LMFDB - Embedded newform 4030.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.3728437.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 6x^{3} + 7x^{2} - 3x - 1 $ x^6 - 2x^5 - 5x^4 + 6x^3 + 7x^2 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.74629$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.31646 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31646 q^{6} -3.47179 q^{7} -1.00000 q^{8} -1.26693 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.31646 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31646 q^{6} -3.47179 q^{7} -1.00000 q^{8} -1.26693 q^{9} -1.00000 q^{10} -2.00462 q^{11} +1.31646 q^{12} +1.00000 q^{13} +3.47179 q^{14} +1.31646 q^{15} +1.00000 q^{16} +3.54211 q^{17} +1.26693 q^{18} +5.85671 q^{19} +1.00000 q^{20} -4.57047 q^{21} +2.00462 q^{22} +1.00512 q^{23} -1.31646 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.61725 q^{27} -3.47179 q^{28} -10.6962 q^{29} -1.31646 q^{30} -1.00000 q^{31} -1.00000 q^{32} -2.63900 q^{33} -3.54211 q^{34} -3.47179 q^{35} -1.26693 q^{36} +2.29547 q^{37} -5.85671 q^{38} +1.31646 q^{39} -1.00000 q^{40} +9.02659 q^{41} +4.57047 q^{42} +0.524270 q^{43} -2.00462 q^{44} -1.26693 q^{45} -1.00512 q^{46} +3.98761 q^{47} +1.31646 q^{48} +5.05332 q^{49} -1.00000 q^{50} +4.66305 q^{51} +1.00000 q^{52} -8.52059 q^{53} +5.61725 q^{54} -2.00462 q^{55} +3.47179 q^{56} +7.71013 q^{57} +10.6962 q^{58} -11.8138 q^{59} +1.31646 q^{60} +1.86374 q^{61} +1.00000 q^{62} +4.39852 q^{63} +1.00000 q^{64} +1.00000 q^{65} +2.63900 q^{66} +4.96520 q^{67} +3.54211 q^{68} +1.32320 q^{69} +3.47179 q^{70} +3.31066 q^{71} +1.26693 q^{72} -15.8329 q^{73} -2.29547 q^{74} +1.31646 q^{75} +5.85671 q^{76} +6.95962 q^{77} -1.31646 q^{78} -0.302504 q^{79} +1.00000 q^{80} -3.59409 q^{81} -9.02659 q^{82} +2.33228 q^{83} -4.57047 q^{84} +3.54211 q^{85} -0.524270 q^{86} -14.0811 q^{87} +2.00462 q^{88} -17.9585 q^{89} +1.26693 q^{90} -3.47179 q^{91} +1.00512 q^{92} -1.31646 q^{93} -3.98761 q^{94} +5.85671 q^{95} -1.31646 q^{96} -15.4285 q^{97} -5.05332 q^{98} +2.53972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - q^9	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - q^{9} - 6 q^{10} - q^{12} + 6 q^{13} + 2 q^{14} - q^{15} + 6 q^{16} - 10 q^{17} + q^{18} + q^{19} + 6 q^{20} + 3 q^{21} - 13 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - 7 q^{27} - 2 q^{28} - 16 q^{29} + q^{30} - 6 q^{31} - 6 q^{32} - 22 q^{33} + 10 q^{34} - 2 q^{35} - q^{36} - 14 q^{37} - q^{38} - q^{39} - 6 q^{40} - 4 q^{41} - 3 q^{42} + 5 q^{43} - q^{45} + 13 q^{46} - 4 q^{47} - q^{48} + 2 q^{49} - 6 q^{50} + 11 q^{51} + 6 q^{52} - 14 q^{53} + 7 q^{54} + 2 q^{56} - 3 q^{57} + 16 q^{58} - 7 q^{59} - q^{60} - 3 q^{61} + 6 q^{62} - 3 q^{63} + 6 q^{64} + 6 q^{65} + 22 q^{66} - 4 q^{67} - 10 q^{68} - 4 q^{69} + 2 q^{70} + q^{72} - 5 q^{73} + 14 q^{74} - q^{75} + q^{76} - 23 q^{77} + q^{78} + 6 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 2 q^{83} + 3 q^{84} - 10 q^{85} - 5 q^{86} - 21 q^{87} - 14 q^{89} + q^{90} - 2 q^{91} - 13 q^{92} + q^{93} + 4 q^{94} + q^{95} + q^{96} - 35 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - q^9 - 6 * q^10 - q^12 + 6 * q^13 + 2 * q^14 - q^15 + 6 * q^16 - 10 * q^17 + q^18 + q^19 + 6 * q^20 + 3 * q^21 - 13 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - 7 * q^27 - 2 * q^28 - 16 * q^29 + q^30 - 6 * q^31 - 6 * q^32 - 22 * q^33 + 10 * q^34 - 2 * q^35 - q^36 - 14 * q^37 - q^38 - q^39 - 6 * q^40 - 4 * q^41 - 3 * q^42 + 5 * q^43 - q^45 + 13 * q^46 - 4 * q^47 - q^48 + 2 * q^49 - 6 * q^50 + 11 * q^51 + 6 * q^52 - 14 * q^53 + 7 * q^54 + 2 * q^56 - 3 * q^57 + 16 * q^58 - 7 * q^59 - q^60 - 3 * q^61 + 6 * q^62 - 3 * q^63 + 6 * q^64 + 6 * q^65 + 22 * q^66 - 4 * q^67 - 10 * q^68 - 4 * q^69 + 2 * q^70 + q^72 - 5 * q^73 + 14 * q^74 - q^75 + q^76 - 23 * q^77 + q^78 + 6 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 2 * q^83 + 3 * q^84 - 10 * q^85 - 5 * q^86 - 21 * q^87 - 14 * q^89 + q^90 - 2 * q^91 - 13 * q^92 + q^93 + 4 * q^94 + q^95 + q^96 - 35 * q^97 - 2 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.31646	0.760059	0.380030	−	0.924974i	$-0.375914\pi$
$3$	1.31646	0.760059	0.380030	+	0.924974i	$0.375914\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.31646	−0.537443
$7$	−3.47179	−1.31221	−0.656106	−	0.754668i	$-0.727798\pi$
$7$	−3.47179	−1.31221	−0.656106	+	0.754668i	$0.727798\pi$
$8$	−1.00000	−0.353553
$9$	−1.26693	−0.422310
$10$	−1.00000	−0.316228
$11$	−2.00462	−0.604416	−0.302208	−	0.953242i	$-0.597724\pi$
$11$	−2.00462	−0.604416	−0.302208	+	0.953242i	$0.597724\pi$
$12$	1.31646	0.380030
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.47179	0.927875
$15$	1.31646	0.339909
$16$	1.00000	0.250000
$17$	3.54211	0.859088	0.429544	−	0.903046i	$-0.358674\pi$
$17$	3.54211	0.859088	0.429544	+	0.903046i	$0.358674\pi$
$18$	1.26693	0.298618
$19$	5.85671	1.34362	0.671811	−	0.740723i	$-0.265517\pi$
$19$	5.85671	1.34362	0.671811	+	0.740723i	$0.265517\pi$
$20$	1.00000	0.223607
$21$	−4.57047	−0.997359
$22$	2.00462	0.427386
$23$	1.00512	0.209582	0.104791	−	0.994494i	$-0.466583\pi$
$23$	1.00512	0.209582	0.104791	+	0.994494i	$0.466583\pi$
$24$	−1.31646	−0.268721
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−5.61725	−1.08104
$28$	−3.47179	−0.656106
$29$	−10.6962	−1.98623	−0.993114	−	0.117148i	$-0.962625\pi$
$29$	−10.6962	−1.98623	−0.993114	+	0.117148i	$0.962625\pi$
$30$	−1.31646	−0.240352
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−2.63900	−0.459392
$34$	−3.54211	−0.607467
$35$	−3.47179	−0.586839
$36$	−1.26693	−0.211155
$37$	2.29547	0.377374	0.188687	−	0.982037i	$-0.439577\pi$
$37$	2.29547	0.377374	0.188687	+	0.982037i	$0.439577\pi$
$38$	−5.85671	−0.950084
$39$	1.31646	0.210802
$40$	−1.00000	−0.158114
$41$	9.02659	1.40972	0.704858	−	0.709348i	$-0.251011\pi$
$41$	9.02659	1.40972	0.704858	+	0.709348i	$0.251011\pi$
$42$	4.57047	0.705239
$43$	0.524270	0.0799504	0.0399752	−	0.999201i	$-0.487272\pi$
$43$	0.524270	0.0799504	0.0399752	+	0.999201i	$0.487272\pi$
$44$	−2.00462	−0.302208
$45$	−1.26693	−0.188863
$46$	−1.00512	−0.148197
$47$	3.98761	0.581653	0.290827	−	0.956776i	$-0.406070\pi$
$47$	3.98761	0.581653	0.290827	+	0.956776i	$0.406070\pi$
$48$	1.31646	0.190015
$49$	5.05332	0.721902
$50$	−1.00000	−0.141421
$51$	4.66305	0.652958
$52$	1.00000	0.138675
$53$	−8.52059	−1.17039	−0.585197	−	0.810891i	$-0.698983\pi$
$53$	−8.52059	−1.17039	−0.585197	+	0.810891i	$0.698983\pi$
$54$	5.61725	0.764411
$55$	−2.00462	−0.270303
$56$	3.47179	0.463937
$57$	7.71013	1.02123
$58$	10.6962	1.40448
$59$	−11.8138	−1.53802	−0.769012	−	0.639235i	$-0.779251\pi$
$59$	−11.8138	−1.53802	−0.769012	+	0.639235i	$0.779251\pi$
$60$	1.31646	0.169954
$61$	1.86374	0.238627	0.119314	−	0.992857i	$-0.461931\pi$
$61$	1.86374	0.238627	0.119314	+	0.992857i	$0.461931\pi$
$62$	1.00000	0.127000
$63$	4.39852	0.554161
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	2.63900	0.324839
$67$	4.96520	0.606596	0.303298	−	0.952896i	$-0.401912\pi$
$67$	4.96520	0.606596	0.303298	+	0.952896i	$0.401912\pi$
$68$	3.54211	0.429544
$69$	1.32320	0.159294
$70$	3.47179	0.414958
$71$	3.31066	0.392903	0.196451	−	0.980514i	$-0.437058\pi$
$71$	3.31066	0.392903	0.196451	+	0.980514i	$0.437058\pi$
$72$	1.26693	0.149309
$73$	−15.8329	−1.85310	−0.926549	−	0.376175i	$-0.877239\pi$
$73$	−15.8329	−1.85310	−0.926549	+	0.376175i	$0.877239\pi$
$74$	−2.29547	−0.266844
$75$	1.31646	0.152012
$76$	5.85671	0.671811
$77$	6.95962	0.793122
$78$	−1.31646	−0.149060
$79$	−0.302504	−0.0340343	−0.0170172	−	0.999855i	$-0.505417\pi$
$79$	−0.302504	−0.0340343	−0.0170172	+	0.999855i	$0.505417\pi$
$80$	1.00000	0.111803
$81$	−3.59409	−0.399344
$82$	−9.02659	−0.996820
$83$	2.33228	0.256001	0.128001	−	0.991774i	$-0.459144\pi$
$83$	2.33228	0.256001	0.128001	+	0.991774i	$0.459144\pi$
$84$	−4.57047	−0.498680
$85$	3.54211	0.384196
$86$	−0.524270	−0.0565334
$87$	−14.0811	−1.50965
$88$	2.00462	0.213693
$89$	−17.9585	−1.90359	−0.951797	−	0.306729i	$-0.900765\pi$
$89$	−17.9585	−1.90359	−0.951797	+	0.306729i	$0.900765\pi$
$90$	1.26693	0.133546
$91$	−3.47179	−0.363942
$92$	1.00512	0.104791
$93$	−1.31646	−0.136511
$94$	−3.98761	−0.411291
$95$	5.85671	0.600886
$96$	−1.31646	−0.134361
$97$	−15.4285	−1.56652	−0.783261	−	0.621693i	$-0.786445\pi$
$97$	−15.4285	−1.56652	−0.783261	+	0.621693i	$0.786445\pi$
$98$	−5.05332	−0.510462
$99$	2.53972	0.255251
$100$	1.00000	0.100000
$101$	10.2414	1.01906	0.509529	−	0.860454i	$-0.329820\pi$
$101$	10.2414	1.01906	0.509529	+	0.860454i	$0.329820\pi$
$102$	−4.66305	−0.461711
$103$	−13.6086	−1.34090	−0.670450	−	0.741955i	$-0.733899\pi$
$103$	−13.6086	−1.34090	−0.670450	+	0.741955i	$0.733899\pi$
$104$	−1.00000	−0.0980581
$105$	−4.57047	−0.446033
$106$	8.52059	0.827593
$107$	−18.6026	−1.79839	−0.899193	−	0.437552i	$-0.855845\pi$
$107$	−18.6026	−1.79839	−0.899193	+	0.437552i	$0.855845\pi$
$108$	−5.61725	−0.540520
$109$	−3.91146	−0.374650	−0.187325	−	0.982298i	$-0.559982\pi$
$109$	−3.91146	−0.374650	−0.187325	+	0.982298i	$0.559982\pi$
$110$	2.00462	0.191133
$111$	3.02190	0.286826
$112$	−3.47179	−0.328053
$113$	−15.0726	−1.41791	−0.708957	−	0.705252i	$-0.750834\pi$
$113$	−15.0726	−1.41791	−0.708957	+	0.705252i	$0.750834\pi$
$114$	−7.71013	−0.722120
$115$	1.00512	0.0937277
$116$	−10.6962	−0.993114
$117$	−1.26693	−0.117128
$118$	11.8138	1.08755
$119$	−12.2975	−1.12731
$120$	−1.31646	−0.120176
$121$	−6.98150	−0.634682
$122$	−1.86374	−0.168735
$123$	11.8832	1.07147
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	−4.39852	−0.391851
$127$	−18.7643	−1.66507	−0.832533	−	0.553975i	$-0.813110\pi$
$127$	−18.7643	−1.66507	−0.832533	+	0.553975i	$0.813110\pi$
$128$	−1.00000	−0.0883883
$129$	0.690180	0.0607670
$130$	−1.00000	−0.0877058
$131$	−2.40956	−0.210524	−0.105262	−	0.994445i	$-0.533568\pi$
$131$	−2.40956	−0.210524	−0.105262	+	0.994445i	$0.533568\pi$
$132$	−2.63900	−0.229696
$133$	−20.3333	−1.76312
$134$	−4.96520	−0.428928
$135$	−5.61725	−0.483456
$136$	−3.54211	−0.303734
$137$	7.88123	0.673339	0.336669	−	0.941623i	$-0.390700\pi$
$137$	7.88123	0.673339	0.336669	+	0.941623i	$0.390700\pi$
$138$	−1.32320	−0.112638
$139$	−7.32267	−0.621101	−0.310550	−	0.950557i	$-0.600513\pi$
$139$	−7.32267	−0.621101	−0.310550	+	0.950557i	$0.600513\pi$
$140$	−3.47179	−0.293420
$141$	5.24954	0.442091
$142$	−3.31066	−0.277824
$143$	−2.00462	−0.167635
$144$	−1.26693	−0.105578
$145$	−10.6962	−0.888269
$146$	15.8329	1.31034
$147$	6.65249	0.548688
$148$	2.29547	0.188687
$149$	−5.58207	−0.457301	−0.228651	−	0.973509i	$-0.573431\pi$
$149$	−5.58207	−0.457301	−0.228651	+	0.973509i	$0.573431\pi$
$150$	−1.31646	−0.107489
$151$	18.1771	1.47923	0.739614	−	0.673031i	$-0.235008\pi$
$151$	18.1771	1.47923	0.739614	+	0.673031i	$0.235008\pi$
$152$	−5.85671	−0.475042
$153$	−4.48761	−0.362802
$154$	−6.95962	−0.560822
$155$	−1.00000	−0.0803219
$156$	1.31646	0.105401
$157$	11.3774	0.908016	0.454008	−	0.890998i	$-0.349994\pi$
$157$	11.3774	0.908016	0.454008	+	0.890998i	$0.349994\pi$
$158$	0.302504	0.0240659
$159$	−11.2170	−0.889568
$160$	−1.00000	−0.0790569
$161$	−3.48956	−0.275016
$162$	3.59409	0.282379
$163$	−11.2593	−0.881893	−0.440946	−	0.897533i	$-0.645357\pi$
$163$	−11.2593	−0.881893	−0.440946	+	0.897533i	$0.645357\pi$
$164$	9.02659	0.704858
$165$	−2.63900	−0.205446
$166$	−2.33228	−0.181020
$167$	23.2813	1.80156	0.900780	−	0.434276i	$-0.142996\pi$
$167$	23.2813	1.80156	0.900780	+	0.434276i	$0.142996\pi$
$168$	4.57047	0.352620
$169$	1.00000	0.0769231
$170$	−3.54211	−0.271668
$171$	−7.42004	−0.567425
$172$	0.524270	0.0399752
$173$	4.13870	0.314659	0.157330	−	0.987546i	$-0.449711\pi$
$173$	4.13870	0.314659	0.157330	+	0.987546i	$0.449711\pi$
$174$	14.0811	1.06748
$175$	−3.47179	−0.262443
$176$	−2.00462	−0.151104
$177$	−15.5524	−1.16899
$178$	17.9585	1.34604
$179$	−3.28901	−0.245832	−0.122916	−	0.992417i	$-0.539225\pi$
$179$	−3.28901	−0.245832	−0.122916	+	0.992417i	$0.539225\pi$
$180$	−1.26693	−0.0944314
$181$	−3.24388	−0.241116	−0.120558	−	0.992706i	$-0.538468\pi$
$181$	−3.24388	−0.241116	−0.120558	+	0.992706i	$0.538468\pi$
$182$	3.47179	0.257346
$183$	2.45354	0.181371
$184$	−1.00512	−0.0740983
$185$	2.29547	0.168767
$186$	1.31646	0.0965276
$187$	−7.10059	−0.519246
$188$	3.98761	0.290827
$189$	19.5019	1.41855
$190$	−5.85671	−0.424890
$191$	−4.59190	−0.332259	−0.166129	−	0.986104i	$-0.553127\pi$
$191$	−4.59190	−0.332259	−0.166129	+	0.986104i	$0.553127\pi$
$192$	1.31646	0.0950074
$193$	−5.31717	−0.382739	−0.191369	−	0.981518i	$-0.561293\pi$
$193$	−5.31717	−0.382739	−0.191369	+	0.981518i	$0.561293\pi$
$194$	15.4285	1.10770
$195$	1.31646	0.0942737
$196$	5.05332	0.360951
$197$	−11.2996	−0.805067	−0.402533	−	0.915405i	$-0.631870\pi$
$197$	−11.2996	−0.805067	−0.402533	+	0.915405i	$0.631870\pi$
$198$	−2.53972	−0.180490
$199$	19.3635	1.37264	0.686322	−	0.727297i	$-0.259224\pi$
$199$	19.3635	1.37264	0.686322	+	0.727297i	$0.259224\pi$
$200$	−1.00000	−0.0707107
$201$	6.53650	0.461049
$202$	−10.2414	−0.720582
$203$	37.1348	2.60636
$204$	4.66305	0.326479
$205$	9.02659	0.630444
$206$	13.6086	0.948159
$207$	−1.27341	−0.0885084
$208$	1.00000	0.0693375
$209$	−11.7405	−0.812106
$210$	4.57047	0.315393
$211$	−4.79901	−0.330378	−0.165189	−	0.986262i	$-0.552823\pi$
$211$	−4.79901	−0.330378	−0.165189	+	0.986262i	$0.552823\pi$
$212$	−8.52059	−0.585197
$213$	4.35835	0.298629
$214$	18.6026	1.27165
$215$	0.524270	0.0357549
$216$	5.61725	0.382205
$217$	3.47179	0.235680
$218$	3.91146	0.264918
$219$	−20.8434	−1.40846
$220$	−2.00462	−0.135151
$221$	3.54211	0.238268
$222$	−3.02190	−0.202817
$223$	12.1514	0.813716	0.406858	−	0.913492i	$-0.366624\pi$
$223$	12.1514	0.813716	0.406858	+	0.913492i	$0.366624\pi$
$224$	3.47179	0.231969
$225$	−1.26693	−0.0844620
$226$	15.0726	1.00262
$227$	20.9306	1.38921	0.694607	−	0.719389i	$-0.255578\pi$
$227$	20.9306	1.38921	0.694607	+	0.719389i	$0.255578\pi$
$228$	7.71013	0.510616
$229$	15.7740	1.04238	0.521189	−	0.853441i	$-0.325489\pi$
$229$	15.7740	1.04238	0.521189	+	0.853441i	$0.325489\pi$
$230$	−1.00512	−0.0662755
$231$	9.16207	0.602820
$232$	10.6962	0.702238
$233$	−24.6372	−1.61403	−0.807017	−	0.590528i	$-0.798919\pi$
$233$	−24.6372	−1.61403	−0.807017	+	0.590528i	$0.798919\pi$
$234$	1.26693	0.0828219
$235$	3.98761	0.260123
$236$	−11.8138	−0.769012
$237$	−0.398235	−0.0258681
$238$	12.2975	0.797126
$239$	−10.7894	−0.697909	−0.348955	−	0.937140i	$-0.613463\pi$
$239$	−10.7894	−0.697909	−0.348955	+	0.937140i	$0.613463\pi$
$240$	1.31646	0.0849772
$241$	−1.96468	−0.126556	−0.0632781	−	0.997996i	$-0.520156\pi$
$241$	−1.96468	−0.126556	−0.0632781	+	0.997996i	$0.520156\pi$
$242$	6.98150	0.448788
$243$	12.1203	0.777515
$244$	1.86374	0.119314
$245$	5.05332	0.322845
$246$	−11.8832	−0.757642
$247$	5.85671	0.372653
$248$	1.00000	0.0635001
$249$	3.07036	0.194576
$250$	−1.00000	−0.0632456
$251$	10.0753	0.635950	0.317975	−	0.948099i	$-0.396997\pi$
$251$	10.0753	0.635950	0.317975	+	0.948099i	$0.396997\pi$
$252$	4.39852	0.277080
$253$	−2.01488	−0.126674
$254$	18.7643	1.17738
$255$	4.66305	0.292012
$256$	1.00000	0.0625000
$257$	−28.9232	−1.80418	−0.902090	−	0.431548i	$-0.857967\pi$
$257$	−28.9232	−1.80418	−0.902090	+	0.431548i	$0.857967\pi$
$258$	−0.690180	−0.0429688
$259$	−7.96940	−0.495195
$260$	1.00000	0.0620174
$261$	13.5513	0.838805
$262$	2.40956	0.148863
$263$	−23.3212	−1.43805	−0.719024	−	0.694986i	$-0.755411\pi$
$263$	−23.3212	−1.43805	−0.719024	+	0.694986i	$0.755411\pi$
$264$	2.63900	0.162419
$265$	−8.52059	−0.523416
$266$	20.3333	1.24671
$267$	−23.6416	−1.44684
$268$	4.96520	0.303298
$269$	8.22606	0.501552	0.250776	−	0.968045i	$-0.419314\pi$
$269$	8.22606	0.501552	0.250776	+	0.968045i	$0.419314\pi$
$270$	5.61725	0.341855
$271$	−8.75484	−0.531819	−0.265909	−	0.963998i	$-0.585672\pi$
$271$	−8.75484	−0.531819	−0.265909	+	0.963998i	$0.585672\pi$
$272$	3.54211	0.214772
$273$	−4.57047	−0.276618
$274$	−7.88123	−0.476122
$275$	−2.00462	−0.120883
$276$	1.32320	0.0796472
$277$	−14.8801	−0.894060	−0.447030	−	0.894519i	$-0.647518\pi$
$277$	−14.8801	−0.894060	−0.447030	+	0.894519i	$0.647518\pi$
$278$	7.32267	0.439184
$279$	1.26693	0.0758492
$280$	3.47179	0.207479
$281$	15.2964	0.912504	0.456252	−	0.889851i	$-0.349191\pi$
$281$	15.2964	0.912504	0.456252	+	0.889851i	$0.349191\pi$
$282$	−5.24954	−0.312605
$283$	3.80880	0.226410	0.113205	−	0.993572i	$-0.463888\pi$
$283$	3.80880	0.226410	0.113205	+	0.993572i	$0.463888\pi$
$284$	3.31066	0.196451
$285$	7.71013	0.456709
$286$	2.00462	0.118536
$287$	−31.3384	−1.84985
$288$	1.26693	0.0746546
$289$	−4.45345	−0.261968
$290$	10.6962	0.628101
$291$	−20.3110	−1.19065
$292$	−15.8329	−0.926549
$293$	−21.6727	−1.26613	−0.633066	−	0.774098i	$-0.718204\pi$
$293$	−21.6727	−1.26613	−0.633066	+	0.774098i	$0.718204\pi$
$294$	−6.65249	−0.387981
$295$	−11.8138	−0.687825
$296$	−2.29547	−0.133422
$297$	11.2604	0.653397
$298$	5.58207	0.323361
$299$	1.00512	0.0581275
$300$	1.31646	0.0760059
$301$	−1.82015	−0.104912
$302$	−18.1771	−1.04597
$303$	13.4824	0.774544
$304$	5.85671	0.335905
$305$	1.86374	0.106717
$306$	4.48761	0.256540
$307$	−21.7515	−1.24142	−0.620711	−	0.784039i	$-0.713156\pi$
$307$	−21.7515	−1.24142	−0.620711	+	0.784039i	$0.713156\pi$
$308$	6.95962	0.396561
$309$	−17.9153	−1.01916
$310$	1.00000	0.0567962
$311$	19.0498	1.08021	0.540107	−	0.841596i	$-0.318384\pi$
$311$	19.0498	1.08021	0.540107	+	0.841596i	$0.318384\pi$
$312$	−1.31646	−0.0745299
$313$	5.63232	0.318357	0.159179	−	0.987250i	$-0.449115\pi$
$313$	5.63232	0.318357	0.159179	+	0.987250i	$0.449115\pi$
$314$	−11.3774	−0.642064
$315$	4.39852	0.247828
$316$	−0.302504	−0.0170172
$317$	7.04210	0.395524	0.197762	−	0.980250i	$-0.436633\pi$
$317$	7.04210	0.395524	0.197762	+	0.980250i	$0.436633\pi$
$318$	11.2170	0.629020
$319$	21.4418	1.20051
$320$	1.00000	0.0559017
$321$	−24.4897	−1.36688
$322$	3.48956	0.194465
$323$	20.7451	1.15429
$324$	−3.59409	−0.199672
$325$	1.00000	0.0554700
$326$	11.2593	0.623592
$327$	−5.14929	−0.284756
$328$	−9.02659	−0.498410
$329$	−13.8442	−0.763253
$330$	2.63900	0.145272
$331$	35.7315	1.96398	0.981989	−	0.188936i	$-0.0605037\pi$
$331$	35.7315	1.96398	0.981989	+	0.188936i	$0.0605037\pi$
$332$	2.33228	0.128001
$333$	−2.90821	−0.159369
$334$	−23.2813	−1.27389
$335$	4.96520	0.271278
$336$	−4.57047	−0.249340
$337$	−25.2399	−1.37491	−0.687453	−	0.726229i	$-0.741271\pi$
$337$	−25.2399	−1.37491	−0.687453	+	0.726229i	$0.741271\pi$
$338$	−1.00000	−0.0543928
$339$	−19.8425	−1.07770
$340$	3.54211	0.192098
$341$	2.00462	0.108556
$342$	7.42004	0.401230
$343$	6.75847	0.364923
$344$	−0.524270	−0.0282667
$345$	1.32320	0.0712386
$346$	−4.13870	−0.222498
$347$	−3.44303	−0.184832	−0.0924159	−	0.995720i	$-0.529459\pi$
$347$	−3.44303	−0.184832	−0.0924159	+	0.995720i	$0.529459\pi$
$348$	−14.0811	−0.754826
$349$	−9.39547	−0.502928	−0.251464	−	0.967867i	$-0.580912\pi$
$349$	−9.39547	−0.502928	−0.251464	+	0.967867i	$0.580912\pi$
$350$	3.47179	0.185575
$351$	−5.61725	−0.299826
$352$	2.00462	0.106847
$353$	−17.5968	−0.936582	−0.468291	−	0.883574i	$-0.655130\pi$
$353$	−17.5968	−0.936582	−0.468291	+	0.883574i	$0.655130\pi$
$354$	15.5524	0.826600
$355$	3.31066	0.175711
$356$	−17.9585	−0.951797
$357$	−16.1891	−0.856819
$358$	3.28901	0.173829
$359$	6.14275	0.324202	0.162101	−	0.986774i	$-0.448173\pi$
$359$	6.14275	0.324202	0.162101	+	0.986774i	$0.448173\pi$
$360$	1.26693	0.0667731
$361$	15.3010	0.805318
$362$	3.24388	0.170495
$363$	−9.19087	−0.482395
$364$	−3.47179	−0.181971
$365$	−15.8329	−0.828730
$366$	−2.45354	−0.128248
$367$	11.2291	0.586156	0.293078	−	0.956089i	$-0.405320\pi$
$367$	11.2291	0.586156	0.293078	+	0.956089i	$0.405320\pi$
$368$	1.00512	0.0523954
$369$	−11.4361	−0.595338
$370$	−2.29547	−0.119336
$371$	29.5817	1.53581
$372$	−1.31646	−0.0682553
$373$	17.2271	0.891985	0.445992	−	0.895037i	$-0.352851\pi$
$373$	17.2271	0.891985	0.445992	+	0.895037i	$0.352851\pi$
$374$	7.10059	0.367163
$375$	1.31646	0.0679817
$376$	−3.98761	−0.205646
$377$	−10.6962	−0.550881
$378$	−19.5019	−1.00307
$379$	38.0099	1.95244	0.976218	−	0.216792i	$-0.0695592\pi$
$379$	38.0099	1.95244	0.976218	+	0.216792i	$0.0695592\pi$
$380$	5.85671	0.300443
$381$	−24.7025	−1.26555
$382$	4.59190	0.234942
$383$	27.3824	1.39917	0.699587	−	0.714548i	$-0.253367\pi$
$383$	27.3824	1.39917	0.699587	+	0.714548i	$0.253367\pi$
$384$	−1.31646	−0.0671804
$385$	6.95962	0.354695
$386$	5.31717	0.270637
$387$	−0.664213	−0.0337639
$388$	−15.4285	−0.783261
$389$	10.0285	0.508466	0.254233	−	0.967143i	$-0.418177\pi$
$389$	10.0285	0.508466	0.254233	+	0.967143i	$0.418177\pi$
$390$	−1.31646	−0.0666616
$391$	3.56024	0.180049
$392$	−5.05332	−0.255231
$393$	−3.17209	−0.160011
$394$	11.2996	0.569268
$395$	−0.302504	−0.0152206
$396$	2.53972	0.127625
$397$	12.1492	0.609751	0.304875	−	0.952392i	$-0.401385\pi$
$397$	12.1492	0.609751	0.304875	+	0.952392i	$0.401385\pi$
$398$	−19.3635	−0.970607
$399$	−26.7679	−1.34007
$400$	1.00000	0.0500000
$401$	−37.5868	−1.87699	−0.938497	−	0.345288i	$-0.887781\pi$
$401$	−37.5868	−1.87699	−0.938497	+	0.345288i	$0.887781\pi$
$402$	−6.53650	−0.326011
$403$	−1.00000	−0.0498135
$404$	10.2414	0.509529
$405$	−3.59409	−0.178592
$406$	−37.1348	−1.84297
$407$	−4.60156	−0.228091
$408$	−4.66305	−0.230855
$409$	25.2394	1.24801	0.624004	−	0.781421i	$-0.285505\pi$
$409$	25.2394	1.24801	0.624004	+	0.781421i	$0.285505\pi$
$410$	−9.02659	−0.445791
$411$	10.3753	0.511777
$412$	−13.6086	−0.670450
$413$	41.0150	2.01821
$414$	1.27341	0.0625849
$415$	2.33228	0.114487
$416$	−1.00000	−0.0490290
$417$	−9.64000	−0.472073
$418$	11.7405	0.574245
$419$	−26.5558	−1.29733	−0.648667	−	0.761072i	$-0.724673\pi$
$419$	−26.5558	−1.29733	−0.648667	+	0.761072i	$0.724673\pi$
$420$	−4.57047	−0.223016
$421$	−0.406423	−0.0198078	−0.00990392	−	0.999951i	$-0.503153\pi$
$421$	−0.406423	−0.0198078	−0.00990392	+	0.999951i	$0.503153\pi$
$422$	4.79901	0.233612
$423$	−5.05203	−0.245638
$424$	8.52059	0.413797
$425$	3.54211	0.171818
$426$	−4.35835	−0.211163
$427$	−6.47050	−0.313130
$428$	−18.6026	−0.899193
$429$	−2.63900	−0.127412
$430$	−0.524270	−0.0252825
$431$	3.44247	0.165818	0.0829090	−	0.996557i	$-0.473579\pi$
$431$	3.44247	0.165818	0.0829090	+	0.996557i	$0.473579\pi$
$432$	−5.61725	−0.270260
$433$	22.8848	1.09977	0.549887	−	0.835239i	$-0.314671\pi$
$433$	22.8848	1.09977	0.549887	+	0.835239i	$0.314671\pi$
$434$	−3.47179	−0.166651
$435$	−14.0811	−0.675137
$436$	−3.91146	−0.187325
$437$	5.88668	0.281598
$438$	20.8434	0.995934
$439$	−1.41165	−0.0673743	−0.0336871	−	0.999432i	$-0.510725\pi$
$439$	−1.41165	−0.0673743	−0.0336871	+	0.999432i	$0.510725\pi$
$440$	2.00462	0.0955665
$441$	−6.40220	−0.304867
$442$	−3.54211	−0.168481
$443$	5.78273	0.274746	0.137373	−	0.990519i	$-0.456134\pi$
$443$	5.78273	0.274746	0.137373	+	0.990519i	$0.456134\pi$
$444$	3.02190	0.143413
$445$	−17.9585	−0.851313
$446$	−12.1514	−0.575384
$447$	−7.34858	−0.347576
$448$	−3.47179	−0.164027
$449$	27.5093	1.29825	0.649123	−	0.760683i	$-0.275136\pi$
$449$	27.5093	1.29825	0.649123	+	0.760683i	$0.275136\pi$
$450$	1.26693	0.0597237
$451$	−18.0949	−0.852055
$452$	−15.0726	−0.708957
$453$	23.9294	1.12430
$454$	−20.9306	−0.982323
$455$	−3.47179	−0.162760
$456$	−7.71013	−0.361060
$457$	31.8436	1.48958	0.744791	−	0.667298i	$-0.232549\pi$
$457$	31.8436	1.48958	0.744791	+	0.667298i	$0.232549\pi$
$458$	−15.7740	−0.737073
$459$	−19.8969	−0.928708
$460$	1.00512	0.0468639
$461$	−2.43581	−0.113447	−0.0567236	−	0.998390i	$-0.518065\pi$
$461$	−2.43581	−0.113447	−0.0567236	+	0.998390i	$0.518065\pi$
$462$	−9.16207	−0.426258
$463$	5.28464	0.245598	0.122799	−	0.992432i	$-0.460813\pi$
$463$	5.28464	0.245598	0.122799	+	0.992432i	$0.460813\pi$
$464$	−10.6962	−0.496557
$465$	−1.31646	−0.0610494
$466$	24.6372	1.14129
$467$	−26.5954	−1.23069	−0.615343	−	0.788259i	$-0.710983\pi$
$467$	−26.5954	−1.23069	−0.615343	+	0.788259i	$0.710983\pi$
$468$	−1.26693	−0.0585639
$469$	−17.2381	−0.795983
$470$	−3.98761	−0.183935
$471$	14.9779	0.690145
$472$	11.8138	0.543774
$473$	−1.05096	−0.0483233
$474$	0.398235	0.0182915
$475$	5.85671	0.268724
$476$	−12.2975	−0.563653
$477$	10.7950	0.494269
$478$	10.7894	0.493496
$479$	−17.4414	−0.796920	−0.398460	−	0.917186i	$-0.630455\pi$
$479$	−17.4414	−0.796920	−0.398460	+	0.917186i	$0.630455\pi$
$480$	−1.31646	−0.0600879
$481$	2.29547	0.104665
$482$	1.96468	0.0894887
$483$	−4.59386	−0.209028
$484$	−6.98150	−0.317341
$485$	−15.4285	−0.700570
$486$	−12.1203	−0.549786
$487$	23.5744	1.06826	0.534129	−	0.845403i	$-0.320640\pi$
$487$	23.5744	1.06826	0.534129	+	0.845403i	$0.320640\pi$
$488$	−1.86374	−0.0843674
$489$	−14.8224	−0.670291
$490$	−5.05332	−0.228286
$491$	−13.6671	−0.616788	−0.308394	−	0.951259i	$-0.599792\pi$
$491$	−13.6671	−0.616788	−0.308394	+	0.951259i	$0.599792\pi$
$492$	11.8832	0.535734
$493$	−37.8870	−1.70635
$494$	−5.85671	−0.263506
$495$	2.53972	0.114152
$496$	−1.00000	−0.0449013
$497$	−11.4939	−0.515572
$498$	−3.07036	−0.137586
$499$	−7.81859	−0.350008	−0.175004	−	0.984568i	$-0.555994\pi$
$499$	−7.81859	−0.350008	−0.175004	+	0.984568i	$0.555994\pi$
$500$	1.00000	0.0447214
$501$	30.6489	1.36929
$502$	−10.0753	−0.449685
$503$	14.4897	0.646065	0.323033	−	0.946388i	$-0.395298\pi$
$503$	14.4897	0.646065	0.323033	+	0.946388i	$0.395298\pi$
$504$	−4.39852	−0.195925
$505$	10.2414	0.455736
$506$	2.01488	0.0895723
$507$	1.31646	0.0584661
$508$	−18.7643	−0.832533
$509$	−33.5164	−1.48559	−0.742795	−	0.669519i	$-0.766500\pi$
$509$	−33.5164	−1.48559	−0.742795	+	0.669519i	$0.766500\pi$
$510$	−4.66305	−0.206483
$511$	54.9684	2.43166
$512$	−1.00000	−0.0441942
$513$	−32.8986	−1.45251
$514$	28.9232	1.27575
$515$	−13.6086	−0.599669
$516$	0.690180	0.0303835
$517$	−7.99365	−0.351560
$518$	7.96940	0.350156
$519$	5.44843	0.239160
$520$	−1.00000	−0.0438529
$521$	39.0399	1.71037	0.855184	−	0.518324i	$-0.173444\pi$
$521$	39.0399	1.71037	0.855184	+	0.518324i	$0.173444\pi$
$522$	−13.5513	−0.593125
$523$	−6.68063	−0.292123	−0.146062	−	0.989275i	$-0.546660\pi$
$523$	−6.68063	−0.292123	−0.146062	+	0.989275i	$0.546660\pi$
$524$	−2.40956	−0.105262
$525$	−4.57047	−0.199472
$526$	23.3212	1.01685
$527$	−3.54211	−0.154297
$528$	−2.63900	−0.114848
$529$	−21.9897	−0.956076
$530$	8.52059	0.370111
$531$	14.9672	0.649523
$532$	−20.3333	−0.881558
$533$	9.02659	0.390985
$534$	23.6416	1.02307
$535$	−18.6026	−0.804263
$536$	−4.96520	−0.214464
$537$	−4.32985	−0.186847
$538$	−8.22606	−0.354651
$539$	−10.1300	−0.436329
$540$	−5.61725	−0.241728
$541$	38.7923	1.66781	0.833906	−	0.551907i	$-0.186100\pi$
$541$	38.7923	1.66781	0.833906	+	0.551907i	$0.186100\pi$
$542$	8.75484	0.376053
$543$	−4.27044	−0.183262
$544$	−3.54211	−0.151867
$545$	−3.91146	−0.167549
$546$	4.57047	0.195598
$547$	37.9415	1.62226	0.811131	−	0.584865i	$-0.198853\pi$
$547$	37.9415	1.62226	0.811131	+	0.584865i	$0.198853\pi$
$548$	7.88123	0.336669
$549$	−2.36123	−0.100775
$550$	2.00462	0.0854773
$551$	−62.6444	−2.66874
$552$	−1.32320	−0.0563191
$553$	1.05023	0.0446603
$554$	14.8801	0.632196
$555$	3.02190	0.128273
$556$	−7.32267	−0.310550
$557$	−34.7310	−1.47160	−0.735801	−	0.677198i	$-0.763194\pi$
$557$	−34.7310	−1.47160	−0.735801	+	0.677198i	$0.763194\pi$
$558$	−1.26693	−0.0536335
$559$	0.524270	0.0221742
$560$	−3.47179	−0.146710
$561$	−9.34765	−0.394658
$562$	−15.2964	−0.645238
$563$	−23.1683	−0.976428	−0.488214	−	0.872724i	$-0.662351\pi$
$563$	−23.1683	−0.976428	−0.488214	+	0.872724i	$0.662351\pi$
$564$	5.24954	0.221045
$565$	−15.0726	−0.634111
$566$	−3.80880	−0.160096
$567$	12.4779	0.524024
$568$	−3.31066	−0.138912
$569$	16.2957	0.683152	0.341576	−	0.939854i	$-0.389039\pi$
$569$	16.2957	0.683152	0.341576	+	0.939854i	$0.389039\pi$
$570$	−7.71013	−0.322942
$571$	−13.2418	−0.554151	−0.277076	−	0.960848i	$-0.589365\pi$
$571$	−13.2418	−0.554151	−0.277076	+	0.960848i	$0.589365\pi$
$572$	−2.00462	−0.0838174
$573$	−6.04506	−0.252536
$574$	31.3384	1.30804
$575$	1.00512	0.0419163
$576$	−1.26693	−0.0527888
$577$	−42.3138	−1.76155	−0.880773	−	0.473538i	$-0.842977\pi$
$577$	−42.3138	−1.76155	−0.880773	+	0.473538i	$0.842977\pi$
$578$	4.45345	0.185239
$579$	−6.99985	−0.290904
$580$	−10.6962	−0.444134
$581$	−8.09719	−0.335928
$582$	20.3110	0.841916
$583$	17.0806	0.707404
$584$	15.8329	0.655169
$585$	−1.26693	−0.0523811
$586$	21.6727	0.895291
$587$	27.3005	1.12681	0.563405	−	0.826181i	$-0.309491\pi$
$587$	27.3005	1.12681	0.563405	+	0.826181i	$0.309491\pi$
$588$	6.65249	0.274344
$589$	−5.85671	−0.241321
$590$	11.8138	0.486366
$591$	−14.8755	−0.611898
$592$	2.29547	0.0943434
$593$	−29.3655	−1.20590	−0.602949	−	0.797780i	$-0.706008\pi$
$593$	−29.3655	−1.20590	−0.602949	+	0.797780i	$0.706008\pi$
$594$	−11.2604	−0.462022
$595$	−12.2975	−0.504147
$596$	−5.58207	−0.228651
$597$	25.4913	1.04329
$598$	−1.00512	−0.0411023
$599$	−12.5867	−0.514277	−0.257139	−	0.966375i	$-0.582780\pi$
$599$	−12.5867	−0.514277	−0.257139	+	0.966375i	$0.582780\pi$
$600$	−1.31646	−0.0537443
$601$	16.0040	0.652816	0.326408	−	0.945229i	$-0.394162\pi$
$601$	16.0040	0.652816	0.326408	+	0.945229i	$0.394162\pi$
$602$	1.82015	0.0741839
$603$	−6.29057	−0.256172
$604$	18.1771	0.739614
$605$	−6.98150	−0.283838
$606$	−13.4824	−0.547685
$607$	7.51163	0.304888	0.152444	−	0.988312i	$-0.451286\pi$
$607$	7.51163	0.304888	0.152444	+	0.988312i	$0.451286\pi$
$608$	−5.85671	−0.237521
$609$	48.8866	1.98098
$610$	−1.86374	−0.0754605
$611$	3.98761	0.161322
$612$	−4.48761	−0.181401
$613$	−37.9479	−1.53270	−0.766350	−	0.642424i	$-0.777929\pi$
$613$	−37.9479	−1.53270	−0.766350	+	0.642424i	$0.777929\pi$
$614$	21.7515	0.877818
$615$	11.8832	0.479175
$616$	−6.95962	−0.280411
$617$	39.8526	1.60441	0.802203	−	0.597051i	$-0.203661\pi$
$617$	39.8526	1.60441	0.802203	+	0.597051i	$0.203661\pi$
$618$	17.9153	0.720657
$619$	−17.9824	−0.722773	−0.361386	−	0.932416i	$-0.617696\pi$
$619$	−17.9824	−0.722773	−0.361386	+	0.932416i	$0.617696\pi$
$620$	−1.00000	−0.0401610
$621$	−5.64600	−0.226566
$622$	−19.0498	−0.763827
$623$	62.3480	2.49792
$624$	1.31646	0.0527006
$625$	1.00000	0.0400000
$626$	−5.63232	−0.225113
$627$	−15.4559	−0.617248
$628$	11.3774	0.454008
$629$	8.13083	0.324197
$630$	−4.39852	−0.175241
$631$	−5.70939	−0.227287	−0.113644	−	0.993522i	$-0.536252\pi$
$631$	−5.70939	−0.227287	−0.113644	+	0.993522i	$0.536252\pi$
$632$	0.302504	0.0120330
$633$	−6.31771	−0.251106
$634$	−7.04210	−0.279677
$635$	−18.7643	−0.744640
$636$	−11.2170	−0.444784
$637$	5.05332	0.200220
$638$	−21.4418	−0.848887
$639$	−4.19437	−0.165927
$640$	−1.00000	−0.0395285
$641$	44.0678	1.74057	0.870287	−	0.492546i	$-0.163934\pi$
$641$	44.0678	1.74057	0.870287	+	0.492546i	$0.163934\pi$
$642$	24.4897	0.966530
$643$	−34.8018	−1.37245	−0.686224	−	0.727391i	$-0.740733\pi$
$643$	−34.8018	−1.37245	−0.686224	+	0.727391i	$0.740733\pi$
$644$	−3.48956	−0.137508
$645$	0.690180	0.0271758
$646$	−20.7451	−0.816205
$647$	−22.2306	−0.873974	−0.436987	−	0.899468i	$-0.643954\pi$
$647$	−22.2306	−0.873974	−0.436987	+	0.899468i	$0.643954\pi$
$648$	3.59409	0.141189
$649$	23.6822	0.929606
$650$	−1.00000	−0.0392232
$651$	4.57047	0.179131
$652$	−11.2593	−0.440946
$653$	33.3224	1.30401	0.652004	−	0.758216i	$-0.273929\pi$
$653$	33.3224	1.30401	0.652004	+	0.758216i	$0.273929\pi$
$654$	5.14929	0.201353
$655$	−2.40956	−0.0941493
$656$	9.02659	0.352429
$657$	20.0592	0.782582
$658$	13.8442	0.539701
$659$	−21.9862	−0.856462	−0.428231	−	0.903669i	$-0.640863\pi$
$659$	−21.9862	−0.856462	−0.428231	+	0.903669i	$0.640863\pi$
$660$	−2.63900	−0.102723
$661$	−23.5678	−0.916680	−0.458340	−	0.888777i	$-0.651556\pi$
$661$	−23.5678	−0.916680	−0.458340	+	0.888777i	$0.651556\pi$
$662$	−35.7315	−1.38874
$663$	4.66305	0.181098
$664$	−2.33228	−0.0905101
$665$	−20.3333	−0.788490
$666$	2.90821	0.112691
$667$	−10.7509	−0.416277
$668$	23.2813	0.900780
$669$	15.9968	0.618472
$670$	−4.96520	−0.191823
$671$	−3.73609	−0.144230
$672$	4.57047	0.176310
$673$	13.0647	0.503605	0.251803	−	0.967779i	$-0.418977\pi$
$673$	13.0647	0.503605	0.251803	+	0.967779i	$0.418977\pi$
$674$	25.2399	0.972206
$675$	−5.61725	−0.216208
$676$	1.00000	0.0384615
$677$	−19.8607	−0.763308	−0.381654	−	0.924305i	$-0.624645\pi$
$677$	−19.8607	−0.763308	−0.381654	+	0.924305i	$0.624645\pi$
$678$	19.8425	0.762048
$679$	53.5643	2.05561
$680$	−3.54211	−0.135834
$681$	27.5544	1.05589
$682$	−2.00462	−0.0767609
$683$	16.9955	0.650313	0.325156	−	0.945660i	$-0.394583\pi$
$683$	16.9955	0.650313	0.325156	+	0.945660i	$0.394583\pi$
$684$	−7.42004	−0.283712
$685$	7.88123	0.301126
$686$	−6.75847	−0.258040
$687$	20.7659	0.792269
$688$	0.524270	0.0199876
$689$	−8.52059	−0.324609
$690$	−1.32320	−0.0503733
$691$	−7.52735	−0.286354	−0.143177	−	0.989697i	$-0.545732\pi$
$691$	−7.52735	−0.286354	−0.143177	+	0.989697i	$0.545732\pi$
$692$	4.13870	0.157330
$693$	−8.81735	−0.334944
$694$	3.44303	0.130696
$695$	−7.32267	−0.277765
$696$	14.0811	0.533742
$697$	31.9732	1.21107
$698$	9.39547	0.355624
$699$	−32.4339	−1.22676
$700$	−3.47179	−0.131221
$701$	−36.8812	−1.39298	−0.696492	−	0.717565i	$-0.745257\pi$
$701$	−36.8812	−1.39298	−0.696492	+	0.717565i	$0.745257\pi$
$702$	5.61725	0.212009
$703$	13.4439	0.507047
$704$	−2.00462	−0.0755520
$705$	5.24954	0.197709
$706$	17.5968	0.662263
$707$	−35.5560	−1.33722
$708$	−15.5524	−0.584494
$709$	33.6477	1.26366	0.631832	−	0.775105i	$-0.282303\pi$
$709$	33.6477	1.26366	0.631832	+	0.775105i	$0.282303\pi$
$710$	−3.31066	−0.124247
$711$	0.383251	0.0143731
$712$	17.9585	0.673022
$713$	−1.00512	−0.0376420
$714$	16.1891	0.605863
$715$	−2.00462	−0.0749685
$716$	−3.28901	−0.122916
$717$	−14.2038	−0.530452
$718$	−6.14275	−0.229245
$719$	−13.6389	−0.508644	−0.254322	−	0.967120i	$-0.581852\pi$
$719$	−13.6389	−0.508644	−0.254322	+	0.967120i	$0.581852\pi$
$720$	−1.26693	−0.0472157
$721$	47.2464	1.75955
$722$	−15.3010	−0.569445
$723$	−2.58642	−0.0961902
$724$	−3.24388	−0.120558
$725$	−10.6962	−0.397246
$726$	9.19087	0.341105
$727$	−9.10948	−0.337852	−0.168926	−	0.985629i	$-0.554030\pi$
$727$	−9.10948	−0.337852	−0.168926	+	0.985629i	$0.554030\pi$
$728$	3.47179	0.128673
$729$	26.7381	0.990301
$730$	15.8329	0.586001
$731$	1.85702	0.0686844
$732$	2.45354	0.0906853
$733$	−34.5239	−1.27517	−0.637585	−	0.770380i	$-0.720067\pi$
$733$	−34.5239	−1.27517	−0.637585	+	0.770380i	$0.720067\pi$
$734$	−11.2291	−0.414475
$735$	6.65249	0.245381
$736$	−1.00512	−0.0370491
$737$	−9.95335	−0.366636
$738$	11.4361	0.420967
$739$	−0.362837	−0.0133472	−0.00667359	−	0.999978i	$-0.502124\pi$
$739$	−0.362837	−0.0133472	−0.00667359	+	0.999978i	$0.502124\pi$
$740$	2.29547	0.0843833
$741$	7.71013	0.283239
$742$	−29.5817	−1.08598
$743$	−50.6122	−1.85678	−0.928391	−	0.371605i	$-0.878808\pi$
$743$	−50.6122	−1.85678	−0.928391	+	0.371605i	$0.878808\pi$
$744$	1.31646	0.0482638
$745$	−5.58207	−0.204511
$746$	−17.2271	−0.630729
$747$	−2.95484	−0.108112
$748$	−7.10059	−0.259623
$749$	64.5845	2.35986
$750$	−1.31646	−0.0480704
$751$	9.30312	0.339476	0.169738	−	0.985489i	$-0.445708\pi$
$751$	9.30312	0.339476	0.169738	+	0.985489i	$0.445708\pi$
$752$	3.98761	0.145413
$753$	13.2638	0.483360
$754$	10.6962	0.389532
$755$	18.1771	0.661531
$756$	19.5019	0.709277
$757$	30.5918	1.11188	0.555939	−	0.831223i	$-0.312359\pi$
$757$	30.5918	1.11188	0.555939	+	0.831223i	$0.312359\pi$
$758$	−38.0099	−1.38058
$759$	−2.65251	−0.0962800
$760$	−5.85671	−0.212445
$761$	−9.19833	−0.333439	−0.166720	−	0.986004i	$-0.553317\pi$
$761$	−9.19833	−0.333439	−0.166720	+	0.986004i	$0.553317\pi$
$762$	24.7025	0.894878
$763$	13.5798	0.491621
$764$	−4.59190	−0.166129
$765$	−4.48761	−0.162250
$766$	−27.3824	−0.989365
$767$	−11.8138	−0.426571
$768$	1.31646	0.0475037
$769$	−21.9871	−0.792876	−0.396438	−	0.918062i	$-0.629754\pi$
$769$	−21.9871	−0.792876	−0.396438	+	0.918062i	$0.629754\pi$
$770$	−6.95962	−0.250807
$771$	−38.0763	−1.37128
$772$	−5.31717	−0.191369
$773$	−11.1024	−0.399327	−0.199664	−	0.979865i	$-0.563985\pi$
$773$	−11.1024	−0.399327	−0.199664	+	0.979865i	$0.563985\pi$
$774$	0.664213	0.0238746
$775$	−1.00000	−0.0359211
$776$	15.4285	0.553849
$777$	−10.4914	−0.376377
$778$	−10.0285	−0.359540
$779$	52.8661	1.89412
$780$	1.31646	0.0471369
$781$	−6.63661	−0.237476
$782$	−3.56024	−0.127314
$783$	60.0830	2.14719
$784$	5.05332	0.180476
$785$	11.3774	0.406077
$786$	3.17209	0.113145
$787$	7.43961	0.265194	0.132597	−	0.991170i	$-0.457668\pi$
$787$	7.43961	0.265194	0.132597	+	0.991170i	$0.457668\pi$
$788$	−11.2996	−0.402533
$789$	−30.7015	−1.09300
$790$	0.302504	0.0107626
$791$	52.3290	1.86061
$792$	−2.53972	−0.0902448
$793$	1.86374	0.0661833
$794$	−12.1492	−0.431159
$795$	−11.2170	−0.397827
$796$	19.3635	0.686322
$797$	−16.9861	−0.601678	−0.300839	−	0.953675i	$-0.597267\pi$
$797$	−16.9861	−0.601678	−0.300839	+	0.953675i	$0.597267\pi$
$798$	26.7679	0.947575
$799$	14.1246	0.499692
$800$	−1.00000	−0.0353553
$801$	22.7521	0.803907
$802$	37.5868	1.32723
$803$	31.7389	1.12004
$804$	6.53650	0.230524
$805$	−3.48956	−0.122991
$806$	1.00000	0.0352235
$807$	10.8293	0.381209
$808$	−10.2414	−0.360291
$809$	−52.6439	−1.85086	−0.925431	−	0.378915i	$-0.876297\pi$
$809$	−52.6439	−1.85086	−0.925431	+	0.378915i	$0.876297\pi$
$810$	3.59409	0.126284
$811$	2.80087	0.0983520	0.0491760	−	0.998790i	$-0.484340\pi$
$811$	2.80087	0.0983520	0.0491760	+	0.998790i	$0.484340\pi$
$812$	37.1348	1.30318
$813$	−11.5254	−0.404214
$814$	4.60156	0.161284
$815$	−11.2593	−0.394394
$816$	4.66305	0.163239
$817$	3.07049	0.107423
$818$	−25.2394	−0.882475
$819$	4.39852	0.153697
$820$	9.02659	0.315222
$821$	−10.8887	−0.380018	−0.190009	−	0.981782i	$-0.560852\pi$
$821$	−10.8887	−0.380018	−0.190009	+	0.981782i	$0.560852\pi$
$822$	−10.3753	−0.361881
$823$	37.6277	1.31162	0.655809	−	0.754927i	$-0.272328\pi$
$823$	37.6277	1.31162	0.655809	+	0.754927i	$0.272328\pi$
$824$	13.6086	0.474080
$825$	−2.63900	−0.0918783
$826$	−41.0150	−1.42709
$827$	−37.1076	−1.29036	−0.645179	−	0.764031i	$-0.723217\pi$
$827$	−37.1076	−1.29036	−0.645179	+	0.764031i	$0.723217\pi$
$828$	−1.27341	−0.0442542
$829$	24.1791	0.839774	0.419887	−	0.907576i	$-0.362070\pi$
$829$	24.1791	0.839774	0.419887	+	0.907576i	$0.362070\pi$
$830$	−2.33228	−0.0809547
$831$	−19.5891	−0.679538
$832$	1.00000	0.0346688
$833$	17.8994	0.620178
$834$	9.64000	0.333806
$835$	23.2813	0.805682
$836$	−11.7405	−0.406053
$837$	5.61725	0.194160
$838$	26.5558	0.917354
$839$	5.66676	0.195638	0.0978192	−	0.995204i	$-0.468813\pi$
$839$	5.66676	0.195638	0.0978192	+	0.995204i	$0.468813\pi$
$840$	4.57047	0.157696
$841$	85.4081	2.94511
$842$	0.406423	0.0140063
$843$	20.1371	0.693557
$844$	−4.79901	−0.165189
$845$	1.00000	0.0344010
$846$	5.05203	0.173692
$847$	24.2383	0.832837
$848$	−8.52059	−0.292598
$849$	5.01414	0.172085
$850$	−3.54211	−0.121493
$851$	2.30722	0.0790906
$852$	4.35835	0.149315
$853$	−15.6920	−0.537284	−0.268642	−	0.963240i	$-0.586575\pi$
$853$	−15.6920	−0.537284	−0.268642	+	0.963240i	$0.586575\pi$
$854$	6.47050	0.221416
$855$	−7.42004	−0.253760
$856$	18.6026	0.635825
$857$	32.9665	1.12611	0.563057	−	0.826418i	$-0.309625\pi$
$857$	32.9665	1.12611	0.563057	+	0.826418i	$0.309625\pi$
$858$	2.63900	0.0900941
$859$	23.3719	0.797438	0.398719	−	0.917073i	$-0.369455\pi$
$859$	23.3719	0.797438	0.398719	+	0.917073i	$0.369455\pi$
$860$	0.524270	0.0178774
$861$	−41.2558	−1.40599
$862$	−3.44247	−0.117251
$863$	19.6340	0.668350	0.334175	−	0.942511i	$-0.391542\pi$
$863$	19.6340	0.668350	0.334175	+	0.942511i	$0.391542\pi$
$864$	5.61725	0.191103
$865$	4.13870	0.140720
$866$	−22.8848	−0.777657
$867$	−5.86279	−0.199111
$868$	3.47179	0.117840
$869$	0.606405	0.0205709
$870$	14.0811	0.477394
$871$	4.96520	0.168239
$872$	3.91146	0.132459
$873$	19.5468	0.661558
$874$	−5.88668	−0.199120
$875$	−3.47179	−0.117368
$876$	−20.8434	−0.704232
$877$	−17.7469	−0.599270	−0.299635	−	0.954054i	$-0.596865\pi$
$877$	−17.7469	−0.599270	−0.299635	+	0.954054i	$0.596865\pi$
$878$	1.41165	0.0476408
$879$	−28.5313	−0.962335
$880$	−2.00462	−0.0675757
$881$	−23.5215	−0.792461	−0.396230	−	0.918151i	$-0.629682\pi$
$881$	−23.5215	−0.792461	−0.396230	+	0.918151i	$0.629682\pi$
$882$	6.40220	0.215573
$883$	−26.8682	−0.904188	−0.452094	−	0.891970i	$-0.649323\pi$
$883$	−26.8682	−0.904188	−0.452094	+	0.891970i	$0.649323\pi$
$884$	3.54211	0.119134
$885$	−15.5524	−0.522788
$886$	−5.78273	−0.194275
$887$	−48.7650	−1.63737	−0.818684	−	0.574244i	$-0.805296\pi$
$887$	−48.7650	−1.63737	−0.818684	+	0.574244i	$0.805296\pi$
$888$	−3.02190	−0.101408
$889$	65.1458	2.18492
$890$	17.9585	0.601969
$891$	7.20479	0.241370
$892$	12.1514	0.406858
$893$	23.3543	0.781522
$894$	7.34858	0.245773
$895$	−3.28901	−0.109939
$896$	3.47179	0.115984
$897$	1.32320	0.0441803
$898$	−27.5093	−0.917999
$899$	10.6962	0.356737
$900$	−1.26693	−0.0422310
$901$	−30.1809	−1.00547
$902$	18.0949	0.602494
$903$	−2.39616	−0.0797392
$904$	15.0726	0.501308
$905$	−3.24388	−0.107830
$906$	−23.9294	−0.795000
$907$	−46.5896	−1.54698	−0.773491	−	0.633807i	$-0.781491\pi$
$907$	−46.5896	−1.54698	−0.773491	+	0.633807i	$0.781491\pi$
$908$	20.9306	0.694607
$909$	−12.9751	−0.430358
$910$	3.47179	0.115089
$911$	−12.3108	−0.407874	−0.203937	−	0.978984i	$-0.565374\pi$
$911$	−12.3108	−0.407874	−0.203937	+	0.978984i	$0.565374\pi$
$912$	7.71013	0.255308
$913$	−4.67534	−0.154731
$914$	−31.8436	−1.05329
$915$	2.45354	0.0811114
$916$	15.7740	0.521189
$917$	8.36549	0.276253
$918$	19.8969	0.656696
$919$	43.9133	1.44857	0.724284	−	0.689502i	$-0.242171\pi$
$919$	43.9133	1.44857	0.724284	+	0.689502i	$0.242171\pi$
$920$	−1.00512	−0.0331378
$921$	−28.6350	−0.943555
$922$	2.43581	0.0802193
$923$	3.31066	0.108972
$924$	9.16207	0.301410
$925$	2.29547	0.0754748
$926$	−5.28464	−0.173664
$927$	17.2412	0.566276
$928$	10.6962	0.351119
$929$	49.6325	1.62839	0.814195	−	0.580592i	$-0.197179\pi$
$929$	49.6325	1.62839	0.814195	+	0.580592i	$0.197179\pi$
$930$	1.31646	0.0431685
$931$	29.5958	0.969963
$932$	−24.6372	−0.807017
$933$	25.0783	0.821027
$934$	26.5954	0.870227
$935$	−7.10059	−0.232214
$936$	1.26693	0.0414109
$937$	−1.46374	−0.0478182	−0.0239091	−	0.999714i	$-0.507611\pi$
$937$	−1.46374	−0.0478182	−0.0239091	+	0.999714i	$0.507611\pi$
$938$	17.2381	0.562845
$939$	7.41473	0.241970
$940$	3.98761	0.130062
$941$	−50.9672	−1.66148	−0.830742	−	0.556658i	$-0.812083\pi$
$941$	−50.9672	−1.66148	−0.830742	+	0.556658i	$0.812083\pi$
$942$	−14.9779	−0.488007
$943$	9.07278	0.295451
$944$	−11.8138	−0.384506
$945$	19.5019	0.634397
$946$	1.05096	0.0341697
$947$	−14.4646	−0.470037	−0.235019	−	0.971991i	$-0.575515\pi$
$947$	−14.4646	−0.470037	−0.235019	+	0.971991i	$0.575515\pi$
$948$	−0.398235	−0.0129341
$949$	−15.8329	−0.513957
$950$	−5.85671	−0.190017
$951$	9.27064	0.300621
$952$	12.2975	0.398563
$953$	−30.8289	−0.998646	−0.499323	−	0.866416i	$-0.666418\pi$
$953$	−30.8289	−0.998646	−0.499323	+	0.866416i	$0.666418\pi$
$954$	−10.7950	−0.349501
$955$	−4.59190	−0.148591
$956$	−10.7894	−0.348955
$957$	28.2272	0.912457
$958$	17.4414	0.563508
$959$	−27.3620	−0.883564
$960$	1.31646	0.0424886
$961$	1.00000	0.0322581
$962$	−2.29547	−0.0740091
$963$	23.5683	0.759477
$964$	−1.96468	−0.0632781
$965$	−5.31717	−0.171166
$966$	4.59386	0.147805
$967$	6.30779	0.202845	0.101422	−	0.994843i	$-0.467661\pi$
$967$	6.30779	0.202845	0.101422	+	0.994843i	$0.467661\pi$
$968$	6.98150	0.224394
$969$	27.3101	0.877328
$970$	15.4285	0.495378
$971$	27.5095	0.882821	0.441411	−	0.897305i	$-0.354478\pi$
$971$	27.5095	0.882821	0.441411	+	0.897305i	$0.354478\pi$
$972$	12.1203	0.388757
$973$	25.4228	0.815016
$974$	−23.5744	−0.755373
$975$	1.31646	0.0421605
$976$	1.86374	0.0596568
$977$	−28.0420	−0.897144	−0.448572	−	0.893747i	$-0.648067\pi$
$977$	−28.0420	−0.897144	−0.448572	+	0.893747i	$0.648067\pi$
$978$	14.8224	0.473967
$979$	35.9999	1.15056
$980$	5.05332	0.161422
$981$	4.95555	0.158219
$982$	13.6671	0.436135
$983$	34.2967	1.09389	0.546947	−	0.837167i	$-0.315790\pi$
$983$	34.2967	1.09389	0.546947	+	0.837167i	$0.315790\pi$
$984$	−11.8832	−0.378821
$985$	−11.2996	−0.360037
$986$	37.8870	1.20657
$987$	−18.2253	−0.580117
$988$	5.85671	0.186327
$989$	0.526953	0.0167561
$990$	−2.53972	−0.0807174
$991$	16.6647	0.529371	0.264686	−	0.964335i	$-0.414732\pi$
$991$	16.6647	0.529371	0.264686	+	0.964335i	$0.414732\pi$
$992$	1.00000	0.0317500
$993$	47.0391	1.49274
$994$	11.4939	0.364564
$995$	19.3635	0.613865
$996$	3.07036	0.0972880
$997$	−4.88859	−0.154823	−0.0774116	−	0.996999i	$-0.524666\pi$
$997$	−4.88859	−0.154823	−0.0774116	+	0.996999i	$0.524666\pi$
$998$	7.81859	0.247493
$999$	−12.8943	−0.407956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.d.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.d.1.5	✓	6	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.31646 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31646 q^{6} -3.47179 q^{7} -1.00000 q^{8} -1.26693 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.31646 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.31646 q^{6} -3.47179 q^{7} -1.00000 q^{8} -1.26693 q^{9} -1.00000 q^{10} -2.00462 q^{11} +1.31646 q^{12} +1.00000 q^{13} +3.47179 q^{14} +1.31646 q^{15} +1.00000 q^{16} +3.54211 q^{17} +1.26693 q^{18} +5.85671 q^{19} +1.00000 q^{20} -4.57047 q^{21} +2.00462 q^{22} +1.00512 q^{23} -1.31646 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.61725 q^{27} -3.47179 q^{28} -10.6962 q^{29} -1.31646 q^{30} -1.00000 q^{31} -1.00000 q^{32} -2.63900 q^{33} -3.54211 q^{34} -3.47179 q^{35} -1.26693 q^{36} +2.29547 q^{37} -5.85671 q^{38} +1.31646 q^{39} -1.00000 q^{40} +9.02659 q^{41} +4.57047 q^{42} +0.524270 q^{43} -2.00462 q^{44} -1.26693 q^{45} -1.00512 q^{46} +3.98761 q^{47} +1.31646 q^{48} +5.05332 q^{49} -1.00000 q^{50} +4.66305 q^{51} +1.00000 q^{52} -8.52059 q^{53} +5.61725 q^{54} -2.00462 q^{55} +3.47179 q^{56} +7.71013 q^{57} +10.6962 q^{58} -11.8138 q^{59} +1.31646 q^{60} +1.86374 q^{61} +1.00000 q^{62} +4.39852 q^{63} +1.00000 q^{64} +1.00000 q^{65} +2.63900 q^{66} +4.96520 q^{67} +3.54211 q^{68} +1.32320 q^{69} +3.47179 q^{70} +3.31066 q^{71} +1.26693 q^{72} -15.8329 q^{73} -2.29547 q^{74} +1.31646 q^{75} +5.85671 q^{76} +6.95962 q^{77} -1.31646 q^{78} -0.302504 q^{79} +1.00000 q^{80} -3.59409 q^{81} -9.02659 q^{82} +2.33228 q^{83} -4.57047 q^{84} +3.54211 q^{85} -0.524270 q^{86} -14.0811 q^{87} +2.00462 q^{88} -17.9585 q^{89} +1.26693 q^{90} -3.47179 q^{91} +1.00512 q^{92} -1.31646 q^{93} -3.98761 q^{94} +5.85671 q^{95} -1.31646 q^{96} -15.4285 q^{97} -5.05332 q^{98} +2.53972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} + 6 q^{5} + q^{6} - 2 q^{7} - 6 q^{8} - q^{9} - 6 q^{10} - q^{12} + 6 q^{13} + 2 q^{14} - q^{15} + 6 q^{16} - 10 q^{17} + q^{18} + q^{19} + 6 q^{20} + 3 q^{21} - 13 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - 7 q^{27} - 2 q^{28} - 16 q^{29} + q^{30} - 6 q^{31} - 6 q^{32} - 22 q^{33} + 10 q^{34} - 2 q^{35} - q^{36} - 14 q^{37} - q^{38} - q^{39} - 6 q^{40} - 4 q^{41} - 3 q^{42} + 5 q^{43} - q^{45} + 13 q^{46} - 4 q^{47} - q^{48} + 2 q^{49} - 6 q^{50} + 11 q^{51} + 6 q^{52} - 14 q^{53} + 7 q^{54} + 2 q^{56} - 3 q^{57} + 16 q^{58} - 7 q^{59} - q^{60} - 3 q^{61} + 6 q^{62} - 3 q^{63} + 6 q^{64} + 6 q^{65} + 22 q^{66} - 4 q^{67} - 10 q^{68} - 4 q^{69} + 2 q^{70} + q^{72} - 5 q^{73} + 14 q^{74} - q^{75} + q^{76} - 23 q^{77} + q^{78} + 6 q^{79} + 6 q^{80} - 18 q^{81} + 4 q^{82} - 2 q^{83} + 3 q^{84} - 10 q^{85} - 5 q^{86} - 21 q^{87} - 14 q^{89} + q^{90} - 2 q^{91} - 13 q^{92} + q^{93} + 4 q^{94} + q^{95} + q^{96} - 35 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 + 6 * q^5 + q^6 - 2 * q^7 - 6 * q^8 - q^9 - 6 * q^10 - q^12 + 6 * q^13 + 2 * q^14 - q^15 + 6 * q^16 - 10 * q^17 + q^18 + q^19 + 6 * q^20 + 3 * q^21 - 13 * q^23 + q^24 + 6 * q^25 - 6 * q^26 - 7 * q^27 - 2 * q^28 - 16 * q^29 + q^30 - 6 * q^31 - 6 * q^32 - 22 * q^33 + 10 * q^34 - 2 * q^35 - q^36 - 14 * q^37 - q^38 - q^39 - 6 * q^40 - 4 * q^41 - 3 * q^42 + 5 * q^43 - q^45 + 13 * q^46 - 4 * q^47 - q^48 + 2 * q^49 - 6 * q^50 + 11 * q^51 + 6 * q^52 - 14 * q^53 + 7 * q^54 + 2 * q^56 - 3 * q^57 + 16 * q^58 - 7 * q^59 - q^60 - 3 * q^61 + 6 * q^62 - 3 * q^63 + 6 * q^64 + 6 * q^65 + 22 * q^66 - 4 * q^67 - 10 * q^68 - 4 * q^69 + 2 * q^70 + q^72 - 5 * q^73 + 14 * q^74 - q^75 + q^76 - 23 * q^77 + q^78 + 6 * q^79 + 6 * q^80 - 18 * q^81 + 4 * q^82 - 2 * q^83 + 3 * q^84 - 10 * q^85 - 5 * q^86 - 21 * q^87 - 14 * q^89 + q^90 - 2 * q^91 - 13 * q^92 + q^93 + 4 * q^94 + q^95 + q^96 - 35 * q^97 - 2 * q^98 + 3 * q^99

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