LMFDB - Embedded newform 384.2.v.a.325.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			325.14
Character	$\chi$	$=$	384.325
Dual form			384.2.v.a.13.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.283082 - 1.38559i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.83973 + 0.784471i) q^{4} +(-0.166665 + 1.69218i) q^{5} +(-1.40810 - 0.131324i) q^{6} +(1.76235 + 2.63755i) q^{7} +(1.60775 + 2.32704i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})$	\(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+O(q^{10}) $ 512 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{17}{32}\right)$	$1$

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	0.883177	+	0.469039i	$0.155400\pi$
$5$	−0.166665	+	1.69218i	−0.0745350	+	0.756767i	−0.957712	+	0.287727i	$0.907100\pi$
$6$	−1.40810	−	0.131324i	−0.574856	−	0.0536127i
$7$	1.76235	+	2.63755i	0.666106	+	0.996899i	0.998553	+	0.0537767i	$0.0171259\pi$
$7$	1.76235	+	2.63755i	0.666106	+	0.996899i	−0.332447	+	0.943122i	$0.607874\pi$
$8$	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	0.567662	−	0.823262i	$-0.307848\pi$
$11$	0.658421	+	0.351933i	0.198521	+	0.106112i	−0.369141	+	0.929373i	$0.620348\pi$
$12$	0.216647	+	1.98823i	0.0625406	+	0.573953i
$13$	5.74062	−	0.565402i	1.59216	−	0.156814i	0.737262	−	0.675607i	$-0.236119\pi$
$13$	5.74062	−	0.565402i	1.59216	−	0.156814i	0.854900	+	0.518793i	$0.173619\pi$
$14$	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	−0.533946	−	0.845519i	$-0.679291\pi$
$17$	−1.29313	+	0.535633i	−0.313630	+	0.129910i	0.220315	+	0.975429i	$0.429291\pi$
$18$	−0.534420	+	1.30935i	−0.125964	+	0.308617i
$19$	−1.14115	−	0.936520i	−0.261799	−	0.214853i	0.494332	−	0.869273i	$-0.335413\pi$
$19$	−1.14115	−	0.936520i	−0.261799	−	0.214853i	−0.756131	+	0.654421i	$0.772913\pi$
$20$	−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	0.948850	+	0.315726i	$0.102248\pi$
$23$	0.925835	+	4.65449i	0.193050	+	0.970528i	−0.755800	+	0.654802i	$0.772752\pi$
$24$	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	0.729031	−	0.684480i	$-0.239971\pi$
$29$	−1.32002	−	2.46958i	−0.245121	−	0.458590i	−0.974153	+	0.225890i	$0.927471\pi$
$30$	0.456906	−	2.36088i	0.0834192	−	0.431036i
$31$	−4.43521	−	4.43521i	−0.796587	−	0.796587i	0.185969	−	0.982556i	$-0.440458\pi$
$31$	−4.43521	−	4.43521i	−0.796587	−	0.796587i	−0.982556	+	0.185969i	$0.940458\pi$
$32$	−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	0.890027	+	0.455909i	$0.150686\pi$
$37$	7.07753	+	8.62400i	1.16354	+	1.41778i	0.273513	+	0.961868i	$0.411814\pi$
$38$	−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	−0.366895	−	0.930262i	$-0.619579\pi$
$41$	−2.24024	+	0.445611i	−0.349866	+	0.0695928i	0.0170289	+	0.999855i	$0.494579\pi$
$42$	−2.13520	−	3.94538i	−0.329469	−	0.608785i
$43$	1.80544	+	5.95173i	0.275327	+	0.907631i	0.980152	+	0.198249i	$0.0635256\pi$
$43$	1.80544	+	5.95173i	0.275327	+	0.907631i	−0.704825	+	0.709381i	$0.748974\pi$
$44$	−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	−0.972586	−	0.232545i	$-0.925295\pi$
$47$	−3.08023	−	7.43634i	−0.449298	−	1.08470i	0.523288	−	0.852156i	$-0.324705\pi$
$48$	−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	−0.279548	−	0.960132i	$-0.590184\pi$
$53$	4.90739	−	9.18107i	0.674081	−	1.26112i	0.953629	−	0.300985i	$-0.0973155\pi$
$54$	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	−0.0508707	−	0.998705i	$-0.516200\pi$
$59$	−2.27056	−	0.223631i	−0.295602	−	0.0291142i	−0.244731	+	0.969591i	$0.578700\pi$
$60$	−3.40056	+	0.0352365i	−0.439010	+	0.00454901i
$61$	9.80077	+	2.97303i	1.25486	+	0.380658i	0.846611	−	0.532213i	$-0.178639\pi$
$61$	9.80077	+	2.97303i	1.25486	+	0.380658i	0.408249	+	0.912870i	$0.366139\pi$
$62$	−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	−0.0840552	−	0.996461i	$-0.526787\pi$
$67$	−5.79154	−	1.75684i	−0.707549	−	0.214633i	−0.623493	+	0.781829i	$0.714287\pi$
$68$	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	−0.916401	−	0.400261i	$-0.868920\pi$
$71$	−7.56079	+	5.05196i	−0.897300	+	0.599557i	0.0191011	+	0.999818i	$0.493920\pi$
$72$	−0.0439588	−	2.82809i	−0.00518060	−	0.333293i
$73$	−1.08352	+	1.62161i	−0.126817	+	0.189795i	−0.889445	−	0.457042i	$-0.848909\pi$
$73$	−1.08352	+	1.62161i	−0.126817	+	0.189795i	0.762628	+	0.646837i	$0.223909\pi$
$74$	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	−0.612634	−	0.790367i	$-0.709890\pi$
$79$	3.37251	−	8.14197i	0.379438	−	0.916043i	0.992071	−	0.125676i	$-0.0401101\pi$
$80$	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	0.266426	−	0.963855i	$-0.414157\pi$
$83$	10.5661	−	12.8749i	1.15978	−	1.41320i	0.893358	−	0.449346i	$-0.148343\pi$
$84$	−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	0.696684	+	0.717378i	$0.254658\pi$
$89$	−2.08960	+	10.5051i	−0.221497	+	1.11354i	−0.918181	+	0.396162i	$0.870342\pi$
$90$	−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	0.807634	−	0.589683i	$-0.200748\pi$
$97$	2.14657	+	2.14657i	0.217951	+	0.217951i	−0.589683	+	0.807634i	$0.700748\pi$
$98$	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	−0.932161	−	0.362043i	$-0.882079\pi$
$101$	−7.62715	+	6.25944i	−0.758930	+	0.622838i	0.173231	+	0.984881i	$0.444579\pi$
$102$	1.89120	−	0.584407i	0.187257	−	0.0578649i
$103$	−6.71089	−	1.33488i	−0.661244	−	0.131530i	−0.146950	−	0.989144i	$-0.546946\pi$
$103$	−6.71089	−	1.33488i	−0.661244	−	0.131530i	−0.514293	+	0.857614i	$0.671946\pi$
$104$	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	−0.885977	−	0.463730i	$-0.846511\pi$
$107$	−14.1197	+	4.28317i	−1.36500	+	0.414070i	−0.479028	+	0.877800i	$0.659011\pi$
$108$	0.924467	−	1.77352i	0.0889569	−	0.170657i
$109$	−6.21427	−	5.09992i	−0.595219	−	0.488483i	0.287883	−	0.957666i	$-0.407049\pi$
$109$	−6.21427	−	5.09992i	−0.595219	−	0.488483i	−0.883101	+	0.469182i	$0.844549\pi$
$110$	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	0.235483	−	0.971879i	$-0.424333\pi$
$113$	−3.03201	−	1.25590i	−0.285228	−	0.118145i	−0.520711	+	0.853733i	$0.674333\pi$
$114$	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	−0.953767	−	0.300548i	$-0.902830\pi$
$131$	0.0713865	−	0.235330i	0.00623707	−	0.0205608i	0.960004	+	0.279988i	$0.0903303\pi$
$132$	−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	0.0450059	−	0.998987i	$-0.485669\pi$
$137$	−10.0744	−	6.73150i	−0.860715	−	0.575111i	−0.905720	+	0.423876i	$0.860669\pi$
$138$	−0.692426	−	6.67558i	−0.0589432	−	0.568263i
$139$	2.52406	+	1.34914i	0.214088	+	0.114432i	0.574956	−	0.818185i	$-0.305019\pi$
$139$	2.52406	+	1.34914i	0.214088	+	0.114432i	−0.360868	+	0.932617i	$0.617519\pi$
$140$	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	0.668701	−	0.743531i	$-0.266851\pi$
$149$	19.9918	−	6.06444i	1.63779	−	0.496818i	0.969088	+	0.246713i	$0.0793506\pi$
$150$	−2.85825	−	0.850894i	−0.233375	−	0.0694752i
$151$	−2.19670	−	11.0436i	−0.178765	−	0.898711i	−0.961173	−	0.275946i	$-0.911009\pi$
$151$	−2.19670	−	11.0436i	−0.178765	−	0.898711i	0.782408	−	0.622766i	$-0.213991\pi$
$152$	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	−0.996172	−	0.0874188i	$-0.972138\pi$
$157$	−6.45812	−	12.0823i	−0.515414	−	0.964273i	0.480757	−	0.876854i	$-0.340362\pi$
$158$	−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	−0.606247	−	0.795276i	$-0.707326\pi$
$163$	−3.59793	+	1.92313i	−0.281812	+	0.150631i	0.324435	+	0.945908i	$0.394826\pi$
$164$	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	−0.985093	−	0.172025i	$-0.944969\pi$
$167$	−0.118302	+	0.594747i	−0.00915452	+	0.0460229i	0.975938	+	0.218048i	$0.0699690\pi$
$168$	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	−0.549528	−	0.835475i	$-0.685192\pi$
$173$	4.95999	−	6.04377i	0.377101	−	0.459499i	0.926629	+	0.375976i	$0.122692\pi$
$174$	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	0.967261	+	0.253785i	$0.0816756\pi$
$179$	0.911071	+	9.25026i	0.0680966	+	0.691397i	−0.899164	+	0.437612i	$0.855824\pi$
$180$	−0.953410	+	3.26436i	−0.0710630	+	0.243311i
$181$	8.24235	−	15.4203i	0.612649	−	1.14619i	−0.364011	−	0.931395i	$-0.618593\pi$
$181$	8.24235	−	15.4203i	0.612649	−	1.14619i	0.976660	−	0.214791i	$-0.0689070\pi$
$182$	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	$-0.920074\pi$
$191$		−	6.86774i		−	0.496932i	0.968641	−	0.248466i	$-0.0799264\pi$
$192$	6.33883	+	4.88049i	0.457466	+	0.352219i
$193$		−	12.2028i		−	0.878379i	−0.898394	−	0.439190i	$-0.855266\pi$
$193$		−	12.2028i		−	0.878379i	0.898394	−	0.439190i	$-0.144734\pi$
$194$	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	0.953476	−	0.301469i	$-0.0974770\pi$
$197$	25.6827	+	2.52953i	1.82982	+	0.180221i	0.876342	+	0.481690i	$0.159977\pi$
$198$	−0.812677	+	0.674023i	−0.0577544	+	0.0479007i
$199$	−15.6230	+	10.4389i	−1.10748	+	0.739997i	−0.968181	−	0.250253i	$-0.919486\pi$
$199$	−15.6230	+	10.4389i	−1.10748	+	0.739997i	−0.139303	+	0.990250i	$0.544486\pi$
$200$	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	−0.898686	−	0.438593i	$-0.855477\pi$
$211$	−4.25891	+	5.18949i	−0.293195	+	0.357260i	0.605490	+	0.795853i	$0.292977\pi$
$212$	−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	−0.170690	−	0.985325i	$-0.554600\pi$
$223$	12.1651	−	12.1651i	0.814635	−	0.814635i	0.985325	+	0.170690i	$0.0545997\pi$
$224$	−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	−0.985496	−	0.169697i	$-0.945721\pi$
$227$	−8.72474	−	16.3228i	−0.579081	−	1.08339i	0.406415	−	0.913689i	$-0.366779\pi$
$228$	1.61479	−	2.47177i	0.106942	−	0.163697i
$229$	13.6638	−	11.2136i	0.902927	−	0.741013i	−0.0634922	−	0.997982i	$-0.520224\pi$
$229$	13.6638	−	11.2136i	0.902927	−	0.741013i	0.966420	+	0.256969i	$0.0827238\pi$
$230$	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	−0.877383	−	0.479791i	$-0.840712\pi$
$233$	−3.82211	−	19.2151i	−0.250395	−	1.25882i	0.626988	−	0.779029i	$-0.284288\pi$
$234$	−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	−0.286189	−	0.958173i	$-0.592389\pi$
$239$	2.92148	−	1.21012i	0.188975	−	0.0782760i	0.475164	+	0.879897i	$0.342389\pi$
$240$	6.22846	−	2.73246i	0.402046	−	0.176380i
$241$	−13.7607	−	5.69985i	−0.886402	−	0.367160i	−0.107425	−	0.994213i	$-0.534261\pi$
$241$	−13.7607	−	5.69985i	−0.886402	−	0.367160i	−0.778976	+	0.627054i	$0.784261\pi$
$242$	−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	−0.993828	−	0.110928i	$-0.964618\pi$
$251$	0.0403178	−	0.409353i	0.00254483	−	0.0258381i	0.996373	+	0.0850898i	$0.0271177\pi$
$252$	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	0.947995	+	0.318286i	$0.103107\pi$
$263$	14.2594	+	21.3407i	0.879271	+	1.31592i	−0.0687239	+	0.997636i	$0.521893\pi$
$264$	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	−0.101807	−	0.994804i	$-0.532462\pi$
$269$	−0.124330	+	0.0122454i	−0.00758051	+	0.000746615i	0.0942262	+	0.995551i	$0.469962\pi$
$270$	−1.69154	+	1.70916i	−0.102944	+	0.104016i
$271$	18.2311	+	7.55156i	1.10746	+	0.458725i	0.860062	−	0.510189i	$-0.170425\pi$
$271$	18.2311	+	7.55156i	1.10746	+	0.458725i	0.247397	+	0.968914i	$0.420425\pi$
$272$	−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	−0.712573	−	0.701598i	$-0.752470\pi$
$277$	−15.2331	+	4.62091i	−0.915268	+	0.277644i	−0.202695	+	0.979242i	$0.564970\pi$
$278$	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	−0.410440	−	0.911888i	$-0.634625\pi$
$281$	−19.0864	−	3.79653i	−1.13860	−	0.226482i	−0.728161	+	0.685406i	$0.759625\pi$
$282$	3.36072	+	10.8756i	0.200128	+	0.647635i
$283$	25.0995	−	20.5986i	1.49201	−	1.22446i	0.579789	−	0.814767i	$-0.303135\pi$
$283$	25.0995	−	20.5986i	1.49201	−	1.22446i	0.912223	−	0.409695i	$-0.134365\pi$
$284$	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	0.814890	−	0.579615i	$-0.196797\pi$
$293$	1.49664	+	1.82366i	0.0874348	+	0.106540i	−0.727455	+	0.686155i	$0.759297\pi$
$294$	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	0.998375	−	0.0569918i	$-0.0181509\pi$
$307$	0.141309	+	1.43474i	0.00806494	+	0.0818847i	−0.990310	+	0.138877i	$0.955651\pi$
$308$	−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	−0.770340	−	0.637634i	$-0.779913\pi$
$311$	2.00253	−	2.99700i	0.113553	−	0.169944i	0.883893	+	0.467689i	$0.154913\pi$
$312$	14.9747	−	6.47718i	0.847775	−	0.366698i
$313$	−1.81952	+	1.21577i	−0.102846	+	0.0687192i	−0.605930	−	0.795518i	$-0.707199\pi$
$313$	−1.81952	+	1.21577i	−0.102846	+	0.0687192i	0.503084	+	0.864238i	$0.332199\pi$
$314$	−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	0.456674	−	0.889634i	$-0.349041\pi$
$317$	6.09144	+	1.84782i	0.342129	+	0.103784i	−0.114544	+	0.993418i	$0.536541\pi$
$318$	−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	−0.187871	+	0.982194i	$0.560159\pi$
$331$	−16.3770	+	30.6392i	−0.900160	+	1.68408i	−0.712289	+	0.701887i	$0.752341\pi$
$332$	−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	0.874517	+	0.484996i	$0.161179\pi$
$337$	10.9977	+	26.5508i	0.599084	+	1.44632i	−0.275433	+	0.961320i	$0.588821\pi$
$338$	−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	0.561021	−	0.827802i	$-0.310409\pi$
$347$	−6.71210	−	8.17872i	−0.360324	−	0.439056i	−0.921345	+	0.388745i	$0.872909\pi$
$348$	4.62412	−	3.15953i	0.247879	−	0.169369i
$349$	−29.7212	+	15.8863i	−1.59094	+	0.850374i	−0.591924	+	0.805994i	$0.701631\pi$
$349$	−29.7212	+	15.8863i	−1.59094	+	0.850374i	−0.999015	+	0.0443807i	$0.985869\pi$
$350$	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	0.906653	−	0.421877i	$-0.138629\pi$
$353$	9.10812	+	9.10812i	0.484776	+	0.484776i	−0.421877	+	0.906653i	$0.638629\pi$
$354$	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	0.715608	−	0.698502i	$-0.246150\pi$
$359$	21.0209	+	4.18131i	1.10944	+	0.220681i	0.393830	+	0.919183i	$0.371150\pi$
$360$	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	−0.722942	−	0.690909i	$-0.757210\pi$
$367$	−14.2835	+	5.91641i	−0.745592	+	0.308834i	−0.0226504	+	0.999743i	$0.507210\pi$
$368$	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	0.198409	−	0.980119i	$-0.436423\pi$
$373$	−9.77829	−	5.22661i	−0.506301	−	0.270623i	−0.704710	+	0.709496i	$0.748923\pi$
$374$	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	−0.952974	−	0.303051i	$-0.901995\pi$
$379$	0.794511	−	8.06680i	0.0408113	−	0.414364i	0.993785	−	0.111312i	$-0.0355054\pi$
$380$	−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	0.799731	+	0.600359i	$0.204976\pi$
$389$	−2.00697	+	20.3771i	−0.101758	+	1.03316i	−0.901488	+	0.432803i	$0.857524\pi$
$390$	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	0.773129	−	0.634249i	$-0.218691\pi$
$397$	32.9784	−	3.24809i	1.65514	−	0.163017i	0.882009	+	0.471232i	$0.156191\pi$
$398$	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	0.490102	−	0.871665i	$-0.336960\pi$
$401$	29.0966	−	12.0522i	1.45302	−	0.601859i	0.962915	+	0.269806i	$0.0869597\pi$
$402$	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	−0.111102	−	0.993809i	$-0.535438\pi$
$409$	−12.0142	−	2.38976i	−0.594062	−	0.118166i	−0.482959	+	0.875643i	$0.660438\pi$
$410$	−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	−0.936910	−	0.349571i	$-0.886327\pi$
$419$	−23.8832	+	12.7658i	−1.16677	+	0.623652i	−0.229861	+	0.973223i	$0.573827\pi$
$420$	−6.08592	−	8.90703i	−0.296962	−	0.434618i
$421$	−15.5513	−	18.9493i	−0.757923	−	0.923532i	0.240972	−	0.970532i	$-0.422534\pi$
$421$	−15.5513	−	18.9493i	−0.757923	−	0.923532i	−0.998895	+	0.0470003i	$0.985034\pi$
$422$	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	0.859977	+	0.510332i	$0.170478\pi$
$431$	12.7208	+	30.7108i	0.612741	+	1.47929i	−0.247237	+	0.968955i	$0.579522\pi$
$432$	−0.309497	+	3.98801i	−0.0148907	+	0.191873i
$433$	0.114350	−	0.276065i	0.00549530	−	0.0132668i	−0.921108	−	0.389307i	$-0.872715\pi$
$433$	0.114350	−	0.276065i	0.00549530	−	0.0132668i	0.926603	+	0.376040i	$0.122715\pi$
$434$	−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	−0.712393	−	0.701781i	$-0.752389\pi$
$439$	4.37042	−	6.54079i	0.208589	−	0.312175i	0.920982	+	0.389606i	$0.127389\pi$
$440$	−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	−0.246082	−	0.969249i	$-0.579143\pi$
$443$	−14.2392	−	1.40244i	−0.676527	−	0.0666320i	−0.430445	+	0.902617i	$0.641643\pi$
$444$	−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	$0.0151341\pi$
$449$			2.01417i			0.0950544i	−0.998870	+	0.0475272i	$0.984866\pi$
$450$	−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	−0.729468	−	0.684015i	$-0.760232\pi$
$457$	3.88292	−	5.81119i	0.181635	−	0.271836i	0.911103	+	0.412179i	$0.135232\pi$
$458$	−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	0.949336	+	0.314262i	$0.101757\pi$
$461$	1.70803	+	17.3419i	0.0795508	+	0.807692i	−0.869785	+	0.493430i	$0.835743\pi$
$462$	−0.0173515	−	3.34917i	−0.000807266	−	0.155817i
$463$	−0.266781	+	0.644067i	−0.0123984	+	0.0299323i	−0.929957	−	0.367667i	$-0.880157\pi$
$463$	−0.266781	+	0.644067i	−0.0123984	+	0.0299323i	0.917559	+	0.397599i	$0.130157\pi$
$464$	−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	−0.618697	−	0.785630i	$-0.712339\pi$
$467$	5.88962	−	7.17652i	0.272539	−	0.332090i	0.891236	+	0.453540i	$0.149839\pi$
$468$	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	0.207336	−	0.978270i	$-0.433521\pi$
$479$	25.9482	−	25.9482i	1.18561	−	1.18561i	0.978270	−	0.207336i	$-0.0664792\pi$
$480$	−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	0.154654	−	0.987969i	$-0.450574\pi$
$487$	−1.77746	−	0.353558i	−0.0805443	−	0.0160212i	−0.235198	+	0.971947i	$0.575574\pi$
$488$	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	0.320660	−	0.947194i	$-0.396095\pi$
$491$	24.6738	−	7.48471i	1.11351	−	0.337780i	0.792852	+	0.609414i	$0.208595\pi$
$492$	−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	0.141043	−	0.990003i	$-0.454954\pi$
$499$	10.5552	−	1.03960i	0.472516	−	0.0465388i	0.331473	+	0.943465i	$0.392454\pi$
$500$	−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	0.974481	−	0.224470i	$-0.0720651\pi$
$503$	25.5679	+	17.0839i	1.14002	+	0.761734i	0.165534	+	0.986204i	$0.447065\pi$
$504$	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	−0.0226495	−	0.999743i	$-0.507210\pi$
$509$	12.4449	−	41.0253i	0.551611	−	1.81842i	0.574260	−	0.818673i	$-0.305290\pi$
$510$	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	0.835082	−	0.550126i	$-0.185420\pi$
$521$	14.7544	+	9.85860i	0.646404	+	0.431913i	−0.188678	+	0.982039i	$0.560420\pi$
$522$	3.93899	−	0.408573i	0.172405	−	0.0178827i
$523$	−2.13073	−	1.13890i	−0.0931704	−	0.0498006i	0.424153	−	0.905590i	$-0.360572\pi$
$523$	−2.13073	−	1.13890i	−0.0931704	−	0.0498006i	−0.517324	+	0.855790i	$0.673072\pi$
$524$	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	0.841523	+	0.540221i	$0.181659\pi$
$541$	19.1466	+	35.8207i	0.823175	+	1.54005i	−0.0183483	+	0.999832i	$0.505841\pi$
$542$	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	−0.713283	−	0.700876i	$-0.752793\pi$
$547$	−12.3209	+	6.58567i	−0.526804	+	0.281583i	0.186478	+	0.982459i	$0.440293\pi$
$548$	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	−0.562219	−	0.826988i	$-0.690052\pi$
$557$	8.46237	−	10.3114i	0.358562	−	0.436909i	0.920781	+	0.390079i	$0.127552\pi$
$558$	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	−0.598441	−	0.801167i	$-0.704213\pi$
$563$	−3.98147	−	40.4245i	−0.167799	−	1.70369i	0.430642	−	0.902523i	$-0.358287\pi$
$564$	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	−0.765500	−	0.643436i	$-0.777508\pi$
$569$	−11.0678	+	7.39527i	−0.463986	+	0.310026i	0.301513	+	0.953462i	$0.402508\pi$
$570$	−2.73241	+	2.26622i	−0.114448	+	0.0949217i
$571$	−24.5643	−	2.41937i	−1.02798	−	0.101247i	−0.430059	−	0.902801i	$-0.641507\pi$
$571$	−24.5643	−	2.41937i	−1.02798	−	0.101247i	−0.597923	+	0.801553i	$0.704007\pi$
$572$	−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	$-0.980776\pi$
$577$		−	2.89971i		−	0.120717i	0.998177	−	0.0603583i	$-0.0192243\pi$
$578$	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	0.254162	−	0.967162i	$-0.418200\pi$
$587$	22.2201	−	41.5709i	0.917123	−	1.71582i	0.662961	−	0.748654i	$-0.269300\pi$
$588$	−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	0.978939	−	0.204152i	$-0.0654438\pi$
$593$	3.46687	+	8.36976i	0.142367	+	0.343705i	−0.836572	+	0.547857i	$0.815444\pi$
$594$	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	−0.476840	−	0.878990i	$-0.658218\pi$
$599$	−14.2199	+	2.82851i	−0.581008	+	0.115570i	−0.104168	+	0.994560i	$0.533218\pi$
$600$	5.92590	−	0.676797i	0.241924	−	0.0276301i
$601$	4.03786	−	20.2997i	0.164708	−	0.828043i	−0.806761	−	0.590877i	$-0.798782\pi$
$601$	4.03786	−	20.2997i	0.164708	−	0.828043i	0.971469	−	0.237165i	$-0.0762183\pi$
$602$	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	−0.0342308	+	0.999414i	$0.510898\pi$
$607$	−25.4663	+	25.4663i	−1.03364	+	1.03364i	−0.999414	+	0.0342308i	$0.989102\pi$
$608$	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	−0.993336	−	0.115256i	$-0.963231\pi$
$613$	−26.5931	+	21.8244i	−1.07408	+	0.881479i	−0.0807489	+	0.996734i	$0.525731\pi$
$614$	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	0.668880	+	0.743371i	$0.266774\pi$
$617$	8.33094	+	41.8825i	0.335391	+	1.68613i	−0.333488	+	0.942754i	$0.608226\pi$
$618$	9.27433	+	2.76095i	0.373068	+	0.111062i
$619$	20.4152	−	6.19287i	0.820555	−	0.248913i	0.148026	−	0.988983i	$-0.452708\pi$
$619$	20.4152	−	6.19287i	0.820555	−	0.248913i	0.672529	+	0.740071i	$0.265208\pi$
$620$	−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	0.939419	−	0.342772i	$-0.111366\pi$
$631$	24.6736	+	16.4863i	0.982239	+	0.656311i	0.0428203	+	0.999083i	$0.486366\pi$
$632$	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	−0.999372	−	0.0354447i	$-0.988715\pi$
$643$	−3.77148	+	12.4329i	−0.148732	+	0.490305i	0.850639	+	0.525750i	$0.176215\pi$
$644$	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	0.999927	−	0.0120509i	$-0.00383601\pi$
$647$	15.4178	+	23.0744i	0.606138	+	0.907150i	−0.393789	+	0.919201i	$0.628836\pi$
$648$	−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	−0.00699875	−	0.999976i	$-0.502228\pi$
$653$	4.63094	−	0.456107i	0.181223	−	0.0178489i	0.188221	+	0.982127i	$0.439728\pi$
$654$	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	0.783219	−	0.621745i	$-0.213576\pi$
$659$	8.37437	+	6.87267i	0.326219	+	0.267721i	−0.457000	+	0.889467i	$0.651076\pi$
$660$	−2.25140	−	1.17357i	−0.0876356	−	0.0456811i
$661$	−36.2042	+	10.9824i	−1.40818	+	0.427167i	−0.900680	−	0.434484i	$-0.856931\pi$
$661$	−36.2042	+	10.9824i	−1.40818	+	0.427167i	−0.507501	+	0.861651i	$0.669431\pi$
$662$	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	−0.378260	+	0.925699i	$0.623477\pi$
$673$	−33.8276	+	33.8276i	−1.30396	+	1.30396i	−0.925699	+	0.378260i	$0.876523\pi$
$674$	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	0.961917	−	0.273342i	$-0.0881290\pi$
$677$	13.1701	+	16.0478i	0.506167	+	0.616766i	−0.455750	+	0.890108i	$0.650629\pi$
$678$	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	−0.928154	−	0.372197i	$-0.878605\pi$
$683$	−9.49206	−	31.2911i	−0.363204	−	1.19732i	0.564950	−	0.825125i	$-0.308895\pi$
$684$	−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	−0.999734	−	0.0230538i	$-0.992661\pi$
$691$	−0.623188	−	6.32733i	−0.0237072	−	0.240703i	0.976027	−	0.217649i	$-0.0698389\pi$
$692$	−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	−0.212435	−	0.977175i	$-0.568139\pi$
$701$	−24.6749	−	7.48505i	−0.931958	−	0.282706i	−0.719523	+	0.694469i	$0.755639\pi$
$702$	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	−0.0946494	−	0.995511i	$-0.530173\pi$
$709$	−10.1634	−	1.00101i	−0.381695	−	0.0375936i	−0.287045	+	0.957917i	$0.592673\pi$
$710$	−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	−0.929576	−	0.368630i	$-0.879827\pi$
$719$	−0.311191	+	0.751282i	−0.0116055	+	0.0280181i	0.917971	+	0.396648i	$0.129827\pi$
$720$	−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	−0.401541	−	0.915841i	$-0.631525\pi$
$727$	−11.3794	+	2.26351i	−0.422039	+	0.0839488i	−0.0204983	+	0.999790i	$0.506525\pi$
$728$	−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	−0.895157	−	0.445752i	$-0.852936\pi$
$733$	−27.6655	+	14.7875i	−1.02185	+	0.546190i	−0.126693	+	0.991942i	$0.540436\pi$
$734$	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	0.814399	−	0.580305i	$-0.197067\pi$
$739$	−3.27745	−	6.13168i	−0.120563	−	0.225557i	−0.934962	+	0.354748i	$0.884567\pi$
$740$	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	−0.103522	−	0.994627i	$-0.533011\pi$
$743$	−15.8039	−	3.14360i	−0.579791	−	0.115328i	−0.476269	+	0.879300i	$0.658011\pi$
$744$	−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	−0.425422	−	0.904995i	$-0.639874\pi$
$751$	−2.36533	+	0.979754i	−0.0863123	+	0.0357517i	0.339110	+	0.940747i	$0.389874\pi$
$752$	−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	0.597622	−	0.801778i	$-0.296112\pi$
$757$	7.23578	+	3.86761i	0.262989	+	0.140571i	−0.334633	+	0.942349i	$0.608612\pi$
$758$	−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	0.894407	−	0.447254i	$-0.147598\pi$
$761$	3.83236	+	5.73554i	0.138923	+	0.207913i	−0.755484	+	0.655167i	$0.772598\pi$
$762$	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	−0.974261	−	0.225424i	$-0.927623\pi$
$773$	0.702243	−	7.12999i	0.0252579	−	0.256448i	0.999519	−	0.0310238i	$-0.00987677\pi$
$774$	−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	0.162866	−	0.986648i	$-0.447926\pi$
$787$	−21.6868	−	17.7979i	−0.773051	−	0.634427i	−0.935917	+	0.352222i	$0.885426\pi$
$788$	−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	0.971642	−	0.236457i	$-0.0759861\pi$
$797$	6.64055	+	12.4236i	0.235220	+	0.440066i	−0.736422	+	0.676523i	$0.763486\pi$
$798$	−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	−0.819678	−	0.572825i	$-0.805848\pi$
$809$	−38.6184	+	7.68168i	−1.35775	+	0.270073i	−0.538073	+	0.842898i	$0.680848\pi$
$810$	1.14453	+	2.11484i	0.0402148	+	0.0743080i
$811$	0.234584	+	0.773321i	0.00823737	+	0.0271550i	0.960963	−	0.276678i	$-0.0892335\pi$
$811$	0.234584	+	0.773321i	0.00823737	+	0.0271550i	−0.952725	+	0.303833i	$0.901734\pi$
$812$	−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	−0.993703	−	0.112049i	$-0.964259\pi$
$821$	−9.98463	+	18.6799i	−0.348466	+	0.651934i	0.645237	+	0.763983i	$0.276759\pi$
$822$	13.3018	+	10.8017i	0.463953	+	0.376751i
$823$	26.4923	−	39.6486i	0.923465	−	1.38206i	−0.000670818	−	1.00000i	$-0.500214\pi$
$823$	26.4923	−	39.6486i	0.923465	−	1.38206i	0.924136	−	0.382064i	$-0.124786\pi$
$824$	−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	−0.740778	−	0.671750i	$-0.765543\pi$
$827$	−45.9654	−	4.52720i	−1.59837	−	0.157426i	−0.857596	+	0.514324i	$0.828043\pi$
$828$	0.0983439	+	9.49084i	0.00341769	+	0.329829i
$829$	28.0287	+	8.50241i	0.973477	+	0.295301i	0.736667	−	0.676255i	$-0.236398\pi$
$829$	28.0287	+	8.50241i	0.973477	+	0.295301i	0.236809	+	0.971556i	$0.423898\pi$
$830$	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	−0.970217	−	0.242239i	$-0.922118\pi$
$839$	−32.3748	+	21.6322i	−1.11770	+	0.746825i	−0.147486	+	0.989064i	$0.547118\pi$
$840$	−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	0.985612	−	0.169024i	$-0.0540616\pi$
$853$	2.10871	+	6.95148i	0.0722008	+	0.238014i	−0.913411	+	0.407038i	$0.866562\pi$
$854$	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	−0.970760	−	0.240052i	$-0.922836\pi$
$857$	0.526039	−	2.64458i	0.0179692	−	0.0903371i	0.988729	+	0.149715i	$0.0478356\pi$
$858$	−5.38603	−	2.84312i	−0.183876	−	0.0970624i
$859$	25.7285	+	31.3503i	0.877846	+	1.06966i	0.997047	+	0.0767882i	$0.0244665\pi$
$859$	25.7285	+	31.3503i	0.877846	+	1.06966i	−0.119202	+	0.992870i	$0.538033\pi$
$860$	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	−0.214449	+	0.976735i	$0.568796\pi$
$863$	−34.9933	+	34.9933i	−1.19118	+	1.19118i	−0.976735	+	0.214449i	$0.931204\pi$
$864$	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	0.826638	−	0.562735i	$-0.190251\pi$
$877$	12.9113	+	10.5961i	0.435985	+	0.357804i	−0.390653	+	0.920538i	$0.627751\pi$
$878$	−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	0.999528	−	0.0307082i	$-0.00977627\pi$
$881$	50.0013	+	20.7112i	1.68459	+	0.697779i	0.685059	+	0.728487i	$0.259776\pi$
$882$	−3.07836	−	3.04663i	−0.103654	−	0.102585i
$883$	29.9009	−	2.94499i	1.00625	−	0.0991067i	0.418555	−	0.908191i	$-0.362537\pi$
$883$	29.9009	−	2.94499i	1.00625	−	0.0991067i	0.587692	+	0.809085i	$0.300037\pi$
$884$	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	−0.304986	−	0.952357i	$-0.598652\pi$
$887$	−38.7638	−	25.9012i	−1.30156	−	0.869676i	−0.996576	+	0.0826807i	$0.973652\pi$
$888$	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	−0.0336734	−	0.999433i	$-0.510721\pi$
$907$	−26.6042	−	14.2203i	−0.883379	−	0.472176i	−0.849706	+	0.527257i	$0.823221\pi$
$908$	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	0.948618	−	0.316425i	$-0.102482\pi$
$911$	42.1245	+	17.4485i	1.39565	+	0.578095i	0.447028	+	0.894520i	$0.352482\pi$
$912$	−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	−0.993040	−	0.117781i	$-0.962422\pi$
$919$	−3.65792	−	18.3896i	−0.120664	−	0.606617i	0.872376	−	0.488836i	$-0.162578\pi$
$920$	−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	−0.747720	−	0.664014i	$-0.768852\pi$
$929$	−2.55132	+	2.55132i	−0.0837062	+	0.0837062i	0.664014	+	0.747720i	$0.268852\pi$
$930$	−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	−0.339756	−	0.940513i	$-0.610345\pi$
$937$	−8.99125	+	1.78847i	−0.293731	+	0.0584268i	0.0460250	+	0.998940i	$0.485345\pi$
$938$	−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	−0.674151	−	0.738594i	$-0.735490\pi$
$941$	5.57597	−	6.79434i	0.181772	−	0.221489i	0.855922	+	0.517105i	$0.172990\pi$
$942$	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	0.852269	+	0.523104i	$0.175226\pi$
$947$	3.64445	+	37.0027i	0.118429	+	1.20243i	−0.733840	+	0.679322i	$0.762274\pi$
$948$	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	−0.547671	+	0.836694i	$0.684486\pi$
$953$	−47.2402	+	31.5649i	−1.53026	+	1.02249i	−0.982589	+	0.185794i	$0.940514\pi$
$954$	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	0.350869	−	0.936424i	$-0.385886\pi$
$967$	41.9893	−	28.0563i	1.35028	−	0.902231i	0.999415	+	0.0341932i	$0.0108861\pi$
$968$	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	−0.654572	−	0.756000i	$-0.727151\pi$
$971$	10.5224	−	19.6860i	0.337680	−	0.631754i	0.992251	+	0.124246i	$0.0396511\pi$
$972$	−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	0.723434	−	0.690393i	$-0.242562\pi$
$977$	−8.63608	−	20.8493i	−0.276293	−	0.667029i	−0.999727	+	0.0233638i	$0.992562\pi$
$978$	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	0.193763	−	0.981048i	$-0.437931\pi$
$983$	23.4584	−	4.66617i	0.748208	−	0.148828i	0.554445	+	0.832221i	$0.312931\pi$
$984$	−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	−0.972356	−	0.233502i	$-0.924982\pi$
$991$	−23.2593	+	23.2593i	−0.738855	+	0.738855i	0.233502	+	0.972356i	$0.424982\pi$
$992$	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	−0.869966	−	0.493112i	$-0.835859\pi$
$997$	−17.5575	+	14.4090i	−0.556050	+	0.456339i	0.313915	+	0.949451i	$0.398359\pi$
$998$	−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.325.14	yes	512
128.13	even	32	inner	384.2.v.a.13.14	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.14	✓	512	128.13	even	32	inner
384.2.v.a.325.14	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.283082 - 1.38559i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.83973 + 0.784471i) q^{4} +(-0.166665 + 1.69218i) q^{5} +(-1.40810 - 0.131324i) q^{6} +(1.76235 + 2.63755i) q^{7} +(1.60775 + 2.32704i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * 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

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