LMFDB - Embedded newform 6041.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65744 q^{2} +2.58260 q^{3} +5.06196 q^{4} +1.09780 q^{5} -6.86308 q^{6} +1.00000 q^{7} -8.13696 q^{8} +3.66980 q^{9} +O(q^{10})$	\(q-2.65744 q^{2} +2.58260 q^{3} +5.06196 q^{4} +1.09780 q^{5} -6.86308 q^{6} +1.00000 q^{7} -8.13696 q^{8} +3.66980 q^{9} -2.91732 q^{10} -0.201709 q^{11} +13.0730 q^{12} +6.89294 q^{13} -2.65744 q^{14} +2.83516 q^{15} +11.4995 q^{16} -3.73459 q^{17} -9.75226 q^{18} -0.944972 q^{19} +5.55700 q^{20} +2.58260 q^{21} +0.536029 q^{22} +9.13542 q^{23} -21.0145 q^{24} -3.79484 q^{25} -18.3175 q^{26} +1.72982 q^{27} +5.06196 q^{28} +1.11926 q^{29} -7.53426 q^{30} -3.58061 q^{31} -14.2853 q^{32} -0.520934 q^{33} +9.92444 q^{34} +1.09780 q^{35} +18.5764 q^{36} -0.763262 q^{37} +2.51120 q^{38} +17.8017 q^{39} -8.93273 q^{40} +2.89507 q^{41} -6.86308 q^{42} +2.11050 q^{43} -1.02104 q^{44} +4.02869 q^{45} -24.2768 q^{46} +1.83346 q^{47} +29.6986 q^{48} +1.00000 q^{49} +10.0845 q^{50} -9.64495 q^{51} +34.8918 q^{52} -4.73158 q^{53} -4.59689 q^{54} -0.221436 q^{55} -8.13696 q^{56} -2.44048 q^{57} -2.97437 q^{58} +12.8856 q^{59} +14.3515 q^{60} +5.93740 q^{61} +9.51523 q^{62} +3.66980 q^{63} +14.9633 q^{64} +7.56704 q^{65} +1.38435 q^{66} +12.7010 q^{67} -18.9044 q^{68} +23.5931 q^{69} -2.91732 q^{70} -10.9366 q^{71} -29.8610 q^{72} +7.90022 q^{73} +2.02832 q^{74} -9.80055 q^{75} -4.78341 q^{76} -0.201709 q^{77} -47.3068 q^{78} +1.83529 q^{79} +12.6241 q^{80} -6.54197 q^{81} -7.69347 q^{82} -15.4099 q^{83} +13.0730 q^{84} -4.09982 q^{85} -5.60851 q^{86} +2.89061 q^{87} +1.64130 q^{88} -4.53745 q^{89} -10.7060 q^{90} +6.89294 q^{91} +46.2431 q^{92} -9.24726 q^{93} -4.87231 q^{94} -1.03739 q^{95} -36.8932 q^{96} +3.12512 q^{97} -2.65744 q^{98} -0.740233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.65744	−1.87909	−0.939545	−	0.342425i	$-0.888752\pi$
$2$	−2.65744	−1.87909	−0.939545	+	0.342425i	$0.888752\pi$
$3$	2.58260	1.49106	0.745531	−	0.666471i	$-0.232196\pi$
$3$	2.58260	1.49106	0.745531	+	0.666471i	$0.232196\pi$
$4$	5.06196	2.53098
$5$	1.09780	0.490949	0.245475	−	0.969403i	$-0.421056\pi$
$5$	1.09780	0.490949	0.245475	+	0.969403i	$0.421056\pi$
$6$	−6.86308	−2.80184
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−8.13696	−2.87685
$9$	3.66980	1.22327
$10$	−2.91732	−0.922538
$11$	−0.201709	−0.0608176	−0.0304088	−	0.999538i	$-0.509681\pi$
$11$	−0.201709	−0.0608176	−0.0304088	+	0.999538i	$0.509681\pi$
$12$	13.0730	3.77385
$13$	6.89294	1.91176	0.955879	−	0.293761i	$-0.0949070\pi$
$13$	6.89294	1.91176	0.955879	+	0.293761i	$0.0949070\pi$
$14$	−2.65744	−0.710229
$15$	2.83516	0.732036
$16$	11.4995	2.87488
$17$	−3.73459	−0.905772	−0.452886	−	0.891568i	$-0.649606\pi$
$17$	−3.73459	−0.905772	−0.452886	+	0.891568i	$0.649606\pi$
$18$	−9.75226	−2.29863
$19$	−0.944972	−0.216792	−0.108396	−	0.994108i	$-0.534571\pi$
$19$	−0.944972	−0.216792	−0.108396	+	0.994108i	$0.534571\pi$
$20$	5.55700	1.24258
$21$	2.58260	0.563569
$22$	0.536029	0.114282
$23$	9.13542	1.90487	0.952433	−	0.304747i	$-0.0985718\pi$
$23$	9.13542	1.90487	0.952433	+	0.304747i	$0.0985718\pi$
$24$	−21.0145	−4.28956
$25$	−3.79484	−0.758969
$26$	−18.3175	−3.59237
$27$	1.72982	0.332905
$28$	5.06196	0.956621
$29$	1.11926	0.207842	0.103921	−	0.994586i	$-0.466861\pi$
$29$	1.11926	0.207842	0.103921	+	0.994586i	$0.466861\pi$
$30$	−7.53426	−1.37556
$31$	−3.58061	−0.643096	−0.321548	−	0.946893i	$-0.604203\pi$
$31$	−3.58061	−0.643096	−0.321548	+	0.946893i	$0.604203\pi$
$32$	−14.2853	−2.52531
$33$	−0.520934	−0.0906829
$34$	9.92444	1.70203
$35$	1.09780	0.185561
$36$	18.5764	3.09606
$37$	−0.763262	−0.125479	−0.0627397	−	0.998030i	$-0.519984\pi$
$37$	−0.763262	−0.125479	−0.0627397	+	0.998030i	$0.519984\pi$
$38$	2.51120	0.407371
$39$	17.8017	2.85055
$40$	−8.93273	−1.41239
$41$	2.89507	0.452134	0.226067	−	0.974112i	$-0.427413\pi$
$41$	2.89507	0.452134	0.226067	+	0.974112i	$0.427413\pi$
$42$	−6.86308	−1.05900
$43$	2.11050	0.321848	0.160924	−	0.986967i	$-0.448553\pi$
$43$	2.11050	0.321848	0.160924	+	0.986967i	$0.448553\pi$
$44$	−1.02104	−0.153928
$45$	4.02869	0.600562
$46$	−24.2768	−3.57942
$47$	1.83346	0.267438	0.133719	−	0.991019i	$-0.457308\pi$
$47$	1.83346	0.267438	0.133719	+	0.991019i	$0.457308\pi$
$48$	29.6986	4.28663
$49$	1.00000	0.142857
$50$	10.0845	1.42617
$51$	−9.64495	−1.35056
$52$	34.8918	4.83862
$53$	−4.73158	−0.649933	−0.324966	−	0.945726i	$-0.605353\pi$
$53$	−4.73158	−0.649933	−0.324966	+	0.945726i	$0.605353\pi$
$54$	−4.59689	−0.625558
$55$	−0.221436	−0.0298584
$56$	−8.13696	−1.08735
$57$	−2.44048	−0.323250
$58$	−2.97437	−0.390554
$59$	12.8856	1.67756	0.838781	−	0.544468i	$-0.183269\pi$
$59$	12.8856	1.67756	0.838781	+	0.544468i	$0.183269\pi$
$60$	14.3515	1.85277
$61$	5.93740	0.760206	0.380103	−	0.924944i	$-0.375889\pi$
$61$	5.93740	0.760206	0.380103	+	0.924944i	$0.375889\pi$
$62$	9.51523	1.20844
$63$	3.66980	0.462351
$64$	14.9633	1.87041
$65$	7.56704	0.938576
$66$	1.38435	0.170401
$67$	12.7010	1.55167	0.775834	−	0.630937i	$-0.217329\pi$
$67$	12.7010	1.55167	0.775834	+	0.630937i	$0.217329\pi$
$68$	−18.9044	−2.29249
$69$	23.5931	2.84028
$70$	−2.91732	−0.348687
$71$	−10.9366	−1.29794	−0.648969	−	0.760815i	$-0.724800\pi$
$71$	−10.9366	−1.29794	−0.648969	+	0.760815i	$0.724800\pi$
$72$	−29.8610	−3.51916
$73$	7.90022	0.924651	0.462326	−	0.886710i	$-0.347015\pi$
$73$	7.90022	0.924651	0.462326	+	0.886710i	$0.347015\pi$
$74$	2.02832	0.235787
$75$	−9.80055	−1.13167
$76$	−4.78341	−0.548695
$77$	−0.201709	−0.0229869
$78$	−47.3068	−5.35644
$79$	1.83529	0.206486	0.103243	−	0.994656i	$-0.467078\pi$
$79$	1.83529	0.206486	0.103243	+	0.994656i	$0.467078\pi$
$80$	12.6241	1.41142
$81$	−6.54197	−0.726885
$82$	−7.69347	−0.849601
$83$	−15.4099	−1.69145	−0.845727	−	0.533615i	$-0.820833\pi$
$83$	−15.4099	−1.69145	−0.845727	+	0.533615i	$0.820833\pi$
$84$	13.0730	1.42638
$85$	−4.09982	−0.444688
$86$	−5.60851	−0.604781
$87$	2.89061	0.309906
$88$	1.64130	0.174963
$89$	−4.53745	−0.480969	−0.240485	−	0.970653i	$-0.577306\pi$
$89$	−4.53745	−0.480969	−0.240485	+	0.970653i	$0.577306\pi$
$90$	−10.7060	−1.12851
$91$	6.89294	0.722576
$92$	46.2431	4.82118
$93$	−9.24726	−0.958896
$94$	−4.87231	−0.502540
$95$	−1.03739	−0.106434
$96$	−36.8932	−3.76540
$97$	3.12512	0.317308	0.158654	−	0.987334i	$-0.449285\pi$
$97$	3.12512	0.317308	0.158654	+	0.987334i	$0.449285\pi$
$98$	−2.65744	−0.268441
$99$	−0.740233	−0.0743962
$100$	−19.2093	−1.92093
$101$	6.23661	0.620566	0.310283	−	0.950644i	$-0.399576\pi$
$101$	6.23661	0.620566	0.310283	+	0.950644i	$0.399576\pi$
$102$	25.6308	2.53783
$103$	19.7729	1.94829	0.974143	−	0.225933i	$-0.0725429\pi$
$103$	19.7729	1.94829	0.974143	+	0.225933i	$0.0725429\pi$
$104$	−56.0876	−5.49984
$105$	2.83516	0.276684
$106$	12.5739	1.22128
$107$	−15.1879	−1.46827	−0.734137	−	0.679002i	$-0.762413\pi$
$107$	−15.1879	−1.46827	−0.734137	+	0.679002i	$0.762413\pi$
$108$	8.75630	0.842575
$109$	2.73020	0.261506	0.130753	−	0.991415i	$-0.458261\pi$
$109$	2.73020	0.261506	0.130753	+	0.991415i	$0.458261\pi$
$110$	0.588451	0.0561066
$111$	−1.97120	−0.187098
$112$	11.4995	1.08660
$113$	7.22884	0.680032	0.340016	−	0.940420i	$-0.389568\pi$
$113$	7.22884	0.680032	0.340016	+	0.940420i	$0.389568\pi$
$114$	6.48542	0.607415
$115$	10.0288	0.935193
$116$	5.66567	0.526044
$117$	25.2957	2.33859
$118$	−34.2427	−3.15229
$119$	−3.73459	−0.342350
$120$	−23.0696	−2.10596
$121$	−10.9593	−0.996301
$122$	−15.7782	−1.42850
$123$	7.47680	0.674160
$124$	−18.1249	−1.62766
$125$	−9.65495	−0.863565
$126$	−9.75226	−0.868800
$127$	9.33001	0.827904	0.413952	−	0.910299i	$-0.364148\pi$
$127$	9.33001	0.827904	0.413952	+	0.910299i	$0.364148\pi$
$128$	−11.1932	−0.989352
$129$	5.45056	0.479895
$130$	−20.1089	−1.76367
$131$	−12.8113	−1.11933	−0.559663	−	0.828720i	$-0.689070\pi$
$131$	−12.8113	−1.11933	−0.559663	+	0.828720i	$0.689070\pi$
$132$	−2.63695	−0.229517
$133$	−0.944972	−0.0819395
$134$	−33.7520	−2.91573
$135$	1.89899	0.163439
$136$	30.3882	2.60577
$137$	9.59042	0.819365	0.409682	−	0.912228i	$-0.365640\pi$
$137$	9.59042	0.819365	0.409682	+	0.912228i	$0.365640\pi$
$138$	−62.6971	−5.33713
$139$	7.32695	0.621464	0.310732	−	0.950498i	$-0.399426\pi$
$139$	7.32695	0.621464	0.310732	+	0.950498i	$0.399426\pi$
$140$	5.55700	0.469652
$141$	4.73509	0.398767
$142$	29.0634	2.43894
$143$	−1.39037	−0.116269
$144$	42.2010	3.51675
$145$	1.22872	0.102040
$146$	−20.9943	−1.73750
$147$	2.58260	0.213009
$148$	−3.86360	−0.317586
$149$	−16.1427	−1.32246	−0.661232	−	0.750181i	$-0.729966\pi$
$149$	−16.1427	−1.32246	−0.661232	+	0.750181i	$0.729966\pi$
$150$	26.0443	2.12651
$151$	−8.66249	−0.704943	−0.352472	−	0.935823i	$-0.614659\pi$
$151$	−8.66249	−0.704943	−0.352472	+	0.935823i	$0.614659\pi$
$152$	7.68920	0.623677
$153$	−13.7052	−1.10800
$154$	0.536029	0.0431945
$155$	−3.93078	−0.315728
$156$	90.1114	7.21469
$157$	−13.9430	−1.11278	−0.556388	−	0.830923i	$-0.687813\pi$
$157$	−13.9430	−1.11278	−0.556388	+	0.830923i	$0.687813\pi$
$158$	−4.87717	−0.388007
$159$	−12.2198	−0.969090
$160$	−15.6824	−1.23980
$161$	9.13542	0.719972
$162$	17.3848	1.36588
$163$	19.8922	1.55808	0.779038	−	0.626977i	$-0.215708\pi$
$163$	19.8922	1.55808	0.779038	+	0.626977i	$0.215708\pi$
$164$	14.6547	1.14434
$165$	−0.571879	−0.0445207
$166$	40.9508	3.17840
$167$	−19.3471	−1.49713	−0.748563	−	0.663063i	$-0.769256\pi$
$167$	−19.3471	−1.49713	−0.748563	+	0.663063i	$0.769256\pi$
$168$	−21.0145	−1.62130
$169$	34.5126	2.65482
$170$	10.8950	0.835610
$171$	−3.46786	−0.265194
$172$	10.6833	0.814591
$173$	11.9286	0.906917	0.453459	−	0.891277i	$-0.350190\pi$
$173$	11.9286	0.906917	0.453459	+	0.891277i	$0.350190\pi$
$174$	−7.68160	−0.582340
$175$	−3.79484	−0.286863
$176$	−2.31956	−0.174844
$177$	33.2783	2.50135
$178$	12.0580	0.903785
$179$	24.0119	1.79473	0.897366	−	0.441287i	$-0.145478\pi$
$179$	24.0119	1.79473	0.897366	+	0.441287i	$0.145478\pi$
$180$	20.3931	1.52001
$181$	19.0889	1.41887	0.709433	−	0.704773i	$-0.248951\pi$
$181$	19.0889	1.41887	0.709433	+	0.704773i	$0.248951\pi$
$182$	−18.3175	−1.35779
$183$	15.3339	1.13351
$184$	−74.3346	−5.48002
$185$	−0.837906	−0.0616041
$186$	24.5740	1.80185
$187$	0.753302	0.0550869
$188$	9.28092	0.676881
$189$	1.72982	0.125826
$190$	2.75679	0.199998
$191$	−4.94147	−0.357552	−0.178776	−	0.983890i	$-0.557214\pi$
$191$	−4.94147	−0.357552	−0.178776	+	0.983890i	$0.557214\pi$
$192$	38.6440	2.78889
$193$	16.7400	1.20497	0.602487	−	0.798129i	$-0.294176\pi$
$193$	16.7400	1.20497	0.602487	+	0.798129i	$0.294176\pi$
$194$	−8.30480	−0.596250
$195$	19.5426	1.39948
$196$	5.06196	0.361569
$197$	−15.2947	−1.08970	−0.544851	−	0.838533i	$-0.683414\pi$
$197$	−15.2947	−1.08970	−0.544851	+	0.838533i	$0.683414\pi$
$198$	1.96712	0.139797
$199$	3.44503	0.244212	0.122106	−	0.992517i	$-0.461035\pi$
$199$	3.44503	0.244212	0.122106	+	0.992517i	$0.461035\pi$
$200$	30.8785	2.18344
$201$	32.8014	2.31364
$202$	−16.5734	−1.16610
$203$	1.11926	0.0785569
$204$	−48.8223	−3.41825
$205$	3.17820	0.221975
$206$	−52.5453	−3.66101
$207$	33.5252	2.33016
$208$	79.2655	5.49608
$209$	0.190610	0.0131847
$210$	−7.53426	−0.519914
$211$	3.02911	0.208532	0.104266	−	0.994549i	$-0.466751\pi$
$211$	3.02911	0.208532	0.104266	+	0.994549i	$0.466751\pi$
$212$	−23.9511	−1.64497
$213$	−28.2449	−1.93531
$214$	40.3610	2.75902
$215$	2.31690	0.158011
$216$	−14.0755	−0.957717
$217$	−3.58061	−0.243067
$218$	−7.25533	−0.491393
$219$	20.4031	1.37871
$220$	−1.12090	−0.0755710
$221$	−25.7423	−1.73162
$222$	5.23833	0.351573
$223$	−23.7583	−1.59097	−0.795487	−	0.605971i	$-0.792785\pi$
$223$	−23.7583	−1.59097	−0.795487	+	0.605971i	$0.792785\pi$
$224$	−14.2853	−0.954478
$225$	−13.9263	−0.928421
$226$	−19.2102	−1.27784
$227$	3.07064	0.203805	0.101903	−	0.994794i	$-0.467507\pi$
$227$	3.07064	0.203805	0.101903	+	0.994794i	$0.467507\pi$
$228$	−12.3536	−0.818139
$229$	10.3733	0.685484	0.342742	−	0.939430i	$-0.388644\pi$
$229$	10.3733	0.685484	0.342742	+	0.939430i	$0.388644\pi$
$230$	−26.6510	−1.75731
$231$	−0.520934	−0.0342749
$232$	−9.10741	−0.597931
$233$	26.6664	1.74697	0.873486	−	0.486849i	$-0.161854\pi$
$233$	26.6664	1.74697	0.873486	+	0.486849i	$0.161854\pi$
$234$	−67.2217	−4.39442
$235$	2.01277	0.131299
$236$	65.2264	4.24588
$237$	4.73981	0.307884
$238$	9.92444	0.643306
$239$	2.85091	0.184410	0.0922049	−	0.995740i	$-0.470609\pi$
$239$	2.85091	0.184410	0.0922049	+	0.995740i	$0.470609\pi$
$240$	32.6030	2.10452
$241$	16.6970	1.07555	0.537775	−	0.843088i	$-0.319265\pi$
$241$	16.6970	1.07555	0.537775	+	0.843088i	$0.319265\pi$
$242$	29.1237	1.87214
$243$	−22.0847	−1.41674
$244$	30.0549	1.92407
$245$	1.09780	0.0701356
$246$	−19.8691	−1.26681
$247$	−6.51364	−0.414453
$248$	29.1353	1.85009
$249$	−39.7975	−2.52206
$250$	25.6574	1.62272
$251$	−12.2581	−0.773723	−0.386861	−	0.922138i	$-0.626441\pi$
$251$	−12.2581	−0.773723	−0.386861	+	0.922138i	$0.626441\pi$
$252$	18.5764	1.17020
$253$	−1.84270	−0.115850
$254$	−24.7939	−1.55571
$255$	−10.5882	−0.663058
$256$	−0.181202	−0.0113251
$257$	18.7470	1.16940	0.584702	−	0.811248i	$-0.301211\pi$
$257$	18.7470	1.16940	0.584702	+	0.811248i	$0.301211\pi$
$258$	−14.4845	−0.901766
$259$	−0.763262	−0.0474268
$260$	38.3041	2.37552
$261$	4.10748	0.254246
$262$	34.0451	2.10332
$263$	−4.93348	−0.304212	−0.152106	−	0.988364i	$-0.548605\pi$
$263$	−4.93348	−0.304212	−0.152106	+	0.988364i	$0.548605\pi$
$264$	4.23882	0.260881
$265$	−5.19431	−0.319084
$266$	2.51120	0.153972
$267$	−11.7184	−0.717155
$268$	64.2918	3.92724
$269$	−1.78068	−0.108570	−0.0542851	−	0.998525i	$-0.517288\pi$
$269$	−1.78068	−0.108570	−0.0542851	+	0.998525i	$0.517288\pi$
$270$	−5.04645	−0.307117
$271$	−12.0063	−0.729329	−0.364665	−	0.931139i	$-0.618816\pi$
$271$	−12.0063	−0.729329	−0.364665	+	0.931139i	$0.618816\pi$
$272$	−42.9461	−2.60399
$273$	17.8017	1.07741
$274$	−25.4859	−1.53966
$275$	0.765455	0.0461587
$276$	119.427	7.18868
$277$	−7.22540	−0.434132	−0.217066	−	0.976157i	$-0.569649\pi$
$277$	−7.22540	−0.434132	−0.217066	+	0.976157i	$0.569649\pi$
$278$	−19.4709	−1.16779
$279$	−13.1401	−0.786678
$280$	−8.93273	−0.533833
$281$	−9.73464	−0.580720	−0.290360	−	0.956918i	$-0.593775\pi$
$281$	−9.73464	−0.580720	−0.290360	+	0.956918i	$0.593775\pi$
$282$	−12.5832	−0.749319
$283$	−2.40515	−0.142971	−0.0714856	−	0.997442i	$-0.522774\pi$
$283$	−2.40515	−0.142971	−0.0714856	+	0.997442i	$0.522774\pi$
$284$	−55.3608	−3.28506
$285$	−2.67915	−0.158699
$286$	3.69482	0.218479
$287$	2.89507	0.170891
$288$	−52.4243	−3.08913
$289$	−3.05281	−0.179577
$290$	−3.26525	−0.191742
$291$	8.07092	0.473126
$292$	39.9906	2.34027
$293$	−6.60931	−0.386120	−0.193060	−	0.981187i	$-0.561841\pi$
$293$	−6.60931	−0.386120	−0.193060	+	0.981187i	$0.561841\pi$
$294$	−6.86308	−0.400263
$295$	14.1458	0.823598
$296$	6.21063	0.360986
$297$	−0.348922	−0.0202465
$298$	42.8983	2.48503
$299$	62.9699	3.64164
$300$	−49.6100	−2.86423
$301$	2.11050	0.121647
$302$	23.0200	1.32465
$303$	16.1066	0.925302
$304$	−10.8667	−0.623250
$305$	6.51805	0.373223
$306$	36.4207	2.08203
$307$	−30.6581	−1.74975	−0.874875	−	0.484349i	$-0.839057\pi$
$307$	−30.6581	−1.74975	−0.874875	+	0.484349i	$0.839057\pi$
$308$	−1.02104	−0.0581794
$309$	51.0655	2.90502
$310$	10.4458	0.593281
$311$	−3.30973	−0.187678	−0.0938388	−	0.995587i	$-0.529914\pi$
$311$	−3.30973	−0.187678	−0.0938388	+	0.995587i	$0.529914\pi$
$312$	−144.852	−8.20061
$313$	7.35994	0.416009	0.208004	−	0.978128i	$-0.433303\pi$
$313$	7.35994	0.416009	0.208004	+	0.978128i	$0.433303\pi$
$314$	37.0527	2.09101
$315$	4.02869	0.226991
$316$	9.29017	0.522613
$317$	−11.7650	−0.660787	−0.330393	−	0.943843i	$-0.607181\pi$
$317$	−11.7650	−0.660787	−0.330393	+	0.943843i	$0.607181\pi$
$318$	32.4732	1.82101
$319$	−0.225766	−0.0126405
$320$	16.4266	0.918275
$321$	−39.2243	−2.18929
$322$	−24.2768	−1.35289
$323$	3.52909	0.196364
$324$	−33.1152	−1.83973
$325$	−26.1576	−1.45096
$326$	−52.8622	−2.92777
$327$	7.05100	0.389921
$328$	−23.5571	−1.30072
$329$	1.83346	0.101082
$330$	1.51973	0.0836584
$331$	18.1959	1.00014	0.500068	−	0.865986i	$-0.333308\pi$
$331$	18.1959	1.00014	0.500068	+	0.865986i	$0.333308\pi$
$332$	−78.0042	−4.28104
$333$	−2.80102	−0.153495
$334$	51.4138	2.81324
$335$	13.9431	0.761791
$336$	29.6986	1.62019
$337$	16.9310	0.922290	0.461145	−	0.887325i	$-0.347439\pi$
$337$	16.9310	0.922290	0.461145	+	0.887325i	$0.347439\pi$
$338$	−91.7151	−4.98864
$339$	18.6692	1.01397
$340$	−20.7531	−1.12550
$341$	0.722242	0.0391116
$342$	9.21561	0.498323
$343$	1.00000	0.0539949
$344$	−17.1730	−0.925908
$345$	25.9004	1.39443
$346$	−31.6996	−1.70418
$347$	−2.89197	−0.155249	−0.0776246	−	0.996983i	$-0.524734\pi$
$347$	−2.89197	−0.155249	−0.0776246	+	0.996983i	$0.524734\pi$
$348$	14.6321	0.784365
$349$	−6.48634	−0.347206	−0.173603	−	0.984816i	$-0.555541\pi$
$349$	−6.48634	−0.347206	−0.173603	+	0.984816i	$0.555541\pi$
$350$	10.0845	0.539042
$351$	11.9236	0.636433
$352$	2.88148	0.153583
$353$	2.63388	0.140187	0.0700936	−	0.997540i	$-0.477670\pi$
$353$	2.63388	0.140187	0.0700936	+	0.997540i	$0.477670\pi$
$354$	−88.4349	−4.70026
$355$	−12.0062	−0.637222
$356$	−22.9684	−1.21732
$357$	−9.64495	−0.510465
$358$	−63.8100	−3.37246
$359$	−12.7545	−0.673156	−0.336578	−	0.941656i	$-0.609270\pi$
$359$	−12.7545	−0.673156	−0.336578	+	0.941656i	$0.609270\pi$
$360$	−32.7813	−1.72773
$361$	−18.1070	−0.953001
$362$	−50.7275	−2.66618
$363$	−28.3035	−1.48555
$364$	34.8918	1.82883
$365$	8.67284	0.453957
$366$	−40.7488	−2.12998
$367$	−10.0193	−0.523001	−0.261501	−	0.965203i	$-0.584217\pi$
$367$	−10.0193	−0.523001	−0.261501	+	0.965203i	$0.584217\pi$
$368$	105.053	5.47627
$369$	10.6243	0.553081
$370$	2.22668	0.115760
$371$	−4.73158	−0.245652
$372$	−46.8093	−2.42695
$373$	−5.03488	−0.260696	−0.130348	−	0.991468i	$-0.541610\pi$
$373$	−5.03488	−0.260696	−0.130348	+	0.991468i	$0.541610\pi$
$374$	−2.00185	−0.103513
$375$	−24.9348	−1.28763
$376$	−14.9188	−0.769379
$377$	7.71502	0.397344
$378$	−4.59689	−0.236439
$379$	−14.4989	−0.744758	−0.372379	−	0.928081i	$-0.621458\pi$
$379$	−14.4989	−0.744758	−0.372379	+	0.928081i	$0.621458\pi$
$380$	−5.25121	−0.269382
$381$	24.0956	1.23446
$382$	13.1316	0.671873
$383$	17.0756	0.872522	0.436261	−	0.899820i	$-0.356302\pi$
$383$	17.0756	0.872522	0.436261	+	0.899820i	$0.356302\pi$
$384$	−28.9076	−1.47519
$385$	−0.221436	−0.0112854
$386$	−44.4856	−2.26426
$387$	7.74510	0.393706
$388$	15.8192	0.803100
$389$	−15.1910	−0.770215	−0.385107	−	0.922872i	$-0.625836\pi$
$389$	−15.1910	−0.770215	−0.385107	+	0.922872i	$0.625836\pi$
$390$	−51.9332	−2.62974
$391$	−34.1171	−1.72538
$392$	−8.13696	−0.410979
$393$	−33.0864	−1.66899
$394$	40.6447	2.04765
$395$	2.01478	0.101374
$396$	−3.74703	−0.188295
$397$	28.4481	1.42777	0.713885	−	0.700263i	$-0.246934\pi$
$397$	28.4481	1.42777	0.713885	+	0.700263i	$0.246934\pi$
$398$	−9.15495	−0.458896
$399$	−2.44048	−0.122177
$400$	−43.6389	−2.18194
$401$	−33.4919	−1.67251	−0.836254	−	0.548343i	$-0.815259\pi$
$401$	−33.4919	−1.67251	−0.836254	+	0.548343i	$0.815259\pi$
$402$	−87.1677	−4.34753
$403$	−24.6809	−1.22944
$404$	31.5695	1.57064
$405$	−7.18175	−0.356864
$406$	−2.97437	−0.147616
$407$	0.153957	0.00763136
$408$	78.4806	3.88537
$409$	−35.5569	−1.75818	−0.879088	−	0.476659i	$-0.841848\pi$
$409$	−35.5569	−1.75818	−0.879088	+	0.476659i	$0.841848\pi$
$410$	−8.44586	−0.417111
$411$	24.7682	1.22172
$412$	100.090	4.93107
$413$	12.8856	0.634059
$414$	−89.0910	−4.37858
$415$	−16.9169	−0.830419
$416$	−98.4679	−4.82778
$417$	18.9225	0.926641
$418$	−0.506533	−0.0247753
$419$	22.1475	1.08198	0.540989	−	0.841030i	$-0.318050\pi$
$419$	22.1475	1.08198	0.540989	+	0.841030i	$0.318050\pi$
$420$	14.3515	0.700281
$421$	14.6863	0.715764	0.357882	−	0.933767i	$-0.383499\pi$
$421$	14.6863	0.715764	0.357882	+	0.933767i	$0.383499\pi$
$422$	−8.04965	−0.391851
$423$	6.72844	0.327148
$424$	38.5007	1.86976
$425$	14.1722	0.687453
$426$	75.0589	3.63662
$427$	5.93740	0.287331
$428$	−76.8808	−3.71617
$429$	−3.59076	−0.173364
$430$	−6.15700	−0.296917
$431$	12.5056	0.602372	0.301186	−	0.953565i	$-0.402618\pi$
$431$	12.5056	0.602372	0.301186	+	0.953565i	$0.402618\pi$
$432$	19.8922	0.957062
$433$	−22.4937	−1.08098	−0.540489	−	0.841351i	$-0.681761\pi$
$433$	−22.4937	−1.08098	−0.540489	+	0.841351i	$0.681761\pi$
$434$	9.51523	0.456746
$435$	3.17330	0.152148
$436$	13.8202	0.661866
$437$	−8.63272	−0.412959
$438$	−54.2199	−2.59073
$439$	−28.8453	−1.37671	−0.688355	−	0.725374i	$-0.741667\pi$
$439$	−28.8453	−1.37671	−0.688355	+	0.725374i	$0.741667\pi$
$440$	1.80181	0.0858981
$441$	3.66980	0.174752
$442$	68.4086	3.25386
$443$	14.5488	0.691236	0.345618	−	0.938375i	$-0.387669\pi$
$443$	14.5488	0.691236	0.345618	+	0.938375i	$0.387669\pi$
$444$	−9.97812	−0.473540
$445$	−4.98120	−0.236132
$446$	63.1361	2.98958
$447$	−41.6902	−1.97188
$448$	14.9633	0.706947
$449$	−37.5508	−1.77213	−0.886066	−	0.463558i	$-0.846573\pi$
$449$	−37.5508	−1.77213	−0.886066	+	0.463558i	$0.846573\pi$
$450$	37.0083	1.74459
$451$	−0.583963	−0.0274977
$452$	36.5921	1.72115
$453$	−22.3717	−1.05111
$454$	−8.16002	−0.382969
$455$	7.56704	0.354749
$456$	19.8581	0.929941
$457$	−9.27077	−0.433668	−0.216834	−	0.976208i	$-0.569573\pi$
$457$	−9.27077	−0.433668	−0.216834	+	0.976208i	$0.569573\pi$
$458$	−27.5663	−1.28809
$459$	−6.46019	−0.301536
$460$	50.7655	2.36696
$461$	6.04166	0.281388	0.140694	−	0.990053i	$-0.455067\pi$
$461$	6.04166	0.281388	0.140694	+	0.990053i	$0.455067\pi$
$462$	1.38435	0.0644057
$463$	29.4709	1.36963	0.684814	−	0.728718i	$-0.259884\pi$
$463$	29.4709	1.36963	0.684814	+	0.728718i	$0.259884\pi$
$464$	12.8710	0.597521
$465$	−10.1516	−0.470770
$466$	−70.8642	−3.28272
$467$	5.00460	0.231585	0.115793	−	0.993273i	$-0.463059\pi$
$467$	5.00460	0.231585	0.115793	+	0.993273i	$0.463059\pi$
$468$	128.046	5.91893
$469$	12.7010	0.586476
$470$	−5.34880	−0.246722
$471$	−36.0092	−1.65922
$472$	−104.850	−4.82610
$473$	−0.425707	−0.0195740
$474$	−12.5957	−0.578542
$475$	3.58602	0.164538
$476$	−18.9044	−0.866480
$477$	−17.3640	−0.795041
$478$	−7.57610	−0.346523
$479$	14.1068	0.644554	0.322277	−	0.946645i	$-0.395552\pi$
$479$	14.1068	0.644554	0.322277	+	0.946645i	$0.395552\pi$
$480$	−40.5012	−1.84862
$481$	−5.26112	−0.239886
$482$	−44.3713	−2.02106
$483$	23.5931	1.07352
$484$	−55.4756	−2.52162
$485$	3.43074	0.155782
$486$	58.6887	2.66217
$487$	−3.48237	−0.157801	−0.0789005	−	0.996882i	$-0.525141\pi$
$487$	−3.48237	−0.157801	−0.0789005	+	0.996882i	$0.525141\pi$
$488$	−48.3124	−2.18700
$489$	51.3735	2.32319
$490$	−2.91732	−0.131791
$491$	−25.2607	−1.14000	−0.570001	−	0.821644i	$-0.693057\pi$
$491$	−25.2607	−1.14000	−0.570001	+	0.821644i	$0.693057\pi$
$492$	37.8473	1.70629
$493$	−4.18000	−0.188258
$494$	17.3096	0.778794
$495$	−0.812625	−0.0365248
$496$	−41.1753	−1.84883
$497$	−10.9366	−0.490575
$498$	105.759	4.73919
$499$	23.5572	1.05457	0.527283	−	0.849690i	$-0.323211\pi$
$499$	23.5572	1.05457	0.527283	+	0.849690i	$0.323211\pi$
$500$	−48.8730	−2.18567
$501$	−49.9658	−2.23231
$502$	32.5750	1.45390
$503$	−11.5947	−0.516984	−0.258492	−	0.966013i	$-0.583226\pi$
$503$	−11.5947	−0.516984	−0.258492	+	0.966013i	$0.583226\pi$
$504$	−29.8610	−1.33012
$505$	6.84653	0.304666
$506$	4.89685	0.217692
$507$	89.1322	3.95850
$508$	47.2281	2.09541
$509$	−23.2492	−1.03050	−0.515251	−	0.857039i	$-0.672301\pi$
$509$	−23.2492	−1.03050	−0.515251	+	0.857039i	$0.672301\pi$
$510$	28.1374	1.24595
$511$	7.90022	0.349485
$512$	22.8680	1.01063
$513$	−1.63464	−0.0721709
$514$	−49.8189	−2.19742
$515$	21.7067	0.956510
$516$	27.5905	1.21461
$517$	−0.369827	−0.0162650
$518$	2.02832	0.0891192
$519$	30.8068	1.35227
$520$	−61.5728	−2.70014
$521$	28.3399	1.24159	0.620797	−	0.783972i	$-0.286809\pi$
$521$	28.3399	1.24159	0.620797	+	0.783972i	$0.286809\pi$
$522$	−10.9153	−0.477752
$523$	26.8051	1.17210	0.586052	−	0.810273i	$-0.300681\pi$
$523$	26.8051	1.17210	0.586052	+	0.810273i	$0.300681\pi$
$524$	−64.8502	−2.83299
$525$	−9.80055	−0.427731
$526$	13.1104	0.571641
$527$	13.3721	0.582498
$528$	−5.99049	−0.260703
$529$	60.4559	2.62852
$530$	13.8036	0.599588
$531$	47.2876	2.05211
$532$	−4.78341	−0.207387
$533$	19.9556	0.864371
$534$	31.1409	1.34760
$535$	−16.6733	−0.720848
$536$	−103.347	−4.46392
$537$	62.0130	2.67606
$538$	4.73205	0.204013
$539$	−0.201709	−0.00868823
$540$	9.61264	0.413662
$541$	−35.3368	−1.51925	−0.759624	−	0.650362i	$-0.774617\pi$
$541$	−35.3368	−1.51925	−0.759624	+	0.650362i	$0.774617\pi$
$542$	31.9059	1.37048
$543$	49.2989	2.11562
$544$	53.3499	2.28736
$545$	2.99720	0.128386
$546$	−47.3068	−2.02454
$547$	−18.4131	−0.787288	−0.393644	−	0.919263i	$-0.628786\pi$
$547$	−18.4131	−0.787288	−0.393644	+	0.919263i	$0.628786\pi$
$548$	48.5463	2.07380
$549$	21.7891	0.929935
$550$	−2.03415	−0.0867363
$551$	−1.05767	−0.0450584
$552$	−191.976	−8.17105
$553$	1.83529	0.0780445
$554$	19.2010	0.815773
$555$	−2.16397	−0.0918555
$556$	37.0887	1.57291
$557$	−5.77220	−0.244576	−0.122288	−	0.992495i	$-0.539023\pi$
$557$	−5.77220	−0.244576	−0.122288	+	0.992495i	$0.539023\pi$
$558$	34.9190	1.47824
$559$	14.5475	0.615295
$560$	12.6241	0.533467
$561$	1.94548	0.0821380
$562$	25.8692	1.09123
$563$	−34.1916	−1.44100	−0.720502	−	0.693453i	$-0.756089\pi$
$563$	−34.1916	−1.44100	−0.720502	+	0.693453i	$0.756089\pi$
$564$	23.9689	1.00927
$565$	7.93579	0.333861
$566$	6.39153	0.268656
$567$	−6.54197	−0.274737
$568$	88.9909	3.73398
$569$	31.9694	1.34023	0.670114	−	0.742258i	$-0.266245\pi$
$569$	31.9694	1.34023	0.670114	+	0.742258i	$0.266245\pi$
$570$	7.11967	0.298210
$571$	−15.5859	−0.652251	−0.326125	−	0.945326i	$-0.605743\pi$
$571$	−15.5859	−0.652251	−0.326125	+	0.945326i	$0.605743\pi$
$572$	−7.03800	−0.294274
$573$	−12.7618	−0.533132
$574$	−7.69347	−0.321119
$575$	−34.6675	−1.44573
$576$	54.9122	2.28801
$577$	−24.3062	−1.01188	−0.505939	−	0.862569i	$-0.668854\pi$
$577$	−24.3062	−1.01188	−0.505939	+	0.862569i	$0.668854\pi$
$578$	8.11264	0.337441
$579$	43.2328	1.79669
$580$	6.21975	0.258261
$581$	−15.4099	−0.639310
$582$	−21.4479	−0.889046
$583$	0.954404	0.0395274
$584$	−64.2838	−2.66008
$585$	27.7695	1.14813
$586$	17.5638	0.725554
$587$	−9.05280	−0.373649	−0.186824	−	0.982393i	$-0.559820\pi$
$587$	−9.05280	−0.373649	−0.186824	+	0.982393i	$0.559820\pi$
$588$	13.0730	0.539121
$589$	3.38358	0.139418
$590$	−37.5915	−1.54762
$591$	−39.5000	−1.62481
$592$	−8.77715	−0.360738
$593$	6.99060	0.287069	0.143535	−	0.989645i	$-0.454153\pi$
$593$	6.99060	0.287069	0.143535	+	0.989645i	$0.454153\pi$
$594$	0.927236	0.0380450
$595$	−4.09982	−0.168076
$596$	−81.7139	−3.34713
$597$	8.89712	0.364135
$598$	−167.338	−6.84298
$599$	39.1328	1.59892	0.799461	−	0.600718i	$-0.205118\pi$
$599$	39.1328	1.59892	0.799461	+	0.600718i	$0.205118\pi$
$600$	79.7467	3.25564
$601$	15.3010	0.624140	0.312070	−	0.950059i	$-0.398978\pi$
$601$	15.3010	0.624140	0.312070	+	0.950059i	$0.398978\pi$
$602$	−5.60851	−0.228586
$603$	46.6100	1.89811
$604$	−43.8492	−1.78420
$605$	−12.0311	−0.489134
$606$	−42.8024	−1.73873
$607$	−24.1083	−0.978524	−0.489262	−	0.872137i	$-0.662734\pi$
$607$	−24.1083	−0.978524	−0.489262	+	0.872137i	$0.662734\pi$
$608$	13.4992	0.547466
$609$	2.89061	0.117133
$610$	−17.3213	−0.701319
$611$	12.6380	0.511277
$612$	−69.3753	−2.80433
$613$	−2.78503	−0.112486	−0.0562431	−	0.998417i	$-0.517912\pi$
$613$	−2.78503	−0.112486	−0.0562431	+	0.998417i	$0.517912\pi$
$614$	81.4719	3.28794
$615$	8.20800	0.330979
$616$	1.64130	0.0661299
$617$	−3.63539	−0.146355	−0.0731777	−	0.997319i	$-0.523314\pi$
$617$	−3.63539	−0.146355	−0.0731777	+	0.997319i	$0.523314\pi$
$618$	−135.703	−5.45879
$619$	26.9666	1.08388	0.541939	−	0.840418i	$-0.317690\pi$
$619$	26.9666	1.08388	0.541939	+	0.840418i	$0.317690\pi$
$620$	−19.8974	−0.799101
$621$	15.8027	0.634139
$622$	8.79539	0.352663
$623$	−4.53745	−0.181789
$624$	204.711	8.19499
$625$	8.37505	0.335002
$626$	−19.5586	−0.781718
$627$	0.492268	0.0196593
$628$	−70.5791	−2.81641
$629$	2.85047	0.113656
$630$	−10.7060	−0.426537
$631$	12.3049	0.489850	0.244925	−	0.969542i	$-0.421237\pi$
$631$	12.3049	0.489850	0.244925	+	0.969542i	$0.421237\pi$
$632$	−14.9337	−0.594030
$633$	7.82295	0.310935
$634$	31.2647	1.24168
$635$	10.2425	0.406459
$636$	−61.8560	−2.45275
$637$	6.89294	0.273108
$638$	0.599958	0.0237526
$639$	−40.1352	−1.58773
$640$	−12.2879	−0.485722
$641$	14.2533	0.562973	0.281487	−	0.959565i	$-0.409173\pi$
$641$	14.2533	0.562973	0.281487	+	0.959565i	$0.409173\pi$
$642$	104.236	4.11387
$643$	−3.20817	−0.126518	−0.0632590	−	0.997997i	$-0.520149\pi$
$643$	−3.20817	−0.126518	−0.0632590	+	0.997997i	$0.520149\pi$
$644$	46.2431	1.82223
$645$	5.98361	0.235604
$646$	−9.37832	−0.368985
$647$	21.8809	0.860228	0.430114	−	0.902775i	$-0.358473\pi$
$647$	21.8809	0.860228	0.430114	+	0.902775i	$0.358473\pi$
$648$	53.2317	2.09114
$649$	−2.59915	−0.102025
$650$	69.5122	2.72649
$651$	−9.24726	−0.362429
$652$	100.693	3.94346
$653$	−39.1116	−1.53056	−0.765278	−	0.643699i	$-0.777399\pi$
$653$	−39.1116	−1.53056	−0.765278	+	0.643699i	$0.777399\pi$
$654$	−18.7376	−0.732697
$655$	−14.0642	−0.549533
$656$	33.2920	1.29983
$657$	28.9922	1.13110
$658$	−4.87231	−0.189942
$659$	28.9293	1.12693	0.563463	−	0.826142i	$-0.309469\pi$
$659$	28.9293	1.12693	0.563463	+	0.826142i	$0.309469\pi$
$660$	−2.89483	−0.112681
$661$	20.3113	0.790017	0.395009	−	0.918677i	$-0.370742\pi$
$661$	20.3113	0.790017	0.395009	+	0.918677i	$0.370742\pi$
$662$	−48.3543	−1.87934
$663$	−66.4820	−2.58195
$664$	125.390	4.86606
$665$	−1.03739	−0.0402282
$666$	7.44352	0.288431
$667$	10.2249	0.395912
$668$	−97.9345	−3.78920
$669$	−61.3581	−2.37224
$670$	−37.0528	−1.43147
$671$	−1.19763	−0.0462339
$672$	−36.8932	−1.42319
$673$	−26.7623	−1.03161	−0.515805	−	0.856706i	$-0.672507\pi$
$673$	−26.7623	−1.03161	−0.515805	+	0.856706i	$0.672507\pi$
$674$	−44.9930	−1.73307
$675$	−6.56441	−0.252664
$676$	174.702	6.71929
$677$	36.4205	1.39975	0.699876	−	0.714264i	$-0.253239\pi$
$677$	36.4205	1.39975	0.699876	+	0.714264i	$0.253239\pi$
$678$	−49.6121	−1.90534
$679$	3.12512	0.119931
$680$	33.3601	1.27930
$681$	7.93022	0.303887
$682$	−1.91931	−0.0734942
$683$	−37.7085	−1.44288	−0.721438	−	0.692479i	$-0.756519\pi$
$683$	−37.7085	−1.44288	−0.721438	+	0.692479i	$0.756519\pi$
$684$	−17.5542	−0.671201
$685$	10.5283	0.402267
$686$	−2.65744	−0.101461
$687$	26.7899	1.02210
$688$	24.2697	0.925274
$689$	−32.6145	−1.24251
$690$	−68.8287	−2.62026
$691$	−19.1993	−0.730377	−0.365188	−	0.930934i	$-0.618995\pi$
$691$	−19.1993	−0.730377	−0.365188	+	0.930934i	$0.618995\pi$
$692$	60.3823	2.29539
$693$	−0.740233	−0.0281191
$694$	7.68522	0.291727
$695$	8.04350	0.305107
$696$	−23.5208	−0.891552
$697$	−10.8119	−0.409531
$698$	17.2370	0.652431
$699$	68.8685	2.60485
$700$	−19.2093	−0.726045
$701$	18.1163	0.684241	0.342121	−	0.939656i	$-0.388855\pi$
$701$	18.1163	0.684241	0.342121	+	0.939656i	$0.388855\pi$
$702$	−31.6861	−1.19592
$703$	0.721261	0.0272029
$704$	−3.01823	−0.113754
$705$	5.19817	0.195774
$706$	−6.99936	−0.263424
$707$	6.23661	0.234552
$708$	168.453	6.33087
$709$	−6.09378	−0.228857	−0.114428	−	0.993432i	$-0.536504\pi$
$709$	−6.09378	−0.228857	−0.114428	+	0.993432i	$0.536504\pi$
$710$	31.9057	1.19740
$711$	6.73515	0.252588
$712$	36.9211	1.38368
$713$	−32.7104	−1.22501
$714$	25.6308	0.959209
$715$	−1.52634	−0.0570820
$716$	121.547	4.54243
$717$	7.36274	0.274967
$718$	33.8942	1.26492
$719$	20.5232	0.765387	0.382693	−	0.923875i	$-0.374997\pi$
$719$	20.5232	0.765387	0.382693	+	0.923875i	$0.374997\pi$
$720$	46.3281	1.72655
$721$	19.7729	0.736383
$722$	48.1182	1.79078
$723$	43.1217	1.60371
$724$	96.6272	3.59112
$725$	−4.24743	−0.157746
$726$	75.2146	2.79148
$727$	−45.4401	−1.68528	−0.842639	−	0.538479i	$-0.818999\pi$
$727$	−45.4401	−1.68528	−0.842639	+	0.538479i	$0.818999\pi$
$728$	−56.0876	−2.07874
$729$	−37.4100	−1.38556
$730$	−23.0475	−0.853026
$731$	−7.88185	−0.291521
$732$	77.6196	2.86890
$733$	−16.7882	−0.620088	−0.310044	−	0.950722i	$-0.600344\pi$
$733$	−16.7882	−0.620088	−0.310044	+	0.950722i	$0.600344\pi$
$734$	26.6255	0.982767
$735$	2.83516	0.104577
$736$	−130.502	−4.81038
$737$	−2.56190	−0.0943688
$738$	−28.2335	−1.03929
$739$	38.1328	1.40274	0.701369	−	0.712799i	$-0.252573\pi$
$739$	38.1328	1.40274	0.701369	+	0.712799i	$0.252573\pi$
$740$	−4.24145	−0.155919
$741$	−16.8221	−0.617975
$742$	12.5739	0.461601
$743$	−36.3387	−1.33314	−0.666569	−	0.745443i	$-0.732238\pi$
$743$	−36.3387	−1.33314	−0.666569	+	0.745443i	$0.732238\pi$
$744$	75.2446	2.75860
$745$	−17.7214	−0.649263
$746$	13.3799	0.489872
$747$	−56.5512	−2.06910
$748$	3.81319	0.139424
$749$	−15.1879	−0.554955
$750$	66.2627	2.41957
$751$	21.3400	0.778709	0.389354	−	0.921088i	$-0.372698\pi$
$751$	21.3400	0.778709	0.389354	+	0.921088i	$0.372698\pi$
$752$	21.0840	0.768853
$753$	−31.6577	−1.15367
$754$	−20.5022	−0.746645
$755$	−9.50965	−0.346091
$756$	8.75630	0.318464
$757$	−21.3199	−0.774884	−0.387442	−	0.921894i	$-0.626641\pi$
$757$	−21.3199	−0.774884	−0.387442	+	0.921894i	$0.626641\pi$
$758$	38.5299	1.39947
$759$	−4.75895	−0.172739
$760$	8.44118	0.306194
$761$	−28.4371	−1.03084	−0.515422	−	0.856937i	$-0.672365\pi$
$761$	−28.4371	−1.03084	−0.515422	+	0.856937i	$0.672365\pi$
$762$	−64.0326	−2.31966
$763$	2.73020	0.0988399
$764$	−25.0135	−0.904957
$765$	−15.0455	−0.543972
$766$	−45.3773	−1.63955
$767$	88.8197	3.20709
$768$	−0.467972	−0.0168865
$769$	−38.5724	−1.39096	−0.695478	−	0.718548i	$-0.744807\pi$
$769$	−38.5724	−1.39096	−0.695478	+	0.718548i	$0.744807\pi$
$770$	0.588451	0.0212063
$771$	48.4159	1.74366
$772$	84.7374	3.04977
$773$	26.8384	0.965311	0.482655	−	0.875810i	$-0.339672\pi$
$773$	26.8384	0.965311	0.482655	+	0.875810i	$0.339672\pi$
$774$	−20.5821	−0.739809
$775$	13.5878	0.488090
$776$	−25.4290	−0.912847
$777$	−1.97120	−0.0707163
$778$	40.3691	1.44730
$779$	−2.73576	−0.0980189
$780$	98.9240	3.54205
$781$	2.20602	0.0789376
$782$	90.6639	3.24214
$783$	1.93613	0.0691916
$784$	11.4995	0.410697
$785$	−15.3066	−0.546316
$786$	87.9249	3.13618
$787$	45.1165	1.60823	0.804114	−	0.594475i	$-0.202640\pi$
$787$	45.1165	1.60823	0.804114	+	0.594475i	$0.202640\pi$
$788$	−77.4212	−2.75801
$789$	−12.7412	−0.453598
$790$	−5.35414	−0.190492
$791$	7.22884	0.257028
$792$	6.02325	0.214027
$793$	40.9261	1.45333
$794$	−75.5990	−2.68291
$795$	−13.4148	−0.475774
$796$	17.4386	0.618095
$797$	−16.4931	−0.584215	−0.292108	−	0.956385i	$-0.594357\pi$
$797$	−16.4931	−0.584215	−0.292108	+	0.956385i	$0.594357\pi$
$798$	6.48542	0.229581
$799$	−6.84724	−0.242238
$800$	54.2105	1.91663
$801$	−16.6516	−0.588354
$802$	89.0026	3.14279
$803$	−1.59355	−0.0562351
$804$	166.040	5.85577
$805$	10.0288	0.353470
$806$	65.5879	2.31024
$807$	−4.59878	−0.161885
$808$	−50.7471	−1.78528
$809$	40.5318	1.42502	0.712511	−	0.701661i	$-0.247558\pi$
$809$	40.5318	1.42502	0.712511	+	0.701661i	$0.247558\pi$
$810$	19.0850	0.670579
$811$	−47.1625	−1.65610	−0.828050	−	0.560654i	$-0.810550\pi$
$811$	−47.1625	−1.65610	−0.828050	+	0.560654i	$0.810550\pi$
$812$	5.66567	0.198826
$813$	−31.0074	−1.08748
$814$	−0.409131	−0.0143400
$815$	21.8376	0.764936
$816$	−110.912	−3.88271
$817$	−1.99436	−0.0697739
$818$	94.4902	3.30377
$819$	25.2957	0.883904
$820$	16.0879	0.561815
$821$	16.1751	0.564516	0.282258	−	0.959338i	$-0.408917\pi$
$821$	16.1751	0.564516	0.282258	+	0.959338i	$0.408917\pi$
$822$	−65.8198	−2.29573
$823$	−8.17106	−0.284825	−0.142413	−	0.989807i	$-0.545486\pi$
$823$	−8.17106	−0.284825	−0.142413	+	0.989807i	$0.545486\pi$
$824$	−160.892	−5.60493
$825$	1.97686	0.0688255
$826$	−34.2427	−1.19145
$827$	−38.1759	−1.32751	−0.663753	−	0.747952i	$-0.731037\pi$
$827$	−38.1759	−1.32751	−0.663753	+	0.747952i	$0.731037\pi$
$828$	169.703	5.89759
$829$	−21.2420	−0.737765	−0.368883	−	0.929476i	$-0.620260\pi$
$829$	−21.2420	−0.737765	−0.368883	+	0.929476i	$0.620260\pi$
$830$	44.9556	1.56043
$831$	−18.6603	−0.647318
$832$	103.141	3.57576
$833$	−3.73459	−0.129396
$834$	−50.2854	−1.74124
$835$	−21.2392	−0.735014
$836$	0.964859	0.0333703
$837$	−6.19382	−0.214090
$838$	−58.8556	−2.03313
$839$	43.1075	1.48824	0.744118	−	0.668048i	$-0.232870\pi$
$839$	43.1075	1.48824	0.744118	+	0.668048i	$0.232870\pi$
$840$	−23.0696	−0.795978
$841$	−27.7472	−0.956802
$842$	−39.0278	−1.34499
$843$	−25.1406	−0.865889
$844$	15.3332	0.527791
$845$	37.8878	1.30338
$846$	−17.8804	−0.614741
$847$	−10.9593	−0.376566
$848$	−54.4110	−1.86848
$849$	−6.21153	−0.213179
$850$	−37.6617	−1.29179
$851$	−6.97271	−0.239022
$852$	−142.974	−4.89822
$853$	−38.3179	−1.31198	−0.655990	−	0.754769i	$-0.727749\pi$
$853$	−38.3179	−1.31198	−0.655990	+	0.754769i	$0.727749\pi$
$854$	−15.7782	−0.539920
$855$	−3.80700	−0.130197
$856$	123.584	4.22400
$857$	6.33448	0.216382	0.108191	−	0.994130i	$-0.465494\pi$
$857$	6.33448	0.216382	0.108191	+	0.994130i	$0.465494\pi$
$858$	9.54222	0.325766
$859$	−1.61931	−0.0552501	−0.0276250	−	0.999618i	$-0.508794\pi$
$859$	−1.61931	−0.0552501	−0.0276250	+	0.999618i	$0.508794\pi$
$860$	11.7280	0.399923
$861$	7.47680	0.254809
$862$	−33.2327	−1.13191
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−24.7111	−0.840688
$865$	13.0952	0.445251
$866$	59.7755	2.03125
$867$	−7.88417	−0.267760
$868$	−18.1249	−0.615199
$869$	−0.370195	−0.0125580
$870$	−8.43283	−0.285900
$871$	87.5469	2.96642
$872$	−22.2155	−0.752313
$873$	11.4686	0.388152
$874$	22.9409	0.775987
$875$	−9.65495	−0.326397
$876$	103.280	3.48950
$877$	3.21481	0.108556	0.0542782	−	0.998526i	$-0.482714\pi$
$877$	3.21481	0.108556	0.0542782	+	0.998526i	$0.482714\pi$
$878$	76.6545	2.58696
$879$	−17.0692	−0.575729
$880$	−2.54641	−0.0858393
$881$	−12.7458	−0.429415	−0.214708	−	0.976678i	$-0.568880\pi$
$881$	−12.7458	−0.429415	−0.214708	+	0.976678i	$0.568880\pi$
$882$	−9.75226	−0.328376
$883$	52.0451	1.75146	0.875729	−	0.482803i	$-0.160381\pi$
$883$	52.0451	1.75146	0.875729	+	0.482803i	$0.160381\pi$
$884$	−130.307	−4.38269
$885$	36.5328	1.22804
$886$	−38.6626	−1.29889
$887$	27.0434	0.908027	0.454014	−	0.890995i	$-0.349992\pi$
$887$	27.0434	0.908027	0.454014	+	0.890995i	$0.349992\pi$
$888$	16.0395	0.538252
$889$	9.33001	0.312918
$890$	13.2372	0.443713
$891$	1.31958	0.0442074
$892$	−120.264	−4.02672
$893$	−1.73257	−0.0579783
$894$	110.789	3.70534
$895$	26.3602	0.881123
$896$	−11.1932	−0.373940
$897$	162.626	5.42992
$898$	99.7889	3.33000
$899$	−4.00764	−0.133662
$900$	−70.4945	−2.34982
$901$	17.6705	0.588691
$902$	1.55184	0.0516707
$903$	5.45056	0.181383
$904$	−58.8208	−1.95635
$905$	20.9557	0.696591
$906$	59.4513	1.97514
$907$	−36.7548	−1.22042	−0.610212	−	0.792238i	$-0.708916\pi$
$907$	−36.7548	−1.22042	−0.610212	+	0.792238i	$0.708916\pi$
$908$	15.5435	0.515828
$909$	22.8871	0.759118
$910$	−20.1089	−0.666605
$911$	46.5940	1.54373	0.771864	−	0.635787i	$-0.219324\pi$
$911$	46.5940	1.54373	0.771864	+	0.635787i	$0.219324\pi$
$912$	−28.0644	−0.929305
$913$	3.10832	0.102870
$914$	24.6365	0.814902
$915$	16.8335	0.556498
$916$	52.5090	1.73495
$917$	−12.8113	−0.423066
$918$	17.1675	0.566613
$919$	16.6303	0.548582	0.274291	−	0.961647i	$-0.411557\pi$
$919$	16.6303	0.548582	0.274291	+	0.961647i	$0.411557\pi$
$920$	−81.6042	−2.69041
$921$	−79.1775	−2.60899
$922$	−16.0553	−0.528754
$923$	−75.3855	−2.48134
$924$	−2.63695	−0.0867491
$925$	2.89646	0.0952349
$926$	−78.3169	−2.57365
$927$	72.5628	2.38327
$928$	−15.9890	−0.524866
$929$	−3.18717	−0.104568	−0.0522838	−	0.998632i	$-0.516650\pi$
$929$	−3.18717	−0.104568	−0.0522838	+	0.998632i	$0.516650\pi$
$930$	26.9772	0.884619
$931$	−0.944972	−0.0309702
$932$	134.984	4.42155
$933$	−8.54770	−0.279839
$934$	−13.2994	−0.435170
$935$	0.826973	0.0270449
$936$	−205.830	−6.72777
$937$	24.2766	0.793082	0.396541	−	0.918017i	$-0.370210\pi$
$937$	24.2766	0.793082	0.396541	+	0.918017i	$0.370210\pi$
$938$	−33.7520	−1.10204
$939$	19.0078	0.620295
$940$	10.1886	0.332314
$941$	43.0560	1.40358	0.701792	−	0.712382i	$-0.252383\pi$
$941$	43.0560	1.40358	0.701792	+	0.712382i	$0.252383\pi$
$942$	95.6922	3.11782
$943$	26.4477	0.861256
$944$	148.178	4.82279
$945$	1.89899	0.0617743
$946$	1.13129	0.0367814
$947$	−15.6826	−0.509615	−0.254807	−	0.966992i	$-0.582012\pi$
$947$	−15.6826	−0.509615	−0.254807	+	0.966992i	$0.582012\pi$
$948$	23.9928	0.779248
$949$	54.4558	1.76771
$950$	−9.52962	−0.309182
$951$	−30.3842	−0.985274
$952$	30.3882	0.984889
$953$	−33.6534	−1.09014	−0.545071	−	0.838390i	$-0.683497\pi$
$953$	−33.6534	−1.09014	−0.545071	+	0.838390i	$0.683497\pi$
$954$	46.1436	1.49395
$955$	−5.42473	−0.175540
$956$	14.4312	0.466738
$957$	−0.583062	−0.0188477
$958$	−37.4878	−1.21118
$959$	9.59042	0.309691
$960$	42.4233	1.36921
$961$	−18.1793	−0.586427
$962$	13.9811	0.450768
$963$	−55.7367	−1.79609
$964$	84.5198	2.72220
$965$	18.3772	0.591581
$966$	−62.6971	−2.01725
$967$	15.6080	0.501919	0.250959	−	0.967998i	$-0.419254\pi$
$967$	15.6080	0.501919	0.250959	+	0.967998i	$0.419254\pi$
$968$	89.1755	2.86621
$969$	9.11421	0.292791
$970$	−9.11698	−0.292729
$971$	29.5832	0.949370	0.474685	−	0.880156i	$-0.342562\pi$
$971$	29.5832	0.949370	0.474685	+	0.880156i	$0.342562\pi$
$972$	−111.792	−3.58573
$973$	7.32695	0.234891
$974$	9.25416	0.296522
$975$	−67.5546	−2.16348
$976$	68.2773	2.18550
$977$	50.5527	1.61733	0.808663	−	0.588273i	$-0.200192\pi$
$977$	50.5527	1.61733	0.808663	+	0.588273i	$0.200192\pi$
$978$	−136.522	−4.36548
$979$	0.915247	0.0292514
$980$	5.55700	0.177512
$981$	10.0193	0.319891
$982$	67.1288	2.14217
$983$	29.7400	0.948558	0.474279	−	0.880375i	$-0.342709\pi$
$983$	29.7400	0.948558	0.474279	+	0.880375i	$0.342709\pi$
$984$	−60.8384	−1.93946
$985$	−16.7905	−0.534989
$986$	11.1081	0.353753
$987$	4.73509	0.150720
$988$	−32.9718	−1.04897
$989$	19.2803	0.613077
$990$	2.15950	0.0686334
$991$	−33.5539	−1.06588	−0.532938	−	0.846154i	$-0.678912\pi$
$991$	−33.5539	−1.06588	−0.532938	+	0.846154i	$0.678912\pi$
$992$	51.1501	1.62402
$993$	46.9926	1.49126
$994$	29.0634	0.921834
$995$	3.78194	0.119896
$996$	−201.453	−6.38330
$997$	−3.59942	−0.113995	−0.0569974	−	0.998374i	$-0.518153\pi$
$997$	−3.59942	−0.113995	−0.0569974	+	0.998374i	$0.518153\pi$
$998$	−62.6017	−1.98162
$999$	−1.32031	−0.0417727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.6	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.6	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65744 q^{2} +2.58260 q^{3} +5.06196 q^{4} +1.09780 q^{5} -6.86308 q^{6} +1.00000 q^{7} -8.13696 q^{8} +3.66980 q^{9} +O(q^{10})\)	\(q-2.65744 q^{2} +2.58260 q^{3} +5.06196 q^{4} +1.09780 q^{5} -6.86308 q^{6} +1.00000 q^{7} -8.13696 q^{8} +3.66980 q^{9} -2.91732 q^{10} -0.201709 q^{11} +13.0730 q^{12} +6.89294 q^{13} -2.65744 q^{14} +2.83516 q^{15} +11.4995 q^{16} -3.73459 q^{17} -9.75226 q^{18} -0.944972 q^{19} +5.55700 q^{20} +2.58260 q^{21} +0.536029 q^{22} +9.13542 q^{23} -21.0145 q^{24} -3.79484 q^{25} -18.3175 q^{26} +1.72982 q^{27} +5.06196 q^{28} +1.11926 q^{29} -7.53426 q^{30} -3.58061 q^{31} -14.2853 q^{32} -0.520934 q^{33} +9.92444 q^{34} +1.09780 q^{35} +18.5764 q^{36} -0.763262 q^{37} +2.51120 q^{38} +17.8017 q^{39} -8.93273 q^{40} +2.89507 q^{41} -6.86308 q^{42} +2.11050 q^{43} -1.02104 q^{44} +4.02869 q^{45} -24.2768 q^{46} +1.83346 q^{47} +29.6986 q^{48} +1.00000 q^{49} +10.0845 q^{50} -9.64495 q^{51} +34.8918 q^{52} -4.73158 q^{53} -4.59689 q^{54} -0.221436 q^{55} -8.13696 q^{56} -2.44048 q^{57} -2.97437 q^{58} +12.8856 q^{59} +14.3515 q^{60} +5.93740 q^{61} +9.51523 q^{62} +3.66980 q^{63} +14.9633 q^{64} +7.56704 q^{65} +1.38435 q^{66} +12.7010 q^{67} -18.9044 q^{68} +23.5931 q^{69} -2.91732 q^{70} -10.9366 q^{71} -29.8610 q^{72} +7.90022 q^{73} +2.02832 q^{74} -9.80055 q^{75} -4.78341 q^{76} -0.201709 q^{77} -47.3068 q^{78} +1.83529 q^{79} +12.6241 q^{80} -6.54197 q^{81} -7.69347 q^{82} -15.4099 q^{83} +13.0730 q^{84} -4.09982 q^{85} -5.60851 q^{86} +2.89061 q^{87} +1.64130 q^{88} -4.53745 q^{89} -10.7060 q^{90} +6.89294 q^{91} +46.2431 q^{92} -9.24726 q^{93} -4.87231 q^{94} -1.03739 q^{95} -36.8932 q^{96} +3.12512 q^{97} -2.65744 q^{98} -0.740233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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