LMFDB - Embedded newform 6013.2.a.e.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.53130 q^{2} +1.72523 q^{3} +4.40746 q^{4} -1.30306 q^{5} -4.36707 q^{6} +1.00000 q^{7} -6.09399 q^{8} -0.0235740 q^{9} +O(q^{10})$	\(q-2.53130 q^{2} +1.72523 q^{3} +4.40746 q^{4} -1.30306 q^{5} -4.36707 q^{6} +1.00000 q^{7} -6.09399 q^{8} -0.0235740 q^{9} +3.29843 q^{10} -0.721143 q^{11} +7.60389 q^{12} +0.841919 q^{13} -2.53130 q^{14} -2.24808 q^{15} +6.61079 q^{16} +7.21849 q^{17} +0.0596727 q^{18} -3.82019 q^{19} -5.74318 q^{20} +1.72523 q^{21} +1.82543 q^{22} +0.353318 q^{23} -10.5136 q^{24} -3.30204 q^{25} -2.13115 q^{26} -5.21637 q^{27} +4.40746 q^{28} +3.12979 q^{29} +5.69055 q^{30} +5.64160 q^{31} -4.54587 q^{32} -1.24414 q^{33} -18.2721 q^{34} -1.30306 q^{35} -0.103901 q^{36} +0.891975 q^{37} +9.67003 q^{38} +1.45251 q^{39} +7.94083 q^{40} +5.49875 q^{41} -4.36707 q^{42} -8.06585 q^{43} -3.17841 q^{44} +0.0307183 q^{45} -0.894353 q^{46} -3.08589 q^{47} +11.4051 q^{48} +1.00000 q^{49} +8.35844 q^{50} +12.4536 q^{51} +3.71072 q^{52} +9.23293 q^{53} +13.2042 q^{54} +0.939691 q^{55} -6.09399 q^{56} -6.59071 q^{57} -7.92242 q^{58} +2.08753 q^{59} -9.90832 q^{60} -5.39601 q^{61} -14.2806 q^{62} -0.0235740 q^{63} -1.71464 q^{64} -1.09707 q^{65} +3.14928 q^{66} +4.81531 q^{67} +31.8152 q^{68} +0.609556 q^{69} +3.29843 q^{70} +1.37071 q^{71} +0.143660 q^{72} +6.46357 q^{73} -2.25785 q^{74} -5.69678 q^{75} -16.8373 q^{76} -0.721143 q^{77} -3.67672 q^{78} +8.56828 q^{79} -8.61424 q^{80} -8.92872 q^{81} -13.9190 q^{82} +2.89335 q^{83} +7.60389 q^{84} -9.40611 q^{85} +20.4171 q^{86} +5.39961 q^{87} +4.39464 q^{88} -5.28524 q^{89} -0.0777571 q^{90} +0.841919 q^{91} +1.55724 q^{92} +9.73306 q^{93} +7.81131 q^{94} +4.97793 q^{95} -7.84267 q^{96} -13.9376 q^{97} -2.53130 q^{98} +0.0170002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.53130	−1.78990	−0.894948	−	0.446170i	$-0.852788\pi$
$2$	−2.53130	−1.78990	−0.894948	+	0.446170i	$0.852788\pi$
$3$	1.72523	0.996063	0.498032	−	0.867159i	$-0.334056\pi$
$3$	1.72523	0.996063	0.498032	+	0.867159i	$0.334056\pi$
$4$	4.40746	2.20373
$5$	−1.30306	−0.582745	−0.291373	−	0.956610i	$-0.594112\pi$
$5$	−1.30306	−0.582745	−0.291373	+	0.956610i	$0.594112\pi$
$6$	−4.36707	−1.78285
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−6.09399	−2.15455
$9$	−0.0235740	−0.00785799
$10$	3.29843	1.04305
$11$	−0.721143	−0.217433	−0.108716	−	0.994073i	$-0.534674\pi$
$11$	−0.721143	−0.217433	−0.108716	+	0.994073i	$0.534674\pi$
$12$	7.60389	2.19505
$13$	0.841919	0.233506	0.116753	−	0.993161i	$-0.462751\pi$
$13$	0.841919	0.233506	0.116753	+	0.993161i	$0.462751\pi$
$14$	−2.53130	−0.676517
$15$	−2.24808	−0.580451
$16$	6.61079	1.65270
$17$	7.21849	1.75074	0.875371	−	0.483453i	$-0.160617\pi$
$17$	7.21849	1.75074	0.875371	+	0.483453i	$0.160617\pi$
$18$	0.0596727	0.0140650
$19$	−3.82019	−0.876412	−0.438206	−	0.898875i	$-0.644386\pi$
$19$	−3.82019	−0.876412	−0.438206	+	0.898875i	$0.644386\pi$
$20$	−5.74318	−1.28421
$21$	1.72523	0.376477
$22$	1.82543	0.389182
$23$	0.353318	0.0736720	0.0368360	−	0.999321i	$-0.488272\pi$
$23$	0.353318	0.0736720	0.0368360	+	0.999321i	$0.488272\pi$
$24$	−10.5136	−2.14607
$25$	−3.30204	−0.660408
$26$	−2.13115	−0.417952
$27$	−5.21637	−1.00389
$28$	4.40746	0.832932
$29$	3.12979	0.581187	0.290593	−	0.956847i	$-0.406147\pi$
$29$	3.12979	0.581187	0.290593	+	0.956847i	$0.406147\pi$
$30$	5.69055	1.03895
$31$	5.64160	1.01326	0.506630	−	0.862163i	$-0.330891\pi$
$31$	5.64160	1.01326	0.506630	+	0.862163i	$0.330891\pi$
$32$	−4.54587	−0.803603
$33$	−1.24414	−0.216577
$34$	−18.2721	−3.13365
$35$	−1.30306	−0.220257
$36$	−0.103901	−0.0173169
$37$	0.891975	0.146640	0.0733199	−	0.997308i	$-0.476641\pi$
$37$	0.891975	0.146640	0.0733199	+	0.997308i	$0.476641\pi$
$38$	9.67003	1.56869
$39$	1.45251	0.232587
$40$	7.94083	1.25556
$41$	5.49875	0.858761	0.429380	−	0.903124i	$-0.358732\pi$
$41$	5.49875	0.858761	0.429380	+	0.903124i	$0.358732\pi$
$42$	−4.36707	−0.673854
$43$	−8.06585	−1.23003	−0.615015	−	0.788515i	$-0.710850\pi$
$43$	−8.06585	−1.23003	−0.615015	+	0.788515i	$0.710850\pi$
$44$	−3.17841	−0.479163
$45$	0.0307183	0.00457921
$46$	−0.894353	−0.131865
$47$	−3.08589	−0.450124	−0.225062	−	0.974344i	$-0.572258\pi$
$47$	−3.08589	−0.450124	−0.225062	+	0.974344i	$0.572258\pi$
$48$	11.4051	1.64619
$49$	1.00000	0.142857
$50$	8.35844	1.18206
$51$	12.4536	1.74385
$52$	3.71072	0.514585
$53$	9.23293	1.26824	0.634120	−	0.773235i	$-0.281362\pi$
$53$	9.23293	1.26824	0.634120	+	0.773235i	$0.281362\pi$
$54$	13.2042	1.79686
$55$	0.939691	0.126708
$56$	−6.09399	−0.814344
$57$	−6.59071	−0.872961
$58$	−7.92242	−1.04026
$59$	2.08753	0.271773	0.135887	−	0.990724i	$-0.456612\pi$
$59$	2.08753	0.271773	0.135887	+	0.990724i	$0.456612\pi$
$60$	−9.90832	−1.27916
$61$	−5.39601	−0.690888	−0.345444	−	0.938439i	$-0.612272\pi$
$61$	−5.39601	−0.690888	−0.345444	+	0.938439i	$0.612272\pi$
$62$	−14.2806	−1.81363
$63$	−0.0235740	−0.00297004
$64$	−1.71464	−0.214330
$65$	−1.09707	−0.136075
$66$	3.14928	0.387650
$67$	4.81531	0.588284	0.294142	−	0.955762i	$-0.404966\pi$
$67$	4.81531	0.588284	0.294142	+	0.955762i	$0.404966\pi$
$68$	31.8152	3.85816
$69$	0.609556	0.0733819
$70$	3.29843	0.394237
$71$	1.37071	0.162674	0.0813368	−	0.996687i	$-0.474081\pi$
$71$	1.37071	0.162674	0.0813368	+	0.996687i	$0.474081\pi$
$72$	0.143660	0.0169305
$73$	6.46357	0.756503	0.378252	−	0.925703i	$-0.376525\pi$
$73$	6.46357	0.756503	0.378252	+	0.925703i	$0.376525\pi$
$74$	−2.25785	−0.262470
$75$	−5.69678	−0.657808
$76$	−16.8373	−1.93137
$77$	−0.721143	−0.0821818
$78$	−3.67672	−0.416307
$79$	8.56828	0.964007	0.482003	−	0.876169i	$-0.339909\pi$
$79$	8.56828	0.964007	0.482003	+	0.876169i	$0.339909\pi$
$80$	−8.61424	−0.963101
$81$	−8.92872	−0.992080
$82$	−13.9190	−1.53709
$83$	2.89335	0.317586	0.158793	−	0.987312i	$-0.449240\pi$
$83$	2.89335	0.317586	0.158793	+	0.987312i	$0.449240\pi$
$84$	7.60389	0.829653
$85$	−9.40611	−1.02024
$86$	20.4171	2.20163
$87$	5.39961	0.578899
$88$	4.39464	0.468470
$89$	−5.28524	−0.560235	−0.280117	−	0.959966i	$-0.590373\pi$
$89$	−5.28524	−0.560235	−0.280117	+	0.959966i	$0.590373\pi$
$90$	−0.0777571	−0.00819631
$91$	0.841919	0.0882571
$92$	1.55724	0.162353
$93$	9.73306	1.00927
$94$	7.81131	0.805675
$95$	4.97793	0.510725
$96$	−7.84267	−0.800440
$97$	−13.9376	−1.41515	−0.707576	−	0.706637i	$-0.750211\pi$
$97$	−13.9376	−1.41515	−0.707576	+	0.706637i	$0.750211\pi$
$98$	−2.53130	−0.255700
$99$	0.0170002	0.00170859
$100$	−14.5536	−1.45536
$101$	10.3686	1.03171	0.515855	−	0.856676i	$-0.327474\pi$
$101$	10.3686	1.03171	0.515855	+	0.856676i	$0.327474\pi$
$102$	−31.5237	−3.12131
$103$	−15.6779	−1.54479	−0.772397	−	0.635140i	$-0.780942\pi$
$103$	−15.6779	−1.54479	−0.772397	+	0.635140i	$0.780942\pi$
$104$	−5.13065	−0.503102
$105$	−2.24808	−0.219390
$106$	−23.3713	−2.27002
$107$	−17.4175	−1.68381	−0.841907	−	0.539622i	$-0.818567\pi$
$107$	−17.4175	−1.68381	−0.841907	+	0.539622i	$0.818567\pi$
$108$	−22.9909	−2.21230
$109$	3.01641	0.288920	0.144460	−	0.989511i	$-0.453856\pi$
$109$	3.01641	0.288920	0.144460	+	0.989511i	$0.453856\pi$
$110$	−2.37864	−0.226794
$111$	1.53886	0.146062
$112$	6.61079	0.624661
$113$	5.61041	0.527783	0.263891	−	0.964552i	$-0.414994\pi$
$113$	5.61041	0.527783	0.263891	+	0.964552i	$0.414994\pi$
$114$	16.6830	1.56251
$115$	−0.460394	−0.0429320
$116$	13.7944	1.28078
$117$	−0.0198474	−0.00183489
$118$	−5.28416	−0.486446
$119$	7.21849	0.661718
$120$	13.6998	1.25061
$121$	−10.4800	−0.952723
$122$	13.6589	1.23662
$123$	9.48662	0.855380
$124$	24.8651	2.23295
$125$	10.8180	0.967595
$126$	0.0596727	0.00531607
$127$	3.02753	0.268650	0.134325	−	0.990937i	$-0.457113\pi$
$127$	3.02753	0.268650	0.134325	+	0.990937i	$0.457113\pi$
$128$	13.4320	1.18723
$129$	−13.9155	−1.22519
$130$	2.77701	0.243560
$131$	10.3355	0.903016	0.451508	−	0.892267i	$-0.350886\pi$
$131$	10.3355	0.903016	0.451508	+	0.892267i	$0.350886\pi$
$132$	−5.48349	−0.477277
$133$	−3.82019	−0.331252
$134$	−12.1890	−1.05297
$135$	6.79723	0.585012
$136$	−43.9894	−3.77206
$137$	10.6889	0.913214	0.456607	−	0.889668i	$-0.349064\pi$
$137$	10.6889	0.913214	0.456607	+	0.889668i	$0.349064\pi$
$138$	−1.54297	−0.131346
$139$	22.0592	1.87104	0.935519	−	0.353277i	$-0.114933\pi$
$139$	22.0592	1.87104	0.935519	+	0.353277i	$0.114933\pi$
$140$	−5.74318	−0.485387
$141$	−5.32388	−0.448352
$142$	−3.46968	−0.291169
$143$	−0.607144	−0.0507719
$144$	−0.155843	−0.0129869
$145$	−4.07829	−0.338684
$146$	−16.3612	−1.35406
$147$	1.72523	0.142295
$148$	3.93134	0.323154
$149$	−4.94614	−0.405204	−0.202602	−	0.979261i	$-0.564940\pi$
$149$	−4.94614	−0.405204	−0.202602	+	0.979261i	$0.564940\pi$
$150$	14.4202	1.17741
$151$	5.57117	0.453375	0.226688	−	0.973968i	$-0.427210\pi$
$151$	5.57117	0.453375	0.226688	+	0.973968i	$0.427210\pi$
$152$	23.2802	1.88827
$153$	−0.170169	−0.0137573
$154$	1.82543	0.147097
$155$	−7.35133	−0.590473
$156$	6.40186	0.512559
$157$	1.46140	0.116633	0.0583163	−	0.998298i	$-0.481427\pi$
$157$	1.46140	0.116633	0.0583163	+	0.998298i	$0.481427\pi$
$158$	−21.6889	−1.72547
$159$	15.9289	1.26325
$160$	5.92353	0.468296
$161$	0.353318	0.0278454
$162$	22.6012	1.77572
$163$	14.8377	1.16218	0.581091	−	0.813839i	$-0.302626\pi$
$163$	14.8377	1.16218	0.581091	+	0.813839i	$0.302626\pi$
$164$	24.2355	1.89248
$165$	1.62119	0.126209
$166$	−7.32392	−0.568447
$167$	20.2138	1.56419	0.782094	−	0.623161i	$-0.214152\pi$
$167$	20.2138	1.56419	0.782094	+	0.623161i	$0.214152\pi$
$168$	−10.5136	−0.811138
$169$	−12.2912	−0.945475
$170$	23.8097	1.82612
$171$	0.0900571	0.00688684
$172$	−35.5499	−2.71066
$173$	−19.3943	−1.47452	−0.737259	−	0.675610i	$-0.763880\pi$
$173$	−19.3943	−1.47452	−0.737259	+	0.675610i	$0.763880\pi$
$174$	−13.6680	−1.03617
$175$	−3.30204	−0.249611
$176$	−4.76732	−0.359350
$177$	3.60147	0.270703
$178$	13.3785	1.00276
$179$	16.3504	1.22209	0.611043	−	0.791598i	$-0.290750\pi$
$179$	16.3504	1.22209	0.611043	+	0.791598i	$0.290750\pi$
$180$	0.135390	0.0100913
$181$	12.6634	0.941266	0.470633	−	0.882329i	$-0.344026\pi$
$181$	12.6634	0.941266	0.470633	+	0.882329i	$0.344026\pi$
$182$	−2.13115	−0.157971
$183$	−9.30937	−0.688168
$184$	−2.15312	−0.158730
$185$	−1.16230	−0.0854536
$186$	−24.6373	−1.80649
$187$	−5.20556	−0.380668
$188$	−13.6009	−0.991951
$189$	−5.21637	−0.379435
$190$	−12.6006	−0.914145
$191$	−10.1547	−0.734766	−0.367383	−	0.930070i	$-0.619746\pi$
$191$	−10.1547	−0.734766	−0.367383	+	0.930070i	$0.619746\pi$
$192$	−2.95815	−0.213486
$193$	8.35507	0.601411	0.300706	−	0.953717i	$-0.402778\pi$
$193$	8.35507	0.601411	0.300706	+	0.953717i	$0.402778\pi$
$194$	35.2803	2.53298
$195$	−1.89270	−0.135539
$196$	4.40746	0.314819
$197$	−11.5488	−0.822816	−0.411408	−	0.911451i	$-0.634963\pi$
$197$	−11.5488	−0.822816	−0.411408	+	0.911451i	$0.634963\pi$
$198$	−0.0430326	−0.00305819
$199$	−12.1635	−0.862250	−0.431125	−	0.902292i	$-0.641883\pi$
$199$	−12.1635	−0.862250	−0.431125	+	0.902292i	$0.641883\pi$
$200$	20.1226	1.42288
$201$	8.30753	0.585968
$202$	−26.2459	−1.84665
$203$	3.12979	0.219668
$204$	54.8886	3.84297
$205$	−7.16519	−0.500439
$206$	39.6855	2.76502
$207$	−0.00832912	−0.000578914 0
$208$	5.56575	0.385915
$209$	2.75490	0.190561
$210$	5.69055	0.392685
$211$	−4.71501	−0.324595	−0.162297	−	0.986742i	$-0.551890\pi$
$211$	−4.71501	−0.324595	−0.162297	+	0.986742i	$0.551890\pi$
$212$	40.6938	2.79486
$213$	2.36480	0.162033
$214$	44.0889	3.01385
$215$	10.5103	0.716795
$216$	31.7885	2.16293
$217$	5.64160	0.382977
$218$	−7.63543	−0.517136
$219$	11.1512	0.753525
$220$	4.14165	0.279230
$221$	6.07738	0.408809
$222$	−3.89532	−0.261437
$223$	10.8126	0.724066	0.362033	−	0.932165i	$-0.382083\pi$
$223$	10.8126	0.724066	0.362033	+	0.932165i	$0.382083\pi$
$224$	−4.54587	−0.303733
$225$	0.0778422	0.00518948
$226$	−14.2016	−0.944677
$227$	14.3050	0.949457	0.474729	−	0.880132i	$-0.342546\pi$
$227$	14.3050	0.949457	0.474729	+	0.880132i	$0.342546\pi$
$228$	−29.0483	−1.92377
$229$	21.2236	1.40249	0.701246	−	0.712920i	$-0.252628\pi$
$229$	21.2236	1.40249	0.701246	+	0.712920i	$0.252628\pi$
$230$	1.16539	0.0768438
$231$	−1.24414	−0.0818583
$232$	−19.0729	−1.25220
$233$	22.4807	1.47276	0.736380	−	0.676568i	$-0.236534\pi$
$233$	22.4807	1.47276	0.736380	+	0.676568i	$0.236534\pi$
$234$	0.0502396	0.00328427
$235$	4.02110	0.262307
$236$	9.20070	0.598915
$237$	14.7823	0.960212
$238$	−18.2721	−1.18441
$239$	25.7090	1.66298	0.831489	−	0.555541i	$-0.187489\pi$
$239$	25.7090	1.66298	0.831489	+	0.555541i	$0.187489\pi$
$240$	−14.8616	−0.959310
$241$	−29.5350	−1.90252	−0.951259	−	0.308392i	$-0.900209\pi$
$241$	−29.5350	−1.90252	−0.951259	+	0.308392i	$0.900209\pi$
$242$	26.5279	1.70528
$243$	0.244982	0.0157156
$244$	−23.7827	−1.52253
$245$	−1.30306	−0.0832493
$246$	−24.0135	−1.53104
$247$	−3.21629	−0.204648
$248$	−34.3799	−2.18312
$249$	4.99170	0.316336
$250$	−27.3837	−1.73190
$251$	−16.3953	−1.03486	−0.517431	−	0.855725i	$-0.673112\pi$
$251$	−16.3953	−1.03486	−0.517431	+	0.855725i	$0.673112\pi$
$252$	−0.103901	−0.00654517
$253$	−0.254793	−0.0160187
$254$	−7.66358	−0.480856
$255$	−16.2277	−1.01622
$256$	−30.5711	−1.91069
$257$	29.9290	1.86692	0.933459	−	0.358683i	$-0.116774\pi$
$257$	29.9290	1.86692	0.933459	+	0.358683i	$0.116774\pi$
$258$	35.2242	2.19296
$259$	0.891975	0.0554246
$260$	−4.83529	−0.299872
$261$	−0.0737815	−0.00456696
$262$	−26.1622	−1.61631
$263$	24.2003	1.49226	0.746128	−	0.665802i	$-0.231911\pi$
$263$	24.2003	1.49226	0.746128	+	0.665802i	$0.231911\pi$
$264$	7.58177	0.466626
$265$	−12.0310	−0.739061
$266$	9.67003	0.592908
$267$	−9.11827	−0.558029
$268$	21.2233	1.29642
$269$	−17.0955	−1.04233	−0.521165	−	0.853456i	$-0.674502\pi$
$269$	−17.0955	−1.04233	−0.521165	+	0.853456i	$0.674502\pi$
$270$	−17.2058	−1.04711
$271$	29.5525	1.79519	0.897593	−	0.440824i	$-0.145314\pi$
$271$	29.5525	1.79519	0.897593	+	0.440824i	$0.145314\pi$
$272$	47.7199	2.89344
$273$	1.45251	0.0879096
$274$	−27.0568	−1.63456
$275$	2.38124	0.143594
$276$	2.68659	0.161714
$277$	−4.45754	−0.267828	−0.133914	−	0.990993i	$-0.542755\pi$
$277$	−4.45754	−0.267828	−0.133914	+	0.990993i	$0.542755\pi$
$278$	−55.8384	−3.34896
$279$	−0.132995	−0.00796220
$280$	7.94083	0.474555
$281$	16.2924	0.971921	0.485961	−	0.873981i	$-0.338470\pi$
$281$	16.2924	0.971921	0.485961	+	0.873981i	$0.338470\pi$
$282$	13.4763	0.802503
$283$	−7.23941	−0.430338	−0.215169	−	0.976577i	$-0.569030\pi$
$283$	−7.23941	−0.430338	−0.215169	+	0.976577i	$0.569030\pi$
$284$	6.04136	0.358489
$285$	8.58809	0.508714
$286$	1.53686	0.0908765
$287$	5.49875	0.324581
$288$	0.107164	0.00631471
$289$	35.1066	2.06509
$290$	10.3234	0.606209
$291$	−24.0457	−1.40958
$292$	28.4879	1.66713
$293$	−17.3033	−1.01087	−0.505435	−	0.862865i	$-0.668668\pi$
$293$	−17.3033	−1.01087	−0.505435	+	0.862865i	$0.668668\pi$
$294$	−4.36707	−0.254693
$295$	−2.72017	−0.158375
$296$	−5.43569	−0.315943
$297$	3.76175	0.218279
$298$	12.5201	0.725272
$299$	0.297465	0.0172029
$300$	−25.1083	−1.44963
$301$	−8.06585	−0.464908
$302$	−14.1023	−0.811495
$303$	17.8882	1.02765
$304$	−25.2545	−1.44844
$305$	7.03132	0.402612
$306$	0.430747	0.0246242
$307$	−7.64360	−0.436243	−0.218122	−	0.975922i	$-0.569993\pi$
$307$	−7.64360	−0.436243	−0.218122	+	0.975922i	$0.569993\pi$
$308$	−3.17841	−0.181107
$309$	−27.0481	−1.53871
$310$	18.6084	1.05689
$311$	21.0490	1.19358	0.596789	−	0.802398i	$-0.296443\pi$
$311$	21.0490	1.19358	0.596789	+	0.802398i	$0.296443\pi$
$312$	−8.85156	−0.501121
$313$	−25.1947	−1.42409	−0.712043	−	0.702135i	$-0.752230\pi$
$313$	−25.1947	−1.42409	−0.712043	+	0.702135i	$0.752230\pi$
$314$	−3.69924	−0.208760
$315$	0.0307183	0.00173078
$316$	37.7643	2.12441
$317$	23.8691	1.34062	0.670312	−	0.742080i	$-0.266160\pi$
$317$	23.8691	1.34062	0.670312	+	0.742080i	$0.266160\pi$
$318$	−40.3209	−2.26108
$319$	−2.25702	−0.126369
$320$	2.23427	0.124900
$321$	−30.0493	−1.67719
$322$	−0.894353	−0.0498404
$323$	−27.5760	−1.53437
$324$	−39.3530	−2.18628
$325$	−2.78005	−0.154209
$326$	−37.5587	−2.08018
$327$	5.20401	0.287782
$328$	−33.5094	−1.85024
$329$	−3.08589	−0.170131
$330$	−4.10370	−0.225901
$331$	26.3966	1.45089	0.725444	−	0.688282i	$-0.241635\pi$
$331$	26.3966	1.45089	0.725444	+	0.688282i	$0.241635\pi$
$332$	12.7523	0.699875
$333$	−0.0210274	−0.00115229
$334$	−51.1670	−2.79973
$335$	−6.27463	−0.342820
$336$	11.4051	0.622201
$337$	−17.0247	−0.927396	−0.463698	−	0.885993i	$-0.653478\pi$
$337$	−17.0247	−0.927396	−0.463698	+	0.885993i	$0.653478\pi$
$338$	31.1126	1.69230
$339$	9.67926	0.525705
$340$	−41.4571	−2.24833
$341$	−4.06840	−0.220316
$342$	−0.227961	−0.0123267
$343$	1.00000	0.0539949
$344$	49.1533	2.65017
$345$	−0.794287	−0.0427630
$346$	49.0926	2.63924
$347$	−4.94361	−0.265387	−0.132693	−	0.991157i	$-0.542363\pi$
$347$	−4.94361	−0.265387	−0.132693	+	0.991157i	$0.542363\pi$
$348$	23.7986	1.27574
$349$	17.3781	0.930229	0.465114	−	0.885251i	$-0.346013\pi$
$349$	17.3781	0.930229	0.465114	+	0.885251i	$0.346013\pi$
$350$	8.35844	0.446777
$351$	−4.39176	−0.234415
$352$	3.27822	0.174730
$353$	−1.25769	−0.0669400	−0.0334700	−	0.999440i	$-0.510656\pi$
$353$	−1.25769	−0.0669400	−0.0334700	+	0.999440i	$0.510656\pi$
$354$	−9.11640	−0.484531
$355$	−1.78612	−0.0947972
$356$	−23.2945	−1.23461
$357$	12.4536	0.659113
$358$	−41.3877	−2.18741
$359$	−31.2615	−1.64992	−0.824958	−	0.565193i	$-0.808802\pi$
$359$	−31.2615	−1.64992	−0.824958	+	0.565193i	$0.808802\pi$
$360$	−0.187197	−0.00986615
$361$	−4.40615	−0.231903
$362$	−32.0549	−1.68477
$363$	−18.0804	−0.948972
$364$	3.71072	0.194495
$365$	−8.42241	−0.440849
$366$	23.5648	1.23175
$367$	−24.2682	−1.26679	−0.633395	−	0.773828i	$-0.718339\pi$
$367$	−24.2682	−1.26679	−0.633395	+	0.773828i	$0.718339\pi$
$368$	2.33571	0.121757
$369$	−0.129627	−0.00674814
$370$	2.94211	0.152953
$371$	9.23293	0.479350
$372$	42.8981	2.22416
$373$	23.2261	1.20260	0.601302	−	0.799022i	$-0.294649\pi$
$373$	23.2261	1.20260	0.601302	+	0.799022i	$0.294649\pi$
$374$	13.1768	0.681357
$375$	18.6636	0.963786
$376$	18.8054	0.969815
$377$	2.63503	0.135711
$378$	13.2042	0.679149
$379$	33.1981	1.70527	0.852635	−	0.522507i	$-0.175003\pi$
$379$	33.1981	1.70527	0.852635	+	0.522507i	$0.175003\pi$
$380$	21.9400	1.12550
$381$	5.22320	0.267592
$382$	25.7045	1.31516
$383$	−1.70574	−0.0871592	−0.0435796	−	0.999050i	$-0.513876\pi$
$383$	−1.70574	−0.0871592	−0.0435796	+	0.999050i	$0.513876\pi$
$384$	23.1733	1.18256
$385$	0.939691	0.0478911
$386$	−21.1492	−1.07646
$387$	0.190144	0.00966558
$388$	−61.4296	−3.11861
$389$	−1.99761	−0.101283	−0.0506414	−	0.998717i	$-0.516127\pi$
$389$	−1.99761	−0.101283	−0.0506414	+	0.998717i	$0.516127\pi$
$390$	4.79098	0.242601
$391$	2.55042	0.128981
$392$	−6.09399	−0.307793
$393$	17.8311	0.899461
$394$	29.2334	1.47276
$395$	−11.1650	−0.561770
$396$	0.0749277	0.00376526
$397$	−20.7005	−1.03893	−0.519465	−	0.854492i	$-0.673869\pi$
$397$	−20.7005	−1.03893	−0.519465	+	0.854492i	$0.673869\pi$
$398$	30.7895	1.54334
$399$	−6.59071	−0.329948
$400$	−21.8291	−1.09145
$401$	8.40382	0.419667	0.209833	−	0.977737i	$-0.432708\pi$
$401$	8.40382	0.419667	0.209833	+	0.977737i	$0.432708\pi$
$402$	−21.0288	−1.04882
$403$	4.74977	0.236603
$404$	45.6990	2.27361
$405$	11.6346	0.578130
$406$	−7.92242	−0.393183
$407$	−0.643241	−0.0318843
$408$	−75.8920	−3.75721
$409$	−37.1213	−1.83553	−0.917765	−	0.397125i	$-0.870008\pi$
$409$	−37.1213	−1.83553	−0.917765	+	0.397125i	$0.870008\pi$
$410$	18.1372	0.895734
$411$	18.4408	0.909619
$412$	−69.0999	−3.40431
$413$	2.08753	0.102721
$414$	0.0210835	0.00103620
$415$	−3.77020	−0.185072
$416$	−3.82725	−0.187646
$417$	38.0572	1.86367
$418$	−6.97347	−0.341084
$419$	17.3588	0.848032	0.424016	−	0.905655i	$-0.360620\pi$
$419$	17.3588	0.848032	0.424016	+	0.905655i	$0.360620\pi$
$420$	−9.90832	−0.483476
$421$	6.83181	0.332962	0.166481	−	0.986045i	$-0.446760\pi$
$421$	6.83181	0.332962	0.166481	+	0.986045i	$0.446760\pi$
$422$	11.9351	0.580991
$423$	0.0727468	0.00353707
$424$	−56.2654	−2.73249
$425$	−23.8357	−1.15620
$426$	−5.98600	−0.290023
$427$	−5.39601	−0.261131
$428$	−76.7670	−3.71067
$429$	−1.04746	−0.0505720
$430$	−26.6046	−1.28299
$431$	−23.6055	−1.13704	−0.568518	−	0.822671i	$-0.692483\pi$
$431$	−23.6055	−1.13704	−0.568518	+	0.822671i	$0.692483\pi$
$432$	−34.4843	−1.65913
$433$	18.9735	0.911808	0.455904	−	0.890029i	$-0.349316\pi$
$433$	18.9735	0.911808	0.455904	+	0.890029i	$0.349316\pi$
$434$	−14.2806	−0.685488
$435$	−7.03600	−0.337351
$436$	13.2947	0.636701
$437$	−1.34974	−0.0645670
$438$	−28.2269	−1.34873
$439$	−10.5105	−0.501638	−0.250819	−	0.968034i	$-0.580700\pi$
$439$	−10.5105	−0.501638	−0.250819	+	0.968034i	$0.580700\pi$
$440$	−5.72647	−0.272999
$441$	−0.0235740	−0.00112257
$442$	−15.3837	−0.731726
$443$	4.48793	0.213228	0.106614	−	0.994300i	$-0.465999\pi$
$443$	4.48793	0.213228	0.106614	+	0.994300i	$0.465999\pi$
$444$	6.78248	0.321882
$445$	6.88698	0.326474
$446$	−27.3699	−1.29600
$447$	−8.53324	−0.403608
$448$	−1.71464	−0.0810090
$449$	−31.2102	−1.47290	−0.736449	−	0.676493i	$-0.763499\pi$
$449$	−31.2102	−1.47290	−0.736449	+	0.676493i	$0.763499\pi$
$450$	−0.197042	−0.00928863
$451$	−3.96538	−0.186723
$452$	24.7276	1.16309
$453$	9.61156	0.451590
$454$	−36.2102	−1.69943
$455$	−1.09707	−0.0514314
$456$	40.1638	1.88084
$457$	−6.27089	−0.293340	−0.146670	−	0.989185i	$-0.546856\pi$
$457$	−6.27089	−0.293340	−0.146670	+	0.989185i	$0.546856\pi$
$458$	−53.7231	−2.51032
$459$	−37.6543	−1.75755
$460$	−2.02917	−0.0946105
$461$	11.6575	0.542944	0.271472	−	0.962446i	$-0.412490\pi$
$461$	11.6575	0.542944	0.271472	+	0.962446i	$0.412490\pi$
$462$	3.14928	0.146518
$463$	12.6268	0.586818	0.293409	−	0.955987i	$-0.405210\pi$
$463$	12.6268	0.586818	0.293409	+	0.955987i	$0.405210\pi$
$464$	20.6903	0.960525
$465$	−12.6828	−0.588148
$466$	−56.9053	−2.63609
$467$	−40.3467	−1.86702	−0.933510	−	0.358550i	$-0.883271\pi$
$467$	−40.3467	−1.86702	−0.933510	+	0.358550i	$0.883271\pi$
$468$	−0.0874766	−0.00404361
$469$	4.81531	0.222350
$470$	−10.1786	−0.469503
$471$	2.52126	0.116173
$472$	−12.7214	−0.585550
$473$	5.81663	0.267449
$474$	−37.4183	−1.71868
$475$	12.6144	0.578789
$476$	31.8152	1.45825
$477$	−0.217657	−0.00996582
$478$	−65.0771	−2.97656
$479$	38.8981	1.77730	0.888650	−	0.458586i	$-0.151644\pi$
$479$	38.8981	1.77730	0.888650	+	0.458586i	$0.151644\pi$
$480$	10.2195	0.466452
$481$	0.750971	0.0342413
$482$	74.7619	3.40531
$483$	0.609556	0.0277358
$484$	−46.1900	−2.09954
$485$	18.1615	0.824673
$486$	−0.620123	−0.0281293
$487$	8.00409	0.362700	0.181350	−	0.983419i	$-0.441953\pi$
$487$	8.00409	0.362700	0.181350	+	0.983419i	$0.441953\pi$
$488$	32.8833	1.48856
$489$	25.5985	1.15761
$490$	3.29843	0.149008
$491$	8.27877	0.373616	0.186808	−	0.982396i	$-0.440186\pi$
$491$	8.27877	0.373616	0.186808	+	0.982396i	$0.440186\pi$
$492$	41.8119	1.88503
$493$	22.5923	1.01751
$494$	8.14138	0.366298
$495$	−0.0221523	−0.000995670 0
$496$	37.2954	1.67461
$497$	1.37071	0.0614848
$498$	−12.6355	−0.566209
$499$	27.0555	1.21117	0.605586	−	0.795780i	$-0.292939\pi$
$499$	27.0555	1.21117	0.605586	+	0.795780i	$0.292939\pi$
$500$	47.6801	2.13232
$501$	34.8734	1.55803
$502$	41.5013	1.85230
$503$	−0.897705	−0.0400267	−0.0200133	−	0.999800i	$-0.506371\pi$
$503$	−0.897705	−0.0400267	−0.0200133	+	0.999800i	$0.506371\pi$
$504$	0.143660	0.00639911
$505$	−13.5108	−0.601224
$506$	0.644956	0.0286718
$507$	−21.2051	−0.941753
$508$	13.3437	0.592032
$509$	7.86666	0.348684	0.174342	−	0.984685i	$-0.444220\pi$
$509$	7.86666	0.348684	0.174342	+	0.984685i	$0.444220\pi$
$510$	41.0772	1.81893
$511$	6.46357	0.285931
$512$	50.5204	2.23271
$513$	19.9275	0.879821
$514$	−75.7591	−3.34159
$515$	20.4293	0.900221
$516$	−61.3319	−2.69998
$517$	2.22537	0.0978716
$518$	−2.25785	−0.0992043
$519$	−33.4596	−1.46871
$520$	6.68554	0.293180
$521$	−17.6662	−0.773969	−0.386985	−	0.922086i	$-0.626483\pi$
$521$	−17.6662	−0.773969	−0.386985	+	0.922086i	$0.626483\pi$
$522$	0.186763	0.00817439
$523$	−39.5190	−1.72805	−0.864023	−	0.503452i	$-0.832063\pi$
$523$	−39.5190	−1.72805	−0.864023	+	0.503452i	$0.832063\pi$
$524$	45.5533	1.99000
$525$	−5.69678	−0.248628
$526$	−61.2582	−2.67099
$527$	40.7238	1.77396
$528$	−8.22473	−0.357936
$529$	−22.8752	−0.994572
$530$	30.4541	1.32284
$531$	−0.0492114	−0.00213559
$532$	−16.8373	−0.729991
$533$	4.62950	0.200526
$534$	23.0811	0.998815
$535$	22.6960	0.981235
$536$	−29.3445	−1.26749
$537$	28.2082	1.21727
$538$	43.2738	1.86566
$539$	−0.721143	−0.0310618
$540$	29.9585	1.28921
$541$	24.4309	1.05037	0.525184	−	0.850989i	$-0.323996\pi$
$541$	24.4309	1.05037	0.525184	+	0.850989i	$0.323996\pi$
$542$	−74.8061	−3.21320
$543$	21.8474	0.937561
$544$	−32.8143	−1.40690
$545$	−3.93056	−0.168367
$546$	−3.67672	−0.157349
$547$	37.7618	1.61458	0.807289	−	0.590156i	$-0.200934\pi$
$547$	37.7618	1.61458	0.807289	+	0.590156i	$0.200934\pi$
$548$	47.1109	2.01248
$549$	0.127205	0.00542900
$550$	−6.02763	−0.257019
$551$	−11.9564	−0.509359
$552$	−3.71463	−0.158105
$553$	8.56828	0.364360
$554$	11.2834	0.479384
$555$	−2.00523	−0.0851172
$556$	97.2251	4.12326
$557$	11.4267	0.484164	0.242082	−	0.970256i	$-0.422170\pi$
$557$	11.4267	0.484164	0.242082	+	0.970256i	$0.422170\pi$
$558$	0.336649	0.0142515
$559$	−6.79079	−0.287220
$560$	−8.61424	−0.364018
$561$	−8.98080	−0.379170
$562$	−41.2408	−1.73964
$563$	2.97078	0.125203	0.0626017	−	0.998039i	$-0.480060\pi$
$563$	2.97078	0.125203	0.0626017	+	0.998039i	$0.480060\pi$
$564$	−23.4648	−0.988046
$565$	−7.31069	−0.307563
$566$	18.3251	0.770261
$567$	−8.92872	−0.374971
$568$	−8.35311	−0.350489
$569$	−34.4412	−1.44385	−0.721924	−	0.691972i	$-0.756742\pi$
$569$	−34.4412	−1.44385	−0.721924	+	0.691972i	$0.756742\pi$
$570$	−21.7390	−0.910546
$571$	13.1595	0.550707	0.275353	−	0.961343i	$-0.411205\pi$
$571$	13.1595	0.550707	0.275353	+	0.961343i	$0.411205\pi$
$572$	−2.67596	−0.111888
$573$	−17.5192	−0.731874
$574$	−13.9190	−0.580966
$575$	−1.16667	−0.0486535
$576$	0.0404208	0.00168420
$577$	−17.7916	−0.740673	−0.370336	−	0.928898i	$-0.620758\pi$
$577$	−17.7916	−0.740673	−0.370336	+	0.928898i	$0.620758\pi$
$578$	−88.8652	−3.69631
$579$	14.4144	0.599044
$580$	−17.9749	−0.746368
$581$	2.89335	0.120036
$582$	60.8667	2.52300
$583$	−6.65826	−0.275757
$584$	−39.3889	−1.62993
$585$	0.0258623	0.00106927
$586$	43.7998	1.80935
$587$	31.6925	1.30809	0.654044	−	0.756456i	$-0.273071\pi$
$587$	31.6925	1.30809	0.654044	+	0.756456i	$0.273071\pi$
$588$	7.60389	0.313579
$589$	−21.5520	−0.888033
$590$	6.88556	0.283474
$591$	−19.9243	−0.819577
$592$	5.89665	0.242351
$593$	29.0118	1.19137	0.595686	−	0.803217i	$-0.296880\pi$
$593$	29.0118	1.19137	0.595686	+	0.803217i	$0.296880\pi$
$594$	−9.52209	−0.390696
$595$	−9.40611	−0.385613
$596$	−21.7999	−0.892959
$597$	−20.9849	−0.858855
$598$	−0.752973	−0.0307914
$599$	−38.7779	−1.58442	−0.792211	−	0.610247i	$-0.791070\pi$
$599$	−38.7779	−1.58442	−0.792211	+	0.610247i	$0.791070\pi$
$600$	34.7162	1.41728
$601$	10.7421	0.438181	0.219090	−	0.975705i	$-0.429691\pi$
$601$	10.7421	0.438181	0.219090	+	0.975705i	$0.429691\pi$
$602$	20.4171	0.832137
$603$	−0.113516	−0.00462273
$604$	24.5547	0.999116
$605$	13.6560	0.555195
$606$	−45.2803	−1.83938
$607$	40.7250	1.65298	0.826489	−	0.562952i	$-0.190335\pi$
$607$	40.7250	1.65298	0.826489	+	0.562952i	$0.190335\pi$
$608$	17.3661	0.704287
$609$	5.39961	0.218803
$610$	−17.7983	−0.720634
$611$	−2.59807	−0.105107
$612$	−0.750011	−0.0303174
$613$	−30.1012	−1.21578	−0.607889	−	0.794022i	$-0.707983\pi$
$613$	−30.1012	−1.21578	−0.607889	+	0.794022i	$0.707983\pi$
$614$	19.3482	0.780831
$615$	−12.3616	−0.498469
$616$	4.39464	0.177065
$617$	32.6160	1.31307	0.656534	−	0.754296i	$-0.272022\pi$
$617$	32.6160	1.31307	0.656534	+	0.754296i	$0.272022\pi$
$618$	68.4667	2.75414
$619$	22.3052	0.896521	0.448261	−	0.893903i	$-0.352044\pi$
$619$	22.3052	0.896521	0.448261	+	0.893903i	$0.352044\pi$
$620$	−32.4007	−1.30124
$621$	−1.84304	−0.0739586
$622$	−53.2812	−2.13638
$623$	−5.28524	−0.211749
$624$	9.60220	0.384396
$625$	2.41366	0.0965462
$626$	63.7752	2.54897
$627$	4.75285	0.189810
$628$	6.44107	0.257027
$629$	6.43871	0.256728
$630$	−0.0777571	−0.00309792
$631$	−15.8887	−0.632517	−0.316259	−	0.948673i	$-0.602427\pi$
$631$	−15.8887	−0.632517	−0.316259	+	0.948673i	$0.602427\pi$
$632$	−52.2150	−2.07700
$633$	−8.13448	−0.323317
$634$	−60.4198	−2.39958
$635$	−3.94505	−0.156555
$636$	70.2062	2.78386
$637$	0.841919	0.0333580
$638$	5.71319	0.226187
$639$	−0.0323131	−0.00127829
$640$	−17.5027	−0.691854
$641$	10.7468	0.424473	0.212237	−	0.977218i	$-0.431925\pi$
$641$	10.7468	0.424473	0.212237	+	0.977218i	$0.431925\pi$
$642$	76.0636	3.00199
$643$	19.4609	0.767465	0.383732	−	0.923444i	$-0.374638\pi$
$643$	19.4609	0.767465	0.383732	+	0.923444i	$0.374638\pi$
$644$	1.55724	0.0613637
$645$	18.1327	0.713973
$646$	69.8030	2.74636
$647$	50.1856	1.97300	0.986500	−	0.163760i	$-0.0523622\pi$
$647$	50.1856	1.97300	0.986500	+	0.163760i	$0.0523622\pi$
$648$	54.4116	2.13749
$649$	−1.50541	−0.0590924
$650$	7.03713	0.276019
$651$	9.73306	0.381469
$652$	65.3967	2.56113
$653$	10.3850	0.406395	0.203197	−	0.979138i	$-0.434867\pi$
$653$	10.3850	0.406395	0.203197	+	0.979138i	$0.434867\pi$
$654$	−13.1729	−0.515100
$655$	−13.4677	−0.526229
$656$	36.3511	1.41927
$657$	−0.152372	−0.00594460
$658$	7.81131	0.304516
$659$	0.140891	0.00548833	0.00274416	−	0.999996i	$-0.499127\pi$
$659$	0.140891	0.00548833	0.00274416	+	0.999996i	$0.499127\pi$
$660$	7.14531	0.278131
$661$	−3.30832	−0.128679	−0.0643395	−	0.997928i	$-0.520494\pi$
$661$	−3.30832	−0.128679	−0.0643395	+	0.997928i	$0.520494\pi$
$662$	−66.8176	−2.59694
$663$	10.4849	0.407200
$664$	−17.6321	−0.684256
$665$	4.97793	0.193036
$666$	0.0532266	0.00206249
$667$	1.10581	0.0428172
$668$	89.0913	3.44705
$669$	18.6543	0.721216
$670$	15.8829	0.613612
$671$	3.89129	0.150222
$672$	−7.84267	−0.302538
$673$	18.0308	0.695037	0.347519	−	0.937673i	$-0.387024\pi$
$673$	18.0308	0.695037	0.347519	+	0.937673i	$0.387024\pi$
$674$	43.0946	1.65994
$675$	17.2246	0.662977
$676$	−54.1729	−2.08357
$677$	1.73646	0.0667374	0.0333687	−	0.999443i	$-0.489376\pi$
$677$	1.73646	0.0667374	0.0333687	+	0.999443i	$0.489376\pi$
$678$	−24.5011	−0.940958
$679$	−13.9376	−0.534877
$680$	57.3208	2.19815
$681$	24.6795	0.945720
$682$	10.2983	0.394343
$683$	20.6257	0.789221	0.394610	−	0.918849i	$-0.370880\pi$
$683$	20.6257	0.789221	0.394610	+	0.918849i	$0.370880\pi$
$684$	0.396923	0.0151767
$685$	−13.9283	−0.532172
$686$	−2.53130	−0.0966453
$687$	36.6156	1.39697
$688$	−53.3216	−2.03287
$689$	7.77338	0.296142
$690$	2.01058	0.0765413
$691$	4.11720	0.156626	0.0783128	−	0.996929i	$-0.475047\pi$
$691$	4.11720	0.156626	0.0783128	+	0.996929i	$0.475047\pi$
$692$	−85.4794	−3.24944
$693$	0.0170002	0.000645784 0
$694$	12.5137	0.475015
$695$	−28.7444	−1.09034
$696$	−32.9052	−1.24727
$697$	39.6927	1.50347
$698$	−43.9891	−1.66501
$699$	38.7844	1.46696
$700$	−14.5536	−0.550075
$701$	24.5896	0.928735	0.464368	−	0.885642i	$-0.346282\pi$
$701$	24.5896	0.928735	0.464368	+	0.885642i	$0.346282\pi$
$702$	11.1168	0.419578
$703$	−3.40751	−0.128517
$704$	1.23650	0.0466023
$705$	6.93733	0.261275
$706$	3.18358	0.119816
$707$	10.3686	0.389950
$708$	15.8734	0.596557
$709$	22.9289	0.861114	0.430557	−	0.902563i	$-0.358317\pi$
$709$	22.9289	0.861114	0.430557	+	0.902563i	$0.358317\pi$
$710$	4.52119	0.169677
$711$	−0.201988	−0.00757516
$712$	32.2083	1.20706
$713$	1.99328	0.0746489
$714$	−31.5237	−1.17974
$715$	0.791144	0.0295871
$716$	72.0637	2.69315
$717$	44.3540	1.65643
$718$	79.1320	2.95318
$719$	27.3228	1.01897	0.509485	−	0.860480i	$-0.329836\pi$
$719$	27.3228	1.01897	0.509485	+	0.860480i	$0.329836\pi$
$720$	0.203072	0.00756804
$721$	−15.6779	−0.583877
$722$	11.1533	0.415082
$723$	−50.9548	−1.89503
$724$	55.8136	2.07430
$725$	−10.3347	−0.383820
$726$	45.7667	1.69856
$727$	6.59392	0.244555	0.122277	−	0.992496i	$-0.460980\pi$
$727$	6.59392	0.244555	0.122277	+	0.992496i	$0.460980\pi$
$728$	−5.13065	−0.190155
$729$	27.2088	1.00773
$730$	21.3196	0.789074
$731$	−58.2233	−2.15347
$732$	−41.0307	−1.51654
$733$	−10.6378	−0.392914	−0.196457	−	0.980512i	$-0.562944\pi$
$733$	−10.6378	−0.392914	−0.196457	+	0.980512i	$0.562944\pi$
$734$	61.4300	2.26742
$735$	−2.24808	−0.0829216
$736$	−1.60614	−0.0592030
$737$	−3.47253	−0.127912
$738$	0.328126	0.0120785
$739$	20.2306	0.744194	0.372097	−	0.928194i	$-0.378639\pi$
$739$	20.2306	0.744194	0.372097	+	0.928194i	$0.378639\pi$
$740$	−5.12277	−0.188317
$741$	−5.54885	−0.203842
$742$	−23.3713	−0.857986
$743$	−32.8780	−1.20618	−0.603088	−	0.797675i	$-0.706063\pi$
$743$	−32.8780	−1.20618	−0.603088	+	0.797675i	$0.706063\pi$
$744$	−59.3132	−2.17453
$745$	6.44511	0.236131
$746$	−58.7922	−2.15254
$747$	−0.0682078	−0.00249559
$748$	−22.9433	−0.838890
$749$	−17.4175	−0.636422
$750$	−47.2432	−1.72508
$751$	28.1426	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$751$	28.1426	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$752$	−20.4002	−0.743918
$753$	−28.2857	−1.03079
$754$	−6.67003	−0.242908
$755$	−7.25956	−0.264202
$756$	−22.9909	−0.836172
$757$	11.7670	0.427678	0.213839	−	0.976869i	$-0.431403\pi$
$757$	11.7670	0.427678	0.213839	+	0.976869i	$0.431403\pi$
$758$	−84.0341	−3.05226
$759$	−0.439577	−0.0159556
$760$	−30.3355	−1.10038
$761$	−25.4656	−0.923128	−0.461564	−	0.887107i	$-0.652712\pi$
$761$	−25.4656	−0.923128	−0.461564	+	0.887107i	$0.652712\pi$
$762$	−13.2215	−0.478963
$763$	3.01641	0.109201
$764$	−44.7563	−1.61923
$765$	0.221740	0.00801701
$766$	4.31773	0.156006
$767$	1.75753	0.0634608
$768$	−52.7422	−1.90317
$769$	−26.6857	−0.962310	−0.481155	−	0.876635i	$-0.659783\pi$
$769$	−26.6857	−0.962310	−0.481155	+	0.876635i	$0.659783\pi$
$770$	−2.37864	−0.0857201
$771$	51.6344	1.85957
$772$	36.8247	1.32535
$773$	51.7495	1.86130	0.930650	−	0.365912i	$-0.119243\pi$
$773$	51.7495	1.86130	0.930650	+	0.365912i	$0.119243\pi$
$774$	−0.481311	−0.0173004
$775$	−18.6288	−0.669165
$776$	84.9359	3.04902
$777$	1.53886	0.0552064
$778$	5.05654	0.181286
$779$	−21.0063	−0.752628
$780$	−8.34200	−0.298691
$781$	−0.988479	−0.0353705
$782$	−6.45588	−0.230862
$783$	−16.3261	−0.583448
$784$	6.61079	0.236099
$785$	−1.90429	−0.0679671
$786$	−45.1359	−1.60994
$787$	15.2801	0.544676	0.272338	−	0.962202i	$-0.412203\pi$
$787$	15.2801	0.544676	0.272338	+	0.962202i	$0.412203\pi$
$788$	−50.9008	−1.81327
$789$	41.7512	1.48638
$790$	28.2618	1.00551
$791$	5.61041	0.199483
$792$	−0.103599	−0.00368124
$793$	−4.54300	−0.161327
$794$	52.3992	1.85958
$795$	−20.7563	−0.736152
$796$	−53.6103	−1.90017
$797$	12.2004	0.432159	0.216080	−	0.976376i	$-0.430673\pi$
$797$	12.2004	0.432159	0.216080	+	0.976376i	$0.430673\pi$
$798$	16.6830	0.590574
$799$	−22.2755	−0.788050
$800$	15.0106	0.530706
$801$	0.124594	0.00440232
$802$	−21.2726	−0.751160
$803$	−4.66115	−0.164489
$804$	36.6151	1.29131
$805$	−0.460394	−0.0162268
$806$	−12.0231	−0.423495
$807$	−29.4937	−1.03823
$808$	−63.1859	−2.22287
$809$	10.9534	0.385101	0.192550	−	0.981287i	$-0.438324\pi$
$809$	10.9534	0.385101	0.192550	+	0.981287i	$0.438324\pi$
$810$	−29.4507	−1.03479
$811$	36.0109	1.26451	0.632257	−	0.774759i	$-0.282129\pi$
$811$	36.0109	1.26451	0.632257	+	0.774759i	$0.282129\pi$
$812$	13.7944	0.484089
$813$	50.9849	1.78812
$814$	1.62823	0.0570696
$815$	−19.3344	−0.677256
$816$	82.3279	2.88205
$817$	30.8131	1.07801
$818$	93.9649	3.28541
$819$	−0.0198474	−0.000693524 0
$820$	−31.5803	−1.10283
$821$	12.3969	0.432656	0.216328	−	0.976321i	$-0.430592\pi$
$821$	12.3969	0.432656	0.216328	+	0.976321i	$0.430592\pi$
$822$	−46.6792	−1.62812
$823$	−17.9161	−0.624515	−0.312258	−	0.949997i	$-0.601085\pi$
$823$	−17.9161	−0.624515	−0.312258	+	0.949997i	$0.601085\pi$
$824$	95.5413	3.32834
$825$	4.10819	0.143029
$826$	−5.28416	−0.183859
$827$	−31.9229	−1.11007	−0.555034	−	0.831828i	$-0.687295\pi$
$827$	−31.9229	−1.11007	−0.555034	+	0.831828i	$0.687295\pi$
$828$	−0.0367103	−0.00127577
$829$	−18.1689	−0.631031	−0.315515	−	0.948920i	$-0.602177\pi$
$829$	−18.1689	−0.631031	−0.315515	+	0.948920i	$0.602177\pi$
$830$	9.54350	0.331260
$831$	−7.69029	−0.266773
$832$	−1.44359	−0.0500474
$833$	7.21849	0.250106
$834$	−96.3342	−3.33578
$835$	−26.3397	−0.911523
$836$	12.1421	0.419944
$837$	−29.4286	−1.01720
$838$	−43.9402	−1.51789
$839$	−39.2360	−1.35458	−0.677289	−	0.735717i	$-0.736845\pi$
$839$	−39.2360	−1.35458	−0.677289	+	0.735717i	$0.736845\pi$
$840$	13.6998	0.472687
$841$	−19.2044	−0.662222
$842$	−17.2933	−0.595968
$843$	28.1081	0.968095
$844$	−20.7812	−0.715319
$845$	16.0161	0.550971
$846$	−0.184144	−0.00633099
$847$	−10.4800	−0.360095
$848$	61.0369	2.09602
$849$	−12.4897	−0.428644
$850$	60.3353	2.06948
$851$	0.315151	0.0108032
$852$	10.4227	0.357077
$853$	3.92968	0.134550	0.0672748	−	0.997734i	$-0.478570\pi$
$853$	3.92968	0.134550	0.0672748	+	0.997734i	$0.478570\pi$
$854$	13.6589	0.467398
$855$	−0.117350	−0.00401327
$856$	106.142	3.62787
$857$	−4.29732	−0.146794	−0.0733968	−	0.997303i	$-0.523384\pi$
$857$	−4.29732	−0.146794	−0.0733968	+	0.997303i	$0.523384\pi$
$858$	2.65144	0.0905187
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	46.3236	1.57962
$861$	9.48662	0.323303
$862$	59.7525	2.03518
$863$	35.6307	1.21288	0.606441	−	0.795129i	$-0.292597\pi$
$863$	35.6307	1.21288	0.606441	+	0.795129i	$0.292597\pi$
$864$	23.7129	0.806729
$865$	25.2719	0.859269
$866$	−48.0275	−1.63204
$867$	60.5670	2.05696
$868$	24.8651	0.843977
$869$	−6.17895	−0.209607
$870$	17.8102	0.603823
$871$	4.05410	0.137368
$872$	−18.3820	−0.622492
$873$	0.328566	0.0111203
$874$	3.41660	0.115568
$875$	10.8180	0.365717
$876$	49.1483	1.66057
$877$	−10.0328	−0.338785	−0.169392	−	0.985549i	$-0.554181\pi$
$877$	−10.0328	−0.338785	−0.169392	+	0.985549i	$0.554181\pi$
$878$	26.6052	0.897881
$879$	−29.8522	−1.00689
$880$	6.21210	0.209410
$881$	13.5260	0.455703	0.227851	−	0.973696i	$-0.426830\pi$
$881$	13.5260	0.455703	0.227851	+	0.973696i	$0.426830\pi$
$882$	0.0596727	0.00200929
$883$	35.9934	1.21127	0.605637	−	0.795741i	$-0.292919\pi$
$883$	35.9934	1.21127	0.605637	+	0.795741i	$0.292919\pi$
$884$	26.7858	0.900905
$885$	−4.69293	−0.157751
$886$	−11.3603	−0.381656
$887$	−54.7566	−1.83855	−0.919273	−	0.393620i	$-0.871222\pi$
$887$	−54.7566	−1.83855	−0.919273	+	0.393620i	$0.871222\pi$
$888$	−9.37783	−0.314699
$889$	3.02753	0.101540
$890$	−17.4330	−0.584355
$891$	6.43888	0.215711
$892$	47.6562	1.59565
$893$	11.7887	0.394494
$894$	21.6002	0.722417
$895$	−21.3055	−0.712165
$896$	13.4320	0.448731
$897$	0.513197	0.0171351
$898$	79.0021	2.63634
$899$	17.6570	0.588894
$900$	0.343086	0.0114362
$901$	66.6478	2.22036
$902$	10.0376	0.334214
$903$	−13.9155	−0.463078
$904$	−34.1898	−1.13714
$905$	−16.5012	−0.548519
$906$	−24.3297	−0.808300
$907$	4.93892	0.163994	0.0819971	−	0.996633i	$-0.473870\pi$
$907$	4.93892	0.163994	0.0819971	+	0.996633i	$0.473870\pi$
$908$	63.0488	2.09235
$909$	−0.244428	−0.00810717
$910$	2.77701	0.0920569
$911$	−39.7087	−1.31561	−0.657803	−	0.753190i	$-0.728514\pi$
$911$	−39.7087	−1.31561	−0.657803	+	0.753190i	$0.728514\pi$
$912$	−43.5698	−1.44274
$913$	−2.08652	−0.0690537
$914$	15.8735	0.525048
$915$	12.1307	0.401027
$916$	93.5420	3.09071
$917$	10.3355	0.341308
$918$	95.3142	3.14584
$919$	−34.2537	−1.12992	−0.564962	−	0.825117i	$-0.691109\pi$
$919$	−34.2537	−1.12992	−0.564962	+	0.825117i	$0.691109\pi$
$920$	2.80564	0.0924992
$921$	−13.1870	−0.434526
$922$	−29.5086	−0.971813
$923$	1.15403	0.0379853
$924$	−5.48349	−0.180394
$925$	−2.94534	−0.0968420
$926$	−31.9622	−1.05034
$927$	0.369592	0.0121390
$928$	−14.2276	−0.467044
$929$	35.0451	1.14979	0.574896	−	0.818226i	$-0.305042\pi$
$929$	35.0451	1.14979	0.574896	+	0.818226i	$0.305042\pi$
$930$	32.1038	1.05272
$931$	−3.82019	−0.125202
$932$	99.0828	3.24557
$933$	36.3144	1.18888
$934$	102.129	3.34177
$935$	6.78315	0.221833
$936$	0.120950	0.00395337
$937$	61.0833	1.99550	0.997752	−	0.0670201i	$-0.0213492\pi$
$937$	61.0833	1.99550	0.997752	+	0.0670201i	$0.0213492\pi$
$938$	−12.1890	−0.397984
$939$	−43.4666	−1.41848
$940$	17.7228	0.578055
$941$	0.806963	0.0263063	0.0131531	−	0.999913i	$-0.495813\pi$
$941$	0.806963	0.0263063	0.0131531	+	0.999913i	$0.495813\pi$
$942$	−6.38205	−0.207938
$943$	1.94281	0.0632666
$944$	13.8002	0.449159
$945$	6.79723	0.221114
$946$	−14.7236	−0.478706
$947$	−4.22403	−0.137263	−0.0686313	−	0.997642i	$-0.521863\pi$
$947$	−4.22403	−0.137263	−0.0686313	+	0.997642i	$0.521863\pi$
$948$	65.1523	2.11605
$949$	5.44180	0.176648
$950$	−31.9308	−1.03597
$951$	41.1798	1.33535
$952$	−43.9894	−1.42571
$953$	21.7187	0.703538	0.351769	−	0.936087i	$-0.385580\pi$
$953$	21.7187	0.703538	0.351769	+	0.936087i	$0.385580\pi$
$954$	0.550954	0.0178378
$955$	13.2321	0.428182
$956$	113.311	3.66475
$957$	−3.89389	−0.125872
$958$	−98.4627	−3.18118
$959$	10.6889	0.345163
$960$	3.85464	0.124408
$961$	0.827611	0.0266971
$962$	−1.90093	−0.0612884
$963$	0.410600	0.0132314
$964$	−130.174	−4.19264
$965$	−10.8871	−0.350470
$966$	−1.54297	−0.0496441
$967$	14.4520	0.464746	0.232373	−	0.972627i	$-0.425351\pi$
$967$	14.4520	0.464746	0.232373	+	0.972627i	$0.425351\pi$
$968$	63.8648	2.05269
$969$	−47.5750	−1.52833
$970$	−45.9723	−1.47608
$971$	17.4354	0.559528	0.279764	−	0.960069i	$-0.409744\pi$
$971$	17.4354	0.559528	0.279764	+	0.960069i	$0.409744\pi$
$972$	1.07975	0.0346330
$973$	22.0592	0.707186
$974$	−20.2607	−0.649196
$975$	−4.79623	−0.153602
$976$	−35.6719	−1.14183
$977$	−0.920220	−0.0294404	−0.0147202	−	0.999892i	$-0.504686\pi$
$977$	−0.920220	−0.0294404	−0.0147202	+	0.999892i	$0.504686\pi$
$978$	−64.7975	−2.07200
$979$	3.81142	0.121813
$980$	−5.74318	−0.183459
$981$	−0.0711088	−0.00227033
$982$	−20.9560	−0.668733
$983$	−41.2655	−1.31616	−0.658082	−	0.752946i	$-0.728632\pi$
$983$	−41.2655	−1.31616	−0.658082	+	0.752946i	$0.728632\pi$
$984$	−57.8114	−1.84296
$985$	15.0487	0.479493
$986$	−57.1879	−1.82123
$987$	−5.32388	−0.169461
$988$	−14.1757	−0.450988
$989$	−2.84981	−0.0906188
$990$	0.0560739	0.00178215
$991$	4.49250	0.142709	0.0713544	−	0.997451i	$-0.477268\pi$
$991$	4.49250	0.142709	0.0713544	+	0.997451i	$0.477268\pi$
$992$	−25.6459	−0.814259
$993$	45.5402	1.44518
$994$	−3.46968	−0.110051
$995$	15.8498	0.502472
$996$	22.0007	0.697119
$997$	29.1720	0.923886	0.461943	−	0.886910i	$-0.347153\pi$
$997$	29.1720	0.923886	0.461943	+	0.886910i	$0.347153\pi$
$998$	−68.4855	−2.16787
$999$	−4.65287	−0.147210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.e.1.5	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.e.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.53130 q^{2} +1.72523 q^{3} +4.40746 q^{4} -1.30306 q^{5} -4.36707 q^{6} +1.00000 q^{7} -6.09399 q^{8} -0.0235740 q^{9} +O(q^{10})\)	\(q-2.53130 q^{2} +1.72523 q^{3} +4.40746 q^{4} -1.30306 q^{5} -4.36707 q^{6} +1.00000 q^{7} -6.09399 q^{8} -0.0235740 q^{9} +3.29843 q^{10} -0.721143 q^{11} +7.60389 q^{12} +0.841919 q^{13} -2.53130 q^{14} -2.24808 q^{15} +6.61079 q^{16} +7.21849 q^{17} +0.0596727 q^{18} -3.82019 q^{19} -5.74318 q^{20} +1.72523 q^{21} +1.82543 q^{22} +0.353318 q^{23} -10.5136 q^{24} -3.30204 q^{25} -2.13115 q^{26} -5.21637 q^{27} +4.40746 q^{28} +3.12979 q^{29} +5.69055 q^{30} +5.64160 q^{31} -4.54587 q^{32} -1.24414 q^{33} -18.2721 q^{34} -1.30306 q^{35} -0.103901 q^{36} +0.891975 q^{37} +9.67003 q^{38} +1.45251 q^{39} +7.94083 q^{40} +5.49875 q^{41} -4.36707 q^{42} -8.06585 q^{43} -3.17841 q^{44} +0.0307183 q^{45} -0.894353 q^{46} -3.08589 q^{47} +11.4051 q^{48} +1.00000 q^{49} +8.35844 q^{50} +12.4536 q^{51} +3.71072 q^{52} +9.23293 q^{53} +13.2042 q^{54} +0.939691 q^{55} -6.09399 q^{56} -6.59071 q^{57} -7.92242 q^{58} +2.08753 q^{59} -9.90832 q^{60} -5.39601 q^{61} -14.2806 q^{62} -0.0235740 q^{63} -1.71464 q^{64} -1.09707 q^{65} +3.14928 q^{66} +4.81531 q^{67} +31.8152 q^{68} +0.609556 q^{69} +3.29843 q^{70} +1.37071 q^{71} +0.143660 q^{72} +6.46357 q^{73} -2.25785 q^{74} -5.69678 q^{75} -16.8373 q^{76} -0.721143 q^{77} -3.67672 q^{78} +8.56828 q^{79} -8.61424 q^{80} -8.92872 q^{81} -13.9190 q^{82} +2.89335 q^{83} +7.60389 q^{84} -9.40611 q^{85} +20.4171 q^{86} +5.39961 q^{87} +4.39464 q^{88} -5.28524 q^{89} -0.0777571 q^{90} +0.841919 q^{91} +1.55724 q^{92} +9.73306 q^{93} +7.81131 q^{94} +4.97793 q^{95} -7.84267 q^{96} -13.9376 q^{97} -2.53130 q^{98} +0.0170002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q + 19 q^{2} + 38 q^{3} + 111 q^{4} + 43 q^{5} + 14 q^{6} + 109 q^{7} + 48 q^{8} + 119 q^{9}+O(q^{10}) \) 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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