LMFDB - Embedded newform 6010.2.a.i.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.19430 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.19430 q^{6} -4.31508 q^{7} -1.00000 q^{8} +1.81494 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.19430 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.19430 q^{6} -4.31508 q^{7} -1.00000 q^{8} +1.81494 q^{9} +1.00000 q^{10} -0.0662417 q^{11} -2.19430 q^{12} +0.0541913 q^{13} +4.31508 q^{14} +2.19430 q^{15} +1.00000 q^{16} -4.82060 q^{17} -1.81494 q^{18} +3.98279 q^{19} -1.00000 q^{20} +9.46858 q^{21} +0.0662417 q^{22} -5.13895 q^{23} +2.19430 q^{24} +1.00000 q^{25} -0.0541913 q^{26} +2.60037 q^{27} -4.31508 q^{28} -1.42992 q^{29} -2.19430 q^{30} +1.71418 q^{31} -1.00000 q^{32} +0.145354 q^{33} +4.82060 q^{34} +4.31508 q^{35} +1.81494 q^{36} -0.606775 q^{37} -3.98279 q^{38} -0.118912 q^{39} +1.00000 q^{40} -8.04158 q^{41} -9.46858 q^{42} +1.27497 q^{43} -0.0662417 q^{44} -1.81494 q^{45} +5.13895 q^{46} -1.86363 q^{47} -2.19430 q^{48} +11.6199 q^{49} -1.00000 q^{50} +10.5778 q^{51} +0.0541913 q^{52} +13.1197 q^{53} -2.60037 q^{54} +0.0662417 q^{55} +4.31508 q^{56} -8.73944 q^{57} +1.42992 q^{58} -5.78132 q^{59} +2.19430 q^{60} +9.94732 q^{61} -1.71418 q^{62} -7.83163 q^{63} +1.00000 q^{64} -0.0541913 q^{65} -0.145354 q^{66} +4.12669 q^{67} -4.82060 q^{68} +11.2764 q^{69} -4.31508 q^{70} +2.43841 q^{71} -1.81494 q^{72} -2.77590 q^{73} +0.606775 q^{74} -2.19430 q^{75} +3.98279 q^{76} +0.285839 q^{77} +0.118912 q^{78} +11.6810 q^{79} -1.00000 q^{80} -11.1508 q^{81} +8.04158 q^{82} +1.36527 q^{83} +9.46858 q^{84} +4.82060 q^{85} -1.27497 q^{86} +3.13766 q^{87} +0.0662417 q^{88} -3.38869 q^{89} +1.81494 q^{90} -0.233840 q^{91} -5.13895 q^{92} -3.76141 q^{93} +1.86363 q^{94} -3.98279 q^{95} +2.19430 q^{96} +15.8779 q^{97} -11.6199 q^{98} -0.120225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * 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
$3$	−2.19430	−1.26688	−0.633439	−	0.773793i	$-0.718357\pi$
$3$	−2.19430	−1.26688	−0.633439	+	0.773793i	$0.718357\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.19430	0.895818
$7$	−4.31508	−1.63095	−0.815474	−	0.578793i	$-0.803524\pi$
$7$	−4.31508	−1.63095	−0.815474	+	0.578793i	$0.803524\pi$
$8$	−1.00000	−0.353553
$9$	1.81494	0.604981
$10$	1.00000	0.316228
$11$	−0.0662417	−0.0199726	−0.00998631	−	0.999950i	$-0.503179\pi$
$11$	−0.0662417	−0.0199726	−0.00998631	+	0.999950i	$0.503179\pi$
$12$	−2.19430	−0.633439
$13$	0.0541913	0.0150300	0.00751498	−	0.999972i	$-0.497608\pi$
$13$	0.0541913	0.0150300	0.00751498	+	0.999972i	$0.497608\pi$
$14$	4.31508	1.15325
$15$	2.19430	0.566565
$16$	1.00000	0.250000
$17$	−4.82060	−1.16917	−0.584583	−	0.811334i	$-0.698742\pi$
$17$	−4.82060	−1.16917	−0.584583	+	0.811334i	$0.698742\pi$
$18$	−1.81494	−0.427786
$19$	3.98279	0.913716	0.456858	−	0.889540i	$-0.348975\pi$
$19$	3.98279	0.913716	0.456858	+	0.889540i	$0.348975\pi$
$20$	−1.00000	−0.223607
$21$	9.46858	2.06621
$22$	0.0662417	0.0141228
$23$	−5.13895	−1.07155	−0.535773	−	0.844362i	$-0.679980\pi$
$23$	−5.13895	−1.07155	−0.535773	+	0.844362i	$0.679980\pi$
$24$	2.19430	0.447909
$25$	1.00000	0.200000
$26$	−0.0541913	−0.0106278
$27$	2.60037	0.500441
$28$	−4.31508	−0.815474
$29$	−1.42992	−0.265529	−0.132764	−	0.991148i	$-0.542385\pi$
$29$	−1.42992	−0.265529	−0.132764	+	0.991148i	$0.542385\pi$
$30$	−2.19430	−0.400622
$31$	1.71418	0.307875	0.153938	−	0.988081i	$-0.450805\pi$
$31$	1.71418	0.307875	0.153938	+	0.988081i	$0.450805\pi$
$32$	−1.00000	−0.176777
$33$	0.145354	0.0253029
$34$	4.82060	0.826726
$35$	4.31508	0.729382
$36$	1.81494	0.302490
$37$	−0.606775	−0.0997532	−0.0498766	−	0.998755i	$-0.515883\pi$
$37$	−0.606775	−0.0997532	−0.0498766	+	0.998755i	$0.515883\pi$
$38$	−3.98279	−0.646095
$39$	−0.118912	−0.0190411
$40$	1.00000	0.158114
$41$	−8.04158	−1.25588	−0.627942	−	0.778260i	$-0.716102\pi$
$41$	−8.04158	−1.25588	−0.627942	+	0.778260i	$0.716102\pi$
$42$	−9.46858	−1.46103
$43$	1.27497	0.194431	0.0972153	−	0.995263i	$-0.469006\pi$
$43$	1.27497	0.194431	0.0972153	+	0.995263i	$0.469006\pi$
$44$	−0.0662417	−0.00998631
$45$	−1.81494	−0.270556
$46$	5.13895	0.757697
$47$	−1.86363	−0.271839	−0.135919	−	0.990720i	$-0.543399\pi$
$47$	−1.86363	−0.271839	−0.135919	+	0.990720i	$0.543399\pi$
$48$	−2.19430	−0.316720
$49$	11.6199	1.65999
$50$	−1.00000	−0.141421
$51$	10.5778	1.48119
$52$	0.0541913	0.00751498
$53$	13.1197	1.80213	0.901066	−	0.433682i	$-0.142786\pi$
$53$	13.1197	1.80213	0.901066	+	0.433682i	$0.142786\pi$
$54$	−2.60037	−0.353866
$55$	0.0662417	0.00893203
$56$	4.31508	0.576627
$57$	−8.73944	−1.15757
$58$	1.42992	0.187757
$59$	−5.78132	−0.752664	−0.376332	−	0.926485i	$-0.622815\pi$
$59$	−5.78132	−0.752664	−0.376332	+	0.926485i	$0.622815\pi$
$60$	2.19430	0.283283
$61$	9.94732	1.27362	0.636812	−	0.771019i	$-0.280253\pi$
$61$	9.94732	1.27362	0.636812	+	0.771019i	$0.280253\pi$
$62$	−1.71418	−0.217701
$63$	−7.83163	−0.986692
$64$	1.00000	0.125000
$65$	−0.0541913	−0.00672160
$66$	−0.145354	−0.0178918
$67$	4.12669	0.504156	0.252078	−	0.967707i	$-0.418886\pi$
$67$	4.12669	0.504156	0.252078	+	0.967707i	$0.418886\pi$
$68$	−4.82060	−0.584583
$69$	11.2764	1.35752
$70$	−4.31508	−0.515751
$71$	2.43841	0.289386	0.144693	−	0.989477i	$-0.453781\pi$
$71$	2.43841	0.289386	0.144693	+	0.989477i	$0.453781\pi$
$72$	−1.81494	−0.213893
$73$	−2.77590	−0.324895	−0.162447	−	0.986717i	$-0.551939\pi$
$73$	−2.77590	−0.324895	−0.162447	+	0.986717i	$0.551939\pi$
$74$	0.606775	0.0705361
$75$	−2.19430	−0.253376
$76$	3.98279	0.456858
$77$	0.285839	0.0325743
$78$	0.118912	0.0134641
$79$	11.6810	1.31422	0.657110	−	0.753795i	$-0.271779\pi$
$79$	11.6810	1.31422	0.657110	+	0.753795i	$0.271779\pi$
$80$	−1.00000	−0.111803
$81$	−11.1508	−1.23898
$82$	8.04158	0.888044
$83$	1.36527	0.149857	0.0749287	−	0.997189i	$-0.476127\pi$
$83$	1.36527	0.149857	0.0749287	+	0.997189i	$0.476127\pi$
$84$	9.46858	1.03311
$85$	4.82060	0.522867
$86$	−1.27497	−0.137483
$87$	3.13766	0.336393
$88$	0.0662417	0.00706139
$89$	−3.38869	−0.359200	−0.179600	−	0.983740i	$-0.557480\pi$
$89$	−3.38869	−0.359200	−0.179600	+	0.983740i	$0.557480\pi$
$90$	1.81494	0.191312
$91$	−0.233840	−0.0245131
$92$	−5.13895	−0.535773
$93$	−3.76141	−0.390041
$94$	1.86363	0.192219
$95$	−3.98279	−0.408626
$96$	2.19430	0.223955
$97$	15.8779	1.61216	0.806080	−	0.591807i	$-0.201585\pi$
$97$	15.8779	1.61216	0.806080	+	0.591807i	$0.201585\pi$
$98$	−11.6199	−1.17379
$99$	−0.120225	−0.0120831
$100$	1.00000	0.100000
$101$	18.5807	1.84885	0.924425	−	0.381364i	$-0.124545\pi$
$101$	18.5807	1.84885	0.924425	+	0.381364i	$0.124545\pi$
$102$	−10.5778	−1.04736
$103$	−9.88328	−0.973829	−0.486914	−	0.873450i	$-0.661878\pi$
$103$	−9.88328	−0.973829	−0.486914	+	0.873450i	$0.661878\pi$
$104$	−0.0541913	−0.00531389
$105$	−9.46858	−0.924039
$106$	−13.1197	−1.27430
$107$	−6.48595	−0.627020	−0.313510	−	0.949585i	$-0.601505\pi$
$107$	−6.48595	−0.627020	−0.313510	+	0.949585i	$0.601505\pi$
$108$	2.60037	0.250221
$109$	14.7328	1.41115	0.705574	−	0.708636i	$-0.250689\pi$
$109$	14.7328	1.41115	0.705574	+	0.708636i	$0.250689\pi$
$110$	−0.0662417	−0.00631590
$111$	1.33144	0.126375
$112$	−4.31508	−0.407737
$113$	7.66754	0.721302	0.360651	−	0.932701i	$-0.382555\pi$
$113$	7.66754	0.721302	0.360651	+	0.932701i	$0.382555\pi$
$114$	8.73944	0.818523
$115$	5.13895	0.479210
$116$	−1.42992	−0.132764
$117$	0.0983540	0.00909283
$118$	5.78132	0.532214
$119$	20.8013	1.90685
$120$	−2.19430	−0.200311
$121$	−10.9956	−0.999601
$122$	−9.94732	−0.900588
$123$	17.6456	1.59105
$124$	1.71418	0.153938
$125$	−1.00000	−0.0894427
$126$	7.83163	0.697697
$127$	−20.0564	−1.77972	−0.889860	−	0.456234i	$-0.849198\pi$
$127$	−20.0564	−1.77972	−0.889860	+	0.456234i	$0.849198\pi$
$128$	−1.00000	−0.0883883
$129$	−2.79766	−0.246320
$130$	0.0541913	0.00475289
$131$	13.1144	1.14581	0.572907	−	0.819621i	$-0.305816\pi$
$131$	13.1144	1.14581	0.572907	+	0.819621i	$0.305816\pi$
$132$	0.145354	0.0126514
$133$	−17.1861	−1.49022
$134$	−4.12669	−0.356492
$135$	−2.60037	−0.223804
$136$	4.82060	0.413363
$137$	4.38725	0.374828	0.187414	−	0.982281i	$-0.439989\pi$
$137$	4.38725	0.374828	0.187414	+	0.982281i	$0.439989\pi$
$138$	−11.2764	−0.959910
$139$	1.82934	0.155163	0.0775814	−	0.996986i	$-0.475280\pi$
$139$	1.82934	0.155163	0.0775814	+	0.996986i	$0.475280\pi$
$140$	4.31508	0.364691
$141$	4.08937	0.344387
$142$	−2.43841	−0.204627
$143$	−0.00358972	−0.000300188 0
$144$	1.81494	0.151245
$145$	1.42992	0.118748
$146$	2.77590	0.229735
$147$	−25.4976	−2.10301
$148$	−0.606775	−0.0498766
$149$	−7.33097	−0.600577	−0.300288	−	0.953848i	$-0.597083\pi$
$149$	−7.33097	−0.600577	−0.300288	+	0.953848i	$0.597083\pi$
$150$	2.19430	0.179164
$151$	−9.80549	−0.797959	−0.398980	−	0.916960i	$-0.630636\pi$
$151$	−9.80549	−0.797959	−0.398980	+	0.916960i	$0.630636\pi$
$152$	−3.98279	−0.323047
$153$	−8.74911	−0.707323
$154$	−0.285839	−0.0230335
$155$	−1.71418	−0.137686
$156$	−0.118912	−0.00952056
$157$	−8.42739	−0.672579	−0.336290	−	0.941759i	$-0.609172\pi$
$157$	−8.42739	−0.672579	−0.336290	+	0.941759i	$0.609172\pi$
$158$	−11.6810	−0.929294
$159$	−28.7886	−2.28308
$160$	1.00000	0.0790569
$161$	22.1750	1.74763
$162$	11.1508	0.876091
$163$	19.1915	1.50319	0.751596	−	0.659623i	$-0.229284\pi$
$163$	19.1915	1.50319	0.751596	+	0.659623i	$0.229284\pi$
$164$	−8.04158	−0.627942
$165$	−0.145354	−0.0113158
$166$	−1.36527	−0.105965
$167$	−2.89654	−0.224141	−0.112070	−	0.993700i	$-0.535748\pi$
$167$	−2.89654	−0.224141	−0.112070	+	0.993700i	$0.535748\pi$
$168$	−9.46858	−0.730517
$169$	−12.9971	−0.999774
$170$	−4.82060	−0.369723
$171$	7.22854	0.552780
$172$	1.27497	0.0972153
$173$	−0.364956	−0.0277471	−0.0138735	−	0.999904i	$-0.504416\pi$
$173$	−0.364956	−0.0277471	−0.0138735	+	0.999904i	$0.504416\pi$
$174$	−3.13766	−0.237865
$175$	−4.31508	−0.326190
$176$	−0.0662417	−0.00499316
$177$	12.6859	0.953534
$178$	3.38869	0.253993
$179$	10.4261	0.779285	0.389642	−	0.920966i	$-0.372599\pi$
$179$	10.4261	0.779285	0.389642	+	0.920966i	$0.372599\pi$
$180$	−1.81494	−0.135278
$181$	22.5485	1.67601	0.838007	−	0.545660i	$-0.183721\pi$
$181$	22.5485	1.67601	0.838007	+	0.545660i	$0.183721\pi$
$182$	0.233840	0.0173334
$183$	−21.8274	−1.61353
$184$	5.13895	0.378848
$185$	0.606775	0.0446110
$186$	3.76141	0.275800
$187$	0.319325	0.0233513
$188$	−1.86363	−0.135919
$189$	−11.2208	−0.816194
$190$	3.98279	0.288942
$191$	−12.8673	−0.931047	−0.465524	−	0.885035i	$-0.654134\pi$
$191$	−12.8673	−0.931047	−0.465524	+	0.885035i	$0.654134\pi$
$192$	−2.19430	−0.158360
$193$	17.2481	1.24155	0.620774	−	0.783989i	$-0.286818\pi$
$193$	17.2481	1.24155	0.620774	+	0.783989i	$0.286818\pi$
$194$	−15.8779	−1.13997
$195$	0.118912	0.00851545
$196$	11.6199	0.829996
$197$	−5.04832	−0.359678	−0.179839	−	0.983696i	$-0.557558\pi$
$197$	−5.04832	−0.359678	−0.179839	+	0.983696i	$0.557558\pi$
$198$	0.120225	0.00854401
$199$	−4.82441	−0.341993	−0.170997	−	0.985272i	$-0.554699\pi$
$199$	−4.82441	−0.341993	−0.170997	+	0.985272i	$0.554699\pi$
$200$	−1.00000	−0.0707107
$201$	−9.05519	−0.638704
$202$	−18.5807	−1.30733
$203$	6.17021	0.433064
$204$	10.5778	0.740596
$205$	8.04158	0.561648
$206$	9.88328	0.688601
$207$	−9.32689	−0.648264
$208$	0.0541913	0.00375749
$209$	−0.263827	−0.0182493
$210$	9.46858	0.653394
$211$	−13.4421	−0.925391	−0.462695	−	0.886517i	$-0.653118\pi$
$211$	−13.4421	−0.925391	−0.462695	+	0.886517i	$0.653118\pi$
$212$	13.1197	0.901066
$213$	−5.35060	−0.366617
$214$	6.48595	0.443370
$215$	−1.27497	−0.0869520
$216$	−2.60037	−0.176933
$217$	−7.39682	−0.502129
$218$	−14.7328	−0.997833
$219$	6.09115	0.411602
$220$	0.0662417	0.00446602
$221$	−0.261234	−0.0175725
$222$	−1.33144	−0.0893607
$223$	−6.54599	−0.438352	−0.219176	−	0.975685i	$-0.570337\pi$
$223$	−6.54599	−0.438352	−0.219176	+	0.975685i	$0.570337\pi$
$224$	4.31508	0.288314
$225$	1.81494	0.120996
$226$	−7.66754	−0.510037
$227$	−5.45316	−0.361939	−0.180970	−	0.983489i	$-0.557924\pi$
$227$	−5.45316	−0.361939	−0.180970	+	0.983489i	$0.557924\pi$
$228$	−8.73944	−0.578783
$229$	19.0008	1.25561	0.627805	−	0.778371i	$-0.283954\pi$
$229$	19.0008	1.25561	0.627805	+	0.778371i	$0.283954\pi$
$230$	−5.13895	−0.338852
$231$	−0.627215	−0.0412677
$232$	1.42992	0.0938786
$233$	14.8386	0.972109	0.486055	−	0.873928i	$-0.338436\pi$
$233$	14.8386	0.972109	0.486055	+	0.873928i	$0.338436\pi$
$234$	−0.0983540	−0.00642960
$235$	1.86363	0.121570
$236$	−5.78132	−0.376332
$237$	−25.6317	−1.66496
$238$	−20.8013	−1.34835
$239$	26.5313	1.71617	0.858083	−	0.513510i	$-0.171655\pi$
$239$	26.5313	1.71617	0.858083	+	0.513510i	$0.171655\pi$
$240$	2.19430	0.141641
$241$	−6.83681	−0.440398	−0.220199	−	0.975455i	$-0.570671\pi$
$241$	−6.83681	−0.440398	−0.220199	+	0.975455i	$0.570671\pi$
$242$	10.9956	0.706825
$243$	16.6671	1.06919
$244$	9.94732	0.636812
$245$	−11.6199	−0.742371
$246$	−17.6456	−1.12504
$247$	0.215833	0.0137331
$248$	−1.71418	−0.108850
$249$	−2.99580	−0.189851
$250$	1.00000	0.0632456
$251$	−18.5243	−1.16924	−0.584622	−	0.811306i	$-0.698757\pi$
$251$	−18.5243	−1.16924	−0.584622	+	0.811306i	$0.698757\pi$
$252$	−7.83163	−0.493346
$253$	0.340413	0.0214016
$254$	20.0564	1.25845
$255$	−10.5778	−0.662409
$256$	1.00000	0.0625000
$257$	25.2032	1.57213	0.786065	−	0.618143i	$-0.212115\pi$
$257$	25.2032	1.57213	0.786065	+	0.618143i	$0.212115\pi$
$258$	2.79766	0.174174
$259$	2.61828	0.162692
$260$	−0.0541913	−0.00336080
$261$	−2.59521	−0.160640
$262$	−13.1144	−0.810212
$263$	−16.3683	−1.00931	−0.504656	−	0.863321i	$-0.668381\pi$
$263$	−16.3683	−1.00931	−0.504656	+	0.863321i	$0.668381\pi$
$264$	−0.145354	−0.00894592
$265$	−13.1197	−0.805938
$266$	17.1861	1.05375
$267$	7.43578	0.455063
$268$	4.12669	0.252078
$269$	−15.0739	−0.919069	−0.459535	−	0.888160i	$-0.651984\pi$
$269$	−15.0739	−0.919069	−0.459535	+	0.888160i	$0.651984\pi$
$270$	2.60037	0.158253
$271$	−15.4917	−0.941051	−0.470526	−	0.882386i	$-0.655936\pi$
$271$	−15.4917	−0.941051	−0.470526	+	0.882386i	$0.655936\pi$
$272$	−4.82060	−0.292292
$273$	0.513114	0.0310551
$274$	−4.38725	−0.265043
$275$	−0.0662417	−0.00399453
$276$	11.2764	0.678759
$277$	4.65077	0.279438	0.139719	−	0.990191i	$-0.455380\pi$
$277$	4.65077	0.279438	0.139719	+	0.990191i	$0.455380\pi$
$278$	−1.82934	−0.109717
$279$	3.11113	0.186259
$280$	−4.31508	−0.257876
$281$	−14.0142	−0.836016	−0.418008	−	0.908443i	$-0.637272\pi$
$281$	−14.0142	−0.836016	−0.418008	+	0.908443i	$0.637272\pi$
$282$	−4.08937	−0.243518
$283$	−7.76117	−0.461353	−0.230677	−	0.973030i	$-0.574094\pi$
$283$	−7.76117	−0.461353	−0.230677	+	0.973030i	$0.574094\pi$
$284$	2.43841	0.144693
$285$	8.73944	0.517680
$286$	0.00358972	0.000212265 0
$287$	34.7001	2.04828
$288$	−1.81494	−0.106946
$289$	6.23817	0.366951
$290$	−1.42992	−0.0839676
$291$	−34.8409	−2.04241
$292$	−2.77590	−0.162447
$293$	25.6620	1.49919	0.749594	−	0.661898i	$-0.230249\pi$
$293$	25.6620	1.49919	0.749594	+	0.661898i	$0.230249\pi$
$294$	25.4976	1.48705
$295$	5.78132	0.336602
$296$	0.606775	0.0352681
$297$	−0.172253	−0.00999513
$298$	7.33097	0.424672
$299$	−0.278486	−0.0161053
$300$	−2.19430	−0.126688
$301$	−5.50159	−0.317106
$302$	9.80549	0.564242
$303$	−40.7716	−2.34227
$304$	3.98279	0.228429
$305$	−9.94732	−0.569582
$306$	8.74911	0.500153
$307$	−8.81675	−0.503198	−0.251599	−	0.967832i	$-0.580956\pi$
$307$	−8.81675	−0.503198	−0.251599	+	0.967832i	$0.580956\pi$
$308$	0.285839	0.0162872
$309$	21.6869	1.23372
$310$	1.71418	0.0973587
$311$	0.857921	0.0486482	0.0243241	−	0.999704i	$-0.492257\pi$
$311$	0.857921	0.0486482	0.0243241	+	0.999704i	$0.492257\pi$
$312$	0.118912	0.00673205
$313$	−10.3858	−0.587042	−0.293521	−	0.955953i	$-0.594827\pi$
$313$	−10.3858	−0.587042	−0.293521	+	0.955953i	$0.594827\pi$
$314$	8.42739	0.475585
$315$	7.83163	0.441262
$316$	11.6810	0.657110
$317$	−19.5926	−1.10043	−0.550215	−	0.835023i	$-0.685454\pi$
$317$	−19.5926	−1.10043	−0.550215	+	0.835023i	$0.685454\pi$
$318$	28.7886	1.61438
$319$	0.0947201	0.00530331
$320$	−1.00000	−0.0559017
$321$	14.2321	0.794358
$322$	−22.1750	−1.23576
$323$	−19.1995	−1.06829
$324$	−11.1508	−0.619490
$325$	0.0541913	0.00300599
$326$	−19.1915	−1.06292
$327$	−32.3282	−1.78775
$328$	8.04158	0.444022
$329$	8.04173	0.443355
$330$	0.145354	0.00800148
$331$	−8.98651	−0.493943	−0.246972	−	0.969023i	$-0.579435\pi$
$331$	−8.98651	−0.493943	−0.246972	+	0.969023i	$0.579435\pi$
$332$	1.36527	0.0749287
$333$	−1.10126	−0.0603487
$334$	2.89654	0.158492
$335$	−4.12669	−0.225465
$336$	9.46858	0.516553
$337$	12.1432	0.661480	0.330740	−	0.943722i	$-0.392702\pi$
$337$	12.1432	0.661480	0.330740	+	0.943722i	$0.392702\pi$
$338$	12.9971	0.706947
$339$	−16.8249	−0.913801
$340$	4.82060	0.261434
$341$	−0.113550	−0.00614908
$342$	−7.22854	−0.390875
$343$	−19.9355	−1.07641
$344$	−1.27497	−0.0687416
$345$	−11.2764	−0.607100
$346$	0.364956	0.0196202
$347$	8.51249	0.456974	0.228487	−	0.973547i	$-0.426622\pi$
$347$	8.51249	0.456974	0.228487	+	0.973547i	$0.426622\pi$
$348$	3.13766	0.168196
$349$	−1.84807	−0.0989250	−0.0494625	−	0.998776i	$-0.515751\pi$
$349$	−1.84807	−0.0989250	−0.0494625	+	0.998776i	$0.515751\pi$
$350$	4.31508	0.230651
$351$	0.140917	0.00752161
$352$	0.0662417	0.00353070
$353$	−18.5251	−0.985991	−0.492996	−	0.870032i	$-0.664098\pi$
$353$	−18.5251	−0.985991	−0.492996	+	0.870032i	$0.664098\pi$
$354$	−12.6859	−0.674250
$355$	−2.43841	−0.129417
$356$	−3.38869	−0.179600
$357$	−45.6442	−2.41575
$358$	−10.4261	−0.551037
$359$	−14.5348	−0.767115	−0.383558	−	0.923517i	$-0.625301\pi$
$359$	−14.5348	−0.767115	−0.383558	+	0.923517i	$0.625301\pi$
$360$	1.81494	0.0956558
$361$	−3.13734	−0.165123
$362$	−22.5485	−1.18512
$363$	24.1276	1.26637
$364$	−0.233840	−0.0122565
$365$	2.77590	0.145297
$366$	21.8274	1.14094
$367$	−18.7842	−0.980526	−0.490263	−	0.871574i	$-0.663099\pi$
$367$	−18.7842	−0.980526	−0.490263	+	0.871574i	$0.663099\pi$
$368$	−5.13895	−0.267886
$369$	−14.5950	−0.759785
$370$	−0.606775	−0.0315447
$371$	−56.6127	−2.93918
$372$	−3.76141	−0.195020
$373$	14.5991	0.755910	0.377955	−	0.925824i	$-0.376627\pi$
$373$	14.5991	0.755910	0.377955	+	0.925824i	$0.376627\pi$
$374$	−0.319325	−0.0165119
$375$	2.19430	0.113313
$376$	1.86363	0.0961095
$377$	−0.0774890	−0.00399088
$378$	11.2208	0.577136
$379$	−1.03534	−0.0531817	−0.0265908	−	0.999646i	$-0.508465\pi$
$379$	−1.03534	−0.0531817	−0.0265908	+	0.999646i	$0.508465\pi$
$380$	−3.98279	−0.204313
$381$	44.0098	2.25469
$382$	12.8673	0.658350
$383$	−12.1048	−0.618527	−0.309264	−	0.950976i	$-0.600083\pi$
$383$	−12.1048	−0.618527	−0.309264	+	0.950976i	$0.600083\pi$
$384$	2.19430	0.111977
$385$	−0.285839	−0.0145677
$386$	−17.2481	−0.877908
$387$	2.31399	0.117627
$388$	15.8779	0.806080
$389$	−31.7441	−1.60949	−0.804744	−	0.593622i	$-0.797698\pi$
$389$	−31.7441	−1.60949	−0.804744	+	0.593622i	$0.797698\pi$
$390$	−0.118912	−0.00602133
$391$	24.7728	1.25282
$392$	−11.6199	−0.586896
$393$	−28.7770	−1.45161
$394$	5.04832	0.254331
$395$	−11.6810	−0.587737
$396$	−0.120225	−0.00604153
$397$	35.3985	1.77660	0.888301	−	0.459262i	$-0.151886\pi$
$397$	35.3985	1.77660	0.888301	+	0.459262i	$0.151886\pi$
$398$	4.82441	0.241826
$399$	37.7114	1.88793
$400$	1.00000	0.0500000
$401$	20.2963	1.01355	0.506774	−	0.862079i	$-0.330838\pi$
$401$	20.2963	1.01355	0.506774	+	0.862079i	$0.330838\pi$
$402$	9.05519	0.451632
$403$	0.0928934	0.00462735
$404$	18.5807	0.924425
$405$	11.1508	0.554088
$406$	−6.17021	−0.306222
$407$	0.0401938	0.00199233
$408$	−10.5778	−0.523681
$409$	7.00402	0.346327	0.173163	−	0.984893i	$-0.444601\pi$
$409$	7.00402	0.346327	0.173163	+	0.984893i	$0.444601\pi$
$410$	−8.04158	−0.397145
$411$	−9.62693	−0.474861
$412$	−9.88328	−0.486914
$413$	24.9469	1.22756
$414$	9.32689	0.458392
$415$	−1.36527	−0.0670182
$416$	−0.0541913	−0.00265695
$417$	−4.01412	−0.196573
$418$	0.263827	0.0129042
$419$	−19.8953	−0.971950	−0.485975	−	0.873973i	$-0.661535\pi$
$419$	−19.8953	−0.971950	−0.485975	+	0.873973i	$0.661535\pi$
$420$	−9.46858	−0.462019
$421$	0.0991055	0.00483011	0.00241505	−	0.999997i	$-0.499231\pi$
$421$	0.0991055	0.00483011	0.00241505	+	0.999997i	$0.499231\pi$
$422$	13.4421	0.654350
$423$	−3.38239	−0.164457
$424$	−13.1197	−0.637150
$425$	−4.82060	−0.233833
$426$	5.35060	0.259237
$427$	−42.9235	−2.07722
$428$	−6.48595	−0.313510
$429$	0.00787692	0.000380301 0
$430$	1.27497	0.0614843
$431$	−25.5837	−1.23232	−0.616162	−	0.787620i	$-0.711313\pi$
$431$	−25.5837	−1.23232	−0.616162	+	0.787620i	$0.711313\pi$
$432$	2.60037	0.125110
$433$	−12.5321	−0.602255	−0.301128	−	0.953584i	$-0.597363\pi$
$433$	−12.5321	−0.602255	−0.301128	+	0.953584i	$0.597363\pi$
$434$	7.39682	0.355059
$435$	−3.13766	−0.150439
$436$	14.7328	0.705574
$437$	−20.4674	−0.979088
$438$	−6.09115	−0.291047
$439$	11.7705	0.561774	0.280887	−	0.959741i	$-0.409371\pi$
$439$	11.7705	0.561774	0.280887	+	0.959741i	$0.409371\pi$
$440$	−0.0662417	−0.00315795
$441$	21.0895	1.00426
$442$	0.261234	0.0124257
$443$	21.2953	1.01177	0.505885	−	0.862601i	$-0.331166\pi$
$443$	21.2953	1.01177	0.505885	+	0.862601i	$0.331166\pi$
$444$	1.33144	0.0631876
$445$	3.38869	0.160639
$446$	6.54599	0.309962
$447$	16.0863	0.760858
$448$	−4.31508	−0.203869
$449$	34.4718	1.62682	0.813412	−	0.581688i	$-0.197608\pi$
$449$	34.4718	1.62682	0.813412	+	0.581688i	$0.197608\pi$
$450$	−1.81494	−0.0855572
$451$	0.532688	0.0250833
$452$	7.66754	0.360651
$453$	21.5162	1.01092
$454$	5.45316	0.255930
$455$	0.233840	0.0109626
$456$	8.73944	0.409262
$457$	30.1186	1.40889	0.704445	−	0.709758i	$-0.251196\pi$
$457$	30.1186	1.40889	0.704445	+	0.709758i	$0.251196\pi$
$458$	−19.0008	−0.887850
$459$	−12.5353	−0.585100
$460$	5.13895	0.239605
$461$	−9.69215	−0.451408	−0.225704	−	0.974196i	$-0.572468\pi$
$461$	−9.69215	−0.451408	−0.225704	+	0.974196i	$0.572468\pi$
$462$	0.627215	0.0291807
$463$	8.82806	0.410275	0.205137	−	0.978733i	$-0.434236\pi$
$463$	8.82806	0.410275	0.205137	+	0.978733i	$0.434236\pi$
$464$	−1.42992	−0.0663822
$465$	3.76141	0.174431
$466$	−14.8386	−0.687385
$467$	11.6580	0.539469	0.269734	−	0.962935i	$-0.413064\pi$
$467$	11.6580	0.539469	0.269734	+	0.962935i	$0.413064\pi$
$468$	0.0983540	0.00454642
$469$	−17.8070	−0.822252
$470$	−1.86363	−0.0859630
$471$	18.4922	0.852076
$472$	5.78132	0.266107
$473$	−0.0844560	−0.00388329
$474$	25.6317	1.17730
$475$	3.98279	0.182743
$476$	20.8013	0.953425
$477$	23.8115	1.09025
$478$	−26.5313	−1.21351
$479$	−41.1535	−1.88035	−0.940175	−	0.340692i	$-0.889339\pi$
$479$	−41.1535	−1.88035	−0.940175	+	0.340692i	$0.889339\pi$
$480$	−2.19430	−0.100156
$481$	−0.0328819	−0.00149929
$482$	6.83681	0.311408
$483$	−48.6585	−2.21404
$484$	−10.9956	−0.499801
$485$	−15.8779	−0.720980
$486$	−16.6671	−0.756034
$487$	4.65074	0.210745	0.105373	−	0.994433i	$-0.466396\pi$
$487$	4.65074	0.210745	0.105373	+	0.994433i	$0.466396\pi$
$488$	−9.94732	−0.450294
$489$	−42.1118	−1.90436
$490$	11.6199	0.524936
$491$	−39.1159	−1.76527	−0.882637	−	0.470055i	$-0.844234\pi$
$491$	−39.1159	−1.76527	−0.882637	+	0.470055i	$0.844234\pi$
$492$	17.6456	0.795526
$493$	6.89305	0.310447
$494$	−0.215833	−0.00971077
$495$	0.120225	0.00540371
$496$	1.71418	0.0769688
$497$	−10.5219	−0.471974
$498$	2.99580	0.134245
$499$	7.89965	0.353637	0.176818	−	0.984243i	$-0.443419\pi$
$499$	7.89965	0.353637	0.176818	+	0.984243i	$0.443419\pi$
$500$	−1.00000	−0.0447214
$501$	6.35587	0.283959
$502$	18.5243	0.826780
$503$	−22.3362	−0.995924	−0.497962	−	0.867199i	$-0.665918\pi$
$503$	−22.3362	−0.995924	−0.497962	+	0.867199i	$0.665918\pi$
$504$	7.83163	0.348848
$505$	−18.5807	−0.826831
$506$	−0.340413	−0.0151332
$507$	28.5194	1.26659
$508$	−20.0564	−0.889860
$509$	−11.0310	−0.488941	−0.244470	−	0.969657i	$-0.578614\pi$
$509$	−11.0310	−0.488941	−0.244470	+	0.969657i	$0.578614\pi$
$510$	10.5778	0.468394
$511$	11.9782	0.529886
$512$	−1.00000	−0.0441942
$513$	10.3567	0.457261
$514$	−25.2032	−1.11166
$515$	9.88328	0.435509
$516$	−2.79766	−0.123160
$517$	0.123450	0.00542934
$518$	−2.61828	−0.115041
$519$	0.800822	0.0351522
$520$	0.0541913	0.00237644
$521$	−35.7606	−1.56670	−0.783350	−	0.621581i	$-0.786491\pi$
$521$	−35.7606	−1.56670	−0.783350	+	0.621581i	$0.786491\pi$
$522$	2.59521	0.113589
$523$	−37.5807	−1.64329	−0.821645	−	0.570000i	$-0.806943\pi$
$523$	−37.5807	−1.64329	−0.821645	+	0.570000i	$0.806943\pi$
$524$	13.1144	0.572907
$525$	9.46858	0.413243
$526$	16.3683	0.713691
$527$	−8.26336	−0.359958
$528$	0.145354	0.00632572
$529$	3.40880	0.148209
$530$	13.1197	0.569884
$531$	−10.4928	−0.455347
$532$	−17.1861	−0.745112
$533$	−0.435783	−0.0188759
$534$	−7.43578	−0.321778
$535$	6.48595	0.280412
$536$	−4.12669	−0.178246
$537$	−22.8780	−0.987259
$538$	15.0739	0.649880
$539$	−0.769725	−0.0331544
$540$	−2.60037	−0.111902
$541$	−0.649328	−0.0279168	−0.0139584	−	0.999903i	$-0.504443\pi$
$541$	−0.649328	−0.0279168	−0.0139584	+	0.999903i	$0.504443\pi$
$542$	15.4917	0.665424
$543$	−49.4780	−2.12331
$544$	4.82060	0.206681
$545$	−14.7328	−0.631085
$546$	−0.513114	−0.0219593
$547$	25.4912	1.08993	0.544963	−	0.838460i	$-0.316544\pi$
$547$	25.4912	1.08993	0.544963	+	0.838460i	$0.316544\pi$
$548$	4.38725	0.187414
$549$	18.0538	0.770518
$550$	0.0662417	0.00282456
$551$	−5.69506	−0.242618
$552$	−11.2764	−0.479955
$553$	−50.4047	−2.14342
$554$	−4.65077	−0.197592
$555$	−1.33144	−0.0565167
$556$	1.82934	0.0775814
$557$	25.7384	1.09057	0.545286	−	0.838250i	$-0.316421\pi$
$557$	25.7384	1.09057	0.545286	+	0.838250i	$0.316421\pi$
$558$	−3.11113	−0.131705
$559$	0.0690921	0.00292228
$560$	4.31508	0.182346
$561$	−0.700694	−0.0295833
$562$	14.0142	0.591153
$563$	−17.2228	−0.725855	−0.362927	−	0.931817i	$-0.618223\pi$
$563$	−17.2228	−0.725855	−0.362927	+	0.931817i	$0.618223\pi$
$564$	4.08937	0.172193
$565$	−7.66754	−0.322576
$566$	7.76117	0.326226
$567$	48.1167	2.02071
$568$	−2.43841	−0.102313
$569$	3.06373	0.128438	0.0642191	−	0.997936i	$-0.479544\pi$
$569$	3.06373	0.128438	0.0642191	+	0.997936i	$0.479544\pi$
$570$	−8.73944	−0.366055
$571$	−21.0132	−0.879374	−0.439687	−	0.898151i	$-0.644911\pi$
$571$	−21.0132	−0.879374	−0.439687	+	0.898151i	$0.644911\pi$
$572$	−0.00358972	−0.000150094 0
$573$	28.2348	1.17952
$574$	−34.7001	−1.44835
$575$	−5.13895	−0.214309
$576$	1.81494	0.0756226
$577$	−45.8624	−1.90928	−0.954638	−	0.297768i	$-0.903758\pi$
$577$	−45.8624	−1.90928	−0.954638	+	0.297768i	$0.903758\pi$
$578$	−6.23817	−0.259474
$579$	−37.8476	−1.57289
$580$	1.42992	0.0593740
$581$	−5.89123	−0.244410
$582$	34.8409	1.44420
$583$	−0.869073	−0.0359933
$584$	2.77590	0.114868
$585$	−0.0983540	−0.00406644
$586$	−25.6620	−1.06009
$587$	4.35082	0.179578	0.0897888	−	0.995961i	$-0.471381\pi$
$587$	4.35082	0.179578	0.0897888	+	0.995961i	$0.471381\pi$
$588$	−25.4976	−1.05150
$589$	6.82722	0.281311
$590$	−5.78132	−0.238013
$591$	11.0775	0.455668
$592$	−0.606775	−0.0249383
$593$	−6.67845	−0.274251	−0.137126	−	0.990554i	$-0.543786\pi$
$593$	−6.67845	−0.274251	−0.137126	+	0.990554i	$0.543786\pi$
$594$	0.172253	0.00706763
$595$	−20.8013	−0.852770
$596$	−7.33097	−0.300288
$597$	10.5862	0.433264
$598$	0.278486	0.0113881
$599$	4.31331	0.176237	0.0881185	−	0.996110i	$-0.471915\pi$
$599$	4.31331	0.176237	0.0881185	+	0.996110i	$0.471915\pi$
$600$	2.19430	0.0895818
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	5.50159	0.224228
$603$	7.48971	0.305004
$604$	−9.80549	−0.398980
$605$	10.9956	0.447035
$606$	40.7716	1.65623
$607$	−23.6174	−0.958601	−0.479300	−	0.877651i	$-0.659110\pi$
$607$	−23.6174	−0.958601	−0.479300	+	0.877651i	$0.659110\pi$
$608$	−3.98279	−0.161524
$609$	−13.5393	−0.548639
$610$	9.94732	0.402755
$611$	−0.100993	−0.00408573
$612$	−8.74911	−0.353662
$613$	−19.7813	−0.798959	−0.399480	−	0.916742i	$-0.630809\pi$
$613$	−19.7813	−0.798959	−0.399480	+	0.916742i	$0.630809\pi$
$614$	8.81675	0.355815
$615$	−17.6456	−0.711540
$616$	−0.285839	−0.0115168
$617$	−14.5048	−0.583941	−0.291970	−	0.956427i	$-0.594311\pi$
$617$	−14.5048	−0.583941	−0.291970	+	0.956427i	$0.594311\pi$
$618$	−21.6869	−0.872374
$619$	25.4749	1.02392	0.511962	−	0.859008i	$-0.328919\pi$
$619$	25.4749	1.02392	0.511962	+	0.859008i	$0.328919\pi$
$620$	−1.71418	−0.0688430
$621$	−13.3632	−0.536246
$622$	−0.857921	−0.0343995
$623$	14.6225	0.585837
$624$	−0.118912	−0.00476028
$625$	1.00000	0.0400000
$626$	10.3858	0.415102
$627$	0.578915	0.0231197
$628$	−8.42739	−0.336290
$629$	2.92502	0.116628
$630$	−7.83163	−0.312019
$631$	31.8166	1.26660	0.633300	−	0.773907i	$-0.281700\pi$
$631$	31.8166	1.26660	0.633300	+	0.773907i	$0.281700\pi$
$632$	−11.6810	−0.464647
$633$	29.4959	1.17236
$634$	19.5926	0.778122
$635$	20.0564	0.795915
$636$	−28.7886	−1.14154
$637$	0.629700	0.0249496
$638$	−0.0947201	−0.00375000
$639$	4.42557	0.175073
$640$	1.00000	0.0395285
$641$	3.55435	0.140388	0.0701941	−	0.997533i	$-0.477638\pi$
$641$	3.55435	0.140388	0.0701941	+	0.997533i	$0.477638\pi$
$642$	−14.2321	−0.561696
$643$	−42.1467	−1.66210	−0.831051	−	0.556196i	$-0.812260\pi$
$643$	−42.1467	−1.66210	−0.831051	+	0.556196i	$0.812260\pi$
$644$	22.1750	0.873817
$645$	2.79766	0.110158
$646$	19.1995	0.755393
$647$	36.9972	1.45451	0.727255	−	0.686368i	$-0.240796\pi$
$647$	36.9972	1.45451	0.727255	+	0.686368i	$0.240796\pi$
$648$	11.1508	0.438045
$649$	0.382965	0.0150327
$650$	−0.0541913	−0.00212556
$651$	16.2308	0.636136
$652$	19.1915	0.751596
$653$	−42.6246	−1.66803	−0.834015	−	0.551741i	$-0.813964\pi$
$653$	−42.6246	−1.66803	−0.834015	+	0.551741i	$0.813964\pi$
$654$	32.3282	1.26413
$655$	−13.1144	−0.512423
$656$	−8.04158	−0.313971
$657$	−5.03810	−0.196555
$658$	−8.04173	−0.313499
$659$	50.7280	1.97608	0.988040	−	0.154195i	$-0.0492785\pi$
$659$	50.7280	1.97608	0.988040	+	0.154195i	$0.0492785\pi$
$660$	−0.145354	−0.00565790
$661$	−7.90028	−0.307285	−0.153643	−	0.988126i	$-0.549100\pi$
$661$	−7.90028	−0.307285	−0.153643	+	0.988126i	$0.549100\pi$
$662$	8.98651	0.349270
$663$	0.573226	0.0222623
$664$	−1.36527	−0.0529826
$665$	17.1861	0.666448
$666$	1.10126	0.0426730
$667$	7.34827	0.284526
$668$	−2.89654	−0.112070
$669$	14.3639	0.555339
$670$	4.12669	0.159428
$671$	−0.658928	−0.0254376
$672$	−9.46858	−0.365258
$673$	9.64103	0.371634	0.185817	−	0.982584i	$-0.440507\pi$
$673$	9.64103	0.371634	0.185817	+	0.982584i	$0.440507\pi$
$674$	−12.1432	−0.467737
$675$	2.60037	0.100088
$676$	−12.9971	−0.499887
$677$	2.81697	0.108265	0.0541325	−	0.998534i	$-0.482761\pi$
$677$	2.81697	0.108265	0.0541325	+	0.998534i	$0.482761\pi$
$678$	16.8249	0.646155
$679$	−68.5146	−2.62935
$680$	−4.82060	−0.184862
$681$	11.9659	0.458533
$682$	0.113550	0.00434806
$683$	−13.3320	−0.510135	−0.255068	−	0.966923i	$-0.582098\pi$
$683$	−13.3320	−0.510135	−0.255068	+	0.966923i	$0.582098\pi$
$684$	7.22854	0.276390
$685$	−4.38725	−0.167628
$686$	19.9355	0.761140
$687$	−41.6935	−1.59071
$688$	1.27497	0.0486076
$689$	0.710974	0.0270860
$690$	11.2764	0.429285
$691$	−8.56864	−0.325967	−0.162983	−	0.986629i	$-0.552112\pi$
$691$	−8.56864	−0.325967	−0.162983	+	0.986629i	$0.552112\pi$
$692$	−0.364956	−0.0138735
$693$	0.518780	0.0197068
$694$	−8.51249	−0.323130
$695$	−1.82934	−0.0693910
$696$	−3.13766	−0.118933
$697$	38.7652	1.46834
$698$	1.84807	0.0699505
$699$	−32.5603	−1.23154
$700$	−4.31508	−0.163095
$701$	−30.5543	−1.15402	−0.577010	−	0.816737i	$-0.695781\pi$
$701$	−30.5543	−1.15402	−0.577010	+	0.816737i	$0.695781\pi$
$702$	−0.140917	−0.00531858
$703$	−2.41666	−0.0911460
$704$	−0.0662417	−0.00249658
$705$	−4.08937	−0.154014
$706$	18.5251	0.697201
$707$	−80.1773	−3.01538
$708$	12.6859	0.476767
$709$	39.8886	1.49805	0.749024	−	0.662543i	$-0.230523\pi$
$709$	39.8886	1.49805	0.749024	+	0.662543i	$0.230523\pi$
$710$	2.43841	0.0915119
$711$	21.2004	0.795077
$712$	3.38869	0.126996
$713$	−8.80907	−0.329902
$714$	45.6442	1.70819
$715$	0.00358972	0.000134248 0
$716$	10.4261	0.389642
$717$	−58.2176	−2.17417
$718$	14.5348	0.542433
$719$	30.8986	1.15232	0.576161	−	0.817336i	$-0.304550\pi$
$719$	30.8986	1.15232	0.576161	+	0.817336i	$0.304550\pi$
$720$	−1.81494	−0.0676389
$721$	42.6472	1.58826
$722$	3.13734	0.116760
$723$	15.0020	0.557930
$724$	22.5485	0.838007
$725$	−1.42992	−0.0531058
$726$	−24.1276	−0.895461
$727$	−2.09074	−0.0775411	−0.0387706	−	0.999248i	$-0.512344\pi$
$727$	−2.09074	−0.0775411	−0.0387706	+	0.999248i	$0.512344\pi$
$728$	0.233840	0.00866668
$729$	−3.12012	−0.115560
$730$	−2.77590	−0.102741
$731$	−6.14610	−0.227322
$732$	−21.8274	−0.806764
$733$	−43.5506	−1.60858	−0.804290	−	0.594237i	$-0.797454\pi$
$733$	−43.5506	−1.60858	−0.804290	+	0.594237i	$0.797454\pi$
$734$	18.7842	0.693337
$735$	25.4976	0.940494
$736$	5.13895	0.189424
$737$	−0.273359	−0.0100693
$738$	14.5950	0.537249
$739$	25.9784	0.955631	0.477815	−	0.878460i	$-0.341429\pi$
$739$	25.9784	0.955631	0.477815	+	0.878460i	$0.341429\pi$
$740$	0.606775	0.0223055
$741$	−0.473601	−0.0173982
$742$	56.6127	2.07832
$743$	−13.4297	−0.492689	−0.246345	−	0.969182i	$-0.579230\pi$
$743$	−13.4297	−0.492689	−0.246345	+	0.969182i	$0.579230\pi$
$744$	3.76141	0.137900
$745$	7.33097	0.268586
$746$	−14.5991	−0.534509
$747$	2.47788	0.0906608
$748$	0.319325	0.0116757
$749$	27.9874	1.02264
$750$	−2.19430	−0.0801244
$751$	20.7461	0.757037	0.378519	−	0.925594i	$-0.376434\pi$
$751$	20.7461	0.757037	0.378519	+	0.925594i	$0.376434\pi$
$752$	−1.86363	−0.0679597
$753$	40.6478	1.48129
$754$	0.0774890	0.00282198
$755$	9.80549	0.356858
$756$	−11.2208	−0.408097
$757$	26.1391	0.950041	0.475021	−	0.879975i	$-0.342441\pi$
$757$	26.1391	0.950041	0.475021	+	0.879975i	$0.342441\pi$
$758$	1.03534	0.0376051
$759$	−0.746967	−0.0271132
$760$	3.98279	0.144471
$761$	−4.71931	−0.171075	−0.0855374	−	0.996335i	$-0.527261\pi$
$761$	−4.71931	−0.171075	−0.0855374	+	0.996335i	$0.527261\pi$
$762$	−44.0098	−1.59431
$763$	−63.5734	−2.30151
$764$	−12.8673	−0.465524
$765$	8.74911	0.316325
$766$	12.1048	0.437365
$767$	−0.313297	−0.0113125
$768$	−2.19430	−0.0791799
$769$	−49.5965	−1.78850	−0.894248	−	0.447571i	$-0.852289\pi$
$769$	−49.5965	−1.78850	−0.894248	+	0.447571i	$0.852289\pi$
$770$	0.285839	0.0103009
$771$	−55.3033	−1.99170
$772$	17.2481	0.620774
$773$	−20.2105	−0.726921	−0.363460	−	0.931610i	$-0.618405\pi$
$773$	−20.2105	−0.726921	−0.363460	+	0.931610i	$0.618405\pi$
$774$	−2.31399	−0.0831747
$775$	1.71418	0.0615751
$776$	−15.8779	−0.569984
$777$	−5.74529	−0.206111
$778$	31.7441	1.13808
$779$	−32.0280	−1.14752
$780$	0.118912	0.00425772
$781$	−0.161524	−0.00577980
$782$	−24.7728	−0.885874
$783$	−3.71831	−0.132882
$784$	11.6199	0.414998
$785$	8.42739	0.300787
$786$	28.7770	1.02644
$787$	−24.2959	−0.866055	−0.433028	−	0.901381i	$-0.642555\pi$
$787$	−24.2959	−0.866055	−0.433028	+	0.901381i	$0.642555\pi$
$788$	−5.04832	−0.179839
$789$	35.9169	1.27867
$790$	11.6810	0.415593
$791$	−33.0861	−1.17641
$792$	0.120225	0.00427200
$793$	0.539058	0.0191425
$794$	−35.3985	−1.25625
$795$	28.7886	1.02103
$796$	−4.82441	−0.170997
$797$	2.83740	0.100506	0.0502529	−	0.998737i	$-0.483997\pi$
$797$	2.83740	0.100506	0.0502529	+	0.998737i	$0.483997\pi$
$798$	−37.7114	−1.33497
$799$	8.98383	0.317825
$800$	−1.00000	−0.0353553
$801$	−6.15027	−0.217309
$802$	−20.2963	−0.716687
$803$	0.183880	0.00648900
$804$	−9.05519	−0.319352
$805$	−22.1750	−0.781566
$806$	−0.0928934	−0.00327203
$807$	33.0765	1.16435
$808$	−18.5807	−0.653667
$809$	−7.36365	−0.258892	−0.129446	−	0.991586i	$-0.541320\pi$
$809$	−7.36365	−0.258892	−0.129446	+	0.991586i	$0.541320\pi$
$810$	−11.1508	−0.391800
$811$	17.0412	0.598398	0.299199	−	0.954191i	$-0.403281\pi$
$811$	17.0412	0.598398	0.299199	+	0.954191i	$0.403281\pi$
$812$	6.17021	0.216532
$813$	33.9933	1.19220
$814$	−0.0401938	−0.00140879
$815$	−19.1915	−0.672248
$816$	10.5778	0.370298
$817$	5.07793	0.177654
$818$	−7.00402	−0.244890
$819$	−0.424406	−0.0148299
$820$	8.04158	0.280824
$821$	4.00697	0.139844	0.0699220	−	0.997552i	$-0.477725\pi$
$821$	4.00697	0.139844	0.0699220	+	0.997552i	$0.477725\pi$
$822$	9.62693	0.335778
$823$	−12.8945	−0.449472	−0.224736	−	0.974420i	$-0.572152\pi$
$823$	−12.8945	−0.449472	−0.224736	+	0.974420i	$0.572152\pi$
$824$	9.88328	0.344300
$825$	0.145354	0.00506058
$826$	−24.9469	−0.868013
$827$	−11.2446	−0.391012	−0.195506	−	0.980703i	$-0.562635\pi$
$827$	−11.2446	−0.391012	−0.195506	+	0.980703i	$0.562635\pi$
$828$	−9.32689	−0.324132
$829$	49.4985	1.71916	0.859578	−	0.511005i	$-0.170727\pi$
$829$	49.4985	1.71916	0.859578	+	0.511005i	$0.170727\pi$
$830$	1.36527	0.0473890
$831$	−10.2052	−0.354013
$832$	0.0541913	0.00187874
$833$	−56.0151	−1.94081
$834$	4.01412	0.138998
$835$	2.89654	0.100239
$836$	−0.263827	−0.00912465
$837$	4.45750	0.154074
$838$	19.8953	0.687273
$839$	1.30128	0.0449252	0.0224626	−	0.999748i	$-0.492849\pi$
$839$	1.30128	0.0449252	0.0224626	+	0.999748i	$0.492849\pi$
$840$	9.46858	0.326697
$841$	−26.9553	−0.929494
$842$	−0.0991055	−0.00341540
$843$	30.7513	1.05913
$844$	−13.4421	−0.462695
$845$	12.9971	0.447113
$846$	3.38239	0.116289
$847$	47.4470	1.63030
$848$	13.1197	0.450533
$849$	17.0303	0.584479
$850$	4.82060	0.165345
$851$	3.11819	0.106890
$852$	−5.35060	−0.183308
$853$	41.8471	1.43282	0.716408	−	0.697681i	$-0.245785\pi$
$853$	41.8471	1.43282	0.716408	+	0.697681i	$0.245785\pi$
$854$	42.9235	1.46881
$855$	−7.22854	−0.247211
$856$	6.48595	0.221685
$857$	−8.10341	−0.276807	−0.138404	−	0.990376i	$-0.544197\pi$
$857$	−8.10341	−0.276807	−0.138404	+	0.990376i	$0.544197\pi$
$858$	−0.00787692	−0.000268914 0
$859$	−22.6248	−0.771948	−0.385974	−	0.922510i	$-0.626135\pi$
$859$	−22.6248	−0.771948	−0.385974	+	0.922510i	$0.626135\pi$
$860$	−1.27497	−0.0434760
$861$	−76.1423	−2.59492
$862$	25.5837	0.871384
$863$	−21.2223	−0.722414	−0.361207	−	0.932486i	$-0.617635\pi$
$863$	−21.2223	−0.722414	−0.361207	+	0.932486i	$0.617635\pi$
$864$	−2.60037	−0.0884664
$865$	0.364956	0.0124089
$866$	12.5321	0.425859
$867$	−13.6884	−0.464883
$868$	−7.39682	−0.251064
$869$	−0.773772	−0.0262484
$870$	3.13766	0.106377
$871$	0.223631	0.00757744
$872$	−14.7328	−0.498916
$873$	28.8175	0.975325
$874$	20.4674	0.692320
$875$	4.31508	0.145876
$876$	6.09115	0.205801
$877$	51.6960	1.74565	0.872825	−	0.488033i	$-0.162285\pi$
$877$	51.6960	1.74565	0.872825	+	0.488033i	$0.162285\pi$
$878$	−11.7705	−0.397234
$879$	−56.3100	−1.89929
$880$	0.0662417	0.00223301
$881$	−31.0039	−1.04455	−0.522274	−	0.852778i	$-0.674916\pi$
$881$	−31.0039	−1.04455	−0.522274	+	0.852778i	$0.674916\pi$
$882$	−21.0895	−0.710121
$883$	−57.0337	−1.91934	−0.959668	−	0.281136i	$-0.909289\pi$
$883$	−57.0337	−1.91934	−0.959668	+	0.281136i	$0.909289\pi$
$884$	−0.261234	−0.00878626
$885$	−12.6859	−0.426433
$886$	−21.2953	−0.715429
$887$	16.3779	0.549917	0.274959	−	0.961456i	$-0.411336\pi$
$887$	16.3779	0.549917	0.274959	+	0.961456i	$0.411336\pi$
$888$	−1.33144	−0.0446804
$889$	86.5451	2.90263
$890$	−3.38869	−0.113589
$891$	0.738649	0.0247457
$892$	−6.54599	−0.219176
$893$	−7.42247	−0.248383
$894$	−16.0863	−0.538008
$895$	−10.4261	−0.348507
$896$	4.31508	0.144157
$897$	0.611082	0.0204034
$898$	−34.4718	−1.15034
$899$	−2.45113	−0.0817497
$900$	1.81494	0.0604981
$901$	−63.2449	−2.10699
$902$	−0.532688	−0.0177366
$903$	12.0721	0.401735
$904$	−7.66754	−0.255019
$905$	−22.5485	−0.749536
$906$	−21.5162	−0.714826
$907$	−15.9569	−0.529840	−0.264920	−	0.964270i	$-0.585345\pi$
$907$	−15.9569	−0.529840	−0.264920	+	0.964270i	$0.585345\pi$
$908$	−5.45316	−0.180970
$909$	33.7229	1.11852
$910$	−0.233840	−0.00775172
$911$	6.57519	0.217846	0.108923	−	0.994050i	$-0.465260\pi$
$911$	6.57519	0.217846	0.108923	+	0.994050i	$0.465260\pi$
$912$	−8.73944	−0.289392
$913$	−0.0904375	−0.00299304
$914$	−30.1186	−0.996236
$915$	21.8274	0.721591
$916$	19.0008	0.627805
$917$	−56.5899	−1.86876
$918$	12.5353	0.413728
$919$	−9.04334	−0.298312	−0.149156	−	0.988814i	$-0.547656\pi$
$919$	−9.04334	−0.298312	−0.149156	+	0.988814i	$0.547656\pi$
$920$	−5.13895	−0.169426
$921$	19.3466	0.637491
$922$	9.69215	0.319194
$923$	0.132141	0.00434946
$924$	−0.627215	−0.0206339
$925$	−0.606775	−0.0199506
$926$	−8.82806	−0.290108
$927$	−17.9376	−0.589147
$928$	1.42992	0.0469393
$929$	47.9506	1.57321	0.786603	−	0.617459i	$-0.211838\pi$
$929$	47.9506	1.57321	0.786603	+	0.617459i	$0.211838\pi$
$930$	−3.76141	−0.123342
$931$	46.2799	1.51676
$932$	14.8386	0.486055
$933$	−1.88253	−0.0616314
$934$	−11.6580	−0.381462
$935$	−0.319325	−0.0104430
$936$	−0.0983540	−0.00321480
$937$	−36.5701	−1.19469	−0.597347	−	0.801983i	$-0.703779\pi$
$937$	−36.5701	−1.19469	−0.597347	+	0.801983i	$0.703779\pi$
$938$	17.8070	0.581420
$939$	22.7896	0.743711
$940$	1.86363	0.0607850
$941$	−40.6006	−1.32354	−0.661772	−	0.749705i	$-0.730195\pi$
$941$	−40.6006	−1.32354	−0.661772	+	0.749705i	$0.730195\pi$
$942$	−18.4922	−0.602509
$943$	41.3253	1.34574
$944$	−5.78132	−0.188166
$945$	11.2208	0.365013
$946$	0.0844560	0.00274590
$947$	17.9173	0.582233	0.291117	−	0.956688i	$-0.405973\pi$
$947$	17.9173	0.582233	0.291117	+	0.956688i	$0.405973\pi$
$948$	−25.6317	−0.832478
$949$	−0.150430	−0.00488315
$950$	−3.98279	−0.129219
$951$	42.9920	1.39411
$952$	−20.8013	−0.674174
$953$	−34.8772	−1.12978	−0.564892	−	0.825165i	$-0.691082\pi$
$953$	−34.8772	−1.12978	−0.564892	+	0.825165i	$0.691082\pi$
$954$	−23.8115	−0.770927
$955$	12.8673	0.416377
$956$	26.5313	0.858083
$957$	−0.207844	−0.00671864
$958$	41.1535	1.32961
$959$	−18.9313	−0.611325
$960$	2.19430	0.0708206
$961$	−28.0616	−0.905213
$962$	0.0328819	0.00106015
$963$	−11.7716	−0.379335
$964$	−6.83681	−0.220199
$965$	−17.2481	−0.555238
$966$	48.6585	1.56556
$967$	−37.5373	−1.20712	−0.603559	−	0.797318i	$-0.706251\pi$
$967$	−37.5373	−1.20712	−0.603559	+	0.797318i	$0.706251\pi$
$968$	10.9956	0.353412
$969$	42.1293	1.35339
$970$	15.8779	0.509810
$971$	29.1439	0.935273	0.467637	−	0.883921i	$-0.345106\pi$
$971$	29.1439	0.935273	0.467637	+	0.883921i	$0.345106\pi$
$972$	16.6671	0.534597
$973$	−7.89377	−0.253063
$974$	−4.65074	−0.149019
$975$	−0.118912	−0.00380822
$976$	9.94732	0.318406
$977$	27.7804	0.888775	0.444388	−	0.895835i	$-0.353421\pi$
$977$	27.7804	0.888775	0.444388	+	0.895835i	$0.353421\pi$
$978$	42.1118	1.34659
$979$	0.224472	0.00717417
$980$	−11.6199	−0.371186
$981$	26.7392	0.853718
$982$	39.1159	1.24824
$983$	−9.00067	−0.287077	−0.143538	−	0.989645i	$-0.545848\pi$
$983$	−9.00067	−0.287077	−0.143538	+	0.989645i	$0.545848\pi$
$984$	−17.6456	−0.562522
$985$	5.04832	0.160853
$986$	−6.89305	−0.219519
$987$	−17.6460	−0.561677
$988$	0.215833	0.00686655
$989$	−6.55199	−0.208341
$990$	−0.120225	−0.00382100
$991$	33.7626	1.07250	0.536252	−	0.844058i	$-0.319840\pi$
$991$	33.7626	1.07250	0.536252	+	0.844058i	$0.319840\pi$
$992$	−1.71418	−0.0544252
$993$	19.7191	0.625766
$994$	10.5219	0.333736
$995$	4.82441	0.152944
$996$	−2.99580	−0.0949255
$997$	9.82516	0.311166	0.155583	−	0.987823i	$-0.450274\pi$
$997$	9.82516	0.311166	0.155583	+	0.987823i	$0.450274\pi$
$998$	−7.89965	−0.250059
$999$	−1.57784	−0.0499206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.i.1.7	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.i.1.7	✓	29	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.19430 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.19430 q^{6} -4.31508 q^{7} -1.00000 q^{8} +1.81494 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.19430 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.19430 q^{6} -4.31508 q^{7} -1.00000 q^{8} +1.81494 q^{9} +1.00000 q^{10} -0.0662417 q^{11} -2.19430 q^{12} +0.0541913 q^{13} +4.31508 q^{14} +2.19430 q^{15} +1.00000 q^{16} -4.82060 q^{17} -1.81494 q^{18} +3.98279 q^{19} -1.00000 q^{20} +9.46858 q^{21} +0.0662417 q^{22} -5.13895 q^{23} +2.19430 q^{24} +1.00000 q^{25} -0.0541913 q^{26} +2.60037 q^{27} -4.31508 q^{28} -1.42992 q^{29} -2.19430 q^{30} +1.71418 q^{31} -1.00000 q^{32} +0.145354 q^{33} +4.82060 q^{34} +4.31508 q^{35} +1.81494 q^{36} -0.606775 q^{37} -3.98279 q^{38} -0.118912 q^{39} +1.00000 q^{40} -8.04158 q^{41} -9.46858 q^{42} +1.27497 q^{43} -0.0662417 q^{44} -1.81494 q^{45} +5.13895 q^{46} -1.86363 q^{47} -2.19430 q^{48} +11.6199 q^{49} -1.00000 q^{50} +10.5778 q^{51} +0.0541913 q^{52} +13.1197 q^{53} -2.60037 q^{54} +0.0662417 q^{55} +4.31508 q^{56} -8.73944 q^{57} +1.42992 q^{58} -5.78132 q^{59} +2.19430 q^{60} +9.94732 q^{61} -1.71418 q^{62} -7.83163 q^{63} +1.00000 q^{64} -0.0541913 q^{65} -0.145354 q^{66} +4.12669 q^{67} -4.82060 q^{68} +11.2764 q^{69} -4.31508 q^{70} +2.43841 q^{71} -1.81494 q^{72} -2.77590 q^{73} +0.606775 q^{74} -2.19430 q^{75} +3.98279 q^{76} +0.285839 q^{77} +0.118912 q^{78} +11.6810 q^{79} -1.00000 q^{80} -11.1508 q^{81} +8.04158 q^{82} +1.36527 q^{83} +9.46858 q^{84} +4.82060 q^{85} -1.27497 q^{86} +3.13766 q^{87} +0.0662417 q^{88} -3.38869 q^{89} +1.81494 q^{90} -0.233840 q^{91} -5.13895 q^{92} -3.76141 q^{93} +1.86363 q^{94} -3.98279 q^{95} +2.19430 q^{96} +15.8779 q^{97} -11.6199 q^{98} -0.120225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9	\( 29 q - 29 q^{2} - 10 q^{3} + 29 q^{4} - 29 q^{5} + 10 q^{6} - 29 q^{8} + 29 q^{9} + 29 q^{10} - 10 q^{12} - 4 q^{13} + 10 q^{15} + 29 q^{16} - 23 q^{17} - 29 q^{18} + q^{19} - 29 q^{20} + 2 q^{21} - 9 q^{23} + 10 q^{24} + 29 q^{25} + 4 q^{26} - 43 q^{27} - 5 q^{29} - 10 q^{30} + 21 q^{31} - 29 q^{32} - 19 q^{33} + 23 q^{34} + 29 q^{36} - 6 q^{37} - q^{38} + 18 q^{39} + 29 q^{40} - 17 q^{41} - 2 q^{42} - 19 q^{43} - 29 q^{45} + 9 q^{46} - 21 q^{47} - 10 q^{48} + 45 q^{49} - 29 q^{50} + 11 q^{51} - 4 q^{52} - 53 q^{53} + 43 q^{54} - 16 q^{57} + 5 q^{58} - 30 q^{59} + 10 q^{60} + 16 q^{61} - 21 q^{62} - 17 q^{63} + 29 q^{64} + 4 q^{65} + 19 q^{66} - 35 q^{67} - 23 q^{68} + 13 q^{69} + 2 q^{71} - 29 q^{72} - q^{73} + 6 q^{74} - 10 q^{75} + q^{76} - 50 q^{77} - 18 q^{78} + 26 q^{79} - 29 q^{80} + 33 q^{81} + 17 q^{82} - 54 q^{83} + 2 q^{84} + 23 q^{85} + 19 q^{86} - 56 q^{87} - 2 q^{89} + 29 q^{90} + 27 q^{91} - 9 q^{92} - 26 q^{93} + 21 q^{94} - q^{95} + 10 q^{96} + 15 q^{97} - 45 q^{98} + 27 q^{99}+O(q^{100}) \) 29 * q - 29 * q^2 - 10 * q^3 + 29 * q^4 - 29 * q^5 + 10 * q^6 - 29 * q^8 + 29 * q^9 + 29 * q^10 - 10 * q^12 - 4 * q^13 + 10 * q^15 + 29 * q^16 - 23 * q^17 - 29 * q^18 + q^19 - 29 * q^20 + 2 * q^21 - 9 * q^23 + 10 * q^24 + 29 * q^25 + 4 * q^26 - 43 * q^27 - 5 * q^29 - 10 * q^30 + 21 * q^31 - 29 * q^32 - 19 * q^33 + 23 * q^34 + 29 * q^36 - 6 * q^37 - q^38 + 18 * q^39 + 29 * q^40 - 17 * q^41 - 2 * q^42 - 19 * q^43 - 29 * q^45 + 9 * q^46 - 21 * q^47 - 10 * q^48 + 45 * q^49 - 29 * q^50 + 11 * q^51 - 4 * q^52 - 53 * q^53 + 43 * q^54 - 16 * q^57 + 5 * q^58 - 30 * q^59 + 10 * q^60 + 16 * q^61 - 21 * q^62 - 17 * q^63 + 29 * q^64 + 4 * q^65 + 19 * q^66 - 35 * q^67 - 23 * q^68 + 13 * q^69 + 2 * q^71 - 29 * q^72 - q^73 + 6 * q^74 - 10 * q^75 + q^76 - 50 * q^77 - 18 * q^78 + 26 * q^79 - 29 * q^80 + 33 * q^81 + 17 * q^82 - 54 * q^83 + 2 * q^84 + 23 * q^85 + 19 * q^86 - 56 * q^87 - 2 * q^89 + 29 * q^90 + 27 * q^91 - 9 * q^92 - 26 * q^93 + 21 * q^94 - q^95 + 10 * q^96 + 15 * q^97 - 45 * q^98 + 27 * q^99

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