LMFDB - Embedded newform 6014.2.a.j.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.01996 q^{3} +1.00000 q^{4} -1.74888 q^{5} +1.01996 q^{6} +2.14281 q^{7} -1.00000 q^{8} -1.95968 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.01996 q^{3} +1.00000 q^{4} -1.74888 q^{5} +1.01996 q^{6} +2.14281 q^{7} -1.00000 q^{8} -1.95968 q^{9} +1.74888 q^{10} +5.24727 q^{11} -1.01996 q^{12} +4.79853 q^{13} -2.14281 q^{14} +1.78378 q^{15} +1.00000 q^{16} +7.10961 q^{17} +1.95968 q^{18} -1.80956 q^{19} -1.74888 q^{20} -2.18557 q^{21} -5.24727 q^{22} +6.24486 q^{23} +1.01996 q^{24} -1.94143 q^{25} -4.79853 q^{26} +5.05867 q^{27} +2.14281 q^{28} +1.28412 q^{29} -1.78378 q^{30} -1.00000 q^{31} -1.00000 q^{32} -5.35199 q^{33} -7.10961 q^{34} -3.74751 q^{35} -1.95968 q^{36} +7.18808 q^{37} +1.80956 q^{38} -4.89430 q^{39} +1.74888 q^{40} -2.43112 q^{41} +2.18557 q^{42} +9.45570 q^{43} +5.24727 q^{44} +3.42725 q^{45} -6.24486 q^{46} +12.6892 q^{47} -1.01996 q^{48} -2.40837 q^{49} +1.94143 q^{50} -7.25151 q^{51} +4.79853 q^{52} +1.23640 q^{53} -5.05867 q^{54} -9.17682 q^{55} -2.14281 q^{56} +1.84567 q^{57} -1.28412 q^{58} +8.42442 q^{59} +1.78378 q^{60} +13.1705 q^{61} +1.00000 q^{62} -4.19923 q^{63} +1.00000 q^{64} -8.39204 q^{65} +5.35199 q^{66} +11.5344 q^{67} +7.10961 q^{68} -6.36949 q^{69} +3.74751 q^{70} -11.7865 q^{71} +1.95968 q^{72} -8.28427 q^{73} -7.18808 q^{74} +1.98018 q^{75} -1.80956 q^{76} +11.2439 q^{77} +4.89430 q^{78} -15.1495 q^{79} -1.74888 q^{80} +0.719420 q^{81} +2.43112 q^{82} -6.79688 q^{83} -2.18557 q^{84} -12.4338 q^{85} -9.45570 q^{86} -1.30975 q^{87} -5.24727 q^{88} -16.5698 q^{89} -3.42725 q^{90} +10.2823 q^{91} +6.24486 q^{92} +1.01996 q^{93} -12.6892 q^{94} +3.16469 q^{95} +1.01996 q^{96} +1.00000 q^{97} +2.40837 q^{98} -10.2830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.01996	−0.588873	−0.294437	−	0.955671i	$-0.595132\pi$
$3$	−1.01996	−0.588873	−0.294437	+	0.955671i	$0.595132\pi$
$4$	1.00000	0.500000
$5$	−1.74888	−0.782121	−0.391061	−	0.920365i	$-0.627892\pi$
$5$	−1.74888	−0.782121	−0.391061	+	0.920365i	$0.627892\pi$
$6$	1.01996	0.416396
$7$	2.14281	0.809905	0.404953	−	0.914338i	$-0.367288\pi$
$7$	2.14281	0.809905	0.404953	+	0.914338i	$0.367288\pi$
$8$	−1.00000	−0.353553
$9$	−1.95968	−0.653228
$10$	1.74888	0.553043
$11$	5.24727	1.58211	0.791055	−	0.611745i	$-0.209532\pi$
$11$	5.24727	1.58211	0.791055	+	0.611745i	$0.209532\pi$
$12$	−1.01996	−0.294437
$13$	4.79853	1.33087	0.665437	−	0.746454i	$-0.268245\pi$
$13$	4.79853	1.33087	0.665437	+	0.746454i	$0.268245\pi$
$14$	−2.14281	−0.572690
$15$	1.78378	0.460570
$16$	1.00000	0.250000
$17$	7.10961	1.72433	0.862167	−	0.506624i	$-0.169107\pi$
$17$	7.10961	1.72433	0.862167	+	0.506624i	$0.169107\pi$
$18$	1.95968	0.461902
$19$	−1.80956	−0.415141	−0.207570	−	0.978220i	$-0.566556\pi$
$19$	−1.80956	−0.415141	−0.207570	+	0.978220i	$0.566556\pi$
$20$	−1.74888	−0.391061
$21$	−2.18557	−0.476932
$22$	−5.24727	−1.11872
$23$	6.24486	1.30214	0.651071	−	0.759017i	$-0.274320\pi$
$23$	6.24486	1.30214	0.651071	+	0.759017i	$0.274320\pi$
$24$	1.01996	0.208198
$25$	−1.94143	−0.388286
$26$	−4.79853	−0.941069
$27$	5.05867	0.973542
$28$	2.14281	0.404953
$29$	1.28412	0.238456	0.119228	−	0.992867i	$-0.461958\pi$
$29$	1.28412	0.238456	0.119228	+	0.992867i	$0.461958\pi$
$30$	−1.78378	−0.325672
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−5.35199	−0.931662
$34$	−7.10961	−1.21929
$35$	−3.74751	−0.633444
$36$	−1.95968	−0.326614
$37$	7.18808	1.18171	0.590857	−	0.806776i	$-0.298790\pi$
$37$	7.18808	1.18171	0.590857	+	0.806776i	$0.298790\pi$
$38$	1.80956	0.293549
$39$	−4.89430	−0.783716
$40$	1.74888	0.276522
$41$	−2.43112	−0.379678	−0.189839	−	0.981815i	$-0.560797\pi$
$41$	−2.43112	−0.379678	−0.189839	+	0.981815i	$0.560797\pi$
$42$	2.18557	0.337242
$43$	9.45570	1.44198	0.720990	−	0.692945i	$-0.243687\pi$
$43$	9.45570	1.44198	0.720990	+	0.692945i	$0.243687\pi$
$44$	5.24727	0.791055
$45$	3.42725	0.510904
$46$	−6.24486	−0.920754
$47$	12.6892	1.85091	0.925453	−	0.378863i	$-0.123685\pi$
$47$	12.6892	1.85091	0.925453	+	0.378863i	$0.123685\pi$
$48$	−1.01996	−0.147218
$49$	−2.40837	−0.344053
$50$	1.94143	0.274560
$51$	−7.25151	−1.01541
$52$	4.79853	0.665437
$53$	1.23640	0.169832	0.0849162	−	0.996388i	$-0.472938\pi$
$53$	1.23640	0.169832	0.0849162	+	0.996388i	$0.472938\pi$
$54$	−5.05867	−0.688398
$55$	−9.17682	−1.23740
$56$	−2.14281	−0.286345
$57$	1.84567	0.244465
$58$	−1.28412	−0.168614
$59$	8.42442	1.09677	0.548383	−	0.836227i	$-0.315244\pi$
$59$	8.42442	1.09677	0.548383	+	0.836227i	$0.315244\pi$
$60$	1.78378	0.230285
$61$	13.1705	1.68631	0.843153	−	0.537674i	$-0.180697\pi$
$61$	13.1705	1.68631	0.843153	+	0.537674i	$0.180697\pi$
$62$	1.00000	0.127000
$63$	−4.19923	−0.529053
$64$	1.00000	0.125000
$65$	−8.39204	−1.04090
$66$	5.35199	0.658785
$67$	11.5344	1.40915	0.704574	−	0.709631i	$-0.251138\pi$
$67$	11.5344	1.40915	0.704574	+	0.709631i	$0.251138\pi$
$68$	7.10961	0.862167
$69$	−6.36949	−0.766797
$70$	3.74751	0.447913
$71$	−11.7865	−1.39880	−0.699399	−	0.714731i	$-0.746549\pi$
$71$	−11.7865	−1.39880	−0.699399	+	0.714731i	$0.746549\pi$
$72$	1.95968	0.230951
$73$	−8.28427	−0.969601	−0.484801	−	0.874625i	$-0.661108\pi$
$73$	−8.28427	−0.969601	−0.484801	+	0.874625i	$0.661108\pi$
$74$	−7.18808	−0.835598
$75$	1.98018	0.228651
$76$	−1.80956	−0.207570
$77$	11.2439	1.28136
$78$	4.89430	0.554171
$79$	−15.1495	−1.70445	−0.852225	−	0.523176i	$-0.824747\pi$
$79$	−15.1495	−1.70445	−0.852225	+	0.523176i	$0.824747\pi$
$80$	−1.74888	−0.195530
$81$	0.719420	0.0799355
$82$	2.43112	0.268473
$83$	−6.79688	−0.746055	−0.373027	−	0.927820i	$-0.621680\pi$
$83$	−6.79688	−0.746055	−0.373027	+	0.927820i	$0.621680\pi$
$84$	−2.18557	−0.238466
$85$	−12.4338	−1.34864
$86$	−9.45570	−1.01963
$87$	−1.30975	−0.140420
$88$	−5.24727	−0.559360
$89$	−16.5698	−1.75640	−0.878199	−	0.478295i	$-0.841255\pi$
$89$	−16.5698	−1.75640	−0.878199	+	0.478295i	$0.841255\pi$
$90$	−3.42725	−0.361264
$91$	10.2823	1.07788
$92$	6.24486	0.651071
$93$	1.01996	0.105765
$94$	−12.6892	−1.30879
$95$	3.16469	0.324690
$96$	1.01996	0.104099
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	2.40837	0.243282
$99$	−10.2830	−1.03348
$100$	−1.94143	−0.194143
$101$	3.28023	0.326395	0.163198	−	0.986593i	$-0.447819\pi$
$101$	3.28023	0.326395	0.163198	+	0.986593i	$0.447819\pi$
$102$	7.25151	0.718006
$103$	−5.10139	−0.502655	−0.251328	−	0.967902i	$-0.580867\pi$
$103$	−5.10139	−0.502655	−0.251328	+	0.967902i	$0.580867\pi$
$104$	−4.79853	−0.470535
$105$	3.82230	0.373018
$106$	−1.23640	−0.120090
$107$	−10.8137	−1.04540	−0.522699	−	0.852517i	$-0.675075\pi$
$107$	−10.8137	−1.04540	−0.522699	+	0.852517i	$0.675075\pi$
$108$	5.05867	0.486771
$109$	−3.67037	−0.351558	−0.175779	−	0.984430i	$-0.556244\pi$
$109$	−3.67037	−0.351558	−0.175779	+	0.984430i	$0.556244\pi$
$110$	9.17682	0.874976
$111$	−7.33154	−0.695879
$112$	2.14281	0.202476
$113$	−10.8187	−1.01773	−0.508867	−	0.860845i	$-0.669936\pi$
$113$	−10.8187	−1.01773	−0.508867	+	0.860845i	$0.669936\pi$
$114$	−1.84567	−0.172863
$115$	−10.9215	−1.01843
$116$	1.28412	0.119228
$117$	−9.40361	−0.869364
$118$	−8.42442	−0.775531
$119$	15.2345	1.39655
$120$	−1.78378	−0.162836
$121$	16.5338	1.50307
$122$	−13.1705	−1.19240
$123$	2.47964	0.223582
$124$	−1.00000	−0.0898027
$125$	12.1397	1.08581
$126$	4.19923	0.374097
$127$	16.5026	1.46437	0.732184	−	0.681107i	$-0.238501\pi$
$127$	16.5026	1.46437	0.732184	+	0.681107i	$0.238501\pi$
$128$	−1.00000	−0.0883883
$129$	−9.64442	−0.849144
$130$	8.39204	0.736031
$131$	−8.37895	−0.732072	−0.366036	−	0.930601i	$-0.619285\pi$
$131$	−8.37895	−0.732072	−0.366036	+	0.930601i	$0.619285\pi$
$132$	−5.35199	−0.465831
$133$	−3.87753	−0.336225
$134$	−11.5344	−0.996418
$135$	−8.84699	−0.761428
$136$	−7.10961	−0.609644
$137$	−1.89331	−0.161757	−0.0808783	−	0.996724i	$-0.525773\pi$
$137$	−1.89331	−0.161757	−0.0808783	+	0.996724i	$0.525773\pi$
$138$	6.36949	0.542207
$139$	−9.25610	−0.785092	−0.392546	−	0.919732i	$-0.628406\pi$
$139$	−9.25610	−0.785092	−0.392546	+	0.919732i	$0.628406\pi$
$140$	−3.74751	−0.316722
$141$	−12.9424	−1.08995
$142$	11.7865	0.989099
$143$	25.1792	2.10559
$144$	−1.95968	−0.163307
$145$	−2.24577	−0.186501
$146$	8.28427	0.685611
$147$	2.45644	0.202604
$148$	7.18808	0.590857
$149$	−20.7777	−1.70217	−0.851086	−	0.525027i	$-0.824055\pi$
$149$	−20.7777	−1.70217	−0.851086	+	0.525027i	$0.824055\pi$
$150$	−1.98018	−0.161681
$151$	16.9544	1.37973	0.689863	−	0.723940i	$-0.257671\pi$
$151$	16.9544	1.37973	0.689863	+	0.723940i	$0.257671\pi$
$152$	1.80956	0.146774
$153$	−13.9326	−1.12638
$154$	−11.2439	−0.906058
$155$	1.74888	0.140473
$156$	−4.89430	−0.391858
$157$	17.0072	1.35732	0.678659	−	0.734453i	$-0.262561\pi$
$157$	17.0072	1.35732	0.678659	+	0.734453i	$0.262561\pi$
$158$	15.1495	1.20523
$159$	−1.26108	−0.100010
$160$	1.74888	0.138261
$161$	13.3815	1.05461
$162$	−0.719420	−0.0565230
$163$	22.1536	1.73520	0.867601	−	0.497260i	$-0.165661\pi$
$163$	22.1536	1.73520	0.867601	+	0.497260i	$0.165661\pi$
$164$	−2.43112	−0.189839
$165$	9.35998	0.728673
$166$	6.79688	0.527540
$167$	−19.6564	−1.52106	−0.760530	−	0.649302i	$-0.775061\pi$
$167$	−19.6564	−1.52106	−0.760530	+	0.649302i	$0.775061\pi$
$168$	2.18557	0.168621
$169$	10.0259	0.771224
$170$	12.4338	0.953632
$171$	3.54616	0.271182
$172$	9.45570	0.720990
$173$	0.660237	0.0501969	0.0250984	−	0.999685i	$-0.492010\pi$
$173$	0.660237	0.0501969	0.0250984	+	0.999685i	$0.492010\pi$
$174$	1.30975	0.0992921
$175$	−4.16011	−0.314475
$176$	5.24727	0.395528
$177$	−8.59256	−0.645856
$178$	16.5698	1.24196
$179$	0.678004	0.0506764	0.0253382	−	0.999679i	$-0.491934\pi$
$179$	0.678004	0.0506764	0.0253382	+	0.999679i	$0.491934\pi$
$180$	3.42725	0.255452
$181$	−25.6950	−1.90989	−0.954946	−	0.296780i	$-0.904087\pi$
$181$	−25.6950	−1.90989	−0.954946	+	0.296780i	$0.904087\pi$
$182$	−10.2823	−0.762177
$183$	−13.4333	−0.993020
$184$	−6.24486	−0.460377
$185$	−12.5711	−0.924243
$186$	−1.01996	−0.0747870
$187$	37.3060	2.72809
$188$	12.6892	0.925453
$189$	10.8398	0.788477
$190$	−3.16469	−0.229591
$191$	13.9890	1.01221	0.506103	−	0.862473i	$-0.331086\pi$
$191$	13.9890	1.01221	0.506103	+	0.862473i	$0.331086\pi$
$192$	−1.01996	−0.0736092
$193$	−11.7080	−0.842763	−0.421381	−	0.906883i	$-0.638455\pi$
$193$	−11.7080	−0.842763	−0.421381	+	0.906883i	$0.638455\pi$
$194$	−1.00000	−0.0717958
$195$	8.55953	0.612961
$196$	−2.40837	−0.172027
$197$	−12.0155	−0.856071	−0.428035	−	0.903762i	$-0.640794\pi$
$197$	−12.0155	−0.856071	−0.428035	+	0.903762i	$0.640794\pi$
$198$	10.2830	0.730780
$199$	18.0595	1.28020	0.640102	−	0.768290i	$-0.278892\pi$
$199$	18.0595	1.28020	0.640102	+	0.768290i	$0.278892\pi$
$200$	1.94143	0.137280
$201$	−11.7646	−0.829809
$202$	−3.28023	−0.230796
$203$	2.75163	0.193127
$204$	−7.25151	−0.507707
$205$	4.25173	0.296954
$206$	5.10139	0.355431
$207$	−12.2380	−0.850597
$208$	4.79853	0.332718
$209$	−9.49523	−0.656798
$210$	−3.82230	−0.263764
$211$	−18.7555	−1.29118	−0.645590	−	0.763684i	$-0.723389\pi$
$211$	−18.7555	−1.29118	−0.645590	+	0.763684i	$0.723389\pi$
$212$	1.23640	0.0849162
$213$	12.0217	0.823715
$214$	10.8137	0.739208
$215$	−16.5369	−1.12780
$216$	−5.05867	−0.344199
$217$	−2.14281	−0.145463
$218$	3.67037	0.248589
$219$	8.44962	0.570972
$220$	−9.17682	−0.618701
$221$	34.1157	2.29487
$222$	7.33154	0.492061
$223$	29.4327	1.97096	0.985479	−	0.169796i	$-0.0543108\pi$
$223$	29.4327	1.97096	0.985479	+	0.169796i	$0.0543108\pi$
$224$	−2.14281	−0.143172
$225$	3.80459	0.253639
$226$	10.8187	0.719647
$227$	−12.2104	−0.810430	−0.405215	−	0.914221i	$-0.632803\pi$
$227$	−12.2104	−0.810430	−0.405215	+	0.914221i	$0.632803\pi$
$228$	1.84567	0.122233
$229$	2.51537	0.166221	0.0831103	−	0.996540i	$-0.473515\pi$
$229$	2.51537	0.166221	0.0831103	+	0.996540i	$0.473515\pi$
$230$	10.9215	0.720141
$231$	−11.4683	−0.754558
$232$	−1.28412	−0.0843069
$233$	2.30608	0.151076	0.0755380	−	0.997143i	$-0.475933\pi$
$233$	2.30608	0.151076	0.0755380	+	0.997143i	$0.475933\pi$
$234$	9.40361	0.614733
$235$	−22.1918	−1.44763
$236$	8.42442	0.548383
$237$	15.4518	1.00370
$238$	−15.2345	−0.987508
$239$	−1.64078	−0.106133	−0.0530666	−	0.998591i	$-0.516900\pi$
$239$	−1.64078	−0.106133	−0.0530666	+	0.998591i	$0.516900\pi$
$240$	1.78378	0.115143
$241$	−16.6362	−1.07163	−0.535814	−	0.844336i	$-0.679995\pi$
$241$	−16.6362	−1.07163	−0.535814	+	0.844336i	$0.679995\pi$
$242$	−16.5338	−1.06283
$243$	−15.9098	−1.02061
$244$	13.1705	0.843153
$245$	4.21195	0.269092
$246$	−2.47964	−0.158096
$247$	−8.68321	−0.552500
$248$	1.00000	0.0635001
$249$	6.93254	0.439332
$250$	−12.1397	−0.767782
$251$	2.90688	0.183481	0.0917403	−	0.995783i	$-0.470757\pi$
$251$	2.90688	0.183481	0.0917403	+	0.995783i	$0.470757\pi$
$252$	−4.19923	−0.264527
$253$	32.7684	2.06013
$254$	−16.5026	−1.03546
$255$	12.6820	0.794177
$256$	1.00000	0.0625000
$257$	13.7750	0.859260	0.429630	−	0.903005i	$-0.358644\pi$
$257$	13.7750	0.859260	0.429630	+	0.903005i	$0.358644\pi$
$258$	9.64442	0.600435
$259$	15.4027	0.957076
$260$	−8.39204	−0.520452
$261$	−2.51648	−0.155766
$262$	8.37895	0.517653
$263$	−20.4852	−1.26317	−0.631586	−	0.775306i	$-0.717596\pi$
$263$	−20.4852	−1.26317	−0.631586	+	0.775306i	$0.717596\pi$
$264$	5.35199	0.329392
$265$	−2.16231	−0.132830
$266$	3.87753	0.237747
$267$	16.9005	1.03430
$268$	11.5344	0.704574
$269$	−1.17983	−0.0719358	−0.0359679	−	0.999353i	$-0.511451\pi$
$269$	−1.17983	−0.0719358	−0.0359679	+	0.999353i	$0.511451\pi$
$270$	8.84699	0.538411
$271$	17.2608	1.04852	0.524260	−	0.851558i	$-0.324342\pi$
$271$	17.2608	1.04852	0.524260	+	0.851558i	$0.324342\pi$
$272$	7.10961	0.431084
$273$	−10.4876	−0.634735
$274$	1.89331	0.114379
$275$	−10.1872	−0.614311
$276$	−6.36949	−0.383399
$277$	−11.5229	−0.692347	−0.346173	−	0.938171i	$-0.612519\pi$
$277$	−11.5229	−0.692347	−0.346173	+	0.938171i	$0.612519\pi$
$278$	9.25610	0.555144
$279$	1.95968	0.117323
$280$	3.74751	0.223956
$281$	26.6224	1.58816	0.794080	−	0.607814i	$-0.207953\pi$
$281$	26.6224	1.58816	0.794080	+	0.607814i	$0.207953\pi$
$282$	12.9424	0.770710
$283$	−7.31417	−0.434782	−0.217391	−	0.976085i	$-0.569755\pi$
$283$	−7.31417	−0.434782	−0.217391	+	0.976085i	$0.569755\pi$
$284$	−11.7865	−0.699399
$285$	−3.22785	−0.191202
$286$	−25.1792	−1.48888
$287$	−5.20943	−0.307503
$288$	1.95968	0.115476
$289$	33.5466	1.97333
$290$	2.24577	0.131876
$291$	−1.01996	−0.0597910
$292$	−8.28427	−0.484801
$293$	−11.1339	−0.650450	−0.325225	−	0.945637i	$-0.605440\pi$
$293$	−11.1339	−0.650450	−0.325225	+	0.945637i	$0.605440\pi$
$294$	−2.45644	−0.143263
$295$	−14.7333	−0.857804
$296$	−7.18808	−0.417799
$297$	26.5442	1.54025
$298$	20.7777	1.20362
$299$	29.9661	1.73299
$300$	1.98018	0.114326
$301$	20.2617	1.16787
$302$	−16.9544	−0.975613
$303$	−3.34570	−0.192206
$304$	−1.80956	−0.103785
$305$	−23.0335	−1.31890
$306$	13.9326	0.796474
$307$	7.31686	0.417595	0.208798	−	0.977959i	$-0.433045\pi$
$307$	7.31686	0.417595	0.208798	+	0.977959i	$0.433045\pi$
$308$	11.2439	0.640680
$309$	5.20321	0.296000
$310$	−1.74888	−0.0993295
$311$	−26.2560	−1.48884	−0.744420	−	0.667711i	$-0.767274\pi$
$311$	−26.2560	−1.48884	−0.744420	+	0.667711i	$0.767274\pi$
$312$	4.89430	0.277085
$313$	2.22060	0.125515	0.0627577	−	0.998029i	$-0.480010\pi$
$313$	2.22060	0.125515	0.0627577	+	0.998029i	$0.480010\pi$
$314$	−17.0072	−0.959769
$315$	7.34393	0.413784
$316$	−15.1495	−0.852225
$317$	−18.6030	−1.04485	−0.522424	−	0.852686i	$-0.674972\pi$
$317$	−18.6030	−1.04485	−0.522424	+	0.852686i	$0.674972\pi$
$318$	1.26108	0.0707176
$319$	6.73814	0.377263
$320$	−1.74888	−0.0977652
$321$	11.0295	0.615607
$322$	−13.3815	−0.745724
$323$	−12.8652	−0.715841
$324$	0.719420	0.0399678
$325$	−9.31601	−0.516759
$326$	−22.1536	−1.22697
$327$	3.74363	0.207023
$328$	2.43112	0.134236
$329$	27.1905	1.49906
$330$	−9.35998	−0.515250
$331$	12.4533	0.684494	0.342247	−	0.939610i	$-0.388812\pi$
$331$	12.4533	0.684494	0.342247	+	0.939610i	$0.388812\pi$
$332$	−6.79688	−0.373027
$333$	−14.0864	−0.771929
$334$	19.6564	1.07555
$335$	−20.1722	−1.10212
$336$	−2.18557	−0.119233
$337$	−4.13308	−0.225143	−0.112572	−	0.993644i	$-0.535909\pi$
$337$	−4.13308	−0.225143	−0.112572	+	0.993644i	$0.535909\pi$
$338$	−10.0259	−0.545337
$339$	11.0346	0.599316
$340$	−12.4338	−0.674319
$341$	−5.24727	−0.284155
$342$	−3.54616	−0.191754
$343$	−20.1603	−1.08856
$344$	−9.45570	−0.509817
$345$	11.1395	0.599728
$346$	−0.660237	−0.0354945
$347$	1.87083	0.100432	0.0502158	−	0.998738i	$-0.484009\pi$
$347$	1.87083	0.100432	0.0502158	+	0.998738i	$0.484009\pi$
$348$	−1.30975	−0.0702101
$349$	−8.28349	−0.443405	−0.221702	−	0.975114i	$-0.571161\pi$
$349$	−8.28349	−0.443405	−0.221702	+	0.975114i	$0.571161\pi$
$350$	4.16011	0.222367
$351$	24.2742	1.29566
$352$	−5.24727	−0.279680
$353$	18.0324	0.959766	0.479883	−	0.877333i	$-0.340679\pi$
$353$	18.0324	0.959766	0.479883	+	0.877333i	$0.340679\pi$
$354$	8.59256	0.456689
$355$	20.6131	1.09403
$356$	−16.5698	−0.878199
$357$	−15.5386	−0.822390
$358$	−0.678004	−0.0358336
$359$	19.4968	1.02900	0.514501	−	0.857490i	$-0.327977\pi$
$359$	19.4968	1.02900	0.514501	+	0.857490i	$0.327977\pi$
$360$	−3.42725	−0.180632
$361$	−15.7255	−0.827658
$362$	25.6950	1.35050
$363$	−16.8638	−0.885120
$364$	10.2823	0.538941
$365$	14.4882	0.758346
$366$	13.4333	0.702171
$367$	27.5069	1.43585	0.717925	−	0.696120i	$-0.245092\pi$
$367$	27.5069	1.43585	0.717925	+	0.696120i	$0.245092\pi$
$368$	6.24486	0.325536
$369$	4.76423	0.248016
$370$	12.5711	0.653539
$371$	2.64936	0.137548
$372$	1.01996	0.0528824
$373$	13.0007	0.673152	0.336576	−	0.941656i	$-0.390731\pi$
$373$	13.0007	0.673152	0.336576	+	0.941656i	$0.390731\pi$
$374$	−37.3060	−1.92905
$375$	−12.3820	−0.639403
$376$	−12.6892	−0.654394
$377$	6.16191	0.317355
$378$	−10.8398	−0.557537
$379$	18.9358	0.972667	0.486333	−	0.873773i	$-0.338334\pi$
$379$	18.9358	0.972667	0.486333	+	0.873773i	$0.338334\pi$
$380$	3.16469	0.162345
$381$	−16.8319	−0.862327
$382$	−13.9890	−0.715738
$383$	−26.7188	−1.36527	−0.682633	−	0.730762i	$-0.739165\pi$
$383$	−26.7188	−1.36527	−0.682633	+	0.730762i	$0.739165\pi$
$384$	1.01996	0.0520495
$385$	−19.6642	−1.00218
$386$	11.7080	0.595923
$387$	−18.5302	−0.941943
$388$	1.00000	0.0507673
$389$	29.1540	1.47817	0.739084	−	0.673613i	$-0.235259\pi$
$389$	29.1540	1.47817	0.739084	+	0.673613i	$0.235259\pi$
$390$	−8.55953	−0.433429
$391$	44.3985	2.24533
$392$	2.40837	0.121641
$393$	8.54618	0.431098
$394$	12.0155	0.605333
$395$	26.4946	1.33309
$396$	−10.2830	−0.516740
$397$	11.1789	0.561054	0.280527	−	0.959846i	$-0.409491\pi$
$397$	11.1789	0.561054	0.280527	+	0.959846i	$0.409491\pi$
$398$	−18.0595	−0.905241
$399$	3.95492	0.197994
$400$	−1.94143	−0.0970715
$401$	1.72506	0.0861453	0.0430727	−	0.999072i	$-0.486285\pi$
$401$	1.72506	0.0861453	0.0430727	+	0.999072i	$0.486285\pi$
$402$	11.7646	0.586764
$403$	−4.79853	−0.239032
$404$	3.28023	0.163198
$405$	−1.25818	−0.0625193
$406$	−2.75163	−0.136561
$407$	37.7178	1.86960
$408$	7.25151	0.359003
$409$	−19.5701	−0.967682	−0.483841	−	0.875156i	$-0.660759\pi$
$409$	−19.5701	−0.967682	−0.483841	+	0.875156i	$0.660759\pi$
$410$	−4.25173	−0.209978
$411$	1.93110	0.0952541
$412$	−5.10139	−0.251328
$413$	18.0519	0.888277
$414$	12.2380	0.601463
$415$	11.8869	0.583505
$416$	−4.79853	−0.235267
$417$	9.44084	0.462320
$418$	9.49523	0.464427
$419$	−2.59803	−0.126922	−0.0634610	−	0.997984i	$-0.520214\pi$
$419$	−2.59803	−0.126922	−0.0634610	+	0.997984i	$0.520214\pi$
$420$	3.82230	0.186509
$421$	−31.1283	−1.51710	−0.758551	−	0.651614i	$-0.774092\pi$
$421$	−31.1283	−1.51710	−0.758551	+	0.651614i	$0.774092\pi$
$422$	18.7555	0.913003
$423$	−24.8668	−1.20906
$424$	−1.23640	−0.0600448
$425$	−13.8028	−0.669535
$426$	−12.0217	−0.582454
$427$	28.2218	1.36575
$428$	−10.8137	−0.522699
$429$	−25.6817	−1.23992
$430$	16.5369	0.797478
$431$	18.3373	0.883278	0.441639	−	0.897193i	$-0.354397\pi$
$431$	18.3373	0.883278	0.441639	+	0.897193i	$0.354397\pi$
$432$	5.05867	0.243385
$433$	26.3673	1.26713	0.633566	−	0.773688i	$-0.281590\pi$
$433$	26.3673	1.26713	0.633566	+	0.773688i	$0.281590\pi$
$434$	2.14281	0.102858
$435$	2.29060	0.109826
$436$	−3.67037	−0.175779
$437$	−11.3004	−0.540572
$438$	−8.44962	−0.403738
$439$	13.4431	0.641605	0.320802	−	0.947146i	$-0.396047\pi$
$439$	13.4431	0.641605	0.320802	+	0.947146i	$0.396047\pi$
$440$	9.17682	0.437488
$441$	4.71965	0.224745
$442$	−34.1157	−1.62272
$443$	−4.26407	−0.202592	−0.101296	−	0.994856i	$-0.532299\pi$
$443$	−4.26407	−0.202592	−0.101296	+	0.994856i	$0.532299\pi$
$444$	−7.33154	−0.347940
$445$	28.9786	1.37372
$446$	−29.4327	−1.39368
$447$	21.1923	1.00236
$448$	2.14281	0.101238
$449$	−39.2624	−1.85291	−0.926453	−	0.376411i	$-0.877158\pi$
$449$	−39.2624	−1.85291	−0.926453	+	0.376411i	$0.877158\pi$
$450$	−3.80459	−0.179350
$451$	−12.7567	−0.600692
$452$	−10.8187	−0.508867
$453$	−17.2927	−0.812483
$454$	12.2104	0.573060
$455$	−17.9825	−0.843034
$456$	−1.84567	−0.0864315
$457$	8.69259	0.406622	0.203311	−	0.979114i	$-0.434830\pi$
$457$	8.69259	0.406622	0.203311	+	0.979114i	$0.434830\pi$
$458$	−2.51537	−0.117536
$459$	35.9652	1.67871
$460$	−10.9215	−0.509217
$461$	16.7561	0.780408	0.390204	−	0.920728i	$-0.372405\pi$
$461$	16.7561	0.780408	0.390204	+	0.920728i	$0.372405\pi$
$462$	11.4683	0.533553
$463$	21.2963	0.989721	0.494861	−	0.868972i	$-0.335219\pi$
$463$	21.2963	0.989721	0.494861	+	0.868972i	$0.335219\pi$
$464$	1.28412	0.0596140
$465$	−1.78378	−0.0827209
$466$	−2.30608	−0.106827
$467$	−8.55218	−0.395747	−0.197874	−	0.980228i	$-0.563404\pi$
$467$	−8.55218	−0.395747	−0.197874	+	0.980228i	$0.563404\pi$
$468$	−9.40361	−0.434682
$469$	24.7159	1.14128
$470$	22.1918	1.02363
$471$	−17.3466	−0.799289
$472$	−8.42442	−0.387765
$473$	49.6166	2.28137
$474$	−15.4518	−0.709726
$475$	3.51313	0.161193
$476$	15.2345	0.698274
$477$	−2.42295	−0.110939
$478$	1.64078	0.0750475
$479$	−43.5393	−1.98936	−0.994681	−	0.103004i	$-0.967155\pi$
$479$	−43.5393	−1.98936	−0.994681	+	0.103004i	$0.967155\pi$
$480$	−1.78378	−0.0814181
$481$	34.4922	1.57271
$482$	16.6362	0.757756
$483$	−13.6486	−0.621033
$484$	16.5338	0.751537
$485$	−1.74888	−0.0794124
$486$	15.9098	0.721683
$487$	43.5868	1.97511	0.987554	−	0.157279i	$-0.0502722\pi$
$487$	43.5868	1.97511	0.987554	+	0.157279i	$0.0502722\pi$
$488$	−13.1705	−0.596199
$489$	−22.5957	−1.02181
$490$	−4.21195	−0.190276
$491$	−20.6857	−0.933530	−0.466765	−	0.884381i	$-0.654581\pi$
$491$	−20.6857	−0.933530	−0.466765	+	0.884381i	$0.654581\pi$
$492$	2.47964	0.111791
$493$	9.12963	0.411178
$494$	8.68321	0.390676
$495$	17.9837	0.808306
$496$	−1.00000	−0.0449013
$497$	−25.2562	−1.13289
$498$	−6.93254	−0.310654
$499$	−8.91207	−0.398959	−0.199479	−	0.979902i	$-0.563925\pi$
$499$	−8.91207	−0.398959	−0.199479	+	0.979902i	$0.563925\pi$
$500$	12.1397	0.542904
$501$	20.0487	0.895712
$502$	−2.90688	−0.129740
$503$	−28.8896	−1.28812	−0.644061	−	0.764974i	$-0.722752\pi$
$503$	−28.8896	−1.28812	−0.644061	+	0.764974i	$0.722752\pi$
$504$	4.19923	0.187049
$505$	−5.73672	−0.255281
$506$	−32.7684	−1.45673
$507$	−10.2260	−0.454153
$508$	16.5026	0.732184
$509$	17.0783	0.756984	0.378492	−	0.925605i	$-0.376443\pi$
$509$	17.0783	0.756984	0.378492	+	0.925605i	$0.376443\pi$
$510$	−12.6820	−0.561568
$511$	−17.7516	−0.785285
$512$	−1.00000	−0.0441942
$513$	−9.15395	−0.404157
$514$	−13.7750	−0.607589
$515$	8.92171	0.393137
$516$	−9.64442	−0.424572
$517$	66.5834	2.92834
$518$	−15.4027	−0.676755
$519$	−0.673414	−0.0295596
$520$	8.39204	0.368015
$521$	−9.26019	−0.405696	−0.202848	−	0.979210i	$-0.565020\pi$
$521$	−9.26019	−0.405696	−0.202848	+	0.979210i	$0.565020\pi$
$522$	2.51648	0.110143
$523$	−39.6640	−1.73438	−0.867192	−	0.497974i	$-0.834077\pi$
$523$	−39.6640	−1.73438	−0.867192	+	0.497974i	$0.834077\pi$
$524$	−8.37895	−0.366036
$525$	4.24314	0.185186
$526$	20.4852	0.893197
$527$	−7.10961	−0.309700
$528$	−5.35199	−0.232916
$529$	15.9982	0.695576
$530$	2.16231	0.0939247
$531$	−16.5092	−0.716439
$532$	−3.87753	−0.168112
$533$	−11.6658	−0.505303
$534$	−16.9005	−0.731358
$535$	18.9118	0.817628
$536$	−11.5344	−0.498209
$537$	−0.691536	−0.0298420
$538$	1.17983	0.0508663
$539$	−12.6374	−0.544330
$540$	−8.84699	−0.380714
$541$	−4.47662	−0.192465	−0.0962324	−	0.995359i	$-0.530679\pi$
$541$	−4.47662	−0.192465	−0.0962324	+	0.995359i	$0.530679\pi$
$542$	−17.2608	−0.741415
$543$	26.2078	1.12468
$544$	−7.10961	−0.304822
$545$	6.41903	0.274961
$546$	10.4876	0.448826
$547$	7.71912	0.330046	0.165023	−	0.986290i	$-0.447230\pi$
$547$	7.71912	0.330046	0.165023	+	0.986290i	$0.447230\pi$
$548$	−1.89331	−0.0808783
$549$	−25.8100	−1.10154
$550$	10.1872	0.434384
$551$	−2.32370	−0.0989927
$552$	6.36949	0.271104
$553$	−32.4624	−1.38044
$554$	11.5229	0.489563
$555$	12.8220	0.544262
$556$	−9.25610	−0.392546
$557$	9.87713	0.418508	0.209254	−	0.977861i	$-0.432897\pi$
$557$	9.87713	0.418508	0.209254	+	0.977861i	$0.432897\pi$
$558$	−1.95968	−0.0829601
$559$	45.3735	1.91909
$560$	−3.74751	−0.158361
$561$	−38.0506	−1.60650
$562$	−26.6224	−1.12300
$563$	8.02596	0.338254	0.169127	−	0.985594i	$-0.445905\pi$
$563$	8.02596	0.338254	0.169127	+	0.985594i	$0.445905\pi$
$564$	−12.9424	−0.544974
$565$	18.9205	0.795992
$566$	7.31417	0.307437
$567$	1.54158	0.0647402
$568$	11.7865	0.494550
$569$	−5.75778	−0.241379	−0.120689	−	0.992690i	$-0.538510\pi$
$569$	−5.75778	−0.241379	−0.120689	+	0.992690i	$0.538510\pi$
$570$	3.22785	0.135200
$571$	−6.70363	−0.280538	−0.140269	−	0.990113i	$-0.544797\pi$
$571$	−6.70363	−0.280538	−0.140269	+	0.990113i	$0.544797\pi$
$572$	25.1792	1.05279
$573$	−14.2682	−0.596061
$574$	5.20943	0.217437
$575$	−12.1240	−0.505604
$576$	−1.95968	−0.0816535
$577$	8.64178	0.359762	0.179881	−	0.983688i	$-0.442429\pi$
$577$	8.64178	0.359762	0.179881	+	0.983688i	$0.442429\pi$
$578$	−33.5466	−1.39535
$579$	11.9417	0.496281
$580$	−2.24577	−0.0932507
$581$	−14.5644	−0.604234
$582$	1.01996	0.0422786
$583$	6.48771	0.268694
$584$	8.28427	0.342806
$585$	16.4458	0.679948
$586$	11.1339	0.459937
$587$	−19.0898	−0.787921	−0.393961	−	0.919127i	$-0.628895\pi$
$587$	−19.0898	−0.787921	−0.393961	+	0.919127i	$0.628895\pi$
$588$	2.45644	0.101302
$589$	1.80956	0.0745615
$590$	14.7333	0.606559
$591$	12.2553	0.504117
$592$	7.18808	0.295428
$593$	23.9244	0.982457	0.491229	−	0.871031i	$-0.336548\pi$
$593$	23.9244	0.982457	0.491229	+	0.871031i	$0.336548\pi$
$594$	−26.5442	−1.08912
$595$	−26.6433	−1.09227
$596$	−20.7777	−0.851086
$597$	−18.4199	−0.753878
$598$	−29.9661	−1.22541
$599$	39.5717	1.61686	0.808428	−	0.588595i	$-0.200319\pi$
$599$	39.5717	1.61686	0.808428	+	0.588595i	$0.200319\pi$
$600$	−1.98018	−0.0808404
$601$	34.7578	1.41780	0.708899	−	0.705310i	$-0.249192\pi$
$601$	34.7578	1.41780	0.708899	+	0.705310i	$0.249192\pi$
$602$	−20.2617	−0.825807
$603$	−22.6037	−0.920495
$604$	16.9544	0.689863
$605$	−28.9156	−1.17559
$606$	3.34570	0.135910
$607$	−3.33410	−0.135327	−0.0676634	−	0.997708i	$-0.521554\pi$
$607$	−3.33410	−0.135327	−0.0676634	+	0.997708i	$0.521554\pi$
$608$	1.80956	0.0733872
$609$	−2.80655	−0.113727
$610$	23.0335	0.932600
$611$	60.8894	2.46332
$612$	−13.9326	−0.563192
$613$	−11.4932	−0.464206	−0.232103	−	0.972691i	$-0.574561\pi$
$613$	−11.4932	−0.464206	−0.232103	+	0.972691i	$0.574561\pi$
$614$	−7.31686	−0.295284
$615$	−4.33659	−0.174868
$616$	−11.2439	−0.453029
$617$	20.8330	0.838706	0.419353	−	0.907823i	$-0.362257\pi$
$617$	20.8330	0.838706	0.419353	+	0.907823i	$0.362257\pi$
$618$	−5.20321	−0.209304
$619$	−41.2447	−1.65776	−0.828881	−	0.559425i	$-0.811022\pi$
$619$	−41.2447	−1.65776	−0.828881	+	0.559425i	$0.811022\pi$
$620$	1.74888	0.0702366
$621$	31.5907	1.26769
$622$	26.2560	1.05277
$623$	−35.5060	−1.42252
$624$	−4.89430	−0.195929
$625$	−11.5237	−0.460948
$626$	−2.22060	−0.0887528
$627$	9.68473	0.386771
$628$	17.0072	0.678659
$629$	51.1045	2.03767
$630$	−7.34393	−0.292589
$631$	25.6196	1.01990	0.509949	−	0.860204i	$-0.329664\pi$
$631$	25.6196	1.01990	0.509949	+	0.860204i	$0.329664\pi$
$632$	15.1495	0.602614
$633$	19.1298	0.760342
$634$	18.6030	0.738819
$635$	−28.8610	−1.14531
$636$	−1.26108	−0.0500049
$637$	−11.5567	−0.457891
$638$	−6.73814	−0.266766
$639$	23.0978	0.913734
$640$	1.74888	0.0691304
$641$	−6.25799	−0.247176	−0.123588	−	0.992334i	$-0.539440\pi$
$641$	−6.25799	−0.247176	−0.123588	+	0.992334i	$0.539440\pi$
$642$	−11.0295	−0.435300
$643$	19.0201	0.750081	0.375041	−	0.927008i	$-0.377629\pi$
$643$	19.0201	0.750081	0.375041	+	0.927008i	$0.377629\pi$
$644$	13.3815	0.527306
$645$	16.8669	0.664134
$646$	12.8652	0.506176
$647$	19.7460	0.776295	0.388147	−	0.921597i	$-0.373115\pi$
$647$	19.7460	0.776295	0.388147	+	0.921597i	$0.373115\pi$
$648$	−0.719420	−0.0282615
$649$	44.2052	1.73521
$650$	9.31601	0.365404
$651$	2.18557	0.0856594
$652$	22.1536	0.867601
$653$	25.4592	0.996295	0.498147	−	0.867092i	$-0.334014\pi$
$653$	25.4592	0.996295	0.498147	+	0.867092i	$0.334014\pi$
$654$	−3.74363	−0.146387
$655$	14.6538	0.572570
$656$	−2.43112	−0.0949194
$657$	16.2346	0.633371
$658$	−27.1905	−1.05999
$659$	−12.9712	−0.505287	−0.252644	−	0.967559i	$-0.581300\pi$
$659$	−12.9712	−0.505287	−0.252644	+	0.967559i	$0.581300\pi$
$660$	9.35998	0.364337
$661$	24.3388	0.946671	0.473335	−	0.880882i	$-0.343050\pi$
$661$	24.3388	0.946671	0.473335	+	0.880882i	$0.343050\pi$
$662$	−12.4533	−0.484010
$663$	−34.7966	−1.35139
$664$	6.79688	0.263770
$665$	6.78133	0.262969
$666$	14.0864	0.545836
$667$	8.01917	0.310504
$668$	−19.6564	−0.760530
$669$	−30.0201	−1.16064
$670$	20.1722	0.779320
$671$	69.1090	2.66792
$672$	2.18557	0.0843104
$673$	13.5471	0.522204	0.261102	−	0.965311i	$-0.415914\pi$
$673$	13.5471	0.522204	0.261102	+	0.965311i	$0.415914\pi$
$674$	4.13308	0.159200
$675$	−9.82106	−0.378013
$676$	10.0259	0.385612
$677$	−18.6475	−0.716683	−0.358342	−	0.933590i	$-0.616658\pi$
$677$	−18.6475	−0.716683	−0.358342	+	0.933590i	$0.616658\pi$
$678$	−11.0346	−0.423781
$679$	2.14281	0.0822334
$680$	12.4338	0.476816
$681$	12.4541	0.477240
$682$	5.24727	0.200928
$683$	−32.8852	−1.25832	−0.629158	−	0.777278i	$-0.716600\pi$
$683$	−32.8852	−1.25832	−0.629158	+	0.777278i	$0.716600\pi$
$684$	3.54616	0.135591
$685$	3.31117	0.126513
$686$	20.1603	0.769725
$687$	−2.56558	−0.0978828
$688$	9.45570	0.360495
$689$	5.93290	0.226025
$690$	−11.1395	−0.424072
$691$	47.6423	1.81240	0.906200	−	0.422849i	$-0.138970\pi$
$691$	47.6423	1.81240	0.906200	+	0.422849i	$0.138970\pi$
$692$	0.660237	0.0250984
$693$	−22.0345	−0.837020
$694$	−1.87083	−0.0710159
$695$	16.1878	0.614037
$696$	1.30975	0.0496461
$697$	−17.2843	−0.654691
$698$	8.28349	0.313535
$699$	−2.35210	−0.0889646
$700$	−4.16011	−0.157237
$701$	14.1613	0.534866	0.267433	−	0.963576i	$-0.413825\pi$
$701$	14.1613	0.534866	0.267433	+	0.963576i	$0.413825\pi$
$702$	−24.2742	−0.916171
$703$	−13.0072	−0.490577
$704$	5.24727	0.197764
$705$	22.6347	0.852472
$706$	−18.0324	−0.678657
$707$	7.02891	0.264349
$708$	−8.59256	−0.322928
$709$	8.04181	0.302016	0.151008	−	0.988533i	$-0.451748\pi$
$709$	8.04181	0.302016	0.151008	+	0.988533i	$0.451748\pi$
$710$	−20.6131	−0.773596
$711$	29.6882	1.11339
$712$	16.5698	0.620981
$713$	−6.24486	−0.233872
$714$	15.5386	0.581517
$715$	−44.0353	−1.64683
$716$	0.678004	0.0253382
$717$	1.67353	0.0624990
$718$	−19.4968	−0.727614
$719$	−38.8453	−1.44869	−0.724343	−	0.689440i	$-0.757857\pi$
$719$	−38.8453	−1.44869	−0.724343	+	0.689440i	$0.757857\pi$
$720$	3.42725	0.127726
$721$	−10.9313	−0.407103
$722$	15.7255	0.585243
$723$	16.9682	0.631053
$724$	−25.6950	−0.954946
$725$	−2.49304	−0.0925891
$726$	16.8638	0.625874
$727$	−5.88657	−0.218321	−0.109160	−	0.994024i	$-0.534816\pi$
$727$	−5.88657	−0.218321	−0.109160	+	0.994024i	$0.534816\pi$
$728$	−10.2823	−0.381089
$729$	14.0691	0.521077
$730$	−14.4882	−0.536231
$731$	67.2264	2.48646
$732$	−13.4333	−0.496510
$733$	0.680002	0.0251164	0.0125582	−	0.999921i	$-0.496002\pi$
$733$	0.680002	0.0251164	0.0125582	+	0.999921i	$0.496002\pi$
$734$	−27.5069	−1.01530
$735$	−4.29601	−0.158461
$736$	−6.24486	−0.230188
$737$	60.5239	2.22943
$738$	−4.76423	−0.175374
$739$	−8.44534	−0.310667	−0.155333	−	0.987862i	$-0.549645\pi$
$739$	−8.44534	−0.310667	−0.155333	+	0.987862i	$0.549645\pi$
$740$	−12.5711	−0.462122
$741$	8.85652	0.325352
$742$	−2.64936	−0.0972612
$743$	13.2277	0.485278	0.242639	−	0.970117i	$-0.421987\pi$
$743$	13.2277	0.485278	0.242639	+	0.970117i	$0.421987\pi$
$744$	−1.01996	−0.0373935
$745$	36.3376	1.33130
$746$	−13.0007	−0.475991
$747$	13.3197	0.487344
$748$	37.3060	1.36404
$749$	−23.1716	−0.846673
$750$	12.3820	0.452127
$751$	−48.9425	−1.78594	−0.892969	−	0.450119i	$-0.851382\pi$
$751$	−48.9425	−1.78594	−0.892969	+	0.450119i	$0.851382\pi$
$752$	12.6892	0.462726
$753$	−2.96490	−0.108047
$754$	−6.16191	−0.224404
$755$	−29.6511	−1.07911
$756$	10.8398	0.394238
$757$	−50.6302	−1.84018	−0.920092	−	0.391702i	$-0.871886\pi$
$757$	−50.6302	−1.84018	−0.920092	+	0.391702i	$0.871886\pi$
$758$	−18.9358	−0.687779
$759$	−33.4224	−1.21316
$760$	−3.16469	−0.114795
$761$	−3.02117	−0.109517	−0.0547587	−	0.998500i	$-0.517439\pi$
$761$	−3.02117	−0.109517	−0.0547587	+	0.998500i	$0.517439\pi$
$762$	16.8319	0.609757
$763$	−7.86491	−0.284729
$764$	13.9890	0.506103
$765$	24.3664	0.880969
$766$	26.7188	0.965389
$767$	40.4249	1.45966
$768$	−1.01996	−0.0368046
$769$	12.8196	0.462287	0.231144	−	0.972920i	$-0.425753\pi$
$769$	12.8196	0.462287	0.231144	+	0.972920i	$0.425753\pi$
$770$	19.6642	0.708647
$771$	−14.0499	−0.505995
$772$	−11.7080	−0.421381
$773$	−29.3870	−1.05698	−0.528489	−	0.848940i	$-0.677241\pi$
$773$	−29.3870	−1.05698	−0.528489	+	0.848940i	$0.677241\pi$
$774$	18.5302	0.666054
$775$	1.94143	0.0697382
$776$	−1.00000	−0.0358979
$777$	−15.7101	−0.563596
$778$	−29.1540	−1.04522
$779$	4.39925	0.157620
$780$	8.55953	0.306480
$781$	−61.8468	−2.21305
$782$	−44.3985	−1.58769
$783$	6.49596	0.232147
$784$	−2.40837	−0.0860133
$785$	−29.7434	−1.06159
$786$	−8.54618	−0.304832
$787$	2.99149	0.106635	0.0533175	−	0.998578i	$-0.483020\pi$
$787$	2.99149	0.106635	0.0533175	+	0.998578i	$0.483020\pi$
$788$	−12.0155	−0.428035
$789$	20.8940	0.743848
$790$	−26.4946	−0.942634
$791$	−23.1823	−0.824268
$792$	10.2830	0.365390
$793$	63.1989	2.24426
$794$	−11.1789	−0.396725
$795$	2.20546	0.0782198
$796$	18.0595	0.640102
$797$	−51.4207	−1.82142	−0.910708	−	0.413051i	$-0.864463\pi$
$797$	−51.4207	−1.82142	−0.910708	+	0.413051i	$0.864463\pi$
$798$	−3.95492	−0.140003
$799$	90.2151	3.19158
$800$	1.94143	0.0686399
$801$	32.4716	1.14733
$802$	−1.72506	−0.0609140
$803$	−43.4698	−1.53402
$804$	−11.7646	−0.414905
$805$	−23.4026	−0.824835
$806$	4.79853	0.169021
$807$	1.20338	0.0423611
$808$	−3.28023	−0.115398
$809$	12.4214	0.436712	0.218356	−	0.975869i	$-0.429931\pi$
$809$	12.4214	0.436712	0.218356	+	0.975869i	$0.429931\pi$
$810$	1.25818	0.0442078
$811$	−53.3592	−1.87369	−0.936847	−	0.349740i	$-0.886270\pi$
$811$	−53.3592	−1.87369	−0.936847	+	0.349740i	$0.886270\pi$
$812$	2.75163	0.0965633
$813$	−17.6053	−0.617445
$814$	−37.7178	−1.32201
$815$	−38.7439	−1.35714
$816$	−7.25151	−0.253854
$817$	−17.1106	−0.598625
$818$	19.5701	0.684254
$819$	−20.1501	−0.704103
$820$	4.25173	0.148477
$821$	−11.0783	−0.386636	−0.193318	−	0.981136i	$-0.561925\pi$
$821$	−11.0783	−0.386636	−0.193318	+	0.981136i	$0.561925\pi$
$822$	−1.93110	−0.0673548
$823$	−41.9198	−1.46123	−0.730617	−	0.682788i	$-0.760767\pi$
$823$	−41.9198	−1.46123	−0.730617	+	0.682788i	$0.760767\pi$
$824$	5.10139	0.177715
$825$	10.3905	0.361751
$826$	−18.0519	−0.628107
$827$	−51.8711	−1.80374	−0.901868	−	0.432011i	$-0.857804\pi$
$827$	−51.8711	−1.80374	−0.901868	+	0.432011i	$0.857804\pi$
$828$	−12.2380	−0.425298
$829$	−1.50437	−0.0522490	−0.0261245	−	0.999659i	$-0.508317\pi$
$829$	−1.50437	−0.0522490	−0.0261245	+	0.999659i	$0.508317\pi$
$830$	−11.8869	−0.412601
$831$	11.7529	0.407704
$832$	4.79853	0.166359
$833$	−17.1226	−0.593263
$834$	−9.44084	−0.326909
$835$	34.3767	1.18965
$836$	−9.49523	−0.328399
$837$	−5.05867	−0.174853
$838$	2.59803	0.0897474
$839$	11.1627	0.385379	0.192689	−	0.981260i	$-0.438279\pi$
$839$	11.1627	0.385379	0.192689	+	0.981260i	$0.438279\pi$
$840$	−3.82230	−0.131882
$841$	−27.3510	−0.943139
$842$	31.1283	1.07275
$843$	−27.1537	−0.935225
$844$	−18.7555	−0.645590
$845$	−17.5341	−0.603191
$846$	24.8668	0.854937
$847$	35.4288	1.21735
$848$	1.23640	0.0424581
$849$	7.46015	0.256032
$850$	13.8028	0.473433
$851$	44.8885	1.53876
$852$	12.0217	0.411857
$853$	12.9331	0.442821	0.221411	−	0.975181i	$-0.428934\pi$
$853$	12.9331	0.442821	0.221411	+	0.975181i	$0.428934\pi$
$854$	−28.2218	−0.965730
$855$	−6.20180	−0.212097
$856$	10.8137	0.369604
$857$	39.1689	1.33799	0.668993	−	0.743269i	$-0.266726\pi$
$857$	39.1689	1.33799	0.668993	+	0.743269i	$0.266726\pi$
$858$	25.6817	0.876759
$859$	8.36826	0.285521	0.142761	−	0.989757i	$-0.454402\pi$
$859$	8.36826	0.285521	0.142761	+	0.989757i	$0.454402\pi$
$860$	−16.5369	−0.563902
$861$	5.31340	0.181080
$862$	−18.3373	−0.624572
$863$	9.37262	0.319048	0.159524	−	0.987194i	$-0.449004\pi$
$863$	9.37262	0.319048	0.159524	+	0.987194i	$0.449004\pi$
$864$	−5.05867	−0.172100
$865$	−1.15467	−0.0392600
$866$	−26.3673	−0.895998
$867$	−34.2161	−1.16204
$868$	−2.14281	−0.0727316
$869$	−79.4933	−2.69663
$870$	−2.29060	−0.0776585
$871$	55.3480	1.87540
$872$	3.67037	0.124295
$873$	−1.95968	−0.0663253
$874$	11.3004	0.382242
$875$	26.0131	0.879402
$876$	8.44962	0.285486
$877$	−23.7240	−0.801101	−0.400550	−	0.916275i	$-0.631181\pi$
$877$	−23.7240	−0.801101	−0.400550	+	0.916275i	$0.631181\pi$
$878$	−13.4431	−0.453683
$879$	11.3561	0.383032
$880$	−9.17682	−0.309351
$881$	2.25026	0.0758133	0.0379067	−	0.999281i	$-0.487931\pi$
$881$	2.25026	0.0758133	0.0379067	+	0.999281i	$0.487931\pi$
$882$	−4.71965	−0.158919
$883$	−2.86979	−0.0965760	−0.0482880	−	0.998833i	$-0.515377\pi$
$883$	−2.86979	−0.0965760	−0.0482880	+	0.998833i	$0.515377\pi$
$884$	34.1157	1.14744
$885$	15.0273	0.505138
$886$	4.26407	0.143254
$887$	−40.1544	−1.34825	−0.674126	−	0.738617i	$-0.735479\pi$
$887$	−40.1544	−1.34825	−0.674126	+	0.738617i	$0.735479\pi$
$888$	7.33154	0.246031
$889$	35.3619	1.18600
$890$	−28.9786	−0.971365
$891$	3.77499	0.126467
$892$	29.4327	0.985479
$893$	−22.9618	−0.768386
$894$	−21.1923	−0.708778
$895$	−1.18574	−0.0396351
$896$	−2.14281	−0.0715862
$897$	−30.5642	−1.02051
$898$	39.2624	1.31020
$899$	−1.28412	−0.0428279
$900$	3.80459	0.126820
$901$	8.79032	0.292848
$902$	12.7567	0.424753
$903$	−20.6661	−0.687726
$904$	10.8187	0.359823
$905$	44.9373	1.49377
$906$	17.2927	0.574513
$907$	−9.55063	−0.317124	−0.158562	−	0.987349i	$-0.550686\pi$
$907$	−9.55063	−0.317124	−0.158562	+	0.987349i	$0.550686\pi$
$908$	−12.2104	−0.405215
$909$	−6.42822	−0.213211
$910$	17.9825	0.596115
$911$	−41.7634	−1.38368	−0.691842	−	0.722049i	$-0.743200\pi$
$911$	−41.7634	−1.38368	−0.691842	+	0.722049i	$0.743200\pi$
$912$	1.84567	0.0611163
$913$	−35.6650	−1.18034
$914$	−8.69259	−0.287525
$915$	23.4932	0.776662
$916$	2.51537	0.0831103
$917$	−17.9545	−0.592909
$918$	−35.9652	−1.18703
$919$	−3.27551	−0.108049	−0.0540246	−	0.998540i	$-0.517205\pi$
$919$	−3.27551	−0.108049	−0.0540246	+	0.998540i	$0.517205\pi$
$920$	10.9215	0.360071
$921$	−7.46289	−0.245911
$922$	−16.7561	−0.551832
$923$	−56.5578	−1.86162
$924$	−11.4683	−0.377279
$925$	−13.9552	−0.458843
$926$	−21.2963	−0.699838
$927$	9.99712	0.328349
$928$	−1.28412	−0.0421534
$929$	−10.2550	−0.336457	−0.168228	−	0.985748i	$-0.553805\pi$
$929$	−10.2550	−0.336457	−0.168228	+	0.985748i	$0.553805\pi$
$930$	1.78378	0.0584925
$931$	4.35809	0.142831
$932$	2.30608	0.0755380
$933$	26.7800	0.876738
$934$	8.55218	0.279836
$935$	−65.2437	−2.13370
$936$	9.40361	0.307367
$937$	18.4701	0.603392	0.301696	−	0.953404i	$-0.402447\pi$
$937$	18.4701	0.603392	0.301696	+	0.953404i	$0.402447\pi$
$938$	−24.7159	−0.807004
$939$	−2.26491	−0.0739127
$940$	−22.1918	−0.723816
$941$	6.23518	0.203261	0.101631	−	0.994822i	$-0.467594\pi$
$941$	6.23518	0.203261	0.101631	+	0.994822i	$0.467594\pi$
$942$	17.3466	0.565182
$943$	−15.1820	−0.494394
$944$	8.42442	0.274192
$945$	−18.9574	−0.616685
$946$	−49.6166	−1.61317
$947$	36.3031	1.17969	0.589846	−	0.807516i	$-0.299189\pi$
$947$	36.3031	1.17969	0.589846	+	0.807516i	$0.299189\pi$
$948$	15.4518	0.501852
$949$	−39.7524	−1.29042
$950$	−3.51313	−0.113981
$951$	18.9743	0.615283
$952$	−15.2345	−0.493754
$953$	−55.5128	−1.79823	−0.899117	−	0.437708i	$-0.855790\pi$
$953$	−55.5128	−1.79823	−0.899117	+	0.437708i	$0.855790\pi$
$954$	2.42295	0.0784460
$955$	−24.4650	−0.791668
$956$	−1.64078	−0.0530666
$957$	−6.87262	−0.222160
$958$	43.5393	1.40669
$959$	−4.05701	−0.131008
$960$	1.78378	0.0575713
$961$	1.00000	0.0322581
$962$	−34.4922	−1.11207
$963$	21.1914	0.682883
$964$	−16.6362	−0.535814
$965$	20.4759	0.659143
$966$	13.6486	0.439137
$967$	−23.0081	−0.739889	−0.369945	−	0.929054i	$-0.620623\pi$
$967$	−23.0081	−0.739889	−0.369945	+	0.929054i	$0.620623\pi$
$968$	−16.5338	−0.531417
$969$	13.1220	0.421540
$970$	1.74888	0.0561530
$971$	45.5692	1.46238	0.731192	−	0.682172i	$-0.238964\pi$
$971$	45.5692	1.46238	0.731192	+	0.682172i	$0.238964\pi$
$972$	−15.9098	−0.510307
$973$	−19.8340	−0.635850
$974$	−43.5868	−1.39661
$975$	9.50195	0.304306
$976$	13.1705	0.421576
$977$	40.2715	1.28840	0.644200	−	0.764857i	$-0.277190\pi$
$977$	40.2715	1.28840	0.644200	+	0.764857i	$0.277190\pi$
$978$	22.5957	0.722532
$979$	−86.9463	−2.77882
$980$	4.21195	0.134546
$981$	7.19278	0.229648
$982$	20.6857	0.660106
$983$	47.5151	1.51550	0.757749	−	0.652547i	$-0.226299\pi$
$983$	47.5151	1.51550	0.757749	+	0.652547i	$0.226299\pi$
$984$	−2.47964	−0.0790482
$985$	21.0137	0.669551
$986$	−9.12963	−0.290746
$987$	−27.7331	−0.882755
$988$	−8.68321	−0.276250
$989$	59.0495	1.87766
$990$	−17.9837	−0.571559
$991$	−52.4561	−1.66632	−0.833161	−	0.553031i	$-0.813471\pi$
$991$	−52.4561	−1.66632	−0.833161	+	0.553031i	$0.813471\pi$
$992$	1.00000	0.0317500
$993$	−12.7018	−0.403080
$994$	25.2562	0.801077
$995$	−31.5838	−1.00127
$996$	6.93254	0.219666
$997$	−35.0252	−1.10926	−0.554629	−	0.832098i	$-0.687140\pi$
$997$	−35.0252	−1.10926	−0.554629	+	0.832098i	$0.687140\pi$
$998$	8.91207	0.282107
$999$	36.3622	1.15045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.11	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.01996 q^{3} +1.00000 q^{4} -1.74888 q^{5} +1.01996 q^{6} +2.14281 q^{7} -1.00000 q^{8} -1.95968 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.01996 q^{3} +1.00000 q^{4} -1.74888 q^{5} +1.01996 q^{6} +2.14281 q^{7} -1.00000 q^{8} -1.95968 q^{9} +1.74888 q^{10} +5.24727 q^{11} -1.01996 q^{12} +4.79853 q^{13} -2.14281 q^{14} +1.78378 q^{15} +1.00000 q^{16} +7.10961 q^{17} +1.95968 q^{18} -1.80956 q^{19} -1.74888 q^{20} -2.18557 q^{21} -5.24727 q^{22} +6.24486 q^{23} +1.01996 q^{24} -1.94143 q^{25} -4.79853 q^{26} +5.05867 q^{27} +2.14281 q^{28} +1.28412 q^{29} -1.78378 q^{30} -1.00000 q^{31} -1.00000 q^{32} -5.35199 q^{33} -7.10961 q^{34} -3.74751 q^{35} -1.95968 q^{36} +7.18808 q^{37} +1.80956 q^{38} -4.89430 q^{39} +1.74888 q^{40} -2.43112 q^{41} +2.18557 q^{42} +9.45570 q^{43} +5.24727 q^{44} +3.42725 q^{45} -6.24486 q^{46} +12.6892 q^{47} -1.01996 q^{48} -2.40837 q^{49} +1.94143 q^{50} -7.25151 q^{51} +4.79853 q^{52} +1.23640 q^{53} -5.05867 q^{54} -9.17682 q^{55} -2.14281 q^{56} +1.84567 q^{57} -1.28412 q^{58} +8.42442 q^{59} +1.78378 q^{60} +13.1705 q^{61} +1.00000 q^{62} -4.19923 q^{63} +1.00000 q^{64} -8.39204 q^{65} +5.35199 q^{66} +11.5344 q^{67} +7.10961 q^{68} -6.36949 q^{69} +3.74751 q^{70} -11.7865 q^{71} +1.95968 q^{72} -8.28427 q^{73} -7.18808 q^{74} +1.98018 q^{75} -1.80956 q^{76} +11.2439 q^{77} +4.89430 q^{78} -15.1495 q^{79} -1.74888 q^{80} +0.719420 q^{81} +2.43112 q^{82} -6.79688 q^{83} -2.18557 q^{84} -12.4338 q^{85} -9.45570 q^{86} -1.30975 q^{87} -5.24727 q^{88} -16.5698 q^{89} -3.42725 q^{90} +10.2823 q^{91} +6.24486 q^{92} +1.01996 q^{93} -12.6892 q^{94} +3.16469 q^{95} +1.01996 q^{96} +1.00000 q^{97} +2.40837 q^{98} -10.2830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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