LMFDB - Embedded newform 5041.2.a.t.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5041,2,Mod(1,5041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5041, 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("5041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5041 = 71^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5041.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:	$40.2525876589$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 71)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	5041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12199 q^{2} -0.878312 q^{3} +2.50286 q^{4} +0.714152 q^{5} +1.86377 q^{6} +0.230934 q^{7} -1.06706 q^{8} -2.22857 q^{9} +O(q^{10})$	\(q-2.12199 q^{2} -0.878312 q^{3} +2.50286 q^{4} +0.714152 q^{5} +1.86377 q^{6} +0.230934 q^{7} -1.06706 q^{8} -2.22857 q^{9} -1.51543 q^{10} -1.25561 q^{11} -2.19829 q^{12} +2.68043 q^{13} -0.490041 q^{14} -0.627248 q^{15} -2.74142 q^{16} +1.65037 q^{17} +4.72901 q^{18} +6.53601 q^{19} +1.78742 q^{20} -0.202832 q^{21} +2.66439 q^{22} +6.48014 q^{23} +0.937212 q^{24} -4.48999 q^{25} -5.68785 q^{26} +4.59231 q^{27} +0.577996 q^{28} -0.829664 q^{29} +1.33102 q^{30} -7.70653 q^{31} +7.95140 q^{32} +1.10281 q^{33} -3.50207 q^{34} +0.164922 q^{35} -5.57779 q^{36} +7.90336 q^{37} -13.8694 q^{38} -2.35425 q^{39} -0.762043 q^{40} +6.96040 q^{41} +0.430409 q^{42} +6.00348 q^{43} -3.14260 q^{44} -1.59154 q^{45} -13.7508 q^{46} -8.55648 q^{47} +2.40782 q^{48} -6.94667 q^{49} +9.52773 q^{50} -1.44954 q^{51} +6.70873 q^{52} -1.93032 q^{53} -9.74486 q^{54} -0.896693 q^{55} -0.246421 q^{56} -5.74065 q^{57} +1.76054 q^{58} -3.18358 q^{59} -1.56991 q^{60} +9.76929 q^{61} +16.3532 q^{62} -0.514653 q^{63} -11.3900 q^{64} +1.91423 q^{65} -2.34016 q^{66} +3.60862 q^{67} +4.13063 q^{68} -5.69159 q^{69} -0.349964 q^{70} +2.37802 q^{72} -6.57900 q^{73} -16.7709 q^{74} +3.94361 q^{75} +16.3587 q^{76} -0.289962 q^{77} +4.99571 q^{78} -5.66006 q^{79} -1.95779 q^{80} +2.65222 q^{81} -14.7699 q^{82} -4.54846 q^{83} -0.507660 q^{84} +1.17861 q^{85} -12.7393 q^{86} +0.728703 q^{87} +1.33981 q^{88} +11.2664 q^{89} +3.37723 q^{90} +0.619002 q^{91} +16.2189 q^{92} +6.76874 q^{93} +18.1568 q^{94} +4.66770 q^{95} -6.98381 q^{96} -10.6082 q^{97} +14.7408 q^{98} +2.79820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 2 q^{2} - 2 q^{3} + 46 q^{4} + 10 q^{5} + 4 q^{6} + 25 q^{7} + 9 q^{8} + 32 q^{9}+O(q^{10}) $ 60 * q - 2 * q^2 - 2 * q^3 + 46 * q^4 + 10 * q^5 + 4 * q^6 + 25 * q^7 + 9 * q^8 + 32 * q^9	\( 60 q - 2 q^{2} - 2 q^{3} + 46 q^{4} + 10 q^{5} + 4 q^{6} + 25 q^{7} + 9 q^{8} + 32 q^{9} + 18 q^{10} + 53 q^{11} + 44 q^{12} + 13 q^{13} + 49 q^{14} - 20 q^{15} + 26 q^{16} + 33 q^{17} - 48 q^{18} + 3 q^{19} - 48 q^{20} + 18 q^{21} + 16 q^{22} + 59 q^{23} - 85 q^{24} + 24 q^{25} + 63 q^{26} - 26 q^{27} + 63 q^{28} + 22 q^{29} - 66 q^{30} + 72 q^{31} + 16 q^{32} + 46 q^{33} + 4 q^{34} + 101 q^{35} - 10 q^{36} + 17 q^{37} - 48 q^{38} + 55 q^{39} + 91 q^{40} + 61 q^{41} + 25 q^{42} + 24 q^{43} + 121 q^{44} + 43 q^{45} - 12 q^{46} + 64 q^{47} - 8 q^{48} + 13 q^{49} + 12 q^{50} + 45 q^{51} + 47 q^{52} + 55 q^{53} + 5 q^{54} + 94 q^{55} + 167 q^{56} + 45 q^{57} - 9 q^{58} + 109 q^{59} - 110 q^{60} + 68 q^{61} + 128 q^{62} + 61 q^{63} + 89 q^{64} - 10 q^{65} + 72 q^{66} + 71 q^{67} + 110 q^{68} + q^{69} + 32 q^{70} - 72 q^{72} - 17 q^{73} - 63 q^{74} - 122 q^{75} + 69 q^{76} + 88 q^{77} - 6 q^{78} - 17 q^{79} - 130 q^{80} + 40 q^{81} - 71 q^{82} + 31 q^{83} - 26 q^{84} + 9 q^{85} + q^{86} - 142 q^{87} + 56 q^{88} - 11 q^{89} - 29 q^{90} + 9 q^{91} + 134 q^{92} - 91 q^{93} + 39 q^{94} - 5 q^{95} - 130 q^{96} - 15 q^{97} - 55 q^{98} + 135 q^{99}+O(q^{100}) \) 60 * q - 2 * q^2 - 2 * q^3 + 46 * q^4 + 10 * q^5 + 4 * q^6 + 25 * q^7 + 9 * q^8 + 32 * q^9 + 18 * q^10 + 53 * q^11 + 44 * q^12 + 13 * q^13 + 49 * q^14 - 20 * q^15 + 26 * q^16 + 33 * q^17 - 48 * q^18 + 3 * q^19 - 48 * q^20 + 18 * q^21 + 16 * q^22 + 59 * q^23 - 85 * q^24 + 24 * q^25 + 63 * q^26 - 26 * q^27 + 63 * q^28 + 22 * q^29 - 66 * q^30 + 72 * q^31 + 16 * q^32 + 46 * q^33 + 4 * q^34 + 101 * q^35 - 10 * q^36 + 17 * q^37 - 48 * q^38 + 55 * q^39 + 91 * q^40 + 61 * q^41 + 25 * q^42 + 24 * q^43 + 121 * q^44 + 43 * q^45 - 12 * q^46 + 64 * q^47 - 8 * q^48 + 13 * q^49 + 12 * q^50 + 45 * q^51 + 47 * q^52 + 55 * q^53 + 5 * q^54 + 94 * q^55 + 167 * q^56 + 45 * q^57 - 9 * q^58 + 109 * q^59 - 110 * q^60 + 68 * q^61 + 128 * q^62 + 61 * q^63 + 89 * q^64 - 10 * q^65 + 72 * q^66 + 71 * q^67 + 110 * q^68 + q^69 + 32 * q^70 - 72 * q^72 - 17 * q^73 - 63 * q^74 - 122 * q^75 + 69 * q^76 + 88 * q^77 - 6 * q^78 - 17 * q^79 - 130 * q^80 + 40 * q^81 - 71 * q^82 + 31 * q^83 - 26 * q^84 + 9 * q^85 + q^86 - 142 * q^87 + 56 * q^88 - 11 * q^89 - 29 * q^90 + 9 * q^91 + 134 * q^92 - 91 * q^93 + 39 * q^94 - 5 * q^95 - 130 * q^96 - 15 * q^97 - 55 * q^98 + 135 * 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 $

$2$	−2.12199	−1.50048	−0.750238	−	0.661168i	$-0.770061\pi$
$2$	−2.12199	−1.50048	−0.750238	+	0.661168i	$0.770061\pi$
$3$	−0.878312	−0.507094	−0.253547	−	0.967323i	$-0.581597\pi$
$3$	−0.878312	−0.507094	−0.253547	+	0.967323i	$0.581597\pi$
$4$	2.50286	1.25143
$5$	0.714152	0.319378	0.159689	−	0.987167i	$-0.448951\pi$
$5$	0.714152	0.319378	0.159689	+	0.987167i	$0.448951\pi$
$6$	1.86377	0.760882
$7$	0.230934	0.0872849	0.0436425	−	0.999047i	$-0.486104\pi$
$7$	0.230934	0.0872849	0.0436425	+	0.999047i	$0.486104\pi$
$8$	−1.06706	−0.377263
$9$	−2.22857	−0.742856
$10$	−1.51543	−0.479220
$11$	−1.25561	−0.378580	−0.189290	−	0.981921i	$-0.560619\pi$
$11$	−1.25561	−0.378580	−0.189290	+	0.981921i	$0.560619\pi$
$12$	−2.19829	−0.634592
$13$	2.68043	0.743417	0.371708	−	0.928350i	$-0.378772\pi$
$13$	2.68043	0.743417	0.371708	+	0.928350i	$0.378772\pi$
$14$	−0.490041	−0.130969
$15$	−0.627248	−0.161955
$16$	−2.74142	−0.685355
$17$	1.65037	0.400272	0.200136	−	0.979768i	$-0.435862\pi$
$17$	1.65037	0.400272	0.200136	+	0.979768i	$0.435862\pi$
$18$	4.72901	1.11464
$19$	6.53601	1.49946	0.749731	−	0.661742i	$-0.230183\pi$
$19$	6.53601	1.49946	0.749731	+	0.661742i	$0.230183\pi$
$20$	1.78742	0.399679
$21$	−0.202832	−0.0442616
$22$	2.66439	0.568050
$23$	6.48014	1.35120	0.675602	−	0.737267i	$-0.263884\pi$
$23$	6.48014	1.35120	0.675602	+	0.737267i	$0.263884\pi$
$24$	0.937212	0.191308
$25$	−4.48999	−0.897998
$26$	−5.68785	−1.11548
$27$	4.59231	0.883791
$28$	0.577996	0.109231
$29$	−0.829664	−0.154065	−0.0770323	−	0.997029i	$-0.524544\pi$
$29$	−0.829664	−0.154065	−0.0770323	+	0.997029i	$0.524544\pi$
$30$	1.33102	0.243009
$31$	−7.70653	−1.38413	−0.692067	−	0.721833i	$-0.743300\pi$
$31$	−7.70653	−1.38413	−0.692067	+	0.721833i	$0.743300\pi$
$32$	7.95140	1.40562
$33$	1.10281	0.191975
$34$	−3.50207	−0.600599
$35$	0.164922	0.0278769
$36$	−5.57779	−0.929631
$37$	7.90336	1.29930	0.649652	−	0.760232i	$-0.274915\pi$
$37$	7.90336	1.29930	0.649652	+	0.760232i	$0.274915\pi$
$38$	−13.8694	−2.24991
$39$	−2.35425	−0.376982
$40$	−0.762043	−0.120490
$41$	6.96040	1.08703	0.543516	−	0.839399i	$-0.317093\pi$
$41$	6.96040	1.08703	0.543516	+	0.839399i	$0.317093\pi$
$42$	0.430409	0.0664135
$43$	6.00348	0.915522	0.457761	−	0.889075i	$-0.348652\pi$
$43$	6.00348	0.915522	0.457761	+	0.889075i	$0.348652\pi$
$44$	−3.14260	−0.473765
$45$	−1.59154	−0.237252
$46$	−13.7508	−2.02745
$47$	−8.55648	−1.24809	−0.624045	−	0.781388i	$-0.714512\pi$
$47$	−8.55648	−1.24809	−0.624045	+	0.781388i	$0.714512\pi$
$48$	2.40782	0.347539
$49$	−6.94667	−0.992381
$50$	9.52773	1.34742
$51$	−1.44954	−0.202976
$52$	6.70873	0.930333
$53$	−1.93032	−0.265150	−0.132575	−	0.991173i	$-0.542325\pi$
$53$	−1.93032	−0.265150	−0.132575	+	0.991173i	$0.542325\pi$
$54$	−9.74486	−1.32611
$55$	−0.896693	−0.120910
$56$	−0.246421	−0.0329294
$57$	−5.74065	−0.760368
$58$	1.76054	0.231170
$59$	−3.18358	−0.414467	−0.207233	−	0.978292i	$-0.566446\pi$
$59$	−3.18358	−0.414467	−0.207233	+	0.978292i	$0.566446\pi$
$60$	−1.56991	−0.202675
$61$	9.76929	1.25083	0.625415	−	0.780292i	$-0.284930\pi$
$61$	9.76929	1.25083	0.625415	+	0.780292i	$0.284930\pi$
$62$	16.3532	2.07686
$63$	−0.514653	−0.0648402
$64$	−11.3900	−1.42375
$65$	1.91423	0.237431
$66$	−2.34016	−0.288054
$67$	3.60862	0.440863	0.220431	−	0.975402i	$-0.429253\pi$
$67$	3.60862	0.440863	0.220431	+	0.975402i	$0.429253\pi$
$68$	4.13063	0.500912
$69$	−5.69159	−0.685186
$70$	−0.349964	−0.0418286
$71$	0	0
$71$	0	0
$72$	2.37802	0.280252
$73$	−6.57900	−0.770014	−0.385007	−	0.922914i	$-0.625801\pi$
$73$	−6.57900	−0.770014	−0.385007	+	0.922914i	$0.625801\pi$
$74$	−16.7709	−1.94957
$75$	3.94361	0.455369
$76$	16.3587	1.87647
$77$	−0.289962	−0.0330443
$78$	4.99571	0.565652
$79$	−5.66006	−0.636806	−0.318403	−	0.947955i	$-0.603147\pi$
$79$	−5.66006	−0.636806	−0.318403	+	0.947955i	$0.603147\pi$
$80$	−1.95779	−0.218887
$81$	2.65222	0.294691
$82$	−14.7699	−1.63106
$83$	−4.54846	−0.499258	−0.249629	−	0.968342i	$-0.580309\pi$
$83$	−4.54846	−0.499258	−0.249629	+	0.968342i	$0.580309\pi$
$84$	−0.507660	−0.0553903
$85$	1.17861	0.127838
$86$	−12.7393	−1.37372
$87$	0.728703	0.0781252
$88$	1.33981	0.142824
$89$	11.2664	1.19423	0.597117	−	0.802154i	$-0.296313\pi$
$89$	11.2664	1.19423	0.597117	+	0.802154i	$0.296313\pi$
$90$	3.37723	0.355991
$91$	0.619002	0.0648891
$92$	16.2189	1.69093
$93$	6.76874	0.701886
$94$	18.1568	1.87273
$95$	4.66770	0.478896
$96$	−6.98381	−0.712782
$97$	−10.6082	−1.07710	−0.538551	−	0.842593i	$-0.681028\pi$
$97$	−10.6082	−1.07710	−0.538551	+	0.842593i	$0.681028\pi$
$98$	14.7408	1.48904
$99$	2.79820	0.281230
$100$	−11.2378	−1.12378
$101$	8.85816	0.881420	0.440710	−	0.897650i	$-0.354727\pi$
$101$	8.85816	0.881420	0.440710	+	0.897650i	$0.354727\pi$
$102$	3.07591	0.304560
$103$	19.5631	1.92761	0.963804	−	0.266612i	$-0.0859044\pi$
$103$	19.5631	1.92761	0.963804	+	0.266612i	$0.0859044\pi$
$104$	−2.86018	−0.280463
$105$	−0.144853	−0.0141362
$106$	4.09613	0.397851
$107$	8.48757	0.820524	0.410262	−	0.911968i	$-0.365437\pi$
$107$	8.48757	0.820524	0.410262	+	0.911968i	$0.365437\pi$
$108$	11.4939	1.10600
$109$	−16.2826	−1.55959	−0.779797	−	0.626032i	$-0.784678\pi$
$109$	−16.2826	−1.55959	−0.779797	+	0.626032i	$0.784678\pi$
$110$	1.90278	0.181423
$111$	−6.94161	−0.658869
$112$	−0.633088	−0.0598212
$113$	8.99671	0.846339	0.423169	−	0.906051i	$-0.360917\pi$
$113$	8.99671	0.846339	0.423169	+	0.906051i	$0.360917\pi$
$114$	12.1816	1.14091
$115$	4.62780	0.431545
$116$	−2.07653	−0.192801
$117$	−5.97351	−0.552252
$118$	6.75554	0.621898
$119$	0.381126	0.0349378
$120$	0.669311	0.0610995
$121$	−9.42345	−0.856678
$122$	−20.7304	−1.87684
$123$	−6.11340	−0.551227
$124$	−19.2884	−1.73215
$125$	−6.77729	−0.606179
$126$	1.09209	0.0972911
$127$	−10.1143	−0.897503	−0.448752	−	0.893657i	$-0.648131\pi$
$127$	−10.1143	−0.897503	−0.448752	+	0.893657i	$0.648131\pi$
$128$	8.26666	0.730676
$129$	−5.27293	−0.464255
$130$	−4.06199	−0.356260
$131$	−11.1779	−0.976620	−0.488310	−	0.872670i	$-0.662387\pi$
$131$	−11.1779	−0.976620	−0.488310	+	0.872670i	$0.662387\pi$
$132$	2.76019	0.240243
$133$	1.50939	0.130881
$134$	−7.65747	−0.661504
$135$	3.27961	0.282264
$136$	−1.76104	−0.151008
$137$	20.9993	1.79409	0.897045	−	0.441939i	$-0.145709\pi$
$137$	20.9993	1.79409	0.897045	+	0.441939i	$0.145709\pi$
$138$	12.0775	1.02811
$139$	13.0663	1.10827	0.554134	−	0.832428i	$-0.313050\pi$
$139$	13.0663	1.10827	0.554134	+	0.832428i	$0.313050\pi$
$140$	0.412776	0.0348860
$141$	7.51526	0.632899
$142$	0	0
$143$	−3.36556	−0.281442
$144$	6.10944	0.509120
$145$	−0.592505	−0.0492049
$146$	13.9606	1.15539
$147$	6.10134	0.503230
$148$	19.7810	1.62599
$149$	13.7712	1.12818	0.564092	−	0.825712i	$-0.309226\pi$
$149$	13.7712	1.12818	0.564092	+	0.825712i	$0.309226\pi$
$150$	−8.36831	−0.683270
$151$	−0.993603	−0.0808583	−0.0404291	−	0.999182i	$-0.512873\pi$
$151$	−0.993603	−0.0808583	−0.0404291	+	0.999182i	$0.512873\pi$
$152$	−6.97431	−0.565692
$153$	−3.67795	−0.297345
$154$	0.615299	0.0495822
$155$	−5.50363	−0.442062
$156$	−5.89235	−0.471766
$157$	8.59039	0.685588	0.342794	−	0.939411i	$-0.388627\pi$
$157$	8.59039	0.685588	0.342794	+	0.939411i	$0.388627\pi$
$158$	12.0106	0.955512
$159$	1.69542	0.134456
$160$	5.67850	0.448925
$161$	1.49649	0.117940
$162$	−5.62800	−0.442177
$163$	−0.502754	−0.0393788	−0.0196894	−	0.999806i	$-0.506268\pi$
$163$	−0.502754	−0.0393788	−0.0196894	+	0.999806i	$0.506268\pi$
$164$	17.4209	1.36034
$165$	0.787576	0.0613127
$166$	9.65180	0.749125
$167$	−2.19608	−0.169938	−0.0849689	−	0.996384i	$-0.527079\pi$
$167$	−2.19608	−0.169938	−0.0849689	+	0.996384i	$0.527079\pi$
$168$	0.216434	0.0166983
$169$	−5.81531	−0.447332
$170$	−2.50101	−0.191818
$171$	−14.5659	−1.11388
$172$	15.0259	1.14571
$173$	−13.0905	−0.995254	−0.497627	−	0.867391i	$-0.665795\pi$
$173$	−13.0905	−0.995254	−0.497627	+	0.867391i	$0.665795\pi$
$174$	−1.54630	−0.117225
$175$	−1.03689	−0.0783817
$176$	3.44214	0.259461
$177$	2.79618	0.210173
$178$	−23.9072	−1.79192
$179$	−16.2136	−1.21186	−0.605930	−	0.795518i	$-0.707199\pi$
$179$	−16.2136	−1.21186	−0.605930	+	0.795518i	$0.707199\pi$
$180$	−3.98339	−0.296904
$181$	−2.50657	−0.186312	−0.0931559	−	0.995652i	$-0.529695\pi$
$181$	−2.50657	−0.186312	−0.0931559	+	0.995652i	$0.529695\pi$
$182$	−1.31352	−0.0973645
$183$	−8.58049	−0.634288
$184$	−6.91470	−0.509759
$185$	5.64420	0.414969
$186$	−14.3632	−1.05316
$187$	−2.07221	−0.151535
$188$	−21.4156	−1.56190
$189$	1.06052	0.0771417
$190$	−9.90483	−0.718572
$191$	9.96211	0.720833	0.360416	−	0.932792i	$-0.382635\pi$
$191$	9.96211	0.720833	0.360416	+	0.932792i	$0.382635\pi$
$192$	10.0039	0.721973
$193$	−26.6012	−1.91480	−0.957398	−	0.288773i	$-0.906753\pi$
$193$	−26.6012	−1.91480	−0.957398	+	0.288773i	$0.906753\pi$
$194$	22.5106	1.61616
$195$	−1.68129	−0.120400
$196$	−17.3865	−1.24189
$197$	−2.91391	−0.207608	−0.103804	−	0.994598i	$-0.533101\pi$
$197$	−2.91391	−0.207608	−0.103804	+	0.994598i	$0.533101\pi$
$198$	−5.93777	−0.421979
$199$	11.8304	0.838638	0.419319	−	0.907839i	$-0.362269\pi$
$199$	11.8304	0.838638	0.419319	+	0.907839i	$0.362269\pi$
$200$	4.79109	0.338781
$201$	−3.16949	−0.223559
$202$	−18.7970	−1.32255
$203$	−0.191598	−0.0134475
$204$	−3.62798	−0.254009
$205$	4.97078	0.347174
$206$	−41.5127	−2.89233
$207$	−14.4414	−1.00375
$208$	−7.34817	−0.509504
$209$	−8.20665	−0.567666
$210$	0.307377	0.0212110
$211$	6.18184	0.425575	0.212788	−	0.977098i	$-0.431746\pi$
$211$	6.18184	0.425575	0.212788	+	0.977098i	$0.431746\pi$
$212$	−4.83132	−0.331816
$213$	0	0
$214$	−18.0106	−1.23118
$215$	4.28739	0.292398
$216$	−4.90028	−0.333422
$217$	−1.77970	−0.120814
$218$	34.5517	2.34014
$219$	5.77842	0.390469
$220$	−2.24430	−0.151310
$221$	4.42368	0.297569
$222$	14.7301	0.988617
$223$	4.57409	0.306304	0.153152	−	0.988203i	$-0.451058\pi$
$223$	4.57409	0.306304	0.153152	+	0.988203i	$0.451058\pi$
$224$	1.83625	0.122690
$225$	10.0062	0.667083
$226$	−19.0910	−1.26991
$227$	9.16184	0.608093	0.304046	−	0.952657i	$-0.401662\pi$
$227$	9.16184	0.608093	0.304046	+	0.952657i	$0.401662\pi$
$228$	−14.3680	−0.951546
$229$	0.220736	0.0145866	0.00729331	−	0.999973i	$-0.497678\pi$
$229$	0.220736	0.0145866	0.00729331	+	0.999973i	$0.497678\pi$
$230$	−9.82017	−0.647523
$231$	0.254677	0.0167565
$232$	0.885301	0.0581229
$233$	−8.43914	−0.552867	−0.276433	−	0.961033i	$-0.589153\pi$
$233$	−8.43914	−0.552867	−0.276433	+	0.961033i	$0.589153\pi$
$234$	12.6758	0.828640
$235$	−6.11062	−0.398613
$236$	−7.96805	−0.518676
$237$	4.97129	0.322920
$238$	−0.808747	−0.0524233
$239$	−26.8741	−1.73834	−0.869171	−	0.494512i	$-0.835347\pi$
$239$	−26.8741	−1.73834	−0.869171	+	0.494512i	$0.835347\pi$
$240$	1.71955	0.110996
$241$	−28.0516	−1.80696	−0.903481	−	0.428628i	$-0.858997\pi$
$241$	−28.0516	−1.80696	−0.903481	+	0.428628i	$0.858997\pi$
$242$	19.9965	1.28542
$243$	−16.1064	−1.03323
$244$	24.4512	1.56532
$245$	−4.96097	−0.316945
$246$	12.9726	0.827103
$247$	17.5193	1.11473
$248$	8.22334	0.522182
$249$	3.99497	0.253171
$250$	14.3814	0.909557
$251$	23.1897	1.46372	0.731860	−	0.681455i	$-0.238652\pi$
$251$	23.1897	1.46372	0.731860	+	0.681455i	$0.238652\pi$
$252$	−1.28810	−0.0811428
$253$	−8.13651	−0.511538
$254$	21.4626	1.34668
$255$	−1.03519	−0.0648260
$256$	5.23814	0.327384
$257$	0.428617	0.0267364	0.0133682	−	0.999911i	$-0.495745\pi$
$257$	0.428617	0.0267364	0.0133682	+	0.999911i	$0.495745\pi$
$258$	11.1891	0.696604
$259$	1.82516	0.113410
$260$	4.79105	0.297128
$261$	1.84896	0.114448
$262$	23.7195	1.46540
$263$	−25.3323	−1.56206	−0.781029	−	0.624495i	$-0.785305\pi$
$263$	−25.3323	−1.56206	−0.781029	+	0.624495i	$0.785305\pi$
$264$	−1.17677	−0.0724251
$265$	−1.37854	−0.0846832
$266$	−3.20291	−0.196383
$267$	−9.89539	−0.605588
$268$	9.03186	0.551709
$269$	8.80121	0.536619	0.268310	−	0.963333i	$-0.413535\pi$
$269$	8.80121	0.536619	0.268310	+	0.963333i	$0.413535\pi$
$270$	−6.95931	−0.423530
$271$	−7.42857	−0.451254	−0.225627	−	0.974214i	$-0.572443\pi$
$271$	−7.42857	−0.451254	−0.225627	+	0.974214i	$0.572443\pi$
$272$	−4.52434	−0.274329
$273$	−0.543677	−0.0329048
$274$	−44.5604	−2.69199
$275$	5.63766	0.339963
$276$	−14.2452	−0.857462
$277$	17.4632	1.04926	0.524631	−	0.851330i	$-0.324203\pi$
$277$	17.4632	1.04926	0.524631	+	0.851330i	$0.324203\pi$
$278$	−27.7266	−1.66293
$279$	17.1745	1.02821
$280$	−0.175982	−0.0105169
$281$	12.7367	0.759806	0.379903	−	0.925026i	$-0.375957\pi$
$281$	12.7367	0.759806	0.379903	+	0.925026i	$0.375957\pi$
$282$	−15.9473	−0.949649
$283$	4.19397	0.249306	0.124653	−	0.992200i	$-0.460218\pi$
$283$	4.19397	0.249306	0.124653	+	0.992200i	$0.460218\pi$
$284$	0	0
$285$	−4.09970	−0.242845
$286$	7.14170	0.422298
$287$	1.60739	0.0948815
$288$	−17.7202	−1.04417
$289$	−14.2763	−0.839782
$290$	1.25729	0.0738308
$291$	9.31732	0.546191
$292$	−16.4663	−0.963618
$293$	17.0263	0.994685	0.497343	−	0.867554i	$-0.334309\pi$
$293$	17.0263	0.994685	0.497343	+	0.867554i	$0.334309\pi$
$294$	−12.9470	−0.755085
$295$	−2.27356	−0.132372
$296$	−8.43336	−0.490179
$297$	−5.76614	−0.334585
$298$	−29.2225	−1.69281
$299$	17.3695	1.00451
$300$	9.87029	0.569862
$301$	1.38641	0.0799113
$302$	2.10842	0.121326
$303$	−7.78023	−0.446962
$304$	−17.9179	−1.02766
$305$	6.97676	0.399488
$306$	7.80459	0.446159
$307$	3.00237	0.171355	0.0856773	−	0.996323i	$-0.472695\pi$
$307$	3.00237	0.171355	0.0856773	+	0.996323i	$0.472695\pi$
$308$	−0.725735	−0.0413526
$309$	−17.1825	−0.977477
$310$	11.6787	0.663304
$311$	−15.3548	−0.870692	−0.435346	−	0.900263i	$-0.643374\pi$
$311$	−15.3548	−0.870692	−0.435346	+	0.900263i	$0.643374\pi$
$312$	2.51213	0.142221
$313$	−13.8053	−0.780323	−0.390161	−	0.920747i	$-0.627581\pi$
$313$	−13.8053	−0.780323	−0.390161	+	0.920747i	$0.627581\pi$
$314$	−18.2288	−1.02871
$315$	−0.367540	−0.0207085
$316$	−14.1663	−0.796917
$317$	34.2658	1.92456	0.962280	−	0.272059i	$-0.0877047\pi$
$317$	34.2658	1.92456	0.962280	+	0.272059i	$0.0877047\pi$
$318$	−3.59768	−0.201748
$319$	1.04173	0.0583257
$320$	−8.13417	−0.454714
$321$	−7.45473	−0.416083
$322$	−3.17554	−0.176966
$323$	10.7868	0.600194
$324$	6.63813	0.368785
$325$	−12.0351	−0.667586
$326$	1.06684	0.0590869
$327$	14.3012	0.790861
$328$	−7.42716	−0.410097
$329$	−1.97598	−0.108939
$330$	−1.67123	−0.0919983
$331$	20.2907	1.11528	0.557640	−	0.830083i	$-0.311707\pi$
$331$	20.2907	1.11528	0.557640	+	0.830083i	$0.311707\pi$
$332$	−11.3841	−0.624786
$333$	−17.6132	−0.965196
$334$	4.66007	0.254988
$335$	2.57710	0.140802
$336$	0.556048	0.0303349
$337$	24.5163	1.33549	0.667745	−	0.744390i	$-0.267260\pi$
$337$	24.5163	1.33549	0.667745	+	0.744390i	$0.267260\pi$
$338$	12.3401	0.671210
$339$	−7.90191	−0.429173
$340$	2.94990	0.159981
$341$	9.67637	0.524005
$342$	30.9088	1.67136
$343$	−3.22076	−0.173905
$344$	−6.40607	−0.345392
$345$	−4.06466	−0.218834
$346$	27.7780	1.49335
$347$	0.662519	0.0355659	0.0177830	−	0.999842i	$-0.494339\pi$
$347$	0.662519	0.0355659	0.0177830	+	0.999842i	$0.494339\pi$
$348$	1.82384	0.0977681
$349$	18.9120	1.01233	0.506167	−	0.862436i	$-0.331062\pi$
$349$	18.9120	1.01233	0.506167	+	0.862436i	$0.331062\pi$
$350$	2.20028	0.117610
$351$	12.3094	0.657025
$352$	−9.98382	−0.532139
$353$	20.2531	1.07796	0.538982	−	0.842317i	$-0.318809\pi$
$353$	20.2531	1.07796	0.538982	+	0.842317i	$0.318809\pi$
$354$	−5.93347	−0.315360
$355$	0	0
$356$	28.1981	1.49450
$357$	−0.334747	−0.0177167
$358$	34.4051	1.81837
$359$	11.3651	0.599826	0.299913	−	0.953967i	$-0.403042\pi$
$359$	11.3651	0.599826	0.299913	+	0.953967i	$0.403042\pi$
$360$	1.69826	0.0895064
$361$	23.7194	1.24839
$362$	5.31892	0.279556
$363$	8.27673	0.434416
$364$	1.54927	0.0812041
$365$	−4.69841	−0.245926
$366$	18.2077	0.951734
$367$	9.19524	0.479987	0.239994	−	0.970774i	$-0.422855\pi$
$367$	9.19524	0.479987	0.239994	+	0.970774i	$0.422855\pi$
$368$	−17.7648	−0.926054
$369$	−15.5117	−0.807508
$370$	−11.9769	−0.622652
$371$	−0.445777	−0.0231436
$372$	16.9412	0.878360
$373$	−1.26579	−0.0655400	−0.0327700	−	0.999463i	$-0.510433\pi$
$373$	−1.26579	−0.0655400	−0.0327700	+	0.999463i	$0.510433\pi$
$374$	4.39722	0.227375
$375$	5.95257	0.307390
$376$	9.13028	0.470858
$377$	−2.22385	−0.114534
$378$	−2.25042	−0.115749
$379$	6.04582	0.310553	0.155277	−	0.987871i	$-0.450373\pi$
$379$	6.04582	0.310553	0.155277	+	0.987871i	$0.450373\pi$
$380$	11.6826	0.599304
$381$	8.88355	0.455118
$382$	−21.1395	−1.08159
$383$	9.47580	0.484191	0.242095	−	0.970252i	$-0.422165\pi$
$383$	9.47580	0.484191	0.242095	+	0.970252i	$0.422165\pi$
$384$	−7.26071	−0.370521
$385$	−0.207077	−0.0105536
$386$	56.4476	2.87310
$387$	−13.3792	−0.680101
$388$	−26.5509	−1.34792
$389$	32.5186	1.64876	0.824380	−	0.566037i	$-0.191524\pi$
$389$	32.5186	1.64876	0.824380	+	0.566037i	$0.191524\pi$
$390$	3.56769	0.180657
$391$	10.6946	0.540849
$392$	7.41252	0.374389
$393$	9.81771	0.495238
$394$	6.18331	0.311510
$395$	−4.04214	−0.203382
$396$	7.00351	0.351939
$397$	−25.6623	−1.28795	−0.643976	−	0.765046i	$-0.722716\pi$
$397$	−25.6623	−1.28795	−0.643976	+	0.765046i	$0.722716\pi$
$398$	−25.1041	−1.25836
$399$	−1.32571	−0.0663687
$400$	12.3089	0.615447
$401$	29.0260	1.44949	0.724745	−	0.689017i	$-0.241958\pi$
$401$	29.0260	1.44949	0.724745	+	0.689017i	$0.241958\pi$
$402$	6.72564	0.335445
$403$	−20.6568	−1.02899
$404$	22.1707	1.10303
$405$	1.89409	0.0941180
$406$	0.406569	0.0201777
$407$	−9.92351	−0.491890
$408$	1.54674	0.0765751
$409$	18.0449	0.892260	0.446130	−	0.894968i	$-0.352802\pi$
$409$	18.0449	0.892260	0.446130	+	0.894968i	$0.352802\pi$
$410$	−10.5480	−0.520927
$411$	−18.4439	−0.909772
$412$	48.9636	2.41226
$413$	−0.735198	−0.0361767
$414$	30.6446	1.50610
$415$	−3.24829	−0.159452
$416$	21.3131	1.04496
$417$	−11.4763	−0.561995
$418$	17.4145	0.851769
$419$	12.3233	0.602033	0.301017	−	0.953619i	$-0.402674\pi$
$419$	12.3233	0.602033	0.301017	+	0.953619i	$0.402674\pi$
$420$	−0.362546	−0.0176905
$421$	−11.2167	−0.546668	−0.273334	−	0.961919i	$-0.588126\pi$
$421$	−11.2167	−0.546668	−0.273334	+	0.961919i	$0.588126\pi$
$422$	−13.1178	−0.638566
$423$	19.0687	0.927152
$424$	2.05977	0.100031
$425$	−7.41012	−0.359444
$426$	0	0
$427$	2.25606	0.109179
$428$	21.2432	1.02683
$429$	2.95601	0.142718
$430$	−9.09782	−0.438736
$431$	0.712414	0.0343158	0.0171579	−	0.999853i	$-0.494538\pi$
$431$	0.712414	0.0343158	0.0171579	+	0.999853i	$0.494538\pi$
$432$	−12.5895	−0.605711
$433$	−26.2408	−1.26105	−0.630527	−	0.776168i	$-0.717161\pi$
$433$	−26.2408	−1.26105	−0.630527	+	0.776168i	$0.717161\pi$
$434$	3.77652	0.181279
$435$	0.520405	0.0249515
$436$	−40.7532	−1.95172
$437$	42.3543	2.02608
$438$	−12.2618	−0.585890
$439$	7.24521	0.345795	0.172897	−	0.984940i	$-0.444687\pi$
$439$	7.24521	0.345795	0.172897	+	0.984940i	$0.444687\pi$
$440$	0.956826	0.0456149
$441$	15.4811	0.737197
$442$	−9.38703	−0.446496
$443$	35.9117	1.70622	0.853108	−	0.521735i	$-0.174715\pi$
$443$	35.9117	1.70622	0.853108	+	0.521735i	$0.174715\pi$
$444$	−17.3739	−0.824527
$445$	8.04590	0.381412
$446$	−9.70620	−0.459602
$447$	−12.0954	−0.572095
$448$	−2.63033	−0.124272
$449$	−22.8929	−1.08038	−0.540192	−	0.841542i	$-0.681648\pi$
$449$	−22.8929	−1.08038	−0.540192	+	0.841542i	$0.681648\pi$
$450$	−21.2332	−1.00094
$451$	−8.73952	−0.411528
$452$	22.5175	1.05913
$453$	0.872694	0.0410027
$454$	−19.4414	−0.912429
$455$	0.442062	0.0207242
$456$	6.12562	0.286859
$457$	−6.56676	−0.307180	−0.153590	−	0.988135i	$-0.549084\pi$
$457$	−6.56676	−0.307180	−0.153590	+	0.988135i	$0.549084\pi$
$458$	−0.468399	−0.0218869
$459$	7.57900	0.353757
$460$	11.5827	0.540048
$461$	35.6949	1.66248	0.831240	−	0.555914i	$-0.187632\pi$
$461$	35.6949	1.66248	0.831240	+	0.555914i	$0.187632\pi$
$462$	−0.540424	−0.0251428
$463$	−3.86618	−0.179677	−0.0898383	−	0.995956i	$-0.528635\pi$
$463$	−3.86618	−0.179677	−0.0898383	+	0.995956i	$0.528635\pi$
$464$	2.27446	0.105589
$465$	4.83391	0.224167
$466$	17.9078	0.829563
$467$	32.2797	1.49373	0.746863	−	0.664978i	$-0.231559\pi$
$467$	32.2797	1.49373	0.746863	+	0.664978i	$0.231559\pi$
$468$	−14.9509	−0.691104
$469$	0.833354	0.0384807
$470$	12.9667	0.598109
$471$	−7.54504	−0.347657
$472$	3.39707	0.156363
$473$	−7.53800	−0.346598
$474$	−10.5491	−0.484534
$475$	−29.3466	−1.34651
$476$	0.953904	0.0437221
$477$	4.30185	0.196968
$478$	57.0267	2.60834
$479$	35.5216	1.62302	0.811512	−	0.584336i	$-0.198645\pi$
$479$	35.5216	1.62302	0.811512	+	0.584336i	$0.198645\pi$
$480$	−4.98750	−0.227647
$481$	21.1844	0.965924
$482$	59.5253	2.71130
$483$	−1.31438	−0.0598065
$484$	−23.5856	−1.07207
$485$	−7.57587	−0.344003
$486$	34.1777	1.55033
$487$	−0.115057	−0.00521374	−0.00260687	−	0.999997i	$-0.500830\pi$
$487$	−0.115057	−0.00521374	−0.00260687	+	0.999997i	$0.500830\pi$
$488$	−10.4244	−0.471892
$489$	0.441575	0.0199687
$490$	10.5272	0.475568
$491$	36.8435	1.66272	0.831362	−	0.555731i	$-0.187561\pi$
$491$	36.8435	1.66272	0.831362	+	0.555731i	$0.187561\pi$
$492$	−15.3010	−0.689821
$493$	−1.36925	−0.0616678
$494$	−37.1758	−1.67262
$495$	1.99834	0.0898188
$496$	21.1268	0.948623
$497$	0	0
$498$	−8.47729	−0.379877
$499$	−4.20767	−0.188361	−0.0941807	−	0.995555i	$-0.530023\pi$
$499$	−4.20767	−0.188361	−0.0941807	+	0.995555i	$0.530023\pi$
$500$	−16.9626	−0.758590
$501$	1.92884	0.0861743
$502$	−49.2084	−2.19628
$503$	−31.2636	−1.39397	−0.696987	−	0.717084i	$-0.745476\pi$
$503$	−31.2636	−1.39397	−0.696987	+	0.717084i	$0.745476\pi$
$504$	0.549166	0.0244618
$505$	6.32607	0.281506
$506$	17.2656	0.767550
$507$	5.10766	0.226839
$508$	−25.3148	−1.12316
$509$	−11.8878	−0.526917	−0.263458	−	0.964671i	$-0.584863\pi$
$509$	−11.8878	−0.526917	−0.263458	+	0.964671i	$0.584863\pi$
$510$	2.19666	0.0972699
$511$	−1.51932	−0.0672106
$512$	−27.6486	−1.22191
$513$	30.0154	1.32521
$514$	−0.909523	−0.0401173
$515$	13.9710	0.615636
$516$	−13.1974	−0.580982
$517$	10.7436	0.472501
$518$	−3.87297	−0.170169
$519$	11.4976	0.504687
$520$	−2.04260	−0.0895739
$521$	−39.1819	−1.71659	−0.858295	−	0.513157i	$-0.828476\pi$
$521$	−39.1819	−1.71659	−0.858295	+	0.513157i	$0.828476\pi$
$522$	−3.92349	−0.171726
$523$	18.9682	0.829423	0.414711	−	0.909953i	$-0.363883\pi$
$523$	18.9682	0.829423	0.414711	+	0.909953i	$0.363883\pi$
$524$	−27.9768	−1.22217
$525$	0.910715	0.0397468
$526$	53.7550	2.34383
$527$	−12.7186	−0.554031
$528$	−3.02328	−0.131571
$529$	18.9922	0.825750
$530$	2.92526	0.127065
$531$	7.09483	0.307889
$532$	3.77778	0.163788
$533$	18.6568	0.808117
$534$	20.9980	0.908670
$535$	6.06141	0.262058
$536$	−3.85061	−0.166321
$537$	14.2406	0.614527
$538$	−18.6761	−0.805184
$539$	8.72228	0.375695
$540$	8.20839	0.353233
$541$	44.7586	1.92432	0.962161	−	0.272482i	$-0.0878444\pi$
$541$	44.7586	1.92432	0.962161	+	0.272482i	$0.0878444\pi$
$542$	15.7634	0.677095
$543$	2.20155	0.0944775
$544$	13.1227	0.562632
$545$	−11.6283	−0.498101
$546$	1.15368	0.0493729
$547$	−36.1831	−1.54708	−0.773538	−	0.633750i	$-0.781515\pi$
$547$	−36.1831	−1.54708	−0.773538	+	0.633750i	$0.781515\pi$
$548$	52.5582	2.24518
$549$	−21.7715	−0.929187
$550$	−11.9631	−0.510107
$551$	−5.42269	−0.231014
$552$	6.07327	0.258495
$553$	−1.30710	−0.0555836
$554$	−37.0568	−1.57439
$555$	−4.95736	−0.210428
$556$	32.7030	1.38692
$557$	−20.2235	−0.856899	−0.428449	−	0.903566i	$-0.640940\pi$
$557$	−20.2235	−0.856899	−0.428449	+	0.903566i	$0.640940\pi$
$558$	−36.4443	−1.54281
$559$	16.0919	0.680614
$560$	−0.452121	−0.0191056
$561$	1.82005	0.0768424
$562$	−27.0271	−1.14007
$563$	7.42943	0.313113	0.156557	−	0.987669i	$-0.449961\pi$
$563$	7.42943	0.313113	0.156557	+	0.987669i	$0.449961\pi$
$564$	18.8096	0.792028
$565$	6.42501	0.270302
$566$	−8.89958	−0.374077
$567$	0.612489	0.0257221
$568$	0	0
$569$	29.3544	1.23060	0.615299	−	0.788293i	$-0.289035\pi$
$569$	29.3544	1.23060	0.615299	+	0.788293i	$0.289035\pi$
$570$	8.69953	0.364383
$571$	36.3259	1.52019	0.760095	−	0.649811i	$-0.225152\pi$
$571$	36.3259	1.52019	0.760095	+	0.649811i	$0.225152\pi$
$572$	−8.42352	−0.352205
$573$	−8.74984	−0.365530
$574$	−3.41088	−0.142367
$575$	−29.0958	−1.21338
$576$	25.3833	1.05764
$577$	−19.6962	−0.819963	−0.409982	−	0.912094i	$-0.634465\pi$
$577$	−19.6962	−0.819963	−0.409982	+	0.912094i	$0.634465\pi$
$578$	30.2942	1.26007
$579$	23.3641	0.970981
$580$	−1.48296	−0.0615764
$581$	−1.05040	−0.0435777
$582$	−19.7713	−0.819547
$583$	2.42372	0.100380
$584$	7.02019	0.290498
$585$	−4.26599	−0.176377
$586$	−36.1296	−1.49250
$587$	−1.03575	−0.0427501	−0.0213750	−	0.999772i	$-0.506804\pi$
$587$	−1.03575	−0.0427501	−0.0213750	+	0.999772i	$0.506804\pi$
$588$	15.2708	0.629757
$589$	−50.3700	−2.07546
$590$	4.82448	0.198621
$591$	2.55932	0.105277
$592$	−21.6664	−0.890484
$593$	−25.0404	−1.02829	−0.514143	−	0.857704i	$-0.671890\pi$
$593$	−25.0404	−1.02829	−0.514143	+	0.857704i	$0.671890\pi$
$594$	12.2357	0.502037
$595$	0.272182	0.0111584
$596$	34.4674	1.41184
$597$	−10.3908	−0.425268
$598$	−36.8581	−1.50724
$599$	18.0395	0.737072	0.368536	−	0.929613i	$-0.379859\pi$
$599$	18.0395	0.737072	0.368536	+	0.929613i	$0.379859\pi$
$600$	−4.20807	−0.171794
$601$	−34.2517	−1.39716	−0.698578	−	0.715534i	$-0.746184\pi$
$601$	−34.2517	−1.39716	−0.698578	+	0.715534i	$0.746184\pi$
$602$	−2.94195	−0.119905
$603$	−8.04205	−0.327498
$604$	−2.48685	−0.101188
$605$	−6.72977	−0.273604
$606$	16.5096	0.670657
$607$	−31.8572	−1.29304	−0.646521	−	0.762896i	$-0.723777\pi$
$607$	−31.8572	−1.29304	−0.646521	+	0.762896i	$0.723777\pi$
$608$	51.9704	2.10768
$609$	0.168283	0.00681915
$610$	−14.8046	−0.599422
$611$	−22.9350	−0.927851
$612$	−9.20539	−0.372106
$613$	11.7551	0.474784	0.237392	−	0.971414i	$-0.423707\pi$
$613$	11.7551	0.474784	0.237392	+	0.971414i	$0.423707\pi$
$614$	−6.37102	−0.257113
$615$	−4.36589	−0.176050
$616$	0.309407	0.0124664
$617$	−7.82632	−0.315076	−0.157538	−	0.987513i	$-0.550356\pi$
$617$	−7.82632	−0.315076	−0.157538	+	0.987513i	$0.550356\pi$
$618$	36.4611	1.46668
$619$	26.1546	1.05124	0.525621	−	0.850719i	$-0.323833\pi$
$619$	26.1546	1.05124	0.525621	+	0.850719i	$0.323833\pi$
$620$	−13.7748	−0.553210
$621$	29.7588	1.19418
$622$	32.5828	1.30645
$623$	2.60179	0.104239
$624$	6.45399	0.258366
$625$	17.6099	0.704397
$626$	29.2948	1.17086
$627$	7.20800	0.287860
$628$	21.5005	0.857964
$629$	13.0434	0.520076
$630$	0.779918	0.0310727
$631$	34.7128	1.38189	0.690947	−	0.722905i	$-0.257194\pi$
$631$	34.7128	1.38189	0.690947	+	0.722905i	$0.257194\pi$
$632$	6.03962	0.240243
$633$	−5.42958	−0.215807
$634$	−72.7119	−2.88776
$635$	−7.22318	−0.286643
$636$	4.24341	0.168262
$637$	−18.6200	−0.737753
$638$	−2.21055	−0.0875164
$639$	0	0
$640$	5.90365	0.233362
$641$	1.99964	0.0789812	0.0394906	−	0.999220i	$-0.487426\pi$
$641$	1.99964	0.0789812	0.0394906	+	0.999220i	$0.487426\pi$
$642$	15.8189	0.624322
$643$	23.6005	0.930714	0.465357	−	0.885123i	$-0.345926\pi$
$643$	23.6005	0.930714	0.465357	+	0.885123i	$0.345926\pi$
$644$	3.74549	0.147593
$645$	−3.76567	−0.148273
$646$	−22.8895	−0.900576
$647$	43.9762	1.72888	0.864442	−	0.502733i	$-0.167672\pi$
$647$	43.9762	1.72888	0.864442	+	0.502733i	$0.167672\pi$
$648$	−2.83008	−0.111176
$649$	3.99732	0.156909
$650$	25.5384	1.00170
$651$	1.56313	0.0612641
$652$	−1.25832	−0.0492797
$653$	46.2728	1.81079	0.905397	−	0.424566i	$-0.139573\pi$
$653$	46.2728	1.81079	0.905397	+	0.424566i	$0.139573\pi$
$654$	−30.3472	−1.18667
$655$	−7.98274	−0.311911
$656$	−19.0814	−0.745002
$657$	14.6618	0.572010
$658$	4.19302	0.163461
$659$	20.3122	0.791249	0.395625	−	0.918412i	$-0.370528\pi$
$659$	20.3122	0.791249	0.395625	+	0.918412i	$0.370528\pi$
$660$	1.97119	0.0767285
$661$	27.7309	1.07861	0.539303	−	0.842112i	$-0.318688\pi$
$661$	27.7309	1.07861	0.539303	+	0.842112i	$0.318688\pi$
$662$	−43.0568	−1.67345
$663$	−3.88537	−0.150895
$664$	4.85348	0.188352
$665$	1.07793	0.0418004
$666$	37.3750	1.44825
$667$	−5.37634	−0.208173
$668$	−5.49647	−0.212665
$669$	−4.01748	−0.155325
$670$	−5.46859	−0.211270
$671$	−12.2664	−0.473539
$672$	−1.61280	−0.0622151
$673$	−34.1920	−1.31801	−0.659003	−	0.752140i	$-0.729022\pi$
$673$	−34.1920	−1.31801	−0.659003	+	0.752140i	$0.729022\pi$
$674$	−52.0235	−2.00387
$675$	−20.6194	−0.793642
$676$	−14.5549	−0.559804
$677$	20.3383	0.781664	0.390832	−	0.920462i	$-0.372187\pi$
$677$	20.3383	0.781664	0.390832	+	0.920462i	$0.372187\pi$
$678$	16.7678	0.643964
$679$	−2.44980	−0.0940147
$680$	−1.25765	−0.0482286
$681$	−8.04695	−0.308360
$682$	−20.5332	−0.786257
$683$	34.7927	1.33130	0.665652	−	0.746262i	$-0.268154\pi$
$683$	34.7927	1.33130	0.665652	+	0.746262i	$0.268154\pi$
$684$	−36.4565	−1.39395
$685$	14.9967	0.572993
$686$	6.83444	0.260940
$687$	−0.193875	−0.00739678
$688$	−16.4581	−0.627457
$689$	−5.17409	−0.197117
$690$	8.62517	0.328355
$691$	19.2319	0.731615	0.365808	−	0.930690i	$-0.380793\pi$
$691$	19.2319	0.731615	0.365808	+	0.930690i	$0.380793\pi$
$692$	−32.7637	−1.24549
$693$	0.646201	0.0245472
$694$	−1.40586	−0.0533658
$695$	9.33130	0.353956
$696$	−0.777570	−0.0294737
$697$	11.4872	0.435109
$698$	−40.1310	−1.51898
$699$	7.41220	0.280355
$700$	−2.59519	−0.0980891
$701$	4.79928	0.181266	0.0906332	−	0.995884i	$-0.471111\pi$
$701$	4.79928	0.181266	0.0906332	+	0.995884i	$0.471111\pi$
$702$	−26.1204	−0.985850
$703$	51.6564	1.94826
$704$	14.3013	0.539001
$705$	5.36703	0.202134
$706$	−42.9769	−1.61746
$707$	2.04565	0.0769347
$708$	6.99843	0.263017
$709$	−4.23128	−0.158909	−0.0794545	−	0.996838i	$-0.525318\pi$
$709$	−4.23128	−0.158909	−0.0794545	+	0.996838i	$0.525318\pi$
$710$	0	0
$711$	12.6138	0.473055
$712$	−12.0219	−0.450540
$713$	−49.9394	−1.87025
$714$	0.710332	0.0265835
$715$	−2.40352	−0.0898866
$716$	−40.5803	−1.51656
$717$	23.6038	0.881502
$718$	−24.1166	−0.900024
$719$	3.09745	0.115516	0.0577578	−	0.998331i	$-0.481605\pi$
$719$	3.09745	0.115516	0.0577578	+	0.998331i	$0.481605\pi$
$720$	4.36307	0.162602
$721$	4.51779	0.168251
$722$	−50.3324	−1.87318
$723$	24.6380	0.916299
$724$	−6.27358	−0.233156
$725$	3.72518	0.138350
$726$	−17.5632	−0.651830
$727$	28.3430	1.05119	0.525593	−	0.850736i	$-0.323844\pi$
$727$	28.3430	1.05119	0.525593	+	0.850736i	$0.323844\pi$
$728$	−0.660513	−0.0244802
$729$	6.18980	0.229252
$730$	9.96999	0.369006
$731$	9.90793	0.366458
$732$	−21.4757	−0.793766
$733$	22.6475	0.836506	0.418253	−	0.908331i	$-0.362643\pi$
$733$	22.6475	0.836506	0.418253	+	0.908331i	$0.362643\pi$
$734$	−19.5122	−0.720210
$735$	4.35728	0.160721
$736$	51.5262	1.89928
$737$	−4.53100	−0.166902
$738$	32.9158	1.21165
$739$	−6.32443	−0.232648	−0.116324	−	0.993211i	$-0.537111\pi$
$739$	−6.32443	−0.232648	−0.116324	+	0.993211i	$0.537111\pi$
$740$	14.1266	0.519305
$741$	−15.3874	−0.565270
$742$	0.945937	0.0347264
$743$	16.4803	0.604603	0.302302	−	0.953212i	$-0.402245\pi$
$743$	16.4803	0.604603	0.302302	+	0.953212i	$0.402245\pi$
$744$	−7.22266	−0.264795
$745$	9.83475	0.360317
$746$	2.68599	0.0983411
$747$	10.1366	0.370877
$748$	−5.18644	−0.189635
$749$	1.96007	0.0716194
$750$	−12.6313	−0.461231
$751$	5.01554	0.183020	0.0915098	−	0.995804i	$-0.470831\pi$
$751$	5.01554	0.183020	0.0915098	+	0.995804i	$0.470831\pi$
$752$	23.4569	0.855385
$753$	−20.3678	−0.742243
$754$	4.71900	0.171856
$755$	−0.709583	−0.0258244
$756$	2.65434	0.0965373
$757$	−37.2794	−1.35494	−0.677472	−	0.735548i	$-0.736925\pi$
$757$	−37.2794	−1.35494	−0.677472	+	0.735548i	$0.736925\pi$
$758$	−12.8292	−0.465978
$759$	7.14639	0.259398
$760$	−4.98072	−0.180670
$761$	26.3896	0.956623	0.478311	−	0.878190i	$-0.341249\pi$
$761$	26.3896	0.956623	0.478311	+	0.878190i	$0.341249\pi$
$762$	−18.8508	−0.682894
$763$	−3.76022	−0.136129
$764$	24.9337	0.902071
$765$	−2.62662	−0.0949655
$766$	−20.1076	−0.726517
$767$	−8.53335	−0.308122
$768$	−4.60072	−0.166014
$769$	18.4921	0.666841	0.333421	−	0.942778i	$-0.391797\pi$
$769$	18.4921	0.666841	0.333421	+	0.942778i	$0.391797\pi$
$770$	0.439416	0.0158355
$771$	−0.376459	−0.0135579
$772$	−66.5790	−2.39623
$773$	−26.2468	−0.944031	−0.472015	−	0.881590i	$-0.656473\pi$
$773$	−26.2468	−0.944031	−0.472015	+	0.881590i	$0.656473\pi$
$774$	28.3905	1.02048
$775$	34.6022	1.24295
$776$	11.3196	0.406350
$777$	−1.60306	−0.0575093
$778$	−69.0043	−2.47392
$779$	45.4932	1.62996
$780$	−4.20803	−0.150672
$781$	0	0
$782$	−22.6939	−0.811532
$783$	−3.81008	−0.136161
$784$	19.0437	0.680133
$785$	6.13484	0.218962
$786$	−20.8331	−0.743093
$787$	36.6930	1.30796	0.653981	−	0.756511i	$-0.273097\pi$
$787$	36.6930	1.30796	0.653981	+	0.756511i	$0.273097\pi$
$788$	−7.29311	−0.259806
$789$	22.2497	0.792110
$790$	8.57739	0.305170
$791$	2.07765	0.0738726
$792$	−2.98585	−0.106098
$793$	26.1859	0.929888
$794$	54.4552	1.93254
$795$	1.21079	0.0429423
$796$	29.6099	1.04950
$797$	−1.47484	−0.0522415	−0.0261207	−	0.999659i	$-0.508315\pi$
$797$	−1.47484	−0.0522415	−0.0261207	+	0.999659i	$0.508315\pi$
$798$	2.81315	0.0995846
$799$	−14.1213	−0.499576
$800$	−35.7017	−1.26224
$801$	−25.1079	−0.887143
$802$	−61.5930	−2.17492
$803$	8.26064	0.291512
$804$	−7.93279	−0.279768
$805$	1.06872	0.0376674
$806$	43.8336	1.54397
$807$	−7.73021	−0.272116
$808$	−9.45219	−0.332527
$809$	11.2826	0.396676	0.198338	−	0.980134i	$-0.436446\pi$
$809$	11.2826	0.396676	0.198338	+	0.980134i	$0.436446\pi$
$810$	−4.01924	−0.141222
$811$	27.8430	0.977699	0.488849	−	0.872368i	$-0.337417\pi$
$811$	27.8430	0.977699	0.488849	+	0.872368i	$0.337417\pi$
$812$	−0.479542	−0.0168286
$813$	6.52460	0.228828
$814$	21.0576	0.738069
$815$	−0.359043	−0.0125767
$816$	3.97379	0.139110
$817$	39.2388	1.37279
$818$	−38.2911	−1.33882
$819$	−1.37949	−0.0482032
$820$	12.4412	0.434464
$821$	−37.4592	−1.30733	−0.653667	−	0.756782i	$-0.726770\pi$
$821$	−37.4592	−1.30733	−0.653667	+	0.756782i	$0.726770\pi$
$822$	39.1379	1.36509
$823$	−20.4516	−0.712898	−0.356449	−	0.934315i	$-0.616013\pi$
$823$	−20.4516	−0.712898	−0.356449	+	0.934315i	$0.616013\pi$
$824$	−20.8750	−0.727215
$825$	−4.95162	−0.172393
$826$	1.56008	0.0542823
$827$	9.39773	0.326791	0.163396	−	0.986561i	$-0.447755\pi$
$827$	9.39773	0.326791	0.163396	+	0.986561i	$0.447755\pi$
$828$	−36.1449	−1.25612
$829$	−10.3409	−0.359153	−0.179576	−	0.983744i	$-0.557473\pi$
$829$	−10.3409	−0.359153	−0.179576	+	0.983744i	$0.557473\pi$
$830$	6.89285	0.239254
$831$	−15.3381	−0.532074
$832$	−30.5300	−1.05844
$833$	−11.4645	−0.397223
$834$	24.3526	0.843260
$835$	−1.56833	−0.0542744
$836$	−20.5401	−0.710393
$837$	−35.3908	−1.22329
$838$	−26.1500	−0.903337
$839$	−21.0974	−0.728363	−0.364181	−	0.931328i	$-0.618651\pi$
$839$	−21.0974	−0.728363	−0.364181	+	0.931328i	$0.618651\pi$
$840$	0.154567	0.00533306
$841$	−28.3117	−0.976264
$842$	23.8018	0.820263
$843$	−11.1868	−0.385293
$844$	15.4723	0.532577
$845$	−4.15301	−0.142868
$846$	−40.4636	−1.39117
$847$	−2.17620	−0.0747751
$848$	5.29182	0.181722
$849$	−3.68361	−0.126421
$850$	15.7242	0.539337
$851$	51.2149	1.75562
$852$	0	0
$853$	−18.7837	−0.643141	−0.321570	−	0.946886i	$-0.604211\pi$
$853$	−18.7837	−0.643141	−0.321570	+	0.946886i	$0.604211\pi$
$854$	−4.78736	−0.163820
$855$	−10.4023	−0.355751
$856$	−9.05675	−0.309553
$857$	−23.2235	−0.793301	−0.396650	−	0.917970i	$-0.629827\pi$
$857$	−23.2235	−0.793301	−0.396650	+	0.917970i	$0.629827\pi$
$858$	−6.27264	−0.214144
$859$	−7.33333	−0.250210	−0.125105	−	0.992143i	$-0.539927\pi$
$859$	−7.33333	−0.250210	−0.125105	+	0.992143i	$0.539927\pi$
$860$	10.7307	0.365915
$861$	−1.41179	−0.0481138
$862$	−1.51174	−0.0514900
$863$	−6.24210	−0.212484	−0.106242	−	0.994340i	$-0.533882\pi$
$863$	−6.24210	−0.212484	−0.106242	+	0.994340i	$0.533882\pi$
$864$	36.5153	1.24228
$865$	−9.34862	−0.317862
$866$	55.6829	1.89218
$867$	12.5390	0.425848
$868$	−4.45434	−0.151190
$869$	7.10680	0.241082
$870$	−1.10430	−0.0374391
$871$	9.67264	0.327745
$872$	17.3746	0.588377
$873$	23.6411	0.800131
$874$	−89.8755	−3.04008
$875$	−1.56511	−0.0529103
$876$	14.4626	0.488644
$877$	−20.7484	−0.700624	−0.350312	−	0.936633i	$-0.613924\pi$
$877$	−20.7484	−0.700624	−0.350312	+	0.936633i	$0.613924\pi$
$878$	−15.3743	−0.518857
$879$	−14.9544	−0.504399
$880$	2.45821	0.0828663
$881$	−1.42986	−0.0481733	−0.0240867	−	0.999710i	$-0.507668\pi$
$881$	−1.42986	−0.0481733	−0.0240867	+	0.999710i	$0.507668\pi$
$882$	−32.8509	−1.10615
$883$	−35.6145	−1.19852	−0.599262	−	0.800553i	$-0.704539\pi$
$883$	−35.6145	−1.19852	−0.599262	+	0.800553i	$0.704539\pi$
$884$	11.0719	0.372387
$885$	1.99689	0.0671248
$886$	−76.2044	−2.56014
$887$	−9.30456	−0.312417	−0.156208	−	0.987724i	$-0.549927\pi$
$887$	−9.30456	−0.312417	−0.156208	+	0.987724i	$0.549927\pi$
$888$	7.40712	0.248567
$889$	−2.33575	−0.0783385
$890$	−17.0733	−0.572300
$891$	−3.33015	−0.111564
$892$	11.4483	0.383318
$893$	−55.9252	−1.87146
$894$	25.6664	0.858414
$895$	−11.5790	−0.387042
$896$	1.90906	0.0637771
$897$	−15.2559	−0.509379
$898$	48.5786	1.62109
$899$	6.39383	0.213246
$900$	25.0442	0.834807
$901$	−3.18574	−0.106132
$902$	18.5452	0.617488
$903$	−1.21770	−0.0405225
$904$	−9.60003	−0.319292
$905$	−1.79007	−0.0595039
$906$	−1.85185	−0.0615236
$907$	19.9614	0.662809	0.331404	−	0.943489i	$-0.392478\pi$
$907$	19.9614	0.662809	0.331404	+	0.943489i	$0.392478\pi$
$908$	22.9308	0.760985
$909$	−19.7410	−0.654768
$910$	−0.938052	−0.0310961
$911$	15.6300	0.517845	0.258923	−	0.965898i	$-0.416633\pi$
$911$	15.6300	0.517845	0.258923	+	0.965898i	$0.416633\pi$
$912$	15.7375	0.521122
$913$	5.71107	0.189009
$914$	13.9346	0.460916
$915$	−6.12777	−0.202578
$916$	0.552470	0.0182541
$917$	−2.58137	−0.0852443
$918$	−16.0826	−0.530804
$919$	16.7671	0.553097	0.276548	−	0.961000i	$-0.410809\pi$
$919$	16.7671	0.553097	0.276548	+	0.961000i	$0.410809\pi$
$920$	−4.93815	−0.162806
$921$	−2.63702	−0.0868928
$922$	−75.7445	−2.49451
$923$	0	0
$924$	0.637421	0.0209696
$925$	−35.4860	−1.16677
$926$	8.20401	0.269601
$927$	−43.5977	−1.43194
$928$	−6.59698	−0.216557
$929$	−10.8356	−0.355505	−0.177753	−	0.984075i	$-0.556883\pi$
$929$	−10.8356	−0.355505	−0.177753	+	0.984075i	$0.556883\pi$
$930$	−10.2575	−0.336357
$931$	−45.4035	−1.48804
$932$	−21.1220	−0.691873
$933$	13.4863	0.441522
$934$	−68.4973	−2.24130
$935$	−1.47987	−0.0483970
$936$	6.37410	0.208344
$937$	−21.9915	−0.718430	−0.359215	−	0.933255i	$-0.616956\pi$
$937$	−21.9915	−0.718430	−0.359215	+	0.933255i	$0.616956\pi$
$938$	−1.76837	−0.0577394
$939$	12.1254	0.395697
$940$	−15.2940	−0.498836
$941$	−5.87845	−0.191632	−0.0958160	−	0.995399i	$-0.530546\pi$
$941$	−5.87845	−0.191632	−0.0958160	+	0.995399i	$0.530546\pi$
$942$	16.0105	0.521651
$943$	45.1044	1.46880
$944$	8.72753	0.284057
$945$	0.757374	0.0246374
$946$	15.9956	0.520062
$947$	30.0989	0.978083	0.489041	−	0.872261i	$-0.337347\pi$
$947$	30.0989	0.978083	0.489041	+	0.872261i	$0.337347\pi$
$948$	12.4424	0.404112
$949$	−17.6345	−0.572441
$950$	62.2733	2.02041
$951$	−30.0961	−0.975933
$952$	−0.406684	−0.0131807
$953$	2.89963	0.0939282	0.0469641	−	0.998897i	$-0.485045\pi$
$953$	2.89963	0.0939282	0.0469641	+	0.998897i	$0.485045\pi$
$954$	−9.12851	−0.295546
$955$	7.11446	0.230218
$956$	−67.2620	−2.17541
$957$	−0.914964	−0.0295766
$958$	−75.3766	−2.43531
$959$	4.84946	0.156597
$960$	7.14434	0.230582
$961$	28.3907	0.915828
$962$	−44.9531	−1.44935
$963$	−18.9151	−0.609531
$964$	−70.2091	−2.26128
$965$	−18.9973	−0.611544
$966$	2.78911	0.0897382
$967$	−21.1359	−0.679684	−0.339842	−	0.940483i	$-0.610374\pi$
$967$	−21.1359	−0.679684	−0.339842	+	0.940483i	$0.610374\pi$
$968$	10.0554	0.323193
$969$	−9.47417	−0.304354
$970$	16.0760	0.516168
$971$	30.2825	0.971810	0.485905	−	0.874012i	$-0.338490\pi$
$971$	30.2825	0.971810	0.485905	+	0.874012i	$0.338490\pi$
$972$	−40.3121	−1.29301
$973$	3.01745	0.0967350
$974$	0.244151	0.00782309
$975$	10.5706	0.338529
$976$	−26.7817	−0.857262
$977$	11.6219	0.371817	0.185909	−	0.982567i	$-0.440477\pi$
$977$	11.6219	0.371817	0.185909	+	0.982567i	$0.440477\pi$
$978$	−0.937020	−0.0299626
$979$	−14.1461	−0.452112
$980$	−12.4166	−0.396634
$981$	36.2870	1.15855
$982$	−78.1817	−2.49488
$983$	28.1757	0.898666	0.449333	−	0.893364i	$-0.351662\pi$
$983$	28.1757	0.898666	0.449333	+	0.893364i	$0.351662\pi$
$984$	6.52337	0.207957
$985$	−2.08098	−0.0663054
$986$	2.90554	0.0925311
$987$	1.73553	0.0552425
$988$	43.8483	1.39500
$989$	38.9034	1.23706
$990$	−4.24047	−0.134771
$991$	47.9328	1.52264	0.761318	−	0.648379i	$-0.224553\pi$
$991$	47.9328	1.52264	0.761318	+	0.648379i	$0.224553\pi$
$992$	−61.2777	−1.94557
$993$	−17.8216	−0.565551
$994$	0	0
$995$	8.44873	0.267843
$996$	9.99883	0.316825
$997$	−0.0700155	−0.00221741	−0.00110871	−	0.999999i	$-0.500353\pi$
$997$	−0.0700155	−0.00221741	−0.00110871	+	0.999999i	$0.500353\pi$
$998$	8.92866	0.282632
$999$	36.2947	1.14831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5041.2.a.t.1.8		60
71.52	odd	70		71.2.g.a.6.5	✓	120
71.56	odd	70		71.2.g.a.12.5	yes	120
71.70	odd	2		5041.2.a.s.1.8		60
213.56	even	70		639.2.v.a.154.1		120
213.194	even	70		639.2.v.a.361.1		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.6.5	✓	120	71.52	odd	70
71.2.g.a.12.5	yes	120	71.56	odd	70
639.2.v.a.154.1		120	213.56	even	70
639.2.v.a.361.1		120	213.194	even	70
5041.2.a.s.1.8		60	71.70	odd	2
5041.2.a.t.1.8		60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5041 = 71^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12199 q^{2} -0.878312 q^{3} +2.50286 q^{4} +0.714152 q^{5} +1.86377 q^{6} +0.230934 q^{7} -1.06706 q^{8} -2.22857 q^{9} +O(q^{10})\)	\(q-2.12199 q^{2} -0.878312 q^{3} +2.50286 q^{4} +0.714152 q^{5} +1.86377 q^{6} +0.230934 q^{7} -1.06706 q^{8} -2.22857 q^{9} -1.51543 q^{10} -1.25561 q^{11} -2.19829 q^{12} +2.68043 q^{13} -0.490041 q^{14} -0.627248 q^{15} -2.74142 q^{16} +1.65037 q^{17} +4.72901 q^{18} +6.53601 q^{19} +1.78742 q^{20} -0.202832 q^{21} +2.66439 q^{22} +6.48014 q^{23} +0.937212 q^{24} -4.48999 q^{25} -5.68785 q^{26} +4.59231 q^{27} +0.577996 q^{28} -0.829664 q^{29} +1.33102 q^{30} -7.70653 q^{31} +7.95140 q^{32} +1.10281 q^{33} -3.50207 q^{34} +0.164922 q^{35} -5.57779 q^{36} +7.90336 q^{37} -13.8694 q^{38} -2.35425 q^{39} -0.762043 q^{40} +6.96040 q^{41} +0.430409 q^{42} +6.00348 q^{43} -3.14260 q^{44} -1.59154 q^{45} -13.7508 q^{46} -8.55648 q^{47} +2.40782 q^{48} -6.94667 q^{49} +9.52773 q^{50} -1.44954 q^{51} +6.70873 q^{52} -1.93032 q^{53} -9.74486 q^{54} -0.896693 q^{55} -0.246421 q^{56} -5.74065 q^{57} +1.76054 q^{58} -3.18358 q^{59} -1.56991 q^{60} +9.76929 q^{61} +16.3532 q^{62} -0.514653 q^{63} -11.3900 q^{64} +1.91423 q^{65} -2.34016 q^{66} +3.60862 q^{67} +4.13063 q^{68} -5.69159 q^{69} -0.349964 q^{70} +2.37802 q^{72} -6.57900 q^{73} -16.7709 q^{74} +3.94361 q^{75} +16.3587 q^{76} -0.289962 q^{77} +4.99571 q^{78} -5.66006 q^{79} -1.95779 q^{80} +2.65222 q^{81} -14.7699 q^{82} -4.54846 q^{83} -0.507660 q^{84} +1.17861 q^{85} -12.7393 q^{86} +0.728703 q^{87} +1.33981 q^{88} +11.2664 q^{89} +3.37723 q^{90} +0.619002 q^{91} +16.2189 q^{92} +6.76874 q^{93} +18.1568 q^{94} +4.66770 q^{95} -6.98381 q^{96} -10.6082 q^{97} +14.7408 q^{98} +2.79820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 2 q^{2} - 2 q^{3} + 46 q^{4} + 10 q^{5} + 4 q^{6} + 25 q^{7} + 9 q^{8} + 32 q^{9}+O(q^{10}) \) 60 * q - 2 * q^2 - 2 * q^3 + 46 * q^4 + 10 * q^5 + 4 * q^6 + 25 * q^7 + 9 * q^8 + 32 * q^9	\( 60 q - 2 q^{2} - 2 q^{3} + 46 q^{4} + 10 q^{5} + 4 q^{6} + 25 q^{7} + 9 q^{8} + 32 q^{9} + 18 q^{10} + 53 q^{11} + 44 q^{12} + 13 q^{13} + 49 q^{14} - 20 q^{15} + 26 q^{16} + 33 q^{17} - 48 q^{18} + 3 q^{19} - 48 q^{20} + 18 q^{21} + 16 q^{22} + 59 q^{23} - 85 q^{24} + 24 q^{25} + 63 q^{26} - 26 q^{27} + 63 q^{28} + 22 q^{29} - 66 q^{30} + 72 q^{31} + 16 q^{32} + 46 q^{33} + 4 q^{34} + 101 q^{35} - 10 q^{36} + 17 q^{37} - 48 q^{38} + 55 q^{39} + 91 q^{40} + 61 q^{41} + 25 q^{42} + 24 q^{43} + 121 q^{44} + 43 q^{45} - 12 q^{46} + 64 q^{47} - 8 q^{48} + 13 q^{49} + 12 q^{50} + 45 q^{51} + 47 q^{52} + 55 q^{53} + 5 q^{54} + 94 q^{55} + 167 q^{56} + 45 q^{57} - 9 q^{58} + 109 q^{59} - 110 q^{60} + 68 q^{61} + 128 q^{62} + 61 q^{63} + 89 q^{64} - 10 q^{65} + 72 q^{66} + 71 q^{67} + 110 q^{68} + q^{69} + 32 q^{70} - 72 q^{72} - 17 q^{73} - 63 q^{74} - 122 q^{75} + 69 q^{76} + 88 q^{77} - 6 q^{78} - 17 q^{79} - 130 q^{80} + 40 q^{81} - 71 q^{82} + 31 q^{83} - 26 q^{84} + 9 q^{85} + q^{86} - 142 q^{87} + 56 q^{88} - 11 q^{89} - 29 q^{90} + 9 q^{91} + 134 q^{92} - 91 q^{93} + 39 q^{94} - 5 q^{95} - 130 q^{96} - 15 q^{97} - 55 q^{98} + 135 q^{99}+O(q^{100}) \) 60 * q - 2 * q^2 - 2 * q^3 + 46 * q^4 + 10 * q^5 + 4 * q^6 + 25 * q^7 + 9 * q^8 + 32 * q^9 + 18 * q^10 + 53 * q^11 + 44 * q^12 + 13 * q^13 + 49 * q^14 - 20 * q^15 + 26 * q^16 + 33 * q^17 - 48 * q^18 + 3 * q^19 - 48 * q^20 + 18 * q^21 + 16 * q^22 + 59 * q^23 - 85 * q^24 + 24 * q^25 + 63 * q^26 - 26 * q^27 + 63 * q^28 + 22 * q^29 - 66 * q^30 + 72 * q^31 + 16 * q^32 + 46 * q^33 + 4 * q^34 + 101 * q^35 - 10 * q^36 + 17 * q^37 - 48 * q^38 + 55 * q^39 + 91 * q^40 + 61 * q^41 + 25 * q^42 + 24 * q^43 + 121 * q^44 + 43 * q^45 - 12 * q^46 + 64 * q^47 - 8 * q^48 + 13 * q^49 + 12 * q^50 + 45 * q^51 + 47 * q^52 + 55 * q^53 + 5 * q^54 + 94 * q^55 + 167 * q^56 + 45 * q^57 - 9 * q^58 + 109 * q^59 - 110 * q^60 + 68 * q^61 + 128 * q^62 + 61 * q^63 + 89 * q^64 - 10 * q^65 + 72 * q^66 + 71 * q^67 + 110 * q^68 + q^69 + 32 * q^70 - 72 * q^72 - 17 * q^73 - 63 * q^74 - 122 * q^75 + 69 * q^76 + 88 * q^77 - 6 * q^78 - 17 * q^79 - 130 * q^80 + 40 * q^81 - 71 * q^82 + 31 * q^83 - 26 * q^84 + 9 * q^85 + q^86 - 142 * q^87 + 56 * q^88 - 11 * q^89 - 29 * q^90 + 9 * q^91 + 134 * q^92 - 91 * q^93 + 39 * q^94 - 5 * q^95 - 130 * q^96 - 15 * q^97 - 55 * q^98 + 135 * q^99

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