LMFDB - Embedded newform 8027.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +O(q^{10})$	\(q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +3.59355 q^{10} -1.30714 q^{11} -6.88502 q^{12} +0.398449 q^{13} +13.1641 q^{14} +2.06836 q^{15} +8.26112 q^{16} +2.72438 q^{17} +2.06098 q^{18} +0.445059 q^{19} -6.47223 q^{20} +7.57695 q^{21} +3.36868 q^{22} +1.00000 q^{23} +10.0981 q^{24} -3.05565 q^{25} -1.02685 q^{26} +5.63625 q^{27} -23.7094 q^{28} -7.89244 q^{29} -5.33043 q^{30} -1.20169 q^{31} -7.67456 q^{32} +1.93893 q^{33} -7.02107 q^{34} +7.12267 q^{35} -3.71196 q^{36} +1.57974 q^{37} -1.14697 q^{38} -0.591032 q^{39} +9.49265 q^{40} +0.346533 q^{41} -19.5268 q^{42} +1.60026 q^{43} -6.06722 q^{44} +1.11513 q^{45} -2.57713 q^{46} +10.7518 q^{47} -12.2540 q^{48} +19.0922 q^{49} +7.87479 q^{50} -4.04116 q^{51} +1.84943 q^{52} -1.77650 q^{53} -14.5253 q^{54} +1.82268 q^{55} +34.7740 q^{56} -0.660172 q^{57} +20.3398 q^{58} -3.20814 q^{59} +9.60048 q^{60} -11.0073 q^{61} +3.09690 q^{62} +4.08500 q^{63} +3.25609 q^{64} -0.555597 q^{65} -4.99687 q^{66} -9.27987 q^{67} +12.6454 q^{68} -1.48333 q^{69} -18.3560 q^{70} -6.33448 q^{71} +5.44424 q^{72} +2.18771 q^{73} -4.07118 q^{74} +4.53255 q^{75} +2.06578 q^{76} +6.67696 q^{77} +1.52317 q^{78} -16.0251 q^{79} -11.5193 q^{80} -5.96129 q^{81} -0.893059 q^{82} -8.96465 q^{83} +35.1690 q^{84} -3.79888 q^{85} -4.12407 q^{86} +11.7071 q^{87} +8.89864 q^{88} -14.8082 q^{89} -2.87383 q^{90} -2.03530 q^{91} +4.64158 q^{92} +1.78250 q^{93} -27.7089 q^{94} -0.620591 q^{95} +11.3839 q^{96} +4.83280 q^{97} -49.2030 q^{98} +1.04535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.57713	−1.82230	−0.911152	−	0.412071i	$-0.864806\pi$
$2$	−2.57713	−1.82230	−0.911152	+	0.412071i	$0.864806\pi$
$3$	−1.48333	−0.856404	−0.428202	−	0.903683i	$-0.640853\pi$
$3$	−1.48333	−0.856404	−0.428202	+	0.903683i	$0.640853\pi$
$4$	4.64158	2.32079
$5$	−1.39440	−0.623595	−0.311798	−	0.950149i	$-0.600931\pi$
$5$	−1.39440	−0.623595	−0.311798	+	0.950149i	$0.600931\pi$
$6$	3.82274	1.56063
$7$	−5.10805	−1.93066	−0.965331	−	0.261029i	$-0.915938\pi$
$7$	−5.10805	−1.93066	−0.965331	+	0.261029i	$0.915938\pi$
$8$	−6.80769	−2.40688
$9$	−0.799719	−0.266573
$10$	3.59355	1.13638
$11$	−1.30714	−0.394119	−0.197059	−	0.980392i	$-0.563139\pi$
$11$	−1.30714	−0.394119	−0.197059	+	0.980392i	$0.563139\pi$
$12$	−6.88502	−1.98753
$13$	0.398449	0.110510	0.0552549	−	0.998472i	$-0.482403\pi$
$13$	0.398449	0.110510	0.0552549	+	0.998472i	$0.482403\pi$
$14$	13.1641	3.51825
$15$	2.06836	0.534049
$16$	8.26112	2.06528
$17$	2.72438	0.660759	0.330379	−	0.943848i	$-0.392823\pi$
$17$	2.72438	0.660759	0.330379	+	0.943848i	$0.392823\pi$
$18$	2.06098	0.485777
$19$	0.445059	0.102104	0.0510518	−	0.998696i	$-0.483743\pi$
$19$	0.445059	0.102104	0.0510518	+	0.998696i	$0.483743\pi$
$20$	−6.47223	−1.44723
$21$	7.57695	1.65343
$22$	3.36868	0.718204
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	10.0981	2.06126
$25$	−3.05565	−0.611129
$26$	−1.02685	−0.201382
$27$	5.63625	1.08470
$28$	−23.7094	−4.48066
$29$	−7.89244	−1.46559	−0.732794	−	0.680450i	$-0.761784\pi$
$29$	−7.89244	−1.46559	−0.732794	+	0.680450i	$0.761784\pi$
$30$	−5.33043	−0.973200
$31$	−1.20169	−0.215829	−0.107915	−	0.994160i	$-0.534417\pi$
$31$	−1.20169	−0.215829	−0.107915	+	0.994160i	$0.534417\pi$
$32$	−7.67456	−1.35668
$33$	1.93893	0.337525
$34$	−7.02107	−1.20410
$35$	7.12267	1.20395
$36$	−3.71196	−0.618660
$37$	1.57974	0.259707	0.129854	−	0.991533i	$-0.458549\pi$
$37$	1.57974	0.259707	0.129854	+	0.991533i	$0.458549\pi$
$38$	−1.14697	−0.186064
$39$	−0.591032	−0.0946409
$40$	9.49265	1.50092
$41$	0.346533	0.0541193	0.0270597	−	0.999634i	$-0.491386\pi$
$41$	0.346533	0.0541193	0.0270597	+	0.999634i	$0.491386\pi$
$42$	−19.5268	−3.01304
$43$	1.60026	0.244037	0.122018	−	0.992528i	$-0.461063\pi$
$43$	1.60026	0.244037	0.122018	+	0.992528i	$0.461063\pi$
$44$	−6.06722	−0.914668
$45$	1.11513	0.166234
$46$	−2.57713	−0.379977
$47$	10.7518	1.56832	0.784159	−	0.620560i	$-0.213095\pi$
$47$	10.7518	1.56832	0.784159	+	0.620560i	$0.213095\pi$
$48$	−12.2540	−1.76871
$49$	19.0922	2.72745
$50$	7.87479	1.11366
$51$	−4.04116	−0.565876
$52$	1.84943	0.256470
$53$	−1.77650	−0.244020	−0.122010	−	0.992529i	$-0.538934\pi$
$53$	−1.77650	−0.244020	−0.122010	+	0.992529i	$0.538934\pi$
$54$	−14.5253	−1.97665
$55$	1.82268	0.245771
$56$	34.7740	4.64688
$57$	−0.660172	−0.0874419
$58$	20.3398	2.67075
$59$	−3.20814	−0.417665	−0.208832	−	0.977951i	$-0.566966\pi$
$59$	−3.20814	−0.417665	−0.208832	+	0.977951i	$0.566966\pi$
$60$	9.60048	1.23942
$61$	−11.0073	−1.40935	−0.704673	−	0.709533i	$-0.748906\pi$
$61$	−11.0073	−1.40935	−0.704673	+	0.709533i	$0.748906\pi$
$62$	3.09690	0.393307
$63$	4.08500	0.514662
$64$	3.25609	0.407011
$65$	−0.555597	−0.0689133
$66$	−4.99687	−0.615073
$67$	−9.27987	−1.13372	−0.566859	−	0.823815i	$-0.691841\pi$
$67$	−9.27987	−1.13372	−0.566859	+	0.823815i	$0.691841\pi$
$68$	12.6454	1.53348
$69$	−1.48333	−0.178572
$70$	−18.3560	−2.19396
$71$	−6.33448	−0.751765	−0.375882	−	0.926667i	$-0.622660\pi$
$71$	−6.33448	−0.751765	−0.375882	+	0.926667i	$0.622660\pi$
$72$	5.44424	0.641610
$73$	2.18771	0.256052	0.128026	−	0.991771i	$-0.459136\pi$
$73$	2.18771	0.256052	0.128026	+	0.991771i	$0.459136\pi$
$74$	−4.07118	−0.473265
$75$	4.53255	0.523373
$76$	2.06578	0.236961
$77$	6.67696	0.760910
$78$	1.52317	0.172465
$79$	−16.0251	−1.80297	−0.901485	−	0.432811i	$-0.857522\pi$
$79$	−16.0251	−1.80297	−0.901485	+	0.432811i	$0.857522\pi$
$80$	−11.5193	−1.28790
$81$	−5.96129	−0.662366
$82$	−0.893059	−0.0986218
$83$	−8.96465	−0.983998	−0.491999	−	0.870596i	$-0.663734\pi$
$83$	−8.96465	−0.983998	−0.491999	+	0.870596i	$0.663734\pi$
$84$	35.1690	3.83726
$85$	−3.79888	−0.412046
$86$	−4.12407	−0.444710
$87$	11.7071	1.25514
$88$	8.89864	0.948598
$89$	−14.8082	−1.56967	−0.784833	−	0.619708i	$-0.787251\pi$
$89$	−14.8082	−1.56967	−0.784833	+	0.619708i	$0.787251\pi$
$90$	−2.87383	−0.302928
$91$	−2.03530	−0.213357
$92$	4.64158	0.483918
$93$	1.78250	0.184837
$94$	−27.7089	−2.85795
$95$	−0.620591	−0.0636713
$96$	11.3839	1.16187
$97$	4.83280	0.490696	0.245348	−	0.969435i	$-0.421098\pi$
$97$	4.83280	0.490696	0.245348	+	0.969435i	$0.421098\pi$
$98$	−49.2030	−4.97025
$99$	1.04535	0.105061
$100$	−14.1830	−1.41830
$101$	−3.37474	−0.335799	−0.167900	−	0.985804i	$-0.553698\pi$
$101$	−3.37474	−0.335799	−0.167900	+	0.985804i	$0.553698\pi$
$102$	10.4146	1.03120
$103$	3.48034	0.342928	0.171464	−	0.985190i	$-0.445150\pi$
$103$	3.48034	0.342928	0.171464	+	0.985190i	$0.445150\pi$
$104$	−2.71251	−0.265984
$105$	−10.5653	−1.03107
$106$	4.57825	0.444679
$107$	−15.2318	−1.47251	−0.736256	−	0.676703i	$-0.763408\pi$
$107$	−15.2318	−1.47251	−0.736256	+	0.676703i	$0.763408\pi$
$108$	26.1611	2.51736
$109$	19.7275	1.88955	0.944774	−	0.327723i	$-0.106281\pi$
$109$	19.7275	1.88955	0.944774	+	0.327723i	$0.106281\pi$
$110$	−4.69729	−0.447869
$111$	−2.34328	−0.222414
$112$	−42.1982	−3.98736
$113$	−14.4365	−1.35808	−0.679038	−	0.734103i	$-0.737603\pi$
$113$	−14.4365	−1.35808	−0.679038	+	0.734103i	$0.737603\pi$
$114$	1.70135	0.159346
$115$	−1.39440	−0.130029
$116$	−36.6334	−3.40132
$117$	−0.318647	−0.0294589
$118$	8.26779	0.761112
$119$	−13.9163	−1.27570
$120$	−14.0808	−1.28539
$121$	−9.29137	−0.844670
$122$	28.3673	2.56825
$123$	−0.514024	−0.0463480
$124$	−5.57773	−0.500895
$125$	11.2328	1.00469
$126$	−10.5276	−0.937871
$127$	0.742296	0.0658681	0.0329341	−	0.999458i	$-0.489515\pi$
$127$	0.742296	0.0658681	0.0329341	+	0.999458i	$0.489515\pi$
$128$	6.95777	0.614986
$129$	−2.37372	−0.208994
$130$	1.43184	0.125581
$131$	−21.1656	−1.84924	−0.924622	−	0.380885i	$-0.875619\pi$
$131$	−21.1656	−1.84924	−0.924622	+	0.380885i	$0.875619\pi$
$132$	8.99971	0.783325
$133$	−2.27338	−0.197127
$134$	23.9154	2.06598
$135$	−7.85920	−0.676412
$136$	−18.5467	−1.59037
$137$	−18.4154	−1.57333	−0.786666	−	0.617378i	$-0.788195\pi$
$137$	−18.4154	−1.57333	−0.786666	+	0.617378i	$0.788195\pi$
$138$	3.82274	0.325413
$139$	1.46667	0.124402	0.0622008	−	0.998064i	$-0.480188\pi$
$139$	1.46667	0.124402	0.0622008	+	0.998064i	$0.480188\pi$
$140$	33.0605	2.79412
$141$	−15.9486	−1.34311
$142$	16.3248	1.36994
$143$	−0.520830	−0.0435540
$144$	−6.60657	−0.550548
$145$	11.0052	0.913934
$146$	−5.63801	−0.466605
$147$	−28.3201	−2.33580
$148$	7.33248	0.602726
$149$	−10.0619	−0.824303	−0.412152	−	0.911115i	$-0.635223\pi$
$149$	−10.0619	−0.824303	−0.412152	+	0.911115i	$0.635223\pi$
$150$	−11.6809	−0.953745
$151$	−18.4316	−1.49994	−0.749972	−	0.661469i	$-0.769933\pi$
$151$	−18.4316	−1.49994	−0.749972	+	0.661469i	$0.769933\pi$
$152$	−3.02983	−0.245751
$153$	−2.17874	−0.176140
$154$	−17.2074	−1.38661
$155$	1.67563	0.134590
$156$	−2.74333	−0.219642
$157$	−1.37048	−0.109377	−0.0546883	−	0.998503i	$-0.517417\pi$
$157$	−1.37048	−0.109377	−0.0546883	+	0.998503i	$0.517417\pi$
$158$	41.2988	3.28556
$159$	2.63514	0.208980
$160$	10.7014	0.846022
$161$	−5.10805	−0.402571
$162$	15.3630	1.20703
$163$	2.11634	0.165765	0.0828823	−	0.996559i	$-0.473587\pi$
$163$	2.11634	0.165765	0.0828823	+	0.996559i	$0.473587\pi$
$164$	1.60846	0.125600
$165$	−2.70365	−0.210479
$166$	23.1030	1.79314
$167$	14.0825	1.08974	0.544870	−	0.838521i	$-0.316579\pi$
$167$	14.0825	1.08974	0.544870	+	0.838521i	$0.316579\pi$
$168$	−51.5815	−3.97960
$169$	−12.8412	−0.987788
$170$	9.79018	0.750873
$171$	−0.355922	−0.0272181
$172$	7.42773	0.566359
$173$	8.39769	0.638464	0.319232	−	0.947677i	$-0.396575\pi$
$173$	8.39769	0.638464	0.319232	+	0.947677i	$0.396575\pi$
$174$	−30.1707	−2.28724
$175$	15.6084	1.17988
$176$	−10.7985	−0.813966
$177$	4.75875	0.357690
$178$	38.1626	2.86041
$179$	2.18758	0.163507	0.0817535	−	0.996653i	$-0.473948\pi$
$179$	2.18758	0.163507	0.0817535	+	0.996653i	$0.473948\pi$
$180$	5.17596	0.385793
$181$	4.16691	0.309724	0.154862	−	0.987936i	$-0.450507\pi$
$181$	4.16691	0.309724	0.154862	+	0.987936i	$0.450507\pi$
$182$	5.24521	0.388801
$183$	16.3276	1.20697
$184$	−6.80769	−0.501870
$185$	−2.20279	−0.161952
$186$	−4.59374	−0.336829
$187$	−3.56116	−0.260418
$188$	49.9056	3.63974
$189$	−28.7903	−2.09418
$190$	1.59934	0.116028
$191$	−12.8424	−0.929246	−0.464623	−	0.885509i	$-0.653810\pi$
$191$	−12.8424	−0.929246	−0.464623	+	0.885509i	$0.653810\pi$
$192$	−4.82987	−0.348566
$193$	9.13829	0.657788	0.328894	−	0.944367i	$-0.393324\pi$
$193$	9.13829	0.657788	0.328894	+	0.944367i	$0.393324\pi$
$194$	−12.4547	−0.894198
$195$	0.824136	0.0590176
$196$	88.6179	6.32985
$197$	−12.3586	−0.880512	−0.440256	−	0.897872i	$-0.645112\pi$
$197$	−12.3586	−0.880512	−0.440256	+	0.897872i	$0.645112\pi$
$198$	−2.69399	−0.191454
$199$	−17.1797	−1.21784	−0.608918	−	0.793233i	$-0.708396\pi$
$199$	−17.1797	−1.21784	−0.608918	+	0.793233i	$0.708396\pi$
$200$	20.8019	1.47092
$201$	13.7652	0.970919
$202$	8.69713	0.611928
$203$	40.3150	2.82956
$204$	−18.7574	−1.31328
$205$	−0.483205	−0.0337485
$206$	−8.96928	−0.624919
$207$	−0.799719	−0.0555843
$208$	3.29163	0.228233
$209$	−0.581757	−0.0402409
$210$	27.2281	1.87892
$211$	24.5039	1.68692	0.843458	−	0.537196i	$-0.180516\pi$
$211$	24.5039	1.68692	0.843458	+	0.537196i	$0.180516\pi$
$212$	−8.24575	−0.566320
$213$	9.39615	0.643814
$214$	39.2543	2.68337
$215$	−2.23140	−0.152180
$216$	−38.3699	−2.61074
$217$	6.13828	0.416694
$218$	−50.8402	−3.44333
$219$	−3.24511	−0.219284
$220$	8.46013	0.570382
$221$	1.08552	0.0730203
$222$	6.03893	0.405306
$223$	8.19877	0.549030	0.274515	−	0.961583i	$-0.411483\pi$
$223$	8.19877	0.549030	0.274515	+	0.961583i	$0.411483\pi$
$224$	39.2021	2.61930
$225$	2.44366	0.162911
$226$	37.2048	2.47483
$227$	−21.0455	−1.39684	−0.698419	−	0.715690i	$-0.746113\pi$
$227$	−21.0455	−1.39684	−0.698419	+	0.715690i	$0.746113\pi$
$228$	−3.06424	−0.202934
$229$	20.9003	1.38113	0.690564	−	0.723271i	$-0.257362\pi$
$229$	20.9003	1.38113	0.690564	+	0.723271i	$0.257362\pi$
$230$	3.59355	0.236952
$231$	−9.90417	−0.651646
$232$	53.7293	3.52750
$233$	−4.17523	−0.273528	−0.136764	−	0.990604i	$-0.543670\pi$
$233$	−4.17523	−0.273528	−0.136764	+	0.990604i	$0.543670\pi$
$234$	0.821193	0.0536831
$235$	−14.9924	−0.977995
$236$	−14.8909	−0.969313
$237$	23.7706	1.54407
$238$	35.8640	2.32472
$239$	−24.4798	−1.58347	−0.791733	−	0.610867i	$-0.790821\pi$
$239$	−24.4798	−1.58347	−0.791733	+	0.610867i	$0.790821\pi$
$240$	17.0870	1.10296
$241$	10.7187	0.690450	0.345225	−	0.938520i	$-0.387803\pi$
$241$	10.7187	0.690450	0.345225	+	0.938520i	$0.387803\pi$
$242$	23.9450	1.53925
$243$	−8.06617	−0.517445
$244$	−51.0915	−3.27080
$245$	−26.6222	−1.70083
$246$	1.32470	0.0844601
$247$	0.177333	0.0112834
$248$	8.18072	0.519476
$249$	13.2976	0.842700
$250$	−28.9483	−1.83085
$251$	19.6196	1.23838	0.619188	−	0.785243i	$-0.287462\pi$
$251$	19.6196	1.23838	0.619188	+	0.785243i	$0.287462\pi$
$252$	18.9609	1.19442
$253$	−1.30714	−0.0821795
$254$	−1.91299	−0.120032
$255$	5.63500	0.352878
$256$	−24.4432	−1.52770
$257$	11.1300	0.694270	0.347135	−	0.937815i	$-0.387155\pi$
$257$	11.1300	0.694270	0.347135	+	0.937815i	$0.387155\pi$
$258$	6.11737	0.380851
$259$	−8.06938	−0.501407
$260$	−2.57885	−0.159933
$261$	6.31173	0.390686
$262$	54.5464	3.36989
$263$	−10.9676	−0.676293	−0.338147	−	0.941093i	$-0.609800\pi$
$263$	−10.9676	−0.676293	−0.338147	+	0.941093i	$0.609800\pi$
$264$	−13.1997	−0.812382
$265$	2.47715	0.152170
$266$	5.85880	0.359226
$267$	21.9655	1.34427
$268$	−43.0733	−2.63112
$269$	11.9210	0.726833	0.363417	−	0.931627i	$-0.381610\pi$
$269$	11.9210	0.726833	0.363417	+	0.931627i	$0.381610\pi$
$270$	20.2541	1.23263
$271$	10.8169	0.657080	0.328540	−	0.944490i	$-0.393443\pi$
$271$	10.8169	0.657080	0.328540	+	0.944490i	$0.393443\pi$
$272$	22.5064	1.36465
$273$	3.01902	0.182720
$274$	47.4588	2.86709
$275$	3.99417	0.240858
$276$	−6.88502	−0.414429
$277$	−13.9071	−0.835594	−0.417797	−	0.908540i	$-0.637198\pi$
$277$	−13.9071	−0.835594	−0.417797	+	0.908540i	$0.637198\pi$
$278$	−3.77980	−0.226698
$279$	0.961012	0.0575343
$280$	−48.4889	−2.89777
$281$	−25.9454	−1.54777	−0.773886	−	0.633325i	$-0.781690\pi$
$281$	−25.9454	−1.54777	−0.773886	+	0.633325i	$0.781690\pi$
$282$	41.1015	2.44756
$283$	0.100939	0.00600020	0.00300010	−	0.999995i	$-0.499045\pi$
$283$	0.100939	0.00600020	0.00300010	+	0.999995i	$0.499045\pi$
$284$	−29.4020	−1.74469
$285$	0.920544	0.0545283
$286$	1.34224	0.0793686
$287$	−1.77011	−0.104486
$288$	6.13749	0.361655
$289$	−9.57776	−0.563398
$290$	−28.3618	−1.66546
$291$	−7.16866	−0.420234
$292$	10.1544	0.594244
$293$	−23.3528	−1.36429	−0.682143	−	0.731218i	$-0.738952\pi$
$293$	−23.3528	−1.36429	−0.682143	+	0.731218i	$0.738952\pi$
$294$	72.9845	4.25654
$295$	4.47344	0.260454
$296$	−10.7544	−0.625085
$297$	−7.36740	−0.427500
$298$	25.9308	1.50213
$299$	0.398449	0.0230429
$300$	21.0382	1.21464
$301$	−8.17420	−0.471153
$302$	47.5006	2.73336
$303$	5.00587	0.287580
$304$	3.67669	0.210872
$305$	15.3486	0.878861
$306$	5.61488	0.320981
$307$	−10.2083	−0.582618	−0.291309	−	0.956629i	$-0.594091\pi$
$307$	−10.2083	−0.582618	−0.291309	+	0.956629i	$0.594091\pi$
$308$	30.9917	1.76591
$309$	−5.16251	−0.293685
$310$	−4.31832	−0.245264
$311$	−29.5659	−1.67653	−0.838265	−	0.545263i	$-0.816430\pi$
$311$	−29.5659	−1.67653	−0.838265	+	0.545263i	$0.816430\pi$
$312$	4.02357	0.227790
$313$	−1.11389	−0.0629605	−0.0314803	−	0.999504i	$-0.510022\pi$
$313$	−1.11389	−0.0629605	−0.0314803	+	0.999504i	$0.510022\pi$
$314$	3.53191	0.199317
$315$	−5.69613	−0.320941
$316$	−74.3820	−4.18431
$317$	−26.8444	−1.50773	−0.753867	−	0.657027i	$-0.771814\pi$
$317$	−26.8444	−1.50773	−0.753867	+	0.657027i	$0.771814\pi$
$318$	−6.79108	−0.380825
$319$	10.3166	0.577616
$320$	−4.54030	−0.253810
$321$	22.5938	1.26107
$322$	13.1641	0.733606
$323$	1.21251	0.0674658
$324$	−27.6698	−1.53721
$325$	−1.21752	−0.0675357
$326$	−5.45408	−0.302074
$327$	−29.2624	−1.61822
$328$	−2.35909	−0.130259
$329$	−54.9210	−3.02789
$330$	6.96765	0.383556
$331$	−19.1758	−1.05400	−0.526999	−	0.849866i	$-0.676683\pi$
$331$	−19.1758	−1.05400	−0.526999	+	0.849866i	$0.676683\pi$
$332$	−41.6102	−2.28365
$333$	−1.26335	−0.0692309
$334$	−36.2925	−1.98584
$335$	12.9399	0.706980
$336$	62.5941	3.41479
$337$	6.91681	0.376783	0.188391	−	0.982094i	$-0.439673\pi$
$337$	6.91681	0.376783	0.188391	+	0.982094i	$0.439673\pi$
$338$	33.0935	1.80005
$339$	21.4142	1.16306
$340$	−17.6328	−0.956272
$341$	1.57078	0.0850624
$342$	0.917257	0.0495996
$343$	−61.7675	−3.33513
$344$	−10.8941	−0.587368
$345$	2.06836	0.111357
$346$	−21.6419	−1.16348
$347$	8.49468	0.456019	0.228009	−	0.973659i	$-0.426778\pi$
$347$	8.49468	0.456019	0.228009	+	0.973659i	$0.426778\pi$
$348$	54.3396	2.91291
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−40.2248	−2.15011
$351$	2.24576	0.119870
$352$	10.0318	0.534695
$353$	13.2769	0.706657	0.353328	−	0.935499i	$-0.385050\pi$
$353$	13.2769	0.706657	0.353328	+	0.935499i	$0.385050\pi$
$354$	−12.2639	−0.651819
$355$	8.83281	0.468797
$356$	−68.7335	−3.64287
$357$	20.6425	1.09252
$358$	−5.63766	−0.297960
$359$	10.6397	0.561539	0.280770	−	0.959775i	$-0.409410\pi$
$359$	10.6397	0.561539	0.280770	+	0.959775i	$0.409410\pi$
$360$	−7.59145	−0.400105
$361$	−18.8019	−0.989575
$362$	−10.7386	−0.564411
$363$	13.7822	0.723379
$364$	−9.44699	−0.495157
$365$	−3.05055	−0.159673
$366$	−42.0782	−2.19946
$367$	−21.0542	−1.09902	−0.549511	−	0.835487i	$-0.685186\pi$
$367$	−21.0542	−1.09902	−0.549511	+	0.835487i	$0.685186\pi$
$368$	8.26112	0.430641
$369$	−0.277129	−0.0144267
$370$	5.67686	0.295126
$371$	9.07443	0.471121
$372$	8.27364	0.428968
$373$	−4.43210	−0.229485	−0.114743	−	0.993395i	$-0.536604\pi$
$373$	−4.43210	−0.229485	−0.114743	+	0.993395i	$0.536604\pi$
$374$	9.17755	0.474560
$375$	−16.6620	−0.860422
$376$	−73.1952	−3.77475
$377$	−3.14473	−0.161962
$378$	74.1962	3.81624
$379$	−7.85223	−0.403342	−0.201671	−	0.979453i	$-0.564637\pi$
$379$	−7.85223	−0.403342	−0.201671	+	0.979453i	$0.564637\pi$
$380$	−2.88052	−0.147768
$381$	−1.10107	−0.0564097
$382$	33.0966	1.69337
$383$	−0.669281	−0.0341987	−0.0170993	−	0.999854i	$-0.505443\pi$
$383$	−0.669281	−0.0341987	−0.0170993	+	0.999854i	$0.505443\pi$
$384$	−10.3207	−0.526676
$385$	−9.31036	−0.474500
$386$	−23.5505	−1.19869
$387$	−1.27976	−0.0650537
$388$	22.4318	1.13880
$389$	−27.3821	−1.38833	−0.694164	−	0.719817i	$-0.744226\pi$
$389$	−27.3821	−1.38833	−0.694164	+	0.719817i	$0.744226\pi$
$390$	−2.12390	−0.107548
$391$	2.72438	0.137778
$392$	−129.974	−6.56466
$393$	31.3956	1.58370
$394$	31.8496	1.60456
$395$	22.3455	1.12432
$396$	4.85207	0.243826
$397$	30.8072	1.54617	0.773085	−	0.634302i	$-0.218713\pi$
$397$	30.8072	1.54617	0.773085	+	0.634302i	$0.218713\pi$
$398$	44.2742	2.21927
$399$	3.37219	0.168821
$400$	−25.2431	−1.26215
$401$	25.2006	1.25846	0.629230	−	0.777220i	$-0.283371\pi$
$401$	25.2006	1.25846	0.629230	+	0.777220i	$0.283371\pi$
$402$	−35.4746	−1.76931
$403$	−0.478810	−0.0238512
$404$	−15.6641	−0.779320
$405$	8.31243	0.413048
$406$	−103.897	−5.15631
$407$	−2.06495	−0.102356
$408$	27.5110	1.36200
$409$	1.69505	0.0838150	0.0419075	−	0.999121i	$-0.486657\pi$
$409$	1.69505	0.0838150	0.0419075	+	0.999121i	$0.486657\pi$
$410$	1.24528	0.0615001
$411$	27.3162	1.34741
$412$	16.1543	0.795865
$413$	16.3874	0.806369
$414$	2.06098	0.101291
$415$	12.5003	0.613617
$416$	−3.05792	−0.149927
$417$	−2.17557	−0.106538
$418$	1.49926	0.0733312
$419$	11.6073	0.567053	0.283527	−	0.958964i	$-0.408496\pi$
$419$	11.6073	0.567053	0.283527	+	0.958964i	$0.408496\pi$
$420$	−49.0397	−2.39289
$421$	−19.5786	−0.954203	−0.477102	−	0.878848i	$-0.658313\pi$
$421$	−19.5786	−0.954203	−0.477102	+	0.878848i	$0.658313\pi$
$422$	−63.1496	−3.07407
$423$	−8.59845	−0.418071
$424$	12.0938	0.587328
$425$	−8.32474	−0.403809
$426$	−24.2151	−1.17322
$427$	56.2260	2.72097
$428$	−70.6996	−3.41739
$429$	0.772565	0.0372998
$430$	5.75060	0.277319
$431$	−35.9552	−1.73190	−0.865951	−	0.500129i	$-0.833286\pi$
$431$	−35.9552	−1.73190	−0.865951	+	0.500129i	$0.833286\pi$
$432$	46.5618	2.24020
$433$	35.0490	1.68435	0.842173	−	0.539207i	$-0.181276\pi$
$433$	35.0490	1.68435	0.842173	+	0.539207i	$0.181276\pi$
$434$	−15.8191	−0.759342
$435$	−16.3244	−0.782696
$436$	91.5666	4.38525
$437$	0.445059	0.0212901
$438$	8.36306	0.399602
$439$	−5.50875	−0.262918	−0.131459	−	0.991322i	$-0.541966\pi$
$439$	−5.50875	−0.262918	−0.131459	+	0.991322i	$0.541966\pi$
$440$	−12.4083	−0.591541
$441$	−15.2684	−0.727066
$442$	−2.79753	−0.133065
$443$	−11.5802	−0.550194	−0.275097	−	0.961416i	$-0.588710\pi$
$443$	−11.5802	−0.550194	−0.275097	+	0.961416i	$0.588710\pi$
$444$	−10.8765	−0.516177
$445$	20.6486	0.978836
$446$	−21.1293	−1.00050
$447$	14.9252	0.705936
$448$	−16.6323	−0.785801
$449$	22.1291	1.04434	0.522168	−	0.852843i	$-0.325123\pi$
$449$	22.1291	1.04434	0.522168	+	0.852843i	$0.325123\pi$
$450$	−6.29762	−0.296872
$451$	−0.452968	−0.0213294
$452$	−67.0084	−3.15181
$453$	27.3403	1.28456
$454$	54.2368	2.54546
$455$	2.83802	0.133048
$456$	4.49424	0.210462
$457$	−19.7964	−0.926035	−0.463018	−	0.886349i	$-0.653233\pi$
$457$	−19.7964	−0.926035	−0.463018	+	0.886349i	$0.653233\pi$
$458$	−53.8626	−2.51683
$459$	15.3553	0.716723
$460$	−6.47223	−0.301769
$461$	23.6559	1.10176	0.550882	−	0.834583i	$-0.314292\pi$
$461$	23.6559	1.10176	0.550882	+	0.834583i	$0.314292\pi$
$462$	25.5243	1.18750
$463$	4.52171	0.210141	0.105071	−	0.994465i	$-0.466493\pi$
$463$	4.52171	0.210141	0.105071	+	0.994465i	$0.466493\pi$
$464$	−65.2003	−3.02685
$465$	−2.48553	−0.115263
$466$	10.7601	0.498451
$467$	−23.2913	−1.07779	−0.538896	−	0.842373i	$-0.681158\pi$
$467$	−23.2913	−1.07779	−0.538896	+	0.842373i	$0.681158\pi$
$468$	−1.47903	−0.0683680
$469$	47.4021	2.18882
$470$	38.6373	1.78220
$471$	2.03289	0.0936705
$472$	21.8401	1.00527
$473$	−2.09177	−0.0961796
$474$	−61.2600	−2.81376
$475$	−1.35994	−0.0623985
$476$	−64.5935	−2.96064
$477$	1.42070	0.0650493
$478$	63.0875	2.88556
$479$	−17.0813	−0.780463	−0.390232	−	0.920717i	$-0.627605\pi$
$479$	−17.0813	−0.780463	−0.390232	+	0.920717i	$0.627605\pi$
$480$	−15.8738	−0.724536
$481$	0.629444	0.0287002
$482$	−27.6234	−1.25821
$483$	7.57695	0.344763
$484$	−43.1267	−1.96030
$485$	−6.73886	−0.305996
$486$	20.7875	0.942942
$487$	−9.66394	−0.437915	−0.218957	−	0.975734i	$-0.570266\pi$
$487$	−9.66394	−0.437915	−0.218957	+	0.975734i	$0.570266\pi$
$488$	74.9345	3.39213
$489$	−3.13924	−0.141961
$490$	68.6087	3.09942
$491$	19.9216	0.899051	0.449526	−	0.893267i	$-0.351593\pi$
$491$	19.9216	0.899051	0.449526	+	0.893267i	$0.351593\pi$
$492$	−2.38588	−0.107564
$493$	−21.5020	−0.968401
$494$	−0.457010	−0.0205619
$495$	−1.45763	−0.0655158
$496$	−9.92728	−0.445748
$497$	32.3568	1.45140
$498$	−34.2695	−1.53565
$499$	−29.1900	−1.30672	−0.653361	−	0.757046i	$-0.726642\pi$
$499$	−29.1900	−1.30672	−0.653361	+	0.757046i	$0.726642\pi$
$500$	52.1380	2.33168
$501$	−20.8891	−0.933257
$502$	−50.5621	−2.25670
$503$	30.0883	1.34157	0.670785	−	0.741652i	$-0.265957\pi$
$503$	30.0883	1.34157	0.670785	+	0.741652i	$0.265957\pi$
$504$	−27.8094	−1.23873
$505$	4.70574	0.209403
$506$	3.36868	0.149756
$507$	19.0479	0.845945
$508$	3.44543	0.152866
$509$	−11.7322	−0.520022	−0.260011	−	0.965606i	$-0.583726\pi$
$509$	−11.7322	−0.520022	−0.260011	+	0.965606i	$0.583726\pi$
$510$	−14.5221	−0.643050
$511$	−11.1749	−0.494350
$512$	49.0778	2.16895
$513$	2.50847	0.110751
$514$	−28.6834	−1.26517
$515$	−4.85299	−0.213848
$516$	−11.0178	−0.485032
$517$	−14.0542	−0.618103
$518$	20.7958	0.913716
$519$	−12.4566	−0.546783
$520$	3.78233	0.165866
$521$	14.8599	0.651026	0.325513	−	0.945538i	$-0.394463\pi$
$521$	14.8599	0.651026	0.325513	+	0.945538i	$0.394463\pi$
$522$	−16.2661	−0.711949
$523$	12.4343	0.543714	0.271857	−	0.962338i	$-0.412362\pi$
$523$	12.4343	0.543714	0.271857	+	0.962338i	$0.412362\pi$
$524$	−98.2417	−4.29171
$525$	−23.1525	−1.01046
$526$	28.2650	1.23241
$527$	−3.27385	−0.142611
$528$	16.0177	0.697083
$529$	1.00000	0.0434783
$530$	−6.38392	−0.277300
$531$	2.56561	0.111338
$532$	−10.5521	−0.457492
$533$	0.138075	0.00598071
$534$	−56.6079	−2.44966
$535$	21.2392	0.918252
$536$	63.1745	2.72872
$537$	−3.24491	−0.140028
$538$	−30.7218	−1.32451
$539$	−24.9562	−1.07494
$540$	−36.4791	−1.56981
$541$	23.1728	0.996277	0.498138	−	0.867098i	$-0.334017\pi$
$541$	23.1728	0.996277	0.498138	+	0.867098i	$0.334017\pi$
$542$	−27.8765	−1.19740
$543$	−6.18092	−0.265248
$544$	−20.9084	−0.896441
$545$	−27.5080	−1.17831
$546$	−7.78041	−0.332971
$547$	−10.3513	−0.442591	−0.221295	−	0.975207i	$-0.571029\pi$
$547$	−10.3513	−0.442591	−0.221295	+	0.975207i	$0.571029\pi$
$548$	−85.4765	−3.65138
$549$	8.80278	0.375693
$550$	−10.2935	−0.438916
$551$	−3.51260	−0.149642
$552$	10.0981	0.429803
$553$	81.8572	3.48092
$554$	35.8402	1.52271
$555$	3.26747	0.138696
$556$	6.80769	0.288710
$557$	12.8719	0.545401	0.272700	−	0.962099i	$-0.412083\pi$
$557$	12.8719	0.545401	0.272700	+	0.962099i	$0.412083\pi$
$558$	−2.47665	−0.104845
$559$	0.637620	0.0269685
$560$	58.8412	2.48650
$561$	5.28239	0.223023
$562$	66.8645	2.82051
$563$	−39.0661	−1.64644	−0.823219	−	0.567724i	$-0.807824\pi$
$563$	−39.0661	−1.64644	−0.823219	+	0.567724i	$0.807824\pi$
$564$	−74.0266	−3.11708
$565$	20.1303	0.846889
$566$	−0.260133	−0.0109342
$567$	30.4506	1.27880
$568$	43.1232	1.80941
$569$	6.17098	0.258701	0.129350	−	0.991599i	$-0.458711\pi$
$569$	6.17098	0.258701	0.129350	+	0.991599i	$0.458711\pi$
$570$	−2.37236	−0.0993671
$571$	−26.1851	−1.09581	−0.547906	−	0.836540i	$-0.684575\pi$
$571$	−26.1851	−1.09581	−0.547906	+	0.836540i	$0.684575\pi$
$572$	−2.41747	−0.101080
$573$	19.0496	0.795810
$574$	4.56179	0.190405
$575$	−3.05565	−0.127429
$576$	−2.60396	−0.108498
$577$	−36.2820	−1.51044	−0.755221	−	0.655471i	$-0.772470\pi$
$577$	−36.2820	−1.51044	−0.755221	+	0.655471i	$0.772470\pi$
$578$	24.6831	1.02668
$579$	−13.5551	−0.563332
$580$	51.0816	2.12105
$581$	45.7919	1.89977
$582$	18.4745	0.765794
$583$	2.32214	0.0961731
$584$	−14.8933	−0.616288
$585$	0.444321	0.0183704
$586$	60.1832	2.48614
$587$	4.99302	0.206084	0.103042	−	0.994677i	$-0.467142\pi$
$587$	4.99302	0.206084	0.103042	+	0.994677i	$0.467142\pi$
$588$	−131.450	−5.42091
$589$	−0.534822	−0.0220370
$590$	−11.5286	−0.474626
$591$	18.3319	0.754074
$592$	13.0504	0.536368
$593$	−19.3131	−0.793094	−0.396547	−	0.918014i	$-0.629792\pi$
$593$	−19.3131	−0.793094	−0.396547	+	0.918014i	$0.629792\pi$
$594$	18.9867	0.779034
$595$	19.4049	0.795521
$596$	−46.7031	−1.91304
$597$	25.4832	1.04296
$598$	−1.02685	−0.0419911
$599$	2.19955	0.0898710	0.0449355	−	0.998990i	$-0.485692\pi$
$599$	2.19955	0.0898710	0.0449355	+	0.998990i	$0.485692\pi$
$600$	−30.8562	−1.25970
$601$	−16.2205	−0.661647	−0.330823	−	0.943693i	$-0.607326\pi$
$601$	−16.2205	−0.661647	−0.330823	+	0.943693i	$0.607326\pi$
$602$	21.0659	0.858584
$603$	7.42129	0.302218
$604$	−85.5519	−3.48106
$605$	12.9559	0.526732
$606$	−12.9008	−0.524058
$607$	1.14499	0.0464736	0.0232368	−	0.999730i	$-0.492603\pi$
$607$	1.14499	0.0464736	0.0232368	+	0.999730i	$0.492603\pi$
$608$	−3.41564	−0.138522
$609$	−59.8006	−2.42324
$610$	−39.5554	−1.60155
$611$	4.28406	0.173314
$612$	−10.1128	−0.408785
$613$	33.0046	1.33304	0.666521	−	0.745486i	$-0.267782\pi$
$613$	33.0046	1.33304	0.666521	+	0.745486i	$0.267782\pi$
$614$	26.3081	1.06171
$615$	0.716755	0.0289024
$616$	−45.4547	−1.83142
$617$	33.8515	1.36281	0.681405	−	0.731907i	$-0.261369\pi$
$617$	33.8515	1.36281	0.681405	+	0.731907i	$0.261369\pi$
$618$	13.3044	0.535183
$619$	18.4249	0.740559	0.370279	−	0.928920i	$-0.379262\pi$
$619$	18.4249	0.740559	0.370279	+	0.928920i	$0.379262\pi$
$620$	7.77759	0.312356
$621$	5.63625	0.226175
$622$	76.1952	3.05515
$623$	75.6410	3.03049
$624$	−4.88259	−0.195460
$625$	−0.384797	−0.0153919
$626$	2.87062	0.114733
$627$	0.862940	0.0344625
$628$	−6.36122	−0.253840
$629$	4.30380	0.171604
$630$	14.6797	0.584852
$631$	24.6723	0.982190	0.491095	−	0.871106i	$-0.336597\pi$
$631$	24.6723	0.982190	0.491095	+	0.871106i	$0.336597\pi$
$632$	109.094	4.33953
$633$	−36.3474	−1.44468
$634$	69.1815	2.74755
$635$	−1.03506	−0.0410751
$636$	12.2312	0.484999
$637$	7.60725	0.301410
$638$	−26.5871	−1.05259
$639$	5.06580	0.200400
$640$	−9.70192	−0.383502
$641$	33.2574	1.31359	0.656795	−	0.754069i	$-0.271912\pi$
$641$	33.2574	1.31359	0.656795	+	0.754069i	$0.271912\pi$
$642$	−58.2272	−2.29804
$643$	−37.3997	−1.47490	−0.737450	−	0.675402i	$-0.763970\pi$
$643$	−37.3997	−1.47490	−0.737450	+	0.675402i	$0.763970\pi$
$644$	−23.7094	−0.934283
$645$	3.30991	0.130328
$646$	−3.12479	−0.122943
$647$	34.1333	1.34192	0.670960	−	0.741493i	$-0.265882\pi$
$647$	34.1333	1.34192	0.670960	+	0.741493i	$0.265882\pi$
$648$	40.5826	1.59424
$649$	4.19351	0.164610
$650$	3.13770	0.123071
$651$	−9.10512	−0.356858
$652$	9.82317	0.384705
$653$	−9.37924	−0.367038	−0.183519	−	0.983016i	$-0.558749\pi$
$653$	−9.37924	−0.367038	−0.183519	+	0.983016i	$0.558749\pi$
$654$	75.4130	2.94888
$655$	29.5133	1.15318
$656$	2.86275	0.111771
$657$	−1.74955	−0.0682566
$658$	141.538	5.51774
$659$	−40.8007	−1.58937	−0.794685	−	0.607022i	$-0.792364\pi$
$659$	−40.8007	−1.58937	−0.794685	+	0.607022i	$0.792364\pi$
$660$	−12.5492	−0.488477
$661$	−32.2817	−1.25561	−0.627807	−	0.778369i	$-0.716047\pi$
$661$	−32.2817	−1.25561	−0.627807	+	0.778369i	$0.716047\pi$
$662$	49.4185	1.92071
$663$	−1.61020	−0.0625348
$664$	61.0286	2.36837
$665$	3.17001	0.122928
$666$	3.25580	0.126160
$667$	−7.89244	−0.305596
$668$	65.3653	2.52906
$669$	−12.1615	−0.470191
$670$	−33.3477	−1.28833
$671$	14.3882	0.555450
$672$	−58.1498	−2.24318
$673$	13.9329	0.537075	0.268538	−	0.963269i	$-0.413460\pi$
$673$	13.9329	0.537075	0.268538	+	0.963269i	$0.413460\pi$
$674$	−17.8255	−0.686613
$675$	−17.2224	−0.662890
$676$	−59.6037	−2.29245
$677$	−46.5802	−1.79022	−0.895112	−	0.445842i	$-0.852904\pi$
$677$	−46.5802	−1.79022	−0.895112	+	0.445842i	$0.852904\pi$
$678$	−55.1872	−2.11945
$679$	−24.6862	−0.947369
$680$	25.8616	0.991746
$681$	31.2175	1.19626
$682$	−4.04810	−0.155010
$683$	−21.7737	−0.833146	−0.416573	−	0.909102i	$-0.636769\pi$
$683$	−21.7737	−0.833146	−0.416573	+	0.909102i	$0.636769\pi$
$684$	−1.65204	−0.0631674
$685$	25.6784	0.981123
$686$	159.183	6.07762
$687$	−31.0021	−1.18280
$688$	13.2199	0.504005
$689$	−0.707842	−0.0269666
$690$	−5.33043	−0.202926
$691$	−25.6002	−0.973877	−0.486938	−	0.873436i	$-0.661886\pi$
$691$	−25.6002	−0.973877	−0.486938	+	0.873436i	$0.661886\pi$
$692$	38.9785	1.48174
$693$	−5.33969	−0.202838
$694$	−21.8919	−0.831004
$695$	−2.04513	−0.0775762
$696$	−79.6985	−3.02096
$697$	0.944086	0.0357598
$698$	2.57713	0.0975457
$699$	6.19326	0.234250
$700$	72.4476	2.73826
$701$	−51.0469	−1.92801	−0.964007	−	0.265875i	$-0.914339\pi$
$701$	−51.0469	−1.92801	−0.964007	+	0.265875i	$0.914339\pi$
$702$	−5.78760	−0.218439
$703$	0.703077	0.0265170
$704$	−4.25618	−0.160411
$705$	22.2387	0.837558
$706$	−34.2162	−1.28774
$707$	17.2383	0.648315
$708$	22.0881	0.830123
$709$	38.1066	1.43112	0.715561	−	0.698550i	$-0.246171\pi$
$709$	38.1066	1.43112	0.715561	+	0.698550i	$0.246171\pi$
$710$	−22.7633	−0.854290
$711$	12.8156	0.480623
$712$	100.810	3.77800
$713$	−1.20169	−0.0450035
$714$	−53.1983	−1.99090
$715$	0.726246	0.0271600
$716$	10.1538	0.379466
$717$	36.3117	1.35609
$718$	−27.4197	−1.02330
$719$	1.47212	0.0549009	0.0274504	−	0.999623i	$-0.491261\pi$
$719$	1.47212	0.0549009	0.0274504	+	0.999623i	$0.491261\pi$
$720$	9.21221	0.343319
$721$	−17.7778	−0.662078
$722$	48.4549	1.80331
$723$	−15.8994	−0.591304
$724$	19.3410	0.718804
$725$	24.1165	0.895664
$726$	−35.5185	−1.31822
$727$	−6.01668	−0.223146	−0.111573	−	0.993756i	$-0.535589\pi$
$727$	−6.01668	−0.223146	−0.111573	+	0.993756i	$0.535589\pi$
$728$	13.8557	0.513525
$729$	29.8487	1.10551
$730$	7.86165	0.290973
$731$	4.35971	0.161250
$732$	75.7857	2.80112
$733$	31.9758	1.18105	0.590527	−	0.807018i	$-0.298920\pi$
$733$	31.9758	1.18105	0.590527	+	0.807018i	$0.298920\pi$
$734$	54.2594	2.00275
$735$	39.4896	1.45659
$736$	−7.67456	−0.282888
$737$	12.1301	0.446819
$738$	0.714196	0.0262899
$739$	18.6155	0.684783	0.342391	−	0.939557i	$-0.388763\pi$
$739$	18.6155	0.684783	0.342391	+	0.939557i	$0.388763\pi$
$740$	−10.2244	−0.375857
$741$	−0.263044	−0.00966318
$742$	−23.3860	−0.858525
$743$	−46.4828	−1.70529	−0.852645	−	0.522491i	$-0.825003\pi$
$743$	−46.4828	−1.70529	−0.852645	+	0.522491i	$0.825003\pi$
$744$	−12.1347	−0.444881
$745$	14.0303	0.514031
$746$	11.4221	0.418192
$747$	7.16920	0.262307
$748$	−16.5294	−0.604375
$749$	77.8048	2.84292
$750$	42.9401	1.56795
$751$	−22.4885	−0.820615	−0.410308	−	0.911947i	$-0.634579\pi$
$751$	−22.4885	−0.820615	−0.410308	+	0.911947i	$0.634579\pi$
$752$	88.8222	3.23901
$753$	−29.1024	−1.06055
$754$	8.10437	0.295144
$755$	25.7011	0.935358
$756$	−133.632	−4.86016
$757$	12.6799	0.460859	0.230430	−	0.973089i	$-0.425987\pi$
$757$	12.6799	0.460859	0.230430	+	0.973089i	$0.425987\pi$
$758$	20.2362	0.735011
$759$	1.93893	0.0703788
$760$	4.22479	0.153249
$761$	1.85880	0.0673813	0.0336907	−	0.999432i	$-0.489274\pi$
$761$	1.85880	0.0673813	0.0336907	+	0.999432i	$0.489274\pi$
$762$	2.83761	0.102796
$763$	−100.769	−3.64808
$764$	−59.6092	−2.15659
$765$	3.03803	0.109840
$766$	1.72482	0.0623204
$767$	−1.27828	−0.0461560
$768$	36.2575	1.30833
$769$	9.94177	0.358509	0.179255	−	0.983803i	$-0.442631\pi$
$769$	9.94177	0.358509	0.179255	+	0.983803i	$0.442631\pi$
$770$	23.9940	0.864683
$771$	−16.5095	−0.594575
$772$	42.4161	1.52659
$773$	−29.4283	−1.05846	−0.529232	−	0.848477i	$-0.677520\pi$
$773$	−29.4283	−1.05846	−0.529232	+	0.848477i	$0.677520\pi$
$774$	3.29809	0.118548
$775$	3.67193	0.131900
$776$	−32.9002	−1.18105
$777$	11.9696	0.429407
$778$	70.5671	2.52995
$779$	0.154228	0.00552577
$780$	3.82530	0.136968
$781$	8.28008	0.296285
$782$	−7.02107	−0.251073
$783$	−44.4838	−1.58972
$784$	157.723	5.63296
$785$	1.91100	0.0682067
$786$	−80.9105	−2.88598
$787$	−2.99186	−0.106648	−0.0533241	−	0.998577i	$-0.516982\pi$
$787$	−2.99186	−0.106648	−0.0533241	+	0.998577i	$0.516982\pi$
$788$	−57.3633	−2.04348
$789$	16.2687	0.579180
$790$	−57.5871	−2.04886
$791$	73.7426	2.62198
$792$	−7.11641	−0.252870
$793$	−4.38586	−0.155746
$794$	−79.3941	−2.81759
$795$	−3.67444	−0.130319
$796$	−79.7409	−2.82634
$797$	9.36981	0.331896	0.165948	−	0.986135i	$-0.446932\pi$
$797$	9.36981	0.331896	0.165948	+	0.986135i	$0.446932\pi$
$798$	−8.69056	−0.307643
$799$	29.2921	1.03628
$800$	23.4508	0.829109
$801$	11.8424	0.418430
$802$	−64.9452	−2.29329
$803$	−2.85966	−0.100915
$804$	63.8921	2.25330
$805$	7.12267	0.251041
$806$	1.23396	0.0434642
$807$	−17.6828	−0.622463
$808$	22.9742	0.808229
$809$	−40.8294	−1.43549	−0.717743	−	0.696308i	$-0.754825\pi$
$809$	−40.8294	−1.43549	−0.717743	+	0.696308i	$0.754825\pi$
$810$	−21.4222	−0.752699
$811$	−30.5752	−1.07364	−0.536820	−	0.843697i	$-0.680375\pi$
$811$	−30.5752	−1.07364	−0.536820	+	0.843697i	$0.680375\pi$
$812$	187.125	6.56681
$813$	−16.0451	−0.562726
$814$	5.32163	0.186523
$815$	−2.95103	−0.103370
$816$	−33.3845	−1.16869
$817$	0.712209	0.0249170
$818$	−4.36837	−0.152736
$819$	1.62766	0.0568752
$820$	−2.24284	−0.0783233
$821$	8.68466	0.303097	0.151548	−	0.988450i	$-0.451574\pi$
$821$	8.68466	0.303097	0.151548	+	0.988450i	$0.451574\pi$
$822$	−70.3973	−2.45539
$823$	20.8804	0.727843	0.363922	−	0.931430i	$-0.381438\pi$
$823$	20.8804	0.727843	0.363922	+	0.931430i	$0.381438\pi$
$824$	−23.6931	−0.825388
$825$	−5.92469	−0.206271
$826$	−42.2323	−1.46945
$827$	−38.3866	−1.33483	−0.667416	−	0.744685i	$-0.732600\pi$
$827$	−38.3866	−1.33483	−0.667416	+	0.744685i	$0.732600\pi$
$828$	−3.71196	−0.129000
$829$	18.8152	0.653478	0.326739	−	0.945115i	$-0.394050\pi$
$829$	18.8152	0.653478	0.326739	+	0.945115i	$0.394050\pi$
$830$	−32.2149	−1.11820
$831$	20.6288	0.715606
$832$	1.29738	0.0449787
$833$	52.0143	1.80219
$834$	5.60671	0.194145
$835$	−19.6367	−0.679556
$836$	−2.70027	−0.0933908
$837$	−6.77301	−0.234110
$838$	−29.9135	−1.03334
$839$	−16.0948	−0.555653	−0.277827	−	0.960631i	$-0.589614\pi$
$839$	−16.0948	−0.555653	−0.277827	+	0.960631i	$0.589614\pi$
$840$	71.9253	2.48166
$841$	33.2905	1.14795
$842$	50.4566	1.73885
$843$	38.4857	1.32552
$844$	113.737	3.91498
$845$	17.9058	0.615979
$846$	22.1593	0.761852
$847$	47.4608	1.63077
$848$	−14.6758	−0.503970
$849$	−0.149726	−0.00513860
$850$	21.4539	0.735863
$851$	1.57974	0.0541527
$852$	43.6130	1.49416
$853$	3.31300	0.113435	0.0567175	−	0.998390i	$-0.481937\pi$
$853$	3.31300	0.113435	0.0567175	+	0.998390i	$0.481937\pi$
$854$	−144.902	−4.95843
$855$	0.496298	0.0169730
$856$	103.693	3.54417
$857$	−13.4082	−0.458017	−0.229008	−	0.973424i	$-0.573548\pi$
$857$	−13.4082	−0.458017	−0.229008	+	0.973424i	$0.573548\pi$
$858$	−1.99100	−0.0679715
$859$	7.28956	0.248717	0.124358	−	0.992237i	$-0.460313\pi$
$859$	7.28956	0.248717	0.124358	+	0.992237i	$0.460313\pi$
$860$	−10.3572	−0.353179
$861$	2.62566	0.0894823
$862$	92.6612	3.15605
$863$	−30.7582	−1.04702	−0.523511	−	0.852019i	$-0.675378\pi$
$863$	−30.7582	−1.04702	−0.523511	+	0.852019i	$0.675378\pi$
$864$	−43.2558	−1.47159
$865$	−11.7097	−0.398143
$866$	−90.3257	−3.06939
$867$	14.2070	0.482496
$868$	28.4913	0.967059
$869$	20.9472	0.710584
$870$	42.0701	1.42631
$871$	−3.69755	−0.125287
$872$	−134.298	−4.54792
$873$	−3.86488	−0.130806
$874$	−1.14697	−0.0387970
$875$	−57.3777	−1.93972
$876$	−15.0624	−0.508913
$877$	22.2242	0.750458	0.375229	−	0.926932i	$-0.377564\pi$
$877$	22.2242	0.750458	0.375229	+	0.926932i	$0.377564\pi$
$878$	14.1967	0.479117
$879$	34.6401	1.16838
$880$	15.0574	0.507585
$881$	22.2191	0.748581	0.374290	−	0.927312i	$-0.377886\pi$
$881$	22.2191	0.748581	0.374290	+	0.927312i	$0.377886\pi$
$882$	39.3485	1.32493
$883$	−30.7186	−1.03376	−0.516882	−	0.856057i	$-0.672907\pi$
$883$	−30.7186	−1.03376	−0.516882	+	0.856057i	$0.672907\pi$
$884$	5.03855	0.169465
$885$	−6.63561	−0.223053
$886$	29.8438	1.00262
$887$	−44.0256	−1.47823	−0.739117	−	0.673577i	$-0.764757\pi$
$887$	−44.0256	−1.47823	−0.739117	+	0.673577i	$0.764757\pi$
$888$	15.9523	0.535325
$889$	−3.79169	−0.127169
$890$	−53.2140	−1.78374
$891$	7.79227	0.261051
$892$	38.0552	1.27418
$893$	4.78521	0.160131
$894$	−38.4640	−1.28643
$895$	−3.05036	−0.101962
$896$	−35.5407	−1.18733
$897$	−0.591032	−0.0197340
$898$	−57.0295	−1.90310
$899$	9.48424	0.316317
$900$	11.3424	0.378081
$901$	−4.83985	−0.161239
$902$	1.16736	0.0388687
$903$	12.1251	0.403497
$904$	98.2795	3.26873
$905$	−5.81034	−0.193142
$906$	−70.4593	−2.34086
$907$	56.6376	1.88062	0.940310	−	0.340320i	$-0.110536\pi$
$907$	56.6376	1.88062	0.940310	+	0.340320i	$0.110536\pi$
$908$	−97.6843	−3.24177
$909$	2.69884	0.0895150
$910$	−7.31393	−0.242454
$911$	52.0959	1.72601	0.863006	−	0.505193i	$-0.168579\pi$
$911$	52.0959	1.72601	0.863006	+	0.505193i	$0.168579\pi$
$912$	−5.45376	−0.180592
$913$	11.7181	0.387812
$914$	51.0178	1.68752
$915$	−22.7672	−0.752659
$916$	97.0103	3.20531
$917$	108.115	3.57027
$918$	−39.5725	−1.30609
$919$	−48.5347	−1.60101	−0.800506	−	0.599325i	$-0.795436\pi$
$919$	−48.5347	−1.60101	−0.800506	+	0.599325i	$0.795436\pi$
$920$	9.49265	0.312963
$921$	15.1423	0.498956
$922$	−60.9642	−2.00775
$923$	−2.52396	−0.0830773
$924$	−45.9710	−1.51233
$925$	−4.82712	−0.158715
$926$	−11.6530	−0.382942
$927$	−2.78329	−0.0914154
$928$	60.5710	1.98834
$929$	19.4642	0.638601	0.319300	−	0.947654i	$-0.396552\pi$
$929$	19.4642	0.638601	0.319300	+	0.947654i	$0.396552\pi$
$930$	6.40551	0.210045
$931$	8.49715	0.278483
$932$	−19.3797	−0.634802
$933$	43.8562	1.43579
$934$	60.0245	1.96406
$935$	4.96568	0.162395
$936$	2.16925	0.0709041
$937$	−12.2487	−0.400149	−0.200074	−	0.979781i	$-0.564118\pi$
$937$	−12.2487	−0.400149	−0.200074	+	0.979781i	$0.564118\pi$
$938$	−122.161	−3.98870
$939$	1.65226	0.0539196
$940$	−69.5883	−2.26972
$941$	41.7106	1.35973	0.679863	−	0.733339i	$-0.262039\pi$
$941$	41.7106	1.35973	0.679863	+	0.733339i	$0.262039\pi$
$942$	−5.23901	−0.170696
$943$	0.346533	0.0112847
$944$	−26.5029	−0.862594
$945$	40.1452	1.30592
$946$	5.39075	0.175268
$947$	14.4171	0.468494	0.234247	−	0.972177i	$-0.424737\pi$
$947$	14.4171	0.468494	0.234247	+	0.972177i	$0.424737\pi$
$948$	110.333	3.58346
$949$	0.871691	0.0282963
$950$	3.50475	0.113709
$951$	39.8193	1.29123
$952$	94.7376	3.07046
$953$	−53.0174	−1.71740	−0.858701	−	0.512476i	$-0.828728\pi$
$953$	−53.0174	−1.71740	−0.858701	+	0.512476i	$0.828728\pi$
$954$	−3.66132	−0.118539
$955$	17.9075	0.579473
$956$	−113.625	−3.67489
$957$	−15.3029	−0.494672
$958$	44.0206	1.42224
$959$	94.0667	3.03757
$960$	6.73478	0.217364
$961$	−29.5559	−0.953418
$962$	−1.62216	−0.0523004
$963$	12.1812	0.392532
$964$	49.7515	1.60239
$965$	−12.7424	−0.410193
$966$	−19.5268	−0.628263
$967$	57.6772	1.85477	0.927386	−	0.374106i	$-0.122050\pi$
$967$	57.6772	1.85477	0.927386	+	0.374106i	$0.122050\pi$
$968$	63.2528	2.03302
$969$	−1.79856	−0.0577780
$970$	17.3669	0.557617
$971$	2.69869	0.0866050	0.0433025	−	0.999062i	$-0.486212\pi$
$971$	2.69869	0.0866050	0.0433025	+	0.999062i	$0.486212\pi$
$972$	−37.4398	−1.20088
$973$	−7.49184	−0.240177
$974$	24.9052	0.798014
$975$	1.80599	0.0578378
$976$	−90.9329	−2.91069
$977$	−16.1484	−0.516633	−0.258317	−	0.966060i	$-0.583168\pi$
$977$	−16.1484	−0.516633	−0.258317	+	0.966060i	$0.583168\pi$
$978$	8.09023	0.258697
$979$	19.3565	0.618635
$980$	−123.569	−3.94726
$981$	−15.7764	−0.503702
$982$	−51.3406	−1.63834
$983$	41.5219	1.32434	0.662172	−	0.749352i	$-0.269635\pi$
$983$	41.5219	1.32434	0.662172	+	0.749352i	$0.269635\pi$
$984$	3.49932	0.111554
$985$	17.2328	0.549083
$986$	55.4133	1.76472
$987$	81.4661	2.59310
$988$	0.823106	0.0261865
$989$	1.60026	0.0508852
$990$	3.75651	0.119390
$991$	−4.85513	−0.154228	−0.0771142	−	0.997022i	$-0.524571\pi$
$991$	−4.85513	−0.154228	−0.0771142	+	0.997022i	$0.524571\pi$
$992$	9.22243	0.292812
$993$	28.4442	0.902648
$994$	−83.3877	−2.64490
$995$	23.9554	0.759436
$996$	61.7218	1.95573
$997$	42.4359	1.34396	0.671980	−	0.740570i	$-0.265444\pi$
$997$	42.4359	1.34396	0.671980	+	0.740570i	$0.265444\pi$
$998$	75.2263	2.38125
$999$	8.90380	0.281704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.11	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.11	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +O(q^{10})\)	\(q-2.57713 q^{2} -1.48333 q^{3} +4.64158 q^{4} -1.39440 q^{5} +3.82274 q^{6} -5.10805 q^{7} -6.80769 q^{8} -0.799719 q^{9} +3.59355 q^{10} -1.30714 q^{11} -6.88502 q^{12} +0.398449 q^{13} +13.1641 q^{14} +2.06836 q^{15} +8.26112 q^{16} +2.72438 q^{17} +2.06098 q^{18} +0.445059 q^{19} -6.47223 q^{20} +7.57695 q^{21} +3.36868 q^{22} +1.00000 q^{23} +10.0981 q^{24} -3.05565 q^{25} -1.02685 q^{26} +5.63625 q^{27} -23.7094 q^{28} -7.89244 q^{29} -5.33043 q^{30} -1.20169 q^{31} -7.67456 q^{32} +1.93893 q^{33} -7.02107 q^{34} +7.12267 q^{35} -3.71196 q^{36} +1.57974 q^{37} -1.14697 q^{38} -0.591032 q^{39} +9.49265 q^{40} +0.346533 q^{41} -19.5268 q^{42} +1.60026 q^{43} -6.06722 q^{44} +1.11513 q^{45} -2.57713 q^{46} +10.7518 q^{47} -12.2540 q^{48} +19.0922 q^{49} +7.87479 q^{50} -4.04116 q^{51} +1.84943 q^{52} -1.77650 q^{53} -14.5253 q^{54} +1.82268 q^{55} +34.7740 q^{56} -0.660172 q^{57} +20.3398 q^{58} -3.20814 q^{59} +9.60048 q^{60} -11.0073 q^{61} +3.09690 q^{62} +4.08500 q^{63} +3.25609 q^{64} -0.555597 q^{65} -4.99687 q^{66} -9.27987 q^{67} +12.6454 q^{68} -1.48333 q^{69} -18.3560 q^{70} -6.33448 q^{71} +5.44424 q^{72} +2.18771 q^{73} -4.07118 q^{74} +4.53255 q^{75} +2.06578 q^{76} +6.67696 q^{77} +1.52317 q^{78} -16.0251 q^{79} -11.5193 q^{80} -5.96129 q^{81} -0.893059 q^{82} -8.96465 q^{83} +35.1690 q^{84} -3.79888 q^{85} -4.12407 q^{86} +11.7071 q^{87} +8.89864 q^{88} -14.8082 q^{89} -2.87383 q^{90} -2.03530 q^{91} +4.64158 q^{92} +1.78250 q^{93} -27.7089 q^{94} -0.620591 q^{95} +11.3839 q^{96} +4.83280 q^{97} -49.2030 q^{98} +1.04535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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