LMFDB - Embedded newform 459.2.l.a.406.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(298,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.298"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.l (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,0,-16,0,0,0,0,0,-48,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == traces)

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

Self dual:	no
Analytic conductor:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			406.6
Character	$\chi$	$=$	459.406
Dual form			459.2.l.a.433.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0801657 - 0.0801657i) q^{2} -1.98715i q^{4} +(3.34287 - 1.38466i) q^{5} +(4.49973 + 1.86385i) q^{7} +(-0.319632 + 0.319632i) q^{8} +(-0.378985 - 0.156981i) q^{10} +(-1.42762 + 3.44659i) q^{11} -2.58136i q^{13} +(-0.211307 - 0.510141i) q^{14} -3.92305 q^{16} +(-3.41014 + 2.31754i) q^{17} +(2.74781 + 2.74781i) q^{19} +(-2.75152 - 6.64277i) q^{20} +(0.390745 - 0.161852i) q^{22} +(-0.547342 + 1.32140i) q^{23} +(5.72194 - 5.72194i) q^{25} +(-0.206936 + 0.206936i) q^{26} +(3.70374 - 8.94163i) q^{28} +(-7.31781 + 3.03114i) q^{29} +(-1.24327 - 3.00153i) q^{31} +(0.953759 + 0.953759i) q^{32} +(0.459163 + 0.0875890i) q^{34} +17.6228 q^{35} +(-2.51967 - 6.08303i) q^{37} -0.440560i q^{38} +(-0.625906 + 1.51107i) q^{40} +(-6.29901 - 2.60913i) q^{41} +(-0.977765 + 0.977765i) q^{43} +(6.84888 + 2.83690i) q^{44} +(0.149809 - 0.0620530i) q^{46} -7.36992i q^{47} +(11.8239 + 11.8239i) q^{49} -0.917406 q^{50} -5.12954 q^{52} +(3.65552 + 3.65552i) q^{53} +13.4983i q^{55} +(-2.03401 + 0.842513i) q^{56} +(0.829630 + 0.343644i) q^{58} +(4.57252 - 4.57252i) q^{59} +(-4.30238 - 1.78211i) q^{61} +(-0.140952 + 0.340287i) q^{62} +7.69318i q^{64} +(-3.57430 - 8.62913i) q^{65} -7.37261 q^{67} +(4.60529 + 6.77644i) q^{68} +(-1.41274 - 1.41274i) q^{70} +(-0.518078 - 1.25075i) q^{71} +(-10.5442 + 4.36755i) q^{73} +(-0.285659 + 0.689642i) q^{74} +(5.46029 - 5.46029i) q^{76} +(-12.8479 + 12.8479i) q^{77} +(-0.978074 + 2.36128i) q^{79} +(-13.1142 + 5.43209i) q^{80} +(0.295801 + 0.714127i) q^{82} +(-6.27135 - 6.27135i) q^{83} +(-8.19063 + 12.4691i) q^{85} +0.156766 q^{86} +(-0.645327 - 1.55796i) q^{88} -8.62930i q^{89} +(4.81126 - 11.6154i) q^{91} +(2.62582 + 1.08765i) q^{92} +(-0.590814 + 0.590814i) q^{94} +(12.9903 + 5.38077i) q^{95} +(-3.35874 + 1.39124i) q^{97} -1.89574i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) $ 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.0801657	−	0.0801657i	−0.0566857	−	0.0566857i	0.678196	−	0.734881i	$-0.262762\pi$
$2$	−0.0801657	−	0.0801657i	−0.0566857	−	0.0566857i	−0.734881	+	0.678196i	$0.762762\pi$
$3$		0			0
$3$		0			0
$4$		−	1.98715i		−	0.993573i
$5$	3.34287	−	1.38466i	1.49498	−	0.619239i	0.522582	−	0.852589i	$-0.324969\pi$
$5$	3.34287	−	1.38466i	1.49498	−	0.619239i	0.972393	+	0.233350i	$0.0749687\pi$
$6$		0			0
$7$	4.49973	+	1.86385i	1.70074	+	0.704469i	0.999960	−	0.00891072i	$-0.00283641\pi$
$7$	4.49973	+	1.86385i	1.70074	+	0.704469i	0.700778	+	0.713380i	$0.252836\pi$
$8$	−0.319632	+	0.319632i	−0.113007	+	0.113007i
$9$		0			0
$10$	−0.378985	−	0.156981i	−0.119846	−	0.0496417i
$11$	−1.42762	+	3.44659i	−0.430445	+	1.03919i	0.548699	+	0.836020i	$0.315123\pi$
$11$	−1.42762	+	3.44659i	−0.430445	+	1.03919i	−0.979144	+	0.203166i	$0.934877\pi$
$12$		0			0
$13$		−	2.58136i		−	0.715940i	−0.933733	−	0.357970i	$-0.883469\pi$
$13$		−	2.58136i		−	0.715940i	0.933733	−	0.357970i	$-0.116531\pi$
$14$	−0.211307	−	0.510141i	−0.0564742	−	0.136341i
$15$		0			0
$16$	−3.92305			−0.980762
$17$	−3.41014	+	2.31754i	−0.827079	+	0.562085i
$17$	−3.41014	+	2.31754i	−0.827079	+	0.562085i
$18$		0			0
$19$	2.74781	+	2.74781i	0.630390	+	0.630390i	0.948166	−	0.317776i	$-0.102936\pi$
$19$	2.74781	+	2.74781i	0.630390	+	0.630390i	−0.317776	+	0.948166i	$0.602936\pi$
$20$	−2.75152	−	6.64277i	−0.615259	−	1.48537i
$21$		0			0
$22$	0.390745	−	0.161852i	0.0833071	−	0.0345069i
$23$	−0.547342	+	1.32140i	−0.114129	+	0.275531i	−0.970615	−	0.240639i	$-0.922643\pi$
$23$	−0.547342	+	1.32140i	−0.114129	+	0.275531i	0.856486	+	0.516170i	$0.172643\pi$
$24$		0			0
$25$	5.72194	−	5.72194i	1.14439	−	1.14439i
$26$	−0.206936	+	0.206936i	−0.0405835	+	0.0405835i
$27$		0			0
$28$	3.70374	−	8.94163i	0.699942	−	1.68981i
$29$	−7.31781	+	3.03114i	−1.35888	+	0.562868i	−0.938751	−	0.344595i	$-0.888016\pi$
$29$	−7.31781	+	3.03114i	−1.35888	+	0.562868i	−0.420132	+	0.907463i	$0.638016\pi$
$30$		0			0
$31$	−1.24327	−	3.00153i	−0.223298	−	0.539090i	0.772036	−	0.635579i	$-0.219239\pi$
$31$	−1.24327	−	3.00153i	−0.223298	−	0.539090i	−0.995334	+	0.0964891i	$0.969239\pi$
$32$	0.953759	+	0.953759i	0.168602	+	0.168602i
$33$		0			0
$34$	0.459163	+	0.0875890i	0.0787458	+	0.0150214i
$35$	17.6228			2.97880
$36$		0			0
$37$	−2.51967	−	6.08303i	−0.414232	−	1.00004i	−0.983989	−	0.178231i	$-0.942963\pi$
$37$	−2.51967	−	6.08303i	−0.414232	−	1.00004i	0.569757	−	0.821813i	$-0.307037\pi$
$38$		−	0.440560i		−	0.0714682i
$39$		0			0
$40$	−0.625906	+	1.51107i	−0.0989644	+	0.238921i
$41$	−6.29901	−	2.60913i	−0.983740	−	0.407478i	−0.167930	−	0.985799i	$-0.553708\pi$
$41$	−6.29901	−	2.60913i	−0.983740	−	0.407478i	−0.815810	+	0.578321i	$0.803708\pi$
$42$		0			0
$43$	−0.977765	+	0.977765i	−0.149108	+	0.149108i	−0.777719	−	0.628612i	$-0.783624\pi$
$43$	−0.977765	+	0.977765i	−0.149108	+	0.149108i	0.628612	+	0.777719i	$0.283624\pi$
$44$	6.84888	+	2.83690i	1.03251	+	0.427679i
$45$		0			0
$46$	0.149809	−	0.0620530i	0.0220881	−	0.00914921i
$47$		−	7.36992i		−	1.07501i	−0.843260	−	0.537506i	$-0.819366\pi$
$47$		−	7.36992i		−	1.07501i	0.843260	−	0.537506i	$-0.180634\pi$
$48$		0			0
$49$	11.8239	+	11.8239i	1.68913	+	1.68913i
$50$	−0.917406			−0.129741
$51$		0			0
$52$	−5.12954			−0.711339
$53$	3.65552	+	3.65552i	0.502124	+	0.502124i	0.912098	−	0.409973i	$-0.134462\pi$
$53$	3.65552	+	3.65552i	0.502124	+	0.502124i	−0.409973	+	0.912098i	$0.634462\pi$
$54$		0			0
$55$			13.4983i			1.82011i
$56$	−2.03401	+	0.842513i	−0.271805	+	0.112586i
$57$		0			0
$58$	0.829630	+	0.343644i	0.108936	+	0.0451227i
$59$	4.57252	−	4.57252i	0.595292	−	0.595292i	−0.343764	−	0.939056i	$-0.611702\pi$
$59$	4.57252	−	4.57252i	0.595292	−	0.595292i	0.939056	+	0.343764i	$0.111702\pi$
$60$		0			0
$61$	−4.30238	−	1.78211i	−0.550864	−	0.228175i	0.0898497	−	0.995955i	$-0.471361\pi$
$61$	−4.30238	−	1.78211i	−0.550864	−	0.228175i	−0.640713	+	0.767780i	$0.721361\pi$
$62$	−0.140952	+	0.340287i	−0.0179009	+	0.0432165i
$63$		0			0
$64$			7.69318i			0.961647i
$65$	−3.57430	−	8.62913i	−0.443338	−	1.07031i
$66$		0			0
$67$	−7.37261			−0.900708			−0.450354	−	0.892850i	$-0.648702\pi$
$67$	−7.37261			−0.900708			−0.450354	+	0.892850i	$0.648702\pi$
$68$	4.60529	+	6.77644i	0.558473	+	0.821764i
$69$		0			0
$70$	−1.41274	−	1.41274i	−0.168855	−	0.168855i
$71$	−0.518078	−	1.25075i	−0.0614845	−	0.148437i	0.890151	−	0.455665i	$-0.150598\pi$
$71$	−0.518078	−	1.25075i	−0.0614845	−	0.148437i	−0.951636	+	0.307228i	$0.900598\pi$
$72$		0			0
$73$	−10.5442	+	4.36755i	−1.23411	+	0.511184i	−0.901868	−	0.432012i	$-0.857804\pi$
$73$	−10.5442	+	4.36755i	−1.23411	+	0.511184i	−0.332238	+	0.943195i	$0.607804\pi$
$74$	−0.285659	+	0.689642i	−0.0332072	+	0.0801692i
$75$		0			0
$76$	5.46029	−	5.46029i	0.626339	−	0.626339i
$77$	−12.8479	+	12.8479i	−1.46415	+	1.46415i
$78$		0			0
$79$	−0.978074	+	2.36128i	−0.110042	+	0.265665i	−0.969302	−	0.245875i	$-0.920925\pi$
$79$	−0.978074	+	2.36128i	−0.110042	+	0.265665i	0.859260	+	0.511540i	$0.170925\pi$
$80$	−13.1142	+	5.43209i	−1.46621	+	0.607326i
$81$		0			0
$82$	0.295801	+	0.714127i	0.0326658	+	0.0788622i
$83$	−6.27135	−	6.27135i	−0.688371	−	0.688371i	0.273501	−	0.961872i	$-0.411818\pi$
$83$	−6.27135	−	6.27135i	−0.688371	−	0.688371i	−0.961872	+	0.273501i	$0.911818\pi$
$84$		0			0
$85$	−8.19063	+	12.4691i	−0.888398	+	1.35246i
$86$	0.156766			0.0169046
$87$		0			0
$88$	−0.645327	−	1.55796i	−0.0687921	−	0.166079i
$89$		−	8.62930i		−	0.914704i	−0.889286	−	0.457352i	$-0.848798\pi$
$89$		−	8.62930i		−	0.914704i	0.889286	−	0.457352i	$-0.151202\pi$
$90$		0			0
$91$	4.81126	−	11.6154i	0.504357	−	1.21763i
$92$	2.62582	+	1.08765i	0.273760	+	0.113395i
$93$		0			0
$94$	−0.590814	+	0.590814i	−0.0609379	+	0.0609379i
$95$	12.9903	+	5.38077i	1.33278	+	0.552055i
$96$		0			0
$97$	−3.35874	+	1.39124i	−0.341029	+	0.141259i	−0.546623	−	0.837379i	$-0.684087\pi$
$97$	−3.35874	+	1.39124i	−0.341029	+	0.141259i	0.205595	+	0.978637i	$0.434087\pi$
$98$		−	1.89574i		−	0.191499i
$99$		0			0
$100$	−11.3703	−	11.3703i	−1.13703	−	1.13703i
$101$	2.32609			0.231455			0.115728	−	0.993281i	$-0.463080\pi$
$101$	2.32609			0.231455			0.115728	+	0.993281i	$0.463080\pi$
$102$		0			0
$103$	4.01072			0.395188			0.197594	−	0.980284i	$-0.436687\pi$
$103$	4.01072			0.395188			0.197594	+	0.980284i	$0.436687\pi$
$104$	0.825085	+	0.825085i	0.0809063	+	0.0809063i
$105$		0			0
$106$		−	0.586095i		−	0.0569265i
$107$	−4.62870	+	1.91727i	−0.447474	+	0.185350i	−0.595029	−	0.803704i	$-0.702860\pi$
$107$	−4.62870	+	1.91727i	−0.447474	+	0.185350i	0.147555	+	0.989054i	$0.452860\pi$
$108$		0			0
$109$	8.07699	+	3.34560i	0.773635	+	0.320450i	0.734344	−	0.678778i	$-0.237490\pi$
$109$	8.07699	+	3.34560i	0.773635	+	0.320450i	0.0392911	+	0.999228i	$0.487490\pi$
$110$	1.08210	−	1.08210i	0.103174	−	0.103174i
$111$		0			0
$112$	−17.6527	−	7.31197i	−1.66802	−	0.690916i
$113$	2.01362	−	4.86132i	0.189426	−	0.457314i	−0.800424	−	0.599435i	$-0.795392\pi$
$113$	2.01362	−	4.86132i	0.189426	−	0.457314i	0.989849	+	0.142121i	$0.0453921\pi$
$114$		0			0
$115$			5.17515i			0.482585i
$116$	6.02331	+	14.5416i	0.559251	+	1.35015i
$117$		0			0
$118$	−0.733119			−0.0674891
$119$	−19.6642	+	4.07231i	−1.80262	+	0.373308i
$120$		0			0
$121$	−2.06270	−	2.06270i	−0.187518	−	0.187518i
$122$	0.202040	+	0.487767i	0.0182918	+	0.0441604i
$123$		0			0
$124$	−5.96448	+	2.47057i	−0.535626	+	0.221863i
$125$	4.28142	−	10.3363i	0.382942	−	0.924504i
$126$		0			0
$127$	−2.21554	+	2.21554i	−0.196597	+	0.196597i	−0.798540	−	0.601942i	$-0.794394\pi$
$127$	−2.21554	+	2.21554i	−0.196597	+	0.196597i	0.601942	+	0.798540i	$0.294394\pi$
$128$	2.52425	−	2.52425i	0.223114	−	0.223114i
$129$		0			0
$130$	−0.405224	+	0.978297i	−0.0355405	+	0.0858023i
$131$	2.25005	−	0.932002i	0.196588	−	0.0814294i	−0.282217	−	0.959350i	$-0.591070\pi$
$131$	2.25005	−	0.932002i	0.196588	−	0.0814294i	0.478805	+	0.877921i	$0.341070\pi$
$132$		0			0
$133$	7.24289	+	17.4859i	0.628038	+	1.51622i
$134$	0.591031	+	0.591031i	0.0510573	+	0.0510573i
$135$		0			0
$136$	0.349230	−	1.83075i	0.0299462	−	0.156985i
$137$	21.8938			1.87051			0.935256	−	0.353971i	$-0.115169\pi$
$137$	21.8938			1.87051			0.935256	+	0.353971i	$0.115169\pi$
$138$		0			0
$139$	−1.93443	−	4.67012i	−0.164076	−	0.396114i	0.820363	−	0.571844i	$-0.193772\pi$
$139$	−1.93443	−	4.67012i	−0.164076	−	0.396114i	−0.984439	+	0.175729i	$0.943772\pi$
$140$		−	35.0191i		−	2.95965i
$141$		0			0
$142$	−0.0587352	+	0.141799i	−0.00492895	+	0.0118995i
$143$	8.89688	+	3.68521i	0.743995	+	0.308173i
$144$		0			0
$145$	−20.2654	+	20.2654i	−1.68295	+	1.68295i
$146$	1.19541	+	0.495156i	0.0989330	+	0.0409794i
$147$		0			0
$148$	−12.0879	+	5.00696i	−0.993617	+	0.411570i
$149$			21.1635i			1.73378i	0.498497	+	0.866891i	$0.333885\pi$
$149$			21.1635i			1.73378i	−0.498497	+	0.866891i	$0.666115\pi$
$150$		0			0
$151$	4.40041	+	4.40041i	0.358100	+	0.358100i	0.863112	−	0.505012i	$-0.168512\pi$
$151$	4.40041	+	4.40041i	0.358100	+	0.358100i	−0.505012	+	0.863112i	$0.668512\pi$
$152$	−1.75658			−0.142477
$153$		0			0
$154$	2.05991			0.165993
$155$	−8.31219	−	8.31219i	−0.667651	−	0.667651i
$156$		0			0
$157$		−	8.20400i		−	0.654751i	−0.944894	−	0.327375i	$-0.893836\pi$
$157$		−	8.20400i		−	0.654751i	0.944894	−	0.327375i	$-0.106164\pi$
$158$	0.267702	−	0.110886i	0.0212972	−	0.00882159i
$159$		0			0
$160$	4.50892	+	1.86766i	0.356461	+	0.147651i
$161$	−4.92579	+	4.92579i	−0.388206	+	0.388206i
$162$		0			0
$163$	14.7382	+	6.10477i	1.15439	+	0.478163i	0.876002	−	0.482307i	$-0.160201\pi$
$163$	14.7382	+	6.10477i	1.15439	+	0.478163i	0.278385	+	0.960470i	$0.410201\pi$
$164$	−5.18473	+	12.5171i	−0.404860	+	0.977418i
$165$		0			0
$166$			1.00549i			0.0780415i
$167$	6.05669	+	14.6221i	0.468681	+	1.13150i	0.964740	+	0.263206i	$0.0847800\pi$
$167$	6.05669	+	14.6221i	0.468681	+	1.13150i	−0.496059	+	0.868289i	$0.665220\pi$
$168$		0			0
$169$	6.33660			0.487430
$170$	1.65620	−	0.342986i	0.127025	−	0.0263058i
$171$		0			0
$172$	1.94296	+	1.94296i	0.148150	+	0.148150i
$173$	7.66748	+	18.5109i	0.582948	+	1.40736i	0.890129	+	0.455709i	$0.150614\pi$
$173$	7.66748	+	18.5109i	0.582948	+	1.40736i	−0.307181	+	0.951651i	$0.599386\pi$
$174$		0			0
$175$	36.4120	−	15.0823i	2.75249	−	1.14012i
$176$	5.60064	−	13.5211i	0.422164	−	1.01919i
$177$		0			0
$178$	−0.691774	+	0.691774i	−0.0518507	+	0.0518507i
$179$	13.0791	−	13.0791i	0.977581	−	0.977581i	−0.0221730	−	0.999754i	$-0.507058\pi$
$179$	13.0791	−	13.0791i	0.977581	−	0.977581i	0.999754	+	0.0221730i	$0.00705846\pi$
$180$		0			0
$181$	1.85648	−	4.48194i	0.137991	−	0.333140i	−0.839744	−	0.542982i	$-0.817295\pi$
$181$	1.85648	−	4.48194i	0.137991	−	0.333140i	0.977735	+	0.209842i	$0.0672951\pi$
$182$	−1.31686	+	0.545459i	−0.0976118	+	0.0404321i
$183$		0			0
$184$	−0.247414	−	0.597311i	−0.0182396	−	0.0440343i
$185$	−16.8459	−	16.8459i	−1.23853	−	1.23853i
$186$		0			0
$187$	−3.11921	−	15.0619i	−0.228099	−	1.10144i
$188$	−14.6451			−1.06810
$189$		0			0
$190$	−0.610025	−	1.47273i	−0.0442559	−	0.106843i
$191$			4.66086i			0.337248i	0.985680	+	0.168624i	$0.0539323\pi$
$191$			4.66086i			0.337248i	−0.985680	+	0.168624i	$0.946068\pi$
$192$		0			0
$193$	−3.79180	+	9.15422i	−0.272940	+	0.658935i	−0.999606	−	0.0280551i	$-0.991069\pi$
$193$	−3.79180	+	9.15422i	−0.272940	+	0.658935i	0.726666	+	0.686990i	$0.241069\pi$
$194$	0.380785	+	0.157726i	0.0273388	+	0.0113241i
$195$		0			0
$196$	23.4958	−	23.4958i	1.67827	−	1.67827i
$197$	−11.9679	−	4.95725i	−0.852674	−	0.353189i	−0.0868362	−	0.996223i	$-0.527676\pi$
$197$	−11.9679	−	4.95725i	−0.852674	−	0.353189i	−0.765838	+	0.643033i	$0.777676\pi$
$198$		0			0
$199$	25.6051	−	10.6060i	1.81510	−	0.751839i	0.835919	−	0.548853i	$-0.184935\pi$
$199$	25.6051	−	10.6060i	1.81510	−	0.751839i	0.979182	−	0.202987i	$-0.0650648\pi$
$200$			3.65783i			0.258648i
$201$		0			0
$202$	−0.186473	−	0.186473i	−0.0131202	−	0.0131202i
$203$	−38.5778			−2.70763
$204$		0			0
$205$	−24.6695			−1.72299
$206$	−0.321522	−	0.321522i	−0.0224015	−	0.0224015i
$207$		0			0
$208$			10.1268i			0.702166i
$209$	−13.3934	+	5.54773i	−0.926441	+	0.383744i
$210$		0			0
$211$	−20.9994	−	8.69824i	−1.44566	−	0.598812i	−0.484496	−	0.874793i	$-0.660997\pi$
$211$	−20.9994	−	8.69824i	−1.44566	−	0.598812i	−0.961163	+	0.275982i	$0.910997\pi$
$212$	7.26406	−	7.26406i	0.498897	−	0.498897i
$213$		0			0
$214$	0.524763	+	0.217364i	0.0358720	+	0.0148587i
$215$	−1.91467	+	4.62241i	−0.130579	+	0.315246i
$216$		0			0
$217$		−	15.8233i		−	1.07416i
$218$	−0.379295	−	0.915699i	−0.0256891	−	0.0620190i
$219$		0			0
$220$	26.8230			1.80841
$221$	5.98239	+	8.80278i	0.402419	+	0.592139i
$222$		0			0
$223$	8.50375	+	8.50375i	0.569453	+	0.569453i	0.931975	−	0.362522i	$-0.118084\pi$
$223$	8.50375	+	8.50375i	0.569453	+	0.569453i	−0.362522	+	0.931975i	$0.618084\pi$
$224$	2.51399	+	6.06932i	0.167973	+	0.405523i
$225$		0			0
$226$	−0.551134	+	0.228287i	−0.0366609	+	0.0151854i
$227$	5.65533	−	13.6532i	0.375357	−	0.906192i	−0.617466	−	0.786598i	$-0.711841\pi$
$227$	5.65533	−	13.6532i	0.375357	−	0.906192i	0.992823	−	0.119595i	$-0.0381595\pi$
$228$		0			0
$229$	−10.0487	+	10.0487i	−0.664039	+	0.664039i	−0.956330	−	0.292291i	$-0.905583\pi$
$229$	−10.0487	+	10.0487i	−0.664039	+	0.664039i	0.292291	+	0.956330i	$0.405583\pi$
$230$	0.414870	−	0.414870i	0.0273557	−	0.0273557i
$231$		0			0
$232$	1.37016	−	3.30786i	0.0899554	−	0.217172i
$233$	7.96496	−	3.29919i	0.521802	−	0.216137i	−0.106206	−	0.994344i	$-0.533870\pi$
$233$	7.96496	−	3.29919i	0.521802	−	0.216137i	0.628008	+	0.778207i	$0.283870\pi$
$234$		0			0
$235$	−10.2048	−	24.6366i	−0.665690	−	1.60712i
$236$	−9.08628	−	9.08628i	−0.591466	−	0.591466i
$237$		0			0
$238$	1.90286	+	1.24994i	0.123344	+	0.0810214i
$239$	16.0848			1.04044			0.520221	−	0.854032i	$-0.325850\pi$
$239$	16.0848			1.04044			0.520221	+	0.854032i	$0.325850\pi$
$240$		0			0
$241$	1.25013	+	3.01808i	0.0805280	+	0.194412i	0.959016	−	0.283353i	$-0.0914469\pi$
$241$	1.25013	+	3.01808i	0.0805280	+	0.194412i	−0.878488	+	0.477765i	$0.841447\pi$
$242$			0.330716i			0.0212592i
$243$		0			0
$244$	−3.54131	+	8.54947i	−0.226709	+	0.547324i
$245$	55.8978	+	23.1536i	3.57118	+	1.47923i
$246$		0			0
$247$	7.09307	−	7.09307i	0.451321	−	0.451321i
$248$	1.35678	+	0.561995i	0.0861553	+	0.0356867i
$249$		0			0
$250$	−1.17184	+	0.485391i	−0.0741135	+	0.0306988i
$251$		−	0.393311i		−	0.0248256i	−0.999923	−	0.0124128i	$-0.996049\pi$
$251$		−	0.393311i		−	0.0248256i	0.999923	−	0.0124128i	$-0.00395121\pi$
$252$		0			0
$253$	−3.77293	−	3.77293i	−0.237202	−	0.237202i
$254$	0.355220			0.0222885
$255$		0			0
$256$	14.9816			0.936352
$257$	−1.08185	−	1.08185i	−0.0674841	−	0.0674841i	0.672559	−	0.740043i	$-0.265195\pi$
$257$	−1.08185	−	1.08185i	−0.0674841	−	0.0674841i	−0.740043	+	0.672559i	$0.765195\pi$
$258$		0			0
$259$		−	32.0683i		−	1.99263i
$260$	−17.1474	+	7.10267i	−1.06343	+	0.440489i
$261$		0			0
$262$	−0.255092	−	0.105662i	−0.0157596	−	0.00652785i
$263$	−7.33600	+	7.33600i	−0.452357	+	0.452357i	−0.896136	−	0.443779i	$-0.853637\pi$
$263$	−7.33600	+	7.33600i	−0.452357	+	0.452357i	0.443779	+	0.896136i	$0.353637\pi$
$264$		0			0
$265$	17.2816	+	7.15826i	1.06160	+	0.439728i
$266$	0.821137	−	1.98240i	0.0503471	−	0.121549i
$267$		0			0
$268$			14.6505i			0.894920i
$269$	−10.9570	−	26.4525i	−0.668059	−	1.61284i	−0.784854	−	0.619681i	$-0.787262\pi$
$269$	−10.9570	−	26.4525i	−0.668059	−	1.61284i	0.116795	−	0.993156i	$-0.462738\pi$
$270$		0			0
$271$	−3.90958			−0.237490			−0.118745	−	0.992925i	$-0.537887\pi$
$271$	−3.90958			−0.237490			−0.118745	+	0.992925i	$0.537887\pi$
$272$	13.3781	−	9.09180i	0.811168	−	0.551272i
$273$		0			0
$274$	−1.75513	−	1.75513i	−0.106031	−	0.106031i
$275$	11.5524	+	27.8899i	0.696635	+	1.68183i
$276$		0			0
$277$	−16.4926	+	6.83146i	−0.990944	+	0.410462i	−0.818469	−	0.574551i	$-0.805177\pi$
$277$	−16.4926	+	6.83146i	−0.990944	+	0.410462i	−0.172475	+	0.985014i	$0.555177\pi$
$278$	−0.219309	+	0.529458i	−0.0131533	+	0.0317548i
$279$		0			0
$280$	−5.63282	+	5.63282i	−0.336625	+	0.336625i
$281$	18.8752	−	18.8752i	1.12600	−	1.12600i	0.135182	−	0.990821i	$-0.456838\pi$
$281$	18.8752	−	18.8752i	1.12600	−	1.12600i	0.990821	−	0.135182i	$-0.0431619\pi$
$282$		0			0
$283$	−7.01288	+	16.9306i	−0.416872	+	1.00642i	0.566376	+	0.824147i	$0.308345\pi$
$283$	−7.01288	+	16.9306i	−0.416872	+	1.00642i	−0.983248	+	0.182272i	$0.941655\pi$
$284$	−2.48542	+	1.02950i	−0.147483	+	0.0610894i
$285$		0			0
$286$	−0.417797	−	1.00865i	−0.0247049	−	0.0596428i
$287$	−23.4808	−	23.4808i	−1.38603	−	1.38603i
$288$		0			0
$289$	6.25805	−	15.8062i	0.368121	−	0.929778i
$290$	3.24917			0.190798
$291$		0			0
$292$	8.67897	+	20.9529i	0.507898	+	1.22618i
$293$		−	16.6305i		−	0.971564i	−0.874080	−	0.485782i	$-0.838535\pi$
$293$		−	16.6305i		−	0.971564i	0.874080	−	0.485782i	$-0.161465\pi$
$294$		0			0
$295$	8.95394	−	21.6167i	0.521319	−	1.25857i
$296$	2.74970	+	1.13896i	0.159823	+	0.0662010i
$297$		0			0
$298$	1.69659	−	1.69659i	0.0982807	−	0.0982807i
$299$	3.41101	+	1.41289i	0.197264	+	0.0817093i
$300$		0			0
$301$	−6.22209	+	2.57727i	−0.358635	+	0.148552i
$302$		−	0.705524i		−	0.0405983i
$303$		0			0
$304$	−10.7798	−	10.7798i	−0.618262	−	0.618262i
$305$	−16.8499			−0.964823
$306$		0			0
$307$	27.9347			1.59432			0.797158	−	0.603771i	$-0.206336\pi$
$307$	27.9347			1.59432			0.797158	+	0.603771i	$0.206336\pi$
$308$	25.5306	+	25.5306i	1.45474	+	1.45474i
$309$		0			0
$310$			1.33271i			0.0756926i
$311$	−11.8431	+	4.90558i	−0.671561	+	0.278170i	−0.692294	−	0.721615i	$-0.743400\pi$
$311$	−11.8431	+	4.90558i	−0.671561	+	0.278170i	0.0207330	+	0.999785i	$0.493400\pi$
$312$		0			0
$313$	0.211315	+	0.0875297i	0.0119443	+	0.00494747i	0.388648	−	0.921386i	$-0.372942\pi$
$313$	0.211315	+	0.0875297i	0.0119443	+	0.00494747i	−0.376703	+	0.926334i	$0.622942\pi$
$314$	−0.657680	+	0.657680i	−0.0371150	+	0.0371150i
$315$		0			0
$316$	4.69221	+	1.94358i	0.263957	+	0.109335i
$317$	−4.88171	+	11.7855i	−0.274184	+	0.661939i	−0.999654	−	0.0263150i	$-0.991623\pi$
$317$	−4.88171	+	11.7855i	−0.274184	+	0.661939i	0.725469	+	0.688254i	$0.241623\pi$
$318$		0			0
$319$		−	29.5488i		−	1.65442i
$320$	10.6524	+	25.7173i	0.595489	+	1.43764i
$321$		0			0
$322$	0.789758			0.0440115
$323$	−15.7385	−	3.00225i	−0.875715	−	0.167050i
$324$		0			0
$325$	−14.7704	−	14.7704i	−0.819312	−	0.819312i
$326$	−0.692107	−	1.67089i	−0.0383323	−	0.0925423i
$327$		0			0
$328$	2.84733	−	1.17940i	0.157218	−	0.0651216i
$329$	13.7364	−	33.1626i	0.757313	−	1.82832i
$330$		0			0
$331$	−2.85034	+	2.85034i	−0.156669	+	0.156669i	−0.781089	−	0.624420i	$-0.785335\pi$
$331$	−2.85034	+	2.85034i	−0.156669	+	0.156669i	0.624420	+	0.781089i	$0.285335\pi$
$332$	−12.4621	+	12.4621i	−0.683947	+	0.683947i
$333$		0			0
$334$	0.686655	−	1.65773i	0.0375721	−	0.0907071i
$335$	−24.6457	+	10.2086i	−1.34654	+	0.557754i
$336$		0			0
$337$	1.25974	+	3.04128i	0.0686223	+	0.165669i	0.954470	−	0.298308i	$-0.0964222\pi$
$337$	1.25974	+	3.04128i	0.0686223	+	0.165669i	−0.885847	+	0.463977i	$0.846422\pi$
$338$	−0.507978	−	0.507978i	−0.0276303	−	0.0276303i
$339$		0			0
$340$	24.7779	+	16.2760i	1.34377	+	0.882689i
$341$	12.1200			0.656333
$342$		0			0
$343$	18.1194	+	43.7442i	0.978357	+	2.36196i
$344$		−	0.625051i		−	0.0337005i
$345$		0			0
$346$	0.869273	−	2.09861i	0.0467324	−	0.112822i
$347$	9.65633	+	3.99978i	0.518379	+	0.214719i	0.626505	−	0.779418i	$-0.284485\pi$
$347$	9.65633	+	3.99978i	0.518379	+	0.214719i	−0.108126	+	0.994137i	$0.534485\pi$
$348$		0			0
$349$	0.354817	−	0.354817i	0.0189929	−	0.0189929i	−0.697547	−	0.716539i	$-0.745725\pi$
$349$	0.354817	−	0.354817i	0.0189929	−	0.0189929i	0.716539	+	0.697547i	$0.245725\pi$
$350$	−4.12808	−	1.70991i	−0.220655	−	0.0913983i
$351$		0			0
$352$	−4.64882	+	1.92561i	−0.247783	+	0.102635i
$353$		−	29.9020i		−	1.59152i	−0.605611	−	0.795761i	$-0.707071\pi$
$353$		−	29.9020i		−	1.59152i	0.605611	−	0.795761i	$-0.292929\pi$
$354$		0			0
$355$	−3.46373	−	3.46373i	−0.183836	−	0.183836i
$356$	−17.1477			−0.908826
$357$		0			0
$358$	−2.09700			−0.110830
$359$	−9.63876	−	9.63876i	−0.508714	−	0.508714i	0.405417	−	0.914132i	$-0.367126\pi$
$359$	−9.63876	−	9.63876i	−0.508714	−	0.508714i	−0.914132	+	0.405417i	$0.867126\pi$
$360$		0			0
$361$		−	3.89912i		−	0.205217i
$362$	−0.508124	+	0.210472i	−0.0267064	+	0.0110621i
$363$		0			0
$364$	−23.0815	−	9.56068i	−1.20980	−	0.501116i
$365$	−29.2003	+	29.2003i	−1.52841	+	1.52841i
$366$		0			0
$367$	12.3474	+	5.11447i	0.644530	+	0.266973i	0.680912	−	0.732365i	$-0.261583\pi$
$367$	12.3474	+	5.11447i	0.644530	+	0.266973i	−0.0363823	+	0.999338i	$0.511583\pi$
$368$	2.14725	−	5.18392i	0.111933	−	0.270230i
$369$		0			0
$370$			2.70092i			0.140414i
$371$	9.63552	+	23.2622i	0.500251	+	1.20771i
$372$		0			0
$373$	−16.3768			−0.847961			−0.423980	−	0.905671i	$-0.639367\pi$
$373$	−16.3768			−0.847961			−0.423980	+	0.905671i	$0.639367\pi$
$374$	−0.957395	+	1.45750i	−0.0495057	+	0.0753656i
$375$		0			0
$376$	2.35566	+	2.35566i	0.121484	+	0.121484i
$377$	7.82445	+	18.8899i	0.402979	+	0.972878i
$378$		0			0
$379$	−19.6644	+	8.14528i	−1.01009	+	0.418395i	−0.825489	−	0.564418i	$-0.809101\pi$
$379$	−19.6644	+	8.14528i	−1.01009	+	0.418395i	−0.184605	+	0.982813i	$0.559101\pi$
$380$	10.6924	−	25.8137i	0.548508	−	1.32421i
$381$		0			0
$382$	0.373641	−	0.373641i	0.0191171	−	0.0191171i
$383$	−6.90474	+	6.90474i	−0.352816	+	0.352816i	−0.861156	−	0.508340i	$-0.830259\pi$
$383$	−6.90474	+	6.90474i	−0.352816	+	0.352816i	0.508340	+	0.861156i	$0.330259\pi$
$384$		0			0
$385$	−25.1587	+	60.7386i	−1.28221	+	3.09552i
$386$	1.03783	−	0.429882i	0.0528240	−	0.0218804i
$387$		0			0
$388$	2.76459	+	6.67431i	0.140351	+	0.338837i
$389$	0.129554	+	0.129554i	0.00656866	+	0.00656866i	0.710383	−	0.703815i	$-0.248522\pi$
$389$	0.129554	+	0.129554i	0.00656866	+	0.00656866i	−0.703815	+	0.710383i	$0.748522\pi$
$390$		0			0
$391$	−1.19588	−	5.77464i	−0.0604784	−	0.292036i
$392$	−7.55860			−0.381767
$393$		0			0
$394$	0.562010	+	1.35681i	0.0283137	+	0.0683552i
$395$			9.24774i			0.465304i
$396$		0			0
$397$	−10.3800	+	25.0595i	−0.520957	+	1.25770i	0.416352	+	0.909203i	$0.363308\pi$
$397$	−10.3800	+	25.0595i	−0.520957	+	1.25770i	−0.937309	+	0.348499i	$0.886692\pi$
$398$	−2.90289	−	1.20242i	−0.145509	−	0.0602717i
$399$		0			0
$400$	−22.4474	+	22.4474i	−1.12237	+	1.12237i
$401$	−23.1218	−	9.57735i	−1.15465	−	0.478270i	−0.278557	−	0.960420i	$-0.589856\pi$
$401$	−23.1218	−	9.57735i	−1.15465	−	0.478270i	−0.876089	+	0.482150i	$0.839856\pi$
$402$		0			0
$403$	−7.74801	+	3.20933i	−0.385956	+	0.159868i
$404$		−	4.62229i		−	0.229968i
$405$		0			0
$406$	3.09261	+	3.09261i	0.153484	+	0.153484i
$407$	24.5629			1.21754
$408$		0			0
$409$	2.02920			0.100337			0.0501687	−	0.998741i	$-0.484024\pi$
$409$	2.02920			0.100337			0.0501687	+	0.998741i	$0.484024\pi$
$410$	1.97765	+	1.97765i	0.0976691	+	0.0976691i
$411$		0			0
$412$		−	7.96990i		−	0.392649i
$413$	29.0976	−	12.0526i	1.43180	−	0.593071i
$414$		0			0
$415$	−29.6480	−	12.2806i	−1.45536	−	0.602831i
$416$	2.46199	−	2.46199i	0.120709	−	0.120709i
$417$		0			0
$418$	1.51843	+	0.628954i	0.0742688	+	0.0307631i
$419$	3.28491	−	7.93049i	0.160479	−	0.387430i	−0.823103	−	0.567892i	$-0.807759\pi$
$419$	3.28491	−	7.93049i	0.160479	−	0.387430i	0.983582	+	0.180462i	$0.0577593\pi$
$420$		0			0
$421$		−	15.1592i		−	0.738815i	−0.929267	−	0.369408i	$-0.879561\pi$
$421$		−	15.1592i		−	0.738815i	0.929267	−	0.369408i	$-0.120439\pi$
$422$	0.986132	+	2.38073i	0.0480041	+	0.115892i
$423$		0			0
$424$	−2.33685			−0.113487
$425$	−6.25178	+	32.7734i	−0.303256	+	1.58974i
$426$		0			0
$427$	−16.0380	−	16.0380i	−0.776133	−	0.776133i
$428$	3.80990	+	9.19792i	0.184159	+	0.444598i
$429$		0			0
$430$	0.524049	−	0.217068i	0.0252719	−	0.0104680i
$431$	11.3632	−	27.4331i	0.547345	−	1.32141i	−0.372102	−	0.928192i	$-0.621363\pi$
$431$	11.3632	−	27.4331i	0.547345	−	1.32141i	0.919447	−	0.393215i	$-0.128637\pi$
$432$		0			0
$433$	−11.2374	+	11.2374i	−0.540037	+	0.540037i	−0.923540	−	0.383503i	$-0.874718\pi$
$433$	−11.2374	+	11.2374i	−0.540037	+	0.540037i	0.383503	+	0.923540i	$0.374718\pi$
$434$	−1.26849	+	1.26849i	−0.0608894	+	0.0608894i
$435$		0			0
$436$	6.64819	−	16.0502i	0.318391	−	0.768663i
$437$	−5.13495	+	2.12696i	−0.245638	+	0.101746i
$438$		0			0
$439$	−3.93225	−	9.49330i	−0.187676	−	0.453091i	0.801835	−	0.597545i	$-0.203857\pi$
$439$	−3.93225	−	9.49330i	−0.187676	−	0.453091i	−0.989511	+	0.144455i	$0.953857\pi$
$440$	−4.31448	−	4.31448i	−0.205685	−	0.205685i
$441$		0			0
$442$	0.226098	−	1.18526i	0.0107544	−	0.0563772i
$443$	−4.79437			−0.227787			−0.113894	−	0.993493i	$-0.536332\pi$
$443$	−4.79437			−0.227787			−0.113894	+	0.993493i	$0.536332\pi$
$444$		0			0
$445$	−11.9487	−	28.8466i	−0.566421	−	1.36746i
$446$		−	1.36342i		−	0.0645597i
$447$		0			0
$448$	−14.3389	+	34.6172i	−0.677450	+	1.63551i
$449$	17.6923	+	7.32837i	0.834949	+	0.345847i	0.758860	−	0.651254i	$-0.225757\pi$
$449$	17.6923	+	7.32837i	0.834949	+	0.345847i	0.0760891	+	0.997101i	$0.475757\pi$
$450$		0			0
$451$	17.9852	−	17.9852i	0.846892	−	0.846892i
$452$	−9.66015	−	4.00137i	−0.454375	−	0.188208i
$453$		0			0
$454$	−1.54788	+	0.641152i	−0.0726455	+	0.0300908i
$455$		−	45.4907i		−	2.13264i
$456$		0			0
$457$	−3.68753	−	3.68753i	−0.172495	−	0.172495i	0.615579	−	0.788075i	$-0.288922\pi$
$457$	−3.68753	−	3.68753i	−0.172495	−	0.172495i	−0.788075	+	0.615579i	$0.788922\pi$
$458$	1.61113			0.0752830
$459$		0			0
$460$	10.2838			0.479484
$461$	−13.1053	−	13.1053i	−0.610374	−	0.610374i	0.332670	−	0.943043i	$-0.392051\pi$
$461$	−13.1053	−	13.1053i	−0.610374	−	0.610374i	−0.943043	+	0.332670i	$0.892051\pi$
$462$		0			0
$463$			36.3578i			1.68969i	0.535009	+	0.844846i	$0.320308\pi$
$463$			36.3578i			1.68969i	−0.535009	+	0.844846i	$0.679692\pi$
$464$	28.7081	−	11.8913i	1.33274	−	0.552039i
$465$		0			0
$466$	−0.902999	−	0.374034i	−0.0418306	−	0.0173268i
$467$	10.8866	−	10.8866i	0.503772	−	0.503772i	−0.408836	−	0.912608i	$-0.634065\pi$
$467$	10.8866	−	10.8866i	0.503772	−	0.503772i	0.912608	+	0.408836i	$0.134065\pi$
$468$		0			0
$469$	−33.1748	−	13.7414i	−1.53187	−	0.634521i
$470$	−1.15694	+	2.79309i	−0.0533655	+	0.128836i
$471$		0			0
$472$			2.92305i			0.134544i
$473$	−1.97407	−	4.76584i	−0.0907681	−	0.219133i
$474$		0			0
$475$	31.4455			1.44282
$476$	8.09228	+	39.0757i	0.370909	+	1.79103i
$477$		0			0
$478$	−1.28945	−	1.28945i	−0.0589782	−	0.0589782i
$479$	5.31206	+	12.8244i	0.242714	+	0.585964i	0.997551	−	0.0699493i	$-0.0222838\pi$
$479$	5.31206	+	12.8244i	0.242714	+	0.585964i	−0.754836	+	0.655913i	$0.772284\pi$
$480$		0			0
$481$	−15.7025	+	6.50418i	−0.715971	+	0.296565i
$482$	0.141729	−	0.342164i	0.00645559	−	0.0155852i
$483$		0			0
$484$	−4.09889	+	4.09889i	−0.186313	+	0.186313i
$485$	−9.30143	+	9.30143i	−0.422356	+	0.422356i
$486$		0			0
$487$	9.09789	−	21.9642i	0.412265	−	0.995295i	−0.572264	−	0.820070i	$-0.693935\pi$
$487$	9.09789	−	21.9642i	0.412265	−	0.995295i	0.984528	−	0.175225i	$-0.0560654\pi$
$488$	1.94480	−	0.805562i	0.0880369	−	0.0364661i
$489$		0			0
$490$	−2.62496	−	6.33721i	−0.118583	−	0.286286i
$491$	8.20903	+	8.20903i	0.370468	+	0.370468i	0.867648	−	0.497179i	$-0.165631\pi$
$491$	8.20903	+	8.20903i	0.370468	+	0.370468i	−0.497179	+	0.867648i	$0.665631\pi$
$492$		0			0
$493$	17.9300	−	27.2959i	0.807525	−	1.22934i
$494$	−1.13724			−0.0511669
$495$		0			0
$496$	4.87742	+	11.7751i	0.219003	+	0.528719i
$497$		−	6.59366i		−	0.295766i
$498$		0			0
$499$	0.150251	−	0.362737i	0.00672614	−	0.0162383i	−0.920481	−	0.390788i	$-0.872203\pi$
$499$	0.150251	−	0.362737i	0.00672614	−	0.0162383i	0.927207	+	0.374549i	$0.122203\pi$
$500$	−20.5397	−	8.50782i	−0.918563	−	0.380481i
$501$		0			0
$502$	−0.0315300	+	0.0315300i	−0.00140725	+	0.00140725i
$503$	22.8920	+	9.48218i	1.02070	+	0.422789i	0.829349	−	0.558732i	$-0.188712\pi$
$503$	22.8920	+	9.48218i	1.02070	+	0.422789i	0.191355	+	0.981521i	$0.438712\pi$
$504$		0			0
$505$	7.77582	−	3.22085i	0.346020	−	0.143326i
$506$			0.604919i			0.0268919i
$507$		0			0
$508$	4.40260	+	4.40260i	0.195334	+	0.195334i
$509$	17.1712			0.761100			0.380550	−	0.924760i	$-0.375735\pi$
$509$	17.1712			0.761100			0.380550	+	0.924760i	$0.375735\pi$
$510$		0			0
$511$	−55.5866			−2.45900
$512$	−6.24950	−	6.24950i	−0.276192	−	0.276192i
$513$		0			0
$514$			0.173455i			0.00765077i
$515$	13.4073	−	5.55349i	0.590797	−	0.244716i
$516$		0			0
$517$	25.4011	+	10.5215i	1.11714	+	0.462734i
$518$	−2.57078	+	2.57078i	−0.112953	+	0.112953i
$519$		0			0
$520$	3.90061	+	1.61569i	0.171053	+	0.0708525i
$521$	−11.5679	+	27.9275i	−0.506801	+	1.22353i	0.438914	+	0.898529i	$0.355363\pi$
$521$	−11.5679	+	27.9275i	−0.506801	+	1.22353i	−0.945715	+	0.324997i	$0.894637\pi$
$522$		0			0
$523$			32.1131i			1.40421i	0.712074	+	0.702104i	$0.247756\pi$
$523$			32.1131i			1.40421i	−0.712074	+	0.702104i	$0.752244\pi$
$524$	−1.85203	−	4.47119i	−0.0809061	−	0.195325i
$525$		0			0
$526$	1.17619			0.0512843
$527$	11.1959	+	7.35428i	0.487700	+	0.320358i
$528$		0			0
$529$	14.8169	+	14.8169i	0.644215	+	0.644215i
$530$	−0.811542	−	1.95924i	−0.0352511	−	0.0851038i
$531$		0			0
$532$	34.7470	−	14.3927i	1.50647	−	0.624002i
$533$	−6.73511	+	16.2600i	−0.291730	+	0.704298i
$534$		0			0
$535$	−12.8184	+	12.8184i	−0.554186	+	0.554186i
$536$	2.35653	−	2.35653i	0.101786	−	0.101786i
$537$		0			0
$538$	−1.24221	+	2.99896i	−0.0535554	+	0.129294i
$539$	−57.6322	+	23.8720i	−2.48239	+	1.02824i
$540$		0			0
$541$	−4.49686	−	10.8564i	−0.193335	−	0.466752i	0.797250	−	0.603649i	$-0.206287\pi$
$541$	−4.49686	−	10.8564i	−0.193335	−	0.466752i	−0.990585	+	0.136897i	$0.956287\pi$
$542$	0.313414	+	0.313414i	0.0134623	+	0.0134623i
$543$		0			0
$544$	−5.46282	−	1.04208i	−0.234216	−	0.0446786i
$545$	31.6328			1.35500
$546$		0			0
$547$	−9.35821	−	22.5927i	−0.400128	−	0.965995i	−0.987634	−	0.156775i	$-0.949890\pi$
$547$	−9.35821	−	22.5927i	−0.400128	−	0.965995i	0.587506	−	0.809220i	$-0.300110\pi$
$548$		−	43.5062i		−	1.85849i
$549$		0			0
$550$	1.30971	−	3.16192i	0.0558463	−	0.134825i
$551$	−28.4369	−	11.7790i	−1.21145	−	0.501800i
$552$		0			0
$553$	−8.80214	+	8.80214i	−0.374305	+	0.374305i
$554$	1.86979	+	0.774492i	0.0794397	+	0.0329050i
$555$		0			0
$556$	−9.28021	+	3.84399i	−0.393569	+	0.163021i
$557$		−	31.7081i		−	1.34351i	−0.740772	−	0.671757i	$-0.765540\pi$
$557$		−	31.7081i		−	1.34351i	0.740772	−	0.671757i	$-0.234460\pi$
$558$		0			0
$559$	2.52396	+	2.52396i	0.106752	+	0.106752i
$560$	−69.1350			−2.92149
$561$		0			0
$562$	−3.02629			−0.127657
$563$	25.3596	+	25.3596i	1.06878	+	1.06878i	0.997453	+	0.0713245i	$0.0227226\pi$
$563$	25.3596	+	25.3596i	1.06878	+	1.06878i	0.0713245	+	0.997453i	$0.477277\pi$
$564$		0			0
$565$		−	19.0389i		−	0.800973i
$566$	1.91944	−	0.795060i	0.0806803	−	0.0334189i
$567$		0			0
$568$	0.565375	+	0.234186i	0.0237226	+	0.00982622i
$569$	−20.7901	+	20.7901i	−0.871567	+	0.871567i	−0.992643	−	0.121076i	$-0.961366\pi$
$569$	−20.7901	+	20.7901i	−0.871567	+	0.871567i	0.121076	+	0.992643i	$0.461366\pi$
$570$		0			0
$571$	37.6782	+	15.6068i	1.57678	+	0.653124i	0.987900	−	0.155095i	$-0.0495683\pi$
$571$	37.6782	+	15.6068i	1.57678	+	0.653124i	0.588882	+	0.808219i	$0.299568\pi$
$572$	7.32305	−	17.6794i	0.306192	−	0.739213i
$573$		0			0
$574$			3.76471i			0.157136i
$575$	4.42911	+	10.6928i	0.184707	+	0.445922i
$576$		0			0
$577$	−8.38687			−0.349150			−0.174575	−	0.984644i	$-0.555855\pi$
$577$	−8.38687			−0.349150			−0.174575	+	0.984644i	$0.555855\pi$
$578$	−1.76880	+	0.765436i	−0.0735723	+	0.0318379i
$579$		0			0
$580$	40.2703	+	40.2703i	1.67213	+	1.67213i
$581$	−16.5305	−	39.9083i	−0.685803	−	1.65567i
$582$		0			0
$583$	−17.8178	+	7.38037i	−0.737938	+	0.305664i
$584$	1.97426	−	4.76628i	0.0816954	−	0.197230i
$585$		0			0
$586$	−1.33320	+	1.33320i	−0.0550738	+	0.0550738i
$587$	−17.4929	+	17.4929i	−0.722011	+	0.722011i	−0.969015	−	0.247004i	$-0.920554\pi$
$587$	−17.4929	+	17.4929i	−0.722011	+	0.722011i	0.247004	+	0.969015i	$0.420554\pi$
$588$		0			0
$589$	4.83134	−	11.6639i	0.199072	−	0.480602i
$590$	−2.45072	+	1.01512i	−0.100895	+	0.0417919i
$591$		0			0
$592$	9.88480	+	23.8640i	0.406263	+	0.980805i
$593$	−0.504383	−	0.504383i	−0.0207125	−	0.0207125i	0.696675	−	0.717387i	$-0.254662\pi$
$593$	−0.504383	−	0.504383i	−0.0207125	−	0.0207125i	−0.717387	+	0.696675i	$0.754662\pi$
$594$		0			0
$595$	−60.0961	+	40.8415i	−2.46370	+	1.67434i
$596$	42.0550			1.72264
$597$		0			0
$598$	−0.160181	−	0.386711i	−0.00655028	−	0.0158138i
$599$			26.1042i			1.06659i	0.845930	+	0.533294i	$0.179046\pi$
$599$			26.1042i			1.06659i	−0.845930	+	0.533294i	$0.820954\pi$
$600$		0			0
$601$	13.8000	−	33.3162i	0.562915	−	1.35900i	−0.344510	−	0.938783i	$-0.611955\pi$
$601$	13.8000	−	33.3162i	0.562915	−	1.35900i	0.907425	−	0.420214i	$-0.138045\pi$
$602$	0.705407	+	0.292189i	0.0287502	+	0.0119087i
$603$		0			0
$604$	8.74426	−	8.74426i	0.355799	−	0.355799i
$605$	−9.75147	−	4.03919i	−0.396454	−	0.164216i
$606$		0			0
$607$	30.4241	−	12.6021i	1.23488	−	0.511503i	0.332767	−	0.943009i	$-0.392018\pi$
$607$	30.4241	−	12.6021i	1.23488	−	0.511503i	0.902110	+	0.431507i	$0.142018\pi$
$608$			5.24149i			0.212570i
$609$		0			0
$610$	1.35078	+	1.35078i	0.0546916	+	0.0546916i
$611$	−19.0244			−0.769644
$612$		0			0
$613$	16.1615			0.652756			0.326378	−	0.945239i	$-0.394172\pi$
$613$	16.1615			0.652756			0.326378	+	0.945239i	$0.394172\pi$
$614$	−2.23940	−	2.23940i	−0.0903749	−	0.0903749i
$615$		0			0
$616$		−	8.21318i		−	0.330918i
$617$	−27.6059	+	11.4347i	−1.11137	+	0.460345i	−0.861410	−	0.507910i	$-0.830418\pi$
$617$	−27.6059	+	11.4347i	−1.11137	+	0.460345i	−0.249962	+	0.968256i	$0.580418\pi$
$618$		0			0
$619$	34.8056	+	14.4170i	1.39896	+	0.579467i	0.949481	−	0.313825i	$-0.101611\pi$
$619$	34.8056	+	14.4170i	1.39896	+	0.579467i	0.449476	+	0.893292i	$0.351611\pi$
$620$	−16.5175	+	16.5175i	−0.663361	+	0.663361i
$621$		0			0
$622$	1.34267	+	0.556152i	0.0538362	+	0.0222997i
$623$	16.0837	−	38.8295i	0.644381	−	1.55567i
$624$		0			0
$625$		−	0.0208904i		−	0.000835616i
$626$	−0.00992337	−	0.0239571i	−0.000396618	−	0.000957520i
$627$		0			0
$628$	−16.3026			−0.650543
$629$	22.6901	+	14.9045i	0.904713	+	0.594282i
$630$		0			0
$631$	−14.2914	−	14.2914i	−0.568930	−	0.568930i	0.362899	−	0.931829i	$-0.381787\pi$
$631$	−14.2914	−	14.2914i	−0.568930	−	0.568930i	−0.931829	+	0.362899i	$0.881787\pi$
$632$	−0.442117	−	1.06737i	−0.0175865	−	0.0424575i
$633$		0			0
$634$	1.33614	−	0.553447i	0.0530648	−	0.0219802i
$635$	−4.33848	+	10.4740i	−0.172167	+	0.415649i
$636$		0			0
$637$	30.5217	−	30.5217i	1.20931	−	1.20931i
$638$	−2.36880	+	2.36880i	−0.0937818	+	0.0937818i
$639$		0			0
$640$	4.94299	−	11.9334i	0.195389	−	0.471711i
$641$	10.1347	−	4.19794i	0.400297	−	0.165809i	−0.173447	−	0.984843i	$-0.555490\pi$
$641$	10.1347	−	4.19794i	0.400297	−	0.165809i	0.573744	+	0.819035i	$0.305490\pi$
$642$		0			0
$643$	1.55897	+	3.76370i	0.0614800	+	0.148426i	0.951634	−	0.307234i	$-0.0994034\pi$
$643$	1.55897	+	3.76370i	0.0614800	+	0.148426i	−0.890154	+	0.455660i	$0.849403\pi$
$644$	9.78826	+	9.78826i	0.385711	+	0.385711i
$645$		0			0
$646$	1.02101	+	1.50237i	0.0401712	+	0.0591099i
$647$	17.4383			0.685570			0.342785	−	0.939414i	$-0.388630\pi$
$647$	17.4383			0.685570			0.342785	+	0.939414i	$0.388630\pi$
$648$		0			0
$649$	9.23177	+	22.2875i	0.362379	+	0.874860i
$650$			2.36815i			0.0928866i
$651$		0			0
$652$	12.1311	−	29.2870i	0.475090	−	1.14697i
$653$	19.7152	+	8.16629i	0.771514	+	0.319572i	0.733485	−	0.679705i	$-0.237892\pi$
$653$	19.7152	+	8.16629i	0.771514	+	0.319572i	0.0380284	+	0.999277i	$0.487892\pi$
$654$		0			0
$655$	6.23112	−	6.23112i	0.243470	−	0.243470i
$656$	24.7113	+	10.2358i	0.964814	+	0.399639i
$657$		0			0
$658$	−3.75969	+	1.55732i	−0.146568	+	0.0607105i
$659$		−	31.9158i		−	1.24326i	−0.783310	−	0.621631i	$-0.786470\pi$
$659$		−	31.9158i		−	1.24326i	0.783310	−	0.621631i	$-0.213530\pi$
$660$		0			0
$661$	−27.9585	−	27.9585i	−1.08746	−	1.08746i	−0.995790	−	0.0916692i	$-0.970780\pi$
$661$	−27.9585	−	27.9585i	−1.08746	−	1.08746i	−0.0916692	−	0.995790i	$-0.529220\pi$
$662$	0.456999			0.0177618
$663$		0			0
$664$	4.00906			0.155582
$665$	48.4240	+	48.4240i	1.87780	+	1.87780i
$666$		0			0
$667$		−	11.3288i		−	0.438654i
$668$	29.0563	−	12.0355i	1.12422	−	0.465669i
$669$		0			0
$670$	2.79411	+	1.15736i	0.107946	+	0.0447127i
$671$	12.2844	−	12.2844i	0.474233	−	0.474233i
$672$		0			0
$673$	−25.1388	−	10.4128i	−0.969030	−	0.401386i	−0.158679	−	0.987330i	$-0.550724\pi$
$673$	−25.1388	−	10.4128i	−0.969030	−	0.401386i	−0.810351	+	0.585945i	$0.800724\pi$
$674$	0.142818	−	0.344794i	0.00550116	−	0.0132810i
$675$		0			0
$676$		−	12.5917i		−	0.484298i
$677$	−9.20473	−	22.2222i	−0.353766	−	0.854068i	−0.996148	−	0.0876831i	$-0.972054\pi$
$677$	−9.20473	−	22.2222i	−0.353766	−	0.854068i	0.642382	−	0.766385i	$-0.277946\pi$
$678$		0			0
$679$	−17.7065			−0.679513
$680$	−1.36754	−	6.60352i	−0.0524426	−	0.253233i
$681$		0			0
$682$	−0.971605	−	0.971605i	−0.0372047	−	0.0372047i
$683$	−4.93467	−	11.9133i	−0.188820	−	0.455851i	0.800913	−	0.598781i	$-0.204348\pi$
$683$	−4.93467	−	11.9133i	−0.188820	−	0.455851i	−0.989733	+	0.142929i	$0.954348\pi$
$684$		0			0
$685$	73.1880	−	30.3155i	2.79637	−	1.15829i
$686$	2.05422	−	4.95934i	0.0784307	−	0.189348i
$687$		0			0
$688$	3.83582	−	3.83582i	0.146239	−	0.146239i
$689$	9.43620	−	9.43620i	0.359491	−	0.359491i
$690$		0			0
$691$	18.6705	−	45.0746i	0.710260	−	1.71472i	0.0109088	−	0.999940i	$-0.496528\pi$
$691$	18.6705	−	45.0746i	0.710260	−	1.71472i	0.699351	−	0.714778i	$-0.253472\pi$
$692$	36.7839	−	15.2364i	1.39832	−	0.579201i
$693$		0			0
$694$	−0.453461	−	1.09475i	−0.0172131	−	0.0415562i
$695$	−12.9331	−	12.9331i	−0.490579	−	0.490579i
$696$		0			0
$697$	27.5272	−	5.70068i	1.04267	−	0.215929i
$698$	−0.0568884			−0.00215326
$699$		0			0
$700$	−29.9708	−	72.3560i	−1.13279	−	2.73480i
$701$			13.4261i			0.507097i	0.967323	+	0.253548i	$0.0815977\pi$
$701$			13.4261i			0.507097i	−0.967323	+	0.253548i	$0.918402\pi$
$702$		0			0
$703$	9.79141	−	23.6386i	0.369290	−	0.891545i
$704$	−26.5152	−	10.9830i	−0.999330	−	0.413936i
$705$		0			0
$706$	−2.39711	+	2.39711i	−0.0902165	+	0.0902165i
$707$	10.4668	+	4.33549i	0.393644	+	0.163053i
$708$		0			0
$709$	−26.5494	+	10.9971i	−0.997083	+	0.413005i	−0.820727	−	0.571321i	$-0.806431\pi$
$709$	−26.5494	+	10.9971i	−0.997083	+	0.413005i	−0.176356	+	0.984326i	$0.556431\pi$
$710$			0.555344i			0.0208417i
$711$		0			0
$712$	2.75821	+	2.75821i	0.103368	+	0.103368i
$713$	4.64672			0.174021
$714$		0			0
$715$	34.8438			1.30309
$716$	−25.9902	−	25.9902i	−0.971299	−	0.971299i
$717$		0			0
$718$			1.54540i			0.0576737i
$719$	10.1716	−	4.21320i	0.379335	−	0.157126i	−0.184865	−	0.982764i	$-0.559185\pi$
$719$	10.1716	−	4.21320i	0.379335	−	0.157126i	0.564200	+	0.825638i	$0.309185\pi$
$720$		0			0
$721$	18.0472	+	7.47538i	0.672112	+	0.278398i
$722$	−0.312576	+	0.312576i	−0.0116329	+	0.0116329i
$723$		0			0
$724$	−8.90627	−	3.68910i	−0.330999	−	0.137104i
$725$	−24.5281	+	59.2160i	−0.910950	+	2.19923i
$726$		0			0
$727$			5.45319i			0.202248i	0.994874	+	0.101124i	$0.0322438\pi$
$727$			5.45319i			0.202248i	−0.994874	+	0.101124i	$0.967756\pi$
$728$	2.17483	+	5.25050i	0.0806044	+	0.194596i
$729$		0			0
$730$	4.68172			0.173278
$731$	1.06831	−	5.60032i	0.0395127	−	0.207135i
$732$		0			0
$733$	−11.2048	−	11.2048i	−0.413858	−	0.413858i	0.469222	−	0.883080i	$-0.344534\pi$
$733$	−11.2048	−	11.2048i	−0.413858	−	0.413858i	−0.883080	+	0.469222i	$0.844534\pi$
$734$	−0.579835	−	1.39984i	−0.0214021	−	0.0516692i
$735$		0			0
$736$	−1.78233	+	0.738265i	−0.0656976	+	0.0272128i
$737$	10.5253	−	25.4104i	0.387705	−	0.936003i
$738$		0			0
$739$	23.3188	−	23.3188i	0.857795	−	0.857795i	−0.133283	−	0.991078i	$-0.542552\pi$
$739$	23.3188	−	23.3188i	0.857795	−	0.857795i	0.991078	+	0.133283i	$0.0425519\pi$
$740$	−33.4752	+	33.4752i	−1.23057	+	1.23057i
$741$		0			0
$742$	1.09239	−	2.63727i	0.0401030	−	0.0968171i
$743$	−38.7942	+	16.0691i	−1.42322	+	0.589517i	−0.955668	−	0.294448i	$-0.904864\pi$
$743$	−38.7942	+	16.0691i	−1.42322	+	0.589517i	−0.467553	+	0.883965i	$0.654864\pi$
$744$		0			0
$745$	29.3043	+	70.7468i	1.07363	+	2.59196i
$746$	1.31286	+	1.31286i	0.0480673	+	0.0480673i
$747$		0			0
$748$	−29.9302	+	6.19832i	−1.09436	+	0.226633i
$749$	−24.4014			−0.891609
$750$		0			0
$751$	−5.58970	−	13.4947i	−0.203971	−	0.492430i	0.788481	−	0.615059i	$-0.210868\pi$
$751$	−5.58970	−	13.4947i	−0.203971	−	0.492430i	−0.992453	+	0.122629i	$0.960868\pi$
$752$			28.9125i			1.05433i
$753$		0			0
$754$	0.887068	−	2.14157i	0.0323051	−	0.0779915i
$755$	20.8031	+	8.61691i	0.757101	+	0.313601i
$756$		0			0
$757$	−24.1046	+	24.1046i	−0.876098	+	0.876098i	−0.993128	−	0.117031i	$-0.962662\pi$
$757$	−24.1046	+	24.1046i	−0.876098	+	0.876098i	0.117031	+	0.993128i	$0.462662\pi$
$758$	2.22939	+	0.923442i	0.0809749	+	0.0335409i
$759$		0			0
$760$	−5.87200	+	2.43226i	−0.213000	+	0.0882274i
$761$		−	0.721195i		−	0.0261433i	−0.999915	−	0.0130716i	$-0.995839\pi$
$761$		−	0.721195i		−	0.0261433i	0.999915	−	0.0130716i	$-0.00416095\pi$
$762$		0			0
$763$	30.1086	+	30.1086i	1.09000	+	1.09000i
$764$	9.26180			0.335080
$765$		0			0
$766$	1.10705			0.0399992
$767$	−11.8033	−	11.8033i	−0.426193	−	0.426193i
$768$		0			0
$769$			34.6936i			1.25108i	0.780191	+	0.625542i	$0.215122\pi$
$769$			34.6936i			1.25108i	−0.780191	+	0.625542i	$0.784878\pi$
$770$	6.88602	−	2.85228i	0.248155	−	0.102789i
$771$		0			0
$772$	18.1908	+	7.53487i	0.654701	+	0.271186i
$773$	7.39294	−	7.39294i	0.265906	−	0.265906i	−0.561542	−	0.827448i	$-0.689792\pi$
$773$	7.39294	−	7.39294i	0.265906	−	0.265906i	0.827448	+	0.561542i	$0.189792\pi$
$774$		0			0
$775$	−24.2885	−	10.0606i	−0.872468	−	0.361388i
$776$	0.628878	−	1.51825i	0.0225754	−	0.0545019i
$777$		0			0
$778$		−	0.0207716i		−	0.000744698i
$779$	−10.1391	−	24.4779i	−0.363269	−	0.877010i
$780$		0			0
$781$	5.05044			0.180719
$782$	−0.367059	+	0.558797i	−0.0131260	+	0.0199825i
$783$		0			0
$784$	−46.3857	−	46.3857i	−1.65663	−	1.65663i
$785$	−11.3598	−	27.4249i	−0.405447	−	0.978836i
$786$		0			0
$787$	−48.5309	+	20.1022i	−1.72994	+	0.716565i	−0.730508	+	0.682904i	$0.760717\pi$
$787$	−48.5309	+	20.1022i	−1.72994	+	0.716565i	−0.999433	+	0.0336613i	$0.989283\pi$
$788$	−9.85078	+	23.7819i	−0.350920	+	0.847195i
$789$		0			0
$790$	0.741351	−	0.741351i	0.0263761	−	0.0263761i
$791$	18.1215	−	18.1215i	0.644327	−	0.644327i
$792$		0			0
$793$	−4.60025	+	11.1060i	−0.163360	+	0.394385i
$794$	2.84103	−	1.17680i	0.100825	−	0.0417629i
$795$		0			0
$796$	−21.0757	−	50.8812i	−0.747008	−	1.80344i
$797$	−13.5472	−	13.5472i	−0.479866	−	0.479866i	0.425223	−	0.905089i	$-0.360196\pi$
$797$	−13.5472	−	13.5472i	−0.479866	−	0.479866i	−0.905089	+	0.425223i	$0.860196\pi$
$798$		0			0
$799$	17.0800	+	25.1324i	0.604249	+	0.889121i
$800$	10.9147			0.385893
$801$		0			0
$802$	1.08580	+	2.62135i	0.0383409	+	0.0925630i
$803$		−	42.5768i		−	1.50250i
$804$		0			0
$805$	−9.64570	+	23.2868i	−0.339966	+	0.820751i
$806$	0.878403	+	0.363847i	0.0309404	+	0.0128159i
$807$		0			0
$808$	−0.743495	+	0.743495i	−0.0261561	+	0.0261561i
$809$	−37.3957	−	15.4898i	−1.31476	−	0.544592i	−0.388492	−	0.921452i	$-0.627004\pi$
$809$	−37.3957	−	15.4898i	−1.31476	−	0.544592i	−0.926270	+	0.376860i	$0.877004\pi$
$810$		0			0
$811$	48.2917	−	20.0031i	1.69575	−	0.702403i	0.695876	−	0.718162i	$-0.255016\pi$
$811$	48.2917	−	20.0031i	1.69575	−	0.702403i	0.999876	+	0.0157590i	$0.00501646\pi$
$812$			76.6597i			2.69023i
$813$		0			0
$814$	−1.96910	−	1.96910i	−0.0690169	−	0.0690169i
$815$	57.7210			2.02188
$816$		0			0
$817$	−5.37342			−0.187992
$818$	−0.162672	−	0.162672i	−0.00568770	−	0.00568770i
$819$		0			0
$820$			49.0219i			1.71192i
$821$	−41.7614	+	17.2982i	−1.45748	+	0.603710i	−0.963966	−	0.266026i	$-0.914289\pi$
$821$	−41.7614	+	17.2982i	−1.45748	+	0.603710i	−0.493518	+	0.869735i	$0.664289\pi$
$822$		0			0
$823$	18.1831	+	7.53171i	0.633825	+	0.262539i	0.676377	−	0.736555i	$-0.263549\pi$
$823$	18.1831	+	7.53171i	0.633825	+	0.262539i	−0.0425525	+	0.999094i	$0.513549\pi$
$824$	−1.28196	+	1.28196i	−0.0446591	+	0.0446591i
$825$		0			0
$826$	−3.29884	−	1.36642i	−0.114781	−	0.0475440i
$827$	−13.0577	+	31.5241i	−0.454061	+	1.09620i	0.516703	+	0.856165i	$0.327159\pi$
$827$	−13.0577	+	31.5241i	−0.454061	+	1.09620i	−0.970764	+	0.240036i	$0.922841\pi$
$828$		0			0
$829$			43.1191i			1.49759i	0.662802	+	0.748794i	$0.269367\pi$
$829$			43.1191i			1.49759i	−0.662802	+	0.748794i	$0.730633\pi$
$830$	1.39227	+	3.36123i	0.0483264	+	0.116670i
$831$		0			0
$832$	19.8588			0.688481
$833$	−67.7234	−	12.9188i	−2.34648	−	0.447609i
$834$		0			0
$835$	40.4934	+	40.4934i	1.40133	+	1.40133i
$836$	11.0241	+	26.6147i	0.381278	+	0.920487i
$837$		0			0
$838$	−0.899090	+	0.372415i	−0.0310586	+	0.0128649i
$839$	4.12300	−	9.95380i	0.142342	−	0.343643i	−0.836590	−	0.547829i	$-0.815455\pi$
$839$	4.12300	−	9.95380i	0.142342	−	0.343643i	0.978932	+	0.204185i	$0.0654545\pi$
$840$		0			0
$841$	23.8565	−	23.8565i	0.822637	−	0.822637i
$842$	−1.21525	+	1.21525i	−0.0418803	+	0.0418803i
$843$		0			0
$844$	−17.2847	+	41.7289i	−0.594963	+	1.43637i
$845$	21.1824	−	8.77403i	0.728696	−	0.301836i
$846$		0			0
$847$	−5.43703	−	13.1262i	−0.186819	−	0.451020i
$848$	−14.3408	−	14.3408i	−0.492464	−	0.492464i
$849$		0			0
$850$	3.12848	−	2.12612i	0.107306	−	0.0729254i
$851$	9.41725			0.322819
$852$		0			0
$853$	−13.0379	−	31.4763i	−0.446410	−	1.07773i	−0.973657	−	0.228016i	$-0.926776\pi$
$853$	−13.0379	−	31.4763i	−0.446410	−	1.07773i	0.527248	−	0.849712i	$-0.323224\pi$
$854$			2.57139i			0.0879912i
$855$		0			0
$856$	0.866662	−	2.09231i	0.0296219	−	0.0715136i
$857$	−22.8837	−	9.47874i	−0.781692	−	0.323787i	−0.0440939	−	0.999027i	$-0.514040\pi$
$857$	−22.8837	−	9.47874i	−0.781692	−	0.323787i	−0.737598	+	0.675240i	$0.764040\pi$
$858$		0			0
$859$	0.681709	−	0.681709i	0.0232596	−	0.0232596i	−0.695381	−	0.718641i	$-0.744765\pi$
$859$	0.681709	−	0.681709i	0.0232596	−	0.0232596i	0.718641	+	0.695381i	$0.244765\pi$
$860$	9.18541	+	3.80472i	0.313220	+	0.129740i
$861$		0			0
$862$	−3.11013	+	1.28826i	−0.105931	+	0.0438783i
$863$			42.1294i			1.43410i	0.697022	+	0.717050i	$0.254508\pi$
$863$			42.1294i			1.43410i	−0.697022	+	0.717050i	$0.745492\pi$
$864$		0			0
$865$	51.2627	+	51.2627i	1.74298	+	1.74298i
$866$	1.80172			0.0612248
$867$		0			0
$868$	−31.4433			−1.06725
$869$	−6.74204	−	6.74204i	−0.228708	−	0.228708i
$870$		0			0
$871$			19.0313i			0.644853i
$872$	−3.65103	+	1.51230i	−0.123639	+	0.0512131i
$873$		0			0
$874$	0.582156	+	0.241137i	0.0196917	+	0.00815658i
$875$	38.5305	−	38.5305i	1.30257	−	1.30257i
$876$		0			0
$877$	−48.1715	−	19.9533i	−1.62664	−	0.673775i	−0.631788	−	0.775141i	$-0.717679\pi$
$877$	−48.1715	−	19.9533i	−1.62664	−	0.673775i	−0.994849	+	0.101366i	$0.967679\pi$
$878$	−0.445805	+	1.07627i	−0.0150452	+	0.0363223i
$879$		0			0
$880$		−	52.9543i		−	1.78509i
$881$	6.59863	+	15.9305i	0.222313	+	0.536712i	0.995203	−	0.0978281i	$-0.0311895\pi$
$881$	6.59863	+	15.9305i	0.222313	+	0.536712i	−0.772890	+	0.634540i	$0.781190\pi$
$882$		0			0
$883$	−19.4857			−0.655747			−0.327873	−	0.944722i	$-0.606332\pi$
$883$	−19.4857			−0.655747			−0.327873	+	0.944722i	$0.606332\pi$
$884$	17.4924	−	11.8879i	0.588334	−	0.399833i
$885$		0			0
$886$	0.384344	+	0.384344i	0.0129123	+	0.0129123i
$887$	2.12565	+	5.13176i	0.0713722	+	0.172308i	0.955540	−	0.294862i	$-0.0952737\pi$
$887$	2.12565	+	5.13176i	0.0713722	+	0.172308i	−0.884168	+	0.467170i	$0.845274\pi$
$888$		0			0
$889$	−14.0987	+	5.83989i	−0.472857	+	0.195864i
$890$	−1.35464	+	3.27038i	−0.0454075	+	0.109623i
$891$		0			0
$892$	16.8982	−	16.8982i	0.565794	−	0.565794i
$893$	20.2511	−	20.2511i	0.677677	−	0.677677i
$894$		0			0
$895$	25.6117	−	61.8320i	0.856103	−	2.06682i
$896$	16.0632	−	6.65361i	0.536635	−	0.222282i
$897$		0			0
$898$	−0.830828	−	2.00580i	−0.0277251	−	0.0669343i
$899$	18.1961	+	18.1961i	0.606873	+	0.606873i
$900$		0			0
$901$	−20.9376	−	3.99402i	−0.697533	−	0.133060i
$902$	−2.88360			−0.0960133
$903$		0			0
$904$	0.910215	+	2.19745i	0.0302733	+	0.0730862i
$905$		−	17.5531i		−	0.583485i
$906$		0			0
$907$	−4.25298	+	10.2676i	−0.141218	+	0.340930i	−0.978626	−	0.205648i	$-0.934070\pi$
$907$	−4.25298	+	10.2676i	−0.141218	+	0.340930i	0.837408	+	0.546578i	$0.184070\pi$
$908$	−27.1308	−	11.2380i	−0.900369	−	0.372945i
$909$		0			0
$910$	−3.64680	+	3.64680i	−0.120890	+	0.120890i
$911$	28.5444	+	11.8235i	0.945717	+	0.391729i	0.801619	−	0.597835i	$-0.203972\pi$
$911$	28.5444	+	11.8235i	0.945717	+	0.391729i	0.144097	+	0.989564i	$0.453972\pi$
$912$		0			0
$913$	30.5679	−	12.6617i	1.01165	−	0.419040i
$914$			0.591227i			0.0195560i
$915$		0			0
$916$	19.9683	+	19.9683i	0.659771	+	0.659771i
$917$	11.8617			0.391709
$918$		0			0
$919$	−26.7590			−0.882699			−0.441349	−	0.897335i	$-0.645500\pi$
$919$	−26.7590			−0.882699			−0.441349	+	0.897335i	$0.645500\pi$
$920$	−1.65415	−	1.65415i	−0.0545356	−	0.0545356i
$921$		0			0
$922$			2.10119i			0.0691989i
$923$	−3.22863	+	1.33734i	−0.106272	+	0.0440192i
$924$		0			0
$925$	−49.2241	−	20.3893i	−1.61848	−	0.670396i
$926$	2.91465	−	2.91465i	0.0957814	−	0.0957814i
$927$		0			0
$928$	−9.87040	−	4.08845i	−0.324012	−	0.134210i
$929$	−4.52207	+	10.9172i	−0.148364	+	0.358183i	−0.980537	−	0.196333i	$-0.937097\pi$
$929$	−4.52207	+	10.9172i	−0.148364	+	0.358183i	0.832173	+	0.554516i	$0.187097\pi$
$930$		0			0
$931$			64.9795i			2.12962i
$932$	−6.55599	−	15.8275i	−0.214748	−	0.518449i
$933$		0			0
$934$	−1.74547			−0.0571134
$935$	−31.2827	−	46.0309i	−1.02305	−	1.50537i
$936$		0			0
$937$	−10.1101	−	10.1101i	−0.330284	−	0.330284i	0.522410	−	0.852694i	$-0.325033\pi$
$937$	−10.1101	−	10.1101i	−0.330284	−	0.330284i	−0.852694	+	0.522410i	$0.825033\pi$
$938$	1.55789	+	3.76107i	0.0508668	+	0.122803i
$939$		0			0
$940$	−48.9566	+	20.2785i	−1.59679	+	0.661412i
$941$	−6.62017	+	15.9825i	−0.215811	+	0.521015i	−0.994297	−	0.106648i	$-0.965988\pi$
$941$	−6.62017	+	15.9825i	−0.215811	+	0.521015i	0.778485	+	0.627663i	$0.215988\pi$
$942$		0			0
$943$	6.89543	−	6.89543i	0.224546	−	0.224546i
$944$	−17.9382	+	17.9382i	−0.583840	+	0.583840i
$945$		0			0
$946$	−0.223804	+	0.540310i	−0.00727648	+	0.0175670i
$947$	−38.0356	+	15.7549i	−1.23599	+	0.511964i	−0.902460	−	0.430774i	$-0.858240\pi$
$947$	−38.0356	+	15.7549i	−1.23599	+	0.511964i	−0.333532	+	0.942739i	$0.608240\pi$
$948$		0			0
$949$	11.2742	+	27.2184i	0.365977	+	0.883546i
$950$	−2.52085	−	2.52085i	−0.0817873	−	0.0817873i
$951$		0			0
$952$	4.98368	−	7.58697i	0.161522	−	0.245895i
$953$	−11.2870			−0.365623			−0.182812	−	0.983148i	$-0.558520\pi$
$953$	−11.2870			−0.365623			−0.182812	+	0.983148i	$0.558520\pi$
$954$		0			0
$955$	6.45370	+	15.5806i	0.208837	+	0.504177i
$956$		−	31.9629i		−	1.03375i
$957$		0			0
$958$	0.602236	−	1.45393i	0.0194573	−	0.0469742i
$959$	98.5162	+	40.8067i	3.18125	+	1.31772i
$960$		0			0
$961$	14.4569	−	14.4569i	0.466351	−	0.466351i
$962$	1.78021	+	0.737388i	0.0573963	+	0.0237743i
$963$		0			0
$964$	5.99738	−	2.48419i	0.193163	−	0.0800105i
$965$			35.8517i			1.15411i
$966$		0			0
$967$	−10.5780	−	10.5780i	−0.340164	−	0.340164i	0.516265	−	0.856429i	$-0.327322\pi$
$967$	−10.5780	−	10.5780i	−0.340164	−	0.340164i	−0.856429	+	0.516265i	$0.827322\pi$
$968$	1.31861			0.0423818
$969$		0			0
$970$	1.49131			0.0478831
$971$	−36.2522	−	36.2522i	−1.16339	−	1.16339i	−0.983729	−	0.179661i	$-0.942500\pi$
$971$	−36.2522	−	36.2522i	−1.16339	−	1.16339i	−0.179661	−	0.983729i	$-0.557500\pi$
$972$		0			0
$973$		−	24.6198i		−	0.789273i
$974$	−2.49012	+	1.03144i	−0.0797885	+	0.0330495i
$975$		0			0
$976$	16.8785	+	6.99128i	0.540266	+	0.223786i
$977$	25.1236	−	25.1236i	0.803775	−	0.803775i	−0.179908	−	0.983683i	$-0.557580\pi$
$977$	25.1236	−	25.1236i	0.803775	−	0.803775i	0.983683	+	0.179908i	$0.0575801\pi$
$978$		0			0
$979$	29.7417	+	12.3194i	0.950548	+	0.393730i
$980$	46.0096	−	111.077i	1.46972	−	3.54823i
$981$		0			0
$982$		−	1.31617i		−	0.0420005i
$983$	22.2990	+	53.8345i	0.711227	+	1.71705i	0.696912	+	0.717157i	$0.254557\pi$
$983$	22.2990	+	53.8345i	0.711227	+	1.71705i	0.0143153	+	0.999898i	$0.495443\pi$
$984$		0			0
$985$	−46.8710			−1.49344
$986$	−3.62556	+	0.750825i	−0.115461	+	0.0239112i
$987$		0			0
$988$	−14.0950	−	14.0950i	−0.448421	−	0.448421i
$989$	−0.756848	−	1.82719i	−0.0240664	−	0.0581013i
$990$		0			0
$991$	2.64825	−	1.09694i	0.0841244	−	0.0348455i	−0.340224	−	0.940344i	$-0.610503\pi$
$991$	2.64825	−	1.09694i	0.0841244	−	0.0348455i	0.424349	+	0.905499i	$0.360503\pi$
$992$	1.67695	−	4.04851i	0.0532432	−	0.128540i
$993$		0			0
$994$	−0.528585	+	0.528585i	−0.0167657	+	0.0167657i
$995$	70.9089	−	70.9089i	2.24796	−	2.24796i
$996$		0			0
$997$	−14.6016	+	35.2515i	−0.462439	+	1.11643i	0.504954	+	0.863146i	$0.331509\pi$
$997$	−14.6016	+	35.2515i	−0.462439	+	1.11643i	−0.967393	+	0.253280i	$0.918491\pi$
$998$	−0.0411240	+	0.0170341i	−0.00130176	+	0.000539205i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.l.a.406.6	✓	48
3.2	odd	2	inner	459.2.l.a.406.7	yes	48
17.5	odd	16		7803.2.a.cd.1.13		24
17.8	even	8	inner	459.2.l.a.433.6	yes	48
17.12	odd	16		7803.2.a.cg.1.13		24
51.5	even	16		7803.2.a.cg.1.12		24
51.8	odd	8	inner	459.2.l.a.433.7	yes	48
51.29	even	16		7803.2.a.cd.1.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.l.a.406.6	✓	48	1.1	even	1	trivial
459.2.l.a.406.7	yes	48	3.2	odd	2	inner
459.2.l.a.433.6	yes	48	17.8	even	8	inner
459.2.l.a.433.7	yes	48	51.8	odd	8	inner
7803.2.a.cd.1.12		24	51.29	even	16
7803.2.a.cd.1.13		24	17.5	odd	16
7803.2.a.cg.1.12		24	51.5	even	16
7803.2.a.cg.1.13		24	17.12	odd	16

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0801657 - 0.0801657i) q^{2} -1.98715i q^{4} +(3.34287 - 1.38466i) q^{5} +(4.49973 + 1.86385i) q^{7} +(-0.319632 + 0.319632i) q^{8} +(-0.378985 - 0.156981i) q^{10} +(-1.42762 + 3.44659i) q^{11} -2.58136i q^{13} +(-0.211307 - 0.510141i) q^{14} -3.92305 q^{16} +(-3.41014 + 2.31754i) q^{17} +(2.74781 + 2.74781i) q^{19} +(-2.75152 - 6.64277i) q^{20} +(0.390745 - 0.161852i) q^{22} +(-0.547342 + 1.32140i) q^{23} +(5.72194 - 5.72194i) q^{25} +(-0.206936 + 0.206936i) q^{26} +(3.70374 - 8.94163i) q^{28} +(-7.31781 + 3.03114i) q^{29} +(-1.24327 - 3.00153i) q^{31} +(0.953759 + 0.953759i) q^{32} +(0.459163 + 0.0875890i) q^{34} +17.6228 q^{35} +(-2.51967 - 6.08303i) q^{37} -0.440560i q^{38} +(-0.625906 + 1.51107i) q^{40} +(-6.29901 - 2.60913i) q^{41} +(-0.977765 + 0.977765i) q^{43} +(6.84888 + 2.83690i) q^{44} +(0.149809 - 0.0620530i) q^{46} -7.36992i q^{47} +(11.8239 + 11.8239i) q^{49} -0.917406 q^{50} -5.12954 q^{52} +(3.65552 + 3.65552i) q^{53} +13.4983i q^{55} +(-2.03401 + 0.842513i) q^{56} +(0.829630 + 0.343644i) q^{58} +(4.57252 - 4.57252i) q^{59} +(-4.30238 - 1.78211i) q^{61} +(-0.140952 + 0.340287i) q^{62} +7.69318i q^{64} +(-3.57430 - 8.62913i) q^{65} -7.37261 q^{67} +(4.60529 + 6.77644i) q^{68} +(-1.41274 - 1.41274i) q^{70} +(-0.518078 - 1.25075i) q^{71} +(-10.5442 + 4.36755i) q^{73} +(-0.285659 + 0.689642i) q^{74} +(5.46029 - 5.46029i) q^{76} +(-12.8479 + 12.8479i) q^{77} +(-0.978074 + 2.36128i) q^{79} +(-13.1142 + 5.43209i) q^{80} +(0.295801 + 0.714127i) q^{82} +(-6.27135 - 6.27135i) q^{83} +(-8.19063 + 12.4691i) q^{85} +0.156766 q^{86} +(-0.645327 - 1.55796i) q^{88} -8.62930i q^{89} +(4.81126 - 11.6154i) q^{91} +(2.62582 + 1.08765i) q^{92} +(-0.590814 + 0.590814i) q^{94} +(12.9903 + 5.38077i) q^{95} +(-3.35874 + 1.39124i) q^{97} -1.89574i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{10} - 48 q^{16} - 16 q^{19} - 24 q^{22} + 16 q^{25} + 24 q^{28} - 40 q^{31} + 64 q^{34} + 48 q^{37} - 48 q^{40} - 8 q^{43} + 24 q^{46} - 16 q^{49} + 32 q^{52} + 64 q^{58} - 24 q^{61} - 32 q^{67}+ \cdots - 88 q^{97}+O(q^{100}) \) 48 * q - 16 * q^10 - 48 * q^16 - 16 * q^19 - 24 * q^22 + 16 * q^25 + 24 * q^28 - 40 * q^31 + 64 * q^34 + 48 * q^37 - 48 * q^40 - 8 * q^43 + 24 * q^46 - 16 * q^49 + 32 * q^52 + 64 * q^58 - 24 * q^61 - 32 * q^67 + 96 * q^70 + 48 * q^73 + 96 * q^76 - 48 * q^79 + 112 * q^82 - 56 * q^85 - 160 * q^88 - 80 * q^91 - 40 * q^94 - 88 * q^97

Introduction

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