LMFDB - Embedded newform 361.2.e.m.234.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] 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("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,24,0,0,0,30,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			234.3
Character	$\chi$	$=$	361.234
Dual form			361.2.e.m.54.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.900539 - 0.755642i) q^{2} +(1.10467 + 0.402069i) q^{3} +(-0.107320 + 0.608645i) q^{4} +(0.214641 + 1.21729i) q^{5} +(1.29862 - 0.472660i) q^{6} +(2.11803 - 3.66854i) q^{7} +(1.53884 + 2.66535i) q^{8} +(-1.23949 - 1.04005i) q^{9} +(1.11313 + 0.934025i) q^{10} +(1.80902 + 3.13331i) q^{11} +(-0.363271 + 0.629204i) q^{12} +(-2.89208 + 1.05263i) q^{13} +(-0.864733 - 4.90414i) q^{14} +(-0.252326 + 1.43101i) q^{15} +(2.23832 + 0.814680i) q^{16} +(1.89377 - 1.58906i) q^{17} -1.90211 q^{18} -0.763932 q^{20} +(3.81475 - 3.20095i) q^{21} +(3.99675 + 1.45470i) q^{22} +(-0.454617 + 2.57826i) q^{23} +(0.628265 + 3.56307i) q^{24} +(3.26274 - 1.18754i) q^{25} +(-1.80902 + 3.13331i) q^{26} +(-2.71441 - 4.70150i) q^{27} +(2.00553 + 1.68284i) q^{28} +(-2.01367 - 1.68967i) q^{29} +(0.854102 + 1.47935i) q^{30} +(0.587785 - 1.01807i) q^{31} +(-3.15285 + 1.14755i) q^{32} +(0.738570 + 4.18864i) q^{33} +(0.504651 - 2.86202i) q^{34} +(4.92029 + 1.79084i) q^{35} +(0.766044 - 0.642788i) q^{36} -6.43288 q^{37} -3.61803 q^{39} +(-2.91421 + 2.44531i) q^{40} +(-8.67623 - 3.15789i) q^{41} +(1.01655 - 5.76517i) q^{42} +(-1.09854 - 6.23013i) q^{43} +(-2.10122 + 0.764780i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.53884 + 2.66535i) q^{46} +(-1.93646 - 1.62488i) q^{47} +(2.14505 + 1.79991i) q^{48} +(-5.47214 - 9.47802i) q^{49} +(2.04087 - 3.53489i) q^{50} +(2.73091 - 0.993969i) q^{51} +(-0.330298 - 1.87322i) q^{52} +(0.0779729 - 0.442206i) q^{53} +(-5.99709 - 2.18276i) q^{54} +(-3.42585 + 2.87463i) q^{55} +13.0373 q^{56} -3.09017 q^{58} +(-2.14505 + 1.79991i) q^{59} +(-0.843897 - 0.307153i) q^{60} +(-0.0916626 + 0.519845i) q^{61} +(-0.239976 - 1.36097i) q^{62} +(-6.44075 + 2.34424i) q^{63} +(-4.35410 + 7.54153i) q^{64} +(-1.90211 - 3.29456i) q^{65} +(3.83022 + 3.21394i) q^{66} +(-0.131387 - 0.110247i) q^{67} +(0.763932 + 1.32317i) q^{68} +(-1.53884 + 2.66535i) q^{69} +(5.78415 - 2.10526i) q^{70} +(2.10795 + 11.9548i) q^{71} +(0.864733 - 4.90414i) q^{72} +(-8.45723 - 3.07818i) q^{73} +(-5.79306 + 4.86096i) q^{74} +4.08174 q^{75} +15.3262 q^{77} +(-3.25818 + 2.73394i) q^{78} +(7.14961 + 2.60224i) q^{79} +(-0.511267 + 2.89954i) q^{80} +(-0.265311 - 1.50465i) q^{81} +(-10.1995 + 3.71232i) q^{82} +(-0.618034 + 1.07047i) q^{83} +(1.53884 + 2.66535i) q^{84} +(2.34082 + 1.96418i) q^{85} +(-5.69703 - 4.78037i) q^{86} +(-1.54508 - 2.67617i) q^{87} +(-5.56758 + 9.64333i) q^{88} +(16.6697 - 6.06729i) q^{89} +(-0.408271 - 2.31542i) q^{90} +(-2.26390 + 12.8392i) q^{91} +(-1.52045 - 0.553400i) q^{92} +(1.05865 - 0.888311i) q^{93} -2.97168 q^{94} -3.94427 q^{96} +(-12.0008 + 10.0699i) q^{97} +(-12.0899 - 4.40035i) q^{98} +(1.01655 - 5.76517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) $ 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.900539	−	0.755642i	0.636777	−	0.534320i	−0.266249	−	0.963904i	$-0.585784\pi$
$2$	0.900539	−	0.755642i	0.636777	−	0.534320i	0.903027	+	0.429585i	$0.141340\pi$
$3$	1.10467	+	0.402069i	0.637784	+	0.232135i	0.640616	−	0.767861i	$-0.278679\pi$
$3$	1.10467	+	0.402069i	0.637784	+	0.232135i	−0.00283156	+	0.999996i	$0.500901\pi$
$4$	−0.107320	+	0.608645i	−0.0536602	+	0.304322i
$5$	0.214641	+	1.21729i	0.0959904	+	0.544388i	0.994439	+	0.105311i	$0.0335837\pi$
$5$	0.214641	+	1.21729i	0.0959904	+	0.544388i	−0.898449	+	0.439078i	$0.855305\pi$
$6$	1.29862	−	0.472660i	0.530161	−	0.192963i
$7$	2.11803	−	3.66854i	0.800542	−	1.38658i	−0.118718	−	0.992928i	$-0.537879\pi$
$7$	2.11803	−	3.66854i	0.800542	−	1.38658i	0.919260	−	0.393651i	$-0.128788\pi$
$8$	1.53884	+	2.66535i	0.544063	+	0.942344i
$9$	−1.23949	−	1.04005i	−0.413162	−	0.346684i
$10$	1.11313	+	0.934025i	0.352002	+	0.295365i
$11$	1.80902	+	3.13331i	0.545439	+	0.944728i	0.998579	+	0.0532889i	$0.0169704\pi$
$11$	1.80902	+	3.13331i	0.545439	+	0.944728i	−0.453140	+	0.891439i	$0.649696\pi$
$12$	−0.363271	+	0.629204i	−0.104867	+	0.181636i
$13$	−2.89208	+	1.05263i	−0.802118	+	0.291947i	−0.710364	−	0.703835i	$-0.751470\pi$
$13$	−2.89208	+	1.05263i	−0.802118	+	0.291947i	−0.0917540	+	0.995782i	$0.529247\pi$
$14$	−0.864733	−	4.90414i	−0.231110	−	1.31069i
$15$	−0.252326	+	1.43101i	−0.0651502	+	0.369485i
$16$	2.23832	+	0.814680i	0.559579	+	0.203670i
$17$	1.89377	−	1.58906i	0.459306	−	0.385403i	−0.383570	−	0.923512i	$-0.625305\pi$
$17$	1.89377	−	1.58906i	0.459306	−	0.385403i	0.842875	+	0.538109i	$0.180861\pi$
$18$	−1.90211			−0.448332
$19$		0			0
$19$		0			0
$20$	−0.763932			−0.170820
$21$	3.81475	−	3.20095i	0.832446	−	0.698505i
$22$	3.99675	+	1.45470i	0.852110	+	0.310143i
$23$	−0.454617	+	2.57826i	−0.0947942	+	0.537604i	0.900016	+	0.435857i	$0.143555\pi$
$23$	−0.454617	+	2.57826i	−0.0947942	+	0.537604i	−0.994810	+	0.101748i	$0.967557\pi$
$24$	0.628265	+	3.56307i	0.128244	+	0.727308i
$25$	3.26274	−	1.18754i	0.652548	−	0.237508i
$26$	−1.80902	+	3.13331i	−0.354777	+	0.614493i
$27$	−2.71441	−	4.70150i	−0.522389	−	0.904804i
$28$	2.00553	+	1.68284i	0.379010	+	0.318027i
$29$	−2.01367	−	1.68967i	−0.373929	−	0.313763i	0.436385	−	0.899760i	$-0.356259\pi$
$29$	−2.01367	−	1.68967i	−0.373929	−	0.313763i	−0.810313	+	0.585997i	$0.800703\pi$
$30$	0.854102	+	1.47935i	0.155937	+	0.270091i
$31$	0.587785	−	1.01807i	0.105569	−	0.182851i	−0.808401	−	0.588632i	$-0.799667\pi$
$31$	0.587785	−	1.01807i	0.105569	−	0.182851i	0.913971	+	0.405780i	$0.133000\pi$
$32$	−3.15285	+	1.14755i	−0.557351	+	0.202859i
$33$	0.738570	+	4.18864i	0.128569	+	0.729148i
$34$	0.504651	−	2.86202i	0.0865470	−	0.490832i
$35$	4.92029	+	1.79084i	0.831682	+	0.302707i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−6.43288			−1.05756			−0.528780	−	0.848759i	$-0.677350\pi$
$37$	−6.43288			−1.05756			−0.528780	+	0.848759i	$0.677350\pi$
$38$		0			0
$39$	−3.61803			−0.579349
$40$	−2.91421	+	2.44531i	−0.460776	+	0.386637i
$41$	−8.67623	−	3.15789i	−1.35500	−	0.493179i	−0.440495	−	0.897755i	$-0.645197\pi$
$41$	−8.67623	−	3.15789i	−1.35500	−	0.493179i	−0.914505	+	0.404576i	$0.867419\pi$
$42$	1.01655	−	5.76517i	0.156858	−	0.889584i
$43$	−1.09854	−	6.23013i	−0.167526	−	0.950086i	−0.946422	−	0.322933i	$-0.895331\pi$
$43$	−1.09854	−	6.23013i	−0.167526	−	0.950086i	0.778896	−	0.627153i	$-0.215780\pi$
$44$	−2.10122	+	0.764780i	−0.316770	+	0.115295i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$	1.53884	+	2.66535i	0.226890	+	0.392985i
$47$	−1.93646	−	1.62488i	−0.282461	−	0.237013i	0.490538	−	0.871420i	$-0.336800\pi$
$47$	−1.93646	−	1.62488i	−0.282461	−	0.237013i	−0.773000	+	0.634406i	$0.781245\pi$
$48$	2.14505	+	1.79991i	0.309612	+	0.259795i
$49$	−5.47214	−	9.47802i	−0.781734	−	1.35400i
$50$	2.04087	−	3.53489i	0.288623	−	0.499909i
$51$	2.73091	−	0.993969i	0.382403	−	0.139183i
$52$	−0.330298	−	1.87322i	−0.0458042	−	0.259768i
$53$	0.0779729	−	0.442206i	0.0107104	−	0.0607417i	−0.978984	−	0.203936i	$-0.934626\pi$
$53$	0.0779729	−	0.442206i	0.0107104	−	0.0607417i	0.989695	+	0.143195i	$0.0457375\pi$
$54$	−5.99709	−	2.18276i	−0.816100	−	0.297036i
$55$	−3.42585	+	2.87463i	−0.461942	+	0.387616i
$56$	13.0373			1.74218
$57$		0			0
$58$	−3.09017			−0.405759
$59$	−2.14505	+	1.79991i	−0.279262	+	0.234329i	−0.771650	−	0.636047i	$-0.780568\pi$
$59$	−2.14505	+	1.79991i	−0.279262	+	0.234329i	0.492388	+	0.870376i	$0.336124\pi$
$60$	−0.843897	−	0.307153i	−0.108947	−	0.0396533i
$61$	−0.0916626	+	0.519845i	−0.0117362	+	0.0665593i	−0.990113	−	0.140269i	$-0.955203\pi$
$61$	−0.0916626	+	0.519845i	−0.0117362	+	0.0665593i	0.978377	+	0.206829i	$0.0663143\pi$
$62$	−0.239976	−	1.36097i	−0.0304770	−	0.172843i
$63$	−6.44075	+	2.34424i	−0.811458	+	0.295347i
$64$	−4.35410	+	7.54153i	−0.544263	+	0.942691i
$65$	−1.90211	−	3.29456i	−0.235928	−	0.408639i
$66$	3.83022	+	3.21394i	0.471468	+	0.395608i
$67$	−0.131387	−	0.110247i	−0.0160515	−	0.0134688i	0.634727	−	0.772737i	$-0.281113\pi$
$67$	−0.131387	−	0.110247i	−0.0160515	−	0.0134688i	−0.650778	+	0.759268i	$0.725557\pi$
$68$	0.763932	+	1.32317i	0.0926404	+	0.160458i
$69$	−1.53884	+	2.66535i	−0.185255	+	0.320871i
$70$	5.78415	−	2.10526i	0.691339	−	0.251627i
$71$	2.10795	+	11.9548i	0.250168	+	1.41877i	0.808178	+	0.588939i	$0.200454\pi$
$71$	2.10795	+	11.9548i	0.250168	+	1.41877i	−0.558009	+	0.829835i	$0.688435\pi$
$72$	0.864733	−	4.90414i	0.101910	−	0.577959i
$73$	−8.45723	−	3.07818i	−0.989844	−	0.360274i	−0.204184	−	0.978932i	$-0.565454\pi$
$73$	−8.45723	−	3.07818i	−0.989844	−	0.360274i	−0.785660	+	0.618659i	$0.787676\pi$
$74$	−5.79306	+	4.86096i	−0.673430	+	0.565075i
$75$	4.08174			0.471319
$76$		0			0
$77$	15.3262			1.74659
$78$	−3.25818	+	2.73394i	−0.368916	+	0.309558i
$79$	7.14961	+	2.60224i	0.804394	+	0.292775i	0.711306	−	0.702883i	$-0.248104\pi$
$79$	7.14961	+	2.60224i	0.804394	+	0.292775i	0.0930877	+	0.995658i	$0.470326\pi$
$80$	−0.511267	+	2.89954i	−0.0571614	+	0.324179i
$81$	−0.265311	−	1.50465i	−0.0294790	−	0.167184i
$82$	−10.1995	+	3.71232i	−1.12635	+	0.409957i
$83$	−0.618034	+	1.07047i	−0.0678380	+	0.117499i	−0.897949	−	0.440099i	$-0.854943\pi$
$83$	−0.618034	+	1.07047i	−0.0678380	+	0.117499i	0.830111	+	0.557598i	$0.188277\pi$
$84$	1.53884	+	2.66535i	0.167901	+	0.290814i
$85$	2.34082	+	1.96418i	0.253898	+	0.213046i
$86$	−5.69703	−	4.78037i	−0.614326	−	0.515481i
$87$	−1.54508	−	2.67617i	−0.165650	−	0.286915i
$88$	−5.56758	+	9.64333i	−0.593506	+	1.02798i
$89$	16.6697	−	6.06729i	1.76699	−	0.643131i	0.766989	−	0.641660i	$-0.221754\pi$
$89$	16.6697	−	6.06729i	1.76699	−	0.643131i	0.999999	−	0.00147104i	$-0.000468248\pi$
$90$	−0.408271	−	2.31542i	−0.0430356	−	0.244067i
$91$	−2.26390	+	12.8392i	−0.237321	+	1.34592i
$92$	−1.52045	−	0.553400i	−0.158518	−	0.0576960i
$93$	1.05865	−	0.888311i	0.109777	−	0.0921135i
$94$	−2.97168			−0.306506
$95$		0			0
$96$	−3.94427			−0.402561
$97$	−12.0008	+	10.0699i	−1.21850	+	1.02244i	−0.219595	+	0.975591i	$0.570473\pi$
$97$	−12.0008	+	10.0699i	−1.21850	+	1.02244i	−0.998902	+	0.0468489i	$0.985082\pi$
$98$	−12.0899	−	4.40035i	−1.22126	−	0.444502i
$99$	1.01655	−	5.76517i	0.102168	−	0.579421i
$100$	0.372631	+	2.11330i	0.0372631	+	0.211330i
$101$	13.1033	−	4.76922i	1.30383	−	0.474555i	0.405588	−	0.914056i	$-0.367067\pi$
$101$	13.1033	−	4.76922i	1.30383	−	0.474555i	0.898242	+	0.439501i	$0.144845\pi$
$102$	1.70820	−	2.95870i	0.169137	−	0.292955i
$103$	−0.502029	−	0.869539i	−0.0494663	−	0.0856782i	0.840232	−	0.542227i	$-0.182419\pi$
$103$	−0.502029	−	0.869539i	−0.0494663	−	0.0856782i	−0.889698	+	0.456549i	$0.849085\pi$
$104$	−7.25608	−	6.08857i	−0.711517	−	0.597034i
$105$	4.71528	+	3.95659i	0.460165	+	0.386124i
$106$	−0.263932	−	0.457144i	−0.0256353	−	0.0444017i
$107$	5.79210	−	10.0322i	0.559943	−	0.969850i	−0.437557	−	0.899190i	$-0.644156\pi$
$107$	5.79210	−	10.0322i	0.559943	−	0.969850i	0.997501	−	0.0706593i	$-0.0225103\pi$
$108$	3.15285	−	1.14755i	0.303384	−	0.110423i
$109$	−0.126163	−	0.715505i	−0.0120842	−	0.0685329i	0.978169	−	0.207809i	$-0.0666334\pi$
$109$	−0.126163	−	0.715505i	−0.0120842	−	0.0685329i	−0.990254	+	0.139277i	$0.955522\pi$
$110$	−0.912922	+	5.17744i	−0.0870437	+	0.493650i
$111$	−7.10624	−	2.58646i	−0.674495	−	0.245496i
$112$	7.72952	−	6.48584i	0.730371	−	0.612854i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	−3.23607			−0.301765
$116$	1.24451	−	1.04427i	0.115550	−	0.0969582i
$117$	4.67948	+	1.70319i	0.432618	+	0.157460i
$118$	−0.571614	+	3.24179i	−0.0526214	+	0.298431i
$119$	−1.81847	−	10.3130i	−0.166699	−	0.945395i
$120$	−4.20243	+	1.52956i	−0.383628	+	0.139629i
$121$	−1.04508	+	1.81014i	−0.0950077	+	0.164558i
$122$	0.310271	+	0.537405i	0.0280906	+	0.0486543i
$123$	−8.31472	−	6.97688i	−0.749713	−	0.629084i
$124$	0.556564	+	0.467013i	0.0499809	+	0.0419390i
$125$	5.23607	+	9.06914i	0.468328	+	0.811168i
$126$	−4.02874	+	6.97798i	−0.358909	+	0.621648i
$127$	−14.9819	+	5.45298i	−1.32943	+	0.483874i	−0.906469	−	0.422273i	$-0.861232\pi$
$127$	−14.9819	+	5.45298i	−1.32943	+	0.483874i	−0.422963	+	0.906147i	$0.639010\pi$
$128$	0.612407	+	3.47313i	0.0541296	+	0.306984i
$129$	1.29141	−	7.32395i	0.113702	−	0.644838i
$130$	−4.20243	−	1.52956i	−0.368578	−	0.134151i
$131$	−3.89930	+	3.27190i	−0.340683	+	0.285867i	−0.797036	−	0.603932i	$-0.793600\pi$
$131$	−3.89930	+	3.27190i	−0.340683	+	0.285867i	0.456353	+	0.889799i	$0.349155\pi$
$132$	−2.62866			−0.228795
$133$		0			0
$134$	−0.201626			−0.0174178
$135$	5.14046	−	4.31336i	0.442421	−	0.371235i
$136$	7.14961	+	2.60224i	0.613074	+	0.223141i
$137$	−0.817571	+	4.63668i	−0.0698498	+	0.396138i	0.929759	+	0.368169i	$0.120015\pi$
$137$	−0.817571	+	4.63668i	−0.0698498	+	0.396138i	−0.999609	+	0.0279692i	$0.991096\pi$
$138$	0.628265	+	3.56307i	0.0534815	+	0.303308i
$139$	0.854961	−	0.311180i	0.0725168	−	0.0263940i	−0.305507	−	0.952190i	$-0.598826\pi$
$139$	0.854961	−	0.311180i	0.0725168	−	0.0263940i	0.378024	+	0.925796i	$0.376604\pi$
$140$	−1.61803	+	2.80252i	−0.136749	+	0.236856i
$141$	−1.48584	−	2.57355i	−0.125130	−	0.216732i
$142$	10.9318	+	9.17291i	0.917380	+	0.769773i
$143$	−8.53003	−	7.15755i	−0.713317	−	0.598544i
$144$	−1.92705	−	3.33775i	−0.160588	−	0.278146i
$145$	1.62460	−	2.81389i	0.134916	−	0.233681i
$146$	−9.94207	+	3.61862i	−0.822812	+	0.299479i
$147$	−2.23412	−	12.6703i	−0.184267	−	1.04503i
$148$	0.690380	−	3.91534i	0.0567489	−	0.321839i
$149$	21.6453	+	7.87824i	1.77325	+	0.645411i	0.999935	+	0.0113907i	$0.00362585\pi$
$149$	21.6453	+	7.87824i	1.77325	+	0.645411i	0.773317	+	0.634020i	$0.218596\pi$
$150$	3.67577	−	3.08434i	0.300125	−	0.251835i
$151$	−2.45714			−0.199959			−0.0999797	−	0.994989i	$-0.531878\pi$
$151$	−2.45714			−0.199959			−0.0999797	+	0.994989i	$0.531878\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	13.8019	−	11.5812i	1.11219	−	0.933236i
$155$	1.36545	+	0.496984i	0.109676	+	0.0399187i
$156$	0.388289	−	2.20210i	0.0310880	−	0.176309i
$157$	2.70237	+	15.3259i	0.215672	+	1.22314i	0.879736	+	0.475462i	$0.157719\pi$
$157$	2.70237	+	15.3259i	0.215672	+	1.22314i	−0.664064	+	0.747676i	$0.731170\pi$
$158$	8.40487	−	3.05912i	0.668655	−	0.243371i
$159$	0.263932	−	0.457144i	0.0209312	−	0.0362539i
$160$	−2.07363	−	3.59163i	−0.163935	−	0.283943i
$161$	8.49556	+	7.12862i	0.669544	+	0.561814i
$162$	−1.37590	−	1.15452i	−0.108101	−	0.0907075i
$163$	−3.26393	−	5.65330i	−0.255651	−	0.442800i	0.709421	−	0.704785i	$-0.248956\pi$
$163$	−3.26393	−	5.65330i	−0.255651	−	0.442800i	−0.965072	+	0.261984i	$0.915623\pi$
$164$	2.85317	−	4.94183i	0.222795	−	0.385892i
$165$	−4.94026	+	1.79811i	−0.384598	+	0.139982i
$166$	0.252326	+	1.43101i	0.0195843	+	0.111068i
$167$	1.19503	−	6.77736i	0.0924743	−	0.524448i	−0.903018	−	0.429603i	$-0.858653\pi$
$167$	1.19503	−	6.77736i	0.0924743	−	0.524448i	0.995492	−	0.0948446i	$-0.0302354\pi$
$168$	14.4020	+	5.24188i	1.11113	+	0.404420i
$169$	−2.70250	+	2.26767i	−0.207885	+	0.174436i
$170$	3.59222			0.275511
$171$		0			0
$172$	3.90983			0.298122
$173$	11.9196	−	10.0017i	0.906230	−	0.760418i	−0.0651678	−	0.997874i	$-0.520758\pi$
$173$	11.9196	−	10.0017i	0.906230	−	0.760418i	0.971398	+	0.237457i	$0.0763138\pi$
$174$	−3.41363	−	1.24246i	−0.258787	−	0.0941907i
$175$	2.55405	−	14.4848i	0.193068	−	1.09494i
$176$	1.49651	+	8.48711i	0.112803	+	0.639740i
$177$	−3.09328	+	1.12586i	−0.232505	+	0.0846249i
$178$	10.4271	−	18.0602i	0.781541	−	1.35367i
$179$	9.14729	+	15.8436i	0.683701	+	1.18420i	0.973843	+	0.227221i	$0.0729640\pi$
$179$	9.14729	+	15.8436i	0.683701	+	1.18420i	−0.290142	+	0.956983i	$0.593703\pi$
$180$	0.946883	+	0.794529i	0.0705765	+	0.0592207i
$181$	18.8611	+	15.8264i	1.40194	+	1.17637i	0.960231	+	0.279205i	$0.0900710\pi$
$181$	18.8611	+	15.8264i	1.40194	+	1.17637i	0.441706	+	0.897160i	$0.354373\pi$
$182$	7.66312	+	13.2729i	0.568028	+	0.983854i
$183$	−0.310271	+	0.537405i	−0.0229359	+	0.0397261i
$184$	−7.57155	+	2.75582i	−0.558182	+	0.203162i
$185$	−1.38076	−	7.83068i	−0.101515	−	0.575723i
$186$	0.282109	−	1.59992i	0.0206852	−	0.117312i
$187$	8.40487	+	3.05912i	0.614625	+	0.223705i
$188$	1.19680	−	1.00423i	0.0872853	−	0.0732411i
$189$	−22.9969			−1.67278
$190$		0			0
$191$	−17.0000			−1.23008			−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000			−1.23008			−0.615038	+	0.788497i	$0.710860\pi$
$192$	−7.84208	+	6.58029i	−0.565953	+	0.474891i
$193$	−4.94026	−	1.79811i	−0.355607	−	0.129431i	0.158038	−	0.987433i	$-0.449483\pi$
$193$	−4.94026	−	1.79811i	−0.355607	−	0.129431i	−0.513646	+	0.858002i	$0.671705\pi$
$194$	−3.19798	+	18.1366i	−0.229601	+	1.30213i
$195$	−0.776578	−	4.40419i	−0.0556119	−	0.315391i
$196$	6.35602	−	2.31340i	0.454001	−	0.165243i
$197$	−1.26393	+	2.18919i	−0.0900514	+	0.155974i	−0.907533	−	0.419982i	$-0.862036\pi$
$197$	−1.26393	+	2.18919i	−0.0900514	+	0.155974i	0.817481	+	0.575955i	$0.195370\pi$
$198$	−3.44095	−	5.95991i	−0.244538	−	0.423552i
$199$	−14.5122	−	12.1771i	−1.02874	−	0.863215i	−0.0380389	−	0.999276i	$-0.512111\pi$
$199$	−14.5122	−	12.1771i	−1.02874	−	0.863215i	−0.990700	+	0.136061i	$0.956556\pi$
$200$	8.18605	+	6.86892i	0.578841	+	0.485706i
$201$	−0.100813	−	0.174613i	−0.00711081	−	0.0123163i
$202$	8.19624	−	14.1963i	0.576685	−	0.998848i
$203$	−10.4636	+	3.80845i	−0.734403	+	0.267301i
$204$	0.311892	+	1.76882i	0.0218368	+	0.123843i
$205$	1.98179	−	11.2393i	0.138414	−	0.784986i
$206$	−1.10916	−	0.403700i	−0.0772786	−	0.0281271i
$207$	3.24502	−	2.72289i	0.225544	−	0.189254i
$208$	−7.33094			−0.508309
$209$		0			0
$210$	7.23607			0.499336
$211$	13.8019	−	11.5812i	0.950161	−	0.797279i	−0.0291640	−	0.999575i	$-0.509285\pi$
$211$	13.8019	−	11.5812i	0.950161	−	0.797279i	0.979325	+	0.202295i	$0.0648401\pi$
$212$	0.260778	+	0.0949156i	0.0179103	+	0.00651883i
$213$	−2.47805	+	14.0537i	−0.169793	+	0.962944i
$214$	−2.36475	−	13.4111i	−0.161651	−	0.916767i
$215$	7.34808	−	2.67448i	0.501135	−	0.182398i
$216$	8.35410	−	14.4697i	0.568425	−	0.984540i
$217$	−2.48990	−	4.31263i	−0.169025	−	0.292760i
$218$	−0.654280	−	0.549006i	−0.0443134	−	0.0371834i
$219$	−8.10485	−	6.80078i	−0.547675	−	0.459554i
$220$	−1.38197	−	2.39364i	−0.0931721	−	0.161379i
$221$	−3.80423	+	6.58911i	−0.255900	+	0.443232i
$222$	−8.35389	+	3.04057i	−0.560676	+	0.204070i
$223$	−2.36028	−	13.3858i	−0.158056	−	0.896380i	−0.955938	−	0.293567i	$-0.905158\pi$
$223$	−2.36028	−	13.3858i	−0.158056	−	0.896380i	0.797883	−	0.602813i	$-0.205953\pi$
$224$	−2.46804	+	13.9969i	−0.164903	+	0.935209i
$225$	−5.27923	−	1.92148i	−0.351948	−	0.128099i
$226$		0			0
$227$	29.7073			1.97174			0.985870	−	0.167511i	$-0.0535729\pi$
$227$	29.7073			1.97174			0.985870	+	0.167511i	$0.0535729\pi$
$228$		0			0
$229$	4.09017			0.270286			0.135143	−	0.990826i	$-0.456851\pi$
$229$	4.09017			0.270286			0.135143	+	0.990826i	$0.456851\pi$
$230$	−2.91421	+	2.44531i	−0.192157	+	0.161239i
$231$	16.9305	+	6.16220i	1.11395	+	0.405443i
$232$	1.40484	−	7.96726i	0.0922325	−	0.523076i
$233$	2.33941	+	13.2675i	0.153260	+	0.869180i	0.960359	+	0.278765i	$0.0899250\pi$
$233$	2.33941	+	13.2675i	0.153260	+	0.869180i	−0.807099	+	0.590416i	$0.798964\pi$
$234$	5.50106	−	2.00222i	0.359615	−	0.130889i
$235$	1.56231	−	2.70599i	0.101914	−	0.176520i
$236$	−0.865300	−	1.49874i	−0.0563262	−	0.0975599i
$237$	6.85171	+	5.74927i	0.445066	+	0.373455i
$238$	−9.43057	−	7.91319i	−0.611293	−	0.512936i
$239$	7.92705	+	13.7301i	0.512758	+	0.888123i	0.999891	+	0.0147952i	$0.00470963\pi$
$239$	7.92705	+	13.7301i	0.512758	+	0.888123i	−0.487132	+	0.873328i	$0.661957\pi$
$240$	−1.73060	+	2.99749i	−0.111710	+	0.193487i
$241$	21.2876	−	7.74807i	1.37126	−	0.499097i	0.451742	−	0.892149i	$-0.350803\pi$
$241$	21.2876	−	7.74807i	1.37126	−	0.499097i	0.919516	+	0.393052i	$0.128581\pi$
$242$	0.426678	+	2.41981i	0.0274279	+	0.155551i
$243$	−2.51622	+	14.2702i	−0.161416	+	0.915435i
$244$	−0.306563	−	0.111580i	−0.0196257	−	0.00714317i
$245$	10.3629	−	8.69554i	0.662064	−	0.555538i
$246$	−12.7598			−0.813533
$247$		0			0
$248$	3.61803			0.229745
$249$	−1.11313	+	0.934025i	−0.0705416	+	0.0591914i
$250$	11.5683	+	4.21052i	0.731644	+	0.266297i
$251$	1.80879	−	10.2582i	0.114170	−	0.647489i	−0.872988	−	0.487742i	$-0.837821\pi$
$251$	1.80879	−	10.2582i	0.114170	−	0.647489i	0.987158	−	0.159748i	$-0.0510681\pi$
$252$	−0.735585	−	4.17171i	−0.0463375	−	0.262793i
$253$	−8.90090	+	3.23966i	−0.559595	+	0.203676i
$254$	−9.37132	+	16.2316i	−0.588009	+	1.01846i
$255$	1.79611	+	3.11096i	0.112477	+	0.194816i
$256$	−10.1658	−	8.53012i	−0.635363	−	0.533132i
$257$	−6.94154	−	5.82464i	−0.433001	−	0.363331i	0.400081	−	0.916480i	$-0.368982\pi$
$257$	−6.94154	−	5.82464i	−0.433001	−	0.363331i	−0.833083	+	0.553148i	$0.813426\pi$
$258$	−4.37132	−	7.57135i	−0.272147	−	0.471372i
$259$	−13.6251	+	23.5993i	−0.846620	+	1.46639i
$260$	2.20935	−	0.804138i	0.137018	−	0.0498705i
$261$	0.738570	+	4.18864i	0.0457163	+	0.259270i
$262$	−1.03909	+	5.89295i	−0.0641949	+	0.364067i
$263$	−11.1716	−	4.06612i	−0.688869	−	0.250728i	−0.0262181	−	0.999656i	$-0.508346\pi$
$263$	−11.1716	−	4.06612i	−0.688869	−	0.250728i	−0.662651	+	0.748928i	$0.730569\pi$
$264$	−10.0277	+	8.41420i	−0.617159	+	0.517858i
$265$	0.555029			0.0340952
$266$		0			0
$267$	20.8541			1.27625
$268$	0.0812016	−	0.0681362i	0.00496018	−	0.00416208i
$269$	−7.24921	−	2.63850i	−0.441992	−	0.160872i	0.111431	−	0.993772i	$-0.464457\pi$
$269$	−7.24921	−	2.63850i	−0.441992	−	0.160872i	−0.553423	+	0.832900i	$0.686679\pi$
$270$	1.36983	−	7.76870i	0.0833653	−	0.472788i
$271$	2.47805	+	14.0537i	0.150531	+	0.853702i	0.962759	+	0.270362i	$0.0871434\pi$
$271$	2.47805	+	14.0537i	0.150531	+	0.853702i	−0.812228	+	0.583340i	$0.801746\pi$
$272$	5.53342	−	2.01400i	0.335513	−	0.122117i
$273$	−7.66312	+	13.2729i	−0.463793	+	0.803313i
$274$	2.76741	+	4.79330i	0.167186	+	0.289574i
$275$	9.62328	+	8.07489i	0.580306	+	0.486934i
$276$	−1.45710	−	1.22265i	−0.0877073	−	0.0735952i
$277$	9.61803	+	16.6589i	0.577892	+	1.00094i	0.995721	+	0.0924121i	$0.0294577\pi$
$277$	9.61803	+	16.6589i	0.577892	+	1.00094i	−0.417829	+	0.908526i	$0.637209\pi$
$278$	0.534785	−	0.926274i	0.0320743	−	0.0555542i
$279$	−1.78740	+	0.650561i	−0.107009	+	0.0389481i
$280$	2.79833	+	15.8701i	0.167232	+	0.948422i
$281$	0.768353	−	4.35755i	0.0458361	−	0.259949i	−0.953275	−	0.302104i	$-0.902311\pi$
$281$	0.768353	−	4.35755i	0.0458361	−	0.259949i	0.999111	+	0.0421545i	$0.0134222\pi$
$282$	−3.28274	−	1.19482i	−0.195485	−	0.0711505i
$283$	−0.696970	+	0.584827i	−0.0414306	+	0.0347644i	−0.663268	−	0.748382i	$-0.730831\pi$
$283$	−0.696970	+	0.584827i	−0.0414306	+	0.0347644i	0.621837	+	0.783146i	$0.286387\pi$
$284$	−7.50245			−0.445189
$285$		0			0
$286$	−13.0902			−0.774038
$287$	−29.9614	+	25.1406i	−1.76857	+	1.48400i
$288$	5.10143	+	1.85677i	0.300604	+	0.109411i
$289$	−1.89078	+	10.7231i	−0.111222	+	0.630772i
$290$	−0.663277	−	3.76163i	−0.0389490	−	0.220891i
$291$	−17.3058	+	6.29878i	−1.01448	+	0.369241i
$292$	2.78115	−	4.81710i	0.162755	−	0.281899i
$293$	12.3637	+	21.4146i	0.722297	+	1.25106i	0.960077	+	0.279736i	$0.0902470\pi$
$293$	12.3637	+	21.4146i	0.722297	+	1.25106i	−0.237780	+	0.971319i	$0.576420\pi$
$294$	−11.5861	−	9.72191i	−0.675717	−	0.566993i
$295$	−2.65143	−	2.22482i	−0.154372	−	0.129534i
$296$	−9.89919	−	17.1459i	−0.575379	−	0.996585i
$297$	9.82084	−	17.0102i	0.569863	−	0.987031i
$298$	25.4456	−	9.26143i	1.47402	−	0.536500i
$299$	−1.39917	−	7.93507i	−0.0809159	−	0.458897i
$300$	−0.438054	+	2.48433i	−0.0252911	+	0.143433i
$301$	−25.1822	−	9.16558i	−1.45148	−	0.528295i
$302$	−2.21275	+	1.85672i	−0.127330	+	0.106842i
$303$	16.3925			0.941723
$304$		0			0
$305$	−0.652476			−0.0373607
$306$	−3.60216	+	3.02257i	−0.205922	+	0.172789i
$307$	−25.9291	−	9.43741i	−1.47985	−	0.538622i	−0.529095	−	0.848563i	$-0.677468\pi$
$307$	−25.9291	−	9.43741i	−1.47985	−	0.538622i	−0.950756	+	0.309941i	$0.899691\pi$
$308$	−1.64482	+	9.32823i	−0.0937223	+	0.531525i
$309$	−0.204964	−	1.16241i	−0.0116600	−	0.0661271i
$310$	1.60519	−	0.584240i	0.0911685	−	0.0331826i
$311$	2.76393	−	4.78727i	0.156728	−	0.271461i	−0.776959	−	0.629551i	$-0.783239\pi$
$311$	2.76393	−	4.78727i	0.156728	−	0.271461i	0.933687	+	0.358090i	$0.116572\pi$
$312$	−5.56758	−	9.64333i	−0.315202	−	0.545946i
$313$	5.83575	+	4.89678i	0.329856	+	0.276782i	0.792641	−	0.609688i	$-0.208705\pi$
$313$	5.83575	+	4.89678i	0.329856	+	0.276782i	−0.462785	+	0.886471i	$0.653150\pi$
$314$	14.0145	+	11.7595i	0.790882	+	0.663629i
$315$	−4.23607	−	7.33708i	−0.238675	−	0.413398i
$316$	−2.35114	+	4.07230i	−0.132262	+	0.229085i
$317$	8.31584	−	3.02672i	0.467064	−	0.169997i	−0.0977578	−	0.995210i	$-0.531167\pi$
$317$	8.31584	−	3.02672i	0.467064	−	0.169997i	0.564822	+	0.825213i	$0.308945\pi$
$318$	−0.107756	−	0.611114i	−0.00604265	−	0.0342696i
$319$	1.65149	−	9.36608i	0.0924658	−	0.524400i
$320$	−10.1148	−	3.68148i	−0.565434	−	0.205801i
$321$	10.4320	−	8.75350i	0.582259	−	0.488573i
$322$	13.0373			0.726539
$323$		0			0
$324$	0.944272			0.0524596
$325$	−8.18605	+	6.86892i	−0.454081	+	0.381019i
$326$	−7.21117	−	2.62465i	−0.399390	−	0.145366i
$327$	0.148313	−	0.841126i	0.00820174	−	0.0465144i
$328$	−4.93446	−	27.9847i	−0.272460	−	1.54520i
$329$	−10.0624	+	3.66242i	−0.554759	+	0.201916i
$330$	−3.09017	+	5.35233i	−0.170108	+	0.294636i
$331$	−12.1392	−	21.0257i	−0.667232	−	1.15568i	−0.978675	−	0.205415i	$-0.934146\pi$
$331$	−12.1392	−	21.0257i	−0.667232	−	1.15568i	0.311443	−	0.950265i	$-0.399188\pi$
$332$	−0.585206	−	0.491046i	−0.0321173	−	0.0269497i
$333$	7.97347	+	6.69053i	0.436943	+	0.366639i
$334$	−4.04508	−	7.00629i	−0.221337	−	0.383367i
$335$	0.106001	−	0.183599i	0.00579146	−	0.0100311i
$336$	11.1464	−	4.05694i	0.608084	−	0.221324i
$337$	2.79833	+	15.8701i	0.152435	+	0.864501i	0.961094	+	0.276223i	$0.0890829\pi$
$337$	2.79833	+	15.8701i	0.152435	+	0.864501i	−0.808659	+	0.588278i	$0.799806\pi$
$338$	−0.720163	+	4.08425i	−0.0391717	+	0.222154i
$339$		0			0
$340$	−1.44671	+	1.21393i	−0.0784588	+	0.0658347i
$341$	4.25325			0.230327
$342$		0			0
$343$	−16.7082			−0.902158
$344$	14.9150	−	12.5152i	0.804163	−	0.674773i
$345$	−3.57480	−	1.30112i	−0.192461	−	0.0700501i
$346$	3.17634	−	18.0139i	0.170761	−	0.968433i
$347$	−4.31217	−	24.4555i	−0.231490	−	1.31284i	−0.849882	−	0.526973i	$-0.823327\pi$
$347$	−4.31217	−	24.4555i	−0.231490	−	1.31284i	0.618392	−	0.785870i	$-0.287784\pi$
$348$	1.79465	−	0.653200i	0.0962035	−	0.0350152i
$349$	−5.69098	+	9.85707i	−0.304631	+	0.527637i	−0.977179	−	0.212417i	$-0.931867\pi$
$349$	−5.69098	+	9.85707i	−0.304631	+	0.527637i	0.672548	+	0.740054i	$0.265200\pi$
$350$	−8.64527	−	14.9740i	−0.462109	−	0.800396i
$351$	12.7992	+	10.7398i	0.683172	+	0.573250i
$352$	−9.29918	−	7.80294i	−0.495648	−	0.415898i
$353$	−13.8090	−	23.9179i	−0.734980	−	1.27302i	−0.954732	−	0.297467i	$-0.903858\pi$
$353$	−13.8090	−	23.9179i	−0.734980	−	1.27302i	0.219752	−	0.975556i	$-0.429475\pi$
$354$	−1.93487	+	3.35129i	−0.102837	+	0.178119i
$355$	−14.1000	+	5.13198i	−0.748350	+	0.272377i
$356$	1.90382	+	10.7971i	0.100902	+	0.572245i
$357$	2.13774	−	12.1237i	0.113141	−	0.641655i
$358$	20.2096	+	7.35568i	1.06811	+	0.388760i
$359$	−28.8171	+	24.1804i	−1.52091	+	1.27619i	−0.682938	+	0.730477i	$0.739298\pi$
$359$	−28.8171	+	24.1804i	−1.52091	+	1.27619i	−0.837970	+	0.545716i	$0.816258\pi$
$360$	6.15537			0.324416
$361$		0			0
$362$	28.9443			1.52128
$363$	−1.88228	+	1.57942i	−0.0987941	+	0.0828981i
$364$	−7.57155	−	2.75582i	−0.396857	−	0.144444i
$365$	1.93177	−	10.9556i	0.101113	−	0.573443i
$366$	0.126675	+	0.718408i	0.00662139	+	0.0375518i
$367$	−20.1772	+	7.34390i	−1.05324	+	0.383349i	−0.809885	−	0.586588i	$-0.800471\pi$
$367$	−20.1772	+	7.34390i	−1.05324	+	0.383349i	−0.243356	+	0.969937i	$0.578248\pi$
$368$	−3.11803	+	5.40059i	−0.162539	+	0.281525i
$369$	7.46969	+	12.9379i	0.388857	+	0.673520i
$370$	−7.16062	−	6.00847i	−0.372263	−	0.312366i
$371$	−1.45710	−	1.22265i	−0.0756490	−	0.0634771i
$372$	0.427051	+	0.739674i	0.0221416	+	0.0383503i
$373$	−2.15938	+	3.74016i	−0.111809	+	0.193658i	−0.916500	−	0.400036i	$-0.868998\pi$
$373$	−2.15938	+	3.74016i	−0.111809	+	0.193658i	0.804691	+	0.593694i	$0.202331\pi$
$374$	9.88051	−	3.59621i	0.510909	−	0.185956i
$375$	2.13774	+	12.1237i	0.110392	+	0.626066i
$376$	1.35098	−	7.66177i	0.0696713	−	0.395126i
$377$	7.60227	+	2.76700i	0.391537	+	0.142508i
$378$	−20.7096	+	17.3774i	−1.06519	+	0.893797i
$379$	7.95148			0.408440			0.204220	−	0.978925i	$-0.434534\pi$
$379$	7.95148			0.408440			0.204220	+	0.978925i	$0.434534\pi$
$380$		0			0
$381$	−18.7426			−0.960215
$382$	−15.3092	+	12.8459i	−0.783285	+	0.657254i
$383$	13.1945	+	4.80242i	0.674209	+	0.245392i	0.656359	−	0.754449i	$-0.272096\pi$
$383$	13.1945	+	4.80242i	0.674209	+	0.245392i	0.0178502	+	0.999841i	$0.494318\pi$
$384$	−0.719928	+	4.08291i	−0.0367387	+	0.208355i
$385$	3.28964	+	18.6565i	0.167655	+	0.950822i
$386$	−5.80762	+	2.11380i	−0.295600	+	0.107590i
$387$	−5.11803	+	8.86469i	−0.260164	+	0.450618i
$388$	−4.84104	−	8.38493i	−0.245767	−	0.425680i
$389$	10.0277	+	8.41420i	0.508422	+	0.426617i	0.860574	−	0.509326i	$-0.170105\pi$
$389$	10.0277	+	8.41420i	0.508422	+	0.426617i	−0.352151	+	0.935943i	$0.614550\pi$
$390$	−4.02733	−	3.37933i	−0.203932	−	0.171119i
$391$	3.23607	+	5.60503i	0.163655	+	0.283459i
$392$	16.8415	−	29.1703i	0.850624	−	1.47332i
$393$	−5.62298	+	2.04660i	−0.283642	+	0.103237i
$394$	0.516027	+	2.92654i	0.0259971	+	0.147437i
$395$	−1.63309	+	9.26169i	−0.0821694	+	0.466006i
$396$	3.39984	+	1.23744i	0.170848	+	0.0621837i
$397$	11.2671	−	9.45425i	0.565481	−	0.474495i	−0.314662	−	0.949204i	$-0.601891\pi$
$397$	11.2671	−	9.45425i	0.565481	−	0.474495i	0.880143	+	0.474709i	$0.157447\pi$
$398$	−22.2703			−1.11631
$399$		0			0
$400$	8.27051			0.413525
$401$	5.82841	−	4.89062i	0.291057	−	0.244226i	−0.485553	−	0.874207i	$-0.661382\pi$
$401$	5.82841	−	4.89062i	0.291057	−	0.244226i	0.776610	+	0.629981i	$0.216937\pi$
$402$	−0.222731	−	0.0810676i	−0.0111088	−	0.00404328i
$403$	−0.628265	+	3.56307i	−0.0312961	+	0.177489i
$404$	1.49651	+	8.48711i	0.0744540	+	0.422249i
$405$	1.77465	−	0.645920i	0.0881831	−	0.0320960i
$406$	−6.54508	+	11.3364i	−0.324827	+	0.562617i
$407$	−11.6372	−	20.1562i	−0.576834	−	0.999106i
$408$	6.85171	+	5.74927i	0.339210	+	0.284631i
$409$	−16.7973	−	14.0946i	−0.830572	−	0.696933i	0.124850	−	0.992176i	$-0.460155\pi$
$409$	−16.7973	−	14.0946i	−0.830572	−	0.696933i	−0.955422	+	0.295243i	$0.904600\pi$
$410$	−6.70820	−	11.6190i	−0.331295	−	0.573819i
$411$	−2.76741	+	4.79330i	−0.136506	+	0.236436i
$412$	0.583118	−	0.212238i	0.0287282	−	0.0104562i
$413$	2.05976	+	11.6815i	0.101354	+	0.574809i
$414$	0.864733	−	4.90414i	0.0424993	−	0.241025i
$415$	−1.43572	−	0.522560i	−0.0704768	−	0.0256515i
$416$	7.91036	−	6.63758i	0.387837	−	0.325434i
$417$	1.06957			0.0523770
$418$		0			0
$419$	−33.4164			−1.63250			−0.816249	−	0.577700i	$-0.803950\pi$
$419$	−33.4164			−1.63250			−0.816249	+	0.577700i	$0.803950\pi$
$420$	−2.91421	+	2.44531i	−0.142199	+	0.119319i
$421$	−13.2941	−	4.83867i	−0.647917	−	0.235823i	−0.00290601	−	0.999996i	$-0.500925\pi$
$421$	−13.2941	−	4.83867i	−0.647917	−	0.235823i	−0.645011	+	0.764173i	$0.723147\pi$
$422$	3.67793	−	20.8586i	0.179039	−	1.01538i
$423$	0.710251	+	4.02803i	0.0345336	+	0.195850i
$424$	1.29862	−	0.472660i	0.0630667	−	0.0229544i
$425$	4.29180	−	7.43361i	0.208183	−	0.360583i
$426$	8.38800	+	14.5284i	0.406400	+	0.703905i
$427$	1.71293	+	1.43732i	0.0828944	+	0.0695566i
$428$	5.48444	+	4.60199i	0.265100	+	0.222446i
$429$	−6.54508	−	11.3364i	−0.316000	−	0.547328i
$430$	4.59628	−	7.96099i	0.221652	−	0.383913i
$431$	−14.9819	+	5.45298i	−0.721655	+	0.262661i	−0.676628	−	0.736325i	$-0.736559\pi$
$431$	−14.9819	+	5.45298i	−0.721655	+	0.262661i	−0.0450266	+	0.998986i	$0.514337\pi$
$432$	−2.24549	−	12.7348i	−0.108036	−	0.612704i
$433$	1.62171	−	9.19717i	0.0779344	−	0.441988i	−0.920724	−	0.390213i	$-0.872401\pi$
$433$	1.62171	−	9.19717i	0.0779344	−	0.441988i	0.998659	−	0.0517744i	$-0.0164877\pi$
$434$	−5.50106	−	2.00222i	−0.264059	−	0.0961097i
$435$	2.92603	−	2.45523i	0.140292	−	0.117719i
$436$	0.449028			0.0215045
$437$		0			0
$438$	−12.4377			−0.594296
$439$	8.87401	−	7.44617i	0.423533	−	0.355387i	−0.405972	−	0.913885i	$-0.633067\pi$
$439$	8.87401	−	7.44617i	0.423533	−	0.355387i	0.829505	+	0.558499i	$0.188623\pi$
$440$	−12.9338	−	4.70750i	−0.616593	−	0.224421i
$441$	−3.07500	+	17.4392i	−0.146428	+	0.830437i
$442$	1.55316	+	8.80839i	0.0738761	+	0.418972i
$443$	6.74731	−	2.45582i	0.320574	−	0.116680i	−0.176721	−	0.984261i	$-0.556549\pi$
$443$	6.74731	−	2.45582i	0.320574	−	0.116680i	0.497295	+	0.867581i	$0.334327\pi$
$444$	2.33688	−	4.04760i	0.110903	−	0.192090i
$445$	10.9637	+	18.9896i	0.519727	+	0.900193i
$446$	−12.2404	−	10.2709i	−0.579600	−	0.486342i
$447$	20.7434	+	17.4058i	0.981130	+	0.823266i
$448$	18.4443	+	31.9464i	0.871410	+	1.50933i
$449$	−17.4823	+	30.2802i	−0.825040	+	1.42901i	0.0768484	+	0.997043i	$0.475514\pi$
$449$	−17.4823	+	30.2802i	−0.825040	+	1.42901i	−0.901889	+	0.431969i	$0.857819\pi$
$450$	−6.20610	+	2.25884i	−0.292558	+	0.106483i
$451$	−5.80080	−	32.8980i	−0.273149	−	1.54911i
$452$		0			0
$453$	−2.71434	−	0.987940i	−0.127531	−	0.0464175i
$454$	26.7526	−	22.4481i	1.25556	−	1.05354i
$455$	−16.1150			−0.755481
$456$		0			0
$457$	19.7082			0.921911			0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082			0.921911			0.460955	+	0.887423i	$0.347507\pi$
$458$	3.68336	−	3.09070i	0.172112	−	0.144419i
$459$	−12.6114	−	4.59018i	−0.588651	−	0.214251i
$460$	0.347296	−	1.96962i	0.0161928	−	0.0918338i
$461$	−5.93535	−	33.6611i	−0.276437	−	1.56775i	−0.734360	−	0.678760i	$-0.762518\pi$
$461$	−5.93535	−	33.6611i	−0.276437	−	1.56775i	0.457923	−	0.888992i	$-0.348594\pi$
$462$	19.9030	−	7.24410i	0.925972	−	0.337026i
$463$	−8.42705	+	14.5961i	−0.391638	+	0.678337i	−0.992666	−	0.120891i	$-0.961425\pi$
$463$	−8.42705	+	14.5961i	−0.391638	+	0.678337i	0.601028	+	0.799228i	$0.294758\pi$
$464$	−3.13068	−	5.42250i	−0.145338	−	0.251733i
$465$	1.30856	+	1.09801i	0.0606830	+	0.0509191i
$466$	12.1322	+	10.1801i	0.562013	+	0.471585i
$467$	0.118034	+	0.204441i	0.00546196	+	0.00946040i	0.868743	−	0.495262i	$-0.164928\pi$
$467$	0.118034	+	0.204441i	0.00546196	+	0.00946040i	−0.863282	+	0.504723i	$0.831595\pi$
$468$	−1.53884	+	2.66535i	−0.0711330	+	0.123206i
$469$	−0.682727	+	0.248492i	−0.0315254	+	0.0114743i
$470$	−0.637845	−	3.61740i	−0.0294216	−	0.166858i
$471$	−3.17682	+	18.0167i	−0.146380	+	0.830163i
$472$	−8.09830	−	2.94754i	−0.372755	−	0.135672i
$473$	17.5336	−	14.7125i	0.806198	−	0.676480i
$474$	10.5146			0.482953
$475$		0			0
$476$	6.47214			0.296650
$477$	−0.556564	+	0.467013i	−0.0254833	+	0.0213830i
$478$	17.5136	+	6.37444i	0.801055	+	0.291560i
$479$	−4.70416	+	26.6786i	−0.214938	+	1.21898i	0.666075	+	0.745885i	$0.267973\pi$
$479$	−4.70416	+	26.6786i	−0.214938	+	1.21898i	−0.881013	+	0.473092i	$0.843138\pi$
$480$	−0.846602	−	4.80132i	−0.0386419	−	0.219149i
$481$	18.6044	−	6.77144i	0.848287	−	0.308751i
$482$	13.3156	−	23.0633i	0.606509	−	1.05050i
$483$	6.51864	+	11.2906i	0.296608	+	0.513741i
$484$	−0.989573	−	0.830351i	−0.0449806	−	0.0377432i
$485$	−14.8338	−	12.4470i	−0.673568	−	0.565191i
$486$	8.51722	+	14.7523i	0.386349	+	0.669176i
$487$	7.77997	−	13.4753i	0.352544	−	0.610624i	−0.634151	−	0.773210i	$-0.718650\pi$
$487$	7.77997	−	13.4753i	0.352544	−	0.610624i	0.986694	+	0.162586i	$0.0519834\pi$
$488$	−1.52662	+	0.555645i	−0.0691070	+	0.0251529i
$489$	−1.33257	−	7.55738i	−0.0602609	−	0.341757i
$490$	2.76152	−	15.6614i	0.124753	−	0.707508i
$491$	15.2893	+	5.56484i	0.689995	+	0.251138i	0.663133	−	0.748501i	$-0.269226\pi$
$491$	15.2893	+	5.56484i	0.689995	+	0.251138i	0.0268622	+	0.999639i	$0.491448\pi$
$492$	5.13878	−	4.31195i	0.231674	−	0.194398i
$493$	−6.49839			−0.292673
$494$		0			0
$495$	7.23607			0.325237
$496$	2.14505	−	1.79991i	0.0963158	−	0.0808185i
$497$	48.3214	+	17.5876i	2.16751	+	0.788910i
$498$	−0.296626	+	1.68225i	−0.0132922	+	0.0753835i
$499$	3.73827	+	21.2008i	0.167348	+	0.949078i	0.946610	+	0.322380i	$0.104483\pi$
$499$	3.73827	+	21.2008i	0.167348	+	0.949078i	−0.779262	+	0.626698i	$0.784406\pi$
$500$	−6.08182	+	2.21360i	−0.271987	+	0.0989952i
$501$	4.04508	−	7.00629i	0.180721	−	0.313018i
$502$	−6.12261	−	10.6047i	−0.273265	−	0.473310i
$503$	−21.9064	−	18.3816i	−0.976757	−	0.819597i	0.00683980	−	0.999977i	$-0.497823\pi$
$503$	−21.9064	−	18.3816i	−0.976757	−	0.819597i	−0.983597	+	0.180380i	$0.942267\pi$
$504$	−16.1595	−	13.5594i	−0.719802	−	0.603986i
$505$	8.61803	+	14.9269i	0.383497	+	0.664237i
$506$	−5.56758	+	9.64333i	−0.247509	+	0.428699i
$507$	−3.89714	+	1.41844i	−0.173078	+	0.0629953i
$508$	−1.71106	−	9.70389i	−0.0759159	−	0.430541i
$509$	−2.15614	+	12.2281i	−0.0955694	+	0.542001i	0.899002	+	0.437944i	$0.144293\pi$
$509$	−2.15614	+	12.2281i	−0.0955694	+	0.542001i	−0.994571	+	0.104056i	$0.966818\pi$
$510$	3.96824	+	1.44432i	0.175717	+	0.0639556i
$511$	−29.2051	+	24.5060i	−1.29196	+	1.08408i
$512$	−22.6538			−1.00117
$513$		0			0
$514$	−10.6525			−0.469861
$515$	0.950725	−	0.797753i	0.0418939	−	0.0351532i
$516$	4.31909	+	1.57202i	0.190137	+	0.0692044i
$517$	1.58817	−	9.00695i	0.0698476	−	0.396125i
$518$	5.56272	+	31.5478i	0.244412	+	1.38613i
$519$	17.1887	−	6.25616i	0.754499	−	0.274615i
$520$	5.85410	−	10.1396i	0.256719	−	0.444651i
$521$	1.48584	+	2.57355i	0.0650959	+	0.112749i	0.896737	−	0.442565i	$-0.145931\pi$
$521$	1.48584	+	2.57355i	0.0650959	+	0.112749i	−0.831641	+	0.555314i	$0.812598\pi$
$522$	3.83022	+	3.21394i	0.167644	+	0.140670i
$523$	−6.22257	−	5.22136i	−0.272094	−	0.228314i	0.496522	−	0.868024i	$-0.334610\pi$
$523$	−6.22257	−	5.22136i	−0.272094	−	0.228314i	−0.768616	+	0.639710i	$0.779055\pi$
$524$	−1.57295	−	2.72443i	−0.0687146	−	0.119017i
$525$	8.64527	−	14.9740i	0.377310	−	0.653521i
$526$	−13.1330	+	4.78001i	−0.572625	+	0.208418i
$527$	−0.504651	−	2.86202i	−0.0219829	−	0.124671i
$528$	−1.75925	+	9.97719i	−0.0765615	+	0.434202i
$529$	15.1722	+	5.52222i	0.659660	+	0.240097i
$530$	0.499825	−	0.419403i	0.0217110	−	0.0182177i
$531$	4.53077			0.196619
$532$		0			0
$533$	28.4164			1.23085
$534$	18.7799	−	15.7582i	0.812687	−	0.681926i
$535$	13.4553	+	4.89733i	0.581724	+	0.211730i
$536$	0.0916626	−	0.519845i	0.00395922	−	0.0224539i
$537$	3.73458	+	21.1798i	0.161159	+	0.913978i
$538$	−8.52196	+	3.10174i	−0.367408	+	0.133726i
$539$	19.7984	−	34.2918i	0.852776	−	1.47705i
$540$	2.07363	+	3.59163i	0.0892347	+	0.154559i
$541$	−5.13878	−	4.31195i	−0.220934	−	0.185385i	0.525602	−	0.850730i	$-0.323840\pi$
$541$	−5.13878	−	4.31195i	−0.220934	−	0.185385i	−0.746536	+	0.665345i	$0.768284\pi$
$542$	12.8512	+	10.7834i	0.552004	+	0.463187i
$543$	14.4721	+	25.0665i	0.621059	+	1.07571i
$544$	−4.14725	+	7.18325i	−0.177812	+	0.307979i
$545$	0.843897	−	0.307153i	0.0361486	−	0.0131570i
$546$	3.12863	+	17.7434i	0.133893	+	0.759345i
$547$	−5.08064	+	28.8137i	−0.217232	+	1.23199i	0.659758	+	0.751478i	$0.270659\pi$
$547$	−5.08064	+	28.8137i	−0.217232	+	1.23199i	−0.876990	+	0.480508i	$0.840452\pi$
$548$	−2.73435	−	0.995220i	−0.116805	−	0.0425137i
$549$	0.654280	−	0.549006i	0.0279240	−	0.0234310i
$550$	14.7679			0.629704
$551$		0			0
$552$	−9.47214			−0.403161
$553$	24.6896	−	20.7170i	1.04991	−	0.880976i
$554$	21.2496	+	7.73422i	0.902809	+	0.328596i
$555$	1.62318	−	9.20551i	0.0689002	−	0.390752i
$556$	0.0976434	+	0.553763i	0.00414100	+	0.0234848i
$557$	−5.03739	+	1.83346i	−0.213441	+	0.0776862i	−0.446528	−	0.894770i	$-0.647340\pi$
$557$	−5.03739	+	1.83346i	−0.213441	+	0.0776862i	0.233087	+	0.972456i	$0.425117\pi$
$558$	−1.11803	+	1.93649i	−0.0473302	+	0.0819782i
$559$	9.73508	+	16.8617i	0.411750	+	0.713172i
$560$	9.55421	+	8.01693i	0.403739	+	0.338777i
$561$	8.05467	+	6.75867i	0.340068	+	0.285351i
$562$	−2.60081	−	4.50474i	−0.109709	−	0.190021i
$563$	−9.06154	+	15.6950i	−0.381898	+	0.661467i	−0.991334	−	0.131369i	$-0.958063\pi$
$563$	−9.06154	+	15.6950i	−0.381898	+	0.661467i	0.609435	+	0.792836i	$0.291396\pi$
$564$	1.72584	−	0.628154i	0.0726710	−	0.0264501i
$565$		0			0
$566$	−0.185729	+	1.05332i	−0.00780676	+	0.0442744i
$567$	−6.08182	−	2.21360i	−0.255412	−	0.0929625i
$568$	−28.6199	+	24.0150i	−1.20087	+	1.00765i
$569$	−18.3601			−0.769695			−0.384848	−	0.922980i	$-0.625746\pi$
$569$	−18.3601			−0.769695			−0.384848	+	0.922980i	$0.625746\pi$
$570$		0			0
$571$	41.1033			1.72012			0.860060	−	0.510192i	$-0.170426\pi$
$571$	41.1033			1.72012			0.860060	+	0.510192i	$0.170426\pi$
$572$	5.27185	−	4.42361i	0.220427	−	0.184960i
$573$	−18.7795	−	6.83517i	−0.784524	−	0.285543i
$574$	−7.98412	+	45.2802i	−0.333251	+	1.88996i
$575$	1.57849	+	8.95207i	0.0658276	+	0.373327i
$576$	13.2404	−	4.81912i	0.551685	−	0.200797i
$577$	14.3541	−	24.8620i	0.597569	−	1.03502i	−0.395610	−	0.918419i	$-0.629467\pi$
$577$	14.3541	−	24.8620i	0.597569	−	1.03502i	0.993179	−	0.116601i	$-0.0372000\pi$
$578$	6.40013	+	11.0853i	0.266210	+	0.461089i
$579$	−4.73442	−	3.97265i	−0.196756	−	0.165098i
$580$	1.53830	+	1.29079i	0.0638746	+	0.0535972i
$581$	2.61803	+	4.53457i	0.108614	+	0.188126i
$582$	−10.8249	+	18.7493i	−0.448706	+	0.777182i
$583$	1.52662	−	0.555645i	0.0632263	−	0.0230125i
$584$	−4.80991	−	27.2783i	−0.199035	−	1.12879i
$585$	−1.06887	+	6.06185i	−0.0441923	+	0.250627i
$586$	27.3158	+	9.94214i	1.12841	+	0.410706i
$587$	30.0139	−	25.1846i	1.23881	−	1.03948i	0.241189	−	0.970478i	$-0.422463\pi$
$587$	30.0139	−	25.1846i	1.23881	−	1.03948i	0.997616	−	0.0690031i	$-0.0219818\pi$
$588$	7.95148			0.327913
$589$		0			0
$590$	−4.06888			−0.167513
$591$	−2.27644	+	1.91016i	−0.0936403	+	0.0785735i
$592$	−14.3988	−	5.24074i	−0.591788	−	0.215393i
$593$	5.33242	−	30.2417i	0.218976	−	1.24188i	−0.654895	−	0.755720i	$-0.727287\pi$
$593$	5.33242	−	30.2417i	0.218976	−	1.24188i	0.873871	−	0.486157i	$-0.161602\pi$
$594$	−4.00957	−	22.7394i	−0.164514	−	0.933008i
$595$	12.1636	−	4.42720i	0.498660	−	0.181498i
$596$	−7.11803	+	12.3288i	−0.291566	+	0.505007i
$597$	−11.1352	−	19.2867i	−0.455732	−	0.789351i
$598$	−7.25608	−	6.08857i	−0.296723	−	0.248980i
$599$	15.8155	+	13.2708i	0.646206	+	0.542231i	0.905917	−	0.423455i	$-0.139183\pi$
$599$	15.8155	+	13.2708i	0.646206	+	0.542231i	−0.259711	+	0.965686i	$0.583627\pi$
$600$	6.28115	+	10.8793i	0.256427	+	0.444145i
$601$	20.6457	−	35.7595i	0.842157	−	1.45866i	−0.0459108	−	0.998946i	$-0.514619\pi$
$601$	20.6457	−	35.7595i	0.842157	−	1.45866i	0.888068	−	0.459713i	$-0.152048\pi$
$602$	−29.6035	+	10.7748i	−1.20655	+	0.439148i
$603$	0.0481899	+	0.273298i	0.00196244	+	0.0111296i
$604$	0.263702	−	1.49553i	0.0107299	−	0.0608521i
$605$	−2.42778	−	0.883641i	−0.0987034	−	0.0359251i
$606$	14.7621	−	12.3868i	0.599668	−	0.503181i
$607$	1.51860			0.0616380			0.0308190	−	0.999525i	$-0.490188\pi$
$607$	1.51860			0.0616380			0.0308190	+	0.999525i	$0.490188\pi$
$608$		0			0
$609$	−13.0902			−0.530440
$610$	−0.587580	+	0.493038i	−0.0237904	+	0.0199625i
$611$	7.31078	+	2.66090i	0.295762	+	0.107649i
$612$	0.429282	−	2.43458i	0.0173527	−	0.0984120i
$613$	−4.25922	−	24.1552i	−0.172028	−	0.975621i	−0.941518	−	0.336962i	$-0.890601\pi$
$613$	−4.25922	−	24.1552i	−0.172028	−	0.975621i	0.769490	−	0.638659i	$-0.220510\pi$
$614$	−30.4815	+	11.0943i	−1.23013	+	0.447731i
$615$	6.70820	−	11.6190i	0.270501	−	0.468521i
$616$	23.5847	+	40.8498i	0.950253	+	1.64589i
$617$	13.2300	+	11.1013i	0.532619	+	0.446920i	0.869005	−	0.494804i	$-0.164760\pi$
$617$	13.2300	+	11.1013i	0.532619	+	0.446920i	−0.336386	+	0.941724i	$0.609205\pi$
$618$	−1.06294	−	0.891915i	−0.0427578	−	0.0358781i
$619$	−18.3885	−	31.8499i	−0.739098	−	1.28016i	−0.952902	−	0.303279i	$-0.901919\pi$
$619$	−18.3885	−	31.8499i	−0.739098	−	1.28016i	0.213804	−	0.976877i	$-0.431415\pi$
$620$	−0.449028	+	0.777739i	−0.0180334	+	0.0312348i
$621$	13.3557	−	4.86108i	0.535946	−	0.195068i
$622$	−1.12843	−	6.39967i	−0.0452461	−	0.256603i
$623$	13.0490	−	74.0043i	0.522796	−	2.96492i
$624$	−8.09830	−	2.94754i	−0.324192	−	0.117996i
$625$	3.38316	−	2.83881i	0.135327	−	0.113552i
$626$	8.95554			0.357935
$627$		0			0
$628$	−9.61803			−0.383801
$629$	−12.1824	+	10.2222i	−0.485743	+	0.407587i
$630$	−9.35896	−	3.40638i	−0.372870	−	0.135713i
$631$	−4.34120	+	24.6202i	−0.172821	+	0.980114i	0.767809	+	0.640679i	$0.221347\pi$
$631$	−4.34120	+	24.6202i	−0.172821	+	0.980114i	−0.940629	+	0.339435i	$0.889764\pi$
$632$	4.06622	+	23.0607i	0.161745	+	0.917304i
$633$	19.9030	−	7.24410i	0.791074	−	0.287927i
$634$	5.20163	−	9.00948i	0.206583	−	0.357812i
$635$	−9.85359	−	17.0669i	−0.391028	−	0.677280i
$636$	0.249913	+	0.209702i	0.00990969	+	0.00831521i
$637$	25.8027	+	21.6510i	1.02234	+	0.857845i
$638$	−5.59017	−	9.68246i	−0.221317	−	0.383332i
$639$	9.82084	−	17.0102i	0.388506	−	0.672913i
$640$	−4.09636	+	1.49095i	−0.161923	+	0.0589351i
$641$	−5.02107	−	28.4759i	−0.198320	−	1.12473i	−0.907610	−	0.419814i	$-0.862095\pi$
$641$	−5.02107	−	28.4759i	−0.198320	−	1.12473i	0.709290	−	0.704917i	$-0.249016\pi$
$642$	2.77993	−	15.7657i	0.109715	−	0.622224i
$643$	−7.24334	−	2.63636i	−0.285650	−	0.103968i	0.195222	−	0.980759i	$-0.437457\pi$
$643$	−7.24334	−	2.63636i	−0.285650	−	0.103968i	−0.480871	+	0.876791i	$0.659680\pi$
$644$	−5.25055	+	4.40573i	−0.206901	+	0.173610i
$645$	9.19256			0.361957
$646$		0			0
$647$	−32.1246			−1.26295			−0.631474	−	0.775397i	$-0.717550\pi$
$647$	−32.1246			−1.26295			−0.631474	+	0.775397i	$0.717550\pi$
$648$	3.60216	−	3.02257i	0.141506	−	0.118738i
$649$	−9.52013	−	3.46504i	−0.373698	−	0.136015i
$650$	−2.18142	+	12.3715i	−0.0855624	+	0.485248i
$651$	−1.01655	−	5.76517i	−0.0398419	−	0.225955i
$652$	3.79114	−	1.37986i	0.148472	−	0.0540395i
$653$	−9.87132	+	17.0976i	−0.386295	+	0.669082i	−0.991948	−	0.126647i	$-0.959579\pi$
$653$	−9.87132	+	17.0976i	−0.386295	+	0.669082i	0.605653	+	0.795729i	$0.292912\pi$
$654$	−0.502029	−	0.869539i	−0.0196309	−	0.0340017i
$655$	−4.81980	−	4.04429i	−0.188325	−	0.158023i
$656$	−16.8475	−	14.1367i	−0.657783	−	0.551946i
$657$	7.28115	+	12.6113i	0.284065	+	0.492015i
$658$	−6.29412	+	10.9017i	−0.245371	+	0.424994i
$659$	17.5517	−	6.38829i	0.683716	−	0.248852i	0.0232739	−	0.999729i	$-0.492591\pi$
$659$	17.5517	−	6.38829i	0.683716	−	0.248852i	0.660442	+	0.750877i	$0.270369\pi$
$660$	−0.564217	−	3.19983i	−0.0219621	−	0.124553i
$661$	−0.876109	+	4.96866i	−0.0340767	+	0.193258i	−0.997094	−	0.0761810i	$-0.975727\pi$
$661$	−0.876109	+	4.96866i	−0.0340767	+	0.193258i	0.963017	+	0.269439i	$0.0868384\pi$
$662$	−26.8198	−	9.76160i	−1.04238	−	0.379395i
$663$	−6.85171	+	5.74927i	−0.266098	+	0.223283i
$664$	−3.80423			−0.147633
$665$		0			0
$666$	12.2361			0.474138
$667$	5.27185	−	4.42361i	0.204127	−	0.171283i
$668$	3.99675	+	1.45470i	0.154639	+	0.0562840i
$669$	2.77467	−	15.7360i	0.107275	−	0.608387i
$670$	−0.0432772	−	0.245437i	−0.00167194	−	0.00948207i
$671$	−1.79465	+	0.653200i	−0.0692818	+	0.0252165i
$672$	−8.35410	+	14.4697i	−0.322266	+	0.558182i
$673$	−14.1271	−	24.4688i	−0.544559	−	0.943204i	−0.998635	−	0.0522410i	$-0.983364\pi$
$673$	−14.1271	−	24.4688i	−0.544559	−	0.943204i	0.454075	−	0.890963i	$-0.349970\pi$
$674$	14.5122	+	12.1771i	0.558987	+	0.469046i
$675$	−14.4396	−	12.1163i	−0.555782	−	0.466357i
$676$	−1.09017	−	1.88823i	−0.0419296	−	0.0726242i
$677$	−5.84510	+	10.1240i	−0.224645	+	0.389097i	−0.956213	−	0.292672i	$-0.905456\pi$
$677$	−5.84510	+	10.1240i	−0.224645	+	0.389097i	0.731568	+	0.681769i	$0.238789\pi$
$678$		0			0
$679$	11.5236	+	65.3538i	0.442236	+	2.50805i
$680$	−1.63309	+	9.26169i	−0.0626260	+	0.355170i
$681$	32.8169	+	11.9444i	1.25755	+	0.457709i
$682$	3.83022	−	3.21394i	0.146667	−	0.123068i
$683$	−32.7445			−1.25293			−0.626466	−	0.779449i	$-0.715499\pi$
$683$	−32.7445			−1.25293			−0.626466	+	0.779449i	$0.715499\pi$
$684$		0			0
$685$	−5.81966			−0.222358
$686$	−15.0464	+	12.6254i	−0.574474	+	0.482041i
$687$	4.51831	+	1.64453i	0.172384	+	0.0627427i
$688$	2.61668	−	14.8400i	0.0997601	−	0.565768i
$689$	0.239976	+	1.36097i	0.00914235	+	0.0518489i
$690$	−4.20243	+	1.52956i	−0.159984	+	0.0582294i
$691$	−23.1525	+	40.1013i	−0.880762	+	1.52552i	−0.0302661	+	0.999542i	$0.509635\pi$
$691$	−23.1525	+	40.1013i	−0.880762	+	1.52552i	−0.850496	+	0.525982i	$0.823698\pi$
$692$	4.80828	+	8.32819i	0.182783	+	0.316590i
$693$	−18.9967	−	15.9401i	−0.721623	−	0.605514i
$694$	−22.3629	−	18.7647i	−0.848885	−	0.712299i
$695$	0.562306	+	0.973942i	0.0213295	+	0.0369437i
$696$	4.75528	−	8.23639i	0.180249	−	0.312200i
$697$	−21.4488	+	7.80673i	−0.812432	+	0.295701i
$698$	2.32347	+	13.1770i	0.0879445	+	0.498758i
$699$	−2.75014	+	15.5968i	−0.104020	+	0.589927i
$700$	8.54197	+	3.10902i	0.322856	+	0.117510i
$701$	−25.8484	+	21.6894i	−0.976279	+	0.819196i	−0.983524	−	0.180778i	$-0.942138\pi$
$701$	−25.8484	+	21.6894i	−0.976279	+	0.819196i	0.00724458	+	0.999974i	$0.497694\pi$
$702$	19.6417			0.741327
$703$		0			0
$704$	−31.5066			−1.18745
$705$	2.81384	−	2.36109i	0.105975	−	0.0889237i
$706$	−30.5089	−	11.1043i	−1.14822	−	0.417918i
$707$	10.2572	−	58.1715i	0.385762	−	2.18776i
$708$	−0.353277	−	2.00353i	−0.0132770	−	0.0752974i
$709$	−12.6073	+	4.58868i	−0.473477	+	0.172332i	−0.567727	−	0.823217i	$-0.692177\pi$
$709$	−12.6073	+	4.58868i	−0.473477	+	0.172332i	0.0942497	+	0.995549i	$0.469955\pi$
$710$	−8.81966	+	15.2761i	−0.330996	+	0.573302i
$711$	−6.15537	−	10.6614i	−0.230844	−	0.399834i
$712$	41.8235	+	35.0941i	1.56740	+	1.31521i
$713$	2.35764	+	1.97830i	0.0882944	+	0.0740878i
$714$	−7.23607	−	12.5332i	−0.270803	−	0.469045i
$715$	6.88191	−	11.9198i	0.257369	−	0.445776i
$716$	−10.6248	+	3.86711i	−0.397067	+	0.144521i
$717$	3.23639	+	18.3545i	0.120865	+	0.685460i
$718$	−7.67918	+	43.5508i	−0.286585	+	1.62530i
$719$	−11.6352	−	4.23488i	−0.433921	−	0.157934i	0.115818	−	0.993270i	$-0.463051\pi$
$719$	−11.6352	−	4.23488i	−0.433921	−	0.157934i	−0.549740	+	0.835336i	$0.685273\pi$
$720$	3.64938	−	3.06220i	0.136004	−	0.114121i
$721$	−4.25325			−0.158399
$722$		0			0
$723$	26.6312			0.990425
$724$	−11.6568	+	9.78124i	−0.433222	+	0.363517i
$725$	−8.57662	−	3.12163i	−0.318528	−	0.115935i
$726$	−0.501590	+	2.84466i	−0.0186158	+	0.105575i
$727$	−3.30899	−	18.7662i	−0.122724	−	0.696001i	−0.982634	−	0.185555i	$-0.940592\pi$
$727$	−3.30899	−	18.7662i	−0.122724	−	0.696001i	0.859910	−	0.510446i	$-0.170520\pi$
$728$	−37.7048	+	13.7234i	−1.39743	+	0.508624i
$729$	−10.8090	+	18.7218i	−0.400334	+	0.693399i
$730$	−6.53888	−	11.3257i	−0.242015	−	0.419182i
$731$	−11.9804	−	10.0528i	−0.443112	−	0.371815i
$732$	−0.293790	−	0.246519i	−0.0108588	−	0.00911161i
$733$	−17.5902	−	30.4671i	−0.649708	−	1.12533i	−0.983193	−	0.182571i	$-0.941558\pi$
$733$	−17.5902	−	30.4671i	−0.649708	−	1.12533i	0.333485	−	0.942755i	$-0.391775\pi$
$734$	−12.6210	+	21.8602i	−0.465850	+	0.806876i
$735$	14.9439	−	5.43913i	0.551214	−	0.200625i
$736$	−1.52533	−	8.65057i	−0.0562244	−	0.318864i
$737$	0.107756	−	0.611114i	0.00396924	−	0.0225107i
$738$	16.5032	+	6.00666i	0.607490	+	0.221108i
$739$	8.06481	−	6.76718i	0.296669	−	0.248935i	−0.482287	−	0.876013i	$-0.660194\pi$
$739$	8.06481	−	6.76718i	0.296669	−	0.248935i	0.778956	+	0.627078i	$0.215749\pi$
$740$	4.91428			0.180653
$741$		0			0
$742$	−2.23607			−0.0820886
$743$	−3.30837	+	2.77605i	−0.121372	+	0.101843i	−0.701454	−	0.712715i	$-0.747465\pi$
$743$	−3.30837	+	2.77605i	−0.121372	+	0.101843i	0.580081	+	0.814559i	$0.303021\pi$
$744$	3.99675	+	1.45470i	0.146528	+	0.0533318i
$745$	−4.94413	+	28.0396i	−0.181139	+	1.02729i
$746$	0.881614	+	4.99988i	0.0322782	+	0.183059i
$747$	1.87939	−	0.684040i	0.0687631	−	0.0250277i
$748$	−2.76393	+	4.78727i	−0.101059	+	0.175040i
$749$	−24.5357	−	42.4971i	−0.896515	−	1.55281i
$750$	11.0863	+	9.30251i	0.404814	+	0.339680i
$751$	−33.9075	−	28.4518i	−1.23730	−	1.03822i	−0.997730	−	0.0673426i	$-0.978548\pi$
$751$	−33.9075	−	28.4518i	−1.23730	−	1.03822i	−0.239574	−	0.970878i	$-0.577008\pi$
$752$	−3.01064	−	5.21459i	−0.109787	−	0.190156i
$753$	6.12261	−	10.6047i	0.223120	−	0.386456i
$754$	8.93701	−	3.25280i	0.325467	−	0.118460i
$755$	−0.527403	−	2.99105i	−0.0191942	−	0.108856i
$756$	2.46804	−	13.9969i	0.0897616	−	0.509063i
$757$	3.50457	+	1.27556i	0.127376	+	0.0463610i	0.404922	−	0.914351i	$-0.367299\pi$
$757$	3.50457	+	1.27556i	0.127376	+	0.0463610i	−0.277546	+	0.960712i	$0.589521\pi$
$758$	7.16062	−	6.00847i	0.260085	−	0.218238i
$759$	−11.1352			−0.404181
$760$		0			0
$761$	−6.05573			−0.219520			−0.109760	−	0.993958i	$-0.535008\pi$
$761$	−6.05573			−0.219520			−0.109760	+	0.993958i	$0.535008\pi$
$762$	−16.8785	+	14.1627i	−0.611443	+	0.513062i
$763$	−2.89208	−	1.05263i	−0.104700	−	0.0381078i
$764$	1.82445	−	10.3470i	0.0660062	−	0.374340i
$765$	−0.858564	−	4.86916i	−0.0310414	−	0.176045i
$766$	15.5111	−	5.64558i	0.560439	−	0.203983i
$767$	4.30902	−	7.46344i	0.155590	−	0.269489i
$768$	−7.80021	−	13.5104i	−0.281466	−	0.487513i
$769$	−27.6994	−	23.2426i	−0.998867	−	0.838149i	−0.0120403	−	0.999928i	$-0.503833\pi$
$769$	−27.6994	−	23.2426i	−0.998867	−	0.838149i	−0.986827	+	0.161778i	$0.948277\pi$
$770$	17.0601	+	14.3151i	0.614802	+	0.515880i
$771$	−5.32624	−	9.22531i	−0.191820	−	0.332242i
$772$	1.62460	−	2.81389i	0.0584706	−	0.101274i
$773$	34.8045	−	12.6678i	1.25183	−	0.455630i	0.370812	−	0.928708i	$-0.379080\pi$
$773$	34.8045	−	12.6678i	1.25183	−	0.455630i	0.881020	+	0.473079i	$0.156857\pi$
$774$	2.08955	+	11.8504i	0.0751072	+	0.425954i
$775$	0.708787	−	4.01973i	0.0254604	−	0.144393i
$776$	−45.3071	−	16.4904i	−1.62643	−	0.591972i
$777$	−24.5398	+	20.5913i	−0.880361	+	0.738710i
$778$	15.3884			0.551702
$779$		0			0
$780$	2.76393			0.0989646
$781$	−33.6448	+	28.2313i	−1.20390	+	1.01020i
$782$	7.14961	+	2.60224i	0.255669	+	0.0930561i
$783$	−2.47805	+	14.0537i	−0.0885582	+	0.502239i
$784$	−4.52681	−	25.6728i	−0.161672	−	0.916887i
$785$	−18.0760	+	6.57912i	−0.645160	+	0.234819i
$786$	−3.51722	+	6.09201i	−0.125455	+	0.217295i
$787$	7.15942	+	12.4005i	0.255206	+	0.442030i	0.964951	−	0.262429i	$-0.0845234\pi$
$787$	7.15942	+	12.4005i	0.255206	+	0.442030i	−0.709746	+	0.704458i	$0.751190\pi$
$788$	−1.19680	−	1.00423i	−0.0426341	−	0.0357742i
$789$	−10.7061	−	8.98348i	−0.381147	−	0.319821i
$790$	5.52786	+	9.57454i	0.196673	+	0.340647i
$791$		0			0
$792$	16.9305	−	6.16220i	0.601600	−	0.218964i
$793$	−0.282109	−	1.59992i	−0.0100180	−	0.0568147i
$794$	3.00247	−	17.0278i	0.106554	−	0.604296i
$795$	0.613127	+	0.223160i	0.0217454	+	0.00791467i
$796$	8.96900	−	7.52589i	0.317898	−	0.266748i
$797$	12.8658			0.455729			0.227864	−	0.973693i	$-0.426826\pi$
$797$	12.8658			0.455729			0.227864	+	0.973693i	$0.426826\pi$
$798$		0			0
$799$	−6.24922			−0.221082
$800$	−8.92419	+	7.48829i	−0.315518	+	0.264751i
$801$	−26.9722	−	9.81708i	−0.953016	−	0.346869i
$802$	1.55316	−	8.80839i	0.0548439	−	0.311035i
$803$	−5.65439	−	32.0676i	−0.199539	−	1.13164i
$804$	0.117097	−	0.0426197i	0.00412969	−	0.00150308i
$805$	−6.85410	+	11.8717i	−0.241575	+	0.418421i
$806$	2.12663	+	3.68343i	0.0749072	+	0.129743i
$807$	−6.94717	−	5.82937i	−0.244552	−	0.205203i
$808$	32.8756	+	27.5859i	1.15656	+	0.970469i
$809$	0.364745	+	0.631757i	0.0128238	+	0.0222114i	0.872366	−	0.488853i	$-0.162585\pi$
$809$	0.364745	+	0.631757i	0.0128238	+	0.0222114i	−0.859542	+	0.511065i	$0.829251\pi$
$810$	1.11006	−	1.92268i	0.0390035	−	0.0675560i
$811$	30.1866	−	10.9870i	1.06000	−	0.385807i	0.247569	−	0.968870i	$-0.420368\pi$
$811$	30.1866	−	10.9870i	1.06000	−	0.385807i	0.812427	+	0.583064i	$0.198146\pi$
$812$	−1.19503	−	6.77736i	−0.0419374	−	0.237839i
$813$	−2.91312	+	16.5211i	−0.102168	+	0.579421i
$814$	−25.7106	−	9.35790i	−0.901157	−	0.327994i
$815$	6.18112	−	5.18658i	0.216515	−	0.181678i
$816$	6.92240			0.242332
$817$		0			0
$818$	−25.7771			−0.901275
$819$	16.1595	−	13.5594i	0.564659	−	0.473805i
$820$	6.62805	+	2.41241i	0.231462	+	0.0842451i
$821$	−3.30530	+	18.7453i	−0.115356	+	0.654214i	0.871218	+	0.490897i	$0.163331\pi$
$821$	−3.30530	+	18.7453i	−0.115356	+	0.654214i	−0.986574	+	0.163318i	$0.947780\pi$
$822$	1.12986	+	6.40773i	0.0394082	+	0.223495i
$823$	36.3862	−	13.2435i	1.26834	−	0.461639i	0.381782	−	0.924252i	$-0.375310\pi$
$823$	36.3862	−	13.2435i	1.26834	−	0.461639i	0.886560	+	0.462613i	$0.153088\pi$
$824$	1.54508	−	2.67617i	0.0538256	−	0.0932286i
$825$	7.38394	+	12.7894i	0.257076	+	0.445268i
$826$	10.6819	+	8.96321i	0.371672	+	0.311870i
$827$	12.0510	+	10.1120i	0.419054	+	0.351628i	0.827803	−	0.561019i	$-0.189590\pi$
$827$	12.0510	+	10.1120i	0.419054	+	0.351628i	−0.408749	+	0.912647i	$0.634035\pi$
$828$	1.30902	+	2.26728i	0.0454915	+	0.0787936i
$829$	−5.84510	+	10.1240i	−0.203009	+	0.351621i	−0.949496	−	0.313778i	$-0.898405\pi$
$829$	−5.84510	+	10.1240i	−0.203009	+	0.351621i	0.746488	+	0.665399i	$0.231739\pi$
$830$	−1.68779	+	0.614306i	−0.0585842	+	0.0213229i
$831$	3.92677	+	22.2698i	0.136218	+	0.772531i
$832$	4.65396	−	26.3939i	0.161347	−	0.915045i
$833$	−25.4241	−	9.25360i	−0.880892	−	0.320618i
$834$	0.963189	−	0.808212i	0.0333525	−	0.0279861i
$835$	8.50651			0.294380
$836$		0			0
$837$	−6.38197			−0.220593
$838$	−30.0928	+	25.2508i	−1.03954	+	0.872276i
$839$	−22.1931	−	8.07763i	−0.766191	−	0.278871i	−0.0707887	−	0.997491i	$-0.522552\pi$
$839$	−22.1931	−	8.07763i	−0.766191	−	0.278871i	−0.695402	+	0.718621i	$0.744774\pi$
$840$	−3.28964	+	18.6565i	−0.113503	+	0.643709i
$841$	−3.83592	−	21.7546i	−0.132273	−	0.750158i
$842$	−15.6282	+	5.68820i	−0.538584	+	0.196028i
$843$	2.60081	−	4.50474i	0.0895768	−	0.155151i
$844$	5.56758	+	9.64333i	0.191644	+	0.331937i
$845$	−3.34047	−	2.80299i	−0.114916	−	0.0964258i
$846$	3.68336	+	3.09070i	0.126636	+	0.106261i
$847$	4.42705	+	7.66788i	0.152115	+	0.263471i
$848$	0.534785	−	0.926274i	0.0183646	−	0.0318084i
$849$	−1.00507	+	0.365814i	−0.0344938	+	0.0125547i
$850$	−1.75222	−	9.93732i	−0.0601006	−	0.340847i
$851$	2.92450	−	16.5856i	0.100250	−	0.568549i
$852$	−8.28777	−	3.01650i	−0.283934	−	0.103344i
$853$	−17.0866	+	14.3373i	−0.585034	+	0.490901i	−0.886596	−	0.462545i	$-0.846936\pi$
$853$	−17.0866	+	14.3373i	−0.585034	+	0.490901i	0.301562	+	0.953446i	$0.402492\pi$
$854$	2.62866			0.0899507
$855$		0			0
$856$	35.6525			1.21858
$857$	16.1285	−	13.5334i	0.550939	−	0.462293i	−0.324320	−	0.945948i	$-0.605135\pi$
$857$	16.1285	−	13.5334i	0.550939	−	0.462293i	0.875259	+	0.483655i	$0.160691\pi$
$858$	−14.4604	−	5.26315i	−0.493669	−	0.179681i
$859$	3.65629	−	20.7358i	0.124751	−	0.707498i	−0.856704	−	0.515808i	$-0.827492\pi$
$859$	3.65629	−	20.7358i	0.124751	−	0.707498i	0.981455	−	0.191690i	$-0.0613969\pi$
$860$	0.839210	+	4.75939i	0.0286168	+	0.162294i
$861$	−43.2059	+	15.7256i	−1.47245	+	0.535929i
$862$	−9.37132	+	16.2316i	−0.319189	+	0.552851i
$863$	13.5923	+	23.5426i	0.462687	+	0.801398i	0.999094	−	0.0425616i	$-0.0135519\pi$
$863$	13.5923	+	23.5426i	0.462687	+	0.801398i	−0.536406	+	0.843960i	$0.680219\pi$
$864$	13.9533	+	11.7082i	0.474702	+	0.398322i
$865$	14.7334	+	12.3628i	0.500952	+	0.420348i
$866$	−5.48936	−	9.50785i	−0.186536	−	0.323090i
$867$	−6.40013	+	11.0853i	−0.217360	+	0.376478i
$868$	2.89208	−	1.05263i	0.0981635	−	0.0357286i
$869$	4.78012	+	27.1094i	0.162155	+	0.919624i
$870$	0.779729	−	4.42206i	0.0264353	−	0.149922i
$871$	0.496030	+	0.180540i	0.0168073	+	0.00611737i
$872$	1.71293	−	1.43732i	0.0580070	−	0.0486737i
$873$	25.3480			0.857900
$874$		0			0
$875$	44.3607			1.49966
$876$	5.00907	−	4.20311i	0.169241	−	0.142010i
$877$	38.8013	+	14.1225i	1.31023	+	0.476883i	0.900314	−	0.435242i	$-0.143337\pi$
$877$	38.8013	+	14.1225i	1.31023	+	0.476883i	0.409912	+	0.912125i	$0.365559\pi$
$878$	2.36475	−	13.4111i	0.0798063	−	0.452604i
$879$	5.04776	+	28.6273i	0.170257	+	0.965574i
$880$	−10.0101	+	3.64336i	−0.337439	+	0.122818i
$881$	27.7877	−	48.1298i	0.936192	−	1.62153i	0.163699	−	0.986510i	$-0.447657\pi$
$881$	27.7877	−	48.1298i	0.936192	−	1.62153i	0.772494	−	0.635022i	$-0.219009\pi$
$882$	10.4086	+	18.0283i	0.350477	+	0.607043i
$883$	32.9663	+	27.6620i	1.10940	+	0.930901i	0.998021	−	0.0628769i	$-0.0200276\pi$
$883$	32.9663	+	27.6620i	1.10940	+	0.930901i	0.111383	+	0.993778i	$0.464472\pi$
$884$	−3.60216	−	3.02257i	−0.121154	−	0.101660i
$885$	−2.03444	−	3.52376i	−0.0683870	−	0.118450i
$886$	4.22050	−	7.31012i	0.141790	−	0.245588i
$887$	25.0236	−	9.10785i	0.840211	−	0.305812i	0.114168	−	0.993461i	$-0.463580\pi$
$887$	25.0236	−	9.10785i	0.840211	−	0.305812i	0.726043	+	0.687650i	$0.241357\pi$
$888$	−4.04155	−	22.9208i	−0.135626	−	0.769171i
$889$	−11.7278	+	66.5115i	−0.393337	+	2.23072i
$890$	24.2225	+	8.81628i	0.811941	+	0.295522i
$891$	4.23459	−	3.55324i	0.141864	−	0.119038i
$892$	8.40051			0.281270
$893$		0			0
$894$	31.8328			1.06465
$895$	−17.3228	+	14.5356i	−0.579038	+	0.485871i
$896$	14.0384	+	5.10957i	0.468991	+	0.170699i
$897$	1.64482	−	9.32823i	0.0549189	−	0.311461i
$898$	7.13752	+	40.4789i	0.238182	+	1.35080i
$899$	−2.90381	+	1.05690i	−0.0968475	+	0.0352496i
$900$	1.73607	−	3.00696i	0.0578689	−	0.100232i
$901$	−0.555029	−	0.961339i	−0.0184907	−	0.0320268i
$902$	−30.0830	−	25.2426i	−1.00165	−	0.840487i
$903$	−24.1330	−	20.2500i	−0.803096	−	0.673877i
$904$		0			0
$905$	−15.2169	+	26.3565i	−0.505827	+	0.876118i
$906$	−3.19090	+	1.16139i	−0.106011	+	0.0385847i
$907$	−2.19730	−	12.4615i	−0.0729602	−	0.413778i	−0.999311	−	0.0371160i	$-0.988183\pi$
$907$	−2.19730	−	12.4615i	−0.0729602	−	0.413778i	0.926351	−	0.376662i	$-0.122928\pi$
$908$	−3.18820	+	18.0812i	−0.105804	+	0.600045i
$909$	−21.2016	−	7.71676i	−0.703214	−	0.255949i
$910$	−14.5122	+	12.1771i	−0.481073	+	0.403668i
$911$	−18.3601			−0.608297			−0.304149	−	0.952625i	$-0.598372\pi$
$911$	−18.3601			−0.608297			−0.304149	+	0.952625i	$0.598372\pi$
$912$		0			0
$913$	−4.47214			−0.148006
$914$	17.7480	−	14.8923i	0.587052	−	0.492595i
$915$	−0.720774	−	0.262340i	−0.0238280	−	0.00867270i
$916$	−0.438959	+	2.48946i	−0.0145036	+	0.0822541i
$917$	3.74426	+	21.2347i	0.123646	+	0.701232i
$918$	−14.8256	+	5.39608i	−0.489318	+	0.178097i
$919$	1.31966	−	2.28572i	0.0435316	−	0.0753989i	−0.843439	−	0.537225i	$-0.819472\pi$
$919$	1.31966	−	2.28572i	0.0435316	−	0.0753989i	0.886970	+	0.461827i	$0.152806\pi$
$920$	−4.97980	−	8.62526i	−0.164179	−	0.284366i
$921$	−24.8487	−	20.8505i	−0.818793	−	0.687049i
$922$	−30.7807	−	25.8281i	−1.01371	−	0.850603i
$923$	−18.6803	−	32.3553i	−0.614871	−	1.06499i
$924$	−5.56758	+	9.64333i	−0.183160	+	0.317242i
$925$	−20.9888	+	7.63931i	−0.690108	+	0.251179i
$926$	3.44052	+	19.5122i	0.113063	+	0.641210i
$927$	−0.282109	+	1.59992i	−0.00926566	+	0.0525482i
$928$	8.28777	+	3.01650i	0.272059	+	0.0990215i
$929$	−16.4750	+	13.8242i	−0.540527	+	0.453556i	−0.871718	−	0.490008i	$-0.836994\pi$
$929$	−16.4750	+	13.8242i	−0.540527	+	0.453556i	0.331191	+	0.943564i	$0.392550\pi$
$930$	2.00811			0.0658487
$931$		0			0
$932$	−8.32624			−0.272735
$933$	4.97806	−	4.17709i	0.162974	−	0.136752i
$934$	0.260778	+	0.0949156i	0.00853293	+	0.00310573i
$935$	−1.91981	+	10.8878i	−0.0627844	+	0.356068i
$936$	2.66137	+	15.0934i	0.0869897	+	0.493343i
$937$	39.2776	−	14.2959i	1.28314	−	0.467026i	0.391673	−	0.920104i	$-0.371896\pi$
$937$	39.2776	−	14.2959i	1.28314	−	0.467026i	0.891471	+	0.453078i	$0.149674\pi$
$938$	−0.427051	+	0.739674i	−0.0139437	+	0.0241512i
$939$	4.47777	+	7.75572i	0.146126	+	0.253098i
$940$	1.47932	+	1.24130i	0.0482501	+	0.0404867i
$941$	−11.1504	−	9.35634i	−0.363494	−	0.305008i	0.442687	−	0.896676i	$-0.354025\pi$
$941$	−11.1504	−	9.35634i	−0.363494	−	0.305008i	−0.806182	+	0.591668i	$0.798470\pi$
$942$	10.7533	+	18.6252i	0.350361	+	0.606843i
$943$	12.0862	−	20.9339i	0.393581	−	0.681703i
$944$	−6.26766	+	2.28124i	−0.203995	+	0.0742481i
$945$	−4.93607	−	27.9938i	−0.160570	−	0.910640i
$946$	4.67237	−	26.4983i	0.151912	−	0.861535i
$947$	5.46869	+	1.99044i	0.177709	+	0.0646806i	0.429342	−	0.903142i	$-0.358746\pi$
$947$	5.46869	+	1.99044i	0.177709	+	0.0646806i	−0.251633	+	0.967823i	$0.580968\pi$
$948$	−4.23459	+	3.55324i	−0.137533	+	0.115404i
$949$	27.6992			0.899153
$950$		0			0
$951$	10.4033			0.337349
$952$	24.6896	−	20.7170i	0.800193	−	0.671442i
$953$	35.0653	+	12.7627i	1.13588	+	0.413425i	0.840423	−	0.541932i	$-0.182307\pi$
$953$	35.0653	+	12.7627i	1.13588	+	0.413425i	0.295454	+	0.955357i	$0.404529\pi$
$954$	−0.148313	+	0.841126i	−0.00480182	+	0.0272325i
$955$	−3.64890	−	20.6939i	−0.118076	−	0.669639i
$956$	−9.20746	+	3.35124i	−0.297791	+	0.108387i
$957$	5.59017	−	9.68246i	0.180705	−	0.312989i
$958$	15.9232	+	27.5798i	0.514455	+	0.891063i
$959$	15.2782	+	12.8199i	0.493359	+	0.413977i
$960$	−9.69334	−	8.13368i	−0.312851	−	0.262513i
$961$	14.8090	+	25.6500i	0.477710	+	0.827418i
$962$	11.6372	−	20.1562i	0.375198	−	0.649862i
$963$	−17.6132	+	6.41069i	−0.567579	+	0.206582i
$964$	2.43122	+	13.7881i	0.0783044	+	0.444086i
$965$	1.12843	−	6.39967i	0.0363256	−	0.206013i
$966$	14.4020	+	5.24188i	0.463375	+	0.168655i
$967$	25.8220	−	21.6672i	0.830379	−	0.696771i	−0.124999	−	0.992157i	$-0.539893\pi$
$967$	25.8220	−	21.6672i	0.830379	−	0.696771i	0.955378	+	0.295386i	$0.0954483\pi$
$968$	−6.43288			−0.206761
$969$		0			0
$970$	−22.7639			−0.730906
$971$	13.0829	−	10.9779i	0.419851	−	0.352297i	−0.408256	−	0.912868i	$-0.633863\pi$
$971$	13.0829	−	10.9779i	0.419851	−	0.352297i	0.828106	+	0.560571i	$0.189418\pi$
$972$	−8.41545	−	3.06297i	−0.269926	−	0.0982449i
$973$	0.669258	−	3.79555i	0.0214554	−	0.121680i
$974$	−3.17634	−	18.0139i	−0.101776	−	0.577203i
$975$	−11.8047	+	4.29656i	−0.378053	+	0.137600i
$976$	−0.628677	+	1.08890i	−0.0201235	+	0.0348549i
$977$	−14.1271	−	24.4688i	−0.451966	−	0.782827i	0.546542	−	0.837431i	$-0.315944\pi$
$977$	−14.1271	−	24.4688i	−0.451966	−	0.782827i	−0.998508	+	0.0546039i	$0.982610\pi$
$978$	−6.91071	−	5.79877i	−0.220980	−	0.185424i
$979$	49.1665	+	41.2556i	1.57137	+	1.31853i
$980$	4.18034	+	7.24056i	0.133536	+	0.231291i
$981$	−0.587785	+	1.01807i	−0.0187665	+	0.0325046i
$982$	17.9736	−	6.54186i	0.573561	−	0.208759i
$983$	3.75242	+	21.2810i	0.119683	+	0.678759i	0.984324	+	0.176368i	$0.0564349\pi$
$983$	3.75242	+	21.2810i	0.119683	+	0.678759i	−0.864641	+	0.502391i	$0.832454\pi$
$984$	5.80080	−	32.8980i	0.184923	−	1.04875i
$985$	−2.93617	−	1.06868i	−0.0935543	−	0.0340510i
$986$	−5.85206	+	4.91046i	−0.186368	+	0.156381i
$987$	−12.5882			−0.400688
$988$		0			0
$989$	16.5623			0.526651
$990$	6.51636	−	5.46788i	0.207104	−	0.173781i
$991$	19.7845	+	7.20098i	0.628477	+	0.228747i	0.636568	−	0.771220i	$-0.280353\pi$
$991$	19.7845	+	7.20098i	0.628477	+	0.228747i	−0.00809149	+	0.999967i	$0.502576\pi$
$992$	−0.684916	+	3.88435i	−0.0217461	+	0.123328i
$993$	−4.95610	−	28.1074i	−0.157277	−	0.891962i
$994$	56.8052	−	20.6754i	1.80175	−	0.655784i
$995$	11.7082	−	20.2792i	0.371175	−	0.642894i
$996$	−0.449028	−	0.777739i	−0.0142280	−	0.0246436i
$997$	5.45777	+	4.57961i	0.172849	+	0.145038i	0.725108	−	0.688635i	$-0.241790\pi$
$997$	5.45777	+	4.57961i	0.172849	+	0.145038i	−0.552259	+	0.833673i	$0.686234\pi$
$998$	19.3867	+	16.2674i	0.613675	+	0.514934i
$999$	17.4615	+	30.2442i	0.552457	+	0.956884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.m.234.3		24
19.2	odd	18	inner	361.2.e.m.62.3		24
19.3	odd	18	inner	361.2.e.m.54.2		24
19.4	even	9		361.2.a.i.1.3	yes	4
19.5	even	9	inner	361.2.e.m.245.3		24
19.6	even	9		361.2.c.j.292.2		8
19.7	even	3	inner	361.2.e.m.28.3		24
19.8	odd	6	inner	361.2.e.m.99.3		24
19.9	even	9		361.2.c.j.68.2		8
19.10	odd	18		361.2.c.j.68.3		8
19.11	even	3	inner	361.2.e.m.99.2		24
19.12	odd	6	inner	361.2.e.m.28.2		24
19.13	odd	18		361.2.c.j.292.3		8
19.14	odd	18	inner	361.2.e.m.245.2		24
19.15	odd	18		361.2.a.i.1.2	✓	4
19.16	even	9	inner	361.2.e.m.54.3		24
19.17	even	9	inner	361.2.e.m.62.2		24
19.18	odd	2	inner	361.2.e.m.234.2		24
57.23	odd	18		3249.2.a.bc.1.2		4
57.53	even	18		3249.2.a.bc.1.3		4
76.15	even	18		5776.2.a.bu.1.2		4
76.23	odd	18		5776.2.a.bu.1.3		4
95.4	even	18		9025.2.a.bj.1.2		4
95.34	odd	18		9025.2.a.bj.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.i.1.2	✓	4	19.15	odd	18
361.2.a.i.1.3	yes	4	19.4	even	9
361.2.c.j.68.2		8	19.9	even	9
361.2.c.j.68.3		8	19.10	odd	18
361.2.c.j.292.2		8	19.6	even	9
361.2.c.j.292.3		8	19.13	odd	18
361.2.e.m.28.2		24	19.12	odd	6	inner
361.2.e.m.28.3		24	19.7	even	3	inner
361.2.e.m.54.2		24	19.3	odd	18	inner
361.2.e.m.54.3		24	19.16	even	9	inner
361.2.e.m.62.2		24	19.17	even	9	inner
361.2.e.m.62.3		24	19.2	odd	18	inner
361.2.e.m.99.2		24	19.11	even	3	inner
361.2.e.m.99.3		24	19.8	odd	6	inner
361.2.e.m.234.2		24	19.18	odd	2	inner
361.2.e.m.234.3		24	1.1	even	1	trivial
361.2.e.m.245.2		24	19.14	odd	18	inner
361.2.e.m.245.3		24	19.5	even	9	inner
3249.2.a.bc.1.2		4	57.23	odd	18
3249.2.a.bc.1.3		4	57.53	even	18
5776.2.a.bu.1.2		4	76.15	even	18
5776.2.a.bu.1.3		4	76.23	odd	18
9025.2.a.bj.1.2		4	95.4	even	18
9025.2.a.bj.1.3		4	95.34	odd	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.900539 - 0.755642i) q^{2} +(1.10467 + 0.402069i) q^{3} +(-0.107320 + 0.608645i) q^{4} +(0.214641 + 1.21729i) q^{5} +(1.29862 - 0.472660i) q^{6} +(2.11803 - 3.66854i) q^{7} +(1.53884 + 2.66535i) q^{8} +(-1.23949 - 1.04005i) q^{9} +(1.11313 + 0.934025i) q^{10} +(1.80902 + 3.13331i) q^{11} +(-0.363271 + 0.629204i) q^{12} +(-2.89208 + 1.05263i) q^{13} +(-0.864733 - 4.90414i) q^{14} +(-0.252326 + 1.43101i) q^{15} +(2.23832 + 0.814680i) q^{16} +(1.89377 - 1.58906i) q^{17} -1.90211 q^{18} -0.763932 q^{20} +(3.81475 - 3.20095i) q^{21} +(3.99675 + 1.45470i) q^{22} +(-0.454617 + 2.57826i) q^{23} +(0.628265 + 3.56307i) q^{24} +(3.26274 - 1.18754i) q^{25} +(-1.80902 + 3.13331i) q^{26} +(-2.71441 - 4.70150i) q^{27} +(2.00553 + 1.68284i) q^{28} +(-2.01367 - 1.68967i) q^{29} +(0.854102 + 1.47935i) q^{30} +(0.587785 - 1.01807i) q^{31} +(-3.15285 + 1.14755i) q^{32} +(0.738570 + 4.18864i) q^{33} +(0.504651 - 2.86202i) q^{34} +(4.92029 + 1.79084i) q^{35} +(0.766044 - 0.642788i) q^{36} -6.43288 q^{37} -3.61803 q^{39} +(-2.91421 + 2.44531i) q^{40} +(-8.67623 - 3.15789i) q^{41} +(1.01655 - 5.76517i) q^{42} +(-1.09854 - 6.23013i) q^{43} +(-2.10122 + 0.764780i) q^{44} +(1.00000 - 1.73205i) q^{45} +(1.53884 + 2.66535i) q^{46} +(-1.93646 - 1.62488i) q^{47} +(2.14505 + 1.79991i) q^{48} +(-5.47214 - 9.47802i) q^{49} +(2.04087 - 3.53489i) q^{50} +(2.73091 - 0.993969i) q^{51} +(-0.330298 - 1.87322i) q^{52} +(0.0779729 - 0.442206i) q^{53} +(-5.99709 - 2.18276i) q^{54} +(-3.42585 + 2.87463i) q^{55} +13.0373 q^{56} -3.09017 q^{58} +(-2.14505 + 1.79991i) q^{59} +(-0.843897 - 0.307153i) q^{60} +(-0.0916626 + 0.519845i) q^{61} +(-0.239976 - 1.36097i) q^{62} +(-6.44075 + 2.34424i) q^{63} +(-4.35410 + 7.54153i) q^{64} +(-1.90211 - 3.29456i) q^{65} +(3.83022 + 3.21394i) q^{66} +(-0.131387 - 0.110247i) q^{67} +(0.763932 + 1.32317i) q^{68} +(-1.53884 + 2.66535i) q^{69} +(5.78415 - 2.10526i) q^{70} +(2.10795 + 11.9548i) q^{71} +(0.864733 - 4.90414i) q^{72} +(-8.45723 - 3.07818i) q^{73} +(-5.79306 + 4.86096i) q^{74} +4.08174 q^{75} +15.3262 q^{77} +(-3.25818 + 2.73394i) q^{78} +(7.14961 + 2.60224i) q^{79} +(-0.511267 + 2.89954i) q^{80} +(-0.265311 - 1.50465i) q^{81} +(-10.1995 + 3.71232i) q^{82} +(-0.618034 + 1.07047i) q^{83} +(1.53884 + 2.66535i) q^{84} +(2.34082 + 1.96418i) q^{85} +(-5.69703 - 4.78037i) q^{86} +(-1.54508 - 2.67617i) q^{87} +(-5.56758 + 9.64333i) q^{88} +(16.6697 - 6.06729i) q^{89} +(-0.408271 - 2.31542i) q^{90} +(-2.26390 + 12.8392i) q^{91} +(-1.52045 - 0.553400i) q^{92} +(1.05865 - 0.888311i) q^{93} -2.97168 q^{94} -3.94427 q^{96} +(-12.0008 + 10.0699i) q^{97} +(-12.0899 - 4.40035i) q^{98} +(1.01655 - 5.76517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{7} + 30 q^{11} - 72 q^{20} - 30 q^{26} - 60 q^{30} - 60 q^{39} + 24 q^{45} - 24 q^{49} + 60 q^{58} - 24 q^{64} + 72 q^{68} + 180 q^{77} + 12 q^{83} + 30 q^{87} + 120 q^{96}+O(q^{100}) \) 24 * q + 24 * q^7 + 30 * q^11 - 72 * q^20 - 30 * q^26 - 60 * q^30 - 60 * q^39 + 24 * q^45 - 24 * q^49 + 60 * q^58 - 24 * q^64 + 72 * q^68 + 180 * q^77 + 12 * q^83 + 30 * q^87 + 120 * q^96

Introduction

L-functions

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