LMFDB - Embedded newform 6041.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78355 q^{2} +3.33951 q^{3} +5.74813 q^{4} +2.68755 q^{5} -9.29568 q^{6} +1.00000 q^{7} -10.4331 q^{8} +8.15233 q^{9} +O(q^{10})$	\(q-2.78355 q^{2} +3.33951 q^{3} +5.74813 q^{4} +2.68755 q^{5} -9.29568 q^{6} +1.00000 q^{7} -10.4331 q^{8} +8.15233 q^{9} -7.48091 q^{10} -2.52684 q^{11} +19.1959 q^{12} -4.90685 q^{13} -2.78355 q^{14} +8.97509 q^{15} +17.5447 q^{16} -0.898319 q^{17} -22.6924 q^{18} +1.96499 q^{19} +15.4484 q^{20} +3.33951 q^{21} +7.03359 q^{22} -7.40366 q^{23} -34.8414 q^{24} +2.22291 q^{25} +13.6585 q^{26} +17.2063 q^{27} +5.74813 q^{28} +3.52400 q^{29} -24.9826 q^{30} +5.35439 q^{31} -27.9703 q^{32} -8.43842 q^{33} +2.50051 q^{34} +2.68755 q^{35} +46.8606 q^{36} +10.1575 q^{37} -5.46964 q^{38} -16.3865 q^{39} -28.0394 q^{40} +3.52367 q^{41} -9.29568 q^{42} +2.64184 q^{43} -14.5246 q^{44} +21.9098 q^{45} +20.6084 q^{46} +4.92135 q^{47} +58.5907 q^{48} +1.00000 q^{49} -6.18756 q^{50} -2.99995 q^{51} -28.2052 q^{52} +10.7700 q^{53} -47.8944 q^{54} -6.79101 q^{55} -10.4331 q^{56} +6.56211 q^{57} -9.80922 q^{58} -3.69514 q^{59} +51.5900 q^{60} +4.74191 q^{61} -14.9042 q^{62} +8.15233 q^{63} +42.7673 q^{64} -13.1874 q^{65} +23.4887 q^{66} +15.0912 q^{67} -5.16365 q^{68} -24.7246 q^{69} -7.48091 q^{70} -4.59300 q^{71} -85.0539 q^{72} +0.997451 q^{73} -28.2740 q^{74} +7.42342 q^{75} +11.2950 q^{76} -2.52684 q^{77} +45.6126 q^{78} -2.20739 q^{79} +47.1522 q^{80} +33.0035 q^{81} -9.80830 q^{82} +6.11616 q^{83} +19.1959 q^{84} -2.41427 q^{85} -7.35367 q^{86} +11.7684 q^{87} +26.3628 q^{88} -0.258006 q^{89} -60.9869 q^{90} -4.90685 q^{91} -42.5571 q^{92} +17.8810 q^{93} -13.6988 q^{94} +5.28100 q^{95} -93.4072 q^{96} -12.8683 q^{97} -2.78355 q^{98} -20.5997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.78355	−1.96826	−0.984132	−	0.177438i	$-0.943219\pi$
$2$	−2.78355	−1.96826	−0.984132	+	0.177438i	$0.943219\pi$
$3$	3.33951	1.92807	0.964034	−	0.265780i	$-0.0856294\pi$
$3$	3.33951	1.92807	0.964034	+	0.265780i	$0.0856294\pi$
$4$	5.74813	2.87406
$5$	2.68755	1.20191	0.600954	−	0.799284i	$-0.294788\pi$
$5$	2.68755	1.20191	0.600954	+	0.799284i	$0.294788\pi$
$6$	−9.29568	−3.79495
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−10.4331	−3.68865
$9$	8.15233	2.71744
$10$	−7.48091	−2.36567
$11$	−2.52684	−0.761872	−0.380936	−	0.924601i	$-0.624398\pi$
$11$	−2.52684	−0.761872	−0.380936	+	0.924601i	$0.624398\pi$
$12$	19.1959	5.54139
$13$	−4.90685	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$13$	−4.90685	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$14$	−2.78355	−0.743934
$15$	8.97509	2.31736
$16$	17.5447	4.38618
$17$	−0.898319	−0.217874	−0.108937	−	0.994049i	$-0.534745\pi$
$17$	−0.898319	−0.217874	−0.108937	+	0.994049i	$0.534745\pi$
$18$	−22.6924	−5.34865
$19$	1.96499	0.450800	0.225400	−	0.974266i	$-0.427631\pi$
$19$	1.96499	0.450800	0.225400	+	0.974266i	$0.427631\pi$
$20$	15.4484	3.45436
$21$	3.33951	0.728741
$22$	7.03359	1.49957
$23$	−7.40366	−1.54377	−0.771884	−	0.635763i	$-0.780686\pi$
$23$	−7.40366	−1.54377	−0.771884	+	0.635763i	$0.780686\pi$
$24$	−34.8414	−7.11197
$25$	2.22291	0.444581
$26$	13.6585	2.67864
$27$	17.2063	3.31135
$28$	5.74813	1.08629
$29$	3.52400	0.654391	0.327195	−	0.944957i	$-0.393896\pi$
$29$	3.52400	0.654391	0.327195	+	0.944957i	$0.393896\pi$
$30$	−24.9826	−4.56117
$31$	5.35439	0.961677	0.480838	−	0.876809i	$-0.340332\pi$
$31$	5.35439	0.961677	0.480838	+	0.876809i	$0.340332\pi$
$32$	−27.9703	−4.94450
$33$	−8.43842	−1.46894
$34$	2.50051	0.428834
$35$	2.68755	0.454278
$36$	46.8606	7.81011
$37$	10.1575	1.66989	0.834945	−	0.550333i	$-0.185499\pi$
$37$	10.1575	1.66989	0.834945	+	0.550333i	$0.185499\pi$
$38$	−5.46964	−0.887293
$39$	−16.3865	−2.62394
$40$	−28.0394	−4.43342
$41$	3.52367	0.550305	0.275153	−	0.961401i	$-0.411272\pi$
$41$	3.52367	0.550305	0.275153	+	0.961401i	$0.411272\pi$
$42$	−9.29568	−1.43435
$43$	2.64184	0.402876	0.201438	−	0.979501i	$-0.435439\pi$
$43$	2.64184	0.402876	0.201438	+	0.979501i	$0.435439\pi$
$44$	−14.5246	−2.18967
$45$	21.9098	3.26612
$46$	20.6084	3.03854
$47$	4.92135	0.717852	0.358926	−	0.933366i	$-0.383143\pi$
$47$	4.92135	0.717852	0.358926	+	0.933366i	$0.383143\pi$
$48$	58.5907	8.45684
$49$	1.00000	0.142857
$50$	−6.18756	−0.875053
$51$	−2.99995	−0.420077
$52$	−28.2052	−3.91136
$53$	10.7700	1.47938	0.739689	−	0.672949i	$-0.234973\pi$
$53$	10.7700	1.47938	0.739689	+	0.672949i	$0.234973\pi$
$54$	−47.8944	−6.51761
$55$	−6.79101	−0.915700
$56$	−10.4331	−1.39418
$57$	6.56211	0.869172
$58$	−9.80922	−1.28801
$59$	−3.69514	−0.481067	−0.240533	−	0.970641i	$-0.577322\pi$
$59$	−3.69514	−0.481067	−0.240533	+	0.970641i	$0.577322\pi$
$60$	51.5900	6.66023
$61$	4.74191	0.607139	0.303570	−	0.952809i	$-0.401821\pi$
$61$	4.74191	0.607139	0.303570	+	0.952809i	$0.401821\pi$
$62$	−14.9042	−1.89283
$63$	8.15233	1.02710
$64$	42.7673	5.34591
$65$	−13.1874	−1.63570
$66$	23.4887	2.89126
$67$	15.0912	1.84368	0.921840	−	0.387570i	$-0.126685\pi$
$67$	15.0912	1.84368	0.921840	+	0.387570i	$0.126685\pi$
$68$	−5.16365	−0.626185
$69$	−24.7246	−2.97649
$70$	−7.48091	−0.894140
$71$	−4.59300	−0.545089	−0.272545	−	0.962143i	$-0.587865\pi$
$71$	−4.59300	−0.545089	−0.272545	+	0.962143i	$0.587865\pi$
$72$	−85.0539	−10.0237
$73$	0.997451	0.116743	0.0583714	−	0.998295i	$-0.481409\pi$
$73$	0.997451	0.116743	0.0583714	+	0.998295i	$0.481409\pi$
$74$	−28.2740	−3.28679
$75$	7.42342	0.857182
$76$	11.2950	1.29563
$77$	−2.52684	−0.287961
$78$	45.6126	5.16461
$79$	−2.20739	−0.248351	−0.124175	−	0.992260i	$-0.539629\pi$
$79$	−2.20739	−0.248351	−0.124175	+	0.992260i	$0.539629\pi$
$80$	47.1522	5.27178
$81$	33.0035	3.66706
$82$	−9.80830	−1.08315
$83$	6.11616	0.671336	0.335668	−	0.941980i	$-0.391038\pi$
$83$	6.11616	0.671336	0.335668	+	0.941980i	$0.391038\pi$
$84$	19.1959	2.09445
$85$	−2.41427	−0.261865
$86$	−7.35367	−0.792967
$87$	11.7684	1.26171
$88$	26.3628	2.81028
$89$	−0.258006	−0.0273486	−0.0136743	−	0.999907i	$-0.504353\pi$
$89$	−0.258006	−0.0273486	−0.0136743	+	0.999907i	$0.504353\pi$
$90$	−60.9869	−6.42858
$91$	−4.90685	−0.514378
$92$	−42.5571	−4.43689
$93$	17.8810	1.85418
$94$	−13.6988	−1.41292
$95$	5.28100	0.541820
$96$	−93.4072	−9.53333
$97$	−12.8683	−1.30658	−0.653289	−	0.757109i	$-0.726611\pi$
$97$	−12.8683	−1.30658	−0.653289	+	0.757109i	$0.726611\pi$
$98$	−2.78355	−0.281181
$99$	−20.5997	−2.07035
$100$	12.7775	1.27775
$101$	8.24089	0.820000	0.410000	−	0.912086i	$-0.365529\pi$
$101$	8.24089	0.820000	0.410000	+	0.912086i	$0.365529\pi$
$102$	8.35049	0.826822
$103$	−15.5304	−1.53025	−0.765126	−	0.643881i	$-0.777323\pi$
$103$	−15.5304	−1.53025	−0.765126	+	0.643881i	$0.777323\pi$
$104$	51.1936	5.01995
$105$	8.97509	0.875879
$106$	−29.9789	−2.91181
$107$	−9.87896	−0.955035	−0.477518	−	0.878622i	$-0.658463\pi$
$107$	−9.87896	−0.955035	−0.477518	+	0.878622i	$0.658463\pi$
$108$	98.9038	9.51703
$109$	−13.9776	−1.33881	−0.669407	−	0.742895i	$-0.733452\pi$
$109$	−13.9776	−1.33881	−0.669407	+	0.742895i	$0.733452\pi$
$110$	18.9031	1.80234
$111$	33.9212	3.21966
$112$	17.5447	1.65782
$113$	6.40810	0.602824	0.301412	−	0.953494i	$-0.402542\pi$
$113$	6.40810	0.602824	0.301412	+	0.953494i	$0.402542\pi$
$114$	−18.2659	−1.71076
$115$	−19.8977	−1.85547
$116$	20.2564	1.88076
$117$	−40.0023	−3.69822
$118$	10.2856	0.946866
$119$	−0.898319	−0.0823488
$120$	−93.6378	−8.54793
$121$	−4.61506	−0.419551
$122$	−13.1993	−1.19501
$123$	11.7673	1.06103
$124$	30.7777	2.76392
$125$	−7.46357	−0.667562
$126$	−22.6924	−2.02160
$127$	14.9068	1.32277	0.661383	−	0.750048i	$-0.269970\pi$
$127$	14.9068	1.32277	0.661383	+	0.750048i	$0.269970\pi$
$128$	−63.1040	−5.57765
$129$	8.82244	0.776772
$130$	36.7077	3.21948
$131$	15.7376	1.37500	0.687499	−	0.726185i	$-0.258708\pi$
$131$	15.7376	1.37500	0.687499	+	0.726185i	$0.258708\pi$
$132$	−48.5051	−4.22183
$133$	1.96499	0.170386
$134$	−42.0070	−3.62885
$135$	46.2427	3.97993
$136$	9.37224	0.803663
$137$	−13.4824	−1.15188	−0.575938	−	0.817493i	$-0.695363\pi$
$137$	−13.4824	−1.15188	−0.575938	+	0.817493i	$0.695363\pi$
$138$	68.8220	5.85852
$139$	19.3976	1.64528	0.822641	−	0.568560i	$-0.192499\pi$
$139$	19.3976	1.64528	0.822641	+	0.568560i	$0.192499\pi$
$140$	15.4484	1.30562
$141$	16.4349	1.38407
$142$	12.7848	1.07288
$143$	12.3989	1.03684
$144$	143.030	11.9192
$145$	9.47092	0.786517
$146$	−2.77645	−0.229781
$147$	3.33951	0.275438
$148$	58.3869	4.79937
$149$	−15.4967	−1.26954	−0.634771	−	0.772700i	$-0.718906\pi$
$149$	−15.4967	−1.26954	−0.634771	+	0.772700i	$0.718906\pi$
$150$	−20.6634	−1.68716
$151$	6.75090	0.549380	0.274690	−	0.961533i	$-0.411425\pi$
$151$	6.75090	0.549380	0.274690	+	0.961533i	$0.411425\pi$
$152$	−20.5009	−1.66284
$153$	−7.32340	−0.592062
$154$	7.03359	0.566782
$155$	14.3902	1.15585
$156$	−94.1916	−7.54137
$157$	16.2790	1.29920	0.649602	−	0.760275i	$-0.274936\pi$
$157$	16.2790	1.29920	0.649602	+	0.760275i	$0.274936\pi$
$158$	6.14437	0.488820
$159$	35.9666	2.85234
$160$	−75.1715	−5.94283
$161$	−7.40366	−0.583490
$162$	−91.8669	−7.21774
$163$	−19.5637	−1.53235	−0.766174	−	0.642633i	$-0.777842\pi$
$163$	−19.5637	−1.53235	−0.766174	+	0.642633i	$0.777842\pi$
$164$	20.2545	1.58161
$165$	−22.6787	−1.76553
$166$	−17.0246	−1.32137
$167$	−17.3096	−1.33946	−0.669730	−	0.742604i	$-0.733590\pi$
$167$	−17.3096	−1.33946	−0.669730	+	0.742604i	$0.733590\pi$
$168$	−34.8414	−2.68807
$169$	11.0772	0.852094
$170$	6.72024	0.515419
$171$	16.0193	1.22502
$172$	15.1856	1.15789
$173$	0.548365	0.0416915	0.0208457	−	0.999783i	$-0.493364\pi$
$173$	0.548365	0.0416915	0.0208457	+	0.999783i	$0.493364\pi$
$174$	−32.7580	−2.48338
$175$	2.22291	0.168036
$176$	−44.3327	−3.34170
$177$	−12.3400	−0.927529
$178$	0.718172	0.0538292
$179$	−0.833334	−0.0622863	−0.0311432	−	0.999515i	$-0.509915\pi$
$179$	−0.833334	−0.0622863	−0.0311432	+	0.999515i	$0.509915\pi$
$180$	125.940	9.38702
$181$	4.58760	0.340994	0.170497	−	0.985358i	$-0.445463\pi$
$181$	4.58760	0.340994	0.170497	+	0.985358i	$0.445463\pi$
$182$	13.6585	1.01243
$183$	15.8357	1.17061
$184$	77.2429	5.69442
$185$	27.2989	2.00705
$186$	−49.7727	−3.64951
$187$	2.26991	0.165992
$188$	28.2885	2.06315
$189$	17.2063	1.25157
$190$	−14.6999	−1.06644
$191$	8.06570	0.583614	0.291807	−	0.956477i	$-0.405744\pi$
$191$	8.06570	0.583614	0.291807	+	0.956477i	$0.405744\pi$
$192$	142.822	10.3073
$193$	−17.8443	−1.28446	−0.642230	−	0.766512i	$-0.721990\pi$
$193$	−17.8443	−1.28446	−0.642230	+	0.766512i	$0.721990\pi$
$194$	35.8195	2.57169
$195$	−44.0395	−3.15373
$196$	5.74813	0.410580
$197$	18.2105	1.29744	0.648721	−	0.761026i	$-0.275304\pi$
$197$	18.2105	1.29744	0.648721	+	0.761026i	$0.275304\pi$
$198$	57.3401	4.07499
$199$	7.39789	0.524422	0.262211	−	0.965011i	$-0.415548\pi$
$199$	7.39789	0.524422	0.262211	+	0.965011i	$0.415548\pi$
$200$	−23.1918	−1.63990
$201$	50.3971	3.55474
$202$	−22.9389	−1.61398
$203$	3.52400	0.247336
$204$	−17.2441	−1.20733
$205$	9.47003	0.661416
$206$	43.2295	3.01194
$207$	−60.3571	−4.19511
$208$	−86.0893	−5.96922
$209$	−4.96522	−0.343452
$210$	−24.9826	−1.72396
$211$	15.7152	1.08188	0.540940	−	0.841061i	$-0.318069\pi$
$211$	15.7152	1.08188	0.540940	+	0.841061i	$0.318069\pi$
$212$	61.9075	4.25182
$213$	−15.3384	−1.05097
$214$	27.4985	1.87976
$215$	7.10005	0.484220
$216$	−179.514	−12.2144
$217$	5.35439	0.363480
$218$	38.9074	2.63514
$219$	3.33100	0.225088
$220$	−39.0356	−2.63178
$221$	4.40792	0.296509
$222$	−94.4213	−6.33714
$223$	18.1665	1.21652	0.608260	−	0.793738i	$-0.291868\pi$
$223$	18.1665	1.21652	0.608260	+	0.793738i	$0.291868\pi$
$224$	−27.9703	−1.86885
$225$	18.1219	1.20812
$226$	−17.8372	−1.18652
$227$	−16.9383	−1.12423	−0.562116	−	0.827058i	$-0.690013\pi$
$227$	−16.9383	−1.12423	−0.562116	+	0.827058i	$0.690013\pi$
$228$	37.7198	2.49806
$229$	7.58780	0.501416	0.250708	−	0.968063i	$-0.419337\pi$
$229$	7.58780	0.501416	0.250708	+	0.968063i	$0.419337\pi$
$230$	55.3861	3.65205
$231$	−8.43842	−0.555207
$232$	−36.7662	−2.41382
$233$	1.43260	0.0938528	0.0469264	−	0.998898i	$-0.485057\pi$
$233$	1.43260	0.0938528	0.0469264	+	0.998898i	$0.485057\pi$
$234$	111.348	7.27906
$235$	13.2263	0.862792
$236$	−21.2401	−1.38262
$237$	−7.37160	−0.478837
$238$	2.50051	0.162084
$239$	19.8979	1.28709	0.643545	−	0.765409i	$-0.277463\pi$
$239$	19.8979	1.28709	0.643545	+	0.765409i	$0.277463\pi$
$240$	157.465	10.1643
$241$	9.23048	0.594587	0.297294	−	0.954786i	$-0.403916\pi$
$241$	9.23048	0.594587	0.297294	+	0.954786i	$0.403916\pi$
$242$	12.8462	0.825787
$243$	58.5969	3.75899
$244$	27.2571	1.74496
$245$	2.68755	0.171701
$246$	−32.7549	−2.08838
$247$	−9.64192	−0.613501
$248$	−55.8628	−3.54729
$249$	20.4250	1.29438
$250$	20.7752	1.31394
$251$	−16.1184	−1.01739	−0.508694	−	0.860948i	$-0.669871\pi$
$251$	−16.1184	−1.01739	−0.508694	+	0.860948i	$0.669871\pi$
$252$	46.8606	2.95194
$253$	18.7079	1.17615
$254$	−41.4938	−2.60355
$255$	−8.06250	−0.504893
$256$	90.1182	5.63239
$257$	11.4760	0.715856	0.357928	−	0.933749i	$-0.383483\pi$
$257$	11.4760	0.715856	0.357928	+	0.933749i	$0.383483\pi$
$258$	−24.5577	−1.52889
$259$	10.1575	0.631159
$260$	−75.8028	−4.70109
$261$	28.7288	1.77827
$262$	−43.8063	−2.70636
$263$	−20.6072	−1.27070	−0.635348	−	0.772226i	$-0.719143\pi$
$263$	−20.6072	−1.27070	−0.635348	+	0.772226i	$0.719143\pi$
$264$	88.0387	5.41841
$265$	28.9450	1.77807
$266$	−5.46964	−0.335365
$267$	−0.861614	−0.0527299
$268$	86.7460	5.29885
$269$	−21.2595	−1.29621	−0.648107	−	0.761550i	$-0.724439\pi$
$269$	−21.2595	−1.29621	−0.648107	+	0.761550i	$0.724439\pi$
$270$	−128.719	−7.83356
$271$	3.13508	0.190443	0.0952213	−	0.995456i	$-0.469644\pi$
$271$	3.13508	0.190443	0.0952213	+	0.995456i	$0.469644\pi$
$272$	−15.7607	−0.955636
$273$	−16.3865	−0.991756
$274$	37.5288	2.26720
$275$	−5.61694	−0.338714
$276$	−142.120	−8.55462
$277$	1.68902	0.101483	0.0507416	−	0.998712i	$-0.483842\pi$
$277$	1.68902	0.101483	0.0507416	+	0.998712i	$0.483842\pi$
$278$	−53.9941	−3.23835
$279$	43.6508	2.61330
$280$	−28.0394	−1.67567
$281$	30.7213	1.83268	0.916340	−	0.400401i	$-0.131129\pi$
$281$	30.7213	1.83268	0.916340	+	0.400401i	$0.131129\pi$
$282$	−45.7473	−2.72421
$283$	7.82297	0.465027	0.232514	−	0.972593i	$-0.425305\pi$
$283$	7.82297	0.465027	0.232514	+	0.972593i	$0.425305\pi$
$284$	−26.4012	−1.56662
$285$	17.6360	1.04466
$286$	−34.5128	−2.04078
$287$	3.52367	0.207996
$288$	−228.023	−13.4364
$289$	−16.1930	−0.952531
$290$	−26.3627	−1.54807
$291$	−42.9738	−2.51917
$292$	5.73347	0.335526
$293$	−14.1345	−0.825746	−0.412873	−	0.910789i	$-0.635475\pi$
$293$	−14.1345	−0.825746	−0.412873	+	0.910789i	$0.635475\pi$
$294$	−9.29568	−0.542135
$295$	−9.93087	−0.578197
$296$	−105.975	−6.15964
$297$	−43.4776	−2.52282
$298$	43.1359	2.49879
$299$	36.3287	2.10094
$300$	42.6707	2.46360
$301$	2.64184	0.152273
$302$	−18.7914	−1.08133
$303$	27.5206	1.58101
$304$	34.4752	1.97729
$305$	12.7441	0.729725
$306$	20.3850	1.16533
$307$	−12.1644	−0.694259	−0.347130	−	0.937817i	$-0.612844\pi$
$307$	−12.1644	−0.694259	−0.347130	+	0.937817i	$0.612844\pi$
$308$	−14.5246	−0.827617
$309$	−51.8638	−2.95043
$310$	−40.0557	−2.27501
$311$	12.5605	0.712240	0.356120	−	0.934440i	$-0.384099\pi$
$311$	12.5605	0.712240	0.356120	+	0.934440i	$0.384099\pi$
$312$	170.962	9.67880
$313$	−26.9599	−1.52386	−0.761932	−	0.647657i	$-0.775749\pi$
$313$	−26.9599	−1.52386	−0.761932	+	0.647657i	$0.775749\pi$
$314$	−45.3133	−2.55717
$315$	21.9098	1.23448
$316$	−12.6883	−0.713775
$317$	0.212403	0.0119297	0.00596486	−	0.999982i	$-0.498101\pi$
$317$	0.212403	0.0119297	0.00596486	+	0.999982i	$0.498101\pi$
$318$	−100.115	−5.61416
$319$	−8.90460	−0.498562
$320$	114.939	6.42528
$321$	−32.9909	−1.84137
$322$	20.6084	1.14846
$323$	−1.76519	−0.0982178
$324$	189.709	10.5394
$325$	−10.9075	−0.605038
$326$	54.4565	3.01607
$327$	−46.6785	−2.58133
$328$	−36.7628	−2.02988
$329$	4.92135	0.271323
$330$	63.1271	3.47503
$331$	32.4629	1.78432	0.892161	−	0.451717i	$-0.149188\pi$
$331$	32.4629	1.78432	0.892161	+	0.451717i	$0.149188\pi$
$332$	35.1564	1.92946
$333$	82.8077	4.53784
$334$	48.1822	2.63641
$335$	40.5582	2.21593
$336$	58.5907	3.19639
$337$	−18.4264	−1.00375	−0.501875	−	0.864940i	$-0.667356\pi$
$337$	−18.4264	−1.00375	−0.501875	+	0.864940i	$0.667356\pi$
$338$	−30.8340	−1.67715
$339$	21.3999	1.16228
$340$	−13.8776	−0.752616
$341$	−13.5297	−0.732675
$342$	−44.5903	−2.41117
$343$	1.00000	0.0539949
$344$	−27.5625	−1.48607
$345$	−66.4485	−3.57747
$346$	−1.52640	−0.0820598
$347$	−4.83747	−0.259689	−0.129845	−	0.991534i	$-0.541448\pi$
$347$	−4.83747	−0.259689	−0.129845	+	0.991534i	$0.541448\pi$
$348$	67.6465	3.62623
$349$	−27.2657	−1.45950	−0.729749	−	0.683715i	$-0.760363\pi$
$349$	−27.2657	−1.45950	−0.729749	+	0.683715i	$0.760363\pi$
$350$	−6.18756	−0.330739
$351$	−84.4287	−4.50647
$352$	70.6766	3.76708
$353$	−28.4196	−1.51262	−0.756311	−	0.654212i	$-0.773000\pi$
$353$	−28.4196	−1.51262	−0.756311	+	0.654212i	$0.773000\pi$
$354$	34.3489	1.82562
$355$	−12.3439	−0.655147
$356$	−1.48305	−0.0786016
$357$	−2.99995	−0.158774
$358$	2.31962	0.122596
$359$	−11.5307	−0.608566	−0.304283	−	0.952582i	$-0.598417\pi$
$359$	−11.5307	−0.608566	−0.304283	+	0.952582i	$0.598417\pi$
$360$	−228.586	−12.0476
$361$	−15.1388	−0.796780
$362$	−12.7698	−0.671166
$363$	−15.4120	−0.808922
$364$	−28.2052	−1.47836
$365$	2.68070	0.140314
$366$	−44.0793	−2.30406
$367$	−27.2059	−1.42014	−0.710069	−	0.704133i	$-0.751336\pi$
$367$	−27.2059	−1.42014	−0.710069	+	0.704133i	$0.751336\pi$
$368$	−129.895	−6.77124
$369$	28.7262	1.49542
$370$	−75.9877	−3.95041
$371$	10.7700	0.559152
$372$	102.782	5.32902
$373$	23.8295	1.23384	0.616922	−	0.787025i	$-0.288380\pi$
$373$	23.8295	1.23384	0.616922	+	0.787025i	$0.288380\pi$
$374$	−6.31841	−0.326717
$375$	−24.9247	−1.28710
$376$	−51.3448	−2.64791
$377$	−17.2918	−0.890571
$378$	−47.8944	−2.46342
$379$	−10.2577	−0.526902	−0.263451	−	0.964673i	$-0.584861\pi$
$379$	−10.2577	−0.526902	−0.263451	+	0.964673i	$0.584861\pi$
$380$	30.3559	1.55722
$381$	49.7815	2.55038
$382$	−22.4512	−1.14871
$383$	−34.2465	−1.74991	−0.874957	−	0.484200i	$-0.839111\pi$
$383$	−34.2465	−1.74991	−0.874957	+	0.484200i	$0.839111\pi$
$384$	−210.736	−10.7541
$385$	−6.79101	−0.346102
$386$	49.6704	2.52815
$387$	21.5371	1.09479
$388$	−73.9686	−3.75519
$389$	11.2757	0.571701	0.285850	−	0.958274i	$-0.407724\pi$
$389$	11.2757	0.571701	0.285850	+	0.958274i	$0.407724\pi$
$390$	122.586	6.20738
$391$	6.65085	0.336348
$392$	−10.4331	−0.526950
$393$	52.5558	2.65109
$394$	−50.6897	−2.55371
$395$	−5.93246	−0.298494
$396$	−118.410	−5.95030
$397$	3.68603	0.184996	0.0924982	−	0.995713i	$-0.470515\pi$
$397$	3.68603	0.184996	0.0924982	+	0.995713i	$0.470515\pi$
$398$	−20.5924	−1.03220
$399$	6.56211	0.328516
$400$	39.0002	1.95001
$401$	−15.1300	−0.755555	−0.377777	−	0.925896i	$-0.623312\pi$
$401$	−15.1300	−0.755555	−0.377777	+	0.925896i	$0.623312\pi$
$402$	−140.283	−6.99667
$403$	−26.2732	−1.30876
$404$	47.3697	2.35673
$405$	88.6985	4.40747
$406$	−9.80922	−0.486824
$407$	−25.6665	−1.27224
$408$	31.2987	1.54952
$409$	11.7652	0.581751	0.290876	−	0.956761i	$-0.406053\pi$
$409$	11.7652	0.581751	0.290876	+	0.956761i	$0.406053\pi$
$410$	−26.3603	−1.30184
$411$	−45.0245	−2.22090
$412$	−89.2705	−4.39804
$413$	−3.69514	−0.181826
$414$	168.007	8.25708
$415$	16.4375	0.806883
$416$	137.246	6.72905
$417$	64.7785	3.17222
$418$	13.8209	0.676004
$419$	−4.40570	−0.215233	−0.107616	−	0.994193i	$-0.534322\pi$
$419$	−4.40570	−0.215233	−0.107616	+	0.994193i	$0.534322\pi$
$420$	51.5900	2.51733
$421$	2.54369	0.123972	0.0619860	−	0.998077i	$-0.480257\pi$
$421$	2.54369	0.123972	0.0619860	+	0.998077i	$0.480257\pi$
$422$	−43.7440	−2.12943
$423$	40.1204	1.95072
$424$	−112.365	−5.45691
$425$	−1.99688	−0.0968629
$426$	42.6951	2.06858
$427$	4.74191	0.229477
$428$	−56.7855	−2.74483
$429$	41.4061	1.99911
$430$	−19.7633	−0.953072
$431$	−34.5764	−1.66548	−0.832742	−	0.553661i	$-0.813230\pi$
$431$	−34.5764	−1.66548	−0.832742	+	0.553661i	$0.813230\pi$
$432$	301.879	14.5242
$433$	1.26053	0.0605774	0.0302887	−	0.999541i	$-0.490357\pi$
$433$	1.26053	0.0605774	0.0302887	+	0.999541i	$0.490357\pi$
$434$	−14.9042	−0.715424
$435$	31.6282	1.51646
$436$	−80.3452	−3.84784
$437$	−14.5481	−0.695931
$438$	−9.27199	−0.443033
$439$	38.1478	1.82070	0.910348	−	0.413844i	$-0.135814\pi$
$439$	38.1478	1.82070	0.910348	+	0.413844i	$0.135814\pi$
$440$	70.8512	3.37770
$441$	8.15233	0.388206
$442$	−12.2697	−0.583608
$443$	5.85895	0.278367	0.139184	−	0.990267i	$-0.455552\pi$
$443$	5.85895	0.278367	0.139184	+	0.990267i	$0.455552\pi$
$444$	194.984	9.25351
$445$	−0.693403	−0.0328705
$446$	−50.5674	−2.39443
$447$	−51.7515	−2.44776
$448$	42.7673	2.02056
$449$	8.75706	0.413271	0.206636	−	0.978418i	$-0.433749\pi$
$449$	8.75706	0.413271	0.206636	+	0.978418i	$0.433749\pi$
$450$	−50.4430	−2.37791
$451$	−8.90377	−0.419262
$452$	36.8346	1.73255
$453$	22.5447	1.05924
$454$	47.1484	2.21279
$455$	−13.1874	−0.618235
$456$	−68.4630	−3.20607
$457$	24.3779	1.14035	0.570174	−	0.821524i	$-0.306876\pi$
$457$	24.3779	1.14035	0.570174	+	0.821524i	$0.306876\pi$
$458$	−21.1210	−0.986920
$459$	−15.4567	−0.721458
$460$	−114.374	−5.33273
$461$	5.55811	0.258867	0.129433	−	0.991588i	$-0.458684\pi$
$461$	5.55811	0.258867	0.129433	+	0.991588i	$0.458684\pi$
$462$	23.4887	1.09279
$463$	−36.1419	−1.67966	−0.839828	−	0.542852i	$-0.817344\pi$
$463$	−36.1419	−1.67966	−0.839828	+	0.542852i	$0.817344\pi$
$464$	61.8276	2.87027
$465$	48.0561	2.22855
$466$	−3.98771	−0.184727
$467$	25.8200	1.19481	0.597403	−	0.801941i	$-0.296199\pi$
$467$	25.8200	1.19481	0.597403	+	0.801941i	$0.296199\pi$
$468$	−229.938	−10.6289
$469$	15.0912	0.696846
$470$	−36.8161	−1.69820
$471$	54.3638	2.50495
$472$	38.5517	1.77449
$473$	−6.67551	−0.306940
$474$	20.5192	0.942477
$475$	4.36799	0.200417
$476$	−5.16365	−0.236676
$477$	87.8009	4.02013
$478$	−55.3868	−2.53333
$479$	−22.7515	−1.03954	−0.519771	−	0.854306i	$-0.673983\pi$
$479$	−22.7515	−1.03954	−0.519771	+	0.854306i	$0.673983\pi$
$480$	−251.036	−11.4582
$481$	−49.8416	−2.27258
$482$	−25.6935	−1.17030
$483$	−24.7246	−1.12501
$484$	−26.5279	−1.20582
$485$	−34.5841	−1.57039
$486$	−163.107	−7.39869
$487$	19.5000	0.883631	0.441815	−	0.897106i	$-0.354335\pi$
$487$	19.5000	0.883631	0.441815	+	0.897106i	$0.354335\pi$
$488$	−49.4727	−2.23953
$489$	−65.3333	−2.95447
$490$	−7.48091	−0.337953
$491$	0.825638	0.0372605	0.0186303	−	0.999826i	$-0.494069\pi$
$491$	0.825638	0.0372605	0.0186303	+	0.999826i	$0.494069\pi$
$492$	67.6402	3.04945
$493$	−3.16568	−0.142575
$494$	26.8387	1.20753
$495$	−55.3626	−2.48836
$496$	93.9412	4.21808
$497$	−4.59300	−0.206024
$498$	−56.8539	−2.54768
$499$	−6.39391	−0.286231	−0.143115	−	0.989706i	$-0.545712\pi$
$499$	−6.39391	−0.286231	−0.143115	+	0.989706i	$0.545712\pi$
$500$	−42.9015	−1.91862
$501$	−57.8058	−2.58257
$502$	44.8664	2.00249
$503$	−1.65864	−0.0739551	−0.0369776	−	0.999316i	$-0.511773\pi$
$503$	−1.65864	−0.0739551	−0.0369776	+	0.999316i	$0.511773\pi$
$504$	−85.0539	−3.78860
$505$	22.1478	0.985563
$506$	−52.0742	−2.31498
$507$	36.9925	1.64290
$508$	85.6863	3.80172
$509$	−32.8921	−1.45792	−0.728959	−	0.684557i	$-0.759996\pi$
$509$	−32.8921	−1.45792	−0.728959	+	0.684557i	$0.759996\pi$
$510$	22.4423	0.993763
$511$	0.997451	0.0441246
$512$	−124.640	−5.50838
$513$	33.8102	1.49276
$514$	−31.9441	−1.40899
$515$	−41.7386	−1.83922
$516$	50.7125	2.23249
$517$	−12.4355	−0.546911
$518$	−28.2740	−1.24229
$519$	1.83127	0.0803839
$520$	137.585	6.03351
$521$	−25.7490	−1.12809	−0.564043	−	0.825746i	$-0.690755\pi$
$521$	−25.7490	−1.12809	−0.564043	+	0.825746i	$0.690755\pi$
$522$	−79.9680	−3.50011
$523$	8.38881	0.366817	0.183408	−	0.983037i	$-0.441287\pi$
$523$	8.38881	0.366817	0.183408	+	0.983037i	$0.441287\pi$
$524$	90.4616	3.95183
$525$	7.42342	0.323985
$526$	57.3611	2.50106
$527$	−4.80995	−0.209525
$528$	−148.050	−6.44303
$529$	31.8141	1.38322
$530$	−80.5696	−3.49972
$531$	−30.1240	−1.30727
$532$	11.2950	0.489701
$533$	−17.2902	−0.748920
$534$	2.39834	0.103786
$535$	−26.5502	−1.14786
$536$	−157.447	−6.80069
$537$	−2.78293	−0.120092
$538$	59.1767	2.55129
$539$	−2.52684	−0.108839
$540$	265.809	11.4386
$541$	−15.9640	−0.686347	−0.343173	−	0.939272i	$-0.611502\pi$
$541$	−15.9640	−0.686347	−0.343173	+	0.939272i	$0.611502\pi$
$542$	−8.72664	−0.374841
$543$	15.3203	0.657459
$544$	25.1263	1.07728
$545$	−37.5655	−1.60913
$546$	45.6126	1.95204
$547$	−12.7862	−0.546697	−0.273349	−	0.961915i	$-0.588131\pi$
$547$	−12.7862	−0.546697	−0.273349	+	0.961915i	$0.588131\pi$
$548$	−77.4984	−3.31057
$549$	38.6576	1.64987
$550$	15.6350	0.666679
$551$	6.92463	0.294999
$552$	257.954	10.9792
$553$	−2.20739	−0.0938677
$554$	−4.70146	−0.199746
$555$	91.1649	3.86974
$556$	111.500	4.72865
$557$	32.8370	1.39135	0.695675	−	0.718357i	$-0.255106\pi$
$557$	32.8370	1.39135	0.695675	+	0.718357i	$0.255106\pi$
$558$	−121.504	−5.14367
$559$	−12.9631	−0.548281
$560$	47.1522	1.99254
$561$	7.58040	0.320045
$562$	−85.5142	−3.60720
$563$	−4.79678	−0.202160	−0.101080	−	0.994878i	$-0.532230\pi$
$563$	−4.79678	−0.202160	−0.101080	+	0.994878i	$0.532230\pi$
$564$	94.4698	3.97790
$565$	17.2221	0.724538
$566$	−21.7756	−0.915296
$567$	33.0035	1.38602
$568$	47.9192	2.01064
$569$	−28.2119	−1.18270	−0.591352	−	0.806413i	$-0.701406\pi$
$569$	−28.2119	−1.18270	−0.591352	+	0.806413i	$0.701406\pi$
$570$	−49.0905	−2.05618
$571$	12.8718	0.538666	0.269333	−	0.963047i	$-0.413197\pi$
$571$	12.8718	0.538666	0.269333	+	0.963047i	$0.413197\pi$
$572$	71.2702	2.97996
$573$	26.9355	1.12525
$574$	−9.80830	−0.409391
$575$	−16.4576	−0.686331
$576$	348.653	14.5272
$577$	−5.28478	−0.220008	−0.110004	−	0.993931i	$-0.535086\pi$
$577$	−5.28478	−0.220008	−0.110004	+	0.993931i	$0.535086\pi$
$578$	45.0740	1.87483
$579$	−59.5912	−2.47652
$580$	54.4400	2.26050
$581$	6.11616	0.253741
$582$	119.620	4.95839
$583$	−27.2142	−1.12710
$584$	−10.4065	−0.430623
$585$	−107.508	−4.44491
$586$	39.3440	1.62529
$587$	−5.85564	−0.241688	−0.120844	−	0.992672i	$-0.538560\pi$
$587$	−5.85564	−0.241688	−0.120844	+	0.992672i	$0.538560\pi$
$588$	19.1959	0.791627
$589$	10.5213	0.433524
$590$	27.6430	1.13805
$591$	60.8141	2.50156
$592$	178.211	7.32443
$593$	−39.8727	−1.63737	−0.818687	−	0.574240i	$-0.805297\pi$
$593$	−39.8727	−1.63737	−0.818687	+	0.574240i	$0.805297\pi$
$594$	121.022	4.96558
$595$	−2.41427	−0.0989756
$596$	−89.0772	−3.64874
$597$	24.7053	1.01112
$598$	−101.122	−4.13521
$599$	21.6257	0.883602	0.441801	−	0.897113i	$-0.354340\pi$
$599$	21.6257	0.883602	0.441801	+	0.897113i	$0.354340\pi$
$600$	−77.4491	−3.16185
$601$	6.15561	0.251092	0.125546	−	0.992088i	$-0.459932\pi$
$601$	6.15561	0.251092	0.125546	+	0.992088i	$0.459932\pi$
$602$	−7.35367	−0.299713
$603$	123.028	5.01010
$604$	38.8050	1.57895
$605$	−12.4032	−0.504261
$606$	−76.6047	−3.11185
$607$	−32.1224	−1.30381	−0.651904	−	0.758301i	$-0.726030\pi$
$607$	−32.1224	−1.30381	−0.651904	+	0.758301i	$0.726030\pi$
$608$	−54.9614	−2.22898
$609$	11.7684	0.476881
$610$	−35.4738	−1.43629
$611$	−24.1483	−0.976937
$612$	−42.0958	−1.70162
$613$	24.4930	0.989263	0.494632	−	0.869103i	$-0.335303\pi$
$613$	24.4930	0.989263	0.494632	+	0.869103i	$0.335303\pi$
$614$	33.8602	1.36649
$615$	31.6253	1.27525
$616$	26.3628	1.06219
$617$	−11.9827	−0.482407	−0.241203	−	0.970475i	$-0.577542\pi$
$617$	−11.9827	−0.482407	−0.241203	+	0.970475i	$0.577542\pi$
$618$	144.365	5.80722
$619$	10.5974	0.425944	0.212972	−	0.977058i	$-0.431686\pi$
$619$	10.5974	0.425944	0.212972	+	0.977058i	$0.431686\pi$
$620$	82.7165	3.32198
$621$	−127.389	−5.11196
$622$	−34.9627	−1.40188
$623$	−0.258006	−0.0103368
$624$	−287.496	−11.5091
$625$	−31.1732	−1.24693
$626$	75.0441	2.99937
$627$	−16.5814	−0.662198
$628$	93.5736	3.73399
$629$	−9.12472	−0.363826
$630$	−60.9869	−2.42977
$631$	−19.8811	−0.791454	−0.395727	−	0.918368i	$-0.629507\pi$
$631$	−19.8811	−0.791454	−0.395727	+	0.918368i	$0.629507\pi$
$632$	23.0299	0.916079
$633$	52.4811	2.08594
$634$	−0.591232	−0.0234808
$635$	40.0628	1.58984
$636$	206.741	8.19780
$637$	−4.90685	−0.194417
$638$	24.7864	0.981302
$639$	−37.4437	−1.48125
$640$	−169.595	−6.70382
$641$	−25.1021	−0.991474	−0.495737	−	0.868473i	$-0.665102\pi$
$641$	−25.1021	−0.991474	−0.495737	+	0.868473i	$0.665102\pi$
$642$	91.8317	3.62431
$643$	26.5726	1.04792	0.523961	−	0.851742i	$-0.324454\pi$
$643$	26.5726	1.04792	0.523961	+	0.851742i	$0.324454\pi$
$644$	−42.5571	−1.67699
$645$	23.7107	0.933608
$646$	4.91348	0.193318
$647$	20.7820	0.817024	0.408512	−	0.912753i	$-0.366048\pi$
$647$	20.7820	0.817024	0.408512	+	0.912753i	$0.366048\pi$
$648$	−344.329	−13.5265
$649$	9.33705	0.366511
$650$	30.3615	1.19087
$651$	17.8810	0.700813
$652$	−112.455	−4.40407
$653$	−12.8734	−0.503775	−0.251887	−	0.967757i	$-0.581051\pi$
$653$	−12.8734	−0.503775	−0.251887	+	0.967757i	$0.581051\pi$
$654$	129.932	5.08073
$655$	42.2955	1.65262
$656$	61.8218	2.41374
$657$	8.13155	0.317242
$658$	−13.6988	−0.534034
$659$	−22.9558	−0.894231	−0.447116	−	0.894476i	$-0.647549\pi$
$659$	−22.9558	−0.894231	−0.447116	+	0.894476i	$0.647549\pi$
$660$	−130.360	−5.07425
$661$	32.9435	1.28135	0.640677	−	0.767811i	$-0.278654\pi$
$661$	32.9435	1.28135	0.640677	+	0.767811i	$0.278654\pi$
$662$	−90.3620	−3.51202
$663$	14.7203	0.571689
$664$	−63.8104	−2.47632
$665$	5.28100	0.204789
$666$	−230.499	−8.93166
$667$	−26.0905	−1.01023
$668$	−99.4981	−3.84970
$669$	60.6673	2.34553
$670$	−112.896	−4.36154
$671$	−11.9821	−0.462563
$672$	−93.4072	−3.60326
$673$	−23.0069	−0.886852	−0.443426	−	0.896311i	$-0.646237\pi$
$673$	−23.0069	−0.886852	−0.443426	+	0.896311i	$0.646237\pi$
$674$	51.2907	1.97565
$675$	38.2479	1.47216
$676$	63.6733	2.44897
$677$	0.672321	0.0258394	0.0129197	−	0.999917i	$-0.495887\pi$
$677$	0.672321	0.0258394	0.0129197	+	0.999917i	$0.495887\pi$
$678$	−59.5677	−2.28768
$679$	−12.8683	−0.493840
$680$	25.1883	0.965928
$681$	−56.5655	−2.16760
$682$	37.6606	1.44210
$683$	−13.2574	−0.507282	−0.253641	−	0.967298i	$-0.581628\pi$
$683$	−13.2574	−0.507282	−0.253641	+	0.967298i	$0.581628\pi$
$684$	92.0807	3.52079
$685$	−36.2345	−1.38445
$686$	−2.78355	−0.106276
$687$	25.3396	0.966764
$688$	46.3502	1.76709
$689$	−52.8470	−2.01331
$690$	184.962	7.04140
$691$	48.8133	1.85695	0.928473	−	0.371400i	$-0.121122\pi$
$691$	48.8133	1.85695	0.928473	+	0.371400i	$0.121122\pi$
$692$	3.15207	0.119824
$693$	−20.5997	−0.782517
$694$	13.4653	0.511137
$695$	52.1319	1.97748
$696$	−122.781	−4.65401
$697$	−3.16538	−0.119897
$698$	75.8952	2.87268
$699$	4.78419	0.180955
$700$	12.7775	0.482946
$701$	34.6479	1.30863	0.654316	−	0.756221i	$-0.272957\pi$
$701$	34.6479	1.30863	0.654316	+	0.756221i	$0.272957\pi$
$702$	235.011	8.86992
$703$	19.9595	0.752786
$704$	−108.066	−4.07290
$705$	44.1695	1.66352
$706$	79.1072	2.97724
$707$	8.24089	0.309931
$708$	−70.9317	−2.66578
$709$	−33.1037	−1.24323	−0.621617	−	0.783321i	$-0.713524\pi$
$709$	−33.1037	−1.24323	−0.621617	+	0.783321i	$0.713524\pi$
$710$	34.3598	1.28950
$711$	−17.9954	−0.674879
$712$	2.69180	0.100879
$713$	−39.6421	−1.48461
$714$	8.35049	0.312509
$715$	33.3225	1.24619
$716$	−4.79011	−0.179015
$717$	66.4493	2.48160
$718$	32.0962	1.19782
$719$	−14.6559	−0.546573	−0.273287	−	0.961933i	$-0.588111\pi$
$719$	−14.6559	−0.546573	−0.273287	+	0.961933i	$0.588111\pi$
$720$	384.400	14.3258
$721$	−15.5304	−0.578381
$722$	42.1396	1.56827
$723$	30.8253	1.14640
$724$	26.3701	0.980037
$725$	7.83353	0.290930
$726$	42.9001	1.59217
$727$	27.5681	1.02244	0.511222	−	0.859449i	$-0.329193\pi$
$727$	27.5681	1.02244	0.511222	+	0.859449i	$0.329193\pi$
$728$	51.1936	1.89736
$729$	96.6743	3.58053
$730$	−7.46184	−0.276175
$731$	−2.37321	−0.0877764
$732$	91.0254	3.36439
$733$	31.0660	1.14745	0.573724	−	0.819049i	$-0.305498\pi$
$733$	31.0660	1.14745	0.573724	+	0.819049i	$0.305498\pi$
$734$	75.7289	2.79520
$735$	8.97509	0.331051
$736$	207.083	7.63317
$737$	−38.1330	−1.40465
$738$	−79.9606	−2.94339
$739$	52.1990	1.92017	0.960087	−	0.279703i	$-0.0902361\pi$
$739$	52.1990	1.92017	0.960087	+	0.279703i	$0.0902361\pi$
$740$	156.917	5.76840
$741$	−32.1993	−1.18287
$742$	−29.9789	−1.10056
$743$	0.203467	0.00746447	0.00373224	−	0.999993i	$-0.498812\pi$
$743$	0.203467	0.00746447	0.00373224	+	0.999993i	$0.498812\pi$
$744$	−186.554	−6.83941
$745$	−41.6482	−1.52587
$746$	−66.3304	−2.42853
$747$	49.8610	1.82432
$748$	13.0477	0.477073
$749$	−9.87896	−0.360969
$750$	69.3790	2.53336
$751$	−34.0461	−1.24236	−0.621181	−	0.783667i	$-0.713347\pi$
$751$	−34.0461	−1.24236	−0.621181	+	0.783667i	$0.713347\pi$
$752$	86.3435	3.14862
$753$	−53.8277	−1.96159
$754$	48.1324	1.75288
$755$	18.1434	0.660304
$756$	98.9038	3.59710
$757$	−34.4288	−1.25134	−0.625668	−	0.780090i	$-0.715173\pi$
$757$	−34.4288	−1.25134	−0.625668	+	0.780090i	$0.715173\pi$
$758$	28.5527	1.03708
$759$	62.4752	2.26771
$760$	−55.0971	−1.99858
$761$	−19.1195	−0.693082	−0.346541	−	0.938035i	$-0.612644\pi$
$761$	−19.1195	−0.693082	−0.346541	+	0.938035i	$0.612644\pi$
$762$	−138.569	−5.01983
$763$	−13.9776	−0.506024
$764$	46.3627	1.67734
$765$	−19.6820	−0.711603
$766$	95.3267	3.44429
$767$	18.1315	0.654692
$768$	300.951	10.8596
$769$	−38.5267	−1.38931	−0.694654	−	0.719344i	$-0.744442\pi$
$769$	−38.5267	−1.38931	−0.694654	+	0.719344i	$0.744442\pi$
$770$	18.9031	0.681220
$771$	38.3244	1.38022
$772$	−102.571	−3.69162
$773$	−4.05449	−0.145830	−0.0729149	−	0.997338i	$-0.523230\pi$
$773$	−4.05449	−0.145830	−0.0729149	+	0.997338i	$0.523230\pi$
$774$	−59.9496	−2.15484
$775$	11.9023	0.427543
$776$	134.256	4.81951
$777$	33.9212	1.21692
$778$	−31.3864	−1.12526
$779$	6.92398	0.248077
$780$	−253.144	−9.06402
$781$	11.6058	0.415288
$782$	−18.5129	−0.662021
$783$	60.6350	2.16692
$784$	17.5447	0.626597
$785$	43.7505	1.56152
$786$	−146.292	−5.21805
$787$	−50.4683	−1.79900	−0.899501	−	0.436920i	$-0.856069\pi$
$787$	−50.4683	−1.79900	−0.899501	+	0.436920i	$0.856069\pi$
$788$	104.676	3.72893
$789$	−68.8180	−2.44999
$790$	16.5133	0.587516
$791$	6.40810	0.227846
$792$	214.918	7.63678
$793$	−23.2679	−0.826266
$794$	−10.2602	−0.364122
$795$	96.6620	3.42825
$796$	42.5240	1.50722
$797$	52.0598	1.84405	0.922026	−	0.387129i	$-0.126533\pi$
$797$	52.0598	1.84405	0.922026	+	0.387129i	$0.126533\pi$
$798$	−18.2659	−0.646607
$799$	−4.42094	−0.156402
$800$	−62.1754	−2.19823
$801$	−2.10335	−0.0743183
$802$	42.1150	1.48713
$803$	−2.52040	−0.0889431
$804$	289.689	10.2165
$805$	−19.8977	−0.701301
$806$	73.1327	2.57599
$807$	−70.9963	−2.49919
$808$	−85.9779	−3.02469
$809$	27.0305	0.950343	0.475171	−	0.879893i	$-0.342386\pi$
$809$	27.0305	0.950343	0.475171	+	0.879893i	$0.342386\pi$
$810$	−246.896	−8.67506
$811$	−45.0723	−1.58270	−0.791352	−	0.611361i	$-0.790622\pi$
$811$	−45.0723	−1.58270	−0.791352	+	0.611361i	$0.790622\pi$
$812$	20.2564	0.710861
$813$	10.4696	0.367186
$814$	71.4440	2.50411
$815$	−52.5784	−1.84174
$816$	−52.6332	−1.84253
$817$	5.19118	0.181616
$818$	−32.7489	−1.14504
$819$	−40.0023	−1.39779
$820$	54.4349	1.90095
$821$	34.1637	1.19232	0.596160	−	0.802866i	$-0.296692\pi$
$821$	34.1637	1.19232	0.596160	+	0.802866i	$0.296692\pi$
$822$	125.328	4.37131
$823$	19.7111	0.687086	0.343543	−	0.939137i	$-0.388373\pi$
$823$	19.7111	0.687086	0.343543	+	0.939137i	$0.388373\pi$
$824$	162.029	5.64456
$825$	−18.7578	−0.653063
$826$	10.2856	0.357882
$827$	−16.1912	−0.563022	−0.281511	−	0.959558i	$-0.590836\pi$
$827$	−16.1912	−0.563022	−0.281511	+	0.959558i	$0.590836\pi$
$828$	−346.940	−12.0570
$829$	18.5905	0.645673	0.322837	−	0.946455i	$-0.395364\pi$
$829$	18.5905	0.645673	0.322837	+	0.946455i	$0.395364\pi$
$830$	−45.7544	−1.58816
$831$	5.64049	0.195667
$832$	−209.853	−7.27533
$833$	−0.898319	−0.0311249
$834$	−180.314	−6.24376
$835$	−46.5205	−1.60991
$836$	−28.5407	−0.987102
$837$	92.1291	3.18445
$838$	12.2635	0.423635
$839$	−37.2509	−1.28604	−0.643022	−	0.765848i	$-0.722320\pi$
$839$	−37.2509	−1.28604	−0.643022	+	0.765848i	$0.722320\pi$
$840$	−93.6378	−3.23081
$841$	−16.5814	−0.571773
$842$	−7.08048	−0.244010
$843$	102.594	3.53353
$844$	90.3330	3.10939
$845$	29.7706	1.02414
$846$	−111.677	−3.83954
$847$	−4.61506	−0.158575
$848$	188.957	6.48881
$849$	26.1249	0.896604
$850$	5.55840	0.190652
$851$	−75.2030	−2.57793
$852$	−88.1670	−3.02055
$853$	−15.3883	−0.526887	−0.263444	−	0.964675i	$-0.584858\pi$
$853$	−15.3883	−0.526887	−0.263444	+	0.964675i	$0.584858\pi$
$854$	−13.1993	−0.451672
$855$	43.0525	1.47236
$856$	103.068	3.52279
$857$	−26.6079	−0.908907	−0.454454	−	0.890770i	$-0.650165\pi$
$857$	−26.6079	−0.908907	−0.454454	+	0.890770i	$0.650165\pi$
$858$	−115.256	−3.93477
$859$	17.4030	0.593781	0.296891	−	0.954911i	$-0.404050\pi$
$859$	17.4030	0.593781	0.296891	+	0.954911i	$0.404050\pi$
$860$	40.8120	1.39168
$861$	11.7673	0.401030
$862$	96.2449	3.27811
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−481.265	−16.3730
$865$	1.47376	0.0501093
$866$	−3.50876	−0.119232
$867$	−54.0768	−1.83654
$868$	30.7777	1.04466
$869$	5.57773	0.189211
$870$	−88.0387	−2.98479
$871$	−74.0502	−2.50910
$872$	145.830	4.93842
$873$	−104.907	−3.55055
$874$	40.4953	1.36978
$875$	−7.46357	−0.252315
$876$	19.1470	0.646917
$877$	24.6938	0.833851	0.416925	−	0.908941i	$-0.363108\pi$
$877$	24.6938	0.833851	0.416925	+	0.908941i	$0.363108\pi$
$878$	−106.186	−3.58361
$879$	−47.2023	−1.59209
$880$	−119.146	−4.01642
$881$	−30.7811	−1.03704	−0.518521	−	0.855065i	$-0.673517\pi$
$881$	−30.7811	−1.03704	−0.518521	+	0.855065i	$0.673517\pi$
$882$	−22.6924	−0.764093
$883$	42.6404	1.43496	0.717482	−	0.696578i	$-0.245295\pi$
$883$	42.6404	1.43496	0.717482	+	0.696578i	$0.245295\pi$
$884$	25.3373	0.852185
$885$	−33.1642	−1.11480
$886$	−16.3086	−0.547900
$887$	57.5076	1.93092	0.965458	−	0.260560i	$-0.0839071\pi$
$887$	57.5076	1.93092	0.965458	+	0.260560i	$0.0839071\pi$
$888$	−353.903	−11.8762
$889$	14.9068	0.499959
$890$	1.93012	0.0646978
$891$	−83.3948	−2.79383
$892$	104.423	3.49636
$893$	9.67040	0.323608
$894$	144.053	4.81784
$895$	−2.23962	−0.0748624
$896$	−63.1040	−2.10816
$897$	121.320	4.05076
$898$	−24.3757	−0.813427
$899$	18.8689	0.629312
$900$	104.167	3.47223
$901$	−9.67493	−0.322319
$902$	24.7841	0.825219
$903$	8.82244	0.293592
$904$	−66.8563	−2.22361
$905$	12.3294	0.409843
$906$	−62.7542	−2.08487
$907$	−31.2796	−1.03862	−0.519312	−	0.854585i	$-0.673812\pi$
$907$	−31.2796	−1.03862	−0.519312	+	0.854585i	$0.673812\pi$
$908$	−97.3633	−3.23111
$909$	67.1825	2.22830
$910$	36.7077	1.21685
$911$	51.8378	1.71746	0.858731	−	0.512427i	$-0.171253\pi$
$911$	51.8378	1.71746	0.858731	+	0.512427i	$0.171253\pi$
$912$	115.130	3.81234
$913$	−15.4546	−0.511472
$914$	−67.8569	−2.24451
$915$	42.5591	1.40696
$916$	43.6157	1.44110
$917$	15.7376	0.519701
$918$	43.0245	1.42002
$919$	17.4053	0.574149	0.287075	−	0.957908i	$-0.407317\pi$
$919$	17.4053	0.574149	0.287075	+	0.957908i	$0.407317\pi$
$920$	207.594	6.84417
$921$	−40.6232	−1.33858
$922$	−15.4713	−0.509519
$923$	22.5372	0.741821
$924$	−48.5051	−1.59570
$925$	22.5793	0.742402
$926$	100.603	3.30601
$927$	−126.609	−4.15837
$928$	−98.5675	−3.23564
$929$	−6.59507	−0.216377	−0.108189	−	0.994130i	$-0.534505\pi$
$929$	−6.59507	−0.216377	−0.108189	+	0.994130i	$0.534505\pi$
$930$	−133.766	−4.38637
$931$	1.96499	0.0644000
$932$	8.23477	0.269739
$933$	41.9459	1.37325
$934$	−71.8711	−2.35169
$935$	6.10050	0.199508
$936$	417.347	13.6414
$937$	−18.8613	−0.616170	−0.308085	−	0.951359i	$-0.599688\pi$
$937$	−18.8613	−0.616170	−0.308085	+	0.951359i	$0.599688\pi$
$938$	−42.0070	−1.37158
$939$	−90.0329	−2.93811
$940$	76.0267	2.47972
$941$	17.9991	0.586755	0.293378	−	0.955997i	$-0.405221\pi$
$941$	17.9991	0.586755	0.293378	+	0.955997i	$0.405221\pi$
$942$	−151.324	−4.93041
$943$	−26.0881	−0.849544
$944$	−64.8302	−2.11004
$945$	46.2427	1.50427
$946$	18.5816	0.604139
$947$	12.9401	0.420496	0.210248	−	0.977648i	$-0.432573\pi$
$947$	12.9401	0.420496	0.210248	+	0.977648i	$0.432573\pi$
$948$	−42.3729	−1.37621
$949$	−4.89435	−0.158877
$950$	−12.1585	−0.394474
$951$	0.709321	0.0230013
$952$	9.37224	0.303756
$953$	−21.0421	−0.681620	−0.340810	−	0.940132i	$-0.610701\pi$
$953$	−21.0421	−0.681620	−0.340810	+	0.940132i	$0.610701\pi$
$954$	−244.398	−7.91267
$955$	21.6769	0.701450
$956$	114.376	3.69918
$957$	−29.7370	−0.961261
$958$	63.3298	2.04609
$959$	−13.4824	−0.435368
$960$	383.840	12.3884
$961$	−2.33051	−0.0751778
$962$	138.736	4.47304
$963$	−80.5366	−2.59526
$964$	53.0580	1.70888
$965$	−47.9573	−1.54380
$966$	68.8220	2.21431
$967$	−29.3495	−0.943816	−0.471908	−	0.881648i	$-0.656435\pi$
$967$	−29.3495	−0.943816	−0.471908	+	0.881648i	$0.656435\pi$
$968$	48.1493	1.54758
$969$	−5.89487	−0.189370
$970$	96.2665	3.09093
$971$	47.3344	1.51903	0.759517	−	0.650488i	$-0.225435\pi$
$971$	47.3344	1.51903	0.759517	+	0.650488i	$0.225435\pi$
$972$	336.822	10.8036
$973$	19.3976	0.621858
$974$	−54.2792	−1.73922
$975$	−36.4256	−1.16655
$976$	83.1954	2.66302
$977$	−24.5942	−0.786840	−0.393420	−	0.919359i	$-0.628708\pi$
$977$	−24.5942	−0.786840	−0.393420	+	0.919359i	$0.628708\pi$
$978$	181.858	5.81518
$979$	0.651941	0.0208361
$980$	15.4484	0.493480
$981$	−113.950	−3.63816
$982$	−2.29820	−0.0733386
$983$	−39.8918	−1.27235	−0.636175	−	0.771545i	$-0.719484\pi$
$983$	−39.8918	−1.27235	−0.636175	+	0.771545i	$0.719484\pi$
$984$	−122.770	−3.91375
$985$	48.9415	1.55941
$986$	8.81181	0.280625
$987$	16.4349	0.523128
$988$	−55.4230	−1.76324
$989$	−19.5592	−0.621948
$990$	154.104	4.89776
$991$	50.0976	1.59140	0.795701	−	0.605690i	$-0.207103\pi$
$991$	50.0976	1.59140	0.795701	+	0.605690i	$0.207103\pi$
$992$	−149.764	−4.75501
$993$	108.410	3.44029
$994$	12.7848	0.405510
$995$	19.8822	0.630307
$996$	117.405	3.72013
$997$	13.3312	0.422203	0.211101	−	0.977464i	$-0.432295\pi$
$997$	13.3312	0.422203	0.211101	+	0.977464i	$0.432295\pi$
$998$	17.7977	0.563377
$999$	174.774	5.52959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.2	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.2	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78355 q^{2} +3.33951 q^{3} +5.74813 q^{4} +2.68755 q^{5} -9.29568 q^{6} +1.00000 q^{7} -10.4331 q^{8} +8.15233 q^{9} +O(q^{10})\)	\(q-2.78355 q^{2} +3.33951 q^{3} +5.74813 q^{4} +2.68755 q^{5} -9.29568 q^{6} +1.00000 q^{7} -10.4331 q^{8} +8.15233 q^{9} -7.48091 q^{10} -2.52684 q^{11} +19.1959 q^{12} -4.90685 q^{13} -2.78355 q^{14} +8.97509 q^{15} +17.5447 q^{16} -0.898319 q^{17} -22.6924 q^{18} +1.96499 q^{19} +15.4484 q^{20} +3.33951 q^{21} +7.03359 q^{22} -7.40366 q^{23} -34.8414 q^{24} +2.22291 q^{25} +13.6585 q^{26} +17.2063 q^{27} +5.74813 q^{28} +3.52400 q^{29} -24.9826 q^{30} +5.35439 q^{31} -27.9703 q^{32} -8.43842 q^{33} +2.50051 q^{34} +2.68755 q^{35} +46.8606 q^{36} +10.1575 q^{37} -5.46964 q^{38} -16.3865 q^{39} -28.0394 q^{40} +3.52367 q^{41} -9.29568 q^{42} +2.64184 q^{43} -14.5246 q^{44} +21.9098 q^{45} +20.6084 q^{46} +4.92135 q^{47} +58.5907 q^{48} +1.00000 q^{49} -6.18756 q^{50} -2.99995 q^{51} -28.2052 q^{52} +10.7700 q^{53} -47.8944 q^{54} -6.79101 q^{55} -10.4331 q^{56} +6.56211 q^{57} -9.80922 q^{58} -3.69514 q^{59} +51.5900 q^{60} +4.74191 q^{61} -14.9042 q^{62} +8.15233 q^{63} +42.7673 q^{64} -13.1874 q^{65} +23.4887 q^{66} +15.0912 q^{67} -5.16365 q^{68} -24.7246 q^{69} -7.48091 q^{70} -4.59300 q^{71} -85.0539 q^{72} +0.997451 q^{73} -28.2740 q^{74} +7.42342 q^{75} +11.2950 q^{76} -2.52684 q^{77} +45.6126 q^{78} -2.20739 q^{79} +47.1522 q^{80} +33.0035 q^{81} -9.80830 q^{82} +6.11616 q^{83} +19.1959 q^{84} -2.41427 q^{85} -7.35367 q^{86} +11.7684 q^{87} +26.3628 q^{88} -0.258006 q^{89} -60.9869 q^{90} -4.90685 q^{91} -42.5571 q^{92} +17.8810 q^{93} -13.6988 q^{94} +5.28100 q^{95} -93.4072 q^{96} -12.8683 q^{97} -2.78355 q^{98} -20.5997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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