LMFDB - Embedded newform 6037.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +O(q^{10})$	\(q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +1.27074 q^{10} -0.629601 q^{11} +13.5484 q^{12} -2.17206 q^{13} +4.43418 q^{14} -1.26611 q^{15} +11.8294 q^{16} +1.89267 q^{17} -10.7953 q^{18} +4.87194 q^{19} -2.43291 q^{20} -4.41804 q^{21} +1.67790 q^{22} -2.42543 q^{23} -21.9539 q^{24} -4.77264 q^{25} +5.78859 q^{26} +2.79004 q^{27} -8.48953 q^{28} +2.79052 q^{29} +3.37422 q^{30} -9.28173 q^{31} -14.9899 q^{32} -1.67179 q^{33} -5.04400 q^{34} +0.793353 q^{35} +20.6683 q^{36} +10.4951 q^{37} -12.9839 q^{38} -5.76751 q^{39} +3.94229 q^{40} +10.1975 q^{41} +11.7742 q^{42} -3.90292 q^{43} -3.21246 q^{44} -1.93147 q^{45} +6.46383 q^{46} -2.47028 q^{47} +31.4109 q^{48} -4.23163 q^{49} +12.7192 q^{50} +5.02564 q^{51} -11.0826 q^{52} +5.57028 q^{53} -7.43552 q^{54} +0.300206 q^{55} +13.7565 q^{56} +12.9366 q^{57} -7.43681 q^{58} +6.84689 q^{59} -6.46016 q^{60} +3.24232 q^{61} +24.7361 q^{62} -6.73978 q^{63} +16.2897 q^{64} +1.03568 q^{65} +4.45537 q^{66} +2.16066 q^{67} +9.65707 q^{68} -6.44029 q^{69} -2.11431 q^{70} +8.34707 q^{71} -33.4910 q^{72} +8.10565 q^{73} -27.9698 q^{74} -12.6729 q^{75} +24.8584 q^{76} +1.04756 q^{77} +15.3706 q^{78} -15.2822 q^{79} -5.64049 q^{80} -4.74376 q^{81} -27.1767 q^{82} +9.31489 q^{83} -22.5424 q^{84} -0.902460 q^{85} +10.4014 q^{86} +7.40973 q^{87} +5.20547 q^{88} +1.68083 q^{89} +5.14742 q^{90} +3.61396 q^{91} -12.3754 q^{92} -24.6460 q^{93} +6.58336 q^{94} -2.32304 q^{95} -39.8030 q^{96} +8.74411 q^{97} +11.2774 q^{98} -2.55035 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * 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 $

$2$	−2.66503	−1.88446	−0.942229	−	0.334969i	$-0.891274\pi$
$2$	−2.66503	−1.88446	−0.942229	+	0.334969i	$0.891274\pi$
$3$	2.65532	1.53305	0.766525	−	0.642214i	$-0.221984\pi$
$3$	2.65532	1.53305	0.766525	+	0.642214i	$0.221984\pi$
$4$	5.10237	2.55118
$5$	−0.476820	−0.213240	−0.106620	−	0.994300i	$-0.534003\pi$
$5$	−0.476820	−0.213240	−0.106620	+	0.994300i	$0.534003\pi$
$6$	−7.07650	−2.88897
$7$	−1.66384	−0.628873	−0.314437	−	0.949278i	$-0.601816\pi$
$7$	−1.66384	−0.628873	−0.314437	+	0.949278i	$0.601816\pi$
$8$	−8.26789	−2.92314
$9$	4.05073	1.35024
$10$	1.27074	0.401842
$11$	−0.629601	−0.189832	−0.0949159	−	0.995485i	$-0.530258\pi$
$11$	−0.629601	−0.189832	−0.0949159	+	0.995485i	$0.530258\pi$
$12$	13.5484	3.91109
$13$	−2.17206	−0.602420	−0.301210	−	0.953558i	$-0.597391\pi$
$13$	−2.17206	−0.602420	−0.301210	+	0.953558i	$0.597391\pi$
$14$	4.43418	1.18509
$15$	−1.26611	−0.326908
$16$	11.8294	2.95735
$17$	1.89267	0.459039	0.229519	−	0.973304i	$-0.426285\pi$
$17$	1.89267	0.459039	0.229519	+	0.973304i	$0.426285\pi$
$18$	−10.7953	−2.54448
$19$	4.87194	1.11770	0.558850	−	0.829269i	$-0.311243\pi$
$19$	4.87194	1.11770	0.558850	+	0.829269i	$0.311243\pi$
$20$	−2.43291	−0.544015
$21$	−4.41804	−0.964094
$22$	1.67790	0.357730
$23$	−2.42543	−0.505736	−0.252868	−	0.967501i	$-0.581374\pi$
$23$	−2.42543	−0.505736	−0.252868	+	0.967501i	$0.581374\pi$
$24$	−21.9539	−4.48132
$25$	−4.77264	−0.954529
$26$	5.78859	1.13524
$27$	2.79004	0.536943
$28$	−8.48953	−1.60437
$29$	2.79052	0.518187	0.259093	−	0.965852i	$-0.416576\pi$
$29$	2.79052	0.518187	0.259093	+	0.965852i	$0.416576\pi$
$30$	3.37422	0.616045
$31$	−9.28173	−1.66705	−0.833524	−	0.552483i	$-0.813680\pi$
$31$	−9.28173	−1.66705	−0.833524	+	0.552483i	$0.813680\pi$
$32$	−14.9899	−2.64987
$33$	−1.67179	−0.291022
$34$	−5.04400	−0.865039
$35$	0.793353	0.134101
$36$	20.6683	3.44472
$37$	10.4951	1.72539	0.862694	−	0.505727i	$-0.168776\pi$
$37$	10.4951	1.72539	0.862694	+	0.505727i	$0.168776\pi$
$38$	−12.9839	−2.10626
$39$	−5.76751	−0.923540
$40$	3.94229	0.623331
$41$	10.1975	1.59259	0.796293	−	0.604912i	$-0.206792\pi$
$41$	10.1975	1.59259	0.796293	+	0.604912i	$0.206792\pi$
$42$	11.7742	1.81680
$43$	−3.90292	−0.595190	−0.297595	−	0.954692i	$-0.596184\pi$
$43$	−3.90292	−0.595190	−0.297595	+	0.954692i	$0.596184\pi$
$44$	−3.21246	−0.484296
$45$	−1.93147	−0.287927
$46$	6.46383	0.953039
$47$	−2.47028	−0.360327	−0.180164	−	0.983637i	$-0.557663\pi$
$47$	−2.47028	−0.360327	−0.180164	+	0.983637i	$0.557663\pi$
$48$	31.4109	4.53377
$49$	−4.23163	−0.604519
$50$	12.7192	1.79877
$51$	5.02564	0.703730
$52$	−11.0826	−1.53688
$53$	5.57028	0.765136	0.382568	−	0.923927i	$-0.375040\pi$
$53$	5.57028	0.765136	0.382568	+	0.923927i	$0.375040\pi$
$54$	−7.43552	−1.01185
$55$	0.300206	0.0404798
$56$	13.7565	1.83828
$57$	12.9366	1.71349
$58$	−7.43681	−0.976501
$59$	6.84689	0.891389	0.445694	−	0.895185i	$-0.352957\pi$
$59$	6.84689	0.891389	0.445694	+	0.895185i	$0.352957\pi$
$60$	−6.46016	−0.834003
$61$	3.24232	0.415137	0.207568	−	0.978220i	$-0.433445\pi$
$61$	3.24232	0.415137	0.207568	+	0.978220i	$0.433445\pi$
$62$	24.7361	3.14148
$63$	−6.73978	−0.849133
$64$	16.2897	2.03621
$65$	1.03568	0.128460
$66$	4.45537	0.548419
$67$	2.16066	0.263966	0.131983	−	0.991252i	$-0.457866\pi$
$67$	2.16066	0.263966	0.131983	+	0.991252i	$0.457866\pi$
$68$	9.65707	1.17109
$69$	−6.44029	−0.775320
$70$	−2.11431	−0.252708
$71$	8.34707	0.990615	0.495307	−	0.868718i	$-0.335055\pi$
$71$	8.34707	0.990615	0.495307	+	0.868718i	$0.335055\pi$
$72$	−33.4910	−3.94695
$73$	8.10565	0.948695	0.474347	−	0.880338i	$-0.342684\pi$
$73$	8.10565	0.948695	0.474347	+	0.880338i	$0.342684\pi$
$74$	−27.9698	−3.25142
$75$	−12.6729	−1.46334
$76$	24.8584	2.85146
$77$	1.04756	0.119380
$78$	15.3706	1.74037
$79$	−15.2822	−1.71939	−0.859694	−	0.510810i	$-0.829345\pi$
$79$	−15.2822	−1.71939	−0.859694	+	0.510810i	$0.829345\pi$
$80$	−5.64049	−0.630627
$81$	−4.74376	−0.527084
$82$	−27.1767	−3.00116
$83$	9.31489	1.02244	0.511221	−	0.859449i	$-0.329193\pi$
$83$	9.31489	1.02244	0.511221	+	0.859449i	$0.329193\pi$
$84$	−22.5424	−2.45958
$85$	−0.902460	−0.0978856
$86$	10.4014	1.12161
$87$	7.40973	0.794406
$88$	5.20547	0.554905
$89$	1.68083	0.178168	0.0890840	−	0.996024i	$-0.471606\pi$
$89$	1.68083	0.178168	0.0890840	+	0.996024i	$0.471606\pi$
$90$	5.14742	0.542586
$91$	3.61396	0.378846
$92$	−12.3754	−1.29023
$93$	−24.6460	−2.55567
$94$	6.58336	0.679022
$95$	−2.32304	−0.238339
$96$	−39.8030	−4.06238
$97$	8.74411	0.887830	0.443915	−	0.896069i	$-0.353589\pi$
$97$	8.74411	0.887830	0.443915	+	0.896069i	$0.353589\pi$
$98$	11.2774	1.13919
$99$	−2.55035	−0.256319
$100$	−24.3518	−2.43518
$101$	−9.12625	−0.908096	−0.454048	−	0.890977i	$-0.650020\pi$
$101$	−9.12625	−0.908096	−0.454048	+	0.890977i	$0.650020\pi$
$102$	−13.3935	−1.32615
$103$	7.27485	0.716812	0.358406	−	0.933566i	$-0.383320\pi$
$103$	7.27485	0.716812	0.358406	+	0.933566i	$0.383320\pi$
$104$	17.9583	1.76096
$105$	2.10661	0.205584
$106$	−14.8449	−1.44187
$107$	17.6960	1.71073	0.855366	−	0.518024i	$-0.173332\pi$
$107$	17.6960	1.71073	0.855366	+	0.518024i	$0.173332\pi$
$108$	14.2358	1.36984
$109$	−0.528860	−0.0506556	−0.0253278	−	0.999679i	$-0.508063\pi$
$109$	−0.528860	−0.0506556	−0.0253278	+	0.999679i	$0.508063\pi$
$110$	−0.800058	−0.0762825
$111$	27.8679	2.64511
$112$	−19.6823	−1.85980
$113$	−8.84180	−0.831767	−0.415883	−	0.909418i	$-0.636528\pi$
$113$	−8.84180	−0.831767	−0.415883	+	0.909418i	$0.636528\pi$
$114$	−34.4763	−3.22900
$115$	1.15649	0.107843
$116$	14.2383	1.32199
$117$	−8.79842	−0.813414
$118$	−18.2471	−1.67979
$119$	−3.14910	−0.288677
$120$	10.4681	0.955598
$121$	−10.6036	−0.963964
$122$	−8.64088	−0.782308
$123$	27.0777	2.44151
$124$	−47.3588	−4.25295
$125$	4.65979	0.416784
$126$	17.9617	1.60015
$127$	12.4634	1.10594	0.552972	−	0.833200i	$-0.313494\pi$
$127$	12.4634	1.10594	0.552972	+	0.833200i	$0.313494\pi$
$128$	−13.4326	−1.18729
$129$	−10.3635	−0.912456
$130$	−2.76011	−0.242078
$131$	3.61022	0.315427	0.157713	−	0.987485i	$-0.449588\pi$
$131$	3.61022	0.315427	0.157713	+	0.987485i	$0.449588\pi$
$132$	−8.53010	−0.742450
$133$	−8.10614	−0.702892
$134$	−5.75820	−0.497433
$135$	−1.33034	−0.114498
$136$	−15.6483	−1.34183
$137$	−9.65300	−0.824712	−0.412356	−	0.911023i	$-0.635294\pi$
$137$	−9.65300	−0.824712	−0.412356	+	0.911023i	$0.635294\pi$
$138$	17.1635	1.46106
$139$	−2.95693	−0.250804	−0.125402	−	0.992106i	$-0.540022\pi$
$139$	−2.95693	−0.250804	−0.125402	+	0.992106i	$0.540022\pi$
$140$	4.04798	0.342116
$141$	−6.55939	−0.552400
$142$	−22.2452	−1.86677
$143$	1.36753	0.114359
$144$	47.9178	3.99315
$145$	−1.33057	−0.110498
$146$	−21.6018	−1.78778
$147$	−11.2363	−0.926758
$148$	53.5499	4.40178
$149$	−7.73243	−0.633465	−0.316733	−	0.948515i	$-0.602586\pi$
$149$	−7.73243	−0.633465	−0.316733	+	0.948515i	$0.602586\pi$
$150$	33.7736	2.75760
$151$	0.790890	0.0643617	0.0321808	−	0.999482i	$-0.489755\pi$
$151$	0.790890	0.0643617	0.0321808	+	0.999482i	$0.489755\pi$
$152$	−40.2807	−3.26720
$153$	7.66668	0.619815
$154$	−2.79177	−0.224967
$155$	4.42571	0.355482
$156$	−29.4279	−2.35612
$157$	11.8652	0.946944	0.473472	−	0.880809i	$-0.343000\pi$
$157$	11.8652	0.946944	0.473472	+	0.880809i	$0.343000\pi$
$158$	40.7276	3.24011
$159$	14.7909	1.17299
$160$	7.14748	0.565058
$161$	4.03553	0.318044
$162$	12.6422	0.993268
$163$	−1.90792	−0.149440	−0.0747200	−	0.997205i	$-0.523806\pi$
$163$	−1.90792	−0.149440	−0.0747200	+	0.997205i	$0.523806\pi$
$164$	52.0315	4.06298
$165$	0.797144	0.0620576
$166$	−24.8244	−1.92675
$167$	0.838151	0.0648581	0.0324291	−	0.999474i	$-0.489676\pi$
$167$	0.838151	0.0648581	0.0324291	+	0.999474i	$0.489676\pi$
$168$	36.5278	2.81818
$169$	−8.28217	−0.637090
$170$	2.40508	0.184461
$171$	19.7349	1.50917
$172$	−19.9141	−1.51844
$173$	19.0906	1.45143	0.725716	−	0.687994i	$-0.241509\pi$
$173$	19.0906	1.45143	0.725716	+	0.687994i	$0.241509\pi$
$174$	−19.7471	−1.49703
$175$	7.94092	0.600277
$176$	−7.44781	−0.561400
$177$	18.1807	1.36654
$178$	−4.47947	−0.335750
$179$	16.5224	1.23494	0.617472	−	0.786593i	$-0.288157\pi$
$179$	16.5224	1.23494	0.617472	+	0.786593i	$0.288157\pi$
$180$	−9.85507	−0.734553
$181$	−3.25226	−0.241739	−0.120869	−	0.992668i	$-0.538568\pi$
$181$	−3.25226	−0.241739	−0.120869	+	0.992668i	$0.538568\pi$
$182$	−9.63129	−0.713919
$183$	8.60941	0.636426
$184$	20.0532	1.47834
$185$	−5.00428	−0.367922
$186$	65.6822	4.81605
$187$	−1.19162	−0.0871402
$188$	−12.6043	−0.919261
$189$	−4.64218	−0.337669
$190$	6.19096	0.449139
$191$	17.8176	1.28924	0.644619	−	0.764504i	$-0.277016\pi$
$191$	17.8176	1.28924	0.644619	+	0.764504i	$0.277016\pi$
$192$	43.2544	3.12161
$193$	11.4990	0.827713	0.413857	−	0.910342i	$-0.364181\pi$
$193$	11.4990	0.827713	0.413857	+	0.910342i	$0.364181\pi$
$194$	−23.3033	−1.67308
$195$	2.75006	0.196936
$196$	−21.5913	−1.54224
$197$	1.99176	0.141907	0.0709534	−	0.997480i	$-0.477396\pi$
$197$	1.99176	0.141907	0.0709534	+	0.997480i	$0.477396\pi$
$198$	6.79674	0.483023
$199$	9.41249	0.667234	0.333617	−	0.942709i	$-0.391731\pi$
$199$	9.41249	0.667234	0.333617	+	0.942709i	$0.391731\pi$
$200$	39.4597	2.79022
$201$	5.73723	0.404673
$202$	24.3217	1.71127
$203$	−4.64298	−0.325874
$204$	25.6426	1.79534
$205$	−4.86238	−0.339603
$206$	−19.3877	−1.35080
$207$	−9.82476	−0.682868
$208$	−25.6941	−1.78157
$209$	−3.06738	−0.212175
$210$	−5.61416	−0.387414
$211$	−10.8751	−0.748673	−0.374337	−	0.927293i	$-0.622130\pi$
$211$	−10.8751	−0.748673	−0.374337	+	0.927293i	$0.622130\pi$
$212$	28.4216	1.95200
$213$	22.1642	1.51866
$214$	−47.1602	−3.22380
$215$	1.86099	0.126918
$216$	−23.0677	−1.56956
$217$	15.4433	1.04836
$218$	1.40943	0.0954584
$219$	21.5231	1.45440
$220$	1.53176	0.103271
$221$	−4.11098	−0.276534
$222$	−74.2687	−4.98459
$223$	17.2972	1.15831	0.579154	−	0.815218i	$-0.303383\pi$
$223$	17.2972	1.15831	0.579154	+	0.815218i	$0.303383\pi$
$224$	24.9408	1.66643
$225$	−19.3327	−1.28885
$226$	23.5636	1.56743
$227$	26.8714	1.78352	0.891759	−	0.452512i	$-0.149472\pi$
$227$	26.8714	1.78352	0.891759	+	0.452512i	$0.149472\pi$
$228$	66.0072	4.37143
$229$	−20.1702	−1.33288	−0.666441	−	0.745558i	$-0.732183\pi$
$229$	−20.1702	−1.33288	−0.666441	+	0.745558i	$0.732183\pi$
$230$	−3.08208	−0.203226
$231$	2.78160	0.183016
$232$	−23.0717	−1.51473
$233$	16.7885	1.09985	0.549925	−	0.835214i	$-0.314656\pi$
$233$	16.7885	1.09985	0.549925	+	0.835214i	$0.314656\pi$
$234$	23.4480	1.53285
$235$	1.17788	0.0768363
$236$	34.9353	2.27410
$237$	−40.5793	−2.63591
$238$	8.39242	0.544000
$239$	1.79676	0.116223	0.0581113	−	0.998310i	$-0.481492\pi$
$239$	1.79676	0.116223	0.0581113	+	0.998310i	$0.481492\pi$
$240$	−14.9773	−0.966782
$241$	17.4288	1.12269	0.561343	−	0.827583i	$-0.310285\pi$
$241$	17.4288	1.12269	0.561343	+	0.827583i	$0.310285\pi$
$242$	28.2589	1.81655
$243$	−20.9663	−1.34499
$244$	16.5435	1.05909
$245$	2.01772	0.128908
$246$	−72.1628	−4.60093
$247$	−10.5821	−0.673325
$248$	76.7403	4.87302
$249$	24.7340	1.56746
$250$	−12.4185	−0.785412
$251$	16.6108	1.04846	0.524232	−	0.851576i	$-0.324352\pi$
$251$	16.6108	1.04846	0.524232	+	0.851576i	$0.324352\pi$
$252$	−34.3888	−2.16629
$253$	1.52705	0.0960049
$254$	−33.2152	−2.08411
$255$	−2.39632	−0.150064
$256$	3.21895	0.201184
$257$	13.4851	0.841180	0.420590	−	0.907251i	$-0.361823\pi$
$257$	13.4851	0.841180	0.420590	+	0.907251i	$0.361823\pi$
$258$	27.6190	1.71948
$259$	−17.4622	−1.08505
$260$	5.28441	0.327725
$261$	11.3037	0.699679
$262$	−9.62134	−0.594408
$263$	−20.9271	−1.29042	−0.645211	−	0.764004i	$-0.723231\pi$
$263$	−20.9271	−1.29042	−0.645211	+	0.764004i	$0.723231\pi$
$264$	13.8222	0.850698
$265$	−2.65602	−0.163158
$266$	21.6031	1.32457
$267$	4.46316	0.273141
$268$	11.0245	0.673426
$269$	4.57948	0.279216	0.139608	−	0.990207i	$-0.455416\pi$
$269$	4.57948	0.279216	0.139608	+	0.990207i	$0.455416\pi$
$270$	3.54540	0.215766
$271$	0.282769	0.0171770	0.00858849	−	0.999963i	$-0.497266\pi$
$271$	0.282769	0.0171770	0.00858849	+	0.999963i	$0.497266\pi$
$272$	22.3891	1.35754
$273$	9.59622	0.580790
$274$	25.7255	1.55413
$275$	3.00486	0.181200
$276$	−32.8607	−1.97798
$277$	−20.2951	−1.21941	−0.609707	−	0.792627i	$-0.708713\pi$
$277$	−20.2951	−1.21941	−0.609707	+	0.792627i	$0.708713\pi$
$278$	7.88030	0.472629
$279$	−37.5978	−2.25092
$280$	−6.55935	−0.391996
$281$	3.24315	0.193470	0.0967351	−	0.995310i	$-0.469160\pi$
$281$	3.24315	0.193470	0.0967351	+	0.995310i	$0.469160\pi$
$282$	17.4809	1.04098
$283$	27.9086	1.65899	0.829496	−	0.558512i	$-0.188628\pi$
$283$	27.9086	1.65899	0.829496	+	0.558512i	$0.188628\pi$
$284$	42.5898	2.52724
$285$	−6.16842	−0.365385
$286$	−3.64450	−0.215504
$287$	−16.9671	−1.00153
$288$	−60.7201	−3.57797
$289$	−13.4178	−0.789283
$290$	3.54602	0.208229
$291$	23.2184	1.36109
$292$	41.3580	2.42029
$293$	21.7248	1.26918	0.634588	−	0.772850i	$-0.281170\pi$
$293$	21.7248	1.26918	0.634588	+	0.772850i	$0.281170\pi$
$294$	29.9451	1.74644
$295$	−3.26473	−0.190080
$296$	−86.7725	−5.04355
$297$	−1.75661	−0.101929
$298$	20.6071	1.19374
$299$	5.26816	0.304666
$300$	−64.6618	−3.73325
$301$	6.49384	0.374299
$302$	−2.10774	−0.121287
$303$	−24.2331	−1.39216
$304$	57.6322	3.30543
$305$	−1.54600	−0.0885239
$306$	−20.4319	−1.16801
$307$	22.3117	1.27340	0.636698	−	0.771113i	$-0.280300\pi$
$307$	22.3117	1.27340	0.636698	+	0.771113i	$0.280300\pi$
$308$	5.34502	0.304561
$309$	19.3171	1.09891
$310$	−11.7946	−0.669891
$311$	5.81204	0.329571	0.164785	−	0.986329i	$-0.447307\pi$
$311$	5.81204	0.329571	0.164785	+	0.986329i	$0.447307\pi$
$312$	47.6851	2.69964
$313$	13.8227	0.781304	0.390652	−	0.920538i	$-0.372250\pi$
$313$	13.8227	0.781304	0.390652	+	0.920538i	$0.372250\pi$
$314$	−31.6210	−1.78448
$315$	3.21366	0.181069
$316$	−77.9756	−4.38647
$317$	−29.6147	−1.66333	−0.831665	−	0.555278i	$-0.812612\pi$
$317$	−29.6147	−1.66333	−0.831665	+	0.555278i	$0.812612\pi$
$318$	−39.4181	−2.21046
$319$	−1.75691	−0.0983683
$320$	−7.76725	−0.434202
$321$	46.9885	2.62264
$322$	−10.7548	−0.599341
$323$	9.22096	0.513068
$324$	−24.2044	−1.34469
$325$	10.3664	0.575027
$326$	5.08466	0.281613
$327$	−1.40429	−0.0776576
$328$	−84.3120	−4.65535
$329$	4.11016	0.226600
$330$	−2.12441	−0.116945
$331$	−18.2723	−1.00433	−0.502167	−	0.864771i	$-0.667464\pi$
$331$	−18.2723	−1.00433	−0.502167	+	0.864771i	$0.667464\pi$
$332$	47.5280	2.60844
$333$	42.5129	2.32969
$334$	−2.23370	−0.122222
$335$	−1.03024	−0.0562882
$336$	−52.2627	−2.85117
$337$	1.67030	0.0909871	0.0454935	−	0.998965i	$-0.485514\pi$
$337$	1.67030	0.0909871	0.0454935	+	0.998965i	$0.485514\pi$
$338$	22.0722	1.20057
$339$	−23.4778	−1.27514
$340$	−4.60468	−0.249724
$341$	5.84379	0.316459
$342$	−52.5942	−2.84397
$343$	18.6877	1.00904
$344$	32.2689	1.73982
$345$	3.07086	0.165329
$346$	−50.8770	−2.73516
$347$	−22.2192	−1.19279	−0.596393	−	0.802692i	$-0.703400\pi$
$347$	−22.2192	−1.19279	−0.596393	+	0.802692i	$0.703400\pi$
$348$	37.8071	2.02668
$349$	2.55806	0.136930	0.0684648	−	0.997654i	$-0.478190\pi$
$349$	2.55806	0.136930	0.0684648	+	0.997654i	$0.478190\pi$
$350$	−21.1628	−1.13120
$351$	−6.06011	−0.323465
$352$	9.43766	0.503029
$353$	−9.84088	−0.523777	−0.261888	−	0.965098i	$-0.584345\pi$
$353$	−9.84088	−0.523777	−0.261888	+	0.965098i	$0.584345\pi$
$354$	−48.4520	−2.57520
$355$	−3.98005	−0.211239
$356$	8.57623	0.454539
$357$	−8.36186	−0.442557
$358$	−44.0327	−2.32720
$359$	−12.2530	−0.646687	−0.323344	−	0.946282i	$-0.604807\pi$
$359$	−12.2530	−0.646687	−0.323344	+	0.946282i	$0.604807\pi$
$360$	15.9692	0.841649
$361$	4.73584	0.249255
$362$	8.66736	0.455546
$363$	−28.1560	−1.47781
$364$	18.4397	0.966505
$365$	−3.86493	−0.202300
$366$	−22.9443	−1.19932
$367$	−4.70231	−0.245459	−0.122729	−	0.992440i	$-0.539165\pi$
$367$	−4.70231	−0.245459	−0.122729	+	0.992440i	$0.539165\pi$
$368$	−28.6914	−1.49564
$369$	41.3074	2.15038
$370$	13.3365	0.693334
$371$	−9.26806	−0.481174
$372$	−125.753	−6.51998
$373$	−1.64294	−0.0850684	−0.0425342	−	0.999095i	$-0.513543\pi$
$373$	−1.64294	−0.0850684	−0.0425342	+	0.999095i	$0.513543\pi$
$374$	3.17571	0.164212
$375$	12.3732	0.638951
$376$	20.4240	1.05329
$377$	−6.06117	−0.312166
$378$	12.3715	0.636323
$379$	−1.45615	−0.0747976	−0.0373988	−	0.999300i	$-0.511907\pi$
$379$	−1.45615	−0.0747976	−0.0373988	+	0.999300i	$0.511907\pi$
$380$	−11.8530	−0.608046
$381$	33.0942	1.69547
$382$	−47.4845	−2.42952
$383$	27.8637	1.42377	0.711884	−	0.702297i	$-0.247842\pi$
$383$	27.8637	1.42377	0.711884	+	0.702297i	$0.247842\pi$
$384$	−35.6680	−1.82017
$385$	−0.499496	−0.0254567
$386$	−30.6450	−1.55979
$387$	−15.8097	−0.803651
$388$	44.6156	2.26502
$389$	−15.2793	−0.774692	−0.387346	−	0.921934i	$-0.626608\pi$
$389$	−15.2793	−0.774692	−0.387346	+	0.921934i	$0.626608\pi$
$390$	−7.32899	−0.371118
$391$	−4.59052	−0.232153
$392$	34.9866	1.76709
$393$	9.58630	0.483565
$394$	−5.30809	−0.267418
$395$	7.28688	0.366643
$396$	−13.0128	−0.653918
$397$	−1.50186	−0.0753764	−0.0376882	−	0.999290i	$-0.511999\pi$
$397$	−1.50186	−0.0753764	−0.0376882	+	0.999290i	$0.511999\pi$
$398$	−25.0845	−1.25737
$399$	−21.5244	−1.07757
$400$	−56.4575	−2.82288
$401$	17.6776	0.882775	0.441387	−	0.897317i	$-0.354486\pi$
$401$	17.6776	0.882775	0.441387	+	0.897317i	$0.354486\pi$
$402$	−15.2899	−0.762590
$403$	20.1604	1.00426
$404$	−46.5655	−2.31672
$405$	2.26192	0.112396
$406$	12.3737	0.614095
$407$	−6.60774	−0.327533
$408$	−41.5514	−2.05710
$409$	14.2535	0.704790	0.352395	−	0.935851i	$-0.385367\pi$
$409$	14.2535	0.704790	0.352395	+	0.935851i	$0.385367\pi$
$410$	12.9584	0.639968
$411$	−25.6318	−1.26432
$412$	37.1189	1.82872
$413$	−11.3921	−0.560571
$414$	26.1832	1.28684
$415$	−4.44153	−0.218026
$416$	32.5589	1.59633
$417$	−7.85161	−0.384495
$418$	8.17465	0.399835
$419$	−25.1630	−1.22929	−0.614647	−	0.788802i	$-0.710701\pi$
$419$	−25.1630	−1.22929	−0.614647	+	0.788802i	$0.710701\pi$
$420$	10.7487	0.524482
$421$	−37.2496	−1.81543	−0.907716	−	0.419584i	$-0.862176\pi$
$421$	−37.2496	−1.81543	−0.907716	+	0.419584i	$0.862176\pi$
$422$	28.9825	1.41084
$423$	−10.0064	−0.486530
$424$	−46.0544	−2.23660
$425$	−9.03302	−0.438166
$426$	−59.0681	−2.86186
$427$	−5.39471	−0.261068
$428$	90.2912	4.36439
$429$	3.63123	0.175317
$430$	−4.95958	−0.239172
$431$	26.7250	1.28730	0.643649	−	0.765321i	$-0.277420\pi$
$431$	26.7250	1.28730	0.643649	+	0.765321i	$0.277420\pi$
$432$	33.0045	1.58793
$433$	−23.7427	−1.14100	−0.570501	−	0.821297i	$-0.693251\pi$
$433$	−23.7427	−1.14100	−0.570501	+	0.821297i	$0.693251\pi$
$434$	−41.1569	−1.97559
$435$	−3.53310	−0.169399
$436$	−2.69844	−0.129232
$437$	−11.8165	−0.565262
$438$	−57.3597	−2.74075
$439$	31.2161	1.48986	0.744931	−	0.667141i	$-0.232482\pi$
$439$	31.2161	1.48986	0.744931	+	0.667141i	$0.232482\pi$
$440$	−2.48207	−0.118328
$441$	−17.1412	−0.816248
$442$	10.9559	0.521117
$443$	−18.8952	−0.897739	−0.448870	−	0.893597i	$-0.648173\pi$
$443$	−18.8952	−0.897739	−0.448870	+	0.893597i	$0.648173\pi$
$444$	142.192	6.74815
$445$	−0.801455	−0.0379926
$446$	−46.0976	−2.18278
$447$	−20.5321	−0.971135
$448$	−27.1035	−1.28052
$449$	13.2907	0.627226	0.313613	−	0.949551i	$-0.398461\pi$
$449$	13.2907	0.627226	0.313613	+	0.949551i	$0.398461\pi$
$450$	51.5222	2.42878
$451$	−6.42037	−0.302323
$452$	−45.1141	−2.12199
$453$	2.10007	0.0986697
$454$	−71.6130	−3.36096
$455$	−1.72321	−0.0807852
$456$	−106.958	−5.00878
$457$	37.8519	1.77064	0.885318	−	0.464987i	$-0.153941\pi$
$457$	37.8519	1.77064	0.885318	+	0.464987i	$0.153941\pi$
$458$	53.7540	2.51176
$459$	5.28061	0.246478
$460$	5.90084	0.275128
$461$	−10.5862	−0.493050	−0.246525	−	0.969136i	$-0.579289\pi$
$461$	−10.5862	−0.493050	−0.246525	+	0.969136i	$0.579289\pi$
$462$	−7.41304	−0.344886
$463$	−0.691953	−0.0321578	−0.0160789	−	0.999871i	$-0.505118\pi$
$463$	−0.691953	−0.0321578	−0.0160789	+	0.999871i	$0.505118\pi$
$464$	33.0102	1.53246
$465$	11.7517	0.544972
$466$	−44.7417	−2.07262
$467$	22.9608	1.06250	0.531251	−	0.847215i	$-0.321722\pi$
$467$	22.9608	1.06250	0.531251	+	0.847215i	$0.321722\pi$
$468$	−44.8928	−2.07517
$469$	−3.59499	−0.166001
$470$	−3.13908	−0.144795
$471$	31.5059	1.45171
$472$	−56.6093	−2.60565
$473$	2.45728	0.112986
$474$	108.145	4.96726
$475$	−23.2520	−1.06688
$476$	−16.0678	−0.736468
$477$	22.5637	1.03312
$478$	−4.78840	−0.219017
$479$	24.8439	1.13515	0.567573	−	0.823323i	$-0.307882\pi$
$479$	24.8439	1.13515	0.567573	+	0.823323i	$0.307882\pi$
$480$	18.9789	0.866263
$481$	−22.7960	−1.03941
$482$	−46.4481	−2.11565
$483$	10.7156	0.487578
$484$	−54.1035	−2.45925
$485$	−4.16936	−0.189321
$486$	55.8758	2.53458
$487$	−23.1251	−1.04790	−0.523949	−	0.851750i	$-0.675542\pi$
$487$	−23.1251	−1.04790	−0.523949	+	0.851750i	$0.675542\pi$
$488$	−26.8072	−1.21350
$489$	−5.06615	−0.229099
$490$	−5.37729	−0.242921
$491$	−41.0083	−1.85068	−0.925339	−	0.379142i	$-0.876219\pi$
$491$	−41.0083	−1.85068	−0.925339	+	0.379142i	$0.876219\pi$
$492$	138.160	6.22875
$493$	5.28152	0.237868
$494$	28.2017	1.26885
$495$	1.21606	0.0546576
$496$	−109.797	−4.93005
$497$	−13.8882	−0.622971
$498$	−65.9169	−2.95381
$499$	2.53732	0.113586	0.0567931	−	0.998386i	$-0.481912\pi$
$499$	2.53732	0.113586	0.0567931	+	0.998386i	$0.481912\pi$
$500$	23.7759	1.06329
$501$	2.22556	0.0994308
$502$	−44.2682	−1.97579
$503$	−20.3136	−0.905736	−0.452868	−	0.891577i	$-0.649599\pi$
$503$	−20.3136	−0.905736	−0.452868	+	0.891577i	$0.649599\pi$
$504$	55.7237	2.48213
$505$	4.35158	0.193643
$506$	−4.06963	−0.180917
$507$	−21.9918	−0.976692
$508$	63.5926	2.82147
$509$	−1.84315	−0.0816963	−0.0408481	−	0.999165i	$-0.513006\pi$
$509$	−1.84315	−0.0816963	−0.0408481	+	0.999165i	$0.513006\pi$
$510$	6.38626	0.282788
$511$	−13.4865	−0.596609
$512$	18.2867	0.808165
$513$	13.5929	0.600141
$514$	−35.9383	−1.58517
$515$	−3.46879	−0.152853
$516$	−52.8784	−2.32784
$517$	1.55529	0.0684016
$518$	46.5373	2.04473
$519$	50.6917	2.22512
$520$	−8.56288	−0.375507
$521$	−2.10028	−0.0920150	−0.0460075	−	0.998941i	$-0.514650\pi$
$521$	−2.10028	−0.0920150	−0.0460075	+	0.998941i	$0.514650\pi$
$522$	−30.1245	−1.31852
$523$	−23.1459	−1.01210	−0.506051	−	0.862504i	$-0.668895\pi$
$523$	−23.1459	−1.01210	−0.506051	+	0.862504i	$0.668895\pi$
$524$	18.4207	0.804711
$525$	21.0857	0.920256
$526$	55.7713	2.43175
$527$	−17.5672	−0.765240
$528$	−19.7763	−0.860654
$529$	−17.1173	−0.744231
$530$	7.07836	0.307464
$531$	27.7349	1.20359
$532$	−41.3605	−1.79321
$533$	−22.1496	−0.959405
$534$	−11.8944	−0.514722
$535$	−8.43778	−0.364797
$536$	−17.8641	−0.771610
$537$	43.8724	1.89323
$538$	−12.2044	−0.526171
$539$	2.66424	0.114757
$540$	−6.78790	−0.292105
$541$	30.8543	1.32653	0.663264	−	0.748385i	$-0.269171\pi$
$541$	30.8543	1.32653	0.663264	+	0.748385i	$0.269171\pi$
$542$	−0.753586	−0.0323693
$543$	−8.63579	−0.370597
$544$	−28.3709	−1.21639
$545$	0.252171	0.0108018
$546$	−25.5742	−1.09447
$547$	39.4572	1.68707	0.843535	−	0.537074i	$-0.180471\pi$
$547$	39.4572	1.68707	0.843535	+	0.537074i	$0.180471\pi$
$548$	−49.2532	−2.10399
$549$	13.1338	0.560536
$550$	−8.00803	−0.341464
$551$	13.5953	0.579177
$552$	53.2476	2.26637
$553$	25.4272	1.08128
$554$	54.0869	2.29793
$555$	−13.2880	−0.564043
$556$	−15.0874	−0.639846
$557$	−5.56036	−0.235600	−0.117800	−	0.993037i	$-0.537584\pi$
$557$	−5.56036	−0.235600	−0.117800	+	0.993037i	$0.537584\pi$
$558$	100.199	4.24177
$559$	8.47736	0.358554
$560$	9.38489	0.396584
$561$	−3.16415	−0.133590
$562$	−8.64308	−0.364586
$563$	19.1706	0.807945	0.403972	−	0.914771i	$-0.367629\pi$
$563$	19.1706	0.807945	0.403972	+	0.914771i	$0.367629\pi$
$564$	−33.4684	−1.40927
$565$	4.21595	0.177366
$566$	−74.3771	−3.12630
$567$	7.89286	0.331469
$568$	−69.0126	−2.89571
$569$	11.1814	0.468750	0.234375	−	0.972146i	$-0.424696\pi$
$569$	11.1814	0.468750	0.234375	+	0.972146i	$0.424696\pi$
$570$	16.4390	0.688554
$571$	10.6580	0.446023	0.223011	−	0.974816i	$-0.428411\pi$
$571$	10.6580	0.446023	0.223011	+	0.974816i	$0.428411\pi$
$572$	6.97763	0.291749
$573$	47.3116	1.97647
$574$	45.2177	1.88735
$575$	11.5757	0.482740
$576$	65.9852	2.74938
$577$	41.6013	1.73189	0.865943	−	0.500143i	$-0.166719\pi$
$577$	41.6013	1.73189	0.865943	+	0.500143i	$0.166719\pi$
$578$	35.7588	1.48737
$579$	30.5334	1.26893
$580$	−6.78908	−0.281901
$581$	−15.4985	−0.642987
$582$	−61.8777	−2.56491
$583$	−3.50705	−0.145247
$584$	−67.0166	−2.77317
$585$	4.19526	0.173453
$586$	−57.8972	−2.39171
$587$	33.6324	1.38816	0.694080	−	0.719898i	$-0.255812\pi$
$587$	33.6324	1.38816	0.694080	+	0.719898i	$0.255812\pi$
$588$	−57.3319	−2.36433
$589$	−45.2201	−1.86326
$590$	8.70060	0.358198
$591$	5.28876	0.217550
$592$	124.151	5.10258
$593$	−23.1396	−0.950229	−0.475114	−	0.879924i	$-0.657593\pi$
$593$	−23.1396	−0.950229	−0.475114	+	0.879924i	$0.657593\pi$
$594$	4.68141	0.192081
$595$	1.50155	0.0615576
$596$	−39.4537	−1.61609
$597$	24.9932	1.02290
$598$	−14.0398	−0.574130
$599$	−15.6251	−0.638424	−0.319212	−	0.947683i	$-0.603418\pi$
$599$	−15.6251	−0.638424	−0.319212	+	0.947683i	$0.603418\pi$
$600$	104.778	4.27755
$601$	21.1450	0.862522	0.431261	−	0.902227i	$-0.358069\pi$
$601$	21.1450	0.862522	0.431261	+	0.902227i	$0.358069\pi$
$602$	−17.3063	−0.705350
$603$	8.75224	0.356419
$604$	4.03541	0.164198
$605$	5.05601	0.205556
$606$	64.5819	2.62346
$607$	−30.9275	−1.25531	−0.627655	−	0.778492i	$-0.715985\pi$
$607$	−30.9275	−1.25531	−0.627655	+	0.778492i	$0.715985\pi$
$608$	−73.0300	−2.96176
$609$	−12.3286	−0.499581
$610$	4.12014	0.166820
$611$	5.36559	0.217068
$612$	39.1182	1.58126
$613$	−20.1976	−0.815773	−0.407886	−	0.913033i	$-0.633734\pi$
$613$	−20.1976	−0.815773	−0.407886	+	0.913033i	$0.633734\pi$
$614$	−59.4612	−2.39966
$615$	−12.9112	−0.520629
$616$	−8.66108	−0.348965
$617$	10.3812	0.417932	0.208966	−	0.977923i	$-0.432990\pi$
$617$	10.3812	0.417932	0.208966	+	0.977923i	$0.432990\pi$
$618$	−51.4805	−2.07085
$619$	17.0984	0.687244	0.343622	−	0.939108i	$-0.388346\pi$
$619$	17.0984	0.687244	0.343622	+	0.939108i	$0.388346\pi$
$620$	22.5816	0.906899
$621$	−6.76703	−0.271551
$622$	−15.4893	−0.621062
$623$	−2.79664	−0.112045
$624$	−68.2262	−2.73123
$625$	21.6413	0.865653
$626$	−36.8378	−1.47234
$627$	−8.14488	−0.325275
$628$	60.5405	2.41583
$629$	19.8638	0.792020
$630$	−8.56449	−0.341217
$631$	−35.3022	−1.40536	−0.702679	−	0.711507i	$-0.748013\pi$
$631$	−35.3022	−1.40536	−0.702679	+	0.711507i	$0.748013\pi$
$632$	126.352	5.02601
$633$	−28.8769	−1.14775
$634$	78.9241	3.13447
$635$	−5.94278	−0.235832
$636$	75.4684	2.99252
$637$	9.19134	0.364174
$638$	4.68222	0.185371
$639$	33.8118	1.33757
$640$	6.40494	0.253178
$641$	−11.2592	−0.444712	−0.222356	−	0.974966i	$-0.571375\pi$
$641$	−11.2592	−0.444712	−0.222356	+	0.974966i	$0.571375\pi$
$642$	−125.225	−4.94226
$643$	−36.5342	−1.44077	−0.720385	−	0.693575i	$-0.756035\pi$
$643$	−36.5342	−1.44077	−0.720385	+	0.693575i	$0.756035\pi$
$644$	20.5907	0.811389
$645$	4.94152	0.194572
$646$	−24.5741	−0.966855
$647$	−33.4960	−1.31686	−0.658432	−	0.752640i	$-0.728780\pi$
$647$	−33.4960	−1.31686	−0.658432	+	0.752640i	$0.728780\pi$
$648$	39.2209	1.54074
$649$	−4.31081	−0.169214
$650$	−27.6269	−1.08361
$651$	41.0070	1.60719
$652$	−9.73492	−0.381249
$653$	32.2965	1.26386	0.631930	−	0.775026i	$-0.282263\pi$
$653$	32.2965	1.26386	0.631930	+	0.775026i	$0.282263\pi$
$654$	3.74248	0.146343
$655$	−1.72143	−0.0672617
$656$	120.631	4.70984
$657$	32.8338	1.28097
$658$	−10.9537	−0.427019
$659$	17.0705	0.664973	0.332487	−	0.943108i	$-0.392112\pi$
$659$	17.0705	0.664973	0.332487	+	0.943108i	$0.392112\pi$
$660$	4.06732	0.158320
$661$	−12.0076	−0.467041	−0.233521	−	0.972352i	$-0.575025\pi$
$661$	−12.0076	−0.467041	−0.233521	+	0.972352i	$0.575025\pi$
$662$	48.6961	1.89263
$663$	−10.9160	−0.423941
$664$	−77.0145	−2.98874
$665$	3.86517	0.149885
$666$	−113.298	−4.39021
$667$	−6.76820	−0.262066
$668$	4.27656	0.165465
$669$	45.9297	1.77575
$670$	2.74562	0.106073
$671$	−2.04137	−0.0788062
$672$	66.2260	2.55472
$673$	50.2827	1.93826	0.969129	−	0.246555i	$-0.0792987\pi$
$673$	50.2827	1.93826	0.969129	+	0.246555i	$0.0792987\pi$
$674$	−4.45140	−0.171461
$675$	−13.3158	−0.512527
$676$	−42.2587	−1.62533
$677$	−18.2257	−0.700472	−0.350236	−	0.936661i	$-0.613899\pi$
$677$	−18.2257	−0.700472	−0.350236	+	0.936661i	$0.613899\pi$
$678$	62.5691	2.40295
$679$	−14.5488	−0.558332
$680$	7.46144	0.286133
$681$	71.3522	2.73422
$682$	−15.5739	−0.596354
$683$	−0.621821	−0.0237933	−0.0118967	−	0.999929i	$-0.503787\pi$
$683$	−0.621821	−0.0237933	−0.0118967	+	0.999929i	$0.503787\pi$
$684$	100.695	3.85017
$685$	4.60274	0.175862
$686$	−49.8031	−1.90149
$687$	−53.5583	−2.04338
$688$	−46.1692	−1.76018
$689$	−12.0989	−0.460933
$690$	−8.18391	−0.311556
$691$	35.9372	1.36711	0.683557	−	0.729897i	$-0.260432\pi$
$691$	35.9372	1.36711	0.683557	+	0.729897i	$0.260432\pi$
$692$	97.4073	3.70287
$693$	4.24337	0.161192
$694$	59.2146	2.24776
$695$	1.40992	0.0534815
$696$	−61.2628	−2.32216
$697$	19.3005	0.731058
$698$	−6.81728	−0.258038
$699$	44.5788	1.68612
$700$	40.5175	1.53142
$701$	19.0812	0.720687	0.360344	−	0.932820i	$-0.382659\pi$
$701$	19.0812	0.720687	0.360344	+	0.932820i	$0.382659\pi$
$702$	16.1504	0.609556
$703$	51.1316	1.92847
$704$	−10.2560	−0.386538
$705$	3.12765	0.117794
$706$	26.2262	0.987036
$707$	15.1846	0.571077
$708$	92.7646	3.48631
$709$	−37.0067	−1.38982	−0.694908	−	0.719099i	$-0.744555\pi$
$709$	−37.0067	−1.38982	−0.694908	+	0.719099i	$0.744555\pi$
$710$	10.6069	0.398071
$711$	−61.9043	−2.32159
$712$	−13.8969	−0.520810
$713$	22.5122	0.843087
$714$	22.2846	0.833980
$715$	−0.652065	−0.0243858
$716$	84.3035	3.15057
$717$	4.77097	0.178175
$718$	32.6545	1.21865
$719$	32.7839	1.22263	0.611316	−	0.791387i	$-0.290640\pi$
$719$	32.7839	1.22263	0.611316	+	0.791387i	$0.290640\pi$
$720$	−22.8481	−0.851500
$721$	−12.1042	−0.450784
$722$	−12.6211	−0.469710
$723$	46.2790	1.72113
$724$	−16.5942	−0.616719
$725$	−13.3182	−0.494624
$726$	75.0364	2.78486
$727$	38.7643	1.43769	0.718844	−	0.695172i	$-0.244672\pi$
$727$	38.7643	1.43769	0.718844	+	0.695172i	$0.244672\pi$
$728$	−29.8798	−1.10742
$729$	−41.4410	−1.53485
$730$	10.3002	0.381226
$731$	−7.38692	−0.273215
$732$	43.9284	1.62364
$733$	−31.7198	−1.17160	−0.585799	−	0.810456i	$-0.699219\pi$
$733$	−31.7198	−1.17160	−0.585799	+	0.810456i	$0.699219\pi$
$734$	12.5318	0.462557
$735$	5.35771	0.197622
$736$	36.3569	1.34013
$737$	−1.36035	−0.0501092
$738$	−110.085	−4.05230
$739$	15.4728	0.569177	0.284588	−	0.958650i	$-0.408143\pi$
$739$	15.4728	0.569177	0.284588	+	0.958650i	$0.408143\pi$
$740$	−25.5337	−0.938636
$741$	−28.0990	−1.03224
$742$	24.6996	0.906751
$743$	31.9261	1.17126	0.585628	−	0.810580i	$-0.300848\pi$
$743$	31.9261	1.17126	0.585628	+	0.810580i	$0.300848\pi$
$744$	203.770	7.47058
$745$	3.68698	0.135080
$746$	4.37849	0.160308
$747$	37.7322	1.38055
$748$	−6.08010	−0.222311
$749$	−29.4433	−1.07583
$750$	−32.9750	−1.20408
$751$	10.0729	0.367564	0.183782	−	0.982967i	$-0.441166\pi$
$751$	10.0729	0.367564	0.183782	+	0.982967i	$0.441166\pi$
$752$	−29.2220	−1.06561
$753$	44.1070	1.60735
$754$	16.1532	0.588264
$755$	−0.377112	−0.0137245
$756$	−23.6861	−0.861455
$757$	−54.2042	−1.97009	−0.985043	−	0.172306i	$-0.944878\pi$
$757$	−54.2042	−1.97009	−0.985043	+	0.172306i	$0.944878\pi$
$758$	3.88069	0.140953
$759$	4.05481	0.147180
$760$	19.2066	0.696698
$761$	−17.6664	−0.640406	−0.320203	−	0.947349i	$-0.603751\pi$
$761$	−17.6664	−0.640406	−0.320203	+	0.947349i	$0.603751\pi$
$762$	−88.1970	−3.19504
$763$	0.879939	0.0318559
$764$	90.9121	3.28908
$765$	−3.65563	−0.132169
$766$	−74.2575	−2.68303
$767$	−14.8718	−0.536991
$768$	8.54734	0.308426
$769$	26.3359	0.949697	0.474848	−	0.880068i	$-0.342503\pi$
$769$	26.3359	0.949697	0.474848	+	0.880068i	$0.342503\pi$
$770$	1.33117	0.0479720
$771$	35.8074	1.28957
$772$	58.6719	2.11165
$773$	−24.2415	−0.871907	−0.435953	−	0.899969i	$-0.643589\pi$
$773$	−24.2415	−0.871907	−0.435953	+	0.899969i	$0.643589\pi$
$774$	42.1332	1.51445
$775$	44.2984	1.59125
$776$	−72.2953	−2.59525
$777$	−46.3678	−1.66344
$778$	40.7198	1.45988
$779$	49.6818	1.78003
$780$	14.0318	0.502420
$781$	−5.25532	−0.188050
$782$	12.2339	0.437482
$783$	7.78565	0.278236
$784$	−50.0577	−1.78777
$785$	−5.65755	−0.201927
$786$	−25.5478	−0.911258
$787$	4.69371	0.167313	0.0836564	−	0.996495i	$-0.473340\pi$
$787$	4.69371	0.167313	0.0836564	+	0.996495i	$0.473340\pi$
$788$	10.1627	0.362030
$789$	−55.5683	−1.97828
$790$	−19.4197	−0.690923
$791$	14.7114	0.523076
$792$	21.0860	0.749258
$793$	−7.04251	−0.250087
$794$	4.00251	0.142044
$795$	−7.05258	−0.250129
$796$	48.0260	1.70223
$797$	−45.1053	−1.59771	−0.798855	−	0.601524i	$-0.794561\pi$
$797$	−45.1053	−1.59771	−0.798855	+	0.601524i	$0.794561\pi$
$798$	57.3632	2.03063
$799$	−4.67541	−0.165404
$800$	71.5415	2.52937
$801$	6.80861	0.240570
$802$	−47.1112	−1.66355
$803$	−5.10333	−0.180093
$804$	29.2735	1.03240
$805$	−1.92422	−0.0678198
$806$	−53.7281	−1.89249
$807$	12.1600	0.428052
$808$	75.4548	2.65449
$809$	−6.74598	−0.237176	−0.118588	−	0.992944i	$-0.537837\pi$
$809$	−6.74598	−0.237176	−0.118588	+	0.992944i	$0.537837\pi$
$810$	−6.02807	−0.211805
$811$	−11.5613	−0.405971	−0.202986	−	0.979182i	$-0.565064\pi$
$811$	−11.5613	−0.405971	−0.202986	+	0.979182i	$0.565064\pi$
$812$	−23.6902	−0.831363
$813$	0.750842	0.0263332
$814$	17.6098	0.617223
$815$	0.909735	0.0318666
$816$	59.4503	2.08118
$817$	−19.0148	−0.665244
$818$	−37.9860	−1.32815
$819$	14.6392	0.511534
$820$	−24.8096	−0.866390
$821$	18.2734	0.637745	0.318873	−	0.947798i	$-0.396696\pi$
$821$	18.2734	0.637745	0.318873	+	0.947798i	$0.396696\pi$
$822$	68.3095	2.38257
$823$	20.7578	0.723572	0.361786	−	0.932261i	$-0.382167\pi$
$823$	20.7578	0.723572	0.361786	+	0.932261i	$0.382167\pi$
$824$	−60.1476	−2.09534
$825$	7.97887	0.277789
$826$	30.3604	1.05637
$827$	17.3850	0.604536	0.302268	−	0.953223i	$-0.402256\pi$
$827$	17.3850	0.604536	0.302268	+	0.953223i	$0.402256\pi$
$828$	−50.1295	−1.74212
$829$	4.50263	0.156383	0.0781914	−	0.996938i	$-0.475085\pi$
$829$	4.50263	0.156383	0.0781914	+	0.996938i	$0.475085\pi$
$830$	11.8368	0.410861
$831$	−53.8900	−1.86942
$832$	−35.3821	−1.22665
$833$	−8.00906	−0.277497
$834$	20.9247	0.724565
$835$	−0.399647	−0.0138304
$836$	−15.6509	−0.541298
$837$	−25.8964	−0.895110
$838$	67.0601	2.31655
$839$	10.6023	0.366033	0.183016	−	0.983110i	$-0.441414\pi$
$839$	10.6023	0.366033	0.183016	+	0.983110i	$0.441414\pi$
$840$	−17.4172	−0.600950
$841$	−21.2130	−0.731483
$842$	99.2711	3.42111
$843$	8.61161	0.296599
$844$	−55.4888	−1.91000
$845$	3.94910	0.135853
$846$	26.6674	0.916846
$847$	17.6427	0.606211
$848$	65.8931	2.26278
$849$	74.1063	2.54332
$850$	24.0732	0.825705
$851$	−25.4551	−0.872591
$852$	113.090	3.87439
$853$	−3.31605	−0.113539	−0.0567697	−	0.998387i	$-0.518080\pi$
$853$	−3.31605	−0.113539	−0.0567697	+	0.998387i	$0.518080\pi$
$854$	14.3771	0.491973
$855$	−9.41001	−0.321816
$856$	−146.308	−5.00071
$857$	−10.7568	−0.367444	−0.183722	−	0.982978i	$-0.558815\pi$
$857$	−10.7568	−0.367444	−0.183722	+	0.982978i	$0.558815\pi$
$858$	−9.67732	−0.330378
$859$	−39.5786	−1.35041	−0.675203	−	0.737632i	$-0.735944\pi$
$859$	−39.5786	−1.35041	−0.675203	+	0.737632i	$0.735944\pi$
$860$	9.49545	0.323792
$861$	−45.0530	−1.53540
$862$	−71.2229	−2.42586
$863$	35.1070	1.19506	0.597528	−	0.801848i	$-0.296150\pi$
$863$	35.1070	1.19506	0.597528	+	0.801848i	$0.296150\pi$
$864$	−41.8224	−1.42283
$865$	−9.10278	−0.309504
$866$	63.2749	2.15017
$867$	−35.6286	−1.21001
$868$	78.7976	2.67456
$869$	9.62172	0.326394
$870$	9.41582	0.319226
$871$	−4.69306	−0.159018
$872$	4.37256	0.148073
$873$	35.4201	1.19879
$874$	31.4914	1.06521
$875$	−7.75315	−0.262104
$876$	109.819	3.71043
$877$	−52.0002	−1.75592	−0.877961	−	0.478732i	$-0.841096\pi$
$877$	−52.0002	−1.75592	−0.877961	+	0.478732i	$0.841096\pi$
$878$	−83.1917	−2.80758
$879$	57.6863	1.94571
$880$	3.55126	0.119713
$881$	12.3669	0.416650	0.208325	−	0.978060i	$-0.433199\pi$
$881$	12.3669	0.416650	0.208325	+	0.978060i	$0.433199\pi$
$882$	45.6818	1.53819
$883$	−37.4088	−1.25891	−0.629453	−	0.777039i	$-0.716721\pi$
$883$	−37.4088	−1.25891	−0.629453	+	0.777039i	$0.716721\pi$
$884$	−20.9757	−0.705489
$885$	−8.66891	−0.291402
$886$	50.3563	1.69175
$887$	−37.4655	−1.25797	−0.628984	−	0.777418i	$-0.716529\pi$
$887$	−37.4655	−1.25797	−0.628984	+	0.777418i	$0.716529\pi$
$888$	−230.409	−7.73201
$889$	−20.7371	−0.695499
$890$	2.13590	0.0715955
$891$	2.98667	0.100057
$892$	88.2568	2.95506
$893$	−12.0351	−0.402738
$894$	54.7186	1.83006
$895$	−7.87822	−0.263340
$896$	22.3498	0.746654
$897$	13.9887	0.467068
$898$	−35.4200	−1.18198
$899$	−25.9009	−0.863842
$900$	−98.6425	−3.28808
$901$	10.5427	0.351227
$902$	17.1105	0.569716
$903$	17.2432	0.573819
$904$	73.1030	2.43137
$905$	1.55074	0.0515484
$906$	−5.59673	−0.185939
$907$	32.8195	1.08976	0.544878	−	0.838516i	$-0.316576\pi$
$907$	32.8195	1.08976	0.544878	+	0.838516i	$0.316576\pi$
$908$	137.108	4.55008
$909$	−36.9680	−1.22615
$910$	4.59239	0.152236
$911$	−1.29703	−0.0429726	−0.0214863	−	0.999769i	$-0.506840\pi$
$911$	−1.29703	−0.0429726	−0.0214863	+	0.999769i	$0.506840\pi$
$912$	153.032	5.06740
$913$	−5.86467	−0.194092
$914$	−100.876	−3.33669
$915$	−4.10514	−0.135712
$916$	−102.916	−3.40043
$917$	−6.00684	−0.198363
$918$	−14.0730	−0.464477
$919$	−6.23139	−0.205555	−0.102777	−	0.994704i	$-0.532773\pi$
$919$	−6.23139	−0.205555	−0.102777	+	0.994704i	$0.532773\pi$
$920$	−9.56174	−0.315241
$921$	59.2447	1.95218
$922$	28.2126	0.929132
$923$	−18.1303	−0.596766
$924$	14.1927	0.466907
$925$	−50.0895	−1.64693
$926$	1.84407	0.0606000
$927$	29.4685	0.967872
$928$	−41.8296	−1.37313
$929$	19.6391	0.644337	0.322169	−	0.946682i	$-0.395588\pi$
$929$	19.6391	0.644337	0.322169	+	0.946682i	$0.395588\pi$
$930$	−31.3186	−1.02698
$931$	−20.6163	−0.675671
$932$	85.6609	2.80592
$933$	15.4328	0.505249
$934$	−61.1913	−2.00224
$935$	0.568190	0.0185818
$936$	72.7444	2.37772
$937$	9.54113	0.311695	0.155848	−	0.987781i	$-0.450189\pi$
$937$	9.54113	0.311695	0.155848	+	0.987781i	$0.450189\pi$
$938$	9.58074	0.312822
$939$	36.7037	1.19778
$940$	6.00997	0.196024
$941$	−7.75937	−0.252948	−0.126474	−	0.991970i	$-0.540366\pi$
$941$	−7.75937	−0.252948	−0.126474	+	0.991970i	$0.540366\pi$
$942$	−83.9640	−2.73569
$943$	−24.7333	−0.805428
$944$	80.9946	2.63615
$945$	2.21348	0.0720046
$946$	−6.54872	−0.212917
$947$	−26.9880	−0.876991	−0.438496	−	0.898733i	$-0.644489\pi$
$947$	−26.9880	−0.876991	−0.438496	+	0.898733i	$0.644489\pi$
$948$	−207.050	−6.72468
$949$	−17.6059	−0.571513
$950$	61.9673	2.01049
$951$	−78.6367	−2.54997
$952$	26.0364	0.843844
$953$	35.8155	1.16018	0.580090	−	0.814553i	$-0.303017\pi$
$953$	35.8155	1.16018	0.580090	+	0.814553i	$0.303017\pi$
$954$	−60.1329	−1.94687
$955$	−8.49580	−0.274918
$956$	9.16771	0.296505
$957$	−4.66517	−0.150804
$958$	−66.2096	−2.13914
$959$	16.0611	0.518639
$960$	−20.6245	−0.665654
$961$	55.1506	1.77905
$962$	60.7519	1.95872
$963$	71.6816	2.30991
$964$	88.9280	2.86418
$965$	−5.48293	−0.176502
$966$	−28.5574	−0.918820
$967$	−6.75120	−0.217104	−0.108552	−	0.994091i	$-0.534621\pi$
$967$	−6.75120	−0.217104	−0.108552	+	0.994091i	$0.534621\pi$
$968$	87.6694	2.81780
$969$	24.4846	0.786559
$970$	11.1115	0.356768
$971$	9.20648	0.295450	0.147725	−	0.989028i	$-0.452805\pi$
$971$	9.20648	0.295450	0.147725	+	0.989028i	$0.452805\pi$
$972$	−106.978	−3.43131
$973$	4.91987	0.157724
$974$	61.6290	1.97472
$975$	27.5263	0.881546
$976$	38.3548	1.22771
$977$	30.8382	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$977$	30.8382	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$978$	13.5014	0.431728
$979$	−1.05826	−0.0338220
$980$	10.2952	0.328867
$981$	−2.14227	−0.0683975
$982$	109.288	3.48752
$983$	55.7554	1.77832	0.889160	−	0.457596i	$-0.151290\pi$
$983$	55.7554	1.77832	0.889160	+	0.457596i	$0.151290\pi$
$984$	−223.875	−7.13689
$985$	−0.949710	−0.0302603
$986$	−14.0754	−0.448252
$987$	10.9138	0.347390
$988$	−53.9939	−1.71778
$989$	9.46624	0.301009
$990$	−3.24082	−0.103000
$991$	−50.9029	−1.61698	−0.808492	−	0.588508i	$-0.799716\pi$
$991$	−50.9029	−1.61698	−0.808492	+	0.588508i	$0.799716\pi$
$992$	139.132	4.41746
$993$	−48.5187	−1.53970
$994$	37.0124	1.17396
$995$	−4.48806	−0.142281
$996$	126.202	3.99887
$997$	25.3506	0.802863	0.401431	−	0.915889i	$-0.368513\pi$
$997$	25.3506	0.802863	0.401431	+	0.915889i	$0.368513\pi$
$998$	−6.76203	−0.214048
$999$	29.2818	0.926434

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.b.1.2	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.b.1.2	✓	259	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +O(q^{10})\)	\(q-2.66503 q^{2} +2.65532 q^{3} +5.10237 q^{4} -0.476820 q^{5} -7.07650 q^{6} -1.66384 q^{7} -8.26789 q^{8} +4.05073 q^{9} +1.27074 q^{10} -0.629601 q^{11} +13.5484 q^{12} -2.17206 q^{13} +4.43418 q^{14} -1.26611 q^{15} +11.8294 q^{16} +1.89267 q^{17} -10.7953 q^{18} +4.87194 q^{19} -2.43291 q^{20} -4.41804 q^{21} +1.67790 q^{22} -2.42543 q^{23} -21.9539 q^{24} -4.77264 q^{25} +5.78859 q^{26} +2.79004 q^{27} -8.48953 q^{28} +2.79052 q^{29} +3.37422 q^{30} -9.28173 q^{31} -14.9899 q^{32} -1.67179 q^{33} -5.04400 q^{34} +0.793353 q^{35} +20.6683 q^{36} +10.4951 q^{37} -12.9839 q^{38} -5.76751 q^{39} +3.94229 q^{40} +10.1975 q^{41} +11.7742 q^{42} -3.90292 q^{43} -3.21246 q^{44} -1.93147 q^{45} +6.46383 q^{46} -2.47028 q^{47} +31.4109 q^{48} -4.23163 q^{49} +12.7192 q^{50} +5.02564 q^{51} -11.0826 q^{52} +5.57028 q^{53} -7.43552 q^{54} +0.300206 q^{55} +13.7565 q^{56} +12.9366 q^{57} -7.43681 q^{58} +6.84689 q^{59} -6.46016 q^{60} +3.24232 q^{61} +24.7361 q^{62} -6.73978 q^{63} +16.2897 q^{64} +1.03568 q^{65} +4.45537 q^{66} +2.16066 q^{67} +9.65707 q^{68} -6.44029 q^{69} -2.11431 q^{70} +8.34707 q^{71} -33.4910 q^{72} +8.10565 q^{73} -27.9698 q^{74} -12.6729 q^{75} +24.8584 q^{76} +1.04756 q^{77} +15.3706 q^{78} -15.2822 q^{79} -5.64049 q^{80} -4.74376 q^{81} -27.1767 q^{82} +9.31489 q^{83} -22.5424 q^{84} -0.902460 q^{85} +10.4014 q^{86} +7.40973 q^{87} +5.20547 q^{88} +1.68083 q^{89} +5.14742 q^{90} +3.61396 q^{91} -12.3754 q^{92} -24.6460 q^{93} +6.58336 q^{94} -2.32304 q^{95} -39.8030 q^{96} +8.74411 q^{97} +11.2774 q^{98} -2.55035 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9	\( 259 q + 47 q^{2} + 29 q^{3} + 273 q^{4} + 38 q^{5} + 24 q^{6} + 42 q^{7} + 141 q^{8} + 286 q^{9} + 18 q^{10} + 108 q^{11} + 46 q^{12} + 33 q^{13} + 35 q^{14} + 40 q^{15} + 301 q^{16} + 67 q^{17} + 117 q^{18} + 69 q^{19} + 103 q^{20} + 24 q^{21} + 42 q^{22} + 162 q^{23} + 45 q^{24} + 291 q^{25} + 41 q^{26} + 101 q^{27} + 87 q^{28} + 78 q^{29} + 48 q^{30} + 25 q^{31} + 314 q^{32} + 67 q^{33} + 9 q^{34} + 252 q^{35} + 337 q^{36} + 49 q^{37} + 59 q^{38} + 93 q^{39} + 44 q^{40} + 60 q^{41} + 38 q^{42} + 178 q^{43} + 171 q^{44} + 67 q^{45} + 43 q^{46} + 185 q^{47} + 67 q^{48} + 273 q^{49} + 204 q^{50} + 145 q^{51} + 83 q^{52} + 112 q^{53} + 60 q^{54} + 57 q^{55} + 93 q^{56} + 109 q^{57} + 63 q^{58} + 228 q^{59} + 53 q^{60} + 20 q^{61} + 126 q^{62} + 153 q^{63} + 345 q^{64} + 113 q^{65} + 5 q^{66} + 208 q^{67} + 166 q^{68} + 10 q^{69} + 69 q^{70} + 150 q^{71} + 331 q^{72} + 75 q^{73} + 84 q^{74} + 72 q^{75} + 102 q^{76} + 166 q^{77} + 69 q^{78} + 52 q^{79} + 180 q^{80} + 327 q^{81} + 43 q^{82} + 434 q^{83} + 75 q^{85} + 133 q^{86} + 144 q^{87} + 111 q^{88} + 78 q^{89} - 8 q^{90} + 35 q^{91} + 372 q^{92} + 160 q^{93} + 36 q^{94} + 154 q^{95} + 60 q^{96} + 35 q^{97} + 254 q^{98} + 234 q^{99}+O(q^{100}) \) 259 * q + 47 * q^2 + 29 * q^3 + 273 * q^4 + 38 * q^5 + 24 * q^6 + 42 * q^7 + 141 * q^8 + 286 * q^9 + 18 * q^10 + 108 * q^11 + 46 * q^12 + 33 * q^13 + 35 * q^14 + 40 * q^15 + 301 * q^16 + 67 * q^17 + 117 * q^18 + 69 * q^19 + 103 * q^20 + 24 * q^21 + 42 * q^22 + 162 * q^23 + 45 * q^24 + 291 * q^25 + 41 * q^26 + 101 * q^27 + 87 * q^28 + 78 * q^29 + 48 * q^30 + 25 * q^31 + 314 * q^32 + 67 * q^33 + 9 * q^34 + 252 * q^35 + 337 * q^36 + 49 * q^37 + 59 * q^38 + 93 * q^39 + 44 * q^40 + 60 * q^41 + 38 * q^42 + 178 * q^43 + 171 * q^44 + 67 * q^45 + 43 * q^46 + 185 * q^47 + 67 * q^48 + 273 * q^49 + 204 * q^50 + 145 * q^51 + 83 * q^52 + 112 * q^53 + 60 * q^54 + 57 * q^55 + 93 * q^56 + 109 * q^57 + 63 * q^58 + 228 * q^59 + 53 * q^60 + 20 * q^61 + 126 * q^62 + 153 * q^63 + 345 * q^64 + 113 * q^65 + 5 * q^66 + 208 * q^67 + 166 * q^68 + 10 * q^69 + 69 * q^70 + 150 * q^71 + 331 * q^72 + 75 * q^73 + 84 * q^74 + 72 * q^75 + 102 * q^76 + 166 * q^77 + 69 * q^78 + 52 * q^79 + 180 * q^80 + 327 * q^81 + 43 * q^82 + 434 * q^83 + 75 * q^85 + 133 * q^86 + 144 * q^87 + 111 * q^88 + 78 * q^89 - 8 * q^90 + 35 * q^91 + 372 * q^92 + 160 * q^93 + 36 * q^94 + 154 * q^95 + 60 * q^96 + 35 * q^97 + 254 * q^98 + 234 * q^99

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