LMFDB - Embedded newform 6013.2.a.e.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.82060 q^{2} +2.13458 q^{3} +1.31457 q^{4} -4.26535 q^{5} -3.88622 q^{6} +1.00000 q^{7} +1.24789 q^{8} +1.55645 q^{9} +O(q^{10})$	\(q-1.82060 q^{2} +2.13458 q^{3} +1.31457 q^{4} -4.26535 q^{5} -3.88622 q^{6} +1.00000 q^{7} +1.24789 q^{8} +1.55645 q^{9} +7.76548 q^{10} +5.61533 q^{11} +2.80606 q^{12} +3.58656 q^{13} -1.82060 q^{14} -9.10475 q^{15} -4.90105 q^{16} +6.50418 q^{17} -2.83366 q^{18} +1.68108 q^{19} -5.60710 q^{20} +2.13458 q^{21} -10.2232 q^{22} +3.27680 q^{23} +2.66373 q^{24} +13.1932 q^{25} -6.52967 q^{26} -3.08138 q^{27} +1.31457 q^{28} +2.92030 q^{29} +16.5761 q^{30} -0.235003 q^{31} +6.42704 q^{32} +11.9864 q^{33} -11.8415 q^{34} -4.26535 q^{35} +2.04606 q^{36} +9.23601 q^{37} -3.06056 q^{38} +7.65581 q^{39} -5.32269 q^{40} -7.75357 q^{41} -3.88622 q^{42} -0.257386 q^{43} +7.38174 q^{44} -6.63880 q^{45} -5.96572 q^{46} +4.49731 q^{47} -10.4617 q^{48} +1.00000 q^{49} -24.0195 q^{50} +13.8837 q^{51} +4.71478 q^{52} -1.70941 q^{53} +5.60995 q^{54} -23.9514 q^{55} +1.24789 q^{56} +3.58840 q^{57} -5.31668 q^{58} +0.207733 q^{59} -11.9688 q^{60} +2.18300 q^{61} +0.427845 q^{62} +1.55645 q^{63} -1.89896 q^{64} -15.2979 q^{65} -21.8224 q^{66} +0.0456908 q^{67} +8.55020 q^{68} +6.99460 q^{69} +7.76548 q^{70} +7.95734 q^{71} +1.94228 q^{72} +3.04428 q^{73} -16.8150 q^{74} +28.1620 q^{75} +2.20990 q^{76} +5.61533 q^{77} -13.9381 q^{78} -10.9791 q^{79} +20.9047 q^{80} -11.2468 q^{81} +14.1161 q^{82} +7.07037 q^{83} +2.80606 q^{84} -27.7426 q^{85} +0.468596 q^{86} +6.23362 q^{87} +7.00732 q^{88} +18.3857 q^{89} +12.0866 q^{90} +3.58656 q^{91} +4.30758 q^{92} -0.501633 q^{93} -8.18779 q^{94} -7.17039 q^{95} +13.7191 q^{96} -11.9692 q^{97} -1.82060 q^{98} +8.73997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) $ 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.82060	−1.28736	−0.643678	−	0.765297i	$-0.722592\pi$
$2$	−1.82060	−1.28736	−0.643678	+	0.765297i	$0.722592\pi$
$3$	2.13458	1.23240	0.616201	−	0.787589i	$-0.288671\pi$
$3$	2.13458	1.23240	0.616201	+	0.787589i	$0.288671\pi$
$4$	1.31457	0.657285
$5$	−4.26535	−1.90752	−0.953762	−	0.300564i	$-0.902825\pi$
$5$	−4.26535	−1.90752	−0.953762	+	0.300564i	$0.902825\pi$
$6$	−3.88622	−1.58654
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.24789	0.441196
$9$	1.55645	0.518816
$10$	7.76548	2.45566
$11$	5.61533	1.69309	0.846543	−	0.532321i	$-0.178680\pi$
$11$	5.61533	1.69309	0.846543	+	0.532321i	$0.178680\pi$
$12$	2.80606	0.810040
$13$	3.58656	0.994732	0.497366	−	0.867541i	$-0.334301\pi$
$13$	3.58656	0.994732	0.497366	+	0.867541i	$0.334301\pi$
$14$	−1.82060	−0.486575
$15$	−9.10475	−2.35084
$16$	−4.90105	−1.22526
$17$	6.50418	1.57750	0.788748	−	0.614717i	$-0.210730\pi$
$17$	6.50418	1.57750	0.788748	+	0.614717i	$0.210730\pi$
$18$	−2.83366	−0.667901
$19$	1.68108	0.385666	0.192833	−	0.981232i	$-0.438232\pi$
$19$	1.68108	0.385666	0.192833	+	0.981232i	$0.438232\pi$
$20$	−5.60710	−1.25379
$21$	2.13458	0.465804
$22$	−10.2232	−2.17960
$23$	3.27680	0.683259	0.341630	−	0.939835i	$-0.389021\pi$
$23$	3.27680	0.683259	0.341630	+	0.939835i	$0.389021\pi$
$24$	2.66373	0.543731
$25$	13.1932	2.63864
$26$	−6.52967	−1.28057
$27$	−3.08138	−0.593012
$28$	1.31457	0.248430
$29$	2.92030	0.542286	0.271143	−	0.962539i	$-0.412598\pi$
$29$	2.92030	0.542286	0.271143	+	0.962539i	$0.412598\pi$
$30$	16.5761	3.02636
$31$	−0.235003	−0.0422077	−0.0211039	−	0.999777i	$-0.506718\pi$
$31$	−0.235003	−0.0422077	−0.0211039	+	0.999777i	$0.506718\pi$
$32$	6.42704	1.13615
$33$	11.9864	2.08656
$34$	−11.8415	−2.03080
$35$	−4.26535	−0.720976
$36$	2.04606	0.341010
$37$	9.23601	1.51839	0.759196	−	0.650863i	$-0.225593\pi$
$37$	9.23601	1.51839	0.759196	+	0.650863i	$0.225593\pi$
$38$	−3.06056	−0.496489
$39$	7.65581	1.22591
$40$	−5.32269	−0.841592
$41$	−7.75357	−1.21090	−0.605452	−	0.795882i	$-0.707008\pi$
$41$	−7.75357	−1.21090	−0.605452	+	0.795882i	$0.707008\pi$
$42$	−3.88622	−0.599656
$43$	−0.257386	−0.0392510	−0.0196255	−	0.999807i	$-0.506247\pi$
$43$	−0.257386	−0.0392510	−0.0196255	+	0.999807i	$0.506247\pi$
$44$	7.38174	1.11284
$45$	−6.63880	−0.989654
$46$	−5.96572	−0.879598
$47$	4.49731	0.656000	0.328000	−	0.944678i	$-0.393625\pi$
$47$	4.49731	0.656000	0.328000	+	0.944678i	$0.393625\pi$
$48$	−10.4617	−1.51002
$49$	1.00000	0.142857
$50$	−24.0195	−3.39687
$51$	13.8837	1.94411
$52$	4.71478	0.653822
$53$	−1.70941	−0.234805	−0.117403	−	0.993084i	$-0.537457\pi$
$53$	−1.70941	−0.234805	−0.117403	+	0.993084i	$0.537457\pi$
$54$	5.60995	0.763418
$55$	−23.9514	−3.22960
$56$	1.24789	0.166756
$57$	3.58840	0.475296
$58$	−5.31668	−0.698115
$59$	0.207733	0.0270446	0.0135223	−	0.999909i	$-0.495696\pi$
$59$	0.207733	0.0270446	0.0135223	+	0.999909i	$0.495696\pi$
$60$	−11.9688	−1.54517
$61$	2.18300	0.279505	0.139753	−	0.990186i	$-0.455369\pi$
$61$	2.18300	0.279505	0.139753	+	0.990186i	$0.455369\pi$
$62$	0.427845	0.0543364
$63$	1.55645	0.196094
$64$	−1.89896	−0.237370
$65$	−15.2979	−1.89747
$66$	−21.8224	−2.68615
$67$	0.0456908	0.00558203	0.00279101	−	0.999996i	$-0.499112\pi$
$67$	0.0456908	0.00558203	0.00279101	+	0.999996i	$0.499112\pi$
$68$	8.55020	1.03686
$69$	6.99460	0.842050
$70$	7.76548	0.928153
$71$	7.95734	0.944363	0.472181	−	0.881501i	$-0.343467\pi$
$71$	7.95734	0.944363	0.472181	+	0.881501i	$0.343467\pi$
$72$	1.94228	0.228900
$73$	3.04428	0.356306	0.178153	−	0.984003i	$-0.442988\pi$
$73$	3.04428	0.356306	0.178153	+	0.984003i	$0.442988\pi$
$74$	−16.8150	−1.95471
$75$	28.1620	3.25187
$76$	2.20990	0.253492
$77$	5.61533	0.639926
$78$	−13.9381	−1.57818
$79$	−10.9791	−1.23525	−0.617625	−	0.786473i	$-0.711905\pi$
$79$	−10.9791	−1.23525	−0.617625	+	0.786473i	$0.711905\pi$
$80$	20.9047	2.33721
$81$	−11.2468	−1.24965
$82$	14.1161	1.55886
$83$	7.07037	0.776074	0.388037	−	0.921644i	$-0.373153\pi$
$83$	7.07037	0.776074	0.388037	+	0.921644i	$0.373153\pi$
$84$	2.80606	0.306166
$85$	−27.7426	−3.00911
$86$	0.468596	0.0505300
$87$	6.23362	0.668314
$88$	7.00732	0.746983
$89$	18.3857	1.94888	0.974442	−	0.224638i	$-0.0721198\pi$
$89$	18.3857	1.94888	0.974442	+	0.224638i	$0.0721198\pi$
$90$	12.0866	1.27404
$91$	3.58656	0.375973
$92$	4.30758	0.449096
$93$	−0.501633	−0.0520169
$94$	−8.18779	−0.844506
$95$	−7.17039	−0.735667
$96$	13.7191	1.40020
$97$	−11.9692	−1.21528	−0.607642	−	0.794211i	$-0.707884\pi$
$97$	−11.9692	−1.21528	−0.607642	+	0.794211i	$0.707884\pi$
$98$	−1.82060	−0.183908
$99$	8.73997	0.878400
$100$	17.3434	1.73434
$101$	8.20118	0.816048	0.408024	−	0.912971i	$-0.366218\pi$
$101$	8.20118	0.816048	0.408024	+	0.912971i	$0.366218\pi$
$102$	−25.2766	−2.50276
$103$	−11.8039	−1.16307	−0.581535	−	0.813521i	$-0.697548\pi$
$103$	−11.8039	−1.16307	−0.581535	+	0.813521i	$0.697548\pi$
$104$	4.47563	0.438872
$105$	−9.10475	−0.888533
$106$	3.11214	0.302278
$107$	−3.24876	−0.314069	−0.157035	−	0.987593i	$-0.550193\pi$
$107$	−3.24876	−0.314069	−0.157035	+	0.987593i	$0.550193\pi$
$108$	−4.05069	−0.389778
$109$	−15.8052	−1.51386	−0.756931	−	0.653495i	$-0.773302\pi$
$109$	−15.8052	−1.51386	−0.756931	+	0.653495i	$0.773302\pi$
$110$	43.6057	4.15764
$111$	19.7150	1.87127
$112$	−4.90105	−0.463105
$113$	−1.58337	−0.148951	−0.0744754	−	0.997223i	$-0.523728\pi$
$113$	−1.58337	−0.148951	−0.0744754	+	0.997223i	$0.523728\pi$
$114$	−6.53303	−0.611874
$115$	−13.9767	−1.30333
$116$	3.83894	0.356436
$117$	5.58229	0.516083
$118$	−0.378199	−0.0348160
$119$	6.50418	0.596237
$120$	−11.3617	−1.03718
$121$	20.5319	1.86654
$122$	−3.97437	−0.359823
$123$	−16.5506	−1.49232
$124$	−0.308928	−0.0277425
$125$	−34.9470	−3.12575
$126$	−2.83366	−0.252443
$127$	−10.0100	−0.888241	−0.444121	−	0.895967i	$-0.646484\pi$
$127$	−10.0100	−0.888241	−0.444121	+	0.895967i	$0.646484\pi$
$128$	−9.39685	−0.830572
$129$	−0.549412	−0.0483731
$130$	27.8513	2.44272
$131$	7.46642	0.652344	0.326172	−	0.945310i	$-0.394241\pi$
$131$	7.46642	0.652344	0.326172	+	0.945310i	$0.394241\pi$
$132$	15.7569	1.37147
$133$	1.68108	0.145768
$134$	−0.0831846	−0.00718605
$135$	13.1432	1.13118
$136$	8.11651	0.695985
$137$	0.580775	0.0496190	0.0248095	−	0.999692i	$-0.492102\pi$
$137$	0.580775	0.0496190	0.0248095	+	0.999692i	$0.492102\pi$
$138$	−12.7343	−1.08402
$139$	9.51874	0.807369	0.403684	−	0.914898i	$-0.367729\pi$
$139$	9.51874	0.807369	0.403684	+	0.914898i	$0.367729\pi$
$140$	−5.60710	−0.473887
$141$	9.59989	0.808457
$142$	−14.4871	−1.21573
$143$	20.1397	1.68417
$144$	−7.62823	−0.635685
$145$	−12.4561	−1.03442
$146$	−5.54240	−0.458693
$147$	2.13458	0.176058
$148$	12.1414	0.998016
$149$	−9.72554	−0.796748	−0.398374	−	0.917223i	$-0.630425\pi$
$149$	−9.72554	−0.796748	−0.398374	+	0.917223i	$0.630425\pi$
$150$	−51.2717	−4.18632
$151$	−10.9342	−0.889810	−0.444905	−	0.895578i	$-0.646763\pi$
$151$	−10.9342	−0.889810	−0.444905	+	0.895578i	$0.646763\pi$
$152$	2.09780	0.170154
$153$	10.1234	0.818430
$154$	−10.2232	−0.823813
$155$	1.00237	0.0805122
$156$	10.0641	0.805772
$157$	−14.1466	−1.12902	−0.564510	−	0.825426i	$-0.690935\pi$
$157$	−14.1466	−1.12902	−0.564510	+	0.825426i	$0.690935\pi$
$158$	19.9886	1.59021
$159$	−3.64887	−0.289374
$160$	−27.4136	−2.16723
$161$	3.27680	0.258248
$162$	20.4759	1.60874
$163$	−16.9021	−1.32388	−0.661938	−	0.749559i	$-0.730266\pi$
$163$	−16.9021	−1.32388	−0.661938	+	0.749559i	$0.730266\pi$
$164$	−10.1926	−0.795909
$165$	−51.1262	−3.98017
$166$	−12.8723	−0.999083
$167$	−11.0074	−0.851777	−0.425888	−	0.904776i	$-0.640038\pi$
$167$	−11.0074	−0.851777	−0.425888	+	0.904776i	$0.640038\pi$
$168$	2.66373	0.205511
$169$	−0.136615	−0.0105088
$170$	50.5081	3.87379
$171$	2.61651	0.200090
$172$	−0.338352	−0.0257991
$173$	−9.84735	−0.748680	−0.374340	−	0.927291i	$-0.622131\pi$
$173$	−9.84735	−0.748680	−0.374340	+	0.927291i	$0.622131\pi$
$174$	−11.3489	−0.860358
$175$	13.1932	0.997314
$176$	−27.5210	−2.07447
$177$	0.443424	0.0333298
$178$	−33.4730	−2.50891
$179$	−10.6460	−0.795719	−0.397859	−	0.917446i	$-0.630247\pi$
$179$	−10.6460	−0.795719	−0.397859	+	0.917446i	$0.630247\pi$
$180$	−8.72717	−0.650485
$181$	16.5515	1.23026	0.615131	−	0.788425i	$-0.289103\pi$
$181$	16.5515	1.23026	0.615131	+	0.788425i	$0.289103\pi$
$182$	−6.52967	−0.484011
$183$	4.65981	0.344463
$184$	4.08909	0.301451
$185$	−39.3948	−2.89637
$186$	0.913271	0.0669643
$187$	36.5231	2.67083
$188$	5.91203	0.431179
$189$	−3.08138	−0.224138
$190$	13.0544	0.947065
$191$	−3.89190	−0.281608	−0.140804	−	0.990037i	$-0.544969\pi$
$191$	−3.89190	−0.281608	−0.140804	+	0.990037i	$0.544969\pi$
$192$	−4.05348	−0.292535
$193$	−12.9598	−0.932868	−0.466434	−	0.884556i	$-0.654462\pi$
$193$	−12.9598	−0.932868	−0.466434	+	0.884556i	$0.654462\pi$
$194$	21.7910	1.56450
$195$	−32.6547	−2.33845
$196$	1.31457	0.0938979
$197$	0.703936	0.0501534	0.0250767	−	0.999686i	$-0.492017\pi$
$197$	0.703936	0.0501534	0.0250767	+	0.999686i	$0.492017\pi$
$198$	−15.9120	−1.13081
$199$	2.09958	0.148835	0.0744176	−	0.997227i	$-0.476290\pi$
$199$	2.09958	0.148835	0.0744176	+	0.997227i	$0.476290\pi$
$200$	16.4637	1.16416
$201$	0.0975309	0.00687930
$202$	−14.9310	−1.05054
$203$	2.92030	0.204965
$204$	18.2511	1.27783
$205$	33.0717	2.30983
$206$	21.4901	1.49729
$207$	5.10016	0.354486
$208$	−17.5779	−1.21881
$209$	9.43981	0.652965
$210$	16.5761	1.14386
$211$	12.4870	0.859643	0.429822	−	0.902914i	$-0.358576\pi$
$211$	12.4870	0.859643	0.429822	+	0.902914i	$0.358576\pi$
$212$	−2.24714	−0.154334
$213$	16.9856	1.16384
$214$	5.91467	0.404319
$215$	1.09784	0.0748722
$216$	−3.84523	−0.261635
$217$	−0.235003	−0.0159530
$218$	28.7749	1.94888
$219$	6.49827	0.439113
$220$	−31.4857	−2.12277
$221$	23.3276	1.56918
$222$	−35.8931	−2.40899
$223$	17.5345	1.17419	0.587097	−	0.809516i	$-0.300271\pi$
$223$	17.5345	1.17419	0.587097	+	0.809516i	$0.300271\pi$
$224$	6.42704	0.429425
$225$	20.5346	1.36897
$226$	2.88267	0.191753
$227$	13.7706	0.913990	0.456995	−	0.889469i	$-0.348926\pi$
$227$	13.7706	0.913990	0.456995	+	0.889469i	$0.348926\pi$
$228$	4.71721	0.312405
$229$	−27.8043	−1.83736	−0.918681	−	0.395000i	$-0.870745\pi$
$229$	−27.8043	−1.83736	−0.918681	+	0.395000i	$0.870745\pi$
$230$	25.4459	1.67785
$231$	11.9864	0.788647
$232$	3.64421	0.239254
$233$	−1.10960	−0.0726926	−0.0363463	−	0.999339i	$-0.511572\pi$
$233$	−1.10960	−0.0726926	−0.0363463	+	0.999339i	$0.511572\pi$
$234$	−10.1631	−0.664382
$235$	−19.1826	−1.25134
$236$	0.273080	0.0177760
$237$	−23.4359	−1.52233
$238$	−11.8415	−0.767569
$239$	5.19532	0.336057	0.168028	−	0.985782i	$-0.446260\pi$
$239$	5.19532	0.336057	0.168028	+	0.985782i	$0.446260\pi$
$240$	44.6228	2.88039
$241$	20.2803	1.30637	0.653184	−	0.757199i	$-0.273433\pi$
$241$	20.2803	1.30637	0.653184	+	0.757199i	$0.273433\pi$
$242$	−37.3803	−2.40290
$243$	−14.7631	−0.947055
$244$	2.86971	0.183715
$245$	−4.26535	−0.272503
$246$	30.1320	1.92115
$247$	6.02928	0.383634
$248$	−0.293258	−0.0186219
$249$	15.0923	0.956436
$250$	63.6243	4.02396
$251$	20.2166	1.27606	0.638030	−	0.770012i	$-0.279750\pi$
$251$	20.2166	1.27606	0.638030	+	0.770012i	$0.279750\pi$
$252$	2.04606	0.128890
$253$	18.4003	1.15682
$254$	18.2241	1.14348
$255$	−59.2189	−3.70843
$256$	20.9058	1.30661
$257$	−9.89146	−0.617012	−0.308506	−	0.951222i	$-0.599829\pi$
$257$	−9.89146	−0.617012	−0.308506	+	0.951222i	$0.599829\pi$
$258$	1.00026	0.0622733
$259$	9.23601	0.573898
$260$	−20.1102	−1.24718
$261$	4.54529	0.281347
$262$	−13.5933	−0.839799
$263$	29.3137	1.80756	0.903779	−	0.428000i	$-0.140782\pi$
$263$	29.3137	1.80756	0.903779	+	0.428000i	$0.140782\pi$
$264$	14.9577	0.920583
$265$	7.29122	0.447896
$266$	−3.06056	−0.187655
$267$	39.2459	2.40181
$268$	0.0600638	0.00366898
$269$	13.6832	0.834279	0.417139	−	0.908842i	$-0.363033\pi$
$269$	13.6832	0.834279	0.417139	+	0.908842i	$0.363033\pi$
$270$	−23.9284	−1.45624
$271$	−2.04532	−0.124244	−0.0621221	−	0.998069i	$-0.519787\pi$
$271$	−2.04532	−0.124244	−0.0621221	+	0.998069i	$0.519787\pi$
$272$	−31.8773	−1.93284
$273$	7.65581	0.463350
$274$	−1.05736	−0.0638773
$275$	74.0843	4.46745
$276$	9.19489	0.553467
$277$	−1.46575	−0.0880687	−0.0440343	−	0.999030i	$-0.514021\pi$
$277$	−1.46575	−0.0880687	−0.0440343	+	0.999030i	$0.514021\pi$
$278$	−17.3298	−1.03937
$279$	−0.365770	−0.0218981
$280$	−5.32269	−0.318092
$281$	−0.981284	−0.0585385	−0.0292693	−	0.999572i	$-0.509318\pi$
$281$	−0.981284	−0.0585385	−0.0292693	+	0.999572i	$0.509318\pi$
$282$	−17.4775	−1.04077
$283$	17.4400	1.03670	0.518349	−	0.855169i	$-0.326547\pi$
$283$	17.4400	1.03670	0.518349	+	0.855169i	$0.326547\pi$
$284$	10.4605	0.620715
$285$	−15.3058	−0.906637
$286$	−36.6662	−2.16812
$287$	−7.75357	−0.457679
$288$	10.0034	0.589454
$289$	25.3044	1.48849
$290$	22.6775	1.33167
$291$	−25.5492	−1.49772
$292$	4.00192	0.234195
$293$	15.3193	0.894960	0.447480	−	0.894294i	$-0.352321\pi$
$293$	15.3193	0.894960	0.447480	+	0.894294i	$0.352321\pi$
$294$	−3.88622	−0.226649
$295$	−0.886056	−0.0515882
$296$	11.5255	0.669908
$297$	−17.3030	−1.00402
$298$	17.7063	1.02570
$299$	11.7524	0.679660
$300$	37.0210	2.13741
$301$	−0.257386	−0.0148355
$302$	19.9067	1.14550
$303$	17.5061	1.00570
$304$	−8.23904	−0.472541
$305$	−9.31128	−0.533162
$306$	−18.4307	−1.05361
$307$	18.3167	1.04539	0.522695	−	0.852520i	$-0.324927\pi$
$307$	18.3167	1.04539	0.522695	+	0.852520i	$0.324927\pi$
$308$	7.38174	0.420614
$309$	−25.1964	−1.43337
$310$	−1.82491	−0.103648
$311$	29.6733	1.68262	0.841310	−	0.540553i	$-0.181785\pi$
$311$	29.6733	1.68262	0.841310	+	0.540553i	$0.181785\pi$
$312$	9.55361	0.540867
$313$	15.8373	0.895179	0.447589	−	0.894239i	$-0.352283\pi$
$313$	15.8373	0.895179	0.447589	+	0.894239i	$0.352283\pi$
$314$	25.7552	1.45345
$315$	−6.63880	−0.374054
$316$	−14.4329	−0.811911
$317$	−24.4618	−1.37391	−0.686954	−	0.726701i	$-0.741053\pi$
$317$	−24.4618	−1.37391	−0.686954	+	0.726701i	$0.741053\pi$
$318$	6.64312	0.372528
$319$	16.3984	0.918136
$320$	8.09972	0.452788
$321$	−6.93474	−0.387060
$322$	−5.96572	−0.332457
$323$	10.9340	0.608386
$324$	−14.7847	−0.821374
$325$	47.3182	2.62474
$326$	30.7719	1.70430
$327$	−33.7375	−1.86569
$328$	−9.67561	−0.534246
$329$	4.49731	0.247945
$330$	93.0801	5.12389
$331$	10.2857	0.565354	0.282677	−	0.959215i	$-0.408778\pi$
$331$	10.2857	0.565354	0.282677	+	0.959215i	$0.408778\pi$
$332$	9.29450	0.510102
$333$	14.3754	0.787766
$334$	20.0400	1.09654
$335$	−0.194888	−0.0106478
$336$	−10.4617	−0.570732
$337$	24.8172	1.35188	0.675939	−	0.736958i	$-0.263738\pi$
$337$	24.8172	1.35188	0.675939	+	0.736958i	$0.263738\pi$
$338$	0.248721	0.0135286
$339$	−3.37983	−0.183567
$340$	−36.4696	−1.97784
$341$	−1.31962	−0.0714613
$342$	−4.76361	−0.257587
$343$	1.00000	0.0539949
$344$	−0.321190	−0.0173174
$345$	−29.8344	−1.60623
$346$	17.9281	0.963818
$347$	−7.04715	−0.378311	−0.189156	−	0.981947i	$-0.560575\pi$
$347$	−7.04715	−0.378311	−0.189156	+	0.981947i	$0.560575\pi$
$348$	8.19453	0.439273
$349$	−30.3701	−1.62567	−0.812837	−	0.582491i	$-0.802078\pi$
$349$	−30.3701	−1.62567	−0.812837	+	0.582491i	$0.802078\pi$
$350$	−24.0195	−1.28390
$351$	−11.0515	−0.589888
$352$	36.0900	1.92360
$353$	23.5215	1.25192	0.625960	−	0.779855i	$-0.284707\pi$
$353$	23.5215	1.25192	0.625960	+	0.779855i	$0.284707\pi$
$354$	−0.807297	−0.0429073
$355$	−33.9409	−1.80139
$356$	24.1693	1.28097
$357$	13.8837	0.734804
$358$	19.3820	1.02437
$359$	29.7328	1.56924	0.784619	−	0.619978i	$-0.212858\pi$
$359$	29.7328	1.56924	0.784619	+	0.619978i	$0.212858\pi$
$360$	−8.28450	−0.436631
$361$	−16.1740	−0.851262
$362$	−30.1335	−1.58378
$363$	43.8271	2.30033
$364$	4.71478	0.247122
$365$	−12.9849	−0.679662
$366$	−8.48363	−0.443446
$367$	−16.1997	−0.845619	−0.422809	−	0.906219i	$-0.638956\pi$
$367$	−16.1997	−0.845619	−0.422809	+	0.906219i	$0.638956\pi$
$368$	−16.0597	−0.837171
$369$	−12.0680	−0.628237
$370$	71.7221	3.72865
$371$	−1.70941	−0.0887480
$372$	−0.659432	−0.0341899
$373$	−4.44785	−0.230301	−0.115150	−	0.993348i	$-0.536735\pi$
$373$	−4.44785	−0.230301	−0.115150	+	0.993348i	$0.536735\pi$
$374$	−66.4938	−3.43831
$375$	−74.5973	−3.85219
$376$	5.61216	0.289425
$377$	10.4738	0.539429
$378$	5.60995	0.288545
$379$	−18.9489	−0.973338	−0.486669	−	0.873587i	$-0.661788\pi$
$379$	−18.9489	−0.973338	−0.486669	+	0.873587i	$0.661788\pi$
$380$	−9.42598	−0.483543
$381$	−21.3671	−1.09467
$382$	7.08558	0.362530
$383$	−24.4184	−1.24772	−0.623862	−	0.781535i	$-0.714437\pi$
$383$	−24.4184	−1.24772	−0.623862	+	0.781535i	$0.714437\pi$
$384$	−20.0584	−1.02360
$385$	−23.9514	−1.22067
$386$	23.5946	1.20093
$387$	−0.400608	−0.0203641
$388$	−15.7343	−0.798788
$389$	−21.9115	−1.11096	−0.555479	−	0.831531i	$-0.687465\pi$
$389$	−21.9115	−1.11096	−0.555479	+	0.831531i	$0.687465\pi$
$390$	59.4510	3.01042
$391$	21.3129	1.07784
$392$	1.24789	0.0630280
$393$	15.9377	0.803950
$394$	−1.28158	−0.0645653
$395$	46.8299	2.35627
$396$	11.4893	0.577359
$397$	26.7193	1.34100	0.670501	−	0.741908i	$-0.266079\pi$
$397$	26.7193	1.34100	0.670501	+	0.741908i	$0.266079\pi$
$398$	−3.82248	−0.191604
$399$	3.58840	0.179645
$400$	−64.6606	−3.23303
$401$	−1.20324	−0.0600872	−0.0300436	−	0.999549i	$-0.509565\pi$
$401$	−1.20324	−0.0600872	−0.0300436	+	0.999549i	$0.509565\pi$
$402$	−0.177564	−0.00885611
$403$	−0.842851	−0.0419854
$404$	10.7810	0.536376
$405$	47.9716	2.38373
$406$	−5.31668	−0.263863
$407$	51.8632	2.57077
$408$	17.3254	0.857734
$409$	6.40723	0.316817	0.158409	−	0.987374i	$-0.449364\pi$
$409$	6.40723	0.316817	0.158409	+	0.987374i	$0.449364\pi$
$410$	−60.2102	−2.97357
$411$	1.23971	0.0611505
$412$	−15.5170	−0.764469
$413$	0.207733	0.0102219
$414$	−9.28534	−0.456350
$415$	−30.1576	−1.48038
$416$	23.0509	1.13017
$417$	20.3185	0.995004
$418$	−17.1861	−0.840598
$419$	−22.8724	−1.11739	−0.558694	−	0.829374i	$-0.688697\pi$
$419$	−22.8724	−1.11739	−0.558694	+	0.829374i	$0.688697\pi$
$420$	−11.9688	−0.584019
$421$	−19.1397	−0.932814	−0.466407	−	0.884570i	$-0.654452\pi$
$421$	−19.1397	−0.932814	−0.466407	+	0.884570i	$0.654452\pi$
$422$	−22.7339	−1.10667
$423$	6.99984	0.340344
$424$	−2.13315	−0.103595
$425$	85.8111	4.16245
$426$	−30.9239	−1.49827
$427$	2.18300	0.105643
$428$	−4.27072	−0.206433
$429$	42.9899	2.07557
$430$	−1.99873	−0.0963872
$431$	21.7704	1.04864	0.524321	−	0.851521i	$-0.324319\pi$
$431$	21.7704	1.04864	0.524321	+	0.851521i	$0.324319\pi$
$432$	15.1020	0.726595
$433$	−9.98779	−0.479983	−0.239991	−	0.970775i	$-0.577145\pi$
$433$	−9.98779	−0.479983	−0.239991	+	0.970775i	$0.577145\pi$
$434$	0.427845	0.0205372
$435$	−26.5886	−1.27483
$436$	−20.7770	−0.995039
$437$	5.50855	0.263510
$438$	−11.8307	−0.565294
$439$	15.7465	0.751541	0.375770	−	0.926713i	$-0.377378\pi$
$439$	15.7465	0.751541	0.375770	+	0.926713i	$0.377378\pi$
$440$	−29.8887	−1.42489
$441$	1.55645	0.0741166
$442$	−42.4701	−2.02010
$443$	−19.8878	−0.944899	−0.472449	−	0.881358i	$-0.656630\pi$
$443$	−19.8878	−0.944899	−0.472449	+	0.881358i	$0.656630\pi$
$444$	25.9168	1.22996
$445$	−78.4217	−3.71754
$446$	−31.9232	−1.51161
$447$	−20.7600	−0.981914
$448$	−1.89896	−0.0897172
$449$	−10.7474	−0.507200	−0.253600	−	0.967309i	$-0.581615\pi$
$449$	−10.7474	−0.507200	−0.253600	+	0.967309i	$0.581615\pi$
$450$	−37.3852	−1.76235
$451$	−43.5388	−2.05016
$452$	−2.08145	−0.0979031
$453$	−23.3399	−1.09660
$454$	−25.0708	−1.17663
$455$	−15.2979	−0.717178
$456$	4.47794	0.209699
$457$	25.2525	1.18126	0.590630	−	0.806942i	$-0.298879\pi$
$457$	25.2525	1.18126	0.590630	+	0.806942i	$0.298879\pi$
$458$	50.6205	2.36534
$459$	−20.0419	−0.935474
$460$	−18.3733	−0.856661
$461$	17.5848	0.819007	0.409504	−	0.912309i	$-0.365702\pi$
$461$	17.5848	0.819007	0.409504	+	0.912309i	$0.365702\pi$
$462$	−21.8224	−1.01527
$463$	−36.5263	−1.69752	−0.848761	−	0.528776i	$-0.822651\pi$
$463$	−36.5263	−1.69752	−0.848761	+	0.528776i	$0.822651\pi$
$464$	−14.3125	−0.664442
$465$	2.13964	0.0992235
$466$	2.02014	0.0935813
$467$	−7.55266	−0.349495	−0.174748	−	0.984613i	$-0.555911\pi$
$467$	−7.55266	−0.349495	−0.174748	+	0.984613i	$0.555911\pi$
$468$	7.33831	0.339214
$469$	0.0456908	0.00210981
$470$	34.9238	1.61091
$471$	−30.1971	−1.39141
$472$	0.259229	0.0119320
$473$	−1.44531	−0.0664553
$474$	42.6673	1.95977
$475$	22.1788	1.01764
$476$	8.55020	0.391898
$477$	−2.66060	−0.121821
$478$	−9.45857	−0.432625
$479$	39.2183	1.79193	0.895966	−	0.444123i	$-0.146485\pi$
$479$	39.2183	1.79193	0.895966	+	0.444123i	$0.146485\pi$
$480$	−58.5166	−2.67091
$481$	33.1255	1.51039
$482$	−36.9222	−1.68176
$483$	6.99460	0.318265
$484$	26.9906	1.22685
$485$	51.0527	2.31818
$486$	26.8777	1.21920
$487$	10.6747	0.483717	0.241859	−	0.970311i	$-0.422243\pi$
$487$	10.6747	0.483717	0.241859	+	0.970311i	$0.422243\pi$
$488$	2.72415	0.123317
$489$	−36.0790	−1.63155
$490$	7.76548	0.350809
$491$	−12.5081	−0.564483	−0.282242	−	0.959343i	$-0.591078\pi$
$491$	−12.5081	−0.564483	−0.282242	+	0.959343i	$0.591078\pi$
$492$	−21.7570	−0.980880
$493$	18.9941	0.855453
$494$	−10.9769	−0.493873
$495$	−37.2790	−1.67557
$496$	1.15176	0.0517155
$497$	7.95734	0.356936
$498$	−27.4770	−1.23127
$499$	11.1949	0.501154	0.250577	−	0.968097i	$-0.419380\pi$
$499$	11.1949	0.501154	0.250577	+	0.968097i	$0.419380\pi$
$500$	−45.9403	−2.05451
$501$	−23.4962	−1.04973
$502$	−36.8062	−1.64274
$503$	−39.3965	−1.75660	−0.878301	−	0.478109i	$-0.841322\pi$
$503$	−39.3965	−1.75660	−0.878301	+	0.478109i	$0.841322\pi$
$504$	1.94228	0.0865160
$505$	−34.9809	−1.55663
$506$	−33.4995	−1.48923
$507$	−0.291616	−0.0129511
$508$	−13.1588	−0.583828
$509$	−27.1255	−1.20232	−0.601159	−	0.799130i	$-0.705294\pi$
$509$	−27.1255	−1.20232	−0.601159	+	0.799130i	$0.705294\pi$
$510$	107.814	4.77407
$511$	3.04428	0.134671
$512$	−19.2673	−0.851502
$513$	−5.18004	−0.228705
$514$	18.0083	0.794314
$515$	50.3477	2.21858
$516$	−0.722241	−0.0317949
$517$	25.2539	1.11066
$518$	−16.8150	−0.738811
$519$	−21.0200	−0.922676
$520$	−19.0901	−0.837158
$521$	21.0533	0.922362	0.461181	−	0.887306i	$-0.347426\pi$
$521$	21.0533	0.922362	0.461181	+	0.887306i	$0.347426\pi$
$522$	−8.27514	−0.362193
$523$	37.9110	1.65773	0.828867	−	0.559446i	$-0.188986\pi$
$523$	37.9110	1.65773	0.828867	+	0.559446i	$0.188986\pi$
$524$	9.81513	0.428776
$525$	28.1620	1.22909
$526$	−53.3683	−2.32697
$527$	−1.52850	−0.0665825
$528$	−58.7458	−2.55658
$529$	−12.2626	−0.533157
$530$	−13.2744	−0.576602
$531$	0.323326	0.0140312
$532$	2.20990	0.0958111
$533$	−27.8086	−1.20452
$534$	−71.4509	−3.09198
$535$	13.8571	0.599094
$536$	0.0570172	0.00246277
$537$	−22.7248	−0.980646
$538$	−24.9116	−1.07401
$539$	5.61533	0.241869
$540$	17.2776	0.743511
$541$	−18.8947	−0.812348	−0.406174	−	0.913796i	$-0.633137\pi$
$541$	−18.8947	−0.812348	−0.406174	+	0.913796i	$0.633137\pi$
$542$	3.72370	0.159946
$543$	35.3305	1.51618
$544$	41.8026	1.79227
$545$	67.4147	2.88773
$546$	−13.9381	−0.596497
$547$	−33.9922	−1.45340	−0.726701	−	0.686954i	$-0.758947\pi$
$547$	−33.9922	−1.45340	−0.726701	+	0.686954i	$0.758947\pi$
$548$	0.763469	0.0326138
$549$	3.39773	0.145012
$550$	−134.878	−5.75120
$551$	4.90925	0.209141
$552$	8.72850	0.371509
$553$	−10.9791	−0.466881
$554$	2.66855	0.113376
$555$	−84.0916	−3.56949
$556$	12.5130	0.530672
$557$	45.1875	1.91466	0.957329	−	0.289001i	$-0.0933231\pi$
$557$	45.1875	1.91466	0.957329	+	0.289001i	$0.0933231\pi$
$558$	0.665919	0.0281906
$559$	−0.923130	−0.0390442
$560$	20.9047	0.883384
$561$	77.9616	3.29154
$562$	1.78652	0.0753599
$563$	7.47593	0.315073	0.157536	−	0.987513i	$-0.449645\pi$
$563$	7.47593	0.315073	0.157536	+	0.987513i	$0.449645\pi$
$564$	12.6197	0.531386
$565$	6.75362	0.284127
$566$	−31.7511	−1.33460
$567$	−11.2468	−0.472322
$568$	9.92990	0.416649
$569$	7.29330	0.305751	0.152875	−	0.988245i	$-0.451147\pi$
$569$	7.29330	0.305751	0.152875	+	0.988245i	$0.451147\pi$
$570$	27.8657	1.16716
$571$	−10.6713	−0.446581	−0.223290	−	0.974752i	$-0.571680\pi$
$571$	−10.6713	−0.446581	−0.223290	+	0.974752i	$0.571680\pi$
$572$	26.4750	1.10698
$573$	−8.30758	−0.347054
$574$	14.1161	0.589195
$575$	43.2315	1.80288
$576$	−2.95563	−0.123151
$577$	20.0993	0.836743	0.418372	−	0.908276i	$-0.362601\pi$
$577$	20.0993	0.836743	0.418372	+	0.908276i	$0.362601\pi$
$578$	−46.0690	−1.91622
$579$	−27.6638	−1.14967
$580$	−16.3744	−0.679911
$581$	7.07037	0.293328
$582$	46.5147	1.92810
$583$	−9.59888	−0.397545
$584$	3.79893	0.157201
$585$	−23.8104	−0.984440
$586$	−27.8902	−1.15213
$587$	−3.49847	−0.144397	−0.0721986	−	0.997390i	$-0.523002\pi$
$587$	−3.49847	−0.144397	−0.0721986	+	0.997390i	$0.523002\pi$
$588$	2.80606	0.115720
$589$	−0.395058	−0.0162781
$590$	1.61315	0.0664124
$591$	1.50261	0.0618092
$592$	−45.2661	−1.86043
$593$	33.0720	1.35810	0.679052	−	0.734090i	$-0.262391\pi$
$593$	33.0720	1.35810	0.679052	+	0.734090i	$0.262391\pi$
$594$	31.5017	1.29253
$595$	−27.7426	−1.13734
$596$	−12.7849	−0.523690
$597$	4.48172	0.183425
$598$	−21.3964	−0.874964
$599$	−0.987390	−0.0403437	−0.0201718	−	0.999797i	$-0.506421\pi$
$599$	−0.987390	−0.0403437	−0.0201718	+	0.999797i	$0.506421\pi$
$600$	35.1432	1.43471
$601$	−26.0016	−1.06063	−0.530313	−	0.847802i	$-0.677926\pi$
$601$	−26.0016	−1.06063	−0.530313	+	0.847802i	$0.677926\pi$
$602$	0.468596	0.0190986
$603$	0.0711154	0.00289604
$604$	−14.3737	−0.584859
$605$	−87.5759	−3.56046
$606$	−31.8716	−1.29469
$607$	−45.5582	−1.84915	−0.924576	−	0.380999i	$-0.875580\pi$
$607$	−45.5582	−1.84915	−0.924576	+	0.380999i	$0.875580\pi$
$608$	10.8044	0.438175
$609$	6.23362	0.252599
$610$	16.9521	0.686370
$611$	16.1299	0.652544
$612$	13.3079	0.537942
$613$	−37.6967	−1.52255	−0.761277	−	0.648427i	$-0.775427\pi$
$613$	−37.6967	−1.52255	−0.761277	+	0.648427i	$0.775427\pi$
$614$	−33.3473	−1.34579
$615$	70.5943	2.84664
$616$	7.00732	0.282333
$617$	2.09344	0.0842788	0.0421394	−	0.999112i	$-0.486583\pi$
$617$	2.09344	0.0842788	0.0421394	+	0.999112i	$0.486583\pi$
$618$	45.8724	1.84526
$619$	3.89000	0.156352	0.0781762	−	0.996940i	$-0.475090\pi$
$619$	3.89000	0.156352	0.0781762	+	0.996940i	$0.475090\pi$
$620$	1.31768	0.0529195
$621$	−10.0971	−0.405181
$622$	−54.0231	−2.16613
$623$	18.3857	0.736609
$624$	−37.5215	−1.50206
$625$	83.0950	3.32380
$626$	−28.8334	−1.15241
$627$	20.1501	0.804716
$628$	−18.5967	−0.742088
$629$	60.0727	2.39525
$630$	12.0866	0.481541
$631$	11.0173	0.438591	0.219296	−	0.975658i	$-0.429624\pi$
$631$	11.0173	0.438591	0.219296	+	0.975658i	$0.429624\pi$
$632$	−13.7008	−0.544988
$633$	26.6546	1.05943
$634$	44.5350	1.76871
$635$	42.6961	1.69434
$636$	−4.79670	−0.190201
$637$	3.58656	0.142105
$638$	−29.8549	−1.18197
$639$	12.3852	0.489951
$640$	40.0809	1.58434
$641$	20.8626	0.824021	0.412011	−	0.911179i	$-0.364827\pi$
$641$	20.8626	0.824021	0.412011	+	0.911179i	$0.364827\pi$
$642$	12.6254	0.498283
$643$	−22.9451	−0.904867	−0.452433	−	0.891798i	$-0.649444\pi$
$643$	−22.9451	−0.904867	−0.452433	+	0.891798i	$0.649444\pi$
$644$	4.30758	0.169742
$645$	2.34344	0.0922727
$646$	−19.9065	−0.783209
$647$	−21.9113	−0.861421	−0.430710	−	0.902490i	$-0.641737\pi$
$647$	−21.9113	−0.861421	−0.430710	+	0.902490i	$0.641737\pi$
$648$	−14.0348	−0.551339
$649$	1.16649	0.0457888
$650$	−86.1474	−3.37898
$651$	−0.501633	−0.0196606
$652$	−22.2190	−0.870164
$653$	23.8261	0.932388	0.466194	−	0.884683i	$-0.345625\pi$
$653$	23.8261	0.932388	0.466194	+	0.884683i	$0.345625\pi$
$654$	61.4223	2.40180
$655$	−31.8469	−1.24436
$656$	38.0006	1.48367
$657$	4.73827	0.184857
$658$	−8.18779	−0.319193
$659$	36.5573	1.42407	0.712034	−	0.702145i	$-0.247774\pi$
$659$	36.5573	1.42407	0.712034	+	0.702145i	$0.247774\pi$
$660$	−67.2089	−2.61610
$661$	0.293241	0.0114058	0.00570288	−	0.999984i	$-0.498185\pi$
$661$	0.293241	0.0114058	0.00570288	+	0.999984i	$0.498185\pi$
$662$	−18.7261	−0.727812
$663$	49.7947	1.93387
$664$	8.82305	0.342401
$665$	−7.17039	−0.278056
$666$	−26.1718	−1.01413
$667$	9.56922	0.370522
$668$	−14.4700	−0.559860
$669$	37.4288	1.44708
$670$	0.354811	0.0137076
$671$	12.2583	0.473226
$672$	13.7191	0.529224
$673$	−2.80263	−0.108033	−0.0540166	−	0.998540i	$-0.517202\pi$
$673$	−2.80263	−0.108033	−0.0540166	+	0.998540i	$0.517202\pi$
$674$	−45.1820	−1.74035
$675$	−40.6534	−1.56475
$676$	−0.179590	−0.00690731
$677$	−31.9674	−1.22861	−0.614304	−	0.789069i	$-0.710563\pi$
$677$	−31.9674	−1.22861	−0.614304	+	0.789069i	$0.710563\pi$
$678$	6.15331	0.236316
$679$	−11.9692	−0.459334
$680$	−34.6198	−1.32761
$681$	29.3946	1.12640
$682$	2.40249	0.0919961
$683$	38.9838	1.49167	0.745837	−	0.666128i	$-0.232050\pi$
$683$	38.9838	1.49167	0.745837	+	0.666128i	$0.232050\pi$
$684$	3.43959	0.131516
$685$	−2.47721	−0.0946493
$686$	−1.82060	−0.0695107
$687$	−59.3507	−2.26437
$688$	1.26146	0.0480928
$689$	−6.13088	−0.233568
$690$	54.3164	2.06779
$691$	27.9256	1.06234	0.531170	−	0.847266i	$-0.321753\pi$
$691$	27.9256	1.06234	0.531170	+	0.847266i	$0.321753\pi$
$692$	−12.9450	−0.492096
$693$	8.73997	0.332004
$694$	12.8300	0.487021
$695$	−40.6008	−1.54008
$696$	7.77888	0.294858
$697$	−50.4306	−1.91020
$698$	55.2917	2.09282
$699$	−2.36854	−0.0895866
$700$	17.3434	0.655520
$701$	−41.0731	−1.55131	−0.775655	−	0.631157i	$-0.782580\pi$
$701$	−41.0731	−1.55131	−0.775655	+	0.631157i	$0.782580\pi$
$702$	20.1204	0.759396
$703$	15.5265	0.585592
$704$	−10.6633	−0.401887
$705$	−40.9469	−1.54215
$706$	−42.8231	−1.61167
$707$	8.20118	0.308437
$708$	0.582913	0.0219072
$709$	14.9751	0.562400	0.281200	−	0.959649i	$-0.409268\pi$
$709$	14.9751	0.562400	0.281200	+	0.959649i	$0.409268\pi$
$710$	61.7926	2.31903
$711$	−17.0885	−0.640868
$712$	22.9434	0.859840
$713$	−0.770056	−0.0288388
$714$	−25.2766	−0.945955
$715$	−85.9029	−3.21259
$716$	−13.9949	−0.523014
$717$	11.0898	0.414158
$718$	−54.1315	−2.02017
$719$	−49.8307	−1.85837	−0.929186	−	0.369614i	$-0.879490\pi$
$719$	−49.8307	−1.85837	−0.929186	+	0.369614i	$0.879490\pi$
$720$	32.5371	1.21258
$721$	−11.8039	−0.439599
$722$	29.4463	1.09588
$723$	43.2900	1.60997
$724$	21.7581	0.808632
$725$	38.5282	1.43090
$726$	−79.7914	−2.96134
$727$	−44.1039	−1.63572	−0.817862	−	0.575414i	$-0.804841\pi$
$727$	−44.1039	−1.63572	−0.817862	+	0.575414i	$0.804841\pi$
$728$	4.47563	0.165878
$729$	2.22732	0.0824933
$730$	23.6403	0.874967
$731$	−1.67409	−0.0619183
$732$	6.12564	0.226410
$733$	−43.1951	−1.59545	−0.797723	−	0.603024i	$-0.793962\pi$
$733$	−43.1951	−1.59545	−0.797723	+	0.603024i	$0.793962\pi$
$734$	29.4932	1.08861
$735$	−9.10475	−0.335834
$736$	21.0601	0.776286
$737$	0.256569	0.00945085
$738$	21.9710	0.808764
$739$	−35.3058	−1.29874	−0.649372	−	0.760471i	$-0.724968\pi$
$739$	−35.3058	−1.29874	−0.649372	+	0.760471i	$0.724968\pi$
$740$	−51.7873	−1.90374
$741$	12.8700	0.472792
$742$	3.11214	0.114250
$743$	−21.6573	−0.794531	−0.397265	−	0.917704i	$-0.630041\pi$
$743$	−21.6573	−0.794531	−0.397265	+	0.917704i	$0.630041\pi$
$744$	−0.625983	−0.0229497
$745$	41.4829	1.51981
$746$	8.09773	0.296479
$747$	11.0047	0.402640
$748$	48.0122	1.75550
$749$	−3.24876	−0.118707
$750$	135.811	4.95913
$751$	−41.3517	−1.50894	−0.754472	−	0.656332i	$-0.772107\pi$
$751$	−41.3517	−1.50894	−0.754472	+	0.656332i	$0.772107\pi$
$752$	−22.0415	−0.803772
$753$	43.1540	1.57262
$754$	−19.0686	−0.694437
$755$	46.6381	1.69733
$756$	−4.05069	−0.147322
$757$	36.7061	1.33410	0.667052	−	0.745011i	$-0.267556\pi$
$757$	36.7061	1.33410	0.667052	+	0.745011i	$0.267556\pi$
$758$	34.4982	1.25303
$759$	39.2770	1.42566
$760$	−8.94787	−0.324573
$761$	41.9058	1.51908	0.759542	−	0.650458i	$-0.225423\pi$
$761$	41.9058	1.51908	0.759542	+	0.650458i	$0.225423\pi$
$762$	38.9009	1.40923
$763$	−15.8052	−0.572186
$764$	−5.11617	−0.185097
$765$	−43.1799	−1.56117
$766$	44.4561	1.60626
$767$	0.745048	0.0269021
$768$	44.6252	1.61027
$769$	23.8829	0.861239	0.430619	−	0.902534i	$-0.358295\pi$
$769$	23.8829	0.861239	0.430619	+	0.902534i	$0.358295\pi$
$770$	43.6057	1.57144
$771$	−21.1141	−0.760407
$772$	−17.0366	−0.613160
$773$	−38.7478	−1.39366	−0.696831	−	0.717235i	$-0.745407\pi$
$773$	−38.7478	−1.39366	−0.696831	+	0.717235i	$0.745407\pi$
$774$	0.729346	0.0262158
$775$	−3.10044	−0.111371
$776$	−14.9362	−0.536179
$777$	19.7150	0.707273
$778$	39.8920	1.43020
$779$	−13.0344	−0.467004
$780$	−42.9269	−1.53703
$781$	44.6831	1.59889
$782$	−38.8021	−1.38756
$783$	−8.99855	−0.321582
$784$	−4.90105	−0.175037
$785$	60.3401	2.15363
$786$	−29.0161	−1.03497
$787$	−44.7902	−1.59660	−0.798298	−	0.602262i	$-0.794266\pi$
$787$	−44.7902	−1.59660	−0.798298	+	0.602262i	$0.794266\pi$
$788$	0.925374	0.0329651
$789$	62.5725	2.22764
$790$	−85.2583	−3.03336
$791$	−1.58337	−0.0562981
$792$	10.9065	0.387547
$793$	7.82947	0.278033
$794$	−48.6450	−1.72635
$795$	15.5637	0.551988
$796$	2.76004	0.0978271
$797$	26.0812	0.923842	0.461921	−	0.886921i	$-0.347160\pi$
$797$	26.0812	0.923842	0.461921	+	0.886921i	$0.347160\pi$
$798$	−6.53303	−0.231267
$799$	29.2513	1.03484
$800$	84.7934	2.99790
$801$	28.6165	1.01111
$802$	2.19062	0.0773536
$803$	17.0946	0.603257
$804$	0.128211	0.00452166
$805$	−13.9767	−0.492614
$806$	1.53449	0.0540501
$807$	29.2079	1.02817
$808$	10.2342	0.360037
$809$	−4.53939	−0.159596	−0.0797982	−	0.996811i	$-0.525428\pi$
$809$	−4.53939	−0.159596	−0.0797982	+	0.996811i	$0.525428\pi$
$810$	−87.3369	−3.06871
$811$	37.3724	1.31232	0.656161	−	0.754621i	$-0.272179\pi$
$811$	37.3724	1.31232	0.656161	+	0.754621i	$0.272179\pi$
$812$	3.83894	0.134720
$813$	−4.36590	−0.153119
$814$	−94.4220	−3.30949
$815$	72.0935	2.52532
$816$	−68.0447	−2.38204
$817$	−0.432686	−0.0151378
$818$	−11.6650	−0.407856
$819$	5.58229	0.195061
$820$	43.4751	1.51821
$821$	11.0612	0.386039	0.193019	−	0.981195i	$-0.438172\pi$
$821$	11.0612	0.386039	0.193019	+	0.981195i	$0.438172\pi$
$822$	−2.25702	−0.0787225
$823$	4.79314	0.167078	0.0835392	−	0.996504i	$-0.473378\pi$
$823$	4.79314	0.167078	0.0835392	+	0.996504i	$0.473378\pi$
$824$	−14.7300	−0.513142
$825$	158.139	5.50570
$826$	−0.378199	−0.0131592
$827$	−3.83408	−0.133324	−0.0666620	−	0.997776i	$-0.521235\pi$
$827$	−3.83408	−0.133324	−0.0666620	+	0.997776i	$0.521235\pi$
$828$	6.70452	0.232998
$829$	6.48471	0.225223	0.112612	−	0.993639i	$-0.464078\pi$
$829$	6.48471	0.225223	0.112612	+	0.993639i	$0.464078\pi$
$830$	54.9048	1.90577
$831$	−3.12878	−0.108536
$832$	−6.81071	−0.236119
$833$	6.50418	0.225356
$834$	−36.9919	−1.28092
$835$	46.9504	1.62478
$836$	12.4093	0.429184
$837$	0.724133	0.0250297
$838$	41.6413	1.43848
$839$	3.63196	0.125389	0.0626946	−	0.998033i	$-0.480031\pi$
$839$	3.63196	0.125389	0.0626946	+	0.998033i	$0.480031\pi$
$840$	−11.3617	−0.392017
$841$	−20.4719	−0.705926
$842$	34.8457	1.20086
$843$	−2.09463	−0.0721430
$844$	16.4151	0.565031
$845$	0.582711	0.0200459
$846$	−12.7439	−0.438143
$847$	20.5319	0.705485
$848$	8.37788	0.287698
$849$	37.2270	1.27763
$850$	−156.227	−5.35855
$851$	30.2645	1.03745
$852$	22.3288	0.764971
$853$	52.4757	1.79673	0.898367	−	0.439245i	$-0.144754\pi$
$853$	52.4757	1.79673	0.898367	+	0.439245i	$0.144754\pi$
$854$	−3.97437	−0.136000
$855$	−11.1603	−0.381676
$856$	−4.05409	−0.138566
$857$	−49.3632	−1.68622	−0.843108	−	0.537744i	$-0.819277\pi$
$857$	−49.3632	−1.68622	−0.843108	+	0.537744i	$0.819277\pi$
$858$	−78.2672	−2.67200
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	1.44319	0.0492124
$861$	−16.5506	−0.564044
$862$	−39.6350	−1.34998
$863$	−2.40054	−0.0817154	−0.0408577	−	0.999165i	$-0.513009\pi$
$863$	−2.40054	−0.0817154	−0.0408577	+	0.999165i	$0.513009\pi$
$864$	−19.8042	−0.673752
$865$	42.0024	1.42813
$866$	18.1837	0.617908
$867$	54.0143	1.83442
$868$	−0.308928	−0.0104857
$869$	−61.6515	−2.09138
$870$	48.4071	1.64115
$871$	0.163873	0.00555262
$872$	−19.7231	−0.667910
$873$	−18.6294	−0.630509
$874$	−10.0288	−0.339231
$875$	−34.9470	−1.18142
$876$	8.54243	0.288622
$877$	46.4409	1.56820	0.784099	−	0.620636i	$-0.213126\pi$
$877$	46.4409	1.56820	0.784099	+	0.620636i	$0.213126\pi$
$878$	−28.6681	−0.967500
$879$	32.7002	1.10295
$880$	117.387	3.95710
$881$	−58.2585	−1.96278	−0.981389	−	0.192029i	$-0.938493\pi$
$881$	−58.2585	−1.96278	−0.981389	+	0.192029i	$0.938493\pi$
$882$	−2.83366	−0.0954144
$883$	−29.7742	−1.00198	−0.500991	−	0.865453i	$-0.667031\pi$
$883$	−29.7742	−1.00198	−0.500991	+	0.865453i	$0.667031\pi$
$884$	30.6658	1.03140
$885$	−1.89136	−0.0635774
$886$	36.2077	1.21642
$887$	−43.8807	−1.47337	−0.736684	−	0.676237i	$-0.763610\pi$
$887$	−43.8807	−1.47337	−0.736684	+	0.676237i	$0.763610\pi$
$888$	24.6022	0.825597
$889$	−10.0100	−0.335724
$890$	142.774	4.78580
$891$	−63.1546	−2.11576
$892$	23.0503	0.771780
$893$	7.56033	0.252997
$894$	37.7956	1.26407
$895$	45.4089	1.51785
$896$	−9.39685	−0.313927
$897$	25.0865	0.837614
$898$	19.5666	0.652946
$899$	−0.686278	−0.0228887
$900$	26.9941	0.899804
$901$	−11.1183	−0.370404
$902$	79.2666	2.63929
$903$	−0.549412	−0.0182833
$904$	−1.97587	−0.0657165
$905$	−70.5978	−2.34675
$906$	42.4925	1.41172
$907$	−54.9548	−1.82474	−0.912372	−	0.409363i	$-0.865751\pi$
$907$	−54.9548	−1.82474	−0.912372	+	0.409363i	$0.865751\pi$
$908$	18.1025	0.600752
$909$	12.7647	0.423379
$910$	27.8513	0.923263
$911$	−23.1905	−0.768337	−0.384168	−	0.923263i	$-0.625512\pi$
$911$	−23.1905	−0.768337	−0.384168	+	0.923263i	$0.625512\pi$
$912$	−17.5869	−0.582361
$913$	39.7025	1.31396
$914$	−45.9745	−1.52070
$915$	−19.8757	−0.657071
$916$	−36.5508	−1.20767
$917$	7.46642	0.246563
$918$	36.4881	1.20429
$919$	−49.7989	−1.64271	−0.821356	−	0.570416i	$-0.806782\pi$
$919$	−49.7989	−1.64271	−0.821356	+	0.570416i	$0.806782\pi$
$920$	−17.4414	−0.575025
$921$	39.0986	1.28834
$922$	−32.0149	−1.05435
$923$	28.5395	0.939388
$924$	15.7569	0.518366
$925$	121.853	4.00649
$926$	66.4997	2.18532
$927$	−18.3721	−0.603420
$928$	18.7689	0.616119
$929$	18.0642	0.592668	0.296334	−	0.955084i	$-0.404236\pi$
$929$	18.0642	0.592668	0.296334	+	0.955084i	$0.404236\pi$
$930$	−3.89542	−0.127736
$931$	1.68108	0.0550951
$932$	−1.45865	−0.0477798
$933$	63.3402	2.07366
$934$	13.7503	0.449925
$935$	−155.784	−5.09468
$936$	6.96609	0.227694
$937$	28.9035	0.944235	0.472118	−	0.881536i	$-0.343490\pi$
$937$	28.9035	0.944235	0.472118	+	0.881536i	$0.343490\pi$
$938$	−0.0831846	−0.00271607
$939$	33.8061	1.10322
$940$	−25.2169	−0.822484
$941$	19.0503	0.621023	0.310512	−	0.950570i	$-0.399500\pi$
$941$	19.0503	0.621023	0.310512	+	0.950570i	$0.399500\pi$
$942$	54.9766	1.79124
$943$	−25.4069	−0.827361
$944$	−1.01811	−0.0331367
$945$	13.1432	0.427548
$946$	2.63132	0.0855517
$947$	48.9196	1.58967	0.794837	−	0.606822i	$-0.207556\pi$
$947$	48.9196	1.58967	0.794837	+	0.606822i	$0.207556\pi$
$948$	−30.8081	−1.00060
$949$	10.9185	0.354429
$950$	−40.3787	−1.31006
$951$	−52.2157	−1.69321
$952$	8.11651	0.263058
$953$	2.60148	0.0842702	0.0421351	−	0.999112i	$-0.486584\pi$
$953$	2.60148	0.0842702	0.0421351	+	0.999112i	$0.486584\pi$
$954$	4.84389	0.156827
$955$	16.6003	0.537174
$956$	6.82961	0.220885
$957$	35.0038	1.13151
$958$	−71.4008	−2.30685
$959$	0.580775	0.0187542
$960$	17.2895	0.558017
$961$	−30.9448	−0.998219
$962$	−60.3081	−1.94441
$963$	−5.05652	−0.162944
$964$	26.6599	0.858656
$965$	55.2782	1.77947
$966$	−12.7343	−0.409721
$967$	25.6453	0.824698	0.412349	−	0.911026i	$-0.364709\pi$
$967$	25.6453	0.824698	0.412349	+	0.911026i	$0.364709\pi$
$968$	25.6216	0.823509
$969$	23.3396	0.749777
$970$	−92.9463	−2.98433
$971$	1.26687	0.0406558	0.0203279	−	0.999793i	$-0.493529\pi$
$971$	1.26687	0.0406558	0.0203279	+	0.999793i	$0.493529\pi$
$972$	−19.4072	−0.622485
$973$	9.51874	0.305157
$974$	−19.4343	−0.622716
$975$	101.005	3.23474
$976$	−10.6990	−0.342467
$977$	37.9536	1.21424	0.607121	−	0.794609i	$-0.292324\pi$
$977$	37.9536	1.21424	0.607121	+	0.794609i	$0.292324\pi$
$978$	65.6852	2.10038
$979$	103.242	3.29963
$980$	−5.60710	−0.179112
$981$	−24.6000	−0.785416
$982$	22.7722	0.726691
$983$	0.385613	0.0122992	0.00614958	−	0.999981i	$-0.498043\pi$
$983$	0.385613	0.0122992	0.00614958	+	0.999981i	$0.498043\pi$
$984$	−20.6534	−0.658406
$985$	−3.00254	−0.0956688
$986$	−34.5807	−1.10127
$987$	9.59989	0.305568
$988$	7.92591	0.252157
$989$	−0.843402	−0.0268186
$990$	67.8701	2.15705
$991$	−47.3175	−1.50309	−0.751544	−	0.659682i	$-0.770691\pi$
$991$	−47.3175	−1.50309	−0.751544	+	0.659682i	$0.770691\pi$
$992$	−1.51037	−0.0479544
$993$	21.9557	0.696744
$994$	−14.4871	−0.459503
$995$	−8.95544	−0.283906
$996$	19.8399	0.628651
$997$	−38.9599	−1.23387	−0.616936	−	0.787013i	$-0.711626\pi$
$997$	−38.9599	−1.23387	−0.616936	+	0.787013i	$0.711626\pi$
$998$	−20.3814	−0.645163
$999$	−28.4597	−0.900424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.19	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.19	✓	109	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.82060 q^{2} +2.13458 q^{3} +1.31457 q^{4} -4.26535 q^{5} -3.88622 q^{6} +1.00000 q^{7} +1.24789 q^{8} +1.55645 q^{9} +O(q^{10})\)	\(q-1.82060 q^{2} +2.13458 q^{3} +1.31457 q^{4} -4.26535 q^{5} -3.88622 q^{6} +1.00000 q^{7} +1.24789 q^{8} +1.55645 q^{9} +7.76548 q^{10} +5.61533 q^{11} +2.80606 q^{12} +3.58656 q^{13} -1.82060 q^{14} -9.10475 q^{15} -4.90105 q^{16} +6.50418 q^{17} -2.83366 q^{18} +1.68108 q^{19} -5.60710 q^{20} +2.13458 q^{21} -10.2232 q^{22} +3.27680 q^{23} +2.66373 q^{24} +13.1932 q^{25} -6.52967 q^{26} -3.08138 q^{27} +1.31457 q^{28} +2.92030 q^{29} +16.5761 q^{30} -0.235003 q^{31} +6.42704 q^{32} +11.9864 q^{33} -11.8415 q^{34} -4.26535 q^{35} +2.04606 q^{36} +9.23601 q^{37} -3.06056 q^{38} +7.65581 q^{39} -5.32269 q^{40} -7.75357 q^{41} -3.88622 q^{42} -0.257386 q^{43} +7.38174 q^{44} -6.63880 q^{45} -5.96572 q^{46} +4.49731 q^{47} -10.4617 q^{48} +1.00000 q^{49} -24.0195 q^{50} +13.8837 q^{51} +4.71478 q^{52} -1.70941 q^{53} +5.60995 q^{54} -23.9514 q^{55} +1.24789 q^{56} +3.58840 q^{57} -5.31668 q^{58} +0.207733 q^{59} -11.9688 q^{60} +2.18300 q^{61} +0.427845 q^{62} +1.55645 q^{63} -1.89896 q^{64} -15.2979 q^{65} -21.8224 q^{66} +0.0456908 q^{67} +8.55020 q^{68} +6.99460 q^{69} +7.76548 q^{70} +7.95734 q^{71} +1.94228 q^{72} +3.04428 q^{73} -16.8150 q^{74} +28.1620 q^{75} +2.20990 q^{76} +5.61533 q^{77} -13.9381 q^{78} -10.9791 q^{79} +20.9047 q^{80} -11.2468 q^{81} +14.1161 q^{82} +7.07037 q^{83} +2.80606 q^{84} -27.7426 q^{85} +0.468596 q^{86} +6.23362 q^{87} +7.00732 q^{88} +18.3857 q^{89} +12.0866 q^{90} +3.58656 q^{91} +4.30758 q^{92} -0.501633 q^{93} -8.18779 q^{94} -7.17039 q^{95} +13.7191 q^{96} -11.9692 q^{97} -1.82060 q^{98} +8.73997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9} + 15 q^{10} + 48 q^{11} + 72 q^{12} + 29 q^{13} + 19 q^{14} + 29 q^{15} + 115 q^{16} + 72 q^{17} + 33 q^{18} + 58 q^{19} + 88 q^{20} + 38 q^{21} + 4 q^{22} + 65 q^{23} + 46 q^{24} + 124 q^{25} + 49 q^{26} + 131 q^{27} + 111 q^{28} + 25 q^{29} + 2 q^{30} + 41 q^{31} + 75 q^{32} + 54 q^{33} + 23 q^{34} + 43 q^{35} + 111 q^{36} + 25 q^{37} + 54 q^{38} + 27 q^{39} + 30 q^{40} + 109 q^{41} + 14 q^{42} + 38 q^{43} + 68 q^{44} + 84 q^{45} - 9 q^{46} + 121 q^{47} + 106 q^{48} + 109 q^{49} + 14 q^{50} + 36 q^{51} + 38 q^{52} + 61 q^{53} + 31 q^{54} + 50 q^{55} + 48 q^{56} + 5 q^{57} - 20 q^{58} + 181 q^{59} + 25 q^{60} + 34 q^{61} + 75 q^{62} + 119 q^{63} + 96 q^{64} + 12 q^{65} + 19 q^{66} + 87 q^{67} + 150 q^{68} + 89 q^{69} + 15 q^{70} + 83 q^{71} + 65 q^{72} + 32 q^{73} - 19 q^{74} + 112 q^{75} + 84 q^{76} + 48 q^{77} - 34 q^{78} - 9 q^{79} + 137 q^{80} + 109 q^{81} - 19 q^{82} + 136 q^{83} + 72 q^{84} - 32 q^{85} - 24 q^{86} + 28 q^{87} - 24 q^{88} + 142 q^{89} + 19 q^{90} + 29 q^{91} + 96 q^{92} + 29 q^{93} + 9 q^{94} + 52 q^{95} + 88 q^{96} + 75 q^{97} + 19 q^{98} + 84 q^{99}+O(q^{100}) \) 109 * q + 19 * q^2 + 38 * q^3 + 111 * q^4 + 43 * q^5 + 14 * q^6 + 109 * q^7 + 48 * q^8 + 119 * q^9 + 15 * q^10 + 48 * q^11 + 72 * q^12 + 29 * q^13 + 19 * q^14 + 29 * q^15 + 115 * q^16 + 72 * q^17 + 33 * q^18 + 58 * q^19 + 88 * q^20 + 38 * q^21 + 4 * q^22 + 65 * q^23 + 46 * q^24 + 124 * q^25 + 49 * q^26 + 131 * q^27 + 111 * q^28 + 25 * q^29 + 2 * q^30 + 41 * q^31 + 75 * q^32 + 54 * q^33 + 23 * q^34 + 43 * q^35 + 111 * q^36 + 25 * q^37 + 54 * q^38 + 27 * q^39 + 30 * q^40 + 109 * q^41 + 14 * q^42 + 38 * q^43 + 68 * q^44 + 84 * q^45 - 9 * q^46 + 121 * q^47 + 106 * q^48 + 109 * q^49 + 14 * q^50 + 36 * q^51 + 38 * q^52 + 61 * q^53 + 31 * q^54 + 50 * q^55 + 48 * q^56 + 5 * q^57 - 20 * q^58 + 181 * q^59 + 25 * q^60 + 34 * q^61 + 75 * q^62 + 119 * q^63 + 96 * q^64 + 12 * q^65 + 19 * q^66 + 87 * q^67 + 150 * q^68 + 89 * q^69 + 15 * q^70 + 83 * q^71 + 65 * q^72 + 32 * q^73 - 19 * q^74 + 112 * q^75 + 84 * q^76 + 48 * q^77 - 34 * q^78 - 9 * q^79 + 137 * q^80 + 109 * q^81 - 19 * q^82 + 136 * q^83 + 72 * q^84 - 32 * q^85 - 24 * q^86 + 28 * q^87 - 24 * q^88 + 142 * q^89 + 19 * q^90 + 29 * q^91 + 96 * q^92 + 29 * q^93 + 9 * q^94 + 52 * q^95 + 88 * q^96 + 75 * q^97 + 19 * q^98 + 84 * q^99

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