0.705526	−	0.708684i	$-0.250711\pi$
$313$	24.9640	1.41105	0.705526	+	0.708684i	$0.250711\pi$
$314$	−3.06225	−0.172813
$315$	−2.32574	−0.131041
$316$	2.38319	0.134065
$317$	22.9749	1.29040	0.645201	−	0.764013i	$-0.276774\pi$
$317$	22.9749	1.29040	0.645201	+	0.764013i	$0.276774\pi$
$318$	−18.4038	−1.03203
$319$	22.7374	1.27305
$320$	−3.72741	−0.208369
$321$	14.9296	0.833288
$322$	−7.03281	−0.391923
$323$	−5.29154	−0.294429
$324$	−10.4825	−0.582364
$325$	7.63448	0.423485
$326$	−0.739064	−0.0409330
$327$	2.08748	0.115438
$328$	−4.82573	−0.266456
$329$	−5.24240	−0.289023
$330$	−20.6704	−1.13787
$331$	−14.7306	−0.809667	−0.404834	−	0.914390i	$-0.632671\pi$
$331$	−14.7306	−0.809667	−0.404834	+	0.914390i	$0.632671\pi$
$332$	−1.46787	−0.0805600
$333$	0.128722	0.00705394
$334$	11.7550	0.643204
$335$	−31.7250	−1.73332
$336$	−1.90367	−0.103854
$337$	0.881637	0.0480258	0.0240129	−	0.999712i	$-0.492356\pi$
$337$	0.881637	0.0480258	0.0240129	+	0.999712i	$0.492356\pi$
$338$	12.2631	0.667025
$339$	−37.4334	−2.03311
$340$	−11.1105	−0.602550
$341$	2.33800	0.126610
$342$	1.10767	0.0598959
$343$	1.00000	0.0539949
$344$	−1.00633	−0.0542576
$345$	49.9031	2.68669
$346$	0.571790	0.0307396
$347$	34.3470	1.84385	0.921923	−	0.387373i	$-0.126617\pi$
$347$	34.3470	1.84385	0.921923	+	0.387373i	$0.126617\pi$
$348$	−14.8588	−0.796514
$349$	−8.66725	−0.463947	−0.231974	−	0.972722i	$-0.574518\pi$
$349$	−8.66725	−0.463947	−0.231974	+	0.972722i	$0.574518\pi$
$350$	−8.89359	−0.475383
$351$	3.88283	0.207250
$352$	−2.91306	−0.155267
$353$	18.3899	0.978794	0.489397	−	0.872061i	$-0.337217\pi$
$353$	18.3899	0.978794	0.489397	+	0.872061i	$0.337217\pi$
$354$	−9.54123	−0.507111
$355$	−47.6679	−2.52995
$356$	8.13689	0.431254
$357$	−5.67436	−0.300319
$358$	15.1293	0.799609
$359$	−0.178842	−0.00943891	−0.00471945	−	0.999989i	$-0.501502\pi$
$359$	−0.178842	−0.00943891	−0.00471945	+	0.999989i	$0.501502\pi$
$360$	2.32574	0.122577
$361$	−15.8485	−0.834133
$362$	−6.97258	−0.366470
$363$	4.78599	0.251200
$364$	0.858424	0.0449937
$365$	3.16021	0.165413
$366$	−22.6724	−1.18511
$367$	−24.7090	−1.28980	−0.644899	−	0.764268i	$-0.723100\pi$
$367$	−24.7090	−1.28980	−0.644899	+	0.764268i	$0.723100\pi$
$368$	7.03281	0.366610
$369$	3.01104	0.156748
$370$	0.768967	0.0399767
$371$	−9.66754	−0.501914
$372$	−1.52787	−0.0792163
$373$	2.66705	0.138095	0.0690474	−	0.997613i	$-0.478004\pi$
$373$	2.66705	0.138095	0.0690474	+	0.997613i	$0.478004\pi$
$374$	−8.68309	−0.448992
$375$	27.6280	1.42670
$376$	5.24240	0.270356
$377$	6.70029	0.345082
$378$	−4.52320	−0.232648
$379$	6.15096	0.315953	0.157977	−	0.987443i	$-0.449503\pi$
$379$	6.15096	0.315953	0.157977	+	0.987443i	$0.449503\pi$
$380$	6.61704	0.339447
$381$	37.7076	1.93182
$382$	−27.2529	−1.39438
$383$	−2.38838	−0.122040	−0.0610202	−	0.998137i	$-0.519435\pi$
$383$	−2.38838	−0.122040	−0.0610202	+	0.998137i	$0.519435\pi$
$384$	1.90367	0.0971462
$385$	−10.8582	−0.553383
$386$	4.63269	0.235798
$387$	0.627904	0.0319181
$388$	14.3308	0.727538
$389$	−33.9102	−1.71932	−0.859658	−	0.510871i	$-0.829323\pi$
$389$	−33.9102	−1.71932	−0.859658	+	0.510871i	$0.829323\pi$
$390$	−6.09117	−0.308438
$391$	20.9630	1.06015
$392$	−1.00000	−0.0505076
$393$	27.1190	1.36797
$394$	−14.2844	−0.719637
$395$	−8.88314	−0.446959
$396$	1.81762	0.0913388
$397$	2.76592	0.138818	0.0694089	−	0.997588i	$-0.477889\pi$
$397$	2.76592	0.138818	0.0694089	+	0.997588i	$0.477889\pi$
$398$	−3.98333	−0.199666
$399$	3.37946	0.169185
$400$	8.89359	0.444680
$401$	28.3809	1.41728	0.708638	−	0.705572i	$-0.249310\pi$
$401$	28.3809	1.41728	0.708638	+	0.705572i	$0.249310\pi$
$402$	16.2026	0.808114
$403$	0.688964	0.0343198
$404$	14.4359	0.718214
$405$	39.0728	1.94154
$406$	−7.80533	−0.387372
$407$	0.600966	0.0297888
$408$	5.67436	0.280923
$409$	−10.5586	−0.522091	−0.261046	−	0.965326i	$-0.584067\pi$
$409$	−10.5586	−0.522091	−0.261046	+	0.965326i	$0.584067\pi$
$410$	17.9875	0.888338
$411$	18.2366	0.899547
$412$	−9.76032	−0.480857
$413$	−5.01202	−0.246626
$414$	−4.38816	−0.215666
$415$	5.47136	0.268579
$416$	−0.858424	−0.0420877
$417$	15.1488	0.741838
$418$	5.17137	0.252940
$419$	31.6464	1.54603	0.773015	−	0.634388i	$-0.218748\pi$
$419$	31.6464	1.54603	0.773015	+	0.634388i	$0.218748\pi$
$420$	7.09576	0.346237
$421$	27.7514	1.35252	0.676260	−	0.736663i	$-0.263599\pi$
$421$	27.7514	1.35252	0.676260	+	0.736663i	$0.263599\pi$
$422$	−5.02415	−0.244572
$423$	−3.27103	−0.159043
$424$	9.66754	0.469497
$425$	26.5096	1.28590
$426$	24.3450	1.17952
$427$	−11.9098	−0.576358
$428$	−7.84253	−0.379083
$429$	−4.76039	−0.229834
$430$	3.75100	0.180889
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	4.52320	0.217623
$433$	−28.9055	−1.38911	−0.694555	−	0.719440i	$-0.744399\pi$
$433$	−28.9055	−1.38911	−0.694555	+	0.719440i	$0.744399\pi$
$434$	−0.802592	−0.0385257
$435$	55.3847	2.65549
$436$	−1.09655	−0.0525154
$437$	−12.4849	−0.597234
$438$	−1.61399	−0.0771193
$439$	22.2721	1.06299	0.531495	−	0.847062i	$-0.321631\pi$
$439$	22.2721	1.06299	0.531495	+	0.847062i	$0.321631\pi$
$440$	10.8582	0.517643
$441$	0.623956	0.0297122
$442$	−2.55875	−0.121707
$443$	2.32911	0.110659	0.0553297	−	0.998468i	$-0.482379\pi$
$443$	2.32911	0.110659	0.0553297	+	0.998468i	$0.482379\pi$
$444$	−0.392728	−0.0186380
$445$	−30.3295	−1.43776
$446$	−1.21846	−0.0576957
$447$	7.89912	0.373616
$448$	1.00000	0.0472456
$449$	0.956283	0.0451298	0.0225649	−	0.999745i	$-0.492817\pi$
$449$	0.956283	0.0451298	0.0225649	+	0.999745i	$0.492817\pi$
$450$	−5.54921	−0.261592
$451$	14.0576	0.661948
$452$	19.6638	0.924909
$453$	−27.8964	−1.31069
$454$	11.2629	0.528592
$455$	−3.19970	−0.150004
$456$	−3.37946	−0.158258
$457$	−34.0425	−1.59244	−0.796220	−	0.605007i	$-0.793170\pi$
$457$	−34.0425	−1.59244	−0.796220	+	0.605007i	$0.793170\pi$
$458$	1.13912	0.0532278
$459$	13.4825	0.629311
$460$	−26.2142	−1.22224
$461$	33.0036	1.53713	0.768565	−	0.639772i	$-0.220971\pi$
$461$	33.0036	1.53713	0.768565	+	0.639772i	$0.220971\pi$
$462$	5.54550	0.258000
$463$	−31.5144	−1.46460	−0.732298	−	0.680984i	$-0.761552\pi$
$463$	−31.5144	−1.46460	−0.732298	+	0.680984i	$0.761552\pi$
$464$	7.80533	0.362353
$465$	5.69500	0.264099
$466$	17.3780	0.805020
$467$	28.8027	1.33283	0.666414	−	0.745582i	$-0.267828\pi$
$467$	28.8027	1.33283	0.666414	+	0.745582i	$0.267828\pi$
$468$	0.535618	0.0247590
$469$	8.51127	0.393014
$470$	−19.5406	−0.901340
$471$	−5.82951	−0.268610
$472$	5.01202	0.230697
$473$	2.93149	0.134790
$474$	4.53681	0.208383
$475$	−15.7882	−0.724414
$476$	2.98075	0.136622
$477$	−6.03211	−0.276192
$478$	−18.0333	−0.824824
$479$	3.08293	0.140863	0.0704313	−	0.997517i	$-0.477562\pi$
$479$	3.08293	0.140863	0.0704313	+	0.997517i	$0.477562\pi$
$480$	−7.09576	−0.323876
$481$	0.177093	0.00807476
$482$	0.947127	0.0431405
$483$	−13.3881	−0.609181
$484$	−2.51409	−0.114277
$485$	−53.4169	−2.42554
$486$	−6.38569	−0.289661
$487$	−2.47113	−0.111977	−0.0559887	−	0.998431i	$-0.517831\pi$
$487$	−2.47113	−0.111977	−0.0559887	+	0.998431i	$0.517831\pi$
$488$	11.9098	0.539133
$489$	−1.40693	−0.0636237
$490$	3.72741	0.168387
$491$	−33.8624	−1.52819	−0.764095	−	0.645104i	$-0.776814\pi$
$491$	−33.8624	−1.52819	−0.764095	+	0.645104i	$0.776814\pi$
$492$	−9.18659	−0.414163
$493$	23.2657	1.04784
$494$	1.52391	0.0685638
$495$	−6.77501	−0.304514
$496$	0.802592	0.0360374
$497$	12.7885	0.573642
$498$	−2.79434	−0.125218
$499$	36.8515	1.64970	0.824850	−	0.565352i	$-0.191259\pi$
$499$	36.8515	1.64970	0.824850	+	0.565352i	$0.191259\pi$
$500$	−14.5130	−0.649042
$501$	22.3776	0.999756
$502$	−2.98951	−0.133428
$503$	6.27919	0.279975	0.139988	−	0.990153i	$-0.455294\pi$
$503$	6.27919	0.279975	0.139988	+	0.990153i	$0.455294\pi$
$504$	−0.623956	−0.0277932
$505$	−53.8086	−2.39445
$506$	−20.4870	−0.910757
$507$	23.3449	1.03678
$508$	−19.8079	−0.878833
$509$	38.1696	1.69184	0.845918	−	0.533313i	$-0.179053\pi$
$509$	38.1696	1.69184	0.845918	+	0.533313i	$0.179053\pi$
$510$	−21.1507	−0.936567
$511$	−0.847830	−0.0375058
$512$	−1.00000	−0.0441942
$513$	−8.02976	−0.354522
$514$	−12.3344	−0.544048
$515$	36.3807	1.60313
$516$	−1.91572	−0.0843347
$517$	−15.2714	−0.671636
$518$	−0.206301	−0.00906433
$519$	1.08850	0.0477798
$520$	3.19970	0.140316
$521$	−11.6956	−0.512392	−0.256196	−	0.966625i	$-0.582469\pi$
$521$	−11.6956	−0.512392	−0.256196	+	0.966625i	$0.582469\pi$
$522$	−4.87018	−0.213162
$523$	−28.5438	−1.24813	−0.624066	−	0.781372i	$-0.714520\pi$
$523$	−28.5438	−1.24813	−0.624066	+	0.781372i	$0.714520\pi$
$524$	−14.2456	−0.622324
$525$	−16.9305	−0.738906
$526$	−20.4794	−0.892946
$527$	2.39233	0.104211
$528$	−5.54550	−0.241337
$529$	26.4604	1.15045
$530$	−36.0349	−1.56526
$531$	−3.12728	−0.135712
$532$	−1.77524	−0.0769663
$533$	4.14252	0.179432
$534$	15.4899	0.670316
$535$	29.2323	1.26382
$536$	−8.51127	−0.367631
$537$	28.8012	1.24286
$538$	−13.2997	−0.573390
$539$	2.91306	0.125474
$540$	−16.8598	−0.725532
$541$	12.6694	0.544699	0.272349	−	0.962198i	$-0.412199\pi$
$541$	12.6694	0.544699	0.272349	+	0.962198i	$0.412199\pi$
$542$	19.3315	0.830358
$543$	−13.2735	−0.569619
$544$	−2.98075	−0.127799
$545$	4.08731	0.175081
$546$	1.63416	0.0699354
$547$	−35.0361	−1.49804	−0.749019	−	0.662549i	$-0.769475\pi$
$547$	−35.0361	−1.49804	−0.749019	+	0.662549i	$0.769475\pi$
$548$	−9.57973	−0.409226
$549$	−7.43121	−0.317157
$550$	−25.9076	−1.10470
$551$	−13.8563	−0.590299
$552$	13.3881	0.569837
$553$	2.38319	0.101344
$554$	−15.0762	−0.640524
$555$	1.46386	0.0621373
$556$	−7.95766	−0.337480
$557$	40.1089	1.69947	0.849734	−	0.527212i	$-0.176763\pi$
$557$	40.1089	1.69947	0.849734	+	0.527212i	$0.176763\pi$
$558$	−0.500782	−0.0211998
$559$	0.863856	0.0365372
$560$	−3.72741	−0.157512
$561$	−16.5297	−0.697886
$562$	13.5077	0.569789
$563$	−17.8295	−0.751423	−0.375711	−	0.926737i	$-0.622602\pi$
$563$	−17.8295	−0.751423	−0.375711	+	0.926737i	$0.622602\pi$
$564$	9.97980	0.420225
$565$	−73.2952	−3.08355
$566$	−9.66089	−0.406078
$567$	−10.4825	−0.440226
$568$	−12.7885	−0.536593
$569$	2.69928	0.113160	0.0565799	−	0.998398i	$-0.481980\pi$
$569$	2.69928	0.113160	0.0565799	+	0.998398i	$0.481980\pi$
$570$	12.5967	0.527616
$571$	41.9535	1.75570	0.877849	−	0.478937i	$-0.158978\pi$
$571$	41.9535	1.75570	0.877849	+	0.478937i	$0.158978\pi$
$572$	2.50064	0.104557
$573$	−51.8805	−2.16734
$574$	−4.82573	−0.201422
$575$	62.5469	2.60839
$576$	0.623956	0.0259981
$577$	−11.2451	−0.468138	−0.234069	−	0.972220i	$-0.575204\pi$
$577$	−11.2451	−0.468138	−0.234069	+	0.972220i	$0.575204\pi$
$578$	8.11514	0.337545
$579$	8.81910	0.366509
$580$	−29.0937	−1.20805
$581$	−1.46787	−0.0608976
$582$	27.2812	1.13084
$583$	−28.1621	−1.16636
$584$	0.847830	0.0350835
$585$	−1.99647	−0.0825439
$586$	23.7302	0.980286
$587$	11.7812	0.486263	0.243132	−	0.969993i	$-0.421825\pi$
$587$	11.7812	0.486263	0.243132	+	0.969993i	$0.421825\pi$
$588$	−1.90367	−0.0785060
$589$	−1.42479	−0.0587075
$590$	−18.6819	−0.769120
$591$	−27.1927	−1.11856
$592$	0.206301	0.00847890
$593$	9.12303	0.374638	0.187319	−	0.982299i	$-0.440020\pi$
$593$	9.12303	0.374638	0.187319	+	0.982299i	$0.440020\pi$
$594$	−13.1764	−0.540632
$595$	−11.1105	−0.455485
$596$	−4.14942	−0.169967
$597$	−7.58293	−0.310349
$598$	−6.03713	−0.246877
$599$	−21.8588	−0.893128	−0.446564	−	0.894752i	$-0.647352\pi$
$599$	−21.8588	−0.893128	−0.446564	+	0.894752i	$0.647352\pi$
$600$	16.9305	0.691183
$601$	0.758674	0.0309470	0.0154735	−	0.999880i	$-0.495074\pi$
$601$	0.758674	0.0309470	0.0154735	+	0.999880i	$0.495074\pi$
$602$	−1.00633	−0.0410149
$603$	5.31065	0.216267
$604$	14.6540	0.596263
$605$	9.37105	0.380987
$606$	27.4812	1.11635
$607$	−5.45318	−0.221338	−0.110669	−	0.993857i	$-0.535299\pi$
$607$	−5.45318	−0.221338	−0.110669	+	0.993857i	$0.535299\pi$
$608$	1.77524	0.0719954
$609$	−14.8588	−0.602108
$610$	−44.3929	−1.79742
$611$	−4.50020	−0.182059
$612$	1.85985	0.0751802
$613$	4.43417	0.179094	0.0895472	−	0.995983i	$-0.471458\pi$
$613$	4.43417	0.179094	0.0895472	+	0.995983i	$0.471458\pi$
$614$	19.0227	0.767693
$615$	34.2422	1.38078
$616$	−2.91306	−0.117370
$617$	30.6054	1.23213	0.616064	−	0.787696i	$-0.288726\pi$
$617$	30.6054	1.23213	0.616064	+	0.787696i	$0.288726\pi$
$618$	−18.5804	−0.747414
$619$	45.1412	1.81438	0.907189	−	0.420722i	$-0.138223\pi$
$619$	45.1412	1.81438	0.907189	+	0.420722i	$0.138223\pi$
$620$	−2.99159	−0.120145
$621$	31.8108	1.27652
$622$	−31.3009	−1.25505
$623$	8.13689	0.325998
$624$	−1.63416	−0.0654186
$625$	9.62804	0.385122
$626$	−24.9640	−0.997764
$627$	9.84458	0.393155
$628$	3.06225	0.122197
$629$	0.614930	0.0245189
$630$	2.32574	0.0926596
$631$	35.9418	1.43082	0.715410	−	0.698704i	$-0.246240\pi$
$631$	35.9418	1.43082	0.715410	+	0.698704i	$0.246240\pi$
$632$	−2.38319	−0.0947983
$633$	−9.56432	−0.380147
$634$	−22.9749	−0.912452
$635$	73.8321	2.92994
$636$	18.4038	0.729758
$637$	0.858424	0.0340120
$638$	−22.7374	−0.900182
$639$	7.97944	0.315662
$640$	3.72741	0.147339
$641$	30.6669	1.21127	0.605635	−	0.795742i	$-0.292919\pi$
$641$	30.6669	1.21127	0.605635	+	0.795742i	$0.292919\pi$
$642$	−14.9296	−0.589224
$643$	1.10669	0.0436436	0.0218218	−	0.999762i	$-0.493053\pi$
$643$	1.10669	0.0436436	0.0218218	+	0.999762i	$0.493053\pi$
$644$	7.03281	0.277131
$645$	7.14066	0.281163
$646$	5.29154	0.208193
$647$	40.0622	1.57501	0.787505	−	0.616309i	$-0.211373\pi$
$647$	40.0622	1.57501	0.787505	+	0.616309i	$0.211373\pi$
$648$	10.4825	0.411793
$649$	−14.6003	−0.573113
$650$	−7.63448	−0.299449
$651$	−1.52787	−0.0598819
$652$	0.739064	0.0289440
$653$	−29.3311	−1.14781	−0.573907	−	0.818921i	$-0.694573\pi$
$653$	−29.3311	−1.14781	−0.573907	+	0.818921i	$0.694573\pi$
$654$	−2.08748	−0.0816268
$655$	53.0994	2.07476
$656$	4.82573	0.188413
$657$	−0.529008	−0.0206386
$658$	5.24240	0.204370
$659$	−18.9021	−0.736322	−0.368161	−	0.929762i	$-0.620012\pi$
$659$	−18.9021	−0.736322	−0.368161	+	0.929762i	$0.620012\pi$
$660$	20.6704	0.804592
$661$	−34.9014	−1.35751	−0.678753	−	0.734367i	$-0.737479\pi$
$661$	−34.9014	−1.35751	−0.678753	+	0.734367i	$0.737479\pi$
$662$	14.7306	0.572521
$663$	−4.87101	−0.189174
$664$	1.46787	0.0569645
$665$	6.61704	0.256598
$666$	−0.128722	−0.00498789
$667$	54.8934	2.12548
$668$	−11.7550	−0.454814
$669$	−2.31954	−0.0896787
$670$	31.7250	1.22564
$671$	−34.6941	−1.33935
$672$	1.90367	0.0734356
$673$	2.18760	0.0843258	0.0421629	−	0.999111i	$-0.486575\pi$
$673$	2.18760	0.0843258	0.0421629	+	0.999111i	$0.486575\pi$
$674$	−0.881637	−0.0339594
$675$	40.2275	1.54836
$676$	−12.2631	−0.471658
$677$	−26.7315	−1.02737	−0.513687	−	0.857978i	$-0.671721\pi$
$677$	−26.7315	−1.02737	−0.513687	+	0.857978i	$0.671721\pi$
$678$	37.4334	1.43762
$679$	14.3308	0.549967
$680$	11.1105	0.426067
$681$	21.4408	0.821612
$682$	−2.33800	−0.0895266
$683$	9.82778	0.376049	0.188025	−	0.982164i	$-0.439792\pi$
$683$	9.82778	0.376049	0.188025	+	0.982164i	$0.439792\pi$
$684$	−1.10767	−0.0423528
$685$	35.7076	1.36432
$686$	−1.00000	−0.0381802
$687$	2.16852	0.0827340
$688$	1.00633	0.0383659
$689$	−8.29885	−0.316161
$690$	−49.9031	−1.89978
$691$	33.1081	1.25949	0.629746	−	0.776801i	$-0.283159\pi$
$691$	33.1081	1.25949	0.629746	+	0.776801i	$0.283159\pi$
$692$	−0.571790	−0.0217362
$693$	1.81762	0.0690456
$694$	−34.3470	−1.30380
$695$	29.6615	1.12512
$696$	14.8588	0.563220
$697$	14.3843	0.544843
$698$	8.66725	0.328060
$699$	33.0820	1.25127
$700$	8.89359	0.336146
$701$	−44.4148	−1.67752	−0.838761	−	0.544499i	$-0.816720\pi$
$701$	−44.4148	−1.67752	−0.838761	+	0.544499i	$0.816720\pi$
$702$	−3.88283	−0.146548
$703$	−0.366232	−0.0138127
$704$	2.91306	0.109790
$705$	−37.1988	−1.40099
$706$	−18.3899	−0.692112
$707$	14.4359	0.542919
$708$	9.54123	0.358581
$709$	−36.7461	−1.38003	−0.690014	−	0.723796i	$-0.742396\pi$
$709$	−36.7461	−1.38003	−0.690014	+	0.723796i	$0.742396\pi$
$710$	47.6679	1.78895
$711$	1.48701	0.0557671
$712$	−8.13689	−0.304943
$713$	5.64447	0.211387
$714$	5.67436	0.212358
$715$	−9.32091	−0.348582
$716$	−15.1293	−0.565409
$717$	−34.3294	−1.28206
$718$	0.178842	0.00667432
$719$	11.4609	0.427419	0.213709	−	0.976897i	$-0.431445\pi$
$719$	11.4609	0.427419	0.213709	+	0.976897i	$0.431445\pi$
$720$	−2.32574	−0.0866752
$721$	−9.76032	−0.363493
$722$	15.8485	0.589821
$723$	1.80302	0.0670549
$724$	6.97258	0.259134
$725$	69.4175	2.57810
$726$	−4.78599	−0.177625
$727$	−31.9309	−1.18425	−0.592125	−	0.805846i	$-0.701711\pi$
$727$	−31.9309	−1.18425	−0.592125	+	0.805846i	$0.701711\pi$
$728$	−0.858424	−0.0318153
$729$	19.2914	0.714496
$730$	−3.16021	−0.116965
$731$	2.99961	0.110945
$732$	22.6724	0.837996
$733$	−38.7241	−1.43031	−0.715153	−	0.698968i	$-0.753643\pi$
$733$	−38.7241	−1.43031	−0.715153	+	0.698968i	$0.753643\pi$
$734$	24.7090	0.912024
$735$	7.09576	0.261731
$736$	−7.03281	−0.259233
$737$	24.7938	0.913292
$738$	−3.01104	−0.110838
$739$	17.7540	0.653092	0.326546	−	0.945181i	$-0.394115\pi$
$739$	17.7540	0.653092	0.326546	+	0.945181i	$0.394115\pi$
$740$	−0.768967	−0.0282678
$741$	2.90101	0.106571
$742$	9.66754	0.354907
$743$	−6.16383	−0.226129	−0.113064	−	0.993588i	$-0.536067\pi$
$743$	−6.16383	−0.226129	−0.113064	+	0.993588i	$0.536067\pi$
$744$	1.52787	0.0560144
$745$	15.4666	0.566652
$746$	−2.66705	−0.0976478
$747$	−0.915887	−0.0335106
$748$	8.68309	0.317485
$749$	−7.84253	−0.286560
$750$	−27.6280	−1.00883
$751$	43.1997	1.57638	0.788189	−	0.615433i	$-0.211019\pi$
$751$	43.1997	1.57638	0.788189	+	0.615433i	$0.211019\pi$
$752$	−5.24240	−0.191171
$753$	−5.69103	−0.207393
$754$	−6.70029	−0.244010
$755$	−54.6215	−1.98788
$756$	4.52320	0.164507
$757$	10.9375	0.397529	0.198765	−	0.980047i	$-0.436307\pi$
$757$	10.9375	0.397529	0.198765	+	0.980047i	$0.436307\pi$
$758$	−6.15096	−0.223413
$759$	−39.0004	−1.41563
$760$	−6.61704	−0.240025
$761$	30.2068	1.09500	0.547498	−	0.836807i	$-0.315580\pi$
$761$	30.2068	1.09500	0.547498	+	0.836807i	$0.315580\pi$
$762$	−37.7076	−1.36600
$763$	−1.09655	−0.0396979
$764$	27.2529	0.985976
$765$	−6.93244	−0.250643
$766$	2.38838	0.0862957
$767$	−4.30244	−0.155352
$768$	−1.90367	−0.0686927
$769$	−10.1063	−0.364443	−0.182222	−	0.983257i	$-0.558329\pi$
$769$	−10.1063	−0.364443	−0.182222	+	0.983257i	$0.558329\pi$
$770$	10.8582	0.391301
$771$	−23.4807	−0.845636
$772$	−4.63269	−0.166734
$773$	−15.4312	−0.555022	−0.277511	−	0.960722i	$-0.589509\pi$
$773$	−15.4312	−0.555022	−0.277511	+	0.960722i	$0.589509\pi$
$774$	−0.627904	−0.0225695
$775$	7.13793	0.256402
$776$	−14.3308	−0.514447
$777$	−0.392728	−0.0140890
$778$	33.9102	1.21574
$779$	−8.56681	−0.306938
$780$	6.09117	0.218099
$781$	37.2536	1.33304
$782$	−20.9630	−0.749636
$783$	35.3051	1.26170
$784$	1.00000	0.0357143
$785$	−11.4143	−0.407393
$786$	−27.1190	−0.967302
$787$	−13.5513	−0.483051	−0.241525	−	0.970395i	$-0.577648\pi$
$787$	−13.5513	−0.483051	−0.241525	+	0.970395i	$0.577648\pi$
$788$	14.2844	0.508860
$789$	−38.9861	−1.38794
$790$	8.88314	0.316048
$791$	19.6638	0.699166
$792$	−1.81762	−0.0645863
$793$	−10.2237	−0.363054
$794$	−2.76592	−0.0981590
$795$	−68.5985	−2.43294
$796$	3.98333	0.141185
$797$	−16.6848	−0.591006	−0.295503	−	0.955342i	$-0.595487\pi$
$797$	−16.6848	−0.591006	−0.295503	+	0.955342i	$0.595487\pi$
$798$	−3.37946	−0.119632
$799$	−15.6263	−0.552818
$800$	−8.89359	−0.314436
$801$	5.07706	0.179389
$802$	−28.3809	−1.00217
$803$	−2.46978	−0.0871566
$804$	−16.2026	−0.571423
$805$	−26.2142	−0.923928
$806$	−0.688964	−0.0242677
$807$	−25.3182	−0.891243
$808$	−14.4359	−0.507854
$809$	3.25257	0.114354	0.0571771	−	0.998364i	$-0.481790\pi$
$809$	3.25257	0.114354	0.0571771	+	0.998364i	$0.481790\pi$
$810$	−39.0728	−1.37288
$811$	0.948085	0.0332918	0.0166459	−	0.999861i	$-0.494701\pi$
$811$	0.948085	0.0332918	0.0166459	+	0.999861i	$0.494701\pi$
$812$	7.80533	0.273913
$813$	36.8007	1.29066
$814$	−0.600966	−0.0210638
$815$	−2.75480	−0.0964963
$816$	−5.67436	−0.198642
$817$	−1.78647	−0.0625007
$818$	10.5586	0.369174
$819$	0.535618	0.0187160
$820$	−17.9875	−0.628150
$821$	−11.4265	−0.398787	−0.199394	−	0.979919i	$-0.563897\pi$
$821$	−11.4265	−0.398787	−0.199394	+	0.979919i	$0.563897\pi$
$822$	−18.2366	−0.636076
$823$	13.2382	0.461456	0.230728	−	0.973018i	$-0.425889\pi$
$823$	13.2382	0.461456	0.230728	+	0.973018i	$0.425889\pi$
$824$	9.76032	0.340017
$825$	−49.3194	−1.71708
$826$	5.01202	0.174391
$827$	−28.2114	−0.981005	−0.490503	−	0.871440i	$-0.663187\pi$
$827$	−28.2114	−0.981005	−0.490503	+	0.871440i	$0.663187\pi$
$828$	4.38816	0.152499
$829$	12.5306	0.435206	0.217603	−	0.976037i	$-0.430176\pi$
$829$	12.5306	0.435206	0.217603	+	0.976037i	$0.430176\pi$
$830$	−5.47136	−0.189914
$831$	−28.7000	−0.995592
$832$	0.858424	0.0297605
$833$	2.98075	0.103277
$834$	−15.1488	−0.524559
$835$	43.8156	1.51630
$836$	−5.17137	−0.178856
$837$	3.63029	0.125481
$838$	−31.6464	−1.09321
$839$	12.0597	0.416346	0.208173	−	0.978092i	$-0.433248\pi$
$839$	12.0597	0.416346	0.208173	+	0.978092i	$0.433248\pi$
$840$	−7.09576	−0.244827
$841$	31.9232	1.10080
$842$	−27.7514	−0.956377
$843$	25.7142	0.885645
$844$	5.02415	0.172938
$845$	45.7096	1.57246
$846$	3.27103	0.112460
$847$	−2.51409	−0.0863852
$848$	−9.66754	−0.331985
$849$	−18.3911	−0.631182
$850$	−26.5096	−0.909271
$851$	1.45087	0.0497352
$852$	−24.3450	−0.834047
$853$	−57.6635	−1.97436	−0.987180	−	0.159608i	$-0.948977\pi$
$853$	−57.6635	−1.97436	−0.987180	+	0.159608i	$0.948977\pi$
$854$	11.9098	0.407547
$855$	4.12874	0.141200
$856$	7.84253	0.268052
$857$	−40.1915	−1.37292	−0.686458	−	0.727170i	$-0.740835\pi$
$857$	−40.1915	−1.37292	−0.686458	+	0.727170i	$0.740835\pi$
$858$	4.76039	0.162517
$859$	−3.52290	−0.120200	−0.0601000	−	0.998192i	$-0.519142\pi$
$859$	−3.52290	−0.120200	−0.0601000	+	0.998192i	$0.519142\pi$
$860$	−3.75100	−0.127908
$861$	−9.18659	−0.313078
$862$	1.00000	0.0340601
$863$	32.9820	1.12272	0.561360	−	0.827572i	$-0.310278\pi$
$863$	32.9820	1.12272	0.561360	+	0.827572i	$0.310278\pi$
$864$	−4.52320	−0.153882
$865$	2.13130	0.0724663
$866$	28.9055	0.982249
$867$	15.4485	0.524660
$868$	0.802592	0.0272417
$869$	6.94238	0.235504
$870$	−55.3847	−1.87772
$871$	7.30628	0.247564
$872$	1.09655	0.0371340
$873$	8.94181	0.302634
$874$	12.4849	0.422308
$875$	−14.5130	−0.490630
$876$	1.61399	0.0545316
$877$	22.7575	0.768467	0.384234	−	0.923236i	$-0.374466\pi$
$877$	22.7575	0.768467	0.384234	+	0.923236i	$0.374466\pi$
$878$	−22.2721	−0.751647
$879$	45.1745	1.52370
$880$	−10.8582	−0.366029
$881$	31.7901	1.07104	0.535519	−	0.844523i	$-0.320116\pi$
$881$	31.7901	1.07104	0.535519	+	0.844523i	$0.320116\pi$
$882$	−0.623956	−0.0210097
$883$	−8.08296	−0.272013	−0.136007	−	0.990708i	$-0.543427\pi$
$883$	−8.08296	−0.272013	−0.136007	+	0.990708i	$0.543427\pi$
$884$	2.55875	0.0860600
$885$	−35.5641	−1.19547
$886$	−2.32911	−0.0782480
$887$	−12.8923	−0.432881	−0.216440	−	0.976296i	$-0.569445\pi$
$887$	−12.8923	−0.432881	−0.216440	+	0.976296i	$0.569445\pi$
$888$	0.392728	0.0131791
$889$	−19.8079	−0.664335
$890$	30.3295	1.01665
$891$	−30.5363	−1.02300
$892$	1.21846	0.0407970
$893$	9.30651	0.311430
$894$	−7.89912	−0.264186
$895$	56.3931	1.88501
$896$	−1.00000	−0.0334077
$897$	−11.4927	−0.383730
$898$	−0.956283	−0.0319116
$899$	6.26450	0.208933
$900$	5.54921	0.184974
$901$	−28.8165	−0.960017
$902$	−14.0576	−0.468068
$903$	−1.91572	−0.0637510
$904$	−19.6638	−0.654009
$905$	−25.9897	−0.863925
$906$	27.8964	0.926795
$907$	−52.9811	−1.75921	−0.879605	−	0.475706i	$-0.842193\pi$
$907$	−52.9811	−1.75921	−0.879605	+	0.475706i	$0.842193\pi$
$908$	−11.2629	−0.373771
$909$	9.00737	0.298756
$910$	3.19970	0.106069
$911$	11.8761	0.393472	0.196736	−	0.980457i	$-0.436966\pi$
$911$	11.8761	0.393472	0.196736	+	0.980457i	$0.436966\pi$
$912$	3.37946	0.111905
$913$	−4.27600	−0.141515
$914$	34.0425	1.12603
$915$	−84.5094	−2.79379
$916$	−1.13912	−0.0376377
$917$	−14.2456	−0.470433
$918$	−13.4825	−0.444990
$919$	46.7794	1.54311	0.771555	−	0.636162i	$-0.219479\pi$
$919$	46.7794	1.54311	0.771555	+	0.636162i	$0.219479\pi$
$920$	26.2142	0.864255
$921$	36.2129	1.19326
$922$	−33.0036	−1.08691
$923$	10.9779	0.361343
$924$	−5.54550	−0.182434
$925$	1.83475	0.0603263
$926$	31.5144	1.03563
$927$	−6.09001	−0.200022
$928$	−7.80533	−0.256223
$929$	23.9724	0.786507	0.393254	−	0.919430i	$-0.371349\pi$
$929$	23.9724	0.786507	0.393254	+	0.919430i	$0.371349\pi$
$930$	−5.69500	−0.186746
$931$	−1.77524	−0.0581811
$932$	−17.3780	−0.569235
$933$	−59.5866	−1.95078
$934$	−28.8027	−0.942452
$935$	−32.3655	−1.05846
$936$	−0.535618	−0.0175072
$937$	10.5748	0.345465	0.172732	−	0.984969i	$-0.444740\pi$
$937$	10.5748	0.345465	0.172732	+	0.984969i	$0.444740\pi$
$938$	−8.51127	−0.277903
$939$	−47.5233	−1.55086
$940$	19.5406	0.637344
$941$	−46.0615	−1.50156	−0.750781	−	0.660551i	$-0.770323\pi$
$941$	−46.0615	−1.50156	−0.750781	+	0.660551i	$0.770323\pi$
$942$	5.82951	0.189936
$943$	33.9384	1.10519
$944$	−5.01202	−0.163127
$945$	−16.8598	−0.548450
$946$	−2.93149	−0.0953110
$947$	19.3816	0.629816	0.314908	−	0.949122i	$-0.398026\pi$
$947$	19.3816	0.629816	0.314908	+	0.949122i	$0.398026\pi$
$948$	−4.53681	−0.147349
$949$	−0.727798	−0.0236253
$950$	15.7882	0.512238
$951$	−43.7367	−1.41826
$952$	−2.98075	−0.0966066
$953$	−1.46579	−0.0474814	−0.0237407	−	0.999718i	$-0.507558\pi$
$953$	−1.46579	−0.0474814	−0.0237407	+	0.999718i	$0.507558\pi$
$954$	6.03211	0.195297
$955$	−101.583	−3.28714
$956$	18.0333	0.583239
$957$	−43.2845	−1.39919
$958$	−3.08293	−0.0996049
$959$	−9.57973	−0.309346
$960$	7.09576	0.229015
$961$	−30.3558	−0.979221
$962$	−0.177093	−0.00570972
$963$	−4.89339	−0.157687
$964$	−0.947127	−0.0305049
$965$	17.2679	0.555874
$966$	13.3881	0.430756
$967$	−17.6070	−0.566204	−0.283102	−	0.959090i	$-0.591363\pi$
$967$	−17.6070	−0.566204	−0.283102	+	0.959090i	$0.591363\pi$
$968$	2.51409	0.0808059
$969$	10.0733	0.323602
$970$	53.4169	1.71511
$971$	−20.3946	−0.654493	−0.327246	−	0.944939i	$-0.606121\pi$
$971$	−20.3946	−0.654493	−0.327246	+	0.944939i	$0.606121\pi$
$972$	6.38569	0.204821
$973$	−7.95766	−0.255111
$974$	2.47113	0.0791800
$975$	−14.5335	−0.465445
$976$	−11.9098	−0.381225
$977$	−14.6917	−0.470029	−0.235015	−	0.971992i	$-0.575514\pi$
$977$	−14.6917	−0.470029	−0.235015	+	0.971992i	$0.575514\pi$
$978$	1.40693	0.0449888
$979$	23.7032	0.757559
$980$	−3.72741	−0.119068
$981$	−0.684201	−0.0218449
$982$	33.8624	1.08059
$983$	−29.0008	−0.924982	−0.462491	−	0.886624i	$-0.653044\pi$
$983$	−29.0008	−0.924982	−0.462491	+	0.886624i	$0.653044\pi$
$984$	9.18659	0.292858
$985$	−53.2438	−1.69649
$986$	−23.2657	−0.740932
$987$	9.97980	0.317660
$988$	−1.52391	−0.0484819
$989$	7.07731	0.225045
$990$	6.77501	0.215324
$991$	20.1901	0.641361	0.320680	−	0.947187i	$-0.396088\pi$
$991$	20.1901	0.641361	0.320680	+	0.947187i	$0.396088\pi$
$992$	−0.802592	−0.0254823
$993$	28.0422	0.889892
$994$	−12.7885	−0.405626
$995$	−14.8475	−0.470697
$996$	2.79434	0.0885422
$997$	23.5371	0.745428	0.372714	−	0.927946i	$-0.378427\pi$
$997$	23.5371	0.745428	0.372714	+	0.927946i	$0.378427\pi$
$998$	−36.8515	−1.16651
$999$	0.933139	0.0295232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.6	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90367 q^{3} +1.00000 q^{4} -3.72741 q^{5} +1.90367 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.623956 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.90367 q^{3} +1.00000 q^{4} -3.72741 q^{5} +1.90367 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.623956 q^{9} +3.72741 q^{10} +2.91306 q^{11} -1.90367 q^{12} +0.858424 q^{13} -1.00000 q^{14} +7.09576 q^{15} +1.00000 q^{16} +2.98075 q^{17} -0.623956 q^{18} -1.77524 q^{19} -3.72741 q^{20} -1.90367 q^{21} -2.91306 q^{22} +7.03281 q^{23} +1.90367 q^{24} +8.89359 q^{25} -0.858424 q^{26} +4.52320 q^{27} +1.00000 q^{28} +7.80533 q^{29} -7.09576 q^{30} +0.802592 q^{31} -1.00000 q^{32} -5.54550 q^{33} -2.98075 q^{34} -3.72741 q^{35} +0.623956 q^{36} +0.206301 q^{37} +1.77524 q^{38} -1.63416 q^{39} +3.72741 q^{40} +4.82573 q^{41} +1.90367 q^{42} +1.00633 q^{43} +2.91306 q^{44} -2.32574 q^{45} -7.03281 q^{46} -5.24240 q^{47} -1.90367 q^{48} +1.00000 q^{49} -8.89359 q^{50} -5.67436 q^{51} +0.858424 q^{52} -9.66754 q^{53} -4.52320 q^{54} -10.8582 q^{55} -1.00000 q^{56} +3.37946 q^{57} -7.80533 q^{58} -5.01202 q^{59} +7.09576 q^{60} -11.9098 q^{61} -0.802592 q^{62} +0.623956 q^{63} +1.00000 q^{64} -3.19970 q^{65} +5.54550 q^{66} +8.51127 q^{67} +2.98075 q^{68} -13.3881 q^{69} +3.72741 q^{70} +12.7885 q^{71} -0.623956 q^{72} -0.847830 q^{73} -0.206301 q^{74} -16.9305 q^{75} -1.77524 q^{76} +2.91306 q^{77} +1.63416 q^{78} +2.38319 q^{79} -3.72741 q^{80} -10.4825 q^{81} -4.82573 q^{82} -1.46787 q^{83} -1.90367 q^{84} -11.1105 q^{85} -1.00633 q^{86} -14.8588 q^{87} -2.91306 q^{88} +8.13689 q^{89} +2.32574 q^{90} +0.858424 q^{91} +7.03281 q^{92} -1.52787 q^{93} +5.24240 q^{94} +6.61704 q^{95} +1.90367 q^{96} +14.3308 q^{97} -1.00000 q^{98} +1.81762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 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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