LMFDB - Embedded newform 8015.2.a.j.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.647127 q^{2} -0.415940 q^{3} -1.58123 q^{4} -1.00000 q^{5} +0.269166 q^{6} +1.00000 q^{7} +2.31751 q^{8} -2.82699 q^{9} +O(q^{10})$	\(q-0.647127 q^{2} -0.415940 q^{3} -1.58123 q^{4} -1.00000 q^{5} +0.269166 q^{6} +1.00000 q^{7} +2.31751 q^{8} -2.82699 q^{9} +0.647127 q^{10} -1.53447 q^{11} +0.657696 q^{12} -0.279783 q^{13} -0.647127 q^{14} +0.415940 q^{15} +1.66273 q^{16} +3.36362 q^{17} +1.82943 q^{18} -0.328010 q^{19} +1.58123 q^{20} -0.415940 q^{21} +0.992994 q^{22} +1.30774 q^{23} -0.963946 q^{24} +1.00000 q^{25} +0.181056 q^{26} +2.42368 q^{27} -1.58123 q^{28} -4.22927 q^{29} -0.269166 q^{30} -7.55250 q^{31} -5.71102 q^{32} +0.638246 q^{33} -2.17669 q^{34} -1.00000 q^{35} +4.47012 q^{36} -0.586735 q^{37} +0.212264 q^{38} +0.116373 q^{39} -2.31751 q^{40} +5.90603 q^{41} +0.269166 q^{42} +3.99443 q^{43} +2.42634 q^{44} +2.82699 q^{45} -0.846276 q^{46} -2.35624 q^{47} -0.691596 q^{48} +1.00000 q^{49} -0.647127 q^{50} -1.39906 q^{51} +0.442401 q^{52} -0.955461 q^{53} -1.56843 q^{54} +1.53447 q^{55} +2.31751 q^{56} +0.136433 q^{57} +2.73688 q^{58} +0.727704 q^{59} -0.657696 q^{60} -4.22986 q^{61} +4.88743 q^{62} -2.82699 q^{63} +0.370299 q^{64} +0.279783 q^{65} -0.413026 q^{66} +15.1496 q^{67} -5.31864 q^{68} -0.543943 q^{69} +0.647127 q^{70} -3.93571 q^{71} -6.55159 q^{72} +9.31891 q^{73} +0.379692 q^{74} -0.415940 q^{75} +0.518658 q^{76} -1.53447 q^{77} -0.0753083 q^{78} -9.64065 q^{79} -1.66273 q^{80} +7.47287 q^{81} -3.82196 q^{82} +10.0563 q^{83} +0.657696 q^{84} -3.36362 q^{85} -2.58491 q^{86} +1.75912 q^{87} -3.55614 q^{88} -7.40727 q^{89} -1.82943 q^{90} -0.279783 q^{91} -2.06784 q^{92} +3.14139 q^{93} +1.52479 q^{94} +0.328010 q^{95} +2.37544 q^{96} -7.42669 q^{97} -0.647127 q^{98} +4.33792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−0.647127	−0.457588	−0.228794	−	0.973475i	$-0.573478\pi$
$2$	−0.647127	−0.457588	−0.228794	+	0.973475i	$0.573478\pi$
$3$	−0.415940	−0.240143	−0.120072	−	0.992765i	$-0.538312\pi$
$3$	−0.415940	−0.240143	−0.120072	+	0.992765i	$0.538312\pi$
$4$	−1.58123	−0.790613
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.269166	0.109887
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.31751	0.819363
$9$	−2.82699	−0.942331
$10$	0.647127	0.204640
$11$	−1.53447	−0.462659	−0.231329	−	0.972876i	$-0.574307\pi$
$11$	−1.53447	−0.462659	−0.231329	+	0.972876i	$0.574307\pi$
$12$	0.657696	0.189860
$13$	−0.279783	−0.0775980	−0.0387990	−	0.999247i	$-0.512353\pi$
$13$	−0.279783	−0.0775980	−0.0387990	+	0.999247i	$0.512353\pi$
$14$	−0.647127	−0.172952
$15$	0.415940	0.107395
$16$	1.66273	0.415682
$17$	3.36362	0.815797	0.407899	−	0.913027i	$-0.366262\pi$
$17$	3.36362	0.815797	0.407899	+	0.913027i	$0.366262\pi$
$18$	1.82943	0.431200
$19$	−0.328010	−0.0752507	−0.0376253	−	0.999292i	$-0.511979\pi$
$19$	−0.328010	−0.0752507	−0.0376253	+	0.999292i	$0.511979\pi$
$20$	1.58123	0.353573
$21$	−0.415940	−0.0907656
$22$	0.992994	0.211707
$23$	1.30774	0.272683	0.136342	−	0.990662i	$-0.456466\pi$
$23$	1.30774	0.272683	0.136342	+	0.990662i	$0.456466\pi$
$24$	−0.963946	−0.196765
$25$	1.00000	0.200000
$26$	0.181056	0.0355079
$27$	2.42368	0.466438
$28$	−1.58123	−0.298824
$29$	−4.22927	−0.785356	−0.392678	−	0.919676i	$-0.628451\pi$
$29$	−4.22927	−0.785356	−0.392678	+	0.919676i	$0.628451\pi$
$30$	−0.269166	−0.0491428
$31$	−7.55250	−1.35647	−0.678234	−	0.734846i	$-0.737255\pi$
$31$	−7.55250	−1.35647	−0.678234	+	0.734846i	$0.737255\pi$
$32$	−5.71102	−1.00957
$33$	0.638246	0.111104
$34$	−2.17669	−0.373299
$35$	−1.00000	−0.169031
$36$	4.47012	0.745019
$37$	−0.586735	−0.0964587	−0.0482293	−	0.998836i	$-0.515358\pi$
$37$	−0.586735	−0.0964587	−0.0482293	+	0.998836i	$0.515358\pi$
$38$	0.212264	0.0344338
$39$	0.116373	0.0186346
$40$	−2.31751	−0.366430
$41$	5.90603	0.922367	0.461184	−	0.887305i	$-0.347425\pi$
$41$	5.90603	0.922367	0.461184	+	0.887305i	$0.347425\pi$
$42$	0.269166	0.0415333
$43$	3.99443	0.609145	0.304572	−	0.952489i	$-0.401486\pi$
$43$	3.99443	0.609145	0.304572	+	0.952489i	$0.401486\pi$
$44$	2.42634	0.365784
$45$	2.82699	0.421423
$46$	−0.846276	−0.124777
$47$	−2.35624	−0.343693	−0.171846	−	0.985124i	$-0.554973\pi$
$47$	−2.35624	−0.343693	−0.171846	+	0.985124i	$0.554973\pi$
$48$	−0.691596	−0.0998232
$49$	1.00000	0.142857
$50$	−0.647127	−0.0915176
$51$	−1.39906	−0.195908
$52$	0.442401	0.0613500
$53$	−0.955461	−0.131243	−0.0656213	−	0.997845i	$-0.520903\pi$
$53$	−0.955461	−0.131243	−0.0656213	+	0.997845i	$0.520903\pi$
$54$	−1.56843	−0.213436
$55$	1.53447	0.206907
$56$	2.31751	0.309690
$57$	0.136433	0.0180709
$58$	2.73688	0.359370
$59$	0.727704	0.0947389	0.0473695	−	0.998877i	$-0.484916\pi$
$59$	0.727704	0.0947389	0.0473695	+	0.998877i	$0.484916\pi$
$60$	−0.657696	−0.0849081
$61$	−4.22986	−0.541578	−0.270789	−	0.962639i	$-0.587285\pi$
$61$	−4.22986	−0.541578	−0.270789	+	0.962639i	$0.587285\pi$
$62$	4.88743	0.620704
$63$	−2.82699	−0.356168
$64$	0.370299	0.0462874
$65$	0.279783	0.0347029
$66$	−0.413026	−0.0508400
$67$	15.1496	1.85081	0.925407	−	0.378976i	$-0.123724\pi$
$67$	15.1496	1.85081	0.925407	+	0.378976i	$0.123724\pi$
$68$	−5.31864	−0.644980
$69$	−0.543943	−0.0654830
$70$	0.647127	0.0773465
$71$	−3.93571	−0.467082	−0.233541	−	0.972347i	$-0.575031\pi$
$71$	−3.93571	−0.467082	−0.233541	+	0.972347i	$0.575031\pi$
$72$	−6.55159	−0.772112
$73$	9.31891	1.09070	0.545348	−	0.838210i	$-0.316397\pi$
$73$	9.31891	1.09070	0.545348	+	0.838210i	$0.316397\pi$
$74$	0.379692	0.0441384
$75$	−0.415940	−0.0480286
$76$	0.518658	0.0594941
$77$	−1.53447	−0.174869
$78$	−0.0753083	−0.00852699
$79$	−9.64065	−1.08466	−0.542329	−	0.840166i	$-0.682457\pi$
$79$	−9.64065	−1.08466	−0.542329	+	0.840166i	$0.682457\pi$
$80$	−1.66273	−0.185899
$81$	7.47287	0.830319
$82$	−3.82196	−0.422064
$83$	10.0563	1.10382	0.551908	−	0.833905i	$-0.313900\pi$
$83$	10.0563	1.10382	0.551908	+	0.833905i	$0.313900\pi$
$84$	0.657696	0.0717605
$85$	−3.36362	−0.364836
$86$	−2.58491	−0.278738
$87$	1.75912	0.188598
$88$	−3.55614	−0.379086
$89$	−7.40727	−0.785169	−0.392585	−	0.919716i	$-0.628419\pi$
$89$	−7.40727	−0.785169	−0.392585	+	0.919716i	$0.628419\pi$
$90$	−1.82943	−0.192838
$91$	−0.279783	−0.0293293
$92$	−2.06784	−0.215587
$93$	3.14139	0.325747
$94$	1.52479	0.157270
$95$	0.328010	0.0336531
$96$	2.37544	0.242443
$97$	−7.42669	−0.754067	−0.377033	−	0.926200i	$-0.623056\pi$
$97$	−7.42669	−0.754067	−0.377033	+	0.926200i	$0.623056\pi$
$98$	−0.647127	−0.0653697
$99$	4.33792	0.435978
$100$	−1.58123	−0.158123
$101$	12.1062	1.20461	0.602306	−	0.798265i	$-0.294249\pi$
$101$	12.1062	1.20461	0.602306	+	0.798265i	$0.294249\pi$
$102$	0.905373	0.0896453
$103$	10.1128	0.996446	0.498223	−	0.867049i	$-0.333986\pi$
$103$	10.1128	0.996446	0.498223	+	0.867049i	$0.333986\pi$
$104$	−0.648401	−0.0635809
$105$	0.415940	0.0405916
$106$	0.618305	0.0600551
$107$	2.16196	0.209005	0.104502	−	0.994525i	$-0.466675\pi$
$107$	2.16196	0.209005	0.104502	+	0.994525i	$0.466675\pi$
$108$	−3.83239	−0.368772
$109$	3.63113	0.347800	0.173900	−	0.984763i	$-0.444363\pi$
$109$	3.63113	0.347800	0.173900	+	0.984763i	$0.444363\pi$
$110$	−0.992994	−0.0946783
$111$	0.244047	0.0231639
$112$	1.66273	0.157113
$113$	11.2881	1.06190	0.530948	−	0.847404i	$-0.321836\pi$
$113$	11.2881	1.06190	0.530948	+	0.847404i	$0.321836\pi$
$114$	−0.0882893	−0.00826905
$115$	−1.30774	−0.121948
$116$	6.68743	0.620913
$117$	0.790946	0.0731230
$118$	−0.470917	−0.0433514
$119$	3.36362	0.308342
$120$	0.963946	0.0879958
$121$	−8.64542	−0.785947
$122$	2.73726	0.247820
$123$	−2.45656	−0.221500
$124$	11.9422	1.07244
$125$	−1.00000	−0.0894427
$126$	1.82943	0.162978
$127$	6.04679	0.536566	0.268283	−	0.963340i	$-0.413544\pi$
$127$	6.04679	0.536566	0.268283	+	0.963340i	$0.413544\pi$
$128$	11.1824	0.988394
$129$	−1.66144	−0.146282
$130$	−0.181056	−0.0158796
$131$	−17.7005	−1.54650	−0.773250	−	0.634102i	$-0.781370\pi$
$131$	−17.7005	−1.54650	−0.773250	+	0.634102i	$0.781370\pi$
$132$	−1.00921	−0.0878405
$133$	−0.328010	−0.0284421
$134$	−9.80369	−0.846910
$135$	−2.42368	−0.208597
$136$	7.79522	0.668434
$137$	−0.415115	−0.0354657	−0.0177328	−	0.999843i	$-0.505645\pi$
$137$	−0.415115	−0.0354657	−0.0177328	+	0.999843i	$0.505645\pi$
$138$	0.352000	0.0299643
$139$	−16.2555	−1.37877	−0.689386	−	0.724394i	$-0.742120\pi$
$139$	−16.2555	−1.37877	−0.689386	+	0.724394i	$0.742120\pi$
$140$	1.58123	0.133638
$141$	0.980055	0.0825355
$142$	2.54690	0.213731
$143$	0.429318	0.0359014
$144$	−4.70052	−0.391710
$145$	4.22927	0.351222
$146$	−6.03052	−0.499090
$147$	−0.415940	−0.0343062
$148$	0.927761	0.0762615
$149$	−1.96239	−0.160766	−0.0803828	−	0.996764i	$-0.525614\pi$
$149$	−1.96239	−0.160766	−0.0803828	+	0.996764i	$0.525614\pi$
$150$	0.269166	0.0219773
$151$	17.6594	1.43710	0.718551	−	0.695474i	$-0.244806\pi$
$151$	17.6594	1.43710	0.718551	+	0.695474i	$0.244806\pi$
$152$	−0.760166	−0.0616576
$153$	−9.50893	−0.768751
$154$	0.992994	0.0800178
$155$	7.55250	0.606631
$156$	−0.184012	−0.0147328
$157$	9.02740	0.720465	0.360233	−	0.932863i	$-0.382697\pi$
$157$	9.02740	0.720465	0.360233	+	0.932863i	$0.382697\pi$
$158$	6.23873	0.496327
$159$	0.397415	0.0315170
$160$	5.71102	0.451495
$161$	1.30774	0.103065
$162$	−4.83590	−0.379944
$163$	12.2117	0.956492	0.478246	−	0.878226i	$-0.341273\pi$
$163$	12.2117	0.956492	0.478246	+	0.878226i	$0.341273\pi$
$164$	−9.33877	−0.729236
$165$	−0.638246	−0.0496874
$166$	−6.50768	−0.505094
$167$	23.8376	1.84461	0.922306	−	0.386460i	$-0.126302\pi$
$167$	23.8376	1.84461	0.922306	+	0.386460i	$0.126302\pi$
$168$	−0.963946	−0.0743700
$169$	−12.9217	−0.993979
$170$	2.17669	0.166944
$171$	0.927282	0.0709110
$172$	−6.31610	−0.481598
$173$	−9.36766	−0.712210	−0.356105	−	0.934446i	$-0.615895\pi$
$173$	−9.36766	−0.712210	−0.356105	+	0.934446i	$0.615895\pi$
$174$	−1.13838	−0.0863002
$175$	1.00000	0.0755929
$176$	−2.55140	−0.192319
$177$	−0.302681	−0.0227509
$178$	4.79345	0.359284
$179$	1.90633	0.142486	0.0712431	−	0.997459i	$-0.477303\pi$
$179$	1.90633	0.142486	0.0712431	+	0.997459i	$0.477303\pi$
$180$	−4.47012	−0.333183
$181$	13.8556	1.02988	0.514940	−	0.857226i	$-0.327814\pi$
$181$	13.8556	1.02988	0.514940	+	0.857226i	$0.327814\pi$
$182$	0.181056	0.0134207
$183$	1.75937	0.130056
$184$	3.03071	0.223427
$185$	0.586735	0.0431376
$186$	−2.03288	−0.149058
$187$	−5.16135	−0.377436
$188$	3.72575	0.271728
$189$	2.42368	0.176297
$190$	−0.212264	−0.0153993
$191$	8.38294	0.606568	0.303284	−	0.952900i	$-0.401917\pi$
$191$	8.38294	0.606568	0.303284	+	0.952900i	$0.401917\pi$
$192$	−0.154022	−0.0111156
$193$	−0.214867	−0.0154665	−0.00773323	−	0.999970i	$-0.502462\pi$
$193$	−0.214867	−0.0154665	−0.00773323	+	0.999970i	$0.502462\pi$
$194$	4.80602	0.345052
$195$	−0.116373	−0.00833366
$196$	−1.58123	−0.112945
$197$	−17.5555	−1.25078	−0.625388	−	0.780314i	$-0.715059\pi$
$197$	−17.5555	−1.25078	−0.625388	+	0.780314i	$0.715059\pi$
$198$	−2.80719	−0.199498
$199$	−16.6085	−1.17735	−0.588673	−	0.808371i	$-0.700350\pi$
$199$	−16.6085	−1.17735	−0.588673	+	0.808371i	$0.700350\pi$
$200$	2.31751	0.163873
$201$	−6.30131	−0.444460
$202$	−7.83426	−0.551216
$203$	−4.22927	−0.296837
$204$	2.21224	0.154888
$205$	−5.90603	−0.412495
$206$	−6.54428	−0.455962
$207$	−3.69698	−0.256958
$208$	−0.465204	−0.0322561
$209$	0.503320	0.0348154
$210$	−0.269166	−0.0185742
$211$	−16.8072	−1.15706	−0.578529	−	0.815662i	$-0.696373\pi$
$211$	−16.8072	−1.15706	−0.578529	+	0.815662i	$0.696373\pi$
$212$	1.51080	0.103762
$213$	1.63702	0.112167
$214$	−1.39907	−0.0956382
$215$	−3.99443	−0.272418
$216$	5.61691	0.382182
$217$	−7.55250	−0.512697
$218$	−2.34981	−0.159149
$219$	−3.87611	−0.261923
$220$	−2.42634	−0.163584
$221$	−0.941085	−0.0633042
$222$	−0.157929	−0.0105995
$223$	−2.28775	−0.153199	−0.0765995	−	0.997062i	$-0.524406\pi$
$223$	−2.28775	−0.153199	−0.0765995	+	0.997062i	$0.524406\pi$
$224$	−5.71102	−0.381583
$225$	−2.82699	−0.188466
$226$	−7.30484	−0.485911
$227$	−4.20682	−0.279216	−0.139608	−	0.990207i	$-0.544584\pi$
$227$	−4.20682	−0.279216	−0.139608	+	0.990207i	$0.544584\pi$
$228$	−0.215731	−0.0142871
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.846276	0.0558018
$231$	0.638246	0.0419935
$232$	−9.80138	−0.643492
$233$	−12.9529	−0.848575	−0.424287	−	0.905528i	$-0.639475\pi$
$233$	−12.9529	−0.848575	−0.424287	+	0.905528i	$0.639475\pi$
$234$	−0.511843	−0.0334602
$235$	2.35624	0.153704
$236$	−1.15066	−0.0749018
$237$	4.00994	0.260473
$238$	−2.17669	−0.141094
$239$	−27.6351	−1.78756	−0.893782	−	0.448501i	$-0.851958\pi$
$239$	−27.6351	−1.78756	−0.893782	+	0.448501i	$0.851958\pi$
$240$	0.691596	0.0446423
$241$	10.6838	0.688204	0.344102	−	0.938932i	$-0.388183\pi$
$241$	10.6838	0.688204	0.344102	+	0.938932i	$0.388183\pi$
$242$	5.59469	0.359640
$243$	−10.3793	−0.665833
$244$	6.68837	0.428179
$245$	−1.00000	−0.0638877
$246$	1.58971	0.101356
$247$	0.0917718	0.00583930
$248$	−17.5030	−1.11144
$249$	−4.18280	−0.265074
$250$	0.647127	0.0409279
$251$	−14.3355	−0.904846	−0.452423	−	0.891804i	$-0.649440\pi$
$251$	−14.3355	−0.904846	−0.452423	+	0.891804i	$0.649440\pi$
$252$	4.47012	0.281591
$253$	−2.00669	−0.126159
$254$	−3.91304	−0.245526
$255$	1.39906	0.0876128
$256$	−7.97704	−0.498565
$257$	0.119232	0.00743747	0.00371874	−	0.999993i	$-0.498816\pi$
$257$	0.119232	0.00743747	0.00371874	+	0.999993i	$0.498816\pi$
$258$	1.07517	0.0669369
$259$	−0.586735	−0.0364580
$260$	−0.442401	−0.0274365
$261$	11.9561	0.740065
$262$	11.4545	0.707660
$263$	21.1996	1.30722	0.653611	−	0.756831i	$-0.273253\pi$
$263$	21.1996	1.30722	0.653611	+	0.756831i	$0.273253\pi$
$264$	1.47914	0.0910348
$265$	0.955461	0.0586935
$266$	0.212264	0.0130148
$267$	3.08098	0.188553
$268$	−23.9549	−1.46328
$269$	−26.8060	−1.63439	−0.817196	−	0.576359i	$-0.804473\pi$
$269$	−26.8060	−1.63439	−0.817196	+	0.576359i	$0.804473\pi$
$270$	1.56843	0.0954517
$271$	−0.450507	−0.0273663	−0.0136832	−	0.999906i	$-0.504356\pi$
$271$	−0.450507	−0.0273663	−0.0136832	+	0.999906i	$0.504356\pi$
$272$	5.59278	0.339112
$273$	0.116373	0.00704323
$274$	0.268632	0.0162287
$275$	−1.53447	−0.0925317
$276$	0.860097	0.0517717
$277$	−16.6027	−0.997559	−0.498780	−	0.866729i	$-0.666218\pi$
$277$	−16.6027	−0.997559	−0.498780	+	0.866729i	$0.666218\pi$
$278$	10.5194	0.630910
$279$	21.3509	1.27824
$280$	−2.31751	−0.138498
$281$	16.0717	0.958754	0.479377	−	0.877609i	$-0.340863\pi$
$281$	16.0717	0.958754	0.479377	+	0.877609i	$0.340863\pi$
$282$	−0.634221	−0.0377673
$283$	−0.244921	−0.0145590	−0.00727951	−	0.999974i	$-0.502317\pi$
$283$	−0.244921	−0.0145590	−0.00727951	+	0.999974i	$0.502317\pi$
$284$	6.22324	0.369281
$285$	−0.136433	−0.00808157
$286$	−0.277823	−0.0164280
$287$	5.90603	0.348622
$288$	16.1450	0.951354
$289$	−5.68607	−0.334475
$290$	−2.73688	−0.160715
$291$	3.08906	0.181084
$292$	−14.7353	−0.862319
$293$	26.2555	1.53386	0.766932	−	0.641729i	$-0.221783\pi$
$293$	26.2555	1.53386	0.766932	+	0.641729i	$0.221783\pi$
$294$	0.269166	0.0156981
$295$	−0.727704	−0.0423685
$296$	−1.35976	−0.0790347
$297$	−3.71905	−0.215801
$298$	1.26992	0.0735645
$299$	−0.365885	−0.0211597
$300$	0.657696	0.0379721
$301$	3.99443	0.230235
$302$	−11.4279	−0.657601
$303$	−5.03546	−0.289279
$304$	−0.545391	−0.0312803
$305$	4.22986	0.242201
$306$	6.15349	0.351771
$307$	−27.2172	−1.55337	−0.776685	−	0.629890i	$-0.783100\pi$
$307$	−27.2172	−1.55337	−0.776685	+	0.629890i	$0.783100\pi$
$308$	2.42634	0.138253
$309$	−4.20633	−0.239290
$310$	−4.88743	−0.277587
$311$	−29.9187	−1.69654	−0.848268	−	0.529567i	$-0.822354\pi$
$311$	−29.9187	−1.69654	−0.848268	+	0.529567i	$0.822354\pi$
$312$	0.269696	0.0152685
$313$	−24.9196	−1.40854	−0.704269	−	0.709933i	$-0.748725\pi$
$313$	−24.9196	−1.40854	−0.704269	+	0.709933i	$0.748725\pi$
$314$	−5.84188	−0.329676
$315$	2.82699	0.159283
$316$	15.2441	0.857545
$317$	12.9998	0.730144	0.365072	−	0.930979i	$-0.381044\pi$
$317$	12.9998	0.730144	0.365072	+	0.930979i	$0.381044\pi$
$318$	−0.257178	−0.0144218
$319$	6.48967	0.363352
$320$	−0.370299	−0.0207004
$321$	−0.899248	−0.0501911
$322$	−0.846276	−0.0471611
$323$	−1.10330	−0.0613893
$324$	−11.8163	−0.656461
$325$	−0.279783	−0.0155196
$326$	−7.90251	−0.437679
$327$	−1.51033	−0.0835217
$328$	13.6873	0.755754
$329$	−2.35624	−0.129904
$330$	0.413026	0.0227364
$331$	4.63473	0.254748	0.127374	−	0.991855i	$-0.459345\pi$
$331$	4.63473	0.254748	0.127374	+	0.991855i	$0.459345\pi$
$332$	−15.9012	−0.872692
$333$	1.65870	0.0908960
$334$	−15.4260	−0.844073
$335$	−15.1496	−0.827709
$336$	−0.691596	−0.0377296
$337$	−5.16405	−0.281304	−0.140652	−	0.990059i	$-0.544920\pi$
$337$	−5.16405	−0.281304	−0.140652	+	0.990059i	$0.544920\pi$
$338$	8.36200	0.454833
$339$	−4.69518	−0.255007
$340$	5.31864	0.288444
$341$	11.5890	0.627582
$342$	−0.600070	−0.0324481
$343$	1.00000	0.0539949
$344$	9.25713	0.499111
$345$	0.543943	0.0292849
$346$	6.06207	0.325899
$347$	28.2793	1.51811	0.759055	−	0.651026i	$-0.225661\pi$
$347$	28.2793	1.51811	0.759055	+	0.651026i	$0.225661\pi$
$348$	−2.78157	−0.149108
$349$	30.7370	1.64532	0.822658	−	0.568537i	$-0.192490\pi$
$349$	30.7370	1.64532	0.822658	+	0.568537i	$0.192490\pi$
$350$	−0.647127	−0.0345904
$351$	−0.678106	−0.0361946
$352$	8.76336	0.467088
$353$	−32.0370	−1.70516	−0.852578	−	0.522599i	$-0.824962\pi$
$353$	−32.0370	−1.70516	−0.852578	+	0.522599i	$0.824962\pi$
$354$	0.195873	0.0104106
$355$	3.93571	0.208886
$356$	11.7126	0.620765
$357$	−1.39906	−0.0740463
$358$	−1.23364	−0.0652000
$359$	−4.48453	−0.236684	−0.118342	−	0.992973i	$-0.537758\pi$
$359$	−4.48453	−0.236684	−0.118342	+	0.992973i	$0.537758\pi$
$360$	6.55159	0.345299
$361$	−18.8924	−0.994337
$362$	−8.96635	−0.471261
$363$	3.59598	0.188740
$364$	0.442401	0.0231881
$365$	−9.31891	−0.487774
$366$	−1.13854	−0.0595122
$367$	−3.47096	−0.181183	−0.0905913	−	0.995888i	$-0.528876\pi$
$367$	−3.47096	−0.181183	−0.0905913	+	0.995888i	$0.528876\pi$
$368$	2.17442	0.113350
$369$	−16.6963	−0.869176
$370$	−0.379692	−0.0197393
$371$	−0.955461	−0.0496051
$372$	−4.96725	−0.257540
$373$	−14.4619	−0.748810	−0.374405	−	0.927265i	$-0.622153\pi$
$373$	−14.4619	−0.748810	−0.374405	+	0.927265i	$0.622153\pi$
$374$	3.34005	0.172710
$375$	0.415940	0.0214791
$376$	−5.46061	−0.281609
$377$	1.18328	0.0609420
$378$	−1.56843	−0.0806714
$379$	19.4155	0.997308	0.498654	−	0.866801i	$-0.333828\pi$
$379$	19.4155	0.997308	0.498654	+	0.866801i	$0.333828\pi$
$380$	−0.518658	−0.0266066
$381$	−2.51510	−0.128853
$382$	−5.42483	−0.277558
$383$	5.47064	0.279537	0.139768	−	0.990184i	$-0.455364\pi$
$383$	5.47064	0.279537	0.139768	+	0.990184i	$0.455364\pi$
$384$	−4.65121	−0.237356
$385$	1.53447	0.0782036
$386$	0.139046	0.00707727
$387$	−11.2922	−0.574016
$388$	11.7433	0.596175
$389$	−30.4010	−1.54139	−0.770695	−	0.637204i	$-0.780091\pi$
$389$	−30.4010	−1.54139	−0.770695	+	0.637204i	$0.780091\pi$
$390$	0.0753083	0.00381338
$391$	4.39875	0.222454
$392$	2.31751	0.117052
$393$	7.36235	0.371381
$394$	11.3606	0.572340
$395$	9.64065	0.485074
$396$	−6.85924	−0.344690
$397$	18.0630	0.906556	0.453278	−	0.891369i	$-0.350255\pi$
$397$	18.0630	0.906556	0.453278	+	0.891369i	$0.350255\pi$
$398$	10.7478	0.538740
$399$	0.136433	0.00683017
$400$	1.66273	0.0831364
$401$	11.6638	0.582465	0.291232	−	0.956652i	$-0.405935\pi$
$401$	11.6638	0.582465	0.291232	+	0.956652i	$0.405935\pi$
$402$	4.07775	0.203380
$403$	2.11306	0.105259
$404$	−19.1426	−0.952382
$405$	−7.47287	−0.371330
$406$	2.73688	0.135829
$407$	0.900325	0.0446274
$408$	−3.24235	−0.160520
$409$	1.69748	0.0839349	0.0419675	−	0.999119i	$-0.486637\pi$
$409$	1.69748	0.0839349	0.0419675	+	0.999119i	$0.486637\pi$
$410$	3.82196	0.188753
$411$	0.172663	0.00851684
$412$	−15.9907	−0.787803
$413$	0.727704	0.0358080
$414$	2.39242	0.117581
$415$	−10.0563	−0.493642
$416$	1.59785	0.0783409
$417$	6.76131	0.331103
$418$	−0.325712	−0.0159311
$419$	−9.77843	−0.477708	−0.238854	−	0.971056i	$-0.576772\pi$
$419$	−9.77843	−0.477708	−0.238854	+	0.971056i	$0.576772\pi$
$420$	−0.657696	−0.0320923
$421$	25.1241	1.22447	0.612237	−	0.790674i	$-0.290270\pi$
$421$	25.1241	1.22447	0.612237	+	0.790674i	$0.290270\pi$
$422$	10.8764	0.529456
$423$	6.66108	0.323873
$424$	−2.21429	−0.107535
$425$	3.36362	0.163159
$426$	−1.05936	−0.0513261
$427$	−4.22986	−0.204697
$428$	−3.41855	−0.165242
$429$	−0.178571	−0.00862147
$430$	2.58491	0.124655
$431$	20.9478	1.00902	0.504510	−	0.863406i	$-0.331673\pi$
$431$	20.9478	1.00902	0.504510	+	0.863406i	$0.331673\pi$
$432$	4.02992	0.193890
$433$	0.391179	0.0187989	0.00939944	−	0.999956i	$-0.497008\pi$
$433$	0.391179	0.0187989	0.00939944	+	0.999956i	$0.497008\pi$
$434$	4.88743	0.234604
$435$	−1.75912	−0.0843436
$436$	−5.74164	−0.274975
$437$	−0.428953	−0.0205196
$438$	2.50834	0.119853
$439$	−23.1867	−1.10664	−0.553320	−	0.832969i	$-0.686639\pi$
$439$	−23.1867	−1.10664	−0.553320	+	0.832969i	$0.686639\pi$
$440$	3.55614	0.169532
$441$	−2.82699	−0.134619
$442$	0.609002	0.0289673
$443$	−3.93332	−0.186878	−0.0934389	−	0.995625i	$-0.529786\pi$
$443$	−3.93332	−0.186878	−0.0934389	+	0.995625i	$0.529786\pi$
$444$	−0.385893	−0.0183137
$445$	7.40727	0.351138
$446$	1.48046	0.0701020
$447$	0.816239	0.0386068
$448$	0.370299	0.0174950
$449$	29.7066	1.40194	0.700970	−	0.713191i	$-0.252751\pi$
$449$	29.7066	1.40194	0.700970	+	0.713191i	$0.252751\pi$
$450$	1.82943	0.0862399
$451$	−9.06260	−0.426741
$452$	−17.8491	−0.839549
$453$	−7.34526	−0.345110
$454$	2.72235	0.127766
$455$	0.279783	0.0131165
$456$	0.316184	0.0148067
$457$	−11.8834	−0.555884	−0.277942	−	0.960598i	$-0.589652\pi$
$457$	−11.8834	−0.555884	−0.277942	+	0.960598i	$0.589652\pi$
$458$	−0.647127	−0.0302383
$459$	8.15234	0.380519
$460$	2.06784	0.0964134
$461$	32.6429	1.52033	0.760166	−	0.649729i	$-0.225118\pi$
$461$	32.6429	1.52033	0.760166	+	0.649729i	$0.225118\pi$
$462$	−0.413026	−0.0192157
$463$	−13.6135	−0.632674	−0.316337	−	0.948647i	$-0.602453\pi$
$463$	−13.6135	−0.632674	−0.316337	+	0.948647i	$0.602453\pi$
$464$	−7.03213	−0.326458
$465$	−3.14139	−0.145678
$466$	8.38220	0.388298
$467$	0.437852	0.0202614	0.0101307	−	0.999949i	$-0.496775\pi$
$467$	0.437852	0.0202614	0.0101307	+	0.999949i	$0.496775\pi$
$468$	−1.25066	−0.0578120
$469$	15.1496	0.699542
$470$	−1.52479	−0.0703332
$471$	−3.75486	−0.173015
$472$	1.68646	0.0776256
$473$	−6.12931	−0.281826
$474$	−2.59494	−0.119190
$475$	−0.328010	−0.0150501
$476$	−5.31864	−0.243779
$477$	2.70108	0.123674
$478$	17.8834	0.817968
$479$	15.3313	0.700503	0.350252	−	0.936656i	$-0.386096\pi$
$479$	15.3313	0.700503	0.350252	+	0.936656i	$0.386096\pi$
$480$	−2.37544	−0.108424
$481$	0.164159	0.00748500
$482$	−6.91378	−0.314914
$483$	−0.543943	−0.0247503
$484$	13.6704	0.621380
$485$	7.42669	0.337229
$486$	6.71674	0.304677
$487$	−35.2475	−1.59722	−0.798608	−	0.601852i	$-0.794430\pi$
$487$	−35.2475	−1.59722	−0.798608	+	0.601852i	$0.794430\pi$
$488$	−9.80274	−0.443749
$489$	−5.07933	−0.229695
$490$	0.647127	0.0292342
$491$	−11.8848	−0.536353	−0.268176	−	0.963370i	$-0.586421\pi$
$491$	−11.8848	−0.536353	−0.268176	+	0.963370i	$0.586421\pi$
$492$	3.88437	0.175121
$493$	−14.2257	−0.640691
$494$	−0.0593880	−0.00267199
$495$	−4.33792	−0.194975
$496$	−12.5578	−0.563860
$497$	−3.93571	−0.176541
$498$	2.70680	0.121295
$499$	−25.3568	−1.13512	−0.567562	−	0.823330i	$-0.692113\pi$
$499$	−25.3568	−1.13512	−0.567562	+	0.823330i	$0.692113\pi$
$500$	1.58123	0.0707146
$501$	−9.91504	−0.442971
$502$	9.27687	0.414047
$503$	−16.8831	−0.752781	−0.376390	−	0.926461i	$-0.622835\pi$
$503$	−16.8831	−0.752781	−0.376390	+	0.926461i	$0.622835\pi$
$504$	−6.55159	−0.291831
$505$	−12.1062	−0.538719
$506$	1.29858	0.0577290
$507$	5.37466	0.238697
$508$	−9.56134	−0.424216
$509$	−36.3412	−1.61080	−0.805398	−	0.592735i	$-0.798048\pi$
$509$	−36.3412	−1.61080	−0.805398	+	0.592735i	$0.798048\pi$
$510$	−0.905373	−0.0400906
$511$	9.31891	0.412244
$512$	−17.2026	−0.760257
$513$	−0.794992	−0.0350997
$514$	−0.0771581	−0.00340330
$515$	−10.1128	−0.445624
$516$	2.62712	0.115652
$517$	3.61557	0.159013
$518$	0.379692	0.0166827
$519$	3.89639	0.171032
$520$	0.648401	0.0284343
$521$	−24.0426	−1.05333	−0.526663	−	0.850074i	$-0.676557\pi$
$521$	−24.0426	−1.05333	−0.526663	+	0.850074i	$0.676557\pi$
$522$	−7.73714	−0.338645
$523$	−19.3489	−0.846068	−0.423034	−	0.906114i	$-0.639035\pi$
$523$	−19.3489	−0.846068	−0.423034	+	0.906114i	$0.639035\pi$
$524$	27.9885	1.22268
$525$	−0.415940	−0.0181531
$526$	−13.7188	−0.598169
$527$	−25.4037	−1.10660
$528$	1.06123	0.0461841
$529$	−21.2898	−0.925644
$530$	−0.618305	−0.0268575
$531$	−2.05721	−0.0892755
$532$	0.518658	0.0224867
$533$	−1.65241	−0.0715738
$534$	−1.99379	−0.0862797
$535$	−2.16196	−0.0934698
$536$	35.1092	1.51649
$537$	−0.792921	−0.0342171
$538$	17.3469	0.747879
$539$	−1.53447	−0.0660941
$540$	3.83239	0.164920
$541$	−35.2000	−1.51336	−0.756682	−	0.653783i	$-0.773181\pi$
$541$	−35.2000	−1.51336	−0.756682	+	0.653783i	$0.773181\pi$
$542$	0.291535	0.0125225
$543$	−5.76311	−0.247319
$544$	−19.2097	−0.823608
$545$	−3.63113	−0.155541
$546$	−0.0753083	−0.00322290
$547$	−33.3072	−1.42411	−0.712056	−	0.702123i	$-0.752236\pi$
$547$	−33.3072	−1.42411	−0.712056	+	0.702123i	$0.752236\pi$
$548$	0.656390	0.0280396
$549$	11.9578	0.510346
$550$	0.992994	0.0423414
$551$	1.38724	0.0590985
$552$	−1.26059	−0.0536544
$553$	−9.64065	−0.409962
$554$	10.7441	0.456471
$555$	−0.244047	−0.0103592
$556$	25.7036	1.09008
$557$	24.9990	1.05924	0.529622	−	0.848234i	$-0.322334\pi$
$557$	24.9990	1.05924	0.529622	+	0.848234i	$0.322334\pi$
$558$	−13.8167	−0.584909
$559$	−1.11758	−0.0472684
$560$	−1.66273	−0.0702631
$561$	2.14682	0.0906386
$562$	−10.4004	−0.438715
$563$	−40.8160	−1.72019	−0.860094	−	0.510135i	$-0.829595\pi$
$563$	−40.8160	−1.72019	−0.860094	+	0.510135i	$0.829595\pi$
$564$	−1.54969	−0.0652537
$565$	−11.2881	−0.474894
$566$	0.158495	0.00666204
$567$	7.47287	0.313831
$568$	−9.12104	−0.382710
$569$	−43.6027	−1.82792	−0.913961	−	0.405803i	$-0.866992\pi$
$569$	−43.6027	−1.82792	−0.913961	+	0.405803i	$0.866992\pi$
$570$	0.0882893	0.00369803
$571$	4.54766	0.190314	0.0951568	−	0.995462i	$-0.469665\pi$
$571$	4.54766	0.190314	0.0951568	+	0.995462i	$0.469665\pi$
$572$	−0.678849	−0.0283841
$573$	−3.48680	−0.145663
$574$	−3.82196	−0.159525
$575$	1.30774	0.0545366
$576$	−1.04683	−0.0436181
$577$	−11.5704	−0.481683	−0.240841	−	0.970564i	$-0.577423\pi$
$577$	−11.5704	−0.481683	−0.240841	+	0.970564i	$0.577423\pi$
$578$	3.67961	0.153052
$579$	0.0893718	0.00371416
$580$	−6.68743	−0.277681
$581$	10.0563	0.417204
$582$	−1.99902	−0.0828619
$583$	1.46612	0.0607206
$584$	21.5967	0.893677
$585$	−0.790946	−0.0327016
$586$	−16.9907	−0.701878
$587$	−17.5464	−0.724218	−0.362109	−	0.932136i	$-0.617943\pi$
$587$	−17.5464	−0.724218	−0.362109	+	0.932136i	$0.617943\pi$
$588$	0.657696	0.0271229
$589$	2.47730	0.102075
$590$	0.470917	0.0193873
$591$	7.30203	0.300365
$592$	−0.975581	−0.0400961
$593$	−31.8960	−1.30981	−0.654905	−	0.755711i	$-0.727291\pi$
$593$	−31.8960	−1.30981	−0.654905	+	0.755711i	$0.727291\pi$
$594$	2.40670	0.0987482
$595$	−3.36362	−0.137895
$596$	3.10299	0.127103
$597$	6.90815	0.282732
$598$	0.236774	0.00968241
$599$	−4.74934	−0.194053	−0.0970263	−	0.995282i	$-0.530933\pi$
$599$	−4.74934	−0.194053	−0.0970263	+	0.995282i	$0.530933\pi$
$600$	−0.963946	−0.0393529
$601$	47.9576	1.95623	0.978116	−	0.208062i	$-0.0667156\pi$
$601$	47.9576	1.95623	0.978116	+	0.208062i	$0.0667156\pi$
$602$	−2.58491	−0.105353
$603$	−42.8277	−1.74408
$604$	−27.9235	−1.13619
$605$	8.64542	0.351486
$606$	3.25858	0.132371
$607$	31.1593	1.26472	0.632359	−	0.774676i	$-0.282087\pi$
$607$	31.1593	1.26472	0.632359	+	0.774676i	$0.282087\pi$
$608$	1.87327	0.0759711
$609$	1.75912	0.0712833
$610$	−2.73726	−0.110828
$611$	0.659237	0.0266699
$612$	15.0358	0.607785
$613$	−49.2925	−1.99091	−0.995453	−	0.0952560i	$-0.969633\pi$
$613$	−49.2925	−1.99091	−0.995453	+	0.0952560i	$0.969633\pi$
$614$	17.6130	0.710803
$615$	2.45656	0.0990579
$616$	−3.55614	−0.143281
$617$	−26.2397	−1.05637	−0.528185	−	0.849129i	$-0.677127\pi$
$617$	−26.2397	−1.05637	−0.528185	+	0.849129i	$0.677127\pi$
$618$	2.72203	0.109496
$619$	−5.29831	−0.212957	−0.106479	−	0.994315i	$-0.533958\pi$
$619$	−5.29831	−0.212957	−0.106479	+	0.994315i	$0.533958\pi$
$620$	−11.9422	−0.479611
$621$	3.16955	0.127190
$622$	19.3612	0.776315
$623$	−7.40727	−0.296766
$624$	0.193497	0.00774608
$625$	1.00000	0.0400000
$626$	16.1262	0.644531
$627$	−0.209351	−0.00836067
$628$	−14.2744	−0.569609
$629$	−1.97355	−0.0786907
$630$	−1.82943	−0.0728860
$631$	−27.0466	−1.07671	−0.538354	−	0.842719i	$-0.680954\pi$
$631$	−27.0466	−1.07671	−0.538354	+	0.842719i	$0.680954\pi$
$632$	−22.3423	−0.888729
$633$	6.99080	0.277860
$634$	−8.41256	−0.334105
$635$	−6.04679	−0.239960
$636$	−0.628403	−0.0249178
$637$	−0.279783	−0.0110854
$638$	−4.19964	−0.166265
$639$	11.1262	0.440146
$640$	−11.1824	−0.442023
$641$	39.3126	1.55276	0.776378	−	0.630268i	$-0.217055\pi$
$641$	39.3126	1.55276	0.776378	+	0.630268i	$0.217055\pi$
$642$	0.581928	0.0229669
$643$	−44.3337	−1.74835	−0.874175	−	0.485612i	$-0.838597\pi$
$643$	−44.3337	−1.74835	−0.874175	+	0.485612i	$0.838597\pi$
$644$	−2.06784	−0.0814842
$645$	1.66144	0.0654193
$646$	0.713976	0.0280910
$647$	11.2342	0.441661	0.220830	−	0.975312i	$-0.429123\pi$
$647$	11.2342	0.441661	0.220830	+	0.975312i	$0.429123\pi$
$648$	17.3185	0.680333
$649$	−1.11664	−0.0438318
$650$	0.181056	0.00710158
$651$	3.14139	0.123121
$652$	−19.3094	−0.756215
$653$	31.2515	1.22297	0.611483	−	0.791257i	$-0.290573\pi$
$653$	31.2515	1.22297	0.611483	+	0.791257i	$0.290573\pi$
$654$	0.977379	0.0382185
$655$	17.7005	0.691615
$656$	9.82013	0.383412
$657$	−26.3445	−1.02780
$658$	1.52479	0.0594424
$659$	−34.6628	−1.35027	−0.675136	−	0.737693i	$-0.735915\pi$
$659$	−34.6628	−1.35027	−0.675136	+	0.737693i	$0.735915\pi$
$660$	1.00921	0.0392835
$661$	−50.6904	−1.97163	−0.985814	−	0.167843i	$-0.946320\pi$
$661$	−50.6904	−1.97163	−0.985814	+	0.167843i	$0.946320\pi$
$662$	−2.99926	−0.116569
$663$	0.391435	0.0152021
$664$	23.3055	0.904427
$665$	0.328010	0.0127197
$666$	−1.07339	−0.0415929
$667$	−5.53080	−0.214153
$668$	−37.6927	−1.45837
$669$	0.951566	0.0367897
$670$	9.80369	0.378750
$671$	6.49057	0.250566
$672$	2.37544	0.0916347
$673$	11.9851	0.461993	0.230997	−	0.972955i	$-0.425801\pi$
$673$	11.9851	0.461993	0.230997	+	0.972955i	$0.425801\pi$
$674$	3.34180	0.128721
$675$	2.42368	0.0932875
$676$	20.4322	0.785852
$677$	−23.6553	−0.909148	−0.454574	−	0.890709i	$-0.650208\pi$
$677$	−23.6553	−0.909148	−0.454574	+	0.890709i	$0.650208\pi$
$678$	3.03838	0.116688
$679$	−7.42669	−0.285010
$680$	−7.79522	−0.298933
$681$	1.74979	0.0670519
$682$	−7.49959	−0.287174
$683$	23.3464	0.893327	0.446663	−	0.894702i	$-0.352612\pi$
$683$	23.3464	0.893327	0.446663	+	0.894702i	$0.352612\pi$
$684$	−1.46624	−0.0560632
$685$	0.415115	0.0158607
$686$	−0.647127	−0.0247074
$687$	−0.415940	−0.0158691
$688$	6.64165	0.253211
$689$	0.267322	0.0101842
$690$	−0.352000	−0.0134004
$691$	3.18235	0.121062	0.0605312	−	0.998166i	$-0.480721\pi$
$691$	3.18235	0.121062	0.0605312	+	0.998166i	$0.480721\pi$
$692$	14.8124	0.563082
$693$	4.33792	0.164784
$694$	−18.3003	−0.694669
$695$	16.2555	0.616606
$696$	4.07679	0.154530
$697$	19.8656	0.752465
$698$	−19.8908	−0.752877
$699$	5.38765	0.203779
$700$	−1.58123	−0.0597647
$701$	36.2584	1.36946	0.684731	−	0.728796i	$-0.259920\pi$
$701$	36.2584	1.36946	0.684731	+	0.728796i	$0.259920\pi$
$702$	0.438821	0.0165622
$703$	0.192455	0.00725858
$704$	−0.568212	−0.0214153
$705$	−0.980055	−0.0369110
$706$	20.7320	0.780260
$707$	12.1062	0.455301
$708$	0.478608	0.0179872
$709$	−27.1864	−1.02101	−0.510504	−	0.859875i	$-0.670541\pi$
$709$	−27.1864	−1.02101	−0.510504	+	0.859875i	$0.670541\pi$
$710$	−2.54690	−0.0955836
$711$	27.2541	1.02211
$712$	−17.1664	−0.643339
$713$	−9.87673	−0.369886
$714$	0.905373	0.0338827
$715$	−0.429318	−0.0160556
$716$	−3.01435	−0.112651
$717$	11.4945	0.429271
$718$	2.90206	0.108304
$719$	23.3731	0.871669	0.435835	−	0.900027i	$-0.356453\pi$
$719$	23.3731	0.871669	0.435835	+	0.900027i	$0.356453\pi$
$720$	4.70052	0.175178
$721$	10.1128	0.376621
$722$	12.2258	0.454997
$723$	−4.44382	−0.165268
$724$	−21.9089	−0.814237
$725$	−4.22927	−0.157071
$726$	−2.32706	−0.0863651
$727$	23.2856	0.863614	0.431807	−	0.901966i	$-0.357876\pi$
$727$	23.2856	0.863614	0.431807	+	0.901966i	$0.357876\pi$
$728$	−0.648401	−0.0240313
$729$	−18.1014	−0.670424
$730$	6.03052	0.223200
$731$	13.4357	0.496939
$732$	−2.78196	−0.102824
$733$	20.5611	0.759443	0.379722	−	0.925101i	$-0.376020\pi$
$733$	20.5611	0.759443	0.379722	+	0.925101i	$0.376020\pi$
$734$	2.24615	0.0829070
$735$	0.415940	0.0153422
$736$	−7.46854	−0.275294
$737$	−23.2465	−0.856295
$738$	10.8046	0.397725
$739$	−13.0416	−0.479744	−0.239872	−	0.970805i	$-0.577105\pi$
$739$	−13.0416	−0.479744	−0.239872	+	0.970805i	$0.577105\pi$
$740$	−0.927761	−0.0341052
$741$	−0.0381716	−0.00140227
$742$	0.618305	0.0226987
$743$	31.1376	1.14233	0.571163	−	0.820836i	$-0.306492\pi$
$743$	31.1376	1.14233	0.571163	+	0.820836i	$0.306492\pi$
$744$	7.28020	0.266905
$745$	1.96239	0.0718966
$746$	9.35871	0.342647
$747$	−28.4290	−1.04016
$748$	8.16127	0.298406
$749$	2.16196	0.0789964
$750$	−0.269166	−0.00982857
$751$	19.3992	0.707886	0.353943	−	0.935267i	$-0.384841\pi$
$751$	19.3992	0.707886	0.353943	+	0.935267i	$0.384841\pi$
$752$	−3.91779	−0.142867
$753$	5.96269	0.217293
$754$	−0.765733	−0.0278864
$755$	−17.6594	−0.642691
$756$	−3.83239	−0.139383
$757$	−45.9028	−1.66836	−0.834182	−	0.551489i	$-0.814060\pi$
$757$	−45.9028	−1.66836	−0.834182	+	0.551489i	$0.814060\pi$
$758$	−12.5643	−0.456356
$759$	0.834661	0.0302963
$760$	0.760166	0.0275741
$761$	−48.2100	−1.74761	−0.873806	−	0.486275i	$-0.838355\pi$
$761$	−48.2100	−1.74761	−0.873806	+	0.486275i	$0.838355\pi$
$762$	1.62759	0.0589615
$763$	3.63113	0.131456
$764$	−13.2553	−0.479560
$765$	9.50893	0.343796
$766$	−3.54020	−0.127913
$767$	−0.203599	−0.00735155
$768$	3.31797	0.119727
$769$	−28.8931	−1.04191	−0.520956	−	0.853584i	$-0.674424\pi$
$769$	−28.8931	−1.04191	−0.520956	+	0.853584i	$0.674424\pi$
$770$	−0.992994	−0.0357850
$771$	−0.0495933	−0.00178606
$772$	0.339753	0.0122280
$773$	29.0404	1.04451	0.522255	−	0.852789i	$-0.325091\pi$
$773$	29.0404	1.04451	0.522255	+	0.852789i	$0.325091\pi$
$774$	7.30751	0.262663
$775$	−7.55250	−0.271294
$776$	−17.2114	−0.617855
$777$	0.244047	0.00875513
$778$	19.6733	0.705322
$779$	−1.93724	−0.0694088
$780$	0.184012	0.00658870
$781$	6.03920	0.216100
$782$	−2.84655	−0.101792
$783$	−10.2504	−0.366320
$784$	1.66273	0.0593831
$785$	−9.02740	−0.322202
$786$	−4.76438	−0.169940
$787$	22.2000	0.791345	0.395673	−	0.918392i	$-0.370512\pi$
$787$	22.2000	0.791345	0.395673	+	0.918392i	$0.370512\pi$
$788$	27.7592	0.988879
$789$	−8.81775	−0.313920
$790$	−6.23873	−0.221964
$791$	11.2881	0.401359
$792$	10.0532	0.357224
$793$	1.18345	0.0420254
$794$	−11.6891	−0.414829
$795$	−0.397415	−0.0140949
$796$	26.2618	0.930826
$797$	29.1837	1.03374	0.516870	−	0.856064i	$-0.327097\pi$
$797$	29.1837	1.03374	0.516870	+	0.856064i	$0.327097\pi$
$798$	−0.0882893	−0.00312541
$799$	−7.92549	−0.280384
$800$	−5.71102	−0.201915
$801$	20.9403	0.739890
$802$	−7.54799	−0.266529
$803$	−14.2995	−0.504620
$804$	9.96380	0.351396
$805$	−1.30774	−0.0460919
$806$	−1.36742	−0.0481654
$807$	11.1497	0.392488
$808$	28.0562	0.987015
$809$	−12.5612	−0.441627	−0.220813	−	0.975316i	$-0.570871\pi$
$809$	−12.5612	−0.441627	−0.220813	+	0.975316i	$0.570871\pi$
$810$	4.83590	0.169916
$811$	−28.1672	−0.989086	−0.494543	−	0.869153i	$-0.664665\pi$
$811$	−28.1672	−0.989086	−0.494543	+	0.869153i	$0.664665\pi$
$812$	6.68743	0.234683
$813$	0.187384	0.00657184
$814$	−0.582625	−0.0204210
$815$	−12.2117	−0.427756
$816$	−2.32626	−0.0814355
$817$	−1.31021	−0.0458386
$818$	−1.09849	−0.0384076
$819$	0.790946	0.0276379
$820$	9.33877	0.326124
$821$	14.1218	0.492853	0.246427	−	0.969161i	$-0.420744\pi$
$821$	14.1218	0.492853	0.246427	+	0.969161i	$0.420744\pi$
$822$	−0.111735	−0.00389720
$823$	29.7052	1.03546	0.517730	−	0.855544i	$-0.326777\pi$
$823$	29.7052	1.03546	0.517730	+	0.855544i	$0.326777\pi$
$824$	23.4366	0.816451
$825$	0.638246	0.0222209
$826$	−0.470917	−0.0163853
$827$	10.4688	0.364036	0.182018	−	0.983295i	$-0.441737\pi$
$827$	10.4688	0.364036	0.182018	+	0.983295i	$0.441737\pi$
$828$	5.84576	0.203154
$829$	52.5809	1.82621	0.913105	−	0.407724i	$-0.133677\pi$
$829$	52.5809	1.82621	0.913105	+	0.407724i	$0.133677\pi$
$830$	6.50768	0.225885
$831$	6.90573	0.239557
$832$	−0.103604	−0.00359181
$833$	3.36362	0.116542
$834$	−4.37543	−0.151509
$835$	−23.8376	−0.824936
$836$	−0.795863	−0.0275255
$837$	−18.3049	−0.632708
$838$	6.32789	0.218593
$839$	35.0254	1.20921	0.604605	−	0.796525i	$-0.293331\pi$
$839$	35.0254	1.20921	0.604605	+	0.796525i	$0.293331\pi$
$840$	0.963946	0.0332593
$841$	−11.1133	−0.383216
$842$	−16.2585	−0.560305
$843$	−6.68485	−0.230238
$844$	26.5760	0.914785
$845$	12.9217	0.444521
$846$	−4.31057	−0.148200
$847$	−8.64542	−0.297060
$848$	−1.58867	−0.0545552
$849$	0.101872	0.00349625
$850$	−2.17669	−0.0746598
$851$	−0.767299	−0.0263027
$852$	−2.58850	−0.0886804
$853$	13.0542	0.446966	0.223483	−	0.974708i	$-0.428257\pi$
$853$	13.0542	0.446966	0.223483	+	0.974708i	$0.428257\pi$
$854$	2.73726	0.0936671
$855$	−0.927282	−0.0317124
$856$	5.01037	0.171251
$857$	39.7400	1.35749	0.678746	−	0.734373i	$-0.262524\pi$
$857$	39.7400	1.35749	0.678746	+	0.734373i	$0.262524\pi$
$858$	0.115558	0.00394508
$859$	20.4390	0.697369	0.348684	−	0.937240i	$-0.386628\pi$
$859$	20.4390	0.697369	0.348684	+	0.937240i	$0.386628\pi$
$860$	6.31610	0.215377
$861$	−2.45656	−0.0837192
$862$	−13.5559	−0.461715
$863$	−23.4927	−0.799700	−0.399850	−	0.916581i	$-0.630938\pi$
$863$	−23.4927	−0.799700	−0.399850	+	0.916581i	$0.630938\pi$
$864$	−13.8417	−0.470904
$865$	9.36766	0.318510
$866$	−0.253143	−0.00860215
$867$	2.36507	0.0803219
$868$	11.9422	0.405345
$869$	14.7932	0.501826
$870$	1.13838	0.0385946
$871$	−4.23860	−0.143619
$872$	8.41519	0.284974
$873$	20.9952	0.710581
$874$	0.277587	0.00938952
$875$	−1.00000	−0.0338062
$876$	6.12901	0.207080
$877$	−48.6494	−1.64277	−0.821387	−	0.570372i	$-0.806799\pi$
$877$	−48.6494	−1.64277	−0.821387	+	0.570372i	$0.806799\pi$
$878$	15.0047	0.506385
$879$	−10.9207	−0.368347
$880$	2.55140	0.0860076
$881$	−39.4716	−1.32983	−0.664915	−	0.746919i	$-0.731532\pi$
$881$	−39.4716	−1.32983	−0.664915	+	0.746919i	$0.731532\pi$
$882$	1.82943	0.0616000
$883$	−20.5313	−0.690934	−0.345467	−	0.938431i	$-0.612279\pi$
$883$	−20.5313	−0.690934	−0.345467	+	0.938431i	$0.612279\pi$
$884$	1.48807	0.0500491
$885$	0.302681	0.0101745
$886$	2.54536	0.0855131
$887$	−23.0531	−0.774049	−0.387024	−	0.922069i	$-0.626497\pi$
$887$	−23.0531	−0.774049	−0.387024	+	0.922069i	$0.626497\pi$
$888$	0.565581	0.0189797
$889$	6.04679	0.202803
$890$	−4.79345	−0.160677
$891$	−11.4669	−0.384154
$892$	3.61745	0.121121
$893$	0.772870	0.0258631
$894$	−0.528211	−0.0176660
$895$	−1.90633	−0.0637217
$896$	11.1824	0.373578
$897$	0.152186	0.00508135
$898$	−19.2239	−0.641511
$899$	31.9416	1.06531
$900$	4.47012	0.149004
$901$	−3.21381	−0.107067
$902$	5.86466	0.195272
$903$	−1.66144	−0.0552894
$904$	26.1603	0.870079
$905$	−13.8556	−0.460576
$906$	4.75332	0.157918
$907$	−7.33115	−0.243427	−0.121713	−	0.992565i	$-0.538839\pi$
$907$	−7.33115	−0.243427	−0.121713	+	0.992565i	$0.538839\pi$
$908$	6.65193	0.220752
$909$	−34.2242	−1.13514
$910$	−0.181056	−0.00600193
$911$	−18.9621	−0.628244	−0.314122	−	0.949383i	$-0.601710\pi$
$911$	−18.9621	−0.628244	−0.314122	+	0.949383i	$0.601710\pi$
$912$	0.226850	0.00751176
$913$	−15.4310	−0.510690
$914$	7.69010	0.254366
$915$	−1.75937	−0.0581630
$916$	−1.58123	−0.0522452
$917$	−17.7005	−0.584522
$918$	−5.27560	−0.174121
$919$	−20.3218	−0.670354	−0.335177	−	0.942155i	$-0.608796\pi$
$919$	−20.3218	−0.670354	−0.335177	+	0.942155i	$0.608796\pi$
$920$	−3.03071	−0.0999194
$921$	11.3207	0.373031
$922$	−21.1241	−0.695686
$923$	1.10115	0.0362446
$924$	−1.00921	−0.0332006
$925$	−0.586735	−0.0192917
$926$	8.80968	0.289504
$927$	−28.5889	−0.938982
$928$	24.1534	0.792875
$929$	−9.24471	−0.303309	−0.151655	−	0.988434i	$-0.548460\pi$
$929$	−9.24471	−0.303309	−0.151655	+	0.988434i	$0.548460\pi$
$930$	2.03288	0.0666607
$931$	−0.328010	−0.0107501
$932$	20.4815	0.670894
$933$	12.4444	0.407412
$934$	−0.283346	−0.00927137
$935$	5.16135	0.168794
$936$	1.83303	0.0599143
$937$	−5.22853	−0.170809	−0.0854043	−	0.996346i	$-0.527218\pi$
$937$	−5.22853	−0.170809	−0.0854043	+	0.996346i	$0.527218\pi$
$938$	−9.80369	−0.320102
$939$	10.3651	0.338251
$940$	−3.72575	−0.121521
$941$	−2.43487	−0.0793744	−0.0396872	−	0.999212i	$-0.512636\pi$
$941$	−2.43487	−0.0793744	−0.0396872	+	0.999212i	$0.512636\pi$
$942$	2.42987	0.0791695
$943$	7.72357	0.251514
$944$	1.20997	0.0393813
$945$	−2.42368	−0.0788424
$946$	3.96645	0.128960
$947$	57.4053	1.86542	0.932710	−	0.360626i	$-0.117437\pi$
$947$	57.4053	1.86542	0.932710	+	0.360626i	$0.117437\pi$
$948$	−6.34061	−0.205934
$949$	−2.60728	−0.0846358
$950$	0.212264	0.00688676
$951$	−5.40716	−0.175339
$952$	7.79522	0.252644
$953$	4.15114	0.134469	0.0672343	−	0.997737i	$-0.478583\pi$
$953$	4.15114	0.134469	0.0672343	+	0.997737i	$0.478583\pi$
$954$	−1.74794	−0.0565918
$955$	−8.38294	−0.271265
$956$	43.6973	1.41327
$957$	−2.69931	−0.0872565
$958$	−9.92128	−0.320542
$959$	−0.415115	−0.0134048
$960$	0.154022	0.00497105
$961$	26.0402	0.840008
$962$	−0.106232	−0.00342505
$963$	−6.11186	−0.196952
$964$	−16.8935	−0.544103
$965$	0.214867	0.00691681
$966$	0.352000	0.0113254
$967$	−33.6579	−1.08237	−0.541183	−	0.840905i	$-0.682023\pi$
$967$	−33.6579	−1.08237	−0.541183	+	0.840905i	$0.682023\pi$
$968$	−20.0358	−0.643976
$969$	0.458907	0.0147422
$970$	−4.80602	−0.154312
$971$	−57.8500	−1.85650	−0.928248	−	0.371962i	$-0.878685\pi$
$971$	−57.8500	−1.85650	−0.928248	+	0.371962i	$0.878685\pi$
$972$	16.4120	0.526416
$973$	−16.2555	−0.521127
$974$	22.8096	0.730867
$975$	0.116373	0.00372693
$976$	−7.03311	−0.225124
$977$	−23.0686	−0.738029	−0.369014	−	0.929424i	$-0.620305\pi$
$977$	−23.0686	−0.738029	−0.369014	+	0.929424i	$0.620305\pi$
$978$	3.28697	0.105106
$979$	11.3662	0.363265
$980$	1.58123	0.0505104
$981$	−10.2652	−0.327742
$982$	7.69097	0.245429
$983$	−1.36933	−0.0436750	−0.0218375	−	0.999762i	$-0.506952\pi$
$983$	−1.36933	−0.0436750	−0.0218375	+	0.999762i	$0.506952\pi$
$984$	−5.69309	−0.181489
$985$	17.5555	0.559364
$986$	9.20581	0.293173
$987$	0.980055	0.0311955
$988$	−0.145112	−0.00461663
$989$	5.22369	0.166104
$990$	2.80719	0.0892183
$991$	−13.1193	−0.416749	−0.208374	−	0.978049i	$-0.566817\pi$
$991$	−13.1193	−0.416749	−0.208374	+	0.978049i	$0.566817\pi$
$992$	43.1324	1.36946
$993$	−1.92777	−0.0611759
$994$	2.54690	0.0807829
$995$	16.6085	0.526526
$996$	6.61395	0.209571
$997$	8.37324	0.265183	0.132592	−	0.991171i	$-0.457670\pi$
$997$	8.37324	0.265183	0.132592	+	0.991171i	$0.457670\pi$
$998$	16.4091	0.519420
$999$	−1.42206	−0.0449920

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.19	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.19	✓	45	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.647127 q^{2} -0.415940 q^{3} -1.58123 q^{4} -1.00000 q^{5} +0.269166 q^{6} +1.00000 q^{7} +2.31751 q^{8} -2.82699 q^{9} +O(q^{10})\)	\(q-0.647127 q^{2} -0.415940 q^{3} -1.58123 q^{4} -1.00000 q^{5} +0.269166 q^{6} +1.00000 q^{7} +2.31751 q^{8} -2.82699 q^{9} +0.647127 q^{10} -1.53447 q^{11} +0.657696 q^{12} -0.279783 q^{13} -0.647127 q^{14} +0.415940 q^{15} +1.66273 q^{16} +3.36362 q^{17} +1.82943 q^{18} -0.328010 q^{19} +1.58123 q^{20} -0.415940 q^{21} +0.992994 q^{22} +1.30774 q^{23} -0.963946 q^{24} +1.00000 q^{25} +0.181056 q^{26} +2.42368 q^{27} -1.58123 q^{28} -4.22927 q^{29} -0.269166 q^{30} -7.55250 q^{31} -5.71102 q^{32} +0.638246 q^{33} -2.17669 q^{34} -1.00000 q^{35} +4.47012 q^{36} -0.586735 q^{37} +0.212264 q^{38} +0.116373 q^{39} -2.31751 q^{40} +5.90603 q^{41} +0.269166 q^{42} +3.99443 q^{43} +2.42634 q^{44} +2.82699 q^{45} -0.846276 q^{46} -2.35624 q^{47} -0.691596 q^{48} +1.00000 q^{49} -0.647127 q^{50} -1.39906 q^{51} +0.442401 q^{52} -0.955461 q^{53} -1.56843 q^{54} +1.53447 q^{55} +2.31751 q^{56} +0.136433 q^{57} +2.73688 q^{58} +0.727704 q^{59} -0.657696 q^{60} -4.22986 q^{61} +4.88743 q^{62} -2.82699 q^{63} +0.370299 q^{64} +0.279783 q^{65} -0.413026 q^{66} +15.1496 q^{67} -5.31864 q^{68} -0.543943 q^{69} +0.647127 q^{70} -3.93571 q^{71} -6.55159 q^{72} +9.31891 q^{73} +0.379692 q^{74} -0.415940 q^{75} +0.518658 q^{76} -1.53447 q^{77} -0.0753083 q^{78} -9.64065 q^{79} -1.66273 q^{80} +7.47287 q^{81} -3.82196 q^{82} +10.0563 q^{83} +0.657696 q^{84} -3.36362 q^{85} -2.58491 q^{86} +1.75912 q^{87} -3.55614 q^{88} -7.40727 q^{89} -1.82943 q^{90} -0.279783 q^{91} -2.06784 q^{92} +3.14139 q^{93} +1.52479 q^{94} +0.328010 q^{95} +2.37544 q^{96} -7.42669 q^{97} -0.647127 q^{98} +4.33792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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