LMFDB - Embedded newform 6034.2.a.r.1.10

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:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.40540 q^{3} +1.00000 q^{4} +2.72818 q^{5} -1.40540 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.02486 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.40540 q^{3} +1.00000 q^{4} +2.72818 q^{5} -1.40540 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.02486 q^{9} +2.72818 q^{10} +2.81327 q^{11} -1.40540 q^{12} +4.13755 q^{13} -1.00000 q^{14} -3.83417 q^{15} +1.00000 q^{16} -7.12854 q^{17} -1.02486 q^{18} -5.00196 q^{19} +2.72818 q^{20} +1.40540 q^{21} +2.81327 q^{22} -7.67310 q^{23} -1.40540 q^{24} +2.44298 q^{25} +4.13755 q^{26} +5.65653 q^{27} -1.00000 q^{28} +4.14386 q^{29} -3.83417 q^{30} +7.50865 q^{31} +1.00000 q^{32} -3.95376 q^{33} -7.12854 q^{34} -2.72818 q^{35} -1.02486 q^{36} +5.81619 q^{37} -5.00196 q^{38} -5.81489 q^{39} +2.72818 q^{40} +6.11752 q^{41} +1.40540 q^{42} +5.49122 q^{43} +2.81327 q^{44} -2.79602 q^{45} -7.67310 q^{46} -5.67066 q^{47} -1.40540 q^{48} +1.00000 q^{49} +2.44298 q^{50} +10.0184 q^{51} +4.13755 q^{52} +5.80450 q^{53} +5.65653 q^{54} +7.67512 q^{55} -1.00000 q^{56} +7.02974 q^{57} +4.14386 q^{58} +9.67513 q^{59} -3.83417 q^{60} +14.0428 q^{61} +7.50865 q^{62} +1.02486 q^{63} +1.00000 q^{64} +11.2880 q^{65} -3.95376 q^{66} -5.47721 q^{67} -7.12854 q^{68} +10.7837 q^{69} -2.72818 q^{70} +14.6492 q^{71} -1.02486 q^{72} +14.1064 q^{73} +5.81619 q^{74} -3.43335 q^{75} -5.00196 q^{76} -2.81327 q^{77} -5.81489 q^{78} -6.15766 q^{79} +2.72818 q^{80} -4.87506 q^{81} +6.11752 q^{82} -10.8943 q^{83} +1.40540 q^{84} -19.4480 q^{85} +5.49122 q^{86} -5.82376 q^{87} +2.81327 q^{88} +8.75964 q^{89} -2.79602 q^{90} -4.13755 q^{91} -7.67310 q^{92} -10.5526 q^{93} -5.67066 q^{94} -13.6463 q^{95} -1.40540 q^{96} -14.5730 q^{97} +1.00000 q^{98} -2.88322 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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
$3$	−1.40540	−0.811405	−0.405703	−	0.914005i	$-0.632973\pi$
$3$	−1.40540	−0.811405	−0.405703	+	0.914005i	$0.632973\pi$
$4$	1.00000	0.500000
$5$	2.72818	1.22008	0.610040	−	0.792371i	$-0.291153\pi$
$5$	2.72818	1.22008	0.610040	+	0.792371i	$0.291153\pi$
$6$	−1.40540	−0.573750
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−1.02486	−0.341622
$10$	2.72818	0.862727
$11$	2.81327	0.848234	0.424117	−	0.905607i	$-0.360585\pi$
$11$	2.81327	0.848234	0.424117	+	0.905607i	$0.360585\pi$
$12$	−1.40540	−0.405703
$13$	4.13755	1.14755	0.573775	−	0.819013i	$-0.305478\pi$
$13$	4.13755	1.14755	0.573775	+	0.819013i	$0.305478\pi$
$14$	−1.00000	−0.267261
$15$	−3.83417	−0.989979
$16$	1.00000	0.250000
$17$	−7.12854	−1.72893	−0.864463	−	0.502697i	$-0.832341\pi$
$17$	−7.12854	−1.72893	−0.864463	+	0.502697i	$0.832341\pi$
$18$	−1.02486	−0.241563
$19$	−5.00196	−1.14753	−0.573765	−	0.819020i	$-0.694518\pi$
$19$	−5.00196	−1.14753	−0.573765	+	0.819020i	$0.694518\pi$
$20$	2.72818	0.610040
$21$	1.40540	0.306682
$22$	2.81327	0.599792
$23$	−7.67310	−1.59995	−0.799976	−	0.600032i	$-0.795154\pi$
$23$	−7.67310	−1.59995	−0.799976	+	0.600032i	$0.795154\pi$
$24$	−1.40540	−0.286875
$25$	2.44298	0.488595
$26$	4.13755	0.811441
$27$	5.65653	1.08860
$28$	−1.00000	−0.188982
$29$	4.14386	0.769495	0.384748	−	0.923022i	$-0.374288\pi$
$29$	4.14386	0.769495	0.384748	+	0.923022i	$0.374288\pi$
$30$	−3.83417	−0.700021
$31$	7.50865	1.34859	0.674296	−	0.738461i	$-0.264447\pi$
$31$	7.50865	1.34859	0.674296	+	0.738461i	$0.264447\pi$
$32$	1.00000	0.176777
$33$	−3.95376	−0.688261
$34$	−7.12854	−1.22254
$35$	−2.72818	−0.461147
$36$	−1.02486	−0.170811
$37$	5.81619	0.956176	0.478088	−	0.878312i	$-0.341330\pi$
$37$	5.81619	0.956176	0.478088	+	0.878312i	$0.341330\pi$
$38$	−5.00196	−0.811426
$39$	−5.81489	−0.931128
$40$	2.72818	0.431363
$41$	6.11752	0.955396	0.477698	−	0.878524i	$-0.341471\pi$
$41$	6.11752	0.955396	0.477698	+	0.878524i	$0.341471\pi$
$42$	1.40540	0.216857
$43$	5.49122	0.837403	0.418702	−	0.908124i	$-0.362485\pi$
$43$	5.49122	0.837403	0.418702	+	0.908124i	$0.362485\pi$
$44$	2.81327	0.424117
$45$	−2.79602	−0.416806
$46$	−7.67310	−1.13134
$47$	−5.67066	−0.827150	−0.413575	−	0.910470i	$-0.635720\pi$
$47$	−5.67066	−0.827150	−0.413575	+	0.910470i	$0.635720\pi$
$48$	−1.40540	−0.202851
$49$	1.00000	0.142857
$50$	2.44298	0.345489
$51$	10.0184	1.40286
$52$	4.13755	0.573775
$53$	5.80450	0.797309	0.398655	−	0.917101i	$-0.369477\pi$
$53$	5.80450	0.797309	0.398655	+	0.917101i	$0.369477\pi$
$54$	5.65653	0.769756
$55$	7.67512	1.03491
$56$	−1.00000	−0.133631
$57$	7.02974	0.931111
$58$	4.14386	0.544115
$59$	9.67513	1.25959	0.629797	−	0.776760i	$-0.283138\pi$
$59$	9.67513	1.25959	0.629797	+	0.776760i	$0.283138\pi$
$60$	−3.83417	−0.494990
$61$	14.0428	1.79800	0.898999	−	0.437951i	$-0.144296\pi$
$61$	14.0428	1.79800	0.898999	+	0.437951i	$0.144296\pi$
$62$	7.50865	0.953599
$63$	1.02486	0.129121
$64$	1.00000	0.125000
$65$	11.2880	1.40010
$66$	−3.95376	−0.486674
$67$	−5.47721	−0.669147	−0.334574	−	0.942370i	$-0.608592\pi$
$67$	−5.47721	−0.669147	−0.334574	+	0.942370i	$0.608592\pi$
$68$	−7.12854	−0.864463
$69$	10.7837	1.29821
$70$	−2.72818	−0.326080
$71$	14.6492	1.73854	0.869268	−	0.494341i	$-0.164590\pi$
$71$	14.6492	1.73854	0.869268	+	0.494341i	$0.164590\pi$
$72$	−1.02486	−0.120781
$73$	14.1064	1.65103	0.825515	−	0.564381i	$-0.190885\pi$
$73$	14.1064	1.65103	0.825515	+	0.564381i	$0.190885\pi$
$74$	5.81619	0.676119
$75$	−3.43335	−0.396449
$76$	−5.00196	−0.573765
$77$	−2.81327	−0.320602
$78$	−5.81489	−0.658407
$79$	−6.15766	−0.692790	−0.346395	−	0.938089i	$-0.612594\pi$
$79$	−6.15766	−0.692790	−0.346395	+	0.938089i	$0.612594\pi$
$80$	2.72818	0.305020
$81$	−4.87506	−0.541673
$82$	6.11752	0.675567
$83$	−10.8943	−1.19581	−0.597904	−	0.801568i	$-0.703999\pi$
$83$	−10.8943	−1.19581	−0.597904	+	0.801568i	$0.703999\pi$
$84$	1.40540	0.153341
$85$	−19.4480	−2.10943
$86$	5.49122	0.592134
$87$	−5.82376	−0.624373
$88$	2.81327	0.299896
$89$	8.75964	0.928520	0.464260	−	0.885699i	$-0.346320\pi$
$89$	8.75964	0.928520	0.464260	+	0.885699i	$0.346320\pi$
$90$	−2.79602	−0.294726
$91$	−4.13755	−0.433733
$92$	−7.67310	−0.799976
$93$	−10.5526	−1.09426
$94$	−5.67066	−0.584884
$95$	−13.6463	−1.40008
$96$	−1.40540	−0.143438
$97$	−14.5730	−1.47966	−0.739832	−	0.672791i	$-0.765095\pi$
$97$	−14.5730	−1.47966	−0.739832	+	0.672791i	$0.765095\pi$
$98$	1.00000	0.101015
$99$	−2.88322	−0.289775
$100$	2.44298	0.244298
$101$	−5.47966	−0.545247	−0.272623	−	0.962121i	$-0.587891\pi$
$101$	−5.47966	−0.545247	−0.272623	+	0.962121i	$0.587891\pi$
$102$	10.0184	0.991971
$103$	−1.54542	−0.152275	−0.0761374	−	0.997097i	$-0.524259\pi$
$103$	−1.54542	−0.152275	−0.0761374	+	0.997097i	$0.524259\pi$
$104$	4.13755	0.405720
$105$	3.83417	0.374177
$106$	5.80450	0.563783
$107$	15.2426	1.47356	0.736778	−	0.676135i	$-0.236346\pi$
$107$	15.2426	1.47356	0.736778	+	0.676135i	$0.236346\pi$
$108$	5.65653	0.544299
$109$	−17.1338	−1.64112	−0.820559	−	0.571561i	$-0.806338\pi$
$109$	−17.1338	−1.64112	−0.820559	+	0.571561i	$0.806338\pi$
$110$	7.67512	0.731794
$111$	−8.17405	−0.775846
$112$	−1.00000	−0.0944911
$113$	13.0842	1.23086	0.615429	−	0.788192i	$-0.288983\pi$
$113$	13.0842	1.23086	0.615429	+	0.788192i	$0.288983\pi$
$114$	7.02974	0.658395
$115$	−20.9336	−1.95207
$116$	4.14386	0.384748
$117$	−4.24043	−0.392028
$118$	9.67513	0.890668
$119$	7.12854	0.653473
$120$	−3.83417	−0.350011
$121$	−3.08549	−0.280499
$122$	14.0428	1.27138
$123$	−8.59753	−0.775213
$124$	7.50865	0.674296
$125$	−6.97603	−0.623955
$126$	1.02486	0.0913022
$127$	−5.01080	−0.444636	−0.222318	−	0.974974i	$-0.571362\pi$
$127$	−5.01080	−0.444636	−0.222318	+	0.974974i	$0.571362\pi$
$128$	1.00000	0.0883883
$129$	−7.71734	−0.679474
$130$	11.2880	0.990023
$131$	3.65865	0.319658	0.159829	−	0.987145i	$-0.448906\pi$
$131$	3.65865	0.319658	0.159829	+	0.987145i	$0.448906\pi$
$132$	−3.95376	−0.344131
$133$	5.00196	0.433725
$134$	−5.47721	−0.473159
$135$	15.4320	1.32818
$136$	−7.12854	−0.611268
$137$	8.27616	0.707080	0.353540	−	0.935419i	$-0.384978\pi$
$137$	8.27616	0.707080	0.353540	+	0.935419i	$0.384978\pi$
$138$	10.7837	0.917972
$139$	3.28911	0.278978	0.139489	−	0.990224i	$-0.455454\pi$
$139$	3.28911	0.278978	0.139489	+	0.990224i	$0.455454\pi$
$140$	−2.72818	−0.230573
$141$	7.96951	0.671154
$142$	14.6492	1.22933
$143$	11.6401	0.973391
$144$	−1.02486	−0.0854054
$145$	11.3052	0.938846
$146$	14.1064	1.16745
$147$	−1.40540	−0.115915
$148$	5.81619	0.478088
$149$	14.4507	1.18385	0.591923	−	0.805994i	$-0.298369\pi$
$149$	14.4507	1.18385	0.591923	+	0.805994i	$0.298369\pi$
$150$	−3.43335	−0.280332
$151$	−12.4700	−1.01479	−0.507395	−	0.861713i	$-0.669392\pi$
$151$	−12.4700	−1.01479	−0.507395	+	0.861713i	$0.669392\pi$
$152$	−5.00196	−0.405713
$153$	7.30579	0.590638
$154$	−2.81327	−0.226700
$155$	20.4850	1.64539
$156$	−5.81489	−0.465564
$157$	17.3324	1.38328	0.691640	−	0.722243i	$-0.256889\pi$
$157$	17.3324	1.38328	0.691640	+	0.722243i	$0.256889\pi$
$158$	−6.15766	−0.489877
$159$	−8.15761	−0.646941
$160$	2.72818	0.215682
$161$	7.67310	0.604725
$162$	−4.87506	−0.383021
$163$	−14.2160	−1.11349	−0.556743	−	0.830685i	$-0.687949\pi$
$163$	−14.2160	−1.11349	−0.556743	+	0.830685i	$0.687949\pi$
$164$	6.11752	0.477698
$165$	−10.7866	−0.839734
$166$	−10.8943	−0.845563
$167$	10.9949	0.850811	0.425406	−	0.905003i	$-0.360131\pi$
$167$	10.9949	0.850811	0.425406	+	0.905003i	$0.360131\pi$
$168$	1.40540	0.108429
$169$	4.11933	0.316872
$170$	−19.4480	−1.49159
$171$	5.12634	0.392021
$172$	5.49122	0.418702
$173$	−14.6248	−1.11191	−0.555953	−	0.831214i	$-0.687646\pi$
$173$	−14.6248	−1.11191	−0.555953	+	0.831214i	$0.687646\pi$
$174$	−5.82376	−0.441498
$175$	−2.44298	−0.184672
$176$	2.81327	0.212058
$177$	−13.5974	−1.02204
$178$	8.75964	0.656563
$179$	−13.9885	−1.04555	−0.522777	−	0.852470i	$-0.675104\pi$
$179$	−13.9885	−1.04555	−0.522777	+	0.852470i	$0.675104\pi$
$180$	−2.79602	−0.208403
$181$	12.8296	0.953619	0.476810	−	0.879007i	$-0.341793\pi$
$181$	12.8296	0.953619	0.476810	+	0.879007i	$0.341793\pi$
$182$	−4.13755	−0.306696
$183$	−19.7357	−1.45891
$184$	−7.67310	−0.565668
$185$	15.8676	1.16661
$186$	−10.5526	−0.773755
$187$	−20.0545	−1.46653
$188$	−5.67066	−0.413575
$189$	−5.65653	−0.411452
$190$	−13.6463	−0.990004
$191$	8.38764	0.606908	0.303454	−	0.952846i	$-0.401860\pi$
$191$	8.38764	0.606908	0.303454	+	0.952846i	$0.401860\pi$
$192$	−1.40540	−0.101426
$193$	−1.17050	−0.0842546	−0.0421273	−	0.999112i	$-0.513413\pi$
$193$	−1.17050	−0.0842546	−0.0421273	+	0.999112i	$0.513413\pi$
$194$	−14.5730	−1.04628
$195$	−15.8641	−1.13605
$196$	1.00000	0.0714286
$197$	9.49551	0.676527	0.338264	−	0.941051i	$-0.390160\pi$
$197$	9.49551	0.676527	0.338264	+	0.941051i	$0.390160\pi$
$198$	−2.88322	−0.204902
$199$	25.2225	1.78797	0.893987	−	0.448092i	$-0.147896\pi$
$199$	25.2225	1.78797	0.893987	+	0.448092i	$0.147896\pi$
$200$	2.44298	0.172745
$201$	7.69764	0.542950
$202$	−5.47966	−0.385548
$203$	−4.14386	−0.290842
$204$	10.0184	0.701430
$205$	16.6897	1.16566
$206$	−1.54542	−0.107675
$207$	7.86389	0.546578
$208$	4.13755	0.286888
$209$	−14.0719	−0.973373
$210$	3.83417	0.264583
$211$	23.7830	1.63729	0.818645	−	0.574300i	$-0.194726\pi$
$211$	23.7830	1.63729	0.818645	+	0.574300i	$0.194726\pi$
$212$	5.80450	0.398655
$213$	−20.5879	−1.41066
$214$	15.2426	1.04196
$215$	14.9811	1.02170
$216$	5.65653	0.384878
$217$	−7.50865	−0.509720
$218$	−17.1338	−1.16045
$219$	−19.8251	−1.33965
$220$	7.67512	0.517457
$221$	−29.4947	−1.98403
$222$	−8.17405	−0.548606
$223$	−6.94501	−0.465072	−0.232536	−	0.972588i	$-0.574702\pi$
$223$	−6.94501	−0.465072	−0.232536	+	0.972588i	$0.574702\pi$
$224$	−1.00000	−0.0668153
$225$	−2.50372	−0.166915
$226$	13.0842	0.870348
$227$	18.0709	1.19941	0.599703	−	0.800223i	$-0.295286\pi$
$227$	18.0709	1.19941	0.599703	+	0.800223i	$0.295286\pi$
$228$	7.02974	0.465556
$229$	−2.82925	−0.186962	−0.0934811	−	0.995621i	$-0.529799\pi$
$229$	−2.82925	−0.186962	−0.0934811	+	0.995621i	$0.529799\pi$
$230$	−20.9336	−1.38032
$231$	3.95376	0.260138
$232$	4.14386	0.272058
$233$	−16.5649	−1.08520	−0.542602	−	0.839990i	$-0.682561\pi$
$233$	−16.5649	−1.08520	−0.542602	+	0.839990i	$0.682561\pi$
$234$	−4.24043	−0.277206
$235$	−15.4706	−1.00919
$236$	9.67513	0.629797
$237$	8.65394	0.562134
$238$	7.12854	0.462075
$239$	−4.06901	−0.263202	−0.131601	−	0.991303i	$-0.542012\pi$
$239$	−4.06901	−0.263202	−0.131601	+	0.991303i	$0.542012\pi$
$240$	−3.83417	−0.247495
$241$	20.7908	1.33925	0.669626	−	0.742698i	$-0.266454\pi$
$241$	20.7908	1.33925	0.669626	+	0.742698i	$0.266454\pi$
$242$	−3.08549	−0.198343
$243$	−10.1182	−0.649082
$244$	14.0428	0.898999
$245$	2.72818	0.174297
$246$	−8.59753	−0.548158
$247$	−20.6959	−1.31685
$248$	7.50865	0.476800
$249$	15.3108	0.970284
$250$	−6.97603	−0.441203
$251$	−11.2183	−0.708093	−0.354047	−	0.935228i	$-0.615195\pi$
$251$	−11.2183	−0.708093	−0.354047	+	0.935228i	$0.615195\pi$
$252$	1.02486	0.0645604
$253$	−21.5865	−1.35713
$254$	−5.01080	−0.314405
$255$	27.3321	1.71160
$256$	1.00000	0.0625000
$257$	6.45425	0.402605	0.201303	−	0.979529i	$-0.435483\pi$
$257$	6.45425	0.402605	0.201303	+	0.979529i	$0.435483\pi$
$258$	−7.71734	−0.480460
$259$	−5.81619	−0.361401
$260$	11.2880	0.700052
$261$	−4.24690	−0.262876
$262$	3.65865	0.226032
$263$	−5.79528	−0.357352	−0.178676	−	0.983908i	$-0.557181\pi$
$263$	−5.79528	−0.357352	−0.178676	+	0.983908i	$0.557181\pi$
$264$	−3.95376	−0.243337
$265$	15.8357	0.972781
$266$	5.00196	0.306690
$267$	−12.3108	−0.753406
$268$	−5.47721	−0.334574
$269$	−19.7908	−1.20667	−0.603334	−	0.797489i	$-0.706161\pi$
$269$	−19.7908	−1.20667	−0.603334	+	0.797489i	$0.706161\pi$
$270$	15.4320	0.939163
$271$	10.9108	0.662785	0.331393	−	0.943493i	$-0.392482\pi$
$271$	10.9108	0.662785	0.331393	+	0.943493i	$0.392482\pi$
$272$	−7.12854	−0.432231
$273$	5.81489	0.351933
$274$	8.27616	0.499981
$275$	6.87276	0.414443
$276$	10.7837	0.649104
$277$	22.2133	1.33467	0.667334	−	0.744759i	$-0.267435\pi$
$277$	22.2133	1.33467	0.667334	+	0.744759i	$0.267435\pi$
$278$	3.28911	0.197267
$279$	−7.69535	−0.460708
$280$	−2.72818	−0.163040
$281$	18.5512	1.10667	0.553335	−	0.832959i	$-0.313355\pi$
$281$	18.5512	1.10667	0.553335	+	0.832959i	$0.313355\pi$
$282$	7.96951	0.474578
$283$	−12.4292	−0.738837	−0.369419	−	0.929263i	$-0.620443\pi$
$283$	−12.4292	−0.738837	−0.369419	+	0.929263i	$0.620443\pi$
$284$	14.6492	0.869268
$285$	19.1784	1.13603
$286$	11.6401	0.688291
$287$	−6.11752	−0.361106
$288$	−1.02486	−0.0603907
$289$	33.8161	1.98918
$290$	11.3052	0.663864
$291$	20.4808	1.20061
$292$	14.1064	0.825515
$293$	10.3506	0.604686	0.302343	−	0.953199i	$-0.402231\pi$
$293$	10.3506	0.604686	0.302343	+	0.953199i	$0.402231\pi$
$294$	−1.40540	−0.0819643
$295$	26.3955	1.53681
$296$	5.81619	0.338059
$297$	15.9133	0.923386
$298$	14.4507	0.837106
$299$	−31.7478	−1.83602
$300$	−3.43335	−0.198224
$301$	−5.49122	−0.316509
$302$	−12.4700	−0.717565
$303$	7.70109	0.442416
$304$	−5.00196	−0.286882
$305$	38.3114	2.19370
$306$	7.30579	0.417644
$307$	−3.17768	−0.181360	−0.0906800	−	0.995880i	$-0.528904\pi$
$307$	−3.17768	−0.181360	−0.0906800	+	0.995880i	$0.528904\pi$
$308$	−2.81327	−0.160301
$309$	2.17193	0.123557
$310$	20.4850	1.16347
$311$	25.1234	1.42462	0.712308	−	0.701868i	$-0.247650\pi$
$311$	25.1234	1.42462	0.712308	+	0.701868i	$0.247650\pi$
$312$	−5.81489	−0.329204
$313$	−26.3471	−1.48923	−0.744613	−	0.667496i	$-0.767366\pi$
$313$	−26.3471	−1.48923	−0.744613	+	0.667496i	$0.767366\pi$
$314$	17.3324	0.978126
$315$	2.79602	0.157538
$316$	−6.15766	−0.346395
$317$	−13.7972	−0.774927	−0.387463	−	0.921885i	$-0.626649\pi$
$317$	−13.7972	−0.774927	−0.387463	+	0.921885i	$0.626649\pi$
$318$	−8.15761	−0.457456
$319$	11.6578	0.652712
$320$	2.72818	0.152510
$321$	−21.4218	−1.19565
$322$	7.67310	0.427605
$323$	35.6567	1.98399
$324$	−4.87506	−0.270837
$325$	10.1079	0.560688
$326$	−14.2160	−0.787353
$327$	24.0797	1.33161
$328$	6.11752	0.337783
$329$	5.67066	0.312633
$330$	−10.7866	−0.593782
$331$	−22.7890	−1.25259	−0.626297	−	0.779585i	$-0.715430\pi$
$331$	−22.7890	−1.25259	−0.626297	+	0.779585i	$0.715430\pi$
$332$	−10.8943	−0.597904
$333$	−5.96081	−0.326650
$334$	10.9949	0.601614
$335$	−14.9428	−0.816413
$336$	1.40540	0.0766706
$337$	−22.8791	−1.24631	−0.623153	−	0.782100i	$-0.714149\pi$
$337$	−22.8791	−1.24631	−0.623153	+	0.782100i	$0.714149\pi$
$338$	4.11933	0.224062
$339$	−18.3885	−0.998725
$340$	−19.4480	−1.05471
$341$	21.1239	1.14392
$342$	5.12634	0.277201
$343$	−1.00000	−0.0539949
$344$	5.49122	0.296067
$345$	29.4200	1.58392
$346$	−14.6248	−0.786236
$347$	−20.3831	−1.09422	−0.547111	−	0.837060i	$-0.684273\pi$
$347$	−20.3831	−1.09422	−0.547111	+	0.837060i	$0.684273\pi$
$348$	−5.82376	−0.312186
$349$	13.2429	0.708878	0.354439	−	0.935079i	$-0.384672\pi$
$349$	13.2429	0.708878	0.354439	+	0.935079i	$0.384672\pi$
$350$	−2.44298	−0.130583
$351$	23.4042	1.24922
$352$	2.81327	0.149948
$353$	−4.81850	−0.256463	−0.128231	−	0.991744i	$-0.540930\pi$
$353$	−4.81850	−0.256463	−0.128231	+	0.991744i	$0.540930\pi$
$354$	−13.5974	−0.722692
$355$	39.9656	2.12115
$356$	8.75964	0.464260
$357$	−10.0184	−0.530231
$358$	−13.9885	−0.739318
$359$	−31.5828	−1.66688	−0.833439	−	0.552612i	$-0.813631\pi$
$359$	−31.5828	−1.66688	−0.833439	+	0.552612i	$0.813631\pi$
$360$	−2.79602	−0.147363
$361$	6.01965	0.316824
$362$	12.8296	0.674311
$363$	4.33634	0.227599
$364$	−4.13755	−0.216867
$365$	38.4848	2.01439
$366$	−19.7357	−1.03160
$367$	1.73876	0.0907626	0.0453813	−	0.998970i	$-0.485550\pi$
$367$	1.73876	0.0907626	0.0453813	+	0.998970i	$0.485550\pi$
$368$	−7.67310	−0.399988
$369$	−6.26963	−0.326384
$370$	15.8676	0.824919
$371$	−5.80450	−0.301355
$372$	−10.5526	−0.547128
$373$	−20.1179	−1.04166	−0.520832	−	0.853659i	$-0.674378\pi$
$373$	−20.1179	−1.04166	−0.520832	+	0.853659i	$0.674378\pi$
$374$	−20.0545	−1.03700
$375$	9.80407	0.506280
$376$	−5.67066	−0.292442
$377$	17.1454	0.883035
$378$	−5.65653	−0.290940
$379$	−3.63675	−0.186807	−0.0934036	−	0.995628i	$-0.529775\pi$
$379$	−3.63675	−0.186807	−0.0934036	+	0.995628i	$0.529775\pi$
$380$	−13.6463	−0.700039
$381$	7.04215	0.360780
$382$	8.38764	0.429149
$383$	−20.2388	−1.03415	−0.517076	−	0.855939i	$-0.672980\pi$
$383$	−20.2388	−1.03415	−0.517076	+	0.855939i	$0.672980\pi$
$384$	−1.40540	−0.0717188
$385$	−7.67512	−0.391160
$386$	−1.17050	−0.0595770
$387$	−5.62776	−0.286075
$388$	−14.5730	−0.739832
$389$	−0.996074	−0.0505029	−0.0252515	−	0.999681i	$-0.508039\pi$
$389$	−0.996074	−0.0505029	−0.0252515	+	0.999681i	$0.508039\pi$
$390$	−15.8641	−0.803309
$391$	54.6980	2.76620
$392$	1.00000	0.0505076
$393$	−5.14185	−0.259372
$394$	9.49551	0.478377
$395$	−16.7992	−0.845260
$396$	−2.88322	−0.144887
$397$	36.2799	1.82084	0.910418	−	0.413689i	$-0.135760\pi$
$397$	36.2799	1.82084	0.910418	+	0.413689i	$0.135760\pi$
$398$	25.2225	1.26429
$399$	−7.02974	−0.351927
$400$	2.44298	0.122149
$401$	15.9837	0.798186	0.399093	−	0.916910i	$-0.369325\pi$
$401$	15.9837	0.798186	0.399093	+	0.916910i	$0.369325\pi$
$402$	7.69764	0.383923
$403$	31.0674	1.54758
$404$	−5.47966	−0.272623
$405$	−13.3000	−0.660885
$406$	−4.14386	−0.205656
$407$	16.3625	0.811061
$408$	10.0184	0.495986
$409$	3.98098	0.196847	0.0984234	−	0.995145i	$-0.468620\pi$
$409$	3.98098	0.196847	0.0984234	+	0.995145i	$0.468620\pi$
$410$	16.6897	0.824245
$411$	−11.6313	−0.573729
$412$	−1.54542	−0.0761374
$413$	−9.67513	−0.476082
$414$	7.86389	0.386489
$415$	−29.7217	−1.45898
$416$	4.13755	0.202860
$417$	−4.62249	−0.226364
$418$	−14.0719	−0.688279
$419$	−11.3926	−0.556564	−0.278282	−	0.960499i	$-0.589765\pi$
$419$	−11.3926	−0.556564	−0.278282	+	0.960499i	$0.589765\pi$
$420$	3.83417	0.187089
$421$	13.3816	0.652180	0.326090	−	0.945339i	$-0.394269\pi$
$421$	13.3816	0.652180	0.326090	+	0.945339i	$0.394269\pi$
$422$	23.7830	1.15774
$423$	5.81166	0.282572
$424$	5.80450	0.281891
$425$	−17.4149	−0.844745
$426$	−20.5879	−0.997486
$427$	−14.0428	−0.679579
$428$	15.2426	0.736778
$429$	−16.3589	−0.789815
$430$	14.9811	0.722450
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.65653	0.272150
$433$	−24.6778	−1.18594	−0.592970	−	0.805224i	$-0.702045\pi$
$433$	−24.6778	−1.18594	−0.592970	+	0.805224i	$0.702045\pi$
$434$	−7.50865	−0.360427
$435$	−15.8883	−0.761785
$436$	−17.1338	−0.820559
$437$	38.3806	1.83599
$438$	−19.8251	−0.947278
$439$	15.4552	0.737638	0.368819	−	0.929501i	$-0.379762\pi$
$439$	15.4552	0.737638	0.368819	+	0.929501i	$0.379762\pi$
$440$	7.67512	0.365897
$441$	−1.02486	−0.0488031
$442$	−29.4947	−1.40292
$443$	5.89420	0.280042	0.140021	−	0.990149i	$-0.455283\pi$
$443$	5.89420	0.280042	0.140021	+	0.990149i	$0.455283\pi$
$444$	−8.17405	−0.387923
$445$	23.8979	1.13287
$446$	−6.94501	−0.328856
$447$	−20.3089	−0.960579
$448$	−1.00000	−0.0472456
$449$	11.5822	0.546596	0.273298	−	0.961929i	$-0.411885\pi$
$449$	11.5822	0.546596	0.273298	+	0.961929i	$0.411885\pi$
$450$	−2.50372	−0.118027
$451$	17.2102	0.810399
$452$	13.0842	0.615429
$453$	17.5252	0.823406
$454$	18.0709	0.848107
$455$	−11.2880	−0.529189
$456$	7.02974	0.329198
$457$	10.0648	0.470811	0.235405	−	0.971897i	$-0.424358\pi$
$457$	10.0648	0.470811	0.235405	+	0.971897i	$0.424358\pi$
$458$	−2.82925	−0.132202
$459$	−40.3228	−1.88211
$460$	−20.9336	−0.976034
$461$	8.76695	0.408317	0.204159	−	0.978938i	$-0.434554\pi$
$461$	8.76695	0.408317	0.204159	+	0.978938i	$0.434554\pi$
$462$	3.95376	0.183946
$463$	−21.2979	−0.989797	−0.494898	−	0.868951i	$-0.664795\pi$
$463$	−21.2979	−0.989797	−0.494898	+	0.868951i	$0.664795\pi$
$464$	4.14386	0.192374
$465$	−28.7895	−1.33508
$466$	−16.5649	−0.767355
$467$	−24.2695	−1.12306	−0.561530	−	0.827456i	$-0.689787\pi$
$467$	−24.2695	−1.12306	−0.561530	+	0.827456i	$0.689787\pi$
$468$	−4.24043	−0.196014
$469$	5.47721	0.252914
$470$	−15.4706	−0.713605
$471$	−24.3589	−1.12240
$472$	9.67513	0.445334
$473$	15.4483	0.710314
$474$	8.65394	0.397489
$475$	−12.2197	−0.560677
$476$	7.12854	0.326736
$477$	−5.94883	−0.272378
$478$	−4.06901	−0.186112
$479$	10.2803	0.469720	0.234860	−	0.972029i	$-0.424537\pi$
$479$	10.2803	0.469720	0.234860	+	0.972029i	$0.424537\pi$
$480$	−3.83417	−0.175005
$481$	24.0648	1.09726
$482$	20.7908	0.946995
$483$	−10.7837	−0.490677
$484$	−3.08549	−0.140250
$485$	−39.7578	−1.80531
$486$	−10.1182	−0.458970
$487$	9.98175	0.452316	0.226158	−	0.974091i	$-0.427383\pi$
$487$	9.98175	0.452316	0.226158	+	0.974091i	$0.427383\pi$
$488$	14.0428	0.635688
$489$	19.9791	0.903488
$490$	2.72818	0.123247
$491$	−34.0271	−1.53562	−0.767811	−	0.640677i	$-0.778654\pi$
$491$	−34.0271	−1.53562	−0.767811	+	0.640677i	$0.778654\pi$
$492$	−8.59753	−0.387607
$493$	−29.5397	−1.33040
$494$	−20.6959	−0.931152
$495$	−7.86596	−0.353549
$496$	7.50865	0.337148
$497$	−14.6492	−0.657105
$498$	15.3108	0.686095
$499$	−10.9485	−0.490124	−0.245062	−	0.969507i	$-0.578808\pi$
$499$	−10.9485	−0.490124	−0.245062	+	0.969507i	$0.578808\pi$
$500$	−6.97603	−0.311977
$501$	−15.4522	−0.690353
$502$	−11.2183	−0.500697
$503$	42.8272	1.90957	0.954786	−	0.297294i	$-0.0960843\pi$
$503$	42.8272	1.90957	0.954786	+	0.297294i	$0.0960843\pi$
$504$	1.02486	0.0456511
$505$	−14.9495	−0.665245
$506$	−21.5865	−0.959638
$507$	−5.78929	−0.257111
$508$	−5.01080	−0.222318
$509$	−17.2862	−0.766199	−0.383099	−	0.923707i	$-0.625143\pi$
$509$	−17.2862	−0.766199	−0.383099	+	0.923707i	$0.625143\pi$
$510$	27.3321	1.21028
$511$	−14.1064	−0.624030
$512$	1.00000	0.0441942
$513$	−28.2937	−1.24920
$514$	6.45425	0.284685
$515$	−4.21619	−0.185787
$516$	−7.71734	−0.339737
$517$	−15.9531	−0.701617
$518$	−5.81619	−0.255549
$519$	20.5537	0.902206
$520$	11.2880	0.495011
$521$	32.2585	1.41327	0.706636	−	0.707577i	$-0.250212\pi$
$521$	32.2585	1.41327	0.706636	+	0.707577i	$0.250212\pi$
$522$	−4.24690	−0.185882
$523$	−20.8584	−0.912072	−0.456036	−	0.889961i	$-0.650731\pi$
$523$	−20.8584	−0.912072	−0.456036	+	0.889961i	$0.650731\pi$
$524$	3.65865	0.159829
$525$	3.43335	0.149844
$526$	−5.79528	−0.252686
$527$	−53.5257	−2.33162
$528$	−3.95376	−0.172065
$529$	35.8764	1.55984
$530$	15.8357	0.687860
$531$	−9.91569	−0.430304
$532$	5.00196	0.216863
$533$	25.3115	1.09636
$534$	−12.3108	−0.532739
$535$	41.5845	1.79786
$536$	−5.47721	−0.236579
$537$	19.6594	0.848367
$538$	−19.7908	−0.853243
$539$	2.81327	0.121176
$540$	15.4320	0.664089
$541$	−9.12905	−0.392489	−0.196244	−	0.980555i	$-0.562875\pi$
$541$	−9.12905	−0.392489	−0.196244	+	0.980555i	$0.562875\pi$
$542$	10.9108	0.468660
$543$	−18.0307	−0.773772
$544$	−7.12854	−0.305634
$545$	−46.7441	−2.00230
$546$	5.81489	0.248855
$547$	6.79039	0.290336	0.145168	−	0.989407i	$-0.453628\pi$
$547$	6.79039	0.290336	0.145168	+	0.989407i	$0.453628\pi$
$548$	8.27616	0.353540
$549$	−14.3920	−0.614235
$550$	6.87276	0.293055
$551$	−20.7274	−0.883019
$552$	10.7837	0.458986
$553$	6.15766	0.261850
$554$	22.2133	0.943752
$555$	−22.3003	−0.946595
$556$	3.28911	0.139489
$557$	−19.4639	−0.824711	−0.412356	−	0.911023i	$-0.635294\pi$
$557$	−19.4639	−0.824711	−0.412356	+	0.911023i	$0.635294\pi$
$558$	−7.69535	−0.325770
$559$	22.7202	0.960963
$560$	−2.72818	−0.115287
$561$	28.1846	1.18995
$562$	18.5512	0.782534
$563$	11.8112	0.497784	0.248892	−	0.968531i	$-0.419934\pi$
$563$	11.8112	0.497784	0.248892	+	0.968531i	$0.419934\pi$
$564$	7.96951	0.335577
$565$	35.6961	1.50175
$566$	−12.4292	−0.522437
$567$	4.87506	0.204733
$568$	14.6492	0.614665
$569$	−44.1946	−1.85273	−0.926367	−	0.376622i	$-0.877086\pi$
$569$	−44.1946	−1.85273	−0.926367	+	0.376622i	$0.877086\pi$
$570$	19.1784	0.803295
$571$	−36.2058	−1.51517	−0.757583	−	0.652739i	$-0.773620\pi$
$571$	−36.2058	−1.51517	−0.757583	+	0.652739i	$0.773620\pi$
$572$	11.6401	0.486695
$573$	−11.7880	−0.492449
$574$	−6.11752	−0.255340
$575$	−18.7452	−0.781729
$576$	−1.02486	−0.0427027
$577$	22.2733	0.927248	0.463624	−	0.886032i	$-0.346549\pi$
$577$	22.2733	0.927248	0.463624	+	0.886032i	$0.346549\pi$
$578$	33.8161	1.40657
$579$	1.64502	0.0683646
$580$	11.3052	0.469423
$581$	10.8943	0.451973
$582$	20.4808	0.848958
$583$	16.3296	0.676305
$584$	14.1064	0.583727
$585$	−11.5687	−0.478305
$586$	10.3506	0.427577
$587$	−7.68574	−0.317224	−0.158612	−	0.987341i	$-0.550702\pi$
$587$	−7.68574	−0.317224	−0.158612	+	0.987341i	$0.550702\pi$
$588$	−1.40540	−0.0579575
$589$	−37.5580	−1.54755
$590$	26.3955	1.08669
$591$	−13.3449	−0.548938
$592$	5.81619	0.239044
$593$	8.79723	0.361259	0.180629	−	0.983551i	$-0.442187\pi$
$593$	8.79723	0.361259	0.180629	+	0.983551i	$0.442187\pi$
$594$	15.9133	0.652933
$595$	19.4480	0.797289
$596$	14.4507	0.591923
$597$	−35.4476	−1.45077
$598$	−31.7478	−1.29827
$599$	−29.4892	−1.20490	−0.602448	−	0.798158i	$-0.705808\pi$
$599$	−29.4892	−1.20490	−0.602448	+	0.798158i	$0.705808\pi$
$600$	−3.43335	−0.140166
$601$	2.68854	0.109668	0.0548340	−	0.998495i	$-0.482537\pi$
$601$	2.68854	0.109668	0.0548340	+	0.998495i	$0.482537\pi$
$602$	−5.49122	−0.223805
$603$	5.61340	0.228595
$604$	−12.4700	−0.507395
$605$	−8.41779	−0.342232
$606$	7.70109	0.312835
$607$	1.00088	0.0406247	0.0203123	−	0.999794i	$-0.493534\pi$
$607$	1.00088	0.0406247	0.0203123	+	0.999794i	$0.493534\pi$
$608$	−5.00196	−0.202856
$609$	5.82376	0.235991
$610$	38.3114	1.55118
$611$	−23.4626	−0.949197
$612$	7.30579	0.295319
$613$	19.4496	0.785561	0.392781	−	0.919632i	$-0.371513\pi$
$613$	19.4496	0.785561	0.392781	+	0.919632i	$0.371513\pi$
$614$	−3.17768	−0.128241
$615$	−23.4556	−0.945822
$616$	−2.81327	−0.113350
$617$	39.7748	1.60127	0.800637	−	0.599149i	$-0.204494\pi$
$617$	39.7748	1.60127	0.800637	+	0.599149i	$0.204494\pi$
$618$	2.17193	0.0873677
$619$	−4.06568	−0.163414	−0.0817068	−	0.996656i	$-0.526037\pi$
$619$	−4.06568	−0.163414	−0.0817068	+	0.996656i	$0.526037\pi$
$620$	20.4850	0.822696
$621$	−43.4031	−1.74170
$622$	25.1234	1.00735
$623$	−8.75964	−0.350948
$624$	−5.81489	−0.232782
$625$	−31.2467	−1.24987
$626$	−26.3471	−1.05304
$627$	19.7766	0.789800
$628$	17.3324	0.691640
$629$	−41.4610	−1.65316
$630$	2.79602	0.111396
$631$	18.0688	0.719308	0.359654	−	0.933086i	$-0.382895\pi$
$631$	18.0688	0.719308	0.359654	+	0.933086i	$0.382895\pi$
$632$	−6.15766	−0.244938
$633$	−33.4245	−1.32851
$634$	−13.7972	−0.547956
$635$	−13.6704	−0.542492
$636$	−8.15761	−0.323470
$637$	4.13755	0.163936
$638$	11.6578	0.461537
$639$	−15.0134	−0.593922
$640$	2.72818	0.107841
$641$	−4.29058	−0.169468	−0.0847338	−	0.996404i	$-0.527004\pi$
$641$	−4.29058	−0.169468	−0.0847338	+	0.996404i	$0.527004\pi$
$642$	−21.4218	−0.845453
$643$	24.3675	0.960962	0.480481	−	0.877005i	$-0.340462\pi$
$643$	24.3675	0.960962	0.480481	+	0.877005i	$0.340462\pi$
$644$	7.67310	0.302362
$645$	−21.0543	−0.829012
$646$	35.6567	1.40290
$647$	26.4551	1.04006	0.520029	−	0.854148i	$-0.325921\pi$
$647$	26.4551	1.04006	0.520029	+	0.854148i	$0.325921\pi$
$648$	−4.87506	−0.191510
$649$	27.2188	1.06843
$650$	10.1079	0.396466
$651$	10.5526	0.413590
$652$	−14.2160	−0.556743
$653$	41.7600	1.63420	0.817098	−	0.576499i	$-0.195582\pi$
$653$	41.7600	1.63420	0.817098	+	0.576499i	$0.195582\pi$
$654$	24.0797	0.941592
$655$	9.98146	0.390008
$656$	6.11752	0.238849
$657$	−14.4572	−0.564027
$658$	5.67066	0.221065
$659$	−21.2566	−0.828040	−0.414020	−	0.910268i	$-0.635876\pi$
$659$	−21.2566	−0.828040	−0.414020	+	0.910268i	$0.635876\pi$
$660$	−10.7866	−0.419867
$661$	−2.93508	−0.114161	−0.0570806	−	0.998370i	$-0.518179\pi$
$661$	−2.93508	−0.114161	−0.0570806	+	0.998370i	$0.518179\pi$
$662$	−22.7890	−0.885718
$663$	41.4517	1.60985
$664$	−10.8943	−0.422782
$665$	13.6463	0.529180
$666$	−5.96081	−0.230977
$667$	−31.7962	−1.23116
$668$	10.9949	0.425406
$669$	9.76049	0.377362
$670$	−14.9428	−0.577292
$671$	39.5063	1.52512
$672$	1.40540	0.0542143
$673$	−46.8778	−1.80700	−0.903502	−	0.428583i	$-0.859013\pi$
$673$	−46.8778	−1.80700	−0.903502	+	0.428583i	$0.859013\pi$
$674$	−22.8791	−0.881272
$675$	13.8188	0.531884
$676$	4.11933	0.158436
$677$	38.1862	1.46761	0.733807	−	0.679358i	$-0.237741\pi$
$677$	38.1862	1.46761	0.733807	+	0.679358i	$0.237741\pi$
$678$	−18.3885	−0.706205
$679$	14.5730	0.559261
$680$	−19.4480	−0.745795
$681$	−25.3967	−0.973204
$682$	21.1239	0.808875
$683$	30.6658	1.17339	0.586697	−	0.809806i	$-0.300428\pi$
$683$	30.6658	1.17339	0.586697	+	0.809806i	$0.300428\pi$
$684$	5.12634	0.196010
$685$	22.5789	0.862694
$686$	−1.00000	−0.0381802
$687$	3.97622	0.151702
$688$	5.49122	0.209351
$689$	24.0164	0.914952
$690$	29.4200	1.12000
$691$	−46.4408	−1.76669	−0.883345	−	0.468723i	$-0.844714\pi$
$691$	−46.4408	−1.76669	−0.883345	+	0.468723i	$0.844714\pi$
$692$	−14.6248	−0.555953
$693$	2.88322	0.109525
$694$	−20.3831	−0.773732
$695$	8.97328	0.340376
$696$	−5.82376	−0.220749
$697$	−43.6090	−1.65181
$698$	13.2429	0.501252
$699$	23.2802	0.880540
$700$	−2.44298	−0.0923358
$701$	−15.0099	−0.566918	−0.283459	−	0.958984i	$-0.591482\pi$
$701$	−15.0099	−0.566918	−0.283459	+	0.958984i	$0.591482\pi$
$702$	23.4042	0.883333
$703$	−29.0924	−1.09724
$704$	2.81327	0.106029
$705$	21.7423	0.818862
$706$	−4.81850	−0.181347
$707$	5.47966	0.206084
$708$	−13.5974	−0.511021
$709$	44.2924	1.66343	0.831717	−	0.555199i	$-0.187358\pi$
$709$	44.2924	1.66343	0.831717	+	0.555199i	$0.187358\pi$
$710$	39.9656	1.49988
$711$	6.31076	0.236672
$712$	8.75964	0.328281
$713$	−57.6146	−2.15768
$714$	−10.0184	−0.374930
$715$	31.7562	1.18761
$716$	−13.9885	−0.522777
$717$	5.71856	0.213564
$718$	−31.5828	−1.17866
$719$	30.7814	1.14795	0.573976	−	0.818872i	$-0.305400\pi$
$719$	30.7814	1.14795	0.573976	+	0.818872i	$0.305400\pi$
$720$	−2.79602	−0.104201
$721$	1.54542	0.0575544
$722$	6.01965	0.224028
$723$	−29.2193	−1.08668
$724$	12.8296	0.476810
$725$	10.1234	0.375972
$726$	4.33634	0.160937
$727$	17.0141	0.631018	0.315509	−	0.948923i	$-0.397825\pi$
$727$	17.0141	0.631018	0.315509	+	0.948923i	$0.397825\pi$
$728$	−4.13755	−0.153348
$729$	28.8452	1.06834
$730$	38.4848	1.42439
$731$	−39.1444	−1.44781
$732$	−19.7357	−0.729453
$733$	−48.5920	−1.79479	−0.897394	−	0.441231i	$-0.854542\pi$
$733$	−48.5920	−1.79479	−0.897394	+	0.441231i	$0.854542\pi$
$734$	1.73876	0.0641788
$735$	−3.83417	−0.141426
$736$	−7.67310	−0.282834
$737$	−15.4089	−0.567593
$738$	−6.26963	−0.230788
$739$	−19.9223	−0.732854	−0.366427	−	0.930447i	$-0.619419\pi$
$739$	−19.9223	−0.732854	−0.366427	+	0.930447i	$0.619419\pi$
$740$	15.8676	0.583306
$741$	29.0859	1.06850
$742$	−5.80450	−0.213090
$743$	8.43942	0.309612	0.154806	−	0.987945i	$-0.450525\pi$
$743$	8.43942	0.309612	0.154806	+	0.987945i	$0.450525\pi$
$744$	−10.5526	−0.386878
$745$	39.4241	1.44439
$746$	−20.1179	−0.736568
$747$	11.1652	0.408514
$748$	−20.0545	−0.733267
$749$	−15.2426	−0.556952
$750$	9.80407	0.357994
$751$	5.81726	0.212275	0.106137	−	0.994351i	$-0.466152\pi$
$751$	5.81726	0.212275	0.106137	+	0.994351i	$0.466152\pi$
$752$	−5.67066	−0.206788
$753$	15.7661	0.574550
$754$	17.1454	0.624400
$755$	−34.0203	−1.23813
$756$	−5.65653	−0.205726
$757$	−27.7297	−1.00785	−0.503927	−	0.863746i	$-0.668112\pi$
$757$	−27.7297	−1.00785	−0.503927	+	0.863746i	$0.668112\pi$
$758$	−3.63675	−0.132093
$759$	30.3376	1.10118
$760$	−13.6463	−0.495002
$761$	30.1400	1.09258	0.546288	−	0.837597i	$-0.316040\pi$
$761$	30.1400	1.09258	0.546288	+	0.837597i	$0.316040\pi$
$762$	7.04215	0.255110
$763$	17.1338	0.620285
$764$	8.38764	0.303454
$765$	19.9315	0.720626
$766$	−20.2388	−0.731256
$767$	40.0313	1.44545
$768$	−1.40540	−0.0507128
$769$	12.8887	0.464780	0.232390	−	0.972623i	$-0.425345\pi$
$769$	12.8887	0.464780	0.232390	+	0.972623i	$0.425345\pi$
$770$	−7.67512	−0.276592
$771$	−9.07078	−0.326676
$772$	−1.17050	−0.0421273
$773$	19.9443	0.717347	0.358674	−	0.933463i	$-0.383229\pi$
$773$	19.9443	0.717347	0.358674	+	0.933463i	$0.383229\pi$
$774$	−5.62776	−0.202286
$775$	18.3434	0.658916
$776$	−14.5730	−0.523140
$777$	8.17405	0.293242
$778$	−0.996074	−0.0357110
$779$	−30.5996	−1.09634
$780$	−15.8641	−0.568026
$781$	41.2121	1.47469
$782$	54.6980	1.95600
$783$	23.4398	0.837672
$784$	1.00000	0.0357143
$785$	47.2860	1.68771
$786$	−5.14185	−0.183404
$787$	−25.0635	−0.893416	−0.446708	−	0.894680i	$-0.647404\pi$
$787$	−25.0635	−0.893416	−0.446708	+	0.894680i	$0.647404\pi$
$788$	9.49551	0.338264
$789$	8.14466	0.289958
$790$	−16.7992	−0.597689
$791$	−13.0842	−0.465221
$792$	−2.88322	−0.102451
$793$	58.1029	2.06329
$794$	36.2799	1.28753
$795$	−22.2555	−0.789320
$796$	25.2225	0.893987
$797$	−42.2784	−1.49758	−0.748788	−	0.662809i	$-0.769364\pi$
$797$	−42.2784	−1.49758	−0.748788	+	0.662809i	$0.769364\pi$
$798$	−7.02974	−0.248850
$799$	40.4235	1.43008
$800$	2.44298	0.0863723
$801$	−8.97745	−0.317202
$802$	15.9837	0.564403
$803$	39.6852	1.40046
$804$	7.69764	0.271475
$805$	20.9336	0.737813
$806$	31.0674	1.09430
$807$	27.8139	0.979097
$808$	−5.47966	−0.192774
$809$	−23.8550	−0.838696	−0.419348	−	0.907826i	$-0.637741\pi$
$809$	−23.8550	−0.838696	−0.419348	+	0.907826i	$0.637741\pi$
$810$	−13.3000	−0.467316
$811$	0.690318	0.0242403	0.0121202	−	0.999927i	$-0.496142\pi$
$811$	0.690318	0.0242403	0.0121202	+	0.999927i	$0.496142\pi$
$812$	−4.14386	−0.145421
$813$	−15.3340	−0.537787
$814$	16.3625	0.573507
$815$	−38.7839	−1.35854
$816$	10.0184	0.350715
$817$	−27.4669	−0.960945
$818$	3.98098	0.139192
$819$	4.24043	0.148173
$820$	16.6897	0.582830
$821$	−7.70669	−0.268965	−0.134483	−	0.990916i	$-0.542937\pi$
$821$	−7.70669	−0.268965	−0.134483	+	0.990916i	$0.542937\pi$
$822$	−11.6313	−0.405687
$823$	−42.6123	−1.48537	−0.742685	−	0.669640i	$-0.766448\pi$
$823$	−42.6123	−1.48537	−0.742685	+	0.669640i	$0.766448\pi$
$824$	−1.54542	−0.0538373
$825$	−9.65894	−0.336281
$826$	−9.67513	−0.336641
$827$	−23.5051	−0.817351	−0.408675	−	0.912680i	$-0.634009\pi$
$827$	−23.5051	−0.817351	−0.408675	+	0.912680i	$0.634009\pi$
$828$	7.86389	0.273289
$829$	−12.8556	−0.446494	−0.223247	−	0.974762i	$-0.571666\pi$
$829$	−12.8556	−0.446494	−0.223247	+	0.974762i	$0.571666\pi$
$830$	−29.7217	−1.03165
$831$	−31.2185	−1.08296
$832$	4.13755	0.143444
$833$	−7.12854	−0.246989
$834$	−4.62249	−0.160064
$835$	29.9961	1.03806
$836$	−14.0719	−0.486687
$837$	42.4729	1.46808
$838$	−11.3926	−0.393550
$839$	−25.9651	−0.896415	−0.448207	−	0.893930i	$-0.647937\pi$
$839$	−25.9651	−0.896415	−0.448207	+	0.893930i	$0.647937\pi$
$840$	3.83417	0.132292
$841$	−11.8284	−0.407877
$842$	13.3816	0.461161
$843$	−26.0717	−0.897958
$844$	23.7830	0.818645
$845$	11.2383	0.386609
$846$	5.81166	0.199809
$847$	3.08549	0.106019
$848$	5.80450	0.199327
$849$	17.4679	0.599497
$850$	−17.4149	−0.597325
$851$	−44.6282	−1.52984
$852$	−20.5879	−0.705329
$853$	34.7704	1.19052	0.595258	−	0.803535i	$-0.297050\pi$
$853$	34.7704	1.19052	0.595258	+	0.803535i	$0.297050\pi$
$854$	−14.0428	−0.480535
$855$	13.9856	0.478297
$856$	15.2426	0.520981
$857$	8.55804	0.292337	0.146169	−	0.989260i	$-0.453306\pi$
$857$	8.55804	0.292337	0.146169	+	0.989260i	$0.453306\pi$
$858$	−16.3589	−0.558483
$859$	7.99614	0.272825	0.136412	−	0.990652i	$-0.456443\pi$
$859$	7.99614	0.272825	0.136412	+	0.990652i	$0.456443\pi$
$860$	14.9811	0.510850
$861$	8.59753	0.293003
$862$	−1.00000	−0.0340601
$863$	−36.8002	−1.25269	−0.626347	−	0.779545i	$-0.715451\pi$
$863$	−36.8002	−1.25269	−0.626347	+	0.779545i	$0.715451\pi$
$864$	5.65653	0.192439
$865$	−39.8992	−1.35661
$866$	−24.6778	−0.838587
$867$	−47.5250	−1.61403
$868$	−7.50865	−0.254860
$869$	−17.3232	−0.587648
$870$	−15.8883	−0.538663
$871$	−22.6622	−0.767880
$872$	−17.1338	−0.580223
$873$	14.9354	0.505485
$874$	38.3806	1.29824
$875$	6.97603	0.235833
$876$	−19.8251	−0.669827
$877$	12.3078	0.415606	0.207803	−	0.978171i	$-0.433369\pi$
$877$	12.3078	0.415606	0.207803	+	0.978171i	$0.433369\pi$
$878$	15.4552	0.521589
$879$	−14.5466	−0.490645
$880$	7.67512	0.258728
$881$	−26.4300	−0.890450	−0.445225	−	0.895419i	$-0.646876\pi$
$881$	−26.4300	−0.890450	−0.445225	+	0.895419i	$0.646876\pi$
$882$	−1.02486	−0.0345090
$883$	27.8260	0.936419	0.468210	−	0.883617i	$-0.344899\pi$
$883$	27.8260	0.936419	0.468210	+	0.883617i	$0.344899\pi$
$884$	−29.4947	−0.992015
$885$	−37.0961	−1.24697
$886$	5.89420	0.198019
$887$	−56.1846	−1.88649	−0.943247	−	0.332092i	$-0.892246\pi$
$887$	−56.1846	−1.88649	−0.943247	+	0.332092i	$0.892246\pi$
$888$	−8.17405	−0.274303
$889$	5.01080	0.168057
$890$	23.8979	0.801059
$891$	−13.7149	−0.459465
$892$	−6.94501	−0.232536
$893$	28.3644	0.949179
$894$	−20.3089	−0.679232
$895$	−38.1633	−1.27566
$896$	−1.00000	−0.0334077
$897$	44.6183	1.48976
$898$	11.5822	0.386502
$899$	31.1148	1.03774
$900$	−2.50372	−0.0834573
$901$	−41.3776	−1.37849
$902$	17.2102	0.573038
$903$	7.71734	0.256817
$904$	13.0842	0.435174
$905$	35.0016	1.16349
$906$	17.5252	0.582236
$907$	−52.7320	−1.75094	−0.875469	−	0.483273i	$-0.839448\pi$
$907$	−52.7320	−1.75094	−0.875469	+	0.483273i	$0.839448\pi$
$908$	18.0709	0.599703
$909$	5.61591	0.186268
$910$	−11.2880	−0.374193
$911$	0.715472	0.0237046	0.0118523	−	0.999930i	$-0.496227\pi$
$911$	0.715472	0.0237046	0.0118523	+	0.999930i	$0.496227\pi$
$912$	7.02974	0.232778
$913$	−30.6487	−1.01432
$914$	10.0648	0.332914
$915$	−53.8426	−1.77998
$916$	−2.82925	−0.0934811
$917$	−3.65865	−0.120819
$918$	−40.3228	−1.33085
$919$	−4.78571	−0.157866	−0.0789330	−	0.996880i	$-0.525151\pi$
$919$	−4.78571	−0.157866	−0.0789330	+	0.996880i	$0.525151\pi$
$920$	−20.9336	−0.690160
$921$	4.46590	0.147156
$922$	8.76695	0.288724
$923$	60.6117	1.99506
$924$	3.95376	0.130069
$925$	14.2088	0.467183
$926$	−21.2979	−0.699892
$927$	1.58385	0.0520203
$928$	4.14386	0.136029
$929$	2.82023	0.0925288	0.0462644	−	0.998929i	$-0.485268\pi$
$929$	2.82023	0.0925288	0.0462644	+	0.998929i	$0.485268\pi$
$930$	−28.7895	−0.944043
$931$	−5.00196	−0.163933
$932$	−16.5649	−0.542602
$933$	−35.3082	−1.15594
$934$	−24.2695	−0.794124
$935$	−54.7124	−1.78929
$936$	−4.24043	−0.138603
$937$	1.86005	0.0607652	0.0303826	−	0.999538i	$-0.490327\pi$
$937$	1.86005	0.0607652	0.0303826	+	0.999538i	$0.490327\pi$
$938$	5.47721	0.178837
$939$	37.0281	1.20837
$940$	−15.4706	−0.504595
$941$	46.2620	1.50810	0.754049	−	0.656818i	$-0.228098\pi$
$941$	46.2620	1.50810	0.754049	+	0.656818i	$0.228098\pi$
$942$	−24.3589	−0.793657
$943$	−46.9403	−1.52859
$944$	9.67513	0.314899
$945$	−15.4320	−0.502004
$946$	15.4483	0.502268
$947$	−26.7099	−0.867955	−0.433978	−	0.900924i	$-0.642890\pi$
$947$	−26.7099	−0.867955	−0.433978	+	0.900924i	$0.642890\pi$
$948$	8.65394	0.281067
$949$	58.3660	1.89464
$950$	−12.2197	−0.396459
$951$	19.3905	0.628780
$952$	7.12854	0.231037
$953$	12.0308	0.389715	0.194858	−	0.980832i	$-0.437576\pi$
$953$	12.0308	0.389715	0.194858	+	0.980832i	$0.437576\pi$
$954$	−5.94883	−0.192600
$955$	22.8830	0.740477
$956$	−4.06901	−0.131601
$957$	−16.3838	−0.529614
$958$	10.2803	0.332142
$959$	−8.27616	−0.267251
$960$	−3.83417	−0.123747
$961$	25.3798	0.818703
$962$	24.0648	0.775880
$963$	−15.6216	−0.503398
$964$	20.7908	0.669626
$965$	−3.19334	−0.102797
$966$	−10.7837	−0.346961
$967$	−23.6378	−0.760142	−0.380071	−	0.924957i	$-0.624100\pi$
$967$	−23.6378	−0.760142	−0.380071	+	0.924957i	$0.624100\pi$
$968$	−3.08549	−0.0991715
$969$	−50.1118	−1.60982
$970$	−39.7578	−1.27655
$971$	36.7807	1.18035	0.590174	−	0.807276i	$-0.299059\pi$
$971$	36.7807	1.18035	0.590174	+	0.807276i	$0.299059\pi$
$972$	−10.1182	−0.324541
$973$	−3.28911	−0.105444
$974$	9.98175	0.319836
$975$	−14.2057	−0.454945
$976$	14.0428	0.449500
$977$	5.90479	0.188911	0.0944556	−	0.995529i	$-0.469889\pi$
$977$	5.90479	0.188911	0.0944556	+	0.995529i	$0.469889\pi$
$978$	19.9791	0.638862
$979$	24.6433	0.787602
$980$	2.72818	0.0871486
$981$	17.5598	0.560642
$982$	−34.0271	−1.08585
$983$	30.9459	0.987022	0.493511	−	0.869739i	$-0.335713\pi$
$983$	30.9459	0.987022	0.493511	+	0.869739i	$0.335713\pi$
$984$	−8.59753	−0.274079
$985$	25.9055	0.825418
$986$	−29.5397	−0.940735
$987$	−7.96951	−0.253672
$988$	−20.6959	−0.658424
$989$	−42.1347	−1.33980
$990$	−7.86596	−0.249997
$991$	6.37932	0.202646	0.101323	−	0.994854i	$-0.467692\pi$
$991$	6.37932	0.202646	0.101323	+	0.994854i	$0.467692\pi$
$992$	7.50865	0.238400
$993$	32.0275	1.01636
$994$	−14.6492	−0.464643
$995$	68.8115	2.18147
$996$	15.3108	0.485142
$997$	18.9580	0.600407	0.300203	−	0.953875i	$-0.402945\pi$
$997$	18.9580	0.600407	0.300203	+	0.953875i	$0.402945\pi$
$998$	−10.9485	−0.346570
$999$	32.8994	1.04089

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.10	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.10	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.40540 q^{3} +1.00000 q^{4} +2.72818 q^{5} -1.40540 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.02486 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.40540 q^{3} +1.00000 q^{4} +2.72818 q^{5} -1.40540 q^{6} -1.00000 q^{7} +1.00000 q^{8} -1.02486 q^{9} +2.72818 q^{10} +2.81327 q^{11} -1.40540 q^{12} +4.13755 q^{13} -1.00000 q^{14} -3.83417 q^{15} +1.00000 q^{16} -7.12854 q^{17} -1.02486 q^{18} -5.00196 q^{19} +2.72818 q^{20} +1.40540 q^{21} +2.81327 q^{22} -7.67310 q^{23} -1.40540 q^{24} +2.44298 q^{25} +4.13755 q^{26} +5.65653 q^{27} -1.00000 q^{28} +4.14386 q^{29} -3.83417 q^{30} +7.50865 q^{31} +1.00000 q^{32} -3.95376 q^{33} -7.12854 q^{34} -2.72818 q^{35} -1.02486 q^{36} +5.81619 q^{37} -5.00196 q^{38} -5.81489 q^{39} +2.72818 q^{40} +6.11752 q^{41} +1.40540 q^{42} +5.49122 q^{43} +2.81327 q^{44} -2.79602 q^{45} -7.67310 q^{46} -5.67066 q^{47} -1.40540 q^{48} +1.00000 q^{49} +2.44298 q^{50} +10.0184 q^{51} +4.13755 q^{52} +5.80450 q^{53} +5.65653 q^{54} +7.67512 q^{55} -1.00000 q^{56} +7.02974 q^{57} +4.14386 q^{58} +9.67513 q^{59} -3.83417 q^{60} +14.0428 q^{61} +7.50865 q^{62} +1.02486 q^{63} +1.00000 q^{64} +11.2880 q^{65} -3.95376 q^{66} -5.47721 q^{67} -7.12854 q^{68} +10.7837 q^{69} -2.72818 q^{70} +14.6492 q^{71} -1.02486 q^{72} +14.1064 q^{73} +5.81619 q^{74} -3.43335 q^{75} -5.00196 q^{76} -2.81327 q^{77} -5.81489 q^{78} -6.15766 q^{79} +2.72818 q^{80} -4.87506 q^{81} +6.11752 q^{82} -10.8943 q^{83} +1.40540 q^{84} -19.4480 q^{85} +5.49122 q^{86} -5.82376 q^{87} +2.81327 q^{88} +8.75964 q^{89} -2.79602 q^{90} -4.13755 q^{91} -7.67310 q^{92} -10.5526 q^{93} -5.67066 q^{94} -13.6463 q^{95} -1.40540 q^{96} -14.5730 q^{97} +1.00000 q^{98} -2.88322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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