LMFDB - Embedded newform 6029.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6029,2,Mod(1,6029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6029 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6029.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:	$48.1418073786$
Analytic rank:	$0$
Dimension:	$268$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66582 q^{2} -1.97296 q^{3} +5.10658 q^{4} +1.39801 q^{5} +5.25954 q^{6} -2.57413 q^{7} -8.28157 q^{8} +0.892553 q^{9} +O(q^{10})$	\(q-2.66582 q^{2} -1.97296 q^{3} +5.10658 q^{4} +1.39801 q^{5} +5.25954 q^{6} -2.57413 q^{7} -8.28157 q^{8} +0.892553 q^{9} -3.72685 q^{10} +0.893416 q^{11} -10.0751 q^{12} -6.35418 q^{13} +6.86216 q^{14} -2.75822 q^{15} +11.8640 q^{16} +2.33836 q^{17} -2.37938 q^{18} -4.59710 q^{19} +7.13907 q^{20} +5.07864 q^{21} -2.38168 q^{22} -2.01132 q^{23} +16.3392 q^{24} -3.04556 q^{25} +16.9391 q^{26} +4.15790 q^{27} -13.1450 q^{28} -1.57412 q^{29} +7.35290 q^{30} +2.49877 q^{31} -15.0641 q^{32} -1.76267 q^{33} -6.23365 q^{34} -3.59867 q^{35} +4.55789 q^{36} -10.0025 q^{37} +12.2550 q^{38} +12.5365 q^{39} -11.5777 q^{40} +5.91415 q^{41} -13.5387 q^{42} -1.66886 q^{43} +4.56230 q^{44} +1.24780 q^{45} +5.36181 q^{46} -9.15484 q^{47} -23.4071 q^{48} -0.373861 q^{49} +8.11890 q^{50} -4.61349 q^{51} -32.4481 q^{52} -4.74313 q^{53} -11.0842 q^{54} +1.24901 q^{55} +21.3178 q^{56} +9.06987 q^{57} +4.19632 q^{58} -3.94384 q^{59} -14.0851 q^{60} -1.96247 q^{61} -6.66125 q^{62} -2.29755 q^{63} +16.4301 q^{64} -8.88323 q^{65} +4.69896 q^{66} +1.25674 q^{67} +11.9410 q^{68} +3.96824 q^{69} +9.59338 q^{70} -10.6822 q^{71} -7.39174 q^{72} +4.28386 q^{73} +26.6647 q^{74} +6.00875 q^{75} -23.4755 q^{76} -2.29977 q^{77} -33.4201 q^{78} -3.70832 q^{79} +16.5860 q^{80} -10.8810 q^{81} -15.7660 q^{82} -15.2669 q^{83} +25.9345 q^{84} +3.26906 q^{85} +4.44886 q^{86} +3.10567 q^{87} -7.39889 q^{88} -10.6159 q^{89} -3.32641 q^{90} +16.3565 q^{91} -10.2710 q^{92} -4.92995 q^{93} +24.4051 q^{94} -6.42681 q^{95} +29.7208 q^{96} -1.50014 q^{97} +0.996645 q^{98} +0.797421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) $ 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * 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 $

$2$	−2.66582	−1.88502	−0.942509	−	0.334182i	$-0.891540\pi$
$2$	−2.66582	−1.88502	−0.942509	+	0.334182i	$0.891540\pi$
$3$	−1.97296	−1.13909	−0.569543	−	0.821961i	$-0.692880\pi$
$3$	−1.97296	−1.13909	−0.569543	+	0.821961i	$0.692880\pi$
$4$	5.10658	2.55329
$5$	1.39801	0.625211	0.312605	−	0.949883i	$-0.398798\pi$
$5$	1.39801	0.625211	0.312605	+	0.949883i	$0.398798\pi$
$6$	5.25954	2.14720
$7$	−2.57413	−0.972929	−0.486465	−	0.873700i	$-0.661714\pi$
$7$	−2.57413	−0.972929	−0.486465	+	0.873700i	$0.661714\pi$
$8$	−8.28157	−2.92798
$9$	0.892553	0.297518
$10$	−3.72685	−1.17853
$11$	0.893416	0.269375	0.134688	−	0.990888i	$-0.456997\pi$
$11$	0.893416	0.269375	0.134688	+	0.990888i	$0.456997\pi$
$12$	−10.0751	−2.90842
$13$	−6.35418	−1.76233	−0.881167	−	0.472805i	$-0.843241\pi$
$13$	−6.35418	−1.76233	−0.881167	+	0.472805i	$0.843241\pi$
$14$	6.86216	1.83399
$15$	−2.75822	−0.712169
$16$	11.8640	2.96600
$17$	2.33836	0.567136	0.283568	−	0.958952i	$-0.408482\pi$
$17$	2.33836	0.567136	0.283568	+	0.958952i	$0.408482\pi$
$18$	−2.37938	−0.560826
$19$	−4.59710	−1.05465	−0.527324	−	0.849665i	$-0.676804\pi$
$19$	−4.59710	−1.05465	−0.527324	+	0.849665i	$0.676804\pi$
$20$	7.13907	1.59634
$21$	5.07864	1.10825
$22$	−2.38168	−0.507777
$23$	−2.01132	−0.419389	−0.209694	−	0.977767i	$-0.567247\pi$
$23$	−2.01132	−0.419389	−0.209694	+	0.977767i	$0.567247\pi$
$24$	16.3392	3.33522
$25$	−3.04556	−0.609112
$26$	16.9391	3.32203
$27$	4.15790	0.800188
$28$	−13.1450	−2.48417
$29$	−1.57412	−0.292307	−0.146153	−	0.989262i	$-0.546689\pi$
$29$	−1.57412	−0.292307	−0.146153	+	0.989262i	$0.546689\pi$
$30$	7.35290	1.34245
$31$	2.49877	0.448792	0.224396	−	0.974498i	$-0.427959\pi$
$31$	2.49877	0.448792	0.224396	+	0.974498i	$0.427959\pi$
$32$	−15.0641	−2.66298
$33$	−1.76267	−0.306841
$34$	−6.23365	−1.06906
$35$	−3.59867	−0.608286
$36$	4.55789	0.759649
$37$	−10.0025	−1.64439	−0.822197	−	0.569202i	$-0.807252\pi$
$37$	−10.0025	−1.64439	−0.822197	+	0.569202i	$0.807252\pi$
$38$	12.2550	1.98803
$39$	12.5365	2.00745
$40$	−11.5777	−1.83060
$41$	5.91415	0.923636	0.461818	−	0.886975i	$-0.347197\pi$
$41$	5.91415	0.923636	0.461818	+	0.886975i	$0.347197\pi$
$42$	−13.5387	−2.08907
$43$	−1.66886	−0.254498	−0.127249	−	0.991871i	$-0.540615\pi$
$43$	−1.66886	−0.254498	−0.127249	+	0.991871i	$0.540615\pi$
$44$	4.56230	0.687793
$45$	1.24780	0.186011
$46$	5.36181	0.790555
$47$	−9.15484	−1.33537	−0.667686	−	0.744443i	$-0.732715\pi$
$47$	−9.15484	−1.33537	−0.667686	+	0.744443i	$0.732715\pi$
$48$	−23.4071	−3.37853
$49$	−0.373861	−0.0534087
$50$	8.11890	1.14819
$51$	−4.61349	−0.646017
$52$	−32.4481	−4.49975
$53$	−4.74313	−0.651519	−0.325760	−	0.945453i	$-0.605620\pi$
$53$	−4.74313	−0.651519	−0.325760	+	0.945453i	$0.605620\pi$
$54$	−11.0842	−1.50837
$55$	1.24901	0.168416
$56$	21.3178	2.84871
$57$	9.06987	1.20133
$58$	4.19632	0.551004
$59$	−3.94384	−0.513444	−0.256722	−	0.966485i	$-0.582643\pi$
$59$	−3.94384	−0.513444	−0.256722	+	0.966485i	$0.582643\pi$
$60$	−14.0851	−1.81837
$61$	−1.96247	−0.251269	−0.125634	−	0.992077i	$-0.540097\pi$
$61$	−1.96247	−0.251269	−0.125634	+	0.992077i	$0.540097\pi$
$62$	−6.66125	−0.845980
$63$	−2.29755	−0.289464
$64$	16.4301	2.05376
$65$	−8.88323	−1.10183
$66$	4.69896	0.578401
$67$	1.25674	0.153535	0.0767674	−	0.997049i	$-0.475540\pi$
$67$	1.25674	0.153535	0.0767674	+	0.997049i	$0.475540\pi$
$68$	11.9410	1.44806
$69$	3.96824	0.477720
$70$	9.59338	1.14663
$71$	−10.6822	−1.26774	−0.633870	−	0.773439i	$-0.718535\pi$
$71$	−10.6822	−1.26774	−0.633870	+	0.773439i	$0.718535\pi$
$72$	−7.39174	−0.871125
$73$	4.28386	0.501388	0.250694	−	0.968066i	$-0.419341\pi$
$73$	4.28386	0.501388	0.250694	+	0.968066i	$0.419341\pi$
$74$	26.6647	3.09971
$75$	6.00875	0.693831
$76$	−23.4755	−2.69282
$77$	−2.29977	−0.262083
$78$	−33.4201	−3.78408
$79$	−3.70832	−0.417218	−0.208609	−	0.977999i	$-0.566894\pi$
$79$	−3.70832	−0.417218	−0.208609	+	0.977999i	$0.566894\pi$
$80$	16.5860	1.85437
$81$	−10.8810	−1.20900
$82$	−15.7660	−1.74107
$83$	−15.2669	−1.67576	−0.837881	−	0.545853i	$-0.816206\pi$
$83$	−15.2669	−1.67576	−0.837881	+	0.545853i	$0.816206\pi$
$84$	25.9345	2.82968
$85$	3.26906	0.354580
$86$	4.44886	0.479733
$87$	3.10567	0.332963
$88$	−7.39889	−0.788724
$89$	−10.6159	−1.12528	−0.562642	−	0.826700i	$-0.690215\pi$
$89$	−10.6159	−1.12528	−0.562642	+	0.826700i	$0.690215\pi$
$90$	−3.32641	−0.350634
$91$	16.3565	1.71463
$92$	−10.2710	−1.07082
$93$	−4.92995	−0.511212
$94$	24.4051	2.51720
$95$	−6.42681	−0.659377
$96$	29.7208	3.03336
$97$	−1.50014	−0.152316	−0.0761581	−	0.997096i	$-0.524265\pi$
$97$	−1.50014	−0.152316	−0.0761581	+	0.997096i	$0.524265\pi$
$98$	0.996645	0.100676
$99$	0.797421	0.0801438
$100$	−15.5524	−1.55524
$101$	−7.51123	−0.747395	−0.373698	−	0.927551i	$-0.621910\pi$
$101$	−7.51123	−0.747395	−0.373698	+	0.927551i	$0.621910\pi$
$102$	12.2987	1.21775
$103$	−1.47293	−0.145132	−0.0725662	−	0.997364i	$-0.523119\pi$
$103$	−1.47293	−0.145132	−0.0725662	+	0.997364i	$0.523119\pi$
$104$	52.6226	5.16007
$105$	7.10001	0.692890
$106$	12.6443	1.22812
$107$	18.5237	1.79075	0.895377	−	0.445309i	$-0.146906\pi$
$107$	18.5237	1.79075	0.895377	+	0.445309i	$0.146906\pi$
$108$	21.2326	2.04311
$109$	8.29777	0.794782	0.397391	−	0.917649i	$-0.369916\pi$
$109$	8.29777	0.794782	0.397391	+	0.917649i	$0.369916\pi$
$110$	−3.32963	−0.317467
$111$	19.7344	1.87311
$112$	−30.5394	−2.88571
$113$	14.7623	1.38872	0.694360	−	0.719628i	$-0.255687\pi$
$113$	14.7623	1.38872	0.694360	+	0.719628i	$0.255687\pi$
$114$	−24.1786	−2.26454
$115$	−2.81185	−0.262206
$116$	−8.03837	−0.746344
$117$	−5.67145	−0.524325
$118$	10.5136	0.967851
$119$	−6.01925	−0.551783
$120$	22.8424	2.08521
$121$	−10.2018	−0.927437
$122$	5.23159	0.473646
$123$	−11.6684	−1.05210
$124$	12.7601	1.14590
$125$	−11.2478	−1.00603
$126$	6.12484	0.545644
$127$	15.3921	1.36583	0.682916	−	0.730497i	$-0.260712\pi$
$127$	15.3921	1.36583	0.682916	+	0.730497i	$0.260712\pi$
$128$	−13.6715	−1.20840
$129$	3.29258	0.289895
$130$	23.6811	2.07697
$131$	4.52303	0.395179	0.197589	−	0.980285i	$-0.436689\pi$
$131$	4.52303	0.395179	0.197589	+	0.980285i	$0.436689\pi$
$132$	−9.00121	−0.783455
$133$	11.8335	1.02610
$134$	−3.35023	−0.289416
$135$	5.81280	0.500286
$136$	−19.3653	−1.66056
$137$	−20.8196	−1.77874	−0.889371	−	0.457186i	$-0.848857\pi$
$137$	−20.8196	−1.77874	−0.889371	+	0.457186i	$0.848857\pi$
$138$	−10.5786	−0.900511
$139$	20.0007	1.69644	0.848219	−	0.529645i	$-0.177675\pi$
$139$	20.0007	1.69644	0.848219	+	0.529645i	$0.177675\pi$
$140$	−18.3769	−1.55313
$141$	18.0621	1.52110
$142$	28.4767	2.38971
$143$	−5.67693	−0.474729
$144$	10.5892	0.882437
$145$	−2.20064	−0.182753
$146$	−11.4200	−0.945124
$147$	0.737611	0.0608371
$148$	−51.0784	−4.19862
$149$	0.613362	0.0502486	0.0251243	−	0.999684i	$-0.492002\pi$
$149$	0.613362	0.0502486	0.0251243	+	0.999684i	$0.492002\pi$
$150$	−16.0182	−1.30788
$151$	−9.79810	−0.797358	−0.398679	−	0.917091i	$-0.630531\pi$
$151$	−9.79810	−0.797358	−0.398679	+	0.917091i	$0.630531\pi$
$152$	38.0712	3.08798
$153$	2.08711	0.168733
$154$	6.13076	0.494031
$155$	3.49331	0.280589
$156$	64.0187	5.12560
$157$	−9.02067	−0.719928	−0.359964	−	0.932966i	$-0.617211\pi$
$157$	−9.02067	−0.719928	−0.359964	+	0.932966i	$0.617211\pi$
$158$	9.88569	0.786463
$159$	9.35799	0.742137
$160$	−21.0598	−1.66492
$161$	5.17739	0.408036
$162$	29.0068	2.27899
$163$	−24.8898	−1.94952	−0.974762	−	0.223248i	$-0.928334\pi$
$163$	−24.8898	−1.94952	−0.974762	+	0.223248i	$0.928334\pi$
$164$	30.2011	2.35831
$165$	−2.46424	−0.191841
$166$	40.6988	3.15884
$167$	−3.62683	−0.280653	−0.140326	−	0.990105i	$-0.544815\pi$
$167$	−3.62683	−0.280653	−0.140326	+	0.990105i	$0.544815\pi$
$168$	−42.0591	−3.24493
$169$	27.3757	2.10582
$170$	−8.71472	−0.668389
$171$	−4.10316	−0.313776
$172$	−8.52214	−0.649807
$173$	−15.5703	−1.18379	−0.591893	−	0.806017i	$-0.701619\pi$
$173$	−15.5703	−1.18379	−0.591893	+	0.806017i	$0.701619\pi$
$174$	−8.27915	−0.627641
$175$	7.83966	0.592623
$176$	10.5995	0.798966
$177$	7.78102	0.584857
$178$	28.3001	2.12118
$179$	26.3462	1.96921	0.984603	−	0.174804i	$-0.0559293\pi$
$179$	26.3462	1.96921	0.984603	+	0.174804i	$0.0559293\pi$
$180$	6.37199	0.474940
$181$	17.0197	1.26506	0.632532	−	0.774534i	$-0.282016\pi$
$181$	17.0197	1.26506	0.632532	+	0.774534i	$0.282016\pi$
$182$	−43.6034	−3.23210
$183$	3.87187	0.286217
$184$	16.6569	1.22796
$185$	−13.9836	−1.02809
$186$	13.1424	0.963644
$187$	2.08913	0.152772
$188$	−46.7499	−3.40959
$189$	−10.7030	−0.778526
$190$	17.1327	1.24294
$191$	0.964672	0.0698012	0.0349006	−	0.999391i	$-0.488889\pi$
$191$	0.964672	0.0698012	0.0349006	+	0.999391i	$0.488889\pi$
$192$	−32.4159	−2.33941
$193$	−23.9239	−1.72208	−0.861041	−	0.508536i	$-0.830187\pi$
$193$	−23.9239	−1.72208	−0.861041	+	0.508536i	$0.830187\pi$
$194$	3.99910	0.287118
$195$	17.5262	1.25508
$196$	−1.90915	−0.136368
$197$	−2.03555	−0.145027	−0.0725134	−	0.997367i	$-0.523102\pi$
$197$	−2.03555	−0.145027	−0.0725134	+	0.997367i	$0.523102\pi$
$198$	−2.12578	−0.151073
$199$	14.8892	1.05546	0.527732	−	0.849411i	$-0.323042\pi$
$199$	14.8892	1.05546	0.527732	+	0.849411i	$0.323042\pi$
$200$	25.2220	1.78347
$201$	−2.47949	−0.174889
$202$	20.0236	1.40885
$203$	4.05199	0.284394
$204$	−23.5591	−1.64947
$205$	8.26806	0.577467
$206$	3.92657	0.273577
$207$	−1.79521	−0.124776
$208$	−75.3860	−5.22708
$209$	−4.10712	−0.284096
$210$	−18.9273	−1.30611
$211$	−20.5745	−1.41641	−0.708204	−	0.706008i	$-0.750494\pi$
$211$	−20.5745	−1.41641	−0.708204	+	0.706008i	$0.750494\pi$
$212$	−24.2212	−1.66352
$213$	21.0755	1.44407
$214$	−49.3808	−3.37560
$215$	−2.33308	−0.159115
$216$	−34.4339	−2.34293
$217$	−6.43215	−0.436643
$218$	−22.1203	−1.49818
$219$	−8.45186	−0.571124
$220$	6.37816	0.430015
$221$	−14.8584	−0.999483
$222$	−52.6083	−3.53084
$223$	−9.03300	−0.604894	−0.302447	−	0.953166i	$-0.597804\pi$
$223$	−9.03300	−0.604894	−0.302447	+	0.953166i	$0.597804\pi$
$224$	38.7769	2.59089
$225$	−2.71832	−0.181222
$226$	−39.3536	−2.61776
$227$	−15.8091	−1.04929	−0.524643	−	0.851322i	$-0.675801\pi$
$227$	−15.8091	−1.04929	−0.524643	+	0.851322i	$0.675801\pi$
$228$	46.3160	3.06735
$229$	−22.3252	−1.47529	−0.737647	−	0.675187i	$-0.764063\pi$
$229$	−22.3252	−1.47529	−0.737647	+	0.675187i	$0.764063\pi$
$230$	7.49588	0.494263
$231$	4.53734	0.298535
$232$	13.0362	0.855868
$233$	−20.7630	−1.36023	−0.680115	−	0.733106i	$-0.738070\pi$
$233$	−20.7630	−1.36023	−0.680115	+	0.733106i	$0.738070\pi$
$234$	15.1190	0.988362
$235$	−12.7986	−0.834888
$236$	−20.1395	−1.31097
$237$	7.31634	0.475248
$238$	16.0462	1.04012
$239$	−11.9365	−0.772109	−0.386055	−	0.922476i	$-0.626162\pi$
$239$	−11.9365	−0.772109	−0.386055	+	0.922476i	$0.626162\pi$
$240$	−32.7235	−2.11229
$241$	22.5001	1.44936	0.724678	−	0.689087i	$-0.241988\pi$
$241$	22.5001	1.44936	0.724678	+	0.689087i	$0.241988\pi$
$242$	27.1962	1.74823
$243$	8.99405	0.576968
$244$	−10.0215	−0.641562
$245$	−0.522663	−0.0333917
$246$	31.1057	1.98323
$247$	29.2108	1.85864
$248$	−20.6937	−1.31405
$249$	30.1210	1.90884
$250$	29.9846	1.89639
$251$	−2.05028	−0.129412	−0.0647062	−	0.997904i	$-0.520611\pi$
$251$	−2.05028	−0.129412	−0.0647062	+	0.997904i	$0.520611\pi$
$252$	−11.7326	−0.739084
$253$	−1.79694	−0.112973
$254$	−41.0326	−2.57462
$255$	−6.44971	−0.403897
$256$	3.58548	0.224092
$257$	−6.16532	−0.384582	−0.192291	−	0.981338i	$-0.561592\pi$
$257$	−6.16532	−0.384582	−0.192291	+	0.981338i	$0.561592\pi$
$258$	−8.77741	−0.546458
$259$	25.7476	1.59988
$260$	−45.3629	−2.81329
$261$	−1.40499	−0.0869665
$262$	−12.0576	−0.744919
$263$	−6.72075	−0.414419	−0.207210	−	0.978297i	$-0.566438\pi$
$263$	−6.72075	−0.414419	−0.207210	+	0.978297i	$0.566438\pi$
$264$	14.5977	0.898425
$265$	−6.63096	−0.407337
$266$	−31.5460	−1.93421
$267$	20.9447	1.28180
$268$	6.41763	0.392019
$269$	−8.42003	−0.513379	−0.256689	−	0.966494i	$-0.582632\pi$
$269$	−8.42003	−0.513379	−0.256689	+	0.966494i	$0.582632\pi$
$270$	−15.4959	−0.943048
$271$	−14.1847	−0.861660	−0.430830	−	0.902433i	$-0.641779\pi$
$271$	−14.1847	−0.861660	−0.430830	+	0.902433i	$0.641779\pi$
$272$	27.7423	1.68212
$273$	−32.2706	−1.95311
$274$	55.5014	3.35296
$275$	−2.72095	−0.164080
$276$	20.2641	1.21976
$277$	17.5299	1.05327	0.526635	−	0.850091i	$-0.323453\pi$
$277$	17.5299	1.05327	0.526635	+	0.850091i	$0.323453\pi$
$278$	−53.3183	−3.19782
$279$	2.23028	0.133523
$280$	29.8026	1.78105
$281$	−7.85218	−0.468422	−0.234211	−	0.972186i	$-0.575251\pi$
$281$	−7.85218	−0.468422	−0.234211	+	0.972186i	$0.575251\pi$
$282$	−48.1502	−2.86731
$283$	0.945967	0.0562319	0.0281160	−	0.999605i	$-0.491049\pi$
$283$	0.945967	0.0562319	0.0281160	+	0.999605i	$0.491049\pi$
$284$	−54.5494	−3.23691
$285$	12.6798	0.751087
$286$	15.1337	0.894872
$287$	−15.2238	−0.898632
$288$	−13.4455	−0.792283
$289$	−11.5321	−0.678356
$290$	5.86651	0.344493
$291$	2.95971	0.173501
$292$	21.8759	1.28019
$293$	−0.964990	−0.0563753	−0.0281877	−	0.999603i	$-0.508974\pi$
$293$	−0.964990	−0.0563753	−0.0281877	+	0.999603i	$0.508974\pi$
$294$	−1.96634	−0.114679
$295$	−5.51354	−0.321011
$296$	82.8361	4.81475
$297$	3.71473	0.215551
$298$	−1.63511	−0.0947195
$299$	12.7803	0.739103
$300$	30.6842	1.77155
$301$	4.29585	0.247609
$302$	26.1199	1.50303
$303$	14.8193	0.851348
$304$	−54.5400	−3.12808
$305$	−2.74356	−0.157096
$306$	−5.56386	−0.318065
$307$	20.8670	1.19094	0.595471	−	0.803377i	$-0.296965\pi$
$307$	20.8670	1.19094	0.595471	+	0.803377i	$0.296965\pi$
$308$	−11.7439	−0.669173
$309$	2.90603	0.165318
$310$	−9.31252	−0.528916
$311$	−25.0277	−1.41919	−0.709594	−	0.704611i	$-0.751122\pi$
$311$	−25.0277	−1.41919	−0.709594	+	0.704611i	$0.751122\pi$
$312$	−103.822	−5.87777
$313$	2.99366	0.169212	0.0846058	−	0.996415i	$-0.473037\pi$
$313$	2.99366	0.169212	0.0846058	+	0.996415i	$0.473037\pi$
$314$	24.0475	1.35708
$315$	−3.21200	−0.180976
$316$	−18.9368	−1.06528
$317$	−19.3741	−1.08816	−0.544079	−	0.839034i	$-0.683121\pi$
$317$	−19.3741	−1.08816	−0.544079	+	0.839034i	$0.683121\pi$
$318$	−24.9467	−1.39894
$319$	−1.40635	−0.0787402
$320$	22.9695	1.28403
$321$	−36.5464	−2.03982
$322$	−13.8020	−0.769154
$323$	−10.7497	−0.598129
$324$	−55.5647	−3.08693
$325$	19.3520	1.07346
$326$	66.3518	3.67488
$327$	−16.3711	−0.905326
$328$	−48.9785	−2.70438
$329$	23.5657	1.29922
$330$	6.56920	0.361623
$331$	19.8398	1.09049	0.545247	−	0.838276i	$-0.316436\pi$
$331$	19.8398	1.09049	0.545247	+	0.838276i	$0.316436\pi$
$332$	−77.9618	−4.27871
$333$	−8.92773	−0.489237
$334$	9.66848	0.529035
$335$	1.75693	0.0959916
$336$	60.2530	3.28707
$337$	29.0227	1.58097	0.790485	−	0.612482i	$-0.209829\pi$
$337$	29.0227	1.58097	0.790485	+	0.612482i	$0.209829\pi$
$338$	−72.9785	−3.96951
$339$	−29.1254	−1.58187
$340$	16.6937	0.905344
$341$	2.23244	0.120893
$342$	10.9383	0.591473
$343$	18.9813	1.02489
$344$	13.8207	0.745165
$345$	5.54765	0.298676
$346$	41.5075	2.23146
$347$	3.86516	0.207493	0.103746	−	0.994604i	$-0.466917\pi$
$347$	3.86516	0.207493	0.103746	+	0.994604i	$0.466917\pi$
$348$	15.8594	0.850151
$349$	−13.7312	−0.735015	−0.367507	−	0.930021i	$-0.619789\pi$
$349$	−13.7312	−0.735015	−0.367507	+	0.930021i	$0.619789\pi$
$350$	−20.8991	−1.11710
$351$	−26.4201	−1.41020
$352$	−13.4585	−0.717340
$353$	1.95967	0.104302	0.0521512	−	0.998639i	$-0.483392\pi$
$353$	1.95967	0.104302	0.0521512	+	0.998639i	$0.483392\pi$
$354$	−20.7428	−1.10247
$355$	−14.9338	−0.792605
$356$	−54.2110	−2.87318
$357$	11.8757	0.628529
$358$	−70.2341	−3.71199
$359$	11.6483	0.614774	0.307387	−	0.951585i	$-0.400545\pi$
$359$	11.6483	0.614774	0.307387	+	0.951585i	$0.400545\pi$
$360$	−10.3338	−0.544637
$361$	2.13333	0.112281
$362$	−45.3714	−2.38467
$363$	20.1277	1.05643
$364$	83.5257	4.37794
$365$	5.98889	0.313473
$366$	−10.3217	−0.539524
$367$	1.45332	0.0758629	0.0379314	−	0.999280i	$-0.487923\pi$
$367$	1.45332	0.0758629	0.0379314	+	0.999280i	$0.487923\pi$
$368$	−23.8623	−1.24391
$369$	5.27870	0.274798
$370$	37.2777	1.93797
$371$	12.2094	0.633882
$372$	−25.1752	−1.30527
$373$	−13.9331	−0.721426	−0.360713	−	0.932677i	$-0.617467\pi$
$373$	−13.9331	−0.721426	−0.360713	+	0.932677i	$0.617467\pi$
$374$	−5.56924	−0.287979
$375$	22.1914	1.14596
$376$	75.8165	3.90994
$377$	10.0023	0.515142
$378$	28.5321	1.46754
$379$	30.7219	1.57808	0.789039	−	0.614344i	$-0.210579\pi$
$379$	30.7219	1.57808	0.789039	+	0.614344i	$0.210579\pi$
$380$	−32.8190	−1.68358
$381$	−30.3680	−1.55580
$382$	−2.57164	−0.131577
$383$	6.94586	0.354917	0.177458	−	0.984128i	$-0.443212\pi$
$383$	6.94586	0.354917	0.177458	+	0.984128i	$0.443212\pi$
$384$	26.9732	1.37647
$385$	−3.21511	−0.163857
$386$	63.7768	3.24615
$387$	−1.48954	−0.0757177
$388$	−7.66058	−0.388907
$389$	−7.75927	−0.393411	−0.196705	−	0.980463i	$-0.563024\pi$
$389$	−7.75927	−0.393411	−0.196705	+	0.980463i	$0.563024\pi$
$390$	−46.7217	−2.36585
$391$	−4.70319	−0.237851
$392$	3.09616	0.156379
$393$	−8.92373	−0.450143
$394$	5.42640	0.273378
$395$	−5.18428	−0.260849
$396$	4.07209	0.204630
$397$	4.92252	0.247054	0.123527	−	0.992341i	$-0.460579\pi$
$397$	4.92252	0.247054	0.123527	+	0.992341i	$0.460579\pi$
$398$	−39.6918	−1.98957
$399$	−23.3470	−1.16881
$400$	−36.1325	−1.80662
$401$	−8.35398	−0.417178	−0.208589	−	0.978003i	$-0.566887\pi$
$401$	−8.35398	−0.417178	−0.208589	+	0.978003i	$0.566887\pi$
$402$	6.60985	0.329670
$403$	−15.8776	−0.790921
$404$	−38.3567	−1.90832
$405$	−15.2118	−0.755880
$406$	−10.8019	−0.536088
$407$	−8.93636	−0.442959
$408$	38.2069	1.89152
$409$	−24.9806	−1.23521	−0.617606	−	0.786487i	$-0.711898\pi$
$409$	−24.9806	−1.23521	−0.617606	+	0.786487i	$0.711898\pi$
$410$	−22.0411	−1.08853
$411$	41.0762	2.02614
$412$	−7.52165	−0.370565
$413$	10.1520	0.499545
$414$	4.78570	0.235204
$415$	−21.3434	−1.04770
$416$	95.7200	4.69306
$417$	−39.4605	−1.93239
$418$	10.9488	0.535525
$419$	3.62255	0.176973	0.0884866	−	0.996077i	$-0.471797\pi$
$419$	3.62255	0.176973	0.0884866	+	0.996077i	$0.471797\pi$
$420$	36.2568	1.76915
$421$	16.8940	0.823363	0.411681	−	0.911328i	$-0.364942\pi$
$421$	16.8940	0.823363	0.411681	+	0.911328i	$0.364942\pi$
$422$	54.8479	2.66995
$423$	−8.17118	−0.397297
$424$	39.2806	1.90763
$425$	−7.12162	−0.345449
$426$	−56.1833	−2.72209
$427$	5.05166	0.244467
$428$	94.5927	4.57231
$429$	11.2003	0.540757
$430$	6.21957	0.299934
$431$	0.290673	0.0140012	0.00700062	−	0.999975i	$-0.497772\pi$
$431$	0.290673	0.0140012	0.00700062	+	0.999975i	$0.497772\pi$
$432$	49.3293	2.37336
$433$	−0.712918	−0.0342607	−0.0171303	−	0.999853i	$-0.505453\pi$
$433$	−0.712918	−0.0342607	−0.0171303	+	0.999853i	$0.505453\pi$
$434$	17.1469	0.823079
$435$	4.34177	0.208172
$436$	42.3732	2.02931
$437$	9.24623	0.442307
$438$	22.5311	1.07658
$439$	−27.1841	−1.29743	−0.648714	−	0.761032i	$-0.724693\pi$
$439$	−27.1841	−1.29743	−0.648714	+	0.761032i	$0.724693\pi$
$440$	−10.3437	−0.493119
$441$	−0.333691	−0.0158900
$442$	39.6097	1.88404
$443$	−10.8259	−0.514353	−0.257177	−	0.966364i	$-0.582792\pi$
$443$	−10.8259	−0.514353	−0.257177	+	0.966364i	$0.582792\pi$
$444$	100.775	4.78259
$445$	−14.8412	−0.703540
$446$	24.0803	1.14024
$447$	−1.21014	−0.0572375
$448$	−42.2932	−1.99817
$449$	−4.38508	−0.206945	−0.103472	−	0.994632i	$-0.532995\pi$
$449$	−4.38508	−0.206945	−0.103472	+	0.994632i	$0.532995\pi$
$450$	7.24655	0.341606
$451$	5.28380	0.248804
$452$	75.3849	3.54581
$453$	19.3312	0.908259
$454$	42.1441	1.97792
$455$	22.8666	1.07200
$456$	−75.1128	−3.51748
$457$	13.9276	0.651507	0.325753	−	0.945455i	$-0.394382\pi$
$457$	13.9276	0.651507	0.325753	+	0.945455i	$0.394382\pi$
$458$	59.5150	2.78095
$459$	9.72268	0.453816
$460$	−14.3589	−0.669489
$461$	−2.05317	−0.0956258	−0.0478129	−	0.998856i	$-0.515225\pi$
$461$	−2.05317	−0.0956258	−0.0478129	+	0.998856i	$0.515225\pi$
$462$	−12.0957	−0.562744
$463$	37.1948	1.72859	0.864295	−	0.502984i	$-0.167765\pi$
$463$	37.1948	1.72859	0.864295	+	0.502984i	$0.167765\pi$
$464$	−18.6754	−0.866982
$465$	−6.89214	−0.319615
$466$	55.3503	2.56406
$467$	−6.45712	−0.298800	−0.149400	−	0.988777i	$-0.547734\pi$
$467$	−6.45712	−0.298800	−0.149400	+	0.988777i	$0.547734\pi$
$468$	−28.9617	−1.33875
$469$	−3.23500	−0.149379
$470$	34.1187	1.57378
$471$	17.7974	0.820060
$472$	32.6612	1.50335
$473$	−1.49098	−0.0685554
$474$	−19.5040	−0.895850
$475$	14.0007	0.642398
$476$	−30.7378	−1.40886
$477$	−4.23350	−0.193838
$478$	31.8206	1.45544
$479$	−33.6499	−1.53750	−0.768751	−	0.639548i	$-0.779121\pi$
$479$	−33.6499	−1.53750	−0.768751	+	0.639548i	$0.779121\pi$
$480$	41.5500	1.89649
$481$	63.5575	2.89797
$482$	−59.9810	−2.73206
$483$	−10.2148	−0.464788
$484$	−52.0963	−2.36802
$485$	−2.09722	−0.0952296
$486$	−23.9765	−1.08760
$487$	−2.83399	−0.128420	−0.0642102	−	0.997936i	$-0.520453\pi$
$487$	−2.83399	−0.128420	−0.0642102	+	0.997936i	$0.520453\pi$
$488$	16.2524	0.735710
$489$	49.1066	2.22068
$490$	1.39332	0.0629439
$491$	27.8049	1.25482	0.627408	−	0.778691i	$-0.284116\pi$
$491$	27.8049	1.25482	0.627408	+	0.778691i	$0.284116\pi$
$492$	−59.5854	−2.68632
$493$	−3.68087	−0.165778
$494$	−77.8707	−3.50357
$495$	1.11481	0.0501068
$496$	29.6453	1.33112
$497$	27.4973	1.23342
$498$	−80.2970	−3.59819
$499$	17.7247	0.793466	0.396733	−	0.917934i	$-0.370144\pi$
$499$	17.7247	0.793466	0.396733	+	0.917934i	$0.370144\pi$
$500$	−57.4378	−2.56870
$501$	7.15558	0.319688
$502$	5.46566	0.243944
$503$	26.7348	1.19204	0.596022	−	0.802968i	$-0.296747\pi$
$503$	26.7348	1.19204	0.596022	+	0.802968i	$0.296747\pi$
$504$	19.0273	0.847543
$505$	−10.5008	−0.467279
$506$	4.79032	0.212956
$507$	−54.0110	−2.39871
$508$	78.6012	3.48736
$509$	35.8226	1.58781	0.793904	−	0.608044i	$-0.208045\pi$
$509$	35.8226	1.58781	0.793904	+	0.608044i	$0.208045\pi$
$510$	17.1938	0.761352
$511$	−11.0272	−0.487815
$512$	17.7848	0.785983
$513$	−19.1143	−0.843916
$514$	16.4356	0.724944
$515$	−2.05918	−0.0907383
$516$	16.8138	0.740187
$517$	−8.17908	−0.359716
$518$	−68.6385	−3.01580
$519$	30.7194	1.34843
$520$	73.5671	3.22613
$521$	−20.9416	−0.917466	−0.458733	−	0.888574i	$-0.651697\pi$
$521$	−20.9416	−0.917466	−0.458733	+	0.888574i	$0.651697\pi$
$522$	3.74544	0.163933
$523$	31.6802	1.38528	0.692638	−	0.721285i	$-0.256448\pi$
$523$	31.6802	1.38528	0.692638	+	0.721285i	$0.256448\pi$
$524$	23.0972	1.00901
$525$	−15.4673	−0.675048
$526$	17.9163	0.781188
$527$	5.84302	0.254526
$528$	−20.9123	−0.910091
$529$	−18.9546	−0.824113
$530$	17.6769	0.767836
$531$	−3.52009	−0.152759
$532$	60.4289	2.61992
$533$	−37.5796	−1.62775
$534$	−55.8348	−2.41621
$535$	25.8964	1.11960
$536$	−10.4078	−0.449546
$537$	−51.9798	−2.24310
$538$	22.4463	0.967727
$539$	−0.334013	−0.0143870
$540$	29.6835	1.27737
$541$	2.01187	0.0864972	0.0432486	−	0.999064i	$-0.486229\pi$
$541$	2.01187	0.0864972	0.0432486	+	0.999064i	$0.486229\pi$
$542$	37.8138	1.62424
$543$	−33.5791	−1.44102
$544$	−35.2253	−1.51027
$545$	11.6004	0.496906
$546$	86.0276	3.68164
$547$	−10.0786	−0.430928	−0.215464	−	0.976512i	$-0.569126\pi$
$547$	−10.0786	−0.430928	−0.215464	+	0.976512i	$0.569126\pi$
$548$	−106.317	−4.54164
$549$	−1.75161	−0.0747569
$550$	7.25356	0.309293
$551$	7.23639	0.308281
$552$	−32.8633	−1.39875
$553$	9.54568	0.405924
$554$	−46.7315	−1.98543
$555$	27.5890	1.17109
$556$	102.135	4.33150
$557$	−3.03815	−0.128731	−0.0643654	−	0.997926i	$-0.520502\pi$
$557$	−3.03815	−0.128731	−0.0643654	+	0.997926i	$0.520502\pi$
$558$	−5.94552	−0.251694
$559$	10.6042	0.448511
$560$	−42.6945	−1.80417
$561$	−4.12176	−0.174021
$562$	20.9325	0.882983
$563$	−28.8336	−1.21519	−0.607595	−	0.794247i	$-0.707866\pi$
$563$	−28.8336	−1.21519	−0.607595	+	0.794247i	$0.707866\pi$
$564$	92.2355	3.88382
$565$	20.6379	0.868243
$566$	−2.52177	−0.105998
$567$	28.0091	1.17627
$568$	88.4652	3.71192
$569$	4.08934	0.171434	0.0857170	−	0.996320i	$-0.472682\pi$
$569$	4.08934	0.171434	0.0857170	+	0.996320i	$0.472682\pi$
$570$	−33.8020	−1.41581
$571$	−14.5756	−0.609969	−0.304985	−	0.952357i	$-0.598651\pi$
$571$	−14.5756	−0.609969	−0.304985	+	0.952357i	$0.598651\pi$
$572$	−28.9897	−1.21212
$573$	−1.90326	−0.0795096
$574$	40.5838	1.69394
$575$	6.12559	0.255455
$576$	14.6647	0.611031
$577$	6.46188	0.269012	0.134506	−	0.990913i	$-0.457055\pi$
$577$	6.46188	0.269012	0.134506	+	0.990913i	$0.457055\pi$
$578$	30.7424	1.27871
$579$	47.2008	1.96160
$580$	−11.2378	−0.466622
$581$	39.2990	1.63040
$582$	−7.89004	−0.327053
$583$	−4.23759	−0.175503
$584$	−35.4771	−1.46805
$585$	−7.92876	−0.327814
$586$	2.57249	0.106268
$587$	26.0672	1.07591	0.537953	−	0.842975i	$-0.319198\pi$
$587$	26.0672	1.07591	0.537953	+	0.842975i	$0.319198\pi$
$588$	3.76667	0.155335
$589$	−11.4871	−0.473317
$590$	14.6981	0.605111
$591$	4.01605	0.165198
$592$	−118.669	−4.87727
$593$	26.7712	1.09936	0.549681	−	0.835374i	$-0.314749\pi$
$593$	26.7712	1.09936	0.549681	+	0.835374i	$0.314749\pi$
$594$	−9.90280	−0.406317
$595$	−8.41499	−0.344981
$596$	3.13218	0.128299
$597$	−29.3756	−1.20226
$598$	−34.0699	−1.39322
$599$	22.2173	0.907773	0.453887	−	0.891059i	$-0.350037\pi$
$599$	22.2173	0.907773	0.453887	+	0.891059i	$0.350037\pi$
$600$	−49.7619	−2.03152
$601$	−46.5899	−1.90044	−0.950221	−	0.311577i	$-0.899143\pi$
$601$	−46.5899	−1.90044	−0.950221	+	0.311577i	$0.899143\pi$
$602$	−11.4519	−0.466746
$603$	1.12170	0.0456793
$604$	−50.0348	−2.03589
$605$	−14.2623	−0.579843
$606$	−39.5056	−1.60480
$607$	−44.0394	−1.78750	−0.893752	−	0.448561i	$-0.851937\pi$
$607$	−44.0394	−1.78750	−0.893752	+	0.448561i	$0.851937\pi$
$608$	69.2511	2.80850
$609$	−7.99440	−0.323949
$610$	7.31384	0.296129
$611$	58.1716	2.35337
$612$	10.6580	0.430824
$613$	41.3396	1.66969	0.834844	−	0.550486i	$-0.185558\pi$
$613$	41.3396	1.66969	0.834844	+	0.550486i	$0.185558\pi$
$614$	−55.6276	−2.24495
$615$	−16.3125	−0.657784
$616$	19.0457	0.767373
$617$	−3.53351	−0.142254	−0.0711269	−	0.997467i	$-0.522660\pi$
$617$	−3.53351	−0.142254	−0.0711269	+	0.997467i	$0.522660\pi$
$618$	−7.74695	−0.311628
$619$	−34.9368	−1.40423	−0.702113	−	0.712065i	$-0.747760\pi$
$619$	−34.9368	−1.40423	−0.702113	+	0.712065i	$0.747760\pi$
$620$	17.8389	0.716426
$621$	−8.36286	−0.335590
$622$	66.7191	2.67519
$623$	27.3267	1.09482
$624$	148.733	5.95409
$625$	−0.496776	−0.0198710
$626$	−7.98055	−0.318967
$627$	8.10317	0.323609
$628$	−46.0648	−1.83819
$629$	−23.3894	−0.932596
$630$	8.56260	0.341142
$631$	−15.2387	−0.606642	−0.303321	−	0.952888i	$-0.598095\pi$
$631$	−15.2387	−0.606642	−0.303321	+	0.952888i	$0.598095\pi$
$632$	30.7107	1.22161
$633$	40.5926	1.61341
$634$	51.6478	2.05120
$635$	21.5184	0.853932
$636$	47.7873	1.89489
$637$	2.37558	0.0941240
$638$	3.74906	0.148427
$639$	−9.53441	−0.377175
$640$	−19.1129	−0.755505
$641$	33.1319	1.30863	0.654315	−	0.756222i	$-0.272957\pi$
$641$	33.1319	1.30863	0.654315	+	0.756222i	$0.272957\pi$
$642$	97.4261	3.84510
$643$	−28.7589	−1.13414	−0.567070	−	0.823669i	$-0.691923\pi$
$643$	−28.7589	−1.13414	−0.567070	+	0.823669i	$0.691923\pi$
$644$	26.4388	1.04183
$645$	4.60307	0.181246
$646$	28.6567	1.12748
$647$	22.7809	0.895611	0.447805	−	0.894131i	$-0.352206\pi$
$647$	22.7809	0.895611	0.447805	+	0.894131i	$0.352206\pi$
$648$	90.1118	3.53993
$649$	−3.52349	−0.138309
$650$	−51.5890	−2.02349
$651$	12.6903	0.497374
$652$	−127.102	−4.97770
$653$	−46.3312	−1.81308	−0.906541	−	0.422119i	$-0.861287\pi$
$653$	−46.3312	−1.81308	−0.906541	+	0.422119i	$0.861287\pi$
$654$	43.6424	1.70655
$655$	6.32325	0.247070
$656$	70.1655	2.73950
$657$	3.82357	0.149172
$658$	−62.8220	−2.44905
$659$	45.3833	1.76788	0.883941	−	0.467599i	$-0.154881\pi$
$659$	45.3833	1.76788	0.883941	+	0.467599i	$0.154881\pi$
$660$	−12.5838	−0.489824
$661$	17.3164	0.673530	0.336765	−	0.941589i	$-0.390667\pi$
$661$	17.3164	0.673530	0.336765	+	0.941589i	$0.390667\pi$
$662$	−52.8892	−2.05560
$663$	29.3149	1.13850
$664$	126.434	4.90659
$665$	16.5434	0.641527
$666$	23.7997	0.922219
$667$	3.16606	0.122590
$668$	−18.5207	−0.716588
$669$	17.8217	0.689027
$670$	−4.68367	−0.180946
$671$	−1.75330	−0.0676856
$672$	−76.5051	−2.95125
$673$	−24.3532	−0.938747	−0.469374	−	0.883000i	$-0.655520\pi$
$673$	−24.3532	−0.938747	−0.469374	+	0.883000i	$0.655520\pi$
$674$	−77.3693	−2.98015
$675$	−12.6631	−0.487404
$676$	139.796	5.37677
$677$	25.0177	0.961509	0.480754	−	0.876855i	$-0.340363\pi$
$677$	25.0177	0.961509	0.480754	+	0.876855i	$0.340363\pi$
$678$	77.6429	2.98186
$679$	3.86155	0.148193
$680$	−27.0730	−1.03820
$681$	31.1906	1.19523
$682$	−5.95127	−0.227886
$683$	−8.93453	−0.341870	−0.170935	−	0.985282i	$-0.554679\pi$
$683$	−8.93453	−0.341870	−0.170935	+	0.985282i	$0.554679\pi$
$684$	−20.9531	−0.801161
$685$	−29.1061	−1.11209
$686$	−50.6006	−1.93194
$687$	44.0467	1.68049
$688$	−19.7993	−0.754841
$689$	30.1387	1.14819
$690$	−14.7890	−0.563009
$691$	21.0602	0.801167	0.400583	−	0.916260i	$-0.368807\pi$
$691$	21.0602	0.801167	0.400583	+	0.916260i	$0.368807\pi$
$692$	−79.5108	−3.02255
$693$	−2.05266	−0.0779743
$694$	−10.3038	−0.391127
$695$	27.9613	1.06063
$696$	−25.7198	−0.974908
$697$	13.8294	0.523827
$698$	36.6049	1.38552
$699$	40.9645	1.54942
$700$	40.0338	1.51314
$701$	−22.4928	−0.849542	−0.424771	−	0.905301i	$-0.639645\pi$
$701$	−22.4928	−0.849542	−0.424771	+	0.905301i	$0.639645\pi$
$702$	70.4310	2.65825
$703$	45.9823	1.73426
$704$	14.6789	0.553233
$705$	25.2511	0.951010
$706$	−5.22411	−0.196612
$707$	19.3349	0.727163
$708$	39.7344	1.49331
$709$	−45.2203	−1.69828	−0.849141	−	0.528166i	$-0.822880\pi$
$709$	−45.2203	−1.69828	−0.849141	+	0.528166i	$0.822880\pi$
$710$	39.8108	1.49407
$711$	−3.30987	−0.124130
$712$	87.9165	3.29481
$713$	−5.02581	−0.188218
$714$	−31.6585	−1.18479
$715$	−7.93642	−0.296805
$716$	134.539	5.02795
$717$	23.5502	0.879499
$718$	−31.0522	−1.15886
$719$	29.2273	1.09000	0.544998	−	0.838437i	$-0.316530\pi$
$719$	29.2273	1.09000	0.544998	+	0.838437i	$0.316530\pi$
$720$	14.8039	0.551709
$721$	3.79152	0.141204
$722$	−5.68708	−0.211651
$723$	−44.3916	−1.65094
$724$	86.9124	3.23007
$725$	4.79408	0.178048
$726$	−53.6568	−1.99139
$727$	2.82367	0.104724	0.0523621	−	0.998628i	$-0.483325\pi$
$727$	2.82367	0.104724	0.0523621	+	0.998628i	$0.483325\pi$
$728$	−135.457	−5.02039
$729$	14.8982	0.551784
$730$	−15.9653	−0.590902
$731$	−3.90239	−0.144335
$732$	19.7720	0.730795
$733$	43.5569	1.60881	0.804405	−	0.594081i	$-0.202484\pi$
$733$	43.5569	1.60881	0.804405	+	0.594081i	$0.202484\pi$
$734$	−3.87430	−0.143003
$735$	1.03119	0.0380360
$736$	30.2987	1.11682
$737$	1.12279	0.0413585
$738$	−14.0720	−0.517999
$739$	22.1914	0.816325	0.408163	−	0.912909i	$-0.366170\pi$
$739$	22.1914	0.816325	0.408163	+	0.912909i	$0.366170\pi$
$740$	−71.4082	−2.62502
$741$	−57.6317	−2.11715
$742$	−32.5481	−1.19488
$743$	16.6445	0.610629	0.305314	−	0.952252i	$-0.401238\pi$
$743$	16.6445	0.610629	0.305314	+	0.952252i	$0.401238\pi$
$744$	40.8278	1.49682
$745$	0.857489	0.0314160
$746$	37.1430	1.35990
$747$	−13.6265	−0.498569
$748$	10.6683	0.390072
$749$	−47.6824	−1.74228
$750$	−59.1582	−2.16015
$751$	−15.2073	−0.554921	−0.277461	−	0.960737i	$-0.589493\pi$
$751$	−15.2073	−0.554921	−0.277461	+	0.960737i	$0.589493\pi$
$752$	−108.613	−3.96071
$753$	4.04511	0.147412
$754$	−26.6642	−0.971052
$755$	−13.6979	−0.498517
$756$	−54.6555	−1.98780
$757$	11.3188	0.411389	0.205694	−	0.978616i	$-0.434055\pi$
$757$	11.3188	0.411389	0.205694	+	0.978616i	$0.434055\pi$
$758$	−81.8989	−2.97470
$759$	3.54529	0.128686
$760$	53.2241	1.93064
$761$	6.85251	0.248403	0.124202	−	0.992257i	$-0.460363\pi$
$761$	6.85251	0.248403	0.124202	+	0.992257i	$0.460363\pi$
$762$	80.9555	2.93271
$763$	−21.3595	−0.773267
$764$	4.92617	0.178223
$765$	2.91781	0.105494
$766$	−18.5164	−0.669024
$767$	25.0599	0.904860
$768$	−7.07398	−0.255260
$769$	−0.343866	−0.0124001	−0.00620006	−	0.999981i	$-0.501974\pi$
$769$	−0.343866	−0.0124001	−0.00620006	+	0.999981i	$0.501974\pi$
$770$	8.57088	0.308873
$771$	12.1639	0.438072
$772$	−122.169	−4.39697
$773$	−6.76043	−0.243156	−0.121578	−	0.992582i	$-0.538795\pi$
$773$	−6.76043	−0.243156	−0.121578	+	0.992582i	$0.538795\pi$
$774$	3.97085	0.142729
$775$	−7.61014	−0.273364
$776$	12.4235	0.445978
$777$	−50.7989	−1.82240
$778$	20.6848	0.741586
$779$	−27.1880	−0.974110
$780$	89.4991	3.20458
$781$	−9.54363	−0.341498
$782$	12.5378	0.448352
$783$	−6.54504	−0.233901
$784$	−4.43548	−0.158410
$785$	−12.6110	−0.450107
$786$	23.7890	0.848527
$787$	50.0719	1.78487	0.892436	−	0.451174i	$-0.148995\pi$
$787$	50.0719	1.78487	0.892436	+	0.451174i	$0.148995\pi$
$788$	−10.3947	−0.370296
$789$	13.2597	0.472059
$790$	13.8203	0.491705
$791$	−38.0001	−1.35113
$792$	−6.60390	−0.234659
$793$	12.4699	0.442820
$794$	−13.1225	−0.465701
$795$	13.0826	0.463992
$796$	76.0327	2.69491
$797$	3.24086	0.114797	0.0573985	−	0.998351i	$-0.481719\pi$
$797$	3.24086	0.114797	0.0573985	+	0.998351i	$0.481719\pi$
$798$	62.2389	2.20323
$799$	−21.4073	−0.757337
$800$	45.8786	1.62205
$801$	−9.47527	−0.334792
$802$	22.2702	0.786387
$803$	3.82727	0.135061
$804$	−12.6617	−0.446543
$805$	7.23806	0.255108
$806$	42.3268	1.49090
$807$	16.6124	0.584782
$808$	62.2048	2.18836
$809$	2.23533	0.0785901	0.0392951	−	0.999228i	$-0.487489\pi$
$809$	2.23533	0.0785901	0.0392951	+	0.999228i	$0.487489\pi$
$810$	40.5519	1.42485
$811$	25.6624	0.901129	0.450564	−	0.892744i	$-0.351223\pi$
$811$	25.6624	0.901129	0.450564	+	0.892744i	$0.351223\pi$
$812$	20.6918	0.726140
$813$	27.9858	0.981505
$814$	23.8227	0.834985
$815$	−34.7963	−1.21886
$816$	−54.7343	−1.91609
$817$	7.67190	0.268406
$818$	66.5938	2.32840
$819$	14.5990	0.510132
$820$	42.2215	1.47444
$821$	−34.8075	−1.21479	−0.607395	−	0.794400i	$-0.707785\pi$
$821$	−34.8075	−1.21479	−0.607395	+	0.794400i	$0.707785\pi$
$822$	−109.502	−3.81931
$823$	−10.8442	−0.378005	−0.189003	−	0.981977i	$-0.560525\pi$
$823$	−10.8442	−0.378005	−0.189003	+	0.981977i	$0.560525\pi$
$824$	12.1982	0.424944
$825$	5.36832	0.186901
$826$	−27.0632	−0.941651
$827$	30.4925	1.06033	0.530164	−	0.847895i	$-0.322130\pi$
$827$	30.4925	1.06033	0.530164	+	0.847895i	$0.322130\pi$
$828$	−9.16737	−0.318588
$829$	35.0501	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$829$	35.0501	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$830$	56.8975	1.97494
$831$	−34.5857	−1.19977
$832$	−104.400	−3.61942
$833$	−0.874222	−0.0302900
$834$	105.195	3.64259
$835$	−5.07036	−0.175467
$836$	−20.9734	−0.725378
$837$	10.3896	0.359118
$838$	−9.65706	−0.333597
$839$	−3.02288	−0.104361	−0.0521807	−	0.998638i	$-0.516617\pi$
$839$	−3.02288	−0.104361	−0.0521807	+	0.998638i	$0.516617\pi$
$840$	−58.7992	−2.02877
$841$	−26.5221	−0.914557
$842$	−45.0363	−1.55205
$843$	15.4920	0.533573
$844$	−105.065	−3.61650
$845$	38.2715	1.31658
$846$	21.7829	0.748911
$847$	26.2608	0.902331
$848$	−56.2725	−1.93240
$849$	−1.86635	−0.0640530
$850$	18.9849	0.651178
$851$	20.1181	0.689641
$852$	107.623	3.68712
$853$	26.3875	0.903491	0.451745	−	0.892147i	$-0.350802\pi$
$853$	26.3875	0.903491	0.451745	+	0.892147i	$0.350802\pi$
$854$	−13.4668	−0.460824
$855$	−5.73627	−0.196176
$856$	−153.405	−5.24329
$857$	−54.0405	−1.84599	−0.922995	−	0.384812i	$-0.874266\pi$
$857$	−54.0405	−1.84599	−0.922995	+	0.384812i	$0.874266\pi$
$858$	−29.8580	−1.01934
$859$	−4.42022	−0.150816	−0.0754079	−	0.997153i	$-0.524026\pi$
$859$	−4.42022	−0.150816	−0.0754079	+	0.997153i	$0.524026\pi$
$860$	−11.9141	−0.406266
$861$	30.0359	1.02362
$862$	−0.774881	−0.0263926
$863$	3.14609	0.107094	0.0535471	−	0.998565i	$-0.482947\pi$
$863$	3.14609	0.107094	0.0535471	+	0.998565i	$0.482947\pi$
$864$	−62.6349	−2.13088
$865$	−21.7674	−0.740115
$866$	1.90051	0.0645819
$867$	22.7522	0.772707
$868$	−32.8463	−1.11487
$869$	−3.31307	−0.112388
$870$	−11.5744	−0.392408
$871$	−7.98554	−0.270580
$872$	−68.7186	−2.32710
$873$	−1.33895	−0.0453167
$874$	−24.6488	−0.833757
$875$	28.9533	0.978800
$876$	−43.1601	−1.45824
$877$	−3.38964	−0.114460	−0.0572300	−	0.998361i	$-0.518227\pi$
$877$	−3.38964	−0.114460	−0.0572300	+	0.998361i	$0.518227\pi$
$878$	72.4679	2.44567
$879$	1.90388	0.0642164
$880$	14.8182	0.499522
$881$	16.6955	0.562486	0.281243	−	0.959637i	$-0.409253\pi$
$881$	16.6955	0.562486	0.281243	+	0.959637i	$0.409253\pi$
$882$	0.889558	0.0299530
$883$	43.1769	1.45302	0.726508	−	0.687158i	$-0.241142\pi$
$883$	43.1769	1.45302	0.726508	+	0.687158i	$0.241142\pi$
$884$	−75.8755	−2.55197
$885$	10.8780	0.365659
$886$	28.8598	0.969565
$887$	32.0746	1.07696	0.538481	−	0.842638i	$-0.318999\pi$
$887$	32.0746	1.07696	0.538481	+	0.842638i	$0.318999\pi$
$888$	−163.432	−5.48442
$889$	−39.6213	−1.32886
$890$	39.5639	1.32618
$891$	−9.72127	−0.325675
$892$	−46.1277	−1.54447
$893$	42.0857	1.40835
$894$	3.22600	0.107894
$895$	36.8323	1.23117
$896$	35.1922	1.17569
$897$	−25.2149	−0.841902
$898$	11.6898	0.390095
$899$	−3.93336	−0.131185
$900$	−13.8813	−0.462711
$901$	−11.0912	−0.369500
$902$	−14.0856	−0.469001
$903$	−8.47552	−0.282048
$904$	−122.255	−4.06614
$905$	23.7938	0.790931
$906$	−51.5335	−1.71208
$907$	30.2045	1.00292	0.501462	−	0.865179i	$-0.332796\pi$
$907$	30.2045	1.00292	0.501462	+	0.865179i	$0.332796\pi$
$908$	−80.7304	−2.67913
$909$	−6.70417	−0.222363
$910$	−60.9581	−2.02074
$911$	−15.1180	−0.500881	−0.250441	−	0.968132i	$-0.580575\pi$
$911$	−15.1180	−0.500881	−0.250441	+	0.968132i	$0.580575\pi$
$912$	107.605	3.56315
$913$	−13.6397	−0.451409
$914$	−37.1285	−1.22810
$915$	5.41293	0.178946
$916$	−114.006	−3.76685
$917$	−11.6429	−0.384481
$918$	−25.9189	−0.855450
$919$	−14.7701	−0.487220	−0.243610	−	0.969873i	$-0.578332\pi$
$919$	−14.7701	−0.487220	−0.243610	+	0.969873i	$0.578332\pi$
$920$	23.2865	0.767734
$921$	−41.1696	−1.35659
$922$	5.47338	0.180256
$923$	67.8765	2.23418
$924$	23.1703	0.762246
$925$	30.4631	1.00162
$926$	−99.1546	−3.25842
$927$	−1.31467	−0.0431795
$928$	23.7127	0.778407
$929$	−18.9424	−0.621479	−0.310739	−	0.950495i	$-0.600577\pi$
$929$	−18.9424	−0.621479	−0.310739	+	0.950495i	$0.600577\pi$
$930$	18.3732	0.602481
$931$	1.71868	0.0563273
$932$	−106.028	−3.47306
$933$	49.3784	1.61658
$934$	17.2135	0.563243
$935$	2.92063	0.0955149
$936$	46.9685	1.53521
$937$	−35.5594	−1.16168	−0.580838	−	0.814019i	$-0.697275\pi$
$937$	−35.5594	−1.16168	−0.580838	+	0.814019i	$0.697275\pi$
$938$	8.62392	0.281581
$939$	−5.90636	−0.192747
$940$	−65.3570	−2.13171
$941$	−49.7909	−1.62314	−0.811568	−	0.584258i	$-0.801386\pi$
$941$	−49.7909	−1.62314	−0.811568	+	0.584258i	$0.801386\pi$
$942$	−47.4446	−1.54583
$943$	−11.8952	−0.387362
$944$	−46.7897	−1.52287
$945$	−14.9629	−0.486743
$946$	3.97469	0.129228
$947$	43.1162	1.40109	0.700544	−	0.713609i	$-0.252941\pi$
$947$	43.1162	1.40109	0.700544	+	0.713609i	$0.252941\pi$
$948$	37.3615	1.21344
$949$	−27.2204	−0.883612
$950$	−37.3234	−1.21093
$951$	38.2242	1.23951
$952$	49.8488	1.61561
$953$	39.7062	1.28621	0.643105	−	0.765778i	$-0.277646\pi$
$953$	39.7062	1.28621	0.643105	+	0.765778i	$0.277646\pi$
$954$	11.2857	0.365389
$955$	1.34862	0.0436405
$956$	−60.9548	−1.97142
$957$	2.77466	0.0896919
$958$	89.7044	2.89822
$959$	53.5924	1.73059
$960$	−45.3178	−1.46263
$961$	−24.7562	−0.798586
$962$	−169.433	−5.46273
$963$	16.5334	0.532781
$964$	114.898	3.70063
$965$	−33.4460	−1.07666
$966$	27.2307	0.876133
$967$	−33.7516	−1.08538	−0.542690	−	0.839933i	$-0.682594\pi$
$967$	−33.7516	−1.08538	−0.542690	+	0.839933i	$0.682594\pi$
$968$	84.4870	2.71551
$969$	21.2087	0.681320
$970$	5.59079	0.179509
$971$	11.6697	0.374497	0.187249	−	0.982313i	$-0.440043\pi$
$971$	11.6697	0.374497	0.187249	+	0.982313i	$0.440043\pi$
$972$	45.9288	1.47317
$973$	−51.4844	−1.65052
$974$	7.55490	0.242074
$975$	−38.1807	−1.22276
$976$	−23.2828	−0.745263
$977$	−20.8144	−0.665911	−0.332955	−	0.942943i	$-0.608046\pi$
$977$	−20.8144	−0.665911	−0.332955	+	0.942943i	$0.608046\pi$
$978$	−130.909	−4.18601
$979$	−9.48443	−0.303124
$980$	−2.66902	−0.0852586
$981$	7.40620	0.236462
$982$	−74.1227	−2.36535
$983$	14.0826	0.449166	0.224583	−	0.974455i	$-0.427898\pi$
$983$	14.0826	0.449166	0.224583	+	0.974455i	$0.427898\pi$
$984$	96.6324	3.08053
$985$	−2.84572	−0.0906723
$986$	9.81252	0.312494
$987$	−46.4942	−1.47993
$988$	149.167	4.74565
$989$	3.35660	0.106734
$990$	−2.97187	−0.0944521
$991$	−30.1595	−0.958047	−0.479023	−	0.877802i	$-0.659009\pi$
$991$	−30.1595	−0.958047	−0.479023	+	0.877802i	$0.659009\pi$
$992$	−37.6416	−1.19512
$993$	−39.1430	−1.24217
$994$	−73.3027	−2.32502
$995$	20.8152	0.659887
$996$	153.815	4.87382
$997$	0.0449906	0.00142487	0.000712433	−	1.00000i	$-0.499773\pi$
$997$	0.0449906	0.00142487	0.000712433		1.00000i	$0.499773\pi$
$998$	−47.2508	−1.49570
$999$	−41.5892	−1.31583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6029.2.a.b.1.10	✓	268

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6029.2.a.b.1.10	✓	268	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:	\( N \)	\(=\)	\( 6029 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66582 q^{2} -1.97296 q^{3} +5.10658 q^{4} +1.39801 q^{5} +5.25954 q^{6} -2.57413 q^{7} -8.28157 q^{8} +0.892553 q^{9} +O(q^{10})\)	\(q-2.66582 q^{2} -1.97296 q^{3} +5.10658 q^{4} +1.39801 q^{5} +5.25954 q^{6} -2.57413 q^{7} -8.28157 q^{8} +0.892553 q^{9} -3.72685 q^{10} +0.893416 q^{11} -10.0751 q^{12} -6.35418 q^{13} +6.86216 q^{14} -2.75822 q^{15} +11.8640 q^{16} +2.33836 q^{17} -2.37938 q^{18} -4.59710 q^{19} +7.13907 q^{20} +5.07864 q^{21} -2.38168 q^{22} -2.01132 q^{23} +16.3392 q^{24} -3.04556 q^{25} +16.9391 q^{26} +4.15790 q^{27} -13.1450 q^{28} -1.57412 q^{29} +7.35290 q^{30} +2.49877 q^{31} -15.0641 q^{32} -1.76267 q^{33} -6.23365 q^{34} -3.59867 q^{35} +4.55789 q^{36} -10.0025 q^{37} +12.2550 q^{38} +12.5365 q^{39} -11.5777 q^{40} +5.91415 q^{41} -13.5387 q^{42} -1.66886 q^{43} +4.56230 q^{44} +1.24780 q^{45} +5.36181 q^{46} -9.15484 q^{47} -23.4071 q^{48} -0.373861 q^{49} +8.11890 q^{50} -4.61349 q^{51} -32.4481 q^{52} -4.74313 q^{53} -11.0842 q^{54} +1.24901 q^{55} +21.3178 q^{56} +9.06987 q^{57} +4.19632 q^{58} -3.94384 q^{59} -14.0851 q^{60} -1.96247 q^{61} -6.66125 q^{62} -2.29755 q^{63} +16.4301 q^{64} -8.88323 q^{65} +4.69896 q^{66} +1.25674 q^{67} +11.9410 q^{68} +3.96824 q^{69} +9.59338 q^{70} -10.6822 q^{71} -7.39174 q^{72} +4.28386 q^{73} +26.6647 q^{74} +6.00875 q^{75} -23.4755 q^{76} -2.29977 q^{77} -33.4201 q^{78} -3.70832 q^{79} +16.5860 q^{80} -10.8810 q^{81} -15.7660 q^{82} -15.2669 q^{83} +25.9345 q^{84} +3.26906 q^{85} +4.44886 q^{86} +3.10567 q^{87} -7.39889 q^{88} -10.6159 q^{89} -3.32641 q^{90} +16.3565 q^{91} -10.2710 q^{92} -4.92995 q^{93} +24.4051 q^{94} -6.42681 q^{95} +29.7208 q^{96} -1.50014 q^{97} +0.996645 q^{98} +0.797421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9}+O(q^{10}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9	\( 268 q + 8 q^{2} + 43 q^{3} + 300 q^{4} + 18 q^{5} + 34 q^{6} + 59 q^{7} + 21 q^{8} + 295 q^{9} + 91 q^{10} + 49 q^{11} + 77 q^{12} + 45 q^{13} + 42 q^{14} + 37 q^{15} + 356 q^{16} + 40 q^{17} + 36 q^{18} + 245 q^{19} + 40 q^{20} + 66 q^{21} + 51 q^{22} + 26 q^{23} + 90 q^{24} + 314 q^{25} + 24 q^{26} + 160 q^{27} + 117 q^{28} + 54 q^{29} + 25 q^{30} + 181 q^{31} + 35 q^{32} + 49 q^{33} + 84 q^{34} + 73 q^{35} + 348 q^{36} + 77 q^{37} + 20 q^{38} + 96 q^{39} + 257 q^{40} + 62 q^{41} + 22 q^{42} + 199 q^{43} + 59 q^{44} + 60 q^{45} + 116 q^{46} + 41 q^{47} + 106 q^{48} + 381 q^{49} + 21 q^{50} + 248 q^{51} + 101 q^{52} + 4 q^{53} + 98 q^{54} + 136 q^{55} + 79 q^{56} + 47 q^{57} + 14 q^{58} + 170 q^{59} + 31 q^{60} + 247 q^{61} + 17 q^{62} + 143 q^{63} + 437 q^{64} + 29 q^{65} + 38 q^{66} + 114 q^{67} + 62 q^{68} + 101 q^{69} + 48 q^{70} + 64 q^{71} + 54 q^{72} + 115 q^{73} + 22 q^{74} + 250 q^{75} + 448 q^{76} + 8 q^{77} - 50 q^{78} + 271 q^{79} + 39 q^{80} + 336 q^{81} + 132 q^{82} + 74 q^{83} + 122 q^{84} + 58 q^{85} + 27 q^{86} + 105 q^{87} + 127 q^{88} + 63 q^{89} + 179 q^{90} + 406 q^{91} + 13 q^{92} + q^{93} + 263 q^{94} + 76 q^{95} + 161 q^{96} + 123 q^{97} - 7 q^{98} + 180 q^{99}+O(q^{100}) \) 268 * q + 8 * q^2 + 43 * q^3 + 300 * q^4 + 18 * q^5 + 34 * q^6 + 59 * q^7 + 21 * q^8 + 295 * q^9 + 91 * q^10 + 49 * q^11 + 77 * q^12 + 45 * q^13 + 42 * q^14 + 37 * q^15 + 356 * q^16 + 40 * q^17 + 36 * q^18 + 245 * q^19 + 40 * q^20 + 66 * q^21 + 51 * q^22 + 26 * q^23 + 90 * q^24 + 314 * q^25 + 24 * q^26 + 160 * q^27 + 117 * q^28 + 54 * q^29 + 25 * q^30 + 181 * q^31 + 35 * q^32 + 49 * q^33 + 84 * q^34 + 73 * q^35 + 348 * q^36 + 77 * q^37 + 20 * q^38 + 96 * q^39 + 257 * q^40 + 62 * q^41 + 22 * q^42 + 199 * q^43 + 59 * q^44 + 60 * q^45 + 116 * q^46 + 41 * q^47 + 106 * q^48 + 381 * q^49 + 21 * q^50 + 248 * q^51 + 101 * q^52 + 4 * q^53 + 98 * q^54 + 136 * q^55 + 79 * q^56 + 47 * q^57 + 14 * q^58 + 170 * q^59 + 31 * q^60 + 247 * q^61 + 17 * q^62 + 143 * q^63 + 437 * q^64 + 29 * q^65 + 38 * q^66 + 114 * q^67 + 62 * q^68 + 101 * q^69 + 48 * q^70 + 64 * q^71 + 54 * q^72 + 115 * q^73 + 22 * q^74 + 250 * q^75 + 448 * q^76 + 8 * q^77 - 50 * q^78 + 271 * q^79 + 39 * q^80 + 336 * q^81 + 132 * q^82 + 74 * q^83 + 122 * q^84 + 58 * q^85 + 27 * q^86 + 105 * q^87 + 127 * q^88 + 63 * q^89 + 179 * q^90 + 406 * q^91 + 13 * q^92 + q^93 + 263 * q^94 + 76 * q^95 + 161 * q^96 + 123 * q^97 - 7 * q^98 + 180 * q^99

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