LMFDB - Embedded newform 8022.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 30 x^{9} + 36 x^{8} + 260 x^{7} - 346 x^{6} - 842 x^{5} + 1317 x^{4} + 736 x^{3} + \cdots + 68 $ x^11 - x^10 - 30x^9 + 36x^8 + 260x^7 - 346x^6 - 842x^5 + 1317x^4 + 736x^3 - 1771x^2 + 576*x + 68
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.14797$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.14797 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.14797 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.14797 q^{10} +3.47625 q^{11} +1.00000 q^{12} -0.0772172 q^{13} +1.00000 q^{14} -2.14797 q^{15} +1.00000 q^{16} +4.42189 q^{17} -1.00000 q^{18} -1.01908 q^{19} -2.14797 q^{20} -1.00000 q^{21} -3.47625 q^{22} -5.61622 q^{23} -1.00000 q^{24} -0.386210 q^{25} +0.0772172 q^{26} +1.00000 q^{27} -1.00000 q^{28} -2.74035 q^{29} +2.14797 q^{30} -8.48363 q^{31} -1.00000 q^{32} +3.47625 q^{33} -4.42189 q^{34} +2.14797 q^{35} +1.00000 q^{36} +2.75015 q^{37} +1.01908 q^{38} -0.0772172 q^{39} +2.14797 q^{40} +3.14192 q^{41} +1.00000 q^{42} +9.50884 q^{43} +3.47625 q^{44} -2.14797 q^{45} +5.61622 q^{46} +2.79076 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.386210 q^{50} +4.42189 q^{51} -0.0772172 q^{52} -8.16679 q^{53} -1.00000 q^{54} -7.46690 q^{55} +1.00000 q^{56} -1.01908 q^{57} +2.74035 q^{58} +4.10546 q^{59} -2.14797 q^{60} -1.83736 q^{61} +8.48363 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.165861 q^{65} -3.47625 q^{66} +2.92787 q^{67} +4.42189 q^{68} -5.61622 q^{69} -2.14797 q^{70} -13.9158 q^{71} -1.00000 q^{72} -2.95201 q^{73} -2.75015 q^{74} -0.386210 q^{75} -1.01908 q^{76} -3.47625 q^{77} +0.0772172 q^{78} -1.97446 q^{79} -2.14797 q^{80} +1.00000 q^{81} -3.14192 q^{82} -1.13355 q^{83} -1.00000 q^{84} -9.49811 q^{85} -9.50884 q^{86} -2.74035 q^{87} -3.47625 q^{88} +5.39256 q^{89} +2.14797 q^{90} +0.0772172 q^{91} -5.61622 q^{92} -8.48363 q^{93} -2.79076 q^{94} +2.18897 q^{95} -1.00000 q^{96} -11.7514 q^{97} -1.00000 q^{98} +3.47625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9	$ 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9} - q^{10} + 11 q^{12} - 15 q^{13} + 11 q^{14} + q^{15} + 11 q^{16} - q^{17} - 11 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 5 q^{23} - 11 q^{24} + 6 q^{25} + 15 q^{26} + 11 q^{27} - 11 q^{28} - 12 q^{29} - q^{30} - q^{31} - 11 q^{32} + q^{34} - q^{35} + 11 q^{36} - 12 q^{37} + 3 q^{38} - 15 q^{39} - q^{40} + 8 q^{41} + 11 q^{42} - 14 q^{43} + q^{45} + 5 q^{46} - 3 q^{47} + 11 q^{48} + 11 q^{49} - 6 q^{50} - q^{51} - 15 q^{52} - 14 q^{53} - 11 q^{54} - 27 q^{55} + 11 q^{56} - 3 q^{57} + 12 q^{58} + 33 q^{59} + q^{60} - 46 q^{61} + q^{62} - 11 q^{63} + 11 q^{64} + 12 q^{65} - 8 q^{67} - q^{68} - 5 q^{69} + q^{70} - 16 q^{71} - 11 q^{72} - 26 q^{73} + 12 q^{74} + 6 q^{75} - 3 q^{76} + 15 q^{78} - 24 q^{79} + q^{80} + 11 q^{81} - 8 q^{82} - 4 q^{83} - 11 q^{84} - 32 q^{85} + 14 q^{86} - 12 q^{87} + 5 q^{89} - q^{90} + 15 q^{91} - 5 q^{92} - q^{93} + 3 q^{94} - 19 q^{95} - 11 q^{96} - 36 q^{97} - 11 q^{98}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9 - q^10 + 11 * q^12 - 15 * q^13 + 11 * q^14 + q^15 + 11 * q^16 - q^17 - 11 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 5 * q^23 - 11 * q^24 + 6 * q^25 + 15 * q^26 + 11 * q^27 - 11 * q^28 - 12 * q^29 - q^30 - q^31 - 11 * q^32 + q^34 - q^35 + 11 * q^36 - 12 * q^37 + 3 * q^38 - 15 * q^39 - q^40 + 8 * q^41 + 11 * q^42 - 14 * q^43 + q^45 + 5 * q^46 - 3 * q^47 + 11 * q^48 + 11 * q^49 - 6 * q^50 - q^51 - 15 * q^52 - 14 * q^53 - 11 * q^54 - 27 * q^55 + 11 * q^56 - 3 * q^57 + 12 * q^58 + 33 * q^59 + q^60 - 46 * q^61 + q^62 - 11 * q^63 + 11 * q^64 + 12 * q^65 - 8 * q^67 - q^68 - 5 * q^69 + q^70 - 16 * q^71 - 11 * q^72 - 26 * q^73 + 12 * q^74 + 6 * q^75 - 3 * q^76 + 15 * q^78 - 24 * q^79 + q^80 + 11 * q^81 - 8 * q^82 - 4 * q^83 - 11 * q^84 - 32 * q^85 + 14 * q^86 - 12 * q^87 + 5 * q^89 - q^90 + 15 * q^91 - 5 * q^92 - q^93 + 3 * q^94 - 19 * q^95 - 11 * q^96 - 36 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.14797	−0.960603	−0.480301	−	0.877103i	$-0.659473\pi$
$5$	−2.14797	−0.960603	−0.480301	+	0.877103i	$0.659473\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.14797	0.679249
$11$	3.47625	1.04813	0.524065	−	0.851678i	$-0.324415\pi$
$11$	3.47625	1.04813	0.524065	+	0.851678i	$0.324415\pi$
$12$	1.00000	0.288675
$13$	−0.0772172	−0.0214162	−0.0107081	−	0.999943i	$-0.503409\pi$
$13$	−0.0772172	−0.0214162	−0.0107081	+	0.999943i	$0.503409\pi$
$14$	1.00000	0.267261
$15$	−2.14797	−0.554604
$16$	1.00000	0.250000
$17$	4.42189	1.07247	0.536233	−	0.844070i	$-0.319847\pi$
$17$	4.42189	1.07247	0.536233	+	0.844070i	$0.319847\pi$
$18$	−1.00000	−0.235702
$19$	−1.01908	−0.233794	−0.116897	−	0.993144i	$-0.537295\pi$
$19$	−1.01908	−0.233794	−0.116897	+	0.993144i	$0.537295\pi$
$20$	−2.14797	−0.480301
$21$	−1.00000	−0.218218
$22$	−3.47625	−0.741140
$23$	−5.61622	−1.17106	−0.585532	−	0.810649i	$-0.699114\pi$
$23$	−5.61622	−1.17106	−0.585532	+	0.810649i	$0.699114\pi$
$24$	−1.00000	−0.204124
$25$	−0.386210	−0.0772421
$26$	0.0772172	0.0151435
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−2.74035	−0.508870	−0.254435	−	0.967090i	$-0.581889\pi$
$29$	−2.74035	−0.508870	−0.254435	+	0.967090i	$0.581889\pi$
$30$	2.14797	0.392164
$31$	−8.48363	−1.52371	−0.761853	−	0.647750i	$-0.775710\pi$
$31$	−8.48363	−1.52371	−0.761853	+	0.647750i	$0.775710\pi$
$32$	−1.00000	−0.176777
$33$	3.47625	0.605138
$34$	−4.42189	−0.758348
$35$	2.14797	0.363074
$36$	1.00000	0.166667
$37$	2.75015	0.452121	0.226061	−	0.974113i	$-0.427415\pi$
$37$	2.75015	0.452121	0.226061	+	0.974113i	$0.427415\pi$
$38$	1.01908	0.165317
$39$	−0.0772172	−0.0123647
$40$	2.14797	0.339624
$41$	3.14192	0.490686	0.245343	−	0.969436i	$-0.421099\pi$
$41$	3.14192	0.490686	0.245343	+	0.969436i	$0.421099\pi$
$42$	1.00000	0.154303
$43$	9.50884	1.45009	0.725043	−	0.688704i	$-0.241820\pi$
$43$	9.50884	1.45009	0.725043	+	0.688704i	$0.241820\pi$
$44$	3.47625	0.524065
$45$	−2.14797	−0.320201
$46$	5.61622	0.828067
$47$	2.79076	0.407074	0.203537	−	0.979067i	$-0.434756\pi$
$47$	2.79076	0.407074	0.203537	+	0.979067i	$0.434756\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	0.386210	0.0546184
$51$	4.42189	0.619189
$52$	−0.0772172	−0.0107081
$53$	−8.16679	−1.12179	−0.560897	−	0.827885i	$-0.689544\pi$
$53$	−8.16679	−1.12179	−0.560897	+	0.827885i	$0.689544\pi$
$54$	−1.00000	−0.136083
$55$	−7.46690	−1.00684
$56$	1.00000	0.133631
$57$	−1.01908	−0.134981
$58$	2.74035	0.359825
$59$	4.10546	0.534485	0.267243	−	0.963629i	$-0.413887\pi$
$59$	4.10546	0.534485	0.267243	+	0.963629i	$0.413887\pi$
$60$	−2.14797	−0.277302
$61$	−1.83736	−0.235250	−0.117625	−	0.993058i	$-0.537528\pi$
$61$	−1.83736	−0.235250	−0.117625	+	0.993058i	$0.537528\pi$
$62$	8.48363	1.07742
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0.165861	0.0205725
$66$	−3.47625	−0.427897
$67$	2.92787	0.357697	0.178848	−	0.983877i	$-0.442763\pi$
$67$	2.92787	0.357697	0.178848	+	0.983877i	$0.442763\pi$
$68$	4.42189	0.536233
$69$	−5.61622	−0.676114
$70$	−2.14797	−0.256732
$71$	−13.9158	−1.65150	−0.825748	−	0.564039i	$-0.809247\pi$
$71$	−13.9158	−1.65150	−0.825748	+	0.564039i	$0.809247\pi$
$72$	−1.00000	−0.117851
$73$	−2.95201	−0.345506	−0.172753	−	0.984965i	$-0.555266\pi$
$73$	−2.95201	−0.345506	−0.172753	+	0.984965i	$0.555266\pi$
$74$	−2.75015	−0.319698
$75$	−0.386210	−0.0445957
$76$	−1.01908	−0.116897
$77$	−3.47625	−0.396156
$78$	0.0772172	0.00874313
$79$	−1.97446	−0.222144	−0.111072	−	0.993812i	$-0.535428\pi$
$79$	−1.97446	−0.222144	−0.111072	+	0.993812i	$0.535428\pi$
$80$	−2.14797	−0.240151
$81$	1.00000	0.111111
$82$	−3.14192	−0.346967
$83$	−1.13355	−0.124424	−0.0622118	−	0.998063i	$-0.519815\pi$
$83$	−1.13355	−0.124424	−0.0622118	+	0.998063i	$0.519815\pi$
$84$	−1.00000	−0.109109
$85$	−9.49811	−1.03021
$86$	−9.50884	−1.02537
$87$	−2.74035	−0.293796
$88$	−3.47625	−0.370570
$89$	5.39256	0.571611	0.285805	−	0.958288i	$-0.407739\pi$
$89$	5.39256	0.571611	0.285805	+	0.958288i	$0.407739\pi$
$90$	2.14797	0.226416
$91$	0.0772172	0.00809457
$92$	−5.61622	−0.585532
$93$	−8.48363	−0.879712
$94$	−2.79076	−0.287845
$95$	2.18897	0.224583
$96$	−1.00000	−0.102062
$97$	−11.7514	−1.19318	−0.596588	−	0.802547i	$-0.703477\pi$
$97$	−11.7514	−1.19318	−0.596588	+	0.802547i	$0.703477\pi$
$98$	−1.00000	−0.101015
$99$	3.47625	0.349377
$100$	−0.386210	−0.0386210
$101$	3.56521	0.354751	0.177376	−	0.984143i	$-0.443239\pi$
$101$	3.56521	0.354751	0.177376	+	0.984143i	$0.443239\pi$
$102$	−4.42189	−0.437833
$103$	−17.2744	−1.70209	−0.851047	−	0.525089i	$-0.824032\pi$
$103$	−17.2744	−1.70209	−0.851047	+	0.525089i	$0.824032\pi$
$104$	0.0772172	0.00757177
$105$	2.14797	0.209621
$106$	8.16679	0.793229
$107$	9.89573	0.956656	0.478328	−	0.878181i	$-0.341243\pi$
$107$	9.89573	0.956656	0.478328	+	0.878181i	$0.341243\pi$
$108$	1.00000	0.0962250
$109$	9.10825	0.872412	0.436206	−	0.899847i	$-0.356322\pi$
$109$	9.10825	0.872412	0.436206	+	0.899847i	$0.356322\pi$
$110$	7.46690	0.711941
$111$	2.75015	0.261032
$112$	−1.00000	−0.0944911
$113$	−6.25694	−0.588604	−0.294302	−	0.955713i	$-0.595087\pi$
$113$	−6.25694	−0.588604	−0.294302	+	0.955713i	$0.595087\pi$
$114$	1.01908	0.0954460
$115$	12.0635	1.12493
$116$	−2.74035	−0.254435
$117$	−0.0772172	−0.00713874
$118$	−4.10546	−0.377938
$119$	−4.42189	−0.405354
$120$	2.14797	0.196082
$121$	1.08434	0.0985765
$122$	1.83736	0.166347
$123$	3.14192	0.283298
$124$	−8.48363	−0.761853
$125$	11.5694	1.03480
$126$	1.00000	0.0890871
$127$	−4.55181	−0.403908	−0.201954	−	0.979395i	$-0.564729\pi$
$127$	−4.55181	−0.403908	−0.201954	+	0.979395i	$0.564729\pi$
$128$	−1.00000	−0.0883883
$129$	9.50884	0.837207
$130$	−0.165861	−0.0145469
$131$	18.1426	1.58513	0.792563	−	0.609789i	$-0.208746\pi$
$131$	18.1426	1.58513	0.792563	+	0.609789i	$0.208746\pi$
$132$	3.47625	0.302569
$133$	1.01908	0.0883658
$134$	−2.92787	−0.252930
$135$	−2.14797	−0.184868
$136$	−4.42189	−0.379174
$137$	−8.12779	−0.694404	−0.347202	−	0.937790i	$-0.612868\pi$
$137$	−8.12779	−0.694404	−0.347202	+	0.937790i	$0.612868\pi$
$138$	5.61622	0.478085
$139$	8.74398	0.741655	0.370828	−	0.928702i	$-0.379074\pi$
$139$	8.74398	0.741655	0.370828	+	0.928702i	$0.379074\pi$
$140$	2.14797	0.181537
$141$	2.79076	0.235024
$142$	13.9158	1.16778
$143$	−0.268427	−0.0224470
$144$	1.00000	0.0833333
$145$	5.88620	0.488822
$146$	2.95201	0.244310
$147$	1.00000	0.0824786
$148$	2.75015	0.226061
$149$	−6.88239	−0.563827	−0.281914	−	0.959440i	$-0.590969\pi$
$149$	−6.88239	−0.563827	−0.281914	+	0.959440i	$0.590969\pi$
$150$	0.386210	0.0315340
$151$	−7.25396	−0.590319	−0.295159	−	0.955448i	$-0.595373\pi$
$151$	−7.25396	−0.590319	−0.295159	+	0.955448i	$0.595373\pi$
$152$	1.01908	0.0826586
$153$	4.42189	0.357489
$154$	3.47625	0.280125
$155$	18.2226	1.46368
$156$	−0.0772172	−0.00618233
$157$	−4.76551	−0.380329	−0.190165	−	0.981752i	$-0.560902\pi$
$157$	−4.76551	−0.380329	−0.190165	+	0.981752i	$0.560902\pi$
$158$	1.97446	0.157079
$159$	−8.16679	−0.647669
$160$	2.14797	0.169812
$161$	5.61622	0.442620
$162$	−1.00000	−0.0785674
$163$	20.9022	1.63719	0.818593	−	0.574375i	$-0.194755\pi$
$163$	20.9022	1.63719	0.818593	+	0.574375i	$0.194755\pi$
$164$	3.14192	0.245343
$165$	−7.46690	−0.581297
$166$	1.13355	0.0879808
$167$	−14.7482	−1.14125	−0.570624	−	0.821212i	$-0.693298\pi$
$167$	−14.7482	−1.14125	−0.570624	+	0.821212i	$0.693298\pi$
$168$	1.00000	0.0771517
$169$	−12.9940	−0.999541
$170$	9.49811	0.728472
$171$	−1.01908	−0.0779313
$172$	9.50884	0.725043
$173$	20.8315	1.58379	0.791893	−	0.610660i	$-0.209096\pi$
$173$	20.8315	1.58379	0.791893	+	0.610660i	$0.209096\pi$
$174$	2.74035	0.207745
$175$	0.386210	0.0291948
$176$	3.47625	0.262032
$177$	4.10546	0.308585
$178$	−5.39256	−0.404190
$179$	1.87095	0.139842	0.0699209	−	0.997553i	$-0.477725\pi$
$179$	1.87095	0.139842	0.0699209	+	0.997553i	$0.477725\pi$
$180$	−2.14797	−0.160100
$181$	−21.5410	−1.60113	−0.800566	−	0.599244i	$-0.795468\pi$
$181$	−21.5410	−1.60113	−0.800566	+	0.599244i	$0.795468\pi$
$182$	−0.0772172	−0.00572372
$183$	−1.83736	−0.135822
$184$	5.61622	0.414034
$185$	−5.90724	−0.434309
$186$	8.48363	0.622050
$187$	15.3716	1.12408
$188$	2.79076	0.203537
$189$	−1.00000	−0.0727393
$190$	−2.18897	−0.158804
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	1.00000	0.0721688
$193$	−19.8317	−1.42752	−0.713759	−	0.700391i	$-0.753009\pi$
$193$	−19.8317	−1.42752	−0.713759	+	0.700391i	$0.753009\pi$
$194$	11.7514	0.843703
$195$	0.165861	0.0118775
$196$	1.00000	0.0714286
$197$	13.2899	0.946864	0.473432	−	0.880830i	$-0.343015\pi$
$197$	13.2899	0.946864	0.473432	+	0.880830i	$0.343015\pi$
$198$	−3.47625	−0.247047
$199$	−8.59370	−0.609191	−0.304596	−	0.952482i	$-0.598521\pi$
$199$	−8.59370	−0.609191	−0.304596	+	0.952482i	$0.598521\pi$
$200$	0.386210	0.0273092
$201$	2.92787	0.206516
$202$	−3.56521	−0.250847
$203$	2.74035	0.192335
$204$	4.42189	0.309594
$205$	−6.74877	−0.471354
$206$	17.2744	1.20356
$207$	−5.61622	−0.390355
$208$	−0.0772172	−0.00535405
$209$	−3.54259	−0.245046
$210$	−2.14797	−0.148224
$211$	−8.10695	−0.558105	−0.279053	−	0.960276i	$-0.590020\pi$
$211$	−8.10695	−0.558105	−0.279053	+	0.960276i	$0.590020\pi$
$212$	−8.16679	−0.560897
$213$	−13.9158	−0.953492
$214$	−9.89573	−0.676458
$215$	−20.4247	−1.39296
$216$	−1.00000	−0.0680414
$217$	8.48363	0.575906
$218$	−9.10825	−0.616889
$219$	−2.95201	−0.199478
$220$	−7.46690	−0.503418
$221$	−0.341446	−0.0229682
$222$	−2.75015	−0.184578
$223$	−6.88895	−0.461318	−0.230659	−	0.973035i	$-0.574088\pi$
$223$	−6.88895	−0.461318	−0.230659	+	0.973035i	$0.574088\pi$
$224$	1.00000	0.0668153
$225$	−0.386210	−0.0257474
$226$	6.25694	0.416206
$227$	6.37965	0.423433	0.211716	−	0.977331i	$-0.432095\pi$
$227$	6.37965	0.423433	0.211716	+	0.977331i	$0.432095\pi$
$228$	−1.01908	−0.0674905
$229$	−2.39729	−0.158417	−0.0792087	−	0.996858i	$-0.525239\pi$
$229$	−2.39729	−0.158417	−0.0792087	+	0.996858i	$0.525239\pi$
$230$	−12.0635	−0.795444
$231$	−3.47625	−0.228721
$232$	2.74035	0.179913
$233$	12.9987	0.851574	0.425787	−	0.904823i	$-0.359997\pi$
$233$	12.9987	0.851574	0.425787	+	0.904823i	$0.359997\pi$
$234$	0.0772172	0.00504785
$235$	−5.99448	−0.391037
$236$	4.10546	0.267243
$237$	−1.97446	−0.128255
$238$	4.42189	0.286629
$239$	2.23057	0.144283	0.0721416	−	0.997394i	$-0.477017\pi$
$239$	2.23057	0.144283	0.0721416	+	0.997394i	$0.477017\pi$
$240$	−2.14797	−0.138651
$241$	−19.9844	−1.28731	−0.643654	−	0.765317i	$-0.722582\pi$
$241$	−19.9844	−1.28731	−0.643654	+	0.765317i	$0.722582\pi$
$242$	−1.08434	−0.0697041
$243$	1.00000	0.0641500
$244$	−1.83736	−0.117625
$245$	−2.14797	−0.137229
$246$	−3.14192	−0.200322
$247$	0.0786909	0.00500698
$248$	8.48363	0.538711
$249$	−1.13355	−0.0718360
$250$	−11.5694	−0.731715
$251$	−9.78178	−0.617420	−0.308710	−	0.951156i	$-0.599897\pi$
$251$	−9.78178	−0.617420	−0.308710	+	0.951156i	$0.599897\pi$
$252$	−1.00000	−0.0629941
$253$	−19.5234	−1.22743
$254$	4.55181	0.285606
$255$	−9.49811	−0.594795
$256$	1.00000	0.0625000
$257$	13.6841	0.853594	0.426797	−	0.904348i	$-0.359642\pi$
$257$	13.6841	0.853594	0.426797	+	0.904348i	$0.359642\pi$
$258$	−9.50884	−0.591995
$259$	−2.75015	−0.170886
$260$	0.165861	0.0102862
$261$	−2.74035	−0.169623
$262$	−18.1426	−1.12085
$263$	4.58939	0.282994	0.141497	−	0.989939i	$-0.454808\pi$
$263$	4.58939	0.282994	0.141497	+	0.989939i	$0.454808\pi$
$264$	−3.47625	−0.213949
$265$	17.5420	1.07760
$266$	−1.01908	−0.0624841
$267$	5.39256	0.330020
$268$	2.92787	0.178848
$269$	−11.8634	−0.723327	−0.361664	−	0.932309i	$-0.617791\pi$
$269$	−11.8634	−0.723327	−0.361664	+	0.932309i	$0.617791\pi$
$270$	2.14797	0.130721
$271$	19.0521	1.15733	0.578666	−	0.815565i	$-0.303573\pi$
$271$	19.0521	1.15733	0.578666	+	0.815565i	$0.303573\pi$
$272$	4.42189	0.268117
$273$	0.0772172	0.00467340
$274$	8.12779	0.491017
$275$	−1.34257	−0.0809598
$276$	−5.61622	−0.338057
$277$	−23.4518	−1.40908	−0.704540	−	0.709665i	$-0.748846\pi$
$277$	−23.4518	−1.40908	−0.704540	+	0.709665i	$0.748846\pi$
$278$	−8.74398	−0.524429
$279$	−8.48363	−0.507902
$280$	−2.14797	−0.128366
$281$	19.6552	1.17253	0.586266	−	0.810119i	$-0.300598\pi$
$281$	19.6552	1.17253	0.586266	+	0.810119i	$0.300598\pi$
$282$	−2.79076	−0.166187
$283$	−32.7288	−1.94553	−0.972764	−	0.231798i	$-0.925539\pi$
$283$	−32.7288	−1.94553	−0.972764	+	0.231798i	$0.925539\pi$
$284$	−13.9158	−0.825748
$285$	2.18897	0.129663
$286$	0.268427	0.0158724
$287$	−3.14192	−0.185462
$288$	−1.00000	−0.0589256
$289$	2.55314	0.150185
$290$	−5.88620	−0.345649
$291$	−11.7514	−0.688881
$292$	−2.95201	−0.172753
$293$	11.1669	0.652376	0.326188	−	0.945305i	$-0.394236\pi$
$293$	11.1669	0.652376	0.326188	+	0.945305i	$0.394236\pi$
$294$	−1.00000	−0.0583212
$295$	−8.81842	−0.513428
$296$	−2.75015	−0.159849
$297$	3.47625	0.201713
$298$	6.88239	0.398686
$299$	0.433669	0.0250797
$300$	−0.386210	−0.0222979
$301$	−9.50884	−0.548081
$302$	7.25396	0.417418
$303$	3.56521	0.204816
$304$	−1.01908	−0.0584485
$305$	3.94661	0.225982
$306$	−4.42189	−0.252783
$307$	−29.8280	−1.70237	−0.851186	−	0.524865i	$-0.824116\pi$
$307$	−29.8280	−1.70237	−0.851186	+	0.524865i	$0.824116\pi$
$308$	−3.47625	−0.198078
$309$	−17.2744	−0.982705
$310$	−18.2226	−1.03497
$311$	−5.29558	−0.300285	−0.150142	−	0.988664i	$-0.547973\pi$
$311$	−5.29558	−0.300285	−0.150142	+	0.988664i	$0.547973\pi$
$312$	0.0772172	0.00437157
$313$	0.214788	0.0121405	0.00607026	−	0.999982i	$-0.498068\pi$
$313$	0.214788	0.0121405	0.00607026	+	0.999982i	$0.498068\pi$
$314$	4.76551	0.268933
$315$	2.14797	0.121025
$316$	−1.97446	−0.111072
$317$	−1.17847	−0.0661894	−0.0330947	−	0.999452i	$-0.510536\pi$
$317$	−1.17847	−0.0661894	−0.0330947	+	0.999452i	$0.510536\pi$
$318$	8.16679	0.457971
$319$	−9.52615	−0.533362
$320$	−2.14797	−0.120075
$321$	9.89573	0.552326
$322$	−5.61622	−0.312980
$323$	−4.50628	−0.250736
$324$	1.00000	0.0555556
$325$	0.0298221	0.00165423
$326$	−20.9022	−1.15766
$327$	9.10825	0.503688
$328$	−3.14192	−0.173484
$329$	−2.79076	−0.153860
$330$	7.46690	0.411039
$331$	3.84117	0.211130	0.105565	−	0.994412i	$-0.466335\pi$
$331$	3.84117	0.211130	0.105565	+	0.994412i	$0.466335\pi$
$332$	−1.13355	−0.0622118
$333$	2.75015	0.150707
$334$	14.7482	0.806984
$335$	−6.28900	−0.343605
$336$	−1.00000	−0.0545545
$337$	−29.3516	−1.59889	−0.799443	−	0.600743i	$-0.794872\pi$
$337$	−29.3516	−1.59889	−0.799443	+	0.600743i	$0.794872\pi$
$338$	12.9940	0.706782
$339$	−6.25694	−0.339830
$340$	−9.49811	−0.515107
$341$	−29.4913	−1.59704
$342$	1.01908	0.0551058
$343$	−1.00000	−0.0539949
$344$	−9.50884	−0.512683
$345$	12.0635	0.649477
$346$	−20.8315	−1.11991
$347$	−15.3234	−0.822602	−0.411301	−	0.911500i	$-0.634926\pi$
$347$	−15.3234	−0.822602	−0.411301	+	0.911500i	$0.634926\pi$
$348$	−2.74035	−0.146898
$349$	−3.13224	−0.167665	−0.0838325	−	0.996480i	$-0.526716\pi$
$349$	−3.13224	−0.167665	−0.0838325	+	0.996480i	$0.526716\pi$
$350$	−0.386210	−0.0206438
$351$	−0.0772172	−0.00412155
$352$	−3.47625	−0.185285
$353$	−30.2141	−1.60813	−0.804067	−	0.594539i	$-0.797335\pi$
$353$	−30.2141	−1.60813	−0.804067	+	0.594539i	$0.797335\pi$
$354$	−4.10546	−0.218203
$355$	29.8907	1.58643
$356$	5.39256	0.285805
$357$	−4.42189	−0.234031
$358$	−1.87095	−0.0988830
$359$	16.5080	0.871260	0.435630	−	0.900126i	$-0.356526\pi$
$359$	16.5080	0.871260	0.435630	+	0.900126i	$0.356526\pi$
$360$	2.14797	0.113208
$361$	−17.9615	−0.945340
$362$	21.5410	1.13217
$363$	1.08434	0.0569131
$364$	0.0772172	0.00404728
$365$	6.34083	0.331894
$366$	1.83736	0.0960405
$367$	17.2245	0.899113	0.449556	−	0.893252i	$-0.351582\pi$
$367$	17.2245	0.899113	0.449556	+	0.893252i	$0.351582\pi$
$368$	−5.61622	−0.292766
$369$	3.14192	0.163562
$370$	5.90724	0.307103
$371$	8.16679	0.423999
$372$	−8.48363	−0.439856
$373$	−0.631417	−0.0326936	−0.0163468	−	0.999866i	$-0.505204\pi$
$373$	−0.631417	−0.0326936	−0.0163468	+	0.999866i	$0.505204\pi$
$374$	−15.3716	−0.794848
$375$	11.5694	0.597443
$376$	−2.79076	−0.143922
$377$	0.211602	0.0108981
$378$	1.00000	0.0514344
$379$	−25.8672	−1.32871	−0.664354	−	0.747418i	$-0.731293\pi$
$379$	−25.8672	−1.32871	−0.664354	+	0.747418i	$0.731293\pi$
$380$	2.18897	0.112292
$381$	−4.55181	−0.233196
$382$	−1.00000	−0.0511645
$383$	5.33476	0.272594	0.136297	−	0.990668i	$-0.456480\pi$
$383$	5.33476	0.272594	0.136297	+	0.990668i	$0.456480\pi$
$384$	−1.00000	−0.0510310
$385$	7.46690	0.380548
$386$	19.8317	1.00941
$387$	9.50884	0.483362
$388$	−11.7514	−0.596588
$389$	−29.2200	−1.48151	−0.740757	−	0.671773i	$-0.765533\pi$
$389$	−29.2200	−1.48151	−0.740757	+	0.671773i	$0.765533\pi$
$390$	−0.165861	−0.00839868
$391$	−24.8343	−1.25593
$392$	−1.00000	−0.0505076
$393$	18.1426	0.915173
$394$	−13.2899	−0.669534
$395$	4.24108	0.213392
$396$	3.47625	0.174688
$397$	11.2410	0.564172	0.282086	−	0.959389i	$-0.408974\pi$
$397$	11.2410	0.564172	0.282086	+	0.959389i	$0.408974\pi$
$398$	8.59370	0.430763
$399$	1.01908	0.0510180
$400$	−0.386210	−0.0193105
$401$	−15.6411	−0.781079	−0.390539	−	0.920586i	$-0.627711\pi$
$401$	−15.6411	−0.781079	−0.390539	+	0.920586i	$0.627711\pi$
$402$	−2.92787	−0.146029
$403$	0.655083	0.0326320
$404$	3.56521	0.177376
$405$	−2.14797	−0.106734
$406$	−2.74035	−0.136001
$407$	9.56021	0.473882
$408$	−4.42189	−0.218916
$409$	27.1117	1.34059	0.670295	−	0.742095i	$-0.266168\pi$
$409$	27.1117	1.34059	0.670295	+	0.742095i	$0.266168\pi$
$410$	6.74877	0.333298
$411$	−8.12779	−0.400914
$412$	−17.2744	−0.851047
$413$	−4.10546	−0.202016
$414$	5.61622	0.276022
$415$	2.43484	0.119522
$416$	0.0772172	0.00378589
$417$	8.74398	0.428195
$418$	3.54259	0.173274
$419$	−0.770596	−0.0376461	−0.0188230	−	0.999823i	$-0.505992\pi$
$419$	−0.770596	−0.0376461	−0.0188230	+	0.999823i	$0.505992\pi$
$420$	2.14797	0.104810
$421$	−2.37863	−0.115927	−0.0579637	−	0.998319i	$-0.518461\pi$
$421$	−2.37863	−0.115927	−0.0579637	+	0.998319i	$0.518461\pi$
$422$	8.10695	0.394640
$423$	2.79076	0.135691
$424$	8.16679	0.396614
$425$	−1.70778	−0.0828396
$426$	13.9158	0.674221
$427$	1.83736	0.0889162
$428$	9.89573	0.478328
$429$	−0.268427	−0.0129598
$430$	20.4247	0.984969
$431$	−15.6149	−0.752143	−0.376072	−	0.926591i	$-0.622725\pi$
$431$	−15.6149	−0.752143	−0.376072	+	0.926591i	$0.622725\pi$
$432$	1.00000	0.0481125
$433$	−36.7028	−1.76382	−0.881912	−	0.471414i	$-0.843744\pi$
$433$	−36.7028	−1.76382	−0.881912	+	0.471414i	$0.843744\pi$
$434$	−8.48363	−0.407227
$435$	5.88620	0.282221
$436$	9.10825	0.436206
$437$	5.72340	0.273788
$438$	2.95201	0.141052
$439$	−3.09958	−0.147935	−0.0739675	−	0.997261i	$-0.523566\pi$
$439$	−3.09958	−0.147935	−0.0739675	+	0.997261i	$0.523566\pi$
$440$	7.46690	0.355971
$441$	1.00000	0.0476190
$442$	0.341446	0.0162409
$443$	−23.2723	−1.10570	−0.552850	−	0.833281i	$-0.686460\pi$
$443$	−23.2723	−1.10570	−0.552850	+	0.833281i	$0.686460\pi$
$444$	2.75015	0.130516
$445$	−11.5831	−0.549091
$446$	6.88895	0.326201
$447$	−6.88239	−0.325526
$448$	−1.00000	−0.0472456
$449$	15.9262	0.751603	0.375802	−	0.926700i	$-0.377367\pi$
$449$	15.9262	0.751603	0.375802	+	0.926700i	$0.377367\pi$
$450$	0.386210	0.0182061
$451$	10.9221	0.514303
$452$	−6.25694	−0.294302
$453$	−7.25396	−0.340821
$454$	−6.37965	−0.299412
$455$	−0.165861	−0.00777566
$456$	1.01908	0.0477230
$457$	28.4656	1.33157	0.665783	−	0.746146i	$-0.268098\pi$
$457$	28.4656	1.33157	0.665783	+	0.746146i	$0.268098\pi$
$458$	2.39729	0.112018
$459$	4.42189	0.206396
$460$	12.0635	0.562464
$461$	14.2828	0.665217	0.332609	−	0.943065i	$-0.392071\pi$
$461$	14.2828	0.665217	0.332609	+	0.943065i	$0.392071\pi$
$462$	3.47625	0.161730
$463$	−31.3037	−1.45481	−0.727404	−	0.686210i	$-0.759273\pi$
$463$	−31.3037	−1.45481	−0.727404	+	0.686210i	$0.759273\pi$
$464$	−2.74035	−0.127217
$465$	18.2226	0.845053
$466$	−12.9987	−0.602154
$467$	−25.8852	−1.19783	−0.598913	−	0.800814i	$-0.704400\pi$
$467$	−25.8852	−1.19783	−0.598913	+	0.800814i	$0.704400\pi$
$468$	−0.0772172	−0.00356937
$469$	−2.92787	−0.135197
$470$	5.99448	0.276505
$471$	−4.76551	−0.219583
$472$	−4.10546	−0.188969
$473$	33.0552	1.51988
$474$	1.97446	0.0906898
$475$	0.393581	0.0180587
$476$	−4.42189	−0.202677
$477$	−8.16679	−0.373932
$478$	−2.23057	−0.102024
$479$	32.5875	1.48896	0.744481	−	0.667644i	$-0.232697\pi$
$479$	32.5875	1.48896	0.744481	+	0.667644i	$0.232697\pi$
$480$	2.14797	0.0980411
$481$	−0.212359	−0.00968272
$482$	19.9844	0.910264
$483$	5.61622	0.255547
$484$	1.08434	0.0492882
$485$	25.2417	1.14617
$486$	−1.00000	−0.0453609
$487$	−32.8098	−1.48675	−0.743377	−	0.668873i	$-0.766777\pi$
$487$	−32.8098	−1.48675	−0.743377	+	0.668873i	$0.766777\pi$
$488$	1.83736	0.0831735
$489$	20.9022	0.945229
$490$	2.14797	0.0970355
$491$	−39.7145	−1.79229	−0.896144	−	0.443762i	$-0.853643\pi$
$491$	−39.7145	−1.79229	−0.896144	+	0.443762i	$0.853643\pi$
$492$	3.14192	0.141649
$493$	−12.1175	−0.545746
$494$	−0.0786909	−0.00354047
$495$	−7.46690	−0.335612
$496$	−8.48363	−0.380926
$497$	13.9158	0.624207
$498$	1.13355	0.0507957
$499$	−6.98528	−0.312704	−0.156352	−	0.987701i	$-0.549973\pi$
$499$	−6.98528	−0.312704	−0.156352	+	0.987701i	$0.549973\pi$
$500$	11.5694	0.517401
$501$	−14.7482	−0.658899
$502$	9.78178	0.436582
$503$	2.63510	0.117493	0.0587467	−	0.998273i	$-0.481290\pi$
$503$	2.63510	0.117493	0.0587467	+	0.998273i	$0.481290\pi$
$504$	1.00000	0.0445435
$505$	−7.65797	−0.340775
$506$	19.5234	0.867922
$507$	−12.9940	−0.577085
$508$	−4.55181	−0.201954
$509$	−38.2098	−1.69362	−0.846809	−	0.531897i	$-0.821479\pi$
$509$	−38.2098	−1.69362	−0.846809	+	0.531897i	$0.821479\pi$
$510$	9.49811	0.420583
$511$	2.95201	0.130589
$512$	−1.00000	−0.0441942
$513$	−1.01908	−0.0449937
$514$	−13.6841	−0.603582
$515$	37.1049	1.63504
$516$	9.50884	0.418604
$517$	9.70139	0.426667
$518$	2.75015	0.120834
$519$	20.8315	0.914399
$520$	−0.165861	−0.00727347
$521$	22.4864	0.985149	0.492575	−	0.870270i	$-0.336056\pi$
$521$	22.4864	0.985149	0.492575	+	0.870270i	$0.336056\pi$
$522$	2.74035	0.119942
$523$	4.73272	0.206947	0.103474	−	0.994632i	$-0.467004\pi$
$523$	4.73272	0.206947	0.103474	+	0.994632i	$0.467004\pi$
$524$	18.1426	0.792563
$525$	0.386210	0.0168556
$526$	−4.58939	−0.200107
$527$	−37.5137	−1.63412
$528$	3.47625	0.151285
$529$	8.54197	0.371390
$530$	−17.5420	−0.761978
$531$	4.10546	0.178162
$532$	1.01908	0.0441829
$533$	−0.242611	−0.0105086
$534$	−5.39256	−0.233359
$535$	−21.2558	−0.918967
$536$	−2.92787	−0.126465
$537$	1.87095	0.0807377
$538$	11.8634	0.511470
$539$	3.47625	0.149733
$540$	−2.14797	−0.0924341
$541$	−2.88685	−0.124115	−0.0620577	−	0.998073i	$-0.519766\pi$
$541$	−2.88685	−0.124115	−0.0620577	+	0.998073i	$0.519766\pi$
$542$	−19.0521	−0.818357
$543$	−21.5410	−0.924414
$544$	−4.42189	−0.189587
$545$	−19.5643	−0.838042
$546$	−0.0772172	−0.00330459
$547$	18.3875	0.786192	0.393096	−	0.919497i	$-0.371404\pi$
$547$	18.3875	0.786192	0.393096	+	0.919497i	$0.371404\pi$
$548$	−8.12779	−0.347202
$549$	−1.83736	−0.0784167
$550$	1.34257	0.0572472
$551$	2.79265	0.118971
$552$	5.61622	0.239042
$553$	1.97446	0.0839624
$554$	23.4518	0.996369
$555$	−5.90724	−0.250748
$556$	8.74398	0.370828
$557$	20.3330	0.861538	0.430769	−	0.902462i	$-0.358242\pi$
$557$	20.3330	0.861538	0.430769	+	0.902462i	$0.358242\pi$
$558$	8.48363	0.359141
$559$	−0.734247	−0.0310553
$560$	2.14797	0.0907684
$561$	15.3716	0.648990
$562$	−19.6552	−0.829105
$563$	−30.2015	−1.27284	−0.636420	−	0.771342i	$-0.719586\pi$
$563$	−30.2015	−1.27284	−0.636420	+	0.771342i	$0.719586\pi$
$564$	2.79076	0.117512
$565$	13.4397	0.565414
$566$	32.7288	1.37570
$567$	−1.00000	−0.0419961
$568$	13.9158	0.583892
$569$	−33.1741	−1.39073	−0.695366	−	0.718656i	$-0.744758\pi$
$569$	−33.1741	−1.39073	−0.695366	+	0.718656i	$0.744758\pi$
$570$	−2.18897	−0.0916857
$571$	−38.6209	−1.61623	−0.808117	−	0.589022i	$-0.799513\pi$
$571$	−38.6209	−1.61623	−0.808117	+	0.589022i	$0.799513\pi$
$572$	−0.268427	−0.0112235
$573$	1.00000	0.0417756
$574$	3.14192	0.131141
$575$	2.16904	0.0904554
$576$	1.00000	0.0416667
$577$	3.99974	0.166511	0.0832556	−	0.996528i	$-0.473468\pi$
$577$	3.99974	0.166511	0.0832556	+	0.996528i	$0.473468\pi$
$578$	−2.55314	−0.106197
$579$	−19.8317	−0.824178
$580$	5.88620	0.244411
$581$	1.13355	0.0470277
$582$	11.7514	0.487112
$583$	−28.3898	−1.17579
$584$	2.95201	0.122155
$585$	0.165861	0.00685749
$586$	−11.1669	−0.461299
$587$	−29.6415	−1.22344	−0.611718	−	0.791076i	$-0.709521\pi$
$587$	−29.6415	−1.22344	−0.611718	+	0.791076i	$0.709521\pi$
$588$	1.00000	0.0412393
$589$	8.64553	0.356233
$590$	8.81842	0.363049
$591$	13.2899	0.546672
$592$	2.75015	0.113030
$593$	35.1306	1.44264	0.721321	−	0.692601i	$-0.243535\pi$
$593$	35.1306	1.44264	0.721321	+	0.692601i	$0.243535\pi$
$594$	−3.47625	−0.142632
$595$	9.49811	0.389384
$596$	−6.88239	−0.281914
$597$	−8.59370	−0.351717
$598$	−0.433669	−0.0177341
$599$	−19.1645	−0.783039	−0.391520	−	0.920170i	$-0.628050\pi$
$599$	−19.1645	−0.783039	−0.391520	+	0.920170i	$0.628050\pi$
$600$	0.386210	0.0157670
$601$	−17.5542	−0.716050	−0.358025	−	0.933712i	$-0.616550\pi$
$601$	−17.5542	−0.716050	−0.358025	+	0.933712i	$0.616550\pi$
$602$	9.50884	0.387552
$603$	2.92787	0.119232
$604$	−7.25396	−0.295159
$605$	−2.32914	−0.0946928
$606$	−3.56521	−0.144827
$607$	−1.29892	−0.0527214	−0.0263607	−	0.999652i	$-0.508392\pi$
$607$	−1.29892	−0.0527214	−0.0263607	+	0.999652i	$0.508392\pi$
$608$	1.01908	0.0413293
$609$	2.74035	0.111045
$610$	−3.94661	−0.159793
$611$	−0.215495	−0.00871799
$612$	4.42189	0.178744
$613$	−8.53940	−0.344903	−0.172452	−	0.985018i	$-0.555169\pi$
$613$	−8.53940	−0.344903	−0.172452	+	0.985018i	$0.555169\pi$
$614$	29.8280	1.20376
$615$	−6.74877	−0.272137
$616$	3.47625	0.140062
$617$	−24.6078	−0.990671	−0.495336	−	0.868702i	$-0.664955\pi$
$617$	−24.6078	−0.990671	−0.495336	+	0.868702i	$0.664955\pi$
$618$	17.2744	0.694877
$619$	24.0443	0.966422	0.483211	−	0.875504i	$-0.339470\pi$
$619$	24.0443	0.966422	0.483211	+	0.875504i	$0.339470\pi$
$620$	18.2226	0.731838
$621$	−5.61622	−0.225371
$622$	5.29558	0.212333
$623$	−5.39256	−0.216049
$624$	−0.0772172	−0.00309116
$625$	−22.9198	−0.916792
$626$	−0.214788	−0.00858464
$627$	−3.54259	−0.141478
$628$	−4.76551	−0.190165
$629$	12.1609	0.484885
$630$	−2.14797	−0.0855773
$631$	34.8843	1.38872	0.694361	−	0.719626i	$-0.255687\pi$
$631$	34.8843	1.38872	0.694361	+	0.719626i	$0.255687\pi$
$632$	1.97446	0.0785396
$633$	−8.10695	−0.322222
$634$	1.17847	0.0468029
$635$	9.77716	0.387995
$636$	−8.16679	−0.323834
$637$	−0.0772172	−0.00305946
$638$	9.52615	0.377144
$639$	−13.9158	−0.550499
$640$	2.14797	0.0849061
$641$	−5.72077	−0.225957	−0.112978	−	0.993597i	$-0.536039\pi$
$641$	−5.72077	−0.225957	−0.112978	+	0.993597i	$0.536039\pi$
$642$	−9.89573	−0.390553
$643$	10.1159	0.398931	0.199465	−	0.979905i	$-0.436079\pi$
$643$	10.1159	0.398931	0.199465	+	0.979905i	$0.436079\pi$
$644$	5.61622	0.221310
$645$	−20.4247	−0.804224
$646$	4.50628	0.177297
$647$	38.5504	1.51557	0.757786	−	0.652503i	$-0.226281\pi$
$647$	38.5504	1.51557	0.757786	+	0.652503i	$0.226281\pi$
$648$	−1.00000	−0.0392837
$649$	14.2716	0.560210
$650$	−0.0298221	−0.00116972
$651$	8.48363	0.332500
$652$	20.9022	0.818593
$653$	24.1029	0.943220	0.471610	−	0.881807i	$-0.343673\pi$
$653$	24.1029	0.943220	0.471610	+	0.881807i	$0.343673\pi$
$654$	−9.10825	−0.356161
$655$	−38.9698	−1.52268
$656$	3.14192	0.122672
$657$	−2.95201	−0.115169
$658$	2.79076	0.108795
$659$	21.1348	0.823295	0.411648	−	0.911343i	$-0.364953\pi$
$659$	21.1348	0.823295	0.411648	+	0.911343i	$0.364953\pi$
$660$	−7.46690	−0.290649
$661$	34.2251	1.33120	0.665600	−	0.746308i	$-0.268176\pi$
$661$	34.2251	1.33120	0.665600	+	0.746308i	$0.268176\pi$
$662$	−3.84117	−0.149291
$663$	−0.341446	−0.0132607
$664$	1.13355	0.0439904
$665$	−2.18897	−0.0848844
$666$	−2.75015	−0.106566
$667$	15.3904	0.595919
$668$	−14.7482	−0.570624
$669$	−6.88895	−0.266342
$670$	6.28900	0.242965
$671$	−6.38714	−0.246573
$672$	1.00000	0.0385758
$673$	−28.3523	−1.09290	−0.546450	−	0.837492i	$-0.684021\pi$
$673$	−28.3523	−1.09290	−0.546450	+	0.837492i	$0.684021\pi$
$674$	29.3516	1.13058
$675$	−0.386210	−0.0148652
$676$	−12.9940	−0.499771
$677$	−35.2781	−1.35585	−0.677923	−	0.735133i	$-0.737120\pi$
$677$	−35.2781	−1.35585	−0.677923	+	0.735133i	$0.737120\pi$
$678$	6.25694	0.240296
$679$	11.7514	0.450978
$680$	9.49811	0.364236
$681$	6.37965	0.244469
$682$	29.4913	1.12928
$683$	−26.4436	−1.01184	−0.505919	−	0.862581i	$-0.668846\pi$
$683$	−26.4436	−1.01184	−0.505919	+	0.862581i	$0.668846\pi$
$684$	−1.01908	−0.0389657
$685$	17.4583	0.667046
$686$	1.00000	0.0381802
$687$	−2.39729	−0.0914623
$688$	9.50884	0.362521
$689$	0.630617	0.0240246
$690$	−12.0635	−0.459250
$691$	0.933692	0.0355193	0.0177597	−	0.999842i	$-0.494347\pi$
$691$	0.933692	0.0355193	0.0177597	+	0.999842i	$0.494347\pi$
$692$	20.8315	0.791893
$693$	−3.47625	−0.132052
$694$	15.3234	0.581668
$695$	−18.7818	−0.712436
$696$	2.74035	0.103873
$697$	13.8933	0.526244
$698$	3.13224	0.118557
$699$	12.9987	0.491656
$700$	0.386210	0.0145974
$701$	−34.1682	−1.29051	−0.645257	−	0.763966i	$-0.723250\pi$
$701$	−34.1682	−1.29051	−0.645257	+	0.763966i	$0.723250\pi$
$702$	0.0772172	0.00291438
$703$	−2.80263	−0.105703
$704$	3.47625	0.131016
$705$	−5.99448	−0.225765
$706$	30.2141	1.13712
$707$	−3.56521	−0.134083
$708$	4.10546	0.154293
$709$	46.6121	1.75055	0.875277	−	0.483622i	$-0.160679\pi$
$709$	46.6121	1.75055	0.875277	+	0.483622i	$0.160679\pi$
$710$	−29.8907	−1.12178
$711$	−1.97446	−0.0740479
$712$	−5.39256	−0.202095
$713$	47.6460	1.78436
$714$	4.42189	0.165485
$715$	0.576573	0.0215626
$716$	1.87095	0.0699209
$717$	2.23057	0.0833020
$718$	−16.5080	−0.616074
$719$	−3.42965	−0.127904	−0.0639522	−	0.997953i	$-0.520371\pi$
$719$	−3.42965	−0.127904	−0.0639522	+	0.997953i	$0.520371\pi$
$720$	−2.14797	−0.0800502
$721$	17.2744	0.643331
$722$	17.9615	0.668457
$723$	−19.9844	−0.743227
$724$	−21.5410	−0.800566
$725$	1.05835	0.0393062
$726$	−1.08434	−0.0402437
$727$	−0.124383	−0.00461311	−0.00230655	−	0.999997i	$-0.500734\pi$
$727$	−0.124383	−0.00461311	−0.00230655	+	0.999997i	$0.500734\pi$
$728$	−0.0772172	−0.00286186
$729$	1.00000	0.0370370
$730$	−6.34083	−0.234685
$731$	42.0471	1.55517
$732$	−1.83736	−0.0679109
$733$	−38.1084	−1.40757	−0.703783	−	0.710415i	$-0.748507\pi$
$733$	−38.1084	−1.40757	−0.703783	+	0.710415i	$0.748507\pi$
$734$	−17.2245	−0.635769
$735$	−2.14797	−0.0792292
$736$	5.61622	0.207017
$737$	10.1780	0.374913
$738$	−3.14192	−0.115656
$739$	−3.22850	−0.118762	−0.0593811	−	0.998235i	$-0.518913\pi$
$739$	−3.22850	−0.118762	−0.0593811	+	0.998235i	$0.518913\pi$
$740$	−5.90724	−0.217154
$741$	0.0786909	0.00289078
$742$	−8.16679	−0.299812
$743$	27.9466	1.02526	0.512631	−	0.858609i	$-0.328671\pi$
$743$	27.9466	1.02526	0.512631	+	0.858609i	$0.328671\pi$
$744$	8.48363	0.311025
$745$	14.7832	0.541614
$746$	0.631417	0.0231178
$747$	−1.13355	−0.0414745
$748$	15.3716	0.562042
$749$	−9.89573	−0.361582
$750$	−11.5694	−0.422456
$751$	−26.4276	−0.964358	−0.482179	−	0.876073i	$-0.660155\pi$
$751$	−26.4276	−0.964358	−0.482179	+	0.876073i	$0.660155\pi$
$752$	2.79076	0.101769
$753$	−9.78178	−0.356468
$754$	−0.211602	−0.00770610
$755$	15.5813	0.567062
$756$	−1.00000	−0.0363696
$757$	−20.9524	−0.761527	−0.380763	−	0.924672i	$-0.624339\pi$
$757$	−20.9524	−0.761527	−0.380763	+	0.924672i	$0.624339\pi$
$758$	25.8672	0.939538
$759$	−19.5234	−0.708655
$760$	−2.18897	−0.0794021
$761$	14.6970	0.532765	0.266383	−	0.963867i	$-0.414172\pi$
$761$	14.6970	0.532765	0.266383	+	0.963867i	$0.414172\pi$
$762$	4.55181	0.164895
$763$	−9.10825	−0.329741
$764$	1.00000	0.0361787
$765$	−9.49811	−0.343405
$766$	−5.33476	−0.192753
$767$	−0.317012	−0.0114466
$768$	1.00000	0.0360844
$769$	3.51474	0.126745	0.0633724	−	0.997990i	$-0.479814\pi$
$769$	3.51474	0.126745	0.0633724	+	0.997990i	$0.479814\pi$
$770$	−7.46690	−0.269088
$771$	13.6841	0.492823
$772$	−19.8317	−0.713759
$773$	28.0806	1.00999	0.504995	−	0.863122i	$-0.331494\pi$
$773$	28.0806	1.00999	0.504995	+	0.863122i	$0.331494\pi$
$774$	−9.50884	−0.341788
$775$	3.27647	0.117694
$776$	11.7514	0.421852
$777$	−2.75015	−0.0986609
$778$	29.2200	1.04759
$779$	−3.20188	−0.114719
$780$	0.165861	0.00593876
$781$	−48.3747	−1.73098
$782$	24.8343	0.888074
$783$	−2.74035	−0.0979321
$784$	1.00000	0.0357143
$785$	10.2362	0.365345
$786$	−18.1426	−0.647125
$787$	−7.09654	−0.252964	−0.126482	−	0.991969i	$-0.540369\pi$
$787$	−7.09654	−0.252964	−0.126482	+	0.991969i	$0.540369\pi$
$788$	13.2899	0.473432
$789$	4.58939	0.163387
$790$	−4.24108	−0.150891
$791$	6.25694	0.222471
$792$	−3.47625	−0.123523
$793$	0.141876	0.00503817
$794$	−11.2410	−0.398930
$795$	17.5420	0.622152
$796$	−8.59370	−0.304596
$797$	6.15236	0.217928	0.108964	−	0.994046i	$-0.465247\pi$
$797$	6.15236	0.217928	0.108964	+	0.994046i	$0.465247\pi$
$798$	−1.01908	−0.0360752
$799$	12.3404	0.436574
$800$	0.386210	0.0136546
$801$	5.39256	0.190537
$802$	15.6411	0.552306
$803$	−10.2619	−0.362136
$804$	2.92787	0.103258
$805$	−12.0635	−0.425182
$806$	−0.655083	−0.0230743
$807$	−11.8634	−0.417613
$808$	−3.56521	−0.125424
$809$	23.2254	0.816560	0.408280	−	0.912857i	$-0.366129\pi$
$809$	23.2254	0.816560	0.408280	+	0.912857i	$0.366129\pi$
$810$	2.14797	0.0754721
$811$	19.6473	0.689911	0.344955	−	0.938619i	$-0.387894\pi$
$811$	19.6473	0.689911	0.344955	+	0.938619i	$0.387894\pi$
$812$	2.74035	0.0961674
$813$	19.0521	0.668186
$814$	−9.56021	−0.335085
$815$	−44.8973	−1.57268
$816$	4.42189	0.154797
$817$	−9.69031	−0.339021
$818$	−27.1117	−0.947940
$819$	0.0772172	0.00269819
$820$	−6.74877	−0.235677
$821$	48.9980	1.71004	0.855021	−	0.518593i	$-0.173544\pi$
$821$	48.9980	1.71004	0.855021	+	0.518593i	$0.173544\pi$
$822$	8.12779	0.283489
$823$	5.43163	0.189335	0.0946673	−	0.995509i	$-0.469821\pi$
$823$	5.43163	0.189335	0.0946673	+	0.995509i	$0.469821\pi$
$824$	17.2744	0.601781
$825$	−1.34257	−0.0467421
$826$	4.10546	0.142847
$827$	−24.1087	−0.838341	−0.419170	−	0.907908i	$-0.637679\pi$
$827$	−24.1087	−0.838341	−0.419170	+	0.907908i	$0.637679\pi$
$828$	−5.61622	−0.195177
$829$	29.2595	1.01622	0.508112	−	0.861291i	$-0.330344\pi$
$829$	29.2595	1.01622	0.508112	+	0.861291i	$0.330344\pi$
$830$	−2.43484	−0.0845146
$831$	−23.4518	−0.813532
$832$	−0.0772172	−0.00267703
$833$	4.42189	0.153210
$834$	−8.74398	−0.302779
$835$	31.6787	1.09629
$836$	−3.54259	−0.122523
$837$	−8.48363	−0.293237
$838$	0.770596	0.0266198
$839$	−15.6467	−0.540184	−0.270092	−	0.962834i	$-0.587054\pi$
$839$	−15.6467	−0.540184	−0.270092	+	0.962834i	$0.587054\pi$
$840$	−2.14797	−0.0741121
$841$	−21.4905	−0.741051
$842$	2.37863	0.0819730
$843$	19.6552	0.676961
$844$	−8.10695	−0.279053
$845$	27.9108	0.960162
$846$	−2.79076	−0.0959483
$847$	−1.08434	−0.0372584
$848$	−8.16679	−0.280449
$849$	−32.7288	−1.12325
$850$	1.70778	0.0585764
$851$	−15.4454	−0.529463
$852$	−13.9158	−0.476746
$853$	29.3027	1.00331	0.501653	−	0.865069i	$-0.332725\pi$
$853$	29.3027	1.00331	0.501653	+	0.865069i	$0.332725\pi$
$854$	−1.83736	−0.0628733
$855$	2.18897	0.0748610
$856$	−9.89573	−0.338229
$857$	−24.3292	−0.831071	−0.415536	−	0.909577i	$-0.636406\pi$
$857$	−24.3292	−0.831071	−0.415536	+	0.909577i	$0.636406\pi$
$858$	0.268427	0.00916394
$859$	46.2260	1.57721	0.788605	−	0.614900i	$-0.210804\pi$
$859$	46.2260	1.57721	0.788605	+	0.614900i	$0.210804\pi$
$860$	−20.4247	−0.696478
$861$	−3.14192	−0.107076
$862$	15.6149	0.531846
$863$	−42.0969	−1.43299	−0.716497	−	0.697590i	$-0.754256\pi$
$863$	−42.0969	−1.43299	−0.716497	+	0.697590i	$0.754256\pi$
$864$	−1.00000	−0.0340207
$865$	−44.7454	−1.52139
$866$	36.7028	1.24721
$867$	2.55314	0.0867091
$868$	8.48363	0.287953
$869$	−6.86371	−0.232835
$870$	−5.88620	−0.199561
$871$	−0.226082	−0.00766051
$872$	−9.10825	−0.308444
$873$	−11.7514	−0.397725
$874$	−5.72340	−0.193597
$875$	−11.5694	−0.391118
$876$	−2.95201	−0.0997391
$877$	4.43196	0.149657	0.0748283	−	0.997196i	$-0.476159\pi$
$877$	4.43196	0.149657	0.0748283	+	0.997196i	$0.476159\pi$
$878$	3.09958	0.104606
$879$	11.1669	0.376649
$880$	−7.46690	−0.251709
$881$	48.7745	1.64326	0.821628	−	0.570025i	$-0.193066\pi$
$881$	48.7745	1.64326	0.821628	+	0.570025i	$0.193066\pi$
$882$	−1.00000	−0.0336718
$883$	−16.9155	−0.569253	−0.284627	−	0.958638i	$-0.591870\pi$
$883$	−16.9155	−0.569253	−0.284627	+	0.958638i	$0.591870\pi$
$884$	−0.341446	−0.0114841
$885$	−8.81842	−0.296428
$886$	23.2723	0.781848
$887$	−31.9829	−1.07388	−0.536940	−	0.843620i	$-0.680420\pi$
$887$	−31.9829	−1.07388	−0.536940	+	0.843620i	$0.680420\pi$
$888$	−2.75015	−0.0922889
$889$	4.55181	0.152663
$890$	11.5831	0.388266
$891$	3.47625	0.116459
$892$	−6.88895	−0.230659
$893$	−2.84402	−0.0951715
$894$	6.88239	0.230181
$895$	−4.01876	−0.134332
$896$	1.00000	0.0334077
$897$	0.433669	0.0144798
$898$	−15.9262	−0.531464
$899$	23.2481	0.775368
$900$	−0.386210	−0.0128737
$901$	−36.1127	−1.20309
$902$	−10.9221	−0.363667
$903$	−9.50884	−0.316435
$904$	6.25694	0.208103
$905$	46.2696	1.53805
$906$	7.25396	0.240997
$907$	37.0907	1.23158	0.615788	−	0.787912i	$-0.288838\pi$
$907$	37.0907	1.23158	0.615788	+	0.787912i	$0.288838\pi$
$908$	6.37965	0.211716
$909$	3.56521	0.118250
$910$	0.165861	0.00549822
$911$	7.18017	0.237890	0.118945	−	0.992901i	$-0.462049\pi$
$911$	7.18017	0.237890	0.118945	+	0.992901i	$0.462049\pi$
$912$	−1.01908	−0.0337452
$913$	−3.94052	−0.130412
$914$	−28.4656	−0.941559
$915$	3.94661	0.130471
$916$	−2.39729	−0.0792087
$917$	−18.1426	−0.599122
$918$	−4.42189	−0.145944
$919$	30.1889	0.995840	0.497920	−	0.867223i	$-0.334097\pi$
$919$	30.1889	0.995840	0.497920	+	0.867223i	$0.334097\pi$
$920$	−12.0635	−0.397722
$921$	−29.8280	−0.982864
$922$	−14.2828	−0.470380
$923$	1.07454	0.0353688
$924$	−3.47625	−0.114360
$925$	−1.06214	−0.0349228
$926$	31.3037	1.02870
$927$	−17.2744	−0.567365
$928$	2.74035	0.0899564
$929$	−24.1365	−0.791894	−0.395947	−	0.918273i	$-0.629584\pi$
$929$	−24.1365	−0.791894	−0.395947	+	0.918273i	$0.629584\pi$
$930$	−18.2226	−0.597543
$931$	−1.01908	−0.0333991
$932$	12.9987	0.425787
$933$	−5.29558	−0.173370
$934$	25.8852	0.846990
$935$	−33.0178	−1.07980
$936$	0.0772172	0.00252392
$937$	−15.6638	−0.511713	−0.255857	−	0.966715i	$-0.582358\pi$
$937$	−15.6638	−0.511713	−0.255857	+	0.966715i	$0.582358\pi$
$938$	2.92787	0.0955985
$939$	0.214788	0.00700933
$940$	−5.99448	−0.195518
$941$	1.99661	0.0650875	0.0325437	−	0.999470i	$-0.489639\pi$
$941$	1.99661	0.0650875	0.0325437	+	0.999470i	$0.489639\pi$
$942$	4.76551	0.155269
$943$	−17.6457	−0.574625
$944$	4.10546	0.133621
$945$	2.14797	0.0698736
$946$	−33.0552	−1.07472
$947$	−32.3752	−1.05205	−0.526027	−	0.850468i	$-0.676319\pi$
$947$	−32.3752	−1.05205	−0.526027	+	0.850468i	$0.676319\pi$
$948$	−1.97446	−0.0641273
$949$	0.227946	0.00739944
$950$	−0.393581	−0.0127695
$951$	−1.17847	−0.0382144
$952$	4.42189	0.143314
$953$	−37.8821	−1.22712	−0.613561	−	0.789648i	$-0.710263\pi$
$953$	−37.8821	−1.22712	−0.613561	+	0.789648i	$0.710263\pi$
$954$	8.16679	0.264410
$955$	−2.14797	−0.0695068
$956$	2.23057	0.0721416
$957$	−9.52615	−0.307937
$958$	−32.5875	−1.05285
$959$	8.12779	0.262460
$960$	−2.14797	−0.0693255
$961$	40.9720	1.32168
$962$	0.212359	0.00684672
$963$	9.89573	0.318885
$964$	−19.9844	−0.643654
$965$	42.5980	1.37128
$966$	−5.61622	−0.180699
$967$	−49.2695	−1.58440	−0.792200	−	0.610262i	$-0.791064\pi$
$967$	−49.2695	−1.58440	−0.792200	+	0.610262i	$0.791064\pi$
$968$	−1.08434	−0.0348520
$969$	−4.50628	−0.144763
$970$	−25.2417	−0.810464
$971$	−14.7204	−0.472400	−0.236200	−	0.971704i	$-0.575902\pi$
$971$	−14.7204	−0.472400	−0.236200	+	0.971704i	$0.575902\pi$
$972$	1.00000	0.0320750
$973$	−8.74398	−0.280319
$974$	32.8098	1.05129
$975$	0.0298221	0.000955072 0
$976$	−1.83736	−0.0588126
$977$	−22.2861	−0.712996	−0.356498	−	0.934296i	$-0.616029\pi$
$977$	−22.2861	−0.712996	−0.356498	+	0.934296i	$0.616029\pi$
$978$	−20.9022	−0.668378
$979$	18.7459	0.599122
$980$	−2.14797	−0.0686145
$981$	9.10825	0.290804
$982$	39.7145	1.26734
$983$	7.63315	0.243460	0.121730	−	0.992563i	$-0.461156\pi$
$983$	7.63315	0.243460	0.121730	+	0.992563i	$0.461156\pi$
$984$	−3.14192	−0.100161
$985$	−28.5463	−0.909560
$986$	12.1175	0.385901
$987$	−2.79076	−0.0888309
$988$	0.0786909	0.00250349
$989$	−53.4038	−1.69814
$990$	7.46690	0.237314
$991$	−20.0360	−0.636463	−0.318232	−	0.948013i	$-0.603089\pi$
$991$	−20.0360	−0.636463	−0.318232	+	0.948013i	$0.603089\pi$
$992$	8.48363	0.269356
$993$	3.84117	0.121896
$994$	−13.9158	−0.441381
$995$	18.4590	0.585191
$996$	−1.13355	−0.0359180
$997$	8.59352	0.272160	0.136080	−	0.990698i	$-0.456550\pi$
$997$	8.59352	0.272160	0.136080	+	0.990698i	$0.456550\pi$
$998$	6.98528	0.221115
$999$	2.75015	0.0870108

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.t.1.2	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.t.1.2	✓	11	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.14797 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.14797 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.14797 q^{10} +3.47625 q^{11} +1.00000 q^{12} -0.0772172 q^{13} +1.00000 q^{14} -2.14797 q^{15} +1.00000 q^{16} +4.42189 q^{17} -1.00000 q^{18} -1.01908 q^{19} -2.14797 q^{20} -1.00000 q^{21} -3.47625 q^{22} -5.61622 q^{23} -1.00000 q^{24} -0.386210 q^{25} +0.0772172 q^{26} +1.00000 q^{27} -1.00000 q^{28} -2.74035 q^{29} +2.14797 q^{30} -8.48363 q^{31} -1.00000 q^{32} +3.47625 q^{33} -4.42189 q^{34} +2.14797 q^{35} +1.00000 q^{36} +2.75015 q^{37} +1.01908 q^{38} -0.0772172 q^{39} +2.14797 q^{40} +3.14192 q^{41} +1.00000 q^{42} +9.50884 q^{43} +3.47625 q^{44} -2.14797 q^{45} +5.61622 q^{46} +2.79076 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.386210 q^{50} +4.42189 q^{51} -0.0772172 q^{52} -8.16679 q^{53} -1.00000 q^{54} -7.46690 q^{55} +1.00000 q^{56} -1.01908 q^{57} +2.74035 q^{58} +4.10546 q^{59} -2.14797 q^{60} -1.83736 q^{61} +8.48363 q^{62} -1.00000 q^{63} +1.00000 q^{64} +0.165861 q^{65} -3.47625 q^{66} +2.92787 q^{67} +4.42189 q^{68} -5.61622 q^{69} -2.14797 q^{70} -13.9158 q^{71} -1.00000 q^{72} -2.95201 q^{73} -2.75015 q^{74} -0.386210 q^{75} -1.01908 q^{76} -3.47625 q^{77} +0.0772172 q^{78} -1.97446 q^{79} -2.14797 q^{80} +1.00000 q^{81} -3.14192 q^{82} -1.13355 q^{83} -1.00000 q^{84} -9.49811 q^{85} -9.50884 q^{86} -2.74035 q^{87} -3.47625 q^{88} +5.39256 q^{89} +2.14797 q^{90} +0.0772172 q^{91} -5.61622 q^{92} -8.48363 q^{93} -2.79076 q^{94} +2.18897 q^{95} -1.00000 q^{96} -11.7514 q^{97} -1.00000 q^{98} +3.47625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} + 11 q^{3} + 11 q^{4} + q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} + 11 q^{9} - q^{10} + 11 q^{12} - 15 q^{13} + 11 q^{14} + q^{15} + 11 q^{16} - q^{17} - 11 q^{18} - 3 q^{19} + q^{20} - 11 q^{21} - 5 q^{23} - 11 q^{24} + 6 q^{25} + 15 q^{26} + 11 q^{27} - 11 q^{28} - 12 q^{29} - q^{30} - q^{31} - 11 q^{32} + q^{34} - q^{35} + 11 q^{36} - 12 q^{37} + 3 q^{38} - 15 q^{39} - q^{40} + 8 q^{41} + 11 q^{42} - 14 q^{43} + q^{45} + 5 q^{46} - 3 q^{47} + 11 q^{48} + 11 q^{49} - 6 q^{50} - q^{51} - 15 q^{52} - 14 q^{53} - 11 q^{54} - 27 q^{55} + 11 q^{56} - 3 q^{57} + 12 q^{58} + 33 q^{59} + q^{60} - 46 q^{61} + q^{62} - 11 q^{63} + 11 q^{64} + 12 q^{65} - 8 q^{67} - q^{68} - 5 q^{69} + q^{70} - 16 q^{71} - 11 q^{72} - 26 q^{73} + 12 q^{74} + 6 q^{75} - 3 q^{76} + 15 q^{78} - 24 q^{79} + q^{80} + 11 q^{81} - 8 q^{82} - 4 q^{83} - 11 q^{84} - 32 q^{85} + 14 q^{86} - 12 q^{87} + 5 q^{89} - q^{90} + 15 q^{91} - 5 q^{92} - q^{93} + 3 q^{94} - 19 q^{95} - 11 q^{96} - 36 q^{97} - 11 q^{98}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^3 + 11 * q^4 + q^5 - 11 * q^6 - 11 * q^7 - 11 * q^8 + 11 * q^9 - q^10 + 11 * q^12 - 15 * q^13 + 11 * q^14 + q^15 + 11 * q^16 - q^17 - 11 * q^18 - 3 * q^19 + q^20 - 11 * q^21 - 5 * q^23 - 11 * q^24 + 6 * q^25 + 15 * q^26 + 11 * q^27 - 11 * q^28 - 12 * q^29 - q^30 - q^31 - 11 * q^32 + q^34 - q^35 + 11 * q^36 - 12 * q^37 + 3 * q^38 - 15 * q^39 - q^40 + 8 * q^41 + 11 * q^42 - 14 * q^43 + q^45 + 5 * q^46 - 3 * q^47 + 11 * q^48 + 11 * q^49 - 6 * q^50 - q^51 - 15 * q^52 - 14 * q^53 - 11 * q^54 - 27 * q^55 + 11 * q^56 - 3 * q^57 + 12 * q^58 + 33 * q^59 + q^60 - 46 * q^61 + q^62 - 11 * q^63 + 11 * q^64 + 12 * q^65 - 8 * q^67 - q^68 - 5 * q^69 + q^70 - 16 * q^71 - 11 * q^72 - 26 * q^73 + 12 * q^74 + 6 * q^75 - 3 * q^76 + 15 * q^78 - 24 * q^79 + q^80 + 11 * q^81 - 8 * q^82 - 4 * q^83 - 11 * q^84 - 32 * q^85 + 14 * q^86 - 12 * q^87 + 5 * q^89 - q^90 + 15 * q^91 - 5 * q^92 - q^93 + 3 * q^94 - 19 * q^95 - 11 * q^96 - 36 * q^97 - 11 * q^98

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