LMFDB - Embedded newform 1155.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.470683 q^{2} -1.00000 q^{3} -1.77846 q^{4} +1.00000 q^{5} -0.470683 q^{6} -1.00000 q^{7} -1.77846 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.470683 q^{2} -1.00000 q^{3} -1.77846 q^{4} +1.00000 q^{5} -0.470683 q^{6} -1.00000 q^{7} -1.77846 q^{8} +1.00000 q^{9} +0.470683 q^{10} -1.00000 q^{11} +1.77846 q^{12} -0.249141 q^{13} -0.470683 q^{14} -1.00000 q^{15} +2.71982 q^{16} +1.22154 q^{17} +0.470683 q^{18} -1.83709 q^{19} -1.77846 q^{20} +1.00000 q^{21} -0.470683 q^{22} +3.71982 q^{23} +1.77846 q^{24} +1.00000 q^{25} -0.117266 q^{26} -1.00000 q^{27} +1.77846 q^{28} -3.96896 q^{29} -0.470683 q^{30} +7.80605 q^{31} +4.83709 q^{32} +1.00000 q^{33} +0.574960 q^{34} -1.00000 q^{35} -1.77846 q^{36} +4.24914 q^{37} -0.864688 q^{38} +0.249141 q^{39} -1.77846 q^{40} +3.19051 q^{41} +0.470683 q^{42} +3.02760 q^{43} +1.77846 q^{44} +1.00000 q^{45} +1.75086 q^{46} -1.19051 q^{47} -2.71982 q^{48} +1.00000 q^{49} +0.470683 q^{50} -1.22154 q^{51} +0.443086 q^{52} +13.3940 q^{53} -0.470683 q^{54} -1.00000 q^{55} +1.77846 q^{56} +1.83709 q^{57} -1.86813 q^{58} +3.02760 q^{59} +1.77846 q^{60} +9.15947 q^{61} +3.67418 q^{62} -1.00000 q^{63} -3.16291 q^{64} -0.249141 q^{65} +0.470683 q^{66} +7.67418 q^{67} -2.17246 q^{68} -3.71982 q^{69} -0.470683 q^{70} -4.13187 q^{71} -1.77846 q^{72} -0.941367 q^{73} +2.00000 q^{74} -1.00000 q^{75} +3.26719 q^{76} +1.00000 q^{77} +0.117266 q^{78} -8.36641 q^{79} +2.71982 q^{80} +1.00000 q^{81} +1.50172 q^{82} +1.10428 q^{83} -1.77846 q^{84} +1.22154 q^{85} +1.42504 q^{86} +3.96896 q^{87} +1.77846 q^{88} +5.26213 q^{89} +0.470683 q^{90} +0.249141 q^{91} -6.61555 q^{92} -7.80605 q^{93} -0.560352 q^{94} -1.83709 q^{95} -4.83709 q^{96} +11.1449 q^{97} +0.470683 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 8 q^{13} - q^{14} - 3 q^{15} - q^{16} + 12 q^{17} + q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - q^{22} + 2 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} + 6 q^{29} - q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} + 4 q^{37} + 22 q^{38} - 8 q^{39} + 3 q^{40} + q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 14 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + q^{50} - 12 q^{51} + 18 q^{52} + 16 q^{53} - q^{54} - 3 q^{55} - 3 q^{56} - 2 q^{57} - 16 q^{58} - 8 q^{59} - 3 q^{60} - 4 q^{62} - 3 q^{63} - 17 q^{64} + 8 q^{65} + q^{66} + 8 q^{67} + 26 q^{68} - 2 q^{69} - q^{70} - 2 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} + 24 q^{76} + 3 q^{77} + 2 q^{78} - 18 q^{79} - q^{80} + 3 q^{81} + 22 q^{82} + 10 q^{83} + 3 q^{84} + 12 q^{85} - 2 q^{86} - 6 q^{87} - 3 q^{88} + 2 q^{89} + q^{90} - 8 q^{91} - 4 q^{92} + 2 q^{93} - 20 q^{94} + 2 q^{95} - 7 q^{96} + 18 q^{97} + q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 8 * q^13 - q^14 - 3 * q^15 - q^16 + 12 * q^17 + q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - q^22 + 2 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 + 4 * q^37 + 22 * q^38 - 8 * q^39 + 3 * q^40 + q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 14 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + q^50 - 12 * q^51 + 18 * q^52 + 16 * q^53 - q^54 - 3 * q^55 - 3 * q^56 - 2 * q^57 - 16 * q^58 - 8 * q^59 - 3 * q^60 - 4 * q^62 - 3 * q^63 - 17 * q^64 + 8 * q^65 + q^66 + 8 * q^67 + 26 * q^68 - 2 * q^69 - q^70 - 2 * q^71 + 3 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 + 24 * q^76 + 3 * q^77 + 2 * q^78 - 18 * q^79 - q^80 + 3 * q^81 + 22 * q^82 + 10 * q^83 + 3 * q^84 + 12 * q^85 - 2 * q^86 - 6 * q^87 - 3 * q^88 + 2 * q^89 + q^90 - 8 * q^91 - 4 * q^92 + 2 * q^93 - 20 * q^94 + 2 * q^95 - 7 * q^96 + 18 * q^97 + q^98 - 3 * 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 $

$2$	0.470683	0.332823	0.166412	−	0.986056i	$-0.446782\pi$
$2$	0.470683	0.332823	0.166412	+	0.986056i	$0.446782\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.77846	−0.889229
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.470683	−0.192156
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.77846	−0.628780
$9$	1.00000	0.333333
$10$	0.470683	0.148843
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.77846	0.513396
$13$	−0.249141	−0.0690992	−0.0345496	−	0.999403i	$-0.511000\pi$
$13$	−0.249141	−0.0690992	−0.0345496	+	0.999403i	$0.511000\pi$
$14$	−0.470683	−0.125795
$15$	−1.00000	−0.258199
$16$	2.71982	0.679956
$17$	1.22154	0.296268	0.148134	−	0.988967i	$-0.452673\pi$
$17$	1.22154	0.296268	0.148134	+	0.988967i	$0.452673\pi$
$18$	0.470683	0.110941
$19$	−1.83709	−0.421457	−0.210729	−	0.977545i	$-0.567584\pi$
$19$	−1.83709	−0.421457	−0.210729	+	0.977545i	$0.567584\pi$
$20$	−1.77846	−0.397675
$21$	1.00000	0.218218
$22$	−0.470683	−0.100350
$23$	3.71982	0.775637	0.387818	−	0.921736i	$-0.373229\pi$
$23$	3.71982	0.775637	0.387818	+	0.921736i	$0.373229\pi$
$24$	1.77846	0.363026
$25$	1.00000	0.200000
$26$	−0.117266	−0.0229978
$27$	−1.00000	−0.192450
$28$	1.77846	0.336097
$29$	−3.96896	−0.737018	−0.368509	−	0.929624i	$-0.620132\pi$
$29$	−3.96896	−0.737018	−0.368509	+	0.929624i	$0.620132\pi$
$30$	−0.470683	−0.0859346
$31$	7.80605	1.40201	0.701004	−	0.713157i	$-0.252735\pi$
$31$	7.80605	1.40201	0.701004	+	0.713157i	$0.252735\pi$
$32$	4.83709	0.855085
$33$	1.00000	0.174078
$34$	0.574960	0.0986048
$35$	−1.00000	−0.169031
$36$	−1.77846	−0.296410
$37$	4.24914	0.698554	0.349277	−	0.937019i	$-0.386427\pi$
$37$	4.24914	0.698554	0.349277	+	0.937019i	$0.386427\pi$
$38$	−0.864688	−0.140271
$39$	0.249141	0.0398944
$40$	−1.77846	−0.281199
$41$	3.19051	0.498274	0.249137	−	0.968468i	$-0.419853\pi$
$41$	3.19051	0.498274	0.249137	+	0.968468i	$0.419853\pi$
$42$	0.470683	0.0726280
$43$	3.02760	0.461704	0.230852	−	0.972989i	$-0.425849\pi$
$43$	3.02760	0.461704	0.230852	+	0.972989i	$0.425849\pi$
$44$	1.77846	0.268112
$45$	1.00000	0.149071
$46$	1.75086	0.258150
$47$	−1.19051	−0.173653	−0.0868267	−	0.996223i	$-0.527673\pi$
$47$	−1.19051	−0.173653	−0.0868267	+	0.996223i	$0.527673\pi$
$48$	−2.71982	−0.392573
$49$	1.00000	0.142857
$50$	0.470683	0.0665647
$51$	−1.22154	−0.171050
$52$	0.443086	0.0614449
$53$	13.3940	1.83981	0.919904	−	0.392144i	$-0.128266\pi$
$53$	13.3940	1.83981	0.919904	+	0.392144i	$0.128266\pi$
$54$	−0.470683	−0.0640519
$55$	−1.00000	−0.134840
$56$	1.77846	0.237656
$57$	1.83709	0.243329
$58$	−1.86813	−0.245297
$59$	3.02760	0.394160	0.197080	−	0.980387i	$-0.436854\pi$
$59$	3.02760	0.394160	0.197080	+	0.980387i	$0.436854\pi$
$60$	1.77846	0.229598
$61$	9.15947	1.17275	0.586375	−	0.810040i	$-0.300554\pi$
$61$	9.15947	1.17275	0.586375	+	0.810040i	$0.300554\pi$
$62$	3.67418	0.466621
$63$	−1.00000	−0.125988
$64$	−3.16291	−0.395364
$65$	−0.249141	−0.0309021
$66$	0.470683	0.0579371
$67$	7.67418	0.937550	0.468775	−	0.883318i	$-0.344695\pi$
$67$	7.67418	0.937550	0.468775	+	0.883318i	$0.344695\pi$
$68$	−2.17246	−0.263450
$69$	−3.71982	−0.447814
$70$	−0.470683	−0.0562574
$71$	−4.13187	−0.490363	−0.245182	−	0.969477i	$-0.578848\pi$
$71$	−4.13187	−0.490363	−0.245182	+	0.969477i	$0.578848\pi$
$72$	−1.77846	−0.209593
$73$	−0.941367	−0.110179	−0.0550893	−	0.998481i	$-0.517544\pi$
$73$	−0.941367	−0.110179	−0.0550893	+	0.998481i	$0.517544\pi$
$74$	2.00000	0.232495
$75$	−1.00000	−0.115470
$76$	3.26719	0.374772
$77$	1.00000	0.113961
$78$	0.117266	0.0132778
$79$	−8.36641	−0.941294	−0.470647	−	0.882322i	$-0.655980\pi$
$79$	−8.36641	−0.941294	−0.470647	+	0.882322i	$0.655980\pi$
$80$	2.71982	0.304086
$81$	1.00000	0.111111
$82$	1.50172	0.165837
$83$	1.10428	0.121210	0.0606050	−	0.998162i	$-0.480697\pi$
$83$	1.10428	0.121210	0.0606050	+	0.998162i	$0.480697\pi$
$84$	−1.77846	−0.194046
$85$	1.22154	0.132495
$86$	1.42504	0.153666
$87$	3.96896	0.425518
$88$	1.77846	0.189584
$89$	5.26213	0.557785	0.278892	−	0.960322i	$-0.410033\pi$
$89$	5.26213	0.557785	0.278892	+	0.960322i	$0.410033\pi$
$90$	0.470683	0.0496144
$91$	0.249141	0.0261170
$92$	−6.61555	−0.689718
$93$	−7.80605	−0.809450
$94$	−0.560352	−0.0577959
$95$	−1.83709	−0.188481
$96$	−4.83709	−0.493683
$97$	11.1449	1.13159	0.565795	−	0.824546i	$-0.308569\pi$
$97$	11.1449	1.13159	0.565795	+	0.824546i	$0.308569\pi$
$98$	0.470683	0.0475462
$99$	−1.00000	−0.100504
$100$	−1.77846	−0.177846
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−0.574960	−0.0569295
$103$	−3.52588	−0.347415	−0.173708	−	0.984797i	$-0.555575\pi$
$103$	−3.52588	−0.347415	−0.173708	+	0.984797i	$0.555575\pi$
$104$	0.443086	0.0434481
$105$	1.00000	0.0975900
$106$	6.30434	0.612331
$107$	9.42504	0.911153	0.455577	−	0.890197i	$-0.349433\pi$
$107$	9.42504	0.911153	0.455577	+	0.890197i	$0.349433\pi$
$108$	1.77846	0.171132
$109$	−6.13187	−0.587327	−0.293664	−	0.955909i	$-0.594875\pi$
$109$	−6.13187	−0.587327	−0.293664	+	0.955909i	$0.594875\pi$
$110$	−0.470683	−0.0448779
$111$	−4.24914	−0.403311
$112$	−2.71982	−0.256999
$113$	−7.77502	−0.731412	−0.365706	−	0.930730i	$-0.619172\pi$
$113$	−7.77502	−0.731412	−0.365706	+	0.930730i	$0.619172\pi$
$114$	0.864688	0.0809854
$115$	3.71982	0.346875
$116$	7.05863	0.655378
$117$	−0.249141	−0.0230331
$118$	1.42504	0.131186
$119$	−1.22154	−0.111979
$120$	1.77846	0.162350
$121$	1.00000	0.0909091
$122$	4.31121	0.390319
$123$	−3.19051	−0.287678
$124$	−13.8827	−1.24671
$125$	1.00000	0.0894427
$126$	−0.470683	−0.0419318
$127$	−10.5293	−0.934326	−0.467163	−	0.884171i	$-0.654724\pi$
$127$	−10.5293	−0.934326	−0.467163	+	0.884171i	$0.654724\pi$
$128$	−11.1629	−0.986671
$129$	−3.02760	−0.266565
$130$	−0.117266	−0.0102849
$131$	−1.68879	−0.147550	−0.0737751	−	0.997275i	$-0.523505\pi$
$131$	−1.68879	−0.147550	−0.0737751	+	0.997275i	$0.523505\pi$
$132$	−1.77846	−0.154795
$133$	1.83709	0.159296
$134$	3.61211	0.312039
$135$	−1.00000	−0.0860663
$136$	−2.17246	−0.186287
$137$	21.9379	1.87428	0.937142	−	0.348949i	$-0.113461\pi$
$137$	21.9379	1.87428	0.937142	+	0.348949i	$0.113461\pi$
$138$	−1.75086	−0.149043
$139$	−2.70683	−0.229591	−0.114795	−	0.993389i	$-0.536621\pi$
$139$	−2.70683	−0.229591	−0.114795	+	0.993389i	$0.536621\pi$
$140$	1.77846	0.150307
$141$	1.19051	0.100259
$142$	−1.94480	−0.163204
$143$	0.249141	0.0208342
$144$	2.71982	0.226652
$145$	−3.96896	−0.329605
$146$	−0.443086	−0.0366700
$147$	−1.00000	−0.0824786
$148$	−7.55691	−0.621175
$149$	11.4948	0.941694	0.470847	−	0.882215i	$-0.343948\pi$
$149$	11.4948	0.941694	0.470847	+	0.882215i	$0.343948\pi$
$150$	−0.470683	−0.0384311
$151$	−12.6707	−1.03113	−0.515565	−	0.856850i	$-0.672418\pi$
$151$	−12.6707	−1.03113	−0.515565	+	0.856850i	$0.672418\pi$
$152$	3.26719	0.265004
$153$	1.22154	0.0987559
$154$	0.470683	0.0379288
$155$	7.80605	0.626997
$156$	−0.443086	−0.0354753
$157$	1.35342	0.108014	0.0540072	−	0.998541i	$-0.482801\pi$
$157$	1.35342	0.108014	0.0540072	+	0.998541i	$0.482801\pi$
$158$	−3.93793	−0.313285
$159$	−13.3940	−1.06221
$160$	4.83709	0.382406
$161$	−3.71982	−0.293163
$162$	0.470683	0.0369804
$163$	−22.9199	−1.79522	−0.897612	−	0.440787i	$-0.854700\pi$
$163$	−22.9199	−1.79522	−0.897612	+	0.440787i	$0.854700\pi$
$164$	−5.67418	−0.443079
$165$	1.00000	0.0778499
$166$	0.519765	0.0403416
$167$	1.29317	0.100068	0.0500341	−	0.998748i	$-0.484067\pi$
$167$	1.29317	0.100068	0.0500341	+	0.998748i	$0.484067\pi$
$168$	−1.77846	−0.137211
$169$	−12.9379	−0.995225
$170$	0.574960	0.0440974
$171$	−1.83709	−0.140486
$172$	−5.38445	−0.410561
$173$	15.8207	1.20282	0.601411	−	0.798940i	$-0.294605\pi$
$173$	15.8207	1.20282	0.601411	+	0.798940i	$0.294605\pi$
$174$	1.86813	0.141622
$175$	−1.00000	−0.0755929
$176$	−2.71982	−0.205014
$177$	−3.02760	−0.227568
$178$	2.47680	0.185644
$179$	−8.13187	−0.607805	−0.303902	−	0.952703i	$-0.598290\pi$
$179$	−8.13187	−0.607805	−0.303902	+	0.952703i	$0.598290\pi$
$180$	−1.77846	−0.132558
$181$	9.11383	0.677426	0.338713	−	0.940890i	$-0.390009\pi$
$181$	9.11383	0.677426	0.338713	+	0.940890i	$0.390009\pi$
$182$	0.117266	0.00869236
$183$	−9.15947	−0.677088
$184$	−6.61555	−0.487705
$185$	4.24914	0.312403
$186$	−3.67418	−0.269404
$187$	−1.22154	−0.0893281
$188$	2.11727	0.154418
$189$	1.00000	0.0727393
$190$	−0.864688	−0.0627311
$191$	−2.11727	−0.153200	−0.0766000	−	0.997062i	$-0.524406\pi$
$191$	−2.11727	−0.153200	−0.0766000	+	0.997062i	$0.524406\pi$
$192$	3.16291	0.228263
$193$	−3.61899	−0.260500	−0.130250	−	0.991481i	$-0.541578\pi$
$193$	−3.61899	−0.260500	−0.130250	+	0.991481i	$0.541578\pi$
$194$	5.24570	0.376620
$195$	0.249141	0.0178413
$196$	−1.77846	−0.127033
$197$	−8.05520	−0.573909	−0.286954	−	0.957944i	$-0.592643\pi$
$197$	−8.05520	−0.573909	−0.286954	+	0.957944i	$0.592643\pi$
$198$	−0.470683	−0.0334500
$199$	−14.8793	−1.05477	−0.527383	−	0.849628i	$-0.676827\pi$
$199$	−14.8793	−1.05477	−0.527383	+	0.849628i	$0.676827\pi$
$200$	−1.77846	−0.125756
$201$	−7.67418	−0.541295
$202$	2.82410	0.198703
$203$	3.96896	0.278567
$204$	2.17246	0.152103
$205$	3.19051	0.222835
$206$	−1.65957	−0.115628
$207$	3.71982	0.258546
$208$	−0.677618	−0.0469844
$209$	1.83709	0.127074
$210$	0.470683	0.0324802
$211$	−12.8241	−0.882847	−0.441424	−	0.897299i	$-0.645526\pi$
$211$	−12.8241	−0.882847	−0.441424	+	0.897299i	$0.645526\pi$
$212$	−23.8207	−1.63601
$213$	4.13187	0.283111
$214$	4.43621	0.303253
$215$	3.02760	0.206480
$216$	1.77846	0.121009
$217$	−7.80605	−0.529910
$218$	−2.88617	−0.195476
$219$	0.941367	0.0636117
$220$	1.77846	0.119904
$221$	−0.304336	−0.0204718
$222$	−2.00000	−0.134231
$223$	−4.08623	−0.273634	−0.136817	−	0.990596i	$-0.543687\pi$
$223$	−4.08623	−0.273634	−0.136817	+	0.990596i	$0.543687\pi$
$224$	−4.83709	−0.323192
$225$	1.00000	0.0666667
$226$	−3.65957	−0.243431
$227$	12.7785	0.848136	0.424068	−	0.905630i	$-0.360602\pi$
$227$	12.7785	0.848136	0.424068	+	0.905630i	$0.360602\pi$
$228$	−3.26719	−0.216375
$229$	−20.3595	−1.34540	−0.672698	−	0.739917i	$-0.734865\pi$
$229$	−20.3595	−1.34540	−0.672698	+	0.739917i	$0.734865\pi$
$230$	1.75086	0.115448
$231$	−1.00000	−0.0657952
$232$	7.05863	0.463422
$233$	−0.311212	−0.0203881	−0.0101941	−	0.999948i	$-0.503245\pi$
$233$	−0.311212	−0.0203881	−0.0101941	+	0.999948i	$0.503245\pi$
$234$	−0.117266	−0.00766594
$235$	−1.19051	−0.0776601
$236$	−5.38445	−0.350498
$237$	8.36641	0.543457
$238$	−0.574960	−0.0372691
$239$	−19.7896	−1.28008	−0.640042	−	0.768340i	$-0.721083\pi$
$239$	−19.7896	−1.28008	−0.640042	+	0.768340i	$0.721083\pi$
$240$	−2.71982	−0.175564
$241$	22.6707	1.46035	0.730175	−	0.683260i	$-0.239438\pi$
$241$	22.6707	1.46035	0.730175	+	0.683260i	$0.239438\pi$
$242$	0.470683	0.0302567
$243$	−1.00000	−0.0641500
$244$	−16.2897	−1.04284
$245$	1.00000	0.0638877
$246$	−1.50172	−0.0957461
$247$	0.457694	0.0291224
$248$	−13.8827	−0.881554
$249$	−1.10428	−0.0699807
$250$	0.470683	0.0297686
$251$	27.2242	1.71838	0.859189	−	0.511659i	$-0.170969\pi$
$251$	27.2242	1.71838	0.859189	+	0.511659i	$0.170969\pi$
$252$	1.77846	0.112032
$253$	−3.71982	−0.233863
$254$	−4.95597	−0.310966
$255$	−1.22154	−0.0764960
$256$	1.07162	0.0669764
$257$	8.42160	0.525325	0.262663	−	0.964888i	$-0.415399\pi$
$257$	8.42160	0.525325	0.262663	+	0.964888i	$0.415399\pi$
$258$	−1.42504	−0.0887191
$259$	−4.24914	−0.264029
$260$	0.443086	0.0274790
$261$	−3.96896	−0.245673
$262$	−0.794885	−0.0491081
$263$	16.2637	1.00287	0.501433	−	0.865197i	$-0.332806\pi$
$263$	16.2637	1.00287	0.501433	+	0.865197i	$0.332806\pi$
$264$	−1.77846	−0.109456
$265$	13.3940	0.822787
$266$	0.864688	0.0530174
$267$	−5.26213	−0.322037
$268$	−13.6482	−0.833697
$269$	−0.763849	−0.0465727	−0.0232864	−	0.999729i	$-0.507413\pi$
$269$	−0.763849	−0.0465727	−0.0232864	+	0.999729i	$0.507413\pi$
$270$	−0.470683	−0.0286449
$271$	−10.9870	−0.667413	−0.333707	−	0.942677i	$-0.608300\pi$
$271$	−10.9870	−0.667413	−0.333707	+	0.942677i	$0.608300\pi$
$272$	3.32238	0.201449
$273$	−0.249141	−0.0150787
$274$	10.3258	0.623806
$275$	−1.00000	−0.0603023
$276$	6.61555	0.398209
$277$	−15.3224	−0.920633	−0.460316	−	0.887755i	$-0.652264\pi$
$277$	−15.3224	−0.920633	−0.460316	+	0.887755i	$0.652264\pi$
$278$	−1.27406	−0.0764132
$279$	7.80605	0.467336
$280$	1.77846	0.106283
$281$	−17.6742	−1.05435	−0.527177	−	0.849756i	$-0.676749\pi$
$281$	−17.6742	−1.05435	−0.527177	+	0.849756i	$0.676749\pi$
$282$	0.560352	0.0333685
$283$	27.4182	1.62984	0.814920	−	0.579573i	$-0.196781\pi$
$283$	27.4182	1.62984	0.814920	+	0.579573i	$0.196781\pi$
$284$	7.34836	0.436045
$285$	1.83709	0.108820
$286$	0.117266	0.00693410
$287$	−3.19051	−0.188330
$288$	4.83709	0.285028
$289$	−15.5078	−0.912225
$290$	−1.86813	−0.109700
$291$	−11.1449	−0.653323
$292$	1.67418	0.0979740
$293$	6.04564	0.353190	0.176595	−	0.984284i	$-0.443492\pi$
$293$	6.04564	0.353190	0.176595	+	0.984284i	$0.443492\pi$
$294$	−0.470683	−0.0274508
$295$	3.02760	0.176274
$296$	−7.55691	−0.439237
$297$	1.00000	0.0580259
$298$	5.41043	0.313418
$299$	−0.926759	−0.0535959
$300$	1.77846	0.102679
$301$	−3.02760	−0.174508
$302$	−5.96391	−0.343184
$303$	−6.00000	−0.344691
$304$	−4.99656	−0.286572
$305$	9.15947	0.524470
$306$	0.574960	0.0328683
$307$	0.0620710	0.00354258	0.00177129	−	0.999998i	$-0.499436\pi$
$307$	0.0620710	0.00354258	0.00177129	+	0.999998i	$0.499436\pi$
$308$	−1.77846	−0.101337
$309$	3.52588	0.200580
$310$	3.67418	0.208679
$311$	−8.73281	−0.495192	−0.247596	−	0.968863i	$-0.579641\pi$
$311$	−8.73281	−0.495192	−0.247596	+	0.968863i	$0.579641\pi$
$312$	−0.443086	−0.0250848
$313$	7.37940	0.417108	0.208554	−	0.978011i	$-0.433124\pi$
$313$	7.37940	0.417108	0.208554	+	0.978011i	$0.433124\pi$
$314$	0.637031	0.0359497
$315$	−1.00000	−0.0563436
$316$	14.8793	0.837026
$317$	23.5569	1.32309	0.661544	−	0.749906i	$-0.269901\pi$
$317$	23.5569	1.32309	0.661544	+	0.749906i	$0.269901\pi$
$318$	−6.30434	−0.353530
$319$	3.96896	0.222219
$320$	−3.16291	−0.176812
$321$	−9.42504	−0.526054
$322$	−1.75086	−0.0975716
$323$	−2.24408	−0.124864
$324$	−1.77846	−0.0988032
$325$	−0.249141	−0.0138198
$326$	−10.7880	−0.597493
$327$	6.13187	0.339093
$328$	−5.67418	−0.313304
$329$	1.19051	0.0656348
$330$	0.470683	0.0259103
$331$	−1.01299	−0.0556790	−0.0278395	−	0.999612i	$-0.508863\pi$
$331$	−1.01299	−0.0556790	−0.0278395	+	0.999612i	$0.508863\pi$
$332$	−1.96391	−0.107783
$333$	4.24914	0.232851
$334$	0.608672	0.0333050
$335$	7.67418	0.419285
$336$	2.71982	0.148379
$337$	9.20006	0.501159	0.250580	−	0.968096i	$-0.419379\pi$
$337$	9.20006	0.501159	0.250580	+	0.968096i	$0.419379\pi$
$338$	−6.08967	−0.331234
$339$	7.77502	0.422281
$340$	−2.17246	−0.117818
$341$	−7.80605	−0.422722
$342$	−0.864688	−0.0467570
$343$	−1.00000	−0.0539949
$344$	−5.38445	−0.290310
$345$	−3.71982	−0.200269
$346$	7.44652	0.400328
$347$	23.3776	1.25497	0.627487	−	0.778627i	$-0.284084\pi$
$347$	23.3776	1.25497	0.627487	+	0.778627i	$0.284084\pi$
$348$	−7.05863	−0.378382
$349$	33.3319	1.78422	0.892109	−	0.451821i	$-0.149225\pi$
$349$	33.3319	1.78422	0.892109	+	0.451821i	$0.149225\pi$
$350$	−0.470683	−0.0251591
$351$	0.249141	0.0132981
$352$	−4.83709	−0.257818
$353$	10.2637	0.546284	0.273142	−	0.961974i	$-0.411937\pi$
$353$	10.2637	0.546284	0.273142	+	0.961974i	$0.411937\pi$
$354$	−1.42504	−0.0757400
$355$	−4.13187	−0.219297
$356$	−9.35847	−0.495998
$357$	1.22154	0.0646509
$358$	−3.82754	−0.202292
$359$	22.2948	1.17667	0.588337	−	0.808616i	$-0.299783\pi$
$359$	22.2948	1.17667	0.588337	+	0.808616i	$0.299783\pi$
$360$	−1.77846	−0.0937329
$361$	−15.6251	−0.822374
$362$	4.28973	0.225463
$363$	−1.00000	−0.0524864
$364$	−0.443086	−0.0232240
$365$	−0.941367	−0.0492734
$366$	−4.31121	−0.225351
$367$	6.03104	0.314817	0.157409	−	0.987534i	$-0.449686\pi$
$367$	6.03104	0.314817	0.157409	+	0.987534i	$0.449686\pi$
$368$	10.1173	0.527399
$369$	3.19051	0.166091
$370$	2.00000	0.103975
$371$	−13.3940	−0.695382
$372$	13.8827	0.719786
$373$	26.5224	1.37328	0.686640	−	0.726998i	$-0.259085\pi$
$373$	26.5224	1.37328	0.686640	+	0.726998i	$0.259085\pi$
$374$	−0.574960	−0.0297305
$375$	−1.00000	−0.0516398
$376$	2.11727	0.109190
$377$	0.988830	0.0509273
$378$	0.470683	0.0242093
$379$	−0.371463	−0.0190808	−0.00954038	−	0.999954i	$-0.503037\pi$
$379$	−0.371463	−0.0190808	−0.00954038	+	0.999954i	$0.503037\pi$
$380$	3.26719	0.167603
$381$	10.5293	0.539433
$382$	−0.996562	−0.0509886
$383$	34.7474	1.77551	0.887755	−	0.460316i	$-0.152264\pi$
$383$	34.7474	1.77551	0.887755	+	0.460316i	$0.152264\pi$
$384$	11.1629	0.569655
$385$	1.00000	0.0509647
$386$	−1.70340	−0.0867006
$387$	3.02760	0.153901
$388$	−19.8207	−1.00624
$389$	10.1319	0.513706	0.256853	−	0.966450i	$-0.417314\pi$
$389$	10.1319	0.513706	0.256853	+	0.966450i	$0.417314\pi$
$390$	0.117266	0.00593801
$391$	4.54392	0.229796
$392$	−1.77846	−0.0898256
$393$	1.68879	0.0851881
$394$	−3.79145	−0.191010
$395$	−8.36641	−0.420960
$396$	1.77846	0.0893708
$397$	−8.44309	−0.423746	−0.211873	−	0.977297i	$-0.567956\pi$
$397$	−8.44309	−0.423746	−0.211873	+	0.977297i	$0.567956\pi$
$398$	−7.00344	−0.351051
$399$	−1.83709	−0.0919695
$400$	2.71982	0.135991
$401$	−22.8026	−1.13871	−0.569354	−	0.822092i	$-0.692807\pi$
$401$	−22.8026	−1.13871	−0.569354	+	0.822092i	$0.692807\pi$
$402$	−3.61211	−0.180156
$403$	−1.94480	−0.0968776
$404$	−10.6707	−0.530889
$405$	1.00000	0.0496904
$406$	1.86813	0.0927135
$407$	−4.24914	−0.210622
$408$	2.17246	0.107553
$409$	−28.6639	−1.41734	−0.708669	−	0.705542i	$-0.750704\pi$
$409$	−28.6639	−1.41734	−0.708669	+	0.705542i	$0.750704\pi$
$410$	1.50172	0.0741646
$411$	−21.9379	−1.08212
$412$	6.27062	0.308931
$413$	−3.02760	−0.148978
$414$	1.75086	0.0860500
$415$	1.10428	0.0542068
$416$	−1.20512	−0.0590856
$417$	2.70683	0.132554
$418$	0.864688	0.0422933
$419$	−5.31733	−0.259768	−0.129884	−	0.991529i	$-0.541461\pi$
$419$	−5.31733	−0.259768	−0.129884	+	0.991529i	$0.541461\pi$
$420$	−1.77846	−0.0867798
$421$	23.3871	1.13982	0.569909	−	0.821707i	$-0.306978\pi$
$421$	23.3871	1.13982	0.569909	+	0.821707i	$0.306978\pi$
$422$	−6.03609	−0.293832
$423$	−1.19051	−0.0578844
$424$	−23.8207	−1.15683
$425$	1.22154	0.0592535
$426$	1.94480	0.0942261
$427$	−9.15947	−0.443258
$428$	−16.7620	−0.810223
$429$	−0.249141	−0.0120286
$430$	1.42504	0.0687215
$431$	−23.6121	−1.13736	−0.568678	−	0.822560i	$-0.692545\pi$
$431$	−23.6121	−1.13736	−0.568678	+	0.822560i	$0.692545\pi$
$432$	−2.71982	−0.130858
$433$	9.26719	0.445353	0.222676	−	0.974892i	$-0.428521\pi$
$433$	9.26719	0.445353	0.222676	+	0.974892i	$0.428521\pi$
$434$	−3.67418	−0.176366
$435$	3.96896	0.190297
$436$	10.9053	0.522268
$437$	−6.83365	−0.326898
$438$	0.443086	0.0211715
$439$	20.8888	0.996970	0.498485	−	0.866898i	$-0.333890\pi$
$439$	20.8888	0.996970	0.498485	+	0.866898i	$0.333890\pi$
$440$	1.77846	0.0847846
$441$	1.00000	0.0476190
$442$	−0.143246	−0.00681351
$443$	−31.1621	−1.48056	−0.740279	−	0.672300i	$-0.765307\pi$
$443$	−31.1621	−1.48056	−0.740279	+	0.672300i	$0.765307\pi$
$444$	7.55691	0.358635
$445$	5.26213	0.249449
$446$	−1.92332	−0.0910719
$447$	−11.4948	−0.543687
$448$	3.16291	0.149433
$449$	−23.5354	−1.11071	−0.555353	−	0.831615i	$-0.687417\pi$
$449$	−23.5354	−1.11071	−0.555353	+	0.831615i	$0.687417\pi$
$450$	0.470683	0.0221882
$451$	−3.19051	−0.150235
$452$	13.8275	0.650393
$453$	12.6707	0.595323
$454$	6.01461	0.282280
$455$	0.249141	0.0116799
$456$	−3.26719	−0.153000
$457$	−5.02760	−0.235181	−0.117591	−	0.993062i	$-0.537517\pi$
$457$	−5.02760	−0.235181	−0.117591	+	0.993062i	$0.537517\pi$
$458$	−9.58289	−0.447779
$459$	−1.22154	−0.0570167
$460$	−6.61555	−0.308451
$461$	−10.6087	−0.494095	−0.247048	−	0.969003i	$-0.579460\pi$
$461$	−10.6087	−0.494095	−0.247048	+	0.969003i	$0.579460\pi$
$462$	−0.470683	−0.0218982
$463$	10.2897	0.478204	0.239102	−	0.970994i	$-0.423147\pi$
$463$	10.2897	0.478204	0.239102	+	0.970994i	$0.423147\pi$
$464$	−10.7949	−0.501140
$465$	−7.80605	−0.361997
$466$	−0.146482	−0.00678565
$467$	9.61899	0.445114	0.222557	−	0.974920i	$-0.428560\pi$
$467$	9.61899	0.445114	0.222557	+	0.974920i	$0.428560\pi$
$468$	0.443086	0.0204816
$469$	−7.67418	−0.354361
$470$	−0.560352	−0.0258471
$471$	−1.35342	−0.0623622
$472$	−5.38445	−0.247840
$473$	−3.02760	−0.139209
$474$	3.93793	0.180875
$475$	−1.83709	−0.0842915
$476$	2.17246	0.0995746
$477$	13.3940	0.613269
$478$	−9.31465	−0.426042
$479$	−23.1544	−1.05795	−0.528976	−	0.848637i	$-0.677424\pi$
$479$	−23.1544	−1.05795	−0.528976	+	0.848637i	$0.677424\pi$
$480$	−4.83709	−0.220782
$481$	−1.05863	−0.0482695
$482$	10.6707	0.486039
$483$	3.71982	0.169258
$484$	−1.77846	−0.0808390
$485$	11.1449	0.506062
$486$	−0.470683	−0.0213506
$487$	−1.94480	−0.0881275	−0.0440638	−	0.999029i	$-0.514030\pi$
$487$	−1.94480	−0.0881275	−0.0440638	+	0.999029i	$0.514030\pi$
$488$	−16.2897	−0.737401
$489$	22.9199	1.03647
$490$	0.470683	0.0212633
$491$	−4.23959	−0.191330	−0.0956650	−	0.995414i	$-0.530498\pi$
$491$	−4.23959	−0.191330	−0.0956650	+	0.995414i	$0.530498\pi$
$492$	5.67418	0.255812
$493$	−4.84826	−0.218355
$494$	0.215429	0.00969260
$495$	−1.00000	−0.0449467
$496$	21.2311	0.953304
$497$	4.13187	0.185340
$498$	−0.519765	−0.0232912
$499$	39.3319	1.76074	0.880370	−	0.474288i	$-0.157295\pi$
$499$	39.3319	1.76074	0.880370	+	0.474288i	$0.157295\pi$
$500$	−1.77846	−0.0795350
$501$	−1.29317	−0.0577744
$502$	12.8140	0.571916
$503$	23.8302	1.06254	0.531268	−	0.847204i	$-0.321716\pi$
$503$	23.8302	1.06254	0.531268	+	0.847204i	$0.321716\pi$
$504$	1.77846	0.0792188
$505$	6.00000	0.266996
$506$	−1.75086	−0.0778352
$507$	12.9379	0.574594
$508$	18.7259	0.830829
$509$	−5.18096	−0.229642	−0.114821	−	0.993386i	$-0.536629\pi$
$509$	−5.18096	−0.229642	−0.114821	+	0.993386i	$0.536629\pi$
$510$	−0.574960	−0.0254597
$511$	0.941367	0.0416436
$512$	22.8302	1.00896
$513$	1.83709	0.0811095
$514$	3.96391	0.174841
$515$	−3.52588	−0.155369
$516$	5.38445	0.237037
$517$	1.19051	0.0523585
$518$	−2.00000	−0.0878750
$519$	−15.8207	−0.694450
$520$	0.443086	0.0194306
$521$	27.4898	1.20435	0.602175	−	0.798364i	$-0.294301\pi$
$521$	27.4898	1.20435	0.602175	+	0.798364i	$0.294301\pi$
$522$	−1.86813	−0.0817656
$523$	−41.8398	−1.82953	−0.914763	−	0.403992i	$-0.867622\pi$
$523$	−41.8398	−1.82953	−0.914763	+	0.403992i	$0.867622\pi$
$524$	3.00344	0.131206
$525$	1.00000	0.0436436
$526$	7.65508	0.333777
$527$	9.53543	0.415370
$528$	2.71982	0.118365
$529$	−9.16291	−0.398387
$530$	6.30434	0.273843
$531$	3.02760	0.131387
$532$	−3.26719	−0.141650
$533$	−0.794885	−0.0344303
$534$	−2.47680	−0.107182
$535$	9.42504	0.407480
$536$	−13.6482	−0.589512
$537$	8.13187	0.350916
$538$	−0.359531	−0.0155005
$539$	−1.00000	−0.0430730
$540$	1.77846	0.0765326
$541$	−26.8939	−1.15626	−0.578130	−	0.815945i	$-0.696217\pi$
$541$	−26.8939	−1.15626	−0.578130	+	0.815945i	$0.696217\pi$
$542$	−5.17140	−0.222131
$543$	−9.11383	−0.391112
$544$	5.90871	0.253334
$545$	−6.13187	−0.262661
$546$	−0.117266	−0.00501854
$547$	−37.3173	−1.59557	−0.797787	−	0.602940i	$-0.793996\pi$
$547$	−37.3173	−1.59557	−0.797787	+	0.602940i	$0.793996\pi$
$548$	−39.0157	−1.66667
$549$	9.15947	0.390917
$550$	−0.470683	−0.0200700
$551$	7.29135	0.310622
$552$	6.61555	0.281576
$553$	8.36641	0.355776
$554$	−7.21199	−0.306408
$555$	−4.24914	−0.180366
$556$	4.81399	0.204159
$557$	16.3810	0.694086	0.347043	−	0.937849i	$-0.387186\pi$
$557$	16.3810	0.694086	0.347043	+	0.937849i	$0.387186\pi$
$558$	3.67418	0.155540
$559$	−0.754297	−0.0319034
$560$	−2.71982	−0.114934
$561$	1.22154	0.0515736
$562$	−8.31894	−0.350913
$563$	−6.55348	−0.276196	−0.138098	−	0.990419i	$-0.544099\pi$
$563$	−6.55348	−0.276196	−0.138098	+	0.990419i	$0.544099\pi$
$564$	−2.11727	−0.0891530
$565$	−7.77502	−0.327098
$566$	12.9053	0.542449
$567$	−1.00000	−0.0419961
$568$	7.34836	0.308330
$569$	38.4312	1.61112	0.805559	−	0.592516i	$-0.201865\pi$
$569$	38.4312	1.61112	0.805559	+	0.592516i	$0.201865\pi$
$570$	0.864688	0.0362178
$571$	2.90078	0.121394	0.0606969	−	0.998156i	$-0.480668\pi$
$571$	2.90078	0.121394	0.0606969	+	0.998156i	$0.480668\pi$
$572$	−0.443086	−0.0185263
$573$	2.11727	0.0884501
$574$	−1.50172	−0.0626805
$575$	3.71982	0.155127
$576$	−3.16291	−0.131788
$577$	36.6448	1.52554	0.762771	−	0.646669i	$-0.223838\pi$
$577$	36.6448	1.52554	0.762771	+	0.646669i	$0.223838\pi$
$578$	−7.29928	−0.303610
$579$	3.61899	0.150400
$580$	7.05863	0.293094
$581$	−1.10428	−0.0458131
$582$	−5.24570	−0.217441
$583$	−13.3940	−0.554723
$584$	1.67418	0.0692781
$585$	−0.249141	−0.0103007
$586$	2.84558	0.117550
$587$	−24.2130	−0.999379	−0.499690	−	0.866204i	$-0.666553\pi$
$587$	−24.2130	−0.999379	−0.499690	+	0.866204i	$0.666553\pi$
$588$	1.77846	0.0733423
$589$	−14.3404	−0.590887
$590$	1.42504	0.0586680
$591$	8.05520	0.331346
$592$	11.5569	0.474986
$593$	14.6707	0.602455	0.301228	−	0.953552i	$-0.402604\pi$
$593$	14.6707	0.602455	0.301228	+	0.953552i	$0.402604\pi$
$594$	0.470683	0.0193124
$595$	−1.22154	−0.0500784
$596$	−20.4431	−0.837381
$597$	14.8793	0.608969
$598$	−0.436210	−0.0178380
$599$	5.05863	0.206690	0.103345	−	0.994646i	$-0.467045\pi$
$599$	5.05863	0.206690	0.103345	+	0.994646i	$0.467045\pi$
$600$	1.77846	0.0726052
$601$	13.3319	0.543821	0.271910	−	0.962323i	$-0.412345\pi$
$601$	13.3319	0.543821	0.271910	+	0.962323i	$0.412345\pi$
$602$	−1.42504	−0.0580803
$603$	7.67418	0.312517
$604$	22.5344	0.916911
$605$	1.00000	0.0406558
$606$	−2.82410	−0.114721
$607$	−8.94824	−0.363198	−0.181599	−	0.983373i	$-0.558127\pi$
$607$	−8.94824	−0.363198	−0.181599	+	0.983373i	$0.558127\pi$
$608$	−8.88617	−0.360382
$609$	−3.96896	−0.160831
$610$	4.31121	0.174556
$611$	0.296604	0.0119993
$612$	−2.17246	−0.0878166
$613$	−9.53093	−0.384951	−0.192475	−	0.981302i	$-0.561652\pi$
$613$	−9.53093	−0.384951	−0.192475	+	0.981302i	$0.561652\pi$
$614$	0.0292158	0.00117905
$615$	−3.19051	−0.128654
$616$	−1.77846	−0.0716561
$617$	27.4328	1.10440	0.552201	−	0.833711i	$-0.313788\pi$
$617$	27.4328	1.10440	0.552201	+	0.833711i	$0.313788\pi$
$618$	1.65957	0.0667578
$619$	−6.20855	−0.249543	−0.124771	−	0.992186i	$-0.539820\pi$
$619$	−6.20855	−0.249543	−0.124771	+	0.992186i	$0.539820\pi$
$620$	−13.8827	−0.557544
$621$	−3.71982	−0.149271
$622$	−4.11039	−0.164812
$623$	−5.26213	−0.210823
$624$	0.677618	0.0271264
$625$	1.00000	0.0400000
$626$	3.47336	0.138823
$627$	−1.83709	−0.0733663
$628$	−2.40699	−0.0960495
$629$	5.19051	0.206959
$630$	−0.470683	−0.0187525
$631$	12.1560	0.483924	0.241962	−	0.970286i	$-0.422209\pi$
$631$	12.1560	0.483924	0.241962	+	0.970286i	$0.422209\pi$
$632$	14.8793	0.591867
$633$	12.8241	0.509712
$634$	11.0878	0.440355
$635$	−10.5293	−0.417843
$636$	23.8207	0.944551
$637$	−0.249141	−0.00987131
$638$	1.86813	0.0739598
$639$	−4.13187	−0.163454
$640$	−11.1629	−0.441253
$641$	14.1104	0.557327	0.278663	−	0.960389i	$-0.410109\pi$
$641$	14.1104	0.557327	0.278663	+	0.960389i	$0.410109\pi$
$642$	−4.43621	−0.175083
$643$	24.5224	0.967071	0.483535	−	0.875325i	$-0.339352\pi$
$643$	24.5224	0.967071	0.483535	+	0.875325i	$0.339352\pi$
$644$	6.61555	0.260689
$645$	−3.02760	−0.119212
$646$	−1.05625	−0.0415577
$647$	−18.3810	−0.722632	−0.361316	−	0.932443i	$-0.617672\pi$
$647$	−18.3810	−0.722632	−0.361316	+	0.932443i	$0.617672\pi$
$648$	−1.77846	−0.0698644
$649$	−3.02760	−0.118844
$650$	−0.117266	−0.00459956
$651$	7.80605	0.305943
$652$	40.7620	1.59636
$653$	−2.39057	−0.0935501	−0.0467751	−	0.998905i	$-0.514894\pi$
$653$	−2.39057	−0.0935501	−0.0467751	+	0.998905i	$0.514894\pi$
$654$	2.88617	0.112858
$655$	−1.68879	−0.0659864
$656$	8.67762	0.338804
$657$	−0.941367	−0.0367262
$658$	0.560352	0.0218448
$659$	20.4932	0.798303	0.399151	−	0.916885i	$-0.369305\pi$
$659$	20.4932	0.798303	0.399151	+	0.916885i	$0.369305\pi$
$660$	−1.77846	−0.0692263
$661$	−4.35953	−0.169566	−0.0847831	−	0.996399i	$-0.527020\pi$
$661$	−4.35953	−0.169566	−0.0847831	+	0.996399i	$0.527020\pi$
$662$	−0.476797	−0.0185313
$663$	0.304336	0.0118194
$664$	−1.96391	−0.0762144
$665$	1.83709	0.0712393
$666$	2.00000	0.0774984
$667$	−14.7638	−0.571659
$668$	−2.29984	−0.0889835
$669$	4.08623	0.157983
$670$	3.61211	0.139548
$671$	−9.15947	−0.353597
$672$	4.83709	0.186595
$673$	−17.2621	−0.665406	−0.332703	−	0.943032i	$-0.607961\pi$
$673$	−17.2621	−0.665406	−0.332703	+	0.943032i	$0.607961\pi$
$674$	4.33032	0.166798
$675$	−1.00000	−0.0384900
$676$	23.0096	0.884983
$677$	3.57334	0.137335	0.0686673	−	0.997640i	$-0.478125\pi$
$677$	3.57334	0.137335	0.0686673	+	0.997640i	$0.478125\pi$
$678$	3.65957	0.140545
$679$	−11.1449	−0.427701
$680$	−2.17246	−0.0833101
$681$	−12.7785	−0.489672
$682$	−3.67418	−0.140692
$683$	30.4622	1.16560	0.582802	−	0.812614i	$-0.301956\pi$
$683$	30.4622	1.16560	0.582802	+	0.812614i	$0.301956\pi$
$684$	3.26719	0.124924
$685$	21.9379	0.838205
$686$	−0.470683	−0.0179708
$687$	20.3595	0.776765
$688$	8.23453	0.313939
$689$	−3.33699	−0.127129
$690$	−1.75086	−0.0666541
$691$	34.1364	1.29861	0.649304	−	0.760529i	$-0.275060\pi$
$691$	34.1364	1.29861	0.649304	+	0.760529i	$0.275060\pi$
$692$	−28.1364	−1.06958
$693$	1.00000	0.0379869
$694$	11.0034	0.417685
$695$	−2.70683	−0.102676
$696$	−7.05863	−0.267557
$697$	3.89734	0.147622
$698$	15.6888	0.593829
$699$	0.311212	0.0117711
$700$	1.77846	0.0672194
$701$	−38.2587	−1.44501	−0.722505	−	0.691365i	$-0.757010\pi$
$701$	−38.2587	−1.44501	−0.722505	+	0.691365i	$0.757010\pi$
$702$	0.117266	0.00442593
$703$	−7.80605	−0.294411
$704$	3.16291	0.119207
$705$	1.19051	0.0448371
$706$	4.83098	0.181816
$707$	−6.00000	−0.225653
$708$	5.38445	0.202360
$709$	53.0974	1.99411	0.997057	−	0.0766589i	$-0.0244253\pi$
$709$	53.0974	1.99411	0.997057	+	0.0766589i	$0.0244253\pi$
$710$	−1.94480	−0.0729872
$711$	−8.36641	−0.313765
$712$	−9.35847	−0.350724
$713$	29.0371	1.08745
$714$	0.574960	0.0215173
$715$	0.249141	0.00931733
$716$	14.4622	0.540477
$717$	19.7896	0.739057
$718$	10.4938	0.391625
$719$	28.9103	1.07817	0.539087	−	0.842250i	$-0.318770\pi$
$719$	28.9103	1.07817	0.539087	+	0.842250i	$0.318770\pi$
$720$	2.71982	0.101362
$721$	3.52588	0.131311
$722$	−7.35448	−0.273705
$723$	−22.6707	−0.843134
$724$	−16.2086	−0.602386
$725$	−3.96896	−0.147404
$726$	−0.470683	−0.0174687
$727$	−9.02072	−0.334560	−0.167280	−	0.985909i	$-0.553498\pi$
$727$	−9.02072	−0.334560	−0.167280	+	0.985909i	$0.553498\pi$
$728$	−0.443086	−0.0164219
$729$	1.00000	0.0370370
$730$	−0.443086	−0.0163993
$731$	3.69834	0.136788
$732$	16.2897	0.602086
$733$	−29.7225	−1.09783	−0.548913	−	0.835880i	$-0.684958\pi$
$733$	−29.7225	−1.09783	−0.548913	+	0.835880i	$0.684958\pi$
$734$	2.83871	0.104779
$735$	−1.00000	−0.0368856
$736$	17.9931	0.663235
$737$	−7.67418	−0.282682
$738$	1.50172	0.0552790
$739$	−33.0586	−1.21608	−0.608041	−	0.793906i	$-0.708044\pi$
$739$	−33.0586	−1.21608	−0.608041	+	0.793906i	$0.708044\pi$
$740$	−7.55691	−0.277798
$741$	−0.457694	−0.0168138
$742$	−6.30434	−0.231439
$743$	11.9379	0.437960	0.218980	−	0.975729i	$-0.429727\pi$
$743$	11.9379	0.437960	0.218980	+	0.975729i	$0.429727\pi$
$744$	13.8827	0.508966
$745$	11.4948	0.421138
$746$	12.4837	0.457060
$747$	1.10428	0.0404034
$748$	2.17246	0.0794331
$749$	−9.42504	−0.344383
$750$	−0.470683	−0.0171869
$751$	3.33193	0.121584	0.0607920	−	0.998150i	$-0.480637\pi$
$751$	3.33193	0.121584	0.0607920	+	0.998150i	$0.480637\pi$
$752$	−3.23797	−0.118077
$753$	−27.2242	−0.992106
$754$	0.465426	0.0169498
$755$	−12.6707	−0.461136
$756$	−1.77846	−0.0646819
$757$	−32.9605	−1.19797	−0.598984	−	0.800761i	$-0.704429\pi$
$757$	−32.9605	−1.19797	−0.598984	+	0.800761i	$0.704429\pi$
$758$	−0.174841	−0.00635053
$759$	3.71982	0.135021
$760$	3.26719	0.118513
$761$	−34.1104	−1.23650	−0.618250	−	0.785981i	$-0.712158\pi$
$761$	−34.1104	−1.23650	−0.618250	+	0.785981i	$0.712158\pi$
$762$	4.95597	0.179536
$763$	6.13187	0.221989
$764$	3.76547	0.136230
$765$	1.22154	0.0441650
$766$	16.3550	0.590931
$767$	−0.754297	−0.0272361
$768$	−1.07162	−0.0386689
$769$	43.2147	1.55836	0.779180	−	0.626800i	$-0.215636\pi$
$769$	43.2147	1.55836	0.779180	+	0.626800i	$0.215636\pi$
$770$	0.470683	0.0169623
$771$	−8.42160	−0.303297
$772$	6.43621	0.231644
$773$	−38.8432	−1.39709	−0.698546	−	0.715565i	$-0.746169\pi$
$773$	−38.8432	−1.39709	−0.698546	+	0.715565i	$0.746169\pi$
$774$	1.42504	0.0512220
$775$	7.80605	0.280402
$776$	−19.8207	−0.711520
$777$	4.24914	0.152437
$778$	4.76891	0.170974
$779$	−5.86125	−0.210001
$780$	−0.443086	−0.0158650
$781$	4.13187	0.147850
$782$	2.13875	0.0764815
$783$	3.96896	0.141839
$784$	2.71982	0.0971366
$785$	1.35342	0.0483055
$786$	0.794885	0.0283526
$787$	−50.5726	−1.80272	−0.901359	−	0.433073i	$-0.857429\pi$
$787$	−50.5726	−1.80272	−0.901359	+	0.433073i	$0.857429\pi$
$788$	14.3258	0.510336
$789$	−16.2637	−0.579005
$790$	−3.93793	−0.140105
$791$	7.77502	0.276448
$792$	1.77846	0.0631947
$793$	−2.28200	−0.0810360
$794$	−3.97402	−0.141033
$795$	−13.3940	−0.475036
$796$	26.4622	0.937927
$797$	1.84664	0.0654114	0.0327057	−	0.999465i	$-0.489588\pi$
$797$	1.84664	0.0654114	0.0327057	+	0.999465i	$0.489588\pi$
$798$	−0.864688	−0.0306096
$799$	−1.45426	−0.0514479
$800$	4.83709	0.171017
$801$	5.26213	0.185928
$802$	−10.7328	−0.378989
$803$	0.941367	0.0332201
$804$	13.6482	0.481335
$805$	−3.71982	−0.131107
$806$	−0.915387	−0.0322431
$807$	0.763849	0.0268888
$808$	−10.6707	−0.375395
$809$	−10.9673	−0.385591	−0.192796	−	0.981239i	$-0.561755\pi$
$809$	−10.9673	−0.385591	−0.192796	+	0.981239i	$0.561755\pi$
$810$	0.470683	0.0165381
$811$	10.2277	0.359142	0.179571	−	0.983745i	$-0.442529\pi$
$811$	10.2277	0.359142	0.179571	+	0.983745i	$0.442529\pi$
$812$	−7.05863	−0.247709
$813$	10.9870	0.385331
$814$	−2.00000	−0.0701000
$815$	−22.9199	−0.802848
$816$	−3.32238	−0.116307
$817$	−5.56197	−0.194589
$818$	−13.4916	−0.471723
$819$	0.249141	0.00870567
$820$	−5.67418	−0.198151
$821$	16.3240	0.569712	0.284856	−	0.958570i	$-0.408054\pi$
$821$	16.3240	0.569712	0.284856	+	0.958570i	$0.408054\pi$
$822$	−10.3258	−0.360154
$823$	15.8061	0.550964	0.275482	−	0.961306i	$-0.411162\pi$
$823$	15.8061	0.550964	0.275482	+	0.961306i	$0.411162\pi$
$824$	6.27062	0.218448
$825$	1.00000	0.0348155
$826$	−1.42504	−0.0495835
$827$	−19.0846	−0.663637	−0.331819	−	0.943343i	$-0.607662\pi$
$827$	−19.0846	−0.663637	−0.331819	+	0.943343i	$0.607662\pi$
$828$	−6.61555	−0.229906
$829$	23.7294	0.824155	0.412078	−	0.911149i	$-0.364803\pi$
$829$	23.7294	0.824155	0.412078	+	0.911149i	$0.364803\pi$
$830$	0.519765	0.0180413
$831$	15.3224	0.531528
$832$	0.788009	0.0273193
$833$	1.22154	0.0423240
$834$	1.27406	0.0441172
$835$	1.29317	0.0447518
$836$	−3.26719	−0.112998
$837$	−7.80605	−0.269817
$838$	−2.50278	−0.0864570
$839$	0.196621	0.00678813	0.00339406	−	0.999994i	$-0.498920\pi$
$839$	0.196621	0.00678813	0.00339406	+	0.999994i	$0.498920\pi$
$840$	−1.77846	−0.0613626
$841$	−13.2473	−0.456804
$842$	11.0079	0.379358
$843$	17.6742	0.608731
$844$	22.8071	0.785053
$845$	−12.9379	−0.445078
$846$	−0.560352	−0.0192653
$847$	−1.00000	−0.0343604
$848$	36.4293	1.25099
$849$	−27.4182	−0.940989
$850$	0.574960	0.0197210
$851$	15.8061	0.541825
$852$	−7.34836	−0.251751
$853$	−30.3855	−1.04038	−0.520190	−	0.854051i	$-0.674139\pi$
$853$	−30.3855	−1.04038	−0.520190	+	0.854051i	$0.674139\pi$
$854$	−4.31121	−0.147527
$855$	−1.83709	−0.0628272
$856$	−16.7620	−0.572914
$857$	−20.4102	−0.697200	−0.348600	−	0.937272i	$-0.613343\pi$
$857$	−20.4102	−0.697200	−0.348600	+	0.937272i	$0.613343\pi$
$858$	−0.117266	−0.00400341
$859$	−16.0406	−0.547298	−0.273649	−	0.961830i	$-0.588231\pi$
$859$	−16.0406	−0.547298	−0.273649	+	0.961830i	$0.588231\pi$
$860$	−5.38445	−0.183608
$861$	3.19051	0.108732
$862$	−11.1138	−0.378538
$863$	−11.7198	−0.398947	−0.199474	−	0.979903i	$-0.563923\pi$
$863$	−11.7198	−0.398947	−0.199474	+	0.979903i	$0.563923\pi$
$864$	−4.83709	−0.164561
$865$	15.8207	0.537919
$866$	4.36191	0.148224
$867$	15.5078	0.526674
$868$	13.8827	0.471211
$869$	8.36641	0.283811
$870$	1.86813	0.0633354
$871$	−1.91195	−0.0647839
$872$	10.9053	0.369299
$873$	11.1449	0.377196
$874$	−3.21649	−0.108799
$875$	−1.00000	−0.0338062
$876$	−1.67418	−0.0565653
$877$	−23.5519	−0.795290	−0.397645	−	0.917539i	$-0.630172\pi$
$877$	−23.5519	−0.795290	−0.397645	+	0.917539i	$0.630172\pi$
$878$	9.83203	0.331815
$879$	−6.04564	−0.203914
$880$	−2.71982	−0.0916852
$881$	−51.4707	−1.73409	−0.867046	−	0.498229i	$-0.833984\pi$
$881$	−51.4707	−1.73409	−0.867046	+	0.498229i	$0.833984\pi$
$882$	0.470683	0.0158487
$883$	9.61899	0.323705	0.161852	−	0.986815i	$-0.448253\pi$
$883$	9.61899	0.323705	0.161852	+	0.986815i	$0.448253\pi$
$884$	0.541248	0.0182041
$885$	−3.02760	−0.101772
$886$	−14.6675	−0.492765
$887$	−16.8697	−0.566431	−0.283215	−	0.959056i	$-0.591401\pi$
$887$	−16.8697	−0.566431	−0.283215	+	0.959056i	$0.591401\pi$
$888$	7.55691	0.253593
$889$	10.5293	0.353142
$890$	2.47680	0.0830224
$891$	−1.00000	−0.0335013
$892$	7.26719	0.243323
$893$	2.18707	0.0731875
$894$	−5.41043	−0.180952
$895$	−8.13187	−0.271819
$896$	11.1629	0.372927
$897$	0.926759	0.0309436
$898$	−11.0777	−0.369669
$899$	−30.9820	−1.03331
$900$	−1.77846	−0.0592819
$901$	16.3614	0.545076
$902$	−1.50172	−0.0500018
$903$	3.02760	0.100752
$904$	13.8275	0.459897
$905$	9.11383	0.302954
$906$	5.96391	0.198138
$907$	43.2940	1.43755	0.718777	−	0.695240i	$-0.244702\pi$
$907$	43.2940	1.43755	0.718777	+	0.695240i	$0.244702\pi$
$908$	−22.7259	−0.754187
$909$	6.00000	0.199007
$910$	0.117266	0.00388734
$911$	−22.4914	−0.745174	−0.372587	−	0.927997i	$-0.621529\pi$
$911$	−22.4914	−0.745174	−0.372587	+	0.927997i	$0.621529\pi$
$912$	4.99656	0.165453
$913$	−1.10428	−0.0365462
$914$	−2.36641	−0.0782738
$915$	−9.15947	−0.302803
$916$	36.2086	1.19636
$917$	1.68879	0.0557687
$918$	−0.574960	−0.0189765
$919$	8.78113	0.289663	0.144831	−	0.989456i	$-0.453736\pi$
$919$	8.78113	0.289663	0.144831	+	0.989456i	$0.453736\pi$
$920$	−6.61555	−0.218108
$921$	−0.0620710	−0.00204531
$922$	−4.99333	−0.164446
$923$	1.02942	0.0338837
$924$	1.77846	0.0585069
$925$	4.24914	0.139711
$926$	4.84320	0.159158
$927$	−3.52588	−0.115805
$928$	−19.1982	−0.630213
$929$	−49.8950	−1.63700	−0.818500	−	0.574506i	$-0.805194\pi$
$929$	−49.8950	−1.63700	−0.818500	+	0.574506i	$0.805194\pi$
$930$	−3.67418	−0.120481
$931$	−1.83709	−0.0602082
$932$	0.553476	0.0181297
$933$	8.73281	0.285899
$934$	4.52750	0.148144
$935$	−1.22154	−0.0399487
$936$	0.443086	0.0144827
$937$	−44.7665	−1.46246	−0.731229	−	0.682132i	$-0.761053\pi$
$937$	−44.7665	−1.46246	−0.731229	+	0.682132i	$0.761053\pi$
$938$	−3.61211	−0.117940
$939$	−7.37940	−0.240818
$940$	2.11727	0.0690576
$941$	15.7509	0.513463	0.256732	−	0.966483i	$-0.417354\pi$
$941$	15.7509	0.513463	0.256732	+	0.966483i	$0.417354\pi$
$942$	−0.637031	−0.0207556
$943$	11.8681	0.386479
$944$	8.23453	0.268011
$945$	1.00000	0.0325300
$946$	−1.42504	−0.0463320
$947$	13.3388	0.433453	0.216727	−	0.976232i	$-0.430462\pi$
$947$	13.3388	0.433453	0.216727	+	0.976232i	$0.430462\pi$
$948$	−14.8793	−0.483257
$949$	0.234533	0.00761325
$950$	−0.864688	−0.0280542
$951$	−23.5569	−0.763885
$952$	2.17246	0.0704099
$953$	−29.8759	−0.967774	−0.483887	−	0.875130i	$-0.660775\pi$
$953$	−29.8759	−0.967774	−0.483887	+	0.875130i	$0.660775\pi$
$954$	6.30434	0.204110
$955$	−2.11727	−0.0685131
$956$	35.1950	1.13829
$957$	−3.96896	−0.128298
$958$	−10.8984	−0.352111
$959$	−21.9379	−0.708413
$960$	3.16291	0.102082
$961$	29.9345	0.965629
$962$	−0.498281	−0.0160652
$963$	9.42504	0.303718
$964$	−40.3189	−1.29859
$965$	−3.61899	−0.116499
$966$	1.75086	0.0563330
$967$	−34.4380	−1.10745	−0.553726	−	0.832699i	$-0.686795\pi$
$967$	−34.4380	−1.10745	−0.553726	+	0.832699i	$0.686795\pi$
$968$	−1.77846	−0.0571618
$969$	2.24408	0.0720904
$970$	5.24570	0.168429
$971$	−11.7604	−0.377410	−0.188705	−	0.982034i	$-0.560429\pi$
$971$	−11.7604	−0.377410	−0.188705	+	0.982034i	$0.560429\pi$
$972$	1.77846	0.0570440
$973$	2.70683	0.0867771
$974$	−0.915387	−0.0293309
$975$	0.249141	0.00797888
$976$	24.9122	0.797419
$977$	27.3871	0.876192	0.438096	−	0.898928i	$-0.355653\pi$
$977$	27.3871	0.876192	0.438096	+	0.898928i	$0.355653\pi$
$978$	10.7880	0.344962
$979$	−5.26213	−0.168178
$980$	−1.77846	−0.0568107
$981$	−6.13187	−0.195776
$982$	−1.99550	−0.0636791
$983$	56.7000	1.80845	0.904224	−	0.427059i	$-0.140450\pi$
$983$	56.7000	1.80845	0.904224	+	0.427059i	$0.140450\pi$
$984$	5.67418	0.180886
$985$	−8.05520	−0.256660
$986$	−2.28200	−0.0726735
$987$	−1.19051	−0.0378943
$988$	−0.813989	−0.0258964
$989$	11.2621	0.358115
$990$	−0.470683	−0.0149593
$991$	−9.94748	−0.315992	−0.157996	−	0.987440i	$-0.550503\pi$
$991$	−9.94748	−0.315992	−0.157996	+	0.987440i	$0.550503\pi$
$992$	37.7586	1.19884
$993$	1.01299	0.0321463
$994$	1.94480	0.0616855
$995$	−14.8793	−0.471705
$996$	1.96391	0.0622288
$997$	50.4553	1.59794	0.798968	−	0.601374i	$-0.205380\pi$
$997$	50.4553	1.59794	0.798968	+	0.601374i	$0.205380\pi$
$998$	18.5129	0.586015
$999$	−4.24914	−0.134437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.s.1.2	✓	3
3.2	odd	2		3465.2.a.bc.1.2		3
5.4	even	2		5775.2.a.br.1.2		3
7.6	odd	2		8085.2.a.bm.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.s.1.2	✓	3	1.1	even	1	trivial
3465.2.a.bc.1.2		3	3.2	odd	2
5775.2.a.br.1.2		3	5.4	even	2
8085.2.a.bm.1.2		3	7.6	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+0.470683 q^{2} -1.00000 q^{3} -1.77846 q^{4} +1.00000 q^{5} -0.470683 q^{6} -1.00000 q^{7} -1.77846 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.470683 q^{2} -1.00000 q^{3} -1.77846 q^{4} +1.00000 q^{5} -0.470683 q^{6} -1.00000 q^{7} -1.77846 q^{8} +1.00000 q^{9} +0.470683 q^{10} -1.00000 q^{11} +1.77846 q^{12} -0.249141 q^{13} -0.470683 q^{14} -1.00000 q^{15} +2.71982 q^{16} +1.22154 q^{17} +0.470683 q^{18} -1.83709 q^{19} -1.77846 q^{20} +1.00000 q^{21} -0.470683 q^{22} +3.71982 q^{23} +1.77846 q^{24} +1.00000 q^{25} -0.117266 q^{26} -1.00000 q^{27} +1.77846 q^{28} -3.96896 q^{29} -0.470683 q^{30} +7.80605 q^{31} +4.83709 q^{32} +1.00000 q^{33} +0.574960 q^{34} -1.00000 q^{35} -1.77846 q^{36} +4.24914 q^{37} -0.864688 q^{38} +0.249141 q^{39} -1.77846 q^{40} +3.19051 q^{41} +0.470683 q^{42} +3.02760 q^{43} +1.77846 q^{44} +1.00000 q^{45} +1.75086 q^{46} -1.19051 q^{47} -2.71982 q^{48} +1.00000 q^{49} +0.470683 q^{50} -1.22154 q^{51} +0.443086 q^{52} +13.3940 q^{53} -0.470683 q^{54} -1.00000 q^{55} +1.77846 q^{56} +1.83709 q^{57} -1.86813 q^{58} +3.02760 q^{59} +1.77846 q^{60} +9.15947 q^{61} +3.67418 q^{62} -1.00000 q^{63} -3.16291 q^{64} -0.249141 q^{65} +0.470683 q^{66} +7.67418 q^{67} -2.17246 q^{68} -3.71982 q^{69} -0.470683 q^{70} -4.13187 q^{71} -1.77846 q^{72} -0.941367 q^{73} +2.00000 q^{74} -1.00000 q^{75} +3.26719 q^{76} +1.00000 q^{77} +0.117266 q^{78} -8.36641 q^{79} +2.71982 q^{80} +1.00000 q^{81} +1.50172 q^{82} +1.10428 q^{83} -1.77846 q^{84} +1.22154 q^{85} +1.42504 q^{86} +3.96896 q^{87} +1.77846 q^{88} +5.26213 q^{89} +0.470683 q^{90} +0.249141 q^{91} -6.61555 q^{92} -7.80605 q^{93} -0.560352 q^{94} -1.83709 q^{95} -4.83709 q^{96} +11.1449 q^{97} +0.470683 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} - 3 q^{11} - 3 q^{12} + 8 q^{13} - q^{14} - 3 q^{15} - q^{16} + 12 q^{17} + q^{18} + 2 q^{19} + 3 q^{20} + 3 q^{21} - q^{22} + 2 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} + 6 q^{29} - q^{30} - 2 q^{31} + 7 q^{32} + 3 q^{33} + 8 q^{34} - 3 q^{35} + 3 q^{36} + 4 q^{37} + 22 q^{38} - 8 q^{39} + 3 q^{40} + q^{42} - 8 q^{43} - 3 q^{44} + 3 q^{45} + 14 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + q^{50} - 12 q^{51} + 18 q^{52} + 16 q^{53} - q^{54} - 3 q^{55} - 3 q^{56} - 2 q^{57} - 16 q^{58} - 8 q^{59} - 3 q^{60} - 4 q^{62} - 3 q^{63} - 17 q^{64} + 8 q^{65} + q^{66} + 8 q^{67} + 26 q^{68} - 2 q^{69} - q^{70} - 2 q^{71} + 3 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} + 24 q^{76} + 3 q^{77} + 2 q^{78} - 18 q^{79} - q^{80} + 3 q^{81} + 22 q^{82} + 10 q^{83} + 3 q^{84} + 12 q^{85} - 2 q^{86} - 6 q^{87} - 3 q^{88} + 2 q^{89} + q^{90} - 8 q^{91} - 4 q^{92} + 2 q^{93} - 20 q^{94} + 2 q^{95} - 7 q^{96} + 18 q^{97} + q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 + q^10 - 3 * q^11 - 3 * q^12 + 8 * q^13 - q^14 - 3 * q^15 - q^16 + 12 * q^17 + q^18 + 2 * q^19 + 3 * q^20 + 3 * q^21 - q^22 + 2 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 + 6 * q^29 - q^30 - 2 * q^31 + 7 * q^32 + 3 * q^33 + 8 * q^34 - 3 * q^35 + 3 * q^36 + 4 * q^37 + 22 * q^38 - 8 * q^39 + 3 * q^40 + q^42 - 8 * q^43 - 3 * q^44 + 3 * q^45 + 14 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + q^50 - 12 * q^51 + 18 * q^52 + 16 * q^53 - q^54 - 3 * q^55 - 3 * q^56 - 2 * q^57 - 16 * q^58 - 8 * q^59 - 3 * q^60 - 4 * q^62 - 3 * q^63 - 17 * q^64 + 8 * q^65 + q^66 + 8 * q^67 + 26 * q^68 - 2 * q^69 - q^70 - 2 * q^71 + 3 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 + 24 * q^76 + 3 * q^77 + 2 * q^78 - 18 * q^79 - q^80 + 3 * q^81 + 22 * q^82 + 10 * q^83 + 3 * q^84 + 12 * q^85 - 2 * q^86 - 6 * q^87 - 3 * q^88 + 2 * q^89 + q^90 - 8 * q^91 - 4 * q^92 + 2 * q^93 - 20 * q^94 + 2 * q^95 - 7 * q^96 + 18 * q^97 + q^98 - 3 * q^99

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