LMFDB - Embedded newform 6022.2.a.e.1.13

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:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.26646 q^{3} +1.00000 q^{4} +2.42379 q^{5} -2.26646 q^{6} -1.89494 q^{7} +1.00000 q^{8} +2.13682 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.26646 q^{3} +1.00000 q^{4} +2.42379 q^{5} -2.26646 q^{6} -1.89494 q^{7} +1.00000 q^{8} +2.13682 q^{9} +2.42379 q^{10} +3.42970 q^{11} -2.26646 q^{12} +2.23174 q^{13} -1.89494 q^{14} -5.49340 q^{15} +1.00000 q^{16} +5.22145 q^{17} +2.13682 q^{18} -1.48195 q^{19} +2.42379 q^{20} +4.29480 q^{21} +3.42970 q^{22} +7.63027 q^{23} -2.26646 q^{24} +0.874739 q^{25} +2.23174 q^{26} +1.95635 q^{27} -1.89494 q^{28} -3.57015 q^{29} -5.49340 q^{30} +7.32766 q^{31} +1.00000 q^{32} -7.77326 q^{33} +5.22145 q^{34} -4.59293 q^{35} +2.13682 q^{36} -5.85688 q^{37} -1.48195 q^{38} -5.05815 q^{39} +2.42379 q^{40} +1.41962 q^{41} +4.29480 q^{42} +1.75771 q^{43} +3.42970 q^{44} +5.17920 q^{45} +7.63027 q^{46} -5.20562 q^{47} -2.26646 q^{48} -3.40919 q^{49} +0.874739 q^{50} -11.8342 q^{51} +2.23174 q^{52} -8.52728 q^{53} +1.95635 q^{54} +8.31285 q^{55} -1.89494 q^{56} +3.35878 q^{57} -3.57015 q^{58} +3.82240 q^{59} -5.49340 q^{60} -11.9525 q^{61} +7.32766 q^{62} -4.04915 q^{63} +1.00000 q^{64} +5.40927 q^{65} -7.77326 q^{66} -3.40580 q^{67} +5.22145 q^{68} -17.2937 q^{69} -4.59293 q^{70} +13.9393 q^{71} +2.13682 q^{72} +13.6869 q^{73} -5.85688 q^{74} -1.98256 q^{75} -1.48195 q^{76} -6.49908 q^{77} -5.05815 q^{78} +13.5162 q^{79} +2.42379 q^{80} -10.8445 q^{81} +1.41962 q^{82} -6.59062 q^{83} +4.29480 q^{84} +12.6557 q^{85} +1.75771 q^{86} +8.09158 q^{87} +3.42970 q^{88} +6.11714 q^{89} +5.17920 q^{90} -4.22903 q^{91} +7.63027 q^{92} -16.6078 q^{93} -5.20562 q^{94} -3.59194 q^{95} -2.26646 q^{96} -16.3577 q^{97} -3.40919 q^{98} +7.32865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) $ 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * 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
$3$	−2.26646	−1.30854	−0.654269	−	0.756262i	$-0.727024\pi$
$3$	−2.26646	−1.30854	−0.654269	+	0.756262i	$0.727024\pi$
$4$	1.00000	0.500000
$5$	2.42379	1.08395	0.541975	−	0.840395i	$-0.317677\pi$
$5$	2.42379	1.08395	0.541975	+	0.840395i	$0.317677\pi$
$6$	−2.26646	−0.925277
$7$	−1.89494	−0.716221	−0.358110	−	0.933679i	$-0.616579\pi$
$7$	−1.89494	−0.716221	−0.358110	+	0.933679i	$0.616579\pi$
$8$	1.00000	0.353553
$9$	2.13682	0.712274
$10$	2.42379	0.766468
$11$	3.42970	1.03409	0.517046	−	0.855958i	$-0.327032\pi$
$11$	3.42970	1.03409	0.517046	+	0.855958i	$0.327032\pi$
$12$	−2.26646	−0.654269
$13$	2.23174	0.618975	0.309487	−	0.950904i	$-0.399843\pi$
$13$	2.23174	0.618975	0.309487	+	0.950904i	$0.399843\pi$
$14$	−1.89494	−0.506445
$15$	−5.49340	−1.41839
$16$	1.00000	0.250000
$17$	5.22145	1.26639	0.633194	−	0.773993i	$-0.281744\pi$
$17$	5.22145	1.26639	0.633194	+	0.773993i	$0.281744\pi$
$18$	2.13682	0.503654
$19$	−1.48195	−0.339983	−0.169992	−	0.985446i	$-0.554374\pi$
$19$	−1.48195	−0.339983	−0.169992	+	0.985446i	$0.554374\pi$
$20$	2.42379	0.541975
$21$	4.29480	0.937203
$22$	3.42970	0.731214
$23$	7.63027	1.59102	0.795510	−	0.605940i	$-0.207203\pi$
$23$	7.63027	1.59102	0.795510	+	0.605940i	$0.207203\pi$
$24$	−2.26646	−0.462638
$25$	0.874739	0.174948
$26$	2.23174	0.437681
$27$	1.95635	0.376501
$28$	−1.89494	−0.358110
$29$	−3.57015	−0.662960	−0.331480	−	0.943462i	$-0.607548\pi$
$29$	−3.57015	−0.662960	−0.331480	+	0.943462i	$0.607548\pi$
$30$	−5.49340	−1.00295
$31$	7.32766	1.31609	0.658043	−	0.752980i	$-0.271384\pi$
$31$	7.32766	1.31609	0.658043	+	0.752980i	$0.271384\pi$
$32$	1.00000	0.176777
$33$	−7.77326	−1.35315
$34$	5.22145	0.895471
$35$	−4.59293	−0.776348
$36$	2.13682	0.356137
$37$	−5.85688	−0.962866	−0.481433	−	0.876483i	$-0.659883\pi$
$37$	−5.85688	−0.962866	−0.481433	+	0.876483i	$0.659883\pi$
$38$	−1.48195	−0.240404
$39$	−5.05815	−0.809952
$40$	2.42379	0.383234
$41$	1.41962	0.221707	0.110854	−	0.993837i	$-0.464642\pi$
$41$	1.41962	0.221707	0.110854	+	0.993837i	$0.464642\pi$
$42$	4.29480	0.662702
$43$	1.75771	0.268049	0.134024	−	0.990978i	$-0.457210\pi$
$43$	1.75771	0.268049	0.134024	+	0.990978i	$0.457210\pi$
$44$	3.42970	0.517046
$45$	5.17920	0.772070
$46$	7.63027	1.12502
$47$	−5.20562	−0.759318	−0.379659	−	0.925127i	$-0.623959\pi$
$47$	−5.20562	−0.759318	−0.379659	+	0.925127i	$0.623959\pi$
$48$	−2.26646	−0.327135
$49$	−3.40919	−0.487028
$50$	0.874739	0.123707
$51$	−11.8342	−1.65712
$52$	2.23174	0.309487
$53$	−8.52728	−1.17131	−0.585656	−	0.810560i	$-0.699163\pi$
$53$	−8.52728	−1.17131	−0.585656	+	0.810560i	$0.699163\pi$
$54$	1.95635	0.266226
$55$	8.31285	1.12090
$56$	−1.89494	−0.253222
$57$	3.35878	0.444881
$58$	−3.57015	−0.468783
$59$	3.82240	0.497634	0.248817	−	0.968551i	$-0.419958\pi$
$59$	3.82240	0.497634	0.248817	+	0.968551i	$0.419958\pi$
$60$	−5.49340	−0.709195
$61$	−11.9525	−1.53036	−0.765181	−	0.643815i	$-0.777351\pi$
$61$	−11.9525	−1.53036	−0.765181	+	0.643815i	$0.777351\pi$
$62$	7.32766	0.930614
$63$	−4.04915	−0.510145
$64$	1.00000	0.125000
$65$	5.40927	0.670938
$66$	−7.77326	−0.956822
$67$	−3.40580	−0.416085	−0.208042	−	0.978120i	$-0.566709\pi$
$67$	−3.40580	−0.416085	−0.208042	+	0.978120i	$0.566709\pi$
$68$	5.22145	0.633194
$69$	−17.2937	−2.08191
$70$	−4.59293	−0.548961
$71$	13.9393	1.65429	0.827144	−	0.561990i	$-0.189964\pi$
$71$	13.9393	1.65429	0.827144	+	0.561990i	$0.189964\pi$
$72$	2.13682	0.251827
$73$	13.6869	1.60193	0.800965	−	0.598711i	$-0.204320\pi$
$73$	13.6869	1.60193	0.800965	+	0.598711i	$0.204320\pi$
$74$	−5.85688	−0.680849
$75$	−1.98256	−0.228926
$76$	−1.48195	−0.169992
$77$	−6.49908	−0.740638
$78$	−5.05815	−0.572723
$79$	13.5162	1.52069	0.760344	−	0.649521i	$-0.225030\pi$
$79$	13.5162	1.52069	0.760344	+	0.649521i	$0.225030\pi$
$80$	2.42379	0.270988
$81$	−10.8445	−1.20494
$82$	1.41962	0.156771
$83$	−6.59062	−0.723414	−0.361707	−	0.932292i	$-0.617806\pi$
$83$	−6.59062	−0.723414	−0.361707	+	0.932292i	$0.617806\pi$
$84$	4.29480	0.468601
$85$	12.6557	1.37270
$86$	1.75771	0.189539
$87$	8.09158	0.867509
$88$	3.42970	0.365607
$89$	6.11714	0.648415	0.324208	−	0.945986i	$-0.394902\pi$
$89$	6.11714	0.648415	0.324208	+	0.945986i	$0.394902\pi$
$90$	5.17920	0.545936
$91$	−4.22903	−0.443323
$92$	7.63027	0.795510
$93$	−16.6078	−1.72215
$94$	−5.20562	−0.536919
$95$	−3.59194	−0.368525
$96$	−2.26646	−0.231319
$97$	−16.3577	−1.66087	−0.830437	−	0.557112i	$-0.811909\pi$
$97$	−16.3577	−1.66087	−0.830437	+	0.557112i	$0.811909\pi$
$98$	−3.40919	−0.344381
$99$	7.32865	0.736557
$100$	0.874739	0.0874739
$101$	−12.6725	−1.26096	−0.630480	−	0.776206i	$-0.717142\pi$
$101$	−12.6725	−1.26096	−0.630480	+	0.776206i	$0.717142\pi$
$102$	−11.8342	−1.17176
$103$	11.9495	1.17742	0.588712	−	0.808343i	$-0.299635\pi$
$103$	11.9495	1.17742	0.588712	+	0.808343i	$0.299635\pi$
$104$	2.23174	0.218841
$105$	10.4097	1.01588
$106$	−8.52728	−0.828243
$107$	7.66967	0.741455	0.370727	−	0.928742i	$-0.379108\pi$
$107$	7.66967	0.741455	0.370727	+	0.928742i	$0.379108\pi$
$108$	1.95635	0.188250
$109$	9.64208	0.923544	0.461772	−	0.886999i	$-0.347214\pi$
$109$	9.64208	0.923544	0.461772	+	0.886999i	$0.347214\pi$
$110$	8.31285	0.792599
$111$	13.2744	1.25995
$112$	−1.89494	−0.179055
$113$	17.3480	1.63196	0.815981	−	0.578079i	$-0.196197\pi$
$113$	17.3480	1.63196	0.815981	+	0.578079i	$0.196197\pi$
$114$	3.35878	0.314578
$115$	18.4941	1.72459
$116$	−3.57015	−0.331480
$117$	4.76884	0.440880
$118$	3.82240	0.351880
$119$	−9.89435	−0.907013
$120$	−5.49340	−0.501477
$121$	0.762817	0.0693470
$122$	−11.9525	−1.08213
$123$	−3.21750	−0.290112
$124$	7.32766	0.658043
$125$	−9.99875	−0.894315
$126$	−4.04915	−0.360727
$127$	−20.6975	−1.83661	−0.918305	−	0.395873i	$-0.870442\pi$
$127$	−20.6975	−1.83661	−0.918305	+	0.395873i	$0.870442\pi$
$128$	1.00000	0.0883883
$129$	−3.98378	−0.350752
$130$	5.40927	0.474425
$131$	−1.79353	−0.156701	−0.0783507	−	0.996926i	$-0.524965\pi$
$131$	−1.79353	−0.156701	−0.0783507	+	0.996926i	$0.524965\pi$
$132$	−7.77326	−0.676575
$133$	2.80821	0.243503
$134$	−3.40580	−0.294216
$135$	4.74179	0.408108
$136$	5.22145	0.447736
$137$	15.2665	1.30430	0.652152	−	0.758088i	$-0.273866\pi$
$137$	15.2665	1.30430	0.652152	+	0.758088i	$0.273866\pi$
$138$	−17.2937	−1.47213
$139$	−0.539200	−0.0457343	−0.0228672	−	0.999739i	$-0.507279\pi$
$139$	−0.539200	−0.0457343	−0.0228672	+	0.999739i	$0.507279\pi$
$140$	−4.59293	−0.388174
$141$	11.7983	0.993597
$142$	13.9393	1.16976
$143$	7.65421	0.640077
$144$	2.13682	0.178069
$145$	−8.65327	−0.718615
$146$	13.6869	1.13274
$147$	7.72679	0.637295
$148$	−5.85688	−0.481433
$149$	−9.52633	−0.780427	−0.390214	−	0.920724i	$-0.627599\pi$
$149$	−9.52633	−0.780427	−0.390214	+	0.920724i	$0.627599\pi$
$150$	−1.98256	−0.161875
$151$	9.35761	0.761511	0.380756	−	0.924676i	$-0.375664\pi$
$151$	9.35761	0.761511	0.380756	+	0.924676i	$0.375664\pi$
$152$	−1.48195	−0.120202
$153$	11.1573	0.902015
$154$	−6.49908	−0.523710
$155$	17.7607	1.42657
$156$	−5.05815	−0.404976
$157$	9.65815	0.770805	0.385402	−	0.922749i	$-0.374063\pi$
$157$	9.65815	0.770805	0.385402	+	0.922749i	$0.374063\pi$
$158$	13.5162	1.07529
$159$	19.3267	1.53271
$160$	2.42379	0.191617
$161$	−14.4589	−1.13952
$162$	−10.8445	−0.852021
$163$	5.88875	0.461242	0.230621	−	0.973044i	$-0.425924\pi$
$163$	5.88875	0.461242	0.230621	+	0.973044i	$0.425924\pi$
$164$	1.41962	0.110854
$165$	−18.8407	−1.46675
$166$	−6.59062	−0.511531
$167$	−15.7650	−1.21994	−0.609968	−	0.792426i	$-0.708818\pi$
$167$	−15.7650	−1.21994	−0.609968	+	0.792426i	$0.708818\pi$
$168$	4.29480	0.331351
$169$	−8.01931	−0.616870
$170$	12.6557	0.970646
$171$	−3.16667	−0.242161
$172$	1.75771	0.134024
$173$	4.26658	0.324382	0.162191	−	0.986759i	$-0.448144\pi$
$173$	4.26658	0.324382	0.162191	+	0.986759i	$0.448144\pi$
$174$	8.09158	0.613421
$175$	−1.65758	−0.125301
$176$	3.42970	0.258523
$177$	−8.66330	−0.651173
$178$	6.11714	0.458499
$179$	8.04360	0.601207	0.300603	−	0.953749i	$-0.402812\pi$
$179$	8.04360	0.601207	0.300603	+	0.953749i	$0.402812\pi$
$180$	5.17920	0.386035
$181$	16.0258	1.19119	0.595594	−	0.803285i	$-0.296917\pi$
$181$	16.0258	1.19119	0.595594	+	0.803285i	$0.296917\pi$
$182$	−4.22903	−0.313476
$183$	27.0898	2.00254
$184$	7.63027	0.562511
$185$	−14.1958	−1.04370
$186$	−16.6078	−1.21774
$187$	17.9080	1.30956
$188$	−5.20562	−0.379659
$189$	−3.70718	−0.269658
$190$	−3.59194	−0.260586
$191$	6.27481	0.454029	0.227015	−	0.973891i	$-0.427104\pi$
$191$	6.27481	0.454029	0.227015	+	0.973891i	$0.427104\pi$
$192$	−2.26646	−0.163567
$193$	3.92284	0.282372	0.141186	−	0.989983i	$-0.454908\pi$
$193$	3.92284	0.282372	0.141186	+	0.989983i	$0.454908\pi$
$194$	−16.3577	−1.17442
$195$	−12.2599	−0.877948
$196$	−3.40919	−0.243514
$197$	−9.11751	−0.649595	−0.324798	−	0.945784i	$-0.605296\pi$
$197$	−9.11751	−0.649595	−0.324798	+	0.945784i	$0.605296\pi$
$198$	7.32865	0.520825
$199$	26.6666	1.89034	0.945172	−	0.326574i	$-0.105894\pi$
$199$	26.6666	1.89034	0.945172	+	0.326574i	$0.105894\pi$
$200$	0.874739	0.0618534
$201$	7.71909	0.544463
$202$	−12.6725	−0.891633
$203$	6.76522	0.474826
$204$	−11.8342	−0.828559
$205$	3.44085	0.240320
$206$	11.9495	0.832564
$207$	16.3045	1.13324
$208$	2.23174	0.154744
$209$	−5.08265	−0.351574
$210$	10.4097	0.718336
$211$	5.11195	0.351921	0.175961	−	0.984397i	$-0.443697\pi$
$211$	5.11195	0.351921	0.175961	+	0.984397i	$0.443697\pi$
$212$	−8.52728	−0.585656
$213$	−31.5928	−2.16470
$214$	7.66967	0.524288
$215$	4.26032	0.290551
$216$	1.95635	0.133113
$217$	−13.8855	−0.942609
$218$	9.64208	0.653044
$219$	−31.0207	−2.09619
$220$	8.31285	0.560452
$221$	11.6529	0.783862
$222$	13.2744	0.890917
$223$	−10.2686	−0.687639	−0.343820	−	0.939036i	$-0.611721\pi$
$223$	−10.2686	−0.687639	−0.343820	+	0.939036i	$0.611721\pi$
$224$	−1.89494	−0.126611
$225$	1.86916	0.124611
$226$	17.3480	1.15397
$227$	27.7155	1.83954	0.919771	−	0.392454i	$-0.128374\pi$
$227$	27.7155	1.83954	0.919771	+	0.392454i	$0.128374\pi$
$228$	3.35878	0.222441
$229$	−0.754263	−0.0498431	−0.0249216	−	0.999689i	$-0.507934\pi$
$229$	−0.754263	−0.0498431	−0.0249216	+	0.999689i	$0.507934\pi$
$230$	18.4941	1.21947
$231$	14.7299	0.969154
$232$	−3.57015	−0.234392
$233$	12.8557	0.842203	0.421102	−	0.907013i	$-0.361644\pi$
$233$	12.8557	0.842203	0.421102	+	0.907013i	$0.361644\pi$
$234$	4.76884	0.311749
$235$	−12.6173	−0.823062
$236$	3.82240	0.248817
$237$	−30.6338	−1.98988
$238$	−9.89435	−0.641355
$239$	−15.2467	−0.986227	−0.493114	−	0.869965i	$-0.664141\pi$
$239$	−15.2467	−0.986227	−0.493114	+	0.869965i	$0.664141\pi$
$240$	−5.49340	−0.354598
$241$	9.91861	0.638914	0.319457	−	0.947601i	$-0.396500\pi$
$241$	9.91861	0.638914	0.319457	+	0.947601i	$0.396500\pi$
$242$	0.762817	0.0490358
$243$	18.7094	1.20021
$244$	−11.9525	−0.765181
$245$	−8.26316	−0.527914
$246$	−3.21750	−0.205141
$247$	−3.30734	−0.210441
$248$	7.32766	0.465307
$249$	14.9373	0.946615
$250$	−9.99875	−0.632376
$251$	−23.8775	−1.50713	−0.753567	−	0.657371i	$-0.771668\pi$
$251$	−23.8775	−1.50713	−0.753567	+	0.657371i	$0.771668\pi$
$252$	−4.04915	−0.255073
$253$	26.1695	1.64526
$254$	−20.6975	−1.29868
$255$	−28.6835	−1.79623
$256$	1.00000	0.0625000
$257$	−9.14491	−0.570444	−0.285222	−	0.958462i	$-0.592067\pi$
$257$	−9.14491	−0.570444	−0.285222	+	0.958462i	$0.592067\pi$
$258$	−3.98378	−0.248019
$259$	11.0985	0.689624
$260$	5.40927	0.335469
$261$	−7.62877	−0.472209
$262$	−1.79353	−0.110805
$263$	8.24409	0.508352	0.254176	−	0.967158i	$-0.418196\pi$
$263$	8.24409	0.508352	0.254176	+	0.967158i	$0.418196\pi$
$264$	−7.77326	−0.478411
$265$	−20.6683	−1.26964
$266$	2.80821	0.172183
$267$	−13.8642	−0.848477
$268$	−3.40580	−0.208042
$269$	−7.88919	−0.481013	−0.240506	−	0.970648i	$-0.577313\pi$
$269$	−7.88919	−0.481013	−0.240506	+	0.970648i	$0.577313\pi$
$270$	4.74179	0.288576
$271$	−0.541077	−0.0328681	−0.0164340	−	0.999865i	$-0.505231\pi$
$271$	−0.541077	−0.0328681	−0.0164340	+	0.999865i	$0.505231\pi$
$272$	5.22145	0.316597
$273$	9.58490	0.580105
$274$	15.2665	0.922283
$275$	3.00009	0.180912
$276$	−17.2937	−1.04096
$277$	19.2657	1.15757	0.578783	−	0.815482i	$-0.303528\pi$
$277$	19.2657	1.15757	0.578783	+	0.815482i	$0.303528\pi$
$278$	−0.539200	−0.0323390
$279$	15.6579	0.937414
$280$	−4.59293	−0.274480
$281$	−11.5291	−0.687770	−0.343885	−	0.939012i	$-0.611743\pi$
$281$	−11.5291	−0.687770	−0.343885	+	0.939012i	$0.611743\pi$
$282$	11.7983	0.702579
$283$	8.81217	0.523829	0.261915	−	0.965091i	$-0.415646\pi$
$283$	8.81217	0.523829	0.261915	+	0.965091i	$0.415646\pi$
$284$	13.9393	0.827144
$285$	8.14096	0.482229
$286$	7.65421	0.452603
$287$	−2.69010	−0.158791
$288$	2.13682	0.125913
$289$	10.2636	0.603738
$290$	−8.65327	−0.508138
$291$	37.0741	2.17332
$292$	13.6869	0.800965
$293$	−30.0228	−1.75395	−0.876976	−	0.480534i	$-0.840443\pi$
$293$	−30.0228	−1.75395	−0.876976	+	0.480534i	$0.840443\pi$
$294$	7.72679	0.450635
$295$	9.26468	0.539410
$296$	−5.85688	−0.340424
$297$	6.70970	0.389336
$298$	−9.52633	−0.551845
$299$	17.0288	0.984802
$300$	−1.98256	−0.114463
$301$	−3.33076	−0.191982
$302$	9.35761	0.538470
$303$	28.7216	1.65001
$304$	−1.48195	−0.0849958
$305$	−28.9703	−1.65884
$306$	11.1573	0.637821
$307$	1.17401	0.0670044	0.0335022	−	0.999439i	$-0.489334\pi$
$307$	1.17401	0.0670044	0.0335022	+	0.999439i	$0.489334\pi$
$308$	−6.49908	−0.370319
$309$	−27.0831	−1.54070
$310$	17.7607	1.00874
$311$	−0.454119	−0.0257507	−0.0128753	−	0.999917i	$-0.504098\pi$
$311$	−0.454119	−0.0257507	−0.0128753	+	0.999917i	$0.504098\pi$
$312$	−5.05815	−0.286361
$313$	−6.05215	−0.342087	−0.171044	−	0.985263i	$-0.554714\pi$
$313$	−6.05215	−0.342087	−0.171044	+	0.985263i	$0.554714\pi$
$314$	9.65815	0.545041
$315$	−9.81428	−0.552972
$316$	13.5162	0.760344
$317$	−20.3586	−1.14345	−0.571727	−	0.820444i	$-0.693726\pi$
$317$	−20.3586	−1.14345	−0.571727	+	0.820444i	$0.693726\pi$
$318$	19.3267	1.08379
$319$	−12.2445	−0.685562
$320$	2.42379	0.135494
$321$	−17.3830	−0.970222
$322$	−14.4589	−0.805764
$323$	−7.73794	−0.430551
$324$	−10.8445	−0.602470
$325$	1.95220	0.108288
$326$	5.88875	0.326148
$327$	−21.8533	−1.20849
$328$	1.41962	0.0783853
$329$	9.86435	0.543839
$330$	−18.8407	−1.03715
$331$	−18.3602	−1.00917	−0.504583	−	0.863363i	$-0.668354\pi$
$331$	−18.3602	−1.00917	−0.504583	+	0.863363i	$0.668354\pi$
$332$	−6.59062	−0.361707
$333$	−12.5151	−0.685824
$334$	−15.7650	−0.862625
$335$	−8.25493	−0.451015
$336$	4.29480	0.234301
$337$	18.8841	1.02868	0.514341	−	0.857586i	$-0.328037\pi$
$337$	18.8841	1.02868	0.514341	+	0.857586i	$0.328037\pi$
$338$	−8.01931	−0.436193
$339$	−39.3185	−2.13549
$340$	12.6557	0.686351
$341$	25.1316	1.36096
$342$	−3.16667	−0.171234
$343$	19.7248	1.06504
$344$	1.75771	0.0947695
$345$	−41.9161	−2.25669
$346$	4.26658	0.229373
$347$	9.26492	0.497367	0.248684	−	0.968585i	$-0.420002\pi$
$347$	9.26492	0.497367	0.248684	+	0.968585i	$0.420002\pi$
$348$	8.09158	0.433754
$349$	6.33249	0.338970	0.169485	−	0.985533i	$-0.445790\pi$
$349$	6.33249	0.338970	0.169485	+	0.985533i	$0.445790\pi$
$350$	−1.65758	−0.0886014
$351$	4.36608	0.233044
$352$	3.42970	0.182803
$353$	23.2848	1.23932	0.619662	−	0.784869i	$-0.287270\pi$
$353$	23.2848	1.23932	0.619662	+	0.784869i	$0.287270\pi$
$354$	−8.66330	−0.460449
$355$	33.7858	1.79317
$356$	6.11714	0.324208
$357$	22.4251	1.18686
$358$	8.04360	0.425118
$359$	28.3364	1.49554	0.747769	−	0.663959i	$-0.231125\pi$
$359$	28.3364	1.49554	0.747769	+	0.663959i	$0.231125\pi$
$360$	5.17920	0.272968
$361$	−16.8038	−0.884411
$362$	16.0258	0.842297
$363$	−1.72889	−0.0907433
$364$	−4.22903	−0.221661
$365$	33.1741	1.73641
$366$	27.0898	1.41601
$367$	29.6842	1.54950	0.774751	−	0.632266i	$-0.217875\pi$
$367$	29.6842	1.54950	0.774751	+	0.632266i	$0.217875\pi$
$368$	7.63027	0.397755
$369$	3.03347	0.157916
$370$	−14.1958	−0.738006
$371$	16.1587	0.838918
$372$	−16.6078	−0.861075
$373$	−3.55535	−0.184089	−0.0920444	−	0.995755i	$-0.529340\pi$
$373$	−3.55535	−0.184089	−0.0920444	+	0.995755i	$0.529340\pi$
$374$	17.9080	0.926000
$375$	22.6617	1.17025
$376$	−5.20562	−0.268459
$377$	−7.96766	−0.410355
$378$	−3.70718	−0.190677
$379$	−2.69400	−0.138381	−0.0691907	−	0.997603i	$-0.522042\pi$
$379$	−2.69400	−0.138381	−0.0691907	+	0.997603i	$0.522042\pi$
$380$	−3.59194	−0.184262
$381$	46.9101	2.40328
$382$	6.27481	0.321047
$383$	−6.82266	−0.348622	−0.174311	−	0.984691i	$-0.555770\pi$
$383$	−6.82266	−0.348622	−0.174311	+	0.984691i	$0.555770\pi$
$384$	−2.26646	−0.115660
$385$	−15.7524	−0.802815
$386$	3.92284	0.199667
$387$	3.75592	0.190924
$388$	−16.3577	−0.830437
$389$	2.29193	0.116205	0.0581026	−	0.998311i	$-0.481495\pi$
$389$	2.29193	0.116205	0.0581026	+	0.998311i	$0.481495\pi$
$390$	−12.2599	−0.620803
$391$	39.8411	2.01485
$392$	−3.40919	−0.172190
$393$	4.06495	0.205050
$394$	−9.11751	−0.459333
$395$	32.7603	1.64835
$396$	7.32865	0.368279
$397$	30.3369	1.52257	0.761283	−	0.648420i	$-0.224570\pi$
$397$	30.3369	1.52257	0.761283	+	0.648420i	$0.224570\pi$
$398$	26.6666	1.33667
$399$	−6.36469	−0.318633
$400$	0.874739	0.0437370
$401$	18.5970	0.928689	0.464344	−	0.885655i	$-0.346290\pi$
$401$	18.5970	0.928689	0.464344	+	0.885655i	$0.346290\pi$
$402$	7.71909	0.384993
$403$	16.3535	0.814624
$404$	−12.6725	−0.630480
$405$	−26.2846	−1.30609
$406$	6.76522	0.335752
$407$	−20.0873	−0.995692
$408$	−11.8342	−0.585880
$409$	−13.8231	−0.683510	−0.341755	−	0.939789i	$-0.611021\pi$
$409$	−13.8231	−0.683510	−0.341755	+	0.939789i	$0.611021\pi$
$410$	3.44085	0.169932
$411$	−34.6008	−1.70673
$412$	11.9495	0.588712
$413$	−7.24322	−0.356416
$414$	16.3045	0.801324
$415$	−15.9742	−0.784145
$416$	2.23174	0.109420
$417$	1.22207	0.0598451
$418$	−5.08265	−0.248600
$419$	−22.0960	−1.07946	−0.539731	−	0.841838i	$-0.681474\pi$
$419$	−22.0960	−1.07946	−0.539731	+	0.841838i	$0.681474\pi$
$420$	10.4097	0.507941
$421$	30.3022	1.47684	0.738420	−	0.674342i	$-0.235572\pi$
$421$	30.3022	1.47684	0.738420	+	0.674342i	$0.235572\pi$
$422$	5.11195	0.248846
$423$	−11.1235	−0.540842
$424$	−8.52728	−0.414121
$425$	4.56741	0.221552
$426$	−31.5928	−1.53067
$427$	22.6493	1.09608
$428$	7.66967	0.370727
$429$	−17.3479	−0.837566
$430$	4.26032	0.205451
$431$	−11.7682	−0.566856	−0.283428	−	0.958994i	$-0.591472\pi$
$431$	−11.7682	−0.566856	−0.283428	+	0.958994i	$0.591472\pi$
$432$	1.95635	0.0941252
$433$	39.9921	1.92190	0.960950	−	0.276723i	$-0.0892484\pi$
$433$	39.9921	1.92190	0.960950	+	0.276723i	$0.0892484\pi$
$434$	−13.8855	−0.666525
$435$	19.6123	0.940336
$436$	9.64208	0.461772
$437$	−11.3077	−0.540920
$438$	−31.0207	−1.48223
$439$	26.3829	1.25919	0.629594	−	0.776924i	$-0.283221\pi$
$439$	26.3829	1.25919	0.629594	+	0.776924i	$0.283221\pi$
$440$	8.31285	0.396300
$441$	−7.28484	−0.346897
$442$	11.6529	0.554274
$443$	24.8648	1.18136	0.590682	−	0.806904i	$-0.298859\pi$
$443$	24.8648	1.18136	0.590682	+	0.806904i	$0.298859\pi$
$444$	13.2744	0.629973
$445$	14.8266	0.702850
$446$	−10.2686	−0.486234
$447$	21.5910	1.02122
$448$	−1.89494	−0.0895276
$449$	11.6856	0.551476	0.275738	−	0.961233i	$-0.411078\pi$
$449$	11.6856	0.551476	0.275738	+	0.961233i	$0.411078\pi$
$450$	1.86916	0.0881132
$451$	4.86886	0.229266
$452$	17.3480	0.815981
$453$	−21.2086	−0.996467
$454$	27.7155	1.30075
$455$	−10.2503	−0.480540
$456$	3.35878	0.157289
$457$	25.2786	1.18248	0.591241	−	0.806495i	$-0.298638\pi$
$457$	25.2786	1.18248	0.591241	+	0.806495i	$0.298638\pi$
$458$	−0.754263	−0.0352444
$459$	10.2150	0.476796
$460$	18.4941	0.862294
$461$	11.0927	0.516641	0.258320	−	0.966059i	$-0.416831\pi$
$461$	11.0927	0.516641	0.258320	+	0.966059i	$0.416831\pi$
$462$	14.7299	0.685296
$463$	−35.5687	−1.65302	−0.826510	−	0.562922i	$-0.809677\pi$
$463$	−35.5687	−1.65302	−0.826510	+	0.562922i	$0.809677\pi$
$464$	−3.57015	−0.165740
$465$	−40.2538	−1.86673
$466$	12.8557	0.595528
$467$	−20.9782	−0.970755	−0.485377	−	0.874305i	$-0.661318\pi$
$467$	−20.9782	−0.970755	−0.485377	+	0.874305i	$0.661318\pi$
$468$	4.76884	0.220440
$469$	6.45379	0.298008
$470$	−12.6173	−0.581993
$471$	−21.8898	−1.00863
$472$	3.82240	0.175940
$473$	6.02842	0.277187
$474$	−30.6338	−1.40706
$475$	−1.29632	−0.0594793
$476$	−9.89435	−0.453507
$477$	−18.2213	−0.834295
$478$	−15.2467	−0.697368
$479$	−4.55398	−0.208077	−0.104038	−	0.994573i	$-0.533176\pi$
$479$	−4.55398	−0.208077	−0.104038	+	0.994573i	$0.533176\pi$
$480$	−5.49340	−0.250738
$481$	−13.0711	−0.595989
$482$	9.91861	0.451780
$483$	32.7705	1.49111
$484$	0.762817	0.0346735
$485$	−39.6476	−1.80031
$486$	18.7094	0.848677
$487$	−25.2927	−1.14612	−0.573061	−	0.819513i	$-0.694244\pi$
$487$	−25.2927	−1.14612	−0.573061	+	0.819513i	$0.694244\pi$
$488$	−11.9525	−0.541065
$489$	−13.3466	−0.603553
$490$	−8.26316	−0.373291
$491$	−27.6014	−1.24564	−0.622818	−	0.782367i	$-0.714012\pi$
$491$	−27.6014	−1.24564	−0.622818	+	0.782367i	$0.714012\pi$
$492$	−3.21750	−0.145056
$493$	−18.6414	−0.839564
$494$	−3.30734	−0.148804
$495$	17.7631	0.798391
$496$	7.32766	0.329022
$497$	−26.4141	−1.18484
$498$	14.9373	0.669358
$499$	−27.1841	−1.21693	−0.608464	−	0.793582i	$-0.708214\pi$
$499$	−27.1841	−1.21693	−0.608464	+	0.793582i	$0.708214\pi$
$500$	−9.99875	−0.447158
$501$	35.7308	1.59633
$502$	−23.8775	−1.06570
$503$	16.0083	0.713773	0.356886	−	0.934148i	$-0.383838\pi$
$503$	16.0083	0.713773	0.356886	+	0.934148i	$0.383838\pi$
$504$	−4.04915	−0.180364
$505$	−30.7154	−1.36682
$506$	26.1695	1.16338
$507$	18.1754	0.807199
$508$	−20.6975	−0.918305
$509$	−11.4008	−0.505332	−0.252666	−	0.967554i	$-0.581307\pi$
$509$	−11.4008	−0.505332	−0.252666	+	0.967554i	$0.581307\pi$
$510$	−28.6835	−1.27013
$511$	−25.9359	−1.14734
$512$	1.00000	0.0441942
$513$	−2.89922	−0.128004
$514$	−9.14491	−0.403365
$515$	28.9631	1.27627
$516$	−3.98378	−0.175376
$517$	−17.8537	−0.785204
$518$	11.0985	0.487638
$519$	−9.67001	−0.424466
$520$	5.40927	0.237212
$521$	−20.4170	−0.894484	−0.447242	−	0.894413i	$-0.647594\pi$
$521$	−20.4170	−0.894484	−0.447242	+	0.894413i	$0.647594\pi$
$522$	−7.62877	−0.333902
$523$	22.6230	0.989234	0.494617	−	0.869111i	$-0.335308\pi$
$523$	22.6230	0.989234	0.494617	+	0.869111i	$0.335308\pi$
$524$	−1.79353	−0.0783507
$525$	3.75683	0.163962
$526$	8.24409	0.359459
$527$	38.2610	1.66668
$528$	−7.77326	−0.338288
$529$	35.2210	1.53135
$530$	−20.6683	−0.897774
$531$	8.16779	0.354452
$532$	2.80821	0.121751
$533$	3.16823	0.137231
$534$	−13.8642	−0.599964
$535$	18.5896	0.803700
$536$	−3.40580	−0.147108
$537$	−18.2305	−0.786703
$538$	−7.88919	−0.340127
$539$	−11.6925	−0.503632
$540$	4.74179	0.204054
$541$	−13.6611	−0.587335	−0.293667	−	0.955908i	$-0.594876\pi$
$541$	−13.6611	−0.587335	−0.293667	+	0.955908i	$0.594876\pi$
$542$	−0.541077	−0.0232412
$543$	−36.3218	−1.55872
$544$	5.22145	0.223868
$545$	23.3703	1.00108
$546$	9.58490	0.410196
$547$	11.9754	0.512033	0.256017	−	0.966672i	$-0.417590\pi$
$547$	11.9754	0.512033	0.256017	+	0.966672i	$0.417590\pi$
$548$	15.2665	0.652152
$549$	−25.5404	−1.09004
$550$	3.00009	0.127924
$551$	5.29079	0.225395
$552$	−17.2937	−0.736067
$553$	−25.6124	−1.08915
$554$	19.2657	0.818523
$555$	32.1742	1.36572
$556$	−0.539200	−0.0228672
$557$	−31.4385	−1.33209	−0.666047	−	0.745910i	$-0.732015\pi$
$557$	−31.4385	−1.33209	−0.666047	+	0.745910i	$0.732015\pi$
$558$	15.6579	0.662852
$559$	3.92276	0.165915
$560$	−4.59293	−0.194087
$561$	−40.5877	−1.71361
$562$	−11.5291	−0.486327
$563$	15.6767	0.660692	0.330346	−	0.943860i	$-0.392835\pi$
$563$	15.6767	0.660692	0.330346	+	0.943860i	$0.392835\pi$
$564$	11.7983	0.496798
$565$	42.0478	1.76897
$566$	8.81217	0.370403
$567$	20.5496	0.863003
$568$	13.9393	0.584879
$569$	−8.32468	−0.348989	−0.174494	−	0.984658i	$-0.555829\pi$
$569$	−8.32468	−0.348989	−0.174494	+	0.984658i	$0.555829\pi$
$570$	8.14096	0.340987
$571$	7.63198	0.319389	0.159694	−	0.987167i	$-0.448949\pi$
$571$	7.63198	0.319389	0.159694	+	0.987167i	$0.448949\pi$
$572$	7.65421	0.320039
$573$	−14.2216	−0.594115
$574$	−2.69010	−0.112282
$575$	6.67449	0.278346
$576$	2.13682	0.0890343
$577$	−31.9587	−1.33046	−0.665229	−	0.746639i	$-0.731666\pi$
$577$	−31.9587	−1.33046	−0.665229	+	0.746639i	$0.731666\pi$
$578$	10.2636	0.426907
$579$	−8.89093	−0.369495
$580$	−8.65327	−0.359308
$581$	12.4888	0.518124
$582$	37.0741	1.53677
$583$	−29.2460	−1.21125
$584$	13.6869	0.566368
$585$	11.5587	0.477891
$586$	−30.0228	−1.24023
$587$	22.2003	0.916303	0.458151	−	0.888874i	$-0.348512\pi$
$587$	22.2003	0.916303	0.458151	+	0.888874i	$0.348512\pi$
$588$	7.72679	0.318647
$589$	−10.8592	−0.447447
$590$	9.26468	0.381421
$591$	20.6644	0.850021
$592$	−5.85688	−0.240716
$593$	29.2076	1.19941	0.599706	−	0.800221i	$-0.295284\pi$
$593$	29.2076	1.19941	0.599706	+	0.800221i	$0.295284\pi$
$594$	6.70970	0.275302
$595$	−23.9818	−0.983157
$596$	−9.52633	−0.390214
$597$	−60.4386	−2.47359
$598$	17.0288	0.696360
$599$	−0.621801	−0.0254061	−0.0127031	−	0.999919i	$-0.504044\pi$
$599$	−0.621801	−0.0254061	−0.0127031	+	0.999919i	$0.504044\pi$
$600$	−1.98256	−0.0809376
$601$	−20.4158	−0.832777	−0.416389	−	0.909187i	$-0.636704\pi$
$601$	−20.4158	−0.832777	−0.416389	+	0.909187i	$0.636704\pi$
$602$	−3.33076	−0.135752
$603$	−7.27759	−0.296366
$604$	9.35761	0.380756
$605$	1.84891	0.0751687
$606$	28.7216	1.16674
$607$	−7.48497	−0.303806	−0.151903	−	0.988395i	$-0.548540\pi$
$607$	−7.48497	−0.303806	−0.151903	+	0.988395i	$0.548540\pi$
$608$	−1.48195	−0.0601011
$609$	−15.3331	−0.621328
$610$	−28.9703	−1.17297
$611$	−11.6176	−0.469998
$612$	11.1573	0.451008
$613$	−0.0428500	−0.00173070	−0.000865348	−	1.00000i	$-0.500275\pi$
$613$	−0.0428500	−0.00173070	−0.000865348		1.00000i	$0.500275\pi$
$614$	1.17401	0.0473793
$615$	−7.79854	−0.314467
$616$	−6.49908	−0.261855
$617$	−13.8270	−0.556654	−0.278327	−	0.960486i	$-0.589780\pi$
$617$	−13.8270	−0.556654	−0.278327	+	0.960486i	$0.589780\pi$
$618$	−27.0831	−1.08944
$619$	−15.8911	−0.638716	−0.319358	−	0.947634i	$-0.603467\pi$
$619$	−15.8911	−0.638716	−0.319358	+	0.947634i	$0.603467\pi$
$620$	17.7607	0.713286
$621$	14.9275	0.599020
$622$	−0.454119	−0.0182085
$623$	−11.5916	−0.464408
$624$	−5.05815	−0.202488
$625$	−28.6085	−1.14434
$626$	−6.05215	−0.241892
$627$	11.5196	0.460048
$628$	9.65815	0.385402
$629$	−30.5814	−1.21936
$630$	−9.81428	−0.391010
$631$	−35.0072	−1.39361	−0.696807	−	0.717259i	$-0.745396\pi$
$631$	−35.0072	−1.39361	−0.696807	+	0.717259i	$0.745396\pi$
$632$	13.5162	0.537644
$633$	−11.5860	−0.460503
$634$	−20.3586	−0.808544
$635$	−50.1664	−1.99079
$636$	19.3267	0.766354
$637$	−7.60845	−0.301458
$638$	−12.2445	−0.484765
$639$	29.7858	1.17831
$640$	2.42379	0.0958086
$641$	−33.1020	−1.30745	−0.653725	−	0.756732i	$-0.726795\pi$
$641$	−33.1020	−1.30745	−0.653725	+	0.756732i	$0.726795\pi$
$642$	−17.3830	−0.686051
$643$	29.4054	1.15964	0.579818	−	0.814746i	$-0.303124\pi$
$643$	29.4054	1.15964	0.579818	+	0.814746i	$0.303124\pi$
$644$	−14.4589	−0.569761
$645$	−9.65582	−0.380198
$646$	−7.73794	−0.304445
$647$	−45.0378	−1.77062	−0.885309	−	0.465002i	$-0.846054\pi$
$647$	−45.0378	−1.77062	−0.885309	+	0.465002i	$0.846054\pi$
$648$	−10.8445	−0.426011
$649$	13.1097	0.514599
$650$	1.95220	0.0765714
$651$	31.4709	1.23344
$652$	5.88875	0.230621
$653$	21.0661	0.824382	0.412191	−	0.911097i	$-0.364764\pi$
$653$	21.0661	0.824382	0.412191	+	0.911097i	$0.364764\pi$
$654$	−21.8533	−0.854533
$655$	−4.34713	−0.169856
$656$	1.41962	0.0554268
$657$	29.2465	1.14101
$658$	9.86435	0.384552
$659$	43.2200	1.68361	0.841806	−	0.539780i	$-0.181493\pi$
$659$	43.2200	1.68361	0.841806	+	0.539780i	$0.181493\pi$
$660$	−18.8407	−0.733374
$661$	−7.50691	−0.291985	−0.145992	−	0.989286i	$-0.546638\pi$
$661$	−7.50691	−0.291985	−0.145992	+	0.989286i	$0.546638\pi$
$662$	−18.3602	−0.713588
$663$	−26.4109	−1.02571
$664$	−6.59062	−0.255765
$665$	6.80651	0.263945
$666$	−12.5151	−0.484951
$667$	−27.2412	−1.05478
$668$	−15.7650	−0.609968
$669$	23.2734	0.899802
$670$	−8.25493	−0.318916
$671$	−40.9935	−1.58254
$672$	4.29480	0.165676
$673$	−27.7624	−1.07016	−0.535081	−	0.844801i	$-0.679719\pi$
$673$	−27.7624	−1.07016	−0.535081	+	0.844801i	$0.679719\pi$
$674$	18.8841	0.727387
$675$	1.71130	0.0658680
$676$	−8.01931	−0.308435
$677$	15.1613	0.582696	0.291348	−	0.956617i	$-0.405896\pi$
$677$	15.1613	0.582696	0.291348	+	0.956617i	$0.405896\pi$
$678$	−39.3185	−1.51002
$679$	30.9969	1.18955
$680$	12.6557	0.485323
$681$	−62.8160	−2.40711
$682$	25.1316	0.962341
$683$	−42.9017	−1.64159	−0.820794	−	0.571224i	$-0.806469\pi$
$683$	−42.9017	−1.64159	−0.820794	+	0.571224i	$0.806469\pi$
$684$	−3.16667	−0.121081
$685$	37.0027	1.41380
$686$	19.7248	0.753097
$687$	1.70950	0.0652217
$688$	1.75771	0.0670121
$689$	−19.0307	−0.725013
$690$	−41.9161	−1.59572
$691$	22.6825	0.862883	0.431441	−	0.902141i	$-0.358005\pi$
$691$	22.6825	0.862883	0.431441	+	0.902141i	$0.358005\pi$
$692$	4.26658	0.162191
$693$	−13.8874	−0.527538
$694$	9.26492	0.351692
$695$	−1.30690	−0.0495737
$696$	8.09158	0.306711
$697$	7.41247	0.280767
$698$	6.33249	0.239688
$699$	−29.1368	−1.10206
$700$	−1.65758	−0.0626506
$701$	37.2885	1.40837	0.704183	−	0.710019i	$-0.251314\pi$
$701$	37.2885	1.40837	0.704183	+	0.710019i	$0.251314\pi$
$702$	4.36608	0.164787
$703$	8.67962	0.327358
$704$	3.42970	0.129262
$705$	28.5966	1.07701
$706$	23.2848	0.876334
$707$	24.0136	0.903125
$708$	−8.66330	−0.325587
$709$	20.1388	0.756328	0.378164	−	0.925739i	$-0.376555\pi$
$709$	20.1388	0.756328	0.378164	+	0.925739i	$0.376555\pi$
$710$	33.7858	1.26796
$711$	28.8817	1.08315
$712$	6.11714	0.229249
$713$	55.9120	2.09392
$714$	22.4251	0.839238
$715$	18.5522	0.693812
$716$	8.04360	0.300603
$717$	34.5560	1.29052
$718$	28.3364	1.05750
$719$	−28.3880	−1.05869	−0.529347	−	0.848405i	$-0.677563\pi$
$719$	−28.3880	−1.05869	−0.529347	+	0.848405i	$0.677563\pi$
$720$	5.17920	0.193017
$721$	−22.6437	−0.843295
$722$	−16.8038	−0.625373
$723$	−22.4801	−0.836044
$724$	16.0258	0.595594
$725$	−3.12295	−0.115983
$726$	−1.72889	−0.0641652
$727$	12.3392	0.457637	0.228818	−	0.973469i	$-0.426514\pi$
$727$	12.3392	0.457637	0.228818	+	0.973469i	$0.426514\pi$
$728$	−4.22903	−0.156738
$729$	−9.87070	−0.365582
$730$	33.1741	1.22783
$731$	9.17781	0.339453
$732$	27.0898	1.00127
$733$	−13.6853	−0.505476	−0.252738	−	0.967535i	$-0.581331\pi$
$733$	−13.6853	−0.505476	−0.252738	+	0.967535i	$0.581331\pi$
$734$	29.6842	1.09566
$735$	18.7281	0.690796
$736$	7.63027	0.281255
$737$	−11.6809	−0.430270
$738$	3.03347	0.111664
$739$	−22.4139	−0.824508	−0.412254	−	0.911069i	$-0.635258\pi$
$739$	−22.4139	−0.824508	−0.412254	+	0.911069i	$0.635258\pi$
$740$	−14.1958	−0.521849
$741$	7.49594	0.275370
$742$	16.1587	0.593205
$743$	20.9692	0.769285	0.384642	−	0.923066i	$-0.374325\pi$
$743$	20.9692	0.769285	0.384642	+	0.923066i	$0.374325\pi$
$744$	−16.6078	−0.608872
$745$	−23.0898	−0.845944
$746$	−3.55535	−0.130170
$747$	−14.0830	−0.515269
$748$	17.9080	0.654781
$749$	−14.5336	−0.531045
$750$	22.6617	0.827489
$751$	−47.7341	−1.74184	−0.870921	−	0.491424i	$-0.836477\pi$
$751$	−47.7341	−1.74184	−0.870921	+	0.491424i	$0.836477\pi$
$752$	−5.20562	−0.189829
$753$	54.1173	1.97214
$754$	−7.96766	−0.290165
$755$	22.6808	0.825440
$756$	−3.70718	−0.134829
$757$	−4.25799	−0.154759	−0.0773797	−	0.997002i	$-0.524655\pi$
$757$	−4.25799	−0.154759	−0.0773797	+	0.997002i	$0.524655\pi$
$758$	−2.69400	−0.0978504
$759$	−59.3120	−2.15289
$760$	−3.59194	−0.130293
$761$	−31.4297	−1.13933	−0.569663	−	0.821879i	$-0.692926\pi$
$761$	−31.4297	−1.13933	−0.569663	+	0.821879i	$0.692926\pi$
$762$	46.9101	1.69937
$763$	−18.2712	−0.661461
$764$	6.27481	0.227015
$765$	27.0429	0.977739
$766$	−6.82266	−0.246513
$767$	8.53062	0.308023
$768$	−2.26646	−0.0817837
$769$	52.9652	1.90997	0.954986	−	0.296650i	$-0.0958694\pi$
$769$	52.9652	1.90997	0.954986	+	0.296650i	$0.0958694\pi$
$770$	−15.7524	−0.567676
$771$	20.7265	0.746448
$772$	3.92284	0.141186
$773$	−16.5484	−0.595206	−0.297603	−	0.954690i	$-0.596187\pi$
$773$	−16.5484	−0.595206	−0.297603	+	0.954690i	$0.596187\pi$
$774$	3.75592	0.135004
$775$	6.40979	0.230247
$776$	−16.3577	−0.587208
$777$	−25.1542	−0.902400
$778$	2.29193	0.0821695
$779$	−2.10381	−0.0753767
$780$	−12.2599	−0.438974
$781$	47.8075	1.71069
$782$	39.8411	1.42471
$783$	−6.98448	−0.249605
$784$	−3.40919	−0.121757
$785$	23.4093	0.835514
$786$	4.06495	0.144992
$787$	13.2397	0.471944	0.235972	−	0.971760i	$-0.424173\pi$
$787$	13.2397	0.471944	0.235972	+	0.971760i	$0.424173\pi$
$788$	−9.11751	−0.324798
$789$	−18.6849	−0.665199
$790$	32.7603	1.16556
$791$	−32.8734	−1.16884
$792$	7.32865	0.260412
$793$	−26.6750	−0.947255
$794$	30.3369	1.07662
$795$	46.8438	1.66138
$796$	26.6666	0.945172
$797$	53.3184	1.88863	0.944317	−	0.329037i	$-0.106724\pi$
$797$	53.3184	1.88863	0.944317	+	0.329037i	$0.106724\pi$
$798$	−6.36469	−0.225308
$799$	−27.1809	−0.961591
$800$	0.874739	0.0309267
$801$	13.0712	0.461849
$802$	18.5970	0.656682
$803$	46.9419	1.65654
$804$	7.71909	0.272231
$805$	−35.0453	−1.23519
$806$	16.3535	0.576026
$807$	17.8805	0.629424
$808$	−12.6725	−0.445816
$809$	−14.3632	−0.504982	−0.252491	−	0.967599i	$-0.581250\pi$
$809$	−14.3632	−0.504982	−0.252491	+	0.967599i	$0.581250\pi$
$810$	−26.2846	−0.923548
$811$	−56.3084	−1.97726	−0.988628	−	0.150382i	$-0.951950\pi$
$811$	−56.3084	−1.97726	−0.988628	+	0.150382i	$0.951950\pi$
$812$	6.76522	0.237413
$813$	1.22633	0.0430091
$814$	−20.0873	−0.704060
$815$	14.2731	0.499964
$816$	−11.8342	−0.414279
$817$	−2.60484	−0.0911320
$818$	−13.8231	−0.483315
$819$	−9.03668	−0.315767
$820$	3.44085	0.120160
$821$	−28.1245	−0.981553	−0.490777	−	0.871285i	$-0.663287\pi$
$821$	−28.1245	−0.981553	−0.490777	+	0.871285i	$0.663287\pi$
$822$	−34.6008	−1.20684
$823$	−50.1530	−1.74822	−0.874112	−	0.485724i	$-0.838556\pi$
$823$	−50.1530	−1.74822	−0.874112	+	0.485724i	$0.838556\pi$
$824$	11.9495	0.416282
$825$	−6.79957	−0.236731
$826$	−7.24322	−0.252024
$827$	−37.6576	−1.30948	−0.654742	−	0.755853i	$-0.727223\pi$
$827$	−37.6576	−1.30948	−0.654742	+	0.755853i	$0.727223\pi$
$828$	16.3045	0.566621
$829$	−17.9933	−0.624932	−0.312466	−	0.949929i	$-0.601155\pi$
$829$	−17.9933	−0.624932	−0.312466	+	0.949929i	$0.601155\pi$
$830$	−15.9742	−0.554474
$831$	−43.6649	−1.51472
$832$	2.23174	0.0773718
$833$	−17.8009	−0.616766
$834$	1.22207	0.0423169
$835$	−38.2111	−1.32235
$836$	−5.08265	−0.175787
$837$	14.3355	0.495507
$838$	−22.0960	−0.763295
$839$	−6.92073	−0.238930	−0.119465	−	0.992838i	$-0.538118\pi$
$839$	−6.92073	−0.238930	−0.119465	+	0.992838i	$0.538118\pi$
$840$	10.4097	0.359168
$841$	−16.2540	−0.560484
$842$	30.3022	1.04428
$843$	26.1303	0.899974
$844$	5.11195	0.175961
$845$	−19.4371	−0.668657
$846$	−11.1235	−0.382433
$847$	−1.44549	−0.0496678
$848$	−8.52728	−0.292828
$849$	−19.9724	−0.685451
$850$	4.56741	0.156661
$851$	−44.6896	−1.53194
$852$	−31.5928	−1.08235
$853$	−6.57654	−0.225176	−0.112588	−	0.993642i	$-0.535914\pi$
$853$	−6.57654	−0.225176	−0.112588	+	0.993642i	$0.535914\pi$
$854$	22.6493	0.775044
$855$	−7.67533	−0.262491
$856$	7.66967	0.262144
$857$	2.36421	0.0807600	0.0403800	−	0.999184i	$-0.487143\pi$
$857$	2.36421	0.0807600	0.0403800	+	0.999184i	$0.487143\pi$
$858$	−17.3479	−0.592248
$859$	37.2623	1.27137	0.635687	−	0.771947i	$-0.280717\pi$
$859$	37.2623	1.27137	0.635687	+	0.771947i	$0.280717\pi$
$860$	4.26032	0.145276
$861$	6.09698	0.207785
$862$	−11.7682	−0.400827
$863$	−42.9282	−1.46129	−0.730647	−	0.682756i	$-0.760781\pi$
$863$	−42.9282	−1.46129	−0.730647	+	0.682756i	$0.760781\pi$
$864$	1.95635	0.0665565
$865$	10.3413	0.351614
$866$	39.9921	1.35899
$867$	−23.2619	−0.790015
$868$	−13.8855	−0.471304
$869$	46.3564	1.57253
$870$	19.6123	0.664918
$871$	−7.60087	−0.257546
$872$	9.64208	0.326522
$873$	−34.9535	−1.18300
$874$	−11.3077	−0.382488
$875$	18.9471	0.640527
$876$	−31.0207	−1.04809
$877$	31.9086	1.07748	0.538738	−	0.842474i	$-0.318901\pi$
$877$	31.9086	1.07748	0.538738	+	0.842474i	$0.318901\pi$
$878$	26.3829	0.890381
$879$	68.0454	2.29512
$880$	8.31285	0.280226
$881$	49.2748	1.66011	0.830055	−	0.557682i	$-0.188309\pi$
$881$	49.2748	1.66011	0.830055	+	0.557682i	$0.188309\pi$
$882$	−7.28484	−0.245293
$883$	−52.5298	−1.76777	−0.883884	−	0.467707i	$-0.845080\pi$
$883$	−52.5298	−1.76777	−0.883884	+	0.467707i	$0.845080\pi$
$884$	11.6529	0.391931
$885$	−20.9980	−0.705839
$886$	24.8648	0.835351
$887$	−22.9156	−0.769431	−0.384716	−	0.923035i	$-0.625701\pi$
$887$	−22.9156	−0.769431	−0.384716	+	0.923035i	$0.625701\pi$
$888$	13.2744	0.445459
$889$	39.2206	1.31542
$890$	14.8266	0.496990
$891$	−37.1932	−1.24602
$892$	−10.2686	−0.343820
$893$	7.71448	0.258155
$894$	21.5910	0.722111
$895$	19.4960	0.651678
$896$	−1.89494	−0.0633056
$897$	−38.5950	−1.28865
$898$	11.6856	0.389952
$899$	−26.1608	−0.872512
$900$	1.86916	0.0623054
$901$	−44.5248	−1.48334
$902$	4.86886	0.162115
$903$	7.54902	0.251216
$904$	17.3480	0.576986
$905$	38.8431	1.29119
$906$	−21.2086	−0.704609
$907$	−30.5345	−1.01388	−0.506941	−	0.861981i	$-0.669224\pi$
$907$	−30.5345	−1.01388	−0.506941	+	0.861981i	$0.669224\pi$
$908$	27.7155	0.919771
$909$	−27.0788	−0.898149
$910$	−10.2503	−0.339793
$911$	−35.5044	−1.17631	−0.588157	−	0.808747i	$-0.700146\pi$
$911$	−35.5044	−1.17631	−0.588157	+	0.808747i	$0.700146\pi$
$912$	3.35878	0.111220
$913$	−22.6038	−0.748077
$914$	25.2786	0.836142
$915$	65.6600	2.17065
$916$	−0.754263	−0.0249216
$917$	3.39863	0.112233
$918$	10.2150	0.337146
$919$	−17.3585	−0.572603	−0.286301	−	0.958140i	$-0.592426\pi$
$919$	−17.3585	−0.572603	−0.286301	+	0.958140i	$0.592426\pi$
$920$	18.4941	0.609734
$921$	−2.66085	−0.0876779
$922$	11.0927	0.365320
$923$	31.1089	1.02396
$924$	14.7299	0.484577
$925$	−5.12325	−0.168451
$926$	−35.5687	−1.16886
$927$	25.5341	0.838648
$928$	−3.57015	−0.117196
$929$	24.0674	0.789626	0.394813	−	0.918761i	$-0.370809\pi$
$929$	24.0674	0.789626	0.394813	+	0.918761i	$0.370809\pi$
$930$	−40.2538	−1.31997
$931$	5.05226	0.165581
$932$	12.8557	0.421102
$933$	1.02924	0.0336958
$934$	−20.9782	−0.686427
$935$	43.4051	1.41950
$936$	4.76884	0.155874
$937$	−35.6677	−1.16521	−0.582606	−	0.812755i	$-0.697967\pi$
$937$	−35.6677	−1.16521	−0.582606	+	0.812755i	$0.697967\pi$
$938$	6.45379	0.210724
$939$	13.7169	0.447635
$940$	−12.6173	−0.411531
$941$	−15.1039	−0.492374	−0.246187	−	0.969222i	$-0.579178\pi$
$941$	−15.1039	−0.492374	−0.246187	+	0.969222i	$0.579178\pi$
$942$	−21.8898	−0.713208
$943$	10.8321	0.352741
$944$	3.82240	0.124408
$945$	−8.98541	−0.292295
$946$	6.02842	0.196001
$947$	−8.32933	−0.270667	−0.135333	−	0.990800i	$-0.543211\pi$
$947$	−8.32933	−0.270667	−0.135333	+	0.990800i	$0.543211\pi$
$948$	−30.6338	−0.994940
$949$	30.5457	0.991554
$950$	−1.29632	−0.0420582
$951$	46.1419	1.49625
$952$	−9.89435	−0.320678
$953$	9.49048	0.307427	0.153713	−	0.988115i	$-0.450877\pi$
$953$	9.49048	0.307427	0.153713	+	0.988115i	$0.450877\pi$
$954$	−18.2213	−0.589936
$955$	15.2088	0.492145
$956$	−15.2467	−0.493114
$957$	27.7517	0.897084
$958$	−4.55398	−0.147132
$959$	−28.9291	−0.934170
$960$	−5.49340	−0.177299
$961$	22.6946	0.732084
$962$	−13.0711	−0.421428
$963$	16.3887	0.528119
$964$	9.91861	0.319457
$965$	9.50811	0.306077
$966$	32.7705	1.05437
$967$	21.0160	0.675831	0.337915	−	0.941177i	$-0.390278\pi$
$967$	21.0160	0.675831	0.337915	+	0.941177i	$0.390278\pi$
$968$	0.762817	0.0245179
$969$	17.5377	0.563392
$970$	−39.6476	−1.27301
$971$	47.0774	1.51078	0.755392	−	0.655273i	$-0.227446\pi$
$971$	47.0774	1.51078	0.755392	+	0.655273i	$0.227446\pi$
$972$	18.7094	0.600105
$973$	1.02175	0.0327559
$974$	−25.2927	−0.810430
$975$	−4.42456	−0.141699
$976$	−11.9525	−0.382591
$977$	−6.82337	−0.218299	−0.109149	−	0.994025i	$-0.534813\pi$
$977$	−6.82337	−0.218299	−0.109149	+	0.994025i	$0.534813\pi$
$978$	−13.3466	−0.426777
$979$	20.9799	0.670521
$980$	−8.26316	−0.263957
$981$	20.6034	0.657816
$982$	−27.6014	−0.880797
$983$	30.8977	0.985483	0.492741	−	0.870176i	$-0.335995\pi$
$983$	30.8977	0.985483	0.492741	+	0.870176i	$0.335995\pi$
$984$	−3.21750	−0.102570
$985$	−22.0989	−0.704129
$986$	−18.6414	−0.593662
$987$	−22.3571	−0.711634
$988$	−3.30734	−0.105220
$989$	13.4118	0.426471
$990$	17.7631	0.564548
$991$	24.3024	0.771991	0.385995	−	0.922501i	$-0.373858\pi$
$991$	24.3024	0.771991	0.385995	+	0.922501i	$0.373858\pi$
$992$	7.32766	0.232653
$993$	41.6125	1.32053
$994$	−26.4141	−0.837805
$995$	64.6341	2.04904
$996$	14.9373	0.473308
$997$	−19.2697	−0.610279	−0.305139	−	0.952308i	$-0.598703\pi$
$997$	−19.2697	−0.610279	−0.305139	+	0.952308i	$0.598703\pi$
$998$	−27.1841	−0.860498
$999$	−11.4581	−0.362519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.e.1.13	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.e.1.13	✓	68	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.26646 q^{3} +1.00000 q^{4} +2.42379 q^{5} -2.26646 q^{6} -1.89494 q^{7} +1.00000 q^{8} +2.13682 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.26646 q^{3} +1.00000 q^{4} +2.42379 q^{5} -2.26646 q^{6} -1.89494 q^{7} +1.00000 q^{8} +2.13682 q^{9} +2.42379 q^{10} +3.42970 q^{11} -2.26646 q^{12} +2.23174 q^{13} -1.89494 q^{14} -5.49340 q^{15} +1.00000 q^{16} +5.22145 q^{17} +2.13682 q^{18} -1.48195 q^{19} +2.42379 q^{20} +4.29480 q^{21} +3.42970 q^{22} +7.63027 q^{23} -2.26646 q^{24} +0.874739 q^{25} +2.23174 q^{26} +1.95635 q^{27} -1.89494 q^{28} -3.57015 q^{29} -5.49340 q^{30} +7.32766 q^{31} +1.00000 q^{32} -7.77326 q^{33} +5.22145 q^{34} -4.59293 q^{35} +2.13682 q^{36} -5.85688 q^{37} -1.48195 q^{38} -5.05815 q^{39} +2.42379 q^{40} +1.41962 q^{41} +4.29480 q^{42} +1.75771 q^{43} +3.42970 q^{44} +5.17920 q^{45} +7.63027 q^{46} -5.20562 q^{47} -2.26646 q^{48} -3.40919 q^{49} +0.874739 q^{50} -11.8342 q^{51} +2.23174 q^{52} -8.52728 q^{53} +1.95635 q^{54} +8.31285 q^{55} -1.89494 q^{56} +3.35878 q^{57} -3.57015 q^{58} +3.82240 q^{59} -5.49340 q^{60} -11.9525 q^{61} +7.32766 q^{62} -4.04915 q^{63} +1.00000 q^{64} +5.40927 q^{65} -7.77326 q^{66} -3.40580 q^{67} +5.22145 q^{68} -17.2937 q^{69} -4.59293 q^{70} +13.9393 q^{71} +2.13682 q^{72} +13.6869 q^{73} -5.85688 q^{74} -1.98256 q^{75} -1.48195 q^{76} -6.49908 q^{77} -5.05815 q^{78} +13.5162 q^{79} +2.42379 q^{80} -10.8445 q^{81} +1.41962 q^{82} -6.59062 q^{83} +4.29480 q^{84} +12.6557 q^{85} +1.75771 q^{86} +8.09158 q^{87} +3.42970 q^{88} +6.11714 q^{89} +5.17920 q^{90} -4.22903 q^{91} +7.63027 q^{92} -16.6078 q^{93} -5.20562 q^{94} -3.59194 q^{95} -2.26646 q^{96} -16.3577 q^{97} -3.40919 q^{98} +7.32865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9}+O(q^{10}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9	\( 68 q + 68 q^{2} + 25 q^{3} + 68 q^{4} + 20 q^{5} + 25 q^{6} + 29 q^{7} + 68 q^{8} + 87 q^{9} + 20 q^{10} + 46 q^{11} + 25 q^{12} + 30 q^{13} + 29 q^{14} + 13 q^{15} + 68 q^{16} + 73 q^{17} + 87 q^{18} + 56 q^{19} + 20 q^{20} - 5 q^{21} + 46 q^{22} + 63 q^{23} + 25 q^{24} + 88 q^{25} + 30 q^{26} + 67 q^{27} + 29 q^{28} + 43 q^{29} + 13 q^{30} + 68 q^{31} + 68 q^{32} + 26 q^{33} + 73 q^{34} + 50 q^{35} + 87 q^{36} + 8 q^{37} + 56 q^{38} + 6 q^{39} + 20 q^{40} + 64 q^{41} - 5 q^{42} + 52 q^{43} + 46 q^{44} + 7 q^{45} + 63 q^{46} + 94 q^{47} + 25 q^{48} + 91 q^{49} + 88 q^{50} + 20 q^{51} + 30 q^{52} + 38 q^{53} + 67 q^{54} + 37 q^{55} + 29 q^{56} + 4 q^{57} + 43 q^{58} + 84 q^{59} + 13 q^{60} + 26 q^{61} + 68 q^{62} + 22 q^{63} + 68 q^{64} - 20 q^{65} + 26 q^{66} + 54 q^{67} + 73 q^{68} - 11 q^{69} + 50 q^{70} + 46 q^{71} + 87 q^{72} + 62 q^{73} + 8 q^{74} + 54 q^{75} + 56 q^{76} + 67 q^{77} + 6 q^{78} + 67 q^{79} + 20 q^{80} + 120 q^{81} + 64 q^{82} + 130 q^{83} - 5 q^{84} - 24 q^{85} + 52 q^{86} + 72 q^{87} + 46 q^{88} + 61 q^{89} + 7 q^{90} + 43 q^{91} + 63 q^{92} + 40 q^{93} + 94 q^{94} + 55 q^{95} + 25 q^{96} + 41 q^{97} + 91 q^{98} + 106 q^{99}+O(q^{100}) \) 68 * q + 68 * q^2 + 25 * q^3 + 68 * q^4 + 20 * q^5 + 25 * q^6 + 29 * q^7 + 68 * q^8 + 87 * q^9 + 20 * q^10 + 46 * q^11 + 25 * q^12 + 30 * q^13 + 29 * q^14 + 13 * q^15 + 68 * q^16 + 73 * q^17 + 87 * q^18 + 56 * q^19 + 20 * q^20 - 5 * q^21 + 46 * q^22 + 63 * q^23 + 25 * q^24 + 88 * q^25 + 30 * q^26 + 67 * q^27 + 29 * q^28 + 43 * q^29 + 13 * q^30 + 68 * q^31 + 68 * q^32 + 26 * q^33 + 73 * q^34 + 50 * q^35 + 87 * q^36 + 8 * q^37 + 56 * q^38 + 6 * q^39 + 20 * q^40 + 64 * q^41 - 5 * q^42 + 52 * q^43 + 46 * q^44 + 7 * q^45 + 63 * q^46 + 94 * q^47 + 25 * q^48 + 91 * q^49 + 88 * q^50 + 20 * q^51 + 30 * q^52 + 38 * q^53 + 67 * q^54 + 37 * q^55 + 29 * q^56 + 4 * q^57 + 43 * q^58 + 84 * q^59 + 13 * q^60 + 26 * q^61 + 68 * q^62 + 22 * q^63 + 68 * q^64 - 20 * q^65 + 26 * q^66 + 54 * q^67 + 73 * q^68 - 11 * q^69 + 50 * q^70 + 46 * q^71 + 87 * q^72 + 62 * q^73 + 8 * q^74 + 54 * q^75 + 56 * q^76 + 67 * q^77 + 6 * q^78 + 67 * q^79 + 20 * q^80 + 120 * q^81 + 64 * q^82 + 130 * q^83 - 5 * q^84 - 24 * q^85 + 52 * q^86 + 72 * q^87 + 46 * q^88 + 61 * q^89 + 7 * q^90 + 43 * q^91 + 63 * q^92 + 40 * q^93 + 94 * q^94 + 55 * q^95 + 25 * q^96 + 41 * q^97 + 91 * q^98 + 106 * q^99

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