LMFDB - Embedded newform 8007.2.a.g.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35489 q^{2} -1.00000 q^{3} -0.164276 q^{4} +2.92239 q^{5} -1.35489 q^{6} -0.124938 q^{7} -2.93235 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.35489 q^{2} -1.00000 q^{3} -0.164276 q^{4} +2.92239 q^{5} -1.35489 q^{6} -0.124938 q^{7} -2.93235 q^{8} +1.00000 q^{9} +3.95951 q^{10} -6.11794 q^{11} +0.164276 q^{12} +4.37677 q^{13} -0.169277 q^{14} -2.92239 q^{15} -3.64446 q^{16} -1.00000 q^{17} +1.35489 q^{18} +4.28476 q^{19} -0.480077 q^{20} +0.124938 q^{21} -8.28912 q^{22} +5.01208 q^{23} +2.93235 q^{24} +3.54036 q^{25} +5.93004 q^{26} -1.00000 q^{27} +0.0205243 q^{28} -4.63739 q^{29} -3.95951 q^{30} -6.51022 q^{31} +0.926865 q^{32} +6.11794 q^{33} -1.35489 q^{34} -0.365118 q^{35} -0.164276 q^{36} +4.62925 q^{37} +5.80538 q^{38} -4.37677 q^{39} -8.56948 q^{40} +1.36817 q^{41} +0.169277 q^{42} +7.36121 q^{43} +1.00503 q^{44} +2.92239 q^{45} +6.79081 q^{46} -0.295751 q^{47} +3.64446 q^{48} -6.98439 q^{49} +4.79679 q^{50} +1.00000 q^{51} -0.718997 q^{52} +7.60318 q^{53} -1.35489 q^{54} -17.8790 q^{55} +0.366363 q^{56} -4.28476 q^{57} -6.28314 q^{58} -5.33893 q^{59} +0.480077 q^{60} +12.4422 q^{61} -8.82063 q^{62} -0.124938 q^{63} +8.54472 q^{64} +12.7906 q^{65} +8.28912 q^{66} +2.08210 q^{67} +0.164276 q^{68} -5.01208 q^{69} -0.494694 q^{70} -3.92650 q^{71} -2.93235 q^{72} -3.36174 q^{73} +6.27212 q^{74} -3.54036 q^{75} -0.703883 q^{76} +0.764364 q^{77} -5.93004 q^{78} +5.61545 q^{79} -10.6505 q^{80} +1.00000 q^{81} +1.85372 q^{82} -14.1718 q^{83} -0.0205243 q^{84} -2.92239 q^{85} +9.97362 q^{86} +4.63739 q^{87} +17.9399 q^{88} -2.21883 q^{89} +3.95951 q^{90} -0.546826 q^{91} -0.823362 q^{92} +6.51022 q^{93} -0.400710 q^{94} +12.5217 q^{95} -0.926865 q^{96} +17.5948 q^{97} -9.46307 q^{98} -6.11794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) $ 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * 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 $

$2$	1.35489	0.958051	0.479026	−	0.877801i	$-0.340990\pi$
$2$	1.35489	0.958051	0.479026	+	0.877801i	$0.340990\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.164276	−0.0821379
$5$	2.92239	1.30693	0.653466	−	0.756956i	$-0.273314\pi$
$5$	2.92239	1.30693	0.653466	+	0.756956i	$0.273314\pi$
$6$	−1.35489	−0.553131
$7$	−0.124938	−0.0472222	−0.0236111	−	0.999721i	$-0.507516\pi$
$7$	−0.124938	−0.0472222	−0.0236111	+	0.999721i	$0.507516\pi$
$8$	−2.93235	−1.03674
$9$	1.00000	0.333333
$10$	3.95951	1.25211
$11$	−6.11794	−1.84463	−0.922313	−	0.386443i	$-0.873704\pi$
$11$	−6.11794	−1.84463	−0.922313	+	0.386443i	$0.873704\pi$
$12$	0.164276	0.0474223
$13$	4.37677	1.21390	0.606949	−	0.794741i	$-0.292393\pi$
$13$	4.37677	1.21390	0.606949	+	0.794741i	$0.292393\pi$
$14$	−0.169277	−0.0452413
$15$	−2.92239	−0.754558
$16$	−3.64446	−0.911116
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.35489	0.319350
$19$	4.28476	0.982992	0.491496	−	0.870880i	$-0.336450\pi$
$19$	4.28476	0.982992	0.491496	+	0.870880i	$0.336450\pi$
$20$	−0.480077	−0.107349
$21$	0.124938	0.0272638
$22$	−8.28912	−1.76725
$23$	5.01208	1.04509	0.522545	−	0.852612i	$-0.324983\pi$
$23$	5.01208	1.04509	0.522545	+	0.852612i	$0.324983\pi$
$24$	2.93235	0.598564
$25$	3.54036	0.708071
$26$	5.93004	1.16298
$27$	−1.00000	−0.192450
$28$	0.0205243	0.00387873
$29$	−4.63739	−0.861141	−0.430570	−	0.902557i	$-0.641688\pi$
$29$	−4.63739	−0.861141	−0.430570	+	0.902557i	$0.641688\pi$
$30$	−3.95951	−0.722905
$31$	−6.51022	−1.16927	−0.584635	−	0.811296i	$-0.698762\pi$
$31$	−6.51022	−1.16927	−0.584635	+	0.811296i	$0.698762\pi$
$32$	0.926865	0.163848
$33$	6.11794	1.06500
$34$	−1.35489	−0.232362
$35$	−0.365118	−0.0617162
$36$	−0.164276	−0.0273793
$37$	4.62925	0.761043	0.380522	−	0.924772i	$-0.375744\pi$
$37$	4.62925	0.761043	0.380522	+	0.924772i	$0.375744\pi$
$38$	5.80538	0.941757
$39$	−4.37677	−0.700844
$40$	−8.56948	−1.35495
$41$	1.36817	0.213672	0.106836	−	0.994277i	$-0.465928\pi$
$41$	1.36817	0.213672	0.106836	+	0.994277i	$0.465928\pi$
$42$	0.169277	0.0261201
$43$	7.36121	1.12257	0.561287	−	0.827621i	$-0.310306\pi$
$43$	7.36121	1.12257	0.561287	+	0.827621i	$0.310306\pi$
$44$	1.00503	0.151514
$45$	2.92239	0.435644
$46$	6.79081	1.00125
$47$	−0.295751	−0.0431397	−0.0215699	−	0.999767i	$-0.506866\pi$
$47$	−0.295751	−0.0431397	−0.0215699	+	0.999767i	$0.506866\pi$
$48$	3.64446	0.526033
$49$	−6.98439	−0.997770
$50$	4.79679	0.678368
$51$	1.00000	0.140028
$52$	−0.718997	−0.0997069
$53$	7.60318	1.04438	0.522188	−	0.852830i	$-0.325116\pi$
$53$	7.60318	1.04438	0.522188	+	0.852830i	$0.325116\pi$
$54$	−1.35489	−0.184377
$55$	−17.8790	−2.41080
$56$	0.366363	0.0489573
$57$	−4.28476	−0.567531
$58$	−6.28314	−0.825017
$59$	−5.33893	−0.695070	−0.347535	−	0.937667i	$-0.612981\pi$
$59$	−5.33893	−0.695070	−0.347535	+	0.937667i	$0.612981\pi$
$60$	0.480077	0.0619777
$61$	12.4422	1.59306	0.796532	−	0.604597i	$-0.206666\pi$
$61$	12.4422	1.59306	0.796532	+	0.604597i	$0.206666\pi$
$62$	−8.82063	−1.12022
$63$	−0.124938	−0.0157407
$64$	8.54472	1.06809
$65$	12.7906	1.58648
$66$	8.28912	1.02032
$67$	2.08210	0.254369	0.127185	−	0.991879i	$-0.459406\pi$
$67$	2.08210	0.254369	0.127185	+	0.991879i	$0.459406\pi$
$68$	0.164276	0.0199214
$69$	−5.01208	−0.603383
$70$	−0.494694	−0.0591273
$71$	−3.92650	−0.465989	−0.232995	−	0.972478i	$-0.574852\pi$
$71$	−3.92650	−0.465989	−0.232995	+	0.972478i	$0.574852\pi$
$72$	−2.93235	−0.345581
$73$	−3.36174	−0.393461	−0.196731	−	0.980458i	$-0.563032\pi$
$73$	−3.36174	−0.393461	−0.196731	+	0.980458i	$0.563032\pi$
$74$	6.27212	0.729119
$75$	−3.54036	−0.408805
$76$	−0.703883	−0.0807409
$77$	0.764364	0.0871074
$78$	−5.93004	−0.671444
$79$	5.61545	0.631788	0.315894	−	0.948795i	$-0.397696\pi$
$79$	5.61545	0.631788	0.315894	+	0.948795i	$0.397696\pi$
$80$	−10.6505	−1.19077
$81$	1.00000	0.111111
$82$	1.85372	0.204709
$83$	−14.1718	−1.55556	−0.777780	−	0.628537i	$-0.783654\pi$
$83$	−14.1718	−1.55556	−0.777780	+	0.628537i	$0.783654\pi$
$84$	−0.0205243	−0.00223939
$85$	−2.92239	−0.316978
$86$	9.97362	1.07548
$87$	4.63739	0.497180
$88$	17.9399	1.91240
$89$	−2.21883	−0.235196	−0.117598	−	0.993061i	$-0.537519\pi$
$89$	−2.21883	−0.235196	−0.117598	+	0.993061i	$0.537519\pi$
$90$	3.95951	0.417369
$91$	−0.546826	−0.0573229
$92$	−0.823362	−0.0858415
$93$	6.51022	0.675078
$94$	−0.400710	−0.0413300
$95$	12.5217	1.28470
$96$	−0.926865	−0.0945978
$97$	17.5948	1.78648	0.893242	−	0.449577i	$-0.148425\pi$
$97$	17.5948	1.78648	0.893242	+	0.449577i	$0.148425\pi$
$98$	−9.46307	−0.955915
$99$	−6.11794	−0.614876
$100$	−0.581594	−0.0581594
$101$	4.71104	0.468766	0.234383	−	0.972144i	$-0.424693\pi$
$101$	4.71104	0.468766	0.234383	+	0.972144i	$0.424693\pi$
$102$	1.35489	0.134154
$103$	−0.441669	−0.0435190	−0.0217595	−	0.999763i	$-0.506927\pi$
$103$	−0.441669	−0.0435190	−0.0217595	+	0.999763i	$0.506927\pi$
$104$	−12.8342	−1.25850
$105$	0.365118	0.0356319
$106$	10.3015	1.00057
$107$	2.17831	0.210585	0.105293	−	0.994441i	$-0.466422\pi$
$107$	2.17831	0.210585	0.105293	+	0.994441i	$0.466422\pi$
$108$	0.164276	0.0158074
$109$	20.0602	1.92142	0.960709	−	0.277556i	$-0.0895244\pi$
$109$	20.0602	1.92142	0.960709	+	0.277556i	$0.0895244\pi$
$110$	−24.2240	−2.30967
$111$	−4.62925	−0.439389
$112$	0.455333	0.0430249
$113$	−5.46042	−0.513673	−0.256836	−	0.966455i	$-0.582680\pi$
$113$	−5.46042	−0.513673	−0.256836	+	0.966455i	$0.582680\pi$
$114$	−5.80538	−0.543724
$115$	14.6472	1.36586
$116$	0.761810	0.0707323
$117$	4.37677	0.404632
$118$	−7.23366	−0.665913
$119$	0.124938	0.0114531
$120$	8.56948	0.782283
$121$	26.4291	2.40265
$122$	16.8578	1.52624
$123$	−1.36817	−0.123364
$124$	1.06947	0.0960413
$125$	−4.26565	−0.381531
$126$	−0.169277	−0.0150804
$127$	−2.26111	−0.200641	−0.100320	−	0.994955i	$-0.531987\pi$
$127$	−2.26111	−0.200641	−0.100320	+	0.994955i	$0.531987\pi$
$128$	9.72342	0.859437
$129$	−7.36121	−0.648118
$130$	17.3299	1.51993
$131$	15.0790	1.31746	0.658729	−	0.752381i	$-0.271095\pi$
$131$	15.0790	1.31746	0.658729	+	0.752381i	$0.271095\pi$
$132$	−1.00503	−0.0874765
$133$	−0.535331	−0.0464191
$134$	2.82102	0.243699
$135$	−2.92239	−0.251519
$136$	2.93235	0.251447
$137$	4.35856	0.372377	0.186188	−	0.982514i	$-0.440387\pi$
$137$	4.35856	0.372377	0.186188	+	0.982514i	$0.440387\pi$
$138$	−6.79081	−0.578072
$139$	5.11045	0.433462	0.216731	−	0.976231i	$-0.430460\pi$
$139$	5.11045	0.433462	0.216731	+	0.976231i	$0.430460\pi$
$140$	0.0599800	0.00506924
$141$	0.295751	0.0249067
$142$	−5.31997	−0.446442
$143$	−26.7768	−2.23919
$144$	−3.64446	−0.303705
$145$	−13.5522	−1.12545
$146$	−4.55478	−0.376956
$147$	6.98439	0.576063
$148$	−0.760473	−0.0625105
$149$	6.26406	0.513172	0.256586	−	0.966521i	$-0.417402\pi$
$149$	6.26406	0.513172	0.256586	+	0.966521i	$0.417402\pi$
$150$	−4.79679	−0.391656
$151$	7.58196	0.617011	0.308506	−	0.951222i	$-0.400171\pi$
$151$	7.58196	0.617011	0.308506	+	0.951222i	$0.400171\pi$
$152$	−12.5644	−1.01911
$153$	−1.00000	−0.0808452
$154$	1.03563	0.0834533
$155$	−19.0254	−1.52816
$156$	0.718997	0.0575658
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	7.60831	0.605285
$159$	−7.60318	−0.602971
$160$	2.70866	0.214138
$161$	−0.626200	−0.0493515
$162$	1.35489	0.106450
$163$	13.9145	1.08986	0.544932	−	0.838480i	$-0.316555\pi$
$163$	13.9145	1.08986	0.544932	+	0.838480i	$0.316555\pi$
$164$	−0.224757	−0.0175506
$165$	17.8790	1.39188
$166$	−19.2012	−1.49031
$167$	10.0701	0.779245	0.389622	−	0.920975i	$-0.372606\pi$
$167$	10.0701	0.779245	0.389622	+	0.920975i	$0.372606\pi$
$168$	−0.366363	−0.0282655
$169$	6.15610	0.473546
$170$	−3.95951	−0.303681
$171$	4.28476	0.327664
$172$	−1.20927	−0.0922058
$173$	15.3516	1.16716	0.583579	−	0.812056i	$-0.301652\pi$
$173$	15.3516	1.16716	0.583579	+	0.812056i	$0.301652\pi$
$174$	6.28314	0.476324
$175$	−0.442326	−0.0334367
$176$	22.2966	1.68067
$177$	5.33893	0.401299
$178$	−3.00627	−0.225330
$179$	4.64851	0.347446	0.173723	−	0.984795i	$-0.444420\pi$
$179$	4.64851	0.347446	0.173723	+	0.984795i	$0.444420\pi$
$180$	−0.480077	−0.0357829
$181$	14.3933	1.06984	0.534921	−	0.844902i	$-0.320341\pi$
$181$	14.3933	1.06984	0.534921	+	0.844902i	$0.320341\pi$
$182$	−0.740888	−0.0549183
$183$	−12.4422	−0.919756
$184$	−14.6972	−1.08349
$185$	13.5285	0.994632
$186$	8.82063	0.646760
$187$	6.11794	0.447388
$188$	0.0485847	0.00354340
$189$	0.124938	0.00908792
$190$	16.9656	1.23081
$191$	−23.8477	−1.72556	−0.862781	−	0.505577i	$-0.831279\pi$
$191$	−23.8477	−1.72556	−0.862781	+	0.505577i	$0.831279\pi$
$192$	−8.54472	−0.616662
$193$	−2.59213	−0.186586	−0.0932929	−	0.995639i	$-0.529739\pi$
$193$	−2.59213	−0.186586	−0.0932929	+	0.995639i	$0.529739\pi$
$194$	23.8390	1.71154
$195$	−12.7906	−0.915955
$196$	1.14737	0.0819547
$197$	4.80666	0.342460	0.171230	−	0.985231i	$-0.445226\pi$
$197$	4.80666	0.342460	0.171230	+	0.985231i	$0.445226\pi$
$198$	−8.28912	−0.589082
$199$	−11.7620	−0.833787	−0.416894	−	0.908955i	$-0.636881\pi$
$199$	−11.7620	−0.833787	−0.416894	+	0.908955i	$0.636881\pi$
$200$	−10.3816	−0.734088
$201$	−2.08210	−0.146860
$202$	6.38293	0.449102
$203$	0.579387	0.0406650
$204$	−0.164276	−0.0115016
$205$	3.99832	0.279255
$206$	−0.598413	−0.0416934
$207$	5.01208	0.348363
$208$	−15.9510	−1.10600
$209$	−26.2139	−1.81325
$210$	0.494694	0.0341372
$211$	6.84445	0.471191	0.235596	−	0.971851i	$-0.424296\pi$
$211$	6.84445	0.471191	0.235596	+	0.971851i	$0.424296\pi$
$212$	−1.24902	−0.0857829
$213$	3.92650	0.269039
$214$	2.95137	0.201751
$215$	21.5123	1.46713
$216$	2.93235	0.199521
$217$	0.813375	0.0552155
$218$	27.1793	1.84082
$219$	3.36174	0.227165
$220$	2.93708	0.198018
$221$	−4.37677	−0.294413
$222$	−6.27212	−0.420957
$223$	−20.4723	−1.37093	−0.685464	−	0.728106i	$-0.740401\pi$
$223$	−20.4723	−1.37093	−0.685464	+	0.728106i	$0.740401\pi$
$224$	−0.115801	−0.00773727
$225$	3.54036	0.236024
$226$	−7.39826	−0.492125
$227$	10.2437	0.679901	0.339951	−	0.940443i	$-0.389590\pi$
$227$	10.2437	0.679901	0.339951	+	0.940443i	$0.389590\pi$
$228$	0.703883	0.0466158
$229$	−8.04681	−0.531748	−0.265874	−	0.964008i	$-0.585660\pi$
$229$	−8.04681	−0.531748	−0.265874	+	0.964008i	$0.585660\pi$
$230$	19.8454	1.30857
$231$	−0.764364	−0.0502915
$232$	13.5985	0.892782
$233$	1.66084	0.108805	0.0544027	−	0.998519i	$-0.482675\pi$
$233$	1.66084	0.108805	0.0544027	+	0.998519i	$0.482675\pi$
$234$	5.93004	0.387659
$235$	−0.864299	−0.0563807
$236$	0.877057	0.0570916
$237$	−5.61545	−0.364763
$238$	0.169277	0.0109726
$239$	1.41267	0.0913782	0.0456891	−	0.998956i	$-0.485452\pi$
$239$	1.41267	0.0913782	0.0456891	+	0.998956i	$0.485452\pi$
$240$	10.6505	0.687489
$241$	18.4262	1.18694	0.593468	−	0.804858i	$-0.297758\pi$
$241$	18.4262	1.18694	0.593468	+	0.804858i	$0.297758\pi$
$242$	35.8085	2.30186
$243$	−1.00000	−0.0641500
$244$	−2.04396	−0.130851
$245$	−20.4111	−1.30402
$246$	−1.85372	−0.118189
$247$	18.7534	1.19325
$248$	19.0903	1.21223
$249$	14.1718	0.898103
$250$	−5.77948	−0.365526
$251$	0.365766	0.0230869	0.0115435	−	0.999933i	$-0.496326\pi$
$251$	0.365766	0.0230869	0.0115435	+	0.999933i	$0.496326\pi$
$252$	0.0205243	0.00129291
$253$	−30.6636	−1.92780
$254$	−3.06355	−0.192224
$255$	2.92239	0.183007
$256$	−3.91529	−0.244706
$257$	−13.4870	−0.841298	−0.420649	−	0.907223i	$-0.638198\pi$
$257$	−13.4870	−0.841298	−0.420649	+	0.907223i	$0.638198\pi$
$258$	−9.97362	−0.620930
$259$	−0.578370	−0.0359382
$260$	−2.10119	−0.130310
$261$	−4.63739	−0.287047
$262$	20.4304	1.26219
$263$	3.18983	0.196693	0.0983466	−	0.995152i	$-0.468645\pi$
$263$	3.18983	0.196693	0.0983466	+	0.995152i	$0.468645\pi$
$264$	−17.9399	−1.10413
$265$	22.2194	1.36493
$266$	−0.725314	−0.0444718
$267$	2.21883	0.135790
$268$	−0.342039	−0.0208933
$269$	18.0742	1.10200	0.551002	−	0.834504i	$-0.314246\pi$
$269$	18.0742	1.10200	0.551002	+	0.834504i	$0.314246\pi$
$270$	−3.95951	−0.240968
$271$	17.5522	1.06622	0.533111	−	0.846045i	$-0.321023\pi$
$271$	17.5522	1.06622	0.533111	+	0.846045i	$0.321023\pi$
$272$	3.64446	0.220978
$273$	0.546826	0.0330954
$274$	5.90536	0.356756
$275$	−21.6597	−1.30613
$276$	0.823362	0.0495606
$277$	−24.5521	−1.47519	−0.737595	−	0.675244i	$-0.764039\pi$
$277$	−24.5521	−1.47519	−0.737595	+	0.675244i	$0.764039\pi$
$278$	6.92409	0.415279
$279$	−6.51022	−0.389757
$280$	1.07066	0.0639839
$281$	−6.83846	−0.407948	−0.203974	−	0.978976i	$-0.565386\pi$
$281$	−6.83846	−0.407948	−0.203974	+	0.978976i	$0.565386\pi$
$282$	0.400710	0.0238619
$283$	10.6205	0.631321	0.315660	−	0.948872i	$-0.397774\pi$
$283$	10.6205	0.631321	0.315660	+	0.948872i	$0.397774\pi$
$284$	0.645028	0.0382754
$285$	−12.5217	−0.741724
$286$	−36.2796	−2.14526
$287$	−0.170937	−0.0100901
$288$	0.926865	0.0546161
$289$	1.00000	0.0588235
$290$	−18.3618	−1.07824
$291$	−17.5948	−1.03143
$292$	0.552251	0.0323181
$293$	6.01813	0.351583	0.175791	−	0.984427i	$-0.443752\pi$
$293$	6.01813	0.351583	0.175791	+	0.984427i	$0.443752\pi$
$294$	9.46307	0.551898
$295$	−15.6024	−0.908409
$296$	−13.5746	−0.789007
$297$	6.11794	0.354999
$298$	8.48711	0.491645
$299$	21.9367	1.26863
$300$	0.581594	0.0335784
$301$	−0.919696	−0.0530104
$302$	10.2727	0.591129
$303$	−4.71104	−0.270642
$304$	−15.6157	−0.895619
$305$	36.3610	2.08203
$306$	−1.35489	−0.0774539
$307$	8.29187	0.473242	0.236621	−	0.971602i	$-0.423960\pi$
$307$	8.29187	0.473242	0.236621	+	0.971602i	$0.423960\pi$
$308$	−0.125566	−0.00715481
$309$	0.441669	0.0251257
$310$	−25.7773	−1.46405
$311$	−6.40378	−0.363125	−0.181563	−	0.983379i	$-0.558115\pi$
$311$	−6.40378	−0.363125	−0.181563	+	0.983379i	$0.558115\pi$
$312$	12.8342	0.726595
$313$	−3.91430	−0.221249	−0.110625	−	0.993862i	$-0.535285\pi$
$313$	−3.91430	−0.221249	−0.110625	+	0.993862i	$0.535285\pi$
$314$	1.35489	0.0764608
$315$	−0.365118	−0.0205721
$316$	−0.922482	−0.0518937
$317$	−9.49872	−0.533501	−0.266751	−	0.963766i	$-0.585950\pi$
$317$	−9.49872	−0.533501	−0.266751	+	0.963766i	$0.585950\pi$
$318$	−10.3015	−0.577677
$319$	28.3712	1.58848
$320$	24.9710	1.39592
$321$	−2.17831	−0.121581
$322$	−0.848431	−0.0472812
$323$	−4.28476	−0.238411
$324$	−0.164276	−0.00912643
$325$	15.4953	0.859525
$326$	18.8525	1.04415
$327$	−20.0602	−1.10933
$328$	−4.01195	−0.221523
$329$	0.0369506	0.00203715
$330$	24.2240	1.33349
$331$	2.07648	0.114134	0.0570668	−	0.998370i	$-0.481825\pi$
$331$	2.07648	0.114134	0.0570668	+	0.998370i	$0.481825\pi$
$332$	2.32809	0.127770
$333$	4.62925	0.253681
$334$	13.6438	0.746556
$335$	6.08471	0.332443
$336$	−0.455333	−0.0248404
$337$	8.19062	0.446171	0.223086	−	0.974799i	$-0.428387\pi$
$337$	8.19062	0.446171	0.223086	+	0.974799i	$0.428387\pi$
$338$	8.34083	0.453681
$339$	5.46042	0.296569
$340$	0.480077	0.0260359
$341$	39.8291	2.15687
$342$	5.80538	0.313919
$343$	1.74718	0.0943391
$344$	−21.5857	−1.16382
$345$	−14.6472	−0.788581
$346$	20.7997	1.11820
$347$	−0.480630	−0.0258016	−0.0129008	−	0.999917i	$-0.504107\pi$
$347$	−0.480630	−0.0258016	−0.0129008	+	0.999917i	$0.504107\pi$
$348$	−0.761810	−0.0408373
$349$	8.25292	0.441769	0.220884	−	0.975300i	$-0.429106\pi$
$349$	8.25292	0.441769	0.220884	+	0.975300i	$0.429106\pi$
$350$	−0.599302	−0.0320341
$351$	−4.37677	−0.233615
$352$	−5.67050	−0.302239
$353$	−12.7146	−0.676732	−0.338366	−	0.941015i	$-0.609874\pi$
$353$	−12.7146	−0.676732	−0.338366	+	0.941015i	$0.609874\pi$
$354$	7.23366	0.384465
$355$	−11.4747	−0.609016
$356$	0.364500	0.0193185
$357$	−0.124938	−0.00661243
$358$	6.29822	0.332871
$359$	16.3650	0.863712	0.431856	−	0.901943i	$-0.357859\pi$
$359$	16.3650	0.863712	0.431856	+	0.901943i	$0.357859\pi$
$360$	−8.56948	−0.451651
$361$	−0.640804	−0.0337265
$362$	19.5013	1.02496
$363$	−26.4291	−1.38717
$364$	0.0898302	0.00470838
$365$	−9.82430	−0.514227
$366$	−16.8578	−0.881173
$367$	−14.5844	−0.761297	−0.380649	−	0.924720i	$-0.624299\pi$
$367$	−14.5844	−0.761297	−0.380649	+	0.924720i	$0.624299\pi$
$368$	−18.2663	−0.952198
$369$	1.36817	0.0712240
$370$	18.3296	0.952908
$371$	−0.949928	−0.0493178
$372$	−1.06947	−0.0554495
$373$	−19.9392	−1.03241	−0.516207	−	0.856464i	$-0.672656\pi$
$373$	−19.9392	−1.03241	−0.516207	+	0.856464i	$0.672656\pi$
$374$	8.28912	0.428620
$375$	4.26565	0.220277
$376$	0.867246	0.0447248
$377$	−20.2968	−1.04534
$378$	0.169277	0.00870669
$379$	18.0607	0.927715	0.463858	−	0.885910i	$-0.346465\pi$
$379$	18.0607	0.927715	0.463858	+	0.885910i	$0.346465\pi$
$380$	−2.05702	−0.105523
$381$	2.26111	0.115840
$382$	−32.3111	−1.65318
$383$	−23.8392	−1.21813	−0.609063	−	0.793122i	$-0.708455\pi$
$383$	−23.8392	−1.21813	−0.609063	+	0.793122i	$0.708455\pi$
$384$	−9.72342	−0.496196
$385$	2.23377	0.113843
$386$	−3.51205	−0.178759
$387$	7.36121	0.374191
$388$	−2.89040	−0.146738
$389$	14.4213	0.731190	0.365595	−	0.930774i	$-0.380865\pi$
$389$	14.4213	0.731190	0.365595	+	0.930774i	$0.380865\pi$
$390$	−17.3299	−0.877532
$391$	−5.01208	−0.253472
$392$	20.4807	1.03443
$393$	−15.0790	−0.760634
$394$	6.51249	0.328095
$395$	16.4105	0.825703
$396$	1.00503	0.0505046
$397$	33.7427	1.69350	0.846749	−	0.531992i	$-0.178556\pi$
$397$	33.7427	1.69350	0.846749	+	0.531992i	$0.178556\pi$
$398$	−15.9362	−0.798811
$399$	0.535331	0.0268001
$400$	−12.9027	−0.645135
$401$	25.9802	1.29739	0.648694	−	0.761049i	$-0.275315\pi$
$401$	25.9802	1.29739	0.648694	+	0.761049i	$0.275315\pi$
$402$	−2.82102	−0.140700
$403$	−28.4937	−1.41937
$404$	−0.773909	−0.0385034
$405$	2.92239	0.145215
$406$	0.785005	0.0389591
$407$	−28.3214	−1.40384
$408$	−2.93235	−0.145173
$409$	2.07514	0.102609	0.0513045	−	0.998683i	$-0.483662\pi$
$409$	2.07514	0.102609	0.0513045	+	0.998683i	$0.483662\pi$
$410$	5.41728	0.267540
$411$	−4.35856	−0.214992
$412$	0.0725556	0.00357456
$413$	0.667037	0.0328227
$414$	6.79081	0.333750
$415$	−41.4156	−2.03301
$416$	4.05667	0.198895
$417$	−5.11045	−0.250260
$418$	−35.5169	−1.73719
$419$	−14.2308	−0.695220	−0.347610	−	0.937639i	$-0.613007\pi$
$419$	−14.2308	−0.695220	−0.347610	+	0.937639i	$0.613007\pi$
$420$	−0.0599800	−0.00292673
$421$	−8.99703	−0.438489	−0.219244	−	0.975670i	$-0.570359\pi$
$421$	−8.99703	−0.438489	−0.219244	+	0.975670i	$0.570359\pi$
$422$	9.27347	0.451425
$423$	−0.295751	−0.0143799
$424$	−22.2952	−1.08275
$425$	−3.54036	−0.171732
$426$	5.31997	0.257753
$427$	−1.55451	−0.0752280
$428$	−0.357844	−0.0172970
$429$	26.7768	1.29280
$430$	29.1468	1.40558
$431$	35.4068	1.70549	0.852743	−	0.522330i	$-0.174937\pi$
$431$	35.4068	1.70549	0.852743	+	0.522330i	$0.174937\pi$
$432$	3.64446	0.175344
$433$	−17.8077	−0.855783	−0.427892	−	0.903830i	$-0.640743\pi$
$433$	−17.8077	−0.855783	−0.427892	+	0.903830i	$0.640743\pi$
$434$	1.10203	0.0528993
$435$	13.5522	0.649780
$436$	−3.29540	−0.157821
$437$	21.4756	1.02732
$438$	4.55478	0.217636
$439$	9.18195	0.438231	0.219115	−	0.975699i	$-0.429683\pi$
$439$	9.18195	0.438231	0.219115	+	0.975699i	$0.429683\pi$
$440$	52.4275	2.49938
$441$	−6.98439	−0.332590
$442$	−5.93004	−0.282063
$443$	−22.1341	−1.05162	−0.525812	−	0.850601i	$-0.676238\pi$
$443$	−22.1341	−1.05162	−0.525812	+	0.850601i	$0.676238\pi$
$444$	0.760473	0.0360904
$445$	−6.48429	−0.307385
$446$	−27.7377	−1.31342
$447$	−6.26406	−0.296280
$448$	−1.06756	−0.0504376
$449$	2.73518	0.129081	0.0645405	−	0.997915i	$-0.479442\pi$
$449$	2.73518	0.129081	0.0645405	+	0.997915i	$0.479442\pi$
$450$	4.79679	0.226123
$451$	−8.37037	−0.394145
$452$	0.897014	0.0421920
$453$	−7.58196	−0.356232
$454$	13.8791	0.651380
$455$	−1.59804	−0.0749171
$456$	12.5644	0.588384
$457$	24.4307	1.14282	0.571409	−	0.820665i	$-0.306397\pi$
$457$	24.4307	1.14282	0.571409	+	0.820665i	$0.306397\pi$
$458$	−10.9025	−0.509442
$459$	1.00000	0.0466760
$460$	−2.40619	−0.112189
$461$	30.8704	1.43778	0.718889	−	0.695125i	$-0.244651\pi$
$461$	30.8704	1.43778	0.718889	+	0.695125i	$0.244651\pi$
$462$	−1.03563	−0.0481818
$463$	10.9016	0.506641	0.253321	−	0.967382i	$-0.418477\pi$
$463$	10.9016	0.506641	0.253321	+	0.967382i	$0.418477\pi$
$464$	16.9008	0.784599
$465$	19.0254	0.882281
$466$	2.25026	0.104241
$467$	12.6912	0.587281	0.293640	−	0.955916i	$-0.405133\pi$
$467$	12.6912	0.587281	0.293640	+	0.955916i	$0.405133\pi$
$468$	−0.718997	−0.0332356
$469$	−0.260134	−0.0120119
$470$	−1.17103	−0.0540156
$471$	−1.00000	−0.0460776
$472$	15.6556	0.720609
$473$	−45.0354	−2.07073
$474$	−7.60831	−0.349461
$475$	15.1696	0.696028
$476$	−0.0205243	−0.000940730 0
$477$	7.60318	0.348126
$478$	1.91401	0.0875450
$479$	33.9819	1.55267	0.776336	−	0.630320i	$-0.217076\pi$
$479$	33.9819	1.55267	0.776336	+	0.630320i	$0.217076\pi$
$480$	−2.70866	−0.123633
$481$	20.2611	0.923828
$482$	24.9655	1.13715
$483$	0.626200	0.0284931
$484$	−4.34166	−0.197348
$485$	51.4189	2.33481
$486$	−1.35489	−0.0614590
$487$	15.1906	0.688351	0.344176	−	0.938905i	$-0.388158\pi$
$487$	15.1906	0.688351	0.344176	+	0.938905i	$0.388158\pi$
$488$	−36.4850	−1.65160
$489$	−13.9145	−0.629233
$490$	−27.6548	−1.24932
$491$	5.79352	0.261458	0.130729	−	0.991418i	$-0.458268\pi$
$491$	5.79352	0.261458	0.130729	+	0.991418i	$0.458268\pi$
$492$	0.224757	0.0101328
$493$	4.63739	0.208857
$494$	25.4088	1.14320
$495$	−17.8790	−0.803601
$496$	23.7262	1.06534
$497$	0.490569	0.0220050
$498$	19.2012	0.860428
$499$	−36.1043	−1.61625	−0.808126	−	0.589009i	$-0.799518\pi$
$499$	−36.1043	−1.61625	−0.808126	+	0.589009i	$0.799518\pi$
$500$	0.700742	0.0313382
$501$	−10.0701	−0.449897
$502$	0.495572	0.0221185
$503$	23.4154	1.04404	0.522020	−	0.852933i	$-0.325179\pi$
$503$	23.4154	1.04404	0.522020	+	0.852933i	$0.325179\pi$
$504$	0.366363	0.0163191
$505$	13.7675	0.612645
$506$	−41.5457	−1.84693
$507$	−6.15610	−0.273402
$508$	0.371445	0.0164802
$509$	11.3779	0.504318	0.252159	−	0.967686i	$-0.418859\pi$
$509$	11.3779	0.504318	0.252159	+	0.967686i	$0.418859\pi$
$510$	3.95951	0.175330
$511$	0.420009	0.0185801
$512$	−24.7516	−1.09388
$513$	−4.28476	−0.189177
$514$	−18.2734	−0.806007
$515$	−1.29073	−0.0568763
$516$	1.20927	0.0532350
$517$	1.80938	0.0795767
$518$	−0.783627	−0.0344306
$519$	−15.3516	−0.673859
$520$	−37.5066	−1.64477
$521$	−31.4826	−1.37928	−0.689640	−	0.724153i	$-0.742231\pi$
$521$	−31.4826	−1.37928	−0.689640	+	0.724153i	$0.742231\pi$
$522$	−6.28314	−0.275006
$523$	28.3225	1.23846	0.619228	−	0.785211i	$-0.287445\pi$
$523$	28.3225	1.23846	0.619228	+	0.785211i	$0.287445\pi$
$524$	−2.47711	−0.108213
$525$	0.442326	0.0193047
$526$	4.32186	0.188442
$527$	6.51022	0.283590
$528$	−22.2966	−0.970334
$529$	2.12091	0.0922135
$530$	30.1049	1.30767
$531$	−5.33893	−0.231690
$532$	0.0879418	0.00381276
$533$	5.98816	0.259376
$534$	3.00627	0.130094
$535$	6.36587	0.275221
$536$	−6.10546	−0.263716
$537$	−4.64851	−0.200598
$538$	24.4885	1.05578
$539$	42.7300	1.84051
$540$	0.480077	0.0206592
$541$	−14.3260	−0.615923	−0.307961	−	0.951399i	$-0.599647\pi$
$541$	−14.3260	−0.615923	−0.307961	+	0.951399i	$0.599647\pi$
$542$	23.7813	1.02150
$543$	−14.3933	−0.617674
$544$	−0.926865	−0.0397390
$545$	58.6237	2.51116
$546$	0.740888	0.0317071
$547$	−32.5653	−1.39239	−0.696196	−	0.717852i	$-0.745125\pi$
$547$	−32.5653	−1.39239	−0.696196	+	0.717852i	$0.745125\pi$
$548$	−0.716005	−0.0305862
$549$	12.4422	0.531021
$550$	−29.3464	−1.25134
$551$	−19.8701	−0.846495
$552$	14.6972	0.625554
$553$	−0.701584	−0.0298344
$554$	−33.2653	−1.41331
$555$	−13.5285	−0.574251
$556$	−0.839522	−0.0356037
$557$	20.3259	0.861237	0.430619	−	0.902534i	$-0.358295\pi$
$557$	20.3259	0.861237	0.430619	+	0.902534i	$0.358295\pi$
$558$	−8.82063	−0.373407
$559$	32.2183	1.36269
$560$	1.33066	0.0562306
$561$	−6.11794	−0.258299
$562$	−9.26535	−0.390835
$563$	3.99528	0.168381	0.0841904	−	0.996450i	$-0.473170\pi$
$563$	3.99528	0.168381	0.0841904	+	0.996450i	$0.473170\pi$
$564$	−0.0485847	−0.00204578
$565$	−15.9575	−0.671335
$566$	14.3895	0.604838
$567$	−0.124938	−0.00524691
$568$	11.5139	0.483111
$569$	−19.3502	−0.811201	−0.405600	−	0.914051i	$-0.632938\pi$
$569$	−19.3502	−0.811201	−0.405600	+	0.914051i	$0.632938\pi$
$570$	−16.9656	−0.710610
$571$	−29.0109	−1.21407	−0.607033	−	0.794677i	$-0.707640\pi$
$571$	−29.0109	−1.21407	−0.607033	+	0.794677i	$0.707640\pi$
$572$	4.39878	0.183922
$573$	23.8477	0.996254
$574$	−0.231600	−0.00966680
$575$	17.7445	0.739998
$576$	8.54472	0.356030
$577$	−10.5528	−0.439317	−0.219658	−	0.975577i	$-0.570494\pi$
$577$	−10.5528	−0.439317	−0.219658	+	0.975577i	$0.570494\pi$
$578$	1.35489	0.0563560
$579$	2.59213	0.107725
$580$	2.22630	0.0924423
$581$	1.77060	0.0734570
$582$	−23.8390	−0.988160
$583$	−46.5157	−1.92649
$584$	9.85780	0.407918
$585$	12.7906	0.528827
$586$	8.15390	0.336834
$587$	−26.5434	−1.09556	−0.547781	−	0.836621i	$-0.684527\pi$
$587$	−26.5434	−1.09556	−0.547781	+	0.836621i	$0.684527\pi$
$588$	−1.14737	−0.0473166
$589$	−27.8948	−1.14938
$590$	−21.1396	−0.870302
$591$	−4.80666	−0.197720
$592$	−16.8711	−0.693399
$593$	−11.2023	−0.460022	−0.230011	−	0.973188i	$-0.573876\pi$
$593$	−11.2023	−0.460022	−0.230011	+	0.973188i	$0.573876\pi$
$594$	8.28912	0.340107
$595$	0.365118	0.0149684
$596$	−1.02903	−0.0421508
$597$	11.7620	0.481387
$598$	29.7218	1.21541
$599$	6.88839	0.281452	0.140726	−	0.990049i	$-0.455056\pi$
$599$	6.88839	0.281452	0.140726	+	0.990049i	$0.455056\pi$
$600$	10.3816	0.423826
$601$	25.3667	1.03473	0.517365	−	0.855765i	$-0.326913\pi$
$601$	25.3667	1.03473	0.517365	+	0.855765i	$0.326913\pi$
$602$	−1.24609	−0.0507867
$603$	2.08210	0.0847898
$604$	−1.24553	−0.0506800
$605$	77.2362	3.14010
$606$	−6.38293	−0.259289
$607$	19.7306	0.800841	0.400420	−	0.916332i	$-0.368864\pi$
$607$	19.7306	0.800841	0.400420	+	0.916332i	$0.368864\pi$
$608$	3.97140	0.161061
$609$	−0.579387	−0.0234779
$610$	49.2651	1.99469
$611$	−1.29443	−0.0523672
$612$	0.164276	0.00664045
$613$	13.3077	0.537493	0.268747	−	0.963211i	$-0.413391\pi$
$613$	13.3077	0.537493	0.268747	+	0.963211i	$0.413391\pi$
$614$	11.2346	0.453390
$615$	−3.99832	−0.161228
$616$	−2.24139	−0.0903080
$617$	−22.9216	−0.922790	−0.461395	−	0.887195i	$-0.652651\pi$
$617$	−22.9216	−0.922790	−0.461395	+	0.887195i	$0.652651\pi$
$618$	0.598413	0.0240717
$619$	1.73372	0.0696840	0.0348420	−	0.999393i	$-0.488907\pi$
$619$	1.73372	0.0696840	0.0348420	+	0.999393i	$0.488907\pi$
$620$	3.12541	0.125519
$621$	−5.01208	−0.201128
$622$	−8.67641	−0.347892
$623$	0.277217	0.0111065
$624$	15.9510	0.638550
$625$	−30.1677	−1.20671
$626$	−5.30344	−0.211968
$627$	26.2139	1.04688
$628$	−0.164276	−0.00655531
$629$	−4.62925	−0.184580
$630$	−0.494694	−0.0197091
$631$	20.9565	0.834265	0.417133	−	0.908846i	$-0.363035\pi$
$631$	20.9565	0.834265	0.417133	+	0.908846i	$0.363035\pi$
$632$	−16.4665	−0.655002
$633$	−6.84445	−0.272042
$634$	−12.8697	−0.511122
$635$	−6.60783	−0.262224
$636$	1.24902	0.0495268
$637$	−30.5691	−1.21119
$638$	38.4399	1.52185
$639$	−3.92650	−0.155330
$640$	28.4156	1.12323
$641$	36.1203	1.42667	0.713333	−	0.700826i	$-0.247185\pi$
$641$	36.1203	1.42667	0.713333	+	0.700826i	$0.247185\pi$
$642$	−2.95137	−0.116481
$643$	−14.6322	−0.577036	−0.288518	−	0.957474i	$-0.593163\pi$
$643$	−14.6322	−0.577036	−0.288518	+	0.957474i	$0.593163\pi$
$644$	0.102869	0.00405362
$645$	−21.5123	−0.847046
$646$	−5.80538	−0.228410
$647$	−22.6475	−0.890365	−0.445183	−	0.895440i	$-0.646861\pi$
$647$	−22.6475	−0.890365	−0.445183	+	0.895440i	$0.646861\pi$
$648$	−2.93235	−0.115194
$649$	32.6632	1.28214
$650$	20.9944	0.823469
$651$	−0.813375	−0.0318787
$652$	−2.28581	−0.0895191
$653$	12.4295	0.486402	0.243201	−	0.969976i	$-0.421803\pi$
$653$	12.4295	0.486402	0.243201	+	0.969976i	$0.421803\pi$
$654$	−27.1793	−1.06280
$655$	44.0667	1.72183
$656$	−4.98624	−0.194680
$657$	−3.36174	−0.131154
$658$	0.0500639	0.00195170
$659$	20.5319	0.799808	0.399904	−	0.916557i	$-0.369043\pi$
$659$	20.5319	0.799808	0.399904	+	0.916557i	$0.369043\pi$
$660$	−2.93708	−0.114326
$661$	19.1758	0.745851	0.372925	−	0.927861i	$-0.378355\pi$
$661$	19.1758	0.745851	0.372925	+	0.927861i	$0.378355\pi$
$662$	2.81340	0.109346
$663$	4.37677	0.169980
$664$	41.5568	1.61272
$665$	−1.56444	−0.0606665
$666$	6.27212	0.243040
$667$	−23.2429	−0.899970
$668$	−1.65427	−0.0640055
$669$	20.4723	0.791506
$670$	8.24411	0.318498
$671$	−76.1207	−2.93861
$672$	0.115801	0.00446712
$673$	−30.8555	−1.18939	−0.594695	−	0.803951i	$-0.702727\pi$
$673$	−30.8555	−1.18939	−0.594695	+	0.803951i	$0.702727\pi$
$674$	11.0974	0.427455
$675$	−3.54036	−0.136268
$676$	−1.01130	−0.0388961
$677$	−14.0260	−0.539062	−0.269531	−	0.962992i	$-0.586869\pi$
$677$	−14.0260	−0.539062	−0.269531	+	0.962992i	$0.586869\pi$
$678$	7.39826	0.284128
$679$	−2.19827	−0.0843617
$680$	8.56948	0.328624
$681$	−10.2437	−0.392541
$682$	53.9640	2.06639
$683$	25.3352	0.969424	0.484712	−	0.874674i	$-0.338924\pi$
$683$	25.3352	0.969424	0.484712	+	0.874674i	$0.338924\pi$
$684$	−0.703883	−0.0269136
$685$	12.7374	0.486671
$686$	2.36724	0.0903817
$687$	8.04681	0.307005
$688$	−26.8276	−1.02279
$689$	33.2773	1.26777
$690$	−19.8454	−0.755501
$691$	20.0479	0.762656	0.381328	−	0.924440i	$-0.375467\pi$
$691$	20.0479	0.762656	0.381328	+	0.924440i	$0.375467\pi$
$692$	−2.52189	−0.0958679
$693$	0.764364	0.0290358
$694$	−0.651200	−0.0247192
$695$	14.9347	0.566506
$696$	−13.5985	−0.515448
$697$	−1.36817	−0.0518231
$698$	11.1818	0.423237
$699$	−1.66084	−0.0628188
$700$	0.0726634	0.00274642
$701$	−47.6324	−1.79905	−0.899525	−	0.436870i	$-0.856087\pi$
$701$	−47.6324	−1.79905	−0.899525	+	0.436870i	$0.856087\pi$
$702$	−5.93004	−0.223815
$703$	19.8352	0.748100
$704$	−52.2761	−1.97023
$705$	0.864299	0.0325514
$706$	−17.2269	−0.648344
$707$	−0.588589	−0.0221362
$708$	−0.877057	−0.0329618
$709$	−8.26869	−0.310537	−0.155269	−	0.987872i	$-0.549624\pi$
$709$	−8.26869	−0.310537	−0.155269	+	0.987872i	$0.549624\pi$
$710$	−15.5470	−0.583469
$711$	5.61545	0.210596
$712$	6.50640	0.243838
$713$	−32.6297	−1.22199
$714$	−0.169277	−0.00633505
$715$	−78.2522	−2.92647
$716$	−0.763637	−0.0285385
$717$	−1.41267	−0.0527572
$718$	22.1728	0.827480
$719$	−33.9154	−1.26483	−0.632415	−	0.774630i	$-0.717936\pi$
$719$	−33.9154	−1.26483	−0.632415	+	0.774630i	$0.717936\pi$
$720$	−10.6505	−0.396922
$721$	0.0551814	0.00205506
$722$	−0.868218	−0.0323117
$723$	−18.4262	−0.685278
$724$	−2.36446	−0.0878746
$725$	−16.4180	−0.609749
$726$	−35.8085	−1.32898
$727$	−45.7104	−1.69530	−0.847652	−	0.530553i	$-0.821984\pi$
$727$	−45.7104	−1.69530	−0.847652	+	0.530553i	$0.821984\pi$
$728$	1.60349	0.0594291
$729$	1.00000	0.0370370
$730$	−13.3108	−0.492656
$731$	−7.36121	−0.272264
$732$	2.04396	0.0755468
$733$	−26.2073	−0.967989	−0.483994	−	0.875071i	$-0.660814\pi$
$733$	−26.2073	−0.967989	−0.483994	+	0.875071i	$0.660814\pi$
$734$	−19.7602	−0.729362
$735$	20.4111	0.752875
$736$	4.64552	0.171236
$737$	−12.7382	−0.469216
$738$	1.85372	0.0682362
$739$	36.6766	1.34917	0.674585	−	0.738198i	$-0.264323\pi$
$739$	36.6766	1.34917	0.674585	+	0.738198i	$0.264323\pi$
$740$	−2.22240	−0.0816969
$741$	−18.7534	−0.688924
$742$	−1.28705	−0.0472490
$743$	−37.9892	−1.39369	−0.696843	−	0.717223i	$-0.745413\pi$
$743$	−37.9892	−1.39369	−0.696843	+	0.717223i	$0.745413\pi$
$744$	−19.0903	−0.699883
$745$	18.3060	0.670681
$746$	−27.0154	−0.989105
$747$	−14.1718	−0.518520
$748$	−1.00503	−0.0367475
$749$	−0.272154	−0.00994430
$750$	5.77948	0.211037
$751$	20.4166	0.745011	0.372505	−	0.928030i	$-0.378499\pi$
$751$	20.4166	0.745011	0.372505	+	0.928030i	$0.378499\pi$
$752$	1.07785	0.0393053
$753$	−0.365766	−0.0133292
$754$	−27.4999	−1.00149
$755$	22.1574	0.806392
$756$	−0.0205243	−0.000746462 0
$757$	−33.3373	−1.21166	−0.605832	−	0.795593i	$-0.707160\pi$
$757$	−33.3373	−1.21166	−0.605832	+	0.795593i	$0.707160\pi$
$758$	24.4702	0.888799
$759$	30.6636	1.11302
$760$	−36.7182	−1.33191
$761$	−25.8019	−0.935320	−0.467660	−	0.883908i	$-0.654903\pi$
$761$	−25.8019	−0.935320	−0.467660	+	0.883908i	$0.654903\pi$
$762$	3.06355	0.110981
$763$	−2.50629	−0.0907336
$764$	3.91761	0.141734
$765$	−2.92239	−0.105659
$766$	−32.2995	−1.16703
$767$	−23.3673	−0.843743
$768$	3.91529	0.141281
$769$	−34.9253	−1.25944	−0.629719	−	0.776823i	$-0.716830\pi$
$769$	−34.9253	−1.25944	−0.629719	+	0.776823i	$0.716830\pi$
$770$	3.02651	0.109068
$771$	13.4870	0.485724
$772$	0.425824	0.0153258
$773$	25.4581	0.915665	0.457832	−	0.889039i	$-0.348626\pi$
$773$	25.4581	0.915665	0.457832	+	0.889039i	$0.348626\pi$
$774$	9.97362	0.358494
$775$	−23.0485	−0.827926
$776$	−51.5942	−1.85213
$777$	0.578370	0.0207489
$778$	19.5393	0.700518
$779$	5.86228	0.210038
$780$	2.10119	0.0752346
$781$	24.0220	0.859576
$782$	−6.79081	−0.242839
$783$	4.63739	0.165727
$784$	25.4543	0.909084
$785$	2.92239	0.104305
$786$	−20.4304	−0.728727
$787$	−42.7258	−1.52301	−0.761506	−	0.648158i	$-0.775540\pi$
$787$	−42.7258	−1.52301	−0.761506	+	0.648158i	$0.775540\pi$
$788$	−0.789618	−0.0281290
$789$	−3.18983	−0.113561
$790$	22.2344	0.791066
$791$	0.682215	0.0242568
$792$	17.9399	0.637468
$793$	54.4567	1.93382
$794$	45.7176	1.62246
$795$	−22.2194	−0.788042
$796$	1.93221	0.0684855
$797$	36.0748	1.27783	0.638917	−	0.769276i	$-0.279383\pi$
$797$	36.0748	1.27783	0.638917	+	0.769276i	$0.279383\pi$
$798$	0.725314	0.0256758
$799$	0.295751	0.0104629
$800$	3.28143	0.116016
$801$	−2.21883	−0.0783986
$802$	35.2003	1.24296
$803$	20.5669	0.725789
$804$	0.342039	0.0120628
$805$	−1.83000	−0.0644990
$806$	−38.6058	−1.35983
$807$	−18.0742	−0.636242
$808$	−13.8144	−0.485990
$809$	−20.1604	−0.708801	−0.354401	−	0.935094i	$-0.615315\pi$
$809$	−20.1604	−0.708801	−0.354401	+	0.935094i	$0.615315\pi$
$810$	3.95951	0.139123
$811$	−6.37600	−0.223892	−0.111946	−	0.993714i	$-0.535708\pi$
$811$	−6.37600	−0.223892	−0.111946	+	0.993714i	$0.535708\pi$
$812$	−0.0951792	−0.00334013
$813$	−17.5522	−0.615583
$814$	−38.3724	−1.34495
$815$	40.6634	1.42438
$816$	−3.64446	−0.127582
$817$	31.5410	1.10348
$818$	2.81158	0.0983047
$819$	−0.546826	−0.0191076
$820$	−0.656827	−0.0229374
$821$	18.4749	0.644779	0.322390	−	0.946607i	$-0.395514\pi$
$821$	18.4749	0.644779	0.322390	+	0.946607i	$0.395514\pi$
$822$	−5.90536	−0.205973
$823$	−43.0099	−1.49923	−0.749615	−	0.661874i	$-0.769761\pi$
$823$	−43.0099	−1.49923	−0.749615	+	0.661874i	$0.769761\pi$
$824$	1.29513	0.0451180
$825$	21.6597	0.754093
$826$	0.903761	0.0314459
$827$	−22.5399	−0.783788	−0.391894	−	0.920010i	$-0.628180\pi$
$827$	−22.5399	−0.783788	−0.391894	+	0.920010i	$0.628180\pi$
$828$	−0.823362	−0.0286138
$829$	−52.8250	−1.83469	−0.917344	−	0.398095i	$-0.869671\pi$
$829$	−52.8250	−1.83469	−0.917344	+	0.398095i	$0.869671\pi$
$830$	−56.1135	−1.94773
$831$	24.5521	0.851701
$832$	37.3983	1.29655
$833$	6.98439	0.241995
$834$	−6.92409	−0.239762
$835$	29.4286	1.01842
$836$	4.30631	0.148937
$837$	6.51022	0.225026
$838$	−19.2812	−0.666056
$839$	15.9905	0.552054	0.276027	−	0.961150i	$-0.410982\pi$
$839$	15.9905	0.552054	0.276027	+	0.961150i	$0.410982\pi$
$840$	−1.07066	−0.0369411
$841$	−7.49466	−0.258436
$842$	−12.1900	−0.420095
$843$	6.83846	0.235529
$844$	−1.12438	−0.0387026
$845$	17.9905	0.618892
$846$	−0.400710	−0.0137767
$847$	−3.30201	−0.113458
$848$	−27.7095	−0.951548
$849$	−10.6205	−0.364493
$850$	−4.79679	−0.164528
$851$	23.2021	0.795359
$852$	−0.645028	−0.0220983
$853$	15.6852	0.537051	0.268525	−	0.963273i	$-0.413464\pi$
$853$	15.6852	0.537051	0.268525	+	0.963273i	$0.413464\pi$
$854$	−2.10619	−0.0720723
$855$	12.5217	0.428235
$856$	−6.38758	−0.218323
$857$	29.5087	1.00800	0.503998	−	0.863705i	$-0.331862\pi$
$857$	29.5087	1.00800	0.503998	+	0.863705i	$0.331862\pi$
$858$	36.2796	1.23856
$859$	24.3462	0.830683	0.415342	−	0.909666i	$-0.363662\pi$
$859$	24.3462	0.830683	0.415342	+	0.909666i	$0.363662\pi$
$860$	−3.53395	−0.120507
$861$	0.170937	0.00582550
$862$	47.9723	1.63394
$863$	20.0593	0.682828	0.341414	−	0.939913i	$-0.389094\pi$
$863$	20.0593	0.682828	0.341414	+	0.939913i	$0.389094\pi$
$864$	−0.926865	−0.0315326
$865$	44.8633	1.52540
$866$	−24.1274	−0.819884
$867$	−1.00000	−0.0339618
$868$	−0.133618	−0.00453528
$869$	−34.3550	−1.16541
$870$	18.3618	0.622523
$871$	9.11288	0.308778
$872$	−58.8236	−1.99202
$873$	17.5948	0.595494
$874$	29.0970	0.984221
$875$	0.532943	0.0180167
$876$	−0.552251	−0.0186588
$877$	39.4651	1.33264	0.666320	−	0.745666i	$-0.267868\pi$
$877$	39.4651	1.33264	0.666320	+	0.745666i	$0.267868\pi$
$878$	12.4405	0.419847
$879$	−6.01813	−0.202986
$880$	65.1593	2.19652
$881$	54.2608	1.82809	0.914046	−	0.405611i	$-0.132941\pi$
$881$	54.2608	1.82809	0.914046	+	0.405611i	$0.132941\pi$
$882$	−9.46307	−0.318638
$883$	17.7457	0.597189	0.298595	−	0.954380i	$-0.403482\pi$
$883$	17.7457	0.597189	0.298595	+	0.954380i	$0.403482\pi$
$884$	0.718997	0.0241825
$885$	15.6024	0.524470
$886$	−29.9893	−1.00751
$887$	−10.6222	−0.356659	−0.178329	−	0.983971i	$-0.557069\pi$
$887$	−10.6222	−0.356659	−0.178329	+	0.983971i	$0.557069\pi$
$888$	13.5746	0.455533
$889$	0.282499	0.00947470
$890$	−8.78549	−0.294490
$891$	−6.11794	−0.204959
$892$	3.36311	0.112605
$893$	−1.26722	−0.0424060
$894$	−8.48711	−0.283851
$895$	13.5848	0.454088
$896$	−1.21483	−0.0405845
$897$	−21.9367	−0.732445
$898$	3.70586	0.123666
$899$	30.1904	1.00691
$900$	−0.581594	−0.0193865
$901$	−7.60318	−0.253299
$902$	−11.3409	−0.377611
$903$	0.919696	0.0306056
$904$	16.0119	0.532547
$905$	42.0627	1.39821
$906$	−10.2727	−0.341288
$907$	2.60722	0.0865713	0.0432857	−	0.999063i	$-0.486217\pi$
$907$	2.60722	0.0865713	0.0432857	+	0.999063i	$0.486217\pi$
$908$	−1.68280	−0.0558456
$909$	4.71104	0.156255
$910$	−2.16516	−0.0717744
$911$	−50.8058	−1.68327	−0.841635	−	0.540047i	$-0.818407\pi$
$911$	−50.8058	−1.68327	−0.841635	+	0.540047i	$0.818407\pi$
$912$	15.6157	0.517086
$913$	86.7023	2.86943
$914$	33.1008	1.09488
$915$	−36.3610	−1.20206
$916$	1.32189	0.0436766
$917$	−1.88394	−0.0622132
$918$	1.35489	0.0447180
$919$	4.87118	0.160685	0.0803427	−	0.996767i	$-0.474399\pi$
$919$	4.87118	0.160685	0.0803427	+	0.996767i	$0.474399\pi$
$920$	−42.9509	−1.41605
$921$	−8.29187	−0.273227
$922$	41.8260	1.37746
$923$	−17.1854	−0.565663
$924$	0.125566	0.00413083
$925$	16.3892	0.538873
$926$	14.7705	0.485388
$927$	−0.441669	−0.0145063
$928$	−4.29823	−0.141096
$929$	−50.4125	−1.65398	−0.826990	−	0.562217i	$-0.809948\pi$
$929$	−50.4125	−1.65398	−0.826990	+	0.562217i	$0.809948\pi$
$930$	25.7773	0.845271
$931$	−29.9265	−0.980800
$932$	−0.272836	−0.00893704
$933$	6.40378	0.209650
$934$	17.1952	0.562645
$935$	17.8790	0.584705
$936$	−12.8342	−0.419500
$937$	53.5191	1.74839	0.874197	−	0.485572i	$-0.161389\pi$
$937$	53.5191	1.74839	0.874197	+	0.485572i	$0.161389\pi$
$938$	−0.352453	−0.0115080
$939$	3.91430	0.127738
$940$	0.141983	0.00463099
$941$	−37.6237	−1.22650	−0.613248	−	0.789890i	$-0.710137\pi$
$941$	−37.6237	−1.22650	−0.613248	+	0.789890i	$0.710137\pi$
$942$	−1.35489	−0.0441447
$943$	6.85736	0.223307
$944$	19.4575	0.633289
$945$	0.365118	0.0118773
$946$	−61.0179	−1.98386
$947$	−6.20920	−0.201772	−0.100886	−	0.994898i	$-0.532168\pi$
$947$	−6.20920	−0.201772	−0.100886	+	0.994898i	$0.532168\pi$
$948$	0.922482	0.0299608
$949$	−14.7135	−0.477622
$950$	20.5531	0.666831
$951$	9.49872	0.308017
$952$	−0.366363	−0.0118739
$953$	35.4358	1.14788	0.573938	−	0.818898i	$-0.305415\pi$
$953$	35.4358	1.14788	0.573938	+	0.818898i	$0.305415\pi$
$954$	10.3015	0.333522
$955$	−69.6924	−2.25519
$956$	−0.232068	−0.00750561
$957$	−28.3712	−0.917111
$958$	46.0417	1.48754
$959$	−0.544550	−0.0175845
$960$	−24.9710	−0.805936
$961$	11.3830	0.367192
$962$	27.4516	0.885075
$963$	2.17831	0.0701951
$964$	−3.02698	−0.0974924
$965$	−7.57522	−0.243855
$966$	0.848431	0.0272978
$967$	58.1790	1.87091	0.935455	−	0.353445i	$-0.114990\pi$
$967$	58.1790	1.87091	0.935455	+	0.353445i	$0.114990\pi$
$968$	−77.4995	−2.49093
$969$	4.28476	0.137646
$970$	69.6669	2.23687
$971$	−6.32396	−0.202945	−0.101473	−	0.994838i	$-0.532355\pi$
$971$	−6.32396	−0.202945	−0.101473	+	0.994838i	$0.532355\pi$
$972$	0.164276	0.00526915
$973$	−0.638490	−0.0204690
$974$	20.5816	0.659476
$975$	−15.4953	−0.496247
$976$	−45.3452	−1.45147
$977$	−47.3660	−1.51537	−0.757686	−	0.652619i	$-0.773670\pi$
$977$	−47.3660	−1.51537	−0.757686	+	0.652619i	$0.773670\pi$
$978$	−18.8525	−0.602838
$979$	13.5747	0.433848
$980$	3.35305	0.107109
$981$	20.0602	0.640473
$982$	7.84958	0.250490
$983$	2.74745	0.0876302	0.0438151	−	0.999040i	$-0.486049\pi$
$983$	2.74745	0.0876302	0.0438151	+	0.999040i	$0.486049\pi$
$984$	4.01195	0.127896
$985$	14.0469	0.447573
$986$	6.28314	0.200096
$987$	−0.0369506	−0.00117615
$988$	−3.08073	−0.0980111
$989$	36.8949	1.17319
$990$	−24.2240	−0.769891
$991$	−20.7999	−0.660731	−0.330365	−	0.943853i	$-0.607172\pi$
$991$	−20.7999	−0.660731	−0.330365	+	0.943853i	$0.607172\pi$
$992$	−6.03410	−0.191583
$993$	−2.07648	−0.0658950
$994$	0.664667	0.0210820
$995$	−34.3732	−1.08970
$996$	−2.32809	−0.0737682
$997$	3.42504	0.108472	0.0542361	−	0.998528i	$-0.482728\pi$
$997$	3.42504	0.108472	0.0542361	+	0.998528i	$0.482728\pi$
$998$	−48.9174	−1.54845
$999$	−4.62925	−0.146463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.g.1.39	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.g.1.39	✓	56	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.35489 q^{2} -1.00000 q^{3} -0.164276 q^{4} +2.92239 q^{5} -1.35489 q^{6} -0.124938 q^{7} -2.93235 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.35489 q^{2} -1.00000 q^{3} -0.164276 q^{4} +2.92239 q^{5} -1.35489 q^{6} -0.124938 q^{7} -2.93235 q^{8} +1.00000 q^{9} +3.95951 q^{10} -6.11794 q^{11} +0.164276 q^{12} +4.37677 q^{13} -0.169277 q^{14} -2.92239 q^{15} -3.64446 q^{16} -1.00000 q^{17} +1.35489 q^{18} +4.28476 q^{19} -0.480077 q^{20} +0.124938 q^{21} -8.28912 q^{22} +5.01208 q^{23} +2.93235 q^{24} +3.54036 q^{25} +5.93004 q^{26} -1.00000 q^{27} +0.0205243 q^{28} -4.63739 q^{29} -3.95951 q^{30} -6.51022 q^{31} +0.926865 q^{32} +6.11794 q^{33} -1.35489 q^{34} -0.365118 q^{35} -0.164276 q^{36} +4.62925 q^{37} +5.80538 q^{38} -4.37677 q^{39} -8.56948 q^{40} +1.36817 q^{41} +0.169277 q^{42} +7.36121 q^{43} +1.00503 q^{44} +2.92239 q^{45} +6.79081 q^{46} -0.295751 q^{47} +3.64446 q^{48} -6.98439 q^{49} +4.79679 q^{50} +1.00000 q^{51} -0.718997 q^{52} +7.60318 q^{53} -1.35489 q^{54} -17.8790 q^{55} +0.366363 q^{56} -4.28476 q^{57} -6.28314 q^{58} -5.33893 q^{59} +0.480077 q^{60} +12.4422 q^{61} -8.82063 q^{62} -0.124938 q^{63} +8.54472 q^{64} +12.7906 q^{65} +8.28912 q^{66} +2.08210 q^{67} +0.164276 q^{68} -5.01208 q^{69} -0.494694 q^{70} -3.92650 q^{71} -2.93235 q^{72} -3.36174 q^{73} +6.27212 q^{74} -3.54036 q^{75} -0.703883 q^{76} +0.764364 q^{77} -5.93004 q^{78} +5.61545 q^{79} -10.6505 q^{80} +1.00000 q^{81} +1.85372 q^{82} -14.1718 q^{83} -0.0205243 q^{84} -2.92239 q^{85} +9.97362 q^{86} +4.63739 q^{87} +17.9399 q^{88} -2.21883 q^{89} +3.95951 q^{90} -0.546826 q^{91} -0.823362 q^{92} +6.51022 q^{93} -0.400710 q^{94} +12.5217 q^{95} -0.926865 q^{96} +17.5948 q^{97} -9.46307 q^{98} -6.11794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9}+O(q^{10}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9	\( 56 q + q^{2} - 56 q^{3} + 61 q^{4} + q^{5} - q^{6} + 19 q^{7} + 56 q^{9} + 8 q^{10} - 7 q^{11} - 61 q^{12} + 8 q^{13} - 8 q^{14} - q^{15} + 71 q^{16} - 56 q^{17} + q^{18} - 2 q^{19} - 4 q^{20} - 19 q^{21} + 47 q^{22} + 16 q^{23} + 85 q^{25} - 11 q^{26} - 56 q^{27} + 52 q^{28} + 17 q^{29} - 8 q^{30} + 23 q^{31} + 11 q^{32} + 7 q^{33} - q^{34} - 41 q^{35} + 61 q^{36} + 58 q^{37} - 22 q^{38} - 8 q^{39} + 38 q^{40} - q^{41} + 8 q^{42} + 27 q^{43} + 2 q^{44} + q^{45} + 46 q^{46} + 5 q^{47} - 71 q^{48} + 59 q^{49} - 4 q^{50} + 56 q^{51} + 25 q^{52} + 15 q^{53} - q^{54} + 9 q^{55} - 36 q^{56} + 2 q^{57} + 89 q^{58} - 61 q^{59} + 4 q^{60} + 47 q^{61} + 8 q^{62} + 19 q^{63} + 88 q^{64} + 39 q^{65} - 47 q^{66} + 20 q^{67} - 61 q^{68} - 16 q^{69} + 36 q^{70} - 2 q^{71} + 93 q^{73} + 48 q^{74} - 85 q^{75} + 38 q^{76} + 26 q^{77} + 11 q^{78} + 72 q^{79} + 42 q^{80} + 56 q^{81} + 33 q^{82} - 11 q^{83} - 52 q^{84} - q^{85} - 4 q^{86} - 17 q^{87} + 130 q^{88} - 6 q^{89} + 8 q^{90} + 37 q^{91} + 132 q^{92} - 23 q^{93} - 32 q^{94} + 12 q^{95} - 11 q^{96} + 100 q^{97} + 42 q^{98} - 7 q^{99}+O(q^{100}) \) 56 * q + q^2 - 56 * q^3 + 61 * q^4 + q^5 - q^6 + 19 * q^7 + 56 * q^9 + 8 * q^10 - 7 * q^11 - 61 * q^12 + 8 * q^13 - 8 * q^14 - q^15 + 71 * q^16 - 56 * q^17 + q^18 - 2 * q^19 - 4 * q^20 - 19 * q^21 + 47 * q^22 + 16 * q^23 + 85 * q^25 - 11 * q^26 - 56 * q^27 + 52 * q^28 + 17 * q^29 - 8 * q^30 + 23 * q^31 + 11 * q^32 + 7 * q^33 - q^34 - 41 * q^35 + 61 * q^36 + 58 * q^37 - 22 * q^38 - 8 * q^39 + 38 * q^40 - q^41 + 8 * q^42 + 27 * q^43 + 2 * q^44 + q^45 + 46 * q^46 + 5 * q^47 - 71 * q^48 + 59 * q^49 - 4 * q^50 + 56 * q^51 + 25 * q^52 + 15 * q^53 - q^54 + 9 * q^55 - 36 * q^56 + 2 * q^57 + 89 * q^58 - 61 * q^59 + 4 * q^60 + 47 * q^61 + 8 * q^62 + 19 * q^63 + 88 * q^64 + 39 * q^65 - 47 * q^66 + 20 * q^67 - 61 * q^68 - 16 * q^69 + 36 * q^70 - 2 * q^71 + 93 * q^73 + 48 * q^74 - 85 * q^75 + 38 * q^76 + 26 * q^77 + 11 * q^78 + 72 * q^79 + 42 * q^80 + 56 * q^81 + 33 * q^82 - 11 * q^83 - 52 * q^84 - q^85 - 4 * q^86 - 17 * q^87 + 130 * q^88 - 6 * q^89 + 8 * q^90 + 37 * q^91 + 132 * q^92 - 23 * q^93 - 32 * q^94 + 12 * q^95 - 11 * q^96 + 100 * q^97 + 42 * q^98 - 7 * q^99

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