LMFDB - Embedded newform 6022.2.a.b.1.4

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:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.17082 q^{3} +1.00000 q^{4} +0.413863 q^{5} -3.17082 q^{6} -1.62952 q^{7} +1.00000 q^{8} +7.05407 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.17082 q^{3} +1.00000 q^{4} +0.413863 q^{5} -3.17082 q^{6} -1.62952 q^{7} +1.00000 q^{8} +7.05407 q^{9} +0.413863 q^{10} -3.27309 q^{11} -3.17082 q^{12} +4.72308 q^{13} -1.62952 q^{14} -1.31228 q^{15} +1.00000 q^{16} +3.11616 q^{17} +7.05407 q^{18} -6.74230 q^{19} +0.413863 q^{20} +5.16691 q^{21} -3.27309 q^{22} +2.90001 q^{23} -3.17082 q^{24} -4.82872 q^{25} +4.72308 q^{26} -12.8547 q^{27} -1.62952 q^{28} -4.63047 q^{29} -1.31228 q^{30} +0.519955 q^{31} +1.00000 q^{32} +10.3784 q^{33} +3.11616 q^{34} -0.674398 q^{35} +7.05407 q^{36} +9.26223 q^{37} -6.74230 q^{38} -14.9760 q^{39} +0.413863 q^{40} -5.31208 q^{41} +5.16691 q^{42} +1.05730 q^{43} -3.27309 q^{44} +2.91942 q^{45} +2.90001 q^{46} +4.86074 q^{47} -3.17082 q^{48} -4.34467 q^{49} -4.82872 q^{50} -9.88077 q^{51} +4.72308 q^{52} -2.85863 q^{53} -12.8547 q^{54} -1.35461 q^{55} -1.62952 q^{56} +21.3786 q^{57} -4.63047 q^{58} -8.66170 q^{59} -1.31228 q^{60} +11.2567 q^{61} +0.519955 q^{62} -11.4947 q^{63} +1.00000 q^{64} +1.95471 q^{65} +10.3784 q^{66} +10.4930 q^{67} +3.11616 q^{68} -9.19539 q^{69} -0.674398 q^{70} -2.42860 q^{71} +7.05407 q^{72} +2.13923 q^{73} +9.26223 q^{74} +15.3110 q^{75} -6.74230 q^{76} +5.33357 q^{77} -14.9760 q^{78} +9.49729 q^{79} +0.413863 q^{80} +19.5977 q^{81} -5.31208 q^{82} -4.28807 q^{83} +5.16691 q^{84} +1.28966 q^{85} +1.05730 q^{86} +14.6824 q^{87} -3.27309 q^{88} +1.50007 q^{89} +2.91942 q^{90} -7.69635 q^{91} +2.90001 q^{92} -1.64868 q^{93} +4.86074 q^{94} -2.79039 q^{95} -3.17082 q^{96} -6.71078 q^{97} -4.34467 q^{98} -23.0886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−3.17082	−1.83067	−0.915336	−	0.402692i	$-0.868075\pi$
$3$	−3.17082	−1.83067	−0.915336	+	0.402692i	$0.868075\pi$
$4$	1.00000	0.500000
$5$	0.413863	0.185085	0.0925426	−	0.995709i	$-0.470501\pi$
$5$	0.413863	0.185085	0.0925426	+	0.995709i	$0.470501\pi$
$6$	−3.17082	−1.29448
$7$	−1.62952	−0.615901	−0.307950	−	0.951402i	$-0.599643\pi$
$7$	−1.62952	−0.615901	−0.307950	+	0.951402i	$0.599643\pi$
$8$	1.00000	0.353553
$9$	7.05407	2.35136
$10$	0.413863	0.130875
$11$	−3.27309	−0.986875	−0.493437	−	0.869781i	$-0.664260\pi$
$11$	−3.27309	−0.986875	−0.493437	+	0.869781i	$0.664260\pi$
$12$	−3.17082	−0.915336
$13$	4.72308	1.30995	0.654973	−	0.755652i	$-0.272680\pi$
$13$	4.72308	1.30995	0.654973	+	0.755652i	$0.272680\pi$
$14$	−1.62952	−0.435507
$15$	−1.31228	−0.338830
$16$	1.00000	0.250000
$17$	3.11616	0.755780	0.377890	−	0.925851i	$-0.376650\pi$
$17$	3.11616	0.755780	0.377890	+	0.925851i	$0.376650\pi$
$18$	7.05407	1.66266
$19$	−6.74230	−1.54679	−0.773395	−	0.633925i	$-0.781443\pi$
$19$	−6.74230	−1.54679	−0.773395	+	0.633925i	$0.781443\pi$
$20$	0.413863	0.0925426
$21$	5.16691	1.12751
$22$	−3.27309	−0.697826
$23$	2.90001	0.604694	0.302347	−	0.953198i	$-0.402230\pi$
$23$	2.90001	0.604694	0.302347	+	0.953198i	$0.402230\pi$
$24$	−3.17082	−0.647240
$25$	−4.82872	−0.965743
$26$	4.72308	0.926272
$27$	−12.8547	−2.47389
$28$	−1.62952	−0.307950
$29$	−4.63047	−0.859856	−0.429928	−	0.902863i	$-0.641461\pi$
$29$	−4.63047	−0.859856	−0.429928	+	0.902863i	$0.641461\pi$
$30$	−1.31228	−0.239589
$31$	0.519955	0.0933867	0.0466934	−	0.998909i	$-0.485132\pi$
$31$	0.519955	0.0933867	0.0466934	+	0.998909i	$0.485132\pi$
$32$	1.00000	0.176777
$33$	10.3784	1.80664
$34$	3.11616	0.534417
$35$	−0.674398	−0.113994
$36$	7.05407	1.17568
$37$	9.26223	1.52270	0.761351	−	0.648340i	$-0.224537\pi$
$37$	9.26223	1.52270	0.761351	+	0.648340i	$0.224537\pi$
$38$	−6.74230	−1.09375
$39$	−14.9760	−2.39808
$40$	0.413863	0.0654375
$41$	−5.31208	−0.829607	−0.414804	−	0.909911i	$-0.636150\pi$
$41$	−5.31208	−0.829607	−0.414804	+	0.909911i	$0.636150\pi$
$42$	5.16691	0.797271
$43$	1.05730	0.161236	0.0806182	−	0.996745i	$-0.474311\pi$
$43$	1.05730	0.161236	0.0806182	+	0.996745i	$0.474311\pi$
$44$	−3.27309	−0.493437
$45$	2.91942	0.435201
$46$	2.90001	0.427583
$47$	4.86074	0.709011	0.354506	−	0.935054i	$-0.384649\pi$
$47$	4.86074	0.709011	0.354506	+	0.935054i	$0.384649\pi$
$48$	−3.17082	−0.457668
$49$	−4.34467	−0.620667
$50$	−4.82872	−0.682884
$51$	−9.88077	−1.38358
$52$	4.72308	0.654973
$53$	−2.85863	−0.392663	−0.196331	−	0.980538i	$-0.562903\pi$
$53$	−2.85863	−0.392663	−0.196331	+	0.980538i	$0.562903\pi$
$54$	−12.8547	−1.74930
$55$	−1.35461	−0.182656
$56$	−1.62952	−0.217754
$57$	21.3786	2.83166
$58$	−4.63047	−0.608010
$59$	−8.66170	−1.12766	−0.563828	−	0.825892i	$-0.690672\pi$
$59$	−8.66170	−1.12766	−0.563828	+	0.825892i	$0.690672\pi$
$60$	−1.31228	−0.169415
$61$	11.2567	1.44127	0.720635	−	0.693315i	$-0.243850\pi$
$61$	11.2567	1.44127	0.720635	+	0.693315i	$0.243850\pi$
$62$	0.519955	0.0660344
$63$	−11.4947	−1.44820
$64$	1.00000	0.125000
$65$	1.95471	0.242452
$66$	10.3784	1.27749
$67$	10.4930	1.28192	0.640962	−	0.767573i	$-0.278536\pi$
$67$	10.4930	1.28192	0.640962	+	0.767573i	$0.278536\pi$
$68$	3.11616	0.377890
$69$	−9.19539	−1.10700
$70$	−0.674398	−0.0806060
$71$	−2.42860	−0.288222	−0.144111	−	0.989562i	$-0.546032\pi$
$71$	−2.42860	−0.288222	−0.144111	+	0.989562i	$0.546032\pi$
$72$	7.05407	0.831330
$73$	2.13923	0.250378	0.125189	−	0.992133i	$-0.460046\pi$
$73$	2.13923	0.250378	0.125189	+	0.992133i	$0.460046\pi$
$74$	9.26223	1.07671
$75$	15.3110	1.76796
$76$	−6.74230	−0.773395
$77$	5.33357	0.607817
$78$	−14.9760	−1.69570
$79$	9.49729	1.06853	0.534264	−	0.845317i	$-0.320589\pi$
$79$	9.49729	1.06853	0.534264	+	0.845317i	$0.320589\pi$
$80$	0.413863	0.0462713
$81$	19.5977	2.17752
$82$	−5.31208	−0.586621
$83$	−4.28807	−0.470677	−0.235339	−	0.971913i	$-0.575620\pi$
$83$	−4.28807	−0.470677	−0.235339	+	0.971913i	$0.575620\pi$
$84$	5.16691	0.563756
$85$	1.28966	0.139884
$86$	1.05730	0.114011
$87$	14.6824	1.57411
$88$	−3.27309	−0.348913
$89$	1.50007	0.159007	0.0795034	−	0.996835i	$-0.474667\pi$
$89$	1.50007	0.159007	0.0795034	+	0.996835i	$0.474667\pi$
$90$	2.91942	0.307734
$91$	−7.69635	−0.806797
$92$	2.90001	0.302347
$93$	−1.64868	−0.170960
$94$	4.86074	0.501347
$95$	−2.79039	−0.286288
$96$	−3.17082	−0.323620
$97$	−6.71078	−0.681376	−0.340688	−	0.940176i	$-0.610660\pi$
$97$	−6.71078	−0.681376	−0.340688	+	0.940176i	$0.610660\pi$
$98$	−4.34467	−0.438878
$99$	−23.0886	−2.32050
$100$	−4.82872	−0.482872
$101$	8.89797	0.885381	0.442691	−	0.896674i	$-0.354024\pi$
$101$	8.89797	0.885381	0.442691	+	0.896674i	$0.354024\pi$
$102$	−9.88077	−0.978342
$103$	−6.78778	−0.668820	−0.334410	−	0.942428i	$-0.608537\pi$
$103$	−6.78778	−0.668820	−0.334410	+	0.942428i	$0.608537\pi$
$104$	4.72308	0.463136
$105$	2.13839	0.208686
$106$	−2.85863	−0.277655
$107$	10.1040	0.976786	0.488393	−	0.872624i	$-0.337583\pi$
$107$	10.1040	0.976786	0.488393	+	0.872624i	$0.337583\pi$
$108$	−12.8547	−1.23695
$109$	6.00910	0.575567	0.287784	−	0.957695i	$-0.407082\pi$
$109$	6.00910	0.575567	0.287784	+	0.957695i	$0.407082\pi$
$110$	−1.35461	−0.129157
$111$	−29.3688	−2.78757
$112$	−1.62952	−0.153975
$113$	−3.66157	−0.344452	−0.172226	−	0.985057i	$-0.555096\pi$
$113$	−3.66157	−0.344452	−0.172226	+	0.985057i	$0.555096\pi$
$114$	21.3786	2.00229
$115$	1.20021	0.111920
$116$	−4.63047	−0.429928
$117$	33.3169	3.08015
$118$	−8.66170	−0.797374
$119$	−5.07784	−0.465485
$120$	−1.31228	−0.119795
$121$	−0.286859	−0.0260781
$122$	11.2567	1.01913
$123$	16.8436	1.51874
$124$	0.519955	0.0466934
$125$	−4.06774	−0.363830
$126$	−11.4947	−1.02403
$127$	−18.2468	−1.61915	−0.809573	−	0.587019i	$-0.800301\pi$
$127$	−18.2468	−1.61915	−0.809573	+	0.587019i	$0.800301\pi$
$128$	1.00000	0.0883883
$129$	−3.35249	−0.295171
$130$	1.95471	0.171439
$131$	−1.19949	−0.104800	−0.0524000	−	0.998626i	$-0.516687\pi$
$131$	−1.19949	−0.104800	−0.0524000	+	0.998626i	$0.516687\pi$
$132$	10.3784	0.903322
$133$	10.9867	0.952668
$134$	10.4930	0.906457
$135$	−5.32009	−0.457881
$136$	3.11616	0.267208
$137$	−20.9520	−1.79005	−0.895024	−	0.446018i	$-0.852842\pi$
$137$	−20.9520	−1.79005	−0.895024	+	0.446018i	$0.852842\pi$
$138$	−9.19539	−0.782764
$139$	−11.0365	−0.936102	−0.468051	−	0.883702i	$-0.655044\pi$
$139$	−11.0365	−0.936102	−0.468051	+	0.883702i	$0.655044\pi$
$140$	−0.674398	−0.0569970
$141$	−15.4125	−1.29797
$142$	−2.42860	−0.203803
$143$	−15.4591	−1.29275
$144$	7.05407	0.587839
$145$	−1.91638	−0.159147
$146$	2.13923	0.177044
$147$	13.7761	1.13624
$148$	9.26223	0.761351
$149$	−13.9404	−1.14205	−0.571023	−	0.820934i	$-0.693453\pi$
$149$	−13.9404	−1.14205	−0.571023	+	0.820934i	$0.693453\pi$
$150$	15.3110	1.25014
$151$	−20.7548	−1.68901	−0.844503	−	0.535551i	$-0.820104\pi$
$151$	−20.7548	−1.68901	−0.844503	+	0.535551i	$0.820104\pi$
$152$	−6.74230	−0.546873
$153$	21.9816	1.77711
$154$	5.33357	0.429791
$155$	0.215190	0.0172845
$156$	−14.9760	−1.19904
$157$	4.20294	0.335431	0.167716	−	0.985835i	$-0.446361\pi$
$157$	4.20294	0.335431	0.167716	+	0.985835i	$0.446361\pi$
$158$	9.49729	0.755564
$159$	9.06419	0.718837
$160$	0.413863	0.0327188
$161$	−4.72562	−0.372431
$162$	19.5977	1.53974
$163$	11.6120	0.909524	0.454762	−	0.890613i	$-0.349724\pi$
$163$	11.6120	0.909524	0.454762	+	0.890613i	$0.349724\pi$
$164$	−5.31208	−0.414804
$165$	4.29523	0.334383
$166$	−4.28807	−0.332819
$167$	−1.13561	−0.0878762	−0.0439381	−	0.999034i	$-0.513990\pi$
$167$	−1.13561	−0.0878762	−0.0439381	+	0.999034i	$0.513990\pi$
$168$	5.16691	0.398635
$169$	9.30746	0.715959
$170$	1.28966	0.0989127
$171$	−47.5607	−3.63705
$172$	1.05730	0.0806182
$173$	−2.99167	−0.227452	−0.113726	−	0.993512i	$-0.536279\pi$
$173$	−2.99167	−0.227452	−0.113726	+	0.993512i	$0.536279\pi$
$174$	14.6824	1.11307
$175$	7.86849	0.594802
$176$	−3.27309	−0.246719
$177$	27.4646	2.06437
$178$	1.50007	0.112435
$179$	17.2059	1.28603	0.643015	−	0.765853i	$-0.277683\pi$
$179$	17.2059	1.28603	0.643015	+	0.765853i	$0.277683\pi$
$180$	2.91942	0.217601
$181$	3.05519	0.227090	0.113545	−	0.993533i	$-0.463779\pi$
$181$	3.05519	0.227090	0.113545	+	0.993533i	$0.463779\pi$
$182$	−7.69635	−0.570491
$183$	−35.6929	−2.63849
$184$	2.90001	0.213791
$185$	3.83330	0.281830
$186$	−1.64868	−0.120887
$187$	−10.1995	−0.745860
$188$	4.86074	0.354506
$189$	20.9470	1.52367
$190$	−2.79039	−0.202436
$191$	0.804818	0.0582346	0.0291173	−	0.999576i	$-0.490730\pi$
$191$	0.804818	0.0582346	0.0291173	+	0.999576i	$0.490730\pi$
$192$	−3.17082	−0.228834
$193$	−13.7669	−0.990966	−0.495483	−	0.868618i	$-0.665009\pi$
$193$	−13.7669	−0.990966	−0.495483	+	0.868618i	$0.665009\pi$
$194$	−6.71078	−0.481806
$195$	−6.19802	−0.443849
$196$	−4.34467	−0.310333
$197$	0.429086	0.0305711	0.0152855	−	0.999883i	$-0.495134\pi$
$197$	0.429086	0.0305711	0.0152855	+	0.999883i	$0.495134\pi$
$198$	−23.0886	−1.64084
$199$	−9.96272	−0.706239	−0.353119	−	0.935578i	$-0.614879\pi$
$199$	−9.96272	−0.706239	−0.353119	+	0.935578i	$0.614879\pi$
$200$	−4.82872	−0.341442
$201$	−33.2714	−2.34678
$202$	8.89797	0.626059
$203$	7.54544	0.529586
$204$	−9.88077	−0.691792
$205$	−2.19847	−0.153548
$206$	−6.78778	−0.472927
$207$	20.4569	1.42185
$208$	4.72308	0.327487
$209$	22.0682	1.52649
$210$	2.13839	0.147563
$211$	2.04863	0.141033	0.0705167	−	0.997511i	$-0.477535\pi$
$211$	2.04863	0.141033	0.0705167	+	0.997511i	$0.477535\pi$
$212$	−2.85863	−0.196331
$213$	7.70064	0.527639
$214$	10.1040	0.690692
$215$	0.437576	0.0298425
$216$	−12.8547	−0.874652
$217$	−0.847277	−0.0575169
$218$	6.00910	0.406987
$219$	−6.78310	−0.458360
$220$	−1.35461	−0.0913280
$221$	14.7179	0.990031
$222$	−29.3688	−1.97111
$223$	−7.57668	−0.507372	−0.253686	−	0.967287i	$-0.581643\pi$
$223$	−7.57668	−0.507372	−0.253686	+	0.967287i	$0.581643\pi$
$224$	−1.62952	−0.108877
$225$	−34.0621	−2.27081
$226$	−3.66157	−0.243564
$227$	−29.3962	−1.95109	−0.975546	−	0.219796i	$-0.929461\pi$
$227$	−29.3962	−1.95109	−0.975546	+	0.219796i	$0.929461\pi$
$228$	21.3786	1.41583
$229$	−6.96211	−0.460069	−0.230035	−	0.973182i	$-0.573884\pi$
$229$	−6.96211	−0.460069	−0.230035	+	0.973182i	$0.573884\pi$
$230$	1.20021	0.0791393
$231$	−16.9118	−1.11271
$232$	−4.63047	−0.304005
$233$	−5.76973	−0.377988	−0.188994	−	0.981978i	$-0.560523\pi$
$233$	−5.76973	−0.377988	−0.188994	+	0.981978i	$0.560523\pi$
$234$	33.3169	2.17800
$235$	2.01168	0.131228
$236$	−8.66170	−0.563828
$237$	−30.1142	−1.95613
$238$	−5.07784	−0.329148
$239$	−1.24285	−0.0803931	−0.0401965	−	0.999192i	$-0.512798\pi$
$239$	−1.24285	−0.0803931	−0.0401965	+	0.999192i	$0.512798\pi$
$240$	−1.31228	−0.0847075
$241$	−4.88693	−0.314795	−0.157398	−	0.987535i	$-0.550310\pi$
$241$	−4.88693	−0.314795	−0.157398	+	0.987535i	$0.550310\pi$
$242$	−0.286859	−0.0184400
$243$	−23.5766	−1.51244
$244$	11.2567	0.720635
$245$	−1.79810	−0.114876
$246$	16.8436	1.07391
$247$	−31.8444	−2.02621
$248$	0.519955	0.0330172
$249$	13.5967	0.861655
$250$	−4.06774	−0.257267
$251$	5.84026	0.368634	0.184317	−	0.982867i	$-0.440993\pi$
$251$	5.84026	0.368634	0.184317	+	0.982867i	$0.440993\pi$
$252$	−11.4947	−0.724101
$253$	−9.49200	−0.596757
$254$	−18.2468	−1.14491
$255$	−4.08928	−0.256081
$256$	1.00000	0.0625000
$257$	−7.90816	−0.493297	−0.246649	−	0.969105i	$-0.579329\pi$
$257$	−7.90816	−0.493297	−0.246649	+	0.969105i	$0.579329\pi$
$258$	−3.35249	−0.208717
$259$	−15.0930	−0.937833
$260$	1.95471	0.121226
$261$	−32.6636	−2.02183
$262$	−1.19949	−0.0741049
$263$	3.93731	0.242785	0.121392	−	0.992605i	$-0.461264\pi$
$263$	3.93731	0.242785	0.121392	+	0.992605i	$0.461264\pi$
$264$	10.3784	0.638745
$265$	−1.18308	−0.0726761
$266$	10.9867	0.673638
$267$	−4.75643	−0.291089
$268$	10.4930	0.640962
$269$	3.23195	0.197055	0.0985277	−	0.995134i	$-0.468587\pi$
$269$	3.23195	0.197055	0.0985277	+	0.995134i	$0.468587\pi$
$270$	−5.32009	−0.323770
$271$	−23.9118	−1.45254	−0.726268	−	0.687412i	$-0.758747\pi$
$271$	−23.9118	−1.45254	−0.726268	+	0.687412i	$0.758747\pi$
$272$	3.11616	0.188945
$273$	24.4037	1.47698
$274$	−20.9520	−1.26575
$275$	15.8048	0.953068
$276$	−9.19539	−0.553498
$277$	−6.03078	−0.362355	−0.181177	−	0.983450i	$-0.557991\pi$
$277$	−6.03078	−0.362355	−0.181177	+	0.983450i	$0.557991\pi$
$278$	−11.0365	−0.661924
$279$	3.66780	0.219586
$280$	−0.674398	−0.0403030
$281$	3.60969	0.215336	0.107668	−	0.994187i	$-0.465662\pi$
$281$	3.60969	0.215336	0.107668	+	0.994187i	$0.465662\pi$
$282$	−15.4125	−0.917801
$283$	−15.4291	−0.917167	−0.458583	−	0.888651i	$-0.651643\pi$
$283$	−15.4291	−0.917167	−0.458583	+	0.888651i	$0.651643\pi$
$284$	−2.42860	−0.144111
$285$	8.84781	0.524099
$286$	−15.4591	−0.914114
$287$	8.65614	0.510956
$288$	7.05407	0.415665
$289$	−7.28955	−0.428797
$290$	−1.91638	−0.112534
$291$	21.2786	1.24738
$292$	2.13923	0.125189
$293$	−15.9436	−0.931432	−0.465716	−	0.884934i	$-0.654203\pi$
$293$	−15.9436	−0.931432	−0.465716	+	0.884934i	$0.654203\pi$
$294$	13.7761	0.803440
$295$	−3.58476	−0.208713
$296$	9.26223	0.538356
$297$	42.0747	2.44142
$298$	−13.9404	−0.807548
$299$	13.6970	0.792116
$300$	15.3110	0.883979
$301$	−1.72289	−0.0993055
$302$	−20.7548	−1.19431
$303$	−28.2138	−1.62084
$304$	−6.74230	−0.386697
$305$	4.65872	0.266758
$306$	21.9816	1.25660
$307$	−3.78978	−0.216294	−0.108147	−	0.994135i	$-0.534492\pi$
$307$	−3.78978	−0.216294	−0.108147	+	0.994135i	$0.534492\pi$
$308$	5.33357	0.303908
$309$	21.5228	1.22439
$310$	0.215190	0.0122220
$311$	10.1458	0.575317	0.287659	−	0.957733i	$-0.407123\pi$
$311$	10.1458	0.575317	0.287659	+	0.957733i	$0.407123\pi$
$312$	−14.9760	−0.847850
$313$	24.7830	1.40082	0.700409	−	0.713741i	$-0.253001\pi$
$313$	24.7830	1.40082	0.700409	+	0.713741i	$0.253001\pi$
$314$	4.20294	0.237186
$315$	−4.75725	−0.268041
$316$	9.49729	0.534264
$317$	6.38529	0.358634	0.179317	−	0.983791i	$-0.442611\pi$
$317$	6.38529	0.358634	0.179317	+	0.983791i	$0.442611\pi$
$318$	9.06419	0.508294
$319$	15.1560	0.848570
$320$	0.413863	0.0231357
$321$	−32.0378	−1.78817
$322$	−4.72562	−0.263349
$323$	−21.0101	−1.16903
$324$	19.5977	1.08876
$325$	−22.8064	−1.26507
$326$	11.6120	0.643131
$327$	−19.0537	−1.05367
$328$	−5.31208	−0.293310
$329$	−7.92067	−0.436681
$330$	4.29523	0.236444
$331$	30.4778	1.67521	0.837606	−	0.546276i	$-0.183955\pi$
$331$	30.4778	1.67521	0.837606	+	0.546276i	$0.183955\pi$
$332$	−4.28807	−0.235339
$333$	65.3364	3.58042
$334$	−1.13561	−0.0621379
$335$	4.34267	0.237265
$336$	5.16691	0.281878
$337$	−32.4569	−1.76804	−0.884020	−	0.467449i	$-0.845173\pi$
$337$	−32.4569	−1.76804	−0.884020	+	0.467449i	$0.845173\pi$
$338$	9.30746	0.506259
$339$	11.6102	0.630578
$340$	1.28966	0.0699418
$341$	−1.70186	−0.0921610
$342$	−47.5607	−2.57179
$343$	18.4864	0.998169
$344$	1.05730	0.0570056
$345$	−3.80563	−0.204888
$346$	−2.99167	−0.160833
$347$	28.8026	1.54620	0.773102	−	0.634282i	$-0.218704\pi$
$347$	28.8026	1.54620	0.773102	+	0.634282i	$0.218704\pi$
$348$	14.6824	0.787057
$349$	−3.49402	−0.187031	−0.0935153	−	0.995618i	$-0.529810\pi$
$349$	−3.49402	−0.187031	−0.0935153	+	0.995618i	$0.529810\pi$
$350$	7.86849	0.420588
$351$	−60.7138	−3.24066
$352$	−3.27309	−0.174456
$353$	−16.1201	−0.857987	−0.428993	−	0.903308i	$-0.641132\pi$
$353$	−16.1201	−0.857987	−0.428993	+	0.903308i	$0.641132\pi$
$354$	27.4646	1.45973
$355$	−1.00511	−0.0533456
$356$	1.50007	0.0795034
$357$	16.1009	0.852150
$358$	17.2059	0.909361
$359$	−27.1099	−1.43081	−0.715404	−	0.698711i	$-0.753757\pi$
$359$	−27.1099	−1.43081	−0.715404	+	0.698711i	$0.753757\pi$
$360$	2.91942	0.153867
$361$	26.4586	1.39256
$362$	3.05519	0.160577
$363$	0.909578	0.0477404
$364$	−7.69635	−0.403398
$365$	0.885348	0.0463413
$366$	−35.6929	−1.86570
$367$	−23.3761	−1.22022	−0.610112	−	0.792315i	$-0.708876\pi$
$367$	−23.3761	−1.22022	−0.610112	+	0.792315i	$0.708876\pi$
$368$	2.90001	0.151173
$369$	−37.4718	−1.95070
$370$	3.83330	0.199284
$371$	4.65819	0.241841
$372$	−1.64868	−0.0854802
$373$	−8.26909	−0.428157	−0.214079	−	0.976816i	$-0.568675\pi$
$373$	−8.26909	−0.428157	−0.214079	+	0.976816i	$0.568675\pi$
$374$	−10.1995	−0.527403
$375$	12.8981	0.666053
$376$	4.86074	0.250673
$377$	−21.8701	−1.12637
$378$	20.9470	1.07740
$379$	−17.2928	−0.888273	−0.444136	−	0.895959i	$-0.646489\pi$
$379$	−17.2928	−0.888273	−0.444136	+	0.895959i	$0.646489\pi$
$380$	−2.79039	−0.143144
$381$	57.8574	2.96412
$382$	0.804818	0.0411781
$383$	−13.8268	−0.706519	−0.353259	−	0.935525i	$-0.614927\pi$
$383$	−13.8268	−0.706519	−0.353259	+	0.935525i	$0.614927\pi$
$384$	−3.17082	−0.161810
$385$	2.20737	0.112498
$386$	−13.7669	−0.700719
$387$	7.45825	0.379124
$388$	−6.71078	−0.340688
$389$	−37.9044	−1.92183	−0.960916	−	0.276841i	$-0.910713\pi$
$389$	−37.9044	−1.92183	−0.960916	+	0.276841i	$0.910713\pi$
$390$	−6.19802	−0.313849
$391$	9.03689	0.457015
$392$	−4.34467	−0.219439
$393$	3.80337	0.191855
$394$	0.429086	0.0216170
$395$	3.93058	0.197769
$396$	−23.0886	−1.16025
$397$	−28.8021	−1.44553	−0.722767	−	0.691091i	$-0.757130\pi$
$397$	−28.8021	−1.44553	−0.722767	+	0.691091i	$0.757130\pi$
$398$	−9.96272	−0.499386
$399$	−34.8368	−1.74402
$400$	−4.82872	−0.241436
$401$	−20.5714	−1.02729	−0.513644	−	0.858003i	$-0.671705\pi$
$401$	−20.5714	−1.02729	−0.513644	+	0.858003i	$0.671705\pi$
$402$	−33.2714	−1.65942
$403$	2.45579	0.122332
$404$	8.89797	0.442691
$405$	8.11077	0.403027
$406$	7.54544	0.374474
$407$	−30.3162	−1.50272
$408$	−9.88077	−0.489171
$409$	15.1343	0.748342	0.374171	−	0.927360i	$-0.377927\pi$
$409$	15.1343	0.748342	0.374171	+	0.927360i	$0.377927\pi$
$410$	−2.19847	−0.108575
$411$	66.4348	3.27699
$412$	−6.78778	−0.334410
$413$	14.1144	0.694524
$414$	20.4569	1.00540
$415$	−1.77468	−0.0871154
$416$	4.72308	0.231568
$417$	34.9946	1.71369
$418$	22.0682	1.07939
$419$	−10.7317	−0.524277	−0.262139	−	0.965030i	$-0.584428\pi$
$419$	−10.7317	−0.524277	−0.262139	+	0.965030i	$0.584428\pi$
$420$	2.13839	0.104343
$421$	−10.4485	−0.509227	−0.254613	−	0.967043i	$-0.581948\pi$
$421$	−10.4485	−0.509227	−0.254613	+	0.967043i	$0.581948\pi$
$422$	2.04863	0.0997256
$423$	34.2880	1.66714
$424$	−2.85863	−0.138827
$425$	−15.0471	−0.729889
$426$	7.70064	0.373097
$427$	−18.3430	−0.887679
$428$	10.1040	0.488393
$429$	49.0179	2.36661
$430$	0.437576	0.0211018
$431$	−25.0828	−1.20820	−0.604098	−	0.796910i	$-0.706466\pi$
$431$	−25.0828	−1.20820	−0.604098	+	0.796910i	$0.706466\pi$
$432$	−12.8547	−0.618473
$433$	−11.0723	−0.532102	−0.266051	−	0.963959i	$-0.585719\pi$
$433$	−11.0723	−0.532102	−0.266051	+	0.963959i	$0.585719\pi$
$434$	−0.847277	−0.0406706
$435$	6.07649	0.291345
$436$	6.00910	0.287784
$437$	−19.5527	−0.935334
$438$	−6.78310	−0.324109
$439$	−16.1276	−0.769730	−0.384865	−	0.922973i	$-0.625752\pi$
$439$	−16.1276	−0.769730	−0.384865	+	0.922973i	$0.625752\pi$
$440$	−1.35461	−0.0645786
$441$	−30.6476	−1.45941
$442$	14.7179	0.700057
$443$	16.9689	0.806215	0.403107	−	0.915153i	$-0.367930\pi$
$443$	16.9689	0.806215	0.403107	+	0.915153i	$0.367930\pi$
$444$	−29.3688	−1.39378
$445$	0.620822	0.0294298
$446$	−7.57668	−0.358766
$447$	44.2026	2.09071
$448$	−1.62952	−0.0769876
$449$	30.0683	1.41901	0.709505	−	0.704701i	$-0.248919\pi$
$449$	30.0683	1.41901	0.709505	+	0.704701i	$0.248919\pi$
$450$	−34.0621	−1.60570
$451$	17.3869	0.818719
$452$	−3.66157	−0.172226
$453$	65.8098	3.09201
$454$	−29.3962	−1.37963
$455$	−3.18523	−0.149326
$456$	21.3786	1.00114
$457$	9.92951	0.464483	0.232242	−	0.972658i	$-0.425394\pi$
$457$	9.92951	0.464483	0.232242	+	0.972658i	$0.425394\pi$
$458$	−6.96211	−0.325318
$459$	−40.0573	−1.86972
$460$	1.20021	0.0559599
$461$	1.65674	0.0771620	0.0385810	−	0.999255i	$-0.487716\pi$
$461$	1.65674	0.0771620	0.0385810	+	0.999255i	$0.487716\pi$
$462$	−16.9118	−0.786807
$463$	6.02438	0.279977	0.139988	−	0.990153i	$-0.455293\pi$
$463$	6.02438	0.279977	0.139988	+	0.990153i	$0.455293\pi$
$464$	−4.63047	−0.214964
$465$	−0.682329	−0.0316422
$466$	−5.76973	−0.267278
$467$	−37.1755	−1.72028	−0.860139	−	0.510059i	$-0.829623\pi$
$467$	−37.1755	−1.72028	−0.860139	+	0.510059i	$0.829623\pi$
$468$	33.3169	1.54008
$469$	−17.0985	−0.789538
$470$	2.01168	0.0927919
$471$	−13.3268	−0.614065
$472$	−8.66170	−0.398687
$473$	−3.46063	−0.159120
$474$	−30.1142	−1.38319
$475$	32.5567	1.49380
$476$	−5.07784	−0.232743
$477$	−20.1650	−0.923291
$478$	−1.24285	−0.0568465
$479$	−36.5862	−1.67167	−0.835834	−	0.548982i	$-0.815015\pi$
$479$	−36.5862	−1.67167	−0.835834	+	0.548982i	$0.815015\pi$
$480$	−1.31228	−0.0598973
$481$	43.7462	1.99466
$482$	−4.88693	−0.222594
$483$	14.9841	0.681799
$484$	−0.286859	−0.0130391
$485$	−2.77734	−0.126113
$486$	−23.5766	−1.06946
$487$	24.4204	1.10659	0.553297	−	0.832984i	$-0.313369\pi$
$487$	24.4204	1.10659	0.553297	+	0.832984i	$0.313369\pi$
$488$	11.2567	0.509566
$489$	−36.8196	−1.66504
$490$	−1.79810	−0.0812297
$491$	−16.9503	−0.764958	−0.382479	−	0.923964i	$-0.624929\pi$
$491$	−16.9503	−0.764958	−0.382479	+	0.923964i	$0.624929\pi$
$492$	16.8436	0.759369
$493$	−14.4293	−0.649862
$494$	−31.8444	−1.43275
$495$	−9.55553	−0.429489
$496$	0.519955	0.0233467
$497$	3.95745	0.177516
$498$	13.5967	0.609282
$499$	22.9830	1.02886	0.514430	−	0.857532i	$-0.328004\pi$
$499$	22.9830	1.02886	0.514430	+	0.857532i	$0.328004\pi$
$500$	−4.06774	−0.181915
$501$	3.60081	0.160873
$502$	5.84026	0.260664
$503$	−34.3790	−1.53288	−0.766442	−	0.642314i	$-0.777975\pi$
$503$	−34.3790	−1.53288	−0.766442	+	0.642314i	$0.777975\pi$
$504$	−11.4947	−0.512017
$505$	3.68254	0.163871
$506$	−9.49200	−0.421971
$507$	−29.5123	−1.31069
$508$	−18.2468	−0.809573
$509$	12.2399	0.542524	0.271262	−	0.962506i	$-0.412559\pi$
$509$	12.2399	0.542524	0.271262	+	0.962506i	$0.412559\pi$
$510$	−4.08928	−0.181077
$511$	−3.48592	−0.154208
$512$	1.00000	0.0441942
$513$	86.6703	3.82659
$514$	−7.90816	−0.348814
$515$	−2.80921	−0.123789
$516$	−3.35249	−0.147585
$517$	−15.9096	−0.699706
$518$	−15.0930	−0.663148
$519$	9.48603	0.416391
$520$	1.95471	0.0857196
$521$	−13.9470	−0.611030	−0.305515	−	0.952187i	$-0.598829\pi$
$521$	−13.9470	−0.611030	−0.305515	+	0.952187i	$0.598829\pi$
$522$	−32.6636	−1.42965
$523$	7.63031	0.333650	0.166825	−	0.985986i	$-0.446648\pi$
$523$	7.63031	0.333650	0.166825	+	0.985986i	$0.446648\pi$
$524$	−1.19949	−0.0524000
$525$	−24.9495	−1.08889
$526$	3.93731	0.171675
$527$	1.62026	0.0705798
$528$	10.3784	0.451661
$529$	−14.5900	−0.634346
$530$	−1.18308	−0.0513898
$531$	−61.1002	−2.65152
$532$	10.9867	0.476334
$533$	−25.0894	−1.08674
$534$	−4.75643	−0.205831
$535$	4.18166	0.180789
$536$	10.4930	0.453229
$537$	−54.5568	−2.35430
$538$	3.23195	0.139339
$539$	14.2205	0.612520
$540$	−5.32009	−0.228940
$541$	6.78253	0.291604	0.145802	−	0.989314i	$-0.453424\pi$
$541$	6.78253	0.291604	0.145802	+	0.989314i	$0.453424\pi$
$542$	−23.9118	−1.02710
$543$	−9.68743	−0.415728
$544$	3.11616	0.133604
$545$	2.48694	0.106529
$546$	24.4037	1.04438
$547$	−8.72787	−0.373177	−0.186588	−	0.982438i	$-0.559743\pi$
$547$	−8.72787	−0.373177	−0.186588	+	0.982438i	$0.559743\pi$
$548$	−20.9520	−0.895024
$549$	79.4054	3.38894
$550$	15.8048	0.673921
$551$	31.2200	1.33002
$552$	−9.19539	−0.391382
$553$	−15.4760	−0.658108
$554$	−6.03078	−0.256223
$555$	−12.1547	−0.515937
$556$	−11.0365	−0.468051
$557$	12.8845	0.545935	0.272967	−	0.962023i	$-0.411995\pi$
$557$	12.8845	0.545935	0.272967	+	0.962023i	$0.411995\pi$
$558$	3.66780	0.155270
$559$	4.99370	0.211211
$560$	−0.674398	−0.0284985
$561$	32.3407	1.36542
$562$	3.60969	0.152266
$563$	25.0922	1.05751	0.528756	−	0.848774i	$-0.322659\pi$
$563$	25.0922	1.05751	0.528756	+	0.848774i	$0.322659\pi$
$564$	−15.4125	−0.648983
$565$	−1.51539	−0.0637529
$566$	−15.4291	−0.648535
$567$	−31.9348	−1.34114
$568$	−2.42860	−0.101902
$569$	3.45179	0.144706	0.0723532	−	0.997379i	$-0.476949\pi$
$569$	3.45179	0.144706	0.0723532	+	0.997379i	$0.476949\pi$
$570$	8.84781	0.370594
$571$	10.2351	0.428324	0.214162	−	0.976798i	$-0.431298\pi$
$571$	10.2351	0.428324	0.214162	+	0.976798i	$0.431298\pi$
$572$	−15.4591	−0.646376
$573$	−2.55193	−0.106608
$574$	8.65614	0.361300
$575$	−14.0033	−0.583979
$576$	7.05407	0.293920
$577$	7.56435	0.314908	0.157454	−	0.987526i	$-0.449671\pi$
$577$	7.56435	0.314908	0.157454	+	0.987526i	$0.449671\pi$
$578$	−7.28955	−0.303205
$579$	43.6524	1.81413
$580$	−1.91638	−0.0795733
$581$	6.98750	0.289890
$582$	21.2786	0.882028
$583$	9.35656	0.387509
$584$	2.13923	0.0885220
$585$	13.7886	0.570090
$586$	−15.9436	−0.658622
$587$	22.9231	0.946137	0.473068	−	0.881026i	$-0.343146\pi$
$587$	22.9231	0.946137	0.473068	+	0.881026i	$0.343146\pi$
$588$	13.7761	0.568118
$589$	−3.50569	−0.144450
$590$	−3.58476	−0.147582
$591$	−1.36055	−0.0559656
$592$	9.26223	0.380675
$593$	−38.0316	−1.56177	−0.780885	−	0.624675i	$-0.785231\pi$
$593$	−38.0316	−1.56177	−0.780885	+	0.624675i	$0.785231\pi$
$594$	42.0747	1.72634
$595$	−2.10153	−0.0861544
$596$	−13.9404	−0.571023
$597$	31.5900	1.29289
$598$	13.6970	0.560111
$599$	8.02028	0.327700	0.163850	−	0.986485i	$-0.447609\pi$
$599$	8.02028	0.327700	0.163850	+	0.986485i	$0.447609\pi$
$600$	15.3110	0.625068
$601$	26.5036	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$601$	26.5036	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$602$	−1.72289	−0.0702196
$603$	74.0184	3.01426
$604$	−20.7548	−0.844503
$605$	−0.118720	−0.00482667
$606$	−28.2138	−1.14611
$607$	2.28993	0.0929455	0.0464727	−	0.998920i	$-0.485202\pi$
$607$	2.28993	0.0929455	0.0464727	+	0.998920i	$0.485202\pi$
$608$	−6.74230	−0.273436
$609$	−23.9252	−0.969498
$610$	4.65872	0.188626
$611$	22.9576	0.928767
$612$	21.9816	0.888554
$613$	33.9061	1.36945	0.684727	−	0.728800i	$-0.259922\pi$
$613$	33.9061	1.36945	0.684727	+	0.728800i	$0.259922\pi$
$614$	−3.78978	−0.152943
$615$	6.97095	0.281096
$616$	5.33357	0.214896
$617$	14.4379	0.581250	0.290625	−	0.956837i	$-0.406137\pi$
$617$	14.4379	0.581250	0.290625	+	0.956837i	$0.406137\pi$
$618$	21.5228	0.865775
$619$	−13.7128	−0.551162	−0.275581	−	0.961278i	$-0.588870\pi$
$619$	−13.7128	−0.551162	−0.275581	+	0.961278i	$0.588870\pi$
$620$	0.215190	0.00864225
$621$	−37.2788	−1.49595
$622$	10.1458	0.406811
$623$	−2.44439	−0.0979323
$624$	−14.9760	−0.599520
$625$	22.4601	0.898404
$626$	24.7830	0.990528
$627$	−69.9741	−2.79450
$628$	4.20294	0.167716
$629$	28.8626	1.15083
$630$	−4.75725	−0.189533
$631$	22.7521	0.905747	0.452873	−	0.891575i	$-0.350399\pi$
$631$	22.7521	0.905747	0.452873	+	0.891575i	$0.350399\pi$
$632$	9.49729	0.377782
$633$	−6.49582	−0.258186
$634$	6.38529	0.253592
$635$	−7.55170	−0.299680
$636$	9.06419	0.359418
$637$	−20.5202	−0.813040
$638$	15.1560	0.600030
$639$	−17.1315	−0.677712
$640$	0.413863	0.0163594
$641$	29.9485	1.18289	0.591447	−	0.806344i	$-0.298557\pi$
$641$	29.9485	1.18289	0.591447	+	0.806344i	$0.298557\pi$
$642$	−32.0378	−1.26443
$643$	50.4357	1.98899	0.994494	−	0.104792i	$-0.0334177\pi$
$643$	50.4357	1.98899	0.994494	+	0.104792i	$0.0334177\pi$
$644$	−4.72562	−0.186216
$645$	−1.38747	−0.0546317
$646$	−21.0101	−0.826630
$647$	25.8944	1.01802	0.509008	−	0.860762i	$-0.330012\pi$
$647$	25.8944	1.01802	0.509008	+	0.860762i	$0.330012\pi$
$648$	19.5977	0.769871
$649$	28.3505	1.11286
$650$	−22.8064	−0.894541
$651$	2.68656	0.105295
$652$	11.6120	0.454762
$653$	−18.3527	−0.718198	−0.359099	−	0.933299i	$-0.616916\pi$
$653$	−18.3527	−0.718198	−0.359099	+	0.933299i	$0.616916\pi$
$654$	−19.0537	−0.745060
$655$	−0.496425	−0.0193969
$656$	−5.31208	−0.207402
$657$	15.0903	0.588728
$658$	−7.92067	−0.308780
$659$	2.67229	0.104098	0.0520489	−	0.998645i	$-0.483425\pi$
$659$	2.67229	0.104098	0.0520489	+	0.998645i	$0.483425\pi$
$660$	4.29523	0.167191
$661$	−24.3429	−0.946828	−0.473414	−	0.880840i	$-0.656978\pi$
$661$	−24.3429	−0.946828	−0.473414	+	0.880840i	$0.656978\pi$
$662$	30.4778	1.18455
$663$	−46.6676	−1.81242
$664$	−4.28807	−0.166410
$665$	4.54699	0.176325
$666$	65.3364	2.53174
$667$	−13.4284	−0.519950
$668$	−1.13561	−0.0439381
$669$	24.0243	0.928831
$670$	4.34267	0.167772
$671$	−36.8442	−1.42235
$672$	5.16691	0.199318
$673$	14.9022	0.574437	0.287219	−	0.957865i	$-0.407269\pi$
$673$	14.9022	0.574437	0.287219	+	0.957865i	$0.407269\pi$
$674$	−32.4569	−1.25019
$675$	62.0718	2.38914
$676$	9.30746	0.357979
$677$	−40.9896	−1.57536	−0.787679	−	0.616086i	$-0.788718\pi$
$677$	−40.9896	−1.57536	−0.787679	+	0.616086i	$0.788718\pi$
$678$	11.6102	0.445886
$679$	10.9353	0.419660
$680$	1.28966	0.0494563
$681$	93.2098	3.57181
$682$	−1.70186	−0.0651677
$683$	13.3641	0.511362	0.255681	−	0.966761i	$-0.417700\pi$
$683$	13.3641	0.511362	0.255681	+	0.966761i	$0.417700\pi$
$684$	−47.5607	−1.81853
$685$	−8.67125	−0.331311
$686$	18.4864	0.705812
$687$	22.0756	0.842236
$688$	1.05730	0.0403091
$689$	−13.5015	−0.514367
$690$	−3.80563	−0.144878
$691$	−7.59488	−0.288923	−0.144461	−	0.989510i	$-0.546145\pi$
$691$	−7.59488	−0.288923	−0.144461	+	0.989510i	$0.546145\pi$
$692$	−2.99167	−0.113726
$693$	37.6234	1.42919
$694$	28.8026	1.09333
$695$	−4.56759	−0.173259
$696$	14.6824	0.556533
$697$	−16.5533	−0.627000
$698$	−3.49402	−0.132251
$699$	18.2948	0.691971
$700$	7.86849	0.297401
$701$	−0.798293	−0.0301511	−0.0150756	−	0.999886i	$-0.504799\pi$
$701$	−0.798293	−0.0301511	−0.0150756	+	0.999886i	$0.504799\pi$
$702$	−60.7138	−2.29149
$703$	−62.4487	−2.35530
$704$	−3.27309	−0.123359
$705$	−6.37867	−0.240234
$706$	−16.1201	−0.606688
$707$	−14.4994	−0.545307
$708$	27.4646	1.03218
$709$	36.0838	1.35515	0.677577	−	0.735451i	$-0.263030\pi$
$709$	36.0838	1.35515	0.677577	+	0.735451i	$0.263030\pi$
$710$	−1.00511	−0.0377210
$711$	66.9946	2.51249
$712$	1.50007	0.0562174
$713$	1.50787	0.0564703
$714$	16.1009	0.602561
$715$	−6.39794	−0.239269
$716$	17.2059	0.643015
$717$	3.94084	0.147173
$718$	−27.1099	−1.01173
$719$	8.21652	0.306425	0.153212	−	0.988193i	$-0.451038\pi$
$719$	8.21652	0.306425	0.153212	+	0.988193i	$0.451038\pi$
$720$	2.91942	0.108800
$721$	11.0608	0.411927
$722$	26.4586	0.984687
$723$	15.4956	0.576286
$724$	3.05519	0.113545
$725$	22.3592	0.830401
$726$	0.909578	0.0337576
$727$	45.5029	1.68761	0.843804	−	0.536651i	$-0.180311\pi$
$727$	45.5029	1.68761	0.843804	+	0.536651i	$0.180311\pi$
$728$	−7.69635	−0.285246
$729$	15.9639	0.591254
$730$	0.885348	0.0327682
$731$	3.29471	0.121859
$732$	−35.6929	−1.31925
$733$	−30.2945	−1.11895	−0.559477	−	0.828846i	$-0.688998\pi$
$733$	−30.2945	−1.11895	−0.559477	+	0.828846i	$0.688998\pi$
$734$	−23.3761	−0.862829
$735$	5.70143	0.210301
$736$	2.90001	0.106896
$737$	−34.3446	−1.26510
$738$	−37.4718	−1.37936
$739$	−32.2136	−1.18500	−0.592498	−	0.805572i	$-0.701858\pi$
$739$	−32.2136	−1.18500	−0.592498	+	0.805572i	$0.701858\pi$
$740$	3.83330	0.140915
$741$	100.973	3.70933
$742$	4.65819	0.171008
$743$	16.0884	0.590227	0.295113	−	0.955462i	$-0.404643\pi$
$743$	16.0884	0.590227	0.295113	+	0.955462i	$0.404643\pi$
$744$	−1.64868	−0.0604436
$745$	−5.76944	−0.211376
$746$	−8.26909	−0.302753
$747$	−30.2484	−1.10673
$748$	−10.1995	−0.372930
$749$	−16.4646	−0.601603
$750$	12.8981	0.470971
$751$	−6.93428	−0.253035	−0.126518	−	0.991964i	$-0.540380\pi$
$751$	−6.93428	−0.253035	−0.126518	+	0.991964i	$0.540380\pi$
$752$	4.86074	0.177253
$753$	−18.5184	−0.674848
$754$	−21.8701	−0.796461
$755$	−8.58967	−0.312610
$756$	20.9470	0.761835
$757$	−14.5613	−0.529240	−0.264620	−	0.964353i	$-0.585247\pi$
$757$	−14.5613	−0.529240	−0.264620	+	0.964353i	$0.585247\pi$
$758$	−17.2928	−0.628104
$759$	30.0974	1.09247
$760$	−2.79039	−0.101218
$761$	10.1445	0.367737	0.183868	−	0.982951i	$-0.441138\pi$
$761$	10.1445	0.367737	0.183868	+	0.982951i	$0.441138\pi$
$762$	57.8574	2.09595
$763$	−9.79194	−0.354492
$764$	0.804818	0.0291173
$765$	9.09738	0.328916
$766$	−13.8268	−0.499584
$767$	−40.9099	−1.47717
$768$	−3.17082	−0.114417
$769$	26.8360	0.967730	0.483865	−	0.875143i	$-0.339233\pi$
$769$	26.8360	0.967730	0.483865	+	0.875143i	$0.339233\pi$
$770$	2.20737	0.0795480
$771$	25.0753	0.903065
$772$	−13.7669	−0.495483
$773$	−1.46915	−0.0528417	−0.0264209	−	0.999651i	$-0.508411\pi$
$773$	−1.46915	−0.0528417	−0.0264209	+	0.999651i	$0.508411\pi$
$774$	7.45825	0.268081
$775$	−2.51072	−0.0901876
$776$	−6.71078	−0.240903
$777$	47.8571	1.71686
$778$	−37.9044	−1.35894
$779$	35.8156	1.28323
$780$	−6.19802	−0.221925
$781$	7.94903	0.284439
$782$	9.03689	0.323158
$783$	59.5233	2.12719
$784$	−4.34467	−0.155167
$785$	1.73944	0.0620834
$786$	3.80337	0.135662
$787$	4.04238	0.144095	0.0720476	−	0.997401i	$-0.477047\pi$
$787$	4.04238	0.144095	0.0720476	+	0.997401i	$0.477047\pi$
$788$	0.429086	0.0152855
$789$	−12.4845	−0.444459
$790$	3.93058	0.139844
$791$	5.96661	0.212148
$792$	−23.0886	−0.820419
$793$	53.1662	1.88799
$794$	−28.8021	−1.02215
$795$	3.75133	0.133046
$796$	−9.96272	−0.353119
$797$	−33.1825	−1.17539	−0.587693	−	0.809084i	$-0.699964\pi$
$797$	−33.1825	−1.17539	−0.587693	+	0.809084i	$0.699964\pi$
$798$	−34.8368	−1.23321
$799$	15.1468	0.535856
$800$	−4.82872	−0.170721
$801$	10.5816	0.373882
$802$	−20.5714	−0.726403
$803$	−7.00190	−0.247092
$804$	−33.2714	−1.17339
$805$	−1.95576	−0.0689315
$806$	2.45579	0.0865015
$807$	−10.2479	−0.360744
$808$	8.89797	0.313030
$809$	33.1082	1.16402	0.582011	−	0.813181i	$-0.302266\pi$
$809$	33.1082	1.16402	0.582011	+	0.813181i	$0.302266\pi$
$810$	8.11077	0.284983
$811$	35.0546	1.23093	0.615467	−	0.788162i	$-0.288967\pi$
$811$	35.0546	1.23093	0.615467	+	0.788162i	$0.288967\pi$
$812$	7.54544	0.264793
$813$	75.8198	2.65912
$814$	−30.3162	−1.06258
$815$	4.80579	0.168339
$816$	−9.88077	−0.345896
$817$	−7.12861	−0.249399
$818$	15.1343	0.529157
$819$	−54.2906	−1.89707
$820$	−2.19847	−0.0767740
$821$	3.91108	0.136498	0.0682488	−	0.997668i	$-0.478259\pi$
$821$	3.91108	0.136498	0.0682488	+	0.997668i	$0.478259\pi$
$822$	66.4348	2.31718
$823$	−28.6991	−1.00039	−0.500194	−	0.865913i	$-0.666738\pi$
$823$	−28.6991	−1.00039	−0.500194	+	0.865913i	$0.666738\pi$
$824$	−6.78778	−0.236464
$825$	−50.1142	−1.74475
$826$	14.1144	0.491103
$827$	10.5872	0.368152	0.184076	−	0.982912i	$-0.441071\pi$
$827$	10.5872	0.368152	0.184076	+	0.982912i	$0.441071\pi$
$828$	20.4569	0.710925
$829$	−53.6064	−1.86183	−0.930914	−	0.365238i	$-0.880988\pi$
$829$	−53.6064	−1.86183	−0.930914	+	0.365238i	$0.880988\pi$
$830$	−1.77468	−0.0615999
$831$	19.1225	0.663352
$832$	4.72308	0.163743
$833$	−13.5387	−0.469087
$834$	34.9946	1.21177
$835$	−0.469988	−0.0162646
$836$	22.0682	0.763244
$837$	−6.68387	−0.231029
$838$	−10.7317	−0.370720
$839$	35.2379	1.21655	0.608273	−	0.793728i	$-0.291862\pi$
$839$	35.2379	1.21655	0.608273	+	0.793728i	$0.291862\pi$
$840$	2.13839	0.0737815
$841$	−7.55877	−0.260647
$842$	−10.4485	−0.360078
$843$	−11.4457	−0.394210
$844$	2.04863	0.0705167
$845$	3.85202	0.132513
$846$	34.2880	1.17885
$847$	0.467443	0.0160615
$848$	−2.85863	−0.0981657
$849$	48.9229	1.67903
$850$	−15.0471	−0.516110
$851$	26.8606	0.920768
$852$	7.70064	0.263819
$853$	−12.2828	−0.420554	−0.210277	−	0.977642i	$-0.567437\pi$
$853$	−12.2828	−0.420554	−0.210277	+	0.977642i	$0.567437\pi$
$854$	−18.3430	−0.627684
$855$	−19.6836	−0.673165
$856$	10.1040	0.345346
$857$	−53.0183	−1.81107	−0.905535	−	0.424272i	$-0.860530\pi$
$857$	−53.0183	−1.81107	−0.905535	+	0.424272i	$0.860530\pi$
$858$	49.0179	1.67344
$859$	−45.8331	−1.56380	−0.781902	−	0.623402i	$-0.785750\pi$
$859$	−45.8331	−1.56380	−0.781902	+	0.623402i	$0.785750\pi$
$860$	0.437576	0.0149212
$861$	−27.4470	−0.935392
$862$	−25.0828	−0.854323
$863$	−3.89509	−0.132590	−0.0662952	−	0.997800i	$-0.521118\pi$
$863$	−3.89509	−0.132590	−0.0662952	+	0.997800i	$0.521118\pi$
$864$	−12.8547	−0.437326
$865$	−1.23814	−0.0420981
$866$	−11.0723	−0.376253
$867$	23.1138	0.784987
$868$	−0.847277	−0.0287585
$869$	−31.0855	−1.05450
$870$	6.07649	0.206012
$871$	49.5593	1.67925
$872$	6.00910	0.203494
$873$	−47.3383	−1.60216
$874$	−19.5527	−0.661381
$875$	6.62847	0.224083
$876$	−6.78310	−0.229180
$877$	−1.82114	−0.0614954	−0.0307477	−	0.999527i	$-0.509789\pi$
$877$	−1.82114	−0.0614954	−0.0307477	+	0.999527i	$0.509789\pi$
$878$	−16.1276	−0.544281
$879$	50.5541	1.70515
$880$	−1.35461	−0.0456640
$881$	−21.1436	−0.712345	−0.356172	−	0.934420i	$-0.615918\pi$
$881$	−21.1436	−0.712345	−0.356172	+	0.934420i	$0.615918\pi$
$882$	−30.6476	−1.03196
$883$	−48.1378	−1.61997	−0.809983	−	0.586454i	$-0.800524\pi$
$883$	−48.1378	−1.61997	−0.809983	+	0.586454i	$0.800524\pi$
$884$	14.7179	0.495015
$885$	11.3666	0.382084
$886$	16.9689	0.570080
$887$	25.8593	0.868271	0.434136	−	0.900848i	$-0.357054\pi$
$887$	25.8593	0.868271	0.434136	+	0.900848i	$0.357054\pi$
$888$	−29.3688	−0.985553
$889$	29.7336	0.997233
$890$	0.620822	0.0208100
$891$	−64.1451	−2.14894
$892$	−7.57668	−0.253686
$893$	−32.7725	−1.09669
$894$	44.2026	1.47836
$895$	7.12090	0.238025
$896$	−1.62952	−0.0544384
$897$	−43.4306	−1.45010
$898$	30.0683	1.00339
$899$	−2.40764	−0.0802991
$900$	−34.0621	−1.13540
$901$	−8.90794	−0.296767
$902$	17.3869	0.578921
$903$	5.46296	0.181796
$904$	−3.66157	−0.121782
$905$	1.26443	0.0420310
$906$	65.8098	2.18638
$907$	−24.8631	−0.825567	−0.412783	−	0.910829i	$-0.635443\pi$
$907$	−24.8631	−0.825567	−0.412783	+	0.910829i	$0.635443\pi$
$908$	−29.3962	−0.975546
$909$	62.7669	2.08185
$910$	−3.18523	−0.105589
$911$	−12.4362	−0.412030	−0.206015	−	0.978549i	$-0.566050\pi$
$911$	−12.4362	−0.412030	−0.206015	+	0.978549i	$0.566050\pi$
$912$	21.3786	0.707916
$913$	14.0353	0.464499
$914$	9.92951	0.328439
$915$	−14.7720	−0.488346
$916$	−6.96211	−0.230035
$917$	1.95460	0.0645464
$918$	−40.0573	−1.32209
$919$	−4.45929	−0.147098	−0.0735492	−	0.997292i	$-0.523433\pi$
$919$	−4.45929	−0.147098	−0.0735492	+	0.997292i	$0.523433\pi$
$920$	1.20021	0.0395696
$921$	12.0167	0.395963
$922$	1.65674	0.0545618
$923$	−11.4705	−0.377555
$924$	−16.9118	−0.556356
$925$	−44.7247	−1.47054
$926$	6.02438	0.197974
$927$	−47.8815	−1.57264
$928$	−4.63047	−0.152003
$929$	−10.2470	−0.336194	−0.168097	−	0.985770i	$-0.553762\pi$
$929$	−10.2470	−0.336194	−0.168097	+	0.985770i	$0.553762\pi$
$930$	−0.682329	−0.0223744
$931$	29.2930	0.960040
$932$	−5.76973	−0.188994
$933$	−32.1706	−1.05322
$934$	−37.1755	−1.21642
$935$	−4.22119	−0.138048
$936$	33.3169	1.08900
$937$	−44.4253	−1.45131	−0.725655	−	0.688058i	$-0.758463\pi$
$937$	−44.4253	−1.45131	−0.725655	+	0.688058i	$0.758463\pi$
$938$	−17.0985	−0.558287
$939$	−78.5824	−2.56444
$940$	2.01168	0.0656138
$941$	31.1377	1.01506	0.507530	−	0.861634i	$-0.330559\pi$
$941$	31.1377	1.01506	0.507530	+	0.861634i	$0.330559\pi$
$942$	−13.3268	−0.434209
$943$	−15.4051	−0.501658
$944$	−8.66170	−0.281914
$945$	8.66919	0.282009
$946$	−3.46063	−0.112515
$947$	8.43265	0.274024	0.137012	−	0.990569i	$-0.456250\pi$
$947$	8.43265	0.274024	0.137012	+	0.990569i	$0.456250\pi$
$948$	−30.1142	−0.978063
$949$	10.1038	0.327982
$950$	32.5567	1.05628
$951$	−20.2466	−0.656540
$952$	−5.07784	−0.164574
$953$	1.87613	0.0607737	0.0303868	−	0.999538i	$-0.490326\pi$
$953$	1.87613	0.0607737	0.0303868	+	0.999538i	$0.490326\pi$
$954$	−20.1650	−0.652865
$955$	0.333084	0.0107784
$956$	−1.24285	−0.0401965
$957$	−48.0567	−1.55345
$958$	−36.5862	−1.18205
$959$	34.1417	1.10249
$960$	−1.31228	−0.0423538
$961$	−30.7296	−0.991279
$962$	43.7462	1.41044
$963$	71.2740	2.29677
$964$	−4.88693	−0.157398
$965$	−5.69763	−0.183413
$966$	14.9841	0.482105
$967$	48.3640	1.55528	0.777640	−	0.628709i	$-0.216416\pi$
$967$	48.3640	1.55528	0.777640	+	0.628709i	$0.216416\pi$
$968$	−0.286859	−0.00922000
$969$	66.6191	2.14011
$970$	−2.77734	−0.0891751
$971$	10.0552	0.322687	0.161344	−	0.986898i	$-0.448417\pi$
$971$	10.0552	0.322687	0.161344	+	0.986898i	$0.448417\pi$
$972$	−23.5766	−0.756219
$973$	17.9842	0.576546
$974$	24.4204	0.782480
$975$	72.3149	2.31593
$976$	11.2567	0.360318
$977$	−2.15985	−0.0690998	−0.0345499	−	0.999403i	$-0.511000\pi$
$977$	−2.15985	−0.0690998	−0.0345499	+	0.999403i	$0.511000\pi$
$978$	−36.8196	−1.17736
$979$	−4.90986	−0.156920
$980$	−1.79810	−0.0574381
$981$	42.3886	1.35336
$982$	−16.9503	−0.540907
$983$	−38.0182	−1.21259	−0.606297	−	0.795239i	$-0.707346\pi$
$983$	−38.0182	−1.21259	−0.606297	+	0.795239i	$0.707346\pi$
$984$	16.8436	0.536955
$985$	0.177583	0.00565826
$986$	−14.4293	−0.459522
$987$	25.1150	0.799419
$988$	−31.8444	−1.01311
$989$	3.06617	0.0974986
$990$	−9.55553	−0.303695
$991$	−30.2003	−0.959345	−0.479672	−	0.877448i	$-0.659244\pi$
$991$	−30.2003	−0.959345	−0.479672	+	0.877448i	$0.659244\pi$
$992$	0.519955	0.0165086
$993$	−96.6395	−3.06676
$994$	3.95745	0.125523
$995$	−4.12320	−0.130714
$996$	13.5967	0.430828
$997$	26.2271	0.830622	0.415311	−	0.909680i	$-0.363673\pi$
$997$	26.2271	0.830622	0.415311	+	0.909680i	$0.363673\pi$
$998$	22.9830	0.727514
$999$	−119.063	−3.76700

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.4	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.4	✓	54	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.17082 q^{3} +1.00000 q^{4} +0.413863 q^{5} -3.17082 q^{6} -1.62952 q^{7} +1.00000 q^{8} +7.05407 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.17082 q^{3} +1.00000 q^{4} +0.413863 q^{5} -3.17082 q^{6} -1.62952 q^{7} +1.00000 q^{8} +7.05407 q^{9} +0.413863 q^{10} -3.27309 q^{11} -3.17082 q^{12} +4.72308 q^{13} -1.62952 q^{14} -1.31228 q^{15} +1.00000 q^{16} +3.11616 q^{17} +7.05407 q^{18} -6.74230 q^{19} +0.413863 q^{20} +5.16691 q^{21} -3.27309 q^{22} +2.90001 q^{23} -3.17082 q^{24} -4.82872 q^{25} +4.72308 q^{26} -12.8547 q^{27} -1.62952 q^{28} -4.63047 q^{29} -1.31228 q^{30} +0.519955 q^{31} +1.00000 q^{32} +10.3784 q^{33} +3.11616 q^{34} -0.674398 q^{35} +7.05407 q^{36} +9.26223 q^{37} -6.74230 q^{38} -14.9760 q^{39} +0.413863 q^{40} -5.31208 q^{41} +5.16691 q^{42} +1.05730 q^{43} -3.27309 q^{44} +2.91942 q^{45} +2.90001 q^{46} +4.86074 q^{47} -3.17082 q^{48} -4.34467 q^{49} -4.82872 q^{50} -9.88077 q^{51} +4.72308 q^{52} -2.85863 q^{53} -12.8547 q^{54} -1.35461 q^{55} -1.62952 q^{56} +21.3786 q^{57} -4.63047 q^{58} -8.66170 q^{59} -1.31228 q^{60} +11.2567 q^{61} +0.519955 q^{62} -11.4947 q^{63} +1.00000 q^{64} +1.95471 q^{65} +10.3784 q^{66} +10.4930 q^{67} +3.11616 q^{68} -9.19539 q^{69} -0.674398 q^{70} -2.42860 q^{71} +7.05407 q^{72} +2.13923 q^{73} +9.26223 q^{74} +15.3110 q^{75} -6.74230 q^{76} +5.33357 q^{77} -14.9760 q^{78} +9.49729 q^{79} +0.413863 q^{80} +19.5977 q^{81} -5.31208 q^{82} -4.28807 q^{83} +5.16691 q^{84} +1.28966 q^{85} +1.05730 q^{86} +14.6824 q^{87} -3.27309 q^{88} +1.50007 q^{89} +2.91942 q^{90} -7.69635 q^{91} +2.90001 q^{92} -1.64868 q^{93} +4.86074 q^{94} -2.79039 q^{95} -3.17082 q^{96} -6.71078 q^{97} -4.34467 q^{98} -23.0886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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