LMFDB - Embedded newform 875.2.bb.a.768.14

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			768.14
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.a.507.14

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.33031	−	0.863911i	0.940669	−	0.610877i	0.0194031	−	0.999812i	$-0.493823\pi$
$2$	1.33031	−	0.863911i	0.940669	−	0.610877i	0.921265	+	0.388934i	$0.127157\pi$
$3$	−1.82975	+	0.702377i	−1.05641	+	0.405518i	−0.823698	−	0.567028i	$-0.808093\pi$
$3$	−1.82975	+	0.702377i	−1.05641	+	0.405518i	−0.232711	+	0.972546i	$0.574760\pi$
$4$	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	−0.495392	−	0.868670i	$-0.664975\pi$
$11$	1.39398	−	1.54818i	0.420302	−	0.466792i	0.915694	+	0.401877i	$0.131642\pi$
$12$	−0.0529345	+	1.01005i	−0.0152809	+	0.291576i
$13$	−0.992394	−	1.94768i	−0.275241	−	0.540190i	0.711462	−	0.702724i	$-0.248033\pi$
$13$	−0.992394	−	1.94768i	−0.275241	−	0.540190i	−0.986703	+	0.162534i	$0.948033\pi$
$14$	−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	$-0.506085\pi$
$17$	3.93706	−	3.18817i	0.954878	−	0.773245i	0.973994	+	0.226572i	$0.0727519\pi$
$18$	0.345403	−	1.28906i	0.0814123	−	0.303835i
$19$	6.86927	−	3.05840i	1.57592	−	0.701644i	0.582148	−	0.813083i	$-0.302212\pi$
$19$	6.86927	−	3.05840i	1.57592	−	0.701644i	0.993771	+	0.111438i	$0.0355458\pi$
$20$		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	$-0.116187\pi$
$23$	1.09383	+	1.68435i	0.228079	+	0.351210i	−0.706041	+	0.708171i	$0.749520\pi$
$24$	−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	0.996684	+	0.0813721i	$0.0259302\pi$
$29$	4.12547	+	5.67823i	0.766081	+	1.05442i	−0.230603	+	0.973048i	$0.574070\pi$
$30$		0			0
$31$	6.31745	+	0.663990i	1.13465	+	0.119256i	0.653176	−	0.757206i	$-0.273436\pi$
$31$	6.31745	+	0.663990i	1.13465	+	0.119256i	0.481471	+	0.876462i	$0.340103\pi$
$32$	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	$-0.413494\pi$
$37$	2.64422	+	0.138578i	0.434707	+	0.0227820i	0.166272	+	0.986080i	$0.446827\pi$
$38$	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	−0.440339	−	0.897832i	$-0.645142\pi$
$41$	−8.47974	−	2.75523i	−1.32431	−	0.430295i	−0.883974	+	0.467536i	$0.845142\pi$
$42$	8.22005	−	0.293115i	1.26838	−	0.0452287i
$43$	−0.986332	−	0.986332i	−0.150414	−	0.150414i	0.627889	−	0.778303i	$-0.283919\pi$
$43$	−0.986332	−	0.986332i	−0.150414	−	0.150414i	−0.778303	+	0.627889i	$0.783919\pi$
$44$	−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	$-0.844705\pi$
$47$	−1.65339	+	2.04177i	−0.241172	+	0.297822i	0.642160	+	0.766571i	$0.278038\pi$
$48$	−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	−0.949019	−	0.315220i	$-0.897922\pi$
$53$	−3.31015	−	8.62323i	−0.454684	−	1.18449i	0.494335	−	0.869271i	$-0.335412\pi$
$54$	−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	0.518498	−	0.855079i	$-0.326491\pi$
$59$	10.2924	−	2.18773i	1.33996	−	0.284818i	0.821464	+	0.570261i	$0.193158\pi$
$60$		0			0
$61$	1.78346	−	8.39053i	0.228349	−	1.07430i	−0.703288	−	0.710905i	$-0.748285\pi$
$61$	1.78346	−	8.39053i	0.228349	−	1.07430i	0.931637	−	0.363391i	$-0.118381\pi$
$62$	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	$-0.280950\pi$
$67$	−2.06649	−	2.55191i	−0.252462	−	0.311765i	−0.887583	+	0.460648i	$0.847617\pi$
$68$	−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	−0.218094	−	0.975928i	$-0.569984\pi$
$71$	5.41526	−	3.93442i	0.642673	−	0.466930i	0.860768	+	0.508998i	$0.169984\pi$
$72$	1.53904	+	1.24629i	0.181378	+	0.146877i
$73$	−0.433401	−	8.26979i	−0.0507258	−	0.967906i	−0.898891	−	0.438173i	$-0.855626\pi$
$73$	−0.433401	−	8.26979i	−0.0507258	−	0.967906i	0.848165	−	0.529733i	$-0.177708\pi$
$74$	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	0.0461216	−	0.998936i	$-0.485314\pi$
$79$	2.65691	−	0.279252i	0.298926	−	0.0314184i	0.252804	+	0.967517i	$0.418647\pi$
$80$		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	$-0.601230\pi$
$83$	−2.88395	+	0.456772i	−0.316554	+	0.0501373i	−0.00386431	+	0.999993i	$0.501230\pi$
$84$	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	−0.502327	−	0.864678i	$-0.667523\pi$
$89$	−12.3861	−	2.63274i	−1.31292	−	0.279070i	−0.810595	+	0.585608i	$0.800856\pi$
$90$		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	$-0.504773\pi$
$97$	−3.33125	−	0.527619i	−0.338237	−	0.0535716i	−0.323243	+	0.946316i	$0.604773\pi$
$98$	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	−0.617333	−	0.786702i	$-0.711787\pi$
$101$	−2.45915	+	1.41979i	−0.244695	+	0.141275i	0.372638	+	0.927977i	$0.378453\pi$
$102$	0.824274	+	15.7281i	0.0816152	+	1.55731i
$103$	5.67198	+	4.59308i	0.558877	+	0.452570i	0.866669	−	0.498884i	$-0.166257\pi$
$103$	5.67198	+	4.59308i	0.558877	+	0.452570i	−0.307792	+	0.951454i	$0.599590\pi$
$104$	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	0.945011	+	0.327040i	$0.106051\pi$
$107$	3.00110	+	11.2003i	0.290127	+	1.08277i	−0.654883	+	0.755730i	$0.727282\pi$
$108$	−1.37403	−	1.69678i	−0.132216	−	0.163273i
$109$	2.03244	+	9.56186i	0.194672	+	0.915860i	0.961670	+	0.274210i	$0.0884164\pi$
$109$	2.03244	+	9.56186i	0.194672	+	0.915860i	−0.766998	+	0.641650i	$0.778250\pi$
$110$		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	$-0.508113\pi$
$113$	8.16704	−	4.16132i	0.768291	−	0.391464i	0.793775	+	0.608212i	$0.208113\pi$
$114$	−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	$-0.315222\pi$
$127$	2.18980	+	1.11576i	0.194313	+	0.0990074i	−0.354127	+	0.935197i	$0.615222\pi$
$128$	−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	0.985069	−	0.172159i	$-0.0550742\pi$
$131$	2.26610	+	5.08975i	0.197990	+	0.444693i	−0.787079	+	0.616852i	$0.788408\pi$
$132$	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	$-0.689850\pi$
$137$	4.94623	−	7.61653i	0.422585	−	0.650724i	0.984279	+	0.176621i	$0.0565167\pi$
$138$	−6.23513	−	0.326769i	−0.530770	−	0.0278165i
$139$	5.50579	+	16.9451i	0.466995	+	1.43726i	0.856456	+	0.516220i	$0.172661\pi$
$139$	5.50579	+	16.9451i	0.466995	+	1.43726i	−0.389461	+	0.921043i	$0.627339\pi$
$140$		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	−0.119185	−	0.992872i	$-0.538028\pi$
$149$	−12.6781	−	7.31970i	−1.03863	−	0.599653i	−0.919445	+	0.393219i	$0.871362\pi$
$150$		0			0
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	−0.981816	−	0.189833i	$-0.939205\pi$
$151$	−8.05257	−	13.9475i	−0.655309	−	1.13503i	0.326508	−	0.945195i	$-0.394128\pi$
$152$	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	$-0.861836\pi$
$157$	1.11174	−	4.14906i	0.0887263	−	0.331131i	0.995994	+	0.0894230i	$0.0285023\pi$
$158$	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	0.769591	+	0.638537i	$0.220460\pi$
$163$	−0.798321	+	15.2329i	−0.0625294	+	1.19313i	−0.832121	+	0.554595i	$0.812873\pi$
$164$	−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	0.849289	+	0.527929i	$0.177031\pi$
$167$	2.64539	+	16.7023i	0.204706	+	1.29246i	−0.644583	+	0.764535i	$0.722969\pi$
$168$	−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	$-0.935816\pi$
$173$	−15.7214	+	10.2096i	−1.19527	+	0.776219i	−0.215533	+	0.976496i	$0.569149\pi$
$174$	−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	−0.700845	−	0.713314i	$-0.747193\pi$
$179$	3.98974	−	8.96111i	0.298207	−	0.669785i	0.999052	+	0.0435289i	$0.0138601\pi$
$180$		0			0
$181$	−0.493376	+	0.679074i	−0.0366723	+	0.0504751i	−0.826959	−	0.562262i	$-0.809931\pi$
$181$	−0.493376	+	0.679074i	−0.0366723	+	0.0504751i	0.790287	+	0.612737i	$0.209931\pi$
$182$	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	0.673670	−	0.739032i	$-0.264717\pi$
$191$	−1.82056	−	2.02194i	−0.131731	−	0.146302i	−0.805401	+	0.592730i	$0.798050\pi$
$192$	7.62788	−	6.17693i	0.550494	−	0.445782i
$193$	−1.81427	+	6.77095i	−0.130594	+	0.487384i	−0.999977	−	0.00675479i	$-0.997850\pi$
$193$	−1.81427	+	6.77095i	−0.130594	+	0.487384i	0.869383	+	0.494139i	$0.164517\pi$
$194$	−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	0.756190	+	0.654352i	$0.227058\pi$
$197$	−2.31863	+	14.6392i	−0.165195	+	1.04300i	−0.921385	+	0.388650i	$0.872942\pi$
$198$	−1.51421	−	2.33167i	−0.107610	−	0.165705i
$199$	−10.5072	−	18.1990i	−0.744835	−	1.29009i	−0.950272	−	0.311422i	$-0.899195\pi$
$199$	−10.5072	−	18.1990i	−0.744835	−	1.29009i	0.205437	−	0.978670i	$-0.434138\pi$
$200$		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	−0.751912	−	0.659263i	$-0.770868\pi$
$211$	−7.71478	−	23.7437i	−0.531108	−	1.63458i	0.220805	−	0.975318i	$-0.429132\pi$
$212$	−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	$-0.206339\pi$
$223$	11.6067	+	5.91390i	0.777241	+	0.396024i	−0.0199118	+	0.999802i	$0.506339\pi$
$224$	−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	$-0.549443\pi$
$227$	−3.09307	+	0.162101i	−0.205294	+	0.0107590i	−0.0505884	+	0.998720i	$0.516110\pi$
$228$	2.72551	+	7.10021i	0.180502	+	0.470223i
$229$	−0.0558012	−	0.530913i	−0.00368745	−	0.0350837i	0.992523	−	0.122054i	$-0.0389481\pi$
$229$	−0.0558012	−	0.530913i	−0.00368745	−	0.0350837i	−0.996211	+	0.0869703i	$0.972281\pi$
$230$		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	$-0.0811757\pi$
$233$	23.1708	+	8.89443i	1.51797	+	0.582694i	0.550311	+	0.834960i	$0.314509\pi$
$234$	−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	0.693736	−	0.720229i	$-0.255963\pi$
$239$	25.9462	−	8.43043i	1.67832	−	0.545320i	0.984585	+	0.174910i	$0.0559633\pi$
$240$		0			0
$241$	−3.97979	−	18.7235i	−0.256361	−	1.20608i	−0.898319	−	0.439344i	$-0.855211\pi$
$241$	−3.97979	−	18.7235i	−0.256361	−	1.20608i	0.641958	−	0.766740i	$-0.278122\pi$
$242$	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	$-0.923964\pi$
$251$		−	7.49714i		−	0.473215i	0.971605	−	0.236608i	$-0.0760356\pi$
$252$	−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	$-0.442918\pi$
$257$	13.2229	−	3.54307i	0.824824	−	0.221011i	0.646454	+	0.762953i	$0.276251\pi$
$258$	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	$-0.110528\pi$
$263$	16.4103	+	10.6570i	1.01190	+	0.657137i	0.0715841	+	0.997435i	$0.477195\pi$
$264$	−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	0.924881	+	0.380257i	$0.124164\pi$
$269$	−0.965195	+	9.18322i	−0.0588490	+	0.559911i	−0.983730	+	0.179654i	$0.942502\pi$
$270$		0			0
$271$	1.10014	−	0.115630i	0.0668289	−	0.00702400i	−0.0710550	−	0.997472i	$-0.522637\pi$
$271$	1.10014	−	0.115630i	0.0668289	−	0.00702400i	0.137884	+	0.990448i	$0.455970\pi$
$272$	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	−0.841175	−	0.540763i	$-0.818136\pi$
$277$	−1.01746	−	19.4143i	−0.0611331	−	1.16649i	0.780042	−	0.625727i	$-0.215198\pi$
$278$	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	0.545614	−	0.838036i	$-0.316296\pi$
$281$	−1.38801	−	1.00845i	−0.0828017	−	0.0601589i	−0.628416	+	0.777878i	$0.716296\pi$
$282$	−2.11398	−	7.88949i	−0.125886	−	0.469812i
$283$	−16.6132	−	20.5156i	−0.987553	−	1.21953i	−0.975590	−	0.219598i	$-0.929525\pi$
$283$	−16.6132	−	20.5156i	−0.987553	−	1.21953i	−0.0119625	−	0.999928i	$-0.503808\pi$
$284$	−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	$-0.807350\pi$
$293$	−4.33790	+	4.33790i	−0.253423	+	0.253423i	0.568950	+	0.822372i	$0.307350\pi$
$294$	−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	$-0.0808379\pi$
$307$	12.5574	+	12.5574i	0.716687	+	0.716687i	−0.251239	+	0.967925i	$0.580838\pi$
$308$	−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	0.792161	−	0.610312i	$-0.208956\pi$
$311$	4.72615	+	4.25544i	0.267995	+	0.241304i	−0.524166	+	0.851616i	$0.675623\pi$
$312$	−5.49244	+	8.45761i	−0.310948	+	0.478818i
$313$	−7.62782	−	0.399757i	−0.431150	−	0.0225956i	−0.164473	−	0.986382i	$-0.552592\pi$
$313$	−7.62782	−	0.399757i	−0.431150	−	0.0225956i	−0.266677	+	0.963786i	$0.585926\pi$
$314$	−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	0.715101	+	0.699021i	$0.246381\pi$
$317$	−5.05753	+	13.1753i	−0.284059	+	0.740000i	−0.999160	+	0.0409785i	$0.986952\pi$
$318$	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	−0.648613	−	0.761118i	$-0.724651\pi$
$331$	−9.40598	+	4.18781i	−0.516999	+	0.230183i	0.131614	+	0.991301i	$0.457984\pi$
$332$	−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	0.954056	+	0.299629i	$0.0968628\pi$
$337$	11.6695	+	22.9028i	0.635681	+	1.24759i	−0.318375	+	0.947965i	$0.603137\pi$
$338$	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	$-0.655754\pi$
$347$	−4.26035	+	1.63539i	−0.228707	+	0.0877926i	0.241316	+	0.970447i	$0.422421\pi$
$348$	−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	$-0.708518\pi$
$353$	−9.98297	+	3.83210i	−0.531340	+	0.203962i	0.0778814	+	0.996963i	$0.475184\pi$
$354$	−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	−0.590873	−	0.806765i	$-0.701216\pi$
$359$	2.83659	−	2.55408i	0.149710	−	0.134799i	0.740582	+	0.671966i	$0.234550\pi$
$360$		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	$-0.786399\pi$
$367$	−6.47094	+	5.24006i	−0.337780	+	0.273529i	0.445390	+	0.895337i	$0.353065\pi$
$368$	−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	$-0.0343028\pi$
$373$	9.49367	+	14.6190i	0.491563	+	0.756941i	−0.502635	+	0.864498i	$0.667636\pi$
$374$	−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	0.941372	−	0.337370i	$-0.109537\pi$
$379$	6.41691	+	8.83212i	0.329614	+	0.453675i	−0.611758	+	0.791045i	$0.709537\pi$
$380$		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	−0.693612	−	0.720349i	$-0.743982\pi$
$383$	5.94645	−	15.4910i	0.303849	−	0.791555i	0.997462	−	0.0712062i	$-0.0226848\pi$
$384$	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	0.222133	−	0.975016i	$-0.428698\pi$
$389$	−14.2859	−	12.8631i	−0.724323	−	0.652183i	−0.946456	+	0.322833i	$0.895365\pi$
$390$		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	$-0.793053\pi$
$397$	−0.765657	+	0.945508i	−0.0384272	+	0.0474537i	0.757570	+	0.652754i	$0.226386\pi$
$398$	−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	−0.800710	−	0.599052i	$-0.795544\pi$
$401$	2.37174	−	4.10797i	0.118439	−	0.205142i	0.919149	+	0.393910i	$0.128878\pi$
$402$	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	−0.763827	−	0.645421i	$-0.776682\pi$
$409$	−24.2503	+	5.15456i	−1.19910	+	0.254877i	−0.435274	+	0.900298i	$0.643349\pi$
$410$		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	0.953678	−	0.300828i	$-0.0972631\pi$
$419$	19.6973	+	14.3109i	0.962276	+	0.699135i	0.00859807	+	0.999963i	$0.497263\pi$
$420$		0			0
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	−0.724335	−	0.689448i	$-0.757853\pi$
$421$	−6.00083	+	4.35986i	−0.292463	+	0.212486i	0.431872	+	0.901935i	$0.357853\pi$
$422$	−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	0.850169	+	0.526511i	$0.176500\pi$
$431$	−1.88691	+	17.9528i	−0.0908895	+	0.864756i	−0.941058	+	0.338245i	$0.890167\pi$
$432$	19.4763	−	5.21865i	0.937052	−	0.251082i
$433$	−24.9324	+	3.94891i	−1.19818	+	0.189773i	−0.723460	−	0.690366i	$-0.757449\pi$
$433$	−24.9324	+	3.94891i	−1.19818	+	0.189773i	−0.474717	+	0.880139i	$0.657449\pi$
$434$	−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	−0.495977	−	0.868335i	$-0.665190\pi$
$439$	−27.2854	−	5.79968i	−1.30226	−	0.276804i	−0.806282	+	0.591532i	$0.798523\pi$
$440$		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	$-0.842626\pi$
$443$	−29.5785	+	7.92554i	−1.40532	+	0.376554i	−0.525066	+	0.851061i	$0.675960\pi$
$444$	−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	$0.254879\pi$
$449$			30.4224i			1.43572i	−0.696187	+	0.717861i	$0.745121\pi$
$450$		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	−0.562628	−	0.826710i	$-0.690210\pi$
$457$	−10.4479	−	38.9922i	−0.488733	−	1.82398i	0.0738955	−	0.997266i	$-0.476457\pi$
$458$	−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	−0.676705	−	0.736255i	$-0.736593\pi$
$461$	−16.9923	+	5.52114i	−0.791411	+	0.257145i	−0.114706	+	0.993399i	$0.536593\pi$
$462$	11.0048	−	13.1347i	0.511990	−	0.611080i
$463$	−30.4814	+	15.5311i	−1.41659	+	0.721790i	−0.983727	−	0.179668i	$-0.942498\pi$
$463$	−30.4814	+	15.5311i	−1.41659	+	0.721790i	−0.432866	+	0.901458i	$0.642498\pi$
$464$	−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	$-0.333957\pi$
$467$	6.23404	+	2.39302i	0.288477	+	0.110736i	−0.209826	+	0.977739i	$0.567290\pi$
$468$	−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	0.298298	−	0.954473i	$-0.403581\pi$
$479$	−4.62700	−	2.06007i	−0.211413	−	0.0941271i	−0.509711	+	0.860346i	$0.670248\pi$
$480$		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	$-0.956748\pi$
$487$	−10.2405	+	15.7690i	−0.464043	+	0.714563i	0.526740	+	0.850027i	$0.323414\pi$
$488$	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	0.583555	+	0.812073i	$0.301661\pi$
$491$	−8.10726	+	24.9516i	−0.365876	+	1.12605i	−0.949431	+	0.313976i	$0.898339\pi$
$492$	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	0.440263	−	0.897869i	$-0.354885\pi$
$499$	−2.61768	−	1.51132i	−0.117183	−	0.0676558i	−0.557446	+	0.830213i	$0.688219\pi$
$500$		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	−0.889178	−	0.457562i	$-0.848723\pi$
$503$	2.19511	−	13.8594i	0.0978750	−	0.617958i	0.987053	−	0.160396i	$-0.0512772\pi$
$504$	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	0.978796	−	0.204838i	$-0.0656667\pi$
$509$	15.1783	+	16.8573i	0.672768	+	0.747185i	−0.306028	+	0.952023i	$0.599000\pi$
$510$		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	−0.0166856	+	0.999861i	$0.505311\pi$
$521$	−17.0862	+	38.3763i	−0.748562	+	1.68130i	−0.731877	+	0.681437i	$0.761355\pi$
$522$	8.74454	−	3.35671i	0.382738	−	0.146919i
$523$	22.1618	−	14.3920i	0.969068	−	0.629320i	0.0399883	−	0.999200i	$-0.487268\pi$
$523$	22.1618	−	14.3920i	0.969068	−	0.629320i	0.929079	+	0.369880i	$0.120601\pi$
$524$	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	0.667553	−	0.744562i	$-0.267342\pi$
$541$	−3.31932	−	3.68648i	−0.142709	−	0.158494i	−0.810262	+	0.586068i	$0.800675\pi$
$542$	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	−0.858638	−	0.512582i	$-0.828689\pi$
$547$	2.72171	−	17.1842i	0.116372	−	0.734743i	0.975010	−	0.222161i	$-0.0713110\pi$
$548$	−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	$-0.342161\pi$
$557$	10.5747	+	2.83348i	0.448064	+	0.120058i	−0.0277296	+	0.999615i	$0.508828\pi$
$558$	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	$-0.830034\pi$
$563$	−1.08507	+	1.67086i	−0.0457302	+	0.0704183i	0.815066	+	0.579368i	$0.196701\pi$
$564$	−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	−0.950959	−	0.309318i	$-0.899899\pi$
$569$	−12.9886	−	29.1729i	−0.544511	−	1.22299i	0.406447	−	0.913674i	$-0.366768\pi$
$570$		0			0
$571$	−13.4872	−	6.00488i	−0.564421	−	0.251297i	0.104632	−	0.994511i	$-0.466634\pi$
$571$	−13.4872	−	6.00488i	−0.564421	−	0.251297i	−0.669053	+	0.743214i	$0.733300\pi$
$572$	−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	$-0.570728\pi$
$577$	−8.10906	+	0.424978i	−0.337585	+	0.0176921i	−0.117209	+	0.993107i	$0.537395\pi$
$578$	−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	$-0.696020\pi$
$587$	−6.22031	+	3.16940i	−0.256739	+	0.130815i	0.320884	+	0.947118i	$0.396020\pi$
$588$	−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	$-0.139019\pi$
$593$	−2.19397	−	8.18799i	−0.0900954	−	0.336240i	−0.996230	+	0.0867484i	$0.972352\pi$
$594$	−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	−0.858880	−	0.512177i	$-0.828839\pi$
$599$	−20.6751	+	11.9368i	−0.844762	+	0.487723i	0.0141183	+	0.999900i	$0.495506\pi$
$600$		0			0
$601$		−	9.32470i		−	0.380362i	−0.981749	−	0.190181i	$-0.939092\pi$
$601$		−	9.32470i		−	0.380362i	0.981749	−	0.190181i	$-0.0609075\pi$
$602$	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	$-0.433901\pi$
$607$	21.5323	−	5.76957i	0.873971	−	0.234180i	0.667804	+	0.744337i	$0.267234\pi$
$608$	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	$-0.453516\pi$
$613$	−17.3094	−	11.2408i	−0.699118	−	0.454013i	−0.844635	+	0.535343i	$0.820182\pi$
$614$	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	$-0.471566\pi$
$617$	11.9685	−	1.89563i	0.481835	−	0.0763151i	0.392627	+	0.919698i	$0.371566\pi$
$618$	−21.9168	+	5.87259i	−0.881624	+	0.236230i
$619$	−1.68698	+	16.0505i	−0.0678054	+	0.645125i	0.906856	+	0.421440i	$0.138475\pi$
$619$	−1.68698	+	16.0505i	−0.0678054	+	0.645125i	−0.974662	+	0.223685i	$0.928191\pi$
$620$		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	0.999797	−	0.0201409i	$-0.00641148\pi$
$631$	32.3943	+	23.5358i	1.28960	+	0.936947i	0.289799	+	0.957087i	$0.406411\pi$
$632$	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	0.570406	−	0.821363i	$-0.306786\pi$
$641$	36.0927	−	7.67174i	1.42558	−	0.303015i	0.855170	+	0.518348i	$0.173453\pi$
$642$	−33.6541	−	12.9186i	−1.32822	−	0.509856i
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	−0.335406	−	0.942074i	$-0.608874\pi$
$643$	15.3835	−	15.3835i	0.606667	−	0.606667i	0.942074	+	0.335406i	$0.108874\pi$
$644$	−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	0.921936	+	0.387343i	$0.126607\pi$
$647$	12.6160	+	32.8659i	0.495987	+	1.29209i	−0.425949	+	0.904747i	$0.640060\pi$
$648$	−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	$-0.990790\pi$
$653$	−19.5093	+	24.0920i	−0.763459	+	0.942794i	0.236122	+	0.971723i	$0.424124\pi$
$654$	−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	0.174479	−	0.984661i	$-0.444176\pi$
$659$	−6.75492	−	2.19481i	−0.263134	−	0.0854976i	−0.437613	+	0.899163i	$0.644176\pi$
$660$		0			0
$661$	3.56987	+	3.21432i	0.138852	+	0.125023i	0.735630	−	0.677383i	$-0.236886\pi$
$661$	3.56987	+	3.21432i	0.138852	+	0.125023i	−0.596778	+	0.802406i	$0.703553\pi$
$662$	−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	$-0.931667\pi$
$673$	−5.97729	+	11.7311i	−0.230408	+	0.452201i	0.746638	+	0.665231i	$0.231667\pi$
$674$	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	0.840937	+	0.541134i	$0.182005\pi$
$677$	25.8435	+	39.7955i	0.993247	+	1.52947i	0.152311	+	0.988333i	$0.451329\pi$
$678$	−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	$-0.827618\pi$
$683$	−13.8738	+	11.2348i	−0.530865	+	0.429886i	0.326043	+	0.945355i	$0.394284\pi$
$684$	−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	−0.772819	−	0.634626i	$-0.781154\pi$
$691$	−5.84754	+	5.26515i	−0.222451	+	0.200296i	0.550368	+	0.834922i	$0.314487\pi$
$692$	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	−0.708212	−	0.706000i	$-0.750498\pi$
$709$	−2.13303	+	1.92059i	−0.0801077	+	0.0721293i	0.628104	+	0.778129i	$0.283831\pi$
$710$		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	−0.501202	−	0.865330i	$-0.667109\pi$
$719$	−5.18872	+	2.31017i	−0.193507	+	0.0861547i	0.307696	+	0.951485i	$0.400442\pi$
$720$		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	−0.213294	−	0.976988i	$-0.568419\pi$
$727$	18.9408	−	37.1735i	0.702477	−	1.37869i	0.915771	−	0.401701i	$-0.131581\pi$
$728$	−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	0.489513	+	0.871996i	$0.337175\pi$
$733$	−12.3930	+	32.2848i	−0.457745	+	1.19247i	−0.947258	+	0.320471i	$0.896159\pi$
$734$	−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	0.547597	−	0.836742i	$-0.315543\pi$
$739$	−6.17964	−	5.56417i	−0.227322	−	0.204681i	−0.774919	+	0.632061i	$0.782209\pi$
$740$		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	$-0.333862\pi$
$743$	−10.0390	−	10.0390i	−0.368295	−	0.368295i	−0.866855	+	0.498560i	$0.833862\pi$
$744$	−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	−0.227365	−	0.973810i	$-0.573011\pi$
$751$	19.9959	−	34.6339i	0.729661	−	1.26381i	0.957026	−	0.290000i	$-0.0936555\pi$
$752$	−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	$-0.851485\pi$
$757$	−12.1964	+	12.1964i	−0.443287	+	0.443287i	0.449828	+	0.893115i	$0.351485\pi$
$758$	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	−0.999636	−	0.0269835i	$-0.991410\pi$
$761$	−2.08132	+	9.79185i	−0.0754479	+	0.354954i	0.924188	+	0.381938i	$0.124743\pi$
$762$	−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	0.995929	−	0.0901368i	$-0.0287304\pi$
$769$	33.7752	+	24.5391i	1.21796	+	0.884902i	0.222034	+	0.975039i	$0.428730\pi$
$770$		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	−0.883533	−	0.468370i	$-0.844842\pi$
$773$	−1.49574	−	28.5404i	−0.0537980	−	1.02653i	0.829735	−	0.558158i	$-0.188492\pi$
$774$	−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	$-0.527700\pi$
$787$	−28.9611	−	18.8075i	−1.03235	−	0.670416i	−0.945439	+	0.325800i	$0.894366\pi$
$788$	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	$-0.763021\pi$
$797$	−46.4194	−	7.35212i	−1.64426	−	0.260425i	−0.908828	+	0.417172i	$0.863021\pi$
$798$	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	0.922176	+	0.386770i	$0.126409\pi$
$809$	6.74211	+	31.7191i	0.237040	+	1.11519i	−0.685136	+	0.728415i	$0.740257\pi$
$810$		0			0
$811$	8.85993	−	2.87877i	0.311114	−	0.101087i	−0.149298	−	0.988792i	$-0.547701\pi$
$811$	8.85993	−	2.87877i	0.311114	−	0.101087i	0.460413	+	0.887705i	$0.347701\pi$
$812$	−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	0.824366	+	0.566058i	$0.191532\pi$
$821$	3.88835	+	36.9952i	0.135704	+	1.29114i	−0.688661	+	0.725083i	$0.741801\pi$
$822$	10.1180	+	26.3584i	0.352907	+	0.919354i
$823$	−29.7808	+	1.56075i	−1.03809	+	0.0544042i	−0.563758	−	0.825940i	$-0.690645\pi$
$823$	−29.7808	+	1.56075i	−1.03809	+	0.0544042i	−0.474335	+	0.880344i	$0.657312\pi$
$824$	−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	$-0.182160\pi$
$827$	25.7867	+	13.1390i	0.896691	+	0.456887i	0.0560176	+	0.998430i	$0.482160\pi$
$828$	0.548755	−	0.677656i	0.0190706	−	0.0235502i
$829$	−8.61441	−	3.83538i	−0.299191	−	0.133208i	0.251651	−	0.967818i	$-0.419027\pi$
$829$	−8.61441	−	3.83538i	−0.299191	−	0.133208i	−0.550842	+	0.834610i	$0.685693\pi$
$830$		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	0.604101	+	0.796907i	$0.293532\pi$
$839$	16.9096	+	52.0423i	0.583784	+	1.79670i	−0.0203179	+	0.999794i	$0.506468\pi$
$840$		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	−0.00773601	+	0.999970i	$0.502462\pi$
$853$	−9.03599	+	57.0510i	−0.309386	+	1.95339i	−0.301650	+	0.953419i	$0.597538\pi$
$854$	−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	$-0.839302\pi$
$857$	3.64690	−	13.6104i	0.124576	−	0.464923i	0.999824	+	0.0187505i	$0.00596883\pi$
$858$	11.0024	−	8.90958i	0.375616	−	0.304168i
$859$	14.0269	+	15.5785i	0.478592	+	0.531530i	0.933294	−	0.359113i	$-0.116921\pi$
$859$	14.0269	+	15.5785i	0.478592	+	0.531530i	−0.454702	+	0.890644i	$0.650254\pi$
$860$		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	0.950577	+	0.310490i	$0.100493\pi$
$863$	−0.800451	+	15.2735i	−0.0272477	+	0.519916i	−0.977824	+	0.209427i	$0.932840\pi$
$864$	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	$-0.764650\pi$
$877$	−12.5522	+	8.15148i	−0.423857	+	0.275256i	0.315035	+	0.949080i	$0.397984\pi$
$878$	−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	−0.604967	−	0.796250i	$-0.706814\pi$
$881$	10.0697	−	13.8597i	0.339257	−	0.466947i	0.944224	+	0.329303i	$0.106814\pi$
$882$	8.17714	+	4.51692i	0.275339	+	0.152093i
$883$	−4.27148	−	26.9691i	−0.143747	−	0.907581i	−0.949143	−	0.314845i	$-0.898048\pi$
$883$	−4.27148	−	26.9691i	−0.143747	−	0.907581i	0.805397	−	0.592736i	$-0.201952\pi$
$884$	−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	−0.817298	−	0.576216i	$-0.804529\pi$
$887$	1.66049	−	31.6840i	0.0557537	−	1.06384i	0.873051	−	0.487628i	$-0.162138\pi$
$888$	−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	$-0.484793\pi$
$907$	−12.3572	−	3.31110i	−0.410314	−	0.109943i	−0.458071	+	0.888916i	$0.651459\pi$
$908$	−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	0.892089	−	0.451860i	$-0.149239\pi$
$911$	−2.87409	−	8.84554i	−0.0952228	−	0.293066i	−0.987312	+	0.158794i	$0.949239\pi$
$912$	−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	−0.871369	−	0.490629i	$-0.836767\pi$
$919$	−19.7932	−	44.4563i	−0.652917	−	1.46648i	0.218451	−	0.975848i	$-0.429899\pi$
$920$		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	0.995302	−	0.0968214i	$-0.0308676\pi$
$929$	0.0493594	+	0.469623i	0.00161943	+	0.0154078i	−0.993682	+	0.112229i	$0.964201\pi$
$930$		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	$-0.841498\pi$
$937$	−30.8727	+	15.7304i	−1.00857	+	0.513890i	−0.130002	+	0.991514i	$0.541498\pi$
$938$	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	0.999671	−	0.0256647i	$-0.00817023\pi$
$941$	2.33096	+	10.9663i	0.0759873	+	0.357492i	−0.923683	+	0.383157i	$0.874837\pi$
$942$	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	0.952946	+	0.303139i	$0.0980347\pi$
$947$	44.5472	+	36.0736i	1.44759	+	1.17224i	0.494644	+	0.869096i	$0.335299\pi$
$948$	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	$-0.359649\pi$
$953$	17.0778	+	2.70486i	0.553204	+	0.0876189i	0.126427	+	0.991976i	$0.459649\pi$
$954$	−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	$-0.477041\pi$
$967$	13.9567	−	2.21053i	0.448819	−	0.0710859i	0.376753	+	0.926314i	$0.377041\pi$
$968$	−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	−0.269328	−	0.963048i	$-0.586802\pi$
$971$	−10.3623	+	1.08912i	−0.332542	+	0.0349516i	−0.0632139	+	0.998000i	$0.520135\pi$
$972$	−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	−0.936740	−	0.350025i	$-0.886173\pi$
$977$	−1.30401	−	24.8821i	−0.0417191	−	0.796048i	0.895021	−	0.446023i	$-0.147160\pi$
$978$	−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	$-0.276346\pi$
$983$	−7.35536	−	9.08311i	−0.234600	−	0.289706i	−0.880827	+	0.473439i	$0.843013\pi$
$984$	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	−0.0372721	−	0.999305i	$-0.511867\pi$
$991$	10.5500	−	2.24247i	0.335132	−	0.0712345i	0.372404	+	0.928071i	$0.378533\pi$
$992$	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	$-0.179507\pi$
$997$	−4.43884	−	11.5636i	−0.140580	−	0.366222i	−0.985737	+	0.168296i	$0.946174\pi$
$998$	−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.768.14		288
5.2	odd	4		875.2.bb.c.607.14		288
5.3	odd	4		175.2.x.a.117.5	yes	288
5.4	even	2		875.2.bb.b.768.5		288
7.3	odd	6	inner	875.2.bb.a.143.14		288
25.3	odd	20		875.2.bb.b.257.5		288
25.4	even	10		175.2.x.a.103.14	yes	288
25.21	even	5		875.2.bb.c.243.5		288
25.22	odd	20	inner	875.2.bb.a.257.14		288
35.3	even	12		175.2.x.a.17.14	yes	288
35.17	even	12		875.2.bb.c.857.5		288
35.24	odd	6		875.2.bb.b.143.5		288
175.3	even	60		875.2.bb.b.507.5		288
175.122	even	60	inner	875.2.bb.a.507.14		288
175.129	odd	30		175.2.x.a.3.5	✓	288
175.171	odd	30		875.2.bb.c.493.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.5	✓	288	175.129	odd	30
175.2.x.a.17.14	yes	288	35.3	even	12
175.2.x.a.103.14	yes	288	25.4	even	10
175.2.x.a.117.5	yes	288	5.3	odd	4
875.2.bb.a.143.14		288	7.3	odd	6	inner
875.2.bb.a.257.14		288	25.22	odd	20	inner
875.2.bb.a.507.14		288	175.122	even	60	inner
875.2.bb.a.768.14		288	1.1	even	1	trivial
875.2.bb.b.143.5		288	35.24	odd	6
875.2.bb.b.257.5		288	25.3	odd	20
875.2.bb.b.507.5		288	175.3	even	60
875.2.bb.b.768.5		288	5.4	even	2
875.2.bb.c.243.5		288	25.21	even	5
875.2.bb.c.493.14		288	175.171	odd	30
875.2.bb.c.607.14		288	5.2	odd	4
875.2.bb.c.857.5		288	35.17	even	12

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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