LMFDB - Embedded newform 6033.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52431 q^{2} -1.00000 q^{3} +0.323513 q^{4} -2.18374 q^{5} +1.52431 q^{6} -1.69385 q^{7} +2.55548 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52431 q^{2} -1.00000 q^{3} +0.323513 q^{4} -2.18374 q^{5} +1.52431 q^{6} -1.69385 q^{7} +2.55548 q^{8} +1.00000 q^{9} +3.32869 q^{10} -1.01182 q^{11} -0.323513 q^{12} -3.11695 q^{13} +2.58194 q^{14} +2.18374 q^{15} -4.54237 q^{16} -6.06101 q^{17} -1.52431 q^{18} -0.777411 q^{19} -0.706468 q^{20} +1.69385 q^{21} +1.54233 q^{22} +4.17796 q^{23} -2.55548 q^{24} -0.231289 q^{25} +4.75119 q^{26} -1.00000 q^{27} -0.547981 q^{28} +1.68764 q^{29} -3.32869 q^{30} +0.180862 q^{31} +1.81300 q^{32} +1.01182 q^{33} +9.23885 q^{34} +3.69892 q^{35} +0.323513 q^{36} +3.59051 q^{37} +1.18501 q^{38} +3.11695 q^{39} -5.58050 q^{40} -4.01383 q^{41} -2.58194 q^{42} -5.71739 q^{43} -0.327337 q^{44} -2.18374 q^{45} -6.36850 q^{46} -7.50806 q^{47} +4.54237 q^{48} -4.13089 q^{49} +0.352555 q^{50} +6.06101 q^{51} -1.00837 q^{52} -11.4311 q^{53} +1.52431 q^{54} +2.20955 q^{55} -4.32859 q^{56} +0.777411 q^{57} -2.57248 q^{58} -12.6128 q^{59} +0.706468 q^{60} -0.523975 q^{61} -0.275690 q^{62} -1.69385 q^{63} +6.32116 q^{64} +6.80660 q^{65} -1.54233 q^{66} +5.53427 q^{67} -1.96082 q^{68} -4.17796 q^{69} -5.63828 q^{70} -6.37808 q^{71} +2.55548 q^{72} -0.219734 q^{73} -5.47304 q^{74} +0.231289 q^{75} -0.251502 q^{76} +1.71387 q^{77} -4.75119 q^{78} -16.3262 q^{79} +9.91934 q^{80} +1.00000 q^{81} +6.11830 q^{82} +13.8044 q^{83} +0.547981 q^{84} +13.2357 q^{85} +8.71506 q^{86} -1.68764 q^{87} -2.58569 q^{88} +4.42538 q^{89} +3.32869 q^{90} +5.27963 q^{91} +1.35163 q^{92} -0.180862 q^{93} +11.4446 q^{94} +1.69766 q^{95} -1.81300 q^{96} -7.70080 q^{97} +6.29674 q^{98} -1.01182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) $ 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * 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 $

$2$	−1.52431	−1.07785	−0.538924	−	0.842354i	$-0.681169\pi$
$2$	−1.52431	−1.07785	−0.538924	+	0.842354i	$0.681169\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.323513	0.161757
$5$	−2.18374	−0.976597	−0.488299	−	0.872677i	$-0.662382\pi$
$5$	−2.18374	−0.976597	−0.488299	+	0.872677i	$0.662382\pi$
$6$	1.52431	0.622296
$7$	−1.69385	−0.640214	−0.320107	−	0.947381i	$-0.603719\pi$
$7$	−1.69385	−0.640214	−0.320107	+	0.947381i	$0.603719\pi$
$8$	2.55548	0.903499
$9$	1.00000	0.333333
$10$	3.32869	1.05262
$11$	−1.01182	−0.305075	−0.152538	−	0.988298i	$-0.548745\pi$
$11$	−1.01182	−0.305075	−0.152538	+	0.988298i	$0.548745\pi$
$12$	−0.323513	−0.0933902
$13$	−3.11695	−0.864486	−0.432243	−	0.901757i	$-0.642278\pi$
$13$	−3.11695	−0.864486	−0.432243	+	0.901757i	$0.642278\pi$
$14$	2.58194	0.690053
$15$	2.18374	0.563839
$16$	−4.54237	−1.13559
$17$	−6.06101	−1.47001	−0.735006	−	0.678061i	$-0.762821\pi$
$17$	−6.06101	−1.47001	−0.735006	+	0.678061i	$0.762821\pi$
$18$	−1.52431	−0.359283
$19$	−0.777411	−0.178350	−0.0891751	−	0.996016i	$-0.528423\pi$
$19$	−0.777411	−0.178350	−0.0891751	+	0.996016i	$0.528423\pi$
$20$	−0.706468	−0.157971
$21$	1.69385	0.369627
$22$	1.54233	0.328825
$23$	4.17796	0.871166	0.435583	−	0.900149i	$-0.356542\pi$
$23$	4.17796	0.871166	0.435583	+	0.900149i	$0.356542\pi$
$24$	−2.55548	−0.521635
$25$	−0.231289	−0.0462578
$26$	4.75119	0.931785
$27$	−1.00000	−0.192450
$28$	−0.547981	−0.103559
$29$	1.68764	0.313387	0.156693	−	0.987647i	$-0.449917\pi$
$29$	1.68764	0.313387	0.156693	+	0.987647i	$0.449917\pi$
$30$	−3.32869	−0.607732
$31$	0.180862	0.0324838	0.0162419	−	0.999868i	$-0.494830\pi$
$31$	0.180862	0.0324838	0.0162419	+	0.999868i	$0.494830\pi$
$32$	1.81300	0.320496
$33$	1.01182	0.176135
$34$	9.23885	1.58445
$35$	3.69892	0.625231
$36$	0.323513	0.0539188
$37$	3.59051	0.590276	0.295138	−	0.955455i	$-0.404634\pi$
$37$	3.59051	0.590276	0.295138	+	0.955455i	$0.404634\pi$
$38$	1.18501	0.192234
$39$	3.11695	0.499111
$40$	−5.58050	−0.882355
$41$	−4.01383	−0.626854	−0.313427	−	0.949612i	$-0.601477\pi$
$41$	−4.01383	−0.626854	−0.313427	+	0.949612i	$0.601477\pi$
$42$	−2.58194	−0.398402
$43$	−5.71739	−0.871894	−0.435947	−	0.899972i	$-0.643587\pi$
$43$	−5.71739	−0.871894	−0.435947	+	0.899972i	$0.643587\pi$
$44$	−0.327337	−0.0493479
$45$	−2.18374	−0.325532
$46$	−6.36850	−0.938984
$47$	−7.50806	−1.09516	−0.547582	−	0.836752i	$-0.684451\pi$
$47$	−7.50806	−1.09516	−0.547582	+	0.836752i	$0.684451\pi$
$48$	4.54237	0.655634
$49$	−4.13089	−0.590127
$50$	0.352555	0.0498589
$51$	6.06101	0.848712
$52$	−1.00837	−0.139836
$53$	−11.4311	−1.57018	−0.785088	−	0.619384i	$-0.787382\pi$
$53$	−11.4311	−1.57018	−0.785088	+	0.619384i	$0.787382\pi$
$54$	1.52431	0.207432
$55$	2.20955	0.297936
$56$	−4.32859	−0.578432
$57$	0.777411	0.102971
$58$	−2.57248	−0.337784
$59$	−12.6128	−1.64205	−0.821025	−	0.570892i	$-0.806597\pi$
$59$	−12.6128	−1.64205	−0.821025	+	0.570892i	$0.806597\pi$
$60$	0.706468	0.0912046
$61$	−0.523975	−0.0670882	−0.0335441	−	0.999437i	$-0.510679\pi$
$61$	−0.523975	−0.0670882	−0.0335441	+	0.999437i	$0.510679\pi$
$62$	−0.275690	−0.0350126
$63$	−1.69385	−0.213405
$64$	6.32116	0.790146
$65$	6.80660	0.844255
$66$	−1.54233	−0.189847
$67$	5.53427	0.676119	0.338060	−	0.941125i	$-0.390229\pi$
$67$	5.53427	0.676119	0.338060	+	0.941125i	$0.390229\pi$
$68$	−1.96082	−0.237784
$69$	−4.17796	−0.502968
$70$	−5.63828	−0.673904
$71$	−6.37808	−0.756939	−0.378469	−	0.925614i	$-0.623549\pi$
$71$	−6.37808	−0.756939	−0.378469	+	0.925614i	$0.623549\pi$
$72$	2.55548	0.301166
$73$	−0.219734	−0.0257180	−0.0128590	−	0.999917i	$-0.504093\pi$
$73$	−0.219734	−0.0257180	−0.0128590	+	0.999917i	$0.504093\pi$
$74$	−5.47304	−0.636228
$75$	0.231289	0.0267069
$76$	−0.251502	−0.0288493
$77$	1.71387	0.195313
$78$	−4.75119	−0.537966
$79$	−16.3262	−1.83684	−0.918419	−	0.395610i	$-0.870533\pi$
$79$	−16.3262	−1.83684	−0.918419	+	0.395610i	$0.870533\pi$
$80$	9.91934	1.10902
$81$	1.00000	0.111111
$82$	6.11830	0.675654
$83$	13.8044	1.51523	0.757615	−	0.652702i	$-0.226365\pi$
$83$	13.8044	1.51523	0.757615	+	0.652702i	$0.226365\pi$
$84$	0.547981	0.0597896
$85$	13.2357	1.43561
$86$	8.71506	0.939769
$87$	−1.68764	−0.180934
$88$	−2.58569	−0.275635
$89$	4.42538	0.469089	0.234545	−	0.972105i	$-0.424640\pi$
$89$	4.42538	0.469089	0.234545	+	0.972105i	$0.424640\pi$
$90$	3.32869	0.350875
$91$	5.27963	0.553456
$92$	1.35163	0.140917
$93$	−0.180862	−0.0187545
$94$	11.4446	1.18042
$95$	1.69766	0.174176
$96$	−1.81300	−0.185038
$97$	−7.70080	−0.781897	−0.390949	−	0.920412i	$-0.627853\pi$
$97$	−7.70080	−0.781897	−0.390949	+	0.920412i	$0.627853\pi$
$98$	6.29674	0.636067
$99$	−1.01182	−0.101692
$100$	−0.0748250	−0.00748250
$101$	6.91729	0.688296	0.344148	−	0.938915i	$-0.388168\pi$
$101$	6.91729	0.688296	0.344148	+	0.938915i	$0.388168\pi$
$102$	−9.23885	−0.914782
$103$	−8.08650	−0.796786	−0.398393	−	0.917215i	$-0.630432\pi$
$103$	−8.08650	−0.796786	−0.398393	+	0.917215i	$0.630432\pi$
$104$	−7.96530	−0.781062
$105$	−3.69892	−0.360977
$106$	17.4244	1.69241
$107$	2.43786	0.235677	0.117839	−	0.993033i	$-0.462403\pi$
$107$	2.43786	0.235677	0.117839	+	0.993033i	$0.462403\pi$
$108$	−0.323513	−0.0311301
$109$	−8.52982	−0.817008	−0.408504	−	0.912756i	$-0.633949\pi$
$109$	−8.52982	−0.817008	−0.408504	+	0.912756i	$0.633949\pi$
$110$	−3.36804	−0.321130
$111$	−3.59051	−0.340796
$112$	7.69407	0.727021
$113$	2.55954	0.240781	0.120391	−	0.992727i	$-0.461585\pi$
$113$	2.55954	0.240781	0.120391	+	0.992727i	$0.461585\pi$
$114$	−1.18501	−0.110987
$115$	−9.12358	−0.850778
$116$	0.545974	0.0506924
$117$	−3.11695	−0.288162
$118$	19.2258	1.76988
$119$	10.2664	0.941121
$120$	5.58050	0.509428
$121$	−9.97622	−0.906929
$122$	0.798700	0.0723109
$123$	4.01383	0.361914
$124$	0.0585113	0.00525447
$125$	11.4238	1.02177
$126$	2.58194	0.230018
$127$	−8.44644	−0.749501	−0.374750	−	0.927126i	$-0.622272\pi$
$127$	−8.44644	−0.749501	−0.374750	+	0.927126i	$0.622272\pi$
$128$	−13.2614	−1.17215
$129$	5.71739	0.503388
$130$	−10.3753	−0.909978
$131$	−15.0008	−1.31063	−0.655315	−	0.755356i	$-0.727464\pi$
$131$	−15.0008	−1.31063	−0.655315	+	0.755356i	$0.727464\pi$
$132$	0.327337	0.0284910
$133$	1.31681	0.114182
$134$	−8.43593	−0.728754
$135$	2.18374	0.187946
$136$	−15.4888	−1.32815
$137$	13.0582	1.11563	0.557817	−	0.829964i	$-0.311639\pi$
$137$	13.0582	1.11563	0.557817	+	0.829964i	$0.311639\pi$
$138$	6.36850	0.542123
$139$	−17.5506	−1.48862	−0.744309	−	0.667835i	$-0.767221\pi$
$139$	−17.5506	−1.48862	−0.744309	+	0.667835i	$0.767221\pi$
$140$	1.19665	0.101135
$141$	7.50806	0.632293
$142$	9.72215	0.815865
$143$	3.15379	0.263733
$144$	−4.54237	−0.378530
$145$	−3.68536	−0.306053
$146$	0.334943	0.0277201
$147$	4.13089	0.340710
$148$	1.16158	0.0954810
$149$	8.36558	0.685335	0.342667	−	0.939457i	$-0.388670\pi$
$149$	8.36558	0.685335	0.342667	+	0.939457i	$0.388670\pi$
$150$	−0.352555	−0.0287860
$151$	−21.5447	−1.75328	−0.876641	−	0.481145i	$-0.840221\pi$
$151$	−21.5447	−1.75328	−0.876641	+	0.481145i	$0.840221\pi$
$152$	−1.98666	−0.161139
$153$	−6.06101	−0.490004
$154$	−2.61246	−0.210518
$155$	−0.394956	−0.0317236
$156$	1.00837	0.0807345
$157$	−22.4135	−1.78879	−0.894396	−	0.447275i	$-0.852394\pi$
$157$	−22.4135	−1.78879	−0.894396	+	0.447275i	$0.852394\pi$
$158$	24.8861	1.97983
$159$	11.4311	0.906542
$160$	−3.95911	−0.312995
$161$	−7.07683	−0.557732
$162$	−1.52431	−0.119761
$163$	−1.61177	−0.126244	−0.0631219	−	0.998006i	$-0.520106\pi$
$163$	−1.61177	−0.126244	−0.0631219	+	0.998006i	$0.520106\pi$
$164$	−1.29852	−0.101398
$165$	−2.20955	−0.172013
$166$	−21.0422	−1.63319
$167$	0.174819	0.0135279	0.00676397	−	0.999977i	$-0.497847\pi$
$167$	0.174819	0.0135279	0.00676397	+	0.999977i	$0.497847\pi$
$168$	4.32859	0.333958
$169$	−3.28463	−0.252664
$170$	−20.1752	−1.54737
$171$	−0.777411	−0.0594501
$172$	−1.84965	−0.141035
$173$	−16.2588	−1.23613	−0.618065	−	0.786127i	$-0.712083\pi$
$173$	−16.2588	−1.23613	−0.618065	+	0.786127i	$0.712083\pi$
$174$	2.57248	0.195019
$175$	0.391768	0.0296149
$176$	4.59606	0.346441
$177$	12.6128	0.948038
$178$	−6.74564	−0.505607
$179$	−18.4630	−1.37999	−0.689996	−	0.723813i	$-0.742388\pi$
$179$	−18.4630	−1.37999	−0.689996	+	0.723813i	$0.742388\pi$
$180$	−0.706468	−0.0526570
$181$	−16.4530	−1.22294	−0.611470	−	0.791268i	$-0.709421\pi$
$181$	−16.4530	−1.22294	−0.611470	+	0.791268i	$0.709421\pi$
$182$	−8.04778	−0.596541
$183$	0.523975	0.0387334
$184$	10.6767	0.787097
$185$	−7.84073	−0.576462
$186$	0.275690	0.0202146
$187$	6.13266	0.448464
$188$	−2.42896	−0.177150
$189$	1.69385	0.123209
$190$	−2.58776	−0.187736
$191$	6.60049	0.477595	0.238798	−	0.971069i	$-0.423247\pi$
$191$	6.60049	0.477595	0.238798	+	0.971069i	$0.423247\pi$
$192$	−6.32116	−0.456191
$193$	−5.85021	−0.421107	−0.210554	−	0.977582i	$-0.567527\pi$
$193$	−5.85021	−0.421107	−0.210554	+	0.977582i	$0.567527\pi$
$194$	11.7384	0.842767
$195$	−6.80660	−0.487431
$196$	−1.33640	−0.0954568
$197$	7.04160	0.501693	0.250847	−	0.968027i	$-0.419291\pi$
$197$	7.04160	0.501693	0.250847	+	0.968027i	$0.419291\pi$
$198$	1.54233	0.109608
$199$	−9.21110	−0.652958	−0.326479	−	0.945204i	$-0.605862\pi$
$199$	−9.21110	−0.652958	−0.326479	+	0.945204i	$0.605862\pi$
$200$	−0.591054	−0.0417939
$201$	−5.53427	−0.390358
$202$	−10.5441	−0.741879
$203$	−2.85860	−0.200635
$204$	1.96082	0.137285
$205$	8.76514	0.612184
$206$	12.3263	0.858815
$207$	4.17796	0.290389
$208$	14.1583	0.981703
$209$	0.786600	0.0544103
$210$	5.63828	0.389079
$211$	17.3484	1.19431	0.597157	−	0.802124i	$-0.296297\pi$
$211$	17.3484	1.19431	0.597157	+	0.802124i	$0.296297\pi$
$212$	−3.69809	−0.253986
$213$	6.37808	0.437019
$214$	−3.71605	−0.254024
$215$	12.4853	0.851489
$216$	−2.55548	−0.173878
$217$	−0.306353	−0.0207966
$218$	13.0021	0.880611
$219$	0.219734	0.0148483
$220$	0.714819	0.0481931
$221$	18.8919	1.27080
$222$	5.47304	0.367326
$223$	−19.3790	−1.29771	−0.648857	−	0.760910i	$-0.724753\pi$
$223$	−19.3790	−1.29771	−0.648857	+	0.760910i	$0.724753\pi$
$224$	−3.07094	−0.205186
$225$	−0.231289	−0.0154193
$226$	−3.90153	−0.259526
$227$	−28.5285	−1.89351	−0.946753	−	0.321962i	$-0.895658\pi$
$227$	−28.5285	−1.89351	−0.946753	+	0.321962i	$0.895658\pi$
$228$	0.251502	0.0166562
$229$	5.61351	0.370951	0.185476	−	0.982649i	$-0.440617\pi$
$229$	5.61351	0.370951	0.185476	+	0.982649i	$0.440617\pi$
$230$	13.9071	0.917010
$231$	−1.71387	−0.112764
$232$	4.31273	0.283145
$233$	19.6889	1.28986	0.644932	−	0.764240i	$-0.276886\pi$
$233$	19.6889	1.28986	0.644932	+	0.764240i	$0.276886\pi$
$234$	4.75119	0.310595
$235$	16.3956	1.06953
$236$	−4.08041	−0.265612
$237$	16.3262	1.06050
$238$	−15.6492	−1.01439
$239$	−19.2525	−1.24534	−0.622670	−	0.782484i	$-0.713952\pi$
$239$	−19.2525	−1.24534	−0.622670	+	0.782484i	$0.713952\pi$
$240$	−9.91934	−0.640290
$241$	−15.6255	−1.00652	−0.503262	−	0.864134i	$-0.667867\pi$
$241$	−15.6255	−1.00652	−0.503262	+	0.864134i	$0.667867\pi$
$242$	15.2068	0.977532
$243$	−1.00000	−0.0641500
$244$	−0.169513	−0.0108519
$245$	9.02077	0.576316
$246$	−6.11830	−0.390089
$247$	2.42315	0.154181
$248$	0.462190	0.0293491
$249$	−13.8044	−0.874818
$250$	−17.4133	−1.10132
$251$	2.55866	0.161501	0.0807507	−	0.996734i	$-0.474268\pi$
$251$	2.55866	0.161501	0.0807507	+	0.996734i	$0.474268\pi$
$252$	−0.547981	−0.0345196
$253$	−4.22735	−0.265771
$254$	12.8750	0.807848
$255$	−13.2357	−0.828850
$256$	7.57211	0.473257
$257$	−5.54769	−0.346056	−0.173028	−	0.984917i	$-0.555355\pi$
$257$	−5.54769	−0.346056	−0.173028	+	0.984917i	$0.555355\pi$
$258$	−8.71506	−0.542576
$259$	−6.08177	−0.377903
$260$	2.20202	0.136564
$261$	1.68764	0.104462
$262$	22.8659	1.41266
$263$	18.6631	1.15082	0.575408	−	0.817867i	$-0.304843\pi$
$263$	18.6631	1.15082	0.575408	+	0.817867i	$0.304843\pi$
$264$	2.58569	0.159138
$265$	24.9624	1.53343
$266$	−2.00723	−0.123071
$267$	−4.42538	−0.270829
$268$	1.79041	0.109367
$269$	5.48256	0.334278	0.167139	−	0.985933i	$-0.446547\pi$
$269$	5.48256	0.334278	0.167139	+	0.985933i	$0.446547\pi$
$270$	−3.32869	−0.202577
$271$	14.4509	0.877832	0.438916	−	0.898528i	$-0.355363\pi$
$271$	14.4509	0.877832	0.438916	+	0.898528i	$0.355363\pi$
$272$	27.5313	1.66933
$273$	−5.27963	−0.319538
$274$	−19.9047	−1.20248
$275$	0.234023	0.0141121
$276$	−1.35163	−0.0813583
$277$	−25.0082	−1.50260	−0.751300	−	0.659961i	$-0.770573\pi$
$277$	−25.0082	−1.50260	−0.751300	+	0.659961i	$0.770573\pi$
$278$	26.7524	1.60451
$279$	0.180862	0.0108279
$280$	9.45251	0.564895
$281$	−5.92401	−0.353397	−0.176698	−	0.984265i	$-0.556542\pi$
$281$	−5.92401	−0.353397	−0.176698	+	0.984265i	$0.556542\pi$
$282$	−11.4446	−0.681516
$283$	19.1369	1.13757	0.568784	−	0.822487i	$-0.307414\pi$
$283$	19.1369	1.13757	0.568784	+	0.822487i	$0.307414\pi$
$284$	−2.06339	−0.122440
$285$	−1.69766	−0.100561
$286$	−4.80735	−0.284265
$287$	6.79880	0.401321
$288$	1.81300	0.106832
$289$	19.7359	1.16093
$290$	5.61763	0.329878
$291$	7.70080	0.451429
$292$	−0.0710869	−0.00416005
$293$	22.0672	1.28918	0.644589	−	0.764529i	$-0.277029\pi$
$293$	22.0672	1.28918	0.644589	+	0.764529i	$0.277029\pi$
$294$	−6.29674	−0.367233
$295$	27.5431	1.60362
$296$	9.17548	0.533314
$297$	1.01182	0.0587118
$298$	−12.7517	−0.738687
$299$	−13.0225	−0.753111
$300$	0.0748250	0.00432002
$301$	9.68438	0.558198
$302$	32.8407	1.88977
$303$	−6.91729	−0.397388
$304$	3.53128	0.202533
$305$	1.14422	0.0655181
$306$	9.23885	0.528150
$307$	4.00046	0.228318	0.114159	−	0.993462i	$-0.463583\pi$
$307$	4.00046	0.228318	0.114159	+	0.993462i	$0.463583\pi$
$308$	0.554459	0.0315932
$309$	8.08650	0.460025
$310$	0.602034	0.0341932
$311$	−4.32822	−0.245431	−0.122715	−	0.992442i	$-0.539160\pi$
$311$	−4.32822	−0.245431	−0.122715	+	0.992442i	$0.539160\pi$
$312$	7.96530	0.450947
$313$	17.4225	0.984778	0.492389	−	0.870375i	$-0.336124\pi$
$313$	17.4225	0.984778	0.492389	+	0.870375i	$0.336124\pi$
$314$	34.1651	1.92805
$315$	3.69892	0.208410
$316$	−5.28173	−0.297120
$317$	−9.21955	−0.517821	−0.258911	−	0.965901i	$-0.583364\pi$
$317$	−9.21955	−0.517821	−0.258911	+	0.965901i	$0.583364\pi$
$318$	−17.4244	−0.977114
$319$	−1.70759	−0.0956067
$320$	−13.8038	−0.771654
$321$	−2.43786	−0.136068
$322$	10.7873	0.601150
$323$	4.71190	0.262177
$324$	0.323513	0.0179729
$325$	0.720916	0.0399892
$326$	2.45684	0.136072
$327$	8.52982	0.471700
$328$	−10.2573	−0.566362
$329$	12.7175	0.701138
$330$	3.36804	0.185404
$331$	12.1947	0.670283	0.335141	−	0.942168i	$-0.391216\pi$
$331$	12.1947	0.670283	0.335141	+	0.942168i	$0.391216\pi$
$332$	4.46590	0.245098
$333$	3.59051	0.196759
$334$	−0.266479	−0.0145811
$335$	−12.0854	−0.660296
$336$	−7.69407	−0.419746
$337$	9.39830	0.511958	0.255979	−	0.966682i	$-0.417602\pi$
$337$	9.39830	0.511958	0.255979	+	0.966682i	$0.417602\pi$
$338$	5.00679	0.272333
$339$	−2.55954	−0.139015
$340$	4.28191	0.232219
$341$	−0.183000	−0.00991002
$342$	1.18501	0.0640781
$343$	18.8540	1.01802
$344$	−14.6107	−0.787756
$345$	9.12358	0.491197
$346$	24.7833	1.33236
$347$	−18.3450	−0.984811	−0.492406	−	0.870366i	$-0.663882\pi$
$347$	−18.3450	−0.984811	−0.492406	+	0.870366i	$0.663882\pi$
$348$	−0.545974	−0.0292673
$349$	−19.3706	−1.03688	−0.518441	−	0.855113i	$-0.673488\pi$
$349$	−19.3706	−1.03688	−0.518441	+	0.855113i	$0.673488\pi$
$350$	−0.597174	−0.0319203
$351$	3.11695	0.166370
$352$	−1.83443	−0.0977754
$353$	18.9147	1.00673	0.503364	−	0.864074i	$-0.332095\pi$
$353$	18.9147	1.00673	0.503364	+	0.864074i	$0.332095\pi$
$354$	−19.2258	−1.02184
$355$	13.9281	0.739224
$356$	1.43167	0.0758782
$357$	−10.2664	−0.543357
$358$	28.1434	1.48742
$359$	12.3535	0.651993	0.325996	−	0.945371i	$-0.394300\pi$
$359$	12.3535	0.651993	0.325996	+	0.945371i	$0.394300\pi$
$360$	−5.58050	−0.294118
$361$	−18.3956	−0.968191
$362$	25.0794	1.31814
$363$	9.97622	0.523616
$364$	1.70803	0.0895251
$365$	0.479842	0.0251161
$366$	−0.798700	−0.0417487
$367$	23.0784	1.20468	0.602341	−	0.798239i	$-0.294235\pi$
$367$	23.0784	1.20468	0.602341	+	0.798239i	$0.294235\pi$
$368$	−18.9778	−0.989288
$369$	−4.01383	−0.208951
$370$	11.9517	0.621338
$371$	19.3624	1.00525
$372$	−0.0585113	−0.00303367
$373$	−17.4217	−0.902061	−0.451030	−	0.892509i	$-0.648943\pi$
$373$	−17.4217	−0.902061	−0.451030	+	0.892509i	$0.648943\pi$
$374$	−9.34806	−0.483377
$375$	−11.4238	−0.589921
$376$	−19.1867	−0.989479
$377$	−5.26029	−0.270919
$378$	−2.58194	−0.132801
$379$	−5.47596	−0.281281	−0.140640	−	0.990061i	$-0.544916\pi$
$379$	−5.47596	−0.281281	−0.140640	+	0.990061i	$0.544916\pi$
$380$	0.549215	0.0281742
$381$	8.44644	0.432724
$382$	−10.0612	−0.514775
$383$	14.9541	0.764119	0.382059	−	0.924138i	$-0.375215\pi$
$383$	14.9541	0.764119	0.382059	+	0.924138i	$0.375215\pi$
$384$	13.2614	0.676743
$385$	−3.74264	−0.190743
$386$	8.91752	0.453890
$387$	−5.71739	−0.290631
$388$	−2.49131	−0.126477
$389$	19.0543	0.966093	0.483046	−	0.875595i	$-0.339530\pi$
$389$	19.0543	0.966093	0.483046	+	0.875595i	$0.339530\pi$
$390$	10.3753	0.525376
$391$	−25.3227	−1.28062
$392$	−10.5564	−0.533179
$393$	15.0008	0.756692
$394$	−10.7336	−0.540749
$395$	35.6521	1.79385
$396$	−0.327337	−0.0164493
$397$	26.9050	1.35033	0.675163	−	0.737669i	$-0.264073\pi$
$397$	26.9050	1.35033	0.675163	+	0.737669i	$0.264073\pi$
$398$	14.0406	0.703789
$399$	−1.31681	−0.0659231
$400$	1.05060	0.0525299
$401$	−18.6550	−0.931587	−0.465794	−	0.884893i	$-0.654231\pi$
$401$	−18.6550	−0.931587	−0.465794	+	0.884893i	$0.654231\pi$
$402$	8.43593	0.420746
$403$	−0.563738	−0.0280818
$404$	2.23783	0.111336
$405$	−2.18374	−0.108511
$406$	4.35739	0.216254
$407$	−3.63295	−0.180079
$408$	15.4888	0.766810
$409$	21.7613	1.07603	0.538014	−	0.842936i	$-0.319175\pi$
$409$	21.7613	1.07603	0.538014	+	0.842936i	$0.319175\pi$
$410$	−13.3608	−0.659841
$411$	−13.0582	−0.644112
$412$	−2.61609	−0.128885
$413$	21.3642	1.05126
$414$	−6.36850	−0.312995
$415$	−30.1452	−1.47977
$416$	−5.65102	−0.277064
$417$	17.5506	0.859455
$418$	−1.19902	−0.0586460
$419$	−26.5441	−1.29677	−0.648383	−	0.761314i	$-0.724554\pi$
$419$	−26.5441	−1.29677	−0.648383	+	0.761314i	$0.724554\pi$
$420$	−1.19665	−0.0583904
$421$	18.9564	0.923877	0.461938	−	0.886912i	$-0.347154\pi$
$421$	18.9564	0.923877	0.461938	+	0.886912i	$0.347154\pi$
$422$	−26.4443	−1.28729
$423$	−7.50806	−0.365054
$424$	−29.2118	−1.41865
$425$	1.40185	0.0679995
$426$	−9.72215	−0.471040
$427$	0.887533	0.0429508
$428$	0.788680	0.0381223
$429$	−3.15379	−0.152267
$430$	−19.0314	−0.917776
$431$	27.4076	1.32018	0.660089	−	0.751187i	$-0.270519\pi$
$431$	27.4076	1.32018	0.660089	+	0.751187i	$0.270519\pi$
$432$	4.54237	0.218545
$433$	12.5875	0.604919	0.302459	−	0.953162i	$-0.402192\pi$
$433$	12.5875	0.604919	0.302459	+	0.953162i	$0.402192\pi$
$434$	0.466976	0.0224156
$435$	3.68536	0.176700
$436$	−2.75951	−0.132156
$437$	−3.24799	−0.155373
$438$	−0.334943	−0.0160042
$439$	−0.825547	−0.0394012	−0.0197006	−	0.999806i	$-0.506271\pi$
$439$	−0.825547	−0.0394012	−0.0197006	+	0.999806i	$0.506271\pi$
$440$	5.64647	0.269185
$441$	−4.13089	−0.196709
$442$	−28.7970	−1.36973
$443$	39.0188	1.85384	0.926920	−	0.375260i	$-0.122447\pi$
$443$	39.0188	1.85384	0.926920	+	0.375260i	$0.122447\pi$
$444$	−1.16158	−0.0551260
$445$	−9.66386	−0.458111
$446$	29.5396	1.39874
$447$	−8.36558	−0.395678
$448$	−10.7071	−0.505862
$449$	−0.812881	−0.0383622	−0.0191811	−	0.999816i	$-0.506106\pi$
$449$	−0.812881	−0.0383622	−0.0191811	+	0.999816i	$0.506106\pi$
$450$	0.352555	0.0166196
$451$	4.06127	0.191238
$452$	0.828045	0.0389479
$453$	21.5447	1.01226
$454$	43.4863	2.04091
$455$	−11.5293	−0.540503
$456$	1.98666	0.0930338
$457$	−35.1967	−1.64643	−0.823217	−	0.567727i	$-0.807823\pi$
$457$	−35.1967	−1.64643	−0.823217	+	0.567727i	$0.807823\pi$
$458$	−8.55672	−0.399829
$459$	6.06101	0.282904
$460$	−2.95160	−0.137619
$461$	20.9066	0.973719	0.486859	−	0.873480i	$-0.338142\pi$
$461$	20.9066	0.973719	0.486859	+	0.873480i	$0.338142\pi$
$462$	2.61246	0.121543
$463$	−5.03858	−0.234163	−0.117081	−	0.993122i	$-0.537354\pi$
$463$	−5.03858	−0.234163	−0.117081	+	0.993122i	$0.537354\pi$
$464$	−7.66588	−0.355879
$465$	0.394956	0.0183156
$466$	−30.0120	−1.39028
$467$	−8.52137	−0.394322	−0.197161	−	0.980371i	$-0.563172\pi$
$467$	−8.52137	−0.394322	−0.197161	+	0.980371i	$0.563172\pi$
$468$	−1.00837	−0.0466121
$469$	−9.37420	−0.432861
$470$	−24.9920	−1.15279
$471$	22.4135	1.03276
$472$	−32.2318	−1.48359
$473$	5.78498	0.265993
$474$	−24.8861	−1.14306
$475$	0.179806	0.00825008
$476$	3.32132	0.152233
$477$	−11.4311	−0.523392
$478$	29.3467	1.34229
$479$	36.2200	1.65494	0.827468	−	0.561513i	$-0.189781\pi$
$479$	36.2200	1.65494	0.827468	+	0.561513i	$0.189781\pi$
$480$	3.95911	0.180708
$481$	−11.1914	−0.510285
$482$	23.8180	1.08488
$483$	7.07683	0.322007
$484$	−3.22744	−0.146702
$485$	16.8165	0.763599
$486$	1.52431	0.0691440
$487$	35.5435	1.61063	0.805315	−	0.592848i	$-0.201996\pi$
$487$	35.5435	1.61063	0.805315	+	0.592848i	$0.201996\pi$
$488$	−1.33901	−0.0606141
$489$	1.61177	0.0728869
$490$	−13.7504	−0.621181
$491$	1.48366	0.0669566	0.0334783	−	0.999439i	$-0.489342\pi$
$491$	1.48366	0.0669566	0.0334783	+	0.999439i	$0.489342\pi$
$492$	1.29852	0.0585420
$493$	−10.2288	−0.460682
$494$	−3.69362	−0.166184
$495$	2.20955	0.0993119
$496$	−0.821543	−0.0368883
$497$	10.8035	0.484603
$498$	21.0422	0.942921
$499$	8.54663	0.382600	0.191300	−	0.981532i	$-0.438730\pi$
$499$	8.54663	0.382600	0.191300	+	0.981532i	$0.438730\pi$
$500$	3.69574	0.165278
$501$	−0.174819	−0.00781036
$502$	−3.90019	−0.174074
$503$	35.6425	1.58922	0.794610	−	0.607120i	$-0.207675\pi$
$503$	35.6425	1.58922	0.794610	+	0.607120i	$0.207675\pi$
$504$	−4.32859	−0.192811
$505$	−15.1056	−0.672188
$506$	6.44378	0.286461
$507$	3.28463	0.145876
$508$	−2.73253	−0.121237
$509$	−28.7330	−1.27357	−0.636783	−	0.771043i	$-0.719735\pi$
$509$	−28.7330	−1.27357	−0.636783	+	0.771043i	$0.719735\pi$
$510$	20.1752	0.893374
$511$	0.372196	0.0164650
$512$	14.9806	0.662054
$513$	0.777411	0.0343235
$514$	8.45639	0.372995
$515$	17.6588	0.778139
$516$	1.84965	0.0814263
$517$	7.59681	0.334107
$518$	9.27048	0.407322
$519$	16.2588	0.713680
$520$	17.3941	0.762783
$521$	−0.415732	−0.0182136	−0.00910678	−	0.999959i	$-0.502899\pi$
$521$	−0.415732	−0.0182136	−0.00910678	+	0.999959i	$0.502899\pi$
$522$	−2.57248	−0.112595
$523$	0.885917	0.0387385	0.0193692	−	0.999812i	$-0.493834\pi$
$523$	0.885917	0.0387385	0.0193692	+	0.999812i	$0.493834\pi$
$524$	−4.85297	−0.212003
$525$	−0.391768	−0.0170981
$526$	−28.4483	−1.24040
$527$	−1.09621	−0.0477516
$528$	−4.59606	−0.200018
$529$	−5.54462	−0.241070
$530$	−38.0504	−1.65280
$531$	−12.6128	−0.547350
$532$	0.426006	0.0184697
$533$	12.5109	0.541907
$534$	6.74564	0.291912
$535$	−5.32365	−0.230162
$536$	14.1427	0.610873
$537$	18.4630	0.796739
$538$	−8.35711	−0.360300
$539$	4.17972	0.180033
$540$	0.706468	0.0304015
$541$	19.3153	0.830431	0.415216	−	0.909723i	$-0.363706\pi$
$541$	19.3153	0.830431	0.415216	+	0.909723i	$0.363706\pi$
$542$	−22.0277	−0.946169
$543$	16.4530	0.706064
$544$	−10.9886	−0.471133
$545$	18.6269	0.797888
$546$	8.04778	0.344413
$547$	−13.2848	−0.568018	−0.284009	−	0.958822i	$-0.591665\pi$
$547$	−13.2848	−0.568018	−0.284009	+	0.958822i	$0.591665\pi$
$548$	4.22449	0.180461
$549$	−0.523975	−0.0223627
$550$	−0.356723	−0.0152107
$551$	−1.31199	−0.0558926
$552$	−10.6767	−0.454431
$553$	27.6540	1.17597
$554$	38.1203	1.61957
$555$	7.84073	0.332820
$556$	−5.67783	−0.240794
$557$	−3.15237	−0.133570	−0.0667850	−	0.997767i	$-0.521274\pi$
$557$	−3.15237	−0.133570	−0.0667850	+	0.997767i	$0.521274\pi$
$558$	−0.275690	−0.0116709
$559$	17.8208	0.753740
$560$	−16.8018	−0.710007
$561$	−6.13266	−0.258921
$562$	9.03002	0.380908
$563$	−35.1720	−1.48232	−0.741162	−	0.671326i	$-0.765725\pi$
$563$	−35.1720	−1.48232	−0.741162	+	0.671326i	$0.765725\pi$
$564$	2.42896	0.102277
$565$	−5.58937	−0.235146
$566$	−29.1704	−1.22613
$567$	−1.69385	−0.0711348
$568$	−16.2991	−0.683894
$569$	13.5107	0.566400	0.283200	−	0.959061i	$-0.408604\pi$
$569$	13.5107	0.566400	0.283200	+	0.959061i	$0.408604\pi$
$570$	2.58776	0.108389
$571$	46.3150	1.93822	0.969112	−	0.246622i	$-0.0793206\pi$
$571$	46.3150	1.93822	0.969112	+	0.246622i	$0.0793206\pi$
$572$	1.02029	0.0426606
$573$	−6.60049	−0.275740
$574$	−10.3635	−0.432563
$575$	−0.966317	−0.0402982
$576$	6.32116	0.263382
$577$	−46.2031	−1.92346	−0.961730	−	0.273998i	$-0.911654\pi$
$577$	−46.2031	−1.92346	−0.961730	+	0.273998i	$0.911654\pi$
$578$	−30.0836	−1.25131
$579$	5.85021	0.243126
$580$	−1.19226	−0.0495060
$581$	−23.3825	−0.970071
$582$	−11.7384	−0.486572
$583$	11.5662	0.479022
$584$	−0.561527	−0.0232362
$585$	6.80660	0.281418
$586$	−33.6371	−1.38954
$587$	20.2898	0.837450	0.418725	−	0.908113i	$-0.362477\pi$
$587$	20.2898	0.837450	0.418725	+	0.908113i	$0.362477\pi$
$588$	1.33640	0.0551120
$589$	−0.140604	−0.00579350
$590$	−41.9842	−1.72846
$591$	−7.04160	−0.289653
$592$	−16.3094	−0.670312
$593$	5.81088	0.238624	0.119312	−	0.992857i	$-0.461931\pi$
$593$	5.81088	0.238624	0.119312	+	0.992857i	$0.461931\pi$
$594$	−1.54233	−0.0632824
$595$	−22.4192	−0.919097
$596$	2.70637	0.110857
$597$	9.21110	0.376985
$598$	19.8503	0.811739
$599$	−13.1280	−0.536394	−0.268197	−	0.963364i	$-0.586428\pi$
$599$	−13.1280	−0.536394	−0.268197	+	0.963364i	$0.586428\pi$
$600$	0.591054	0.0241297
$601$	−13.7436	−0.560614	−0.280307	−	0.959910i	$-0.590436\pi$
$601$	−13.7436	−0.560614	−0.280307	+	0.959910i	$0.590436\pi$
$602$	−14.7620	−0.601653
$603$	5.53427	0.225373
$604$	−6.96999	−0.283605
$605$	21.7854	0.885704
$606$	10.5441	0.428324
$607$	−7.66141	−0.310967	−0.155483	−	0.987838i	$-0.549694\pi$
$607$	−7.66141	−0.310967	−0.155483	+	0.987838i	$0.549694\pi$
$608$	−1.40944	−0.0571605
$609$	2.85860	0.115836
$610$	−1.74415	−0.0706186
$611$	23.4022	0.946753
$612$	−1.96082	−0.0792613
$613$	14.8045	0.597949	0.298974	−	0.954261i	$-0.403355\pi$
$613$	14.8045	0.597949	0.298974	+	0.954261i	$0.403355\pi$
$614$	−6.09793	−0.246093
$615$	−8.76514	−0.353445
$616$	4.37976	0.176466
$617$	33.0579	1.33086	0.665430	−	0.746460i	$-0.268248\pi$
$617$	33.0579	1.33086	0.665430	+	0.746460i	$0.268248\pi$
$618$	−12.3263	−0.495837
$619$	−15.8115	−0.635518	−0.317759	−	0.948172i	$-0.602930\pi$
$619$	−15.8115	−0.635518	−0.317759	+	0.948172i	$0.602930\pi$
$620$	−0.127773	−0.00513150
$621$	−4.17796	−0.167656
$622$	6.59754	0.264537
$623$	−7.49591	−0.300317
$624$	−14.1583	−0.566786
$625$	−23.7901	−0.951602
$626$	−26.5572	−1.06144
$627$	−0.786600	−0.0314138
$628$	−7.25106	−0.289349
$629$	−21.7621	−0.867712
$630$	−5.63828	−0.224635
$631$	−43.4226	−1.72863	−0.864313	−	0.502954i	$-0.832246\pi$
$631$	−43.4226	−1.72863	−0.864313	+	0.502954i	$0.832246\pi$
$632$	−41.7212	−1.65958
$633$	−17.3484	−0.689537
$634$	14.0534	0.558133
$635$	18.4448	0.731960
$636$	3.69809	0.146639
$637$	12.8758	0.510156
$638$	2.60289	0.103049
$639$	−6.37808	−0.252313
$640$	28.9594	1.14472
$641$	−0.760315	−0.0300307	−0.0150153	−	0.999887i	$-0.504780\pi$
$641$	−0.760315	−0.0300307	−0.0150153	+	0.999887i	$0.504780\pi$
$642$	3.71605	0.146661
$643$	9.55349	0.376753	0.188376	−	0.982097i	$-0.439678\pi$
$643$	9.55349	0.376753	0.188376	+	0.982097i	$0.439678\pi$
$644$	−2.28945	−0.0902168
$645$	−12.4853	−0.491608
$646$	−7.18238	−0.282587
$647$	−32.0564	−1.26027	−0.630133	−	0.776487i	$-0.717000\pi$
$647$	−32.0564	−1.26027	−0.630133	+	0.776487i	$0.717000\pi$
$648$	2.55548	0.100389
$649$	12.7619	0.500949
$650$	−1.09890	−0.0431023
$651$	0.306353	0.0120069
$652$	−0.521429	−0.0204207
$653$	8.08185	0.316267	0.158134	−	0.987418i	$-0.449452\pi$
$653$	8.08185	0.316267	0.158134	+	0.987418i	$0.449452\pi$
$654$	−13.0021	−0.508421
$655$	32.7579	1.27996
$656$	18.2323	0.711850
$657$	−0.219734	−0.00857266
$658$	−19.3854	−0.755721
$659$	−40.3781	−1.57291	−0.786453	−	0.617650i	$-0.788085\pi$
$659$	−40.3781	−1.57291	−0.786453	+	0.617650i	$0.788085\pi$
$660$	−0.714819	−0.0278243
$661$	−1.91603	−0.0745248	−0.0372624	−	0.999306i	$-0.511864\pi$
$661$	−1.91603	−0.0745248	−0.0372624	+	0.999306i	$0.511864\pi$
$662$	−18.5885	−0.722463
$663$	−18.8919	−0.733699
$664$	35.2769	1.36901
$665$	−2.87558	−0.111510
$666$	−5.47304	−0.212076
$667$	7.05090	0.273012
$668$	0.0565564	0.00218823
$669$	19.3790	0.749236
$670$	18.4219	0.711699
$671$	0.530169	0.0204670
$672$	3.07094	0.118464
$673$	−21.0142	−0.810038	−0.405019	−	0.914308i	$-0.632735\pi$
$673$	−21.0142	−0.810038	−0.405019	+	0.914308i	$0.632735\pi$
$674$	−14.3259	−0.551813
$675$	0.231289	0.00890231
$676$	−1.06262	−0.0408700
$677$	−41.3036	−1.58742	−0.793712	−	0.608293i	$-0.791855\pi$
$677$	−41.3036	−1.58742	−0.793712	+	0.608293i	$0.791855\pi$
$678$	3.90153	0.149837
$679$	13.0440	0.500581
$680$	33.8235	1.29707
$681$	28.5285	1.09322
$682$	0.278949	0.0106815
$683$	7.41299	0.283650	0.141825	−	0.989892i	$-0.454703\pi$
$683$	7.41299	0.283650	0.141825	+	0.989892i	$0.454703\pi$
$684$	−0.251502	−0.00961644
$685$	−28.5156	−1.08953
$686$	−28.7393	−1.09727
$687$	−5.61351	−0.214169
$688$	25.9705	0.990115
$689$	35.6300	1.35740
$690$	−13.9071	−0.529436
$691$	3.34908	0.127405	0.0637024	−	0.997969i	$-0.479709\pi$
$691$	3.34908	0.127405	0.0637024	+	0.997969i	$0.479709\pi$
$692$	−5.25992	−0.199952
$693$	1.71387	0.0651045
$694$	27.9634	1.06148
$695$	38.3258	1.45378
$696$	−4.31273	−0.163474
$697$	24.3279	0.921483
$698$	29.5267	1.11760
$699$	−19.6889	−0.744703
$700$	0.126742	0.00479040
$701$	36.6478	1.38417	0.692084	−	0.721817i	$-0.256693\pi$
$701$	36.6478	1.38417	0.692084	+	0.721817i	$0.256693\pi$
$702$	−4.75119	−0.179322
$703$	−2.79130	−0.105276
$704$	−6.39589	−0.241054
$705$	−16.3956	−0.617495
$706$	−28.8318	−1.08510
$707$	−11.7168	−0.440657
$708$	4.08041	0.153351
$709$	−42.8190	−1.60810	−0.804050	−	0.594561i	$-0.797326\pi$
$709$	−42.8190	−1.60810	−0.804050	+	0.594561i	$0.797326\pi$
$710$	−21.2306	−0.796772
$711$	−16.3262	−0.612279
$712$	11.3090	0.423822
$713$	0.755636	0.0282988
$714$	15.6492	0.585656
$715$	−6.88706	−0.257561
$716$	−5.97304	−0.223223
$717$	19.2525	0.718998
$718$	−18.8305	−0.702749
$719$	34.3201	1.27992	0.639962	−	0.768407i	$-0.278950\pi$
$719$	34.3201	1.27992	0.639962	+	0.768407i	$0.278950\pi$
$720$	9.91934	0.369672
$721$	13.6973	0.510113
$722$	28.0406	1.04356
$723$	15.6255	0.581117
$724$	−5.32275	−0.197818
$725$	−0.390332	−0.0144966
$726$	−15.2068	−0.564378
$727$	51.3158	1.90320	0.951599	−	0.307343i	$-0.0994398\pi$
$727$	51.3158	1.90320	0.951599	+	0.307343i	$0.0994398\pi$
$728$	13.4920	0.500047
$729$	1.00000	0.0370370
$730$	−0.731427	−0.0270713
$731$	34.6532	1.28169
$732$	0.169513	0.00626538
$733$	−36.5148	−1.34870	−0.674352	−	0.738410i	$-0.735577\pi$
$733$	−36.5148	−1.34870	−0.674352	+	0.738410i	$0.735577\pi$
$734$	−35.1785	−1.29846
$735$	−9.02077	−0.332736
$736$	7.57464	0.279205
$737$	−5.59969	−0.206267
$738$	6.11830	0.225218
$739$	−7.47510	−0.274976	−0.137488	−	0.990503i	$-0.543903\pi$
$739$	−7.47510	−0.274976	−0.137488	+	0.990503i	$0.543903\pi$
$740$	−2.53658	−0.0932464
$741$	−2.42315	−0.0890166
$742$	−29.5143	−1.08350
$743$	32.7383	1.20105	0.600526	−	0.799605i	$-0.294958\pi$
$743$	32.7383	1.20105	0.600526	+	0.799605i	$0.294958\pi$
$744$	−0.462190	−0.0169447
$745$	−18.2682	−0.669296
$746$	26.5560	0.972284
$747$	13.8044	0.505077
$748$	1.98400	0.0725421
$749$	−4.12936	−0.150884
$750$	17.4133	0.635845
$751$	−6.68412	−0.243907	−0.121954	−	0.992536i	$-0.538916\pi$
$751$	−6.68412	−0.243907	−0.121954	+	0.992536i	$0.538916\pi$
$752$	34.1044	1.24366
$753$	−2.55866	−0.0932429
$754$	8.01830	0.292009
$755$	47.0480	1.71225
$756$	0.547981	0.0199299
$757$	7.37000	0.267867	0.133934	−	0.990990i	$-0.457239\pi$
$757$	7.37000	0.267867	0.133934	+	0.990990i	$0.457239\pi$
$758$	8.34704	0.303178
$759$	4.22735	0.153443
$760$	4.33834	0.157368
$761$	−38.5355	−1.39691	−0.698455	−	0.715654i	$-0.746129\pi$
$761$	−38.5355	−1.39691	−0.698455	+	0.715654i	$0.746129\pi$
$762$	−12.8750	−0.466411
$763$	14.4482	0.523060
$764$	2.13535	0.0772541
$765$	13.2357	0.478536
$766$	−22.7946	−0.823604
$767$	39.3135	1.41953
$768$	−7.57211	−0.273235
$769$	22.3994	0.807741	0.403871	−	0.914816i	$-0.367665\pi$
$769$	22.3994	0.807741	0.403871	+	0.914816i	$0.367665\pi$
$770$	5.70493	0.205592
$771$	5.54769	0.199795
$772$	−1.89262	−0.0681169
$773$	−53.7666	−1.93385	−0.966925	−	0.255059i	$-0.917905\pi$
$773$	−53.7666	−1.93385	−0.966925	+	0.255059i	$0.917905\pi$
$774$	8.71506	0.313256
$775$	−0.0418314	−0.00150263
$776$	−19.6792	−0.706444
$777$	6.08177	0.218182
$778$	−29.0446	−1.04130
$779$	3.12039	0.111800
$780$	−2.20202	−0.0788451
$781$	6.45347	0.230923
$782$	38.5996	1.38032
$783$	−1.68764	−0.0603113
$784$	18.7640	0.670143
$785$	48.9452	1.74693
$786$	−22.8659	−0.815600
$787$	−16.3130	−0.581495	−0.290747	−	0.956800i	$-0.593904\pi$
$787$	−16.3130	−0.581495	−0.290747	+	0.956800i	$0.593904\pi$
$788$	2.27805	0.0811522
$789$	−18.6631	−0.664424
$790$	−54.3447	−1.93350
$791$	−4.33547	−0.154151
$792$	−2.58569	−0.0918785
$793$	1.63320	0.0579968
$794$	−41.0116	−1.45545
$795$	−24.9624	−0.885326
$796$	−2.97991	−0.105620
$797$	−43.5094	−1.54118	−0.770591	−	0.637330i	$-0.780039\pi$
$797$	−43.5094	−1.54118	−0.770591	+	0.637330i	$0.780039\pi$
$798$	2.00723	0.0710551
$799$	45.5065	1.60990
$800$	−0.419326	−0.0148254
$801$	4.42538	0.156363
$802$	28.4360	1.00411
$803$	0.222332	0.00784592
$804$	−1.79041	−0.0631429
$805$	15.4539	0.544680
$806$	0.859311	0.0302679
$807$	−5.48256	−0.192995
$808$	17.6770	0.621875
$809$	43.4947	1.52919	0.764596	−	0.644510i	$-0.222938\pi$
$809$	43.4947	1.52919	0.764596	+	0.644510i	$0.222938\pi$
$810$	3.32869	0.116958
$811$	−22.4872	−0.789633	−0.394817	−	0.918760i	$-0.629192\pi$
$811$	−22.4872	−0.789633	−0.394817	+	0.918760i	$0.629192\pi$
$812$	−0.924795	−0.0324539
$813$	−14.4509	−0.506816
$814$	5.53773	0.194097
$815$	3.51969	0.123289
$816$	−27.5313	−0.963790
$817$	4.44476	0.155503
$818$	−33.1710	−1.15980
$819$	5.27963	0.184485
$820$	2.83564	0.0990248
$821$	−20.2652	−0.707259	−0.353630	−	0.935386i	$-0.615053\pi$
$821$	−20.2652	−0.707259	−0.353630	+	0.935386i	$0.615053\pi$
$822$	19.9047	0.694255
$823$	−13.6668	−0.476393	−0.238197	−	0.971217i	$-0.576556\pi$
$823$	−13.6668	−0.476393	−0.238197	+	0.971217i	$0.576556\pi$
$824$	−20.6649	−0.719896
$825$	−0.234023	−0.00814763
$826$	−32.5656	−1.13310
$827$	9.27578	0.322550	0.161275	−	0.986909i	$-0.448439\pi$
$827$	9.27578	0.322550	0.161275	+	0.986909i	$0.448439\pi$
$828$	1.35163	0.0469722
$829$	27.5006	0.955134	0.477567	−	0.878595i	$-0.341519\pi$
$829$	27.5006	0.955134	0.477567	+	0.878595i	$0.341519\pi$
$830$	45.9505	1.59497
$831$	25.0082	0.867526
$832$	−19.7027	−0.683070
$833$	25.0374	0.867493
$834$	−26.7524	−0.926361
$835$	−0.381760	−0.0132113
$836$	0.254475	0.00880122
$837$	−0.180862	−0.00625151
$838$	40.4614	1.39772
$839$	−28.4195	−0.981151	−0.490575	−	0.871399i	$-0.663213\pi$
$839$	−28.4195	−0.981151	−0.490575	+	0.871399i	$0.663213\pi$
$840$	−9.45251	−0.326143
$841$	−26.1519	−0.901789
$842$	−28.8953	−0.995799
$843$	5.92401	0.204034
$844$	5.61244	0.193188
$845$	7.17277	0.246751
$846$	11.4446	0.393473
$847$	16.8982	0.580628
$848$	51.9240	1.78308
$849$	−19.1369	−0.656775
$850$	−2.13684	−0.0732931
$851$	15.0010	0.514228
$852$	2.06339	0.0706906
$853$	3.90826	0.133816	0.0669082	−	0.997759i	$-0.478687\pi$
$853$	3.90826	0.133816	0.0669082	+	0.997759i	$0.478687\pi$
$854$	−1.35287	−0.0462944
$855$	1.69766	0.0580588
$856$	6.22991	0.212934
$857$	−43.7999	−1.49618	−0.748088	−	0.663599i	$-0.769028\pi$
$857$	−43.7999	−1.49618	−0.748088	+	0.663599i	$0.769028\pi$
$858$	4.80735	0.164120
$859$	−28.0667	−0.957625	−0.478812	−	0.877917i	$-0.658933\pi$
$859$	−28.0667	−0.957625	−0.478812	+	0.877917i	$0.658933\pi$
$860$	4.03915	0.137734
$861$	−6.79880	−0.231703
$862$	−41.7776	−1.42295
$863$	17.8017	0.605977	0.302989	−	0.952994i	$-0.402016\pi$
$863$	17.8017	0.605977	0.302989	+	0.952994i	$0.402016\pi$
$864$	−1.81300	−0.0616794
$865$	35.5049	1.20720
$866$	−19.1873	−0.652010
$867$	−19.7359	−0.670266
$868$	−0.0991091	−0.00336398
$869$	16.5192	0.560374
$870$	−5.61763	−0.190455
$871$	−17.2500	−0.584495
$872$	−21.7978	−0.738166
$873$	−7.70080	−0.260632
$874$	4.95094	0.167468
$875$	−19.3501	−0.654153
$876$	0.0710869	0.00240181
$877$	45.3217	1.53040	0.765202	−	0.643790i	$-0.222639\pi$
$877$	45.3217	1.53040	0.765202	+	0.643790i	$0.222639\pi$
$878$	1.25839	0.0424685
$879$	−22.0672	−0.744307
$880$	−10.0366	−0.338333
$881$	49.8467	1.67938	0.839690	−	0.543066i	$-0.182737\pi$
$881$	49.8467	1.67938	0.839690	+	0.543066i	$0.182737\pi$
$882$	6.29674	0.212022
$883$	6.47776	0.217994	0.108997	−	0.994042i	$-0.465236\pi$
$883$	6.47776	0.217994	0.108997	+	0.994042i	$0.465236\pi$
$884$	6.11177	0.205561
$885$	−27.5431	−0.925851
$886$	−59.4767	−1.99816
$887$	23.0261	0.773141	0.386570	−	0.922260i	$-0.373660\pi$
$887$	23.0261	0.773141	0.386570	+	0.922260i	$0.373660\pi$
$888$	−9.17548	−0.307909
$889$	14.3070	0.479841
$890$	14.7307	0.493774
$891$	−1.01182	−0.0338973
$892$	−6.26936	−0.209914
$893$	5.83685	0.195323
$894$	12.7517	0.426481
$895$	40.3185	1.34770
$896$	22.4628	0.750428
$897$	13.0225	0.434809
$898$	1.23908	0.0413486
$899$	0.305230	0.0101800
$900$	−0.0748250	−0.00249417
$901$	69.2838	2.30818
$902$	−6.19063	−0.206125
$903$	−9.68438	−0.322276
$904$	6.54086	0.217546
$905$	35.9290	1.19432
$906$	−32.8407	−1.09106
$907$	52.3626	1.73867	0.869336	−	0.494221i	$-0.164547\pi$
$907$	52.3626	1.73867	0.869336	+	0.494221i	$0.164547\pi$
$908$	−9.22935	−0.306287
$909$	6.91729	0.229432
$910$	17.5742	0.582580
$911$	−25.0945	−0.831417	−0.415708	−	0.909498i	$-0.636466\pi$
$911$	−25.0945	−0.831417	−0.415708	+	0.909498i	$0.636466\pi$
$912$	−3.53128	−0.116932
$913$	−13.9676	−0.462259
$914$	53.6506	1.77461
$915$	−1.14422	−0.0378269
$916$	1.81604	0.0600038
$917$	25.4091	0.839083
$918$	−9.23885	−0.304927
$919$	34.8763	1.15046	0.575231	−	0.817991i	$-0.304912\pi$
$919$	34.8763	1.15046	0.575231	+	0.817991i	$0.304912\pi$
$920$	−23.3151	−0.768677
$921$	−4.00046	−0.131820
$922$	−31.8681	−1.04952
$923$	19.8801	0.654363
$924$	−0.554459	−0.0182404
$925$	−0.830444	−0.0273048
$926$	7.68035	0.252392
$927$	−8.08650	−0.265595
$928$	3.05969	0.100439
$929$	13.5869	0.445772	0.222886	−	0.974844i	$-0.428452\pi$
$929$	13.5869	0.445772	0.222886	+	0.974844i	$0.428452\pi$
$930$	−0.602034	−0.0197415
$931$	3.21139	0.105249
$932$	6.36962	0.208644
$933$	4.32822	0.141700
$934$	12.9892	0.425019
$935$	−13.3921	−0.437969
$936$	−7.96530	−0.260354
$937$	11.1195	0.363257	0.181628	−	0.983367i	$-0.441863\pi$
$937$	11.1195	0.363257	0.181628	+	0.983367i	$0.441863\pi$
$938$	14.2892	0.466558
$939$	−17.4225	−0.568562
$940$	5.30420	0.173004
$941$	−13.3688	−0.435811	−0.217905	−	0.975970i	$-0.569922\pi$
$941$	−13.3688	−0.435811	−0.217905	+	0.975970i	$0.569922\pi$
$942$	−34.1651	−1.11316
$943$	−16.7696	−0.546094
$944$	57.2921	1.86470
$945$	−3.69892	−0.120326
$946$	−8.81808	−0.286701
$947$	1.74096	0.0565737	0.0282868	−	0.999600i	$-0.490995\pi$
$947$	1.74096	0.0565737	0.0282868	+	0.999600i	$0.490995\pi$
$948$	5.28173	0.171543
$949$	0.684901	0.0222328
$950$	−0.274080	−0.00889234
$951$	9.21955	0.298964
$952$	26.2357	0.850302
$953$	38.9296	1.26105	0.630527	−	0.776168i	$-0.282839\pi$
$953$	38.9296	1.26105	0.630527	+	0.776168i	$0.282839\pi$
$954$	17.4244	0.564137
$955$	−14.4138	−0.466418
$956$	−6.22844	−0.201442
$957$	1.70759	0.0551985
$958$	−55.2105	−1.78377
$959$	−22.1185	−0.714244
$960$	13.8038	0.445515
$961$	−30.9673	−0.998945
$962$	17.0592	0.550010
$963$	2.43786	0.0785590
$964$	−5.05504	−0.162812
$965$	12.7753	0.411252
$966$	−10.7873	−0.347074
$967$	−38.4183	−1.23545	−0.617725	−	0.786394i	$-0.711946\pi$
$967$	−38.4183	−1.23545	−0.617725	+	0.786394i	$0.711946\pi$
$968$	−25.4940	−0.819410
$969$	−4.71190	−0.151368
$970$	−25.6335	−0.823044
$971$	−54.2050	−1.73952	−0.869761	−	0.493474i	$-0.835727\pi$
$971$	−54.2050	−1.73952	−0.869761	+	0.493474i	$0.835727\pi$
$972$	−0.323513	−0.0103767
$973$	29.7279	0.953034
$974$	−54.1792	−1.73601
$975$	−0.720916	−0.0230878
$976$	2.38009	0.0761847
$977$	−15.7805	−0.504864	−0.252432	−	0.967615i	$-0.581230\pi$
$977$	−15.7805	−0.504864	−0.252432	+	0.967615i	$0.581230\pi$
$978$	−2.45684	−0.0785610
$979$	−4.47769	−0.143108
$980$	2.91834	0.0932229
$981$	−8.52982	−0.272336
$982$	−2.26155	−0.0721690
$983$	−57.0410	−1.81932	−0.909662	−	0.415348i	$-0.863660\pi$
$983$	−57.0410	−1.81932	−0.909662	+	0.415348i	$0.863660\pi$
$984$	10.2573	0.326989
$985$	−15.3770	−0.489952
$986$	15.5919	0.496546
$987$	−12.7175	−0.404802
$988$	0.783920	0.0249398
$989$	−23.8871	−0.759564
$990$	−3.36804	−0.107043
$991$	14.9146	0.473778	0.236889	−	0.971537i	$-0.423872\pi$
$991$	14.9146	0.473778	0.236889	+	0.971537i	$0.423872\pi$
$992$	0.327903	0.0104109
$993$	−12.1947	−0.386988
$994$	−16.4678	−0.522328
$995$	20.1146	0.637677
$996$	−4.46590	−0.141508
$997$	0.689947	0.0218509	0.0109254	−	0.999940i	$-0.496522\pi$
$997$	0.689947	0.0218509	0.0109254	+	0.999940i	$0.496522\pi$
$998$	−13.0277	−0.412384
$999$	−3.59051	−0.113599

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.c.1.18	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.c.1.18	✓	82	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52431 q^{2} -1.00000 q^{3} +0.323513 q^{4} -2.18374 q^{5} +1.52431 q^{6} -1.69385 q^{7} +2.55548 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52431 q^{2} -1.00000 q^{3} +0.323513 q^{4} -2.18374 q^{5} +1.52431 q^{6} -1.69385 q^{7} +2.55548 q^{8} +1.00000 q^{9} +3.32869 q^{10} -1.01182 q^{11} -0.323513 q^{12} -3.11695 q^{13} +2.58194 q^{14} +2.18374 q^{15} -4.54237 q^{16} -6.06101 q^{17} -1.52431 q^{18} -0.777411 q^{19} -0.706468 q^{20} +1.69385 q^{21} +1.54233 q^{22} +4.17796 q^{23} -2.55548 q^{24} -0.231289 q^{25} +4.75119 q^{26} -1.00000 q^{27} -0.547981 q^{28} +1.68764 q^{29} -3.32869 q^{30} +0.180862 q^{31} +1.81300 q^{32} +1.01182 q^{33} +9.23885 q^{34} +3.69892 q^{35} +0.323513 q^{36} +3.59051 q^{37} +1.18501 q^{38} +3.11695 q^{39} -5.58050 q^{40} -4.01383 q^{41} -2.58194 q^{42} -5.71739 q^{43} -0.327337 q^{44} -2.18374 q^{45} -6.36850 q^{46} -7.50806 q^{47} +4.54237 q^{48} -4.13089 q^{49} +0.352555 q^{50} +6.06101 q^{51} -1.00837 q^{52} -11.4311 q^{53} +1.52431 q^{54} +2.20955 q^{55} -4.32859 q^{56} +0.777411 q^{57} -2.57248 q^{58} -12.6128 q^{59} +0.706468 q^{60} -0.523975 q^{61} -0.275690 q^{62} -1.69385 q^{63} +6.32116 q^{64} +6.80660 q^{65} -1.54233 q^{66} +5.53427 q^{67} -1.96082 q^{68} -4.17796 q^{69} -5.63828 q^{70} -6.37808 q^{71} +2.55548 q^{72} -0.219734 q^{73} -5.47304 q^{74} +0.231289 q^{75} -0.251502 q^{76} +1.71387 q^{77} -4.75119 q^{78} -16.3262 q^{79} +9.91934 q^{80} +1.00000 q^{81} +6.11830 q^{82} +13.8044 q^{83} +0.547981 q^{84} +13.2357 q^{85} +8.71506 q^{86} -1.68764 q^{87} -2.58569 q^{88} +4.42538 q^{89} +3.32869 q^{90} +5.27963 q^{91} +1.35163 q^{92} -0.180862 q^{93} +11.4446 q^{94} +1.69766 q^{95} -1.81300 q^{96} -7.70080 q^{97} +6.29674 q^{98} -1.01182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9}+O(q^{10}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9	\( 82 q + 13 q^{2} - 82 q^{3} + 87 q^{4} + 7 q^{5} - 13 q^{6} + 30 q^{7} + 39 q^{8} + 82 q^{9} - 9 q^{10} + 28 q^{11} - 87 q^{12} - 14 q^{13} + 21 q^{14} - 7 q^{15} + 93 q^{16} + 25 q^{17} + 13 q^{18} - 7 q^{19} + 40 q^{20} - 30 q^{21} + 31 q^{22} + 97 q^{23} - 39 q^{24} + 83 q^{25} + 22 q^{26} - 82 q^{27} + 53 q^{28} + 45 q^{29} + 9 q^{30} - 11 q^{31} + 86 q^{32} - 28 q^{33} - 30 q^{34} + 69 q^{35} + 87 q^{36} + 8 q^{37} + 33 q^{38} + 14 q^{39} - 38 q^{40} + 12 q^{41} - 21 q^{42} + 68 q^{43} + 77 q^{44} + 7 q^{45} - 14 q^{46} + 85 q^{47} - 93 q^{48} + 68 q^{49} + 56 q^{50} - 25 q^{51} - 18 q^{52} + 58 q^{53} - 13 q^{54} + 68 q^{55} + 59 q^{56} + 7 q^{57} + 27 q^{58} + 40 q^{59} - 40 q^{60} - 116 q^{61} + 79 q^{62} + 30 q^{63} + 127 q^{64} + 66 q^{65} - 31 q^{66} + 51 q^{67} + 94 q^{68} - 97 q^{69} + q^{70} + 101 q^{71} + 39 q^{72} + 12 q^{73} + 72 q^{74} - 83 q^{75} - 3 q^{76} + 101 q^{77} - 22 q^{78} + 26 q^{79} + 61 q^{80} + 82 q^{81} + 31 q^{82} + 94 q^{83} - 53 q^{84} - 8 q^{85} + 68 q^{86} - 45 q^{87} + 91 q^{88} + 40 q^{89} - 9 q^{90} - 6 q^{91} + 180 q^{92} + 11 q^{93} - 31 q^{94} + 153 q^{95} - 86 q^{96} - 39 q^{97} + 115 q^{98} + 28 q^{99}+O(q^{100}) \) 82 * q + 13 * q^2 - 82 * q^3 + 87 * q^4 + 7 * q^5 - 13 * q^6 + 30 * q^7 + 39 * q^8 + 82 * q^9 - 9 * q^10 + 28 * q^11 - 87 * q^12 - 14 * q^13 + 21 * q^14 - 7 * q^15 + 93 * q^16 + 25 * q^17 + 13 * q^18 - 7 * q^19 + 40 * q^20 - 30 * q^21 + 31 * q^22 + 97 * q^23 - 39 * q^24 + 83 * q^25 + 22 * q^26 - 82 * q^27 + 53 * q^28 + 45 * q^29 + 9 * q^30 - 11 * q^31 + 86 * q^32 - 28 * q^33 - 30 * q^34 + 69 * q^35 + 87 * q^36 + 8 * q^37 + 33 * q^38 + 14 * q^39 - 38 * q^40 + 12 * q^41 - 21 * q^42 + 68 * q^43 + 77 * q^44 + 7 * q^45 - 14 * q^46 + 85 * q^47 - 93 * q^48 + 68 * q^49 + 56 * q^50 - 25 * q^51 - 18 * q^52 + 58 * q^53 - 13 * q^54 + 68 * q^55 + 59 * q^56 + 7 * q^57 + 27 * q^58 + 40 * q^59 - 40 * q^60 - 116 * q^61 + 79 * q^62 + 30 * q^63 + 127 * q^64 + 66 * q^65 - 31 * q^66 + 51 * q^67 + 94 * q^68 - 97 * q^69 + q^70 + 101 * q^71 + 39 * q^72 + 12 * q^73 + 72 * q^74 - 83 * q^75 - 3 * q^76 + 101 * q^77 - 22 * q^78 + 26 * q^79 + 61 * q^80 + 82 * q^81 + 31 * q^82 + 94 * q^83 - 53 * q^84 - 8 * q^85 + 68 * q^86 - 45 * q^87 + 91 * q^88 + 40 * q^89 - 9 * q^90 - 6 * q^91 + 180 * q^92 + 11 * q^93 - 31 * q^94 + 153 * q^95 - 86 * q^96 - 39 * q^97 + 115 * q^98 + 28 * q^99

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