LMFDB - Embedded newform 432.2.v.a.395.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(35,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.v (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			395.17
Character	$\chi$	$=$	432.395
Dual form			432.2.v.a.35.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.09161 + 0.899102i) q^{2} +(0.383232 + 1.96294i) q^{4} +(0.726024 + 2.70956i) q^{5} +(-0.00424642 - 0.00735502i) q^{7} +(-1.34654 + 2.48733i) q^{8} +(-1.64363 + 3.61055i) q^{10} +(-0.804193 + 3.00129i) q^{11} +(-1.72108 - 6.42317i) q^{13} +(0.00197747 - 0.0118468i) q^{14} +(-3.70627 + 1.50452i) q^{16} -3.37812i q^{17} +(1.35881 + 1.35881i) q^{19} +(-5.04046 + 2.46353i) q^{20} +(-3.57633 + 2.55319i) q^{22} +(5.38718 + 3.11029i) q^{23} +(-2.48446 + 1.43441i) q^{25} +(3.89633 - 8.55903i) q^{26} +(0.0128101 - 0.0111542i) q^{28} +(-0.878030 + 3.27685i) q^{29} +(6.70211 + 3.86947i) q^{31} +(-5.39852 - 1.68996i) q^{32} +(3.03727 - 3.68759i) q^{34} +(0.0168459 - 0.0168459i) q^{35} +(0.769697 + 0.769697i) q^{37} +(0.261585 + 2.70501i) q^{38} +(-7.71719 - 1.84267i) q^{40} +(2.64756 - 4.58570i) q^{41} +(-5.99790 - 1.60713i) q^{43} +(-6.19954 - 0.428394i) q^{44} +(3.08424 + 8.23886i) q^{46} +(0.0955284 + 0.165460i) q^{47} +(3.49996 - 6.06212i) q^{49} +(-4.00175 - 0.667972i) q^{50} +(11.9487 - 5.83994i) q^{52} +(0.750557 - 0.750557i) q^{53} -8.71603 q^{55} +(0.0240124 - 0.000658413i) q^{56} +(-3.90469 + 2.78761i) q^{58} +(9.08809 - 2.43515i) q^{59} +(9.85796 + 2.64143i) q^{61} +(3.83706 + 10.2498i) q^{62} +(-4.37364 - 6.69860i) q^{64} +(16.1544 - 9.32674i) q^{65} +(-7.77154 + 2.08238i) q^{67} +(6.63104 - 1.29460i) q^{68} +(0.0335353 - 0.00324299i) q^{70} -1.02260i q^{71} -7.30911i q^{73} +(0.148174 + 1.53225i) q^{74} +(-2.14653 + 3.18801i) q^{76} +(0.0254895 - 0.00682989i) q^{77} +(4.36074 - 2.51768i) q^{79} +(-6.76742 - 8.95003i) q^{80} +(7.01311 - 2.62538i) q^{82} +(-12.5030 - 3.35017i) q^{83} +(9.15320 - 2.45259i) q^{85} +(-5.10240 - 7.14709i) q^{86} +(-6.38232 - 6.04166i) q^{88} -18.1774 q^{89} +(-0.0399341 + 0.0399341i) q^{91} +(-4.04078 + 11.7667i) q^{92} +(-0.0444856 + 0.266508i) q^{94} +(-2.69525 + 4.66831i) q^{95} +(1.64497 + 2.84917i) q^{97} +(9.27106 - 3.47065i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.09161	+	0.899102i	0.771886	+	0.635761i
$2$	1.09161	+	0.899102i	0.771886	+	0.635761i
$3$		0			0
$3$		0			0
$4$	0.383232	+	1.96294i	0.191616	+	0.981470i
$5$	0.726024	+	2.70956i	0.324688	+	1.21175i	0.914625	+	0.404302i	$0.132486\pi$
$5$	0.726024	+	2.70956i	0.324688	+	1.21175i	−0.589938	+	0.807449i	$0.700848\pi$
$6$		0			0
$7$	−0.00424642	−	0.00735502i	−0.00160500	−	0.00277994i	0.865222	−	0.501389i	$-0.167178\pi$
$7$	−0.00424642	−	0.00735502i	−0.00160500	−	0.00277994i	−0.866827	+	0.498609i	$0.833844\pi$
$8$	−1.34654	+	2.48733i	−0.476075	+	0.879405i
$9$		0			0
$10$	−1.64363	+	3.61055i	−0.519762	+	1.14176i
$11$	−0.804193	+	3.00129i	−0.242473	+	0.904923i	0.732163	+	0.681129i	$0.238511\pi$
$11$	−0.804193	+	3.00129i	−0.242473	+	0.904923i	−0.974637	+	0.223794i	$0.928156\pi$
$12$		0			0
$13$	−1.72108	−	6.42317i	−0.477342	−	1.78147i	−0.612312	−	0.790616i	$-0.709760\pi$
$13$	−1.72108	−	6.42317i	−0.477342	−	1.78147i	0.134969	−	0.990850i	$-0.456906\pi$
$14$	0.00197747	−	0.0118468i	0.000528501	−	0.00316619i
$15$		0			0
$16$	−3.70627	+	1.50452i	−0.926567	+	0.376130i
$17$		−	3.37812i		−	0.819314i	−0.912240	−	0.409657i	$-0.865648\pi$
$17$		−	3.37812i		−	0.819314i	0.912240	−	0.409657i	$-0.134352\pi$
$18$		0			0
$19$	1.35881	+	1.35881i	0.311733	+	0.311733i	0.845581	−	0.533848i	$-0.179254\pi$
$19$	1.35881	+	1.35881i	0.311733	+	0.311733i	−0.533848	+	0.845581i	$0.679254\pi$
$20$	−5.04046	+	2.46353i	−1.12708	+	0.550862i
$21$		0			0
$22$	−3.57633	+	2.55319i	−0.762477	+	0.544342i
$23$	5.38718	+	3.11029i	1.12331	+	0.648541i	0.942243	−	0.334931i	$-0.108713\pi$
$23$	5.38718	+	3.11029i	1.12331	+	0.648541i	0.181062	+	0.983472i	$0.442046\pi$
$24$		0			0
$25$	−2.48446	+	1.43441i	−0.496893	+	0.286881i
$26$	3.89633	−	8.55903i	0.764133	−	1.67856i
$27$		0			0
$28$	0.0128101	−	0.0111542i	0.00242088	−	0.00210794i
$29$	−0.878030	+	3.27685i	−0.163046	+	0.608496i	0.835235	+	0.549893i	$0.185331\pi$
$29$	−0.878030	+	3.27685i	−0.163046	+	0.608496i	−0.998281	+	0.0586036i	$0.981335\pi$
$30$		0			0
$31$	6.70211	+	3.86947i	1.20374	+	0.694977i	0.961384	−	0.275212i	$-0.0887479\pi$
$31$	6.70211	+	3.86947i	1.20374	+	0.694977i	0.242352	+	0.970188i	$0.422081\pi$
$32$	−5.39852	−	1.68996i	−0.954333	−	0.298745i
$33$		0			0
$34$	3.03727	−	3.68759i	0.520888	−	0.632417i
$35$	0.0168459	−	0.0168459i	0.00284747	−	0.00284747i
$36$		0			0
$37$	0.769697	+	0.769697i	0.126537	+	0.126537i	0.767539	−	0.641002i	$-0.221481\pi$
$37$	0.769697	+	0.769697i	0.126537	+	0.126537i	−0.641002	+	0.767539i	$0.721481\pi$
$38$	0.261585	+	2.70501i	0.0424346	+	0.438810i
$39$		0			0
$40$	−7.71719	−	1.84267i	−1.22020	−	0.291352i
$41$	2.64756	−	4.58570i	0.413479	−	0.716166i	−0.581789	−	0.813340i	$-0.697647\pi$
$41$	2.64756	−	4.58570i	0.413479	−	0.716166i	0.995267	+	0.0971739i	$0.0309803\pi$
$42$		0			0
$43$	−5.99790	−	1.60713i	−0.914672	−	0.245086i	−0.229365	−	0.973340i	$-0.573665\pi$
$43$	−5.99790	−	1.60713i	−0.914672	−	0.245086i	−0.685306	+	0.728255i	$0.740332\pi$
$44$	−6.19954	−	0.428394i	−0.934617	−	0.0645828i
$45$		0			0
$46$	3.08424	+	8.23886i	0.454747	+	1.21475i
$47$	0.0955284	+	0.165460i	0.0139343	+	0.0241348i	0.872908	−	0.487884i	$-0.162231\pi$
$47$	0.0955284	+	0.165460i	0.0139343	+	0.0241348i	−0.858974	+	0.512019i	$0.828898\pi$
$48$		0			0
$49$	3.49996	−	6.06212i	0.499995	−	0.866016i
$50$	−4.00175	−	0.667972i	−0.565932	−	0.0944655i
$51$		0			0
$52$	11.9487	−	5.83994i	1.65699	−	0.809854i
$53$	0.750557	−	0.750557i	0.103097	−	0.103097i	−0.653677	−	0.756774i	$-0.726774\pi$
$53$	0.750557	−	0.750557i	0.103097	−	0.103097i	0.756774	+	0.653677i	$0.226774\pi$
$54$		0			0
$55$	−8.71603			−1.17527
$56$	0.0240124		0.000658413i	0.00320879		8.79842e-5i
$57$		0			0
$58$	−3.90469	+	2.78761i	−0.512711	+	0.366031i
$59$	9.08809	−	2.43515i	1.18317	−	0.317029i	0.386986	−	0.922086i	$-0.373516\pi$
$59$	9.08809	−	2.43515i	1.18317	−	0.317029i	0.796182	+	0.605057i	$0.206850\pi$
$60$		0			0
$61$	9.85796	+	2.64143i	1.26218	+	0.338201i	0.827031	−	0.562156i	$-0.190028\pi$
$61$	9.85796	+	2.64143i	1.26218	+	0.338201i	0.435152	+	0.900357i	$0.356695\pi$
$62$	3.83706	+	10.2498i	0.487307	+	1.30173i
$63$		0			0
$64$	−4.37364	−	6.69860i	−0.546705	−	0.837325i
$65$	16.1544	−	9.32674i	2.00371	−	1.15684i
$66$		0			0
$67$	−7.77154	+	2.08238i	−0.949445	+	0.254403i	−0.700127	−	0.714019i	$-0.746873\pi$
$67$	−7.77154	+	2.08238i	−0.949445	+	0.254403i	−0.249318	+	0.968422i	$0.580206\pi$
$68$	6.63104	−	1.29460i	0.804132	−	0.156993i
$69$		0			0
$70$	0.0335353	−	0.00324299i	0.00400823	−	0.000387611i
$71$		−	1.02260i		−	0.121360i	−0.998157	−	0.0606801i	$-0.980673\pi$
$71$		−	1.02260i		−	0.121360i	0.998157	−	0.0606801i	$-0.0193269\pi$
$72$		0			0
$73$		−	7.30911i		−	0.855467i	−0.903905	−	0.427734i	$-0.859312\pi$
$73$		−	7.30911i		−	0.855467i	0.903905	−	0.427734i	$-0.140688\pi$
$74$	0.148174	+	1.53225i	0.0172249	+	0.178120i
$75$		0			0
$76$	−2.14653	+	3.18801i	−0.246224	+	0.365690i
$77$	0.0254895	−	0.00682989i	0.00290480	−	0.000778338i
$78$		0			0
$79$	4.36074	−	2.51768i	0.490622	−	0.283261i	−0.234211	−	0.972186i	$-0.575251\pi$
$79$	4.36074	−	2.51768i	0.490622	−	0.283261i	0.724832	+	0.688925i	$0.241917\pi$
$80$	−6.76742	−	8.95003i	−0.756621	−	1.00064i
$81$		0			0
$82$	7.01311	−	2.62538i	0.774469	−	0.289925i
$83$	−12.5030	−	3.35017i	−1.37238	−	0.367729i	−0.504034	−	0.863684i	$-0.668151\pi$
$83$	−12.5030	−	3.35017i	−1.37238	−	0.367729i	−0.868348	+	0.495955i	$0.834818\pi$
$84$		0			0
$85$	9.15320	−	2.45259i	0.992804	−	0.266021i
$86$	−5.10240	−	7.14709i	−0.550206	−	0.770691i
$87$		0			0
$88$	−6.38232	−	6.04166i	−0.680358	−	0.644043i
$89$	−18.1774			−1.92680			−0.963399	−	0.268070i	$-0.913614\pi$
$89$	−18.1774			−1.92680			−0.963399	+	0.268070i	$0.913614\pi$
$90$		0			0
$91$	−0.0399341	+	0.0399341i	−0.00418623	+	0.00418623i
$92$	−4.04078	+	11.7667i	−0.421280	+	1.22676i
$93$		0			0
$94$	−0.0444856	+	0.266508i	−0.00458833	+	0.0274882i
$95$	−2.69525	+	4.66831i	−0.276527	+	0.478959i
$96$		0			0
$97$	1.64497	+	2.84917i	0.167021	+	0.289289i	0.937371	−	0.348332i	$-0.113252\pi$
$97$	1.64497	+	2.84917i	0.167021	+	0.289289i	−0.770350	+	0.637621i	$0.779918\pi$
$98$	9.27106	−	3.47065i	0.936519	−	0.350589i
$99$		0			0
$100$	−3.76778	−	4.32714i	−0.376778	−	0.432714i
$101$	−2.66775	−	0.714822i	−0.265451	−	0.0711275i	0.123638	−	0.992327i	$-0.460544\pi$
$101$	−2.66775	−	0.714822i	−0.265451	−	0.0711275i	−0.389090	+	0.921200i	$0.627210\pi$
$102$		0			0
$103$	5.52502	−	9.56961i	0.544396	−	0.942922i	−0.454249	−	0.890875i	$-0.650092\pi$
$103$	5.52502	−	9.56961i	0.544396	−	0.942922i	0.998645	−	0.0520466i	$-0.0165744\pi$
$104$	18.2941	+	4.36817i	1.79388	+	0.428334i
$105$		0			0
$106$	1.49414	−	0.144490i	0.145124	−	0.0140341i
$107$	1.93562	+	1.93562i	0.187124	+	0.187124i	0.794451	−	0.607328i	$-0.207759\pi$
$107$	1.93562	+	1.93562i	0.187124	+	0.187124i	−0.607328	+	0.794451i	$0.707759\pi$
$108$		0			0
$109$	5.98392	−	5.98392i	0.573155	−	0.573155i	−0.359853	−	0.933009i	$-0.617173\pi$
$109$	5.98392	−	5.98392i	0.573155	−	0.573155i	0.933009	+	0.359853i	$0.117173\pi$
$110$	−9.51452	−	7.83660i	−0.907174	−	0.747190i
$111$		0			0
$112$	0.0268042	+	0.0208708i	0.00253276	+	0.00197211i
$113$	−11.7864	−	6.80488i	−1.10877	−	0.640149i	−0.170260	−	0.985399i	$-0.554461\pi$
$113$	−11.7864	−	6.80488i	−1.10877	−	0.640149i	−0.938511	+	0.345250i	$0.887794\pi$
$114$		0			0
$115$	−4.51629	+	16.8550i	−0.421146	+	1.57174i
$116$	−6.76876	−	0.467727i	−0.628463	−	0.0434274i
$117$		0			0
$118$	12.1101	+	5.51288i	1.11483	+	0.507502i
$119$	−0.0248461	+	0.0143449i	−0.00227764	+	0.00131500i
$120$		0			0
$121$	1.16526	+	0.672766i	0.105933	+	0.0611605i
$122$	8.38615	+	11.7467i	0.759246	+	1.06350i
$123$		0			0
$124$	−5.02707	+	14.6388i	−0.451444	+	1.31460i
$125$	4.22728	+	4.22728i	0.378100	+	0.378100i
$126$		0			0
$127$		−	7.01184i		−	0.622200i	−0.950377	−	0.311100i	$-0.899303\pi$
$127$		−	7.01184i		−	0.622200i	0.950377	−	0.311100i	$-0.100697\pi$
$128$	1.24840	−	11.2446i	0.110344	−	0.993893i
$129$		0			0
$130$	26.0200	+	4.34327i	2.28211	+	0.380930i
$131$	2.15546	+	8.04427i	0.188323	+	0.702831i	0.993895	+	0.110333i	$0.0351916\pi$
$131$	2.15546	+	8.04427i	0.188323	+	0.702831i	−0.805572	+	0.592498i	$0.798142\pi$
$132$		0			0
$133$	0.00422400	−	0.0157642i	0.000366268	−	0.00136693i
$134$	−10.3558	−	4.71426i	−0.894603	−	0.407250i
$135$		0			0
$136$	8.40250	+	4.54878i	0.720508	+	0.390055i
$137$	−2.71852	−	4.70861i	−0.232259	−	0.402284i	0.726214	−	0.687469i	$-0.241278\pi$
$137$	−2.71852	−	4.70861i	−0.232259	−	0.402284i	−0.958472	+	0.285185i	$0.907945\pi$
$138$		0			0
$139$	3.64349	+	13.5977i	0.309037	+	1.15334i	0.929414	+	0.369038i	$0.120313\pi$
$139$	3.64349	+	13.5977i	0.309037	+	1.15334i	−0.620378	+	0.784303i	$0.713021\pi$
$140$	0.0395233	+	0.0266115i	0.00334033	+	0.00224909i
$141$		0			0
$142$	0.919421	−	1.11628i	0.0771561	−	0.0936762i
$143$	20.6619			1.72783
$144$		0			0
$145$	−9.51629			−0.790285
$146$	6.57164	−	7.97871i	0.543873	−	0.660323i
$147$		0			0
$148$	−1.21590	+	1.80584i	−0.0999461	+	0.148439i
$149$	−2.45769	−	9.17223i	−0.201342	−	0.751419i	−0.990533	−	0.137271i	$-0.956167\pi$
$149$	−2.45769	−	9.17223i	−0.201342	−	0.751419i	0.789191	−	0.614147i	$-0.210500\pi$
$150$		0			0
$151$	−2.26744	−	3.92732i	−0.184522	−	0.319601i	0.758893	−	0.651215i	$-0.225740\pi$
$151$	−2.26744	−	3.92732i	−0.184522	−	0.319601i	−0.943415	+	0.331614i	$0.892407\pi$
$152$	−5.20952	+	1.55012i	−0.422548	+	0.125731i
$153$		0			0
$154$	0.0339654	+	0.0154621i	0.00273701	+	0.00124597i
$155$	−5.61865	+	20.9691i	−0.451301	+	1.68428i
$156$		0			0
$157$	5.12011	+	19.1085i	0.408629	+	1.52502i	0.797263	+	0.603632i	$0.206280\pi$
$157$	5.12011	+	19.1085i	0.408629	+	1.52502i	−0.388634	+	0.921392i	$0.627053\pi$
$158$	7.02388	+	1.17243i	0.558790	+	0.0932733i
$159$		0			0
$160$	0.659586	−	15.8546i	0.0521449	−	1.25341i
$161$		−	0.0528305i		−	0.00416362i
$162$		0			0
$163$	−6.31776	−	6.31776i	−0.494845	−	0.494845i	0.414984	−	0.909829i	$-0.363787\pi$
$163$	−6.31776	−	6.31776i	−0.494845	−	0.494845i	−0.909829	+	0.414984i	$0.863787\pi$
$164$	10.0161	+	3.43961i	0.782125	+	0.268588i
$165$		0			0
$166$	−10.6363	−	14.8985i	−0.825535	−	1.15635i
$167$	−10.2973	−	5.94513i	−0.796827	−	0.460048i	0.0455334	−	0.998963i	$-0.485501\pi$
$167$	−10.2973	−	5.94513i	−0.796827	−	0.460048i	−0.842360	+	0.538915i	$0.818835\pi$
$168$		0			0
$169$	−27.0366	+	15.6096i	−2.07974	+	1.20074i
$170$	12.1969	+	5.55238i	0.935457	+	0.425848i
$171$		0			0
$172$	0.856120	−	12.3894i	0.0652786	−	0.944685i
$173$	0.125524	−	0.468462i	0.00954341	−	0.0356165i	−0.960990	−	0.276583i	$-0.910798\pi$
$173$	0.125524	−	0.468462i	0.00954341	−	0.0356165i	0.970533	+	0.240967i	$0.0774645\pi$
$174$		0			0
$175$	0.0211002	+	0.0121822i	0.00159502	+	0.000920887i
$176$	−1.53495	−	12.3335i	−0.115701	−	0.929673i
$177$		0			0
$178$	−19.8426	−	16.3433i	−1.48727	−	1.22498i
$179$	−6.91661	+	6.91661i	−0.516971	+	0.516971i	−0.916654	−	0.399682i	$-0.869120\pi$
$179$	−6.91661	+	6.91661i	−0.516971	+	0.516971i	0.399682	+	0.916654i	$0.369120\pi$
$180$		0			0
$181$	−2.19753	−	2.19753i	−0.163341	−	0.163341i	0.620704	−	0.784045i	$-0.286847\pi$
$181$	−2.19753	−	2.19753i	−0.163341	−	0.163341i	−0.784045	+	0.620704i	$0.786847\pi$
$182$	−0.0794974	+	0.00768770i	−0.00589274	+	0.000569850i
$183$		0			0
$184$	−14.9904	+	9.21157i	−1.10511	+	0.679086i
$185$	−1.52672	+	2.64436i	−0.112247	+	0.194417i
$186$		0			0
$187$	10.1387	+	2.71666i	0.741416	+	0.198662i
$188$	−0.288179	+	0.250926i	−0.0210176	+	0.0183007i
$189$		0			0
$190$	−7.13946	+	2.67268i	−0.517951	+	0.193896i
$191$	6.33144	+	10.9664i	0.458127	+	0.793499i	0.998862	−	0.0476936i	$-0.0151871\pi$
$191$	6.33144	+	10.9664i	0.458127	+	0.793499i	−0.540735	+	0.841193i	$0.681854\pi$
$192$		0			0
$193$	4.99499	−	8.65157i	0.359547	−	0.622754i	−0.628338	−	0.777940i	$-0.716265\pi$
$193$	4.99499	−	8.65157i	0.359547	−	0.622754i	0.987885	+	0.155187i	$0.0495979\pi$
$194$	−0.766026	+	4.58918i	−0.0549975	+	0.329484i
$195$		0			0
$196$	13.2409	+	4.54703i	0.945776	+	0.324788i
$197$	−0.273888	+	0.273888i	−0.0195137	+	0.0195137i	−0.716796	−	0.697283i	$-0.754392\pi$
$197$	−0.273888	+	0.273888i	−0.0195137	+	0.0195137i	0.697283	+	0.716796i	$0.254392\pi$
$198$		0			0
$199$	−18.0544			−1.27984			−0.639920	−	0.768441i	$-0.721033\pi$
$199$	−18.0544			−1.27984			−0.639920	+	0.768441i	$0.721033\pi$
$200$	−0.222406	−	8.11118i	−0.0157265	−	0.573547i
$201$		0			0
$202$	−2.26945	−	3.17889i	−0.159678	−	0.223666i
$203$	0.0278298	−	0.00745698i	0.00195327	−	0.000523377i
$204$		0			0
$205$	14.3474	+	3.84438i	1.00207	+	0.268503i
$206$	14.6352	−	5.47874i	1.01968	−	0.381722i
$207$		0			0
$208$	16.0426	+	21.2166i	1.11235	+	1.47110i
$209$	−5.17094	+	2.98544i	−0.357681	+	0.206507i
$210$		0			0
$211$	−2.33428	+	0.625467i	−0.160698	+	0.0430589i	−0.338271	−	0.941049i	$-0.609842\pi$
$211$	−2.33428	+	0.625467i	−0.160698	+	0.0430589i	0.177573	+	0.984108i	$0.443175\pi$
$212$	1.76094	+	1.18566i	0.120942	+	0.0814316i
$213$		0			0
$214$	0.372626	+	3.85327i	0.0254722	+	0.263404i
$215$		−	17.4185i		−	1.18793i
$216$		0			0
$217$		−	0.0657256i		−	0.00446175i
$218$	11.9123	−	1.15196i	0.806800	−	0.0780207i
$219$		0			0
$220$	−3.34026	−	17.1090i	−0.225200	−	1.15349i
$221$	−21.6982	+	5.81402i	−1.45958	+	0.391093i
$222$		0			0
$223$	0.0284597	−	0.0164312i	0.00190581	−	0.00110032i	−0.499047	−	0.866575i	$-0.666316\pi$
$223$	0.0284597	−	0.0164312i	0.00190581	−	0.00110032i	0.500953	+	0.865475i	$0.332983\pi$
$224$	0.0104947	+	0.0468825i	0.000701209	+	0.00313247i
$225$		0			0
$226$	−6.74788	−	18.0254i	−0.448863	−	1.19903i
$227$	−17.9063	−	4.79797i	−1.18848	−	0.318453i	−0.390196	−	0.920732i	$-0.627593\pi$
$227$	−17.9063	−	4.79797i	−1.18848	−	0.318453i	−0.798285	+	0.602279i	$0.794259\pi$
$228$		0			0
$229$	−26.3567	+	7.06225i	−1.74170	+	0.466687i	−0.982823	−	0.184549i	$-0.940918\pi$
$229$	−26.3567	+	7.06225i	−1.74170	+	0.466687i	−0.758875	+	0.651236i	$0.774251\pi$
$230$	−20.0844	+	14.3385i	−1.32433	+	0.945455i
$231$		0			0
$232$	−6.96832	−	6.59638i	−0.457493	−	0.433073i
$233$	7.42838			0.486649			0.243325	−	0.969945i	$-0.421762\pi$
$233$	7.42838			0.486649			0.243325	+	0.969945i	$0.421762\pi$
$234$		0			0
$235$	−0.378968	+	0.378968i	−0.0247211	+	0.0247211i
$236$	8.26289	+	16.9061i	0.537868	+	1.10050i
$237$		0			0
$238$	−0.0400199	−	0.00668012i	−0.00259410	−	0.000433008i
$239$	−2.67225	+	4.62848i	−0.172854	+	0.299391i	−0.939416	−	0.342778i	$-0.888632\pi$
$239$	−2.67225	+	4.62848i	−0.172854	+	0.299391i	0.766563	+	0.642169i	$0.221965\pi$
$240$		0			0
$241$	−10.9314	−	18.9337i	−0.704151	−	1.21963i	−0.966997	−	0.254788i	$-0.917994\pi$
$241$	−10.9314	−	18.9337i	−0.704151	−	1.21963i	0.262845	−	0.964838i	$-0.415339\pi$
$242$	0.667131	+	1.78209i	0.0428848	+	0.114557i
$243$		0			0
$244$	−1.40709	+	20.3629i	−0.0900799	+	1.30360i
$245$	18.9667	+	5.08211i	1.21174	+	0.324684i
$246$		0			0
$247$	6.38925	−	11.0665i	0.406538	−	0.704145i
$248$	−18.6493	+	11.4600i	−1.18423	+	0.727709i
$249$		0			0
$250$	0.813793	+	8.41531i	0.0514688	+	0.532231i
$251$	−18.4081	−	18.4081i	−1.16191	−	1.16191i	−0.984057	−	0.177854i	$-0.943085\pi$
$251$	−18.4081	−	18.4081i	−1.16191	−	1.16191i	−0.177854	−	0.984057i	$-0.556915\pi$
$252$		0			0
$253$	−13.6672	+	13.6672i	−0.859251	+	0.859251i
$254$	6.30436	−	7.65421i	0.395571	−	0.480268i
$255$		0			0
$256$	11.4728	−	11.1523i	0.717052	−	0.697020i
$257$	6.96658	+	4.02216i	0.434563	+	0.250895i	0.701289	−	0.712877i	$-0.252608\pi$
$257$	6.96658	+	4.02216i	0.434563	+	0.250895i	−0.266726	+	0.963773i	$0.585942\pi$
$258$		0			0
$259$	0.00239268	−	0.00892960i	0.000148674	−	0.000554858i
$260$	24.4987	+	28.1358i	1.51935	+	1.74491i
$261$		0			0
$262$	−4.87970	+	10.7192i	−0.301469	+	0.662234i
$263$	3.65553	−	2.11052i	0.225409	−	0.130140i	−0.383043	−	0.923730i	$-0.625124\pi$
$263$	3.65553	−	2.11052i	0.225409	−	0.130140i	0.608452	+	0.793590i	$0.291791\pi$
$264$		0			0
$265$	2.57860	+	1.48876i	0.158402	+	0.0914535i
$266$	0.0187846	−	0.0134106i	0.00115176	−	0.000822255i
$267$		0			0
$268$	−7.06588	−	14.4570i	−0.431618	−	0.883104i
$269$	13.7834	+	13.7834i	0.840386	+	0.840386i	0.988909	−	0.148523i	$-0.0474518\pi$
$269$	13.7834	+	13.7834i	0.840386	+	0.840386i	−0.148523	+	0.988909i	$0.547452\pi$
$270$		0			0
$271$			14.3202i			0.869889i	0.900457	+	0.434945i	$0.143232\pi$
$271$			14.3202i			0.869889i	−0.900457	+	0.434945i	$0.856768\pi$
$272$	5.08245	+	12.5202i	0.308169	+	0.759149i
$273$		0			0
$274$	1.26596	−	7.58420i	0.0764792	−	0.458178i
$275$	−2.30708	−	8.61014i	−0.139122	−	0.519211i
$276$		0			0
$277$	1.71354	−	6.39501i	0.102956	−	0.384239i	−0.895149	−	0.445767i	$-0.852931\pi$
$277$	1.71354	−	6.39501i	0.102956	−	0.384239i	0.998105	+	0.0615286i	$0.0195975\pi$
$278$	−8.24843	+	18.1193i	−0.494708	+	1.08672i
$279$		0			0
$280$	0.0192176	+	0.0645849i	0.00114847	+	0.00385969i
$281$	−1.84037	−	3.18761i	−0.109787	−	0.190157i	0.805897	−	0.592056i	$-0.201684\pi$
$281$	−1.84037	−	3.18761i	−0.109787	−	0.190157i	−0.915684	+	0.401899i	$0.868350\pi$
$282$		0			0
$283$	−1.12390	−	4.19445i	−0.0668089	−	0.249334i	0.924442	−	0.381321i	$-0.124531\pi$
$283$	−1.12390	−	4.19445i	−0.0668089	−	0.249334i	−0.991251	+	0.131987i	$0.957864\pi$
$284$	2.00730	−	0.391892i	0.119111	−	0.0232545i
$285$		0			0
$286$	22.5547	+	18.5771i	1.33369	+	1.09849i
$287$	−0.0449706			−0.00265453
$288$		0			0
$289$	5.58832			0.328725
$290$	−10.3881	−	8.55612i	−0.610010	−	0.502433i
$291$		0			0
$292$	14.3474	−	2.80108i	0.839615	−	0.163921i
$293$	−3.93269	−	14.6770i	−0.229750	−	0.857439i	−0.980446	−	0.196791i	$-0.936948\pi$
$293$	−3.93269	−	14.6770i	−0.229750	−	0.857439i	0.750695	−	0.660649i	$-0.229719\pi$
$294$		0			0
$295$	13.1963	+	22.8567i	0.768320	+	1.33077i
$296$	−2.95092	+	0.878062i	−0.171519	+	0.0510363i
$297$		0			0
$298$	5.56393	−	12.2222i	0.322310	−	0.708015i
$299$	10.7061	−	39.9558i	0.619152	−	2.31071i
$300$		0			0
$301$	0.0136491	+	0.0509393i	0.000786723	+	0.00293609i
$302$	1.05590	−	6.32577i	0.0607602	−	0.364007i
$303$		0			0
$304$	−7.08049	−	2.99176i	−0.406094	−	0.171589i
$305$			28.6285i			1.63926i
$306$		0			0
$307$	23.4294	+	23.4294i	1.33718	+	1.33718i	0.898776	+	0.438408i	$0.144457\pi$
$307$	23.4294	+	23.4294i	1.33718	+	1.33718i	0.438408	+	0.898776i	$0.355543\pi$
$308$	0.0231751	+	0.0474169i	0.00132052	+	0.00270183i
$309$		0			0
$310$	−24.9867	+	17.8384i	−1.41915	+	1.01315i
$311$	25.9086	+	14.9583i	1.46914	+	0.848210i	0.999401	−	0.0345940i	$-0.0110138\pi$
$311$	25.9086	+	14.9583i	1.46914	+	0.848210i	0.469741	+	0.882804i	$0.344347\pi$
$312$		0			0
$313$	13.0513	−	7.53519i	0.737705	−	0.425914i	−0.0835293	−	0.996505i	$-0.526619\pi$
$313$	13.0513	−	7.53519i	0.737705	−	0.425914i	0.821234	+	0.570591i	$0.193286\pi$
$314$	−11.5913	+	25.4626i	−0.654136	+	1.43694i
$315$		0			0
$316$	6.61322	+	7.59502i	0.372023	+	0.427253i
$317$	−5.40325	+	20.1652i	−0.303477	+	1.13259i	0.630772	+	0.775969i	$0.282739\pi$
$317$	−5.40325	+	20.1652i	−0.303477	+	1.13259i	−0.934248	+	0.356623i	$0.883928\pi$
$318$		0			0
$319$	−9.12868	−	5.27045i	−0.511108	−	0.295088i
$320$	14.9749	−	16.7140i	0.837121	−	0.934340i
$321$		0			0
$322$	0.0475000	−	0.0576703i	0.00264707	−	0.00321384i
$323$	4.59023	−	4.59023i	0.255407	−	0.255407i
$324$		0			0
$325$	13.4894	+	13.4894i	0.748257	+	0.748257i
$326$	−1.21623	−	12.5769i	−0.0673608	−	0.696567i
$327$		0			0
$328$	7.84111	+	12.7602i	0.432953	+	0.704564i
$329$	0.000811309	−	0.00140523i	4.47289e−5	−	7.74727e-5i
$330$		0			0
$331$	−18.4453	−	4.94242i	−1.01385	−	0.271660i	−0.286612	−	0.958047i	$-0.592529\pi$
$331$	−18.4453	−	4.94242i	−1.01385	−	0.271660i	−0.727236	+	0.686387i	$0.759196\pi$
$332$	1.78463	−	25.8265i	0.0979446	−	1.41741i
$333$		0			0
$334$	−5.89534	−	15.7481i	−0.322579	−	0.861696i
$335$	−11.2846	−	19.5456i	−0.616546	−	1.06789i
$336$		0			0
$337$	−9.91944	+	17.1810i	−0.540346	+	0.935907i	0.458538	+	0.888675i	$0.348373\pi$
$337$	−9.91944	+	17.1810i	−0.540346	+	0.935907i	−0.998884	+	0.0472324i	$0.984960\pi$
$338$	−43.5481	−	7.26906i	−2.36871	−	0.395385i
$339$		0			0
$340$	8.32209	+	17.0273i	0.451329	+	0.923434i
$341$	−17.0032	+	17.0032i	−0.920774	+	0.920774i
$342$		0			0
$343$	−0.118899			−0.00641996
$344$	12.0739	−	12.7547i	0.650982	−	0.687687i
$345$		0			0
$346$	0.558219	−	0.398520i	0.0300100	−	0.0214245i
$347$	−20.9225	+	5.60618i	−1.12318	+	0.300955i	−0.772170	−	0.635416i	$-0.780829\pi$
$347$	−20.9225	+	5.60618i	−1.12318	+	0.300955i	−0.351011	+	0.936372i	$0.614162\pi$
$348$		0			0
$349$	1.59139	+	0.426410i	0.0851849	+	0.0228252i	0.301160	−	0.953574i	$-0.402626\pi$
$349$	1.59139	+	0.426410i	0.0851849	+	0.0228252i	−0.215975	+	0.976399i	$0.569293\pi$
$350$	0.0120802	+	0.0322694i	0.000645712	+	0.00172487i
$351$		0			0
$352$	9.41351	−	14.8435i	0.501742	−	0.791160i
$353$	3.91868	−	2.26245i	0.208570	−	0.120418i	−0.392076	−	0.919933i	$-0.628243\pi$
$353$	3.91868	−	2.26245i	0.208570	−	0.120418i	0.600647	+	0.799514i	$0.294910\pi$
$354$		0			0
$355$	2.77079	−	0.742431i	0.147058	−	0.0394042i
$356$	−6.96615	−	35.6811i	−0.369205	−	1.89110i
$357$		0			0
$358$	−13.7690	+	1.33151i	−0.727713	+	0.0703727i
$359$		−	11.0661i		−	0.584046i	−0.956411	−	0.292023i	$-0.905672\pi$
$359$		−	11.0661i		−	0.584046i	0.956411	−	0.292023i	$-0.0943284\pi$
$360$		0			0
$361$		−	15.3073i		−	0.805645i
$362$	−0.423045	−	4.37465i	−0.0222348	−	0.229926i
$363$		0			0
$364$	−0.0936923	−	0.0630842i	−0.00491081	−	0.00330651i
$365$	19.8045	−	5.30659i	1.03661	−	0.277760i
$366$		0			0
$367$	4.77772	−	2.75842i	0.249395	−	0.143988i	−0.370092	−	0.928995i	$-0.620674\pi$
$367$	4.77772	−	2.75842i	0.249395	−	0.143988i	0.619487	+	0.785007i	$0.287341\pi$
$368$	−24.6458	−	3.42244i	−1.28475	−	0.178407i
$369$		0			0
$370$	−4.04413	+	1.51393i	−0.210244	+	0.0787056i
$371$	−0.00870755	−	0.00233318i	−0.000452074	−	0.000121133i
$372$		0			0
$373$	−8.16763	+	2.18851i	−0.422904	+	0.113317i	−0.463993	−	0.885839i	$-0.653584\pi$
$373$	−8.16763	+	2.18851i	−0.422904	+	0.113317i	0.0410893	+	0.999155i	$0.486917\pi$
$374$	8.62498	+	12.0813i	0.445987	+	0.624708i
$375$		0			0
$376$	−0.540187	+	0.0148118i	−0.0278580	+	0.000763860i
$377$	22.5589			1.16184
$378$		0			0
$379$	20.4820	−	20.4820i	1.05209	−	1.05209i	0.0535254	−	0.998566i	$-0.482954\pi$
$379$	20.4820	−	20.4820i	1.05209	−	1.05209i	0.998566	−	0.0535254i	$-0.0170458\pi$
$380$	−10.1965	−	3.50157i	−0.523071	−	0.179627i
$381$		0			0
$382$	−2.94842	+	17.6636i	−0.150854	+	0.903750i
$383$	2.14427	−	3.71398i	0.109567	−	0.189776i	−0.806028	−	0.591878i	$-0.798387\pi$
$383$	2.14427	−	3.71398i	0.109567	−	0.189776i	0.915595	+	0.402102i	$0.131720\pi$
$384$		0			0
$385$	0.0370120	+	0.0641066i	0.00188630	+	0.00326718i
$386$	13.2312	−	4.95315i	0.673452	−	0.252109i
$387$		0			0
$388$	−4.96234	+	4.32086i	−0.251925	+	0.219359i
$389$	15.6680	+	4.19823i	0.794400	+	0.212859i	0.633124	−	0.774051i	$-0.281772\pi$
$389$	15.6680	+	4.19823i	0.794400	+	0.212859i	0.161276	+	0.986909i	$0.448439\pi$
$390$		0			0
$391$	10.5069	−	18.1985i	0.531358	−	0.920339i
$392$	10.3656	+	16.8685i	0.523544	+	0.851987i
$393$		0			0
$394$	−0.545232	+	0.0527260i	−0.0274684	+	0.00265630i
$395$	9.98779	+	9.98779i	0.502540	+	0.502540i
$396$		0			0
$397$	−2.22738	+	2.22738i	−0.111789	+	0.111789i	−0.760789	−	0.649000i	$-0.775188\pi$
$397$	−2.22738	+	2.22738i	−0.111789	+	0.111789i	0.649000	+	0.760789i	$0.275188\pi$
$398$	−19.7084	−	16.2327i	−0.987891	−	0.813673i
$399$		0			0
$400$	7.04999	−	9.05422i	0.352500	−	0.452711i
$401$	−7.43343	−	4.29169i	−0.371208	−	0.214317i	0.302778	−	0.953061i	$-0.402086\pi$
$401$	−7.43343	−	4.29169i	−0.371208	−	0.214317i	−0.673986	+	0.738744i	$0.735419\pi$
$402$		0			0
$403$	13.3193	−	49.7085i	0.663484	−	2.47616i
$404$	0.380786	−	5.51058i	0.0189448	−	0.274162i
$405$		0			0
$406$	0.0370839	+	0.0168817i	0.00184045	+	0.000837826i
$407$	−2.92907	+	1.69110i	−0.145189	+	0.0838246i
$408$		0			0
$409$	32.0886	+	18.5263i	1.58668	+	0.916068i	0.993850	+	0.110739i	$0.0353218\pi$
$409$	32.0886	+	18.5263i	1.58668	+	0.916068i	0.592828	+	0.805329i	$0.298012\pi$
$410$	12.2053	+	17.0963i	0.602777	+	0.844328i
$411$		0			0
$412$	20.9019	+	7.17790i	1.02976	+	0.353630i
$413$	−0.0565024	−	0.0565024i	−0.00278030	−	0.00278030i
$414$		0			0
$415$		−	36.3099i		−	1.78238i
$416$	−1.56359	+	37.5842i	−0.0766612	+	1.84272i
$417$		0			0
$418$	−8.32888	−	1.39026i	−0.407379	−	0.0679997i
$419$	5.35101	+	19.9702i	0.261414	+	0.975609i	0.964409	+	0.264415i	$0.0851788\pi$
$419$	5.35101	+	19.9702i	0.261414	+	0.975609i	−0.702995	+	0.711195i	$0.748155\pi$
$420$		0			0
$421$	2.50791	−	9.35966i	0.122228	−	0.456162i	−0.877497	−	0.479581i	$-0.840789\pi$
$421$	2.50791	−	9.35966i	0.122228	−	0.456162i	0.999726	+	0.0234192i	$0.00745525\pi$
$422$	−3.11048	−	1.41598i	−0.151416	−	0.0689290i
$423$		0			0
$424$	0.856228	+	2.87754i	0.0415821	+	0.139746i
$425$	4.84559	+	8.39281i	0.235046	+	0.407111i
$426$		0			0
$427$	−0.0224333	−	0.0837222i	−0.00108562	−	0.00405160i
$428$	−3.05772	+	4.54130i	−0.147800	+	0.219512i
$429$		0			0
$430$	15.6610	−	19.0142i	0.755240	−	0.916947i
$431$	−25.3669			−1.22188			−0.610941	−	0.791676i	$-0.709209\pi$
$431$	−25.3669			−1.22188			−0.610941	+	0.791676i	$0.709209\pi$
$432$		0			0
$433$	−10.5243			−0.505764			−0.252882	−	0.967497i	$-0.581378\pi$
$433$	−10.5243			−0.505764			−0.252882	+	0.967497i	$0.581378\pi$
$434$	0.0590940	−	0.0717468i	0.00283660	−	0.00344396i
$435$		0			0
$436$	14.0393	+	9.45285i	0.672360	+	0.452709i
$437$	3.09387	+	11.5465i	0.148000	+	0.552343i
$438$		0			0
$439$	1.65348	+	2.86391i	0.0789163	+	0.136687i	0.902783	−	0.430097i	$-0.141521\pi$
$439$	1.65348	+	2.86391i	0.0789163	+	0.136687i	−0.823866	+	0.566784i	$0.808187\pi$
$440$	11.7365	−	21.6797i	0.559516	−	1.03354i
$441$		0			0
$442$	−28.9134	−	13.1623i	−1.37527	−	0.626065i
$443$	1.45346	−	5.42439i	0.0690560	−	0.257721i	−0.922764	−	0.385366i	$-0.874075\pi$
$443$	1.45346	−	5.42439i	0.0690560	−	0.257721i	0.991820	+	0.127645i	$0.0407419\pi$
$444$		0			0
$445$	−13.1972	−	49.2527i	−0.625608	−	2.33480i
$446$	0.0458403	+	0.00765168i	0.00217060	+	0.000362317i
$447$		0			0
$448$	−0.0306960	+	0.0606134i	−0.00145025	+	0.00286371i
$449$			3.76456i			0.177661i	0.996047	+	0.0888303i	$0.0283129\pi$
$449$			3.76456i			0.177661i	−0.996047	+	0.0888303i	$0.971687\pi$
$450$		0			0
$451$	11.6339	+	11.6339i	0.547818	+	0.547818i
$452$	8.84065	−	25.7438i	0.415829	−	1.21089i
$453$		0			0
$454$	−15.2328	−	21.3371i	−0.714912	−	1.00140i
$455$	−0.137197	−	0.0792106i	−0.00643189	−	0.00371345i
$456$		0			0
$457$	−18.4633	+	10.6598i	−0.863675	+	0.498643i	−0.865241	−	0.501356i	$-0.832835\pi$
$457$	−18.4633	+	10.6598i	−0.863675	+	0.498643i	0.00156649	+	0.999999i	$0.499501\pi$
$458$	−35.1209	−	15.9881i	−1.64109	−	0.747075i
$459$		0			0
$460$	−34.8162	−	2.40583i	−1.62331	−	0.112172i
$461$	10.0471	−	37.4962i	0.467938	−	1.74637i	−0.179021	−	0.983845i	$-0.557293\pi$
$461$	10.0471	−	37.4962i	0.467938	−	1.74637i	0.646959	−	0.762525i	$-0.276040\pi$
$462$		0			0
$463$	−7.29597	−	4.21233i	−0.339073	−	0.195764i	0.320789	−	0.947151i	$-0.396052\pi$
$463$	−7.29597	−	4.21233i	−0.339073	−	0.195764i	−0.659862	+	0.751387i	$0.729385\pi$
$464$	−1.67588	−	13.4659i	−0.0778008	−	0.625139i
$465$		0			0
$466$	8.10891	+	6.67887i	0.375638	+	0.309393i
$467$	19.4539	−	19.4539i	0.900219	−	0.900219i	−0.0952358	−	0.995455i	$-0.530361\pi$
$467$	19.4539	−	19.4539i	0.900219	−	0.900219i	0.995455	+	0.0952358i	$0.0303605\pi$
$468$		0			0
$469$	0.0483172	+	0.0483172i	0.00223108	+	0.00223108i
$470$	−0.754416	+	0.0729550i	−0.0347986	+	0.00336516i
$471$		0			0
$472$	−6.18049	+	25.8841i	−0.284480	+	1.19141i
$473$	9.64695	−	16.7090i	0.443567	−	0.768281i
$474$		0			0
$475$	−5.32501	−	1.42683i	−0.244328	−	0.0654676i
$476$	−0.0376800	−	0.0432740i	−0.00172706	−	0.00198346i
$477$		0			0
$478$	−7.07854	+	2.64987i	−0.323765	+	0.121202i
$479$	10.4276	+	18.0611i	0.476450	+	0.825235i	0.999636	−	0.0269835i	$-0.00859016\pi$
$479$	10.4276	+	18.0611i	0.476450	+	0.825235i	−0.523186	+	0.852218i	$0.675257\pi$
$480$		0			0
$481$	3.61918	−	6.26860i	0.165020	−	0.285824i
$482$	5.09051	−	30.4966i	0.231866	−	1.38908i
$483$		0			0
$484$	−0.874033	+	2.54517i	−0.0397288	+	0.115689i
$485$	−6.52570	+	6.52570i	−0.296317	+	0.296317i
$486$		0			0
$487$	34.0126			1.54126			0.770629	−	0.637284i	$-0.219942\pi$
$487$	34.0126			1.54126			0.770629	+	0.637284i	$0.219942\pi$
$488$	−19.8443	+	20.9632i	−0.898309	+	0.948961i
$489$		0			0
$490$	16.1349	+	22.6007i	0.728902	+	1.02100i
$491$	−1.41342	+	0.378725i	−0.0637868	+	0.0170916i	−0.290571	−	0.956853i	$-0.593845\pi$
$491$	−1.41342	+	0.378725i	−0.0637868	+	0.0170916i	0.226785	+	0.973945i	$0.427179\pi$
$492$		0			0
$493$	11.0696	+	2.96609i	0.498550	+	0.133586i
$494$	16.9245	−	6.33574i	0.761469	−	0.285059i
$495$		0			0
$496$	−30.6615	−	4.25781i	−1.37674	−	0.191181i
$497$	−0.00752124	+	0.00434239i	−0.000337374	+	0.000194783i
$498$		0			0
$499$	−35.2078	+	9.43390i	−1.57612	+	0.422319i	−0.937721	−	0.347389i	$-0.887068\pi$
$499$	−35.2078	+	9.43390i	−1.57612	+	0.422319i	−0.638396	+	0.769708i	$0.720402\pi$
$500$	−6.67788	+	9.91793i	−0.298644	+	0.443543i
$501$		0			0
$502$	−3.54374	−	36.6453i	−0.158165	−	1.63556i
$503$		−	10.8529i		−	0.483908i	−0.970288	−	0.241954i	$-0.922212\pi$
$503$		−	10.8529i		−	0.483908i	0.970288	−	0.241954i	$-0.0777882\pi$
$504$		0			0
$505$		−	7.74741i		−	0.344755i
$506$	−27.2075	+	2.63107i	−1.20952	+	0.116965i
$507$		0			0
$508$	13.7638	−	2.68716i	0.610671	−	0.119223i
$509$	−3.94598	+	1.05732i	−0.174903	+	0.0468650i	−0.345207	−	0.938526i	$-0.612191\pi$
$509$	−3.94598	+	1.05732i	−0.174903	+	0.0468650i	0.170305	+	0.985391i	$0.445525\pi$
$510$		0			0
$511$	−0.0537587	+	0.0310376i	−0.00237814	+	0.00137302i
$512$	22.5509	−	1.85875i	0.996620	−	0.0821460i
$513$		0			0
$514$	3.98847	+	10.6543i	0.175924	+	0.469941i
$515$	29.9407	+	8.02259i	1.31934	+	0.353517i
$516$		0			0
$517$	−0.573417	+	0.153647i	−0.0252189	+	0.00675737i
$518$	0.0106405	−	0.00759639i	0.000467516	−	0.000333766i
$519$		0			0
$520$	1.44612	+	52.7402i	0.0634167	+	2.31281i
$521$	−13.4286			−0.588318			−0.294159	−	0.955757i	$-0.595039\pi$
$521$	−13.4286			−0.588318			−0.294159	+	0.955757i	$0.595039\pi$
$522$		0			0
$523$	23.5806	−	23.5806i	1.03111	−	1.03111i	0.0316083	−	0.999500i	$-0.489937\pi$
$523$	23.5806	−	23.5806i	1.03111	−	1.03111i	0.999500	−	0.0316083i	$-0.0100629\pi$
$524$	−14.9644	+	7.31385i	−0.653722	+	0.319507i
$525$		0			0
$526$	5.88799	+	0.982823i	0.256728	+	0.0428531i
$527$	13.0715	−	22.6405i	0.569404	−	0.986237i
$528$		0			0
$529$	7.84782	+	13.5928i	0.341210	+	0.590992i
$530$	1.47629	+	3.94357i	0.0641258	+	0.171298i
$531$		0			0
$532$	0.0325629	+	0.00225013i	0.00141178	+	9.75554e-5i
$533$	−34.0114	−	9.11332i	−1.47320	−	0.394742i
$534$		0			0
$535$	−3.83937	+	6.64999i	−0.165991	+	0.287504i
$536$	5.28515	−	22.1344i	0.228284	−	0.956061i
$537$		0			0
$538$	2.65343	+	27.4387i	0.114397	+	1.18297i
$539$	15.3795	+	15.3795i	0.662443	+	0.662443i
$540$		0			0
$541$	−31.9545	+	31.9545i	−1.37383	+	1.37383i	−0.519148	+	0.854684i	$0.673751\pi$
$541$	−31.9545	+	31.9545i	−1.37383	+	1.37383i	−0.854684	+	0.519148i	$0.826249\pi$
$542$	−12.8753	+	15.6321i	−0.553042	+	0.671455i
$543$		0			0
$544$	−5.70888	+	18.2368i	−0.244766	+	0.781898i
$545$	20.5582	+	11.8693i	0.880618	+	0.508425i
$546$		0			0
$547$	2.76131	−	10.3053i	0.118065	−	0.440625i	−0.881433	−	0.472309i	$-0.843421\pi$
$547$	2.76131	−	10.3053i	0.118065	−	0.440625i	0.999498	+	0.0316846i	$0.0100872\pi$
$548$	8.20090	−	7.14078i	0.350325	−	0.305039i
$549$		0			0
$550$	5.22296	−	11.4732i	0.222708	−	0.489220i
$551$	−5.64571	+	3.25955i	−0.240515	+	0.138862i
$552$		0			0
$553$	−0.0370351	−	0.0213822i	−0.00157489	−	0.000909265i
$554$	7.62028	−	5.44022i	0.323755	−	0.231133i
$555$		0			0
$556$	−25.2951	+	12.3630i	−1.07275	+	0.524309i
$557$	−11.6850	−	11.6850i	−0.495109	−	0.495109i	0.414802	−	0.909912i	$-0.363851\pi$
$557$	−11.6850	−	11.6850i	−0.495109	−	0.495109i	−0.909912	+	0.414802i	$0.863851\pi$
$558$		0			0
$559$			41.2915i			1.74645i
$560$	−0.0370903	+	0.0877802i	−0.00156735	+	0.00370939i
$561$		0			0
$562$	0.857020	−	5.13431i	0.0361512	−	0.216578i
$563$	−2.31677	−	8.64631i	−0.0976403	−	0.364398i	0.899766	−	0.436372i	$-0.143737\pi$
$563$	−2.31677	−	8.64631i	−0.0976403	−	0.364398i	−0.997407	+	0.0719737i	$0.977070\pi$
$564$		0			0
$565$	9.88100	−	36.8764i	0.415697	−	1.55140i
$566$	2.54438	−	5.58921i	0.106948	−	0.234932i
$567$		0			0
$568$	2.54354	+	1.37697i	0.106725	+	0.0577765i
$569$	−6.28570	−	10.8872i	−0.263510	−	0.456413i	0.703662	−	0.710535i	$-0.251547\pi$
$569$	−6.28570	−	10.8872i	−0.263510	−	0.456413i	−0.967172	+	0.254122i	$0.918214\pi$
$570$		0			0
$571$	−3.72510	−	13.9023i	−0.155890	−	0.581791i	−0.999027	−	0.0440924i	$-0.985960\pi$
$571$	−3.72510	−	13.9023i	−0.155890	−	0.581791i	0.843137	−	0.537699i	$-0.180706\pi$
$572$	7.91828	+	40.5580i	0.331080	+	1.69582i
$573$		0			0
$574$	−0.0490904	−	0.0404331i	−0.00204899	−	0.00168765i
$575$	−17.8457			−0.744216
$576$		0			0
$577$	17.0561			0.710056			0.355028	−	0.934856i	$-0.384471\pi$
$577$	17.0561			0.710056			0.355028	+	0.934856i	$0.384471\pi$
$578$	6.10028	+	5.02447i	0.253738	+	0.208990i
$579$		0			0
$580$	−3.64694	−	18.6799i	−0.151431	−	0.775641i
$581$	0.0284525	+	0.106186i	0.00118041	+	0.00440534i
$582$		0			0
$583$	1.64905	+	2.85623i	0.0682965	+	0.118293i
$584$	18.1802	+	9.84204i	0.752302	+	0.407266i
$585$		0			0
$586$	8.90315	−	19.5575i	0.367786	−	0.807912i
$587$	−4.63428	+	17.2954i	−0.191277	+	0.713856i	0.801922	+	0.597428i	$0.203811\pi$
$587$	−4.63428	+	17.2954i	−0.191277	+	0.713856i	−0.993199	+	0.116427i	$0.962856\pi$
$588$		0			0
$589$	3.84904	+	14.3648i	0.158597	+	0.591891i
$590$	−6.14525	+	36.8155i	−0.252996	+	1.51567i
$591$		0			0
$592$	−4.01073	−	1.69468i	−0.164840	−	0.0696508i
$593$		−	25.5455i		−	1.04903i	−0.851402	−	0.524514i	$-0.824247\pi$
$593$		−	25.5455i		−	1.04903i	0.851402	−	0.524514i	$-0.175753\pi$
$594$		0			0
$595$	−0.0569073	−	0.0569073i	−0.00233297	−	0.00233297i
$596$	17.0627	−	8.33939i	0.698914	−	0.341595i
$597$		0			0
$598$	47.6113	−	33.9904i	1.94697	−	1.38997i
$599$	−1.66118	−	0.959083i	−0.0678740	−	0.0391871i	0.465679	−	0.884954i	$-0.345810\pi$
$599$	−1.66118	−	0.959083i	−0.0678740	−	0.0391871i	−0.533553	+	0.845767i	$0.679143\pi$
$600$		0			0
$601$	7.76786	−	4.48478i	0.316858	−	0.182938i	−0.333133	−	0.942880i	$-0.608106\pi$
$601$	7.76786	−	4.48478i	0.316858	−	0.182938i	0.649991	+	0.759942i	$0.274773\pi$
$602$	−0.0309000	+	0.0678779i	−0.00125939	+	0.00276650i
$603$		0			0
$604$	6.84015	−	5.95593i	0.278322	−	0.242343i
$605$	−0.976888	+	3.64579i	−0.0397161	+	0.148223i
$606$		0			0
$607$	20.1239	+	11.6185i	0.816802	+	0.471581i	0.849312	−	0.527890i	$-0.177017\pi$
$607$	20.1239	+	11.6185i	0.816802	+	0.471581i	−0.0325103	+	0.999471i	$0.510350\pi$
$608$	−5.03924	−	9.63192i	−0.204368	−	0.390626i
$609$		0			0
$610$	−25.7399	+	31.2512i	−1.04218	+	1.26532i
$611$	0.898366	−	0.898366i	0.0363440	−	0.0363440i
$612$		0			0
$613$	18.6158	+	18.6158i	0.751886	+	0.751886i	0.974831	−	0.222945i	$-0.0715670\pi$
$613$	18.6158	+	18.6158i	0.751886	+	0.751886i	−0.222945	+	0.974831i	$0.571567\pi$
$614$	4.51038	+	46.6411i	0.182024	+	1.88228i
$615$		0			0
$616$	−0.0173345	+	0.0725976i	−0.000698427	+	0.00292504i
$617$	−18.3062	+	31.7073i	−0.736981	+	1.27649i	0.216868	+	0.976201i	$0.430416\pi$
$617$	−18.3062	+	31.7073i	−0.736981	+	1.27649i	−0.953849	+	0.300288i	$0.902917\pi$
$618$		0			0
$619$	−25.6443	−	6.87138i	−1.03073	−	0.276184i	−0.296465	−	0.955044i	$-0.595808\pi$
$619$	−25.6443	−	6.87138i	−1.03073	−	0.276184i	−0.734268	+	0.678860i	$0.762474\pi$
$620$	−43.3143	−	2.99306i	−1.73954	−	0.120204i
$621$		0			0
$622$	14.8331	+	39.6232i	0.594752	+	1.58875i
$623$	0.0771889	+	0.133695i	0.00309251	+	0.00535638i
$624$		0			0
$625$	−15.5570	+	26.9455i	−0.622280	+	1.07782i
$626$	21.0219	+	3.50898i	0.840204	+	0.140247i
$627$		0			0
$628$	−35.5467	+	17.3734i	−1.41847	+	0.693276i
$629$	2.60013	−	2.60013i	0.103674	−	0.103674i
$630$		0			0
$631$	−28.2467			−1.12449			−0.562243	−	0.826972i	$-0.690061\pi$
$631$	−28.2467			−1.12449			−0.562243	+	0.826972i	$0.690061\pi$
$632$	0.390369	+	14.2368i	0.0155280	+	0.566308i
$633$		0			0
$634$	−24.0288	+	17.1545i	−0.954307	+	0.681293i
$635$	18.9990	−	5.09076i	0.753952	−	0.202021i
$636$		0			0
$637$	−44.9617	−	12.0475i	−1.78145	−	0.477338i
$638$	−5.22631	−	13.9609i	−0.206911	−	0.552717i
$639$		0			0
$640$	31.3743	−	4.78124i	1.24018	−	0.188995i
$641$	−14.4080	+	8.31845i	−0.569081	+	0.328559i	−0.756782	−	0.653667i	$-0.773230\pi$
$641$	−14.4080	+	8.31845i	−0.569081	+	0.328559i	0.187701	+	0.982226i	$0.439896\pi$
$642$		0			0
$643$	5.68404	−	1.52303i	0.224157	−	0.0600626i	−0.144993	−	0.989433i	$-0.546316\pi$
$643$	5.68404	−	1.52303i	0.224157	−	0.0600626i	0.369149	+	0.929370i	$0.379649\pi$
$644$	0.103703	−	0.0202463i	0.00408647	−	0.000797816i
$645$		0			0
$646$	9.13783	−	0.883664i	0.359523	−	0.0347673i
$647$			37.4518i			1.47238i	0.676773	+	0.736192i	$0.263378\pi$
$647$			37.4518i			1.47238i	−0.676773	+	0.736192i	$0.736622\pi$
$648$		0			0
$649$			29.2343i			1.14755i
$650$	2.59684	+	26.8535i	0.101856	+	1.05328i
$651$		0			0
$652$	9.98022	−	14.8226i	0.390856	−	0.580496i
$653$	21.2854	−	5.70340i	0.832962	−	0.223191i	0.182956	−	0.983121i	$-0.441433\pi$
$653$	21.2854	−	5.70340i	0.832962	−	0.223191i	0.650005	+	0.759930i	$0.274767\pi$
$654$		0			0
$655$	−20.2315	+	11.6807i	−0.790510	+	0.456401i
$656$	−2.91326	+	20.9791i	−0.113744	+	0.819098i
$657$		0			0
$658$	0.00214908		0.000804514i	8.37797e−5		3.13632e-5i
$659$	23.8609	+	6.39350i	0.929487	+	0.249055i	0.691636	−	0.722246i	$-0.256890\pi$
$659$	23.8609	+	6.39350i	0.929487	+	0.249055i	0.237851	+	0.971302i	$0.423557\pi$
$660$		0			0
$661$	3.57782	−	0.958674i	0.139161	−	0.0372881i	−0.188566	−	0.982060i	$-0.560384\pi$
$661$	3.57782	−	0.958674i	0.139161	−	0.0372881i	0.327727	+	0.944772i	$0.393717\pi$
$662$	−15.6914	−	21.9794i	−0.609864	−	0.854255i
$663$		0			0
$664$	25.1688	−	26.5879i	0.976739	−	1.03181i
$665$	0.0457807			0.00177530
$666$		0			0
$667$	−14.9221	+	14.9221i	−0.577785	+	0.577785i
$668$	7.72370	−	22.4913i	0.298839	−	0.870214i
$669$		0			0
$670$	5.25502	−	31.4822i	0.203019	−	1.21626i
$671$	−15.8554	+	27.4624i	−0.612091	+	1.06017i
$672$		0			0
$673$	17.3782	+	30.0999i	0.669880	+	1.16027i	0.977937	+	0.208898i	$0.0669877\pi$
$673$	17.3782	+	30.0999i	0.669880	+	1.16027i	−0.308058	+	0.951368i	$0.599679\pi$
$674$	−26.2756	+	9.83636i	−1.01210	+	0.378883i
$675$		0			0
$676$	−41.0020	−	47.0892i	−1.57700	−	1.81112i
$677$	24.4928	+	6.56283i	0.941335	+	0.252230i	0.696681	−	0.717381i	$-0.254659\pi$
$677$	24.4928	+	6.56283i	0.941335	+	0.252230i	0.244654	+	0.969611i	$0.421326\pi$
$678$		0			0
$679$	0.0139705	−	0.0241976i	0.000536137	−	0.000928617i
$680$	−6.22477	+	26.0696i	−0.238709	+	0.999723i
$681$		0			0
$682$	−33.8485	+	3.27328i	−1.29613	+	0.125340i
$683$	1.88928	+	1.88928i	0.0722912	+	0.0722912i	0.742328	−	0.670037i	$-0.233722\pi$
$683$	1.88928	+	1.88928i	0.0722912	+	0.0722912i	−0.670037	+	0.742328i	$0.733722\pi$
$684$		0			0
$685$	10.7845	−	10.7845i	0.412056	−	0.412056i
$686$	−0.129792	−	0.106903i	−0.00495548	−	0.00408156i
$687$		0			0
$688$	24.6478	−	3.06751i	0.939688	−	0.116948i
$689$	−6.11273	−	3.52918i	−0.232876	−	0.134451i
$690$		0			0
$691$	−5.19868	+	19.4017i	−0.197767	+	0.738077i	0.793766	+	0.608223i	$0.208117\pi$
$691$	−5.19868	+	19.4017i	−0.197767	+	0.738077i	−0.991533	+	0.129854i	$0.958549\pi$
$692$	0.967668	+	0.0668667i	0.0367852	+	0.00254189i
$693$		0			0
$694$	−27.8798	−	12.6917i	−1.05830	−	0.481771i
$695$	−34.1985	+	19.7445i	−1.29722	+	0.748951i
$696$		0			0
$697$	−15.4910	−	8.94375i	−0.586765	−	0.338769i
$698$	1.35379	+	1.89629i	0.0512416	+	0.0717757i
$699$		0			0
$700$	−0.0158267	+	0.0460870i	−0.000598192	+	0.00174192i
$701$	10.9010	+	10.9010i	0.411725	+	0.411725i	0.882339	−	0.470614i	$-0.155968\pi$
$701$	10.9010	+	10.9010i	0.411725	+	0.411725i	−0.470614	+	0.882339i	$0.655968\pi$
$702$		0			0
$703$			2.09175i			0.0788918i
$704$	23.6217	−	7.73960i	0.890276	−	0.291697i
$705$		0			0
$706$	6.31185	+	1.05358i	0.237550	+	0.0396518i
$707$	0.00607088	+	0.0226568i	0.000228319	+	0.000852098i
$708$		0			0
$709$	−4.14803	+	15.4807i	−0.155783	+	0.581389i	0.843254	+	0.537515i	$0.180637\pi$
$709$	−4.14803	+	15.4807i	−0.155783	+	0.581389i	−0.999037	+	0.0438741i	$0.986030\pi$
$710$	3.69215	+	1.68078i	0.138564	+	0.0630784i
$711$		0			0
$712$	24.4766	−	45.2132i	0.917300	−	1.69444i
$713$	24.0703	+	41.6911i	0.901441	+	1.56134i
$714$		0			0
$715$	15.0010	+	55.9845i	0.561006	+	2.09370i
$716$	−16.2275	−	10.9262i	−0.606452	−	0.408332i
$717$		0			0
$718$	9.94954	−	12.0799i	0.371314	−	0.450817i
$719$	−21.7763			−0.812119			−0.406060	−	0.913847i	$-0.633097\pi$
$719$	−21.7763			−0.812119			−0.406060	+	0.913847i	$0.633097\pi$
$720$		0			0
$721$	−0.0938463			−0.00349502
$722$	13.7628	−	16.7096i	0.512198	−	0.621866i
$723$		0			0
$724$	3.47145	−	5.15578i	0.129016	−	0.191613i
$725$	−2.51890	−	9.40068i	−0.0935497	−	0.349132i
$726$		0			0
$727$	−2.62325	−	4.54360i	−0.0972908	−	0.168513i	0.813272	−	0.581884i	$-0.197684\pi$
$727$	−2.62325	−	4.54360i	−0.0972908	−	0.168513i	−0.910562	+	0.413372i	$0.864351\pi$
$728$	−0.0455564	−	0.153102i	−0.00168843	−	0.00567435i
$729$		0			0
$730$	26.3899	+	12.0135i	0.976736	+	0.444639i
$731$	−5.42908	+	20.2616i	−0.200802	+	0.749403i
$732$		0			0
$733$	−3.41408	−	12.7415i	−0.126102	−	0.470618i	0.873775	−	0.486331i	$-0.161665\pi$
$733$	−3.41408	−	12.7415i	−0.126102	−	0.470618i	−0.999877	+	0.0157124i	$0.994998\pi$
$734$	7.69552	+	1.28454i	0.284047	+	0.0474131i
$735$		0			0
$736$	−23.8266	−	25.8951i	−0.878258	−	0.954506i
$737$		−	24.9993i		−	0.920860i
$738$		0			0
$739$	−23.2424	−	23.2424i	−0.854984	−	0.854984i	0.135758	−	0.990742i	$-0.456653\pi$
$739$	−23.2424	−	23.2424i	−0.854984	−	0.854984i	−0.990742	+	0.135758i	$0.956653\pi$
$740$	−5.77580	−	1.98346i	−0.212323	−	0.0729134i
$741$		0			0
$742$	−0.00740750	−	0.0103759i	−0.000271938	−	0.000380911i
$743$	−24.5336	−	14.1645i	−0.900049	−	0.519643i	−0.0228329	−	0.999739i	$-0.507269\pi$
$743$	−24.5336	−	14.1645i	−0.900049	−	0.519643i	−0.877216	+	0.480096i	$0.840602\pi$
$744$		0			0
$745$	23.0683	−	13.3185i	0.845159	−	0.487953i
$746$	−10.8836	−	4.95453i	−0.398476	−	0.181398i
$747$		0			0
$748$	−1.44717	+	20.9428i	−0.0529136	+	0.765744i
$749$	0.00601707	−	0.0224560i	0.000219859	−	0.000820525i
$750$		0			0
$751$	−22.5527	−	13.0208i	−0.822960	−	0.475136i	0.0284763	−	0.999594i	$-0.490934\pi$
$751$	−22.5527	−	13.0208i	−0.822960	−	0.475136i	−0.851436	+	0.524458i	$0.824268\pi$
$752$	−0.602992	−	0.469515i	−0.0219889	−	0.0171214i
$753$		0			0
$754$	24.6256	+	20.2828i	0.896812	+	0.738656i
$755$	8.99509	−	8.99509i	0.327365	−	0.327365i
$756$		0			0
$757$	4.87465	+	4.87465i	0.177172	+	0.177172i	0.790122	−	0.612950i	$-0.210017\pi$
$757$	4.87465	+	4.87465i	0.177172	+	0.177172i	−0.612950	+	0.790122i	$0.710017\pi$
$758$	40.7739	−	3.94299i	1.48097	−	0.143216i
$759$		0			0
$760$	−7.98237	−	12.9901i	−0.289551	−	0.471199i
$761$	−3.18964	+	5.52462i	−0.115624	+	0.200267i	−0.918029	−	0.396513i	$-0.870220\pi$
$761$	−3.18964	+	5.52462i	−0.115624	+	0.200267i	0.802405	+	0.596780i	$0.203554\pi$
$762$		0			0
$763$	−0.0694221	−	0.0186016i	−0.00251325	−	0.000673423i
$764$	−19.0999	+	16.6309i	−0.691012	+	0.601685i
$765$		0			0
$766$	5.67996	−	2.12631i	0.205225	−	0.0768267i
$767$	−31.2827	−	54.1832i	−1.12955	−	1.95644i
$768$		0			0
$769$	−9.57641	+	16.5868i	−0.345334	+	0.598136i	−0.985414	−	0.170172i	$-0.945568\pi$
$769$	−9.57641	+	16.5868i	−0.345334	+	0.598136i	0.640080	+	0.768308i	$0.278901\pi$
$770$	−0.0172357	+	0.103257i	−0.000621131	+	0.00372113i
$771$		0			0
$772$	18.8967	+	6.48930i	0.680109	+	0.233555i
$773$	26.0627	−	26.0627i	0.937411	−	0.937411i	−0.0607427	−	0.998153i	$-0.519347\pi$
$773$	26.0627	−	26.0627i	0.937411	−	0.937411i	0.998153	+	0.0607427i	$0.0193469\pi$
$774$		0			0
$775$	−22.2015			−0.797503
$776$	−9.30185	+	0.255054i	−0.333917	+	0.00915592i
$777$		0			0
$778$	13.3287	+	18.6700i	0.477859	+	0.669351i
$779$	9.82864	−	2.63358i	0.352148	−	0.0943577i
$780$		0			0
$781$	3.06912	+	0.822367i	0.109822	+	0.0294266i
$782$	27.8318	−	10.4189i	0.995264	−	0.372580i
$783$		0			0
$784$	−3.85122	+	27.7336i	−0.137544	+	0.990485i
$785$	−48.0583	+	27.7464i	−1.71527	+	0.990313i
$786$		0			0
$787$	11.0575	−	2.96285i	0.394158	−	0.105614i	−0.0562956	−	0.998414i	$-0.517929\pi$
$787$	11.0575	−	2.96285i	0.394158	−	0.105614i	0.450454	+	0.892800i	$0.351262\pi$
$788$	−0.642587	−	0.432663i	−0.0228912	−	0.0154130i
$789$		0			0
$790$	1.92275	+	19.8828i	0.0684082	+	0.707399i
$791$			0.115586i			0.00410975i
$792$		0			0
$793$		−	67.8655i		−	2.40997i
$794$	−4.43408	+	0.428793i	−0.157360	+	0.0152173i
$795$		0			0
$796$	−6.91901	−	35.4397i	−0.245238	−	1.25613i
$797$	4.17990	−	1.12000i	0.148060	−	0.0396725i	−0.184028	−	0.982921i	$-0.558914\pi$
$797$	4.17990	−	1.12000i	0.148060	−	0.0396725i	0.332088	+	0.943249i	$0.392247\pi$
$798$		0			0
$799$	0.558944	−	0.322706i	0.0197740	−	0.0114165i
$800$	15.8365	−	3.54503i	0.559906	−	0.125336i
$801$		0			0
$802$	−4.25575	−	11.3683i	−0.150276	−	0.401427i
$803$	21.9368	+	5.87794i	0.774132	+	0.207428i
$804$		0			0
$805$	0.143147	−	0.0383562i	0.00504528	−	0.00135188i
$806$	59.2325	−	42.2869i	2.08638	−	1.48949i
$807$		0			0
$808$	5.37025	−	5.67305i	0.188925	−	0.199577i
$809$	22.7884			0.801198			0.400599	−	0.916253i	$-0.368802\pi$
$809$	22.7884			0.801198			0.400599	+	0.916253i	$0.368802\pi$
$810$		0			0
$811$	−14.9053	+	14.9053i	−0.523396	+	0.523396i	−0.918595	−	0.395200i	$-0.870675\pi$
$811$	−14.9053	+	14.9053i	−0.523396	+	0.523396i	0.395200	+	0.918595i	$0.370675\pi$
$812$	0.0253029	+	0.0517705i	0.000887957	+	0.00181679i
$813$		0			0
$814$	−4.71787	−	0.787508i	−0.165361	−	0.0276022i
$815$	12.5315	−	21.7052i	0.438959	−	0.760299i
$816$		0			0
$817$	−5.96623	−	10.3338i	−0.208732	−	0.361535i
$818$	18.3712	+	49.0744i	0.642333	+	1.71585i
$819$		0			0
$820$	−2.04790	+	29.6364i	−0.0715158	+	1.03495i
$821$	−43.8854	−	11.7591i	−1.53161	−	0.410394i	−0.608067	−	0.793886i	$-0.708055\pi$
$821$	−43.8854	−	11.7591i	−1.53161	−	0.410394i	−0.923544	+	0.383492i	$0.874721\pi$
$822$		0			0
$823$	−22.8842	+	39.6366i	−0.797694	+	1.38165i	0.123421	+	0.992354i	$0.460614\pi$
$823$	−22.8842	+	39.6366i	−0.797694	+	1.38165i	−0.921115	+	0.389292i	$0.872720\pi$
$824$	16.3631	+	26.6284i	0.570036	+	0.927646i
$825$		0			0
$826$	−0.0108773	−	0.112480i	−0.000378468	−	0.00391369i
$827$	−22.0262	−	22.0262i	−0.765925	−	0.765925i	0.211461	−	0.977386i	$-0.432178\pi$
$827$	−22.0262	−	22.0262i	−0.765925	−	0.765925i	−0.977386	+	0.211461i	$0.932178\pi$
$828$		0			0
$829$	28.3392	−	28.3392i	0.984261	−	0.984261i	−0.0156173	−	0.999878i	$-0.504971\pi$
$829$	28.3392	−	28.3392i	0.984261	−	0.984261i	0.999878	+	0.0156173i	$0.00497134\pi$
$830$	32.6463	−	39.6363i	1.13317	−	1.37580i
$831$		0			0
$832$	−35.4988	+	39.6215i	−1.23070	+	1.37363i
$833$	−20.4785	−	11.8233i	−0.709539	−	0.409653i
$834$		0			0
$835$	8.63262	−	32.2174i	0.298744	−	1.11493i
$836$	−7.84191	−	9.00613i	−0.271218	−	0.311483i
$837$		0			0
$838$	−12.1140	+	26.6108i	−0.418473	+	0.919256i
$839$	−15.8724	+	9.16393i	−0.547976	+	0.316374i	−0.748305	−	0.663355i	$-0.769132\pi$
$839$	−15.8724	+	9.16393i	−0.547976	+	0.316374i	0.200329	+	0.979729i	$0.435799\pi$
$840$		0			0
$841$	15.1479	+	8.74565i	0.522342	+	0.301574i
$842$	11.1530	−	7.96225i	0.384356	−	0.274397i
$843$		0			0
$844$	−2.12232	−	4.34234i	−0.0730534	−	0.149470i
$845$	−61.9244	−	61.9244i	−2.13026	−	2.13026i
$846$		0			0
$847$		−	0.0114274i		−	0.000392650i
$848$	−1.65254	+	3.91100i	−0.0567483	+	0.134304i
$849$		0			0
$850$	−2.25649	+	13.5184i	−0.0773969	+	0.463676i
$851$	1.75252	+	6.54048i	0.0600755	+	0.224205i
$852$		0			0
$853$	6.36992	−	23.7728i	0.218102	−	0.813967i	−0.766950	−	0.641707i	$-0.778227\pi$
$853$	6.36992	−	23.7728i	0.218102	−	0.813967i	0.985052	−	0.172260i	$-0.0551068\pi$
$854$	0.0507863	−	0.111562i	0.00173787	−	0.00381757i
$855$		0			0
$856$	−7.42093	+	2.20814i	−0.253642	+	0.0754726i
$857$	−0.838395	−	1.45214i	−0.0286390	−	0.0496043i	0.851351	−	0.524597i	$-0.175784\pi$
$857$	−0.838395	−	1.45214i	−0.0286390	−	0.0496043i	−0.879990	+	0.474993i	$0.842451\pi$
$858$		0			0
$859$	3.61213	+	13.4806i	0.123244	+	0.459954i	0.999771	−	0.0213994i	$-0.00681216\pi$
$859$	3.61213	+	13.4806i	0.123244	+	0.459954i	−0.876527	+	0.481353i	$0.840145\pi$
$860$	34.1914	−	6.67531i	1.16592	−	0.227626i
$861$		0			0
$862$	−27.6908	−	22.8075i	−0.943154	−	0.776825i
$863$	31.6409			1.07707			0.538535	−	0.842603i	$-0.318978\pi$
$863$	31.6409			1.07707			0.538535	+	0.842603i	$0.318978\pi$
$864$		0			0
$865$	1.36046			0.0462570
$866$	−11.4884	−	9.46238i	−0.390392	−	0.321545i
$867$		0			0
$868$	0.129015	−	0.0251881i	0.00437907	−	0.000854941i
$869$	4.04940	+	15.1126i	0.137366	+	0.512658i
$870$		0			0
$871$	26.7509	+	46.3340i	0.906421	+	1.56997i
$872$	6.82639	+	22.9416i	0.231171	+	0.776900i
$873$		0			0
$874$	−7.00416	+	15.3860i	−0.236919	+	0.520438i
$875$	0.0131409	−	0.0490426i	0.000444244	−	0.00165794i
$876$		0			0
$877$	−7.88760	−	29.4369i	−0.266345	−	0.994014i	−0.961422	−	0.275078i	$-0.911296\pi$
$877$	−7.88760	−	29.4369i	−0.266345	−	0.994014i	0.695077	−	0.718936i	$-0.255370\pi$
$878$	−0.769991	+	4.61293i	−0.0259859	+	0.155679i
$879$		0			0
$880$	32.3039	−	13.1135i	1.08897	−	0.442054i
$881$			10.2116i			0.344037i	0.985094	+	0.172019i	$0.0550290\pi$
$881$			10.2116i			0.344037i	−0.985094	+	0.172019i	$0.944971\pi$
$882$		0			0
$883$	7.98299	+	7.98299i	0.268649	+	0.268649i	0.828556	−	0.559907i	$-0.189163\pi$
$883$	7.98299	+	7.98299i	0.268649	+	0.268649i	−0.559907	+	0.828556i	$0.689163\pi$
$884$	−19.7280	−	40.3642i	−0.663525	−	1.35759i
$885$		0			0
$886$	6.46370	−	4.61452i	0.217152	−	0.155028i
$887$	−9.34850	−	5.39736i	−0.313892	−	0.181226i	0.334775	−	0.942298i	$-0.391340\pi$
$887$	−9.34850	−	5.39736i	−0.313892	−	0.181226i	−0.648667	+	0.761073i	$0.724673\pi$
$888$		0			0
$889$	−0.0515723	+	0.0297753i	−0.00172968	+	0.000998630i
$890$	29.8769	−	65.6304i	1.00148	−	2.19994i
$891$		0			0
$892$	0.0431602	+	0.0495678i	0.00144511	+	0.00165965i
$893$	−0.0950241	+	0.354635i	−0.00317986	+	0.0118674i
$894$		0			0
$895$	−23.7626	−	13.7193i	−0.794295	−	0.458586i
$896$	−0.0880057	+	0.0385674i	−0.00294006	+	0.00128845i
$897$		0			0
$898$	−3.38472	+	4.10944i	−0.112950	+	0.137134i
$899$	−18.5643	+	18.5643i	−0.619155	+	0.619155i
$900$		0			0
$901$	−2.53547	−	2.53547i	−0.0844688	−	0.0844688i
$902$	2.23963	+	23.1597i	0.0745716	+	0.771134i
$903$		0			0
$904$	32.7969	−	20.1536i	1.09081	−	0.670299i
$905$	4.35887	−	7.54978i	0.144894	−	0.250963i
$906$		0			0
$907$	7.67746	+	2.05717i	0.254926	+	0.0683072i	0.384019	−	0.923325i	$-0.374540\pi$
$907$	7.67746	+	2.05717i	0.254926	+	0.0683072i	−0.129093	+	0.991633i	$0.541206\pi$
$908$	2.55588	−	36.9877i	0.0848199	−	1.22748i
$909$		0			0
$910$	−0.0785472	−	0.209821i	−0.00260382	−	0.00695550i
$911$	17.5142	+	30.3354i	0.580270	+	1.00506i	0.995447	+	0.0953171i	$0.0303865\pi$
$911$	17.5142	+	30.3354i	0.580270	+	1.00506i	−0.415176	+	0.909741i	$0.636280\pi$
$912$		0			0
$913$	20.1096	−	34.8309i	0.665532	−	1.15274i
$914$	−29.7389	−	4.96402i	−0.983676	−	0.164195i
$915$		0			0
$916$	−23.9635	−	49.0301i	−0.791776	−	1.62000i
$917$	0.0500128	−	0.0500128i	0.00165157	−	0.00165157i
$918$		0			0
$919$	25.9311			0.855387			0.427694	−	0.903924i	$-0.359326\pi$
$919$	25.9311			0.855387			0.427694	+	0.903924i	$0.359326\pi$
$920$	−35.8427	−	33.9295i	−1.18170	−	1.11862i
$921$		0			0
$922$	44.6804	−	31.8979i	1.47147	−	1.05050i
$923$	−6.56833	+	1.75998i	−0.216199	+	0.0579304i
$924$		0			0
$925$	−3.01634	−	0.808226i	−0.0991767	−	0.0265743i
$926$	−4.17705	−	11.1580i	−0.137266	−	0.366676i
$927$		0			0
$928$	10.2778	−	16.2063i	0.337386	−	0.531999i
$929$	23.3443	−	13.4779i	0.765903	−	0.442194i	−0.0655082	−	0.997852i	$-0.520867\pi$
$929$	23.3443	−	13.4779i	0.765903	−	0.442194i	0.831411	+	0.555658i	$0.187534\pi$
$930$		0			0
$931$	12.9931	−	3.48148i	0.425831	−	0.114101i
$932$	2.84679	+	14.5815i	0.0932497	+	0.477632i
$933$		0			0
$934$	38.7271	−	3.74506i	1.26719	−	0.122542i
$935$			29.4438i			0.962914i
$936$		0			0
$937$			5.72005i			0.186866i	0.995626	+	0.0934330i	$0.0297841\pi$
$937$			5.72005i			0.186866i	−0.995626	+	0.0934330i	$0.970216\pi$
$938$	0.00930153	+	0.0961857i	0.000303706	+	0.00314057i
$939$		0			0
$940$	−0.889123	−	0.598659i	−0.0290000	−	0.0195261i
$941$	−22.9223	+	6.14201i	−0.747245	+	0.200224i	−0.612296	−	0.790629i	$-0.709754\pi$
$941$	−22.9223	+	6.14201i	−0.747245	+	0.200224i	−0.134949	+	0.990853i	$0.543087\pi$
$942$		0			0
$943$	28.5257	−	16.4693i	0.928925	−	0.536315i
$944$	−30.0192	+	22.6985i	−0.977040	+	0.738774i
$945$		0			0
$946$	25.5538	−	9.56615i	0.830826	−	0.311022i
$947$	−52.2601	−	14.0030i	−1.69822	−	0.455038i	−0.725732	−	0.687977i	$-0.758499\pi$
$947$	−52.2601	−	14.0030i	−1.69822	−	0.455038i	−0.972491	+	0.232940i	$0.925166\pi$
$948$		0			0
$949$	−46.9477	+	12.5796i	−1.52399	+	0.408351i
$950$	−4.52998	−	6.34527i	−0.146972	−	0.205868i
$951$		0			0
$952$	−0.00222420	−	0.0811166i	−7.20867e−5	−	0.00262901i
$953$	2.80246			0.0907805			0.0453902	−	0.998969i	$-0.485547\pi$
$953$	2.80246			0.0907805			0.0453902	+	0.998969i	$0.485547\pi$
$954$		0			0
$955$	−25.1173	+	25.1173i	−0.812775	+	0.812775i
$956$	−10.1095	−	3.47169i	−0.326965	−	0.112283i
$957$		0			0
$958$	−4.85591	+	29.0912i	−0.156887	+	0.939895i
$959$	−0.0230880	+	0.0399895i	−0.000745550	+	0.00129133i
$960$		0			0
$961$	14.4456	+	25.0204i	0.465986	+	0.807111i
$962$	9.58685	−	3.58887i	0.309093	−	0.115710i
$963$		0			0
$964$	32.9764	−	28.7136i	1.06210	−	0.924803i
$965$	27.0684	+	7.25296i	0.871363	+	0.233481i
$966$		0			0
$967$	−7.66141	+	13.2699i	−0.246374	+	0.426733i	−0.962517	−	0.271221i	$-0.912573\pi$
$967$	−7.66141	+	13.2699i	−0.246374	+	0.426733i	0.716143	+	0.697954i	$0.245906\pi$
$968$	−3.24247	+	1.99249i	−0.104217	+	0.0640411i
$969$		0			0
$970$	−12.9908	+	1.25626i	−0.417109	+	0.0403361i
$971$	22.7938	+	22.7938i	0.731487	+	0.731487i	0.970914	−	0.239428i	$-0.0769598\pi$
$971$	22.7938	+	22.7938i	0.731487	+	0.731487i	−0.239428	+	0.970914i	$0.576960\pi$
$972$		0			0
$973$	0.0845395	−	0.0845395i	0.00271021	−	0.00271021i
$974$	37.1286	+	30.5808i	1.18968	+	0.979872i
$975$		0			0
$976$	−40.5103	+	5.04166i	−1.29670	+	0.161380i
$977$	20.2451	+	11.6885i	0.647699	+	0.373949i	0.787574	−	0.616220i	$-0.211337\pi$
$977$	20.2451	+	11.6885i	0.647699	+	0.373949i	−0.139875	+	0.990169i	$0.544670\pi$
$978$		0			0
$979$	14.6181	−	54.5556i	0.467197	−	1.74360i
$980$	−2.70724	+	39.1781i	−0.0864797	+	1.25150i
$981$		0			0
$982$	−1.88342	−	0.857389i	−0.0601023	−	0.0273604i
$983$	30.2556	−	17.4681i	0.965005	−	0.557146i	0.0672949	−	0.997733i	$-0.478563\pi$
$983$	30.2556	−	17.4681i	0.965005	−	0.557146i	0.897710	+	0.440587i	$0.145230\pi$
$984$		0			0
$985$	−0.940963	−	0.543265i	−0.0299816	−	0.0173099i
$986$	9.41688	+	13.1905i	0.299895	+	0.420071i
$987$		0			0
$988$	24.1715	+	8.30069i	0.768997	+	0.264080i
$989$	−27.3131	−	27.3131i	−0.868507	−	0.868507i
$990$		0			0
$991$			58.5560i			1.86009i	0.367440	+	0.930047i	$0.380234\pi$
$991$			58.5560i			1.86009i	−0.367440	+	0.930047i	$0.619766\pi$
$992$	−29.6423	−	32.2157i	−0.941143	−	1.02285i
$993$		0			0
$994$	−0.0121145	−	0.00202216i	−0.000384249	−	6.41390e-5i
$995$	−13.1079	−	48.9194i	−0.415549	−	1.55085i
$996$		0			0
$997$	−11.7727	+	43.9362i	−0.372844	+	1.39147i	0.483624	+	0.875276i	$0.339320\pi$
$997$	−11.7727	+	43.9362i	−0.372844	+	1.39147i	−0.856469	+	0.516199i	$0.827347\pi$
$998$	−46.9153	−	21.3572i	−1.48508	−	0.676051i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.v.a.395.17		88
3.2	odd	2		144.2.u.a.59.6	yes	88
4.3	odd	2		1728.2.z.a.719.18		88
9.2	odd	6	inner	432.2.v.a.251.9		88
9.7	even	3		144.2.u.a.11.14	✓	88
12.11	even	2		576.2.y.a.527.16		88
16.3	odd	4	inner	432.2.v.a.179.9		88
16.13	even	4		1728.2.z.a.1583.18		88
36.7	odd	6		576.2.y.a.335.5		88
36.11	even	6		1728.2.z.a.143.18		88
48.29	odd	4		576.2.y.a.239.5		88
48.35	even	4		144.2.u.a.131.14	yes	88
144.29	odd	12		1728.2.z.a.1007.18		88
144.61	even	12		576.2.y.a.47.16		88
144.83	even	12	inner	432.2.v.a.35.17		88
144.115	odd	12		144.2.u.a.83.6	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.14	✓	88	9.7	even	3
144.2.u.a.59.6	yes	88	3.2	odd	2
144.2.u.a.83.6	yes	88	144.115	odd	12
144.2.u.a.131.14	yes	88	48.35	even	4
432.2.v.a.35.17		88	144.83	even	12	inner
432.2.v.a.179.9		88	16.3	odd	4	inner
432.2.v.a.251.9		88	9.2	odd	6	inner
432.2.v.a.395.17		88	1.1	even	1	trivial
576.2.y.a.47.16		88	144.61	even	12
576.2.y.a.239.5		88	48.29	odd	4
576.2.y.a.335.5		88	36.7	odd	6
576.2.y.a.527.16		88	12.11	even	2
1728.2.z.a.143.18		88	36.11	even	6
1728.2.z.a.719.18		88	4.3	odd	2
1728.2.z.a.1007.18		88	144.29	odd	12
1728.2.z.a.1583.18		88	16.13	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09161 + 0.899102i) q^{2} +(0.383232 + 1.96294i) q^{4} +(0.726024 + 2.70956i) q^{5} +(-0.00424642 - 0.00735502i) q^{7} +(-1.34654 + 2.48733i) q^{8} +(-1.64363 + 3.61055i) q^{10} +(-0.804193 + 3.00129i) q^{11} +(-1.72108 - 6.42317i) q^{13} +(0.00197747 - 0.0118468i) q^{14} +(-3.70627 + 1.50452i) q^{16} -3.37812i q^{17} +(1.35881 + 1.35881i) q^{19} +(-5.04046 + 2.46353i) q^{20} +(-3.57633 + 2.55319i) q^{22} +(5.38718 + 3.11029i) q^{23} +(-2.48446 + 1.43441i) q^{25} +(3.89633 - 8.55903i) q^{26} +(0.0128101 - 0.0111542i) q^{28} +(-0.878030 + 3.27685i) q^{29} +(6.70211 + 3.86947i) q^{31} +(-5.39852 - 1.68996i) q^{32} +(3.03727 - 3.68759i) q^{34} +(0.0168459 - 0.0168459i) q^{35} +(0.769697 + 0.769697i) q^{37} +(0.261585 + 2.70501i) q^{38} +(-7.71719 - 1.84267i) q^{40} +(2.64756 - 4.58570i) q^{41} +(-5.99790 - 1.60713i) q^{43} +(-6.19954 - 0.428394i) q^{44} +(3.08424 + 8.23886i) q^{46} +(0.0955284 + 0.165460i) q^{47} +(3.49996 - 6.06212i) q^{49} +(-4.00175 - 0.667972i) q^{50} +(11.9487 - 5.83994i) q^{52} +(0.750557 - 0.750557i) q^{53} -8.71603 q^{55} +(0.0240124 - 0.000658413i) q^{56} +(-3.90469 + 2.78761i) q^{58} +(9.08809 - 2.43515i) q^{59} +(9.85796 + 2.64143i) q^{61} +(3.83706 + 10.2498i) q^{62} +(-4.37364 - 6.69860i) q^{64} +(16.1544 - 9.32674i) q^{65} +(-7.77154 + 2.08238i) q^{67} +(6.63104 - 1.29460i) q^{68} +(0.0335353 - 0.00324299i) q^{70} -1.02260i q^{71} -7.30911i q^{73} +(0.148174 + 1.53225i) q^{74} +(-2.14653 + 3.18801i) q^{76} +(0.0254895 - 0.00682989i) q^{77} +(4.36074 - 2.51768i) q^{79} +(-6.76742 - 8.95003i) q^{80} +(7.01311 - 2.62538i) q^{82} +(-12.5030 - 3.35017i) q^{83} +(9.15320 - 2.45259i) q^{85} +(-5.10240 - 7.14709i) q^{86} +(-6.38232 - 6.04166i) q^{88} -18.1774 q^{89} +(-0.0399341 + 0.0399341i) q^{91} +(-4.04078 + 11.7667i) q^{92} +(-0.0444856 + 0.266508i) q^{94} +(-2.69525 + 4.66831i) q^{95} +(1.64497 + 2.84917i) q^{97} +(9.27106 - 3.47065i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{2} - 2 q^{4} + 6 q^{5} - 4 q^{7} - 8 q^{10} + 6 q^{11} - 2 q^{13} + 6 q^{14} - 2 q^{16} - 8 q^{19} + 48 q^{20} - 2 q^{22} + 12 q^{23} + 8 q^{28} + 6 q^{29} + 6 q^{32} + 2 q^{34} - 8 q^{37} + 6 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^2 - 2 * q^4 + 6 * q^5 - 4 * q^7 - 8 * q^10 + 6 * q^11 - 2 * q^13 + 6 * q^14 - 2 * q^16 - 8 * q^19 + 48 * q^20 - 2 * q^22 + 12 * q^23 + 8 * q^28 + 6 * q^29 + 6 * q^32 + 2 * q^34 - 8 * q^37 + 6 * q^38 - 2 * q^40 - 2 * q^43 - 40 * q^46 - 24 * q^49 - 72 * q^50 - 2 * q^52 - 16 * q^55 - 36 * q^56 + 16 * q^58 + 42 * q^59 - 2 * q^61 - 44 * q^64 + 12 * q^65 - 2 * q^67 - 96 * q^68 - 16 * q^70 - 78 * q^74 - 14 * q^76 + 6 * q^77 - 36 * q^82 - 54 * q^83 + 8 * q^85 - 54 * q^86 + 22 * q^88 + 20 * q^91 - 108 * q^92 + 6 * q^94 - 4 * q^97

Introduction

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