LMFDB - Embedded newform 575.2.k.g.101.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(26,575)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("575.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.k (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	575.101
Dual form			575.2.k.g.501.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.21797 - 0.651256i) q^{2} +(-0.794936 - 0.917405i) q^{3} +(2.81277 - 1.80765i) q^{4} +(-2.36061 - 1.51707i) q^{6} +(0.779189 - 1.70619i) q^{7} +(2.03383 - 2.34716i) q^{8} +(0.217236 - 1.51091i) q^{9} +O(q^{10})$	\(q+(2.21797 - 0.651256i) q^{2} +(-0.794936 - 0.917405i) q^{3} +(2.81277 - 1.80765i) q^{4} +(-2.36061 - 1.51707i) q^{6} +(0.779189 - 1.70619i) q^{7} +(2.03383 - 2.34716i) q^{8} +(0.217236 - 1.51091i) q^{9} +(2.86226 + 0.840435i) q^{11} +(-3.89432 - 1.14348i) q^{12} +(0.559818 + 1.22583i) q^{13} +(0.617057 - 4.29173i) q^{14} +(0.204462 - 0.447708i) q^{16} +(-2.98466 - 1.91813i) q^{17} +(-0.502165 - 3.49263i) q^{18} +(-2.14666 + 1.37958i) q^{19} +(-2.18467 + 0.641476i) q^{21} +6.89575 q^{22} +(-2.09582 - 4.31364i) q^{23} -3.77006 q^{24} +(2.03999 + 2.35427i) q^{26} +(-4.62240 + 2.97063i) q^{27} +(-0.892519 - 6.20761i) q^{28} +(3.30718 + 2.12540i) q^{29} +(5.50738 - 6.35585i) q^{31} +(-0.722069 + 5.02210i) q^{32} +(-1.50429 - 3.29394i) q^{33} +(-7.86909 - 2.31057i) q^{34} +(-2.12017 - 4.64252i) q^{36} +(0.548587 - 3.81551i) q^{37} +(-3.86278 + 4.45789i) q^{38} +(0.679563 - 1.48803i) q^{39} +(1.67437 + 11.6455i) q^{41} +(-4.42777 + 2.84556i) q^{42} +(8.07159 + 9.31512i) q^{43} +(9.57008 - 2.81003i) q^{44} +(-7.45777 - 8.20263i) q^{46} -2.86157 q^{47} +(-0.573263 + 0.168325i) q^{48} +(2.28009 + 2.63136i) q^{49} +(0.612917 + 4.26293i) q^{51} +(3.79051 + 2.43601i) q^{52} +(2.30922 - 5.05648i) q^{53} +(-8.31771 + 9.59915i) q^{54} +(-2.41996 - 5.29898i) q^{56} +(2.97209 + 0.872683i) q^{57} +(8.71943 + 2.56025i) q^{58} +(4.80538 + 10.5223i) q^{59} +(-9.54961 + 11.0208i) q^{61} +(8.07593 - 17.6838i) q^{62} +(-2.40862 - 1.54793i) q^{63} +(1.80923 + 12.5835i) q^{64} +(-5.48168 - 6.32620i) q^{66} +(-0.423155 + 0.124250i) q^{67} -11.8625 q^{68} +(-2.29131 + 5.35179i) q^{69} +(-2.31436 + 0.679556i) q^{71} +(-3.10453 - 3.58282i) q^{72} +(-2.90643 + 1.86785i) q^{73} +(-1.26812 - 8.81997i) q^{74} +(-3.54426 + 7.76085i) q^{76} +(3.66418 - 4.22869i) q^{77} +(0.538161 - 3.74299i) q^{78} +(-1.76980 - 3.87531i) q^{79} +(2.00594 + 0.588996i) q^{81} +(11.2979 + 24.7389i) q^{82} +(0.302411 - 2.10331i) q^{83} +(-4.98539 + 5.75345i) q^{84} +(23.9691 + 15.4040i) q^{86} +(-0.679148 - 4.72358i) q^{87} +(7.79399 - 5.00889i) q^{88} +(-5.83391 - 6.73270i) q^{89} +2.52770 q^{91} +(-13.6926 - 8.34474i) q^{92} -10.2089 q^{93} +(-6.34689 + 1.86362i) q^{94} +(5.18130 - 3.32982i) q^{96} +(-1.48805 - 10.3496i) q^{97} +(6.77087 + 4.35138i) q^{98} +(1.89161 - 4.14204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	$ 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) $ 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$

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 $

$2$	2.21797	−	0.651256i	1.56834	−	0.460507i	0.621825	−	0.783156i	$-0.286391\pi$
$2$	2.21797	−	0.651256i	1.56834	−	0.460507i	0.946519	+	0.322649i	$0.104573\pi$
$3$	−0.794936	−	0.917405i	−0.458956	−	0.529664i	0.478351	−	0.878169i	$-0.341235\pi$
$3$	−0.794936	−	0.917405i	−0.458956	−	0.529664i	−0.937307	+	0.348505i	$0.886689\pi$
$4$	2.81277	−	1.80765i	1.40638	−	0.903827i
$5$		0			0
$5$		0			0
$6$	−2.36061	−	1.51707i	−0.963715	−	0.619342i
$7$	0.779189	−	1.70619i	0.294506	−	0.644878i	−0.703314	−	0.710880i	$-0.748297\pi$
$7$	0.779189	−	1.70619i	0.294506	−	0.644878i	0.997819	+	0.0660019i	$0.0210244\pi$
$8$	2.03383	−	2.34716i	0.719067	−	0.829848i
$9$	0.217236	−	1.51091i	0.0724120	−	0.503636i
$10$		0			0
$11$	2.86226	+	0.840435i	0.863004	+	0.253401i	0.683137	−	0.730290i	$-0.260615\pi$
$11$	2.86226	+	0.840435i	0.863004	+	0.253401i	0.179867	+	0.983691i	$0.442433\pi$
$12$	−3.89432	−	1.14348i	−1.12419	−	0.330093i
$13$	0.559818	+	1.22583i	0.155265	+	0.339984i	0.971240	−	0.238105i	$-0.0765261\pi$
$13$	0.559818	+	1.22583i	0.155265	+	0.339984i	−0.815974	+	0.578089i	$0.803799\pi$
$14$	0.617057	−	4.29173i	0.164915	−	1.14701i
$15$		0			0
$16$	0.204462	−	0.447708i	0.0511154	−	0.111927i
$17$	−2.98466	−	1.91813i	−0.723887	−	0.465214i	0.126100	−	0.992018i	$-0.459754\pi$
$17$	−2.98466	−	1.91813i	−0.723887	−	0.465214i	−0.849987	+	0.526804i	$0.823390\pi$
$18$	−0.502165	−	3.49263i	−0.118361	−	0.823222i
$19$	−2.14666	+	1.37958i	−0.492478	+	0.316496i	−0.763201	−	0.646161i	$-0.776374\pi$
$19$	−2.14666	+	1.37958i	−0.492478	+	0.316496i	0.270723	+	0.962657i	$0.412737\pi$
$20$		0			0
$21$	−2.18467	+	0.641476i	−0.476734	+	0.139982i
$22$	6.89575			1.47018
$23$	−2.09582	−	4.31364i	−0.437010	−	0.899457i
$23$	−2.09582	−	4.31364i	−0.437010	−	0.899457i
$24$	−3.77006			−0.769561
$25$		0			0
$26$	2.03999	+	2.35427i	0.400075	+	0.461711i
$27$	−4.62240	+	2.97063i	−0.889581	+	0.571699i
$28$	−0.892519	−	6.20761i	−0.168670	−	1.17313i
$29$	3.30718	+	2.12540i	0.614129	+	0.394677i	0.810403	−	0.585872i	$-0.199248\pi$
$29$	3.30718	+	2.12540i	0.614129	+	0.394677i	−0.196275	+	0.980549i	$0.562884\pi$
$30$		0			0
$31$	5.50738	−	6.35585i	0.989154	−	1.14155i	−0.000777292	−	1.00000i	$-0.500247\pi$
$31$	5.50738	−	6.35585i	0.989154	−	1.14155i	0.989932	−	0.141545i	$-0.0452071\pi$
$32$	−0.722069	+	5.02210i	−0.127645	+	0.887791i
$33$	−1.50429	−	3.29394i	−0.261864	−	0.573402i
$34$	−7.86909	−	2.31057i	−1.34954	−	0.396260i
$35$		0			0
$36$	−2.12017	−	4.64252i	−0.353361	−	0.773754i
$37$	0.548587	−	3.81551i	0.0901872	−	0.627266i	−0.893725	−	0.448615i	$-0.851918\pi$
$37$	0.548587	−	3.81551i	0.0901872	−	0.627266i	0.983912	−	0.178651i	$-0.0571733\pi$
$38$	−3.86278	+	4.45789i	−0.626626	+	0.723165i
$39$	0.679563	−	1.48803i	0.108817	−	0.238276i
$40$		0			0
$41$	1.67437	+	11.6455i	0.261492	+	1.81872i	0.521659	+	0.853154i	$0.325313\pi$
$41$	1.67437	+	11.6455i	0.261492	+	1.81872i	−0.260167	+	0.965564i	$0.583777\pi$
$42$	−4.42777	+	2.84556i	−0.683220	+	0.439079i
$43$	8.07159	+	9.31512i	1.23091	+	1.42054i	0.873664	+	0.486531i	$0.161738\pi$
$43$	8.07159	+	9.31512i	1.23091	+	1.42054i	0.357243	+	0.934011i	$0.383717\pi$
$44$	9.57008	−	2.81003i	1.44274	−	0.423628i
$45$		0			0
$46$	−7.45777	−	8.20263i	−1.09959	−	1.20941i
$47$	−2.86157			−0.417403			−0.208702	−	0.977979i	$-0.566924\pi$
$47$	−2.86157			−0.417403			−0.208702	+	0.977979i	$0.566924\pi$
$48$	−0.573263	+	0.168325i	−0.0827434	+	0.0242957i
$49$	2.28009	+	2.63136i	0.325727	+	0.375909i
$50$		0			0
$51$	0.612917	+	4.26293i	0.0858255	+	0.596929i
$52$	3.79051	+	2.43601i	0.525650	+	0.337814i
$53$	2.30922	−	5.05648i	0.317196	−	0.694562i	−0.682132	−	0.731229i	$-0.738947\pi$
$53$	2.30922	−	5.05648i	0.317196	−	0.694562i	0.999328	+	0.0366676i	$0.0116743\pi$
$54$	−8.31771	+	9.59915i	−1.13190	+	1.30628i
$55$		0			0
$56$	−2.41996	−	5.29898i	−0.323381	−	0.708105i
$57$	2.97209	+	0.872683i	0.393662	+	0.115590i
$58$	8.71943	+	2.56025i	1.14492	+	0.336178i
$59$	4.80538	+	10.5223i	0.625607	+	1.36989i	0.911370	+	0.411588i	$0.135026\pi$
$59$	4.80538	+	10.5223i	0.625607	+	1.36989i	−0.285763	+	0.958300i	$0.592247\pi$
$60$		0			0
$61$	−9.54961	+	11.0208i	−1.22270	+	1.41107i	−0.340472	+	0.940255i	$0.610587\pi$
$61$	−9.54961	+	11.0208i	−1.22270	+	1.41107i	−0.882230	+	0.470818i	$0.843959\pi$
$62$	8.07593	−	17.6838i	1.02564	−	2.24585i
$63$	−2.40862	−	1.54793i	−0.303458	−	0.195021i
$64$	1.80923	+	12.5835i	0.226154	+	1.57294i
$65$		0			0
$66$	−5.48168	−	6.32620i	−0.674748	−	0.778701i
$67$	−0.423155	+	0.124250i	−0.0516966	+	0.0151795i	−0.307479	−	0.951555i	$-0.599485\pi$
$67$	−0.423155	+	0.124250i	−0.0516966	+	0.0151795i	0.255782	+	0.966734i	$0.417667\pi$
$68$	−11.8625			−1.43854
$69$	−2.29131	+	5.35179i	−0.275841	+	0.644279i
$70$		0			0
$71$	−2.31436	+	0.679556i	−0.274664	+	0.0806485i	−0.416164	−	0.909290i	$-0.636626\pi$
$71$	−2.31436	+	0.679556i	−0.274664	+	0.0806485i	0.141500	+	0.989938i	$0.454807\pi$
$72$	−3.10453	−	3.58282i	−0.365873	−	0.422240i
$73$	−2.90643	+	1.86785i	−0.340172	+	0.218615i	−0.699562	−	0.714572i	$-0.746621\pi$
$73$	−2.90643	+	1.86785i	−0.340172	+	0.218615i	0.359389	+	0.933188i	$0.382985\pi$
$74$	−1.26812	−	8.81997i	−0.147416	−	1.02530i
$75$		0			0
$76$	−3.54426	+	7.76085i	−0.406554	+	0.890230i
$77$	3.66418	−	4.22869i	0.417572	−	0.481904i
$78$	0.538161	−	3.74299i	0.0609347	−	0.423810i
$79$	−1.76980	−	3.87531i	−0.199118	−	0.436007i	0.783563	−	0.621312i	$-0.213400\pi$
$79$	−1.76980	−	3.87531i	−0.199118	−	0.436007i	−0.982681	+	0.185305i	$0.940673\pi$
$80$		0			0
$81$	2.00594	+	0.588996i	0.222882	+	0.0654440i
$82$	11.2979	+	24.7389i	1.24764	+	2.73196i
$83$	0.302411	−	2.10331i	0.0331939	−	0.230869i	−0.966470	−	0.256778i	$-0.917339\pi$
$83$	0.302411	−	2.10331i	0.0331939	−	0.230869i	0.999664	+	0.0259095i	$0.00824816\pi$
$84$	−4.98539	+	5.75345i	−0.543951	+	0.627753i
$85$		0			0
$86$	23.9691	+	15.4040i	2.58466	+	1.66106i
$87$	−0.679148	−	4.72358i	−0.0728123	−	0.506421i
$88$	7.79399	−	5.00889i	0.830842	−	0.533950i
$89$	−5.83391	−	6.73270i	−0.618394	−	0.713664i	0.357008	−	0.934102i	$-0.383797\pi$
$89$	−5.83391	−	6.73270i	−0.618394	−	0.713664i	−0.975401	+	0.220437i	$0.929252\pi$
$90$		0			0
$91$	2.52770			0.264975
$92$	−13.6926	−	8.34474i	−1.42756	−	0.870000i
$93$	−10.2089			−1.05861
$94$	−6.34689	+	1.86362i	−0.654632	+	0.192217i
$95$		0			0
$96$	5.18130	−	3.32982i	0.528814	−	0.339848i
$97$	−1.48805	−	10.3496i	−0.151089	−	1.05084i	−0.914400	−	0.404813i	$-0.867337\pi$
$97$	−1.48805	−	10.3496i	−0.151089	−	1.05084i	0.763311	−	0.646031i	$-0.223572\pi$
$98$	6.77087	+	4.35138i	0.683961	+	0.439555i
$99$	1.89161	−	4.14204i	0.190114	−	0.416291i
$100$		0			0
$101$	0.716013	−	4.97998i	0.0712459	−	0.495526i	−0.922688	−	0.385548i	$-0.874013\pi$
$101$	0.716013	−	4.97998i	0.0712459	−	0.495526i	0.993934	−	0.109979i	$-0.0350783\pi$
$102$	4.13569	+	9.05590i	0.409494	+	0.896668i
$103$	1.08747	+	0.319309i	0.107151	+	0.0314625i	0.334869	−	0.942265i	$-0.391308\pi$
$103$	1.08747	+	0.319309i	0.107151	+	0.0314625i	−0.227717	+	0.973727i	$0.573126\pi$
$104$	4.01580	+	1.17914i	0.393781	+	0.115625i
$105$		0			0
$106$	1.82872	−	12.7190i	0.177621	−	1.23538i
$107$	−0.662950	+	0.765085i	−0.0640898	+	0.0739635i	−0.786889	−	0.617094i	$-0.788310\pi$
$107$	−0.662950	+	0.765085i	−0.0640898	+	0.0739635i	0.722799	+	0.691058i	$0.242855\pi$
$108$	−7.63184	+	16.7114i	−0.734374	+	1.60806i
$109$	8.52036	+	5.47570i	0.816102	+	0.524477i	0.880834	−	0.473426i	$-0.156983\pi$
$109$	8.52036	+	5.47570i	0.816102	+	0.524477i	−0.0647317	+	0.997903i	$0.520619\pi$
$110$		0			0
$111$	−3.93646	+	2.52981i	−0.373632	+	0.240119i
$112$	−0.604559	−	0.697699i	−0.0571255	−	0.0659263i
$113$	−10.6608	+	3.13031i	−1.00289	+	0.294474i	−0.741641	−	0.670798i	$-0.765952\pi$
$113$	−10.6608	+	3.13031i	−1.00289	+	0.294474i	−0.261247	+	0.965272i	$0.584134\pi$
$114$	7.16035			0.670628
$115$		0			0
$116$	13.1443			1.22042
$117$	1.97373	−	0.579539i	0.182471	−	0.0535784i
$118$	17.5109	+	20.2087i	1.61201	+	1.86036i
$119$	−5.59829	+	3.59781i	−0.513195	+	0.329810i
$120$		0			0
$121$	−1.76759	−	1.13596i	−0.160690	−	0.103269i
$122$	−14.0034	+	30.6632i	−1.26781	+	2.77611i
$123$	9.35260	−	10.7935i	0.843296	−	0.973215i
$124$	4.00178	−	27.8330i	0.359370	−	2.49947i
$125$		0			0
$126$	−6.35036	−	1.86463i	−0.565735	−	0.166115i
$127$	10.7718	+	3.16290i	0.955846	+	0.280662i	0.722219	−	0.691665i	$-0.243122\pi$
$127$	10.7718	+	3.16290i	0.955846	+	0.280662i	0.233627	+	0.972326i	$0.424941\pi$
$128$	7.99249	+	17.5011i	0.706443	+	1.54689i
$129$	2.12933	−	14.8098i	0.187477	−	1.30393i
$130$		0			0
$131$	5.38793	−	11.7979i	0.470745	−	1.03079i	−0.514160	−	0.857694i	$-0.671896\pi$
$131$	5.38793	−	11.7979i	0.470745	−	1.03079i	0.984905	−	0.173094i	$-0.0553766\pi$
$132$	−10.1855	−	6.54584i	−0.886537	−	0.569743i
$133$	0.681157	+	4.73755i	0.0590638	+	0.410798i
$134$	−0.857629	+	0.551165i	−0.0740879	+	0.0476134i
$135$		0			0
$136$	−10.5725	+	3.10435i	−0.906580	+	0.266196i
$137$	−9.36107			−0.799771			−0.399885	−	0.916565i	$-0.630950\pi$
$137$	−9.36107			−0.799771			−0.399885	+	0.916565i	$0.630950\pi$
$138$	−1.59668	+	13.3624i	−0.135919	+	1.13748i
$139$	5.82865			0.494380			0.247190	−	0.968967i	$-0.420493\pi$
$139$	5.82865			0.494380			0.247190	+	0.968967i	$0.420493\pi$
$140$		0			0
$141$	2.27477	+	2.62522i	0.191570	+	0.221083i
$142$	−4.69062	+	3.01448i	−0.393628	+	0.252969i
$143$	0.572113	+	3.97913i	0.0478425	+	0.332752i
$144$	−0.632030	−	0.406181i	−0.0526692	−	0.0338484i
$145$		0			0
$146$	−5.22994	+	6.03568i	−0.432833	+	0.499516i
$147$	0.601501	−	4.18353i	0.0496110	−	0.345052i
$148$	−5.35408	−	11.7238i	−0.440102	−	0.963690i
$149$	−11.5134	−	3.38064i	−0.943214	−	0.276953i	−0.226255	−	0.974068i	$-0.572648\pi$
$149$	−11.5134	−	3.38064i	−0.943214	−	0.276953i	−0.716959	+	0.697115i	$0.754466\pi$
$150$		0			0
$151$	1.76691	+	3.86900i	0.143789	+	0.314855i	0.967800	−	0.251719i	$-0.0809959\pi$
$151$	1.76691	+	3.86900i	0.143789	+	0.314855i	−0.824011	+	0.566574i	$0.808269\pi$
$152$	−1.12785	+	7.84439i	−0.0914809	+	0.636264i
$153$	−3.54649	+	4.09287i	−0.286717	+	0.330889i
$154$	5.37310	−	11.7654i	0.432976	−	0.948086i
$155$		0			0
$156$	−0.778402	−	5.41391i	−0.0623221	−	0.433460i
$157$	−17.8627	+	11.4796i	−1.42560	+	0.916175i	−0.425661	+	0.904883i	$0.639958\pi$
$157$	−17.8627	+	11.4796i	−1.42560	+	0.916175i	−0.999936	+	0.0112926i	$0.996405\pi$
$158$	−6.44918	−	7.44275i	−0.513069	−	0.592113i
$159$	−6.47452	+	1.90109i	−0.513463	+	0.150766i
$160$		0			0
$161$	−8.99292	+	0.214722i	−0.708741	+	0.0169225i
$162$	4.83270			0.379693
$163$	−8.88067	+	2.60760i	−0.695587	+	0.204243i	−0.610366	−	0.792119i	$-0.708978\pi$
$163$	−8.88067	+	2.60760i	−0.695587	+	0.204243i	−0.0852210	+	0.996362i	$0.527160\pi$
$164$	25.7606	+	29.7293i	2.01157	+	2.32147i
$165$		0			0
$166$	−0.699056	−	4.86204i	−0.0542572	−	0.377367i
$167$	8.46100	+	5.43755i	0.654732	+	0.420771i	0.825393	−	0.564559i	$-0.190954\pi$
$167$	8.46100	+	5.43755i	0.654732	+	0.420771i	−0.170661	+	0.985330i	$0.554590\pi$
$168$	−2.93759	+	6.43243i	−0.226640	+	0.496273i
$169$	7.32393	−	8.45226i	0.563379	−	0.650174i
$170$		0			0
$171$	1.61808	+	3.54310i	0.123738	+	0.270948i
$172$	39.5420	+	11.6106i	3.01505	+	0.885299i
$173$	−3.28712	−	0.965186i	−0.249915	−	0.0733818i	0.154376	−	0.988012i	$-0.450663\pi$
$173$	−3.28712	−	0.965186i	−0.249915	−	0.0733818i	−0.404291	+	0.914630i	$0.632482\pi$
$174$	−4.58259	−	10.0345i	−0.347405	−	0.760712i
$175$		0			0
$176$	0.961492	−	1.10962i	0.0724752	−	0.0836408i
$177$	5.83325	−	12.7730i	0.438454	−	0.960080i
$178$	−17.3242	−	11.1336i	−1.29850	−	0.834496i
$179$	−2.16589	−	15.0641i	−0.161886	−	1.12594i	−0.895074	−	0.445917i	$-0.852878\pi$
$179$	−2.16589	−	15.0641i	−0.161886	−	1.12594i	0.733188	−	0.680026i	$-0.238031\pi$
$180$		0			0
$181$	−14.9291	−	17.2291i	−1.10967	−	1.28063i	−0.956276	−	0.292465i	$-0.905525\pi$
$181$	−14.9291	−	17.2291i	−1.10967	−	1.28063i	−0.153396	−	0.988165i	$-0.549021\pi$
$182$	5.60636	−	1.64618i	0.415571	−	0.122023i
$183$	17.7019			1.30856
$184$	−14.3874	−	3.85397i	−1.06065	−	0.284119i
$185$		0			0
$186$	−22.6431	+	6.64861i	−1.66027	+	0.487499i
$187$	−6.93082	−	7.99859i	−0.506831	−	0.584915i
$188$	−8.04894	+	5.17274i	−0.587029	+	0.377261i
$189$	1.46673	+	10.2014i	0.106689	+	0.742039i
$190$		0			0
$191$	8.30108	−	18.1768i	0.600645	−	1.31523i	−0.328146	−	0.944627i	$-0.606424\pi$
$191$	8.30108	−	18.1768i	0.600645	−	1.31523i	0.928791	−	0.370603i	$-0.120849\pi$
$192$	10.1059	−	11.6629i	0.729333	−	0.841695i
$193$	1.04221	−	7.24875i	0.0750202	−	0.521777i	−0.917311	−	0.398171i	$-0.869645\pi$
$193$	1.04221	−	7.24875i	0.0750202	−	0.521777i	0.992331	−	0.123606i	$-0.0394458\pi$
$194$	−10.0407	−	21.9861i	−0.720880	−	1.57851i
$195$		0			0
$196$	11.1700	+	3.27980i	0.797854	+	0.234271i
$197$	−0.491494	−	1.07622i	−0.0350175	−	0.0766776i	0.891315	−	0.453385i	$-0.149784\pi$
$197$	−0.491494	−	1.07622i	−0.0350175	−	0.0766776i	−0.926332	+	0.376707i	$0.877056\pi$
$198$	1.49801	−	10.4189i	0.106459	−	0.740436i
$199$	1.49676	−	1.72735i	0.106102	−	0.122449i	−0.700214	−	0.713933i	$-0.746912\pi$
$199$	1.49676	−	1.72735i	0.106102	−	0.122449i	0.806317	+	0.591484i	$0.201458\pi$
$200$		0			0
$201$	0.450368	+	0.289434i	0.0317665	+	0.0204151i
$202$	−1.65514	−	11.5118i	−0.116455	−	0.809965i
$203$	6.20325	−	3.98658i	0.435383	−	0.279803i
$204$	9.42990	+	10.8827i	0.660225	+	0.761940i
$205$		0			0
$206$	2.61993			0.182539
$207$	−6.97281	+	2.22952i	−0.484644	+	0.154962i
$208$	0.663275			0.0459899
$209$	−7.30374	+	2.14457i	−0.505211	+	0.148343i
$210$		0			0
$211$	17.1270	−	11.0069i	1.17907	−	0.757744i	0.203857	−	0.979001i	$-0.434652\pi$
$211$	17.1270	−	11.0069i	1.17907	−	0.757744i	0.975216	+	0.221257i	$0.0710159\pi$
$212$	−2.64509	−	18.3970i	−0.181665	−	1.26351i
$213$	2.46319	+	1.58300i	0.168775	+	0.108465i
$214$	−0.972139	+	2.12869i	−0.0664540	+	0.145514i
$215$		0			0
$216$	−2.42860	+	16.8913i	−0.165245	+	1.14931i
$217$	−6.55298	−	14.3490i	−0.444845	−	0.974075i
$218$	22.4640	+	6.59603i	1.52145	+	0.446739i
$219$	4.02400	+	1.18155i	0.271917	+	0.0798420i
$220$		0			0
$221$	0.680429	−	4.73249i	0.0457706	−	0.318342i
$222$	−7.08341	+	8.17469i	−0.475407	+	0.548649i
$223$	5.70514	−	12.4925i	0.382044	−	0.836561i	−0.616735	−	0.787171i	$-0.711545\pi$
$223$	5.70514	−	12.4925i	0.382044	−	0.836561i	0.998780	−	0.0493898i	$-0.0157277\pi$
$224$	8.00601	+	5.14515i	0.534924	+	0.343775i
$225$		0			0
$226$	−21.6068	+	13.8859i	−1.43727	+	0.923675i
$227$	−3.47212	−	4.00704i	−0.230453	−	0.265957i	0.628732	−	0.777622i	$-0.283574\pi$
$227$	−3.47212	−	4.00704i	−0.230453	−	0.265957i	−0.859185	+	0.511665i	$0.829029\pi$
$228$	9.93729	−	2.91785i	0.658113	−	0.193240i
$229$	−9.12630			−0.603083			−0.301542	−	0.953453i	$-0.597501\pi$
$229$	−9.12630			−0.603083			−0.301542	+	0.953453i	$0.597501\pi$
$230$		0			0
$231$	−6.79220			−0.446894
$232$	11.7149	−	3.43981i	0.769121	−	0.225834i
$233$	−11.4894	−	13.2595i	−0.752696	−	0.868657i	0.242131	−	0.970244i	$-0.422154\pi$
$233$	−11.4894	−	13.2595i	−0.752696	−	0.868657i	−0.994827	+	0.101586i	$0.967608\pi$
$234$	4.00025	−	2.57081i	0.261505	−	0.168059i
$235$		0			0
$236$	32.5371	+	20.9103i	2.11799	+	1.36115i
$237$	−2.14835	+	4.70424i	−0.139551	+	0.305573i
$238$	−10.0738	+	11.6258i	−0.652986	+	0.753586i
$239$	−2.72097	+	18.9248i	−0.176005	+	1.22414i	0.689889	+	0.723916i	$0.257659\pi$
$239$	−2.72097	+	18.9248i	−0.176005	+	1.22414i	−0.865894	+	0.500228i	$0.833250\pi$
$240$		0			0
$241$	−7.32540	−	2.15093i	−0.471871	−	0.138554i	0.0371469	−	0.999310i	$-0.488173\pi$
$241$	−7.32540	−	2.15093i	−0.471871	−	0.138554i	−0.509018	+	0.860756i	$0.669991\pi$
$242$	−4.66027	−	1.36838i	−0.299574	−	0.0879628i
$243$	5.79344	+	12.6859i	0.371650	+	0.813799i
$244$	−6.93894	+	48.2614i	−0.444220	+	3.08962i
$245$		0			0
$246$	13.7145	−	30.0306i	0.874405	−	1.91468i
$247$	−2.89286	−	1.85913i	−0.184068	−	0.118294i
$248$	−3.71716	−	25.8534i	−0.236040	−	1.64170i
$249$	−2.16999	+	1.39457i	−0.137517	+	0.0883770i
$250$		0			0
$251$	−14.4794	+	4.25153i	−0.913930	+	0.268354i	−0.704694	−	0.709511i	$-0.748916\pi$
$251$	−14.4794	+	4.25153i	−0.913930	+	0.268354i	−0.209236	+	0.977865i	$0.567098\pi$
$252$	−9.57302			−0.603043
$253$	−2.37345	−	14.1082i	−0.149218	−	0.886973i
$254$	25.9515			1.62834
$255$		0			0
$256$	12.4745	+	14.3963i	0.779654	+	0.899769i
$257$	−23.8963	+	15.3572i	−1.49061	+	0.957957i	−0.494563	+	0.869142i	$0.664672\pi$
$257$	−23.8963	+	15.3572i	−1.49061	+	0.957957i	−0.996048	+	0.0888154i	$0.971692\pi$
$258$	−4.92219	−	34.2346i	−0.306442	−	2.13135i
$259$	−6.08251	−	3.90899i	−0.377949	−	0.242893i
$260$		0			0
$261$	3.92972	−	4.53514i	0.243244	−	0.280718i
$262$	4.26682	−	29.6764i	0.263605	−	1.83341i
$263$	9.08900	+	19.9021i	0.560452	+	1.22722i	0.951727	+	0.306944i	$0.0993066\pi$
$263$	9.08900	+	19.9021i	0.560452	+	1.22722i	−0.391276	+	0.920273i	$0.627966\pi$
$264$	−10.7909	−	3.16849i	−0.664134	−	0.195007i
$265$		0			0
$266$	4.59615	+	10.0642i	0.281808	+	0.617073i
$267$	−1.53902	+	10.7041i	−0.0941865	+	0.655081i
$268$	−0.965636	+	1.11440i	−0.0589856	+	0.0680730i
$269$	−3.64720	+	7.98626i	−0.222374	+	0.486931i	−0.987631	−	0.156793i	$-0.949884\pi$
$269$	−3.64720	+	7.98626i	−0.222374	+	0.486931i	0.765258	+	0.643724i	$0.222612\pi$
$270$		0			0
$271$	1.61872	+	11.2585i	0.0983305	+	0.683903i	0.978044	+	0.208399i	$0.0668253\pi$
$271$	1.61872	+	11.2585i	0.0983305	+	0.683903i	−0.879713	+	0.475504i	$0.842266\pi$
$272$	−1.46901	+	0.944075i	−0.0890718	+	0.0572430i
$273$	−2.00936	−	2.31892i	−0.121612	−	0.140347i
$274$	−20.7626	+	6.09645i	−1.25432	+	0.368300i
$275$		0			0
$276$	3.22926	+	19.1952i	0.194379	+	1.15542i
$277$	32.2080			1.93519			0.967596	−	0.252503i	$-0.0812538\pi$
$277$	32.2080			1.93519			0.967596	+	0.252503i	$0.0812538\pi$
$278$	12.9278	−	3.79594i	0.775358	−	0.227666i
$279$	−8.40672	−	9.70187i	−0.503297	−	0.580836i
$280$		0			0
$281$	0.459390	+	3.19513i	0.0274049	+	0.190605i	0.998925	−	0.0463510i	$-0.0147593\pi$
$281$	0.459390	+	3.19513i	0.0274049	+	0.190605i	−0.971520	+	0.236956i	$0.923850\pi$
$282$	6.75506	+	4.34121i	0.402258	+	0.258516i
$283$	−8.00297	+	17.5241i	−0.475727	+	1.04170i	0.507889	+	0.861422i	$0.330426\pi$
$283$	−8.00297	+	17.5241i	−0.475727	+	1.04170i	−0.983616	+	0.180275i	$0.942301\pi$
$284$	−5.28134	+	6.09499i	−0.313390	+	0.361671i
$285$		0			0
$286$	3.86036	+	8.45302i	0.228268	+	0.499837i
$287$	21.1740	+	6.21725i	1.24986	+	0.366992i
$288$	7.43108	+	2.18196i	0.437881	+	0.128573i
$289$	−1.83305	−	4.01383i	−0.107827	−	0.236108i
$290$		0			0
$291$	−8.31188	+	9.59242i	−0.487251	+	0.562318i
$292$	−4.79869	+	10.5077i	−0.280822	+	0.614914i
$293$	−7.56843	−	4.86393i	−0.442152	−	0.284154i	0.300562	−	0.953762i	$-0.402826\pi$
$293$	−7.56843	−	4.86393i	−0.442152	−	0.284154i	−0.742715	+	0.669608i	$0.766462\pi$
$294$	−1.39044	−	9.67069i	−0.0810918	−	0.564006i
$295$		0			0
$296$	−7.83989	−	9.04772i	−0.455685	−	0.525888i
$297$	−15.7271	+	4.61790i	−0.912580	+	0.267958i
$298$	−27.7381			−1.60682
$299$	4.11451	−	4.98398i	0.237948	−	0.288231i
$300$		0			0
$301$	22.1826	−	6.51340i	1.27858	−	0.375426i
$302$	6.43868	+	7.43063i	0.370504	+	0.427585i
$303$	−5.13784	+	3.30189i	−0.295161	+	0.189689i
$304$	0.178738	+	1.24315i	0.0102513	+	0.0712994i
$305$		0			0
$306$	−5.20052	+	11.3875i	−0.297294	+	0.650983i
$307$	−0.347497	+	0.401033i	−0.0198327	+	0.0228882i	−0.765579	−	0.643342i	$-0.777548\pi$
$307$	−0.347497	+	0.401033i	−0.0198327	+	0.0228882i	0.745747	+	0.666230i	$0.232093\pi$
$308$	2.66247	−	18.5179i	0.151708	−	1.05515i
$309$	−0.571531	−	1.25148i	−0.0325133	−	0.0711941i
$310$		0			0
$311$	−13.2849	−	3.90080i	−0.753319	−	0.221194i	−0.117543	−	0.993068i	$-0.537502\pi$
$311$	−13.2849	−	3.90080i	−0.753319	−	0.221194i	−0.635776	+	0.771873i	$0.719320\pi$
$312$	−2.11055	−	4.62145i	−0.119486	−	0.261638i
$313$	0.184462	−	1.28296i	0.0104264	−	0.0725172i	−0.983944	−	0.178478i	$-0.942883\pi$
$313$	0.184462	−	1.28296i	0.0104264	−	0.0725172i	0.994370	+	0.105961i	$0.0337918\pi$
$314$	−32.1428	+	37.0947i	−1.81392	+	2.09338i
$315$		0			0
$316$	−11.9832	−	7.70116i	−0.674110	−	0.433224i
$317$	2.25349	+	15.6734i	0.126569	+	0.880305i	0.949858	+	0.312682i	$0.101228\pi$
$317$	2.25349	+	15.6734i	0.126569	+	0.880305i	−0.823289	+	0.567622i	$0.807863\pi$
$318$	−13.1222	+	8.43314i	−0.735858	+	0.472907i
$319$	7.67976	+	8.86291i	0.429984	+	0.496228i
$320$		0			0
$321$	1.22889			0.0685902
$322$	−19.8062	+	6.33294i	−1.10376	+	0.352921i
$323$	9.05326			0.503737
$324$	6.70693	−	1.96933i	0.372607	−	0.109407i
$325$		0			0
$326$	−17.9989	+	11.5672i	−0.996865	+	0.640646i
$327$	−1.74970	−	12.1694i	−0.0967587	−	0.672972i
$328$	30.7392	+	19.7549i	1.69729	+	1.09078i
$329$	−2.22971	+	4.88238i	−0.122928	+	0.269174i
$330$		0			0
$331$	1.86398	−	12.9643i	0.102454	−	0.712580i	−0.872247	−	0.489065i	$-0.837338\pi$
$331$	1.86398	−	12.9643i	0.102454	−	0.712580i	0.974701	−	0.223515i	$-0.0717530\pi$
$332$	−2.95145	−	6.46278i	−0.161982	−	0.354691i
$333$	−5.64572	−	1.65773i	−0.309383	−	0.0908431i
$334$	22.3075	+	6.55008i	1.22061	+	0.358404i
$335$		0			0
$336$	−0.159486	+	1.10925i	−0.00870069	+	0.0605146i
$337$	3.95131	−	4.56005i	0.215241	−	0.248402i	−0.637853	−	0.770158i	$-0.720177\pi$
$337$	3.95131	−	4.56005i	0.215241	−	0.248402i	0.853095	+	0.521756i	$0.174723\pi$
$338$	10.7397	−	23.5166i	0.584162	−	1.27914i
$339$	11.3464	+	7.29191i	0.616254	+	0.396042i
$340$		0			0
$341$	21.1052	−	13.5635i	1.14291	−	0.734505i
$342$	5.89633	+	6.80473i	0.318837	+	0.367957i
$343$	18.8642	−	5.53902i	1.01857	−	0.299079i
$344$	38.2804			2.06394
$345$		0			0
$346$	−7.91933			−0.425746
$347$	5.60317	−	1.64524i	0.300794	−	0.0883210i	−0.127853	−	0.991793i	$-0.540809\pi$
$347$	5.60317	−	1.64524i	0.300794	−	0.0883210i	0.428647	+	0.903472i	$0.358990\pi$
$348$	−10.4489	−	12.0587i	−0.560119	−	0.646412i
$349$	12.7323	−	8.18254i	0.681543	−	0.438001i	−0.153527	−	0.988144i	$-0.549063\pi$
$349$	12.7323	−	8.18254i	0.681543	−	0.438001i	0.835070	+	0.550143i	$0.185427\pi$
$350$		0			0
$351$	−6.22919	−	4.00326i	−0.332490	−	0.213678i
$352$	−6.28750	+	13.7677i	−0.335125	+	0.733821i
$353$	−14.1233	+	16.2991i	−0.751706	+	0.867514i	−0.994732	−	0.102505i	$-0.967314\pi$
$353$	−14.1233	+	16.2991i	−0.751706	+	0.867514i	0.243027	+	0.970020i	$0.421860\pi$
$354$	4.61948	−	32.1292i	0.245523	−	1.70765i
$355$		0			0
$356$	−28.5798	−	8.39179i	−1.51473	−	0.444764i
$357$	7.75093	+	2.27588i	0.410223	+	0.120452i
$358$	−14.6145	−	32.0012i	−0.772398	−	1.69132i
$359$	−1.73450	+	12.0637i	−0.0915436	+	0.636700i	0.891458	+	0.453103i	$0.149683\pi$
$359$	−1.73450	+	12.0637i	−0.0915436	+	0.636700i	−0.983002	+	0.183597i	$0.941226\pi$
$360$		0			0
$361$	−5.18796	+	11.3600i	−0.273050	+	0.597897i
$362$	−44.3329	−	28.4910i	−2.33009	−	1.49746i
$363$	0.362985	+	2.52461i	0.0190518	+	0.132508i
$364$	7.10982	−	4.56920i	0.372656	−	0.239491i
$365$		0			0
$366$	39.2623	−	11.5285i	2.05227	−	0.602602i
$367$	12.5883			0.657105			0.328552	−	0.944486i	$-0.393439\pi$
$367$	12.5883			0.657105			0.328552	+	0.944486i	$0.393439\pi$
$368$	−2.35977	+	0.0563438i	−0.123011	+	0.00293712i
$369$	17.9590			0.934908
$370$		0			0
$371$	−6.82798	−	7.87991i	−0.354491	−	0.409105i
$372$	−28.7152	+	18.4542i	−1.48882	+	0.956804i
$373$	−3.45226	−	24.0110i	−0.178751	−	1.24324i	−0.859657	−	0.510872i	$-0.829323\pi$
$373$	−3.45226	−	24.0110i	−0.178751	−	1.24324i	0.680906	−	0.732371i	$-0.261586\pi$
$374$	−20.5815	−	13.2269i	−1.06424	−	0.683948i
$375$		0			0
$376$	−5.81995	+	6.71658i	−0.300141	+	0.346381i
$377$	−0.753956	+	5.24388i	−0.0388307	+	0.270074i
$378$	9.89687	+	21.6711i	0.509040	+	1.11464i
$379$	−9.20201	−	2.70195i	−0.472676	−	0.138790i	0.0367145	−	0.999326i	$-0.488311\pi$
$379$	−9.20201	−	2.70195i	−0.472676	−	0.138790i	−0.509390	+	0.860536i	$0.670129\pi$
$380$		0			0
$381$	−5.66126	−	12.3964i	−0.290035	−	0.635088i
$382$	6.57381	−	45.7219i	0.336346	−	2.33933i
$383$	−5.89990	+	6.80884i	−0.301471	+	0.347916i	−0.886192	−	0.463319i	$-0.846658\pi$
$383$	−5.89990	+	6.80884i	−0.301471	+	0.347916i	0.584721	+	0.811234i	$0.301204\pi$
$384$	9.70208	−	21.2446i	0.495107	−	1.08413i
$385$		0			0
$386$	−2.40919	−	16.7563i	−0.122625	−	0.852873i
$387$	15.8277	−	10.1719i	0.804569	−	0.517065i
$388$	−22.8941	−	26.4212i	−1.16227	−	1.34133i
$389$	−18.6610	+	5.47935i	−0.946148	+	0.277814i	−0.718182	−	0.695855i	$-0.755026\pi$
$389$	−18.6610	+	5.47935i	−0.946148	+	0.277814i	−0.227966	+	0.973669i	$0.573207\pi$
$390$		0			0
$391$	−2.01878	+	16.8948i	−0.102094	+	0.854408i
$392$	10.8136			0.546167
$393$	−15.1065	+	4.43567i	−0.762023	+	0.223750i
$394$	−1.79102	−	2.06694i	−0.0902301	−	0.104131i
$395$		0			0
$396$	−2.16673	−	15.0700i	−0.108882	−	0.757294i
$397$	8.17378	+	5.25297i	0.410230	+	0.263639i	0.729440	−	0.684045i	$-0.239781\pi$
$397$	8.17378	+	5.25297i	0.410230	+	0.263639i	−0.319209	+	0.947684i	$0.603417\pi$
$398$	2.19482	−	4.80599i	0.110016	−	0.240902i
$399$	3.80478	−	4.39095i	0.190477	−	0.219822i
$400$		0			0
$401$	4.96742	+	10.8771i	0.248061	+	0.543178i	0.992172	−	0.124878i	$-0.0398540\pi$
$401$	4.96742	+	10.8771i	0.248061	+	0.543178i	−0.744111	+	0.668056i	$0.767127\pi$
$402$	1.18740	+	0.348652i	0.0592222	+	0.0173892i
$403$	10.8743	+	3.19299i	0.541689	+	0.159054i
$404$	−6.98811	−	15.3018i	−0.347671	−	0.761294i
$405$		0			0
$406$	11.1623	−	12.8820i	0.553978	−	0.639325i
$407$	4.77689	−	10.4599i	0.236782	−	0.518479i
$408$	11.2524	+	7.23145i	0.557075	+	0.358010i
$409$	−2.38261	−	16.5714i	−0.117813	−	0.819404i	−0.959956	−	0.280151i	$-0.909616\pi$
$409$	−2.38261	−	16.5714i	−0.117813	−	0.819404i	0.842144	−	0.539253i	$-0.181293\pi$
$410$		0			0
$411$	7.44145	+	8.58789i	0.367060	+	0.423609i
$412$	3.63599	−	1.06762i	0.179133	−	0.0525981i
$413$	21.6973			1.06766
$414$	−14.0135	+	9.48611i	−0.688727	+	0.466217i
$415$		0			0
$416$	−6.56047	+	1.92633i	−0.321653	+	0.0944460i
$417$	−4.63340	−	5.34723i	−0.226899	−	0.261855i
$418$	−14.8028	+	9.51321i	−0.724031	+	0.465306i
$419$	−4.49087	−	31.2347i	−0.219393	−	1.52591i	−0.740286	−	0.672292i	$-0.765310\pi$
$419$	−4.49087	−	31.2347i	−0.219393	−	1.52591i	0.520893	−	0.853622i	$-0.325599\pi$
$420$		0			0
$421$	4.23877	−	9.28162i	0.206585	−	0.452359i	−0.777771	−	0.628548i	$-0.783650\pi$
$421$	4.23877	−	9.28162i	0.206585	−	0.452359i	0.984356	+	0.176189i	$0.0563770\pi$
$422$	30.8190	−	35.5670i	1.50024	−	1.73137i
$423$	−0.621637	+	4.32358i	−0.0302250	+	0.210220i
$424$	−7.17184	−	15.7041i	−0.348296	−	0.762661i
$425$		0			0
$426$	6.49423	+	1.90688i	0.314647	+	0.0923886i
$427$	11.3626	+	24.8807i	0.549877	+	1.20406i
$428$	−0.481713	+	3.35039i	−0.0232845	+	0.161947i
$429$	3.19568	−	3.68801i	0.154289	−	0.178059i
$430$		0			0
$431$	−14.2924	−	9.18518i	−0.688441	−	0.442434i	0.149090	−	0.988824i	$-0.452366\pi$
$431$	−14.2924	−	9.18518i	−0.688441	−	0.442434i	−0.837531	+	0.546389i	$0.816002\pi$
$432$	0.384875	+	2.67687i	0.0185173	+	0.128791i
$433$	12.4830	−	8.02233i	0.599894	−	0.385529i	−0.205161	−	0.978728i	$-0.565772\pi$
$433$	12.4830	−	8.02233i	0.599894	−	0.385529i	0.805055	+	0.593200i	$0.202135\pi$
$434$	−23.8792	−	27.5581i	−1.14624	−	1.32283i
$435$		0			0
$436$	33.8639			1.62179
$437$	10.4500	+	6.36858i	0.499892	+	0.304651i
$438$	9.69462			0.463227
$439$	23.1462	−	6.79633i	1.10471	−	0.324371i	0.321986	−	0.946744i	$-0.395649\pi$
$439$	23.1462	−	6.79633i	1.10471	−	0.324371i	0.782721	+	0.622373i	$0.213831\pi$
$440$		0			0
$441$	4.47107	−	2.87338i	0.212908	−	0.136828i
$442$	−1.57289	−	10.9397i	−0.0748146	−	0.520347i
$443$	−22.9338	−	14.7386i	−1.08962	−	0.700254i	−0.132857	−	0.991135i	$-0.542415\pi$
$443$	−22.9338	−	14.7386i	−1.08962	−	0.700254i	−0.956759	+	0.290882i	$0.906051\pi$
$444$	−6.49931	+	14.2315i	−0.308444	+	0.675398i
$445$		0			0
$446$	4.51803	−	31.4236i	0.213935	−	1.48795i
$447$	6.05099	+	13.2498i	0.286202	+	0.626695i
$448$	22.8795	+	6.71803i	1.08096	+	0.317397i
$449$	5.99141	+	1.75924i	0.282752	+	0.0830235i	0.420034	−	0.907509i	$-0.362018\pi$
$449$	5.99141	+	1.75924i	0.282752	+	0.0830235i	−0.137281	+	0.990532i	$0.543836\pi$
$450$		0			0
$451$	−4.99480	+	34.7396i	−0.235196	+	1.63582i
$452$	−24.3279	+	28.0759i	−1.14429	+	1.32058i
$453$	2.14486	−	4.69658i	0.100774	−	0.220665i
$454$	−10.3107	−	6.62627i	−0.483904	−	0.310986i
$455$		0			0
$456$	8.09305	−	5.20109i	0.378992	−	0.243563i
$457$	10.9561	+	12.6440i	0.512503	+	0.591460i	0.951738	−	0.306912i	$-0.0992958\pi$
$457$	10.9561	+	12.6440i	0.512503	+	0.591460i	−0.439235	+	0.898372i	$0.644750\pi$
$458$	−20.2419	+	5.94356i	−0.945842	+	0.277724i
$459$	19.4943			0.909918
$460$		0			0
$461$	−20.8453			−0.970864			−0.485432	−	0.874274i	$-0.661338\pi$
$461$	−20.8453			−0.970864			−0.485432	+	0.874274i	$0.661338\pi$
$462$	−15.0649	+	4.42346i	−0.700884	+	0.205798i
$463$	6.78522	+	7.83056i	0.315336	+	0.363917i	0.891186	−	0.453638i	$-0.149874\pi$
$463$	6.78522	+	7.83056i	0.315336	+	0.363917i	−0.575850	+	0.817555i	$0.695329\pi$
$464$	1.62775	−	1.04609i	0.0755664	−	0.0485636i
$465$		0			0
$466$	−34.1185	−	21.9266i	−1.58051	−	1.01573i
$467$	7.18857	−	15.7408i	0.332648	−	0.728396i	−0.667217	−	0.744863i	$-0.732515\pi$
$467$	7.18857	−	15.7408i	0.332648	−	0.728396i	0.999864	+	0.0164670i	$0.00524186\pi$
$468$	4.50403	−	5.19793i	0.208199	−	0.240274i
$469$	−0.117725	+	0.818795i	−0.00543604	+	0.0378085i
$470$		0			0
$471$	24.7312	+	7.26172i	1.13955	+	0.334603i
$472$	34.4709	+	10.1216i	1.58665	+	0.465883i
$473$	15.2742	+	33.4459i	0.702311	+	1.53785i
$474$	−1.70133	+	11.8330i	−0.0781447	+	0.543508i
$475$		0			0
$476$	−9.24310	+	20.2396i	−0.423657	+	0.927679i
$477$	−7.13824	−	4.58747i	−0.326838	−	0.210046i
$478$	6.28983	+	43.7468i	0.287690	+	2.00093i
$479$	9.27666	−	5.96175i	0.423862	−	0.272399i	−0.311273	−	0.950321i	$-0.600755\pi$
$479$	9.27666	−	5.96175i	0.423862	−	0.272399i	0.735135	+	0.677921i	$0.237119\pi$
$480$		0			0
$481$	4.98427	−	1.46351i	0.227263	−	0.0667305i
$482$	−17.6484			−0.803861
$483$	7.34578	+	8.07946i	0.334245	+	0.367628i
$484$	−7.02525			−0.319330
$485$		0			0
$486$	21.1114	+	24.3639i	0.957635	+	1.10517i
$487$	−20.3245	+	13.0617i	−0.920989	+	0.591884i	−0.912944	−	0.408084i	$-0.866197\pi$
$487$	−20.3245	+	13.0617i	−0.920989	+	0.591884i	−0.00804472	+	0.999968i	$0.502561\pi$
$488$	6.44544	+	44.8290i	0.291771	+	2.02931i
$489$	9.45178	+	6.07429i	0.427424	+	0.274689i
$490$		0			0
$491$	−13.9624	+	16.1135i	−0.630116	+	0.727193i	−0.977595	−	0.210495i	$-0.932492\pi$
$491$	−13.9624	+	16.1135i	−0.630116	+	0.727193i	0.347479	+	0.937688i	$0.387038\pi$
$492$	6.79580	−	47.2658i	0.306378	−	2.13091i
$493$	−5.79405	−	12.6872i	−0.260951	−	0.571402i
$494$	−7.62706	−	2.23951i	−0.343158	−	0.100760i
$495$		0			0
$496$	−1.71952	−	3.76523i	−0.0772088	−	0.169064i
$497$	−0.643871	+	4.47822i	−0.0288816	+	0.200876i
$498$	−3.90475	+	4.50632i	−0.174976	+	0.201933i
$499$	8.82827	−	19.3312i	0.395208	−	0.865384i	−0.602526	−	0.798099i	$-0.705839\pi$
$499$	8.82827	−	19.3312i	0.395208	−	0.865384i	0.997734	−	0.0672848i	$-0.0214336\pi$
$500$		0			0
$501$	−1.73751	−	12.0847i	−0.0776263	−	0.539903i
$502$	−29.3460	+	18.8595i	−1.30978	+	0.841743i
$503$	9.83541	+	11.3507i	0.438539	+	0.506101i	0.931395	−	0.364010i	$-0.118592\pi$
$503$	9.83541	+	11.3507i	0.438539	+	0.506101i	−0.492856	+	0.870111i	$0.664047\pi$
$504$	−8.53198	+	2.50521i	−0.380044	+	0.111591i
$505$		0			0
$506$	−14.4523	−	29.7458i	−0.642483	−	1.32236i
$507$	−13.5762			−0.602940
$508$	36.0161	−	10.5753i	1.59796	−	0.469202i
$509$	13.6602	+	15.7647i	0.605477	+	0.698757i	0.972882	−	0.231304i	$-0.0742991\pi$
$509$	13.6602	+	15.7647i	0.605477	+	0.698757i	−0.367405	+	0.930061i	$0.619754\pi$
$510$		0			0
$511$	0.922241	+	6.41432i	0.0407975	+	0.283753i
$512$	4.67269	+	3.00295i	0.206506	+	0.132713i
$513$	5.82451	−	12.7539i	0.257158	−	0.563098i
$514$	−42.9999	+	49.6245i	−1.89664	+	2.18884i
$515$		0			0
$516$	−20.7818	−	45.5057i	−0.914866	−	2.00328i
$517$	−8.19056	−	2.40497i	−0.360221	−	0.105770i
$518$	−16.0366	−	4.70877i	−0.704608	−	0.206892i
$519$	1.72758	+	3.78288i	0.0758325	+	0.166050i
$520$		0			0
$521$	−3.48604	+	4.02311i	−0.152726	+	0.176255i	−0.826957	−	0.562265i	$-0.809930\pi$
$521$	−3.48604	+	4.02311i	−0.152726	+	0.176255i	0.674231	+	0.738521i	$0.264475\pi$
$522$	5.76249	−	12.6181i	0.252217	−	0.552278i
$523$	0.660025	+	0.424173i	0.0288609	+	0.0185478i	0.554992	−	0.831856i	$-0.312721\pi$
$523$	0.660025	+	0.424173i	0.0288609	+	0.0185478i	−0.526131	+	0.850404i	$0.676358\pi$
$524$	−6.17158	−	42.9243i	−0.269607	−	1.87516i
$525$		0			0
$526$	33.1205	+	38.2231i	1.44412	+	1.66661i
$527$	−28.6290	+	8.40623i	−1.24710	+	0.366181i
$528$	−1.78229			−0.0775644
$529$	−14.2150	+	18.0813i	−0.618045	+	0.786143i
$530$		0			0
$531$	16.9422	−	4.97467i	0.735227	−	0.215882i
$532$	10.4798	+	12.0943i	0.454357	+	0.524356i
$533$	−13.3380	+	8.57183i	−0.577734	+	0.371287i
$534$	3.55761	+	24.7437i	0.153953	+	1.07077i
$535$		0			0
$536$	−0.568991	+	1.24592i	−0.0245767	+	0.0538154i
$537$	−12.0981	+	13.9620i	−0.522072	+	0.602504i
$538$	−2.88830	+	20.0886i	−0.124523	+	0.866080i
$539$	4.31472	+	9.44792i	0.185848	+	0.406951i
$540$		0			0
$541$	15.6230	+	4.58732i	0.671684	+	0.197224i	0.599753	−	0.800185i	$-0.295266\pi$
$541$	15.6230	+	4.58732i	0.671684	+	0.197224i	0.0719312	+	0.997410i	$0.477084\pi$
$542$	10.9224	+	23.9168i	0.469159	+	1.02731i
$543$	−3.93838	+	27.3921i	−0.169012	+	1.17551i
$544$	11.7882	−	13.6043i	0.505413	−	0.583278i
$545$		0			0
$546$	−5.96691	−	3.83470i	−0.255360	−	0.164110i
$547$	6.03051	+	41.9431i	0.257846	+	1.79336i	0.548104	+	0.836410i	$0.315350\pi$
$547$	6.03051	+	41.9431i	0.257846	+	1.79336i	−0.290258	+	0.956948i	$0.593741\pi$
$548$	−26.3305	+	16.9216i	−1.12478	+	0.722855i
$549$	14.5770	+	16.8227i	0.622130	+	0.717976i
$550$		0			0
$551$	−10.0316			−0.427358
$552$	7.90139	+	16.2627i	0.336305	+	0.692187i
$553$	−7.99101			−0.339812
$554$	71.4365	−	20.9757i	3.03505	−	0.891170i
$555$		0			0
$556$	16.3946	−	10.5362i	0.695287	−	0.446834i
$557$	−5.98682	−	41.6392i	−0.253670	−	1.76431i	−0.575776	−	0.817607i	$-0.695300\pi$
$557$	−5.98682	−	41.6392i	−0.253670	−	1.76431i	0.322106	−	0.946703i	$-0.395609\pi$
$558$	−24.9643	−	16.0436i	−1.05682	−	0.679178i
$559$	−6.90012	+	15.1092i	−0.291844	+	0.639050i
$560$		0			0
$561$	−1.82839	+	12.7167i	−0.0771946	+	0.536900i
$562$	3.09976	+	6.78752i	0.130755	+	0.286314i
$563$	−5.60389	−	1.64545i	−0.236176	−	0.0693475i	0.161503	−	0.986872i	$-0.448366\pi$
$563$	−5.60389	−	1.64545i	−0.236176	−	0.0693475i	−0.397679	+	0.917525i	$0.630184\pi$
$564$	11.1439	+	3.27214i	0.469242	+	0.137782i
$565$		0			0
$566$	−6.33773	+	44.0799i	−0.266395	+	1.85282i
$567$	2.56794	−	2.96356i	0.107843	−	0.124458i
$568$	−3.11198	+	6.81428i	−0.130576	+	0.285921i
$569$	−33.4619	−	21.5047i	−1.40280	−	0.901522i	−0.402890	−	0.915248i	$-0.631994\pi$
$569$	−33.4619	−	21.5047i	−1.40280	−	0.901522i	−0.999906	+	0.0137259i	$0.995631\pi$
$570$		0			0
$571$	1.94014	−	1.24685i	0.0811925	−	0.0521793i	−0.499415	−	0.866363i	$-0.666452\pi$
$571$	1.94014	−	1.24685i	0.0811925	−	0.0521793i	0.580607	+	0.814184i	$0.302815\pi$
$572$	8.80212	+	10.1582i	0.368035	+	0.424735i
$573$	−23.2743	+	6.83396i	−0.972299	+	0.285493i
$574$	51.0124			2.12922
$575$		0			0
$576$	19.4056			0.808565
$577$	−15.6855	+	4.60568i	−0.652995	+	0.191737i	−0.591418	−	0.806366i	$-0.701431\pi$
$577$	−15.6855	+	4.60568i	−0.652995	+	0.191737i	−0.0615780	+	0.998102i	$0.519613\pi$
$578$	−6.67970	−	7.70878i	−0.277839	−	0.320643i
$579$	−7.47853	+	4.80616i	−0.310797	+	0.199737i
$580$		0			0
$581$	−3.35301	−	2.15485i	−0.139106	−	0.0893981i
$582$	−12.1884	+	26.6889i	−0.505226	+	1.10629i
$583$	10.8592	−	12.5322i	0.449743	−	0.519032i
$584$	−1.52704	+	10.6208i	−0.0631892	+	0.439491i
$585$		0			0
$586$	−19.9542	−	5.85909i	−0.824302	−	0.242037i
$587$	43.3180	+	12.7193i	1.78793	+	0.524982i	0.996294	−	0.0860160i	$-0.0274136\pi$
$587$	43.3180	+	12.7193i	1.78793	+	0.524982i	0.791632	+	0.610998i	$0.209232\pi$
$588$	−5.87050	−	12.8546i	−0.242095	−	0.530115i
$589$	−3.05410	+	21.2417i	−0.125842	+	0.875249i
$590$		0			0
$591$	−0.596624	+	1.30643i	−0.0245418	+	0.0537391i
$592$	−1.59607	−	1.02573i	−0.0655981	−	0.0421573i
$593$	−0.233177	−	1.62178i	−0.00957543	−	0.0665986i	0.984473	−	0.175534i	$-0.0561651\pi$
$593$	−0.233177	−	1.62178i	−0.00957543	−	0.0665986i	−0.994049	+	0.108935i	$0.965256\pi$
$594$	−31.8749	+	20.4848i	−1.30784	+	0.840500i
$595$		0			0
$596$	−38.4955	+	11.3033i	−1.57684	+	0.463001i
$597$	−2.77450			−0.113553
$598$	5.88004	−	13.7339i	0.240453	−	0.561622i
$599$	−43.3808			−1.77249			−0.886246	−	0.463216i	$-0.846696\pi$
$599$	−43.3808			−1.77249			−0.886246	+	0.463216i	$0.846696\pi$
$600$		0			0
$601$	−8.84669	−	10.2096i	−0.360864	−	0.416459i	0.546065	−	0.837743i	$-0.316125\pi$
$601$	−8.84669	−	10.2096i	−0.360864	−	0.416459i	−0.906929	+	0.421283i	$0.861580\pi$
$602$	44.9586	−	28.8931i	1.83237	−	1.17760i
$603$	0.0958053	+	0.666341i	0.00390149	+	0.0271355i
$604$	11.9637	+	7.68863i	0.486797	+	0.312846i
$605$		0			0
$606$	−9.24522	+	10.6695i	−0.375561	+	0.433421i
$607$	1.74042	−	12.1049i	0.0706414	−	0.491322i	−0.923531	−	0.383523i	$-0.874711\pi$
$607$	1.74042	−	12.1049i	0.0706414	−	0.491322i	0.994173	−	0.107799i	$-0.0343802\pi$
$608$	−5.37833	−	11.7769i	−0.218120	−	0.477616i
$609$	−8.58849	−	2.52181i	−0.348023	−	0.102189i
$610$		0			0
$611$	−1.60196	−	3.50780i	−0.0648083	−	0.141910i
$612$	−2.57695	+	17.9231i	−0.104167	+	0.724499i
$613$	18.0266	−	20.8038i	0.728088	−	0.840259i	−0.264167	−	0.964477i	$-0.585097\pi$
$613$	18.0266	−	20.8038i	0.728088	−	0.840259i	0.992255	+	0.124218i	$0.0396423\pi$
$614$	−0.509565	+	1.11579i	−0.0205644	+	0.0450297i
$615$		0			0
$616$	−2.47311	−	17.2009i	−0.0996445	−	0.693043i
$617$	−12.4618	+	8.00869i	−0.501692	+	0.322418i	−0.766893	−	0.641775i	$-0.778198\pi$
$617$	−12.4618	+	8.00869i	−0.501692	+	0.322418i	0.265201	+	0.964193i	$0.414562\pi$
$618$	−2.08267	−	2.40353i	−0.0837774	−	0.0966843i
$619$	23.8384	−	6.99958i	0.958145	−	0.281337i	0.234971	−	0.972002i	$-0.424501\pi$
$619$	23.8384	−	6.99958i	0.958145	−	0.281337i	0.723174	+	0.690666i	$0.242682\pi$
$620$		0			0
$621$	22.5020	+	13.7134i	0.902974	+	0.550302i
$622$	−32.0060			−1.28332
$623$	−16.0330	+	4.70770i	−0.642347	+	0.188610i
$624$	−0.527261	−	0.608492i	−0.0211073	−	0.0243592i
$625$		0			0
$626$	−0.426404	−	2.96570i	−0.0170425	−	0.118533i
$627$	7.77345	+	4.99569i	0.310442	+	0.199509i
$628$	−29.4923	+	64.5791i	−1.17687	+	2.57699i
$629$	−8.95597	+	10.3357i	−0.357098	+	0.412113i
$630$		0			0
$631$	6.07083	+	13.2933i	0.241676	+	0.529196i	0.991136	−	0.132854i	$-0.0424140\pi$
$631$	6.07083	+	13.2933i	0.241676	+	0.529196i	−0.749460	+	0.662050i	$0.769687\pi$
$632$	−12.6955	−	3.72772i	−0.504998	−	0.148281i
$633$	−23.7126	−	6.96265i	−0.942492	−	0.276741i
$634$	15.2056	+	33.2955i	0.603890	+	1.32234i
$635$		0			0
$636$	−14.7748	+	17.0510i	−0.585859	+	0.676117i
$637$	−1.94917	+	4.26809i	−0.0772289	+	0.169108i
$638$	22.8055	+	14.6562i	0.902880	+	0.580245i
$639$	0.523987	+	3.64441i	0.0207286	+	0.144170i
$640$		0			0
$641$	29.1393	+	33.6285i	1.15093	+	1.32825i	0.936157	+	0.351582i	$0.114356\pi$
$641$	29.1393	+	33.6285i	1.15093	+	1.32825i	0.214774	+	0.976664i	$0.431098\pi$
$642$	2.72566	−	0.800325i	0.107573	−	0.0315863i
$643$	42.1236			1.66119			0.830597	−	0.556874i	$-0.187999\pi$
$643$	42.1236			1.66119			0.830597	+	0.556874i	$0.187999\pi$
$644$	−24.9068	+	16.8601i	−0.981467	+	0.664379i
$645$		0			0
$646$	20.0799	−	5.89599i	0.790033	−	0.231974i
$647$	−5.07204	−	5.85345i	−0.199403	−	0.230123i	0.647238	−	0.762288i	$-0.275924\pi$
$647$	−5.07204	−	5.85345i	−0.199403	−	0.230123i	−0.846641	+	0.532165i	$0.821379\pi$
$648$	5.46221	−	3.51035i	0.214576	−	0.137899i
$649$	4.91092	+	34.1562i	0.192770	+	1.34075i
$650$		0			0
$651$	−7.95466	+	17.4183i	−0.311768	+	0.682676i
$652$	−20.2656	+	23.3877i	−0.793662	+	0.915935i
$653$	−3.84133	+	26.7170i	−0.150323	+	1.04552i	0.765356	+	0.643608i	$0.222563\pi$
$653$	−3.84133	+	26.7170i	−0.150323	+	1.04552i	−0.915679	+	0.401911i	$0.868346\pi$
$654$	−11.8062	−	25.8520i	−0.461659	−	1.01089i
$655$		0			0
$656$	5.55612	+	1.63142i	0.216930	+	0.0636964i
$657$	2.19077	+	4.79712i	0.0854702	+	0.187154i
$658$	−1.76575	+	12.2811i	−0.0688363	+	0.478767i
$659$	−19.2565	+	22.2232i	−0.750127	+	0.865692i	−0.994581	−	0.103968i	$-0.966846\pi$
$659$	−19.2565	+	22.2232i	−0.750127	+	0.865692i	0.244454	+	0.969661i	$0.421391\pi$
$660$		0			0
$661$	−4.41718	−	2.83875i	−0.171808	−	0.110414i	0.451911	−	0.892063i	$-0.350743\pi$
$661$	−4.41718	−	2.83875i	−0.171808	−	0.110414i	−0.623719	+	0.781649i	$0.714379\pi$
$662$	−4.30879	−	29.9683i	−0.167466	−	1.16475i
$663$	−4.88250	+	3.13779i	−0.189621	+	0.121862i
$664$	−4.32177	−	4.98759i	−0.167717	−	0.193556i
$665$		0			0
$666$	−13.6017			−0.527053
$667$	2.23693	−	18.7205i	0.0866144	−	0.724860i
$668$	33.6280			1.30111
$669$	−15.9959	+	4.69682i	−0.618437	+	0.181590i
$670$		0			0
$671$	−36.5957	+	23.5187i	−1.41276	+	0.907928i
$672$	−1.64408	−	11.4348i	−0.0634217	−	0.441108i
$673$	2.06012	+	1.32396i	0.0794118	+	0.0510349i	0.579744	−	0.814799i	$-0.303152\pi$
$673$	2.06012	+	1.32396i	0.0794118	+	0.0510349i	−0.500332	+	0.865833i	$0.666789\pi$
$674$	5.79413	−	12.6874i	0.223182	−	0.488700i
$675$		0			0
$676$	5.32172	−	37.0134i	0.204682	−	1.42359i
$677$	5.62411	+	12.3151i	0.216152	+	0.473307i	0.986384	−	0.164456i	$-0.0525870\pi$
$677$	5.62411	+	12.3151i	0.216152	+	0.473307i	−0.770232	+	0.637763i	$0.779860\pi$
$678$	29.9150	+	8.78384i	1.14888	+	0.337341i
$679$	−18.8178	−	5.52542i	−0.722162	−	0.212046i
$680$		0			0
$681$	−0.915965	+	6.37068i	−0.0350998	+	0.244125i
$682$	37.9775	−	43.8284i	1.45423	−	1.67828i
$683$	11.8984	−	26.0538i	0.455278	−	0.996920i	−0.533260	−	0.845951i	$-0.679033\pi$
$683$	11.8984	−	26.0538i	0.455278	−	0.996920i	0.988538	−	0.150969i	$-0.0482394\pi$
$684$	10.9560	+	7.04099i	0.418913	+	0.269219i
$685$		0			0
$686$	38.2329	−	24.5708i	1.45974	−	0.938118i
$687$	7.25482	+	8.37251i	0.276789	+	0.319431i
$688$	5.82079	−	1.70914i	0.221915	−	0.0651602i
$689$	7.49113			0.285389
$690$		0			0
$691$	25.8680			0.984066			0.492033	−	0.870577i	$-0.336254\pi$
$691$	25.8680			0.984066			0.492033	+	0.870577i	$0.336254\pi$
$692$	−10.9906	+	3.22714i	−0.417801	+	0.122677i
$693$	−5.59317	−	6.45487i	−0.212467	−	0.245200i
$694$	11.3562	−	7.29819i	0.431076	−	0.277036i
$695$		0			0
$696$	−12.4683	−	8.01289i	−0.472609	−	0.303728i
$697$	17.3401	−	37.9695i	0.656802	−	1.43820i
$698$	22.9109	−	26.4406i	0.867192	−	1.00079i
$699$	−3.03097	+	21.0809i	−0.114642	+	0.797351i
$700$		0			0
$701$	8.32237	+	2.44367i	0.314331	+	0.0922960i	0.435093	−	0.900386i	$-0.356715\pi$
$701$	8.32237	+	2.44367i	0.314331	+	0.0922960i	−0.120762	+	0.992682i	$0.538534\pi$
$702$	−16.4233	−	4.82232i	−0.619858	−	0.182007i
$703$	4.08615	+	8.94742i	0.154112	+	0.337458i
$704$	−5.39712	+	37.5378i	−0.203411	+	1.41476i
$705$		0			0
$706$	−20.7101	+	45.3489i	−0.779436	+	1.70673i
$707$	−7.93886	−	5.10200i	−0.298572	−	0.191880i
$708$	−6.68167	−	46.4721i	−0.251113	−	1.74653i
$709$	30.1136	−	19.3528i	1.13094	−	0.726811i	0.165184	−	0.986263i	$-0.447178\pi$
$709$	30.1136	−	19.3528i	1.13094	−	0.726811i	0.965756	+	0.259452i	$0.0835418\pi$
$710$		0			0
$711$	−6.23971	+	1.83214i	−0.234007	+	0.0687107i
$712$	−27.6679			−1.03690
$713$	−38.9594	−	10.4361i	−1.45904	−	0.390836i
$714$	18.6735			0.698839
$715$		0			0
$716$	−33.3228	−	38.4566i	−1.24533	−	1.43719i
$717$	19.5247	−	12.5478i	0.729163	−	0.468605i
$718$	4.00950	+	27.8867i	0.149633	+	1.04072i
$719$	−9.55550	−	6.14095i	−0.356360	−	0.229019i	0.350195	−	0.936677i	$-0.386115\pi$
$719$	−9.55550	−	6.14095i	−0.356360	−	0.229019i	−0.706555	+	0.707658i	$0.749752\pi$
$720$		0			0
$721$	1.39214	−	1.60662i	0.0518462	−	0.0598336i
$722$	−4.10846	+	28.5750i	−0.152901	+	1.06345i
$723$	3.84995	+	8.43021i	0.143181	+	0.313523i
$724$	−73.1364	−	21.4748i	−2.71809	−	0.798104i
$725$		0			0
$726$	2.44926	+	5.36313i	0.0909006	+	0.199044i
$727$	−0.977049	+	6.79553i	−0.0362368	+	0.252032i	−0.999885	−	0.0151407i	$-0.995180\pi$
$727$	−0.977049	+	6.79553i	−0.0362368	+	0.252032i	0.963649	+	0.267173i	$0.0860895\pi$
$728$	5.14090	−	5.93292i	0.190535	−	0.219889i
$729$	9.63809	−	21.1045i	0.356966	−	0.781647i
$730$		0			0
$731$	−6.22342	−	43.2848i	−0.230181	−	1.60095i
$732$	49.7913	−	31.9989i	1.84034	−	1.18271i
$733$	25.5240	+	29.4563i	0.942750	+	1.08799i	0.995995	+	0.0894105i	$0.0284983\pi$
$733$	25.5240	+	29.4563i	0.942750	+	1.08799i	−0.0532444	+	0.998582i	$0.516956\pi$
$734$	27.9206	−	8.19822i	1.03057	−	0.302602i
$735$		0			0
$736$	23.1769	−	7.41069i	0.854311	−	0.273162i
$737$	−1.31560			−0.0484609
$738$	39.8326	−	11.6959i	1.46626	−	0.430532i
$739$	−14.7255	−	16.9942i	−0.541687	−	0.625140i	0.417239	−	0.908797i	$-0.362998\pi$
$739$	−14.7255	−	16.9942i	−0.541687	−	0.625140i	−0.958926	+	0.283657i	$0.908452\pi$
$740$		0			0
$741$	0.594065	+	4.13181i	0.0218235	+	0.151786i
$742$	−20.2761	−	13.0307i	−0.744360	−	0.478371i
$743$	16.0285	−	35.0976i	0.588029	−	1.28760i	−0.348596	−	0.937273i	$-0.613342\pi$
$743$	16.0285	−	35.0976i	0.588029	−	1.28760i	0.936626	−	0.350332i	$-0.113931\pi$
$744$	−20.7632	+	23.9620i	−0.761215	+	0.878488i
$745$		0			0
$746$	−23.2943	−	51.0075i	−0.852866	−	1.86752i
$747$	−3.11222	−	0.913830i	−0.113870	−	0.0334353i
$748$	−33.9535	−	9.96963i	−1.24146	−	0.364526i
$749$	0.788814	+	1.72726i	0.0288226	+	0.0631127i
$750$		0			0
$751$	19.7499	−	22.7925i	0.720682	−	0.831712i	−0.270707	−	0.962662i	$-0.587257\pi$
$751$	19.7499	−	22.7925i	0.720682	−	0.831712i	0.991389	+	0.130950i	$0.0418028\pi$
$752$	−0.585082	+	1.28115i	−0.0213357	+	0.0467187i
$753$	15.4105	+	9.90375i	0.561591	+	0.360913i
$754$	1.74285	+	12.1218i	0.0634709	+	0.441450i
$755$		0			0
$756$	22.5661	+	26.0427i	0.820721	+	0.947163i
$757$	40.8870	−	12.0055i	1.48606	−	0.436348i	0.564781	−	0.825241i	$-0.308961\pi$
$757$	40.8870	−	12.0055i	1.48606	−	0.436348i	0.921283	+	0.388893i	$0.127142\pi$
$758$	−22.1695			−0.805232
$759$	−11.0562	+	13.3925i	−0.401313	+	0.486117i
$760$		0			0
$761$	34.8771	−	10.2408i	1.26429	−	0.371230i	0.420202	−	0.907430i	$-0.361959\pi$
$761$	34.8771	−	10.2408i	1.26429	−	0.371230i	0.844091	+	0.536200i	$0.180141\pi$
$762$	−20.6298	−	23.8080i	−0.747338	−	0.862474i
$763$	15.9815	−	10.2707i	0.578570	−	0.371824i
$764$	−9.50844	−	66.1327i	−0.344003	−	2.39260i
$765$		0			0
$766$	−8.65151	+	18.9442i	−0.312592	+	0.684481i
$767$	−10.2084	+	11.7811i	−0.368605	+	0.425393i
$768$	3.29084	−	22.8883i	0.118748	−	0.825909i
$769$	0.137465	+	0.301006i	0.00495710	+	0.0108545i	0.912094	−	0.409980i	$-0.134464\pi$
$769$	0.137465	+	0.301006i	0.00495710	+	0.0108545i	−0.907137	+	0.420835i	$0.861737\pi$
$770$		0			0
$771$	33.0848	+	9.71458i	1.19152	+	0.349862i
$772$	−10.1717	−	22.2730i	−0.366089	−	0.801623i
$773$	4.37536	−	30.4313i	0.157371	−	1.09454i	−0.746084	−	0.665852i	$-0.768068\pi$
$773$	4.37536	−	30.4313i	0.157371	−	1.09454i	0.903454	−	0.428684i	$-0.141023\pi$
$774$	28.4810	−	32.8688i	1.02373	−	1.18145i
$775$		0			0
$776$	−27.3187	−	17.5567i	−0.980684	−	0.630247i
$777$	1.24908	+	8.68752i	0.0448104	+	0.311663i
$778$	−37.8210	+	24.3061i	−1.35595	+	0.871416i
$779$	−19.6601	−	22.6890i	−0.704397	−	0.812917i
$780$		0			0
$781$	−7.19541			−0.257472
$782$	6.52524	+	38.7870i	0.233342	+	1.38702i
$783$	−21.6009			−0.771953
$784$	1.64427	−	0.482803i	0.0587241	−	0.0172429i
$785$		0			0
$786$	−30.6171	+	19.6764i	−1.09208	+	0.701835i
$787$	2.39031	+	16.6250i	0.0852053	+	0.592616i	0.987033	+	0.160519i	$0.0513169\pi$
$787$	2.39031	+	16.6250i	0.0852053	+	0.592616i	−0.901827	+	0.432096i	$0.857774\pi$
$788$	−3.32789	−	2.13871i	−0.118551	−	0.0761883i
$789$	11.0331	−	24.1592i	0.392790	−	0.860090i
$790$		0			0
$791$	−2.96593	+	20.6285i	−0.105456	+	0.733464i
$792$	−5.87485	−	12.8641i	−0.208754	−	0.457107i
$793$	−18.8557	−	5.53653i	−0.669586	−	0.196608i
$794$	21.5502	+	6.32772i	0.764790	+	0.224563i
$795$		0			0
$796$	1.08758	−	7.56425i	0.0385481	−	0.268108i
$797$	−11.3221	+	13.0664i	−0.401048	+	0.462834i	−0.919971	−	0.391987i	$-0.871788\pi$
$797$	−11.3221	+	13.0664i	−0.401048	+	0.462834i	0.518923	+	0.854821i	$0.326333\pi$
$798$	5.57926	−	12.2169i	0.197504	−	0.432473i
$799$	8.54083	+	5.48886i	0.302153	+	0.194182i
$800$		0			0
$801$	−11.4398	+	7.35193i	−0.404206	+	0.259768i
$802$	18.1014	+	20.8901i	0.639182	+	0.737656i
$803$	−9.88877	+	2.90361i	−0.348967	+	0.102466i
$804$	1.78998			0.0631276
$805$		0			0
$806$	26.1984			0.922800
$807$	10.2259	−	3.00260i	0.359969	−	0.105697i
$808$	−10.2326	−	11.8090i	−0.359981	−	0.415440i
$809$	−18.0654	+	11.6099i	−0.635146	+	0.408184i	−0.818212	−	0.574917i	$-0.805034\pi$
$809$	−18.0654	+	11.6099i	−0.635146	+	0.408184i	0.183066	+	0.983101i	$0.441398\pi$
$810$		0			0
$811$	−27.6043	−	17.7402i	−0.969317	−	0.622942i	−0.0427558	−	0.999086i	$-0.513614\pi$
$811$	−27.6043	−	17.7402i	−0.969317	−	0.622942i	−0.926562	+	0.376143i	$0.877250\pi$
$812$	10.2419	−	22.4267i	0.359421	−	0.787021i
$813$	9.04179	−	10.4348i	0.317109	−	0.365964i
$814$	3.78292	−	26.3108i	0.132591	−	0.922193i
$815$		0			0
$816$	2.03387	+	0.597197i	0.0711996	+	0.0209061i
$817$	−30.1779	−	8.86103i	−1.05579	−	0.310008i
$818$	−16.0768	−	35.2033i	−0.562112	−	1.23085i
$819$	0.549107	−	3.81912i	0.0191873	−	0.133451i
$820$		0			0
$821$	−10.2757	+	22.5006i	−0.358624	+	0.785278i	0.641215	+	0.767361i	$0.278431\pi$
$821$	−10.2757	+	22.5006i	−0.358624	+	0.785278i	−0.999839	+	0.0179165i	$0.994297\pi$
$822$	22.0979	+	14.2014i	0.770751	+	0.495332i
$823$	4.27087	+	29.7046i	0.148873	+	1.03544i	0.918068	+	0.396422i	$0.129748\pi$
$823$	4.27087	+	29.7046i	0.148873	+	1.03544i	−0.769195	+	0.639014i	$0.779343\pi$
$824$	2.96120	−	1.90305i	0.103158	−	0.0662957i
$825$		0			0
$826$	48.1241	−	14.1305i	1.67445	−	0.491663i
$827$	3.93999			0.137007			0.0685034	−	0.997651i	$-0.478178\pi$
$827$	3.93999			0.137007			0.0685034	+	0.997651i	$0.478178\pi$
$828$	−15.5827	+	18.8756i	−0.541536	+	0.655971i
$829$	0.931445			0.0323504			0.0161752	−	0.999869i	$-0.494851\pi$
$829$	0.931445			0.0323504			0.0161752	+	0.999869i	$0.494851\pi$
$830$		0			0
$831$	−25.6033	−	29.5478i	−0.888169	−	1.02500i
$832$	−14.4124	+	9.26227i	−0.499659	+	0.321112i
$833$	−1.75801	−	12.2272i	−0.0609115	−	0.423649i
$834$	−13.7592	−	8.84249i	−0.476442	−	0.306190i
$835$		0			0
$836$	−16.6671	+	19.2348i	−0.576443	+	0.665251i
$837$	−6.57637	+	45.7397i	−0.227313	+	1.58099i
$838$	−30.3024	−	66.3530i	−1.04678	−	2.29213i
$839$	20.2099	+	5.93417i	0.697724	+	0.204870i	0.611313	−	0.791389i	$-0.290642\pi$
$839$	20.2099	+	5.93417i	0.697724	+	0.204870i	0.0864117	+	0.996260i	$0.472460\pi$
$840$		0			0
$841$	−5.62689	−	12.3212i	−0.194031	−	0.424868i
$842$	3.35678	−	23.3469i	0.115682	−	0.804588i
$843$	2.56604	−	2.96136i	0.0883790	−	0.101995i
$844$	28.2777	−	61.9195i	0.973358	−	2.13136i
$845$		0			0
$846$	1.43698	+	9.99443i	0.0494044	+	0.343615i
$847$	−3.31545	+	2.13071i	−0.113920	+	0.0732121i
$848$	−1.79168	−	2.06771i	−0.0615267	−	0.0710056i
$849$	22.4385	−	6.58853i	0.770087	−	0.226118i
$850$		0			0
$851$	−17.6085	+	5.63023i	−0.603611	+	0.193002i
$852$	9.78990			0.335396
$853$	−21.9800	+	6.45390i	−0.752580	+	0.220977i	−0.635453	−	0.772140i	$-0.719187\pi$
$853$	−21.9800	+	6.45390i	−0.752580	+	0.220977i	−0.117127	+	0.993117i	$0.537368\pi$
$854$	41.4058	+	47.7848i	1.41688	+	1.63516i
$855$		0			0
$856$	0.447453	+	3.11210i	0.0152936	+	0.106370i
$857$	−26.6687	−	17.1389i	−0.910986	−	0.585455i	−0.000956853	−	1.00000i	$-0.500305\pi$
$857$	−26.6687	−	17.1389i	−0.910986	−	0.585455i	−0.910029	+	0.414544i	$0.863941\pi$
$858$	4.68610	−	10.2611i	0.159981	−	0.350309i
$859$	−5.16659	+	5.96256i	−0.176282	+	0.203440i	−0.837014	−	0.547182i	$-0.815701\pi$
$859$	−5.16659	+	5.96256i	−0.176282	+	0.203440i	0.660732	+	0.750622i	$0.270246\pi$
$860$		0			0
$861$	−11.1282	−	24.3674i	−0.379249	−	0.830440i
$862$	−37.6821	−	11.0645i	−1.28346	−	0.376857i
$863$	41.1640	+	12.0868i	1.40124	+	0.411441i	0.893109	−	0.449840i	$-0.148519\pi$
$863$	41.1640	+	12.0868i	1.40124	+	0.411441i	0.508129	+	0.861281i	$0.330337\pi$
$864$	−11.5811	−	25.3592i	−0.393998	−	0.862736i
$865$		0			0
$866$	22.4624	−	25.9229i	0.763302	−	0.880898i
$867$	−2.22515	+	4.87239i	−0.0755699	+	0.165475i
$868$	−44.3701	−	28.5149i	−1.50602	−	0.967859i
$869$	−1.80867	−	12.5795i	−0.0613548	−	0.426732i
$870$		0			0
$871$	−0.389199	−	0.449159i	−0.0131875	−	0.0152192i
$872$	30.1813	−	8.86204i	1.02207	−	0.300106i
$873$	−15.9606			−0.540184
$874$	27.3255	+	7.31971i	0.924297	+	0.247593i
$875$		0			0
$876$	13.4544	−	3.95057i	0.454583	−	0.133478i
$877$	37.2418	+	42.9793i	1.25757	+	1.45131i	0.839931	+	0.542693i	$0.182595\pi$
$877$	37.2418	+	42.9793i	1.25757	+	1.45131i	0.417634	+	0.908615i	$0.362859\pi$
$878$	46.9115	−	30.1482i	1.58319	−	1.01745i
$879$	1.55422	+	10.8098i	0.0524225	+	0.364606i
$880$		0			0
$881$	−0.569858	+	1.24781i	−0.0191990	+	0.0420399i	−0.918989	−	0.394284i	$-0.870993\pi$
$881$	−0.569858	+	1.24781i	−0.0191990	+	0.0420399i	0.899790	+	0.436324i	$0.143720\pi$
$882$	8.04541	−	9.28490i	0.270903	−	0.312639i
$883$	−7.47159	+	51.9661i	−0.251439	+	1.74880i	0.338149	+	0.941093i	$0.390199\pi$
$883$	−7.47159	+	51.9661i	−0.251439	+	1.74880i	−0.589588	+	0.807704i	$0.700710\pi$
$884$	−6.64082	−	14.5414i	−0.223355	−	0.489079i
$885$		0			0
$886$	−60.4651	−	17.7542i	−2.03136	−	0.596463i
$887$	−6.65115	−	14.5640i	−0.223324	−	0.489011i	0.764493	−	0.644632i	$-0.222989\pi$
$887$	−6.65115	−	14.5640i	−0.223324	−	0.489011i	−0.987817	+	0.155621i	$0.950262\pi$
$888$	−2.06821	+	14.3847i	−0.0694045	+	0.482719i
$889$	13.7898	−	15.9143i	0.462495	−	0.533747i
$890$		0			0
$891$	5.24650	+	3.37172i	0.175764	+	0.112957i
$892$	−6.53493	−	45.4514i	−0.218806	−	1.52183i
$893$	6.14283	−	3.94776i	0.205562	−	0.132107i
$894$	22.0500	+	25.4470i	0.737461	+	0.851076i
$895$		0			0
$896$	36.0878			1.20561
$897$	−7.84310	+	0.187268i	−0.261873	+	0.00625270i
$898$	14.4345			0.481685
$899$	31.7226	−	9.31461i	1.05801	−	0.310660i
$900$		0			0
$901$	−16.5912	+	10.6625i	−0.552733	+	0.355220i
$902$	11.5460	+	80.3043i	0.384440	+	2.67384i
$903$	−23.6092	−	15.1727i	−0.785664	−	0.504916i
$904$	−14.3350	+	31.3893i	−0.476775	+	1.04399i
$905$		0			0
$906$	1.69856	−	11.8137i	0.0564309	−	0.392485i
$907$	−11.7834	−	25.8020i	−0.391261	−	0.856742i	−0.998082	−	0.0619038i	$-0.980283\pi$
$907$	−11.7834	−	25.8020i	−0.391261	−	0.856742i	0.606821	−	0.794838i	$-0.292444\pi$
$908$	−17.0096	−	4.99447i	−0.564483	−	0.165747i
$909$	−7.36875	−	2.16366i	−0.244406	−	0.0717641i
$910$		0			0
$911$	−1.18038	+	8.20972i	−0.0391077	+	0.272000i	−0.999988	−	0.00496496i	$-0.998420\pi$
$911$	−1.18038	+	8.20972i	−0.0391077	+	0.272000i	0.960880	+	0.276965i	$0.0893287\pi$
$912$	0.998385	−	1.15220i	0.0330598	−	0.0381531i
$913$	2.63328	−	5.76607i	0.0871487	−	0.190829i
$914$	32.5347	+	20.9088i	1.07615	+	0.691602i
$915$		0			0
$916$	−25.6702	+	16.4972i	−0.848166	+	0.545083i
$917$	−15.9312	−	18.3856i	−0.526095	−	0.607146i
$918$	43.2379	−	12.6958i	1.42706	−	0.419024i
$919$	−18.3970			−0.606862			−0.303431	−	0.952853i	$-0.598132\pi$
$919$	−18.3970			−0.606862			−0.303431	+	0.952853i	$0.598132\pi$
$920$		0			0
$921$	0.644148			0.0212254
$922$	−46.2344	+	13.5756i	−1.52265	+	0.447090i
$923$	−2.12864	−	2.45658i	−0.0700650	−	0.0808593i
$924$	−19.1049	+	12.2780i	−0.628504	+	0.403915i
$925$		0			0
$926$	20.1491	+	12.9491i	0.662142	+	0.425533i
$927$	0.718685	−	1.57370i	0.0236047	−	0.0516871i
$928$	−13.0620	+	15.0743i	−0.428781	+	0.494839i
$929$	6.34797	−	44.1511i	0.208270	−	1.44855i	−0.570529	−	0.821277i	$-0.693262\pi$
$929$	6.34797	−	44.1511i	0.208270	−	1.44855i	0.778799	−	0.627273i	$-0.215829\pi$
$930$		0			0
$931$	−8.52475	−	2.50309i	−0.279387	−	0.0820355i
$932$	−56.2856	−	16.5269i	−1.84369	−	0.541358i
$933$	6.98204	+	15.2885i	0.228582	+	0.500524i
$934$	5.69279	−	39.5942i	0.186274	−	1.29556i
$935$		0			0
$936$	2.65396	−	5.81135i	0.0867473	−	0.189950i
$937$	−16.3838	−	10.5292i	−0.535235	−	0.343975i	0.244937	−	0.969539i	$-0.421233\pi$
$937$	−16.3838	−	10.5292i	−0.535235	−	0.343975i	−0.780173	+	0.625564i	$0.784869\pi$
$938$	0.272134	+	1.89274i	0.00888550	+	0.0618000i
$939$	−1.32363	+	0.850645i	−0.0431950	+	0.0277597i
$940$		0			0
$941$	−9.14286	+	2.68458i	−0.298049	+	0.0875150i	−0.427338	−	0.904092i	$-0.640549\pi$
$941$	−9.14286	+	2.68458i	−0.298049	+	0.0875150i	0.129289	+	0.991607i	$0.458730\pi$
$942$	59.5823			1.94130
$943$	46.7253	−	31.6295i	1.52158	−	1.03000i
$944$	5.69344			0.185306
$945$		0			0
$946$	55.6597	+	64.2348i	1.80965	+	2.08845i
$947$	20.6651	−	13.2806i	0.671525	−	0.431563i	−0.159950	−	0.987125i	$-0.551133\pi$
$947$	20.6651	−	13.2806i	0.671525	−	0.431563i	0.831475	+	0.555562i	$0.187497\pi$
$948$	2.46082	+	17.1154i	0.0799239	+	0.555883i
$949$	−3.91674	−	2.51714i	−0.127143	−	0.0817097i
$950$		0			0
$951$	12.5874	−	14.5267i	0.408176	−	0.471060i
$952$	−2.94134	+	20.4574i	−0.0953293	+	0.663030i
$953$	9.28285	+	20.3266i	0.300701	+	0.658443i	0.998315	−	0.0580306i	$-0.0184821\pi$
$953$	9.28285	+	20.3266i	0.300701	+	0.658443i	−0.697614	+	0.716474i	$0.745755\pi$
$954$	−18.8201	−	5.52607i	−0.609322	−	0.178913i
$955$		0			0
$956$	26.5560	+	58.1496i	0.858884	+	1.88069i
$957$	2.02596	−	14.0909i	0.0654901	−	0.455494i
$958$	16.6928	−	19.2645i	0.539319	−	0.622407i
$959$	−7.29405	+	15.9717i	−0.235537	+	0.515754i
$960$		0			0
$961$	−5.65390	−	39.3237i	−0.182384	−	1.26851i
$962$	10.1019	−	6.49207i	0.325697	−	0.209313i
$963$	1.01196	+	1.16786i	0.0326099	+	0.0376338i
$964$	−24.4928	+	7.19173i	−0.788860	+	0.231630i
$965$		0			0
$966$	21.5545	+	13.1360i	0.693506	+	0.422645i
$967$	−18.2677			−0.587448			−0.293724	−	0.955890i	$-0.594895\pi$
$967$	−18.2677			−0.587448			−0.293724	+	0.955890i	$0.594895\pi$
$968$	−6.26127	+	1.83848i	−0.201245	+	0.0590908i
$969$	−7.19676	−	8.30550i	−0.231193	−	0.266811i
$970$		0			0
$971$	−5.64215	−	39.2420i	−0.181065	−	1.25934i	−0.854250	−	0.519862i	$-0.825983\pi$
$971$	−5.64215	−	39.2420i	−0.181065	−	1.25934i	0.673185	−	0.739474i	$-0.264926\pi$
$972$	39.2273	+	25.2098i	1.25822	+	0.808606i
$973$	4.54162	−	9.94476i	0.145598	−	0.318815i
$974$	−36.5726	+	42.2070i	−1.17186	+	1.35240i
$975$		0			0
$976$	2.98159	+	6.52877i	0.0954384	+	0.208981i
$977$	−41.5735	−	12.2071i	−1.33005	−	0.390539i	−0.461943	−	0.886910i	$-0.652847\pi$
$977$	−41.5735	−	12.2071i	−1.33005	−	0.390539i	−0.868110	+	0.496371i	$0.834666\pi$
$978$	24.9197	+	7.31709i	0.796845	+	0.233975i
$979$	−11.0398	−	24.1737i	−0.352833	−	0.772596i
$980$		0			0
$981$	10.1242	−	11.6840i	0.323241	−	0.373040i
$982$	−20.4743	+	44.8325i	−0.653361	+	1.43066i
$983$	−10.7669	−	6.91945i	−0.343410	−	0.220696i	0.357555	−	0.933892i	$-0.383611\pi$
$983$	−10.7669	−	6.91945i	−0.343410	−	0.220696i	−0.700965	+	0.713196i	$0.747247\pi$
$984$	−6.31247	−	43.9042i	−0.201234	−	1.39961i
$985$		0			0
$986$	−21.1136	−	24.3664i	−0.672396	−	0.775986i
$987$	6.25159	−	1.83563i	0.198990	−	0.0584288i
$988$	−11.4976			−0.365788
$989$	23.2654	−	54.3408i	0.739798	−	1.72794i
$990$		0			0
$991$	−13.4961	+	3.96282i	−0.428718	+	0.125883i	−0.488971	−	0.872300i	$-0.662628\pi$
$991$	−13.4961	+	3.96282i	−0.428718	+	0.125883i	0.0602526	+	0.998183i	$0.480809\pi$
$992$	27.9430	+	32.2480i	0.887192	+	1.02387i
$993$	−13.3752	+	8.59573i	−0.424449	+	0.272777i
$994$	1.48838	+	10.3519i	0.0472085	+	0.328343i
$995$		0			0
$996$	−3.58277	+	7.84517i	−0.113524	+	0.248584i
$997$	25.0620	−	28.9230i	0.793720	−	0.916002i	−0.204299	−	0.978909i	$-0.565492\pi$
$997$	25.0620	−	28.9230i	0.793720	−	0.916002i	0.998019	+	0.0629065i	$0.0200370\pi$
$998$	6.99130	−	48.6256i	0.221306	−	1.53922i
$999$	8.79869	+	19.2665i	0.278378	+	0.609564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.k.g.101.9		100
5.2	odd	4		115.2.j.a.9.9	yes	100
5.3	odd	4		115.2.j.a.9.2	✓	100
5.4	even	2	inner	575.2.k.g.101.2		100
23.18	even	11	inner	575.2.k.g.501.9		100
115.18	odd	44		115.2.j.a.64.9	yes	100
115.64	even	22	inner	575.2.k.g.501.2		100
115.87	odd	44		115.2.j.a.64.2	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.j.a.9.2	✓	100	5.3	odd	4
115.2.j.a.9.9	yes	100	5.2	odd	4
115.2.j.a.64.2	yes	100	115.87	odd	44
115.2.j.a.64.9	yes	100	115.18	odd	44
575.2.k.g.101.2		100	5.4	even	2	inner
575.2.k.g.101.9		100	1.1	even	1	trivial
575.2.k.g.501.2		100	115.64	even	22	inner
575.2.k.g.501.9		100	23.18	even	11	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.k (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.21797 - 0.651256i) q^{2} +(-0.794936 - 0.917405i) q^{3} +(2.81277 - 1.80765i) q^{4} +(-2.36061 - 1.51707i) q^{6} +(0.779189 - 1.70619i) q^{7} +(2.03383 - 2.34716i) q^{8} +(0.217236 - 1.51091i) q^{9} +O(q^{10})\)	\(q+(2.21797 - 0.651256i) q^{2} +(-0.794936 - 0.917405i) q^{3} +(2.81277 - 1.80765i) q^{4} +(-2.36061 - 1.51707i) q^{6} +(0.779189 - 1.70619i) q^{7} +(2.03383 - 2.34716i) q^{8} +(0.217236 - 1.51091i) q^{9} +(2.86226 + 0.840435i) q^{11} +(-3.89432 - 1.14348i) q^{12} +(0.559818 + 1.22583i) q^{13} +(0.617057 - 4.29173i) q^{14} +(0.204462 - 0.447708i) q^{16} +(-2.98466 - 1.91813i) q^{17} +(-0.502165 - 3.49263i) q^{18} +(-2.14666 + 1.37958i) q^{19} +(-2.18467 + 0.641476i) q^{21} +6.89575 q^{22} +(-2.09582 - 4.31364i) q^{23} -3.77006 q^{24} +(2.03999 + 2.35427i) q^{26} +(-4.62240 + 2.97063i) q^{27} +(-0.892519 - 6.20761i) q^{28} +(3.30718 + 2.12540i) q^{29} +(5.50738 - 6.35585i) q^{31} +(-0.722069 + 5.02210i) q^{32} +(-1.50429 - 3.29394i) q^{33} +(-7.86909 - 2.31057i) q^{34} +(-2.12017 - 4.64252i) q^{36} +(0.548587 - 3.81551i) q^{37} +(-3.86278 + 4.45789i) q^{38} +(0.679563 - 1.48803i) q^{39} +(1.67437 + 11.6455i) q^{41} +(-4.42777 + 2.84556i) q^{42} +(8.07159 + 9.31512i) q^{43} +(9.57008 - 2.81003i) q^{44} +(-7.45777 - 8.20263i) q^{46} -2.86157 q^{47} +(-0.573263 + 0.168325i) q^{48} +(2.28009 + 2.63136i) q^{49} +(0.612917 + 4.26293i) q^{51} +(3.79051 + 2.43601i) q^{52} +(2.30922 - 5.05648i) q^{53} +(-8.31771 + 9.59915i) q^{54} +(-2.41996 - 5.29898i) q^{56} +(2.97209 + 0.872683i) q^{57} +(8.71943 + 2.56025i) q^{58} +(4.80538 + 10.5223i) q^{59} +(-9.54961 + 11.0208i) q^{61} +(8.07593 - 17.6838i) q^{62} +(-2.40862 - 1.54793i) q^{63} +(1.80923 + 12.5835i) q^{64} +(-5.48168 - 6.32620i) q^{66} +(-0.423155 + 0.124250i) q^{67} -11.8625 q^{68} +(-2.29131 + 5.35179i) q^{69} +(-2.31436 + 0.679556i) q^{71} +(-3.10453 - 3.58282i) q^{72} +(-2.90643 + 1.86785i) q^{73} +(-1.26812 - 8.81997i) q^{74} +(-3.54426 + 7.76085i) q^{76} +(3.66418 - 4.22869i) q^{77} +(0.538161 - 3.74299i) q^{78} +(-1.76980 - 3.87531i) q^{79} +(2.00594 + 0.588996i) q^{81} +(11.2979 + 24.7389i) q^{82} +(0.302411 - 2.10331i) q^{83} +(-4.98539 + 5.75345i) q^{84} +(23.9691 + 15.4040i) q^{86} +(-0.679148 - 4.72358i) q^{87} +(7.79399 - 5.00889i) q^{88} +(-5.83391 - 6.73270i) q^{89} +2.52770 q^{91} +(-13.6926 - 8.34474i) q^{92} -10.2089 q^{93} +(-6.34689 + 1.86362i) q^{94} +(5.18130 - 3.32982i) q^{96} +(-1.48805 - 10.3496i) q^{97} +(6.77087 + 4.35138i) q^{98} +(1.89161 - 4.14204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9}+O(q^{10}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9	\( 100 q + 14 q^{4} - 18 q^{6} + 12 q^{9} - 26 q^{11} + 26 q^{14} - 18 q^{16} + 14 q^{19} - 22 q^{21} + 68 q^{24} - 42 q^{26} + 24 q^{29} - 12 q^{31} - 8 q^{34} - 10 q^{36} - 14 q^{39} + 8 q^{41} - 166 q^{44} - 18 q^{46} - 32 q^{49} - 22 q^{51} - 116 q^{54} - 116 q^{56} - 50 q^{59} - 38 q^{61} - 10 q^{64} - 28 q^{66} - 80 q^{69} - 110 q^{71} - 22 q^{74} + 4 q^{76} - 42 q^{79} + 204 q^{81} - 56 q^{84} + 132 q^{86} + 66 q^{89} + 76 q^{91} + 70 q^{94} + 236 q^{96} + 60 q^{99}+O(q^{100}) \) 100 * q + 14 * q^4 - 18 * q^6 + 12 * q^9 - 26 * q^11 + 26 * q^14 - 18 * q^16 + 14 * q^19 - 22 * q^21 + 68 * q^24 - 42 * q^26 + 24 * q^29 - 12 * q^31 - 8 * q^34 - 10 * q^36 - 14 * q^39 + 8 * q^41 - 166 * q^44 - 18 * q^46 - 32 * q^49 - 22 * q^51 - 116 * q^54 - 116 * q^56 - 50 * q^59 - 38 * q^61 - 10 * q^64 - 28 * q^66 - 80 * q^69 - 110 * q^71 - 22 * q^74 + 4 * q^76 - 42 * q^79 + 204 * q^81 - 56 * q^84 + 132 * q^86 + 66 * q^89 + 76 * q^91 + 70 * q^94 + 236 * q^96 + 60 * q^99

Introduction

L-functions

Modular forms

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Database

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