LMFDB - Embedded newform 946.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(1,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("946.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	946.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -2.30278 q^{5} +1.30278 q^{6} -2.60555 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -2.30278 q^{5} +1.30278 q^{6} -2.60555 q^{7} -1.00000 q^{8} -1.30278 q^{9} +2.30278 q^{10} -1.00000 q^{11} -1.30278 q^{12} -4.00000 q^{13} +2.60555 q^{14} +3.00000 q^{15} +1.00000 q^{16} +0.697224 q^{17} +1.30278 q^{18} -0.302776 q^{19} -2.30278 q^{20} +3.39445 q^{21} +1.00000 q^{22} -2.30278 q^{23} +1.30278 q^{24} +0.302776 q^{25} +4.00000 q^{26} +5.60555 q^{27} -2.60555 q^{28} +6.69722 q^{29} -3.00000 q^{30} -4.69722 q^{31} -1.00000 q^{32} +1.30278 q^{33} -0.697224 q^{34} +6.00000 q^{35} -1.30278 q^{36} -0.0916731 q^{37} +0.302776 q^{38} +5.21110 q^{39} +2.30278 q^{40} -3.69722 q^{41} -3.39445 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.00000 q^{45} +2.30278 q^{46} +9.90833 q^{47} -1.30278 q^{48} -0.211103 q^{49} -0.302776 q^{50} -0.908327 q^{51} -4.00000 q^{52} -3.21110 q^{53} -5.60555 q^{54} +2.30278 q^{55} +2.60555 q^{56} +0.394449 q^{57} -6.69722 q^{58} +9.21110 q^{59} +3.00000 q^{60} +2.00000 q^{61} +4.69722 q^{62} +3.39445 q^{63} +1.00000 q^{64} +9.21110 q^{65} -1.30278 q^{66} -14.6056 q^{67} +0.697224 q^{68} +3.00000 q^{69} -6.00000 q^{70} +4.60555 q^{71} +1.30278 q^{72} +5.21110 q^{73} +0.0916731 q^{74} -0.394449 q^{75} -0.302776 q^{76} +2.60555 q^{77} -5.21110 q^{78} +16.7250 q^{79} -2.30278 q^{80} -3.39445 q^{81} +3.69722 q^{82} -7.81665 q^{83} +3.39445 q^{84} -1.60555 q^{85} -1.00000 q^{86} -8.72498 q^{87} +1.00000 q^{88} +12.0000 q^{89} -3.00000 q^{90} +10.4222 q^{91} -2.30278 q^{92} +6.11943 q^{93} -9.90833 q^{94} +0.697224 q^{95} +1.30278 q^{96} -14.1194 q^{97} +0.211103 q^{98} +1.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 8 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 5 q^{17} - q^{18} + 3 q^{19} - q^{20} + 14 q^{21} + 2 q^{22} - q^{23} - q^{24} - 3 q^{25} + 8 q^{26} + 4 q^{27} + 2 q^{28} + 17 q^{29} - 6 q^{30} - 13 q^{31} - 2 q^{32} - q^{33} - 5 q^{34} + 12 q^{35} + q^{36} - 11 q^{37} - 3 q^{38} - 4 q^{39} + q^{40} - 11 q^{41} - 14 q^{42} + 2 q^{43} - 2 q^{44} + 6 q^{45} + q^{46} + 9 q^{47} + q^{48} + 14 q^{49} + 3 q^{50} + 9 q^{51} - 8 q^{52} + 8 q^{53} - 4 q^{54} + q^{55} - 2 q^{56} + 8 q^{57} - 17 q^{58} + 4 q^{59} + 6 q^{60} + 4 q^{61} + 13 q^{62} + 14 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 22 q^{67} + 5 q^{68} + 6 q^{69} - 12 q^{70} + 2 q^{71} - q^{72} - 4 q^{73} + 11 q^{74} - 8 q^{75} + 3 q^{76} - 2 q^{77} + 4 q^{78} + q^{79} - q^{80} - 14 q^{81} + 11 q^{82} + 6 q^{83} + 14 q^{84} + 4 q^{85} - 2 q^{86} + 15 q^{87} + 2 q^{88} + 24 q^{89} - 6 q^{90} - 8 q^{91} - q^{92} - 13 q^{93} - 9 q^{94} + 5 q^{95} - q^{96} - 3 q^{97} - 14 q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9 + q^10 - 2 * q^11 + q^12 - 8 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 5 * q^17 - q^18 + 3 * q^19 - q^20 + 14 * q^21 + 2 * q^22 - q^23 - q^24 - 3 * q^25 + 8 * q^26 + 4 * q^27 + 2 * q^28 + 17 * q^29 - 6 * q^30 - 13 * q^31 - 2 * q^32 - q^33 - 5 * q^34 + 12 * q^35 + q^36 - 11 * q^37 - 3 * q^38 - 4 * q^39 + q^40 - 11 * q^41 - 14 * q^42 + 2 * q^43 - 2 * q^44 + 6 * q^45 + q^46 + 9 * q^47 + q^48 + 14 * q^49 + 3 * q^50 + 9 * q^51 - 8 * q^52 + 8 * q^53 - 4 * q^54 + q^55 - 2 * q^56 + 8 * q^57 - 17 * q^58 + 4 * q^59 + 6 * q^60 + 4 * q^61 + 13 * q^62 + 14 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 22 * q^67 + 5 * q^68 + 6 * q^69 - 12 * q^70 + 2 * q^71 - q^72 - 4 * q^73 + 11 * q^74 - 8 * q^75 + 3 * q^76 - 2 * q^77 + 4 * q^78 + q^79 - q^80 - 14 * q^81 + 11 * q^82 + 6 * q^83 + 14 * q^84 + 4 * q^85 - 2 * q^86 + 15 * q^87 + 2 * q^88 + 24 * q^89 - 6 * q^90 - 8 * q^91 - q^92 - 13 * q^93 - 9 * q^94 + 5 * q^95 - q^96 - 3 * q^97 - 14 * q^98 - 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
$3$	−1.30278	−0.752158	−0.376079	−	0.926588i	$-0.622728\pi$
$3$	−1.30278	−0.752158	−0.376079	+	0.926588i	$0.622728\pi$
$4$	1.00000	0.500000
$5$	−2.30278	−1.02983	−0.514916	−	0.857240i	$-0.672177\pi$
$5$	−2.30278	−1.02983	−0.514916	+	0.857240i	$0.672177\pi$
$6$	1.30278	0.531856
$7$	−2.60555	−0.984806	−0.492403	−	0.870367i	$-0.663881\pi$
$7$	−2.60555	−0.984806	−0.492403	+	0.870367i	$0.663881\pi$
$8$	−1.00000	−0.353553
$9$	−1.30278	−0.434259
$10$	2.30278	0.728202
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.30278	−0.376079
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.60555	0.696363
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	0.697224	0.169102	0.0845509	−	0.996419i	$-0.473054\pi$
$17$	0.697224	0.169102	0.0845509	+	0.996419i	$0.473054\pi$
$18$	1.30278	0.307067
$19$	−0.302776	−0.0694615	−0.0347307	−	0.999397i	$-0.511057\pi$
$19$	−0.302776	−0.0694615	−0.0347307	+	0.999397i	$0.511057\pi$
$20$	−2.30278	−0.514916
$21$	3.39445	0.740729
$22$	1.00000	0.213201
$23$	−2.30278	−0.480162	−0.240081	−	0.970753i	$-0.577174\pi$
$23$	−2.30278	−0.480162	−0.240081	+	0.970753i	$0.577174\pi$
$24$	1.30278	0.265928
$25$	0.302776	0.0605551
$26$	4.00000	0.784465
$27$	5.60555	1.07879
$28$	−2.60555	−0.492403
$29$	6.69722	1.24364	0.621822	−	0.783159i	$-0.286393\pi$
$29$	6.69722	1.24364	0.621822	+	0.783159i	$0.286393\pi$
$30$	−3.00000	−0.547723
$31$	−4.69722	−0.843646	−0.421823	−	0.906678i	$-0.638610\pi$
$31$	−4.69722	−0.843646	−0.421823	+	0.906678i	$0.638610\pi$
$32$	−1.00000	−0.176777
$33$	1.30278	0.226784
$34$	−0.697224	−0.119573
$35$	6.00000	1.01419
$36$	−1.30278	−0.217129
$37$	−0.0916731	−0.0150710	−0.00753548	−	0.999972i	$-0.502399\pi$
$37$	−0.0916731	−0.0150710	−0.00753548	+	0.999972i	$0.502399\pi$
$38$	0.302776	0.0491167
$39$	5.21110	0.834444
$40$	2.30278	0.364101
$41$	−3.69722	−0.577409	−0.288705	−	0.957418i	$-0.593225\pi$
$41$	−3.69722	−0.577409	−0.288705	+	0.957418i	$0.593225\pi$
$42$	−3.39445	−0.523775
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	3.00000	0.447214
$46$	2.30278	0.339526
$47$	9.90833	1.44528	0.722639	−	0.691226i	$-0.242929\pi$
$47$	9.90833	1.44528	0.722639	+	0.691226i	$0.242929\pi$
$48$	−1.30278	−0.188039
$49$	−0.211103	−0.0301575
$50$	−0.302776	−0.0428189
$51$	−0.908327	−0.127191
$52$	−4.00000	−0.554700
$53$	−3.21110	−0.441079	−0.220539	−	0.975378i	$-0.570782\pi$
$53$	−3.21110	−0.441079	−0.220539	+	0.975378i	$0.570782\pi$
$54$	−5.60555	−0.762819
$55$	2.30278	0.310506
$56$	2.60555	0.348181
$57$	0.394449	0.0522460
$58$	−6.69722	−0.879389
$59$	9.21110	1.19918	0.599592	−	0.800306i	$-0.295330\pi$
$59$	9.21110	1.19918	0.599592	+	0.800306i	$0.295330\pi$
$60$	3.00000	0.387298
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	4.69722	0.596548
$63$	3.39445	0.427660
$64$	1.00000	0.125000
$65$	9.21110	1.14250
$66$	−1.30278	−0.160361
$67$	−14.6056	−1.78435	−0.892176	−	0.451688i	$-0.850822\pi$
$67$	−14.6056	−1.78435	−0.892176	+	0.451688i	$0.850822\pi$
$68$	0.697224	0.0845509
$69$	3.00000	0.361158
$70$	−6.00000	−0.717137
$71$	4.60555	0.546578	0.273289	−	0.961932i	$-0.411888\pi$
$71$	4.60555	0.546578	0.273289	+	0.961932i	$0.411888\pi$
$72$	1.30278	0.153534
$73$	5.21110	0.609913	0.304957	−	0.952366i	$-0.401358\pi$
$73$	5.21110	0.609913	0.304957	+	0.952366i	$0.401358\pi$
$74$	0.0916731	0.0106568
$75$	−0.394449	−0.0455470
$76$	−0.302776	−0.0347307
$77$	2.60555	0.296930
$78$	−5.21110	−0.590041
$79$	16.7250	1.88171	0.940854	−	0.338813i	$-0.110025\pi$
$79$	16.7250	1.88171	0.940854	+	0.338813i	$0.110025\pi$
$80$	−2.30278	−0.257458
$81$	−3.39445	−0.377161
$82$	3.69722	0.408290
$83$	−7.81665	−0.857989	−0.428995	−	0.903307i	$-0.641132\pi$
$83$	−7.81665	−0.857989	−0.428995	+	0.903307i	$0.641132\pi$
$84$	3.39445	0.370365
$85$	−1.60555	−0.174146
$86$	−1.00000	−0.107833
$87$	−8.72498	−0.935416
$88$	1.00000	0.106600
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	−3.00000	−0.316228
$91$	10.4222	1.09254
$92$	−2.30278	−0.240081
$93$	6.11943	0.634555
$94$	−9.90833	−1.02197
$95$	0.697224	0.0715337
$96$	1.30278	0.132964
$97$	−14.1194	−1.43361	−0.716805	−	0.697273i	$-0.754396\pi$
$97$	−14.1194	−1.43361	−0.716805	+	0.697273i	$0.754396\pi$
$98$	0.211103	0.0213246
$99$	1.30278	0.130934
$100$	0.302776	0.0302776
$101$	10.6056	1.05529	0.527646	−	0.849464i	$-0.323075\pi$
$101$	10.6056	1.05529	0.527646	+	0.849464i	$0.323075\pi$
$102$	0.908327	0.0899378
$103$	19.5139	1.92276	0.961380	−	0.275225i	$-0.0887524\pi$
$103$	19.5139	1.92276	0.961380	+	0.275225i	$0.0887524\pi$
$104$	4.00000	0.392232
$105$	−7.81665	−0.762827
$106$	3.21110	0.311890
$107$	1.39445	0.134806	0.0674032	−	0.997726i	$-0.478529\pi$
$107$	1.39445	0.134806	0.0674032	+	0.997726i	$0.478529\pi$
$108$	5.60555	0.539394
$109$	−11.8167	−1.13183	−0.565915	−	0.824464i	$-0.691477\pi$
$109$	−11.8167	−1.13183	−0.565915	+	0.824464i	$0.691477\pi$
$110$	−2.30278	−0.219561
$111$	0.119429	0.0113357
$112$	−2.60555	−0.246201
$113$	−2.78890	−0.262357	−0.131179	−	0.991359i	$-0.541876\pi$
$113$	−2.78890	−0.262357	−0.131179	+	0.991359i	$0.541876\pi$
$114$	−0.394449	−0.0369435
$115$	5.30278	0.494486
$116$	6.69722	0.621822
$117$	5.21110	0.481767
$118$	−9.21110	−0.847951
$119$	−1.81665	−0.166532
$120$	−3.00000	−0.273861
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	4.81665	0.434303
$124$	−4.69722	−0.421823
$125$	10.8167	0.967471
$126$	−3.39445	−0.302402
$127$	−11.1194	−0.986690	−0.493345	−	0.869834i	$-0.664226\pi$
$127$	−11.1194	−0.986690	−0.493345	+	0.869834i	$0.664226\pi$
$128$	−1.00000	−0.0883883
$129$	−1.30278	−0.114703
$130$	−9.21110	−0.807867
$131$	6.69722	0.585139	0.292570	−	0.956244i	$-0.405490\pi$
$131$	6.69722	0.585139	0.292570	+	0.956244i	$0.405490\pi$
$132$	1.30278	0.113392
$133$	0.788897	0.0684061
$134$	14.6056	1.26173
$135$	−12.9083	−1.11097
$136$	−0.697224	−0.0597865
$137$	−13.8167	−1.18044	−0.590218	−	0.807244i	$-0.700958\pi$
$137$	−13.8167	−1.18044	−0.590218	+	0.807244i	$0.700958\pi$
$138$	−3.00000	−0.255377
$139$	−0.788897	−0.0669134	−0.0334567	−	0.999440i	$-0.510652\pi$
$139$	−0.788897	−0.0669134	−0.0334567	+	0.999440i	$0.510652\pi$
$140$	6.00000	0.507093
$141$	−12.9083	−1.08708
$142$	−4.60555	−0.386489
$143$	4.00000	0.334497
$144$	−1.30278	−0.108565
$145$	−15.4222	−1.28074
$146$	−5.21110	−0.431274
$147$	0.275019	0.0226832
$148$	−0.0916731	−0.00753548
$149$	1.11943	0.0917072	0.0458536	−	0.998948i	$-0.485399\pi$
$149$	1.11943	0.0917072	0.0458536	+	0.998948i	$0.485399\pi$
$150$	0.394449	0.0322066
$151$	18.6056	1.51410	0.757049	−	0.653358i	$-0.226640\pi$
$151$	18.6056	1.51410	0.757049	+	0.653358i	$0.226640\pi$
$152$	0.302776	0.0245583
$153$	−0.908327	−0.0734339
$154$	−2.60555	−0.209961
$155$	10.8167	0.868815
$156$	5.21110	0.417222
$157$	−20.1194	−1.60571	−0.802853	−	0.596178i	$-0.796685\pi$
$157$	−20.1194	−1.60571	−0.802853	+	0.596178i	$0.796685\pi$
$158$	−16.7250	−1.33057
$159$	4.18335	0.331761
$160$	2.30278	0.182050
$161$	6.00000	0.472866
$162$	3.39445	0.266693
$163$	−0.302776	−0.0237152	−0.0118576	−	0.999930i	$-0.503774\pi$
$163$	−0.302776	−0.0237152	−0.0118576	+	0.999930i	$0.503774\pi$
$164$	−3.69722	−0.288705
$165$	−3.00000	−0.233550
$166$	7.81665	0.606690
$167$	18.4222	1.42555	0.712777	−	0.701391i	$-0.247437\pi$
$167$	18.4222	1.42555	0.712777	+	0.701391i	$0.247437\pi$
$168$	−3.39445	−0.261887
$169$	3.00000	0.230769
$170$	1.60555	0.123140
$171$	0.394449	0.0301642
$172$	1.00000	0.0762493
$173$	−7.39445	−0.562190	−0.281095	−	0.959680i	$-0.590698\pi$
$173$	−7.39445	−0.562190	−0.281095	+	0.959680i	$0.590698\pi$
$174$	8.72498	0.661439
$175$	−0.788897	−0.0596350
$176$	−1.00000	−0.0753778
$177$	−12.0000	−0.901975
$178$	−12.0000	−0.899438
$179$	−11.0917	−0.829031	−0.414515	−	0.910042i	$-0.636049\pi$
$179$	−11.0917	−0.829031	−0.414515	+	0.910042i	$0.636049\pi$
$180$	3.00000	0.223607
$181$	−7.21110	−0.535997	−0.267999	−	0.963419i	$-0.586362\pi$
$181$	−7.21110	−0.535997	−0.267999	+	0.963419i	$0.586362\pi$
$182$	−10.4222	−0.772545
$183$	−2.60555	−0.192608
$184$	2.30278	0.169763
$185$	0.211103	0.0155206
$186$	−6.11943	−0.448698
$187$	−0.697224	−0.0509861
$188$	9.90833	0.722639
$189$	−14.6056	−1.06240
$190$	−0.697224	−0.0505820
$191$	10.6056	0.767391	0.383695	−	0.923460i	$-0.374651\pi$
$191$	10.6056	0.767391	0.383695	+	0.923460i	$0.374651\pi$
$192$	−1.30278	−0.0940197
$193$	−6.72498	−0.484075	−0.242037	−	0.970267i	$-0.577816\pi$
$193$	−6.72498	−0.484075	−0.242037	+	0.970267i	$0.577816\pi$
$194$	14.1194	1.01372
$195$	−12.0000	−0.859338
$196$	−0.211103	−0.0150788
$197$	−22.6056	−1.61058	−0.805289	−	0.592882i	$-0.797990\pi$
$197$	−22.6056	−1.61058	−0.805289	+	0.592882i	$0.797990\pi$
$198$	−1.30278	−0.0925842
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	−0.302776	−0.0214095
$201$	19.0278	1.34211
$202$	−10.6056	−0.746204
$203$	−17.4500	−1.22475
$204$	−0.908327	−0.0635956
$205$	8.51388	0.594635
$206$	−19.5139	−1.35960
$207$	3.00000	0.208514
$208$	−4.00000	−0.277350
$209$	0.302776	0.0209434
$210$	7.81665	0.539400
$211$	−21.3028	−1.46654	−0.733272	−	0.679936i	$-0.762008\pi$
$211$	−21.3028	−1.46654	−0.733272	+	0.679936i	$0.762008\pi$
$212$	−3.21110	−0.220539
$213$	−6.00000	−0.411113
$214$	−1.39445	−0.0953226
$215$	−2.30278	−0.157048
$216$	−5.60555	−0.381409
$217$	12.2389	0.830828
$218$	11.8167	0.800325
$219$	−6.78890	−0.458751
$220$	2.30278	0.155253
$221$	−2.78890	−0.187602
$222$	−0.119429	−0.00801558
$223$	−8.60555	−0.576270	−0.288135	−	0.957590i	$-0.593035\pi$
$223$	−8.60555	−0.576270	−0.288135	+	0.957590i	$0.593035\pi$
$224$	2.60555	0.174091
$225$	−0.394449	−0.0262966
$226$	2.78890	0.185515
$227$	−3.69722	−0.245393	−0.122697	−	0.992444i	$-0.539154\pi$
$227$	−3.69722	−0.245393	−0.122697	+	0.992444i	$0.539154\pi$
$228$	0.394449	0.0261230
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	−5.30278	−0.349655
$231$	−3.39445	−0.223338
$232$	−6.69722	−0.439694
$233$	−1.81665	−0.119013	−0.0595065	−	0.998228i	$-0.518953\pi$
$233$	−1.81665	−0.119013	−0.0595065	+	0.998228i	$0.518953\pi$
$234$	−5.21110	−0.340660
$235$	−22.8167	−1.48839
$236$	9.21110	0.599592
$237$	−21.7889	−1.41534
$238$	1.81665	0.117756
$239$	−11.5139	−0.744771	−0.372385	−	0.928078i	$-0.621460\pi$
$239$	−11.5139	−0.744771	−0.372385	+	0.928078i	$0.621460\pi$
$240$	3.00000	0.193649
$241$	3.81665	0.245852	0.122926	−	0.992416i	$-0.460772\pi$
$241$	3.81665	0.245852	0.122926	+	0.992416i	$0.460772\pi$
$242$	−1.00000	−0.0642824
$243$	−12.3944	−0.795104
$244$	2.00000	0.128037
$245$	0.486122	0.0310572
$246$	−4.81665	−0.307099
$247$	1.21110	0.0770606
$248$	4.69722	0.298274
$249$	10.1833	0.645343
$250$	−10.8167	−0.684105
$251$	−10.6056	−0.669416	−0.334708	−	0.942322i	$-0.608638\pi$
$251$	−10.6056	−0.669416	−0.334708	+	0.942322i	$0.608638\pi$
$252$	3.39445	0.213830
$253$	2.30278	0.144774
$254$	11.1194	0.697695
$255$	2.09167	0.130986
$256$	1.00000	0.0625000
$257$	9.21110	0.574573	0.287286	−	0.957845i	$-0.407247\pi$
$257$	9.21110	0.574573	0.287286	+	0.957845i	$0.407247\pi$
$258$	1.30278	0.0811073
$259$	0.238859	0.0148420
$260$	9.21110	0.571248
$261$	−8.72498	−0.540063
$262$	−6.69722	−0.413756
$263$	23.0278	1.41995	0.709976	−	0.704226i	$-0.248706\pi$
$263$	23.0278	1.41995	0.709976	+	0.704226i	$0.248706\pi$
$264$	−1.30278	−0.0801803
$265$	7.39445	0.454237
$266$	−0.788897	−0.0483704
$267$	−15.6333	−0.956743
$268$	−14.6056	−0.892176
$269$	1.39445	0.0850210	0.0425105	−	0.999096i	$-0.486464\pi$
$269$	1.39445	0.0850210	0.0425105	+	0.999096i	$0.486464\pi$
$270$	12.9083	0.785576
$271$	13.0917	0.795263	0.397631	−	0.917545i	$-0.369832\pi$
$271$	13.0917	0.795263	0.397631	+	0.917545i	$0.369832\pi$
$272$	0.697224	0.0422754
$273$	−13.5778	−0.821766
$274$	13.8167	0.834695
$275$	−0.302776	−0.0182581
$276$	3.00000	0.180579
$277$	2.90833	0.174744	0.0873722	−	0.996176i	$-0.472153\pi$
$277$	2.90833	0.174744	0.0873722	+	0.996176i	$0.472153\pi$
$278$	0.788897	0.0473149
$279$	6.11943	0.366361
$280$	−6.00000	−0.358569
$281$	9.90833	0.591081	0.295541	−	0.955330i	$-0.404500\pi$
$281$	9.90833	0.591081	0.295541	+	0.955330i	$0.404500\pi$
$282$	12.9083	0.768680
$283$	23.6333	1.40485	0.702427	−	0.711756i	$-0.252100\pi$
$283$	23.6333	1.40485	0.702427	+	0.711756i	$0.252100\pi$
$284$	4.60555	0.273289
$285$	−0.908327	−0.0538046
$286$	−4.00000	−0.236525
$287$	9.63331	0.568636
$288$	1.30278	0.0767668
$289$	−16.5139	−0.971405
$290$	15.4222	0.905623
$291$	18.3944	1.07830
$292$	5.21110	0.304957
$293$	25.8167	1.50823	0.754113	−	0.656745i	$-0.228067\pi$
$293$	25.8167	1.50823	0.754113	+	0.656745i	$0.228067\pi$
$294$	−0.275019	−0.0160394
$295$	−21.2111	−1.23496
$296$	0.0916731	0.00532839
$297$	−5.60555	−0.325267
$298$	−1.11943	−0.0648468
$299$	9.21110	0.532692
$300$	−0.394449	−0.0227735
$301$	−2.60555	−0.150181
$302$	−18.6056	−1.07063
$303$	−13.8167	−0.793746
$304$	−0.302776	−0.0173654
$305$	−4.60555	−0.263713
$306$	0.908327	0.0519256
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	2.60555	0.148465
$309$	−25.4222	−1.44622
$310$	−10.8167	−0.614345
$311$	−6.42221	−0.364170	−0.182085	−	0.983283i	$-0.558285\pi$
$311$	−6.42221	−0.364170	−0.182085	+	0.983283i	$0.558285\pi$
$312$	−5.21110	−0.295021
$313$	7.02776	0.397232	0.198616	−	0.980077i	$-0.436355\pi$
$313$	7.02776	0.397232	0.198616	+	0.980077i	$0.436355\pi$
$314$	20.1194	1.13541
$315$	−7.81665	−0.440419
$316$	16.7250	0.940854
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	−4.18335	−0.234590
$319$	−6.69722	−0.374973
$320$	−2.30278	−0.128729
$321$	−1.81665	−0.101396
$322$	−6.00000	−0.334367
$323$	−0.211103	−0.0117461
$324$	−3.39445	−0.188580
$325$	−1.21110	−0.0671799
$326$	0.302776	0.0167692
$327$	15.3944	0.851315
$328$	3.69722	0.204145
$329$	−25.8167	−1.42332
$330$	3.00000	0.165145
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−7.81665	−0.428995
$333$	0.119429	0.00654469
$334$	−18.4222	−1.00802
$335$	33.6333	1.83758
$336$	3.39445	0.185182
$337$	25.7250	1.40133	0.700664	−	0.713491i	$-0.252887\pi$
$337$	25.7250	1.40133	0.700664	+	0.713491i	$0.252887\pi$
$338$	−3.00000	−0.163178
$339$	3.63331	0.197334
$340$	−1.60555	−0.0870732
$341$	4.69722	0.254369
$342$	−0.394449	−0.0213293
$343$	18.7889	1.01451
$344$	−1.00000	−0.0539164
$345$	−6.90833	−0.371932
$346$	7.39445	0.397528
$347$	12.9083	0.692955	0.346478	−	0.938058i	$-0.387378\pi$
$347$	12.9083	0.692955	0.346478	+	0.938058i	$0.387378\pi$
$348$	−8.72498	−0.467708
$349$	33.1194	1.77284	0.886421	−	0.462880i	$-0.153184\pi$
$349$	33.1194	1.77284	0.886421	+	0.462880i	$0.153184\pi$
$350$	0.788897	0.0421683
$351$	−22.4222	−1.19681
$352$	1.00000	0.0533002
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	12.0000	0.637793
$355$	−10.6056	−0.562884
$356$	12.0000	0.635999
$357$	2.36669	0.125259
$358$	11.0917	0.586213
$359$	3.48612	0.183990	0.0919952	−	0.995759i	$-0.470676\pi$
$359$	3.48612	0.183990	0.0919952	+	0.995759i	$0.470676\pi$
$360$	−3.00000	−0.158114
$361$	−18.9083	−0.995175
$362$	7.21110	0.379007
$363$	−1.30278	−0.0683780
$364$	10.4222	0.546272
$365$	−12.0000	−0.628109
$366$	2.60555	0.136194
$367$	10.0917	0.526781	0.263391	−	0.964689i	$-0.415159\pi$
$367$	10.0917	0.526781	0.263391	+	0.964689i	$0.415159\pi$
$368$	−2.30278	−0.120040
$369$	4.81665	0.250745
$370$	−0.211103	−0.0109747
$371$	8.36669	0.434377
$372$	6.11943	0.317278
$373$	28.7250	1.48732	0.743662	−	0.668556i	$-0.233087\pi$
$373$	28.7250	1.48732	0.743662	+	0.668556i	$0.233087\pi$
$374$	0.697224	0.0360526
$375$	−14.0917	−0.727691
$376$	−9.90833	−0.510983
$377$	−26.7889	−1.37970
$378$	14.6056	0.751228
$379$	−2.18335	−0.112151	−0.0560755	−	0.998427i	$-0.517859\pi$
$379$	−2.18335	−0.112151	−0.0560755	+	0.998427i	$0.517859\pi$
$380$	0.697224	0.0357669
$381$	14.4861	0.742147
$382$	−10.6056	−0.542627
$383$	−7.39445	−0.377839	−0.188919	−	0.981993i	$-0.560498\pi$
$383$	−7.39445	−0.377839	−0.188919	+	0.981993i	$0.560498\pi$
$384$	1.30278	0.0664820
$385$	−6.00000	−0.305788
$386$	6.72498	0.342293
$387$	−1.30278	−0.0662238
$388$	−14.1194	−0.716805
$389$	−15.2111	−0.771234	−0.385617	−	0.922659i	$-0.626011\pi$
$389$	−15.2111	−0.771234	−0.385617	+	0.922659i	$0.626011\pi$
$390$	12.0000	0.607644
$391$	−1.60555	−0.0811962
$392$	0.211103	0.0106623
$393$	−8.72498	−0.440117
$394$	22.6056	1.13885
$395$	−38.5139	−1.93784
$396$	1.30278	0.0654669
$397$	−33.0278	−1.65762	−0.828808	−	0.559533i	$-0.810980\pi$
$397$	−33.0278	−1.65762	−0.828808	+	0.559533i	$0.810980\pi$
$398$	−14.0000	−0.701757
$399$	−1.02776	−0.0514522
$400$	0.302776	0.0151388
$401$	14.0917	0.703705	0.351852	−	0.936056i	$-0.385552\pi$
$401$	14.0917	0.703705	0.351852	+	0.936056i	$0.385552\pi$
$402$	−19.0278	−0.949018
$403$	18.7889	0.935942
$404$	10.6056	0.527646
$405$	7.81665	0.388413
$406$	17.4500	0.866027
$407$	0.0916731	0.00454407
$408$	0.908327	0.0449689
$409$	9.81665	0.485402	0.242701	−	0.970101i	$-0.421967\pi$
$409$	9.81665	0.485402	0.242701	+	0.970101i	$0.421967\pi$
$410$	−8.51388	−0.420470
$411$	18.0000	0.887875
$412$	19.5139	0.961380
$413$	−24.0000	−1.18096
$414$	−3.00000	−0.147442
$415$	18.0000	0.883585
$416$	4.00000	0.196116
$417$	1.02776	0.0503294
$418$	−0.302776	−0.0148092
$419$	14.7889	0.722485	0.361242	−	0.932472i	$-0.382353\pi$
$419$	14.7889	0.722485	0.361242	+	0.932472i	$0.382353\pi$
$420$	−7.81665	−0.381414
$421$	28.7250	1.39997	0.699985	−	0.714158i	$-0.253190\pi$
$421$	28.7250	1.39997	0.699985	+	0.714158i	$0.253190\pi$
$422$	21.3028	1.03700
$423$	−12.9083	−0.627624
$424$	3.21110	0.155945
$425$	0.211103	0.0102400
$426$	6.00000	0.290701
$427$	−5.21110	−0.252183
$428$	1.39445	0.0674032
$429$	−5.21110	−0.251594
$430$	2.30278	0.111050
$431$	2.09167	0.100752	0.0503762	−	0.998730i	$-0.483958\pi$
$431$	2.09167	0.100752	0.0503762	+	0.998730i	$0.483958\pi$
$432$	5.60555	0.269697
$433$	−11.8167	−0.567872	−0.283936	−	0.958843i	$-0.591640\pi$
$433$	−11.8167	−0.567872	−0.283936	+	0.958843i	$0.591640\pi$
$434$	−12.2389	−0.587484
$435$	20.0917	0.963322
$436$	−11.8167	−0.565915
$437$	0.697224	0.0333528
$438$	6.78890	0.324386
$439$	40.5139	1.93362	0.966811	−	0.255493i	$-0.0822377\pi$
$439$	40.5139	1.93362	0.966811	+	0.255493i	$0.0822377\pi$
$440$	−2.30278	−0.109781
$441$	0.275019	0.0130962
$442$	2.78890	0.132654
$443$	33.6333	1.59797	0.798983	−	0.601353i	$-0.205372\pi$
$443$	33.6333	1.59797	0.798983	+	0.601353i	$0.205372\pi$
$444$	0.119429	0.00566787
$445$	−27.6333	−1.30994
$446$	8.60555	0.407485
$447$	−1.45837	−0.0689783
$448$	−2.60555	−0.123101
$449$	3.63331	0.171466	0.0857332	−	0.996318i	$-0.472677\pi$
$449$	3.63331	0.171466	0.0857332	+	0.996318i	$0.472677\pi$
$450$	0.394449	0.0185945
$451$	3.69722	0.174095
$452$	−2.78890	−0.131179
$453$	−24.2389	−1.13884
$454$	3.69722	0.173519
$455$	−24.0000	−1.12514
$456$	−0.394449	−0.0184718
$457$	20.8444	0.975060	0.487530	−	0.873106i	$-0.337898\pi$
$457$	20.8444	0.975060	0.487530	+	0.873106i	$0.337898\pi$
$458$	22.0000	1.02799
$459$	3.90833	0.182425
$460$	5.30278	0.247243
$461$	12.0000	0.558896	0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000	0.558896	0.279448	+	0.960161i	$0.409849\pi$
$462$	3.39445	0.157924
$463$	−3.02776	−0.140712	−0.0703559	−	0.997522i	$-0.522413\pi$
$463$	−3.02776	−0.140712	−0.0703559	+	0.997522i	$0.522413\pi$
$464$	6.69722	0.310911
$465$	−14.0917	−0.653486
$466$	1.81665	0.0841549
$467$	8.09167	0.374438	0.187219	−	0.982318i	$-0.440053\pi$
$467$	8.09167	0.374438	0.187219	+	0.982318i	$0.440053\pi$
$468$	5.21110	0.240883
$469$	38.0555	1.75724
$470$	22.8167	1.05245
$471$	26.2111	1.20774
$472$	−9.21110	−0.423975
$473$	−1.00000	−0.0459800
$474$	21.7889	1.00080
$475$	−0.0916731	−0.00420625
$476$	−1.81665	−0.0832662
$477$	4.18335	0.191542
$478$	11.5139	0.526633
$479$	−1.33053	−0.0607936	−0.0303968	−	0.999538i	$-0.509677\pi$
$479$	−1.33053	−0.0607936	−0.0303968	+	0.999538i	$0.509677\pi$
$480$	−3.00000	−0.136931
$481$	0.366692	0.0167197
$482$	−3.81665	−0.173844
$483$	−7.81665	−0.355670
$484$	1.00000	0.0454545
$485$	32.5139	1.47638
$486$	12.3944	0.562224
$487$	26.9083	1.21933	0.609666	−	0.792658i	$-0.291303\pi$
$487$	26.9083	1.21933	0.609666	+	0.792658i	$0.291303\pi$
$488$	−2.00000	−0.0905357
$489$	0.394449	0.0178376
$490$	−0.486122	−0.0219607
$491$	12.9083	0.582545	0.291272	−	0.956640i	$-0.405921\pi$
$491$	12.9083	0.582545	0.291272	+	0.956640i	$0.405921\pi$
$492$	4.81665	0.217152
$493$	4.66947	0.210302
$494$	−1.21110	−0.0544901
$495$	−3.00000	−0.134840
$496$	−4.69722	−0.210912
$497$	−12.0000	−0.538274
$498$	−10.1833	−0.456327
$499$	−7.90833	−0.354025	−0.177013	−	0.984209i	$-0.556643\pi$
$499$	−7.90833	−0.354025	−0.177013	+	0.984209i	$0.556643\pi$
$500$	10.8167	0.483735
$501$	−24.0000	−1.07224
$502$	10.6056	0.473349
$503$	−4.60555	−0.205351	−0.102676	−	0.994715i	$-0.532740\pi$
$503$	−4.60555	−0.205351	−0.102676	+	0.994715i	$0.532740\pi$
$504$	−3.39445	−0.151201
$505$	−24.4222	−1.08677
$506$	−2.30278	−0.102371
$507$	−3.90833	−0.173575
$508$	−11.1194	−0.493345
$509$	3.21110	0.142330	0.0711648	−	0.997465i	$-0.477328\pi$
$509$	3.21110	0.142330	0.0711648	+	0.997465i	$0.477328\pi$
$510$	−2.09167	−0.0926208
$511$	−13.5778	−0.600646
$512$	−1.00000	−0.0441942
$513$	−1.69722	−0.0749343
$514$	−9.21110	−0.406284
$515$	−44.9361	−1.98012
$516$	−1.30278	−0.0573515
$517$	−9.90833	−0.435768
$518$	−0.238859	−0.0104949
$519$	9.63331	0.422855
$520$	−9.21110	−0.403934
$521$	27.6333	1.21064	0.605319	−	0.795983i	$-0.293046\pi$
$521$	27.6333	1.21064	0.605319	+	0.795983i	$0.293046\pi$
$522$	8.72498	0.381882
$523$	27.5416	1.20431	0.602156	−	0.798379i	$-0.294309\pi$
$523$	27.5416	1.20431	0.602156	+	0.798379i	$0.294309\pi$
$524$	6.69722	0.292570
$525$	1.02776	0.0448550
$526$	−23.0278	−1.00406
$527$	−3.27502	−0.142662
$528$	1.30278	0.0566960
$529$	−17.6972	−0.769445
$530$	−7.39445	−0.321194
$531$	−12.0000	−0.520756
$532$	0.788897	0.0342030
$533$	14.7889	0.640578
$534$	15.6333	0.676519
$535$	−3.21110	−0.138828
$536$	14.6056	0.630864
$537$	14.4500	0.623562
$538$	−1.39445	−0.0601190
$539$	0.211103	0.00909283
$540$	−12.9083	−0.555486
$541$	−8.60555	−0.369982	−0.184991	−	0.982740i	$-0.559226\pi$
$541$	−8.60555	−0.369982	−0.184991	+	0.982740i	$0.559226\pi$
$542$	−13.0917	−0.562336
$543$	9.39445	0.403154
$544$	−0.697224	−0.0298932
$545$	27.2111	1.16560
$546$	13.5778	0.581076
$547$	−2.60555	−0.111405	−0.0557027	−	0.998447i	$-0.517740\pi$
$547$	−2.60555	−0.111405	−0.0557027	+	0.998447i	$0.517740\pi$
$548$	−13.8167	−0.590218
$549$	−2.60555	−0.111202
$550$	0.302776	0.0129104
$551$	−2.02776	−0.0863853
$552$	−3.00000	−0.127688
$553$	−43.5778	−1.85312
$554$	−2.90833	−0.123563
$555$	−0.275019	−0.0116739
$556$	−0.788897	−0.0334567
$557$	−16.6056	−0.703600	−0.351800	−	0.936075i	$-0.614430\pi$
$557$	−16.6056	−0.703600	−0.351800	+	0.936075i	$0.614430\pi$
$558$	−6.11943	−0.259056
$559$	−4.00000	−0.169182
$560$	6.00000	0.253546
$561$	0.908327	0.0383496
$562$	−9.90833	−0.417958
$563$	22.1833	0.934917	0.467458	−	0.884015i	$-0.345170\pi$
$563$	22.1833	0.934917	0.467458	+	0.884015i	$0.345170\pi$
$564$	−12.9083	−0.543539
$565$	6.42221	0.270184
$566$	−23.6333	−0.993382
$567$	8.84441	0.371430
$568$	−4.60555	−0.193245
$569$	24.4222	1.02383	0.511916	−	0.859035i	$-0.328936\pi$
$569$	24.4222	1.02383	0.511916	+	0.859035i	$0.328936\pi$
$570$	0.908327	0.0380456
$571$	−31.3583	−1.31230	−0.656152	−	0.754629i	$-0.727817\pi$
$571$	−31.3583	−1.31230	−0.656152	+	0.754629i	$0.727817\pi$
$572$	4.00000	0.167248
$573$	−13.8167	−0.577199
$574$	−9.63331	−0.402086
$575$	−0.697224	−0.0290763
$576$	−1.30278	−0.0542823
$577$	−30.2389	−1.25886	−0.629430	−	0.777057i	$-0.716712\pi$
$577$	−30.2389	−1.25886	−0.629430	+	0.777057i	$0.716712\pi$
$578$	16.5139	0.686887
$579$	8.76114	0.364101
$580$	−15.4222	−0.640372
$581$	20.3667	0.844953
$582$	−18.3944	−0.762474
$583$	3.21110	0.132990
$584$	−5.21110	−0.215637
$585$	−12.0000	−0.496139
$586$	−25.8167	−1.06648
$587$	−30.4222	−1.25566	−0.627829	−	0.778351i	$-0.716056\pi$
$587$	−30.4222	−1.25566	−0.627829	+	0.778351i	$0.716056\pi$
$588$	0.275019	0.0113416
$589$	1.42221	0.0586009
$590$	21.2111	0.873247
$591$	29.4500	1.21141
$592$	−0.0916731	−0.00376774
$593$	12.0000	0.492781	0.246390	−	0.969171i	$-0.420755\pi$
$593$	12.0000	0.492781	0.246390	+	0.969171i	$0.420755\pi$
$594$	5.60555	0.229999
$595$	4.18335	0.171500
$596$	1.11943	0.0458536
$597$	−18.2389	−0.746467
$598$	−9.21110	−0.376670
$599$	−16.3305	−0.667247	−0.333624	−	0.942706i	$-0.608271\pi$
$599$	−16.3305	−0.667247	−0.333624	+	0.942706i	$0.608271\pi$
$600$	0.394449	0.0161033
$601$	−4.42221	−0.180386	−0.0901928	−	0.995924i	$-0.528748\pi$
$601$	−4.42221	−0.180386	−0.0901928	+	0.995924i	$0.528748\pi$
$602$	2.60555	0.106194
$603$	19.0278	0.774870
$604$	18.6056	0.757049
$605$	−2.30278	−0.0936211
$606$	13.8167	0.561263
$607$	10.7889	0.437908	0.218954	−	0.975735i	$-0.429736\pi$
$607$	10.7889	0.437908	0.218954	+	0.975735i	$0.429736\pi$
$608$	0.302776	0.0122792
$609$	22.7334	0.921203
$610$	4.60555	0.186473
$611$	−39.6333	−1.60339
$612$	−0.908327	−0.0367169
$613$	−18.2389	−0.736661	−0.368330	−	0.929695i	$-0.620070\pi$
$613$	−18.2389	−0.736661	−0.368330	+	0.929695i	$0.620070\pi$
$614$	10.0000	0.403567
$615$	−11.0917	−0.447259
$616$	−2.60555	−0.104981
$617$	−20.3028	−0.817359	−0.408679	−	0.912678i	$-0.634011\pi$
$617$	−20.3028	−0.817359	−0.408679	+	0.912678i	$0.634011\pi$
$618$	25.4222	1.02263
$619$	35.6333	1.43222	0.716112	−	0.697986i	$-0.245920\pi$
$619$	35.6333	1.43222	0.716112	+	0.697986i	$0.245920\pi$
$620$	10.8167	0.434407
$621$	−12.9083	−0.517993
$622$	6.42221	0.257507
$623$	−31.2666	−1.25267
$624$	5.21110	0.208611
$625$	−26.4222	−1.05689
$626$	−7.02776	−0.280886
$627$	−0.394449	−0.0157528
$628$	−20.1194	−0.802853
$629$	−0.0639167	−0.00254853
$630$	7.81665	0.311423
$631$	40.2389	1.60188	0.800942	−	0.598742i	$-0.204333\pi$
$631$	40.2389	1.60188	0.800942	+	0.598742i	$0.204333\pi$
$632$	−16.7250	−0.665284
$633$	27.7527	1.10307
$634$	0	0
$635$	25.6056	1.01613
$636$	4.18335	0.165880
$637$	0.844410	0.0334568
$638$	6.69722	0.265146
$639$	−6.00000	−0.237356
$640$	2.30278	0.0910252
$641$	11.5778	0.457295	0.228648	−	0.973509i	$-0.426570\pi$
$641$	11.5778	0.457295	0.228648	+	0.973509i	$0.426570\pi$
$642$	1.81665	0.0716976
$643$	30.0555	1.18527	0.592637	−	0.805470i	$-0.298087\pi$
$643$	30.0555	1.18527	0.592637	+	0.805470i	$0.298087\pi$
$644$	6.00000	0.236433
$645$	3.00000	0.118125
$646$	0.211103	0.00830572
$647$	9.63331	0.378724	0.189362	−	0.981907i	$-0.439358\pi$
$647$	9.63331	0.378724	0.189362	+	0.981907i	$0.439358\pi$
$648$	3.39445	0.133347
$649$	−9.21110	−0.361567
$650$	1.21110	0.0475034
$651$	−15.9445	−0.624914
$652$	−0.302776	−0.0118576
$653$	14.3028	0.559711	0.279855	−	0.960042i	$-0.409713\pi$
$653$	14.3028	0.559711	0.279855	+	0.960042i	$0.409713\pi$
$654$	−15.3944	−0.601971
$655$	−15.4222	−0.602595
$656$	−3.69722	−0.144352
$657$	−6.78890	−0.264860
$658$	25.8167	1.00644
$659$	−22.0555	−0.859161	−0.429580	−	0.903029i	$-0.641339\pi$
$659$	−22.0555	−0.859161	−0.429580	+	0.903029i	$0.641339\pi$
$660$	−3.00000	−0.116775
$661$	−13.2111	−0.513852	−0.256926	−	0.966431i	$-0.582710\pi$
$661$	−13.2111	−0.513852	−0.256926	+	0.966431i	$0.582710\pi$
$662$	4.00000	0.155464
$663$	3.63331	0.141106
$664$	7.81665	0.303345
$665$	−1.81665	−0.0704468
$666$	−0.119429	−0.00462780
$667$	−15.4222	−0.597150
$668$	18.4222	0.712777
$669$	11.2111	0.433446
$670$	−33.6333	−1.29937
$671$	−2.00000	−0.0772091
$672$	−3.39445	−0.130944
$673$	30.6056	1.17976	0.589879	−	0.807492i	$-0.299176\pi$
$673$	30.6056	1.17976	0.589879	+	0.807492i	$0.299176\pi$
$674$	−25.7250	−0.990889
$675$	1.69722	0.0653262
$676$	3.00000	0.115385
$677$	−18.9083	−0.726706	−0.363353	−	0.931652i	$-0.618368\pi$
$677$	−18.9083	−0.726706	−0.363353	+	0.931652i	$0.618368\pi$
$678$	−3.63331	−0.139536
$679$	36.7889	1.41183
$680$	1.60555	0.0615701
$681$	4.81665	0.184575
$682$	−4.69722	−0.179866
$683$	−10.1833	−0.389655	−0.194827	−	0.980838i	$-0.562415\pi$
$683$	−10.1833	−0.389655	−0.194827	+	0.980838i	$0.562415\pi$
$684$	0.394449	0.0150821
$685$	31.8167	1.21565
$686$	−18.7889	−0.717363
$687$	28.6611	1.09349
$688$	1.00000	0.0381246
$689$	12.8444	0.489333
$690$	6.90833	0.262996
$691$	−1.21110	−0.0460725	−0.0230363	−	0.999735i	$-0.507333\pi$
$691$	−1.21110	−0.0460725	−0.0230363	+	0.999735i	$0.507333\pi$
$692$	−7.39445	−0.281095
$693$	−3.39445	−0.128944
$694$	−12.9083	−0.489993
$695$	1.81665	0.0689096
$696$	8.72498	0.330720
$697$	−2.57779	−0.0976409
$698$	−33.1194	−1.25359
$699$	2.36669	0.0895165
$700$	−0.788897	−0.0298175
$701$	38.2389	1.44426	0.722131	−	0.691756i	$-0.243163\pi$
$701$	38.2389	1.44426	0.722131	+	0.691756i	$0.243163\pi$
$702$	22.4222	0.846272
$703$	0.0277564	0.00104685
$704$	−1.00000	−0.0376889
$705$	29.7250	1.11951
$706$	6.00000	0.225813
$707$	−27.6333	−1.03926
$708$	−12.0000	−0.450988
$709$	32.4222	1.21764	0.608821	−	0.793308i	$-0.291643\pi$
$709$	32.4222	1.21764	0.608821	+	0.793308i	$0.291643\pi$
$710$	10.6056	0.398019
$711$	−21.7889	−0.817147
$712$	−12.0000	−0.449719
$713$	10.8167	0.405087
$714$	−2.36669	−0.0885712
$715$	−9.21110	−0.344476
$716$	−11.0917	−0.414515
$717$	15.0000	0.560185
$718$	−3.48612	−0.130101
$719$	11.3028	0.421522	0.210761	−	0.977538i	$-0.432406\pi$
$719$	11.3028	0.421522	0.210761	+	0.977538i	$0.432406\pi$
$720$	3.00000	0.111803
$721$	−50.8444	−1.89354
$722$	18.9083	0.703695
$723$	−4.97224	−0.184920
$724$	−7.21110	−0.267999
$725$	2.02776	0.0753090
$726$	1.30278	0.0483505
$727$	−45.0278	−1.66999	−0.834994	−	0.550260i	$-0.814529\pi$
$727$	−45.0278	−1.66999	−0.834994	+	0.550260i	$0.814529\pi$
$728$	−10.4222	−0.386273
$729$	26.3305	0.975205
$730$	12.0000	0.444140
$731$	0.697224	0.0257878
$732$	−2.60555	−0.0963039
$733$	−9.30278	−0.343606	−0.171803	−	0.985131i	$-0.554959\pi$
$733$	−9.30278	−0.343606	−0.171803	+	0.985131i	$0.554959\pi$
$734$	−10.0917	−0.372490
$735$	−0.633308	−0.0233599
$736$	2.30278	0.0848814
$737$	14.6056	0.538002
$738$	−4.81665	−0.177303
$739$	−30.5139	−1.12247	−0.561236	−	0.827656i	$-0.689674\pi$
$739$	−30.5139	−1.12247	−0.561236	+	0.827656i	$0.689674\pi$
$740$	0.211103	0.00776028
$741$	−1.57779	−0.0579617
$742$	−8.36669	−0.307151
$743$	−6.00000	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$744$	−6.11943	−0.224349
$745$	−2.57779	−0.0944431
$746$	−28.7250	−1.05170
$747$	10.1833	0.372589
$748$	−0.697224	−0.0254930
$749$	−3.63331	−0.132758
$750$	14.0917	0.514555
$751$	21.3944	0.780695	0.390347	−	0.920668i	$-0.372355\pi$
$751$	21.3944	0.780695	0.390347	+	0.920668i	$0.372355\pi$
$752$	9.90833	0.361320
$753$	13.8167	0.503507
$754$	26.7889	0.975594
$755$	−42.8444	−1.55927
$756$	−14.6056	−0.531199
$757$	−3.72498	−0.135387	−0.0676934	−	0.997706i	$-0.521564\pi$
$757$	−3.72498	−0.135387	−0.0676934	+	0.997706i	$0.521564\pi$
$758$	2.18335	0.0793027
$759$	−3.00000	−0.108893
$760$	−0.697224	−0.0252910
$761$	−1.81665	−0.0658536	−0.0329268	−	0.999458i	$-0.510483\pi$
$761$	−1.81665	−0.0658536	−0.0329268	+	0.999458i	$0.510483\pi$
$762$	−14.4861	−0.524777
$763$	30.7889	1.11463
$764$	10.6056	0.383695
$765$	2.09167	0.0756246
$766$	7.39445	0.267172
$767$	−36.8444	−1.33037
$768$	−1.30278	−0.0470099
$769$	−10.2750	−0.370527	−0.185263	−	0.982689i	$-0.559314\pi$
$769$	−10.2750	−0.370527	−0.185263	+	0.982689i	$0.559314\pi$
$770$	6.00000	0.216225
$771$	−12.0000	−0.432169
$772$	−6.72498	−0.242037
$773$	39.3583	1.41562	0.707810	−	0.706403i	$-0.249683\pi$
$773$	39.3583	1.41562	0.707810	+	0.706403i	$0.249683\pi$
$774$	1.30278	0.0468273
$775$	−1.42221	−0.0510871
$776$	14.1194	0.506858
$777$	−0.311180	−0.0111635
$778$	15.2111	0.545344
$779$	1.11943	0.0401077
$780$	−12.0000	−0.429669
$781$	−4.60555	−0.164800
$782$	1.60555	0.0574144
$783$	37.5416	1.34163
$784$	−0.211103	−0.00753938
$785$	46.3305	1.65361
$786$	8.72498	0.311210
$787$	9.81665	0.349926	0.174963	−	0.984575i	$-0.444019\pi$
$787$	9.81665	0.349926	0.174963	+	0.984575i	$0.444019\pi$
$788$	−22.6056	−0.805289
$789$	−30.0000	−1.06803
$790$	38.5139	1.37026
$791$	7.26662	0.258371
$792$	−1.30278	−0.0462921
$793$	−8.00000	−0.284088
$794$	33.0278	1.17211
$795$	−9.63331	−0.341658
$796$	14.0000	0.496217
$797$	3.63331	0.128698	0.0643492	−	0.997927i	$-0.479503\pi$
$797$	3.63331	0.128698	0.0643492	+	0.997927i	$0.479503\pi$
$798$	1.02776	0.0363822
$799$	6.90833	0.244399
$800$	−0.302776	−0.0107047
$801$	−15.6333	−0.552376
$802$	−14.0917	−0.497594
$803$	−5.21110	−0.183896
$804$	19.0278	0.671057
$805$	−13.8167	−0.486973
$806$	−18.7889	−0.661811
$807$	−1.81665	−0.0639492
$808$	−10.6056	−0.373102
$809$	−2.09167	−0.0735393	−0.0367697	−	0.999324i	$-0.511707\pi$
$809$	−2.09167	−0.0735393	−0.0367697	+	0.999324i	$0.511707\pi$
$810$	−7.81665	−0.274649
$811$	10.7250	0.376605	0.188303	−	0.982111i	$-0.439701\pi$
$811$	10.7250	0.376605	0.188303	+	0.982111i	$0.439701\pi$
$812$	−17.4500	−0.612374
$813$	−17.0555	−0.598163
$814$	−0.0916731	−0.00321314
$815$	0.697224	0.0244227
$816$	−0.908327	−0.0317978
$817$	−0.302776	−0.0105928
$818$	−9.81665	−0.343231
$819$	−13.5778	−0.474447
$820$	8.51388	0.297318
$821$	−29.4500	−1.02781	−0.513905	−	0.857847i	$-0.671802\pi$
$821$	−29.4500	−1.02781	−0.513905	+	0.857847i	$0.671802\pi$
$822$	−18.0000	−0.627822
$823$	−22.4222	−0.781589	−0.390794	−	0.920478i	$-0.627800\pi$
$823$	−22.4222	−0.781589	−0.390794	+	0.920478i	$0.627800\pi$
$824$	−19.5139	−0.679798
$825$	0.394449	0.0137329
$826$	24.0000	0.835067
$827$	36.4222	1.26652	0.633262	−	0.773937i	$-0.281716\pi$
$827$	36.4222	1.26652	0.633262	+	0.773937i	$0.281716\pi$
$828$	3.00000	0.104257
$829$	−35.5416	−1.23441	−0.617206	−	0.786802i	$-0.711735\pi$
$829$	−35.5416	−1.23441	−0.617206	+	0.786802i	$0.711735\pi$
$830$	−18.0000	−0.624789
$831$	−3.78890	−0.131435
$832$	−4.00000	−0.138675
$833$	−0.147186	−0.00509969
$834$	−1.02776	−0.0355883
$835$	−42.4222	−1.46808
$836$	0.302776	0.0104717
$837$	−26.3305	−0.910116
$838$	−14.7889	−0.510874
$839$	1.39445	0.0481417	0.0240709	−	0.999710i	$-0.492337\pi$
$839$	1.39445	0.0481417	0.0240709	+	0.999710i	$0.492337\pi$
$840$	7.81665	0.269700
$841$	15.8528	0.546649
$842$	−28.7250	−0.989928
$843$	−12.9083	−0.444586
$844$	−21.3028	−0.733272
$845$	−6.90833	−0.237654
$846$	12.9083	0.443797
$847$	−2.60555	−0.0895278
$848$	−3.21110	−0.110270
$849$	−30.7889	−1.05667
$850$	−0.211103	−0.00724076
$851$	0.211103	0.00723650
$852$	−6.00000	−0.205557
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	5.21110	0.178320
$855$	−0.908327	−0.0310641
$856$	−1.39445	−0.0476613
$857$	−11.0917	−0.378884	−0.189442	−	0.981892i	$-0.560668\pi$
$857$	−11.0917	−0.378884	−0.189442	+	0.981892i	$0.560668\pi$
$858$	5.21110	0.177904
$859$	16.3028	0.556244	0.278122	−	0.960546i	$-0.410288\pi$
$859$	16.3028	0.556244	0.278122	+	0.960546i	$0.410288\pi$
$860$	−2.30278	−0.0785240
$861$	−12.5500	−0.427704
$862$	−2.09167	−0.0712427
$863$	−52.4777	−1.78636	−0.893181	−	0.449697i	$-0.851532\pi$
$863$	−52.4777	−1.78636	−0.893181	+	0.449697i	$0.851532\pi$
$864$	−5.60555	−0.190705
$865$	17.0278	0.578961
$866$	11.8167	0.401546
$867$	21.5139	0.730650
$868$	12.2389	0.415414
$869$	−16.7250	−0.567356
$870$	−20.0917	−0.681172
$871$	58.4222	1.97956
$872$	11.8167	0.400162
$873$	18.3944	0.622558
$874$	−0.697224	−0.0235840
$875$	−28.1833	−0.952771
$876$	−6.78890	−0.229376
$877$	56.4222	1.90524	0.952621	−	0.304159i	$-0.0983754\pi$
$877$	56.4222	1.90524	0.952621	+	0.304159i	$0.0983754\pi$
$878$	−40.5139	−1.36728
$879$	−33.6333	−1.13442
$880$	2.30278	0.0776266
$881$	15.4861	0.521741	0.260870	−	0.965374i	$-0.415990\pi$
$881$	15.4861	0.521741	0.260870	+	0.965374i	$0.415990\pi$
$882$	−0.275019	−0.00926038
$883$	−45.4500	−1.52951	−0.764756	−	0.644319i	$-0.777141\pi$
$883$	−45.4500	−1.52951	−0.764756	+	0.644319i	$0.777141\pi$
$884$	−2.78890	−0.0938008
$885$	27.6333	0.928883
$886$	−33.6333	−1.12993
$887$	−4.60555	−0.154639	−0.0773196	−	0.997006i	$-0.524636\pi$
$887$	−4.60555	−0.154639	−0.0773196	+	0.997006i	$0.524636\pi$
$888$	−0.119429	−0.00400779
$889$	28.9722	0.971698
$890$	27.6333	0.926271
$891$	3.39445	0.113718
$892$	−8.60555	−0.288135
$893$	−3.00000	−0.100391
$894$	1.45837	0.0487750
$895$	25.5416	0.853763
$896$	2.60555	0.0870454
$897$	−12.0000	−0.400668
$898$	−3.63331	−0.121245
$899$	−31.4584	−1.04920
$900$	−0.394449	−0.0131483
$901$	−2.23886	−0.0745872
$902$	−3.69722	−0.123104
$903$	3.39445	0.112960
$904$	2.78890	0.0927573
$905$	16.6056	0.551987
$906$	24.2389	0.805282
$907$	12.0555	0.400297	0.200148	−	0.979766i	$-0.435858\pi$
$907$	12.0555	0.400297	0.200148	+	0.979766i	$0.435858\pi$
$908$	−3.69722	−0.122697
$909$	−13.8167	−0.458269
$910$	24.0000	0.795592
$911$	−35.0278	−1.16052	−0.580261	−	0.814431i	$-0.697049\pi$
$911$	−35.0278	−1.16052	−0.580261	+	0.814431i	$0.697049\pi$
$912$	0.394449	0.0130615
$913$	7.81665	0.258693
$914$	−20.8444	−0.689472
$915$	6.00000	0.198354
$916$	−22.0000	−0.726900
$917$	−17.4500	−0.576248
$918$	−3.90833	−0.128994
$919$	−8.33053	−0.274799	−0.137399	−	0.990516i	$-0.543874\pi$
$919$	−8.33053	−0.274799	−0.137399	+	0.990516i	$0.543874\pi$
$920$	−5.30278	−0.174827
$921$	13.0278	0.429279
$922$	−12.0000	−0.395199
$923$	−18.4222	−0.606374
$924$	−3.39445	−0.111669
$925$	−0.0277564	−0.000912624 0
$926$	3.02776	0.0994982
$927$	−25.4222	−0.834975
$928$	−6.69722	−0.219847
$929$	24.0000	0.787414	0.393707	−	0.919236i	$-0.371192\pi$
$929$	24.0000	0.787414	0.393707	+	0.919236i	$0.371192\pi$
$930$	14.0917	0.462084
$931$	0.0639167	0.00209479
$932$	−1.81665	−0.0595065
$933$	8.36669	0.273913
$934$	−8.09167	−0.264768
$935$	1.60555	0.0525071
$936$	−5.21110	−0.170330
$937$	42.0555	1.37389	0.686947	−	0.726708i	$-0.258951\pi$
$937$	42.0555	1.37389	0.686947	+	0.726708i	$0.258951\pi$
$938$	−38.0555	−1.24256
$939$	−9.15559	−0.298781
$940$	−22.8167	−0.744197
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−26.2111	−0.854004
$943$	8.51388	0.277250
$944$	9.21110	0.299796
$945$	33.6333	1.09409
$946$	1.00000	0.0325128
$947$	29.4500	0.956995	0.478498	−	0.878089i	$-0.341182\pi$
$947$	29.4500	0.956995	0.478498	+	0.878089i	$0.341182\pi$
$948$	−21.7889	−0.707670
$949$	−20.8444	−0.676638
$950$	0.0916731	0.00297427
$951$	0	0
$952$	1.81665	0.0588781
$953$	−9.63331	−0.312053	−0.156027	−	0.987753i	$-0.549869\pi$
$953$	−9.63331	−0.312053	−0.156027	+	0.987753i	$0.549869\pi$
$954$	−4.18335	−0.135441
$955$	−24.4222	−0.790284
$956$	−11.5139	−0.372385
$957$	8.72498	0.282039
$958$	1.33053	0.0429875
$959$	36.0000	1.16250
$960$	3.00000	0.0968246
$961$	−8.93608	−0.288261
$962$	−0.366692	−0.0118226
$963$	−1.81665	−0.0585409
$964$	3.81665	0.122926
$965$	15.4861	0.498516
$966$	7.81665	0.251497
$967$	15.8806	0.510685	0.255342	−	0.966851i	$-0.417812\pi$
$967$	15.8806	0.510685	0.255342	+	0.966851i	$0.417812\pi$
$968$	−1.00000	−0.0321412
$969$	0.275019	0.00883489
$970$	−32.5139	−1.04396
$971$	−39.6333	−1.27189	−0.635947	−	0.771733i	$-0.719390\pi$
$971$	−39.6333	−1.27189	−0.635947	+	0.771733i	$0.719390\pi$
$972$	−12.3944	−0.397552
$973$	2.05551	0.0658967
$974$	−26.9083	−0.862198
$975$	1.57779	0.0505299
$976$	2.00000	0.0640184
$977$	−38.0917	−1.21866	−0.609330	−	0.792917i	$-0.708562\pi$
$977$	−38.0917	−1.21866	−0.609330	+	0.792917i	$0.708562\pi$
$978$	−0.394449	−0.0126131
$979$	−12.0000	−0.383522
$980$	0.486122	0.0155286
$981$	15.3944	0.491507
$982$	−12.9083	−0.411921
$983$	−38.6611	−1.23310	−0.616548	−	0.787317i	$-0.711469\pi$
$983$	−38.6611	−1.23310	−0.616548	+	0.787317i	$0.711469\pi$
$984$	−4.81665	−0.153549
$985$	52.0555	1.65863
$986$	−4.66947	−0.148706
$987$	33.6333	1.07056
$988$	1.21110	0.0385303
$989$	−2.30278	−0.0732240
$990$	3.00000	0.0953463
$991$	16.7889	0.533317	0.266658	−	0.963791i	$-0.414080\pi$
$991$	16.7889	0.533317	0.266658	+	0.963791i	$0.414080\pi$
$992$	4.69722	0.149137
$993$	5.21110	0.165369
$994$	12.0000	0.380617
$995$	−32.2389	−1.02204
$996$	10.1833	0.322672
$997$	−45.3028	−1.43475	−0.717377	−	0.696686i	$-0.754657\pi$
$997$	−45.3028	−1.43475	−0.717377	+	0.696686i	$0.754657\pi$
$998$	7.90833	0.250334
$999$	−0.513878	−0.0162584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.a.e.1.1	✓	2
3.2	odd	2		8514.2.a.r.1.2		2
4.3	odd	2		7568.2.a.q.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.a.e.1.1	✓	2	1.1	even	1	trivial
7568.2.a.q.1.2		2	4.3	odd	2
8514.2.a.r.1.2		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -2.30278 q^{5} +1.30278 q^{6} -2.60555 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -2.30278 q^{5} +1.30278 q^{6} -2.60555 q^{7} -1.00000 q^{8} -1.30278 q^{9} +2.30278 q^{10} -1.00000 q^{11} -1.30278 q^{12} -4.00000 q^{13} +2.60555 q^{14} +3.00000 q^{15} +1.00000 q^{16} +0.697224 q^{17} +1.30278 q^{18} -0.302776 q^{19} -2.30278 q^{20} +3.39445 q^{21} +1.00000 q^{22} -2.30278 q^{23} +1.30278 q^{24} +0.302776 q^{25} +4.00000 q^{26} +5.60555 q^{27} -2.60555 q^{28} +6.69722 q^{29} -3.00000 q^{30} -4.69722 q^{31} -1.00000 q^{32} +1.30278 q^{33} -0.697224 q^{34} +6.00000 q^{35} -1.30278 q^{36} -0.0916731 q^{37} +0.302776 q^{38} +5.21110 q^{39} +2.30278 q^{40} -3.69722 q^{41} -3.39445 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.00000 q^{45} +2.30278 q^{46} +9.90833 q^{47} -1.30278 q^{48} -0.211103 q^{49} -0.302776 q^{50} -0.908327 q^{51} -4.00000 q^{52} -3.21110 q^{53} -5.60555 q^{54} +2.30278 q^{55} +2.60555 q^{56} +0.394449 q^{57} -6.69722 q^{58} +9.21110 q^{59} +3.00000 q^{60} +2.00000 q^{61} +4.69722 q^{62} +3.39445 q^{63} +1.00000 q^{64} +9.21110 q^{65} -1.30278 q^{66} -14.6056 q^{67} +0.697224 q^{68} +3.00000 q^{69} -6.00000 q^{70} +4.60555 q^{71} +1.30278 q^{72} +5.21110 q^{73} +0.0916731 q^{74} -0.394449 q^{75} -0.302776 q^{76} +2.60555 q^{77} -5.21110 q^{78} +16.7250 q^{79} -2.30278 q^{80} -3.39445 q^{81} +3.69722 q^{82} -7.81665 q^{83} +3.39445 q^{84} -1.60555 q^{85} -1.00000 q^{86} -8.72498 q^{87} +1.00000 q^{88} +12.0000 q^{89} -3.00000 q^{90} +10.4222 q^{91} -2.30278 q^{92} +6.11943 q^{93} -9.90833 q^{94} +0.697224 q^{95} +1.30278 q^{96} -14.1194 q^{97} +0.211103 q^{98} +1.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{7} - 2 q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} - 8 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 5 q^{17} - q^{18} + 3 q^{19} - q^{20} + 14 q^{21} + 2 q^{22} - q^{23} - q^{24} - 3 q^{25} + 8 q^{26} + 4 q^{27} + 2 q^{28} + 17 q^{29} - 6 q^{30} - 13 q^{31} - 2 q^{32} - q^{33} - 5 q^{34} + 12 q^{35} + q^{36} - 11 q^{37} - 3 q^{38} - 4 q^{39} + q^{40} - 11 q^{41} - 14 q^{42} + 2 q^{43} - 2 q^{44} + 6 q^{45} + q^{46} + 9 q^{47} + q^{48} + 14 q^{49} + 3 q^{50} + 9 q^{51} - 8 q^{52} + 8 q^{53} - 4 q^{54} + q^{55} - 2 q^{56} + 8 q^{57} - 17 q^{58} + 4 q^{59} + 6 q^{60} + 4 q^{61} + 13 q^{62} + 14 q^{63} + 2 q^{64} + 4 q^{65} + q^{66} - 22 q^{67} + 5 q^{68} + 6 q^{69} - 12 q^{70} + 2 q^{71} - q^{72} - 4 q^{73} + 11 q^{74} - 8 q^{75} + 3 q^{76} - 2 q^{77} + 4 q^{78} + q^{79} - q^{80} - 14 q^{81} + 11 q^{82} + 6 q^{83} + 14 q^{84} + 4 q^{85} - 2 q^{86} + 15 q^{87} + 2 q^{88} + 24 q^{89} - 6 q^{90} - 8 q^{91} - q^{92} - 13 q^{93} - 9 q^{94} + 5 q^{95} - q^{96} - 3 q^{97} - 14 q^{98} - q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^7 - 2 * q^8 + q^9 + q^10 - 2 * q^11 + q^12 - 8 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 5 * q^17 - q^18 + 3 * q^19 - q^20 + 14 * q^21 + 2 * q^22 - q^23 - q^24 - 3 * q^25 + 8 * q^26 + 4 * q^27 + 2 * q^28 + 17 * q^29 - 6 * q^30 - 13 * q^31 - 2 * q^32 - q^33 - 5 * q^34 + 12 * q^35 + q^36 - 11 * q^37 - 3 * q^38 - 4 * q^39 + q^40 - 11 * q^41 - 14 * q^42 + 2 * q^43 - 2 * q^44 + 6 * q^45 + q^46 + 9 * q^47 + q^48 + 14 * q^49 + 3 * q^50 + 9 * q^51 - 8 * q^52 + 8 * q^53 - 4 * q^54 + q^55 - 2 * q^56 + 8 * q^57 - 17 * q^58 + 4 * q^59 + 6 * q^60 + 4 * q^61 + 13 * q^62 + 14 * q^63 + 2 * q^64 + 4 * q^65 + q^66 - 22 * q^67 + 5 * q^68 + 6 * q^69 - 12 * q^70 + 2 * q^71 - q^72 - 4 * q^73 + 11 * q^74 - 8 * q^75 + 3 * q^76 - 2 * q^77 + 4 * q^78 + q^79 - q^80 - 14 * q^81 + 11 * q^82 + 6 * q^83 + 14 * q^84 + 4 * q^85 - 2 * q^86 + 15 * q^87 + 2 * q^88 + 24 * q^89 - 6 * q^90 - 8 * q^91 - q^92 - 13 * q^93 - 9 * q^94 + 5 * q^95 - q^96 - 3 * q^97 - 14 * q^98 - q^99

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