LMFDB - Embedded newform 576.2.bd.b.541.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(37,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 9, 0]))

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

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

chi := DirichletCharacter("576.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 192)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			541.11
Character	$\chi$	$=$	576.541
Dual form			576.2.bd.b.181.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.662809 - 1.24927i) q^{2} +(-1.12137 - 1.65606i) q^{4} +(-1.62504 + 2.43205i) q^{5} +(0.294182 - 0.121854i) q^{7} +(-2.81212 + 0.303246i) q^{8} +O(q^{10})$	\(q+(0.662809 - 1.24927i) q^{2} +(-1.12137 - 1.65606i) q^{4} +(-1.62504 + 2.43205i) q^{5} +(0.294182 - 0.121854i) q^{7} +(-2.81212 + 0.303246i) q^{8} +(1.96120 + 3.64211i) q^{10} +(1.07988 + 5.42890i) q^{11} +(2.67591 + 4.00478i) q^{13} +(0.0427572 - 0.448280i) q^{14} +(-1.48506 + 3.71411i) q^{16} +(-0.394520 - 0.394520i) q^{17} +(-2.13690 + 1.42783i) q^{19} +(5.84989 - 0.0360570i) q^{20} +(7.49793 + 2.24926i) q^{22} +(3.37395 - 8.14543i) q^{23} +(-1.36068 - 3.28498i) q^{25} +(6.77668 - 0.688538i) q^{26} +(-0.531684 - 0.350539i) q^{28} +(-0.411462 + 2.06856i) q^{29} +1.31001i q^{31} +(3.65562 + 4.31699i) q^{32} +(-0.754356 + 0.231372i) q^{34} +(-0.181703 + 0.913483i) q^{35} +(1.47533 + 0.985786i) q^{37} +(0.367396 + 3.61595i) q^{38} +(3.83232 - 7.33202i) q^{40} +(-4.39934 + 10.6209i) q^{41} +(-2.25285 + 0.448119i) q^{43} +(7.77964 - 7.87614i) q^{44} +(-7.93958 - 9.61384i) q^{46} +(5.23873 + 5.23873i) q^{47} +(-4.87805 + 4.87805i) q^{49} +(-5.00571 - 0.477448i) q^{50} +(3.63147 - 8.92230i) q^{52} +(-1.88714 - 9.48728i) q^{53} +(-14.9582 - 6.19589i) q^{55} +(-0.790324 + 0.431878i) q^{56} +(2.31148 + 1.88509i) q^{58} +(0.373863 - 0.559526i) q^{59} +(0.868572 + 0.172770i) q^{61} +(1.63656 + 0.868286i) q^{62} +(7.81608 - 1.70553i) q^{64} -14.0883 q^{65} +(10.3046 + 2.04972i) q^{67} +(-0.210946 + 1.09575i) q^{68} +(1.02076 + 0.832462i) q^{70} +(12.4243 - 5.14631i) q^{71} +(-14.5155 - 6.01250i) q^{73} +(2.20938 - 1.18971i) q^{74} +(4.76083 + 1.93771i) q^{76} +(0.979213 + 1.46550i) q^{77} +(-2.55934 + 2.55934i) q^{79} +(-6.61960 - 9.64734i) q^{80} +(10.3525 + 12.5356i) q^{82} +(-0.585536 + 0.391243i) q^{83} +(1.60061 - 0.318380i) q^{85} +(-0.933384 + 3.11144i) q^{86} +(-4.68304 - 14.9393i) q^{88} +(-3.72369 - 8.98978i) q^{89} +(1.27520 + 0.852063i) q^{91} +(-17.2727 + 3.54657i) q^{92} +(10.0169 - 3.07233i) q^{94} -7.51734i q^{95} -0.565484i q^{97} +(2.86081 + 9.32724i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} + 80 q^{26} - 80 q^{28} + 80 q^{32} - 80 q^{34} + 80 q^{38} - 80 q^{40} + 16 q^{44} - 48 q^{50} + 48 q^{52} - 64 q^{55} - 112 q^{56} + 128 q^{59} - 96 q^{62} + 96 q^{64} - 32 q^{67} - 96 q^{68} + 96 q^{70} + 128 q^{71} - 112 q^{74} + 16 q^{76} - 32 q^{79} - 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 + 80 * q^26 - 80 * q^28 + 80 * q^32 - 80 * q^34 + 80 * q^38 - 80 * q^40 + 16 * q^44 - 48 * q^50 + 48 * q^52 - 64 * q^55 - 112 * q^56 + 128 * q^59 - 96 * q^62 + 96 * q^64 - 32 * q^67 - 96 * q^68 + 96 * q^70 + 128 * q^71 - 112 * q^74 + 16 * q^76 - 32 * q^79 - 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	0.662809	−	1.24927i	0.468677	−	0.883370i
$2$	0.662809	−	1.24927i	0.468677	−	0.883370i
$3$		0			0
$3$		0			0
$4$	−1.12137	−	1.65606i	−0.560685	−	0.828030i
$5$	−1.62504	+	2.43205i	−0.726742	+	1.08765i	0.265595	+	0.964085i	$0.414432\pi$
$5$	−1.62504	+	2.43205i	−0.726742	+	1.08765i	−0.992337	+	0.123561i	$0.960568\pi$
$6$		0			0
$7$	0.294182	−	0.121854i	0.111190	−	0.0460565i	−0.326395	−	0.945234i	$-0.605834\pi$
$7$	0.294182	−	0.121854i	0.111190	−	0.0460565i	0.437585	+	0.899177i	$0.355834\pi$
$8$	−2.81212	+	0.303246i	−0.994236	+	0.107214i
$9$		0			0
$10$	1.96120	+	3.64211i	0.620187	+	1.15174i
$11$	1.07988	+	5.42890i	0.325595	+	1.63687i	0.703260	+	0.710932i	$0.251727\pi$
$11$	1.07988	+	5.42890i	0.325595	+	1.63687i	−0.377666	+	0.925942i	$0.623273\pi$
$12$		0			0
$13$	2.67591	+	4.00478i	0.742163	+	1.11073i	0.989882	+	0.141894i	$0.0453192\pi$
$13$	2.67591	+	4.00478i	0.742163	+	1.11073i	−0.247718	+	0.968832i	$0.579681\pi$
$14$	0.0427572	−	0.448280i	0.0114273	−	0.119808i
$15$		0			0
$16$	−1.48506	+	3.71411i	−0.371266	+	0.928527i
$17$	−0.394520	−	0.394520i	−0.0956853	−	0.0956853i	0.657644	−	0.753329i	$-0.271553\pi$
$17$	−0.394520	−	0.394520i	−0.0956853	−	0.0956853i	−0.753329	+	0.657644i	$0.771553\pi$
$18$		0			0
$19$	−2.13690	+	1.42783i	−0.490239	+	0.327567i	−0.775999	−	0.630734i	$-0.782754\pi$
$19$	−2.13690	+	1.42783i	−0.490239	+	0.327567i	0.285760	+	0.958301i	$0.407754\pi$
$20$	5.84989	−	0.0360570i	1.30808	−	0.00806259i
$21$		0			0
$22$	7.49793	+	2.24926i	1.59856	+	0.479544i
$23$	3.37395	−	8.14543i	0.703516	−	1.69844i	−0.0120823	−	0.999927i	$-0.503846\pi$
$23$	3.37395	−	8.14543i	0.703516	−	1.69844i	0.715599	−	0.698512i	$-0.246154\pi$
$24$		0			0
$25$	−1.36068	−	3.28498i	−0.272137	−	0.656996i
$26$	6.77668	−	0.688538i	1.32902	−	0.135033i
$27$		0			0
$28$	−0.531684	−	0.350539i	−0.100479	−	0.0662457i
$29$	−0.411462	+	2.06856i	−0.0764067	+	0.384122i	0.923593	+	0.383374i	$0.125238\pi$
$29$	−0.411462	+	2.06856i	−0.0764067	+	0.384122i	−1.00000		0.000747904i	$0.999762\pi$
$30$		0			0
$31$			1.31001i			0.235285i	0.993056	+	0.117642i	$0.0375336\pi$
$31$			1.31001i			0.235285i	−0.993056	+	0.117642i	$0.962466\pi$
$32$	3.65562	+	4.31699i	0.646229	+	0.763144i
$33$		0			0
$34$	−0.754356	+	0.231372i	−0.129371	+	0.0396800i
$35$	−0.181703	+	0.913483i	−0.0307134	+	0.154407i
$36$		0			0
$37$	1.47533	+	0.985786i	0.242543	+	0.162062i	0.670901	−	0.741547i	$-0.265908\pi$
$37$	1.47533	+	0.985786i	0.242543	+	0.162062i	−0.428358	+	0.903609i	$0.640908\pi$
$38$	0.367396	+	3.61595i	0.0595994	+	0.586585i
$39$		0			0
$40$	3.83232	−	7.33202i	0.605942	−	1.15929i
$41$	−4.39934	+	10.6209i	−0.687061	+	1.65871i	0.0635600	+	0.997978i	$0.479755\pi$
$41$	−4.39934	+	10.6209i	−0.687061	+	1.65871i	−0.750621	+	0.660733i	$0.770245\pi$
$42$		0			0
$43$	−2.25285	+	0.448119i	−0.343556	+	0.0683376i	−0.363853	−	0.931456i	$-0.618539\pi$
$43$	−2.25285	+	0.448119i	−0.343556	+	0.0683376i	0.0202967	+	0.999794i	$0.493539\pi$
$44$	7.77964	−	7.87614i	1.17282	−	1.18737i
$45$		0			0
$46$	−7.93958	−	9.61384i	−1.17063	−	1.41748i
$47$	5.23873	+	5.23873i	0.764147	+	0.764147i	0.977069	−	0.212922i	$-0.0682980\pi$
$47$	5.23873	+	5.23873i	0.764147	+	0.764147i	−0.212922	+	0.977069i	$0.568298\pi$
$48$		0			0
$49$	−4.87805	+	4.87805i	−0.696865	+	0.696865i
$50$	−5.00571	−	0.477448i	−0.707915	−	0.0675213i
$51$		0			0
$52$	3.63147	−	8.92230i	0.503594	−	1.23730i
$53$	−1.88714	−	9.48728i	−0.259218	−	1.30318i	−0.862665	−	0.505775i	$-0.831206\pi$
$53$	−1.88714	−	9.48728i	−0.259218	−	1.30318i	0.603447	−	0.797403i	$-0.293794\pi$
$54$		0			0
$55$	−14.9582	−	6.19589i	−2.01696	−	0.835453i
$56$	−0.790324	+	0.431878i	−0.105611	+	0.0577122i
$57$		0			0
$58$	2.31148	+	1.88509i	0.303512	+	0.247524i
$59$	0.373863	−	0.559526i	0.0486728	−	0.0728441i	−0.806335	−	0.591459i	$-0.798552\pi$
$59$	0.373863	−	0.559526i	0.0486728	−	0.0728441i	0.855008	+	0.518615i	$0.173552\pi$
$60$		0			0
$61$	0.868572	+	0.172770i	0.111209	+	0.0221209i	0.250381	−	0.968147i	$-0.419444\pi$
$61$	0.868572	+	0.172770i	0.111209	+	0.0221209i	−0.139172	+	0.990268i	$0.544444\pi$
$62$	1.63656	+	0.868286i	0.207843	+	0.110272i
$63$		0			0
$64$	7.81608	−	1.70553i	0.977010	−	0.213192i
$65$	−14.0883			−1.74744
$66$		0			0
$67$	10.3046	+	2.04972i	1.25891	+	0.250413i	0.779068	−	0.626940i	$-0.215693\pi$
$67$	10.3046	+	2.04972i	1.25891	+	0.250413i	0.479845	+	0.877353i	$0.340693\pi$
$68$	−0.210946	+	1.09575i	−0.0255810	+	0.132879i
$69$		0			0
$70$	1.02076	+	0.832462i	0.122004	+	0.0994982i
$71$	12.4243	−	5.14631i	1.47449	−	0.610755i	0.506614	−	0.862173i	$-0.330897\pi$
$71$	12.4243	−	5.14631i	1.47449	−	0.610755i	0.967878	+	0.251419i	$0.0808971\pi$
$72$		0			0
$73$	−14.5155	−	6.01250i	−1.69891	−	0.703710i	−0.698971	−	0.715150i	$-0.746359\pi$
$73$	−14.5155	−	6.01250i	−1.69891	−	0.703710i	−0.999935	+	0.0114397i	$0.996359\pi$
$74$	2.20938	−	1.18971i	0.256835	−	0.138301i
$75$		0			0
$76$	4.76083	+	1.93771i	0.546104	+	0.222270i
$77$	0.979213	+	1.46550i	0.111592	+	0.167009i
$78$		0			0
$79$	−2.55934	+	2.55934i	−0.287948	+	0.287948i	−0.836268	−	0.548320i	$-0.815267\pi$
$79$	−2.55934	+	2.55934i	−0.287948	+	0.287948i	0.548320	+	0.836268i	$0.315267\pi$
$80$	−6.61960	−	9.64734i	−0.740094	−	1.07860i
$81$		0			0
$82$	10.3525	+	12.5356i	1.14325	+	1.38433i
$83$	−0.585536	+	0.391243i	−0.0642710	+	0.0429445i	−0.587291	−	0.809376i	$-0.699805\pi$
$83$	−0.585536	+	0.391243i	−0.0642710	+	0.0429445i	0.523020	+	0.852321i	$0.324805\pi$
$84$		0			0
$85$	1.60061	−	0.318380i	0.173610	−	0.0345332i
$86$	−0.933384	+	3.11144i	−0.100649	+	0.335515i
$87$		0			0
$88$	−4.68304	−	14.9393i	−0.499213	−	1.59253i
$89$	−3.72369	−	8.98978i	−0.394710	−	0.952915i	−0.988899	−	0.148589i	$-0.952527\pi$
$89$	−3.72369	−	8.98978i	−0.394710	−	0.952915i	0.594189	−	0.804326i	$-0.297473\pi$
$90$		0			0
$91$	1.27520	+	0.852063i	0.133678	+	0.0893205i
$92$	−17.2727	+	3.54657i	−1.80081	+	0.369756i
$93$		0			0
$94$	10.0169	−	3.07233i	1.03316	−	0.316887i
$95$		−	7.51734i		−	0.771263i
$96$		0			0
$97$		−	0.565484i		−	0.0574162i	−0.999588	−	0.0287081i	$-0.990861\pi$
$97$		−	0.565484i		−	0.0574162i	0.999588	−	0.0287081i	$-0.00913933\pi$
$98$	2.86081	+	9.32724i	0.288985	+	0.942193i
$99$		0			0
$100$	−3.91429	+	5.93705i	−0.391429	+	0.593705i
$101$	−9.22776	−	6.16579i	−0.918196	−	0.613519i	0.00410457	−	0.999992i	$-0.498693\pi$
$101$	−9.22776	−	6.16579i	−0.918196	−	0.613519i	−0.922301	+	0.386472i	$0.873693\pi$
$102$		0			0
$103$	3.23367	+	7.80677i	0.318623	+	0.769223i	0.999328	+	0.0366656i	$0.0116736\pi$
$103$	3.23367	+	7.80677i	0.318623	+	0.769223i	−0.680705	+	0.732558i	$0.738326\pi$
$104$	−8.73942	−	10.4505i	−0.856971	−	1.02475i
$105$		0			0
$106$	−13.1030	−	3.93070i	−1.27268	−	0.381784i
$107$	−8.21391	+	1.63385i	−0.794069	+	0.157950i	−0.575425	−	0.817855i	$-0.695163\pi$
$107$	−8.21391	+	1.63385i	−0.794069	+	0.157950i	−0.218644	+	0.975805i	$0.570163\pi$
$108$		0			0
$109$	0.453546	−	0.303050i	0.0434419	−	0.0290269i	−0.533660	−	0.845699i	$-0.679184\pi$
$109$	0.453546	−	0.303050i	0.0434419	−	0.0290269i	0.577102	+	0.816672i	$0.304184\pi$
$110$	−17.6548	+	14.5802i	−1.68332	+	1.39017i
$111$		0			0
$112$	0.0157006	+	1.27358i	0.00148357	+	0.120342i
$113$	−1.13400	+	1.13400i	−0.106678	+	0.106678i	−0.758431	−	0.651753i	$-0.774034\pi$
$113$	−1.13400	+	1.13400i	−0.106678	+	0.106678i	0.651753	+	0.758431i	$0.274034\pi$
$114$		0			0
$115$	14.3273	+	21.4423i	1.33603	+	1.99950i
$116$	3.88706	−	1.63821i	0.360905	−	0.152104i
$117$		0			0
$118$	−0.451201	−	0.837916i	−0.0415364	−	0.0771364i
$119$	−0.164135	−	0.0679868i	−0.0150462	−	0.00623234i
$120$		0			0
$121$	−18.1441	+	7.51555i	−1.64947	+	0.683231i
$122$	0.791534	−	0.970571i	0.0716621	−	0.0878713i
$123$		0			0
$124$	2.16945	−	1.46900i	0.194823	−	0.131920i
$125$	−4.14359	−	0.824210i	−0.370614	−	0.0737196i
$126$		0			0
$127$	6.16120			0.546718			0.273359	−	0.961912i	$-0.411865\pi$
$127$	6.16120			0.546718			0.273359	+	0.961912i	$0.411865\pi$
$128$	3.04989	−	10.8949i	0.269575	−	0.962979i
$129$		0			0
$130$	−9.33785	+	17.6001i	−0.818983	+	1.54363i
$131$	18.7962	+	3.73880i	1.64223	+	0.326660i	0.927810	−	0.373054i	$-0.121689\pi$
$131$	18.7962	+	3.73880i	1.64223	+	0.326660i	0.714423	+	0.699714i	$0.246689\pi$
$132$		0			0
$133$	−0.454650	+	0.680432i	−0.0394232	+	0.0590010i
$134$	9.39068	−	11.5148i	0.811231	−	0.994723i
$135$		0			0
$136$	1.22908	+	0.989803i	0.105392	+	0.0848749i
$137$	20.4158	+	8.45651i	1.74424	+	0.722488i	0.998411	+	0.0563516i	$0.0179468\pi$
$137$	20.4158	+	8.45651i	1.74424	+	0.722488i	0.745830	+	0.666137i	$0.232053\pi$
$138$		0			0
$139$	−1.51500	−	7.61643i	−0.128501	−	0.646018i	−0.990320	−	0.138802i	$-0.955675\pi$
$139$	−1.51500	−	7.61643i	−0.128501	−	0.646018i	0.861819	−	0.507215i	$-0.169325\pi$
$140$	1.71654	−	0.723441i	0.145074	−	0.0611419i
$141$		0			0
$142$	1.80578	−	18.9324i	0.151538	−	1.58877i
$143$	−18.8519	+	18.8519i	−1.57647	+	1.57647i
$144$		0			0
$145$	−4.36220	−	4.36220i	−0.362261	−	0.362261i
$146$	−17.1322	+	14.1486i	−1.41787	+	1.17095i
$147$		0			0
$148$	−0.0218729	−	3.54867i	−0.00179794	−	0.291699i
$149$	14.4464	−	2.87356i	1.18349	−	0.235411i	0.436165	−	0.899867i	$-0.356336\pi$
$149$	14.4464	−	2.87356i	1.18349	−	0.235411i	0.747328	+	0.664455i	$0.231336\pi$
$150$		0			0
$151$	7.33383	−	17.7054i	0.596819	−	1.44085i	−0.279987	−	0.960004i	$-0.590330\pi$
$151$	7.33383	−	17.7054i	0.596819	−	1.44085i	0.876806	−	0.480845i	$-0.159670\pi$
$152$	5.57625	−	4.66325i	0.452293	−	0.378239i
$153$		0			0
$154$	2.47984	−	0.251962i	0.199831	−	0.0203036i
$155$	−3.18601	−	2.12882i	−0.255906	−	0.170991i
$156$		0			0
$157$	2.49692	−	12.5529i	0.199276	−	1.00183i	−0.743584	−	0.668642i	$-0.766876\pi$
$157$	2.49692	−	12.5529i	0.199276	−	1.00183i	0.942861	−	0.333187i	$-0.108124\pi$
$158$	1.50096	+	4.89366i	0.119410	+	0.389319i
$159$		0			0
$160$	−16.4397	+	1.87535i	−1.29967	+	0.148260i
$161$		−	2.80737i		−	0.221251i
$162$		0			0
$163$	1.62246	−	8.15667i	0.127081	−	0.638880i	−0.863766	−	0.503893i	$-0.831901\pi$
$163$	1.62246	−	8.15667i	0.127081	−	0.638880i	0.990847	−	0.134987i	$-0.0430994\pi$
$164$	22.5222	−	4.62443i	1.75869	−	0.361107i
$165$		0			0
$166$	0.100671	+	0.990814i	0.00781357	+	0.0769021i
$167$	−2.16239	−	5.22048i	−0.167331	−	0.403973i	0.817864	−	0.575412i	$-0.195158\pi$
$167$	−2.16239	−	5.22048i	−0.167331	−	0.403973i	−0.985195	+	0.171439i	$0.945158\pi$
$168$		0			0
$169$	−3.90289	+	9.42242i	−0.300222	+	0.724801i
$170$	0.663152	−	2.21062i	0.0508614	−	0.169547i
$171$		0			0
$172$	3.26839	+	3.22834i	0.249212	+	0.246159i
$173$	−1.03110	+	0.688961i	−0.0783933	+	0.0523808i	−0.594149	−	0.804355i	$-0.702511\pi$
$173$	−1.03110	+	0.688961i	−0.0783933	+	0.0523808i	0.515756	+	0.856736i	$0.327511\pi$
$174$		0			0
$175$	−0.800577	−	0.800577i	−0.0605179	−	0.0605179i
$176$	−21.7672	−	4.05149i	−1.64076	−	0.305392i
$177$		0			0
$178$	−13.6988	−	1.30660i	−1.02677	−	0.0979338i
$179$	−2.80532	−	4.19846i	−0.209680	−	0.313808i	0.711691	−	0.702492i	$-0.247930\pi$
$179$	−2.80532	−	4.19846i	−0.209680	−	0.313808i	−0.921371	+	0.388685i	$0.872930\pi$
$180$		0			0
$181$	2.72985	+	13.7239i	0.202908	+	1.02009i	0.939186	+	0.343408i	$0.111581\pi$
$181$	2.72985	+	13.7239i	0.202908	+	1.02009i	−0.736278	+	0.676679i	$0.763419\pi$
$182$	1.90968	−	1.02832i	0.141555	−	0.0762243i
$183$		0			0
$184$	−7.01788	+	23.9291i	−0.517365	+	1.76408i
$185$	−4.79496	+	1.98614i	−0.352533	+	0.146024i
$186$		0			0
$187$	1.71578	−	2.56784i	0.125470	−	0.187779i
$188$	2.80110	−	14.5502i	0.204291	−	1.06118i
$189$		0			0
$190$	−9.39121	−	4.98256i	−0.681310	−	0.361473i
$191$	3.22178			0.233120			0.116560	−	0.993184i	$-0.462813\pi$
$191$	3.22178			0.233120			0.116560	+	0.993184i	$0.462813\pi$
$192$		0			0
$193$	20.2935			1.46076			0.730381	−	0.683040i	$-0.239343\pi$
$193$	20.2935			1.46076			0.730381	+	0.683040i	$0.239343\pi$
$194$	−0.706444	−	0.374808i	−0.0507197	−	0.0269096i
$195$		0			0
$196$	13.5484	+	2.60825i	0.967746	+	0.186303i
$197$	−10.1421	+	15.1788i	−0.722597	+	1.08144i	0.270336	+	0.962766i	$0.412865\pi$
$197$	−10.1421	+	15.1788i	−0.722597	+	1.08144i	−0.992933	+	0.118677i	$0.962135\pi$
$198$		0			0
$199$	11.3372	−	4.69603i	0.803674	−	0.332893i	0.0572470	−	0.998360i	$-0.481768\pi$
$199$	11.3372	−	4.69603i	0.803674	−	0.332893i	0.746427	+	0.665467i	$0.231768\pi$
$200$	4.82257	+	8.82515i	0.341007	+	0.624032i
$201$		0			0
$202$	−13.8190	+	7.44126i	−0.972302	+	0.523565i
$203$	0.131018	+	0.658672i	0.00919566	+	0.0462297i
$204$		0			0
$205$	−18.6815	−	27.9589i	−1.30477	−	1.95273i
$206$	11.8961	+	1.13466i	0.828840	+	0.0790553i
$207$		0			0
$208$	−18.8481	+	3.99126i	−1.30688	+	0.276744i
$209$	−10.0591	−	10.0591i	−0.695805	−	0.695805i
$210$		0			0
$211$	10.3269	−	6.90024i	0.710935	−	0.475032i	−0.146772	−	0.989170i	$-0.546888\pi$
$211$	10.3269	−	6.90024i	0.710935	−	0.475032i	0.857707	+	0.514139i	$0.171888\pi$
$212$	−13.5953	+	13.7640i	−0.933731	+	0.945312i
$213$		0			0
$214$	−3.40313	+	11.3444i	−0.232633	+	0.775484i
$215$	2.57113	−	6.20726i	0.175350	−	0.423331i
$216$		0			0
$217$	0.159630	+	0.385381i	0.0108364	+	0.0261614i
$218$	−0.0779778	−	0.767468i	−0.00528133	−	0.0519795i
$219$		0			0
$220$	6.51290	+	31.7195i	0.439100	+	2.13853i
$221$	0.524267	−	2.63567i	0.0352660	−	0.177294i
$222$		0			0
$223$		−	16.4720i		−	1.10305i	−0.834158	−	0.551525i	$-0.814046\pi$
$223$		−	16.4720i		−	1.10305i	0.834158	−	0.551525i	$-0.185954\pi$
$224$	1.60146	+	0.824528i	0.107002	+	0.0550911i
$225$		0			0
$226$	0.665051	+	2.16830i	0.0442386	+	0.144233i
$227$	−1.40712	+	7.07407i	−0.0933939	+	0.469523i	0.905578	+	0.424181i	$0.139438\pi$
$227$	−1.40712	+	7.07407i	−0.0933939	+	0.469523i	−0.998972	+	0.0453422i	$0.985562\pi$
$228$		0			0
$229$	4.56486	+	3.05014i	0.301654	+	0.201559i	0.697180	−	0.716896i	$-0.254438\pi$
$229$	4.56486	+	3.05014i	0.301654	+	0.201559i	−0.395526	+	0.918455i	$0.629438\pi$
$230$	36.2835	−	3.68655i	2.39246	−	0.243084i
$231$		0			0
$232$	0.529800	−	5.94183i	0.0347831	−	0.390100i
$233$	−3.73176	+	9.00926i	−0.244476	+	0.590216i	−0.997717	−	0.0675274i	$-0.978489\pi$
$233$	−3.73176	+	9.00926i	−0.244476	+	0.590216i	0.753242	+	0.657744i	$0.228489\pi$
$234$		0			0
$235$	−21.2540	+	4.22769i	−1.38646	+	0.275784i
$236$	−1.34585	+	0.00829540i	−0.0876071	+	0.000539984i
$237$		0			0
$238$	−0.193724	+	0.159987i	−0.0125573	+	0.0103704i
$239$	−15.5694	−	15.5694i	−1.00710	−	1.00710i	−0.999975	−	0.00712806i	$-0.997731\pi$
$239$	−15.5694	−	15.5694i	−1.00710	−	1.00710i	−0.00712806	−	0.999975i	$-0.502269\pi$
$240$		0			0
$241$	−9.69865	+	9.69865i	−0.624745	+	0.624745i	−0.946741	−	0.321996i	$-0.895646\pi$
$241$	−9.69865	+	9.69865i	−0.624745	+	0.624745i	0.321996	+	0.946741i	$0.395646\pi$
$242$	−2.63712	+	27.6484i	−0.169520	+	1.77730i
$243$		0			0
$244$	−0.687873	−	1.63215i	−0.0440365	−	0.104487i
$245$	−3.93662	−	19.7907i	−0.251501	−	1.26438i
$246$		0			0
$247$	−11.4363	−	4.73707i	−0.727675	−	0.301413i
$248$	−0.397256	−	3.68391i	−0.0252258	−	0.233929i
$249$		0			0
$250$	−3.77607	+	4.63018i	−0.238820	+	0.292838i
$251$	−5.88752	+	8.81130i	−0.371617	+	0.556165i	−0.969398	−	0.245495i	$-0.921049\pi$
$251$	−5.88752	+	8.81130i	−0.371617	+	0.556165i	0.597781	+	0.801660i	$0.296049\pi$
$252$		0			0
$253$	47.8641	+	9.52077i	3.00919	+	0.598566i
$254$	4.08370	−	7.69702i	0.256234	−	0.482954i
$255$		0			0
$256$	−11.5892	−	11.0314i	−0.724323	−	0.689460i
$257$	13.3850			0.834934			0.417467	−	0.908692i	$-0.362918\pi$
$257$	13.3850			0.834934			0.417467	+	0.908692i	$0.362918\pi$
$258$		0			0
$259$	0.554139	+	0.110225i	0.0344325	+	0.00684905i
$260$	15.7982	+	23.3310i	0.979761	+	1.44693i
$261$		0			0
$262$	17.1291	−	21.0035i	1.05824	−	1.29760i
$263$	1.95063	−	0.807975i	0.120281	−	0.0498219i	−0.321731	−	0.946831i	$-0.604265\pi$
$263$	1.95063	−	0.807975i	0.120281	−	0.0498219i	0.442012	+	0.897009i	$0.354265\pi$
$264$		0			0
$265$	26.1402	+	10.8276i	1.60578	+	0.665137i
$266$	0.548700	+	1.01898i	0.0336429	+	0.0624776i
$267$		0			0
$268$	−8.16085	−	19.3636i	−0.498504	−	1.18282i
$269$	3.24219	+	4.85228i	0.197680	+	0.295849i	0.917045	−	0.398783i	$-0.130567\pi$
$269$	3.24219	+	4.85228i	0.197680	+	0.295849i	−0.719365	+	0.694632i	$0.755567\pi$
$270$		0			0
$271$	12.0904	−	12.0904i	0.734438	−	0.734438i	−0.237058	−	0.971496i	$-0.576183\pi$
$271$	12.0904	−	12.0904i	0.734438	−	0.734438i	0.971496	+	0.237058i	$0.0761831\pi$
$272$	2.05118	−	0.879403i	0.124371	−	0.0533217i
$273$		0			0
$274$	24.0963	−	19.8999i	1.45571	−	1.20220i
$275$	16.3645	−	10.9344i	0.986814	−	0.659368i
$276$		0			0
$277$	−19.1137	+	3.80195i	−1.14843	+	0.228437i	−0.732375	−	0.680902i	$-0.761588\pi$
$277$	−19.1137	+	3.80195i	−1.14843	+	0.228437i	−0.416056	+	0.909339i	$0.636588\pi$
$278$	−10.5192	−	3.15559i	−0.630898	−	0.189259i
$279$		0			0
$280$	0.233961	−	2.62393i	0.0139819	−	0.156810i
$281$	4.87231	+	11.7628i	0.290658	+	0.701710i	0.999995	−	0.00315921i	$-0.00100561\pi$
$281$	4.87231	+	11.7628i	0.290658	+	0.701710i	−0.709337	+	0.704869i	$0.751006\pi$
$282$		0			0
$283$	14.6616	+	9.79655i	0.871540	+	0.582344i	0.908926	−	0.416957i	$-0.136903\pi$
$283$	14.6616	+	9.79655i	0.871540	+	0.582344i	−0.0373867	+	0.999301i	$0.511903\pi$
$284$	−22.4548	−	14.8044i	−1.33245	−	0.878482i
$285$		0			0
$286$	11.0560	+	36.0464i	0.653753	+	2.13147i
$287$			3.66056i			0.216076i
$288$		0			0
$289$		−	16.6887i		−	0.981689i
$290$	−8.34089	+	2.55828i	−0.489794	+	0.150227i
$291$		0			0
$292$	6.32013	+	30.7807i	0.369858	+	1.80130i
$293$	13.2983	+	8.88565i	0.776896	+	0.519105i	0.879662	−	0.475600i	$-0.157769\pi$
$293$	13.2983	+	8.88565i	0.776896	+	0.519105i	−0.102765	+	0.994706i	$0.532769\pi$
$294$		0			0
$295$	0.753251	+	1.81851i	0.0438560	+	0.105878i
$296$	−4.44776	−	2.32476i	−0.258521	−	0.135124i
$297$		0			0
$298$	5.98532	−	19.9521i	0.346720	−	1.15579i
$299$	41.6490	−	8.28450i	2.40862	−	0.479105i
$300$		0			0
$301$	−0.608142	+	0.406348i	−0.0350527	+	0.0234215i
$302$	−17.2580	−	20.8973i	−0.993087	−	1.20250i
$303$		0			0
$304$	−2.12969	−	10.0571i	−0.122146	−	0.576814i
$305$	−1.83165	+	1.83165i	−0.104880	+	0.104880i
$306$		0			0
$307$	7.73866	+	11.5817i	0.441668	+	0.661004i	0.983796	−	0.179293i	$-0.0573810\pi$
$307$	7.73866	+	11.5817i	0.441668	+	0.661004i	−0.542127	+	0.840296i	$0.682381\pi$
$308$	1.32889	−	3.26500i	0.0757205	−	0.186040i
$309$		0			0
$310$	−4.77120	+	2.56919i	−0.270986	+	0.145920i
$311$	9.17931	+	3.80219i	0.520511	+	0.215603i	0.627441	−	0.778664i	$-0.284102\pi$
$311$	9.17931	+	3.80219i	0.520511	+	0.215603i	−0.106930	+	0.994266i	$0.534102\pi$
$312$		0			0
$313$	14.8947	−	6.16958i	0.841897	−	0.348725i	0.0802956	−	0.996771i	$-0.474414\pi$
$313$	14.8947	−	6.16958i	0.841897	−	0.348725i	0.761601	+	0.648046i	$0.224414\pi$
$314$	−14.0270	−	11.4395i	−0.791590	−	0.645569i
$315$		0			0
$316$	7.10837	+	1.36845i	0.399877	+	0.0769814i
$317$	30.4022	+	6.04738i	1.70756	+	0.339654i	0.949794	−	0.312875i	$-0.101292\pi$
$317$	30.4022	+	6.04738i	1.70756	+	0.339654i	0.757764	+	0.652529i	$0.226292\pi$
$318$		0			0
$319$	−11.6743			−0.653637
$320$	−8.55354	+	21.7807i	−0.478157	+	1.21758i
$321$		0			0
$322$	−3.50717	−	1.86075i	−0.195447	−	0.103695i
$323$	1.40636	+	0.279742i	0.0782519	+	0.0155653i
$324$		0			0
$325$	9.51456	−	14.2395i	0.527773	−	0.789868i
$326$	−9.11454	−	7.43322i	−0.504807	−	0.411688i
$327$		0			0
$328$	9.15072	−	31.2015i	0.505264	−	1.72281i
$329$	2.17950	+	0.902779i	0.120160	+	0.0497718i
$330$		0			0
$331$	−1.73426	−	8.71873i	−0.0953238	−	0.479225i	−0.998727	−	0.0504338i	$-0.983940\pi$
$331$	−1.73426	−	8.71873i	−0.0953238	−	0.479225i	0.903404	−	0.428791i	$-0.141060\pi$
$332$	1.30452	+	0.530955i	0.0715950	+	0.0291400i
$333$		0			0
$334$	−7.95506	−	0.758758i	−0.435281	−	0.0415174i
$335$	−21.7305	+	21.7305i	−1.18727	+	1.18727i
$336$		0			0
$337$	−8.25556	−	8.25556i	−0.449709	−	0.449709i	0.445549	−	0.895258i	$-0.353009\pi$
$337$	−8.25556	−	8.25556i	−0.449709	−	0.449709i	−0.895258	+	0.445549i	$0.853009\pi$
$338$	9.18430	+	11.1210i	0.499560	+	0.604905i
$339$		0			0
$340$	−2.32213	−	2.29368i	−0.125935	−	0.124392i
$341$	−7.11191	+	1.41465i	−0.385131	+	0.0766074i
$342$		0			0
$343$	−1.69360	+	4.08872i	−0.0914459	+	0.220770i
$344$	6.19940	−	1.94334i	0.334249	−	0.104778i
$345$		0			0
$346$	0.177277	+	1.74478i	0.00953046	+	0.0937999i
$347$	−11.1318	−	7.43806i	−0.597588	−	0.399296i	0.219664	−	0.975576i	$-0.429504\pi$
$347$	−11.1318	−	7.43806i	−0.597588	−	0.399296i	−0.817253	+	0.576280i	$0.804504\pi$
$348$		0			0
$349$	0.867225	−	4.35983i	0.0464215	−	0.233377i	−0.950608	−	0.310393i	$-0.899539\pi$
$349$	0.867225	−	4.35983i	0.0464215	−	0.233377i	0.997030	+	0.0770164i	$0.0245394\pi$
$350$	−1.53077	+	0.469510i	−0.0818230	+	0.0250964i
$351$		0			0
$352$	−19.4889	+	24.5078i	−1.03876	+	1.30627i
$353$		−	31.4850i		−	1.67578i	−0.545839	−	0.837890i	$-0.683789\pi$
$353$		−	31.4850i		−	1.67578i	0.545839	−	0.837890i	$-0.316211\pi$
$354$		0			0
$355$	−7.67394	+	38.5795i	−0.407290	+	2.04759i
$356$	−10.7120	+	16.2475i	−0.567734	+	0.861117i
$357$		0			0
$358$	−7.10442	+	0.721838i	−0.375480	+	0.0381503i
$359$	−6.61491	−	15.9698i	−0.349122	−	0.842854i	−0.996724	−	0.0808758i	$-0.974228\pi$
$359$	−6.61491	−	15.9698i	−0.349122	−	0.842854i	0.647603	−	0.761978i	$-0.275772\pi$
$360$		0			0
$361$	−4.74334	+	11.4514i	−0.249650	+	0.602707i
$362$	18.9542	+	5.68597i	0.996212	+	0.298848i
$363$		0			0
$364$	−0.0189059	−	3.06729i	−0.000990936	−	0.160770i
$365$	38.2110	−	25.5318i	2.00005	−	1.33639i
$366$		0			0
$367$	2.68230	+	2.68230i	0.140015	+	0.140015i	0.773640	−	0.633625i	$-0.218434\pi$
$367$	2.68230	+	2.68230i	0.140015	+	0.140015i	−0.633625	+	0.773640i	$0.718434\pi$
$368$	25.2425	+	24.6277i	1.31585	+	1.28381i
$369$		0			0
$370$	−0.696913	+	7.30665i	−0.0362308	+	0.379855i
$371$	−1.71123	−	2.56103i	−0.0888424	−	0.132962i
$372$		0			0
$373$	−6.63396	−	33.3511i	−0.343493	−	1.72686i	−0.636968	−	0.770890i	$-0.719812\pi$
$373$	−6.63396	−	33.3511i	−0.343493	−	1.72686i	0.293475	−	0.955967i	$-0.405188\pi$
$374$	−2.07071	−	3.84547i	−0.107074	−	0.198844i
$375$		0			0
$376$	−16.3206	−	13.1433i	−0.841670	−	0.677816i
$377$	−9.38517	+	3.88746i	−0.483361	+	0.200215i
$378$		0			0
$379$	−2.07239	+	3.10156i	−0.106452	+	0.159316i	−0.880871	−	0.473357i	$-0.843042\pi$
$379$	−2.07239	+	3.10156i	−0.106452	+	0.159316i	0.774419	+	0.632673i	$0.218042\pi$
$380$	−12.4492	+	8.42971i	−0.638628	+	0.432435i
$381$		0			0
$382$	2.13542	−	4.02489i	0.109258	−	0.205931i
$383$	23.4907			1.20032			0.600159	−	0.799880i	$-0.295104\pi$
$383$	23.4907			1.20032			0.600159	+	0.799880i	$0.295104\pi$
$384$		0			0
$385$	−5.15543			−0.262745
$386$	13.4507	−	25.3522i	0.684625	−	1.29039i
$387$		0			0
$388$	−0.936475	+	0.634116i	−0.0475423	+	0.0321924i
$389$	−9.39612	+	14.0623i	−0.476402	+	0.712987i	−0.989370	−	0.145422i	$-0.953546\pi$
$389$	−9.39612	+	14.0623i	−0.476402	+	0.712987i	0.512967	+	0.858408i	$0.328546\pi$
$390$		0			0
$391$	−4.54463	+	1.88245i	−0.229832	+	0.0951994i
$392$	12.2384	−	15.1969i	0.618135	−	0.767561i
$393$		0			0
$394$	12.2401	+	22.7309i	0.616650	+	1.14517i
$395$	−2.06540	−	10.3835i	−0.103922	−	0.522449i
$396$		0			0
$397$	5.92073	+	8.86099i	0.297153	+	0.444720i	0.949762	−	0.312975i	$-0.101325\pi$
$397$	5.92073	+	8.86099i	0.297153	+	0.444720i	−0.652609	+	0.757695i	$0.726325\pi$
$398$	1.64778	−	17.2759i	0.0825958	−	0.865960i
$399$		0			0
$400$	14.2215	−	0.175320i	0.711073	−	0.00876602i
$401$	−12.3125	−	12.3125i	−0.614859	−	0.614859i	0.329349	−	0.944208i	$-0.393171\pi$
$401$	−12.3125	−	12.3125i	−0.614859	−	0.614859i	−0.944208	+	0.329349i	$0.893171\pi$
$402$		0			0
$403$	−5.24630	+	3.50547i	−0.261337	+	0.174620i
$404$	0.136809	+	22.1958i	0.00680648	+	1.10428i
$405$		0			0
$406$	0.909701	+	0.272896i	0.0451477	+	0.0135436i
$407$	−3.75856	+	9.07396i	−0.186305	+	0.449780i
$408$		0			0
$409$	11.9692	+	28.8963i	0.591841	+	1.42883i	0.881723	+	0.471767i	$0.156384\pi$
$409$	11.9692	+	28.8963i	0.591841	+	1.42883i	−0.289882	+	0.957062i	$0.593616\pi$
$410$	−47.3106	+	4.80695i	−2.33650	+	0.237398i
$411$		0			0
$412$	9.30233	−	14.1094i	0.458293	−	0.695121i
$413$	0.0418032	−	0.210159i	0.00205700	−	0.0103413i
$414$		0			0
$415$		−	2.05984i		−	0.101114i
$416$	−7.50649	+	26.1918i	−0.368036	+	1.28416i
$417$		0			0
$418$	−19.2339	+	5.89933i	−0.940761	+	0.288546i
$419$	−6.14582	+	30.8971i	−0.300243	+	1.50942i	0.476257	+	0.879306i	$0.341993\pi$
$419$	−6.14582	+	30.8971i	−0.300243	+	1.50942i	−0.776500	+	0.630117i	$0.783007\pi$
$420$		0			0
$421$	−2.09636	−	1.40074i	−0.102170	−	0.0682681i	0.503435	−	0.864033i	$-0.332069\pi$
$421$	−2.09636	−	1.40074i	−0.102170	−	0.0682681i	−0.605606	+	0.795765i	$0.707069\pi$
$422$	−1.77550	−	17.4747i	−0.0864300	−	0.850655i
$423$		0			0
$424$	8.18385	+	26.1071i	0.397443	+	1.26788i
$425$	−0.759174	+	1.83281i	−0.0368254	+	0.0889043i
$426$		0			0
$427$	0.276571	−	0.0550134i	0.0133842	−	0.00266228i
$428$	11.9166	+	11.7706i	0.576009	+	0.568952i
$429$		0			0
$430$	−6.05039	−	7.32627i	−0.291776	−	0.353304i
$431$	12.1380	+	12.1380i	0.584669	+	0.584669i	0.936183	−	0.351514i	$-0.114333\pi$
$431$	12.1380	+	12.1380i	0.584669	+	0.584669i	−0.351514	+	0.936183i	$0.614333\pi$
$432$		0			0
$433$	−22.3743	+	22.3743i	−1.07524	+	1.07524i	−0.0783126	+	0.996929i	$0.524953\pi$
$433$	−22.3743	+	22.3743i	−1.07524	+	1.07524i	−0.996929	+	0.0783126i	$0.975047\pi$
$434$	0.587251	+	0.0560123i	0.0281889	+	0.00268868i
$435$		0			0
$436$	−1.01046	−	0.411269i	−0.0483923	−	0.0196962i
$437$	4.42051	+	22.2234i	0.211462	+	1.06309i
$438$		0			0
$439$	−0.796259	−	0.329821i	−0.0380034	−	0.0157415i	0.363601	−	0.931555i	$-0.381547\pi$
$439$	−0.796259	−	0.329821i	−0.0380034	−	0.0157415i	−0.401604	+	0.915813i	$0.631547\pi$
$440$	43.9432	+	12.8876i	2.09491	+	0.614392i
$441$		0			0
$442$	−2.94518	−	2.40190i	−0.140088	−	0.114247i
$443$	−6.32934	+	9.47253i	−0.300716	+	0.450053i	−0.950798	−	0.309810i	$-0.899734\pi$
$443$	−6.32934	+	9.47253i	−0.300716	+	0.450053i	0.650082	+	0.759864i	$0.274734\pi$
$444$		0			0
$445$	27.9148	+	5.55259i	1.32329	+	0.263218i
$446$	−20.5781	−	10.9178i	−0.974401	−	0.516974i
$447$		0			0
$448$	2.09152	−	1.45416i	0.0988152	−	0.0687025i
$449$	−23.1176			−1.09099			−0.545495	−	0.838114i	$-0.683658\pi$
$449$	−23.1176			−1.09099			−0.545495	+	0.838114i	$0.683658\pi$
$450$		0			0
$451$	−62.4107	−	12.4143i	−2.93881	−	0.584565i
$452$	3.14960	+	0.606339i	0.148145	+	0.0285198i
$453$		0			0
$454$	7.90480	+	6.44664i	0.370991	+	0.302556i
$455$	−4.14452	+	1.71672i	−0.194298	+	0.0804809i
$456$		0			0
$457$	−17.1139	−	7.08880i	−0.800553	−	0.331600i	−0.0553752	−	0.998466i	$-0.517635\pi$
$457$	−17.1139	−	7.08880i	−0.800553	−	0.331600i	−0.745178	+	0.666866i	$0.767635\pi$
$458$	6.83609	−	3.68110i	0.319429	−	0.172006i
$459$		0			0
$460$	19.4435	−	47.7715i	0.906559	−	2.22736i
$461$	9.72599	+	14.5560i	0.452984	+	0.677939i	0.985730	−	0.168337i	$-0.0538395\pi$
$461$	9.72599	+	14.5560i	0.452984	+	0.677939i	−0.532745	+	0.846276i	$0.678840\pi$
$462$		0			0
$463$	−15.4991	+	15.4991i	−0.720304	+	0.720304i	−0.968667	−	0.248363i	$-0.920107\pi$
$463$	−15.4991	+	15.4991i	−0.720304	+	0.720304i	0.248363	+	0.968667i	$0.420107\pi$
$464$	−7.07181	−	4.60016i	−0.328301	−	0.213557i
$465$		0			0
$466$	8.78159	+	10.6334i	0.406799	+	0.492583i
$467$	19.4918	−	13.0240i	0.901971	−	0.602678i	−0.0157622	−	0.999876i	$-0.505017\pi$
$467$	19.4918	−	13.0240i	0.901971	−	0.602678i	0.917733	+	0.397198i	$0.130017\pi$
$468$		0			0
$469$	3.28121	−	0.652673i	0.151512	−	0.0301376i
$470$	−8.80581	+	29.3542i	−0.406182	+	1.35401i
$471$		0			0
$472$	−0.881676	+	1.68683i	−0.0405824	+	0.0776426i
$473$	−4.86559	−	11.7466i	−0.223720	−	0.540108i
$474$		0			0
$475$	7.59805	+	5.07685i	0.348622	+	0.232942i
$476$	0.0714654	+	0.348055i	0.00327561	+	0.0159531i
$477$		0			0
$478$	−29.7700	+	9.13092i	−1.36165	+	0.417639i
$479$		−	13.5004i		−	0.616849i	−0.951249	−	0.308424i	$-0.900198\pi$
$479$		−	13.5004i		−	0.616849i	0.951249	−	0.308424i	$-0.0998017\pi$
$480$		0			0
$481$			8.54626i			0.389676i
$482$	5.68792	+	18.5446i	0.259078	+	0.844684i
$483$		0			0
$484$	32.7925	+	21.6201i	1.49057	+	0.982730i
$485$	1.37529	+	0.918937i	0.0624485	+	0.0417268i
$486$		0			0
$487$	4.80481	+	11.5998i	0.217727	+	0.525639i	0.994572	−	0.104053i	$-0.0331812\pi$
$487$	4.80481	+	11.5998i	0.217727	+	0.525639i	−0.776845	+	0.629692i	$0.783181\pi$
$488$	−2.49492	−	0.222459i	−0.112940	−	0.0100702i
$489$		0			0
$490$	−27.3333	−	8.19955i	−1.23479	−	0.370418i
$491$	−31.5600	+	6.27768i	−1.42428	+	0.283308i	−0.846286	−	0.532730i	$-0.821166\pi$
$491$	−31.5600	+	6.27768i	−1.42428	+	0.283308i	−0.577999	+	0.816037i	$0.696166\pi$
$492$		0			0
$493$	0.978420	−	0.653759i	0.0440658	−	0.0294438i
$494$	−13.4980	+	11.1473i	−0.607303	+	0.501541i
$495$		0			0
$496$	−4.86552	−	1.94545i	−0.218468	−	0.0873531i
$497$	3.02790	−	3.02790i	0.135820	−	0.135820i
$498$		0			0
$499$	−12.7702	−	19.1119i	−0.571671	−	0.855565i	0.427147	−	0.904182i	$-0.359519\pi$
$499$	−12.7702	−	19.1119i	−0.571671	−	0.855565i	−0.998818	+	0.0486167i	$0.984519\pi$
$500$	3.28155	+	7.78627i	0.146755	+	0.348212i
$501$		0			0
$502$	7.10543	+	13.1953i	0.317131	+	0.588937i
$503$	−26.6111	−	11.0227i	−1.18653	−	0.491476i	−0.299905	−	0.953969i	$-0.596955\pi$
$503$	−26.6111	−	11.0227i	−1.18653	−	0.491476i	−0.886623	+	0.462493i	$0.846955\pi$
$504$		0			0
$505$	29.9910	−	12.4227i	1.33458	−	0.552803i
$506$	43.6188	−	53.4849i	1.93909	−	2.37770i
$507$		0			0
$508$	−6.90898	−	10.2033i	−0.306536	−	0.452699i
$509$	6.48058	+	1.28907i	0.287247	+	0.0571370i	0.336611	−	0.941644i	$-0.390719\pi$
$509$	6.48058	+	1.28907i	0.287247	+	0.0571370i	−0.0493638	+	0.998781i	$0.515719\pi$
$510$		0			0
$511$	−5.00283			−0.221312
$512$	−21.4626	+	7.16637i	−0.948522	+	0.316712i
$513$		0			0
$514$	8.87171	−	16.7215i	0.391314	−	0.737556i
$515$	−24.2413	−	4.82189i	−1.06820	−	0.212478i
$516$		0			0
$517$	−22.7834	+	34.0977i	−1.00201	+	1.49962i
$518$	0.504989	−	0.619213i	0.0221879	−	0.0272066i
$519$		0			0
$520$	39.6180	−	4.27222i	1.73737	−	0.187349i
$521$	4.49853	+	1.86335i	0.197084	+	0.0816349i	0.479042	−	0.877792i	$-0.340984\pi$
$521$	4.49853	+	1.86335i	0.197084	+	0.0816349i	−0.281958	+	0.959427i	$0.590984\pi$
$522$		0			0
$523$	2.98320	+	14.9975i	0.130446	+	0.655797i	0.989573	+	0.144034i	$0.0460074\pi$
$523$	2.98320	+	14.9975i	0.130446	+	0.655797i	−0.859127	+	0.511763i	$0.828993\pi$
$524$	−14.8858	−	35.3202i	−0.650290	−	1.54297i
$525$		0			0
$526$	0.283509	−	2.97240i	0.0123616	−	0.129603i
$527$	0.516826	−	0.516826i	0.0225133	−	0.0225133i
$528$		0			0
$529$	−38.7010	−	38.7010i	−1.68265	−	1.68265i
$530$	30.8527	−	25.4796i	1.34015	−	1.10677i
$531$		0			0
$532$	1.63667	−	0.0100879i	0.0709585	−	0.000437367i
$533$	−54.3067	+	10.8023i	−2.35229	+	0.467899i
$534$		0			0
$535$	9.37437	−	22.6317i	0.405289	−	0.978455i
$536$	−29.5995	−	2.63923i	−1.27850	−	0.113997i
$537$		0			0
$538$	8.21079	−	0.834249i	0.353992	−	0.0359670i
$539$	−31.7501	−	21.2148i	−1.36758	−	0.913785i
$540$		0			0
$541$	2.50762	−	12.6067i	0.107811	−	0.542002i	−0.888696	−	0.458496i	$-0.848388\pi$
$541$	2.50762	−	12.6067i	0.107811	−	0.542002i	0.996507	−	0.0835060i	$-0.0266118\pi$
$542$	−7.09058	−	23.1178i	−0.304566	−	0.992994i
$543$		0			0
$544$	0.260924	−	3.14536i	0.0111870	−	0.134856i
$545$			1.59552i			0.0683444i
$546$		0			0
$547$	4.22387	−	21.2348i	0.180600	−	0.907936i	−0.779098	−	0.626902i	$-0.784323\pi$
$547$	4.22387	−	21.2348i	0.180600	−	0.907936i	0.959698	−	0.281034i	$-0.0906775\pi$
$548$	−8.88919	−	43.2927i	−0.379727	−	1.84937i
$549$		0			0
$550$	−2.81353	−	27.6911i	−0.119969	−	1.18075i
$551$	−2.07430	−	5.00781i	−0.0883683	−	0.213340i
$552$		0			0
$553$	−0.441045	+	1.06478i	−0.0187551	+	0.0452789i
$554$	−7.91905	+	26.3982i	−0.336448	+	1.12155i
$555$		0			0
$556$	−10.9144	+	11.0498i	−0.462873	+	0.468615i
$557$	−17.0377	+	11.3842i	−0.721909	+	0.482364i	−0.861444	−	0.507853i	$-0.830439\pi$
$557$	−17.0377	+	11.3842i	−0.721909	+	0.482364i	0.139535	+	0.990217i	$0.455439\pi$
$558$		0			0
$559$	−7.82304	−	7.82304i	−0.330879	−	0.330879i
$560$	−3.12293	−	2.03145i	−0.131968	−	0.0858442i
$561$		0			0
$562$	17.9244	+	1.70964i	0.756094	+	0.0721167i
$563$	16.4974	+	24.6900i	0.695281	+	1.04056i	0.996216	+	0.0869163i	$0.0277013\pi$
$563$	16.4974	+	24.6900i	0.695281	+	1.04056i	−0.300935	+	0.953645i	$0.597299\pi$
$564$		0			0
$565$	−0.915145	−	4.60075i	−0.0385005	−	0.193555i
$566$	21.9564	−	11.8231i	0.922895	−	0.496961i
$567$		0			0
$568$	−33.3780	+	18.2397i	−1.40051	+	0.765320i
$569$	23.1377	−	9.58394i	0.969982	−	0.401780i	0.159277	−	0.987234i	$-0.449084\pi$
$569$	23.1377	−	9.58394i	0.969982	−	0.401780i	0.810706	+	0.585454i	$0.199084\pi$
$570$		0			0
$571$	−19.8386	+	29.6906i	−0.830222	+	1.24251i	0.137502	+	0.990501i	$0.456093\pi$
$571$	−19.8386	+	29.6906i	−0.830222	+	1.24251i	−0.967724	+	0.252013i	$0.918907\pi$
$572$	52.3598	+	10.0799i	2.18927	+	0.421463i
$573$		0			0
$574$	4.57305	+	2.42625i	0.190875	+	0.101270i
$575$	−31.3484			−1.30732
$576$		0			0
$577$	41.3597			1.72183			0.860914	−	0.508751i	$-0.169893\pi$
$577$	41.3597			1.72183			0.860914	+	0.508751i	$0.169893\pi$
$578$	−20.8488	−	11.0614i	−0.867194	−	0.460094i
$579$		0			0
$580$	−2.33243	+	12.1157i	−0.0968487	+	0.503077i
$581$	−0.124580	+	0.186447i	−0.00516843	+	0.00773511i
$582$		0			0
$583$	49.4676	−	20.4902i	2.04874	−	0.848616i
$584$	42.6425	+	12.5061i	1.76456	+	0.517508i
$585$		0			0
$586$	19.9149	−	10.7237i	0.822675	−	0.442994i
$587$	−6.18128	−	31.0754i	−0.255129	−	1.28262i	−0.869631	−	0.493703i	$-0.835643\pi$
$587$	−6.18128	−	31.0754i	−0.255129	−	1.28262i	0.614502	−	0.788915i	$-0.289357\pi$
$588$		0			0
$589$	−1.87047	−	2.79936i	−0.0770715	−	0.115346i
$590$	2.77108	+	0.264307i	0.114083	+	0.0108813i
$591$		0			0
$592$	−5.85228	+	4.01559i	−0.240527	+	0.165040i
$593$	0.502147	+	0.502147i	0.0206207	+	0.0206207i	0.717342	−	0.696721i	$-0.245359\pi$
$593$	0.502147	+	0.502147i	0.0206207	+	0.0206207i	−0.696721	+	0.717342i	$0.745359\pi$
$594$		0			0
$595$	0.432073	−	0.288702i	0.0177133	−	0.0118356i
$596$	−20.9585	−	20.7017i	−0.858494	−	0.847976i
$597$		0			0
$598$	17.2557	−	57.5220i	0.705639	−	2.35225i
$599$	7.67530	−	18.5298i	0.313604	−	0.757108i	−0.685961	−	0.727638i	$-0.740618\pi$
$599$	7.67530	−	18.5298i	0.313604	−	0.757108i	0.999566	−	0.0294698i	$-0.00938188\pi$
$600$		0			0
$601$	−8.64504	−	20.8710i	−0.352639	−	0.851345i	−0.996293	−	0.0860284i	$-0.972582\pi$
$601$	−8.64504	−	20.8710i	−0.352639	−	0.851345i	0.643654	−	0.765317i	$-0.277418\pi$
$602$	0.104557	+	1.02907i	0.00426144	+	0.0419416i
$603$		0			0
$604$	−37.5452	+	7.70907i	−1.52769	+	0.313678i
$605$	11.2068	−	56.3405i	0.455622	−	2.29057i
$606$		0			0
$607$			18.5694i			0.753711i	0.926272	+	0.376855i	$0.122995\pi$
$607$			18.5694i			0.753711i	−0.926272	+	0.376855i	$0.877005\pi$
$608$	−13.9756	−	4.00537i	−0.566787	−	0.162439i
$609$		0			0
$610$	1.07420	+	3.50227i	0.0434931	+	0.141803i
$611$	−6.96160	+	34.9983i	−0.281636	+	1.41588i
$612$		0			0
$613$	24.5393	+	16.3967i	0.991135	+	0.662255i	0.941676	−	0.336521i	$-0.109250\pi$
$613$	24.5393	+	16.3967i	0.991135	+	0.662255i	0.0494587	+	0.998776i	$0.484250\pi$
$614$	19.5980	−	1.99123i	0.790910	−	0.0803597i
$615$		0			0
$616$	−3.19808	−	3.82421i	−0.128854	−	0.154082i
$617$	−13.0190	+	31.4307i	−0.524126	+	1.26535i	0.411194	+	0.911548i	$0.365112\pi$
$617$	−13.0190	+	31.4307i	−0.524126	+	1.26535i	−0.935320	+	0.353804i	$0.884888\pi$
$618$		0			0
$619$	20.5706	−	4.09174i	0.826802	−	0.164461i	0.236487	−	0.971635i	$-0.424004\pi$
$619$	20.5706	−	4.09174i	0.826802	−	0.164461i	0.590314	+	0.807174i	$0.299004\pi$
$620$	0.0472350	+	7.66342i	0.00189700	+	0.307770i
$621$		0			0
$622$	10.8341	−	8.94734i	0.434408	−	0.358756i
$623$	−2.19088	−	2.19088i	−0.0877759	−	0.0877759i
$624$		0			0
$625$	21.3091	−	21.3091i	0.852364	−	0.852364i
$626$	2.16483	−	22.6968i	0.0865241	−	0.907146i
$627$		0			0
$628$	−23.5883	+	9.94137i	−0.941276	+	0.396704i
$629$	−0.193136	−	0.970962i	−0.00770085	−	0.0387148i
$630$		0			0
$631$	−37.1648	−	15.3942i	−1.47951	−	0.612832i	−0.510503	−	0.859876i	$-0.670541\pi$
$631$	−37.1648	−	15.3942i	−1.47951	−	0.612832i	−0.969004	+	0.247044i	$0.920541\pi$
$632$	6.42106	−	7.97328i	0.255416	−	0.317160i
$633$		0			0
$634$	27.7057	−	33.9724i	1.10033	−	1.34922i
$635$	−10.0122	+	14.9843i	−0.397323	+	0.594636i
$636$		0			0
$637$	−32.5888	−	6.48231i	−1.29121	−	0.256838i
$638$	−7.73785	+	14.5844i	−0.306345	+	0.577404i
$639$		0			0
$640$	21.5407	+	25.1221i	0.851469	+	0.993040i
$641$	35.5138			1.40271			0.701356	−	0.712811i	$-0.252578\pi$
$641$	35.5138			1.40271			0.701356	+	0.712811i	$0.252578\pi$
$642$		0			0
$643$	21.5451	+	4.28559i	0.849656	+	0.169007i	0.600667	−	0.799499i	$-0.294902\pi$
$643$	21.5451	+	4.28559i	0.849656	+	0.169007i	0.248989	+	0.968506i	$0.419902\pi$
$644$	−4.64916	+	3.14809i	−0.183203	+	0.124052i
$645$		0			0
$646$	1.28162	−	1.57151i	0.0504248	−	0.0618303i
$647$	−12.8162	+	5.30863i	−0.503856	+	0.208704i	−0.620109	−	0.784516i	$-0.712912\pi$
$647$	−12.8162	+	5.30863i	−0.503856	+	0.208704i	0.116253	+	0.993220i	$0.462912\pi$
$648$		0			0
$649$	3.44133	+	1.42545i	0.135084	+	0.0559537i
$650$	−11.4828	−	21.3244i	−0.450391	−	0.836411i
$651$		0			0
$652$	−15.3273	+	6.45975i	−0.600264	+	0.252983i
$653$	4.45389	+	6.66572i	0.174294	+	0.260850i	0.908324	−	0.418268i	$-0.137363\pi$
$653$	4.45389	+	6.66572i	0.174294	+	0.260850i	−0.734029	+	0.679118i	$0.762363\pi$
$654$		0			0
$655$	−39.6376	+	39.6376i	−1.54877	+	1.54877i
$656$	−32.9140	−	32.1124i	−1.28508	−	1.25378i
$657$		0			0
$658$	2.57241	−	2.12442i	0.100283	−	0.0828186i
$659$	−17.4455	+	11.6567i	−0.679579	+	0.454080i	−0.846851	−	0.531831i	$-0.821504\pi$
$659$	−17.4455	+	11.6567i	−0.679579	+	0.454080i	0.167272	+	0.985911i	$0.446504\pi$
$660$		0			0
$661$	−14.4368	+	2.87166i	−0.561527	+	0.111695i	−0.467690	−	0.883893i	$-0.654913\pi$
$661$	−14.4368	+	2.87166i	−0.561527	+	0.111695i	−0.0938378	+	0.995588i	$0.529913\pi$
$662$	−12.0416	−	3.61228i	−0.468009	−	0.140395i
$663$		0			0
$664$	1.52796	−	1.27779i	0.0592963	−	0.0495877i
$665$	−0.916019	−	2.21147i	−0.0355217	−	0.0857569i
$666$		0			0
$667$	15.4611	+	10.3308i	0.598655	+	0.400008i
$668$	−6.22058	+	9.43513i	−0.240681	+	0.365056i
$669$		0			0
$670$	12.7442	+	41.5506i	0.492351	+	1.60524i
$671$			4.90196i			0.189238i
$672$		0			0
$673$			9.82761i			0.378826i	0.981897	+	0.189413i	$0.0606586\pi$
$673$			9.82761i			0.378826i	−0.981897	+	0.189413i	$0.939341\pi$
$674$	−15.7853	+	4.84159i	−0.608027	+	0.186491i
$675$		0			0
$676$	19.9807	−	4.10258i	0.768487	−	0.157792i
$677$	18.3376	+	12.2528i	0.704770	+	0.470912i	0.855593	−	0.517648i	$-0.173192\pi$
$677$	18.3376	+	12.2528i	0.704770	+	0.470912i	−0.150823	+	0.988561i	$0.548192\pi$
$678$		0			0
$679$	−0.0689066	−	0.166355i	−0.00264439	−	0.00638413i
$680$	−4.40456	+	1.38070i	−0.168907	+	0.0529476i
$681$		0			0
$682$	−2.94656	+	9.82236i	−0.112829	+	0.376118i
$683$	−39.0856	+	7.77460i	−1.49557	+	0.297487i	−0.874020	−	0.485889i	$-0.838496\pi$
$683$	−39.0856	+	7.77460i	−1.49557	+	0.297487i	−0.621548	+	0.783376i	$0.713496\pi$
$684$		0			0
$685$	−53.7433	+	35.9101i	−2.05342	+	1.37205i
$686$	3.98539	+	4.82581i	0.152163	+	0.184250i
$687$		0			0
$688$	1.68126	−	9.03281i	0.0640974	−	0.344372i
$689$	32.9447	−	32.9447i	1.25509	−	1.25509i
$690$		0			0
$691$	0.586959	+	0.878446i	0.0223290	+	0.0334177i	0.842466	−	0.538749i	$-0.181103\pi$
$691$	0.586959	+	0.878446i	0.0223290	+	0.0334177i	−0.820137	+	0.572167i	$0.806103\pi$
$692$	2.29721	+	0.934988i	0.0873267	+	0.0355429i
$693$		0			0
$694$	−16.6705	+	8.97670i	−0.632802	+	0.340751i
$695$	20.9855	+	8.69248i	0.796025	+	0.329724i
$696$		0			0
$697$	5.92580	−	2.45455i	0.224456	−	0.0929726i
$698$	−4.87182	−	3.97314i	−0.184401	−	0.150385i
$699$		0			0
$700$	−0.428060	+	2.22354i	−0.0161792	+	0.0840421i
$701$	−7.02983	−	1.39832i	−0.265513	−	0.0528138i	0.0605384	−	0.998166i	$-0.480718\pi$
$701$	−7.02983	−	1.39832i	−0.265513	−	0.0528138i	−0.326051	+	0.945352i	$0.605718\pi$
$702$		0			0
$703$	−4.56018			−0.171990
$704$	17.6996	+	40.5910i	0.667077	+	1.52983i
$705$		0			0
$706$	−39.3334	−	20.8686i	−1.48033	−	0.785399i
$707$	−3.46597	−	0.689424i	−0.130351	−	0.0259284i
$708$		0			0
$709$	16.3103	−	24.4101i	0.612546	−	0.916740i	−0.387441	−	0.921895i	$-0.626641\pi$
$709$	16.3103	−	24.4101i	0.612546	−	0.916740i	0.999987	+	0.00515478i	$0.00164083\pi$
$710$	43.1100	+	35.1577i	1.61789	+	1.31944i
$711$		0			0
$712$	13.1976	+	24.1512i	0.494601	+	0.905104i
$713$	10.6706	+	4.41990i	0.399617	+	0.165527i
$714$		0			0
$715$	−15.2136	−	76.4839i	−0.568956	−	2.86034i
$716$	−3.80710	+	9.35380i	−0.142278	+	0.349568i
$717$		0			0
$718$	−24.3351	−	2.32109i	−0.908177	−	0.0866225i
$719$	−2.72562	+	2.72562i	−0.101649	+	0.101649i	−0.756102	−	0.654454i	$-0.772899\pi$
$719$	−2.72562	+	2.72562i	−0.101649	+	0.101649i	0.654454	+	0.756102i	$0.272899\pi$
$720$		0			0
$721$	1.90257	+	1.90257i	0.0708555	+	0.0708555i
$722$	11.1621	+	13.5158i	0.415409	+	0.503008i
$723$		0			0
$724$	19.6664	−	19.9103i	0.730895	−	0.739960i
$725$	7.35505	−	1.46301i	0.273160	−	0.0543349i
$726$		0			0
$727$	−16.6313	+	40.1516i	−0.616823	+	1.48914i	0.238551	+	0.971130i	$0.423328\pi$
$727$	−16.6313	+	40.1516i	−0.616823	+	1.48914i	−0.855374	+	0.518011i	$0.826672\pi$
$728$	−3.84441	−	2.00941i	−0.142483	−	0.0744736i
$729$		0			0
$730$	−6.56958	−	64.6586i	−0.243151	−	2.39312i
$731$	1.06559	+	0.712003i	0.0394122	+	0.0263344i
$732$		0			0
$733$	−1.23293	+	6.19836i	−0.0455393	+	0.228942i	−0.996852	−	0.0792861i	$-0.974736\pi$
$733$	−1.23293	+	6.19836i	−0.0455393	+	0.228942i	0.951313	+	0.308228i	$0.0997359\pi$
$734$	5.12878	−	1.57308i	0.189307	−	0.0580633i
$735$		0			0
$736$	47.4976	−	15.2113i	1.75079	−	0.560696i
$737$			58.1563i			2.14222i
$738$		0			0
$739$	3.58939	−	18.0451i	0.132038	−	0.663799i	−0.856902	−	0.515480i	$-0.827614\pi$
$739$	3.58939	−	18.0451i	0.132038	−	0.663799i	0.988940	−	0.148319i	$-0.0473864\pi$
$740$	8.66609	+	5.71355i	0.318572	+	0.210034i
$741$		0			0
$742$	−4.33364	+	0.440316i	−0.159093	+	0.0161645i
$743$	7.10234	+	17.1466i	0.260560	+	0.629047i	0.998973	−	0.0453012i	$-0.0144248\pi$
$743$	7.10234	+	17.1466i	0.260560	+	0.629047i	−0.738414	+	0.674348i	$0.764425\pi$
$744$		0			0
$745$	−16.4874	+	39.8040i	−0.604050	+	1.45831i
$746$	−46.0617	−	13.8178i	−1.68644	−	0.505906i
$747$		0			0
$748$	−6.17652	+	0.0380702i	−0.225836	+	0.00139199i
$749$	−2.21729	+	1.48155i	−0.0810181	+	0.0541346i
$750$		0			0
$751$	−12.0765	−	12.0765i	−0.440679	−	0.440679i	0.451561	−	0.892240i	$-0.350867\pi$
$751$	−12.0765	−	12.0765i	−0.440679	−	0.440679i	−0.892240	+	0.451561i	$0.850867\pi$
$752$	−27.2370	+	11.6774i	−0.993233	+	0.425829i
$753$		0			0
$754$	−1.36407	+	14.3013i	−0.0496764	+	0.520822i
$755$	31.1427	+	46.6084i	1.13340	+	1.69625i
$756$		0			0
$757$	3.15311	+	15.8517i	0.114602	+	0.576142i	0.994827	+	0.101585i	$0.0323915\pi$
$757$	3.15311	+	15.8517i	0.114602	+	0.576142i	−0.880225	+	0.474556i	$0.842609\pi$
$758$	2.50109	+	4.64473i	0.0908438	+	0.168704i
$759$		0			0
$760$	2.27961	+	21.1397i	0.0826900	+	0.766817i
$761$	12.7704	−	5.28967i	0.462927	−	0.191751i	−0.139015	−	0.990290i	$-0.544394\pi$
$761$	12.7704	−	5.28967i	0.462927	−	0.191751i	0.601942	+	0.798540i	$0.294394\pi$
$762$		0			0
$763$	0.0964972	−	0.144418i	0.00349343	−	0.00522829i
$764$	−3.61281	−	5.33546i	−0.130707	−	0.193030i
$765$		0			0
$766$	15.5698	−	29.3463i	0.562561	−	1.06033i
$767$	3.24120			0.117033
$768$		0			0
$769$	−36.5971			−1.31973			−0.659863	−	0.751386i	$-0.729386\pi$
$769$	−36.5971			−1.31973			−0.659863	+	0.751386i	$0.729386\pi$
$770$	−3.41706	+	6.44054i	−0.123142	+	0.232101i
$771$		0			0
$772$	−22.7566	−	33.6073i	−0.819026	−	1.20955i
$773$	19.3354	−	28.9374i	0.695445	−	1.04081i	−0.300754	−	0.953702i	$-0.597238\pi$
$773$	19.3354	−	28.9374i	0.695445	−	1.04081i	0.996199	−	0.0871053i	$-0.0277617\pi$
$774$		0			0
$775$	4.30336	−	1.78251i	0.154581	−	0.0640296i
$776$	0.171481	+	1.59021i	0.00615581	+	0.0570853i
$777$		0			0
$778$	11.3398	+	21.0589i	0.406552	+	0.755000i
$779$	−5.76396	−	28.9774i	−0.206515	−	1.03822i
$780$		0			0
$781$	41.3555	+	61.8928i	1.47982	+	2.21470i
$782$	−0.660528	+	6.92518i	−0.0236205	+	0.247644i
$783$		0			0
$784$	−10.8734	−	25.3618i	−0.388335	−	0.905779i
$785$	26.4716	+	26.4716i	0.944814	+	0.944814i
$786$		0			0
$787$	39.0123	−	26.0672i	1.39064	−	0.929195i	0.390676	−	0.920528i	$-0.372241\pi$
$787$	39.0123	−	26.0672i	1.39064	−	0.929195i	0.999962	−	0.00866684i	$-0.00275877\pi$
$788$	36.5100	−	0.225037i	1.30062	−	0.00801661i
$789$		0			0
$790$	−14.3408	−	4.30201i	−0.510221	−	0.153058i
$791$	−0.195420	+	0.471785i	−0.00694833	+	0.0167747i
$792$		0			0
$793$	1.63231	+	3.94076i	0.0579652	+	0.139940i
$794$	14.9941	−	1.52346i	0.532121	−	0.0540657i
$795$		0			0
$796$	−20.4901	−	13.5091i	−0.726252	−	0.478818i
$797$	4.26222	−	21.4276i	0.150976	−	0.759005i	−0.828900	−	0.559397i	$-0.811033\pi$
$797$	4.26222	−	21.4276i	0.150976	−	0.759005i	0.979876	−	0.199609i	$-0.0639671\pi$
$798$		0			0
$799$		−	4.13357i		−	0.146235i
$800$	9.20709	−	17.8827i	0.325520	−	0.632249i
$801$		0			0
$802$	−23.5426	+	7.22087i	−0.831318	+	0.254978i
$803$	16.9664	−	85.2957i	0.598730	−	3.01002i
$804$		0			0
$805$	6.82765	+	4.56209i	0.240643	+	0.160793i
$806$	0.901992	+	8.87752i	0.0317713	+	0.312697i
$807$		0			0
$808$	27.8194	+	14.5407i	0.978682	+	0.511540i
$809$	−3.30815	+	7.98658i	−0.116308	+	0.280793i	−0.971304	−	0.237842i	$-0.923560\pi$
$809$	−3.30815	+	7.98658i	−0.116308	+	0.280793i	0.854995	+	0.518636i	$0.173560\pi$
$810$		0			0
$811$	−28.3926	+	5.64764i	−0.996998	+	0.198315i	−0.666511	−	0.745495i	$-0.732213\pi$
$811$	−28.3926	+	5.64764i	−0.996998	+	0.198315i	−0.330487	+	0.943810i	$0.607213\pi$
$812$	0.943880	−	0.955587i	0.0331237	−	0.0335345i
$813$		0			0
$814$	8.84466	+	10.7098i	0.310005	+	0.375377i
$815$	17.2009	+	17.2009i	0.602520	+	0.602520i
$816$		0			0
$817$	4.17428	−	4.17428i	0.146039	−	0.146039i
$818$	44.0327	+	4.19987i	1.53957	+	0.146845i
$819$		0			0
$820$	−25.3527	+	62.2900i	−0.885354	+	2.17526i
$821$	0.523141	+	2.63001i	0.0182578	+	0.0917879i	0.988840	−	0.148983i	$-0.0475999\pi$
$821$	0.523141	+	2.63001i	0.0182578	+	0.0917879i	−0.970582	+	0.240771i	$0.922600\pi$
$822$		0			0
$823$	28.2090	+	11.6845i	0.983304	+	0.407298i	0.815648	−	0.578548i	$-0.196380\pi$
$823$	28.2090	+	11.6845i	0.983304	+	0.407298i	0.167655	+	0.985846i	$0.446380\pi$
$824$	−11.4608	−	20.9730i	−0.399258	−	0.730629i
$825$		0			0
$826$	−0.234839	−	0.191519i	−0.00817108	−	0.00666380i
$827$	3.65599	−	5.47157i	0.127131	−	0.190265i	−0.762444	−	0.647054i	$-0.776001\pi$
$827$	3.65599	−	5.47157i	0.127131	−	0.190265i	0.889575	+	0.456789i	$0.151001\pi$
$828$		0			0
$829$	−39.2725	−	7.81178i	−1.36399	−	0.271314i	−0.541790	−	0.840514i	$-0.682253\pi$
$829$	−39.2725	−	7.81178i	−1.36399	−	0.271314i	−0.822199	+	0.569200i	$0.807253\pi$
$830$	−2.57331	−	1.36528i	−0.0893207	−	0.0473896i
$831$		0			0
$832$	27.7454	+	26.7378i	0.961899	+	0.926968i
$833$	3.84898			0.133359
$834$		0			0
$835$	16.2104	+	3.22446i	0.560986	+	0.111587i
$836$	−5.37852	+	27.9385i	−0.186020	+	0.966274i
$837$		0			0
$838$	34.5255	+	28.1567i	1.19266	+	0.972657i
$839$	0.387077	−	0.160333i	0.0133634	−	0.00553530i	−0.375992	−	0.926623i	$-0.622698\pi$
$839$	0.387077	−	0.160333i	0.0133634	−	0.00553530i	0.389355	+	0.921088i	$0.372698\pi$
$840$		0			0
$841$	22.6829	+	9.39555i	0.782168	+	0.323984i
$842$	−3.13940	+	1.69050i	−0.108191	+	0.0582586i
$843$		0			0
$844$	−23.0075	−	9.36430i	−0.791951	−	0.322333i
$845$	−16.5734	−	24.8039i	−0.570143	−	0.853279i
$846$		0			0
$847$	−4.42187	+	4.42187i	−0.151937	+	0.151937i
$848$	38.0393	+	7.08018i	1.30627	+	0.243134i
$849$		0			0
$850$	1.78649	+	2.16322i	0.0612762	+	0.0741978i
$851$	13.0073	−	8.69123i	0.445886	−	0.297932i
$852$		0			0
$853$	−35.1220	+	6.98620i	−1.20255	+	0.239203i	−0.755406	−	0.655257i	$-0.772560\pi$
$853$	−35.1220	+	6.98620i	−1.20255	+	0.239203i	−0.447148	+	0.894460i	$0.647560\pi$
$854$	0.114587	−	0.381976i	0.00392108	−	0.0130709i
$855$		0			0
$856$	22.6031	−	7.08542i	0.772557	−	0.242175i
$857$	10.0446	+	24.2499i	0.343118	+	0.828361i	0.997397	+	0.0721071i	$0.0229723\pi$
$857$	10.0446	+	24.2499i	0.343118	+	0.828361i	−0.654279	+	0.756253i	$0.727028\pi$
$858$		0			0
$859$	−12.8731	−	8.60156i	−0.439226	−	0.293482i	0.316228	−	0.948683i	$-0.397584\pi$
$859$	−12.8731	−	8.60156i	−0.439226	−	0.293482i	−0.755454	+	0.655202i	$0.772584\pi$
$860$	−13.1628	+	2.70268i	−0.448847	+	0.0921607i
$861$		0			0
$862$	23.2089	−	7.11853i	0.790499	−	0.242458i
$863$			18.1277i			0.617073i	0.951213	+	0.308536i	$0.0998392\pi$
$863$			18.1277i			0.617073i	−0.951213	+	0.308536i	$0.900161\pi$
$864$		0			0
$865$		−	3.62729i		−	0.123331i
$866$	13.1218	+	42.7816i	0.445895	+	1.45378i
$867$		0			0
$868$	0.459210	−	0.696511i	0.0155866	−	0.0236411i
$869$	−16.6581	−	11.1306i	−0.565089	−	0.377580i
$870$		0			0
$871$	19.3656	+	46.7527i	0.656179	+	1.58416i
$872$	−1.18353	+	0.989750i	−0.0400794	+	0.0335172i
$873$		0			0
$874$	30.6931	+	9.20744i	1.03821	+	0.311446i
$875$	−1.31940	+	0.262445i	−0.0446039	+	0.00887227i
$876$		0			0
$877$	−9.44491	+	6.31089i	−0.318932	+	0.213104i	−0.704723	−	0.709483i	$-0.748929\pi$
$877$	−9.44491	+	6.31089i	−0.318932	+	0.213104i	0.385791	+	0.922586i	$0.373929\pi$
$878$	−0.939805	+	0.776137i	−0.0317169	+	0.0261934i
$879$		0			0
$880$	45.2261	−	46.3551i	1.52457	−	1.56263i
$881$	13.7251	−	13.7251i	0.462412	−	0.462412i	−0.437034	−	0.899445i	$-0.643971\pi$
$881$	13.7251	−	13.7251i	0.462412	−	0.462412i	0.899445	+	0.437034i	$0.143971\pi$
$882$		0			0
$883$	2.77069	+	4.14663i	0.0932411	+	0.139545i	0.875158	−	0.483838i	$-0.160758\pi$
$883$	2.77069	+	4.14663i	0.0932411	+	0.139545i	−0.781916	+	0.623383i	$0.785758\pi$
$884$	−4.95272	+	2.08734i	−0.166578	+	0.0702048i
$885$		0			0
$886$	7.63864	+	14.1856i	0.256625	+	0.476573i
$887$	−21.8529	−	9.05179i	−0.733750	−	0.303929i	−0.0156581	−	0.999877i	$-0.504984\pi$
$887$	−21.8529	−	9.05179i	−0.733750	−	0.303929i	−0.718092	+	0.695948i	$0.754984\pi$
$888$		0			0
$889$	1.81251	−	0.750767i	0.0607897	−	0.0251799i
$890$	25.4389	−	31.1929i	0.852712	−	1.04559i
$891$		0			0
$892$	−27.2787	+	18.4712i	−0.913358	+	0.618463i
$893$	−18.6747	−	3.71462i	−0.624924	−	0.124305i
$894$		0			0
$895$	14.7696			0.493695
$896$	−0.430361	−	3.57671i	−0.0143774	−	0.119490i
$897$		0			0
$898$	−15.3226	+	28.8803i	−0.511321	+	0.963747i
$899$	−2.70984	−	0.539020i	−0.0903781	−	0.0179773i
$900$		0			0
$901$	−2.99841	+	4.48744i	−0.0998916	+	0.149498i
$902$	−56.8752	+	69.7398i	−1.89374	+	2.32208i
$903$		0			0
$904$	2.84507	−	3.53283i	0.0946256	−	0.117500i
$905$	−37.8132	−	15.6628i	−1.25695	−	0.520648i
$906$		0			0
$907$	−0.516883	−	2.59855i	−0.0171628	−	0.0862833i	0.971255	−	0.238043i	$-0.0765060\pi$
$907$	−0.516883	−	2.59855i	−0.0171628	−	0.0862833i	−0.988417	+	0.151760i	$0.951506\pi$
$908$	13.2930	−	5.60237i	0.441143	−	0.185921i
$909$		0			0
$910$	−0.602376	+	6.31550i	−0.0199686	+	0.209357i
$911$	30.6239	−	30.6239i	1.01461	−	1.01461i	0.0147224	−	0.999892i	$-0.495314\pi$
$911$	30.6239	−	30.6239i	1.01461	−	1.01461i	0.999892	−	0.0147224i	$-0.00468644\pi$
$912$		0			0
$913$	−2.75632	−	2.75632i	−0.0912210	−	0.0912210i
$914$	−20.1991	+	16.6814i	−0.668126	+	0.551771i
$915$		0			0
$916$	−0.0676775	−	10.9800i	−0.00223613	−	0.362790i
$917$	5.98509	−	1.19051i	0.197645	−	0.0393141i
$918$		0			0
$919$	4.08571	−	9.86378i	0.134775	−	0.325376i	−0.842055	−	0.539392i	$-0.818654\pi$
$919$	4.08571	−	9.86378i	0.134775	−	0.325376i	0.976830	+	0.214015i	$0.0686543\pi$
$920$	−46.7924	−	55.9537i	−1.54270	−	1.84474i
$921$		0			0
$922$	24.6309	−	2.50260i	0.811174	−	0.0824186i
$923$	53.8561	+	35.9855i	1.77270	+	1.18448i
$924$		0			0
$925$	1.23083	−	6.18779i	0.0404693	−	0.203453i
$926$	9.08968	+	29.6356i	0.298705	+	0.973885i
$927$		0			0
$928$	−10.4341	+	5.78560i	−0.342517	+	0.189922i
$929$		−	2.01972i		−	0.0662650i	−0.999451	−	0.0331325i	$-0.989452\pi$
$929$		−	2.01972i		−	0.0662650i	0.999451	−	0.0331325i	$-0.0105483\pi$
$930$		0			0
$931$	3.45888	−	17.3890i	0.113360	−	0.569900i
$932$	19.1045	−	3.92269i	0.625790	−	0.128492i
$933$		0			0
$934$	−3.35120	−	32.9829i	−0.109655	−	1.07923i
$935$	3.45691	+	8.34572i	0.113053	+	0.272934i
$936$		0			0
$937$	9.96228	−	24.0511i	0.325453	−	0.785714i	−0.673465	−	0.739219i	$-0.735195\pi$
$937$	9.96228	−	24.0511i	0.325453	−	0.785714i	0.998919	−	0.0464951i	$-0.0148052\pi$
$938$	1.35945	−	4.53172i	0.0443875	−	0.147966i
$939$		0			0
$940$	30.8349	+	30.4571i	1.00572	+	0.993402i
$941$	−19.7754	+	13.2135i	−0.644659	+	0.430747i	−0.834455	−	0.551076i	$-0.814217\pi$
$941$	−19.7754	+	13.2135i	−0.644659	+	0.430747i	0.189796	+	0.981824i	$0.439217\pi$
$942$		0			0
$943$	71.6689	+	71.6689i	2.33386	+	2.33386i
$944$	1.52293	+	2.21950i	0.0495671	+	0.0722385i
$945$		0			0
$946$	−17.8996	−	1.70728i	−0.581967	−	0.0555084i
$947$	−14.6312	−	21.8971i	−0.475450	−	0.711561i	0.513782	−	0.857921i	$-0.328244\pi$
$947$	−14.6312	−	21.8971i	−0.475450	−	0.711561i	−0.989231	+	0.146360i	$0.953244\pi$
$948$		0			0
$949$	−14.7633	−	74.2201i	−0.479237	−	2.40929i
$950$	11.3784	−	6.12706i	0.369165	−	0.198788i
$951$		0			0
$952$	0.482184	+	0.141414i	0.0156277	+	0.00458326i
$953$	16.4109	−	6.79760i	0.531600	−	0.220196i	−0.100704	−	0.994916i	$-0.532110\pi$
$953$	16.4109	−	6.79760i	0.531600	−	0.220196i	0.632304	+	0.774721i	$0.282110\pi$
$954$		0			0
$955$	−5.23554	+	7.83553i	−0.169418	+	0.253552i
$956$	−8.32482	+	43.2430i	−0.269244	+	1.39858i
$957$		0			0
$958$	−16.8657	−	8.94818i	−0.544906	−	0.289103i
$959$	7.03642			0.227218
$960$		0			0
$961$	29.2839			0.944641
$962$	10.6766	+	5.66454i	0.344228	+	0.182632i
$963$		0			0
$964$	26.9373	+	5.18577i	0.867592	+	0.167022i
$965$	−32.9779	+	49.3549i	−1.06160	+	1.58879i
$966$		0			0
$967$	−30.9379	+	12.8149i	−0.994897	+	0.412100i	−0.819923	−	0.572473i	$-0.805984\pi$
$967$	−30.9379	+	12.8149i	−0.994897	+	0.412100i	−0.174974	+	0.984573i	$0.555984\pi$
$968$	48.7445	−	26.6368i	1.56671	−	0.856139i
$969$		0			0
$970$	2.05955	−	1.10903i	0.0661283	−	0.0356088i
$971$	−9.31325	−	46.8209i	−0.298876	−	1.50255i	−0.779933	−	0.625864i	$-0.784747\pi$
$971$	−9.31325	−	46.8209i	−0.298876	−	1.50255i	0.481056	−	0.876690i	$-0.340253\pi$
$972$		0			0
$973$	−1.37378	−	2.05601i	−0.0440414	−	0.0659126i
$974$	17.6760	+	1.68595i	0.566377	+	0.0540214i
$975$		0			0
$976$	−1.93157	+	2.96939i	−0.0618280	+	0.0950480i
$977$	−26.4810	−	26.4810i	−0.847201	−	0.847201i	0.142582	−	0.989783i	$-0.454460\pi$
$977$	−26.4810	−	26.4810i	−0.847201	−	0.847201i	−0.989783	+	0.142582i	$0.954460\pi$
$978$		0			0
$979$	44.7835	−	29.9234i	1.43129	−	0.956355i
$980$	−28.3602	+	28.7120i	−0.905933	+	0.917170i
$981$		0			0
$982$	−13.0757	+	43.5880i	−0.417263	+	1.39095i
$983$	−9.39257	+	22.6757i	−0.299577	+	0.723242i	0.700379	+	0.713771i	$0.253014\pi$
$983$	−9.39257	+	22.6757i	−0.299577	+	0.723242i	−0.999955	+	0.00947017i	$0.996986\pi$
$984$		0			0
$985$	−20.4341	−	49.3323i	−0.651085	−	1.57186i
$986$	−0.168219	−	1.65563i	−0.00535718	−	0.0527261i
$987$		0			0
$988$	4.97945	+	24.2512i	0.158417	+	0.771533i
$989$	−3.95087	+	19.8623i	−0.125630	+	0.631586i
$990$		0			0
$991$		−	9.05267i		−	0.287567i	−0.989609	−	0.143784i	$-0.954073\pi$
$991$		−	9.05267i		−	0.287567i	0.989609	−	0.143784i	$-0.0459270\pi$
$992$	−5.65530	+	4.78890i	−0.179556	+	0.152048i
$993$		0			0
$994$	−1.77576	−	5.78960i	−0.0563236	−	0.183635i
$995$	−7.00250	+	35.2039i	−0.221994	+	1.11604i
$996$		0			0
$997$	11.0204	+	7.36360i	0.349020	+	0.233207i	0.717706	−	0.696346i	$-0.245192\pi$
$997$	11.0204	+	7.36360i	0.349020	+	0.233207i	−0.368686	+	0.929554i	$0.620192\pi$
$998$	−32.3401	+	3.28589i	−1.02371	+	0.104013i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bd.b.541.11		128
3.2	odd	2		192.2.r.a.157.6	✓	128
12.11	even	2		768.2.r.a.721.7		128
64.53	even	16	inner	576.2.bd.b.181.11		128
192.11	even	16		768.2.r.a.49.7		128
192.53	odd	16		192.2.r.a.181.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.6	✓	128	3.2	odd	2
192.2.r.a.181.6	yes	128	192.53	odd	16
576.2.bd.b.181.11		128	64.53	even	16	inner
576.2.bd.b.541.11		128	1.1	even	1	trivial
768.2.r.a.49.7		128	192.11	even	16
768.2.r.a.721.7		128	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.662809 - 1.24927i) q^{2} +(-1.12137 - 1.65606i) q^{4} +(-1.62504 + 2.43205i) q^{5} +(0.294182 - 0.121854i) q^{7} +(-2.81212 + 0.303246i) q^{8} +O(q^{10})\)	\(q+(0.662809 - 1.24927i) q^{2} +(-1.12137 - 1.65606i) q^{4} +(-1.62504 + 2.43205i) q^{5} +(0.294182 - 0.121854i) q^{7} +(-2.81212 + 0.303246i) q^{8} +(1.96120 + 3.64211i) q^{10} +(1.07988 + 5.42890i) q^{11} +(2.67591 + 4.00478i) q^{13} +(0.0427572 - 0.448280i) q^{14} +(-1.48506 + 3.71411i) q^{16} +(-0.394520 - 0.394520i) q^{17} +(-2.13690 + 1.42783i) q^{19} +(5.84989 - 0.0360570i) q^{20} +(7.49793 + 2.24926i) q^{22} +(3.37395 - 8.14543i) q^{23} +(-1.36068 - 3.28498i) q^{25} +(6.77668 - 0.688538i) q^{26} +(-0.531684 - 0.350539i) q^{28} +(-0.411462 + 2.06856i) q^{29} +1.31001i q^{31} +(3.65562 + 4.31699i) q^{32} +(-0.754356 + 0.231372i) q^{34} +(-0.181703 + 0.913483i) q^{35} +(1.47533 + 0.985786i) q^{37} +(0.367396 + 3.61595i) q^{38} +(3.83232 - 7.33202i) q^{40} +(-4.39934 + 10.6209i) q^{41} +(-2.25285 + 0.448119i) q^{43} +(7.77964 - 7.87614i) q^{44} +(-7.93958 - 9.61384i) q^{46} +(5.23873 + 5.23873i) q^{47} +(-4.87805 + 4.87805i) q^{49} +(-5.00571 - 0.477448i) q^{50} +(3.63147 - 8.92230i) q^{52} +(-1.88714 - 9.48728i) q^{53} +(-14.9582 - 6.19589i) q^{55} +(-0.790324 + 0.431878i) q^{56} +(2.31148 + 1.88509i) q^{58} +(0.373863 - 0.559526i) q^{59} +(0.868572 + 0.172770i) q^{61} +(1.63656 + 0.868286i) q^{62} +(7.81608 - 1.70553i) q^{64} -14.0883 q^{65} +(10.3046 + 2.04972i) q^{67} +(-0.210946 + 1.09575i) q^{68} +(1.02076 + 0.832462i) q^{70} +(12.4243 - 5.14631i) q^{71} +(-14.5155 - 6.01250i) q^{73} +(2.20938 - 1.18971i) q^{74} +(4.76083 + 1.93771i) q^{76} +(0.979213 + 1.46550i) q^{77} +(-2.55934 + 2.55934i) q^{79} +(-6.61960 - 9.64734i) q^{80} +(10.3525 + 12.5356i) q^{82} +(-0.585536 + 0.391243i) q^{83} +(1.60061 - 0.318380i) q^{85} +(-0.933384 + 3.11144i) q^{86} +(-4.68304 - 14.9393i) q^{88} +(-3.72369 - 8.98978i) q^{89} +(1.27520 + 0.852063i) q^{91} +(-17.2727 + 3.54657i) q^{92} +(10.0169 - 3.07233i) q^{94} -7.51734i q^{95} -0.565484i q^{97} +(2.86081 + 9.32724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} + 80 q^{26} - 80 q^{28} + 80 q^{32} - 80 q^{34} + 80 q^{38} - 80 q^{40} + 16 q^{44} - 48 q^{50} + 48 q^{52} - 64 q^{55} - 112 q^{56} + 128 q^{59} - 96 q^{62} + 96 q^{64} - 32 q^{67} - 96 q^{68} + 96 q^{70} + 128 q^{71} - 112 q^{74} + 16 q^{76} - 32 q^{79} - 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 + 80 * q^26 - 80 * q^28 + 80 * q^32 - 80 * q^34 + 80 * q^38 - 80 * q^40 + 16 * q^44 - 48 * q^50 + 48 * q^52 - 64 * q^55 - 112 * q^56 + 128 * q^59 - 96 * q^62 + 96 * q^64 - 32 * q^67 - 96 * q^68 + 96 * q^70 + 128 * q^71 - 112 * q^74 + 16 * q^76 - 32 * q^79 - 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

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