LMFDB - Embedded newform 270.2.m.b.197.2

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			197.2
Root			$0.500000 + 2.74530i$ of defining polynomial
Character	$\chi$	$=$	270.197
Dual form			270.2.m.b.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.29554 - 1.82252i) q^{5} +(1.94786 - 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.29554 - 1.82252i) q^{5} +(1.94786 - 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +(1.70563 + 0.984748i) q^{11} +(-3.92790 - 1.05248i) q^{13} +(-1.00829 - 1.74641i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(-0.210717 + 2.22612i) q^{20} +(0.509743 - 1.90239i) q^{22} +(1.62200 - 6.05338i) q^{23} +(-1.64313 - 4.72230i) q^{25} +4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} +(-3.74863 + 6.49281i) q^{29} +(3.48837 + 6.04204i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.88889 - 1.66790i) q^{34} +(1.57232 - 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-3.58120 + 0.959578i) q^{38} +(2.20480 - 0.372625i) q^{40} +(-6.13601 + 3.54263i) q^{41} +(2.43757 + 9.09714i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(-2.00837 - 7.49533i) q^{47} +(-2.54041 + 1.46671i) q^{49} +(-4.13612 + 2.80936i) q^{50} +(3.92790 - 1.05248i) q^{52} +(7.03027 + 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +(1.74641 + 1.00829i) q^{56} +(7.24179 + 1.94043i) q^{58} +(1.34967 + 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(-7.00693 + 5.79513i) q^{65} +(2.19259 - 8.18285i) q^{67} +(-0.863368 + 3.22213i) q^{68} +(-4.48914 - 0.424926i) q^{70} +5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(3.01717 - 5.22589i) q^{74} +(1.85376 + 3.21081i) q^{76} +(3.83631 + 1.02794i) q^{77} +(10.0535 + 5.80440i) q^{79} +(-0.930573 - 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(1.64569 - 0.440961i) q^{83} +(-1.24300 - 7.35477i) q^{85} +(8.15627 - 4.70902i) q^{86} +(0.509743 + 1.90239i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(1.62200 + 6.05338i) q^{92} +(-6.72013 + 3.87987i) q^{94} +(-6.75702 - 4.80327i) q^{95} +(-9.71905 + 2.60421i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.29554	−	1.82252i	0.579385	−	0.815054i
$5$	1.29554	−	1.82252i	0.579385	−	0.815054i
$6$		0			0
$7$	1.94786	−	0.521929i	0.736223	−	0.197270i	0.128824	−	0.991667i	$-0.458880\pi$
$7$	1.94786	−	0.521929i	0.736223	−	0.197270i	0.607399	+	0.794397i	$0.292213\pi$
$8$	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	0.734586	−	0.678515i	$-0.237376\pi$
$11$	1.70563	+	0.984748i	0.514268	+	0.296913i	−0.220318	+	0.975428i	$0.570710\pi$
$12$		0			0
$13$	−3.92790	−	1.05248i	−1.08940	−	0.291905i	−0.330961	−	0.943644i	$-0.607373\pi$
$13$	−3.92790	−	1.05248i	−1.08940	−	0.291905i	−0.758443	+	0.651739i	$0.774040\pi$
$14$	−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	−0.360626	−	0.932711i	$-0.617437\pi$
$17$	2.35877	−	2.35877i	0.572085	−	0.572085i	0.932711	+	0.360626i	$0.117437\pi$
$18$		0			0
$19$		−	3.70753i		−	0.850565i	−0.905061	−	0.425282i	$-0.860175\pi$
$19$		−	3.70753i		−	0.850565i	0.905061	−	0.425282i	$-0.139825\pi$
$20$	−0.210717	+	2.22612i	−0.0471177	+	0.497775i
$21$		0			0
$22$	0.509743	−	1.90239i	0.108678	−	0.405590i
$23$	1.62200	−	6.05338i	0.338210	−	1.26222i	−0.562137	−	0.827044i	$-0.690021\pi$
$23$	1.62200	−	6.05338i	0.338210	−	1.26222i	0.900347	−	0.435173i	$-0.143313\pi$
$24$		0			0
$25$	−1.64313	−	4.72230i	−0.328626	−	0.944460i
$26$			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	0.273705	+	0.961814i	$0.411751\pi$
$29$	−3.74863	+	6.49281i	−0.696103	+	1.20569i	−0.969808	+	0.243872i	$0.921582\pi$
$30$		0			0
$31$	3.48837	+	6.04204i	0.626530	+	1.08518i	0.988243	+	0.152892i	$0.0488587\pi$
$31$	3.48837	+	6.04204i	0.626530	+	1.08518i	−0.361713	+	0.932289i	$0.617808\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		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	$0.584794\pi$
$38$	−3.58120	+	0.959578i	−0.580947	+	0.155664i
$39$		0			0
$40$	2.20480	−	0.372625i	0.348610	−	0.0589172i
$41$	−6.13601	+	3.54263i	−0.958284	+	0.553266i	−0.895644	−	0.444771i	$-0.853285\pi$
$41$	−6.13601	+	3.54263i	−0.958284	+	0.553266i	−0.0626396	+	0.998036i	$0.519952\pi$
$42$		0			0
$43$	2.43757	+	9.09714i	0.371726	+	1.38730i	0.858070	+	0.513533i	$0.171664\pi$
$43$	2.43757	+	9.09714i	0.371726	+	1.38730i	−0.486344	+	0.873767i	$0.661670\pi$
$44$	−1.96950			−0.296913
$45$		0			0
$46$	−6.26692			−0.924007
$47$	−2.00837	−	7.49533i	−0.292951	−	1.09331i	−0.942831	−	0.333270i	$-0.891848\pi$
$47$	−2.00837	−	7.49533i	−0.292951	−	1.09331i	0.649881	−	0.760036i	$-0.274819\pi$
$48$		0			0
$49$	−2.54041	+	1.46671i	−0.362916	+	0.209530i
$50$	−4.13612	+	2.80936i	−0.584936	+	0.397304i
$51$		0			0
$52$	3.92790	−	1.05248i	0.544702	−	0.145953i
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	0.999430	−	0.0337485i	$-0.0107445\pi$
$53$	7.03027	+	7.03027i	0.965682	+	0.965682i	−0.0337485	+	0.999430i	$0.510745\pi$
$54$		0			0
$55$	4.00444	−	1.83276i	0.539959	−	0.247129i
$56$	1.74641	+	1.00829i	0.233373	+	0.134738i
$57$		0			0
$58$	7.24179	+	1.94043i	0.950894	+	0.254791i
$59$	1.34967	+	2.33769i	0.175712	+	0.304341i	0.940407	−	0.340050i	$-0.110444\pi$
$59$	1.34967	+	2.33769i	0.175712	+	0.304341i	−0.764696	+	0.644392i	$0.777111\pi$
$60$		0			0
$61$	−4.37353	+	7.57518i	−0.559973	+	0.969902i	0.437524	+	0.899207i	$0.355855\pi$
$61$	−4.37353	+	7.57518i	−0.559973	+	0.969902i	−0.997498	+	0.0706960i	$0.977478\pi$
$62$	4.93330	−	4.93330i	0.626530	−	0.626530i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−7.00693	+	5.79513i	−0.869103	+	0.718798i
$66$		0			0
$67$	2.19259	−	8.18285i	0.267867	−	0.999694i	−0.692605	−	0.721317i	$-0.743537\pi$
$67$	2.19259	−	8.18285i	0.267867	−	0.999694i	0.960472	−	0.278377i	$-0.0897964\pi$
$68$	−0.863368	+	3.22213i	−0.104699	+	0.390741i
$69$		0			0
$70$	−4.48914	−	0.424926i	−0.536554	−	0.0507884i
$71$			5.68481i			0.674663i	0.941386	+	0.337332i	$0.109524\pi$
$71$			5.68481i			0.674663i	−0.941386	+	0.337332i	$0.890476\pi$
$72$		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
$77$	3.83631	+	1.02794i	0.437188	+	0.117144i
$78$		0			0
$79$	10.0535	+	5.80440i	1.13111	+	0.653046i	0.944214	−	0.329334i	$-0.106824\pi$
$79$	10.0535	+	5.80440i	1.13111	+	0.653046i	0.186895	+	0.982380i	$0.440158\pi$
$80$	−0.930573	−	2.03323i	−0.104041	−	0.227322i
$81$		0			0
$82$	5.01003	+	5.01003i	0.553266	+	0.553266i
$83$	1.64569	−	0.440961i	0.180638	−	0.0484017i	−0.167366	−	0.985895i	$-0.553526\pi$
$83$	1.64569	−	0.440961i	0.180638	−	0.0484017i	0.348004	+	0.937493i	$0.386860\pi$
$84$		0			0
$85$	−1.24300	−	7.35477i	−0.134822	−	0.797737i
$86$	8.15627	−	4.70902i	0.879513	−	0.507787i
$87$		0			0
$88$	0.509743	+	1.90239i	0.0543388	+	0.202795i
$89$	−2.04989			−0.217288			−0.108644	−	0.994081i	$-0.534651\pi$
$89$	−2.04989			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$90$		0			0
$91$	−8.20034			−0.859629
$92$	1.62200	+	6.05338i	0.169105	+	0.631109i
$93$		0			0
$94$	−6.72013	+	3.87987i	−0.693128	+	0.400178i
$95$	−6.75702	−	4.80327i	−0.693256	−	0.492805i
$96$		0			0
$97$	−9.71905	+	2.60421i	−0.986820	+	0.264418i	−0.715914	−	0.698188i	$-0.753990\pi$
$97$	−9.71905	+	2.60421i	−0.986820	+	0.264418i	−0.270906	+	0.962606i	$0.587323\pi$
$98$	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	0.689493	−	0.724292i	$-0.257833\pi$
$101$	4.09014	+	2.36144i	0.406984	+	0.234972i	−0.282509	+	0.959265i	$0.591167\pi$
$102$		0			0
$103$	−3.86872	−	1.03662i	−0.381196	−	0.102141i	0.0631321	−	0.998005i	$-0.479891\pi$
$103$	−3.86872	−	1.03662i	−0.381196	−	0.102141i	−0.444329	+	0.895864i	$0.646558\pi$
$104$	−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	−0.918273	−	0.395949i	$-0.870416\pi$
$107$	−5.40296	+	5.40296i	−0.522324	+	0.522324i	0.395949	+	0.918273i	$0.370416\pi$
$108$		0			0
$109$		−	4.35357i		−	0.416996i	−0.978023	−	0.208498i	$-0.933142\pi$
$109$		−	4.35357i		−	0.416996i	0.978023	−	0.208498i	$-0.0668575\pi$
$110$	−2.80674	−	3.39364i	−0.267612	−	0.323571i
$111$		0			0
$112$	0.521929	−	1.94786i	0.0493176	−	0.184056i
$113$	−0.767544	+	2.86451i	−0.0722045	+	0.269471i	−0.992585	−	0.121553i	$-0.961212\pi$
$113$	−0.767544	+	2.86451i	−0.0722045	+	0.269471i	0.920380	+	0.391024i	$0.127879\pi$
$114$		0			0
$115$	−8.93101	−	10.7985i	−0.832821	−	1.00697i
$116$		−	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
$122$	8.44902	+	2.26391i	0.764938	+	0.204965i
$123$		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	$0.818787\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	7.41120	+	5.26829i	0.650005	+	0.462059i
$131$	0.411267	−	0.237445i	0.0359326	−	0.0207457i	−0.481926	−	0.876212i	$-0.660063\pi$
$131$	0.411267	−	0.237445i	0.0359326	−	0.0207457i	0.517859	+	0.855466i	$0.326729\pi$
$132$		0			0
$133$	−1.93506	−	7.22176i	−0.167791	−	0.626206i
$134$	−8.47151			−0.731827
$135$		0			0
$136$	3.33580			0.286042
$137$	−2.54985	−	9.51618i	−0.217849	−	0.813022i	−0.985144	−	0.171728i	$-0.945065\pi$
$137$	−2.54985	−	9.51618i	−0.217849	−	0.813022i	0.767296	−	0.641293i	$-0.221602\pi$
$138$		0			0
$139$	−0.608318	+	0.351212i	−0.0515968	+	0.0297894i	−0.525577	−	0.850746i	$-0.676150\pi$
$139$	−0.608318	+	0.351212i	−0.0515968	+	0.0297894i	0.473980	+	0.880536i	$0.342817\pi$
$140$	0.751427	+	4.44615i	0.0635072	+	0.375768i
$141$		0			0
$142$	5.49111	−	1.47134i	0.460803	−	0.123472i
$143$	−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
$148$	−5.82872	−	1.56180i	−0.479118	−	0.128379i
$149$	4.05609	+	7.02536i	0.332288	+	0.575540i	0.982960	−	0.183819i	$-0.0588460\pi$
$149$	4.05609	+	7.02536i	0.332288	+	0.575540i	−0.650672	+	0.759359i	$0.725513\pi$
$150$		0			0
$151$	4.61739	−	7.99755i	0.375758	−	0.650832i	−0.614682	−	0.788775i	$-0.710716\pi$
$151$	4.61739	−	7.99755i	0.375758	−	0.650832i	0.990440	+	0.137943i	$0.0440491\pi$
$152$	2.62162	−	2.62162i	0.212641	−	0.212641i
$153$		0			0
$154$		−	3.97164i		−	0.320044i
$155$	15.5310	+	1.47012i	1.24748	+	0.118083i
$156$		0			0
$157$	−2.80938	+	10.4848i	−0.224213	+	0.836775i	0.758505	+	0.651667i	$0.225930\pi$
$157$	−2.80938	+	10.4848i	−0.224213	+	0.836775i	−0.982718	+	0.185108i	$0.940736\pi$
$158$	3.00458	−	11.2132i	0.239031	−	0.892077i
$159$		0			0
$160$	−1.72310	+	1.42510i	−0.136223	+	0.112664i
$161$		−	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
$167$	−4.93579	−	1.32254i	−0.381943	−	0.102341i	0.0627387	−	0.998030i	$-0.480017\pi$
$167$	−4.93579	−	1.32254i	−0.381943	−	0.102341i	−0.444682	+	0.895689i	$0.646683\pi$
$168$		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
$173$	7.16239	−	1.91916i	0.544546	−	0.145911i	0.0239492	−	0.999713i	$-0.492376\pi$
$173$	7.16239	−	1.91916i	0.544546	−	0.145911i	0.520597	+	0.853802i	$0.325709\pi$
$174$		0			0
$175$	−5.66529	−	8.34080i	−0.428256	−	0.630506i
$176$	1.70563	−	0.984748i	0.128567	−	0.0742282i
$177$		0			0
$178$	0.530550	+	1.98004i	0.0397664	+	0.148410i
$179$	2.73426			0.204369			0.102184	−	0.994765i	$-0.467417\pi$
$179$	2.73426			0.204369			0.102184	+	0.994765i	$0.467417\pi$
$180$		0			0
$181$	−22.7081			−1.68788			−0.843941	−	0.536437i	$-0.819770\pi$
$181$	−22.7081			−1.68788			−0.843941	+	0.536437i	$0.819770\pi$
$182$	2.12240	+	7.92092i	0.157323	+	0.587138i
$183$		0			0
$184$	5.42731	−	3.13346i	0.400107	−	0.231002i
$185$	13.3045	−	2.24855i	0.978168	−	0.165316i
$186$		0			0
$187$	6.34598	−	1.70040i	0.464064	−	0.124346i
$188$	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	0.539675	−	0.841874i	$-0.318547\pi$
$191$	1.11154	+	0.641749i	0.0804283	+	0.0464353i	−0.459246	+	0.888309i	$0.651881\pi$
$192$		0			0
$193$	−5.28063	−	1.41494i	−0.380108	−	0.101850i	0.0637057	−	0.997969i	$-0.479708\pi$
$193$	−5.28063	−	1.41494i	−0.380108	−	0.101850i	−0.443814	+	0.896119i	$0.646375\pi$
$194$	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	−0.991069	−	0.133353i	$-0.957426\pi$
$197$	−12.0386	+	12.0386i	−0.857716	+	0.857716i	0.133353	+	0.991069i	$0.457426\pi$
$198$		0			0
$199$		−	4.43831i		−	0.314623i	−0.987549	−	0.157312i	$-0.949717\pi$
$199$		−	4.43831i		−	0.314623i	0.987549	−	0.157312i	$-0.0502827\pi$
$200$	2.17730	−	4.50104i	0.153959	−	0.318271i
$201$		0			0
$202$	1.22237	−	4.56196i	0.0860058	−	0.320978i
$203$	−3.91303	+	14.6036i	−0.274641	+	1.02497i
$204$		0			0
$205$	−1.49298	+	15.7726i	−0.104274	+	1.10161i
$206$			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	0.898794	+	0.438372i	$0.144445\pi$
$211$	12.0425	+	20.8582i	0.829038	+	1.43594i	−0.0697556	+	0.997564i	$0.522222\pi$
$212$	−9.60353	−	2.57326i	−0.659573	−	0.176732i
$213$		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
$218$	−4.20523	+	1.12679i	−0.284814	+	0.0763156i
$219$		0			0
$220$	−2.55157	+	3.58944i	−0.172027	+	0.242000i
$221$	−11.7476	+	6.78245i	−0.790226	+	0.456237i
$222$		0			0
$223$	4.34272	+	16.2073i	0.290810	+	1.08532i	0.944488	+	0.328546i	$0.106559\pi$
$223$	4.34272	+	16.2073i	0.290810	+	1.08532i	−0.653678	+	0.756773i	$0.726775\pi$
$224$	−2.01658			−0.134738
$225$		0			0
$226$	2.96556			0.197266
$227$	−1.92533	−	7.18543i	−0.127789	−	0.476914i	0.872135	−	0.489265i	$-0.162735\pi$
$227$	−1.92533	−	7.18543i	−0.127789	−	0.476914i	−0.999924	+	0.0123515i	$0.996068\pi$
$228$		0			0
$229$	7.74183	−	4.46975i	0.511595	−	0.295369i	−0.221894	−	0.975071i	$-0.571224\pi$
$229$	7.74183	−	4.46975i	0.511595	−	0.295369i	0.733489	+	0.679701i	$0.237891\pi$
$230$	−8.11908	+	11.4216i	−0.535356	+	0.753116i
$231$		0			0
$232$	−7.24179	+	1.94043i	−0.475447	+	0.127396i
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	0.0133533	−	0.999911i	$-0.495749\pi$
$233$	−15.0591	−	15.0591i	−0.986558	−	0.986558i	−0.999911	+	0.0133533i	$0.995749\pi$
$234$		0			0
$235$	−16.2623	−	6.05025i	−1.06083	−	0.394675i
$236$	−2.33769	−	1.34967i	−0.152171	−	0.0878558i
$237$		0			0
$238$	−6.49768	−	1.74105i	−0.421182	−	0.112855i
$239$	5.42731	+	9.40038i	0.351064	+	0.608060i	0.986436	−	0.164146i	$-0.0524867\pi$
$239$	5.42731	+	9.40038i	0.351064	+	0.608060i	−0.635372	+	0.772206i	$0.719153\pi$
$240$		0			0
$241$	11.6659	−	20.2059i	0.751467	−	1.30158i	−0.195645	−	0.980675i	$-0.562680\pi$
$241$	11.6659	−	20.2059i	0.751467	−	1.30158i	0.947112	−	0.320904i	$-0.103987\pi$
$242$	−5.03537	+	5.03537i	−0.323686	+	0.323686i
$243$		0			0
$244$		−	8.74707i		−	0.559973i
$245$	−0.618120	+	6.53013i	−0.0394902	+	0.417195i
$246$		0			0
$247$	−3.90209	+	14.5628i	−0.248284	+	0.926609i
$248$	−1.80571	+	6.73901i	−0.114663	+	0.427928i
$249$		0			0
$250$	−0.238423	+	11.1778i	−0.0150792	+	0.706946i
$251$		−	13.3860i		−	0.844914i	−0.906383	−	0.422457i	$-0.861168\pi$
$251$		−	13.3860i		−	0.844914i	0.906383	−	0.422457i	$-0.138832\pi$
$252$		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
$257$	7.29595	+	1.95494i	0.455109	+	0.121946i	0.479089	−	0.877766i	$-0.340967\pi$
$257$	7.29595	+	1.95494i	0.455109	+	0.121946i	−0.0239802	+	0.999712i	$0.507634\pi$
$258$		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
$263$	−10.7695	+	2.88569i	−0.664078	+	0.177939i	−0.575086	−	0.818093i	$-0.695031\pi$
$263$	−10.7695	+	2.88569i	−0.664078	+	0.177939i	−0.0889923	+	0.996032i	$0.528365\pi$
$264$		0			0
$265$	21.9208	−	3.70475i	1.34658	−	0.227581i
$266$	−6.47485	+	3.73826i	−0.396998	+	0.229207i
$267$		0			0
$268$	2.19259	+	8.18285i	0.133934	+	0.499847i
$269$	13.4707			0.821326			0.410663	−	0.911787i	$-0.365297\pi$
$269$	13.4707			0.821326			0.410663	+	0.911787i	$0.365297\pi$
$270$		0			0
$271$	20.4402			1.24165			0.620827	−	0.783947i	$-0.286797\pi$
$271$	20.4402			1.24165			0.620827	+	0.783947i	$0.286797\pi$
$272$	−0.863368	−	3.22213i	−0.0523494	−	0.195371i
$273$		0			0
$274$	−8.53197	+	4.92594i	−0.515435	+	0.297587i
$275$	1.84770	−	9.67258i	0.111421	−	0.583279i
$276$		0			0
$277$	−23.4121	+	6.27326i	−1.40670	+	0.376924i	−0.880745	−	0.473590i	$-0.842958\pi$
$277$	−23.4121	+	6.27326i	−1.40670	+	0.376924i	−0.525953	+	0.850514i	$0.676291\pi$
$278$	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	−0.213114	−	0.977027i	$-0.568360\pi$
$281$	−19.5424	−	11.2828i	−1.16580	−	0.673076i	−0.952687	+	0.303952i	$0.901694\pi$
$282$		0			0
$283$	−2.05136	−	0.549660i	−0.121941	−	0.0326739i	0.197333	−	0.980337i	$-0.436772\pi$
$283$	−2.05136	−	0.549660i	−0.121941	−	0.0326739i	−0.319273	+	0.947663i	$0.603439\pi$
$284$	−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
$290$	12.9185	−	10.6844i	0.758602	−	0.627408i
$291$		0			0
$292$	−0.420664	+	1.56994i	−0.0246175	+	0.0918738i
$293$	0.946406	−	3.53204i	0.0552896	−	0.206344i	−0.932755	−	0.360510i	$-0.882603\pi$
$293$	0.946406	−	3.53204i	0.0552896	−	0.206344i	0.988045	+	0.154167i	$0.0492692\pi$
$294$		0			0
$295$	6.00903	+	0.568794i	0.349859	+	0.0331165i
$296$			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
$302$	−8.92011	−	2.39014i	−0.513295	−	0.137537i
$303$		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	$0.889903\pi$
$308$	−3.83631	+	1.02794i	−0.218594	+	0.0585721i
$309$		0			0
$310$	−2.59971	−	15.3823i	−0.147653	−	0.873658i
$311$	9.08436	−	5.24485i	0.515127	−	0.297408i	−0.219812	−	0.975542i	$-0.570544\pi$
$311$	9.08436	−	5.24485i	0.515127	−	0.297408i	0.734938	+	0.678134i	$0.237211\pi$
$312$		0			0
$313$	−4.56901	−	17.0518i	−0.258256	−	0.963824i	−0.966250	−	0.257606i	$-0.917066\pi$
$313$	−4.56901	−	17.0518i	−0.258256	−	0.963824i	0.707994	−	0.706218i	$-0.249600\pi$
$314$	10.8546			0.612562
$315$		0			0
$316$	−11.6088			−0.653046
$317$	6.00131	+	22.3972i	0.337067	+	1.25795i	0.901611	+	0.432549i	$0.142386\pi$
$317$	6.00131	+	22.3972i	0.337067	+	1.25795i	−0.564543	+	0.825403i	$0.690948\pi$
$318$		0			0
$319$	−12.7876	+	7.38291i	−0.715966	+	0.413363i
$320$	1.82252	+	1.29554i	0.101882	+	0.0724231i
$321$		0			0
$322$	−12.2071	+	3.27089i	−0.680276	+	0.182279i
$323$	−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
$328$	−6.84383	−	1.83380i	−0.377887	−	0.101255i
$329$	−7.82405	−	13.5517i	−0.431354	−	0.747127i
$330$		0			0
$331$	12.9130	−	22.3659i	0.709761	−	1.22934i	−0.255185	−	0.966892i	$-0.582136\pi$
$331$	12.9130	−	22.3659i	0.709761	−	1.22934i	0.964946	−	0.262450i	$-0.0845303\pi$
$332$	−1.20473	+	1.20473i	−0.0661180	+	0.0661180i
$333$		0			0
$334$			5.10991i			0.279602i
$335$	−12.0728	−	14.5973i	−0.659606	−	0.797534i
$336$		0			0
$337$	8.30344	−	30.9889i	0.452317	−	1.68807i	−0.243541	−	0.969891i	$-0.578309\pi$
$337$	8.30344	−	30.9889i	0.452317	−	1.68807i	0.695858	−	0.718180i	$-0.255024\pi$
$338$	0.915220	−	3.41565i	0.0497814	−	0.185787i
$339$		0			0
$340$	4.75386	+	5.74792i	0.257814	+	0.311725i
$341$			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
$347$	14.3001	+	3.83170i	0.767670	+	0.205696i	0.621342	−	0.783540i	$-0.286588\pi$
$347$	14.3001	+	3.83170i	0.767670	+	0.205696i	0.146328	+	0.989236i	$0.453255\pi$
$348$		0			0
$349$	−13.3741	−	7.72151i	−0.715897	−	0.413323i	0.0973439	−	0.995251i	$-0.468965\pi$
$349$	−13.3741	−	7.72151i	−0.715897	−	0.413323i	−0.813241	+	0.581928i	$0.802299\pi$
$350$	−6.59031	+	7.63101i	−0.352267	+	0.407895i
$351$		0			0
$352$	−1.39264	−	1.39264i	−0.0742282	−	0.0742282i
$353$	20.1446	−	5.39774i	1.07219	−	0.287293i	0.320798	−	0.947148i	$-0.396049\pi$
$353$	20.1446	−	5.39774i	1.07219	−	0.287293i	0.751393	+	0.659855i	$0.229382\pi$
$354$		0			0
$355$	10.3607	+	7.36493i	0.549887	+	0.390890i
$356$	1.77526	−	1.02494i	0.0940883	−	0.0543219i
$357$		0			0
$358$	−0.707680	−	2.64110i	−0.0374020	−	0.139586i
$359$	−3.39466			−0.179163			−0.0895815	−	0.995979i	$-0.528553\pi$
$359$	−3.39466			−0.179163			−0.0895815	+	0.995979i	$0.528553\pi$
$360$		0			0
$361$	5.25425			0.276540
$362$	5.87729	+	21.9344i	0.308904	+	1.15284i
$363$		0			0
$364$	7.10170	−	4.10017i	0.372230	−	0.214907i
$365$	−0.605635	−	3.58351i	−0.0317004	−	0.187570i
$366$		0			0
$367$	−21.2279	+	5.68801i	−1.10809	+	0.296912i	−0.766054	−	0.642776i	$-0.777783\pi$
$367$	−21.2279	+	5.68801i	−1.10809	+	0.296912i	−0.342035	+	0.939687i	$0.611116\pi$
$368$	−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
$373$	1.42207	+	0.381044i	0.0736322	+	0.0197297i	0.295447	−	0.955359i	$-0.404531\pi$
$373$	1.42207	+	0.381044i	0.0736322	+	0.0197297i	−0.221815	+	0.975089i	$0.571198\pi$
$374$	−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	$0.718306\pi$
$380$	8.25339	+	0.781237i	0.423390	+	0.0400766i
$381$		0			0
$382$	0.332194	−	1.23976i	0.0169965	−	0.0634318i
$383$	4.43826	−	16.5638i	0.226785	−	0.846372i	−0.754897	−	0.655843i	$-0.772313\pi$
$383$	4.43826	−	16.5638i	0.226785	−	0.846372i	0.981682	−	0.190528i	$-0.0610201\pi$
$384$		0			0
$385$	6.84354	−	5.66000i	0.348779	−	0.288460i
$386$			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	−0.173789	−	0.984783i	$-0.555601\pi$
$389$	15.1070	−	26.1660i	0.765953	−	1.32667i	0.939741	−	0.341886i	$-0.111066\pi$
$390$		0			0
$391$	−10.4526	−	18.1044i	−0.528610	−	0.915580i
$392$	−2.83346	−	0.759224i	−0.143112	−	0.0383466i
$393$		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	$0.774534\pi$
$398$	−4.28708	+	1.14872i	−0.214892	+	0.0575801i
$399$		0			0
$400$	−4.91120	−	0.938160i	−0.245560	−	0.0469080i
$401$	12.3209	−	7.11346i	0.615275	−	0.355229i	−0.159752	−	0.987157i	$-0.551069\pi$
$401$	12.3209	−	7.11346i	0.615275	−	0.355229i	0.775027	+	0.631928i	$0.217736\pi$
$402$		0			0
$403$	−7.34287	−	27.4040i	−0.365774	−	1.36509i
$404$	−4.72288			−0.234972
$405$		0			0
$406$	15.1188			0.750333
$407$	3.07596	+	11.4796i	0.152470	+	0.569025i
$408$		0			0
$409$	10.2963	−	5.94456i	0.509118	−	0.293939i	−0.223353	−	0.974738i	$-0.571700\pi$
$409$	10.2963	−	5.94456i	0.509118	−	0.293939i	0.732471	+	0.680798i	$0.238367\pi$
$410$	15.6216	−	2.64014i	0.771495	−	0.130387i
$411$		0			0
$412$	3.86872	−	1.03662i	0.190598	−	0.0510706i
$413$	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
$418$	−7.05315	−	1.88989i	−0.344981	−	0.0924373i
$419$	−19.6354	−	34.0095i	−0.959251	−	1.66147i	−0.724325	−	0.689458i	$-0.757849\pi$
$419$	−19.6354	−	34.0095i	−0.959251	−	1.66147i	−0.234926	−	0.972013i	$-0.575485\pi$
$420$		0			0
$421$	−12.2493	+	21.2163i	−0.596992	+	1.03402i	0.396270	+	0.918134i	$0.370304\pi$
$421$	−12.2493	+	21.2163i	−0.596992	+	1.03402i	−0.993262	+	0.115887i	$0.963029\pi$
$422$	17.0306	−	17.0306i	0.829038	−	0.829038i
$423$		0			0
$424$			9.94230i			0.482841i
$425$	−15.0146	−	7.26305i	−0.728313	−	0.352310i
$426$		0			0
$427$	−4.56534	+	17.0381i	−0.220932	+	0.824531i
$428$	1.97762	−	7.38058i	0.0955920	−	0.356754i
$429$		0			0
$430$	1.98454	−	20.9657i	0.0957030	−	1.01105i
$431$		−	6.10703i		−	0.294165i	−0.989124	−	0.147083i	$-0.953012\pi$
$431$		−	6.10703i		−	0.294165i	0.989124	−	0.147083i	$-0.0469883\pi$
$432$		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
$437$	−22.4431	−	6.01360i	−1.07360	−	0.287670i
$438$		0			0
$439$	−1.96604	−	1.13510i	−0.0938342	−	0.0541752i	0.452349	−	0.891841i	$-0.350586\pi$
$439$	−1.96604	−	1.13510i	−0.0938342	−	0.0541752i	−0.546183	+	0.837666i	$0.683920\pi$
$440$	4.12753	+	1.53561i	0.196772	+	0.0732075i
$441$		0			0
$442$	9.59184	+	9.59184i	0.456237	+	0.456237i
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.832603	−	0.553870i	$-0.813150\pi$
$443$	−26.8719	+	7.20031i	−1.27672	+	0.342097i	−0.444120	+	0.895967i	$0.646484\pi$
$444$		0			0
$445$	−2.65572	+	3.73595i	−0.125893	+	0.177101i
$446$	14.5310	−	8.38950i	0.688065	−	0.397254i
$447$		0			0
$448$	0.521929	+	1.94786i	0.0246588	+	0.0920279i
$449$	11.7712			0.555516			0.277758	−	0.960651i	$-0.410409\pi$
$449$	11.7712			0.555516			0.277758	+	0.960651i	$0.410409\pi$
$450$		0			0
$451$	−13.9544			−0.657086
$452$	−0.767544	−	2.86451i	−0.0361022	−	0.134735i
$453$		0			0
$454$	−6.44228	+	3.71945i	−0.302351	+	0.174562i
$455$	−10.6239	+	14.9452i	−0.498056	+	0.700644i
$456$		0			0
$457$	37.5970	−	10.0741i	1.75871	−	0.471246i	0.772263	−	0.635303i	$-0.219125\pi$
$457$	37.5970	−	10.0741i	1.75871	−	0.471246i	0.986451	+	0.164058i	$0.0524583\pi$
$458$	−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	0.559815	−	0.828618i	$-0.310872\pi$
$461$	2.62200	+	1.51381i	0.122119	+	0.0705053i	−0.437696	+	0.899123i	$0.644205\pi$
$462$		0			0
$463$	−6.60350	−	1.76940i	−0.306891	−	0.0822311i	0.102087	−	0.994775i	$-0.467448\pi$
$463$	−6.60350	−	1.76940i	−0.306891	−	0.0822311i	−0.408978	+	0.912544i	$0.634115\pi$
$464$	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	−0.868451	−	0.495775i	$-0.834884\pi$
$467$	−8.05359	+	8.05359i	−0.372676	+	0.372676i	0.495775	+	0.868451i	$0.334884\pi$
$468$		0			0
$469$		−	17.0835i		−	0.788841i
$470$	−1.63511	+	17.2741i	−0.0754218	+	0.796794i
$471$		0			0
$472$	−0.698639	+	2.60736i	−0.0321575	+	0.120013i
$473$	−4.80079	+	17.9168i	−0.220740	+	0.823814i
$474$		0			0
$475$	−17.5081	+	6.09194i	−0.803325	+	0.279517i
$476$			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	0.187142	+	0.982333i	$0.440078\pi$
$479$	−16.5711	+	28.7020i	−0.757154	+	1.31143i	−0.944296	+	0.329097i	$0.893256\pi$
$480$		0			0
$481$	−12.2692	−	21.2509i	−0.559428	−	0.968958i
$482$	−22.5368	−	6.03872i	−1.02652	−	0.275056i
$483$		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	$0.907558\pi$
$488$	−8.44902	+	2.26391i	−0.382469	+	0.102482i
$489$		0			0
$490$	6.46760	−	1.09306i	0.292177	−	0.0493796i
$491$	−16.1505	+	9.32449i	−0.728861	+	0.420808i	−0.818005	−	0.575210i	$-0.804920\pi$
$491$	−16.1505	+	9.32449i	−0.728861	+	0.420808i	0.0891441	+	0.996019i	$0.471587\pi$
$492$		0			0
$493$	6.47289	+	24.1572i	0.291524	+	1.08798i
$494$	15.0765			0.678325
$495$		0			0
$496$	6.97674			0.313265
$497$	2.96707	+	11.0732i	0.133091	+	0.496703i
$498$		0			0
$499$	−19.6189	+	11.3270i	−0.878263	+	0.507065i	−0.870085	−	0.492901i	$-0.835936\pi$
$499$	−19.6189	+	11.3270i	−0.878263	+	0.507065i	−0.00817742	+	0.999967i	$0.502603\pi$
$500$	10.8586	−	2.66273i	0.485613	−	0.119081i
$501$		0			0
$502$	−12.9298	+	3.46454i	−0.577087	+	0.154630i
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	0.888691	−	0.458507i	$-0.151616\pi$
$503$	9.64801	+	9.64801i	0.430183	+	0.430183i	−0.458507	+	0.888691i	$0.651616\pi$
$504$		0			0
$505$	9.60272	−	4.39499i	0.427315	−	0.195574i
$506$	−10.6891	−	6.17134i	−0.475187	−	0.274349i
$507$		0			0
$508$	4.66818	+	1.25084i	0.207117	+	0.0554968i
$509$	−13.5882	−	23.5355i	−0.602286	−	1.04319i	−0.992474	−	0.122455i	$-0.960923\pi$
$509$	−13.5882	−	23.5355i	−0.602286	−	1.04319i	0.390188	−	0.920735i	$-0.372410\pi$
$510$		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
$515$	−6.90136	+	5.70782i	−0.304110	+	0.251517i
$516$		0			0
$517$	3.95547	−	14.7620i	0.173961	−	0.649233i
$518$	3.14949	−	11.7541i	0.138381	−	0.516444i
$519$		0			0
$520$	−9.05243	−	0.856872i	−0.396975	−	0.0375763i
$521$		−	18.3542i		−	0.804114i	−0.915615	−	0.402057i	$-0.868295\pi$
$521$		−	18.3542i		−	0.804114i	0.915615	−	0.402057i	$-0.131705\pi$
$522$		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
$527$	22.4800	+	6.02350i	0.979244	+	0.262388i
$528$		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
$533$	27.8302	−	7.45708i	1.20546	−	0.323002i
$534$		0			0
$535$	2.84721	+	16.8468i	0.123095	+	0.728349i
$536$	7.33654	−	4.23576i	0.316890	−	0.182957i
$537$		0			0
$538$	−3.48649	−	13.0117i	−0.150313	−	0.560976i
$539$	−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	$0.531170\pi$
$542$	−5.29032	−	19.7437i	−0.227239	−	0.848066i
$543$		0			0
$544$	−2.88889	+	1.66790i	−0.123860	+	0.0715106i
$545$	−7.93445	−	5.64024i	−0.339875	−	0.241602i
$546$		0			0
$547$	21.6180	−	5.79252i	0.924319	−	0.247670i	0.234888	−	0.972022i	$-0.424528\pi$
$547$	21.6180	−	5.79252i	0.924319	−	0.247670i	0.689430	+	0.724352i	$0.257861\pi$
$548$	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
$553$	22.6124	+	6.05896i	0.961575	+	0.257653i
$554$	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	−0.992663	−	0.120914i	$-0.961417\pi$
$557$	−20.5740	+	20.5740i	−0.871749	+	0.871749i	0.120914	+	0.992663i	$0.461417\pi$
$558$		0			0
$559$		−	38.2982i		−	1.61984i
$560$	−2.87383	−	3.47477i	−0.121442	−	0.146836i
$561$		0			0
$562$	−5.84041	+	21.7967i	−0.246363	+	0.919438i
$563$	−9.17805	+	34.2529i	−0.386809	+	1.44359i	0.448487	+	0.893789i	$0.351963\pi$
$563$	−9.17805	+	34.2529i	−0.386809	+	1.44359i	−0.835296	+	0.549800i	$0.814704\pi$
$564$		0			0
$565$	4.22623	+	5.10997i	0.177799	+	0.214978i
$566$			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	0.494430	+	0.869217i	$0.335377\pi$
$569$	−12.0592	+	20.8872i	−0.505549	+	0.875637i	−0.999979	+	0.00641982i	$0.997956\pi$
$570$		0			0
$571$	2.24726	+	3.89236i	0.0940448	+	0.162890i	0.909210	−	0.416339i	$-0.136687\pi$
$571$	2.24726	+	3.89236i	0.0940448	+	0.162890i	−0.815165	+	0.579229i	$0.803354\pi$
$572$	7.73599	+	2.07285i	0.323458	+	0.0866703i
$573$		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	$0.748252\pi$
$578$	5.67235	−	1.51990i	0.235939	−	0.0632196i
$579$		0			0
$580$	−13.6639	−	9.71303i	−0.567361	−	0.403312i
$581$	2.97543	−	1.71786i	0.123441	−	0.0712689i
$582$		0			0
$583$	5.06802	+	18.9141i	0.209896	+	0.783342i
$584$	1.62532			0.0672563
$585$		0			0
$586$	−3.65663			−0.151054
$587$	−11.6992	−	43.6620i	−0.482878	−	1.80212i	−0.589433	−	0.807818i	$-0.700649\pi$
$587$	−11.6992	−	43.6620i	−0.482878	−	1.80212i	0.106555	−	0.994307i	$-0.466018\pi$
$588$		0			0
$589$	22.4010	−	12.9332i	0.923017	−	0.532904i
$590$	−1.00584	−	5.95149i	−0.0414097	−	0.245019i
$591$		0			0
$592$	5.82872	−	1.56180i	0.239559	−	0.0641897i
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	0.777209	−	0.629242i	$-0.216635\pi$
$593$	3.60323	+	3.60323i	0.147967	+	0.147967i	−0.629242	+	0.777209i	$0.716635\pi$
$594$		0			0
$595$	−6.25986	−	13.6773i	−0.256629	−	0.560716i
$596$	−7.02536	−	4.05609i	−0.287770	−	0.166144i
$597$		0			0
$598$	24.6159	+	6.59580i	1.00662	+	0.269722i
$599$	23.4581	+	40.6307i	0.958473	+	1.66012i	0.726213	+	0.687470i	$0.241279\pi$
$599$	23.4581	+	40.6307i	0.958473	+	1.66012i	0.232260	+	0.972654i	$0.425388\pi$
$600$		0			0
$601$	−20.5688	+	35.6263i	−0.839020	+	1.45323i	0.0516943	+	0.998663i	$0.483538\pi$
$601$	−20.5688	+	35.6263i	−0.839020	+	1.45323i	−0.890715	+	0.454563i	$0.849795\pi$
$602$	13.4295	−	13.4295i	0.547347	−	0.547347i
$603$		0			0
$604$			9.23478i			0.375758i
$605$	−15.8524	−	1.50053i	−0.644491	−	0.0610053i
$606$		0			0
$607$	4.28061	−	15.9755i	0.173745	−	0.648424i	−0.823017	−	0.568016i	$-0.807711\pi$
$607$	4.28061	−	15.9755i	0.173745	−	0.648424i	0.996762	−	0.0804079i	$-0.0256223\pi$
$608$	−0.959578	+	3.58120i	−0.0389160	+	0.145237i
$609$		0			0
$610$	15.0721	−	12.4655i	0.610251	−	0.504712i
$611$			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
$617$	10.1671	+	2.72427i	0.409312	+	0.109675i	0.457599	−	0.889159i	$-0.348710\pi$
$617$	10.1671	+	2.72427i	0.409312	+	0.109675i	−0.0482869	+	0.998834i	$0.515376\pi$
$618$		0			0
$619$	2.77044	+	1.59951i	0.111353	+	0.0642898i	0.554642	−	0.832089i	$-0.312855\pi$
$619$	2.77044	+	1.59951i	0.111353	+	0.0642898i	−0.443289	+	0.896379i	$0.646188\pi$
$620$	−14.1853	+	6.49237i	−0.569697	+	0.260740i
$621$		0			0
$622$	−7.41734	−	7.41734i	−0.297408	−	0.297408i
$623$	−3.99290	+	1.06990i	−0.159972	+	0.0428644i
$624$		0			0
$625$	−19.6003	+	15.5187i	−0.784010	+	0.620748i
$626$	−15.2882	+	8.82666i	−0.611040	+	0.352784i
$627$		0			0
$628$	−2.80938	−	10.4848i	−0.112107	−	0.418388i
$629$	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	$0.361102\pi$
$632$	3.00458	+	11.2132i	0.119516	+	0.446039i
$633$		0			0
$634$	20.0808	−	11.5936i	0.797510	−	0.460442i
$635$	−10.6555	+	1.80084i	−0.422850	+	0.0714642i
$636$		0			0
$637$	11.5222	−	3.08736i	0.456525	−	0.122326i
$638$	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	−0.958320	−	0.285698i	$-0.907775\pi$
$641$	−42.6583	−	24.6288i	−1.68490	−	0.972778i	−0.726582	−	0.687080i	$-0.758892\pi$
$642$		0			0
$643$	19.6155	+	5.25595i	0.773559	+	0.207274i	0.623943	−	0.781470i	$-0.285530\pi$
$643$	19.6155	+	5.25595i	0.773559	+	0.207274i	0.149616	+	0.988744i	$0.452196\pi$
$644$	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	$-0.450585\pi$
$647$	29.0632	−	29.0632i	1.14259	−	1.14259i	0.987974	−	0.154619i	$-0.0494151\pi$
$648$		0			0
$649$			5.31632i			0.208684i
$650$	19.2031	−	6.68172i	0.753207	−	0.262079i
$651$		0			0
$652$	−3.54385	+	13.2258i	−0.138788	+	0.517963i
$653$	−0.736931	+	2.75027i	−0.0288384	+	0.107626i	−0.978845	−	0.204604i	$-0.934409\pi$
$653$	−0.736931	+	2.75027i	−0.0288384	+	0.107626i	0.950006	+	0.312230i	$0.101076\pi$
$654$		0			0
$655$	0.100067	−	1.05716i	0.00390995	−	0.0413067i
$656$			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	−0.220822	−	0.975314i	$-0.570874\pi$
$659$	18.8486	−	32.6467i	0.734236	−	1.27173i	0.955058	−	0.296420i	$-0.0957928\pi$
$660$		0			0
$661$	3.68907	+	6.38966i	0.143488	+	0.248529i	0.928808	−	0.370561i	$-0.120835\pi$
$661$	3.68907	+	6.38966i	0.143488	+	0.248529i	−0.785320	+	0.619091i	$0.787501\pi$
$662$	−24.9459	−	6.68424i	−0.969551	−	0.259791i
$663$		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
$668$	4.93579	−	1.32254i	0.190971	−	0.0511707i
$669$		0			0
$670$	−10.9752	+	15.4395i	−0.424010	+	0.596479i
$671$	−14.9193	+	8.61365i	−0.575953	+	0.332526i
$672$		0			0
$673$	1.84460	+	6.88414i	0.0711041	+	0.265364i	0.992322	−	0.123684i	$-0.0394708\pi$
$673$	1.84460	+	6.88414i	0.0711041	+	0.265364i	−0.921218	+	0.389048i	$0.872804\pi$
$674$	−32.0820			−1.23575
$675$		0			0
$676$	−3.53614			−0.136005
$677$	−2.16966	−	8.09727i	−0.0833867	−	0.311203i	0.911617	−	0.411040i	$-0.134834\pi$
$677$	−2.16966	−	8.09727i	−0.0833867	−	0.311203i	−0.995004	+	0.0998372i	$0.968168\pi$
$678$		0			0
$679$	−17.5722	+	10.1453i	−0.674358	+	0.389341i
$680$	4.32168	−	6.07954i	0.165729	−	0.233140i
$681$		0			0
$682$	13.2725	−	3.55635i	0.508229	−	0.136180i
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	0.942400	−	0.334488i	$-0.108564\pi$
$683$	15.8873	+	15.8873i	0.607911	+	0.607911i	−0.334488	+	0.942400i	$0.608564\pi$
$684$		0			0
$685$	−20.6468	−	7.68149i	−0.788875	−	0.293494i
$686$	17.3478	+	10.0158i	0.662342	+	0.382403i
$687$		0			0
$688$	9.09714	+	2.43757i	0.346825	+	0.0929315i
$689$	−20.2150	−	35.0134i	−0.770131	−	1.33391i
$690$		0			0
$691$	9.16297	−	15.8707i	0.348576	−	0.603751i	−0.637421	−	0.770516i	$-0.719999\pi$
$691$	9.16297	−	15.8707i	0.348576	−	0.603751i	0.985997	+	0.166765i	$0.0533321\pi$
$692$	−5.24323	+	5.24323i	−0.199318	+	0.199318i
$693$		0			0
$694$		−	14.8046i		−	0.561973i
$695$	−0.148013	+	1.56368i	−0.00561444	+	0.0593138i
$696$		0			0
$697$	−6.11718	+	22.8296i	−0.231705	+	0.864734i
$698$	−3.99695	+	14.9168i	−0.151287	+	0.564610i
$699$		0			0
$700$	9.07669	+	4.39070i	0.343067	+	0.165953i
$701$		−	21.1738i		−	0.799724i	−0.916575	−	0.399862i	$-0.869058\pi$
$701$		−	21.1738i		−	0.799724i	0.916575	−	0.399862i	$-0.130942\pi$
$702$		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
$707$	9.19953	+	2.46501i	0.345984	+	0.0927062i
$708$		0			0
$709$	−20.4846	−	11.8268i	−0.769316	−	0.444165i	0.0633143	−	0.997994i	$-0.479833\pi$
$709$	−20.4846	−	11.8268i	−0.769316	−	0.444165i	−0.832631	+	0.553829i	$0.813166\pi$
$710$	4.43244	−	11.9138i	0.166346	−	0.447117i
$711$		0			0
$712$	−1.44949	−	1.44949i	−0.0543219	−	0.0543219i
$713$	42.2329	−	11.3163i	1.58163	−	0.423798i
$714$		0			0
$715$	−17.6580	+	2.98431i	−0.660372	+	0.111607i
$716$	−2.36794	+	1.36713i	−0.0884942	+	0.0510921i
$717$		0			0
$718$	0.878601	+	3.27899i	0.0327891	+	0.122371i
$719$	−21.3695			−0.796947			−0.398473	−	0.917180i	$-0.630460\pi$
$719$	−21.3695			−0.796947			−0.398473	+	0.917180i	$0.630460\pi$
$720$		0			0
$721$	−8.07679			−0.300795
$722$	−1.35990	−	5.07522i	−0.0506102	−	0.188880i
$723$		0			0
$724$	19.6658	−	11.3541i	0.730874	−	0.421970i
$725$	36.8205	+	7.03363i	1.36748	+	0.261222i
$726$		0			0
$727$	2.97151	−	0.796213i	0.110207	−	0.0295299i	−0.203294	−	0.979118i	$-0.565165\pi$
$727$	2.97151	−	0.796213i	0.110207	−	0.0295299i	0.313501	+	0.949588i	$0.398498\pi$
$728$	−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
$733$	23.5366	+	6.30661i	0.869343	+	0.232940i	0.665804	−	0.746127i	$-0.268089\pi$
$733$	23.5366	+	6.30661i	0.869343	+	0.232940i	0.203540	+	0.979067i	$0.434755\pi$
$734$	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	$0.966638\pi$
$740$	−10.3978	+	8.59956i	−0.382230	+	0.316126i
$741$		0			0
$742$	5.18917	−	19.3663i	0.190500	−	0.710958i
$743$	4.04871	−	15.1100i	0.148533	−	0.554332i	−0.851040	−	0.525101i	$-0.824027\pi$
$743$	4.04871	−	15.1100i	0.148533	−	0.554332i	0.999573	−	0.0292311i	$-0.00930587\pi$
$744$		0			0
$745$	18.0587	+	1.70937i	0.661619	+	0.0626266i
$746$		−	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	−0.926537	−	0.376203i	$-0.877229\pi$
$751$	−21.6240	−	37.4538i	−0.789070	−	1.36671i	0.137467	−	0.990506i	$-0.456104\pi$
$752$	−7.49533	−	2.00837i	−0.273327	−	0.0732376i
$753$		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	$0.551456\pi$
$758$	29.1055	−	7.79880i	1.05716	−	0.283265i
$759$		0			0
$760$	−1.38152	−	8.17436i	−0.0501129	−	0.296515i
$761$	24.8744	−	14.3612i	0.901696	−	0.520595i	0.0239461	−	0.999713i	$-0.492377\pi$
$761$	24.8744	−	14.3612i	0.901696	−	0.520595i	0.877750	+	0.479119i	$0.159044\pi$
$762$		0			0
$763$	−2.27225	−	8.48016i	−0.0822611	−	0.307002i
$764$	−1.28350			−0.0464353
$765$		0			0
$766$	−17.1481			−0.619587
$767$	−2.84099	−	10.6027i	−0.102582	−	0.382842i
$768$		0			0
$769$	−29.3558	+	16.9486i	−1.05860	+	0.611180i	−0.925043	−	0.379861i	$-0.875972\pi$
$769$	−29.3558	+	16.9486i	−1.05860	+	0.611180i	−0.133552	+	0.991042i	$0.542638\pi$
$770$	−7.23838	−	5.14544i	−0.260853	−	0.185429i
$771$		0			0
$772$	5.28063	−	1.41494i	0.190054	−	0.0509248i
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.996232	−	0.0867231i	$-0.972360\pi$
$773$	−30.1093	−	30.1093i	−1.08296	−	1.08296i	−0.0867231	−	0.996232i	$-0.527640\pi$
$774$		0			0
$775$	22.8005	−	26.4010i	0.819017	−	0.948351i
$776$	−8.71386	−	5.03095i	−0.312809	−	0.180601i
$777$		0			0
$778$	−29.1844	−	7.81993i	−1.04631	−	0.280358i
$779$	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
$785$	15.4690	+	18.7036i	0.552111	+	0.667561i
$786$		0			0
$787$	2.73876	−	10.2212i	0.0976263	−	0.364346i	−0.899778	−	0.436347i	$-0.856272\pi$
$787$	2.73876	−	10.2212i	0.0976263	−	0.364346i	0.997405	+	0.0720011i	$0.0229385\pi$
$788$	4.40644	−	16.4450i	0.156973	−	0.585831i
$789$		0			0
$790$	−16.5437	−	20.0031i	−0.588600	−	0.711680i
$791$			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
$797$	13.1409	+	3.52110i	0.465476	+	0.124724i	0.483932	−	0.875106i	$-0.339208\pi$
$797$	13.1409	+	3.52110i	0.465476	+	0.124724i	−0.0184558	+	0.999830i	$0.505875\pi$
$798$		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
$803$	3.09199	−	0.828496i	0.109114	−	0.0292370i
$804$		0			0
$805$	−23.0325	−	16.3727i	−0.811788	−	0.577063i
$806$	−24.5697	+	14.1853i	−0.865432	+	0.499657i
$807$		0			0
$808$	1.22237	+	4.56196i	0.0430029	+	0.160489i
$809$	−33.4429			−1.17579			−0.587895	−	0.808937i	$-0.700043\pi$
$809$	−33.4429			−1.17579			−0.587895	+	0.808937i	$0.700043\pi$
$810$		0			0
$811$	21.1960			0.744294			0.372147	−	0.928174i	$-0.378622\pi$
$811$	21.1960			0.744294			0.372147	+	0.928174i	$0.378622\pi$
$812$	−3.91303	−	14.6036i	−0.137320	−	0.512487i
$813$		0			0
$814$	10.2924	−	5.94230i	0.360747	−	0.208278i
$815$	−5.10212	−	30.1890i	−0.178720	−	1.05747i
$816$		0			0
$817$	33.7279	−	9.03736i	1.17999	−	0.316177i
$818$	−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	0.987313	−	0.158789i	$-0.0507589\pi$
$821$	38.4941	+	22.2246i	1.34345	+	0.775643i	0.356141	+	0.934432i	$0.384092\pi$
$822$		0			0
$823$	−24.6311	−	6.59989i	−0.858588	−	0.230058i	−0.197441	−	0.980315i	$-0.563263\pi$
$823$	−24.6311	−	6.59989i	−0.858588	−	0.230058i	−0.661146	+	0.750257i	$0.729930\pi$
$824$	−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	−0.869253	−	0.494368i	$-0.835400\pi$
$827$	−10.7808	+	10.7808i	−0.374885	+	0.374885i	0.494368	+	0.869253i	$0.335400\pi$
$828$		0			0
$829$		−	4.02079i		−	0.139648i	−0.997559	−	0.0698239i	$-0.977756\pi$
$829$		−	4.02079i		−	0.139648i	0.997559	−	0.0698239i	$-0.0222437\pi$
$830$	−3.79273	−	0.359007i	−0.131647	−	0.0124613i
$831$		0			0
$832$	1.05248	−	3.92790i	0.0364881	−	0.136176i
$833$	−2.53262	+	9.45186i	−0.0877500	+	0.327488i
$834$		0			0
$835$	−8.80489	+	7.28215i	−0.304706	+	0.252009i
$836$			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	−0.415939	−	0.909393i	$-0.636547\pi$
$839$	16.7880	−	29.0777i	0.579588	−	1.00388i	0.995527	−	0.0944825i	$-0.0301196\pi$
$840$		0			0
$841$	−13.6044	−	23.5635i	−0.469118	−	0.812536i
$842$	23.6637	+	6.34068i	0.815506	+	0.218514i
$843$		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
$848$	9.60353	−	2.57326i	0.329786	−	0.0883660i
$849$		0			0
$850$	−3.12951	+	16.3828i	−0.107341	+	0.561924i
$851$	32.7503	−	18.9084i	1.12266	−	0.648171i
$852$		0			0
$853$	−6.15572	−	22.9734i	−0.210768	−	0.786596i	−0.987614	−	0.156905i	$-0.949848\pi$
$853$	−6.15572	−	22.9734i	−0.210768	−	0.786596i	0.776846	−	0.629691i	$-0.216818\pi$
$854$	17.6391			0.603599
$855$		0			0
$856$	−7.64094			−0.261162
$857$	−3.06736	−	11.4475i	−0.104779	−	0.391040i	0.893541	−	0.448981i	$-0.148213\pi$
$857$	−3.06736	−	11.4475i	−0.104779	−	0.391040i	−0.998320	+	0.0579412i	$0.981546\pi$
$858$		0			0
$859$	34.6670	−	20.0150i	1.18282	−	0.682904i	0.226158	−	0.974091i	$-0.427383\pi$
$859$	34.6670	−	20.0150i	1.18282	−	0.682904i	0.956666	+	0.291187i	$0.0940501\pi$
$860$	−20.7649	+	3.50940i	−0.708078	+	0.119670i
$861$		0			0
$862$	−5.89894	+	1.58062i	−0.200919	+	0.0538360i
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	0.736864	−	0.676041i	$-0.236306\pi$
$863$	1.78680	+	1.78680i	0.0608233	+	0.0608233i	−0.676041	+	0.736864i	$0.736306\pi$
$864$		0			0
$865$	5.78150	−	15.5399i	0.196577	−	0.528373i
$866$	−12.5665	−	7.25527i	−0.427027	−	0.246544i
$867$		0			0
$868$	−13.5897	−	3.64136i	−0.461266	−	0.123596i
$869$	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
$875$	−22.5409	−	0.480797i	−0.762021	−	0.0162539i
$876$		0			0
$877$	−1.78537	+	6.66309i	−0.0602876	+	0.224996i	−0.989496	−	0.144559i	$-0.953824\pi$
$877$	−1.78537	+	6.66309i	−0.0602876	+	0.224996i	0.929208	+	0.369556i	$0.120490\pi$
$878$	−0.587569	+	2.19284i	−0.0198295	+	0.0740047i
$879$		0			0
$880$	0.415006	−	4.38433i	0.0139898	−	0.147796i
$881$		−	3.01999i		−	0.101746i	−0.998705	−	0.0508731i	$-0.983800\pi$
$881$		−	3.01999i		−	0.101746i	0.998705	−	0.0508731i	$-0.0162004\pi$
$882$		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
$887$	17.2055	+	4.61020i	0.577705	+	0.154796i	0.535828	−	0.844327i	$-0.320000\pi$
$887$	17.2055	+	4.61020i	0.577705	+	0.154796i	0.0418769	+	0.999123i	$0.486666\pi$
$888$		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
$893$	−27.7891	+	7.44607i	−0.929928	+	0.249173i
$894$		0			0
$895$	3.54236	−	4.98324i	0.118408	−	0.166571i
$896$	1.74641	−	1.00829i	0.0583434	−	0.0336846i
$897$		0			0
$898$	−3.04660	−	11.3701i	−0.101666	−	0.379424i
$899$	−52.3064			−1.74452
$900$		0			0
$901$	33.1655			1.10490
$902$	3.61166	+	13.4789i	0.120255	+	0.448798i
$903$		0			0
$904$	−2.56825	+	1.48278i	−0.0854188	+	0.0493166i
$905$	−29.4194	+	41.3859i	−0.977933	+	1.37571i
$906$		0			0
$907$	−1.21188	+	0.324723i	−0.0402399	+	0.0107822i	−0.278883	−	0.960325i	$-0.589964\pi$
$907$	−1.21188	+	0.324723i	−0.0402399	+	0.0107822i	0.238643	+	0.971107i	$0.423297\pi$
$908$	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	0.834738	−	0.550647i	$-0.185619\pi$
$911$	23.3987	+	13.5092i	0.775232	+	0.447581i	−0.0595057	+	0.998228i	$0.518952\pi$
$912$		0			0
$913$	3.24117	+	0.868470i	0.107267	+	0.0287422i
$914$	−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	$0.646511\pi$
$920$	1.32054	−	13.9509i	0.0435371	−	0.459948i
$921$		0			0
$922$	0.783607	−	2.92446i	0.0258067	−	0.0963121i
$923$	5.98314	−	22.3294i	0.196938	−	0.734981i
$924$		0			0
$925$	13.1386	−	27.1608i	0.431994	−	0.893041i
$926$			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	$-0.682277\pi$
$929$	13.9274	−	24.1230i	0.456944	−	0.791450i	0.998798	+	0.0490228i	$0.0156107\pi$
$930$		0			0
$931$	5.43786	+	9.41865i	0.178219	+	0.308684i
$932$	20.5712	+	5.51203i	0.673831	+	0.180553i
$933$		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	$0.877477\pi$
$938$	−16.5014	+	4.42152i	−0.538788	+	0.144368i
$939$		0			0
$940$	17.1087	−	2.89147i	0.558024	−	0.0943094i
$941$	−28.5039	+	16.4567i	−0.929201	+	0.536474i	−0.886559	−	0.462616i	$-0.846911\pi$
$941$	−28.5039	+	16.4567i	−0.929201	+	0.536474i	−0.0426420	+	0.999090i	$0.513577\pi$
$942$		0			0
$943$	11.4923	+	42.8898i	0.374240	+	1.39668i
$944$	2.69933			0.0878558
$945$		0			0
$946$	18.5488			0.603074
$947$	−3.08335	−	11.5072i	−0.100195	−	0.373934i	0.897560	−	0.440891i	$-0.145338\pi$
$947$	−3.08335	−	11.5072i	−0.100195	−	0.373934i	−0.997756	+	0.0669572i	$0.978671\pi$
$948$		0			0
$949$	−5.72383	+	3.30466i	−0.185804	+	0.107274i
$950$	10.4158	+	15.3348i	0.337933	+	0.497526i
$951$		0			0
$952$	6.49768	−	1.74105i	0.210591	−	0.0564277i
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	0.890802	−	0.454391i	$-0.150143\pi$
$953$	13.4723	+	13.4723i	0.436411	+	0.436411i	−0.454391	+	0.890802i	$0.650143\pi$
$954$		0			0
$955$	2.60965	−	1.19439i	0.0844463	−	0.0386495i
$956$	−9.40038	−	5.42731i	−0.304030	−	0.175532i
$957$		0			0
$958$	32.0130	+	8.57785i	1.03429	+	0.277138i
$959$	−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
$965$	−9.42004	+	7.79091i	−0.303242	+	0.250798i
$966$		0			0
$967$	−2.40036	+	8.95826i	−0.0771904	+	0.288078i	−0.993721	−	0.111886i	$-0.964311\pi$
$967$	−2.40036	+	8.95826i	−0.0771904	+	0.288078i	0.916531	+	0.399964i	$0.130978\pi$
$968$	1.84307	−	6.87844i	0.0592386	−	0.221081i
$969$		0			0
$970$	22.3990	+	2.12021i	0.719188	+	0.0680758i
$971$		−	24.7290i		−	0.793590i	−0.917907	−	0.396795i	$-0.870122\pi$
$971$		−	24.7290i		−	0.793590i	0.917907	−	0.396795i	$-0.129878\pi$
$972$		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
$977$	−23.7190	−	6.35548i	−0.758837	−	0.203330i	−0.141403	−	0.989952i	$-0.545161\pi$
$977$	−23.7190	−	6.35548i	−0.758837	−	0.203330i	−0.617434	+	0.786622i	$0.711828\pi$
$978$		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
$983$	−40.0954	+	10.7435i	−1.27885	+	0.342666i	−0.833414	−	0.552650i	$-0.813617\pi$
$983$	−40.0954	+	10.7435i	−1.27885	+	0.342666i	−0.445433	+	0.895316i	$0.646950\pi$
$984$		0			0
$985$	6.34400	+	37.5371i	0.202137	+	1.19603i
$986$	21.6587	−	12.5047i	0.689754	−	0.398230i
$987$		0			0
$988$	−3.90209	−	14.5628i	−0.124142	−	0.463305i
$989$	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	$0.302481\pi$
$992$	−1.80571	−	6.73901i	−0.0573315	−	0.213964i
$993$		0			0
$994$	9.92800	−	5.73193i	0.314897	−	0.181806i
$995$	−8.08889	−	5.75003i	−0.256435	−	0.182288i
$996$		0			0
$997$	−11.5550	+	3.09617i	−0.365952	+	0.0980565i	−0.437109	−	0.899409i	$-0.643998\pi$
$997$	−11.5550	+	3.09617i	−0.365952	+	0.0980565i	0.0711569	+	0.997465i	$0.477331\pi$
$998$	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.197.2		16
3.2	odd	2		90.2.l.b.47.4	yes	16
5.2	odd	4		1350.2.q.h.143.4		16
5.3	odd	4	inner	270.2.m.b.143.2		16
5.4	even	2		1350.2.q.h.1007.3		16
9.2	odd	6		810.2.f.c.647.7		16
9.4	even	3		90.2.l.b.77.4	yes	16
9.5	odd	6	inner	270.2.m.b.17.2		16
9.7	even	3		810.2.f.c.647.2		16
12.11	even	2		720.2.cu.b.497.1		16
15.2	even	4		450.2.p.h.443.1		16
15.8	even	4		90.2.l.b.83.4	yes	16
15.14	odd	2		450.2.p.h.407.1		16
36.31	odd	6		720.2.cu.b.257.2		16
45.4	even	6		450.2.p.h.257.1		16
45.13	odd	12		90.2.l.b.23.4	✓	16
45.14	odd	6		1350.2.q.h.557.4		16
45.22	odd	12		450.2.p.h.293.1		16
45.23	even	12	inner	270.2.m.b.233.2		16
45.32	even	12		1350.2.q.h.1043.3		16
45.38	even	12		810.2.f.c.323.2		16
45.43	odd	12		810.2.f.c.323.7		16
60.23	odd	4		720.2.cu.b.353.2		16
180.103	even	12		720.2.cu.b.113.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.4	✓	16	45.13	odd	12
90.2.l.b.47.4	yes	16	3.2	odd	2
90.2.l.b.77.4	yes	16	9.4	even	3
90.2.l.b.83.4	yes	16	15.8	even	4
270.2.m.b.17.2		16	9.5	odd	6	inner
270.2.m.b.143.2		16	5.3	odd	4	inner
270.2.m.b.197.2		16	1.1	even	1	trivial
270.2.m.b.233.2		16	45.23	even	12	inner
450.2.p.h.257.1		16	45.4	even	6
450.2.p.h.293.1		16	45.22	odd	12
450.2.p.h.407.1		16	15.14	odd	2
450.2.p.h.443.1		16	15.2	even	4
720.2.cu.b.113.1		16	180.103	even	12
720.2.cu.b.257.2		16	36.31	odd	6
720.2.cu.b.353.2		16	60.23	odd	4
720.2.cu.b.497.1		16	12.11	even	2
810.2.f.c.323.2		16	45.38	even	12
810.2.f.c.323.7		16	45.43	odd	12
810.2.f.c.647.2		16	9.7	even	3
810.2.f.c.647.7		16	9.2	odd	6
1350.2.q.h.143.4		16	5.2	odd	4
1350.2.q.h.557.4		16	45.14	odd	6
1350.2.q.h.1007.3		16	5.4	even	2
1350.2.q.h.1043.3		16	45.32	even	12

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.29554 - 1.82252i) q^{5} +(1.94786 - 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(1.29554 - 1.82252i) q^{5} +(1.94786 - 0.521929i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.09573 - 0.779698i) q^{10} +(1.70563 + 0.984748i) q^{11} +(-3.92790 - 1.05248i) q^{13} +(-1.00829 - 1.74641i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.35877 - 2.35877i) q^{17} -3.70753i q^{19} +(-0.210717 + 2.22612i) q^{20} +(0.509743 - 1.90239i) q^{22} +(1.62200 - 6.05338i) q^{23} +(-1.64313 - 4.72230i) q^{25} +4.06647i q^{26} +(-1.42594 + 1.42594i) q^{28} +(-3.74863 + 6.49281i) q^{29} +(3.48837 + 6.04204i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.88889 - 1.66790i) q^{34} +(1.57232 - 4.22619i) q^{35} +(4.26692 + 4.26692i) q^{37} +(-3.58120 + 0.959578i) q^{38} +(2.20480 - 0.372625i) q^{40} +(-6.13601 + 3.54263i) q^{41} +(2.43757 + 9.09714i) q^{43} -1.96950 q^{44} -6.26692 q^{46} +(-2.00837 - 7.49533i) q^{47} +(-2.54041 + 1.46671i) q^{49} +(-4.13612 + 2.80936i) q^{50} +(3.92790 - 1.05248i) q^{52} +(7.03027 + 7.03027i) q^{53} +(4.00444 - 1.83276i) q^{55} +(1.74641 + 1.00829i) q^{56} +(7.24179 + 1.94043i) q^{58} +(1.34967 + 2.33769i) q^{59} +(-4.37353 + 7.57518i) q^{61} +(4.93330 - 4.93330i) q^{62} +1.00000i q^{64} +(-7.00693 + 5.79513i) q^{65} +(2.19259 - 8.18285i) q^{67} +(-0.863368 + 3.22213i) q^{68} +(-4.48914 - 0.424926i) q^{70} +5.68481i q^{71} +(1.14928 - 1.14928i) q^{73} +(3.01717 - 5.22589i) q^{74} +(1.85376 + 3.21081i) q^{76} +(3.83631 + 1.02794i) q^{77} +(10.0535 + 5.80440i) q^{79} +(-0.930573 - 2.03323i) q^{80} +(5.01003 + 5.01003i) q^{82} +(1.64569 - 0.440961i) q^{83} +(-1.24300 - 7.35477i) q^{85} +(8.15627 - 4.70902i) q^{86} +(0.509743 + 1.90239i) q^{88} -2.04989 q^{89} -8.20034 q^{91} +(1.62200 + 6.05338i) q^{92} +(-6.72013 + 3.87987i) q^{94} +(-6.75702 - 4.80327i) q^{95} +(-9.71905 + 2.60421i) q^{97} +(2.07424 + 2.07424i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 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

Introduction

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