LMFDB - Embedded newform 6022.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.29982 q^{3} +1.00000 q^{4} +3.94529 q^{5} +3.29982 q^{6} +1.75060 q^{7} -1.00000 q^{8} +7.88881 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.29982 q^{3} +1.00000 q^{4} +3.94529 q^{5} +3.29982 q^{6} +1.75060 q^{7} -1.00000 q^{8} +7.88881 q^{9} -3.94529 q^{10} +3.40402 q^{11} -3.29982 q^{12} +0.0996609 q^{13} -1.75060 q^{14} -13.0188 q^{15} +1.00000 q^{16} +5.91545 q^{17} -7.88881 q^{18} -2.89424 q^{19} +3.94529 q^{20} -5.77666 q^{21} -3.40402 q^{22} +3.94615 q^{23} +3.29982 q^{24} +10.5653 q^{25} -0.0996609 q^{26} -16.1322 q^{27} +1.75060 q^{28} -5.46266 q^{29} +13.0188 q^{30} +1.18703 q^{31} -1.00000 q^{32} -11.2327 q^{33} -5.91545 q^{34} +6.90663 q^{35} +7.88881 q^{36} +2.93586 q^{37} +2.89424 q^{38} -0.328863 q^{39} -3.94529 q^{40} +5.02885 q^{41} +5.77666 q^{42} +3.85790 q^{43} +3.40402 q^{44} +31.1237 q^{45} -3.94615 q^{46} -7.37601 q^{47} -3.29982 q^{48} -3.93540 q^{49} -10.5653 q^{50} -19.5199 q^{51} +0.0996609 q^{52} +5.43670 q^{53} +16.1322 q^{54} +13.4299 q^{55} -1.75060 q^{56} +9.55046 q^{57} +5.46266 q^{58} +5.88277 q^{59} -13.0188 q^{60} +5.09461 q^{61} -1.18703 q^{62} +13.8101 q^{63} +1.00000 q^{64} +0.393191 q^{65} +11.2327 q^{66} +13.6904 q^{67} +5.91545 q^{68} -13.0216 q^{69} -6.90663 q^{70} -8.58441 q^{71} -7.88881 q^{72} +9.10357 q^{73} -2.93586 q^{74} -34.8637 q^{75} -2.89424 q^{76} +5.95908 q^{77} +0.328863 q^{78} +11.5082 q^{79} +3.94529 q^{80} +29.5669 q^{81} -5.02885 q^{82} +4.00345 q^{83} -5.77666 q^{84} +23.3382 q^{85} -3.85790 q^{86} +18.0258 q^{87} -3.40402 q^{88} -3.86645 q^{89} -31.1237 q^{90} +0.174466 q^{91} +3.94615 q^{92} -3.91698 q^{93} +7.37601 q^{94} -11.4186 q^{95} +3.29982 q^{96} +0.434891 q^{97} +3.93540 q^{98} +26.8537 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * 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
$3$	−3.29982	−1.90515	−0.952576	−	0.304301i	$-0.901577\pi$
$3$	−3.29982	−1.90515	−0.952576	+	0.304301i	$0.901577\pi$
$4$	1.00000	0.500000
$5$	3.94529	1.76439	0.882194	−	0.470885i	$-0.156065\pi$
$5$	3.94529	1.76439	0.882194	+	0.470885i	$0.156065\pi$
$6$	3.29982	1.34715
$7$	1.75060	0.661664	0.330832	−	0.943690i	$-0.392671\pi$
$7$	1.75060	0.661664	0.330832	+	0.943690i	$0.392671\pi$
$8$	−1.00000	−0.353553
$9$	7.88881	2.62960
$10$	−3.94529	−1.24761
$11$	3.40402	1.02635	0.513175	−	0.858284i	$-0.328469\pi$
$11$	3.40402	1.02635	0.513175	+	0.858284i	$0.328469\pi$
$12$	−3.29982	−0.952576
$13$	0.0996609	0.0276409	0.0138205	−	0.999904i	$-0.495601\pi$
$13$	0.0996609	0.0276409	0.0138205	+	0.999904i	$0.495601\pi$
$14$	−1.75060	−0.467867
$15$	−13.0188	−3.36143
$16$	1.00000	0.250000
$17$	5.91545	1.43471	0.717354	−	0.696709i	$-0.245353\pi$
$17$	5.91545	1.43471	0.717354	+	0.696709i	$0.245353\pi$
$18$	−7.88881	−1.85941
$19$	−2.89424	−0.663983	−0.331992	−	0.943282i	$-0.607721\pi$
$19$	−2.89424	−0.663983	−0.331992	+	0.943282i	$0.607721\pi$
$20$	3.94529	0.882194
$21$	−5.77666	−1.26057
$22$	−3.40402	−0.725740
$23$	3.94615	0.822829	0.411414	−	0.911448i	$-0.365035\pi$
$23$	3.94615	0.822829	0.411414	+	0.911448i	$0.365035\pi$
$24$	3.29982	0.673573
$25$	10.5653	2.11307
$26$	−0.0996609	−0.0195451
$27$	−16.1322	−3.10464
$28$	1.75060	0.330832
$29$	−5.46266	−1.01439	−0.507195	−	0.861831i	$-0.669318\pi$
$29$	−5.46266	−1.01439	−0.507195	+	0.861831i	$0.669318\pi$
$30$	13.0188	2.37689
$31$	1.18703	0.213197	0.106598	−	0.994302i	$-0.466004\pi$
$31$	1.18703	0.213197	0.106598	+	0.994302i	$0.466004\pi$
$32$	−1.00000	−0.176777
$33$	−11.2327	−1.95535
$34$	−5.91545	−1.01449
$35$	6.90663	1.16743
$36$	7.88881	1.31480
$37$	2.93586	0.482652	0.241326	−	0.970444i	$-0.422418\pi$
$37$	2.93586	0.482652	0.241326	+	0.970444i	$0.422418\pi$
$38$	2.89424	0.469507
$39$	−0.328863	−0.0526602
$40$	−3.94529	−0.623806
$41$	5.02885	0.785374	0.392687	−	0.919672i	$-0.371545\pi$
$41$	5.02885	0.785374	0.392687	+	0.919672i	$0.371545\pi$
$42$	5.77666	0.891358
$43$	3.85790	0.588324	0.294162	−	0.955756i	$-0.404959\pi$
$43$	3.85790	0.588324	0.294162	+	0.955756i	$0.404959\pi$
$44$	3.40402	0.513175
$45$	31.1237	4.63964
$46$	−3.94615	−0.581828
$47$	−7.37601	−1.07590	−0.537951	−	0.842976i	$-0.680801\pi$
$47$	−7.37601	−1.07590	−0.537951	+	0.842976i	$0.680801\pi$
$48$	−3.29982	−0.476288
$49$	−3.93540	−0.562200
$50$	−10.5653	−1.49416
$51$	−19.5199	−2.73334
$52$	0.0996609	0.0138205
$53$	5.43670	0.746789	0.373394	−	0.927673i	$-0.378194\pi$
$53$	5.43670	0.746789	0.373394	+	0.927673i	$0.378194\pi$
$54$	16.1322	2.19531
$55$	13.4299	1.81088
$56$	−1.75060	−0.233934
$57$	9.55046	1.26499
$58$	5.46266	0.717282
$59$	5.88277	0.765872	0.382936	−	0.923775i	$-0.374913\pi$
$59$	5.88277	0.765872	0.382936	+	0.923775i	$0.374913\pi$
$60$	−13.0188	−1.68071
$61$	5.09461	0.652298	0.326149	−	0.945318i	$-0.394249\pi$
$61$	5.09461	0.652298	0.326149	+	0.945318i	$0.394249\pi$
$62$	−1.18703	−0.150753
$63$	13.8101	1.73992
$64$	1.00000	0.125000
$65$	0.393191	0.0487694
$66$	11.2327	1.38264
$67$	13.6904	1.67255	0.836273	−	0.548313i	$-0.184730\pi$
$67$	13.6904	1.67255	0.836273	+	0.548313i	$0.184730\pi$
$68$	5.91545	0.717354
$69$	−13.0216	−1.56761
$70$	−6.90663	−0.825500
$71$	−8.58441	−1.01878	−0.509391	−	0.860535i	$-0.670129\pi$
$71$	−8.58441	−1.01878	−0.509391	+	0.860535i	$0.670129\pi$
$72$	−7.88881	−0.929705
$73$	9.10357	1.06549	0.532746	−	0.846275i	$-0.321160\pi$
$73$	9.10357	1.06549	0.532746	+	0.846275i	$0.321160\pi$
$74$	−2.93586	−0.341286
$75$	−34.8637	−4.02572
$76$	−2.89424	−0.331992
$77$	5.95908	0.679100
$78$	0.328863	0.0372364
$79$	11.5082	1.29477	0.647387	−	0.762162i	$-0.275862\pi$
$79$	11.5082	1.29477	0.647387	+	0.762162i	$0.275862\pi$
$80$	3.94529	0.441097
$81$	29.5669	3.28521
$82$	−5.02885	−0.555344
$83$	4.00345	0.439436	0.219718	−	0.975563i	$-0.429486\pi$
$83$	4.00345	0.439436	0.219718	+	0.975563i	$0.429486\pi$
$84$	−5.77666	−0.630286
$85$	23.3382	2.53138
$86$	−3.85790	−0.416008
$87$	18.0258	1.93257
$88$	−3.40402	−0.362870
$89$	−3.86645	−0.409842	−0.204921	−	0.978778i	$-0.565694\pi$
$89$	−3.86645	−0.409842	−0.204921	+	0.978778i	$0.565694\pi$
$90$	−31.1237	−3.28072
$91$	0.174466	0.0182890
$92$	3.94615	0.411414
$93$	−3.91698	−0.406172
$94$	7.37601	0.760777
$95$	−11.4186	−1.17152
$96$	3.29982	0.336786
$97$	0.434891	0.0441565	0.0220782	−	0.999756i	$-0.492972\pi$
$97$	0.434891	0.0441565	0.0220782	+	0.999756i	$0.492972\pi$
$98$	3.93540	0.397536
$99$	26.8537	2.69890
$100$	10.5653	1.05653
$101$	4.89979	0.487548	0.243774	−	0.969832i	$-0.421615\pi$
$101$	4.89979	0.487548	0.243774	+	0.969832i	$0.421615\pi$
$102$	19.5199	1.93276
$103$	−14.9613	−1.47418	−0.737092	−	0.675793i	$-0.763801\pi$
$103$	−14.9613	−1.47418	−0.737092	+	0.675793i	$0.763801\pi$
$104$	−0.0996609	−0.00977255
$105$	−22.7906	−2.22414
$106$	−5.43670	−0.528059
$107$	−11.4982	−1.11157	−0.555785	−	0.831326i	$-0.687582\pi$
$107$	−11.4982	−1.11157	−0.555785	+	0.831326i	$0.687582\pi$
$108$	−16.1322	−1.55232
$109$	−2.81033	−0.269180	−0.134590	−	0.990901i	$-0.542972\pi$
$109$	−2.81033	−0.269180	−0.134590	+	0.990901i	$0.542972\pi$
$110$	−13.4299	−1.28049
$111$	−9.68780	−0.919525
$112$	1.75060	0.165416
$113$	15.2497	1.43458	0.717288	−	0.696777i	$-0.245383\pi$
$113$	15.2497	1.43458	0.717288	+	0.696777i	$0.245383\pi$
$114$	−9.55046	−0.894483
$115$	15.5687	1.45179
$116$	−5.46266	−0.507195
$117$	0.786206	0.0726847
$118$	−5.88277	−0.541553
$119$	10.3556	0.949296
$120$	13.0188	1.18844
$121$	0.587354	0.0533959
$122$	−5.09461	−0.461244
$123$	−16.5943	−1.49626
$124$	1.18703	0.106598
$125$	21.9569	1.96388
$126$	−13.8101	−1.23031
$127$	−0.187288	−0.0166191	−0.00830957	−	0.999965i	$-0.502645\pi$
$127$	−0.187288	−0.0166191	−0.00830957	+	0.999965i	$0.502645\pi$
$128$	−1.00000	−0.0883883
$129$	−12.7304	−1.12085
$130$	−0.393191	−0.0344852
$131$	2.11858	0.185101	0.0925505	−	0.995708i	$-0.470498\pi$
$131$	2.11858	0.185101	0.0925505	+	0.995708i	$0.470498\pi$
$132$	−11.2327	−0.977677
$133$	−5.06665	−0.439334
$134$	−13.6904	−1.18267
$135$	−63.6462	−5.47780
$136$	−5.91545	−0.507246
$137$	−9.80772	−0.837930	−0.418965	−	0.908002i	$-0.637607\pi$
$137$	−9.80772	−0.837930	−0.418965	+	0.908002i	$0.637607\pi$
$138$	13.0216	1.10847
$139$	3.47731	0.294941	0.147471	−	0.989066i	$-0.452887\pi$
$139$	3.47731	0.294941	0.147471	+	0.989066i	$0.452887\pi$
$140$	6.90663	0.583717
$141$	24.3395	2.04976
$142$	8.58441	0.720387
$143$	0.339248	0.0283693
$144$	7.88881	0.657401
$145$	−21.5518	−1.78978
$146$	−9.10357	−0.753417
$147$	12.9861	1.07108
$148$	2.93586	0.241326
$149$	−7.44337	−0.609784	−0.304892	−	0.952387i	$-0.598620\pi$
$149$	−7.44337	−0.609784	−0.304892	+	0.952387i	$0.598620\pi$
$150$	34.8637	2.84661
$151$	−22.6135	−1.84026	−0.920131	−	0.391611i	$-0.871918\pi$
$151$	−22.6135	−1.84026	−0.920131	+	0.391611i	$0.871918\pi$
$152$	2.89424	0.234754
$153$	46.6659	3.77271
$154$	−5.95908	−0.480196
$155$	4.68318	0.376162
$156$	−0.328863	−0.0263301
$157$	10.3109	0.822900	0.411450	−	0.911432i	$-0.365022\pi$
$157$	10.3109	0.822900	0.411450	+	0.911432i	$0.365022\pi$
$158$	−11.5082	−0.915543
$159$	−17.9401	−1.42275
$160$	−3.94529	−0.311903
$161$	6.90813	0.544437
$162$	−29.5669	−2.32300
$163$	−2.14002	−0.167619	−0.0838097	−	0.996482i	$-0.526709\pi$
$163$	−2.14002	−0.167619	−0.0838097	+	0.996482i	$0.526709\pi$
$164$	5.02885	0.392687
$165$	−44.3161	−3.45000
$166$	−4.00345	−0.310728
$167$	−19.6102	−1.51748	−0.758742	−	0.651391i	$-0.774186\pi$
$167$	−19.6102	−1.51748	−0.758742	+	0.651391i	$0.774186\pi$
$168$	5.77666	0.445679
$169$	−12.9901	−0.999236
$170$	−23.3382	−1.78996
$171$	−22.8321	−1.74601
$172$	3.85790	0.294162
$173$	11.9129	0.905724	0.452862	−	0.891581i	$-0.350403\pi$
$173$	11.9129	0.905724	0.452862	+	0.891581i	$0.350403\pi$
$174$	−18.0258	−1.36653
$175$	18.4957	1.39814
$176$	3.40402	0.256588
$177$	−19.4121	−1.45910
$178$	3.86645	0.289802
$179$	−5.91881	−0.442393	−0.221196	−	0.975229i	$-0.570996\pi$
$179$	−5.91881	−0.442393	−0.221196	+	0.975229i	$0.570996\pi$
$180$	31.1237	2.31982
$181$	−0.708900	−0.0526921	−0.0263461	−	0.999653i	$-0.508387\pi$
$181$	−0.708900	−0.0526921	−0.0263461	+	0.999653i	$0.508387\pi$
$182$	−0.174466	−0.0129323
$183$	−16.8113	−1.24273
$184$	−3.94615	−0.290914
$185$	11.5828	0.851586
$186$	3.91698	0.287207
$187$	20.1363	1.47251
$188$	−7.37601	−0.537951
$189$	−28.2410	−2.05423
$190$	11.4186	0.828393
$191$	−25.3926	−1.83734	−0.918670	−	0.395025i	$-0.870736\pi$
$191$	−25.3926	−1.83734	−0.918670	+	0.395025i	$0.870736\pi$
$192$	−3.29982	−0.238144
$193$	22.4514	1.61608	0.808042	−	0.589125i	$-0.200527\pi$
$193$	22.4514	1.61608	0.808042	+	0.589125i	$0.200527\pi$
$194$	−0.434891	−0.0312233
$195$	−1.29746	−0.0929131
$196$	−3.93540	−0.281100
$197$	1.18198	0.0842127	0.0421063	−	0.999113i	$-0.486593\pi$
$197$	1.18198	0.0842127	0.0421063	+	0.999113i	$0.486593\pi$
$198$	−26.8537	−1.90841
$199$	2.46910	0.175030	0.0875151	−	0.996163i	$-0.472107\pi$
$199$	2.46910	0.175030	0.0875151	+	0.996163i	$0.472107\pi$
$200$	−10.5653	−0.747082
$201$	−45.1758	−3.18645
$202$	−4.89979	−0.344748
$203$	−9.56293	−0.671186
$204$	−19.5199	−1.36667
$205$	19.8403	1.38571
$206$	14.9613	1.04241
$207$	31.1304	2.16371
$208$	0.0996609	0.00691024
$209$	−9.85204	−0.681480
$210$	22.7906	1.57270
$211$	9.10494	0.626810	0.313405	−	0.949620i	$-0.398530\pi$
$211$	9.10494	0.626810	0.313405	+	0.949620i	$0.398530\pi$
$212$	5.43670	0.373394
$213$	28.3270	1.94093
$214$	11.4982	0.785998
$215$	15.2205	1.03803
$216$	16.1322	1.09766
$217$	2.07801	0.141065
$218$	2.81033	0.190339
$219$	−30.0402	−2.02993
$220$	13.4299	0.905441
$221$	0.589539	0.0396567
$222$	9.68780	0.650203
$223$	−10.8738	−0.728164	−0.364082	−	0.931367i	$-0.618617\pi$
$223$	−10.8738	−0.728164	−0.364082	+	0.931367i	$0.618617\pi$
$224$	−1.75060	−0.116967
$225$	83.3480	5.55653
$226$	−15.2497	−1.01440
$227$	12.3770	0.821491	0.410746	−	0.911750i	$-0.365268\pi$
$227$	12.3770	0.821491	0.410746	+	0.911750i	$0.365268\pi$
$228$	9.55046	0.632495
$229$	0.251682	0.0166316	0.00831582	−	0.999965i	$-0.497353\pi$
$229$	0.251682	0.0166316	0.00831582	+	0.999965i	$0.497353\pi$
$230$	−15.5687	−1.02657
$231$	−19.6639	−1.29379
$232$	5.46266	0.358641
$233$	−29.9584	−1.96264	−0.981321	−	0.192377i	$-0.938380\pi$
$233$	−29.9584	−1.96264	−0.981321	+	0.192377i	$0.938380\pi$
$234$	−0.786206	−0.0513959
$235$	−29.1005	−1.89831
$236$	5.88277	0.382936
$237$	−37.9750	−2.46674
$238$	−10.3556	−0.671253
$239$	−30.5970	−1.97915	−0.989577	−	0.144003i	$-0.954002\pi$
$239$	−30.5970	−1.97915	−0.989577	+	0.144003i	$0.954002\pi$
$240$	−13.0188	−0.840357
$241$	−17.5979	−1.13358	−0.566792	−	0.823861i	$-0.691816\pi$
$241$	−17.5979	−1.13358	−0.566792	+	0.823861i	$0.691816\pi$
$242$	−0.587354	−0.0377566
$243$	−49.1689	−3.15419
$244$	5.09461	0.326149
$245$	−15.5263	−0.991940
$246$	16.5943	1.05801
$247$	−0.288442	−0.0183531
$248$	−1.18703	−0.0753764
$249$	−13.2107	−0.837192
$250$	−21.9569	−1.38868
$251$	−4.62223	−0.291753	−0.145876	−	0.989303i	$-0.546600\pi$
$251$	−4.62223	−0.291753	−0.145876	+	0.989303i	$0.546600\pi$
$252$	13.8101	0.869958
$253$	13.4328	0.844511
$254$	0.187288	0.0117515
$255$	−77.0119	−4.82267
$256$	1.00000	0.0625000
$257$	0.121347	0.00756945	0.00378472	−	0.999993i	$-0.498795\pi$
$257$	0.121347	0.00756945	0.00378472	+	0.999993i	$0.498795\pi$
$258$	12.7304	0.792558
$259$	5.13951	0.319354
$260$	0.393191	0.0243847
$261$	−43.0939	−2.66744
$262$	−2.11858	−0.130886
$263$	5.93623	0.366044	0.183022	−	0.983109i	$-0.441412\pi$
$263$	5.93623	0.366044	0.183022	+	0.983109i	$0.441412\pi$
$264$	11.2327	0.691322
$265$	21.4494	1.31763
$266$	5.06665	0.310656
$267$	12.7586	0.780812
$268$	13.6904	0.836273
$269$	−2.98917	−0.182253	−0.0911264	−	0.995839i	$-0.529047\pi$
$269$	−2.98917	−0.182253	−0.0911264	+	0.995839i	$0.529047\pi$
$270$	63.6462	3.87339
$271$	25.8286	1.56897	0.784487	−	0.620145i	$-0.212926\pi$
$271$	25.8286	1.56897	0.784487	+	0.620145i	$0.212926\pi$
$272$	5.91545	0.358677
$273$	−0.575707	−0.0348434
$274$	9.80772	0.592506
$275$	35.9646	2.16875
$276$	−13.0216	−0.783807
$277$	−15.1222	−0.908605	−0.454303	−	0.890847i	$-0.650112\pi$
$277$	−15.1222	−0.908605	−0.454303	+	0.890847i	$0.650112\pi$
$278$	−3.47731	−0.208555
$279$	9.36424	0.560623
$280$	−6.90663	−0.412750
$281$	3.93914	0.234989	0.117495	−	0.993074i	$-0.462514\pi$
$281$	3.93914	0.234989	0.117495	+	0.993074i	$0.462514\pi$
$282$	−24.3395	−1.44940
$283$	12.8942	0.766480	0.383240	−	0.923649i	$-0.374808\pi$
$283$	12.8942	0.766480	0.383240	+	0.923649i	$0.374808\pi$
$284$	−8.58441	−0.509391
$285$	37.6794	2.23193
$286$	−0.339248	−0.0200601
$287$	8.80350	0.519654
$288$	−7.88881	−0.464853
$289$	17.9926	1.05839
$290$	21.5518	1.26556
$291$	−1.43506	−0.0841248
$292$	9.10357	0.532746
$293$	5.17850	0.302531	0.151266	−	0.988493i	$-0.451665\pi$
$293$	5.17850	0.302531	0.151266	+	0.988493i	$0.451665\pi$
$294$	−12.9861	−0.757366
$295$	23.2093	1.35130
$296$	−2.93586	−0.170643
$297$	−54.9143	−3.18645
$298$	7.44337	0.431183
$299$	0.393277	0.0227438
$300$	−34.8637	−2.01286
$301$	6.75363	0.389273
$302$	22.6135	1.30126
$303$	−16.1684	−0.928853
$304$	−2.89424	−0.165996
$305$	20.0997	1.15091
$306$	−46.6659	−2.66771
$307$	4.47260	0.255265	0.127632	−	0.991822i	$-0.459262\pi$
$307$	4.47260	0.255265	0.127632	+	0.991822i	$0.459262\pi$
$308$	5.95908	0.339550
$309$	49.3697	2.80854
$310$	−4.68318	−0.265987
$311$	−15.3778	−0.871995	−0.435997	−	0.899948i	$-0.643604\pi$
$311$	−15.3778	−0.871995	−0.435997	+	0.899948i	$0.643604\pi$
$312$	0.328863	0.0186182
$313$	−0.292424	−0.0165288	−0.00826440	−	0.999966i	$-0.502631\pi$
$313$	−0.292424	−0.0165288	−0.00826440	+	0.999966i	$0.502631\pi$
$314$	−10.3109	−0.581878
$315$	54.4851	3.06989
$316$	11.5082	0.647387
$317$	34.6034	1.94352	0.971761	−	0.235966i	$-0.0758253\pi$
$317$	34.6034	1.94352	0.971761	+	0.235966i	$0.0758253\pi$
$318$	17.9401	1.00603
$319$	−18.5950	−1.04112
$320$	3.94529	0.220549
$321$	37.9419	2.11771
$322$	−6.90813	−0.384975
$323$	−17.1207	−0.952623
$324$	29.5669	1.64261
$325$	1.05295	0.0584072
$326$	2.14002	0.118525
$327$	9.27357	0.512830
$328$	−5.02885	−0.277672
$329$	−12.9124	−0.711886
$330$	44.3161	2.43952
$331$	−31.0847	−1.70857	−0.854285	−	0.519804i	$-0.826005\pi$
$331$	−31.0847	−1.70857	−0.854285	+	0.519804i	$0.826005\pi$
$332$	4.00345	0.219718
$333$	23.1604	1.26918
$334$	19.6102	1.07302
$335$	54.0126	2.95102
$336$	−5.77666	−0.315143
$337$	−27.1126	−1.47692	−0.738459	−	0.674298i	$-0.764446\pi$
$337$	−27.1126	−1.47692	−0.738459	+	0.674298i	$0.764446\pi$
$338$	12.9901	0.706567
$339$	−50.3214	−2.73308
$340$	23.3382	1.26569
$341$	4.04067	0.218815
$342$	22.8321	1.23462
$343$	−19.1435	−1.03365
$344$	−3.85790	−0.208004
$345$	−51.3740	−2.76588
$346$	−11.9129	−0.640444
$347$	−0.965702	−0.0518416	−0.0259208	−	0.999664i	$-0.508252\pi$
$347$	−0.965702	−0.0518416	−0.0259208	+	0.999664i	$0.508252\pi$
$348$	18.0258	0.966284
$349$	−0.306048	−0.0163824	−0.00819119	−	0.999966i	$-0.502607\pi$
$349$	−0.306048	−0.0163824	−0.00819119	+	0.999966i	$0.502607\pi$
$350$	−18.4957	−0.988636
$351$	−1.60775	−0.0858153
$352$	−3.40402	−0.181435
$353$	30.1039	1.60227	0.801134	−	0.598484i	$-0.204230\pi$
$353$	30.1039	1.60227	0.801134	+	0.598484i	$0.204230\pi$
$354$	19.4121	1.03174
$355$	−33.8680	−1.79753
$356$	−3.86645	−0.204921
$357$	−34.1716	−1.80855
$358$	5.91881	0.312819
$359$	7.14042	0.376857	0.188428	−	0.982087i	$-0.439661\pi$
$359$	7.14042	0.376857	0.188428	+	0.982087i	$0.439661\pi$
$360$	−31.1237	−1.64036
$361$	−10.6234	−0.559126
$362$	0.708900	0.0372590
$363$	−1.93816	−0.101727
$364$	0.174466	0.00914452
$365$	35.9163	1.87994
$366$	16.8113	0.878741
$367$	−11.5265	−0.601679	−0.300840	−	0.953675i	$-0.597267\pi$
$367$	−11.5265	−0.601679	−0.300840	+	0.953675i	$0.597267\pi$
$368$	3.94615	0.205707
$369$	39.6717	2.06522
$370$	−11.5828	−0.602162
$371$	9.51749	0.494123
$372$	−3.91698	−0.203086
$373$	5.27177	0.272962	0.136481	−	0.990643i	$-0.456421\pi$
$373$	5.27177	0.272962	0.136481	+	0.990643i	$0.456421\pi$
$374$	−20.1363	−1.04122
$375$	−72.4538	−3.74150
$376$	7.37601	0.380389
$377$	−0.544413	−0.0280387
$378$	28.2410	1.45256
$379$	32.3403	1.66121	0.830605	−	0.556862i	$-0.187995\pi$
$379$	32.3403	1.66121	0.830605	+	0.556862i	$0.187995\pi$
$380$	−11.4186	−0.585762
$381$	0.618018	0.0316620
$382$	25.3926	1.29920
$383$	11.0204	0.563118	0.281559	−	0.959544i	$-0.409149\pi$
$383$	11.0204	0.563118	0.281559	+	0.959544i	$0.409149\pi$
$384$	3.29982	0.168393
$385$	23.5103	1.19820
$386$	−22.4514	−1.14274
$387$	30.4342	1.54706
$388$	0.434891	0.0220782
$389$	−5.47194	−0.277438	−0.138719	−	0.990332i	$-0.544299\pi$
$389$	−5.47194	−0.277438	−0.138719	+	0.990332i	$0.544299\pi$
$390$	1.29746	0.0656995
$391$	23.3433	1.18052
$392$	3.93540	0.198768
$393$	−6.99092	−0.352645
$394$	−1.18198	−0.0595474
$395$	45.4032	2.28448
$396$	26.8537	1.34945
$397$	12.3097	0.617809	0.308904	−	0.951093i	$-0.400038\pi$
$397$	12.3097	0.617809	0.308904	+	0.951093i	$0.400038\pi$
$398$	−2.46910	−0.123765
$399$	16.7190	0.836998
$400$	10.5653	0.528267
$401$	14.4593	0.722063	0.361031	−	0.932554i	$-0.382425\pi$
$401$	14.4593	0.722063	0.361031	+	0.932554i	$0.382425\pi$
$402$	45.1758	2.25316
$403$	0.118300	0.00589296
$404$	4.89979	0.243774
$405$	116.650	5.79639
$406$	9.56293	0.474600
$407$	9.99372	0.495370
$408$	19.5199	0.966381
$409$	−18.4999	−0.914762	−0.457381	−	0.889271i	$-0.651212\pi$
$409$	−18.4999	−0.914762	−0.457381	+	0.889271i	$0.651212\pi$
$410$	−19.8403	−0.979842
$411$	32.3637	1.59638
$412$	−14.9613	−0.737092
$413$	10.2984	0.506750
$414$	−31.1304	−1.52998
$415$	15.7948	0.775336
$416$	−0.0996609	−0.00488628
$417$	−11.4745	−0.561908
$418$	9.85204	0.481879
$419$	16.4570	0.803977	0.401989	−	0.915645i	$-0.368319\pi$
$419$	16.4570	0.803977	0.401989	+	0.915645i	$0.368319\pi$
$420$	−22.7906	−1.11207
$421$	−18.3465	−0.894154	−0.447077	−	0.894496i	$-0.647535\pi$
$421$	−18.3465	−0.894154	−0.447077	+	0.894496i	$0.647535\pi$
$422$	−9.10494	−0.443222
$423$	−58.1880	−2.82920
$424$	−5.43670	−0.264030
$425$	62.4988	3.03164
$426$	−28.3270	−1.37245
$427$	8.91862	0.431602
$428$	−11.4982	−0.555785
$429$	−1.11946	−0.0540478
$430$	−15.2205	−0.734000
$431$	20.7128	0.997701	0.498850	−	0.866688i	$-0.333756\pi$
$431$	20.7128	0.997701	0.498850	+	0.866688i	$0.333756\pi$
$432$	−16.1322	−0.776161
$433$	3.25393	0.156374	0.0781869	−	0.996939i	$-0.475087\pi$
$433$	3.25393	0.156374	0.0781869	+	0.996939i	$0.475087\pi$
$434$	−2.07801	−0.0997478
$435$	71.1170	3.40980
$436$	−2.81033	−0.134590
$437$	−11.4211	−0.546345
$438$	30.0402	1.43537
$439$	−24.9095	−1.18886	−0.594432	−	0.804146i	$-0.702623\pi$
$439$	−24.9095	−1.18886	−0.594432	+	0.804146i	$0.702623\pi$
$440$	−13.4299	−0.640243
$441$	−31.0456	−1.47836
$442$	−0.589539	−0.0280415
$443$	24.1333	1.14661	0.573305	−	0.819342i	$-0.305661\pi$
$443$	24.1333	1.14661	0.573305	+	0.819342i	$0.305661\pi$
$444$	−9.68780	−0.459763
$445$	−15.2543	−0.723121
$446$	10.8738	0.514890
$447$	24.5618	1.16173
$448$	1.75060	0.0827081
$449$	−21.1536	−0.998298	−0.499149	−	0.866516i	$-0.666354\pi$
$449$	−21.1536	−0.998298	−0.499149	+	0.866516i	$0.666354\pi$
$450$	−83.3480	−3.92906
$451$	17.1183	0.806070
$452$	15.2497	0.717288
$453$	74.6205	3.50598
$454$	−12.3770	−0.580882
$455$	0.688321	0.0322690
$456$	−9.55046	−0.447241
$457$	−2.45565	−0.114870	−0.0574352	−	0.998349i	$-0.518292\pi$
$457$	−2.45565	−0.114870	−0.0574352	+	0.998349i	$0.518292\pi$
$458$	−0.251682	−0.0117603
$459$	−95.4293	−4.45426
$460$	15.5687	0.725895
$461$	33.4990	1.56020	0.780102	−	0.625653i	$-0.215167\pi$
$461$	33.4990	1.56020	0.780102	+	0.625653i	$0.215167\pi$
$462$	19.6639	0.914846
$463$	8.03955	0.373630	0.186815	−	0.982395i	$-0.440184\pi$
$463$	8.03955	0.373630	0.186815	+	0.982395i	$0.440184\pi$
$464$	−5.46266	−0.253598
$465$	−15.4536	−0.716645
$466$	29.9584	1.38780
$467$	−7.06006	−0.326701	−0.163350	−	0.986568i	$-0.552230\pi$
$467$	−7.06006	−0.326701	−0.163350	+	0.986568i	$0.552230\pi$
$468$	0.786206	0.0363424
$469$	23.9664	1.10666
$470$	29.1005	1.34231
$471$	−34.0242	−1.56775
$472$	−5.88277	−0.270777
$473$	13.1324	0.603827
$474$	37.9750	1.74425
$475$	−30.5786	−1.40304
$476$	10.3556	0.474648
$477$	42.8891	1.96376
$478$	30.5970	1.39947
$479$	36.8115	1.68196	0.840980	−	0.541067i	$-0.181979\pi$
$479$	36.8115	1.68196	0.840980	+	0.541067i	$0.181979\pi$
$480$	13.0188	0.594222
$481$	0.292590	0.0133410
$482$	17.5979	0.801564
$483$	−22.7956	−1.03723
$484$	0.587354	0.0266979
$485$	1.71577	0.0779092
$486$	49.1689	2.23035
$487$	−41.3563	−1.87403	−0.937016	−	0.349286i	$-0.886424\pi$
$487$	−41.3563	−1.87403	−0.937016	+	0.349286i	$0.886424\pi$
$488$	−5.09461	−0.230622
$489$	7.06168	0.319340
$490$	15.5263	0.701407
$491$	−24.6486	−1.11238	−0.556188	−	0.831057i	$-0.687737\pi$
$491$	−24.6486	−1.11238	−0.556188	+	0.831057i	$0.687737\pi$
$492$	−16.5943	−0.748129
$493$	−32.3141	−1.45535
$494$	0.288442	0.0129776
$495$	105.946	4.76190
$496$	1.18703	0.0532992
$497$	−15.0279	−0.674092
$498$	13.2107	0.591984
$499$	29.6603	1.32778	0.663890	−	0.747831i	$-0.268904\pi$
$499$	29.6603	1.32778	0.663890	+	0.747831i	$0.268904\pi$
$500$	21.9569	0.981942
$501$	64.7102	2.89104
$502$	4.62223	0.206300
$503$	−0.866764	−0.0386471	−0.0193236	−	0.999813i	$-0.506151\pi$
$503$	−0.866764	−0.0386471	−0.0193236	+	0.999813i	$0.506151\pi$
$504$	−13.8101	−0.615153
$505$	19.3311	0.860224
$506$	−13.4328	−0.597159
$507$	42.8649	1.90370
$508$	−0.187288	−0.00830957
$509$	−3.99456	−0.177056	−0.0885279	−	0.996074i	$-0.528216\pi$
$509$	−3.99456	−0.177056	−0.0885279	+	0.996074i	$0.528216\pi$
$510$	77.0119	3.41014
$511$	15.9367	0.704999
$512$	−1.00000	−0.0441942
$513$	46.6904	2.06143
$514$	−0.121347	−0.00535241
$515$	−59.0268	−2.60103
$516$	−12.7304	−0.560423
$517$	−25.1081	−1.10425
$518$	−5.13951	−0.225817
$519$	−39.3106	−1.72554
$520$	−0.393191	−0.0172426
$521$	39.5266	1.73169	0.865847	−	0.500309i	$-0.166780\pi$
$521$	39.5266	1.73169	0.865847	+	0.500309i	$0.166780\pi$
$522$	43.0939	1.88617
$523$	22.4878	0.983321	0.491661	−	0.870787i	$-0.336390\pi$
$523$	22.4878	0.983321	0.491661	+	0.870787i	$0.336390\pi$
$524$	2.11858	0.0925505
$525$	−61.0324	−2.66367
$526$	−5.93623	−0.258832
$527$	7.02181	0.305875
$528$	−11.2327	−0.488839
$529$	−7.42791	−0.322953
$530$	−21.4494	−0.931702
$531$	46.4081	2.01394
$532$	−5.06665	−0.219667
$533$	0.501180	0.0217085
$534$	−12.7586	−0.552117
$535$	−45.3636	−1.96124
$536$	−13.6904	−0.591334
$537$	19.5310	0.842825
$538$	2.98917	0.128872
$539$	−13.3962	−0.577015
$540$	−63.6462	−2.73890
$541$	−24.5930	−1.05733	−0.528667	−	0.848829i	$-0.677308\pi$
$541$	−24.5930	−1.05733	−0.528667	+	0.848829i	$0.677308\pi$
$542$	−25.8286	−1.10943
$543$	2.33924	0.100386
$544$	−5.91545	−0.253623
$545$	−11.0876	−0.474939
$546$	0.575707	0.0246380
$547$	−28.3709	−1.21305	−0.606527	−	0.795063i	$-0.707438\pi$
$547$	−28.3709	−1.21305	−0.606527	+	0.795063i	$0.707438\pi$
$548$	−9.80772	−0.418965
$549$	40.1904	1.71529
$550$	−35.9646	−1.53354
$551$	15.8102	0.673538
$552$	13.0216	0.554235
$553$	20.1462	0.856706
$554$	15.1222	0.642481
$555$	−38.2212	−1.62240
$556$	3.47731	0.147471
$557$	7.09443	0.300601	0.150300	−	0.988640i	$-0.451976\pi$
$557$	7.09443	0.300601	0.150300	+	0.988640i	$0.451976\pi$
$558$	−9.36424	−0.396420
$559$	0.384481	0.0162618
$560$	6.90663	0.291858
$561$	−66.4462	−2.80536
$562$	−3.93914	−0.166163
$563$	−41.7716	−1.76046	−0.880232	−	0.474544i	$-0.842613\pi$
$563$	−41.7716	−1.76046	−0.880232	+	0.474544i	$0.842613\pi$
$564$	24.3395	1.02488
$565$	60.1647	2.53115
$566$	−12.8942	−0.541984
$567$	51.7598	2.17371
$568$	8.58441	0.360194
$569$	−39.7823	−1.66776	−0.833880	−	0.551946i	$-0.813885\pi$
$569$	−39.7823	−1.66776	−0.833880	+	0.551946i	$0.813885\pi$
$570$	−37.6794	−1.57821
$571$	−20.5269	−0.859024	−0.429512	−	0.903061i	$-0.641314\pi$
$571$	−20.5269	−0.859024	−0.429512	+	0.903061i	$0.641314\pi$
$572$	0.339248	0.0141847
$573$	83.7908	3.50041
$574$	−8.80350	−0.367451
$575$	41.6924	1.73869
$576$	7.88881	0.328700
$577$	−31.6874	−1.31916	−0.659581	−	0.751633i	$-0.729266\pi$
$577$	−31.6874	−1.31916	−0.659581	+	0.751633i	$0.729266\pi$
$578$	−17.9926	−0.748393
$579$	−74.0854	−3.07889
$580$	−21.5518	−0.894890
$581$	7.00844	0.290759
$582$	1.43506	0.0594852
$583$	18.5066	0.766467
$584$	−9.10357	−0.376709
$585$	3.10181	0.128244
$586$	−5.17850	−0.213922
$587$	−46.0924	−1.90244	−0.951219	−	0.308516i	$-0.900168\pi$
$587$	−46.0924	−1.90244	−0.951219	+	0.308516i	$0.900168\pi$
$588$	12.9861	0.535538
$589$	−3.43554	−0.141559
$590$	−23.2093	−0.955511
$591$	−3.90033	−0.160438
$592$	2.93586	0.120663
$593$	−33.9285	−1.39328	−0.696639	−	0.717422i	$-0.745322\pi$
$593$	−33.9285	−1.39328	−0.696639	+	0.717422i	$0.745322\pi$
$594$	54.9143	2.25316
$595$	40.8558	1.67493
$596$	−7.44337	−0.304892
$597$	−8.14760	−0.333459
$598$	−0.393277	−0.0160823
$599$	41.6513	1.70183	0.850913	−	0.525306i	$-0.176049\pi$
$599$	41.6513	1.70183	0.850913	+	0.525306i	$0.176049\pi$
$600$	34.8637	1.42331
$601$	−33.8498	−1.38076	−0.690380	−	0.723446i	$-0.742557\pi$
$601$	−33.8498	−1.38076	−0.690380	+	0.723446i	$0.742557\pi$
$602$	−6.75363	−0.275258
$603$	108.001	4.39813
$604$	−22.6135	−0.920131
$605$	2.31729	0.0942110
$606$	16.1684	0.656798
$607$	−0.763236	−0.0309788	−0.0154894	−	0.999880i	$-0.504931\pi$
$607$	−0.763236	−0.0309788	−0.0154894	+	0.999880i	$0.504931\pi$
$608$	2.89424	0.117377
$609$	31.5559	1.27871
$610$	−20.0997	−0.813814
$611$	−0.735100	−0.0297389
$612$	46.6659	1.88636
$613$	−4.93194	−0.199199	−0.0995995	−	0.995028i	$-0.531756\pi$
$613$	−4.93194	−0.199199	−0.0995995	+	0.995028i	$0.531756\pi$
$614$	−4.47260	−0.180499
$615$	−65.4694	−2.63998
$616$	−5.95908	−0.240098
$617$	−16.5080	−0.664589	−0.332294	−	0.943176i	$-0.607823\pi$
$617$	−16.5080	−0.664589	−0.332294	+	0.943176i	$0.607823\pi$
$618$	−49.3697	−1.98594
$619$	15.8216	0.635925	0.317963	−	0.948103i	$-0.397001\pi$
$619$	15.8216	0.635925	0.317963	+	0.948103i	$0.397001\pi$
$620$	4.68318	0.188081
$621$	−63.6600	−2.55459
$622$	15.3778	0.616593
$623$	−6.76860	−0.271178
$624$	−0.328863	−0.0131651
$625$	33.7997	1.35199
$626$	0.292424	0.0116876
$627$	32.5100	1.29832
$628$	10.3109	0.411450
$629$	17.3669	0.692465
$630$	−54.4851	−2.17074
$631$	36.3408	1.44670	0.723352	−	0.690479i	$-0.242600\pi$
$631$	36.3408	1.44670	0.723352	+	0.690479i	$0.242600\pi$
$632$	−11.5082	−0.457772
$633$	−30.0447	−1.19417
$634$	−34.6034	−1.37428
$635$	−0.738907	−0.0293226
$636$	−17.9401	−0.711373
$637$	−0.392205	−0.0155397
$638$	18.5950	0.736183
$639$	−67.7208	−2.67899
$640$	−3.94529	−0.155951
$641$	−38.3999	−1.51671	−0.758353	−	0.651844i	$-0.773996\pi$
$641$	−38.3999	−1.51671	−0.758353	+	0.651844i	$0.773996\pi$
$642$	−37.9419	−1.49745
$643$	−25.4879	−1.00514	−0.502572	−	0.864535i	$-0.667613\pi$
$643$	−25.4879	−1.00514	−0.502572	+	0.864535i	$0.667613\pi$
$644$	6.90813	0.272218
$645$	−50.2250	−1.97761
$646$	17.1207	0.673606
$647$	10.1309	0.398287	0.199143	−	0.979970i	$-0.436184\pi$
$647$	10.1309	0.398287	0.199143	+	0.979970i	$0.436184\pi$
$648$	−29.5669	−1.16150
$649$	20.0251	0.786053
$650$	−1.05295	−0.0413001
$651$	−6.85706	−0.268750
$652$	−2.14002	−0.0838097
$653$	33.4694	1.30976	0.654880	−	0.755733i	$-0.272719\pi$
$653$	33.4694	1.30976	0.654880	+	0.755733i	$0.272719\pi$
$654$	−9.27357	−0.362625
$655$	8.35841	0.326590
$656$	5.02885	0.196344
$657$	71.8164	2.80182
$658$	12.9124	0.503379
$659$	−15.9800	−0.622491	−0.311245	−	0.950330i	$-0.600746\pi$
$659$	−15.9800	−0.622491	−0.311245	+	0.950330i	$0.600746\pi$
$660$	−44.3161	−1.72500
$661$	−10.7869	−0.419562	−0.209781	−	0.977748i	$-0.567275\pi$
$661$	−10.7869	−0.419562	−0.209781	+	0.977748i	$0.567275\pi$
$662$	31.0847	1.20814
$663$	−1.94537	−0.0755520
$664$	−4.00345	−0.155364
$665$	−19.9894	−0.775156
$666$	−23.1604	−0.897448
$667$	−21.5565	−0.834670
$668$	−19.6102	−0.758742
$669$	35.8816	1.38726
$670$	−54.0126	−2.08669
$671$	17.3422	0.669487
$672$	5.77666	0.222840
$673$	49.0231	1.88970	0.944851	−	0.327501i	$-0.106207\pi$
$673$	49.0231	1.88970	0.944851	+	0.327501i	$0.106207\pi$
$674$	27.1126	1.04434
$675$	−170.442	−6.56032
$676$	−12.9901	−0.499618
$677$	−0.0969338	−0.00372547	−0.00186273	−	0.999998i	$-0.500593\pi$
$677$	−0.0969338	−0.00372547	−0.00186273	+	0.999998i	$0.500593\pi$
$678$	50.3214	1.93258
$679$	0.761319	0.0292168
$680$	−23.3382	−0.894979
$681$	−40.8419	−1.56507
$682$	−4.04067	−0.154725
$683$	29.1913	1.11697	0.558487	−	0.829513i	$-0.311382\pi$
$683$	29.1913	1.11697	0.558487	+	0.829513i	$0.311382\pi$
$684$	−22.8321	−0.873007
$685$	−38.6943	−1.47843
$686$	19.1435	0.730903
$687$	−0.830506	−0.0316858
$688$	3.85790	0.147081
$689$	0.541826	0.0206419
$690$	51.3740	1.95577
$691$	−35.8440	−1.36357	−0.681784	−	0.731553i	$-0.738796\pi$
$691$	−35.8440	−1.36357	−0.681784	+	0.731553i	$0.738796\pi$
$692$	11.9129	0.452862
$693$	47.0100	1.78576
$694$	0.965702	0.0366575
$695$	13.7190	0.520391
$696$	−18.0258	−0.683266
$697$	29.7479	1.12678
$698$	0.306048	0.0115841
$699$	98.8574	3.73913
$700$	18.4957	0.699071
$701$	−36.7651	−1.38860	−0.694299	−	0.719687i	$-0.744286\pi$
$701$	−36.7651	−1.38860	−0.694299	+	0.719687i	$0.744286\pi$
$702$	1.60775	0.0606806
$703$	−8.49707	−0.320473
$704$	3.40402	0.128294
$705$	96.0265	3.61657
$706$	−30.1039	−1.13298
$707$	8.57758	0.322593
$708$	−19.4121	−0.729551
$709$	8.16375	0.306596	0.153298	−	0.988180i	$-0.451011\pi$
$709$	8.16375	0.306596	0.153298	+	0.988180i	$0.451011\pi$
$710$	33.8680	1.27104
$711$	90.7860	3.40474
$712$	3.86645	0.144901
$713$	4.68419	0.175424
$714$	34.1716	1.27884
$715$	1.33843	0.0500545
$716$	−5.91881	−0.221196
$717$	100.965	3.77059
$718$	−7.14042	−0.266478
$719$	38.0057	1.41737	0.708686	−	0.705524i	$-0.249288\pi$
$719$	38.0057	1.41737	0.708686	+	0.705524i	$0.249288\pi$
$720$	31.1237	1.15991
$721$	−26.1913	−0.975415
$722$	10.6234	0.395362
$723$	58.0700	2.15965
$724$	−0.708900	−0.0263461
$725$	−57.7148	−2.14348
$726$	1.93816	0.0719320
$727$	39.4428	1.46285	0.731427	−	0.681920i	$-0.238855\pi$
$727$	39.4428	1.46285	0.731427	+	0.681920i	$0.238855\pi$
$728$	−0.174466	−0.00646615
$729$	73.5477	2.72399
$730$	−35.9163	−1.32932
$731$	22.8212	0.844073
$732$	−16.8113	−0.621363
$733$	23.5831	0.871063	0.435531	−	0.900174i	$-0.356560\pi$
$733$	23.5831	0.871063	0.435531	+	0.900174i	$0.356560\pi$
$734$	11.5265	0.425451
$735$	51.2340	1.88980
$736$	−3.94615	−0.145457
$737$	46.6023	1.71662
$738$	−39.6717	−1.46033
$739$	45.2082	1.66301	0.831505	−	0.555518i	$-0.187480\pi$
$739$	45.2082	1.66301	0.831505	+	0.555518i	$0.187480\pi$
$740$	11.5828	0.425793
$741$	0.951807	0.0349655
$742$	−9.51749	−0.349398
$743$	48.9178	1.79462	0.897310	−	0.441401i	$-0.145518\pi$
$743$	48.9178	1.79462	0.897310	+	0.441401i	$0.145518\pi$
$744$	3.91698	0.143603
$745$	−29.3663	−1.07590
$746$	−5.27177	−0.193013
$747$	31.5825	1.15554
$748$	20.1363	0.736257
$749$	−20.1287	−0.735486
$750$	72.4538	2.64564
$751$	−37.7800	−1.37861	−0.689306	−	0.724471i	$-0.742084\pi$
$751$	−37.7800	−1.37861	−0.689306	+	0.724471i	$0.742084\pi$
$752$	−7.37601	−0.268975
$753$	15.2525	0.555833
$754$	0.544413	0.0198264
$755$	−89.2169	−3.24694
$756$	−28.2410	−1.02712
$757$	−24.2583	−0.881684	−0.440842	−	0.897585i	$-0.645320\pi$
$757$	−24.2583	−0.881684	−0.440842	+	0.897585i	$0.645320\pi$
$758$	−32.3403	−1.17465
$759$	−44.3257	−1.60892
$760$	11.4186	0.414197
$761$	−7.38714	−0.267784	−0.133892	−	0.990996i	$-0.542747\pi$
$761$	−7.38714	−0.267784	−0.133892	+	0.990996i	$0.542747\pi$
$762$	−0.618018	−0.0223884
$763$	−4.91976	−0.178107
$764$	−25.3926	−0.918670
$765$	184.111	6.65654
$766$	−11.0204	−0.398184
$767$	0.586282	0.0211694
$768$	−3.29982	−0.119072
$769$	−21.6613	−0.781127	−0.390564	−	0.920576i	$-0.627720\pi$
$769$	−21.6613	−0.781127	−0.390564	+	0.920576i	$0.627720\pi$
$770$	−23.5103	−0.847253
$771$	−0.400425	−0.0144209
$772$	22.4514	0.808042
$773$	19.5780	0.704170	0.352085	−	0.935968i	$-0.385473\pi$
$773$	19.5780	0.704170	0.352085	+	0.935968i	$0.385473\pi$
$774$	−30.4342	−1.09394
$775$	12.5414	0.450499
$776$	−0.434891	−0.0156117
$777$	−16.9595	−0.608417
$778$	5.47194	0.196179
$779$	−14.5547	−0.521476
$780$	−1.29746	−0.0464565
$781$	−29.2215	−1.04563
$782$	−23.3433	−0.834753
$783$	88.1247	3.14932
$784$	−3.93540	−0.140550
$785$	40.6796	1.45192
$786$	6.99092	0.249358
$787$	45.0847	1.60709	0.803547	−	0.595241i	$-0.202943\pi$
$787$	45.0847	1.60709	0.803547	+	0.595241i	$0.202943\pi$
$788$	1.18198	0.0421063
$789$	−19.5885	−0.697369
$790$	−45.4032	−1.61537
$791$	26.6962	0.949208
$792$	−26.8537	−0.954204
$793$	0.507733	0.0180301
$794$	−12.3097	−0.436857
$795$	−70.7791	−2.51028
$796$	2.46910	0.0875151
$797$	−43.8333	−1.55265	−0.776327	−	0.630331i	$-0.782919\pi$
$797$	−43.8333	−1.55265	−0.776327	+	0.630331i	$0.782919\pi$
$798$	−16.7190	−0.591847
$799$	−43.6325	−1.54361
$800$	−10.5653	−0.373541
$801$	−30.5017	−1.07772
$802$	−14.4593	−0.510575
$803$	30.9887	1.09357
$804$	−45.1758	−1.59323
$805$	27.2546	0.960598
$806$	−0.118300	−0.00416695
$807$	9.86372	0.347219
$808$	−4.89979	−0.172374
$809$	−22.7293	−0.799119	−0.399559	−	0.916707i	$-0.630837\pi$
$809$	−22.7293	−0.799119	−0.399559	+	0.916707i	$0.630837\pi$
$810$	−116.650	−4.09867
$811$	−6.31370	−0.221704	−0.110852	−	0.993837i	$-0.535358\pi$
$811$	−6.31370	−0.221704	−0.110852	+	0.993837i	$0.535358\pi$
$812$	−9.56293	−0.335593
$813$	−85.2297	−2.98913
$814$	−9.99372	−0.350280
$815$	−8.44301	−0.295746
$816$	−19.5199	−0.683334
$817$	−11.1657	−0.390637
$818$	18.4999	0.646834
$819$	1.37633	0.0480929
$820$	19.8403	0.692853
$821$	−29.6186	−1.03370	−0.516848	−	0.856077i	$-0.672895\pi$
$821$	−29.6186	−1.03370	−0.516848	+	0.856077i	$0.672895\pi$
$822$	−32.3637	−1.12881
$823$	52.6166	1.83410	0.917049	−	0.398775i	$-0.130564\pi$
$823$	52.6166	1.83410	0.917049	+	0.398775i	$0.130564\pi$
$824$	14.9613	0.521203
$825$	−118.677	−4.13180
$826$	−10.2984	−0.358327
$827$	22.9805	0.799112	0.399556	−	0.916709i	$-0.369164\pi$
$827$	22.9805	0.799112	0.399556	+	0.916709i	$0.369164\pi$
$828$	31.1304	1.08186
$829$	42.1434	1.46370	0.731850	−	0.681466i	$-0.238657\pi$
$829$	42.1434	1.46370	0.731850	+	0.681466i	$0.238657\pi$
$830$	−15.7948	−0.548245
$831$	49.9006	1.73103
$832$	0.0996609	0.00345512
$833$	−23.2797	−0.806593
$834$	11.4745	0.397329
$835$	−77.3681	−2.67743
$836$	−9.85204	−0.340740
$837$	−19.1494	−0.661899
$838$	−16.4570	−0.568498
$839$	32.2925	1.11486	0.557430	−	0.830224i	$-0.311788\pi$
$839$	32.2925	1.11486	0.557430	+	0.830224i	$0.311788\pi$
$840$	22.7906	0.786351
$841$	0.840648	0.0289879
$842$	18.3465	0.632262
$843$	−12.9985	−0.447691
$844$	9.10494	0.313405
$845$	−51.2496	−1.76304
$846$	58.1880	2.00054
$847$	1.02822	0.0353301
$848$	5.43670	0.186697
$849$	−42.5485	−1.46026
$850$	−62.4988	−2.14369
$851$	11.5853	0.397140
$852$	28.3270	0.970467
$853$	10.2814	0.352027	0.176014	−	0.984388i	$-0.443680\pi$
$853$	10.2814	0.352027	0.176014	+	0.984388i	$0.443680\pi$
$854$	−8.91862	−0.305189
$855$	−90.0793	−3.08065
$856$	11.4982	0.392999
$857$	27.7486	0.947873	0.473936	−	0.880559i	$-0.342833\pi$
$857$	27.7486	0.947873	0.473936	+	0.880559i	$0.342833\pi$
$858$	1.11946	0.0382176
$859$	−41.5058	−1.41616	−0.708080	−	0.706132i	$-0.750439\pi$
$859$	−41.5058	−1.41616	−0.708080	+	0.706132i	$0.750439\pi$
$860$	15.2205	0.519016
$861$	−29.0500	−0.990020
$862$	−20.7128	−0.705481
$863$	31.8168	1.08306	0.541529	−	0.840682i	$-0.317846\pi$
$863$	31.8168	1.08306	0.541529	+	0.840682i	$0.317846\pi$
$864$	16.1322	0.548828
$865$	47.0001	1.59805
$866$	−3.25393	−0.110573
$867$	−59.3723	−2.01639
$868$	2.07801	0.0705323
$869$	39.1741	1.32889
$870$	−71.1170	−2.41109
$871$	1.36439	0.0462308
$872$	2.81033	0.0951697
$873$	3.43077	0.116114
$874$	11.4211	0.386324
$875$	38.4377	1.29943
$876$	−30.0402	−1.01496
$877$	12.7738	0.431340	0.215670	−	0.976466i	$-0.430806\pi$
$877$	12.7738	0.431340	0.215670	+	0.976466i	$0.430806\pi$
$878$	24.9095	0.840654
$879$	−17.0881	−0.576368
$880$	13.4299	0.452720
$881$	−17.3978	−0.586147	−0.293073	−	0.956090i	$-0.594678\pi$
$881$	−17.3978	−0.586147	−0.293073	+	0.956090i	$0.594678\pi$
$882$	31.0456	1.04536
$883$	46.1967	1.55464	0.777322	−	0.629103i	$-0.216578\pi$
$883$	46.1967	1.55464	0.777322	+	0.629103i	$0.216578\pi$
$884$	0.589539	0.0198284
$885$	−76.5864	−2.57442
$886$	−24.1333	−0.810775
$887$	46.3976	1.55788	0.778940	−	0.627099i	$-0.215758\pi$
$887$	46.3976	1.55788	0.778940	+	0.627099i	$0.215758\pi$
$888$	9.68780	0.325101
$889$	−0.327867	−0.0109963
$890$	15.2543	0.511324
$891$	100.646	3.37178
$892$	−10.8738	−0.364082
$893$	21.3479	0.714381
$894$	−24.5618	−0.821469
$895$	−23.3514	−0.780552
$896$	−1.75060	−0.0584834
$897$	−1.29774	−0.0433303
$898$	21.1536	0.705903
$899$	−6.48433	−0.216265
$900$	83.3480	2.77827
$901$	32.1606	1.07142
$902$	−17.1183	−0.569977
$903$	−22.2858	−0.741624
$904$	−15.2497	−0.507199
$905$	−2.79682	−0.0929694
$906$	−74.6205	−2.47910
$907$	−17.0414	−0.565850	−0.282925	−	0.959142i	$-0.591305\pi$
$907$	−17.0414	−0.565850	−0.282925	+	0.959142i	$0.591305\pi$
$908$	12.3770	0.410746
$909$	38.6536	1.28206
$910$	−0.688321	−0.0228176
$911$	22.6017	0.748826	0.374413	−	0.927262i	$-0.377844\pi$
$911$	22.6017	0.748826	0.374413	+	0.927262i	$0.377844\pi$
$912$	9.55046	0.316247
$913$	13.6278	0.451015
$914$	2.45565	0.0812256
$915$	−66.3255	−2.19265
$916$	0.251682	0.00831582
$917$	3.70878	0.122475
$918$	95.4293	3.14964
$919$	2.59147	0.0854845	0.0427423	−	0.999086i	$-0.486391\pi$
$919$	2.59147	0.0854845	0.0427423	+	0.999086i	$0.486391\pi$
$920$	−15.5687	−0.513285
$921$	−14.7588	−0.486318
$922$	−33.4990	−1.10323
$923$	−0.855529	−0.0281601
$924$	−19.6639	−0.646894
$925$	31.0183	1.01988
$926$	−8.03955	−0.264196
$927$	−118.027	−3.87652
$928$	5.46266	0.179321
$929$	−42.6171	−1.39822	−0.699110	−	0.715014i	$-0.746420\pi$
$929$	−42.6171	−1.39822	−0.699110	+	0.715014i	$0.746420\pi$
$930$	15.4536	0.506745
$931$	11.3900	0.373292
$932$	−29.9584	−0.981321
$933$	50.7440	1.66128
$934$	7.06006	0.231012
$935$	79.4437	2.59809
$936$	−0.786206	−0.0256979
$937$	−23.6392	−0.772258	−0.386129	−	0.922445i	$-0.626188\pi$
$937$	−23.6392	−0.772258	−0.386129	+	0.922445i	$0.626188\pi$
$938$	−23.9664	−0.782530
$939$	0.964947	0.0314899
$940$	−29.1005	−0.949155
$941$	13.9758	0.455597	0.227798	−	0.973708i	$-0.426847\pi$
$941$	13.9758	0.455597	0.227798	+	0.973708i	$0.426847\pi$
$942$	34.0242	1.10857
$943$	19.8446	0.646229
$944$	5.88277	0.191468
$945$	−111.419	−3.62446
$946$	−13.1324	−0.426970
$947$	−19.4430	−0.631813	−0.315906	−	0.948790i	$-0.602309\pi$
$947$	−19.4430	−0.631813	−0.315906	+	0.948790i	$0.602309\pi$
$948$	−37.9750	−1.23337
$949$	0.907270	0.0294512
$950$	30.5786	0.992101
$951$	−114.185	−3.70271
$952$	−10.3556	−0.335627
$953$	15.3274	0.496504	0.248252	−	0.968696i	$-0.420144\pi$
$953$	15.3274	0.496504	0.248252	+	0.968696i	$0.420144\pi$
$954$	−42.8891	−1.38859
$955$	−100.181	−3.24178
$956$	−30.5970	−0.989577
$957$	61.3602	1.98349
$958$	−36.8115	−1.18933
$959$	−17.1694	−0.554428
$960$	−13.0188	−0.420179
$961$	−29.5910	−0.954547
$962$	−0.292590	−0.00943348
$963$	−90.7068	−2.92299
$964$	−17.5979	−0.566792
$965$	88.5772	2.85140
$966$	22.7956	0.733435
$967$	20.3228	0.653537	0.326768	−	0.945104i	$-0.394040\pi$
$967$	20.3228	0.653537	0.326768	+	0.945104i	$0.394040\pi$
$968$	−0.587354	−0.0188783
$969$	56.4953	1.81489
$970$	−1.71577	−0.0550901
$971$	−24.5516	−0.787899	−0.393949	−	0.919132i	$-0.628891\pi$
$971$	−24.5516	−0.787899	−0.393949	+	0.919132i	$0.628891\pi$
$972$	−49.1689	−1.57709
$973$	6.08737	0.195152
$974$	41.3563	1.32514
$975$	−3.47455	−0.111275
$976$	5.09461	0.163074
$977$	−31.0885	−0.994608	−0.497304	−	0.867576i	$-0.665677\pi$
$977$	−31.0885	−0.994608	−0.497304	+	0.867576i	$0.665677\pi$
$978$	−7.06168	−0.225808
$979$	−13.1615	−0.420642
$980$	−15.5263	−0.495970
$981$	−22.1701	−0.707838
$982$	24.6486	0.786568
$983$	−39.0102	−1.24423	−0.622117	−	0.782925i	$-0.713727\pi$
$983$	−39.0102	−1.24423	−0.622117	+	0.782925i	$0.713727\pi$
$984$	16.5943	0.529007
$985$	4.66326	0.148584
$986$	32.3141	1.02909
$987$	42.6087	1.35625
$988$	−0.288442	−0.00917657
$989$	15.2238	0.484090
$990$	−105.946	−3.36717
$991$	31.0547	0.986486	0.493243	−	0.869892i	$-0.335811\pi$
$991$	31.0547	0.986486	0.493243	+	0.869892i	$0.335811\pi$
$992$	−1.18703	−0.0376882
$993$	102.574	3.25509
$994$	15.0279	0.476655
$995$	9.74134	0.308821
$996$	−13.2107	−0.418596
$997$	−35.9219	−1.13766	−0.568828	−	0.822456i	$-0.692603\pi$
$997$	−35.9219	−1.13766	−0.568828	+	0.822456i	$0.692603\pi$
$998$	−29.6603	−0.938882
$999$	−47.3618	−1.49846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.2	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.2	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.29982 q^{3} +1.00000 q^{4} +3.94529 q^{5} +3.29982 q^{6} +1.75060 q^{7} -1.00000 q^{8} +7.88881 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.29982 q^{3} +1.00000 q^{4} +3.94529 q^{5} +3.29982 q^{6} +1.75060 q^{7} -1.00000 q^{8} +7.88881 q^{9} -3.94529 q^{10} +3.40402 q^{11} -3.29982 q^{12} +0.0996609 q^{13} -1.75060 q^{14} -13.0188 q^{15} +1.00000 q^{16} +5.91545 q^{17} -7.88881 q^{18} -2.89424 q^{19} +3.94529 q^{20} -5.77666 q^{21} -3.40402 q^{22} +3.94615 q^{23} +3.29982 q^{24} +10.5653 q^{25} -0.0996609 q^{26} -16.1322 q^{27} +1.75060 q^{28} -5.46266 q^{29} +13.0188 q^{30} +1.18703 q^{31} -1.00000 q^{32} -11.2327 q^{33} -5.91545 q^{34} +6.90663 q^{35} +7.88881 q^{36} +2.93586 q^{37} +2.89424 q^{38} -0.328863 q^{39} -3.94529 q^{40} +5.02885 q^{41} +5.77666 q^{42} +3.85790 q^{43} +3.40402 q^{44} +31.1237 q^{45} -3.94615 q^{46} -7.37601 q^{47} -3.29982 q^{48} -3.93540 q^{49} -10.5653 q^{50} -19.5199 q^{51} +0.0996609 q^{52} +5.43670 q^{53} +16.1322 q^{54} +13.4299 q^{55} -1.75060 q^{56} +9.55046 q^{57} +5.46266 q^{58} +5.88277 q^{59} -13.0188 q^{60} +5.09461 q^{61} -1.18703 q^{62} +13.8101 q^{63} +1.00000 q^{64} +0.393191 q^{65} +11.2327 q^{66} +13.6904 q^{67} +5.91545 q^{68} -13.0216 q^{69} -6.90663 q^{70} -8.58441 q^{71} -7.88881 q^{72} +9.10357 q^{73} -2.93586 q^{74} -34.8637 q^{75} -2.89424 q^{76} +5.95908 q^{77} +0.328863 q^{78} +11.5082 q^{79} +3.94529 q^{80} +29.5669 q^{81} -5.02885 q^{82} +4.00345 q^{83} -5.77666 q^{84} +23.3382 q^{85} -3.85790 q^{86} +18.0258 q^{87} -3.40402 q^{88} -3.86645 q^{89} -31.1237 q^{90} +0.174466 q^{91} +3.94615 q^{92} -3.91698 q^{93} +7.37601 q^{94} -11.4186 q^{95} +3.29982 q^{96} +0.434891 q^{97} +3.93540 q^{98} +26.8537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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