LMFDB - Embedded newform 875.2.bb.a.507.14

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			507.14
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.a.768.14

$q$-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	0.921265	−	0.388934i	$-0.127157\pi$
$2$	1.33031	+	0.863911i	0.940669	+	0.610877i	0.0194031	+	0.999812i	$0.493823\pi$
$3$	−1.82975	−	0.702377i	−1.05641	−	0.405518i	−0.232711	−	0.972546i	$-0.574760\pi$
$3$	−1.82975	−	0.702377i	−1.05641	−	0.405518i	−0.823698	+	0.567028i	$0.808093\pi$
$4$	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	−0.986703	−	0.162534i	$-0.948033\pi$
$13$	−0.992394	+	1.94768i	−0.275241	+	0.540190i	0.711462	+	0.702724i	$0.248033\pi$
$14$	−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	0.973994	−	0.226572i	$-0.0727519\pi$
$17$	3.93706	+	3.18817i	0.954878	+	0.773245i	−0.0191163	+	0.999817i	$0.506085\pi$
$18$	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	−0.706041	−	0.708171i	$-0.749520\pi$
$23$	1.09383	−	1.68435i	0.228079	−	0.351210i	0.934119	+	0.356961i	$0.116187\pi$
$24$	−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	0.166272	−	0.986080i	$-0.446827\pi$
$37$	2.64422	−	0.138578i	0.434707	−	0.0227820i	0.268435	+	0.963298i	$0.413494\pi$
$38$	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	−0.778303	−	0.627889i	$-0.783919\pi$
$43$	−0.986332	+	0.986332i	−0.150414	+	0.150414i	0.627889	+	0.778303i	$0.283919\pi$
$44$	−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	0.642160	−	0.766571i	$-0.278038\pi$
$47$	−1.65339	−	2.04177i	−0.241172	−	0.297822i	−0.883332	+	0.468748i	$0.844705\pi$
$48$	−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	$0.335412\pi$
$53$	−3.31015	+	8.62323i	−0.454684	+	1.18449i	−0.949019	+	0.315220i	$0.897922\pi$
$54$	−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	−0.887583	−	0.460648i	$-0.847617\pi$
$67$	−2.06649	+	2.55191i	−0.252462	+	0.311765i	0.635121	+	0.772413i	$0.280950\pi$
$68$	−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	$0.177708\pi$
$73$	−0.433401	+	8.26979i	−0.0507258	+	0.967906i	−0.898891	+	0.438173i	$0.855626\pi$
$74$	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	−0.00386431	−	0.999993i	$-0.501230\pi$
$83$	−2.88395	−	0.456772i	−0.316554	−	0.0501373i	−0.312690	+	0.949855i	$0.601230\pi$
$84$	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	−0.323243	−	0.946316i	$-0.604773\pi$
$97$	−3.33125	+	0.527619i	−0.338237	+	0.0535716i	−0.0149946	+	0.999888i	$0.504773\pi$
$98$	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	−0.307792	−	0.951454i	$-0.599590\pi$
$103$	5.67198	−	4.59308i	0.558877	−	0.452570i	0.866669	+	0.498884i	$0.166257\pi$
$104$	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	$-0.727282\pi$
$107$	3.00110	−	11.2003i	0.290127	−	1.08277i	0.945011	−	0.327040i	$-0.106051\pi$
$108$	−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	0.793775	−	0.608212i	$-0.208113\pi$
$113$	8.16704	+	4.16132i	0.768291	+	0.391464i	−0.0254843	+	0.999675i	$0.508113\pi$
$114$	−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	−0.354127	−	0.935197i	$-0.615222\pi$
$127$	2.18980	−	1.11576i	0.194313	−	0.0990074i	0.548440	+	0.836190i	$0.315222\pi$
$128$	−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	0.984279	−	0.176621i	$-0.0565167\pi$
$137$	4.94623	+	7.61653i	0.422585	+	0.650724i	−0.561694	+	0.827345i	$0.689850\pi$
$138$	−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	0.995994	−	0.0894230i	$-0.0285023\pi$
$157$	1.11174	+	4.14906i	0.0887263	+	0.331131i	−0.907267	+	0.420554i	$0.861836\pi$
$158$	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	$-0.812873\pi$
$163$	−0.798321	−	15.2329i	−0.0625294	−	1.19313i	0.769591	−	0.638537i	$-0.220460\pi$
$164$	−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	$-0.722969\pi$
$167$	2.64539	−	16.7023i	0.204706	−	1.29246i	0.849289	−	0.527929i	$-0.177031\pi$
$168$	−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	−0.215533	−	0.976496i	$-0.569149\pi$
$173$	−15.7214	−	10.2096i	−1.19527	−	0.776219i	−0.979739	+	0.200277i	$0.935816\pi$
$174$	−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	0.869383	−	0.494139i	$-0.164517\pi$
$193$	−1.81427	−	6.77095i	−0.130594	−	0.487384i	−0.999977	+	0.00675479i	$0.997850\pi$
$194$	−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	$-0.872942\pi$
$197$	−2.31863	−	14.6392i	−0.165195	−	1.04300i	0.756190	−	0.654352i	$-0.227058\pi$
$198$	−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	−0.0199118	−	0.999802i	$-0.506339\pi$
$223$	11.6067	−	5.91390i	0.777241	−	0.396024i	0.797153	+	0.603778i	$0.206339\pi$
$224$	−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	−0.0505884	−	0.998720i	$-0.516110\pi$
$227$	−3.09307	−	0.162101i	−0.205294	−	0.0107590i	−0.154706	+	0.987961i	$0.549443\pi$
$228$	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	0.550311	−	0.834960i	$-0.314509\pi$
$233$	23.1708	−	8.89443i	1.51797	−	0.582694i	0.967658	+	0.252266i	$0.0811757\pi$
$234$	−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	0.646454	−	0.762953i	$-0.276251\pi$
$257$	13.2229	+	3.54307i	0.824824	+	0.221011i	0.178369	+	0.983964i	$0.442918\pi$
$258$	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	0.0715841	−	0.997435i	$-0.477195\pi$
$263$	16.4103	−	10.6570i	1.01190	−	0.657137i	0.940318	+	0.340298i	$0.110528\pi$
$264$	−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	$0.215198\pi$
$277$	−1.01746	+	19.4143i	−0.0611331	+	1.16649i	−0.841175	+	0.540763i	$0.818136\pi$
$278$	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	$0.503808\pi$
$283$	−16.6132	+	20.5156i	−0.987553	+	1.21953i	−0.975590	+	0.219598i	$0.929525\pi$
$284$	−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	0.568950	−	0.822372i	$-0.307350\pi$
$293$	−4.33790	−	4.33790i	−0.253423	−	0.253423i	−0.822372	+	0.568950i	$0.807350\pi$
$294$	−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	−0.251239	−	0.967925i	$-0.580838\pi$
$307$	12.5574	−	12.5574i	0.716687	−	0.716687i	0.967925	+	0.251239i	$0.0808379\pi$
$308$	−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	−0.266677	−	0.963786i	$-0.585926\pi$
$313$	−7.62782	+	0.399757i	−0.431150	+	0.0225956i	−0.164473	+	0.986382i	$0.552592\pi$
$314$	−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	$-0.986952\pi$
$317$	−5.05753	−	13.1753i	−0.284059	−	0.740000i	0.715101	−	0.699021i	$-0.246381\pi$
$318$	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	$-0.603137\pi$
$337$	11.6695	−	22.9028i	0.635681	−	1.24759i	0.954056	−	0.299629i	$-0.0968628\pi$
$338$	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	0.241316	−	0.970447i	$-0.422421\pi$
$347$	−4.26035	−	1.63539i	−0.228707	−	0.0877926i	−0.470023	+	0.882654i	$0.655754\pi$
$348$	−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	0.0778814	−	0.996963i	$-0.475184\pi$
$353$	−9.98297	−	3.83210i	−0.531340	−	0.203962i	−0.609221	+	0.793000i	$0.708518\pi$
$354$	−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	0.445390	−	0.895337i	$-0.353065\pi$
$367$	−6.47094	−	5.24006i	−0.337780	−	0.273529i	−0.783170	+	0.621808i	$0.786399\pi$
$368$	−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	−0.502635	−	0.864498i	$-0.667636\pi$
$373$	9.49367	−	14.6190i	0.491563	−	0.756941i	0.994199	+	0.107557i	$0.0343028\pi$
$374$	−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	$0.0226848\pi$
$383$	5.94645	+	15.4910i	0.303849	+	0.791555i	−0.693612	+	0.720349i	$0.743982\pi$
$384$	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	0.757570	−	0.652754i	$-0.226386\pi$
$397$	−0.765657	−	0.945508i	−0.0384272	−	0.0474537i	−0.795997	+	0.605300i	$0.793053\pi$
$398$	−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	−0.474717	−	0.880139i	$-0.657449\pi$
$433$	−24.9324	−	3.94891i	−1.19818	−	0.189773i	−0.723460	+	0.690366i	$0.757449\pi$
$434$	−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	−0.525066	−	0.851061i	$-0.675960\pi$
$443$	−29.5785	−	7.92554i	−1.40532	−	0.376554i	−0.880252	+	0.474507i	$0.842626\pi$
$444$	−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	$0.476457\pi$
$457$	−10.4479	+	38.9922i	−0.488733	+	1.82398i	−0.562628	+	0.826710i	$0.690210\pi$
$458$	−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	−0.432866	−	0.901458i	$-0.642498\pi$
$463$	−30.4814	−	15.5311i	−1.41659	−	0.721790i	−0.983727	+	0.179668i	$0.942498\pi$
$464$	−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	−0.209826	−	0.977739i	$-0.567290\pi$
$467$	6.23404	−	2.39302i	0.288477	−	0.110736i	0.498303	+	0.867003i	$0.333957\pi$
$468$	−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	0.526740	−	0.850027i	$-0.323414\pi$
$487$	−10.2405	−	15.7690i	−0.464043	−	0.714563i	−0.990782	+	0.135464i	$0.956748\pi$
$488$	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	$0.0512772\pi$
$503$	2.19511	+	13.8594i	0.0978750	+	0.617958i	−0.889178	+	0.457562i	$0.848723\pi$
$504$	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	0.929079	−	0.369880i	$-0.120601\pi$
$523$	22.1618	+	14.3920i	0.969068	+	0.629320i	0.0399883	+	0.999200i	$0.487268\pi$
$524$	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	$0.0713110\pi$
$547$	2.72171	+	17.1842i	0.116372	+	0.734743i	−0.858638	+	0.512582i	$0.828689\pi$
$548$	−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	−0.0277296	−	0.999615i	$-0.508828\pi$
$557$	10.5747	−	2.83348i	0.448064	−	0.120058i	0.475793	+	0.879557i	$0.342161\pi$
$558$	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	0.815066	−	0.579368i	$-0.196701\pi$
$563$	−1.08507	−	1.67086i	−0.0457302	−	0.0704183i	−0.860796	+	0.508950i	$0.830034\pi$
$564$	−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	−0.117209	−	0.993107i	$-0.537395\pi$
$577$	−8.10906	−	0.424978i	−0.337585	−	0.0176921i	−0.220375	+	0.975415i	$0.570728\pi$
$578$	−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	0.320884	−	0.947118i	$-0.396020\pi$
$587$	−6.22031	−	3.16940i	−0.256739	−	0.130815i	−0.577624	+	0.816303i	$0.696020\pi$
$588$	−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	−0.996230	−	0.0867484i	$-0.972352\pi$
$593$	−2.19397	+	8.18799i	−0.0900954	+	0.336240i	0.906135	+	0.422989i	$0.139019\pi$
$594$	−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	0.667804	−	0.744337i	$-0.267234\pi$
$607$	21.5323	+	5.76957i	0.873971	+	0.234180i	0.206167	+	0.978517i	$0.433901\pi$
$608$	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	−0.844635	−	0.535343i	$-0.820182\pi$
$613$	−17.3094	+	11.2408i	−0.699118	+	0.454013i	0.145516	+	0.989356i	$0.453516\pi$
$614$	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	0.392627	−	0.919698i	$-0.371566\pi$
$617$	11.9685	+	1.89563i	0.481835	+	0.0763151i	0.0892079	+	0.996013i	$0.471566\pi$
$618$	−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	0.942074	−	0.335406i	$-0.108874\pi$
$643$	15.3835	+	15.3835i	0.606667	+	0.606667i	−0.335406	+	0.942074i	$0.608874\pi$
$644$	−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	$-0.640060\pi$
$647$	12.6160	−	32.8659i	0.495987	−	1.29209i	0.921936	−	0.387343i	$-0.126607\pi$
$648$	−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	0.236122	−	0.971723i	$-0.424124\pi$
$653$	−19.5093	−	24.0920i	−0.763459	−	0.942794i	−0.999581	+	0.0289295i	$0.990790\pi$
$654$	−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	0.746638	−	0.665231i	$-0.231667\pi$
$673$	−5.97729	−	11.7311i	−0.230408	−	0.452201i	−0.977046	+	0.213030i	$0.931667\pi$
$674$	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	$-0.451329\pi$
$677$	25.8435	−	39.7955i	0.993247	−	1.52947i	0.840937	−	0.541134i	$-0.182005\pi$
$678$	−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	0.326043	−	0.945355i	$-0.394284\pi$
$683$	−13.8738	−	11.2348i	−0.530865	−	0.429886i	−0.856908	+	0.515469i	$0.827618\pi$
$684$	−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	$0.131581\pi$
$727$	18.9408	+	37.1735i	0.702477	+	1.37869i	−0.213294	+	0.976988i	$0.568419\pi$
$728$	−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	$-0.896159\pi$
$733$	−12.3930	−	32.2848i	−0.457745	−	1.19247i	0.489513	−	0.871996i	$-0.337175\pi$
$734$	−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	−0.866855	−	0.498560i	$-0.833862\pi$
$743$	−10.0390	+	10.0390i	−0.368295	+	0.368295i	0.498560	+	0.866855i	$0.333862\pi$
$744$	−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	0.449828	−	0.893115i	$-0.351485\pi$
$757$	−12.1964	−	12.1964i	−0.443287	−	0.443287i	−0.893115	+	0.449828i	$0.851485\pi$
$758$	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	$0.188492\pi$
$773$	−1.49574	+	28.5404i	−0.0537980	+	1.02653i	−0.883533	+	0.468370i	$0.844842\pi$
$774$	−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	−0.945439	−	0.325800i	$-0.894366\pi$
$787$	−28.9611	+	18.8075i	−1.03235	+	0.670416i	−0.0869114	+	0.996216i	$0.527700\pi$
$788$	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	−0.908828	−	0.417172i	$-0.863021\pi$
$797$	−46.4194	+	7.35212i	−1.64426	+	0.260425i	−0.735433	+	0.677597i	$0.763021\pi$
$798$	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	−0.474335	−	0.880344i	$-0.657312\pi$
$823$	−29.7808	−	1.56075i	−1.03809	−	0.0544042i	−0.563758	+	0.825940i	$0.690645\pi$
$824$	−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	0.0560176	−	0.998430i	$-0.482160\pi$
$827$	25.7867	−	13.1390i	0.896691	−	0.456887i	0.840673	+	0.541543i	$0.182160\pi$
$828$	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	$-0.597538\pi$
$853$	−9.03599	−	57.0510i	−0.309386	−	1.95339i	−0.00773601	−	0.999970i	$-0.502462\pi$
$854$	−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	0.999824	−	0.0187505i	$-0.00596883\pi$
$857$	3.64690	+	13.6104i	0.124576	+	0.464923i	−0.875248	+	0.483674i	$0.839302\pi$
$858$	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	$-0.932840\pi$
$863$	−0.800451	−	15.2735i	−0.0272477	−	0.519916i	0.950577	−	0.310490i	$-0.100493\pi$
$864$	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	0.315035	−	0.949080i	$-0.397984\pi$
$877$	−12.5522	−	8.15148i	−0.423857	−	0.275256i	−0.738892	+	0.673824i	$0.764650\pi$
$878$	−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	$0.201952\pi$
$883$	−4.27148	+	26.9691i	−0.143747	+	0.907581i	−0.949143	+	0.314845i	$0.898048\pi$
$884$	−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	$0.162138\pi$
$887$	1.66049	+	31.6840i	0.0557537	+	1.06384i	−0.817298	+	0.576216i	$0.804529\pi$
$888$	−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	−0.458071	−	0.888916i	$-0.651459\pi$
$907$	−12.3572	+	3.31110i	−0.410314	+	0.109943i	0.0477567	+	0.998859i	$0.484793\pi$
$908$	−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	−0.130002	−	0.991514i	$-0.541498\pi$
$937$	−30.8727	−	15.7304i	−1.00857	−	0.513890i	−0.878565	+	0.477624i	$0.841498\pi$
$938$	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	$-0.335299\pi$
$947$	44.5472	−	36.0736i	1.44759	−	1.17224i	0.952946	−	0.303139i	$-0.0980347\pi$
$948$	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	0.126427	−	0.991976i	$-0.459649\pi$
$953$	17.0778	−	2.70486i	0.553204	−	0.0876189i	0.426777	+	0.904357i	$0.359649\pi$
$954$	−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	0.376753	−	0.926314i	$-0.377041\pi$
$967$	13.9567	+	2.21053i	0.448819	+	0.0710859i	0.0720662	+	0.997400i	$0.477041\pi$
$968$	−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	$0.147160\pi$
$977$	−1.30401	+	24.8821i	−0.0417191	+	0.796048i	−0.936740	+	0.350025i	$0.886173\pi$
$978$	−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	−0.880827	−	0.473439i	$-0.843013\pi$
$983$	−7.35536	+	9.08311i	−0.234600	+	0.289706i	0.646227	+	0.763145i	$0.276346\pi$
$984$	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	−0.985737	−	0.168296i	$-0.946174\pi$
$997$	−4.43884	+	11.5636i	−0.140580	+	0.366222i	0.845157	+	0.534518i	$0.179507\pi$
$998$	−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.a.507.14		288
5.2	odd	4		175.2.x.a.3.5	✓	288
5.3	odd	4		875.2.bb.c.493.14		288
5.4	even	2		875.2.bb.b.507.5		288
7.5	odd	6	inner	875.2.bb.a.257.14		288
25.6	even	5		875.2.bb.c.857.5		288
25.8	odd	20	inner	875.2.bb.a.143.14		288
25.17	odd	20		875.2.bb.b.143.5		288
25.19	even	10		175.2.x.a.17.14	yes	288
35.12	even	12		175.2.x.a.103.14	yes	288
35.19	odd	6		875.2.bb.b.257.5		288
35.33	even	12		875.2.bb.c.243.5		288
175.19	odd	30		175.2.x.a.117.5	yes	288
175.33	even	60	inner	875.2.bb.a.768.14		288
175.117	even	60		875.2.bb.b.768.5		288
175.131	odd	30		875.2.bb.c.607.14		288

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

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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