LMFDB - Embedded newform 384.2.v.a.37.17

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			37.17
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0822429 - 1.41182i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.98647 - 0.232224i) q^{4} +(0.859670 - 0.705513i) q^{5} +(1.28388 - 0.592996i) q^{6} +(0.637437 - 0.425922i) q^{7} +(-0.491232 + 2.78544i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(0.0822429 - 1.41182i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.98647 - 0.232224i) q^{4} +(0.859670 - 0.705513i) q^{5} +(1.28388 - 0.592996i) q^{6} +(0.637437 - 0.425922i) q^{7} +(-0.491232 + 2.78544i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-0.925356 - 1.27172i) q^{10} +(-1.67516 - 5.52225i) q^{11} +(-0.731613 - 1.86138i) q^{12} +(2.52301 - 3.07430i) q^{13} +(-0.548900 - 0.934976i) q^{14} +(1.02745 + 0.425585i) q^{15} +(3.89214 + 0.922614i) q^{16} +(3.77043 - 1.56176i) q^{17} +(1.12819 + 0.852748i) q^{18} +(5.73443 - 0.564793i) q^{19} +(-1.87155 + 1.20185i) q^{20} +(0.676115 + 0.361391i) q^{21} +(-7.93419 + 1.91085i) q^{22} +(-1.83052 + 0.364113i) q^{23} +(-2.68811 + 0.879821i) q^{24} +(-0.734168 + 3.69091i) q^{25} +(-4.13286 - 3.81488i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-1.36516 + 0.698054i) q^{28} +(-0.0937668 - 0.0284438i) q^{29} +(0.685350 - 1.41558i) q^{30} +(-5.49926 - 5.49926i) q^{31} +(1.62267 - 5.41913i) q^{32} +(4.08053 - 4.08053i) q^{33} +(-1.89484 - 5.45161i) q^{34} +(0.247492 - 0.815873i) q^{35} +(1.29671 - 1.52267i) q^{36} +(-0.816007 + 8.28506i) q^{37} +(-0.325769 - 8.14244i) q^{38} +(3.90063 + 0.775883i) q^{39} +(1.54287 + 2.74113i) q^{40} +(-0.339303 - 1.70579i) q^{41} +(0.565825 - 0.924831i) q^{42} +(-3.93471 + 7.36133i) q^{43} +(2.04525 + 11.3588i) q^{44} +(0.109006 + 1.10675i) q^{45} +(0.363515 + 2.61431i) q^{46} +(-2.64233 - 6.37916i) q^{47} +(1.02107 + 3.86748i) q^{48} +(-2.45387 + 5.92416i) q^{49} +(5.15052 + 1.34006i) q^{50} +(3.15472 + 2.58901i) q^{51} +(-5.72582 + 5.52110i) q^{52} +(5.14669 - 1.56123i) q^{53} +(-0.220229 + 1.39696i) q^{54} +(-5.33610 - 3.56547i) q^{55} +(0.873251 + 1.98477i) q^{56} +(3.20130 + 4.79108i) q^{57} +(-0.0478692 + 0.130043i) q^{58} +(6.14668 + 7.48975i) q^{59} +(-1.94217 - 1.08401i) q^{60} +(6.79010 - 3.62938i) q^{61} +(-8.21625 + 7.31170i) q^{62} +0.766639i q^{63} +(-7.51738 - 2.73660i) q^{64} -4.42290i q^{65} +(-5.42538 - 6.09656i) q^{66} +(-9.47973 + 5.06702i) q^{67} +(-7.85253 + 2.22681i) q^{68} +(-1.18402 - 1.44273i) q^{69} +(-1.13151 - 0.416514i) q^{70} +(-3.73039 - 5.58292i) q^{71} +(-2.04310 - 1.95595i) q^{72} +(10.6588 + 7.12196i) q^{73} +(11.6299 + 1.83344i) q^{74} +(-3.60118 + 1.09240i) q^{75} +(-11.5225 - 0.209730i) q^{76} +(-3.41985 - 2.80660i) q^{77} +(1.41621 - 5.44317i) q^{78} +(-4.05478 + 9.78910i) q^{79} +(3.99688 - 1.95281i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.43617 + 0.338745i) q^{82} +(1.29496 + 13.1479i) q^{83} +(-1.25916 - 0.874904i) q^{84} +(2.13948 - 4.00269i) q^{85} +(10.0693 + 6.16052i) q^{86} +(-0.0191161 - 0.0961033i) q^{87} +(16.2048 - 1.95335i) q^{88} +(-0.603595 - 0.120062i) q^{89} +(1.57150 - 0.0628738i) q^{90} +(0.298850 - 3.03428i) q^{91} +(3.72083 - 0.298209i) q^{92} +(2.25758 - 7.44225i) q^{93} +(-9.22353 + 3.20586i) q^{94} +(4.53125 - 4.53125i) q^{95} +(5.54416 - 1.12350i) q^{96} +(0.245404 + 0.245404i) q^{97} +(8.16204 + 3.95164i) q^{98} +(5.52225 + 1.67516i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	0.0822429	−	1.41182i	0.0581545	−	0.998308i
$2$	0.0822429	−	1.41182i	0.0581545	−	0.998308i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$4$	−1.98647	−	0.232224i	−0.993236	−	0.116112i
$5$	0.859670	−	0.705513i	0.384456	−	0.315515i	−0.422237	−	0.906485i	$-0.638755\pi$
$5$	0.859670	−	0.705513i	0.384456	−	0.315515i	0.806693	+	0.590970i	$0.201255\pi$
$6$	1.28388	−	0.592996i	0.524143	−	0.242089i
$7$	0.637437	−	0.425922i	0.240929	−	0.160983i	−0.429244	−	0.903189i	$-0.641220\pi$
$7$	0.637437	−	0.425922i	0.240929	−	0.160983i	0.670173	+	0.742205i	$0.266220\pi$
$8$	−0.491232	+	2.78544i	−0.173677	+	0.984803i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	−0.925356	−	1.27172i	−0.292623	−	0.402154i
$11$	−1.67516	−	5.52225i	−0.505079	−	1.66502i	−0.724409	−	0.689371i	$-0.757887\pi$
$11$	−1.67516	−	5.52225i	−0.505079	−	1.66502i	0.219330	−	0.975651i	$-0.429613\pi$
$12$	−0.731613	−	1.86138i	−0.211198	−	0.537335i
$13$	2.52301	−	3.07430i	0.699757	−	0.852657i	−0.294938	−	0.955516i	$-0.595299\pi$
$13$	2.52301	−	3.07430i	0.699757	−	0.852657i	0.994696	+	0.102859i	$0.0327992\pi$
$14$	−0.548900	−	0.934976i	−0.146700	−	0.249883i
$15$	1.02745	+	0.425585i	0.265287	+	0.109886i
$16$	3.89214	+	0.922614i	0.973036	+	0.230654i
$17$	3.77043	−	1.56176i	0.914463	−	0.378783i	0.124699	−	0.992195i	$-0.460203\pi$
$17$	3.77043	−	1.56176i	0.914463	−	0.378783i	0.789763	+	0.613412i	$0.210203\pi$
$18$	1.12819	+	0.852748i	0.265918	+	0.200995i
$19$	5.73443	−	0.564793i	1.31557	−	0.129572i	0.584231	−	0.811587i	$-0.301396\pi$
$19$	5.73443	−	0.564793i	1.31557	−	0.129572i	0.731338	+	0.682015i	$0.238896\pi$
$20$	−1.87155	+	1.20185i	−0.418491	+	0.268741i
$21$	0.676115	+	0.361391i	0.147540	+	0.0788620i
$22$	−7.93419	+	1.91085i	−1.69158	+	0.407395i
$23$	−1.83052	+	0.364113i	−0.381690	+	0.0759228i	−0.382206	−	0.924077i	$-0.624836\pi$
$23$	−1.83052	+	0.364113i	−0.381690	+	0.0759228i	0.000516401		1.00000i	$0.499836\pi$
$24$	−2.68811	+	0.879821i	−0.548707	+	0.179593i
$25$	−0.734168	+	3.69091i	−0.146834	+	0.738182i
$26$	−4.13286	−	3.81488i	−0.810520	−	0.748159i
$27$	−0.995185	−	0.0980171i	−0.191523	−	0.0188634i
$28$	−1.36516	+	0.698054i	−0.257991	+	0.131920i
$29$	−0.0937668	−	0.0284438i	−0.0174121	−	0.00528189i	0.281567	−	0.959542i	$-0.409146\pi$
$29$	−0.0937668	−	0.0284438i	−0.0174121	−	0.00528189i	−0.298979	+	0.954260i	$0.596646\pi$
$30$	0.685350	−	1.41558i	0.125127	−	0.258448i
$31$	−5.49926	−	5.49926i	−0.987697	−	0.987697i	0.0122284	−	0.999925i	$-0.496107\pi$
$31$	−5.49926	−	5.49926i	−0.987697	−	0.987697i	−0.999925	+	0.0122284i	$0.996107\pi$
$32$	1.62267	−	5.41913i	0.286850	−	0.957976i
$33$	4.08053	−	4.08053i	0.710329	−	0.710329i
$34$	−1.89484	−	5.45161i	−0.324962	−	0.934943i
$35$	0.247492	−	0.815873i	0.0418338	−	0.137908i
$36$	1.29671	−	1.52267i	0.216119	−	0.253779i
$37$	−0.816007	+	8.28506i	−0.134151	+	1.36206i	0.658593	+	0.752500i	$0.271152\pi$
$37$	−0.816007	+	8.28506i	−0.134151	+	1.36206i	−0.792743	+	0.609556i	$0.791348\pi$
$38$	−0.325769	−	8.14244i	−0.0528467	−	1.32088i
$39$	3.90063	+	0.775883i	0.624600	+	0.124241i
$40$	1.54287	+	2.74113i	0.243949	+	0.433411i
$41$	−0.339303	−	1.70579i	−0.0529902	−	0.266400i	0.945203	−	0.326483i	$-0.105863\pi$
$41$	−0.339303	−	1.70579i	−0.0529902	−	0.266400i	−0.998193	+	0.0600830i	$0.980863\pi$
$42$	0.565825	−	0.924831i	0.0873087	−	0.142705i
$43$	−3.93471	+	7.36133i	−0.600038	+	1.12259i	0.380225	+	0.924894i	$0.375847\pi$
$43$	−3.93471	+	7.36133i	−0.600038	+	1.12259i	−0.980263	+	0.197698i	$0.936653\pi$
$44$	2.04525	+	11.3588i	0.308333	+	1.71240i
$45$	0.109006	+	1.10675i	0.0162496	+	0.164985i
$46$	0.363515	+	2.61431i	0.0535974	+	0.385459i
$47$	−2.64233	−	6.37916i	−0.385424	−	0.930496i	−0.990896	−	0.134629i	$-0.957016\pi$
$47$	−2.64233	−	6.37916i	−0.385424	−	0.930496i	0.605472	−	0.795866i	$-0.292984\pi$
$48$	1.02107	+	3.86748i	0.147379	+	0.558223i
$49$	−2.45387	+	5.92416i	−0.350552	+	0.846309i
$50$	5.15052	+	1.34006i	0.728394	+	0.189514i
$51$	3.15472	+	2.58901i	0.441749	+	0.362534i
$52$	−5.72582	+	5.52110i	−0.794028	+	0.765639i
$53$	5.14669	−	1.56123i	0.706952	−	0.214452i	0.0837209	−	0.996489i	$-0.473320\pi$
$53$	5.14669	−	1.56123i	0.706952	−	0.214452i	0.623231	+	0.782038i	$0.285820\pi$
$54$	−0.220229	+	1.39696i	−0.0299694	+	0.190102i
$55$	−5.33610	−	3.56547i	−0.719520	−	0.480768i
$56$	0.873251	+	1.98477i	0.116693	+	0.265226i
$57$	3.20130	+	4.79108i	0.424022	+	0.634594i
$58$	−0.0478692	+	0.130043i	−0.00628554	+	0.0170754i
$59$	6.14668	+	7.48975i	0.800229	+	0.975082i	0.999989	−	0.00476306i	$-0.00151613\pi$
$59$	6.14668	+	7.48975i	0.800229	+	0.975082i	−0.199760	+	0.979845i	$0.564016\pi$
$60$	−1.94217	−	1.08401i	−0.250734	−	0.139945i
$61$	6.79010	−	3.62938i	0.869383	−	0.464695i	0.0245335	−	0.999699i	$-0.492190\pi$
$61$	6.79010	−	3.62938i	0.869383	−	0.464695i	0.844849	+	0.535004i	$0.179690\pi$
$62$	−8.21625	+	7.31170i	−1.04346	+	0.928586i
$63$			0.766639i			0.0965875i
$64$	−7.51738	−	2.73660i	−0.939673	−	0.342075i
$65$		−	4.42290i		−	0.548593i
$66$	−5.42538	−	6.09656i	−0.667818	−	0.750435i
$67$	−9.47973	+	5.06702i	−1.15813	+	0.619035i	−0.934614	−	0.355664i	$-0.884255\pi$
$67$	−9.47973	+	5.06702i	−1.15813	+	0.619035i	−0.223520	+	0.974699i	$0.571755\pi$
$68$	−7.85253	+	2.22681i	−0.952259	+	0.270041i
$69$	−1.18402	−	1.44273i	−0.142539	−	0.173685i
$70$	−1.13151	−	0.416514i	−0.135241	−	0.0497830i
$71$	−3.73039	−	5.58292i	−0.442716	−	0.662571i	0.541264	−	0.840853i	$-0.317946\pi$
$71$	−3.73039	−	5.58292i	−0.442716	−	0.662571i	−0.983979	+	0.178282i	$0.942946\pi$
$72$	−2.04310	−	1.95595i	−0.240781	−	0.230511i
$73$	10.6588	+	7.12196i	1.24751	+	0.833562i	0.991115	−	0.133009i	$-0.0424639\pi$
$73$	10.6588	+	7.12196i	1.24751	+	0.833562i	0.256399	+	0.966571i	$0.417464\pi$
$74$	11.6299	+	1.83344i	1.35195	+	0.213133i
$75$	−3.60118	+	1.09240i	−0.415828	+	0.126140i
$76$	−11.5225	−	0.209730i	−1.32172	−	0.0240577i
$77$	−3.41985	−	2.80660i	−0.389729	−	0.319842i
$78$	1.41621	−	5.44317i	0.160354	−	0.616318i
$79$	−4.05478	+	9.78910i	−0.456198	+	1.10136i	0.513727	+	0.857954i	$0.328265\pi$
$79$	−4.05478	+	9.78910i	−0.456198	+	1.10136i	−0.969925	+	0.243405i	$0.921735\pi$
$80$	3.99688	−	1.95281i	0.446864	−	0.218331i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−2.43617	+	0.338745i	−0.269030	+	0.0374082i
$83$	1.29496	+	13.1479i	0.142140	+	1.44317i	0.756422	+	0.654084i	$0.226946\pi$
$83$	1.29496	+	13.1479i	0.142140	+	1.44317i	−0.614282	+	0.789086i	$0.710554\pi$
$84$	−1.25916	−	0.874904i	−0.137386	−	0.0954599i
$85$	2.13948	−	4.00269i	0.232059	−	0.434152i
$86$	10.0693	+	6.16052i	1.08580	+	0.664306i
$87$	−0.0191161	−	0.0961033i	−0.00204946	−	0.0103034i
$88$	16.2048	−	1.95335i	1.72744	−	0.208227i
$89$	−0.603595	−	0.120062i	−0.0639809	−	0.0127266i	0.162996	−	0.986627i	$-0.447884\pi$
$89$	−0.603595	−	0.120062i	−0.0639809	−	0.0127266i	−0.226977	+	0.973900i	$0.572884\pi$
$90$	1.57150	−	0.0628738i	0.165651	−	0.00662748i
$91$	0.298850	−	3.03428i	0.0313280	−	0.318079i
$92$	3.72083	−	0.298209i	0.387924	−	0.0310905i
$93$	2.25758	−	7.44225i	0.234100	−	0.771726i
$94$	−9.22353	+	3.20586i	−0.951335	+	0.330659i
$95$	4.53125	−	4.53125i	0.464897	−	0.464897i
$96$	5.54416	−	1.12350i	0.565849	−	0.114666i
$97$	0.245404	+	0.245404i	0.0249170	+	0.0249170i	0.719456	−	0.694539i	$-0.244391\pi$
$97$	0.245404	+	0.245404i	0.0249170	+	0.0249170i	−0.694539	+	0.719456i	$0.744391\pi$
$98$	8.16204	+	3.95164i	0.824490	+	0.399176i
$99$	5.52225	+	1.67516i	0.555007	+	0.168360i
$100$	2.31552	−	7.16140i	0.231552	−	0.716140i
$101$	1.58780	+	0.156385i	0.157992	+	0.0155609i	0.176704	−	0.984264i	$-0.443456\pi$
$101$	1.58780	+	0.156385i	0.157992	+	0.0155609i	−0.0187118	+	0.999825i	$0.505956\pi$
$102$	3.91467	−	4.24097i	0.387610	−	0.419918i
$103$	0.170804	−	0.858690i	0.0168298	−	0.0846093i	−0.971458	−	0.237213i	$-0.923766\pi$
$103$	0.170804	−	0.858690i	0.0168298	−	0.0846093i	0.988287	+	0.152604i	$0.0487659\pi$
$104$	7.32390	+	8.53790i	0.718167	+	0.837210i
$105$	0.836202	−	0.166331i	0.0816050	−	0.0162322i
$106$	−1.78090	−	7.39460i	−0.172976	−	0.718227i
$107$	3.76301	+	2.01137i	0.363784	+	0.194446i	0.643154	−	0.765737i	$-0.277626\pi$
$107$	3.76301	+	2.01137i	0.363784	+	0.194446i	−0.279370	+	0.960184i	$0.590126\pi$
$108$	1.95414	+	0.425814i	0.188038	+	0.0409740i
$109$	14.6445	−	1.44235i	1.40268	−	0.138152i	0.631802	−	0.775130i	$-0.282316\pi$
$109$	14.6445	−	1.44235i	1.40268	−	0.138152i	0.770882	+	0.636978i	$0.219816\pi$
$110$	−5.47266	+	7.24038i	−0.521797	+	0.690343i
$111$	−7.69143	+	3.18590i	−0.730039	+	0.302392i
$112$	2.87396	−	1.06964i	0.271564	−	0.101072i
$113$	−10.0706	−	4.17139i	−0.947365	−	0.392411i	−0.145125	−	0.989413i	$-0.546358\pi$
$113$	−10.0706	−	4.17139i	−0.947365	−	0.392411i	−0.802240	+	0.597002i	$0.796358\pi$
$114$	7.02742	−	4.12562i	0.658179	−	0.386400i
$115$	−1.31676	+	1.60447i	−0.122788	+	0.149618i
$116$	0.179660	+	0.0782778i	0.0166810	+	0.00726791i
$117$	1.15448	+	3.80580i	0.106731	+	0.351846i
$118$	11.0797	−	8.06202i	1.01997	−	0.742169i
$119$	1.73822	−	2.60143i	0.159343	−	0.238473i
$120$	−1.69016	+	2.65285i	−0.154290	+	0.242171i
$121$	−18.5429	+	12.3900i	−1.68572	+	1.12636i
$122$	−4.56560	−	9.88489i	−0.413350	−	0.894936i
$123$	1.34443	−	1.10334i	0.121223	−	0.0994850i
$124$	9.64707	+	12.2012i	0.866333	+	1.09570i
$125$	4.59406	+	8.59488i	0.410905	+	0.768750i
$126$	1.08236	+	0.0630506i	0.0964240	+	0.00561699i
$127$	2.05619			0.182458			0.0912289	−	0.995830i	$-0.470921\pi$
$127$	2.05619			0.182458			0.0912289	+	0.995830i	$0.470921\pi$
$128$	−4.48184	+	10.3881i	−0.396142	+	0.918189i
$129$	−8.34692			−0.734906
$130$	−6.24434	−	0.363752i	−0.547665	−	0.0319032i
$131$	−1.32288	−	2.47493i	−0.115580	−	0.216235i	0.817479	−	0.575959i	$-0.195371\pi$
$131$	−1.32288	−	2.47493i	−0.115580	−	0.216235i	−0.933059	+	0.359723i	$0.882871\pi$
$132$	−9.05345	+	7.15826i	−0.788002	+	0.623046i
$133$	3.41478	−	2.80244i	0.296099	−	0.243002i
$134$	6.37408	+	13.8004i	0.550637	+	1.19217i
$135$	−0.924683	+	0.617853i	−0.0795840	+	0.0531764i
$136$	2.49804	+	11.2695i	0.214205	+	0.966351i
$137$	3.17490	−	4.75158i	0.271250	−	0.405955i	−0.670689	−	0.741739i	$-0.734001\pi$
$137$	3.17490	−	4.75158i	0.271250	−	0.405955i	0.941939	+	0.335784i	$0.109001\pi$
$138$	−2.13426	+	1.55297i	−0.181680	+	0.132198i
$139$	−3.32693	−	10.9674i	−0.282186	−	0.930243i	−0.977393	−	0.211433i	$-0.932187\pi$
$139$	−3.32693	−	10.9674i	−0.282186	−	0.930243i	0.695206	−	0.718810i	$-0.255313\pi$
$140$	−0.681102	+	1.56323i	−0.0575636	+	0.132117i
$141$	4.38033	−	5.33744i	0.368890	−	0.449494i
$142$	−8.18888	+	4.80748i	−0.687195	+	0.403435i
$143$	−21.2035	−	8.78277i	−1.77312	−	0.734452i
$144$	−2.92948	+	2.72362i	−0.244124	+	0.226969i
$145$	−0.100676	+	0.0417014i	−0.00836069	+	0.00346311i
$146$	10.9315	−	14.4625i	0.904700	−	1.19693i
$147$	−6.38139	+	0.628512i	−0.526328	+	0.0518388i
$148$	3.54497	−	16.2685i	0.291395	−	1.33727i
$149$	−12.2884	−	6.56831i	−1.00671	−	0.538097i	−0.116278	−	0.993217i	$-0.537096\pi$
$149$	−12.2884	−	6.56831i	−1.00671	−	0.538097i	−0.890430	+	0.455120i	$0.849596\pi$
$150$	1.24611	+	5.17406i	0.101744	+	0.422460i
$151$	7.31724	−	1.45549i	0.595469	−	0.118446i	0.111850	−	0.993725i	$-0.464322\pi$
$151$	7.31724	−	1.45549i	0.595469	−	0.118446i	0.483618	+	0.875279i	$0.339322\pi$
$152$	−1.24374	+	16.2504i	−0.100881	+	1.31808i
$153$	−0.796179	+	4.00266i	−0.0643673	+	0.323596i
$154$	−4.24368	+	4.59740i	−0.341965	+	0.370469i
$155$	−8.60735	−	0.847750i	−0.691359	−	0.0680929i
$156$	−7.56831	−	2.44709i	−0.605950	−	0.195924i
$157$	14.2953	+	4.33643i	1.14089	+	0.346085i	0.803514	−	0.595286i	$-0.202961\pi$
$157$	14.2953	+	4.33643i	1.14089	+	0.346085i	0.337374	+	0.941371i	$0.390461\pi$
$158$	13.4870	+	6.52970i	1.07297	+	0.519475i
$159$	3.80301	+	3.80301i	0.301599	+	0.301599i
$160$	−2.42831	−	5.80347i	−0.191975	−	0.458805i
$161$	−1.01176	+	1.01176i	−0.0797377	+	0.0797377i
$162$	−1.33582	+	0.464298i	−0.104952	+	0.0364787i
$163$	4.84154	−	15.9604i	0.379219	−	1.25012i	−0.534985	−	0.844862i	$-0.679683\pi$
$163$	4.84154	−	15.9604i	0.379219	−	1.25012i	0.914204	−	0.405255i	$-0.132817\pi$
$164$	0.277890	+	3.46730i	0.0216995	+	0.270751i
$165$	0.629042	−	6.38677i	0.0489709	−	0.497210i
$166$	18.6690	−	0.746923i	1.44899	−	0.0579724i
$167$	−22.8090	−	4.53698i	−1.76501	−	0.351082i	−0.797384	−	0.603472i	$-0.793784\pi$
$167$	−22.8090	−	4.53698i	−1.76501	−	0.351082i	−0.967626	+	0.252389i	$0.918784\pi$
$168$	−1.33876	+	1.70575i	−0.103288	+	0.131602i
$169$	−0.549549	−	2.76277i	−0.0422730	−	0.212521i
$170$	−5.47511	−	3.34975i	−0.419922	−	0.256914i
$171$	−2.71627	+	5.08179i	−0.207719	+	0.388614i
$172$	9.52568	−	13.7093i	0.726326	−	1.04533i
$173$	−1.19644	−	12.1476i	−0.0909635	−	0.923568i	−0.927042	−	0.374958i	$-0.877657\pi$
$173$	−1.19644	−	12.1476i	−0.0909635	−	0.923568i	0.836078	−	0.548610i	$-0.184843\pi$
$174$	−0.137253	+	0.0190847i	−0.0104051	+	0.00144681i
$175$	1.10405	+	2.66542i	0.0834586	+	0.201487i
$176$	−1.42504	−	23.0389i	−0.107417	−	1.73662i
$177$	−3.70784	+	8.95153i	−0.278699	+	0.672838i
$178$	−0.219148	+	0.842293i	−0.0164258	+	0.0631325i
$179$	13.0505	+	10.7102i	0.975438	+	0.800521i	0.979904	−	0.199469i	$-0.0639216\pi$
$179$	13.0505	+	10.7102i	0.975438	+	0.800521i	−0.00446606	+	0.999990i	$0.501422\pi$
$180$	0.0404782	−	2.22385i	0.00301707	−	0.165756i
$181$	−21.2813	+	6.45562i	−1.58183	+	0.479843i	−0.954325	−	0.298770i	$-0.903424\pi$
$181$	−21.2813	+	6.45562i	−1.58183	+	0.479843i	−0.627504	+	0.778613i	$0.715924\pi$
$182$	−4.25928	−	0.671471i	−0.315719	−	0.0497727i
$183$	6.40166	+	4.27745i	0.473224	+	0.316198i
$184$	−0.115006	−	5.27767i	−0.00847835	−	0.389075i
$185$	5.14372	+	7.69812i	0.378174	+	0.565977i
$186$	−10.3215	−	3.79937i	−0.756806	−	0.278584i
$187$	−14.9405	−	18.2050i	−1.09256	−	1.33128i
$188$	3.76753	+	13.2856i	0.274775	+	0.968954i
$189$	−0.676115	+	0.361391i	−0.0491802	+	0.0262873i
$190$	−6.02465	−	6.76998i	−0.437074	−	0.491146i
$191$			12.4746i			0.902633i	0.892364	+	0.451317i	$0.149046\pi$
$191$			12.4746i			0.902633i	−0.892364	+	0.451317i	$0.850954\pi$
$192$	−1.13021	−	7.91976i	−0.0815656	−	0.571560i
$193$			13.5694i			0.976750i	0.872634	+	0.488375i	$0.162410\pi$
$193$			13.5694i			0.976750i	−0.872634	+	0.488375i	$0.837590\pi$
$194$	0.366649	−	0.326284i	0.0263239	−	0.0234258i
$195$	3.90065	−	2.08494i	0.279331	−	0.149306i
$196$	6.25027	−	11.1983i	0.446448	−	0.799881i
$197$	4.74390	+	5.78046i	0.337989	+	0.411841i	0.914073	−	0.405550i	$-0.132920\pi$
$197$	4.74390	+	5.78046i	0.337989	+	0.411841i	−0.576084	+	0.817390i	$0.695420\pi$
$198$	2.81919	−	7.65866i	0.200351	−	0.544277i
$199$	−12.9196	−	19.3355i	−0.915843	−	1.37066i	−0.928737	−	0.370739i	$-0.879104\pi$
$199$	−12.9196	−	19.3355i	−0.915843	−	1.37066i	0.0128939	−	0.999917i	$-0.495896\pi$
$200$	−9.92017	−	3.85807i	−0.701462	−	0.272807i
$201$	−8.93743	−	5.97180i	−0.630398	−	0.421218i
$202$	0.351373	−	2.22883i	0.0247225	−	0.156820i
$203$	−0.0718853	+	0.0218062i	−0.00504536	+	0.00153049i
$204$	−5.66553	−	5.87560i	−0.396666	−	0.411374i
$205$	−1.49515	−	1.22703i	−0.104426	−	0.0856998i
$206$	−1.19827	−	0.311766i	−0.0834873	−	0.0217218i
$207$	0.714234	−	1.72431i	0.0496427	−	0.119848i
$208$	12.6563	−	9.63784i	0.877557	−	0.668264i
$209$	−12.7250	−	30.7209i	−0.880207	−	2.12501i
$210$	−0.166058	−	1.19425i	−0.0114591	−	0.0824109i
$211$	1.13691	+	11.5433i	0.0782684	+	0.794672i	0.951558	+	0.307470i	$0.0994825\pi$
$211$	1.13691	+	11.5433i	0.0782684	+	0.794672i	−0.873289	+	0.487202i	$0.838018\pi$
$212$	−10.5863	+	1.90616i	−0.727071	+	0.130915i
$213$	3.16520	−	5.92168i	0.216876	−	0.405747i
$214$	3.14917	−	5.14727i	0.215273	−	0.351860i
$215$	1.81096	+	9.10431i	0.123506	+	0.620909i
$216$	0.761888	−	2.72388i	0.0518399	−	0.185337i
$217$	−5.84769	−	1.16318i	−0.396967	−	0.0789617i
$218$	−0.831941	−	20.7940i	−0.0563461	−	1.40834i
$219$	−1.25650	+	12.7575i	−0.0849064	+	0.862069i
$220$	9.77203	+	8.32188i	0.658830	+	0.561061i
$221$	4.71151	−	15.5318i	0.316930	−	1.04478i
$222$	3.86535	+	11.1209i	0.259425	+	0.746388i
$223$	3.66393	−	3.66393i	0.245355	−	0.245355i	−0.573706	−	0.819061i	$-0.694495\pi$
$223$	3.66393	−	3.66393i	0.245355	−	0.245355i	0.819061	+	0.573706i	$0.194495\pi$
$224$	−1.27378	−	4.14548i	−0.0851078	−	0.276982i
$225$	−2.66100	−	2.66100i	−0.177400	−	0.177400i
$226$	−6.71749	+	13.8748i	−0.446841	+	0.922941i
$227$	18.5142	+	5.61623i	1.22883	+	0.372762i	0.836964	−	0.547259i	$-0.184329\pi$
$227$	18.5142	+	5.61623i	1.22883	+	0.372762i	0.391869	+	0.920021i	$0.371829\pi$
$228$	−5.24668	−	10.2608i	−0.347470	−	0.679536i
$229$	2.74710	+	0.270566i	0.181534	+	0.0178795i	0.188375	−	0.982097i	$-0.439678\pi$
$229$	2.74710	+	0.270566i	0.181534	+	0.0178795i	−0.00684180	+	0.999977i	$0.502178\pi$
$230$	2.15693	+	1.99098i	0.142224	+	0.131281i
$231$	0.863094	−	4.33907i	0.0567874	−	0.285490i
$232$	0.125290	−	0.247209i	0.00822569	−	0.0162301i
$233$	−15.6564	+	3.11425i	−1.02568	+	0.204021i	−0.679137	−	0.734011i	$-0.737646\pi$
$233$	−15.6564	+	3.11425i	−1.02568	+	0.204021i	−0.346547	+	0.938033i	$0.612646\pi$
$234$	5.46805	−	1.31691i	0.357457	−	0.0860892i
$235$	−6.77211	−	3.61977i	−0.441764	−	0.236128i
$236$	−10.4709	−	16.3056i	−0.681597	−	1.06140i
$237$	−10.5446	+	1.03855i	−0.684947	+	0.0674614i
$238$	−3.52980	−	2.66801i	−0.228803	−	0.172941i
$239$	−13.2923	+	5.50586i	−0.859809	+	0.356145i	−0.768633	−	0.639690i	$-0.779063\pi$
$239$	−13.2923	+	5.50586i	−0.859809	+	0.356145i	−0.0911764	+	0.995835i	$0.529063\pi$
$240$	3.60634	+	2.60438i	0.232788	+	0.168112i
$241$	0.213990	+	0.0886375i	0.0137843	+	0.00570965i	0.389565	−	0.920999i	$-0.372625\pi$
$241$	0.213990	+	0.0886375i	0.0137843	+	0.00570965i	−0.375781	+	0.926709i	$0.622625\pi$
$242$	15.9674	+	27.1983i	1.02642	+	1.74837i
$243$	0.634393	−	0.773010i	0.0406963	−	0.0495886i
$244$	−14.3312	+	5.63284i	−0.917459	+	0.360606i
$245$	2.07006	+	6.82406i	0.132251	+	0.435973i
$246$	−1.44715	−	1.98883i	−0.0922670	−	0.126803i
$247$	12.7317	−	19.0543i	0.810099	−	1.21240i
$248$	18.0193	−	12.6165i	1.14423	−	0.801147i
$249$	−10.9850	+	7.33993i	−0.696145	+	0.465149i
$250$	12.5123	−	5.77912i	0.791345	−	0.365504i
$251$	−9.23988	+	7.58298i	−0.583216	+	0.478633i	−0.879130	−	0.476581i	$-0.841876\pi$
$251$	−9.23988	+	7.58298i	−0.583216	+	0.478633i	0.295914	+	0.955215i	$0.404376\pi$
$252$	0.178032	−	1.52291i	0.0112150	−	0.0959342i
$253$	5.07713	+	9.49865i	0.319197	+	0.597175i
$254$	0.169107	−	2.90298i	0.0106107	−	0.182149i
$255$	4.53860			0.284218
$256$	14.2976	+	7.18189i	0.893598	+	0.448868i
$257$	9.37031			0.584504			0.292252	−	0.956341i	$-0.405595\pi$
$257$	9.37031			0.584504			0.292252	+	0.956341i	$0.405595\pi$
$258$	−0.686475	+	11.7844i	−0.0427381	+	0.733662i
$259$	3.00863	+	5.62876i	0.186947	+	0.349754i
$260$	−1.02710	+	8.78597i	−0.0636983	+	0.544883i
$261$	0.0757442	−	0.0621617i	0.00468845	−	0.00384771i
$262$	−3.60295	+	1.66412i	−0.222591	+	0.102810i
$263$	20.4734	−	13.6799i	1.26244	−	0.843538i	0.269602	−	0.962972i	$-0.413108\pi$
$263$	20.4734	−	13.6799i	1.26244	−	0.843538i	0.992842	+	0.119434i	$0.0381079\pi$
$264$	9.36159	+	13.3706i	0.576166	+	0.822901i
$265$	3.32299	−	4.97320i	0.204129	−	0.305501i
$266$	−3.67570	−	5.05154i	−0.225372	−	0.309730i
$267$	−0.178647	−	0.588920i	−0.0109330	−	0.0360413i
$268$	20.0079	−	7.86407i	1.22218	−	0.480375i
$269$	−12.9949	+	15.8343i	−0.792311	+	0.965434i	−0.999918	−	0.0127785i	$-0.995932\pi$
$269$	−12.9949	+	15.8343i	−0.792311	+	0.965434i	0.207607	+	0.978212i	$0.433432\pi$
$270$	0.796249	+	1.35630i	0.0484582	+	0.0825418i
$271$	11.3703	+	4.70975i	0.690699	+	0.286097i	0.700291	−	0.713857i	$-0.253053\pi$
$271$	11.3703	+	4.70975i	0.690699	+	0.286097i	−0.00959234	+	0.999954i	$0.503053\pi$
$272$	16.1159	−	2.59995i	0.977173	−	0.157645i
$273$	2.81687	−	1.16679i	0.170485	−	0.0706171i
$274$	−6.44726	−	4.87318i	−0.389493	−	0.294399i
$275$	21.6120	−	2.12859i	1.30325	−	0.128359i
$276$	2.01699	+	3.14091i	0.121408	+	0.189060i
$277$	−10.8591	−	5.80428i	−0.652457	−	0.348746i	0.111731	−	0.993738i	$-0.464360\pi$
$277$	−10.8591	−	5.80428i	−0.652457	−	0.348746i	−0.764189	+	0.644993i	$0.776860\pi$
$278$	−15.7576	+	3.79503i	−0.945079	+	0.227611i
$279$	7.62770	−	1.51724i	0.456658	−	0.0908350i
$280$	2.15099	+	1.09016i	0.128546	+	0.0651494i
$281$	−3.18823	+	16.0283i	−0.190194	+	0.956168i	0.761276	+	0.648427i	$0.224573\pi$
$281$	−3.18823	+	16.0283i	−0.190194	+	0.956168i	−0.951470	+	0.307741i	$0.900427\pi$
$282$	−7.17526	−	6.62320i	−0.427280	−	0.394406i
$283$	19.2501	+	1.89597i	1.14430	+	0.112704i	0.652350	−	0.757918i	$-0.273783\pi$
$283$	19.2501	+	1.89597i	1.14430	+	0.112704i	0.491953	+	0.870622i	$0.336283\pi$
$284$	6.11382	+	11.9566i	0.362789	+	0.709494i
$285$	6.13223	+	1.86019i	0.363242	+	0.110188i
$286$	−14.1435	+	29.2132i	−0.836324	+	1.72741i
$287$	−0.942818	−	0.942818i	−0.0556528	−	0.0556528i
$288$	3.60434	+	4.35990i	0.212388	+	0.256910i
$289$	−0.243798	+	0.243798i	−0.0143410	+	0.0143410i
$290$	0.0505949	+	0.145566i	0.00297104	+	0.00854793i
$291$	−0.100744	+	0.332110i	−0.00590574	+	0.0194686i
$292$	−19.5194	−	16.6228i	−1.14229	−	0.972775i
$293$	2.83665	−	28.8010i	0.165719	−	1.68257i	−0.448772	−	0.893646i	$-0.648139\pi$
$293$	2.83665	−	28.8010i	0.165719	−	1.68257i	0.614491	−	0.788924i	$-0.289361\pi$
$294$	0.362522	+	9.06106i	0.0211427	+	0.528452i
$295$	10.5682	+	2.10215i	0.615306	+	0.122392i
$296$	−22.6767	−	6.34283i	−1.31806	−	0.368669i
$297$	1.12581	+	5.65985i	0.0653264	+	0.328418i
$298$	−10.2839	+	16.8089i	−0.595731	+	0.973712i
$299$	−3.49903	+	6.54623i	−0.202354	+	0.378578i
$300$	7.40732	−	1.33375i	0.427662	−	0.0770042i
$301$	0.627219	+	6.36827i	0.0361523	+	0.367061i
$302$	−1.45310	−	10.4503i	−0.0836164	−	0.601349i
$303$	0.610565	+	1.47404i	0.0350761	+	0.0846811i
$304$	22.8403	+	3.09242i	1.30998	+	0.177362i
$305$	3.27667	−	7.91057i	0.187621	−	0.452958i
$306$	5.58556	+	1.45325i	0.319305	+	0.0830769i
$307$	12.8355	+	10.5338i	0.732561	+	0.601197i	0.924935	−	0.380124i	$-0.124119\pi$
$307$	12.8355	+	10.5338i	0.732561	+	0.601197i	−0.192375	+	0.981322i	$0.561619\pi$
$308$	6.14168	+	6.36941i	0.349955	+	0.362931i
$309$	0.837814	−	0.254148i	0.0476616	−	0.0144580i
$310$	−1.90476	+	12.0823i	−0.108183	+	0.686229i
$311$	−10.1204	−	6.76221i	−0.573873	−	0.383450i	0.234504	−	0.972115i	$-0.424654\pi$
$311$	−10.1204	−	6.76221i	−0.573873	−	0.383450i	−0.808377	+	0.588666i	$0.799654\pi$
$312$	−4.07729	+	10.4838i	−0.230831	+	0.593530i
$313$	13.5991	+	20.3524i	0.768665	+	1.15039i	0.984743	+	0.174012i	$0.0556732\pi$
$313$	13.5991	+	20.3524i	0.768665	+	1.15039i	−0.216079	+	0.976376i	$0.569327\pi$
$314$	7.29794	−	19.8257i	0.411847	−	1.11883i
$315$	0.540874	+	0.659057i	0.0304748	+	0.0371336i
$316$	10.3280	−	18.5042i	0.580994	−	1.04094i
$317$	−14.4308	+	7.71344i	−0.810516	+	0.433230i	−0.823938	−	0.566680i	$-0.808228\pi$
$317$	−14.4308	+	7.71344i	−0.810516	+	0.433230i	0.0134218	+	0.999910i	$0.495728\pi$
$318$	5.68194	−	5.05640i	0.318628	−	0.283549i
$319$			0.565452i			0.0316592i
$320$	−8.39317	+	2.95104i	−0.469193	+	0.164968i
$321$			4.26683i			0.238151i
$322$	1.34521	+	1.51163i	0.0749656	+	0.0842399i
$323$	20.7392	−	11.0853i	1.15396	−	0.616804i
$324$	0.545643	+	1.92413i	0.0303135	+	0.106896i
$325$	9.49464	+	11.5693i	0.526668	+	0.641747i
$326$	−22.1351	−	8.14802i	−1.22595	−	0.451277i
$327$	8.17539	+	12.2353i	0.452100	+	0.676615i
$328$	4.91806	−	0.107169i	0.271554	−	0.00591744i
$329$	−4.40134	−	2.94088i	−0.242654	−	0.162136i
$330$	−8.96524	−	1.41336i	−0.493520	−	0.0778030i
$331$	12.2562	−	3.71788i	0.673662	−	0.204353i	0.0651233	−	0.997877i	$-0.479256\pi$
$331$	12.2562	−	3.71788i	0.673662	−	0.204353i	0.608539	+	0.793524i	$0.291756\pi$
$332$	0.480870	−	26.4187i	0.0263911	−	1.44991i
$333$	−6.43543	−	5.28142i	−0.352659	−	0.289420i
$334$	−8.28128	+	31.8290i	−0.453131	+	1.74161i
$335$	−4.57459	+	11.0440i	−0.249937	+	0.603400i
$336$	2.29811	+	2.03038i	0.125372	+	0.110766i
$337$	−5.97300	−	14.4201i	−0.325370	−	0.785513i	−0.998924	−	0.0463750i	$-0.985233\pi$
$337$	−5.97300	−	14.4201i	−0.325370	−	0.785513i	0.673554	−	0.739138i	$-0.264767\pi$
$338$	−3.94573	+	0.548646i	−0.214619	+	0.0298424i
$339$	−1.06842	−	10.8479i	−0.0580288	−	0.589176i
$340$	−5.17954	+	7.45438i	−0.280900	+	0.404271i
$341$	−21.1562	+	39.5804i	−1.14567	+	2.14340i
$342$	6.95118	+	4.25283i	0.375877	+	0.229967i
$343$	2.00599	+	10.0848i	0.108313	+	0.544528i
$344$	−18.5717	−	14.5760i	−1.00132	−	0.785887i
$345$	−2.03573	−	0.404933i	−0.109600	−	0.0218008i
$346$	−17.2487	+	0.690099i	−0.927295	+	0.0370999i
$347$	1.91472	−	19.4404i	0.102787	−	1.04362i	−0.796019	−	0.605272i	$-0.793064\pi$
$347$	1.91472	−	19.4404i	0.102787	−	1.04362i	0.898806	−	0.438346i	$-0.144436\pi$
$348$	0.0156561	+	0.195346i	0.000839257	+	0.0104716i
$349$	0.967491	−	3.18939i	0.0517886	−	0.170724i	−0.927231	−	0.374490i	$-0.877818\pi$
$349$	0.967491	−	3.18939i	0.0517886	−	0.170724i	0.979020	+	0.203765i	$0.0653180\pi$
$350$	3.85390	−	1.33951i	0.205999	−	0.0716000i
$351$	−2.81220	+	2.81220i	−0.150104	+	0.150104i
$352$	−32.6440	+	0.117117i	−1.73993	+	0.00624236i
$353$	−3.58969	−	3.58969i	−0.191060	−	0.191060i	0.605094	−	0.796154i	$-0.293135\pi$
$353$	−3.58969	−	3.58969i	−0.191060	−	0.191060i	−0.796154	+	0.605094i	$0.793135\pi$
$354$	12.3330	+	5.97101i	0.655492	+	0.317355i
$355$	−7.14573	−	2.16763i	−0.379256	−	0.115046i
$356$	1.17114	+	0.378670i	0.0620704	+	0.0200695i
$357$	3.11365	+	0.306668i	0.164792	+	0.0162306i
$358$	16.1943	−	17.5441i	0.855893	−	0.927233i
$359$	−3.50166	+	17.6040i	−0.184810	+	0.929105i	0.771383	+	0.636371i	$0.219565\pi$
$359$	−3.50166	+	17.6040i	−0.184810	+	0.929105i	−0.956194	+	0.292734i	$0.905435\pi$
$360$	−3.13634	−	0.240043i	−0.165300	−	0.0126514i
$361$	13.9298	−	2.77082i	0.733149	−	0.145832i
$362$	7.36394	+	30.5764i	0.387040	+	1.60706i
$363$	−19.6681	−	10.5128i	−1.03231	−	0.551779i
$364$	−1.29829	+	5.95811i	−0.0680489	+	0.312290i
$365$	14.1877	−	1.39736i	0.742616	−	0.0731413i
$366$	6.56548	−	8.68620i	0.343183	−	0.454035i
$367$	−2.19319	+	0.908449i	−0.114484	+	0.0474207i	−0.439190	−	0.898394i	$-0.644735\pi$
$367$	−2.19319	+	0.908449i	−0.114484	+	0.0474207i	0.324706	+	0.945815i	$0.394735\pi$
$368$	−7.46058	−	0.271683i	−0.388910	−	0.0141625i
$369$	1.60682	+	0.665566i	0.0836477	+	0.0346480i
$370$	11.2914	−	6.62889i	0.587012	−	0.344620i
$371$	2.61573	−	3.18727i	0.135802	−	0.165475i
$372$	−6.21290	+	14.2596i	−0.322124	+	0.739324i
$373$	−6.37763	−	21.0242i	−0.330221	−	1.08859i	−0.952179	−	0.305542i	$-0.901162\pi$
$373$	−6.37763	−	21.0242i	−0.330221	−	1.08859i	0.621957	−	0.783051i	$-0.286338\pi$
$374$	−26.9310	+	19.5961i	−1.39257	+	1.01329i
$375$	−5.41438	+	8.10320i	−0.279598	+	0.418447i
$376$	19.0668	−	4.22642i	0.983294	−	0.217961i
$377$	−0.324020	+	0.216503i	−0.0166879	+	0.0111505i
$378$	0.454614	+	0.984275i	0.0233828	+	0.0506257i
$379$	15.8429	−	13.0020i	0.813796	−	0.667866i	−0.132494	−	0.991184i	$-0.542298\pi$
$379$	15.8429	−	13.0020i	0.813796	−	0.667866i	0.946290	+	0.323318i	$0.104798\pi$
$380$	−10.0535	+	7.94894i	−0.515732	+	0.407772i
$381$	0.969283	+	1.81340i	0.0496579	+	0.0929034i
$382$	17.6120	+	1.02595i	0.901106	+	0.0524922i
$383$	13.4958			0.689602			0.344801	−	0.938676i	$-0.387946\pi$
$383$	13.4958			0.689602			0.344801	+	0.938676i	$0.387946\pi$
$384$	−11.2742	+	0.944303i	−0.575336	+	0.0481888i
$385$	−4.92004			−0.250749
$386$	19.1576	+	1.11599i	0.975097	+	0.0568024i
$387$	−3.93471	−	7.36133i	−0.200013	−	0.374197i
$388$	−0.430499	−	0.544477i	−0.0218553	−	0.0276416i
$389$	−17.8321	+	14.6344i	−0.904122	+	0.741994i	−0.966664	−	0.256049i	$-0.917579\pi$
$389$	−17.8321	+	14.6344i	−0.904122	+	0.741994i	0.0625419	+	0.998042i	$0.480079\pi$
$390$	−2.62276	−	5.67849i	−0.132809	−	0.287541i
$391$	−6.33319	+	4.23170i	−0.320283	+	0.214006i
$392$	−15.2960	−	9.74524i	−0.772564	−	0.492209i
$393$	1.55909	−	2.33334i	0.0786457	−	0.117702i
$394$	8.55112	−	6.22213i	0.430799	−	0.313466i
$395$	3.42056	+	11.2761i	0.172107	+	0.567362i
$396$	−10.5808	−	4.61005i	−0.531704	−	0.231664i
$397$	10.7625	−	13.1141i	0.540152	−	0.658177i	−0.429385	−	0.903121i	$-0.641270\pi$
$397$	10.7625	−	13.1141i	0.540152	−	0.658177i	0.969537	+	0.244944i	$0.0787697\pi$
$398$	−28.3608	+	16.6499i	−1.42160	+	0.834583i
$399$	4.08125	+	1.69051i	0.204318	+	0.0846313i
$400$	−6.26277	+	13.6882i	−0.313139	+	0.684410i
$401$	2.63393	−	1.09101i	0.131532	−	0.0544823i	−0.315947	−	0.948777i	$-0.602322\pi$
$401$	2.63393	−	1.09101i	0.131532	−	0.0544823i	0.447479	+	0.894295i	$0.352322\pi$
$402$	−9.16614	+	12.1269i	−0.457166	+	0.604835i
$403$	−30.7811	+	3.03167i	−1.53331	+	0.151018i
$404$	−3.11781	−	0.679380i	−0.155117	−	0.0338004i
$405$	−0.980791	−	0.524243i	−0.0487359	−	0.0260499i
$406$	0.0248743	+	0.103283i	0.00123449	+	0.00512582i
$407$	47.1191	−	9.37257i	2.33561	−	0.464581i
$408$	−8.76124	+	7.51548i	−0.433746	+	0.372072i
$409$	3.34624	−	16.8227i	0.165461	−	0.831828i	−0.805501	−	0.592594i	$-0.798104\pi$
$409$	3.34624	−	16.8227i	0.165461	−	0.831828i	0.970962	−	0.239234i	$-0.0768962\pi$
$410$	−1.85532	+	2.00996i	−0.0916276	+	0.0992650i
$411$	5.68716	+	0.560136i	0.280527	+	0.0276295i
$412$	−0.538706	+	1.66610i	−0.0265402	+	0.0820828i
$413$	7.10817	+	2.15624i	0.349770	+	0.106102i
$414$	−2.37568	−	1.15018i	−0.116758	−	0.0565284i
$415$	10.3893	+	10.3893i	0.509988	+	0.509988i
$416$	−12.5660	−	18.6611i	−0.616099	−	0.914935i
$417$	8.10408	−	8.10408i	0.396859	−	0.396859i
$418$	−44.4189	+	15.4388i	−2.17260	+	0.755138i
$419$	0.926293	−	3.05358i	0.0452524	−	0.149177i	−0.931403	−	0.363990i	$-0.881414\pi$
$419$	0.926293	−	3.05358i	0.0452524	−	0.149177i	0.976655	+	0.214813i	$0.0689142\pi$
$420$	−1.69972	+	0.136225i	−0.0829378	+	0.00664712i
$421$	2.72157	−	27.6325i	0.132641	−	1.34673i	−0.666465	−	0.745537i	$-0.732193\pi$
$421$	2.72157	−	27.6325i	0.132641	−	1.34673i	0.799106	−	0.601190i	$-0.205307\pi$
$422$	16.3905	−	0.655765i	0.797879	−	0.0319222i
$423$	6.77208	+	1.34705i	0.329270	+	0.0654958i
$424$	1.82050	+	15.1027i	0.0884113	+	0.733453i
$425$	2.99620	+	15.0629i	0.145337	+	0.730658i
$426$	−8.10003	−	4.95571i	−0.392448	−	0.240105i
$427$	2.78243	−	5.20556i	0.134651	−	0.251914i
$428$	−7.00802	−	4.86939i	−0.338746	−	0.235371i
$429$	−2.24954	−	22.8400i	−0.108609	−	1.10272i
$430$	13.0026	−	1.80798i	0.627040	−	0.0871887i
$431$	12.5426	+	30.2804i	0.604154	+	1.45856i	0.869269	+	0.494340i	$0.164590\pi$
$431$	12.5426	+	30.2804i	0.604154	+	1.45856i	−0.265115	+	0.964217i	$0.585410\pi$
$432$	−3.78297	−	1.29967i	−0.182008	−	0.0625303i
$433$	−12.3725	+	29.8699i	−0.594586	+	1.43546i	0.284446	+	0.958692i	$0.408191\pi$
$433$	−12.3725	+	29.8699i	−0.594586	+	1.43546i	−0.879031	+	0.476764i	$0.841809\pi$
$434$	−2.12313	+	8.16023i	−0.101913	+	0.391703i
$435$	−0.0842357	−	0.0691304i	−0.00403879	−	0.00331455i
$436$	−29.4257	−	0.535604i	−1.40924	−	0.0256508i
$437$	−10.2914	+	3.12185i	−0.492302	+	0.149338i
$438$	17.9079	+	2.82316i	0.855672	+	0.134896i
$439$	−18.1934	−	12.1564i	−0.868322	−	0.580194i	0.0396557	−	0.999213i	$-0.487374\pi$
$439$	−18.1934	−	12.1564i	−0.868322	−	0.580194i	−0.907977	+	0.419019i	$0.862374\pi$
$440$	12.5527	−	13.1119i	0.598425	−	0.625087i
$441$	−3.56246	−	5.33160i	−0.169641	−	0.253886i
$442$	−21.5406	−	7.92918i	−1.02458	−	0.377153i
$443$	5.41737	+	6.60108i	0.257387	+	0.313627i	0.885631	−	0.464389i	$-0.153726\pi$
$443$	5.41737	+	6.60108i	0.257387	+	0.313627i	−0.628244	+	0.778016i	$0.716226\pi$
$444$	16.0187	−	4.54256i	0.760212	−	0.215580i
$445$	−0.603598	+	0.322630i	−0.0286133	+	0.0152941i
$446$	−4.87147	−	5.47414i	−0.230671	−	0.259208i
$447$		−	13.9337i		−	0.659042i
$448$	−5.95744	+	1.45741i	−0.281462	+	0.0688561i
$449$		−	24.0135i		−	1.13327i	−0.823969	−	0.566635i	$-0.808245\pi$
$449$		−	24.0135i		−	1.13327i	0.823969	−	0.566635i	$-0.191755\pi$
$450$	−3.97570	+	3.53800i	−0.187416	+	0.166783i
$451$	−8.85142	+	4.73118i	−0.416797	+	0.222783i
$452$	19.0363	+	10.6250i	0.895393	+	0.499758i
$453$	4.73295	+	5.76712i	0.222373	+	0.270963i
$454$	9.45177	−	25.6769i	0.443594	−	1.20508i
$455$	−1.88381	−	2.81932i	−0.0883144	−	0.132172i
$456$	−14.9179	+	6.56350i	−0.698593	+	0.307364i
$457$	−16.4018	−	10.9594i	−0.767246	−	0.512657i	0.109281	−	0.994011i	$-0.465145\pi$
$457$	−16.4018	−	10.9594i	−0.767246	−	0.512657i	−0.876527	+	0.481354i	$0.840145\pi$
$458$	0.607920	−	3.85616i	0.0284062	−	0.180187i
$459$	−3.90535	+	1.18468i	−0.182286	+	0.0552959i
$460$	2.98830	−	2.88146i	0.139330	−	0.134349i
$461$	15.7334	+	12.9121i	0.732778	+	0.601375i	0.924996	−	0.379977i	$-0.124068\pi$
$461$	15.7334	+	12.9121i	0.732778	+	0.601375i	−0.192218	+	0.981352i	$0.561568\pi$
$462$	−6.05500	−	1.57539i	−0.281704	−	0.0732938i
$463$	−5.54355	+	13.3833i	−0.257631	+	0.621975i	−0.998781	−	0.0493640i	$-0.984281\pi$
$463$	−5.54355	+	13.3833i	−0.257631	+	0.621975i	0.741150	+	0.671339i	$0.234281\pi$
$464$	−0.338711	−	0.197218i	−0.0157243	−	0.00915562i
$465$	−3.30983	−	7.99064i	−0.153490	−	0.370557i
$466$	3.10913	+	22.3601i	0.144028	+	1.03581i
$467$	2.52597	+	25.6466i	0.116888	+	1.18678i	0.857368	+	0.514704i	$0.172098\pi$
$467$	2.52597	+	25.6466i	0.116888	+	1.18678i	−0.740480	+	0.672078i	$0.765402\pi$
$468$	−1.40954	−	7.82820i	−0.0651558	−	0.361859i
$469$	−3.88458	+	7.26753i	−0.179373	+	0.335583i
$470$	−5.66742	+	9.26330i	−0.261419	+	0.427284i
$471$	2.91436	+	14.6515i	0.134287	+	0.675105i
$472$	−23.8817	+	13.4420i	−1.09924	+	0.618719i
$473$	47.2424	+	9.39709i	2.17221	+	0.432079i
$474$	0.599032	+	14.9725i	0.0275145	+	0.687711i
$475$	−2.12544	+	21.5799i	−0.0975218	+	0.990155i
$476$	−4.05704	+	4.76402i	−0.185954	+	0.218358i
$477$	−1.56123	+	5.14669i	−0.0714838	+	0.235651i
$478$	6.68009	+	19.2192i	0.305540	+	0.879066i
$479$	−9.62518	+	9.62518i	−0.439786	+	0.439786i	−0.891940	−	0.452154i	$-0.850656\pi$
$479$	−9.62518	+	9.62518i	−0.439786	+	0.439786i	0.452154	+	0.891940i	$0.350656\pi$
$480$	3.97351	−	4.87732i	0.181365	−	0.222618i
$481$	23.4119	+	23.4119i	1.06749	+	1.06749i
$482$	0.142739	−	0.294826i	0.00650160	−	0.0134289i
$483$	−1.36923	−	0.415351i	−0.0623021	−	0.0188991i
$484$	39.7123	−	20.3063i	1.80510	−	0.923012i
$485$	0.384102	+	0.0378308i	0.0174412	+	0.00171781i
$486$	−1.03918	−	0.959224i	−0.0471380	−	0.0435113i
$487$	7.55370	−	37.9750i	0.342291	−	1.72081i	−0.299642	−	0.954052i	$-0.596867\pi$
$487$	7.55370	−	37.9750i	0.342291	−	1.72081i	0.641933	−	0.766761i	$-0.278133\pi$
$488$	6.77392	+	20.6963i	0.306641	+	0.936877i
$489$	16.3581	−	3.25383i	0.739740	−	0.147143i
$490$	9.80459	−	2.36132i	0.442926	−	0.106673i
$491$	−20.3609	−	10.8831i	−0.918875	−	0.491149i	−0.0570593	−	0.998371i	$-0.518172\pi$
$491$	−20.3609	−	10.8831i	−0.918875	−	0.491149i	−0.861815	+	0.507222i	$0.830672\pi$
$492$	−2.92689	+	1.87955i	−0.131954	+	0.0847367i
$493$	−0.397963	+	0.0391960i	−0.0179234	+	0.00176530i
$494$	−25.8542	−	19.5420i	−1.16324	−	0.879234i
$495$	5.92916	−	2.45594i	0.266496	−	0.110386i
$496$	−16.3302	−	26.4776i	−0.733249	−	1.18888i
$497$	−4.75578	−	1.96991i	−0.213326	−	0.0883624i
$498$	9.45922	+	16.1125i	0.423878	+	0.722017i
$499$	−14.6863	+	17.8953i	−0.657448	+	0.801102i	−0.989862	−	0.142031i	$-0.954637\pi$
$499$	−14.6863	+	17.8953i	−0.657448	+	0.801102i	0.332415	+	0.943133i	$0.392137\pi$
$500$	−7.13003	−	18.1403i	−0.318865	−	0.811261i
$501$	−6.75081	−	22.2544i	−0.301604	−	0.994254i
$502$	9.94589	+	13.6687i	0.443907	+	0.610064i
$503$	10.0824	−	15.0893i	0.449550	−	0.672799i	−0.535605	−	0.844469i	$-0.679916\pi$
$503$	10.0824	−	15.0893i	0.449550	−	0.672799i	0.985155	+	0.171670i	$0.0549162\pi$
$504$	−2.13543	−	0.376598i	−0.0951196	−	0.0167750i
$505$	1.47532	−	0.985775i	0.0656508	−	0.0438664i
$506$	13.8279	−	6.38680i	0.614727	−	0.283928i
$507$	2.17749	−	1.78702i	0.0967057	−	0.0793643i
$508$	−4.08457	−	0.477498i	−0.181224	−	0.0211856i
$509$	18.1348	+	33.9278i	0.803810	+	1.50382i	0.862789	+	0.505564i	$0.168716\pi$
$509$	18.1348	+	33.9278i	0.803810	+	1.50382i	−0.0589786	+	0.998259i	$0.518784\pi$
$510$	0.373267	−	6.40768i	0.0165286	−	0.283737i
$511$	9.82769			0.434751
$512$	11.3154	−	19.5949i	0.500075	−	0.865982i
$513$	−5.76218			−0.254407
$514$	0.770641	−	13.2292i	0.0339915	−	0.583514i
$515$	−0.458982	−	0.858695i	−0.0202252	−	0.0378386i
$516$	16.5809	+	1.93836i	0.729935	+	0.0853315i
$517$	−30.8010	+	25.2777i	−1.35463	+	1.11171i
$518$	8.19424	−	3.78473i	0.360034	−	0.166291i
$519$	10.1493	−	6.78152i	0.445503	−	0.297676i
$520$	12.3197	+	2.17267i	0.540256	+	0.0952779i
$521$	9.36926	−	14.0221i	0.410475	−	0.614319i	−0.567417	−	0.823431i	$-0.692057\pi$
$521$	9.36926	−	14.0221i	0.410475	−	0.614319i	0.977892	+	0.209112i	$0.0670573\pi$
$522$	−0.0815317	−	0.112050i	−0.00356855	−	0.00490428i
$523$	−6.27717	−	20.6931i	−0.274481	−	0.904844i	−0.980478	−	0.196629i	$-0.937001\pi$
$523$	−6.27717	−	20.6931i	−0.274481	−	0.904844i	0.705997	−	0.708215i	$-0.250499\pi$
$524$	2.05312	+	5.22358i	0.0896909	+	0.228193i
$525$	−1.83024	+	2.23016i	−0.0798784	+	0.0973321i
$526$	−17.6298	−	30.0298i	−0.768694	−	1.30936i
$527$	−29.3231	−	12.1460i	−1.27733	−	0.529089i
$528$	19.6468	−	12.1172i	0.855015	−	0.527335i
$529$	−18.0310	+	7.46869i	−0.783957	+	0.324725i
$530$	−6.74797	−	5.10047i	−0.293113	−	0.221550i
$531$	−9.64241	+	0.949694i	−0.418445	+	0.0412132i
$532$	−7.43417	+	4.77398i	−0.322312	+	0.206978i
$533$	−6.10017	−	3.26061i	−0.264228	−	0.141233i
$534$	−0.846141	+	0.203783i	−0.0366161	+	0.00881855i
$535$	4.65399	−	0.925737i	0.201210	−	0.0400231i
$536$	−9.45715	−	28.8943i	−0.408487	−	1.24804i
$537$	−3.29364	+	16.5583i	−0.142131	+	0.714542i
$538$	21.2864	+	19.6487i	0.917723	+	0.847114i
$539$	36.8253	+	3.62698i	1.58618	+	0.156225i
$540$	1.98034	−	1.01261i	0.0852202	−	0.0435760i
$541$	20.2475	+	6.14200i	0.870506	+	0.264065i	0.693773	−	0.720194i	$-0.255947\pi$
$541$	20.2475	+	6.14200i	0.870506	+	0.264065i	0.176733	+	0.984259i	$0.443447\pi$
$542$	7.58445	−	15.6655i	0.325780	−	0.672892i
$543$	−15.7253	−	15.7253i	−0.674837	−	0.674837i
$544$	−2.34524	−	22.9666i	−0.100551	−	0.984687i
$545$	11.5718	−	11.5718i	0.495681	−	0.495681i
$546$	−1.41562	−	4.07288i	−0.0605831	−	0.174303i
$547$	7.34085	−	24.1996i	0.313872	−	1.03470i	−0.648101	−	0.761554i	$-0.724437\pi$
$547$	7.34085	−	24.1996i	0.313872	−	1.03470i	0.961973	−	0.273144i	$-0.0880635\pi$
$548$	−7.41029	+	8.70159i	−0.316552	+	0.371713i
$549$	−0.754655	+	7.66214i	−0.0322079	+	0.327012i
$550$	−1.22776	−	30.6873i	−0.0523519	−	1.30851i
$551$	−0.553764	−	0.110151i	−0.0235912	−	0.00469257i
$552$	4.60028	−	2.58930i	0.195801	−	0.110208i
$553$	1.58473	+	7.96695i	0.0673894	+	0.338789i
$554$	−9.08768	+	14.8537i	−0.386099	+	0.631072i
$555$	−4.36440	+	8.16523i	−0.185259	+	0.346595i
$556$	4.06195	+	22.5590i	0.172265	+	0.956716i
$557$	−2.99915	−	30.4508i	−0.127078	−	1.29024i	−0.821306	−	0.570488i	$-0.806754\pi$
$557$	−2.99915	−	30.4508i	−0.127078	−	1.29024i	0.694228	−	0.719755i	$-0.255746\pi$
$558$	−1.51475	−	10.8937i	−0.0641245	−	0.461168i
$559$	12.7036	+	30.6692i	0.537305	+	1.29717i
$560$	1.71601	−	2.94715i	0.0725147	−	0.124540i
$561$	9.01252	−	21.7581i	0.380509	−	0.918629i
$562$	22.3669	+	5.81942i	0.943490	+	0.245477i
$563$	12.6584	+	10.3885i	0.533490	+	0.437824i	0.862171	−	0.506617i	$-0.169104\pi$
$563$	12.6584	+	10.3885i	0.533490	+	0.437824i	−0.328681	+	0.944441i	$0.606604\pi$
$564$	−9.94088	+	9.58546i	−0.418587	+	0.403621i
$565$	−11.6004	+	3.51894i	−0.488032	+	0.148043i
$566$	4.25996	−	27.0218i	0.179060	−	1.13581i
$567$	−0.637437	−	0.425922i	−0.0267698	−	0.0178870i
$568$	17.3834	−	7.64827i	0.729391	−	0.320914i
$569$	−17.0951	−	25.5847i	−0.716665	−	1.07257i	−0.993740	−	0.111717i	$-0.964365\pi$
$569$	−17.0951	−	25.5847i	−0.716665	−	1.07257i	0.277075	−	0.960848i	$-0.410635\pi$
$570$	3.13059	−	8.50461i	0.131126	−	0.356219i
$571$	6.25306	+	7.61937i	0.261682	+	0.318861i	0.887232	−	0.461324i	$-0.152625\pi$
$571$	6.25306	+	7.61937i	0.261682	+	0.318861i	−0.625550	+	0.780184i	$0.715125\pi$
$572$	40.0806	+	22.3707i	1.67585	+	0.935366i
$573$	−11.0017	+	5.88051i	−0.459601	+	0.245662i
$574$	−1.40863	+	1.25355i	−0.0587950	+	0.0523221i
$575$		−	7.02361i		−	0.292905i
$576$	6.45183	−	4.73010i	0.268826	−	0.197088i
$577$		−	21.8507i		−	0.909655i	−0.890580	−	0.454827i	$-0.849701\pi$
$577$		−	21.8507i		−	0.909655i	0.890580	−	0.454827i	$-0.150299\pi$
$578$	0.324148	+	0.364249i	0.0134828	+	0.0151508i
$579$	−11.9672	+	6.39659i	−0.497339	+	0.265833i
$580$	0.209674	−	0.0594592i	0.00870625	−	0.00246891i
$581$	6.42543	+	7.82941i	0.266572	+	0.324819i
$582$	0.460594	+	0.169547i	0.0190922	+	0.00702793i
$583$	−17.2430	−	25.8060i	−0.714133	−	1.06878i
$584$	−25.0737	+	26.1908i	−1.03756	+	1.08378i
$585$	3.67751	+	2.45723i	0.152046	+	0.101594i
$586$	−40.4285	−	6.37351i	−1.67009	−	0.263287i
$587$	19.6366	−	5.95671i	0.810491	−	0.245860i	0.142275	−	0.989827i	$-0.454558\pi$
$587$	19.6366	−	5.95671i	0.810491	−	0.245860i	0.668216	+	0.743967i	$0.267058\pi$
$588$	12.8224	+	0.233392i	0.528787	+	0.00962492i
$589$	−34.6411	−	28.4292i	−1.42736	−	1.17141i
$590$	3.83702	−	14.7475i	0.157968	−	0.607147i
$591$	−2.86165	+	6.90863i	−0.117713	+	0.284183i
$592$	−10.8199	+	31.4938i	−0.444696	+	1.29439i
$593$	1.42534	+	3.44108i	0.0585317	+	0.141308i	0.950440	−	0.310909i	$-0.100633\pi$
$593$	1.42534	+	3.44108i	0.0585317	+	0.141308i	−0.891908	+	0.452217i	$0.850633\pi$
$594$	8.08329	−	1.12397i	0.331661	−	0.0461169i
$595$	−0.341047	−	3.46271i	−0.0139816	−	0.141957i
$596$	22.8853	+	15.9014i	0.937419	+	0.651348i
$597$	10.9621	−	20.5087i	0.448650	−	0.839366i
$598$	8.95432	+	5.47838i	0.366170	+	0.224028i
$599$	0.771631	+	3.87925i	0.0315280	+	0.158502i	0.993342	−	0.115201i	$-0.0367514\pi$
$599$	0.771631	+	3.87925i	0.0315280	+	0.158502i	−0.961814	+	0.273703i	$0.911751\pi$
$600$	−1.27382	−	10.5675i	−0.0520034	−	0.431416i
$601$	−4.27956	−	0.851257i	−0.174567	−	0.0347235i	0.107033	−	0.994255i	$-0.465865\pi$
$601$	−4.27956	−	0.851257i	−0.174567	−	0.0347235i	−0.281600	+	0.959532i	$0.590865\pi$
$602$	9.04243	−	0.361777i	0.368542	−	0.0147449i
$603$	1.05358	−	10.6972i	0.0429052	−	0.435623i
$604$	−14.8735	+	1.19205i	−0.605194	+	0.0485038i
$605$	−7.19951	+	23.7336i	−0.292702	+	0.964908i
$606$	2.13129	−	0.740780i	0.0865776	−	0.0300921i
$607$	14.1173	−	14.1173i	0.573002	−	0.573002i	−0.359964	−	0.932966i	$-0.617211\pi$
$607$	14.1173	−	14.1173i	0.573002	−	0.573002i	0.932966	+	0.359964i	$0.117211\pi$
$608$	6.24439	−	31.9921i	0.253244	−	1.29745i
$609$	−0.0531178	−	0.0531178i	−0.00215244	−	0.00215244i
$610$	−10.8988	−	5.27665i	−0.441281	−	0.213645i
$611$	−26.2781	−	7.97136i	−1.06310	−	0.322487i
$612$	2.51110	−	7.76629i	0.101505	−	0.313934i
$613$	7.01067	+	0.690490i	0.283158	+	0.0278886i	0.238599	−	0.971118i	$-0.423312\pi$
$613$	7.01067	+	0.690490i	0.283158	+	0.0278886i	0.0445589	+	0.999007i	$0.485812\pi$
$614$	15.9275	−	17.2551i	0.642781	−	0.696359i
$615$	0.377341	−	1.89702i	0.0152159	−	0.0764953i
$616$	9.49757	−	8.14712i	0.382668	−	0.328257i
$617$	33.9476	−	6.75259i	1.36668	−	0.271849i	0.543393	−	0.839478i	$-0.317139\pi$
$617$	33.9476	−	6.75259i	1.36668	−	0.271849i	0.823284	+	0.567629i	$0.192139\pi$
$618$	−0.289907	−	1.20374i	−0.0116618	−	0.0484217i
$619$	−32.7471	−	17.5037i	−1.31622	−	0.703532i	−0.344300	−	0.938860i	$-0.611884\pi$
$619$	−32.7471	−	17.5037i	−1.31622	−	0.703532i	−0.971916	+	0.235328i	$0.924384\pi$
$620$	16.9014	+	3.68287i	0.678777	+	0.147908i
$621$	1.85740	−	0.182937i	0.0745347	−	0.00734103i
$622$	−10.3793	+	13.7320i	−0.416174	+	0.550602i
$623$	−0.435891	+	0.180552i	−0.0174636	+	0.00723366i
$624$	14.4660	+	6.61862i	0.579102	+	0.264957i
$625$	−7.37063	−	3.05301i	−0.294825	−	0.122121i
$626$	29.8524	−	17.5256i	1.19314	−	0.700464i
$627$	21.0949	−	25.7042i	0.842448	−	1.02653i
$628$	−27.3902	−	11.9339i	−1.09299	−	0.476215i
$629$	9.86259	+	32.5126i	0.393247	+	1.29636i
$630$	0.974953	−	0.709414i	0.0388430	−	0.0282637i
$631$	−21.4276	+	32.0687i	−0.853020	+	1.27663i	0.106306	+	0.994333i	$0.466098\pi$
$631$	−21.4276	+	32.0687i	−0.853020	+	1.27663i	−0.959326	+	0.282301i	$0.908902\pi$
$632$	−25.2751	−	16.1031i	−1.00539	−	0.640546i
$633$	−9.64433	+	6.44413i	−0.383328	+	0.256131i
$634$	9.70316	+	21.0081i	0.385362	+	0.834339i
$635$	1.76765	−	1.45067i	0.0701470	−	0.0575682i
$636$	−6.67143	−	8.43774i	−0.264539	−	0.334578i
$637$	12.0215	+	22.4906i	0.476309	+	0.891112i
$638$	0.798316	+	0.0465044i	0.0316056	+	0.00184113i
$639$	6.71452			0.265622
$640$	3.47606	+	12.0924i	0.137403	+	0.477992i
$641$	0.661561			0.0261301			0.0130650	−	0.999915i	$-0.495841\pi$
$641$	0.661561			0.0261301			0.0130650	+	0.999915i	$0.495841\pi$
$642$	6.02400	+	0.350916i	0.237748	+	0.0138496i
$643$	−1.18649	−	2.21976i	−0.0467904	−	0.0875387i	0.857439	−	0.514585i	$-0.172054\pi$
$643$	−1.18649	−	2.21976i	−0.0467904	−	0.0875387i	−0.904230	+	0.427046i	$0.859554\pi$
$644$	2.24478	−	1.77487i	0.0884569	−	0.0699398i
$645$	−7.17560	+	5.88886i	−0.282539	+	0.231874i
$646$	−13.9448	−	30.1917i	−0.548652	−	1.18788i
$647$	−24.0580	+	16.0750i	−0.945816	+	0.631974i	−0.929866	−	0.367898i	$-0.880077\pi$
$647$	−24.0580	+	16.0750i	−0.945816	+	0.631974i	−0.0159505	+	0.999873i	$0.505077\pi$
$648$	2.76140	−	0.612103i	0.108478	−	0.0240457i
$649$	31.0636	−	46.4900i	1.21935	−	1.82489i
$650$	17.1146	−	12.4532i	0.671289	−	0.488456i
$651$	−1.73075	−	5.70552i	−0.0678335	−	0.223617i
$652$	−13.3240	+	30.5806i	−0.521808	+	1.19763i
$653$	−3.37890	+	4.11720i	−0.132227	+	0.161118i	−0.834915	−	0.550380i	$-0.814483\pi$
$653$	−3.37890	+	4.11720i	−0.132227	+	0.161118i	0.702688	+	0.711498i	$0.251983\pi$
$654$	17.9465	−	10.5359i	0.701762	−	0.411987i
$655$	−2.88333	−	1.19431i	−0.112661	−	0.0466657i
$656$	0.253171	−	6.95223i	0.00988467	−	0.271439i
$657$	−11.8434	+	4.90569i	−0.462054	+	0.191389i
$658$	−4.51398	+	5.97204i	−0.175973	+	0.232814i
$659$	−41.9940	+	4.13605i	−1.63586	+	0.161118i	−0.873764	−	0.486351i	$-0.838328\pi$
$659$	−41.9940	+	4.13605i	−1.63586	+	0.161118i	−0.762092	+	0.647469i	$0.775828\pi$
$660$	−2.73274	+	12.5411i	−0.106372	+	0.488160i
$661$	−32.8063	−	17.5353i	−1.27602	−	0.682046i	−0.312558	−	0.949899i	$-0.601186\pi$
$661$	−32.8063	−	17.5353i	−1.27602	−	0.682046i	−0.963460	+	0.267853i	$0.913686\pi$
$662$	−4.24099	−	17.6093i	−0.164831	−	0.684406i
$663$	15.9188	−	3.16644i	0.618234	−	0.122974i
$664$	−37.2589	−	2.85165i	−1.44592	−	0.110665i
$665$	0.958429	−	4.81835i	0.0371663	−	0.186848i
$666$	−7.98568	+	8.65130i	−0.309439	+	0.335231i
$667$	0.181999	+	0.0179253i	0.00704702	+	0.000694071i
$668$	44.2558	+	14.3094i	1.71231	+	0.553647i
$669$	4.95846	+	1.50413i	0.191705	+	0.0581531i
$670$	15.2160	+	7.36679i	0.587844	+	0.284604i
$671$	−31.4168	−	31.4168i	−1.21283	−	1.21283i
$672$	3.05554	−	3.07754i	0.117870	−	0.118719i
$673$	5.89475	−	5.89475i	0.227226	−	0.227226i	−0.584307	−	0.811533i	$-0.698634\pi$
$673$	5.89475	−	5.89475i	0.227226	−	0.227226i	0.811533	+	0.584307i	$0.198634\pi$
$674$	−20.8498	+	7.24685i	−0.803105	+	0.279138i
$675$	1.09240	−	3.60118i	0.0420467	−	0.138609i
$676$	0.450082	+	5.61578i	0.0173108	+	0.215992i
$677$	0.274415	−	2.78618i	0.0105466	−	0.107082i	−0.988470	−	0.151416i	$-0.951617\pi$
$677$	0.274415	−	2.78618i	0.0105466	−	0.107082i	0.999017	+	0.0443344i	$0.0141167\pi$
$678$	−15.4031	+	0.616260i	−0.591553	+	0.0236673i
$679$	0.260953	+	0.0519067i	0.0100144	+	0.00199200i
$680$	10.0983	+	7.92565i	0.387251	+	0.303935i
$681$	3.77448	+	18.9756i	0.144638	+	0.727145i
$682$	54.1405	+	33.1239i	2.07315	+	1.26838i
$683$	−18.7081	+	35.0004i	−0.715846	+	1.33925i	0.215999	+	0.976394i	$0.430699\pi$
$683$	−18.7081	+	35.0004i	−0.715846	+	1.33925i	−0.931844	+	0.362859i	$0.881801\pi$
$684$	6.57592	−	9.46405i	0.251436	−	0.361867i
$685$	−0.622931	−	6.32473i	−0.0238010	−	0.241655i
$686$	14.4029	−	2.00270i	0.549905	−	0.0764633i
$687$	1.05636	+	2.55027i	0.0403025	+	0.0972989i
$688$	−22.1061	+	25.0211i	−0.842789	+	0.953922i
$689$	8.18546	−	19.7615i	0.311841	−	0.752852i
$690$	−0.739117	+	2.84079i	−0.0281377	+	0.108147i
$691$	−7.36696	−	6.04591i	−0.280252	−	0.229997i	0.483757	−	0.875202i	$-0.339272\pi$
$691$	−7.36696	−	6.04591i	−0.280252	−	0.229997i	−0.764009	+	0.645205i	$0.776772\pi$
$692$	−0.444286	+	24.4088i	−0.0168892	+	0.927883i
$693$	4.23357	−	1.28424i	0.160820	−	0.0487843i
$694$	−27.2889	−	4.30207i	−1.03587	−	0.163304i
$695$	−10.5977	−	7.08116i	−0.401994	−	0.268604i
$696$	0.277081	−	0.00603787i	0.0105027	−	0.000228865i
$697$	−3.94335	−	5.90165i	−0.149365	−	0.223541i
$698$	−4.42328	−	1.62823i	−0.167424	−	0.0616294i
$699$	−10.1269	−	12.3397i	−0.383034	−	0.466729i
$700$	−1.57420	−	5.55117i	−0.0594990	−	0.209815i
$701$	−46.0752	+	24.6277i	−1.74023	+	0.930175i	−0.793250	+	0.608896i	$0.791613\pi$
$701$	−46.0752	+	24.6277i	−1.74023	+	0.930175i	−0.946985	+	0.321279i	$0.895887\pi$
$702$	3.73903	+	4.20160i	0.141121	+	0.158579i
$703$			47.9710i			1.80926i
$704$	−2.51939	+	46.0971i	−0.0949530	+	1.73735i
$705$		−	7.67882i		−	0.289201i
$706$	−5.36322	+	4.77277i	−0.201847	+	0.179625i
$707$	1.07873	−	0.576594i	0.0405699	−	0.0216851i
$708$	9.44429	−	16.9209i	0.354938	−	0.635927i
$709$	−24.0765	−	29.3373i	−0.904211	−	1.10178i	−0.994381	−	0.105858i	$-0.966241\pi$
$709$	−24.0765	−	29.3373i	−0.904211	−	1.10178i	0.0901706	−	0.995926i	$-0.471259\pi$
$710$	−3.64799	+	9.91021i	−0.136907	+	0.371923i
$711$	−5.88662	−	8.80995i	−0.220766	−	0.330399i
$712$	0.630932	−	1.62230i	0.0236452	−	0.0607982i
$713$	12.0689	+	8.06416i	0.451983	+	0.302005i
$714$	0.689035	−	4.37069i	0.0257865	−	0.163569i
$715$	−24.4244	+	7.40905i	−0.913419	+	0.277083i
$716$	−23.4372	−	24.3062i	−0.875890	−	0.908367i
$717$	−11.1217	−	9.12734i	−0.415347	−	0.340867i
$718$	24.5657	+	6.39152i	0.916785	+	0.238529i
$719$	−0.455104	+	1.09872i	−0.0169725	+	0.0409753i	−0.932139	−	0.362102i	$-0.882059\pi$
$719$	−0.455104	+	1.09872i	−0.0169725	+	0.0409753i	0.915166	+	0.403077i	$0.132059\pi$
$720$	−0.596840	+	4.40821i	−0.0222429	+	0.164284i
$721$	−0.256858	−	0.620110i	−0.00956589	−	0.0230941i
$722$	−2.76626	−	19.8943i	−0.102950	−	0.740389i
$723$	0.0227028	+	0.230506i	0.000844328	+	0.00857260i
$724$	43.7739	−	7.88187i	1.62685	−	0.292928i
$725$	0.173824	−	0.325202i	0.00645567	−	0.0120777i
$726$	−16.4598	+	26.9032i	−0.610879	+	0.998471i
$727$	6.71490	+	33.7581i	0.249042	+	1.25202i	0.879539	+	0.475827i	$0.157851\pi$
$727$	6.71490	+	33.7581i	0.249042	+	1.25202i	−0.630497	+	0.776192i	$0.717149\pi$
$728$	8.30500	+	2.32296i	0.307804	+	0.0860948i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−0.805990	−	20.1453i	−0.0298310	−	0.745612i
$731$	−3.33890	+	33.9004i	−0.123494	+	1.25385i
$732$	−11.7234	−	9.98366i	−0.433309	−	0.369007i
$733$	2.04906	−	6.75484i	0.0756837	−	0.249496i	−0.910933	−	0.412555i	$-0.864636\pi$
$733$	2.04906	−	6.75484i	0.0756837	−	0.249496i	0.986616	+	0.163060i	$0.0521363\pi$
$734$	1.10219	+	3.17110i	0.0406827	+	0.117048i
$735$	−5.04246	+	5.04246i	−0.185994	+	0.185994i
$736$	−0.997148	+	10.5107i	−0.0367554	+	0.387428i
$737$	43.8614	+	43.8614i	1.61566	+	1.61566i
$738$	1.07181	−	2.21380i	0.0394539	−	0.0814912i
$739$	2.38916	+	0.724745i	0.0878868	+	0.0266602i	0.333922	−	0.942601i	$-0.391628\pi$
$739$	2.38916	+	0.724745i	0.0878868	+	0.0266602i	−0.246035	+	0.969261i	$0.579128\pi$
$740$	−8.43017	−	16.4866i	−0.309899	−	0.606059i
$741$	22.8061	+	2.24621i	0.837803	+	0.0825164i
$742$	−4.28473	−	3.95507i	−0.157297	−	0.145195i
$743$	−5.88174	+	29.5695i	−0.215780	+	1.08480i	0.709265	+	0.704942i	$0.249027\pi$
$743$	−5.88174	+	29.5695i	−0.215780	+	1.08480i	−0.925045	+	0.379858i	$0.875973\pi$
$744$	19.6210	+	9.94424i	0.719340	+	0.364574i
$745$	−15.1980	+	3.02308i	−0.556813	+	0.110757i
$746$	−30.2069	+	7.27497i	−1.10595	+	0.266356i
$747$	−11.6515	−	6.22787i	−0.426307	−	0.227866i
$748$	25.4512	+	39.6334i	0.930589	+	1.44914i
$749$	3.25537	−	0.320626i	0.118949	−	0.0117154i
$750$	10.9950	+	8.31057i	0.401479	+	0.303459i
$751$	−2.68270	+	1.11121i	−0.0978930	+	0.0405486i	−0.431092	−	0.902308i	$-0.641872\pi$
$751$	−2.68270	+	1.11121i	−0.0978930	+	0.0405486i	0.333200	+	0.942856i	$0.391872\pi$
$752$	−4.39884	−	27.2664i	−0.160409	−	0.994305i
$753$	−11.0432	−	4.57426i	−0.402438	−	0.166695i
$754$	0.279015	+	0.475263i	0.0101611	+	0.0173081i
$755$	5.26355	−	6.41365i	0.191560	−	0.233417i
$756$	1.42701	−	0.560883i	0.0518998	−	0.0203991i
$757$	13.6108	+	44.8688i	0.494693	+	1.63078i	0.748217	+	0.663454i	$0.230910\pi$
$757$	13.6108	+	44.8688i	0.494693	+	1.63078i	−0.253524	+	0.967329i	$0.581590\pi$
$758$	−17.0535	−	23.4367i	−0.619409	−	0.851259i
$759$	−5.98371	+	8.95526i	−0.217195	+	0.325055i
$760$	10.3956	+	14.8474i	0.377090	+	0.538573i
$761$	−19.5224	+	13.0445i	−0.707687	+	0.472861i	−0.856595	−	0.515990i	$-0.827424\pi$
$761$	−19.5224	+	13.0445i	−0.707687	+	0.472861i	0.148908	+	0.988851i	$0.452424\pi$
$762$	2.63991	−	1.21931i	0.0956340	−	0.0441711i
$763$	8.72059	−	7.15680i	0.315706	−	0.259094i
$764$	2.89692	−	24.7805i	0.104807	−	0.896528i
$765$	2.13948	+	4.00269i	0.0773531	+	0.144717i
$766$	1.10993	−	19.0536i	0.0401034	−	0.688435i
$767$	38.5338			1.39138
$768$	0.405961	+	15.9948i	0.0146488	+	0.577164i
$769$	13.0231			0.469625			0.234812	−	0.972041i	$-0.424552\pi$
$769$	13.0231			0.469625			0.234812	+	0.972041i	$0.424552\pi$
$770$	−0.404638	+	6.94621i	−0.0145822	+	0.250324i
$771$	4.41713	+	8.26387i	0.159079	+	0.297616i
$772$	3.15116	−	26.9553i	0.113413	−	0.970144i
$773$	28.2782	−	23.2073i	1.01710	−	0.834710i	0.0307728	−	0.999526i	$-0.490203\pi$
$773$	28.2782	−	23.2073i	1.01710	−	0.834710i	0.986324	+	0.164816i	$0.0527032\pi$
$774$	−10.7165	+	4.94969i	−0.385196	+	0.177913i
$775$	24.3347	−	16.2599i	0.874127	−	0.584073i
$776$	−0.804109	+	0.563008i	−0.0288658	+	0.0202108i
$777$	−3.54586	+	5.30676i	−0.127207	+	0.190379i
$778$	19.1946	+	26.3793i	0.688159	+	0.945742i
$779$	−2.90913	−	9.59011i	−0.104230	−	0.343601i
$780$	−8.23270	+	3.23585i	−0.294778	+	0.115862i
$781$	−24.5813	+	29.9524i	−0.879588	+	1.07178i
$782$	5.45354	+	9.28935i	0.195018	+	0.332186i
$783$	0.0905273	+	0.0374976i	0.00323518	+	0.00134006i
$784$	−15.0165	+	20.7937i	−0.536304	+	0.742632i
$785$	15.3486	−	6.35761i	0.547816	−	0.226913i
$786$	−3.16604	−	2.39306i	−0.112929	−	0.0853575i
$787$	−27.0571	+	2.66490i	−0.964483	+	0.0949933i	−0.567982	−	0.823041i	$-0.692276\pi$
$787$	−27.0571	+	2.66490i	−0.964483	+	0.0949933i	−0.396501	+	0.918034i	$0.629776\pi$
$788$	−8.08126	−	12.5844i	−0.287883	−	0.448300i
$789$	21.7157	+	11.6073i	0.773099	+	0.413230i
$790$	16.2011	−	3.90184i	0.576410	−	0.138821i
$791$	−8.19608	+	1.63030i	−0.291419	+	0.0579668i
$792$	−7.37876	+	14.5590i	−0.262193	+	0.517332i
$793$	5.97369	−	30.0318i	0.212132	−	1.06646i
$794$	−17.6296	−	16.2732i	−0.625651	−	0.577514i
$795$	5.95241	+	0.586262i	0.211110	+	0.0207926i
$796$	21.1742	+	41.4096i	0.750499	+	1.46773i
$797$	−38.0769	−	11.5505i	−1.34875	−	0.409140i	−0.468424	−	0.883504i	$-0.655178\pi$
$797$	−38.0769	−	11.5505i	−1.34875	−	0.409140i	−0.880329	+	0.474364i	$0.842678\pi$
$798$	2.72235	−	5.62296i	0.0963701	−	0.199051i
$799$	−19.9254	−	19.9254i	−0.704912	−	0.704912i
$800$	18.8102	+	9.96766i	0.665041	+	0.352410i
$801$	0.435167	−	0.435167i	0.0153759	−	0.0153759i
$802$	−1.32369	−	3.80836i	−0.0467410	−	0.134478i
$803$	21.4741	−	70.7907i	0.757806	−	2.49815i
$804$	16.3672	+	13.9383i	0.577225	+	0.491566i
$805$	−0.155970	+	1.58359i	−0.00549721	+	0.0558141i
$806$	1.74865	+	43.7067i	0.0615936	+	1.53950i
$807$	−20.0903	−	3.99622i	−0.707213	−	0.140673i
$808$	−1.21558	+	4.34591i	−0.0427640	+	0.152889i
$809$	−3.04698	−	15.3182i	−0.107126	−	0.538560i	−0.996658	−	0.0816865i	$-0.973969\pi$
$809$	−3.04698	−	15.3182i	−0.107126	−	0.538560i	0.889532	−	0.456873i	$-0.151031\pi$
$810$	−0.820801	+	1.34158i	−0.0288400	+	0.0471385i
$811$	−5.14517	+	9.62594i	−0.180671	+	0.338013i	−0.955912	−	0.293654i	$-0.905129\pi$
$811$	−5.14517	+	9.62594i	−0.180671	+	0.338013i	0.775240	+	0.631666i	$0.217629\pi$
$812$	0.147862	−	0.0266238i	0.00518894	−	0.000934313i
$813$	1.20631	+	12.2479i	0.0423073	+	0.429553i
$814$	−9.35718	−	67.2945i	−0.327969	−	2.35867i
$815$	−7.09816	−	17.1365i	−0.248638	−	0.600264i
$816$	9.88996	+	12.9874i	0.346218	+	0.454649i
$817$	−18.4057	+	44.4354i	−0.643935	+	1.55460i
$818$	−23.4754	−	6.10783i	−0.820798	−	0.213555i
$819$	2.35688	+	1.93424i	0.0823560	+	0.0675878i
$820$	2.68512	+	2.78468i	0.0937684	+	0.0972452i
$821$	−26.7352	+	8.11003i	−0.933065	+	0.283042i	−0.719982	−	0.693992i	$-0.755850\pi$
$821$	−26.7352	+	8.11003i	−0.933065	+	0.283042i	−0.213082	+	0.977034i	$0.568350\pi$
$822$	1.25854	−	7.98318i	0.0438966	−	0.278445i
$823$	45.5378	+	30.4274i	1.58735	+	1.06063i	0.959274	+	0.282478i	$0.0911563\pi$
$823$	45.5378	+	30.4274i	1.58735	+	1.06063i	0.628073	+	0.778154i	$0.283844\pi$
$824$	2.30793	+	0.897581i	0.0804005	+	0.0312687i
$825$	12.0651	+	18.0566i	0.420052	+	0.628652i
$826$	3.62882	−	9.85812i	0.126263	−	0.343008i
$827$	−31.6028	−	38.5081i	−1.09894	−	1.33906i	−0.935832	−	0.352448i	$-0.885349\pi$
$827$	−31.6028	−	38.5081i	−1.09894	−	1.33906i	−0.163104	−	0.986609i	$-0.552151\pi$
$828$	−1.81923	+	3.25944i	−0.0632227	+	0.113273i
$829$	41.8082	−	22.3469i	1.45206	−	0.776141i	0.458417	−	0.888737i	$-0.348417\pi$
$829$	41.8082	−	22.3469i	1.45206	−	0.776141i	0.993641	+	0.112596i	$0.0359165\pi$
$830$	15.5222	−	13.8133i	0.538783	−	0.479467i
$831$		−	12.3129i		−	0.427131i
$832$	−27.3796	+	16.2062i	−0.949215	+	0.561849i
$833$			26.1690i			0.906701i
$834$	−10.7750	−	12.1080i	−0.373108	−	0.419266i
$835$	−22.8091	+	12.1917i	−0.789341	+	0.421911i
$836$	18.1437	+	63.9812i	0.627514	+	2.21284i
$837$	4.93376	+	6.01180i	0.170536	+	0.207798i
$838$	−4.23492	−	1.55889i	−0.146293	−	0.0538511i
$839$	6.23926	+	9.33771i	0.215403	+	0.322373i	0.923398	−	0.383844i	$-0.125400\pi$
$839$	6.23926	+	9.33771i	0.215403	+	0.322373i	−0.707995	+	0.706218i	$0.750400\pi$
$840$	0.0525360	+	2.41090i	0.00181266	+	0.0831840i
$841$	−24.1046	−	16.1062i	−0.831194	−	0.555386i
$842$	−38.7883	−	6.11494i	−1.33673	−	0.210735i
$843$	−15.6386	+	4.74392i	−0.538623	+	0.163389i
$844$	0.422182	−	23.1944i	0.0145321	−	0.798385i
$845$	−2.42160	−	1.98736i	−0.0833056	−	0.0683671i
$846$	2.45875	−	9.45017i	0.0845335	−	0.324903i
$847$	−6.54279	+	15.7957i	−0.224813	+	0.542746i
$848$	21.4721	−	1.32813i	0.737354	−	0.0456081i
$849$	7.40236	+	17.8709i	0.254048	+	0.613327i
$850$	21.5125	−	2.99127i	0.737873	−	0.102600i
$851$	−1.52298	−	15.4631i	−0.0522071	−	0.530068i
$852$	−7.66275	+	11.0282i	−0.262521	+	0.377820i
$853$	−16.0077	+	29.9483i	−0.548093	+	1.02541i	0.443532	+	0.896258i	$0.353725\pi$
$853$	−16.0077	+	29.9483i	−0.548093	+	1.02541i	−0.991625	+	0.129151i	$0.958775\pi$
$854$	−7.12047	−	4.35641i	−0.243658	−	0.149073i
$855$	1.25017	+	6.28503i	0.0427549	+	0.214943i
$856$	−7.45107	+	9.49359i	−0.254672	+	0.324484i
$857$	−19.8131	−	3.94108i	−0.676804	−	0.134625i	−0.155292	−	0.987869i	$-0.549632\pi$
$857$	−19.8131	−	3.94108i	−0.676804	−	0.134625i	−0.521512	+	0.853244i	$0.674632\pi$
$858$	−32.4309	+	1.29752i	−1.10717	+	0.0442967i
$859$	3.01393	−	30.6009i	0.102834	−	1.04409i	−0.795850	−	0.605493i	$-0.792976\pi$
$859$	3.01393	−	30.6009i	0.102834	−	1.04409i	0.898684	−	0.438596i	$-0.144524\pi$
$860$	−1.48318	−	18.5060i	−0.0505760	−	0.631049i
$861$	0.387050	−	1.27593i	0.0131906	−	0.0434837i
$862$	43.7821	−	15.2175i	1.49122	−	0.518310i
$863$	20.6455	−	20.6455i	0.702782	−	0.702782i	−0.262225	−	0.965007i	$-0.584456\pi$
$863$	20.6455	−	20.6455i	0.702782	−	0.702782i	0.965007	+	0.262225i	$0.0844561\pi$
$864$	−2.14602	+	5.23398i	−0.0730091	+	0.178064i
$865$	−9.59886	−	9.59886i	−0.326371	−	0.326371i
$866$	41.1534	+	19.9244i	1.39845	+	0.677058i
$867$	−0.329936	−	0.100085i	−0.0112052	−	0.00339906i
$868$	11.3462	+	3.66860i	0.385114	+	0.124520i
$869$	60.8502	+	5.99322i	2.06420	+	0.203306i
$870$	−0.104528	+	0.113240i	−0.00354381	+	0.00383920i
$871$	−8.33993	+	41.9277i	−0.282588	+	1.42066i
$872$	−3.17623	+	41.4998i	−0.107561	+	1.40536i
$873$	−0.340385	+	0.0677068i	−0.0115203	+	0.00229153i
$874$	3.56110	+	14.7863i	0.120456	+	0.500154i
$875$	6.58917	+	3.52199i	0.222755	+	0.119065i
$876$	5.45859	−	25.0505i	0.184429	−	0.846379i
$877$	48.6245	−	4.78909i	1.64193	−	0.161716i	0.765564	−	0.643360i	$-0.222460\pi$
$877$	48.6245	−	4.78909i	1.64193	−	0.161716i	0.876367	+	0.481643i	$0.159960\pi$
$878$	−18.6589	+	24.6860i	−0.629709	+	0.833111i
$879$	26.7374	−	11.0750i	0.901829	−	0.373550i
$880$	−17.4793	−	18.8005i	−0.589228	−	0.633764i
$881$	−24.0849	−	9.97627i	−0.811439	−	0.336109i	−0.0619111	−	0.998082i	$-0.519720\pi$
$881$	−24.0849	−	9.97627i	−0.811439	−	0.336109i	−0.749528	+	0.661973i	$0.769720\pi$
$882$	−7.82025	+	4.59107i	−0.263322	+	0.154589i
$883$	1.93030	−	2.35208i	0.0649598	−	0.0791537i	−0.739517	−	0.673138i	$-0.764946\pi$
$883$	1.93030	−	2.35208i	0.0649598	−	0.0791537i	0.804477	+	0.593984i	$0.202446\pi$
$884$	−12.9661	+	29.7593i	−0.436098	+	1.00091i
$885$	3.12790	+	10.3113i	0.105143	+	0.346610i
$886$	9.76508	−	7.10546i	0.328064	−	0.238713i
$887$	−9.37872	+	14.0362i	−0.314907	+	0.471291i	−0.954832	−	0.297146i	$-0.903965\pi$
$887$	−9.37872	+	14.0362i	−0.314907	+	0.471291i	0.639925	+	0.768437i	$0.278965\pi$
$888$	−5.09585	−	22.9891i	−0.171006	−	0.771462i
$889$	1.31069	−	0.875778i	0.0439593	−	0.0293727i
$890$	0.405854	+	0.878706i	0.0136042	+	0.0294543i
$891$	−4.46084	+	3.66092i	−0.149444	+	0.122645i
$892$	−8.12914	+	6.42744i	−0.272184	+	0.215206i
$893$	−18.7552	−	35.0885i	−0.627618	−	1.17419i
$894$	−19.6719	−	1.14595i	−0.657927	−	0.0383263i
$895$	18.7753			0.627590
$896$	1.56764	+	8.53069i	0.0523712	+	0.284990i
$897$	−7.42269			−0.247836
$898$	−33.9028	−	1.97494i	−1.13135	−	0.0659047i
$899$	0.359228	+	0.672068i	0.0119809	+	0.0224147i
$900$	4.66805	+	5.90395i	0.155602	+	0.196798i
$901$	16.9669	−	13.9244i	0.565251	−	0.463889i
$902$	5.95161	+	12.8857i	0.198167	+	0.429047i
$903$	−5.32064	+	3.55514i	−0.177060	+	0.118308i
$904$	16.5662	−	26.0020i	0.550983	−	0.864815i
$905$	−13.7404	+	20.5640i	−0.456747	+	0.683569i
$906$	8.53138	−	6.20777i	0.283436	−	0.206239i
$907$	−12.9278	−	42.6172i	−0.429260	−	1.41508i	−0.858929	−	0.512094i	$-0.828870\pi$
$907$	−12.9278	−	42.6172i	−0.429260	−	1.41508i	0.429669	−	0.902986i	$-0.358630\pi$
$908$	−35.4738	−	15.4559i	−1.17724	−	0.512923i
$909$	−1.01216	+	1.23333i	−0.0335714	+	0.0409068i
$910$	−4.13530	+	2.42773i	−0.137084	+	0.0804785i
$911$	−43.4291	−	17.9889i	−1.43887	−	0.596000i	−0.479346	−	0.877626i	$-0.659126\pi$
$911$	−43.4291	−	17.9889i	−1.43887	−	0.596000i	−0.959524	+	0.281626i	$0.909126\pi$
$912$	8.03959	+	21.6011i	0.266217	+	0.715285i
$913$	70.4368	−	29.1759i	2.33112	−	0.965580i
$914$	−16.8216	+	22.2551i	−0.556409	+	0.736134i
$915$	8.52111	−	0.839256i	0.281699	−	0.0277450i
$916$	−5.39421	−	1.17542i	−0.178230	−	0.0388368i
$917$	−1.89738	−	1.01417i	−0.0626569	−	0.0334908i
$918$	1.35136	+	5.61108i	0.0446016	+	0.185193i
$919$	−29.7104	+	5.90977i	−0.980056	+	0.194945i	−0.659023	−	0.752123i	$-0.729030\pi$
$919$	−29.7104	+	5.90977i	−0.980056	+	0.194945i	−0.321033	+	0.947068i	$0.604030\pi$
$920$	−3.82233	−	4.45592i	−0.126019	−	0.146907i
$921$	−3.23939	+	16.2855i	−0.106742	+	0.536626i
$922$	19.5235	−	21.1508i	0.642972	−	0.696565i
$923$	−26.5754	−	2.61745i	−0.874739	−	0.0861543i
$924$	−2.72215	+	8.41900i	−0.0895521	+	0.276965i
$925$	−29.9803	−	9.09443i	−0.985747	−	0.299023i
$926$	18.4389	+	8.92717i	0.605940	+	0.293365i
$927$	0.619081	+	0.619081i	0.0203333	+	0.0203333i
$928$	−0.306293	+	0.461979i	−0.0100546	+	0.0151652i
$929$	7.29903	−	7.29903i	0.239473	−	0.239473i	−0.577159	−	0.816632i	$-0.695839\pi$
$929$	7.29903	−	7.29903i	0.239473	−	0.239473i	0.816632	+	0.577159i	$0.195839\pi$
$930$	−11.5535	+	4.01571i	−0.378856	+	0.131680i
$931$	−10.7256	+	35.3576i	−0.351518	+	1.15880i
$932$	31.8242	−	2.55058i	1.04244	−	0.0835469i
$933$	1.19303	−	12.1130i	0.0390581	−	0.396563i
$934$	36.4161	−	1.45696i	1.19157	−	0.0476733i
$935$	−25.6878	−	5.10962i	−0.840081	−	0.167102i
$936$	−11.1679	+	1.34620i	−0.365036	+	0.0440018i
$937$	2.34675	+	11.7979i	0.0766651	+	0.385421i	0.999999	+	0.00142330i	$0.000453051\pi$
$937$	2.34675	+	11.7979i	0.0766651	+	0.385421i	−0.923334	+	0.383998i	$0.874547\pi$
$938$	9.94097	+	6.08203i	0.324584	+	0.198585i
$939$	−11.5387	+	21.5874i	−0.376551	+	0.704478i
$940$	12.6120	+	8.76322i	0.411359	+	0.285825i
$941$	3.73796	+	37.9521i	0.121854	+	1.23720i	0.840494	+	0.541821i	$0.182265\pi$
$941$	3.73796	+	37.9521i	0.121854	+	1.23720i	−0.718640	+	0.695382i	$0.755235\pi$
$942$	20.9250	−	2.90958i	0.681772	−	0.0947991i
$943$	1.24220	+	2.99894i	0.0404516	+	0.0976589i
$944$	17.0136	+	34.8222i	0.553745	+	1.13337i
$945$	−0.326270	+	0.787685i	−0.0106136	+	0.0256234i
$946$	17.1524	−	65.9249i	0.557671	−	2.14340i
$947$	2.90403	+	2.38327i	0.0943682	+	0.0774460i	0.680394	−	0.732846i	$-0.261808\pi$
$947$	2.90403	+	2.38327i	0.0943682	+	0.0774460i	−0.586026	+	0.810292i	$0.699308\pi$
$948$	21.1878	+	0.385657i	0.688147	+	0.0125256i
$949$	48.7872	−	14.7994i	1.58370	−	0.480410i
$950$	30.2922	+	4.77553i	0.982808	+	0.154939i
$951$	−13.6053	−	9.09077i	−0.441182	−	0.294788i
$952$	6.39227	+	6.11962i	0.207175	+	0.198338i
$953$	12.6137	+	18.8778i	0.408599	+	0.611511i	0.977510	−	0.210887i	$-0.0676354\pi$
$953$	12.6137	+	18.8778i	0.408599	+	0.611511i	−0.568912	+	0.822399i	$0.692635\pi$
$954$	7.13780	+	2.62746i	0.231095	+	0.0850670i
$955$	8.80102	+	10.7241i	0.284794	+	0.347023i
$956$	27.6834	−	7.85044i	0.895346	−	0.253901i
$957$	−0.498684	+	0.266552i	−0.0161202	+	0.00861640i
$958$	12.7974	+	14.3806i	0.413466	+	0.464617i
$959$		−	4.38109i		−	0.141473i
$960$	−6.55910	−	6.01101i	−0.211694	−	0.194004i
$961$			29.4838i			0.951090i
$962$	34.9789	−	31.1280i	1.12777	−	1.00361i
$963$	−3.76301	+	2.01137i	−0.121261	+	0.0648155i
$964$	−0.404501	−	0.225770i	−0.0130281	−	0.00727155i
$965$	9.57342	+	11.6652i	0.308179	+	0.375518i
$966$	−0.699011	+	1.89895i	−0.0224903	+	0.0610976i
$967$	−10.6373	−	15.9198i	−0.342072	−	0.511947i	0.620051	−	0.784561i	$-0.287112\pi$
$967$	−10.6373	−	15.9198i	−0.342072	−	0.511947i	−0.962123	+	0.272614i	$0.912112\pi$
$968$	−25.4027	−	57.7367i	−0.816475	−	1.85573i
$969$	19.5528	+	13.0647i	0.628126	+	0.419700i
$970$	0.0849999	−	0.539172i	0.00272918	−	0.0173118i
$971$	31.1545	−	9.45061i	0.999795	−	0.303285i	0.252370	−	0.967631i	$-0.418790\pi$
$971$	31.1545	−	9.45061i	0.999795	−	0.303285i	0.747425	+	0.664346i	$0.231290\pi$
$972$	−1.43972	+	1.38824i	−0.0461789	+	0.0445279i
$973$	−6.79196	−	5.57402i	−0.217740	−	0.178695i
$974$	−52.9927	−	13.7876i	−1.69799	−	0.441785i
$975$	−5.72743	+	13.8272i	−0.183425	+	0.442826i
$976$	29.7766	−	7.86144i	0.953124	−	0.251639i
$977$	−17.8567	−	43.1099i	−0.571287	−	1.37921i	−0.900460	−	0.434939i	$-0.856770\pi$
$977$	−17.8567	−	43.1099i	−0.571287	−	1.37921i	0.329173	−	0.944270i	$-0.393230\pi$
$978$	−3.24849	−	23.3623i	−0.103875	−	0.747045i
$979$	0.348101	+	3.53432i	0.0111253	+	0.112957i
$980$	−2.52740	−	14.0365i	−0.0807347	−	0.448380i
$981$	−6.93675	+	12.9777i	−0.221473	+	0.414347i
$982$	−17.0396	+	27.8509i	−0.543754	+	0.888757i
$983$	6.46359	+	32.4947i	0.206156	+	1.03642i	0.935784	+	0.352574i	$0.114693\pi$
$983$	6.46359	+	32.4947i	0.206156	+	1.03642i	−0.729628	+	0.683845i	$0.760307\pi$
$984$	2.41287	+	4.28682i	0.0769195	+	0.136659i
$985$	8.15638	+	1.62240i	0.259884	+	0.0516941i
$986$	0.0226080	+	0.565076i	0.000719986	+	0.0179957i
$987$	0.518849	−	5.26796i	0.0165151	−	0.167681i
$988$	−29.7161	+	34.8943i	−0.945394	+	1.11014i
$989$	4.52222	−	14.9077i	0.143798	−	0.474039i
$990$	−2.97971	−	8.57289i	−0.0947014	−	0.272464i
$991$	19.5286	−	19.5286i	0.620348	−	0.620348i	−0.325272	−	0.945620i	$-0.605456\pi$
$991$	19.5286	−	19.5286i	0.620348	−	0.620348i	0.945620	+	0.325272i	$0.105456\pi$
$992$	−38.7247	+	20.8777i	−1.22951	+	0.662869i
$993$	9.05642	+	9.05642i	0.287397	+	0.287397i
$994$	−3.17228	+	6.55229i	−0.100619	+	0.207826i
$995$	−24.7480	−	7.50722i	−0.784564	−	0.237995i
$996$	23.5259	−	12.0296i	0.745445	−	0.381172i
$997$	−15.9643	−	1.57235i	−0.505594	−	0.0497967i	−0.157995	−	0.987440i	$-0.550503\pi$
$997$	−15.9643	−	1.57235i	−0.505594	−	0.0497967i	−0.347599	+	0.937643i	$0.613003\pi$
$998$	24.0571	+	22.2061i	0.761513	+	0.702923i
$999$	1.62416	−	8.16518i	0.0513860	−	0.258335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.17	✓	512
128.45	even	32	inner	384.2.v.a.301.17	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.17	✓	512	1.1	even	1	trivial
384.2.v.a.301.17	yes	512	128.45	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.0822429 - 1.41182i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.98647 - 0.232224i) q^{4} +(0.859670 - 0.705513i) q^{5} +(1.28388 - 0.592996i) q^{6} +(0.637437 - 0.425922i) q^{7} +(-0.491232 + 2.78544i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.0822429 - 1.41182i) q^{2} +(0.471397 + 0.881921i) q^{3} +(-1.98647 - 0.232224i) q^{4} +(0.859670 - 0.705513i) q^{5} +(1.28388 - 0.592996i) q^{6} +(0.637437 - 0.425922i) q^{7} +(-0.491232 + 2.78544i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-0.925356 - 1.27172i) q^{10} +(-1.67516 - 5.52225i) q^{11} +(-0.731613 - 1.86138i) q^{12} +(2.52301 - 3.07430i) q^{13} +(-0.548900 - 0.934976i) q^{14} +(1.02745 + 0.425585i) q^{15} +(3.89214 + 0.922614i) q^{16} +(3.77043 - 1.56176i) q^{17} +(1.12819 + 0.852748i) q^{18} +(5.73443 - 0.564793i) q^{19} +(-1.87155 + 1.20185i) q^{20} +(0.676115 + 0.361391i) q^{21} +(-7.93419 + 1.91085i) q^{22} +(-1.83052 + 0.364113i) q^{23} +(-2.68811 + 0.879821i) q^{24} +(-0.734168 + 3.69091i) q^{25} +(-4.13286 - 3.81488i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-1.36516 + 0.698054i) q^{28} +(-0.0937668 - 0.0284438i) q^{29} +(0.685350 - 1.41558i) q^{30} +(-5.49926 - 5.49926i) q^{31} +(1.62267 - 5.41913i) q^{32} +(4.08053 - 4.08053i) q^{33} +(-1.89484 - 5.45161i) q^{34} +(0.247492 - 0.815873i) q^{35} +(1.29671 - 1.52267i) q^{36} +(-0.816007 + 8.28506i) q^{37} +(-0.325769 - 8.14244i) q^{38} +(3.90063 + 0.775883i) q^{39} +(1.54287 + 2.74113i) q^{40} +(-0.339303 - 1.70579i) q^{41} +(0.565825 - 0.924831i) q^{42} +(-3.93471 + 7.36133i) q^{43} +(2.04525 + 11.3588i) q^{44} +(0.109006 + 1.10675i) q^{45} +(0.363515 + 2.61431i) q^{46} +(-2.64233 - 6.37916i) q^{47} +(1.02107 + 3.86748i) q^{48} +(-2.45387 + 5.92416i) q^{49} +(5.15052 + 1.34006i) q^{50} +(3.15472 + 2.58901i) q^{51} +(-5.72582 + 5.52110i) q^{52} +(5.14669 - 1.56123i) q^{53} +(-0.220229 + 1.39696i) q^{54} +(-5.33610 - 3.56547i) q^{55} +(0.873251 + 1.98477i) q^{56} +(3.20130 + 4.79108i) q^{57} +(-0.0478692 + 0.130043i) q^{58} +(6.14668 + 7.48975i) q^{59} +(-1.94217 - 1.08401i) q^{60} +(6.79010 - 3.62938i) q^{61} +(-8.21625 + 7.31170i) q^{62} +0.766639i q^{63} +(-7.51738 - 2.73660i) q^{64} -4.42290i q^{65} +(-5.42538 - 6.09656i) q^{66} +(-9.47973 + 5.06702i) q^{67} +(-7.85253 + 2.22681i) q^{68} +(-1.18402 - 1.44273i) q^{69} +(-1.13151 - 0.416514i) q^{70} +(-3.73039 - 5.58292i) q^{71} +(-2.04310 - 1.95595i) q^{72} +(10.6588 + 7.12196i) q^{73} +(11.6299 + 1.83344i) q^{74} +(-3.60118 + 1.09240i) q^{75} +(-11.5225 - 0.209730i) q^{76} +(-3.41985 - 2.80660i) q^{77} +(1.41621 - 5.44317i) q^{78} +(-4.05478 + 9.78910i) q^{79} +(3.99688 - 1.95281i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-2.43617 + 0.338745i) q^{82} +(1.29496 + 13.1479i) q^{83} +(-1.25916 - 0.874904i) q^{84} +(2.13948 - 4.00269i) q^{85} +(10.0693 + 6.16052i) q^{86} +(-0.0191161 - 0.0961033i) q^{87} +(16.2048 - 1.95335i) q^{88} +(-0.603595 - 0.120062i) q^{89} +(1.57150 - 0.0628738i) q^{90} +(0.298850 - 3.03428i) q^{91} +(3.72083 - 0.298209i) q^{92} +(2.25758 - 7.44225i) q^{93} +(-9.22353 + 3.20586i) q^{94} +(4.53125 - 4.53125i) q^{95} +(5.54416 - 1.12350i) q^{96} +(0.245404 + 0.245404i) q^{97} +(8.16204 + 3.95164i) q^{98} +(5.52225 + 1.67516i) 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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