LMFDB - Embedded newform 6019.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26442 q^{2} +2.63903 q^{3} +3.12758 q^{4} +3.87429 q^{5} -5.97587 q^{6} +0.802453 q^{7} -2.55330 q^{8} +3.96450 q^{9} +O(q^{10})$	\(q-2.26442 q^{2} +2.63903 q^{3} +3.12758 q^{4} +3.87429 q^{5} -5.97587 q^{6} +0.802453 q^{7} -2.55330 q^{8} +3.96450 q^{9} -8.77301 q^{10} +0.433904 q^{11} +8.25378 q^{12} -1.00000 q^{13} -1.81709 q^{14} +10.2244 q^{15} -0.473417 q^{16} +2.38319 q^{17} -8.97729 q^{18} +1.47809 q^{19} +12.1171 q^{20} +2.11770 q^{21} -0.982539 q^{22} +5.68999 q^{23} -6.73825 q^{24} +10.0101 q^{25} +2.26442 q^{26} +2.54536 q^{27} +2.50973 q^{28} -2.63630 q^{29} -23.1523 q^{30} +2.85989 q^{31} +6.17862 q^{32} +1.14509 q^{33} -5.39653 q^{34} +3.10894 q^{35} +12.3993 q^{36} +10.2570 q^{37} -3.34701 q^{38} -2.63903 q^{39} -9.89224 q^{40} -6.13152 q^{41} -4.79535 q^{42} +9.63413 q^{43} +1.35707 q^{44} +15.3596 q^{45} -12.8845 q^{46} -3.17636 q^{47} -1.24936 q^{48} -6.35607 q^{49} -22.6671 q^{50} +6.28932 q^{51} -3.12758 q^{52} +13.1051 q^{53} -5.76376 q^{54} +1.68107 q^{55} -2.04890 q^{56} +3.90073 q^{57} +5.96968 q^{58} -9.50197 q^{59} +31.9776 q^{60} -7.19562 q^{61} -6.47598 q^{62} +3.18133 q^{63} -13.0441 q^{64} -3.87429 q^{65} -2.59295 q^{66} +7.81503 q^{67} +7.45361 q^{68} +15.0161 q^{69} -7.03992 q^{70} -2.97290 q^{71} -10.1226 q^{72} -11.0982 q^{73} -23.2261 q^{74} +26.4171 q^{75} +4.62284 q^{76} +0.348187 q^{77} +5.97587 q^{78} -12.2794 q^{79} -1.83416 q^{80} -5.17622 q^{81} +13.8843 q^{82} -5.47133 q^{83} +6.62327 q^{84} +9.23317 q^{85} -21.8157 q^{86} -6.95729 q^{87} -1.10789 q^{88} +2.93473 q^{89} -34.7806 q^{90} -0.802453 q^{91} +17.7959 q^{92} +7.54735 q^{93} +7.19260 q^{94} +5.72655 q^{95} +16.3056 q^{96} +7.89432 q^{97} +14.3928 q^{98} +1.72021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.26442	−1.60118	−0.800592	−	0.599210i	$-0.795481\pi$
$2$	−2.26442	−1.60118	−0.800592	+	0.599210i	$0.795481\pi$
$3$	2.63903	1.52365	0.761824	−	0.647784i	$-0.224304\pi$
$3$	2.63903	1.52365	0.761824	+	0.647784i	$0.224304\pi$
$4$	3.12758	1.56379
$5$	3.87429	1.73264	0.866318	−	0.499493i	$-0.166480\pi$
$5$	3.87429	1.73264	0.866318	+	0.499493i	$0.166480\pi$
$6$	−5.97587	−2.43964
$7$	0.802453	0.303299	0.151649	−	0.988434i	$-0.451542\pi$
$7$	0.802453	0.303299	0.151649	+	0.988434i	$0.451542\pi$
$8$	−2.55330	−0.902729
$9$	3.96450	1.32150
$10$	−8.77301	−2.77427
$11$	0.433904	0.130827	0.0654135	−	0.997858i	$-0.479163\pi$
$11$	0.433904	0.130827	0.0654135	+	0.997858i	$0.479163\pi$
$12$	8.25378	2.38266
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.81709	−0.485637
$15$	10.2244	2.63993
$16$	−0.473417	−0.118354
$17$	2.38319	0.578008	0.289004	−	0.957328i	$-0.406676\pi$
$17$	2.38319	0.578008	0.289004	+	0.957328i	$0.406676\pi$
$18$	−8.97729	−2.11597
$19$	1.47809	0.339097	0.169548	−	0.985522i	$-0.445769\pi$
$19$	1.47809	0.339097	0.169548	+	0.985522i	$0.445769\pi$
$20$	12.1171	2.70948
$21$	2.11770	0.462120
$22$	−0.982539	−0.209478
$23$	5.68999	1.18645	0.593223	−	0.805039i	$-0.297855\pi$
$23$	5.68999	1.18645	0.593223	+	0.805039i	$0.297855\pi$
$24$	−6.73825	−1.37544
$25$	10.0101	2.00203
$26$	2.26442	0.444088
$27$	2.54536	0.489855
$28$	2.50973	0.474295
$29$	−2.63630	−0.489549	−0.244775	−	0.969580i	$-0.578714\pi$
$29$	−2.63630	−0.489549	−0.244775	+	0.969580i	$0.578714\pi$
$30$	−23.1523	−4.22701
$31$	2.85989	0.513651	0.256826	−	0.966458i	$-0.417323\pi$
$31$	2.85989	0.513651	0.256826	+	0.966458i	$0.417323\pi$
$32$	6.17862	1.09224
$33$	1.14509	0.199334
$34$	−5.39653	−0.925497
$35$	3.10894	0.525506
$36$	12.3993	2.06655
$37$	10.2570	1.68624	0.843119	−	0.537727i	$-0.180717\pi$
$37$	10.2570	1.68624	0.843119	+	0.537727i	$0.180717\pi$
$38$	−3.34701	−0.542956
$39$	−2.63903	−0.422584
$40$	−9.89224	−1.56410
$41$	−6.13152	−0.957582	−0.478791	−	0.877929i	$-0.658925\pi$
$41$	−6.13152	−0.957582	−0.478791	+	0.877929i	$0.658925\pi$
$42$	−4.79535	−0.739939
$43$	9.63413	1.46919	0.734595	−	0.678506i	$-0.237372\pi$
$43$	9.63413	1.46919	0.734595	+	0.678506i	$0.237372\pi$
$44$	1.35707	0.204586
$45$	15.3596	2.28968
$46$	−12.8845	−1.89972
$47$	−3.17636	−0.463320	−0.231660	−	0.972797i	$-0.574416\pi$
$47$	−3.17636	−0.463320	−0.231660	+	0.972797i	$0.574416\pi$
$48$	−1.24936	−0.180330
$49$	−6.35607	−0.908010
$50$	−22.6671	−3.20561
$51$	6.28932	0.880681
$52$	−3.12758	−0.433717
$53$	13.1051	1.80012	0.900062	−	0.435761i	$-0.143521\pi$
$53$	13.1051	1.80012	0.900062	+	0.435761i	$0.143521\pi$
$54$	−5.76376	−0.784348
$55$	1.68107	0.226675
$56$	−2.04890	−0.273796
$57$	3.90073	0.516664
$58$	5.96968	0.783858
$59$	−9.50197	−1.23705	−0.618525	−	0.785765i	$-0.712270\pi$
$59$	−9.50197	−1.23705	−0.618525	+	0.785765i	$0.712270\pi$
$60$	31.9776	4.12829
$61$	−7.19562	−0.921305	−0.460653	−	0.887580i	$-0.652385\pi$
$61$	−7.19562	−0.921305	−0.460653	+	0.887580i	$0.652385\pi$
$62$	−6.47598	−0.822450
$63$	3.18133	0.400810
$64$	−13.0441	−1.63052
$65$	−3.87429	−0.480547
$66$	−2.59295	−0.319171
$67$	7.81503	0.954757	0.477379	−	0.878698i	$-0.341587\pi$
$67$	7.81503	0.954757	0.477379	+	0.878698i	$0.341587\pi$
$68$	7.45361	0.903882
$69$	15.0161	1.80772
$70$	−7.03992	−0.841431
$71$	−2.97290	−0.352818	−0.176409	−	0.984317i	$-0.556448\pi$
$71$	−2.97290	−0.352818	−0.176409	+	0.984317i	$0.556448\pi$
$72$	−10.1226	−1.19296
$73$	−11.0982	−1.29895	−0.649475	−	0.760383i	$-0.725011\pi$
$73$	−11.0982	−1.29895	−0.649475	+	0.760383i	$0.725011\pi$
$74$	−23.2261	−2.69998
$75$	26.4171	3.05038
$76$	4.62284	0.530276
$77$	0.348187	0.0396796
$78$	5.97587	0.676634
$79$	−12.2794	−1.38154	−0.690771	−	0.723074i	$-0.742729\pi$
$79$	−12.2794	−1.38154	−0.690771	+	0.723074i	$0.742729\pi$
$80$	−1.83416	−0.205065
$81$	−5.17622	−0.575135
$82$	13.8843	1.53326
$83$	−5.47133	−0.600556	−0.300278	−	0.953852i	$-0.597079\pi$
$83$	−5.47133	−0.600556	−0.300278	+	0.953852i	$0.597079\pi$
$84$	6.62327	0.722658
$85$	9.23317	1.00148
$86$	−21.8157	−2.35244
$87$	−6.95729	−0.745900
$88$	−1.10789	−0.118101
$89$	2.93473	0.311081	0.155540	−	0.987830i	$-0.450288\pi$
$89$	2.93473	0.311081	0.155540	+	0.987830i	$0.450288\pi$
$90$	−34.7806	−3.66620
$91$	−0.802453	−0.0841199
$92$	17.7959	1.85535
$93$	7.54735	0.782623
$94$	7.19260	0.741861
$95$	5.72655	0.587531
$96$	16.3056	1.66418
$97$	7.89432	0.801546	0.400773	−	0.916177i	$-0.368742\pi$
$97$	7.89432	0.801546	0.400773	+	0.916177i	$0.368742\pi$
$98$	14.3928	1.45389
$99$	1.72021	0.172888
$100$	31.3075	3.13075
$101$	−7.28620	−0.725004	−0.362502	−	0.931983i	$-0.618077\pi$
$101$	−7.28620	−0.725004	−0.362502	+	0.931983i	$0.618077\pi$
$102$	−14.2416	−1.41013
$103$	−14.6915	−1.44759	−0.723797	−	0.690012i	$-0.757605\pi$
$103$	−14.6915	−1.44759	−0.723797	+	0.690012i	$0.757605\pi$
$104$	2.55330	0.250372
$105$	8.20459	0.800686
$106$	−29.6754	−2.88233
$107$	1.83900	0.177783	0.0888915	−	0.996041i	$-0.471668\pi$
$107$	1.83900	0.177783	0.0888915	+	0.996041i	$0.471668\pi$
$108$	7.96082	0.766030
$109$	−4.59395	−0.440021	−0.220011	−	0.975498i	$-0.570609\pi$
$109$	−4.59395	−0.440021	−0.220011	+	0.975498i	$0.570609\pi$
$110$	−3.80664	−0.362949
$111$	27.0685	2.56923
$112$	−0.379895	−0.0358967
$113$	−16.2813	−1.53162	−0.765810	−	0.643067i	$-0.777661\pi$
$113$	−16.2813	−1.53162	−0.765810	+	0.643067i	$0.777661\pi$
$114$	−8.83287	−0.827274
$115$	22.0447	2.05568
$116$	−8.24524	−0.765551
$117$	−3.96450	−0.366519
$118$	21.5164	1.98074
$119$	1.91240	0.175309
$120$	−26.1060	−2.38314
$121$	−10.8117	−0.982884
$122$	16.2939	1.47518
$123$	−16.1813	−1.45902
$124$	8.94452	0.803242
$125$	19.4107	1.73615
$126$	−7.20385	−0.641770
$127$	9.73398	0.863751	0.431875	−	0.901933i	$-0.357852\pi$
$127$	9.73398	0.863751	0.431875	+	0.901933i	$0.357852\pi$
$128$	17.1801	1.51852
$129$	25.4248	2.23853
$130$	8.77301	0.769443
$131$	−7.77577	−0.679372	−0.339686	−	0.940539i	$-0.610321\pi$
$131$	−7.77577	−0.679372	−0.339686	+	0.940539i	$0.610321\pi$
$132$	3.58135	0.311716
$133$	1.18610	0.102848
$134$	−17.6965	−1.52874
$135$	9.86148	0.848741
$136$	−6.08500	−0.521784
$137$	17.3421	1.48164	0.740819	−	0.671704i	$-0.234437\pi$
$137$	17.3421	1.48164	0.740819	+	0.671704i	$0.234437\pi$
$138$	−34.0027	−2.89450
$139$	12.9352	1.09715	0.548574	−	0.836102i	$-0.315171\pi$
$139$	12.9352	1.09715	0.548574	+	0.836102i	$0.315171\pi$
$140$	9.72343	0.821780
$141$	−8.38253	−0.705937
$142$	6.73187	0.564926
$143$	−0.433904	−0.0362849
$144$	−1.87686	−0.156405
$145$	−10.2138	−0.848210
$146$	25.1310	2.07986
$147$	−16.7739	−1.38349
$148$	32.0795	2.63692
$149$	−5.15917	−0.422655	−0.211328	−	0.977415i	$-0.567779\pi$
$149$	−5.15917	−0.422655	−0.211328	+	0.977415i	$0.567779\pi$
$150$	−59.8193	−4.88422
$151$	−14.7280	−1.19854	−0.599272	−	0.800545i	$-0.704543\pi$
$151$	−14.7280	−1.19854	−0.599272	+	0.800545i	$0.704543\pi$
$152$	−3.77401	−0.306112
$153$	9.44816	0.763839
$154$	−0.788441	−0.0635343
$155$	11.0800	0.889971
$156$	−8.25378	−0.660832
$157$	2.31141	0.184470	0.0922352	−	0.995737i	$-0.470599\pi$
$157$	2.31141	0.184470	0.0922352	+	0.995737i	$0.470599\pi$
$158$	27.8057	2.21210
$159$	34.5848	2.74276
$160$	23.9378	1.89245
$161$	4.56595	0.359847
$162$	11.7211	0.920897
$163$	16.9578	1.32824	0.664118	−	0.747628i	$-0.268807\pi$
$163$	16.9578	1.32824	0.664118	+	0.747628i	$0.268807\pi$
$164$	−19.1768	−1.49746
$165$	4.43640	0.345373
$166$	12.3894	0.961601
$167$	−13.6215	−1.05407	−0.527033	−	0.849845i	$-0.676695\pi$
$167$	−13.6215	−1.05407	−0.527033	+	0.849845i	$0.676695\pi$
$168$	−5.40713	−0.417169
$169$	1.00000	0.0769231
$170$	−20.9077	−1.60355
$171$	5.85989	0.448117
$172$	30.1315	2.29750
$173$	16.7927	1.27673	0.638363	−	0.769735i	$-0.279612\pi$
$173$	16.7927	1.27673	0.638363	+	0.769735i	$0.279612\pi$
$174$	15.7542	1.19432
$175$	8.03266	0.607212
$176$	−0.205418	−0.0154839
$177$	−25.0760	−1.88483
$178$	−6.64545	−0.498098
$179$	−21.4716	−1.60487	−0.802433	−	0.596743i	$-0.796461\pi$
$179$	−21.4716	−1.60487	−0.802433	+	0.596743i	$0.796461\pi$
$180$	48.0385	3.58058
$181$	−2.96788	−0.220600	−0.110300	−	0.993898i	$-0.535181\pi$
$181$	−2.96788	−0.220600	−0.110300	+	0.993898i	$0.535181\pi$
$182$	1.81709	0.134691
$183$	−18.9895	−1.40374
$184$	−14.5283	−1.07104
$185$	39.7385	2.92164
$186$	−17.0903	−1.25312
$187$	1.03407	0.0756190
$188$	−9.93432	−0.724535
$189$	2.04253	0.148572
$190$	−12.9673	−0.940745
$191$	18.8570	1.36445	0.682223	−	0.731144i	$-0.261013\pi$
$191$	18.8570	1.36445	0.682223	+	0.731144i	$0.261013\pi$
$192$	−34.4239	−2.48433
$193$	23.5903	1.69807	0.849033	−	0.528339i	$-0.177185\pi$
$193$	23.5903	1.69807	0.849033	+	0.528339i	$0.177185\pi$
$194$	−17.8760	−1.28342
$195$	−10.2244	−0.732184
$196$	−19.8791	−1.41994
$197$	−24.0900	−1.71634	−0.858170	−	0.513366i	$-0.828398\pi$
$197$	−24.0900	−1.71634	−0.858170	+	0.513366i	$0.828398\pi$
$198$	−3.89528	−0.276825
$199$	−16.2258	−1.15022	−0.575108	−	0.818077i	$-0.695040\pi$
$199$	−16.2258	−1.15022	−0.575108	+	0.818077i	$0.695040\pi$
$200$	−25.5589	−1.80729
$201$	20.6241	1.45471
$202$	16.4990	1.16086
$203$	−2.11551	−0.148480
$204$	19.6703	1.37720
$205$	−23.7553	−1.65914
$206$	33.2676	2.31787
$207$	22.5580	1.56789
$208$	0.473417	0.0328256
$209$	0.641348	0.0443630
$210$	−18.5786	−1.28204
$211$	10.1053	0.695676	0.347838	−	0.937555i	$-0.386916\pi$
$211$	10.1053	0.695676	0.347838	+	0.937555i	$0.386916\pi$
$212$	40.9872	2.81501
$213$	−7.84558	−0.537570
$214$	−4.16426	−0.284663
$215$	37.3254	2.54557
$216$	−6.49908	−0.442206
$217$	2.29493	0.155790
$218$	10.4026	0.704554
$219$	−29.2886	−1.97914
$220$	5.25768	0.354472
$221$	−2.38319	−0.160311
$222$	−61.2944	−4.11381
$223$	−5.89682	−0.394880	−0.197440	−	0.980315i	$-0.563263\pi$
$223$	−5.89682	−0.394880	−0.197440	+	0.980315i	$0.563263\pi$
$224$	4.95805	0.331273
$225$	39.6852	2.64568
$226$	36.8677	2.45240
$227$	15.1297	1.00419	0.502097	−	0.864811i	$-0.332562\pi$
$227$	15.1297	1.00419	0.502097	+	0.864811i	$0.332562\pi$
$228$	12.1998	0.807953
$229$	16.6477	1.10011	0.550056	−	0.835128i	$-0.314606\pi$
$229$	16.6477	1.10011	0.550056	+	0.835128i	$0.314606\pi$
$230$	−49.9183	−3.29152
$231$	0.918878	0.0604578
$232$	6.73128	0.441930
$233$	−19.7854	−1.29618	−0.648092	−	0.761562i	$-0.724433\pi$
$233$	−19.7854	−1.29618	−0.648092	+	0.761562i	$0.724433\pi$
$234$	8.97729	0.586864
$235$	−12.3062	−0.802765
$236$	−29.7181	−1.93449
$237$	−32.4058	−2.10498
$238$	−4.33046	−0.280702
$239$	6.09079	0.393980	0.196990	−	0.980405i	$-0.436883\pi$
$239$	6.09079	0.393980	0.196990	+	0.980405i	$0.436883\pi$
$240$	−4.84040	−0.312447
$241$	9.80767	0.631768	0.315884	−	0.948798i	$-0.397699\pi$
$241$	9.80767	0.631768	0.315884	+	0.948798i	$0.397699\pi$
$242$	24.4822	1.57378
$243$	−21.2963	−1.36616
$244$	−22.5049	−1.44073
$245$	−24.6253	−1.57325
$246$	36.6412	2.33616
$247$	−1.47809	−0.0940485
$248$	−7.30216	−0.463688
$249$	−14.4390	−0.915036
$250$	−43.9540	−2.77989
$251$	4.42098	0.279050	0.139525	−	0.990219i	$-0.455442\pi$
$251$	4.42098	0.279050	0.139525	+	0.990219i	$0.455442\pi$
$252$	9.94984	0.626781
$253$	2.46891	0.155219
$254$	−22.0418	−1.38302
$255$	24.3667	1.52590
$256$	−12.8146	−0.800911
$257$	9.06722	0.565598	0.282799	−	0.959179i	$-0.408737\pi$
$257$	9.06722	0.565598	0.282799	+	0.959179i	$0.408737\pi$
$258$	−57.5723	−3.58429
$259$	8.23074	0.511433
$260$	−12.1171	−0.751473
$261$	−10.4516	−0.646940
$262$	17.6076	1.08780
$263$	31.0640	1.91549	0.957743	−	0.287625i	$-0.0928656\pi$
$263$	31.0640	1.91549	0.957743	+	0.287625i	$0.0928656\pi$
$264$	−2.92375	−0.179945
$265$	50.7730	3.11896
$266$	−2.68581	−0.164678
$267$	7.74486	0.473978
$268$	24.4421	1.49304
$269$	8.00018	0.487780	0.243890	−	0.969803i	$-0.421576\pi$
$269$	8.00018	0.487780	0.243890	+	0.969803i	$0.421576\pi$
$270$	−22.3305	−1.35899
$271$	0.674378	0.0409656	0.0204828	−	0.999790i	$-0.493480\pi$
$271$	0.674378	0.0409656	0.0204828	+	0.999790i	$0.493480\pi$
$272$	−1.12824	−0.0684097
$273$	−2.11770	−0.128169
$274$	−39.2698	−2.37238
$275$	4.34344	0.261919
$276$	46.9640	2.82690
$277$	−27.3046	−1.64057	−0.820287	−	0.571952i	$-0.806186\pi$
$277$	−27.3046	−1.64057	−0.820287	+	0.571952i	$0.806186\pi$
$278$	−29.2906	−1.75674
$279$	11.3380	0.678791
$280$	−7.93805	−0.474389
$281$	26.2604	1.56656	0.783282	−	0.621667i	$-0.213544\pi$
$281$	26.2604	1.56656	0.783282	+	0.621667i	$0.213544\pi$
$282$	18.9815	1.13033
$283$	−22.9524	−1.36438	−0.682188	−	0.731177i	$-0.738971\pi$
$283$	−22.9524	−1.36438	−0.682188	+	0.731177i	$0.738971\pi$
$284$	−9.29796	−0.551732
$285$	15.1126	0.895190
$286$	0.982539	0.0580987
$287$	−4.92025	−0.290433
$288$	24.4952	1.44339
$289$	−11.3204	−0.665907
$290$	23.1283	1.35814
$291$	20.8334	1.22127
$292$	−34.7106	−2.03128
$293$	2.74816	0.160549	0.0802745	−	0.996773i	$-0.474420\pi$
$293$	2.74816	0.160549	0.0802745	+	0.996773i	$0.474420\pi$
$294$	37.9831	2.21522
$295$	−36.8134	−2.14336
$296$	−26.1892	−1.52222
$297$	1.10444	0.0640862
$298$	11.6825	0.676749
$299$	−5.68999	−0.329061
$300$	82.6215	4.77015
$301$	7.73093	0.445603
$302$	33.3502	1.91909
$303$	−19.2285	−1.10465
$304$	−0.699752	−0.0401336
$305$	−27.8779	−1.59629
$306$	−21.3946	−1.22305
$307$	13.2854	0.758235	0.379118	−	0.925349i	$-0.376228\pi$
$307$	13.2854	0.758235	0.379118	+	0.925349i	$0.376228\pi$
$308$	1.08898	0.0620505
$309$	−38.7713	−2.20562
$310$	−25.0898	−1.42501
$311$	0.272018	0.0154247	0.00771236	−	0.999970i	$-0.497545\pi$
$311$	0.272018	0.0154247	0.00771236	+	0.999970i	$0.497545\pi$
$312$	6.73825	0.381478
$313$	25.1783	1.42316	0.711582	−	0.702603i	$-0.247979\pi$
$313$	25.1783	1.42316	0.711582	+	0.702603i	$0.247979\pi$
$314$	−5.23398	−0.295371
$315$	12.3254	0.694457
$316$	−38.4048	−2.16044
$317$	9.05128	0.508371	0.254185	−	0.967156i	$-0.418193\pi$
$317$	9.05128	0.508371	0.254185	+	0.967156i	$0.418193\pi$
$318$	−78.3144	−4.39165
$319$	−1.14390	−0.0640462
$320$	−50.5367	−2.82509
$321$	4.85319	0.270879
$322$	−10.3392	−0.576181
$323$	3.52256	0.196001
$324$	−16.1890	−0.899390
$325$	−10.0101	−0.555262
$326$	−38.3995	−2.12675
$327$	−12.1236	−0.670437
$328$	15.6556	0.864437
$329$	−2.54888	−0.140524
$330$	−10.0459	−0.553006
$331$	7.43268	0.408537	0.204268	−	0.978915i	$-0.434518\pi$
$331$	7.43268	0.408537	0.204268	+	0.978915i	$0.434518\pi$
$332$	−17.1120	−0.939143
$333$	40.6639	2.22837
$334$	30.8448	1.68775
$335$	30.2777	1.65425
$336$	−1.00256	−0.0546939
$337$	−20.0019	−1.08957	−0.544786	−	0.838575i	$-0.683389\pi$
$337$	−20.0019	−1.08957	−0.544786	+	0.838575i	$0.683389\pi$
$338$	−2.26442	−0.123168
$339$	−42.9670	−2.33365
$340$	28.8774	1.56610
$341$	1.24092	0.0671994
$342$	−13.2692	−0.717517
$343$	−10.7176	−0.578697
$344$	−24.5988	−1.32628
$345$	58.1767	3.13213
$346$	−38.0257	−2.04427
$347$	16.1717	0.868142	0.434071	−	0.900879i	$-0.357077\pi$
$347$	16.1717	0.868142	0.434071	+	0.900879i	$0.357077\pi$
$348$	−21.7595	−1.16643
$349$	16.8715	0.903108	0.451554	−	0.892244i	$-0.350870\pi$
$349$	16.8715	0.903108	0.451554	+	0.892244i	$0.350870\pi$
$350$	−18.1893	−0.972258
$351$	−2.54536	−0.135861
$352$	2.68093	0.142894
$353$	−23.6860	−1.26068	−0.630340	−	0.776319i	$-0.717084\pi$
$353$	−23.6860	−1.26068	−0.630340	+	0.776319i	$0.717084\pi$
$354$	56.7825	3.01796
$355$	−11.5179	−0.611305
$356$	9.17860	0.486465
$357$	5.04688	0.267109
$358$	48.6207	2.56968
$359$	−12.7799	−0.674496	−0.337248	−	0.941416i	$-0.609496\pi$
$359$	−12.7799	−0.674496	−0.337248	+	0.941416i	$0.609496\pi$
$360$	−39.2178	−2.06696
$361$	−16.8153	−0.885013
$362$	6.72050	0.353222
$363$	−28.5325	−1.49757
$364$	−2.50973	−0.131546
$365$	−42.9978	−2.25061
$366$	43.0001	2.24765
$367$	−21.7495	−1.13531	−0.567656	−	0.823266i	$-0.692150\pi$
$367$	−21.7495	−1.13531	−0.567656	+	0.823266i	$0.692150\pi$
$368$	−2.69374	−0.140421
$369$	−24.3084	−1.26545
$370$	−89.9846	−4.67808
$371$	10.5162	0.545975
$372$	23.6049	1.22386
$373$	−25.7239	−1.33193	−0.665966	−	0.745982i	$-0.731981\pi$
$373$	−25.7239	−1.33193	−0.665966	+	0.745982i	$0.731981\pi$
$374$	−2.34157	−0.121080
$375$	51.2256	2.64528
$376$	8.11021	0.418252
$377$	2.63630	0.135776
$378$	−4.62514	−0.237892
$379$	−28.1033	−1.44357	−0.721785	−	0.692118i	$-0.756678\pi$
$379$	−28.1033	−1.44357	−0.721785	+	0.692118i	$0.756678\pi$
$380$	17.9102	0.918775
$381$	25.6883	1.31605
$382$	−42.7001	−2.18473
$383$	15.3674	0.785238	0.392619	−	0.919701i	$-0.371569\pi$
$383$	15.3674	0.785238	0.392619	+	0.919701i	$0.371569\pi$
$384$	45.3388	2.31369
$385$	1.34898	0.0687503
$386$	−53.4182	−2.71892
$387$	38.1945	1.94154
$388$	24.6901	1.25345
$389$	−10.7092	−0.542978	−0.271489	−	0.962441i	$-0.587516\pi$
$389$	−10.7092	−0.542978	−0.271489	+	0.962441i	$0.587516\pi$
$390$	23.1523	1.17236
$391$	13.5603	0.685775
$392$	16.2290	0.819687
$393$	−20.5205	−1.03512
$394$	54.5497	2.74817
$395$	−47.5740	−2.39371
$396$	5.38010	0.270360
$397$	−22.1395	−1.11115	−0.555576	−	0.831466i	$-0.687502\pi$
$397$	−22.1395	−1.11115	−0.555576	+	0.831466i	$0.687502\pi$
$398$	36.7419	1.84171
$399$	3.13015	0.156703
$400$	−4.73897	−0.236948
$401$	13.9396	0.696108	0.348054	−	0.937474i	$-0.386843\pi$
$401$	13.9396	0.696108	0.348054	+	0.937474i	$0.386843\pi$
$402$	−46.7016	−2.32926
$403$	−2.85989	−0.142461
$404$	−22.7881	−1.13375
$405$	−20.0542	−0.996500
$406$	4.79039	0.237743
$407$	4.45054	0.220605
$408$	−16.0585	−0.795016
$409$	0.195887	0.00968597	0.00484299	−	0.999988i	$-0.498458\pi$
$409$	0.195887	0.00968597	0.00484299	+	0.999988i	$0.498458\pi$
$410$	53.7918	2.65659
$411$	45.7665	2.25749
$412$	−45.9487	−2.26373
$413$	−7.62488	−0.375196
$414$	−51.0807	−2.51048
$415$	−21.1975	−1.04055
$416$	−6.17862	−0.302932
$417$	34.1364	1.67167
$418$	−1.45228	−0.0710333
$419$	8.29149	0.405066	0.202533	−	0.979275i	$-0.435083\pi$
$419$	8.29149	0.405066	0.202533	+	0.979275i	$0.435083\pi$
$420$	25.6605	1.25210
$421$	−30.5835	−1.49055	−0.745275	−	0.666757i	$-0.767682\pi$
$421$	−30.5835	−1.49055	−0.745275	+	0.666757i	$0.767682\pi$
$422$	−22.8826	−1.11391
$423$	−12.5927	−0.612278
$424$	−33.4613	−1.62502
$425$	23.8560	1.15719
$426$	17.7656	0.860748
$427$	−5.77415	−0.279431
$428$	5.75162	0.278015
$429$	−1.14509	−0.0552853
$430$	−84.5202	−4.07593
$431$	17.5525	0.845474	0.422737	−	0.906252i	$-0.361069\pi$
$431$	17.5525	0.845474	0.422737	+	0.906252i	$0.361069\pi$
$432$	−1.20502	−0.0579765
$433$	15.7794	0.758309	0.379154	−	0.925333i	$-0.376215\pi$
$433$	15.7794	0.758309	0.379154	+	0.925333i	$0.376215\pi$
$434$	−5.19666	−0.249448
$435$	−26.9546	−1.29237
$436$	−14.3679	−0.688100
$437$	8.41031	0.402320
$438$	66.3216	3.16897
$439$	−7.00935	−0.334538	−0.167269	−	0.985911i	$-0.553495\pi$
$439$	−7.00935	−0.334538	−0.167269	+	0.985911i	$0.553495\pi$
$440$	−4.29228	−0.204626
$441$	−25.1987	−1.19994
$442$	5.39653	0.256687
$443$	−11.8736	−0.564130	−0.282065	−	0.959395i	$-0.591019\pi$
$443$	−11.8736	−0.564130	−0.282065	+	0.959395i	$0.591019\pi$
$444$	84.6589	4.01773
$445$	11.3700	0.538990
$446$	13.3528	0.632275
$447$	−13.6152	−0.643978
$448$	−10.4673	−0.494533
$449$	15.3992	0.726735	0.363368	−	0.931646i	$-0.381627\pi$
$449$	15.3992	0.726735	0.363368	+	0.931646i	$0.381627\pi$
$450$	−89.8639	−4.23622
$451$	−2.66049	−0.125278
$452$	−50.9211	−2.39513
$453$	−38.8676	−1.82616
$454$	−34.2600	−1.60790
$455$	−3.10894	−0.145749
$456$	−9.95973	−0.466407
$457$	−2.07088	−0.0968715	−0.0484358	−	0.998826i	$-0.515424\pi$
$457$	−2.07088	−0.0968715	−0.0484358	+	0.998826i	$0.515424\pi$
$458$	−37.6973	−1.76148
$459$	6.06608	0.283140
$460$	68.9464	3.21464
$461$	−12.9894	−0.604978	−0.302489	−	0.953153i	$-0.597818\pi$
$461$	−12.9894	−0.604978	−0.302489	+	0.953153i	$0.597818\pi$
$462$	−2.08072	−0.0968039
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	1.24807	0.0579402
$465$	29.2406	1.35600
$466$	44.8024	2.07543
$467$	−19.6635	−0.909916	−0.454958	−	0.890513i	$-0.650346\pi$
$467$	−19.6635	−0.909916	−0.454958	+	0.890513i	$0.650346\pi$
$468$	−12.3993	−0.573158
$469$	6.27119	0.289577
$470$	27.8662	1.28537
$471$	6.09988	0.281068
$472$	24.2614	1.11672
$473$	4.18028	0.192210
$474$	73.3801	3.37046
$475$	14.7959	0.678881
$476$	5.98116	0.274146
$477$	51.9552	2.37887
$478$	−13.7921	−0.630835
$479$	6.33279	0.289353	0.144676	−	0.989479i	$-0.453786\pi$
$479$	6.33279	0.289353	0.144676	+	0.989479i	$0.453786\pi$
$480$	63.1726	2.88342
$481$	−10.2570	−0.467678
$482$	−22.2086	−1.01158
$483$	12.0497	0.548280
$484$	−33.8145	−1.53702
$485$	30.5849	1.38879
$486$	48.2237	2.18747
$487$	11.8832	0.538481	0.269241	−	0.963073i	$-0.413227\pi$
$487$	11.8832	0.538481	0.269241	+	0.963073i	$0.413227\pi$
$488$	18.3726	0.831689
$489$	44.7522	2.02376
$490$	55.7618	2.51906
$491$	21.5226	0.971301	0.485651	−	0.874153i	$-0.338583\pi$
$491$	21.5226	0.971301	0.485651	+	0.874153i	$0.338583\pi$
$492$	−50.6082	−2.28160
$493$	−6.28281	−0.282963
$494$	3.34701	0.150589
$495$	6.66461	0.299552
$496$	−1.35392	−0.0607928
$497$	−2.38561	−0.107009
$498$	32.6959	1.46514
$499$	−4.22705	−0.189229	−0.0946143	−	0.995514i	$-0.530162\pi$
$499$	−4.22705	−0.189229	−0.0946143	+	0.995514i	$0.530162\pi$
$500$	60.7085	2.71497
$501$	−35.9477	−1.60602
$502$	−10.0109	−0.446810
$503$	40.4119	1.80188	0.900940	−	0.433944i	$-0.142879\pi$
$503$	40.4119	1.80188	0.900940	+	0.433944i	$0.142879\pi$
$504$	−8.12289	−0.361822
$505$	−28.2288	−1.25617
$506$	−5.59064	−0.248534
$507$	2.63903	0.117204
$508$	30.4438	1.35072
$509$	9.43657	0.418268	0.209134	−	0.977887i	$-0.432935\pi$
$509$	9.43657	0.418268	0.209134	+	0.977887i	$0.432935\pi$
$510$	−55.1762	−2.44324
$511$	−8.90580	−0.393970
$512$	−5.34262	−0.236113
$513$	3.76227	0.166108
$514$	−20.5320	−0.905626
$515$	−56.9191	−2.50816
$516$	79.5180	3.50058
$517$	−1.37824	−0.0606148
$518$	−18.6378	−0.818899
$519$	44.3165	1.94528
$520$	9.89224	0.433803
$521$	23.9399	1.04883	0.524413	−	0.851464i	$-0.324285\pi$
$521$	23.9399	1.04883	0.524413	+	0.851464i	$0.324285\pi$
$522$	23.6668	1.03587
$523$	−9.46167	−0.413730	−0.206865	−	0.978369i	$-0.566326\pi$
$523$	−9.46167	−0.413730	−0.206865	+	0.978369i	$0.566326\pi$
$524$	−24.3193	−1.06239
$525$	21.1985	0.925177
$526$	−70.3417	−3.06704
$527$	6.81565	0.296895
$528$	−0.542104	−0.0235920
$529$	9.37599	0.407652
$530$	−114.971	−4.99403
$531$	−37.6706	−1.63476
$532$	3.70961	0.160832
$533$	6.13152	0.265586
$534$	−17.5376	−0.758925
$535$	7.12483	0.308033
$536$	−19.9541	−0.861887
$537$	−56.6644	−2.44525
$538$	−18.1157	−0.781025
$539$	−2.75792	−0.118792
$540$	30.8425	1.32725
$541$	−7.09995	−0.305251	−0.152625	−	0.988284i	$-0.548773\pi$
$541$	−7.09995	−0.305251	−0.152625	+	0.988284i	$0.548773\pi$
$542$	−1.52707	−0.0655934
$543$	−7.83233	−0.336117
$544$	14.7248	0.631321
$545$	−17.7983	−0.762396
$546$	4.79535	0.205222
$547$	−16.3934	−0.700930	−0.350465	−	0.936576i	$-0.613977\pi$
$547$	−16.3934	−0.700930	−0.350465	+	0.936576i	$0.613977\pi$
$548$	54.2389	2.31697
$549$	−28.5271	−1.21751
$550$	−9.83534	−0.419381
$551$	−3.89669	−0.166004
$552$	−38.3406	−1.63188
$553$	−9.85364	−0.419019
$554$	61.8289	2.62686
$555$	104.871	4.45154
$556$	40.4558	1.71571
$557$	20.4796	0.867747	0.433874	−	0.900974i	$-0.357146\pi$
$557$	20.4796	0.867747	0.433874	+	0.900974i	$0.357146\pi$
$558$	−25.6740	−1.08687
$559$	−9.63413	−0.407480
$560$	−1.47182	−0.0621959
$561$	2.72896	0.115217
$562$	−59.4644	−2.50836
$563$	−45.8657	−1.93301	−0.966505	−	0.256646i	$-0.917382\pi$
$563$	−45.8657	−1.93301	−0.966505	+	0.256646i	$0.917382\pi$
$564$	−26.2170	−1.10394
$565$	−63.0786	−2.65374
$566$	51.9737	2.18462
$567$	−4.15367	−0.174438
$568$	7.59070	0.318499
$569$	25.5652	1.07175	0.535875	−	0.844297i	$-0.319982\pi$
$569$	25.5652	1.07175	0.535875	+	0.844297i	$0.319982\pi$
$570$	−34.2211	−1.43336
$571$	−4.38431	−0.183478	−0.0917388	−	0.995783i	$-0.529242\pi$
$571$	−4.38431	−0.183478	−0.0917388	+	0.995783i	$0.529242\pi$
$572$	−1.35707	−0.0567418
$573$	49.7643	2.07894
$574$	11.1415	0.465037
$575$	56.9576	2.37530
$576$	−51.7135	−2.15473
$577$	17.8482	0.743031	0.371516	−	0.928427i	$-0.378838\pi$
$577$	17.8482	0.743031	0.371516	+	0.928427i	$0.378838\pi$
$578$	25.6341	1.06624
$579$	62.2556	2.58726
$580$	−31.9445	−1.32642
$581$	−4.39048	−0.182148
$582$	−47.1754	−1.95548
$583$	5.68636	0.235505
$584$	28.3371	1.17260
$585$	−15.3596	−0.635043
$586$	−6.22297	−0.257069
$587$	28.9106	1.19327	0.596635	−	0.802513i	$-0.296504\pi$
$587$	28.9106	1.19327	0.596635	+	0.802513i	$0.296504\pi$
$588$	−52.4616	−2.16348
$589$	4.22717	0.174177
$590$	83.3608	3.43191
$591$	−63.5743	−2.61510
$592$	−4.85583	−0.199573
$593$	−6.01023	−0.246811	−0.123405	−	0.992356i	$-0.539382\pi$
$593$	−6.01023	−0.246811	−0.123405	+	0.992356i	$0.539382\pi$
$594$	−2.50092	−0.102614
$595$	7.40918	0.303747
$596$	−16.1357	−0.660944
$597$	−42.8204	−1.75252
$598$	12.8845	0.526886
$599$	−33.2748	−1.35957	−0.679785	−	0.733412i	$-0.737927\pi$
$599$	−33.2748	−1.35957	−0.679785	+	0.733412i	$0.737927\pi$
$600$	−67.4508	−2.75367
$601$	−39.7505	−1.62145	−0.810727	−	0.585424i	$-0.800928\pi$
$601$	−39.7505	−1.62145	−0.810727	+	0.585424i	$0.800928\pi$
$602$	−17.5060	−0.713493
$603$	30.9827	1.26171
$604$	−46.0628	−1.87427
$605$	−41.8878	−1.70298
$606$	43.5414	1.76875
$607$	−31.5419	−1.28024	−0.640122	−	0.768273i	$-0.721116\pi$
$607$	−31.5419	−1.28024	−0.640122	+	0.768273i	$0.721116\pi$
$608$	9.13254	0.370374
$609$	−5.58290	−0.226230
$610$	63.1273	2.55595
$611$	3.17636	0.128502
$612$	29.5499	1.19448
$613$	35.5526	1.43595	0.717977	−	0.696067i	$-0.245068\pi$
$613$	35.5526	1.43595	0.717977	+	0.696067i	$0.245068\pi$
$614$	−30.0836	−1.21407
$615$	−62.6910	−2.52795
$616$	−0.889027	−0.0358199
$617$	23.2437	0.935757	0.467879	−	0.883793i	$-0.345018\pi$
$617$	23.2437	0.935757	0.467879	+	0.883793i	$0.345018\pi$
$618$	87.7944	3.53161
$619$	−4.77654	−0.191986	−0.0959928	−	0.995382i	$-0.530603\pi$
$619$	−4.77654	−0.191986	−0.0959928	+	0.995382i	$0.530603\pi$
$620$	34.6537	1.39173
$621$	14.4831	0.581186
$622$	−0.615961	−0.0246978
$623$	2.35498	0.0943504
$624$	1.24936	0.0500146
$625$	25.1522	1.00609
$626$	−57.0142	−2.27875
$627$	1.69254	0.0675936
$628$	7.22910	0.288473
$629$	24.4443	0.974659
$630$	−27.9098	−1.11195
$631$	30.0386	1.19582	0.597909	−	0.801564i	$-0.295998\pi$
$631$	30.0386	1.19582	0.597909	+	0.801564i	$0.295998\pi$
$632$	31.3530	1.24716
$633$	26.6682	1.05997
$634$	−20.4959	−0.813995
$635$	37.7123	1.49657
$636$	108.167	4.28909
$637$	6.35607	0.251837
$638$	2.59027	0.102550
$639$	−11.7861	−0.466249
$640$	66.5606	2.63104
$641$	−41.6008	−1.64313	−0.821566	−	0.570114i	$-0.806899\pi$
$641$	−41.6008	−1.64313	−0.821566	+	0.570114i	$0.806899\pi$
$642$	−10.9896	−0.433726
$643$	1.37333	0.0541587	0.0270793	−	0.999633i	$-0.491379\pi$
$643$	1.37333	0.0541587	0.0270793	+	0.999633i	$0.491379\pi$
$644$	14.2804	0.562725
$645$	98.5031	3.87855
$646$	−7.97655	−0.313833
$647$	−44.8989	−1.76516	−0.882579	−	0.470163i	$-0.844195\pi$
$647$	−44.8989	−1.76516	−0.882579	+	0.470163i	$0.844195\pi$
$648$	13.2164	0.519191
$649$	−4.12294	−0.161840
$650$	22.6671	0.889077
$651$	6.05639	0.237369
$652$	53.0368	2.07708
$653$	45.8818	1.79549	0.897747	−	0.440512i	$-0.145203\pi$
$653$	45.8818	1.79549	0.897747	+	0.440512i	$0.145203\pi$
$654$	27.4529	1.07349
$655$	−30.1256	−1.17710
$656$	2.90277	0.113334
$657$	−43.9990	−1.71656
$658$	5.77172	0.225005
$659$	−0.0486521	−0.00189522	−0.000947608	−	1.00000i	$-0.500302\pi$
$659$	−0.0486521	−0.00189522	−0.000947608		1.00000i	$0.500302\pi$
$660$	13.8752	0.540091
$661$	20.7632	0.807594	0.403797	−	0.914849i	$-0.367690\pi$
$661$	20.7632	0.807594	0.403797	+	0.914849i	$0.367690\pi$
$662$	−16.8307	−0.654143
$663$	−6.28932	−0.244257
$664$	13.9700	0.542139
$665$	4.59528	0.178197
$666$	−92.0799	−3.56802
$667$	−15.0005	−0.580823
$668$	−42.6024	−1.64833
$669$	−15.5619	−0.601658
$670$	−68.5613	−2.64875
$671$	−3.12221	−0.120532
$672$	13.0845	0.504744
$673$	27.5800	1.06313	0.531566	−	0.847017i	$-0.321604\pi$
$673$	27.5800	1.06313	0.531566	+	0.847017i	$0.321604\pi$
$674$	45.2926	1.74461
$675$	25.4794	0.980703
$676$	3.12758	0.120291
$677$	−47.8750	−1.83998	−0.919992	−	0.391936i	$-0.871805\pi$
$677$	−47.8750	−1.83998	−0.919992	+	0.391936i	$0.871805\pi$
$678$	97.2952	3.73660
$679$	6.33481	0.243108
$680$	−23.5751	−0.904063
$681$	39.9279	1.53004
$682$	−2.80995	−0.107599
$683$	34.8298	1.33272	0.666362	−	0.745628i	$-0.267850\pi$
$683$	34.8298	1.33272	0.666362	+	0.745628i	$0.267850\pi$
$684$	18.3273	0.700760
$685$	67.1885	2.56714
$686$	24.2691	0.926599
$687$	43.9339	1.67618
$688$	−4.56096	−0.173885
$689$	−13.1051	−0.499265
$690$	−131.736	−5.01511
$691$	−0.365400	−0.0139005	−0.00695024	−	0.999976i	$-0.502212\pi$
$691$	−0.365400	−0.0139005	−0.00695024	+	0.999976i	$0.502212\pi$
$692$	52.5205	1.99653
$693$	1.38039	0.0524367
$694$	−36.6194	−1.39005
$695$	50.1147	1.90096
$696$	17.7641	0.673345
$697$	−14.6126	−0.553490
$698$	−38.2040	−1.44604
$699$	−52.2144	−1.97493
$700$	25.1228	0.949551
$701$	3.52619	0.133182	0.0665911	−	0.997780i	$-0.478788\pi$
$701$	3.52619	0.133182	0.0665911	+	0.997780i	$0.478788\pi$
$702$	5.76376	0.217539
$703$	15.1607	0.571798
$704$	−5.65989	−0.213315
$705$	−32.4764	−1.22313
$706$	53.6350	2.01858
$707$	−5.84683	−0.219893
$708$	−78.4272	−2.94747
$709$	19.0321	0.714765	0.357382	−	0.933958i	$-0.383669\pi$
$709$	19.0321	0.714765	0.357382	+	0.933958i	$0.383669\pi$
$710$	26.0812	0.978811
$711$	−48.6818	−1.82571
$712$	−7.49325	−0.280822
$713$	16.2727	0.609419
$714$	−11.4282	−0.427691
$715$	−1.68107	−0.0628685
$716$	−67.1542	−2.50967
$717$	16.0738	0.600287
$718$	28.9390	1.07999
$719$	42.5124	1.58544	0.792722	−	0.609584i	$-0.208663\pi$
$719$	42.5124	1.58544	0.792722	+	0.609584i	$0.208663\pi$
$720$	−7.27152	−0.270994
$721$	−11.7892	−0.439053
$722$	38.0767	1.41707
$723$	25.8828	0.962591
$724$	−9.28226	−0.344972
$725$	−26.3897	−0.980091
$726$	64.6095	2.39788
$727$	17.7425	0.658031	0.329016	−	0.944324i	$-0.393283\pi$
$727$	17.7425	0.658031	0.329016	+	0.944324i	$0.393283\pi$
$728$	2.04890	0.0759374
$729$	−40.6730	−1.50641
$730$	97.3648	3.60363
$731$	22.9599	0.849204
$732$	−59.3911	−2.19516
$733$	−37.3130	−1.37819	−0.689094	−	0.724672i	$-0.741991\pi$
$733$	−37.3130	−1.37819	−0.689094	+	0.724672i	$0.741991\pi$
$734$	49.2498	1.81784
$735$	−64.9869	−2.39708
$736$	35.1563	1.29588
$737$	3.39097	0.124908
$738$	55.0444	2.02621
$739$	7.56816	0.278399	0.139200	−	0.990264i	$-0.455547\pi$
$739$	7.56816	0.278399	0.139200	+	0.990264i	$0.455547\pi$
$740$	124.285	4.56882
$741$	−3.90073	−0.143297
$742$	−23.8131	−0.874206
$743$	32.7450	1.20130	0.600649	−	0.799513i	$-0.294909\pi$
$743$	32.7450	1.20130	0.600649	+	0.799513i	$0.294909\pi$
$744$	−19.2707	−0.706497
$745$	−19.9881	−0.732308
$746$	58.2496	2.13267
$747$	−21.6911	−0.793636
$748$	3.23415	0.118252
$749$	1.47571	0.0539213
$750$	−115.996	−4.23558
$751$	−22.0189	−0.803482	−0.401741	−	0.915753i	$-0.631595\pi$
$751$	−22.0189	−0.803482	−0.401741	+	0.915753i	$0.631595\pi$
$752$	1.50374	0.0548359
$753$	11.6671	0.425174
$754$	−5.96968	−0.217403
$755$	−57.0604	−2.07664
$756$	6.38818	0.232336
$757$	−13.4631	−0.489325	−0.244662	−	0.969608i	$-0.578677\pi$
$757$	−13.4631	−0.489325	−0.244662	+	0.969608i	$0.578677\pi$
$758$	63.6375	2.31142
$759$	6.51554	0.236499
$760$	−14.6216	−0.530381
$761$	20.4413	0.740998	0.370499	−	0.928833i	$-0.379187\pi$
$761$	20.4413	0.740998	0.370499	+	0.928833i	$0.379187\pi$
$762$	−58.1690	−2.10724
$763$	−3.68643	−0.133458
$764$	58.9768	2.13371
$765$	36.6049	1.32345
$766$	−34.7982	−1.25731
$767$	9.50197	0.343096
$768$	−33.8181	−1.22031
$769$	37.3403	1.34653	0.673263	−	0.739403i	$-0.264892\pi$
$769$	37.3403	1.34653	0.673263	+	0.739403i	$0.264892\pi$
$770$	−3.05465	−0.110082
$771$	23.9287	0.861771
$772$	73.7805	2.65542
$773$	49.1487	1.76776	0.883878	−	0.467717i	$-0.154923\pi$
$773$	49.1487	1.76776	0.883878	+	0.467717i	$0.154923\pi$
$774$	−86.4883	−3.10876
$775$	28.6279	1.02834
$776$	−20.1566	−0.723579
$777$	21.7212	0.779244
$778$	24.2501	0.869408
$779$	−9.06293	−0.324713
$780$	−31.9776	−1.14498
$781$	−1.28995	−0.0461581
$782$	−30.7062	−1.09805
$783$	−6.71034	−0.239808
$784$	3.00907	0.107467
$785$	8.95506	0.319620
$786$	46.4670	1.65742
$787$	−50.2050	−1.78961	−0.894807	−	0.446453i	$-0.852687\pi$
$787$	−50.2050	−1.78961	−0.894807	+	0.446453i	$0.852687\pi$
$788$	−75.3433	−2.68399
$789$	81.9789	2.91853
$790$	107.727	3.83277
$791$	−13.0650	−0.464538
$792$	−4.39223	−0.156071
$793$	7.19562	0.255524
$794$	50.1331	1.77916
$795$	133.992	4.75220
$796$	−50.7474	−1.79869
$797$	33.9166	1.20139	0.600694	−	0.799479i	$-0.294891\pi$
$797$	33.9166	1.20139	0.600694	+	0.799479i	$0.294891\pi$
$798$	−7.08796	−0.250911
$799$	−7.56987	−0.267803
$800$	61.8488	2.18669
$801$	11.6348	0.411094
$802$	−31.5649	−1.11460
$803$	−4.81557	−0.169938
$804$	64.5035	2.27486
$805$	17.6898	0.623484
$806$	6.47598	0.228107
$807$	21.1128	0.743204
$808$	18.6039	0.654482
$809$	30.5704	1.07480	0.537398	−	0.843329i	$-0.319407\pi$
$809$	30.5704	1.07480	0.537398	+	0.843329i	$0.319407\pi$
$810$	45.4110	1.59558
$811$	42.8697	1.50536	0.752679	−	0.658388i	$-0.228761\pi$
$811$	42.8697	1.50536	0.752679	+	0.658388i	$0.228761\pi$
$812$	−6.61641	−0.232191
$813$	1.77971	0.0624171
$814$	−10.0779	−0.353230
$815$	65.6994	2.30135
$816$	−2.97747	−0.104232
$817$	14.2401	0.498198
$818$	−0.443569	−0.0155090
$819$	−3.18133	−0.111165
$820$	−74.2965	−2.59455
$821$	−7.58635	−0.264765	−0.132383	−	0.991199i	$-0.542263\pi$
$821$	−7.58635	−0.264765	−0.132383	+	0.991199i	$0.542263\pi$
$822$	−103.634	−3.61466
$823$	24.1751	0.842692	0.421346	−	0.906900i	$-0.361558\pi$
$823$	24.1751	0.842692	0.421346	+	0.906900i	$0.361558\pi$
$824$	37.5118	1.30679
$825$	11.4625	0.399072
$826$	17.2659	0.600757
$827$	−24.0007	−0.834585	−0.417293	−	0.908772i	$-0.637021\pi$
$827$	−24.0007	−0.834585	−0.417293	+	0.908772i	$0.637021\pi$
$828$	70.5519	2.45185
$829$	1.15534	0.0401267	0.0200634	−	0.999799i	$-0.493613\pi$
$829$	1.15534	0.0401267	0.0200634	+	0.999799i	$0.493613\pi$
$830$	48.0000	1.66610
$831$	−72.0578	−2.49966
$832$	13.0441	0.452224
$833$	−15.1477	−0.524837
$834$	−77.2990	−2.67665
$835$	−52.7738	−1.82631
$836$	2.00587	0.0693743
$837$	7.27945	0.251615
$838$	−18.7754	−0.648584
$839$	−23.4707	−0.810297	−0.405148	−	0.914251i	$-0.632780\pi$
$839$	−23.4707	−0.810297	−0.405148	+	0.914251i	$0.632780\pi$
$840$	−20.9488	−0.722802
$841$	−22.0499	−0.760342
$842$	69.2538	2.38664
$843$	69.3021	2.38689
$844$	31.6050	1.08789
$845$	3.87429	0.133280
$846$	28.5151	0.980370
$847$	−8.67590	−0.298107
$848$	−6.20418	−0.213052
$849$	−60.5721	−2.07883
$850$	−54.0200	−1.85287
$851$	58.3621	2.00063
$852$	−24.5376	−0.840646
$853$	26.6318	0.911856	0.455928	−	0.890017i	$-0.349308\pi$
$853$	26.6318	0.911856	0.455928	+	0.890017i	$0.349308\pi$
$854$	13.0751	0.447420
$855$	22.7029	0.776423
$856$	−4.69553	−0.160490
$857$	−4.40959	−0.150629	−0.0753144	−	0.997160i	$-0.523996\pi$
$857$	−4.40959	−0.150629	−0.0753144	+	0.997160i	$0.523996\pi$
$858$	2.59295	0.0885220
$859$	−38.4178	−1.31080	−0.655400	−	0.755282i	$-0.727500\pi$
$859$	−38.4178	−1.31080	−0.655400	+	0.755282i	$0.727500\pi$
$860$	116.738	3.98074
$861$	−12.9847	−0.442518
$862$	−39.7462	−1.35376
$863$	−22.2370	−0.756956	−0.378478	−	0.925610i	$-0.623552\pi$
$863$	−22.2370	−0.756956	−0.378478	+	0.925610i	$0.623552\pi$
$864$	15.7268	0.535037
$865$	65.0599	2.21210
$866$	−35.7311	−1.21419
$867$	−29.8750	−1.01461
$868$	7.17755	0.243622
$869$	−5.32808	−0.180743
$870$	61.0364	2.06933
$871$	−7.81503	−0.264802
$872$	11.7298	0.397220
$873$	31.2971	1.05925
$874$	−19.0444	−0.644188
$875$	15.5762	0.526571
$876$	−91.6024	−3.09496
$877$	−53.1910	−1.79613	−0.898066	−	0.439860i	$-0.855028\pi$
$877$	−53.1910	−1.79613	−0.898066	+	0.439860i	$0.855028\pi$
$878$	15.8721	0.535657
$879$	7.25248	0.244620
$880$	−0.795847	−0.0268280
$881$	−41.4007	−1.39482	−0.697412	−	0.716670i	$-0.745665\pi$
$881$	−41.4007	−1.39482	−0.697412	+	0.716670i	$0.745665\pi$
$882$	57.0603	1.92132
$883$	−5.49640	−0.184969	−0.0924844	−	0.995714i	$-0.529481\pi$
$883$	−5.49640	−0.184969	−0.0924844	+	0.995714i	$0.529481\pi$
$884$	−7.45361	−0.250692
$885$	−97.1518	−3.26572
$886$	26.8867	0.903276
$887$	11.2044	0.376208	0.188104	−	0.982149i	$-0.439766\pi$
$887$	11.2044	0.376208	0.188104	+	0.982149i	$0.439766\pi$
$888$	−69.1142	−2.31932
$889$	7.81105	0.261974
$890$	−25.7464	−0.863022
$891$	−2.24598	−0.0752432
$892$	−18.4427	−0.617509
$893$	−4.69495	−0.157110
$894$	30.8305	1.03113
$895$	−83.1874	−2.78065
$896$	13.7862	0.460564
$897$	−15.0161	−0.501372
$898$	−34.8703	−1.16364
$899$	−7.53953	−0.251457
$900$	124.119	4.13729
$901$	31.2319	1.04049
$902$	6.02445	0.200592
$903$	20.4022	0.678942
$904$	41.5712	1.38264
$905$	−11.4984	−0.382220
$906$	88.0124	2.92402
$907$	−30.8711	−1.02506	−0.512529	−	0.858670i	$-0.671291\pi$
$907$	−30.8711	−1.02506	−0.512529	+	0.858670i	$0.671291\pi$
$908$	47.3194	1.57035
$909$	−28.8862	−0.958093
$910$	7.03992	0.233371
$911$	32.3975	1.07338	0.536688	−	0.843781i	$-0.319675\pi$
$911$	32.3975	1.07338	0.536688	+	0.843781i	$0.319675\pi$
$912$	−1.84667	−0.0611494
$913$	−2.37403	−0.0785689
$914$	4.68933	0.155109
$915$	−73.5709	−2.43218
$916$	52.0670	1.72034
$917$	−6.23969	−0.206053
$918$	−13.7361	−0.453360
$919$	−16.5926	−0.547338	−0.273669	−	0.961824i	$-0.588237\pi$
$919$	−16.5926	−0.547338	−0.273669	+	0.961824i	$0.588237\pi$
$920$	−56.2867	−1.85572
$921$	35.0605	1.15528
$922$	29.4134	0.968680
$923$	2.97290	0.0978541
$924$	2.87386	0.0945431
$925$	102.674	3.37589
$926$	−2.26442	−0.0744133
$927$	−58.2445	−1.91300
$928$	−16.2887	−0.534703
$929$	−26.5543	−0.871220	−0.435610	−	0.900136i	$-0.643467\pi$
$929$	−26.5543	−0.871220	−0.435610	+	0.900136i	$0.643467\pi$
$930$	−66.2129	−2.17121
$931$	−9.39483	−0.307903
$932$	−61.8804	−2.02696
$933$	0.717865	0.0235018
$934$	44.5262	1.45694
$935$	4.00631	0.131020
$936$	10.1226	0.330867
$937$	36.0079	1.17633	0.588163	−	0.808742i	$-0.299851\pi$
$937$	36.0079	1.17633	0.588163	+	0.808742i	$0.299851\pi$
$938$	−14.2006	−0.463665
$939$	66.4465	2.16840
$940$	−38.4884	−1.25535
$941$	−38.5169	−1.25561	−0.627807	−	0.778369i	$-0.716047\pi$
$941$	−38.5169	−1.25561	−0.627807	+	0.778369i	$0.716047\pi$
$942$	−13.8127	−0.450041
$943$	−34.8883	−1.13612
$944$	4.49839	0.146410
$945$	7.91337	0.257422
$946$	−9.46590	−0.307763
$947$	19.1426	0.622051	0.311026	−	0.950402i	$-0.399328\pi$
$947$	19.1426	0.622051	0.311026	+	0.950402i	$0.399328\pi$
$948$	−101.352	−3.29175
$949$	11.0982	0.360264
$950$	−33.5040	−1.08701
$951$	23.8867	0.774578
$952$	−4.88292	−0.158256
$953$	42.0400	1.36181	0.680905	−	0.732372i	$-0.261587\pi$
$953$	42.0400	1.36181	0.680905	+	0.732372i	$0.261587\pi$
$954$	−117.648	−3.80900
$955$	73.0576	2.36409
$956$	19.0494	0.616102
$957$	−3.01880	−0.0975838
$958$	−14.3401	−0.463307
$959$	13.9162	0.449379
$960$	−133.368	−4.30444
$961$	−22.8210	−0.736162
$962$	23.2261	0.748839
$963$	7.29073	0.234941
$964$	30.6742	0.987951
$965$	91.3957	2.94213
$966$	−27.2855	−0.877897
$967$	−2.43583	−0.0783312	−0.0391656	−	0.999233i	$-0.512470\pi$
$967$	−2.43583	−0.0783312	−0.0391656	+	0.999233i	$0.512470\pi$
$968$	27.6056	0.887278
$969$	9.29617	0.298636
$970$	−69.2569	−2.22370
$971$	−27.3978	−0.879237	−0.439618	−	0.898185i	$-0.644886\pi$
$971$	−27.3978	−0.879237	−0.439618	+	0.898185i	$0.644886\pi$
$972$	−66.6058	−2.13638
$973$	10.3799	0.332763
$974$	−26.9086	−0.862207
$975$	−26.4171	−0.846024
$976$	3.40653	0.109040
$977$	−18.3382	−0.586690	−0.293345	−	0.956007i	$-0.594768\pi$
$977$	−18.3382	−0.586690	−0.293345	+	0.956007i	$0.594768\pi$
$978$	−101.338	−3.24042
$979$	1.27339	0.0406978
$980$	−77.0174	−2.46023
$981$	−18.2128	−0.581488
$982$	−48.7361	−1.55523
$983$	6.10172	0.194615	0.0973073	−	0.995254i	$-0.468977\pi$
$983$	6.10172	0.194615	0.0973073	+	0.995254i	$0.468977\pi$
$984$	41.3157	1.31710
$985$	−93.3316	−2.97379
$986$	14.2269	0.453076
$987$	−6.72658	−0.214110
$988$	−4.62284	−0.147072
$989$	54.8181	1.74311
$990$	−15.0914	−0.479638
$991$	10.5105	0.333879	0.166939	−	0.985967i	$-0.446612\pi$
$991$	10.5105	0.333879	0.166939	+	0.985967i	$0.446612\pi$
$992$	17.6702	0.561028
$993$	19.6151	0.622466
$994$	5.40201	0.171341
$995$	−62.8635	−1.99291
$996$	−45.1592	−1.43092
$997$	37.8923	1.20006	0.600031	−	0.799977i	$-0.295155\pi$
$997$	37.8923	1.20006	0.600031	+	0.799977i	$0.295155\pi$
$998$	9.57179	0.302990
$999$	26.1077	0.826012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.13	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.13	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26442 q^{2} +2.63903 q^{3} +3.12758 q^{4} +3.87429 q^{5} -5.97587 q^{6} +0.802453 q^{7} -2.55330 q^{8} +3.96450 q^{9} +O(q^{10})\)	\(q-2.26442 q^{2} +2.63903 q^{3} +3.12758 q^{4} +3.87429 q^{5} -5.97587 q^{6} +0.802453 q^{7} -2.55330 q^{8} +3.96450 q^{9} -8.77301 q^{10} +0.433904 q^{11} +8.25378 q^{12} -1.00000 q^{13} -1.81709 q^{14} +10.2244 q^{15} -0.473417 q^{16} +2.38319 q^{17} -8.97729 q^{18} +1.47809 q^{19} +12.1171 q^{20} +2.11770 q^{21} -0.982539 q^{22} +5.68999 q^{23} -6.73825 q^{24} +10.0101 q^{25} +2.26442 q^{26} +2.54536 q^{27} +2.50973 q^{28} -2.63630 q^{29} -23.1523 q^{30} +2.85989 q^{31} +6.17862 q^{32} +1.14509 q^{33} -5.39653 q^{34} +3.10894 q^{35} +12.3993 q^{36} +10.2570 q^{37} -3.34701 q^{38} -2.63903 q^{39} -9.89224 q^{40} -6.13152 q^{41} -4.79535 q^{42} +9.63413 q^{43} +1.35707 q^{44} +15.3596 q^{45} -12.8845 q^{46} -3.17636 q^{47} -1.24936 q^{48} -6.35607 q^{49} -22.6671 q^{50} +6.28932 q^{51} -3.12758 q^{52} +13.1051 q^{53} -5.76376 q^{54} +1.68107 q^{55} -2.04890 q^{56} +3.90073 q^{57} +5.96968 q^{58} -9.50197 q^{59} +31.9776 q^{60} -7.19562 q^{61} -6.47598 q^{62} +3.18133 q^{63} -13.0441 q^{64} -3.87429 q^{65} -2.59295 q^{66} +7.81503 q^{67} +7.45361 q^{68} +15.0161 q^{69} -7.03992 q^{70} -2.97290 q^{71} -10.1226 q^{72} -11.0982 q^{73} -23.2261 q^{74} +26.4171 q^{75} +4.62284 q^{76} +0.348187 q^{77} +5.97587 q^{78} -12.2794 q^{79} -1.83416 q^{80} -5.17622 q^{81} +13.8843 q^{82} -5.47133 q^{83} +6.62327 q^{84} +9.23317 q^{85} -21.8157 q^{86} -6.95729 q^{87} -1.10789 q^{88} +2.93473 q^{89} -34.7806 q^{90} -0.802453 q^{91} +17.7959 q^{92} +7.54735 q^{93} +7.19260 q^{94} +5.72655 q^{95} +16.3056 q^{96} +7.89432 q^{97} +14.3928 q^{98} +1.72021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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