LMFDB - Embedded newform 875.2.bb.b.507.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			507.5
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.b.768.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33031 - 0.863911i) q^{2} +(1.82975 + 0.702377i) q^{3} +(0.209899 + 0.471441i) q^{4} +(-1.82734 - 2.51512i) q^{6} +(1.63042 - 2.08368i) q^{7} +(-0.368222 + 2.32486i) q^{8} +(0.625235 + 0.562964i) q^{9} +(1.39398 + 1.54818i) q^{11} +(0.0529345 + 1.01005i) q^{12} +(0.992394 - 1.94768i) q^{13} +(-3.96908 + 1.36339i) q^{14} +(3.18894 - 3.54168i) q^{16} +(-3.93706 - 3.18817i) q^{17} +(-0.345403 - 1.28906i) q^{18} +(6.86927 + 3.05840i) q^{19} +(4.44680 - 2.66745i) q^{21} +(-0.516939 - 3.26382i) q^{22} +(-1.09383 + 1.68435i) q^{23} +(-2.30669 + 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(-1.92076 - 3.76970i) q^{27} +(1.32456 + 0.331286i) q^{28} +(4.12547 - 5.67823i) q^{29} +(6.31745 - 0.663990i) q^{31} +(-2.75469 + 0.738117i) q^{32} +(1.46324 + 3.81188i) q^{33} +(2.48320 + 7.64252i) q^{34} +(-0.134168 + 0.412927i) q^{36} +(-2.64422 + 0.138578i) q^{37} +(-6.49605 - 10.0030i) q^{38} +(3.18385 - 2.86675i) q^{39} +(-8.47974 + 2.75523i) q^{41} +(-8.22005 - 0.293115i) q^{42} +(0.986332 - 0.986332i) q^{43} +(-0.437278 + 0.982142i) q^{44} +(2.91025 - 1.29573i) q^{46} +(1.65339 + 2.04177i) q^{47} +(8.32258 - 4.24056i) q^{48} +(-1.68344 - 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(1.12652 + 0.0590385i) q^{52} +(3.31015 - 8.62323i) q^{53} +(-0.701489 + 6.67422i) q^{54} +(4.24391 + 4.55777i) q^{56} +(10.4209 + 10.4209i) q^{57} +(-10.3936 + 3.98974i) q^{58} +(10.2924 + 2.18773i) q^{59} +(1.78346 + 8.39053i) q^{61} +(-8.97777 - 4.57440i) q^{62} +(2.19243 - 0.384920i) q^{63} +(-4.76284 - 1.54754i) q^{64} +(1.34656 - 6.33508i) q^{66} +(2.06649 - 2.55191i) q^{67} +(0.676649 - 2.52529i) q^{68} +(-3.18448 + 2.31366i) q^{69} +(5.41526 + 3.93442i) q^{71} +(-1.53904 + 1.24629i) q^{72} +(0.433401 - 8.26979i) q^{73} +(3.63734 + 2.10002i) q^{74} +3.88041i q^{76} +(5.49868 - 0.380434i) q^{77} +(-6.71211 + 1.06309i) q^{78} +(2.65691 + 0.279252i) q^{79} +(-1.13060 - 10.7569i) q^{81} +(13.6609 + 3.66043i) q^{82} +(2.88395 + 0.456772i) q^{83} +(2.19093 + 1.53651i) q^{84} +(-2.16423 + 0.460021i) q^{86} +(11.5369 - 7.49212i) q^{87} +(-4.11259 + 2.67075i) q^{88} +(-12.3861 + 2.63274i) q^{89} +(-2.44033 - 5.24338i) q^{91} +(-1.02366 - 0.162132i) q^{92} +(12.0258 + 3.22229i) q^{93} +(-0.435611 - 4.14456i) q^{94} +(-5.55884 - 0.584258i) q^{96} +(3.33125 - 0.527619i) q^{97} +(-3.63040 + 10.4932i) q^{98} +1.75274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) $ 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.33031	−	0.863911i	−0.940669	−	0.610877i	−0.0194031	−	0.999812i	$-0.506177\pi$
$2$	−1.33031	−	0.863911i	−0.940669	−	0.610877i	−0.921265	+	0.388934i	$0.872843\pi$
$3$	1.82975	+	0.702377i	1.05641	+	0.405518i	0.823698	−	0.567028i	$-0.191907\pi$
$3$	1.82975	+	0.702377i	1.05641	+	0.405518i	0.232711	+	0.972546i	$0.425240\pi$
$4$	0.209899	+	0.471441i	0.104950	+	0.235721i
$5$		0			0
$5$		0			0
$6$	−1.82734	−	2.51512i	−0.746010	−	1.02679i
$7$	1.63042	−	2.08368i	0.616242	−	0.787557i
$7$	1.63042	−	2.08368i	0.616242	−	0.787557i
$8$	−0.368222	+	2.32486i	−0.130186	+	0.821963i
$9$	0.625235	+	0.562964i	0.208412	+	0.187655i
$10$		0			0
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	0.915694	−	0.401877i	$-0.131642\pi$
$11$	1.39398	+	1.54818i	0.420302	+	0.466792i	−0.495392	+	0.868670i	$0.664975\pi$
$12$	0.0529345	+	1.01005i	0.0152809	+	0.291576i
$13$	0.992394	−	1.94768i	0.275241	−	0.540190i	−0.711462	−	0.702724i	$-0.751967\pi$
$13$	0.992394	−	1.94768i	0.275241	−	0.540190i	0.986703	+	0.162534i	$0.0519667\pi$
$14$	−3.96908	+	1.36339i	−1.06078	+	0.364382i
$15$		0			0
$16$	3.18894	−	3.54168i	0.797235	−	0.885420i
$17$	−3.93706	−	3.18817i	−0.954878	−	0.773245i	0.0191163	−	0.999817i	$-0.493915\pi$
$17$	−3.93706	−	3.18817i	−0.954878	−	0.773245i	−0.973994	+	0.226572i	$0.927248\pi$
$18$	−0.345403	−	1.28906i	−0.0814123	−	0.303835i
$19$	6.86927	+	3.05840i	1.57592	+	0.701644i	0.993771	−	0.111438i	$-0.0355458\pi$
$19$	6.86927	+	3.05840i	1.57592	+	0.701644i	0.582148	+	0.813083i	$0.302212\pi$
$20$		0			0
$21$	4.44680	−	2.66745i	0.970372	−	0.582086i
$22$	−0.516939	−	3.26382i	−0.110212	−	0.695850i
$23$	−1.09383	+	1.68435i	−0.228079	+	0.351210i	−0.934119	−	0.356961i	$-0.883813\pi$
$23$	−1.09383	+	1.68435i	−0.228079	+	0.351210i	0.706041	+	0.708171i	$0.250480\pi$
$24$	−2.30669	+	3.99530i	−0.470851	+	0.815537i
$25$		0			0
$26$	−3.00281	+	1.73368i	−0.588900	+	0.340002i
$27$	−1.92076	−	3.76970i	−0.369650	−	0.725479i
$28$	1.32456	+	0.331286i	0.250318	+	0.0626072i
$29$	4.12547	−	5.67823i	0.766081	−	1.05442i	−0.230603	−	0.973048i	$-0.574070\pi$
$29$	4.12547	−	5.67823i	0.766081	−	1.05442i	0.996684	−	0.0813721i	$-0.0259302\pi$
$30$		0			0
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.481471	−	0.876462i	$-0.340103\pi$
$31$	6.31745	−	0.663990i	1.13465	−	0.119256i	0.653176	+	0.757206i	$0.273436\pi$
$32$	−2.75469	+	0.738117i	−0.486965	+	0.130482i
$33$	1.46324	+	3.81188i	0.254718	+	0.663564i
$34$	2.48320	+	7.64252i	0.425866	+	1.31068i
$35$		0			0
$36$	−0.134168	+	0.412927i	−0.0223614	+	0.0688212i
$37$	−2.64422	+	0.138578i	−0.434707	+	0.0227820i	−0.268435	−	0.963298i	$-0.586506\pi$
$37$	−2.64422	+	0.138578i	−0.434707	+	0.0227820i	−0.166272	+	0.986080i	$0.553173\pi$
$38$	−6.49605	−	10.0030i	−1.05380	−	1.62271i
$39$	3.18385	−	2.86675i	0.509823	−	0.459047i
$40$		0			0
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.883974	−	0.467536i	$-0.845142\pi$
$41$	−8.47974	+	2.75523i	−1.32431	+	0.430295i	−0.440339	+	0.897832i	$0.645142\pi$
$42$	−8.22005	−	0.293115i	−1.26838	−	0.0452287i
$43$	0.986332	−	0.986332i	0.150414	−	0.150414i	−0.627889	−	0.778303i	$-0.716081\pi$
$43$	0.986332	−	0.986332i	0.150414	−	0.150414i	0.778303	+	0.627889i	$0.216081\pi$
$44$	−0.437278	+	0.982142i	−0.0659221	+	0.148063i
$45$		0			0
$46$	2.91025	−	1.29573i	0.429093	−	0.191044i
$47$	1.65339	+	2.04177i	0.241172	+	0.297822i	0.883332	−	0.468748i	$-0.155295\pi$
$47$	1.65339	+	2.04177i	0.241172	+	0.297822i	−0.642160	+	0.766571i	$0.721962\pi$
$48$	8.32258	−	4.24056i	1.20126	−	0.612073i
$49$	−1.68344	−	6.79456i	−0.240492	−	0.970651i
$50$		0			0
$51$	−4.96456	−	8.59887i	−0.695178	−	1.20408i
$52$	1.12652	+	0.0590385i	0.156220	+	0.00818716i
$53$	3.31015	−	8.62323i	0.454684	−	1.18449i	−0.494335	−	0.869271i	$-0.664588\pi$
$53$	3.31015	−	8.62323i	0.454684	−	1.18449i	0.949019	−	0.315220i	$-0.102078\pi$
$54$	−0.701489	+	6.67422i	−0.0954606	+	0.908247i
$55$		0			0
$56$	4.24391	+	4.55777i	0.567117	+	0.609057i
$57$	10.4209	+	10.4209i	1.38029	+	1.38029i
$58$	−10.3936	+	3.98974i	−1.36475	+	0.523878i
$59$	10.2924	+	2.18773i	1.33996	+	0.284818i	0.821464	−	0.570261i	$-0.193158\pi$
$59$	10.2924	+	2.18773i	1.33996	+	0.284818i	0.518498	+	0.855079i	$0.326491\pi$
$60$		0			0
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	0.931637	+	0.363391i	$0.118381\pi$
$61$	1.78346	+	8.39053i	0.228349	+	1.07430i	−0.703288	+	0.710905i	$0.748285\pi$
$62$	−8.97777	−	4.57440i	−1.14018	−	0.580949i
$63$	2.19243	−	0.384920i	0.276221	−	0.0484953i
$64$	−4.76284	−	1.54754i	−0.595355	−	0.193443i
$65$		0			0
$66$	1.34656	−	6.33508i	0.165751	−	0.779795i
$67$	2.06649	−	2.55191i	0.252462	−	0.311765i	−0.635121	−	0.772413i	$-0.719050\pi$
$67$	2.06649	−	2.55191i	0.252462	−	0.311765i	0.887583	+	0.460648i	$0.152383\pi$
$68$	0.676649	−	2.52529i	0.0820558	−	0.306236i
$69$	−3.18448	+	2.31366i	−0.383366	+	0.278532i
$70$		0			0
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	0.860768	−	0.508998i	$-0.169984\pi$
$71$	5.41526	+	3.93442i	0.642673	+	0.466930i	−0.218094	+	0.975928i	$0.569984\pi$
$72$	−1.53904	+	1.24629i	−0.181378	+	0.146877i
$73$	0.433401	−	8.26979i	0.0507258	−	0.967906i	−0.848165	−	0.529733i	$-0.822292\pi$
$73$	0.433401	−	8.26979i	0.0507258	−	0.967906i	0.898891	−	0.438173i	$-0.144374\pi$
$74$	3.63734	+	2.10002i	0.422832	+	0.244122i
$75$		0			0
$76$			3.88041i			0.445114i
$77$	5.49868	−	0.380434i	0.626633	−	0.0433545i
$78$	−6.71211	+	1.06309i	−0.759996	+	0.120372i
$79$	2.65691	+	0.279252i	0.298926	+	0.0314184i	0.252804	−	0.967517i	$-0.418647\pi$
$79$	2.65691	+	0.279252i	0.298926	+	0.0314184i	0.0461216	+	0.998936i	$0.485314\pi$
$80$		0			0
$81$	−1.13060	−	10.7569i	−0.125622	−	1.19521i
$82$	13.6609	+	3.66043i	1.50860	+	0.404227i
$83$	2.88395	+	0.456772i	0.316554	+	0.0501373i	0.312690	−	0.949855i	$-0.398770\pi$
$83$	2.88395	+	0.456772i	0.316554	+	0.0501373i	0.00386431	+	0.999993i	$0.498770\pi$
$84$	2.19093	+	1.53651i	0.239050	+	0.167647i
$85$		0			0
$86$	−2.16423	+	0.460021i	−0.233375	+	0.0496053i
$87$	11.5369	−	7.49212i	1.23688	−	0.803240i
$88$	−4.11259	+	2.67075i	−0.438404	+	0.284703i
$89$	−12.3861	+	2.63274i	−1.31292	+	0.279070i	−0.810595	−	0.585608i	$-0.800856\pi$
$89$	−12.3861	+	2.63274i	−1.31292	+	0.279070i	−0.502327	+	0.864678i	$0.667523\pi$
$90$		0			0
$91$	−2.44033	−	5.24338i	−0.255816	−	0.549656i
$92$	−1.02366	−	0.162132i	−0.106724	−	0.0169035i
$93$	12.0258	+	3.22229i	1.24701	+	0.334136i
$94$	−0.435611	−	4.14456i	−0.0449298	−	0.427479i
$95$		0			0
$96$	−5.55884	−	0.584258i	−0.567347	−	0.0596306i
$97$	3.33125	−	0.527619i	0.338237	−	0.0535716i	0.0149946	−	0.999888i	$-0.495227\pi$
$97$	3.33125	−	0.527619i	0.338237	−	0.0535716i	0.323243	+	0.946316i	$0.395227\pi$
$98$	−3.63040	+	10.4932i	−0.366726	+	1.05997i
$99$			1.75274i			0.176157i
$100$		0			0
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	0.372638	−	0.927977i	$-0.378453\pi$
$101$	−2.45915	−	1.41979i	−0.244695	−	0.141275i	−0.617333	+	0.786702i	$0.711787\pi$
$102$	−0.824274	+	15.7281i	−0.0816152	+	1.55731i
$103$	−5.67198	+	4.59308i	−0.558877	+	0.452570i	−0.866669	−	0.498884i	$-0.833743\pi$
$103$	−5.67198	+	4.59308i	−0.558877	+	0.452570i	0.307792	+	0.951454i	$0.400410\pi$
$104$	4.16268	+	3.02436i	0.408184	+	0.296563i
$105$		0			0
$106$	−11.8532	+	8.61186i	−1.15129	+	0.836458i
$107$	−3.00110	+	11.2003i	−0.290127	+	1.08277i	0.654883	+	0.755730i	$0.272718\pi$
$107$	−3.00110	+	11.2003i	−0.290127	+	1.08277i	−0.945011	+	0.327040i	$0.893949\pi$
$108$	1.37403	−	1.69678i	0.132216	−	0.163273i
$109$	2.03244	−	9.56186i	0.194672	−	0.915860i	−0.766998	−	0.641650i	$-0.778250\pi$
$109$	2.03244	−	9.56186i	0.194672	−	0.915860i	0.961670	−	0.274210i	$-0.0884164\pi$
$110$		0			0
$111$	−4.93560	−	1.60367i	−0.468467	−	0.152214i
$112$	−2.18040	−	12.4192i	−0.206028	−	1.17350i
$113$	−8.16704	−	4.16132i	−0.768291	−	0.391464i	0.0254843	−	0.999675i	$-0.491887\pi$
$113$	−8.16704	−	4.16132i	−0.768291	−	0.391464i	−0.793775	+	0.608212i	$0.791887\pi$
$114$	−4.86028	−	22.8658i	−0.455207	−	2.14158i
$115$		0			0
$116$	3.54288	+	0.753063i	0.328949	+	0.0699202i
$117$	1.71696	−	0.659077i	0.158733	−	0.0609317i
$118$	−11.8021	−	11.8021i	−1.08647	−	1.08647i
$119$	−13.0622	+	3.00551i	−1.19741	+	0.275515i
$120$		0			0
$121$	0.696156	−	6.62348i	0.0632869	−	0.602135i
$122$	4.87612	−	12.7027i	0.441463	−	1.15005i
$123$	−17.4511	−	0.914571i	−1.57351	−	0.0824641i
$124$	1.63906	+	2.83893i	0.147192	+	0.254944i
$125$		0			0
$126$	−3.24914	−	1.38201i	−0.289457	−	0.123119i
$127$	−2.18980	+	1.11576i	−0.194313	+	0.0990074i	−0.548440	−	0.836190i	$-0.684778\pi$
$127$	−2.18980	+	1.11576i	−0.194313	+	0.0990074i	0.354127	+	0.935197i	$0.384778\pi$
$128$	8.58857	+	10.6060i	0.759130	+	0.937447i
$129$	2.49752	−	1.11197i	0.219895	−	0.0979034i
$130$		0			0
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	−0.787079	−	0.616852i	$-0.788408\pi$
$131$	2.26610	−	5.08975i	0.197990	−	0.444693i	0.985069	+	0.172159i	$0.0550742\pi$
$132$	−1.48995	+	1.48995i	−0.129683	+	0.129683i
$133$	17.5725	−	9.32688i	1.52373	−	0.808743i
$134$	−4.95369	+	1.60955i	−0.427934	+	0.139044i
$135$		0			0
$136$	8.86178	−	7.97918i	0.759891	−	0.684209i
$137$	−4.94623	−	7.61653i	−0.422585	−	0.650724i	0.561694	−	0.827345i	$-0.310150\pi$
$137$	−4.94623	−	7.61653i	−0.422585	−	0.650724i	−0.984279	+	0.176621i	$0.943483\pi$
$138$	6.23513	−	0.326769i	0.530770	−	0.0278165i
$139$	5.50579	−	16.9451i	0.466995	−	1.43726i	−0.389461	−	0.921043i	$-0.627339\pi$
$139$	5.50579	−	16.9451i	0.466995	−	1.43726i	0.856456	−	0.516220i	$-0.172661\pi$
$140$		0			0
$141$	1.59121	+	4.89724i	0.134004	+	0.412422i
$142$	−3.80497	−	9.91229i	−0.319306	−	0.831821i
$143$	4.39874	−	1.17864i	0.367841	−	0.0985627i
$144$	3.98768	−	0.419122i	0.332306	−	0.0349268i
$145$		0			0
$146$	−7.72092	+	10.6269i	−0.638988	+	0.879491i
$147$	1.69206	−	13.6148i	0.139559	−	1.12293i
$148$	−0.620350	−	1.21751i	−0.0509925	−	0.100078i
$149$	−12.6781	+	7.31970i	−1.03863	+	0.599653i	−0.919445	−	0.393219i	$-0.871362\pi$
$149$	−12.6781	+	7.31970i	−1.03863	+	0.599653i	−0.119185	+	0.992872i	$0.538028\pi$
$150$		0			0
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	0.326508	+	0.945195i	$0.394128\pi$
$151$	−8.05257	+	13.9475i	−0.655309	+	1.13503i	−0.981816	+	0.189833i	$0.939205\pi$
$152$	−9.63977	+	14.8440i	−0.781889	+	1.20400i
$153$	−0.666764	−	4.20978i	−0.0539047	−	0.340341i
$154$	−7.64359	−	4.24428i	−0.615938	−	0.342014i
$155$		0			0
$156$	2.01979	+	0.899269i	0.161713	+	0.0719991i
$157$	−1.11174	−	4.14906i	−0.0887263	−	0.331131i	0.907267	−	0.420554i	$-0.138164\pi$
$157$	−1.11174	−	4.14906i	−0.0887263	−	0.331131i	−0.995994	+	0.0894230i	$0.971498\pi$
$158$	−3.29325	−	2.66682i	−0.261997	−	0.212161i
$159$	12.1135	−	13.4534i	0.960664	−	1.06693i
$160$		0			0
$161$	1.72624	+	5.02538i	0.136046	+	0.396055i
$162$	−7.78897	+	15.2867i	−0.611959	+	1.20104i
$163$	0.798321	+	15.2329i	0.0625294	+	1.19313i	0.832121	+	0.554595i	$0.187127\pi$
$163$	0.798321	+	15.2329i	0.0625294	+	1.19313i	−0.769591	+	0.638537i	$0.779540\pi$
$164$	−3.07882	−	3.41938i	−0.240416	−	0.267009i
$165$		0			0
$166$	−3.44192	−	3.09912i	−0.267145	−	0.240538i
$167$	−2.64539	+	16.7023i	−0.204706	+	1.29246i	0.644583	+	0.764535i	$0.277031\pi$
$167$	−2.64539	+	16.7023i	−0.204706	+	1.29246i	−0.849289	+	0.527929i	$0.822969\pi$
$168$	4.56405	+	11.3204i	0.352124	+	0.873390i
$169$	4.83258	+	6.65148i	0.371737	+	0.511652i
$170$		0			0
$171$	2.57314	+	5.77937i	0.196773	+	0.441959i
$172$	0.672028	+	0.257967i	0.0512417	+	0.0196698i
$173$	15.7214	+	10.2096i	1.19527	+	0.776219i	0.979739	−	0.200277i	$-0.0641844\pi$
$173$	15.7214	+	10.2096i	1.19527	+	0.776219i	0.215533	+	0.976496i	$0.430851\pi$
$174$	−21.8201			−1.65418
$175$		0			0
$176$	9.92847			0.748387
$177$	17.2960	+	11.2322i	1.30005	+	0.844262i
$178$	18.7517	+	7.19811i	1.40550	+	0.539521i
$179$	3.98974	+	8.96111i	0.298207	+	0.669785i	0.999052	−	0.0435289i	$-0.0138601\pi$
$179$	3.98974	+	8.96111i	0.298207	+	0.669785i	−0.700845	+	0.713314i	$0.747193\pi$
$180$		0			0
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	0.790287	−	0.612737i	$-0.209931\pi$
$181$	−0.493376	−	0.679074i	−0.0366723	−	0.0504751i	−0.826959	+	0.562262i	$0.809931\pi$
$182$	−1.28343	+	9.08353i	−0.0951344	+	0.673316i
$183$	−2.63002	+	16.6053i	−0.194416	+	1.22750i
$184$	−3.51310	−	3.16321i	−0.258989	−	0.233195i
$185$		0			0
$186$	−13.2142	−	14.6758i	−0.968909	−	1.07608i
$187$	−0.552353	−	10.5395i	−0.0403920	−	0.770726i
$188$	−0.615528	+	1.20804i	−0.0448920	+	0.0881055i
$189$	−10.9865	−	2.14396i	−0.799150	−	0.155950i
$190$		0			0
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	−0.805401	−	0.592730i	$-0.798050\pi$
$191$	−1.82056	+	2.02194i	−0.131731	+	0.146302i	0.673670	+	0.739032i	$0.264717\pi$
$192$	−7.62788	−	6.17693i	−0.550494	−	0.445782i
$193$	1.81427	+	6.77095i	0.130594	+	0.487384i	0.999977	−	0.00675479i	$-0.00215013\pi$
$193$	1.81427	+	6.77095i	0.130594	+	0.487384i	−0.869383	+	0.494139i	$0.835483\pi$
$194$	−4.88740	−	2.17601i	−0.350895	−	0.156229i
$195$		0			0
$196$	2.84988	−	2.21982i	0.203563	−	0.158558i
$197$	2.31863	+	14.6392i	0.165195	+	1.04300i	0.921385	+	0.388650i	$0.127058\pi$
$197$	2.31863	+	14.6392i	0.165195	+	1.04300i	−0.756190	+	0.654352i	$0.772942\pi$
$198$	1.51421	−	2.33167i	0.107610	−	0.165705i
$199$	−10.5072	+	18.1990i	−0.744835	+	1.29009i	0.205437	+	0.978670i	$0.434138\pi$
$199$	−10.5072	+	18.1990i	−0.744835	+	1.29009i	−0.950272	+	0.311422i	$0.899195\pi$
$200$		0			0
$201$	5.57358	−	3.21791i	0.393130	−	0.226974i
$202$	2.04485	+	4.01325i	0.143875	+	0.282371i
$203$	−5.10534	−	17.8541i	−0.358324	−	1.25311i
$204$	3.01181	−	4.14540i	0.210869	−	0.290236i
$205$		0			0
$206$	11.5135	−	1.21012i	0.802183	−	0.0843128i
$207$	−1.63212	+	0.437326i	−0.113440	+	0.0303963i
$208$	−3.73338	−	9.72579i	−0.258863	−	0.674362i
$209$	4.84072	+	14.8982i	0.334839	+	1.03053i
$210$		0			0
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	0.220805	+	0.975318i	$0.429132\pi$
$211$	−7.71478	+	23.7437i	−0.531108	+	1.63458i	−0.751912	+	0.659263i	$0.770868\pi$
$212$	4.76014	−	0.249468i	0.326928	−	0.0171336i
$213$	7.14516	+	11.0026i	0.489578	+	0.753884i
$214$	13.6684	−	12.3071i	0.934353	−	0.841295i
$215$		0			0
$216$	9.47131	−	3.07741i	0.644441	−	0.209392i
$217$	8.91657	−	14.2461i	0.605296	−	0.967090i
$218$	−10.9644	+	10.9644i	−0.742600	+	0.742600i
$219$	6.60153	−	14.8273i	0.446090	−	1.00193i
$220$		0			0
$221$	−10.1167	+	4.50423i	−0.680521	+	0.302987i
$222$	5.18043	+	6.39730i	0.347688	+	0.429359i
$223$	−11.6067	+	5.91390i	−0.777241	+	0.396024i	−0.797153	−	0.603778i	$-0.793661\pi$
$223$	−11.6067	+	5.91390i	−0.777241	+	0.396024i	0.0199118	+	0.999802i	$0.493661\pi$
$224$	−2.95331	+	6.94333i	−0.197326	+	0.463921i
$225$		0			0
$226$	7.26966	+	12.5914i	0.483571	+	0.837569i
$227$	3.09307	+	0.162101i	0.205294	+	0.0107590i	0.154706	−	0.987961i	$-0.450557\pi$
$227$	3.09307	+	0.162101i	0.205294	+	0.0107590i	0.0505884	+	0.998720i	$0.483890\pi$
$228$	−2.72551	+	7.10021i	−0.180502	+	0.470223i
$229$	−0.0558012	+	0.530913i	−0.00368745	+	0.0350837i	−0.996211	−	0.0869703i	$-0.972281\pi$
$229$	−0.0558012	+	0.530913i	−0.00368745	+	0.0350837i	0.992523	+	0.122054i	$0.0389481\pi$
$230$		0			0
$231$	10.3285	+	3.16605i	0.679562	+	0.208311i
$232$	11.6820	+	11.6820i	0.766961	+	0.766961i
$233$	−23.1708	+	8.89443i	−1.51797	+	0.582694i	−0.967658	−	0.252266i	$-0.918824\pi$
$233$	−23.1708	+	8.89443i	−1.51797	+	0.582694i	−0.550311	+	0.834960i	$0.685491\pi$
$234$	−2.85346	−	0.606522i	−0.186537	−	0.0396496i
$235$		0			0
$236$	1.12899	+	5.31148i	0.0734910	+	0.345748i
$237$	4.66535	+	2.37712i	0.303047	+	0.154410i
$238$	19.9732	+	7.28633i	1.29467	+	0.472303i
$239$	25.9462	+	8.43043i	1.67832	+	0.545320i	0.984585	−	0.174910i	$-0.0559633\pi$
$239$	25.9462	+	8.43043i	1.67832	+	0.545320i	0.693736	+	0.720229i	$0.255963\pi$
$240$		0			0
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	0.641958	+	0.766740i	$0.278122\pi$
$241$	−3.97979	+	18.7235i	−0.256361	+	1.20608i	−0.898319	+	0.439344i	$0.855211\pi$
$242$	−6.64820	+	8.20984i	−0.427362	+	0.527749i
$243$	2.20163	−	8.21660i	0.141235	−	0.527095i
$244$	−3.58129	+	2.60196i	−0.229269	+	0.166574i
$245$		0			0
$246$	22.4251	+	16.2928i	1.42977	+	1.03879i
$247$	12.7738	−	10.3440i	0.812779	−	0.658175i
$248$	−0.782537	+	14.9317i	−0.0496912	+	0.948164i
$249$	4.95609	+	2.86140i	0.314079	+	0.181334i
$250$		0			0
$251$			7.49714i			0.473215i	0.971605	+	0.236608i	$0.0760356\pi$
$251$			7.49714i			0.473215i	−0.971605	+	0.236608i	$0.923964\pi$
$252$	0.641657	+	0.952810i	0.0404206	+	0.0600214i
$253$	−4.13244	+	0.654514i	−0.259804	+	0.0411489i
$254$	3.87701	+	0.407490i	0.243265	+	0.0255682i
$255$		0			0
$256$	−1.21584	−	11.5680i	−0.0759901	−	0.722998i
$257$	−13.2229	−	3.54307i	−0.824824	−	0.221011i	−0.178369	−	0.983964i	$-0.557082\pi$
$257$	−13.2229	−	3.54307i	−0.824824	−	0.221011i	−0.646454	+	0.762953i	$0.723749\pi$
$258$	−4.28311	−	0.678378i	−0.266655	−	0.0422340i
$259$	−4.02244	+	5.73564i	−0.249942	+	0.356395i
$260$		0			0
$261$	5.77603	−	1.22773i	0.357527	−	0.0759947i
$262$	−7.41170	+	4.81321i	−0.457896	+	0.297361i
$263$	−16.4103	+	10.6570i	−1.01190	+	0.657137i	−0.940318	−	0.340298i	$-0.889472\pi$
$263$	−16.4103	+	10.6570i	−1.01190	+	0.657137i	−0.0715841	+	0.997435i	$0.522805\pi$
$264$	−9.40091	+	1.99822i	−0.578586	+	0.122982i
$265$		0			0
$266$	−31.4345	−	2.77350i	−1.92737	−	0.170054i
$267$	−24.5127	−	3.88242i	−1.50015	−	0.237600i
$268$	1.63683	+	0.438587i	0.0999853	+	0.0267910i
$269$	−0.965195	−	9.18322i	−0.0588490	−	0.559911i	−0.983730	−	0.179654i	$-0.942502\pi$
$269$	−0.965195	−	9.18322i	−0.0588490	−	0.559911i	0.924881	−	0.380257i	$-0.124164\pi$
$270$		0			0
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	0.137884	−	0.990448i	$-0.455970\pi$
$271$	1.10014	+	0.115630i	0.0668289	+	0.00702400i	−0.0710550	+	0.997472i	$0.522637\pi$
$272$	−23.8465	+	3.77692i	−1.44591	+	0.229010i
$273$	−0.782368	−	11.3081i	−0.0473511	−	0.684399i
$274$			14.4054i			0.870263i
$275$		0			0
$276$	−1.75918	−	1.01566i	−0.105890	−	0.0611356i
$277$	1.01746	−	19.4143i	0.0611331	−	1.16649i	−0.780042	−	0.625727i	$-0.784802\pi$
$277$	1.01746	−	19.4143i	0.0611331	−	1.16649i	0.841175	−	0.540763i	$-0.181864\pi$
$278$	−21.9634	+	17.7856i	−1.31728	+	1.06671i
$279$	4.32369	+	3.14135i	0.258853	+	0.188067i
$280$		0			0
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	−0.628416	−	0.777878i	$-0.716296\pi$
$281$	−1.38801	+	1.00845i	−0.0828017	+	0.0601589i	0.545614	+	0.838036i	$0.316296\pi$
$282$	2.11398	−	7.88949i	0.125886	−	0.469812i
$283$	16.6132	−	20.5156i	0.987553	−	1.21953i	0.0119625	−	0.999928i	$-0.496192\pi$
$283$	16.6132	−	20.5156i	0.987553	−	1.21953i	0.975590	−	0.219598i	$-0.0704745\pi$
$284$	−0.718188	+	3.37881i	−0.0426166	+	0.200495i
$285$		0			0
$286$	−6.86990	−	2.23217i	−0.406226	−	0.131991i
$287$	−8.08454	+	22.1613i	−0.477215	+	1.30814i
$288$	−2.13786	−	1.08929i	−0.125975	−	0.0641873i
$289$	1.80153	+	8.47555i	0.105973	+	0.498562i
$290$		0			0
$291$	6.46596	+	1.37438i	0.379041	+	0.0805678i
$292$	3.98969	−	1.53150i	0.233479	−	0.0896242i
$293$	4.33790	+	4.33790i	0.253423	+	0.253423i	0.822372	−	0.568950i	$-0.192650\pi$
$293$	4.33790	+	4.33790i	0.253423	+	0.253423i	−0.568950	+	0.822372i	$0.692650\pi$
$294$	−14.0129	+	16.6500i	−0.817250	+	0.971051i
$295$		0			0
$296$	0.651485	−	6.19847i	0.0378668	−	0.360279i
$297$	3.15865	−	8.22857i	0.183284	−	0.477470i
$298$	23.1893	+	1.21530i	1.34332	+	0.0704005i
$299$	2.19506	+	3.80196i	0.126944	+	0.219873i
$300$		0			0
$301$	−0.447061	−	3.66334i	−0.0257682	−	0.211151i
$302$	22.7617	−	11.5977i	1.30979	−	0.667372i
$303$	−3.50242	−	4.32512i	−0.201209	−	0.248472i
$304$	32.7376	−	14.5757i	1.87763	−	0.835974i
$305$		0			0
$306$	−2.74988	+	6.17632i	−0.157200	+	0.353077i
$307$	−12.5574	+	12.5574i	−0.716687	+	0.716687i	−0.967925	−	0.251239i	$-0.919162\pi$
$307$	−12.5574	+	12.5574i	−0.716687	+	0.716687i	0.251239	+	0.967925i	$0.419162\pi$
$308$	1.33352	+	2.51245i	0.0759844	+	0.143160i
$309$	−13.6044	+	4.42034i	−0.773928	+	0.251464i
$310$		0			0
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	−0.524166	−	0.851616i	$-0.675623\pi$
$311$	4.72615	−	4.25544i	0.267995	−	0.241304i	0.792161	+	0.610312i	$0.208956\pi$
$312$	5.49244	+	8.45761i	0.310948	+	0.478818i
$313$	7.62782	−	0.399757i	0.431150	−	0.0225956i	0.164473	−	0.986382i	$-0.447408\pi$
$313$	7.62782	−	0.399757i	0.431150	−	0.0225956i	0.266677	+	0.963786i	$0.414074\pi$
$314$	−2.10547	+	6.47997i	−0.118818	+	0.365686i
$315$		0			0
$316$	0.426032	+	1.31119i	0.0239662	+	0.0737603i
$317$	5.05753	+	13.1753i	0.284059	+	0.740000i	0.999160	+	0.0409785i	$0.0130475\pi$
$317$	5.05753	+	13.1753i	0.284059	+	0.740000i	−0.715101	+	0.699021i	$0.753619\pi$
$318$	−27.7372	+	7.43217i	−1.55543	+	0.416775i
$319$	14.5417	−	1.52840i	0.814181	−	0.0855738i
$320$		0			0
$321$	−13.3581	+	18.3858i	−0.745575	+	1.02620i
$322$	2.04506	−	8.17661i	0.113967	−	0.455665i
$323$	−17.2941	−	33.9415i	−0.962268	−	1.88856i
$324$	4.83394	−	2.79088i	0.268552	−	0.155049i
$325$		0			0
$326$	12.0978	−	20.9541i	0.670037	−	1.16054i
$327$	10.4349	−	16.0683i	0.577051	−	0.888580i
$328$	−3.28311	−	20.7288i	−0.181280	−	1.14455i
$329$	6.95011	−	0.116192i	0.383172	−	0.00640585i
$330$		0			0
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	0.131614	−	0.991301i	$-0.457984\pi$
$331$	−9.40598	−	4.18781i	−0.516999	−	0.230183i	−0.648613	+	0.761118i	$0.724651\pi$
$332$	0.389997	+	1.45549i	0.0214038	+	0.0798802i
$333$	−1.73127	−	1.40196i	−0.0948730	−	0.0768267i
$334$	17.9485	−	19.9338i	0.982097	−	1.09073i
$335$		0			0
$336$	4.73334	−	24.2555i	0.258225	−	1.32325i
$337$	−11.6695	+	22.9028i	−0.635681	+	1.24759i	0.318375	+	0.947965i	$0.396863\pi$
$337$	−11.6695	+	22.9028i	−0.635681	+	1.24759i	−0.954056	+	0.299629i	$0.903137\pi$
$338$	−0.682529	−	13.0234i	−0.0371247	−	0.708381i
$339$	−12.0209	−	13.3505i	−0.652884	−	0.725101i
$340$		0			0
$341$	9.83439	+	8.85492i	0.532562	+	0.479521i
$342$	1.56980	−	9.91130i	0.0848848	−	0.535942i
$343$	−16.9024	−	7.57025i	−0.912644	−	0.408755i
$344$	1.92990	+	2.65628i	0.104053	+	0.143217i
$345$		0			0
$346$	−12.0941	−	27.1637i	−0.650181	−	1.46033i
$347$	4.26035	+	1.63539i	0.228707	+	0.0877926i	0.470023	−	0.882654i	$-0.344246\pi$
$347$	4.26035	+	1.63539i	0.228707	+	0.0877926i	−0.241316	+	0.970447i	$0.577579\pi$
$348$	5.95367	+	3.86636i	0.319150	+	0.207259i
$349$	−35.4204			−1.89601			−0.948005	−	0.318256i	$-0.896903\pi$
$349$	−35.4204			−1.89601			−0.948005	+	0.318256i	$0.896903\pi$
$350$		0			0
$351$	−9.24834			−0.493640
$352$	−4.98272	−	3.23582i	−0.265580	−	0.172470i
$353$	9.98297	+	3.83210i	0.531340	+	0.203962i	0.609221	−	0.793000i	$-0.291482\pi$
$353$	9.98297	+	3.83210i	0.531340	+	0.203962i	−0.0778814	+	0.996963i	$0.524816\pi$
$354$	−13.3054	−	29.8845i	−0.707175	−	1.58834i
$355$		0			0
$356$	−3.84101	−	5.28670i	−0.203573	−	0.280194i
$357$	−26.0116	−	3.67525i	−1.37668	−	0.194515i
$358$	2.43402	−	15.3678i	0.128642	−	0.812214i
$359$	2.83659	+	2.55408i	0.149710	+	0.134799i	0.740582	−	0.671966i	$-0.234550\pi$
$359$	2.83659	+	2.55408i	0.149710	+	0.134799i	−0.590873	+	0.806765i	$0.701216\pi$
$360$		0			0
$361$	25.1196	+	27.8982i	1.32209	+	1.46833i
$362$	0.0696818	+	1.32961i	0.00366240	+	0.0698827i
$363$	5.92598	−	11.6304i	0.311033	−	0.610437i
$364$	1.95972	−	2.25105i	0.102717	−	0.117987i
$365$		0			0
$366$	17.8442	−	19.8180i	0.932731	−	1.03590i
$367$	6.47094	+	5.24006i	0.337780	+	0.273529i	0.783170	−	0.621808i	$-0.213601\pi$
$367$	6.47094	+	5.24006i	0.337780	+	0.273529i	−0.445390	+	0.895337i	$0.646935\pi$
$368$	2.47726	+	9.24526i	0.129136	+	0.481943i
$369$	−6.85293	−	3.05112i	−0.356749	−	0.158835i
$370$		0			0
$371$	−12.5711	−	20.9568i	−0.652659	−	1.08802i
$372$	1.00507	+	6.34579i	0.0521107	+	0.329014i
$373$	−9.49367	+	14.6190i	−0.491563	+	0.756941i	−0.994199	−	0.107557i	$-0.965697\pi$
$373$	−9.49367	+	14.6190i	−0.491563	+	0.756941i	0.502635	+	0.864498i	$0.332364\pi$
$374$	−8.37041	+	14.4980i	−0.432824	+	0.749672i
$375$		0			0
$376$	−5.35564	+	3.09208i	−0.276196	+	0.159462i
$377$	−6.96529	−	13.6702i	−0.358731	−	0.704049i
$378$	12.7632	+	12.3435i	0.656469	+	0.634880i
$379$	6.41691	−	8.83212i	0.329614	−	0.453675i	−0.611758	−	0.791045i	$-0.709537\pi$
$379$	6.41691	−	8.83212i	0.329614	−	0.453675i	0.941372	+	0.337370i	$0.109537\pi$
$380$		0			0
$381$	−4.79047	+	0.503499i	−0.245423	+	0.0257950i
$382$	4.16868	−	1.11699i	0.213288	−	0.0571504i
$383$	−5.94645	−	15.4910i	−0.303849	−	0.791555i	−0.997462	−	0.0712062i	$-0.977315\pi$
$383$	−5.94645	−	15.4910i	−0.303849	−	0.791555i	0.693612	−	0.720349i	$-0.256018\pi$
$384$	8.26557	+	25.4388i	0.421800	+	1.29817i
$385$		0			0
$386$	3.43596	−	10.5748i	0.174886	−	0.538244i
$387$	1.17196	−	0.0614198i	0.0595740	−	0.00312214i
$388$	0.947969	+	1.45974i	0.0481258	+	0.0741072i
$389$	−14.2859	+	12.8631i	−0.724323	+	0.652183i	−0.946456	−	0.322833i	$-0.895365\pi$
$389$	−14.2859	+	12.8631i	−0.724323	+	0.652183i	0.222133	+	0.975016i	$0.428698\pi$
$390$		0			0
$391$	9.67645	−	3.14407i	0.489359	−	0.159002i
$392$	16.4163	−	1.41186i	0.829148	−	0.0713099i
$393$	7.72133	−	7.72133i	0.389490	−	0.389490i
$394$	9.56251	−	21.4777i	0.481752	−	1.08203i
$395$		0			0
$396$	−0.826312	+	0.367898i	−0.0415237	+	0.0184876i
$397$	0.765657	+	0.945508i	0.0384272	+	0.0474537i	0.795997	−	0.605300i	$-0.206947\pi$
$397$	0.765657	+	0.945508i	0.0384272	+	0.0474537i	−0.757570	+	0.652754i	$0.773614\pi$
$398$	29.7001	−	15.1329i	1.48873	−	0.758546i
$399$	38.7044	−	4.72336i	1.93765	−	0.236464i
$400$		0			0
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	0.919149	−	0.393910i	$-0.128878\pi$
$401$	2.37174	+	4.10797i	0.118439	+	0.205142i	−0.800710	+	0.599052i	$0.795544\pi$
$402$	−10.1945	−	0.534274i	−0.508458	−	0.0266471i
$403$	4.97615	−	12.9633i	0.247880	−	0.645749i
$404$	0.153175	−	1.45736i	0.00762072	−	0.0725063i
$405$		0			0
$406$	−8.63267	+	28.1619i	−0.428432	+	1.39765i
$407$	−3.90054	−	3.90054i	−0.193342	−	0.193342i
$408$	21.8193	−	8.37563i	1.08021	−	0.414656i
$409$	−24.2503	−	5.15456i	−1.19910	−	0.254877i	−0.435274	−	0.900298i	$-0.643349\pi$
$409$	−24.2503	−	5.15456i	−1.19910	−	0.254877i	−0.763827	+	0.645421i	$0.776682\pi$
$410$		0			0
$411$	−3.70072	−	17.4105i	−0.182543	−	0.858797i
$412$	−3.35591	−	1.70992i	−0.165334	−	0.0842419i
$413$	21.3396	−	17.8792i	1.05005	−	0.879779i
$414$	2.54904	+	0.828232i	0.125278	+	0.0407054i
$415$		0			0
$416$	−1.29612	+	6.09776i	−0.0635475	+	0.298968i
$417$	21.9761	−	27.1382i	1.07617	−	1.32896i
$418$	6.43108	−	24.0011i	0.314554	−	1.17393i
$419$	19.6973	−	14.3109i	0.962276	−	0.699135i	0.00859807	−	0.999963i	$-0.497263\pi$
$419$	19.6973	−	14.3109i	0.962276	−	0.699135i	0.953678	+	0.300828i	$0.0972631\pi$
$420$		0			0
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	0.431872	−	0.901935i	$-0.357853\pi$
$421$	−6.00083	−	4.35986i	−0.292463	−	0.212486i	−0.724335	+	0.689448i	$0.757853\pi$
$422$	30.7754	−	24.9215i	1.49812	−	1.21316i
$423$	−0.115684	+	2.20738i	−0.00562475	+	0.107327i
$424$	18.8290	+	10.8709i	0.914415	+	0.527938i
$425$		0			0
$426$		−	20.8096i		−	1.00823i
$427$	20.3910	+	9.96394i	0.986788	+	0.482189i
$428$	−5.91019	+	0.936083i	−0.285680	+	0.0452473i
$429$	8.87646	+	0.932953i	0.428559	+	0.0450434i
$430$		0			0
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	−0.941058	−	0.338245i	$-0.890167\pi$
$431$	−1.88691	−	17.9528i	−0.0908895	−	0.864756i	0.850169	−	0.526511i	$-0.176500\pi$
$432$	−19.4763	−	5.21865i	−0.937052	−	0.251082i
$433$	24.9324	+	3.94891i	1.19818	+	0.189773i	0.723460	−	0.690366i	$-0.242551\pi$
$433$	24.9324	+	3.94891i	1.19818	+	0.189773i	0.474717	+	0.880139i	$0.342551\pi$
$434$	−24.1691	+	11.2486i	−1.16016	+	0.539949i
$435$		0			0
$436$	4.93446	−	1.04885i	0.236318	−	0.0502309i
$437$	−12.6652	+	8.22487i	−0.605858	+	0.393449i
$438$	−21.5915	+	14.0217i	−1.03168	+	0.669982i
$439$	−27.2854	+	5.79968i	−1.30226	+	0.276804i	−0.806282	−	0.591532i	$-0.798523\pi$
$439$	−27.2854	+	5.79968i	−1.30226	+	0.276804i	−0.495977	+	0.868335i	$0.665190\pi$
$440$		0			0
$441$	2.77255	−	5.19591i	0.132026	−	0.247424i
$442$	17.3495	+	2.74789i	0.825232	+	0.130704i
$443$	29.5785	+	7.92554i	1.40532	+	0.376554i	0.880252	−	0.474507i	$-0.157374\pi$
$443$	29.5785	+	7.92554i	1.40532	+	0.376554i	0.525066	+	0.851061i	$0.324040\pi$
$444$	−0.279941	−	2.66346i	−0.0132854	−	0.126402i
$445$		0			0
$446$	20.5495	+	2.15984i	0.973048	+	0.102271i
$447$	−28.3390	+	4.48846i	−1.34039	+	0.212297i
$448$	−10.9900	+	7.40109i	−0.519230	+	0.349669i
$449$		−	30.4224i		−	1.43572i	−0.696187	−	0.717861i	$-0.745121\pi$
$449$		−	30.4224i		−	1.43572i	0.696187	−	0.717861i	$-0.254879\pi$
$450$		0			0
$451$	−16.0862	−	9.28737i	−0.757469	−	0.437325i
$452$	0.247561	−	4.72374i	0.0116443	−	0.222186i
$453$	−24.5306	+	19.8645i	−1.15255	+	0.933315i
$454$	−3.97469	−	2.88778i	−0.186541	−	0.135530i
$455$		0			0
$456$	−28.0645	+	20.3900i	−1.31424	+	0.954851i
$457$	10.4479	−	38.9922i	0.488733	−	1.82398i	−0.0738955	−	0.997266i	$-0.523543\pi$
$457$	10.4479	−	38.9922i	0.488733	−	1.82398i	0.562628	−	0.826710i	$-0.309790\pi$
$458$	0.532894	−	0.658070i	0.0249005	−	0.0307496i
$459$	−4.45630	+	20.9653i	−0.208002	+	0.978575i
$460$		0			0
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.114706	−	0.993399i	$-0.536593\pi$
$461$	−16.9923	−	5.52114i	−0.791411	−	0.257145i	−0.676705	+	0.736255i	$0.736593\pi$
$462$	−11.0048	−	13.1347i	−0.511990	−	0.611080i
$463$	30.4814	+	15.5311i	1.41659	+	0.721790i	0.983727	−	0.179668i	$-0.0575024\pi$
$463$	30.4814	+	15.5311i	1.41659	+	0.721790i	0.432866	+	0.901458i	$0.357502\pi$
$464$	−6.95456	−	32.7186i	−0.322857	−	1.51892i
$465$		0			0
$466$	38.5083	+	8.18518i	1.78386	+	0.379171i
$467$	−6.23404	+	2.39302i	−0.288477	+	0.110736i	−0.498303	−	0.867003i	$-0.666043\pi$
$467$	−6.23404	+	2.39302i	−0.288477	+	0.110736i	0.209826	+	0.977739i	$0.432710\pi$
$468$	0.671104	+	0.671104i	0.0310218	+	0.0310218i
$469$	−1.94810	−	8.46660i	−0.0899548	−	0.390951i
$470$		0			0
$471$	0.879999	−	8.37263i	0.0405482	−	0.385790i
$472$	−8.87607	+	23.1230i	−0.408554	+	1.06432i
$473$	2.90195	+	0.152085i	0.133432	+	0.00699285i
$474$	−4.15273	−	7.19274i	−0.190741	−	0.330374i
$475$		0			0
$476$	−4.15867	−	5.52721i	−0.190612	−	0.253339i
$477$	6.92419	−	3.52805i	0.317037	−	0.161538i
$478$	−27.2333	−	33.6303i	−1.24562	−	1.53821i
$479$	−4.62700	+	2.06007i	−0.211413	+	0.0941271i	−0.509711	−	0.860346i	$-0.670248\pi$
$479$	−4.62700	+	2.06007i	−0.211413	+	0.0941271i	0.298298	+	0.954473i	$0.403581\pi$
$480$		0			0
$481$	−2.35420	+	5.28762i	−0.107342	+	0.241095i
$482$	21.4697	−	21.4697i	0.977920	−	0.977920i
$483$	−0.371123	+	10.4077i	−0.0168867	+	0.473566i
$484$	3.26870	−	1.06207i	0.148577	−	0.0482758i
$485$		0			0
$486$	−10.0272	+	9.02858i	−0.454845	+	0.409544i
$487$	10.2405	+	15.7690i	0.464043	+	0.714563i	0.990782	−	0.135464i	$-0.0432524\pi$
$487$	10.2405	+	15.7690i	0.464043	+	0.714563i	−0.526740	+	0.850027i	$0.676586\pi$
$488$	−20.1635	+	1.05673i	−0.912760	+	0.0478357i
$489$	−9.23849	+	28.4332i	−0.417779	+	1.28579i
$490$		0			0
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	−0.949431	−	0.313976i	$-0.898339\pi$
$491$	−8.10726	−	24.9516i	−0.365876	−	1.12605i	0.583555	−	0.812073i	$-0.301661\pi$
$492$	−3.23180	−	8.41912i	−0.145701	−	0.379563i
$493$	−34.3454	+	9.20282i	−1.54684	+	0.414474i
$494$	−25.9294	+	2.72529i	−1.16662	+	0.122617i
$495$		0			0
$496$	17.7943	−	24.4918i	0.798989	−	1.09971i
$497$	17.0272	−	4.86891i	0.763776	−	0.218400i
$498$	−4.12112	−	8.08815i	−0.184672	−	0.362439i
$499$	−2.61768	+	1.51132i	−0.117183	+	0.0676558i	−0.557446	−	0.830213i	$-0.688219\pi$
$499$	−2.61768	+	1.51132i	−0.117183	+	0.0676558i	0.440263	+	0.897869i	$0.354885\pi$
$500$		0			0
$501$	−16.5717	+	28.7031i	−0.740370	+	1.28236i
$502$	6.47686	−	9.97349i	0.289076	−	0.445139i
$503$	−2.19511	−	13.8594i	−0.0978750	−	0.617958i	−0.987053	−	0.160396i	$-0.948723\pi$
$503$	−2.19511	−	13.8594i	−0.0978750	−	0.617958i	0.889178	−	0.457562i	$-0.151277\pi$
$504$	0.0875827	+	5.23885i	0.00390124	+	0.233357i
$505$		0			0
$506$	6.06285	+	2.69935i	0.269527	+	0.120001i
$507$	4.17060	+	15.5649i	0.185223	+	0.691260i
$508$	−0.985650	−	0.798164i	−0.0437311	−	0.0354128i
$509$	15.1783	−	16.8573i	0.672768	−	0.747185i	−0.306028	−	0.952023i	$-0.599000\pi$
$509$	15.1783	−	16.8573i	0.672768	−	0.747185i	0.978796	+	0.204838i	$0.0656667\pi$
$510$		0			0
$511$	−16.5250	−	14.3863i	−0.731022	−	0.636414i
$512$	4.01531	−	7.88049i	0.177453	−	0.348272i
$513$	−1.66497	−	31.7696i	−0.0735103	−	1.40266i
$514$	14.5296	+	16.1368i	0.640875	+	0.711764i
$515$		0			0
$516$	1.04846	+	0.944034i	0.0461557	+	0.0415588i
$517$	−0.856215	+	5.40593i	−0.0376563	+	0.237752i
$518$	10.3062	−	4.15513i	0.452827	−	0.182566i
$519$	21.5953	+	29.7233i	0.947927	+	1.30471i
$520$		0			0
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.731877	−	0.681437i	$-0.761355\pi$
$521$	−17.0862	−	38.3763i	−0.748562	−	1.68130i	−0.0166856	−	0.999861i	$-0.505311\pi$
$522$	−8.74454	−	3.35671i	−0.382738	−	0.146919i
$523$	−22.1618	−	14.3920i	−0.969068	−	0.629320i	−0.0399883	−	0.999200i	$-0.512732\pi$
$523$	−22.1618	−	14.3920i	−0.969068	−	0.629320i	−0.929079	+	0.369880i	$0.879399\pi$
$524$	2.87517			0.125602
$525$		0			0
$526$	31.0374			1.35329
$527$	−26.9891	−	17.5269i	−1.17566	−	0.763485i
$528$	18.1667	+	6.97353i	0.790603	+	0.303484i
$529$	7.71438	+	17.3268i	0.335408	+	0.753338i
$530$		0			0
$531$	5.20358	+	7.16212i	0.225816	+	0.310809i
$532$	8.08554	+	6.32672i	0.350553	+	0.274298i
$533$	−3.04892	+	19.2501i	−0.132063	+	0.833815i
$534$	29.2553	+	26.3416i	1.26600	+	1.13991i
$535$		0			0
$536$	5.17191	+	5.74398i	0.223392	+	0.248102i
$537$	1.00617	+	19.1989i	0.0434196	+	0.828496i
$538$	−6.64948	+	13.0503i	−0.286679	+	0.562640i
$539$	8.17248	−	12.0778i	0.352014	−	0.520226i
$540$		0			0
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	−0.810262	−	0.586068i	$-0.800675\pi$
$541$	−3.31932	+	3.68648i	−0.142709	+	0.158494i	0.667553	+	0.744562i	$0.267342\pi$
$542$	−1.36363	−	1.10425i	−0.0585731	−	0.0474315i
$543$	−0.425791	−	1.58907i	−0.0182724	−	0.0681937i
$544$	13.1986	+	5.87641i	0.565886	+	0.251949i
$545$		0			0
$546$	−8.72843	+	15.7192i	−0.373542	+	0.672718i
$547$	−2.72171	−	17.1842i	−0.116372	−	0.734743i	−0.975010	−	0.222161i	$-0.928689\pi$
$547$	−2.72171	−	17.1842i	−0.116372	−	0.734743i	0.858638	−	0.512582i	$-0.171311\pi$
$548$	2.55254	−	3.93056i	0.109039	−	0.167905i
$549$	−3.60848	+	6.25007i	−0.154006	+	0.266747i
$550$		0			0
$551$	45.7053	−	26.3880i	1.94711	−	1.12416i
$552$	−4.20635	−	8.25542i	−0.179034	−	0.351374i
$553$	4.91376	−	5.08085i	0.208954	−	0.216060i
$554$	−18.1257	+	24.9479i	−0.770088	+	1.05994i
$555$		0			0
$556$	9.14427	−	0.961102i	0.387804	−	0.0407598i
$557$	−10.5747	+	2.83348i	−0.448064	+	0.120058i	−0.475793	−	0.879557i	$-0.657839\pi$
$557$	−10.5747	+	2.83348i	−0.448064	+	0.120058i	0.0277296	+	0.999615i	$0.491172\pi$
$558$	−3.03799	−	7.91423i	−0.128608	−	0.335036i
$559$	−0.942233	−	2.89989i	−0.0398522	−	0.122652i
$560$		0			0
$561$	6.39205	−	19.6727i	0.269872	−	0.830582i
$562$	2.71769	−	0.142428i	0.114639	−	0.00600796i
$563$	1.08507	+	1.67086i	0.0457302	+	0.0704183i	0.860796	−	0.508950i	$-0.169966\pi$
$563$	1.08507	+	1.67086i	0.0457302	+	0.0704183i	−0.815066	+	0.579368i	$0.803299\pi$
$564$	−1.97477	+	1.77809i	−0.0831527	+	0.0748710i
$565$		0			0
$566$	−39.8243	+	12.9397i	−1.67394	+	0.543896i
$567$	−24.2573	−	15.1825i	−1.01871	−	0.637606i
$568$	−11.1410	+	11.1410i	−0.467466	+	0.467466i
$569$	−12.9886	+	29.1729i	−0.544511	+	1.22299i	0.406447	+	0.913674i	$0.366768\pi$
$569$	−12.9886	+	29.1729i	−0.544511	+	1.22299i	−0.950959	+	0.309318i	$0.899899\pi$
$570$		0			0
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	−0.669053	−	0.743214i	$-0.733300\pi$
$571$	−13.4872	+	6.00488i	−0.564421	+	0.251297i	0.104632	+	0.994511i	$0.466634\pi$
$572$	1.47895	+	1.82635i	0.0618380	+	0.0763636i
$573$	−4.75134	+	2.42093i	−0.198490	+	0.101136i
$574$	29.9003	−	22.4969i	1.24801	−	0.939004i
$575$		0			0
$576$	−2.10668	−	3.64889i	−0.0877785	−	0.152037i
$577$	8.10906	+	0.424978i	0.337585	+	0.0176921i	0.220375	−	0.975415i	$-0.429272\pi$
$577$	8.10906	+	0.424978i	0.337585	+	0.0176921i	0.117209	+	0.993107i	$0.462605\pi$
$578$	4.92553	−	12.8314i	0.204875	−	0.533718i
$579$	−1.43609	+	13.6635i	−0.0596819	+	0.567835i
$580$		0			0
$581$	5.65382	−	5.26449i	0.234560	−	0.218408i
$582$	−7.41437	−	7.41437i	−0.307335	−	0.307335i
$583$	17.9646	−	6.89595i	0.744016	−	0.285601i
$584$	19.0665	+	4.05272i	0.788979	+	0.167703i
$585$		0			0
$586$	−2.02318	−	9.51830i	−0.0835767	−	0.393197i
$587$	6.22031	+	3.16940i	0.256739	+	0.130815i	0.577624	−	0.816303i	$-0.303980\pi$
$587$	6.22031	+	3.16940i	0.256739	+	0.130815i	−0.320884	+	0.947118i	$0.603980\pi$
$588$	6.77373	−	2.06003i	0.279344	−	0.0849541i
$589$	45.4270	+	14.7601i	1.87179	+	0.608181i
$590$		0			0
$591$	−6.03974	+	28.4148i	−0.248442	+	1.16883i
$592$	−7.94146	+	9.80688i	−0.326392	+	0.403060i
$593$	2.19397	−	8.18799i	0.0900954	−	0.336240i	−0.906135	−	0.422989i	$-0.860981\pi$
$593$	2.19397	−	8.18799i	0.0900954	−	0.336240i	0.996230	+	0.0867484i	$0.0276476\pi$
$594$	−11.3107	+	8.21773i	−0.464085	+	0.337177i
$595$		0			0
$596$	−6.11193	−	4.44058i	−0.250355	−	0.181893i
$597$	−32.0081	+	25.9197i	−1.31001	+	1.06082i
$598$	0.364450	−	6.95412i	0.0149035	−	0.284375i
$599$	−20.6751	−	11.9368i	−0.844762	−	0.487723i	0.0141183	−	0.999900i	$-0.495506\pi$
$599$	−20.6751	−	11.9368i	−0.844762	−	0.487723i	−0.858880	+	0.512177i	$0.828839\pi$
$600$		0			0
$601$			9.32470i			0.380362i	0.981749	+	0.190181i	$0.0609075\pi$
$601$			9.32470i			0.380362i	−0.981749	+	0.190181i	$0.939092\pi$
$602$	−2.57007	+	5.25958i	−0.104748	+	0.214365i
$603$	2.72868	−	0.432180i	0.111120	−	0.0175997i
$604$	−8.26564	−	0.868753i	−0.336324	−	0.0353491i
$605$		0			0
$606$	0.922764	+	8.77952i	0.0374847	+	0.356643i
$607$	−21.5323	−	5.76957i	−0.873971	−	0.234180i	−0.206167	−	0.978517i	$-0.566099\pi$
$607$	−21.5323	−	5.76957i	−0.873971	−	0.234180i	−0.667804	+	0.744337i	$0.732766\pi$
$608$	−21.1802	−	3.35461i	−0.858969	−	0.136047i
$609$	3.19878	−	36.2545i	0.129621	−	1.46910i
$610$		0			0
$611$	5.61753	−	1.19404i	0.227261	−	0.0483058i
$612$	1.84471	−	1.19797i	0.0745680	−	0.0484250i
$613$	17.3094	−	11.2408i	0.699118	−	0.454013i	−0.145516	−	0.989356i	$-0.546484\pi$
$613$	17.3094	−	11.2408i	0.699118	−	0.454013i	0.844635	+	0.535343i	$0.179818\pi$
$614$	27.5536	−	5.85669i	1.11197	−	0.236357i
$615$		0			0
$616$	−1.14028	+	12.9238i	−0.0459432	+	0.520714i
$617$	−11.9685	−	1.89563i	−0.481835	−	0.0763151i	−0.0892079	−	0.996013i	$-0.528434\pi$
$617$	−11.9685	−	1.89563i	−0.481835	−	0.0763151i	−0.392627	+	0.919698i	$0.628434\pi$
$618$	21.9168	+	5.87259i	0.881624	+	0.236230i
$619$	−1.68698	−	16.0505i	−0.0678054	−	0.645125i	−0.974662	−	0.223685i	$-0.928191\pi$
$619$	−1.68698	−	16.0505i	−0.0678054	−	0.645125i	0.906856	−	0.421440i	$-0.138475\pi$
$620$		0			0
$621$	8.45046	+	0.888179i	0.339105	+	0.0356414i
$622$	−9.96354	+	1.57807i	−0.399502	+	0.0632749i
$623$	−14.7088	+	30.1011i	−0.589294	+	1.20597i
$624$		−	20.4181i		−	0.817376i
$625$		0			0
$626$	−10.4927	−	6.05796i	−0.419372	−	0.242125i
$627$	−1.60683	+	30.6600i	−0.0641704	+	1.22444i
$628$	1.72269	−	1.39500i	0.0687427	−	0.0556667i
$629$	10.8523	+	7.88463i	0.432708	+	0.314381i
$630$		0			0
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.289799	−	0.957087i	$-0.406411\pi$
$631$	32.3943	−	23.5358i	1.28960	−	0.936947i	0.999797	+	0.0201409i	$0.00641148\pi$
$632$	−1.62756	+	6.07412i	−0.0647407	+	0.241616i
$633$	−30.7932	+	38.0264i	−1.22392	+	1.51141i
$634$	4.65424	−	21.8965i	0.184843	−	0.869620i
$635$		0			0
$636$	8.88511	+	2.88695i	0.352318	+	0.114475i
$637$	−14.9043	−	3.46407i	−0.590529	−	0.137251i
$638$	−20.6654	−	10.5295i	−0.818149	−	0.416868i
$639$	1.17088	+	5.50853i	0.0463191	+	0.217914i
$640$		0			0
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.855170	−	0.518348i	$-0.173453\pi$
$641$	36.0927	+	7.67174i	1.42558	+	0.303015i	0.570406	+	0.821363i	$0.306786\pi$
$642$	33.6541	−	12.9186i	1.32822	−	0.509856i
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	0.335406	−	0.942074i	$-0.391126\pi$
$643$	−15.3835	−	15.3835i	−0.606667	−	0.606667i	−0.942074	+	0.335406i	$0.891126\pi$
$644$	−2.00684	+	1.86864i	−0.0790804	+	0.0736348i
$645$		0			0
$646$	−6.31604	+	60.0932i	−0.248501	+	2.36433i
$647$	−12.6160	+	32.8659i	−0.495987	+	1.29209i	0.425949	+	0.904747i	$0.359940\pi$
$647$	−12.6160	+	32.8659i	−0.495987	+	1.29209i	−0.921936	+	0.387343i	$0.873393\pi$
$648$	25.4247	+	1.33245i	0.998775	+	0.0523436i
$649$	10.9605	+	18.9842i	0.430238	+	0.745193i
$650$		0			0
$651$	26.3213	−	19.8041i	1.03161	−	0.776184i
$652$	−7.01384	+	3.57373i	−0.274683	+	0.139958i
$653$	19.5093	+	24.0920i	0.763459	+	0.942794i	0.999581	−	0.0289295i	$-0.00920982\pi$
$653$	19.5093	+	24.0920i	0.763459	+	0.942794i	−0.236122	+	0.971723i	$0.575876\pi$
$654$	−27.7632	+	12.3610i	−1.08563	+	0.483352i
$655$		0			0
$656$	−17.2832	+	38.8188i	−0.674797	+	1.51562i
$657$	4.92657	−	4.92657i	0.192204	−	0.192204i
$658$	−9.34616	−	5.84971i	−0.364351	−	0.228045i
$659$	−6.75492	+	2.19481i	−0.263134	+	0.0854976i	−0.437613	−	0.899163i	$-0.644176\pi$
$659$	−6.75492	+	2.19481i	−0.263134	+	0.0854976i	0.174479	+	0.984661i	$0.444176\pi$
$660$		0			0
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	−0.596778	−	0.802406i	$-0.703553\pi$
$661$	3.56987	−	3.21432i	0.138852	−	0.125023i	0.735630	+	0.677383i	$0.236886\pi$
$662$	8.89494	+	13.6970i	0.345712	+	0.532349i
$663$	−21.6747	+	1.13592i	−0.841775	+	0.0441156i
$664$	−2.12387	+	6.53659i	−0.0824220	+	0.253669i
$665$		0			0
$666$	1.09196	+	3.36069i	0.0423124	+	0.130224i
$667$	5.05154	+	13.1597i	0.195596	+	0.509546i
$668$	−8.42942	+	2.25866i	−0.326144	+	0.0873901i
$669$	−25.3912	+	2.66872i	−0.981679	+	0.103179i
$670$		0			0
$671$	−10.5039	+	14.4574i	−0.405498	+	0.558120i
$672$	−10.2807	+	10.6303i	−0.396585	+	0.410071i
$673$	5.97729	+	11.7311i	0.230408	+	0.452201i	0.977046	−	0.213030i	$-0.0683332\pi$
$673$	5.97729	+	11.7311i	0.230408	+	0.452201i	−0.746638	+	0.665231i	$0.768333\pi$
$674$	35.3100	−	20.3863i	1.36009	−	0.785249i
$675$		0			0
$676$	−2.12143	+	3.67442i	−0.0815934	+	0.141324i
$677$	−25.8435	+	39.7955i	−0.993247	+	1.52947i	−0.152311	+	0.988333i	$0.548671\pi$
$677$	−25.8435	+	39.7955i	−0.993247	+	1.52947i	−0.840937	+	0.541134i	$0.817995\pi$
$678$	4.45777	+	28.1453i	0.171200	+	1.08091i
$679$	4.33196	−	7.80151i	0.166245	−	0.299394i
$680$		0			0
$681$	5.54570	+	2.46911i	0.212512	+	0.0946164i
$682$	−5.43288	−	20.2758i	−0.208036	−	0.776400i
$683$	13.8738	+	11.2348i	0.530865	+	0.429886i	0.856908	−	0.515469i	$-0.172382\pi$
$683$	13.8738	+	11.2348i	0.530865	+	0.429886i	−0.326043	+	0.945355i	$0.605716\pi$
$684$	−2.18453	+	2.42617i	−0.0835277	+	0.0927669i
$685$		0			0
$686$	15.9453	+	24.6729i	0.608796	+	0.942017i
$687$	−0.475004	+	0.932248i	−0.0181225	+	0.0355675i
$688$	−0.347916	−	6.63863i	−0.0132642	−	0.253095i
$689$	−13.5103	−	15.0048i	−0.514703	−	0.571636i
$690$		0			0
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	0.550368	−	0.834922i	$-0.314487\pi$
$691$	−5.84754	−	5.26515i	−0.222451	−	0.200296i	−0.772819	+	0.634626i	$0.781154\pi$
$692$	−1.51331	+	9.55468i	−0.0575275	+	0.363214i
$693$	3.65214	+	2.85770i	0.138733	+	0.108555i
$694$	−4.25473	−	5.85614i	−0.161507	−	0.222296i
$695$		0			0
$696$	13.1700	+	29.5804i	0.499209	+	1.12124i
$697$	42.1694	+	16.1873i	1.59728	+	0.613139i
$698$	47.1199	+	30.6001i	1.78352	+	1.15823i
$699$	−48.6441			−1.83989
$700$		0			0
$701$	21.0860			0.796406			0.398203	−	0.917297i	$-0.369634\pi$
$701$	21.0860			0.796406			0.398203	+	0.917297i	$0.369634\pi$
$702$	12.3031	+	7.98974i	0.464351	+	0.301553i
$703$	−18.5877	−	7.13514i	−0.701047	−	0.269107i
$704$	−4.24346	−	9.53096i	−0.159931	−	0.359212i
$705$		0			0
$706$	−9.96981	−	13.7223i	−0.375219	−	0.516444i
$707$	−6.96785	+	2.80922i	−0.262053	+	0.105652i
$708$	−1.66489	+	10.5117i	−0.0625703	+	0.395054i
$709$	−2.13303	−	1.92059i	−0.0801077	−	0.0721293i	0.628104	−	0.778129i	$-0.283831\pi$
$709$	−2.13303	−	1.92059i	−0.0801077	−	0.0721293i	−0.708212	+	0.706000i	$0.750498\pi$
$710$		0			0
$711$	1.50398	+	1.67034i	0.0564038	+	0.0626427i
$712$	−1.55994	−	29.7654i	−0.0584611	−	1.11550i
$713$	−5.79180	+	11.3671i	−0.216905	+	0.425699i
$714$	31.4284	+	27.3609i	1.17618	+	1.02396i
$715$		0			0
$716$	−3.38719	+	3.76186i	−0.126585	+	0.140587i
$717$	41.5539	+	33.6497i	1.55186	+	1.25667i
$718$	−1.56704	−	5.84827i	−0.0584814	−	0.218256i
$719$	−5.18872	−	2.31017i	−0.193507	−	0.0861547i	0.307696	−	0.951485i	$-0.400442\pi$
$719$	−5.18872	−	2.31017i	−0.193507	−	0.0861547i	−0.501202	+	0.865330i	$0.667109\pi$
$720$		0			0
$721$	0.322778	+	19.3073i	0.0120209	+	0.719040i
$722$	−9.31526	−	58.8143i	−0.346678	−	2.18884i
$723$	−20.4330	+	31.4640i	−0.759911	+	1.17016i
$724$	0.216584	−	0.375135i	0.00804929	−	0.0139418i
$725$		0			0
$726$	−17.9310	+	10.3525i	−0.665481	+	0.384216i
$727$	−18.9408	−	37.1735i	−0.702477	−	1.37869i	−0.915771	−	0.401701i	$-0.868419\pi$
$727$	−18.9408	−	37.1735i	−0.702477	−	1.37869i	0.213294	−	0.976988i	$-0.431581\pi$
$728$	13.0887	−	3.74270i	0.485100	−	0.138714i
$729$	−9.27315	+	12.7634i	−0.343450	+	0.472718i
$730$		0			0
$731$	−7.02785	+	0.738657i	−0.259934	+	0.0273202i
$732$	−8.38045	+	2.24553i	−0.309750	+	0.0829973i
$733$	12.3930	+	32.2848i	0.457745	+	1.19247i	0.947258	+	0.320471i	$0.103841\pi$
$733$	12.3930	+	32.2848i	0.457745	+	1.19247i	−0.489513	+	0.871996i	$0.662825\pi$
$734$	−4.08138	−	12.5612i	−0.150647	−	0.463642i
$735$		0			0
$736$	1.76991	−	5.44722i	0.0652397	−	0.200787i
$737$	6.83146	−	0.358021i	0.251640	−	0.0131879i
$738$	6.48059	+	9.97924i	0.238554	+	0.367341i
$739$	−6.17964	+	5.56417i	−0.227322	+	0.204681i	−0.774919	−	0.632061i	$-0.782209\pi$
$739$	−6.17964	+	5.56417i	−0.227322	+	0.204681i	0.547597	+	0.836742i	$0.315543\pi$
$740$		0			0
$741$	30.6384	−	9.95501i	1.12553	−	0.365706i
$742$	−1.38139	+	38.7393i	−0.0507123	+	1.42216i
$743$	10.0390	−	10.0390i	0.368295	−	0.368295i	−0.498560	−	0.866855i	$-0.666138\pi$
$743$	10.0390	−	10.0390i	0.368295	−	0.368295i	0.866855	+	0.498560i	$0.166138\pi$
$744$	−11.9195	+	26.7717i	−0.436991	+	0.981498i
$745$		0			0
$746$	25.2590	−	11.2460i	0.924797	−	0.411746i
$747$	1.54600	+	1.90915i	0.0565651	+	0.0698521i
$748$	4.85283	−	2.47264i	0.177437	−	0.0904086i
$749$	18.4447	+	24.5145i	0.673954	+	0.895740i
$750$		0			0
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	0.957026	+	0.290000i	$0.0936555\pi$
$751$	19.9959	+	34.6339i	0.729661	+	1.26381i	−0.227365	+	0.973810i	$0.573011\pi$
$752$	12.5039	+	0.655299i	0.455968	+	0.0238963i
$753$	−5.26582	+	13.7179i	−0.191897	+	0.499909i
$754$	−2.54383	+	24.2029i	−0.0926407	+	0.881417i
$755$		0			0
$756$	−1.29531	−	5.62951i	−0.0471098	−	0.204743i
$757$	12.1964	+	12.1964i	0.443287	+	0.443287i	0.893115	−	0.449828i	$-0.148515\pi$
$757$	12.1964	+	12.1964i	0.443287	+	0.443287i	−0.449828	+	0.893115i	$0.648515\pi$
$758$	−16.1666	+	6.20578i	−0.587198	+	0.225404i
$759$	−8.02106	−	1.70493i	−0.291146	−	0.0618850i
$760$		0			0
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	0.924188	−	0.381938i	$-0.124743\pi$
$761$	−2.08132	−	9.79185i	−0.0754479	−	0.354954i	−0.999636	+	0.0269835i	$0.991410\pi$
$762$	6.80777	+	3.46873i	0.246619	+	0.125659i
$763$	−16.6101	−	19.8248i	−0.601327	−	0.717707i
$764$	−1.33536	−	0.433884i	−0.0483116	−	0.0156974i
$765$		0			0
$766$	−5.47227	+	25.7450i	−0.197721	+	0.930205i
$767$	14.4752	−	17.8753i	0.522668	−	0.645441i
$768$	5.90038	−	22.0205i	0.212912	−	0.794597i
$769$	33.7752	−	24.5391i	1.21796	−	0.884902i	0.222034	−	0.975039i	$-0.428730\pi$
$769$	33.7752	−	24.5391i	1.21796	−	0.884902i	0.995929	+	0.0901368i	$0.0287304\pi$
$770$		0			0
$771$	−21.7061	−	15.7704i	−0.781728	−	0.567959i
$772$	−2.81129	+	2.27654i	−0.101181	+	0.0819345i
$773$	1.49574	−	28.5404i	0.0537980	−	1.02653i	−0.829735	−	0.558158i	$-0.811508\pi$
$773$	1.49574	−	28.5404i	0.0537980	−	1.02653i	0.883533	−	0.468370i	$-0.155158\pi$
$774$	−1.61213	−	0.930761i	−0.0579466	−	0.0334555i
$775$		0			0
$776$			7.93899i			0.284993i
$777$	−11.3887	+	7.66955i	−0.408566	+	0.275143i
$778$	30.1171	−	4.77008i	1.07975	−	0.171016i
$779$	−66.6762	−	7.00795i	−2.38892	−	0.251086i
$780$		0			0
$781$	1.45762	+	13.8683i	0.0521576	+	0.496246i
$782$	−15.5888	−	4.17702i	−0.557456	−	0.149370i
$783$	−29.3293	−	4.64530i	−1.04814	−	0.166009i
$784$	−29.4325	−	15.7052i	−1.05116	−	0.560902i
$785$		0			0
$786$	−16.9423	+	3.60119i	−0.604311	+	0.128450i
$787$	28.9611	−	18.8075i	1.03235	−	0.670416i	0.0869114	−	0.996216i	$-0.472300\pi$
$787$	28.9611	−	18.8075i	1.03235	−	0.670416i	0.945439	+	0.325800i	$0.105634\pi$
$788$	−6.41486	+	4.16586i	−0.228520	+	0.148403i
$789$	−37.5120	+	7.97342i	−1.33546	+	0.283861i
$790$		0			0
$791$	−21.9866	+	10.2328i	−0.781753	+	0.363836i
$792$	−4.07487	−	0.645396i	−0.144794	−	0.0229332i
$793$	18.1120	+	4.85309i	0.643175	+	0.172338i
$794$	−0.201724	−	1.91927i	−0.00715891	−	0.0681125i
$795$		0			0
$796$	−10.7852	−	1.13357i	−0.382271	−	0.0401783i
$797$	46.4194	−	7.35212i	1.64426	−	0.260425i	0.735433	−	0.677597i	$-0.236979\pi$
$797$	46.4194	−	7.35212i	1.64426	−	0.260425i	0.908828	+	0.417172i	$0.136979\pi$
$798$	−55.5693	−	27.1537i	−1.96713	−	0.961230i
$799$		−	13.3099i		−	0.470869i
$800$		0			0
$801$	−9.22634	−	5.32683i	−0.325997	−	0.188214i
$802$	0.393783	−	7.51383i	0.0139050	−	0.265322i
$803$	13.4072	−	10.8570i	0.473131	−	0.383134i
$804$	2.68694	+	1.95218i	0.0947612	+	0.0688480i
$805$		0			0
$806$	−17.8190	+	12.9462i	−0.627646	+	0.456012i
$807$	4.68401	−	17.4810i	0.164885	−	0.615359i
$808$	4.20634	−	5.19439i	0.147978	−	0.182738i
$809$	6.74211	−	31.7191i	0.237040	−	1.11519i	−0.685136	−	0.728415i	$-0.740257\pi$
$809$	6.74211	−	31.7191i	0.237040	−	1.11519i	0.922176	−	0.386770i	$-0.126409\pi$
$810$		0			0
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	0.460413	−	0.887705i	$-0.347701\pi$
$811$	8.85993	+	2.87877i	0.311114	+	0.101087i	−0.149298	+	0.988792i	$0.547701\pi$
$812$	7.34554	−	6.15442i	0.257778	−	0.215978i
$813$	1.93178	+	0.984289i	0.0677503	+	0.0345205i
$814$	1.81919	+	8.55862i	0.0637626	+	0.299980i
$815$		0			0
$816$	−46.2862	−	9.83843i	−1.62034	−	0.344414i
$817$	9.79198	−	3.75879i	0.342578	−	0.131503i
$818$	27.8073	+	27.8073i	0.972258	+	0.972258i
$819$	1.42606	−	4.65216i	0.0498305	−	0.162560i
$820$		0			0
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	−0.688661	−	0.725083i	$-0.741801\pi$
$821$	3.88835	−	36.9952i	0.135704	−	1.29114i	0.824366	−	0.566058i	$-0.191532\pi$
$822$	−10.1180	+	26.3584i	−0.352907	+	0.919354i
$823$	29.7808	+	1.56075i	1.03809	+	0.0544042i	0.563758	−	0.825940i	$-0.309355\pi$
$823$	29.7808	+	1.56075i	1.03809	+	0.0544042i	0.474335	+	0.880344i	$0.342688\pi$
$824$	−8.58974	−	14.8779i	−0.299238	−	0.518295i
$825$		0			0
$826$	−43.8342	+	5.34938i	−1.52519	+	0.186129i
$827$	−25.7867	+	13.1390i	−0.896691	+	0.456887i	−0.840673	−	0.541543i	$-0.817840\pi$
$827$	−25.7867	+	13.1390i	−0.896691	+	0.456887i	−0.0560176	+	0.998430i	$0.517840\pi$
$828$	−0.548755	−	0.677656i	−0.0190706	−	0.0235502i
$829$	−8.61441	+	3.83538i	−0.299191	+	0.133208i	−0.550842	−	0.834610i	$-0.685693\pi$
$829$	−8.61441	+	3.83538i	−0.299191	+	0.133208i	0.251651	+	0.967818i	$0.419027\pi$
$830$		0			0
$831$	15.4978	−	34.8087i	0.537614	−	1.20750i
$832$	−7.74074	+	7.74074i	−0.268362	+	0.268362i
$833$	−15.0344	+	32.1177i	−0.520911	+	1.11281i
$834$	−52.6799	+	17.1167i	−1.82416	+	0.592704i
$835$		0			0
$836$	−6.00756	+	5.40923i	−0.207776	+	0.187082i
$837$	−14.6373	−	22.5395i	−0.505940	−	0.779080i
$838$	−38.5668	+	2.02120i	−1.33227	+	0.0698212i
$839$	16.9096	−	52.0423i	0.583784	−	1.79670i	−0.0203179	−	0.999794i	$-0.506468\pi$
$839$	16.9096	−	52.0423i	0.583784	−	1.79670i	0.604101	−	0.796907i	$-0.293532\pi$
$840$		0			0
$841$	−6.26123	−	19.2701i	−0.215905	−	0.664486i
$842$	4.21641	+	10.9841i	0.145307	+	0.378538i
$843$	−3.24803	+	0.870306i	−0.111868	+	0.0299749i
$844$	−12.8131	+	1.34671i	−0.441044	+	0.0463556i
$845$		0			0
$846$	2.06088	−	2.83656i	0.0708544	−	0.0975228i
$847$	−12.6662	−	12.2496i	−0.435215	−	0.420903i
$848$	−19.9848	−	39.2224i	−0.686282	−	1.34690i
$849$	44.8078	−	25.8698i	1.53780	−	0.887849i
$850$		0			0
$851$	2.65890	−	4.60535i	0.0911460	−	0.157870i
$852$	−3.68731	+	5.67796i	−0.126325	+	0.194524i
$853$	9.03599	+	57.0510i	0.309386	+	1.95339i	0.301650	+	0.953419i	$0.402462\pi$
$853$	9.03599	+	57.0510i	0.309386	+	1.95339i	0.00773601	+	0.999970i	$0.497538\pi$
$854$	−18.5183	−	30.8711i	−0.633682	−	1.05639i
$855$		0			0
$856$	−24.9340	−	11.1013i	−0.852226	−	0.379436i
$857$	−3.64690	−	13.6104i	−0.124576	−	0.464923i	0.875248	−	0.483674i	$-0.160698\pi$
$857$	−3.64690	−	13.6104i	−0.124576	−	0.464923i	−0.999824	+	0.0187505i	$0.994031\pi$
$858$	−11.0024	−	8.90958i	−0.375616	−	0.304168i
$859$	14.0269	−	15.5785i	0.478592	−	0.531530i	−0.454702	−	0.890644i	$-0.650254\pi$
$859$	14.0269	−	15.5785i	0.478592	−	0.531530i	0.933294	+	0.359113i	$0.116921\pi$
$860$		0			0
$861$	−30.3583	+	34.8713i	−1.03461	+	1.18841i
$862$	−12.9994	+	25.5128i	−0.442763	+	0.868971i
$863$	0.800451	+	15.2735i	0.0272477	+	0.519916i	0.977824	+	0.209427i	$0.0671597\pi$
$863$	0.800451	+	15.2735i	0.0272477	+	0.519916i	−0.950577	+	0.310490i	$0.899507\pi$
$864$	8.07357	+	8.96661i	0.274669	+	0.305050i
$865$		0			0
$866$	−29.7563	−	26.7927i	−1.01116	−	0.910452i
$867$	−2.65667	+	16.7735i	−0.0902252	+	0.569659i
$868$	8.58779	+	1.21339i	0.291489	+	0.0411851i
$869$	3.27136	+	4.50263i	0.110973	+	0.152741i
$870$		0			0
$871$	−2.91953	−	6.55737i	−0.0989245	−	0.222188i
$872$	21.4816	+	8.24602i	0.727460	+	0.279246i
$873$	2.37985	+	1.54549i	0.0805456	+	0.0523069i
$874$	23.9541			0.810261
$875$		0			0
$876$	8.37585			0.282994
$877$	12.5522	+	8.15148i	0.423857	+	0.275256i	0.738892	−	0.673824i	$-0.235350\pi$
$877$	12.5522	+	8.15148i	0.423857	+	0.275256i	−0.315035	+	0.949080i	$0.602016\pi$
$878$	41.3083	+	15.8568i	1.39409	+	0.535140i
$879$	4.89045	+	10.9841i	0.164951	+	0.370486i
$880$		0			0
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	0.944224	−	0.329303i	$-0.106814\pi$
$881$	10.0697	+	13.8597i	0.339257	+	0.466947i	−0.604967	+	0.796250i	$0.706814\pi$
$882$	−8.17714	+	4.51692i	−0.275339	+	0.152093i
$883$	4.27148	−	26.9691i	0.143747	−	0.907581i	−0.805397	−	0.592736i	$-0.798048\pi$
$883$	4.27148	−	26.9691i	0.143747	−	0.907581i	0.949143	−	0.314845i	$-0.101952\pi$
$884$	−4.24696	−	3.82398i	−0.142841	−	0.128614i
$885$		0			0
$886$	−32.5015	−	36.0966i	−1.09191	−	1.21269i
$887$	−1.66049	−	31.6840i	−0.0557537	−	1.06384i	−0.873051	−	0.487628i	$-0.837862\pi$
$887$	−1.66049	−	31.6840i	−0.0557537	−	1.06384i	0.817298	−	0.576216i	$-0.195471\pi$
$888$	5.54572	−	10.8841i	0.186102	−	0.365246i
$889$	−1.24541	+	6.38199i	−0.0417698	+	0.214045i
$890$		0			0
$891$	15.0775	−	16.7453i	0.505117	−	0.560989i
$892$	−5.22429	−	4.23055i	−0.174922	−	0.141649i
$893$	5.11306	+	19.0822i	0.171102	+	0.638561i
$894$	41.5772	+	18.5114i	1.39055	+	0.619112i
$895$		0			0
$896$	36.1025	−	0.603560i	1.20610	−	0.0201635i
$897$	1.34602	+	8.49842i	0.0449422	+	0.283754i
$898$	−26.2822	+	40.4711i	−0.877050	+	1.35054i
$899$	22.2922	−	38.6112i	0.743485	−	1.28775i
$900$		0			0
$901$	−40.5246	+	23.3969i	−1.35007	+	0.779463i
$902$	13.3761	+	26.2521i	0.445376	+	0.874099i
$903$	1.75503	−	7.01702i	0.0584038	−	0.233512i
$904$	12.6818	−	17.4550i	0.421790	−	0.580544i
$905$		0			0
$906$	49.7944	−	5.23360i	1.65431	−	0.173875i
$907$	12.3572	−	3.31110i	0.410314	−	0.109943i	−0.0477567	−	0.998859i	$-0.515207\pi$
$907$	12.3572	−	3.31110i	0.410314	−	0.109943i	0.458071	+	0.888916i	$0.348541\pi$
$908$	0.572812	+	1.49223i	0.0190094	+	0.0495212i
$909$	−0.738256	−	2.27212i	−0.0244864	−	0.0753614i
$910$		0			0
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	−0.987312	−	0.158794i	$-0.949239\pi$
$911$	−2.87409	+	8.84554i	−0.0952228	+	0.293066i	0.892089	+	0.451860i	$0.149239\pi$
$912$	70.1394	−	3.67585i	2.32255	−	0.121720i
$913$	3.31301	+	5.10159i	0.109645	+	0.168838i
$914$	−47.5847	+	42.8454i	−1.57396	+	1.41720i
$915$		0			0
$916$	−0.262007	+	0.0851313i	−0.00865696	+	0.00281282i
$917$	−6.91070	−	13.0203i	−0.228211	−	0.429967i
$918$	24.0404	−	24.0404i	0.793450	−	0.793450i
$919$	−19.7932	+	44.4563i	−0.652917	+	1.46648i	0.218451	+	0.975848i	$0.429899\pi$
$919$	−19.7932	+	44.4563i	−0.652917	+	1.46648i	−0.871369	+	0.490629i	$0.836767\pi$
$920$		0			0
$921$	−31.7969	+	14.1569i	−1.04774	+	0.466485i
$922$	17.8352	+	22.0246i	0.587371	+	0.725343i
$923$	13.0371	−	6.64272i	0.429121	−	0.218648i
$924$	0.675327	+	5.53381i	0.0222166	+	0.182049i
$925$		0			0
$926$	−27.1322	−	46.9943i	−0.891619	−	1.54433i
$927$	−6.13206	−	0.321368i	−0.201403	−	0.0105551i
$928$	−7.17320	+	18.6868i	−0.235472	+	0.613425i
$929$	0.0493594	−	0.469623i	0.00161943	−	0.0154078i	−0.993682	−	0.112229i	$-0.964201\pi$
$929$	0.0493594	−	0.469623i	0.00161943	−	0.0154078i	0.995302	+	0.0968214i	$0.0308676\pi$
$930$		0			0
$931$	9.21644	−	51.8223i	0.302057	−	1.69841i
$932$	−9.05674	−	9.05674i	−0.296663	−	0.296663i
$933$	11.6366	−	4.46688i	0.380966	−	0.146239i
$934$	10.3605	+	2.20220i	0.339007	+	0.0720582i
$935$		0			0
$936$	0.900044	+	4.23437i	0.0294189	+	0.138405i
$937$	30.8727	+	15.7304i	1.00857	+	0.513890i	0.878565	−	0.477624i	$-0.158502\pi$
$937$	30.8727	+	15.7304i	1.00857	+	0.513890i	0.130002	+	0.991514i	$0.458502\pi$
$938$	−4.72282	+	12.9462i	−0.154206	+	0.422707i
$939$	14.2378	+	4.62615i	0.464634	+	0.150969i
$940$		0			0
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	−0.923683	−	0.383157i	$-0.874837\pi$
$941$	2.33096	−	10.9663i	0.0759873	−	0.357492i	0.999671	+	0.0256647i	$0.00817023\pi$
$942$	−8.40387	+	10.3779i	−0.273813	+	0.338131i
$943$	4.63460	−	17.2966i	0.150923	−	0.563253i
$944$	40.5702	−	29.4760i	1.32045	−	0.959362i
$945$		0			0
$946$	−3.72909	−	2.70934i	−0.121243	−	0.0880883i
$947$	−44.5472	+	36.0736i	−1.44759	+	1.17224i	−0.494644	+	0.869096i	$0.664701\pi$
$947$	−44.5472	+	36.0736i	−1.44759	+	1.17224i	−0.952946	+	0.303139i	$0.901965\pi$
$948$	−0.141417	+	2.69839i	−0.00459301	+	0.0876398i
$949$	−15.6768	−	9.05102i	−0.508892	−	0.293809i
$950$		0			0
$951$			27.6599i			0.896934i
$952$	−2.17761	−	31.4745i	−0.0705767	−	1.02010i
$953$	−17.0778	+	2.70486i	−0.553204	+	0.0876189i	−0.426777	−	0.904357i	$-0.640351\pi$
$953$	−17.0778	+	2.70486i	−0.553204	+	0.0876189i	−0.126427	+	0.991976i	$0.540351\pi$
$954$	−12.2592	−	1.28849i	−0.396906	−	0.0417165i
$955$		0			0
$956$	1.47163	+	14.0017i	0.0475960	+	0.452846i
$957$	27.6813	+	7.41718i	0.894810	+	0.239764i
$958$	7.93504	+	1.25679i	0.256370	+	0.0406050i
$959$	−23.9349	−	2.11180i	−0.772897	−	0.0681937i
$960$		0			0
$961$	9.14667	−	1.94419i	0.295054	−	0.0627156i
$962$	7.69984	−	5.00034i	0.248253	−	0.161217i
$963$	−8.18173	+	5.31328i	−0.263653	+	0.171218i
$964$	−9.66237	+	2.05380i	−0.311204	+	0.0661484i
$965$		0			0
$966$	9.48502	−	13.5248i	0.305175	−	0.435153i
$967$	−13.9567	−	2.21053i	−0.448819	−	0.0710859i	−0.0720662	−	0.997400i	$-0.522959\pi$
$967$	−13.9567	−	2.21053i	−0.448819	−	0.0710859i	−0.376753	+	0.926314i	$0.622959\pi$
$968$	15.1423	+	4.05738i	0.486693	+	0.130409i
$969$	−7.80416	−	74.2516i	−0.250706	−	2.38531i
$970$		0			0
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.0632139	−	0.998000i	$-0.520135\pi$
$971$	−10.3623	−	1.08912i	−0.332542	−	0.0349516i	−0.269328	+	0.963048i	$0.586802\pi$
$972$	4.33576	−	0.686717i	0.139070	−	0.0220265i
$973$	−26.3314	−	39.1000i	−0.844144	−	1.25349i
$974$		−	29.8245i		−	0.955640i
$975$		0			0
$976$	35.4039	+	20.4405i	1.13325	+	0.654283i
$977$	1.30401	−	24.8821i	0.0417191	−	0.796048i	−0.895021	−	0.446023i	$-0.852840\pi$
$977$	1.30401	−	24.8821i	0.0417191	−	0.796048i	0.936740	−	0.350025i	$-0.113827\pi$
$978$	36.8537	−	29.8436i	1.17845	−	0.954292i
$979$	−21.3419	−	15.5058i	−0.682091	−	0.495568i
$980$		0			0
$981$	6.65373	−	4.83422i	0.212437	−	0.154345i
$982$	−10.7708	+	40.1972i	−0.343710	+	1.28274i
$983$	7.35536	−	9.08311i	0.234600	−	0.289706i	−0.646227	−	0.763145i	$-0.723654\pi$
$983$	7.35536	−	9.08311i	0.234600	−	0.289706i	0.880827	+	0.473439i	$0.156987\pi$
$984$	8.55212	−	40.2346i	0.272632	−	1.28263i
$985$		0			0
$986$	53.6403	+	17.4288i	1.70826	+	0.555046i
$987$	12.7986	+	4.66900i	0.407384	+	0.148616i
$988$	7.55782	+	3.85090i	0.240446	+	0.122513i
$989$	0.582448	+	2.74020i	0.0185208	+	0.0871333i
$990$		0			0
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	0.372404	−	0.928071i	$-0.378533\pi$
$991$	10.5500	+	2.24247i	0.335132	+	0.0712345i	−0.0372721	+	0.999305i	$0.511867\pi$
$992$	−16.9125	+	6.49210i	−0.536972	+	0.206124i
$993$	−14.2692	−	14.2692i	−0.452820	−	0.452820i
$994$	−26.8577	−	8.23288i	−0.851876	−	0.261131i
$995$		0			0
$996$	−0.308703	+	2.93711i	−0.00978162	+	0.0930659i
$997$	4.43884	−	11.5636i	0.140580	−	0.366222i	−0.845157	−	0.534518i	$-0.820493\pi$
$997$	4.43884	−	11.5636i	0.140580	−	0.366222i	0.985737	+	0.168296i	$0.0538264\pi$
$998$	4.78795	+	0.250926i	0.151560	+	0.00794293i
$999$	5.60130	+	9.70173i	0.177217	+	0.306949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.b.507.5		288
5.2	odd	4		875.2.bb.c.493.14		288
5.3	odd	4		175.2.x.a.3.5	✓	288
5.4	even	2		875.2.bb.a.507.14		288
7.5	odd	6	inner	875.2.bb.b.257.5		288
25.6	even	5		175.2.x.a.17.14	yes	288
25.8	odd	20	inner	875.2.bb.b.143.5		288
25.17	odd	20		875.2.bb.a.143.14		288
25.19	even	10		875.2.bb.c.857.5		288
35.12	even	12		875.2.bb.c.243.5		288
35.19	odd	6		875.2.bb.a.257.14		288
35.33	even	12		175.2.x.a.103.14	yes	288
175.19	odd	30		875.2.bb.c.607.14		288
175.33	even	60	inner	875.2.bb.b.768.5		288
175.117	even	60		875.2.bb.a.768.14		288
175.131	odd	30		175.2.x.a.117.5	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	5.3	odd	4
175.2.x.a.17.14	yes	288	25.6	even	5
175.2.x.a.103.14	yes	288	35.33	even	12
175.2.x.a.117.5	yes	288	175.131	odd	30
875.2.bb.a.143.14		288	25.17	odd	20
875.2.bb.a.257.14		288	35.19	odd	6
875.2.bb.a.507.14		288	5.4	even	2
875.2.bb.a.768.14		288	175.117	even	60
875.2.bb.b.143.5		288	25.8	odd	20	inner
875.2.bb.b.257.5		288	7.5	odd	6	inner
875.2.bb.b.507.5		288	1.1	even	1	trivial
875.2.bb.b.768.5		288	175.33	even	60	inner
875.2.bb.c.243.5		288	35.12	even	12
875.2.bb.c.493.14		288	5.2	odd	4
875.2.bb.c.607.14		288	175.19	odd	30
875.2.bb.c.857.5		288	25.19	even	10

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33031 - 0.863911i) q^{2} +(1.82975 + 0.702377i) q^{3} +(0.209899 + 0.471441i) q^{4} +(-1.82734 - 2.51512i) q^{6} +(1.63042 - 2.08368i) q^{7} +(-0.368222 + 2.32486i) q^{8} +(0.625235 + 0.562964i) q^{9} +(1.39398 + 1.54818i) q^{11} +(0.0529345 + 1.01005i) q^{12} +(0.992394 - 1.94768i) q^{13} +(-3.96908 + 1.36339i) q^{14} +(3.18894 - 3.54168i) q^{16} +(-3.93706 - 3.18817i) q^{17} +(-0.345403 - 1.28906i) q^{18} +(6.86927 + 3.05840i) q^{19} +(4.44680 - 2.66745i) q^{21} +(-0.516939 - 3.26382i) q^{22} +(-1.09383 + 1.68435i) q^{23} +(-2.30669 + 3.99530i) q^{24} +(-3.00281 + 1.73368i) q^{26} +(-1.92076 - 3.76970i) q^{27} +(1.32456 + 0.331286i) q^{28} +(4.12547 - 5.67823i) q^{29} +(6.31745 - 0.663990i) q^{31} +(-2.75469 + 0.738117i) q^{32} +(1.46324 + 3.81188i) q^{33} +(2.48320 + 7.64252i) q^{34} +(-0.134168 + 0.412927i) q^{36} +(-2.64422 + 0.138578i) q^{37} +(-6.49605 - 10.0030i) q^{38} +(3.18385 - 2.86675i) q^{39} +(-8.47974 + 2.75523i) q^{41} +(-8.22005 - 0.293115i) q^{42} +(0.986332 - 0.986332i) q^{43} +(-0.437278 + 0.982142i) q^{44} +(2.91025 - 1.29573i) q^{46} +(1.65339 + 2.04177i) q^{47} +(8.32258 - 4.24056i) q^{48} +(-1.68344 - 6.79456i) q^{49} +(-4.96456 - 8.59887i) q^{51} +(1.12652 + 0.0590385i) q^{52} +(3.31015 - 8.62323i) q^{53} +(-0.701489 + 6.67422i) q^{54} +(4.24391 + 4.55777i) q^{56} +(10.4209 + 10.4209i) q^{57} +(-10.3936 + 3.98974i) q^{58} +(10.2924 + 2.18773i) q^{59} +(1.78346 + 8.39053i) q^{61} +(-8.97777 - 4.57440i) q^{62} +(2.19243 - 0.384920i) q^{63} +(-4.76284 - 1.54754i) q^{64} +(1.34656 - 6.33508i) q^{66} +(2.06649 - 2.55191i) q^{67} +(0.676649 - 2.52529i) q^{68} +(-3.18448 + 2.31366i) q^{69} +(5.41526 + 3.93442i) q^{71} +(-1.53904 + 1.24629i) q^{72} +(0.433401 - 8.26979i) q^{73} +(3.63734 + 2.10002i) q^{74} +3.88041i q^{76} +(5.49868 - 0.380434i) q^{77} +(-6.71211 + 1.06309i) q^{78} +(2.65691 + 0.279252i) q^{79} +(-1.13060 - 10.7569i) q^{81} +(13.6609 + 3.66043i) q^{82} +(2.88395 + 0.456772i) q^{83} +(2.19093 + 1.53651i) q^{84} +(-2.16423 + 0.460021i) q^{86} +(11.5369 - 7.49212i) q^{87} +(-4.11259 + 2.67075i) q^{88} +(-12.3861 + 2.63274i) q^{89} +(-2.44033 - 5.24338i) q^{91} +(-1.02366 - 0.162132i) q^{92} +(12.0258 + 3.22229i) q^{93} +(-0.435611 - 4.14456i) q^{94} +(-5.55884 - 0.584258i) q^{96} +(3.33125 - 0.527619i) q^{97} +(-3.63040 + 10.4932i) q^{98} +1.75274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 2 q^{2} + 6 q^{3} + 10 q^{4} - 10 q^{7} + 64 q^{8} + 10 q^{9} - 6 q^{11} - 6 q^{12} + 20 q^{14} - 30 q^{16} - 12 q^{17} - 14 q^{18} + 30 q^{19} - 12 q^{21} - 8 q^{22} + 30 q^{23} - 48 q^{26} - 58 q^{28}+ \cdots + 62 q^{98}+O(q^{100}) \) 288 * q + 2 * q^2 + 6 * q^3 + 10 * q^4 - 10 * q^7 + 64 * q^8 + 10 * q^9 - 6 * q^11 - 6 * q^12 + 20 * q^14 - 30 * q^16 - 12 * q^17 - 14 * q^18 + 30 * q^19 - 12 * q^21 - 8 * q^22 + 30 * q^23 - 48 * q^26 - 58 * q^28 - 18 * q^31 + 8 * q^32 - 150 * q^33 + 40 * q^36 + 12 * q^38 - 30 * q^39 + 166 * q^42 - 108 * q^43 + 10 * q^44 - 6 * q^46 - 24 * q^47 - 16 * q^51 - 24 * q^52 - 40 * q^53 + 30 * q^54 + 4 * q^56 - 216 * q^57 - 114 * q^58 - 90 * q^59 - 18 * q^61 - 16 * q^63 + 100 * q^64 - 90 * q^66 + 74 * q^67 + 342 * q^68 - 24 * q^71 - 222 * q^72 - 216 * q^73 + 90 * q^77 - 32 * q^78 + 10 * q^79 - 10 * q^81 + 216 * q^82 - 20 * q^84 - 6 * q^86 - 18 * q^87 + 58 * q^88 - 120 * q^89 - 12 * q^91 - 24 * q^92 + 106 * q^93 + 30 * q^94 - 90 * q^96 + 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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