LMFDB - Embedded newform 966.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -3.12311 q^{11} -1.00000 q^{12} +0.561553 q^{13} +1.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} +7.12311 q^{17} -1.00000 q^{18} +3.12311 q^{19} +2.56155 q^{20} +1.00000 q^{21} +3.12311 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.56155 q^{25} -0.561553 q^{26} -1.00000 q^{27} -1.00000 q^{28} +3.43845 q^{29} +2.56155 q^{30} -5.12311 q^{31} -1.00000 q^{32} +3.12311 q^{33} -7.12311 q^{34} -2.56155 q^{35} +1.00000 q^{36} +2.56155 q^{37} -3.12311 q^{38} -0.561553 q^{39} -2.56155 q^{40} -0.561553 q^{41} -1.00000 q^{42} -5.68466 q^{43} -3.12311 q^{44} +2.56155 q^{45} -1.00000 q^{46} +6.56155 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.56155 q^{50} -7.12311 q^{51} +0.561553 q^{52} -2.24621 q^{53} +1.00000 q^{54} -8.00000 q^{55} +1.00000 q^{56} -3.12311 q^{57} -3.43845 q^{58} +13.1231 q^{59} -2.56155 q^{60} +9.12311 q^{61} +5.12311 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.43845 q^{65} -3.12311 q^{66} +7.12311 q^{67} +7.12311 q^{68} -1.00000 q^{69} +2.56155 q^{70} +15.3693 q^{71} -1.00000 q^{72} +0.876894 q^{73} -2.56155 q^{74} -1.56155 q^{75} +3.12311 q^{76} +3.12311 q^{77} +0.561553 q^{78} -2.24621 q^{79} +2.56155 q^{80} +1.00000 q^{81} +0.561553 q^{82} -0.876894 q^{83} +1.00000 q^{84} +18.2462 q^{85} +5.68466 q^{86} -3.43845 q^{87} +3.12311 q^{88} +14.0000 q^{89} -2.56155 q^{90} -0.561553 q^{91} +1.00000 q^{92} +5.12311 q^{93} -6.56155 q^{94} +8.00000 q^{95} +1.00000 q^{96} -16.5616 q^{97} -1.00000 q^{98} -3.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + q^{20} + 2 q^{21} - 2 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} + 3 q^{26} - 2 q^{27} - 2 q^{28} + 11 q^{29} + q^{30} - 2 q^{31} - 2 q^{32} - 2 q^{33} - 6 q^{34} - q^{35} + 2 q^{36} + q^{37} + 2 q^{38} + 3 q^{39} - q^{40} + 3 q^{41} - 2 q^{42} + q^{43} + 2 q^{44} + q^{45} - 2 q^{46} + 9 q^{47} - 2 q^{48} + 2 q^{49} + q^{50} - 6 q^{51} - 3 q^{52} + 12 q^{53} + 2 q^{54} - 16 q^{55} + 2 q^{56} + 2 q^{57} - 11 q^{58} + 18 q^{59} - q^{60} + 10 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 7 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - 2 q^{69} + q^{70} + 6 q^{71} - 2 q^{72} + 10 q^{73} - q^{74} + q^{75} - 2 q^{76} - 2 q^{77} - 3 q^{78} + 12 q^{79} + q^{80} + 2 q^{81} - 3 q^{82} - 10 q^{83} + 2 q^{84} + 20 q^{85} - q^{86} - 11 q^{87} - 2 q^{88} + 28 q^{89} - q^{90} + 3 q^{91} + 2 q^{92} + 2 q^{93} - 9 q^{94} + 16 q^{95} + 2 q^{96} - 29 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 2 * q^19 + q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 + 2 * q^24 - q^25 + 3 * q^26 - 2 * q^27 - 2 * q^28 + 11 * q^29 + q^30 - 2 * q^31 - 2 * q^32 - 2 * q^33 - 6 * q^34 - q^35 + 2 * q^36 + q^37 + 2 * q^38 + 3 * q^39 - q^40 + 3 * q^41 - 2 * q^42 + q^43 + 2 * q^44 + q^45 - 2 * q^46 + 9 * q^47 - 2 * q^48 + 2 * q^49 + q^50 - 6 * q^51 - 3 * q^52 + 12 * q^53 + 2 * q^54 - 16 * q^55 + 2 * q^56 + 2 * q^57 - 11 * q^58 + 18 * q^59 - q^60 + 10 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 7 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - 2 * q^69 + q^70 + 6 * q^71 - 2 * q^72 + 10 * q^73 - q^74 + q^75 - 2 * q^76 - 2 * q^77 - 3 * q^78 + 12 * q^79 + q^80 + 2 * q^81 - 3 * q^82 - 10 * q^83 + 2 * q^84 + 20 * q^85 - q^86 - 11 * q^87 - 2 * q^88 + 28 * q^89 - q^90 + 3 * q^91 + 2 * q^92 + 2 * q^93 - 9 * q^94 + 16 * q^95 + 2 * q^96 - 29 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.56155	1.14556	0.572781	−	0.819709i	$-0.305865\pi$
$5$	2.56155	1.14556	0.572781	+	0.819709i	$0.305865\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56155	−0.810034
$11$	−3.12311	−0.941652	−0.470826	−	0.882226i	$-0.656044\pi$
$11$	−3.12311	−0.941652	−0.470826	+	0.882226i	$0.656044\pi$
$12$	−1.00000	−0.288675
$13$	0.561553	0.155747	0.0778734	−	0.996963i	$-0.475187\pi$
$13$	0.561553	0.155747	0.0778734	+	0.996963i	$0.475187\pi$
$14$	1.00000	0.267261
$15$	−2.56155	−0.661390
$16$	1.00000	0.250000
$17$	7.12311	1.72761	0.863803	−	0.503829i	$-0.168076\pi$
$17$	7.12311	1.72761	0.863803	+	0.503829i	$0.168076\pi$
$18$	−1.00000	−0.235702
$19$	3.12311	0.716490	0.358245	−	0.933628i	$-0.383375\pi$
$19$	3.12311	0.716490	0.358245	+	0.933628i	$0.383375\pi$
$20$	2.56155	0.572781
$21$	1.00000	0.218218
$22$	3.12311	0.665848
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.56155	0.312311
$26$	−0.561553	−0.110130
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	3.43845	0.638504	0.319252	−	0.947670i	$-0.396568\pi$
$29$	3.43845	0.638504	0.319252	+	0.947670i	$0.396568\pi$
$30$	2.56155	0.467673
$31$	−5.12311	−0.920137	−0.460068	−	0.887883i	$-0.652175\pi$
$31$	−5.12311	−0.920137	−0.460068	+	0.887883i	$0.652175\pi$
$32$	−1.00000	−0.176777
$33$	3.12311	0.543663
$34$	−7.12311	−1.22160
$35$	−2.56155	−0.432981
$36$	1.00000	0.166667
$37$	2.56155	0.421117	0.210558	−	0.977581i	$-0.432472\pi$
$37$	2.56155	0.421117	0.210558	+	0.977581i	$0.432472\pi$
$38$	−3.12311	−0.506635
$39$	−0.561553	−0.0899204
$40$	−2.56155	−0.405017
$41$	−0.561553	−0.0876998	−0.0438499	−	0.999038i	$-0.513962\pi$
$41$	−0.561553	−0.0876998	−0.0438499	+	0.999038i	$0.513962\pi$
$42$	−1.00000	−0.154303
$43$	−5.68466	−0.866902	−0.433451	−	0.901177i	$-0.642704\pi$
$43$	−5.68466	−0.866902	−0.433451	+	0.901177i	$0.642704\pi$
$44$	−3.12311	−0.470826
$45$	2.56155	0.381854
$46$	−1.00000	−0.147442
$47$	6.56155	0.957101	0.478550	−	0.878060i	$-0.341162\pi$
$47$	6.56155	0.957101	0.478550	+	0.878060i	$0.341162\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.56155	−0.220837
$51$	−7.12311	−0.997434
$52$	0.561553	0.0778734
$53$	−2.24621	−0.308541	−0.154270	−	0.988029i	$-0.549303\pi$
$53$	−2.24621	−0.308541	−0.154270	+	0.988029i	$0.549303\pi$
$54$	1.00000	0.136083
$55$	−8.00000	−1.07872
$56$	1.00000	0.133631
$57$	−3.12311	−0.413665
$58$	−3.43845	−0.451490
$59$	13.1231	1.70848	0.854241	−	0.519877i	$-0.174022\pi$
$59$	13.1231	1.70848	0.854241	+	0.519877i	$0.174022\pi$
$60$	−2.56155	−0.330695
$61$	9.12311	1.16809	0.584047	−	0.811720i	$-0.301468\pi$
$61$	9.12311	1.16809	0.584047	+	0.811720i	$0.301468\pi$
$62$	5.12311	0.650635
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	1.43845	0.178417
$66$	−3.12311	−0.384428
$67$	7.12311	0.870226	0.435113	−	0.900376i	$-0.356708\pi$
$67$	7.12311	0.870226	0.435113	+	0.900376i	$0.356708\pi$
$68$	7.12311	0.863803
$69$	−1.00000	−0.120386
$70$	2.56155	0.306164
$71$	15.3693	1.82400	0.912001	−	0.410188i	$-0.134537\pi$
$71$	15.3693	1.82400	0.912001	+	0.410188i	$0.134537\pi$
$72$	−1.00000	−0.117851
$73$	0.876894	0.102633	0.0513164	−	0.998682i	$-0.483658\pi$
$73$	0.876894	0.102633	0.0513164	+	0.998682i	$0.483658\pi$
$74$	−2.56155	−0.297774
$75$	−1.56155	−0.180313
$76$	3.12311	0.358245
$77$	3.12311	0.355911
$78$	0.561553	0.0635833
$79$	−2.24621	−0.252719	−0.126359	−	0.991985i	$-0.540329\pi$
$79$	−2.24621	−0.252719	−0.126359	+	0.991985i	$0.540329\pi$
$80$	2.56155	0.286390
$81$	1.00000	0.111111
$82$	0.561553	0.0620131
$83$	−0.876894	−0.0962517	−0.0481258	−	0.998841i	$-0.515325\pi$
$83$	−0.876894	−0.0962517	−0.0481258	+	0.998841i	$0.515325\pi$
$84$	1.00000	0.109109
$85$	18.2462	1.97908
$86$	5.68466	0.612992
$87$	−3.43845	−0.368640
$88$	3.12311	0.332924
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	−2.56155	−0.270011
$91$	−0.561553	−0.0588667
$92$	1.00000	0.104257
$93$	5.12311	0.531241
$94$	−6.56155	−0.676772
$95$	8.00000	0.820783
$96$	1.00000	0.102062
$97$	−16.5616	−1.68157	−0.840785	−	0.541368i	$-0.817906\pi$
$97$	−16.5616	−1.68157	−0.840785	+	0.541368i	$0.817906\pi$
$98$	−1.00000	−0.101015
$99$	−3.12311	−0.313884
$100$	1.56155	0.156155
$101$	−0.246211	−0.0244989	−0.0122495	−	0.999925i	$-0.503899\pi$
$101$	−0.246211	−0.0244989	−0.0122495	+	0.999925i	$0.503899\pi$
$102$	7.12311	0.705293
$103$	−9.93087	−0.978518	−0.489259	−	0.872139i	$-0.662733\pi$
$103$	−9.93087	−0.978518	−0.489259	+	0.872139i	$0.662733\pi$
$104$	−0.561553	−0.0550648
$105$	2.56155	0.249982
$106$	2.24621	0.218171
$107$	3.12311	0.301922	0.150961	−	0.988540i	$-0.451763\pi$
$107$	3.12311	0.301922	0.150961	+	0.988540i	$0.451763\pi$
$108$	−1.00000	−0.0962250
$109$	14.5616	1.39474	0.697372	−	0.716709i	$-0.254353\pi$
$109$	14.5616	1.39474	0.697372	+	0.716709i	$0.254353\pi$
$110$	8.00000	0.762770
$111$	−2.56155	−0.243132
$112$	−1.00000	−0.0944911
$113$	9.68466	0.911056	0.455528	−	0.890221i	$-0.349450\pi$
$113$	9.68466	0.911056	0.455528	+	0.890221i	$0.349450\pi$
$114$	3.12311	0.292506
$115$	2.56155	0.238866
$116$	3.43845	0.319252
$117$	0.561553	0.0519156
$118$	−13.1231	−1.20808
$119$	−7.12311	−0.652974
$120$	2.56155	0.233837
$121$	−1.24621	−0.113292
$122$	−9.12311	−0.825967
$123$	0.561553	0.0506335
$124$	−5.12311	−0.460068
$125$	−8.80776	−0.787790
$126$	1.00000	0.0890871
$127$	−4.31534	−0.382925	−0.191462	−	0.981500i	$-0.561323\pi$
$127$	−4.31534	−0.382925	−0.191462	+	0.981500i	$0.561323\pi$
$128$	−1.00000	−0.0883883
$129$	5.68466	0.500506
$130$	−1.43845	−0.126160
$131$	13.1231	1.14657	0.573286	−	0.819356i	$-0.305669\pi$
$131$	13.1231	1.14657	0.573286	+	0.819356i	$0.305669\pi$
$132$	3.12311	0.271831
$133$	−3.12311	−0.270808
$134$	−7.12311	−0.615343
$135$	−2.56155	−0.220463
$136$	−7.12311	−0.610801
$137$	−4.56155	−0.389720	−0.194860	−	0.980831i	$-0.562425\pi$
$137$	−4.56155	−0.389720	−0.194860	+	0.980831i	$0.562425\pi$
$138$	1.00000	0.0851257
$139$	−16.8078	−1.42562	−0.712808	−	0.701359i	$-0.752577\pi$
$139$	−16.8078	−1.42562	−0.712808	+	0.701359i	$0.752577\pi$
$140$	−2.56155	−0.216491
$141$	−6.56155	−0.552582
$142$	−15.3693	−1.28976
$143$	−1.75379	−0.146659
$144$	1.00000	0.0833333
$145$	8.80776	0.731445
$146$	−0.876894	−0.0725723
$147$	−1.00000	−0.0824786
$148$	2.56155	0.210558
$149$	10.2462	0.839402	0.419701	−	0.907662i	$-0.362135\pi$
$149$	10.2462	0.839402	0.419701	+	0.907662i	$0.362135\pi$
$150$	1.56155	0.127500
$151$	19.6847	1.60191	0.800957	−	0.598721i	$-0.204324\pi$
$151$	19.6847	1.60191	0.800957	+	0.598721i	$0.204324\pi$
$152$	−3.12311	−0.253317
$153$	7.12311	0.575869
$154$	−3.12311	−0.251667
$155$	−13.1231	−1.05407
$156$	−0.561553	−0.0449602
$157$	−2.24621	−0.179267	−0.0896336	−	0.995975i	$-0.528570\pi$
$157$	−2.24621	−0.179267	−0.0896336	+	0.995975i	$0.528570\pi$
$158$	2.24621	0.178699
$159$	2.24621	0.178136
$160$	−2.56155	−0.202509
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	−0.561553	−0.0438499
$165$	8.00000	0.622799
$166$	0.876894	0.0680602
$167$	2.24621	0.173817	0.0869085	−	0.996216i	$-0.472301\pi$
$167$	2.24621	0.173817	0.0869085	+	0.996216i	$0.472301\pi$
$168$	−1.00000	−0.0771517
$169$	−12.6847	−0.975743
$170$	−18.2462	−1.39942
$171$	3.12311	0.238830
$172$	−5.68466	−0.433451
$173$	−14.4924	−1.10184	−0.550919	−	0.834559i	$-0.685723\pi$
$173$	−14.4924	−1.10184	−0.550919	+	0.834559i	$0.685723\pi$
$174$	3.43845	0.260668
$175$	−1.56155	−0.118042
$176$	−3.12311	−0.235413
$177$	−13.1231	−0.986393
$178$	−14.0000	−1.04934
$179$	16.8078	1.25627	0.628136	−	0.778104i	$-0.283818\pi$
$179$	16.8078	1.25627	0.628136	+	0.778104i	$0.283818\pi$
$180$	2.56155	0.190927
$181$	−6.87689	−0.511156	−0.255578	−	0.966789i	$-0.582266\pi$
$181$	−6.87689	−0.511156	−0.255578	+	0.966789i	$0.582266\pi$
$182$	0.561553	0.0416251
$183$	−9.12311	−0.674399
$184$	−1.00000	−0.0737210
$185$	6.56155	0.482415
$186$	−5.12311	−0.375644
$187$	−22.2462	−1.62680
$188$	6.56155	0.478550
$189$	1.00000	0.0727393
$190$	−8.00000	−0.580381
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	−1.00000	−0.0721688
$193$	−9.68466	−0.697117	−0.348558	−	0.937287i	$-0.613329\pi$
$193$	−9.68466	−0.697117	−0.348558	+	0.937287i	$0.613329\pi$
$194$	16.5616	1.18905
$195$	−1.43845	−0.103009
$196$	1.00000	0.0714286
$197$	−3.93087	−0.280063	−0.140031	−	0.990147i	$-0.544720\pi$
$197$	−3.93087	−0.280063	−0.140031	+	0.990147i	$0.544720\pi$
$198$	3.12311	0.221949
$199$	24.1771	1.71387	0.856934	−	0.515426i	$-0.172366\pi$
$199$	24.1771	1.71387	0.856934	+	0.515426i	$0.172366\pi$
$200$	−1.56155	−0.110418
$201$	−7.12311	−0.502425
$202$	0.246211	0.0173234
$203$	−3.43845	−0.241332
$204$	−7.12311	−0.498717
$205$	−1.43845	−0.100466
$206$	9.93087	0.691916
$207$	1.00000	0.0695048
$208$	0.561553	0.0389367
$209$	−9.75379	−0.674684
$210$	−2.56155	−0.176764
$211$	16.4924	1.13539	0.567693	−	0.823241i	$-0.307836\pi$
$211$	16.4924	1.13539	0.567693	+	0.823241i	$0.307836\pi$
$212$	−2.24621	−0.154270
$213$	−15.3693	−1.05309
$214$	−3.12311	−0.213491
$215$	−14.5616	−0.993090
$216$	1.00000	0.0680414
$217$	5.12311	0.347779
$218$	−14.5616	−0.986233
$219$	−0.876894	−0.0592550
$220$	−8.00000	−0.539360
$221$	4.00000	0.269069
$222$	2.56155	0.171920
$223$	−5.12311	−0.343069	−0.171534	−	0.985178i	$-0.554872\pi$
$223$	−5.12311	−0.343069	−0.171534	+	0.985178i	$0.554872\pi$
$224$	1.00000	0.0668153
$225$	1.56155	0.104104
$226$	−9.68466	−0.644214
$227$	−26.8078	−1.77929	−0.889647	−	0.456649i	$-0.849049\pi$
$227$	−26.8078	−1.77929	−0.889647	+	0.456649i	$0.849049\pi$
$228$	−3.12311	−0.206833
$229$	−14.2462	−0.941416	−0.470708	−	0.882289i	$-0.656001\pi$
$229$	−14.2462	−0.941416	−0.470708	+	0.882289i	$0.656001\pi$
$230$	−2.56155	−0.168904
$231$	−3.12311	−0.205485
$232$	−3.43845	−0.225745
$233$	14.4924	0.949430	0.474715	−	0.880140i	$-0.342551\pi$
$233$	14.4924	0.949430	0.474715	+	0.880140i	$0.342551\pi$
$234$	−0.561553	−0.0367099
$235$	16.8078	1.09642
$236$	13.1231	0.854241
$237$	2.24621	0.145907
$238$	7.12311	0.461722
$239$	−28.4924	−1.84302	−0.921511	−	0.388353i	$-0.873044\pi$
$239$	−28.4924	−1.84302	−0.921511	+	0.388353i	$0.873044\pi$
$240$	−2.56155	−0.165348
$241$	17.0540	1.09854	0.549272	−	0.835644i	$-0.314905\pi$
$241$	17.0540	1.09854	0.549272	+	0.835644i	$0.314905\pi$
$242$	1.24621	0.0801095
$243$	−1.00000	−0.0641500
$244$	9.12311	0.584047
$245$	2.56155	0.163652
$246$	−0.561553	−0.0358033
$247$	1.75379	0.111591
$248$	5.12311	0.325318
$249$	0.876894	0.0555709
$250$	8.80776	0.557052
$251$	−4.56155	−0.287923	−0.143961	−	0.989583i	$-0.545984\pi$
$251$	−4.56155	−0.287923	−0.143961	+	0.989583i	$0.545984\pi$
$252$	−1.00000	−0.0629941
$253$	−3.12311	−0.196348
$254$	4.31534	0.270769
$255$	−18.2462	−1.14262
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	−5.68466	−0.353911
$259$	−2.56155	−0.159167
$260$	1.43845	0.0892087
$261$	3.43845	0.212835
$262$	−13.1231	−0.810748
$263$	−5.93087	−0.365713	−0.182857	−	0.983140i	$-0.558534\pi$
$263$	−5.93087	−0.365713	−0.182857	+	0.983140i	$0.558534\pi$
$264$	−3.12311	−0.192214
$265$	−5.75379	−0.353452
$266$	3.12311	0.191490
$267$	−14.0000	−0.856786
$268$	7.12311	0.435113
$269$	−4.24621	−0.258896	−0.129448	−	0.991586i	$-0.541321\pi$
$269$	−4.24621	−0.258896	−0.129448	+	0.991586i	$0.541321\pi$
$270$	2.56155	0.155891
$271$	−2.24621	−0.136448	−0.0682238	−	0.997670i	$-0.521733\pi$
$271$	−2.24621	−0.136448	−0.0682238	+	0.997670i	$0.521733\pi$
$272$	7.12311	0.431902
$273$	0.561553	0.0339867
$274$	4.56155	0.275573
$275$	−4.87689	−0.294088
$276$	−1.00000	−0.0601929
$277$	4.87689	0.293024	0.146512	−	0.989209i	$-0.453195\pi$
$277$	4.87689	0.293024	0.146512	+	0.989209i	$0.453195\pi$
$278$	16.8078	1.00806
$279$	−5.12311	−0.306712
$280$	2.56155	0.153082
$281$	−23.9309	−1.42760	−0.713798	−	0.700352i	$-0.753027\pi$
$281$	−23.9309	−1.42760	−0.713798	+	0.700352i	$0.753027\pi$
$282$	6.56155	0.390735
$283$	22.4924	1.33704	0.668518	−	0.743696i	$-0.266929\pi$
$283$	22.4924	1.33704	0.668518	+	0.743696i	$0.266929\pi$
$284$	15.3693	0.912001
$285$	−8.00000	−0.473879
$286$	1.75379	0.103704
$287$	0.561553	0.0331474
$288$	−1.00000	−0.0589256
$289$	33.7386	1.98463
$290$	−8.80776	−0.517210
$291$	16.5616	0.970855
$292$	0.876894	0.0513164
$293$	−13.6155	−0.795428	−0.397714	−	0.917510i	$-0.630196\pi$
$293$	−13.6155	−0.795428	−0.397714	+	0.917510i	$0.630196\pi$
$294$	1.00000	0.0583212
$295$	33.6155	1.95717
$296$	−2.56155	−0.148887
$297$	3.12311	0.181221
$298$	−10.2462	−0.593547
$299$	0.561553	0.0324754
$300$	−1.56155	−0.0901563
$301$	5.68466	0.327658
$302$	−19.6847	−1.13272
$303$	0.246211	0.0141445
$304$	3.12311	0.179122
$305$	23.3693	1.33812
$306$	−7.12311	−0.407201
$307$	−25.9309	−1.47995	−0.739976	−	0.672633i	$-0.765163\pi$
$307$	−25.9309	−1.47995	−0.739976	+	0.672633i	$0.765163\pi$
$308$	3.12311	0.177955
$309$	9.93087	0.564947
$310$	13.1231	0.745342
$311$	−30.7386	−1.74303	−0.871514	−	0.490371i	$-0.836861\pi$
$311$	−30.7386	−1.74303	−0.871514	+	0.490371i	$0.836861\pi$
$312$	0.561553	0.0317917
$313$	−12.2462	−0.692197	−0.346098	−	0.938198i	$-0.612494\pi$
$313$	−12.2462	−0.692197	−0.346098	+	0.938198i	$0.612494\pi$
$314$	2.24621	0.126761
$315$	−2.56155	−0.144327
$316$	−2.24621	−0.126359
$317$	2.80776	0.157700	0.0788499	−	0.996887i	$-0.474875\pi$
$317$	2.80776	0.157700	0.0788499	+	0.996887i	$0.474875\pi$
$318$	−2.24621	−0.125961
$319$	−10.7386	−0.601248
$320$	2.56155	0.143195
$321$	−3.12311	−0.174315
$322$	1.00000	0.0557278
$323$	22.2462	1.23781
$324$	1.00000	0.0555556
$325$	0.876894	0.0486413
$326$	8.00000	0.443079
$327$	−14.5616	−0.805256
$328$	0.561553	0.0310066
$329$	−6.56155	−0.361750
$330$	−8.00000	−0.440386
$331$	8.49242	0.466786	0.233393	−	0.972383i	$-0.425017\pi$
$331$	8.49242	0.466786	0.233393	+	0.972383i	$0.425017\pi$
$332$	−0.876894	−0.0481258
$333$	2.56155	0.140372
$334$	−2.24621	−0.122907
$335$	18.2462	0.996897
$336$	1.00000	0.0545545
$337$	2.63068	0.143302	0.0716512	−	0.997430i	$-0.477173\pi$
$337$	2.63068	0.143302	0.0716512	+	0.997430i	$0.477173\pi$
$338$	12.6847	0.689954
$339$	−9.68466	−0.525998
$340$	18.2462	0.989540
$341$	16.0000	0.866449
$342$	−3.12311	−0.168878
$343$	−1.00000	−0.0539949
$344$	5.68466	0.306496
$345$	−2.56155	−0.137909
$346$	14.4924	0.779117
$347$	−13.9309	−0.747848	−0.373924	−	0.927459i	$-0.621988\pi$
$347$	−13.9309	−0.747848	−0.373924	+	0.927459i	$0.621988\pi$
$348$	−3.43845	−0.184320
$349$	0.246211	0.0131794	0.00658969	−	0.999978i	$-0.497902\pi$
$349$	0.246211	0.0131794	0.00658969	+	0.999978i	$0.497902\pi$
$350$	1.56155	0.0834685
$351$	−0.561553	−0.0299735
$352$	3.12311	0.166462
$353$	−13.1922	−0.702152	−0.351076	−	0.936347i	$-0.614184\pi$
$353$	−13.1922	−0.702152	−0.351076	+	0.936347i	$0.614184\pi$
$354$	13.1231	0.697485
$355$	39.3693	2.08951
$356$	14.0000	0.741999
$357$	7.12311	0.376995
$358$	−16.8078	−0.888318
$359$	−10.5616	−0.557417	−0.278709	−	0.960376i	$-0.589906\pi$
$359$	−10.5616	−0.557417	−0.278709	+	0.960376i	$0.589906\pi$
$360$	−2.56155	−0.135006
$361$	−9.24621	−0.486643
$362$	6.87689	0.361442
$363$	1.24621	0.0654091
$364$	−0.561553	−0.0294334
$365$	2.24621	0.117572
$366$	9.12311	0.476872
$367$	−22.5616	−1.17770	−0.588852	−	0.808241i	$-0.700420\pi$
$367$	−22.5616	−1.17770	−0.588852	+	0.808241i	$0.700420\pi$
$368$	1.00000	0.0521286
$369$	−0.561553	−0.0292333
$370$	−6.56155	−0.341119
$371$	2.24621	0.116617
$372$	5.12311	0.265621
$373$	6.87689	0.356072	0.178036	−	0.984024i	$-0.443026\pi$
$373$	6.87689	0.356072	0.178036	+	0.984024i	$0.443026\pi$
$374$	22.2462	1.15032
$375$	8.80776	0.454831
$376$	−6.56155	−0.338386
$377$	1.93087	0.0994448
$378$	−1.00000	−0.0514344
$379$	−17.0540	−0.876004	−0.438002	−	0.898974i	$-0.644314\pi$
$379$	−17.0540	−0.876004	−0.438002	+	0.898974i	$0.644314\pi$
$380$	8.00000	0.410391
$381$	4.31534	0.221082
$382$	20.0000	1.02329
$383$	10.2462	0.523557	0.261778	−	0.965128i	$-0.415691\pi$
$383$	10.2462	0.523557	0.261778	+	0.965128i	$0.415691\pi$
$384$	1.00000	0.0510310
$385$	8.00000	0.407718
$386$	9.68466	0.492936
$387$	−5.68466	−0.288967
$388$	−16.5616	−0.840785
$389$	−4.63068	−0.234785	−0.117392	−	0.993086i	$-0.537454\pi$
$389$	−4.63068	−0.234785	−0.117392	+	0.993086i	$0.537454\pi$
$390$	1.43845	0.0728386
$391$	7.12311	0.360231
$392$	−1.00000	−0.0505076
$393$	−13.1231	−0.661973
$394$	3.93087	0.198034
$395$	−5.75379	−0.289505
$396$	−3.12311	−0.156942
$397$	−24.2462	−1.21688	−0.608441	−	0.793599i	$-0.708205\pi$
$397$	−24.2462	−1.21688	−0.608441	+	0.793599i	$0.708205\pi$
$398$	−24.1771	−1.21189
$399$	3.12311	0.156351
$400$	1.56155	0.0780776
$401$	−0.246211	−0.0122952	−0.00614760	−	0.999981i	$-0.501957\pi$
$401$	−0.246211	−0.0122952	−0.00614760	+	0.999981i	$0.501957\pi$
$402$	7.12311	0.355268
$403$	−2.87689	−0.143308
$404$	−0.246211	−0.0122495
$405$	2.56155	0.127285
$406$	3.43845	0.170647
$407$	−8.00000	−0.396545
$408$	7.12311	0.352646
$409$	−7.61553	−0.376564	−0.188282	−	0.982115i	$-0.560292\pi$
$409$	−7.61553	−0.376564	−0.188282	+	0.982115i	$0.560292\pi$
$410$	1.43845	0.0710398
$411$	4.56155	0.225005
$412$	−9.93087	−0.489259
$413$	−13.1231	−0.645746
$414$	−1.00000	−0.0491473
$415$	−2.24621	−0.110262
$416$	−0.561553	−0.0275324
$417$	16.8078	0.823080
$418$	9.75379	0.477073
$419$	−33.8617	−1.65425	−0.827127	−	0.562015i	$-0.810026\pi$
$419$	−33.8617	−1.65425	−0.827127	+	0.562015i	$0.810026\pi$
$420$	2.56155	0.124991
$421$	−12.1771	−0.593475	−0.296737	−	0.954959i	$-0.595899\pi$
$421$	−12.1771	−0.593475	−0.296737	+	0.954959i	$0.595899\pi$
$422$	−16.4924	−0.802839
$423$	6.56155	0.319034
$424$	2.24621	0.109086
$425$	11.1231	0.539550
$426$	15.3693	0.744646
$427$	−9.12311	−0.441498
$428$	3.12311	0.150961
$429$	1.75379	0.0846737
$430$	14.5616	0.702220
$431$	−15.6847	−0.755503	−0.377752	−	0.925907i	$-0.623303\pi$
$431$	−15.6847	−0.755503	−0.377752	+	0.925907i	$0.623303\pi$
$432$	−1.00000	−0.0481125
$433$	2.31534	0.111268	0.0556341	−	0.998451i	$-0.482282\pi$
$433$	2.31534	0.111268	0.0556341	+	0.998451i	$0.482282\pi$
$434$	−5.12311	−0.245917
$435$	−8.80776	−0.422300
$436$	14.5616	0.697372
$437$	3.12311	0.149398
$438$	0.876894	0.0418996
$439$	17.6155	0.840743	0.420372	−	0.907352i	$-0.361900\pi$
$439$	17.6155	0.840743	0.420372	+	0.907352i	$0.361900\pi$
$440$	8.00000	0.381385
$441$	1.00000	0.0476190
$442$	−4.00000	−0.190261
$443$	37.9309	1.80215	0.901075	−	0.433663i	$-0.142779\pi$
$443$	37.9309	1.80215	0.901075	+	0.433663i	$0.142779\pi$
$444$	−2.56155	−0.121566
$445$	35.8617	1.70001
$446$	5.12311	0.242586
$447$	−10.2462	−0.484629
$448$	−1.00000	−0.0472456
$449$	16.2462	0.766706	0.383353	−	0.923602i	$-0.374769\pi$
$449$	16.2462	0.766706	0.383353	+	0.923602i	$0.374769\pi$
$450$	−1.56155	−0.0736123
$451$	1.75379	0.0825827
$452$	9.68466	0.455528
$453$	−19.6847	−0.924866
$454$	26.8078	1.25815
$455$	−1.43845	−0.0674354
$456$	3.12311	0.146253
$457$	−17.3693	−0.812502	−0.406251	−	0.913761i	$-0.633164\pi$
$457$	−17.3693	−0.812502	−0.406251	+	0.913761i	$0.633164\pi$
$458$	14.2462	0.665682
$459$	−7.12311	−0.332478
$460$	2.56155	0.119433
$461$	−8.73863	−0.406999	−0.203499	−	0.979075i	$-0.565231\pi$
$461$	−8.73863	−0.406999	−0.203499	+	0.979075i	$0.565231\pi$
$462$	3.12311	0.145300
$463$	−9.43845	−0.438642	−0.219321	−	0.975653i	$-0.570384\pi$
$463$	−9.43845	−0.438642	−0.219321	+	0.975653i	$0.570384\pi$
$464$	3.43845	0.159626
$465$	13.1231	0.608569
$466$	−14.4924	−0.671349
$467$	−9.68466	−0.448153	−0.224076	−	0.974572i	$-0.571936\pi$
$467$	−9.68466	−0.448153	−0.224076	+	0.974572i	$0.571936\pi$
$468$	0.561553	0.0259578
$469$	−7.12311	−0.328914
$470$	−16.8078	−0.775284
$471$	2.24621	0.103500
$472$	−13.1231	−0.604040
$473$	17.7538	0.816320
$474$	−2.24621	−0.103172
$475$	4.87689	0.223767
$476$	−7.12311	−0.326487
$477$	−2.24621	−0.102847
$478$	28.4924	1.30321
$479$	−9.61553	−0.439345	−0.219672	−	0.975574i	$-0.570499\pi$
$479$	−9.61553	−0.439345	−0.219672	+	0.975574i	$0.570499\pi$
$480$	2.56155	0.116918
$481$	1.43845	0.0655875
$482$	−17.0540	−0.776787
$483$	1.00000	0.0455016
$484$	−1.24621	−0.0566460
$485$	−42.4233	−1.92634
$486$	1.00000	0.0453609
$487$	−1.43845	−0.0651823	−0.0325911	−	0.999469i	$-0.510376\pi$
$487$	−1.43845	−0.0651823	−0.0325911	+	0.999469i	$0.510376\pi$
$488$	−9.12311	−0.412984
$489$	8.00000	0.361773
$490$	−2.56155	−0.115719
$491$	22.7386	1.02618	0.513090	−	0.858335i	$-0.328501\pi$
$491$	22.7386	1.02618	0.513090	+	0.858335i	$0.328501\pi$
$492$	0.561553	0.0253168
$493$	24.4924	1.10308
$494$	−1.75379	−0.0789067
$495$	−8.00000	−0.359573
$496$	−5.12311	−0.230034
$497$	−15.3693	−0.689408
$498$	−0.876894	−0.0392946
$499$	16.6307	0.744492	0.372246	−	0.928134i	$-0.378588\pi$
$499$	16.6307	0.744492	0.372246	+	0.928134i	$0.378588\pi$
$500$	−8.80776	−0.393895
$501$	−2.24621	−0.100353
$502$	4.56155	0.203592
$503$	42.1080	1.87750	0.938750	−	0.344598i	$-0.111985\pi$
$503$	42.1080	1.87750	0.938750	+	0.344598i	$0.111985\pi$
$504$	1.00000	0.0445435
$505$	−0.630683	−0.0280650
$506$	3.12311	0.138839
$507$	12.6847	0.563345
$508$	−4.31534	−0.191462
$509$	21.3693	0.947178	0.473589	−	0.880746i	$-0.342958\pi$
$509$	21.3693	0.947178	0.473589	+	0.880746i	$0.342958\pi$
$510$	18.2462	0.807956
$511$	−0.876894	−0.0387915
$512$	−1.00000	−0.0441942
$513$	−3.12311	−0.137888
$514$	2.00000	0.0882162
$515$	−25.4384	−1.12095
$516$	5.68466	0.250253
$517$	−20.4924	−0.901256
$518$	2.56155	0.112548
$519$	14.4924	0.636147
$520$	−1.43845	−0.0630801
$521$	−16.2462	−0.711759	−0.355880	−	0.934532i	$-0.615819\pi$
$521$	−16.2462	−0.711759	−0.355880	+	0.934532i	$0.615819\pi$
$522$	−3.43845	−0.150497
$523$	14.0000	0.612177	0.306089	−	0.952003i	$-0.400980\pi$
$523$	14.0000	0.612177	0.306089	+	0.952003i	$0.400980\pi$
$524$	13.1231	0.573286
$525$	1.56155	0.0681518
$526$	5.93087	0.258598
$527$	−36.4924	−1.58963
$528$	3.12311	0.135916
$529$	1.00000	0.0434783
$530$	5.75379	0.249929
$531$	13.1231	0.569494
$532$	−3.12311	−0.135404
$533$	−0.315342	−0.0136590
$534$	14.0000	0.605839
$535$	8.00000	0.345870
$536$	−7.12311	−0.307671
$537$	−16.8078	−0.725309
$538$	4.24621	0.183067
$539$	−3.12311	−0.134522
$540$	−2.56155	−0.110232
$541$	9.36932	0.402818	0.201409	−	0.979507i	$-0.435448\pi$
$541$	9.36932	0.402818	0.201409	+	0.979507i	$0.435448\pi$
$542$	2.24621	0.0964830
$543$	6.87689	0.295116
$544$	−7.12311	−0.305401
$545$	37.3002	1.59776
$546$	−0.561553	−0.0240322
$547$	37.6155	1.60832	0.804162	−	0.594410i	$-0.202614\pi$
$547$	37.6155	1.60832	0.804162	+	0.594410i	$0.202614\pi$
$548$	−4.56155	−0.194860
$549$	9.12311	0.389365
$550$	4.87689	0.207951
$551$	10.7386	0.457481
$552$	1.00000	0.0425628
$553$	2.24621	0.0955186
$554$	−4.87689	−0.207199
$555$	−6.56155	−0.278522
$556$	−16.8078	−0.712808
$557$	36.9848	1.56710	0.783549	−	0.621330i	$-0.213407\pi$
$557$	36.9848	1.56710	0.783549	+	0.621330i	$0.213407\pi$
$558$	5.12311	0.216878
$559$	−3.19224	−0.135017
$560$	−2.56155	−0.108245
$561$	22.2462	0.939236
$562$	23.9309	1.00946
$563$	15.4384	0.650653	0.325326	−	0.945602i	$-0.394526\pi$
$563$	15.4384	0.650653	0.325326	+	0.945602i	$0.394526\pi$
$564$	−6.56155	−0.276291
$565$	24.8078	1.04367
$566$	−22.4924	−0.945427
$567$	−1.00000	−0.0419961
$568$	−15.3693	−0.644882
$569$	25.5464	1.07096	0.535480	−	0.844548i	$-0.320131\pi$
$569$	25.5464	1.07096	0.535480	+	0.844548i	$0.320131\pi$
$570$	8.00000	0.335083
$571$	18.6307	0.779670	0.389835	−	0.920885i	$-0.372532\pi$
$571$	18.6307	0.779670	0.389835	+	0.920885i	$0.372532\pi$
$572$	−1.75379	−0.0733296
$573$	20.0000	0.835512
$574$	−0.561553	−0.0234388
$575$	1.56155	0.0651213
$576$	1.00000	0.0416667
$577$	−36.2462	−1.50895	−0.754475	−	0.656329i	$-0.772108\pi$
$577$	−36.2462	−1.50895	−0.754475	+	0.656329i	$0.772108\pi$
$578$	−33.7386	−1.40334
$579$	9.68466	0.402481
$580$	8.80776	0.365722
$581$	0.876894	0.0363797
$582$	−16.5616	−0.686498
$583$	7.01515	0.290538
$584$	−0.876894	−0.0362861
$585$	1.43845	0.0594725
$586$	13.6155	0.562452
$587$	40.9848	1.69163	0.845813	−	0.533480i	$-0.179116\pi$
$587$	40.9848	1.69163	0.845813	+	0.533480i	$0.179116\pi$
$588$	−1.00000	−0.0412393
$589$	−16.0000	−0.659269
$590$	−33.6155	−1.38393
$591$	3.93087	0.161694
$592$	2.56155	0.105279
$593$	−23.3002	−0.956824	−0.478412	−	0.878136i	$-0.658787\pi$
$593$	−23.3002	−0.956824	−0.478412	+	0.878136i	$0.658787\pi$
$594$	−3.12311	−0.128143
$595$	−18.2462	−0.748022
$596$	10.2462	0.419701
$597$	−24.1771	−0.989502
$598$	−0.561553	−0.0229636
$599$	38.7386	1.58282	0.791409	−	0.611287i	$-0.209348\pi$
$599$	38.7386	1.58282	0.791409	+	0.611287i	$0.209348\pi$
$600$	1.56155	0.0637501
$601$	21.3693	0.871673	0.435836	−	0.900026i	$-0.356453\pi$
$601$	21.3693	0.871673	0.435836	+	0.900026i	$0.356453\pi$
$602$	−5.68466	−0.231689
$603$	7.12311	0.290075
$604$	19.6847	0.800957
$605$	−3.19224	−0.129783
$606$	−0.246211	−0.0100016
$607$	−6.38447	−0.259138	−0.129569	−	0.991570i	$-0.541359\pi$
$607$	−6.38447	−0.259138	−0.129569	+	0.991570i	$0.541359\pi$
$608$	−3.12311	−0.126659
$609$	3.43845	0.139333
$610$	−23.3693	−0.946196
$611$	3.68466	0.149065
$612$	7.12311	0.287934
$613$	−16.8078	−0.678859	−0.339430	−	0.940631i	$-0.610234\pi$
$613$	−16.8078	−0.678859	−0.339430	+	0.940631i	$0.610234\pi$
$614$	25.9309	1.04648
$615$	1.43845	0.0580038
$616$	−3.12311	−0.125834
$617$	48.2462	1.94232	0.971160	−	0.238430i	$-0.0766328\pi$
$617$	48.2462	1.94232	0.971160	+	0.238430i	$0.0766328\pi$
$618$	−9.93087	−0.399478
$619$	−8.24621	−0.331443	−0.165722	−	0.986173i	$-0.552995\pi$
$619$	−8.24621	−0.331443	−0.165722	+	0.986173i	$0.552995\pi$
$620$	−13.1231	−0.527037
$621$	−1.00000	−0.0401286
$622$	30.7386	1.23251
$623$	−14.0000	−0.560898
$624$	−0.561553	−0.0224801
$625$	−30.3693	−1.21477
$626$	12.2462	0.489457
$627$	9.75379	0.389529
$628$	−2.24621	−0.0896336
$629$	18.2462	0.727524
$630$	2.56155	0.102055
$631$	−24.4924	−0.975028	−0.487514	−	0.873115i	$-0.662096\pi$
$631$	−24.4924	−0.975028	−0.487514	+	0.873115i	$0.662096\pi$
$632$	2.24621	0.0893495
$633$	−16.4924	−0.655515
$634$	−2.80776	−0.111511
$635$	−11.0540	−0.438664
$636$	2.24621	0.0890681
$637$	0.561553	0.0222495
$638$	10.7386	0.425147
$639$	15.3693	0.608001
$640$	−2.56155	−0.101254
$641$	−25.6847	−1.01448	−0.507242	−	0.861804i	$-0.669335\pi$
$641$	−25.6847	−1.01448	−0.507242	+	0.861804i	$0.669335\pi$
$642$	3.12311	0.123259
$643$	−38.0000	−1.49857	−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000	−1.49857	−0.749287	+	0.662246i	$0.769604\pi$
$644$	−1.00000	−0.0394055
$645$	14.5616	0.573361
$646$	−22.2462	−0.875265
$647$	−36.4924	−1.43467	−0.717333	−	0.696731i	$-0.754637\pi$
$647$	−36.4924	−1.43467	−0.717333	+	0.696731i	$0.754637\pi$
$648$	−1.00000	−0.0392837
$649$	−40.9848	−1.60880
$650$	−0.876894	−0.0343946
$651$	−5.12311	−0.200790
$652$	−8.00000	−0.313304
$653$	−33.5464	−1.31277	−0.656386	−	0.754425i	$-0.727916\pi$
$653$	−33.5464	−1.31277	−0.656386	+	0.754425i	$0.727916\pi$
$654$	14.5616	0.569402
$655$	33.6155	1.31347
$656$	−0.561553	−0.0219250
$657$	0.876894	0.0342109
$658$	6.56155	0.255796
$659$	−35.6155	−1.38738	−0.693692	−	0.720272i	$-0.744017\pi$
$659$	−35.6155	−1.38738	−0.693692	+	0.720272i	$0.744017\pi$
$660$	8.00000	0.311400
$661$	41.1231	1.59950	0.799752	−	0.600331i	$-0.204964\pi$
$661$	41.1231	1.59950	0.799752	+	0.600331i	$0.204964\pi$
$662$	−8.49242	−0.330067
$663$	−4.00000	−0.155347
$664$	0.876894	0.0340301
$665$	−8.00000	−0.310227
$666$	−2.56155	−0.0992582
$667$	3.43845	0.133137
$668$	2.24621	0.0869085
$669$	5.12311	0.198071
$670$	−18.2462	−0.704913
$671$	−28.4924	−1.09994
$672$	−1.00000	−0.0385758
$673$	10.3153	0.397627	0.198814	−	0.980037i	$-0.436291\pi$
$673$	10.3153	0.397627	0.198814	+	0.980037i	$0.436291\pi$
$674$	−2.63068	−0.101330
$675$	−1.56155	−0.0601042
$676$	−12.6847	−0.487871
$677$	27.3693	1.05189	0.525944	−	0.850519i	$-0.323712\pi$
$677$	27.3693	1.05189	0.525944	+	0.850519i	$0.323712\pi$
$678$	9.68466	0.371937
$679$	16.5616	0.635574
$680$	−18.2462	−0.699710
$681$	26.8078	1.02728
$682$	−16.0000	−0.612672
$683$	−40.4924	−1.54940	−0.774700	−	0.632329i	$-0.782099\pi$
$683$	−40.4924	−1.54940	−0.774700	+	0.632329i	$0.782099\pi$
$684$	3.12311	0.119415
$685$	−11.6847	−0.446448
$686$	1.00000	0.0381802
$687$	14.2462	0.543527
$688$	−5.68466	−0.216726
$689$	−1.26137	−0.0480542
$690$	2.56155	0.0975166
$691$	−12.9460	−0.492490	−0.246245	−	0.969208i	$-0.579197\pi$
$691$	−12.9460	−0.492490	−0.246245	+	0.969208i	$0.579197\pi$
$692$	−14.4924	−0.550919
$693$	3.12311	0.118637
$694$	13.9309	0.528809
$695$	−43.0540	−1.63313
$696$	3.43845	0.130334
$697$	−4.00000	−0.151511
$698$	−0.246211	−0.00931923
$699$	−14.4924	−0.548154
$700$	−1.56155	−0.0590211
$701$	17.7538	0.670551	0.335276	−	0.942120i	$-0.391171\pi$
$701$	17.7538	0.670551	0.335276	+	0.942120i	$0.391171\pi$
$702$	0.561553	0.0211944
$703$	8.00000	0.301726
$704$	−3.12311	−0.117706
$705$	−16.8078	−0.633017
$706$	13.1922	0.496496
$707$	0.246211	0.00925973
$708$	−13.1231	−0.493197
$709$	35.3693	1.32832	0.664161	−	0.747589i	$-0.268789\pi$
$709$	35.3693	1.32832	0.664161	+	0.747589i	$0.268789\pi$
$710$	−39.3693	−1.47750
$711$	−2.24621	−0.0842395
$712$	−14.0000	−0.524672
$713$	−5.12311	−0.191862
$714$	−7.12311	−0.266576
$715$	−4.49242	−0.168007
$716$	16.8078	0.628136
$717$	28.4924	1.06407
$718$	10.5616	0.394154
$719$	14.5616	0.543054	0.271527	−	0.962431i	$-0.412471\pi$
$719$	14.5616	0.543054	0.271527	+	0.962431i	$0.412471\pi$
$720$	2.56155	0.0954634
$721$	9.93087	0.369845
$722$	9.24621	0.344108
$723$	−17.0540	−0.634244
$724$	−6.87689	−0.255578
$725$	5.36932	0.199411
$726$	−1.24621	−0.0462512
$727$	−18.2462	−0.676715	−0.338357	−	0.941018i	$-0.609871\pi$
$727$	−18.2462	−0.676715	−0.338357	+	0.941018i	$0.609871\pi$
$728$	0.561553	0.0208125
$729$	1.00000	0.0370370
$730$	−2.24621	−0.0831360
$731$	−40.4924	−1.49767
$732$	−9.12311	−0.337200
$733$	42.2462	1.56040	0.780200	−	0.625531i	$-0.215117\pi$
$733$	42.2462	1.56040	0.780200	+	0.625531i	$0.215117\pi$
$734$	22.5616	0.832762
$735$	−2.56155	−0.0944843
$736$	−1.00000	−0.0368605
$737$	−22.2462	−0.819450
$738$	0.561553	0.0206710
$739$	−17.6155	−0.647998	−0.323999	−	0.946057i	$-0.605027\pi$
$739$	−17.6155	−0.647998	−0.323999	+	0.946057i	$0.605027\pi$
$740$	6.56155	0.241207
$741$	−1.75379	−0.0644270
$742$	−2.24621	−0.0824610
$743$	40.9848	1.50359	0.751794	−	0.659398i	$-0.229189\pi$
$743$	40.9848	1.50359	0.751794	+	0.659398i	$0.229189\pi$
$744$	−5.12311	−0.187822
$745$	26.2462	0.961587
$746$	−6.87689	−0.251781
$747$	−0.876894	−0.0320839
$748$	−22.2462	−0.813402
$749$	−3.12311	−0.114116
$750$	−8.80776	−0.321614
$751$	−8.49242	−0.309893	−0.154946	−	0.987923i	$-0.549521\pi$
$751$	−8.49242	−0.309893	−0.154946	+	0.987923i	$0.549521\pi$
$752$	6.56155	0.239275
$753$	4.56155	0.166232
$754$	−1.93087	−0.0703181
$755$	50.4233	1.83509
$756$	1.00000	0.0363696
$757$	−0.630683	−0.0229226	−0.0114613	−	0.999934i	$-0.503648\pi$
$757$	−0.630683	−0.0229226	−0.0114613	+	0.999934i	$0.503648\pi$
$758$	17.0540	0.619428
$759$	3.12311	0.113362
$760$	−8.00000	−0.290191
$761$	−52.7386	−1.91177	−0.955887	−	0.293735i	$-0.905102\pi$
$761$	−52.7386	−1.91177	−0.955887	+	0.293735i	$0.905102\pi$
$762$	−4.31534	−0.156328
$763$	−14.5616	−0.527164
$764$	−20.0000	−0.723575
$765$	18.2462	0.659693
$766$	−10.2462	−0.370211
$767$	7.36932	0.266091
$768$	−1.00000	−0.0360844
$769$	−1.82292	−0.0657361	−0.0328681	−	0.999460i	$-0.510464\pi$
$769$	−1.82292	−0.0657361	−0.0328681	+	0.999460i	$0.510464\pi$
$770$	−8.00000	−0.288300
$771$	2.00000	0.0720282
$772$	−9.68466	−0.348558
$773$	21.3002	0.766114	0.383057	−	0.923725i	$-0.374871\pi$
$773$	21.3002	0.766114	0.383057	+	0.923725i	$0.374871\pi$
$774$	5.68466	0.204331
$775$	−8.00000	−0.287368
$776$	16.5616	0.594525
$777$	2.56155	0.0918952
$778$	4.63068	0.166018
$779$	−1.75379	−0.0628360
$780$	−1.43845	−0.0515047
$781$	−48.0000	−1.71758
$782$	−7.12311	−0.254722
$783$	−3.43845	−0.122880
$784$	1.00000	0.0357143
$785$	−5.75379	−0.205362
$786$	13.1231	0.468086
$787$	−19.1231	−0.681665	−0.340833	−	0.940124i	$-0.610709\pi$
$787$	−19.1231	−0.681665	−0.340833	+	0.940124i	$0.610709\pi$
$788$	−3.93087	−0.140031
$789$	5.93087	0.211145
$790$	5.75379	0.204711
$791$	−9.68466	−0.344347
$792$	3.12311	0.110975
$793$	5.12311	0.181927
$794$	24.2462	0.860466
$795$	5.75379	0.204066
$796$	24.1771	0.856934
$797$	−34.4233	−1.21934	−0.609668	−	0.792657i	$-0.708697\pi$
$797$	−34.4233	−1.21934	−0.609668	+	0.792657i	$0.708697\pi$
$798$	−3.12311	−0.110557
$799$	46.7386	1.65349
$800$	−1.56155	−0.0552092
$801$	14.0000	0.494666
$802$	0.246211	0.00869402
$803$	−2.73863	−0.0966443
$804$	−7.12311	−0.251213
$805$	−2.56155	−0.0902829
$806$	2.87689	0.101334
$807$	4.24621	0.149474
$808$	0.246211	0.00866168
$809$	−33.8617	−1.19052	−0.595258	−	0.803535i	$-0.702950\pi$
$809$	−33.8617	−1.19052	−0.595258	+	0.803535i	$0.702950\pi$
$810$	−2.56155	−0.0900038
$811$	−12.3153	−0.432450	−0.216225	−	0.976344i	$-0.569374\pi$
$811$	−12.3153	−0.432450	−0.216225	+	0.976344i	$0.569374\pi$
$812$	−3.43845	−0.120666
$813$	2.24621	0.0787781
$814$	8.00000	0.280400
$815$	−20.4924	−0.717818
$816$	−7.12311	−0.249359
$817$	−17.7538	−0.621126
$818$	7.61553	0.266271
$819$	−0.561553	−0.0196222
$820$	−1.43845	−0.0502328
$821$	43.4773	1.51737	0.758684	−	0.651459i	$-0.225843\pi$
$821$	43.4773	1.51737	0.758684	+	0.651459i	$0.225843\pi$
$822$	−4.56155	−0.159102
$823$	35.6847	1.24389	0.621944	−	0.783061i	$-0.286343\pi$
$823$	35.6847	1.24389	0.621944	+	0.783061i	$0.286343\pi$
$824$	9.93087	0.345958
$825$	4.87689	0.169792
$826$	13.1231	0.456611
$827$	−0.738634	−0.0256848	−0.0128424	−	0.999918i	$-0.504088\pi$
$827$	−0.738634	−0.0256848	−0.0128424	+	0.999918i	$0.504088\pi$
$828$	1.00000	0.0347524
$829$	−24.7386	−0.859208	−0.429604	−	0.903017i	$-0.641347\pi$
$829$	−24.7386	−0.859208	−0.429604	+	0.903017i	$0.641347\pi$
$830$	2.24621	0.0779671
$831$	−4.87689	−0.169178
$832$	0.561553	0.0194683
$833$	7.12311	0.246801
$834$	−16.8078	−0.582005
$835$	5.75379	0.199118
$836$	−9.75379	−0.337342
$837$	5.12311	0.177080
$838$	33.8617	1.16973
$839$	−33.6155	−1.16054	−0.580268	−	0.814425i	$-0.697052\pi$
$839$	−33.6155	−1.16054	−0.580268	+	0.814425i	$0.697052\pi$
$840$	−2.56155	−0.0883820
$841$	−17.1771	−0.592313
$842$	12.1771	0.419650
$843$	23.9309	0.824223
$844$	16.4924	0.567693
$845$	−32.4924	−1.11777
$846$	−6.56155	−0.225591
$847$	1.24621	0.0428203
$848$	−2.24621	−0.0771352
$849$	−22.4924	−0.771938
$850$	−11.1231	−0.381519
$851$	2.56155	0.0878089
$852$	−15.3693	−0.526544
$853$	−4.56155	−0.156185	−0.0780923	−	0.996946i	$-0.524883\pi$
$853$	−4.56155	−0.156185	−0.0780923	+	0.996946i	$0.524883\pi$
$854$	9.12311	0.312186
$855$	8.00000	0.273594
$856$	−3.12311	−0.106746
$857$	13.6847	0.467459	0.233730	−	0.972302i	$-0.424907\pi$
$857$	13.6847	0.467459	0.233730	+	0.972302i	$0.424907\pi$
$858$	−1.75379	−0.0598734
$859$	12.1771	0.415477	0.207738	−	0.978184i	$-0.433390\pi$
$859$	12.1771	0.415477	0.207738	+	0.978184i	$0.433390\pi$
$860$	−14.5616	−0.496545
$861$	−0.561553	−0.0191377
$862$	15.6847	0.534222
$863$	−38.7386	−1.31868	−0.659339	−	0.751846i	$-0.729164\pi$
$863$	−38.7386	−1.31868	−0.659339	+	0.751846i	$0.729164\pi$
$864$	1.00000	0.0340207
$865$	−37.1231	−1.26222
$866$	−2.31534	−0.0786785
$867$	−33.7386	−1.14582
$868$	5.12311	0.173890
$869$	7.01515	0.237973
$870$	8.80776	0.298611
$871$	4.00000	0.135535
$872$	−14.5616	−0.493116
$873$	−16.5616	−0.560524
$874$	−3.12311	−0.105641
$875$	8.80776	0.297757
$876$	−0.876894	−0.0296275
$877$	21.8617	0.738218	0.369109	−	0.929386i	$-0.379663\pi$
$877$	21.8617	0.738218	0.369109	+	0.929386i	$0.379663\pi$
$878$	−17.6155	−0.594495
$879$	13.6155	0.459240
$880$	−8.00000	−0.269680
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−1.00000	−0.0336718
$883$	−17.1231	−0.576238	−0.288119	−	0.957595i	$-0.593030\pi$
$883$	−17.1231	−0.576238	−0.288119	+	0.957595i	$0.593030\pi$
$884$	4.00000	0.134535
$885$	−33.6155	−1.12997
$886$	−37.9309	−1.27431
$887$	24.0000	0.805841	0.402921	−	0.915235i	$-0.367995\pi$
$887$	24.0000	0.805841	0.402921	+	0.915235i	$0.367995\pi$
$888$	2.56155	0.0859601
$889$	4.31534	0.144732
$890$	−35.8617	−1.20209
$891$	−3.12311	−0.104628
$892$	−5.12311	−0.171534
$893$	20.4924	0.685753
$894$	10.2462	0.342685
$895$	43.0540	1.43914
$896$	1.00000	0.0334077
$897$	−0.561553	−0.0187497
$898$	−16.2462	−0.542143
$899$	−17.6155	−0.587511
$900$	1.56155	0.0520518
$901$	−16.0000	−0.533037
$902$	−1.75379	−0.0583948
$903$	−5.68466	−0.189174
$904$	−9.68466	−0.322107
$905$	−17.6155	−0.585560
$906$	19.6847	0.653979
$907$	−17.5464	−0.582619	−0.291309	−	0.956629i	$-0.594091\pi$
$907$	−17.5464	−0.582619	−0.291309	+	0.956629i	$0.594091\pi$
$908$	−26.8078	−0.889647
$909$	−0.246211	−0.00816631
$910$	1.43845	0.0476841
$911$	−39.0540	−1.29392	−0.646958	−	0.762526i	$-0.723959\pi$
$911$	−39.0540	−1.29392	−0.646958	+	0.762526i	$0.723959\pi$
$912$	−3.12311	−0.103416
$913$	2.73863	0.0906355
$914$	17.3693	0.574526
$915$	−23.3693	−0.772566
$916$	−14.2462	−0.470708
$917$	−13.1231	−0.433363
$918$	7.12311	0.235098
$919$	−1.26137	−0.0416086	−0.0208043	−	0.999784i	$-0.506623\pi$
$919$	−1.26137	−0.0416086	−0.0208043	+	0.999784i	$0.506623\pi$
$920$	−2.56155	−0.0844519
$921$	25.9309	0.854451
$922$	8.73863	0.287792
$923$	8.63068	0.284082
$924$	−3.12311	−0.102743
$925$	4.00000	0.131519
$926$	9.43845	0.310167
$927$	−9.93087	−0.326173
$928$	−3.43845	−0.112873
$929$	−40.5616	−1.33078	−0.665391	−	0.746495i	$-0.731735\pi$
$929$	−40.5616	−1.33078	−0.665391	+	0.746495i	$0.731735\pi$
$930$	−13.1231	−0.430324
$931$	3.12311	0.102356
$932$	14.4924	0.474715
$933$	30.7386	1.00634
$934$	9.68466	0.316892
$935$	−56.9848	−1.86360
$936$	−0.561553	−0.0183549
$937$	18.1771	0.593819	0.296910	−	0.954906i	$-0.404044\pi$
$937$	18.1771	0.593819	0.296910	+	0.954906i	$0.404044\pi$
$938$	7.12311	0.232578
$939$	12.2462	0.399640
$940$	16.8078	0.548209
$941$	39.0540	1.27312	0.636562	−	0.771226i	$-0.280356\pi$
$941$	39.0540	1.27312	0.636562	+	0.771226i	$0.280356\pi$
$942$	−2.24621	−0.0731855
$943$	−0.561553	−0.0182867
$944$	13.1231	0.427121
$945$	2.56155	0.0833273
$946$	−17.7538	−0.577225
$947$	−26.0691	−0.847133	−0.423566	−	0.905865i	$-0.639222\pi$
$947$	−26.0691	−0.847133	−0.423566	+	0.905865i	$0.639222\pi$
$948$	2.24621	0.0729535
$949$	0.492423	0.0159847
$950$	−4.87689	−0.158227
$951$	−2.80776	−0.0910480
$952$	7.12311	0.230861
$953$	50.0000	1.61966	0.809829	−	0.586665i	$-0.199560\pi$
$953$	50.0000	1.61966	0.809829	+	0.586665i	$0.199560\pi$
$954$	2.24621	0.0727238
$955$	−51.2311	−1.65780
$956$	−28.4924	−0.921511
$957$	10.7386	0.347131
$958$	9.61553	0.310664
$959$	4.56155	0.147300
$960$	−2.56155	−0.0826738
$961$	−4.75379	−0.153348
$962$	−1.43845	−0.0463774
$963$	3.12311	0.100641
$964$	17.0540	0.549272
$965$	−24.8078	−0.798590
$966$	−1.00000	−0.0321745
$967$	−26.2462	−0.844021	−0.422011	−	0.906591i	$-0.638676\pi$
$967$	−26.2462	−0.844021	−0.422011	+	0.906591i	$0.638676\pi$
$968$	1.24621	0.0400547
$969$	−22.2462	−0.714651
$970$	42.4233	1.36213
$971$	39.6155	1.27132	0.635661	−	0.771968i	$-0.280727\pi$
$971$	39.6155	1.27132	0.635661	+	0.771968i	$0.280727\pi$
$972$	−1.00000	−0.0320750
$973$	16.8078	0.538832
$974$	1.43845	0.0460908
$975$	−0.876894	−0.0280831
$976$	9.12311	0.292023
$977$	−46.8078	−1.49751	−0.748757	−	0.662845i	$-0.769349\pi$
$977$	−46.8078	−1.49751	−0.748757	+	0.662845i	$0.769349\pi$
$978$	−8.00000	−0.255812
$979$	−43.7235	−1.39741
$980$	2.56155	0.0818258
$981$	14.5616	0.464915
$982$	−22.7386	−0.725619
$983$	−23.8617	−0.761071	−0.380536	−	0.924766i	$-0.624260\pi$
$983$	−23.8617	−0.761071	−0.380536	+	0.924766i	$0.624260\pi$
$984$	−0.561553	−0.0179016
$985$	−10.0691	−0.320829
$986$	−24.4924	−0.779998
$987$	6.56155	0.208857
$988$	1.75379	0.0557955
$989$	−5.68466	−0.180762
$990$	8.00000	0.254257
$991$	10.2462	0.325482	0.162741	−	0.986669i	$-0.447967\pi$
$991$	10.2462	0.325482	0.162741	+	0.986669i	$0.447967\pi$
$992$	5.12311	0.162659
$993$	−8.49242	−0.269499
$994$	15.3693	0.487485
$995$	61.9309	1.96334
$996$	0.876894	0.0277855
$997$	−47.4773	−1.50362	−0.751810	−	0.659380i	$-0.770819\pi$
$997$	−47.4773	−1.50362	−0.751810	+	0.659380i	$0.770819\pi$
$998$	−16.6307	−0.526435
$999$	−2.56155	−0.0810439

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.l.1.2	✓	2
3.2	odd	2		2898.2.a.ba.1.1		2
4.3	odd	2		7728.2.a.bm.1.2		2
7.6	odd	2		6762.2.a.bw.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.l.1.2	✓	2	1.1	even	1	trivial
2898.2.a.ba.1.1		2	3.2	odd	2
6762.2.a.bw.1.1		2	7.6	odd	2
7728.2.a.bm.1.2		2	4.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56155 q^{10} -3.12311 q^{11} -1.00000 q^{12} +0.561553 q^{13} +1.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} +7.12311 q^{17} -1.00000 q^{18} +3.12311 q^{19} +2.56155 q^{20} +1.00000 q^{21} +3.12311 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.56155 q^{25} -0.561553 q^{26} -1.00000 q^{27} -1.00000 q^{28} +3.43845 q^{29} +2.56155 q^{30} -5.12311 q^{31} -1.00000 q^{32} +3.12311 q^{33} -7.12311 q^{34} -2.56155 q^{35} +1.00000 q^{36} +2.56155 q^{37} -3.12311 q^{38} -0.561553 q^{39} -2.56155 q^{40} -0.561553 q^{41} -1.00000 q^{42} -5.68466 q^{43} -3.12311 q^{44} +2.56155 q^{45} -1.00000 q^{46} +6.56155 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.56155 q^{50} -7.12311 q^{51} +0.561553 q^{52} -2.24621 q^{53} +1.00000 q^{54} -8.00000 q^{55} +1.00000 q^{56} -3.12311 q^{57} -3.43845 q^{58} +13.1231 q^{59} -2.56155 q^{60} +9.12311 q^{61} +5.12311 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.43845 q^{65} -3.12311 q^{66} +7.12311 q^{67} +7.12311 q^{68} -1.00000 q^{69} +2.56155 q^{70} +15.3693 q^{71} -1.00000 q^{72} +0.876894 q^{73} -2.56155 q^{74} -1.56155 q^{75} +3.12311 q^{76} +3.12311 q^{77} +0.561553 q^{78} -2.24621 q^{79} +2.56155 q^{80} +1.00000 q^{81} +0.561553 q^{82} -0.876894 q^{83} +1.00000 q^{84} +18.2462 q^{85} +5.68466 q^{86} -3.43845 q^{87} +3.12311 q^{88} +14.0000 q^{89} -2.56155 q^{90} -0.561553 q^{91} +1.00000 q^{92} +5.12311 q^{93} -6.56155 q^{94} +8.00000 q^{95} +1.00000 q^{96} -16.5616 q^{97} -1.00000 q^{98} -3.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} + 2 q^{11} - 2 q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + q^{20} + 2 q^{21} - 2 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} + 3 q^{26} - 2 q^{27} - 2 q^{28} + 11 q^{29} + q^{30} - 2 q^{31} - 2 q^{32} - 2 q^{33} - 6 q^{34} - q^{35} + 2 q^{36} + q^{37} + 2 q^{38} + 3 q^{39} - q^{40} + 3 q^{41} - 2 q^{42} + q^{43} + 2 q^{44} + q^{45} - 2 q^{46} + 9 q^{47} - 2 q^{48} + 2 q^{49} + q^{50} - 6 q^{51} - 3 q^{52} + 12 q^{53} + 2 q^{54} - 16 q^{55} + 2 q^{56} + 2 q^{57} - 11 q^{58} + 18 q^{59} - q^{60} + 10 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} + 7 q^{65} + 2 q^{66} + 6 q^{67} + 6 q^{68} - 2 q^{69} + q^{70} + 6 q^{71} - 2 q^{72} + 10 q^{73} - q^{74} + q^{75} - 2 q^{76} - 2 q^{77} - 3 q^{78} + 12 q^{79} + q^{80} + 2 q^{81} - 3 q^{82} - 10 q^{83} + 2 q^{84} + 20 q^{85} - q^{86} - 11 q^{87} - 2 q^{88} + 28 q^{89} - q^{90} + 3 q^{91} + 2 q^{92} + 2 q^{93} - 9 q^{94} + 16 q^{95} + 2 q^{96} - 29 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 + 2 * q^11 - 2 * q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 - 2 * q^19 + q^20 + 2 * q^21 - 2 * q^22 + 2 * q^23 + 2 * q^24 - q^25 + 3 * q^26 - 2 * q^27 - 2 * q^28 + 11 * q^29 + q^30 - 2 * q^31 - 2 * q^32 - 2 * q^33 - 6 * q^34 - q^35 + 2 * q^36 + q^37 + 2 * q^38 + 3 * q^39 - q^40 + 3 * q^41 - 2 * q^42 + q^43 + 2 * q^44 + q^45 - 2 * q^46 + 9 * q^47 - 2 * q^48 + 2 * q^49 + q^50 - 6 * q^51 - 3 * q^52 + 12 * q^53 + 2 * q^54 - 16 * q^55 + 2 * q^56 + 2 * q^57 - 11 * q^58 + 18 * q^59 - q^60 + 10 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 + 7 * q^65 + 2 * q^66 + 6 * q^67 + 6 * q^68 - 2 * q^69 + q^70 + 6 * q^71 - 2 * q^72 + 10 * q^73 - q^74 + q^75 - 2 * q^76 - 2 * q^77 - 3 * q^78 + 12 * q^79 + q^80 + 2 * q^81 - 3 * q^82 - 10 * q^83 + 2 * q^84 + 20 * q^85 - q^86 - 11 * q^87 - 2 * q^88 + 28 * q^89 - q^90 + 3 * q^91 + 2 * q^92 + 2 * q^93 - 9 * q^94 + 16 * q^95 + 2 * q^96 - 29 * q^97 - 2 * q^98 + 2 * q^99

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