LMFDB - Embedded newform 384.2.v.a.13.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [384,2,Mod(13,384)] 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("384.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(384, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 15, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.283082 + 1.38559i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.83973 - 0.784471i) q^{4} +(-0.166665 - 1.69218i) q^{5} +(-1.40810 + 0.131324i) q^{6} +(1.76235 - 2.63755i) q^{7} +(1.60775 - 2.32704i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.39185 + 0.248095i) q^{10} +(0.658421 - 0.351933i) q^{11} +(0.216647 - 1.98823i) q^{12} +(5.74062 + 0.565402i) q^{13} +(3.15567 + 3.18854i) q^{14} +(1.57094 - 0.650703i) q^{15} +(2.76921 + 2.88643i) q^{16} +(-1.29313 - 0.535633i) q^{17} +(-0.534420 - 1.30935i) q^{18} +(-1.14115 + 0.936520i) q^{19} +(-1.02085 + 3.24390i) q^{20} +(3.03556 + 0.920827i) q^{21} +(0.301249 + 1.01193i) q^{22} +(0.925835 - 4.65449i) q^{23} +(2.69355 + 0.863016i) q^{24} +(2.06822 - 0.411395i) q^{25} +(-2.40848 + 7.79410i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(-5.31133 + 3.46986i) q^{28} +(-1.32002 + 2.46958i) q^{29} +(0.456906 + 2.36088i) q^{30} +(-4.43521 + 4.43521i) q^{31} +(-4.78333 + 3.01990i) q^{32} +(0.527909 + 0.527909i) q^{33} +(1.10823 - 1.64012i) q^{34} +(-4.75693 - 2.54263i) q^{35} +(1.96551 - 0.369835i) q^{36} +(7.07753 - 8.62400i) q^{37} +(-0.974595 - 1.84628i) q^{38} +(1.12536 + 5.65756i) q^{39} +(-4.20574 - 2.33277i) q^{40} +(-2.24024 - 0.445611i) q^{41} +(-2.13520 + 3.94538i) q^{42} +(1.80544 - 5.95173i) q^{43} +(-1.48740 + 0.130950i) q^{44} +(1.07870 + 1.31440i) q^{45} +(6.18713 + 2.60043i) q^{46} +(-3.08023 + 7.43634i) q^{47} +(-1.95828 + 3.48785i) q^{48} +(-1.17198 - 2.82941i) q^{49} +(-0.0154502 + 2.98217i) q^{50} +(0.137192 - 1.39294i) q^{51} +(-10.1176 - 5.54354i) q^{52} +(4.90739 + 9.18107i) q^{53} +(1.09784 - 0.891492i) q^{54} +(-0.705271 - 1.05551i) q^{55} +(-3.30427 - 8.34159i) q^{56} +(-1.22745 - 0.820158i) q^{57} +(-3.04816 - 2.52810i) q^{58} +(-2.27056 + 0.223631i) q^{59} +(-3.40056 - 0.0352365i) q^{60} +(9.80077 - 2.97303i) q^{61} +(-4.88986 - 7.40091i) q^{62} +3.17215i q^{63} +(-2.83028 - 7.48262i) q^{64} -9.80840i q^{65} +(-0.880907 + 0.582025i) q^{66} +(-5.79154 + 1.75684i) q^{67} +(1.95882 + 1.99984i) q^{68} +(4.72282 - 0.465157i) q^{69} +(4.86965 - 5.87139i) q^{70} +(-7.56079 - 5.05196i) q^{71} +(-0.0439588 + 2.82809i) q^{72} +(-1.08352 - 1.62161i) q^{73} +(9.94582 + 12.2479i) q^{74} +(0.994055 + 1.85975i) q^{75} +(2.83409 - 0.827742i) q^{76} +(0.232129 - 2.35685i) q^{77} +(-8.15763 - 0.0422635i) q^{78} +(3.37251 + 8.14197i) q^{79} +(4.42283 - 5.16707i) q^{80} +(0.382683 - 0.923880i) q^{81} +(1.25161 - 2.97791i) q^{82} +(10.5661 + 12.8749i) q^{83} +(-4.86224 - 4.07538i) q^{84} +(-0.690867 + 2.27748i) q^{85} +(7.73558 + 4.18643i) q^{86} +(-2.74642 - 0.546298i) q^{87} +(0.239612 - 2.09800i) q^{88} +(-2.08960 - 10.5051i) q^{89} +(-2.12659 + 1.12256i) q^{90} +(11.6083 - 14.1447i) q^{91} +(-5.35460 + 7.83671i) q^{92} +(-5.53170 - 2.95676i) q^{93} +(-9.43177 - 6.37303i) q^{94} +(1.77495 + 1.77495i) q^{95} +(-4.27839 - 3.70073i) q^{96} +(2.14657 - 2.14657i) q^{97} +(4.25218 - 0.822933i) q^{98} +(-0.351933 + 0.658421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.283082	+	1.38559i	−0.200169	+	0.979761i
$2$	−0.283082	+	1.38559i	−0.200169	+	0.979761i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$3$	0.290285	+	0.956940i	0.167596	+	0.552490i
$4$	−1.83973	−	0.784471i	−0.919865	−	0.392236i
$5$	−0.166665	−	1.69218i	−0.0745350	−	0.756767i	−0.957712	−	0.287727i	$-0.907100\pi$
$5$	−0.166665	−	1.69218i	−0.0745350	−	0.756767i	0.883177	−	0.469039i	$-0.155400\pi$
$6$	−1.40810	+	0.131324i	−0.574856	+	0.0536127i
$7$	1.76235	−	2.63755i	0.666106	−	0.996899i	−0.332447	−	0.943122i	$-0.607874\pi$
$7$	1.76235	−	2.63755i	0.666106	−	0.996899i	0.998553	−	0.0537767i	$-0.0171259\pi$
$8$	1.60775	−	2.32704i	0.568426	−	0.822735i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	2.39185	+	0.248095i	0.756370	+	0.0784547i
$11$	0.658421	−	0.351933i	0.198521	−	0.106112i	−0.369141	−	0.929373i	$-0.620348\pi$
$11$	0.658421	−	0.351933i	0.198521	−	0.106112i	0.567662	+	0.823262i	$0.307848\pi$
$12$	0.216647	−	1.98823i	0.0625406	−	0.573953i
$13$	5.74062	+	0.565402i	1.59216	+	0.156814i	0.854900	−	0.518793i	$-0.173619\pi$
$13$	5.74062	+	0.565402i	1.59216	+	0.156814i	0.737262	+	0.675607i	$0.236119\pi$
$14$	3.15567	+	3.18854i	0.843389	+	0.852174i
$15$	1.57094	−	0.650703i	0.405614	−	0.168011i
$16$	2.76921	+	2.88643i	0.692302	+	0.721607i
$17$	−1.29313	−	0.535633i	−0.313630	−	0.129910i	0.220315	−	0.975429i	$-0.429291\pi$
$17$	−1.29313	−	0.535633i	−0.313630	−	0.129910i	−0.533946	+	0.845519i	$0.679291\pi$
$18$	−0.534420	−	1.30935i	−0.125964	−	0.308617i
$19$	−1.14115	+	0.936520i	−0.261799	+	0.214853i	−0.756131	−	0.654421i	$-0.772913\pi$
$19$	−1.14115	+	0.936520i	−0.261799	+	0.214853i	0.494332	+	0.869273i	$0.335413\pi$
$20$	−1.02085	+	3.24390i	−0.228269	+	0.725358i
$21$	3.03556	+	0.920827i	0.662413	+	0.200941i
$22$	0.301249	+	1.01193i	0.0642265	+	0.215744i
$23$	0.925835	−	4.65449i	0.193050	−	0.970528i	−0.755800	−	0.654802i	$-0.772752\pi$
$23$	0.925835	−	4.65449i	0.193050	−	0.970528i	0.948850	−	0.315726i	$-0.102248\pi$
$24$	2.69355	+	0.863016i	0.549818	+	0.176162i
$25$	2.06822	−	0.411395i	0.413645	−	0.0822791i
$26$	−2.40848	+	7.79410i	−0.472342	+	1.52855i
$27$	−0.773010	−	0.634393i	−0.148766	−	0.122089i
$28$	−5.31133	+	3.46986i	−1.00375	+	0.655741i
$29$	−1.32002	+	2.46958i	−0.245121	+	0.458590i	−0.974153	−	0.225890i	$-0.927471\pi$
$29$	−1.32002	+	2.46958i	−0.245121	+	0.458590i	0.729031	+	0.684480i	$0.239971\pi$
$30$	0.456906	+	2.36088i	0.0834192	+	0.431036i
$31$	−4.43521	+	4.43521i	−0.796587	+	0.796587i	−0.982556	−	0.185969i	$-0.940458\pi$
$31$	−4.43521	+	4.43521i	−0.796587	+	0.796587i	0.185969	+	0.982556i	$0.440458\pi$
$32$	−4.78333	+	3.01990i	−0.845581	+	0.533848i
$33$	0.527909	+	0.527909i	0.0918971	+	0.0918971i
$34$	1.10823	−	1.64012i	0.190060	−	0.281279i
$35$	−4.75693	−	2.54263i	−0.804068	−	0.429783i
$36$	1.96551	−	0.369835i	0.327585	−	0.0616392i
$37$	7.07753	−	8.62400i	1.16354	−	1.41778i	0.273513	−	0.961868i	$-0.411814\pi$
$37$	7.07753	−	8.62400i	1.16354	−	1.41778i	0.890027	−	0.455909i	$-0.150686\pi$
$38$	−0.974595	−	1.84628i	−0.158100	−	0.299507i
$39$	1.12536	+	5.65756i	0.180202	+	0.905934i
$40$	−4.20574	−	2.33277i	−0.664986	−	0.368843i
$41$	−2.24024	−	0.445611i	−0.349866	−	0.0695928i	0.0170289	−	0.999855i	$-0.494579\pi$
$41$	−2.24024	−	0.445611i	−0.349866	−	0.0695928i	−0.366895	+	0.930262i	$0.619579\pi$
$42$	−2.13520	+	3.94538i	−0.329469	+	0.608785i
$43$	1.80544	−	5.95173i	0.275327	−	0.907631i	−0.704825	−	0.709381i	$-0.748974\pi$
$43$	1.80544	−	5.95173i	0.275327	−	0.907631i	0.980152	−	0.198249i	$-0.0635256\pi$
$44$	−1.48740	+	0.130950i	−0.224234	+	0.0197414i
$45$	1.07870	+	1.31440i	0.160804	+	0.195940i
$46$	6.18713	+	2.60043i	0.912243	+	0.383412i
$47$	−3.08023	+	7.43634i	−0.449298	+	1.08470i	0.523288	+	0.852156i	$0.324705\pi$
$47$	−3.08023	+	7.43634i	−0.449298	+	1.08470i	−0.972586	+	0.232545i	$0.925295\pi$
$48$	−1.95828	+	3.48785i	−0.282654	+	0.503428i
$49$	−1.17198	−	2.82941i	−0.167426	−	0.404202i
$50$	−0.0154502	+	2.98217i	−0.00218499	+	0.421743i
$51$	0.137192	−	1.39294i	0.0192107	−	0.195050i
$52$	−10.1176	−	5.54354i	−1.40307	−	0.768750i
$53$	4.90739	+	9.18107i	0.674081	+	1.26112i	0.953629	+	0.300985i	$0.0973155\pi$
$53$	4.90739	+	9.18107i	0.674081	+	1.26112i	−0.279548	+	0.960132i	$0.590184\pi$
$54$	1.09784	−	0.891492i	0.149396	−	0.121317i
$55$	−0.705271	−	1.05551i	−0.0950987	−	0.142325i
$56$	−3.30427	−	8.34159i	−0.441551	−	1.11469i
$57$	−1.22745	−	0.820158i	−0.162580	−	0.108633i
$58$	−3.04816	−	2.52810i	−0.400243	−	0.331956i
$59$	−2.27056	+	0.223631i	−0.295602	+	0.0291142i	−0.244731	−	0.969591i	$-0.578700\pi$
$59$	−2.27056	+	0.223631i	−0.295602	+	0.0291142i	−0.0508707	+	0.998705i	$0.516200\pi$
$60$	−3.40056	−	0.0352365i	−0.439010	−	0.00454901i
$61$	9.80077	−	2.97303i	1.25486	−	0.380658i	0.408249	−	0.912870i	$-0.366139\pi$
$61$	9.80077	−	2.97303i	1.25486	−	0.380658i	0.846611	+	0.532213i	$0.178639\pi$
$62$	−4.88986	−	7.40091i	−0.621013	−	0.939917i
$63$			3.17215i			0.399653i
$64$	−2.83028	−	7.48262i	−0.353785	−	0.935327i
$65$		−	9.80840i		−	1.21658i
$66$	−0.880907	+	0.582025i	−0.108432	+	0.0716423i
$67$	−5.79154	+	1.75684i	−0.707549	+	0.214633i	−0.623493	−	0.781829i	$-0.714287\pi$
$67$	−5.79154	+	1.75684i	−0.707549	+	0.214633i	−0.0840552	+	0.996461i	$0.526787\pi$
$68$	1.95882	+	1.99984i	0.237542	+	0.242517i
$69$	4.72282	−	0.465157i	0.568561	−	0.0559984i
$70$	4.86965	−	5.87139i	0.582035	−	0.701766i
$71$	−7.56079	−	5.05196i	−0.897300	−	0.599557i	0.0191011	−	0.999818i	$-0.493920\pi$
$71$	−7.56079	−	5.05196i	−0.897300	−	0.599557i	−0.916401	+	0.400261i	$0.868920\pi$
$72$	−0.0439588	+	2.82809i	−0.00518060	+	0.333293i
$73$	−1.08352	−	1.62161i	−0.126817	−	0.189795i	0.762628	−	0.646837i	$-0.223909\pi$
$73$	−1.08352	−	1.62161i	−0.126817	−	0.189795i	−0.889445	+	0.457042i	$0.848909\pi$
$74$	9.94582	+	12.2479i	1.15618	+	1.42379i
$75$	0.994055	+	1.85975i	0.114784	+	0.214745i
$76$	2.83409	−	0.827742i	0.325092	−	0.0949485i
$77$	0.232129	−	2.35685i	0.0264536	−	0.268588i
$78$	−8.15763	−	0.0422635i	−0.923670	−	0.00478540i
$79$	3.37251	+	8.14197i	0.379438	+	0.916043i	0.992071	+	0.125676i	$0.0401101\pi$
$79$	3.37251	+	8.14197i	0.379438	+	0.916043i	−0.612634	+	0.790367i	$0.709890\pi$
$80$	4.42283	−	5.16707i	0.494488	−	0.577696i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	1.25161	−	2.97791i	0.138217	−	0.328855i
$83$	10.5661	+	12.8749i	1.15978	+	1.41320i	0.893358	+	0.449346i	$0.148343\pi$
$83$	10.5661	+	12.8749i	1.15978	+	1.41320i	0.266426	+	0.963855i	$0.414157\pi$
$84$	−4.86224	−	4.07538i	−0.530514	−	0.444660i
$85$	−0.690867	+	2.27748i	−0.0749351	+	0.247028i
$86$	7.73558	+	4.18643i	0.834150	+	0.451434i
$87$	−2.74642	−	0.546298i	−0.294448	−	0.0585693i
$88$	0.239612	−	2.09800i	0.0255427	−	0.223647i
$89$	−2.08960	−	10.5051i	−0.221497	−	1.11354i	−0.918181	−	0.396162i	$-0.870342\pi$
$89$	−2.08960	−	10.5051i	−0.221497	−	1.11354i	0.696684	−	0.717378i	$-0.254658\pi$
$90$	−2.12659	+	1.12256i	−0.224162	+	0.118328i
$91$	11.6083	−	14.1447i	1.21688	−	1.48277i
$92$	−5.35460	+	7.83671i	−0.558255	+	0.817033i
$93$	−5.53170	−	2.95676i	−0.573611	−	0.306601i
$94$	−9.43177	−	6.37303i	−0.972813	−	0.657328i
$95$	1.77495	+	1.77495i	0.182106	+	0.182106i
$96$	−4.27839	−	3.70073i	−0.436661	−	0.377704i
$97$	2.14657	−	2.14657i	0.217951	−	0.217951i	−0.589683	−	0.807634i	$-0.700748\pi$
$97$	2.14657	−	2.14657i	0.217951	−	0.217951i	0.807634	+	0.589683i	$0.200748\pi$
$98$	4.25218	−	0.822933i	0.429535	−	0.0831288i
$99$	−0.351933	+	0.658421i	−0.0353706	+	0.0661738i
$100$	−4.12770	−	0.865606i	−0.412770	−	0.0865606i
$101$	−7.62715	−	6.25944i	−0.758930	−	0.622838i	0.173231	−	0.984881i	$-0.444579\pi$
$101$	−7.62715	−	6.25944i	−0.758930	−	0.622838i	−0.932161	+	0.362043i	$0.882079\pi$
$102$	1.89120	+	0.584407i	0.187257	+	0.0578649i
$103$	−6.71089	+	1.33488i	−0.661244	+	0.131530i	−0.514293	−	0.857614i	$-0.671946\pi$
$103$	−6.71089	+	1.33488i	−0.661244	+	0.131530i	−0.146950	+	0.989144i	$0.546946\pi$
$104$	10.5452	−	12.4497i	1.03404	−	1.22079i
$105$	1.05228	−	5.29019i	0.102692	−	0.516269i
$106$	−14.1104	+	4.20064i	−1.37052	+	0.408002i
$107$	−14.1197	−	4.28317i	−1.36500	−	0.414070i	−0.479028	−	0.877800i	$-0.659011\pi$
$107$	−14.1197	−	4.28317i	−1.36500	−	0.414070i	−0.885977	+	0.463730i	$0.846511\pi$
$108$	0.924467	+	1.77352i	0.0889569	+	0.170657i
$109$	−6.21427	+	5.09992i	−0.595219	+	0.488483i	−0.883101	−	0.469182i	$-0.844549\pi$
$109$	−6.21427	+	5.09992i	−0.595219	+	0.488483i	0.287883	+	0.957666i	$0.407049\pi$
$110$	1.66216	−	0.678422i	0.158481	−	0.0646850i
$111$	10.3072	+	4.26936i	0.978312	+	0.405230i
$112$	12.4934	−	2.21701i	1.18052	−	0.209488i
$113$	−3.03201	+	1.25590i	−0.285228	+	0.118145i	−0.520711	−	0.853733i	$-0.674333\pi$
$113$	−3.03201	+	1.25590i	−0.285228	+	0.118145i	0.235483	+	0.971879i	$0.424333\pi$
$114$	1.48387	−	1.46858i	0.138978	−	0.137545i
$115$	−8.03054	−	0.790940i	−0.748852	−	0.0737555i
$116$	4.36580	−	3.50785i	0.405354	−	0.325695i
$117$	−5.08727	+	2.71920i	−0.470318	+	0.251390i
$118$	0.332893	−	3.20937i	0.0306453	−	0.295447i
$119$	−3.69171	+	2.46672i	−0.338418	+	0.226124i
$120$	1.01146	−	4.70181i	0.0923331	−	0.429214i
$121$	−5.80161	+	8.68273i	−0.527419	+	0.789339i
$122$	1.34499	+	14.4215i	0.121770	+	1.30566i
$123$	−0.223884	−	2.27313i	−0.0201869	−	0.204961i
$124$	11.6389	−	4.68029i	1.04520	−	0.420302i
$125$	−3.50881	−	11.5670i	−0.313838	−	1.03458i
$126$	−4.39531	−	0.897977i	−0.391565	−	0.0799982i
$127$	−20.0664			−1.78061			−0.890304	−	0.455368i	$-0.849508\pi$
$127$	−20.0664			−1.78061			−0.890304	+	0.455368i	$0.849508\pi$
$128$	11.1691	−	1.80342i	0.987214	−	0.159401i
$129$	6.21954			0.547600
$130$	13.5904	+	2.77658i	1.19196	+	0.243522i
$131$	0.0713865	+	0.235330i	0.00623707	+	0.0205608i	0.960004	−	0.279988i	$-0.0903303\pi$
$131$	0.0713865	+	0.235330i	0.00623707	+	0.0205608i	−0.953767	+	0.300548i	$0.902830\pi$
$132$	−0.557080	−	1.38534i	−0.0484876	−	0.120578i
$133$	0.459002	+	4.66032i	0.0398005	+	0.404101i
$134$	−0.794790	−	8.52203i	−0.0686594	−	0.736192i
$135$	−0.944675	+	1.41381i	−0.0813047	+	0.121681i
$136$	−3.32547	+	2.14801i	−0.285157	+	0.184190i
$137$	−10.0744	+	6.73150i	−0.860715	+	0.575111i	−0.905720	−	0.423876i	$-0.860669\pi$
$137$	−10.0744	+	6.73150i	−0.860715	+	0.575111i	0.0450059	+	0.998987i	$0.485669\pi$
$138$	−0.692426	+	6.67558i	−0.0589432	+	0.568263i
$139$	2.52406	−	1.34914i	0.214088	−	0.114432i	−0.360868	−	0.932617i	$-0.617519\pi$
$139$	2.52406	−	1.34914i	0.214088	−	0.114432i	0.574956	+	0.818185i	$0.305019\pi$
$140$	6.75684	+	8.40943i	0.571058	+	0.710727i
$141$	−8.01028	−	0.788943i	−0.674587	−	0.0664410i
$142$	9.14027	−	9.04605i	0.767034	−	0.759127i
$143$	3.97873	−	1.64804i	0.332718	−	0.137816i
$144$	−3.90613	−	0.861488i	−0.325511	−	0.0717907i
$145$	4.39898	+	1.82212i	0.365316	+	0.151319i
$146$	2.55362	−	1.04228i	0.211339	−	0.0862593i
$147$	2.36737	−	1.94285i	0.195258	−	0.160244i
$148$	−19.7860	+	10.3137i	−1.62640	+	0.847781i
$149$	19.9918	+	6.06444i	1.63779	+	0.496818i	0.969088	−	0.246713i	$-0.0793506\pi$
$149$	19.9918	+	6.06444i	1.63779	+	0.496818i	0.668701	+	0.743531i	$0.266851\pi$
$150$	−2.85825	+	0.850894i	−0.233375	+	0.0694752i
$151$	−2.19670	+	11.0436i	−0.178765	+	0.898711i	0.782408	+	0.622766i	$0.213991\pi$
$151$	−2.19670	+	11.0436i	−0.178765	+	0.898711i	−0.961173	+	0.275946i	$0.911009\pi$
$152$	0.344635	+	4.16121i	0.0279536	+	0.337518i
$153$	1.37278	−	0.273063i	0.110983	−	0.0220758i
$154$	3.19991	+	0.988816i	0.257856	+	0.0796811i
$155$	8.24437	+	6.76598i	0.662204	+	0.543457i
$156$	2.36784	−	11.2912i	0.189579	−	0.904018i
$157$	−6.45812	+	12.0823i	−0.515414	+	0.964273i	0.480757	+	0.876854i	$0.340362\pi$
$157$	−6.45812	+	12.0823i	−0.515414	+	0.964273i	−0.996172	+	0.0874188i	$0.972138\pi$
$158$	−12.2361	+	2.36809i	−0.973455	+	0.188395i
$159$	−7.36120	+	7.36120i	−0.583781	+	0.583781i
$160$	5.90743	+	7.59094i	0.467024	+	0.600117i
$161$	−10.6448	−	10.6448i	−0.838926	−	0.838926i
$162$	1.17179	+	0.791776i	0.0920645	+	0.0622078i
$163$	−3.59793	−	1.92313i	−0.281812	−	0.150631i	0.324435	−	0.945908i	$-0.394826\pi$
$163$	−3.59793	−	1.92313i	−0.281812	−	0.150631i	−0.606247	+	0.795276i	$0.707326\pi$
$164$	3.77186	+	2.57721i	0.294533	+	0.201246i
$165$	0.805333	−	0.981301i	0.0626951	−	0.0763942i
$166$	−20.8304	+	10.9957i	−1.61675	+	0.853433i
$167$	−0.118302	−	0.594747i	−0.00915452	−	0.0460229i	0.975938	−	0.218048i	$-0.0699690\pi$
$167$	−0.118302	−	0.594747i	−0.00915452	−	0.0460229i	−0.985093	+	0.172025i	$0.944969\pi$
$168$	7.02323	−	5.58342i	0.541854	−	0.430770i
$169$	19.8848	+	3.95534i	1.52960	+	0.304257i
$170$	−2.96009	−	1.60197i	−0.227029	−	0.122866i
$171$	0.428532	−	1.41268i	0.0327706	−	0.108030i
$172$	−7.99048	+	9.53326i	−0.609268	+	0.726904i
$173$	4.95999	+	6.04377i	0.377101	+	0.459499i	0.926629	−	0.375976i	$-0.122692\pi$
$173$	4.95999	+	6.04377i	0.377101	+	0.459499i	−0.549528	+	0.835475i	$0.685192\pi$
$174$	1.53441	−	3.65078i	0.116323	−	0.276765i
$175$	2.55987	−	6.18006i	0.193508	−	0.467169i
$176$	2.83914	+	0.925908i	0.214008	+	0.0697930i
$177$	−0.873110	−	2.10787i	−0.0656269	−	0.158437i
$178$	15.1473	+	0.0784761i	1.13534	+	0.00588203i
$179$	0.911071	−	9.25026i	0.0680966	−	0.691397i	−0.899164	−	0.437612i	$-0.855824\pi$
$179$	0.911071	−	9.25026i	0.0680966	−	0.691397i	0.967261	−	0.253785i	$-0.0816756\pi$
$180$	−0.953410	−	3.26436i	−0.0710630	−	0.243311i
$181$	8.24235	+	15.4203i	0.612649	+	1.14619i	0.976660	+	0.214791i	$0.0689070\pi$
$181$	8.24235	+	15.4203i	0.612649	+	1.14619i	−0.364011	+	0.931395i	$0.618593\pi$
$182$	16.3127	+	20.0884i	1.20918	+	1.48905i
$183$	5.69003	+	8.51573i	0.420619	+	0.629501i
$184$	−9.34269	−	9.63772i	−0.688752	−	0.710502i
$185$	−15.7730	−	10.5392i	−1.15965	−	0.774854i
$186$	5.66278	−	6.82768i	0.415215	−	0.500630i
$187$	−1.03993	+	0.102424i	−0.0760473	+	0.00749001i
$188$	11.5004	−	11.2645i	0.838752	−	0.821548i
$189$	−3.03556	+	0.920827i	−0.220804	+	0.0669803i
$190$	−2.96182	+	1.95690i	−0.214873	+	0.141969i
$191$			6.86774i			0.496932i	0.968641	+	0.248466i	$0.0799264\pi$
$191$			6.86774i			0.496932i	−0.968641	+	0.248466i	$0.920074\pi$
$192$	6.33883	−	4.88049i	0.457466	−	0.352219i
$193$			12.2028i			0.878379i	0.898394	+	0.439190i	$0.144734\pi$
$193$			12.2028i			0.878379i	−0.898394	+	0.439190i	$0.855266\pi$
$194$	2.36661	+	3.58192i	0.169913	+	0.257167i
$195$	9.38606	−	2.84723i	0.672150	−	0.203894i
$196$	−0.0634645	+	6.12474i	−0.00453318	+	0.437482i
$197$	25.6827	−	2.52953i	1.82982	−	0.180221i	0.876342	−	0.481690i	$-0.159977\pi$
$197$	25.6827	−	2.52953i	1.82982	−	0.180221i	0.953476	+	0.301469i	$0.0974770\pi$
$198$	−0.812677	−	0.674023i	−0.0577544	−	0.0479007i
$199$	−15.6230	−	10.4389i	−1.10748	−	0.739997i	−0.139303	−	0.990250i	$-0.544486\pi$
$199$	−15.6230	−	10.4389i	−1.10748	−	0.739997i	−0.968181	+	0.250253i	$0.919486\pi$
$200$	2.36785	−	5.47427i	0.167433	−	0.387090i
$201$	−3.36239	−	5.03217i	−0.237165	−	0.354942i
$202$	10.8321	−	8.79619i	0.762147	−	0.618897i
$203$	4.18730	+	7.83389i	0.293891	+	0.549831i
$204$	−1.34511	+	2.45500i	−0.0941768	+	0.171884i
$205$	−0.380685	+	3.86516i	−0.0265882	+	0.269954i
$206$	0.0501322	−	9.67644i	0.00349288	−	0.674189i
$207$	1.81609	+	4.38443i	0.126227	+	0.304739i
$208$	14.2650	+	18.1356i	0.989099	+	1.25748i
$209$	−0.421766	+	1.01823i	−0.0291742	+	0.0704327i
$210$	7.03216	+	2.95559i	0.485265	+	0.203955i
$211$	−4.25891	−	5.18949i	−0.293195	−	0.357260i	0.605490	−	0.795853i	$-0.292977\pi$
$211$	−4.25891	−	5.18949i	−0.293195	−	0.357260i	−0.898686	+	0.438593i	$0.855477\pi$
$212$	−1.82598	−	20.7404i	−0.125408	−	1.42446i
$213$	2.63964	−	8.70173i	0.180865	−	0.596232i
$214$	9.93176	−	18.3517i	0.678921	−	1.25449i
$215$	−10.3723	−	2.06318i	−0.707386	−	0.140708i
$216$	−2.71907	+	0.778884i	−0.185009	+	0.0529963i
$217$	3.88167	+	19.5145i	0.263505	+	1.32473i
$218$	−5.30726	−	10.0541i	−0.359453	−	0.680952i
$219$	1.23725	−	1.50760i	0.0836058	−	0.101874i
$220$	0.469489	+	2.49512i	0.0316529	+	0.168221i
$221$	−7.12053	−	3.80600i	−0.478978	−	0.256019i
$222$	−8.83336	+	13.0729i	−0.592856	+	0.877398i
$223$	12.1651	+	12.1651i	0.814635	+	0.814635i	0.985325	−	0.170690i	$-0.0545997\pi$
$223$	12.1651	+	12.1651i	0.814635	+	0.814635i	−0.170690	+	0.985325i	$0.554600\pi$
$224$	−0.464780	+	17.9384i	−0.0310544	+	1.19856i
$225$	−1.49111	+	1.49111i	−0.0994071	+	0.0994071i
$226$	−0.881859	−	4.55666i	−0.0586604	−	0.303104i
$227$	−8.72474	+	16.3228i	−0.579081	+	1.08339i	0.406415	+	0.913689i	$0.366779\pi$
$227$	−8.72474	+	16.3228i	−0.579081	+	1.08339i	−0.985496	+	0.169697i	$0.945721\pi$
$228$	1.61479	+	2.47177i	0.106942	+	0.163697i
$229$	13.6638	+	11.2136i	0.902927	+	0.741013i	0.966420	−	0.256969i	$-0.0827238\pi$
$229$	13.6638	+	11.2136i	0.902927	+	0.741013i	−0.0634922	+	0.997982i	$0.520224\pi$
$230$	3.36922	−	10.9032i	0.222160	−	0.718933i
$231$	2.32274	−	0.462023i	0.152825	−	0.0303989i
$232$	3.62457	+	7.04222i	0.237965	+	0.462344i
$233$	−3.82211	+	19.2151i	−0.250395	+	1.25882i	0.626988	+	0.779029i	$0.284288\pi$
$233$	−3.82211	+	19.2151i	−0.250395	+	1.25882i	−0.877383	+	0.479791i	$0.840712\pi$
$234$	−2.32759	−	7.81864i	−0.152159	−	0.511120i
$235$	13.0970	+	3.97293i	0.854354	+	0.259166i
$236$	4.35265	+	1.36977i	0.283333	+	0.0891643i
$237$	−6.81239	+	5.59078i	−0.442512	+	0.363160i
$238$	−2.37281	−	5.81348i	−0.153807	−	0.376832i
$239$	2.92148	+	1.21012i	0.188975	+	0.0782760i	0.475164	−	0.879897i	$-0.342389\pi$
$239$	2.92148	+	1.21012i	0.188975	+	0.0782760i	−0.286189	+	0.958173i	$0.592389\pi$
$240$	6.22846	+	2.73246i	0.402046	+	0.176380i
$241$	−13.7607	+	5.69985i	−0.886402	+	0.367160i	−0.778976	−	0.627054i	$-0.784261\pi$
$241$	−13.7607	+	5.69985i	−0.886402	+	0.367160i	−0.107425	+	0.994213i	$0.534261\pi$
$242$	−10.3884	−	10.4966i	−0.667791	−	0.674746i
$243$	0.995185	+	0.0980171i	0.0638411	+	0.00628780i
$244$	−20.3630	−	2.21885i	−1.30361	−	0.142047i
$245$	−4.59255	+	2.45477i	−0.293407	+	0.156830i
$246$	3.21301	+	0.333270i	0.204854	+	0.0212485i
$247$	−7.08044	+	4.73100i	−0.450517	+	0.301026i
$248$	3.19022	+	17.4516i	0.202579	+	1.10818i
$249$	−9.25330	+	13.8485i	−0.586404	+	0.877616i
$250$	17.0204	−	1.58738i	1.07647	−	0.100394i
$251$	0.0403178	+	0.409353i	0.00254483	+	0.0258381i	0.996373	−	0.0850898i	$-0.0271177\pi$
$251$	0.0403178	+	0.409353i	0.00254483	+	0.0258381i	−0.993828	+	0.110928i	$0.964618\pi$
$252$	2.48846	−	5.83590i	0.156758	−	0.367627i
$253$	−1.02848	−	3.39044i	−0.0646600	−	0.213155i
$254$	5.68044	−	27.8039i	0.356422	−	1.74457i
$255$	−2.37997			−0.149039
$256$	−0.662953	+	15.9863i	−0.0414346	+	0.999141i
$257$	−20.0902			−1.25319			−0.626595	−	0.779345i	$-0.715552\pi$
$257$	−20.0902			−1.25319			−0.626595	+	0.779345i	$0.715552\pi$
$258$	−1.76064	+	8.61775i	−0.109613	+	0.536518i
$259$	−10.2731	−	33.8658i	−0.638339	−	2.10432i
$260$	−7.69441	+	18.0448i	−0.477187	+	1.11909i
$261$	−0.274471	−	2.78675i	−0.0169893	−	0.172495i
$262$	−0.346279	+	0.0322950i	−0.0213932	+	0.00199519i
$263$	14.2594	−	21.3407i	0.879271	−	1.31592i	−0.0687239	−	0.997636i	$-0.521893\pi$
$263$	14.2594	−	21.3407i	0.879271	−	1.31592i	0.947995	−	0.318286i	$-0.103107\pi$
$264$	2.07721	−	0.379722i	0.127844	−	0.0233703i
$265$	14.7182	−	9.83435i	0.904129	−	0.604120i
$266$	−6.58724	−	0.683263i	−0.403890	−	0.0418935i
$267$	9.44619	−	5.04909i	0.578097	−	0.308999i
$268$	12.0331	+	1.31118i	0.735036	+	0.0800929i
$269$	−0.124330	−	0.0122454i	−0.00758051	−	0.000746615i	0.0942262	−	0.995551i	$-0.469962\pi$
$269$	−0.124330	−	0.0122454i	−0.00758051	−	0.000746615i	−0.101807	+	0.994804i	$0.532462\pi$
$270$	−1.69154	−	1.70916i	−0.102944	−	0.104016i
$271$	18.2311	−	7.55156i	1.10746	−	0.458725i	0.247397	−	0.968914i	$-0.420425\pi$
$271$	18.2311	−	7.55156i	1.10746	−	0.458725i	0.860062	+	0.510189i	$0.170425\pi$
$272$	−2.03489	−	5.21581i	−0.123383	−	0.316255i
$273$	16.9053	+	7.00242i	1.02316	+	0.423806i
$274$	−6.47524	−	15.8646i	−0.391183	−	0.958414i
$275$	1.21698	−	0.998748i	0.0733866	−	0.0602268i
$276$	−9.05362	−	2.84915i	−0.544964	−	0.171499i
$277$	−15.2331	−	4.62091i	−0.915268	−	0.277644i	−0.202695	−	0.979242i	$-0.564970\pi$
$277$	−15.2331	−	4.62091i	−0.915268	−	0.277644i	−0.712573	+	0.701598i	$0.752470\pi$
$278$	1.15484	+	3.87923i	0.0692627	+	0.232661i
$279$	1.22367	−	6.15181i	0.0732593	−	0.368299i
$280$	−13.5648	+	6.98167i	−0.810651	+	0.417235i
$281$	−19.0864	+	3.79653i	−1.13860	+	0.226482i	−0.728161	−	0.685406i	$-0.759625\pi$
$281$	−19.0864	+	3.79653i	−1.13860	+	0.226482i	−0.410440	+	0.911888i	$0.634625\pi$
$282$	3.36072	−	10.8756i	0.200128	−	0.647635i
$283$	25.0995	+	20.5986i	1.49201	+	1.22446i	0.912223	+	0.409695i	$0.134365\pi$
$283$	25.0995	+	20.5986i	1.49201	+	1.22446i	0.579789	+	0.814767i	$0.303135\pi$
$284$	9.94669	+	15.2255i	0.590227	+	0.903464i
$285$	−1.18328	+	2.21377i	−0.0700916	+	0.131132i
$286$	1.15721	+	5.97942i	0.0684273	+	0.353571i
$287$	−5.12341	+	5.12341i	−0.302425	+	0.302425i
$288$	2.29942	−	5.16843i	0.135495	−	0.304553i
$289$	−10.6355	−	10.6355i	−0.625619	−	0.625619i
$290$	−3.76998	+	5.57939i	−0.221381	+	0.327633i
$291$	2.67725	+	1.43102i	0.156943	+	0.0838880i
$292$	0.721287	+	3.83332i	0.0422101	+	0.224328i
$293$	1.49664	−	1.82366i	0.0874348	−	0.106540i	−0.727455	−	0.686155i	$-0.759297\pi$
$293$	1.49664	−	1.82366i	0.0874348	−	0.106540i	0.814890	+	0.579615i	$0.196797\pi$
$294$	2.02184	+	3.83020i	0.117916	+	0.223382i
$295$	0.756847	+	3.80493i	0.0440653	+	0.221531i
$296$	−8.68953	−	30.3350i	−0.505068	−	1.76318i
$297$	−0.732230	−	0.145650i	−0.0424883	−	0.00845145i
$298$	−14.0621	+	25.9837i	−0.814598	+	1.50520i
$299$	7.94652	−	26.1962i	0.459559	−	1.51496i
$300$	−0.369875	−	4.20124i	−0.0213547	−	0.242558i
$301$	−12.5162	−	15.2510i	−0.721419	−	0.879051i
$302$	−14.6800	−	6.16995i	−0.844740	−	0.355041i
$303$	3.77587	−	9.11575i	0.216918	−	0.523686i
$304$	−5.86329	−	0.700438i	−0.336283	−	0.0401729i
$305$	−6.66436	−	16.0892i	−0.381600	−	0.921264i
$306$	−0.0102550	+	1.97941i	−0.000586242	+	0.113156i
$307$	0.141309	−	1.43474i	0.00806494	−	0.0818847i	−0.990310	−	0.138877i	$-0.955651\pi$
$307$	0.141309	−	1.43474i	0.00806494	−	0.0818847i	0.998375	+	0.0569918i	$0.0181509\pi$
$308$	−2.27593	+	4.15386i	−0.129683	+	0.236688i
$309$	−3.22547	−	6.03443i	−0.183491	−	0.343287i
$310$	−11.7087	+	9.50801i	−0.665011	+	0.540019i
$311$	2.00253	+	2.99700i	0.113553	+	0.169944i	0.883893	−	0.467689i	$-0.154913\pi$
$311$	2.00253	+	2.99700i	0.113553	+	0.169944i	−0.770340	+	0.637634i	$0.779913\pi$
$312$	14.9747	+	6.47718i	0.847775	+	0.366698i
$313$	−1.81952	−	1.21577i	−0.102846	−	0.0687192i	0.503084	−	0.864238i	$-0.332199\pi$
$313$	−1.81952	−	1.21577i	−0.102846	−	0.0687192i	−0.605930	+	0.795518i	$0.707199\pi$
$314$	−14.9130	−	12.3686i	−0.841587	−	0.698001i
$315$	5.36785	−	0.528688i	0.302444	−	0.0297882i
$316$	0.182626	−	17.6247i	0.0102735	−	0.991465i
$317$	6.09144	−	1.84782i	0.342129	−	0.103784i	−0.114544	−	0.993418i	$-0.536541\pi$
$317$	6.09144	−	1.84782i	0.342129	−	0.103784i	0.456674	+	0.889634i	$0.349041\pi$
$318$	−8.11580	−	12.2834i	−0.455111	−	0.688821i
$319$			2.09058i			0.117050i
$320$	−12.1902	+	6.03643i	−0.681455	+	0.337447i
$321$		−	14.7551i		−	0.823547i
$322$	17.7627	−	11.7360i	0.989874	−	0.654020i
$323$	1.97729	−	0.599805i	0.110019	−	0.0333740i
$324$	−1.42879	+	1.39948i	−0.0793773	+	0.0777491i
$325$	12.1055	−	1.19229i	0.671492	−	0.0661362i
$326$	3.68319	−	4.44086i	0.203993	−	0.245956i
$327$	−6.68422	−	4.46625i	−0.369638	−	0.246984i
$328$	−4.63870	+	4.49670i	−0.256129	+	0.248289i
$329$	14.1852	+	21.2297i	0.782057	+	1.17043i
$330$	1.13171	+	1.39365i	0.0622985	+	0.0767180i
$331$	−16.3770	−	30.6392i	−0.900160	−	1.68408i	−0.712289	−	0.701887i	$-0.752341\pi$
$331$	−16.3770	−	30.6392i	−0.900160	−	1.68408i	−0.187871	−	0.982194i	$-0.560159\pi$
$332$	−9.33886	−	31.9751i	−0.512537	−	1.75486i
$333$	−1.09352	+	11.1027i	−0.0599243	+	0.608422i
$334$	0.857566	+	0.00444292i	0.0469239	+	0.000243106i
$335$	3.93815	+	9.50753i	0.215164	+	0.519452i
$336$	5.74820	+	11.3119i	0.313590	+	0.617114i
$337$	10.9977	−	26.5508i	0.599084	−	1.44632i	−0.275433	−	0.961320i	$-0.588821\pi$
$337$	10.9977	−	26.5508i	0.599084	−	1.44632i	0.874517	−	0.484996i	$-0.161179\pi$
$338$	−11.1095	+	26.4326i	−0.604278	+	1.43774i
$339$	−2.08197	−	2.53689i	−0.113077	−	0.137785i
$340$	3.05763	−	3.64799i	0.165823	−	0.197840i
$341$	−1.35934	+	4.48113i	−0.0736122	+	0.242667i
$342$	1.83609	+	0.993673i	0.0992842	+	0.0537317i
$343$	12.2502	+	2.43672i	0.661450	+	0.131571i
$344$	−10.9473	−	13.7702i	−0.590236	−	0.742441i
$345$	−1.57426	−	7.91435i	−0.0847554	−	0.426094i
$346$	−9.77828	+	5.16165i	−0.525684	+	0.277492i
$347$	−6.71210	+	8.17872i	−0.360324	+	0.439056i	−0.921345	−	0.388745i	$-0.872909\pi$
$347$	−6.71210	+	8.17872i	−0.360324	+	0.439056i	0.561021	+	0.827802i	$0.310409\pi$
$348$	4.62412	+	3.15953i	0.247879	+	0.169369i
$349$	−29.7212	−	15.8863i	−1.59094	−	0.850374i	−0.999015	−	0.0443807i	$-0.985869\pi$
$349$	−29.7212	−	15.8863i	−1.59094	−	0.850374i	−0.591924	−	0.805994i	$-0.701631\pi$
$350$	7.83839	+	5.29639i	0.418980	+	0.283104i
$351$	−4.07887	−	4.07887i	−0.217714	−	0.217714i
$352$	−2.08664	+	3.67178i	−0.111218	+	0.195706i
$353$	9.10812	−	9.10812i	0.484776	−	0.484776i	−0.421877	−	0.906653i	$-0.638629\pi$
$353$	9.10812	−	9.10812i	0.484776	−	0.484776i	0.906653	+	0.421877i	$0.138629\pi$
$354$	3.16781	−	0.613074i	0.168367	−	0.0325845i
$355$	−7.28871	+	13.6362i	−0.386844	+	0.723735i
$356$	−4.39667	+	20.9658i	−0.233023	+	1.11119i
$357$	−3.43215	−	2.81669i	−0.181649	−	0.149075i
$358$	12.5592	+	3.88095i	0.663773	+	0.205115i
$359$	21.0209	−	4.18131i	1.10944	−	0.220681i	0.393830	−	0.919183i	$-0.371150\pi$
$359$	21.0209	−	4.18131i	1.10944	−	0.220681i	0.715608	+	0.698502i	$0.246150\pi$
$360$	4.79296	−	0.396958i	0.252611	−	0.0209215i
$361$	−3.28156	+	16.4975i	−0.172713	+	0.868289i
$362$	−23.6996	+	7.05531i	−1.24562	+	0.370819i
$363$	−9.99297	−	3.03133i	−0.524495	−	0.159104i
$364$	−32.4522	+	16.9161i	−1.70096	+	0.886644i
$365$	−2.56347	+	2.10379i	−0.134178	+	0.110117i
$366$	−13.4101	+	5.47341i	−0.700955	+	0.286100i
$367$	−14.2835	−	5.91641i	−0.745592	−	0.308834i	−0.0226504	−	0.999743i	$-0.507210\pi$
$367$	−14.2835	−	5.91641i	−0.745592	−	0.308834i	−0.722942	+	0.690909i	$0.757210\pi$
$368$	15.9987	−	10.2169i	0.833989	−	0.532592i
$369$	2.11026	−	0.874097i	0.109856	−	0.0455037i
$370$	19.0680	−	18.8714i	0.991298	−	0.981079i
$371$	32.8640	+	3.23683i	1.70622	+	0.168048i
$372$	7.85735	+	9.77909i	0.407384	+	0.507022i
$373$	−9.77829	+	5.22661i	−0.506301	+	0.270623i	−0.704710	−	0.709496i	$-0.748923\pi$
$373$	−9.77829	+	5.22661i	−0.506301	+	0.270623i	0.198409	+	0.980119i	$0.436423\pi$
$374$	0.152467	−	1.46992i	0.00788389	−	0.0760075i
$375$	10.0504	−	6.71545i	0.518999	−	0.346784i
$376$	12.3524	+	19.1236i	0.637029	+	0.986225i
$377$	−8.97404	+	13.4306i	−0.462186	+	0.691711i
$378$	−0.416579	−	4.46671i	−0.0214265	−	0.229743i
$379$	0.794511	+	8.06680i	0.0408113	+	0.414364i	0.993785	+	0.111312i	$0.0355054\pi$
$379$	0.794511	+	8.06680i	0.0408113	+	0.414364i	−0.952974	+	0.303051i	$0.901995\pi$
$380$	−1.87303	−	4.65783i	−0.0960846	−	0.238942i
$381$	−5.82497	−	19.2024i	−0.298423	−	0.983767i
$382$	−9.51588	−	1.94413i	−0.486875	−	0.0994704i
$383$	8.14470			0.416175			0.208087	−	0.978110i	$-0.433276\pi$
$383$	8.14470			0.416175			0.208087	+	0.978110i	$0.433276\pi$
$384$	4.96797	+	10.1646i	0.253520	+	0.518711i
$385$	−4.02690			−0.205230
$386$	−16.9081	−	3.45440i	−0.860602	−	0.175824i
$387$	1.80544	+	5.95173i	0.0917756	+	0.302544i
$388$	−5.63303	+	2.26518i	−0.285974	+	0.114997i
$389$	−2.00697	−	20.3771i	−0.101758	−	1.03316i	−0.901488	−	0.432803i	$-0.857524\pi$
$389$	−2.00697	−	20.3771i	−0.101758	−	1.03316i	0.799731	−	0.600359i	$-0.204976\pi$
$390$	1.28808	+	13.8112i	0.0652243	+	0.699360i
$391$	−3.69032	+	5.52296i	−0.186628	+	0.279308i
$392$	−8.46843	−	1.82174i	−0.427720	−	0.0920116i
$393$	−0.204474	+	0.136625i	−0.0103144	+	0.00689183i
$394$	−3.76541	+	36.3018i	−0.189699	+	1.82886i
$395$	13.2156	−	7.06389i	0.664950	−	0.355423i
$396$	1.16397	−	0.935235i	0.0584919	−	0.0469973i
$397$	32.9784	+	3.24809i	1.65514	+	0.163017i	0.882009	−	0.471232i	$-0.156191\pi$
$397$	32.9784	+	3.24809i	1.65514	+	0.163017i	0.773129	+	0.634249i	$0.218691\pi$
$398$	18.8867	−	18.6920i	0.946704	−	0.936945i
$399$	−4.32641	+	1.79206i	−0.216591	+	0.0897151i
$400$	6.91481	+	4.83054i	0.345741	+	0.241527i
$401$	29.0966	+	12.0522i	1.45302	+	0.601859i	0.962915	−	0.269806i	$-0.0869597\pi$
$401$	29.0966	+	12.0522i	1.45302	+	0.601859i	0.490102	+	0.871665i	$0.336960\pi$
$402$	7.92436	−	3.23438i	0.395231	−	0.161316i
$403$	−27.9685	+	22.9532i	−1.39321	+	1.14338i
$404$	9.12154	+	17.4990i	0.453814	+	0.870606i
$405$	−1.62715	−	0.493591i	−0.0808538	−	0.0245267i
$406$	−12.0399	+	3.58426i	−0.597531	+	0.177884i
$407$	1.62492	−	8.16904i	0.0805445	−	0.404924i
$408$	−3.02085	−	2.55875i	−0.149554	−	0.126677i
$409$	−12.0142	+	2.38976i	−0.594062	+	0.118166i	−0.482959	−	0.875643i	$-0.660438\pi$
$409$	−12.0142	+	2.38976i	−0.594062	+	0.118166i	−0.111102	+	0.993809i	$0.535438\pi$
$410$	−5.24777	−	1.62163i	−0.259169	−	0.0800865i
$411$	−9.36609	−	7.68655i	−0.461995	−	0.379150i
$412$	13.3934	+	2.80868i	0.659846	+	0.138374i
$413$	−3.41169	+	6.38282i	−0.167878	+	0.314078i
$414$	−6.58913	+	1.27521i	−0.323838	+	0.0626731i
$415$	20.0256	−	20.0256i	0.983019	−	0.983019i
$416$	−29.1667	+	14.6316i	−1.43002	+	0.717373i
$417$	2.02374	+	2.02374i	0.0991030	+	0.0991030i
$418$	−1.29146	−	0.872640i	−0.0631675	−	0.0426822i
$419$	−23.8832	−	12.7658i	−1.16677	−	0.623652i	−0.229861	−	0.973223i	$-0.573827\pi$
$419$	−23.8832	−	12.7658i	−1.16677	−	0.623652i	−0.936910	+	0.349571i	$0.886327\pi$
$420$	−6.08592	+	8.90703i	−0.296962	+	0.434618i
$421$	−15.5513	+	18.9493i	−0.757923	+	0.923532i	−0.998895	−	0.0470003i	$-0.985034\pi$
$421$	−15.5513	+	18.9493i	−0.757923	+	0.923532i	0.240972	+	0.970532i	$0.422534\pi$
$422$	8.39614	−	4.43206i	0.408718	−	0.215749i
$423$	−1.57029	−	7.89437i	−0.0763500	−	0.383838i
$424$	29.2546	+	3.34117i	1.42073	+	0.162261i
$425$	−2.89484	−	0.575820i	−0.140420	−	0.0279314i
$426$	11.3098	+	6.12076i	0.547962	+	0.296552i
$427$	9.43090	−	31.0895i	0.456393	−	1.50453i
$428$	22.6164	+	18.9564i	1.09321	+	0.916291i
$429$	2.73204	+	3.32900i	0.131904	+	0.160726i
$430$	5.79494	−	13.7877i	0.279457	−	0.664904i
$431$	12.7208	−	30.7108i	0.612741	−	1.47929i	−0.247237	−	0.968955i	$-0.579522\pi$
$431$	12.7208	−	30.7108i	0.612741	−	1.47929i	0.859977	−	0.510332i	$-0.170478\pi$
$432$	−0.309497	−	3.98801i	−0.0148907	−	0.191873i
$433$	0.114350	+	0.276065i	0.00549530	+	0.0132668i	0.926603	−	0.376040i	$-0.122715\pi$
$433$	0.114350	+	0.276065i	0.00549530	+	0.0132668i	−0.921108	+	0.389307i	$0.872715\pi$
$434$	−28.1379	−	0.145778i	−1.35066	−	0.00699759i
$435$	−0.466701	+	4.73850i	−0.0223766	+	0.227194i
$436$	15.4333	−	4.50755i	0.739121	−	0.215873i
$437$	3.30250	+	6.17855i	0.157980	+	0.295560i
$438$	1.73867	+	2.14110i	0.0830769	+	0.102306i
$439$	4.37042	+	6.54079i	0.208589	+	0.312175i	0.920982	−	0.389606i	$-0.127389\pi$
$439$	4.37042	+	6.54079i	0.208589	+	0.312175i	−0.712393	+	0.701781i	$0.752389\pi$
$440$	−3.59013	−	0.0558037i	−0.171153	−	0.00266034i
$441$	2.54640	+	1.70145i	0.121257	+	0.0810216i
$442$	7.28925	−	8.78874i	0.346714	−	0.418038i
$443$	−14.2392	+	1.40244i	−0.676527	+	0.0666320i	−0.430445	−	0.902617i	$-0.641643\pi$
$443$	−14.2392	+	1.40244i	−0.676527	+	0.0666320i	−0.246082	+	0.969249i	$0.579143\pi$
$444$	−15.6132	−	15.9401i	−0.740969	−	0.756485i
$445$	−17.4283	+	5.28682i	−0.826181	+	0.250619i
$446$	−20.2996	+	13.4121i	−0.961212	+	0.635083i
$447$			20.8913i			0.988127i
$448$	−24.7237	−	5.72202i	−1.16808	−	0.270340i
$449$		−	2.01417i		−	0.0950544i	−0.998870	−	0.0475272i	$-0.984866\pi$
$449$		−	2.01417i		−	0.0950544i	0.998870	−	0.0475272i	$-0.0151341\pi$
$450$	−1.64396	−	2.48817i	−0.0774970	−	0.117293i
$451$	−1.63184	+	0.495015i	−0.0768406	+	0.0233093i
$452$	6.56330	+	0.0680089i	0.308712	+	0.00319887i
$453$	−11.2057	+	1.10366i	−0.526489	+	0.0518547i
$454$	−20.1470	−	16.7096i	−0.945545	−	0.784222i
$455$	−25.8701	−	17.2859i	−1.21281	−	0.810374i
$456$	−3.88198	+	1.53773i	−0.181791	+	0.0720108i
$457$	3.88292	+	5.81119i	0.181635	+	0.271836i	0.911103	−	0.412179i	$-0.135232\pi$
$457$	3.88292	+	5.81119i	0.181635	+	0.271836i	−0.729468	+	0.684015i	$0.760232\pi$
$458$	−19.4054	+	15.7581i	−0.906754	+	0.736326i
$459$	0.659802	+	1.23440i	0.0307969	+	0.0576170i
$460$	14.1536	+	7.75485i	0.659913	+	0.361572i
$461$	1.70803	−	17.3419i	0.0795508	−	0.807692i	−0.869785	−	0.493430i	$-0.835743\pi$
$461$	1.70803	−	17.3419i	0.0795508	−	0.807692i	0.949336	−	0.314262i	$-0.101757\pi$
$462$	−0.0173515	+	3.34917i	−0.000807266	+	0.155817i
$463$	−0.266781	−	0.644067i	−0.0123984	−	0.0299323i	0.917559	−	0.397599i	$-0.130157\pi$
$463$	−0.266781	−	0.644067i	−0.0123984	−	0.0299323i	−0.929957	+	0.367667i	$0.880157\pi$
$464$	−10.7837	+	3.02865i	−0.500620	+	0.140602i
$465$	−4.08143	+	9.85344i	−0.189272	+	0.456942i
$466$	−25.5423	−	10.7353i	−1.18322	−	0.497304i
$467$	5.88962	+	7.17652i	0.272539	+	0.332090i	0.891236	−	0.453540i	$-0.149839\pi$
$467$	5.88962	+	7.17652i	0.272539	+	0.332090i	−0.618697	+	0.785630i	$0.712339\pi$
$468$	11.4923	−	1.01178i	0.531234	−	0.0467696i
$469$	−5.57297	+	18.3716i	−0.257336	+	0.848323i
$470$	−9.21238	+	17.0224i	−0.424936	+	0.785186i
$471$	−13.4367	−	2.67273i	−0.619132	−	0.123153i
$472$	−3.13009	+	5.64324i	−0.144074	+	0.259751i
$473$	−0.905874	−	4.55414i	−0.0416521	−	0.209399i
$474$	−5.81808	−	11.0218i	−0.267233	−	0.506250i
$475$	−1.97488	+	2.40640i	−0.0906138	+	0.110413i
$476$	8.72682	−	1.64206i	0.399993	−	0.0752637i
$477$	−9.18107	−	4.90739i	−0.420372	−	0.224694i
$478$	−2.50375	+	3.70542i	−0.114519	+	0.169482i
$479$	25.9482	+	25.9482i	1.18561	+	1.18561i	0.978270	+	0.207336i	$0.0664792\pi$
$479$	25.9482	+	25.9482i	1.18561	+	1.18561i	0.207336	+	0.978270i	$0.433521\pi$
$480$	−5.54924	+	7.85660i	−0.253287	+	0.358603i
$481$	45.5055	−	45.5055i	2.07487	−	2.07487i
$482$	−4.00228	−	20.6802i	−0.182299	−	0.941956i
$483$	7.09640	−	13.2764i	0.322897	−	0.604099i
$484$	17.4847	−	11.4227i	0.794761	−	0.519212i
$485$	−3.99014	−	3.27462i	−0.181183	−	0.148693i
$486$	−0.417530	+	1.35117i	−0.0189396	+	0.0612905i
$487$	−1.77746	+	0.353558i	−0.0805443	+	0.0160212i	−0.235198	−	0.971947i	$-0.575574\pi$
$487$	−1.77746	+	0.353558i	−0.0805443	+	0.0160212i	0.154654	+	0.987969i	$0.450574\pi$
$488$	8.83882	−	27.5867i	0.400114	−	1.24879i
$489$	0.795900	−	4.00126i	0.0359919	−	0.180943i
$490$	−2.10124	−	7.05830i	−0.0949245	−	0.318862i
$491$	24.6738	+	7.48471i	1.11351	+	0.337780i	0.792852	−	0.609414i	$-0.208595\pi$
$491$	24.6738	+	7.48471i	1.11351	+	0.337780i	0.320660	+	0.947194i	$0.396095\pi$
$492$	−1.37132	+	4.35757i	−0.0618238	+	0.196454i
$493$	3.02975	−	2.48645i	0.136453	−	0.111984i
$494$	−4.55089	−	11.1499i	−0.204754	−	0.501656i
$495$	1.17282	+	0.485799i	0.0527145	+	0.0218350i
$496$	−25.0839	−	0.519895i	−1.12630	−	0.0233440i
$497$	−26.6495	+	11.0386i	−1.19539	+	0.495149i
$498$	−16.5690	−	16.7416i	−0.742474	−	0.750207i
$499$	10.5552	+	1.03960i	0.472516	+	0.0465388i	0.331473	−	0.943465i	$-0.392454\pi$
$499$	10.5552	+	1.03960i	0.472516	+	0.0465388i	0.141043	+	0.990003i	$0.454954\pi$
$500$	−2.61872	+	24.0327i	−0.117113	+	1.07478i
$501$	0.534796	−	0.285854i	0.0238929	−	0.0127710i
$502$	−0.578610	−	0.0600164i	−0.0258246	−	0.00267866i
$503$	25.5679	−	17.0839i	1.14002	−	0.761734i	0.165534	−	0.986204i	$-0.447065\pi$
$503$	25.5679	−	17.0839i	1.14002	−	0.761734i	0.974481	+	0.224470i	$0.0720651\pi$
$504$	7.38174	+	5.10003i	0.328809	+	0.227173i
$505$	−9.32093	+	13.9498i	−0.414776	+	0.620756i
$506$	4.98892	−	0.465281i	0.221784	−	0.0206843i
$507$	1.98724	+	20.1768i	0.0882563	+	0.896081i
$508$	36.9168	+	15.7415i	1.63792	+	0.698417i
$509$	12.4449	+	41.0253i	0.551611	+	1.81842i	0.574260	+	0.818673i	$0.305290\pi$
$509$	12.4449	+	41.0253i	0.551611	+	1.81842i	−0.0226495	+	0.999743i	$0.507210\pi$
$510$	0.673724	−	3.29766i	0.0298330	−	0.146023i
$511$	−6.18662			−0.273680
$512$	−21.9628	−	5.44400i	−0.970626	−	0.240593i
$513$	1.47625			0.0651778
$514$	5.68716	−	27.8368i	0.250850	−	1.22783i
$515$	3.37733	+	11.1336i	0.148823	+	0.490604i
$516$	−11.4423	−	4.87905i	−0.503718	−	0.214788i
$517$	0.589006	+	5.98028i	0.0259044	+	0.263012i
$518$	49.8324	−	4.64751i	2.18951	−	0.204200i
$519$	−4.34372	+	6.50083i	−0.190668	+	0.285355i
$520$	−22.8246	−	15.7695i	−1.00092	−	0.691537i
$521$	14.7544	−	9.85860i	0.646404	−	0.431913i	−0.188678	−	0.982039i	$-0.560420\pi$
$521$	14.7544	−	9.85860i	0.646404	−	0.431913i	0.835082	+	0.550126i	$0.185420\pi$
$522$	3.93899	+	0.408573i	0.172405	+	0.0178827i
$523$	−2.13073	+	1.13890i	−0.0931704	+	0.0498006i	−0.517324	−	0.855790i	$-0.673072\pi$
$523$	−2.13073	+	1.13890i	−0.0931704	+	0.0498006i	0.424153	+	0.905590i	$0.360572\pi$
$524$	0.0532775	−	0.488944i	0.00232744	−	0.0213596i
$525$	6.65704	+	0.655661i	0.290537	+	0.0286154i
$526$	25.5329	+	25.7988i	1.11329	+	1.12488i
$527$	8.11095	−	3.35966i	0.353318	−	0.146349i
$528$	−0.0618814	+	2.98566i	−0.00269304	+	0.129934i
$529$	0.442143	+	0.183142i	0.0192236	+	0.00796268i
$530$	9.45996	+	23.1773i	0.410915	+	1.00676i
$531$	1.76366	−	1.44740i	0.0765363	−	0.0628117i
$532$	2.81145	−	8.93381i	0.121892	−	0.387330i
$533$	−12.6084	−	3.82472i	−0.546131	−	0.165667i
$534$	4.32194	+	14.5179i	0.187029	+	0.628250i
$535$	−4.89463	+	24.6070i	−0.211613	+	1.06385i
$536$	−5.22309	+	16.3017i	−0.225603	+	0.704127i
$537$	9.11641	−	1.81337i	0.393402	−	0.0782526i
$538$	0.0521626	−	0.168804i	0.00224889	−	0.00727765i
$539$	−1.76742	−	1.45049i	−0.0761282	−	0.0624768i
$540$	2.84704	−	1.85995i	0.122517	−	0.0800395i
$541$	19.1466	−	35.8207i	0.823175	−	1.54005i	−0.0183483	−	0.999832i	$-0.505841\pi$
$541$	19.1466	−	35.8207i	0.823175	−	1.54005i	0.841523	−	0.540221i	$-0.181659\pi$
$542$	5.30250	+	27.3986i	0.227762	+	1.17687i
$543$	−12.3637	+	12.3637i	−0.530578	+	0.530578i
$544$	7.80302	−	1.34302i	0.334552	−	0.0575816i
$545$	9.66569	+	9.66569i	0.414033	+	0.414033i
$546$	−14.4881	+	21.4417i	−0.620033	+	0.917618i
$547$	−12.3209	−	6.58567i	−0.526804	−	0.281583i	0.186478	−	0.982459i	$-0.440293\pi$
$547$	−12.3209	−	6.58567i	−0.526804	−	0.281583i	−0.713283	+	0.700876i	$0.752793\pi$
$548$	23.8149	−	4.48106i	1.01732	−	0.191422i
$549$	−6.49732	+	7.91700i	−0.277299	+	0.337889i
$550$	1.03935	+	1.96896i	0.0443182	+	0.0839568i
$551$	−0.806470	−	4.05440i	−0.0343568	−	0.172723i
$552$	6.51068	−	11.7381i	0.277113	−	0.499606i
$553$	27.4184	+	5.45385i	1.16595	+	0.231922i
$554$	10.7149	−	19.7988i	0.455233	−	0.841169i
$555$	5.50669	−	18.1531i	0.233746	−	0.770558i
$556$	−5.70195	+	0.501997i	−0.241816	+	0.0212894i
$557$	8.46237	+	10.3114i	0.358562	+	0.436909i	0.920781	−	0.390079i	$-0.127552\pi$
$557$	8.46237	+	10.3114i	0.358562	+	0.436909i	−0.562219	+	0.826988i	$0.690052\pi$
$558$	8.17750	+	3.43697i	0.346181	+	0.145499i
$559$	13.7295	−	33.1458i	0.580694	−	1.40192i
$560$	−5.83381	−	20.7716i	−0.246523	−	0.877762i
$561$	−0.399890	−	0.965420i	−0.0168834	−	0.0407601i
$562$	0.142581	−	27.5207i	0.00601441	−	1.16089i
$563$	−3.98147	+	40.4245i	−0.167799	+	1.70369i	0.430642	+	0.902523i	$0.358287\pi$
$563$	−3.98147	+	40.4245i	−0.167799	+	1.70369i	−0.598441	+	0.801167i	$0.704213\pi$
$564$	14.1178	+	7.73527i	0.594468	+	0.325714i
$565$	2.63055	+	4.92140i	0.110668	+	0.207045i
$566$	−35.6465	+	28.9466i	−1.49833	+	1.21672i
$567$	−1.76235	−	2.63755i	−0.0740118	−	0.110767i
$568$	−23.9120	+	9.47200i	−1.00332	+	0.397436i
$569$	−11.0678	−	7.39527i	−0.463986	−	0.310026i	0.301513	−	0.953462i	$-0.402508\pi$
$569$	−11.0678	−	7.39527i	−0.463986	−	0.310026i	−0.765500	+	0.643436i	$0.777508\pi$
$570$	−2.73241	−	2.26622i	−0.114448	−	0.0949217i
$571$	−24.5643	+	2.41937i	−1.02798	+	0.101247i	−0.597923	−	0.801553i	$-0.704007\pi$
$571$	−24.5643	+	2.41937i	−1.02798	+	0.101247i	−0.430059	+	0.902801i	$0.641507\pi$
$572$	−8.61262	−	0.0892439i	−0.360112	−	0.00373147i
$573$	−6.57202	+	1.99360i	−0.274550	+	0.0832838i
$574$	−5.64861	−	8.54929i	−0.235768	−	0.356841i
$575$		−	10.0074i		−	0.417338i
$576$	6.51041	+	4.64915i	0.271267	+	0.193715i
$577$			2.89971i			0.120717i	0.998177	+	0.0603583i	$0.0192243\pi$
$577$			2.89971i			0.120717i	−0.998177	+	0.0603583i	$0.980776\pi$
$578$	17.7472	−	11.7258i	0.738187	−	0.487728i
$579$	−11.6774	+	3.54230i	−0.485295	+	0.147213i
$580$	−6.66354	−	6.80308i	−0.276689	−	0.282483i
$581$	52.5793	−	5.17861i	2.18136	−	0.214845i
$582$	−2.74069	+	3.30448i	−0.113605	+	0.136975i
$583$	6.46225	+	4.31794i	0.267639	+	0.178831i
$584$	−5.51560	−	0.0857326i	−0.228237	−	0.00354764i
$585$	5.44926	+	8.15539i	0.225299	+	0.337184i
$586$	2.10318	+	2.58998i	0.0868816	+	0.106991i
$587$	22.2201	+	41.5709i	0.917123	+	1.71582i	0.662961	+	0.748654i	$0.269300\pi$
$587$	22.2201	+	41.5709i	0.917123	+	1.71582i	0.254162	+	0.967162i	$0.418200\pi$
$588$	−5.87943	+	1.71719i	−0.242464	+	0.0708156i
$589$	0.907590	−	9.21492i	0.0373966	−	0.379694i
$590$	−5.48633	−	0.0284239i	−0.225868	−	0.00117019i
$591$	9.87590	+	23.8425i	0.406240	+	0.980751i
$592$	44.4917	−	3.45286i	1.82860	−	0.141912i
$593$	3.46687	−	8.36976i	0.142367	−	0.343705i	−0.836572	−	0.547857i	$-0.815444\pi$
$593$	3.46687	−	8.36976i	0.142367	−	0.343705i	0.978939	+	0.204152i	$0.0654438\pi$
$594$	0.409092	−	0.973342i	0.0167852	−	0.0399367i
$595$	4.78942	+	5.83592i	0.196347	+	0.239250i
$596$	−32.0221	−	26.8399i	−1.31168	−	1.09940i
$597$	5.45433	−	17.9805i	0.223231	−	0.735894i
$598$	34.0477	+	18.4263i	1.39231	+	0.753507i
$599$	−14.2199	−	2.82851i	−0.581008	−	0.115570i	−0.104168	−	0.994560i	$-0.533218\pi$
$599$	−14.2199	−	2.82851i	−0.581008	−	0.115570i	−0.476840	+	0.878990i	$0.658218\pi$
$600$	5.92590	+	0.676797i	0.241924	+	0.0276301i
$601$	4.03786	+	20.2997i	0.164708	+	0.828043i	0.971469	+	0.237165i	$0.0762183\pi$
$601$	4.03786	+	20.2997i	0.164708	+	0.828043i	−0.806761	+	0.590877i	$0.798782\pi$
$602$	24.6747	−	13.0250i	1.00567	−	0.530860i
$603$	3.83944	−	4.67837i	0.156354	−	0.190518i
$604$	12.7047	−	18.5939i	0.516946	−	0.756575i
$605$	15.6597	+	8.37027i	0.636656	+	0.340300i
$606$	11.5618	+	7.81231i	0.469667	+	0.317353i
$607$	−25.4663	−	25.4663i	−1.03364	−	1.03364i	−0.999414	−	0.0342308i	$-0.989102\pi$
$607$	−25.4663	−	25.4663i	−1.03364	−	1.03364i	−0.0342308	−	0.999414i	$-0.510898\pi$
$608$	2.63031	−	7.92585i	0.106673	−	0.321436i
$609$	−6.28105	+	6.28105i	−0.254521	+	0.254521i
$610$	24.1796	−	4.67953i	0.979003	−	0.189469i
$611$	−21.8870	+	40.9476i	−0.885451	+	1.65656i
$612$	−2.73976	−	0.574545i	−0.110748	−	0.0232246i
$613$	−26.5931	−	21.8244i	−1.07408	−	0.881479i	−0.0807489	−	0.996734i	$-0.525731\pi$
$613$	−26.5931	−	21.8244i	−1.07408	−	0.881479i	−0.993336	+	0.115256i	$0.963231\pi$
$614$	1.94796	+	0.601944i	0.0786131	+	0.0242925i
$615$	−3.80923	+	0.757703i	−0.153603	+	0.0305536i
$616$	−5.11128	−	4.32939i	−0.205939	−	0.174436i
$617$	8.33094	−	41.8825i	0.335391	−	1.68613i	−0.333488	−	0.942754i	$-0.608226\pi$
$617$	8.33094	−	41.8825i	0.335391	−	1.68613i	0.668880	−	0.743371i	$-0.266774\pi$
$618$	9.27433	−	2.76095i	0.373068	−	0.111062i
$619$	20.4152	+	6.19287i	0.820555	+	0.248913i	0.672529	−	0.740071i	$-0.265208\pi$
$619$	20.4152	+	6.19287i	0.820555	+	0.248913i	0.148026	+	0.988983i	$0.452708\pi$
$620$	−9.85970	−	18.9151i	−0.395975	−	0.759647i
$621$	−3.66846	+	3.01062i	−0.147210	+	0.120812i
$622$	−4.71950	+	1.92630i	−0.189235	+	0.0772374i
$623$	−31.3903	−	13.0023i	−1.25763	−	0.520926i
$624$	−13.2138	+	18.9152i	−0.528975	+	0.757215i
$625$	−9.24756	+	3.83046i	−0.369902	+	0.153219i
$626$	2.19963	−	2.17696i	0.0879149	−	0.0870087i
$627$	−1.09682	−	0.108028i	−0.0438028	−	0.00431420i
$628$	21.3594	−	17.1620i	0.852334	−	0.684837i
$629$	−13.7715	+	7.36101i	−0.549105	+	0.293503i
$630$	−0.786996	+	7.58732i	−0.0313547	+	0.302286i
$631$	24.6736	−	16.4863i	0.982239	−	0.656311i	0.0428203	−	0.999083i	$-0.486366\pi$
$631$	24.6736	−	16.4863i	0.982239	−	0.656311i	0.939419	+	0.342772i	$0.111366\pi$
$632$	24.3689	+	5.24226i	0.969342	+	0.208526i
$633$	3.72974	−	5.58195i	0.148244	−	0.221863i
$634$	0.835947	+	8.96333i	0.0331997	+	0.355980i
$635$	3.34438	+	33.9560i	0.132718	+	1.34750i
$636$	19.3173	−	7.76797i	0.765979	−	0.308020i
$637$	−5.12814	−	16.9052i	−0.203184	−	0.669809i
$638$	−2.89670	−	0.591806i	−0.114681	−	0.0234298i
$639$	9.09328			0.359725
$640$	−4.91320	−	18.5995i	−0.194211	−	0.735210i
$641$	−9.45803			−0.373570			−0.186785	−	0.982401i	$-0.559807\pi$
$641$	−9.45803			−0.373570			−0.186785	+	0.982401i	$0.559807\pi$
$642$	20.4445	+	4.17689i	0.806880	+	0.164849i
$643$	−3.77148	−	12.4329i	−0.148732	−	0.490305i	0.850639	−	0.525750i	$-0.176215\pi$
$643$	−3.77148	−	12.4329i	−0.148732	−	0.490305i	−0.999372	+	0.0354447i	$0.988715\pi$
$644$	11.2330	+	27.9340i	0.442642	+	1.10076i
$645$	−1.03658	−	10.5246i	−0.0408154	−	0.414406i
$646$	0.271350	+	2.90951i	0.0106761	+	0.114473i
$647$	15.4178	−	23.0744i	0.606138	−	0.907150i	−0.393789	−	0.919201i	$-0.628836\pi$
$647$	15.4178	−	23.0744i	0.606138	−	0.907150i	0.999927	+	0.0120509i	$0.00383601\pi$
$648$	−1.53465	−	2.37589i	−0.0602867	−	0.0933337i
$649$	−1.41628	+	0.946328i	−0.0555939	+	0.0371466i
$650$	−1.77482	+	17.1108i	−0.0696141	+	0.671140i
$651$	−17.5474	+	9.37928i	−0.687736	+	0.367603i
$652$	5.11058	+	6.36052i	0.200146	+	0.249097i
$653$	4.63094	+	0.456107i	0.181223	+	0.0178489i	0.188221	−	0.982127i	$-0.439728\pi$
$653$	4.63094	+	0.456107i	0.181223	+	0.0178489i	−0.00699875	+	0.999976i	$0.502228\pi$
$654$	8.08059	−	7.99729i	0.315976	−	0.312719i
$655$	0.386323	−	0.160020i	0.0150949	−	0.00625251i
$656$	−4.91746	−	7.70028i	−0.191995	−	0.300645i
$657$	1.80184	+	0.746345i	0.0702963	+	0.0291177i
$658$	−33.4313	+	13.6452i	−1.30329	+	0.531945i
$659$	8.37437	−	6.87267i	0.326219	−	0.267721i	−0.457000	−	0.889467i	$-0.651076\pi$
$659$	8.37437	−	6.87267i	0.326219	−	0.267721i	0.783219	+	0.621745i	$0.213576\pi$
$660$	−2.25140	+	1.17357i	−0.0876356	+	0.0456811i
$661$	−36.2042	−	10.9824i	−1.40818	−	0.427167i	−0.507501	−	0.861651i	$-0.669431\pi$
$661$	−36.2042	−	10.9824i	−1.40818	−	0.427167i	−0.900680	+	0.434484i	$0.856931\pi$
$662$	47.0894	−	14.0184i	1.83018	−	0.544841i
$663$	1.57514	−	7.91874i	0.0611732	−	0.307539i
$664$	46.9481	−	3.88829i	1.82194	−	0.150895i
$665$	7.80961	−	1.55343i	0.302844	−	0.0602394i
$666$	−15.0742	−	4.65813i	−0.584114	−	0.180499i
$667$	10.2725	+	8.43044i	0.397754	+	0.326428i
$668$	−0.248917	+	1.18698i	−0.00963089	+	0.0459256i
$669$	−8.10993	+	15.1726i	−0.313548	+	0.586607i
$670$	−14.2884	+	2.76526i	−0.552008	+	0.106831i
$671$	5.40672	−	5.40672i	0.208724	−	0.208724i
$672$	−17.3009	+	4.76247i	−0.667395	+	0.183716i
$673$	−33.8276	−	33.8276i	−1.30396	−	1.30396i	−0.925699	−	0.378260i	$-0.876523\pi$
$673$	−33.8276	−	33.8276i	−1.30396	−	1.30396i	−0.378260	−	0.925699i	$-0.623477\pi$
$674$	33.6754	+	22.7544i	1.29713	+	0.876467i
$675$	−1.85975	−	0.994055i	−0.0715816	−	0.0382612i
$676$	−33.4798	−	22.8758i	−1.28769	−	0.879839i
$677$	13.1701	−	16.0478i	0.506167	−	0.616766i	−0.455750	−	0.890108i	$-0.650629\pi$
$677$	13.1701	−	16.0478i	0.506167	−	0.616766i	0.961917	+	0.273342i	$0.0881290\pi$
$678$	4.10446	−	2.16661i	0.157631	−	0.0832083i
$679$	−1.87866	−	9.44468i	−0.0720965	−	0.362454i
$680$	4.18907	+	5.26931i	0.160643	+	0.202069i
$681$	−18.1526	−	3.61079i	−0.695611	−	0.138366i
$682$	−5.82422	−	3.15201i	−0.223021	−	0.120697i
$683$	−9.49206	+	31.2911i	−0.363204	+	1.19732i	0.564950	+	0.825125i	$0.308895\pi$
$683$	−9.49206	+	31.2911i	−0.363204	+	1.19732i	−0.928154	+	0.372197i	$0.878605\pi$
$684$	−1.89659	+	2.26278i	−0.0725179	+	0.0865194i
$685$	13.0700	+	15.9258i	0.499378	+	0.608494i
$686$	−6.84412	+	16.2840i	−0.261310	+	0.621727i
$687$	−6.76433	+	16.3305i	−0.258075	+	0.623049i
$688$	22.1789	−	11.2703i	0.845562	−	0.429677i
$689$	22.9804	+	55.4797i	0.875485	+	2.11361i
$690$	11.4117	+	0.0591224i	0.434436	+	0.00225075i
$691$	−0.623188	+	6.32733i	−0.0237072	+	0.240703i	0.976027	+	0.217649i	$0.0698389\pi$
$691$	−0.623188	+	6.32733i	−0.0237072	+	0.240703i	−0.999734	+	0.0230538i	$0.992661\pi$
$692$	−4.38388	−	15.0099i	−0.166650	−	0.570590i
$693$	1.11639	+	2.08861i	0.0424080	+	0.0793397i
$694$	−9.43229	−	11.6155i	−0.358045	−	0.440917i
$695$	−2.70366	−	4.04631i	−0.102556	−	0.153485i
$696$	−5.68683	+	5.51274i	−0.215559	+	0.208960i
$697$	2.65824	+	1.77618i	0.100688	+	0.0672775i
$698$	30.4255	−	36.6843i	1.15162	−	1.38852i
$699$	−19.4972	+	1.92030i	−0.737451	+	0.0726326i
$700$	−9.55754	+	9.36150i	−0.361241	+	0.353831i
$701$	−24.6749	+	7.48505i	−0.931958	+	0.282706i	−0.719523	−	0.694469i	$-0.755639\pi$
$701$	−24.6749	+	7.48505i	−0.931958	+	0.282706i	−0.212435	+	0.977175i	$0.568139\pi$
$702$	6.80631	−	4.49700i	0.256887	−	0.169728i
$703$			16.4696i			0.621161i
$704$	−4.49689	−	3.93064i	−0.169483	−	0.148142i
$705$			13.6863i			0.515457i
$706$	10.0418	+	15.1985i	0.377928	+	0.572002i
$707$	−29.9513	+	9.08562i	−1.12643	+	0.341700i
$708$	−0.0472801	+	4.56285i	−0.00177690	+	0.171482i
$709$	−10.1634	+	1.00101i	−0.381695	+	0.0375936i	−0.287045	−	0.957917i	$-0.592673\pi$
$709$	−10.1634	+	1.00101i	−0.381695	+	0.0375936i	−0.0946494	+	0.995511i	$0.530173\pi$
$710$	−16.8309	−	13.9593i	−0.631653	−	0.523884i
$711$	−7.32758	−	4.89613i	−0.274806	−	0.183619i
$712$	−27.8054	−	12.0270i	−1.04205	−	0.450731i
$713$	16.5374	+	24.7499i	0.619329	+	0.926891i
$714$	4.87437	−	3.95821i	0.182419	−	0.148132i
$715$	−3.45190	−	6.45806i	−0.129094	−	0.241518i
$716$	−8.93268	+	16.3033i	−0.333830	+	0.609282i
$717$	−0.309949	+	3.14696i	−0.0115753	+	0.117525i
$718$	−0.157032	+	30.3100i	−0.00586037	+	1.13116i
$719$	−0.311191	−	0.751282i	−0.0116055	−	0.0280181i	0.917971	−	0.396648i	$-0.129827\pi$
$719$	−0.311191	−	0.751282i	−0.0116055	−	0.0280181i	−0.929576	+	0.368630i	$0.879827\pi$
$720$	−0.806778	+	6.75346i	−0.0300668	+	0.251687i
$721$	−8.30615	+	20.0528i	−0.309337	+	0.746806i
$722$	−21.9298	−	9.21703i	−0.816144	−	0.343022i
$723$	−9.44892	−	11.5135i	−0.351409	−	0.428193i
$724$	−3.06687	−	34.8352i	−0.113979	−	1.29464i
$725$	−1.71412	+	5.65070i	−0.0636609	+	0.209862i
$726$	7.02902	−	12.9881i	0.260871	−	0.482032i
$727$	−11.3794	−	2.26351i	−0.422039	−	0.0839488i	−0.0204983	−	0.999790i	$-0.506525\pi$
$727$	−11.3794	−	2.26351i	−0.422039	−	0.0839488i	−0.401541	+	0.915841i	$0.631525\pi$
$728$	−14.2522	−	49.7541i	−0.528221	−	1.84401i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	−2.18932	−	4.14747i	−0.0810303	−	0.153505i
$731$	−5.52261	+	6.72932i	−0.204261	+	0.248893i
$732$	−3.78777	−	20.1303i	−0.140000	−	0.744037i
$733$	−27.6655	−	14.7875i	−1.02185	−	0.546190i	−0.126693	−	0.991942i	$-0.540436\pi$
$733$	−27.6655	−	14.7875i	−1.02185	−	0.546190i	−0.895157	+	0.445752i	$0.852936\pi$
$734$	12.2411	−	18.1163i	0.451828	−	0.668683i
$735$	−3.68222	−	3.68222i	−0.135821	−	0.135821i
$736$	9.62751	+	25.0599i	0.354875	+	0.923719i
$737$	−3.19498	+	3.19498i	−0.117688	+	0.117688i
$738$	0.613767	+	3.17140i	0.0225931	+	0.116741i
$739$	−3.27745	+	6.13168i	−0.120563	+	0.225557i	−0.934962	−	0.354748i	$-0.884567\pi$
$739$	−3.27745	+	6.13168i	−0.120563	+	0.225557i	0.814399	+	0.580305i	$0.197067\pi$
$740$	20.7503	+	31.7626i	0.762797	+	1.16762i
$741$	−6.58262	−	5.40222i	−0.241819	−	0.198456i
$742$	−13.7881	+	44.6199i	−0.506178	+	1.63805i
$743$	−15.8039	+	3.14360i	−0.579791	+	0.115328i	−0.476269	−	0.879300i	$-0.658011\pi$
$743$	−15.8039	+	3.14360i	−0.579791	+	0.115328i	−0.103522	+	0.994627i	$0.533011\pi$
$744$	−15.7741	+	8.11879i	−0.578307	+	0.297649i
$745$	6.93019	−	34.8404i	0.253903	−	1.27645i
$746$	−4.47389	−	15.0283i	−0.163801	−	0.550224i
$747$	−15.9383	−	4.83484i	−0.583153	−	0.176897i
$748$	1.99354	+	0.627363i	0.0728911	+	0.0229387i
$749$	−36.1810	+	29.6930i	−1.32202	+	1.08496i
$750$	6.45979	+	15.8267i	0.235878	+	0.577911i
$751$	−2.36533	−	0.979754i	−0.0863123	−	0.0357517i	0.339110	−	0.940747i	$-0.389874\pi$
$751$	−2.36533	−	0.979754i	−0.0863123	−	0.0357517i	−0.425422	+	0.904995i	$0.639874\pi$
$752$	−29.9943	+	11.7019i	−1.09378	+	0.426725i
$753$	−0.380023	+	0.157411i	−0.0138488	+	0.00573636i
$754$	−16.0689	−	16.2363i	−0.585196	−	0.591291i
$755$	19.0538	+	1.87664i	0.693439	+	0.0682978i
$756$	6.30697	+	0.687236i	0.229382	+	0.0249945i
$757$	7.23578	−	3.86761i	0.262989	−	0.140571i	−0.334633	−	0.942349i	$-0.608612\pi$
$757$	7.23578	−	3.86761i	0.262989	−	0.140571i	0.597622	+	0.801778i	$0.296112\pi$
$758$	−11.4022	−	1.18270i	−0.414147	−	0.0429575i
$759$	2.94590	−	1.96839i	0.106929	−	0.0714480i
$760$	6.98408	−	1.27671i	0.253339	−	0.0463113i
$761$	3.83236	−	5.73554i	0.138923	−	0.207913i	−0.755484	−	0.655167i	$-0.772598\pi$
$761$	3.83236	−	5.73554i	0.138923	−	0.207913i	0.894407	+	0.447254i	$0.147598\pi$
$762$	28.2556	−	2.63520i	1.02359	−	0.0954632i
$763$	2.49954	+	25.3783i	0.0904895	+	0.918755i
$764$	5.38754	−	12.6348i	0.194914	−	0.457110i
$765$	−0.690867	−	2.27748i	−0.0249784	−	0.0823426i
$766$	−2.30562	+	11.2852i	−0.0833053	+	0.407752i
$767$	−13.1609			−0.475211
$768$	−15.4903	+	4.00616i	−0.558960	+	0.144560i
$769$	−18.9685			−0.684022			−0.342011	−	0.939696i	$-0.611108\pi$
$769$	−18.9685			−0.684022			−0.342011	+	0.939696i	$0.611108\pi$
$770$	1.13994	−	5.57964i	0.0410806	−	0.201076i
$771$	−5.83187	−	19.2251i	−0.210030	−	0.692375i
$772$	9.57277	−	22.4499i	0.344532	−	0.807990i
$773$	0.702243	+	7.12999i	0.0252579	+	0.256448i	0.999519	+	0.0310238i	$0.00987677\pi$
$773$	0.702243	+	7.12999i	0.0252579	+	0.256448i	−0.974261	+	0.225424i	$0.927623\pi$
$774$	−8.75776	+	0.816774i	−0.314791	+	0.0293583i
$775$	−7.34838	+	10.9976i	−0.263962	+	0.395047i
$776$	−1.54401	−	8.44631i	−0.0554269	−	0.303205i
$777$	29.4255	−	19.6615i	1.05563	−	0.705351i
$778$	28.8025	+	2.98755i	1.03262	+	0.107109i
$779$	2.97378	−	1.58952i	0.106547	−	0.0569504i
$780$	−19.5014	−	2.12496i	−0.698261	−	0.0760858i
$781$	−6.75613	−	0.665421i	−0.241753	−	0.0238106i
$782$	−6.60790	−	6.67673i	−0.236298	−	0.238759i
$783$	2.58708	−	1.07160i	0.0924545	−	0.0382959i
$784$	4.92144	−	11.2181i	0.175766	−	0.400646i
$785$	21.5218	+	8.91462i	0.768146	+	0.318176i
$786$	−0.131424	−	0.321994i	−0.00468774	−	0.0114851i
$787$	−21.6868	+	17.7979i	−0.773051	+	0.634427i	−0.935917	−	0.352222i	$-0.885426\pi$
$787$	−21.6868	+	17.7979i	−0.773051	+	0.634427i	0.162866	+	0.986648i	$0.447926\pi$
$788$	−49.2336	−	15.4937i	−1.75387	−	0.551940i
$789$	24.5610	+	7.45050i	0.874396	+	0.265245i
$790$	6.04657	+	20.3111i	0.215127	+	0.722637i
$791$	−2.03098	+	10.2104i	−0.0722133	+	0.363041i
$792$	0.966354	+	1.87754i	0.0343379	+	0.0667155i
$793$	57.9434	−	11.5257i	2.05763	−	0.409288i
$794$	−13.8361	+	44.7751i	−0.491025	+	1.58901i
$795$	13.6833	+	11.2296i	0.485298	+	0.398274i
$796$	20.5530	+	31.4606i	0.728482	+	1.11509i
$797$	6.64055	−	12.4236i	0.235220	−	0.440066i	−0.736422	−	0.676523i	$-0.763486\pi$
$797$	6.64055	−	12.4236i	0.235220	−	0.440066i	0.971642	+	0.236457i	$0.0759861\pi$
$798$	−1.25833	−	6.50194i	−0.0445445	−	0.230166i
$799$	7.96629	−	7.96629i	0.281827	−	0.281827i
$800$	−8.65062	+	8.21367i	−0.305846	+	0.290397i
$801$	7.57376	+	7.57376i	0.267606	+	0.267606i
$802$	−24.9362	+	36.9043i	−0.880527	+	1.30314i
$803$	−1.28411	−	0.686373i	−0.0453154	−	0.0242216i
$804$	2.23829	+	11.8955i	0.0789385	+	0.419523i
$805$	−16.2388	+	19.7870i	−0.572342	+	0.697401i
$806$	−23.8863	−	45.2506i	−0.841361	−	1.59388i
$807$	−0.0243729	−	0.122531i	−0.000857966	−	0.00431329i
$808$	−26.8286	+	7.68510i	−0.943825	+	0.270361i
$809$	−38.6184	−	7.68168i	−1.35775	−	0.270073i	−0.538073	−	0.842898i	$-0.680848\pi$
$809$	−38.6184	−	7.68168i	−1.35775	−	0.270073i	−0.819678	+	0.572825i	$0.805848\pi$
$810$	1.14453	−	2.11484i	0.0402148	−	0.0743080i
$811$	0.234584	−	0.773321i	0.00823737	−	0.0271550i	−0.952725	−	0.303833i	$-0.901734\pi$
$811$	0.234584	−	0.773321i	0.00823737	−	0.0271550i	0.960963	+	0.276678i	$0.0892335\pi$
$812$	−1.55804	−	17.6970i	−0.0546765	−	0.621045i
$813$	12.5186	+	15.2540i	0.439046	+	0.534980i
$814$	10.8590	+	4.56399i	0.380607	+	0.159968i
$815$	−2.65464	+	6.40887i	−0.0929881	+	0.224493i
$816$	4.40052	−	3.46133i	0.154049	−	0.121171i
$817$	3.51364	+	8.48267i	0.122927	+	0.296771i
$818$	0.0897490	−	17.3232i	0.00313800	−	0.605692i
$819$	−1.79354	+	18.2101i	−0.0626713	+	0.636313i
$820$	3.73246	−	6.81221i	0.130343	−	0.237893i
$821$	−9.98463	−	18.6799i	−0.348466	−	0.651934i	0.645237	−	0.763983i	$-0.276759\pi$
$821$	−9.98463	−	18.6799i	−0.348466	−	0.651934i	−0.993703	+	0.112049i	$0.964259\pi$
$822$	13.3018	−	10.8017i	0.463953	−	0.376751i
$823$	26.4923	+	39.6486i	0.923465	+	1.38206i	0.924136	+	0.382064i	$0.124786\pi$
$823$	26.4923	+	39.6486i	0.923465	+	1.38206i	−0.000670818		1.00000i	$0.500214\pi$
$824$	−7.68312	+	17.7627i	−0.267654	+	0.618793i
$825$	1.30901	+	0.874654i	0.0455740	+	0.0304516i
$826$	−7.87820	−	6.53407i	−0.274118	−	0.227349i
$827$	−45.9654	+	4.52720i	−1.59837	+	0.157426i	−0.857596	−	0.514324i	$-0.828043\pi$
$827$	−45.9654	+	4.52720i	−1.59837	+	0.157426i	−0.740778	+	0.671750i	$0.765543\pi$
$828$	0.0983439	−	9.49084i	0.00341769	−	0.329829i
$829$	28.0287	−	8.50241i	0.973477	−	0.295301i	0.236809	−	0.971556i	$-0.423898\pi$
$829$	28.0287	−	8.50241i	0.973477	−	0.295301i	0.736667	+	0.676255i	$0.236398\pi$
$830$	22.0784	+	33.4162i	0.766354	+	1.15989i
$831$		−	15.9185i		−	0.552208i
$832$	−12.0169	−	44.5551i	−0.416610	−	1.54467i
$833$			4.28655i			0.148520i
$834$	−3.37696	+	2.23120i	−0.116935	+	0.0772600i
$835$	−0.986703	+	0.299313i	−0.0341463	+	0.0103582i
$836$	1.57471	−	1.54241i	0.0544625	−	0.0533454i
$837$	6.24213	−	0.614796i	0.215760	−	0.0212505i
$838$	24.4491	−	29.4786i	0.844582	−	1.01832i
$839$	−32.3748	−	21.6322i	−1.11770	−	0.746825i	−0.147486	−	0.989064i	$-0.547118\pi$
$839$	−32.3748	−	21.6322i	−1.11770	−	0.746825i	−0.970217	+	0.242239i	$0.922118\pi$
$840$	−10.6187	−	10.9540i	−0.366380	−	0.377949i
$841$	11.7551	+	17.5928i	0.405350	+	0.606649i
$842$	−21.8537	−	26.9119i	−0.753128	−	0.927446i
$843$	−9.17355	−	17.1625i	−0.315954	−	0.591108i
$844$	3.76423	+	12.8883i	0.129570	+	0.443632i
$845$	3.37904	−	34.3080i	0.116242	−	1.18023i
$846$	11.3829	+	0.0589731i	0.391352	+	0.00202754i
$847$	12.6766	+	30.6040i	0.435573	+	1.05157i
$848$	−12.9109	+	39.5891i	−0.443363	+	1.35950i
$849$	−12.4257	+	29.9982i	−0.426448	+	1.02954i
$850$	1.61733	−	3.84807i	0.0554739	−	0.131988i
$851$	−33.5877	−	40.9267i	−1.15137	−	1.40295i
$852$	−11.6825	+	13.9381i	−0.400235	+	0.477512i
$853$	2.10871	−	6.95148i	0.0722008	−	0.238014i	−0.913411	−	0.407038i	$-0.866562\pi$
$853$	2.10871	−	6.95148i	0.0722008	−	0.238014i	0.985612	+	0.169024i	$0.0540616\pi$
$854$	40.4077	+	21.8682i	1.38272	+	0.748316i
$855$	−2.46193	−	0.489709i	−0.0841963	−	0.0167477i
$856$	−32.6681	+	25.9709i	−1.11657	+	0.887669i
$857$	0.526039	+	2.64458i	0.0179692	+	0.0903371i	0.988729	−	0.149715i	$-0.0478356\pi$
$857$	0.526039	+	2.64458i	0.0179692	+	0.0903371i	−0.970760	+	0.240052i	$0.922836\pi$
$858$	−5.38603	+	2.84312i	−0.183876	+	0.0970624i
$859$	25.7285	−	31.3503i	0.877846	−	1.06966i	−0.119202	−	0.992870i	$-0.538033\pi$
$859$	25.7285	−	31.3503i	0.877846	−	1.06966i	0.997047	−	0.0767882i	$-0.0244665\pi$
$860$	17.4638	+	11.9325i	0.595509	+	0.406894i
$861$	−6.39004	−	3.41555i	−0.217772	−	0.116402i
$862$	38.9516	+	26.3195i	1.32670	+	0.896447i
$863$	−34.9933	−	34.9933i	−1.19118	−	1.19118i	−0.976735	−	0.214449i	$-0.931204\pi$
$863$	−34.9933	−	34.9933i	−1.19118	−	1.19118i	−0.214449	−	0.976735i	$-0.568796\pi$
$864$	5.61336	+	0.700096i	0.190971	+	0.0238178i
$865$	9.40050	−	9.40050i	0.319626	−	0.319626i
$866$	−0.414884	+	0.0802933i	−0.0140983	+	0.00272848i
$867$	7.09024	−	13.2649i	0.240797	−	0.450500i
$868$	8.16732	−	38.9464i	0.277217	−	1.32193i
$869$	5.08596	+	4.17394i	0.172530	+	0.141591i
$870$	−6.43351	−	1.98804i	−0.218116	−	0.0674009i
$871$	−34.2403	+	6.81082i	−1.16019	+	0.230776i
$872$	1.87674	+	22.6603i	0.0635546	+	0.767374i
$873$	−0.592237	+	2.97738i	−0.0200442	+	0.100769i
$874$	−9.49582	+	2.82689i	−0.321201	+	0.0956209i
$875$	−36.6923	−	11.1305i	−1.24043	−	0.376279i
$876$	−3.45888	+	1.80298i	−0.116865	+	0.0609171i
$877$	12.9113	−	10.5961i	0.435985	−	0.357804i	−0.390653	−	0.920538i	$-0.627751\pi$
$877$	12.9113	−	10.5961i	0.435985	−	0.357804i	0.826638	+	0.562735i	$0.190251\pi$
$878$	−10.3001	+	4.20404i	−0.347610	+	0.141879i
$879$	2.17959	+	0.902816i	0.0735157	+	0.0304512i
$880$	1.09362	−	4.95865i	0.0368659	−	0.167156i
$881$	50.0013	−	20.7112i	1.68459	−	0.697779i	0.685059	−	0.728487i	$-0.259776\pi$
$881$	50.0013	−	20.7112i	1.68459	−	0.697779i	0.999528	+	0.0307082i	$0.00977627\pi$
$882$	−3.07836	+	3.04663i	−0.103654	+	0.102585i
$883$	29.9009	+	2.94499i	1.00625	+	0.0991067i	0.587692	−	0.809085i	$-0.300037\pi$
$883$	29.9009	+	2.94499i	1.00625	+	0.0991067i	0.418555	+	0.908191i	$0.362537\pi$
$884$	10.1141	+	12.5879i	0.340176	+	0.423376i
$885$	−3.42139	+	1.82877i	−0.115009	+	0.0614734i
$886$	2.08765	−	20.1268i	0.0701361	−	0.676172i
$887$	−38.7638	+	25.9012i	−1.30156	+	0.869676i	−0.996576	−	0.0826807i	$-0.973652\pi$
$887$	−38.7638	+	25.9012i	−1.30156	+	0.869676i	−0.304986	+	0.952357i	$0.598652\pi$
$888$	26.5063	−	17.1211i	0.889494	−	0.574548i
$889$	−35.3641	+	52.9261i	−1.18607	+	1.77508i
$890$	−2.39174	−	25.6451i	−0.0801713	−	0.859626i
$891$	−0.0731772	−	0.742981i	−0.00245153	−	0.0248908i
$892$	−12.8373	−	31.9236i	−0.429825	−	1.06888i
$893$	−3.44926	−	11.3707i	−0.115425	−	0.380506i
$894$	−28.9469	−	5.91396i	−0.968128	−	0.197792i
$895$	−15.8050			−0.528302
$896$	14.9272	−	32.6371i	0.498683	−	1.09033i
$897$	27.3749			0.914022
$898$	2.79081	+	0.570173i	0.0931306	+	0.0190269i
$899$	−5.09855	−	16.8077i	−0.170046	−	0.560567i
$900$	3.91296	−	1.57350i	0.130432	−	0.0524501i
$901$	−1.42821	−	14.5009i	−0.0475807	−	0.483095i
$902$	−0.223943	−	2.40120i	−0.00745649	−	0.0799512i
$903$	10.9610	−	16.4043i	0.364760	−	0.545902i
$904$	−1.95218	+	9.07481i	−0.0649287	+	0.301824i
$905$	24.7203	−	16.5176i	0.821731	−	0.549063i
$906$	1.64290	−	15.8389i	0.0545816	−	0.526213i
$907$	−26.6042	+	14.2203i	−0.883379	+	0.472176i	−0.849706	−	0.527257i	$-0.823221\pi$
$907$	−26.6042	+	14.2203i	−0.883379	+	0.472176i	−0.0336734	+	0.999433i	$0.510721\pi$
$908$	28.8560	−	23.1853i	0.957619	−	0.769432i
$909$	9.81930	+	0.967117i	0.325686	+	0.0320772i
$910$	31.2745	−	30.9521i	1.03674	−	1.02605i
$911$	42.1245	−	17.4485i	1.39565	−	0.578095i	0.447028	−	0.894520i	$-0.352482\pi$
$911$	42.1245	−	17.4485i	1.39565	−	0.578095i	0.948618	+	0.316425i	$0.102482\pi$
$912$	−1.03175	−	5.81415i	−0.0341646	−	0.192526i
$913$	11.4881	+	4.75851i	0.380199	+	0.157484i
$914$	−9.15113	+	3.73509i	−0.302692	+	0.123546i
$915$	13.4618	−	11.0478i	0.445034	−	0.365230i
$916$	−16.3409	−	31.3488i	−0.539919	−	1.03579i
$917$	0.746501	+	0.226449i	0.0246516	+	0.00747799i
$918$	−1.89716	+	0.564780i	−0.0626155	+	0.0186405i
$919$	−3.65792	+	18.3896i	−0.120664	+	0.606617i	0.872376	+	0.488836i	$0.162578\pi$
$919$	−3.65792	+	18.3896i	−0.120664	+	0.606617i	−0.993040	+	0.117781i	$0.962422\pi$
$920$	−14.7517	+	17.4158i	−0.486348	+	0.574182i
$921$	1.41398	−	0.281258i	0.0465921	−	0.00926775i
$922$	23.5453	+	7.27580i	0.775422	+	0.239616i
$923$	−40.5472	−	33.2762i	−1.33463	−	1.09530i
$924$	−4.63566	−	0.972129i	−0.152502	−	0.0319807i
$925$	11.0901	−	20.7480i	0.364639	−	0.682191i
$926$	0.967935	−	0.187326i	0.0318083	−	0.00615593i
$927$	4.83828	−	4.83828i	0.158910	−	0.158910i
$928$	−1.14381	−	15.7991i	−0.0375473	−	0.518632i
$929$	−2.55132	−	2.55132i	−0.0837062	−	0.0837062i	0.664014	−	0.747720i	$-0.268852\pi$
$929$	−2.55132	−	2.55132i	−0.0837062	−	0.0837062i	−0.747720	+	0.664014i	$0.768852\pi$
$930$	−12.4975	−	8.44452i	−0.409808	−	0.276907i
$931$	3.98721	+	2.13121i	0.130676	+	0.0698476i
$932$	22.1053	−	32.3522i	0.724084	−	1.05973i
$933$	−2.28665	+	2.78629i	−0.0748615	+	0.0912189i
$934$	−11.6110	+	6.12906i	−0.379922	+	0.200549i
$935$	0.346641	+	1.74268i	0.0113364	+	0.0569918i
$936$	−1.85136	+	16.2101i	−0.0605134	+	0.529844i
$937$	−8.99125	−	1.78847i	−0.293731	−	0.0584268i	0.0460250	−	0.998940i	$-0.485345\pi$
$937$	−8.99125	−	1.78847i	−0.293731	−	0.0584268i	−0.339756	+	0.940513i	$0.610345\pi$
$938$	−23.8780	−	12.9225i	−0.779643	−	0.421936i
$939$	0.635237	−	2.09409i	0.0207302	−	0.0683382i
$940$	−20.9783	−	17.5833i	−0.684236	−	0.573505i
$941$	5.57597	+	6.79434i	0.181772	+	0.221489i	0.855922	−	0.517105i	$-0.172990\pi$
$941$	5.57597	+	6.79434i	0.181772	+	0.221489i	−0.674151	+	0.738594i	$0.735490\pi$
$942$	7.50701	−	17.8612i	0.244592	−	0.581950i
$943$	−4.14818	+	10.0146i	−0.135083	+	0.326120i
$944$	−6.93315	−	5.93453i	−0.225655	−	0.193153i
$945$	2.06413	+	4.98325i	0.0671461	+	0.162105i
$946$	6.56661	+	0.0340207i	0.213499	+	0.00110611i
$947$	3.64445	−	37.0027i	0.118429	−	1.20243i	−0.733840	−	0.679322i	$-0.762274\pi$
$947$	3.64445	−	37.0027i	0.118429	−	1.20243i	0.852269	−	0.523104i	$-0.175226\pi$
$948$	16.9188	−	4.94141i	0.549496	−	0.160489i
$949$	−5.30324	−	9.92167i	−0.172151	−	0.322071i
$950$	−2.77524	−	3.41759i	−0.0900405	−	0.110881i
$951$	3.53650	+	5.29275i	0.114679	+	0.171629i
$952$	−0.195176	+	12.5566i	−0.00632570	+	0.406963i
$953$	−47.2402	−	31.5649i	−1.53026	−	1.02249i	−0.982589	−	0.185794i	$-0.940514\pi$
$953$	−47.2402	−	31.5649i	−1.53026	−	1.02249i	−0.547671	−	0.836694i	$-0.684486\pi$
$954$	9.39863	−	11.3320i	0.304292	−	0.366888i
$955$	11.6215	−	1.14461i	0.376062	−	0.0370388i
$956$	−4.42544	−	4.51811i	−0.143129	−	0.146126i
$957$	−2.00056	+	0.606864i	−0.0646690	+	0.0196171i
$958$	−43.2991	+	28.6082i	−1.39893	+	0.924289i
$959$			38.4350i			1.24113i
$960$	−9.31515	−	9.91304i	−0.300645	−	0.319942i
$961$		−	8.34214i		−	0.269101i
$962$	50.1702	+	75.9337i	1.61755	+	2.44820i
$963$	14.1197	−	4.28317i	0.455002	−	0.138023i
$964$	29.7873	+	0.308655i	0.959383	+	0.00994111i
$965$	20.6494	−	2.03379i	0.664728	−	0.0654700i
$966$	16.3869	+	13.5910i	0.527239	+	0.437284i
$967$	41.9893	+	28.0563i	1.35028	+	0.902231i	0.999415	−	0.0341932i	$-0.0108861\pi$
$967$	41.9893	+	28.0563i	1.35028	+	0.902231i	0.350869	+	0.936424i	$0.385886\pi$
$968$	10.8775	+	27.4603i	0.349618	+	0.882606i
$969$	1.14796	+	1.71804i	0.0368776	+	0.0551913i
$970$	5.66683	−	4.60172i	0.181951	−	0.147752i
$971$	10.5224	+	19.6860i	0.337680	+	0.631754i	0.992251	−	0.124246i	$-0.0396511\pi$
$971$	10.5224	+	19.6860i	0.337680	+	0.631754i	−0.654572	+	0.756000i	$0.727151\pi$
$972$	−1.75398	−	0.961019i	−0.0562589	−	0.0308247i
$973$	0.889868	−	9.03498i	0.0285279	−	0.289648i
$974$	0.0132781	−	2.56292i	0.000425457	−	0.0821211i
$975$	4.65499	+	11.2381i	0.149079	+	0.359908i
$976$	35.7218	+	20.0563i	1.14343	+	0.641986i
$977$	−8.63608	+	20.8493i	−0.276293	+	0.667029i	−0.999727	−	0.0233638i	$-0.992562\pi$
$977$	−8.63608	+	20.8493i	−0.276293	+	0.667029i	0.723434	+	0.690393i	$0.242562\pi$
$978$	5.31881	+	2.23548i	0.170077	+	0.0714827i
$979$	−5.07293	−	6.18139i	−0.162132	−	0.197558i
$980$	10.3748	−	0.913389i	0.331409	−	0.0291771i
$981$	2.33361	−	7.69289i	0.0745065	−	0.245615i
$982$	−17.3555	+	32.0690i	−0.553835	+	1.02336i
$983$	23.4584	+	4.66617i	0.748208	+	0.148828i	0.554445	−	0.832221i	$-0.312931\pi$
$983$	23.4584	+	4.66617i	0.748208	+	0.148828i	0.193763	+	0.981048i	$0.437931\pi$
$984$	−5.64962	−	3.13364i	−0.180103	−	0.0998967i
$985$	−8.56084	−	43.0382i	−0.272771	−	1.37131i
$986$	2.58754	+	4.90186i	0.0824040	+	0.156107i
$987$	−16.1978	+	19.7371i	−0.515582	+	0.628238i
$988$	16.7374	−	3.14936i	0.532488	−	0.100194i
$989$	−26.0307	−	13.9137i	−0.827729	−	0.442430i
$990$	−1.00512	+	1.48753i	−0.0319449	+	0.0472769i
$991$	−23.2593	−	23.2593i	−0.738855	−	0.738855i	0.233502	−	0.972356i	$-0.424982\pi$
$991$	−23.2593	−	23.2593i	−0.738855	−	0.738855i	−0.972356	+	0.233502i	$0.924982\pi$
$992$	7.82116	−	34.6089i	0.248322	−	1.09883i
$993$	24.5659	−	24.5659i	0.779574	−	0.779574i
$994$	−7.75100	−	40.0502i	−0.245847	−	1.27032i
$995$	−15.0608	+	28.1767i	−0.477459	+	0.893263i
$996$	27.8873	−	18.2186i	0.883644	−	0.577279i
$997$	−17.5575	−	14.4090i	−0.556050	−	0.456339i	0.313915	−	0.949451i	$-0.398359\pi$
$997$	−17.5575	−	14.4090i	−0.556050	−	0.456339i	−0.869966	+	0.493112i	$0.835859\pi$
$998$	−4.42845	+	14.3309i	−0.140180	+	0.453638i
$999$	−10.9420	+	2.17650i	−0.346190	+	0.0688615i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.14	✓	512
128.69	even	32	inner	384.2.v.a.325.14	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.14	✓	512	1.1	even	1	trivial
384.2.v.a.325.14	yes	512	128.69	even	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.283082 + 1.38559i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.83973 - 0.784471i) q^{4} +(-0.166665 - 1.69218i) q^{5} +(-1.40810 + 0.131324i) q^{6} +(1.76235 - 2.63755i) q^{7} +(1.60775 - 2.32704i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(2.39185 + 0.248095i) q^{10} +(0.658421 - 0.351933i) q^{11} +(0.216647 - 1.98823i) q^{12} +(5.74062 + 0.565402i) q^{13} +(3.15567 + 3.18854i) q^{14} +(1.57094 - 0.650703i) q^{15} +(2.76921 + 2.88643i) q^{16} +(-1.29313 - 0.535633i) q^{17} +(-0.534420 - 1.30935i) q^{18} +(-1.14115 + 0.936520i) q^{19} +(-1.02085 + 3.24390i) q^{20} +(3.03556 + 0.920827i) q^{21} +(0.301249 + 1.01193i) q^{22} +(0.925835 - 4.65449i) q^{23} +(2.69355 + 0.863016i) q^{24} +(2.06822 - 0.411395i) q^{25} +(-2.40848 + 7.79410i) q^{26} +(-0.773010 - 0.634393i) q^{27} +(-5.31133 + 3.46986i) q^{28} +(-1.32002 + 2.46958i) q^{29} +(0.456906 + 2.36088i) q^{30} +(-4.43521 + 4.43521i) q^{31} +(-4.78333 + 3.01990i) q^{32} +(0.527909 + 0.527909i) q^{33} +(1.10823 - 1.64012i) q^{34} +(-4.75693 - 2.54263i) q^{35} +(1.96551 - 0.369835i) q^{36} +(7.07753 - 8.62400i) q^{37} +(-0.974595 - 1.84628i) q^{38} +(1.12536 + 5.65756i) q^{39} +(-4.20574 - 2.33277i) q^{40} +(-2.24024 - 0.445611i) q^{41} +(-2.13520 + 3.94538i) q^{42} +(1.80544 - 5.95173i) q^{43} +(-1.48740 + 0.130950i) q^{44} +(1.07870 + 1.31440i) q^{45} +(6.18713 + 2.60043i) q^{46} +(-3.08023 + 7.43634i) q^{47} +(-1.95828 + 3.48785i) q^{48} +(-1.17198 - 2.82941i) q^{49} +(-0.0154502 + 2.98217i) q^{50} +(0.137192 - 1.39294i) q^{51} +(-10.1176 - 5.54354i) q^{52} +(4.90739 + 9.18107i) q^{53} +(1.09784 - 0.891492i) q^{54} +(-0.705271 - 1.05551i) q^{55} +(-3.30427 - 8.34159i) q^{56} +(-1.22745 - 0.820158i) q^{57} +(-3.04816 - 2.52810i) q^{58} +(-2.27056 + 0.223631i) q^{59} +(-3.40056 - 0.0352365i) q^{60} +(9.80077 - 2.97303i) q^{61} +(-4.88986 - 7.40091i) q^{62} +3.17215i q^{63} +(-2.83028 - 7.48262i) q^{64} -9.80840i q^{65} +(-0.880907 + 0.582025i) q^{66} +(-5.79154 + 1.75684i) q^{67} +(1.95882 + 1.99984i) q^{68} +(4.72282 - 0.465157i) q^{69} +(4.86965 - 5.87139i) q^{70} +(-7.56079 - 5.05196i) q^{71} +(-0.0439588 + 2.82809i) q^{72} +(-1.08352 - 1.62161i) q^{73} +(9.94582 + 12.2479i) q^{74} +(0.994055 + 1.85975i) q^{75} +(2.83409 - 0.827742i) q^{76} +(0.232129 - 2.35685i) q^{77} +(-8.15763 - 0.0422635i) q^{78} +(3.37251 + 8.14197i) q^{79} +(4.42283 - 5.16707i) q^{80} +(0.382683 - 0.923880i) q^{81} +(1.25161 - 2.97791i) q^{82} +(10.5661 + 12.8749i) q^{83} +(-4.86224 - 4.07538i) q^{84} +(-0.690867 + 2.27748i) q^{85} +(7.73558 + 4.18643i) q^{86} +(-2.74642 - 0.546298i) q^{87} +(0.239612 - 2.09800i) q^{88} +(-2.08960 - 10.5051i) q^{89} +(-2.12659 + 1.12256i) q^{90} +(11.6083 - 14.1447i) q^{91} +(-5.35460 + 7.83671i) q^{92} +(-5.53170 - 2.95676i) q^{93} +(-9.43177 - 6.37303i) q^{94} +(1.77495 + 1.77495i) q^{95} +(-4.27839 - 3.70073i) q^{96} +(2.14657 - 2.14657i) q^{97} +(4.25218 - 0.822933i) q^{98} +(-0.351933 + 0.658421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more