LMFDB - Embedded newform 8041.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83493 q^{2} +1.92990 q^{3} +1.36698 q^{4} +0.407070 q^{5} -3.54123 q^{6} +0.437202 q^{7} +1.16155 q^{8} +0.724496 q^{9} +O(q^{10})$	\(q-1.83493 q^{2} +1.92990 q^{3} +1.36698 q^{4} +0.407070 q^{5} -3.54123 q^{6} +0.437202 q^{7} +1.16155 q^{8} +0.724496 q^{9} -0.746946 q^{10} +1.00000 q^{11} +2.63813 q^{12} -2.15306 q^{13} -0.802236 q^{14} +0.785602 q^{15} -4.86533 q^{16} +1.00000 q^{17} -1.32940 q^{18} -7.13276 q^{19} +0.556456 q^{20} +0.843753 q^{21} -1.83493 q^{22} +7.00647 q^{23} +2.24167 q^{24} -4.83429 q^{25} +3.95073 q^{26} -4.39148 q^{27} +0.597645 q^{28} +2.75316 q^{29} -1.44153 q^{30} -0.623741 q^{31} +6.60445 q^{32} +1.92990 q^{33} -1.83493 q^{34} +0.177972 q^{35} +0.990371 q^{36} -4.02076 q^{37} +13.0881 q^{38} -4.15519 q^{39} +0.472832 q^{40} +7.90834 q^{41} -1.54823 q^{42} -1.00000 q^{43} +1.36698 q^{44} +0.294921 q^{45} -12.8564 q^{46} -3.34663 q^{47} -9.38957 q^{48} -6.80885 q^{49} +8.87061 q^{50} +1.92990 q^{51} -2.94319 q^{52} +13.4622 q^{53} +8.05808 q^{54} +0.407070 q^{55} +0.507832 q^{56} -13.7655 q^{57} -5.05186 q^{58} +12.6034 q^{59} +1.07390 q^{60} +5.13870 q^{61} +1.14452 q^{62} +0.316751 q^{63} -2.38806 q^{64} -0.876447 q^{65} -3.54123 q^{66} -11.3344 q^{67} +1.36698 q^{68} +13.5218 q^{69} -0.326566 q^{70} -8.37420 q^{71} +0.841539 q^{72} +1.34000 q^{73} +7.37783 q^{74} -9.32968 q^{75} -9.75034 q^{76} +0.437202 q^{77} +7.62449 q^{78} -9.28169 q^{79} -1.98053 q^{80} -10.6486 q^{81} -14.5113 q^{82} -4.98765 q^{83} +1.15339 q^{84} +0.407070 q^{85} +1.83493 q^{86} +5.31330 q^{87} +1.16155 q^{88} -6.08040 q^{89} -0.541159 q^{90} -0.941323 q^{91} +9.57771 q^{92} -1.20375 q^{93} +6.14084 q^{94} -2.90353 q^{95} +12.7459 q^{96} -6.31891 q^{97} +12.4938 q^{98} +0.724496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) $ 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * 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 $

$2$	−1.83493	−1.29749	−0.648747	−	0.761004i	$-0.724707\pi$
$2$	−1.83493	−1.29749	−0.648747	+	0.761004i	$0.724707\pi$
$3$	1.92990	1.11423	0.557113	−	0.830437i	$-0.311909\pi$
$3$	1.92990	1.11423	0.557113	+	0.830437i	$0.311909\pi$
$4$	1.36698	0.683490
$5$	0.407070	0.182047	0.0910236	−	0.995849i	$-0.470986\pi$
$5$	0.407070	0.182047	0.0910236	+	0.995849i	$0.470986\pi$
$6$	−3.54123	−1.44570
$7$	0.437202	0.165247	0.0826233	−	0.996581i	$-0.473670\pi$
$7$	0.437202	0.165247	0.0826233	+	0.996581i	$0.473670\pi$
$8$	1.16155	0.410670
$9$	0.724496	0.241499
$10$	−0.746946	−0.236205
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.63813	0.761562
$13$	−2.15306	−0.597152	−0.298576	−	0.954386i	$-0.596512\pi$
$13$	−2.15306	−0.597152	−0.298576	+	0.954386i	$0.596512\pi$
$14$	−0.802236	−0.214406
$15$	0.785602	0.202842
$16$	−4.86533	−1.21633
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.32940	−0.313343
$19$	−7.13276	−1.63637	−0.818184	−	0.574956i	$-0.805019\pi$
$19$	−7.13276	−1.63637	−0.818184	+	0.574956i	$0.805019\pi$
$20$	0.556456	0.124427
$21$	0.843753	0.184122
$22$	−1.83493	−0.391209
$23$	7.00647	1.46095	0.730476	−	0.682939i	$-0.239298\pi$
$23$	7.00647	1.46095	0.730476	+	0.682939i	$0.239298\pi$
$24$	2.24167	0.457579
$25$	−4.83429	−0.966859
$26$	3.95073	0.774801
$27$	−4.39148	−0.845142
$28$	0.597645	0.112944
$29$	2.75316	0.511248	0.255624	−	0.966776i	$-0.417719\pi$
$29$	2.75316	0.511248	0.255624	+	0.966776i	$0.417719\pi$
$30$	−1.44153	−0.263186
$31$	−0.623741	−0.112027	−0.0560136	−	0.998430i	$-0.517839\pi$
$31$	−0.623741	−0.112027	−0.0560136	+	0.998430i	$0.517839\pi$
$32$	6.60445	1.16751
$33$	1.92990	0.335952
$34$	−1.83493	−0.314688
$35$	0.177972	0.0300827
$36$	0.990371	0.165062
$37$	−4.02076	−0.661009	−0.330505	−	0.943804i	$-0.607219\pi$
$37$	−4.02076	−0.661009	−0.330505	+	0.943804i	$0.607219\pi$
$38$	13.0881	2.12318
$39$	−4.15519	−0.665362
$40$	0.472832	0.0747613
$41$	7.90834	1.23507	0.617537	−	0.786542i	$-0.288130\pi$
$41$	7.90834	1.23507	0.617537	+	0.786542i	$0.288130\pi$
$42$	−1.54823	−0.238897
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.36698	0.206080
$45$	0.294921	0.0439642
$46$	−12.8564	−1.89557
$47$	−3.34663	−0.488156	−0.244078	−	0.969756i	$-0.578485\pi$
$47$	−3.34663	−0.488156	−0.244078	+	0.969756i	$0.578485\pi$
$48$	−9.38957	−1.35527
$49$	−6.80885	−0.972694
$50$	8.87061	1.25449
$51$	1.92990	0.270239
$52$	−2.94319	−0.408147
$53$	13.4622	1.84918	0.924588	−	0.380970i	$-0.124410\pi$
$53$	13.4622	1.84918	0.924588	+	0.380970i	$0.124410\pi$
$54$	8.05808	1.09657
$55$	0.407070	0.0548893
$56$	0.507832	0.0678619
$57$	−13.7655	−1.82328
$58$	−5.05186	−0.663341
$59$	12.6034	1.64082	0.820409	−	0.571777i	$-0.193746\pi$
$59$	12.6034	1.64082	0.820409	+	0.571777i	$0.193746\pi$
$60$	1.07390	0.138640
$61$	5.13870	0.657944	0.328972	−	0.944340i	$-0.393298\pi$
$61$	5.13870	0.657944	0.328972	+	0.944340i	$0.393298\pi$
$62$	1.14452	0.145354
$63$	0.316751	0.0399069
$64$	−2.38806	−0.298508
$65$	−0.876447	−0.108710
$66$	−3.54123	−0.435895
$67$	−11.3344	−1.38472	−0.692360	−	0.721552i	$-0.743429\pi$
$67$	−11.3344	−1.38472	−0.692360	+	0.721552i	$0.743429\pi$
$68$	1.36698	0.165771
$69$	13.5218	1.62783
$70$	−0.326566	−0.0390321
$71$	−8.37420	−0.993835	−0.496917	−	0.867798i	$-0.665535\pi$
$71$	−8.37420	−0.993835	−0.496917	+	0.867798i	$0.665535\pi$
$72$	0.841539	0.0991764
$73$	1.34000	0.156835	0.0784176	−	0.996921i	$-0.475013\pi$
$73$	1.34000	0.156835	0.0784176	+	0.996921i	$0.475013\pi$
$74$	7.37783	0.857656
$75$	−9.32968	−1.07730
$76$	−9.75034	−1.11844
$77$	0.437202	0.0498237
$78$	7.62449	0.863304
$79$	−9.28169	−1.04427	−0.522136	−	0.852862i	$-0.674865\pi$
$79$	−9.28169	−1.04427	−0.522136	+	0.852862i	$0.674865\pi$
$80$	−1.98053	−0.221430
$81$	−10.6486	−1.18318
$82$	−14.5113	−1.60250
$83$	−4.98765	−0.547466	−0.273733	−	0.961806i	$-0.588258\pi$
$83$	−4.98765	−0.547466	−0.273733	+	0.961806i	$0.588258\pi$
$84$	1.15339	0.125846
$85$	0.407070	0.0441529
$86$	1.83493	0.197866
$87$	5.31330	0.569646
$88$	1.16155	0.123822
$89$	−6.08040	−0.644521	−0.322260	−	0.946651i	$-0.604443\pi$
$89$	−6.08040	−0.644521	−0.322260	+	0.946651i	$0.604443\pi$
$90$	−0.541159	−0.0570432
$91$	−0.941323	−0.0986774
$92$	9.57771	0.998545
$93$	−1.20375	−0.124824
$94$	6.14084	0.633380
$95$	−2.90353	−0.297896
$96$	12.7459	1.30087
$97$	−6.31891	−0.641588	−0.320794	−	0.947149i	$-0.603950\pi$
$97$	−6.31891	−0.641588	−0.320794	+	0.947149i	$0.603950\pi$
$98$	12.4938	1.26206
$99$	0.724496	0.0728146
$100$	−6.60838	−0.660838
$101$	−5.16327	−0.513765	−0.256882	−	0.966443i	$-0.582695\pi$
$101$	−5.16327	−0.513765	−0.256882	+	0.966443i	$0.582695\pi$
$102$	−3.54123	−0.350634
$103$	12.3778	1.21962	0.609811	−	0.792547i	$-0.291245\pi$
$103$	12.3778	1.21962	0.609811	+	0.792547i	$0.291245\pi$
$104$	−2.50089	−0.245233
$105$	0.343466	0.0335189
$106$	−24.7022	−2.39929
$107$	9.59729	0.927805	0.463902	−	0.885886i	$-0.346449\pi$
$107$	9.59729	0.927805	0.463902	+	0.885886i	$0.346449\pi$
$108$	−6.00307	−0.577645
$109$	14.8082	1.41837	0.709184	−	0.705023i	$-0.249063\pi$
$109$	14.8082	1.41837	0.709184	+	0.705023i	$0.249063\pi$
$110$	−0.746946	−0.0712185
$111$	−7.75965	−0.736514
$112$	−2.12713	−0.200995
$113$	−16.0224	−1.50726	−0.753628	−	0.657301i	$-0.771698\pi$
$113$	−16.0224	−1.50726	−0.753628	+	0.657301i	$0.771698\pi$
$114$	25.2587	2.36570
$115$	2.85212	0.265962
$116$	3.76351	0.349433
$117$	−1.55989	−0.144212
$118$	−23.1263	−2.12895
$119$	0.437202	0.0400782
$120$	0.912517	0.0833010
$121$	1.00000	0.0909091
$122$	−9.42918	−0.853678
$123$	15.2623	1.37615
$124$	−0.852641	−0.0765694
$125$	−4.00324	−0.358061
$126$	−0.581217	−0.0517789
$127$	−13.1556	−1.16737	−0.583684	−	0.811981i	$-0.698389\pi$
$127$	−13.1556	−1.16737	−0.583684	+	0.811981i	$0.698389\pi$
$128$	−8.82695	−0.780200
$129$	−1.92990	−0.169918
$130$	1.60822	0.141050
$131$	−12.1053	−1.05764	−0.528820	−	0.848734i	$-0.677365\pi$
$131$	−12.1053	−1.05764	−0.528820	+	0.848734i	$0.677365\pi$
$132$	2.63813	0.229619
$133$	−3.11845	−0.270404
$134$	20.7979	1.79667
$135$	−1.78764	−0.153856
$136$	1.16155	0.0996022
$137$	−8.12249	−0.693951	−0.346975	−	0.937874i	$-0.612791\pi$
$137$	−8.12249	−0.693951	−0.346975	+	0.937874i	$0.612791\pi$
$138$	−24.8115	−2.11210
$139$	−15.6083	−1.32388	−0.661940	−	0.749557i	$-0.730267\pi$
$139$	−15.6083	−1.32388	−0.661940	+	0.749557i	$0.730267\pi$
$140$	0.243283	0.0205612
$141$	−6.45865	−0.543916
$142$	15.3661	1.28949
$143$	−2.15306	−0.180048
$144$	−3.52491	−0.293743
$145$	1.12073	0.0930713
$146$	−2.45881	−0.203493
$147$	−13.1404	−1.08380
$148$	−5.49630	−0.451793
$149$	1.98763	0.162833	0.0814164	−	0.996680i	$-0.474056\pi$
$149$	1.98763	0.162833	0.0814164	+	0.996680i	$0.474056\pi$
$150$	17.1193	1.39779
$151$	−15.9577	−1.29862	−0.649309	−	0.760525i	$-0.724942\pi$
$151$	−15.9577	−1.29862	−0.649309	+	0.760525i	$0.724942\pi$
$152$	−8.28507	−0.672008
$153$	0.724496	0.0585721
$154$	−0.802236	−0.0646460
$155$	−0.253906	−0.0203942
$156$	−5.68005	−0.454768
$157$	−7.48680	−0.597512	−0.298756	−	0.954330i	$-0.596572\pi$
$157$	−7.48680	−0.597512	−0.298756	+	0.954330i	$0.596572\pi$
$158$	17.0313	1.35494
$159$	25.9806	2.06040
$160$	2.68847	0.212542
$161$	3.06324	0.241417
$162$	19.5395	1.53516
$163$	−15.6029	−1.22211	−0.611056	−	0.791588i	$-0.709255\pi$
$163$	−15.6029	−1.22211	−0.611056	+	0.791588i	$0.709255\pi$
$164$	10.8105	0.844161
$165$	0.785602	0.0611590
$166$	9.15201	0.710334
$167$	10.7135	0.829038	0.414519	−	0.910041i	$-0.363950\pi$
$167$	10.7135	0.829038	0.414519	+	0.910041i	$0.363950\pi$
$168$	0.980062	0.0756134
$169$	−8.36432	−0.643409
$170$	−0.746946	−0.0572881
$171$	−5.16766	−0.395181
$172$	−1.36698	−0.104231
$173$	19.7790	1.50377	0.751884	−	0.659295i	$-0.229145\pi$
$173$	19.7790	1.50377	0.751884	+	0.659295i	$0.229145\pi$
$174$	−9.74955	−0.739112
$175$	−2.11356	−0.159770
$176$	−4.86533	−0.366738
$177$	24.3232	1.82824
$178$	11.1571	0.836262
$179$	−15.6176	−1.16731	−0.583656	−	0.812001i	$-0.698378\pi$
$179$	−15.6176	−1.16731	−0.583656	+	0.812001i	$0.698378\pi$
$180$	0.403150	0.0300490
$181$	−4.30606	−0.320067	−0.160033	−	0.987112i	$-0.551160\pi$
$181$	−4.30606	−0.320067	−0.160033	+	0.987112i	$0.551160\pi$
$182$	1.72726	0.128033
$183$	9.91716	0.733098
$184$	8.13838	0.599969
$185$	−1.63673	−0.120335
$186$	2.20881	0.161958
$187$	1.00000	0.0731272
$188$	−4.57477	−0.333650
$189$	−1.91996	−0.139657
$190$	5.32779	0.386518
$191$	−6.60953	−0.478249	−0.239125	−	0.970989i	$-0.576860\pi$
$191$	−6.60953	−0.478249	−0.239125	+	0.970989i	$0.576860\pi$
$192$	−4.60871	−0.332605
$193$	13.1721	0.948146	0.474073	−	0.880485i	$-0.342783\pi$
$193$	13.1721	0.948146	0.474073	+	0.880485i	$0.342783\pi$
$194$	11.5948	0.832456
$195$	−1.69145	−0.121127
$196$	−9.30756	−0.664826
$197$	2.87622	0.204922	0.102461	−	0.994737i	$-0.467328\pi$
$197$	2.87622	0.204922	0.102461	+	0.994737i	$0.467328\pi$
$198$	−1.32940	−0.0944765
$199$	8.30894	0.589005	0.294503	−	0.955651i	$-0.404846\pi$
$199$	8.30894	0.589005	0.294503	+	0.955651i	$0.404846\pi$
$200$	−5.61528	−0.397060
$201$	−21.8743	−1.54289
$202$	9.47426	0.666607
$203$	1.20368	0.0844820
$204$	2.63813	0.184706
$205$	3.21924	0.224842
$206$	−22.7125	−1.58245
$207$	5.07617	0.352818
$208$	10.4754	0.726335
$209$	−7.13276	−0.493384
$210$	−0.630238	−0.0434905
$211$	8.51831	0.586425	0.293212	−	0.956047i	$-0.405276\pi$
$211$	8.51831	0.586425	0.293212	+	0.956047i	$0.405276\pi$
$212$	18.4025	1.26389
$213$	−16.1613	−1.10736
$214$	−17.6104	−1.20382
$215$	−0.407070	−0.0277619
$216$	−5.10093	−0.347074
$217$	−0.272700	−0.0185121
$218$	−27.1721	−1.84032
$219$	2.58606	0.174750
$220$	0.556456	0.0375163
$221$	−2.15306	−0.144831
$222$	14.2384	0.955622
$223$	3.51035	0.235071	0.117535	−	0.993069i	$-0.462501\pi$
$223$	3.51035	0.235071	0.117535	+	0.993069i	$0.462501\pi$
$224$	2.88747	0.192927
$225$	−3.50243	−0.233495
$226$	29.4000	1.95566
$227$	−10.1180	−0.671558	−0.335779	−	0.941941i	$-0.609000\pi$
$227$	−10.1180	−0.671558	−0.335779	+	0.941941i	$0.609000\pi$
$228$	−18.8171	−1.24620
$229$	−4.02412	−0.265921	−0.132961	−	0.991121i	$-0.542448\pi$
$229$	−4.02412	−0.265921	−0.132961	+	0.991121i	$0.542448\pi$
$230$	−5.23346	−0.345084
$231$	0.843753	0.0555149
$232$	3.19793	0.209954
$233$	−12.0153	−0.787146	−0.393573	−	0.919293i	$-0.628761\pi$
$233$	−12.0153	−0.787146	−0.393573	+	0.919293i	$0.628761\pi$
$234$	2.86229	0.187114
$235$	−1.36231	−0.0888675
$236$	17.2285	1.12148
$237$	−17.9127	−1.16355
$238$	−0.802236	−0.0520012
$239$	−24.6458	−1.59420	−0.797101	−	0.603846i	$-0.793634\pi$
$239$	−24.6458	−1.59420	−0.797101	+	0.603846i	$0.793634\pi$
$240$	−3.82221	−0.246723
$241$	13.4443	0.866025	0.433012	−	0.901388i	$-0.357451\pi$
$241$	13.4443	0.866025	0.433012	+	0.901388i	$0.357451\pi$
$242$	−1.83493	−0.117954
$243$	−7.37622	−0.473185
$244$	7.02450	0.449698
$245$	−2.77168	−0.177076
$246$	−28.0052	−1.78555
$247$	15.3573	0.977161
$248$	−0.724507	−0.0460062
$249$	−9.62565	−0.610001
$250$	7.34568	0.464582
$251$	−27.4680	−1.73376	−0.866881	−	0.498515i	$-0.833879\pi$
$251$	−27.4680	−1.73376	−0.866881	+	0.498515i	$0.833879\pi$
$252$	0.432992	0.0272759
$253$	7.00647	0.440493
$254$	24.1396	1.51465
$255$	0.785602	0.0491963
$256$	20.9730	1.31081
$257$	−6.05139	−0.377475	−0.188738	−	0.982028i	$-0.560440\pi$
$257$	−6.05139	−0.377475	−0.188738	+	0.982028i	$0.560440\pi$
$258$	3.54123	0.220467
$259$	−1.75788	−0.109230
$260$	−1.19808	−0.0743021
$261$	1.99465	0.123466
$262$	22.2123	1.37228
$263$	18.9723	1.16988	0.584941	−	0.811076i	$-0.301118\pi$
$263$	18.9723	1.16988	0.584941	+	0.811076i	$0.301118\pi$
$264$	2.24167	0.137965
$265$	5.48005	0.336637
$266$	5.72216	0.350848
$267$	−11.7345	−0.718142
$268$	−15.4939	−0.946442
$269$	27.7161	1.68988	0.844941	−	0.534859i	$-0.179635\pi$
$269$	27.7161	1.68988	0.844941	+	0.534859i	$0.179635\pi$
$270$	3.28020	0.199627
$271$	14.3035	0.868876	0.434438	−	0.900702i	$-0.356947\pi$
$271$	14.3035	0.868876	0.434438	+	0.900702i	$0.356947\pi$
$272$	−4.86533	−0.295004
$273$	−1.81665	−0.109949
$274$	14.9042	0.900397
$275$	−4.83429	−0.291519
$276$	18.4840	1.11260
$277$	−22.8566	−1.37332	−0.686661	−	0.726978i	$-0.740924\pi$
$277$	−22.8566	−1.37332	−0.686661	+	0.726978i	$0.740924\pi$
$278$	28.6402	1.71773
$279$	−0.451898	−0.0270544
$280$	0.206723	0.0123541
$281$	2.90946	0.173564	0.0867820	−	0.996227i	$-0.472342\pi$
$281$	2.90946	0.173564	0.0867820	+	0.996227i	$0.472342\pi$
$282$	11.8512	0.705728
$283$	−7.55561	−0.449134	−0.224567	−	0.974459i	$-0.572097\pi$
$283$	−7.55561	−0.449134	−0.224567	+	0.974459i	$0.572097\pi$
$284$	−11.4474	−0.679276
$285$	−5.60351	−0.331923
$286$	3.95073	0.233611
$287$	3.45754	0.204092
$288$	4.78490	0.281953
$289$	1.00000	0.0588235
$290$	−2.05646	−0.120759
$291$	−12.1948	−0.714874
$292$	1.83175	0.107195
$293$	−23.4723	−1.37126	−0.685632	−	0.727948i	$-0.740474\pi$
$293$	−23.4723	−1.37126	−0.685632	+	0.727948i	$0.740474\pi$
$294$	24.1117	1.40622
$295$	5.13045	0.298706
$296$	−4.67032	−0.271457
$297$	−4.39148	−0.254820
$298$	−3.64716	−0.211274
$299$	−15.0854	−0.872410
$300$	−12.7535	−0.736323
$301$	−0.437202	−0.0251999
$302$	29.2813	1.68495
$303$	−9.96458	−0.572450
$304$	34.7032	1.99037
$305$	2.09181	0.119777
$306$	−1.32940	−0.0759969
$307$	−0.263289	−0.0150267	−0.00751334	−	0.999972i	$-0.502392\pi$
$307$	−0.263289	−0.0150267	−0.00751334	+	0.999972i	$0.502392\pi$
$308$	0.597645	0.0340540
$309$	23.8879	1.35893
$310$	0.465901	0.0264614
$311$	29.8883	1.69481	0.847406	−	0.530945i	$-0.178163\pi$
$311$	29.8883	1.69481	0.847406	+	0.530945i	$0.178163\pi$
$312$	−4.82646	−0.273245
$313$	−28.2844	−1.59873	−0.799364	−	0.600847i	$-0.794830\pi$
$313$	−28.2844	−1.59873	−0.799364	+	0.600847i	$0.794830\pi$
$314$	13.7378	0.775267
$315$	0.128940	0.00726493
$316$	−12.6879	−0.713749
$317$	−13.6803	−0.768363	−0.384182	−	0.923258i	$-0.625516\pi$
$317$	−13.6803	−0.768363	−0.384182	+	0.923258i	$0.625516\pi$
$318$	−47.6727	−2.67335
$319$	2.75316	0.154147
$320$	−0.972109	−0.0543425
$321$	18.5218	1.03378
$322$	−5.62084	−0.313237
$323$	−7.13276	−0.396878
$324$	−14.5564	−0.808689
$325$	10.4085	0.577362
$326$	28.6302	1.58568
$327$	28.5783	1.58038
$328$	9.18593	0.507208
$329$	−1.46315	−0.0806662
$330$	−1.44153	−0.0793535
$331$	−23.5840	−1.29630	−0.648148	−	0.761514i	$-0.724456\pi$
$331$	−23.5840	−1.29630	−0.648148	+	0.761514i	$0.724456\pi$
$332$	−6.81802	−0.374187
$333$	−2.91303	−0.159633
$334$	−19.6586	−1.07567
$335$	−4.61390	−0.252084
$336$	−4.10513	−0.223953
$337$	−5.85444	−0.318911	−0.159456	−	0.987205i	$-0.550974\pi$
$337$	−5.85444	−0.318911	−0.159456	+	0.987205i	$0.550974\pi$
$338$	15.3480	0.834819
$339$	−30.9215	−1.67942
$340$	0.556456	0.0301781
$341$	−0.623741	−0.0337775
$342$	9.48231	0.512745
$343$	−6.03725	−0.325981
$344$	−1.16155	−0.0626266
$345$	5.50430	0.296342
$346$	−36.2931	−1.95113
$347$	−2.70484	−0.145203	−0.0726017	−	0.997361i	$-0.523130\pi$
$347$	−2.70484	−0.145203	−0.0726017	+	0.997361i	$0.523130\pi$
$348$	7.26317	0.389347
$349$	−10.3657	−0.554861	−0.277430	−	0.960746i	$-0.589483\pi$
$349$	−10.3657	−0.554861	−0.277430	+	0.960746i	$0.589483\pi$
$350$	3.87824	0.207301
$351$	9.45514	0.504678
$352$	6.60445	0.352018
$353$	−10.0321	−0.533955	−0.266977	−	0.963703i	$-0.586025\pi$
$353$	−10.0321	−0.533955	−0.266977	+	0.963703i	$0.586025\pi$
$354$	−44.6314	−2.37213
$355$	−3.40888	−0.180925
$356$	−8.31178	−0.440523
$357$	0.843753	0.0446562
$358$	28.6572	1.51458
$359$	22.1632	1.16973	0.584864	−	0.811132i	$-0.301148\pi$
$359$	22.1632	1.16973	0.584864	+	0.811132i	$0.301148\pi$
$360$	0.342565	0.0180548
$361$	31.8763	1.67770
$362$	7.90133	0.415285
$363$	1.92990	0.101293
$364$	−1.28677	−0.0674450
$365$	0.545474	0.0285514
$366$	−18.1973	−0.951190
$367$	9.46977	0.494318	0.247159	−	0.968975i	$-0.420503\pi$
$367$	9.46977	0.494318	0.247159	+	0.968975i	$0.420503\pi$
$368$	−34.0888	−1.77700
$369$	5.72956	0.298269
$370$	3.00329	0.156134
$371$	5.88569	0.305570
$372$	−1.64551	−0.0853156
$373$	−1.82291	−0.0943869	−0.0471934	−	0.998886i	$-0.515028\pi$
$373$	−1.82291	−0.0943869	−0.0471934	+	0.998886i	$0.515028\pi$
$374$	−1.83493	−0.0948821
$375$	−7.72584	−0.398961
$376$	−3.88728	−0.200471
$377$	−5.92772	−0.305293
$378$	3.52300	0.181204
$379$	6.44415	0.331014	0.165507	−	0.986209i	$-0.447074\pi$
$379$	6.44415	0.331014	0.165507	+	0.986209i	$0.447074\pi$
$380$	−3.96907	−0.203609
$381$	−25.3889	−1.30071
$382$	12.1281	0.620525
$383$	−35.5814	−1.81812	−0.909061	−	0.416662i	$-0.863200\pi$
$383$	−35.5814	−1.81812	−0.909061	+	0.416662i	$0.863200\pi$
$384$	−17.0351	−0.869319
$385$	0.177972	0.00907027
$386$	−24.1699	−1.23021
$387$	−0.724496	−0.0368282
$388$	−8.63782	−0.438519
$389$	−15.2140	−0.771379	−0.385689	−	0.922629i	$-0.626036\pi$
$389$	−15.2140	−0.771379	−0.385689	+	0.922629i	$0.626036\pi$
$390$	3.10370	0.157162
$391$	7.00647	0.354333
$392$	−7.90883	−0.399456
$393$	−23.3619	−1.17845
$394$	−5.27767	−0.265885
$395$	−3.77830	−0.190107
$396$	0.990371	0.0497680
$397$	−31.5290	−1.58239	−0.791196	−	0.611562i	$-0.790541\pi$
$397$	−31.5290	−1.58239	−0.791196	+	0.611562i	$0.790541\pi$
$398$	−15.2464	−0.764231
$399$	−6.01829	−0.301291
$400$	23.5204	1.17602
$401$	24.0544	1.20122	0.600609	−	0.799543i	$-0.294925\pi$
$401$	24.0544	1.20122	0.600609	+	0.799543i	$0.294925\pi$
$402$	40.1378	2.00189
$403$	1.34295	0.0668973
$404$	−7.05809	−0.351153
$405$	−4.33472	−0.215394
$406$	−2.20868	−0.109615
$407$	−4.02076	−0.199302
$408$	2.24167	0.110979
$409$	−3.37119	−0.166695	−0.0833473	−	0.996521i	$-0.526561\pi$
$409$	−3.37119	−0.166695	−0.0833473	+	0.996521i	$0.526561\pi$
$410$	−5.90710	−0.291731
$411$	−15.6755	−0.773218
$412$	16.9202	0.833599
$413$	5.51021	0.271140
$414$	−9.31442	−0.457779
$415$	−2.03032	−0.0996646
$416$	−14.2198	−0.697183
$417$	−30.1224	−1.47510
$418$	13.0881	0.640162
$419$	11.3816	0.556029	0.278014	−	0.960577i	$-0.410324\pi$
$419$	11.3816	0.556029	0.278014	+	0.960577i	$0.410324\pi$
$420$	0.469511	0.0229098
$421$	2.33845	0.113969	0.0569844	−	0.998375i	$-0.481851\pi$
$421$	2.33845	0.113969	0.0569844	+	0.998375i	$0.481851\pi$
$422$	−15.6305	−0.760882
$423$	−2.42462	−0.117889
$424$	15.6370	0.759401
$425$	−4.83429	−0.234498
$426$	29.6550	1.43679
$427$	2.24665	0.108723
$428$	13.1193	0.634145
$429$	−4.15519	−0.200614
$430$	0.746946	0.0360209
$431$	−24.1845	−1.16493	−0.582464	−	0.812856i	$-0.697911\pi$
$431$	−24.1845	−1.16493	−0.582464	+	0.812856i	$0.697911\pi$
$432$	21.3660	1.02797
$433$	20.5991	0.989929	0.494965	−	0.868913i	$-0.335181\pi$
$433$	20.5991	0.989929	0.494965	+	0.868913i	$0.335181\pi$
$434$	0.500387	0.0240193
$435$	2.16288	0.103702
$436$	20.2425	0.969440
$437$	−49.9755	−2.39065
$438$	−4.74525	−0.226737
$439$	7.47985	0.356994	0.178497	−	0.983940i	$-0.442877\pi$
$439$	7.47985	0.356994	0.178497	+	0.983940i	$0.442877\pi$
$440$	0.472832	0.0225414
$441$	−4.93299	−0.234904
$442$	3.95073	0.187917
$443$	−29.2587	−1.39012	−0.695062	−	0.718950i	$-0.744623\pi$
$443$	−29.2587	−1.39012	−0.695062	+	0.718950i	$0.744623\pi$
$444$	−10.6073	−0.503399
$445$	−2.47515	−0.117333
$446$	−6.44126	−0.305002
$447$	3.83591	0.181432
$448$	−1.04407	−0.0493275
$449$	21.3644	1.00825	0.504125	−	0.863631i	$-0.331815\pi$
$449$	21.3644	1.00825	0.504125	+	0.863631i	$0.331815\pi$
$450$	6.42672	0.302959
$451$	7.90834	0.372389
$452$	−21.9022	−1.03019
$453$	−30.7966	−1.44695
$454$	18.5659	0.871342
$455$	−0.383184	−0.0179639
$456$	−15.9893	−0.748768
$457$	−6.59312	−0.308413	−0.154207	−	0.988039i	$-0.549282\pi$
$457$	−6.59312	−0.308413	−0.154207	+	0.988039i	$0.549282\pi$
$458$	7.38399	0.345031
$459$	−4.39148	−0.204977
$460$	3.89879	0.181782
$461$	36.6634	1.70758	0.853792	−	0.520614i	$-0.174297\pi$
$461$	36.6634	1.70758	0.853792	+	0.520614i	$0.174297\pi$
$462$	−1.54823	−0.0720302
$463$	−3.57563	−0.166174	−0.0830868	−	0.996542i	$-0.526478\pi$
$463$	−3.57563	−0.166174	−0.0830868	+	0.996542i	$0.526478\pi$
$464$	−13.3950	−0.621847
$465$	−0.490012	−0.0227238
$466$	22.0472	1.02132
$467$	−35.3521	−1.63590	−0.817949	−	0.575290i	$-0.804889\pi$
$467$	−35.3521	−1.63590	−0.817949	+	0.575290i	$0.804889\pi$
$468$	−2.13233	−0.0985671
$469$	−4.95543	−0.228820
$470$	2.49975	0.115305
$471$	−14.4487	−0.665763
$472$	14.6395	0.673835
$473$	−1.00000	−0.0459800
$474$	32.8686	1.50970
$475$	34.4819	1.58214
$476$	0.597645	0.0273930
$477$	9.75331	0.446574
$478$	45.2233	2.06847
$479$	−28.8661	−1.31893	−0.659463	−	0.751737i	$-0.729216\pi$
$479$	−28.8661	−1.31893	−0.659463	+	0.751737i	$0.729216\pi$
$480$	5.18847	0.236820
$481$	8.65696	0.394723
$482$	−24.6694	−1.12366
$483$	5.91174	0.268993
$484$	1.36698	0.0621354
$485$	−2.57224	−0.116799
$486$	13.5349	0.613954
$487$	−10.3979	−0.471173	−0.235586	−	0.971853i	$-0.575701\pi$
$487$	−10.3979	−0.471173	−0.235586	+	0.971853i	$0.575701\pi$
$488$	5.96887	0.270198
$489$	−30.1119	−1.36171
$490$	5.08585	0.229755
$491$	38.6299	1.74334	0.871672	−	0.490089i	$-0.163036\pi$
$491$	38.6299	1.74334	0.871672	+	0.490089i	$0.163036\pi$
$492$	20.8632	0.940585
$493$	2.75316	0.123996
$494$	−28.1796	−1.26786
$495$	0.294921	0.0132557
$496$	3.03470	0.136262
$497$	−3.66121	−0.164228
$498$	17.6624	0.791472
$499$	−26.6934	−1.19496	−0.597481	−	0.801883i	$-0.703832\pi$
$499$	−26.6934	−1.19496	−0.597481	+	0.801883i	$0.703832\pi$
$500$	−5.47235	−0.244731
$501$	20.6760	0.923735
$502$	50.4019	2.24954
$503$	5.57649	0.248643	0.124322	−	0.992242i	$-0.460325\pi$
$503$	5.57649	0.248643	0.124322	+	0.992242i	$0.460325\pi$
$504$	0.367922	0.0163886
$505$	−2.10181	−0.0935294
$506$	−12.8564	−0.571537
$507$	−16.1423	−0.716903
$508$	−17.9834	−0.797884
$509$	−35.7475	−1.58448	−0.792241	−	0.610209i	$-0.791086\pi$
$509$	−35.7475	−1.58448	−0.792241	+	0.610209i	$0.791086\pi$
$510$	−1.44153	−0.0638319
$511$	0.585850	0.0259165
$512$	−20.8301	−0.920571
$513$	31.3234	1.38296
$514$	11.1039	0.489772
$515$	5.03863	0.222029
$516$	−2.63813	−0.116137
$517$	−3.34663	−0.147185
$518$	3.22560	0.141725
$519$	38.1714	1.67554
$520$	−1.01804	−0.0446439
$521$	20.8142	0.911886	0.455943	−	0.890009i	$-0.349302\pi$
$521$	20.8142	0.911886	0.455943	+	0.890009i	$0.349302\pi$
$522$	−3.66005	−0.160196
$523$	29.8331	1.30451	0.652256	−	0.757999i	$-0.273823\pi$
$523$	29.8331	1.30451	0.652256	+	0.757999i	$0.273823\pi$
$524$	−16.5476	−0.722887
$525$	−4.07895	−0.178020
$526$	−34.8129	−1.51791
$527$	−0.623741	−0.0271706
$528$	−9.38957	−0.408629
$529$	26.0907	1.13438
$530$	−10.0555	−0.436784
$531$	9.13109	0.396256
$532$	−4.26286	−0.184819
$533$	−17.0272	−0.737528
$534$	21.5321	0.931784
$535$	3.90677	0.168904
$536$	−13.1655	−0.568663
$537$	−30.1403	−1.30065
$538$	−50.8572	−2.19261
$539$	−6.80885	−0.293278
$540$	−2.44367	−0.105159
$541$	29.9454	1.28745	0.643726	−	0.765256i	$-0.277387\pi$
$541$	29.9454	1.28745	0.643726	+	0.765256i	$0.277387\pi$
$542$	−26.2460	−1.12736
$543$	−8.31025	−0.356627
$544$	6.60445	0.283163
$545$	6.02797	0.258210
$546$	3.33344	0.142658
$547$	41.7537	1.78526	0.892631	−	0.450789i	$-0.148857\pi$
$547$	41.7537	1.78526	0.892631	+	0.450789i	$0.148857\pi$
$548$	−11.1033	−0.474308
$549$	3.72297	0.158893
$550$	8.87061	0.378244
$551$	−19.6376	−0.836590
$552$	15.7062	0.668501
$553$	−4.05797	−0.172562
$554$	41.9404	1.78188
$555$	−3.15872	−0.134080
$556$	−21.3362	−0.904859
$557$	7.51606	0.318466	0.159233	−	0.987241i	$-0.449098\pi$
$557$	7.51606	0.318466	0.159233	+	0.987241i	$0.449098\pi$
$558$	0.829202	0.0351029
$559$	2.15306	0.0910649
$560$	−0.865890	−0.0365905
$561$	1.92990	0.0814802
$562$	−5.33867	−0.225198
$563$	28.1342	1.18572	0.592858	−	0.805307i	$-0.297999\pi$
$563$	28.1342	1.18572	0.592858	+	0.805307i	$0.297999\pi$
$564$	−8.82884	−0.371761
$565$	−6.52222	−0.274392
$566$	13.8640	0.582749
$567$	−4.65558	−0.195516
$568$	−9.72706	−0.408138
$569$	30.7606	1.28955	0.644776	−	0.764372i	$-0.276951\pi$
$569$	30.7606	1.28955	0.644776	+	0.764372i	$0.276951\pi$
$570$	10.2821	0.430669
$571$	−8.49751	−0.355610	−0.177805	−	0.984066i	$-0.556900\pi$
$571$	−8.49751	−0.355610	−0.177805	+	0.984066i	$0.556900\pi$
$572$	−2.94319	−0.123061
$573$	−12.7557	−0.532877
$574$	−6.34435	−0.264808
$575$	−33.8714	−1.41253
$576$	−1.73014	−0.0720893
$577$	0.833991	0.0347195	0.0173597	−	0.999849i	$-0.494474\pi$
$577$	0.833991	0.0347195	0.0173597	+	0.999849i	$0.494474\pi$
$578$	−1.83493	−0.0763232
$579$	25.4207	1.05645
$580$	1.53201	0.0636132
$581$	−2.18061	−0.0904669
$582$	22.3767	0.927544
$583$	13.4622	0.557547
$584$	1.55648	0.0644075
$585$	−0.634983	−0.0262533
$586$	43.0700	1.77921
$587$	46.2948	1.91079	0.955394	−	0.295333i	$-0.0954305\pi$
$587$	46.2948	1.91079	0.955394	+	0.295333i	$0.0954305\pi$
$588$	−17.9626	−0.740766
$589$	4.44899	0.183318
$590$	−9.41403	−0.387570
$591$	5.55080	0.228330
$592$	19.5623	0.804007
$593$	−6.53394	−0.268317	−0.134158	−	0.990960i	$-0.542833\pi$
$593$	−6.53394	−0.268317	−0.134158	+	0.990960i	$0.542833\pi$
$594$	8.05808	0.330627
$595$	0.177972	0.00729612
$596$	2.71705	0.111295
$597$	16.0354	0.656285
$598$	27.6807	1.13195
$599$	37.4600	1.53057	0.765287	−	0.643689i	$-0.222597\pi$
$599$	37.4600	1.53057	0.765287	+	0.643689i	$0.222597\pi$
$600$	−10.8369	−0.442415
$601$	−40.8371	−1.66578	−0.832890	−	0.553439i	$-0.813315\pi$
$601$	−40.8371	−1.66578	−0.832890	+	0.553439i	$0.813315\pi$
$602$	0.802236	0.0326967
$603$	−8.21175	−0.334408
$604$	−21.8138	−0.887591
$605$	0.407070	0.0165497
$606$	18.2843	0.742750
$607$	−11.0263	−0.447545	−0.223772	−	0.974641i	$-0.571837\pi$
$607$	−11.0263	−0.447545	−0.223772	+	0.974641i	$0.571837\pi$
$608$	−47.1079	−1.91048
$609$	2.32298	0.0941321
$610$	−3.83833	−0.155410
$611$	7.20551	0.291504
$612$	0.990371	0.0400334
$613$	−34.9769	−1.41270	−0.706352	−	0.707861i	$-0.749660\pi$
$613$	−34.9769	−1.41270	−0.706352	+	0.707861i	$0.749660\pi$
$614$	0.483117	0.0194970
$615$	6.21281	0.250525
$616$	0.507832	0.0204611
$617$	2.88734	0.116240	0.0581200	−	0.998310i	$-0.481489\pi$
$617$	2.88734	0.116240	0.0581200	+	0.998310i	$0.481489\pi$
$618$	−43.8327	−1.76321
$619$	−29.8001	−1.19777	−0.598883	−	0.800836i	$-0.704389\pi$
$619$	−29.8001	−1.19777	−0.598883	+	0.800836i	$0.704389\pi$
$620$	−0.347084	−0.0139392
$621$	−30.7688	−1.23471
$622$	−54.8431	−2.19901
$623$	−2.65836	−0.106505
$624$	20.2163	0.809301
$625$	22.5419	0.901675
$626$	51.8999	2.07434
$627$	−13.7655	−0.549741
$628$	−10.2343	−0.408393
$629$	−4.02076	−0.160318
$630$	−0.236596	−0.00942620
$631$	16.6127	0.661340	0.330670	−	0.943746i	$-0.392725\pi$
$631$	16.6127	0.661340	0.330670	+	0.943746i	$0.392725\pi$
$632$	−10.7812	−0.428851
$633$	16.4394	0.653409
$634$	25.1025	0.996946
$635$	−5.35524	−0.212516
$636$	35.5150	1.40826
$637$	14.6599	0.580846
$638$	−5.05186	−0.200005
$639$	−6.06708	−0.240010
$640$	−3.59319	−0.142033
$641$	8.81644	0.348228	0.174114	−	0.984725i	$-0.444294\pi$
$641$	8.81644	0.348228	0.174114	+	0.984725i	$0.444294\pi$
$642$	−33.9862	−1.34133
$643$	−24.9623	−0.984416	−0.492208	−	0.870478i	$-0.663810\pi$
$643$	−24.9623	−0.984416	−0.492208	+	0.870478i	$0.663810\pi$
$644$	4.18739	0.165006
$645$	−0.785602	−0.0309331
$646$	13.0881	0.514946
$647$	−3.75849	−0.147761	−0.0738807	−	0.997267i	$-0.523538\pi$
$647$	−3.75849	−0.147761	−0.0738807	+	0.997267i	$0.523538\pi$
$648$	−12.3689	−0.485896
$649$	12.6034	0.494725
$650$	−19.0990	−0.749124
$651$	−0.526283	−0.0206267
$652$	−21.3288	−0.835300
$653$	25.7994	1.00961	0.504804	−	0.863234i	$-0.331565\pi$
$653$	25.7994	1.00961	0.504804	+	0.863234i	$0.331565\pi$
$654$	−52.4392	−2.05054
$655$	−4.92768	−0.192540
$656$	−38.4766	−1.50226
$657$	0.970825	0.0378755
$658$	2.68479	0.104664
$659$	16.2828	0.634289	0.317144	−	0.948377i	$-0.397276\pi$
$659$	16.2828	0.634289	0.317144	+	0.948377i	$0.397276\pi$
$660$	1.07390	0.0418016
$661$	−33.1027	−1.28755	−0.643773	−	0.765216i	$-0.722632\pi$
$661$	−33.1027	−1.28755	−0.643773	+	0.765216i	$0.722632\pi$
$662$	43.2751	1.68194
$663$	−4.15519	−0.161374
$664$	−5.79341	−0.224828
$665$	−1.26943	−0.0492263
$666$	5.34521	0.207123
$667$	19.2899	0.746909
$668$	14.6452	0.566639
$669$	6.77461	0.261922
$670$	8.46620	0.327078
$671$	5.13870	0.198377
$672$	5.57252	0.214965
$673$	−29.6227	−1.14187	−0.570935	−	0.820995i	$-0.693419\pi$
$673$	−29.6227	−1.14187	−0.570935	+	0.820995i	$0.693419\pi$
$674$	10.7425	0.413786
$675$	21.2297	0.817133
$676$	−11.4338	−0.439763
$677$	−29.7859	−1.14476	−0.572382	−	0.819987i	$-0.693981\pi$
$677$	−29.7859	−1.14476	−0.572382	+	0.819987i	$0.693981\pi$
$678$	56.7388	2.17904
$679$	−2.76264	−0.106020
$680$	0.472832	0.0181323
$681$	−19.5268	−0.748267
$682$	1.14452	0.0438260
$683$	8.83755	0.338159	0.169080	−	0.985602i	$-0.445920\pi$
$683$	8.83755	0.338159	0.169080	+	0.985602i	$0.445920\pi$
$684$	−7.06408	−0.270102
$685$	−3.30642	−0.126332
$686$	11.0780	0.422958
$687$	−7.76613	−0.296296
$688$	4.86533	0.185489
$689$	−28.9850	−1.10424
$690$	−10.1000	−0.384501
$691$	−42.4768	−1.61589	−0.807947	−	0.589255i	$-0.799421\pi$
$691$	−42.4768	−1.61589	−0.807947	+	0.589255i	$0.799421\pi$
$692$	27.0375	1.02781
$693$	0.316751	0.0120324
$694$	4.96320	0.188400
$695$	−6.35368	−0.241009
$696$	6.17167	0.233937
$697$	7.90834	0.299550
$698$	19.0203	0.719928
$699$	−23.1882	−0.877058
$700$	−2.88919	−0.109201
$701$	−10.2676	−0.387801	−0.193900	−	0.981021i	$-0.562114\pi$
$701$	−10.2676	−0.387801	−0.193900	+	0.981021i	$0.562114\pi$
$702$	−17.3496	−0.654817
$703$	28.6792	1.08165
$704$	−2.38806	−0.0900036
$705$	−2.62912	−0.0990184
$706$	18.4082	0.692803
$707$	−2.25739	−0.0848979
$708$	33.2493	1.24958
$709$	44.7461	1.68047	0.840237	−	0.542219i	$-0.182416\pi$
$709$	44.7461	1.68047	0.840237	+	0.542219i	$0.182416\pi$
$710$	6.25507	0.234749
$711$	−6.72455	−0.252190
$712$	−7.06269	−0.264686
$713$	−4.37022	−0.163666
$714$	−1.54823	−0.0579411
$715$	−0.876447	−0.0327773
$716$	−21.3489	−0.797846
$717$	−47.5637	−1.77630
$718$	−40.6679	−1.51771
$719$	45.4579	1.69529	0.847646	−	0.530562i	$-0.178019\pi$
$719$	45.4579	1.69529	0.847646	+	0.530562i	$0.178019\pi$
$720$	−1.43488	−0.0534750
$721$	5.41160	0.201538
$722$	−58.4909	−2.17681
$723$	25.9461	0.964947
$724$	−5.88630	−0.218762
$725$	−13.3096	−0.494305
$726$	−3.54123	−0.131427
$727$	−33.0073	−1.22417	−0.612086	−	0.790791i	$-0.709670\pi$
$727$	−33.0073	−1.22417	−0.612086	+	0.790791i	$0.709670\pi$
$728$	−1.09339	−0.0405239
$729$	17.7104	0.655942
$730$	−1.00091	−0.0370452
$731$	−1.00000	−0.0369863
$732$	13.5566	0.501065
$733$	41.7568	1.54232	0.771162	−	0.636639i	$-0.219676\pi$
$733$	41.7568	1.54232	0.771162	+	0.636639i	$0.219676\pi$
$734$	−17.3764	−0.641374
$735$	−5.34905	−0.197303
$736$	46.2739	1.70568
$737$	−11.3344	−0.417509
$738$	−10.5134	−0.387002
$739$	12.0248	0.442339	0.221170	−	0.975235i	$-0.429013\pi$
$739$	12.0248	0.442339	0.221170	+	0.975235i	$0.429013\pi$
$740$	−2.23738	−0.0822476
$741$	29.6380	1.08878
$742$	−10.7999	−0.396475
$743$	17.3715	0.637300	0.318650	−	0.947872i	$-0.396771\pi$
$743$	17.3715	0.637300	0.318650	+	0.947872i	$0.396771\pi$
$744$	−1.39822	−0.0512613
$745$	0.809103	0.0296432
$746$	3.34492	0.122466
$747$	−3.61354	−0.132212
$748$	1.36698	0.0499817
$749$	4.19595	0.153317
$750$	14.1764	0.517649
$751$	26.9212	0.982368	0.491184	−	0.871056i	$-0.336564\pi$
$751$	26.9212	0.982368	0.491184	+	0.871056i	$0.336564\pi$
$752$	16.2825	0.593760
$753$	−53.0103	−1.93180
$754$	10.8770	0.396116
$755$	−6.49589	−0.236410
$756$	−2.62455	−0.0954540
$757$	−21.4461	−0.779471	−0.389735	−	0.920927i	$-0.627434\pi$
$757$	−21.4461	−0.779471	−0.389735	+	0.920927i	$0.627434\pi$
$758$	−11.8246	−0.429488
$759$	13.5218	0.490809
$760$	−3.37260	−0.122337
$761$	27.7694	1.00664	0.503320	−	0.864100i	$-0.332112\pi$
$761$	27.7694	1.00664	0.503320	+	0.864100i	$0.332112\pi$
$762$	46.5869	1.68767
$763$	6.47417	0.234381
$764$	−9.03509	−0.326878
$765$	0.294921	0.0106629
$766$	65.2894	2.35900
$767$	−27.1359	−0.979819
$768$	40.4757	1.46054
$769$	−32.5886	−1.17518	−0.587588	−	0.809160i	$-0.699922\pi$
$769$	−32.5886	−1.17518	−0.587588	+	0.809160i	$0.699922\pi$
$770$	−0.326566	−0.0117686
$771$	−11.6786	−0.420593
$772$	18.0059	0.648048
$773$	22.1704	0.797415	0.398708	−	0.917078i	$-0.369459\pi$
$773$	22.1704	0.797415	0.398708	+	0.917078i	$0.369459\pi$
$774$	1.32940	0.0477844
$775$	3.01535	0.108314
$776$	−7.33973	−0.263481
$777$	−3.39253	−0.121706
$778$	27.9166	1.00086
$779$	−56.4083	−2.02104
$780$	−2.31218	−0.0827893
$781$	−8.37420	−0.299652
$782$	−12.8564	−0.459744
$783$	−12.0904	−0.432077
$784$	33.1273	1.18312
$785$	−3.04765	−0.108775
$786$	42.8675	1.52903
$787$	5.91482	0.210841	0.105420	−	0.994428i	$-0.466381\pi$
$787$	5.91482	0.210841	0.105420	+	0.994428i	$0.466381\pi$
$788$	3.93173	0.140062
$789$	36.6145	1.30351
$790$	6.93292	0.246662
$791$	−7.00500	−0.249069
$792$	0.841539	0.0299028
$793$	−11.0640	−0.392893
$794$	57.8535	2.05314
$795$	10.5759	0.375090
$796$	11.3582	0.402579
$797$	15.8372	0.560982	0.280491	−	0.959857i	$-0.409503\pi$
$797$	15.8372	0.560982	0.280491	+	0.959857i	$0.409503\pi$
$798$	11.0432	0.390924
$799$	−3.34663	−0.118395
$800$	−31.9278	−1.12882
$801$	−4.40523	−0.155651
$802$	−44.1382	−1.55857
$803$	1.34000	0.0472876
$804$	−29.9017	−1.05455
$805$	1.24695	0.0439493
$806$	−2.46423	−0.0867988
$807$	53.4892	1.88291
$808$	−5.99740	−0.210988
$809$	−34.0304	−1.19644	−0.598222	−	0.801330i	$-0.704126\pi$
$809$	−34.0304	−1.19644	−0.598222	+	0.801330i	$0.704126\pi$
$810$	7.95392	0.279472
$811$	15.2127	0.534192	0.267096	−	0.963670i	$-0.413936\pi$
$811$	15.2127	0.534192	0.267096	+	0.963670i	$0.413936\pi$
$812$	1.64541	0.0577426
$813$	27.6043	0.968124
$814$	7.37783	0.258593
$815$	−6.35146	−0.222482
$816$	−9.38957	−0.328701
$817$	7.13276	0.249544
$818$	6.18591	0.216285
$819$	−0.681985	−0.0238305
$820$	4.40064	0.153677
$821$	32.2632	1.12599	0.562997	−	0.826459i	$-0.309648\pi$
$821$	32.2632	1.12599	0.562997	+	0.826459i	$0.309648\pi$
$822$	28.7636	1.00325
$823$	−57.0337	−1.98807	−0.994035	−	0.109060i	$-0.965216\pi$
$823$	−57.0337	−1.98807	−0.994035	+	0.109060i	$0.965216\pi$
$824$	14.3775	0.500862
$825$	−9.32968	−0.324818
$826$	−10.1109	−0.351802
$827$	21.0748	0.732843	0.366421	−	0.930449i	$-0.380583\pi$
$827$	21.0748	0.732843	0.366421	+	0.930449i	$0.380583\pi$
$828$	6.93901	0.241147
$829$	−33.7257	−1.17134	−0.585670	−	0.810549i	$-0.699169\pi$
$829$	−33.7257	−1.17134	−0.585670	+	0.810549i	$0.699169\pi$
$830$	3.72551	0.129314
$831$	−44.1109	−1.53019
$832$	5.14165	0.178255
$833$	−6.80885	−0.235913
$834$	55.2726	1.91393
$835$	4.36115	0.150924
$836$	−9.75034	−0.337223
$837$	2.73915	0.0946788
$838$	−20.8845	−0.721444
$839$	−46.1785	−1.59426	−0.797129	−	0.603808i	$-0.793649\pi$
$839$	−46.1785	−1.59426	−0.797129	+	0.603808i	$0.793649\pi$
$840$	0.398954	0.0137652
$841$	−21.4201	−0.738625
$842$	−4.29089	−0.147874
$843$	5.61496	0.193389
$844$	11.6444	0.400815
$845$	−3.40486	−0.117131
$846$	4.44902	0.152960
$847$	0.437202	0.0150224
$848$	−65.4980	−2.24921
$849$	−14.5815	−0.500437
$850$	8.87061	0.304259
$851$	−28.1714	−0.965702
$852$	−22.0922	−0.756866
$853$	−27.5890	−0.944630	−0.472315	−	0.881430i	$-0.656582\pi$
$853$	−27.5890	−0.944630	−0.472315	+	0.881430i	$0.656582\pi$
$854$	−4.12245	−0.141067
$855$	−2.10360	−0.0719415
$856$	11.1477	0.381022
$857$	6.73065	0.229915	0.114957	−	0.993370i	$-0.463327\pi$
$857$	6.73065	0.229915	0.114957	+	0.993370i	$0.463327\pi$
$858$	7.62449	0.260296
$859$	−25.7040	−0.877008	−0.438504	−	0.898729i	$-0.644491\pi$
$859$	−25.7040	−0.877008	−0.438504	+	0.898729i	$0.644491\pi$
$860$	−0.556456	−0.0189750
$861$	6.67268	0.227404
$862$	44.3770	1.51149
$863$	44.5305	1.51583	0.757917	−	0.652350i	$-0.226217\pi$
$863$	44.5305	1.51583	0.757917	+	0.652350i	$0.226217\pi$
$864$	−29.0033	−0.986713
$865$	8.05143	0.273757
$866$	−37.7979	−1.28443
$867$	1.92990	0.0655427
$868$	−0.372776	−0.0126528
$869$	−9.28169	−0.314860
$870$	−3.96875	−0.134553
$871$	24.4037	0.826889
$872$	17.2005	0.582482
$873$	−4.57803	−0.154943
$874$	91.7017	3.10186
$875$	−1.75022	−0.0591684
$876$	3.53509	0.119440
$877$	−48.1784	−1.62687	−0.813434	−	0.581657i	$-0.802404\pi$
$877$	−48.1784	−1.62687	−0.813434	+	0.581657i	$0.802404\pi$
$878$	−13.7250	−0.463197
$879$	−45.2990	−1.52790
$880$	−1.98053	−0.0667636
$881$	−56.2174	−1.89401	−0.947006	−	0.321215i	$-0.895909\pi$
$881$	−56.2174	−1.89401	−0.947006	+	0.321215i	$0.895909\pi$
$882$	9.05171	0.304787
$883$	−12.1630	−0.409319	−0.204660	−	0.978833i	$-0.565609\pi$
$883$	−12.1630	−0.409319	−0.204660	+	0.978833i	$0.565609\pi$
$884$	−2.94319	−0.0989903
$885$	9.90123	0.332826
$886$	53.6878	1.80368
$887$	9.68336	0.325136	0.162568	−	0.986697i	$-0.448022\pi$
$887$	9.68336	0.325136	0.162568	+	0.986697i	$0.448022\pi$
$888$	−9.01323	−0.302464
$889$	−5.75164	−0.192904
$890$	4.54173	0.152239
$891$	−10.6486	−0.356741
$892$	4.79858	0.160668
$893$	23.8707	0.798803
$894$	−7.03864	−0.235407
$895$	−6.35744	−0.212506
$896$	−3.85916	−0.128925
$897$	−29.1132	−0.972062
$898$	−39.2023	−1.30820
$899$	−1.71726	−0.0572737
$900$	−4.78775	−0.159592
$901$	13.4622	0.448491
$902$	−14.5113	−0.483172
$903$	−0.843753	−0.0280783
$904$	−18.6108	−0.618985
$905$	−1.75287	−0.0582673
$906$	56.5098	1.87741
$907$	−15.1010	−0.501420	−0.250710	−	0.968062i	$-0.580664\pi$
$907$	−15.1010	−0.501420	−0.250710	+	0.968062i	$0.580664\pi$
$908$	−13.8312	−0.459003
$909$	−3.74077	−0.124074
$910$	0.703117	0.0233081
$911$	−43.3446	−1.43607	−0.718035	−	0.696007i	$-0.754958\pi$
$911$	−43.3446	−1.43607	−0.718035	+	0.696007i	$0.754958\pi$
$912$	66.9736	2.21772
$913$	−4.98765	−0.165067
$914$	12.0979	0.400164
$915$	4.03698	0.133458
$916$	−5.50089	−0.181754
$917$	−5.29244	−0.174772
$918$	8.05808	0.265956
$919$	−13.5086	−0.445609	−0.222804	−	0.974863i	$-0.571521\pi$
$919$	−13.5086	−0.445609	−0.222804	+	0.974863i	$0.571521\pi$
$920$	3.31289	0.109223
$921$	−0.508120	−0.0167431
$922$	−67.2749	−2.21558
$923$	18.0302	0.593471
$924$	1.15339	0.0379438
$925$	19.4376	0.639103
$926$	6.56104	0.215609
$927$	8.96768	0.294537
$928$	18.1831	0.596888
$929$	−43.2023	−1.41742	−0.708711	−	0.705499i	$-0.750723\pi$
$929$	−43.2023	−1.41742	−0.708711	+	0.705499i	$0.750723\pi$
$930$	0.899139	0.0294839
$931$	48.5659	1.59168
$932$	−16.4246	−0.538006
$933$	57.6814	1.88840
$934$	64.8687	2.12257
$935$	0.407070	0.0133126
$936$	−1.81189	−0.0592234
$937$	−25.6329	−0.837390	−0.418695	−	0.908127i	$-0.637512\pi$
$937$	−25.6329	−0.837390	−0.418695	+	0.908127i	$0.637512\pi$
$938$	9.09288	0.296893
$939$	−54.5859	−1.78134
$940$	−1.86225	−0.0607400
$941$	−33.5478	−1.09363	−0.546813	−	0.837255i	$-0.684159\pi$
$941$	−33.5478	−1.09363	−0.546813	+	0.837255i	$0.684159\pi$
$942$	26.5125	0.863823
$943$	55.4096	1.80438
$944$	−61.3195	−1.99578
$945$	−0.781559	−0.0254241
$946$	1.83493	0.0596588
$947$	17.7098	0.575492	0.287746	−	0.957707i	$-0.407094\pi$
$947$	17.7098	0.575492	0.287746	+	0.957707i	$0.407094\pi$
$948$	−24.4863	−0.795278
$949$	−2.88511	−0.0936545
$950$	−63.2719	−2.05281
$951$	−26.4016	−0.856130
$952$	0.507832	0.0164589
$953$	42.2445	1.36843	0.684217	−	0.729279i	$-0.260144\pi$
$953$	42.2445	1.36843	0.684217	+	0.729279i	$0.260144\pi$
$954$	−17.8967	−0.579426
$955$	−2.69054	−0.0870639
$956$	−33.6902	−1.08962
$957$	5.31330	0.171755
$958$	52.9673	1.71130
$959$	−3.55116	−0.114673
$960$	−1.87607	−0.0605498
$961$	−30.6109	−0.987450
$962$	−15.8849	−0.512151
$963$	6.95320	0.224064
$964$	18.3781	0.591919
$965$	5.36195	0.172607
$966$	−10.8476	−0.349017
$967$	−15.1444	−0.487011	−0.243505	−	0.969900i	$-0.578297\pi$
$967$	−15.1444	−0.487011	−0.243505	+	0.969900i	$0.578297\pi$
$968$	1.16155	0.0373337
$969$	−13.7655	−0.442211
$970$	4.71988	0.151546
$971$	−52.0050	−1.66892	−0.834460	−	0.551068i	$-0.814220\pi$
$971$	−52.0050	−1.66892	−0.834460	+	0.551068i	$0.814220\pi$
$972$	−10.0831	−0.323417
$973$	−6.82398	−0.218767
$974$	19.0794	0.611343
$975$	20.0874	0.643312
$976$	−25.0015	−0.800278
$977$	18.3179	0.586040	0.293020	−	0.956106i	$-0.405340\pi$
$977$	18.3179	0.586040	0.293020	+	0.956106i	$0.405340\pi$
$978$	55.2533	1.76681
$979$	−6.08040	−0.194330
$980$	−3.78883	−0.121030
$981$	10.7285	0.342534
$982$	−70.8834	−2.26198
$983$	−2.31929	−0.0739739	−0.0369870	−	0.999316i	$-0.511776\pi$
$983$	−2.31929	−0.0739739	−0.0369870	+	0.999316i	$0.511776\pi$
$984$	17.7279	0.565145
$985$	1.17082	0.0373055
$986$	−5.05186	−0.160884
$987$	−2.82373	−0.0898803
$988$	20.9931	0.667879
$989$	−7.00647	−0.222793
$990$	−0.541159	−0.0171992
$991$	−35.8490	−1.13878	−0.569391	−	0.822067i	$-0.692821\pi$
$991$	−35.8490	−1.13878	−0.569391	+	0.822067i	$0.692821\pi$
$992$	−4.11946	−0.130793
$993$	−45.5147	−1.44437
$994$	6.71808	0.213085
$995$	3.38232	0.107227
$996$	−13.1581	−0.416929
$997$	−38.3654	−1.21504	−0.607522	−	0.794303i	$-0.707837\pi$
$997$	−38.3654	−1.21504	−0.607522	+	0.794303i	$0.707837\pi$
$998$	48.9806	1.55045
$999$	17.6571	0.558647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.13	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.13	✓	60	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83493 q^{2} +1.92990 q^{3} +1.36698 q^{4} +0.407070 q^{5} -3.54123 q^{6} +0.437202 q^{7} +1.16155 q^{8} +0.724496 q^{9} +O(q^{10})\)	\(q-1.83493 q^{2} +1.92990 q^{3} +1.36698 q^{4} +0.407070 q^{5} -3.54123 q^{6} +0.437202 q^{7} +1.16155 q^{8} +0.724496 q^{9} -0.746946 q^{10} +1.00000 q^{11} +2.63813 q^{12} -2.15306 q^{13} -0.802236 q^{14} +0.785602 q^{15} -4.86533 q^{16} +1.00000 q^{17} -1.32940 q^{18} -7.13276 q^{19} +0.556456 q^{20} +0.843753 q^{21} -1.83493 q^{22} +7.00647 q^{23} +2.24167 q^{24} -4.83429 q^{25} +3.95073 q^{26} -4.39148 q^{27} +0.597645 q^{28} +2.75316 q^{29} -1.44153 q^{30} -0.623741 q^{31} +6.60445 q^{32} +1.92990 q^{33} -1.83493 q^{34} +0.177972 q^{35} +0.990371 q^{36} -4.02076 q^{37} +13.0881 q^{38} -4.15519 q^{39} +0.472832 q^{40} +7.90834 q^{41} -1.54823 q^{42} -1.00000 q^{43} +1.36698 q^{44} +0.294921 q^{45} -12.8564 q^{46} -3.34663 q^{47} -9.38957 q^{48} -6.80885 q^{49} +8.87061 q^{50} +1.92990 q^{51} -2.94319 q^{52} +13.4622 q^{53} +8.05808 q^{54} +0.407070 q^{55} +0.507832 q^{56} -13.7655 q^{57} -5.05186 q^{58} +12.6034 q^{59} +1.07390 q^{60} +5.13870 q^{61} +1.14452 q^{62} +0.316751 q^{63} -2.38806 q^{64} -0.876447 q^{65} -3.54123 q^{66} -11.3344 q^{67} +1.36698 q^{68} +13.5218 q^{69} -0.326566 q^{70} -8.37420 q^{71} +0.841539 q^{72} +1.34000 q^{73} +7.37783 q^{74} -9.32968 q^{75} -9.75034 q^{76} +0.437202 q^{77} +7.62449 q^{78} -9.28169 q^{79} -1.98053 q^{80} -10.6486 q^{81} -14.5113 q^{82} -4.98765 q^{83} +1.15339 q^{84} +0.407070 q^{85} +1.83493 q^{86} +5.31330 q^{87} +1.16155 q^{88} -6.08040 q^{89} -0.541159 q^{90} -0.941323 q^{91} +9.57771 q^{92} -1.20375 q^{93} +6.14084 q^{94} -2.90353 q^{95} +12.7459 q^{96} -6.31891 q^{97} +12.4938 q^{98} +0.724496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9} + q^{10} + 60 q^{11} - 13 q^{12} - 2 q^{13} - 15 q^{14} - 32 q^{15} + 21 q^{16} + 60 q^{17} - 41 q^{18} - 24 q^{19} - 33 q^{20} - 12 q^{21} - 9 q^{22} - 20 q^{23} + 9 q^{24} + 25 q^{25} - 40 q^{26} - 18 q^{27} - 3 q^{28} - 54 q^{29} - 18 q^{30} - 50 q^{31} - 51 q^{32} - 6 q^{33} - 9 q^{34} - 30 q^{35} + 27 q^{36} - 63 q^{37} - 38 q^{38} - 55 q^{39} - 5 q^{40} - 53 q^{41} - 47 q^{42} - 60 q^{43} + 43 q^{44} - 36 q^{45} - 27 q^{46} - 47 q^{47} - 38 q^{48} + 5 q^{49} - 4 q^{50} - 6 q^{51} - 13 q^{52} - 24 q^{53} - 58 q^{54} - 15 q^{55} - 45 q^{56} + 23 q^{57} + 16 q^{58} - 57 q^{59} - 4 q^{60} - 8 q^{61} - 3 q^{62} - 57 q^{63} - 5 q^{64} - 27 q^{65} - 4 q^{66} - 49 q^{67} + 43 q^{68} - 57 q^{69} - 7 q^{70} - 151 q^{71} - 29 q^{72} - 12 q^{73} + 18 q^{74} - 23 q^{75} - 38 q^{76} - 17 q^{77} + 37 q^{78} - 11 q^{79} - 21 q^{80} + 28 q^{81} + 44 q^{82} - 42 q^{83} + 16 q^{84} - 15 q^{85} + 9 q^{86} - 56 q^{87} - 21 q^{88} - 88 q^{89} + 47 q^{90} - 60 q^{91} + 26 q^{92} - 16 q^{93} + 37 q^{94} - 57 q^{95} + 108 q^{96} - 22 q^{97} + 8 q^{98} + 40 q^{99}+O(q^{100}) \) 60 * q - 9 * q^2 - 6 * q^3 + 43 * q^4 - 15 * q^5 - 4 * q^6 - 17 * q^7 - 21 * q^8 + 40 * q^9 + q^10 + 60 * q^11 - 13 * q^12 - 2 * q^13 - 15 * q^14 - 32 * q^15 + 21 * q^16 + 60 * q^17 - 41 * q^18 - 24 * q^19 - 33 * q^20 - 12 * q^21 - 9 * q^22 - 20 * q^23 + 9 * q^24 + 25 * q^25 - 40 * q^26 - 18 * q^27 - 3 * q^28 - 54 * q^29 - 18 * q^30 - 50 * q^31 - 51 * q^32 - 6 * q^33 - 9 * q^34 - 30 * q^35 + 27 * q^36 - 63 * q^37 - 38 * q^38 - 55 * q^39 - 5 * q^40 - 53 * q^41 - 47 * q^42 - 60 * q^43 + 43 * q^44 - 36 * q^45 - 27 * q^46 - 47 * q^47 - 38 * q^48 + 5 * q^49 - 4 * q^50 - 6 * q^51 - 13 * q^52 - 24 * q^53 - 58 * q^54 - 15 * q^55 - 45 * q^56 + 23 * q^57 + 16 * q^58 - 57 * q^59 - 4 * q^60 - 8 * q^61 - 3 * q^62 - 57 * q^63 - 5 * q^64 - 27 * q^65 - 4 * q^66 - 49 * q^67 + 43 * q^68 - 57 * q^69 - 7 * q^70 - 151 * q^71 - 29 * q^72 - 12 * q^73 + 18 * q^74 - 23 * q^75 - 38 * q^76 - 17 * q^77 + 37 * q^78 - 11 * q^79 - 21 * q^80 + 28 * q^81 + 44 * q^82 - 42 * q^83 + 16 * q^84 - 15 * q^85 + 9 * q^86 - 56 * q^87 - 21 * q^88 - 88 * q^89 + 47 * q^90 - 60 * q^91 + 26 * q^92 - 16 * q^93 + 37 * q^94 - 57 * q^95 + 108 * q^96 - 22 * q^97 + 8 * q^98 + 40 * q^99

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