LMFDB - Embedded newform 6034.2.a.r.1.14

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			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.217225 q^{3} +1.00000 q^{4} +0.607550 q^{5} -0.217225 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.95281 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.217225 q^{3} +1.00000 q^{4} +0.607550 q^{5} -0.217225 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.95281 q^{9} +0.607550 q^{10} -1.76409 q^{11} -0.217225 q^{12} -4.93676 q^{13} -1.00000 q^{14} -0.131975 q^{15} +1.00000 q^{16} -5.28023 q^{17} -2.95281 q^{18} +6.86215 q^{19} +0.607550 q^{20} +0.217225 q^{21} -1.76409 q^{22} +5.49441 q^{23} -0.217225 q^{24} -4.63088 q^{25} -4.93676 q^{26} +1.29310 q^{27} -1.00000 q^{28} +4.61101 q^{29} -0.131975 q^{30} +6.15066 q^{31} +1.00000 q^{32} +0.383204 q^{33} -5.28023 q^{34} -0.607550 q^{35} -2.95281 q^{36} -6.38082 q^{37} +6.86215 q^{38} +1.07238 q^{39} +0.607550 q^{40} -4.87244 q^{41} +0.217225 q^{42} +5.35130 q^{43} -1.76409 q^{44} -1.79398 q^{45} +5.49441 q^{46} +8.05980 q^{47} -0.217225 q^{48} +1.00000 q^{49} -4.63088 q^{50} +1.14700 q^{51} -4.93676 q^{52} +9.02605 q^{53} +1.29310 q^{54} -1.07177 q^{55} -1.00000 q^{56} -1.49063 q^{57} +4.61101 q^{58} +10.5913 q^{59} -0.131975 q^{60} +0.892155 q^{61} +6.15066 q^{62} +2.95281 q^{63} +1.00000 q^{64} -2.99933 q^{65} +0.383204 q^{66} +14.9415 q^{67} -5.28023 q^{68} -1.19352 q^{69} -0.607550 q^{70} +4.37394 q^{71} -2.95281 q^{72} +6.02654 q^{73} -6.38082 q^{74} +1.00594 q^{75} +6.86215 q^{76} +1.76409 q^{77} +1.07238 q^{78} -13.2279 q^{79} +0.607550 q^{80} +8.57755 q^{81} -4.87244 q^{82} +1.72378 q^{83} +0.217225 q^{84} -3.20801 q^{85} +5.35130 q^{86} -1.00163 q^{87} -1.76409 q^{88} +0.880032 q^{89} -1.79398 q^{90} +4.93676 q^{91} +5.49441 q^{92} -1.33607 q^{93} +8.05980 q^{94} +4.16910 q^{95} -0.217225 q^{96} +13.0472 q^{97} +1.00000 q^{98} +5.20903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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
$3$	−0.217225	−0.125415	−0.0627073	−	0.998032i	$-0.519973\pi$
$3$	−0.217225	−0.125415	−0.0627073	+	0.998032i	$0.519973\pi$
$4$	1.00000	0.500000
$5$	0.607550	0.271705	0.135852	−	0.990729i	$-0.456623\pi$
$5$	0.607550	0.271705	0.135852	+	0.990729i	$0.456623\pi$
$6$	−0.217225	−0.0886816
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.95281	−0.984271
$10$	0.607550	0.192124
$11$	−1.76409	−0.531893	−0.265947	−	0.963988i	$-0.585684\pi$
$11$	−1.76409	−0.531893	−0.265947	+	0.963988i	$0.585684\pi$
$12$	−0.217225	−0.0627073
$13$	−4.93676	−1.36921	−0.684605	−	0.728914i	$-0.740025\pi$
$13$	−4.93676	−1.36921	−0.684605	+	0.728914i	$0.740025\pi$
$14$	−1.00000	−0.267261
$15$	−0.131975	−0.0340758
$16$	1.00000	0.250000
$17$	−5.28023	−1.28064	−0.640322	−	0.768106i	$-0.721199\pi$
$17$	−5.28023	−1.28064	−0.640322	+	0.768106i	$0.721199\pi$
$18$	−2.95281	−0.695985
$19$	6.86215	1.57428	0.787142	−	0.616772i	$-0.211560\pi$
$19$	6.86215	1.57428	0.787142	+	0.616772i	$0.211560\pi$
$20$	0.607550	0.135852
$21$	0.217225	0.0474023
$22$	−1.76409	−0.376105
$23$	5.49441	1.14566	0.572832	−	0.819673i	$-0.305845\pi$
$23$	5.49441	1.14566	0.572832	+	0.819673i	$0.305845\pi$
$24$	−0.217225	−0.0443408
$25$	−4.63088	−0.926177
$26$	−4.93676	−0.968178
$27$	1.29310	0.248857
$28$	−1.00000	−0.188982
$29$	4.61101	0.856244	0.428122	−	0.903721i	$-0.359175\pi$
$29$	4.61101	0.856244	0.428122	+	0.903721i	$0.359175\pi$
$30$	−0.131975	−0.0240952
$31$	6.15066	1.10469	0.552345	−	0.833615i	$-0.313733\pi$
$31$	6.15066	1.10469	0.552345	+	0.833615i	$0.313733\pi$
$32$	1.00000	0.176777
$33$	0.383204	0.0667072
$34$	−5.28023	−0.905552
$35$	−0.607550	−0.102695
$36$	−2.95281	−0.492136
$37$	−6.38082	−1.04900	−0.524500	−	0.851410i	$-0.675748\pi$
$37$	−6.38082	−1.04900	−0.524500	+	0.851410i	$0.675748\pi$
$38$	6.86215	1.11319
$39$	1.07238	0.171719
$40$	0.607550	0.0960621
$41$	−4.87244	−0.760948	−0.380474	−	0.924792i	$-0.624239\pi$
$41$	−4.87244	−0.760948	−0.380474	+	0.924792i	$0.624239\pi$
$42$	0.217225	0.0335185
$43$	5.35130	0.816065	0.408032	−	0.912967i	$-0.366215\pi$
$43$	5.35130	0.816065	0.408032	+	0.912967i	$0.366215\pi$
$44$	−1.76409	−0.265947
$45$	−1.79398	−0.267431
$46$	5.49441	0.810107
$47$	8.05980	1.17564	0.587821	−	0.808991i	$-0.299986\pi$
$47$	8.05980	1.17564	0.587821	+	0.808991i	$0.299986\pi$
$48$	−0.217225	−0.0313537
$49$	1.00000	0.142857
$50$	−4.63088	−0.654906
$51$	1.14700	0.160612
$52$	−4.93676	−0.684605
$53$	9.02605	1.23982	0.619912	−	0.784672i	$-0.287168\pi$
$53$	9.02605	1.23982	0.619912	+	0.784672i	$0.287168\pi$
$54$	1.29310	0.175968
$55$	−1.07177	−0.144518
$56$	−1.00000	−0.133631
$57$	−1.49063	−0.197438
$58$	4.61101	0.605456
$59$	10.5913	1.37887	0.689437	−	0.724345i	$-0.257858\pi$
$59$	10.5913	1.37887	0.689437	+	0.724345i	$0.257858\pi$
$60$	−0.131975	−0.0170379
$61$	0.892155	0.114229	0.0571144	−	0.998368i	$-0.481810\pi$
$61$	0.892155	0.114229	0.0571144	+	0.998368i	$0.481810\pi$
$62$	6.15066	0.781134
$63$	2.95281	0.372020
$64$	1.00000	0.125000
$65$	−2.99933	−0.372021
$66$	0.383204	0.0471691
$67$	14.9415	1.82540	0.912700	−	0.408631i	$-0.133994\pi$
$67$	14.9415	1.82540	0.912700	+	0.408631i	$0.133994\pi$
$68$	−5.28023	−0.640322
$69$	−1.19352	−0.143683
$70$	−0.607550	−0.0726162
$71$	4.37394	0.519092	0.259546	−	0.965731i	$-0.416427\pi$
$71$	4.37394	0.519092	0.259546	+	0.965731i	$0.416427\pi$
$72$	−2.95281	−0.347992
$73$	6.02654	0.705353	0.352676	−	0.935745i	$-0.385272\pi$
$73$	6.02654	0.705353	0.352676	+	0.935745i	$0.385272\pi$
$74$	−6.38082	−0.741755
$75$	1.00594	0.116156
$76$	6.86215	0.787142
$77$	1.76409	0.201037
$78$	1.07238	0.121424
$79$	−13.2279	−1.48825	−0.744125	−	0.668040i	$-0.767133\pi$
$79$	−13.2279	−1.48825	−0.744125	+	0.668040i	$0.767133\pi$
$80$	0.607550	0.0679262
$81$	8.57755	0.953061
$82$	−4.87244	−0.538071
$83$	1.72378	0.189209	0.0946047	−	0.995515i	$-0.469841\pi$
$83$	1.72378	0.189209	0.0946047	+	0.995515i	$0.469841\pi$
$84$	0.217225	0.0237011
$85$	−3.20801	−0.347957
$86$	5.35130	0.577045
$87$	−1.00163	−0.107386
$88$	−1.76409	−0.188053
$89$	0.880032	0.0932832	0.0466416	−	0.998912i	$-0.485148\pi$
$89$	0.880032	0.0932832	0.0466416	+	0.998912i	$0.485148\pi$
$90$	−1.79398	−0.189102
$91$	4.93676	0.517513
$92$	5.49441	0.572832
$93$	−1.33607	−0.138544
$94$	8.05980	0.831305
$95$	4.16910	0.427741
$96$	−0.217225	−0.0221704
$97$	13.0472	1.32475	0.662373	−	0.749174i	$-0.269549\pi$
$97$	13.0472	1.32475	0.662373	+	0.749174i	$0.269549\pi$
$98$	1.00000	0.101015
$99$	5.20903	0.523527
$100$	−4.63088	−0.463088
$101$	−7.35097	−0.731449	−0.365725	−	0.930723i	$-0.619179\pi$
$101$	−7.35097	−0.731449	−0.365725	+	0.930723i	$0.619179\pi$
$102$	1.14700	0.113570
$103$	12.8627	1.26740	0.633700	−	0.773579i	$-0.281535\pi$
$103$	12.8627	1.26740	0.633700	+	0.773579i	$0.281535\pi$
$104$	−4.93676	−0.484089
$105$	0.131975	0.0128794
$106$	9.02605	0.876688
$107$	−10.7227	−1.03661	−0.518303	−	0.855197i	$-0.673436\pi$
$107$	−10.7227	−1.03661	−0.518303	+	0.855197i	$0.673436\pi$
$108$	1.29310	0.124428
$109$	−2.13837	−0.204818	−0.102409	−	0.994742i	$-0.532655\pi$
$109$	−2.13837	−0.204818	−0.102409	+	0.994742i	$0.532655\pi$
$110$	−1.07177	−0.102190
$111$	1.38607	0.131560
$112$	−1.00000	−0.0944911
$113$	−4.96754	−0.467307	−0.233653	−	0.972320i	$-0.575068\pi$
$113$	−4.96754	−0.467307	−0.233653	+	0.972320i	$0.575068\pi$
$114$	−1.49063	−0.139610
$115$	3.33813	0.311283
$116$	4.61101	0.428122
$117$	14.5773	1.34767
$118$	10.5913	0.975011
$119$	5.28023	0.484038
$120$	−0.131975	−0.0120476
$121$	−7.88799	−0.717090
$122$	0.892155	0.0807719
$123$	1.05841	0.0954340
$124$	6.15066	0.552345
$125$	−5.85125	−0.523351
$126$	2.95281	0.263058
$127$	19.2160	1.70515	0.852574	−	0.522606i	$-0.175040\pi$
$127$	19.2160	1.70515	0.852574	+	0.522606i	$0.175040\pi$
$128$	1.00000	0.0883883
$129$	−1.16243	−0.102347
$130$	−2.99933	−0.263058
$131$	−18.3095	−1.59971	−0.799856	−	0.600192i	$-0.795091\pi$
$131$	−18.3095	−1.59971	−0.799856	+	0.600192i	$0.795091\pi$
$132$	0.383204	0.0333536
$133$	−6.86215	−0.595024
$134$	14.9415	1.29075
$135$	0.785622	0.0676156
$136$	−5.28023	−0.452776
$137$	6.20962	0.530524	0.265262	−	0.964176i	$-0.414542\pi$
$137$	6.20962	0.530524	0.265262	+	0.964176i	$0.414542\pi$
$138$	−1.19352	−0.101599
$139$	11.6241	0.985947	0.492974	−	0.870044i	$-0.335910\pi$
$139$	11.6241	0.985947	0.492974	+	0.870044i	$0.335910\pi$
$140$	−0.607550	−0.0513474
$141$	−1.75079	−0.147443
$142$	4.37394	0.367053
$143$	8.70888	0.728273
$144$	−2.95281	−0.246068
$145$	2.80142	0.232646
$146$	6.02654	0.498760
$147$	−0.217225	−0.0179164
$148$	−6.38082	−0.524500
$149$	2.75302	0.225536	0.112768	−	0.993621i	$-0.464028\pi$
$149$	2.75302	0.225536	0.112768	+	0.993621i	$0.464028\pi$
$150$	1.00594	0.0821348
$151$	2.87327	0.233823	0.116912	−	0.993142i	$-0.462701\pi$
$151$	2.87327	0.233823	0.116912	+	0.993142i	$0.462701\pi$
$152$	6.86215	0.556594
$153$	15.5915	1.26050
$154$	1.76409	0.142154
$155$	3.73683	0.300150
$156$	1.07238	0.0858595
$157$	5.95783	0.475486	0.237743	−	0.971328i	$-0.423592\pi$
$157$	5.95783	0.475486	0.237743	+	0.971328i	$0.423592\pi$
$158$	−13.2279	−1.05235
$159$	−1.96068	−0.155492
$160$	0.607550	0.0480311
$161$	−5.49441	−0.433021
$162$	8.57755	0.673916
$163$	0.615670	0.0482230	0.0241115	−	0.999709i	$-0.492324\pi$
$163$	0.615670	0.0482230	0.0241115	+	0.999709i	$0.492324\pi$
$164$	−4.87244	−0.380474
$165$	0.232816	0.0181247
$166$	1.72378	0.133791
$167$	15.2552	1.18048	0.590240	−	0.807228i	$-0.299033\pi$
$167$	15.2552	1.18048	0.590240	+	0.807228i	$0.299033\pi$
$168$	0.217225	0.0167592
$169$	11.3716	0.874735
$170$	−3.20801	−0.246043
$171$	−20.2626	−1.54952
$172$	5.35130	0.408032
$173$	−8.83885	−0.672005	−0.336003	−	0.941861i	$-0.609075\pi$
$173$	−8.83885	−0.672005	−0.336003	+	0.941861i	$0.609075\pi$
$174$	−1.00163	−0.0759330
$175$	4.63088	0.350062
$176$	−1.76409	−0.132973
$177$	−2.30070	−0.172931
$178$	0.880032	0.0659612
$179$	18.0968	1.35262	0.676310	−	0.736617i	$-0.263578\pi$
$179$	18.0968	1.35262	0.676310	+	0.736617i	$0.263578\pi$
$180$	−1.79398	−0.133716
$181$	−6.32459	−0.470103	−0.235051	−	0.971983i	$-0.575526\pi$
$181$	−6.32459	−0.470103	−0.235051	+	0.971983i	$0.575526\pi$
$182$	4.93676	0.365937
$183$	−0.193798	−0.0143260
$184$	5.49441	0.405054
$185$	−3.87667	−0.285018
$186$	−1.33607	−0.0979657
$187$	9.31481	0.681166
$188$	8.05980	0.587821
$189$	−1.29310	−0.0940590
$190$	4.16910	0.302458
$191$	−3.08987	−0.223575	−0.111788	−	0.993732i	$-0.535658\pi$
$191$	−3.08987	−0.223575	−0.111788	+	0.993732i	$0.535658\pi$
$192$	−0.217225	−0.0156768
$193$	−20.1073	−1.44735	−0.723676	−	0.690140i	$-0.757549\pi$
$193$	−20.1073	−1.44735	−0.723676	+	0.690140i	$0.757549\pi$
$194$	13.0472	0.936737
$195$	0.651528	0.0466569
$196$	1.00000	0.0714286
$197$	7.06778	0.503558	0.251779	−	0.967785i	$-0.418984\pi$
$197$	7.06778	0.503558	0.251779	+	0.967785i	$0.418984\pi$
$198$	5.20903	0.370190
$199$	14.4734	1.02599	0.512997	−	0.858391i	$-0.328535\pi$
$199$	14.4734	1.02599	0.512997	+	0.858391i	$0.328535\pi$
$200$	−4.63088	−0.327453
$201$	−3.24567	−0.228932
$202$	−7.35097	−0.517213
$203$	−4.61101	−0.323630
$204$	1.14700	0.0803058
$205$	−2.96025	−0.206753
$206$	12.8627	0.896187
$207$	−16.2240	−1.12764
$208$	−4.93676	−0.342302
$209$	−12.1054	−0.837351
$210$	0.131975	0.00910713
$211$	−23.3986	−1.61083	−0.805414	−	0.592713i	$-0.798057\pi$
$211$	−23.3986	−1.61083	−0.805414	+	0.592713i	$0.798057\pi$
$212$	9.02605	0.619912
$213$	−0.950128	−0.0651017
$214$	−10.7227	−0.732992
$215$	3.25118	0.221729
$216$	1.29310	0.0879842
$217$	−6.15066	−0.417534
$218$	−2.13837	−0.144829
$219$	−1.30911	−0.0884616
$220$	−1.07177	−0.0722590
$221$	26.0672	1.75347
$222$	1.38607	0.0930270
$223$	−24.8941	−1.66703	−0.833515	−	0.552497i	$-0.813675\pi$
$223$	−24.8941	−1.66703	−0.833515	+	0.552497i	$0.813675\pi$
$224$	−1.00000	−0.0668153
$225$	13.6741	0.911609
$226$	−4.96754	−0.330436
$227$	−18.7854	−1.24683	−0.623417	−	0.781890i	$-0.714256\pi$
$227$	−18.7854	−1.24683	−0.623417	+	0.781890i	$0.714256\pi$
$228$	−1.49063	−0.0987192
$229$	−9.99878	−0.660738	−0.330369	−	0.943852i	$-0.607173\pi$
$229$	−9.99878	−0.660738	−0.330369	+	0.943852i	$0.607173\pi$
$230$	3.33813	0.220110
$231$	−0.383204	−0.0252130
$232$	4.61101	0.302728
$233$	−2.96629	−0.194328	−0.0971640	−	0.995268i	$-0.530977\pi$
$233$	−2.96629	−0.194328	−0.0971640	+	0.995268i	$0.530977\pi$
$234$	14.5773	0.952949
$235$	4.89673	0.319428
$236$	10.5913	0.689437
$237$	2.87342	0.186648
$238$	5.28023	0.342267
$239$	7.57966	0.490287	0.245144	−	0.969487i	$-0.421165\pi$
$239$	7.57966	0.490287	0.245144	+	0.969487i	$0.421165\pi$
$240$	−0.131975	−0.00851894
$241$	−5.09644	−0.328290	−0.164145	−	0.986436i	$-0.552487\pi$
$241$	−5.09644	−0.328290	−0.164145	+	0.986436i	$0.552487\pi$
$242$	−7.88799	−0.507059
$243$	−5.74255	−0.368385
$244$	0.892155	0.0571144
$245$	0.607550	0.0388150
$246$	1.05841	0.0674820
$247$	−33.8767	−2.15553
$248$	6.15066	0.390567
$249$	−0.374448	−0.0237297
$250$	−5.85125	−0.370065
$251$	6.89774	0.435381	0.217691	−	0.976018i	$-0.430148\pi$
$251$	6.89774	0.435381	0.217691	+	0.976018i	$0.430148\pi$
$252$	2.95281	0.186010
$253$	−9.69264	−0.609371
$254$	19.2160	1.20572
$255$	0.696858	0.0436389
$256$	1.00000	0.0625000
$257$	11.2604	0.702405	0.351203	−	0.936299i	$-0.385773\pi$
$257$	11.2604	0.702405	0.351203	+	0.936299i	$0.385773\pi$
$258$	−1.16243	−0.0723699
$259$	6.38082	0.396485
$260$	−2.99933	−0.186010
$261$	−13.6155	−0.842776
$262$	−18.3095	−1.13117
$263$	−30.8921	−1.90489	−0.952444	−	0.304714i	$-0.901439\pi$
$263$	−30.8921	−1.90489	−0.952444	+	0.304714i	$0.901439\pi$
$264$	0.383204	0.0235846
$265$	5.48378	0.336866
$266$	−6.86215	−0.420745
$267$	−0.191165	−0.0116991
$268$	14.9415	0.912700
$269$	11.4391	0.697453	0.348726	−	0.937225i	$-0.386614\pi$
$269$	11.4391	0.697453	0.348726	+	0.937225i	$0.386614\pi$
$270$	0.785622	0.0478114
$271$	1.81565	0.110293	0.0551465	−	0.998478i	$-0.482437\pi$
$271$	1.81565	0.110293	0.0551465	+	0.998478i	$0.482437\pi$
$272$	−5.28023	−0.320161
$273$	−1.07238	−0.0649037
$274$	6.20962	0.375137
$275$	8.16930	0.492627
$276$	−1.19352	−0.0718416
$277$	−7.43900	−0.446966	−0.223483	−	0.974708i	$-0.571743\pi$
$277$	−7.43900	−0.446966	−0.223483	+	0.974708i	$0.571743\pi$
$278$	11.6241	0.697170
$279$	−18.1617	−1.08732
$280$	−0.607550	−0.0363081
$281$	20.4042	1.21721	0.608605	−	0.793473i	$-0.291729\pi$
$281$	20.4042	1.21721	0.608605	+	0.793473i	$0.291729\pi$
$282$	−1.75079	−0.104258
$283$	−17.6559	−1.04954	−0.524768	−	0.851245i	$-0.675848\pi$
$283$	−17.6559	−1.04954	−0.524768	+	0.851245i	$0.675848\pi$
$284$	4.37394	0.259546
$285$	−0.905631	−0.0536449
$286$	8.70888	0.514967
$287$	4.87244	0.287611
$288$	−2.95281	−0.173996
$289$	10.8809	0.640050
$290$	2.80142	0.164505
$291$	−2.83418	−0.166143
$292$	6.02654	0.352676
$293$	−4.72896	−0.276269	−0.138134	−	0.990414i	$-0.544111\pi$
$293$	−4.72896	−0.276269	−0.138134	+	0.990414i	$0.544111\pi$
$294$	−0.217225	−0.0126688
$295$	6.43477	0.374647
$296$	−6.38082	−0.370878
$297$	−2.28114	−0.132365
$298$	2.75302	0.159478
$299$	−27.1246	−1.56866
$300$	1.00594	0.0580781
$301$	−5.35130	−0.308444
$302$	2.87327	0.165338
$303$	1.59681	0.0917345
$304$	6.86215	0.393571
$305$	0.542029	0.0310365
$306$	15.5915	0.891309
$307$	15.7011	0.896109	0.448055	−	0.894006i	$-0.352117\pi$
$307$	15.7011	0.896109	0.448055	+	0.894006i	$0.352117\pi$
$308$	1.76409	0.100518
$309$	−2.79410	−0.158951
$310$	3.73683	0.212238
$311$	23.8002	1.34958	0.674792	−	0.738008i	$-0.264233\pi$
$311$	23.8002	1.34958	0.674792	+	0.738008i	$0.264233\pi$
$312$	1.07238	0.0607118
$313$	9.18435	0.519130	0.259565	−	0.965726i	$-0.416421\pi$
$313$	9.18435	0.519130	0.259565	+	0.965726i	$0.416421\pi$
$314$	5.95783	0.336220
$315$	1.79398	0.101079
$316$	−13.2279	−0.744125
$317$	−11.4254	−0.641714	−0.320857	−	0.947128i	$-0.603971\pi$
$317$	−11.4254	−0.641714	−0.320857	+	0.947128i	$0.603971\pi$
$318$	−1.96068	−0.109950
$319$	−8.13424	−0.455430
$320$	0.607550	0.0339631
$321$	2.32924	0.130006
$322$	−5.49441	−0.306192
$323$	−36.2337	−2.01610
$324$	8.57755	0.476530
$325$	22.8615	1.26813
$326$	0.615670	0.0340988
$327$	0.464506	0.0256872
$328$	−4.87244	−0.269036
$329$	−8.05980	−0.444351
$330$	0.232816	0.0128161
$331$	12.2767	0.674789	0.337394	−	0.941363i	$-0.390454\pi$
$331$	12.2767	0.674789	0.337394	+	0.941363i	$0.390454\pi$
$332$	1.72378	0.0946047
$333$	18.8414	1.03250
$334$	15.2552	0.834726
$335$	9.07774	0.495970
$336$	0.217225	0.0118506
$337$	−24.1095	−1.31333	−0.656664	−	0.754184i	$-0.728033\pi$
$337$	−24.1095	−1.31333	−0.656664	+	0.754184i	$0.728033\pi$
$338$	11.3716	0.618531
$339$	1.07907	0.0586071
$340$	−3.20801	−0.173979
$341$	−10.8503	−0.587577
$342$	−20.2626	−1.09568
$343$	−1.00000	−0.0539949
$344$	5.35130	0.288523
$345$	−0.725125	−0.0390394
$346$	−8.83885	−0.475179
$347$	−23.1510	−1.24281	−0.621405	−	0.783489i	$-0.713438\pi$
$347$	−23.1510	−1.24281	−0.621405	+	0.783489i	$0.713438\pi$
$348$	−1.00163	−0.0536928
$349$	3.72233	0.199252	0.0996258	−	0.995025i	$-0.468235\pi$
$349$	3.72233	0.199252	0.0996258	+	0.995025i	$0.468235\pi$
$350$	4.63088	0.247531
$351$	−6.38371	−0.340737
$352$	−1.76409	−0.0940263
$353$	4.95866	0.263923	0.131961	−	0.991255i	$-0.457873\pi$
$353$	4.95866	0.263923	0.131961	+	0.991255i	$0.457873\pi$
$354$	−2.30070	−0.122281
$355$	2.65739	0.141040
$356$	0.880032	0.0466416
$357$	−1.14700	−0.0607055
$358$	18.0968	0.956447
$359$	−0.390131	−0.0205903	−0.0102952	−	0.999947i	$-0.503277\pi$
$359$	−0.390131	−0.0205903	−0.0102952	+	0.999947i	$0.503277\pi$
$360$	−1.79398	−0.0945512
$361$	28.0890	1.47837
$362$	−6.32459	−0.332413
$363$	1.71346	0.0899336
$364$	4.93676	0.258756
$365$	3.66142	0.191648
$366$	−0.193798	−0.0101300
$367$	31.2519	1.63134	0.815668	−	0.578521i	$-0.196370\pi$
$367$	31.2519	1.63134	0.815668	+	0.578521i	$0.196370\pi$
$368$	5.49441	0.286416
$369$	14.3874	0.748979
$370$	−3.87667	−0.201538
$371$	−9.02605	−0.468609
$372$	−1.33607	−0.0692722
$373$	5.42004	0.280639	0.140320	−	0.990106i	$-0.455187\pi$
$373$	5.42004	0.280639	0.140320	+	0.990106i	$0.455187\pi$
$374$	9.31481	0.481657
$375$	1.27103	0.0656359
$376$	8.05980	0.415652
$377$	−22.7634	−1.17238
$378$	−1.29310	−0.0665098
$379$	−13.7600	−0.706802	−0.353401	−	0.935472i	$-0.614975\pi$
$379$	−13.7600	−0.706802	−0.353401	+	0.935472i	$0.614975\pi$
$380$	4.16910	0.213870
$381$	−4.17420	−0.213851
$382$	−3.08987	−0.158092
$383$	−0.685800	−0.0350428	−0.0175214	−	0.999846i	$-0.505578\pi$
$383$	−0.685800	−0.0350428	−0.0175214	+	0.999846i	$0.505578\pi$
$384$	−0.217225	−0.0110852
$385$	1.07177	0.0546226
$386$	−20.1073	−1.02343
$387$	−15.8014	−0.803229
$388$	13.0472	0.662373
$389$	2.61903	0.132790	0.0663951	−	0.997793i	$-0.478850\pi$
$389$	2.61903	0.132790	0.0663951	+	0.997793i	$0.478850\pi$
$390$	0.651528	0.0329914
$391$	−29.0118	−1.46719
$392$	1.00000	0.0505076
$393$	3.97728	0.200627
$394$	7.06778	0.356070
$395$	−8.03659	−0.404365
$396$	5.20903	0.261764
$397$	−3.75823	−0.188620	−0.0943102	−	0.995543i	$-0.530065\pi$
$397$	−3.75823	−0.188620	−0.0943102	+	0.995543i	$0.530065\pi$
$398$	14.4734	0.725487
$399$	1.49063	0.0746247
$400$	−4.63088	−0.231544
$401$	24.8598	1.24144	0.620719	−	0.784033i	$-0.286841\pi$
$401$	24.8598	1.24144	0.620719	+	0.784033i	$0.286841\pi$
$402$	−3.24567	−0.161879
$403$	−30.3643	−1.51255
$404$	−7.35097	−0.365725
$405$	5.21129	0.258951
$406$	−4.61101	−0.228841
$407$	11.2563	0.557956
$408$	1.14700	0.0567848
$409$	−12.2643	−0.606429	−0.303215	−	0.952922i	$-0.598060\pi$
$409$	−12.2643	−0.606429	−0.303215	+	0.952922i	$0.598060\pi$
$410$	−2.96025	−0.146197
$411$	−1.34888	−0.0665355
$412$	12.8627	0.633700
$413$	−10.5913	−0.521166
$414$	−16.2240	−0.797365
$415$	1.04728	0.0514091
$416$	−4.93676	−0.242044
$417$	−2.52505	−0.123652
$418$	−12.1054	−0.592097
$419$	18.7825	0.917586	0.458793	−	0.888543i	$-0.348282\pi$
$419$	18.7825	0.917586	0.458793	+	0.888543i	$0.348282\pi$
$420$	0.131975	0.00643972
$421$	16.6950	0.813663	0.406832	−	0.913503i	$-0.366634\pi$
$421$	16.6950	0.813663	0.406832	+	0.913503i	$0.366634\pi$
$422$	−23.3986	−1.13903
$423$	−23.7991	−1.15715
$424$	9.02605	0.438344
$425$	24.4521	1.18610
$426$	−0.950128	−0.0460339
$427$	−0.892155	−0.0431744
$428$	−10.7227	−0.518303
$429$	−1.89178	−0.0913362
$430$	3.25118	0.156786
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.29310	0.0622142
$433$	30.7814	1.47926	0.739629	−	0.673015i	$-0.235001\pi$
$433$	30.7814	1.47926	0.739629	+	0.673015i	$0.235001\pi$
$434$	−6.15066	−0.295241
$435$	−0.608538	−0.0291772
$436$	−2.13837	−0.102409
$437$	37.7035	1.80360
$438$	−1.30911	−0.0625518
$439$	37.7820	1.80323	0.901617	−	0.432534i	$-0.142381\pi$
$439$	37.7820	1.80323	0.901617	+	0.432534i	$0.142381\pi$
$440$	−1.07177	−0.0510948
$441$	−2.95281	−0.140610
$442$	26.0672	1.23989
$443$	40.0752	1.90403	0.952015	−	0.306052i	$-0.0990082\pi$
$443$	40.0752	1.90403	0.952015	+	0.306052i	$0.0990082\pi$
$444$	1.38607	0.0657800
$445$	0.534664	0.0253455
$446$	−24.8941	−1.17877
$447$	−0.598024	−0.0282856
$448$	−1.00000	−0.0472456
$449$	3.12849	0.147642	0.0738212	−	0.997271i	$-0.476481\pi$
$449$	3.12849	0.147642	0.0738212	+	0.997271i	$0.476481\pi$
$450$	13.6741	0.644605
$451$	8.59543	0.404743
$452$	−4.96754	−0.233653
$453$	−0.624145	−0.0293249
$454$	−18.7854	−0.881645
$455$	2.99933	0.140611
$456$	−1.49063	−0.0698050
$457$	−27.2298	−1.27376	−0.636879	−	0.770964i	$-0.719775\pi$
$457$	−27.2298	−1.27376	−0.636879	+	0.770964i	$0.719775\pi$
$458$	−9.99878	−0.467212
$459$	−6.82786	−0.318697
$460$	3.33813	0.155641
$461$	25.0253	1.16554	0.582772	−	0.812636i	$-0.301968\pi$
$461$	25.0253	1.16554	0.582772	+	0.812636i	$0.301968\pi$
$462$	−0.383204	−0.0178283
$463$	27.2736	1.26751	0.633756	−	0.773533i	$-0.281512\pi$
$463$	27.2736	1.26751	0.633756	+	0.773533i	$0.281512\pi$
$464$	4.61101	0.214061
$465$	−0.811732	−0.0376432
$466$	−2.96629	−0.137411
$467$	−13.4445	−0.622135	−0.311068	−	0.950388i	$-0.600687\pi$
$467$	−13.4445	−0.622135	−0.311068	+	0.950388i	$0.600687\pi$
$468$	14.5773	0.673837
$469$	−14.9415	−0.689936
$470$	4.89673	0.225869
$471$	−1.29419	−0.0596330
$472$	10.5913	0.487506
$473$	−9.44017	−0.434059
$474$	2.87342	0.131980
$475$	−31.7778	−1.45807
$476$	5.28023	0.242019
$477$	−26.6522	−1.22032
$478$	7.57966	0.346685
$479$	19.9316	0.910699	0.455350	−	0.890313i	$-0.349514\pi$
$479$	19.9316	0.910699	0.455350	+	0.890313i	$0.349514\pi$
$480$	−0.131975	−0.00602380
$481$	31.5005	1.43630
$482$	−5.09644	−0.232136
$483$	1.19352	0.0543071
$484$	−7.88799	−0.358545
$485$	7.92685	0.359940
$486$	−5.74255	−0.260487
$487$	−9.66008	−0.437740	−0.218870	−	0.975754i	$-0.570237\pi$
$487$	−9.66008	−0.437740	−0.218870	+	0.975754i	$0.570237\pi$
$488$	0.892155	0.0403860
$489$	−0.133739	−0.00604787
$490$	0.607550	0.0274463
$491$	25.3844	1.14558	0.572791	−	0.819701i	$-0.305861\pi$
$491$	25.3844	1.14558	0.572791	+	0.819701i	$0.305861\pi$
$492$	1.05841	0.0477170
$493$	−24.3472	−1.09654
$494$	−33.8767	−1.52419
$495$	3.16475	0.142245
$496$	6.15066	0.276173
$497$	−4.37394	−0.196198
$498$	−0.374448	−0.0167794
$499$	−21.8255	−0.977042	−0.488521	−	0.872552i	$-0.662463\pi$
$499$	−21.8255	−0.977042	−0.488521	+	0.872552i	$0.662463\pi$
$500$	−5.85125	−0.261676
$501$	−3.31380	−0.148050
$502$	6.89774	0.307861
$503$	29.0712	1.29622	0.648110	−	0.761547i	$-0.275560\pi$
$503$	29.0712	1.29622	0.648110	+	0.761547i	$0.275560\pi$
$504$	2.95281	0.131529
$505$	−4.46609	−0.198738
$506$	−9.69264	−0.430891
$507$	−2.47018	−0.109705
$508$	19.2160	0.852574
$509$	5.14662	0.228120	0.114060	−	0.993474i	$-0.463614\pi$
$509$	5.14662	0.228120	0.114060	+	0.993474i	$0.463614\pi$
$510$	0.696858	0.0308574
$511$	−6.02654	−0.266598
$512$	1.00000	0.0441942
$513$	8.87343	0.391771
$514$	11.2604	0.496676
$515$	7.81474	0.344359
$516$	−1.16243	−0.0511733
$517$	−14.2182	−0.625316
$518$	6.38082	0.280357
$519$	1.92002	0.0842793
$520$	−2.99933	−0.131529
$521$	−1.00511	−0.0440347	−0.0220173	−	0.999758i	$-0.507009\pi$
$521$	−1.00511	−0.0440347	−0.0220173	+	0.999758i	$0.507009\pi$
$522$	−13.6155	−0.595933
$523$	42.1299	1.84221	0.921106	−	0.389311i	$-0.127287\pi$
$523$	42.1299	1.84221	0.921106	+	0.389311i	$0.127287\pi$
$524$	−18.3095	−0.799856
$525$	−1.00594	−0.0439029
$526$	−30.8921	−1.34696
$527$	−32.4769	−1.41472
$528$	0.383204	0.0166768
$529$	7.18860	0.312548
$530$	5.48378	0.238200
$531$	−31.2742	−1.35719
$532$	−6.86215	−0.297512
$533$	24.0541	1.04190
$534$	−0.191165	−0.00827250
$535$	−6.51461	−0.281651
$536$	14.9415	0.645376
$537$	−3.93108	−0.169639
$538$	11.4391	0.493174
$539$	−1.76409	−0.0759848
$540$	0.785622	0.0338078
$541$	−10.6945	−0.459794	−0.229897	−	0.973215i	$-0.573839\pi$
$541$	−10.6945	−0.459794	−0.229897	+	0.973215i	$0.573839\pi$
$542$	1.81565	0.0779889
$543$	1.37386	0.0589578
$544$	−5.28023	−0.226388
$545$	−1.29917	−0.0556501
$546$	−1.07238	−0.0458938
$547$	−8.93925	−0.382215	−0.191107	−	0.981569i	$-0.561208\pi$
$547$	−8.93925	−0.382215	−0.191107	+	0.981569i	$0.561208\pi$
$548$	6.20962	0.265262
$549$	−2.63437	−0.112432
$550$	8.16930	0.348340
$551$	31.6414	1.34797
$552$	−1.19352	−0.0507997
$553$	13.2279	0.562506
$554$	−7.43900	−0.316053
$555$	0.842108	0.0357455
$556$	11.6241	0.492974
$557$	41.5481	1.76045	0.880225	−	0.474556i	$-0.157391\pi$
$557$	41.5481	1.76045	0.880225	+	0.474556i	$0.157391\pi$
$558$	−18.1617	−0.768848
$559$	−26.4180	−1.11736
$560$	−0.607550	−0.0256737
$561$	−2.02341	−0.0854282
$562$	20.4042	0.860698
$563$	10.2526	0.432095	0.216047	−	0.976383i	$-0.430683\pi$
$563$	10.2526	0.432095	0.216047	+	0.976383i	$0.430683\pi$
$564$	−1.75079	−0.0737214
$565$	−3.01803	−0.126969
$566$	−17.6559	−0.742134
$567$	−8.57755	−0.360223
$568$	4.37394	0.183527
$569$	10.2111	0.428072	0.214036	−	0.976826i	$-0.431339\pi$
$569$	10.2111	0.428072	0.214036	+	0.976826i	$0.431339\pi$
$570$	−0.905631	−0.0379327
$571$	−10.8538	−0.454218	−0.227109	−	0.973869i	$-0.572927\pi$
$571$	−10.8538	−0.454218	−0.227109	+	0.973869i	$0.572927\pi$
$572$	8.70888	0.364137
$573$	0.671196	0.0280396
$574$	4.87244	0.203372
$575$	−25.4440	−1.06109
$576$	−2.95281	−0.123034
$577$	19.1699	0.798054	0.399027	−	0.916939i	$-0.369348\pi$
$577$	19.1699	0.798054	0.399027	+	0.916939i	$0.369348\pi$
$578$	10.8809	0.452584
$579$	4.36779	0.181519
$580$	2.80142	0.116323
$581$	−1.72378	−0.0715145
$582$	−2.83418	−0.117481
$583$	−15.9228	−0.659454
$584$	6.02654	0.249380
$585$	8.85646	0.366169
$586$	−4.72896	−0.195351
$587$	−41.7767	−1.72431	−0.862154	−	0.506646i	$-0.830885\pi$
$587$	−41.7767	−1.72431	−0.862154	+	0.506646i	$0.830885\pi$
$588$	−0.217225	−0.00895819
$589$	42.2067	1.73910
$590$	6.43477	0.264915
$591$	−1.53530	−0.0631536
$592$	−6.38082	−0.262250
$593$	−44.4404	−1.82495	−0.912475	−	0.409133i	$-0.865831\pi$
$593$	−44.4404	−1.82495	−0.912475	+	0.409133i	$0.865831\pi$
$594$	−2.28114	−0.0935964
$595$	3.20801	0.131515
$596$	2.75302	0.112768
$597$	−3.14398	−0.128675
$598$	−27.1246	−1.10921
$599$	−39.1133	−1.59812	−0.799062	−	0.601248i	$-0.794670\pi$
$599$	−39.1133	−1.59812	−0.799062	+	0.601248i	$0.794670\pi$
$600$	1.00594	0.0410674
$601$	−5.61036	−0.228851	−0.114426	−	0.993432i	$-0.536503\pi$
$601$	−5.61036	−0.228851	−0.114426	+	0.993432i	$0.536503\pi$
$602$	−5.35130	−0.218103
$603$	−44.1196	−1.79669
$604$	2.87327	0.116912
$605$	−4.79235	−0.194837
$606$	1.59681	0.0648661
$607$	16.2819	0.660862	0.330431	−	0.943830i	$-0.392806\pi$
$607$	16.2819	0.660862	0.330431	+	0.943830i	$0.392806\pi$
$608$	6.86215	0.278297
$609$	1.00163	0.0405879
$610$	0.542029	0.0219461
$611$	−39.7893	−1.60970
$612$	15.5915	0.630251
$613$	8.44071	0.340917	0.170459	−	0.985365i	$-0.445475\pi$
$613$	8.44071	0.340917	0.170459	+	0.985365i	$0.445475\pi$
$614$	15.7011	0.633645
$615$	0.643040	0.0259299
$616$	1.76409	0.0710772
$617$	−29.0404	−1.16912	−0.584562	−	0.811349i	$-0.698734\pi$
$617$	−29.0404	−1.16912	−0.584562	+	0.811349i	$0.698734\pi$
$618$	−2.79410	−0.112395
$619$	11.0355	0.443554	0.221777	−	0.975097i	$-0.428814\pi$
$619$	11.0355	0.443554	0.221777	+	0.975097i	$0.428814\pi$
$620$	3.73683	0.150075
$621$	7.10482	0.285106
$622$	23.8002	0.954300
$623$	−0.880032	−0.0352577
$624$	1.07238	0.0429298
$625$	19.5995	0.783979
$626$	9.18435	0.367080
$627$	2.62960	0.105016
$628$	5.95783	0.237743
$629$	33.6922	1.34340
$630$	1.79398	0.0714740
$631$	27.6683	1.10146	0.550729	−	0.834684i	$-0.314350\pi$
$631$	27.6683	1.10146	0.550729	+	0.834684i	$0.314350\pi$
$632$	−13.2279	−0.526176
$633$	5.08276	0.202021
$634$	−11.4254	−0.453760
$635$	11.6747	0.463297
$636$	−1.96068	−0.0777460
$637$	−4.93676	−0.195601
$638$	−8.13424	−0.322038
$639$	−12.9154	−0.510927
$640$	0.607550	0.0240155
$641$	−4.18801	−0.165416	−0.0827082	−	0.996574i	$-0.526357\pi$
$641$	−4.18801	−0.165416	−0.0827082	+	0.996574i	$0.526357\pi$
$642$	2.32924	0.0919279
$643$	−24.1521	−0.952465	−0.476232	−	0.879320i	$-0.657998\pi$
$643$	−24.1521	−0.952465	−0.476232	+	0.879320i	$0.657998\pi$
$644$	−5.49441	−0.216510
$645$	−0.706237	−0.0278080
$646$	−36.2337	−1.42560
$647$	−31.0384	−1.22025	−0.610124	−	0.792306i	$-0.708880\pi$
$647$	−31.0384	−1.22025	−0.610124	+	0.792306i	$0.708880\pi$
$648$	8.57755	0.336958
$649$	−18.6841	−0.733414
$650$	22.8615	0.896703
$651$	1.33607	0.0523649
$652$	0.615670	0.0241115
$653$	29.1322	1.14003	0.570015	−	0.821634i	$-0.306937\pi$
$653$	29.1322	1.14003	0.570015	+	0.821634i	$0.306937\pi$
$654$	0.464506	0.0181636
$655$	−11.1240	−0.434649
$656$	−4.87244	−0.190237
$657$	−17.7952	−0.694258
$658$	−8.05980	−0.314204
$659$	24.5571	0.956611	0.478305	−	0.878194i	$-0.341251\pi$
$659$	24.5571	0.956611	0.478305	+	0.878194i	$0.341251\pi$
$660$	0.232816	0.00906234
$661$	2.63041	0.102311	0.0511555	−	0.998691i	$-0.483710\pi$
$661$	2.63041	0.102311	0.0511555	+	0.998691i	$0.483710\pi$
$662$	12.2767	0.477148
$663$	−5.66244	−0.219911
$664$	1.72378	0.0668957
$665$	−4.16910	−0.161671
$666$	18.8414	0.730088
$667$	25.3348	0.980968
$668$	15.2552	0.590240
$669$	5.40761	0.209070
$670$	9.07774	0.350704
$671$	−1.57384	−0.0607575
$672$	0.217225	0.00837962
$673$	−22.5434	−0.868986	−0.434493	−	0.900675i	$-0.643072\pi$
$673$	−22.5434	−0.868986	−0.434493	+	0.900675i	$0.643072\pi$
$674$	−24.1095	−0.928663
$675$	−5.98818	−0.230485
$676$	11.3716	0.437368
$677$	−1.97745	−0.0759997	−0.0379998	−	0.999278i	$-0.512099\pi$
$677$	−1.97745	−0.0759997	−0.0379998	+	0.999278i	$0.512099\pi$
$678$	1.07907	0.0414415
$679$	−13.0472	−0.500707
$680$	−3.20801	−0.123021
$681$	4.08066	0.156371
$682$	−10.8503	−0.415480
$683$	−23.4029	−0.895486	−0.447743	−	0.894162i	$-0.647772\pi$
$683$	−23.4029	−0.895486	−0.447743	+	0.894162i	$0.647772\pi$
$684$	−20.2626	−0.774761
$685$	3.77266	0.144146
$686$	−1.00000	−0.0381802
$687$	2.17198	0.0828663
$688$	5.35130	0.204016
$689$	−44.5594	−1.69758
$690$	−0.725125	−0.0276050
$691$	48.0504	1.82792	0.913961	−	0.405803i	$-0.133008\pi$
$691$	48.0504	1.82792	0.913961	+	0.405803i	$0.133008\pi$
$692$	−8.83885	−0.336003
$693$	−5.20903	−0.197875
$694$	−23.1510	−0.878800
$695$	7.06225	0.267887
$696$	−1.00163	−0.0379665
$697$	25.7276	0.974503
$698$	3.72233	0.140892
$699$	0.644351	0.0243716
$700$	4.63088	0.175031
$701$	31.8758	1.20393	0.601966	−	0.798521i	$-0.294384\pi$
$701$	31.8758	1.20393	0.601966	+	0.798521i	$0.294384\pi$
$702$	−6.38371	−0.240938
$703$	−43.7861	−1.65142
$704$	−1.76409	−0.0664867
$705$	−1.06369	−0.0400609
$706$	4.95866	0.186622
$707$	7.35097	0.276462
$708$	−2.30070	−0.0864656
$709$	15.2134	0.571350	0.285675	−	0.958327i	$-0.407782\pi$
$709$	15.2134	0.571350	0.285675	+	0.958327i	$0.407782\pi$
$710$	2.65739	0.0997301
$711$	39.0594	1.46484
$712$	0.880032	0.0329806
$713$	33.7943	1.26561
$714$	−1.14700	−0.0429253
$715$	5.29109	0.197875
$716$	18.0968	0.676310
$717$	−1.64649	−0.0614892
$718$	−0.390131	−0.0145596
$719$	28.8533	1.07605	0.538024	−	0.842930i	$-0.319171\pi$
$719$	28.8533	1.07605	0.538024	+	0.842930i	$0.319171\pi$
$720$	−1.79398	−0.0668578
$721$	−12.8627	−0.479032
$722$	28.0890	1.04537
$723$	1.10707	0.0411724
$724$	−6.32459	−0.235051
$725$	−21.3531	−0.793033
$726$	1.71346	0.0635926
$727$	33.6581	1.24831	0.624154	−	0.781301i	$-0.285444\pi$
$727$	33.6581	1.24831	0.624154	+	0.781301i	$0.285444\pi$
$728$	4.93676	0.182968
$729$	−24.4852	−0.906860
$730$	3.66142	0.135515
$731$	−28.2561	−1.04509
$732$	−0.193798	−0.00716298
$733$	−23.4033	−0.864419	−0.432209	−	0.901773i	$-0.642266\pi$
$733$	−23.4033	−0.864419	−0.432209	+	0.901773i	$0.642266\pi$
$734$	31.2519	1.15353
$735$	−0.131975	−0.00486797
$736$	5.49441	0.202527
$737$	−26.3582	−0.970918
$738$	14.3874	0.529608
$739$	−36.6251	−1.34728	−0.673638	−	0.739061i	$-0.735269\pi$
$739$	−36.6251	−1.34728	−0.673638	+	0.739061i	$0.735269\pi$
$740$	−3.87667	−0.142509
$741$	7.35886	0.270335
$742$	−9.02605	−0.331357
$743$	−29.8742	−1.09598	−0.547989	−	0.836485i	$-0.684607\pi$
$743$	−29.8742	−1.09598	−0.547989	+	0.836485i	$0.684607\pi$
$744$	−1.33607	−0.0489829
$745$	1.67260	0.0612793
$746$	5.42004	0.198442
$747$	−5.09000	−0.186233
$748$	9.31481	0.340583
$749$	10.7227	0.391800
$750$	1.27103	0.0464116
$751$	39.2227	1.43126	0.715628	−	0.698481i	$-0.246141\pi$
$751$	39.2227	1.43126	0.715628	+	0.698481i	$0.246141\pi$
$752$	8.05980	0.293911
$753$	−1.49836	−0.0546032
$754$	−22.7634	−0.828996
$755$	1.74566	0.0635309
$756$	−1.29310	−0.0470295
$757$	−20.5595	−0.747247	−0.373624	−	0.927580i	$-0.621885\pi$
$757$	−20.5595	−0.747247	−0.373624	+	0.927580i	$0.621885\pi$
$758$	−13.7600	−0.499784
$759$	2.10548	0.0764241
$760$	4.16910	0.151229
$761$	−4.82685	−0.174973	−0.0874866	−	0.996166i	$-0.527884\pi$
$761$	−4.82685	−0.174973	−0.0874866	+	0.996166i	$0.527884\pi$
$762$	−4.17420	−0.151215
$763$	2.13837	0.0774141
$764$	−3.08987	−0.111788
$765$	9.47265	0.342484
$766$	−0.685800	−0.0247790
$767$	−52.2868	−1.88797
$768$	−0.217225	−0.00783842
$769$	−9.14358	−0.329726	−0.164863	−	0.986316i	$-0.552718\pi$
$769$	−9.14358	−0.329726	−0.164863	+	0.986316i	$0.552718\pi$
$770$	1.07177	0.0386240
$771$	−2.44604	−0.0880920
$772$	−20.1073	−0.723676
$773$	−44.4153	−1.59751	−0.798754	−	0.601658i	$-0.794507\pi$
$773$	−44.4153	−1.59751	−0.798754	+	0.601658i	$0.794507\pi$
$774$	−15.8014	−0.567969
$775$	−28.4830	−1.02314
$776$	13.0472	0.468369
$777$	−1.38607	−0.0497250
$778$	2.61903	0.0938969
$779$	−33.4354	−1.19795
$780$	0.651528	0.0233284
$781$	−7.71603	−0.276101
$782$	−29.0118	−1.03746
$783$	5.96249	0.213082
$784$	1.00000	0.0357143
$785$	3.61968	0.129192
$786$	3.97728	0.141865
$787$	−15.7372	−0.560970	−0.280485	−	0.959858i	$-0.590495\pi$
$787$	−15.7372	−0.560970	−0.280485	+	0.959858i	$0.590495\pi$
$788$	7.06778	0.251779
$789$	6.71052	0.238901
$790$	−8.03659	−0.285929
$791$	4.96754	0.176625
$792$	5.20903	0.185095
$793$	−4.40435	−0.156403
$794$	−3.75823	−0.133375
$795$	−1.19121	−0.0422479
$796$	14.4734	0.512997
$797$	14.0665	0.498262	0.249131	−	0.968470i	$-0.419855\pi$
$797$	14.0665	0.498262	0.249131	+	0.968470i	$0.419855\pi$
$798$	1.49063	0.0527676
$799$	−42.5576	−1.50558
$800$	−4.63088	−0.163726
$801$	−2.59857	−0.0918160
$802$	24.8598	0.877829
$803$	−10.6314	−0.375172
$804$	−3.24567	−0.114466
$805$	−3.33813	−0.117654
$806$	−30.3643	−1.06954
$807$	−2.48485	−0.0874708
$808$	−7.35097	−0.258606
$809$	−6.23526	−0.219220	−0.109610	−	0.993975i	$-0.534960\pi$
$809$	−6.23526	−0.219220	−0.109610	+	0.993975i	$0.534960\pi$
$810$	5.21129	0.183106
$811$	41.7898	1.46744	0.733720	−	0.679452i	$-0.237782\pi$
$811$	41.7898	1.46744	0.733720	+	0.679452i	$0.237782\pi$
$812$	−4.61101	−0.161815
$813$	−0.394404	−0.0138324
$814$	11.2563	0.394535
$815$	0.374051	0.0131024
$816$	1.14700	0.0401529
$817$	36.7214	1.28472
$818$	−12.2643	−0.428810
$819$	−14.5773	−0.509373
$820$	−2.96025	−0.103377
$821$	−23.9191	−0.834782	−0.417391	−	0.908727i	$-0.637055\pi$
$821$	−23.9191	−0.834782	−0.417391	+	0.908727i	$0.637055\pi$
$822$	−1.34888	−0.0470477
$823$	−29.6405	−1.03320	−0.516601	−	0.856226i	$-0.672803\pi$
$823$	−29.6405	−1.03320	−0.516601	+	0.856226i	$0.672803\pi$
$824$	12.8627	0.448093
$825$	−1.77457	−0.0617827
$826$	−10.5913	−0.368520
$827$	9.90188	0.344322	0.172161	−	0.985069i	$-0.444925\pi$
$827$	9.90188	0.344322	0.172161	+	0.985069i	$0.444925\pi$
$828$	−16.2240	−0.563822
$829$	42.4301	1.47366	0.736830	−	0.676078i	$-0.236322\pi$
$829$	42.4301	1.47366	0.736830	+	0.676078i	$0.236322\pi$
$830$	1.04728	0.0363517
$831$	1.61593	0.0560561
$832$	−4.93676	−0.171151
$833$	−5.28023	−0.182949
$834$	−2.52505	−0.0874354
$835$	9.26828	0.320742
$836$	−12.1054	−0.418676
$837$	7.95340	0.274910
$838$	18.7825	0.648831
$839$	27.9275	0.964165	0.482083	−	0.876126i	$-0.339881\pi$
$839$	27.9275	0.964165	0.482083	+	0.876126i	$0.339881\pi$
$840$	0.131975	0.00455357
$841$	−7.73855	−0.266847
$842$	16.6950	0.575347
$843$	−4.43229	−0.152656
$844$	−23.3986	−0.805414
$845$	6.90880	0.237670
$846$	−23.7991	−0.818229
$847$	7.88799	0.271034
$848$	9.02605	0.309956
$849$	3.83530	0.131627
$850$	24.4521	0.838701
$851$	−35.0589	−1.20180
$852$	−0.950128	−0.0325509
$853$	10.5324	0.360623	0.180311	−	0.983610i	$-0.442289\pi$
$853$	10.5324	0.360623	0.180311	+	0.983610i	$0.442289\pi$
$854$	−0.892155	−0.0305289
$855$	−12.3106	−0.421013
$856$	−10.7227	−0.366496
$857$	−8.66553	−0.296009	−0.148004	−	0.988987i	$-0.547285\pi$
$857$	−8.66553	−0.296009	−0.148004	+	0.988987i	$0.547285\pi$
$858$	−1.89178	−0.0645844
$859$	37.3148	1.27316	0.636582	−	0.771209i	$-0.280348\pi$
$859$	37.3148	1.27316	0.636582	+	0.771209i	$0.280348\pi$
$860$	3.25118	0.110864
$861$	−1.05841	−0.0360707
$862$	−1.00000	−0.0340601
$863$	10.9583	0.373026	0.186513	−	0.982453i	$-0.440281\pi$
$863$	10.9583	0.373026	0.186513	+	0.982453i	$0.440281\pi$
$864$	1.29310	0.0439921
$865$	−5.37004	−0.182587
$866$	30.7814	1.04599
$867$	−2.36359	−0.0802717
$868$	−6.15066	−0.208767
$869$	23.3351	0.791590
$870$	−0.608538	−0.0206314
$871$	−73.7627	−2.49935
$872$	−2.13837	−0.0724143
$873$	−38.5261	−1.30391
$874$	37.7035	1.27534
$875$	5.85125	0.197808
$876$	−1.30911	−0.0442308
$877$	17.0674	0.576326	0.288163	−	0.957581i	$-0.406956\pi$
$877$	17.0674	0.576326	0.288163	+	0.957581i	$0.406956\pi$
$878$	37.7820	1.27508
$879$	1.02725	0.0346482
$880$	−1.07177	−0.0361295
$881$	26.2236	0.883495	0.441747	−	0.897139i	$-0.354359\pi$
$881$	26.2236	0.883495	0.441747	+	0.897139i	$0.354359\pi$
$882$	−2.95281	−0.0994264
$883$	−24.6863	−0.830760	−0.415380	−	0.909648i	$-0.636351\pi$
$883$	−24.6863	−0.830760	−0.415380	+	0.909648i	$0.636351\pi$
$884$	26.0672	0.876735
$885$	−1.39779	−0.0469862
$886$	40.0752	1.34635
$887$	−24.5321	−0.823707	−0.411854	−	0.911250i	$-0.635118\pi$
$887$	−24.5321	−0.823707	−0.411854	+	0.911250i	$0.635118\pi$
$888$	1.38607	0.0465135
$889$	−19.2160	−0.644486
$890$	0.534664	0.0179220
$891$	−15.1316	−0.506927
$892$	−24.8941	−0.833515
$893$	55.3075	1.85080
$894$	−0.598024	−0.0200009
$895$	10.9947	0.367513
$896$	−1.00000	−0.0334077
$897$	5.89213	0.196732
$898$	3.12849	0.104399
$899$	28.3608	0.945884
$900$	13.6741	0.455804
$901$	−47.6596	−1.58777
$902$	8.59543	0.286196
$903$	1.16243	0.0386834
$904$	−4.96754	−0.165218
$905$	−3.84250	−0.127729
$906$	−0.624145	−0.0207358
$907$	9.36857	0.311078	0.155539	−	0.987830i	$-0.450289\pi$
$907$	9.36857	0.311078	0.155539	+	0.987830i	$0.450289\pi$
$908$	−18.7854	−0.623417
$909$	21.7061	0.719944
$910$	2.99933	0.0994267
$911$	10.5072	0.348119	0.174060	−	0.984735i	$-0.444311\pi$
$911$	10.5072	0.348119	0.174060	+	0.984735i	$0.444311\pi$
$912$	−1.49063	−0.0493596
$913$	−3.04090	−0.100639
$914$	−27.2298	−0.900682
$915$	−0.117742	−0.00389243
$916$	−9.99878	−0.330369
$917$	18.3095	0.604634
$918$	−6.82786	−0.225353
$919$	−20.8943	−0.689238	−0.344619	−	0.938743i	$-0.611992\pi$
$919$	−20.8943	−0.689238	−0.344619	+	0.938743i	$0.611992\pi$
$920$	3.33813	0.110055
$921$	−3.41067	−0.112385
$922$	25.0253	0.824164
$923$	−21.5931	−0.710745
$924$	−0.383204	−0.0126065
$925$	29.5488	0.971559
$926$	27.2736	0.896266
$927$	−37.9812	−1.24747
$928$	4.61101	0.151364
$929$	27.8860	0.914910	0.457455	−	0.889233i	$-0.348761\pi$
$929$	27.8860	0.914910	0.457455	+	0.889233i	$0.348761\pi$
$930$	−0.811732	−0.0266177
$931$	6.86215	0.224898
$932$	−2.96629	−0.0971640
$933$	−5.16998	−0.169258
$934$	−13.4445	−0.439916
$935$	5.65921	0.185076
$936$	14.5773	0.476475
$937$	42.9282	1.40240	0.701201	−	0.712964i	$-0.252648\pi$
$937$	42.9282	1.40240	0.701201	+	0.712964i	$0.252648\pi$
$938$	−14.9415	−0.487858
$939$	−1.99507	−0.0651065
$940$	4.89673	0.159714
$941$	11.4483	0.373203	0.186602	−	0.982436i	$-0.440253\pi$
$941$	11.4483	0.373203	0.186602	+	0.982436i	$0.440253\pi$
$942$	−1.29419	−0.0421669
$943$	−26.7712	−0.871791
$944$	10.5913	0.344719
$945$	−0.785622	−0.0255563
$946$	−9.44017	−0.306926
$947$	−15.6244	−0.507725	−0.253862	−	0.967240i	$-0.581701\pi$
$947$	−15.6244	−0.507725	−0.253862	+	0.967240i	$0.581701\pi$
$948$	2.87342	0.0933242
$949$	−29.7515	−0.965776
$950$	−31.7778	−1.03101
$951$	2.48188	0.0804804
$952$	5.28023	0.171133
$953$	−14.1242	−0.457528	−0.228764	−	0.973482i	$-0.573468\pi$
$953$	−14.1242	−0.457528	−0.228764	+	0.973482i	$0.573468\pi$
$954$	−26.6522	−0.862898
$955$	−1.87725	−0.0607464
$956$	7.57966	0.245144
$957$	1.76696	0.0571176
$958$	19.9316	0.643962
$959$	−6.20962	−0.200519
$960$	−0.131975	−0.00425947
$961$	6.83058	0.220341
$962$	31.5005	1.01562
$963$	31.6623	1.02030
$964$	−5.09644	−0.164145
$965$	−12.2162	−0.393252
$966$	1.19352	0.0384009
$967$	0.405942	0.0130542	0.00652711	−	0.999979i	$-0.497922\pi$
$967$	0.405942	0.0130542	0.00652711	+	0.999979i	$0.497922\pi$
$968$	−7.88799	−0.253529
$969$	7.87086	0.252848
$970$	7.92685	0.254516
$971$	0.940391	0.0301786	0.0150893	−	0.999886i	$-0.495197\pi$
$971$	0.940391	0.0301786	0.0150893	+	0.999886i	$0.495197\pi$
$972$	−5.74255	−0.184192
$973$	−11.6241	−0.372653
$974$	−9.66008	−0.309529
$975$	−4.96609	−0.159042
$976$	0.892155	0.0285572
$977$	24.6899	0.789900	0.394950	−	0.918703i	$-0.370762\pi$
$977$	24.6899	0.789900	0.394950	+	0.918703i	$0.370762\pi$
$978$	−0.133739	−0.00427649
$979$	−1.55246	−0.0496167
$980$	0.607550	0.0194075
$981$	6.31420	0.201597
$982$	25.3844	0.810049
$983$	−30.0857	−0.959586	−0.479793	−	0.877382i	$-0.659288\pi$
$983$	−30.0857	−0.959586	−0.479793	+	0.877382i	$0.659288\pi$
$984$	1.05841	0.0337410
$985$	4.29403	0.136819
$986$	−24.3472	−0.775374
$987$	1.75079	0.0557282
$988$	−33.8767	−1.07776
$989$	29.4022	0.934937
$990$	3.16475	0.100582
$991$	47.5707	1.51113	0.755567	−	0.655072i	$-0.227362\pi$
$991$	47.5707	1.51113	0.755567	+	0.655072i	$0.227362\pi$
$992$	6.15066	0.195284
$993$	−2.66680	−0.0846284
$994$	−4.37394	−0.138733
$995$	8.79333	0.278767
$996$	−0.374448	−0.0118648
$997$	−32.1582	−1.01846	−0.509231	−	0.860630i	$-0.670070\pi$
$997$	−32.1582	−1.01846	−0.509231	+	0.860630i	$0.670070\pi$
$998$	−21.8255	−0.690873
$999$	−8.25102	−0.261051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.217225 q^{3} +1.00000 q^{4} +0.607550 q^{5} -0.217225 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.95281 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.217225 q^{3} +1.00000 q^{4} +0.607550 q^{5} -0.217225 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.95281 q^{9} +0.607550 q^{10} -1.76409 q^{11} -0.217225 q^{12} -4.93676 q^{13} -1.00000 q^{14} -0.131975 q^{15} +1.00000 q^{16} -5.28023 q^{17} -2.95281 q^{18} +6.86215 q^{19} +0.607550 q^{20} +0.217225 q^{21} -1.76409 q^{22} +5.49441 q^{23} -0.217225 q^{24} -4.63088 q^{25} -4.93676 q^{26} +1.29310 q^{27} -1.00000 q^{28} +4.61101 q^{29} -0.131975 q^{30} +6.15066 q^{31} +1.00000 q^{32} +0.383204 q^{33} -5.28023 q^{34} -0.607550 q^{35} -2.95281 q^{36} -6.38082 q^{37} +6.86215 q^{38} +1.07238 q^{39} +0.607550 q^{40} -4.87244 q^{41} +0.217225 q^{42} +5.35130 q^{43} -1.76409 q^{44} -1.79398 q^{45} +5.49441 q^{46} +8.05980 q^{47} -0.217225 q^{48} +1.00000 q^{49} -4.63088 q^{50} +1.14700 q^{51} -4.93676 q^{52} +9.02605 q^{53} +1.29310 q^{54} -1.07177 q^{55} -1.00000 q^{56} -1.49063 q^{57} +4.61101 q^{58} +10.5913 q^{59} -0.131975 q^{60} +0.892155 q^{61} +6.15066 q^{62} +2.95281 q^{63} +1.00000 q^{64} -2.99933 q^{65} +0.383204 q^{66} +14.9415 q^{67} -5.28023 q^{68} -1.19352 q^{69} -0.607550 q^{70} +4.37394 q^{71} -2.95281 q^{72} +6.02654 q^{73} -6.38082 q^{74} +1.00594 q^{75} +6.86215 q^{76} +1.76409 q^{77} +1.07238 q^{78} -13.2279 q^{79} +0.607550 q^{80} +8.57755 q^{81} -4.87244 q^{82} +1.72378 q^{83} +0.217225 q^{84} -3.20801 q^{85} +5.35130 q^{86} -1.00163 q^{87} -1.76409 q^{88} +0.880032 q^{89} -1.79398 q^{90} +4.93676 q^{91} +5.49441 q^{92} -1.33607 q^{93} +8.05980 q^{94} +4.16910 q^{95} -0.217225 q^{96} +13.0472 q^{97} +1.00000 q^{98} +5.20903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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