LMFDB - Embedded newform 847.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, 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("847.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.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:	$6.76332905120$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.12489$ of defining polynomial
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.12489 q^{2} -3.12489 q^{3} +2.51514 q^{4} +0.484862 q^{5} -6.64002 q^{6} -1.00000 q^{7} +1.09461 q^{8} +6.76491 q^{9} +O(q^{10})$	\(q+2.12489 q^{2} -3.12489 q^{3} +2.51514 q^{4} +0.484862 q^{5} -6.64002 q^{6} -1.00000 q^{7} +1.09461 q^{8} +6.76491 q^{9} +1.03028 q^{10} -7.85952 q^{12} -5.60975 q^{13} -2.12489 q^{14} -1.51514 q^{15} -2.70436 q^{16} -5.60975 q^{17} +14.3747 q^{18} +5.28005 q^{19} +1.21949 q^{20} +3.12489 q^{21} +2.48486 q^{23} -3.42053 q^{24} -4.76491 q^{25} -11.9201 q^{26} -11.7649 q^{27} -2.51514 q^{28} -5.28005 q^{29} -3.21949 q^{30} -7.12489 q^{31} -7.93567 q^{32} -11.9201 q^{34} -0.484862 q^{35} +17.0147 q^{36} -0.235091 q^{37} +11.2195 q^{38} +17.5298 q^{39} +0.530734 q^{40} -2.39025 q^{41} +6.64002 q^{42} -1.03028 q^{43} +3.28005 q^{45} +5.28005 q^{46} -1.60975 q^{47} +8.45080 q^{48} +1.00000 q^{49} -10.1249 q^{50} +17.5298 q^{51} -14.1093 q^{52} -3.03028 q^{53} -24.9991 q^{54} -1.09461 q^{56} -16.4995 q^{57} -11.2195 q^{58} +3.12489 q^{59} -3.81078 q^{60} +2.39025 q^{61} -15.1396 q^{62} -6.76491 q^{63} -11.4537 q^{64} -2.71995 q^{65} +10.0147 q^{67} -14.1093 q^{68} -7.76491 q^{69} -1.03028 q^{70} +12.0752 q^{71} +7.40493 q^{72} -2.39025 q^{73} -0.499542 q^{74} +14.8898 q^{75} +13.2800 q^{76} +37.2489 q^{78} -9.03028 q^{79} -1.31124 q^{80} +16.4693 q^{81} -5.07901 q^{82} +3.21949 q^{83} +7.85952 q^{84} -2.71995 q^{85} -2.18922 q^{86} +16.4995 q^{87} -1.26537 q^{89} +6.96972 q^{90} +5.60975 q^{91} +6.24977 q^{92} +22.2645 q^{93} -3.42053 q^{94} +2.56009 q^{95} +24.7980 q^{96} -8.79518 q^{97} +2.12489 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9	$ 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{20} + q^{21} + 7 q^{23} - 20 q^{24} + 2 q^{25} - 12 q^{26} - 19 q^{27} - 8 q^{28} + 8 q^{30} - 13 q^{31} - 34 q^{32} - 12 q^{34} - q^{35} + 18 q^{36} - 17 q^{37} + 16 q^{38} + 20 q^{39} + 36 q^{40} - 16 q^{41} + 12 q^{42} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 36 q^{48} + 3 q^{49} - 22 q^{50} + 20 q^{51} - 10 q^{53} - 8 q^{54} + 6 q^{56} - 16 q^{57} - 16 q^{58} + q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} - 4 q^{63} + 34 q^{64} - 24 q^{65} - 3 q^{67} - 7 q^{69} - 4 q^{70} + 5 q^{71} - 2 q^{72} - 16 q^{73} + 32 q^{74} + 20 q^{75} + 24 q^{76} + 28 q^{78} - 28 q^{79} - 56 q^{80} + 15 q^{81} + 28 q^{82} - 8 q^{83} - 2 q^{84} - 24 q^{85} + 12 q^{86} + 16 q^{87} - 21 q^{89} + 20 q^{90} + 8 q^{91} + 2 q^{92} + 17 q^{93} - 20 q^{94} - 24 q^{95} - 20 q^{96} - 11 q^{97} - 2 q^{98}+O(q^{100}) $ 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^20 + q^21 + 7 * q^23 - 20 * q^24 + 2 * q^25 - 12 * q^26 - 19 * q^27 - 8 * q^28 + 8 * q^30 - 13 * q^31 - 34 * q^32 - 12 * q^34 - q^35 + 18 * q^36 - 17 * q^37 + 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 + 12 * q^42 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 36 * q^48 + 3 * q^49 - 22 * q^50 + 20 * q^51 - 10 * q^53 - 8 * q^54 + 6 * q^56 - 16 * q^57 - 16 * q^58 + q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 + 34 * q^64 - 24 * q^65 - 3 * q^67 - 7 * q^69 - 4 * q^70 + 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 + 20 * q^75 + 24 * q^76 + 28 * q^78 - 28 * q^79 - 56 * q^80 + 15 * q^81 + 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 + 12 * q^86 + 16 * q^87 - 21 * q^89 + 20 * q^90 + 8 * q^91 + 2 * q^92 + 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 - 11 * q^97 - 2 * q^98

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 $

$2$	2.12489	1.50252	0.751260	−	0.660006i	$-0.229446\pi$
$2$	2.12489	1.50252	0.751260	+	0.660006i	$0.229446\pi$
$3$	−3.12489	−1.80415	−0.902077	−	0.431576i	$-0.857958\pi$
$3$	−3.12489	−1.80415	−0.902077	+	0.431576i	$0.857958\pi$
$4$	2.51514	1.25757
$5$	0.484862	0.216837	0.108418	−	0.994105i	$-0.465421\pi$
$5$	0.484862	0.216837	0.108418	+	0.994105i	$0.465421\pi$
$6$	−6.64002	−2.71078
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.09461	0.387003
$9$	6.76491	2.25497
$10$	1.03028	0.325802
$11$	0	0
$11$	0	0
$12$	−7.85952	−2.26885
$13$	−5.60975	−1.55586	−0.777932	−	0.628348i	$-0.783731\pi$
$13$	−5.60975	−1.55586	−0.777932	+	0.628348i	$0.783731\pi$
$14$	−2.12489	−0.567900
$15$	−1.51514	−0.391207
$16$	−2.70436	−0.676089
$17$	−5.60975	−1.36056	−0.680282	−	0.732951i	$-0.738143\pi$
$17$	−5.60975	−1.36056	−0.680282	+	0.732951i	$0.738143\pi$
$18$	14.3747	3.38814
$19$	5.28005	1.21133	0.605663	−	0.795721i	$-0.292908\pi$
$19$	5.28005	1.21133	0.605663	+	0.795721i	$0.292908\pi$
$20$	1.21949	0.272687
$21$	3.12489	0.681906
$22$	0	0
$23$	2.48486	0.518130	0.259065	−	0.965860i	$-0.416586\pi$
$23$	2.48486	0.518130	0.259065	+	0.965860i	$0.416586\pi$
$24$	−3.42053	−0.698213
$25$	−4.76491	−0.952982
$26$	−11.9201	−2.33772
$27$	−11.7649	−2.26416
$28$	−2.51514	−0.475316
$29$	−5.28005	−0.980480	−0.490240	−	0.871587i	$-0.663091\pi$
$29$	−5.28005	−0.980480	−0.490240	+	0.871587i	$0.663091\pi$
$30$	−3.21949	−0.587797
$31$	−7.12489	−1.27967	−0.639834	−	0.768513i	$-0.720997\pi$
$31$	−7.12489	−1.27967	−0.639834	+	0.768513i	$0.720997\pi$
$32$	−7.93567	−1.40284
$33$	0	0
$34$	−11.9201	−2.04428
$35$	−0.484862	−0.0819566
$36$	17.0147	2.83578
$37$	−0.235091	−0.0386487	−0.0193244	−	0.999813i	$-0.506152\pi$
$37$	−0.235091	−0.0386487	−0.0193244	+	0.999813i	$0.506152\pi$
$38$	11.2195	1.82004
$39$	17.5298	2.80702
$40$	0.530734	0.0839165
$41$	−2.39025	−0.373295	−0.186647	−	0.982427i	$-0.559762\pi$
$41$	−2.39025	−0.373295	−0.186647	+	0.982427i	$0.559762\pi$
$42$	6.64002	1.02458
$43$	−1.03028	−0.157116	−0.0785578	−	0.996910i	$-0.525032\pi$
$43$	−1.03028	−0.157116	−0.0785578	+	0.996910i	$0.525032\pi$
$44$	0	0
$45$	3.28005	0.488961
$46$	5.28005	0.778500
$47$	−1.60975	−0.234806	−0.117403	−	0.993084i	$-0.537457\pi$
$47$	−1.60975	−0.234806	−0.117403	+	0.993084i	$0.537457\pi$
$48$	8.45080	1.21977
$49$	1.00000	0.142857
$50$	−10.1249	−1.43188
$51$	17.5298	2.45467
$52$	−14.1093	−1.95661
$53$	−3.03028	−0.416240	−0.208120	−	0.978103i	$-0.566735\pi$
$53$	−3.03028	−0.416240	−0.208120	+	0.978103i	$0.566735\pi$
$54$	−24.9991	−3.40194
$55$	0	0
$56$	−1.09461	−0.146273
$57$	−16.4995	−2.18542
$58$	−11.2195	−1.47319
$59$	3.12489	0.406825	0.203413	−	0.979093i	$-0.434797\pi$
$59$	3.12489	0.406825	0.203413	+	0.979093i	$0.434797\pi$
$60$	−3.81078	−0.491970
$61$	2.39025	0.306040	0.153020	−	0.988223i	$-0.451100\pi$
$61$	2.39025	0.306040	0.153020	+	0.988223i	$0.451100\pi$
$62$	−15.1396	−1.92273
$63$	−6.76491	−0.852298
$64$	−11.4537	−1.43171
$65$	−2.71995	−0.337369
$66$	0	0
$67$	10.0147	1.22349	0.611744	−	0.791056i	$-0.290468\pi$
$67$	10.0147	1.22349	0.611744	+	0.791056i	$0.290468\pi$
$68$	−14.1093	−1.71100
$69$	−7.76491	−0.934785
$70$	−1.03028	−0.123142
$71$	12.0752	1.43307	0.716533	−	0.697553i	$-0.245728\pi$
$71$	12.0752	1.43307	0.716533	+	0.697553i	$0.245728\pi$
$72$	7.40493	0.872680
$73$	−2.39025	−0.279758	−0.139879	−	0.990169i	$-0.544671\pi$
$73$	−2.39025	−0.279758	−0.139879	+	0.990169i	$0.544671\pi$
$74$	−0.499542	−0.0580705
$75$	14.8898	1.71933
$76$	13.2800	1.52333
$77$	0	0
$78$	37.2489	4.21760
$79$	−9.03028	−1.01599	−0.507993	−	0.861361i	$-0.669612\pi$
$79$	−9.03028	−1.01599	−0.507993	+	0.861361i	$0.669612\pi$
$80$	−1.31124	−0.146601
$81$	16.4693	1.82992
$82$	−5.07901	−0.560883
$83$	3.21949	0.353385	0.176693	−	0.984266i	$-0.443460\pi$
$83$	3.21949	0.353385	0.176693	+	0.984266i	$0.443460\pi$
$84$	7.85952	0.857544
$85$	−2.71995	−0.295020
$86$	−2.18922	−0.236070
$87$	16.4995	1.76894
$88$	0	0
$89$	−1.26537	−0.134129	−0.0670643	−	0.997749i	$-0.521363\pi$
$89$	−1.26537	−0.134129	−0.0670643	+	0.997749i	$0.521363\pi$
$90$	6.96972	0.734673
$91$	5.60975	0.588061
$92$	6.24977	0.651584
$93$	22.2645	2.30872
$94$	−3.42053	−0.352801
$95$	2.56009	0.262660
$96$	24.7980	2.53094
$97$	−8.79518	−0.893016	−0.446508	−	0.894780i	$-0.647333\pi$
$97$	−8.79518	−0.893016	−0.446508	+	0.894780i	$0.647333\pi$
$98$	2.12489	0.214646
$99$	0	0
$100$	−11.9844	−1.19844
$101$	12.9503	1.28861	0.644304	−	0.764770i	$-0.277147\pi$
$101$	12.9503	1.28861	0.644304	+	0.764770i	$0.277147\pi$
$102$	37.2489	3.68819
$103$	12.1698	1.19913	0.599565	−	0.800326i	$-0.295340\pi$
$103$	12.1698	1.19913	0.599565	+	0.800326i	$0.295340\pi$
$104$	−6.14048	−0.602124
$105$	1.51514	0.147862
$106$	−6.43899	−0.625410
$107$	−10.5601	−1.02088	−0.510441	−	0.859913i	$-0.670518\pi$
$107$	−10.5601	−1.02088	−0.510441	+	0.859913i	$0.670518\pi$
$108$	−29.5904	−2.84733
$109$	7.34060	0.703102	0.351551	−	0.936169i	$-0.385654\pi$
$109$	7.34060	0.703102	0.351551	+	0.936169i	$0.385654\pi$
$110$	0	0
$111$	0.734633	0.0697283
$112$	2.70436	0.255538
$113$	13.7649	1.29489	0.647447	−	0.762111i	$-0.275837\pi$
$113$	13.7649	1.29489	0.647447	+	0.762111i	$0.275837\pi$
$114$	−35.0596	−3.28364
$115$	1.20482	0.112350
$116$	−13.2800	−1.23302
$117$	−37.9494	−3.50843
$118$	6.64002	0.611264
$119$	5.60975	0.514245
$120$	−1.65848	−0.151398
$121$	0	0
$122$	5.07901	0.459832
$123$	7.46927	0.673481
$124$	−17.9201	−1.60927
$125$	−4.73463	−0.423478
$126$	−14.3747	−1.28060
$127$	−2.56009	−0.227172	−0.113586	−	0.993528i	$-0.536234\pi$
$127$	−2.56009	−0.227172	−0.113586	+	0.993528i	$0.536234\pi$
$128$	−8.46640	−0.748331
$129$	3.21949	0.283461
$130$	−5.77959	−0.506903
$131$	2.71995	0.237643	0.118822	−	0.992916i	$-0.462088\pi$
$131$	2.71995	0.237643	0.118822	+	0.992916i	$0.462088\pi$
$132$	0	0
$133$	−5.28005	−0.457838
$134$	21.2800	1.83832
$135$	−5.70436	−0.490953
$136$	−6.14048	−0.526542
$137$	−9.70436	−0.829099	−0.414550	−	0.910027i	$-0.636061\pi$
$137$	−9.70436	−0.829099	−0.414550	+	0.910027i	$0.636061\pi$
$138$	−16.4995	−1.40453
$139$	19.7190	1.67255	0.836273	−	0.548313i	$-0.184730\pi$
$139$	19.7190	1.67255	0.836273	+	0.548313i	$0.184730\pi$
$140$	−1.21949	−0.103066
$141$	5.03028	0.423626
$142$	25.6585	2.15321
$143$	0	0
$144$	−18.2947	−1.52456
$145$	−2.56009	−0.212604
$146$	−5.07901	−0.420342
$147$	−3.12489	−0.257736
$148$	−0.591287	−0.0486035
$149$	−10.5601	−0.865117	−0.432558	−	0.901606i	$-0.642389\pi$
$149$	−10.5601	−0.865117	−0.432558	+	0.901606i	$0.642389\pi$
$150$	31.6391	2.58332
$151$	−15.4693	−1.25887	−0.629435	−	0.777053i	$-0.716714\pi$
$151$	−15.4693	−1.25887	−0.629435	+	0.777053i	$0.716714\pi$
$152$	5.77959	0.468787
$153$	−37.9494	−3.06803
$154$	0	0
$155$	−3.45459	−0.277479
$156$	44.0899	3.53002
$157$	9.10551	0.726699	0.363349	−	0.931653i	$-0.381633\pi$
$157$	9.10551	0.726699	0.363349	+	0.931653i	$0.381633\pi$
$158$	−19.1883	−1.52654
$159$	9.46927	0.750962
$160$	−3.84770	−0.304188
$161$	−2.48486	−0.195835
$162$	34.9953	2.74949
$163$	−13.2800	−1.04017	−0.520087	−	0.854113i	$-0.674100\pi$
$163$	−13.2800	−1.04017	−0.520087	+	0.854113i	$0.674100\pi$
$164$	−6.01182	−0.469444
$165$	0	0
$166$	6.84106	0.530969
$167$	−10.0606	−0.778509	−0.389254	−	0.921130i	$-0.627267\pi$
$167$	−10.0606	−0.778509	−0.389254	+	0.921130i	$0.627267\pi$
$168$	3.42053	0.263900
$169$	18.4693	1.42071
$170$	−5.77959	−0.443274
$171$	35.7190	2.73150
$172$	−2.59129	−0.197584
$173$	8.16984	0.621142	0.310571	−	0.950550i	$-0.399480\pi$
$173$	8.16984	0.621142	0.310571	+	0.950550i	$0.399480\pi$
$174$	35.0596	2.65786
$175$	4.76491	0.360193
$176$	0	0
$177$	−9.76491	−0.733975
$178$	−2.68876	−0.201531
$179$	−12.2645	−0.916688	−0.458344	−	0.888775i	$-0.651557\pi$
$179$	−12.2645	−0.916688	−0.458344	+	0.888775i	$0.651557\pi$
$180$	8.24977	0.614902
$181$	−7.04496	−0.523647	−0.261824	−	0.965116i	$-0.584324\pi$
$181$	−7.04496	−0.523647	−0.261824	+	0.965116i	$0.584324\pi$
$182$	11.9201	0.883574
$183$	−7.46927	−0.552144
$184$	2.71995	0.200518
$185$	−0.113987	−0.00838047
$186$	47.3094	3.46889
$187$	0	0
$188$	−4.04874	−0.295284
$189$	11.7649	0.855771
$190$	5.43991	0.394652
$191$	18.7952	1.35997	0.679986	−	0.733225i	$-0.261986\pi$
$191$	18.7952	1.35997	0.679986	+	0.733225i	$0.261986\pi$
$192$	35.7914	2.58302
$193$	−16.4995	−1.18766	−0.593831	−	0.804589i	$-0.702385\pi$
$193$	−16.4995	−1.18766	−0.593831	+	0.804589i	$0.702385\pi$
$194$	−18.6888	−1.34177
$195$	8.49954	0.608665
$196$	2.51514	0.179653
$197$	−24.4995	−1.74552	−0.872760	−	0.488149i	$-0.837672\pi$
$197$	−24.4995	−1.74552	−0.872760	+	0.488149i	$0.837672\pi$
$198$	0	0
$199$	−15.3893	−1.09092	−0.545461	−	0.838136i	$-0.683645\pi$
$199$	−15.3893	−1.09092	−0.545461	+	0.838136i	$0.683645\pi$
$200$	−5.21571	−0.368807
$201$	−31.2947	−2.20736
$202$	27.5180	1.93616
$203$	5.28005	0.370587
$204$	44.0899	3.08691
$205$	−1.15894	−0.0809441
$206$	25.8595	1.80172
$207$	16.8099	1.16837
$208$	15.1708	1.05190
$209$	0	0
$210$	3.21949	0.222166
$211$	14.4390	0.994021	0.497011	−	0.867745i	$-0.334431\pi$
$211$	14.4390	0.994021	0.497011	+	0.867745i	$0.334431\pi$
$212$	−7.62156	−0.523451
$213$	−37.7337	−2.58547
$214$	−22.4390	−1.53390
$215$	−0.499542	−0.0340685
$216$	−12.8780	−0.876235
$217$	7.12489	0.483669
$218$	15.5979	1.05643
$219$	7.46927	0.504726
$220$	0	0
$221$	31.4693	2.11685
$222$	1.56101	0.104768
$223$	17.2536	1.15538	0.577692	−	0.816255i	$-0.303954\pi$
$223$	17.2536	1.15538	0.577692	+	0.816255i	$0.303954\pi$
$224$	7.93567	0.530224
$225$	−32.2342	−2.14894
$226$	29.2489	1.94560
$227$	−10.7200	−0.711508	−0.355754	−	0.934580i	$-0.615776\pi$
$227$	−10.7200	−0.711508	−0.355754	+	0.934580i	$0.615776\pi$
$228$	−41.4986	−2.74831
$229$	5.45459	0.360449	0.180225	−	0.983625i	$-0.442318\pi$
$229$	5.45459	0.360449	0.180225	+	0.983625i	$0.442318\pi$
$230$	2.56009	0.168808
$231$	0	0
$232$	−5.77959	−0.379449
$233$	−29.7796	−1.95093	−0.975463	−	0.220164i	$-0.929341\pi$
$233$	−29.7796	−1.95093	−0.975463	+	0.220164i	$0.929341\pi$
$234$	−80.6382	−5.27148
$235$	−0.780505	−0.0509145
$236$	7.85952	0.511611
$237$	28.2186	1.83299
$238$	11.9201	0.772663
$239$	−2.56009	−0.165599	−0.0827994	−	0.996566i	$-0.526386\pi$
$239$	−2.56009	−0.165599	−0.0827994	+	0.996566i	$0.526386\pi$
$240$	4.09747	0.264491
$241$	−27.3893	−1.76430	−0.882151	−	0.470966i	$-0.843905\pi$
$241$	−27.3893	−1.76430	−0.882151	+	0.470966i	$0.843905\pi$
$242$	0	0
$243$	−16.1698	−1.03730
$244$	6.01182	0.384867
$245$	0.484862	0.0309767
$246$	15.8713	1.01192
$247$	−29.6197	−1.88466
$248$	−7.79897	−0.495235
$249$	−10.0606	−0.637562
$250$	−10.0606	−0.636285
$251$	9.84484	0.621401	0.310700	−	0.950508i	$-0.399436\pi$
$251$	9.84484	0.621401	0.310700	+	0.950508i	$0.399436\pi$
$252$	−17.0147	−1.07182
$253$	0	0
$254$	−5.43991	−0.341330
$255$	8.49954	0.532262
$256$	4.91721	0.307325
$257$	−22.4995	−1.40348	−0.701741	−	0.712432i	$-0.747594\pi$
$257$	−22.4995	−1.40348	−0.701741	+	0.712432i	$0.747594\pi$
$258$	6.84106	0.425906
$259$	0.235091	0.0146079
$260$	−6.84106	−0.424264
$261$	−35.7190	−2.21095
$262$	5.77959	0.357064
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	−1.46927	−0.0902563
$266$	−11.2195	−0.687911
$267$	3.95413	0.241989
$268$	25.1883	1.53862
$269$	9.21949	0.562123	0.281061	−	0.959690i	$-0.409314\pi$
$269$	9.21949	0.562123	0.281061	+	0.959690i	$0.409314\pi$
$270$	−12.1211	−0.737667
$271$	−10.5601	−0.641480	−0.320740	−	0.947167i	$-0.603932\pi$
$271$	−10.5601	−0.641480	−0.320740	+	0.947167i	$0.603932\pi$
$272$	15.1708	0.919862
$273$	−17.5298	−1.06095
$274$	−20.6206	−1.24574
$275$	0	0
$276$	−19.5298	−1.17556
$277$	18.5601	1.11517	0.557584	−	0.830121i	$-0.311728\pi$
$277$	18.5601	1.11517	0.557584	+	0.830121i	$0.311728\pi$
$278$	41.9007	2.51304
$279$	−48.1992	−2.88561
$280$	−0.530734	−0.0317174
$281$	−25.6585	−1.53066	−0.765328	−	0.643640i	$-0.777423\pi$
$281$	−25.6585	−1.53066	−0.765328	+	0.643640i	$0.777423\pi$
$282$	10.6888	0.636506
$283$	−30.2791	−1.79991	−0.899954	−	0.435985i	$-0.856400\pi$
$283$	−30.2791	−1.79991	−0.899954	+	0.435985i	$0.856400\pi$
$284$	30.3709	1.80218
$285$	−8.00000	−0.473879
$286$	0	0
$287$	2.39025	0.141092
$288$	−53.6841	−3.16336
$289$	14.4693	0.851133
$290$	−5.43991	−0.319442
$291$	27.4839	1.61114
$292$	−6.01182	−0.351815
$293$	−3.04965	−0.178163	−0.0890813	−	0.996024i	$-0.528393\pi$
$293$	−3.04965	−0.178163	−0.0890813	+	0.996024i	$0.528393\pi$
$294$	−6.64002	−0.387254
$295$	1.51514	0.0882147
$296$	−0.257333	−0.0149572
$297$	0	0
$298$	−22.4390	−1.29986
$299$	−13.9394	−0.806139
$300$	37.4499	2.16217
$301$	1.03028	0.0593841
$302$	−32.8704	−1.89148
$303$	−40.4683	−2.32485
$304$	−14.2791	−0.818964
$305$	1.15894	0.0663609
$306$	−80.6382	−4.60978
$307$	−3.71904	−0.212257	−0.106128	−	0.994352i	$-0.533845\pi$
$307$	−3.71904	−0.212257	−0.106128	+	0.994352i	$0.533845\pi$
$308$	0	0
$309$	−38.0294	−2.16341
$310$	−7.34060	−0.416918
$311$	4.16984	0.236450	0.118225	−	0.992987i	$-0.462280\pi$
$311$	4.16984	0.236450	0.118225	+	0.992987i	$0.462280\pi$
$312$	19.1883	1.08632
$313$	−11.7044	−0.661569	−0.330785	−	0.943706i	$-0.607313\pi$
$313$	−11.7044	−0.661569	−0.330785	+	0.943706i	$0.607313\pi$
$314$	19.3482	1.09188
$315$	−3.28005	−0.184810
$316$	−22.7124	−1.27767
$317$	−2.23509	−0.125535	−0.0627676	−	0.998028i	$-0.519993\pi$
$317$	−2.23509	−0.125535	−0.0627676	+	0.998028i	$0.519993\pi$
$318$	20.1211	1.12834
$319$	0	0
$320$	−5.55345	−0.310447
$321$	32.9991	1.84183
$322$	−5.28005	−0.294246
$323$	−29.6197	−1.64809
$324$	41.4225	2.30125
$325$	26.7299	1.48271
$326$	−28.2186	−1.56288
$327$	−22.9385	−1.26850
$328$	−2.61639	−0.144466
$329$	1.60975	0.0887482
$330$	0	0
$331$	22.3250	1.22709	0.613547	−	0.789659i	$-0.289742\pi$
$331$	22.3250	1.22709	0.613547	+	0.789659i	$0.289742\pi$
$332$	8.09747	0.444407
$333$	−1.59037	−0.0871517
$334$	−21.3775	−1.16973
$335$	4.85574	0.265297
$336$	−8.45080	−0.461029
$337$	13.2800	0.723410	0.361705	−	0.932293i	$-0.382195\pi$
$337$	13.2800	0.723410	0.361705	+	0.932293i	$0.382195\pi$
$338$	39.2451	2.13465
$339$	−43.0138	−2.33619
$340$	−6.84106	−0.371008
$341$	0	0
$342$	75.8989	4.10414
$343$	−1.00000	−0.0539949
$344$	−1.12775	−0.0608042
$345$	−3.76491	−0.202696
$346$	17.3600	0.933278
$347$	18.0294	0.967867	0.483933	−	0.875105i	$-0.339208\pi$
$347$	18.0294	0.967867	0.483933	+	0.875105i	$0.339208\pi$
$348$	41.4986	2.22456
$349$	21.9494	1.17493	0.587463	−	0.809251i	$-0.300127\pi$
$349$	21.9494	1.17493	0.587463	+	0.809251i	$0.300127\pi$
$350$	10.1249	0.541198
$351$	65.9982	3.52272
$352$	0	0
$353$	18.8557	1.00359	0.501795	−	0.864987i	$-0.332673\pi$
$353$	18.8557	1.00359	0.501795	+	0.864987i	$0.332673\pi$
$354$	−20.7493	−1.10281
$355$	5.85482	0.310742
$356$	−3.18257	−0.168676
$357$	−17.5298	−0.927776
$358$	−26.0606	−1.37734
$359$	−1.52982	−0.0807407	−0.0403703	−	0.999185i	$-0.512854\pi$
$359$	−1.52982	−0.0807407	−0.0403703	+	0.999185i	$0.512854\pi$
$360$	3.59037	0.189229
$361$	8.87890	0.467310
$362$	−14.9697	−0.786791
$363$	0	0
$364$	14.1093	0.739528
$365$	−1.15894	−0.0606618
$366$	−15.8713	−0.829608
$367$	14.6547	0.764969	0.382485	−	0.923962i	$-0.375068\pi$
$367$	14.6547	0.764969	0.382485	+	0.923962i	$0.375068\pi$
$368$	−6.71995	−0.350302
$369$	−16.1698	−0.841768
$370$	−0.242209	−0.0125918
$371$	3.03028	0.157324
$372$	55.9982	2.90337
$373$	−10.0606	−0.520916	−0.260458	−	0.965485i	$-0.583873\pi$
$373$	−10.0606	−0.520916	−0.260458	+	0.965485i	$0.583873\pi$
$374$	0	0
$375$	14.7952	0.764020
$376$	−1.76204	−0.0908705
$377$	29.6197	1.52549
$378$	24.9991	1.28581
$379$	−17.8936	−0.919131	−0.459566	−	0.888144i	$-0.651995\pi$
$379$	−17.8936	−0.919131	−0.459566	+	0.888144i	$0.651995\pi$
$380$	6.43899	0.330313
$381$	8.00000	0.409852
$382$	39.9376	2.04339
$383$	−18.9650	−0.969068	−0.484534	−	0.874773i	$-0.661011\pi$
$383$	−18.9650	−0.969068	−0.484534	+	0.874773i	$0.661011\pi$
$384$	26.4565	1.35010
$385$	0	0
$386$	−35.0596	−1.78449
$387$	−6.96972	−0.354291
$388$	−22.1211	−1.12303
$389$	34.2645	1.73728	0.868638	−	0.495447i	$-0.164996\pi$
$389$	34.2645	1.73728	0.868638	+	0.495447i	$0.164996\pi$
$390$	18.0606	0.914532
$391$	−13.9394	−0.704948
$392$	1.09461	0.0552861
$393$	−8.49954	−0.428745
$394$	−52.0587	−2.62268
$395$	−4.37844	−0.220303
$396$	0	0
$397$	16.2791	0.817026	0.408513	−	0.912752i	$-0.366047\pi$
$397$	16.2791	0.817026	0.408513	+	0.912752i	$0.366047\pi$
$398$	−32.7006	−1.63913
$399$	16.4995	0.826010
$400$	12.8860	0.644301
$401$	28.9385	1.44512	0.722561	−	0.691308i	$-0.242965\pi$
$401$	28.9385	1.44512	0.722561	+	0.691308i	$0.242965\pi$
$402$	−66.4977	−3.31660
$403$	39.9688	1.99099
$404$	32.5719	1.62051
$405$	7.98532	0.396794
$406$	11.2195	0.556814
$407$	0	0
$408$	19.1883	0.949963
$409$	−15.5104	−0.766942	−0.383471	−	0.923553i	$-0.625271\pi$
$409$	−15.5104	−0.766942	−0.383471	+	0.923553i	$0.625271\pi$
$410$	−2.46262	−0.121620
$411$	30.3250	1.49582
$412$	30.6088	1.50799
$413$	−3.12489	−0.153766
$414$	35.7190	1.75549
$415$	1.56101	0.0766270
$416$	44.5171	2.18263
$417$	−61.6197	−3.01753
$418$	0	0
$419$	−12.9503	−0.632666	−0.316333	−	0.948648i	$-0.602452\pi$
$419$	−12.9503	−0.632666	−0.316333	+	0.948648i	$0.602452\pi$
$420$	3.81078	0.185947
$421$	−17.0908	−0.832956	−0.416478	−	0.909146i	$-0.636736\pi$
$421$	−17.0908	−0.832956	−0.416478	+	0.909146i	$0.636736\pi$
$422$	30.6812	1.49354
$423$	−10.8898	−0.529480
$424$	−3.31697	−0.161086
$425$	26.7299	1.29659
$426$	−80.1798	−3.88473
$427$	−2.39025	−0.115672
$428$	−26.5601	−1.28383
$429$	0	0
$430$	−1.06147	−0.0511886
$431$	−19.3482	−0.931968	−0.465984	−	0.884793i	$-0.654300\pi$
$431$	−19.3482	−0.931968	−0.465984	+	0.884793i	$0.654300\pi$
$432$	31.8165	1.53077
$433$	15.8255	0.760523	0.380262	−	0.924879i	$-0.375834\pi$
$433$	15.8255	0.760523	0.380262	+	0.924879i	$0.375834\pi$
$434$	15.1396	0.726722
$435$	8.00000	0.383571
$436$	18.4626	0.884199
$437$	13.1202	0.627624
$438$	15.8713	0.758362
$439$	11.0596	0.527848	0.263924	−	0.964544i	$-0.414983\pi$
$439$	11.0596	0.527848	0.263924	+	0.964544i	$0.414983\pi$
$440$	0	0
$441$	6.76491	0.322139
$442$	66.8686	3.18061
$443$	−34.7034	−1.64881	−0.824405	−	0.566000i	$-0.808490\pi$
$443$	−34.7034	−1.64881	−0.824405	+	0.566000i	$0.808490\pi$
$444$	1.84770	0.0876881
$445$	−0.613528	−0.0290840
$446$	36.6618	1.73599
$447$	32.9991	1.56080
$448$	11.4537	0.541135
$449$	−36.2938	−1.71281	−0.856405	−	0.516304i	$-0.827307\pi$
$449$	−36.2938	−1.71281	−0.856405	+	0.516304i	$0.827307\pi$
$450$	−68.4939	−3.22883
$451$	0	0
$452$	34.6206	1.62842
$453$	48.3397	2.27120
$454$	−22.7787	−1.06906
$455$	2.71995	0.127513
$456$	−18.0606	−0.845763
$457$	2.06055	0.0963886	0.0481943	−	0.998838i	$-0.484653\pi$
$457$	2.06055	0.0963886	0.0481943	+	0.998838i	$0.484653\pi$
$458$	11.5904	0.541582
$459$	65.9982	3.08053
$460$	3.03028	0.141287
$461$	7.17076	0.333975	0.166988	−	0.985959i	$-0.446596\pi$
$461$	7.17076	0.333975	0.166988	+	0.985959i	$0.446596\pi$
$462$	0	0
$463$	3.45459	0.160548	0.0802741	−	0.996773i	$-0.474420\pi$
$463$	3.45459	0.160548	0.0802741	+	0.996773i	$0.474420\pi$
$464$	14.2791	0.662892
$465$	10.7952	0.500615
$466$	−63.2782	−2.93131
$467$	−13.4958	−0.624509	−0.312255	−	0.949998i	$-0.601084\pi$
$467$	−13.4958	−0.624509	−0.312255	+	0.949998i	$0.601084\pi$
$468$	−95.4481	−4.41209
$469$	−10.0147	−0.462435
$470$	−1.65848	−0.0765002
$471$	−28.4537	−1.31108
$472$	3.42053	0.157443
$473$	0	0
$474$	59.9612	2.75411
$475$	−25.1589	−1.15437
$476$	14.1093	0.646698
$477$	−20.4995	−0.938610
$478$	−5.43991	−0.248816
$479$	−35.0596	−1.60192	−0.800958	−	0.598721i	$-0.795676\pi$
$479$	−35.0596	−1.60192	−0.800958	+	0.598721i	$0.795676\pi$
$480$	12.0236	0.548801
$481$	1.31880	0.0601322
$482$	−58.1992	−2.65090
$483$	7.76491	0.353316
$484$	0	0
$485$	−4.26445	−0.193639
$486$	−34.3591	−1.55856
$487$	29.6656	1.34428	0.672138	−	0.740426i	$-0.265376\pi$
$487$	29.6656	1.34428	0.672138	+	0.740426i	$0.265376\pi$
$488$	2.61639	0.118439
$489$	41.4986	1.87663
$490$	1.03028	0.0465431
$491$	−25.5298	−1.15214	−0.576072	−	0.817399i	$-0.695415\pi$
$491$	−25.5298	−1.15214	−0.576072	+	0.817399i	$0.695415\pi$
$492$	18.7862	0.846949
$493$	29.6197	1.33401
$494$	−62.9385	−2.83174
$495$	0	0
$496$	19.2682	0.865169
$497$	−12.0752	−0.541648
$498$	−21.3775	−0.957950
$499$	−25.6585	−1.14863	−0.574316	−	0.818634i	$-0.694732\pi$
$499$	−25.6585	−1.14863	−0.574316	+	0.818634i	$0.694732\pi$
$500$	−11.9083	−0.532553
$501$	31.4381	1.40455
$502$	20.9192	0.933668
$503$	−2.56009	−0.114149	−0.0570745	−	0.998370i	$-0.518177\pi$
$503$	−2.56009	−0.114149	−0.0570745	+	0.998370i	$0.518177\pi$
$504$	−7.40493	−0.329842
$505$	6.27913	0.279418
$506$	0	0
$507$	−57.7143	−2.56318
$508$	−6.43899	−0.285684
$509$	13.4546	0.596364	0.298182	−	0.954509i	$-0.403620\pi$
$509$	13.4546	0.596364	0.298182	+	0.954509i	$0.403620\pi$
$510$	18.0606	0.799735
$511$	2.39025	0.105739
$512$	27.3813	1.21009
$513$	−62.1193	−2.74263
$514$	−47.8089	−2.10876
$515$	5.90069	0.260016
$516$	8.09747	0.356471
$517$	0	0
$518$	0.499542	0.0219486
$519$	−25.5298	−1.12063
$520$	−2.97729	−0.130563
$521$	−32.2333	−1.41216	−0.706082	−	0.708130i	$-0.749539\pi$
$521$	−32.2333	−1.41216	−0.706082	+	0.708130i	$0.749539\pi$
$522$	−75.8989	−3.32200
$523$	32.3397	1.41412	0.707058	−	0.707156i	$-0.250022\pi$
$523$	32.3397	1.41412	0.707058	+	0.707156i	$0.250022\pi$
$524$	6.84106	0.298853
$525$	−14.8898	−0.649844
$526$	33.9982	1.48239
$527$	39.9688	1.74107
$528$	0	0
$529$	−16.8255	−0.731542
$530$	−3.12202	−0.135612
$531$	21.1396	0.917379
$532$	−13.2800	−0.575763
$533$	13.4087	0.580796
$534$	8.40207	0.363593
$535$	−5.12019	−0.221365
$536$	10.9622	0.473493
$537$	38.3250	1.65385
$538$	19.5904	0.844601
$539$	0	0
$540$	−14.3472	−0.617407
$541$	23.5005	1.01036	0.505182	−	0.863013i	$-0.331425\pi$
$541$	23.5005	1.01036	0.505182	+	0.863013i	$0.331425\pi$
$542$	−22.4390	−0.963837
$543$	22.0147	0.944740
$544$	44.5171	1.90865
$545$	3.55918	0.152458
$546$	−37.2489	−1.59410
$547$	4.12110	0.176206	0.0881028	−	0.996111i	$-0.471920\pi$
$547$	4.12110	0.176206	0.0881028	+	0.996111i	$0.471920\pi$
$548$	−24.4078	−1.04265
$549$	16.1698	0.690112
$550$	0	0
$551$	−27.8789	−1.18768
$552$	−8.49954	−0.361765
$553$	9.03028	0.384006
$554$	39.4381	1.67556
$555$	0.356195	0.0151197
$556$	49.5961	2.10334
$557$	13.9394	0.590633	0.295317	−	0.955399i	$-0.404575\pi$
$557$	13.9394	0.590633	0.295317	+	0.955399i	$0.404575\pi$
$558$	−102.418	−4.33569
$559$	5.77959	0.244451
$560$	1.31124	0.0554100
$561$	0	0
$562$	−54.5213	−2.29984
$563$	−2.71995	−0.114632	−0.0573162	−	0.998356i	$-0.518254\pi$
$563$	−2.71995	−0.114632	−0.0573162	+	0.998356i	$0.518254\pi$
$564$	12.6518	0.532739
$565$	6.67408	0.280781
$566$	−64.3397	−2.70440
$567$	−16.4693	−0.691644
$568$	13.2177	0.554601
$569$	27.7190	1.16204	0.581021	−	0.813888i	$-0.302653\pi$
$569$	27.7190	1.16204	0.581021	+	0.813888i	$0.302653\pi$
$570$	−16.9991	−0.712013
$571$	−38.1193	−1.59524	−0.797621	−	0.603159i	$-0.793908\pi$
$571$	−38.1193	−1.59524	−0.797621	+	0.603159i	$0.793908\pi$
$572$	0	0
$573$	−58.7328	−2.45360
$574$	5.07901	0.211994
$575$	−11.8401	−0.493768
$576$	−77.4830	−3.22846
$577$	23.2048	0.966029	0.483015	−	0.875612i	$-0.339542\pi$
$577$	23.2048	0.966029	0.483015	+	0.875612i	$0.339542\pi$
$578$	30.7455	1.27885
$579$	51.5592	2.14273
$580$	−6.43899	−0.267364
$581$	−3.21949	−0.133567
$582$	58.4002	2.42077
$583$	0	0
$584$	−2.61639	−0.108267
$585$	−18.4002	−0.760756
$586$	−6.48016	−0.267693
$587$	−11.0497	−0.456068	−0.228034	−	0.973653i	$-0.573230\pi$
$587$	−11.0497	−0.456068	−0.228034	+	0.973653i	$0.573230\pi$
$588$	−7.85952	−0.324121
$589$	−37.6197	−1.55009
$590$	3.21949	0.132545
$591$	76.5583	3.14919
$592$	0.635770	0.0261300
$593$	36.3884	1.49429	0.747147	−	0.664659i	$-0.231423\pi$
$593$	36.3884	1.49429	0.747147	+	0.664659i	$0.231423\pi$
$594$	0	0
$595$	2.71995	0.111507
$596$	−26.5601	−1.08794
$597$	48.0899	1.96819
$598$	−29.6197	−1.21124
$599$	29.6585	1.21181	0.605906	−	0.795536i	$-0.292811\pi$
$599$	29.6585	1.21181	0.605906	+	0.795536i	$0.292811\pi$
$600$	16.2985	0.665384
$601$	−1.39117	−0.0567470	−0.0283735	−	0.999597i	$-0.509033\pi$
$601$	−1.39117	−0.0567470	−0.0283735	+	0.999597i	$0.509033\pi$
$602$	2.18922	0.0892259
$603$	67.7484	2.75893
$604$	−38.9073	−1.58312
$605$	0	0
$606$	−85.9906	−3.49313
$607$	−30.9385	−1.25576	−0.627878	−	0.778312i	$-0.716076\pi$
$607$	−30.9385	−1.25576	−0.627878	+	0.778312i	$0.716076\pi$
$608$	−41.9007	−1.69930
$609$	−16.4995	−0.668595
$610$	2.46262	0.0997086
$611$	9.03028	0.365326
$612$	−95.4481	−3.85826
$613$	−8.15986	−0.329574	−0.164787	−	0.986329i	$-0.552694\pi$
$613$	−8.15986	−0.329574	−0.164787	+	0.986329i	$0.552694\pi$
$614$	−7.90253	−0.318920
$615$	3.62156	0.146036
$616$	0	0
$617$	−27.5298	−1.10831	−0.554154	−	0.832414i	$-0.686958\pi$
$617$	−27.5298	−1.10831	−0.554154	+	0.832414i	$0.686958\pi$
$618$	−80.8080	−3.25058
$619$	19.9735	0.802803	0.401401	−	0.915902i	$-0.368523\pi$
$619$	19.9735	0.802803	0.401401	+	0.915902i	$0.368523\pi$
$620$	−8.68876	−0.348949
$621$	−29.2342	−1.17313
$622$	8.86043	0.355271
$623$	1.26537	0.0506959
$624$	−47.4069	−1.89779
$625$	21.5289	0.861156
$626$	−24.8704	−0.994022
$627$	0	0
$628$	22.9016	0.913874
$629$	1.31880	0.0525841
$630$	−6.96972	−0.277680
$631$	−17.2342	−0.686082	−0.343041	−	0.939320i	$-0.611457\pi$
$631$	−17.2342	−0.686082	−0.343041	+	0.939320i	$0.611457\pi$
$632$	−9.88462	−0.393189
$633$	−45.1202	−1.79337
$634$	−4.74931	−0.188619
$635$	−1.24129	−0.0492592
$636$	23.8165	0.944386
$637$	−5.60975	−0.222266
$638$	0	0
$639$	81.6878	3.23152
$640$	−4.10504	−0.162266
$641$	−44.4149	−1.75428	−0.877142	−	0.480231i	$-0.840553\pi$
$641$	−44.4149	−1.75428	−0.877142	+	0.480231i	$0.840553\pi$
$642$	70.1193	2.76739
$643$	−22.5336	−0.888638	−0.444319	−	0.895869i	$-0.646554\pi$
$643$	−22.5336	−0.888638	−0.444319	+	0.895869i	$0.646554\pi$
$644$	−6.24977	−0.246275
$645$	1.56101	0.0614647
$646$	−62.9385	−2.47628
$647$	−18.7758	−0.738153	−0.369077	−	0.929399i	$-0.620326\pi$
$647$	−18.7758	−0.738153	−0.369077	+	0.929399i	$0.620326\pi$
$648$	18.0274	0.708184
$649$	0	0
$650$	56.7980	2.22780
$651$	−22.2645	−0.872613
$652$	−33.4012	−1.30809
$653$	31.6126	1.23710	0.618549	−	0.785747i	$-0.287721\pi$
$653$	31.6126	1.23710	0.618549	+	0.785747i	$0.287721\pi$
$654$	−48.7418	−1.90595
$655$	1.31880	0.0515298
$656$	6.46410	0.252381
$657$	−16.1698	−0.630846
$658$	3.42053	0.133346
$659$	−19.8477	−0.773157	−0.386578	−	0.922257i	$-0.626343\pi$
$659$	−19.8477	−0.773157	−0.386578	+	0.922257i	$0.626343\pi$
$660$	0	0
$661$	31.4234	1.22223	0.611114	−	0.791542i	$-0.290722\pi$
$661$	31.4234	1.22223	0.611114	+	0.791542i	$0.290722\pi$
$662$	47.4381	1.84373
$663$	−98.3378	−3.81913
$664$	3.52409	0.136761
$665$	−2.56009	−0.0992762
$666$	−3.37935	−0.130947
$667$	−13.1202	−0.508016
$668$	−25.3037	−0.979029
$669$	−53.9154	−2.08449
$670$	10.3179	0.398615
$671$	0	0
$672$	−24.7980	−0.956606
$673$	19.2195	0.740857	0.370429	−	0.928861i	$-0.379211\pi$
$673$	19.2195	0.740857	0.370429	+	0.928861i	$0.379211\pi$
$674$	28.2186	1.08694
$675$	56.0587	2.15770
$676$	46.4528	1.78664
$677$	−25.7309	−0.988917	−0.494458	−	0.869201i	$-0.664634\pi$
$677$	−25.7309	−0.988917	−0.494458	+	0.869201i	$0.664634\pi$
$678$	−91.3993	−3.51017
$679$	8.79518	0.337528
$680$	−2.97729	−0.114174
$681$	33.4986	1.28367
$682$	0	0
$683$	−11.0596	−0.423185	−0.211593	−	0.977358i	$-0.567865\pi$
$683$	−11.0596	−0.423185	−0.211593	+	0.977358i	$0.567865\pi$
$684$	89.8383	3.43505
$685$	−4.70527	−0.179779
$686$	−2.12489	−0.0811285
$687$	−17.0450	−0.650306
$688$	2.78623	0.106224
$689$	16.9991	0.647613
$690$	−8.00000	−0.304555
$691$	45.0256	1.71285	0.856427	−	0.516268i	$-0.172679\pi$
$691$	45.0256	1.71285	0.856427	+	0.516268i	$0.172679\pi$
$692$	20.5483	0.781128
$693$	0	0
$694$	38.3103	1.45424
$695$	9.56101	0.362670
$696$	18.0606	0.684583
$697$	13.4087	0.507891
$698$	46.6400	1.76535
$699$	93.0578	3.51977
$700$	11.9844	0.452968
$701$	−46.7787	−1.76681	−0.883403	−	0.468614i	$-0.844754\pi$
$701$	−46.7787	−1.76681	−0.883403	+	0.468614i	$0.844754\pi$
$702$	140.239	5.29296
$703$	−1.24129	−0.0468162
$704$	0	0
$705$	2.43899	0.0918577
$706$	40.0663	1.50791
$707$	−12.9503	−0.487048
$708$	−24.5601	−0.923025
$709$	−9.14426	−0.343420	−0.171710	−	0.985148i	$-0.554929\pi$
$709$	−9.14426	−0.343420	−0.171710	+	0.985148i	$0.554929\pi$
$710$	12.4408	0.466896
$711$	−61.0890	−2.29102
$712$	−1.38508	−0.0519082
$713$	−17.7044	−0.663033
$714$	−37.2489	−1.39400
$715$	0	0
$716$	−30.8468	−1.15280
$717$	8.00000	0.298765
$718$	−3.25069	−0.121315
$719$	−30.4655	−1.13617	−0.568085	−	0.822970i	$-0.692316\pi$
$719$	−30.4655	−1.13617	−0.568085	+	0.822970i	$0.692316\pi$
$720$	−8.87042	−0.330581
$721$	−12.1698	−0.453229
$722$	18.8666	0.702143
$723$	85.5885	3.18307
$724$	−17.7190	−0.658523
$725$	25.1589	0.934380
$726$	0	0
$727$	−6.12580	−0.227193	−0.113597	−	0.993527i	$-0.536237\pi$
$727$	−6.12580	−0.227193	−0.113597	+	0.993527i	$0.536237\pi$
$728$	6.14048	0.227581
$729$	1.12110	0.0415224
$730$	−2.46262	−0.0911457
$731$	5.77959	0.213766
$732$	−18.7862	−0.694359
$733$	42.0705	1.55391	0.776955	−	0.629556i	$-0.216763\pi$
$733$	42.0705	1.55391	0.776955	+	0.629556i	$0.216763\pi$
$734$	31.1396	1.14938
$735$	−1.51514	−0.0558867
$736$	−19.7190	−0.726853
$737$	0	0
$738$	−34.3591	−1.26477
$739$	28.8780	1.06229	0.531147	−	0.847280i	$-0.321761\pi$
$739$	28.8780	1.06229	0.531147	+	0.847280i	$0.321761\pi$
$740$	−0.286692	−0.0105390
$741$	92.5583	3.40021
$742$	6.43899	0.236383
$743$	14.6812	0.538601	0.269300	−	0.963056i	$-0.413208\pi$
$743$	14.6812	0.538601	0.269300	+	0.963056i	$0.413208\pi$
$744$	24.3709	0.893480
$745$	−5.12019	−0.187589
$746$	−21.3775	−0.782687
$747$	21.7796	0.796873
$748$	0	0
$749$	10.5601	0.385857
$750$	31.4381	1.14796
$751$	−6.60597	−0.241055	−0.120528	−	0.992710i	$-0.538459\pi$
$751$	−6.60597	−0.241055	−0.120528	+	0.992710i	$0.538459\pi$
$752$	4.35333	0.158750
$753$	−30.7640	−1.12110
$754$	62.9385	2.29209
$755$	−7.50046	−0.272970
$756$	29.5904	1.07619
$757$	2.49954	0.0908474	0.0454237	−	0.998968i	$-0.485536\pi$
$757$	2.49954	0.0908474	0.0454237	+	0.998968i	$0.485536\pi$
$758$	−38.0218	−1.38101
$759$	0	0
$760$	2.80230	0.101650
$761$	12.0487	0.436766	0.218383	−	0.975863i	$-0.429922\pi$
$761$	12.0487	0.436766	0.218383	+	0.975863i	$0.429922\pi$
$762$	16.9991	0.615812
$763$	−7.34060	−0.265748
$764$	47.2725	1.71026
$765$	−18.4002	−0.665262
$766$	−40.2985	−1.45604
$767$	−17.5298	−0.632965
$768$	−15.3657	−0.554462
$769$	−0.489560	−0.0176540	−0.00882699	−	0.999961i	$-0.502810\pi$
$769$	−0.489560	−0.0176540	−0.00882699	+	0.999961i	$0.502810\pi$
$770$	0	0
$771$	70.3085	2.53210
$772$	−41.4986	−1.49357
$773$	−46.7181	−1.68033	−0.840167	−	0.542328i	$-0.817543\pi$
$773$	−46.7181	−1.68033	−0.840167	+	0.542328i	$0.817543\pi$
$774$	−14.8099	−0.532330
$775$	33.9494	1.21950
$776$	−9.62729	−0.345600
$777$	−0.734633	−0.0263548
$778$	72.8080	2.61029
$779$	−12.6206	−0.452182
$780$	21.3775	0.765438
$781$	0	0
$782$	−29.6197	−1.05920
$783$	62.1193	2.21996
$784$	−2.70436	−0.0965842
$785$	4.41491	0.157575
$786$	−18.0606	−0.644199
$787$	8.33968	0.297278	0.148639	−	0.988892i	$-0.452511\pi$
$787$	8.33968	0.297278	0.148639	+	0.988892i	$0.452511\pi$
$788$	−61.6197	−2.19511
$789$	−49.9982	−1.77998
$790$	−9.30368	−0.331010
$791$	−13.7649	−0.489424
$792$	0	0
$793$	−13.4087	−0.476157
$794$	34.5913	1.22760
$795$	4.59129	0.162836
$796$	−38.7063	−1.37191
$797$	−31.5151	−1.11632	−0.558162	−	0.829732i	$-0.688493\pi$
$797$	−31.5151	−1.11632	−0.558162	+	0.829732i	$0.688493\pi$
$798$	35.0596	1.24110
$799$	9.03028	0.319468
$800$	37.8127	1.33688
$801$	−8.56009	−0.302456
$802$	61.4911	2.17132
$803$	0	0
$804$	−78.7106	−2.77591
$805$	−1.20482	−0.0424641
$806$	84.9291	2.99150
$807$	−28.8099	−1.01416
$808$	14.1756	0.498695
$809$	−15.5005	−0.544967	−0.272484	−	0.962160i	$-0.587845\pi$
$809$	−15.5005	−0.544967	−0.272484	+	0.962160i	$0.587845\pi$
$810$	16.9679	0.596191
$811$	48.3397	1.69744	0.848718	−	0.528846i	$-0.177375\pi$
$811$	48.3397	1.69744	0.848718	+	0.528846i	$0.177375\pi$
$812$	13.2800	0.466038
$813$	32.9991	1.15733
$814$	0	0
$815$	−6.43899	−0.225548
$816$	−47.4069	−1.65957
$817$	−5.43991	−0.190318
$818$	−32.9579	−1.15235
$819$	37.9494	1.32606
$820$	−2.91490	−0.101793
$821$	10.5601	0.368550	0.184275	−	0.982875i	$-0.441006\pi$
$821$	10.5601	0.368550	0.184275	+	0.982875i	$0.441006\pi$
$822$	64.4372	2.24750
$823$	19.3241	0.673595	0.336798	−	0.941577i	$-0.390656\pi$
$823$	19.3241	0.673595	0.336798	+	0.941577i	$0.390656\pi$
$824$	13.3212	0.464067
$825$	0	0
$826$	−6.64002	−0.231036
$827$	0.530734	0.0184554	0.00922772	−	0.999957i	$-0.497063\pi$
$827$	0.530734	0.0184554	0.00922772	+	0.999957i	$0.497063\pi$
$828$	42.2791	1.46930
$829$	−47.1954	−1.63916	−0.819582	−	0.572961i	$-0.805794\pi$
$829$	−47.1954	−1.63916	−0.819582	+	0.572961i	$0.805794\pi$
$830$	3.31697	0.115134
$831$	−57.9982	−2.01193
$832$	64.2522	2.22754
$833$	−5.60975	−0.194366
$834$	−130.935	−4.53390
$835$	−4.87798	−0.168809
$836$	0	0
$837$	83.8236	2.89737
$838$	−27.5180	−0.950594
$839$	−37.9036	−1.30858	−0.654288	−	0.756245i	$-0.727032\pi$
$839$	−37.9036	−1.30858	−0.654288	+	0.756245i	$0.727032\pi$
$840$	1.65848	0.0572231
$841$	−1.12110	−0.0386588
$842$	−36.3161	−1.25153
$843$	80.1798	2.76154
$844$	36.3161	1.25005
$845$	8.95504	0.308063
$846$	−23.1396	−0.795555
$847$	0	0
$848$	8.19495	0.281416
$849$	94.6188	3.24731
$850$	56.7980	1.94816
$851$	−0.584169	−0.0200251
$852$	−94.9055	−3.25141
$853$	6.26915	0.214652	0.107326	−	0.994224i	$-0.465771\pi$
$853$	6.26915	0.214652	0.107326	+	0.994224i	$0.465771\pi$
$854$	−5.07901	−0.173800
$855$	17.3188	0.592291
$856$	−11.5592	−0.395085
$857$	−36.9503	−1.26220	−0.631100	−	0.775702i	$-0.717396\pi$
$857$	−36.9503	−1.26220	−0.631100	+	0.775702i	$0.717396\pi$
$858$	0	0
$859$	8.90447	0.303817	0.151908	−	0.988395i	$-0.451458\pi$
$859$	8.90447	0.303817	0.151908	+	0.988395i	$0.451458\pi$
$860$	−1.25642	−0.0428434
$861$	−7.46927	−0.254552
$862$	−41.1126	−1.40030
$863$	−42.1193	−1.43376	−0.716878	−	0.697198i	$-0.754430\pi$
$863$	−42.1193	−1.43376	−0.716878	+	0.697198i	$0.754430\pi$
$864$	93.3624	3.17625
$865$	3.96125	0.134686
$866$	33.6273	1.14270
$867$	−45.2148	−1.53558
$868$	17.9201	0.608247
$869$	0	0
$870$	16.9991	0.576323
$871$	−56.1798	−1.90358
$872$	8.03509	0.272102
$873$	−59.4986	−2.01372
$874$	27.8789	0.943018
$875$	4.73463	0.160060
$876$	18.7862	0.634728
$877$	−24.3397	−0.821893	−0.410946	−	0.911660i	$-0.634802\pi$
$877$	−24.3397	−0.821893	−0.410946	+	0.911660i	$0.634802\pi$
$878$	23.5005	0.793102
$879$	9.52982	0.321433
$880$	0	0
$881$	5.64380	0.190145	0.0950723	−	0.995470i	$-0.469692\pi$
$881$	5.64380	0.190145	0.0950723	+	0.995470i	$0.469692\pi$
$882$	14.3747	0.484020
$883$	15.1807	0.510873	0.255436	−	0.966826i	$-0.417781\pi$
$883$	15.1807	0.510873	0.255436	+	0.966826i	$0.417781\pi$
$884$	79.1495	2.66209
$885$	−4.73463	−0.159153
$886$	−73.7408	−2.47737
$887$	−26.8174	−0.900441	−0.450221	−	0.892917i	$-0.648655\pi$
$887$	−26.8174	−0.900441	−0.450221	+	0.892917i	$0.648655\pi$
$888$	0.804136	0.0269850
$889$	2.56009	0.0858628
$890$	−1.30368	−0.0436994
$891$	0	0
$892$	43.3951	1.45297
$893$	−8.49954	−0.284426
$894$	70.1193	2.34514
$895$	−5.94657	−0.198772
$896$	8.46640	0.282843
$897$	43.5592	1.45440
$898$	−77.1202	−2.57353
$899$	37.6197	1.25469
$900$	−81.0734	−2.70245
$901$	16.9991	0.566322
$902$	0	0
$903$	−3.21949	−0.107138
$904$	15.0672	0.501128
$905$	−3.41583	−0.113546
$906$	102.716	3.41252
$907$	32.0975	1.06578	0.532890	−	0.846185i	$-0.321106\pi$
$907$	32.0975	1.06578	0.532890	+	0.846185i	$0.321106\pi$
$908$	−26.9622	−0.894771
$909$	87.6079	2.90577
$910$	5.77959	0.191591
$911$	12.1599	0.402874	0.201437	−	0.979501i	$-0.435439\pi$
$911$	12.1599	0.402874	0.201437	+	0.979501i	$0.435439\pi$
$912$	44.6206	1.47754
$913$	0	0
$914$	4.37844	0.144826
$915$	−3.62156	−0.119725
$916$	13.7190	0.453290
$917$	−2.71995	−0.0898208
$918$	140.239	4.62856
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	1.31880	0.0434796
$921$	11.6216	0.382944
$922$	15.2370	0.501805
$923$	−67.7390	−2.22966
$924$	0	0
$925$	1.12019	0.0368315
$926$	7.34060	0.241227
$927$	82.3279	2.70400
$928$	41.9007	1.37546
$929$	−21.3794	−0.701434	−0.350717	−	0.936482i	$-0.614062\pi$
$929$	−21.3794	−0.701434	−0.350717	+	0.936482i	$0.614062\pi$
$930$	22.9385	0.752184
$931$	5.28005	0.173047
$932$	−74.8998	−2.45342
$933$	−13.0303	−0.426592
$934$	−28.6769	−0.938338
$935$	0	0
$936$	−41.5398	−1.35777
$937$	31.5104	1.02940	0.514701	−	0.857370i	$-0.327903\pi$
$937$	31.5104	1.02940	0.514701	+	0.857370i	$0.327903\pi$
$938$	−21.2800	−0.694818
$939$	36.5748	1.19357
$940$	−1.96308	−0.0640286
$941$	−42.7299	−1.39296	−0.696478	−	0.717578i	$-0.745251\pi$
$941$	−42.7299	−1.39296	−0.696478	+	0.717578i	$0.745251\pi$
$942$	−60.4608	−1.96992
$943$	−5.93945	−0.193415
$944$	−8.45080	−0.275050
$945$	5.70436	0.185563
$946$	0	0
$947$	3.29473	0.107064	0.0535321	−	0.998566i	$-0.482952\pi$
$947$	3.29473	0.107064	0.0535321	+	0.998566i	$0.482952\pi$
$948$	70.9736	2.30512
$949$	13.4087	0.435265
$950$	−53.4599	−1.73447
$951$	6.98440	0.226485
$952$	6.14048	0.199014
$953$	−38.6812	−1.25301	−0.626503	−	0.779419i	$-0.715515\pi$
$953$	−38.6812	−1.25301	−0.626503	+	0.779419i	$0.715515\pi$
$954$	−43.5592	−1.41028
$955$	9.11307	0.294892
$956$	−6.43899	−0.208252
$957$	0	0
$958$	−74.4977	−2.40691
$959$	9.70436	0.313370
$960$	17.3539	0.560094
$961$	19.7640	0.637548
$962$	2.80230	0.0903499
$963$	−71.4381	−2.30206
$964$	−68.8880	−2.21873
$965$	−8.00000	−0.257529
$966$	16.4995	0.530864
$967$	3.34816	0.107670	0.0538348	−	0.998550i	$-0.482856\pi$
$967$	3.34816	0.107670	0.0538348	+	0.998550i	$0.482856\pi$
$968$	0	0
$969$	92.5583	2.97340
$970$	−9.06147	−0.290946
$971$	58.7134	1.88420	0.942102	−	0.335327i	$-0.108847\pi$
$971$	58.7134	1.88420	0.942102	+	0.335327i	$0.108847\pi$
$972$	−40.6694	−1.30447
$973$	−19.7190	−0.632163
$974$	63.0360	2.01980
$975$	−83.5280	−2.67504
$976$	−6.46410	−0.206911
$977$	13.7649	0.440378	0.220189	−	0.975457i	$-0.429333\pi$
$977$	13.7649	0.440378	0.220189	+	0.975457i	$0.429333\pi$
$978$	88.1798	2.81968
$979$	0	0
$980$	1.21949	0.0389553
$981$	49.6585	1.58547
$982$	−54.2479	−1.73112
$983$	50.2139	1.60157	0.800787	−	0.598949i	$-0.204415\pi$
$983$	50.2139	1.60157	0.800787	+	0.598949i	$0.204415\pi$
$984$	8.17593	0.260639
$985$	−11.8789	−0.378493
$986$	62.9385	2.00437
$987$	−5.03028	−0.160115
$988$	−74.4977	−2.37009
$989$	−2.56009	−0.0814062
$990$	0	0
$991$	−4.65940	−0.148011	−0.0740054	−	0.997258i	$-0.523578\pi$
$991$	−4.65940	−0.148011	−0.0740054	+	0.997258i	$0.523578\pi$
$992$	56.5407	1.79517
$993$	−69.7631	−2.21386
$994$	−25.6585	−0.813838
$995$	−7.46170	−0.236552
$996$	−25.3037	−0.801778
$997$	−3.38934	−0.107341	−0.0536707	−	0.998559i	$-0.517092\pi$
$997$	−3.38934	−0.107341	−0.0536707	+	0.998559i	$0.517092\pi$
$998$	−54.5213	−1.72584
$999$	2.76583	0.0875068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.a.i.1.3	✓	3
3.2	odd	2		7623.2.a.ce.1.1		3
7.6	odd	2		5929.2.a.t.1.3		3
11.2	odd	10		847.2.f.t.323.3		12
11.3	even	5		847.2.f.u.372.3		12
11.4	even	5		847.2.f.u.148.3		12
11.5	even	5		847.2.f.u.729.1		12
11.6	odd	10		847.2.f.t.729.3		12
11.7	odd	10		847.2.f.t.148.1		12
11.8	odd	10		847.2.f.t.372.1		12
11.9	even	5		847.2.f.u.323.1		12
11.10	odd	2		847.2.a.j.1.1	yes	3
33.32	even	2		7623.2.a.bz.1.3		3
77.76	even	2		5929.2.a.y.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.i.1.3	✓	3	1.1	even	1	trivial
847.2.a.j.1.1	yes	3	11.10	odd	2
847.2.f.t.148.1		12	11.7	odd	10
847.2.f.t.323.3		12	11.2	odd	10
847.2.f.t.372.1		12	11.8	odd	10
847.2.f.t.729.3		12	11.6	odd	10
847.2.f.u.148.3		12	11.4	even	5
847.2.f.u.323.1		12	11.9	even	5
847.2.f.u.372.3		12	11.3	even	5
847.2.f.u.729.1		12	11.5	even	5
5929.2.a.t.1.3		3	7.6	odd	2
5929.2.a.y.1.1		3	77.76	even	2
7623.2.a.bz.1.3		3	33.32	even	2
7623.2.a.ce.1.1		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

\(f(q)\)	\(=\)	\(q+2.12489 q^{2} -3.12489 q^{3} +2.51514 q^{4} +0.484862 q^{5} -6.64002 q^{6} -1.00000 q^{7} +1.09461 q^{8} +6.76491 q^{9} +O(q^{10})\)	\(q+2.12489 q^{2} -3.12489 q^{3} +2.51514 q^{4} +0.484862 q^{5} -6.64002 q^{6} -1.00000 q^{7} +1.09461 q^{8} +6.76491 q^{9} +1.03028 q^{10} -7.85952 q^{12} -5.60975 q^{13} -2.12489 q^{14} -1.51514 q^{15} -2.70436 q^{16} -5.60975 q^{17} +14.3747 q^{18} +5.28005 q^{19} +1.21949 q^{20} +3.12489 q^{21} +2.48486 q^{23} -3.42053 q^{24} -4.76491 q^{25} -11.9201 q^{26} -11.7649 q^{27} -2.51514 q^{28} -5.28005 q^{29} -3.21949 q^{30} -7.12489 q^{31} -7.93567 q^{32} -11.9201 q^{34} -0.484862 q^{35} +17.0147 q^{36} -0.235091 q^{37} +11.2195 q^{38} +17.5298 q^{39} +0.530734 q^{40} -2.39025 q^{41} +6.64002 q^{42} -1.03028 q^{43} +3.28005 q^{45} +5.28005 q^{46} -1.60975 q^{47} +8.45080 q^{48} +1.00000 q^{49} -10.1249 q^{50} +17.5298 q^{51} -14.1093 q^{52} -3.03028 q^{53} -24.9991 q^{54} -1.09461 q^{56} -16.4995 q^{57} -11.2195 q^{58} +3.12489 q^{59} -3.81078 q^{60} +2.39025 q^{61} -15.1396 q^{62} -6.76491 q^{63} -11.4537 q^{64} -2.71995 q^{65} +10.0147 q^{67} -14.1093 q^{68} -7.76491 q^{69} -1.03028 q^{70} +12.0752 q^{71} +7.40493 q^{72} -2.39025 q^{73} -0.499542 q^{74} +14.8898 q^{75} +13.2800 q^{76} +37.2489 q^{78} -9.03028 q^{79} -1.31124 q^{80} +16.4693 q^{81} -5.07901 q^{82} +3.21949 q^{83} +7.85952 q^{84} -2.71995 q^{85} -2.18922 q^{86} +16.4995 q^{87} -1.26537 q^{89} +6.96972 q^{90} +5.60975 q^{91} +6.24977 q^{92} +22.2645 q^{93} -3.42053 q^{94} +2.56009 q^{95} +24.7980 q^{96} -8.79518 q^{97} +2.12489 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9	\( 3 q - 2 q^{2} - q^{3} + 8 q^{4} + q^{5} - 12 q^{6} - 3 q^{7} - 6 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{12} - 8 q^{13} + 2 q^{14} - 5 q^{15} + 10 q^{16} - 8 q^{17} + 18 q^{18} - 14 q^{20} + q^{21} + 7 q^{23} - 20 q^{24} + 2 q^{25} - 12 q^{26} - 19 q^{27} - 8 q^{28} + 8 q^{30} - 13 q^{31} - 34 q^{32} - 12 q^{34} - q^{35} + 18 q^{36} - 17 q^{37} + 16 q^{38} + 20 q^{39} + 36 q^{40} - 16 q^{41} + 12 q^{42} - 4 q^{43} - 6 q^{45} + 4 q^{47} + 36 q^{48} + 3 q^{49} - 22 q^{50} + 20 q^{51} - 10 q^{53} - 8 q^{54} + 6 q^{56} - 16 q^{57} - 16 q^{58} + q^{59} - 30 q^{60} + 16 q^{61} - 4 q^{62} - 4 q^{63} + 34 q^{64} - 24 q^{65} - 3 q^{67} - 7 q^{69} - 4 q^{70} + 5 q^{71} - 2 q^{72} - 16 q^{73} + 32 q^{74} + 20 q^{75} + 24 q^{76} + 28 q^{78} - 28 q^{79} - 56 q^{80} + 15 q^{81} + 28 q^{82} - 8 q^{83} - 2 q^{84} - 24 q^{85} + 12 q^{86} + 16 q^{87} - 21 q^{89} + 20 q^{90} + 8 q^{91} + 2 q^{92} + 17 q^{93} - 20 q^{94} - 24 q^{95} - 20 q^{96} - 11 q^{97} - 2 q^{98}+O(q^{100}) \) 3 * q - 2 * q^2 - q^3 + 8 * q^4 + q^5 - 12 * q^6 - 3 * q^7 - 6 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^12 - 8 * q^13 + 2 * q^14 - 5 * q^15 + 10 * q^16 - 8 * q^17 + 18 * q^18 - 14 * q^20 + q^21 + 7 * q^23 - 20 * q^24 + 2 * q^25 - 12 * q^26 - 19 * q^27 - 8 * q^28 + 8 * q^30 - 13 * q^31 - 34 * q^32 - 12 * q^34 - q^35 + 18 * q^36 - 17 * q^37 + 16 * q^38 + 20 * q^39 + 36 * q^40 - 16 * q^41 + 12 * q^42 - 4 * q^43 - 6 * q^45 + 4 * q^47 + 36 * q^48 + 3 * q^49 - 22 * q^50 + 20 * q^51 - 10 * q^53 - 8 * q^54 + 6 * q^56 - 16 * q^57 - 16 * q^58 + q^59 - 30 * q^60 + 16 * q^61 - 4 * q^62 - 4 * q^63 + 34 * q^64 - 24 * q^65 - 3 * q^67 - 7 * q^69 - 4 * q^70 + 5 * q^71 - 2 * q^72 - 16 * q^73 + 32 * q^74 + 20 * q^75 + 24 * q^76 + 28 * q^78 - 28 * q^79 - 56 * q^80 + 15 * q^81 + 28 * q^82 - 8 * q^83 - 2 * q^84 - 24 * q^85 + 12 * q^86 + 16 * q^87 - 21 * q^89 + 20 * q^90 + 8 * q^91 + 2 * q^92 + 17 * q^93 - 20 * q^94 - 24 * q^95 - 20 * q^96 - 11 * q^97 - 2 * q^98

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