LMFDB - Embedded newform 6013.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.87802 q^{2} +0.475349 q^{3} +1.52695 q^{4} -2.58742 q^{5} -0.892713 q^{6} -1.00000 q^{7} +0.888402 q^{8} -2.77404 q^{9} +O(q^{10})$	\(q-1.87802 q^{2} +0.475349 q^{3} +1.52695 q^{4} -2.58742 q^{5} -0.892713 q^{6} -1.00000 q^{7} +0.888402 q^{8} -2.77404 q^{9} +4.85921 q^{10} -1.89227 q^{11} +0.725832 q^{12} +4.50729 q^{13} +1.87802 q^{14} -1.22993 q^{15} -4.72233 q^{16} +0.399775 q^{17} +5.20970 q^{18} -2.10722 q^{19} -3.95085 q^{20} -0.475349 q^{21} +3.55372 q^{22} -0.382528 q^{23} +0.422301 q^{24} +1.69473 q^{25} -8.46477 q^{26} -2.74468 q^{27} -1.52695 q^{28} -6.58659 q^{29} +2.30982 q^{30} -6.80461 q^{31} +7.09181 q^{32} -0.899490 q^{33} -0.750783 q^{34} +2.58742 q^{35} -4.23582 q^{36} -5.14210 q^{37} +3.95739 q^{38} +2.14254 q^{39} -2.29867 q^{40} +4.43357 q^{41} +0.892713 q^{42} -0.361947 q^{43} -2.88940 q^{44} +7.17761 q^{45} +0.718394 q^{46} +6.62600 q^{47} -2.24475 q^{48} +1.00000 q^{49} -3.18272 q^{50} +0.190032 q^{51} +6.88239 q^{52} -6.05812 q^{53} +5.15456 q^{54} +4.89610 q^{55} -0.888402 q^{56} -1.00166 q^{57} +12.3697 q^{58} +10.4108 q^{59} -1.87803 q^{60} +1.75171 q^{61} +12.7792 q^{62} +2.77404 q^{63} -3.87388 q^{64} -11.6622 q^{65} +1.68926 q^{66} -15.1808 q^{67} +0.610434 q^{68} -0.181834 q^{69} -4.85921 q^{70} +5.26665 q^{71} -2.46447 q^{72} +2.73824 q^{73} +9.65695 q^{74} +0.805586 q^{75} -3.21761 q^{76} +1.89227 q^{77} -4.02372 q^{78} -15.1154 q^{79} +12.2186 q^{80} +7.01745 q^{81} -8.32632 q^{82} -11.5879 q^{83} -0.725832 q^{84} -1.03438 q^{85} +0.679743 q^{86} -3.13093 q^{87} -1.68110 q^{88} -14.0507 q^{89} -13.4797 q^{90} -4.50729 q^{91} -0.584100 q^{92} -3.23456 q^{93} -12.4437 q^{94} +5.45225 q^{95} +3.37108 q^{96} +5.67936 q^{97} -1.87802 q^{98} +5.24925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−1.87802	−1.32796	−0.663979	−	0.747751i	$-0.731134\pi$
$2$	−1.87802	−1.32796	−0.663979	+	0.747751i	$0.731134\pi$
$3$	0.475349	0.274443	0.137221	−	0.990540i	$-0.456183\pi$
$3$	0.475349	0.274443	0.137221	+	0.990540i	$0.456183\pi$
$4$	1.52695	0.763473
$5$	−2.58742	−1.15713	−0.578564	−	0.815637i	$-0.696387\pi$
$5$	−2.58742	−1.15713	−0.578564	+	0.815637i	$0.696387\pi$
$6$	−0.892713	−0.364449
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.888402	0.314097
$9$	−2.77404	−0.924681
$10$	4.85921	1.53662
$11$	−1.89227	−0.570542	−0.285271	−	0.958447i	$-0.592084\pi$
$11$	−1.89227	−0.570542	−0.285271	+	0.958447i	$0.592084\pi$
$12$	0.725832	0.209530
$13$	4.50729	1.25010	0.625049	−	0.780586i	$-0.285079\pi$
$13$	4.50729	1.25010	0.625049	+	0.780586i	$0.285079\pi$
$14$	1.87802	0.501921
$15$	−1.22993	−0.317565
$16$	−4.72233	−1.18058
$17$	0.399775	0.0969596	0.0484798	−	0.998824i	$-0.484562\pi$
$17$	0.399775	0.0969596	0.0484798	+	0.998824i	$0.484562\pi$
$18$	5.20970	1.22794
$19$	−2.10722	−0.483429	−0.241715	−	0.970347i	$-0.577710\pi$
$19$	−2.10722	−0.483429	−0.241715	+	0.970347i	$0.577710\pi$
$20$	−3.95085	−0.883436
$21$	−0.475349	−0.103730
$22$	3.55372	0.757656
$23$	−0.382528	−0.0797626	−0.0398813	−	0.999204i	$-0.512698\pi$
$23$	−0.382528	−0.0797626	−0.0398813	+	0.999204i	$0.512698\pi$
$24$	0.422301	0.0862018
$25$	1.69473	0.338945
$26$	−8.46477	−1.66008
$27$	−2.74468	−0.528215
$28$	−1.52695	−0.288566
$29$	−6.58659	−1.22310	−0.611550	−	0.791206i	$-0.709454\pi$
$29$	−6.58659	−1.22310	−0.611550	+	0.791206i	$0.709454\pi$
$30$	2.30982	0.421714
$31$	−6.80461	−1.22214	−0.611072	−	0.791575i	$-0.709262\pi$
$31$	−6.80461	−1.22214	−0.611072	+	0.791575i	$0.709262\pi$
$32$	7.09181	1.25367
$33$	−0.899490	−0.156581
$34$	−0.750783	−0.128758
$35$	2.58742	0.437353
$36$	−4.23582	−0.705969
$37$	−5.14210	−0.845356	−0.422678	−	0.906280i	$-0.638910\pi$
$37$	−5.14210	−0.845356	−0.422678	+	0.906280i	$0.638910\pi$
$38$	3.95739	0.641974
$39$	2.14254	0.343080
$40$	−2.29867	−0.363451
$41$	4.43357	0.692407	0.346204	−	0.938159i	$-0.387471\pi$
$41$	4.43357	0.692407	0.346204	+	0.938159i	$0.387471\pi$
$42$	0.892713	0.137749
$43$	−0.361947	−0.0551964	−0.0275982	−	0.999619i	$-0.508786\pi$
$43$	−0.361947	−0.0551964	−0.0275982	+	0.999619i	$0.508786\pi$
$44$	−2.88940	−0.435593
$45$	7.17761	1.06997
$46$	0.718394	0.105921
$47$	6.62600	0.966501	0.483250	−	0.875482i	$-0.339456\pi$
$47$	6.62600	0.966501	0.483250	+	0.875482i	$0.339456\pi$
$48$	−2.24475	−0.324002
$49$	1.00000	0.142857
$50$	−3.18272	−0.450105
$51$	0.190032	0.0266099
$52$	6.88239	0.954416
$53$	−6.05812	−0.832147	−0.416074	−	0.909331i	$-0.636594\pi$
$53$	−6.05812	−0.832147	−0.416074	+	0.909331i	$0.636594\pi$
$54$	5.15456	0.701447
$55$	4.89610	0.660190
$56$	−0.888402	−0.118718
$57$	−1.00166	−0.132674
$58$	12.3697	1.62423
$59$	10.4108	1.35537	0.677687	−	0.735351i	$-0.262983\pi$
$59$	10.4108	1.35537	0.677687	+	0.735351i	$0.262983\pi$
$60$	−1.87803	−0.242453
$61$	1.75171	0.224283	0.112142	−	0.993692i	$-0.464229\pi$
$61$	1.75171	0.224283	0.112142	+	0.993692i	$0.464229\pi$
$62$	12.7792	1.62296
$63$	2.77404	0.349497
$64$	−3.87388	−0.484234
$65$	−11.6622	−1.44652
$66$	1.68926	0.207933
$67$	−15.1808	−1.85463	−0.927313	−	0.374287i	$-0.877888\pi$
$67$	−15.1808	−1.85463	−0.927313	+	0.374287i	$0.877888\pi$
$68$	0.610434	0.0740261
$69$	−0.181834	−0.0218903
$70$	−4.85921	−0.580787
$71$	5.26665	0.625036	0.312518	−	0.949912i	$-0.398828\pi$
$71$	5.26665	0.625036	0.312518	+	0.949912i	$0.398828\pi$
$72$	−2.46447	−0.290440
$73$	2.73824	0.320487	0.160243	−	0.987078i	$-0.448772\pi$
$73$	2.73824	0.320487	0.160243	+	0.987078i	$0.448772\pi$
$74$	9.65695	1.12260
$75$	0.805586	0.0930211
$76$	−3.21761	−0.369085
$77$	1.89227	0.215644
$78$	−4.02372	−0.455596
$79$	−15.1154	−1.70062	−0.850310	−	0.526283i	$-0.823585\pi$
$79$	−15.1154	−1.70062	−0.850310	+	0.526283i	$0.823585\pi$
$80$	12.2186	1.36608
$81$	7.01745	0.779716
$82$	−8.32632	−0.919488
$83$	−11.5879	−1.27194	−0.635968	−	0.771715i	$-0.719399\pi$
$83$	−11.5879	−1.27194	−0.635968	+	0.771715i	$0.719399\pi$
$84$	−0.725832	−0.0791948
$85$	−1.03438	−0.112195
$86$	0.679743	0.0732985
$87$	−3.13093	−0.335671
$88$	−1.68110	−0.179206
$89$	−14.0507	−1.48937	−0.744687	−	0.667414i	$-0.767401\pi$
$89$	−14.0507	−1.48937	−0.744687	+	0.667414i	$0.767401\pi$
$90$	−13.4797	−1.42088
$91$	−4.50729	−0.472492
$92$	−0.584100	−0.0608966
$93$	−3.23456	−0.335409
$94$	−12.4437	−1.28347
$95$	5.45225	0.559389
$96$	3.37108	0.344060
$97$	5.67936	0.576651	0.288326	−	0.957532i	$-0.406901\pi$
$97$	5.67936	0.576651	0.288326	+	0.957532i	$0.406901\pi$
$98$	−1.87802	−0.189708
$99$	5.24925	0.527569
$100$	2.58776	0.258776
$101$	6.80332	0.676956	0.338478	−	0.940974i	$-0.390088\pi$
$101$	6.80332	0.676956	0.338478	+	0.940974i	$0.390088\pi$
$102$	−0.356884	−0.0353368
$103$	−6.45546	−0.636076	−0.318038	−	0.948078i	$-0.603024\pi$
$103$	−6.45546	−0.636076	−0.318038	+	0.948078i	$0.603024\pi$
$104$	4.00429	0.392652
$105$	1.22993	0.120028
$106$	11.3773	1.10506
$107$	5.64178	0.545412	0.272706	−	0.962097i	$-0.412081\pi$
$107$	5.64178	0.545412	0.272706	+	0.962097i	$0.412081\pi$
$108$	−4.19099	−0.403278
$109$	0.835858	0.0800607	0.0400303	−	0.999198i	$-0.487255\pi$
$109$	0.835858	0.0800607	0.0400303	+	0.999198i	$0.487255\pi$
$110$	−9.19495	−0.876705
$111$	−2.44429	−0.232002
$112$	4.72233	0.446218
$113$	−12.2056	−1.14821	−0.574104	−	0.818782i	$-0.694649\pi$
$113$	−12.2056	−1.14821	−0.574104	+	0.818782i	$0.694649\pi$
$114$	1.88114	0.176185
$115$	0.989760	0.0922956
$116$	−10.0574	−0.933804
$117$	−12.5034	−1.15594
$118$	−19.5517	−1.79988
$119$	−0.399775	−0.0366473
$120$	−1.09267	−0.0997465
$121$	−7.41930	−0.674482
$122$	−3.28974	−0.297839
$123$	2.10749	0.190026
$124$	−10.3903	−0.933075
$125$	8.55212	0.764925
$126$	−5.20970	−0.464117
$127$	−20.2543	−1.79728	−0.898639	−	0.438688i	$-0.855443\pi$
$127$	−20.2543	−1.79728	−0.898639	+	0.438688i	$0.855443\pi$
$128$	−6.90841	−0.610623
$129$	−0.172051	−0.0151483
$130$	21.9019	1.92092
$131$	12.0293	1.05101	0.525503	−	0.850792i	$-0.323877\pi$
$131$	12.0293	1.05101	0.525503	+	0.850792i	$0.323877\pi$
$132$	−1.37347	−0.119545
$133$	2.10722	0.182719
$134$	28.5097	2.46287
$135$	7.10164	0.611212
$136$	0.355160	0.0304548
$137$	−5.36849	−0.458661	−0.229331	−	0.973349i	$-0.573654\pi$
$137$	−5.36849	−0.458661	−0.229331	+	0.973349i	$0.573654\pi$
$138$	0.341488	0.0290694
$139$	5.89903	0.500349	0.250175	−	0.968201i	$-0.419512\pi$
$139$	5.89903	0.500349	0.250175	+	0.968201i	$0.419512\pi$
$140$	3.95085	0.333908
$141$	3.14966	0.265249
$142$	−9.89085	−0.830022
$143$	−8.52902	−0.713233
$144$	13.0999	1.09166
$145$	17.0423	1.41528
$146$	−5.14246	−0.425593
$147$	0.475349	0.0392061
$148$	−7.85171	−0.645407
$149$	−14.0682	−1.15251	−0.576254	−	0.817270i	$-0.695486\pi$
$149$	−14.0682	−1.15251	−0.576254	+	0.817270i	$0.695486\pi$
$150$	−1.51290	−0.123528
$151$	13.4057	1.09094	0.545471	−	0.838129i	$-0.316351\pi$
$151$	13.4057	1.09094	0.545471	+	0.838129i	$0.316351\pi$
$152$	−1.87206	−0.151844
$153$	−1.10899	−0.0896567
$154$	−3.55372	−0.286367
$155$	17.6064	1.41418
$156$	3.27154	0.261933
$157$	−15.6802	−1.25142	−0.625709	−	0.780057i	$-0.715190\pi$
$157$	−15.6802	−1.25142	−0.625709	+	0.780057i	$0.715190\pi$
$158$	28.3870	2.25835
$159$	−2.87972	−0.228377
$160$	−18.3495	−1.45065
$161$	0.382528	0.0301474
$162$	−13.1789	−1.03543
$163$	−19.3156	−1.51292	−0.756459	−	0.654041i	$-0.773072\pi$
$163$	−19.3156	−1.51292	−0.756459	+	0.654041i	$0.773072\pi$
$164$	6.76982	0.528634
$165$	2.32735	0.181184
$166$	21.7623	1.68908
$167$	−20.6285	−1.59628	−0.798140	−	0.602471i	$-0.794183\pi$
$167$	−20.6285	−1.59628	−0.798140	+	0.602471i	$0.794183\pi$
$168$	−0.422301	−0.0325812
$169$	7.31567	0.562744
$170$	1.94259	0.148990
$171$	5.84552	0.447018
$172$	−0.552674	−0.0421410
$173$	3.90310	0.296747	0.148373	−	0.988931i	$-0.452596\pi$
$173$	3.90310	0.296747	0.148373	+	0.988931i	$0.452596\pi$
$174$	5.87994	0.445757
$175$	−1.69473	−0.128109
$176$	8.93593	0.673571
$177$	4.94877	0.371972
$178$	26.3875	1.97783
$179$	10.2907	0.769165	0.384582	−	0.923091i	$-0.374345\pi$
$179$	10.2907	0.769165	0.384582	+	0.923091i	$0.374345\pi$
$180$	10.9598	0.816897
$181$	3.85631	0.286637	0.143319	−	0.989677i	$-0.454223\pi$
$181$	3.85631	0.286637	0.143319	+	0.989677i	$0.454223\pi$
$182$	8.46477	0.627450
$183$	0.832673	0.0615530
$184$	−0.339839	−0.0250532
$185$	13.3048	0.978185
$186$	6.07457	0.445409
$187$	−0.756482	−0.0553195
$188$	10.1175	0.737898
$189$	2.74468	0.199646
$190$	−10.2394	−0.742846
$191$	27.2431	1.97124	0.985619	−	0.168982i	$-0.0540480\pi$
$191$	27.2431	1.97124	0.985619	+	0.168982i	$0.0540480\pi$
$192$	−1.84144	−0.132895
$193$	7.91392	0.569657	0.284828	−	0.958579i	$-0.408063\pi$
$193$	7.91392	0.569657	0.284828	+	0.958579i	$0.408063\pi$
$194$	−10.6659	−0.765769
$195$	−5.54363	−0.396988
$196$	1.52695	0.109068
$197$	−9.13834	−0.651079	−0.325540	−	0.945528i	$-0.605546\pi$
$197$	−9.13834	−0.651079	−0.325540	+	0.945528i	$0.605546\pi$
$198$	−9.85817	−0.700590
$199$	−0.906783	−0.0642801	−0.0321401	−	0.999483i	$-0.510232\pi$
$199$	−0.906783	−0.0642801	−0.0321401	+	0.999483i	$0.510232\pi$
$200$	1.50560	0.106462
$201$	−7.21616	−0.508989
$202$	−12.7768	−0.898969
$203$	6.58659	0.462288
$204$	0.290169	0.0203159
$205$	−11.4715	−0.801204
$206$	12.1235	0.844682
$207$	1.06115	0.0737550
$208$	−21.2849	−1.47584
$209$	3.98743	0.275816
$210$	−2.30982	−0.159393
$211$	18.7342	1.28971	0.644857	−	0.764304i	$-0.276917\pi$
$211$	18.7342	1.28971	0.644857	+	0.764304i	$0.276917\pi$
$212$	−9.25043	−0.635322
$213$	2.50349	0.171537
$214$	−10.5954	−0.724284
$215$	0.936508	0.0638693
$216$	−2.43838	−0.165911
$217$	6.80461	0.461927
$218$	−1.56976	−0.106317
$219$	1.30162	0.0879553
$220$	7.47608	0.504037
$221$	1.80190	0.121209
$222$	4.59042	0.308089
$223$	−11.3544	−0.760344	−0.380172	−	0.924916i	$-0.624135\pi$
$223$	−11.3544	−0.760344	−0.380172	+	0.924916i	$0.624135\pi$
$224$	−7.09181	−0.473841
$225$	−4.70124	−0.313416
$226$	22.9224	1.52477
$227$	25.0182	1.66052	0.830260	−	0.557377i	$-0.188192\pi$
$227$	25.0182	1.66052	0.830260	+	0.557377i	$0.188192\pi$
$228$	−1.52949	−0.101293
$229$	−10.8257	−0.715382	−0.357691	−	0.933840i	$-0.616436\pi$
$229$	−10.8257	−0.715382	−0.357691	+	0.933840i	$0.616436\pi$
$230$	−1.85879	−0.122565
$231$	0.899490	0.0591821
$232$	−5.85154	−0.384173
$233$	7.24855	0.474868	0.237434	−	0.971404i	$-0.423694\pi$
$233$	7.24855	0.474868	0.237434	+	0.971404i	$0.423694\pi$
$234$	23.4816	1.53504
$235$	−17.1442	−1.11837
$236$	15.8968	1.03479
$237$	−7.18511	−0.466723
$238$	0.750783	0.0486661
$239$	−10.1175	−0.654444	−0.327222	−	0.944947i	$-0.606113\pi$
$239$	−10.1175	−0.654444	−0.327222	+	0.944947i	$0.606113\pi$
$240$	5.80811	0.374912
$241$	−18.1066	−1.16635	−0.583176	−	0.812346i	$-0.698190\pi$
$241$	−18.1066	−1.16635	−0.583176	+	0.812346i	$0.698190\pi$
$242$	13.9336	0.895684
$243$	11.5698	0.742202
$244$	2.67477	0.171234
$245$	−2.58742	−0.165304
$246$	−3.95790	−0.252347
$247$	−9.49785	−0.604334
$248$	−6.04523	−0.383872
$249$	−5.50829	−0.349074
$250$	−16.0610	−1.01579
$251$	−12.7498	−0.804760	−0.402380	−	0.915473i	$-0.631817\pi$
$251$	−12.7498	−0.804760	−0.402380	+	0.915473i	$0.631817\pi$
$252$	4.23582	0.266831
$253$	0.723848	0.0455079
$254$	38.0379	2.38671
$255$	−0.491693	−0.0307910
$256$	20.7219	1.29512
$257$	27.3053	1.70326	0.851628	−	0.524147i	$-0.175616\pi$
$257$	27.3053	1.70326	0.851628	+	0.524147i	$0.175616\pi$
$258$	0.323115	0.0201163
$259$	5.14210	0.319515
$260$	−17.8076	−1.10438
$261$	18.2715	1.13098
$262$	−22.5913	−1.39569
$263$	31.8961	1.96680	0.983400	−	0.181452i	$-0.0580796\pi$
$263$	31.8961	1.96680	0.983400	+	0.181452i	$0.0580796\pi$
$264$	−0.799108	−0.0491817
$265$	15.6749	0.962901
$266$	−3.95739	−0.242643
$267$	−6.67900	−0.408748
$268$	−23.1802	−1.41596
$269$	−14.6542	−0.893481	−0.446741	−	0.894664i	$-0.647415\pi$
$269$	−14.6542	−0.893481	−0.446741	+	0.894664i	$0.647415\pi$
$270$	−13.3370	−0.811664
$271$	5.50933	0.334668	0.167334	−	0.985900i	$-0.446484\pi$
$271$	5.50933	0.334668	0.167334	+	0.985900i	$0.446484\pi$
$272$	−1.88787	−0.114469
$273$	−2.14254	−0.129672
$274$	10.0821	0.609083
$275$	−3.20688	−0.193382
$276$	−0.277651	−0.0167126
$277$	6.26882	0.376657	0.188328	−	0.982106i	$-0.439693\pi$
$277$	6.26882	0.376657	0.188328	+	0.982106i	$0.439693\pi$
$278$	−11.0785	−0.664443
$279$	18.8763	1.13009
$280$	2.29867	0.137372
$281$	12.8830	0.768533	0.384267	−	0.923222i	$-0.374454\pi$
$281$	12.8830	0.768533	0.384267	+	0.923222i	$0.374454\pi$
$282$	−5.91511	−0.352240
$283$	3.78707	0.225118	0.112559	−	0.993645i	$-0.464095\pi$
$283$	3.78707	0.225118	0.112559	+	0.993645i	$0.464095\pi$
$284$	8.04189	0.477198
$285$	2.59172	0.153520
$286$	16.0177	0.947144
$287$	−4.43357	−0.261705
$288$	−19.6730	−1.15924
$289$	−16.8402	−0.990599
$290$	−32.0057	−1.87944
$291$	2.69968	0.158258
$292$	4.18115	0.244683
$293$	26.6398	1.55631	0.778157	−	0.628069i	$-0.216155\pi$
$293$	26.6398	1.55631	0.778157	+	0.628069i	$0.216155\pi$
$294$	−0.892713	−0.0520641
$295$	−26.9371	−1.56834
$296$	−4.56825	−0.265524
$297$	5.19369	0.301369
$298$	26.4202	1.53048
$299$	−1.72417	−0.0997111
$300$	1.23009	0.0710191
$301$	0.361947	0.0208623
$302$	−25.1762	−1.44873
$303$	3.23395	0.185786
$304$	9.95098	0.570728
$305$	−4.53240	−0.259525
$306$	2.08271	0.119060
$307$	3.95939	0.225974	0.112987	−	0.993596i	$-0.463958\pi$
$307$	3.95939	0.225974	0.112987	+	0.993596i	$0.463958\pi$
$308$	2.88940	0.164639
$309$	−3.06860	−0.174566
$310$	−33.0651	−1.87797
$311$	18.2183	1.03307	0.516533	−	0.856267i	$-0.327222\pi$
$311$	18.2183	1.03307	0.516533	+	0.856267i	$0.327222\pi$
$312$	1.90343	0.107761
$313$	−4.89348	−0.276596	−0.138298	−	0.990391i	$-0.544163\pi$
$313$	−4.89348	−0.276596	−0.138298	+	0.990391i	$0.544163\pi$
$314$	29.4477	1.66183
$315$	−7.17761	−0.404412
$316$	−23.0805	−1.29838
$317$	−10.0237	−0.562987	−0.281493	−	0.959563i	$-0.590830\pi$
$317$	−10.0237	−0.562987	−0.281493	+	0.959563i	$0.590830\pi$
$318$	5.40817	0.303275
$319$	12.4636	0.697829
$320$	10.0233	0.560321
$321$	2.68182	0.149684
$322$	−0.718394	−0.0400345
$323$	−0.842412	−0.0468731
$324$	10.7153	0.595293
$325$	7.63862	0.423715
$326$	36.2751	2.00909
$327$	0.397324	0.0219721
$328$	3.93879	0.217483
$329$	−6.62600	−0.365303
$330$	−4.37081	−0.240605
$331$	−3.20768	−0.176310	−0.0881551	−	0.996107i	$-0.528097\pi$
$331$	−3.20768	−0.176310	−0.0881551	+	0.996107i	$0.528097\pi$
$332$	−17.6941	−0.971090
$333$	14.2644	0.781685
$334$	38.7407	2.11979
$335$	39.2790	2.14604
$336$	2.24475	0.122461
$337$	30.7917	1.67733	0.838666	−	0.544646i	$-0.183336\pi$
$337$	30.7917	1.67733	0.838666	+	0.544646i	$0.183336\pi$
$338$	−13.7390	−0.747301
$339$	−5.80193	−0.315117
$340$	−1.57945	−0.0856576
$341$	12.8762	0.697284
$342$	−10.9780	−0.593621
$343$	−1.00000	−0.0539949
$344$	−0.321554	−0.0173371
$345$	0.470481	0.0253299
$346$	−7.33008	−0.394068
$347$	−4.98563	−0.267642	−0.133821	−	0.991005i	$-0.542725\pi$
$347$	−4.98563	−0.267642	−0.133821	+	0.991005i	$0.542725\pi$
$348$	−4.78076	−0.256276
$349$	36.7175	1.96544	0.982722	−	0.185089i	$-0.0592572\pi$
$349$	36.7175	1.96544	0.982722	+	0.185089i	$0.0592572\pi$
$350$	3.18272	0.170124
$351$	−12.3711	−0.660320
$352$	−13.4196	−0.715269
$353$	25.6653	1.36603	0.683013	−	0.730407i	$-0.260669\pi$
$353$	25.6653	1.36603	0.683013	+	0.730407i	$0.260669\pi$
$354$	−9.29387	−0.493964
$355$	−13.6270	−0.723247
$356$	−21.4547	−1.13710
$357$	−0.190032	−0.0100576
$358$	−19.3262	−1.02142
$359$	−32.5665	−1.71880	−0.859398	−	0.511307i	$-0.829162\pi$
$359$	−32.5665	−1.71880	−0.859398	+	0.511307i	$0.829162\pi$
$360$	6.37660	0.336076
$361$	−14.5596	−0.766296
$362$	−7.24221	−0.380642
$363$	−3.52676	−0.185107
$364$	−6.88239	−0.360735
$365$	−7.08497	−0.370844
$366$	−1.56377	−0.0817398
$367$	−1.10425	−0.0576412	−0.0288206	−	0.999585i	$-0.509175\pi$
$367$	−1.10425	−0.0576412	−0.0288206	+	0.999585i	$0.509175\pi$
$368$	1.80642	0.0941663
$369$	−12.2989	−0.640256
$370$	−24.9866	−1.29899
$371$	6.05812	0.314522
$372$	−4.93901	−0.256076
$373$	−11.6152	−0.601413	−0.300706	−	0.953717i	$-0.597222\pi$
$373$	−11.6152	−0.601413	−0.300706	+	0.953717i	$0.597222\pi$
$374$	1.42069	0.0734620
$375$	4.06524	0.209928
$376$	5.88655	0.303575
$377$	−29.6877	−1.52899
$378$	−5.15456	−0.265122
$379$	21.8330	1.12149	0.560743	−	0.827990i	$-0.310515\pi$
$379$	21.8330	1.12149	0.560743	+	0.827990i	$0.310515\pi$
$380$	8.32530	0.427079
$381$	−9.62786	−0.493250
$382$	−51.1629	−2.61772
$383$	25.3633	1.29600	0.648002	−	0.761639i	$-0.275605\pi$
$383$	25.3633	1.29600	0.648002	+	0.761639i	$0.275605\pi$
$384$	−3.28390	−0.167581
$385$	−4.89610	−0.249528
$386$	−14.8625	−0.756480
$387$	1.00406	0.0510391
$388$	8.67207	0.440258
$389$	−17.6925	−0.897046	−0.448523	−	0.893771i	$-0.648050\pi$
$389$	−17.6925	−0.897046	−0.448523	+	0.893771i	$0.648050\pi$
$390$	10.4110	0.527183
$391$	−0.152925	−0.00773375
$392$	0.888402	0.0448711
$393$	5.71812	0.288441
$394$	17.1619	0.864606
$395$	39.1099	1.96783
$396$	8.01532	0.402785
$397$	21.8823	1.09824	0.549121	−	0.835743i	$-0.314963\pi$
$397$	21.8823	1.09824	0.549121	+	0.835743i	$0.314963\pi$
$398$	1.70295	0.0853614
$399$	1.00166	0.0501459
$400$	−8.00305	−0.400153
$401$	−18.2875	−0.913233	−0.456617	−	0.889664i	$-0.650939\pi$
$401$	−18.2875	−0.913233	−0.456617	+	0.889664i	$0.650939\pi$
$402$	13.5521	0.675916
$403$	−30.6704	−1.52780
$404$	10.3883	0.516838
$405$	−18.1571	−0.902232
$406$	−12.3697	−0.613900
$407$	9.73026	0.482311
$408$	0.168825	0.00835809
$409$	4.06068	0.200788	0.100394	−	0.994948i	$-0.467990\pi$
$409$	4.06068	0.200788	0.100394	+	0.994948i	$0.467990\pi$
$410$	21.5436	1.06396
$411$	−2.55191	−0.125876
$412$	−9.85715	−0.485627
$413$	−10.4108	−0.512283
$414$	−1.99286	−0.0979436
$415$	29.9827	1.47179
$416$	31.9648	1.56720
$417$	2.80410	0.137317
$418$	−7.48846	−0.366273
$419$	−13.9817	−0.683051	−0.341526	−	0.939873i	$-0.610944\pi$
$419$	−13.9817	−0.683051	−0.341526	+	0.939873i	$0.610944\pi$
$420$	1.87803	0.0916385
$421$	−2.03489	−0.0991744	−0.0495872	−	0.998770i	$-0.515791\pi$
$421$	−2.03489	−0.0991744	−0.0495872	+	0.998770i	$0.515791\pi$
$422$	−35.1831	−1.71269
$423$	−18.3808	−0.893705
$424$	−5.38205	−0.261375
$425$	0.677508	0.0328640
$426$	−4.70160	−0.227793
$427$	−1.75171	−0.0847712
$428$	8.61471	0.416407
$429$	−4.05426	−0.195742
$430$	−1.75878	−0.0848158
$431$	30.8832	1.48759	0.743795	−	0.668408i	$-0.233024\pi$
$431$	30.8832	1.48759	0.743795	+	0.668408i	$0.233024\pi$
$432$	12.9613	0.623601
$433$	36.9341	1.77494	0.887470	−	0.460865i	$-0.152461\pi$
$433$	36.9341	1.77494	0.887470	+	0.460865i	$0.152461\pi$
$434$	−12.7792	−0.613420
$435$	8.10102	0.388414
$436$	1.27631	0.0611242
$437$	0.806070	0.0385596
$438$	−2.44446	−0.116801
$439$	32.9218	1.57127	0.785635	−	0.618690i	$-0.212336\pi$
$439$	32.9218	1.57127	0.785635	+	0.618690i	$0.212336\pi$
$440$	4.34970	0.207364
$441$	−2.77404	−0.132097
$442$	−3.38400	−0.160960
$443$	−9.61370	−0.456761	−0.228380	−	0.973572i	$-0.573343\pi$
$443$	−9.61370	−0.456761	−0.228380	+	0.973572i	$0.573343\pi$
$444$	−3.73230	−0.177127
$445$	36.3551	1.72340
$446$	21.3237	1.00970
$447$	−6.68728	−0.316298
$448$	3.87388	0.183023
$449$	−27.3793	−1.29211	−0.646055	−	0.763291i	$-0.723582\pi$
$449$	−27.3793	−1.29211	−0.646055	+	0.763291i	$0.723582\pi$
$450$	8.82902	0.416204
$451$	−8.38952	−0.395047
$452$	−18.6373	−0.876626
$453$	6.37240	0.299401
$454$	−46.9847	−2.20510
$455$	11.6622	0.546734
$456$	−0.889880	−0.0416724
$457$	−24.0310	−1.12412	−0.562062	−	0.827095i	$-0.689992\pi$
$457$	−24.0310	−1.12412	−0.562062	+	0.827095i	$0.689992\pi$
$458$	20.3308	0.949997
$459$	−1.09726	−0.0512155
$460$	1.51131	0.0704652
$461$	7.76796	0.361790	0.180895	−	0.983502i	$-0.442101\pi$
$461$	7.76796	0.361790	0.180895	+	0.983502i	$0.442101\pi$
$462$	−1.68926	−0.0785913
$463$	26.5468	1.23373	0.616866	−	0.787068i	$-0.288402\pi$
$463$	26.5468	1.23373	0.616866	+	0.787068i	$0.288402\pi$
$464$	31.1041	1.44397
$465$	8.36917	0.388111
$466$	−13.6129	−0.630605
$467$	−30.2122	−1.39805	−0.699027	−	0.715096i	$-0.746383\pi$
$467$	−30.2122	−1.39805	−0.699027	+	0.715096i	$0.746383\pi$
$468$	−19.0921	−0.882531
$469$	15.1808	0.700983
$470$	32.1971	1.48514
$471$	−7.45358	−0.343443
$472$	9.24899	0.425719
$473$	0.684903	0.0314919
$474$	13.4937	0.619788
$475$	−3.57116	−0.163856
$476$	−0.610434	−0.0279792
$477$	16.8055	0.769471
$478$	19.0008	0.869075
$479$	−2.14793	−0.0981414	−0.0490707	−	0.998795i	$-0.515626\pi$
$479$	−2.14793	−0.0981414	−0.0490707	+	0.998795i	$0.515626\pi$
$480$	−8.72239	−0.398121
$481$	−23.1769	−1.05678
$482$	34.0046	1.54887
$483$	0.181834	0.00827375
$484$	−11.3289	−0.514949
$485$	−14.6949	−0.667259
$486$	−21.7283	−0.985614
$487$	17.8271	0.807822	0.403911	−	0.914798i	$-0.367650\pi$
$487$	17.8271	0.807822	0.403911	+	0.914798i	$0.367650\pi$
$488$	1.55622	0.0704468
$489$	−9.18167	−0.415209
$490$	4.85921	0.219517
$491$	39.1408	1.76640	0.883199	−	0.468999i	$-0.155385\pi$
$491$	39.1408	1.76640	0.883199	+	0.468999i	$0.155385\pi$
$492$	3.21803	0.145080
$493$	−2.63315	−0.118591
$494$	17.8371	0.802530
$495$	−13.5820	−0.610465
$496$	32.1336	1.44284
$497$	−5.26665	−0.236241
$498$	10.3447	0.463556
$499$	14.9929	0.671175	0.335588	−	0.942009i	$-0.391065\pi$
$499$	14.9929	0.671175	0.335588	+	0.942009i	$0.391065\pi$
$500$	13.0586	0.584000
$501$	−9.80573	−0.438088
$502$	23.9443	1.06869
$503$	−3.63999	−0.162299	−0.0811496	−	0.996702i	$-0.525859\pi$
$503$	−3.63999	−0.162299	−0.0811496	+	0.996702i	$0.525859\pi$
$504$	2.46447	0.109776
$505$	−17.6030	−0.783325
$506$	−1.35940	−0.0604326
$507$	3.47750	0.154441
$508$	−30.9272	−1.37217
$509$	−8.43060	−0.373680	−0.186840	−	0.982390i	$-0.559825\pi$
$509$	−8.43060	−0.373680	−0.186840	+	0.982390i	$0.559825\pi$
$510$	0.923408	0.0408892
$511$	−2.73824	−0.121133
$512$	−25.0992	−1.10924
$513$	5.78365	0.255354
$514$	−51.2797	−2.26185
$515$	16.7030	0.736021
$516$	−0.262713	−0.0115653
$517$	−12.5382	−0.551429
$518$	−9.65695	−0.424302
$519$	1.85533	0.0814400
$520$	−10.3608	−0.454349
$521$	−42.8426	−1.87697	−0.938485	−	0.345321i	$-0.887770\pi$
$521$	−42.8426	−1.87697	−0.938485	+	0.345321i	$0.887770\pi$
$522$	−34.3142	−1.50189
$523$	−34.0539	−1.48907	−0.744536	−	0.667582i	$-0.767329\pi$
$523$	−34.0539	−1.48907	−0.744536	+	0.667582i	$0.767329\pi$
$524$	18.3681	0.802415
$525$	−0.805586	−0.0351587
$526$	−59.9015	−2.61183
$527$	−2.72031	−0.118499
$528$	4.24768	0.184857
$529$	−22.8537	−0.993638
$530$	−29.4377	−1.27869
$531$	−28.8801	−1.25329
$532$	3.21761	0.139501
$533$	19.9834	0.865576
$534$	12.5433	0.542800
$535$	−14.5976	−0.631111
$536$	−13.4866	−0.582533
$537$	4.89168	0.211092
$538$	27.5208	1.18651
$539$	−1.89227	−0.0815060
$540$	10.8438	0.466644
$541$	7.95060	0.341823	0.170911	−	0.985286i	$-0.445329\pi$
$541$	7.95060	0.341823	0.170911	+	0.985286i	$0.445329\pi$
$542$	−10.3466	−0.444425
$543$	1.83309	0.0786655
$544$	2.83512	0.121555
$545$	−2.16271	−0.0926405
$546$	4.02372	0.172199
$547$	−18.2674	−0.781059	−0.390530	−	0.920590i	$-0.627708\pi$
$547$	−18.2674	−0.781059	−0.390530	+	0.920590i	$0.627708\pi$
$548$	−8.19740	−0.350176
$549$	−4.85932	−0.207391
$550$	6.02258	0.256804
$551$	13.8794	0.591282
$552$	−0.161542	−0.00687568
$553$	15.1154	0.642774
$554$	−11.7729	−0.500185
$555$	6.32440	0.268456
$556$	9.00750	0.382003
$557$	45.5732	1.93100	0.965499	−	0.260408i	$-0.0838572\pi$
$557$	45.5732	1.93100	0.965499	+	0.260408i	$0.0838572\pi$
$558$	−35.4500	−1.50072
$559$	−1.63140	−0.0690009
$560$	−12.2186	−0.516331
$561$	−0.359593	−0.0151820
$562$	−24.1944	−1.02058
$563$	33.2439	1.40106	0.700532	−	0.713621i	$-0.252946\pi$
$563$	33.2439	1.40106	0.700532	+	0.713621i	$0.252946\pi$
$564$	4.80936	0.202511
$565$	31.5810	1.32862
$566$	−7.11219	−0.298947
$567$	−7.01745	−0.294705
$568$	4.67890	0.196322
$569$	9.44782	0.396073	0.198037	−	0.980195i	$-0.436544\pi$
$569$	9.44782	0.396073	0.198037	+	0.980195i	$0.436544\pi$
$570$	−4.86730	−0.203869
$571$	30.9762	1.29631	0.648156	−	0.761507i	$-0.275540\pi$
$571$	30.9762	1.29631	0.648156	+	0.761507i	$0.275540\pi$
$572$	−13.0234	−0.544534
$573$	12.9500	0.540992
$574$	8.32632	0.347534
$575$	−0.648280	−0.0270352
$576$	10.7463	0.447762
$577$	−35.4827	−1.47716	−0.738582	−	0.674164i	$-0.764504\pi$
$577$	−35.4827	−1.47716	−0.738582	+	0.674164i	$0.764504\pi$
$578$	31.6261	1.31547
$579$	3.76187	0.156338
$580$	26.0226	1.08053
$581$	11.5879	0.480747
$582$	−5.07003	−0.210160
$583$	11.4636	0.474775
$584$	2.43266	0.100664
$585$	32.3516	1.33757
$586$	−50.0300	−2.06672
$587$	−22.2207	−0.917147	−0.458574	−	0.888656i	$-0.651639\pi$
$587$	−22.2207	−0.917147	−0.458574	+	0.888656i	$0.651639\pi$
$588$	0.725832	0.0299328
$589$	14.3388	0.590820
$590$	50.5884	2.08269
$591$	−4.34390	−0.178684
$592$	24.2827	0.998012
$593$	15.2260	0.625258	0.312629	−	0.949875i	$-0.398790\pi$
$593$	15.2260	0.625258	0.312629	+	0.949875i	$0.398790\pi$
$594$	−9.75384	−0.400205
$595$	1.03438	0.0424056
$596$	−21.4813	−0.879910
$597$	−0.431038	−0.0176412
$598$	3.23801	0.132412
$599$	−31.2102	−1.27521	−0.637606	−	0.770363i	$-0.720075\pi$
$599$	−31.2102	−1.27521	−0.637606	+	0.770363i	$0.720075\pi$
$600$	0.715684	0.0292177
$601$	23.5584	0.960967	0.480483	−	0.877004i	$-0.340461\pi$
$601$	23.5584	0.960967	0.480483	+	0.877004i	$0.340461\pi$
$602$	−0.679743	−0.0277042
$603$	42.1121	1.71494
$604$	20.4698	0.832906
$605$	19.1968	0.780462
$606$	−6.07342	−0.246716
$607$	12.0232	0.488006	0.244003	−	0.969774i	$-0.421539\pi$
$607$	12.0232	0.488006	0.244003	+	0.969774i	$0.421539\pi$
$608$	−14.9440	−0.606059
$609$	3.13093	0.126872
$610$	8.51193	0.344638
$611$	29.8653	1.20822
$612$	−1.69337	−0.0684505
$613$	−2.77360	−0.112025	−0.0560124	−	0.998430i	$-0.517839\pi$
$613$	−2.77360	−0.112025	−0.0560124	+	0.998430i	$0.517839\pi$
$614$	−7.43580	−0.300084
$615$	−5.45296	−0.219885
$616$	1.68110	0.0677334
$617$	38.9020	1.56613	0.783067	−	0.621937i	$-0.213654\pi$
$617$	38.9020	1.56613	0.783067	+	0.621937i	$0.213654\pi$
$618$	5.76288	0.231817
$619$	15.6475	0.628927	0.314464	−	0.949269i	$-0.398175\pi$
$619$	15.6475	0.628927	0.314464	+	0.949269i	$0.398175\pi$
$620$	26.8840	1.07969
$621$	1.04992	0.0421318
$622$	−34.2143	−1.37187
$623$	14.0507	0.562931
$624$	−10.1178	−0.405034
$625$	−30.6015	−1.22406
$626$	9.19004	0.367308
$627$	1.89542	0.0756958
$628$	−23.9429	−0.955424
$629$	−2.05568	−0.0819654
$630$	13.4797	0.537043
$631$	−27.7385	−1.10425	−0.552126	−	0.833761i	$-0.686183\pi$
$631$	−27.7385	−1.10425	−0.552126	+	0.833761i	$0.686183\pi$
$632$	−13.4286	−0.534160
$633$	8.90526	0.353952
$634$	18.8247	0.747623
$635$	52.4063	2.07968
$636$	−4.39718	−0.174360
$637$	4.50729	0.178585
$638$	−23.4069	−0.926688
$639$	−14.6099	−0.577959
$640$	17.8749	0.706569
$641$	−17.8266	−0.704106	−0.352053	−	0.935980i	$-0.614516\pi$
$641$	−17.8266	−0.704106	−0.352053	+	0.935980i	$0.614516\pi$
$642$	−5.03649	−0.198775
$643$	−38.7002	−1.52619	−0.763094	−	0.646288i	$-0.776321\pi$
$643$	−38.7002	−1.52619	−0.763094	+	0.646288i	$0.776321\pi$
$644$	0.584100	0.0230168
$645$	0.445168	0.0175285
$646$	1.58206	0.0622455
$647$	38.3014	1.50578	0.752891	−	0.658145i	$-0.228659\pi$
$647$	38.3014	1.50578	0.752891	+	0.658145i	$0.228659\pi$
$648$	6.23431	0.244907
$649$	−19.7001	−0.773297
$650$	−14.3455	−0.562675
$651$	3.23456	0.126773
$652$	−29.4940	−1.15507
$653$	−12.1342	−0.474850	−0.237425	−	0.971406i	$-0.576303\pi$
$653$	−12.1342	−0.474850	−0.237425	+	0.971406i	$0.576303\pi$
$654$	−0.746181	−0.0291780
$655$	−31.1248	−1.21615
$656$	−20.9368	−0.817443
$657$	−7.59600	−0.296348
$658$	12.4437	0.485107
$659$	36.9143	1.43798	0.718988	−	0.695022i	$-0.244606\pi$
$659$	36.9143	1.43798	0.718988	+	0.695022i	$0.244606\pi$
$660$	3.55375	0.138329
$661$	18.4689	0.718356	0.359178	−	0.933269i	$-0.383057\pi$
$661$	18.4689	0.718356	0.359178	+	0.933269i	$0.383057\pi$
$662$	6.02409	0.234133
$663$	0.856531	0.0332649
$664$	−10.2947	−0.399512
$665$	−5.45225	−0.211429
$666$	−26.7888	−1.03804
$667$	2.51956	0.0975577
$668$	−31.4986	−1.21872
$669$	−5.39728	−0.208671
$670$	−73.7666	−2.84985
$671$	−3.31471	−0.127963
$672$	−3.37108	−0.130042
$673$	41.0605	1.58277	0.791383	−	0.611320i	$-0.209361\pi$
$673$	41.0605	1.58277	0.791383	+	0.611320i	$0.209361\pi$
$674$	−57.8274	−2.22743
$675$	−4.65149	−0.179036
$676$	11.1706	0.429640
$677$	−19.7133	−0.757643	−0.378822	−	0.925470i	$-0.623671\pi$
$677$	−19.7133	−0.757643	−0.378822	+	0.925470i	$0.623671\pi$
$678$	10.8961	0.418463
$679$	−5.67936	−0.217954
$680$	−0.918948	−0.0352400
$681$	11.8924	0.455718
$682$	−24.1817	−0.925965
$683$	22.8673	0.874994	0.437497	−	0.899220i	$-0.355865\pi$
$683$	22.8673	0.874994	0.437497	+	0.899220i	$0.355865\pi$
$684$	8.92579	0.341286
$685$	13.8905	0.530730
$686$	1.87802	0.0717030
$687$	−5.14598	−0.196331
$688$	1.70923	0.0651639
$689$	−27.3057	−1.04027
$690$	−0.883571	−0.0336370
$691$	3.98944	0.151766	0.0758828	−	0.997117i	$-0.475823\pi$
$691$	3.98944	0.151766	0.0758828	+	0.997117i	$0.475823\pi$
$692$	5.95982	0.226558
$693$	−5.24925	−0.199402
$694$	9.36309	0.355418
$695$	−15.2632	−0.578968
$696$	−2.78152	−0.105433
$697$	1.77243	0.0671355
$698$	−68.9561	−2.61003
$699$	3.44559	0.130324
$700$	−2.58776	−0.0978080
$701$	26.7118	1.00889	0.504445	−	0.863444i	$-0.331697\pi$
$701$	26.7118	1.00889	0.504445	+	0.863444i	$0.331697\pi$
$702$	23.2331	0.876878
$703$	10.8355	0.408670
$704$	7.33043	0.276276
$705$	−8.14948	−0.306927
$706$	−48.1998	−1.81402
$707$	−6.80332	−0.255865
$708$	7.55651	0.283991
$709$	0.877245	0.0329456	0.0164728	−	0.999864i	$-0.494756\pi$
$709$	0.877245	0.0329456	0.0164728	+	0.999864i	$0.494756\pi$
$710$	25.5918	0.960441
$711$	41.9309	1.57253
$712$	−12.4827	−0.467809
$713$	2.60296	0.0974814
$714$	0.356884	0.0133560
$715$	22.0681	0.825302
$716$	15.7134	0.587237
$717$	−4.80933	−0.179608
$718$	61.1605	2.28249
$719$	−14.5295	−0.541860	−0.270930	−	0.962599i	$-0.587331\pi$
$719$	−14.5295	−0.541860	−0.270930	+	0.962599i	$0.587331\pi$
$720$	−33.8950	−1.26319
$721$	6.45546	0.240414
$722$	27.3432	1.01761
$723$	−8.60697	−0.320097
$724$	5.88838	0.218840
$725$	−11.1625	−0.414564
$726$	6.62331	0.245814
$727$	−50.3342	−1.86679	−0.933396	−	0.358849i	$-0.883169\pi$
$727$	−50.3342	−1.86679	−0.933396	+	0.358849i	$0.883169\pi$
$728$	−4.00429	−0.148409
$729$	−15.5527	−0.576024
$730$	13.3057	0.492466
$731$	−0.144697	−0.00535182
$732$	1.27145	0.0469940
$733$	40.4121	1.49265	0.746327	−	0.665579i	$-0.231815\pi$
$733$	40.4121	1.49265	0.746327	+	0.665579i	$0.231815\pi$
$734$	2.07379	0.0765451
$735$	−1.22993	−0.0453665
$736$	−2.71282	−0.0999957
$737$	28.7262	1.05814
$738$	23.0976	0.850233
$739$	−23.4370	−0.862144	−0.431072	−	0.902318i	$-0.641865\pi$
$739$	−23.4370	−0.862144	−0.431072	+	0.902318i	$0.641865\pi$
$740$	20.3157	0.746818
$741$	−4.51479	−0.165855
$742$	−11.3773	−0.417672
$743$	43.0360	1.57884	0.789420	−	0.613854i	$-0.210382\pi$
$743$	43.0360	1.57884	0.789420	+	0.613854i	$0.210382\pi$
$744$	−2.87359	−0.105351
$745$	36.4002	1.33360
$746$	21.8136	0.798651
$747$	32.1453	1.17614
$748$	−1.15511	−0.0422349
$749$	−5.64178	−0.206146
$750$	−7.63459	−0.278776
$751$	−43.0525	−1.57101	−0.785505	−	0.618856i	$-0.787597\pi$
$751$	−43.0525	−1.57101	−0.785505	+	0.618856i	$0.787597\pi$
$752$	−31.2901	−1.14103
$753$	−6.06060	−0.220860
$754$	55.7540	2.03044
$755$	−34.6862	−1.26236
$756$	4.19099	0.152425
$757$	35.7281	1.29856	0.649279	−	0.760550i	$-0.275071\pi$
$757$	35.7281	1.29856	0.649279	+	0.760550i	$0.275071\pi$
$758$	−41.0028	−1.48929
$759$	0.344080	0.0124893
$760$	4.84379	0.175703
$761$	10.1847	0.369195	0.184598	−	0.982814i	$-0.440902\pi$
$761$	10.1847	0.369195	0.184598	+	0.982814i	$0.440902\pi$
$762$	18.0813	0.655016
$763$	−0.835858	−0.0302601
$764$	41.5987	1.50499
$765$	2.86942	0.103744
$766$	−47.6327	−1.72104
$767$	46.9246	1.69435
$768$	9.85011	0.355435
$769$	36.8035	1.32717	0.663585	−	0.748101i	$-0.269034\pi$
$769$	36.8035	1.32717	0.663585	+	0.748101i	$0.269034\pi$
$770$	9.19495	0.331363
$771$	12.9795	0.467446
$772$	12.0841	0.434918
$773$	10.4955	0.377496	0.188748	−	0.982026i	$-0.439557\pi$
$773$	10.4955	0.377496	0.188748	+	0.982026i	$0.439557\pi$
$774$	−1.88564	−0.0677778
$775$	−11.5320	−0.414240
$776$	5.04555	0.181125
$777$	2.44429	0.0876885
$778$	33.2268	1.19124
$779$	−9.34250	−0.334730
$780$	−8.46483	−0.303090
$781$	−9.96593	−0.356609
$782$	0.287196	0.0102701
$783$	18.0781	0.646059
$784$	−4.72233	−0.168655
$785$	40.5713	1.44805
$786$	−10.7387	−0.383038
$787$	3.34393	0.119198	0.0595991	−	0.998222i	$-0.481018\pi$
$787$	3.34393	0.119198	0.0595991	+	0.998222i	$0.481018\pi$
$788$	−13.9538	−0.497082
$789$	15.1618	0.539774
$790$	−73.4491	−2.61320
$791$	12.2056	0.433982
$792$	4.66344	0.165708
$793$	7.89546	0.280376
$794$	−41.0954	−1.45842
$795$	7.45104	0.264261
$796$	−1.38461	−0.0490762
$797$	28.7868	1.01968	0.509840	−	0.860269i	$-0.329705\pi$
$797$	28.7868	1.01968	0.509840	+	0.860269i	$0.329705\pi$
$798$	−1.88114	−0.0665917
$799$	2.64890	0.0937115
$800$	12.0187	0.424924
$801$	38.9773	1.37720
$802$	34.3442	1.21274
$803$	−5.18150	−0.182851
$804$	−11.0187	−0.388599
$805$	−0.989760	−0.0348844
$806$	57.5995	2.02885
$807$	−6.96585	−0.245209
$808$	6.04408	0.212630
$809$	17.8550	0.627748	0.313874	−	0.949465i	$-0.398373\pi$
$809$	17.8550	0.627748	0.313874	+	0.949465i	$0.398373\pi$
$810$	34.0993	1.19813
$811$	−3.04527	−0.106934	−0.0534669	−	0.998570i	$-0.517027\pi$
$811$	−3.04527	−0.106934	−0.0534669	+	0.998570i	$0.517027\pi$
$812$	10.0574	0.352945
$813$	2.61885	0.0918472
$814$	−18.2736	−0.640489
$815$	49.9776	1.75064
$816$	−0.897395	−0.0314151
$817$	0.762702	0.0266836
$818$	−7.62603	−0.266638
$819$	12.5034	0.436905
$820$	−17.5164	−0.611698
$821$	34.9064	1.21824	0.609121	−	0.793077i	$-0.291522\pi$
$821$	34.9064	1.21824	0.609121	+	0.793077i	$0.291522\pi$
$822$	4.79252	0.167158
$823$	30.5661	1.06547	0.532734	−	0.846283i	$-0.321165\pi$
$823$	30.5661	1.06547	0.532734	+	0.846283i	$0.321165\pi$
$824$	−5.73504	−0.199790
$825$	−1.52439	−0.0530724
$826$	19.5517	0.680290
$827$	−8.45164	−0.293892	−0.146946	−	0.989144i	$-0.546944\pi$
$827$	−8.45164	−0.293892	−0.146946	+	0.989144i	$0.546944\pi$
$828$	1.62032	0.0563100
$829$	−37.4945	−1.30224	−0.651119	−	0.758976i	$-0.725700\pi$
$829$	−37.4945	−1.30224	−0.651119	+	0.758976i	$0.725700\pi$
$830$	−56.3080	−1.95448
$831$	2.97988	0.103371
$832$	−17.4607	−0.605340
$833$	0.399775	0.0138514
$834$	−5.26614	−0.182352
$835$	53.3745	1.84710
$836$	6.08860	0.210579
$837$	18.6765	0.645555
$838$	26.2579	0.907063
$839$	14.4397	0.498512	0.249256	−	0.968438i	$-0.419814\pi$
$839$	14.4397	0.498512	0.249256	+	0.968438i	$0.419814\pi$
$840$	1.09267	0.0377006
$841$	14.3832	0.495973
$842$	3.82156	0.131700
$843$	6.12390	0.210918
$844$	28.6061	0.984662
$845$	−18.9287	−0.651167
$846$	34.5195	1.18680
$847$	7.41930	0.254930
$848$	28.6084	0.982418
$849$	1.80018	0.0617820
$850$	−1.27237	−0.0436420
$851$	1.96700	0.0674278
$852$	3.82270	0.130964
$853$	−39.0026	−1.33543	−0.667713	−	0.744419i	$-0.732726\pi$
$853$	−39.0026	−1.33543	−0.667713	+	0.744419i	$0.732726\pi$
$854$	3.28974	0.112573
$855$	−15.1248	−0.517257
$856$	5.01217	0.171312
$857$	19.6518	0.671294	0.335647	−	0.941988i	$-0.391045\pi$
$857$	19.6518	0.671294	0.335647	+	0.941988i	$0.391045\pi$
$858$	7.61397	0.259937
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	1.43000	0.0487625
$861$	−2.10749	−0.0718231
$862$	−57.9991	−1.97546
$863$	−25.8585	−0.880232	−0.440116	−	0.897941i	$-0.645063\pi$
$863$	−25.8585	−0.880232	−0.440116	+	0.897941i	$0.645063\pi$
$864$	−19.4648	−0.662205
$865$	−10.0989	−0.343374
$866$	−69.3629	−2.35705
$867$	−8.00496	−0.271863
$868$	10.3903	0.352669
$869$	28.6025	0.970274
$870$	−15.2139	−0.515798
$871$	−68.4241	−2.31846
$872$	0.742578	0.0251469
$873$	−15.7548	−0.533219
$874$	−1.51381	−0.0512055
$875$	−8.55212	−0.289114
$876$	1.98750	0.0671515
$877$	6.01031	0.202954	0.101477	−	0.994838i	$-0.467643\pi$
$877$	6.01031	0.202954	0.101477	+	0.994838i	$0.467643\pi$
$878$	−61.8276	−2.08658
$879$	12.6632	0.427119
$880$	−23.1210	−0.779408
$881$	−11.4598	−0.386090	−0.193045	−	0.981190i	$-0.561836\pi$
$881$	−11.4598	−0.386090	−0.193045	+	0.981190i	$0.561836\pi$
$882$	5.20970	0.175420
$883$	31.5794	1.06273	0.531366	−	0.847143i	$-0.321679\pi$
$883$	31.5794	1.06273	0.531366	+	0.847143i	$0.321679\pi$
$884$	2.75141	0.0925398
$885$	−12.8045	−0.430420
$886$	18.0547	0.606559
$887$	23.2132	0.779422	0.389711	−	0.920937i	$-0.372575\pi$
$887$	23.2132	0.779422	0.389711	+	0.920937i	$0.372575\pi$
$888$	−2.17151	−0.0728712
$889$	20.2543	0.679308
$890$	−68.2755	−2.28860
$891$	−13.2789	−0.444861
$892$	−17.3375	−0.580502
$893$	−13.9624	−0.467235
$894$	12.5588	0.420030
$895$	−26.6264	−0.890022
$896$	6.90841	0.230794
$897$	−0.819580	−0.0273650
$898$	51.4188	1.71587
$899$	44.8192	1.49480
$900$	−7.17855	−0.239285
$901$	−2.42188	−0.0806846
$902$	15.7557	0.524606
$903$	0.172051	0.00572550
$904$	−10.8435	−0.360649
$905$	−9.97788	−0.331676
$906$	−11.9675	−0.397593
$907$	43.8156	1.45487	0.727437	−	0.686174i	$-0.240711\pi$
$907$	43.8156	1.45487	0.727437	+	0.686174i	$0.240711\pi$
$908$	38.2015	1.26776
$909$	−18.8727	−0.625968
$910$	−21.9019	−0.726040
$911$	7.29805	0.241795	0.120898	−	0.992665i	$-0.461423\pi$
$911$	7.29805	0.241795	0.120898	+	0.992665i	$0.461423\pi$
$912$	4.73018	0.156632
$913$	21.9275	0.725693
$914$	45.1307	1.49279
$915$	−2.15447	−0.0712246
$916$	−16.5303	−0.546175
$917$	−12.0293	−0.397243
$918$	2.06066	0.0680120
$919$	17.9789	0.593070	0.296535	−	0.955022i	$-0.404169\pi$
$919$	17.9789	0.593070	0.296535	+	0.955022i	$0.404169\pi$
$920$	0.879304	0.0289898
$921$	1.88209	0.0620170
$922$	−14.5884	−0.480442
$923$	23.7383	0.781356
$924$	1.37347	0.0451839
$925$	−8.71445	−0.286529
$926$	−49.8553	−1.63835
$927$	17.9077	0.588167
$928$	−46.7108	−1.53336
$929$	53.5887	1.75819	0.879095	−	0.476647i	$-0.158148\pi$
$929$	53.5887	1.75819	0.879095	+	0.476647i	$0.158148\pi$
$930$	−15.7174	−0.515395
$931$	−2.10722	−0.0690613
$932$	11.0682	0.362549
$933$	8.66006	0.283518
$934$	56.7390	1.85656
$935$	1.95734	0.0640117
$936$	−11.1081	−0.363078
$937$	−22.1378	−0.723210	−0.361605	−	0.932331i	$-0.617771\pi$
$937$	−22.1378	−0.723210	−0.361605	+	0.932331i	$0.617771\pi$
$938$	−28.5097	−0.930876
$939$	−2.32611	−0.0759098
$940$	−26.1783	−0.853842
$941$	19.1324	0.623698	0.311849	−	0.950132i	$-0.399052\pi$
$941$	19.1324	0.623698	0.311849	+	0.950132i	$0.399052\pi$
$942$	13.9979	0.456078
$943$	−1.69596	−0.0552282
$944$	−49.1633	−1.60013
$945$	−7.10164	−0.231016
$946$	−1.28626	−0.0418199
$947$	3.88235	0.126159	0.0630797	−	0.998008i	$-0.479908\pi$
$947$	3.88235	0.126159	0.0630797	+	0.998008i	$0.479908\pi$
$948$	−10.9713	−0.356330
$949$	12.3420	0.400640
$950$	6.70670	0.217594
$951$	−4.76475	−0.154508
$952$	−0.355160	−0.0115108
$953$	−50.5859	−1.63864	−0.819319	−	0.573338i	$-0.805648\pi$
$953$	−50.5859	−1.63864	−0.819319	+	0.573338i	$0.805648\pi$
$954$	−31.5610	−1.02183
$955$	−70.4891	−2.28097
$956$	−15.4488	−0.499651
$957$	5.92457	0.191514
$958$	4.03385	0.130328
$959$	5.36849	0.173358
$960$	4.76458	0.153776
$961$	15.3027	0.493637
$962$	43.5267	1.40336
$963$	−15.6506	−0.504332
$964$	−27.6479	−0.890478
$965$	−20.4766	−0.659166
$966$	−0.341488	−0.0109872
$967$	−36.7249	−1.18099	−0.590496	−	0.807041i	$-0.701068\pi$
$967$	−36.7249	−1.18099	−0.590496	+	0.807041i	$0.701068\pi$
$968$	−6.59132	−0.211853
$969$	−0.400440	−0.0128640
$970$	27.5972	0.886093
$971$	43.4351	1.39390	0.696950	−	0.717120i	$-0.254540\pi$
$971$	43.4351	1.39390	0.696950	+	0.717120i	$0.254540\pi$
$972$	17.6665	0.566652
$973$	−5.89903	−0.189114
$974$	−33.4796	−1.07275
$975$	3.63101	0.116285
$976$	−8.27214	−0.264785
$977$	−36.6603	−1.17287	−0.586434	−	0.809997i	$-0.699469\pi$
$977$	−36.6603	−1.17287	−0.586434	+	0.809997i	$0.699469\pi$
$978$	17.2433	0.551381
$979$	26.5878	0.849750
$980$	−3.95085	−0.126205
$981$	−2.31871	−0.0740306
$982$	−73.5070	−2.34570
$983$	−53.8454	−1.71740	−0.858700	−	0.512478i	$-0.828728\pi$
$983$	−53.8454	−1.71740	−0.858700	+	0.512478i	$0.828728\pi$
$984$	1.87230	0.0596867
$985$	23.6447	0.753382
$986$	4.94510	0.157484
$987$	−3.14966	−0.100255
$988$	−14.5027	−0.461393
$989$	0.138455	0.00440261
$990$	25.5072	0.810672
$991$	23.6257	0.750496	0.375248	−	0.926924i	$-0.377558\pi$
$991$	23.6257	0.750496	0.375248	+	0.926924i	$0.377558\pi$
$992$	−48.2570	−1.53216
$993$	−1.52477	−0.0483871
$994$	9.89085	0.313719
$995$	2.34623	0.0743804
$996$	−8.41087	−0.266509
$997$	5.83015	0.184643	0.0923214	−	0.995729i	$-0.470571\pi$
$997$	5.83015	0.184643	0.0923214	+	0.995729i	$0.470571\pi$
$998$	−28.1569	−0.891293
$999$	14.1134	0.446530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.20	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.20	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87802 q^{2} +0.475349 q^{3} +1.52695 q^{4} -2.58742 q^{5} -0.892713 q^{6} -1.00000 q^{7} +0.888402 q^{8} -2.77404 q^{9} +O(q^{10})\)	\(q-1.87802 q^{2} +0.475349 q^{3} +1.52695 q^{4} -2.58742 q^{5} -0.892713 q^{6} -1.00000 q^{7} +0.888402 q^{8} -2.77404 q^{9} +4.85921 q^{10} -1.89227 q^{11} +0.725832 q^{12} +4.50729 q^{13} +1.87802 q^{14} -1.22993 q^{15} -4.72233 q^{16} +0.399775 q^{17} +5.20970 q^{18} -2.10722 q^{19} -3.95085 q^{20} -0.475349 q^{21} +3.55372 q^{22} -0.382528 q^{23} +0.422301 q^{24} +1.69473 q^{25} -8.46477 q^{26} -2.74468 q^{27} -1.52695 q^{28} -6.58659 q^{29} +2.30982 q^{30} -6.80461 q^{31} +7.09181 q^{32} -0.899490 q^{33} -0.750783 q^{34} +2.58742 q^{35} -4.23582 q^{36} -5.14210 q^{37} +3.95739 q^{38} +2.14254 q^{39} -2.29867 q^{40} +4.43357 q^{41} +0.892713 q^{42} -0.361947 q^{43} -2.88940 q^{44} +7.17761 q^{45} +0.718394 q^{46} +6.62600 q^{47} -2.24475 q^{48} +1.00000 q^{49} -3.18272 q^{50} +0.190032 q^{51} +6.88239 q^{52} -6.05812 q^{53} +5.15456 q^{54} +4.89610 q^{55} -0.888402 q^{56} -1.00166 q^{57} +12.3697 q^{58} +10.4108 q^{59} -1.87803 q^{60} +1.75171 q^{61} +12.7792 q^{62} +2.77404 q^{63} -3.87388 q^{64} -11.6622 q^{65} +1.68926 q^{66} -15.1808 q^{67} +0.610434 q^{68} -0.181834 q^{69} -4.85921 q^{70} +5.26665 q^{71} -2.46447 q^{72} +2.73824 q^{73} +9.65695 q^{74} +0.805586 q^{75} -3.21761 q^{76} +1.89227 q^{77} -4.02372 q^{78} -15.1154 q^{79} +12.2186 q^{80} +7.01745 q^{81} -8.32632 q^{82} -11.5879 q^{83} -0.725832 q^{84} -1.03438 q^{85} +0.679743 q^{86} -3.13093 q^{87} -1.68110 q^{88} -14.0507 q^{89} -13.4797 q^{90} -4.50729 q^{91} -0.584100 q^{92} -3.23456 q^{93} -12.4437 q^{94} +5.45225 q^{95} +3.37108 q^{96} +5.67936 q^{97} -1.87802 q^{98} +5.24925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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