LMFDB - Embedded newform 6013.2.a.d.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:	$1$
Dimension:	$104$
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)

$f(q)$	$=$	$q-2.73004 q^{2} -0.655778 q^{3} +5.45311 q^{4} -0.775046 q^{5} +1.79030 q^{6} +1.00000 q^{7} -9.42711 q^{8} -2.56996 q^{9} +O(q^{10})$	\(q-2.73004 q^{2} -0.655778 q^{3} +5.45311 q^{4} -0.775046 q^{5} +1.79030 q^{6} +1.00000 q^{7} -9.42711 q^{8} -2.56996 q^{9} +2.11590 q^{10} -0.469301 q^{11} -3.57602 q^{12} +1.07813 q^{13} -2.73004 q^{14} +0.508258 q^{15} +14.8302 q^{16} -3.06046 q^{17} +7.01608 q^{18} +4.05290 q^{19} -4.22641 q^{20} -0.655778 q^{21} +1.28121 q^{22} -4.17561 q^{23} +6.18209 q^{24} -4.39930 q^{25} -2.94332 q^{26} +3.65265 q^{27} +5.45311 q^{28} -3.92974 q^{29} -1.38756 q^{30} +8.37170 q^{31} -21.6327 q^{32} +0.307757 q^{33} +8.35518 q^{34} -0.775046 q^{35} -14.0142 q^{36} -2.67972 q^{37} -11.0646 q^{38} -0.707011 q^{39} +7.30644 q^{40} +9.61828 q^{41} +1.79030 q^{42} +1.48342 q^{43} -2.55915 q^{44} +1.99183 q^{45} +11.3996 q^{46} +2.36968 q^{47} -9.72528 q^{48} +1.00000 q^{49} +12.0103 q^{50} +2.00698 q^{51} +5.87913 q^{52} -9.09982 q^{53} -9.97188 q^{54} +0.363730 q^{55} -9.42711 q^{56} -2.65780 q^{57} +10.7284 q^{58} +0.330598 q^{59} +2.77158 q^{60} -7.93700 q^{61} -22.8551 q^{62} -2.56996 q^{63} +29.3977 q^{64} -0.835597 q^{65} -0.840188 q^{66} +2.30866 q^{67} -16.6890 q^{68} +2.73827 q^{69} +2.11590 q^{70} +13.6504 q^{71} +24.2273 q^{72} +3.99335 q^{73} +7.31573 q^{74} +2.88496 q^{75} +22.1009 q^{76} -0.469301 q^{77} +1.93017 q^{78} +9.01866 q^{79} -11.4940 q^{80} +5.31454 q^{81} -26.2583 q^{82} -0.937428 q^{83} -3.57602 q^{84} +2.37200 q^{85} -4.04980 q^{86} +2.57704 q^{87} +4.42415 q^{88} -2.67417 q^{89} -5.43778 q^{90} +1.07813 q^{91} -22.7700 q^{92} -5.48997 q^{93} -6.46930 q^{94} -3.14118 q^{95} +14.1862 q^{96} +13.7773 q^{97} -2.73004 q^{98} +1.20608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * 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 $

$2$	−2.73004	−1.93043	−0.965214	−	0.261461i	$-0.915796\pi$
$2$	−2.73004	−1.93043	−0.965214	+	0.261461i	$0.915796\pi$
$3$	−0.655778	−0.378613	−0.189307	−	0.981918i	$-0.560624\pi$
$3$	−0.655778	−0.378613	−0.189307	+	0.981918i	$0.560624\pi$
$4$	5.45311	2.72655
$5$	−0.775046	−0.346611	−0.173306	−	0.984868i	$-0.555445\pi$
$5$	−0.775046	−0.346611	−0.173306	+	0.984868i	$0.555445\pi$
$6$	1.79030	0.730886
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.42711	−3.33299
$9$	−2.56996	−0.856652
$10$	2.11590	0.669108
$11$	−0.469301	−0.141499	−0.0707497	−	0.997494i	$-0.522539\pi$
$11$	−0.469301	−0.141499	−0.0707497	+	0.997494i	$0.522539\pi$
$12$	−3.57602	−1.03231
$13$	1.07813	0.299018	0.149509	−	0.988760i	$-0.452231\pi$
$13$	1.07813	0.299018	0.149509	+	0.988760i	$0.452231\pi$
$14$	−2.73004	−0.729633
$15$	0.508258	0.131232
$16$	14.8302	3.70754
$17$	−3.06046	−0.742271	−0.371136	−	0.928579i	$-0.621031\pi$
$17$	−3.06046	−0.742271	−0.371136	+	0.928579i	$0.621031\pi$
$18$	7.01608	1.65371
$19$	4.05290	0.929799	0.464900	−	0.885363i	$-0.346090\pi$
$19$	4.05290	0.929799	0.464900	+	0.885363i	$0.346090\pi$
$20$	−4.22641	−0.945053
$21$	−0.655778	−0.143102
$22$	1.28121	0.273155
$23$	−4.17561	−0.870675	−0.435337	−	0.900267i	$-0.643371\pi$
$23$	−4.17561	−0.870675	−0.435337	+	0.900267i	$0.643371\pi$
$24$	6.18209	1.26191
$25$	−4.39930	−0.879861
$26$	−2.94332	−0.577233
$27$	3.65265	0.702953
$28$	5.45311	1.03054
$29$	−3.92974	−0.729735	−0.364868	−	0.931059i	$-0.618886\pi$
$29$	−3.92974	−0.729735	−0.364868	+	0.931059i	$0.618886\pi$
$30$	−1.38756	−0.253333
$31$	8.37170	1.50360	0.751801	−	0.659390i	$-0.229185\pi$
$31$	8.37170	1.50360	0.751801	+	0.659390i	$0.229185\pi$
$32$	−21.6327	−3.82415
$33$	0.307757	0.0535736
$34$	8.35518	1.43290
$35$	−0.775046	−0.131007
$36$	−14.0142	−2.33571
$37$	−2.67972	−0.440543	−0.220271	−	0.975439i	$-0.570694\pi$
$37$	−2.67972	−0.440543	−0.220271	+	0.975439i	$0.570694\pi$
$38$	−11.0646	−1.79491
$39$	−0.707011	−0.113212
$40$	7.30644	1.15525
$41$	9.61828	1.50212	0.751061	−	0.660233i	$-0.229542\pi$
$41$	9.61828	1.50212	0.751061	+	0.660233i	$0.229542\pi$
$42$	1.79030	0.276249
$43$	1.48342	0.226220	0.113110	−	0.993582i	$-0.463919\pi$
$43$	1.48342	0.226220	0.113110	+	0.993582i	$0.463919\pi$
$44$	−2.55915	−0.385806
$45$	1.99183	0.296925
$46$	11.3996	1.68078
$47$	2.36968	0.345653	0.172826	−	0.984952i	$-0.444710\pi$
$47$	2.36968	0.345653	0.172826	+	0.984952i	$0.444710\pi$
$48$	−9.72528	−1.40372
$49$	1.00000	0.142857
$50$	12.0103	1.69851
$51$	2.00698	0.281034
$52$	5.87913	0.815289
$53$	−9.09982	−1.24996	−0.624978	−	0.780642i	$-0.714892\pi$
$53$	−9.09982	−1.24996	−0.624978	+	0.780642i	$0.714892\pi$
$54$	−9.97188	−1.35700
$55$	0.363730	0.0490453
$56$	−9.42711	−1.25975
$57$	−2.65780	−0.352034
$58$	10.7284	1.40870
$59$	0.330598	0.0430402	0.0215201	−	0.999768i	$-0.493149\pi$
$59$	0.330598	0.0430402	0.0215201	+	0.999768i	$0.493149\pi$
$60$	2.77158	0.357810
$61$	−7.93700	−1.01623	−0.508114	−	0.861290i	$-0.669657\pi$
$61$	−7.93700	−1.01623	−0.508114	+	0.861290i	$0.669657\pi$
$62$	−22.8551	−2.90260
$63$	−2.56996	−0.323784
$64$	29.3977	3.67471
$65$	−0.835597	−0.103643
$66$	−0.840188	−0.103420
$67$	2.30866	0.282048	0.141024	−	0.990006i	$-0.454960\pi$
$67$	2.30866	0.282048	0.141024	+	0.990006i	$0.454960\pi$
$68$	−16.6890	−2.02384
$69$	2.73827	0.329649
$70$	2.11590	0.252899
$71$	13.6504	1.62000	0.810000	−	0.586430i	$-0.199467\pi$
$71$	13.6504	1.62000	0.810000	+	0.586430i	$0.199467\pi$
$72$	24.2273	2.85521
$73$	3.99335	0.467386	0.233693	−	0.972310i	$-0.424919\pi$
$73$	3.99335	0.467386	0.233693	+	0.972310i	$0.424919\pi$
$74$	7.31573	0.850436
$75$	2.88496	0.333127
$76$	22.1009	2.53515
$77$	−0.469301	−0.0534818
$78$	1.93017	0.218548
$79$	9.01866	1.01468	0.507339	−	0.861746i	$-0.330629\pi$
$79$	9.01866	1.01468	0.507339	+	0.861746i	$0.330629\pi$
$80$	−11.4940	−1.28507
$81$	5.31454	0.590505
$82$	−26.2583	−2.89974
$83$	−0.937428	−0.102896	−0.0514481	−	0.998676i	$-0.516384\pi$
$83$	−0.937428	−0.102896	−0.0514481	+	0.998676i	$0.516384\pi$
$84$	−3.57602	−0.390176
$85$	2.37200	0.257279
$86$	−4.04980	−0.436701
$87$	2.57704	0.276288
$88$	4.42415	0.471616
$89$	−2.67417	−0.283461	−0.141731	−	0.989905i	$-0.545267\pi$
$89$	−2.67417	−0.283461	−0.141731	+	0.989905i	$0.545267\pi$
$90$	−5.43778	−0.573192
$91$	1.07813	0.113018
$92$	−22.7700	−2.37394
$93$	−5.48997	−0.569284
$94$	−6.46930	−0.667258
$95$	−3.14118	−0.322279
$96$	14.1862	1.44787
$97$	13.7773	1.39887	0.699437	−	0.714694i	$-0.253434\pi$
$97$	13.7773	1.39887	0.699437	+	0.714694i	$0.253434\pi$
$98$	−2.73004	−0.275775
$99$	1.20608	0.121216
$100$	−23.9899	−2.39899
$101$	2.36700	0.235525	0.117763	−	0.993042i	$-0.462428\pi$
$101$	2.36700	0.235525	0.117763	+	0.993042i	$0.462428\pi$
$102$	−5.47914	−0.542515
$103$	−3.61195	−0.355896	−0.177948	−	0.984040i	$-0.556946\pi$
$103$	−3.61195	−0.355896	−0.177948	+	0.984040i	$0.556946\pi$
$104$	−10.1636	−0.996624
$105$	0.508258	0.0496009
$106$	24.8428	2.41295
$107$	6.17639	0.597094	0.298547	−	0.954395i	$-0.403498\pi$
$107$	6.17639	0.597094	0.298547	+	0.954395i	$0.403498\pi$
$108$	19.9183	1.91664
$109$	−14.2661	−1.36644	−0.683222	−	0.730210i	$-0.739422\pi$
$109$	−14.2661	−1.36644	−0.683222	+	0.730210i	$0.739422\pi$
$110$	−0.992995	−0.0946784
$111$	1.75730	0.166795
$112$	14.8302	1.40132
$113$	−3.57120	−0.335951	−0.167975	−	0.985791i	$-0.553723\pi$
$113$	−3.57120	−0.335951	−0.167975	+	0.985791i	$0.553723\pi$
$114$	7.25590	0.679577
$115$	3.23629	0.301786
$116$	−21.4293	−1.98966
$117$	−2.77074	−0.256155
$118$	−0.902546	−0.0830861
$119$	−3.06046	−0.280552
$120$	−4.79140	−0.437393
$121$	−10.7798	−0.979978
$122$	21.6683	1.96176
$123$	−6.30745	−0.568724
$124$	45.6518	4.09965
$125$	7.28489	0.651581
$126$	7.01608	0.625042
$127$	8.47327	0.751881	0.375941	−	0.926644i	$-0.377320\pi$
$127$	8.47327	0.751881	0.375941	+	0.926644i	$0.377320\pi$
$128$	−36.9914	−3.26961
$129$	−0.972794	−0.0856498
$130$	2.28121	0.200075
$131$	2.32229	0.202900	0.101450	−	0.994841i	$-0.467652\pi$
$131$	2.32229	0.202900	0.101450	+	0.994841i	$0.467652\pi$
$132$	1.67823	0.146071
$133$	4.05290	0.351431
$134$	−6.30274	−0.544474
$135$	−2.83097	−0.243651
$136$	28.8513	2.47398
$137$	−8.86818	−0.757660	−0.378830	−	0.925466i	$-0.623673\pi$
$137$	−8.86818	−0.757660	−0.378830	+	0.925466i	$0.623673\pi$
$138$	−7.47558	−0.636364
$139$	−4.35303	−0.369220	−0.184610	−	0.982812i	$-0.559102\pi$
$139$	−4.35303	−0.369220	−0.184610	+	0.982812i	$0.559102\pi$
$140$	−4.22641	−0.357197
$141$	−1.55398	−0.130869
$142$	−37.2660	−3.12729
$143$	−0.505965	−0.0423109
$144$	−38.1128	−3.17607
$145$	3.04573	0.252934
$146$	−10.9020	−0.902255
$147$	−0.655778	−0.0540876
$148$	−14.6128	−1.20116
$149$	−12.3239	−1.00961	−0.504805	−	0.863233i	$-0.668436\pi$
$149$	−12.3239	−1.00961	−0.504805	+	0.863233i	$0.668436\pi$
$150$	−7.87606	−0.643078
$151$	−14.3729	−1.16965	−0.584824	−	0.811160i	$-0.698837\pi$
$151$	−14.3729	−1.16965	−0.584824	+	0.811160i	$0.698837\pi$
$152$	−38.2071	−3.09901
$153$	7.86525	0.635868
$154$	1.28121	0.103243
$155$	−6.48845	−0.521165
$156$	−3.85540	−0.308679
$157$	−8.34407	−0.665929	−0.332964	−	0.942939i	$-0.608049\pi$
$157$	−8.34407	−0.665929	−0.332964	+	0.942939i	$0.608049\pi$
$158$	−24.6213	−1.95876
$159$	5.96746	0.473250
$160$	16.7663	1.32549
$161$	−4.17561	−0.329084
$162$	−14.5089	−1.13993
$163$	−6.08815	−0.476860	−0.238430	−	0.971160i	$-0.576633\pi$
$163$	−6.08815	−0.476860	−0.238430	+	0.971160i	$0.576633\pi$
$164$	52.4495	4.09562
$165$	−0.238526	−0.0185692
$166$	2.55921	0.198634
$167$	9.71978	0.752139	0.376070	−	0.926591i	$-0.377275\pi$
$167$	9.71978	0.752139	0.376070	+	0.926591i	$0.377275\pi$
$168$	6.18209	0.476958
$169$	−11.8376	−0.910588
$170$	−6.47564	−0.496659
$171$	−10.4158	−0.796514
$172$	8.08925	0.616800
$173$	−17.1613	−1.30475	−0.652374	−	0.757897i	$-0.726227\pi$
$173$	−17.1613	−1.30475	−0.652374	+	0.757897i	$0.726227\pi$
$174$	−7.03541	−0.533353
$175$	−4.39930	−0.332556
$176$	−6.95980	−0.524615
$177$	−0.216799	−0.0162956
$178$	7.30058	0.547202
$179$	1.33466	0.0997572	0.0498786	−	0.998755i	$-0.484117\pi$
$179$	1.33466	0.0997572	0.0498786	+	0.998755i	$0.484117\pi$
$180$	10.8617	0.809582
$181$	12.3307	0.916532	0.458266	−	0.888815i	$-0.348471\pi$
$181$	12.3307	0.916532	0.458266	+	0.888815i	$0.348471\pi$
$182$	−2.94332	−0.218174
$183$	5.20491	0.384758
$184$	39.3639	2.90195
$185$	2.07690	0.152697
$186$	14.9878	1.09896
$187$	1.43628	0.105031
$188$	12.9221	0.942440
$189$	3.65265	0.265691
$190$	8.57555	0.622136
$191$	12.7245	0.920714	0.460357	−	0.887734i	$-0.347721\pi$
$191$	12.7245	0.920714	0.460357	+	0.887734i	$0.347721\pi$
$192$	−19.2783	−1.39129
$193$	−13.0962	−0.942686	−0.471343	−	0.881950i	$-0.656231\pi$
$193$	−13.0962	−0.942686	−0.471343	+	0.881950i	$0.656231\pi$
$194$	−37.6126	−2.70043
$195$	0.547966	0.0392406
$196$	5.45311	0.389508
$197$	−3.93660	−0.280471	−0.140236	−	0.990118i	$-0.544786\pi$
$197$	−3.93660	−0.280471	−0.140236	+	0.990118i	$0.544786\pi$
$198$	−3.29265	−0.233998
$199$	1.48940	0.105581	0.0527903	−	0.998606i	$-0.483188\pi$
$199$	1.48940	0.105581	0.0527903	+	0.998606i	$0.483188\pi$
$200$	41.4727	2.93256
$201$	−1.51397	−0.106787
$202$	−6.46200	−0.454665
$203$	−3.92974	−0.275814
$204$	10.9443	0.766253
$205$	−7.45461	−0.520652
$206$	9.86076	0.687032
$207$	10.7311	0.745865
$208$	15.9888	1.10862
$209$	−1.90203	−0.131566
$210$	−1.38756	−0.0957509
$211$	−22.8767	−1.57490	−0.787449	−	0.616380i	$-0.788598\pi$
$211$	−22.8767	−1.57490	−0.787449	+	0.616380i	$0.788598\pi$
$212$	−49.6223	−3.40807
$213$	−8.95160	−0.613353
$214$	−16.8618	−1.15265
$215$	−1.14972	−0.0784102
$216$	−34.4339	−2.34293
$217$	8.37170	0.568308
$218$	38.9470	2.63782
$219$	−2.61875	−0.176959
$220$	1.98346	0.133725
$221$	−3.29956	−0.221953
$222$	−4.79749	−0.321986
$223$	5.19838	0.348110	0.174055	−	0.984736i	$-0.444313\pi$
$223$	5.19838	0.348110	0.174055	+	0.984736i	$0.444313\pi$
$224$	−21.6327	−1.44539
$225$	11.3060	0.753734
$226$	9.74952	0.648528
$227$	19.8766	1.31925	0.659627	−	0.751593i	$-0.270714\pi$
$227$	19.8766	1.31925	0.659627	+	0.751593i	$0.270714\pi$
$228$	−14.4933	−0.959840
$229$	1.48154	0.0979027	0.0489513	−	0.998801i	$-0.484412\pi$
$229$	1.48154	0.0979027	0.0489513	+	0.998801i	$0.484412\pi$
$230$	−8.83519	−0.582575
$231$	0.307757	0.0202489
$232$	37.0461	2.43220
$233$	−2.37833	−0.155810	−0.0779049	−	0.996961i	$-0.524823\pi$
$233$	−2.37833	−0.155810	−0.0779049	+	0.996961i	$0.524823\pi$
$234$	7.56421	0.494488
$235$	−1.83661	−0.119807
$236$	1.80279	0.117351
$237$	−5.91423	−0.384171
$238$	8.35518	0.541586
$239$	27.4198	1.77364	0.886819	−	0.462118i	$-0.152910\pi$
$239$	27.4198	1.77364	0.886819	+	0.462118i	$0.152910\pi$
$240$	7.53754	0.486546
$241$	28.1448	1.81296	0.906482	−	0.422244i	$-0.138758\pi$
$241$	28.1448	1.81296	0.906482	+	0.422244i	$0.138758\pi$
$242$	29.4291	1.89178
$243$	−14.4431	−0.926526
$244$	−43.2813	−2.77080
$245$	−0.775046	−0.0495159
$246$	17.2196	1.09788
$247$	4.36954	0.278027
$248$	−78.9209	−5.01149
$249$	0.614744	0.0389578
$250$	−19.8880	−1.25783
$251$	−21.2104	−1.33879	−0.669394	−	0.742908i	$-0.733446\pi$
$251$	−21.2104	−1.33879	−0.669394	+	0.742908i	$0.733446\pi$
$252$	−14.0142	−0.882814
$253$	1.95962	0.123200
$254$	−23.1323	−1.45145
$255$	−1.55550	−0.0974094
$256$	42.1926	2.63704
$257$	−23.1073	−1.44140	−0.720698	−	0.693250i	$-0.756178\pi$
$257$	−23.1073	−1.44140	−0.720698	+	0.693250i	$0.756178\pi$
$258$	2.65577	0.165341
$259$	−2.67972	−0.166509
$260$	−4.55660	−0.282588
$261$	10.0993	0.625129
$262$	−6.33994	−0.391683
$263$	−15.8317	−0.976226	−0.488113	−	0.872781i	$-0.662315\pi$
$263$	−15.8317	−0.976226	−0.488113	+	0.872781i	$0.662315\pi$
$264$	−2.90126	−0.178560
$265$	7.05278	0.433249
$266$	−11.0646	−0.678412
$267$	1.75366	0.107322
$268$	12.5894	0.769019
$269$	25.2960	1.54232	0.771161	−	0.636640i	$-0.219676\pi$
$269$	25.2960	1.54232	0.771161	+	0.636640i	$0.219676\pi$
$270$	7.72866	0.470351
$271$	4.47727	0.271975	0.135987	−	0.990711i	$-0.456579\pi$
$271$	4.47727	0.271975	0.135987	+	0.990711i	$0.456579\pi$
$272$	−45.3871	−2.75200
$273$	−0.707011	−0.0427902
$274$	24.2105	1.46261
$275$	2.06460	0.124500
$276$	14.9321	0.898806
$277$	4.46098	0.268035	0.134017	−	0.990979i	$-0.457212\pi$
$277$	4.46098	0.268035	0.134017	+	0.990979i	$0.457212\pi$
$278$	11.8839	0.712752
$279$	−21.5149	−1.28806
$280$	7.30644	0.436643
$281$	−15.3973	−0.918523	−0.459262	−	0.888301i	$-0.651886\pi$
$281$	−15.3973	−0.918523	−0.459262	+	0.888301i	$0.651886\pi$
$282$	4.24242	0.252633
$283$	17.0292	1.01228	0.506139	−	0.862452i	$-0.331072\pi$
$283$	17.0292	1.01228	0.506139	+	0.862452i	$0.331072\pi$
$284$	74.4368	4.41701
$285$	2.05992	0.122019
$286$	1.38130	0.0816782
$287$	9.61828	0.567749
$288$	55.5950	3.27596
$289$	−7.63357	−0.449034
$290$	−8.31496	−0.488272
$291$	−9.03485	−0.529633
$292$	21.7761	1.27435
$293$	22.9598	1.34133	0.670663	−	0.741762i	$-0.266010\pi$
$293$	22.9598	1.34133	0.670663	+	0.741762i	$0.266010\pi$
$294$	1.79030	0.104412
$295$	−0.256229	−0.0149182
$296$	25.2620	1.46832
$297$	−1.71419	−0.0994675
$298$	33.6446	1.94898
$299$	−4.50183	−0.260348
$300$	15.7320	0.908288
$301$	1.48342	0.0855030
$302$	39.2385	2.25792
$303$	−1.55223	−0.0891730
$304$	60.1051	3.44727
$305$	6.15154	0.352236
$306$	−21.4724	−1.22750
$307$	−2.62949	−0.150073	−0.0750365	−	0.997181i	$-0.523907\pi$
$307$	−2.62949	−0.150073	−0.0750365	+	0.997181i	$0.523907\pi$
$308$	−2.55915	−0.145821
$309$	2.36864	0.134747
$310$	17.7137	1.00607
$311$	27.1128	1.53743	0.768714	−	0.639593i	$-0.220897\pi$
$311$	27.1128	1.53743	0.768714	+	0.639593i	$0.220897\pi$
$312$	6.66507	0.377335
$313$	−2.50375	−0.141520	−0.0707602	−	0.997493i	$-0.522543\pi$
$313$	−2.50375	−0.141520	−0.0707602	+	0.997493i	$0.522543\pi$
$314$	22.7796	1.28553
$315$	1.99183	0.112227
$316$	49.1797	2.76657
$317$	13.8820	0.779689	0.389844	−	0.920881i	$-0.372529\pi$
$317$	13.8820	0.779689	0.389844	+	0.920881i	$0.372529\pi$
$318$	−16.2914	−0.913575
$319$	1.84423	0.103257
$320$	−22.7845	−1.27369
$321$	−4.05034	−0.226068
$322$	11.3996	0.635273
$323$	−12.4037	−0.690163
$324$	28.9808	1.61004
$325$	−4.74300	−0.263094
$326$	16.6209	0.920545
$327$	9.35539	0.517354
$328$	−90.6725	−5.00655
$329$	2.36968	0.130644
$330$	0.651184	0.0358465
$331$	34.8708	1.91667	0.958337	−	0.285640i	$-0.0922060\pi$
$331$	34.8708	1.91667	0.958337	+	0.285640i	$0.0922060\pi$
$332$	−5.11190	−0.280552
$333$	6.88675	0.377392
$334$	−26.5354	−1.45195
$335$	−1.78932	−0.0977610
$336$	−9.72528	−0.530557
$337$	2.93722	0.160001	0.0800003	−	0.996795i	$-0.474508\pi$
$337$	2.93722	0.160001	0.0800003	+	0.996795i	$0.474508\pi$
$338$	32.3172	1.75782
$339$	2.34191	0.127195
$340$	12.9348	0.701486
$341$	−3.92885	−0.212759
$342$	28.4355	1.53761
$343$	1.00000	0.0539949
$344$	−13.9844	−0.753987
$345$	−2.12229	−0.114260
$346$	46.8509	2.51872
$347$	−3.68737	−0.197948	−0.0989741	−	0.995090i	$-0.531556\pi$
$347$	−3.68737	−0.197948	−0.0989741	+	0.995090i	$0.531556\pi$
$348$	14.0529	0.753312
$349$	−4.13476	−0.221329	−0.110664	−	0.993858i	$-0.535298\pi$
$349$	−4.13476	−0.221329	−0.110664	+	0.993858i	$0.535298\pi$
$350$	12.0103	0.641976
$351$	3.93802	0.210196
$352$	10.1522	0.541115
$353$	0.662750	0.0352746	0.0176373	−	0.999844i	$-0.494386\pi$
$353$	0.662750	0.0352746	0.0176373	+	0.999844i	$0.494386\pi$
$354$	0.591869	0.0314575
$355$	−10.5797	−0.561510
$356$	−14.5825	−0.772872
$357$	2.00698	0.106221
$358$	−3.64367	−0.192574
$359$	−15.2248	−0.803532	−0.401766	−	0.915742i	$-0.631603\pi$
$359$	−15.2248	−0.803532	−0.401766	+	0.915742i	$0.631603\pi$
$360$	−18.7772	−0.989647
$361$	−2.57399	−0.135473
$362$	−33.6632	−1.76930
$363$	7.06912	0.371033
$364$	5.87913	0.308150
$365$	−3.09503	−0.162001
$366$	−14.2096	−0.742747
$367$	13.0866	0.683116	0.341558	−	0.939861i	$-0.389045\pi$
$367$	13.0866	0.683116	0.341558	+	0.939861i	$0.389045\pi$
$368$	−61.9249	−3.22806
$369$	−24.7185	−1.28680
$370$	−5.67002	−0.294770
$371$	−9.09982	−0.472439
$372$	−29.9374	−1.55218
$373$	−31.7497	−1.64394	−0.821969	−	0.569533i	$-0.807124\pi$
$373$	−31.7497	−1.64394	−0.821969	+	0.569533i	$0.807124\pi$
$374$	−3.92109	−0.202755
$375$	−4.77727	−0.246697
$376$	−22.3392	−1.15206
$377$	−4.23676	−0.218204
$378$	−9.97188	−0.512898
$379$	29.2597	1.50297	0.751486	−	0.659749i	$-0.229337\pi$
$379$	29.2597	1.50297	0.751486	+	0.659749i	$0.229337\pi$
$380$	−17.1292	−0.878710
$381$	−5.55658	−0.284672
$382$	−34.7384	−1.77737
$383$	−19.2742	−0.984867	−0.492434	−	0.870350i	$-0.663893\pi$
$383$	−19.2742	−0.984867	−0.492434	+	0.870350i	$0.663893\pi$
$384$	24.2581	1.23792
$385$	0.363730	0.0185374
$386$	35.7532	1.81979
$387$	−3.81233	−0.193791
$388$	75.1292	3.81411
$389$	4.17613	0.211738	0.105869	−	0.994380i	$-0.466238\pi$
$389$	4.17613	0.211738	0.105869	+	0.994380i	$0.466238\pi$
$390$	−1.49597	−0.0757512
$391$	12.7793	0.646277
$392$	−9.42711	−0.476141
$393$	−1.52291	−0.0768205
$394$	10.7471	0.541430
$395$	−6.98987	−0.351699
$396$	6.57689	0.330501
$397$	2.75263	0.138151	0.0690753	−	0.997611i	$-0.477995\pi$
$397$	2.75263	0.138151	0.0690753	+	0.997611i	$0.477995\pi$
$398$	−4.06612	−0.203816
$399$	−2.65780	−0.133056
$400$	−65.2423	−3.26212
$401$	−19.4756	−0.972564	−0.486282	−	0.873802i	$-0.661647\pi$
$401$	−19.4756	−0.972564	−0.486282	+	0.873802i	$0.661647\pi$
$402$	4.13320	0.206145
$403$	9.02575	0.449605
$404$	12.9075	0.642172
$405$	−4.11901	−0.204675
$406$	10.7284	0.532439
$407$	1.25759	0.0623366
$408$	−18.9200	−0.936682
$409$	−12.0622	−0.596437	−0.298219	−	0.954498i	$-0.596392\pi$
$409$	−12.0622	−0.596437	−0.298219	+	0.954498i	$0.596392\pi$
$410$	20.3514	1.00508
$411$	5.81555	0.286860
$412$	−19.6964	−0.970370
$413$	0.330598	0.0162677
$414$	−29.2964	−1.43984
$415$	0.726550	0.0356649
$416$	−23.3227	−1.14349
$417$	2.85462	0.139791
$418$	5.19261	0.253979
$419$	−19.8915	−0.971761	−0.485881	−	0.874025i	$-0.661501\pi$
$419$	−19.8915	−0.971761	−0.485881	+	0.874025i	$0.661501\pi$
$420$	2.77158	0.135239
$421$	−17.9858	−0.876576	−0.438288	−	0.898835i	$-0.644415\pi$
$421$	−17.9858	−0.876576	−0.438288	+	0.898835i	$0.644415\pi$
$422$	62.4543	3.04023
$423$	−6.08996	−0.296104
$424$	85.7850	4.16609
$425$	13.4639	0.653095
$426$	24.4382	1.18403
$427$	−7.93700	−0.384098
$428$	33.6805	1.62801
$429$	0.331801	0.0160195
$430$	3.13878	0.151365
$431$	7.02619	0.338440	0.169220	−	0.985578i	$-0.445875\pi$
$431$	7.02619	0.338440	0.169220	+	0.985578i	$0.445875\pi$
$432$	54.1694	2.60623
$433$	−37.8522	−1.81906	−0.909531	−	0.415636i	$-0.863559\pi$
$433$	−37.8522	−1.81906	−0.909531	+	0.415636i	$0.863559\pi$
$434$	−22.8551	−1.09708
$435$	−1.99732	−0.0957643
$436$	−77.7946	−3.72568
$437$	−16.9233	−0.809553
$438$	7.14928	0.341606
$439$	−9.92334	−0.473615	−0.236808	−	0.971557i	$-0.576101\pi$
$439$	−9.92334	−0.473615	−0.236808	+	0.971557i	$0.576101\pi$
$440$	−3.42892	−0.163467
$441$	−2.56996	−0.122379
$442$	9.00793	0.428464
$443$	−19.6000	−0.931225	−0.465612	−	0.884989i	$-0.654166\pi$
$443$	−19.6000	−0.931225	−0.465612	+	0.884989i	$0.654166\pi$
$444$	9.58273	0.454776
$445$	2.07260	0.0982508
$446$	−14.1918	−0.672001
$447$	8.08172	0.382252
$448$	29.3977	1.38891
$449$	4.15627	0.196146	0.0980732	−	0.995179i	$-0.468732\pi$
$449$	4.15627	0.196146	0.0980732	+	0.995179i	$0.468732\pi$
$450$	−30.8659	−1.45503
$451$	−4.51386	−0.212550
$452$	−19.4741	−0.915987
$453$	9.42541	0.442845
$454$	−54.2638	−2.54673
$455$	−0.835597	−0.0391734
$456$	25.0554	1.17333
$457$	−19.7677	−0.924692	−0.462346	−	0.886700i	$-0.652992\pi$
$457$	−19.7677	−0.924692	−0.462346	+	0.886700i	$0.652992\pi$
$458$	−4.04465	−0.188994
$459$	−11.1788	−0.521782
$460$	17.6478	0.822834
$461$	29.3311	1.36609	0.683044	−	0.730377i	$-0.260656\pi$
$461$	29.3311	1.36609	0.683044	+	0.730377i	$0.260656\pi$
$462$	−0.840188	−0.0390891
$463$	−13.9714	−0.649307	−0.324654	−	0.945833i	$-0.605248\pi$
$463$	−13.9714	−0.649307	−0.324654	+	0.945833i	$0.605248\pi$
$464$	−58.2787	−2.70552
$465$	4.25498	0.197320
$466$	6.49294	0.300780
$467$	12.6593	0.585802	0.292901	−	0.956143i	$-0.405379\pi$
$467$	12.6593	0.585802	0.292901	+	0.956143i	$0.405379\pi$
$468$	−15.1091	−0.698419
$469$	2.30866	0.106604
$470$	5.01401	0.231279
$471$	5.47185	0.252130
$472$	−3.11659	−0.143452
$473$	−0.696171	−0.0320100
$474$	16.1461	0.741614
$475$	−17.8299	−0.818094
$476$	−16.6890	−0.764940
$477$	23.3861	1.07078
$478$	−74.8570	−3.42388
$479$	−22.6737	−1.03599	−0.517993	−	0.855385i	$-0.673321\pi$
$479$	−22.6737	−1.03599	−0.517993	+	0.855385i	$0.673321\pi$
$480$	−10.9950	−0.501849
$481$	−2.88907	−0.131730
$482$	−76.8363	−3.49980
$483$	2.73827	0.124596
$484$	−58.7832	−2.67196
$485$	−10.6781	−0.484865
$486$	39.4302	1.78859
$487$	−27.5774	−1.24965	−0.624826	−	0.780764i	$-0.714830\pi$
$487$	−27.5774	−1.24965	−0.624826	+	0.780764i	$0.714830\pi$
$488$	74.8229	3.38708
$489$	3.99247	0.180546
$490$	2.11590	0.0955868
$491$	3.43073	0.154827	0.0774133	−	0.996999i	$-0.475334\pi$
$491$	3.43073	0.154827	0.0774133	+	0.996999i	$0.475334\pi$
$492$	−34.3952	−1.55065
$493$	12.0268	0.541661
$494$	−11.9290	−0.536711
$495$	−0.934769	−0.0420147
$496$	124.154	5.57466
$497$	13.6504	0.612302
$498$	−1.67828	−0.0752053
$499$	−19.4050	−0.868688	−0.434344	−	0.900747i	$-0.643020\pi$
$499$	−19.4050	−0.868688	−0.434344	+	0.900747i	$0.643020\pi$
$500$	39.7253	1.77657
$501$	−6.37401	−0.284770
$502$	57.9052	2.58443
$503$	−21.9630	−0.979283	−0.489641	−	0.871924i	$-0.662872\pi$
$503$	−21.9630	−0.979283	−0.489641	+	0.871924i	$0.662872\pi$
$504$	24.2273	1.07917
$505$	−1.83453	−0.0816357
$506$	−5.34983	−0.237829
$507$	7.76286	0.344761
$508$	46.2056	2.05004
$509$	2.04318	0.0905624	0.0452812	−	0.998974i	$-0.485582\pi$
$509$	2.04318	0.0905624	0.0452812	+	0.998974i	$0.485582\pi$
$510$	4.24658	0.188042
$511$	3.99335	0.176655
$512$	−41.2046	−1.82100
$513$	14.8038	0.653605
$514$	63.0839	2.78251
$515$	2.79943	0.123358
$516$	−5.30475	−0.233529
$517$	−1.11209	−0.0489097
$518$	7.31573	0.321435
$519$	11.2540	0.493995
$520$	7.87726	0.345441
$521$	−36.5240	−1.60014	−0.800072	−	0.599904i	$-0.795205\pi$
$521$	−36.5240	−1.60014	−0.800072	+	0.599904i	$0.795205\pi$
$522$	−27.5714	−1.20677
$523$	−10.5952	−0.463296	−0.231648	−	0.972800i	$-0.574412\pi$
$523$	−10.5952	−0.463296	−0.231648	+	0.972800i	$0.574412\pi$
$524$	12.6637	0.553216
$525$	2.88496	0.125910
$526$	43.2212	1.88453
$527$	−25.6213	−1.11608
$528$	4.56408	0.198626
$529$	−5.56428	−0.241925
$530$	−19.2543	−0.836355
$531$	−0.849623	−0.0368705
$532$	22.1009	0.958195
$533$	10.3697	0.449162
$534$	−4.78756	−0.207178
$535$	−4.78699	−0.206959
$536$	−21.7640	−0.940063
$537$	−0.875240	−0.0377694
$538$	−69.0589	−2.97734
$539$	−0.469301	−0.0202142
$540$	−15.4376	−0.664328
$541$	−26.1899	−1.12599	−0.562996	−	0.826459i	$-0.690351\pi$
$541$	−26.1899	−1.12599	−0.562996	+	0.826459i	$0.690351\pi$
$542$	−12.2231	−0.525028
$543$	−8.08618	−0.347011
$544$	66.2059	2.83855
$545$	11.0569	0.473625
$546$	1.93017	0.0826035
$547$	−15.8372	−0.677151	−0.338576	−	0.940939i	$-0.609945\pi$
$547$	−15.8372	−0.677151	−0.338576	+	0.940939i	$0.609945\pi$
$548$	−48.3591	−2.06580
$549$	20.3977	0.870554
$550$	−5.63643	−0.240338
$551$	−15.9269	−0.678507
$552$	−25.8140	−1.09872
$553$	9.01866	0.383512
$554$	−12.1787	−0.517421
$555$	−1.36199	−0.0578131
$556$	−23.7376	−1.00670
$557$	−20.4335	−0.865797	−0.432898	−	0.901443i	$-0.642509\pi$
$557$	−20.4335	−0.865797	−0.432898	+	0.901443i	$0.642509\pi$
$558$	58.7365	2.48651
$559$	1.59932	0.0676438
$560$	−11.4940	−0.485712
$561$	−0.941878	−0.0397661
$562$	42.0351	1.77314
$563$	−38.3015	−1.61422	−0.807109	−	0.590403i	$-0.798969\pi$
$563$	−38.3015	−1.61422	−0.807109	+	0.590403i	$0.798969\pi$
$564$	−8.47402	−0.356820
$565$	2.76785	0.116444
$566$	−46.4903	−1.95413
$567$	5.31454	0.223190
$568$	−128.683	−5.39944
$569$	11.4692	0.480815	0.240408	−	0.970672i	$-0.422719\pi$
$569$	11.4692	0.480815	0.240408	+	0.970672i	$0.422719\pi$
$570$	−5.62365	−0.235549
$571$	42.9575	1.79771	0.898857	−	0.438243i	$-0.144399\pi$
$571$	42.9575	1.79771	0.898857	+	0.438243i	$0.144399\pi$
$572$	−2.75908	−0.115363
$573$	−8.34445	−0.348595
$574$	−26.2583	−1.09600
$575$	18.3698	0.766073
$576$	−75.5507	−3.14794
$577$	−13.5667	−0.564789	−0.282394	−	0.959298i	$-0.591129\pi$
$577$	−13.5667	−0.564789	−0.282394	+	0.959298i	$0.591129\pi$
$578$	20.8399	0.866827
$579$	8.58820	0.356914
$580$	16.6087	0.689639
$581$	−0.937428	−0.0388911
$582$	24.6655	1.02242
$583$	4.27055	0.176868
$584$	−37.6457	−1.55779
$585$	2.14745	0.0887860
$586$	−62.6811	−2.58933
$587$	17.5918	0.726090	0.363045	−	0.931772i	$-0.381737\pi$
$587$	17.5918	0.726090	0.363045	+	0.931772i	$0.381737\pi$
$588$	−3.57602	−0.147473
$589$	33.9297	1.39805
$590$	0.699514	0.0287985
$591$	2.58154	0.106190
$592$	−39.7406	−1.63333
$593$	32.0989	1.31814	0.659072	−	0.752080i	$-0.270949\pi$
$593$	32.0989	1.31814	0.659072	+	0.752080i	$0.270949\pi$
$594$	4.67981	0.192015
$595$	2.37200	0.0972425
$596$	−67.2034	−2.75276
$597$	−0.976714	−0.0399743
$598$	12.2902	0.502583
$599$	−9.68683	−0.395793	−0.197897	−	0.980223i	$-0.563411\pi$
$599$	−9.68683	−0.395793	−0.197897	+	0.980223i	$0.563411\pi$
$600$	−27.1969	−1.11031
$601$	3.89870	0.159031	0.0795156	−	0.996834i	$-0.474663\pi$
$601$	3.89870	0.159031	0.0795156	+	0.996834i	$0.474663\pi$
$602$	−4.04980	−0.165057
$603$	−5.93317	−0.241617
$604$	−78.3768	−3.18911
$605$	8.35481	0.339671
$606$	4.23763	0.172142
$607$	−21.4845	−0.872030	−0.436015	−	0.899939i	$-0.643611\pi$
$607$	−21.4845	−0.872030	−0.436015	+	0.899939i	$0.643611\pi$
$608$	−87.6750	−3.55569
$609$	2.57704	0.104427
$610$	−16.7939	−0.679966
$611$	2.55481	0.103356
$612$	42.8901	1.73373
$613$	13.7807	0.556599	0.278300	−	0.960494i	$-0.410229\pi$
$613$	13.7807	0.556599	0.278300	+	0.960494i	$0.410229\pi$
$614$	7.17861	0.289705
$615$	4.88856	0.197126
$616$	4.42415	0.178254
$617$	−5.17349	−0.208277	−0.104138	−	0.994563i	$-0.533209\pi$
$617$	−5.17349	−0.208277	−0.104138	+	0.994563i	$0.533209\pi$
$618$	−6.46647	−0.260119
$619$	10.6421	0.427742	0.213871	−	0.976862i	$-0.431393\pi$
$619$	10.6421	0.427742	0.213871	+	0.976862i	$0.431393\pi$
$620$	−35.3822	−1.42098
$621$	−15.2521	−0.612044
$622$	−74.0190	−2.96789
$623$	−2.67417	−0.107138
$624$	−10.4851	−0.419739
$625$	16.3504	0.654016
$626$	6.83534	0.273195
$627$	1.24731	0.0498127
$628$	−45.5011	−1.81569
$629$	8.20117	0.327002
$630$	−5.43778	−0.216646
$631$	−8.78176	−0.349596	−0.174798	−	0.984604i	$-0.555927\pi$
$631$	−8.78176	−0.349596	−0.174798	+	0.984604i	$0.555927\pi$
$632$	−85.0199	−3.38191
$633$	15.0020	0.596277
$634$	−37.8983	−1.50513
$635$	−6.56717	−0.260610
$636$	32.5412	1.29034
$637$	1.07813	0.0427169
$638$	−5.03482	−0.199331
$639$	−35.0808	−1.38778
$640$	28.6700	1.13328
$641$	12.4775	0.492832	0.246416	−	0.969164i	$-0.420747\pi$
$641$	12.4775	0.492832	0.246416	+	0.969164i	$0.420747\pi$
$642$	11.0576	0.436408
$643$	−13.3808	−0.527686	−0.263843	−	0.964566i	$-0.584990\pi$
$643$	−13.3808	−0.527686	−0.263843	+	0.964566i	$0.584990\pi$
$644$	−22.7700	−0.897265
$645$	0.753960	0.0296872
$646$	33.8627	1.33231
$647$	−15.0903	−0.593259	−0.296630	−	0.954993i	$-0.595863\pi$
$647$	−15.0903	−0.593259	−0.296630	+	0.954993i	$0.595863\pi$
$648$	−50.1008	−1.96814
$649$	−0.155150	−0.00609017
$650$	12.9486	0.507885
$651$	−5.48997	−0.215169
$652$	−33.1993	−1.30019
$653$	−22.4516	−0.878598	−0.439299	−	0.898341i	$-0.644773\pi$
$653$	−22.4516	−0.878598	−0.439299	+	0.898341i	$0.644773\pi$
$654$	−25.5406	−0.998715
$655$	−1.79988	−0.0703272
$656$	142.640	5.56918
$657$	−10.2627	−0.400387
$658$	−6.46930	−0.252200
$659$	9.08960	0.354081	0.177040	−	0.984204i	$-0.443348\pi$
$659$	9.08960	0.354081	0.177040	+	0.984204i	$0.443348\pi$
$660$	−1.30071	−0.0506299
$661$	−11.5582	−0.449561	−0.224780	−	0.974409i	$-0.572166\pi$
$661$	−11.5582	−0.449561	−0.224780	+	0.974409i	$0.572166\pi$
$662$	−95.1987	−3.70000
$663$	2.16378	0.0840342
$664$	8.83724	0.342951
$665$	−3.14118	−0.121810
$666$	−18.8011	−0.728528
$667$	16.4091	0.635362
$668$	53.0030	2.05075
$669$	−3.40898	−0.131799
$670$	4.88491	0.188721
$671$	3.72484	0.143796
$672$	14.1862	0.547245
$673$	9.43977	0.363876	0.181938	−	0.983310i	$-0.441763\pi$
$673$	9.43977	0.363876	0.181938	+	0.983310i	$0.441763\pi$
$674$	−8.01872	−0.308870
$675$	−16.0691	−0.618501
$676$	−64.5519	−2.48277
$677$	−31.2182	−1.19981	−0.599907	−	0.800070i	$-0.704796\pi$
$677$	−31.2182	−1.19981	−0.599907	+	0.800070i	$0.704796\pi$
$678$	−6.39351	−0.245541
$679$	13.7773	0.528725
$680$	−22.3611	−0.857509
$681$	−13.0346	−0.499487
$682$	10.7259	0.410716
$683$	35.0846	1.34248	0.671238	−	0.741242i	$-0.265763\pi$
$683$	35.0846	1.34248	0.671238	+	0.741242i	$0.265763\pi$
$684$	−56.7983	−2.17174
$685$	6.87324	0.262613
$686$	−2.73004	−0.104233
$687$	−0.971558	−0.0370673
$688$	21.9994	0.838718
$689$	−9.81075	−0.373760
$690$	5.79392	0.220571
$691$	18.1407	0.690104	0.345052	−	0.938584i	$-0.387861\pi$
$691$	18.1407	0.690104	0.345052	+	0.938584i	$0.387861\pi$
$692$	−93.5823	−3.55746
$693$	1.20608	0.0458153
$694$	10.0666	0.382125
$695$	3.37380	0.127976
$696$	−24.2940	−0.920862
$697$	−29.4364	−1.11498
$698$	11.2881	0.427259
$699$	1.55966	0.0589917
$700$	−23.9899	−0.906732
$701$	−46.7432	−1.76547	−0.882733	−	0.469875i	$-0.844299\pi$
$701$	−46.7432	−1.76547	−0.882733	+	0.469875i	$0.844299\pi$
$702$	−10.7509	−0.405768
$703$	−10.8606	−0.409616
$704$	−13.7963	−0.519969
$705$	1.20441	0.0453605
$706$	−1.80933	−0.0680951
$707$	2.36700	0.0890202
$708$	−1.18223	−0.0444308
$709$	23.8905	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$709$	23.8905	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$710$	28.8828	1.08395
$711$	−23.1776	−0.869226
$712$	25.2097	0.944772
$713$	−34.9570	−1.30915
$714$	−5.47914	−0.205052
$715$	0.392146	0.0146654
$716$	7.27804	0.271993
$717$	−17.9813	−0.671523
$718$	41.5642	1.55116
$719$	−27.9021	−1.04057	−0.520286	−	0.853992i	$-0.674175\pi$
$719$	−27.9021	−1.04057	−0.520286	+	0.853992i	$0.674175\pi$
$720$	29.5392	1.10086
$721$	−3.61195	−0.134516
$722$	7.02710	0.261522
$723$	−18.4567	−0.686412
$724$	67.2405	2.49897
$725$	17.2881	0.642065
$726$	−19.2990	−0.716252
$727$	7.23341	0.268272	0.134136	−	0.990963i	$-0.457174\pi$
$727$	7.23341	0.268272	0.134136	+	0.990963i	$0.457174\pi$
$728$	−10.1636	−0.376688
$729$	−6.47215	−0.239709
$730$	8.44954	0.312732
$731$	−4.53995	−0.167916
$732$	28.3829	1.04906
$733$	−30.5530	−1.12850	−0.564250	−	0.825604i	$-0.690835\pi$
$733$	−30.5530	−1.12850	−0.564250	+	0.825604i	$0.690835\pi$
$734$	−35.7270	−1.31871
$735$	0.508258	0.0187474
$736$	90.3295	3.32959
$737$	−1.08346	−0.0399097
$738$	67.4826	2.48407
$739$	−25.9522	−0.954666	−0.477333	−	0.878722i	$-0.658397\pi$
$739$	−25.9522	−0.954666	−0.477333	+	0.878722i	$0.658397\pi$
$740$	11.3256	0.416336
$741$	−2.86544	−0.105265
$742$	24.8428	0.912009
$743$	50.7358	1.86132	0.930658	−	0.365891i	$-0.119236\pi$
$743$	50.7358	1.86132	0.930658	+	0.365891i	$0.119236\pi$
$744$	51.7546	1.89742
$745$	9.55157	0.349942
$746$	86.6779	3.17350
$747$	2.40915	0.0881462
$748$	7.83217	0.286372
$749$	6.17639	0.225680
$750$	13.0421	0.476231
$751$	32.0335	1.16892	0.584459	−	0.811423i	$-0.301307\pi$
$751$	32.0335	1.16892	0.584459	+	0.811423i	$0.301307\pi$
$752$	35.1426	1.28152
$753$	13.9093	0.506883
$754$	11.5665	0.421228
$755$	11.1396	0.405413
$756$	19.9183	0.724421
$757$	−44.4377	−1.61511	−0.807557	−	0.589789i	$-0.799211\pi$
$757$	−44.4377	−1.61511	−0.807557	+	0.589789i	$0.799211\pi$
$758$	−79.8802	−2.90138
$759$	−1.28507	−0.0466452
$760$	29.6123	1.07415
$761$	−11.4118	−0.413677	−0.206838	−	0.978375i	$-0.566317\pi$
$761$	−11.4118	−0.413677	−0.206838	+	0.978375i	$0.566317\pi$
$762$	15.1697	0.549539
$763$	−14.2661	−0.516468
$764$	69.3881	2.51037
$765$	−6.09593	−0.220399
$766$	52.6194	1.90122
$767$	0.356426	0.0128698
$768$	−27.6690	−0.998418
$769$	19.1142	0.689277	0.344639	−	0.938735i	$-0.388001\pi$
$769$	19.1142	0.689277	0.344639	+	0.938735i	$0.388001\pi$
$770$	−0.992995	−0.0357851
$771$	15.1533	0.545731
$772$	−71.4150	−2.57028
$773$	−35.4593	−1.27538	−0.637691	−	0.770293i	$-0.720110\pi$
$773$	−35.4593	−1.27538	−0.637691	+	0.770293i	$0.720110\pi$
$774$	10.4078	0.374101
$775$	−36.8297	−1.32296
$776$	−129.880	−4.66243
$777$	1.75730	0.0630427
$778$	−11.4010	−0.408745
$779$	38.9819	1.39667
$780$	2.98812	0.106992
$781$	−6.40612	−0.229229
$782$	−34.8880	−1.24759
$783$	−14.3540	−0.512970
$784$	14.8302	0.529648
$785$	6.46703	0.230818
$786$	4.15759	0.148296
$787$	−24.4971	−0.873228	−0.436614	−	0.899649i	$-0.643822\pi$
$787$	−24.4971	−0.873228	−0.436614	+	0.899649i	$0.643822\pi$
$788$	−21.4667	−0.764720
$789$	10.3821	0.369612
$790$	19.0826	0.678929
$791$	−3.57120	−0.126977
$792$	−11.3699	−0.404011
$793$	−8.55708	−0.303871
$794$	−7.51478	−0.266690
$795$	−4.62505	−0.164034
$796$	8.12185	0.287871
$797$	−9.17430	−0.324970	−0.162485	−	0.986711i	$-0.551951\pi$
$797$	−9.17430	−0.324970	−0.162485	+	0.986711i	$0.551951\pi$
$798$	7.25590	0.256856
$799$	−7.25230	−0.256568
$800$	95.1686	3.36472
$801$	6.87249	0.242828
$802$	53.1691	1.87746
$803$	−1.87408	−0.0661349
$804$	−8.25584	−0.291161
$805$	3.23629	0.114064
$806$	−24.6406	−0.867929
$807$	−16.5885	−0.583944
$808$	−22.3140	−0.785003
$809$	0.993617	0.0349337	0.0174669	−	0.999847i	$-0.494440\pi$
$809$	0.993617	0.0349337	0.0174669	+	0.999847i	$0.494440\pi$
$810$	11.2451	0.395111
$811$	−48.1685	−1.69142	−0.845712	−	0.533640i	$-0.820824\pi$
$811$	−48.1685	−1.69142	−0.845712	+	0.533640i	$0.820824\pi$
$812$	−21.4293	−0.752021
$813$	−2.93609	−0.102973
$814$	−3.43328	−0.120336
$815$	4.71859	0.165285
$816$	29.7638	1.04194
$817$	6.01216	0.210339
$818$	32.9303	1.15138
$819$	−2.77074	−0.0968173
$820$	−40.6508	−1.41959
$821$	−11.4646	−0.400119	−0.200059	−	0.979784i	$-0.564114\pi$
$821$	−11.4646	−0.400119	−0.200059	+	0.979784i	$0.564114\pi$
$822$	−15.8767	−0.553763
$823$	−29.7519	−1.03709	−0.518543	−	0.855052i	$-0.673525\pi$
$823$	−29.7519	−1.03709	−0.518543	+	0.855052i	$0.673525\pi$
$824$	34.0503	1.18620
$825$	−1.35392	−0.0471373
$826$	−0.902546	−0.0314036
$827$	−43.6360	−1.51737	−0.758686	−	0.651456i	$-0.774158\pi$
$827$	−43.6360	−1.51737	−0.758686	+	0.651456i	$0.774158\pi$
$828$	58.5180	2.03364
$829$	50.8065	1.76458	0.882291	−	0.470705i	$-0.156000\pi$
$829$	50.8065	1.76458	0.882291	+	0.470705i	$0.156000\pi$
$830$	−1.98351	−0.0688486
$831$	−2.92541	−0.101481
$832$	31.6944	1.09880
$833$	−3.06046	−0.106039
$834$	−7.79323	−0.269857
$835$	−7.53327	−0.260700
$836$	−10.3720	−0.358722
$837$	30.5789	1.05696
$838$	54.3044	1.87592
$839$	5.38397	0.185875	0.0929377	−	0.995672i	$-0.470374\pi$
$839$	5.38397	0.185875	0.0929377	+	0.995672i	$0.470374\pi$
$840$	−4.79140	−0.165319
$841$	−13.5571	−0.467486
$842$	49.1020	1.69217
$843$	10.0972	0.347765
$844$	−124.749	−4.29404
$845$	9.17472	0.315620
$846$	16.6258	0.571608
$847$	−10.7798	−0.370397
$848$	−134.952	−4.63426
$849$	−11.1673	−0.383262
$850$	−36.7570	−1.26075
$851$	11.1895	0.383569
$852$	−48.8140	−1.67234
$853$	−53.5661	−1.83407	−0.917034	−	0.398809i	$-0.869424\pi$
$853$	−53.5661	−1.83407	−0.917034	+	0.398809i	$0.869424\pi$
$854$	21.6683	0.741474
$855$	8.07270	0.276081
$856$	−58.2255	−1.99011
$857$	−2.25572	−0.0770540	−0.0385270	−	0.999258i	$-0.512267\pi$
$857$	−2.25572	−0.0770540	−0.0385270	+	0.999258i	$0.512267\pi$
$858$	−0.905828	−0.0309245
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−6.26954	−0.213790
$861$	−6.30745	−0.214957
$862$	−19.1818	−0.653333
$863$	13.4744	0.458675	0.229337	−	0.973347i	$-0.426344\pi$
$863$	13.4744	0.458675	0.229337	+	0.973347i	$0.426344\pi$
$864$	−79.0165	−2.68820
$865$	13.3008	0.452240
$866$	103.338	3.51157
$867$	5.00593	0.170010
$868$	45.6518	1.54952
$869$	−4.23246	−0.143576
$870$	5.45277	0.184866
$871$	2.48903	0.0843376
$872$	134.488	4.55434
$873$	−35.4071	−1.19835
$874$	46.2013	1.56278
$875$	7.28489	0.246274
$876$	−14.2803	−0.482487
$877$	21.7601	0.734787	0.367394	−	0.930066i	$-0.380250\pi$
$877$	21.7601	0.734787	0.367394	+	0.930066i	$0.380250\pi$
$878$	27.0911	0.914280
$879$	−15.0565	−0.507844
$880$	5.39416	0.181837
$881$	−23.1081	−0.778532	−0.389266	−	0.921125i	$-0.627271\pi$
$881$	−23.1081	−0.778532	−0.389266	+	0.921125i	$0.627271\pi$
$882$	7.01608	0.236244
$883$	6.46251	0.217481	0.108740	−	0.994070i	$-0.465318\pi$
$883$	6.46251	0.217481	0.108740	+	0.994070i	$0.465318\pi$
$884$	−17.9929	−0.605166
$885$	0.168029	0.00564824
$886$	53.5088	1.79766
$887$	37.7471	1.26742	0.633711	−	0.773570i	$-0.281531\pi$
$887$	37.7471	1.26742	0.633711	+	0.773570i	$0.281531\pi$
$888$	−16.5662	−0.555927
$889$	8.47327	0.284184
$890$	−5.65828	−0.189666
$891$	−2.49412	−0.0835561
$892$	28.3473	0.949139
$893$	9.60406	0.321388
$894$	−22.0634	−0.737910
$895$	−1.03442	−0.0345769
$896$	−36.9914	−1.23580
$897$	2.95220	0.0985711
$898$	−11.3468	−0.378646
$899$	−32.8987	−1.09723
$900$	61.6529	2.05510
$901$	27.8496	0.927806
$902$	12.3230	0.410312
$903$	−0.972794	−0.0323726
$904$	33.6661	1.11972
$905$	−9.55684	−0.317680
$906$	−25.7317	−0.854880
$907$	−39.7780	−1.32081	−0.660404	−	0.750911i	$-0.729615\pi$
$907$	−39.7780	−1.32081	−0.660404	+	0.750911i	$0.729615\pi$
$908$	108.389	3.59702
$909$	−6.08309	−0.201763
$910$	2.28121	0.0756214
$911$	−34.7219	−1.15039	−0.575194	−	0.818017i	$-0.695073\pi$
$911$	−34.7219	−1.15039	−0.575194	+	0.818017i	$0.695073\pi$
$912$	−39.4156	−1.30518
$913$	0.439936	0.0145598
$914$	53.9665	1.78505
$915$	−4.03404	−0.133361
$916$	8.07897	0.266937
$917$	2.32229	0.0766888
$918$	30.5186	1.00726
$919$	−29.9206	−0.986989	−0.493494	−	0.869749i	$-0.664281\pi$
$919$	−29.9206	−0.986989	−0.493494	+	0.869749i	$0.664281\pi$
$920$	−30.5089	−1.00585
$921$	1.72436	0.0568197
$922$	−80.0751	−2.63713
$923$	14.7168	0.484409
$924$	1.67823	0.0552097
$925$	11.7889	0.387616
$926$	38.1425	1.25344
$927$	9.28255	0.304879
$928$	85.0108	2.79062
$929$	−46.8662	−1.53763	−0.768815	−	0.639471i	$-0.779153\pi$
$929$	−46.8662	−1.53763	−0.768815	+	0.639471i	$0.779153\pi$
$930$	−11.6163	−0.380912
$931$	4.05290	0.132828
$932$	−12.9693	−0.424824
$933$	−17.7800	−0.582090
$934$	−34.5603	−1.13085
$935$	−1.11318	−0.0364049
$936$	26.1200	0.853760
$937$	31.6731	1.03471	0.517357	−	0.855770i	$-0.326916\pi$
$937$	31.6731	1.03471	0.517357	+	0.855770i	$0.326916\pi$
$938$	−6.30274	−0.205792
$939$	1.64190	0.0535815
$940$	−10.0152	−0.326660
$941$	−35.5198	−1.15791	−0.578956	−	0.815359i	$-0.696540\pi$
$941$	−35.5198	−1.15791	−0.578956	+	0.815359i	$0.696540\pi$
$942$	−14.9384	−0.486718
$943$	−40.1622	−1.30786
$944$	4.90282	0.159573
$945$	−2.83097	−0.0920915
$946$	1.90057	0.0617929
$947$	−36.3870	−1.18242	−0.591210	−	0.806518i	$-0.701350\pi$
$947$	−36.3870	−1.18242	−0.591210	+	0.806518i	$0.701350\pi$
$948$	−32.2509	−1.04746
$949$	4.30533	0.139757
$950$	48.6764	1.57927
$951$	−9.10348	−0.295200
$952$	28.8513	0.935076
$953$	−12.3581	−0.400318	−0.200159	−	0.979763i	$-0.564146\pi$
$953$	−12.3581	−0.400318	−0.200159	+	0.979763i	$0.564146\pi$
$954$	−63.8450	−2.06706
$955$	−9.86208	−0.319130
$956$	149.523	4.83592
$957$	−1.20941	−0.0390945
$958$	61.8999	1.99990
$959$	−8.86818	−0.286368
$960$	14.9416	0.482238
$961$	39.0854	1.26082
$962$	7.88727	0.254296
$963$	−15.8731	−0.511502
$964$	153.476	4.94314
$965$	10.1502	0.326745
$966$	−7.47558	−0.240523
$967$	−38.3079	−1.23190	−0.615950	−	0.787786i	$-0.711228\pi$
$967$	−38.3079	−1.23190	−0.615950	+	0.787786i	$0.711228\pi$
$968$	101.622	3.26625
$969$	8.13410	0.261305
$970$	29.1515	0.935998
$971$	15.7896	0.506712	0.253356	−	0.967373i	$-0.418466\pi$
$971$	15.7896	0.506712	0.253356	+	0.967373i	$0.418466\pi$
$972$	−78.7598	−2.52622
$973$	−4.35303	−0.139552
$974$	75.2874	2.41236
$975$	3.11036	0.0996111
$976$	−117.707	−3.76771
$977$	18.2920	0.585212	0.292606	−	0.956233i	$-0.405478\pi$
$977$	18.2920	0.585212	0.292606	+	0.956233i	$0.405478\pi$
$978$	−10.8996	−0.348530
$979$	1.25499	0.0401096
$980$	−4.22641	−0.135008
$981$	36.6632	1.17057
$982$	−9.36602	−0.298882
$983$	40.4037	1.28868	0.644339	−	0.764740i	$-0.277133\pi$
$983$	40.4037	1.28868	0.644339	+	0.764740i	$0.277133\pi$
$984$	59.4610	1.89555
$985$	3.05105	0.0972145
$986$	−32.8337	−1.04564
$987$	−1.55398	−0.0494637
$988$	23.8276	0.758055
$989$	−6.19419	−0.196964
$990$	2.55195	0.0811064
$991$	58.2743	1.85115	0.925573	−	0.378570i	$-0.123584\pi$
$991$	58.2743	1.85115	0.925573	+	0.378570i	$0.123584\pi$
$992$	−181.102	−5.75000
$993$	−22.8675	−0.725678
$994$	−37.2660	−1.18201
$995$	−1.15435	−0.0365954
$996$	3.35227	0.106221
$997$	4.56711	0.144642	0.0723208	−	0.997381i	$-0.476959\pi$
$997$	4.56711	0.144642	0.0723208	+	0.997381i	$0.476959\pi$
$998$	52.9765	1.67694
$999$	−9.78807	−0.309681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.d.1.5	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.d.1.5	✓	104	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)

\(f(q)\)	\(=\)	\(q-2.73004 q^{2} -0.655778 q^{3} +5.45311 q^{4} -0.775046 q^{5} +1.79030 q^{6} +1.00000 q^{7} -9.42711 q^{8} -2.56996 q^{9} +O(q^{10})\)	\(q-2.73004 q^{2} -0.655778 q^{3} +5.45311 q^{4} -0.775046 q^{5} +1.79030 q^{6} +1.00000 q^{7} -9.42711 q^{8} -2.56996 q^{9} +2.11590 q^{10} -0.469301 q^{11} -3.57602 q^{12} +1.07813 q^{13} -2.73004 q^{14} +0.508258 q^{15} +14.8302 q^{16} -3.06046 q^{17} +7.01608 q^{18} +4.05290 q^{19} -4.22641 q^{20} -0.655778 q^{21} +1.28121 q^{22} -4.17561 q^{23} +6.18209 q^{24} -4.39930 q^{25} -2.94332 q^{26} +3.65265 q^{27} +5.45311 q^{28} -3.92974 q^{29} -1.38756 q^{30} +8.37170 q^{31} -21.6327 q^{32} +0.307757 q^{33} +8.35518 q^{34} -0.775046 q^{35} -14.0142 q^{36} -2.67972 q^{37} -11.0646 q^{38} -0.707011 q^{39} +7.30644 q^{40} +9.61828 q^{41} +1.79030 q^{42} +1.48342 q^{43} -2.55915 q^{44} +1.99183 q^{45} +11.3996 q^{46} +2.36968 q^{47} -9.72528 q^{48} +1.00000 q^{49} +12.0103 q^{50} +2.00698 q^{51} +5.87913 q^{52} -9.09982 q^{53} -9.97188 q^{54} +0.363730 q^{55} -9.42711 q^{56} -2.65780 q^{57} +10.7284 q^{58} +0.330598 q^{59} +2.77158 q^{60} -7.93700 q^{61} -22.8551 q^{62} -2.56996 q^{63} +29.3977 q^{64} -0.835597 q^{65} -0.840188 q^{66} +2.30866 q^{67} -16.6890 q^{68} +2.73827 q^{69} +2.11590 q^{70} +13.6504 q^{71} +24.2273 q^{72} +3.99335 q^{73} +7.31573 q^{74} +2.88496 q^{75} +22.1009 q^{76} -0.469301 q^{77} +1.93017 q^{78} +9.01866 q^{79} -11.4940 q^{80} +5.31454 q^{81} -26.2583 q^{82} -0.937428 q^{83} -3.57602 q^{84} +2.37200 q^{85} -4.04980 q^{86} +2.57704 q^{87} +4.42415 q^{88} -2.67417 q^{89} -5.43778 q^{90} +1.07813 q^{91} -22.7700 q^{92} -5.48997 q^{93} -6.46930 q^{94} -3.14118 q^{95} +14.1862 q^{96} +13.7773 q^{97} -2.73004 q^{98} +1.20608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9	\( 104 q - 17 q^{2} - 34 q^{3} + 99 q^{4} - 46 q^{5} - 18 q^{6} + 104 q^{7} - 48 q^{8} + 98 q^{9} - 17 q^{10} - 46 q^{11} - 62 q^{12} - 37 q^{13} - 17 q^{14} - 17 q^{15} + 93 q^{16} - 75 q^{17} - 41 q^{18} - 40 q^{19} - 106 q^{20} - 34 q^{21} - 14 q^{22} - 57 q^{23} - 38 q^{24} + 102 q^{25} - 45 q^{26} - 121 q^{27} + 99 q^{28} - 29 q^{29} + 26 q^{30} - 42 q^{31} - 113 q^{32} - 42 q^{33} - 7 q^{34} - 46 q^{35} + 99 q^{36} - 31 q^{37} - 62 q^{38} - 9 q^{39} - 36 q^{40} - 106 q^{41} - 18 q^{42} - 29 q^{43} - 60 q^{44} - 121 q^{45} + 21 q^{46} - 141 q^{47} - 88 q^{48} + 104 q^{49} - 70 q^{50} - 2 q^{51} - 58 q^{52} - 70 q^{53} - 49 q^{54} - 14 q^{55} - 48 q^{56} - 11 q^{57} - 28 q^{58} - 202 q^{59} + 17 q^{60} - 79 q^{61} - 41 q^{62} + 98 q^{63} + 110 q^{64} - 34 q^{65} - 21 q^{66} - 57 q^{67} - 180 q^{68} - 99 q^{69} - 17 q^{70} - 109 q^{71} - 73 q^{72} - 46 q^{73} - 7 q^{74} - 146 q^{75} - 54 q^{76} - 46 q^{77} - 42 q^{78} - 12 q^{79} - 187 q^{80} + 100 q^{81} - 45 q^{82} - 156 q^{83} - 62 q^{84} - 13 q^{85} - 8 q^{86} - 76 q^{87} - 6 q^{88} - 140 q^{89} - 5 q^{90} - 37 q^{91} - 98 q^{92} - q^{93} - 17 q^{94} - 48 q^{95} - 12 q^{96} - 63 q^{97} - 17 q^{98} - 78 q^{99}+O(q^{100}) \) 104 * q - 17 * q^2 - 34 * q^3 + 99 * q^4 - 46 * q^5 - 18 * q^6 + 104 * q^7 - 48 * q^8 + 98 * q^9 - 17 * q^10 - 46 * q^11 - 62 * q^12 - 37 * q^13 - 17 * q^14 - 17 * q^15 + 93 * q^16 - 75 * q^17 - 41 * q^18 - 40 * q^19 - 106 * q^20 - 34 * q^21 - 14 * q^22 - 57 * q^23 - 38 * q^24 + 102 * q^25 - 45 * q^26 - 121 * q^27 + 99 * q^28 - 29 * q^29 + 26 * q^30 - 42 * q^31 - 113 * q^32 - 42 * q^33 - 7 * q^34 - 46 * q^35 + 99 * q^36 - 31 * q^37 - 62 * q^38 - 9 * q^39 - 36 * q^40 - 106 * q^41 - 18 * q^42 - 29 * q^43 - 60 * q^44 - 121 * q^45 + 21 * q^46 - 141 * q^47 - 88 * q^48 + 104 * q^49 - 70 * q^50 - 2 * q^51 - 58 * q^52 - 70 * q^53 - 49 * q^54 - 14 * q^55 - 48 * q^56 - 11 * q^57 - 28 * q^58 - 202 * q^59 + 17 * q^60 - 79 * q^61 - 41 * q^62 + 98 * q^63 + 110 * q^64 - 34 * q^65 - 21 * q^66 - 57 * q^67 - 180 * q^68 - 99 * q^69 - 17 * q^70 - 109 * q^71 - 73 * q^72 - 46 * q^73 - 7 * q^74 - 146 * q^75 - 54 * q^76 - 46 * q^77 - 42 * q^78 - 12 * q^79 - 187 * q^80 + 100 * q^81 - 45 * q^82 - 156 * q^83 - 62 * q^84 - 13 * q^85 - 8 * q^86 - 76 * q^87 - 6 * q^88 - 140 * q^89 - 5 * q^90 - 37 * q^91 - 98 * q^92 - q^93 - 17 * q^94 - 48 * q^95 - 12 * q^96 - 63 * q^97 - 17 * q^98 - 78 * q^99

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