LMFDB - Embedded newform 6022.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.16331 q^{3} +1.00000 q^{4} -3.33265 q^{5} +2.16331 q^{6} +3.92579 q^{7} -1.00000 q^{8} +1.67989 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.16331 q^{3} +1.00000 q^{4} -3.33265 q^{5} +2.16331 q^{6} +3.92579 q^{7} -1.00000 q^{8} +1.67989 q^{9} +3.33265 q^{10} -5.16755 q^{11} -2.16331 q^{12} +2.07463 q^{13} -3.92579 q^{14} +7.20954 q^{15} +1.00000 q^{16} -4.04830 q^{17} -1.67989 q^{18} +7.27671 q^{19} -3.33265 q^{20} -8.49268 q^{21} +5.16755 q^{22} -7.19979 q^{23} +2.16331 q^{24} +6.10655 q^{25} -2.07463 q^{26} +2.85580 q^{27} +3.92579 q^{28} +2.06331 q^{29} -7.20954 q^{30} +1.70723 q^{31} -1.00000 q^{32} +11.1790 q^{33} +4.04830 q^{34} -13.0833 q^{35} +1.67989 q^{36} -10.6397 q^{37} -7.27671 q^{38} -4.48807 q^{39} +3.33265 q^{40} +8.07969 q^{41} +8.49268 q^{42} -8.82733 q^{43} -5.16755 q^{44} -5.59848 q^{45} +7.19979 q^{46} +8.84443 q^{47} -2.16331 q^{48} +8.41183 q^{49} -6.10655 q^{50} +8.75772 q^{51} +2.07463 q^{52} +1.40957 q^{53} -2.85580 q^{54} +17.2216 q^{55} -3.92579 q^{56} -15.7417 q^{57} -2.06331 q^{58} -8.34168 q^{59} +7.20954 q^{60} -0.389804 q^{61} -1.70723 q^{62} +6.59490 q^{63} +1.00000 q^{64} -6.91403 q^{65} -11.1790 q^{66} -7.30847 q^{67} -4.04830 q^{68} +15.5753 q^{69} +13.0833 q^{70} +13.7086 q^{71} -1.67989 q^{72} +6.95265 q^{73} +10.6397 q^{74} -13.2103 q^{75} +7.27671 q^{76} -20.2867 q^{77} +4.48807 q^{78} -7.80790 q^{79} -3.33265 q^{80} -11.2176 q^{81} -8.07969 q^{82} +11.1629 q^{83} -8.49268 q^{84} +13.4916 q^{85} +8.82733 q^{86} -4.46357 q^{87} +5.16755 q^{88} +6.49461 q^{89} +5.59848 q^{90} +8.14458 q^{91} -7.19979 q^{92} -3.69326 q^{93} -8.84443 q^{94} -24.2507 q^{95} +2.16331 q^{96} -8.47742 q^{97} -8.41183 q^{98} -8.68092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.16331	−1.24898	−0.624492	−	0.781031i	$-0.714694\pi$
$3$	−2.16331	−1.24898	−0.624492	+	0.781031i	$0.714694\pi$
$4$	1.00000	0.500000
$5$	−3.33265	−1.49041	−0.745203	−	0.666838i	$-0.767647\pi$
$5$	−3.33265	−1.49041	−0.745203	+	0.666838i	$0.767647\pi$
$6$	2.16331	0.883166
$7$	3.92579	1.48381	0.741905	−	0.670505i	$-0.233923\pi$
$7$	3.92579	1.48381	0.741905	+	0.670505i	$0.233923\pi$
$8$	−1.00000	−0.353553
$9$	1.67989	0.559964
$10$	3.33265	1.05388
$11$	−5.16755	−1.55808	−0.779038	−	0.626977i	$-0.784292\pi$
$11$	−5.16755	−1.55808	−0.779038	+	0.626977i	$0.784292\pi$
$12$	−2.16331	−0.624492
$13$	2.07463	0.575400	0.287700	−	0.957721i	$-0.407109\pi$
$13$	2.07463	0.575400	0.287700	+	0.957721i	$0.407109\pi$
$14$	−3.92579	−1.04921
$15$	7.20954	1.86149
$16$	1.00000	0.250000
$17$	−4.04830	−0.981858	−0.490929	−	0.871200i	$-0.663343\pi$
$17$	−4.04830	−0.981858	−0.490929	+	0.871200i	$0.663343\pi$
$18$	−1.67989	−0.395954
$19$	7.27671	1.66939	0.834696	−	0.550711i	$-0.185643\pi$
$19$	7.27671	1.66939	0.834696	+	0.550711i	$0.185643\pi$
$20$	−3.33265	−0.745203
$21$	−8.49268	−1.85326
$22$	5.16755	1.10173
$23$	−7.19979	−1.50126	−0.750630	−	0.660723i	$-0.770250\pi$
$23$	−7.19979	−1.50126	−0.750630	+	0.660723i	$0.770250\pi$
$24$	2.16331	0.441583
$25$	6.10655	1.22131
$26$	−2.07463	−0.406869
$27$	2.85580	0.549599
$28$	3.92579	0.741905
$29$	2.06331	0.383147	0.191574	−	0.981478i	$-0.438641\pi$
$29$	2.06331	0.383147	0.191574	+	0.981478i	$0.438641\pi$
$30$	−7.20954	−1.31628
$31$	1.70723	0.306628	0.153314	−	0.988178i	$-0.451005\pi$
$31$	1.70723	0.306628	0.153314	+	0.988178i	$0.451005\pi$
$32$	−1.00000	−0.176777
$33$	11.1790	1.94601
$34$	4.04830	0.694278
$35$	−13.0833	−2.21148
$36$	1.67989	0.279982
$37$	−10.6397	−1.74915	−0.874574	−	0.484892i	$-0.838859\pi$
$37$	−10.6397	−1.74915	−0.874574	+	0.484892i	$0.838859\pi$
$38$	−7.27671	−1.18044
$39$	−4.48807	−0.718666
$40$	3.33265	0.526938
$41$	8.07969	1.26184	0.630918	−	0.775850i	$-0.282678\pi$
$41$	8.07969	1.26184	0.630918	+	0.775850i	$0.282678\pi$
$42$	8.49268	1.31045
$43$	−8.82733	−1.34616	−0.673078	−	0.739572i	$-0.735028\pi$
$43$	−8.82733	−1.34616	−0.673078	+	0.739572i	$0.735028\pi$
$44$	−5.16755	−0.779038
$45$	−5.59848	−0.834573
$46$	7.19979	1.06155
$47$	8.84443	1.29009	0.645047	−	0.764143i	$-0.276838\pi$
$47$	8.84443	1.29009	0.645047	+	0.764143i	$0.276838\pi$
$48$	−2.16331	−0.312246
$49$	8.41183	1.20169
$50$	−6.10655	−0.863596
$51$	8.75772	1.22633
$52$	2.07463	0.287700
$53$	1.40957	0.193619	0.0968096	−	0.995303i	$-0.469136\pi$
$53$	1.40957	0.193619	0.0968096	+	0.995303i	$0.469136\pi$
$54$	−2.85580	−0.388625
$55$	17.2216	2.32217
$56$	−3.92579	−0.524606
$57$	−15.7417	−2.08505
$58$	−2.06331	−0.270926
$59$	−8.34168	−1.08599	−0.542997	−	0.839735i	$-0.682711\pi$
$59$	−8.34168	−1.08599	−0.542997	+	0.839735i	$0.682711\pi$
$60$	7.20954	0.930747
$61$	−0.389804	−0.0499093	−0.0249547	−	0.999689i	$-0.507944\pi$
$61$	−0.389804	−0.0499093	−0.0249547	+	0.999689i	$0.507944\pi$
$62$	−1.70723	−0.216818
$63$	6.59490	0.830879
$64$	1.00000	0.125000
$65$	−6.91403	−0.857580
$66$	−11.1790	−1.37604
$67$	−7.30847	−0.892872	−0.446436	−	0.894815i	$-0.647307\pi$
$67$	−7.30847	−0.892872	−0.446436	+	0.894815i	$0.647307\pi$
$68$	−4.04830	−0.490929
$69$	15.5753	1.87505
$70$	13.0833	1.56375
$71$	13.7086	1.62691	0.813454	−	0.581629i	$-0.197585\pi$
$71$	13.7086	1.62691	0.813454	+	0.581629i	$0.197585\pi$
$72$	−1.67989	−0.197977
$73$	6.95265	0.813746	0.406873	−	0.913485i	$-0.366619\pi$
$73$	6.95265	0.813746	0.406873	+	0.913485i	$0.366619\pi$
$74$	10.6397	1.23683
$75$	−13.2103	−1.52540
$76$	7.27671	0.834696
$77$	−20.2867	−2.31189
$78$	4.48807	0.508174
$79$	−7.80790	−0.878458	−0.439229	−	0.898375i	$-0.644748\pi$
$79$	−7.80790	−0.878458	−0.439229	+	0.898375i	$0.644748\pi$
$80$	−3.33265	−0.372601
$81$	−11.2176	−1.24640
$82$	−8.07969	−0.892253
$83$	11.1629	1.22529	0.612643	−	0.790360i	$-0.290106\pi$
$83$	11.1629	1.22529	0.612643	+	0.790360i	$0.290106\pi$
$84$	−8.49268	−0.926628
$85$	13.4916	1.46337
$86$	8.82733	0.951876
$87$	−4.46357	−0.478545
$88$	5.16755	0.550863
$89$	6.49461	0.688428	0.344214	−	0.938891i	$-0.388146\pi$
$89$	6.49461	0.688428	0.344214	+	0.938891i	$0.388146\pi$
$90$	5.59848	0.590132
$91$	8.14458	0.853784
$92$	−7.19979	−0.750630
$93$	−3.69326	−0.382973
$94$	−8.84443	−0.912234
$95$	−24.2507	−2.48807
$96$	2.16331	0.220791
$97$	−8.47742	−0.860752	−0.430376	−	0.902650i	$-0.641619\pi$
$97$	−8.47742	−0.860752	−0.430376	+	0.902650i	$0.641619\pi$
$98$	−8.41183	−0.849723
$99$	−8.68092	−0.872466
$100$	6.10655	0.610655
$101$	2.57531	0.256253	0.128126	−	0.991758i	$-0.459104\pi$
$101$	2.57531	0.256253	0.128126	+	0.991758i	$0.459104\pi$
$102$	−8.75772	−0.867143
$103$	−2.60682	−0.256857	−0.128429	−	0.991719i	$-0.540993\pi$
$103$	−2.60682	−0.256857	−0.128429	+	0.991719i	$0.540993\pi$
$104$	−2.07463	−0.203435
$105$	28.3031	2.76210
$106$	−1.40957	−0.136909
$107$	4.94487	0.478039	0.239019	−	0.971015i	$-0.423174\pi$
$107$	4.94487	0.478039	0.239019	+	0.971015i	$0.423174\pi$
$108$	2.85580	0.274799
$109$	11.3732	1.08936	0.544680	−	0.838644i	$-0.316651\pi$
$109$	11.3732	1.08936	0.544680	+	0.838644i	$0.316651\pi$
$110$	−17.2216	−1.64202
$111$	23.0168	2.18466
$112$	3.92579	0.370952
$113$	19.6822	1.85154	0.925771	−	0.378085i	$-0.123417\pi$
$113$	19.6822	1.85154	0.925771	+	0.378085i	$0.123417\pi$
$114$	15.7417	1.47435
$115$	23.9944	2.23749
$116$	2.06331	0.191574
$117$	3.48516	0.322203
$118$	8.34168	0.767914
$119$	−15.8928	−1.45689
$120$	−7.20954	−0.658138
$121$	15.7036	1.42760
$122$	0.389804	0.0352912
$123$	−17.4788	−1.57601
$124$	1.70723	0.153314
$125$	−3.68773	−0.329841
$126$	−6.59490	−0.587520
$127$	−1.91503	−0.169931	−0.0849657	−	0.996384i	$-0.527078\pi$
$127$	−1.91503	−0.169931	−0.0849657	+	0.996384i	$0.527078\pi$
$128$	−1.00000	−0.0883883
$129$	19.0962	1.68133
$130$	6.91403	0.606400
$131$	−9.27409	−0.810281	−0.405140	−	0.914254i	$-0.632777\pi$
$131$	−9.27409	−0.810281	−0.405140	+	0.914254i	$0.632777\pi$
$132$	11.1790	0.973007
$133$	28.5668	2.47706
$134$	7.30847	0.631356
$135$	−9.51738	−0.819126
$136$	4.04830	0.347139
$137$	4.71968	0.403230	0.201615	−	0.979465i	$-0.435381\pi$
$137$	4.71968	0.403230	0.201615	+	0.979465i	$0.435381\pi$
$138$	−15.5753	−1.32586
$139$	14.5816	1.23679	0.618397	−	0.785866i	$-0.287782\pi$
$139$	14.5816	1.23679	0.618397	+	0.785866i	$0.287782\pi$
$140$	−13.0833	−1.10574
$141$	−19.1332	−1.61131
$142$	−13.7086	−1.15040
$143$	−10.7208	−0.896517
$144$	1.67989	0.139991
$145$	−6.87629	−0.571045
$146$	−6.95265	−0.575405
$147$	−18.1974	−1.50089
$148$	−10.6397	−0.874574
$149$	−16.4024	−1.34374	−0.671868	−	0.740671i	$-0.734508\pi$
$149$	−16.4024	−1.34374	−0.671868	+	0.740671i	$0.734508\pi$
$150$	13.2103	1.07862
$151$	−19.2739	−1.56849	−0.784246	−	0.620450i	$-0.786950\pi$
$151$	−19.2739	−1.56849	−0.784246	+	0.620450i	$0.786950\pi$
$152$	−7.27671	−0.590219
$153$	−6.80071	−0.549805
$154$	20.2867	1.63475
$155$	−5.68960	−0.457000
$156$	−4.48807	−0.359333
$157$	9.24013	0.737443	0.368721	−	0.929540i	$-0.379796\pi$
$157$	9.24013	0.737443	0.368721	+	0.929540i	$0.379796\pi$
$158$	7.80790	0.621164
$159$	−3.04933	−0.241827
$160$	3.33265	0.263469
$161$	−28.2649	−2.22758
$162$	11.2176	0.881341
$163$	3.05128	0.238995	0.119497	−	0.992835i	$-0.461872\pi$
$163$	3.05128	0.238995	0.119497	+	0.992835i	$0.461872\pi$
$164$	8.07969	0.630918
$165$	−37.2557	−2.90035
$166$	−11.1629	−0.866408
$167$	7.77640	0.601756	0.300878	−	0.953663i	$-0.402720\pi$
$167$	7.77640	0.601756	0.300878	+	0.953663i	$0.402720\pi$
$168$	8.49268	0.655225
$169$	−8.69589	−0.668915
$170$	−13.4916	−1.03476
$171$	12.2241	0.934798
$172$	−8.82733	−0.673078
$173$	−1.24134	−0.0943776	−0.0471888	−	0.998886i	$-0.515026\pi$
$173$	−1.24134	−0.0943776	−0.0471888	+	0.998886i	$0.515026\pi$
$174$	4.46357	0.338383
$175$	23.9730	1.81219
$176$	−5.16755	−0.389519
$177$	18.0456	1.35639
$178$	−6.49461	−0.486792
$179$	−17.3229	−1.29477	−0.647387	−	0.762161i	$-0.724138\pi$
$179$	−17.3229	−1.29477	−0.647387	+	0.762161i	$0.724138\pi$
$180$	−5.59848	−0.417286
$181$	5.66556	0.421117	0.210559	−	0.977581i	$-0.432472\pi$
$181$	5.66556	0.421117	0.210559	+	0.977581i	$0.432472\pi$
$182$	−8.14458	−0.603716
$183$	0.843266	0.0623360
$184$	7.19979	0.530775
$185$	35.4582	2.60694
$186$	3.69326	0.270803
$187$	20.9198	1.52981
$188$	8.84443	0.645047
$189$	11.2113	0.815500
$190$	24.2507	1.75933
$191$	8.97928	0.649718	0.324859	−	0.945762i	$-0.394683\pi$
$191$	8.97928	0.649718	0.324859	+	0.945762i	$0.394683\pi$
$192$	−2.16331	−0.156123
$193$	6.54338	0.471003	0.235501	−	0.971874i	$-0.424327\pi$
$193$	6.54338	0.471003	0.235501	+	0.971874i	$0.424327\pi$
$194$	8.47742	0.608643
$195$	14.9572	1.07110
$196$	8.41183	0.600845
$197$	−8.41550	−0.599579	−0.299790	−	0.954005i	$-0.596917\pi$
$197$	−8.41550	−0.599579	−0.299790	+	0.954005i	$0.596917\pi$
$198$	8.68092	0.616926
$199$	26.1017	1.85030	0.925150	−	0.379601i	$-0.123939\pi$
$199$	26.1017	1.85030	0.925150	+	0.379601i	$0.123939\pi$
$200$	−6.10655	−0.431798
$201$	15.8105	1.11518
$202$	−2.57531	−0.181198
$203$	8.10013	0.568518
$204$	8.75772	0.613163
$205$	−26.9268	−1.88065
$206$	2.60682	0.181626
$207$	−12.0949	−0.840650
$208$	2.07463	0.143850
$209$	−37.6028	−2.60104
$210$	−28.3031	−1.95310
$211$	25.0831	1.72679	0.863394	−	0.504530i	$-0.168334\pi$
$211$	25.0831	1.72679	0.863394	+	0.504530i	$0.168334\pi$
$212$	1.40957	0.0968096
$213$	−29.6558	−2.03198
$214$	−4.94487	−0.338024
$215$	29.4184	2.00632
$216$	−2.85580	−0.194313
$217$	6.70223	0.454977
$218$	−11.3732	−0.770293
$219$	−15.0407	−1.01636
$220$	17.2216	1.16108
$221$	−8.39875	−0.564961
$222$	−23.0168	−1.54479
$223$	−1.44849	−0.0969977	−0.0484989	−	0.998823i	$-0.515444\pi$
$223$	−1.44849	−0.0969977	−0.0484989	+	0.998823i	$0.515444\pi$
$224$	−3.92579	−0.262303
$225$	10.2583	0.683889
$226$	−19.6822	−1.30924
$227$	18.4378	1.22376	0.611879	−	0.790952i	$-0.290414\pi$
$227$	18.4378	1.22376	0.611879	+	0.790952i	$0.290414\pi$
$228$	−15.7417	−1.04252
$229$	10.6892	0.706359	0.353180	−	0.935556i	$-0.385100\pi$
$229$	10.6892	0.706359	0.353180	+	0.935556i	$0.385100\pi$
$230$	−23.9944	−1.58214
$231$	43.8864	2.88751
$232$	−2.06331	−0.135463
$233$	−7.60514	−0.498229	−0.249115	−	0.968474i	$-0.580140\pi$
$233$	−7.60514	−0.498229	−0.249115	+	0.968474i	$0.580140\pi$
$234$	−3.48516	−0.227832
$235$	−29.4754	−1.92276
$236$	−8.34168	−0.542997
$237$	16.8909	1.09718
$238$	15.8928	1.03018
$239$	10.8358	0.700910	0.350455	−	0.936580i	$-0.386027\pi$
$239$	10.8358	0.700910	0.350455	+	0.936580i	$0.386027\pi$
$240$	7.20954	0.465374
$241$	−1.14427	−0.0737086	−0.0368543	−	0.999321i	$-0.511734\pi$
$241$	−1.14427	−0.0737086	−0.0368543	+	0.999321i	$0.511734\pi$
$242$	−15.7036	−1.00947
$243$	15.6998	1.00714
$244$	−0.389804	−0.0249547
$245$	−28.0337	−1.79101
$246$	17.4788	1.11441
$247$	15.0965	0.960568
$248$	−1.70723	−0.108409
$249$	−24.1487	−1.53036
$250$	3.68773	0.233233
$251$	−12.3625	−0.780317	−0.390159	−	0.920748i	$-0.627580\pi$
$251$	−12.3625	−0.780317	−0.390159	+	0.920748i	$0.627580\pi$
$252$	6.59490	0.415440
$253$	37.2053	2.33908
$254$	1.91503	0.120160
$255$	−29.1864	−1.82772
$256$	1.00000	0.0625000
$257$	22.1073	1.37901	0.689507	−	0.724279i	$-0.257827\pi$
$257$	22.1073	1.37901	0.689507	+	0.724279i	$0.257827\pi$
$258$	−19.0962	−1.18888
$259$	−41.7690	−2.59540
$260$	−6.91403	−0.428790
$261$	3.46614	0.214548
$262$	9.27409	0.572955
$263$	−24.3138	−1.49925	−0.749626	−	0.661861i	$-0.769767\pi$
$263$	−24.3138	−1.49925	−0.749626	+	0.661861i	$0.769767\pi$
$264$	−11.1790	−0.688020
$265$	−4.69760	−0.288571
$266$	−28.5668	−1.75155
$267$	−14.0498	−0.859836
$268$	−7.30847	−0.446436
$269$	−9.37689	−0.571719	−0.285860	−	0.958272i	$-0.592279\pi$
$269$	−9.37689	−0.571719	−0.285860	+	0.958272i	$0.592279\pi$
$270$	9.51738	0.579209
$271$	−16.6600	−1.01202	−0.506011	−	0.862527i	$-0.668880\pi$
$271$	−16.6600	−1.01202	−0.506011	+	0.862527i	$0.668880\pi$
$272$	−4.04830	−0.245464
$273$	−17.6192	−1.06636
$274$	−4.71968	−0.285126
$275$	−31.5559	−1.90289
$276$	15.5753	0.937525
$277$	1.90016	0.114169	0.0570847	−	0.998369i	$-0.481819\pi$
$277$	1.90016	0.114169	0.0570847	+	0.998369i	$0.481819\pi$
$278$	−14.5816	−0.874545
$279$	2.86796	0.171700
$280$	13.0833	0.781876
$281$	22.9693	1.37024	0.685118	−	0.728432i	$-0.259751\pi$
$281$	22.9693	1.37024	0.685118	+	0.728432i	$0.259751\pi$
$282$	19.1332	1.13937
$283$	−15.9272	−0.946773	−0.473387	−	0.880855i	$-0.656969\pi$
$283$	−15.9272	−0.946773	−0.473387	+	0.880855i	$0.656969\pi$
$284$	13.7086	0.813454
$285$	52.4617	3.10756
$286$	10.7208	0.633933
$287$	31.7192	1.87232
$288$	−1.67989	−0.0989885
$289$	−0.611234	−0.0359549
$290$	6.87629	0.403790
$291$	18.3392	1.07507
$292$	6.95265	0.406873
$293$	−30.1750	−1.76284	−0.881421	−	0.472331i	$-0.843413\pi$
$293$	−30.1750	−1.76284	−0.881421	+	0.472331i	$0.843413\pi$
$294$	18.1974	1.06129
$295$	27.7999	1.61857
$296$	10.6397	0.618417
$297$	−14.7575	−0.856317
$298$	16.4024	0.950165
$299$	−14.9369	−0.863825
$300$	−13.2103	−0.762699
$301$	−34.6543	−1.99744
$302$	19.2739	1.10909
$303$	−5.57118	−0.320056
$304$	7.27671	0.417348
$305$	1.29908	0.0743851
$306$	6.80071	0.388771
$307$	4.79991	0.273945	0.136973	−	0.990575i	$-0.456263\pi$
$307$	4.79991	0.273945	0.136973	+	0.990575i	$0.456263\pi$
$308$	−20.2867	−1.15594
$309$	5.63934	0.320811
$310$	5.68960	0.323147
$311$	26.6771	1.51272	0.756360	−	0.654155i	$-0.226976\pi$
$311$	26.6771	1.51272	0.756360	+	0.654155i	$0.226976\pi$
$312$	4.48807	0.254087
$313$	−18.7240	−1.05834	−0.529171	−	0.848515i	$-0.677497\pi$
$313$	−18.7240	−1.05834	−0.529171	+	0.848515i	$0.677497\pi$
$314$	−9.24013	−0.521451
$315$	−21.9785	−1.23835
$316$	−7.80790	−0.439229
$317$	−12.4436	−0.698900	−0.349450	−	0.936955i	$-0.613632\pi$
$317$	−12.4436	−0.698900	−0.349450	+	0.936955i	$0.613632\pi$
$318$	3.04933	0.170998
$319$	−10.6623	−0.596973
$320$	−3.33265	−0.186301
$321$	−10.6973	−0.597063
$322$	28.2649	1.57514
$323$	−29.4583	−1.63911
$324$	−11.2176	−0.623202
$325$	12.6689	0.702741
$326$	−3.05128	−0.168995
$327$	−24.6038	−1.36059
$328$	−8.07969	−0.446126
$329$	34.7214	1.91425
$330$	37.2557	2.05086
$331$	−29.3122	−1.61115	−0.805573	−	0.592496i	$-0.798142\pi$
$331$	−29.3122	−1.61115	−0.805573	+	0.592496i	$0.798142\pi$
$332$	11.1629	0.612643
$333$	−17.8735	−0.979459
$334$	−7.77640	−0.425506
$335$	24.3566	1.33074
$336$	−8.49268	−0.463314
$337$	4.88672	0.266196	0.133098	−	0.991103i	$-0.457507\pi$
$337$	4.88672	0.266196	0.133098	+	0.991103i	$0.457507\pi$
$338$	8.69589	0.472994
$339$	−42.5785	−2.31255
$340$	13.4916	0.731683
$341$	−8.82220	−0.477749
$342$	−12.2241	−0.661002
$343$	5.54256	0.299270
$344$	8.82733	0.475938
$345$	−51.9071	−2.79459
$346$	1.24134	0.0667350
$347$	−28.1576	−1.51158	−0.755788	−	0.654816i	$-0.772746\pi$
$347$	−28.1576	−1.51158	−0.755788	+	0.654816i	$0.772746\pi$
$348$	−4.46357	−0.239273
$349$	−31.1028	−1.66489	−0.832446	−	0.554106i	$-0.813060\pi$
$349$	−31.1028	−1.66489	−0.832446	+	0.554106i	$0.813060\pi$
$350$	−23.9730	−1.28141
$351$	5.92474	0.316239
$352$	5.16755	0.275432
$353$	−12.0820	−0.643058	−0.321529	−	0.946900i	$-0.604197\pi$
$353$	−12.0820	−0.643058	−0.321529	+	0.946900i	$0.604197\pi$
$354$	−18.0456	−0.959113
$355$	−45.6859	−2.42475
$356$	6.49461	0.344214
$357$	34.3810	1.81963
$358$	17.3229	0.915544
$359$	−8.22958	−0.434341	−0.217170	−	0.976134i	$-0.569683\pi$
$359$	−8.22958	−0.434341	−0.217170	+	0.976134i	$0.569683\pi$
$360$	5.59848	0.295066
$361$	33.9505	1.78687
$362$	−5.66556	−0.297775
$363$	−33.9717	−1.78305
$364$	8.14458	0.426892
$365$	−23.1707	−1.21281
$366$	−0.843266	−0.0440782
$367$	−21.5828	−1.12661	−0.563305	−	0.826249i	$-0.690471\pi$
$367$	−21.5828	−1.12661	−0.563305	+	0.826249i	$0.690471\pi$
$368$	−7.19979	−0.375315
$369$	13.5730	0.706582
$370$	−35.4582	−1.84339
$371$	5.53367	0.287294
$372$	−3.69326	−0.191487
$373$	0.798286	0.0413337	0.0206668	−	0.999786i	$-0.493421\pi$
$373$	0.798286	0.0413337	0.0206668	+	0.999786i	$0.493421\pi$
$374$	−20.9198	−1.08174
$375$	7.97769	0.411966
$376$	−8.84443	−0.456117
$377$	4.28062	0.220463
$378$	−11.2113	−0.576646
$379$	−26.6171	−1.36723	−0.683615	−	0.729843i	$-0.739593\pi$
$379$	−26.6171	−1.36723	−0.683615	+	0.729843i	$0.739593\pi$
$380$	−24.2507	−1.24404
$381$	4.14279	0.212242
$382$	−8.97928	−0.459420
$383$	−21.5704	−1.10220	−0.551099	−	0.834440i	$-0.685791\pi$
$383$	−21.5704	−1.10220	−0.551099	+	0.834440i	$0.685791\pi$
$384$	2.16331	0.110396
$385$	67.6086	3.44565
$386$	−6.54338	−0.333049
$387$	−14.8290	−0.753798
$388$	−8.47742	−0.430376
$389$	15.8875	0.805528	0.402764	−	0.915304i	$-0.368050\pi$
$389$	15.8875	0.805528	0.402764	+	0.915304i	$0.368050\pi$
$390$	−14.9572	−0.757385
$391$	29.1469	1.47402
$392$	−8.41183	−0.424862
$393$	20.0627	1.01203
$394$	8.41550	0.423967
$395$	26.0210	1.30926
$396$	−8.68092	−0.436233
$397$	5.24693	0.263336	0.131668	−	0.991294i	$-0.457967\pi$
$397$	5.24693	0.263336	0.131668	+	0.991294i	$0.457967\pi$
$398$	−26.1017	−1.30836
$399$	−61.7988	−3.09381
$400$	6.10655	0.305327
$401$	27.3807	1.36733	0.683663	−	0.729798i	$-0.260386\pi$
$401$	27.3807	1.36733	0.683663	+	0.729798i	$0.260386\pi$
$402$	−15.8105	−0.788554
$403$	3.54188	0.176434
$404$	2.57531	0.128126
$405$	37.3845	1.85765
$406$	−8.10013	−0.402003
$407$	54.9810	2.72531
$408$	−8.75772	−0.433572
$409$	−31.3607	−1.55069	−0.775344	−	0.631539i	$-0.782424\pi$
$409$	−31.3607	−1.55069	−0.775344	+	0.631539i	$0.782424\pi$
$410$	26.9268	1.32982
$411$	−10.2101	−0.503628
$412$	−2.60682	−0.128429
$413$	−32.7477	−1.61141
$414$	12.0949	0.594430
$415$	−37.2020	−1.82617
$416$	−2.07463	−0.101717
$417$	−31.5444	−1.54474
$418$	37.6028	1.83921
$419$	−8.55069	−0.417729	−0.208864	−	0.977945i	$-0.566977\pi$
$419$	−8.55069	−0.417729	−0.208864	+	0.977945i	$0.566977\pi$
$420$	28.3031	1.38105
$421$	−4.83273	−0.235533	−0.117767	−	0.993041i	$-0.537573\pi$
$421$	−4.83273	−0.235533	−0.117767	+	0.993041i	$0.537573\pi$
$422$	−25.0831	−1.22102
$423$	14.8577	0.722405
$424$	−1.40957	−0.0684547
$425$	−24.7212	−1.19915
$426$	29.6558	1.43683
$427$	−1.53029	−0.0740559
$428$	4.94487	0.239019
$429$	23.1923	1.11974
$430$	−29.4184	−1.41868
$431$	−12.1236	−0.583973	−0.291986	−	0.956422i	$-0.594316\pi$
$431$	−12.1236	−0.583973	−0.291986	+	0.956422i	$0.594316\pi$
$432$	2.85580	0.137400
$433$	−19.6533	−0.944476	−0.472238	−	0.881471i	$-0.656554\pi$
$433$	−19.6533	−0.944476	−0.472238	+	0.881471i	$0.656554\pi$
$434$	−6.70223	−0.321717
$435$	14.8755	0.713227
$436$	11.3732	0.544680
$437$	−52.3908	−2.50619
$438$	15.0407	0.718672
$439$	−28.0737	−1.33989	−0.669943	−	0.742412i	$-0.733682\pi$
$439$	−28.0737	−1.33989	−0.669943	+	0.742412i	$0.733682\pi$
$440$	−17.2216	−0.821010
$441$	14.1310	0.672903
$442$	8.39875	0.399488
$443$	22.8274	1.08456	0.542281	−	0.840197i	$-0.317561\pi$
$443$	22.8274	1.08456	0.542281	+	0.840197i	$0.317561\pi$
$444$	23.0168	1.09233
$445$	−21.6443	−1.02604
$446$	1.44849	0.0685878
$447$	35.4834	1.67831
$448$	3.92579	0.185476
$449$	−39.3169	−1.85548	−0.927740	−	0.373227i	$-0.878251\pi$
$449$	−39.3169	−1.85548	−0.927740	+	0.373227i	$0.878251\pi$
$450$	−10.2583	−0.483582
$451$	−41.7522	−1.96604
$452$	19.6822	0.925771
$453$	41.6954	1.95902
$454$	−18.4378	−0.865327
$455$	−27.1430	−1.27248
$456$	15.7417	0.737175
$457$	−15.5641	−0.728056	−0.364028	−	0.931388i	$-0.618599\pi$
$457$	−15.5641	−0.728056	−0.364028	+	0.931388i	$0.618599\pi$
$458$	−10.6892	−0.499472
$459$	−11.5611	−0.539628
$460$	23.9944	1.11874
$461$	−29.4449	−1.37138	−0.685692	−	0.727892i	$-0.740500\pi$
$461$	−29.4449	−1.37138	−0.685692	+	0.727892i	$0.740500\pi$
$462$	−43.8864	−2.04178
$463$	24.7954	1.15234	0.576170	−	0.817330i	$-0.304547\pi$
$463$	24.7954	1.15234	0.576170	+	0.817330i	$0.304547\pi$
$464$	2.06331	0.0957868
$465$	12.3083	0.570786
$466$	7.60514	0.352301
$467$	13.6295	0.630696	0.315348	−	0.948976i	$-0.397879\pi$
$467$	13.6295	0.630696	0.315348	+	0.948976i	$0.397879\pi$
$468$	3.48516	0.161102
$469$	−28.6915	−1.32485
$470$	29.4754	1.35960
$471$	−19.9892	−0.921055
$472$	8.34168	0.383957
$473$	45.6157	2.09741
$474$	−16.8909	−0.775824
$475$	44.4356	2.03884
$476$	−15.8928	−0.728445
$477$	2.36792	0.108420
$478$	−10.8358	−0.495618
$479$	28.8397	1.31772	0.658861	−	0.752265i	$-0.271039\pi$
$479$	28.8397	1.31772	0.658861	+	0.752265i	$0.271039\pi$
$480$	−7.20954	−0.329069
$481$	−22.0734	−1.00646
$482$	1.14427	0.0521199
$483$	61.1455	2.78222
$484$	15.7036	0.713801
$485$	28.2523	1.28287
$486$	−15.6998	−0.712157
$487$	−39.4174	−1.78617	−0.893086	−	0.449886i	$-0.851464\pi$
$487$	−39.4174	−1.78617	−0.893086	+	0.449886i	$0.851464\pi$
$488$	0.389804	0.0176456
$489$	−6.60085	−0.298501
$490$	28.0337	1.26643
$491$	11.4418	0.516362	0.258181	−	0.966097i	$-0.416877\pi$
$491$	11.4418	0.516362	0.258181	+	0.966097i	$0.416877\pi$
$492$	−17.4788	−0.788007
$493$	−8.35291	−0.376196
$494$	−15.0965	−0.679224
$495$	28.9305	1.30033
$496$	1.70723	0.0766569
$497$	53.8170	2.41402
$498$	24.1487	1.08213
$499$	−11.5838	−0.518563	−0.259282	−	0.965802i	$-0.583486\pi$
$499$	−11.5838	−0.518563	−0.259282	+	0.965802i	$0.583486\pi$
$500$	−3.68773	−0.164920
$501$	−16.8227	−0.751584
$502$	12.3625	0.551768
$503$	−25.2422	−1.12549	−0.562746	−	0.826630i	$-0.690255\pi$
$503$	−25.2422	−1.12549	−0.562746	+	0.826630i	$0.690255\pi$
$504$	−6.59490	−0.293760
$505$	−8.58260	−0.381921
$506$	−37.2053	−1.65398
$507$	18.8119	0.835465
$508$	−1.91503	−0.0849657
$509$	−28.6207	−1.26859	−0.634294	−	0.773092i	$-0.718709\pi$
$509$	−28.6207	−1.26859	−0.634294	+	0.773092i	$0.718709\pi$
$510$	29.1864	1.29240
$511$	27.2946	1.20744
$512$	−1.00000	−0.0441942
$513$	20.7808	0.917496
$514$	−22.1073	−0.975110
$515$	8.68761	0.382822
$516$	19.0962	0.840664
$517$	−45.7041	−2.01006
$518$	41.7690	1.83523
$519$	2.68540	0.117876
$520$	6.91403	0.303200
$521$	−25.2461	−1.10605	−0.553026	−	0.833164i	$-0.686527\pi$
$521$	−25.2461	−1.10605	−0.553026	+	0.833164i	$0.686527\pi$
$522$	−3.46614	−0.151709
$523$	−8.60179	−0.376130	−0.188065	−	0.982157i	$-0.560222\pi$
$523$	−8.60179	−0.376130	−0.188065	+	0.982157i	$0.560222\pi$
$524$	−9.27409	−0.405140
$525$	−51.8610	−2.26340
$526$	24.3138	1.06013
$527$	−6.91139	−0.301065
$528$	11.1790	0.486503
$529$	28.8369	1.25378
$530$	4.69760	0.204051
$531$	−14.0131	−0.608117
$532$	28.5668	1.23853
$533$	16.7624	0.726060
$534$	14.0498	0.607996
$535$	−16.4795	−0.712471
$536$	7.30847	0.315678
$537$	37.4747	1.61715
$538$	9.37689	0.404266
$539$	−43.4686	−1.87232
$540$	−9.51738	−0.409563
$541$	−6.10397	−0.262430	−0.131215	−	0.991354i	$-0.541888\pi$
$541$	−6.10397	−0.262430	−0.131215	+	0.991354i	$0.541888\pi$
$542$	16.6600	0.715607
$543$	−12.2563	−0.525969
$544$	4.04830	0.173570
$545$	−37.9030	−1.62359
$546$	17.6192	0.754033
$547$	4.62919	0.197930	0.0989648	−	0.995091i	$-0.468447\pi$
$547$	4.62919	0.197930	0.0989648	+	0.995091i	$0.468447\pi$
$548$	4.71968	0.201615
$549$	−0.654828	−0.0279474
$550$	31.5559	1.34555
$551$	15.0141	0.639623
$552$	−15.5753	−0.662930
$553$	−30.6522	−1.30346
$554$	−1.90016	−0.0807300
$555$	−76.7070	−3.25603
$556$	14.5816	0.618397
$557$	−33.9867	−1.44006	−0.720031	−	0.693942i	$-0.755873\pi$
$557$	−33.9867	−1.44006	−0.720031	+	0.693942i	$0.755873\pi$
$558$	−2.86796	−0.121410
$559$	−18.3135	−0.774578
$560$	−13.0833	−0.552870
$561$	−45.2560	−1.91071
$562$	−22.9693	−0.968903
$563$	−2.36090	−0.0995002	−0.0497501	−	0.998762i	$-0.515842\pi$
$563$	−2.36090	−0.0995002	−0.0497501	+	0.998762i	$0.515842\pi$
$564$	−19.1332	−0.805653
$565$	−65.5937	−2.75955
$566$	15.9272	0.669470
$567$	−44.0381	−1.84943
$568$	−13.7086	−0.575199
$569$	35.2296	1.47690	0.738452	−	0.674306i	$-0.235557\pi$
$569$	35.2296	1.47690	0.738452	+	0.674306i	$0.235557\pi$
$570$	−52.4617	−2.19738
$571$	43.1112	1.80415	0.902073	−	0.431584i	$-0.142045\pi$
$571$	43.1112	1.80415	0.902073	+	0.431584i	$0.142045\pi$
$572$	−10.7208	−0.448259
$573$	−19.4249	−0.811488
$574$	−31.7192	−1.32393
$575$	−43.9658	−1.83350
$576$	1.67989	0.0699954
$577$	18.0101	0.749769	0.374884	−	0.927072i	$-0.377682\pi$
$577$	18.0101	0.749769	0.374884	+	0.927072i	$0.377682\pi$
$578$	0.611234	0.0254240
$579$	−14.1553	−0.588275
$580$	−6.87629	−0.285522
$581$	43.8232	1.81809
$582$	−18.3392	−0.760186
$583$	−7.28402	−0.301673
$584$	−6.95265	−0.287703
$585$	−11.6148	−0.480213
$586$	30.1750	1.24652
$587$	19.1326	0.789686	0.394843	−	0.918749i	$-0.370799\pi$
$587$	19.1326	0.789686	0.394843	+	0.918749i	$0.370799\pi$
$588$	−18.1974	−0.750447
$589$	12.4230	0.511882
$590$	−27.7999	−1.14450
$591$	18.2053	0.748866
$592$	−10.6397	−0.437287
$593$	15.0628	0.618555	0.309277	−	0.950972i	$-0.399913\pi$
$593$	15.0628	0.618555	0.309277	+	0.950972i	$0.399913\pi$
$594$	14.7575	0.605508
$595$	52.9651	2.17136
$596$	−16.4024	−0.671868
$597$	−56.4660	−2.31100
$598$	14.9369	0.610816
$599$	11.5631	0.472457	0.236228	−	0.971698i	$-0.424089\pi$
$599$	11.5631	0.472457	0.236228	+	0.971698i	$0.424089\pi$
$600$	13.2103	0.539309
$601$	−33.5271	−1.36760	−0.683800	−	0.729670i	$-0.739674\pi$
$601$	−33.5271	−1.36760	−0.683800	+	0.729670i	$0.739674\pi$
$602$	34.6543	1.41240
$603$	−12.2774	−0.499976
$604$	−19.2739	−0.784246
$605$	−52.3346	−2.12771
$606$	5.57118	0.226314
$607$	11.4393	0.464308	0.232154	−	0.972679i	$-0.425423\pi$
$607$	11.4393	0.464308	0.232154	+	0.972679i	$0.425423\pi$
$608$	−7.27671	−0.295110
$609$	−17.5231	−0.710070
$610$	−1.29908	−0.0525982
$611$	18.3490	0.742320
$612$	−6.80071	−0.274902
$613$	−17.2593	−0.697095	−0.348547	−	0.937291i	$-0.613325\pi$
$613$	−17.2593	−0.697095	−0.348547	+	0.937291i	$0.613325\pi$
$614$	−4.79991	−0.193709
$615$	58.2508	2.34890
$616$	20.2867	0.817376
$617$	−2.21310	−0.0890959	−0.0445480	−	0.999007i	$-0.514185\pi$
$617$	−2.21310	−0.0890959	−0.0445480	+	0.999007i	$0.514185\pi$
$618$	−5.63934	−0.226848
$619$	24.3779	0.979830	0.489915	−	0.871770i	$-0.337028\pi$
$619$	24.3779	0.979830	0.489915	+	0.871770i	$0.337028\pi$
$620$	−5.68960	−0.228500
$621$	−20.5612	−0.825091
$622$	−26.6771	−1.06966
$623$	25.4965	1.02150
$624$	−4.48807	−0.179666
$625$	−18.2428	−0.729713
$626$	18.7240	0.748361
$627$	81.3463	3.24866
$628$	9.24013	0.368721
$629$	43.0725	1.71742
$630$	21.9785	0.875644
$631$	26.5160	1.05559	0.527793	−	0.849373i	$-0.323020\pi$
$631$	26.5160	1.05559	0.527793	+	0.849373i	$0.323020\pi$
$632$	7.80790	0.310582
$633$	−54.2623	−2.15673
$634$	12.4436	0.494197
$635$	6.38212	0.253267
$636$	−3.04933	−0.120914
$637$	17.4515	0.691453
$638$	10.6623	0.422123
$639$	23.0289	0.911009
$640$	3.33265	0.131735
$641$	23.8661	0.942653	0.471326	−	0.881959i	$-0.343775\pi$
$641$	23.8661	0.942653	0.471326	+	0.881959i	$0.343775\pi$
$642$	10.6973	0.422187
$643$	−28.0841	−1.10753	−0.553765	−	0.832673i	$-0.686809\pi$
$643$	−28.0841	−1.10753	−0.553765	+	0.832673i	$0.686809\pi$
$644$	−28.2649	−1.11379
$645$	−63.6410	−2.50586
$646$	29.4583	1.15902
$647$	−0.612847	−0.0240935	−0.0120468	−	0.999927i	$-0.503835\pi$
$647$	−0.612847	−0.0240935	−0.0120468	+	0.999927i	$0.503835\pi$
$648$	11.2176	0.440670
$649$	43.1061	1.69206
$650$	−12.6689	−0.496913
$651$	−14.4990	−0.568259
$652$	3.05128	0.119497
$653$	−48.3123	−1.89061	−0.945303	−	0.326195i	$-0.894234\pi$
$653$	−48.3123	−1.89061	−0.945303	+	0.326195i	$0.894234\pi$
$654$	24.6038	0.962085
$655$	30.9073	1.20765
$656$	8.07969	0.315459
$657$	11.6797	0.455668
$658$	−34.7214	−1.35358
$659$	−31.3698	−1.22200	−0.610998	−	0.791632i	$-0.709231\pi$
$659$	−31.3698	−1.22200	−0.610998	+	0.791632i	$0.709231\pi$
$660$	−37.2557	−1.45018
$661$	40.4698	1.57409	0.787047	−	0.616894i	$-0.211609\pi$
$661$	40.4698	1.57409	0.787047	+	0.616894i	$0.211609\pi$
$662$	29.3122	1.13925
$663$	18.1691	0.705628
$664$	−11.1629	−0.433204
$665$	−95.2032	−3.69182
$666$	17.8735	0.692582
$667$	−14.8554	−0.575203
$668$	7.77640	0.300878
$669$	3.13352	0.121149
$670$	−24.3566	−0.940977
$671$	2.01433	0.0777625
$672$	8.49268	0.327612
$673$	−15.8878	−0.612430	−0.306215	−	0.951962i	$-0.599063\pi$
$673$	−15.8878	−0.612430	−0.306215	+	0.951962i	$0.599063\pi$
$674$	−4.88672	−0.188229
$675$	17.4391	0.671230
$676$	−8.69589	−0.334457
$677$	−10.4319	−0.400932	−0.200466	−	0.979701i	$-0.564246\pi$
$677$	−10.4319	−0.400932	−0.200466	+	0.979701i	$0.564246\pi$
$678$	42.5785	1.63522
$679$	−33.2806	−1.27719
$680$	−13.4916	−0.517378
$681$	−39.8865	−1.52845
$682$	8.82220	0.337820
$683$	−25.8106	−0.987616	−0.493808	−	0.869571i	$-0.664396\pi$
$683$	−25.8106	−0.987616	−0.493808	+	0.869571i	$0.664396\pi$
$684$	12.2241	0.467399
$685$	−15.7290	−0.600976
$686$	−5.54256	−0.211616
$687$	−23.1239	−0.882232
$688$	−8.82733	−0.336539
$689$	2.92434	0.111409
$690$	51.9071	1.97607
$691$	19.0847	0.726017	0.363009	−	0.931786i	$-0.381750\pi$
$691$	19.0847	0.726017	0.363009	+	0.931786i	$0.381750\pi$
$692$	−1.24134	−0.0471888
$693$	−34.0795	−1.29457
$694$	28.1576	1.06885
$695$	−48.5953	−1.84333
$696$	4.46357	0.169191
$697$	−32.7090	−1.23894
$698$	31.1028	1.17726
$699$	16.4522	0.622281
$700$	23.9730	0.906095
$701$	1.49965	0.0566411	0.0283206	−	0.999599i	$-0.490984\pi$
$701$	1.49965	0.0566411	0.0283206	+	0.999599i	$0.490984\pi$
$702$	−5.92474	−0.223615
$703$	−77.4217	−2.92001
$704$	−5.16755	−0.194760
$705$	63.7643	2.40150
$706$	12.0820	0.454710
$707$	10.1101	0.380231
$708$	18.0456	0.678195
$709$	7.90772	0.296981	0.148490	−	0.988914i	$-0.452559\pi$
$709$	7.90772	0.296981	0.148490	+	0.988914i	$0.452559\pi$
$710$	45.6859	1.71456
$711$	−13.1164	−0.491904
$712$	−6.49461	−0.243396
$713$	−12.2917	−0.460328
$714$	−34.3810	−1.28668
$715$	35.7286	1.33617
$716$	−17.3229	−0.647387
$717$	−23.4412	−0.875426
$718$	8.22958	0.307125
$719$	40.2376	1.50061	0.750304	−	0.661093i	$-0.229907\pi$
$719$	40.2376	1.50061	0.750304	+	0.661093i	$0.229907\pi$
$720$	−5.59848	−0.208643
$721$	−10.2338	−0.381128
$722$	−33.9505	−1.26351
$723$	2.47540	0.0920610
$724$	5.66556	0.210559
$725$	12.5997	0.467941
$726$	33.9717	1.26081
$727$	−9.33793	−0.346325	−0.173162	−	0.984893i	$-0.555399\pi$
$727$	−9.33793	−0.346325	−0.173162	+	0.984893i	$0.555399\pi$
$728$	−8.14458	−0.301858
$729$	−0.310503	−0.0115001
$730$	23.1707	0.857587
$731$	35.7357	1.32173
$732$	0.843266	0.0311680
$733$	−10.8567	−0.401001	−0.200501	−	0.979694i	$-0.564257\pi$
$733$	−10.8567	−0.401001	−0.200501	+	0.979694i	$0.564257\pi$
$734$	21.5828	0.796634
$735$	60.6454	2.23694
$736$	7.19979	0.265388
$737$	37.7669	1.39116
$738$	−13.5730	−0.499629
$739$	−41.6302	−1.53139	−0.765695	−	0.643204i	$-0.777605\pi$
$739$	−41.6302	−1.53139	−0.765695	+	0.643204i	$0.777605\pi$
$740$	35.4582	1.30347
$741$	−32.6584	−1.19974
$742$	−5.53367	−0.203148
$743$	−27.2006	−0.997893	−0.498946	−	0.866633i	$-0.666280\pi$
$743$	−27.2006	−0.997893	−0.498946	+	0.866633i	$0.666280\pi$
$744$	3.69326	0.135401
$745$	54.6634	2.00271
$746$	−0.798286	−0.0292273
$747$	18.7524	0.686116
$748$	20.9198	0.764905
$749$	19.4125	0.709318
$750$	−7.97769	−0.291304
$751$	19.4703	0.710481	0.355240	−	0.934775i	$-0.384399\pi$
$751$	19.4703	0.710481	0.355240	+	0.934775i	$0.384399\pi$
$752$	8.84443	0.322523
$753$	26.7440	0.974604
$754$	−4.28062	−0.155891
$755$	64.2333	2.33769
$756$	11.2113	0.407750
$757$	50.2338	1.82578	0.912889	−	0.408208i	$-0.133846\pi$
$757$	50.2338	1.82578	0.912889	+	0.408208i	$0.133846\pi$
$758$	26.6171	0.966778
$759$	−80.4864	−2.92147
$760$	24.2507	0.879666
$761$	11.2126	0.406455	0.203228	−	0.979132i	$-0.434857\pi$
$761$	11.2126	0.406455	0.203228	+	0.979132i	$0.434857\pi$
$762$	−4.14279	−0.150078
$763$	44.6490	1.61640
$764$	8.97928	0.324859
$765$	22.6644	0.819432
$766$	21.5704	0.779372
$767$	−17.3059	−0.624881
$768$	−2.16331	−0.0780616
$769$	0.470048	0.0169504	0.00847519	−	0.999964i	$-0.497302\pi$
$769$	0.470048	0.0169504	0.00847519	+	0.999964i	$0.497302\pi$
$770$	−67.6086	−2.43644
$771$	−47.8248	−1.72237
$772$	6.54338	0.235501
$773$	−13.4433	−0.483522	−0.241761	−	0.970336i	$-0.577725\pi$
$773$	−13.4433	−0.483522	−0.241761	+	0.970336i	$0.577725\pi$
$774$	14.8290	0.533016
$775$	10.4253	0.374487
$776$	8.47742	0.304322
$777$	90.3592	3.24162
$778$	−15.8875	−0.569594
$779$	58.7936	2.10650
$780$	14.9572	0.535552
$781$	−70.8398	−2.53485
$782$	−29.1469	−1.04229
$783$	5.89240	0.210577
$784$	8.41183	0.300423
$785$	−30.7941	−1.09909
$786$	−20.0627	−0.715612
$787$	35.5933	1.26876	0.634381	−	0.773020i	$-0.281255\pi$
$787$	35.5933	1.26876	0.634381	+	0.773020i	$0.281255\pi$
$788$	−8.41550	−0.299790
$789$	52.5982	1.87254
$790$	−26.0210	−0.925786
$791$	77.2680	2.74734
$792$	8.68092	0.308463
$793$	−0.808701	−0.0287178
$794$	−5.24693	−0.186207
$795$	10.1623	0.360421
$796$	26.1017	0.925150
$797$	−9.41383	−0.333455	−0.166727	−	0.986003i	$-0.553320\pi$
$797$	−9.41383	−0.333455	−0.166727	+	0.986003i	$0.553320\pi$
$798$	61.7988	2.18765
$799$	−35.8050	−1.26669
$800$	−6.10655	−0.215899
$801$	10.9102	0.385494
$802$	−27.3807	−0.966845
$803$	−35.9282	−1.26788
$804$	15.8105	0.557592
$805$	94.1968	3.32000
$806$	−3.54188	−0.124757
$807$	20.2851	0.714069
$808$	−2.57531	−0.0905991
$809$	−13.6219	−0.478921	−0.239461	−	0.970906i	$-0.576971\pi$
$809$	−13.6219	−0.478921	−0.239461	+	0.970906i	$0.576971\pi$
$810$	−37.3845	−1.31356
$811$	−39.6683	−1.39294	−0.696472	−	0.717584i	$-0.745248\pi$
$811$	−39.6683	−1.39294	−0.696472	+	0.717584i	$0.745248\pi$
$812$	8.10013	0.284259
$813$	36.0406	1.26400
$814$	−54.9810	−1.92708
$815$	−10.1688	−0.356199
$816$	8.75772	0.306581
$817$	−64.2339	−2.24726
$818$	31.3607	1.09650
$819$	13.6820	0.478088
$820$	−26.9268	−0.940324
$821$	11.3389	0.395732	0.197866	−	0.980229i	$-0.436599\pi$
$821$	11.3389	0.395732	0.197866	+	0.980229i	$0.436599\pi$
$822$	10.2101	0.356119
$823$	15.6911	0.546958	0.273479	−	0.961878i	$-0.411826\pi$
$823$	15.6911	0.546958	0.273479	+	0.961878i	$0.411826\pi$
$824$	2.60682	0.0908128
$825$	68.2651	2.37668
$826$	32.7477	1.13944
$827$	−22.4157	−0.779472	−0.389736	−	0.920927i	$-0.627434\pi$
$827$	−22.4157	−0.779472	−0.389736	+	0.920927i	$0.627434\pi$
$828$	−12.0949	−0.420325
$829$	−7.06019	−0.245210	−0.122605	−	0.992456i	$-0.539125\pi$
$829$	−7.06019	−0.245210	−0.122605	+	0.992456i	$0.539125\pi$
$830$	37.2020	1.29130
$831$	−4.11062	−0.142596
$832$	2.07463	0.0719250
$833$	−34.0537	−1.17989
$834$	31.5444	1.09229
$835$	−25.9160	−0.896860
$836$	−37.6028	−1.30052
$837$	4.87551	0.168522
$838$	8.55069	0.295379
$839$	18.1463	0.626479	0.313239	−	0.949674i	$-0.398586\pi$
$839$	18.1463	0.626479	0.313239	+	0.949674i	$0.398586\pi$
$840$	−28.3031	−0.976551
$841$	−24.7427	−0.853198
$842$	4.83273	0.166547
$843$	−49.6897	−1.71140
$844$	25.0831	0.863394
$845$	28.9804	0.996955
$846$	−14.8577	−0.510817
$847$	61.6491	2.11829
$848$	1.40957	0.0484048
$849$	34.4554	1.18251
$850$	24.7212	0.847929
$851$	76.6032	2.62593
$852$	−29.6558	−1.01599
$853$	12.7066	0.435066	0.217533	−	0.976053i	$-0.430199\pi$
$853$	12.7066	0.435066	0.217533	+	0.976053i	$0.430199\pi$
$854$	1.53029	0.0523654
$855$	−40.7385	−1.39323
$856$	−4.94487	−0.169012
$857$	−22.3188	−0.762394	−0.381197	−	0.924494i	$-0.624488\pi$
$857$	−22.3188	−0.762394	−0.381197	+	0.924494i	$0.624488\pi$
$858$	−23.1923	−0.791773
$859$	−10.7351	−0.366275	−0.183138	−	0.983087i	$-0.558625\pi$
$859$	−10.7351	−0.366275	−0.183138	+	0.983087i	$0.558625\pi$
$860$	29.4184	1.00316
$861$	−68.6183	−2.33850
$862$	12.1236	0.412931
$863$	41.1539	1.40090	0.700448	−	0.713704i	$-0.252984\pi$
$863$	41.1539	1.40090	0.700448	+	0.713704i	$0.252984\pi$
$864$	−2.85580	−0.0971563
$865$	4.13696	0.140661
$866$	19.6533	0.667846
$867$	1.32229	0.0449072
$868$	6.70223	0.227488
$869$	40.3478	1.36870
$870$	−14.8755	−0.504327
$871$	−15.1624	−0.513759
$872$	−11.3732	−0.385147
$873$	−14.2411	−0.481989
$874$	52.3908	1.77214
$875$	−14.4773	−0.489421
$876$	−15.0407	−0.508178
$877$	−34.4638	−1.16376	−0.581879	−	0.813275i	$-0.697682\pi$
$877$	−34.4638	−1.16376	−0.581879	+	0.813275i	$0.697682\pi$
$878$	28.0737	0.947443
$879$	65.2777	2.20176
$880$	17.2216	0.580541
$881$	−10.5341	−0.354904	−0.177452	−	0.984129i	$-0.556785\pi$
$881$	−10.5341	−0.354904	−0.177452	+	0.984129i	$0.556785\pi$
$882$	−14.1310	−0.475814
$883$	0.878007	0.0295473	0.0147736	−	0.999891i	$-0.495297\pi$
$883$	0.878007	0.0295473	0.0147736	+	0.999891i	$0.495297\pi$
$884$	−8.39875	−0.282481
$885$	−60.1397	−2.02157
$886$	−22.8274	−0.766901
$887$	14.9277	0.501224	0.250612	−	0.968088i	$-0.419368\pi$
$887$	14.9277	0.501224	0.250612	+	0.968088i	$0.419368\pi$
$888$	−23.0168	−0.772394
$889$	−7.51800	−0.252146
$890$	21.6443	0.725517
$891$	57.9678	1.94199
$892$	−1.44849	−0.0484989
$893$	64.3584	2.15367
$894$	−35.4834	−1.18674
$895$	57.7311	1.92974
$896$	−3.92579	−0.131151
$897$	32.3131	1.07890
$898$	39.3169	1.31202
$899$	3.52255	0.117484
$900$	10.2583	0.341944
$901$	−5.70636	−0.190107
$902$	41.7522	1.39020
$903$	74.9677	2.49477
$904$	−19.6822	−0.654619
$905$	−18.8813	−0.627636
$906$	−41.6954	−1.38524
$907$	−19.4522	−0.645899	−0.322950	−	0.946416i	$-0.604674\pi$
$907$	−19.4522	−0.645899	−0.322950	+	0.946416i	$0.604674\pi$
$908$	18.4378	0.611879
$909$	4.32624	0.143492
$910$	27.1430	0.899782
$911$	37.7880	1.25197	0.625986	−	0.779834i	$-0.284697\pi$
$911$	37.7880	1.25197	0.625986	+	0.779834i	$0.284697\pi$
$912$	−15.7417	−0.521261
$913$	−57.6848	−1.90909
$914$	15.5641	0.514813
$915$	−2.81031	−0.0929059
$916$	10.6892	0.353180
$917$	−36.4081	−1.20230
$918$	11.5611	0.381575
$919$	31.2040	1.02933	0.514663	−	0.857393i	$-0.327917\pi$
$919$	31.2040	1.02933	0.514663	+	0.857393i	$0.327917\pi$
$920$	−23.9944	−0.791071
$921$	−10.3837	−0.342154
$922$	29.4449	0.969715
$923$	28.4403	0.936123
$924$	43.8864	1.44376
$925$	−64.9715	−2.13625
$926$	−24.7954	−0.814827
$927$	−4.37917	−0.143831
$928$	−2.06331	−0.0677315
$929$	−23.9236	−0.784907	−0.392454	−	0.919772i	$-0.628374\pi$
$929$	−23.9236	−0.784907	−0.392454	+	0.919772i	$0.628374\pi$
$930$	−12.3083	−0.403606
$931$	61.2105	2.00609
$932$	−7.60514	−0.249115
$933$	−57.7108	−1.88937
$934$	−13.6295	−0.445970
$935$	−69.7184	−2.28004
$936$	−3.48516	−0.113916
$937$	−24.8240	−0.810966	−0.405483	−	0.914103i	$-0.632897\pi$
$937$	−24.8240	−0.810966	−0.405483	+	0.914103i	$0.632897\pi$
$938$	28.6915	0.936812
$939$	40.5057	1.32185
$940$	−29.4754	−0.961381
$941$	1.06517	0.0347237	0.0173618	−	0.999849i	$-0.494473\pi$
$941$	1.06517	0.0347237	0.0173618	+	0.999849i	$0.494473\pi$
$942$	19.9892	0.651284
$943$	−58.1721	−1.89434
$944$	−8.34168	−0.271499
$945$	−37.3632	−1.21543
$946$	−45.6157	−1.48309
$947$	−40.8530	−1.32755	−0.663773	−	0.747934i	$-0.731046\pi$
$947$	−40.8530	−1.32755	−0.663773	+	0.747934i	$0.731046\pi$
$948$	16.8909	0.548590
$949$	14.4242	0.468229
$950$	−44.4356	−1.44168
$951$	26.9192	0.872916
$952$	15.8928	0.515088
$953$	−19.2206	−0.622618	−0.311309	−	0.950309i	$-0.600767\pi$
$953$	−19.2206	−0.622618	−0.311309	+	0.950309i	$0.600767\pi$
$954$	−2.36792	−0.0766643
$955$	−29.9248	−0.968344
$956$	10.8358	0.350455
$957$	23.0658	0.745610
$958$	−28.8397	−0.931770
$959$	18.5285	0.598316
$960$	7.20954	0.232687
$961$	−28.0854	−0.905980
$962$	22.0734	0.711675
$963$	8.30684	0.267684
$964$	−1.14427	−0.0368543
$965$	−21.8068	−0.701985
$966$	−61.1455	−1.96732
$967$	43.1290	1.38693	0.693467	−	0.720488i	$-0.256082\pi$
$967$	43.1290	1.38693	0.693467	+	0.720488i	$0.256082\pi$
$968$	−15.7036	−0.504733
$969$	63.7274	2.04722
$970$	−28.2523	−0.907125
$971$	7.38926	0.237133	0.118566	−	0.992946i	$-0.462170\pi$
$971$	7.38926	0.237133	0.118566	+	0.992946i	$0.462170\pi$
$972$	15.6998	0.503571
$973$	57.2443	1.83517
$974$	39.4174	1.26301
$975$	−27.4066	−0.877714
$976$	−0.389804	−0.0124773
$977$	−50.2310	−1.60703	−0.803516	−	0.595283i	$-0.797040\pi$
$977$	−50.2310	−1.60703	−0.803516	+	0.595283i	$0.797040\pi$
$978$	6.60085	0.211072
$979$	−33.5613	−1.07262
$980$	−28.0337	−0.895503
$981$	19.1058	0.610001
$982$	−11.4418	−0.365123
$983$	−2.10124	−0.0670191	−0.0335095	−	0.999438i	$-0.510668\pi$
$983$	−2.10124	−0.0670191	−0.0335095	+	0.999438i	$0.510668\pi$
$984$	17.4788	0.557205
$985$	28.0459	0.893617
$986$	8.35291	0.266011
$987$	−75.1130	−2.39087
$988$	15.0965	0.480284
$989$	63.5549	2.02093
$990$	−28.9305	−0.919471
$991$	2.39234	0.0759951	0.0379975	−	0.999278i	$-0.487902\pi$
$991$	2.39234	0.0759951	0.0379975	+	0.999278i	$0.487902\pi$
$992$	−1.70723	−0.0542046
$993$	63.4113	2.01230
$994$	−53.8170	−1.70697
$995$	−86.9878	−2.75770
$996$	−24.1487	−0.765182
$997$	20.5656	0.651320	0.325660	−	0.945487i	$-0.394414\pi$
$997$	20.5656	0.651320	0.325660	+	0.945487i	$0.394414\pi$
$998$	11.5838	0.366680
$999$	−30.3847	−0.961330

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.15	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.15	✓	64	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.16331 q^{3} +1.00000 q^{4} -3.33265 q^{5} +2.16331 q^{6} +3.92579 q^{7} -1.00000 q^{8} +1.67989 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.16331 q^{3} +1.00000 q^{4} -3.33265 q^{5} +2.16331 q^{6} +3.92579 q^{7} -1.00000 q^{8} +1.67989 q^{9} +3.33265 q^{10} -5.16755 q^{11} -2.16331 q^{12} +2.07463 q^{13} -3.92579 q^{14} +7.20954 q^{15} +1.00000 q^{16} -4.04830 q^{17} -1.67989 q^{18} +7.27671 q^{19} -3.33265 q^{20} -8.49268 q^{21} +5.16755 q^{22} -7.19979 q^{23} +2.16331 q^{24} +6.10655 q^{25} -2.07463 q^{26} +2.85580 q^{27} +3.92579 q^{28} +2.06331 q^{29} -7.20954 q^{30} +1.70723 q^{31} -1.00000 q^{32} +11.1790 q^{33} +4.04830 q^{34} -13.0833 q^{35} +1.67989 q^{36} -10.6397 q^{37} -7.27671 q^{38} -4.48807 q^{39} +3.33265 q^{40} +8.07969 q^{41} +8.49268 q^{42} -8.82733 q^{43} -5.16755 q^{44} -5.59848 q^{45} +7.19979 q^{46} +8.84443 q^{47} -2.16331 q^{48} +8.41183 q^{49} -6.10655 q^{50} +8.75772 q^{51} +2.07463 q^{52} +1.40957 q^{53} -2.85580 q^{54} +17.2216 q^{55} -3.92579 q^{56} -15.7417 q^{57} -2.06331 q^{58} -8.34168 q^{59} +7.20954 q^{60} -0.389804 q^{61} -1.70723 q^{62} +6.59490 q^{63} +1.00000 q^{64} -6.91403 q^{65} -11.1790 q^{66} -7.30847 q^{67} -4.04830 q^{68} +15.5753 q^{69} +13.0833 q^{70} +13.7086 q^{71} -1.67989 q^{72} +6.95265 q^{73} +10.6397 q^{74} -13.2103 q^{75} +7.27671 q^{76} -20.2867 q^{77} +4.48807 q^{78} -7.80790 q^{79} -3.33265 q^{80} -11.2176 q^{81} -8.07969 q^{82} +11.1629 q^{83} -8.49268 q^{84} +13.4916 q^{85} +8.82733 q^{86} -4.46357 q^{87} +5.16755 q^{88} +6.49461 q^{89} +5.59848 q^{90} +8.14458 q^{91} -7.19979 q^{92} -3.69326 q^{93} -8.84443 q^{94} -24.2507 q^{95} +2.16331 q^{96} -8.47742 q^{97} -8.41183 q^{98} -8.68092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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