LMFDB - Embedded newform 2678.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2678,2,Mod(1,2678)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2678, 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("2678.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2678 = 2 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2678.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:	$21.3839376613$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 8x^{8} + 37x^{7} + 20x^{6} - 106x^{5} - 17x^{4} + 90x^{3} + 2x^{2} - 17x - 2 $ x^10 - 4x^9 - 8x^8 + 37x^7 + 20x^6 - 106x^5 - 17x^4 + 90x^3 + 2x^2 - 17*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.93400$ of defining polynomial
Character	$\chi$	$=$	2678.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.93400 q^{3} +1.00000 q^{4} +1.44285 q^{5} -2.93400 q^{6} +1.07406 q^{7} +1.00000 q^{8} +5.60834 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.93400 q^{3} +1.00000 q^{4} +1.44285 q^{5} -2.93400 q^{6} +1.07406 q^{7} +1.00000 q^{8} +5.60834 q^{9} +1.44285 q^{10} -2.99415 q^{11} -2.93400 q^{12} -1.00000 q^{13} +1.07406 q^{14} -4.23331 q^{15} +1.00000 q^{16} +4.29774 q^{17} +5.60834 q^{18} -7.88191 q^{19} +1.44285 q^{20} -3.15129 q^{21} -2.99415 q^{22} -6.91859 q^{23} -2.93400 q^{24} -2.91819 q^{25} -1.00000 q^{26} -7.65287 q^{27} +1.07406 q^{28} +3.92037 q^{29} -4.23331 q^{30} -7.47501 q^{31} +1.00000 q^{32} +8.78482 q^{33} +4.29774 q^{34} +1.54970 q^{35} +5.60834 q^{36} +8.82875 q^{37} -7.88191 q^{38} +2.93400 q^{39} +1.44285 q^{40} +4.70417 q^{41} -3.15129 q^{42} +8.18721 q^{43} -2.99415 q^{44} +8.09198 q^{45} -6.91859 q^{46} -2.92034 q^{47} -2.93400 q^{48} -5.84640 q^{49} -2.91819 q^{50} -12.6096 q^{51} -1.00000 q^{52} -14.2009 q^{53} -7.65287 q^{54} -4.32009 q^{55} +1.07406 q^{56} +23.1255 q^{57} +3.92037 q^{58} +0.177491 q^{59} -4.23331 q^{60} -1.49439 q^{61} -7.47501 q^{62} +6.02369 q^{63} +1.00000 q^{64} -1.44285 q^{65} +8.78482 q^{66} +13.5332 q^{67} +4.29774 q^{68} +20.2991 q^{69} +1.54970 q^{70} -2.30629 q^{71} +5.60834 q^{72} -7.36814 q^{73} +8.82875 q^{74} +8.56197 q^{75} -7.88191 q^{76} -3.21589 q^{77} +2.93400 q^{78} -2.37238 q^{79} +1.44285 q^{80} +5.62848 q^{81} +4.70417 q^{82} -7.36894 q^{83} -3.15129 q^{84} +6.20098 q^{85} +8.18721 q^{86} -11.5024 q^{87} -2.99415 q^{88} -14.5891 q^{89} +8.09198 q^{90} -1.07406 q^{91} -6.91859 q^{92} +21.9317 q^{93} -2.92034 q^{94} -11.3724 q^{95} -2.93400 q^{96} -11.4639 q^{97} -5.84640 q^{98} -16.7922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9} - 3 q^{10} - 5 q^{11} - 6 q^{12} - 10 q^{13} - 10 q^{14} - 13 q^{15} + 10 q^{16} - 13 q^{17} + 4 q^{18} - 21 q^{19} - 3 q^{20} + 5 q^{21} - 5 q^{22} - 5 q^{23} - 6 q^{24} + 13 q^{25} - 10 q^{26} - 9 q^{27} - 10 q^{28} + 6 q^{29} - 13 q^{30} - 33 q^{31} + 10 q^{32} - 22 q^{33} - 13 q^{34} - 9 q^{35} + 4 q^{36} - 7 q^{37} - 21 q^{38} + 6 q^{39} - 3 q^{40} - 20 q^{41} + 5 q^{42} - 22 q^{43} - 5 q^{44} - 14 q^{45} - 5 q^{46} - 31 q^{47} - 6 q^{48} + 8 q^{49} + 13 q^{50} - 8 q^{51} - 10 q^{52} + q^{53} - 9 q^{54} - 30 q^{55} - 10 q^{56} + 33 q^{57} + 6 q^{58} - 51 q^{59} - 13 q^{60} - 6 q^{61} - 33 q^{62} - 25 q^{63} + 10 q^{64} + 3 q^{65} - 22 q^{66} - 19 q^{67} - 13 q^{68} + 6 q^{69} - 9 q^{70} - 14 q^{71} + 4 q^{72} - 16 q^{73} - 7 q^{74} + 5 q^{75} - 21 q^{76} - 5 q^{77} + 6 q^{78} + 11 q^{79} - 3 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} + 5 q^{84} - 27 q^{85} - 22 q^{86} - 5 q^{88} - 47 q^{89} - 14 q^{90} + 10 q^{91} - 5 q^{92} + 12 q^{93} - 31 q^{94} - 14 q^{95} - 6 q^{96} - 44 q^{97} + 8 q^{98} + 23 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9 - 3 * q^10 - 5 * q^11 - 6 * q^12 - 10 * q^13 - 10 * q^14 - 13 * q^15 + 10 * q^16 - 13 * q^17 + 4 * q^18 - 21 * q^19 - 3 * q^20 + 5 * q^21 - 5 * q^22 - 5 * q^23 - 6 * q^24 + 13 * q^25 - 10 * q^26 - 9 * q^27 - 10 * q^28 + 6 * q^29 - 13 * q^30 - 33 * q^31 + 10 * q^32 - 22 * q^33 - 13 * q^34 - 9 * q^35 + 4 * q^36 - 7 * q^37 - 21 * q^38 + 6 * q^39 - 3 * q^40 - 20 * q^41 + 5 * q^42 - 22 * q^43 - 5 * q^44 - 14 * q^45 - 5 * q^46 - 31 * q^47 - 6 * q^48 + 8 * q^49 + 13 * q^50 - 8 * q^51 - 10 * q^52 + q^53 - 9 * q^54 - 30 * q^55 - 10 * q^56 + 33 * q^57 + 6 * q^58 - 51 * q^59 - 13 * q^60 - 6 * q^61 - 33 * q^62 - 25 * q^63 + 10 * q^64 + 3 * q^65 - 22 * q^66 - 19 * q^67 - 13 * q^68 + 6 * q^69 - 9 * q^70 - 14 * q^71 + 4 * q^72 - 16 * q^73 - 7 * q^74 + 5 * q^75 - 21 * q^76 - 5 * q^77 + 6 * q^78 + 11 * q^79 - 3 * q^80 - 2 * q^81 - 20 * q^82 + q^83 + 5 * q^84 - 27 * q^85 - 22 * q^86 - 5 * q^88 - 47 * q^89 - 14 * q^90 + 10 * q^91 - 5 * q^92 + 12 * q^93 - 31 * q^94 - 14 * q^95 - 6 * q^96 - 44 * q^97 + 8 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.93400	−1.69394	−0.846972	−	0.531637i	$-0.821577\pi$
$3$	−2.93400	−1.69394	−0.846972	+	0.531637i	$0.821577\pi$
$4$	1.00000	0.500000
$5$	1.44285	0.645261	0.322630	−	0.946525i	$-0.395433\pi$
$5$	1.44285	0.645261	0.322630	+	0.946525i	$0.395433\pi$
$6$	−2.93400	−1.19780
$7$	1.07406	0.405956	0.202978	−	0.979183i	$-0.434938\pi$
$7$	1.07406	0.405956	0.202978	+	0.979183i	$0.434938\pi$
$8$	1.00000	0.353553
$9$	5.60834	1.86945
$10$	1.44285	0.456268
$11$	−2.99415	−0.902769	−0.451384	−	0.892330i	$-0.649070\pi$
$11$	−2.99415	−0.902769	−0.451384	+	0.892330i	$0.649070\pi$
$12$	−2.93400	−0.846972
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.07406	0.287055
$15$	−4.23331	−1.09304
$16$	1.00000	0.250000
$17$	4.29774	1.04235	0.521177	−	0.853448i	$-0.325493\pi$
$17$	4.29774	1.04235	0.521177	+	0.853448i	$0.325493\pi$
$18$	5.60834	1.32190
$19$	−7.88191	−1.80823	−0.904117	−	0.427286i	$-0.859470\pi$
$19$	−7.88191	−1.80823	−0.904117	+	0.427286i	$0.859470\pi$
$20$	1.44285	0.322630
$21$	−3.15129	−0.687668
$22$	−2.99415	−0.638354
$23$	−6.91859	−1.44263	−0.721313	−	0.692609i	$-0.756461\pi$
$23$	−6.91859	−1.44263	−0.721313	+	0.692609i	$0.756461\pi$
$24$	−2.93400	−0.598900
$25$	−2.91819	−0.583639
$26$	−1.00000	−0.196116
$27$	−7.65287	−1.47280
$28$	1.07406	0.202978
$29$	3.92037	0.727995	0.363997	−	0.931400i	$-0.381412\pi$
$29$	3.92037	0.727995	0.363997	+	0.931400i	$0.381412\pi$
$30$	−4.23331	−0.772893
$31$	−7.47501	−1.34255	−0.671276	−	0.741208i	$-0.734253\pi$
$31$	−7.47501	−1.34255	−0.671276	+	0.741208i	$0.734253\pi$
$32$	1.00000	0.176777
$33$	8.78482	1.52924
$34$	4.29774	0.737056
$35$	1.54970	0.261948
$36$	5.60834	0.934724
$37$	8.82875	1.45144	0.725719	−	0.687991i	$-0.241507\pi$
$37$	8.82875	1.45144	0.725719	+	0.687991i	$0.241507\pi$
$38$	−7.88191	−1.27861
$39$	2.93400	0.469816
$40$	1.44285	0.228134
$41$	4.70417	0.734668	0.367334	−	0.930089i	$-0.380271\pi$
$41$	4.70417	0.734668	0.367334	+	0.930089i	$0.380271\pi$
$42$	−3.15129	−0.486254
$43$	8.18721	1.24854	0.624269	−	0.781209i	$-0.285397\pi$
$43$	8.18721	1.24854	0.624269	+	0.781209i	$0.285397\pi$
$44$	−2.99415	−0.451384
$45$	8.09198	1.20628
$46$	−6.91859	−1.02009
$47$	−2.92034	−0.425975	−0.212987	−	0.977055i	$-0.568319\pi$
$47$	−2.92034	−0.425975	−0.212987	+	0.977055i	$0.568319\pi$
$48$	−2.93400	−0.423486
$49$	−5.84640	−0.835199
$50$	−2.91819	−0.412695
$51$	−12.6096	−1.76569
$52$	−1.00000	−0.138675
$53$	−14.2009	−1.95064	−0.975319	−	0.220799i	$-0.929134\pi$
$53$	−14.2009	−1.95064	−0.975319	+	0.220799i	$0.929134\pi$
$54$	−7.65287	−1.04142
$55$	−4.32009	−0.582521
$56$	1.07406	0.143527
$57$	23.1255	3.06305
$58$	3.92037	0.514770
$59$	0.177491	0.0231073	0.0115536	−	0.999933i	$-0.496322\pi$
$59$	0.177491	0.0231073	0.0115536	+	0.999933i	$0.496322\pi$
$60$	−4.23331	−0.546518
$61$	−1.49439	−0.191337	−0.0956683	−	0.995413i	$-0.530499\pi$
$61$	−1.49439	−0.191337	−0.0956683	+	0.995413i	$0.530499\pi$
$62$	−7.47501	−0.949328
$63$	6.02369	0.758914
$64$	1.00000	0.125000
$65$	−1.44285	−0.178963
$66$	8.78482	1.08134
$67$	13.5332	1.65335	0.826675	−	0.562680i	$-0.190230\pi$
$67$	13.5332	1.65335	0.826675	+	0.562680i	$0.190230\pi$
$68$	4.29774	0.521177
$69$	20.2991	2.44373
$70$	1.54970	0.185225
$71$	−2.30629	−0.273707	−0.136853	−	0.990591i	$-0.543699\pi$
$71$	−2.30629	−0.273707	−0.136853	+	0.990591i	$0.543699\pi$
$72$	5.60834	0.660949
$73$	−7.36814	−0.862375	−0.431188	−	0.902262i	$-0.641905\pi$
$73$	−7.36814	−0.862375	−0.431188	+	0.902262i	$0.641905\pi$
$74$	8.82875	1.02632
$75$	8.56197	0.988652
$76$	−7.88191	−0.904117
$77$	−3.21589	−0.366485
$78$	2.93400	0.332210
$79$	−2.37238	−0.266914	−0.133457	−	0.991055i	$-0.542608\pi$
$79$	−2.37238	−0.266914	−0.133457	+	0.991055i	$0.542608\pi$
$80$	1.44285	0.161315
$81$	5.62848	0.625386
$82$	4.70417	0.519489
$83$	−7.36894	−0.808846	−0.404423	−	0.914572i	$-0.632528\pi$
$83$	−7.36894	−0.808846	−0.404423	+	0.914572i	$0.632528\pi$
$84$	−3.15129	−0.343834
$85$	6.20098	0.672590
$86$	8.18721	0.882850
$87$	−11.5024	−1.23318
$88$	−2.99415	−0.319177
$89$	−14.5891	−1.54644	−0.773221	−	0.634136i	$-0.781356\pi$
$89$	−14.5891	−1.54644	−0.773221	+	0.634136i	$0.781356\pi$
$90$	8.09198	0.852969
$91$	−1.07406	−0.112592
$92$	−6.91859	−0.721313
$93$	21.9317	2.27421
$94$	−2.92034	−0.301210
$95$	−11.3724	−1.16678
$96$	−2.93400	−0.299450
$97$	−11.4639	−1.16399	−0.581993	−	0.813194i	$-0.697727\pi$
$97$	−11.4639	−1.16399	−0.581993	+	0.813194i	$0.697727\pi$
$98$	−5.84640	−0.590575
$99$	−16.7922	−1.68768
$100$	−2.91819	−0.291819
$101$	5.33412	0.530765	0.265382	−	0.964143i	$-0.414502\pi$
$101$	5.33412	0.530765	0.265382	+	0.964143i	$0.414502\pi$
$102$	−12.6096	−1.24853
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−4.54683	−0.443725
$106$	−14.2009	−1.37931
$107$	−9.08077	−0.877871	−0.438935	−	0.898519i	$-0.644644\pi$
$107$	−9.08077	−0.877871	−0.438935	+	0.898519i	$0.644644\pi$
$108$	−7.65287	−0.736398
$109$	4.28280	0.410218	0.205109	−	0.978739i	$-0.434245\pi$
$109$	4.28280	0.410218	0.205109	+	0.978739i	$0.434245\pi$
$110$	−4.32009	−0.411905
$111$	−25.9035	−2.45865
$112$	1.07406	0.101489
$113$	−1.80141	−0.169463	−0.0847313	−	0.996404i	$-0.527003\pi$
$113$	−1.80141	−0.169463	−0.0847313	+	0.996404i	$0.527003\pi$
$114$	23.1255	2.16590
$115$	−9.98246	−0.930869
$116$	3.92037	0.363997
$117$	−5.60834	−0.518491
$118$	0.177491	0.0163393
$119$	4.61603	0.423151
$120$	−4.23331	−0.386446
$121$	−2.03509	−0.185008
$122$	−1.49439	−0.135295
$123$	−13.8020	−1.24449
$124$	−7.47501	−0.671276
$125$	−11.4247	−1.02186
$126$	6.02369	0.536633
$127$	−3.00863	−0.266973	−0.133487	−	0.991051i	$-0.542617\pi$
$127$	−3.00863	−0.266973	−0.133487	+	0.991051i	$0.542617\pi$
$128$	1.00000	0.0883883
$129$	−24.0213	−2.11495
$130$	−1.44285	−0.126546
$131$	8.26730	0.722317	0.361159	−	0.932504i	$-0.382381\pi$
$131$	8.26730	0.722317	0.361159	+	0.932504i	$0.382381\pi$
$132$	8.78482	0.764620
$133$	−8.46564	−0.734064
$134$	13.5332	1.16909
$135$	−11.0419	−0.950337
$136$	4.29774	0.368528
$137$	−13.1756	−1.12566	−0.562832	−	0.826571i	$-0.690288\pi$
$137$	−13.1756	−1.12566	−0.562832	+	0.826571i	$0.690288\pi$
$138$	20.2991	1.72798
$139$	−2.99669	−0.254176	−0.127088	−	0.991891i	$-0.540563\pi$
$139$	−2.99669	−0.254176	−0.127088	+	0.991891i	$0.540563\pi$
$140$	1.54970	0.130974
$141$	8.56826	0.721578
$142$	−2.30629	−0.193540
$143$	2.99415	0.250383
$144$	5.60834	0.467362
$145$	5.65649	0.469746
$146$	−7.36814	−0.609791
$147$	17.1533	1.41478
$148$	8.82875	0.725719
$149$	−15.2007	−1.24529	−0.622643	−	0.782506i	$-0.713941\pi$
$149$	−15.2007	−1.24529	−0.622643	+	0.782506i	$0.713941\pi$
$150$	8.56197	0.699082
$151$	3.44683	0.280499	0.140250	−	0.990116i	$-0.455210\pi$
$151$	3.44683	0.280499	0.140250	+	0.990116i	$0.455210\pi$
$152$	−7.88191	−0.639307
$153$	24.1032	1.94863
$154$	−3.21589	−0.259144
$155$	−10.7853	−0.866296
$156$	2.93400	0.234908
$157$	19.9168	1.58953	0.794766	−	0.606917i	$-0.207594\pi$
$157$	19.9168	1.58953	0.794766	+	0.606917i	$0.207594\pi$
$158$	−2.37238	−0.188737
$159$	41.6653	3.30427
$160$	1.44285	0.114067
$161$	−7.43098	−0.585643
$162$	5.62848	0.442215
$163$	−10.8879	−0.852807	−0.426403	−	0.904533i	$-0.640220\pi$
$163$	−10.8879	−0.852807	−0.426403	+	0.904533i	$0.640220\pi$
$164$	4.70417	0.367334
$165$	12.6751	0.986758
$166$	−7.36894	−0.571941
$167$	1.06864	0.0826940	0.0413470	−	0.999145i	$-0.486835\pi$
$167$	1.06864	0.0826940	0.0413470	+	0.999145i	$0.486835\pi$
$168$	−3.15129	−0.243127
$169$	1.00000	0.0769231
$170$	6.20098	0.475593
$171$	−44.2044	−3.38040
$172$	8.18721	0.624269
$173$	−22.9837	−1.74742	−0.873710	−	0.486447i	$-0.838293\pi$
$173$	−22.9837	−1.74742	−0.873710	+	0.486447i	$0.838293\pi$
$174$	−11.5024	−0.871992
$175$	−3.13431	−0.236932
$176$	−2.99415	−0.225692
$177$	−0.520757	−0.0391425
$178$	−14.5891	−1.09350
$179$	21.3485	1.59566	0.797830	−	0.602883i	$-0.205981\pi$
$179$	21.3485	1.59566	0.797830	+	0.602883i	$0.205981\pi$
$180$	8.09198	0.603140
$181$	−7.83988	−0.582734	−0.291367	−	0.956611i	$-0.594110\pi$
$181$	−7.83988	−0.582734	−0.291367	+	0.956611i	$0.594110\pi$
$182$	−1.07406	−0.0796146
$183$	4.38453	0.324113
$184$	−6.91859	−0.510045
$185$	12.7385	0.936555
$186$	21.9317	1.60811
$187$	−12.8681	−0.941005
$188$	−2.92034	−0.212987
$189$	−8.21964	−0.597891
$190$	−11.3724	−0.825039
$191$	−13.7458	−0.994614	−0.497307	−	0.867575i	$-0.665678\pi$
$191$	−13.7458	−0.994614	−0.497307	+	0.867575i	$0.665678\pi$
$192$	−2.93400	−0.211743
$193$	−20.4383	−1.47118	−0.735592	−	0.677425i	$-0.763096\pi$
$193$	−20.4383	−1.47118	−0.735592	+	0.677425i	$0.763096\pi$
$194$	−11.4639	−0.823063
$195$	4.23331	0.303153
$196$	−5.84640	−0.417600
$197$	25.2013	1.79552	0.897760	−	0.440485i	$-0.145193\pi$
$197$	25.2013	1.79552	0.897760	+	0.440485i	$0.145193\pi$
$198$	−16.7922	−1.19337
$199$	2.28994	0.162330	0.0811648	−	0.996701i	$-0.474136\pi$
$199$	2.28994	0.162330	0.0811648	+	0.996701i	$0.474136\pi$
$200$	−2.91819	−0.206347
$201$	−39.7065	−2.80068
$202$	5.33412	0.375307
$203$	4.21071	0.295534
$204$	−12.6096	−0.882845
$205$	6.78740	0.474052
$206$	1.00000	0.0696733
$207$	−38.8018	−2.69691
$208$	−1.00000	−0.0693375
$209$	23.5996	1.63242
$210$	−4.54683	−0.313761
$211$	−5.16164	−0.355342	−0.177671	−	0.984090i	$-0.556856\pi$
$211$	−5.16164	−0.355342	−0.177671	+	0.984090i	$0.556856\pi$
$212$	−14.2009	−0.975319
$213$	6.76666	0.463644
$214$	−9.08077	−0.620749
$215$	11.8129	0.805633
$216$	−7.65287	−0.520712
$217$	−8.02861	−0.545018
$218$	4.28280	0.290068
$219$	21.6181	1.46082
$220$	−4.32009	−0.291261
$221$	−4.29774	−0.289097
$222$	−25.9035	−1.73853
$223$	−17.5507	−1.17528	−0.587640	−	0.809122i	$-0.699943\pi$
$223$	−17.5507	−1.17528	−0.587640	+	0.809122i	$0.699943\pi$
$224$	1.07406	0.0717636
$225$	−16.3662	−1.09108
$226$	−1.80141	−0.119828
$227$	15.1420	1.00501	0.502506	−	0.864574i	$-0.332411\pi$
$227$	15.1420	1.00501	0.502506	+	0.864574i	$0.332411\pi$
$228$	23.1255	1.53152
$229$	6.91476	0.456940	0.228470	−	0.973551i	$-0.426628\pi$
$229$	6.91476	0.456940	0.228470	+	0.973551i	$0.426628\pi$
$230$	−9.98246	−0.658224
$231$	9.43542	0.620805
$232$	3.92037	0.257385
$233$	−14.5172	−0.951051	−0.475525	−	0.879702i	$-0.657742\pi$
$233$	−14.5172	−0.951051	−0.475525	+	0.879702i	$0.657742\pi$
$234$	−5.60834	−0.366629
$235$	−4.21360	−0.274865
$236$	0.177491	0.0115536
$237$	6.96057	0.452138
$238$	4.61603	0.299213
$239$	−3.30333	−0.213675	−0.106837	−	0.994277i	$-0.534072\pi$
$239$	−3.30333	−0.213675	−0.106837	+	0.994277i	$0.534072\pi$
$240$	−4.23331	−0.273259
$241$	−14.8991	−0.959734	−0.479867	−	0.877341i	$-0.659315\pi$
$241$	−14.8991	−0.959734	−0.479867	+	0.877341i	$0.659315\pi$
$242$	−2.03509	−0.130821
$243$	6.44467	0.413426
$244$	−1.49439	−0.0956683
$245$	−8.43545	−0.538921
$246$	−13.8020	−0.879985
$247$	7.88191	0.501514
$248$	−7.47501	−0.474664
$249$	21.6205	1.37014
$250$	−11.4247	−0.722564
$251$	26.8338	1.69374	0.846868	−	0.531803i	$-0.178485\pi$
$251$	26.8338	1.69374	0.846868	+	0.531803i	$0.178485\pi$
$252$	6.02369	0.379457
$253$	20.7153	1.30236
$254$	−3.00863	−0.188778
$255$	−18.1937	−1.13933
$256$	1.00000	0.0625000
$257$	11.4611	0.714925	0.357462	−	0.933928i	$-0.383642\pi$
$257$	11.4611	0.714925	0.357462	+	0.933928i	$0.383642\pi$
$258$	−24.0213	−1.49550
$259$	9.48260	0.589220
$260$	−1.44285	−0.0894815
$261$	21.9868	1.36095
$262$	8.26730	0.510755
$263$	5.33572	0.329015	0.164507	−	0.986376i	$-0.447397\pi$
$263$	5.33572	0.329015	0.164507	+	0.986376i	$0.447397\pi$
$264$	8.78482	0.540668
$265$	−20.4897	−1.25867
$266$	−8.46564	−0.519061
$267$	42.8044	2.61959
$268$	13.5332	0.826675
$269$	15.1251	0.922193	0.461096	−	0.887350i	$-0.347456\pi$
$269$	15.1251	0.922193	0.461096	+	0.887350i	$0.347456\pi$
$270$	−11.0419	−0.671990
$271$	−4.37777	−0.265931	−0.132965	−	0.991121i	$-0.542450\pi$
$271$	−4.37777	−0.265931	−0.132965	+	0.991121i	$0.542450\pi$
$272$	4.29774	0.260589
$273$	3.15129	0.190725
$274$	−13.1756	−0.795965
$275$	8.73750	0.526891
$276$	20.2991	1.22186
$277$	−2.05261	−0.123329	−0.0616647	−	0.998097i	$-0.519641\pi$
$277$	−2.05261	−0.123329	−0.0616647	+	0.998097i	$0.519641\pi$
$278$	−2.99669	−0.179730
$279$	−41.9224	−2.50983
$280$	1.54970	0.0926125
$281$	24.1145	1.43855	0.719274	−	0.694727i	$-0.244475\pi$
$281$	24.1145	1.43855	0.719274	+	0.694727i	$0.244475\pi$
$282$	8.56826	0.510233
$283$	7.58433	0.450842	0.225421	−	0.974262i	$-0.427624\pi$
$283$	7.58433	0.450842	0.225421	+	0.974262i	$0.427624\pi$
$284$	−2.30629	−0.136853
$285$	33.3665	1.97646
$286$	2.99415	0.177048
$287$	5.05256	0.298243
$288$	5.60834	0.330475
$289$	1.47056	0.0865032
$290$	5.65649	0.332161
$291$	33.6352	1.97173
$292$	−7.36814	−0.431188
$293$	−26.1822	−1.52958	−0.764789	−	0.644281i	$-0.777157\pi$
$293$	−26.1822	−1.52958	−0.764789	+	0.644281i	$0.777157\pi$
$294$	17.1533	1.00040
$295$	0.256092	0.0149102
$296$	8.82875	0.513161
$297$	22.9138	1.32959
$298$	−15.2007	−0.880550
$299$	6.91859	0.400112
$300$	8.56197	0.494326
$301$	8.79356	0.506852
$302$	3.44683	0.198343
$303$	−15.6503	−0.899086
$304$	−7.88191	−0.452058
$305$	−2.15617	−0.123462
$306$	24.1032	1.37789
$307$	−31.0675	−1.77311	−0.886557	−	0.462619i	$-0.846910\pi$
$307$	−31.0675	−1.77311	−0.886557	+	0.462619i	$0.846910\pi$
$308$	−3.21589	−0.183242
$309$	−2.93400	−0.166909
$310$	−10.7853	−0.612564
$311$	−33.5487	−1.90237	−0.951186	−	0.308618i	$-0.900134\pi$
$311$	−33.5487	−1.90237	−0.951186	+	0.308618i	$0.900134\pi$
$312$	2.93400	0.166105
$313$	−29.2826	−1.65515	−0.827574	−	0.561356i	$-0.810280\pi$
$313$	−29.2826	−1.65515	−0.827574	+	0.561356i	$0.810280\pi$
$314$	19.9168	1.12397
$315$	8.69127	0.489697
$316$	−2.37238	−0.133457
$317$	−5.56307	−0.312453	−0.156226	−	0.987721i	$-0.549933\pi$
$317$	−5.56307	−0.312453	−0.156226	+	0.987721i	$0.549933\pi$
$318$	41.6653	2.33647
$319$	−11.7382	−0.657211
$320$	1.44285	0.0806576
$321$	26.6430	1.48706
$322$	−7.43098	−0.414112
$323$	−33.8744	−1.88482
$324$	5.62848	0.312693
$325$	2.91819	0.161872
$326$	−10.8879	−0.603026
$327$	−12.5657	−0.694886
$328$	4.70417	0.259744
$329$	−3.13662	−0.172927
$330$	12.6751	0.697744
$331$	19.6063	1.07766	0.538829	−	0.842415i	$-0.318867\pi$
$331$	19.6063	1.07766	0.538829	+	0.842415i	$0.318867\pi$
$332$	−7.36894	−0.404423
$333$	49.5147	2.71339
$334$	1.06864	0.0584735
$335$	19.5264	1.06684
$336$	−3.15129	−0.171917
$337$	15.4607	0.842196	0.421098	−	0.907015i	$-0.361645\pi$
$337$	15.4607	0.842196	0.421098	+	0.907015i	$0.361645\pi$
$338$	1.00000	0.0543928
$339$	5.28534	0.287060
$340$	6.20098	0.336295
$341$	22.3813	1.21201
$342$	−44.2044	−2.39030
$343$	−13.7978	−0.745011
$344$	8.18721	0.441425
$345$	29.2885	1.57684
$346$	−22.9837	−1.23561
$347$	−3.15531	−0.169386	−0.0846929	−	0.996407i	$-0.526991\pi$
$347$	−3.15531	−0.169386	−0.0846929	+	0.996407i	$0.526991\pi$
$348$	−11.5024	−0.616591
$349$	21.3376	1.14218	0.571089	−	0.820888i	$-0.306521\pi$
$349$	21.3376	1.14218	0.571089	+	0.820888i	$0.306521\pi$
$350$	−3.13431	−0.167536
$351$	7.65287	0.408480
$352$	−2.99415	−0.159589
$353$	11.2151	0.596920	0.298460	−	0.954422i	$-0.403527\pi$
$353$	11.2151	0.596920	0.298460	+	0.954422i	$0.403527\pi$
$354$	−0.520757	−0.0276779
$355$	−3.32763	−0.176612
$356$	−14.5891	−0.773221
$357$	−13.5434	−0.716793
$358$	21.3485	1.12830
$359$	26.1381	1.37952	0.689759	−	0.724039i	$-0.257716\pi$
$359$	26.1381	1.37952	0.689759	+	0.724039i	$0.257716\pi$
$360$	8.09198	0.426485
$361$	43.1244	2.26971
$362$	−7.83988	−0.412055
$363$	5.97095	0.313394
$364$	−1.07406	−0.0562960
$365$	−10.6311	−0.556457
$366$	4.38453	0.229183
$367$	−4.22487	−0.220536	−0.110268	−	0.993902i	$-0.535171\pi$
$367$	−4.22487	−0.220536	−0.110268	+	0.993902i	$0.535171\pi$
$368$	−6.91859	−0.360656
$369$	26.3826	1.37342
$370$	12.7385	0.662245
$371$	−15.2526	−0.791874
$372$	21.9317	1.13710
$373$	8.46477	0.438289	0.219145	−	0.975692i	$-0.429673\pi$
$373$	8.46477	0.438289	0.219145	+	0.975692i	$0.429673\pi$
$374$	−12.8681	−0.665391
$375$	33.5202	1.73097
$376$	−2.92034	−0.150605
$377$	−3.92037	−0.201909
$378$	−8.21964	−0.422773
$379$	−11.7235	−0.602198	−0.301099	−	0.953593i	$-0.597353\pi$
$379$	−11.7235	−0.602198	−0.301099	+	0.953593i	$0.597353\pi$
$380$	−11.3724	−0.583391
$381$	8.82732	0.452237
$382$	−13.7458	−0.703298
$383$	12.6143	0.644561	0.322281	−	0.946644i	$-0.395551\pi$
$383$	12.6143	0.644561	0.322281	+	0.946644i	$0.395551\pi$
$384$	−2.93400	−0.149725
$385$	−4.64004	−0.236478
$386$	−20.4383	−1.04028
$387$	45.9167	2.33408
$388$	−11.4639	−0.581993
$389$	1.84975	0.0937861	0.0468930	−	0.998900i	$-0.485068\pi$
$389$	1.84975	0.0937861	0.0468930	+	0.998900i	$0.485068\pi$
$390$	4.23331	0.214362
$391$	−29.7343	−1.50373
$392$	−5.84640	−0.295288
$393$	−24.2562	−1.22357
$394$	25.2013	1.26962
$395$	−3.42299	−0.172229
$396$	−16.7922	−0.843840
$397$	16.1243	0.809256	0.404628	−	0.914481i	$-0.367401\pi$
$397$	16.1243	0.809256	0.404628	+	0.914481i	$0.367401\pi$
$398$	2.28994	0.114784
$399$	24.8382	1.24346
$400$	−2.91819	−0.145910
$401$	−15.0926	−0.753689	−0.376844	−	0.926277i	$-0.622991\pi$
$401$	−15.0926	−0.753689	−0.376844	+	0.926277i	$0.622991\pi$
$402$	−39.7065	−1.98038
$403$	7.47501	0.372357
$404$	5.33412	0.265382
$405$	8.12103	0.403537
$406$	4.21071	0.208974
$407$	−26.4346	−1.31031
$408$	−12.6096	−0.624266
$409$	−12.3802	−0.612161	−0.306080	−	0.952006i	$-0.599018\pi$
$409$	−12.3802	−0.612161	−0.306080	+	0.952006i	$0.599018\pi$
$410$	6.78740	0.335206
$411$	38.6571	1.90681
$412$	1.00000	0.0492665
$413$	0.190635	0.00938056
$414$	−38.8018	−1.90701
$415$	−10.6322	−0.521917
$416$	−1.00000	−0.0490290
$417$	8.79229	0.430560
$418$	23.5996	1.15429
$419$	26.8813	1.31324	0.656619	−	0.754222i	$-0.271986\pi$
$419$	26.8813	1.31324	0.656619	+	0.754222i	$0.271986\pi$
$420$	−4.54683	−0.221862
$421$	−13.6791	−0.666680	−0.333340	−	0.942807i	$-0.608176\pi$
$421$	−13.6791	−0.666680	−0.333340	+	0.942807i	$0.608176\pi$
$422$	−5.16164	−0.251265
$423$	−16.3783	−0.796338
$424$	−14.2009	−0.689655
$425$	−12.5416	−0.608359
$426$	6.76666	0.327846
$427$	−1.60506	−0.0776743
$428$	−9.08077	−0.438935
$429$	−8.78482	−0.424135
$430$	11.8129	0.569668
$431$	5.60512	0.269989	0.134995	−	0.990846i	$-0.456898\pi$
$431$	5.60512	0.269989	0.134995	+	0.990846i	$0.456898\pi$
$432$	−7.65287	−0.368199
$433$	5.47408	0.263068	0.131534	−	0.991312i	$-0.458010\pi$
$433$	5.47408	0.263068	0.131534	+	0.991312i	$0.458010\pi$
$434$	−8.02861	−0.385386
$435$	−16.5961	−0.795724
$436$	4.28280	0.205109
$437$	54.5317	2.60860
$438$	21.6181	1.03295
$439$	−7.03409	−0.335719	−0.167859	−	0.985811i	$-0.553685\pi$
$439$	−7.03409	−0.335719	−0.167859	+	0.985811i	$0.553685\pi$
$440$	−4.32009	−0.205952
$441$	−32.7886	−1.56136
$442$	−4.29774	−0.204423
$443$	−1.00244	−0.0476271	−0.0238136	−	0.999716i	$-0.507581\pi$
$443$	−1.00244	−0.0476271	−0.0238136	+	0.999716i	$0.507581\pi$
$444$	−25.9035	−1.22933
$445$	−21.0498	−0.997859
$446$	−17.5507	−0.831049
$447$	44.5987	2.10945
$448$	1.07406	0.0507445
$449$	33.2664	1.56994	0.784970	−	0.619534i	$-0.212678\pi$
$449$	33.2664	1.56994	0.784970	+	0.619534i	$0.212678\pi$
$450$	−16.3662	−0.771512
$451$	−14.0850	−0.663236
$452$	−1.80141	−0.0847313
$453$	−10.1130	−0.475150
$454$	15.1420	0.710651
$455$	−1.54970	−0.0726512
$456$	23.1255	1.08295
$457$	−16.5707	−0.775146	−0.387573	−	0.921839i	$-0.626686\pi$
$457$	−16.5707	−0.775146	−0.387573	+	0.921839i	$0.626686\pi$
$458$	6.91476	0.323105
$459$	−32.8900	−1.53518
$460$	−9.98246	−0.465435
$461$	40.6434	1.89295	0.946475	−	0.322777i	$-0.104617\pi$
$461$	40.6434	1.89295	0.946475	+	0.322777i	$0.104617\pi$
$462$	9.43542	0.438975
$463$	15.0877	0.701183	0.350592	−	0.936528i	$-0.385981\pi$
$463$	15.0877	0.701183	0.350592	+	0.936528i	$0.385981\pi$
$464$	3.92037	0.181999
$465$	31.6440	1.46746
$466$	−14.5172	−0.672494
$467$	−9.24953	−0.428017	−0.214009	−	0.976832i	$-0.568652\pi$
$467$	−9.24953	−0.428017	−0.214009	+	0.976832i	$0.568652\pi$
$468$	−5.60834	−0.259246
$469$	14.5355	0.671188
$470$	−4.21360	−0.194359
$471$	−58.4358	−2.69258
$472$	0.177491	0.00816966
$473$	−24.5137	−1.12714
$474$	6.96057	0.319710
$475$	23.0009	1.05536
$476$	4.61603	0.211575
$477$	−79.6433	−3.64662
$478$	−3.30333	−0.151091
$479$	34.6637	1.58383	0.791913	−	0.610634i	$-0.209085\pi$
$479$	34.6637	1.58383	0.791913	+	0.610634i	$0.209085\pi$
$480$	−4.23331	−0.193223
$481$	−8.82875	−0.402556
$482$	−14.8991	−0.678635
$483$	21.8025	0.992047
$484$	−2.03509	−0.0925041
$485$	−16.5407	−0.751074
$486$	6.44467	0.292336
$487$	29.8637	1.35325	0.676627	−	0.736326i	$-0.263441\pi$
$487$	29.8637	1.35325	0.676627	+	0.736326i	$0.263441\pi$
$488$	−1.49439	−0.0676477
$489$	31.9451	1.44461
$490$	−8.43545	−0.381075
$491$	−1.87608	−0.0846662	−0.0423331	−	0.999104i	$-0.513479\pi$
$491$	−1.87608	−0.0846662	−0.0423331	+	0.999104i	$0.513479\pi$
$492$	−13.8020	−0.622244
$493$	16.8487	0.758829
$494$	7.88191	0.354624
$495$	−24.2286	−1.08899
$496$	−7.47501	−0.335638
$497$	−2.47710	−0.111113
$498$	21.6205	0.968836
$499$	−35.4738	−1.58802	−0.794012	−	0.607902i	$-0.792011\pi$
$499$	−35.4738	−1.58802	−0.794012	+	0.607902i	$0.792011\pi$
$500$	−11.4247	−0.510930
$501$	−3.13539	−0.140079
$502$	26.8338	1.19765
$503$	14.0322	0.625664	0.312832	−	0.949809i	$-0.398722\pi$
$503$	14.0322	0.625664	0.312832	+	0.949809i	$0.398722\pi$
$504$	6.02369	0.268317
$505$	7.69632	0.342482
$506$	20.7153	0.920906
$507$	−2.93400	−0.130303
$508$	−3.00863	−0.133487
$509$	−28.9158	−1.28167	−0.640834	−	0.767679i	$-0.721411\pi$
$509$	−28.9158	−1.28167	−0.640834	+	0.767679i	$0.721411\pi$
$510$	−18.1937	−0.805628
$511$	−7.91382	−0.350087
$512$	1.00000	0.0441942
$513$	60.3192	2.66316
$514$	11.4611	0.505528
$515$	1.44285	0.0635794
$516$	−24.0213	−1.05748
$517$	8.74392	0.384557
$518$	9.48260	0.416642
$519$	67.4342	2.96003
$520$	−1.44285	−0.0632730
$521$	14.2471	0.624175	0.312088	−	0.950053i	$-0.398972\pi$
$521$	14.2471	0.624175	0.312088	+	0.950053i	$0.398972\pi$
$522$	21.9868	0.962335
$523$	−34.0350	−1.48825	−0.744123	−	0.668043i	$-0.767132\pi$
$523$	−34.0350	−1.48825	−0.744123	+	0.668043i	$0.767132\pi$
$524$	8.26730	0.361159
$525$	9.19607	0.401349
$526$	5.33572	0.232648
$527$	−32.1256	−1.39942
$528$	8.78482	0.382310
$529$	24.8669	1.08117
$530$	−20.4897	−0.890014
$531$	0.995428	0.0431979
$532$	−8.46564	−0.367032
$533$	−4.70417	−0.203760
$534$	42.8044	1.85233
$535$	−13.1022	−0.566456
$536$	13.5332	0.584547
$537$	−62.6363	−2.70296
$538$	15.1251	0.652089
$539$	17.5050	0.753992
$540$	−11.0419	−0.475168
$541$	−37.5971	−1.61642	−0.808212	−	0.588891i	$-0.799565\pi$
$541$	−37.5971	−1.61642	−0.808212	+	0.588891i	$0.799565\pi$
$542$	−4.37777	−0.188041
$543$	23.0022	0.987119
$544$	4.29774	0.184264
$545$	6.17942	0.264697
$546$	3.15129	0.134863
$547$	35.6687	1.52508	0.762542	−	0.646939i	$-0.223951\pi$
$547$	35.6687	1.52508	0.762542	+	0.646939i	$0.223951\pi$
$548$	−13.1756	−0.562832
$549$	−8.38103	−0.357694
$550$	8.73750	0.372568
$551$	−30.9000	−1.31638
$552$	20.2991	0.863988
$553$	−2.54808	−0.108355
$554$	−2.05261	−0.0872071
$555$	−37.3748	−1.58647
$556$	−2.99669	−0.127088
$557$	11.3398	0.480484	0.240242	−	0.970713i	$-0.422773\pi$
$557$	11.3398	0.480484	0.240242	+	0.970713i	$0.422773\pi$
$558$	−41.9224	−1.77472
$559$	−8.18721	−0.346282
$560$	1.54970	0.0654869
$561$	37.7548	1.59401
$562$	24.1145	1.01721
$563$	−32.9820	−1.39003	−0.695014	−	0.718997i	$-0.744602\pi$
$563$	−32.9820	−1.39003	−0.695014	+	0.718997i	$0.744602\pi$
$564$	8.56826	0.360789
$565$	−2.59916	−0.109347
$566$	7.58433	0.318793
$567$	6.04532	0.253880
$568$	−2.30629	−0.0967699
$569$	31.8117	1.33362	0.666809	−	0.745229i	$-0.267660\pi$
$569$	31.8117	1.33362	0.666809	+	0.745229i	$0.267660\pi$
$570$	33.3665	1.39757
$571$	31.1966	1.30554	0.652770	−	0.757557i	$-0.273607\pi$
$571$	31.1966	1.30554	0.652770	+	0.757557i	$0.273607\pi$
$572$	2.99415	0.125192
$573$	40.3303	1.68482
$574$	5.05256	0.210890
$575$	20.1898	0.841972
$576$	5.60834	0.233681
$577$	2.01145	0.0837377	0.0418688	−	0.999123i	$-0.486669\pi$
$577$	2.01145	0.0837377	0.0418688	+	0.999123i	$0.486669\pi$
$578$	1.47056	0.0611670
$579$	59.9660	2.49210
$580$	5.65649	0.234873
$581$	−7.91468	−0.328356
$582$	33.6352	1.39422
$583$	42.5195	1.76098
$584$	−7.36814	−0.304896
$585$	−8.09198	−0.334562
$586$	−26.1822	−1.08158
$587$	−41.5548	−1.71515	−0.857576	−	0.514357i	$-0.828031\pi$
$587$	−41.5548	−1.71515	−0.857576	+	0.514357i	$0.828031\pi$
$588$	17.1533	0.707391
$589$	58.9173	2.42765
$590$	0.256092	0.0105431
$591$	−73.9406	−3.04151
$592$	8.82875	0.362859
$593$	−31.6136	−1.29822	−0.649108	−	0.760696i	$-0.724858\pi$
$593$	−31.6136	−1.29822	−0.649108	+	0.760696i	$0.724858\pi$
$594$	22.9138	0.940165
$595$	6.66022	0.273042
$596$	−15.2007	−0.622643
$597$	−6.71868	−0.274977
$598$	6.91859	0.282922
$599$	35.9225	1.46775	0.733876	−	0.679283i	$-0.237709\pi$
$599$	35.9225	1.46775	0.733876	+	0.679283i	$0.237709\pi$
$600$	8.56197	0.349541
$601$	30.9399	1.26207	0.631033	−	0.775756i	$-0.282631\pi$
$601$	30.9399	1.26207	0.631033	+	0.775756i	$0.282631\pi$
$602$	8.79356	0.358399
$603$	75.8991	3.09085
$604$	3.44683	0.140250
$605$	−2.93632	−0.119379
$606$	−15.6503	−0.635750
$607$	11.7999	0.478941	0.239471	−	0.970904i	$-0.423026\pi$
$607$	11.7999	0.478941	0.239471	+	0.970904i	$0.423026\pi$
$608$	−7.88191	−0.319653
$609$	−12.3542	−0.500618
$610$	−2.15617	−0.0873008
$611$	2.92034	0.118144
$612$	24.1032	0.974314
$613$	23.7341	0.958611	0.479306	−	0.877648i	$-0.340889\pi$
$613$	23.7341	0.958611	0.479306	+	0.877648i	$0.340889\pi$
$614$	−31.0675	−1.25378
$615$	−19.9142	−0.803018
$616$	−3.21589	−0.129572
$617$	22.0126	0.886194	0.443097	−	0.896474i	$-0.353880\pi$
$617$	22.0126	0.886194	0.443097	+	0.896474i	$0.353880\pi$
$618$	−2.93400	−0.118023
$619$	−17.0295	−0.684473	−0.342237	−	0.939614i	$-0.611184\pi$
$619$	−17.0295	−0.684473	−0.342237	+	0.939614i	$0.611184\pi$
$620$	−10.7853	−0.433148
$621$	52.9471	2.12469
$622$	−33.5487	−1.34518
$623$	−15.6696	−0.627788
$624$	2.93400	0.117454
$625$	−1.89317	−0.0757269
$626$	−29.2826	−1.17037
$627$	−69.2411	−2.76522
$628$	19.9168	0.794766
$629$	37.9437	1.51291
$630$	8.69127	0.346268
$631$	29.3296	1.16759	0.583796	−	0.811900i	$-0.301567\pi$
$631$	29.3296	1.16759	0.583796	+	0.811900i	$0.301567\pi$
$632$	−2.37238	−0.0943684
$633$	15.1443	0.601930
$634$	−5.56307	−0.220938
$635$	−4.34100	−0.172267
$636$	41.6653	1.65214
$637$	5.84640	0.231643
$638$	−11.7382	−0.464718
$639$	−12.9345	−0.511680
$640$	1.44285	0.0570335
$641$	11.6367	0.459624	0.229812	−	0.973235i	$-0.426189\pi$
$641$	11.6367	0.459624	0.229812	+	0.973235i	$0.426189\pi$
$642$	26.6430	1.05151
$643$	−9.14163	−0.360511	−0.180255	−	0.983620i	$-0.557692\pi$
$643$	−9.14163	−0.360511	−0.180255	+	0.983620i	$0.557692\pi$
$644$	−7.43098	−0.292822
$645$	−34.6590	−1.36470
$646$	−33.8744	−1.33277
$647$	−26.5206	−1.04263	−0.521316	−	0.853364i	$-0.674559\pi$
$647$	−26.5206	−1.04263	−0.521316	+	0.853364i	$0.674559\pi$
$648$	5.62848	0.221107
$649$	−0.531433	−0.0208606
$650$	2.91819	0.114461
$651$	23.5559	0.923229
$652$	−10.8879	−0.426403
$653$	4.49543	0.175920	0.0879599	−	0.996124i	$-0.471965\pi$
$653$	4.49543	0.175920	0.0879599	+	0.996124i	$0.471965\pi$
$654$	−12.5657	−0.491359
$655$	11.9284	0.466083
$656$	4.70417	0.183667
$657$	−41.3230	−1.61216
$658$	−3.13662	−0.122278
$659$	−6.56076	−0.255571	−0.127786	−	0.991802i	$-0.540787\pi$
$659$	−6.56076	−0.255571	−0.127786	+	0.991802i	$0.540787\pi$
$660$	12.6751	0.493379
$661$	−28.9220	−1.12494	−0.562469	−	0.826819i	$-0.690148\pi$
$661$	−28.9220	−1.12494	−0.562469	+	0.826819i	$0.690148\pi$
$662$	19.6063	0.762019
$663$	12.6096	0.489715
$664$	−7.36894	−0.285970
$665$	−12.2146	−0.473662
$666$	49.5147	1.91865
$667$	−27.1234	−1.05022
$668$	1.06864	0.0413470
$669$	51.4936	1.99086
$670$	19.5264	0.754371
$671$	4.47441	0.172733
$672$	−3.15129	−0.121564
$673$	50.8221	1.95905	0.979523	−	0.201332i	$-0.0645270\pi$
$673$	50.8221	1.95905	0.979523	+	0.201332i	$0.0645270\pi$
$674$	15.4607	0.595522
$675$	22.3326	0.859581
$676$	1.00000	0.0384615
$677$	−21.0618	−0.809469	−0.404735	−	0.914434i	$-0.632636\pi$
$677$	−21.0618	−0.809469	−0.404735	+	0.914434i	$0.632636\pi$
$678$	5.28534	0.202982
$679$	−12.3129	−0.472528
$680$	6.20098	0.237797
$681$	−44.4267	−1.70244
$682$	22.3813	0.857023
$683$	21.4048	0.819032	0.409516	−	0.912303i	$-0.365698\pi$
$683$	21.4048	0.819032	0.409516	+	0.912303i	$0.365698\pi$
$684$	−44.2044	−1.69020
$685$	−19.0103	−0.726347
$686$	−13.7978	−0.526802
$687$	−20.2879	−0.774031
$688$	8.18721	0.312135
$689$	14.2009	0.541010
$690$	29.2885	1.11499
$691$	−18.8129	−0.715676	−0.357838	−	0.933784i	$-0.616486\pi$
$691$	−18.8129	−0.715676	−0.357838	+	0.933784i	$0.616486\pi$
$692$	−22.9837	−0.873710
$693$	−18.0358	−0.685124
$694$	−3.15531	−0.119774
$695$	−4.32377	−0.164010
$696$	−11.5024	−0.435996
$697$	20.2173	0.765785
$698$	21.3376	0.807642
$699$	42.5933	1.61103
$700$	−3.13431	−0.118466
$701$	12.1919	0.460480	0.230240	−	0.973134i	$-0.426049\pi$
$701$	12.1919	0.460480	0.230240	+	0.973134i	$0.426049\pi$
$702$	7.65287	0.288839
$703$	−69.5874	−2.62454
$704$	−2.99415	−0.112846
$705$	12.3627	0.465606
$706$	11.2151	0.422086
$707$	5.72916	0.215467
$708$	−0.520757	−0.0195712
$709$	20.3154	0.762959	0.381480	−	0.924377i	$-0.375415\pi$
$709$	20.3154	0.762959	0.381480	+	0.924377i	$0.375415\pi$
$710$	−3.32763	−0.124884
$711$	−13.3051	−0.498982
$712$	−14.5891	−0.546750
$713$	51.7165	1.93680
$714$	−13.5434	−0.506850
$715$	4.32009	0.161562
$716$	21.3485	0.797830
$717$	9.69196	0.361953
$718$	26.1381	0.975467
$719$	−31.6668	−1.18097	−0.590486	−	0.807048i	$-0.701064\pi$
$719$	−31.6668	−1.18097	−0.590486	+	0.807048i	$0.701064\pi$
$720$	8.09198	0.301570
$721$	1.07406	0.0400001
$722$	43.1244	1.60493
$723$	43.7139	1.62574
$724$	−7.83988	−0.291367
$725$	−11.4404	−0.424886
$726$	5.97095	0.221603
$727$	−5.08336	−0.188531	−0.0942657	−	0.995547i	$-0.530050\pi$
$727$	−5.08336	−0.188531	−0.0942657	+	0.995547i	$0.530050\pi$
$728$	−1.07406	−0.0398073
$729$	−35.7941	−1.32571
$730$	−10.6311	−0.393474
$731$	35.1865	1.30142
$732$	4.38453	0.162057
$733$	19.3221	0.713677	0.356839	−	0.934166i	$-0.383855\pi$
$733$	19.3221	0.713677	0.356839	+	0.934166i	$0.383855\pi$
$734$	−4.22487	−0.155943
$735$	24.7496	0.912903
$736$	−6.91859	−0.255023
$737$	−40.5205	−1.49259
$738$	26.3826	0.971157
$739$	17.5707	0.646348	0.323174	−	0.946340i	$-0.395250\pi$
$739$	17.5707	0.646348	0.323174	+	0.946340i	$0.395250\pi$
$740$	12.7385	0.468278
$741$	−23.1255	−0.849536
$742$	−15.2526	−0.559940
$743$	21.9923	0.806820	0.403410	−	0.915019i	$-0.367825\pi$
$743$	21.9923	0.806820	0.403410	+	0.915019i	$0.367825\pi$
$744$	21.9317	0.804054
$745$	−21.9322	−0.803534
$746$	8.46477	0.309917
$747$	−41.3275	−1.51210
$748$	−12.8681	−0.470503
$749$	−9.75329	−0.356377
$750$	33.5202	1.22398
$751$	−49.6906	−1.81324	−0.906618	−	0.421953i	$-0.861345\pi$
$751$	−49.6906	−1.81324	−0.906618	+	0.421953i	$0.861345\pi$
$752$	−2.92034	−0.106494
$753$	−78.7304	−2.86910
$754$	−3.92037	−0.142771
$755$	4.97325	0.180995
$756$	−8.21964	−0.298945
$757$	−42.1934	−1.53355	−0.766773	−	0.641919i	$-0.778139\pi$
$757$	−42.1934	−1.53355	−0.766773	+	0.641919i	$0.778139\pi$
$758$	−11.7235	−0.425818
$759$	−60.7785	−2.20612
$760$	−11.3724	−0.412520
$761$	18.4120	0.667436	0.333718	−	0.942673i	$-0.391697\pi$
$761$	18.4120	0.667436	0.333718	+	0.942673i	$0.391697\pi$
$762$	8.82732	0.319780
$763$	4.59998	0.166531
$764$	−13.7458	−0.497307
$765$	34.7772	1.25737
$766$	12.6143	0.455774
$767$	−0.177491	−0.00640881
$768$	−2.93400	−0.105872
$769$	−17.1982	−0.620182	−0.310091	−	0.950707i	$-0.600360\pi$
$769$	−17.1982	−0.620182	−0.310091	+	0.950707i	$0.600360\pi$
$770$	−4.64004	−0.167215
$771$	−33.6269	−1.21104
$772$	−20.4383	−0.735592
$773$	−24.1977	−0.870329	−0.435165	−	0.900351i	$-0.643310\pi$
$773$	−24.1977	−0.870329	−0.435165	+	0.900351i	$0.643310\pi$
$774$	45.9167	1.65044
$775$	21.8135	0.783565
$776$	−11.4639	−0.411531
$777$	−27.8219	−0.998107
$778$	1.84975	0.0663168
$779$	−37.0778	−1.32845
$780$	4.23331	0.151577
$781$	6.90538	0.247094
$782$	−29.7343	−1.06330
$783$	−30.0021	−1.07219
$784$	−5.84640	−0.208800
$785$	28.7368	1.02566
$786$	−24.2562	−0.865191
$787$	40.0180	1.42649	0.713243	−	0.700917i	$-0.247226\pi$
$787$	40.0180	1.42649	0.713243	+	0.700917i	$0.247226\pi$
$788$	25.2013	0.897760
$789$	−15.6550	−0.557332
$790$	−3.42299	−0.121784
$791$	−1.93482	−0.0687944
$792$	−16.7922	−0.596685
$793$	1.49439	0.0530672
$794$	16.1243	0.572230
$795$	60.1166	2.13212
$796$	2.28994	0.0811648
$797$	−23.8535	−0.844935	−0.422468	−	0.906378i	$-0.638836\pi$
$797$	−23.8535	−0.844935	−0.422468	+	0.906378i	$0.638836\pi$
$798$	24.8382	0.879261
$799$	−12.5508	−0.444017
$800$	−2.91819	−0.103174
$801$	−81.8207	−2.89099
$802$	−15.0926	−0.532938
$803$	22.0613	0.778525
$804$	−39.7065	−1.40034
$805$	−10.7218	−0.377892
$806$	7.47501	0.263296
$807$	−44.3770	−1.56214
$808$	5.33412	0.187654
$809$	25.8850	0.910067	0.455033	−	0.890474i	$-0.349627\pi$
$809$	25.8850	0.910067	0.455033	+	0.890474i	$0.349627\pi$
$810$	8.12103	0.285344
$811$	19.7733	0.694336	0.347168	−	0.937803i	$-0.387143\pi$
$811$	19.7733	0.694336	0.347168	+	0.937803i	$0.387143\pi$
$812$	4.21071	0.147767
$813$	12.8444	0.450472
$814$	−26.4346	−0.926531
$815$	−15.7096	−0.550283
$816$	−12.6096	−0.441423
$817$	−64.5308	−2.25765
$818$	−12.3802	−0.432863
$819$	−6.02369	−0.210485
$820$	6.78740	0.237026
$821$	50.0883	1.74809	0.874047	−	0.485841i	$-0.161487\pi$
$821$	50.0883	1.74809	0.874047	+	0.485841i	$0.161487\pi$
$822$	38.6571	1.34832
$823$	−8.72147	−0.304011	−0.152006	−	0.988380i	$-0.548573\pi$
$823$	−8.72147	−0.304011	−0.152006	+	0.988380i	$0.548573\pi$
$824$	1.00000	0.0348367
$825$	−25.6358	−0.892524
$826$	0.190635	0.00663305
$827$	30.1373	1.04798	0.523989	−	0.851725i	$-0.324443\pi$
$827$	30.1373	1.04798	0.523989	+	0.851725i	$0.324443\pi$
$828$	−38.8018	−1.34846
$829$	31.3010	1.08713	0.543564	−	0.839367i	$-0.317074\pi$
$829$	31.3010	1.08713	0.543564	+	0.839367i	$0.317074\pi$
$830$	−10.6322	−0.369051
$831$	6.02236	0.208913
$832$	−1.00000	−0.0346688
$833$	−25.1263	−0.870574
$834$	8.79229	0.304452
$835$	1.54189	0.0533592
$836$	23.5996	0.816208
$837$	57.2053	1.97730
$838$	26.8813	0.928600
$839$	−29.8169	−1.02939	−0.514697	−	0.857372i	$-0.672096\pi$
$839$	−29.8169	−1.02939	−0.514697	+	0.857372i	$0.672096\pi$
$840$	−4.54683	−0.156880
$841$	−13.6307	−0.470024
$842$	−13.6791	−0.471414
$843$	−70.7517	−2.43682
$844$	−5.16164	−0.177671
$845$	1.44285	0.0496354
$846$	−16.3783	−0.563096
$847$	−2.18581	−0.0751053
$848$	−14.2009	−0.487660
$849$	−22.2524	−0.763700
$850$	−12.5416	−0.430175
$851$	−61.0825	−2.09388
$852$	6.76666	0.231822
$853$	−4.45153	−0.152417	−0.0762087	−	0.997092i	$-0.524282\pi$
$853$	−4.45153	−0.152417	−0.0762087	+	0.997092i	$0.524282\pi$
$854$	−1.60506	−0.0549240
$855$	−63.7802	−2.18124
$856$	−9.08077	−0.310374
$857$	−14.2184	−0.485692	−0.242846	−	0.970065i	$-0.578081\pi$
$857$	−14.2184	−0.485692	−0.242846	+	0.970065i	$0.578081\pi$
$858$	−8.78482	−0.299909
$859$	−30.0618	−1.02570	−0.512848	−	0.858479i	$-0.671410\pi$
$859$	−30.0618	−1.02570	−0.512848	+	0.858479i	$0.671410\pi$
$860$	11.8129	0.402816
$861$	−14.8242	−0.505208
$862$	5.60512	0.190911
$863$	−26.4806	−0.901411	−0.450706	−	0.892673i	$-0.648828\pi$
$863$	−26.4806	−0.901411	−0.450706	+	0.892673i	$0.648828\pi$
$864$	−7.65287	−0.260356
$865$	−33.1620	−1.12754
$866$	5.47408	0.186017
$867$	−4.31461	−0.146532
$868$	−8.02861	−0.272509
$869$	7.10326	0.240962
$870$	−16.5961	−0.562662
$871$	−13.5332	−0.458557
$872$	4.28280	0.145034
$873$	−64.2937	−2.17601
$874$	54.5317	1.84456
$875$	−12.2709	−0.414830
$876$	21.6181	0.730408
$877$	−36.9549	−1.24788	−0.623939	−	0.781473i	$-0.714469\pi$
$877$	−36.9549	−1.24788	−0.623939	+	0.781473i	$0.714469\pi$
$878$	−7.03409	−0.237389
$879$	76.8184	2.59102
$880$	−4.32009	−0.145630
$881$	−16.0760	−0.541615	−0.270808	−	0.962633i	$-0.587291\pi$
$881$	−16.0760	−0.541615	−0.270808	+	0.962633i	$0.587291\pi$
$882$	−32.7886	−1.10405
$883$	−40.8656	−1.37524	−0.687619	−	0.726072i	$-0.741344\pi$
$883$	−40.8656	−1.37524	−0.687619	+	0.726072i	$0.741344\pi$
$884$	−4.29774	−0.144549
$885$	−0.751372	−0.0252571
$886$	−1.00244	−0.0336775
$887$	51.8380	1.74055	0.870275	−	0.492566i	$-0.163941\pi$
$887$	51.8380	1.74055	0.870275	+	0.492566i	$0.163941\pi$
$888$	−25.9035	−0.869266
$889$	−3.23145	−0.108379
$890$	−21.0498	−0.705593
$891$	−16.8525	−0.564579
$892$	−17.5507	−0.587640
$893$	23.0178	0.770262
$894$	44.5987	1.49160
$895$	30.8026	1.02962
$896$	1.07406	0.0358818
$897$	−20.2991	−0.677768
$898$	33.2664	1.11011
$899$	−29.3048	−0.977371
$900$	−16.3662	−0.545541
$901$	−61.0316	−2.03326
$902$	−14.0850	−0.468978
$903$	−25.8003	−0.858579
$904$	−1.80141	−0.0599141
$905$	−11.3117	−0.376015
$906$	−10.1130	−0.335982
$907$	−38.6240	−1.28249	−0.641245	−	0.767337i	$-0.721582\pi$
$907$	−38.6240	−1.28249	−0.641245	+	0.767337i	$0.721582\pi$
$908$	15.1420	0.502506
$909$	29.9156	0.992237
$910$	−1.54970	−0.0513722
$911$	19.0473	0.631064	0.315532	−	0.948915i	$-0.397817\pi$
$911$	19.0473	0.631064	0.315532	+	0.948915i	$0.397817\pi$
$912$	23.1255	0.765762
$913$	22.0637	0.730201
$914$	−16.5707	−0.548111
$915$	6.32620	0.209138
$916$	6.91476	0.228470
$917$	8.87957	0.293229
$918$	−32.8900	−1.08553
$919$	18.1117	0.597449	0.298725	−	0.954339i	$-0.403439\pi$
$919$	18.1117	0.597449	0.298725	+	0.954339i	$0.403439\pi$
$920$	−9.98246	−0.329112
$921$	91.1519	3.00356
$922$	40.6434	1.33852
$923$	2.30629	0.0759126
$924$	9.43542	0.310402
$925$	−25.7640	−0.847115
$926$	15.0877	0.495811
$927$	5.60834	0.184202
$928$	3.92037	0.128692
$929$	−58.8057	−1.92935	−0.964676	−	0.263440i	$-0.915143\pi$
$929$	−58.8057	−1.92935	−0.964676	+	0.263440i	$0.915143\pi$
$930$	31.6440	1.03765
$931$	46.0807	1.51024
$932$	−14.5172	−0.475525
$933$	98.4318	3.22251
$934$	−9.24953	−0.302654
$935$	−18.5666	−0.607194
$936$	−5.60834	−0.183314
$937$	4.43202	0.144788	0.0723938	−	0.997376i	$-0.476936\pi$
$937$	4.43202	0.144788	0.0723938	+	0.997376i	$0.476936\pi$
$938$	14.5355	0.474601
$939$	85.9150	2.80373
$940$	−4.21360	−0.137432
$941$	2.26551	0.0738536	0.0369268	−	0.999318i	$-0.488243\pi$
$941$	2.26551	0.0738536	0.0369268	+	0.999318i	$0.488243\pi$
$942$	−58.4358	−1.90394
$943$	−32.5462	−1.05985
$944$	0.177491	0.00577682
$945$	−11.8597	−0.385795
$946$	−24.5137	−0.797010
$947$	36.2269	1.17722	0.588609	−	0.808418i	$-0.299676\pi$
$947$	36.2269	1.17722	0.588609	+	0.808418i	$0.299676\pi$
$948$	6.96057	0.226069
$949$	7.36814	0.239180
$950$	23.0009	0.746249
$951$	16.3220	0.529278
$952$	4.61603	0.149606
$953$	−7.60384	−0.246313	−0.123156	−	0.992387i	$-0.539302\pi$
$953$	−7.60384	−0.246313	−0.123156	+	0.992387i	$0.539302\pi$
$954$	−79.6433	−2.57855
$955$	−19.8331	−0.641785
$956$	−3.30333	−0.106837
$957$	34.4397	1.11328
$958$	34.6637	1.11993
$959$	−14.1513	−0.456970
$960$	−4.23331	−0.136629
$961$	24.8758	0.802446
$962$	−8.82875	−0.284650
$963$	−50.9281	−1.64113
$964$	−14.8991	−0.479867
$965$	−29.4894	−0.949297
$966$	21.8025	0.701483
$967$	−36.6468	−1.17848	−0.589241	−	0.807957i	$-0.700573\pi$
$967$	−36.6468	−1.17848	−0.589241	+	0.807957i	$0.700573\pi$
$968$	−2.03509	−0.0654103
$969$	99.3873	3.19278
$970$	−16.5407	−0.531090
$971$	7.48447	0.240188	0.120094	−	0.992763i	$-0.461680\pi$
$971$	7.48447	0.240188	0.120094	+	0.992763i	$0.461680\pi$
$972$	6.44467	0.206713
$973$	−3.21863	−0.103184
$974$	29.8637	0.956896
$975$	−8.56197	−0.274203
$976$	−1.49439	−0.0478341
$977$	22.6044	0.723180	0.361590	−	0.932337i	$-0.382234\pi$
$977$	22.6044	0.723180	0.361590	+	0.932337i	$0.382234\pi$
$978$	31.9451	1.02149
$979$	43.6819	1.39608
$980$	−8.43545	−0.269461
$981$	24.0194	0.766881
$982$	−1.87608	−0.0598680
$983$	−35.2915	−1.12562	−0.562812	−	0.826585i	$-0.690281\pi$
$983$	−35.2915	−1.12562	−0.562812	+	0.826585i	$0.690281\pi$
$984$	−13.8020	−0.439993
$985$	36.3616	1.15858
$986$	16.8487	0.536573
$987$	9.20283	0.292929
$988$	7.88191	0.250757
$989$	−56.6440	−1.80117
$990$	−24.2286	−0.770034
$991$	9.52967	0.302720	0.151360	−	0.988479i	$-0.451635\pi$
$991$	9.52967	0.302720	0.151360	+	0.988479i	$0.451635\pi$
$992$	−7.47501	−0.237332
$993$	−57.5247	−1.82549
$994$	−2.47710	−0.0785688
$995$	3.30403	0.104745
$996$	21.6205	0.685070
$997$	−18.8124	−0.595795	−0.297897	−	0.954598i	$-0.596285\pi$
$997$	−18.8124	−0.595795	−0.297897	+	0.954598i	$0.596285\pi$
$998$	−35.4738	−1.12290
$999$	−67.5653	−2.13767

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2678.2.a.s.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2678.2.a.s.1.2	✓	10	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:	\( N \)	\(=\)	\( 2678 = 2 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2678.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.93400 q^{3} +1.00000 q^{4} +1.44285 q^{5} -2.93400 q^{6} +1.07406 q^{7} +1.00000 q^{8} +5.60834 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.93400 q^{3} +1.00000 q^{4} +1.44285 q^{5} -2.93400 q^{6} +1.07406 q^{7} +1.00000 q^{8} +5.60834 q^{9} +1.44285 q^{10} -2.99415 q^{11} -2.93400 q^{12} -1.00000 q^{13} +1.07406 q^{14} -4.23331 q^{15} +1.00000 q^{16} +4.29774 q^{17} +5.60834 q^{18} -7.88191 q^{19} +1.44285 q^{20} -3.15129 q^{21} -2.99415 q^{22} -6.91859 q^{23} -2.93400 q^{24} -2.91819 q^{25} -1.00000 q^{26} -7.65287 q^{27} +1.07406 q^{28} +3.92037 q^{29} -4.23331 q^{30} -7.47501 q^{31} +1.00000 q^{32} +8.78482 q^{33} +4.29774 q^{34} +1.54970 q^{35} +5.60834 q^{36} +8.82875 q^{37} -7.88191 q^{38} +2.93400 q^{39} +1.44285 q^{40} +4.70417 q^{41} -3.15129 q^{42} +8.18721 q^{43} -2.99415 q^{44} +8.09198 q^{45} -6.91859 q^{46} -2.92034 q^{47} -2.93400 q^{48} -5.84640 q^{49} -2.91819 q^{50} -12.6096 q^{51} -1.00000 q^{52} -14.2009 q^{53} -7.65287 q^{54} -4.32009 q^{55} +1.07406 q^{56} +23.1255 q^{57} +3.92037 q^{58} +0.177491 q^{59} -4.23331 q^{60} -1.49439 q^{61} -7.47501 q^{62} +6.02369 q^{63} +1.00000 q^{64} -1.44285 q^{65} +8.78482 q^{66} +13.5332 q^{67} +4.29774 q^{68} +20.2991 q^{69} +1.54970 q^{70} -2.30629 q^{71} +5.60834 q^{72} -7.36814 q^{73} +8.82875 q^{74} +8.56197 q^{75} -7.88191 q^{76} -3.21589 q^{77} +2.93400 q^{78} -2.37238 q^{79} +1.44285 q^{80} +5.62848 q^{81} +4.70417 q^{82} -7.36894 q^{83} -3.15129 q^{84} +6.20098 q^{85} +8.18721 q^{86} -11.5024 q^{87} -2.99415 q^{88} -14.5891 q^{89} +8.09198 q^{90} -1.07406 q^{91} -6.91859 q^{92} +21.9317 q^{93} -2.92034 q^{94} -11.3724 q^{95} -2.93400 q^{96} -11.4639 q^{97} -5.84640 q^{98} -16.7922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9	\( 10 q + 10 q^{2} - 6 q^{3} + 10 q^{4} - 3 q^{5} - 6 q^{6} - 10 q^{7} + 10 q^{8} + 4 q^{9} - 3 q^{10} - 5 q^{11} - 6 q^{12} - 10 q^{13} - 10 q^{14} - 13 q^{15} + 10 q^{16} - 13 q^{17} + 4 q^{18} - 21 q^{19} - 3 q^{20} + 5 q^{21} - 5 q^{22} - 5 q^{23} - 6 q^{24} + 13 q^{25} - 10 q^{26} - 9 q^{27} - 10 q^{28} + 6 q^{29} - 13 q^{30} - 33 q^{31} + 10 q^{32} - 22 q^{33} - 13 q^{34} - 9 q^{35} + 4 q^{36} - 7 q^{37} - 21 q^{38} + 6 q^{39} - 3 q^{40} - 20 q^{41} + 5 q^{42} - 22 q^{43} - 5 q^{44} - 14 q^{45} - 5 q^{46} - 31 q^{47} - 6 q^{48} + 8 q^{49} + 13 q^{50} - 8 q^{51} - 10 q^{52} + q^{53} - 9 q^{54} - 30 q^{55} - 10 q^{56} + 33 q^{57} + 6 q^{58} - 51 q^{59} - 13 q^{60} - 6 q^{61} - 33 q^{62} - 25 q^{63} + 10 q^{64} + 3 q^{65} - 22 q^{66} - 19 q^{67} - 13 q^{68} + 6 q^{69} - 9 q^{70} - 14 q^{71} + 4 q^{72} - 16 q^{73} - 7 q^{74} + 5 q^{75} - 21 q^{76} - 5 q^{77} + 6 q^{78} + 11 q^{79} - 3 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} + 5 q^{84} - 27 q^{85} - 22 q^{86} - 5 q^{88} - 47 q^{89} - 14 q^{90} + 10 q^{91} - 5 q^{92} + 12 q^{93} - 31 q^{94} - 14 q^{95} - 6 q^{96} - 44 q^{97} + 8 q^{98} + 23 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 - 6 * q^3 + 10 * q^4 - 3 * q^5 - 6 * q^6 - 10 * q^7 + 10 * q^8 + 4 * q^9 - 3 * q^10 - 5 * q^11 - 6 * q^12 - 10 * q^13 - 10 * q^14 - 13 * q^15 + 10 * q^16 - 13 * q^17 + 4 * q^18 - 21 * q^19 - 3 * q^20 + 5 * q^21 - 5 * q^22 - 5 * q^23 - 6 * q^24 + 13 * q^25 - 10 * q^26 - 9 * q^27 - 10 * q^28 + 6 * q^29 - 13 * q^30 - 33 * q^31 + 10 * q^32 - 22 * q^33 - 13 * q^34 - 9 * q^35 + 4 * q^36 - 7 * q^37 - 21 * q^38 + 6 * q^39 - 3 * q^40 - 20 * q^41 + 5 * q^42 - 22 * q^43 - 5 * q^44 - 14 * q^45 - 5 * q^46 - 31 * q^47 - 6 * q^48 + 8 * q^49 + 13 * q^50 - 8 * q^51 - 10 * q^52 + q^53 - 9 * q^54 - 30 * q^55 - 10 * q^56 + 33 * q^57 + 6 * q^58 - 51 * q^59 - 13 * q^60 - 6 * q^61 - 33 * q^62 - 25 * q^63 + 10 * q^64 + 3 * q^65 - 22 * q^66 - 19 * q^67 - 13 * q^68 + 6 * q^69 - 9 * q^70 - 14 * q^71 + 4 * q^72 - 16 * q^73 - 7 * q^74 + 5 * q^75 - 21 * q^76 - 5 * q^77 + 6 * q^78 + 11 * q^79 - 3 * q^80 - 2 * q^81 - 20 * q^82 + q^83 + 5 * q^84 - 27 * q^85 - 22 * q^86 - 5 * q^88 - 47 * q^89 - 14 * q^90 + 10 * q^91 - 5 * q^92 + 12 * q^93 - 31 * q^94 - 14 * q^95 - 6 * q^96 - 44 * q^97 + 8 * q^98 + 23 * q^99

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