LMFDB - Embedded newform 6034.2.a.q.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.676569 q^{3} +1.00000 q^{4} +1.60949 q^{5} -0.676569 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.54225 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.676569 q^{3} +1.00000 q^{4} +1.60949 q^{5} -0.676569 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.54225 q^{9} +1.60949 q^{10} -5.23122 q^{11} -0.676569 q^{12} +0.0933098 q^{13} +1.00000 q^{14} -1.08893 q^{15} +1.00000 q^{16} +5.37434 q^{17} -2.54225 q^{18} +0.855428 q^{19} +1.60949 q^{20} -0.676569 q^{21} -5.23122 q^{22} -2.70339 q^{23} -0.676569 q^{24} -2.40954 q^{25} +0.0933098 q^{26} +3.74972 q^{27} +1.00000 q^{28} +4.95849 q^{29} -1.08893 q^{30} +0.399936 q^{31} +1.00000 q^{32} +3.53928 q^{33} +5.37434 q^{34} +1.60949 q^{35} -2.54225 q^{36} +7.13497 q^{37} +0.855428 q^{38} -0.0631305 q^{39} +1.60949 q^{40} +8.10200 q^{41} -0.676569 q^{42} -8.50456 q^{43} -5.23122 q^{44} -4.09173 q^{45} -2.70339 q^{46} -3.65177 q^{47} -0.676569 q^{48} +1.00000 q^{49} -2.40954 q^{50} -3.63611 q^{51} +0.0933098 q^{52} +5.61617 q^{53} +3.74972 q^{54} -8.41959 q^{55} +1.00000 q^{56} -0.578756 q^{57} +4.95849 q^{58} +10.9410 q^{59} -1.08893 q^{60} +11.3535 q^{61} +0.399936 q^{62} -2.54225 q^{63} +1.00000 q^{64} +0.150181 q^{65} +3.53928 q^{66} -4.76271 q^{67} +5.37434 q^{68} +1.82903 q^{69} +1.60949 q^{70} -7.86961 q^{71} -2.54225 q^{72} +8.60330 q^{73} +7.13497 q^{74} +1.63022 q^{75} +0.855428 q^{76} -5.23122 q^{77} -0.0631305 q^{78} +7.19773 q^{79} +1.60949 q^{80} +5.08982 q^{81} +8.10200 q^{82} +3.35167 q^{83} -0.676569 q^{84} +8.64994 q^{85} -8.50456 q^{86} -3.35476 q^{87} -5.23122 q^{88} -2.35957 q^{89} -4.09173 q^{90} +0.0933098 q^{91} -2.70339 q^{92} -0.270584 q^{93} -3.65177 q^{94} +1.37680 q^{95} -0.676569 q^{96} +3.23465 q^{97} +1.00000 q^{98} +13.2991 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * 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
$3$	−0.676569	−0.390617	−0.195309	−	0.980742i	$-0.562571\pi$
$3$	−0.676569	−0.390617	−0.195309	+	0.980742i	$0.562571\pi$
$4$	1.00000	0.500000
$5$	1.60949	0.719786	0.359893	−	0.932994i	$-0.382813\pi$
$5$	1.60949	0.719786	0.359893	+	0.932994i	$0.382813\pi$
$6$	−0.676569	−0.276208
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.54225	−0.847418
$10$	1.60949	0.508965
$11$	−5.23122	−1.57727	−0.788635	−	0.614861i	$-0.789212\pi$
$11$	−5.23122	−1.57727	−0.788635	+	0.614861i	$0.789212\pi$
$12$	−0.676569	−0.195309
$13$	0.0933098	0.0258795	0.0129397	−	0.999916i	$-0.495881\pi$
$13$	0.0933098	0.0258795	0.0129397	+	0.999916i	$0.495881\pi$
$14$	1.00000	0.267261
$15$	−1.08893	−0.281161
$16$	1.00000	0.250000
$17$	5.37434	1.30347	0.651734	−	0.758447i	$-0.274042\pi$
$17$	5.37434	1.30347	0.651734	+	0.758447i	$0.274042\pi$
$18$	−2.54225	−0.599215
$19$	0.855428	0.196249	0.0981243	−	0.995174i	$-0.468716\pi$
$19$	0.855428	0.196249	0.0981243	+	0.995174i	$0.468716\pi$
$20$	1.60949	0.359893
$21$	−0.676569	−0.147639
$22$	−5.23122	−1.11530
$23$	−2.70339	−0.563696	−0.281848	−	0.959459i	$-0.590947\pi$
$23$	−2.70339	−0.563696	−0.281848	+	0.959459i	$0.590947\pi$
$24$	−0.676569	−0.138104
$25$	−2.40954	−0.481909
$26$	0.0933098	0.0182995
$27$	3.74972	0.721633
$28$	1.00000	0.188982
$29$	4.95849	0.920768	0.460384	−	0.887720i	$-0.347712\pi$
$29$	4.95849	0.920768	0.460384	+	0.887720i	$0.347712\pi$
$30$	−1.08893	−0.198811
$31$	0.399936	0.0718307	0.0359153	−	0.999355i	$-0.488565\pi$
$31$	0.399936	0.0718307	0.0359153	+	0.999355i	$0.488565\pi$
$32$	1.00000	0.176777
$33$	3.53928	0.616109
$34$	5.37434	0.921691
$35$	1.60949	0.272053
$36$	−2.54225	−0.423709
$37$	7.13497	1.17298	0.586491	−	0.809956i	$-0.300509\pi$
$37$	7.13497	1.17298	0.586491	+	0.809956i	$0.300509\pi$
$38$	0.855428	0.138769
$39$	−0.0631305	−0.0101090
$40$	1.60949	0.254483
$41$	8.10200	1.26532	0.632660	−	0.774430i	$-0.281963\pi$
$41$	8.10200	1.26532	0.632660	+	0.774430i	$0.281963\pi$
$42$	−0.676569	−0.104397
$43$	−8.50456	−1.29693	−0.648467	−	0.761243i	$-0.724589\pi$
$43$	−8.50456	−1.29693	−0.648467	+	0.761243i	$0.724589\pi$
$44$	−5.23122	−0.788635
$45$	−4.09173	−0.609959
$46$	−2.70339	−0.398593
$47$	−3.65177	−0.532666	−0.266333	−	0.963881i	$-0.585812\pi$
$47$	−3.65177	−0.532666	−0.266333	+	0.963881i	$0.585812\pi$
$48$	−0.676569	−0.0976543
$49$	1.00000	0.142857
$50$	−2.40954	−0.340761
$51$	−3.63611	−0.509157
$52$	0.0933098	0.0129397
$53$	5.61617	0.771440	0.385720	−	0.922616i	$-0.373953\pi$
$53$	5.61617	0.771440	0.385720	+	0.922616i	$0.373953\pi$
$54$	3.74972	0.510272
$55$	−8.41959	−1.13530
$56$	1.00000	0.133631
$57$	−0.578756	−0.0766581
$58$	4.95849	0.651082
$59$	10.9410	1.42440	0.712200	−	0.701977i	$-0.247699\pi$
$59$	10.9410	1.42440	0.712200	+	0.701977i	$0.247699\pi$
$60$	−1.08893	−0.140580
$61$	11.3535	1.45367	0.726833	−	0.686815i	$-0.240992\pi$
$61$	11.3535	1.45367	0.726833	+	0.686815i	$0.240992\pi$
$62$	0.399936	0.0507920
$63$	−2.54225	−0.320294
$64$	1.00000	0.125000
$65$	0.150181	0.0186277
$66$	3.53928	0.435655
$67$	−4.76271	−0.581858	−0.290929	−	0.956745i	$-0.593964\pi$
$67$	−4.76271	−0.581858	−0.290929	+	0.956745i	$0.593964\pi$
$68$	5.37434	0.651734
$69$	1.82903	0.220189
$70$	1.60949	0.192371
$71$	−7.86961	−0.933951	−0.466976	−	0.884270i	$-0.654656\pi$
$71$	−7.86961	−0.933951	−0.466976	+	0.884270i	$0.654656\pi$
$72$	−2.54225	−0.299608
$73$	8.60330	1.00694	0.503470	−	0.864013i	$-0.332056\pi$
$73$	8.60330	1.00694	0.503470	+	0.864013i	$0.332056\pi$
$74$	7.13497	0.829423
$75$	1.63022	0.188242
$76$	0.855428	0.0981243
$77$	−5.23122	−0.596152
$78$	−0.0631305	−0.00714812
$79$	7.19773	0.809808	0.404904	−	0.914359i	$-0.367305\pi$
$79$	7.19773	0.809808	0.404904	+	0.914359i	$0.367305\pi$
$80$	1.60949	0.179946
$81$	5.08982	0.565536
$82$	8.10200	0.894716
$83$	3.35167	0.367894	0.183947	−	0.982936i	$-0.441113\pi$
$83$	3.35167	0.367894	0.183947	+	0.982936i	$0.441113\pi$
$84$	−0.676569	−0.0738197
$85$	8.64994	0.938218
$86$	−8.50456	−0.917070
$87$	−3.35476	−0.359668
$88$	−5.23122	−0.557649
$89$	−2.35957	−0.250114	−0.125057	−	0.992150i	$-0.539911\pi$
$89$	−2.35957	−0.250114	−0.125057	+	0.992150i	$0.539911\pi$
$90$	−4.09173	−0.431306
$91$	0.0933098	0.00978152
$92$	−2.70339	−0.281848
$93$	−0.270584	−0.0280583
$94$	−3.65177	−0.376652
$95$	1.37680	0.141257
$96$	−0.676569	−0.0690520
$97$	3.23465	0.328429	0.164215	−	0.986425i	$-0.447491\pi$
$97$	3.23465	0.328429	0.164215	+	0.986425i	$0.447491\pi$
$98$	1.00000	0.101015
$99$	13.2991	1.33661
$100$	−2.40954	−0.240954
$101$	12.0397	1.19800	0.599000	−	0.800749i	$-0.295565\pi$
$101$	12.0397	1.19800	0.599000	+	0.800749i	$0.295565\pi$
$102$	−3.63611	−0.360029
$103$	13.6037	1.34041	0.670205	−	0.742176i	$-0.266206\pi$
$103$	13.6037	1.34041	0.670205	+	0.742176i	$0.266206\pi$
$104$	0.0933098	0.00914977
$105$	−1.08893	−0.106269
$106$	5.61617	0.545491
$107$	2.96597	0.286731	0.143366	−	0.989670i	$-0.454208\pi$
$107$	2.96597	0.286731	0.143366	+	0.989670i	$0.454208\pi$
$108$	3.74972	0.360817
$109$	1.28035	0.122635	0.0613176	−	0.998118i	$-0.480470\pi$
$109$	1.28035	0.122635	0.0613176	+	0.998118i	$0.480470\pi$
$110$	−8.41959	−0.802776
$111$	−4.82730	−0.458187
$112$	1.00000	0.0944911
$113$	7.55956	0.711143	0.355572	−	0.934649i	$-0.384286\pi$
$113$	7.55956	0.711143	0.355572	+	0.934649i	$0.384286\pi$
$114$	−0.578756	−0.0542054
$115$	−4.35108	−0.405741
$116$	4.95849	0.460384
$117$	−0.237217	−0.0219307
$118$	10.9410	1.00720
$119$	5.37434	0.492665
$120$	−1.08893	−0.0994053
$121$	16.3656	1.48778
$122$	11.3535	1.02790
$123$	−5.48156	−0.494256
$124$	0.399936	0.0359153
$125$	−11.9256	−1.06666
$126$	−2.54225	−0.226482
$127$	3.90690	0.346682	0.173341	−	0.984862i	$-0.444544\pi$
$127$	3.90690	0.346682	0.173341	+	0.984862i	$0.444544\pi$
$128$	1.00000	0.0883883
$129$	5.75392	0.506605
$130$	0.150181	0.0131718
$131$	−10.1809	−0.889512	−0.444756	−	0.895652i	$-0.646710\pi$
$131$	−10.1809	−0.889512	−0.444756	+	0.895652i	$0.646710\pi$
$132$	3.53928	0.308055
$133$	0.855428	0.0741750
$134$	−4.76271	−0.411435
$135$	6.03513	0.519421
$136$	5.37434	0.460846
$137$	−3.62561	−0.309757	−0.154878	−	0.987934i	$-0.549499\pi$
$137$	−3.62561	−0.309757	−0.154878	+	0.987934i	$0.549499\pi$
$138$	1.82903	0.155697
$139$	7.29947	0.619133	0.309567	−	0.950878i	$-0.399816\pi$
$139$	7.29947	0.619133	0.309567	+	0.950878i	$0.399816\pi$
$140$	1.60949	0.136027
$141$	2.47068	0.208069
$142$	−7.86961	−0.660403
$143$	−0.488123	−0.0408189
$144$	−2.54225	−0.211855
$145$	7.98064	0.662756
$146$	8.60330	0.712014
$147$	−0.676569	−0.0558025
$148$	7.13497	0.586491
$149$	−10.7449	−0.880259	−0.440130	−	0.897934i	$-0.645067\pi$
$149$	−10.7449	−0.880259	−0.440130	+	0.897934i	$0.645067\pi$
$150$	1.63022	0.133107
$151$	5.04661	0.410687	0.205344	−	0.978690i	$-0.434169\pi$
$151$	5.04661	0.410687	0.205344	+	0.978690i	$0.434169\pi$
$152$	0.855428	0.0693843
$153$	−13.6629	−1.10458
$154$	−5.23122	−0.421543
$155$	0.643693	0.0517027
$156$	−0.0631305	−0.00505448
$157$	1.51990	0.121301	0.0606504	−	0.998159i	$-0.480683\pi$
$157$	1.51990	0.121301	0.0606504	+	0.998159i	$0.480683\pi$
$158$	7.19773	0.572621
$159$	−3.79973	−0.301338
$160$	1.60949	0.127241
$161$	−2.70339	−0.213057
$162$	5.08982	0.399894
$163$	14.7896	1.15841	0.579204	−	0.815183i	$-0.303364\pi$
$163$	14.7896	1.15841	0.579204	+	0.815183i	$0.303364\pi$
$164$	8.10200	0.632660
$165$	5.69643	0.443467
$166$	3.35167	0.260140
$167$	2.33786	0.180909	0.0904544	−	0.995901i	$-0.471168\pi$
$167$	2.33786	0.180909	0.0904544	+	0.995901i	$0.471168\pi$
$168$	−0.676569	−0.0521984
$169$	−12.9913	−0.999330
$170$	8.64994	0.663420
$171$	−2.17471	−0.166305
$172$	−8.50456	−0.648467
$173$	−9.47306	−0.720224	−0.360112	−	0.932909i	$-0.617261\pi$
$173$	−9.47306	−0.720224	−0.360112	+	0.932909i	$0.617261\pi$
$174$	−3.35476	−0.254324
$175$	−2.40954	−0.182144
$176$	−5.23122	−0.394318
$177$	−7.40236	−0.556395
$178$	−2.35957	−0.176857
$179$	8.04864	0.601584	0.300792	−	0.953690i	$-0.402749\pi$
$179$	8.04864	0.601584	0.300792	+	0.953690i	$0.402749\pi$
$180$	−4.09173	−0.304980
$181$	−5.25925	−0.390917	−0.195458	−	0.980712i	$-0.562619\pi$
$181$	−5.25925	−0.390917	−0.195458	+	0.980712i	$0.562619\pi$
$182$	0.0933098	0.00691658
$183$	−7.68142	−0.567827
$184$	−2.70339	−0.199297
$185$	11.4837	0.844295
$186$	−0.270584	−0.0198402
$187$	−28.1143	−2.05592
$188$	−3.65177	−0.266333
$189$	3.74972	0.272752
$190$	1.37680	0.0998837
$191$	9.45700	0.684284	0.342142	−	0.939648i	$-0.388848\pi$
$191$	9.45700	0.684284	0.342142	+	0.939648i	$0.388848\pi$
$192$	−0.676569	−0.0488272
$193$	−9.77124	−0.703349	−0.351675	−	0.936122i	$-0.614388\pi$
$193$	−9.77124	−0.703349	−0.351675	+	0.936122i	$0.614388\pi$
$194$	3.23465	0.232234
$195$	−0.101608	−0.00727629
$196$	1.00000	0.0714286
$197$	−23.5990	−1.68136	−0.840680	−	0.541532i	$-0.817844\pi$
$197$	−23.5990	−1.68136	−0.840680	+	0.541532i	$0.817844\pi$
$198$	13.2991	0.945125
$199$	−1.38180	−0.0979532	−0.0489766	−	0.998800i	$-0.515596\pi$
$199$	−1.38180	−0.0979532	−0.0489766	+	0.998800i	$0.515596\pi$
$200$	−2.40954	−0.170380
$201$	3.22230	0.227284
$202$	12.0397	0.847114
$203$	4.95849	0.348018
$204$	−3.63611	−0.254579
$205$	13.0401	0.910759
$206$	13.6037	0.947812
$207$	6.87271	0.477686
$208$	0.0933098	0.00646987
$209$	−4.47493	−0.309537
$210$	−1.08893	−0.0751434
$211$	−26.3425	−1.81349	−0.906746	−	0.421677i	$-0.861442\pi$
$211$	−26.3425	−1.81349	−0.906746	+	0.421677i	$0.861442\pi$
$212$	5.61617	0.385720
$213$	5.32434	0.364818
$214$	2.96597	0.202750
$215$	−13.6880	−0.933514
$216$	3.74972	0.255136
$217$	0.399936	0.0271494
$218$	1.28035	0.0867161
$219$	−5.82073	−0.393328
$220$	−8.41959	−0.567649
$221$	0.501478	0.0337331
$222$	−4.82730	−0.323987
$223$	6.92657	0.463837	0.231919	−	0.972735i	$-0.425500\pi$
$223$	6.92657	0.463837	0.231919	+	0.972735i	$0.425500\pi$
$224$	1.00000	0.0668153
$225$	6.12567	0.408378
$226$	7.55956	0.502854
$227$	7.58411	0.503375	0.251688	−	0.967809i	$-0.419014\pi$
$227$	7.58411	0.503375	0.251688	+	0.967809i	$0.419014\pi$
$228$	−0.578756	−0.0383290
$229$	−12.9761	−0.857486	−0.428743	−	0.903426i	$-0.641043\pi$
$229$	−12.9761	−0.857486	−0.428743	+	0.903426i	$0.641043\pi$
$230$	−4.35108	−0.286902
$231$	3.53928	0.232867
$232$	4.95849	0.325541
$233$	22.8305	1.49567	0.747836	−	0.663883i	$-0.231093\pi$
$233$	22.8305	1.49567	0.747836	+	0.663883i	$0.231093\pi$
$234$	−0.237217	−0.0155074
$235$	−5.87749	−0.383405
$236$	10.9410	0.712200
$237$	−4.86976	−0.316325
$238$	5.37434	0.348367
$239$	2.00190	0.129492	0.0647459	−	0.997902i	$-0.479376\pi$
$239$	2.00190	0.129492	0.0647459	+	0.997902i	$0.479376\pi$
$240$	−1.08893	−0.0702902
$241$	−12.3695	−0.796790	−0.398395	−	0.917214i	$-0.630433\pi$
$241$	−12.3695	−0.796790	−0.398395	+	0.917214i	$0.630433\pi$
$242$	16.3656	1.05202
$243$	−14.6928	−0.942541
$244$	11.3535	0.726833
$245$	1.60949	0.102827
$246$	−5.48156	−0.349492
$247$	0.0798197	0.00507881
$248$	0.399936	0.0253960
$249$	−2.26764	−0.143706
$250$	−11.9256	−0.754240
$251$	3.89587	0.245905	0.122953	−	0.992413i	$-0.460764\pi$
$251$	3.89587	0.245905	0.122953	+	0.992413i	$0.460764\pi$
$252$	−2.54225	−0.160147
$253$	14.1420	0.889102
$254$	3.90690	0.245141
$255$	−5.85228	−0.366484
$256$	1.00000	0.0625000
$257$	3.47559	0.216802	0.108401	−	0.994107i	$-0.465427\pi$
$257$	3.47559	0.216802	0.108401	+	0.994107i	$0.465427\pi$
$258$	5.75392	0.358224
$259$	7.13497	0.443345
$260$	0.150181	0.00931384
$261$	−12.6057	−0.780276
$262$	−10.1809	−0.628980
$263$	16.7062	1.03015	0.515074	−	0.857146i	$-0.327765\pi$
$263$	16.7062	1.03015	0.515074	+	0.857146i	$0.327765\pi$
$264$	3.53928	0.217828
$265$	9.03917	0.555272
$266$	0.855428	0.0524496
$267$	1.59641	0.0976989
$268$	−4.76271	−0.290929
$269$	−5.06373	−0.308741	−0.154371	−	0.988013i	$-0.549335\pi$
$269$	−5.06373	−0.308741	−0.154371	+	0.988013i	$0.549335\pi$
$270$	6.03513	0.367286
$271$	20.3645	1.23706	0.618528	−	0.785763i	$-0.287729\pi$
$271$	20.3645	1.23706	0.618528	+	0.785763i	$0.287729\pi$
$272$	5.37434	0.325867
$273$	−0.0631305	−0.00382083
$274$	−3.62561	−0.219031
$275$	12.6048	0.760100
$276$	1.82903	0.110095
$277$	−0.885278	−0.0531912	−0.0265956	−	0.999646i	$-0.508467\pi$
$277$	−0.885278	−0.0531912	−0.0265956	+	0.999646i	$0.508467\pi$
$278$	7.29947	0.437793
$279$	−1.01674	−0.0608706
$280$	1.60949	0.0961854
$281$	13.6707	0.815523	0.407761	−	0.913088i	$-0.366309\pi$
$281$	13.6707	0.815523	0.407761	+	0.913088i	$0.366309\pi$
$282$	2.47068	0.147127
$283$	17.1371	1.01870	0.509348	−	0.860560i	$-0.329886\pi$
$283$	17.1371	1.01870	0.509348	+	0.860560i	$0.329886\pi$
$284$	−7.86961	−0.466976
$285$	−0.931502	−0.0551774
$286$	−0.488123	−0.0288633
$287$	8.10200	0.478246
$288$	−2.54225	−0.149804
$289$	11.8835	0.699030
$290$	7.98064	0.468639
$291$	−2.18847	−0.128290
$292$	8.60330	0.503470
$293$	3.83643	0.224127	0.112063	−	0.993701i	$-0.464254\pi$
$293$	3.83643	0.224127	0.112063	+	0.993701i	$0.464254\pi$
$294$	−0.676569	−0.0394583
$295$	17.6095	1.02526
$296$	7.13497	0.414712
$297$	−19.6156	−1.13821
$298$	−10.7449	−0.622437
$299$	−0.252253	−0.0145882
$300$	1.63022	0.0941209
$301$	−8.50456	−0.490195
$302$	5.04661	0.290400
$303$	−8.14572	−0.467959
$304$	0.855428	0.0490621
$305$	18.2733	1.04633
$306$	−13.6629	−0.781058
$307$	−19.0887	−1.08945	−0.544724	−	0.838615i	$-0.683366\pi$
$307$	−19.0887	−1.08945	−0.544724	+	0.838615i	$0.683366\pi$
$308$	−5.23122	−0.298076
$309$	−9.20382	−0.523587
$310$	0.643693	0.0365593
$311$	−23.1764	−1.31421	−0.657106	−	0.753798i	$-0.728220\pi$
$311$	−23.1764	−1.31421	−0.657106	+	0.753798i	$0.728220\pi$
$312$	−0.0631305	−0.00357406
$313$	15.8587	0.896385	0.448192	−	0.893937i	$-0.352068\pi$
$313$	15.8587	0.896385	0.448192	+	0.893937i	$0.352068\pi$
$314$	1.51990	0.0857727
$315$	−4.09173	−0.230543
$316$	7.19773	0.404904
$317$	20.1623	1.13243	0.566215	−	0.824258i	$-0.308407\pi$
$317$	20.1623	1.13243	0.566215	+	0.824258i	$0.308407\pi$
$318$	−3.79973	−0.213078
$319$	−25.9389	−1.45230
$320$	1.60949	0.0899732
$321$	−2.00668	−0.112002
$322$	−2.70339	−0.150654
$323$	4.59736	0.255804
$324$	5.08982	0.282768
$325$	−0.224834	−0.0124715
$326$	14.7896	0.819118
$327$	−0.866244	−0.0479034
$328$	8.10200	0.447358
$329$	−3.65177	−0.201329
$330$	5.69643	0.313578
$331$	−5.37869	−0.295639	−0.147820	−	0.989014i	$-0.547226\pi$
$331$	−5.37869	−0.295639	−0.147820	+	0.989014i	$0.547226\pi$
$332$	3.35167	0.183947
$333$	−18.1389	−0.994006
$334$	2.33786	0.127922
$335$	−7.66553	−0.418813
$336$	−0.676569	−0.0369099
$337$	−32.6693	−1.77961	−0.889804	−	0.456343i	$-0.849159\pi$
$337$	−32.6693	−1.77961	−0.889804	+	0.456343i	$0.849159\pi$
$338$	−12.9913	−0.706633
$339$	−5.11456	−0.277785
$340$	8.64994	0.469109
$341$	−2.09215	−0.113296
$342$	−2.17471	−0.117595
$343$	1.00000	0.0539949
$344$	−8.50456	−0.458535
$345$	2.94381	0.158489
$346$	−9.47306	−0.509275
$347$	−19.0330	−1.02175	−0.510874	−	0.859656i	$-0.670678\pi$
$347$	−19.0330	−1.02175	−0.510874	+	0.859656i	$0.670678\pi$
$348$	−3.35476	−0.179834
$349$	26.0183	1.39273	0.696365	−	0.717688i	$-0.254799\pi$
$349$	26.0183	1.39273	0.696365	+	0.717688i	$0.254799\pi$
$350$	−2.40954	−0.128795
$351$	0.349885	0.0186755
$352$	−5.23122	−0.278825
$353$	5.94279	0.316303	0.158151	−	0.987415i	$-0.449447\pi$
$353$	5.94279	0.316303	0.158151	+	0.987415i	$0.449447\pi$
$354$	−7.40236	−0.393431
$355$	−12.6661	−0.672245
$356$	−2.35957	−0.125057
$357$	−3.63611	−0.192443
$358$	8.04864	0.425384
$359$	−8.98141	−0.474021	−0.237010	−	0.971507i	$-0.576168\pi$
$359$	−8.98141	−0.474021	−0.237010	+	0.971507i	$0.576168\pi$
$360$	−4.09173	−0.215653
$361$	−18.2682	−0.961487
$362$	−5.25925	−0.276420
$363$	−11.0725	−0.581154
$364$	0.0933098	0.00489076
$365$	13.8469	0.724781
$366$	−7.68142	−0.401514
$367$	−3.32767	−0.173703	−0.0868514	−	0.996221i	$-0.527681\pi$
$367$	−3.32767	−0.173703	−0.0868514	+	0.996221i	$0.527681\pi$
$368$	−2.70339	−0.140924
$369$	−20.5973	−1.07225
$370$	11.4837	0.597007
$371$	5.61617	0.291577
$372$	−0.270584	−0.0140292
$373$	7.62441	0.394777	0.197388	−	0.980325i	$-0.436754\pi$
$373$	7.62441	0.394777	0.197388	+	0.980325i	$0.436754\pi$
$374$	−28.1143	−1.45376
$375$	8.06848	0.416655
$376$	−3.65177	−0.188326
$377$	0.462675	0.0238290
$378$	3.74972	0.192865
$379$	−0.987767	−0.0507382	−0.0253691	−	0.999678i	$-0.508076\pi$
$379$	−0.987767	−0.0507382	−0.0253691	+	0.999678i	$0.508076\pi$
$380$	1.37680	0.0706284
$381$	−2.64329	−0.135420
$382$	9.45700	0.483862
$383$	−16.2919	−0.832476	−0.416238	−	0.909256i	$-0.636652\pi$
$383$	−16.2919	−0.832476	−0.416238	+	0.909256i	$0.636652\pi$
$384$	−0.676569	−0.0345260
$385$	−8.41959	−0.429102
$386$	−9.77124	−0.497343
$387$	21.6208	1.09904
$388$	3.23465	0.164215
$389$	−16.6221	−0.842772	−0.421386	−	0.906881i	$-0.638456\pi$
$389$	−16.6221	−0.842772	−0.421386	+	0.906881i	$0.638456\pi$
$390$	−0.101608	−0.00514511
$391$	−14.5289	−0.734760
$392$	1.00000	0.0505076
$393$	6.88810	0.347459
$394$	−23.5990	−1.18890
$395$	11.5847	0.582888
$396$	13.2991	0.668304
$397$	25.9426	1.30202	0.651011	−	0.759068i	$-0.274345\pi$
$397$	25.9426	1.30202	0.651011	+	0.759068i	$0.274345\pi$
$398$	−1.38180	−0.0692634
$399$	−0.578756	−0.0289740
$400$	−2.40954	−0.120477
$401$	33.0049	1.64819	0.824093	−	0.566455i	$-0.191686\pi$
$401$	33.0049	1.64819	0.824093	+	0.566455i	$0.191686\pi$
$402$	3.22230	0.160714
$403$	0.0373180	0.00185894
$404$	12.0397	0.599000
$405$	8.19201	0.407064
$406$	4.95849	0.246086
$407$	−37.3246	−1.85011
$408$	−3.63611	−0.180014
$409$	−22.8802	−1.13135	−0.565677	−	0.824627i	$-0.691385\pi$
$409$	−22.8802	−1.13135	−0.565677	+	0.824627i	$0.691385\pi$
$410$	13.0401	0.644004
$411$	2.45298	0.120996
$412$	13.6037	0.670205
$413$	10.9410	0.538373
$414$	6.87271	0.337775
$415$	5.39448	0.264805
$416$	0.0933098	0.00457489
$417$	−4.93860	−0.241844
$418$	−4.47493	−0.218876
$419$	−16.3484	−0.798671	−0.399336	−	0.916805i	$-0.630759\pi$
$419$	−16.3484	−0.798671	−0.399336	+	0.916805i	$0.630759\pi$
$420$	−1.08893	−0.0531344
$421$	12.1216	0.590772	0.295386	−	0.955378i	$-0.404552\pi$
$421$	12.1216	0.590772	0.295386	+	0.955378i	$0.404552\pi$
$422$	−26.3425	−1.28233
$423$	9.28374	0.451391
$424$	5.61617	0.272745
$425$	−12.9497	−0.628152
$426$	5.32434	0.257965
$427$	11.3535	0.549434
$428$	2.96597	0.143366
$429$	0.330249	0.0159446
$430$	−13.6880	−0.660094
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	3.74972	0.180408
$433$	−18.6684	−0.897147	−0.448573	−	0.893746i	$-0.648068\pi$
$433$	−18.6684	−0.897147	−0.448573	+	0.893746i	$0.648068\pi$
$434$	0.399936	0.0191976
$435$	−5.39945	−0.258884
$436$	1.28035	0.0613176
$437$	−2.31256	−0.110625
$438$	−5.82073	−0.278125
$439$	0.185183	0.00883828	0.00441914	−	0.999990i	$-0.498593\pi$
$439$	0.185183	0.00883828	0.00441914	+	0.999990i	$0.498593\pi$
$440$	−8.41959	−0.401388
$441$	−2.54225	−0.121060
$442$	0.501478	0.0238529
$443$	33.1745	1.57617	0.788084	−	0.615568i	$-0.211073\pi$
$443$	33.1745	1.57617	0.788084	+	0.615568i	$0.211073\pi$
$444$	−4.82730	−0.229093
$445$	−3.79771	−0.180029
$446$	6.92657	0.327982
$447$	7.26969	0.343844
$448$	1.00000	0.0472456
$449$	13.1462	0.620407	0.310203	−	0.950670i	$-0.399603\pi$
$449$	13.1462	0.620407	0.310203	+	0.950670i	$0.399603\pi$
$450$	6.12567	0.288767
$451$	−42.3833	−1.99575
$452$	7.55956	0.355572
$453$	−3.41438	−0.160422
$454$	7.58411	0.355940
$455$	0.150181	0.00704060
$456$	−0.578756	−0.0271027
$457$	−0.814396	−0.0380959	−0.0190479	−	0.999819i	$-0.506064\pi$
$457$	−0.814396	−0.0380959	−0.0190479	+	0.999819i	$0.506064\pi$
$458$	−12.9761	−0.606334
$459$	20.1522	0.940626
$460$	−4.35108	−0.202870
$461$	14.6980	0.684552	0.342276	−	0.939599i	$-0.388802\pi$
$461$	14.6980	0.684552	0.342276	+	0.939599i	$0.388802\pi$
$462$	3.53928	0.164662
$463$	−27.0353	−1.25644	−0.628219	−	0.778037i	$-0.716216\pi$
$463$	−27.0353	−1.25644	−0.628219	+	0.778037i	$0.716216\pi$
$464$	4.95849	0.230192
$465$	−0.435503	−0.0201960
$466$	22.8305	1.05760
$467$	−2.20684	−0.102121	−0.0510603	−	0.998696i	$-0.516260\pi$
$467$	−2.20684	−0.102121	−0.0510603	+	0.998696i	$0.516260\pi$
$468$	−0.237217	−0.0109654
$469$	−4.76271	−0.219921
$470$	−5.87749	−0.271109
$471$	−1.02831	−0.0473822
$472$	10.9410	0.503601
$473$	44.4892	2.04562
$474$	−4.86976	−0.223676
$475$	−2.06119	−0.0945738
$476$	5.37434	0.246332
$477$	−14.2777	−0.653733
$478$	2.00190	0.0915646
$479$	0.672458	0.0307254	0.0153627	−	0.999882i	$-0.495110\pi$
$479$	0.672458	0.0307254	0.0153627	+	0.999882i	$0.495110\pi$
$480$	−1.08893	−0.0497027
$481$	0.665762	0.0303561
$482$	−12.3695	−0.563416
$483$	1.82903	0.0832238
$484$	16.3656	0.743892
$485$	5.20614	0.236399
$486$	−14.6928	−0.666477
$487$	32.2856	1.46300	0.731500	−	0.681841i	$-0.238820\pi$
$487$	32.2856	1.46300	0.731500	+	0.681841i	$0.238820\pi$
$488$	11.3535	0.513948
$489$	−10.0062	−0.452494
$490$	1.60949	0.0727093
$491$	6.66725	0.300889	0.150444	−	0.988618i	$-0.451930\pi$
$491$	6.66725	0.300889	0.150444	+	0.988618i	$0.451930\pi$
$492$	−5.48156	−0.247128
$493$	26.6486	1.20019
$494$	0.0798197	0.00359126
$495$	21.4047	0.962071
$496$	0.399936	0.0179577
$497$	−7.86961	−0.353000
$498$	−2.26764	−0.101615
$499$	14.3852	0.643970	0.321985	−	0.946745i	$-0.395650\pi$
$499$	14.3852	0.643970	0.321985	+	0.946745i	$0.395650\pi$
$500$	−11.9256	−0.533328
$501$	−1.58172	−0.0706661
$502$	3.89587	0.173881
$503$	9.11981	0.406632	0.203316	−	0.979113i	$-0.434828\pi$
$503$	9.11981	0.406632	0.203316	+	0.979113i	$0.434828\pi$
$504$	−2.54225	−0.113241
$505$	19.3779	0.862303
$506$	14.1420	0.628690
$507$	8.78951	0.390356
$508$	3.90690	0.173341
$509$	15.1476	0.671408	0.335704	−	0.941968i	$-0.391026\pi$
$509$	15.1476	0.671408	0.335704	+	0.941968i	$0.391026\pi$
$510$	−5.85228	−0.259143
$511$	8.60330	0.380588
$512$	1.00000	0.0441942
$513$	3.20761	0.141620
$514$	3.47559	0.153302
$515$	21.8950	0.964807
$516$	5.75392	0.253302
$517$	19.1032	0.840159
$518$	7.13497	0.313493
$519$	6.40918	0.281332
$520$	0.150181	0.00658588
$521$	32.0736	1.40517	0.702584	−	0.711600i	$-0.252029\pi$
$521$	32.0736	1.40517	0.702584	+	0.711600i	$0.252029\pi$
$522$	−12.6057	−0.551738
$523$	−43.0494	−1.88242	−0.941209	−	0.337824i	$-0.890309\pi$
$523$	−43.0494	−1.88242	−0.941209	+	0.337824i	$0.890309\pi$
$524$	−10.1809	−0.444756
$525$	1.63022	0.0711487
$526$	16.7062	0.728424
$527$	2.14939	0.0936290
$528$	3.53928	0.154027
$529$	−15.6917	−0.682247
$530$	9.03917	0.392636
$531$	−27.8149	−1.20706
$532$	0.855428	0.0370875
$533$	0.755995	0.0327458
$534$	1.59641	0.0690836
$535$	4.77370	0.206385
$536$	−4.76271	−0.205718
$537$	−5.44546	−0.234989
$538$	−5.06373	−0.218313
$539$	−5.23122	−0.225324
$540$	6.03513	0.259711
$541$	20.1776	0.867501	0.433750	−	0.901033i	$-0.357190\pi$
$541$	20.1776	0.867501	0.433750	+	0.901033i	$0.357190\pi$
$542$	20.3645	0.874730
$543$	3.55824	0.152699
$544$	5.37434	0.230423
$545$	2.06071	0.0882710
$546$	−0.0631305	−0.00270174
$547$	18.1405	0.775634	0.387817	−	0.921736i	$-0.373229\pi$
$547$	18.1405	0.775634	0.387817	+	0.921736i	$0.373229\pi$
$548$	−3.62561	−0.154878
$549$	−28.8635	−1.23186
$550$	12.6048	0.537472
$551$	4.24163	0.180699
$552$	1.82903	0.0778487
$553$	7.19773	0.306079
$554$	−0.885278	−0.0376119
$555$	−7.76949	−0.329796
$556$	7.29947	0.309567
$557$	32.4416	1.37459	0.687297	−	0.726377i	$-0.258797\pi$
$557$	32.4416	1.37459	0.687297	+	0.726377i	$0.258797\pi$
$558$	−1.01674	−0.0430420
$559$	−0.793559	−0.0335640
$560$	1.60949	0.0680134
$561$	19.0213	0.803079
$562$	13.6707	0.576662
$563$	−11.1077	−0.468134	−0.234067	−	0.972220i	$-0.575204\pi$
$563$	−11.1077	−0.468134	−0.234067	+	0.972220i	$0.575204\pi$
$564$	2.47068	0.104034
$565$	12.1670	0.511871
$566$	17.1371	0.720327
$567$	5.08982	0.213752
$568$	−7.86961	−0.330202
$569$	−10.0374	−0.420791	−0.210395	−	0.977616i	$-0.567475\pi$
$569$	−10.0374	−0.420791	−0.210395	+	0.977616i	$0.567475\pi$
$570$	−0.931502	−0.0390163
$571$	34.3865	1.43903	0.719515	−	0.694477i	$-0.244364\pi$
$571$	34.3865	1.43903	0.719515	+	0.694477i	$0.244364\pi$
$572$	−0.488123	−0.0204095
$573$	−6.39831	−0.267293
$574$	8.10200	0.338171
$575$	6.51394	0.271650
$576$	−2.54225	−0.105927
$577$	−8.24588	−0.343280	−0.171640	−	0.985160i	$-0.554907\pi$
$577$	−8.24588	−0.343280	−0.171640	+	0.985160i	$0.554907\pi$
$578$	11.8835	0.494289
$579$	6.61092	0.274740
$580$	7.98064	0.331378
$581$	3.35167	0.139051
$582$	−2.18847	−0.0907148
$583$	−29.3794	−1.21677
$584$	8.60330	0.356007
$585$	−0.381799	−0.0157854
$586$	3.83643	0.158482
$587$	−39.9376	−1.64840	−0.824200	−	0.566298i	$-0.808375\pi$
$587$	−39.9376	−1.64840	−0.824200	+	0.566298i	$0.808375\pi$
$588$	−0.676569	−0.0279012
$589$	0.342116	0.0140967
$590$	17.6095	0.724970
$591$	15.9664	0.656768
$592$	7.13497	0.293245
$593$	2.34330	0.0962278	0.0481139	−	0.998842i	$-0.484679\pi$
$593$	2.34330	0.0962278	0.0481139	+	0.998842i	$0.484679\pi$
$594$	−19.6156	−0.804837
$595$	8.64994	0.354613
$596$	−10.7449	−0.440130
$597$	0.934883	0.0382622
$598$	−0.252253	−0.0103154
$599$	−7.44129	−0.304043	−0.152021	−	0.988377i	$-0.548578\pi$
$599$	−7.44129	−0.304043	−0.152021	+	0.988377i	$0.548578\pi$
$600$	1.63022	0.0665535
$601$	−36.2949	−1.48050	−0.740250	−	0.672332i	$-0.765293\pi$
$601$	−36.2949	−1.48050	−0.740250	+	0.672332i	$0.765293\pi$
$602$	−8.50456	−0.346620
$603$	12.1080	0.493077
$604$	5.04661	0.205344
$605$	26.3403	1.07089
$606$	−8.14572	−0.330897
$607$	29.7482	1.20744	0.603721	−	0.797195i	$-0.293684\pi$
$607$	29.7482	1.20744	0.603721	+	0.797195i	$0.293684\pi$
$608$	0.855428	0.0346922
$609$	−3.35476	−0.135942
$610$	18.2733	0.739865
$611$	−0.340746	−0.0137851
$612$	−13.6629	−0.552291
$613$	12.7017	0.513019	0.256509	−	0.966542i	$-0.417428\pi$
$613$	12.7017	0.513019	0.256509	+	0.966542i	$0.417428\pi$
$614$	−19.0887	−0.770356
$615$	−8.82252	−0.355758
$616$	−5.23122	−0.210772
$617$	−22.9838	−0.925294	−0.462647	−	0.886543i	$-0.653100\pi$
$617$	−22.9838	−0.925294	−0.462647	+	0.886543i	$0.653100\pi$
$618$	−9.20382	−0.370232
$619$	−43.4294	−1.74557	−0.872787	−	0.488100i	$-0.837690\pi$
$619$	−43.4294	−1.74557	−0.872787	+	0.488100i	$0.837690\pi$
$620$	0.643693	0.0258513
$621$	−10.1370	−0.406782
$622$	−23.1764	−0.929288
$623$	−2.35957	−0.0945343
$624$	−0.0631305	−0.00252724
$625$	−7.14639	−0.285856
$626$	15.8587	0.633840
$627$	3.02760	0.120911
$628$	1.51990	0.0606504
$629$	38.3457	1.52894
$630$	−4.09173	−0.163019
$631$	−21.2471	−0.845834	−0.422917	−	0.906168i	$-0.638994\pi$
$631$	−21.2471	−0.845834	−0.422917	+	0.906168i	$0.638994\pi$
$632$	7.19773	0.286310
$633$	17.8225	0.708381
$634$	20.1623	0.800749
$635$	6.28812	0.249536
$636$	−3.79973	−0.150669
$637$	0.0933098	0.00369707
$638$	−25.9389	−1.02693
$639$	20.0066	0.791447
$640$	1.60949	0.0636207
$641$	−10.9855	−0.433899	−0.216950	−	0.976183i	$-0.569611\pi$
$641$	−10.9855	−0.433899	−0.216950	+	0.976183i	$0.569611\pi$
$642$	−2.00668	−0.0791975
$643$	33.4503	1.31915	0.659576	−	0.751638i	$-0.270736\pi$
$643$	33.4503	1.31915	0.659576	+	0.751638i	$0.270736\pi$
$644$	−2.70339	−0.106529
$645$	9.26088	0.364647
$646$	4.59736	0.180881
$647$	−38.8772	−1.52842	−0.764210	−	0.644967i	$-0.776871\pi$
$647$	−38.8772	−1.52842	−0.764210	+	0.644967i	$0.776871\pi$
$648$	5.08982	0.199947
$649$	−57.2349	−2.24666
$650$	−0.224834	−0.00881871
$651$	−0.270584	−0.0106050
$652$	14.7896	0.579204
$653$	25.9361	1.01496	0.507479	−	0.861664i	$-0.330578\pi$
$653$	25.9361	1.01496	0.507479	+	0.861664i	$0.330578\pi$
$654$	−0.866244	−0.0338728
$655$	−16.3861	−0.640258
$656$	8.10200	0.316330
$657$	−21.8718	−0.853300
$658$	−3.65177	−0.142361
$659$	−4.40616	−0.171640	−0.0858199	−	0.996311i	$-0.527351\pi$
$659$	−4.40616	−0.171640	−0.0858199	+	0.996311i	$0.527351\pi$
$660$	5.69643	0.221733
$661$	−19.5086	−0.758797	−0.379399	−	0.925233i	$-0.623869\pi$
$661$	−19.5086	−0.758797	−0.379399	+	0.925233i	$0.623869\pi$
$662$	−5.37869	−0.209049
$663$	−0.339285	−0.0131767
$664$	3.35167	0.130070
$665$	1.37680	0.0533901
$666$	−18.1389	−0.702868
$667$	−13.4047	−0.519034
$668$	2.33786	0.0904544
$669$	−4.68630	−0.181183
$670$	−7.66553	−0.296145
$671$	−59.3925	−2.29282
$672$	−0.676569	−0.0260992
$673$	22.7108	0.875438	0.437719	−	0.899112i	$-0.355787\pi$
$673$	22.7108	0.875438	0.437719	+	0.899112i	$0.355787\pi$
$674$	−32.6693	−1.25837
$675$	−9.03510	−0.347761
$676$	−12.9913	−0.499665
$677$	32.4096	1.24560	0.622801	−	0.782381i	$-0.285995\pi$
$677$	32.4096	1.24560	0.622801	+	0.782381i	$0.285995\pi$
$678$	−5.11456	−0.196424
$679$	3.23465	0.124135
$680$	8.64994	0.331710
$681$	−5.13118	−0.196627
$682$	−2.09215	−0.0801127
$683$	26.3242	1.00727	0.503633	−	0.863918i	$-0.331996\pi$
$683$	26.3242	1.00727	0.503633	+	0.863918i	$0.331996\pi$
$684$	−2.17471	−0.0831523
$685$	−5.83538	−0.222958
$686$	1.00000	0.0381802
$687$	8.77924	0.334949
$688$	−8.50456	−0.324233
$689$	0.524044	0.0199645
$690$	2.94381	0.112069
$691$	−38.5515	−1.46657	−0.733284	−	0.679923i	$-0.762013\pi$
$691$	−38.5515	−1.46657	−0.733284	+	0.679923i	$0.762013\pi$
$692$	−9.47306	−0.360112
$693$	13.2991	0.505190
$694$	−19.0330	−0.722485
$695$	11.7484	0.445643
$696$	−3.35476	−0.127162
$697$	43.5429	1.64930
$698$	26.0183	0.984809
$699$	−15.4464	−0.584236
$700$	−2.40954	−0.0910721
$701$	11.8835	0.448834	0.224417	−	0.974493i	$-0.427952\pi$
$701$	11.8835	0.448834	0.224417	+	0.974493i	$0.427952\pi$
$702$	0.349885	0.0132056
$703$	6.10345	0.230196
$704$	−5.23122	−0.197159
$705$	3.97653	0.149765
$706$	5.94279	0.223660
$707$	12.0397	0.452801
$708$	−7.40236	−0.278198
$709$	−43.1158	−1.61925	−0.809624	−	0.586949i	$-0.800329\pi$
$709$	−43.1158	−1.61925	−0.809624	+	0.586949i	$0.800329\pi$
$710$	−12.6661	−0.475349
$711$	−18.2985	−0.686246
$712$	−2.35957	−0.0884287
$713$	−1.08118	−0.0404907
$714$	−3.63611	−0.136078
$715$	−0.785630	−0.0293809
$716$	8.04864	0.300792
$717$	−1.35442	−0.0505818
$718$	−8.98141	−0.335183
$719$	−0.0971804	−0.00362422	−0.00181211	−	0.999998i	$-0.500577\pi$
$719$	−0.0971804	−0.00362422	−0.00181211	+	0.999998i	$0.500577\pi$
$720$	−4.09173	−0.152490
$721$	13.6037	0.506627
$722$	−18.2682	−0.679874
$723$	8.36883	0.311240
$724$	−5.25925	−0.195458
$725$	−11.9477	−0.443726
$726$	−11.0725	−0.410938
$727$	−3.81143	−0.141358	−0.0706790	−	0.997499i	$-0.522517\pi$
$727$	−3.81143	−0.141358	−0.0706790	+	0.997499i	$0.522517\pi$
$728$	0.0933098	0.00345829
$729$	−5.32879	−0.197363
$730$	13.8469	0.512498
$731$	−45.7064	−1.69051
$732$	−7.68142	−0.283913
$733$	36.7508	1.35742	0.678710	−	0.734406i	$-0.262539\pi$
$733$	36.7508	1.35742	0.678710	+	0.734406i	$0.262539\pi$
$734$	−3.32767	−0.122826
$735$	−1.08893	−0.0401658
$736$	−2.70339	−0.0996484
$737$	24.9148	0.917747
$738$	−20.5973	−0.758199
$739$	38.3841	1.41198	0.705990	−	0.708221i	$-0.250502\pi$
$739$	38.3841	1.41198	0.705990	+	0.708221i	$0.250502\pi$
$740$	11.4837	0.422148
$741$	−0.0540036	−0.00198387
$742$	5.61617	0.206176
$743$	−29.4394	−1.08003	−0.540014	−	0.841656i	$-0.681581\pi$
$743$	−29.4394	−1.08003	−0.540014	+	0.841656i	$0.681581\pi$
$744$	−0.270584	−0.00992011
$745$	−17.2939	−0.633598
$746$	7.62441	0.279149
$747$	−8.52080	−0.311760
$748$	−28.1143	−1.02796
$749$	2.96597	0.108374
$750$	8.06848	0.294619
$751$	−14.3393	−0.523248	−0.261624	−	0.965170i	$-0.584258\pi$
$751$	−14.3393	−0.523248	−0.261624	+	0.965170i	$0.584258\pi$
$752$	−3.65177	−0.133166
$753$	−2.63583	−0.0960549
$754$	0.462675	0.0168496
$755$	8.12247	0.295607
$756$	3.74972	0.136376
$757$	−49.7909	−1.80968	−0.904841	−	0.425750i	$-0.860010\pi$
$757$	−49.7909	−1.80968	−0.904841	+	0.425750i	$0.860010\pi$
$758$	−0.987767	−0.0358773
$759$	−9.56806	−0.347298
$760$	1.37680	0.0499419
$761$	−26.4197	−0.957714	−0.478857	−	0.877893i	$-0.658949\pi$
$761$	−26.4197	−0.957714	−0.478857	+	0.877893i	$0.658949\pi$
$762$	−2.64329	−0.0957563
$763$	1.28035	0.0463517
$764$	9.45700	0.342142
$765$	−21.9904	−0.795063
$766$	−16.2919	−0.588650
$767$	1.02090	0.0368627
$768$	−0.676569	−0.0244136
$769$	9.17252	0.330769	0.165385	−	0.986229i	$-0.447113\pi$
$769$	9.17252	0.330769	0.165385	+	0.986229i	$0.447113\pi$
$770$	−8.41959	−0.303421
$771$	−2.35148	−0.0846864
$772$	−9.77124	−0.351675
$773$	−24.3961	−0.877467	−0.438734	−	0.898617i	$-0.644573\pi$
$773$	−24.3961	−0.877467	−0.438734	+	0.898617i	$0.644573\pi$
$774$	21.6208	0.777142
$775$	−0.963663	−0.0346158
$776$	3.23465	0.116117
$777$	−4.82730	−0.173178
$778$	−16.6221	−0.595930
$779$	6.93067	0.248317
$780$	−0.101608	−0.00363815
$781$	41.1677	1.47309
$782$	−14.5289	−0.519554
$783$	18.5929	0.664457
$784$	1.00000	0.0357143
$785$	2.44626	0.0873106
$786$	6.88810	0.245690
$787$	25.3745	0.904504	0.452252	−	0.891890i	$-0.350621\pi$
$787$	25.3745	0.904504	0.452252	+	0.891890i	$0.350621\pi$
$788$	−23.5990	−0.840680
$789$	−11.3029	−0.402393
$790$	11.5847	0.412164
$791$	7.55956	0.268787
$792$	13.2991	0.472562
$793$	1.05939	0.0376201
$794$	25.9426	0.920668
$795$	−6.11562	−0.216899
$796$	−1.38180	−0.0489766
$797$	−10.7409	−0.380461	−0.190231	−	0.981739i	$-0.560924\pi$
$797$	−10.7409	−0.380461	−0.190231	+	0.981739i	$0.560924\pi$
$798$	−0.578756	−0.0204877
$799$	−19.6259	−0.694313
$800$	−2.40954	−0.0851902
$801$	5.99863	0.211951
$802$	33.0049	1.16544
$803$	−45.0057	−1.58822
$804$	3.22230	0.113642
$805$	−4.35108	−0.153355
$806$	0.0373180	0.00131447
$807$	3.42596	0.120600
$808$	12.0397	0.423557
$809$	14.3225	0.503553	0.251776	−	0.967785i	$-0.418985\pi$
$809$	14.3225	0.503553	0.251776	+	0.967785i	$0.418985\pi$
$810$	8.19201	0.287838
$811$	28.6079	1.00456	0.502279	−	0.864705i	$-0.332495\pi$
$811$	28.6079	1.00456	0.502279	+	0.864705i	$0.332495\pi$
$812$	4.95849	0.174009
$813$	−13.7780	−0.483215
$814$	−37.3246	−1.30823
$815$	23.8036	0.833805
$816$	−3.63611	−0.127289
$817$	−7.27504	−0.254521
$818$	−22.8802	−0.799988
$819$	−0.237217	−0.00828904
$820$	13.0401	0.455379
$821$	12.0062	0.419018	0.209509	−	0.977807i	$-0.432813\pi$
$821$	12.0062	0.419018	0.209509	+	0.977807i	$0.432813\pi$
$822$	2.45298	0.0855573
$823$	0.798610	0.0278378	0.0139189	−	0.999903i	$-0.495569\pi$
$823$	0.798610	0.0278378	0.0139189	+	0.999903i	$0.495569\pi$
$824$	13.6037	0.473906
$825$	−8.52804	−0.296908
$826$	10.9410	0.380687
$827$	36.0551	1.25376	0.626880	−	0.779116i	$-0.284332\pi$
$827$	36.0551	1.25376	0.626880	+	0.779116i	$0.284332\pi$
$828$	6.87271	0.238843
$829$	12.9237	0.448858	0.224429	−	0.974490i	$-0.427948\pi$
$829$	12.9237	0.448858	0.224429	+	0.974490i	$0.427948\pi$
$830$	5.39448	0.187245
$831$	0.598952	0.0207774
$832$	0.0933098	0.00323493
$833$	5.37434	0.186210
$834$	−4.93860	−0.171010
$835$	3.76276	0.130216
$836$	−4.47493	−0.154769
$837$	1.49965	0.0518354
$838$	−16.3484	−0.564746
$839$	29.3494	1.01325	0.506627	−	0.862165i	$-0.330892\pi$
$839$	29.3494	1.01325	0.506627	+	0.862165i	$0.330892\pi$
$840$	−1.08893	−0.0375717
$841$	−4.41338	−0.152185
$842$	12.1216	0.417739
$843$	−9.24914	−0.318557
$844$	−26.3425	−0.906746
$845$	−20.9094	−0.719304
$846$	9.28374	0.319181
$847$	16.3656	0.562329
$848$	5.61617	0.192860
$849$	−11.5945	−0.397921
$850$	−12.9497	−0.444171
$851$	−19.2886	−0.661205
$852$	5.32434	0.182409
$853$	−43.2906	−1.48224	−0.741120	−	0.671372i	$-0.765705\pi$
$853$	−43.2906	−1.48224	−0.741120	+	0.671372i	$0.765705\pi$
$854$	11.3535	0.388508
$855$	−3.50018	−0.119704
$856$	2.96597	0.101375
$857$	−44.3208	−1.51397	−0.756984	−	0.653433i	$-0.773328\pi$
$857$	−44.3208	−1.51397	−0.756984	+	0.653433i	$0.773328\pi$
$858$	0.330249	0.0112745
$859$	17.4311	0.594741	0.297371	−	0.954762i	$-0.403890\pi$
$859$	17.4311	0.594741	0.297371	+	0.954762i	$0.403890\pi$
$860$	−13.6880	−0.466757
$861$	−5.48156	−0.186811
$862$	1.00000	0.0340601
$863$	43.2887	1.47356	0.736782	−	0.676130i	$-0.236344\pi$
$863$	43.2887	1.47356	0.736782	+	0.676130i	$0.236344\pi$
$864$	3.74972	0.127568
$865$	−15.2468	−0.518407
$866$	−18.6684	−0.634378
$867$	−8.04001	−0.273053
$868$	0.399936	0.0135747
$869$	−37.6529	−1.27729
$870$	−5.39945	−0.183059
$871$	−0.444407	−0.0150582
$872$	1.28035	0.0433581
$873$	−8.22331	−0.278317
$874$	−2.31256	−0.0782234
$875$	−11.9256	−0.403158
$876$	−5.82073	−0.196664
$877$	−17.7200	−0.598362	−0.299181	−	0.954196i	$-0.596713\pi$
$877$	−17.7200	−0.598362	−0.299181	+	0.954196i	$0.596713\pi$
$878$	0.185183	0.00624961
$879$	−2.59561	−0.0875478
$880$	−8.41959	−0.283824
$881$	−2.45842	−0.0828263	−0.0414131	−	0.999142i	$-0.513186\pi$
$881$	−2.45842	−0.0828263	−0.0414131	+	0.999142i	$0.513186\pi$
$882$	−2.54225	−0.0856022
$883$	−21.1595	−0.712074	−0.356037	−	0.934472i	$-0.615872\pi$
$883$	−21.1595	−0.712074	−0.356037	+	0.934472i	$0.615872\pi$
$884$	0.501478	0.0168665
$885$	−11.9140	−0.400485
$886$	33.1745	1.11452
$887$	12.8043	0.429928	0.214964	−	0.976622i	$-0.431037\pi$
$887$	12.8043	0.429928	0.214964	+	0.976622i	$0.431037\pi$
$888$	−4.82730	−0.161994
$889$	3.90690	0.131033
$890$	−3.79771	−0.127299
$891$	−26.6259	−0.892003
$892$	6.92657	0.231919
$893$	−3.12383	−0.104535
$894$	7.26969	0.243135
$895$	12.9542	0.433011
$896$	1.00000	0.0334077
$897$	0.170666	0.00569839
$898$	13.1462	0.438694
$899$	1.98308	0.0661394
$900$	6.12567	0.204189
$901$	30.1832	1.00555
$902$	−42.3833	−1.41121
$903$	5.75392	0.191479
$904$	7.55956	0.251427
$905$	−8.46470	−0.281376
$906$	−3.41438	−0.113435
$907$	−57.2144	−1.89977	−0.949887	−	0.312595i	$-0.898802\pi$
$907$	−57.2144	−1.89977	−0.949887	+	0.312595i	$0.898802\pi$
$908$	7.58411	0.251688
$909$	−30.6081	−1.01521
$910$	0.150181	0.00497845
$911$	−53.5342	−1.77367	−0.886833	−	0.462090i	$-0.847100\pi$
$911$	−53.5342	−1.77367	−0.886833	+	0.462090i	$0.847100\pi$
$912$	−0.578756	−0.0191645
$913$	−17.5333	−0.580268
$914$	−0.814396	−0.0269378
$915$	−12.3632	−0.408714
$916$	−12.9761	−0.428743
$917$	−10.1809	−0.336204
$918$	20.1522	0.665123
$919$	7.27534	0.239991	0.119996	−	0.992774i	$-0.461712\pi$
$919$	7.27534	0.239991	0.119996	+	0.992774i	$0.461712\pi$
$920$	−4.35108	−0.143451
$921$	12.9148	0.425557
$922$	14.6980	0.484051
$923$	−0.734312	−0.0241702
$924$	3.53928	0.116434
$925$	−17.1920	−0.565270
$926$	−27.0353	−0.888436
$927$	−34.5840	−1.13589
$928$	4.95849	0.162770
$929$	−32.6130	−1.07000	−0.534999	−	0.844853i	$-0.679688\pi$
$929$	−32.6130	−1.07000	−0.534999	+	0.844853i	$0.679688\pi$
$930$	−0.435503	−0.0142807
$931$	0.855428	0.0280355
$932$	22.8305	0.747836
$933$	15.6804	0.513354
$934$	−2.20684	−0.0722101
$935$	−45.2497	−1.47982
$936$	−0.237217	−0.00775368
$937$	−2.57057	−0.0839768	−0.0419884	−	0.999118i	$-0.513369\pi$
$937$	−2.57057	−0.0839768	−0.0419884	+	0.999118i	$0.513369\pi$
$938$	−4.76271	−0.155508
$939$	−10.7295	−0.350143
$940$	−5.87749	−0.191703
$941$	5.57516	0.181745	0.0908725	−	0.995863i	$-0.471034\pi$
$941$	5.57516	0.181745	0.0908725	+	0.995863i	$0.471034\pi$
$942$	−1.02831	−0.0335043
$943$	−21.9029	−0.713256
$944$	10.9410	0.356100
$945$	6.03513	0.196323
$946$	44.4892	1.44647
$947$	−56.4051	−1.83292	−0.916460	−	0.400127i	$-0.868966\pi$
$947$	−56.4051	−1.83292	−0.916460	+	0.400127i	$0.868966\pi$
$948$	−4.86976	−0.158163
$949$	0.802772	0.0260591
$950$	−2.06119	−0.0668738
$951$	−13.6412	−0.442347
$952$	5.37434	0.174183
$953$	47.1876	1.52856	0.764278	−	0.644887i	$-0.223096\pi$
$953$	47.1876	1.52856	0.764278	+	0.644887i	$0.223096\pi$
$954$	−14.2777	−0.462259
$955$	15.2209	0.492538
$956$	2.00190	0.0647459
$957$	17.5495	0.567294
$958$	0.672458	0.0217261
$959$	−3.62561	−0.117077
$960$	−1.08893	−0.0351451
$961$	−30.8401	−0.994840
$962$	0.665762	0.0214650
$963$	−7.54025	−0.242981
$964$	−12.3695	−0.398395
$965$	−15.7267	−0.506261
$966$	1.82903	0.0588481
$967$	7.81287	0.251245	0.125622	−	0.992078i	$-0.459907\pi$
$967$	7.81287	0.251245	0.125622	+	0.992078i	$0.459907\pi$
$968$	16.3656	0.526011
$969$	−3.11043	−0.0999214
$970$	5.20614	0.167159
$971$	−24.1147	−0.773877	−0.386939	−	0.922105i	$-0.626467\pi$
$971$	−24.1147	−0.773877	−0.386939	+	0.922105i	$0.626467\pi$
$972$	−14.6928	−0.471271
$973$	7.29947	0.234010
$974$	32.2856	1.03450
$975$	0.152116	0.00487160
$976$	11.3535	0.363416
$977$	−51.3580	−1.64309	−0.821544	−	0.570145i	$-0.806887\pi$
$977$	−51.3580	−1.64309	−0.821544	+	0.570145i	$0.806887\pi$
$978$	−10.0062	−0.319962
$979$	12.3434	0.394498
$980$	1.60949	0.0514133
$981$	−3.25497	−0.103923
$982$	6.66725	0.212760
$983$	16.7939	0.535641	0.267820	−	0.963469i	$-0.413697\pi$
$983$	16.7939	0.535641	0.267820	+	0.963469i	$0.413697\pi$
$984$	−5.48156	−0.174746
$985$	−37.9824	−1.21022
$986$	26.6486	0.848664
$987$	2.47068	0.0786425
$988$	0.0798197	0.00253940
$989$	22.9912	0.731077
$990$	21.4047	0.680287
$991$	−2.57333	−0.0817446	−0.0408723	−	0.999164i	$-0.513014\pi$
$991$	−2.57333	−0.0817446	−0.0408723	+	0.999164i	$0.513014\pi$
$992$	0.399936	0.0126980
$993$	3.63905	0.115482
$994$	−7.86961	−0.249609
$995$	−2.22399	−0.0705053
$996$	−2.26764	−0.0718529
$997$	−21.6385	−0.685297	−0.342648	−	0.939464i	$-0.611324\pi$
$997$	−21.6385	−0.685297	−0.342648	+	0.939464i	$0.611324\pi$
$998$	14.3852	0.455356
$999$	26.7541	0.846463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.13	✓	31	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.676569 q^{3} +1.00000 q^{4} +1.60949 q^{5} -0.676569 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.54225 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.676569 q^{3} +1.00000 q^{4} +1.60949 q^{5} -0.676569 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.54225 q^{9} +1.60949 q^{10} -5.23122 q^{11} -0.676569 q^{12} +0.0933098 q^{13} +1.00000 q^{14} -1.08893 q^{15} +1.00000 q^{16} +5.37434 q^{17} -2.54225 q^{18} +0.855428 q^{19} +1.60949 q^{20} -0.676569 q^{21} -5.23122 q^{22} -2.70339 q^{23} -0.676569 q^{24} -2.40954 q^{25} +0.0933098 q^{26} +3.74972 q^{27} +1.00000 q^{28} +4.95849 q^{29} -1.08893 q^{30} +0.399936 q^{31} +1.00000 q^{32} +3.53928 q^{33} +5.37434 q^{34} +1.60949 q^{35} -2.54225 q^{36} +7.13497 q^{37} +0.855428 q^{38} -0.0631305 q^{39} +1.60949 q^{40} +8.10200 q^{41} -0.676569 q^{42} -8.50456 q^{43} -5.23122 q^{44} -4.09173 q^{45} -2.70339 q^{46} -3.65177 q^{47} -0.676569 q^{48} +1.00000 q^{49} -2.40954 q^{50} -3.63611 q^{51} +0.0933098 q^{52} +5.61617 q^{53} +3.74972 q^{54} -8.41959 q^{55} +1.00000 q^{56} -0.578756 q^{57} +4.95849 q^{58} +10.9410 q^{59} -1.08893 q^{60} +11.3535 q^{61} +0.399936 q^{62} -2.54225 q^{63} +1.00000 q^{64} +0.150181 q^{65} +3.53928 q^{66} -4.76271 q^{67} +5.37434 q^{68} +1.82903 q^{69} +1.60949 q^{70} -7.86961 q^{71} -2.54225 q^{72} +8.60330 q^{73} +7.13497 q^{74} +1.63022 q^{75} +0.855428 q^{76} -5.23122 q^{77} -0.0631305 q^{78} +7.19773 q^{79} +1.60949 q^{80} +5.08982 q^{81} +8.10200 q^{82} +3.35167 q^{83} -0.676569 q^{84} +8.64994 q^{85} -8.50456 q^{86} -3.35476 q^{87} -5.23122 q^{88} -2.35957 q^{89} -4.09173 q^{90} +0.0933098 q^{91} -2.70339 q^{92} -0.270584 q^{93} -3.65177 q^{94} +1.37680 q^{95} -0.676569 q^{96} +3.23465 q^{97} +1.00000 q^{98} +13.2991 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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