LMFDB - Embedded newform 6037.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70464 q^{2} +1.55203 q^{3} +5.31508 q^{4} +0.654263 q^{5} -4.19768 q^{6} +0.835894 q^{7} -8.96611 q^{8} -0.591204 q^{9} +O(q^{10})$	\(q-2.70464 q^{2} +1.55203 q^{3} +5.31508 q^{4} +0.654263 q^{5} -4.19768 q^{6} +0.835894 q^{7} -8.96611 q^{8} -0.591204 q^{9} -1.76955 q^{10} -0.688569 q^{11} +8.24917 q^{12} +3.20921 q^{13} -2.26079 q^{14} +1.01544 q^{15} +13.6199 q^{16} -3.02864 q^{17} +1.59900 q^{18} +5.64870 q^{19} +3.47746 q^{20} +1.29733 q^{21} +1.86233 q^{22} +3.99803 q^{23} -13.9157 q^{24} -4.57194 q^{25} -8.67975 q^{26} -5.57366 q^{27} +4.44285 q^{28} -7.24035 q^{29} -2.74639 q^{30} +7.60677 q^{31} -18.9048 q^{32} -1.06868 q^{33} +8.19138 q^{34} +0.546894 q^{35} -3.14230 q^{36} +3.41844 q^{37} -15.2777 q^{38} +4.98078 q^{39} -5.86619 q^{40} -10.6857 q^{41} -3.50882 q^{42} -10.2333 q^{43} -3.65980 q^{44} -0.386803 q^{45} -10.8132 q^{46} -12.6153 q^{47} +21.1385 q^{48} -6.30128 q^{49} +12.3655 q^{50} -4.70054 q^{51} +17.0572 q^{52} -4.49378 q^{53} +15.0747 q^{54} -0.450505 q^{55} -7.49472 q^{56} +8.76694 q^{57} +19.5825 q^{58} -5.22377 q^{59} +5.39712 q^{60} -0.140427 q^{61} -20.5736 q^{62} -0.494184 q^{63} +23.8909 q^{64} +2.09966 q^{65} +2.89040 q^{66} +7.99352 q^{67} -16.0975 q^{68} +6.20506 q^{69} -1.47915 q^{70} +2.56581 q^{71} +5.30080 q^{72} -13.1396 q^{73} -9.24565 q^{74} -7.09579 q^{75} +30.0233 q^{76} -0.575571 q^{77} -13.4712 q^{78} -9.21355 q^{79} +8.91102 q^{80} -6.87686 q^{81} +28.9010 q^{82} -2.19860 q^{83} +6.89543 q^{84} -1.98152 q^{85} +27.6775 q^{86} -11.2372 q^{87} +6.17379 q^{88} +2.93598 q^{89} +1.04616 q^{90} +2.68256 q^{91} +21.2499 q^{92} +11.8059 q^{93} +34.1198 q^{94} +3.69573 q^{95} -29.3409 q^{96} +0.535520 q^{97} +17.0427 q^{98} +0.407085 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.70464	−1.91247	−0.956235	−	0.292600i	$-0.905480\pi$
$2$	−2.70464	−1.91247	−0.956235	+	0.292600i	$0.905480\pi$
$3$	1.55203	0.896065	0.448032	−	0.894017i	$-0.352125\pi$
$3$	1.55203	0.896065	0.448032	+	0.894017i	$0.352125\pi$
$4$	5.31508	2.65754
$5$	0.654263	0.292595	0.146298	−	0.989241i	$-0.453264\pi$
$5$	0.654263	0.292595	0.146298	+	0.989241i	$0.453264\pi$
$6$	−4.19768	−1.71370
$7$	0.835894	0.315938	0.157969	−	0.987444i	$-0.449505\pi$
$7$	0.835894	0.315938	0.157969	+	0.987444i	$0.449505\pi$
$8$	−8.96611	−3.17000
$9$	−0.591204	−0.197068
$10$	−1.76955	−0.559580
$11$	−0.688569	−0.207611	−0.103806	−	0.994598i	$-0.533102\pi$
$11$	−0.688569	−0.207611	−0.103806	+	0.994598i	$0.533102\pi$
$12$	8.24917	2.38133
$13$	3.20921	0.890073	0.445037	−	0.895512i	$-0.353191\pi$
$13$	3.20921	0.890073	0.445037	+	0.895512i	$0.353191\pi$
$14$	−2.26079	−0.604222
$15$	1.01544	0.262184
$16$	13.6199	3.40499
$17$	−3.02864	−0.734553	−0.367276	−	0.930112i	$-0.619710\pi$
$17$	−3.02864	−0.734553	−0.367276	+	0.930112i	$0.619710\pi$
$18$	1.59900	0.376887
$19$	5.64870	1.29590	0.647950	−	0.761683i	$-0.275627\pi$
$19$	5.64870	1.29590	0.647950	+	0.761683i	$0.275627\pi$
$20$	3.47746	0.777584
$21$	1.29733	0.283101
$22$	1.86233	0.397051
$23$	3.99803	0.833647	0.416823	−	0.908988i	$-0.363143\pi$
$23$	3.99803	0.833647	0.416823	+	0.908988i	$0.363143\pi$
$24$	−13.9157	−2.84052
$25$	−4.57194	−0.914388
$26$	−8.67975	−1.70224
$27$	−5.57366	−1.07265
$28$	4.44285	0.839619
$29$	−7.24035	−1.34450	−0.672250	−	0.740324i	$-0.734672\pi$
$29$	−7.24035	−1.34450	−0.672250	+	0.740324i	$0.734672\pi$
$30$	−2.74639	−0.501419
$31$	7.60677	1.36622	0.683108	−	0.730318i	$-0.260628\pi$
$31$	7.60677	1.36622	0.683108	+	0.730318i	$0.260628\pi$
$32$	−18.9048	−3.34193
$33$	−1.06868	−0.186033
$34$	8.19138	1.40481
$35$	0.546894	0.0924420
$36$	−3.14230	−0.523717
$37$	3.41844	0.561988	0.280994	−	0.959710i	$-0.409336\pi$
$37$	3.41844	0.561988	0.280994	+	0.959710i	$0.409336\pi$
$38$	−15.2777	−2.47837
$39$	4.98078	0.797563
$40$	−5.86619	−0.927526
$41$	−10.6857	−1.66883	−0.834414	−	0.551139i	$-0.814194\pi$
$41$	−10.6857	−1.66883	−0.834414	+	0.551139i	$0.814194\pi$
$42$	−3.50882	−0.541422
$43$	−10.2333	−1.56057	−0.780285	−	0.625424i	$-0.784926\pi$
$43$	−10.2333	−1.56057	−0.780285	+	0.625424i	$0.784926\pi$
$44$	−3.65980	−0.551736
$45$	−0.386803	−0.0576612
$46$	−10.8132	−1.59432
$47$	−12.6153	−1.84013	−0.920065	−	0.391767i	$-0.871864\pi$
$47$	−12.6153	−1.84013	−0.920065	+	0.391767i	$0.871864\pi$
$48$	21.1385	3.05109
$49$	−6.30128	−0.900183
$50$	12.3655	1.74874
$51$	−4.70054	−0.658207
$52$	17.0572	2.36541
$53$	−4.49378	−0.617269	−0.308634	−	0.951181i	$-0.599872\pi$
$53$	−4.49378	−0.617269	−0.308634	+	0.951181i	$0.599872\pi$
$54$	15.0747	2.05141
$55$	−0.450505	−0.0607461
$56$	−7.49472	−1.00152
$57$	8.76694	1.16121
$58$	19.5825	2.57131
$59$	−5.22377	−0.680078	−0.340039	−	0.940411i	$-0.610440\pi$
$59$	−5.22377	−0.680078	−0.340039	+	0.940411i	$0.610440\pi$
$60$	5.39712	0.696765
$61$	−0.140427	−0.0179799	−0.00898993	−	0.999960i	$-0.502862\pi$
$61$	−0.140427	−0.0179799	−0.00898993	+	0.999960i	$0.502862\pi$
$62$	−20.5736	−2.61285
$63$	−0.494184	−0.0622613
$64$	23.8909	2.98636
$65$	2.09966	0.260431
$66$	2.89040	0.355783
$67$	7.99352	0.976564	0.488282	−	0.872686i	$-0.337624\pi$
$67$	7.99352	0.976564	0.488282	+	0.872686i	$0.337624\pi$
$68$	−16.0975	−1.95210
$69$	6.20506	0.747001
$70$	−1.47915	−0.176793
$71$	2.56581	0.304506	0.152253	−	0.988342i	$-0.451347\pi$
$71$	2.56581	0.304506	0.152253	+	0.988342i	$0.451347\pi$
$72$	5.30080	0.624705
$73$	−13.1396	−1.53788	−0.768938	−	0.639324i	$-0.779214\pi$
$73$	−13.1396	−1.53788	−0.768938	+	0.639324i	$0.779214\pi$
$74$	−9.24565	−1.07478
$75$	−7.09579	−0.819351
$76$	30.0233	3.44391
$77$	−0.575571	−0.0655924
$78$	−13.4712	−1.52532
$79$	−9.21355	−1.03661	−0.518303	−	0.855197i	$-0.673436\pi$
$79$	−9.21355	−1.03661	−0.518303	+	0.855197i	$0.673436\pi$
$80$	8.91102	0.996282
$81$	−6.87686	−0.764096
$82$	28.9010	3.19158
$83$	−2.19860	−0.241327	−0.120664	−	0.992693i	$-0.538502\pi$
$83$	−2.19860	−0.241327	−0.120664	+	0.992693i	$0.538502\pi$
$84$	6.89543	0.752353
$85$	−1.98152	−0.214927
$86$	27.6775	2.98455
$87$	−11.2372	−1.20476
$88$	6.17379	0.658128
$89$	2.93598	0.311213	0.155606	−	0.987819i	$-0.450267\pi$
$89$	2.93598	0.311213	0.155606	+	0.987819i	$0.450267\pi$
$90$	1.04616	0.110275
$91$	2.68256	0.281208
$92$	21.2499	2.21545
$93$	11.8059	1.22422
$94$	34.1198	3.51919
$95$	3.69573	0.379174
$96$	−29.3409	−2.99459
$97$	0.535520	0.0543738	0.0271869	−	0.999630i	$-0.491345\pi$
$97$	0.535520	0.0543738	0.0271869	+	0.999630i	$0.491345\pi$
$98$	17.0427	1.72157
$99$	0.407085	0.0409136
$100$	−24.3002	−2.43002
$101$	6.65835	0.662530	0.331265	−	0.943538i	$-0.392525\pi$
$101$	6.65835	0.662530	0.331265	+	0.943538i	$0.392525\pi$
$102$	12.7133	1.25880
$103$	1.66958	0.164508	0.0822542	−	0.996611i	$-0.473788\pi$
$103$	1.66958	0.164508	0.0822542	+	0.996611i	$0.473788\pi$
$104$	−28.7741	−2.82153
$105$	0.848796	0.0828340
$106$	12.1541	1.18051
$107$	13.7829	1.33245	0.666223	−	0.745752i	$-0.267910\pi$
$107$	13.7829	1.33245	0.666223	+	0.745752i	$0.267910\pi$
$108$	−29.6244	−2.85061
$109$	−3.00420	−0.287750	−0.143875	−	0.989596i	$-0.545956\pi$
$109$	−3.00420	−0.287750	−0.143875	+	0.989596i	$0.545956\pi$
$110$	1.21846	0.116175
$111$	5.30552	0.503577
$112$	11.3848	1.07576
$113$	5.49088	0.516539	0.258269	−	0.966073i	$-0.416848\pi$
$113$	5.49088	0.516539	0.258269	+	0.966073i	$0.416848\pi$
$114$	−23.7114	−2.22078
$115$	2.61576	0.243921
$116$	−38.4831	−3.57306
$117$	−1.89730	−0.175405
$118$	14.1284	1.30063
$119$	−2.53162	−0.232073
$120$	−9.10450	−0.831124
$121$	−10.5259	−0.956897
$122$	0.379805	0.0343859
$123$	−16.5845	−1.49538
$124$	40.4306	3.63077
$125$	−6.26256	−0.560141
$126$	1.33659	0.119073
$127$	−9.42358	−0.836208	−0.418104	−	0.908399i	$-0.637305\pi$
$127$	−9.42358	−0.836208	−0.418104	+	0.908399i	$0.637305\pi$
$128$	−26.8066	−2.36939
$129$	−15.8825	−1.39837
$130$	−5.67884	−0.498067
$131$	12.7971	1.11809	0.559043	−	0.829138i	$-0.311169\pi$
$131$	12.7971	1.11809	0.559043	+	0.829138i	$0.311169\pi$
$132$	−5.68012	−0.494391
$133$	4.72171	0.409424
$134$	−21.6196	−1.86765
$135$	−3.64664	−0.313852
$136$	27.1551	2.32853
$137$	1.71417	0.146451	0.0732255	−	0.997315i	$-0.476671\pi$
$137$	1.71417	0.146451	0.0732255	+	0.997315i	$0.476671\pi$
$138$	−16.7825	−1.42862
$139$	6.58532	0.558560	0.279280	−	0.960210i	$-0.409904\pi$
$139$	6.58532	0.558560	0.279280	+	0.960210i	$0.409904\pi$
$140$	2.90679	0.245668
$141$	−19.5793	−1.64887
$142$	−6.93961	−0.582359
$143$	−2.20976	−0.184789
$144$	−8.05217	−0.671014
$145$	−4.73709	−0.393394
$146$	35.5379	2.94114
$147$	−9.77977	−0.806622
$148$	18.1693	1.49351
$149$	11.8037	0.966999	0.483499	−	0.875345i	$-0.339366\pi$
$149$	11.8037	0.966999	0.483499	+	0.875345i	$0.339366\pi$
$150$	19.1916	1.56698
$151$	−7.95433	−0.647314	−0.323657	−	0.946174i	$-0.604912\pi$
$151$	−7.95433	−0.647314	−0.323657	+	0.946174i	$0.604912\pi$
$152$	−50.6468	−4.10800
$153$	1.79054	0.144757
$154$	1.55671	0.125444
$155$	4.97682	0.399748
$156$	26.4733	2.11956
$157$	−19.5433	−1.55973	−0.779864	−	0.625949i	$-0.784712\pi$
$157$	−19.5433	−1.55973	−0.779864	+	0.625949i	$0.784712\pi$
$158$	24.9193	1.98248
$159$	−6.97448	−0.553113
$160$	−12.3687	−0.977834
$161$	3.34193	0.263381
$162$	18.5995	1.46131
$163$	23.3689	1.83040	0.915198	−	0.403005i	$-0.132034\pi$
$163$	23.3689	1.83040	0.915198	+	0.403005i	$0.132034\pi$
$164$	−56.7954	−4.43498
$165$	−0.699198	−0.0544325
$166$	5.94641	0.461531
$167$	−10.7475	−0.831668	−0.415834	−	0.909440i	$-0.636510\pi$
$167$	−10.7475	−0.831668	−0.415834	+	0.909440i	$0.636510\pi$
$168$	−11.6320	−0.897430
$169$	−2.70100	−0.207769
$170$	5.35931	0.411041
$171$	−3.33953	−0.255381
$172$	−54.3911	−4.14728
$173$	−10.9088	−0.829380	−0.414690	−	0.909963i	$-0.636110\pi$
$173$	−10.9088	−0.829380	−0.414690	+	0.909963i	$0.636110\pi$
$174$	30.3927	2.30406
$175$	−3.82166	−0.288890
$176$	−9.37827	−0.706914
$177$	−8.10745	−0.609393
$178$	−7.94076	−0.595185
$179$	3.53078	0.263903	0.131951	−	0.991256i	$-0.457876\pi$
$179$	3.53078	0.263903	0.131951	+	0.991256i	$0.457876\pi$
$180$	−2.05589	−0.153237
$181$	−14.9201	−1.10900	−0.554501	−	0.832183i	$-0.687091\pi$
$181$	−14.9201	−1.10900	−0.554501	+	0.832183i	$0.687091\pi$
$182$	−7.25535	−0.537802
$183$	−0.217947	−0.0161111
$184$	−35.8468	−2.64266
$185$	2.23656	0.164435
$186$	−31.9308	−2.34128
$187$	2.08543	0.152502
$188$	−67.0513	−4.89022
$189$	−4.65898	−0.338891
$190$	−9.99563	−0.725159
$191$	12.7505	0.922594	0.461297	−	0.887246i	$-0.347384\pi$
$191$	12.7505	0.922594	0.461297	+	0.887246i	$0.347384\pi$
$192$	37.0794	2.67597
$193$	−7.64286	−0.550145	−0.275073	−	0.961423i	$-0.588702\pi$
$193$	−7.64286	−0.550145	−0.275073	+	0.961423i	$0.588702\pi$
$194$	−1.44839	−0.103988
$195$	3.25874	0.233363
$196$	−33.4918	−2.39227
$197$	−15.2449	−1.08615	−0.543076	−	0.839684i	$-0.682740\pi$
$197$	−15.2449	−1.08615	−0.543076	+	0.839684i	$0.682740\pi$
$198$	−1.10102	−0.0782460
$199$	7.76084	0.550152	0.275076	−	0.961423i	$-0.411297\pi$
$199$	7.76084	0.550152	0.275076	+	0.961423i	$0.411297\pi$
$200$	40.9925	2.89861
$201$	12.4062	0.875065
$202$	−18.0084	−1.26707
$203$	−6.05217	−0.424779
$204$	−24.9837	−1.74921
$205$	−6.99126	−0.488291
$206$	−4.51561	−0.314617
$207$	−2.36365	−0.164285
$208$	43.7092	3.03069
$209$	−3.88952	−0.269044
$210$	−2.29569	−0.158418
$211$	−16.2574	−1.11921	−0.559604	−	0.828760i	$-0.689047\pi$
$211$	−16.2574	−1.11921	−0.559604	+	0.828760i	$0.689047\pi$
$212$	−23.8848	−1.64042
$213$	3.98222	0.272857
$214$	−37.2779	−2.54826
$215$	−6.69530	−0.456616
$216$	49.9740	3.40030
$217$	6.35845	0.431640
$218$	8.12529	0.550314
$219$	−20.3931	−1.37804
$220$	−2.39447	−0.161435
$221$	−9.71952	−0.653806
$222$	−14.3495	−0.963077
$223$	−8.31067	−0.556524	−0.278262	−	0.960505i	$-0.589758\pi$
$223$	−8.31067	−0.556524	−0.278262	+	0.960505i	$0.589758\pi$
$224$	−15.8024	−1.05584
$225$	2.70295	0.180197
$226$	−14.8509	−0.987865
$227$	22.4587	1.49063	0.745317	−	0.666710i	$-0.232298\pi$
$227$	22.4587	1.49063	0.745317	+	0.666710i	$0.232298\pi$
$228$	46.5970	3.08596
$229$	15.8696	1.04869	0.524345	−	0.851506i	$-0.324310\pi$
$229$	15.8696	1.04869	0.524345	+	0.851506i	$0.324310\pi$
$230$	−7.07470	−0.466492
$231$	−0.893303	−0.0587750
$232$	64.9178	4.26206
$233$	11.1417	0.729915	0.364957	−	0.931024i	$-0.381084\pi$
$233$	11.1417	0.729915	0.364957	+	0.931024i	$0.381084\pi$
$234$	5.13150	0.335457
$235$	−8.25371	−0.538413
$236$	−27.7648	−1.80733
$237$	−14.2997	−0.928865
$238$	6.84712	0.443833
$239$	−13.9636	−0.903232	−0.451616	−	0.892212i	$-0.649152\pi$
$239$	−13.9636	−0.903232	−0.451616	+	0.892212i	$0.649152\pi$
$240$	13.8302	0.892733
$241$	−2.34834	−0.151270	−0.0756350	−	0.997136i	$-0.524098\pi$
$241$	−2.34834	−0.151270	−0.0756350	+	0.997136i	$0.524098\pi$
$242$	28.4687	1.83004
$243$	6.04787	0.387971
$244$	−0.746382	−0.0477822
$245$	−4.12269	−0.263389
$246$	44.8552	2.85986
$247$	18.1278	1.15345
$248$	−68.2031	−4.33090
$249$	−3.41229	−0.216245
$250$	16.9380	1.07125
$251$	24.9145	1.57259	0.786294	−	0.617853i	$-0.211997\pi$
$251$	24.9145	1.57259	0.786294	+	0.617853i	$0.211997\pi$
$252$	−2.62663	−0.165462
$253$	−2.75292	−0.173075
$254$	25.4874	1.59922
$255$	−3.07539	−0.192588
$256$	24.7205	1.54503
$257$	−7.69580	−0.480051	−0.240025	−	0.970767i	$-0.577156\pi$
$257$	−7.69580	−0.480051	−0.240025	+	0.970767i	$0.577156\pi$
$258$	42.9563	2.67435
$259$	2.85745	0.177553
$260$	11.1599	0.692107
$261$	4.28053	0.264958
$262$	−34.6115	−2.13831
$263$	−13.8659	−0.855006	−0.427503	−	0.904014i	$-0.640607\pi$
$263$	−13.8659	−0.855006	−0.427503	+	0.904014i	$0.640607\pi$
$264$	9.58190	0.589725
$265$	−2.94012	−0.180610
$266$	−12.7705	−0.783012
$267$	4.55672	0.278867
$268$	42.4862	2.59526
$269$	−18.5358	−1.13015	−0.565073	−	0.825041i	$-0.691152\pi$
$269$	−18.5358	−1.13015	−0.565073	+	0.825041i	$0.691152\pi$
$270$	9.86284	0.600233
$271$	19.9446	1.21155	0.605774	−	0.795637i	$-0.292864\pi$
$271$	19.9446	1.21155	0.605774	+	0.795637i	$0.292864\pi$
$272$	−41.2499	−2.50114
$273$	4.16340	0.251981
$274$	−4.63620	−0.280083
$275$	3.14810	0.189837
$276$	32.9804	1.98519
$277$	11.7613	0.706666	0.353333	−	0.935498i	$-0.385048\pi$
$277$	11.7613	0.706666	0.353333	+	0.935498i	$0.385048\pi$
$278$	−17.8109	−1.06823
$279$	−4.49715	−0.269237
$280$	−4.90351	−0.293041
$281$	4.16348	0.248372	0.124186	−	0.992259i	$-0.460368\pi$
$281$	4.16348	0.248372	0.124186	+	0.992259i	$0.460368\pi$
$282$	52.9550	3.15342
$283$	12.7844	0.759951	0.379976	−	0.924997i	$-0.375932\pi$
$283$	12.7844	0.759951	0.379976	+	0.924997i	$0.375932\pi$
$284$	13.6375	0.809238
$285$	5.73589	0.339765
$286$	5.97661	0.353404
$287$	−8.93212	−0.527246
$288$	11.1766	0.658588
$289$	−7.82735	−0.460433
$290$	12.8121	0.752354
$291$	0.831142	0.0487224
$292$	−69.8381	−4.08697
$293$	−12.0790	−0.705661	−0.352831	−	0.935687i	$-0.614781\pi$
$293$	−12.0790	−0.705661	−0.352831	+	0.935687i	$0.614781\pi$
$294$	26.4508	1.54264
$295$	−3.41772	−0.198987
$296$	−30.6501	−1.78150
$297$	3.83785	0.222695
$298$	−31.9248	−1.84936
$299$	12.8305	0.742007
$300$	−37.7147	−2.17746
$301$	−8.55399	−0.493044
$302$	21.5136	1.23797
$303$	10.3340	0.593670
$304$	76.9349	4.41252
$305$	−0.0918763	−0.00526082
$306$	−4.84278	−0.276843
$307$	−7.88088	−0.449786	−0.224893	−	0.974383i	$-0.572203\pi$
$307$	−7.88088	−0.449786	−0.224893	+	0.974383i	$0.572203\pi$
$308$	−3.05921	−0.174315
$309$	2.59123	0.147410
$310$	−13.4605	−0.764506
$311$	−3.30939	−0.187658	−0.0938290	−	0.995588i	$-0.529911\pi$
$311$	−3.30939	−0.187658	−0.0938290	+	0.995588i	$0.529911\pi$
$312$	−44.6582	−2.52827
$313$	−16.2966	−0.921140	−0.460570	−	0.887623i	$-0.652355\pi$
$313$	−16.2966	−0.921140	−0.460570	+	0.887623i	$0.652355\pi$
$314$	52.8577	2.98293
$315$	−0.323326	−0.0182174
$316$	−48.9708	−2.75482
$317$	−14.7029	−0.825795	−0.412897	−	0.910778i	$-0.635483\pi$
$317$	−14.7029	−0.825795	−0.412897	+	0.910778i	$0.635483\pi$
$318$	18.8635	1.05781
$319$	4.98548	0.279134
$320$	15.6309	0.873795
$321$	21.3915	1.19396
$322$	−9.03871	−0.503708
$323$	−17.1079	−0.951907
$324$	−36.5511	−2.03062
$325$	−14.6723	−0.813872
$326$	−63.2045	−3.50058
$327$	−4.66261	−0.257843
$328$	95.8092	5.29018
$329$	−10.5450	−0.581367
$330$	1.89108	0.104100
$331$	26.6607	1.46541	0.732703	−	0.680548i	$-0.238258\pi$
$331$	26.6607	1.46541	0.732703	+	0.680548i	$0.238258\pi$
$332$	−11.6857	−0.641337
$333$	−2.02100	−0.110750
$334$	29.0682	1.59054
$335$	5.22986	0.285738
$336$	17.6696	0.963955
$337$	9.65859	0.526137	0.263069	−	0.964777i	$-0.415265\pi$
$337$	9.65859	0.526137	0.263069	+	0.964777i	$0.415265\pi$
$338$	7.30524	0.397353
$339$	8.52201	0.462852
$340$	−10.5320	−0.571176
$341$	−5.23779	−0.283642
$342$	9.03224	0.488408
$343$	−11.1185	−0.600340
$344$	91.7533	4.94701
$345$	4.05974	0.218569
$346$	29.5044	1.58616
$347$	15.1418	0.812856	0.406428	−	0.913683i	$-0.366774\pi$
$347$	15.1418	0.812856	0.406428	+	0.913683i	$0.366774\pi$
$348$	−59.7269	−3.20170
$349$	30.2124	1.61723	0.808617	−	0.588335i	$-0.200217\pi$
$349$	30.2124	1.61723	0.808617	+	0.588335i	$0.200217\pi$
$350$	10.3362	0.552494
$351$	−17.8870	−0.954738
$352$	13.0173	0.693824
$353$	−37.2669	−1.98352	−0.991758	−	0.128124i	$-0.959105\pi$
$353$	−37.2669	−1.98352	−0.991758	+	0.128124i	$0.959105\pi$
$354$	21.9277	1.16545
$355$	1.67872	0.0890970
$356$	15.6050	0.827061
$357$	−3.92915	−0.207953
$358$	−9.54949	−0.504706
$359$	−17.2820	−0.912107	−0.456053	−	0.889952i	$-0.650737\pi$
$359$	−17.2820	−0.912107	−0.456053	+	0.889952i	$0.650737\pi$
$360$	3.46812	0.182786
$361$	12.9078	0.679357
$362$	40.3535	2.12093
$363$	−16.3365	−0.857442
$364$	14.2580	0.747322
$365$	−8.59676	−0.449975
$366$	0.589469	0.0308120
$367$	30.6510	1.59997	0.799983	−	0.600022i	$-0.204842\pi$
$367$	30.6510	1.59997	0.799983	+	0.600022i	$0.204842\pi$
$368$	54.4529	2.83855
$369$	6.31744	0.328873
$370$	−6.04908	−0.314477
$371$	−3.75633	−0.195019
$372$	62.7495	3.25341
$373$	−25.6324	−1.32720	−0.663598	−	0.748089i	$-0.730971\pi$
$373$	−25.6324	−1.32720	−0.663598	+	0.748089i	$0.730971\pi$
$374$	−5.64033	−0.291655
$375$	−9.71968	−0.501922
$376$	113.110	5.83321
$377$	−23.2358	−1.19670
$378$	12.6009	0.648119
$379$	−22.3881	−1.15000	−0.575000	−	0.818153i	$-0.694998\pi$
$379$	−22.3881	−1.15000	−0.575000	+	0.818153i	$0.694998\pi$
$380$	19.6431	1.00767
$381$	−14.6257	−0.749296
$382$	−34.4855	−1.76443
$383$	−8.02017	−0.409811	−0.204906	−	0.978782i	$-0.565689\pi$
$383$	−8.02017	−0.409811	−0.204906	+	0.978782i	$0.565689\pi$
$384$	−41.6047	−2.12313
$385$	−0.376575	−0.0191920
$386$	20.6712	1.05214
$387$	6.05000	0.307539
$388$	2.84633	0.144501
$389$	−13.3117	−0.674932	−0.337466	−	0.941338i	$-0.609570\pi$
$389$	−13.3117	−0.674932	−0.337466	+	0.941338i	$0.609570\pi$
$390$	−8.81372	−0.446300
$391$	−12.1086	−0.612357
$392$	56.4980	2.85358
$393$	19.8615	1.00188
$394$	41.2319	2.07723
$395$	−6.02808	−0.303306
$396$	2.16369	0.108730
$397$	16.7626	0.841292	0.420646	−	0.907225i	$-0.361803\pi$
$397$	16.7626	0.841292	0.420646	+	0.907225i	$0.361803\pi$
$398$	−20.9903	−1.05215
$399$	7.32824	0.366871
$400$	−62.2696	−3.11348
$401$	−14.0346	−0.700853	−0.350427	−	0.936590i	$-0.613963\pi$
$401$	−14.0346	−0.700853	−0.350427	+	0.936590i	$0.613963\pi$
$402$	−33.5543	−1.67353
$403$	24.4117	1.21603
$404$	35.3897	1.76070
$405$	−4.49928	−0.223571
$406$	16.3689	0.812377
$407$	−2.35383	−0.116675
$408$	42.1455	2.08651
$409$	17.9419	0.887170	0.443585	−	0.896232i	$-0.353706\pi$
$409$	17.9419	0.887170	0.443585	+	0.896232i	$0.353706\pi$
$410$	18.9089	0.933842
$411$	2.66044	0.131230
$412$	8.87394	0.437188
$413$	−4.36652	−0.214862
$414$	6.39283	0.314190
$415$	−1.43846	−0.0706112
$416$	−60.6695	−2.97457
$417$	10.2206	0.500505
$418$	10.5198	0.514538
$419$	35.8275	1.75029	0.875144	−	0.483862i	$-0.160766\pi$
$419$	35.8275	1.75029	0.875144	+	0.483862i	$0.160766\pi$
$420$	4.51142	0.220135
$421$	18.9888	0.925455	0.462728	−	0.886501i	$-0.346871\pi$
$421$	18.9888	0.925455	0.462728	+	0.886501i	$0.346871\pi$
$422$	43.9705	2.14045
$423$	7.45821	0.362631
$424$	40.2918	1.95674
$425$	13.8468	0.671666
$426$	−10.7705	−0.521831
$427$	−0.117382	−0.00568053
$428$	73.2575	3.54103
$429$	−3.42961	−0.165583
$430$	18.1084	0.873264
$431$	−15.8086	−0.761474	−0.380737	−	0.924683i	$-0.624330\pi$
$431$	−15.8086	−0.761474	−0.380737	+	0.924683i	$0.624330\pi$
$432$	−75.9128	−3.65236
$433$	−3.82261	−0.183703	−0.0918515	−	0.995773i	$-0.529279\pi$
$433$	−3.82261	−0.183703	−0.0918515	+	0.995773i	$0.529279\pi$
$434$	−17.1973	−0.825498
$435$	−7.35211	−0.352507
$436$	−15.9676	−0.764709
$437$	22.5837	1.08032
$438$	55.1559	2.63545
$439$	−30.6473	−1.46272	−0.731359	−	0.681993i	$-0.761113\pi$
$439$	−30.6473	−1.46272	−0.731359	+	0.681993i	$0.761113\pi$
$440$	4.03928	0.192565
$441$	3.72534	0.177397
$442$	26.2878	1.25038
$443$	−3.91557	−0.186034	−0.0930172	−	0.995665i	$-0.529651\pi$
$443$	−3.91557	−0.186034	−0.0930172	+	0.995665i	$0.529651\pi$
$444$	28.1993	1.33828
$445$	1.92090	0.0910594
$446$	22.4774	1.06434
$447$	18.3197	0.866494
$448$	19.9703	0.943506
$449$	26.6257	1.25655	0.628273	−	0.777993i	$-0.283762\pi$
$449$	26.6257	1.25655	0.628273	+	0.777993i	$0.283762\pi$
$450$	−7.31051	−0.344621
$451$	7.35785	0.346468
$452$	29.1845	1.37272
$453$	−12.3454	−0.580036
$454$	−60.7427	−2.85079
$455$	1.75510	0.0822802
$456$	−78.6054	−3.68103
$457$	−33.3844	−1.56166	−0.780829	−	0.624745i	$-0.785203\pi$
$457$	−33.3844	−1.56166	−0.780829	+	0.624745i	$0.785203\pi$
$458$	−42.9215	−2.00559
$459$	16.8806	0.787918
$460$	13.9030	0.648230
$461$	−28.4489	−1.32500	−0.662499	−	0.749062i	$-0.730504\pi$
$461$	−28.4489	−1.32500	−0.662499	+	0.749062i	$0.730504\pi$
$462$	2.41606	0.112405
$463$	19.0225	0.884052	0.442026	−	0.897002i	$-0.354260\pi$
$463$	19.0225	0.884052	0.442026	+	0.897002i	$0.354260\pi$
$464$	−98.6131	−4.57800
$465$	7.72418	0.358200
$466$	−30.1342	−1.39594
$467$	30.5109	1.41188	0.705939	−	0.708273i	$-0.250525\pi$
$467$	30.5109	1.41188	0.705939	+	0.708273i	$0.250525\pi$
$468$	−10.0843	−0.466146
$469$	6.68174	0.308534
$470$	22.3233	1.02970
$471$	−30.3318	−1.39762
$472$	46.8369	2.15584
$473$	7.04637	0.323992
$474$	38.6756	1.77643
$475$	−25.8255	−1.18496
$476$	−13.4558	−0.616744
$477$	2.65674	0.121644
$478$	37.7666	1.72740
$479$	17.4688	0.798168	0.399084	−	0.916914i	$-0.369328\pi$
$479$	17.4688	0.798168	0.399084	+	0.916914i	$0.369328\pi$
$480$	−19.1966	−0.876202
$481$	10.9705	0.500210
$482$	6.35142	0.289299
$483$	5.18677	0.236006
$484$	−55.9459	−2.54299
$485$	0.350371	0.0159095
$486$	−16.3573	−0.741983
$487$	−17.3114	−0.784455	−0.392227	−	0.919868i	$-0.628295\pi$
$487$	−17.3114	−0.784455	−0.392227	+	0.919868i	$0.628295\pi$
$488$	1.25909	0.0569961
$489$	36.2693	1.64015
$490$	11.1504	0.503724
$491$	31.5606	1.42431	0.712154	−	0.702023i	$-0.247720\pi$
$491$	31.5606	1.42431	0.712154	+	0.702023i	$0.247720\pi$
$492$	−88.1482	−3.97403
$493$	21.9284	0.987605
$494$	−49.0293	−2.20593
$495$	0.266341	0.0119711
$496$	103.604	4.65194
$497$	2.14475	0.0962051
$498$	9.22901	0.413562
$499$	−31.0560	−1.39026	−0.695129	−	0.718885i	$-0.744653\pi$
$499$	−31.0560	−1.39026	−0.695129	+	0.718885i	$0.744653\pi$
$500$	−33.2860	−1.48860
$501$	−16.6805	−0.745229
$502$	−67.3847	−3.00753
$503$	−3.95821	−0.176488	−0.0882439	−	0.996099i	$-0.528125\pi$
$503$	−3.95821	−0.176488	−0.0882439	+	0.996099i	$0.528125\pi$
$504$	4.43091	0.197368
$505$	4.35631	0.193853
$506$	7.44566	0.331000
$507$	−4.19204	−0.186175
$508$	−50.0871	−2.22226
$509$	−24.0115	−1.06429	−0.532144	−	0.846654i	$-0.678614\pi$
$509$	−24.0115	−1.06429	−0.532144	+	0.846654i	$0.678614\pi$
$510$	8.31781	0.368319
$511$	−10.9833	−0.485874
$512$	−13.2469	−0.585437
$513$	−31.4839	−1.39005
$514$	20.8144	0.918082
$515$	1.09234	0.0481343
$516$	−84.4166	−3.71623
$517$	8.68650	0.382032
$518$	−7.72838	−0.339566
$519$	−16.9308	−0.743178
$520$	−18.8258	−0.825566
$521$	−36.3650	−1.59318	−0.796591	−	0.604519i	$-0.793365\pi$
$521$	−36.3650	−1.59318	−0.796591	+	0.604519i	$0.793365\pi$
$522$	−11.5773	−0.506724
$523$	15.9132	0.695834	0.347917	−	0.937525i	$-0.386889\pi$
$523$	15.9132	0.695834	0.347917	+	0.937525i	$0.386889\pi$
$524$	68.0176	2.97136
$525$	−5.93132	−0.258864
$526$	37.5022	1.63517
$527$	−23.0381	−1.00356
$528$	−14.5554	−0.633441
$529$	−7.01577	−0.305033
$530$	7.95196	0.345411
$531$	3.08832	0.134022
$532$	25.0963	1.08806
$533$	−34.2926	−1.48538
$534$	−12.3243	−0.533325
$535$	9.01766	0.389868
$536$	−71.6708	−3.09571
$537$	5.47988	0.236474
$538$	50.1326	2.16137
$539$	4.33887	0.186888
$540$	−19.3822	−0.834076
$541$	16.6370	0.715283	0.357641	−	0.933859i	$-0.383581\pi$
$541$	16.6370	0.715283	0.357641	+	0.933859i	$0.383581\pi$
$542$	−53.9430	−2.31705
$543$	−23.1564	−0.993738
$544$	57.2559	2.45483
$545$	−1.96554	−0.0841944
$546$	−11.2605	−0.481906
$547$	−16.2060	−0.692917	−0.346458	−	0.938065i	$-0.612616\pi$
$547$	−16.2060	−0.692917	−0.346458	+	0.938065i	$0.612616\pi$
$548$	9.11093	0.389200
$549$	0.0830212	0.00354326
$550$	−8.51448	−0.363058
$551$	−40.8985	−1.74234
$552$	−55.6352	−2.36799
$553$	−7.70155	−0.327503
$554$	−31.8100	−1.35148
$555$	3.47120	0.147344
$556$	35.0015	1.48440
$557$	−20.6060	−0.873103	−0.436551	−	0.899679i	$-0.643800\pi$
$557$	−20.6060	−0.873103	−0.436551	+	0.899679i	$0.643800\pi$
$558$	12.1632	0.514909
$559$	−32.8409	−1.38902
$560$	7.44867	0.314764
$561$	3.23664	0.136651
$562$	−11.2607	−0.475005
$563$	13.4340	0.566176	0.283088	−	0.959094i	$-0.408641\pi$
$563$	13.4340	0.566176	0.283088	+	0.959094i	$0.408641\pi$
$564$	−104.066	−4.38195
$565$	3.59248	0.151137
$566$	−34.5771	−1.45338
$567$	−5.74833	−0.241407
$568$	−23.0054	−0.965284
$569$	−33.9557	−1.42350	−0.711748	−	0.702435i	$-0.752096\pi$
$569$	−33.9557	−1.42350	−0.711748	+	0.702435i	$0.752096\pi$
$570$	−15.5135	−0.649789
$571$	−12.7729	−0.534529	−0.267265	−	0.963623i	$-0.586120\pi$
$571$	−12.7729	−0.534529	−0.267265	+	0.963623i	$0.586120\pi$
$572$	−11.7451	−0.491086
$573$	19.7892	0.826704
$574$	24.1582	1.00834
$575$	−18.2787	−0.762276
$576$	−14.1244	−0.588517
$577$	9.15746	0.381230	0.190615	−	0.981665i	$-0.438952\pi$
$577$	9.15746	0.381230	0.190615	+	0.981665i	$0.438952\pi$
$578$	21.1702	0.880563
$579$	−11.8620	−0.492966
$580$	−25.1780	−1.04546
$581$	−1.83779	−0.0762445
$582$	−2.24794	−0.0931802
$583$	3.09428	0.128152
$584$	117.811	4.87506
$585$	−1.24133	−0.0513227
$586$	32.6693	1.34956
$587$	−39.8011	−1.64277	−0.821384	−	0.570375i	$-0.806798\pi$
$587$	−39.8011	−1.64277	−0.821384	+	0.570375i	$0.806798\pi$
$588$	−51.9803	−2.14363
$589$	42.9683	1.77048
$590$	9.24371	0.380557
$591$	−23.6605	−0.973262
$592$	46.5589	1.91356
$593$	4.95233	0.203368	0.101684	−	0.994817i	$-0.467577\pi$
$593$	4.95233	0.203368	0.101684	+	0.994817i	$0.467577\pi$
$594$	−10.3800	−0.425897
$595$	−1.65634	−0.0679035
$596$	62.7378	2.56984
$597$	12.0451	0.492971
$598$	−34.7019	−1.41907
$599$	24.3121	0.993367	0.496683	−	0.867932i	$-0.334551\pi$
$599$	24.3121	0.993367	0.496683	+	0.867932i	$0.334551\pi$
$600$	63.6216	2.59734
$601$	8.05050	0.328387	0.164193	−	0.986428i	$-0.447498\pi$
$601$	8.05050	0.328387	0.164193	+	0.986428i	$0.447498\pi$
$602$	23.1355	0.942932
$603$	−4.72580	−0.192450
$604$	−42.2779	−1.72026
$605$	−6.88669	−0.279984
$606$	−27.9496	−1.13538
$607$	20.6685	0.838907	0.419453	−	0.907777i	$-0.362222\pi$
$607$	20.6685	0.838907	0.419453	+	0.907777i	$0.362222\pi$
$608$	−106.788	−4.33081
$609$	−9.39314	−0.380629
$610$	0.248492	0.0100612
$611$	−40.4851	−1.63785
$612$	9.51689	0.384697
$613$	−29.4090	−1.18782	−0.593909	−	0.804532i	$-0.702416\pi$
$613$	−29.4090	−1.18782	−0.593909	+	0.804532i	$0.702416\pi$
$614$	21.3150	0.860202
$615$	−10.8506	−0.437540
$616$	5.16063	0.207928
$617$	29.8885	1.20327	0.601633	−	0.798773i	$-0.294517\pi$
$617$	29.8885	1.20327	0.601633	+	0.798773i	$0.294517\pi$
$618$	−7.00835	−0.281917
$619$	−44.2827	−1.77987	−0.889935	−	0.456087i	$-0.849251\pi$
$619$	−44.2827	−1.77987	−0.889935	+	0.456087i	$0.849251\pi$
$620$	26.4522	1.06235
$621$	−22.2836	−0.894211
$622$	8.95070	0.358890
$623$	2.45417	0.0983241
$624$	67.8379	2.71569
$625$	18.7623	0.750494
$626$	44.0765	1.76165
$627$	−6.03665	−0.241081
$628$	−103.874	−4.14504
$629$	−10.3532	−0.412810
$630$	0.874481	0.0348402
$631$	27.5192	1.09552	0.547762	−	0.836634i	$-0.315480\pi$
$631$	27.5192	1.09552	0.547762	+	0.836634i	$0.315480\pi$
$632$	82.6097	3.28604
$633$	−25.2320	−1.00288
$634$	39.7660	1.57931
$635$	−6.16550	−0.244670
$636$	−37.0700	−1.46992
$637$	−20.2221	−0.801229
$638$	−13.4839	−0.533834
$639$	−1.51692	−0.0600084
$640$	−17.5386	−0.693274
$641$	−5.30090	−0.209373	−0.104686	−	0.994505i	$-0.533384\pi$
$641$	−5.30090	−0.209373	−0.104686	+	0.994505i	$0.533384\pi$
$642$	−57.8564	−2.28341
$643$	−12.5243	−0.493912	−0.246956	−	0.969027i	$-0.579430\pi$
$643$	−12.5243	−0.493912	−0.246956	+	0.969027i	$0.579430\pi$
$644$	17.7626	0.699945
$645$	−10.3913	−0.409157
$646$	46.2706	1.82049
$647$	−27.9216	−1.09771	−0.548855	−	0.835918i	$-0.684936\pi$
$647$	−27.9216	−1.09771	−0.548855	+	0.835918i	$0.684936\pi$
$648$	61.6587	2.42218
$649$	3.59693	0.141192
$650$	39.6833	1.55651
$651$	9.86850	0.386777
$652$	124.208	4.86435
$653$	−17.1866	−0.672565	−0.336282	−	0.941761i	$-0.609170\pi$
$653$	−17.1866	−0.672565	−0.336282	+	0.941761i	$0.609170\pi$
$654$	12.6107	0.493117
$655$	8.37266	0.327147
$656$	−145.539	−5.68233
$657$	7.76820	0.303066
$658$	28.5206	1.11185
$659$	−33.3224	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$659$	−33.3224	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$660$	−3.71629	−0.144657
$661$	34.8130	1.35407	0.677034	−	0.735951i	$-0.263265\pi$
$661$	34.8130	1.35407	0.677034	+	0.735951i	$0.263265\pi$
$662$	−72.1077	−2.80255
$663$	−15.0850	−0.585852
$664$	19.7128	0.765007
$665$	3.08924	0.119796
$666$	5.46607	0.211806
$667$	−28.9471	−1.12084
$668$	−57.1240	−2.21019
$669$	−12.8984	−0.498681
$670$	−14.1449	−0.546465
$671$	0.0966939	0.00373283
$672$	−24.5258	−0.946105
$673$	−25.7025	−0.990758	−0.495379	−	0.868677i	$-0.664971\pi$
$673$	−25.7025	−0.990758	−0.495379	+	0.868677i	$0.664971\pi$
$674$	−26.1230	−1.00622
$675$	25.4824	0.980819
$676$	−14.3561	−0.552156
$677$	37.7711	1.45166	0.725830	−	0.687874i	$-0.241456\pi$
$677$	37.7711	1.45166	0.725830	+	0.687874i	$0.241456\pi$
$678$	−23.0490	−0.885191
$679$	0.447638	0.0171788
$680$	17.7666	0.681317
$681$	34.8565	1.33571
$682$	14.1663	0.542457
$683$	−11.0102	−0.421295	−0.210648	−	0.977562i	$-0.567557\pi$
$683$	−11.0102	−0.421295	−0.210648	+	0.977562i	$0.567557\pi$
$684$	−17.7499	−0.678684
$685$	1.12151	0.0428509
$686$	30.0714	1.14813
$687$	24.6300	0.939694
$688$	−139.378	−5.31372
$689$	−14.4215	−0.549414
$690$	−10.9801	−0.418007
$691$	37.8684	1.44058	0.720291	−	0.693672i	$-0.244008\pi$
$691$	37.8684	1.44058	0.720291	+	0.693672i	$0.244008\pi$
$692$	−57.9811	−2.20411
$693$	0.340280	0.0129262
$694$	−40.9532	−1.55456
$695$	4.30853	0.163432
$696$	100.754	3.81908
$697$	32.3631	1.22584
$698$	−81.7138	−3.09291
$699$	17.2922	0.654051
$700$	−20.3124	−0.767737
$701$	−14.7412	−0.556766	−0.278383	−	0.960470i	$-0.589798\pi$
$701$	−14.7412	−0.556766	−0.278383	+	0.960470i	$0.589798\pi$
$702$	48.3779	1.82591
$703$	19.3097	0.728280
$704$	−16.4505	−0.620003
$705$	−12.8100	−0.482453
$706$	100.794	3.79342
$707$	5.56567	0.209319
$708$	−43.0918	−1.61949
$709$	−10.9142	−0.409893	−0.204946	−	0.978773i	$-0.565702\pi$
$709$	−10.9142	−0.409893	−0.204946	+	0.978773i	$0.565702\pi$
$710$	−4.54033	−0.170395
$711$	5.44709	0.204282
$712$	−26.3243	−0.986544
$713$	30.4121	1.13894
$714$	10.6269	0.397703
$715$	−1.44576	−0.0540685
$716$	18.7664	0.701333
$717$	−21.6720	−0.809355
$718$	46.7415	1.74438
$719$	−11.6753	−0.435415	−0.217707	−	0.976014i	$-0.569858\pi$
$719$	−11.6753	−0.435415	−0.217707	+	0.976014i	$0.569858\pi$
$720$	−5.26823	−0.196335
$721$	1.39559	0.0519745
$722$	−34.9109	−1.29925
$723$	−3.64470	−0.135548
$724$	−79.3016	−2.94722
$725$	33.1025	1.22939
$726$	44.1843	1.63983
$727$	−28.5063	−1.05724	−0.528621	−	0.848858i	$-0.677291\pi$
$727$	−28.5063	−1.05724	−0.528621	+	0.848858i	$0.677291\pi$
$728$	−24.0521	−0.891429
$729$	30.0171	1.11174
$730$	23.2512	0.860564
$731$	30.9931	1.14632
$732$	−1.15841	−0.0428160
$733$	−37.6163	−1.38939	−0.694695	−	0.719305i	$-0.744461\pi$
$733$	−37.6163	−1.38939	−0.694695	+	0.719305i	$0.744461\pi$
$734$	−82.8998	−3.05989
$735$	−6.39854	−0.236014
$736$	−75.5820	−2.78599
$737$	−5.50409	−0.202746
$738$	−17.0864	−0.628959
$739$	−4.89899	−0.180212	−0.0901062	−	0.995932i	$-0.528721\pi$
$739$	−4.89899	−0.180212	−0.0901062	+	0.995932i	$0.528721\pi$
$740$	11.8875	0.436993
$741$	28.1349	1.03356
$742$	10.1595	0.372968
$743$	−10.6268	−0.389861	−0.194931	−	0.980817i	$-0.562448\pi$
$743$	−10.6268	−0.389861	−0.194931	+	0.980817i	$0.562448\pi$
$744$	−105.853	−3.88077
$745$	7.72274	0.282939
$746$	69.3265	2.53822
$747$	1.29982	0.0475579
$748$	11.0842	0.405279
$749$	11.5211	0.420971
$750$	26.2883	0.959911
$751$	14.4118	0.525893	0.262946	−	0.964810i	$-0.415306\pi$
$751$	14.4118	0.525893	0.262946	+	0.964810i	$0.415306\pi$
$752$	−171.819	−6.26561
$753$	38.6680	1.40914
$754$	62.8444	2.28866
$755$	−5.20422	−0.189401
$756$	−24.7629	−0.900618
$757$	−27.5148	−1.00004	−0.500022	−	0.866013i	$-0.666675\pi$
$757$	−27.5148	−1.00004	−0.500022	+	0.866013i	$0.666675\pi$
$758$	60.5518	2.19934
$759$	−4.27261	−0.155086
$760$	−33.1363	−1.20198
$761$	36.1869	1.31177	0.655887	−	0.754859i	$-0.272295\pi$
$761$	36.1869	1.31177	0.655887	+	0.754859i	$0.272295\pi$
$762$	39.5572	1.43301
$763$	−2.51120	−0.0909114
$764$	67.7700	2.45183
$765$	1.17149	0.0423552
$766$	21.6917	0.783752
$767$	−16.7642	−0.605319
$768$	38.3670	1.38445
$769$	3.08536	0.111261	0.0556304	−	0.998451i	$-0.482283\pi$
$769$	3.08536	0.111261	0.0556304	+	0.998451i	$0.482283\pi$
$770$	1.01850	0.0367042
$771$	−11.9441	−0.430156
$772$	−40.6225	−1.46203
$773$	21.4675	0.772131	0.386065	−	0.922471i	$-0.373834\pi$
$773$	21.4675	0.772131	0.386065	+	0.922471i	$0.373834\pi$
$774$	−16.3631	−0.588159
$775$	−34.7777	−1.24925
$776$	−4.80153	−0.172365
$777$	4.43485	0.159099
$778$	36.0035	1.29079
$779$	−60.3603	−2.16263
$780$	17.3205	0.620172
$781$	−1.76674	−0.0632190
$782$	32.7494	1.17111
$783$	40.3552	1.44218
$784$	−85.8231	−3.06511
$785$	−12.7865	−0.456369
$786$	−53.7181	−1.91606
$787$	1.38563	0.0493922	0.0246961	−	0.999695i	$-0.492138\pi$
$787$	1.38563	0.0493922	0.0246961	+	0.999695i	$0.492138\pi$
$788$	−81.0277	−2.88649
$789$	−21.5202	−0.766141
$790$	16.3038	0.580063
$791$	4.58980	0.163194
$792$	−3.64997	−0.129696
$793$	−0.450660	−0.0160034
$794$	−45.3369	−1.60895
$795$	−4.56315	−0.161838
$796$	41.2495	1.46205
$797$	25.8299	0.914942	0.457471	−	0.889225i	$-0.348755\pi$
$797$	25.8299	0.914942	0.457471	+	0.889225i	$0.348755\pi$
$798$	−19.8202	−0.701629
$799$	38.2071	1.35167
$800$	86.4318	3.05582
$801$	−1.73576	−0.0613301
$802$	37.9585	1.34036
$803$	9.04754	0.319281
$804$	65.9399	2.32552
$805$	2.18650	0.0770640
$806$	−66.0248	−2.32562
$807$	−28.7681	−1.01268
$808$	−59.6995	−2.10022
$809$	20.5729	0.723303	0.361652	−	0.932313i	$-0.382213\pi$
$809$	20.5729	0.723303	0.361652	+	0.932313i	$0.382213\pi$
$810$	12.1689	0.427573
$811$	−45.4124	−1.59465	−0.797323	−	0.603553i	$-0.793751\pi$
$811$	−45.4124	−1.59465	−0.797323	+	0.603553i	$0.793751\pi$
$812$	−32.1678	−1.12887
$813$	30.9546	1.08563
$814$	6.36627	0.223138
$815$	15.2894	0.535565
$816$	−64.0210	−2.24118
$817$	−57.8051	−2.02234
$818$	−48.5264	−1.69669
$819$	−1.58594	−0.0554172
$820$	−37.1591	−1.29765
$821$	35.0243	1.22236	0.611178	−	0.791493i	$-0.290696\pi$
$821$	35.0243	1.22236	0.611178	+	0.791493i	$0.290696\pi$
$822$	−7.19552	−0.250973
$823$	−8.62740	−0.300732	−0.150366	−	0.988630i	$-0.548045\pi$
$823$	−8.62740	−0.300732	−0.150366	+	0.988630i	$0.548045\pi$
$824$	−14.9696	−0.521491
$825$	4.88594	0.170107
$826$	11.8099	0.410918
$827$	18.7137	0.650738	0.325369	−	0.945587i	$-0.394511\pi$
$827$	18.7137	0.650738	0.325369	+	0.945587i	$0.394511\pi$
$828$	−12.5630	−0.436595
$829$	13.8846	0.482234	0.241117	−	0.970496i	$-0.422486\pi$
$829$	13.8846	0.482234	0.241117	+	0.970496i	$0.422486\pi$
$830$	3.89052	0.135042
$831$	18.2538	0.633218
$832$	76.6708	2.65808
$833$	19.0843	0.661232
$834$	−27.6431	−0.957202
$835$	−7.03171	−0.243342
$836$	−20.6731	−0.714995
$837$	−42.3975	−1.46547
$838$	−96.9006	−3.34737
$839$	0.0144394	0.000498505 0	0.000249252	−	1.00000i	$-0.499921\pi$
$839$	0.0144394	0.000498505 0	0.000249252		1.00000i	$0.499921\pi$
$840$	−7.61040	−0.262584
$841$	23.4227	0.807679
$842$	−51.3578	−1.76991
$843$	6.46185	0.222558
$844$	−86.4096	−2.97434
$845$	−1.76717	−0.0607923
$846$	−20.1718	−0.693520
$847$	−8.79851	−0.302320
$848$	−61.2051	−2.10179
$849$	19.8417	0.680965
$850$	−37.4505	−1.28454
$851$	13.6670	0.468499
$852$	21.1658	0.725129
$853$	−25.7202	−0.880643	−0.440321	−	0.897840i	$-0.645135\pi$
$853$	−25.7202	−0.880643	−0.440321	+	0.897840i	$0.645135\pi$
$854$	0.317477	0.0108638
$855$	−2.18493	−0.0747231
$856$	−123.579	−4.22385
$857$	39.8205	1.36024	0.680121	−	0.733100i	$-0.261927\pi$
$857$	39.8205	1.36024	0.680121	+	0.733100i	$0.261927\pi$
$858$	9.27587	0.316673
$859$	53.6866	1.83176	0.915882	−	0.401447i	$-0.131493\pi$
$859$	53.6866	1.83176	0.915882	+	0.401447i	$0.131493\pi$
$860$	−35.5861	−1.21347
$861$	−13.8629	−0.472447
$862$	42.7566	1.45630
$863$	−29.1668	−0.992850	−0.496425	−	0.868080i	$-0.665354\pi$
$863$	−29.1668	−0.992850	−0.496425	+	0.868080i	$0.665354\pi$
$864$	105.369	3.58473
$865$	−7.13722	−0.242673
$866$	10.3388	0.351327
$867$	−12.1483	−0.412577
$868$	33.7957	1.14710
$869$	6.34417	0.215211
$870$	19.8848	0.674158
$871$	25.6529	0.869214
$872$	26.9360	0.912168
$873$	−0.316602	−0.0107153
$874$	−61.0807	−2.06608
$875$	−5.23484	−0.176970
$876$	−108.391	−3.66219
$877$	−7.15580	−0.241634	−0.120817	−	0.992675i	$-0.538551\pi$
$877$	−7.15580	−0.241634	−0.120817	+	0.992675i	$0.538551\pi$
$878$	82.8900	2.79740
$879$	−18.7469	−0.632318
$880$	−6.13586	−0.206840
$881$	−12.5202	−0.421815	−0.210908	−	0.977506i	$-0.567642\pi$
$881$	−12.5202	−0.421815	−0.210908	+	0.977506i	$0.567642\pi$
$882$	−10.0757	−0.339267
$883$	35.8067	1.20499	0.602496	−	0.798122i	$-0.294173\pi$
$883$	35.8067	1.20499	0.602496	+	0.798122i	$0.294173\pi$
$884$	−51.6601	−1.73752
$885$	−5.30440	−0.178306
$886$	10.5902	0.355785
$887$	13.1983	0.443155	0.221578	−	0.975143i	$-0.428879\pi$
$887$	13.1983	0.443155	0.221578	+	0.975143i	$0.428879\pi$
$888$	−47.5699	−1.59634
$889$	−7.87712	−0.264190
$890$	−5.19535	−0.174148
$891$	4.73520	0.158635
$892$	−44.1719	−1.47898
$893$	−71.2599	−2.38462
$894$	−49.5483	−1.65714
$895$	2.31006	0.0772167
$896$	−22.4075	−0.748582
$897$	19.9133	0.664886
$898$	−72.0130	−2.40311
$899$	−55.0756	−1.83688
$900$	14.3664	0.478880
$901$	13.6100	0.453416
$902$	−19.9003	−0.662609
$903$	−13.2761	−0.441799
$904$	−49.2318	−1.63743
$905$	−9.76167	−0.324489
$906$	33.3898	1.10930
$907$	−45.0375	−1.49545	−0.747723	−	0.664010i	$-0.768853\pi$
$907$	−45.0375	−1.49545	−0.747723	+	0.664010i	$0.768853\pi$
$908$	119.370	3.96142
$909$	−3.93644	−0.130564
$910$	−4.74690	−0.157358
$911$	53.4441	1.77068	0.885341	−	0.464942i	$-0.153925\pi$
$911$	53.4441	1.77068	0.885341	+	0.464942i	$0.153925\pi$
$912$	119.405	3.95390
$913$	1.51389	0.0501023
$914$	90.2929	2.98662
$915$	−0.142595	−0.00471404
$916$	84.3480	2.78694
$917$	10.6970	0.353246
$918$	−45.6559	−1.50687
$919$	−3.20348	−0.105673	−0.0528365	−	0.998603i	$-0.516826\pi$
$919$	−3.20348	−0.105673	−0.0528365	+	0.998603i	$0.516826\pi$
$920$	−23.4532	−0.773229
$921$	−12.2314	−0.403037
$922$	76.9441	2.53402
$923$	8.23422	0.271033
$924$	−4.74798	−0.156197
$925$	−15.6289	−0.513875
$926$	−51.4491	−1.69072
$927$	−0.987061	−0.0324193
$928$	136.878	4.49323
$929$	−8.67341	−0.284565	−0.142283	−	0.989826i	$-0.545444\pi$
$929$	−8.67341	−0.284565	−0.142283	+	0.989826i	$0.545444\pi$
$930$	−20.8911	−0.685047
$931$	−35.5940	−1.16655
$932$	59.2189	1.93978
$933$	−5.13627	−0.168154
$934$	−82.5211	−2.70017
$935$	1.36442	0.0446212
$936$	17.0114	0.556034
$937$	−34.3500	−1.12217	−0.561083	−	0.827760i	$-0.689615\pi$
$937$	−34.3500	−1.12217	−0.561083	+	0.827760i	$0.689615\pi$
$938$	−18.0717	−0.590062
$939$	−25.2928	−0.825401
$940$	−43.8692	−1.43085
$941$	−15.5646	−0.507392	−0.253696	−	0.967284i	$-0.581646\pi$
$941$	−15.5646	−0.507392	−0.253696	+	0.967284i	$0.581646\pi$
$942$	82.0367	2.67290
$943$	−42.7218	−1.39121
$944$	−71.1475	−2.31565
$945$	−3.04820	−0.0991580
$946$	−19.0579	−0.619626
$947$	−5.23476	−0.170107	−0.0850534	−	0.996376i	$-0.527106\pi$
$947$	−5.23476	−0.170107	−0.0850534	+	0.996376i	$0.527106\pi$
$948$	−76.0041	−2.46850
$949$	−42.1677	−1.36882
$950$	69.8487	2.26619
$951$	−22.8193	−0.739966
$952$	22.6988	0.735672
$953$	0.566532	0.0183518	0.00917589	−	0.999958i	$-0.497079\pi$
$953$	0.566532	0.0183518	0.00917589	+	0.999958i	$0.497079\pi$
$954$	−7.18554	−0.232640
$955$	8.34218	0.269947
$956$	−74.2179	−2.40038
$957$	7.73762	0.250122
$958$	−47.2467	−1.52647
$959$	1.43286	0.0462695
$960$	24.2597	0.782977
$961$	26.8629	0.866544
$962$	−29.6712	−0.956637
$963$	−8.14853	−0.262583
$964$	−12.4816	−0.402006
$965$	−5.00044	−0.160970
$966$	−14.0284	−0.451355
$967$	6.32251	0.203318	0.101659	−	0.994819i	$-0.467585\pi$
$967$	6.32251	0.203318	0.101659	+	0.994819i	$0.467585\pi$
$968$	94.3761	3.03336
$969$	−26.5519	−0.852970
$970$	−0.947627	−0.0304265
$971$	35.6298	1.14342	0.571708	−	0.820457i	$-0.306281\pi$
$971$	35.6298	1.14342	0.571708	+	0.820457i	$0.306281\pi$
$972$	32.1449	1.03105
$973$	5.50463	0.176470
$974$	46.8211	1.50025
$975$	−22.7718	−0.729282
$976$	−1.91261	−0.0612212
$977$	29.7108	0.950531	0.475266	−	0.879842i	$-0.342352\pi$
$977$	29.7108	0.950531	0.475266	+	0.879842i	$0.342352\pi$
$978$	−98.0953	−3.13674
$979$	−2.02162	−0.0646114
$980$	−21.9125	−0.699968
$981$	1.77610	0.0567064
$982$	−85.3600	−2.72395
$983$	−41.4137	−1.32089	−0.660446	−	0.750874i	$-0.729633\pi$
$983$	−41.4137	−1.32089	−0.660446	+	0.750874i	$0.729633\pi$
$984$	148.699	4.74034
$985$	−9.97415	−0.317803
$986$	−59.3084	−1.88877
$987$	−16.3662	−0.520943
$988$	96.3509	3.06533
$989$	−40.9132	−1.30096
$990$	−0.720356	−0.0228944
$991$	8.77873	0.278866	0.139433	−	0.990232i	$-0.455472\pi$
$991$	8.77873	0.278866	0.139433	+	0.990232i	$0.455472\pi$
$992$	−143.805	−4.56580
$993$	41.3783	1.31310
$994$	−5.80077	−0.183989
$995$	5.07763	0.160972
$996$	−18.1366	−0.574679
$997$	−13.3134	−0.421640	−0.210820	−	0.977525i	$-0.567613\pi$
$997$	−13.3134	−0.421640	−0.210820	+	0.977525i	$0.567613\pi$
$998$	83.9953	2.65882
$999$	−19.0532	−0.602817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.12	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.12	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70464 q^{2} +1.55203 q^{3} +5.31508 q^{4} +0.654263 q^{5} -4.19768 q^{6} +0.835894 q^{7} -8.96611 q^{8} -0.591204 q^{9} +O(q^{10})\)	\(q-2.70464 q^{2} +1.55203 q^{3} +5.31508 q^{4} +0.654263 q^{5} -4.19768 q^{6} +0.835894 q^{7} -8.96611 q^{8} -0.591204 q^{9} -1.76955 q^{10} -0.688569 q^{11} +8.24917 q^{12} +3.20921 q^{13} -2.26079 q^{14} +1.01544 q^{15} +13.6199 q^{16} -3.02864 q^{17} +1.59900 q^{18} +5.64870 q^{19} +3.47746 q^{20} +1.29733 q^{21} +1.86233 q^{22} +3.99803 q^{23} -13.9157 q^{24} -4.57194 q^{25} -8.67975 q^{26} -5.57366 q^{27} +4.44285 q^{28} -7.24035 q^{29} -2.74639 q^{30} +7.60677 q^{31} -18.9048 q^{32} -1.06868 q^{33} +8.19138 q^{34} +0.546894 q^{35} -3.14230 q^{36} +3.41844 q^{37} -15.2777 q^{38} +4.98078 q^{39} -5.86619 q^{40} -10.6857 q^{41} -3.50882 q^{42} -10.2333 q^{43} -3.65980 q^{44} -0.386803 q^{45} -10.8132 q^{46} -12.6153 q^{47} +21.1385 q^{48} -6.30128 q^{49} +12.3655 q^{50} -4.70054 q^{51} +17.0572 q^{52} -4.49378 q^{53} +15.0747 q^{54} -0.450505 q^{55} -7.49472 q^{56} +8.76694 q^{57} +19.5825 q^{58} -5.22377 q^{59} +5.39712 q^{60} -0.140427 q^{61} -20.5736 q^{62} -0.494184 q^{63} +23.8909 q^{64} +2.09966 q^{65} +2.89040 q^{66} +7.99352 q^{67} -16.0975 q^{68} +6.20506 q^{69} -1.47915 q^{70} +2.56581 q^{71} +5.30080 q^{72} -13.1396 q^{73} -9.24565 q^{74} -7.09579 q^{75} +30.0233 q^{76} -0.575571 q^{77} -13.4712 q^{78} -9.21355 q^{79} +8.91102 q^{80} -6.87686 q^{81} +28.9010 q^{82} -2.19860 q^{83} +6.89543 q^{84} -1.98152 q^{85} +27.6775 q^{86} -11.2372 q^{87} +6.17379 q^{88} +2.93598 q^{89} +1.04616 q^{90} +2.68256 q^{91} +21.2499 q^{92} +11.8059 q^{93} +34.1198 q^{94} +3.69573 q^{95} -29.3409 q^{96} +0.535520 q^{97} +17.0427 q^{98} +0.407085 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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