LMFDB - Embedded newform 8041.2.a.c.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.23062 q^{2} -0.724033 q^{3} -0.485567 q^{4} +2.55129 q^{5} +0.891011 q^{6} -2.06260 q^{7} +3.05880 q^{8} -2.47578 q^{9} +O(q^{10})$	\(q-1.23062 q^{2} -0.724033 q^{3} -0.485567 q^{4} +2.55129 q^{5} +0.891011 q^{6} -2.06260 q^{7} +3.05880 q^{8} -2.47578 q^{9} -3.13968 q^{10} +1.00000 q^{11} +0.351567 q^{12} -1.70217 q^{13} +2.53828 q^{14} -1.84722 q^{15} -2.79309 q^{16} +1.00000 q^{17} +3.04675 q^{18} +1.33060 q^{19} -1.23882 q^{20} +1.49339 q^{21} -1.23062 q^{22} -4.90235 q^{23} -2.21467 q^{24} +1.50910 q^{25} +2.09473 q^{26} +3.96464 q^{27} +1.00153 q^{28} +2.06707 q^{29} +2.27323 q^{30} -4.76678 q^{31} -2.68035 q^{32} -0.724033 q^{33} -1.23062 q^{34} -5.26229 q^{35} +1.20216 q^{36} +8.52570 q^{37} -1.63747 q^{38} +1.23243 q^{39} +7.80388 q^{40} +9.72974 q^{41} -1.83780 q^{42} -1.00000 q^{43} -0.485567 q^{44} -6.31643 q^{45} +6.03295 q^{46} +0.420371 q^{47} +2.02229 q^{48} -2.74570 q^{49} -1.85713 q^{50} -0.724033 q^{51} +0.826519 q^{52} +4.45312 q^{53} -4.87898 q^{54} +2.55129 q^{55} -6.30906 q^{56} -0.963398 q^{57} -2.54378 q^{58} +4.74791 q^{59} +0.896949 q^{60} +0.122923 q^{61} +5.86611 q^{62} +5.10653 q^{63} +8.88468 q^{64} -4.34274 q^{65} +0.891011 q^{66} +4.12490 q^{67} -0.485567 q^{68} +3.54946 q^{69} +6.47589 q^{70} -3.39468 q^{71} -7.57290 q^{72} -10.2343 q^{73} -10.4919 q^{74} -1.09263 q^{75} -0.646096 q^{76} -2.06260 q^{77} -1.51665 q^{78} -13.3023 q^{79} -7.12599 q^{80} +4.55680 q^{81} -11.9736 q^{82} -0.161520 q^{83} -0.725140 q^{84} +2.55129 q^{85} +1.23062 q^{86} -1.49663 q^{87} +3.05880 q^{88} -0.138476 q^{89} +7.77314 q^{90} +3.51089 q^{91} +2.38042 q^{92} +3.45130 q^{93} -0.517318 q^{94} +3.39475 q^{95} +1.94066 q^{96} +4.10477 q^{97} +3.37892 q^{98} -2.47578 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.23062	−0.870182	−0.435091	−	0.900387i	$-0.643284\pi$
$2$	−1.23062	−0.870182	−0.435091	+	0.900387i	$0.643284\pi$
$3$	−0.724033	−0.418020	−0.209010	−	0.977913i	$-0.567024\pi$
$3$	−0.724033	−0.418020	−0.209010	+	0.977913i	$0.567024\pi$
$4$	−0.485567	−0.242784
$5$	2.55129	1.14097	0.570486	−	0.821307i	$-0.306755\pi$
$5$	2.55129	1.14097	0.570486	+	0.821307i	$0.306755\pi$
$6$	0.891011	0.363754
$7$	−2.06260	−0.779588	−0.389794	−	0.920902i	$-0.627454\pi$
$7$	−2.06260	−0.779588	−0.389794	+	0.920902i	$0.627454\pi$
$8$	3.05880	1.08145
$9$	−2.47578	−0.825259
$10$	−3.13968	−0.992854
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.351567	0.101489
$13$	−1.70217	−0.472098	−0.236049	−	0.971741i	$-0.575853\pi$
$13$	−1.70217	−0.472098	−0.236049	+	0.971741i	$0.575853\pi$
$14$	2.53828	0.678383
$15$	−1.84722	−0.476950
$16$	−2.79309	−0.698272
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	3.04675	0.718125
$19$	1.33060	0.305261	0.152630	−	0.988283i	$-0.451226\pi$
$19$	1.33060	0.305261	0.152630	+	0.988283i	$0.451226\pi$
$20$	−1.23882	−0.277010
$21$	1.49339	0.325884
$22$	−1.23062	−0.262370
$23$	−4.90235	−1.02221	−0.511106	−	0.859518i	$-0.670764\pi$
$23$	−4.90235	−1.02221	−0.511106	+	0.859518i	$0.670764\pi$
$24$	−2.21467	−0.452067
$25$	1.50910	0.301819
$26$	2.09473	0.410811
$27$	3.96464	0.762996
$28$	1.00153	0.189271
$29$	2.06707	0.383845	0.191923	−	0.981410i	$-0.438528\pi$
$29$	2.06707	0.383845	0.191923	+	0.981410i	$0.438528\pi$
$30$	2.27323	0.415033
$31$	−4.76678	−0.856139	−0.428069	−	0.903746i	$-0.640806\pi$
$31$	−4.76678	−0.856139	−0.428069	+	0.903746i	$0.640806\pi$
$32$	−2.68035	−0.473824
$33$	−0.724033	−0.126038
$34$	−1.23062	−0.211050
$35$	−5.26229	−0.889489
$36$	1.20216	0.200359
$37$	8.52570	1.40162	0.700808	−	0.713350i	$-0.252823\pi$
$37$	8.52570	1.40162	0.700808	+	0.713350i	$0.252823\pi$
$38$	−1.63747	−0.265632
$39$	1.23243	0.197347
$40$	7.80388	1.23390
$41$	9.72974	1.51953	0.759765	−	0.650197i	$-0.225314\pi$
$41$	9.72974	1.51953	0.759765	+	0.650197i	$0.225314\pi$
$42$	−1.83780	−0.283578
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.485567	−0.0732020
$45$	−6.31643	−0.941598
$46$	6.03295	0.889510
$47$	0.420371	0.0613173	0.0306587	−	0.999530i	$-0.490240\pi$
$47$	0.420371	0.0613173	0.0306587	+	0.999530i	$0.490240\pi$
$48$	2.02229	0.291892
$49$	−2.74570	−0.392243
$50$	−1.85713	−0.262637
$51$	−0.724033	−0.101385
$52$	0.826519	0.114618
$53$	4.45312	0.611684	0.305842	−	0.952082i	$-0.401062\pi$
$53$	4.45312	0.611684	0.305842	+	0.952082i	$0.401062\pi$
$54$	−4.87898	−0.663945
$55$	2.55129	0.344016
$56$	−6.30906	−0.843084
$57$	−0.963398	−0.127605
$58$	−2.54378	−0.334015
$59$	4.74791	0.618126	0.309063	−	0.951042i	$-0.399985\pi$
$59$	4.74791	0.618126	0.309063	+	0.951042i	$0.399985\pi$
$60$	0.896949	0.115796
$61$	0.122923	0.0157387	0.00786937	−	0.999969i	$-0.497495\pi$
$61$	0.122923	0.0157387	0.00786937	+	0.999969i	$0.497495\pi$
$62$	5.86611	0.744997
$63$	5.10653	0.643362
$64$	8.88468	1.11059
$65$	−4.34274	−0.538651
$66$	0.891011	0.109676
$67$	4.12490	0.503937	0.251969	−	0.967735i	$-0.418922\pi$
$67$	4.12490	0.503937	0.251969	+	0.967735i	$0.418922\pi$
$68$	−0.485567	−0.0588837
$69$	3.54946	0.427305
$70$	6.47589	0.774017
$71$	−3.39468	−0.402874	−0.201437	−	0.979501i	$-0.564561\pi$
$71$	−3.39468	−0.402874	−0.201437	+	0.979501i	$0.564561\pi$
$72$	−7.57290	−0.892474
$73$	−10.2343	−1.19784	−0.598920	−	0.800809i	$-0.704403\pi$
$73$	−10.2343	−1.19784	−0.598920	+	0.800809i	$0.704403\pi$
$74$	−10.4919	−1.21966
$75$	−1.09263	−0.126167
$76$	−0.646096	−0.0741123
$77$	−2.06260	−0.235055
$78$	−1.51665	−0.171727
$79$	−13.3023	−1.49663	−0.748313	−	0.663346i	$-0.769136\pi$
$79$	−13.3023	−1.49663	−0.748313	+	0.663346i	$0.769136\pi$
$80$	−7.12599	−0.796710
$81$	4.55680	0.506311
$82$	−11.9736	−1.32227
$83$	−0.161520	−0.0177292	−0.00886459	−	0.999961i	$-0.502822\pi$
$83$	−0.161520	−0.0177292	−0.00886459	+	0.999961i	$0.502822\pi$
$84$	−0.725140	−0.0791192
$85$	2.55129	0.276727
$86$	1.23062	0.132701
$87$	−1.49663	−0.160455
$88$	3.05880	0.326069
$89$	−0.138476	−0.0146784	−0.00733921	−	0.999973i	$-0.502336\pi$
$89$	−0.138476	−0.0146784	−0.00733921	+	0.999973i	$0.502336\pi$
$90$	7.77314	0.819361
$91$	3.51089	0.368042
$92$	2.38042	0.248176
$93$	3.45130	0.357884
$94$	−0.517318	−0.0533572
$95$	3.39475	0.348294
$96$	1.94066	0.198068
$97$	4.10477	0.416777	0.208388	−	0.978046i	$-0.433178\pi$
$97$	4.10477	0.416777	0.208388	+	0.978046i	$0.433178\pi$
$98$	3.37892	0.341322
$99$	−2.47578	−0.248825
$100$	−0.732767	−0.0732767
$101$	0.242466	0.0241263	0.0120632	−	0.999927i	$-0.496160\pi$
$101$	0.242466	0.0241263	0.0120632	+	0.999927i	$0.496160\pi$
$102$	0.891011	0.0882233
$103$	−9.25304	−0.911729	−0.455865	−	0.890049i	$-0.650670\pi$
$103$	−9.25304	−0.911729	−0.455865	+	0.890049i	$0.650670\pi$
$104$	−5.20660	−0.510549
$105$	3.81007	0.371824
$106$	−5.48012	−0.532276
$107$	−7.91468	−0.765141	−0.382571	−	0.923926i	$-0.624961\pi$
$107$	−7.91468	−0.765141	−0.382571	+	0.923926i	$0.624961\pi$
$108$	−1.92510	−0.185243
$109$	7.83282	0.750248	0.375124	−	0.926975i	$-0.377600\pi$
$109$	7.83282	0.750248	0.375124	+	0.926975i	$0.377600\pi$
$110$	−3.13968	−0.299357
$111$	−6.17288	−0.585904
$112$	5.76101	0.544365
$113$	13.3261	1.25361	0.626805	−	0.779176i	$-0.284362\pi$
$113$	13.3261	1.25361	0.626805	+	0.779176i	$0.284362\pi$
$114$	1.18558	0.111040
$115$	−12.5073	−1.16632
$116$	−1.00370	−0.0931914
$117$	4.21420	0.389603
$118$	−5.84289	−0.537882
$119$	−2.06260	−0.189078
$120$	−5.65027	−0.515796
$121$	1.00000	0.0909091
$122$	−0.151272	−0.0136956
$123$	−7.04465	−0.635195
$124$	2.31459	0.207857
$125$	−8.90632	−0.796606
$126$	−6.28421	−0.559842
$127$	−11.0755	−0.982790	−0.491395	−	0.870937i	$-0.663513\pi$
$127$	−11.0755	−0.982790	−0.491395	+	0.870937i	$0.663513\pi$
$128$	−5.57299	−0.492587
$129$	0.724033	0.0637475
$130$	5.34428	0.468724
$131$	10.2749	0.897719	0.448860	−	0.893602i	$-0.351830\pi$
$131$	10.2749	0.897719	0.448860	+	0.893602i	$0.351830\pi$
$132$	0.351567	0.0305999
$133$	−2.74449	−0.237978
$134$	−5.07620	−0.438517
$135$	10.1150	0.870557
$136$	3.05880	0.262290
$137$	7.14912	0.610790	0.305395	−	0.952226i	$-0.401211\pi$
$137$	7.14912	0.610790	0.305395	+	0.952226i	$0.401211\pi$
$138$	−4.36805	−0.371833
$139$	12.3340	1.04615	0.523077	−	0.852285i	$-0.324784\pi$
$139$	12.3340	1.04615	0.523077	+	0.852285i	$0.324784\pi$
$140$	2.55519	0.215953
$141$	−0.304362	−0.0256319
$142$	4.17757	0.350574
$143$	−1.70217	−0.142343
$144$	6.91507	0.576256
$145$	5.27370	0.437957
$146$	12.5946	1.04234
$147$	1.98798	0.163965
$148$	−4.13980	−0.340289
$149$	1.10114	0.0902086	0.0451043	−	0.998982i	$-0.485638\pi$
$149$	1.10114	0.0902086	0.0451043	+	0.998982i	$0.485638\pi$
$150$	1.34462	0.109788
$151$	−17.9687	−1.46227	−0.731136	−	0.682231i	$-0.761010\pi$
$151$	−17.9687	−1.46227	−0.731136	+	0.682231i	$0.761010\pi$
$152$	4.07004	0.330123
$153$	−2.47578	−0.200155
$154$	2.53828	0.204540
$155$	−12.1615	−0.976831
$156$	−0.598427	−0.0479125
$157$	1.51222	0.120688	0.0603440	−	0.998178i	$-0.480780\pi$
$157$	1.51222	0.120688	0.0603440	+	0.998178i	$0.480780\pi$
$158$	16.3701	1.30234
$159$	−3.22421	−0.255696
$160$	−6.83836	−0.540620
$161$	10.1116	0.796904
$162$	−5.60770	−0.440583
$163$	4.62010	0.361874	0.180937	−	0.983495i	$-0.442087\pi$
$163$	4.62010	0.361874	0.180937	+	0.983495i	$0.442087\pi$
$164$	−4.72445	−0.368917
$165$	−1.84722	−0.143806
$166$	0.198771	0.0154276
$167$	22.7634	1.76148	0.880742	−	0.473597i	$-0.157045\pi$
$167$	22.7634	1.76148	0.880742	+	0.473597i	$0.157045\pi$
$168$	4.56797	0.352426
$169$	−10.1026	−0.777124
$170$	−3.13968	−0.240802
$171$	−3.29427	−0.251919
$172$	0.485567	0.0370242
$173$	−4.79053	−0.364217	−0.182109	−	0.983278i	$-0.558292\pi$
$173$	−4.79053	−0.364217	−0.182109	+	0.983278i	$0.558292\pi$
$174$	1.84178	0.139625
$175$	−3.11265	−0.235294
$176$	−2.79309	−0.210537
$177$	−3.43764	−0.258389
$178$	0.170412	0.0127729
$179$	10.3155	0.771017	0.385509	−	0.922704i	$-0.374026\pi$
$179$	10.3155	0.771017	0.385509	+	0.922704i	$0.374026\pi$
$180$	3.06705	0.228605
$181$	−16.4030	−1.21923	−0.609613	−	0.792699i	$-0.708675\pi$
$181$	−16.4030	−1.21923	−0.609613	+	0.792699i	$0.708675\pi$
$182$	−4.32059	−0.320263
$183$	−0.0890006	−0.00657912
$184$	−14.9953	−1.10547
$185$	21.7516	1.59921
$186$	−4.24725	−0.311424
$187$	1.00000	0.0731272
$188$	−0.204118	−0.0148869
$189$	−8.17745	−0.594822
$190$	−4.17766	−0.303079
$191$	8.34721	0.603983	0.301991	−	0.953311i	$-0.402349\pi$
$191$	8.34721	0.603983	0.301991	+	0.953311i	$0.402349\pi$
$192$	−6.43280	−0.464247
$193$	−10.6289	−0.765084	−0.382542	−	0.923938i	$-0.624951\pi$
$193$	−10.6289	−0.765084	−0.382542	+	0.923938i	$0.624951\pi$
$194$	−5.05143	−0.362671
$195$	3.14429	0.225167
$196$	1.33322	0.0952301
$197$	−21.3637	−1.52210	−0.761049	−	0.648694i	$-0.775315\pi$
$197$	−21.3637	−1.52210	−0.761049	+	0.648694i	$0.775315\pi$
$198$	3.04675	0.216523
$199$	−11.8966	−0.843330	−0.421665	−	0.906752i	$-0.638554\pi$
$199$	−11.8966	−0.843330	−0.421665	+	0.906752i	$0.638554\pi$
$200$	4.61601	0.326401
$201$	−2.98657	−0.210656
$202$	−0.298385	−0.0209943
$203$	−4.26353	−0.299241
$204$	0.351567	0.0246146
$205$	24.8234	1.73374
$206$	11.3870	0.793370
$207$	12.1371	0.843589
$208$	4.75432	0.329653
$209$	1.33060	0.0920396
$210$	−4.68876	−0.323555
$211$	−8.70840	−0.599511	−0.299755	−	0.954016i	$-0.596905\pi$
$211$	−8.70840	−0.599511	−0.299755	+	0.954016i	$0.596905\pi$
$212$	−2.16229	−0.148507
$213$	2.45786	0.168410
$214$	9.73999	0.665812
$215$	−2.55129	−0.173997
$216$	12.1270	0.825140
$217$	9.83194	0.667436
$218$	−9.63925	−0.652852
$219$	7.41000	0.500722
$220$	−1.23882	−0.0835215
$221$	−1.70217	−0.114501
$222$	7.59649	0.509843
$223$	22.0040	1.47350	0.736748	−	0.676167i	$-0.236360\pi$
$223$	22.0040	1.47350	0.736748	+	0.676167i	$0.236360\pi$
$224$	5.52848	0.369387
$225$	−3.73618	−0.249079
$226$	−16.3994	−1.09087
$227$	3.92613	0.260586	0.130293	−	0.991476i	$-0.458408\pi$
$227$	3.92613	0.260586	0.130293	+	0.991476i	$0.458408\pi$
$228$	0.467795	0.0309805
$229$	−27.1137	−1.79173	−0.895863	−	0.444330i	$-0.853442\pi$
$229$	−27.1137	−1.79173	−0.895863	+	0.444330i	$0.853442\pi$
$230$	15.3918	1.01491
$231$	1.49339	0.0982576
$232$	6.32275	0.415109
$233$	5.02256	0.329039	0.164519	−	0.986374i	$-0.447393\pi$
$233$	5.02256	0.329039	0.164519	+	0.986374i	$0.447393\pi$
$234$	−5.18609	−0.339025
$235$	1.07249	0.0699614
$236$	−2.30543	−0.150071
$237$	9.63130	0.625620
$238$	2.53828	0.164532
$239$	8.17257	0.528640	0.264320	−	0.964435i	$-0.414853\pi$
$239$	8.17257	0.528640	0.264320	+	0.964435i	$0.414853\pi$
$240$	5.15945	0.333041
$241$	−8.43853	−0.543573	−0.271787	−	0.962358i	$-0.587615\pi$
$241$	−8.43853	−0.543573	−0.271787	+	0.962358i	$0.587615\pi$
$242$	−1.23062	−0.0791074
$243$	−15.1932	−0.974644
$244$	−0.0596876	−0.00382111
$245$	−7.00508	−0.447538
$246$	8.66931	0.552735
$247$	−2.26491	−0.144113
$248$	−14.5806	−0.925870
$249$	0.116946	0.00741116
$250$	10.9603	0.693192
$251$	−21.9660	−1.38648	−0.693240	−	0.720707i	$-0.743817\pi$
$251$	−21.9660	−1.38648	−0.693240	+	0.720707i	$0.743817\pi$
$252$	−2.47956	−0.156198
$253$	−4.90235	−0.308208
$254$	13.6297	0.855206
$255$	−1.84722	−0.115677
$256$	−10.9111	−0.681945
$257$	17.1179	1.06779	0.533893	−	0.845552i	$-0.320729\pi$
$257$	17.1179	1.06779	0.533893	+	0.845552i	$0.320729\pi$
$258$	−0.891011	−0.0554719
$259$	−17.5851	−1.09268
$260$	2.10869	0.130776
$261$	−5.11761	−0.316772
$262$	−12.6445	−0.781179
$263$	−27.1804	−1.67602	−0.838008	−	0.545658i	$-0.816280\pi$
$263$	−27.1804	−1.67602	−0.838008	+	0.545658i	$0.816280\pi$
$264$	−2.21467	−0.136303
$265$	11.3612	0.697915
$266$	3.37743	0.207084
$267$	0.100261	0.00613588
$268$	−2.00292	−0.122348
$269$	11.9880	0.730921	0.365460	−	0.930827i	$-0.380912\pi$
$269$	11.9880	0.730921	0.365460	+	0.930827i	$0.380912\pi$
$270$	−12.4477	−0.757543
$271$	−27.7685	−1.68682	−0.843410	−	0.537271i	$-0.819455\pi$
$271$	−27.7685	−1.68682	−0.843410	+	0.537271i	$0.819455\pi$
$272$	−2.79309	−0.169356
$273$	−2.54200	−0.153849
$274$	−8.79787	−0.531498
$275$	1.50910	0.0910019
$276$	−1.72350	−0.103743
$277$	−2.81410	−0.169083	−0.0845415	−	0.996420i	$-0.526943\pi$
$277$	−2.81410	−0.169083	−0.0845415	+	0.996420i	$0.526943\pi$
$278$	−15.1785	−0.910345
$279$	11.8015	0.706536
$280$	−16.0963	−0.961935
$281$	27.7761	1.65698	0.828492	−	0.560001i	$-0.189199\pi$
$281$	27.7761	1.65698	0.828492	+	0.560001i	$0.189199\pi$
$282$	0.374555	0.0223044
$283$	−18.1857	−1.08103	−0.540514	−	0.841335i	$-0.681770\pi$
$283$	−18.1857	−1.08103	−0.540514	+	0.841335i	$0.681770\pi$
$284$	1.64834	0.0978112
$285$	−2.45791	−0.145594
$286$	2.09473	0.123864
$287$	−20.0685	−1.18461
$288$	6.63595	0.391027
$289$	1.00000	0.0588235
$290$	−6.48994	−0.381102
$291$	−2.97199	−0.174221
$292$	4.96947	0.290816
$293$	4.96145	0.289851	0.144925	−	0.989443i	$-0.453706\pi$
$293$	4.96145	0.289851	0.144925	+	0.989443i	$0.453706\pi$
$294$	−2.44645	−0.142680
$295$	12.1133	0.705265
$296$	26.0784	1.51577
$297$	3.96464	0.230052
$298$	−1.35508	−0.0784978
$299$	8.34465	0.482584
$300$	0.530547	0.0306312
$301$	2.06260	0.118886
$302$	22.1127	1.27244
$303$	−0.175554	−0.0100853
$304$	−3.71649	−0.213155
$305$	0.313614	0.0179575
$306$	3.04675	0.174171
$307$	9.94534	0.567610	0.283805	−	0.958882i	$-0.408403\pi$
$307$	9.94534	0.567610	0.283805	+	0.958882i	$0.408403\pi$
$308$	1.00153	0.0570674
$309$	6.69950	0.381121
$310$	14.9662	0.850021
$311$	11.9476	0.677484	0.338742	−	0.940879i	$-0.389999\pi$
$311$	11.9476	0.677484	0.338742	+	0.940879i	$0.389999\pi$
$312$	3.76975	0.213420
$313$	9.04759	0.511400	0.255700	−	0.966756i	$-0.417694\pi$
$313$	9.04759	0.511400	0.255700	+	0.966756i	$0.417694\pi$
$314$	−1.86097	−0.105020
$315$	13.0282	0.734058
$316$	6.45916	0.363356
$317$	2.31430	0.129984	0.0649920	−	0.997886i	$-0.479298\pi$
$317$	2.31430	0.129984	0.0649920	+	0.997886i	$0.479298\pi$
$318$	3.96778	0.222502
$319$	2.06707	0.115734
$320$	22.6674	1.26715
$321$	5.73049	0.319845
$322$	−12.4435	−0.693451
$323$	1.33060	0.0740366
$324$	−2.21263	−0.122924
$325$	−2.56874	−0.142488
$326$	−5.68560	−0.314896
$327$	−5.67122	−0.313619
$328$	29.7613	1.64329
$329$	−0.867055	−0.0478023
$330$	2.27323	0.125137
$331$	4.70110	0.258396	0.129198	−	0.991619i	$-0.458760\pi$
$331$	4.70110	0.258396	0.129198	+	0.991619i	$0.458760\pi$
$332$	0.0784291	0.00430435
$333$	−21.1077	−1.15670
$334$	−28.0131	−1.53281
$335$	10.5238	0.574979
$336$	−4.17116	−0.227556
$337$	−11.1600	−0.607925	−0.303962	−	0.952684i	$-0.598310\pi$
$337$	−11.1600	−0.607925	−0.303962	+	0.952684i	$0.598310\pi$
$338$	12.4325	0.676239
$339$	−9.64850	−0.524035
$340$	−1.23882	−0.0671847
$341$	−4.76678	−0.258136
$342$	4.05400	0.219215
$343$	20.1014	1.08538
$344$	−3.05880	−0.164919
$345$	9.05572	0.487544
$346$	5.89534	0.316935
$347$	24.1946	1.29884	0.649418	−	0.760432i	$-0.275013\pi$
$347$	24.1946	1.29884	0.649418	+	0.760432i	$0.275013\pi$
$348$	0.726713	0.0389559
$349$	−12.9487	−0.693127	−0.346564	−	0.938026i	$-0.612652\pi$
$349$	−12.9487	−0.693127	−0.346564	+	0.938026i	$0.612652\pi$
$350$	3.83050	0.204749
$351$	−6.74850	−0.360209
$352$	−2.68035	−0.142863
$353$	−0.749307	−0.0398816	−0.0199408	−	0.999801i	$-0.506348\pi$
$353$	−0.749307	−0.0398816	−0.0199408	+	0.999801i	$0.506348\pi$
$354$	4.23044	0.224846
$355$	−8.66081	−0.459668
$356$	0.0672394	0.00356368
$357$	1.49339	0.0790384
$358$	−12.6945	−0.670925
$359$	18.6476	0.984183	0.492091	−	0.870544i	$-0.336233\pi$
$359$	18.6476	0.984183	0.492091	+	0.870544i	$0.336233\pi$
$360$	−19.3207	−1.01829
$361$	−17.2295	−0.906816
$362$	20.1859	1.06095
$363$	−0.724033	−0.0380019
$364$	−1.70478	−0.0893545
$365$	−26.1108	−1.36670
$366$	0.109526	0.00572503
$367$	−34.2155	−1.78603	−0.893017	−	0.450022i	$-0.851416\pi$
$367$	−34.2155	−1.78603	−0.893017	+	0.450022i	$0.851416\pi$
$368$	13.6927	0.713782
$369$	−24.0887	−1.25401
$370$	−26.7680	−1.39160
$371$	−9.18500	−0.476861
$372$	−1.67584	−0.0868883
$373$	27.3694	1.41713	0.708567	−	0.705644i	$-0.249342\pi$
$373$	27.3694	1.41713	0.708567	+	0.705644i	$0.249342\pi$
$374$	−1.23062	−0.0636340
$375$	6.44847	0.332997
$376$	1.28583	0.0663115
$377$	−3.51851	−0.181213
$378$	10.0634	0.517603
$379$	−12.0817	−0.620593	−0.310297	−	0.950640i	$-0.600428\pi$
$379$	−12.0817	−0.620593	−0.310297	+	0.950640i	$0.600428\pi$
$380$	−1.64838	−0.0845601
$381$	8.01901	0.410826
$382$	−10.2723	−0.525575
$383$	−12.3332	−0.630197	−0.315099	−	0.949059i	$-0.602038\pi$
$383$	−12.3332	−0.630197	−0.315099	+	0.949059i	$0.602038\pi$
$384$	4.03503	0.205912
$385$	−5.26229	−0.268191
$386$	13.0802	0.665762
$387$	2.47578	0.125851
$388$	−1.99314	−0.101187
$389$	22.6996	1.15092	0.575458	−	0.817831i	$-0.304824\pi$
$389$	22.6996	1.15092	0.575458	+	0.817831i	$0.304824\pi$
$390$	−3.86943	−0.195936
$391$	−4.90235	−0.247923
$392$	−8.39853	−0.424190
$393$	−7.43934	−0.375265
$394$	26.2906	1.32450
$395$	−33.9381	−1.70761
$396$	1.20216	0.0604106
$397$	−28.3781	−1.42426	−0.712128	−	0.702050i	$-0.752268\pi$
$397$	−28.3781	−1.42426	−0.712128	+	0.702050i	$0.752268\pi$
$398$	14.6403	0.733850
$399$	1.98710	0.0994795
$400$	−4.21504	−0.210752
$401$	−34.1374	−1.70474	−0.852371	−	0.522938i	$-0.824836\pi$
$401$	−34.1374	−1.70474	−0.852371	+	0.522938i	$0.824836\pi$
$402$	3.67534	0.183309
$403$	8.11388	0.404181
$404$	−0.117734	−0.00585747
$405$	11.6257	0.577687
$406$	5.24680	0.260394
$407$	8.52570	0.422603
$408$	−2.21467	−0.109642
$409$	24.8229	1.22741	0.613706	−	0.789535i	$-0.289678\pi$
$409$	24.8229	1.22741	0.613706	+	0.789535i	$0.289678\pi$
$410$	−30.5483	−1.50867
$411$	−5.17619	−0.255323
$412$	4.49297	0.221353
$413$	−9.79303	−0.481883
$414$	−14.9362	−0.734076
$415$	−0.412086	−0.0202285
$416$	4.56242	0.223691
$417$	−8.93021	−0.437314
$418$	−1.63747	−0.0800911
$419$	32.2326	1.57467	0.787334	−	0.616527i	$-0.211461\pi$
$419$	32.2326	1.57467	0.787334	+	0.616527i	$0.211461\pi$
$420$	−1.85004	−0.0902729
$421$	−10.2195	−0.498067	−0.249033	−	0.968495i	$-0.580113\pi$
$421$	−10.2195	−0.498067	−0.249033	+	0.968495i	$0.580113\pi$
$422$	10.7168	0.521683
$423$	−1.04074	−0.0506027
$424$	13.6212	0.661504
$425$	1.50910	0.0732019
$426$	−3.02469	−0.146547
$427$	−0.253541	−0.0122697
$428$	3.84311	0.185764
$429$	1.23243	0.0595022
$430$	3.13968	0.151409
$431$	19.6132	0.944733	0.472367	−	0.881402i	$-0.343400\pi$
$431$	19.6132	0.944733	0.472367	+	0.881402i	$0.343400\pi$
$432$	−11.0736	−0.532779
$433$	10.3066	0.495305	0.247653	−	0.968849i	$-0.420341\pi$
$433$	10.3066	0.495305	0.247653	+	0.968849i	$0.420341\pi$
$434$	−12.0994	−0.580790
$435$	−3.81833	−0.183075
$436$	−3.80336	−0.182148
$437$	−6.52307	−0.312041
$438$	−9.11892	−0.435719
$439$	5.03484	0.240300	0.120150	−	0.992756i	$-0.461662\pi$
$439$	5.03484	0.240300	0.120150	+	0.992756i	$0.461662\pi$
$440$	7.80388	0.372036
$441$	6.79774	0.323702
$442$	2.09473	0.0996363
$443$	−38.5195	−1.83012	−0.915059	−	0.403321i	$-0.867856\pi$
$443$	−38.5195	−1.83012	−0.915059	+	0.403321i	$0.867856\pi$
$444$	2.99735	0.142248
$445$	−0.353292	−0.0167477
$446$	−27.0786	−1.28221
$447$	−0.797258	−0.0377090
$448$	−18.3255	−0.865799
$449$	−9.20981	−0.434638	−0.217319	−	0.976101i	$-0.569731\pi$
$449$	−9.20981	−0.434638	−0.217319	+	0.976101i	$0.569731\pi$
$450$	4.59783	0.216744
$451$	9.72974	0.458156
$452$	−6.47070	−0.304356
$453$	13.0099	0.611260
$454$	−4.83159	−0.226758
$455$	8.95732	0.419926
$456$	−2.94684	−0.137998
$457$	38.0073	1.77791	0.888953	−	0.457998i	$-0.151433\pi$
$457$	38.0073	1.77791	0.888953	+	0.457998i	$0.151433\pi$
$458$	33.3668	1.55913
$459$	3.96464	0.185054
$460$	6.07315	0.283162
$461$	29.9323	1.39408	0.697042	−	0.717030i	$-0.254499\pi$
$461$	29.9323	1.39408	0.697042	+	0.717030i	$0.254499\pi$
$462$	−1.83780	−0.0855020
$463$	−18.7756	−0.872575	−0.436288	−	0.899807i	$-0.643707\pi$
$463$	−18.7756	−0.872575	−0.436288	+	0.899807i	$0.643707\pi$
$464$	−5.77351	−0.268029
$465$	8.80529	0.408335
$466$	−6.18087	−0.286323
$467$	−30.9064	−1.43018	−0.715090	−	0.699032i	$-0.753614\pi$
$467$	−30.9064	−1.43018	−0.715090	+	0.699032i	$0.753614\pi$
$468$	−2.04628	−0.0945892
$469$	−8.50801	−0.392863
$470$	−1.31983	−0.0608792
$471$	−1.09489	−0.0504500
$472$	14.5229	0.668471
$473$	−1.00000	−0.0459800
$474$	−11.8525	−0.544403
$475$	2.00800	0.0921335
$476$	1.00153	0.0459050
$477$	−11.0249	−0.504797
$478$	−10.0574	−0.460013
$479$	2.78364	0.127188	0.0635938	−	0.997976i	$-0.479744\pi$
$479$	2.78364	0.127188	0.0635938	+	0.997976i	$0.479744\pi$
$480$	4.95120	0.225990
$481$	−14.5122	−0.661700
$482$	10.3846	0.473008
$483$	−7.32111	−0.333122
$484$	−0.485567	−0.0220712
$485$	10.4725	0.475531
$486$	18.6971	0.848117
$487$	−5.18595	−0.234998	−0.117499	−	0.993073i	$-0.537488\pi$
$487$	−5.18595	−0.234998	−0.117499	+	0.993073i	$0.537488\pi$
$488$	0.375998	0.0170206
$489$	−3.34510	−0.151271
$490$	8.62061	0.389440
$491$	25.8437	1.16631	0.583155	−	0.812361i	$-0.301818\pi$
$491$	25.8437	1.16631	0.583155	+	0.812361i	$0.301818\pi$
$492$	3.42065	0.154215
$493$	2.06707	0.0930962
$494$	2.78725	0.125404
$495$	−6.31643	−0.283902
$496$	13.3140	0.597818
$497$	7.00185	0.314076
$498$	−0.143917	−0.00644905
$499$	−28.0904	−1.25750	−0.628749	−	0.777608i	$-0.716433\pi$
$499$	−28.0904	−1.25750	−0.628749	+	0.777608i	$0.716433\pi$
$500$	4.32462	0.193403
$501$	−16.4814	−0.736336
$502$	27.0318	1.20649
$503$	−29.3877	−1.31033	−0.655167	−	0.755484i	$-0.727402\pi$
$503$	−29.3877	−1.31033	−0.655167	+	0.755484i	$0.727402\pi$
$504$	15.6198	0.695762
$505$	0.618603	0.0275275
$506$	6.03295	0.268197
$507$	7.31462	0.324854
$508$	5.37789	0.238605
$509$	12.9918	0.575851	0.287926	−	0.957653i	$-0.407034\pi$
$509$	12.9918	0.575851	0.287926	+	0.957653i	$0.407034\pi$
$510$	2.27323	0.100660
$511$	21.1093	0.933822
$512$	24.5734	1.08600
$513$	5.27535	0.232913
$514$	−21.0657	−0.929167
$515$	−23.6072	−1.04026
$516$	−0.351567	−0.0154769
$517$	0.420371	0.0184879
$518$	21.6406	0.950833
$519$	3.46850	0.152250
$520$	−13.2836	−0.582523
$521$	−6.96116	−0.304974	−0.152487	−	0.988305i	$-0.548728\pi$
$521$	−6.96116	−0.304974	−0.152487	+	0.988305i	$0.548728\pi$
$522$	6.29784	0.275649
$523$	−6.81286	−0.297905	−0.148953	−	0.988844i	$-0.547590\pi$
$523$	−6.81286	−0.297905	−0.148953	+	0.988844i	$0.547590\pi$
$524$	−4.98914	−0.217952
$525$	2.25366	0.0983579
$526$	33.4488	1.45844
$527$	−4.76678	−0.207644
$528$	2.02229	0.0880088
$529$	1.03306	0.0449158
$530$	−13.9814	−0.607313
$531$	−11.7548	−0.510114
$532$	1.33264	0.0577771
$533$	−16.5617	−0.717367
$534$	−0.123384	−0.00533933
$535$	−20.1927	−0.873005
$536$	12.6172	0.544982
$537$	−7.46877	−0.322301
$538$	−14.7527	−0.636034
$539$	−2.74570	−0.118266
$540$	−4.91149	−0.211357
$541$	−27.9635	−1.20225	−0.601123	−	0.799156i	$-0.705280\pi$
$541$	−27.9635	−1.20225	−0.601123	+	0.799156i	$0.705280\pi$
$542$	34.1726	1.46784
$543$	11.8763	0.509661
$544$	−2.68035	−0.114919
$545$	19.9838	0.856013
$546$	3.12825	0.133877
$547$	1.84789	0.0790100	0.0395050	−	0.999219i	$-0.487422\pi$
$547$	1.84789	0.0790100	0.0395050	+	0.999219i	$0.487422\pi$
$548$	−3.47138	−0.148290
$549$	−0.304331	−0.0129885
$550$	−1.85713	−0.0791882
$551$	2.75045	0.117173
$552$	10.8571	0.462108
$553$	27.4373	1.16675
$554$	3.46310	0.147133
$555$	−15.7488	−0.668501
$556$	−5.98898	−0.253989
$557$	−29.4574	−1.24815	−0.624075	−	0.781364i	$-0.714524\pi$
$557$	−29.4574	−1.24815	−0.624075	+	0.781364i	$0.714524\pi$
$558$	−14.5232	−0.614815
$559$	1.70217	0.0719942
$560$	14.6980	0.621105
$561$	−0.724033	−0.0305687
$562$	−34.1819	−1.44188
$563$	−42.1523	−1.77651	−0.888253	−	0.459355i	$-0.848081\pi$
$563$	−42.1523	−1.77651	−0.888253	+	0.459355i	$0.848081\pi$
$564$	0.147788	0.00622301
$565$	33.9987	1.43034
$566$	22.3797	0.940690
$567$	−9.39884	−0.394714
$568$	−10.3836	−0.435687
$569$	−35.0523	−1.46947	−0.734735	−	0.678355i	$-0.762693\pi$
$569$	−35.0523	−1.46947	−0.734735	+	0.678355i	$0.762693\pi$
$570$	3.02476	0.126693
$571$	2.47386	0.103528	0.0517638	−	0.998659i	$-0.483516\pi$
$571$	2.47386	0.103528	0.0517638	+	0.998659i	$0.483516\pi$
$572$	0.826519	0.0345585
$573$	−6.04365	−0.252477
$574$	24.6968	1.03082
$575$	−7.39812	−0.308523
$576$	−21.9965	−0.916520
$577$	−34.1607	−1.42213	−0.711064	−	0.703128i	$-0.751786\pi$
$577$	−34.1607	−1.42213	−0.711064	+	0.703128i	$0.751786\pi$
$578$	−1.23062	−0.0511872
$579$	7.69566	0.319821
$580$	−2.56074	−0.106329
$581$	0.333151	0.0138215
$582$	3.65740	0.151604
$583$	4.45312	0.184430
$584$	−31.3048	−1.29540
$585$	10.7517	0.444526
$586$	−6.10567	−0.252223
$587$	−2.00704	−0.0828393	−0.0414197	−	0.999142i	$-0.513188\pi$
$587$	−2.00704	−0.0828393	−0.0414197	+	0.999142i	$0.513188\pi$
$588$	−0.965296	−0.0398081
$589$	−6.34268	−0.261346
$590$	−14.9069	−0.613708
$591$	15.4680	0.636268
$592$	−23.8130	−0.978710
$593$	43.8241	1.79964	0.899820	−	0.436261i	$-0.143698\pi$
$593$	43.8241	1.79964	0.899820	+	0.436261i	$0.143698\pi$
$594$	−4.87898	−0.200187
$595$	−5.26229	−0.215733
$596$	−0.534676	−0.0219012
$597$	8.61355	0.352529
$598$	−10.2691	−0.419935
$599$	−27.6933	−1.13152	−0.565758	−	0.824571i	$-0.691416\pi$
$599$	−27.6933	−1.13152	−0.565758	+	0.824571i	$0.691416\pi$
$600$	−3.34215	−0.136443
$601$	−42.4356	−1.73099	−0.865493	−	0.500921i	$-0.832995\pi$
$601$	−42.4356	−1.73099	−0.865493	+	0.500921i	$0.832995\pi$
$602$	−2.53828	−0.103452
$603$	−10.2123	−0.415879
$604$	8.72502	0.355016
$605$	2.55129	0.103725
$606$	0.216040	0.00877604
$607$	−4.66797	−0.189467	−0.0947336	−	0.995503i	$-0.530200\pi$
$607$	−4.66797	−0.189467	−0.0947336	+	0.995503i	$0.530200\pi$
$608$	−3.56648	−0.144640
$609$	3.08694	0.125089
$610$	−0.385940	−0.0156263
$611$	−0.715543	−0.0289478
$612$	1.20216	0.0485943
$613$	−21.6534	−0.874574	−0.437287	−	0.899322i	$-0.644061\pi$
$613$	−21.6534	−0.874574	−0.437287	+	0.899322i	$0.644061\pi$
$614$	−12.2390	−0.493924
$615$	−17.9730	−0.724740
$616$	−6.30906	−0.254199
$617$	1.32307	0.0532647	0.0266323	−	0.999645i	$-0.491522\pi$
$617$	1.32307	0.0532647	0.0266323	+	0.999645i	$0.491522\pi$
$618$	−8.24456	−0.331645
$619$	10.3077	0.414303	0.207151	−	0.978309i	$-0.433581\pi$
$619$	10.3077	0.414303	0.207151	+	0.978309i	$0.433581\pi$
$620$	5.90520	0.237159
$621$	−19.4361	−0.779943
$622$	−14.7029	−0.589534
$623$	0.285620	0.0114431
$624$	−3.44228	−0.137802
$625$	−30.2681	−1.21072
$626$	−11.1342	−0.445011
$627$	−0.963398	−0.0384744
$628$	−0.734283	−0.0293011
$629$	8.52570	0.339942
$630$	−16.0329	−0.638764
$631$	−33.4364	−1.33108	−0.665541	−	0.746362i	$-0.731799\pi$
$631$	−33.4364	−1.33108	−0.665541	+	0.746362i	$0.731799\pi$
$632$	−40.6890	−1.61852
$633$	6.30517	0.250608
$634$	−2.84803	−0.113110
$635$	−28.2568	−1.12134
$636$	1.56557	0.0620789
$637$	4.67365	0.185177
$638$	−2.54378	−0.100709
$639$	8.40446	0.332475
$640$	−14.2183	−0.562029
$641$	23.8883	0.943532	0.471766	−	0.881724i	$-0.343617\pi$
$641$	23.8883	0.943532	0.471766	+	0.881724i	$0.343617\pi$
$642$	−7.05207	−0.278323
$643$	4.89038	0.192858	0.0964289	−	0.995340i	$-0.469258\pi$
$643$	4.89038	0.192858	0.0964289	+	0.995340i	$0.469258\pi$
$644$	−4.90985	−0.193475
$645$	1.84722	0.0727342
$646$	−1.63747	−0.0644253
$647$	14.4863	0.569515	0.284758	−	0.958600i	$-0.408087\pi$
$647$	14.4863	0.569515	0.284758	+	0.958600i	$0.408087\pi$
$648$	13.9383	0.547549
$649$	4.74791	0.186372
$650$	3.16115	0.123991
$651$	−7.11865	−0.279002
$652$	−2.24337	−0.0878571
$653$	−17.3742	−0.679904	−0.339952	−	0.940443i	$-0.610411\pi$
$653$	−17.3742	−0.679904	−0.339952	+	0.940443i	$0.610411\pi$
$654$	6.97913	0.272906
$655$	26.2142	1.02427
$656$	−27.1760	−1.06105
$657$	25.3380	0.988528
$658$	1.06702	0.0415967
$659$	−17.3649	−0.676439	−0.338219	−	0.941067i	$-0.609825\pi$
$659$	−17.3649	−0.676439	−0.338219	+	0.941067i	$0.609825\pi$
$660$	0.896949	0.0349137
$661$	−18.3523	−0.713824	−0.356912	−	0.934138i	$-0.616170\pi$
$661$	−18.3523	−0.713824	−0.356912	+	0.934138i	$0.616170\pi$
$662$	−5.78529	−0.224852
$663$	1.23243	0.0478636
$664$	−0.494058	−0.0191732
$665$	−7.00200	−0.271526
$666$	25.9756	1.00654
$667$	−10.1335	−0.392371
$668$	−11.0532	−0.427659
$669$	−15.9316	−0.615952
$670$	−12.9509	−0.500336
$671$	0.122923	0.00474541
$672$	−4.00280	−0.154411
$673$	−9.53814	−0.367668	−0.183834	−	0.982957i	$-0.558851\pi$
$673$	−9.53814	−0.367668	−0.183834	+	0.982957i	$0.558851\pi$
$674$	13.7338	0.529005
$675$	5.98302	0.230287
$676$	4.90550	0.188673
$677$	−2.57181	−0.0988429	−0.0494214	−	0.998778i	$-0.515738\pi$
$677$	−2.57181	−0.0988429	−0.0494214	+	0.998778i	$0.515738\pi$
$678$	11.8737	0.456005
$679$	−8.46649	−0.324914
$680$	7.80388	0.299265
$681$	−2.84265	−0.108930
$682$	5.86611	0.224625
$683$	−38.8665	−1.48719	−0.743593	−	0.668632i	$-0.766880\pi$
$683$	−38.8665	−1.48719	−0.743593	+	0.668632i	$0.766880\pi$
$684$	1.59959	0.0611618
$685$	18.2395	0.696895
$686$	−24.7373	−0.944474
$687$	19.6312	0.748978
$688$	2.79309	0.106486
$689$	−7.57999	−0.288775
$690$	−11.1442	−0.424252
$691$	−46.6076	−1.77304	−0.886518	−	0.462694i	$-0.846883\pi$
$691$	−46.6076	−1.77304	−0.886518	+	0.462694i	$0.846883\pi$
$692$	2.32612	0.0884260
$693$	5.10653	0.193981
$694$	−29.7744	−1.13022
$695$	31.4676	1.19363
$696$	−4.57788	−0.173524
$697$	9.72974	0.368540
$698$	15.9350	0.603147
$699$	−3.63649	−0.137545
$700$	1.51140	0.0571257
$701$	−20.3251	−0.767670	−0.383835	−	0.923402i	$-0.625397\pi$
$701$	−20.3251	−0.767670	−0.383835	+	0.923402i	$0.625397\pi$
$702$	8.30486	0.313447
$703$	11.3443	0.427858
$704$	8.88468	0.334854
$705$	−0.776517	−0.0292453
$706$	0.922115	0.0347042
$707$	−0.500110	−0.0188086
$708$	1.66921	0.0627327
$709$	−38.5723	−1.44861	−0.724307	−	0.689478i	$-0.757840\pi$
$709$	−38.5723	−1.44861	−0.724307	+	0.689478i	$0.757840\pi$
$710$	10.6582	0.399995
$711$	32.9335	1.23510
$712$	−0.423569	−0.0158739
$713$	23.3684	0.875155
$714$	−1.83780	−0.0687778
$715$	−4.34274	−0.162409
$716$	−5.00887	−0.187190
$717$	−5.91721	−0.220982
$718$	−22.9482	−0.856418
$719$	−39.8883	−1.48758	−0.743792	−	0.668412i	$-0.766974\pi$
$719$	−39.8883	−1.48758	−0.743792	+	0.668412i	$0.766974\pi$
$720$	17.6424	0.657492
$721$	19.0853	0.710773
$722$	21.2030	0.789095
$723$	6.10977	0.227225
$724$	7.96476	0.296008
$725$	3.11941	0.115852
$726$	0.891011	0.0330685
$727$	−44.3011	−1.64304	−0.821518	−	0.570183i	$-0.806872\pi$
$727$	−44.3011	−1.64304	−0.821518	+	0.570183i	$0.806872\pi$
$728$	10.7391	0.398018
$729$	−2.67003	−0.0988899
$730$	32.1326	1.18928
$731$	−1.00000	−0.0369863
$732$	0.0432158	0.00159730
$733$	19.4722	0.719223	0.359611	−	0.933102i	$-0.382909\pi$
$733$	19.4722	0.719223	0.359611	+	0.933102i	$0.382909\pi$
$734$	42.1064	1.55417
$735$	5.07191	0.187080
$736$	13.1400	0.484348
$737$	4.12490	0.151943
$738$	29.6441	1.09121
$739$	−21.7893	−0.801532	−0.400766	−	0.916180i	$-0.631256\pi$
$739$	−21.7893	−0.801532	−0.400766	+	0.916180i	$0.631256\pi$
$740$	−10.5618	−0.388261
$741$	1.63987	0.0602421
$742$	11.3033	0.414956
$743$	1.39570	0.0512033	0.0256016	−	0.999672i	$-0.491850\pi$
$743$	1.39570	0.0512033	0.0256016	+	0.999672i	$0.491850\pi$
$744$	10.5568	0.387032
$745$	2.80932	0.102926
$746$	−33.6814	−1.23316
$747$	0.399889	0.0146312
$748$	−0.485567	−0.0177541
$749$	16.3248	0.596495
$750$	−7.93563	−0.289768
$751$	−42.1287	−1.53730	−0.768649	−	0.639671i	$-0.779071\pi$
$751$	−42.1287	−1.53730	−0.768649	+	0.639671i	$0.779071\pi$
$752$	−1.17413	−0.0428162
$753$	15.9041	0.579577
$754$	4.32996	0.157688
$755$	−45.8434	−1.66841
$756$	3.97070	0.144413
$757$	17.0395	0.619311	0.309655	−	0.950849i	$-0.399786\pi$
$757$	17.0395	0.619311	0.309655	+	0.950849i	$0.399786\pi$
$758$	14.8680	0.540029
$759$	3.54946	0.128837
$760$	10.3839	0.376662
$761$	15.3709	0.557194	0.278597	−	0.960408i	$-0.410131\pi$
$761$	15.3709	0.557194	0.278597	+	0.960408i	$0.410131\pi$
$762$	−9.86837	−0.357493
$763$	−16.1559	−0.584884
$764$	−4.05313	−0.146637
$765$	−6.31643	−0.228371
$766$	15.1775	0.548386
$767$	−8.08177	−0.291816
$768$	7.90000	0.285067
$769$	18.8483	0.679689	0.339844	−	0.940482i	$-0.389626\pi$
$769$	18.8483	0.679689	0.339844	+	0.940482i	$0.389626\pi$
$770$	6.47589	0.233375
$771$	−12.3939	−0.446356
$772$	5.16104	0.185750
$773$	−23.9245	−0.860503	−0.430251	−	0.902709i	$-0.641575\pi$
$773$	−23.9245	−0.860503	−0.430251	+	0.902709i	$0.641575\pi$
$774$	−3.04675	−0.109513
$775$	−7.19352	−0.258399
$776$	12.5557	0.450722
$777$	12.7322	0.456764
$778$	−27.9347	−1.00151
$779$	12.9464	0.463853
$780$	−1.52676	−0.0546669
$781$	−3.39468	−0.121471
$782$	6.03295	0.215738
$783$	8.19519	0.292872
$784$	7.66898	0.273892
$785$	3.85811	0.137702
$786$	9.15502	0.326549
$787$	10.4619	0.372925	0.186463	−	0.982462i	$-0.440298\pi$
$787$	10.4619	0.372925	0.186463	+	0.982462i	$0.440298\pi$
$788$	10.3735	0.369541
$789$	19.6795	0.700609
$790$	41.7650	1.48593
$791$	−27.4863	−0.977299
$792$	−7.57290	−0.269091
$793$	−0.209237	−0.00743022
$794$	34.9227	1.23936
$795$	−8.22590	−0.291743
$796$	5.77662	0.204747
$797$	−29.1601	−1.03291	−0.516453	−	0.856316i	$-0.672748\pi$
$797$	−29.1601	−1.03291	−0.516453	+	0.856316i	$0.672748\pi$
$798$	−2.44537	−0.0865652
$799$	0.420371	0.0148716
$800$	−4.04491	−0.143009
$801$	0.342835	0.0121135
$802$	42.0103	1.48344
$803$	−10.2343	−0.361162
$804$	1.45018	0.0511439
$805$	25.7976	0.909245
$806$	−9.98513	−0.351711
$807$	−8.67970	−0.305540
$808$	0.741655	0.0260913
$809$	2.03074	0.0713970	0.0356985	−	0.999363i	$-0.488634\pi$
$809$	2.03074	0.0713970	0.0356985	+	0.999363i	$0.488634\pi$
$810$	−14.3069	−0.502693
$811$	−10.3763	−0.364362	−0.182181	−	0.983265i	$-0.558316\pi$
$811$	−10.3763	−0.364362	−0.182181	+	0.983265i	$0.558316\pi$
$812$	2.07023	0.0726509
$813$	20.1053	0.705125
$814$	−10.4919	−0.367742
$815$	11.7872	0.412888
$816$	2.02229	0.0707943
$817$	−1.33060	−0.0465518
$818$	−30.5476	−1.06807
$819$	−8.69219	−0.303730
$820$	−12.0534	−0.420924
$821$	−45.5802	−1.59076	−0.795381	−	0.606110i	$-0.792729\pi$
$821$	−45.5802	−1.59076	−0.795381	+	0.606110i	$0.792729\pi$
$822$	6.36994	0.222177
$823$	−13.8649	−0.483301	−0.241650	−	0.970363i	$-0.577689\pi$
$823$	−13.8649	−0.483301	−0.241650	+	0.970363i	$0.577689\pi$
$824$	−28.3032	−0.985987
$825$	−1.09263	−0.0380406
$826$	12.0515	0.419326
$827$	14.8901	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$827$	14.8901	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$828$	−5.89339	−0.204810
$829$	13.4956	0.468722	0.234361	−	0.972150i	$-0.424700\pi$
$829$	13.4956	0.468722	0.234361	+	0.972150i	$0.424700\pi$
$830$	0.507122	0.0176025
$831$	2.03750	0.0706802
$832$	−15.1233	−0.524305
$833$	−2.74570	−0.0951328
$834$	10.9897	0.380543
$835$	58.0761	2.00980
$836$	−0.646096	−0.0223457
$837$	−18.8986	−0.653230
$838$	−39.6662	−1.37025
$839$	46.3349	1.59966	0.799829	−	0.600228i	$-0.204924\pi$
$839$	46.3349	1.59966	0.799829	+	0.600228i	$0.204924\pi$
$840$	11.6542	0.402109
$841$	−24.7272	−0.852663
$842$	12.5763	0.433408
$843$	−20.1108	−0.692653
$844$	4.22851	0.145551
$845$	−25.7747	−0.886677
$846$	1.28076	0.0440335
$847$	−2.06260	−0.0708716
$848$	−12.4380	−0.427122
$849$	13.1670	0.451892
$850$	−1.85713	−0.0636989
$851$	−41.7960	−1.43275
$852$	−1.19345	−0.0408871
$853$	−14.6074	−0.500148	−0.250074	−	0.968227i	$-0.580455\pi$
$853$	−14.6074	−0.500148	−0.250074	+	0.968227i	$0.580455\pi$
$854$	0.312014	0.0106769
$855$	−8.40465	−0.287433
$856$	−24.2094	−0.827460
$857$	−41.6128	−1.42147	−0.710733	−	0.703462i	$-0.751637\pi$
$857$	−41.6128	−1.42147	−0.710733	+	0.703462i	$0.751637\pi$
$858$	−1.51665	−0.0517777
$859$	−39.1949	−1.33731	−0.668656	−	0.743571i	$-0.733130\pi$
$859$	−39.1949	−1.33731	−0.668656	+	0.743571i	$0.733130\pi$
$860$	1.23882	0.0422436
$861$	14.5303	0.495190
$862$	−24.1364	−0.822090
$863$	−32.2281	−1.09706	−0.548528	−	0.836132i	$-0.684812\pi$
$863$	−32.2281	−1.09706	−0.548528	+	0.836132i	$0.684812\pi$
$864$	−10.6266	−0.361525
$865$	−12.2220	−0.415562
$866$	−12.6836	−0.431006
$867$	−0.724033	−0.0245894
$868$	−4.77407	−0.162042
$869$	−13.3023	−0.451250
$870$	4.69893	0.159309
$871$	−7.02130	−0.237908
$872$	23.9590	0.811354
$873$	−10.1625	−0.343949
$874$	8.02744	0.271532
$875$	18.3701	0.621024
$876$	−3.59806	−0.121567
$877$	52.7060	1.77976	0.889878	−	0.456198i	$-0.150789\pi$
$877$	52.7060	1.77976	0.889878	+	0.456198i	$0.150789\pi$
$878$	−6.19599	−0.209105
$879$	−3.59225	−0.121164
$880$	−7.12599	−0.240217
$881$	−28.1073	−0.946958	−0.473479	−	0.880805i	$-0.657002\pi$
$881$	−28.1073	−0.946958	−0.473479	+	0.880805i	$0.657002\pi$
$882$	−8.36545	−0.281679
$883$	21.2667	0.715682	0.357841	−	0.933782i	$-0.383513\pi$
$883$	21.2667	0.715682	0.357841	+	0.933782i	$0.383513\pi$
$884$	0.826519	0.0277989
$885$	−8.77044	−0.294815
$886$	47.4030	1.59253
$887$	−9.51264	−0.319403	−0.159702	−	0.987165i	$-0.551053\pi$
$887$	−9.51264	−0.319403	−0.159702	+	0.987165i	$0.551053\pi$
$888$	−18.8816	−0.633625
$889$	22.8442	0.766171
$890$	0.434770	0.0145735
$891$	4.55680	0.152659
$892$	−10.6844	−0.357741
$893$	0.559345	0.0187178
$894$	0.981124	0.0328137
$895$	26.3179	0.879710
$896$	11.4948	0.384015
$897$	−6.04180	−0.201730
$898$	11.3338	0.378214
$899$	−9.85327	−0.328625
$900$	1.81417	0.0604723
$901$	4.45312	0.148355
$902$	−11.9736	−0.398679
$903$	−1.49339	−0.0496968
$904$	40.7617	1.35571
$905$	−41.8489	−1.39110
$906$	−16.0103	−0.531907
$907$	18.9644	0.629701	0.314851	−	0.949141i	$-0.398046\pi$
$907$	18.9644	0.629701	0.314851	+	0.949141i	$0.398046\pi$
$908$	−1.90640	−0.0632661
$909$	−0.600293	−0.0199104
$910$	−11.0231	−0.365412
$911$	−26.4939	−0.877783	−0.438891	−	0.898540i	$-0.644629\pi$
$911$	−26.4939	−0.877783	−0.438891	+	0.898540i	$0.644629\pi$
$912$	2.69086	0.0891032
$913$	−0.161520	−0.00534555
$914$	−46.7726	−1.54710
$915$	−0.227067	−0.00750659
$916$	13.1655	0.435002
$917$	−21.1929	−0.699851
$918$	−4.87898	−0.161030
$919$	−28.8068	−0.950248	−0.475124	−	0.879919i	$-0.657597\pi$
$919$	−28.8068	−0.950248	−0.475124	+	0.879919i	$0.657597\pi$
$920$	−38.2574	−1.26131
$921$	−7.20075	−0.237273
$922$	−36.8353	−1.21311
$923$	5.77833	0.190196
$924$	−0.725140	−0.0238553
$925$	12.8661	0.423034
$926$	23.1057	0.759299
$927$	22.9085	0.752412
$928$	−5.54048	−0.181875
$929$	24.3981	0.800476	0.400238	−	0.916411i	$-0.368928\pi$
$929$	24.3981	0.800476	0.400238	+	0.916411i	$0.368928\pi$
$930$	−10.8360	−0.355326
$931$	−3.65343	−0.119736
$932$	−2.43879	−0.0798852
$933$	−8.65042	−0.283202
$934$	38.0342	1.24452
$935$	2.55129	0.0834362
$936$	12.8904	0.421335
$937$	−29.7178	−0.970840	−0.485420	−	0.874281i	$-0.661333\pi$
$937$	−29.7178	−0.970840	−0.485420	+	0.874281i	$0.661333\pi$
$938$	10.4702	0.341863
$939$	−6.55075	−0.213776
$940$	−0.520765	−0.0169855
$941$	−51.7810	−1.68801	−0.844007	−	0.536332i	$-0.819809\pi$
$941$	−51.7810	−1.68801	−0.844007	+	0.536332i	$0.819809\pi$
$942$	1.34740	0.0439007
$943$	−47.6986	−1.55328
$944$	−13.2613	−0.431620
$945$	−20.8631	−0.678676
$946$	1.23062	0.0400110
$947$	10.7142	0.348165	0.174083	−	0.984731i	$-0.444304\pi$
$947$	10.7142	0.348165	0.174083	+	0.984731i	$0.444304\pi$
$948$	−4.67664	−0.151890
$949$	17.4206	0.565498
$950$	−2.47109	−0.0801729
$951$	−1.67563	−0.0543360
$952$	−6.30906	−0.204478
$953$	29.2251	0.946695	0.473347	−	0.880876i	$-0.343046\pi$
$953$	29.2251	0.946695	0.473347	+	0.880876i	$0.343046\pi$
$954$	13.5675	0.439266
$955$	21.2962	0.689128
$956$	−3.96833	−0.128345
$957$	−1.49663	−0.0483791
$958$	−3.42561	−0.110676
$959$	−14.7457	−0.476165
$960$	−16.4120	−0.529694
$961$	−8.27781	−0.267026
$962$	17.8591	0.575799
$963$	19.5950	0.631439
$964$	4.09747	0.131971
$965$	−27.1174	−0.872940
$966$	9.00952	0.289877
$967$	34.6058	1.11285	0.556424	−	0.830899i	$-0.312173\pi$
$967$	34.6058	1.11285	0.556424	+	0.830899i	$0.312173\pi$
$968$	3.05880	0.0983134
$969$	−0.963398	−0.0309488
$970$	−12.8877	−0.413798
$971$	6.38228	0.204817	0.102409	−	0.994742i	$-0.467345\pi$
$971$	6.38228	0.204817	0.102409	+	0.994742i	$0.467345\pi$
$972$	7.37732	0.236628
$973$	−25.4400	−0.815570
$974$	6.38195	0.204491
$975$	1.85985	0.0595629
$976$	−0.343336	−0.0109899
$977$	−15.1300	−0.484052	−0.242026	−	0.970270i	$-0.577812\pi$
$977$	−15.1300	−0.484052	−0.242026	+	0.970270i	$0.577812\pi$
$978$	4.11656	0.131633
$979$	−0.138476	−0.00442571
$980$	3.40144	0.108655
$981$	−19.3923	−0.619149
$982$	−31.8038	−1.01490
$983$	42.6640	1.36077	0.680386	−	0.732854i	$-0.261812\pi$
$983$	42.6640	1.36077	0.680386	+	0.732854i	$0.261812\pi$
$984$	−21.5482	−0.686930
$985$	−54.5050	−1.73667
$986$	−2.54378	−0.0810106
$987$	0.627776	0.0199823
$988$	1.09977	0.0349883
$989$	4.90235	0.155886
$990$	7.77314	0.247047
$991$	58.5872	1.86108	0.930542	−	0.366185i	$-0.119336\pi$
$991$	58.5872	1.86108	0.930542	+	0.366185i	$0.119336\pi$
$992$	12.7766	0.405659
$993$	−3.40375	−0.108015
$994$	−8.61663	−0.273303
$995$	−30.3518	−0.962216
$996$	−0.0567852	−0.00179931
$997$	39.7825	1.25993	0.629963	−	0.776625i	$-0.283070\pi$
$997$	39.7825	1.25993	0.629963	+	0.776625i	$0.283070\pi$
$998$	34.5687	1.09425
$999$	33.8013	1.06943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.c.1.20	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.23062 q^{2} -0.724033 q^{3} -0.485567 q^{4} +2.55129 q^{5} +0.891011 q^{6} -2.06260 q^{7} +3.05880 q^{8} -2.47578 q^{9} +O(q^{10})\)	\(q-1.23062 q^{2} -0.724033 q^{3} -0.485567 q^{4} +2.55129 q^{5} +0.891011 q^{6} -2.06260 q^{7} +3.05880 q^{8} -2.47578 q^{9} -3.13968 q^{10} +1.00000 q^{11} +0.351567 q^{12} -1.70217 q^{13} +2.53828 q^{14} -1.84722 q^{15} -2.79309 q^{16} +1.00000 q^{17} +3.04675 q^{18} +1.33060 q^{19} -1.23882 q^{20} +1.49339 q^{21} -1.23062 q^{22} -4.90235 q^{23} -2.21467 q^{24} +1.50910 q^{25} +2.09473 q^{26} +3.96464 q^{27} +1.00153 q^{28} +2.06707 q^{29} +2.27323 q^{30} -4.76678 q^{31} -2.68035 q^{32} -0.724033 q^{33} -1.23062 q^{34} -5.26229 q^{35} +1.20216 q^{36} +8.52570 q^{37} -1.63747 q^{38} +1.23243 q^{39} +7.80388 q^{40} +9.72974 q^{41} -1.83780 q^{42} -1.00000 q^{43} -0.485567 q^{44} -6.31643 q^{45} +6.03295 q^{46} +0.420371 q^{47} +2.02229 q^{48} -2.74570 q^{49} -1.85713 q^{50} -0.724033 q^{51} +0.826519 q^{52} +4.45312 q^{53} -4.87898 q^{54} +2.55129 q^{55} -6.30906 q^{56} -0.963398 q^{57} -2.54378 q^{58} +4.74791 q^{59} +0.896949 q^{60} +0.122923 q^{61} +5.86611 q^{62} +5.10653 q^{63} +8.88468 q^{64} -4.34274 q^{65} +0.891011 q^{66} +4.12490 q^{67} -0.485567 q^{68} +3.54946 q^{69} +6.47589 q^{70} -3.39468 q^{71} -7.57290 q^{72} -10.2343 q^{73} -10.4919 q^{74} -1.09263 q^{75} -0.646096 q^{76} -2.06260 q^{77} -1.51665 q^{78} -13.3023 q^{79} -7.12599 q^{80} +4.55680 q^{81} -11.9736 q^{82} -0.161520 q^{83} -0.725140 q^{84} +2.55129 q^{85} +1.23062 q^{86} -1.49663 q^{87} +3.05880 q^{88} -0.138476 q^{89} +7.77314 q^{90} +3.51089 q^{91} +2.38042 q^{92} +3.45130 q^{93} -0.517318 q^{94} +3.39475 q^{95} +1.94066 q^{96} +4.10477 q^{97} +3.37892 q^{98} -2.47578 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 9 q^{2} - 6 q^{3} + 43 q^{4} - 15 q^{5} - 4 q^{6} - 17 q^{7} - 21 q^{8} + 40 q^{9}+O(q^{10}) \) 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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