LMFDB - Embedded newform 270.2.m.b.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.2
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	270.17
Dual form			270.2.m.b.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.22612 + 0.210717i) q^{5} +(-0.521929 + 1.94786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.22612 + 0.210717i) q^{5} +(-0.521929 + 1.94786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +(1.70563 - 0.984748i) q^{11} +(1.05248 + 3.92790i) q^{13} +(1.00829 - 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.35877 + 2.35877i) q^{17} -3.70753i q^{19} +(1.82252 + 1.29554i) q^{20} +(-1.90239 + 0.509743i) q^{22} +(6.05338 - 1.62200i) q^{23} +(4.91120 + 0.938160i) q^{25} -4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.88889 - 1.66790i) q^{34} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-0.959578 + 3.58120i) q^{38} +(-1.42510 - 1.72310i) q^{40} +(-6.13601 - 3.54263i) q^{41} +(-9.09714 - 2.43757i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(-7.49533 - 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(-4.50104 - 2.17730i) q^{50} +(-1.05248 + 3.92790i) q^{52} +(-7.03027 - 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +(1.74641 - 1.00829i) q^{56} +(-1.94043 - 7.24179i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 + 4.93330i) q^{62} +1.00000i q^{64} +(1.51527 + 8.96575i) q^{65} +(-8.18285 + 2.19259i) q^{67} +(-3.22213 + 0.863368i) q^{68} +(2.61257 - 3.67524i) q^{70} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(1.02794 + 3.83631i) q^{77} +(-10.0535 + 5.80440i) q^{79} +(0.930573 + 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(0.440961 - 1.64569i) q^{83} +(-5.74792 + 4.75386i) q^{85} +(8.15627 + 4.70902i) q^{86} +(-1.90239 - 0.509743i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(6.05338 + 1.62200i) q^{92} +(6.72013 + 3.87987i) q^{94} +(0.781237 - 8.25339i) q^{95} +(2.60421 - 9.71905i) q^{97} +(-2.07424 - 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.22612	+	0.210717i	0.995550	+	0.0942354i
$5$	2.22612	+	0.210717i	0.995550	+	0.0942354i
$6$		0			0
$7$	−0.521929	+	1.94786i	−0.197270	+	0.736223i	0.794397	+	0.607399i	$0.207787\pi$
$7$	−0.521929	+	1.94786i	−0.197270	+	0.736223i	−0.991667	+	0.128824i	$0.958880\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−2.09573	−	0.779698i	−0.662727	−	0.246562i
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	−0.220318	−	0.975428i	$-0.570710\pi$
$11$	1.70563	−	0.984748i	0.514268	−	0.296913i	0.734586	+	0.678515i	$0.237376\pi$
$12$		0			0
$13$	1.05248	+	3.92790i	0.291905	+	1.08940i	0.943644	+	0.330961i	$0.107373\pi$
$13$	1.05248	+	3.92790i	0.291905	+	1.08940i	−0.651739	+	0.758443i	$0.725960\pi$
$14$	1.00829	−	1.74641i	0.269476	−	0.466747i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	−0.932711	−	0.360626i	$-0.882563\pi$
$17$	−2.35877	+	2.35877i	−0.572085	+	0.572085i	0.360626	+	0.932711i	$0.382563\pi$
$18$		0			0
$19$		−	3.70753i		−	0.850565i	−0.905061	−	0.425282i	$-0.860175\pi$
$19$		−	3.70753i		−	0.850565i	0.905061	−	0.425282i	$-0.139825\pi$
$20$	1.82252	+	1.29554i	0.407527	+	0.289693i
$21$		0			0
$22$	−1.90239	+	0.509743i	−0.405590	+	0.108678i
$23$	6.05338	−	1.62200i	1.26222	−	0.338210i	0.435173	−	0.900347i	$-0.356687\pi$
$23$	6.05338	−	1.62200i	1.26222	−	0.338210i	0.827044	+	0.562137i	$0.190021\pi$
$24$		0			0
$25$	4.91120	+	0.938160i	0.982239	+	0.187632i
$26$		−	4.06647i		−	0.797499i
$27$		0			0
$28$	−1.42594	+	1.42594i	−0.269476	+	0.269476i
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	0.969808	+	0.243872i	$0.0784175\pi$
$29$	3.74863	+	6.49281i	0.696103	+	1.20569i	−0.273705	+	0.961814i	$0.588249\pi$
$30$		0			0
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	−0.361713	−	0.932289i	$-0.617808\pi$
$31$	3.48837	−	6.04204i	0.626530	−	1.08518i	0.988243	−	0.152892i	$-0.0488587\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	2.88889	−	1.66790i	0.495440	−	0.286042i
$35$	−1.57232	+	4.22619i	−0.265771	+	0.714357i
$36$		0			0
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	0.964728	−	0.263250i	$-0.0847944\pi$
$37$	4.26692	+	4.26692i	0.701478	+	0.701478i	−0.263250	+	0.964728i	$0.584794\pi$
$38$	−0.959578	+	3.58120i	−0.155664	+	0.580947i
$39$		0			0
$40$	−1.42510	−	1.72310i	−0.225329	−	0.272446i
$41$	−6.13601	−	3.54263i	−0.958284	−	0.553266i	−0.0626396	−	0.998036i	$-0.519952\pi$
$41$	−6.13601	−	3.54263i	−0.958284	−	0.553266i	−0.895644	+	0.444771i	$0.853285\pi$
$42$		0			0
$43$	−9.09714	−	2.43757i	−1.38730	−	0.371726i	−0.513533	−	0.858070i	$-0.671664\pi$
$43$	−9.09714	−	2.43757i	−1.38730	−	0.371726i	−0.873767	+	0.486344i	$0.838330\pi$
$44$	1.96950			0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	−7.49533	−	2.00837i	−1.09331	−	0.292951i	−0.333270	−	0.942831i	$-0.608152\pi$
$47$	−7.49533	−	2.00837i	−1.09331	−	0.292951i	−0.760036	+	0.649881i	$0.774819\pi$
$48$		0			0
$49$	2.54041	+	1.46671i	0.362916	+	0.209530i
$50$	−4.50104	−	2.17730i	−0.636543	−	0.307917i
$51$		0			0
$52$	−1.05248	+	3.92790i	−0.145953	+	0.544702i
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	0.0337485	−	0.999430i	$-0.489255\pi$
$53$	−7.03027	−	7.03027i	−0.965682	−	0.965682i	−0.999430	+	0.0337485i	$0.989255\pi$
$54$		0			0
$55$	4.00444	−	1.83276i	0.539959	−	0.247129i
$56$	1.74641	−	1.00829i	0.233373	−	0.134738i
$57$		0			0
$58$	−1.94043	−	7.24179i	−0.254791	−	0.950894i
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	−0.940407	−	0.340050i	$-0.889556\pi$
$59$	−1.34967	+	2.33769i	−0.175712	+	0.304341i	0.764696	+	0.644392i	$0.222889\pi$
$60$		0			0
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	−0.997498	−	0.0706960i	$-0.977478\pi$
$61$	−4.37353	−	7.57518i	−0.559973	−	0.969902i	0.437524	−	0.899207i	$-0.355855\pi$
$62$	−4.93330	+	4.93330i	−0.626530	+	0.626530i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	1.51527	+	8.96575i	0.187946	+	1.11206i
$66$		0			0
$67$	−8.18285	+	2.19259i	−0.999694	+	0.267867i	−0.721317	−	0.692605i	$-0.756463\pi$
$67$	−8.18285	+	2.19259i	−0.999694	+	0.267867i	−0.278377	+	0.960472i	$0.589796\pi$
$68$	−3.22213	+	0.863368i	−0.390741	+	0.104699i
$69$		0			0
$70$	2.61257	−	3.67524i	0.312261	−	0.439276i
$71$		−	5.68481i		−	0.674663i	−0.941386	−	0.337332i	$-0.890476\pi$
$71$		−	5.68481i		−	0.674663i	0.941386	−	0.337332i	$-0.109524\pi$
$72$		0			0
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	−0.636645	−	0.771157i	$-0.719678\pi$
$73$	1.14928	−	1.14928i	0.134513	−	0.134513i	0.771157	+	0.636645i	$0.219678\pi$
$74$	−3.01717	−	5.22589i	−0.350739	−	0.607498i
$75$		0			0
$76$	1.85376	−	3.21081i	0.212641	−	0.368305i
$77$	1.02794	+	3.83631i	0.117144	+	0.437188i
$78$		0			0
$79$	−10.0535	+	5.80440i	−1.13111	+	0.653046i	−0.944214	−	0.329334i	$-0.893176\pi$
$79$	−10.0535	+	5.80440i	−1.13111	+	0.653046i	−0.186895	+	0.982380i	$0.559842\pi$
$80$	0.930573	+	2.03323i	0.104041	+	0.227322i
$81$		0			0
$82$	5.01003	+	5.01003i	0.553266	+	0.553266i
$83$	0.440961	−	1.64569i	0.0484017	−	0.180638i	−0.937493	−	0.348004i	$-0.886860\pi$
$83$	0.440961	−	1.64569i	0.0484017	−	0.180638i	0.985895	+	0.167366i	$0.0535262\pi$
$84$		0			0
$85$	−5.74792	+	4.75386i	−0.623449	+	0.515628i
$86$	8.15627	+	4.70902i	0.879513	+	0.507787i
$87$		0			0
$88$	−1.90239	−	0.509743i	−0.202795	−	0.0543388i
$89$	2.04989			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$89$	2.04989			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	6.05338	+	1.62200i	0.631109	+	0.169105i
$93$		0			0
$94$	6.72013	+	3.87987i	0.693128	+	0.400178i
$95$	0.781237	−	8.25339i	0.0801533	−	0.846780i
$96$		0			0
$97$	2.60421	−	9.71905i	0.264418	−	0.986820i	−0.698188	−	0.715914i	$-0.746010\pi$
$97$	2.60421	−	9.71905i	0.264418	−	0.986820i	0.962606	−	0.270906i	$-0.0873232\pi$
$98$	−2.07424	−	2.07424i	−0.209530	−	0.209530i
$99$		0			0
$100$	3.78414	+	3.26807i	0.378414	+	0.326807i
$101$	4.09014	−	2.36144i	0.406984	−	0.234972i	−0.282509	−	0.959265i	$-0.591167\pi$
$101$	4.09014	−	2.36144i	0.406984	−	0.234972i	0.689493	+	0.724292i	$0.257833\pi$
$102$		0			0
$103$	1.03662	+	3.86872i	0.102141	+	0.381196i	0.998005	−	0.0631321i	$-0.0201089\pi$
$103$	1.03662	+	3.86872i	0.102141	+	0.381196i	−0.895864	+	0.444329i	$0.853442\pi$
$104$	2.03323	−	3.52166i	0.199375	−	0.345327i
$105$		0			0
$106$	4.97115	+	8.61029i	0.482841	+	0.836305i
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	−0.395949	−	0.918273i	$-0.629584\pi$
$107$	5.40296	−	5.40296i	0.522324	−	0.522324i	0.918273	+	0.395949i	$0.129584\pi$
$108$		0			0
$109$		−	4.35357i		−	0.416996i	−0.978023	−	0.208498i	$-0.933142\pi$
$109$		−	4.35357i		−	0.416996i	0.978023	−	0.208498i	$-0.0668575\pi$
$110$	−4.34235	+	0.733883i	−0.414027	+	0.0699730i
$111$		0			0
$112$	−1.94786	+	0.521929i	−0.184056	+	0.0493176i
$113$	−2.86451	+	0.767544i	−0.269471	+	0.0722045i	−0.391024	−	0.920380i	$-0.627879\pi$
$113$	−2.86451	+	0.767544i	−0.269471	+	0.0722045i	0.121553	+	0.992585i	$0.461212\pi$
$114$		0			0
$115$	13.8173	−	2.33521i	1.28847	−	0.217760i
$116$			7.49726i			0.696103i
$117$		0			0
$118$	1.90872	−	1.90872i	0.175712	−	0.175712i
$119$	−3.36345	−	5.82566i	−0.308327	−	0.534037i
$120$		0			0
$121$	−3.56054	+	6.16704i	−0.323686	+	0.560640i
$122$	2.26391	+	8.44902i	0.204965	+	0.764938i
$123$		0			0
$124$	6.04204	−	3.48837i	0.542591	−	0.313265i
$125$	10.7352	+	3.12333i	0.960187	+	0.279359i
$126$		0			0
$127$	−3.41734	−	3.41734i	−0.303240	−	0.303240i	0.539040	−	0.842280i	$-0.318787\pi$
$127$	−3.41734	−	3.41734i	−0.303240	−	0.303240i	−0.842280	+	0.539040i	$0.818787\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$	0.856872	−	9.05243i	0.0751526	−	0.793950i
$131$	0.411267	+	0.237445i	0.0359326	+	0.0207457i	0.517859	−	0.855466i	$-0.326729\pi$
$131$	0.411267	+	0.237445i	0.0359326	+	0.0207457i	−0.481926	+	0.876212i	$0.660063\pi$
$132$		0			0
$133$	7.22176	+	1.93506i	0.626206	+	0.167791i
$134$	8.47151			0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	−9.51618	−	2.54985i	−0.813022	−	0.217849i	−0.171728	−	0.985144i	$-0.554935\pi$
$137$	−9.51618	−	2.54985i	−0.813022	−	0.217849i	−0.641293	+	0.767296i	$0.721602\pi$
$138$		0			0
$139$	0.608318	+	0.351212i	0.0515968	+	0.0297894i	0.525577	−	0.850746i	$-0.323850\pi$
$139$	0.608318	+	0.351212i	0.0515968	+	0.0297894i	−0.473980	+	0.880536i	$0.657183\pi$
$140$	−3.47477	+	2.87383i	−0.293671	+	0.242883i
$141$		0			0
$142$	−1.47134	+	5.49111i	−0.123472	+	0.460803i
$143$	5.66314	+	5.66314i	0.473575	+	0.473575i
$144$		0			0
$145$	6.97674	+	15.2437i	0.579387	+	1.26592i
$146$	−1.40757	+	0.812661i	−0.116491	+	0.0672563i
$147$		0			0
$148$	1.56180	+	5.82872i	0.128379	+	0.479118i
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	−0.982960	−	0.183819i	$-0.941154\pi$
$149$	−4.05609	+	7.02536i	−0.332288	+	0.575540i	0.650672	+	0.759359i	$0.274487\pi$
$150$		0			0
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	0.990440	−	0.137943i	$-0.0440491\pi$
$151$	4.61739	+	7.99755i	0.375758	+	0.650832i	−0.614682	+	0.788775i	$0.710716\pi$
$152$	−2.62162	+	2.62162i	−0.212641	+	0.212641i
$153$		0			0
$154$		−	3.97164i		−	0.320044i
$155$	9.03868	−	12.7152i	0.726004	−	1.02131i
$156$		0			0
$157$	10.4848	−	2.80938i	0.836775	−	0.224213i	0.185108	−	0.982718i	$-0.440736\pi$
$157$	10.4848	−	2.80938i	0.836775	−	0.224213i	0.651667	+	0.758505i	$0.274070\pi$
$158$	11.2132	−	3.00458i	0.892077	−	0.239031i
$159$		0			0
$160$	−0.372625	−	2.20480i	−0.0294586	−	0.174305i
$161$			12.6377i			0.995993i
$162$		0			0
$163$	9.68197	−	9.68197i	0.758351	−	0.758351i	−0.217671	−	0.976022i	$-0.569846\pi$
$163$	9.68197	−	9.68197i	0.758351	−	0.758351i	0.976022	+	0.217671i	$0.0698461\pi$
$164$	−3.54263	−	6.13601i	−0.276633	−	0.479142i
$165$		0			0
$166$	−0.851871	+	1.47548i	−0.0661180	+	0.114520i
$167$	−1.32254	−	4.93579i	−0.102341	−	0.381943i	0.895689	−	0.444682i	$-0.146683\pi$
$167$	−1.32254	−	4.93579i	−0.102341	−	0.381943i	−0.998030	+	0.0627387i	$0.980017\pi$
$168$		0			0
$169$	−3.06239	+	1.76807i	−0.235568	+	0.136005i
$170$	6.78245	−	3.10420i	0.520190	−	0.238081i
$171$		0			0
$172$	−6.65957	−	6.65957i	−0.507787	−	0.507787i
$173$	1.91916	−	7.16239i	0.145911	−	0.544546i	−0.853802	−	0.520597i	$-0.825709\pi$
$173$	1.91916	−	7.16239i	0.145911	−	0.544546i	0.999713	−	0.0239492i	$-0.00762400\pi$
$174$		0			0
$175$	−4.39070	+	9.07669i	−0.331906	+	0.686133i
$176$	1.70563	+	0.984748i	0.128567	+	0.0742282i
$177$		0			0
$178$	−1.98004	−	0.530550i	−0.148410	−	0.0397664i
$179$	−2.73426			−0.204369			−0.102184	−	0.994765i	$-0.532583\pi$
$179$	−2.73426			−0.204369			−0.102184	+	0.994765i	$0.532583\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	7.92092	+	2.12240i	0.587138	+	0.157323i
$183$		0			0
$184$	−5.42731	−	3.13346i	−0.400107	−	0.231002i
$185$	8.59956	+	10.3978i	0.632252	+	0.764460i
$186$		0			0
$187$	−1.70040	+	6.34598i	−0.124346	+	0.464064i
$188$	−5.48696	−	5.48696i	−0.400178	−	0.400178i
$189$		0			0
$190$	−2.89075	+	7.76996i	−0.209717	+	0.563692i
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	−0.459246	−	0.888309i	$-0.651881\pi$
$191$	1.11154	−	0.641749i	0.0804283	−	0.0464353i	0.539675	+	0.841874i	$0.318547\pi$
$192$		0			0
$193$	1.41494	+	5.28063i	0.101850	+	0.380108i	0.997969	−	0.0637057i	$-0.0202919\pi$
$193$	1.41494	+	5.28063i	0.101850	+	0.380108i	−0.896119	+	0.443814i	$0.853625\pi$
$194$	−5.03095	+	8.71386i	−0.361201	+	0.625619i
$195$		0			0
$196$	1.46671	+	2.54041i	0.104765	+	0.181458i
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	−0.133353	−	0.991069i	$-0.542574\pi$
$197$	12.0386	−	12.0386i	0.857716	−	0.857716i	0.991069	+	0.133353i	$0.0425744\pi$
$198$		0			0
$199$		−	4.43831i		−	0.314623i	−0.987549	−	0.157312i	$-0.949717\pi$
$199$		−	4.43831i		−	0.314623i	0.987549	−	0.157312i	$-0.0502827\pi$
$200$	−2.80936	−	4.13612i	−0.198652	−	0.292468i
$201$		0			0
$202$	−4.56196	+	1.22237i	−0.320978	+	0.0860058i
$203$	−14.6036	+	3.91303i	−1.02497	+	0.274641i
$204$		0			0
$205$	−12.9130	−	9.17927i	−0.901882	−	0.641108i
$206$		−	4.00520i		−	0.279055i
$207$		0			0
$208$	−2.87542	+	2.87542i	−0.199375	+	0.199375i
$209$	−3.65098	−	6.32368i	−0.252543	−	0.437418i
$210$		0			0
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	−0.0697556	−	0.997564i	$-0.522222\pi$
$211$	12.0425	−	20.8582i	0.829038	−	1.43594i	0.898794	−	0.438372i	$-0.144445\pi$
$212$	−2.57326	−	9.60353i	−0.176732	−	0.659573i
$213$		0			0
$214$	−6.61725	+	3.82047i	−0.452346	+	0.261162i
$215$	−19.7377	−	7.34324i	−1.34610	−	0.500805i
$216$		0			0
$217$	9.94838	+	9.94838i	0.675340	+	0.675340i
$218$	−1.12679	+	4.20523i	−0.0763156	+	0.284814i
$219$		0			0
$220$	4.38433	+	0.415006i	0.295591	+	0.0279797i
$221$	−11.7476	−	6.78245i	−0.790226	−	0.456237i
$222$		0			0
$223$	−16.2073	−	4.34272i	−1.08532	−	0.290810i	−0.328546	−	0.944488i	$-0.606559\pi$
$223$	−16.2073	−	4.34272i	−1.08532	−	0.290810i	−0.756773	+	0.653678i	$0.773225\pi$
$224$	2.01658			0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	−7.18543	−	1.92533i	−0.476914	−	0.127789i	0.0123515	−	0.999924i	$-0.496068\pi$
$227$	−7.18543	−	1.92533i	−0.476914	−	0.127789i	−0.489265	+	0.872135i	$0.662735\pi$
$228$		0			0
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	0.221894	−	0.975071i	$-0.428776\pi$
$229$	−7.74183	−	4.46975i	−0.511595	−	0.295369i	−0.733489	+	0.679701i	$0.762109\pi$
$230$	−13.9509	−	1.32054i	−0.919895	−	0.0870742i
$231$		0			0
$232$	1.94043	−	7.24179i	0.127396	−	0.475447i
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	0.999911	−	0.0133533i	$-0.00425061\pi$
$233$	15.0591	+	15.0591i	0.986558	+	0.986558i	−0.0133533	+	0.999911i	$0.504251\pi$
$234$		0			0
$235$	−16.2623	−	6.05025i	−1.06083	−	0.394675i
$236$	−2.33769	+	1.34967i	−0.152171	+	0.0878558i
$237$		0			0
$238$	1.74105	+	6.49768i	0.112855	+	0.421182i
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	−0.986436	−	0.164146i	$-0.947513\pi$
$239$	−5.42731	+	9.40038i	−0.351064	+	0.608060i	0.635372	+	0.772206i	$0.280847\pi$
$240$		0			0
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	0.947112	+	0.320904i	$0.103987\pi$
$241$	11.6659	+	20.2059i	0.751467	+	1.30158i	−0.195645	+	0.980675i	$0.562680\pi$
$242$	5.03537	−	5.03537i	0.323686	−	0.323686i
$243$		0			0
$244$		−	8.74707i		−	0.559973i
$245$	5.34620	+	3.80037i	0.341556	+	0.242797i
$246$		0			0
$247$	14.5628	−	3.90209i	0.926609	−	0.248284i
$248$	−6.73901	+	1.80571i	−0.427928	+	0.114663i
$249$		0			0
$250$	−9.56105	−	5.79538i	−0.604694	−	0.366532i
$251$			13.3860i			0.844914i	0.906383	+	0.422457i	$0.138832\pi$
$251$			13.3860i			0.844914i	−0.906383	+	0.422457i	$0.861168\pi$
$252$		0			0
$253$	8.72759	−	8.72759i	0.548699	−	0.548699i
$254$	2.41643	+	4.18538i	0.151620	+	0.262614i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.95494	+	7.29595i	0.121946	+	0.455109i	0.999712	−	0.0239802i	$-0.00763386\pi$
$257$	1.95494	+	7.29595i	0.121946	+	0.455109i	−0.877766	+	0.479089i	$0.840967\pi$
$258$		0			0
$259$	−10.5384	+	6.08436i	−0.654825	+	0.378063i
$260$	−3.17062	+	8.52220i	−0.196633	+	0.528524i
$261$		0			0
$262$	−0.335798	−	0.335798i	−0.0207457	−	0.0207457i
$263$	−2.88569	+	10.7695i	−0.177939	+	0.664078i	0.818093	+	0.575086i	$0.195031\pi$
$263$	−2.88569	+	10.7695i	−0.177939	+	0.664078i	−0.996032	+	0.0889923i	$0.971635\pi$
$264$		0			0
$265$	−14.1688	−	17.1316i	−0.870383	−	1.05239i
$266$	−6.47485	−	3.73826i	−0.396998	−	0.229207i
$267$		0			0
$268$	−8.18285	−	2.19259i	−0.499847	−	0.133934i
$269$	−13.4707			−0.821326			−0.410663	−	0.911787i	$-0.634703\pi$
$269$	−13.4707			−0.821326			−0.410663	+	0.911787i	$0.634703\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	−3.22213	−	0.863368i	−0.195371	−	0.0523494i
$273$		0			0
$274$	8.53197	+	4.92594i	0.515435	+	0.297587i
$275$	9.30055	−	3.23613i	0.560844	−	0.195146i
$276$		0			0
$277$	6.27326	−	23.4121i	0.376924	−	1.40670i	−0.473590	−	0.880745i	$-0.657042\pi$
$277$	6.27326	−	23.4121i	0.376924	−	1.40670i	0.850514	−	0.525953i	$-0.176291\pi$
$278$	−0.496689	−	0.496689i	−0.0297894	−	0.0297894i
$279$		0			0
$280$	4.10017	−	1.87657i	0.245032	−	0.112147i
$281$	−19.5424	+	11.2828i	−1.16580	+	0.673076i	−0.952687	−	0.303952i	$-0.901694\pi$
$281$	−19.5424	+	11.2828i	−1.16580	+	0.673076i	−0.213114	+	0.977027i	$0.568360\pi$
$282$		0			0
$283$	0.549660	+	2.05136i	0.0326739	+	0.121941i	0.980337	−	0.197333i	$-0.0632279\pi$
$283$	0.549660	+	2.05136i	0.0326739	+	0.121941i	−0.947663	+	0.319273i	$0.896561\pi$
$284$	2.84241	−	4.92319i	0.168666	−	0.292138i
$285$		0			0
$286$	−4.00444	−	6.93590i	−0.236788	−	0.410128i
$287$	10.1031	−	10.1031i	0.596368	−	0.596368i
$288$		0			0
$289$			5.87245i			0.345438i
$290$	−2.79366	−	16.5300i	−0.164050	−	0.970673i
$291$		0			0
$292$	1.56994	−	0.420664i	0.0918738	−	0.0246175i
$293$	3.53204	−	0.946406i	0.206344	−	0.0552896i	−0.154167	−	0.988045i	$-0.549269\pi$
$293$	3.53204	−	0.946406i	0.206344	−	0.0552896i	0.360510	+	0.932755i	$0.382603\pi$
$294$		0			0
$295$	−3.49711	+	4.91958i	−0.203609	+	0.286429i
$296$		−	6.03434i		−	0.350739i
$297$		0			0
$298$	5.73618	−	5.73618i	0.332288	−	0.332288i
$299$	12.7421	+	22.0700i	0.736895	+	1.27634i
$300$		0			0
$301$	9.49611	−	16.4477i	0.547347	−	0.948032i
$302$	−2.39014	−	8.92011i	−0.137537	−	0.513295i
$303$		0			0
$304$	3.21081	−	1.85376i	0.184153	−	0.106321i
$305$	−8.13978	−	17.7848i	−0.466082	−	1.01836i
$306$		0			0
$307$	−10.5436	−	10.5436i	−0.601754	−	0.601754i	0.339024	−	0.940778i	$-0.389903\pi$
$307$	−10.5436	−	10.5436i	−0.601754	−	0.601754i	−0.940778	+	0.339024i	$0.889903\pi$
$308$	−1.02794	+	3.83631i	−0.0585721	+	0.218594i
$309$		0			0
$310$	−12.0216	+	9.94258i	−0.682783	+	0.564701i
$311$	9.08436	+	5.24485i	0.515127	+	0.297408i	0.734938	−	0.678134i	$-0.237211\pi$
$311$	9.08436	+	5.24485i	0.515127	+	0.297408i	−0.219812	+	0.975542i	$0.570544\pi$
$312$		0			0
$313$	17.0518	+	4.56901i	0.963824	+	0.258256i	0.706218	−	0.707994i	$-0.250400\pi$
$313$	17.0518	+	4.56901i	0.963824	+	0.258256i	0.257606	+	0.966250i	$0.417066\pi$
$314$	−10.8546			−0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	22.3972	+	6.00131i	1.25795	+	0.337067i	0.825403	−	0.564543i	$-0.190948\pi$
$317$	22.3972	+	6.00131i	1.25795	+	0.337067i	0.432549	+	0.901611i	$0.357614\pi$
$318$		0			0
$319$	12.7876	+	7.38291i	0.715966	+	0.413363i
$320$	−0.210717	+	2.22612i	−0.0117794	+	0.124444i
$321$		0			0
$322$	3.27089	−	12.2071i	0.182279	−	0.680276i
$323$	8.74518	+	8.74518i	0.486595	+	0.486595i
$324$		0			0
$325$	1.48393	+	20.2781i	0.0823135	+	1.12483i
$326$	−11.8579	+	6.84619i	−0.656751	+	0.379175i
$327$		0			0
$328$	1.83380	+	6.84383i	0.101255	+	0.377887i
$329$	7.82405	−	13.5517i	0.431354	−	0.747127i
$330$		0			0
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	0.964946	+	0.262450i	$0.0845303\pi$
$331$	12.9130	+	22.3659i	0.709761	+	1.22934i	−0.255185	+	0.966892i	$0.582136\pi$
$332$	1.20473	−	1.20473i	0.0661180	−	0.0661180i
$333$		0			0
$334$			5.10991i			0.279602i
$335$	−18.6780	+	3.15670i	−1.02049	+	0.172469i
$336$		0			0
$337$	−30.9889	+	8.30344i	−1.68807	+	0.452317i	−0.969891	−	0.243541i	$-0.921691\pi$
$337$	−30.9889	+	8.30344i	−1.68807	+	0.452317i	−0.718180	+	0.695858i	$0.755024\pi$
$338$	3.41565	−	0.915220i	0.185787	−	0.0497814i
$339$		0			0
$340$	−7.35477	+	1.24300i	−0.398869	+	0.0674112i
$341$		−	13.7407i		−	0.744099i
$342$		0			0
$343$	−14.1644	+	14.1644i	−0.764806	+	0.764806i
$344$	4.70902	+	8.15627i	0.253894	+	0.439757i
$345$		0			0
$346$	−3.70753	+	6.42162i	−0.199318	+	0.345229i
$347$	3.83170	+	14.3001i	0.205696	+	0.767670i	0.989236	+	0.146328i	$0.0467454\pi$
$347$	3.83170	+	14.3001i	0.205696	+	0.767670i	−0.783540	+	0.621342i	$0.786588\pi$
$348$		0			0
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	−0.0973439	−	0.995251i	$-0.531035\pi$
$349$	13.3741	−	7.72151i	0.715897	−	0.413323i	0.813241	+	0.581928i	$0.197701\pi$
$350$	6.59031	−	7.63101i	0.352267	−	0.407895i
$351$		0			0
$352$	−1.39264	−	1.39264i	−0.0742282	−	0.0742282i
$353$	5.39774	−	20.1446i	0.287293	−	1.07219i	−0.659855	−	0.751393i	$-0.729382\pi$
$353$	5.39774	−	20.1446i	0.287293	−	1.07219i	0.947148	−	0.320798i	$-0.103951\pi$
$354$		0			0
$355$	1.19788	−	12.6551i	0.0635771	−	0.671661i
$356$	1.77526	+	1.02494i	0.0940883	+	0.0543219i
$357$		0			0
$358$	2.64110	+	0.707680i	0.139586	+	0.0374020i
$359$	3.39466			0.179163			0.0895815	−	0.995979i	$-0.471447\pi$
$359$	3.39466			0.179163			0.0895815	+	0.995979i	$0.471447\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	21.9344	+	5.87729i	1.15284	+	0.308904i
$363$		0			0
$364$	−7.10170	−	4.10017i	−0.372230	−	0.214907i
$365$	2.80059	−	2.31625i	0.146590	−	0.121238i
$366$		0			0
$367$	5.68801	−	21.2279i	0.296912	−	1.10809i	−0.642776	−	0.766054i	$-0.722217\pi$
$367$	5.68801	−	21.2279i	0.296912	−	1.10809i	0.939687	−	0.342035i	$-0.111116\pi$
$368$	4.43138	+	4.43138i	0.231002	+	0.231002i
$369$		0			0
$370$	−5.61539	−	12.2692i	−0.291930	−	0.637846i
$371$	17.3633	−	10.0247i	0.901458	−	0.520457i
$372$		0			0
$373$	−0.381044	−	1.42207i	−0.0197297	−	0.0736322i	0.955359	−	0.295447i	$-0.0954686\pi$
$373$	−0.381044	−	1.42207i	−0.0197297	−	0.0736322i	−0.975089	+	0.221815i	$0.928802\pi$
$374$	3.28492	−	5.68965i	0.169859	−	0.294205i
$375$		0			0
$376$	3.87987	+	6.72013i	0.200089	+	0.346564i
$377$	−21.5578	+	21.5578i	−1.11028	+	1.11028i
$378$		0			0
$379$			30.1323i			1.54779i	0.633314	+	0.773895i	$0.281694\pi$
$379$			30.1323i			1.54779i	−0.633314	+	0.773895i	$0.718306\pi$
$380$	4.80327	−	6.75702i	0.246402	−	0.346628i
$381$		0			0
$382$	−1.23976	+	0.332194i	−0.0634318	+	0.0169965i
$383$	16.5638	−	4.43826i	0.846372	−	0.226785i	0.190528	−	0.981682i	$-0.438980\pi$
$383$	16.5638	−	4.43826i	0.846372	−	0.226785i	0.655843	+	0.754897i	$0.272313\pi$
$384$		0			0
$385$	1.47993	+	8.75668i	0.0754243	+	0.446282i
$386$		−	5.46691i		−	0.278258i
$387$		0			0
$388$	7.11484	−	7.11484i	0.361201	−	0.361201i
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	−0.939741	−	0.341886i	$-0.888934\pi$
$389$	−15.1070	−	26.1660i	−0.765953	−	1.32667i	0.173789	−	0.984783i	$-0.444399\pi$
$390$		0			0
$391$	−10.4526	+	18.1044i	−0.528610	+	0.915580i
$392$	−0.759224	−	2.83346i	−0.0383466	−	0.143112i
$393$		0			0
$394$	−14.7442	+	8.51258i	−0.742803	+	0.428858i
$395$	−23.6034	+	10.8028i	−1.18762	+	0.543549i
$396$		0			0
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	0.650561	−	0.759454i	$-0.274534\pi$
$397$	−2.16969	−	2.16969i	−0.108893	−	0.108893i	−0.759454	+	0.650561i	$0.774534\pi$
$398$	−1.14872	+	4.28708i	−0.0575801	+	0.214892i
$399$		0			0
$400$	1.64313	+	4.72230i	0.0821564	+	0.236115i
$401$	12.3209	+	7.11346i	0.615275	+	0.355229i	0.775027	−	0.631928i	$-0.217736\pi$
$401$	12.3209	+	7.11346i	0.615275	+	0.355229i	−0.159752	+	0.987157i	$0.551069\pi$
$402$		0			0
$403$	27.4040	+	7.34287i	1.36509	+	0.365774i
$404$	4.72288			0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	11.4796	+	3.07596i	0.569025	+	0.152470i
$408$		0			0
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	0.223353	−	0.974738i	$-0.428300\pi$
$409$	−10.2963	−	5.94456i	−0.509118	−	0.293939i	−0.732471	+	0.680798i	$0.761633\pi$
$410$	10.0972	+	12.2086i	0.498666	+	0.602941i
$411$		0			0
$412$	−1.03662	+	3.86872i	−0.0510706	+	0.190598i
$413$	−3.84907	−	3.84907i	−0.189401	−	0.189401i
$414$		0			0
$415$	1.32840	−	3.57058i	0.0652088	−	0.175273i
$416$	3.52166	−	2.03323i	0.172664	−	0.0996874i
$417$		0			0
$418$	1.88989	+	7.05315i	0.0924373	+	0.344981i
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.234926	−	0.972013i	$-0.424515\pi$
$419$	19.6354	−	34.0095i	0.959251	−	1.66147i	0.724325	−	0.689458i	$-0.242151\pi$
$420$		0			0
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	−0.993262	−	0.115887i	$-0.963029\pi$
$421$	−12.2493	−	21.2163i	−0.596992	−	1.03402i	0.396270	−	0.918134i	$-0.370304\pi$
$422$	−17.0306	+	17.0306i	−0.829038	+	0.829038i
$423$		0			0
$424$			9.94230i			0.482841i
$425$	−13.7973	+	9.37146i	−0.669265	+	0.454583i
$426$		0			0
$427$	17.0381	−	4.56534i	0.824531	−	0.220932i
$428$	7.38058	−	1.97762i	0.356754	−	0.0955920i
$429$		0			0
$430$	17.1645	+	12.2015i	0.827748	+	0.588409i
$431$			6.10703i			0.294165i	0.989124	+	0.147083i	$0.0469883\pi$
$431$			6.10703i			0.294165i	−0.989124	+	0.147083i	$0.953012\pi$
$432$		0			0
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	−0.416190	−	0.909278i	$-0.636635\pi$
$433$	10.2605	−	10.2605i	0.493088	−	0.493088i	0.909278	+	0.416190i	$0.136635\pi$
$434$	−7.03457	−	12.1842i	−0.337670	−	0.584862i
$435$		0			0
$436$	2.17679	−	3.77030i	0.104249	−	0.180565i
$437$	−6.01360	−	22.4431i	−0.287670	−	1.07360i
$438$		0			0
$439$	1.96604	−	1.13510i	0.0938342	−	0.0541752i	−0.452349	−	0.891841i	$-0.649414\pi$
$439$	1.96604	−	1.13510i	0.0938342	−	0.0541752i	0.546183	+	0.837666i	$0.316080\pi$
$440$	−4.12753	−	1.53561i	−0.196772	−	0.0732075i
$441$		0			0
$442$	9.59184	+	9.59184i	0.456237	+	0.456237i
$443$	−7.20031	+	26.8719i	−0.342097	+	1.27672i	0.553870	+	0.832603i	$0.313150\pi$
$443$	−7.20031	+	26.8719i	−0.342097	+	1.27672i	−0.895967	+	0.444120i	$0.853516\pi$
$444$		0			0
$445$	4.56329	+	0.431946i	0.216321	+	0.0204762i
$446$	14.5310	+	8.38950i	0.688065	+	0.397254i
$447$		0			0
$448$	−1.94786	−	0.521929i	−0.0920279	−	0.0246588i
$449$	−11.7712			−0.555516			−0.277758	−	0.960651i	$-0.589591\pi$
$449$	−11.7712			−0.555516			−0.277758	+	0.960651i	$0.589591\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	−2.86451	−	0.767544i	−0.134735	−	0.0361022i
$453$		0			0
$454$	6.44228	+	3.71945i	0.302351	+	0.174562i
$455$	−18.2549	−	1.72795i	−0.855804	−	0.0810075i
$456$		0			0
$457$	−10.0741	+	37.5970i	−0.471246	+	1.75871i	0.164058	+	0.986451i	$0.447542\pi$
$457$	−10.0741	+	37.5970i	−0.471246	+	1.75871i	−0.635303	+	0.772263i	$0.719125\pi$
$458$	6.32118	+	6.32118i	0.295369	+	0.295369i
$459$		0			0
$460$	13.1338	+	4.88631i	0.612365	+	0.227825i
$461$	2.62200	−	1.51381i	0.122119	−	0.0705053i	−0.437696	−	0.899123i	$-0.644205\pi$
$461$	2.62200	−	1.51381i	0.122119	−	0.0705053i	0.559815	+	0.828618i	$0.310872\pi$
$462$		0			0
$463$	1.76940	+	6.60350i	0.0822311	+	0.306891i	0.994775	−	0.102087i	$-0.0325520\pi$
$463$	1.76940	+	6.60350i	0.0822311	+	0.306891i	−0.912544	+	0.408978i	$0.865885\pi$
$464$	−3.74863	+	6.49281i	−0.174026	+	0.301421i
$465$		0			0
$466$	−10.6484	−	18.4436i	−0.493279	−	0.854384i
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	−0.495775	−	0.868451i	$-0.665116\pi$
$467$	8.05359	−	8.05359i	0.372676	−	0.372676i	0.868451	+	0.495775i	$0.165116\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$	14.1422	+	10.0531i	0.652333	+	0.463714i
$471$		0			0
$472$	2.60736	−	0.698639i	0.120013	−	0.0321575i
$473$	−17.9168	+	4.80079i	−0.823814	+	0.220740i
$474$		0			0
$475$	3.47825	−	18.2084i	0.159593	−	0.835458i
$476$		−	6.72689i		−	0.308327i
$477$		0			0
$478$	7.67538	−	7.67538i	0.351064	−	0.351064i
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	0.944296	+	0.329097i	$0.106744\pi$
$479$	16.5711	+	28.7020i	0.757154	+	1.31143i	−0.187142	+	0.982333i	$0.559922\pi$
$480$		0			0
$481$	−12.2692	+	21.2509i	−0.559428	+	0.968958i
$482$	−6.03872	−	22.5368i	−0.275056	−	1.02652i
$483$		0			0
$484$	−6.16704	+	3.56054i	−0.280320	+	0.161843i
$485$	7.84525	−	21.0870i	0.356234	−	0.957511i
$486$		0			0
$487$	−14.8248	−	14.8248i	−0.671777	−	0.671777i	0.286349	−	0.958126i	$-0.407558\pi$
$487$	−14.8248	−	14.8248i	−0.671777	−	0.671777i	−0.958126	+	0.286349i	$0.907558\pi$
$488$	−2.26391	+	8.44902i	−0.102482	+	0.382469i
$489$		0			0
$490$	−4.18042	−	5.05458i	−0.188852	−	0.228343i
$491$	−16.1505	−	9.32449i	−0.728861	−	0.420808i	0.0891441	−	0.996019i	$-0.471587\pi$
$491$	−16.1505	−	9.32449i	−0.728861	−	0.420808i	−0.818005	+	0.575210i	$0.804920\pi$
$492$		0			0
$493$	−24.1572	−	6.47289i	−1.08798	−	0.291524i
$494$	−15.0765			−0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	11.0732	+	2.96707i	0.496703	+	0.133091i
$498$		0			0
$499$	19.6189	+	11.3270i	0.878263	+	0.507065i	0.870085	−	0.492901i	$-0.164064\pi$
$499$	19.6189	+	11.3270i	0.878263	+	0.507065i	0.00817742	+	0.999967i	$0.497397\pi$
$500$	7.73531	+	8.07249i	0.345933	+	0.361013i
$501$		0			0
$502$	3.46454	−	12.9298i	0.154630	−	0.577087i
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	0.458507	−	0.888691i	$-0.348384\pi$
$503$	−9.64801	−	9.64801i	−0.430183	−	0.430183i	−0.888691	+	0.458507i	$0.848384\pi$
$504$		0			0
$505$	9.60272	−	4.39499i	0.427315	−	0.195574i
$506$	−10.6891	+	6.17134i	−0.475187	+	0.274349i
$507$		0			0
$508$	−1.25084	−	4.66818i	−0.0554968	−	0.207117i
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$509$	13.5882	−	23.5355i	0.602286	−	1.04319i	0.992474	−	0.122455i	$-0.0390768\pi$
$510$		0			0
$511$	1.63879	+	2.83847i	0.0724959	+	0.125567i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	7.55332i		−	0.333163i
$515$	1.49244	+	8.83066i	0.0657646	+	0.389125i
$516$		0			0
$517$	−14.7620	+	3.95547i	−0.649233	+	0.173961i
$518$	11.7541	−	3.14949i	0.516444	−	0.138381i
$519$		0			0
$520$	5.26829	−	7.41120i	0.231030	−	0.325002i
$521$			18.3542i			0.804114i	0.915615	+	0.402057i	$0.131705\pi$
$521$			18.3542i			0.804114i	−0.915615	+	0.402057i	$0.868295\pi$
$522$		0			0
$523$	−25.8576	+	25.8576i	−1.13067	+	1.13067i	−0.140607	+	0.990066i	$0.544905\pi$
$523$	−25.8576	+	25.8576i	−1.13067	+	1.13067i	−0.990066	+	0.140607i	$0.955095\pi$
$524$	0.237445	+	0.411267i	0.0103728	+	0.0179663i
$525$		0			0
$526$	5.57472	−	9.65570i	0.243069	−	0.421009i
$527$	6.02350	+	22.4800i	0.262388	+	0.979244i
$528$		0			0
$529$	14.0940	−	8.13716i	0.612781	−	0.353789i
$530$	9.25204	+	20.2150i	0.401883	+	0.878084i
$531$		0			0
$532$	5.28669	+	5.28669i	0.229207	+	0.229207i
$533$	7.45708	−	27.8302i	0.323002	−	1.20546i
$534$		0			0
$535$	13.1661	−	10.8891i	0.569221	−	0.470778i
$536$	7.33654	+	4.23576i	0.316890	+	0.182957i
$537$		0			0
$538$	13.0117	+	3.48649i	0.560976	+	0.150313i
$539$	5.77735			0.248848
$540$		0			0
$541$	−4.54804			−0.195536			−0.0977678	−	0.995209i	$-0.531170\pi$
$541$	−4.54804			−0.195536			−0.0977678	+	0.995209i	$0.531170\pi$
$542$	−19.7437	−	5.29032i	−0.848066	−	0.227239i
$543$		0			0
$544$	2.88889	+	1.66790i	0.123860	+	0.0715106i
$545$	0.917370	−	9.69156i	0.0392958	−	0.415141i
$546$		0			0
$547$	−5.79252	+	21.6180i	−0.247670	+	0.924319i	0.724352	+	0.689430i	$0.242139\pi$
$547$	−5.79252	+	21.6180i	−0.247670	+	0.924319i	−0.972022	+	0.234888i	$0.924528\pi$
$548$	−6.96632	−	6.96632i	−0.297587	−	0.297587i
$549$		0			0
$550$	−9.82122	+	0.718705i	−0.418778	+	0.0306457i
$551$	24.0723	−	13.8981i	1.02551	−	0.592080i
$552$		0			0
$553$	−6.05896	−	22.6124i	−0.257653	−	0.961575i
$554$	−12.1190	+	20.9907i	−0.514887	+	0.891811i
$555$		0			0
$556$	0.351212	+	0.608318i	0.0148947	+	0.0257984i
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	−0.120914	−	0.992663i	$-0.538583\pi$
$557$	20.5740	−	20.5740i	0.871749	−	0.871749i	0.992663	+	0.120914i	$0.0385825\pi$
$558$		0			0
$559$		−	38.2982i		−	1.61984i
$560$	−4.44615	+	0.751427i	−0.187884	+	0.0317536i
$561$		0			0
$562$	21.7967	−	5.84041i	0.919438	−	0.246363i
$563$	−34.2529	+	9.17805i	−1.44359	+	0.386809i	−0.893789	−	0.448487i	$-0.851963\pi$
$563$	−34.2529	+	9.17805i	−1.44359	+	0.386809i	−0.549800	+	0.835296i	$0.685296\pi$
$564$		0			0
$565$	−6.53848	+	1.10504i	−0.275076	+	0.0464895i
$566$		−	2.12372i		−	0.0892668i
$567$		0			0
$568$	−4.01977	+	4.01977i	−0.168666	+	0.168666i
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	0.999979	+	0.00641982i	$0.00204351\pi$
$569$	12.0592	+	20.8872i	0.505549	+	0.875637i	−0.494430	+	0.869217i	$0.664623\pi$
$570$		0			0
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	−0.815165	−	0.579229i	$-0.803354\pi$
$571$	2.24726	−	3.89236i	0.0940448	−	0.162890i	0.909210	+	0.416339i	$0.136687\pi$
$572$	2.07285	+	7.73599i	0.0866703	+	0.323458i
$573$		0			0
$574$	−12.3737	+	7.14398i	−0.516470	+	0.298184i
$575$	31.2510	−	2.28691i	1.30326	−	0.0953709i
$576$		0			0
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	0.710979	−	0.703214i	$-0.248252\pi$
$577$	0.186522	+	0.186522i	0.00776502	+	0.00776502i	−0.703214	+	0.710979i	$0.748252\pi$
$578$	1.51990	−	5.67235i	0.0632196	−	0.235939i
$579$		0			0
$580$	−1.57980	+	16.6898i	−0.0655975	+	0.693005i
$581$	2.97543	+	1.71786i	0.123441	+	0.0712689i
$582$		0			0
$583$	−18.9141	−	5.06802i	−0.783342	−	0.209896i
$584$	−1.62532			−0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	−43.6620	−	11.6992i	−1.80212	−	0.482878i	−0.807818	−	0.589433i	$-0.799351\pi$
$587$	−43.6620	−	11.6992i	−1.80212	−	0.482878i	−0.994307	+	0.106555i	$0.966018\pi$
$588$		0			0
$589$	−22.4010	−	12.9332i	−0.923017	−	0.532904i
$590$	4.65122	−	3.84683i	0.191488	−	0.158371i
$591$		0			0
$592$	−1.56180	+	5.82872i	−0.0641897	+	0.239559i
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	0.629242	−	0.777209i	$-0.283365\pi$
$593$	−3.60323	−	3.60323i	−0.147967	−	0.147967i	−0.777209	+	0.629242i	$0.783365\pi$
$594$		0			0
$595$	−6.25986	−	13.6773i	−0.256629	−	0.560716i
$596$	−7.02536	+	4.05609i	−0.287770	+	0.166144i
$597$		0			0
$598$	−6.59580	−	24.6159i	−0.269722	−	1.00662i
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.232260	+	0.972654i	$0.574612\pi$
$599$	−23.4581	+	40.6307i	−0.958473	+	1.66012i	−0.726213	+	0.687470i	$0.758721\pi$
$600$		0			0
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	−0.890715	−	0.454563i	$-0.849795\pi$
$601$	−20.5688	−	35.6263i	−0.839020	−	1.45323i	0.0516943	−	0.998663i	$-0.483538\pi$
$602$	−13.4295	+	13.4295i	−0.547347	+	0.547347i
$603$		0			0
$604$			9.23478i			0.375758i
$605$	−9.22568	+	12.9783i	−0.375077	+	0.527643i
$606$		0			0
$607$	−15.9755	+	4.28061i	−0.648424	+	0.173745i	−0.568016	−	0.823017i	$-0.692289\pi$
$607$	−15.9755	+	4.28061i	−0.648424	+	0.173745i	−0.0804079	+	0.996762i	$0.525622\pi$
$608$	−3.58120	+	0.959578i	−0.145237	+	0.0389160i
$609$		0			0
$610$	3.25937	+	19.2855i	0.131968	+	0.780849i
$611$		−	31.5547i		−	1.27657i
$612$		0			0
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	−0.990658	−	0.136368i	$-0.956457\pi$
$613$	−21.1512	+	21.1512i	−0.854290	+	0.854290i	0.136368	+	0.990658i	$0.456457\pi$
$614$	7.45544	+	12.9132i	0.300877	+	0.521134i
$615$		0			0
$616$	1.98582	−	3.43954i	0.0800110	−	0.138583i
$617$	2.72427	+	10.1671i	0.109675	+	0.409312i	0.998834	−	0.0482869i	$-0.0153762\pi$
$617$	2.72427	+	10.1671i	0.109675	+	0.409312i	−0.889159	+	0.457599i	$0.848710\pi$
$618$		0			0
$619$	−2.77044	+	1.59951i	−0.111353	+	0.0642898i	−0.554642	−	0.832089i	$-0.687145\pi$
$619$	−2.77044	+	1.59951i	−0.111353	+	0.0642898i	0.443289	+	0.896379i	$0.353812\pi$
$620$	14.1853	−	6.49237i	0.569697	−	0.260740i
$621$		0			0
$622$	−7.41734	−	7.41734i	−0.297408	−	0.297408i
$623$	−1.06990	+	3.99290i	−0.0428644	+	0.159972i
$624$		0			0
$625$	23.2397	+	9.21498i	0.929588	+	0.368599i
$626$	−15.2882	−	8.82666i	−0.611040	−	0.352784i
$627$		0			0
$628$	10.4848	+	2.80938i	0.418388	+	0.112107i
$629$	−20.1293			−0.802609
$630$		0			0
$631$	21.2335			0.845291			0.422645	−	0.906295i	$-0.361102\pi$
$631$	21.2335			0.845291			0.422645	+	0.906295i	$0.361102\pi$
$632$	11.2132	+	3.00458i	0.446039	+	0.119516i
$633$		0			0
$634$	−20.0808	−	11.5936i	−0.797510	−	0.460442i
$635$	−6.88732	−	8.32750i	−0.273315	−	0.330467i
$636$		0			0
$637$	−3.08736	+	11.5222i	−0.122326	+	0.456525i
$638$	−10.4410	−	10.4410i	−0.413363	−	0.413363i
$639$		0			0
$640$	0.779698	−	2.09573i	0.0308203	−	0.0828409i
$641$	−42.6583	+	24.6288i	−1.68490	+	0.972778i	−0.726582	+	0.687080i	$0.758892\pi$
$641$	−42.6583	+	24.6288i	−1.68490	+	0.972778i	−0.958320	+	0.285698i	$0.907775\pi$
$642$		0			0
$643$	−5.25595	−	19.6155i	−0.207274	−	0.773559i	−0.988744	−	0.149616i	$-0.952196\pi$
$643$	−5.25595	−	19.6155i	−0.207274	−	0.773559i	0.781470	−	0.623943i	$-0.214470\pi$
$644$	−6.31887	+	10.9446i	−0.248998	+	0.431278i
$645$		0			0
$646$	−6.18378	−	10.7106i	−0.243298	−	0.421404i
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.154619	+	0.987974i	$0.549415\pi$
$647$	−29.0632	+	29.0632i	−1.14259	+	1.14259i	−0.987974	+	0.154619i	$0.950585\pi$
$648$		0			0
$649$			5.31632i			0.208684i
$650$	3.81499	−	19.9712i	0.149636	−	0.783335i
$651$		0			0
$652$	13.2258	−	3.54385i	0.517963	−	0.138788i
$653$	−2.75027	+	0.736931i	−0.107626	+	0.0288384i	−0.312230	−	0.950006i	$-0.601076\pi$
$653$	−2.75027	+	0.736931i	−0.107626	+	0.0288384i	0.204604	+	0.978845i	$0.434409\pi$
$654$		0			0
$655$	0.865495	+	0.615241i	0.0338177	+	0.0240395i
$656$		−	7.08526i		−	0.276633i
$657$		0			0
$658$	−11.0649	+	11.0649i	−0.431354	+	0.431354i
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	−0.955058	−	0.296420i	$-0.904207\pi$
$659$	−18.8486	−	32.6467i	−0.734236	−	1.27173i	0.220822	−	0.975314i	$-0.429126\pi$
$660$		0			0
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	−0.785320	−	0.619091i	$-0.787501\pi$
$661$	3.68907	−	6.38966i	0.143488	−	0.248529i	0.928808	+	0.370561i	$0.120835\pi$
$662$	−6.68424	−	24.9459i	−0.259791	−	0.969551i
$663$		0			0
$664$	−1.47548	+	0.851871i	−0.0572598	+	0.0330590i
$665$	15.6687	+	5.82942i	0.607607	+	0.226055i
$666$		0			0
$667$	33.2232	+	33.2232i	1.28641	+	1.28641i
$668$	1.32254	−	4.93579i	0.0511707	−	0.190971i
$669$		0			0
$670$	18.8586	+	1.78509i	0.728570	+	0.0689640i
$671$	−14.9193	−	8.61365i	−0.575953	−	0.332526i
$672$		0			0
$673$	−6.88414	−	1.84460i	−0.265364	−	0.0711041i	0.123684	−	0.992322i	$-0.460529\pi$
$673$	−6.88414	−	1.84460i	−0.265364	−	0.0711041i	−0.389048	+	0.921218i	$0.627196\pi$
$674$	32.0820			1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	−8.09727	−	2.16966i	−0.311203	−	0.0833867i	0.0998372	−	0.995004i	$-0.468168\pi$
$677$	−8.09727	−	2.16966i	−0.311203	−	0.0833867i	−0.411040	+	0.911617i	$0.634834\pi$
$678$		0			0
$679$	17.5722	+	10.1453i	0.674358	+	0.389341i
$680$	7.42588	+	0.702908i	0.284769	+	0.0269553i
$681$		0			0
$682$	−3.55635	+	13.2725i	−0.136180	+	0.508229i
$683$	−15.8873	−	15.8873i	−0.607911	−	0.607911i	0.334488	−	0.942400i	$-0.391436\pi$
$683$	−15.8873	−	15.8873i	−0.607911	−	0.607911i	−0.942400	+	0.334488i	$0.891436\pi$
$684$		0			0
$685$	−20.6468	−	7.68149i	−0.788875	−	0.293494i
$686$	17.3478	−	10.0158i	0.662342	−	0.382403i
$687$		0			0
$688$	−2.43757	−	9.09714i	−0.0929315	−	0.346825i
$689$	20.2150	−	35.0134i	0.770131	−	1.33391i
$690$		0			0
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	0.985997	−	0.166765i	$-0.0533321\pi$
$691$	9.16297	+	15.8707i	0.348576	+	0.603751i	−0.637421	+	0.770516i	$0.719999\pi$
$692$	5.24323	−	5.24323i	0.199318	−	0.199318i
$693$		0			0
$694$		−	14.8046i		−	0.561973i
$695$	1.28018	+	0.910023i	0.0485600	+	0.0345191i
$696$		0			0
$697$	22.8296	−	6.11718i	0.864734	−	0.231705i
$698$	−14.9168	+	3.99695i	−0.564610	+	0.151287i
$699$		0			0
$700$	−8.34080	+	5.66529i	−0.315253	+	0.214128i
$701$			21.1738i			0.799724i	0.916575	+	0.399862i	$0.130942\pi$
$701$			21.1738i			0.799724i	−0.916575	+	0.399862i	$0.869058\pi$
$702$		0			0
$703$	15.8197	−	15.8197i	0.596652	−	0.596652i
$704$	0.984748	+	1.70563i	0.0371141	+	0.0642835i
$705$		0			0
$706$	−10.4276	+	18.0612i	−0.392449	+	0.679742i
$707$	2.46501	+	9.19953i	0.0927062	+	0.345984i
$708$		0			0
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	−0.0633143	−	0.997994i	$-0.520167\pi$
$709$	20.4846	−	11.8268i	0.769316	−	0.444165i	0.832631	+	0.553829i	$0.186834\pi$
$710$	−4.43244	+	11.9138i	−0.166346	+	0.447117i
$711$		0			0
$712$	−1.44949	−	1.44949i	−0.0543219	−	0.0543219i
$713$	11.3163	−	42.2329i	0.423798	−	1.58163i
$714$		0			0
$715$	11.4135	+	13.8001i	0.426840	+	0.516095i
$716$	−2.36794	−	1.36713i	−0.0884942	−	0.0510921i
$717$		0			0
$718$	−3.27899	−	0.878601i	−0.122371	−	0.0327891i
$719$	21.3695			0.796947			0.398473	−	0.917180i	$-0.369540\pi$
$719$	21.3695			0.796947			0.398473	+	0.917180i	$0.369540\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	−5.07522	−	1.35990i	−0.188880	−	0.0506102i
$723$		0			0
$724$	−19.6658	−	11.3541i	−0.730874	−	0.421970i
$725$	12.3190	+	35.4043i	0.457514	+	1.31488i
$726$		0			0
$727$	−0.796213	+	2.97151i	−0.0295299	+	0.110207i	−0.979118	−	0.203294i	$-0.934835\pi$
$727$	−0.796213	+	2.97151i	−0.0295299	+	0.110207i	0.949588	+	0.313501i	$0.101502\pi$
$728$	5.79852	+	5.79852i	0.214907	+	0.214907i
$729$		0			0
$730$	−3.30466	+	1.51248i	−0.122311	+	0.0559794i
$731$	27.2077	−	15.7084i	1.00631	−	0.580994i
$732$		0			0
$733$	−6.30661	−	23.5366i	−0.232940	−	0.869343i	−0.979067	−	0.203540i	$-0.934755\pi$
$733$	−6.30661	−	23.5366i	−0.232940	−	0.869343i	0.746127	−	0.665804i	$-0.231911\pi$
$734$	−10.9884	+	19.0324i	−0.405589	+	0.702500i
$735$		0			0
$736$	−3.13346	−	5.42731i	−0.115501	−	0.200053i
$737$	−11.7978	+	11.7978i	−0.434578	+	0.434578i
$738$		0			0
$739$			5.68805i			0.209238i	0.994512	+	0.104619i	$0.0333624\pi$
$739$			5.68805i			0.209238i	−0.994512	+	0.104619i	$0.966638\pi$
$740$	2.24855	+	13.3045i	0.0826582	+	0.489084i
$741$		0			0
$742$	−19.3663	+	5.18917i	−0.710958	+	0.190500i
$743$	15.1100	−	4.04871i	0.554332	−	0.148533i	0.0292311	−	0.999573i	$-0.490694\pi$
$743$	15.1100	−	4.04871i	0.554332	−	0.148533i	0.525101	+	0.851040i	$0.324027\pi$
$744$		0			0
$745$	−10.5097	+	14.7846i	−0.385046	+	0.541665i
$746$			1.47224i			0.0539025i
$747$		0			0
$748$	−4.64558	+	4.64558i	−0.169859	+	0.169859i
$749$	7.70428	+	13.3442i	0.281508	+	0.487586i
$750$		0			0
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	0.137467	+	0.990506i	$0.456104\pi$
$751$	−21.6240	+	37.4538i	−0.789070	+	1.36671i	−0.926537	+	0.376203i	$0.877229\pi$
$752$	−2.00837	−	7.49533i	−0.0732376	−	0.273327i
$753$		0			0
$754$	26.4028	−	15.2437i	0.961533	−	0.555141i
$755$	8.59363	+	18.7764i	0.312754	+	0.683345i
$756$		0			0
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	0.986963	−	0.160950i	$-0.0514557\pi$
$757$	22.7266	+	22.7266i	0.826013	+	0.826013i	−0.160950	+	0.986963i	$0.551456\pi$
$758$	7.79880	−	29.1055i	0.283265	−	1.05716i
$759$		0			0
$760$	−6.38844	+	5.28361i	−0.231733	+	0.191657i
$761$	24.8744	+	14.3612i	0.901696	+	0.520595i	0.877750	−	0.479119i	$-0.159044\pi$
$761$	24.8744	+	14.3612i	0.901696	+	0.520595i	0.0239461	+	0.999713i	$0.492377\pi$
$762$		0			0
$763$	8.48016	+	2.27225i	0.307002	+	0.0822611i
$764$	1.28350			0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	−10.6027	−	2.84099i	−0.382842	−	0.102582i
$768$		0			0
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.925043	−	0.379861i	$-0.124028\pi$
$769$	29.3558	+	16.9486i	1.05860	+	0.611180i	0.133552	+	0.991042i	$0.457362\pi$
$770$	0.836891	−	8.84134i	0.0301594	−	0.318620i
$771$		0			0
$772$	−1.41494	+	5.28063i	−0.0509248	+	0.190054i
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.996232	+	0.0867231i	$0.0276395\pi$
$773$	30.1093	+	30.1093i	1.08296	+	1.08296i	0.0867231	+	0.996232i	$0.472360\pi$
$774$		0			0
$775$	22.8005	−	26.4010i	0.819017	−	0.948351i
$776$	−8.71386	+	5.03095i	−0.312809	+	0.180601i
$777$		0			0
$778$	7.81993	+	29.1844i	0.280358	+	1.04631i
$779$	−13.1344	+	22.7494i	−0.470588	+	0.815083i
$780$		0			0
$781$	−5.59811	−	9.69621i	−0.200316	−	0.346958i
$782$	14.7822	−	14.7822i	0.528610	−	0.528610i
$783$		0			0
$784$			2.93342i			0.104765i
$785$	23.9323	−	4.04470i	0.854181	−	0.144362i
$786$		0			0
$787$	−10.2212	+	2.73876i	−0.364346	+	0.0976263i	−0.436347	−	0.899778i	$-0.643728\pi$
$787$	−10.2212	+	2.73876i	−0.364346	+	0.0976263i	0.0720011	+	0.997405i	$0.477061\pi$
$788$	16.4450	−	4.40644i	0.585831	−	0.156973i
$789$		0			0
$790$	25.5951	−	4.32573i	0.910633	−	0.153902i
$791$		−	5.98028i		−	0.212634i
$792$		0			0
$793$	25.1515	−	25.1515i	0.893157	−	0.893157i
$794$	1.53420	+	2.65731i	0.0544467	+	0.0943045i
$795$		0			0
$796$	2.21916	−	3.84369i	0.0786559	−	0.136236i
$797$	3.52110	+	13.1409i	0.124724	+	0.465476i	0.999830	−	0.0184558i	$-0.00587500\pi$
$797$	3.52110	+	13.1409i	0.124724	+	0.465476i	−0.875106	+	0.483932i	$0.839208\pi$
$798$		0			0
$799$	22.4170	−	12.9425i	0.793056	−	0.457871i
$800$	−0.364918	−	4.98667i	−0.0129018	−	0.176305i
$801$		0			0
$802$	−10.0599	−	10.0599i	−0.355229	−	0.355229i
$803$	0.828496	−	3.09199i	0.0292370	−	0.109114i
$804$		0			0
$805$	−2.66298	+	28.1331i	−0.0938577	+	0.991561i
$806$	−24.5697	−	14.1853i	−0.865432	−	0.499657i
$807$		0			0
$808$	−4.56196	−	1.22237i	−0.160489	−	0.0430029i
$809$	33.4429			1.17579			0.587895	−	0.808937i	$-0.299957\pi$
$809$	33.4429			1.17579			0.587895	+	0.808937i	$0.299957\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	−14.6036	−	3.91303i	−0.512487	−	0.137320i
$813$		0			0
$814$	−10.2924	−	5.94230i	−0.360747	−	0.208278i
$815$	23.5934	−	19.5131i	0.826440	−	0.683513i
$816$		0			0
$817$	−9.03736	+	33.7279i	−0.316177	+	1.17999i
$818$	8.40687	+	8.40687i	0.293939	+	0.293939i
$819$		0			0
$820$	−6.59335	−	14.4060i	−0.230250	−	0.503078i
$821$	38.4941	−	22.2246i	1.34345	−	0.775643i	0.356141	−	0.934432i	$-0.384092\pi$
$821$	38.4941	−	22.2246i	1.34345	−	0.775643i	0.987313	+	0.158789i	$0.0507589\pi$
$822$		0			0
$823$	6.59989	+	24.6311i	0.230058	+	0.858588i	0.980315	+	0.197441i	$0.0632631\pi$
$823$	6.59989	+	24.6311i	0.230058	+	0.858588i	−0.750257	+	0.661146i	$0.770070\pi$
$824$	2.00260	−	3.46860i	0.0697638	−	0.120834i
$825$		0			0
$826$	2.72171	+	4.71413i	0.0947003	+	0.164026i
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	−0.494368	−	0.869253i	$-0.664600\pi$
$827$	10.7808	−	10.7808i	0.374885	−	0.374885i	0.869253	+	0.494368i	$0.164600\pi$
$828$		0			0
$829$		−	4.02079i		−	0.139648i	−0.997559	−	0.0698239i	$-0.977756\pi$
$829$		−	4.02079i		−	0.139648i	0.997559	−	0.0698239i	$-0.0222437\pi$
$830$	−2.20727	+	3.10510i	−0.0766155	+	0.107779i
$831$		0			0
$832$	−3.92790	+	1.05248i	−0.136176	+	0.0364881i
$833$	−9.45186	+	2.53262i	−0.327488	+	0.0877500i
$834$		0			0
$835$	−1.90408	−	11.2663i	−0.0658934	−	0.389887i
$836$		−	7.30196i		−	0.252543i
$837$		0			0
$838$	−27.7686	+	27.7686i	−0.959251	+	0.959251i
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	−0.995527	−	0.0944825i	$-0.969880\pi$
$839$	−16.7880	−	29.0777i	−0.579588	−	1.00388i	0.415939	−	0.909393i	$-0.363453\pi$
$840$		0			0
$841$	−13.6044	+	23.5635i	−0.469118	+	0.812536i
$842$	6.34068	+	23.6637i	0.218514	+	0.815506i
$843$		0			0
$844$	20.8582	−	12.0425i	0.717968	−	0.414519i
$845$	−7.18979	+	3.29063i	−0.247336	+	0.113201i
$846$		0			0
$847$	−10.1542	−	10.1542i	−0.348903	−	0.348903i
$848$	2.57326	−	9.60353i	0.0883660	−	0.329786i
$849$		0			0
$850$	15.7526	−	5.48114i	0.540311	−	0.188002i
$851$	32.7503	+	18.9084i	1.12266	+	0.648171i
$852$		0			0
$853$	22.9734	+	6.15572i	0.786596	+	0.210768i	0.629691	−	0.776846i	$-0.283182\pi$
$853$	22.9734	+	6.15572i	0.786596	+	0.210768i	0.156905	+	0.987614i	$0.449848\pi$
$854$	−17.6391			−0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	−11.4475	−	3.06736i	−0.391040	−	0.104779i	0.0579412	−	0.998320i	$-0.481546\pi$
$857$	−11.4475	−	3.06736i	−0.391040	−	0.104779i	−0.448981	+	0.893541i	$0.648213\pi$
$858$		0			0
$859$	−34.6670	−	20.0150i	−1.18282	−	0.682904i	−0.226158	−	0.974091i	$-0.572617\pi$
$859$	−34.6670	−	20.0150i	−1.18282	−	0.682904i	−0.956666	+	0.291187i	$0.905950\pi$
$860$	−13.4217	−	16.2283i	−0.457676	−	0.553379i
$861$		0			0
$862$	1.58062	−	5.89894i	0.0538360	−	0.200919i
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	0.676041	−	0.736864i	$-0.263694\pi$
$863$	−1.78680	−	1.78680i	−0.0608233	−	0.0608233i	−0.736864	+	0.676041i	$0.763694\pi$
$864$		0			0
$865$	5.78150	−	15.5399i	0.196577	−	0.528373i
$866$	−12.5665	+	7.25527i	−0.427027	+	0.246544i
$867$		0			0
$868$	3.64136	+	13.5897i	0.123596	+	0.461266i
$869$	−11.4317	+	19.8004i	−0.387795	+	0.671681i
$870$		0			0
$871$	−17.2246	−	29.8338i	−0.583632	−	1.01088i
$872$	−3.07844	+	3.07844i	−0.104249	+	0.104249i
$873$		0			0
$874$			23.2348i			0.785928i
$875$	−11.6868	+	19.2806i	−0.395087	+	0.651803i
$876$		0			0
$877$	6.66309	−	1.78537i	0.224996	−	0.0602876i	−0.144559	−	0.989496i	$-0.546176\pi$
$877$	6.66309	−	1.78537i	0.224996	−	0.0602876i	0.369556	+	0.929208i	$0.379510\pi$
$878$	−2.19284	+	0.587569i	−0.0740047	+	0.0198295i
$879$		0			0
$880$	3.58944	+	2.55157i	0.121000	+	0.0860134i
$881$			3.01999i			0.101746i	0.998705	+	0.0508731i	$0.0162004\pi$
$881$			3.01999i			0.101746i	−0.998705	+	0.0508731i	$0.983800\pi$
$882$		0			0
$883$	−8.50404	+	8.50404i	−0.286184	+	0.286184i	−0.835569	−	0.549385i	$-0.814862\pi$
$883$	−8.50404	+	8.50404i	−0.286184	+	0.286184i	0.549385	+	0.835569i	$0.314862\pi$
$884$	−6.78245	−	11.7476i	−0.228119	−	0.395113i
$885$		0			0
$886$	13.9099	−	24.0927i	0.467313	−	0.809410i
$887$	4.61020	+	17.2055i	0.154796	+	0.577705i	0.999123	+	0.0418769i	$0.0133337\pi$
$887$	4.61020	+	17.2055i	0.154796	+	0.577705i	−0.844327	+	0.535828i	$0.820000\pi$
$888$		0			0
$889$	8.44013	−	4.87291i	0.283073	−	0.163432i
$890$	−4.29601	−	1.59829i	−0.144002	−	0.0535749i
$891$		0			0
$892$	−11.8645	−	11.8645i	−0.397254	−	0.397254i
$893$	−7.44607	+	27.7891i	−0.249173	+	0.929928i
$894$		0			0
$895$	−6.08679	−	0.576155i	−0.203459	−	0.0192587i
$896$	1.74641	+	1.00829i	0.0583434	+	0.0336846i
$897$		0			0
$898$	11.3701	+	3.04660i	0.379424	+	0.101666i
$899$	52.3064			1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	13.4789	+	3.61166i	0.448798	+	0.120255i
$903$		0			0
$904$	2.56825	+	1.48278i	0.0854188	+	0.0493166i
$905$	−50.5509	−	4.78498i	−1.68037	−	0.159058i
$906$		0			0
$907$	0.324723	−	1.21188i	0.0107822	−	0.0402399i	−0.960325	−	0.278883i	$-0.910036\pi$
$907$	0.324723	−	1.21188i	0.0107822	−	0.0402399i	0.971107	+	0.238643i	$0.0767026\pi$
$908$	−5.26010	−	5.26010i	−0.174562	−	0.174562i
$909$		0			0
$910$	17.1857	+	6.39379i	0.569699	+	0.211952i
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	−0.0595057	−	0.998228i	$-0.518952\pi$
$911$	23.3987	−	13.5092i	0.775232	−	0.447581i	0.834738	+	0.550647i	$0.185619\pi$
$912$		0			0
$913$	−0.868470	−	3.24117i	−0.0287422	−	0.107267i
$914$	19.4616	−	33.7085i	0.643734	−	1.11498i
$915$		0			0
$916$	−4.46975	−	7.74183i	−0.147685	−	0.255797i
$917$	−0.677163	+	0.677163i	−0.0223619	+	0.0223619i
$918$		0			0
$919$			54.3202i			1.79186i	0.444196	+	0.895930i	$0.353489\pi$
$919$			54.3202i			1.79186i	−0.444196	+	0.895930i	$0.646511\pi$
$920$	−11.4216	−	8.11908i	−0.376558	−	0.267678i
$921$		0			0
$922$	−2.92446	+	0.783607i	−0.0963121	+	0.0258067i
$923$	22.3294	−	5.98314i	0.734981	−	0.196938i
$924$		0			0
$925$	16.9526	+	24.9588i	0.557399	+	0.820639i
$926$		−	6.83645i		−	0.224660i
$927$		0			0
$928$	5.30136	−	5.30136i	0.174026	−	0.174026i
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	0.541854	−	0.840473i	$-0.317723\pi$
$929$	−13.9274	−	24.1230i	−0.456944	−	0.791450i	−0.998798	+	0.0490228i	$0.984389\pi$
$930$		0			0
$931$	5.43786	−	9.41865i	0.178219	−	0.308684i
$932$	5.51203	+	20.5712i	0.180553	+	0.673831i
$933$		0			0
$934$	−9.86360	+	5.69475i	−0.322747	+	0.186338i
$935$	−5.12249	+	13.7686i	−0.167523	+	0.450281i
$936$		0			0
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	0.375481	−	0.926830i	$-0.377477\pi$
$937$	−16.8770	−	16.8770i	−0.551349	−	0.551349i	−0.926830	+	0.375481i	$0.877477\pi$
$938$	−4.42152	+	16.5014i	−0.144368	+	0.538788i
$939$		0			0
$940$	−11.0584	−	13.3708i	−0.360686	−	0.436108i
$941$	−28.5039	−	16.4567i	−0.929201	−	0.536474i	−0.0426420	−	0.999090i	$-0.513577\pi$
$941$	−28.5039	−	16.4567i	−0.929201	−	0.536474i	−0.886559	+	0.462616i	$0.846911\pi$
$942$		0			0
$943$	−42.8898	−	11.4923i	−1.39668	−	0.374240i
$944$	−2.69933			−0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	−11.5072	−	3.08335i	−0.373934	−	0.100195i	0.0669572	−	0.997756i	$-0.478671\pi$
$947$	−11.5072	−	3.08335i	−0.373934	−	0.100195i	−0.440891	+	0.897560i	$0.645338\pi$
$948$		0			0
$949$	5.72383	+	3.30466i	0.185804	+	0.107274i
$950$	−8.07241	+	16.6877i	−0.261904	+	0.541421i
$951$		0			0
$952$	−1.74105	+	6.49768i	−0.0564277	+	0.210591i
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	0.454391	−	0.890802i	$-0.349857\pi$
$953$	−13.4723	−	13.4723i	−0.436411	−	0.436411i	−0.890802	+	0.454391i	$0.849857\pi$
$954$		0			0
$955$	2.60965	−	1.19439i	0.0844463	−	0.0386495i
$956$	−9.40038	+	5.42731i	−0.304030	+	0.175532i
$957$		0			0
$958$	−8.57785	−	32.0130i	−0.277138	−	1.03429i
$959$	9.93353	−	17.2054i	0.320770	−	0.555591i
$960$		0			0
$961$	−8.83746	−	15.3069i	−0.285079	−	0.493772i
$962$	17.3513	−	17.3513i	0.559428	−	0.559428i
$963$		0			0
$964$			23.3318i			0.751467i
$965$	2.03711	+	12.0534i	0.0655768	+	0.388014i
$966$		0			0
$967$	8.95826	−	2.40036i	0.288078	−	0.0771904i	−0.111886	−	0.993721i	$-0.535689\pi$
$967$	8.95826	−	2.40036i	0.288078	−	0.0771904i	0.399964	+	0.916531i	$0.369022\pi$
$968$	6.87844	−	1.84307i	0.221081	−	0.0592386i
$969$		0			0
$970$	−13.0356	+	18.3380i	−0.418549	+	0.588797i
$971$			24.7290i			0.793590i	0.917907	+	0.396795i	$0.129878\pi$
$971$			24.7290i			0.793590i	−0.917907	+	0.396795i	$0.870122\pi$
$972$		0			0
$973$	−1.00161	+	1.00161i	−0.0321102	+	0.0321102i
$974$	10.4827	+	18.1566i	0.335889	+	0.581776i
$975$		0			0
$976$	4.37353	−	7.57518i	0.139993	−	0.242476i
$977$	−6.35548	−	23.7190i	−0.203330	−	0.758837i	−0.989952	−	0.141403i	$-0.954839\pi$
$977$	−6.35548	−	23.7190i	−0.203330	−	0.758837i	0.786622	−	0.617434i	$-0.211828\pi$
$978$		0			0
$979$	3.49636	−	2.01862i	0.111744	−	0.0645155i
$980$	2.72976	+	5.96432i	0.0871989	+	0.190523i
$981$		0			0
$982$	13.1868	+	13.1868i	0.420808	+	0.420808i
$983$	−10.7435	+	40.0954i	−0.342666	+	1.27885i	0.552650	+	0.833414i	$0.313617\pi$
$983$	−10.7435	+	40.0954i	−0.342666	+	1.27885i	−0.895316	+	0.445433i	$0.853050\pi$
$984$		0			0
$985$	29.3361	−	24.2626i	0.934726	−	0.773072i
$986$	21.6587	+	12.5047i	0.689754	+	0.398230i
$987$		0			0
$988$	14.5628	+	3.90209i	0.463305	+	0.124142i
$989$	−59.0222			−1.87680
$990$		0			0
$991$	36.6089			1.16292			0.581460	−	0.813575i	$-0.302481\pi$
$991$	36.6089			1.16292			0.581460	+	0.813575i	$0.302481\pi$
$992$	−6.73901	−	1.80571i	−0.213964	−	0.0573315i
$993$		0			0
$994$	−9.92800	−	5.73193i	−0.314897	−	0.181806i
$995$	0.935226	−	9.88020i	0.0296487	−	0.313223i
$996$		0			0
$997$	3.09617	−	11.5550i	0.0980565	−	0.365952i	−0.899409	−	0.437109i	$-0.856002\pi$
$997$	3.09617	−	11.5550i	0.0980565	−	0.365952i	0.997465	+	0.0711569i	$0.0226691\pi$
$998$	−16.0188	−	16.0188i	−0.507065	−	0.507065i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.b.17.2		16
3.2	odd	2		90.2.l.b.77.4	yes	16
5.2	odd	4		1350.2.q.h.1043.3		16
5.3	odd	4	inner	270.2.m.b.233.2		16
5.4	even	2		1350.2.q.h.557.4		16
9.2	odd	6	inner	270.2.m.b.197.2		16
9.4	even	3		810.2.f.c.647.7		16
9.5	odd	6		810.2.f.c.647.2		16
9.7	even	3		90.2.l.b.47.4	yes	16
12.11	even	2		720.2.cu.b.257.2		16
15.2	even	4		450.2.p.h.293.1		16
15.8	even	4		90.2.l.b.23.4	✓	16
15.14	odd	2		450.2.p.h.257.1		16
36.7	odd	6		720.2.cu.b.497.1		16
45.2	even	12		1350.2.q.h.143.4		16
45.7	odd	12		450.2.p.h.443.1		16
45.13	odd	12		810.2.f.c.323.2		16
45.23	even	12		810.2.f.c.323.7		16
45.29	odd	6		1350.2.q.h.1007.3		16
45.34	even	6		450.2.p.h.407.1		16
45.38	even	12	inner	270.2.m.b.143.2		16
45.43	odd	12		90.2.l.b.83.4	yes	16
60.23	odd	4		720.2.cu.b.113.1		16
180.43	even	12		720.2.cu.b.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	15.8	even	4
90.2.l.b.47.4	yes	16	9.7	even	3
90.2.l.b.77.4	yes	16	3.2	odd	2
90.2.l.b.83.4	yes	16	45.43	odd	12
270.2.m.b.17.2		16	1.1	even	1	trivial
270.2.m.b.143.2		16	45.38	even	12	inner
270.2.m.b.197.2		16	9.2	odd	6	inner
270.2.m.b.233.2		16	5.3	odd	4	inner
450.2.p.h.257.1		16	15.14	odd	2
450.2.p.h.293.1		16	15.2	even	4
450.2.p.h.407.1		16	45.34	even	6
450.2.p.h.443.1		16	45.7	odd	12
720.2.cu.b.113.1		16	60.23	odd	4
720.2.cu.b.257.2		16	12.11	even	2
720.2.cu.b.353.2		16	180.43	even	12
720.2.cu.b.497.1		16	36.7	odd	6
810.2.f.c.323.2		16	45.13	odd	12
810.2.f.c.323.7		16	45.23	even	12
810.2.f.c.647.2		16	9.5	odd	6
810.2.f.c.647.7		16	9.4	even	3
1350.2.q.h.143.4		16	45.2	even	12
1350.2.q.h.557.4		16	5.4	even	2
1350.2.q.h.1007.3		16	45.29	odd	6
1350.2.q.h.1043.3		16	5.2	odd	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.22612 + 0.210717i) q^{5} +(-0.521929 + 1.94786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(2.22612 + 0.210717i) q^{5} +(-0.521929 + 1.94786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +(1.70563 - 0.984748i) q^{11} +(1.05248 + 3.92790i) q^{13} +(1.00829 - 1.74641i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-2.35877 + 2.35877i) q^{17} -3.70753i q^{19} +(1.82252 + 1.29554i) q^{20} +(-1.90239 + 0.509743i) q^{22} +(6.05338 - 1.62200i) q^{23} +(4.91120 + 0.938160i) q^{25} -4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} +(3.74863 + 6.49281i) q^{29} +(3.48837 - 6.04204i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.88889 - 1.66790i) q^{34} +(-1.57232 + 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-0.959578 + 3.58120i) q^{38} +(-1.42510 - 1.72310i) q^{40} +(-6.13601 - 3.54263i) q^{41} +(-9.09714 - 2.43757i) q^{43} +1.96950 q^{44} -6.26692 q^{46} +(-7.49533 - 2.00837i) q^{47} +(2.54041 + 1.46671i) q^{49} +(-4.50104 - 2.17730i) q^{50} +(-1.05248 + 3.92790i) q^{52} +(-7.03027 - 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +(1.74641 - 1.00829i) q^{56} +(-1.94043 - 7.24179i) q^{58} +(-1.34967 + 2.33769i) q^{59} +(-4.37353 - 7.57518i) q^{61} +(-4.93330 + 4.93330i) q^{62} +1.00000i q^{64} +(1.51527 + 8.96575i) q^{65} +(-8.18285 + 2.19259i) q^{67} +(-3.22213 + 0.863368i) q^{68} +(2.61257 - 3.67524i) q^{70} -5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(-3.01717 - 5.22589i) q^{74} +(1.85376 - 3.21081i) q^{76} +(1.02794 + 3.83631i) q^{77} +(-10.0535 + 5.80440i) q^{79} +(0.930573 + 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(0.440961 - 1.64569i) q^{83} +(-5.74792 + 4.75386i) q^{85} +(8.15627 + 4.70902i) q^{86} +(-1.90239 - 0.509743i) q^{88} +2.04989 q^{89} -8.20034 q^{91} +(6.05338 + 1.62200i) q^{92} +(6.72013 + 3.87987i) q^{94} +(0.781237 - 8.25339i) q^{95} +(2.60421 - 9.71905i) q^{97} +(-2.07424 - 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 12 q^{20} + 8 q^{22} + 24 q^{23} - 16 q^{25} - 16 q^{28} - 8 q^{31} - 24 q^{38} - 4 q^{40} - 24 q^{41} - 32 q^{46} - 48 q^{47} - 24 q^{50} + 24 q^{55} - 24 q^{56} + 16 q^{58} - 24 q^{61} - 16 q^{67} + 24 q^{68} + 16 q^{70} + 16 q^{73} + 16 q^{76} + 72 q^{77} - 16 q^{82} - 48 q^{83} - 4 q^{85} + 48 q^{86} + 8 q^{88} + 24 q^{92} - 84 q^{95} - 48 q^{97}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 12 * q^20 + 8 * q^22 + 24 * q^23 - 16 * q^25 - 16 * q^28 - 8 * q^31 - 24 * q^38 - 4 * q^40 - 24 * q^41 - 32 * q^46 - 48 * q^47 - 24 * q^50 + 24 * q^55 - 24 * q^56 + 16 * q^58 - 24 * q^61 - 16 * q^67 + 24 * q^68 + 16 * q^70 + 16 * q^73 + 16 * q^76 + 72 * q^77 - 16 * q^82 - 48 * q^83 - 4 * q^85 + 48 * q^86 + 8 * q^88 + 24 * q^92 - 84 * q^95 - 48 * q^97

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