LMFDB - Embedded newform 6047.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6047,2,Mod(1,6047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6047, 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("6047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6047 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6047.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:	$48.2855381023$
Analytic rank:	$0$
Dimension:	$287$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59210 q^{2} -2.49236 q^{3} +4.71900 q^{4} +2.95307 q^{5} +6.46045 q^{6} -0.174259 q^{7} -7.04794 q^{8} +3.21184 q^{9} +O(q^{10})$	\(q-2.59210 q^{2} -2.49236 q^{3} +4.71900 q^{4} +2.95307 q^{5} +6.46045 q^{6} -0.174259 q^{7} -7.04794 q^{8} +3.21184 q^{9} -7.65466 q^{10} -5.58913 q^{11} -11.7614 q^{12} +1.93148 q^{13} +0.451698 q^{14} -7.36010 q^{15} +8.83100 q^{16} +5.05258 q^{17} -8.32543 q^{18} +2.16780 q^{19} +13.9355 q^{20} +0.434316 q^{21} +14.4876 q^{22} -4.16193 q^{23} +17.5660 q^{24} +3.72060 q^{25} -5.00659 q^{26} -0.527989 q^{27} -0.822330 q^{28} +9.16366 q^{29} +19.0781 q^{30} -4.55043 q^{31} -8.79498 q^{32} +13.9301 q^{33} -13.0968 q^{34} -0.514599 q^{35} +15.1567 q^{36} +0.575414 q^{37} -5.61917 q^{38} -4.81393 q^{39} -20.8130 q^{40} -4.26841 q^{41} -1.12579 q^{42} +4.07742 q^{43} -26.3751 q^{44} +9.48479 q^{45} +10.7881 q^{46} -4.66183 q^{47} -22.0100 q^{48} -6.96963 q^{49} -9.64419 q^{50} -12.5928 q^{51} +9.11465 q^{52} -6.13311 q^{53} +1.36860 q^{54} -16.5051 q^{55} +1.22817 q^{56} -5.40294 q^{57} -23.7532 q^{58} -4.58899 q^{59} -34.7323 q^{60} +9.80384 q^{61} +11.7952 q^{62} -0.559693 q^{63} +5.13551 q^{64} +5.70378 q^{65} -36.1083 q^{66} +6.18437 q^{67} +23.8431 q^{68} +10.3730 q^{69} +1.33389 q^{70} -1.21215 q^{71} -22.6369 q^{72} -1.38954 q^{73} -1.49153 q^{74} -9.27307 q^{75} +10.2299 q^{76} +0.973958 q^{77} +12.4782 q^{78} +6.89203 q^{79} +26.0785 q^{80} -8.31959 q^{81} +11.0642 q^{82} +16.0625 q^{83} +2.04954 q^{84} +14.9206 q^{85} -10.5691 q^{86} -22.8391 q^{87} +39.3919 q^{88} -0.0730410 q^{89} -24.5856 q^{90} -0.336578 q^{91} -19.6401 q^{92} +11.3413 q^{93} +12.0840 q^{94} +6.40166 q^{95} +21.9202 q^{96} +11.0969 q^{97} +18.0660 q^{98} -17.9514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) $ 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * 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 $

$2$	−2.59210	−1.83289	−0.916447	−	0.400155i	$-0.868956\pi$
$2$	−2.59210	−1.83289	−0.916447	+	0.400155i	$0.868956\pi$
$3$	−2.49236	−1.43896	−0.719481	−	0.694512i	$-0.755620\pi$
$3$	−2.49236	−1.43896	−0.719481	+	0.694512i	$0.755620\pi$
$4$	4.71900	2.35950
$5$	2.95307	1.32065	0.660326	−	0.750979i	$-0.270418\pi$
$5$	2.95307	1.32065	0.660326	+	0.750979i	$0.270418\pi$
$6$	6.46045	2.63747
$7$	−0.174259	−0.0658638	−0.0329319	−	0.999458i	$-0.510484\pi$
$7$	−0.174259	−0.0658638	−0.0329319	+	0.999458i	$0.510484\pi$
$8$	−7.04794	−2.49182
$9$	3.21184	1.07061
$10$	−7.65466	−2.42062
$11$	−5.58913	−1.68519	−0.842593	−	0.538550i	$-0.818972\pi$
$11$	−5.58913	−1.68519	−0.842593	+	0.538550i	$0.818972\pi$
$12$	−11.7614	−3.39524
$13$	1.93148	0.535695	0.267848	−	0.963461i	$-0.413688\pi$
$13$	1.93148	0.535695	0.267848	+	0.963461i	$0.413688\pi$
$14$	0.451698	0.120721
$15$	−7.36010	−1.90037
$16$	8.83100	2.20775
$17$	5.05258	1.22543	0.612715	−	0.790304i	$-0.290077\pi$
$17$	5.05258	1.22543	0.612715	+	0.790304i	$0.290077\pi$
$18$	−8.32543	−1.96232
$19$	2.16780	0.497328	0.248664	−	0.968590i	$-0.420009\pi$
$19$	2.16780	0.497328	0.248664	+	0.968590i	$0.420009\pi$
$20$	13.9355	3.11608
$21$	0.434316	0.0947756
$22$	14.4876	3.08877
$23$	−4.16193	−0.867821	−0.433911	−	0.900956i	$-0.642867\pi$
$23$	−4.16193	−0.867821	−0.433911	+	0.900956i	$0.642867\pi$
$24$	17.5660	3.58564
$25$	3.72060	0.744121
$26$	−5.00659	−0.981873
$27$	−0.527989	−0.101612
$28$	−0.822330	−0.155406
$29$	9.16366	1.70165	0.850824	−	0.525451i	$-0.176103\pi$
$29$	9.16366	1.70165	0.850824	+	0.525451i	$0.176103\pi$
$30$	19.0781	3.48318
$31$	−4.55043	−0.817281	−0.408640	−	0.912695i	$-0.633997\pi$
$31$	−4.55043	−0.817281	−0.408640	+	0.912695i	$0.633997\pi$
$32$	−8.79498	−1.55475
$33$	13.9301	2.42492
$34$	−13.0968	−2.24608
$35$	−0.514599	−0.0869831
$36$	15.1567	2.52612
$37$	0.575414	0.0945975	0.0472988	−	0.998881i	$-0.484939\pi$
$37$	0.575414	0.0945975	0.0472988	+	0.998881i	$0.484939\pi$
$38$	−5.61917	−0.911549
$39$	−4.81393	−0.770846
$40$	−20.8130	−3.29083
$41$	−4.26841	−0.666613	−0.333307	−	0.942818i	$-0.608164\pi$
$41$	−4.26841	−0.666613	−0.333307	+	0.942818i	$0.608164\pi$
$42$	−1.12579	−0.173714
$43$	4.07742	0.621800	0.310900	−	0.950443i	$-0.399370\pi$
$43$	4.07742	0.621800	0.310900	+	0.950443i	$0.399370\pi$
$44$	−26.3751	−3.97620
$45$	9.48479	1.41391
$46$	10.7881	1.59063
$47$	−4.66183	−0.679998	−0.339999	−	0.940426i	$-0.610427\pi$
$47$	−4.66183	−0.679998	−0.339999	+	0.940426i	$0.610427\pi$
$48$	−22.0100	−3.17687
$49$	−6.96963	−0.995662
$50$	−9.64419	−1.36389
$51$	−12.5928	−1.76335
$52$	9.11465	1.26397
$53$	−6.13311	−0.842447	−0.421223	−	0.906957i	$-0.638399\pi$
$53$	−6.13311	−0.842447	−0.421223	+	0.906957i	$0.638399\pi$
$54$	1.36860	0.186243
$55$	−16.5051	−2.22554
$56$	1.22817	0.164121
$57$	−5.40294	−0.715636
$58$	−23.7532	−3.11894
$59$	−4.58899	−0.597436	−0.298718	−	0.954341i	$-0.596559\pi$
$59$	−4.58899	−0.597436	−0.298718	+	0.954341i	$0.596559\pi$
$60$	−34.7323	−4.48392
$61$	9.80384	1.25525	0.627627	−	0.778515i	$-0.284026\pi$
$61$	9.80384	1.25525	0.627627	+	0.778515i	$0.284026\pi$
$62$	11.7952	1.49799
$63$	−0.559693	−0.0705147
$64$	5.13551	0.641938
$65$	5.70378	0.707467
$66$	−36.1083	−4.44462
$67$	6.18437	0.755541	0.377771	−	0.925899i	$-0.376691\pi$
$67$	6.18437	0.755541	0.377771	+	0.925899i	$0.376691\pi$
$68$	23.8431	2.89141
$69$	10.3730	1.24876
$70$	1.33389	0.159431
$71$	−1.21215	−0.143856	−0.0719278	−	0.997410i	$-0.522915\pi$
$71$	−1.21215	−0.143856	−0.0719278	+	0.997410i	$0.522915\pi$
$72$	−22.6369	−2.66778
$73$	−1.38954	−0.162634	−0.0813168	−	0.996688i	$-0.525913\pi$
$73$	−1.38954	−0.162634	−0.0813168	+	0.996688i	$0.525913\pi$
$74$	−1.49153	−0.173387
$75$	−9.27307	−1.07076
$76$	10.2299	1.17345
$77$	0.973958	0.110993
$78$	12.4782	1.41288
$79$	6.89203	0.775414	0.387707	−	0.921783i	$-0.373267\pi$
$79$	6.89203	0.775414	0.387707	+	0.921783i	$0.373267\pi$
$80$	26.0785	2.91567
$81$	−8.31959	−0.924399
$82$	11.0642	1.22183
$83$	16.0625	1.76309	0.881544	−	0.472101i	$-0.156504\pi$
$83$	16.0625	1.76309	0.881544	+	0.472101i	$0.156504\pi$
$84$	2.04954	0.223623
$85$	14.9206	1.61837
$86$	−10.5691	−1.13969
$87$	−22.8391	−2.44861
$88$	39.3919	4.19919
$89$	−0.0730410	−0.00774233	−0.00387117	−	0.999993i	$-0.501232\pi$
$89$	−0.0730410	−0.00774233	−0.00387117	+	0.999993i	$0.501232\pi$
$90$	−24.5856	−2.59155
$91$	−0.336578	−0.0352829
$92$	−19.6401	−2.04763
$93$	11.3413	1.17604
$94$	12.0840	1.24637
$95$	6.40166	0.656797
$96$	21.9202	2.23722
$97$	11.0969	1.12672	0.563359	−	0.826212i	$-0.309509\pi$
$97$	11.0969	1.12672	0.563359	+	0.826212i	$0.309509\pi$
$98$	18.0660	1.82494
$99$	−17.9514	−1.80419
$100$	17.5575	1.75575
$101$	12.8220	1.27584	0.637921	−	0.770102i	$-0.279795\pi$
$101$	12.8220	1.27584	0.637921	+	0.770102i	$0.279795\pi$
$102$	32.6419	3.23203
$103$	−0.228961	−0.0225602	−0.0112801	−	0.999936i	$-0.503591\pi$
$103$	−0.228961	−0.0225602	−0.0112801	+	0.999936i	$0.503591\pi$
$104$	−13.6129	−1.33486
$105$	1.28256	0.125165
$106$	15.8977	1.54412
$107$	2.68428	0.259499	0.129750	−	0.991547i	$-0.458583\pi$
$107$	2.68428	0.259499	0.129750	+	0.991547i	$0.458583\pi$
$108$	−2.49158	−0.239753
$109$	1.87614	0.179702	0.0898508	−	0.995955i	$-0.471361\pi$
$109$	1.87614	0.179702	0.0898508	+	0.995955i	$0.471361\pi$
$110$	42.7829	4.07919
$111$	−1.43414	−0.136122
$112$	−1.53888	−0.145411
$113$	−10.7316	−1.00955	−0.504773	−	0.863252i	$-0.668424\pi$
$113$	−10.7316	−1.00955	−0.504773	+	0.863252i	$0.668424\pi$
$114$	14.0050	1.31169
$115$	−12.2904	−1.14609
$116$	43.2433	4.01504
$117$	6.20360	0.573523
$118$	11.8951	1.09504
$119$	−0.880458	−0.0807115
$120$	51.8735	4.73539
$121$	20.2384	1.83985
$122$	−25.4126	−2.30075
$123$	10.6384	0.959232
$124$	−21.4735	−1.92838
$125$	−3.77815	−0.337928
$126$	1.45078	0.129246
$127$	−2.62895	−0.233282	−0.116641	−	0.993174i	$-0.537213\pi$
$127$	−2.62895	−0.233282	−0.116641	+	0.993174i	$0.537213\pi$
$128$	4.27819	0.378142
$129$	−10.1624	−0.894748
$130$	−14.7848	−1.29671
$131$	−6.85030	−0.598514	−0.299257	−	0.954173i	$-0.596739\pi$
$131$	−6.85030	−0.598514	−0.299257	+	0.954173i	$0.596739\pi$
$132$	65.7363	5.72161
$133$	−0.377759	−0.0327559
$134$	−16.0305	−1.38483
$135$	−1.55919	−0.134193
$136$	−35.6103	−3.05356
$137$	−11.2453	−0.960750	−0.480375	−	0.877063i	$-0.659500\pi$
$137$	−11.2453	−0.960750	−0.480375	+	0.877063i	$0.659500\pi$
$138$	−26.8879	−2.28885
$139$	−6.39599	−0.542501	−0.271251	−	0.962509i	$-0.587437\pi$
$139$	−6.39599	−0.542501	−0.271251	+	0.962509i	$0.587437\pi$
$140$	−2.42840	−0.205237
$141$	11.6190	0.978492
$142$	3.14202	0.263672
$143$	−10.7953	−0.902747
$144$	28.3638	2.36365
$145$	27.0609	2.24728
$146$	3.60184	0.298090
$147$	17.3708	1.43272
$148$	2.71538	0.223203
$149$	−8.76421	−0.717992	−0.358996	−	0.933339i	$-0.616881\pi$
$149$	−8.76421	−0.717992	−0.358996	+	0.933339i	$0.616881\pi$
$150$	24.0368	1.96259
$151$	−20.6991	−1.68447	−0.842233	−	0.539114i	$-0.818759\pi$
$151$	−20.6991	−1.68447	−0.842233	+	0.539114i	$0.818759\pi$
$152$	−15.2785	−1.23925
$153$	16.2281	1.31196
$154$	−2.52460	−0.203438
$155$	−13.4377	−1.07934
$156$	−22.7170	−1.81881
$157$	18.4561	1.47296	0.736478	−	0.676462i	$-0.236488\pi$
$157$	18.4561	1.47296	0.736478	+	0.676462i	$0.236488\pi$
$158$	−17.8649	−1.42125
$159$	15.2859	1.21225
$160$	−25.9722	−2.05328
$161$	0.725254	0.0571580
$162$	21.5653	1.69433
$163$	17.3789	1.36122	0.680610	−	0.732646i	$-0.261715\pi$
$163$	17.3789	1.36122	0.680610	+	0.732646i	$0.261715\pi$
$164$	−20.1426	−1.57288
$165$	41.1365	3.20248
$166$	−41.6357	−3.23156
$167$	−1.11129	−0.0859946	−0.0429973	−	0.999075i	$-0.513691\pi$
$167$	−1.11129	−0.0859946	−0.0429973	+	0.999075i	$0.513691\pi$
$168$	−3.06104	−0.236164
$169$	−9.26939	−0.713030
$170$	−38.6757	−2.96629
$171$	6.96264	0.532446
$172$	19.2414	1.46714
$173$	−7.82053	−0.594584	−0.297292	−	0.954787i	$-0.596084\pi$
$173$	−7.82053	−0.594584	−0.297292	+	0.954787i	$0.596084\pi$
$174$	59.2013	4.48804
$175$	−0.648349	−0.0490106
$176$	−49.3576	−3.72047
$177$	11.4374	0.859688
$178$	0.189330	0.0141909
$179$	0.764097	0.0571113	0.0285556	−	0.999592i	$-0.490909\pi$
$179$	0.764097	0.0571113	0.0285556	+	0.999592i	$0.490909\pi$
$180$	44.7588	3.33612
$181$	−9.69342	−0.720506	−0.360253	−	0.932855i	$-0.617310\pi$
$181$	−9.69342	−0.720506	−0.360253	+	0.932855i	$0.617310\pi$
$182$	0.872445	0.0646699
$183$	−24.4347	−1.80626
$184$	29.3330	2.16246
$185$	1.69924	0.124930
$186$	−29.3978	−2.15555
$187$	−28.2395	−2.06508
$188$	−21.9992	−1.60446
$189$	0.0920069	0.00669252
$190$	−16.5938	−1.20384
$191$	−14.6840	−1.06250	−0.531249	−	0.847216i	$-0.678277\pi$
$191$	−14.6840	−1.06250	−0.531249	+	0.847216i	$0.678277\pi$
$192$	−12.7995	−0.923725
$193$	23.4869	1.69063	0.845314	−	0.534271i	$-0.179414\pi$
$193$	23.4869	1.69063	0.845314	+	0.534271i	$0.179414\pi$
$194$	−28.7643	−2.06516
$195$	−14.2159	−1.01802
$196$	−32.8897	−2.34927
$197$	5.91798	0.421638	0.210819	−	0.977525i	$-0.432387\pi$
$197$	5.91798	0.421638	0.210819	+	0.977525i	$0.432387\pi$
$198$	46.5319	3.30688
$199$	16.2709	1.15342	0.576708	−	0.816950i	$-0.304337\pi$
$199$	16.2709	1.15342	0.576708	+	0.816950i	$0.304337\pi$
$200$	−26.2226	−1.85422
$201$	−15.4137	−1.08720
$202$	−33.2361	−2.33848
$203$	−1.59685	−0.112077
$204$	−59.4256	−4.16063
$205$	−12.6049	−0.880364
$206$	0.593492	0.0413506
$207$	−13.3675	−0.929102
$208$	17.0569	1.18268
$209$	−12.1161	−0.838090
$210$	−3.32454	−0.229415
$211$	28.9926	1.99593	0.997966	−	0.0637471i	$-0.0203051\pi$
$211$	28.9926	1.99593	0.997966	+	0.0637471i	$0.0203051\pi$
$212$	−28.9422	−1.98776
$213$	3.02111	0.207003
$214$	−6.95794	−0.475635
$215$	12.0409	0.821182
$216$	3.72124	0.253198
$217$	0.792954	0.0538292
$218$	−4.86315	−0.329374
$219$	3.46323	0.234024
$220$	−77.8875	−5.25118
$221$	9.75894	0.656457
$222$	3.71743	0.249498
$223$	15.4908	1.03734	0.518669	−	0.854975i	$-0.326428\pi$
$223$	15.4908	1.03734	0.518669	+	0.854975i	$0.326428\pi$
$224$	1.53261	0.102402
$225$	11.9500	0.796666
$226$	27.8175	1.85039
$227$	11.2436	0.746266	0.373133	−	0.927778i	$-0.378284\pi$
$227$	11.2436	0.746266	0.373133	+	0.927778i	$0.378284\pi$
$228$	−25.4965	−1.68855
$229$	18.1449	1.19905	0.599524	−	0.800357i	$-0.295357\pi$
$229$	18.1449	1.19905	0.599524	+	0.800357i	$0.295357\pi$
$230$	31.8581	2.10066
$231$	−2.42745	−0.159714
$232$	−64.5849	−4.24021
$233$	9.61460	0.629874	0.314937	−	0.949113i	$-0.398017\pi$
$233$	9.61460	0.629874	0.314937	+	0.949113i	$0.398017\pi$
$234$	−16.0804	−1.05121
$235$	−13.7667	−0.898041
$236$	−21.6555	−1.40965
$237$	−17.1774	−1.11579
$238$	2.28224	0.147936
$239$	3.60082	0.232918	0.116459	−	0.993196i	$-0.462846\pi$
$239$	3.60082	0.232918	0.116459	+	0.993196i	$0.462846\pi$
$240$	−64.9970	−4.19554
$241$	−18.4881	−1.19092	−0.595461	−	0.803385i	$-0.703030\pi$
$241$	−18.4881	−1.19092	−0.595461	+	0.803385i	$0.703030\pi$
$242$	−52.4600	−3.37226
$243$	22.3194	1.43179
$244$	46.2644	2.96177
$245$	−20.5818	−1.31492
$246$	−27.5758	−1.75817
$247$	4.18706	0.266416
$248$	32.0712	2.03652
$249$	−40.0335	−2.53702
$250$	9.79335	0.619386
$251$	−25.4912	−1.60899	−0.804496	−	0.593958i	$-0.797564\pi$
$251$	−25.4912	−1.60899	−0.804496	+	0.593958i	$0.797564\pi$
$252$	−2.64120	−0.166380
$253$	23.2615	1.46244
$254$	6.81451	0.427580
$255$	−37.1875	−2.32877
$256$	−21.3605	−1.33503
$257$	7.74298	0.482994	0.241497	−	0.970402i	$-0.422362\pi$
$257$	7.74298	0.482994	0.241497	+	0.970402i	$0.422362\pi$
$258$	26.3419	1.63998
$259$	−0.100271	−0.00623055
$260$	26.9162	1.66927
$261$	29.4322	1.82181
$262$	17.7567	1.09701
$263$	12.8485	0.792274	0.396137	−	0.918191i	$-0.370351\pi$
$263$	12.8485	0.792274	0.396137	+	0.918191i	$0.370351\pi$
$264$	−98.1787	−6.04248
$265$	−18.1115	−1.11258
$266$	0.979192	0.0600381
$267$	0.182044	0.0111409
$268$	29.1841	1.78270
$269$	3.76110	0.229318	0.114659	−	0.993405i	$-0.463422\pi$
$269$	3.76110	0.229318	0.114659	+	0.993405i	$0.463422\pi$
$270$	4.04157	0.245962
$271$	−5.78316	−0.351302	−0.175651	−	0.984453i	$-0.556203\pi$
$271$	−5.78316	−0.351302	−0.175651	+	0.984453i	$0.556203\pi$
$272$	44.6193	2.70544
$273$	0.838872	0.0507708
$274$	29.1490	1.76095
$275$	−20.7949	−1.25398
$276$	48.9503	2.94646
$277$	−21.4030	−1.28598	−0.642992	−	0.765873i	$-0.722307\pi$
$277$	−21.4030	−1.28598	−0.642992	+	0.765873i	$0.722307\pi$
$278$	16.5791	0.994347
$279$	−14.6153	−0.874993
$280$	3.62687	0.216747
$281$	−1.89917	−0.113295	−0.0566474	−	0.998394i	$-0.518041\pi$
$281$	−1.89917	−0.113295	−0.0566474	+	0.998394i	$0.518041\pi$
$282$	−30.1175	−1.79347
$283$	−12.0658	−0.717236	−0.358618	−	0.933484i	$-0.616752\pi$
$283$	−12.0658	−0.717236	−0.358618	+	0.933484i	$0.616752\pi$
$284$	−5.72014	−0.339428
$285$	−15.9552	−0.945106
$286$	27.9825	1.65464
$287$	0.743809	0.0439057
$288$	−28.2481	−1.66453
$289$	8.52854	0.501679
$290$	−70.1446	−4.11904
$291$	−27.6574	−1.62131
$292$	−6.55726	−0.383734
$293$	23.5564	1.37618	0.688089	−	0.725627i	$-0.258450\pi$
$293$	23.5564	1.37618	0.688089	+	0.725627i	$0.258450\pi$
$294$	−45.0270	−2.62603
$295$	−13.5516	−0.789004
$296$	−4.05549	−0.235720
$297$	2.95100	0.171234
$298$	22.7178	1.31600
$299$	−8.03866	−0.464888
$300$	−43.7597	−2.52647
$301$	−0.710527	−0.0409541
$302$	53.6541	3.08745
$303$	−31.9571	−1.83589
$304$	19.1438	1.09798
$305$	28.9514	1.65775
$306$	−42.0649	−2.40469
$307$	−8.82070	−0.503424	−0.251712	−	0.967802i	$-0.580994\pi$
$307$	−8.82070	−0.503424	−0.251712	+	0.967802i	$0.580994\pi$
$308$	4.59611	0.261888
$309$	0.570654	0.0324634
$310$	34.8320	1.97832
$311$	−17.3107	−0.981599	−0.490799	−	0.871273i	$-0.663295\pi$
$311$	−17.3107	−0.981599	−0.490799	+	0.871273i	$0.663295\pi$
$312$	33.9283	1.92081
$313$	1.70361	0.0962938	0.0481469	−	0.998840i	$-0.484668\pi$
$313$	1.70361	0.0962938	0.0481469	+	0.998840i	$0.484668\pi$
$314$	−47.8401	−2.69977
$315$	−1.65281	−0.0931254
$316$	32.5235	1.82959
$317$	3.83237	0.215248	0.107624	−	0.994192i	$-0.465676\pi$
$317$	3.83237	0.215248	0.107624	+	0.994192i	$0.465676\pi$
$318$	−39.6226	−2.22193
$319$	−51.2169	−2.86759
$320$	15.1655	0.847777
$321$	−6.69019	−0.373410
$322$	−1.87993	−0.104765
$323$	10.9530	0.609440
$324$	−39.2602	−2.18112
$325$	7.18626	0.398622
$326$	−45.0479	−2.49497
$327$	−4.67601	−0.258584
$328$	30.0835	1.66108
$329$	0.812367	0.0447873
$330$	−106.630	−5.86980
$331$	−6.73169	−0.370007	−0.185004	−	0.982738i	$-0.559230\pi$
$331$	−6.73169	−0.370007	−0.185004	+	0.982738i	$0.559230\pi$
$332$	75.7990	4.16001
$333$	1.84814	0.101277
$334$	2.88059	0.157619
$335$	18.2629	0.997807
$336$	3.83544	0.209241
$337$	−9.07489	−0.494341	−0.247170	−	0.968972i	$-0.579501\pi$
$337$	−9.07489	−0.494341	−0.247170	+	0.968972i	$0.579501\pi$
$338$	24.0272	1.30691
$339$	26.7470	1.45270
$340$	70.4104	3.81854
$341$	25.4329	1.37727
$342$	−18.0479	−0.975918
$343$	2.43434	0.131442
$344$	−28.7374	−1.54942
$345$	30.6322	1.64918
$346$	20.2716	1.08981
$347$	−7.23121	−0.388192	−0.194096	−	0.980983i	$-0.562177\pi$
$347$	−7.23121	−0.388192	−0.194096	+	0.980983i	$0.562177\pi$
$348$	−107.778	−5.77750
$349$	−1.94886	−0.104320	−0.0521600	−	0.998639i	$-0.516611\pi$
$349$	−1.94886	−0.104320	−0.0521600	+	0.998639i	$0.516611\pi$
$350$	1.68059	0.0898313
$351$	−1.01980	−0.0544328
$352$	49.1563	2.62004
$353$	−15.6156	−0.831135	−0.415567	−	0.909562i	$-0.636417\pi$
$353$	−15.6156	−0.831135	−0.415567	+	0.909562i	$0.636417\pi$
$354$	−29.6469	−1.57572
$355$	−3.57956	−0.189983
$356$	−0.344681	−0.0182681
$357$	2.19442	0.116141
$358$	−1.98062	−0.104679
$359$	6.75747	0.356646	0.178323	−	0.983972i	$-0.442933\pi$
$359$	6.75747	0.356646	0.178323	+	0.983972i	$0.442933\pi$
$360$	−66.8483	−3.52321
$361$	−14.3006	−0.752665
$362$	25.1263	1.32061
$363$	−50.4413	−2.64748
$364$	−1.58831	−0.0832502
$365$	−4.10341	−0.214782
$366$	63.3372	3.31069
$367$	−22.5514	−1.17717	−0.588587	−	0.808434i	$-0.700316\pi$
$367$	−22.5514	−1.17717	−0.588587	+	0.808434i	$0.700316\pi$
$368$	−36.7540	−1.91593
$369$	−13.7095	−0.713686
$370$	−4.40460	−0.228984
$371$	1.06875	0.0554868
$372$	53.5196	2.77486
$373$	−3.50325	−0.181391	−0.0906956	−	0.995879i	$-0.528909\pi$
$373$	−3.50325	−0.181391	−0.0906956	+	0.995879i	$0.528909\pi$
$374$	73.1998	3.78507
$375$	9.41649	0.486265
$376$	32.8563	1.69444
$377$	17.6994	0.911565
$378$	−0.238492	−0.0122667
$379$	22.2020	1.14044	0.570220	−	0.821492i	$-0.306858\pi$
$379$	22.2020	1.14044	0.570220	+	0.821492i	$0.306858\pi$
$380$	30.2095	1.54971
$381$	6.55228	0.335683
$382$	38.0625	1.94745
$383$	26.1003	1.33366	0.666831	−	0.745209i	$-0.267650\pi$
$383$	26.1003	1.33366	0.666831	+	0.745209i	$0.267650\pi$
$384$	−10.6628	−0.544132
$385$	2.87616	0.146583
$386$	−60.8806	−3.09874
$387$	13.0960	0.665708
$388$	52.3663	2.65850
$389$	−25.0120	−1.26816	−0.634079	−	0.773269i	$-0.718620\pi$
$389$	−25.0120	−1.26816	−0.634079	+	0.773269i	$0.718620\pi$
$390$	36.8490	1.86592
$391$	−21.0285	−1.06345
$392$	49.1216	2.48101
$393$	17.0734	0.861239
$394$	−15.3400	−0.772818
$395$	20.3526	1.02405
$396$	−84.7128	−4.25698
$397$	−20.2144	−1.01453	−0.507267	−	0.861789i	$-0.669344\pi$
$397$	−20.2144	−1.01453	−0.507267	+	0.861789i	$0.669344\pi$
$398$	−42.1760	−2.11409
$399$	0.941511	0.0471345
$400$	32.8566	1.64283
$401$	−13.9438	−0.696322	−0.348161	−	0.937435i	$-0.613194\pi$
$401$	−13.9438	−0.696322	−0.348161	+	0.937435i	$0.613194\pi$
$402$	39.9538	1.99272
$403$	−8.78905	−0.437814
$404$	60.5073	3.01035
$405$	−24.5683	−1.22081
$406$	4.13921	0.205425
$407$	−3.21607	−0.159414
$408$	88.7535	4.39396
$409$	23.0341	1.13896	0.569482	−	0.822004i	$-0.307144\pi$
$409$	23.0341	1.13896	0.569482	+	0.822004i	$0.307144\pi$
$410$	32.6732	1.61361
$411$	28.0273	1.38248
$412$	−1.08047	−0.0532310
$413$	0.799674	0.0393494
$414$	34.6498	1.70295
$415$	47.4336	2.32843
$416$	−16.9873	−0.832871
$417$	15.9411	0.780639
$418$	31.4063	1.53613
$419$	14.6555	0.715966	0.357983	−	0.933728i	$-0.383465\pi$
$419$	14.6555	0.715966	0.357983	+	0.933728i	$0.383465\pi$
$420$	6.05243	0.295328
$421$	12.1591	0.592596	0.296298	−	0.955095i	$-0.404248\pi$
$421$	12.1591	0.592596	0.296298	+	0.955095i	$0.404248\pi$
$422$	−75.1518	−3.65833
$423$	−14.9731	−0.728016
$424$	43.2258	2.09923
$425$	18.7986	0.911868
$426$	−7.83103	−0.379415
$427$	−1.70841	−0.0826757
$428$	12.6671	0.612289
$429$	26.9057	1.29902
$430$	−31.2112	−1.50514
$431$	−21.6405	−1.04238	−0.521192	−	0.853439i	$-0.674512\pi$
$431$	−21.6405	−1.04238	−0.521192	+	0.853439i	$0.674512\pi$
$432$	−4.66267	−0.224333
$433$	33.9741	1.63269	0.816344	−	0.577565i	$-0.195997\pi$
$433$	33.9741	1.63269	0.816344	+	0.577565i	$0.195997\pi$
$434$	−2.05542	−0.0986633
$435$	−67.4454	−3.23376
$436$	8.85351	0.424006
$437$	−9.02223	−0.431592
$438$	−8.97707	−0.428941
$439$	−26.7091	−1.27475	−0.637377	−	0.770552i	$-0.719981\pi$
$439$	−26.7091	−1.27475	−0.637377	+	0.770552i	$0.719981\pi$
$440$	116.327	5.54567
$441$	−22.3854	−1.06597
$442$	−25.2962	−1.20322
$443$	3.91024	0.185781	0.0928905	−	0.995676i	$-0.470389\pi$
$443$	3.91024	0.185781	0.0928905	+	0.995676i	$0.470389\pi$
$444$	−6.76770	−0.321181
$445$	−0.215695	−0.0102249
$446$	−40.1537	−1.90133
$447$	21.8436	1.03316
$448$	−0.894909	−0.0422805
$449$	2.17165	0.102487	0.0512433	−	0.998686i	$-0.483682\pi$
$449$	2.17165	0.102487	0.0512433	+	0.998686i	$0.483682\pi$
$450$	−30.9756	−1.46021
$451$	23.8567	1.12337
$452$	−50.6426	−2.38203
$453$	51.5894	2.42388
$454$	−29.1447	−1.36783
$455$	−0.993936	−0.0465965
$456$	38.0796	1.78324
$457$	34.7775	1.62682	0.813412	−	0.581689i	$-0.197608\pi$
$457$	34.7775	1.62682	0.813412	+	0.581689i	$0.197608\pi$
$458$	−47.0334	−2.19773
$459$	−2.66771	−0.124518
$460$	−57.9987	−2.70420
$461$	−30.5553	−1.42310	−0.711551	−	0.702635i	$-0.752007\pi$
$461$	−30.5553	−1.42310	−0.711551	+	0.702635i	$0.752007\pi$
$462$	6.29220	0.292740
$463$	11.3605	0.527968	0.263984	−	0.964527i	$-0.414963\pi$
$463$	11.3605	0.527968	0.263984	+	0.964527i	$0.414963\pi$
$464$	80.9242	3.75681
$465$	33.4916	1.55313
$466$	−24.9221	−1.15449
$467$	−27.5601	−1.27533	−0.637665	−	0.770314i	$-0.720100\pi$
$467$	−27.5601	−1.27533	−0.637665	+	0.770314i	$0.720100\pi$
$468$	29.2748	1.35323
$469$	−1.07768	−0.0497628
$470$	35.6847	1.64601
$471$	−45.9991	−2.11953
$472$	32.3430	1.48870
$473$	−22.7892	−1.04785
$474$	44.5256	2.04513
$475$	8.06553	0.370072
$476$	−4.15489	−0.190439
$477$	−19.6986	−0.901936
$478$	−9.33371	−0.426914
$479$	36.5018	1.66781	0.833904	−	0.551909i	$-0.186100\pi$
$479$	36.5018	1.66781	0.833904	+	0.551909i	$0.186100\pi$
$480$	64.7319	2.95459
$481$	1.11140	0.0506755
$482$	47.9230	2.18283
$483$	−1.80759	−0.0822483
$484$	95.5051	4.34114
$485$	32.7699	1.48800
$486$	−57.8541	−2.62432
$487$	16.4252	0.744299	0.372150	−	0.928173i	$-0.378621\pi$
$487$	16.4252	0.744299	0.372150	+	0.928173i	$0.378621\pi$
$488$	−69.0969	−3.12787
$489$	−43.3144	−1.95874
$490$	53.3502	2.41011
$491$	−8.92237	−0.402661	−0.201331	−	0.979523i	$-0.564527\pi$
$491$	−8.92237	−0.402661	−0.201331	+	0.979523i	$0.564527\pi$
$492$	50.2026	2.26331
$493$	46.3001	2.08525
$494$	−10.8533	−0.488313
$495$	−53.0117	−2.38270
$496$	−40.1848	−1.80435
$497$	0.211228	0.00947488
$498$	103.771	4.65009
$499$	9.38821	0.420274	0.210137	−	0.977672i	$-0.432609\pi$
$499$	9.38821	0.420274	0.210137	+	0.977672i	$0.432609\pi$
$500$	−17.8291	−0.797341
$501$	2.76974	0.123743
$502$	66.0759	2.94911
$503$	11.9368	0.532237	0.266118	−	0.963940i	$-0.414259\pi$
$503$	11.9368	0.532237	0.266118	+	0.963940i	$0.414259\pi$
$504$	3.94469	0.175710
$505$	37.8644	1.68494
$506$	−60.2964	−2.68050
$507$	23.1026	1.02602
$508$	−12.4060	−0.550428
$509$	28.8201	1.27743	0.638714	−	0.769444i	$-0.279467\pi$
$509$	28.8201	1.27743	0.638714	+	0.769444i	$0.279467\pi$
$510$	96.3938	4.26839
$511$	0.242141	0.0107117
$512$	46.8123	2.06883
$513$	−1.14458	−0.0505342
$514$	−20.0706	−0.885277
$515$	−0.676139	−0.0297942
$516$	−47.9563	−2.11116
$517$	26.0556	1.14592
$518$	0.259913	0.0114199
$519$	19.4916	0.855585
$520$	−40.1999	−1.76288
$521$	14.2539	0.624473	0.312237	−	0.950004i	$-0.398922\pi$
$521$	14.2539	0.624473	0.312237	+	0.950004i	$0.398922\pi$
$522$	−76.2914	−3.33918
$523$	−0.904789	−0.0395637	−0.0197818	−	0.999804i	$-0.506297\pi$
$523$	−0.904789	−0.0395637	−0.0197818	+	0.999804i	$0.506297\pi$
$524$	−32.3266	−1.41219
$525$	1.61592	0.0705244
$526$	−33.3047	−1.45215
$527$	−22.9914	−1.00152
$528$	123.017	5.35362
$529$	−5.67838	−0.246886
$530$	46.9468	2.03924
$531$	−14.7391	−0.639623
$532$	−1.78265	−0.0772876
$533$	−8.24433	−0.357102
$534$	−0.471878	−0.0204201
$535$	7.92686	0.342708
$536$	−43.5871	−1.88268
$537$	−1.90440	−0.0821810
$538$	−9.74917	−0.420317
$539$	38.9542	1.67788
$540$	−7.35781	−0.316630
$541$	3.39416	0.145927	0.0729633	−	0.997335i	$-0.476754\pi$
$541$	3.39416	0.145927	0.0729633	+	0.997335i	$0.476754\pi$
$542$	14.9906	0.643900
$543$	24.1595	1.03678
$544$	−44.4373	−1.90523
$545$	5.54037	0.237323
$546$	−2.17444	−0.0930576
$547$	36.5541	1.56294	0.781471	−	0.623942i	$-0.214470\pi$
$547$	36.5541	1.56294	0.781471	+	0.623942i	$0.214470\pi$
$548$	−53.0666	−2.26689
$549$	31.4884	1.34389
$550$	53.9027	2.29842
$551$	19.8650	0.846277
$552$	−73.1084	−3.11170
$553$	−1.20100	−0.0510717
$554$	55.4789	2.35707
$555$	−4.23510	−0.179770
$556$	−30.1827	−1.28003
$557$	−3.14459	−0.133241	−0.0666203	−	0.997778i	$-0.521222\pi$
$557$	−3.14459	−0.133241	−0.0666203	+	0.997778i	$0.521222\pi$
$558$	37.8843	1.60377
$559$	7.87544	0.333096
$560$	−4.54442	−0.192037
$561$	70.3830	2.97157
$562$	4.92284	0.207657
$563$	12.0605	0.508290	0.254145	−	0.967166i	$-0.418206\pi$
$563$	12.0605	0.508290	0.254145	+	0.967166i	$0.418206\pi$
$564$	54.8299	2.30876
$565$	−31.6912	−1.33326
$566$	31.2758	1.31462
$567$	1.44977	0.0608844
$568$	8.54316	0.358463
$569$	−20.3840	−0.854540	−0.427270	−	0.904124i	$-0.640525\pi$
$569$	−20.3840	−0.854540	−0.427270	+	0.904124i	$0.640525\pi$
$570$	41.3576	1.73228
$571$	−31.6875	−1.32608	−0.663041	−	0.748583i	$-0.730734\pi$
$571$	−31.6875	−1.32608	−0.663041	+	0.748583i	$0.730734\pi$
$572$	−50.9430	−2.13003
$573$	36.5978	1.52890
$574$	−1.92803	−0.0804745
$575$	−15.4849	−0.645764
$576$	16.4944	0.687268
$577$	1.40506	0.0584932	0.0292466	−	0.999572i	$-0.490689\pi$
$577$	1.40506	0.0584932	0.0292466	+	0.999572i	$0.490689\pi$
$578$	−22.1069	−0.919524
$579$	−58.5378	−2.43275
$580$	127.700	5.30247
$581$	−2.79904	−0.116124
$582$	71.6909	2.97168
$583$	34.2787	1.41968
$584$	9.79342	0.405254
$585$	18.3197	0.757424
$586$	−61.0605	−2.52239
$587$	4.13946	0.170854	0.0854269	−	0.996344i	$-0.472775\pi$
$587$	4.13946	0.170854	0.0854269	+	0.996344i	$0.472775\pi$
$588$	81.9730	3.38051
$589$	−9.86442	−0.406456
$590$	35.1271	1.44616
$591$	−14.7497	−0.606722
$592$	5.08148	0.208848
$593$	34.4955	1.41656	0.708280	−	0.705932i	$-0.249472\pi$
$593$	34.4955	1.41656	0.708280	+	0.705932i	$0.249472\pi$
$594$	−7.64930	−0.313855
$595$	−2.60005	−0.106592
$596$	−41.3584	−1.69410
$597$	−40.5530	−1.65972
$598$	20.8371	0.852091
$599$	−38.8206	−1.58617	−0.793083	−	0.609113i	$-0.791525\pi$
$599$	−38.8206	−1.58617	−0.793083	+	0.609113i	$0.791525\pi$
$600$	65.3561	2.66815
$601$	12.7536	0.520230	0.260115	−	0.965578i	$-0.416239\pi$
$601$	12.7536	0.520230	0.260115	+	0.965578i	$0.416239\pi$
$602$	1.84176	0.0750646
$603$	19.8632	0.808893
$604$	−97.6789	−3.97450
$605$	59.7653	2.42981
$606$	82.8362	3.36499
$607$	24.8642	1.00921	0.504603	−	0.863352i	$-0.331639\pi$
$607$	24.8642	1.00921	0.504603	+	0.863352i	$0.331639\pi$
$608$	−19.0658	−0.773219
$609$	3.97992	0.161275
$610$	−75.0450	−3.03848
$611$	−9.00423	−0.364272
$612$	76.5804	3.09558
$613$	−24.8986	−1.00565	−0.502823	−	0.864389i	$-0.667705\pi$
$613$	−24.8986	−1.00565	−0.502823	+	0.864389i	$0.667705\pi$
$614$	22.8642	0.922723
$615$	31.4159	1.26681
$616$	−6.86440	−0.276575
$617$	−42.4910	−1.71062	−0.855312	−	0.518113i	$-0.826635\pi$
$617$	−42.4910	−1.71062	−0.855312	+	0.518113i	$0.826635\pi$
$618$	−1.47919	−0.0595019
$619$	9.85099	0.395945	0.197972	−	0.980208i	$-0.436564\pi$
$619$	9.85099	0.395945	0.197972	+	0.980208i	$0.436564\pi$
$620$	−63.4126	−2.54671
$621$	2.19745	0.0881806
$622$	44.8711	1.79917
$623$	0.0127281	0.000509939 0
$624$	−42.5118	−1.70183
$625$	−29.7601	−1.19041
$626$	−4.41594	−0.176496
$627$	30.1977	1.20598
$628$	87.0943	3.47544
$629$	2.90732	0.115923
$630$	4.28426	0.170689
$631$	22.1744	0.882750	0.441375	−	0.897323i	$-0.354491\pi$
$631$	22.1744	0.882750	0.441375	+	0.897323i	$0.354491\pi$
$632$	−48.5746	−1.93219
$633$	−72.2599	−2.87207
$634$	−9.93391	−0.394526
$635$	−7.76346	−0.308084
$636$	72.1342	2.86031
$637$	−13.4617	−0.533372
$638$	132.759	5.25600
$639$	−3.89323	−0.154014
$640$	12.6338	0.499394
$641$	40.6426	1.60528	0.802642	−	0.596461i	$-0.203427\pi$
$641$	40.6426	1.60528	0.802642	+	0.596461i	$0.203427\pi$
$642$	17.3417	0.684421
$643$	−14.6254	−0.576769	−0.288384	−	0.957515i	$-0.593118\pi$
$643$	−14.6254	−0.576769	−0.288384	+	0.957515i	$0.593118\pi$
$644$	3.42248	0.134864
$645$	−30.0102	−1.18165
$646$	−28.3913	−1.11704
$647$	−2.38796	−0.0938803	−0.0469402	−	0.998898i	$-0.514947\pi$
$647$	−2.38796	−0.0938803	−0.0469402	+	0.998898i	$0.514947\pi$
$648$	58.6360	2.30344
$649$	25.6485	1.00679
$650$	−18.6275	−0.730632
$651$	−1.97632	−0.0774582
$652$	82.0110	3.21180
$653$	−8.00980	−0.313448	−0.156724	−	0.987642i	$-0.550093\pi$
$653$	−8.00980	−0.313448	−0.156724	+	0.987642i	$0.550093\pi$
$654$	12.1207	0.473957
$655$	−20.2294	−0.790428
$656$	−37.6943	−1.47171
$657$	−4.46299	−0.174118
$658$	−2.10574	−0.0820903
$659$	13.0267	0.507449	0.253725	−	0.967277i	$-0.418344\pi$
$659$	13.0267	0.507449	0.253725	+	0.967277i	$0.418344\pi$
$660$	194.124	7.55625
$661$	3.92155	0.152531	0.0762653	−	0.997088i	$-0.475700\pi$
$661$	3.92155	0.152531	0.0762653	+	0.997088i	$0.475700\pi$
$662$	17.4493	0.678185
$663$	−24.3228	−0.944618
$664$	−113.208	−4.39331
$665$	−1.11555	−0.0432591
$666$	−4.79057	−0.185631
$667$	−38.1385	−1.47673
$668$	−5.24421	−0.202904
$669$	−38.6085	−1.49269
$670$	−47.3392	−1.82887
$671$	−54.7950	−2.11534
$672$	−3.81980	−0.147352
$673$	−1.19635	−0.0461157	−0.0230579	−	0.999734i	$-0.507340\pi$
$673$	−1.19635	−0.0461157	−0.0230579	+	0.999734i	$0.507340\pi$
$674$	23.5231	0.906075
$675$	−1.96444	−0.0756112
$676$	−43.7423	−1.68240
$677$	−24.1885	−0.929639	−0.464820	−	0.885405i	$-0.653881\pi$
$677$	−24.1885	−0.929639	−0.464820	+	0.885405i	$0.653881\pi$
$678$	−69.3311	−2.66265
$679$	−1.93374	−0.0742100
$680$	−105.160	−4.03268
$681$	−28.0231	−1.07385
$682$	−65.9248	−2.52439
$683$	31.4899	1.20493	0.602464	−	0.798146i	$-0.294186\pi$
$683$	31.4899	1.20493	0.602464	+	0.798146i	$0.294186\pi$
$684$	32.8567	1.25631
$685$	−33.2081	−1.26882
$686$	−6.31006	−0.240919
$687$	−45.2235	−1.72538
$688$	36.0077	1.37278
$689$	−11.8460	−0.451295
$690$	−79.4018	−3.02277
$691$	40.3551	1.53518	0.767591	−	0.640940i	$-0.221455\pi$
$691$	40.3551	1.53518	0.767591	+	0.640940i	$0.221455\pi$
$692$	−36.9051	−1.40292
$693$	3.12820	0.118830
$694$	18.7441	0.711514
$695$	−18.8878	−0.716455
$696$	160.969	6.10150
$697$	−21.5665	−0.816888
$698$	5.05165	0.191208
$699$	−23.9630	−0.906365
$700$	−3.05956	−0.115641
$701$	−32.2691	−1.21879	−0.609394	−	0.792868i	$-0.708587\pi$
$701$	−32.2691	−1.21879	−0.609394	+	0.792868i	$0.708587\pi$
$702$	2.64342	0.0997696
$703$	1.24738	0.0470460
$704$	−28.7030	−1.08179
$705$	34.3115	1.29225
$706$	40.4773	1.52338
$707$	−2.23436	−0.0840317
$708$	53.9732	2.02844
$709$	−2.25310	−0.0846171	−0.0423085	−	0.999105i	$-0.513471\pi$
$709$	−2.25310	−0.0846171	−0.0423085	+	0.999105i	$0.513471\pi$
$710$	9.27859	0.348219
$711$	22.1361	0.830169
$712$	0.514789	0.0192925
$713$	18.9385	0.709254
$714$	−5.68816	−0.212874
$715$	−31.8792	−1.19221
$716$	3.60578	0.134754
$717$	−8.97454	−0.335160
$718$	−17.5161	−0.653694
$719$	30.4400	1.13522	0.567610	−	0.823298i	$-0.307868\pi$
$719$	30.4400	1.13522	0.567610	+	0.823298i	$0.307868\pi$
$720$	83.7601	3.12156
$721$	0.0398986	0.00148590
$722$	37.0687	1.37956
$723$	46.0789	1.71369
$724$	−45.7433	−1.70004
$725$	34.0943	1.26623
$726$	130.749	4.85256
$727$	44.7359	1.65916	0.829582	−	0.558385i	$-0.188579\pi$
$727$	44.7359	1.65916	0.829582	+	0.558385i	$0.188579\pi$
$728$	2.37218	0.0879189
$729$	−30.6690	−1.13589
$730$	10.6365	0.393673
$731$	20.6015	0.761973
$732$	−115.307	−4.26188
$733$	44.0825	1.62823	0.814113	−	0.580707i	$-0.197224\pi$
$733$	44.0825	1.62823	0.814113	+	0.580707i	$0.197224\pi$
$734$	58.4556	2.15764
$735$	51.2972	1.89212
$736$	36.6040	1.34924
$737$	−34.5653	−1.27323
$738$	35.5363	1.30811
$739$	45.3379	1.66778	0.833891	−	0.551928i	$-0.186108\pi$
$739$	45.3379	1.66778	0.833891	+	0.551928i	$0.186108\pi$
$740$	8.01870	0.294773
$741$	−10.4356	−0.383363
$742$	−2.77031	−0.101701
$743$	1.86736	0.0685068	0.0342534	−	0.999413i	$-0.489095\pi$
$743$	1.86736	0.0685068	0.0342534	+	0.999413i	$0.489095\pi$
$744$	−79.9328	−2.93048
$745$	−25.8813	−0.948218
$746$	9.08078	0.332471
$747$	51.5902	1.88759
$748$	−133.262	−4.87256
$749$	−0.467761	−0.0170916
$750$	−24.4085	−0.891273
$751$	40.1445	1.46489	0.732447	−	0.680824i	$-0.238378\pi$
$751$	40.1445	1.46489	0.732447	+	0.680824i	$0.238378\pi$
$752$	−41.1686	−1.50127
$753$	63.5332	2.31528
$754$	−45.8787	−1.67080
$755$	−61.1257	−2.22459
$756$	0.434181	0.0157910
$757$	36.9263	1.34211	0.671054	−	0.741409i	$-0.265842\pi$
$757$	36.9263	1.34211	0.671054	+	0.741409i	$0.265842\pi$
$758$	−57.5498	−2.09030
$759$	−57.9761	−2.10440
$760$	−45.1186	−1.63662
$761$	20.0754	0.727733	0.363866	−	0.931451i	$-0.381456\pi$
$761$	20.0754	0.727733	0.363866	+	0.931451i	$0.381456\pi$
$762$	−16.9842	−0.615272
$763$	−0.326935	−0.0118358
$764$	−69.2940	−2.50697
$765$	47.9226	1.73265
$766$	−67.6547	−2.44446
$767$	−8.86353	−0.320044
$768$	53.2381	1.92106
$769$	44.1692	1.59278	0.796391	−	0.604782i	$-0.206740\pi$
$769$	44.1692	1.59278	0.796391	+	0.604782i	$0.206740\pi$
$770$	−7.45531	−0.268671
$771$	−19.2983	−0.695010
$772$	110.835	3.98904
$773$	25.4053	0.913766	0.456883	−	0.889527i	$-0.348966\pi$
$773$	25.4053	0.913766	0.456883	+	0.889527i	$0.348966\pi$
$774$	−33.9463	−1.22017
$775$	−16.9303	−0.608155
$776$	−78.2103	−2.80759
$777$	0.249912	0.00896553
$778$	64.8336	2.32440
$779$	−9.25306	−0.331525
$780$	−67.0847	−2.40202
$781$	6.77486	0.242424
$782$	54.5079	1.94920
$783$	−4.83831	−0.172907
$784$	−61.5488	−2.19817
$785$	54.5020	1.94526
$786$	−44.2560	−1.57856
$787$	44.6108	1.59020	0.795102	−	0.606476i	$-0.207417\pi$
$787$	44.6108	1.59020	0.795102	+	0.606476i	$0.207417\pi$
$788$	27.9270	0.994857
$789$	−32.0231	−1.14005
$790$	−52.7561	−1.87698
$791$	1.87008	0.0664926
$792$	126.521	4.49571
$793$	18.9359	0.672433
$794$	52.3980	1.85953
$795$	45.1403	1.60096
$796$	76.7827	2.72149
$797$	−34.6213	−1.22635	−0.613174	−	0.789948i	$-0.710108\pi$
$797$	−34.6213	−1.22635	−0.613174	+	0.789948i	$0.710108\pi$
$798$	−2.44050	−0.0863926
$799$	−23.5543	−0.833290
$800$	−32.7226	−1.15692
$801$	−0.234596	−0.00828905
$802$	36.1439	1.27628
$803$	7.76633	0.274068
$804$	−72.7371	−2.56524
$805$	2.14172	0.0754858
$806$	22.7821	0.802466
$807$	−9.37401	−0.329981
$808$	−90.3691	−3.17917
$809$	−13.5998	−0.478143	−0.239072	−	0.971002i	$-0.576843\pi$
$809$	−13.5998	−0.478143	−0.239072	+	0.971002i	$0.576843\pi$
$810$	63.6836	2.23761
$811$	−7.69690	−0.270275	−0.135137	−	0.990827i	$-0.543148\pi$
$811$	−7.69690	−0.270275	−0.135137	+	0.990827i	$0.543148\pi$
$812$	−7.53555	−0.264446
$813$	14.4137	0.505511
$814$	8.33638	0.292190
$815$	51.3210	1.79770
$816$	−111.207	−3.89303
$817$	8.83903	0.309239
$818$	−59.7068	−2.08760
$819$	−1.08103	−0.0377744
$820$	−59.4825	−2.07722
$821$	−24.0377	−0.838920	−0.419460	−	0.907774i	$-0.637781\pi$
$821$	−24.0377	−0.838920	−0.419460	+	0.907774i	$0.637781\pi$
$822$	−72.6497	−2.53395
$823$	−52.4935	−1.82981	−0.914904	−	0.403672i	$-0.867734\pi$
$823$	−52.4935	−1.82981	−0.914904	+	0.403672i	$0.867734\pi$
$824$	1.61371	0.0562162
$825$	51.8284	1.80443
$826$	−2.07284	−0.0721233
$827$	−30.9344	−1.07569	−0.537847	−	0.843042i	$-0.680762\pi$
$827$	−30.9344	−1.07569	−0.537847	+	0.843042i	$0.680762\pi$
$828$	−63.0811	−2.19222
$829$	13.2558	0.460394	0.230197	−	0.973144i	$-0.426063\pi$
$829$	13.2558	0.460394	0.230197	+	0.973144i	$0.426063\pi$
$830$	−122.953	−4.26776
$831$	53.3440	1.85048
$832$	9.91911	0.343883
$833$	−35.2146	−1.22011
$834$	−41.3210	−1.43083
$835$	−3.28173	−0.113569
$836$	−57.1761	−1.97748
$837$	2.40257	0.0830451
$838$	−37.9885	−1.31229
$839$	−28.2582	−0.975582	−0.487791	−	0.872960i	$-0.662197\pi$
$839$	−28.2582	−0.975582	−0.487791	+	0.872960i	$0.662197\pi$
$840$	−9.03944	−0.311890
$841$	54.9726	1.89561
$842$	−31.5176	−1.08617
$843$	4.73340	0.163027
$844$	136.816	4.70941
$845$	−27.3731	−0.941665
$846$	38.8118	1.33438
$847$	−3.52673	−0.121180
$848$	−54.1614	−1.85991
$849$	30.0722	1.03208
$850$	−48.7280	−1.67136
$851$	−2.39483	−0.0820937
$852$	14.2566	0.488424
$853$	−2.68733	−0.0920125	−0.0460063	−	0.998941i	$-0.514649\pi$
$853$	−2.68733	−0.0920125	−0.0460063	+	0.998941i	$0.514649\pi$
$854$	4.42838	0.151536
$855$	20.5611	0.703176
$856$	−18.9187	−0.646627
$857$	−23.1187	−0.789721	−0.394861	−	0.918741i	$-0.629207\pi$
$857$	−23.1187	−0.789721	−0.394861	+	0.918741i	$0.629207\pi$
$858$	−69.7424	−2.38097
$859$	46.7565	1.59531	0.797655	−	0.603114i	$-0.206073\pi$
$859$	46.7565	1.59531	0.797655	+	0.603114i	$0.206073\pi$
$860$	56.8210	1.93758
$861$	−1.85384	−0.0631786
$862$	56.0943	1.91058
$863$	32.1283	1.09366	0.546830	−	0.837244i	$-0.315835\pi$
$863$	32.1283	1.09366	0.546830	+	0.837244i	$0.315835\pi$
$864$	4.64365	0.157980
$865$	−23.0946	−0.785239
$866$	−88.0643	−2.99255
$867$	−21.2562	−0.721897
$868$	3.74195	0.127010
$869$	−38.5204	−1.30672
$870$	174.825	5.92714
$871$	11.9450	0.404740
$872$	−13.2229	−0.447785
$873$	35.6415	1.20628
$874$	23.3866	0.791062
$875$	0.658377	0.0222572
$876$	16.3430	0.552180
$877$	12.0588	0.407195	0.203598	−	0.979055i	$-0.434737\pi$
$877$	12.0588	0.407195	0.203598	+	0.979055i	$0.434737\pi$
$878$	69.2327	2.33649
$879$	−58.7109	−1.98027
$880$	−145.756	−4.91344
$881$	50.3105	1.69500	0.847502	−	0.530792i	$-0.178105\pi$
$881$	50.3105	1.69500	0.847502	+	0.530792i	$0.178105\pi$
$882$	58.0252	1.95381
$883$	−7.30939	−0.245980	−0.122990	−	0.992408i	$-0.539248\pi$
$883$	−7.30939	−0.245980	−0.122990	+	0.992408i	$0.539248\pi$
$884$	46.0525	1.54891
$885$	33.7754	1.13535
$886$	−10.1357	−0.340517
$887$	39.7966	1.33624	0.668120	−	0.744054i	$-0.267099\pi$
$887$	39.7966	1.33624	0.668120	+	0.744054i	$0.267099\pi$
$888$	10.1077	0.339193
$889$	0.458119	0.0153648
$890$	0.559104	0.0187412
$891$	46.4993	1.55779
$892$	73.1010	2.44760
$893$	−10.1059	−0.338182
$894$	−56.6208	−1.89368
$895$	2.25643	0.0754241
$896$	−0.745514	−0.0249059
$897$	20.0352	0.668957
$898$	−5.62915	−0.187847
$899$	−41.6985	−1.39072
$900$	56.3921	1.87974
$901$	−30.9880	−1.03236
$902$	−61.8390	−2.05901
$903$	1.77089	0.0589315
$904$	75.6359	2.51561
$905$	−28.6253	−0.951537
$906$	−133.725	−4.44272
$907$	8.25803	0.274203	0.137102	−	0.990557i	$-0.456221\pi$
$907$	8.25803	0.274203	0.137102	+	0.990557i	$0.456221\pi$
$908$	53.0588	1.76082
$909$	41.1824	1.36593
$910$	2.57639	0.0854064
$911$	6.48950	0.215007	0.107503	−	0.994205i	$-0.465714\pi$
$911$	6.48950	0.215007	0.107503	+	0.994205i	$0.465714\pi$
$912$	−47.7133	−1.57995
$913$	−89.7754	−2.97113
$914$	−90.1469	−2.98180
$915$	−72.1572	−2.38544
$916$	85.6258	2.82915
$917$	1.19373	0.0394204
$918$	6.91497	0.228228
$919$	5.88933	0.194271	0.0971355	−	0.995271i	$-0.469032\pi$
$919$	5.88933	0.194271	0.0971355	+	0.995271i	$0.469032\pi$
$920$	86.6224	2.85585
$921$	21.9843	0.724408
$922$	79.2025	2.60839
$923$	−2.34124	−0.0770628
$924$	−11.4551	−0.376847
$925$	2.14089	0.0703919
$926$	−29.4477	−0.967710
$927$	−0.735388	−0.0241533
$928$	−80.5941	−2.64563
$929$	−23.3307	−0.765456	−0.382728	−	0.923861i	$-0.625015\pi$
$929$	−23.3307	−0.765456	−0.382728	+	0.923861i	$0.625015\pi$
$930$	−86.8137	−2.84673
$931$	−15.1088	−0.495170
$932$	45.3714	1.48619
$933$	43.1444	1.41248
$934$	71.4387	2.33755
$935$	−83.3932	−2.72725
$936$	−43.7226	−1.42912
$937$	42.1034	1.37546	0.687729	−	0.725967i	$-0.258608\pi$
$937$	42.1034	1.37546	0.687729	+	0.725967i	$0.258608\pi$
$938$	2.79347	0.0912100
$939$	−4.24601	−0.138563
$940$	−64.9651	−2.11893
$941$	14.6507	0.477598	0.238799	−	0.971069i	$-0.423246\pi$
$941$	14.6507	0.477598	0.238799	+	0.971069i	$0.423246\pi$
$942$	119.235	3.88487
$943$	17.7648	0.578501
$944$	−40.5254	−1.31899
$945$	0.271703	0.00883849
$946$	59.0720	1.92060
$947$	−40.1078	−1.30333	−0.651664	−	0.758508i	$-0.725929\pi$
$947$	−40.1078	−1.30333	−0.651664	+	0.758508i	$0.725929\pi$
$948$	−81.0602	−2.63271
$949$	−2.68387	−0.0871221
$950$	−20.9067	−0.678303
$951$	−9.55164	−0.309733
$952$	6.20542	0.201119
$953$	17.8191	0.577218	0.288609	−	0.957447i	$-0.406807\pi$
$953$	17.8191	0.577218	0.288609	+	0.957447i	$0.406807\pi$
$954$	51.0608	1.65315
$955$	−43.3629	−1.40319
$956$	16.9923	0.549571
$957$	127.651	4.12636
$958$	−94.6164	−3.05692
$959$	1.95960	0.0632787
$960$	−37.7978	−1.21992
$961$	−10.2936	−0.332052
$962$	−2.88086	−0.0928828
$963$	8.62149	0.277824
$964$	−87.2453	−2.80998
$965$	69.3585	2.23273
$966$	4.68547	0.150752
$967$	55.7592	1.79310	0.896548	−	0.442947i	$-0.146067\pi$
$967$	55.7592	1.79310	0.896548	+	0.442947i	$0.146067\pi$
$968$	−142.639	−4.58459
$969$	−27.2987	−0.876962
$970$	−84.9429	−2.72735
$971$	3.28179	0.105318	0.0526588	−	0.998613i	$-0.483230\pi$
$971$	3.28179	0.105318	0.0526588	+	0.998613i	$0.483230\pi$
$972$	105.325	3.37831
$973$	1.11456	0.0357312
$974$	−42.5760	−1.36422
$975$	−17.9107	−0.573602
$976$	86.5777	2.77128
$977$	60.8918	1.94810	0.974051	−	0.226331i	$-0.0726729\pi$
$977$	60.8918	1.94810	0.974051	+	0.226331i	$0.0726729\pi$
$978$	112.275	3.59017
$979$	0.408236	0.0130473
$980$	−97.1256	−3.10256
$981$	6.02587	0.192391
$982$	23.1277	0.738035
$983$	14.8731	0.474380	0.237190	−	0.971463i	$-0.423774\pi$
$983$	14.8731	0.474380	0.237190	+	0.971463i	$0.423774\pi$
$984$	−74.9788	−2.39024
$985$	17.4762	0.556837
$986$	−120.015	−3.82204
$987$	−2.02471	−0.0644472
$988$	19.7588	0.628610
$989$	−16.9699	−0.539612
$990$	137.412	4.36724
$991$	30.5251	0.969663	0.484832	−	0.874608i	$-0.338881\pi$
$991$	30.5251	0.969663	0.484832	+	0.874608i	$0.338881\pi$
$992$	40.0209	1.27066
$993$	16.7778	0.532427
$994$	−0.547525	−0.0173665
$995$	48.0492	1.52326
$996$	−188.918	−5.98610
$997$	−54.9438	−1.74009	−0.870044	−	0.492974i	$-0.835910\pi$
$997$	−54.9438	−1.74009	−0.870044	+	0.492974i	$0.835910\pi$
$998$	−24.3352	−0.770318
$999$	−0.303812	−0.00961220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6047.2.a.b.1.15	✓	287

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6047.2.a.b.1.15	✓	287	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:	\( N \)	\(=\)	\( 6047 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59210 q^{2} -2.49236 q^{3} +4.71900 q^{4} +2.95307 q^{5} +6.46045 q^{6} -0.174259 q^{7} -7.04794 q^{8} +3.21184 q^{9} +O(q^{10})\)	\(q-2.59210 q^{2} -2.49236 q^{3} +4.71900 q^{4} +2.95307 q^{5} +6.46045 q^{6} -0.174259 q^{7} -7.04794 q^{8} +3.21184 q^{9} -7.65466 q^{10} -5.58913 q^{11} -11.7614 q^{12} +1.93148 q^{13} +0.451698 q^{14} -7.36010 q^{15} +8.83100 q^{16} +5.05258 q^{17} -8.32543 q^{18} +2.16780 q^{19} +13.9355 q^{20} +0.434316 q^{21} +14.4876 q^{22} -4.16193 q^{23} +17.5660 q^{24} +3.72060 q^{25} -5.00659 q^{26} -0.527989 q^{27} -0.822330 q^{28} +9.16366 q^{29} +19.0781 q^{30} -4.55043 q^{31} -8.79498 q^{32} +13.9301 q^{33} -13.0968 q^{34} -0.514599 q^{35} +15.1567 q^{36} +0.575414 q^{37} -5.61917 q^{38} -4.81393 q^{39} -20.8130 q^{40} -4.26841 q^{41} -1.12579 q^{42} +4.07742 q^{43} -26.3751 q^{44} +9.48479 q^{45} +10.7881 q^{46} -4.66183 q^{47} -22.0100 q^{48} -6.96963 q^{49} -9.64419 q^{50} -12.5928 q^{51} +9.11465 q^{52} -6.13311 q^{53} +1.36860 q^{54} -16.5051 q^{55} +1.22817 q^{56} -5.40294 q^{57} -23.7532 q^{58} -4.58899 q^{59} -34.7323 q^{60} +9.80384 q^{61} +11.7952 q^{62} -0.559693 q^{63} +5.13551 q^{64} +5.70378 q^{65} -36.1083 q^{66} +6.18437 q^{67} +23.8431 q^{68} +10.3730 q^{69} +1.33389 q^{70} -1.21215 q^{71} -22.6369 q^{72} -1.38954 q^{73} -1.49153 q^{74} -9.27307 q^{75} +10.2299 q^{76} +0.973958 q^{77} +12.4782 q^{78} +6.89203 q^{79} +26.0785 q^{80} -8.31959 q^{81} +11.0642 q^{82} +16.0625 q^{83} +2.04954 q^{84} +14.9206 q^{85} -10.5691 q^{86} -22.8391 q^{87} +39.3919 q^{88} -0.0730410 q^{89} -24.5856 q^{90} -0.336578 q^{91} -19.6401 q^{92} +11.3413 q^{93} +12.0840 q^{94} +6.40166 q^{95} +21.9202 q^{96} +11.0969 q^{97} +18.0660 q^{98} -17.9514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9}+O(q^{10}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9	\( 287 q + 21 q^{2} + 29 q^{3} + 319 q^{4} + 19 q^{5} + 15 q^{6} + 52 q^{7} + 60 q^{8} + 352 q^{9} + 38 q^{10} + 32 q^{11} + 80 q^{12} + 86 q^{13} + 14 q^{14} + 41 q^{15} + 375 q^{16} + 59 q^{17} + 93 q^{18} + 39 q^{19} + 27 q^{20} + 51 q^{21} + 99 q^{22} + 68 q^{23} + 31 q^{24} + 492 q^{25} + 19 q^{26} + 107 q^{27} + 142 q^{28} + 39 q^{29} + 12 q^{30} + 104 q^{31} + 131 q^{32} + 139 q^{33} + 71 q^{34} - 5 q^{35} + 410 q^{36} + 298 q^{37} + 19 q^{38} + 37 q^{39} + 98 q^{40} + 90 q^{41} + 32 q^{42} + 105 q^{43} + 85 q^{44} + 73 q^{45} + 97 q^{46} + 66 q^{47} + 161 q^{48} + 473 q^{49} + 85 q^{50} + 34 q^{51} + 179 q^{52} + 95 q^{53} + 28 q^{54} + 62 q^{55} + 16 q^{56} + 247 q^{57} + 247 q^{58} + 32 q^{59} + 51 q^{60} + 106 q^{61} + 22 q^{62} + 104 q^{63} + 480 q^{64} + 150 q^{65} - 27 q^{66} + 232 q^{67} + 88 q^{68} + 57 q^{69} + 123 q^{70} + 46 q^{71} + 240 q^{72} + 372 q^{73} + 13 q^{74} + 81 q^{75} + 82 q^{76} + 65 q^{77} + 154 q^{78} + 143 q^{79} + 17 q^{80} + 519 q^{81} + 98 q^{82} + 49 q^{83} + 79 q^{84} + 236 q^{85} + 61 q^{86} + 31 q^{87} + 254 q^{88} + 114 q^{89} + 36 q^{90} + 96 q^{91} + 151 q^{92} + 189 q^{93} + 8 q^{94} + 30 q^{95} + 23 q^{96} + 503 q^{97} + 91 q^{98} + 130 q^{99}+O(q^{100}) \) 287 * q + 21 * q^2 + 29 * q^3 + 319 * q^4 + 19 * q^5 + 15 * q^6 + 52 * q^7 + 60 * q^8 + 352 * q^9 + 38 * q^10 + 32 * q^11 + 80 * q^12 + 86 * q^13 + 14 * q^14 + 41 * q^15 + 375 * q^16 + 59 * q^17 + 93 * q^18 + 39 * q^19 + 27 * q^20 + 51 * q^21 + 99 * q^22 + 68 * q^23 + 31 * q^24 + 492 * q^25 + 19 * q^26 + 107 * q^27 + 142 * q^28 + 39 * q^29 + 12 * q^30 + 104 * q^31 + 131 * q^32 + 139 * q^33 + 71 * q^34 - 5 * q^35 + 410 * q^36 + 298 * q^37 + 19 * q^38 + 37 * q^39 + 98 * q^40 + 90 * q^41 + 32 * q^42 + 105 * q^43 + 85 * q^44 + 73 * q^45 + 97 * q^46 + 66 * q^47 + 161 * q^48 + 473 * q^49 + 85 * q^50 + 34 * q^51 + 179 * q^52 + 95 * q^53 + 28 * q^54 + 62 * q^55 + 16 * q^56 + 247 * q^57 + 247 * q^58 + 32 * q^59 + 51 * q^60 + 106 * q^61 + 22 * q^62 + 104 * q^63 + 480 * q^64 + 150 * q^65 - 27 * q^66 + 232 * q^67 + 88 * q^68 + 57 * q^69 + 123 * q^70 + 46 * q^71 + 240 * q^72 + 372 * q^73 + 13 * q^74 + 81 * q^75 + 82 * q^76 + 65 * q^77 + 154 * q^78 + 143 * q^79 + 17 * q^80 + 519 * q^81 + 98 * q^82 + 49 * q^83 + 79 * q^84 + 236 * q^85 + 61 * q^86 + 31 * q^87 + 254 * q^88 + 114 * q^89 + 36 * q^90 + 96 * q^91 + 151 * q^92 + 189 * q^93 + 8 * q^94 + 30 * q^95 + 23 * q^96 + 503 * q^97 + 91 * q^98 + 130 * q^99

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