LMFDB - Embedded newform 567.2.v.b.505.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(64,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("567.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.v (of order $9$, degree $6$, not minimal)

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:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			505.5
Character	$\chi$	$=$	567.505
Dual form			567.2.v.b.64.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.252618 - 0.0919454i) q^{2} +(-1.47673 + 1.23912i) q^{4} +(-0.344603 - 1.95434i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-0.527947 + 0.914430i) q^{8} +O(q^{10})$	\(q+(0.252618 - 0.0919454i) q^{2} +(-1.47673 + 1.23912i) q^{4} +(-0.344603 - 1.95434i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-0.527947 + 0.914430i) q^{8} +(-0.266746 - 0.462017i) q^{10} +(0.738567 - 4.18862i) q^{11} +(0.102794 + 0.0374138i) q^{13} +(0.252618 + 0.0919454i) q^{14} +(0.620203 - 3.51734i) q^{16} +(0.533740 + 0.924465i) q^{17} +(3.21121 - 5.56198i) q^{19} +(2.93055 + 2.45902i) q^{20} +(-0.198549 - 1.12603i) q^{22} +(-0.0548097 + 0.0459908i) q^{23} +(0.997769 - 0.363158i) q^{25} +0.0294076 q^{26} -1.92773 q^{28} +(6.83162 - 2.48651i) q^{29} +(-2.06194 + 1.73017i) q^{31} +(-0.533437 - 3.02527i) q^{32} +(0.219833 + 0.184462i) q^{34} +(0.992245 - 1.71862i) q^{35} +(-4.73896 - 8.20813i) q^{37} +(0.299811 - 1.70031i) q^{38} +(1.96904 + 0.716672i) q^{40} +(-2.91868 - 1.06231i) q^{41} +(1.13791 - 6.45340i) q^{43} +(4.09955 + 7.10062i) q^{44} +(-0.00961727 + 0.0166576i) q^{46} +(8.52509 + 7.15340i) q^{47} +(0.173648 + 0.984808i) q^{49} +(0.218664 - 0.183480i) q^{50} +(-0.198158 + 0.0721238i) q^{52} -6.12296 q^{53} -8.44050 q^{55} +(-0.992215 + 0.361137i) q^{56} +(1.49717 - 1.25627i) q^{58} +(-0.933327 - 5.29316i) q^{59} +(3.60454 + 3.02457i) q^{61} +(-0.361801 + 0.626658i) q^{62} +(3.15869 + 5.47101i) q^{64} +(0.0376964 - 0.213787i) q^{65} +(-4.91604 - 1.78929i) q^{67} +(-1.93371 - 0.703814i) q^{68} +(0.0926397 - 0.525386i) q^{70} +(5.76503 + 9.98533i) q^{71} +(-6.92342 + 11.9917i) q^{73} +(-1.95185 - 1.63779i) q^{74} +(2.14989 + 12.1926i) q^{76} +(3.25817 - 2.73393i) q^{77} +(7.78358 - 2.83299i) q^{79} -7.08781 q^{80} -0.834985 q^{82} +(-15.2906 + 5.56533i) q^{83} +(1.62279 - 1.36168i) q^{85} +(-0.305904 - 1.73487i) q^{86} +(3.44028 + 2.88674i) q^{88} +(5.29946 - 9.17893i) q^{89} +(0.0546954 + 0.0947352i) q^{91} +(0.0239508 - 0.135832i) q^{92} +(2.81131 + 1.02323i) q^{94} +(-11.9766 - 4.35913i) q^{95} +(0.306285 - 1.73703i) q^{97} +(0.134415 + 0.232814i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) $ 54 * q + 3 * q^5 + 27 * q^8	$ 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) $ 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.252618	−	0.0919454i	0.178628	−	0.0650152i	−0.251158	−	0.967946i	$-0.580811\pi$
$2$	0.252618	−	0.0919454i	0.178628	−	0.0650152i	0.429786	+	0.902931i	$0.358589\pi$
$3$		0			0
$3$		0			0
$4$	−1.47673	+	1.23912i	−0.738364	+	0.619561i
$5$	−0.344603	−	1.95434i	−0.154111	−	0.874008i	−0.959594	−	0.281388i	$-0.909205\pi$
$5$	−0.344603	−	1.95434i	−0.154111	−	0.874008i	0.805483	−	0.592619i	$-0.201906\pi$
$6$		0			0
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$7$	0.766044	+	0.642788i	0.289538	+	0.242951i
$8$	−0.527947	+	0.914430i	−0.186657	+	0.323300i
$9$		0			0
$10$	−0.266746	−	0.462017i	−0.0843523	−	0.146103i
$11$	0.738567	−	4.18862i	0.222686	−	1.26292i	−0.644373	−	0.764712i	$-0.722881\pi$
$11$	0.738567	−	4.18862i	0.222686	−	1.26292i	0.867059	−	0.498205i	$-0.166007\pi$
$12$		0			0
$13$	0.102794	+	0.0374138i	0.0285098	+	0.0103767i	0.356236	−	0.934396i	$-0.384060\pi$
$13$	0.102794	+	0.0374138i	0.0285098	+	0.0103767i	−0.327726	+	0.944773i	$0.606282\pi$
$14$	0.252618	+	0.0919454i	0.0675150	+	0.0245734i
$15$		0			0
$16$	0.620203	−	3.51734i	0.155051	−	0.879336i
$17$	0.533740	+	0.924465i	0.129451	+	0.224216i	0.923464	−	0.383685i	$-0.125345\pi$
$17$	0.533740	+	0.924465i	0.129451	+	0.224216i	−0.794013	+	0.607901i	$0.792012\pi$
$18$		0			0
$19$	3.21121	−	5.56198i	0.736703	−	1.27601i	−0.217270	−	0.976112i	$-0.569715\pi$
$19$	3.21121	−	5.56198i	0.736703	−	1.27601i	0.953972	−	0.299895i	$-0.0969516\pi$
$20$	2.93055	+	2.45902i	0.655291	+	0.549854i
$21$		0			0
$22$	−0.198549	−	1.12603i	−0.0423308	−	0.240070i
$23$	−0.0548097	+	0.0459908i	−0.0114286	+	0.00958974i	−0.648484	−	0.761228i	$-0.724597\pi$
$23$	−0.0548097	+	0.0459908i	−0.0114286	+	0.00958974i	0.637055	+	0.770818i	$0.280152\pi$
$24$		0			0
$25$	0.997769	−	0.363158i	0.199554	−	0.0726316i
$26$	0.0294076			0.00576730
$27$		0			0
$28$	−1.92773			−0.364307
$29$	6.83162	−	2.48651i	1.26860	−	0.461733i	0.381954	−	0.924181i	$-0.375251\pi$
$29$	6.83162	−	2.48651i	1.26860	−	0.461733i	0.886646	+	0.462449i	$0.153029\pi$
$30$		0			0
$31$	−2.06194	+	1.73017i	−0.370335	+	0.310748i	−0.808894	−	0.587955i	$-0.799933\pi$
$31$	−2.06194	+	1.73017i	−0.370335	+	0.310748i	0.438559	+	0.898702i	$0.355489\pi$
$32$	−0.533437	−	3.02527i	−0.0942993	−	0.534798i
$33$		0			0
$34$	0.219833	+	0.184462i	0.0377010	+	0.0316349i
$35$	0.992245	−	1.71862i	0.167720	−	0.290499i
$36$		0			0
$37$	−4.73896	−	8.20813i	−0.779081	−	1.34941i	−0.932472	−	0.361242i	$-0.882353\pi$
$37$	−4.73896	−	8.20813i	−0.779081	−	1.34941i	0.153391	−	0.988166i	$-0.450981\pi$
$38$	0.299811	−	1.70031i	0.0486358	−	0.275827i
$39$		0			0
$40$	1.96904	+	0.716672i	0.311333	+	0.113316i
$41$	−2.91868	−	1.06231i	−0.455821	−	0.165905i	0.103898	−	0.994588i	$-0.466869\pi$
$41$	−2.91868	−	1.06231i	−0.455821	−	0.165905i	−0.559719	+	0.828683i	$0.689091\pi$
$42$		0			0
$43$	1.13791	−	6.45340i	0.173529	−	0.984134i	−0.766298	−	0.642485i	$-0.777903\pi$
$43$	1.13791	−	6.45340i	0.173529	−	0.984134i	0.939828	−	0.341649i	$-0.110985\pi$
$44$	4.09955	+	7.10062i	0.618030	+	1.07046i
$45$		0			0
$46$	−0.00961727	+	0.0166576i	−0.00141799	+	0.00245603i
$47$	8.52509	+	7.15340i	1.24351	+	1.04343i	0.997241	+	0.0742300i	$0.0236499\pi$
$47$	8.52509	+	7.15340i	1.24351	+	1.04343i	0.246271	+	0.969201i	$0.420795\pi$
$48$		0			0
$49$	0.173648	+	0.984808i	0.0248069	+	0.140687i
$50$	0.218664	−	0.183480i	0.0309237	−	0.0259481i
$51$		0			0
$52$	−0.198158	+	0.0721238i	−0.0274796	+	0.0100018i
$53$	−6.12296			−0.841053			−0.420526	−	0.907280i	$-0.638155\pi$
$53$	−6.12296			−0.841053			−0.420526	+	0.907280i	$0.638155\pi$
$54$		0			0
$55$	−8.44050			−1.13812
$56$	−0.992215	+	0.361137i	−0.132590	+	0.0482589i
$57$		0			0
$58$	1.49717	−	1.25627i	0.196588	−	0.164957i
$59$	−0.933327	−	5.29316i	−0.121509	−	0.689111i	−0.983320	−	0.181882i	$-0.941781\pi$
$59$	−0.933327	−	5.29316i	−0.121509	−	0.689111i	0.861811	−	0.507229i	$-0.169330\pi$
$60$		0			0
$61$	3.60454	+	3.02457i	0.461514	+	0.387256i	0.843688	−	0.536834i	$-0.180380\pi$
$61$	3.60454	+	3.02457i	0.461514	+	0.387256i	−0.382174	+	0.924091i	$0.624824\pi$
$62$	−0.361801	+	0.626658i	−0.0459488	+	0.0795856i
$63$		0			0
$64$	3.15869	+	5.47101i	0.394836	+	0.683876i
$65$	0.0376964	−	0.213787i	0.00467566	−	0.0265170i
$66$		0			0
$67$	−4.91604	−	1.78929i	−0.600589	−	0.218597i	0.0237912	−	0.999717i	$-0.492426\pi$
$67$	−4.91604	−	1.78929i	−0.600589	−	0.218597i	−0.624381	+	0.781120i	$0.714649\pi$
$68$	−1.93371	−	0.703814i	−0.234497	−	0.0853500i
$69$		0			0
$70$	0.0926397	−	0.525386i	0.0110726	−	0.0627956i
$71$	5.76503	+	9.98533i	0.684184	+	1.18504i	0.973693	+	0.227866i	$0.0731747\pi$
$71$	5.76503	+	9.98533i	0.684184	+	1.18504i	−0.289509	+	0.957175i	$0.593492\pi$
$72$		0			0
$73$	−6.92342	+	11.9917i	−0.810325	+	1.40352i	0.102311	+	0.994752i	$0.467376\pi$
$73$	−6.92342	+	11.9917i	−0.810325	+	1.40352i	−0.912637	+	0.408772i	$0.865957\pi$
$74$	−1.95185	−	1.63779i	−0.226898	−	0.190390i
$75$		0			0
$76$	2.14989	+	12.1926i	0.246609	+	1.39859i
$77$	3.25817	−	2.73393i	0.371303	−	0.311560i
$78$		0			0
$79$	7.78358	−	2.83299i	0.875721	−	0.318736i	0.135239	−	0.990813i	$-0.456820\pi$
$79$	7.78358	−	2.83299i	0.875721	−	0.318736i	0.740482	+	0.672077i	$0.234597\pi$
$80$	−7.08781			−0.792441
$81$		0			0
$82$	−0.834985			−0.0922087
$83$	−15.2906	+	5.56533i	−1.67836	+	0.610874i	−0.993084	−	0.117407i	$-0.962542\pi$
$83$	−15.2906	+	5.56533i	−1.67836	+	0.610874i	−0.685279	+	0.728281i	$0.740320\pi$
$84$		0			0
$85$	1.62279	−	1.36168i	0.176016	−	0.147695i
$86$	−0.305904	−	1.73487i	−0.0329865	−	0.187076i
$87$		0			0
$88$	3.44028	+	2.88674i	0.366735	+	0.307727i
$89$	5.29946	−	9.17893i	0.561741	−	0.972965i	−0.435603	−	0.900139i	$-0.643465\pi$
$89$	5.29946	−	9.17893i	0.561741	−	0.972965i	0.997345	−	0.0728258i	$-0.0232017\pi$
$90$		0			0
$91$	0.0546954	+	0.0947352i	0.00573363	+	0.00993094i
$92$	0.0239508	−	0.135832i	0.00249704	−	0.0141614i
$93$		0			0
$94$	2.81131	+	1.02323i	0.289965	+	0.105539i
$95$	−11.9766	−	4.35913i	−1.22877	−	0.447237i
$96$		0			0
$97$	0.306285	−	1.73703i	0.0310985	−	0.176369i	−0.965302	−	0.261135i	$-0.915903\pi$
$97$	0.306285	−	1.73703i	0.0310985	−	0.176369i	0.996401	+	0.0847663i	$0.0270144\pi$
$98$	0.134415	+	0.232814i	0.0135780	+	0.0235178i
$99$		0			0
$100$	−1.02343	+	1.77264i	−0.102343	+	0.177264i
$101$	−5.56107	−	4.66630i	−0.553348	−	0.464314i	0.322725	−	0.946493i	$-0.395401\pi$
$101$	−5.56107	−	4.66630i	−0.553348	−	0.464314i	−0.876073	+	0.482179i	$0.839845\pi$
$102$		0			0
$103$	2.81426	+	15.9605i	0.277298	+	1.57263i	0.731568	+	0.681769i	$0.238789\pi$
$103$	2.81426	+	15.9605i	0.277298	+	1.57263i	−0.454270	+	0.890864i	$0.650100\pi$
$104$	−0.0884819	+	0.0742452i	−0.00867637	+	0.00728034i
$105$		0			0
$106$	−1.54677	+	0.562978i	−0.150235	+	0.0546812i
$107$	−7.58438			−0.733210			−0.366605	−	0.930377i	$-0.619480\pi$
$107$	−7.58438			−0.733210			−0.366605	+	0.930377i	$0.619480\pi$
$108$		0			0
$109$	−4.68262			−0.448513			−0.224257	−	0.974530i	$-0.571995\pi$
$109$	−4.68262			−0.448513			−0.224257	+	0.974530i	$0.571995\pi$
$110$	−2.13222	+	0.776066i	−0.203299	+	0.0739950i
$111$		0			0
$112$	2.73601	−	2.29578i	0.258528	−	0.216931i
$113$	0.585502	+	3.32055i	0.0550794	+	0.312371i	0.999883	−	0.0152651i	$-0.00485922\pi$
$113$	0.585502	+	3.32055i	0.0550794	+	0.312371i	−0.944804	+	0.327636i	$0.893748\pi$
$114$		0			0
$115$	0.108769	+	0.0912682i	0.0101428	+	0.00851081i
$116$	−7.00736	+	12.1371i	−0.650617	+	1.12690i
$117$		0			0
$118$	−0.722457	−	1.25133i	−0.0665076	−	0.115194i
$119$	−0.185366	+	1.05126i	−0.0169925	+	0.0963691i
$120$		0			0
$121$	−6.66245	−	2.42493i	−0.605677	−	0.220449i
$122$	1.18867	+	0.432639i	0.107617	+	0.0391693i
$123$		0			0
$124$	0.901027	−	5.10998i	0.0809146	−	0.458890i
$125$	−6.01479	−	10.4179i	−0.537979	−	0.931807i
$126$		0			0
$127$	4.50609	−	7.80478i	0.399851	−	0.692563i	−0.593856	−	0.804571i	$-0.702395\pi$
$127$	4.50609	−	7.80478i	0.399851	−	0.692563i	0.993707	+	0.112009i	$0.0357285\pi$
$128$	6.00746	+	5.04086i	0.530990	+	0.445553i
$129$		0			0
$130$	−0.0101339	−	0.0574724i	−0.000888805	−	0.00504066i
$131$	−5.66050	+	4.74972i	−0.494560	+	0.414985i	−0.855657	−	0.517543i	$-0.826847\pi$
$131$	−5.66050	+	4.74972i	−0.494560	+	0.414985i	0.361097	+	0.932528i	$0.382402\pi$
$132$		0			0
$133$	6.03510	−	2.19660i	0.523310	−	0.190469i
$134$	−1.40640			−0.121494
$135$		0			0
$136$	−1.12715			−0.0966519
$137$	15.2566	−	5.55297i	1.30346	−	0.474422i	0.405340	−	0.914166i	$-0.367153\pi$
$137$	15.2566	−	5.55297i	1.30346	−	0.474422i	0.898123	+	0.439744i	$0.144931\pi$
$138$		0			0
$139$	−5.62840	+	4.72279i	−0.477395	+	0.400582i	−0.849483	−	0.527615i	$-0.823086\pi$
$139$	−5.62840	+	4.72279i	−0.477395	+	0.400582i	0.372088	+	0.928197i	$0.378642\pi$
$140$	0.664301	+	3.76744i	0.0561437	+	0.318407i
$141$		0			0
$142$	2.37446	+	1.99241i	0.199260	+	0.167199i
$143$	0.232632	−	0.402931i	0.0194537	−	0.0336948i
$144$		0			0
$145$	−7.21368	−	12.4945i	−0.599063	−	1.03761i
$146$	−0.646397	+	3.66590i	−0.0534962	+	0.303392i
$147$		0			0
$148$	17.1690	+	6.24901i	1.41128	+	0.513666i
$149$	15.4400	+	5.61969i	1.26489	+	0.460383i	0.885408	−	0.464815i	$-0.153879\pi$
$149$	15.4400	+	5.61969i	1.26489	+	0.460383i	0.379484	+	0.925198i	$0.376102\pi$
$150$		0			0
$151$	−3.69759	+	20.9701i	−0.300906	+	1.70652i	0.341271	+	0.939965i	$0.389143\pi$
$151$	−3.69759	+	20.9701i	−0.300906	+	1.70652i	−0.642177	+	0.766557i	$0.721968\pi$
$152$	3.39070	+	5.87286i	0.275022	+	0.476352i
$153$		0			0
$154$	0.571700	−	0.990213i	0.0460689	−	0.0797937i
$155$	4.09189	+	3.43350i	0.328669	+	0.275786i
$156$		0			0
$157$	−0.840807	−	4.76845i	−0.0671037	−	0.380564i	−0.999802	−	0.0199061i	$-0.993663\pi$
$157$	−0.840807	−	4.76845i	−0.0671037	−	0.380564i	0.932698	−	0.360658i	$-0.117448\pi$
$158$	1.70579	−	1.43133i	0.135705	−	0.113870i
$159$		0			0
$160$	−5.72859	+	2.08504i	−0.452885	+	0.164837i
$161$	−0.0715490			−0.00563885
$162$		0			0
$163$	17.1250			1.34133			0.670665	−	0.741760i	$-0.266009\pi$
$163$	17.1250			1.34133			0.670665	+	0.741760i	$0.266009\pi$
$164$	5.62642	−	2.04785i	0.439350	−	0.159910i
$165$		0			0
$166$	−3.35098	+	2.81180i	−0.260086	+	0.218238i
$167$	0.441094	+	2.50157i	0.0341329	+	0.193577i	0.997106	−	0.0760189i	$-0.0242209\pi$
$167$	0.441094	+	2.50157i	0.0341329	+	0.193577i	−0.962974	+	0.269596i	$0.913110\pi$
$168$		0			0
$169$	−9.94941	−	8.34855i	−0.765339	−	0.642196i
$170$	0.284746	−	0.493194i	0.0218390	−	0.0378262i
$171$		0			0
$172$	6.31616	+	10.9399i	0.481603	+	0.834161i
$173$	2.04893	−	11.6201i	0.155777	−	0.883457i	−0.802294	−	0.596928i	$-0.796388\pi$
$173$	2.04893	−	11.6201i	0.155777	−	0.883457i	0.958072	−	0.286528i	$-0.0925013\pi$
$174$		0			0
$175$	0.997769	+	0.363158i	0.0754242	+	0.0274522i
$176$	−14.2748	−	5.19559i	−1.07600	−	0.391632i
$177$		0			0
$178$	0.494778	−	2.80602i	0.0370851	−	0.210320i
$179$	11.5564	+	20.0163i	0.863766	+	1.49609i	0.868267	+	0.496097i	$0.165234\pi$
$179$	11.5564	+	20.0163i	0.863766	+	1.49609i	−0.00450080	+	0.999990i	$0.501433\pi$
$180$		0			0
$181$	−6.64660	+	11.5122i	−0.494038	+	0.855699i	−0.999976	−	0.00687081i	$-0.997813\pi$
$181$	−6.64660	+	11.5122i	−0.494038	+	0.855699i	0.505938	+	0.862570i	$0.331146\pi$
$182$	0.0225275	+	0.0189028i	0.00166985	+	0.00140117i
$183$		0			0
$184$	−0.0131188	−	0.0744003i	−0.000967130	−	0.00548487i
$185$	−14.4084	+	12.0901i	−1.05933	+	0.888881i
$186$		0			0
$187$	4.26644	−	1.55286i	0.311993	−	0.113556i
$188$	−21.4532			−1.56463
$189$		0			0
$190$	−3.42631			−0.248570
$191$	5.30959	−	1.93253i	0.384188	−	0.139833i	−0.142704	−	0.989765i	$-0.545580\pi$
$191$	5.30959	−	1.93253i	0.384188	−	0.139833i	0.526892	+	0.849932i	$0.323357\pi$
$192$		0			0
$193$	−9.19450	+	7.71510i	−0.661835	+	0.555345i	−0.910636	−	0.413209i	$-0.864408\pi$
$193$	−9.19450	+	7.71510i	−0.661835	+	0.555345i	0.248801	+	0.968555i	$0.419963\pi$
$194$	−0.0823388	−	0.466966i	−0.00591158	−	0.0335262i
$195$		0			0
$196$	−1.47673	−	1.23912i	−0.105481	−	0.0885086i
$197$	10.5793	−	18.3238i	0.753742	−	1.30552i	−0.192255	−	0.981345i	$-0.561580\pi$
$197$	10.5793	−	18.3238i	0.753742	−	1.30552i	0.945997	−	0.324174i	$-0.105086\pi$
$198$		0			0
$199$	−2.46259	−	4.26534i	−0.174569	−	0.302362i	0.765443	−	0.643503i	$-0.222520\pi$
$199$	−2.46259	−	4.26534i	−0.174569	−	0.302362i	−0.940012	+	0.341142i	$0.889186\pi$
$200$	−0.194686	+	1.10412i	−0.0137664	+	0.0780729i
$201$		0			0
$202$	−1.83387	−	0.667475i	−0.129031	−	0.0469634i
$203$	6.83162	+	2.48651i	0.479486	+	0.174519i
$204$		0			0
$205$	−1.07033	+	6.07017i	−0.0747554	+	0.423959i
$206$	2.17843	+	3.77314i	0.151778	+	0.262887i
$207$		0			0
$208$	0.195350	−	0.338357i	0.0135451	−	0.0234608i
$209$	−20.9253	−	17.5584i	−1.44744	−	1.21454i
$210$		0			0
$211$	−3.39895	−	19.2764i	−0.233994	−	1.32704i	−0.844723	−	0.535204i	$-0.820235\pi$
$211$	−3.39895	−	19.2764i	−0.233994	−	1.32704i	0.610729	−	0.791840i	$-0.290876\pi$
$212$	9.04194	−	7.58709i	0.621003	−	0.521083i
$213$		0			0
$214$	−1.91595	+	0.697349i	−0.130972	+	0.0476698i
$215$	−13.0043			−0.886883
$216$		0			0
$217$	−2.69167			−0.182722
$218$	−1.18291	+	0.430545i	−0.0801170	+	0.0291602i
$219$		0			0
$220$	12.4643	−	10.4588i	0.840344	−	0.705133i
$221$	0.0202773	+	0.114998i	0.00136400	+	0.00773563i
$222$		0			0
$223$	−1.97273	−	1.65532i	−0.132104	−	0.110848i	0.574342	−	0.818616i	$-0.305258\pi$
$223$	−1.97273	−	1.65532i	−0.132104	−	0.110848i	−0.706446	+	0.707767i	$0.749703\pi$
$224$	1.53597	−	2.66038i	0.102626	−	0.177754i
$225$		0			0
$226$	0.453217	+	0.784995i	0.0301476	+	0.0522171i
$227$	−3.15566	+	17.8967i	−0.209449	+	1.18784i	0.680835	+	0.732437i	$0.261617\pi$
$227$	−3.15566	+	17.8967i	−0.209449	+	1.18784i	−0.890284	+	0.455406i	$0.849494\pi$
$228$		0			0
$229$	−22.2811	−	8.10966i	−1.47238	−	0.535902i	−0.523632	−	0.851944i	$-0.675423\pi$
$229$	−22.2811	−	8.10966i	−1.47238	−	0.535902i	−0.948745	+	0.316043i	$0.897646\pi$
$230$	0.0358688	+	0.0130552i	0.00236512	+	0.000860832i
$231$		0			0
$232$	−1.33299	+	7.55979i	−0.0875153	+	0.496324i
$233$	4.81550	+	8.34069i	0.315474	+	0.546417i	0.979538	−	0.201259i	$-0.0645032\pi$
$233$	4.81550	+	8.34069i	0.315474	+	0.546417i	−0.664064	+	0.747676i	$0.731170\pi$
$234$		0			0
$235$	11.0424	−	19.1260i	0.720327	−	1.24764i
$236$	7.93714	+	6.66005i	0.516664	+	0.433532i
$237$		0			0
$238$	0.0498320	+	0.282611i	0.00323013	+	0.0183190i
$239$	7.66286	−	6.42990i	0.495669	−	0.415916i	−0.360384	−	0.932804i	$-0.617354\pi$
$239$	7.66286	−	6.42990i	0.495669	−	0.415916i	0.856053	+	0.516888i	$0.172910\pi$
$240$		0			0
$241$	−1.59677	+	0.581175i	−0.102857	+	0.0374368i	−0.392936	−	0.919566i	$-0.628541\pi$
$241$	−1.59677	+	0.581175i	−0.102857	+	0.0374368i	0.290079	+	0.957003i	$0.406318\pi$
$242$	−1.90602			−0.122523
$243$		0			0
$244$	−9.07073			−0.580694
$245$	1.86481	−	0.678735i	0.119138	−	0.0433628i
$246$		0			0
$247$	0.538187	−	0.451593i	0.0342440	−	0.0287342i
$248$	−0.493528	−	2.79893i	−0.0313390	−	0.177733i
$249$		0			0
$250$	−2.47732	−	2.07872i	−0.156680	−	0.131470i
$251$	10.6265	−	18.4057i	0.670740	−	1.16176i	−0.306954	−	0.951724i	$-0.599310\pi$
$251$	10.6265	−	18.4057i	0.670740	−	1.16176i	0.977695	−	0.210032i	$-0.0673568\pi$
$252$		0			0
$253$	0.152157	+	0.263544i	0.00956605	+	0.0165689i
$254$	0.420706	−	2.38594i	0.0263975	−	0.149707i
$255$		0			0
$256$	−9.89171	−	3.60029i	−0.618232	−	0.225018i
$257$	4.46924	+	1.62667i	0.278783	+	0.101469i	0.477628	−	0.878562i	$-0.341497\pi$
$257$	4.46924	+	1.62667i	0.278783	+	0.101469i	−0.198845	+	0.980031i	$0.563719\pi$
$258$		0			0
$259$	1.64582	−	9.33394i	0.102267	−	0.579983i
$260$	0.209240	+	0.362415i	0.0129765	+	0.0224760i
$261$		0			0
$262$	−0.993229	+	1.72032i	−0.0613619	+	0.106282i
$263$	−0.0349080	−	0.0292913i	−0.00215252	−	0.00180618i	0.641711	−	0.766947i	$-0.278225\pi$
$263$	−0.0349080	−	0.0292913i	−0.00215252	−	0.00180618i	−0.643863	+	0.765141i	$0.722669\pi$
$264$		0			0
$265$	2.10999	+	11.9663i	0.129616	+	0.735087i
$266$	1.32261	−	1.10980i	0.0810943	−	0.0680462i
$267$		0			0
$268$	9.47679	−	3.44927i	0.578887	−	0.210698i
$269$	3.67995			0.224371			0.112185	−	0.993687i	$-0.464215\pi$
$269$	3.67995			0.224371			0.112185	+	0.993687i	$0.464215\pi$
$270$		0			0
$271$	21.3658			1.29788			0.648939	−	0.760841i	$-0.275213\pi$
$271$	21.3658			1.29788			0.648939	+	0.760841i	$0.275213\pi$
$272$	3.58269	−	1.30399i	0.217232	−	0.0790661i
$273$		0			0
$274$	3.34353	−	2.80556i	0.201990	−	0.169490i
$275$	−0.784213	−	4.44749i	−0.0472898	−	0.268194i
$276$		0			0
$277$	11.3697	+	9.54029i	0.683138	+	0.573221i	0.916921	−	0.399068i	$-0.130666\pi$
$277$	11.3697	+	9.54029i	0.683138	+	0.573221i	−0.233784	+	0.972289i	$0.575111\pi$
$278$	−0.987597	+	1.71057i	−0.0592321	+	0.102593i
$279$		0			0
$280$	1.04770	+	1.81468i	0.0626123	+	0.108448i
$281$	1.06190	−	6.02235i	0.0633479	−	0.359264i	−0.936613	−	0.350367i	$-0.886057\pi$
$281$	1.06190	−	6.02235i	0.0633479	−	0.359264i	0.999960	−	0.00889673i	$-0.00283195\pi$
$282$		0			0
$283$	15.1906	+	5.52891i	0.902985	+	0.328660i	0.751448	−	0.659792i	$-0.229356\pi$
$283$	15.1906	+	5.52891i	0.902985	+	0.328660i	0.151537	+	0.988452i	$0.451578\pi$
$284$	−20.8864	−	7.60204i	−1.23938	−	0.451098i
$285$		0			0
$286$	0.0217195	−	0.123177i	0.00128430	−	0.00728362i
$287$	−1.55300	−	2.68987i	−0.0916705	−	0.158778i
$288$		0			0
$289$	7.93024	−	13.7356i	0.466485	−	0.807975i
$290$	−2.97111	−	2.49306i	−0.174470	−	0.146397i
$291$		0			0
$292$	−4.63519	−	26.2874i	−0.271254	−	1.53836i
$293$	6.34637	−	5.32524i	0.370759	−	0.311104i	−0.438303	−	0.898827i	$-0.644420\pi$
$293$	6.34637	−	5.32524i	0.370759	−	0.311104i	0.809062	+	0.587724i	$0.199976\pi$
$294$		0			0
$295$	−10.0230	+	3.64808i	−0.583562	+	0.212399i
$296$	10.0077			0.581685
$297$		0			0
$298$	4.41712			0.255877
$299$	−0.00735478	+	0.00267692i	−0.000425338	+	0.000154810i
$300$		0			0
$301$	5.01985	−	4.21216i	0.289340	−	0.242785i
$302$	0.994025	+	5.63740i	0.0571997	+	0.324396i
$303$		0			0
$304$	−17.5718	−	14.7445i	−1.00781	−	0.845655i
$305$	4.66890	−	8.08677i	0.267341	−	0.463047i
$306$		0			0
$307$	12.6563	+	21.9214i	0.722336	+	1.25112i	0.960061	+	0.279790i	$0.0902649\pi$
$307$	12.6563	+	21.9214i	0.722336	+	1.25112i	−0.237725	+	0.971332i	$0.576402\pi$
$308$	−1.42376	+	8.07453i	−0.0811261	+	0.460089i
$309$		0			0
$310$	1.34938	+	0.491134i	0.0766396	+	0.0278945i
$311$	31.2575	+	11.3768i	1.77245	+	0.645118i	0.999949	+	0.0101028i	$0.00321589\pi$
$311$	31.2575	+	11.3768i	1.77245	+	0.645118i	0.772499	+	0.635016i	$0.219006\pi$
$312$		0			0
$313$	−2.34226	+	13.2836i	−0.132392	+	0.750835i	0.844248	+	0.535953i	$0.180048\pi$
$313$	−2.34226	+	13.2836i	−0.132392	+	0.750835i	−0.976640	+	0.214882i	$0.931063\pi$
$314$	−0.650840	−	1.12729i	−0.0367291	−	0.0636166i
$315$		0			0
$316$	−7.98380	+	13.8283i	−0.449124	+	0.777905i
$317$	−23.3442	−	19.5881i	−1.31114	−	1.10018i	−0.988104	−	0.153788i	$-0.950853\pi$
$317$	−23.3442	−	19.5881i	−1.31114	−	1.10018i	−0.323034	−	0.946387i	$-0.604703\pi$
$318$		0			0
$319$	−5.36943	−	30.4515i	−0.300630	−	1.70496i
$320$	9.60372	−	8.05848i	0.536864	−	0.450483i
$321$		0			0
$322$	−0.0180746	+	0.00657860i	−0.00100726	+	0.000366611i
$323$	6.85581			0.381468
$324$		0			0
$325$	0.116151			0.00644292
$326$	4.32607	−	1.57456i	0.239599	−	0.0872069i
$327$		0			0
$328$	2.51232	−	2.10808i	0.138719	−	0.116399i
$329$	1.93248	+	10.9596i	0.106541	+	0.604225i
$330$		0			0
$331$	−3.07944	−	2.58395i	−0.169261	−	0.142027i	0.554222	−	0.832369i	$-0.313016\pi$
$331$	−3.07944	−	2.58395i	−0.169261	−	0.142027i	−0.723483	+	0.690342i	$0.757460\pi$
$332$	15.6839	−	27.1654i	0.860768	−	1.49089i
$333$		0			0
$334$	0.341436	+	0.591384i	0.0186825	+	0.0323591i
$335$	−1.80280	+	10.2242i	−0.0984976	+	0.558608i
$336$		0			0
$337$	11.1414	+	4.05515i	0.606912	+	0.220898i	0.627152	−	0.778897i	$-0.284221\pi$
$337$	11.1414	+	4.05515i	0.606912	+	0.220898i	−0.0202394	+	0.999795i	$0.506443\pi$
$338$	−3.28101	−	1.19419i	−0.178463	−	0.0649554i
$339$		0			0
$340$	−0.709129	+	4.02167i	−0.0384579	+	0.218106i
$341$	5.72415	+	9.91452i	0.309980	+	0.536901i
$342$		0			0
$343$	−0.500000	+	0.866025i	−0.0269975	+	0.0467610i
$344$	5.30043	+	4.44759i	0.285780	+	0.239798i
$345$		0			0
$346$	−0.550815	−	3.12383i	−0.0296120	−	0.167938i
$347$	−7.87729	+	6.60983i	−0.422875	+	0.354834i	−0.829255	−	0.558870i	$-0.811235\pi$
$347$	−7.87729	+	6.60983i	−0.422875	+	0.354834i	0.406381	+	0.913704i	$0.366791\pi$
$348$		0			0
$349$	−4.01781	+	1.46236i	−0.215069	+	0.0782786i	−0.447308	−	0.894380i	$-0.647617\pi$
$349$	−4.01781	+	1.46236i	−0.215069	+	0.0782786i	0.232239	+	0.972659i	$0.425395\pi$
$350$	0.285445			0.0152577
$351$		0			0
$352$	−13.0657			−0.696404
$353$	−24.8052	+	9.02835i	−1.32025	+	0.480531i	−0.903537	−	0.428509i	$-0.859039\pi$
$353$	−24.8052	+	9.02835i	−1.32025	+	0.480531i	−0.416710	+	0.909040i	$0.636817\pi$
$354$		0			0
$355$	17.5281	−	14.7078i	0.930294	−	0.780610i
$356$	3.54795	+	20.1214i	0.188041	+	1.06643i
$357$		0			0
$358$	4.75976	+	3.99391i	0.251561	+	0.211085i
$359$	10.8174	−	18.7363i	0.570921	−	0.988864i	−0.425551	−	0.904934i	$-0.639920\pi$
$359$	10.8174	−	18.7363i	0.570921	−	0.988864i	0.996472	−	0.0839293i	$-0.0267470\pi$
$360$		0			0
$361$	−11.1238	−	19.2669i	−0.585461	−	1.01405i
$362$	−0.620552	+	3.51933i	−0.0326155	+	0.184972i
$363$		0			0
$364$	−0.198158	−	0.0721238i	−0.0103863	−	0.00378031i
$365$	25.8217	+	9.39834i	1.35157	+	0.491932i
$366$		0			0
$367$	−0.391997	+	2.22313i	−0.0204621	+	0.116046i	−0.993328	−	0.115323i	$-0.963210\pi$
$367$	−0.391997	+	2.22313i	−0.0204621	+	0.116046i	0.972866	+	0.231370i	$0.0743207\pi$
$368$	0.127772	+	0.221308i	0.00666059	+	0.0115365i
$369$		0			0
$370$	−2.52819	+	4.37896i	−0.131435	+	0.227651i
$371$	−4.69046	−	3.93576i	−0.243516	−	0.204335i
$372$		0			0
$373$	1.80257	+	10.2229i	0.0933336	+	0.529321i	0.995245	+	0.0974006i	$0.0310528\pi$
$373$	1.80257	+	10.2229i	0.0933336	+	0.529321i	−0.901912	+	0.431921i	$0.857836\pi$
$374$	0.935001	−	0.784559i	0.0483477	−	0.0405686i
$375$		0			0
$376$	−11.0421	+	4.01899i	−0.569452	+	0.207264i
$377$	0.795277			0.0409589
$378$		0			0
$379$	10.1524			0.521496			0.260748	−	0.965407i	$-0.416031\pi$
$379$	10.1524			0.521496			0.260748	+	0.965407i	$0.416031\pi$
$380$	23.0877	−	8.40322i	1.18437	−	0.431076i
$381$		0			0
$382$	1.16361	−	0.976384i	0.0595354	−	0.0499562i
$383$	−1.32193	−	7.49701i	−0.0675472	−	0.383079i	−0.999775	−	0.0212076i	$-0.993249\pi$
$383$	−1.32193	−	7.49701i	−0.0675472	−	0.383079i	0.932228	−	0.361872i	$-0.117862\pi$
$384$		0			0
$385$	−6.46580	−	5.42545i	−0.329528	−	0.276507i
$386$	−1.61333	+	2.79437i	−0.0821162	+	0.142229i
$387$		0			0
$388$	1.70009	+	2.94464i	0.0863090	+	0.149492i
$389$	−0.781945	+	4.43463i	−0.0396462	+	0.224845i	−0.998193	−	0.0600906i	$-0.980861\pi$
$389$	−0.781945	+	4.43463i	−0.0396462	+	0.224845i	0.958547	+	0.284935i	$0.0919721\pi$
$390$		0			0
$391$	−0.0717710	−	0.0261225i	−0.00362962	−	0.00132107i
$392$	−0.992215	−	0.361137i	−0.0501144	−	0.0182402i
$393$		0			0
$394$	0.987721	−	5.60165i	0.0497607	−	0.282207i
$395$	−8.21887	−	14.2355i	−0.413536	−	0.716266i
$396$		0			0
$397$	0.706624	−	1.22391i	0.0354644	−	0.0614262i	−0.847748	−	0.530399i	$-0.822042\pi$
$397$	0.706624	−	1.22391i	0.0354644	−	0.0614262i	0.883213	+	0.468972i	$0.155376\pi$
$398$	−1.01427	−	0.851077i	−0.0508409	−	0.0426606i
$399$		0			0
$400$	−0.658533	−	3.73473i	−0.0329267	−	0.186736i
$401$	−20.9203	+	17.5543i	−1.04471	+	0.876617i	−0.992528	−	0.122020i	$-0.961063\pi$
$401$	−20.9203	+	17.5543i	−1.04471	+	0.876617i	−0.0521844	+	0.998637i	$0.516618\pi$
$402$		0			0
$403$	−0.276686	+	0.100706i	−0.0137827	+	0.00501650i
$404$	13.9943			0.696242
$405$		0			0
$406$	1.95441			0.0969959
$407$	−37.8808	+	13.7875i	−1.87768	+	0.683420i
$408$		0			0
$409$	−14.4841	+	12.1536i	−0.716193	+	0.600957i	−0.926329	−	0.376715i	$-0.877054\pi$
$409$	−14.4841	+	12.1536i	−0.716193	+	0.600957i	0.210136	+	0.977672i	$0.432609\pi$
$410$	0.287738	+	1.63185i	0.0142104	+	0.0805911i
$411$		0			0
$412$	−23.9329	−	20.0821i	−1.17909	−	0.989372i
$413$	2.68741	−	4.65473i	0.132239	−	0.229044i
$414$		0			0
$415$	16.1457	+	27.9652i	0.792563	+	1.37276i
$416$	0.0583531	−	0.330937i	0.00286100	−	0.0162255i
$417$		0			0
$418$	−6.90054	−	2.51159i	−0.337516	−	0.122846i
$419$	18.7757	+	6.83379i	0.917252	+	0.333852i	0.757145	−	0.653247i	$-0.226594\pi$
$419$	18.7757	+	6.83379i	0.917252	+	0.333852i	0.160107	+	0.987100i	$0.448816\pi$
$420$		0			0
$421$	4.40162	−	24.9629i	0.214522	−	1.21661i	−0.667212	−	0.744868i	$-0.732512\pi$
$421$	4.40162	−	24.9629i	0.214522	−	1.21661i	0.881734	−	0.471747i	$-0.156376\pi$
$422$	−2.63102	−	4.55705i	−0.128076	−	0.221834i
$423$		0			0
$424$	3.23260	−	5.59902i	0.156989	−	0.271912i
$425$	0.868276	+	0.728570i	0.0421176	+	0.0353409i
$426$		0			0
$427$	0.817083	+	4.63391i	0.0395414	+	0.224251i
$428$	11.2001	−	9.39796i	0.541375	−	0.454268i
$429$		0			0
$430$	−3.28511	+	1.19568i	−0.158422	+	0.0576609i
$431$	−9.73667			−0.468999			−0.234499	−	0.972116i	$-0.575345\pi$
$431$	−9.73667			−0.468999			−0.234499	+	0.972116i	$0.575345\pi$
$432$		0			0
$433$	−10.2203			−0.491155			−0.245578	−	0.969377i	$-0.578978\pi$
$433$	−10.2203			−0.491155			−0.245578	+	0.969377i	$0.578978\pi$
$434$	−0.679963	+	0.247486i	−0.0326393	+	0.0118797i
$435$		0			0
$436$	6.91495	−	5.80233i	0.331166	−	0.277881i
$437$	0.0797944	+	0.452537i	0.00381709	+	0.0216478i
$438$		0			0
$439$	25.8368	+	21.6796i	1.23312	+	1.03471i	0.998030	+	0.0627388i	$0.0199835\pi$
$439$	25.8368	+	21.6796i	1.23312	+	1.03471i	0.235092	+	0.971973i	$0.424461\pi$
$440$	4.45614	−	7.71825i	0.212438	−	0.367953i
$441$		0			0
$442$	0.0156960	+	0.0271863i	0.000746583	+	0.00129312i
$443$	−3.66992	+	20.8132i	−0.174363	+	0.988864i	0.764513	+	0.644609i	$0.222980\pi$
$443$	−3.66992	+	20.8132i	−0.174363	+	0.988864i	−0.938876	+	0.344255i	$0.888132\pi$
$444$		0			0
$445$	−19.7650	−	7.19386i	−0.936949	−	0.341022i
$446$	−0.650547	−	0.236780i	−0.0308043	−	0.0112118i
$447$		0			0
$448$	−1.09700	+	6.22140i	−0.0518284	+	0.293934i
$449$	−9.20909	−	15.9506i	−0.434604	−	0.752756i	0.562659	−	0.826689i	$-0.309778\pi$
$449$	−9.20909	−	15.9506i	−0.434604	−	0.752756i	−0.997263	+	0.0739329i	$0.976445\pi$
$450$		0			0
$451$	−6.60526	+	11.4406i	−0.311030	+	0.538719i
$452$	−4.97919	−	4.17803i	−0.234201	−	0.196518i
$453$		0			0
$454$	0.848338	+	4.81117i	0.0398145	+	0.225799i
$455$	0.166297	−	0.139539i	0.00779610	−	0.00654171i
$456$		0			0
$457$	−36.4637	+	13.2717i	−1.70570	+	0.620824i	−0.996454	−	0.0841383i	$-0.973186\pi$
$457$	−36.4637	+	13.2717i	−1.70570	+	0.620824i	−0.709245	+	0.704962i	$0.750964\pi$
$458$	−6.37426			−0.297849
$459$		0			0
$460$	−0.273715			−0.0127620
$461$	−34.3432	+	12.4999i	−1.59952	+	0.582178i	−0.979329	−	0.202272i	$-0.935168\pi$
$461$	−34.3432	+	12.4999i	−1.59952	+	0.582178i	−0.620192	+	0.784450i	$0.712945\pi$
$462$		0			0
$463$	−13.2918	+	11.1532i	−0.617725	+	0.518332i	−0.897087	−	0.441853i	$-0.854321\pi$
$463$	−13.2918	+	11.1532i	−0.617725	+	0.518332i	0.279363	+	0.960186i	$0.409877\pi$
$464$	−4.50891	−	25.5713i	−0.209321	−	1.18712i
$465$		0			0
$466$	1.98337	+	1.66425i	0.0918779	+	0.0770947i
$467$	−11.6410	+	20.1627i	−0.538680	+	0.933021i	0.460296	+	0.887766i	$0.347743\pi$
$467$	−11.6410	+	20.1627i	−0.538680	+	0.933021i	−0.998975	+	0.0452551i	$0.985590\pi$
$468$		0			0
$469$	−2.61577	−	4.53064i	−0.120785	−	0.209206i
$470$	1.03096	−	5.84687i	0.0475547	−	0.269696i
$471$		0			0
$472$	5.33298	+	1.94104i	0.245470	+	0.0893438i
$473$	−26.1904	−	9.53253i	−1.20424	−	0.438306i
$474$		0			0
$475$	1.18417	−	6.71575i	0.0543333	−	0.308140i
$476$	−1.02891	−	1.78212i	−0.0471599	−	0.0816833i
$477$		0			0
$478$	1.34458	−	2.32887i	0.0614995	−	0.106520i
$479$	0.597324	+	0.501215i	0.0272924	+	0.0229011i	0.656332	−	0.754472i	$-0.272107\pi$
$479$	0.597324	+	0.501215i	0.0272924	+	0.0229011i	−0.629039	+	0.777373i	$0.716552\pi$
$480$		0			0
$481$	−0.180038	−	1.02105i	−0.00820903	−	0.0465557i
$482$	−0.349935	+	0.293631i	−0.0159391	+	0.0133745i
$483$		0			0
$484$	12.8434	−	4.67462i	0.583791	−	0.212483i
$485$	−3.50029			−0.158940
$486$		0			0
$487$	35.3660			1.60259			0.801293	−	0.598272i	$-0.204146\pi$
$487$	35.3660			1.60259			0.801293	+	0.598272i	$0.204146\pi$
$488$	−4.66876	+	1.69929i	−0.211345	+	0.0769233i
$489$		0			0
$490$	0.408678	−	0.342921i	0.0184622	−	0.0154916i
$491$	6.97088	+	39.5338i	0.314591	+	1.78414i	0.574501	+	0.818504i	$0.305196\pi$
$491$	6.97088	+	39.5338i	0.314591	+	1.78414i	−0.259910	+	0.965633i	$0.583693\pi$
$492$		0			0
$493$	5.94500	+	4.98845i	0.267749	+	0.224668i
$494$	0.0944339	−	0.163564i	0.00424878	−	0.00735911i
$495$		0			0
$496$	4.80678	+	8.32559i	0.215831	+	0.373830i
$497$	−2.00218	+	11.3549i	−0.0898099	+	0.509337i
$498$		0			0
$499$	−5.50313	−	2.00298i	−0.246354	−	0.0896655i	0.215892	−	0.976417i	$-0.430734\pi$
$499$	−5.50313	−	2.00298i	−0.246354	−	0.0896655i	−0.462246	+	0.886752i	$0.652956\pi$
$500$	21.7913	+	7.93137i	0.974535	+	0.354702i
$501$		0			0
$502$	0.992133	−	5.62666i	0.0442811	−	0.251130i
$503$	4.11805	+	7.13268i	0.183615	+	0.318030i	0.943109	−	0.332484i	$-0.107887\pi$
$503$	4.11805	+	7.13268i	0.183615	+	0.318030i	−0.759494	+	0.650514i	$0.774553\pi$
$504$		0			0
$505$	−7.20317	+	12.4763i	−0.320537	+	0.555186i
$506$	0.0626694	+	0.0525859i	0.00278599	+	0.00233773i
$507$		0			0
$508$	3.01680	+	17.1091i	0.133849	+	0.759095i
$509$	−16.6389	+	13.9617i	−0.737508	+	0.618842i	−0.932167	−	0.362029i	$-0.882084\pi$
$509$	−16.6389	+	13.9617i	−0.737508	+	0.618842i	0.194659	+	0.980871i	$0.437640\pi$
$510$		0			0
$511$	−13.0118	+	4.73590i	−0.575607	+	0.209504i
$512$	−18.5142			−0.818221
$513$		0			0
$514$	1.27857			0.0563955
$515$	30.2224	−	11.0001i	1.33176	−	0.484720i
$516$		0			0
$517$	36.2592	−	30.4251i	1.59468	−	1.33810i
$518$	−0.442448	−	2.50925i	−0.0194400	−	0.110250i
$519$		0			0
$520$	0.175591	+	0.147339i	0.00770019	+	0.00646123i
$521$	3.79475	−	6.57271i	0.166251	−	0.287956i	−0.770848	−	0.637019i	$-0.780167\pi$
$521$	3.79475	−	6.57271i	0.166251	−	0.287956i	0.937099	+	0.349064i	$0.113500\pi$
$522$		0			0
$523$	8.34294	+	14.4504i	0.364811	+	0.631872i	0.988746	−	0.149605i	$-0.0478002\pi$
$523$	8.34294	+	14.4504i	0.364811	+	0.631872i	−0.623935	+	0.781477i	$0.714467\pi$
$524$	2.47353	−	14.0281i	0.108057	−	0.612820i
$525$		0			0
$526$	−0.0115116	−	0.00418988i	−0.000501929	−	0.000182687i
$527$	−2.70002	−	0.982727i	−0.117615	−	0.0428083i
$528$		0			0
$529$	−3.99302	+	22.6455i	−0.173610	+	0.984589i
$530$	1.63327	+	2.82891i	0.0709448	+	0.122880i
$531$		0			0
$532$	−6.19035	+	10.7220i	−0.268386	+	0.464858i
$533$	−0.260276	−	0.218398i	−0.0112738	−	0.00945986i
$534$		0			0
$535$	2.61360	+	14.8225i	0.112996	+	0.640831i
$536$	4.23159	−	3.55072i	0.182777	−	0.153368i
$537$		0			0
$538$	0.929623	−	0.338355i	0.0400789	−	0.0145875i
$539$	4.25324			0.183200
$540$		0			0
$541$	17.7745			0.764187			0.382093	−	0.924124i	$-0.375203\pi$
$541$	17.7745			0.764187			0.382093	+	0.924124i	$0.375203\pi$
$542$	5.39738	−	1.96448i	0.231837	−	0.0843818i
$543$		0			0
$544$	2.51204	−	2.10785i	0.107703	−	0.0903735i
$545$	1.61364	+	9.15142i	0.0691209	+	0.392004i
$546$		0			0
$547$	1.99834	+	1.67681i	0.0854430	+	0.0716952i	0.684509	−	0.729005i	$-0.260017\pi$
$547$	1.99834	+	1.67681i	0.0854430	+	0.0716952i	−0.599066	+	0.800700i	$0.704461\pi$
$548$	−15.6491	+	27.1051i	−0.668497	+	1.15787i
$549$		0			0
$550$	−0.607033	−	1.05141i	−0.0258840	−	0.0448323i
$551$	8.10788	−	45.9821i	0.345407	−	1.95890i
$552$		0			0
$553$	7.78358	+	2.83299i	0.330991	+	0.120471i
$554$	3.74937	+	1.36466i	0.159296	+	0.0579788i
$555$		0			0
$556$	2.45951	−	13.9485i	0.104306	−	0.591550i
$557$	10.2242	+	17.7089i	0.433215	+	0.750350i	0.997148	−	0.0754705i	$-0.0240459\pi$
$557$	10.2242	+	17.7089i	0.433215	+	0.750350i	−0.563933	+	0.825820i	$0.690713\pi$
$558$		0			0
$559$	0.358416	−	0.620795i	0.0151594	−	0.0262568i
$560$	−5.42958	−	4.55596i	−0.229442	−	0.192524i
$561$		0			0
$562$	−0.285472	−	1.61899i	−0.0120419	−	0.0682931i
$563$	−18.5893	+	15.5983i	−0.783448	+	0.657391i	−0.944114	−	0.329618i	$-0.893080\pi$
$563$	−18.5893	+	15.5983i	−0.783448	+	0.657391i	0.160667	+	0.987009i	$0.448636\pi$
$564$		0			0
$565$	6.28771	−	2.28854i	0.264526	−	0.0962796i
$566$	4.34577			0.182666
$567$		0			0
$568$	−12.1745			−0.510832
$569$	3.07417	−	1.11891i	0.128876	−	0.0469071i	−0.276777	−	0.960934i	$-0.589266\pi$
$569$	3.07417	−	1.11891i	0.128876	−	0.0469071i	0.405653	+	0.914027i	$0.367044\pi$
$570$		0			0
$571$	−30.5930	+	25.6706i	−1.28028	+	1.07428i	−0.287070	+	0.957909i	$0.592681\pi$
$571$	−30.5930	+	25.6706i	−1.28028	+	1.07428i	−0.993206	+	0.116370i	$0.962874\pi$
$572$	0.155746	+	0.883279i	0.00651206	+	0.0369318i
$573$		0			0
$574$	−0.639636	−	0.536718i	−0.0266979	−	0.0224022i
$575$	−0.0379855	+	0.0657927i	−0.00158410	+	0.00274375i
$576$		0			0
$577$	14.2518	+	24.6849i	0.593311	+	1.02764i	0.993783	+	0.111336i	$0.0355128\pi$
$577$	14.2518	+	24.6849i	0.593311	+	1.02764i	−0.400472	+	0.916309i	$0.631154\pi$
$578$	0.740398	−	4.19900i	0.0307965	−	0.174656i
$579$		0			0
$580$	26.1348	+	9.51228i	1.08519	+	0.394976i
$581$	−15.2906	−	5.56533i	−0.634361	−	0.230889i
$582$		0			0
$583$	−4.52221	+	25.6468i	−0.187291	+	1.06218i
$584$	−7.31039	−	12.6620i	−0.302506	−	0.523956i
$585$		0			0
$586$	1.11358	−	1.92877i	0.0460014	−	0.0796767i
$587$	28.6772	+	24.0630i	1.18363	+	0.993186i	0.999948	+	0.0102013i	$0.00324723\pi$
$587$	28.6772	+	24.0630i	1.18363	+	0.993186i	0.183685	+	0.982985i	$0.441197\pi$
$588$		0			0
$589$	3.00186	+	17.0244i	0.123690	+	0.701478i
$590$	−2.19657	+	1.84314i	−0.0904313	+	0.0758809i
$591$		0			0
$592$	−31.8099	+	11.5779i	−1.30738	+	0.475847i
$593$	1.95349			0.0802204			0.0401102	−	0.999195i	$-0.487229\pi$
$593$	1.95349			0.0802204			0.0401102	+	0.999195i	$0.487229\pi$
$594$		0			0
$595$	2.11840			0.0868461
$596$	−29.7641	+	10.8332i	−1.21918	+	0.443747i
$597$		0			0
$598$	−0.00161182	+	0.00135248i	−6.59122e−5	+	5.53069e-5i
$599$	−6.63734	−	37.6422i	−0.271194	−	1.53802i	−0.750797	−	0.660533i	$-0.770330\pi$
$599$	−6.63734	−	37.6422i	−0.271194	−	1.53802i	0.479603	−	0.877486i	$-0.340781\pi$
$600$		0			0
$601$	12.3235	+	10.3406i	0.502686	+	0.421804i	0.858547	−	0.512735i	$-0.171368\pi$
$601$	12.3235	+	10.3406i	0.502686	+	0.421804i	−0.355861	+	0.934539i	$0.615812\pi$
$602$	0.880816	−	1.52562i	0.0358994	−	0.0621796i
$603$		0			0
$604$	−20.5241	−	35.5489i	−0.835116	−	1.44646i
$605$	−2.44325	+	13.8563i	−0.0993321	+	0.563340i
$606$		0			0
$607$	−2.63527	−	0.959161i	−0.106962	−	0.0389311i	0.287985	−	0.957635i	$-0.407015\pi$
$607$	−2.63527	−	0.959161i	−0.106962	−	0.0389311i	−0.394947	+	0.918704i	$0.629237\pi$
$608$	−18.5395	−	6.74782i	−0.751876	−	0.273660i
$609$		0			0
$610$	0.435907	−	2.47215i	0.0176493	−	0.100094i
$611$	0.608689	+	1.05428i	0.0246249	+	0.0426516i
$612$		0			0
$613$	12.3228	−	21.3437i	0.497712	−	0.862062i	−0.502285	−	0.864702i	$-0.667507\pi$
$613$	12.3228	−	21.3437i	0.497712	−	0.862062i	0.999997	+	0.00264012i	$0.000840377\pi$
$614$	5.21280	+	4.37406i	0.210371	+	0.176523i
$615$		0			0
$616$	0.779848	+	4.42274i	0.0314210	+	0.178197i
$617$	9.91483	−	8.31953i	0.399156	−	0.334932i	−0.421011	−	0.907055i	$-0.638325\pi$
$617$	9.91483	−	8.31953i	0.399156	−	0.334932i	0.820167	+	0.572124i	$0.193880\pi$
$618$		0			0
$619$	8.18250	−	2.97819i	0.328883	−	0.119703i	−0.172301	−	0.985044i	$-0.555120\pi$
$619$	8.18250	−	2.97819i	0.328883	−	0.119703i	0.501184	+	0.865341i	$0.332898\pi$
$620$	−10.2971			−0.413543
$621$		0			0
$622$	8.94224			0.358551
$623$	9.95972	−	3.62504i	0.399028	−	0.145234i
$624$		0			0
$625$	−14.2205	+	11.9324i	−0.568820	+	0.477297i
$626$	0.629671	+	3.57104i	0.0251667	+	0.142728i
$627$		0			0
$628$	7.15033	+	5.99984i	0.285329	+	0.239420i
$629$	5.05875	−	8.76201i	0.201706	−	0.349364i
$630$		0			0
$631$	−7.41380	−	12.8411i	−0.295139	−	0.511195i	0.679878	−	0.733325i	$-0.262033\pi$
$631$	−7.41380	−	12.8411i	−0.295139	−	0.511195i	−0.975017	+	0.222130i	$0.928699\pi$
$632$	−1.51874	+	8.61321i	−0.0604123	+	0.342615i
$633$		0			0
$634$	−7.69819	−	2.80191i	−0.305734	−	0.111278i
$635$	−16.8060	−	6.11689i	−0.666926	−	0.242741i
$636$		0			0
$637$	−0.0189955	+	0.107729i	−0.000752629	+	0.00426837i
$638$	−4.15629	−	7.19891i	−0.164549	−	0.285008i
$639$		0			0
$640$	7.78137	−	13.4777i	0.307586	−	0.532754i
$641$	10.1580	+	8.52359i	0.401218	+	0.336662i	0.820964	−	0.570980i	$-0.193437\pi$
$641$	10.1580	+	8.52359i	0.401218	+	0.336662i	−0.419746	+	0.907641i	$0.637881\pi$
$642$		0			0
$643$	−5.88721	−	33.3880i	−0.232169	−	1.31670i	−0.848494	−	0.529204i	$-0.822490\pi$
$643$	−5.88721	−	33.3880i	−0.232169	−	1.31670i	0.616325	−	0.787492i	$-0.288621\pi$
$644$	0.105658	−	0.0886578i	0.00416352	−	0.00349361i
$645$		0			0
$646$	1.73190	−	0.630361i	0.0681407	−	0.0248012i
$647$	−15.4959			−0.609207			−0.304604	−	0.952479i	$-0.598524\pi$
$647$	−15.4959			−0.609207			−0.304604	+	0.952479i	$0.598524\pi$
$648$		0			0
$649$	−22.8604			−0.897348
$650$	0.0293419	−	0.0106796i	0.00115089	−	0.000418888i
$651$		0			0
$652$	−25.2889	+	21.2199i	−0.990389	+	0.831035i
$653$	3.15260	+	17.8793i	0.123371	+	0.699670i	0.982262	+	0.187512i	$0.0600425\pi$
$653$	3.15260	+	17.8793i	0.123371	+	0.699670i	−0.858892	+	0.512157i	$0.828846\pi$
$654$		0			0
$655$	11.2332	+	9.42577i	0.438917	+	0.368295i
$656$	−5.54669	+	9.60714i	−0.216562	+	0.375096i
$657$		0			0
$658$	1.49587	+	2.59092i	0.0583150	+	0.101005i
$659$	2.17238	−	12.3202i	0.0846239	−	0.479926i	−0.912813	−	0.408377i	$-0.866095\pi$
$659$	2.17238	−	12.3202i	0.0846239	−	0.479926i	0.997437	−	0.0715487i	$-0.0227941\pi$
$660$		0			0
$661$	22.5610	+	8.21152i	0.877519	+	0.319391i	0.741208	−	0.671275i	$-0.234253\pi$
$661$	22.5610	+	8.21152i	0.877519	+	0.319391i	0.136311	+	0.990666i	$0.456475\pi$
$662$	−1.01550	−	0.369613i	−0.0394687	−	0.0143654i
$663$		0			0
$664$	2.98352	−	16.9204i	0.115783	−	0.656639i
$665$	−6.37262	−	11.0377i	−0.247119	−	0.428023i
$666$		0			0
$667$	−0.260083	+	0.450476i	−0.0100704	+	0.0174425i
$668$	−3.75112	−	3.14756i	−0.145135	−	0.121783i
$669$		0			0
$670$	0.484648	+	2.74858i	0.0187236	+	0.106187i
$671$	15.3310	−	12.8642i	0.591846	−	0.496617i
$672$		0			0
$673$	31.3980	−	11.4279i	1.21031	−	0.440515i	0.343496	−	0.939154i	$-0.388389\pi$
$673$	31.3980	−	11.4279i	1.21031	−	0.440515i	0.866810	+	0.498639i	$0.166167\pi$
$674$	3.18738			0.122773
$675$		0			0
$676$	25.0374			0.962978
$677$	−20.2124	+	7.35671i	−0.776825	+	0.282741i	−0.699848	−	0.714292i	$-0.746749\pi$
$677$	−20.2124	+	7.35671i	−0.776825	+	0.282741i	−0.0769771	+	0.997033i	$0.524527\pi$
$678$		0			0
$679$	1.35117	−	1.13377i	0.0518531	−	0.0435099i
$680$	0.388418	+	2.20283i	0.0148951	+	0.0844745i
$681$		0			0
$682$	2.35762	+	1.97828i	0.0902778	+	0.0757521i
$683$	−21.2205	+	36.7549i	−0.811979	+	1.40639i	0.0994979	+	0.995038i	$0.468276\pi$
$683$	−21.2205	+	36.7549i	−0.811979	+	1.40639i	−0.911477	+	0.411351i	$0.865057\pi$
$684$		0			0
$685$	−16.1099	−	27.9031i	−0.615527	−	1.06612i
$686$	−0.0466819	+	0.264746i	−0.00178232	+	0.0101081i
$687$		0			0
$688$	−21.9931	−	8.00483i	−0.838479	−	0.305181i
$689$	−0.629401	−	0.229083i	−0.0239783	−	0.00872738i
$690$		0			0
$691$	−5.81764	+	32.9935i	−0.221314	+	1.25513i	0.648295	+	0.761390i	$0.275483\pi$
$691$	−5.81764	+	32.9935i	−0.221314	+	1.25513i	−0.869608	+	0.493742i	$0.835629\pi$
$692$	11.3730	+	19.6985i	0.432335	+	0.748826i
$693$		0			0
$694$	−1.38220	+	2.39404i	−0.0524676	+	0.0908766i
$695$	11.1695	+	9.37233i	0.423684	+	0.355513i
$696$		0			0
$697$	−0.575746	−	3.26522i	−0.0218079	−	0.123679i
$698$	−0.880514	+	0.738839i	−0.0333280	+	0.0279655i
$699$		0			0
$700$	−1.92343	+	0.700071i	−0.0726988	+	0.0264602i
$701$	4.77624			0.180396			0.0901980	−	0.995924i	$-0.471250\pi$
$701$	4.77624			0.180396			0.0901980	+	0.995924i	$0.471250\pi$
$702$		0			0
$703$	−60.8713			−2.29580
$704$	25.2489	−	9.18984i	0.951603	−	0.346355i
$705$		0			0
$706$	−5.43612	+	4.56145i	−0.204591	+	0.171672i
$707$	−1.26059	−	7.14918i	−0.0474095	−	0.268873i
$708$		0			0
$709$	2.87376	+	2.41137i	0.107926	+	0.0905610i	0.695154	−	0.718861i	$-0.255336\pi$
$709$	2.87376	+	2.41137i	0.107926	+	0.0905610i	−0.587228	+	0.809422i	$0.699781\pi$
$710$	3.07559	−	5.32709i	0.115425	−	0.199922i
$711$		0			0
$712$	5.59566	+	9.69197i	0.209706	+	0.363222i
$713$	0.0334422	−	0.189660i	0.00125242	−	0.00710283i
$714$		0			0
$715$	−0.867630	−	0.315792i	−0.0324475	−	0.0118099i
$716$	−41.8682	−	15.2388i	−1.56469	−	0.569501i
$717$		0			0
$718$	1.00995	−	5.72774i	0.0376912	−	0.213757i
$719$	16.4027	+	28.4103i	0.611718	+	1.05953i	0.990951	+	0.134225i	$0.0428545\pi$
$719$	16.4027	+	28.4103i	0.611718	+	1.05953i	−0.379233	+	0.925301i	$0.623812\pi$
$720$		0			0
$721$	−8.10335	+	14.0354i	−0.301784	+	0.522706i
$722$	−4.58157	−	3.84439i	−0.170508	−	0.143073i
$723$		0			0
$724$	−4.44986	−	25.2364i	−0.165378	−	0.937903i
$725$	5.91338	−	4.96192i	0.219617	−	0.184281i
$726$		0			0
$727$	3.44816	−	1.25503i	0.127885	−	0.0465464i	−0.277285	−	0.960788i	$-0.589435\pi$
$727$	3.44816	−	1.25503i	0.127885	−	0.0465464i	0.405170	+	0.914241i	$0.367212\pi$
$728$	−0.115505			−0.00428090
$729$		0			0
$730$	7.38717			0.273411
$731$	6.57329	−	2.39248i	0.243122	−	0.0884891i
$732$		0			0
$733$	−20.7398	+	17.4028i	−0.766042	+	0.642786i	−0.939692	−	0.342022i	$-0.888888\pi$
$733$	−20.7398	+	17.4028i	−0.766042	+	0.642786i	0.173650	+	0.984807i	$0.444444\pi$
$734$	0.105381	+	0.597644i	0.00388968	+	0.0220594i
$735$		0			0
$736$	0.168372	+	0.141281i	0.00620628	+	0.00520769i
$737$	−11.1255	+	19.2699i	−0.409813	+	0.709816i
$738$		0			0
$739$	−9.58393	−	16.5999i	−0.352551	−	0.610635i	0.634145	−	0.773214i	$-0.281352\pi$
$739$	−9.58393	−	16.5999i	−0.352551	−	0.610635i	−0.986696	+	0.162579i	$0.948019\pi$
$740$	6.29620	−	35.7075i	0.231453	−	1.31263i
$741$		0			0
$742$	−1.54677	−	0.562978i	−0.0567837	−	0.0206676i
$743$	3.44616	+	1.25430i	0.126427	+	0.0460157i	0.404459	−	0.914556i	$-0.367460\pi$
$743$	3.44616	+	1.25430i	0.126427	+	0.0460157i	−0.278032	+	0.960572i	$0.589682\pi$
$744$		0			0
$745$	5.66213	−	32.1115i	0.207444	−	1.17647i
$746$	1.39531	+	2.41675i	0.0510859	+	0.0884834i
$747$		0			0
$748$	−4.37619	+	7.57978i	−0.160009	+	0.277144i
$749$	−5.80997	−	4.87514i	−0.212292	−	0.178134i
$750$		0			0
$751$	−5.61066	−	31.8197i	−0.204736	−	1.16112i	−0.897855	−	0.440292i	$-0.854875\pi$
$751$	−5.61066	−	31.8197i	−0.204736	−	1.16112i	0.693119	−	0.720824i	$-0.256236\pi$
$752$	30.4483	−	25.5491i	1.11033	−	0.931681i
$753$		0			0
$754$	0.200901	−	0.0731221i	0.00731639	−	0.00266295i
$755$	42.2569			1.53789
$756$		0			0
$757$	−22.9786			−0.835170			−0.417585	−	0.908638i	$-0.637123\pi$
$757$	−22.9786			−0.835170			−0.417585	+	0.908638i	$0.637123\pi$
$758$	2.56469	−	0.933471i	0.0931538	−	0.0339052i
$759$		0			0
$760$	10.3091	−	8.65038i	0.373951	−	0.313782i
$761$	−6.76780	−	38.3821i	−0.245333	−	1.39135i	−0.819719	−	0.572766i	$-0.805870\pi$
$761$	−6.76780	−	38.3821i	−0.245333	−	1.39135i	0.574387	−	0.818584i	$-0.305241\pi$
$762$		0			0
$763$	−3.58709	−	3.00993i	−0.129861	−	0.108967i
$764$	−5.44617	+	9.43304i	−0.197035	+	0.341275i
$765$		0			0
$766$	−1.02326	−	1.77234i	−0.0369718	−	0.0640371i
$767$	0.102097	−	0.579023i	0.00368652	−	0.0209073i
$768$		0			0
$769$	3.76335	+	1.36975i	0.135710	+	0.0493944i	0.408982	−	0.912542i	$-0.365884\pi$
$769$	3.76335	+	1.36975i	0.135710	+	0.0493944i	−0.273272	+	0.961937i	$0.588106\pi$
$770$	−2.13222	−	0.776066i	−0.0768400	−	0.0279675i
$771$		0			0
$772$	4.01782	−	22.7862i	0.144605	−	0.820093i
$773$	−4.49792	−	7.79062i	−0.161779	−	0.280209i	0.773728	−	0.633518i	$-0.218390\pi$
$773$	−4.49792	−	7.79062i	−0.161779	−	0.280209i	−0.935507	+	0.353309i	$0.885056\pi$
$774$		0			0
$775$	−1.42901	+	2.47512i	−0.0513316	+	0.0889089i
$776$	1.42669	+	1.19714i	0.0512152	+	0.0429747i
$777$		0			0
$778$	0.210211	+	1.19216i	0.00753642	+	0.0427412i
$779$	−15.2811	+	12.8223i	−0.547501	+	0.459408i
$780$		0			0
$781$	46.0826	−	16.7727i	1.64897	−	0.600175i
$782$	−0.0205325			−0.000734241
$783$		0			0
$784$	3.57160			0.127557
$785$	−9.02944	+	3.28645i	−0.322274	+	0.117298i
$786$		0			0
$787$	4.70426	−	3.94734i	0.167689	−	0.140708i	−0.555081	−	0.831796i	$-0.687313\pi$
$787$	4.70426	−	3.94734i	0.167689	−	0.140708i	0.722770	+	0.691088i	$0.242868\pi$
$788$	7.08276	+	40.1683i	0.252313	+	1.43094i
$789$		0			0
$790$	−3.38512	−	2.84046i	−0.120437	−	0.101059i
$791$	−1.68589	+	2.92004i	−0.0599432	+	0.103825i
$792$		0			0
$793$	0.257363	+	0.445766i	0.00913924	+	0.0158296i
$794$	0.0659731	−	0.374152i	0.00234130	−	0.0132782i
$795$		0			0
$796$	8.92185	+	3.24729i	0.316227	+	0.115097i
$797$	40.2393	+	14.6459i	1.42535	+	0.518784i	0.935594	−	0.353077i	$-0.114865\pi$
$797$	40.2393	+	14.6459i	1.42535	+	0.518784i	0.489753	+	0.871861i	$0.337087\pi$
$798$		0			0
$799$	−2.06289	+	11.6992i	−0.0729797	+	0.413888i
$800$	−1.63090	−	2.82480i	−0.0576610	−	0.0998718i
$801$		0			0
$802$	−3.67082	+	6.35805i	−0.129621	+	0.224511i
$803$	45.1154	+	37.8563i	1.59209	+	1.33592i
$804$		0			0
$805$	0.0246560	+	0.139831i	0.000869009	+	0.00492840i
$806$	−0.0606365	+	0.0508801i	−0.00213583	+	0.00179217i
$807$		0			0
$808$	7.20295	−	2.62166i	0.253399	−	0.0922297i
$809$	51.9664			1.82704			0.913521	−	0.406791i	$-0.133352\pi$
$809$	51.9664			1.82704			0.913521	+	0.406791i	$0.133352\pi$
$810$		0			0
$811$	0.845745			0.0296981			0.0148491	−	0.999890i	$-0.495273\pi$
$811$	0.845745			0.0296981			0.0148491	+	0.999890i	$0.495273\pi$
$812$	−13.1695	+	4.79331i	−0.462160	+	0.168212i
$813$		0			0
$814$	−8.30167	+	6.96593i	−0.290973	+	0.244156i
$815$	−5.90131	−	33.4680i	−0.206714	−	1.17233i
$816$		0			0
$817$	−32.2396	−	27.0523i	−1.12792	−	0.946439i
$818$	−2.54148	+	4.40197i	−0.0888607	+	0.153911i
$819$		0			0
$820$	−5.94108	−	10.2903i	−0.207471	−	0.359351i
$821$	1.21746	−	6.90458i	0.0424897	−	0.240971i	−0.956165	−	0.292829i	$-0.905403\pi$
$821$	1.21746	−	6.90458i	0.0424897	−	0.240971i	0.998654	+	0.0518580i	$0.0165143\pi$
$822$		0			0
$823$	4.51806	+	1.64444i	0.157490	+	0.0573215i	0.419562	−	0.907727i	$-0.362184\pi$
$823$	4.51806	+	1.64444i	0.157490	+	0.0573215i	−0.262072	+	0.965048i	$0.584406\pi$
$824$	−16.0805	−	5.85283i	−0.560192	−	0.203893i
$825$		0			0
$826$	0.250907	−	1.42296i	0.00873016	−	0.0495112i
$827$	−20.6378	−	35.7457i	−0.717646	−	1.24300i	−0.961930	−	0.273295i	$-0.911886\pi$
$827$	−20.6378	−	35.7457i	−0.717646	−	1.24300i	0.244284	−	0.969704i	$-0.421447\pi$
$828$		0			0
$829$	14.4000	−	24.9416i	0.500133	−	0.866257i	−0.499867	−	0.866102i	$-0.666618\pi$
$829$	14.4000	−	24.9416i	0.500133	−	0.866257i	1.00000		0.000154088i	$-4.90477e-5\pi$
$830$	6.64998	+	5.57999i	0.230824	+	0.193684i
$831$		0			0
$832$	0.120002	+	0.680564i	0.00416031	+	0.0235943i
$833$	−0.817738	+	0.686163i	−0.0283329	+	0.0237741i
$834$		0			0
$835$	4.73691	−	1.72409i	0.163928	−	0.0596648i
$836$	52.6581			1.82122
$837$		0			0
$838$	5.37141			0.185552
$839$	31.3323	−	11.4040i	1.08171	−	0.393710i	0.261167	−	0.965294i	$-0.415893\pi$
$839$	31.3323	−	11.4040i	1.08171	−	0.393710i	0.820544	+	0.571583i	$0.193671\pi$
$840$		0			0
$841$	18.2730	−	15.3329i	0.630105	−	0.528721i
$842$	−1.18329	−	6.71077i	−0.0407789	−	0.231269i
$843$		0			0
$844$	28.9052	+	24.2543i	0.994956	+	0.834868i
$845$	−12.8873	+	22.3215i	−0.443337	+	0.767882i
$846$		0			0
$847$	−3.54502	−	6.14015i	−0.121808	−	0.210978i
$848$	−3.79747	+	21.5365i	−0.130406	+	0.739568i
$849$		0			0
$850$	0.286331	+	0.104216i	0.00982107	+	0.00357458i
$851$	0.637239	+	0.231936i	0.0218443	+	0.00795067i
$852$		0			0
$853$	7.32620	−	41.5489i	0.250844	−	1.42261i	−0.555675	−	0.831400i	$-0.687540\pi$
$853$	7.32620	−	41.5489i	0.250844	−	1.42261i	0.806519	−	0.591208i	$-0.201349\pi$
$854$	0.632477	+	1.09548i	0.0216429	+	0.0374866i
$855$		0			0
$856$	4.00415	−	6.93539i	0.136859	−	0.237047i
$857$	−22.8265	−	19.1537i	−0.779737	−	0.654277i	0.163445	−	0.986552i	$-0.447739\pi$
$857$	−22.8265	−	19.1537i	−0.779737	−	0.654277i	−0.943182	+	0.332275i	$0.892184\pi$
$858$		0			0
$859$	1.56271	+	8.86260i	0.0533191	+	0.302388i	0.999792	−	0.0203956i	$-0.00649256\pi$
$859$	1.56271	+	8.86260i	0.0533191	+	0.302388i	−0.946473	+	0.322783i	$0.895381\pi$
$860$	19.2037	−	16.1139i	0.654842	−	0.549478i
$861$		0			0
$862$	−2.45966	+	0.895242i	−0.0837763	+	0.0304921i
$863$	−7.45910			−0.253911			−0.126955	−	0.991908i	$-0.540521\pi$
$863$	−7.45910			−0.253911			−0.126955	+	0.991908i	$0.540521\pi$
$864$		0			0
$865$	−23.4156			−0.796155
$866$	−2.58183	+	0.939707i	−0.0877340	+	0.0319326i
$867$		0			0
$868$	3.97486	−	3.33530i	0.134915	−	0.113207i
$869$	−6.11763	−	34.6948i	−0.207526	−	1.17694i
$870$		0			0
$871$	−0.438393	−	0.367856i	−0.0148544	−	0.0124643i
$872$	2.47217	−	4.28193i	0.0837183	−	0.145004i
$873$		0			0
$874$	0.0617662	+	0.106982i	0.00208927	+	0.00361873i
$875$	2.08892	−	11.8468i	0.0706182	−	0.400496i
$876$		0			0
$877$	26.7934	+	9.75198i	0.904747	+	0.329301i	0.752154	−	0.658988i	$-0.229015\pi$
$877$	26.7934	+	9.75198i	0.904747	+	0.329301i	0.152594	+	0.988289i	$0.451237\pi$
$878$	8.52017	+	3.10109i	0.287542	+	0.104657i
$879$		0			0
$880$	−5.23482	+	29.6882i	−0.176466	+	1.00079i
$881$	−19.4723	−	33.7270i	−0.656038	−	1.13629i	−0.981633	−	0.190781i	$-0.938898\pi$
$881$	−19.4723	−	33.7270i	−0.656038	−	1.13629i	0.325595	−	0.945509i	$-0.394436\pi$
$882$		0			0
$883$	−10.1720	+	17.6184i	−0.342315	+	0.592908i	−0.984862	−	0.173339i	$-0.944544\pi$
$883$	−10.1720	+	17.6184i	−0.342315	+	0.592908i	0.642547	+	0.766246i	$0.277878\pi$
$884$	−0.172441	−	0.144695i	−0.00579982	−	0.00486663i
$885$		0			0
$886$	0.986587	+	5.59521i	0.0331450	+	0.187975i
$887$	−1.76932	+	1.48463i	−0.0594078	+	0.0498491i	−0.672008	−	0.740544i	$-0.734568\pi$
$887$	−1.76932	+	1.48463i	−0.0594078	+	0.0498491i	0.612600	+	0.790393i	$0.290124\pi$
$888$		0			0
$889$	8.46869	−	3.08235i	0.284031	−	0.103379i
$890$	−5.65443			−0.189537
$891$		0			0
$892$	4.96433			0.166218
$893$	67.1630	−	24.4453i	2.24752	−	0.818032i
$894$		0			0
$895$	35.1363	−	29.4828i	1.17448	−	0.985502i
$896$	1.36178	+	7.72305i	0.0454939	+	0.258009i
$897$		0			0
$898$	−3.79297	−	3.18268i	−0.126573	−	0.106207i
$899$	−9.78429	+	16.9469i	−0.326324	+	0.565210i
$900$		0			0
$901$	−3.26807	−	5.66046i	−0.108875	−	0.188577i
$902$	−0.616693	+	3.49744i	−0.0205336	+	0.116452i
$903$		0			0
$904$	−3.34552	−	1.21767i	−0.111270	−	0.0404991i
$905$	24.7893	+	9.02256i	0.824024	+	0.299920i
$906$		0			0
$907$	2.82975	−	16.0483i	0.0939602	−	0.532875i	−0.901101	−	0.433610i	$-0.857240\pi$
$907$	2.82975	−	16.0483i	0.0939602	−	0.532875i	0.995061	−	0.0992651i	$-0.0316492\pi$
$908$	−17.5161	−	30.3387i	−0.581291	−	1.00683i
$909$		0			0
$910$	0.0291795	−	0.0505404i	0.000967291	−	0.00167540i
$911$	11.3967	+	9.56299i	0.377590	+	0.316836i	0.811756	−	0.583997i	$-0.198512\pi$
$911$	11.3967	+	9.56299i	0.377590	+	0.316836i	−0.434165	+	0.900833i	$0.642957\pi$
$912$		0			0
$913$	12.0179	+	68.1570i	0.397735	+	2.25567i
$914$	−7.99111	+	6.70534i	−0.264322	+	0.221793i
$915$		0			0
$916$	42.9520	−	15.6332i	1.41917	−	0.516537i
$917$	−7.38926			−0.244015
$918$		0			0
$919$	−25.7942			−0.850871			−0.425435	−	0.904989i	$-0.639879\pi$
$919$	−25.7942			−0.850871			−0.425435	+	0.904989i	$0.639879\pi$
$920$	−0.140883	+	0.0512771i	−0.00464477	+	0.00169056i
$921$		0			0
$922$	−7.52640	+	6.31540i	−0.247869	+	0.207987i
$923$	0.219019	+	1.24212i	0.00720911	+	0.0408849i
$924$		0			0
$925$	−7.70924	−	6.46882i	−0.253478	−	0.212693i
$926$	−2.33228	+	4.03962i	−0.0766433	+	0.132750i
$927$		0			0
$928$	−11.1666	−	19.3411i	−0.366562	−	0.634903i
$929$	9.92436	−	56.2838i	0.325608	−	1.84661i	−0.179763	−	0.983710i	$-0.557533\pi$
$929$	9.92436	−	56.2838i	0.325608	−	1.84661i	0.505370	−	0.862903i	$-0.331356\pi$
$930$		0			0
$931$	6.03510	+	2.19660i	0.197793	+	0.0719906i
$932$	−17.4463	−	6.34994i	−0.571473	−	0.207999i
$933$		0			0
$934$	−1.08685	+	6.16381i	−0.0355627	+	0.201686i
$935$	−4.50504	−	7.80295i	−0.147330	−	0.255184i
$936$		0			0
$937$	11.3847	−	19.7189i	0.371922	−	0.644188i	−0.617939	−	0.786226i	$-0.712032\pi$
$937$	11.3847	−	19.7189i	0.371922	−	0.644188i	0.989861	+	0.142038i	$0.0453655\pi$
$938$	−1.07736	−	0.904014i	−0.0351771	−	0.0295171i
$939$		0			0
$940$	7.39282	+	41.9268i	0.241127	+	1.36750i
$941$	−4.54994	+	3.81785i	−0.148324	+	0.124458i	−0.713930	−	0.700217i	$-0.753087\pi$
$941$	−4.54994	+	3.81785i	−0.148324	+	0.124458i	0.565606	+	0.824675i	$0.308642\pi$
$942$		0			0
$943$	0.208828	−	0.0760073i	0.00680039	−	0.00247514i
$944$	−19.1967			−0.624800
$945$		0			0
$946$	−7.49264			−0.243607
$947$	7.62776	−	2.77628i	0.247869	−	0.0902170i	−0.215098	−	0.976592i	$-0.569007\pi$
$947$	7.62776	−	2.77628i	0.247869	−	0.0902170i	0.462967	+	0.886376i	$0.346785\pi$
$948$		0			0
$949$	−1.16034	+	0.973641i	−0.0376662	+	0.0316057i
$950$	−0.318340	−	1.80540i	−0.0103283	−	0.0585748i
$951$		0			0
$952$	−0.863444	−	0.724515i	−0.0279844	−	0.0234817i
$953$	7.23985	−	12.5398i	0.234522	−	0.406204i	−0.724612	−	0.689157i	$-0.757981\pi$
$953$	7.23985	−	12.5398i	0.234522	−	0.406204i	0.959134	+	0.282954i	$0.0913142\pi$
$954$		0			0
$955$	−5.60652	−	9.71078i	−0.181423	−	0.314233i
$956$	−3.34852	+	18.9904i	−0.108299	+	0.614194i
$957$		0			0
$958$	0.196979	+	0.0716946i	0.00636411	+	0.00231635i
$959$	15.2566	+	5.55297i	0.492663	+	0.179315i
$960$		0			0
$961$	−4.12500	+	23.3940i	−0.133065	+	0.754646i
$962$	−0.139361	−	0.241381i	−0.00449319	−	0.00778243i
$963$		0			0
$964$	1.63784	−	2.83682i	0.0527513	−	0.0913679i
$965$	18.2464	+	15.3105i	0.587372	+	0.492864i
$966$		0			0
$967$	5.15678	+	29.2455i	0.165831	+	0.940473i	0.948204	+	0.317663i	$0.102898\pi$
$967$	5.15678	+	29.2455i	0.165831	+	0.940473i	−0.782373	+	0.622810i	$0.785991\pi$
$968$	5.73485	−	4.81211i	0.184325	−	0.154667i
$969$		0			0
$970$	−0.884237	+	0.321836i	−0.0283911	+	0.0103335i
$971$	−40.4986			−1.29966			−0.649831	−	0.760079i	$-0.725160\pi$
$971$	−40.4986			−1.29966			−0.649831	+	0.760079i	$0.725160\pi$
$972$		0			0
$973$	−7.34736			−0.235546
$974$	8.93409	−	3.25174i	0.286267	−	0.104193i
$975$		0			0
$976$	12.8740	−	10.8026i	0.412087	−	0.345782i
$977$	−4.17470	−	23.6759i	−0.133561	−	0.757460i	−0.975851	−	0.218436i	$-0.929904\pi$
$977$	−4.17470	−	23.6759i	−0.133561	−	0.757460i	0.842291	−	0.539024i	$-0.181207\pi$
$978$		0			0
$979$	−34.5331	−	28.9767i	−1.10368	−	0.926099i
$980$	−1.91278	+	3.31303i	−0.0611015	+	0.105831i
$981$		0			0
$982$	5.39592	+	9.34601i	0.172191	+	0.298243i
$983$	−6.92615	+	39.2802i	−0.220910	+	1.25284i	0.649441	+	0.760412i	$0.275003\pi$
$983$	−6.92615	+	39.2802i	−0.220910	+	1.25284i	−0.870351	+	0.492431i	$0.836108\pi$
$984$		0			0
$985$	−39.4567	−	14.3610i	−1.25719	−	0.457581i
$986$	1.96048	+	0.713556i	0.0624344	+	0.0227242i
$987$		0			0
$988$	−0.235178	+	1.33376i	−0.00748200	+	0.0424325i
$989$	0.234429	+	0.406042i	0.00745439	+	0.0129114i
$990$		0			0
$991$	20.5144	−	35.5320i	0.651661	−	1.12871i	−0.331059	−	0.943610i	$-0.607406\pi$
$991$	20.5144	−	35.5320i	0.651661	−	1.12871i	0.982720	−	0.185100i	$-0.0592609\pi$
$992$	6.33415	+	5.31498i	0.201109	+	0.168751i
$993$		0			0
$994$	0.538246	+	3.05254i	0.0170721	+	0.0968208i
$995$	−7.48730	+	6.28259i	−0.237363	+	0.199172i
$996$		0			0
$997$	16.9933	−	6.18504i	0.538182	−	0.195882i	−0.0586062	−	0.998281i	$-0.518666\pi$
$997$	16.9933	−	6.18504i	0.538182	−	0.195882i	0.596788	+	0.802399i	$0.296443\pi$
$998$	−1.57435			−0.0498353
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.v.b.505.5		54
3.2	odd	2		189.2.v.a.169.5	yes	54
27.2	odd	18		5103.2.a.i.1.14		27
27.4	even	9	inner	567.2.v.b.64.5		54
27.23	odd	18		189.2.v.a.85.5	✓	54
27.25	even	9		5103.2.a.f.1.14		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.a.85.5	✓	54	27.23	odd	18
189.2.v.a.169.5	yes	54	3.2	odd	2
567.2.v.b.64.5		54	27.4	even	9	inner
567.2.v.b.505.5		54	1.1	even	1	trivial
5103.2.a.f.1.14		27	27.25	even	9
5103.2.a.i.1.14		27	27.2	odd	18

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.252618 - 0.0919454i) q^{2} +(-1.47673 + 1.23912i) q^{4} +(-0.344603 - 1.95434i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-0.527947 + 0.914430i) q^{8} +O(q^{10})\)	\(q+(0.252618 - 0.0919454i) q^{2} +(-1.47673 + 1.23912i) q^{4} +(-0.344603 - 1.95434i) q^{5} +(0.766044 + 0.642788i) q^{7} +(-0.527947 + 0.914430i) q^{8} +(-0.266746 - 0.462017i) q^{10} +(0.738567 - 4.18862i) q^{11} +(0.102794 + 0.0374138i) q^{13} +(0.252618 + 0.0919454i) q^{14} +(0.620203 - 3.51734i) q^{16} +(0.533740 + 0.924465i) q^{17} +(3.21121 - 5.56198i) q^{19} +(2.93055 + 2.45902i) q^{20} +(-0.198549 - 1.12603i) q^{22} +(-0.0548097 + 0.0459908i) q^{23} +(0.997769 - 0.363158i) q^{25} +0.0294076 q^{26} -1.92773 q^{28} +(6.83162 - 2.48651i) q^{29} +(-2.06194 + 1.73017i) q^{31} +(-0.533437 - 3.02527i) q^{32} +(0.219833 + 0.184462i) q^{34} +(0.992245 - 1.71862i) q^{35} +(-4.73896 - 8.20813i) q^{37} +(0.299811 - 1.70031i) q^{38} +(1.96904 + 0.716672i) q^{40} +(-2.91868 - 1.06231i) q^{41} +(1.13791 - 6.45340i) q^{43} +(4.09955 + 7.10062i) q^{44} +(-0.00961727 + 0.0166576i) q^{46} +(8.52509 + 7.15340i) q^{47} +(0.173648 + 0.984808i) q^{49} +(0.218664 - 0.183480i) q^{50} +(-0.198158 + 0.0721238i) q^{52} -6.12296 q^{53} -8.44050 q^{55} +(-0.992215 + 0.361137i) q^{56} +(1.49717 - 1.25627i) q^{58} +(-0.933327 - 5.29316i) q^{59} +(3.60454 + 3.02457i) q^{61} +(-0.361801 + 0.626658i) q^{62} +(3.15869 + 5.47101i) q^{64} +(0.0376964 - 0.213787i) q^{65} +(-4.91604 - 1.78929i) q^{67} +(-1.93371 - 0.703814i) q^{68} +(0.0926397 - 0.525386i) q^{70} +(5.76503 + 9.98533i) q^{71} +(-6.92342 + 11.9917i) q^{73} +(-1.95185 - 1.63779i) q^{74} +(2.14989 + 12.1926i) q^{76} +(3.25817 - 2.73393i) q^{77} +(7.78358 - 2.83299i) q^{79} -7.08781 q^{80} -0.834985 q^{82} +(-15.2906 + 5.56533i) q^{83} +(1.62279 - 1.36168i) q^{85} +(-0.305904 - 1.73487i) q^{86} +(3.44028 + 2.88674i) q^{88} +(5.29946 - 9.17893i) q^{89} +(0.0546954 + 0.0947352i) q^{91} +(0.0239508 - 0.135832i) q^{92} +(2.81131 + 1.02323i) q^{94} +(-11.9766 - 4.35913i) q^{95} +(0.306285 - 1.73703i) q^{97} +(0.134415 + 0.232814i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{5} + 27 q^{8}+O(q^{10}) \) 54 * q + 3 * q^5 + 27 * q^8	\( 54 q + 3 q^{5} + 27 q^{8} + 6 q^{11} - 9 q^{13} + 30 q^{17} + 12 q^{20} - 9 q^{22} + 12 q^{23} + 27 q^{25} - 18 q^{26} + 54 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 9 q^{34} + 12 q^{35} - 54 q^{38} - 45 q^{40} + 15 q^{41} - 9 q^{43} + 42 q^{44} + 45 q^{47} - 18 q^{50} - 63 q^{52} - 132 q^{53} + 9 q^{56} - 27 q^{58} + 36 q^{62} - 27 q^{64} - 66 q^{65} + 45 q^{67} - 87 q^{68} + 72 q^{71} + 72 q^{74} + 54 q^{76} - 3 q^{77} - 36 q^{79} - 42 q^{80} - 24 q^{83} + 18 q^{85} + 90 q^{86} + 54 q^{88} + 42 q^{89} - 87 q^{92} - 90 q^{94} - 12 q^{95} - 18 q^{97} + 9 q^{98}+O(q^{100}) \) 54 * q + 3 * q^5 + 27 * q^8 + 6 * q^11 - 9 * q^13 + 30 * q^17 + 12 * q^20 - 9 * q^22 + 12 * q^23 + 27 * q^25 - 18 * q^26 + 54 * q^28 - 6 * q^29 - 9 * q^31 + 9 * q^32 - 9 * q^34 + 12 * q^35 - 54 * q^38 - 45 * q^40 + 15 * q^41 - 9 * q^43 + 42 * q^44 + 45 * q^47 - 18 * q^50 - 63 * q^52 - 132 * q^53 + 9 * q^56 - 27 * q^58 + 36 * q^62 - 27 * q^64 - 66 * q^65 + 45 * q^67 - 87 * q^68 + 72 * q^71 + 72 * q^74 + 54 * q^76 - 3 * q^77 - 36 * q^79 - 42 * q^80 - 24 * q^83 + 18 * q^85 + 90 * q^86 + 54 * q^88 + 42 * q^89 - 87 * q^92 - 90 * q^94 - 12 * q^95 - 18 * q^97 + 9 * q^98

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