LMFDB - Embedded newform 384.2.v.a.37.13

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			37.13
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.691080 - 1.23386i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.04482 + 1.70539i) q^{4} +(-1.72328 + 1.41426i) q^{5} +(-0.762394 + 1.19112i) q^{6} +(-0.0630509 + 0.0421293i) q^{7} +(2.82626 + 0.110596i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-0.691080 - 1.23386i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.04482 + 1.70539i) q^{4} +(-1.72328 + 1.41426i) q^{5} +(-0.762394 + 1.19112i) q^{6} +(-0.0630509 + 0.0421293i) q^{7} +(2.82626 + 0.110596i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(2.93592 + 1.14892i) q^{10} +(1.01850 + 3.35754i) q^{11} +(1.99654 + 0.117531i) q^{12} +(4.28528 - 5.22163i) q^{13} +(0.0955548 + 0.0486813i) q^{14} +(2.05961 + 0.853118i) q^{15} +(-1.81671 - 3.56364i) q^{16} +(2.61069 - 1.08138i) q^{17} +(1.40986 + 0.110884i) q^{18} +(5.11307 - 0.503594i) q^{19} +(-0.611351 - 4.41650i) q^{20} +(0.0668767 + 0.0357463i) q^{21} +(3.43887 - 3.57702i) q^{22} +(-5.17657 + 1.02968i) q^{23} +(-1.23475 - 2.54468i) q^{24} +(-0.00589100 + 0.0296161i) q^{25} +(-9.40422 - 1.67887i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-0.00597019 - 0.151544i) q^{28} +(6.63854 + 2.01378i) q^{29} +(-0.370727 - 3.13084i) q^{30} +(6.28402 + 6.28402i) q^{31} +(-3.14154 + 4.70433i) q^{32} +(2.48097 - 2.48097i) q^{33} +(-3.13847 - 2.47390i) q^{34} +(0.0490726 - 0.161771i) q^{35} +(-0.837511 - 1.81620i) q^{36} +(1.11373 - 11.3078i) q^{37} +(-4.15491 - 5.96079i) q^{38} +(-6.62513 - 1.31782i) q^{39} +(-5.02685 + 3.80647i) q^{40} +(1.13902 + 5.72626i) q^{41} +(-0.00211119 - 0.107220i) q^{42} +(-1.45646 + 2.72484i) q^{43} +(-6.79007 - 1.77108i) q^{44} +(-0.218510 - 2.21857i) q^{45} +(4.84790 + 5.67556i) q^{46} +(-2.54277 - 6.13879i) q^{47} +(-2.28646 + 3.28209i) q^{48} +(-2.67658 + 6.46184i) q^{49} +(0.0406132 - 0.0131984i) q^{50} +(-2.18436 - 1.79266i) q^{51} +(4.42758 + 12.7637i) q^{52} +(6.60695 - 2.00420i) q^{53} +(-0.566813 - 1.29566i) q^{54} +(-6.50358 - 4.34556i) q^{55} +(-0.182858 + 0.112095i) q^{56} +(-2.85442 - 4.27194i) q^{57} +(-2.10304 - 9.58271i) q^{58} +(-2.05527 - 2.50436i) q^{59} +(-3.60682 + 2.62109i) q^{60} +(7.68834 - 4.10951i) q^{61} +(3.41084 - 12.0964i) q^{62} -0.0758307i q^{63} +(7.97554 + 0.625148i) q^{64} +15.0588i q^{65} +(-4.77572 - 1.34662i) q^{66} +(-3.37931 + 1.80628i) q^{67} +(-0.883512 + 5.58209i) q^{68} +(3.34832 + 4.07993i) q^{69} +(-0.233515 + 0.0512478i) q^{70} +(-0.353091 - 0.528437i) q^{71} +(-1.66215 + 2.28851i) q^{72} +(12.9362 + 8.64371i) q^{73} +(-14.7220 + 6.44045i) q^{74} +(0.0288960 - 0.00876552i) q^{75} +(-4.48340 + 9.24595i) q^{76} +(-0.205668 - 0.168788i) q^{77} +(2.95249 + 9.08520i) q^{78} +(0.108585 - 0.262147i) q^{79} +(8.17061 + 3.57184i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(6.27824 - 5.36269i) q^{82} +(0.880145 + 8.93626i) q^{83} +(-0.130835 + 0.0767025i) q^{84} +(-2.96959 + 5.55570i) q^{85} +(4.36859 - 0.0860187i) q^{86} +(-1.35339 - 6.80396i) q^{87} +(2.50722 + 9.60195i) q^{88} +(4.54759 + 0.904572i) q^{89} +(-2.58640 + 1.80282i) q^{90} +(-0.0502074 + 0.509764i) q^{91} +(3.65255 - 9.90390i) q^{92} +(2.57974 - 8.50428i) q^{93} +(-5.81714 + 7.37981i) q^{94} +(-8.09903 + 8.09903i) q^{95} +(5.62976 + 0.552983i) q^{96} +(-7.86360 - 7.86360i) q^{97} +(9.82274 - 1.16312i) q^{98} +(-3.35754 - 1.01850i) 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 $

$2$	−0.691080	−	1.23386i	−0.488667	−	0.872470i
$2$	−0.691080	−	1.23386i	−0.488667	−	0.872470i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$4$	−1.04482	+	1.70539i	−0.522409	+	0.852695i
$5$	−1.72328	+	1.41426i	−0.770673	+	0.632475i	−0.935290	−	0.353883i	$-0.884861\pi$
$5$	−1.72328	+	1.41426i	−0.770673	+	0.632475i	0.164617	+	0.986358i	$0.447361\pi$
$6$	−0.762394	+	1.19112i	−0.311246	+	0.486271i
$7$	−0.0630509	+	0.0421293i	−0.0238310	+	0.0159234i	−0.567429	−	0.823423i	$-0.692062\pi$
$7$	−0.0630509	+	0.0421293i	−0.0238310	+	0.0159234i	0.543598	+	0.839346i	$0.317062\pi$
$8$	2.82626	+	0.110596i	0.999235	+	0.0391016i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	2.93592	+	1.14892i	0.928418	+	0.363319i
$11$	1.01850	+	3.35754i	0.307089	+	1.01234i	0.965658	+	0.259817i	$0.0836622\pi$
$11$	1.01850	+	3.35754i	0.307089	+	1.01234i	−0.658569	+	0.752521i	$0.728838\pi$
$12$	1.99654	+	0.117531i	0.576353	+	0.0339283i
$13$	4.28528	−	5.22163i	1.18852	−	1.44822i	0.323686	−	0.946165i	$-0.395078\pi$
$13$	4.28528	−	5.22163i	1.18852	−	1.44822i	0.864836	−	0.502054i	$-0.167422\pi$
$14$	0.0955548	+	0.0486813i	0.0255381	+	0.0130106i
$15$	2.05961	+	0.853118i	0.531789	+	0.220274i
$16$	−1.81671	−	3.56364i	−0.454179	−	0.890911i
$17$	2.61069	−	1.08138i	0.633185	−	0.262274i	−0.0429208	−	0.999078i	$-0.513666\pi$
$17$	2.61069	−	1.08138i	0.633185	−	0.262274i	0.676106	+	0.736805i	$0.263666\pi$
$18$	1.40986	+	0.110884i	0.332307	+	0.0261355i
$19$	5.11307	−	0.503594i	1.17302	−	0.115532i	0.507324	−	0.861756i	$-0.330635\pi$
$19$	5.11307	−	0.503594i	1.17302	−	0.115532i	0.665696	+	0.746223i	$0.268135\pi$
$20$	−0.611351	−	4.41650i	−0.136702	−	0.987559i
$21$	0.0668767	+	0.0357463i	0.0145937	+	0.00780049i
$22$	3.43887	−	3.57702i	0.733170	−	0.762622i
$23$	−5.17657	+	1.02968i	−1.07939	+	0.214704i	−0.702592	−	0.711592i	$-0.747974\pi$
$23$	−5.17657	+	1.02968i	−1.07939	+	0.214704i	−0.376796	+	0.926296i	$0.622974\pi$
$24$	−1.23475	−	2.54468i	−0.252043	−	0.519430i
$25$	−0.00589100	+	0.0296161i	−0.00117820	+	0.00592321i
$26$	−9.40422	−	1.67887i	−1.84432	−	0.329253i
$27$	0.995185	+	0.0980171i	0.191523	+	0.0188634i
$28$	−0.00597019	−	0.151544i	−0.00112826	−	0.0286391i
$29$	6.63854	+	2.01378i	1.23275	+	0.373949i	0.838422	−	0.545022i	$-0.183479\pi$
$29$	6.63854	+	2.01378i	1.23275	+	0.373949i	0.394324	+	0.918971i	$0.370979\pi$
$30$	−0.370727	−	3.13084i	−0.0676852	−	0.571611i
$31$	6.28402	+	6.28402i	1.12864	+	1.12864i	0.990398	+	0.138245i	$0.0441461\pi$
$31$	6.28402	+	6.28402i	1.12864	+	1.12864i	0.138245	+	0.990398i	$0.455854\pi$
$32$	−3.14154	+	4.70433i	−0.555351	+	0.831616i
$33$	2.48097	−	2.48097i	0.431882	−	0.431882i
$34$	−3.13847	−	2.47390i	−0.538243	−	0.424270i
$35$	0.0490726	−	0.161771i	0.00829478	−	0.0273442i
$36$	−0.837511	−	1.81620i	−0.139585	−	0.302700i
$37$	1.11373	−	11.3078i	0.183095	−	1.85900i	−0.264013	−	0.964519i	$-0.585046\pi$
$37$	1.11373	−	11.3078i	0.183095	−	1.85900i	0.447108	−	0.894480i	$-0.352454\pi$
$38$	−4.15491	−	5.96079i	−0.674015	−	0.966968i
$39$	−6.62513	−	1.31782i	−1.06087	−	0.211020i
$40$	−5.02685	+	3.80647i	−0.794814	+	0.601856i
$41$	1.13902	+	5.72626i	0.177886	+	0.894291i	0.961869	+	0.273510i	$0.0881845\pi$
$41$	1.13902	+	5.72626i	0.177886	+	0.894291i	−0.783984	+	0.620781i	$0.786815\pi$
$42$	−0.00211119	−	0.107220i	−0.000325764	−	0.0165444i
$43$	−1.45646	+	2.72484i	−0.222107	+	0.415534i	−0.968152	−	0.250362i	$-0.919450\pi$
$43$	−1.45646	+	2.72484i	−0.222107	+	0.415534i	0.746045	+	0.665896i	$0.231950\pi$
$44$	−6.79007	−	1.77108i	−1.02364	−	0.267000i
$45$	−0.218510	−	2.21857i	−0.0325736	−	0.330725i
$46$	4.84790	+	5.67556i	0.714785	+	0.836816i
$47$	−2.54277	−	6.13879i	−0.370901	−	0.895434i	−0.993598	−	0.112971i	$-0.963963\pi$
$47$	−2.54277	−	6.13879i	−0.370901	−	0.895434i	0.622697	−	0.782463i	$-0.286037\pi$
$48$	−2.28646	+	3.28209i	−0.330022	+	0.473729i
$49$	−2.67658	+	6.46184i	−0.382369	+	0.923121i
$50$	0.0406132	−	0.0131984i	0.00574358	−	0.00186654i
$51$	−2.18436	−	1.79266i	−0.305872	−	0.251023i
$52$	4.42758	+	12.7637i	0.613995	+	1.77001i
$53$	6.60695	−	2.00420i	0.907535	−	0.275298i	0.198194	−	0.980163i	$-0.436493\pi$
$53$	6.60695	−	2.00420i	0.907535	−	0.275298i	0.709341	+	0.704865i	$0.248993\pi$
$54$	−0.566813	−	1.29566i	−0.0771335	−	0.176316i
$55$	−6.50358	−	4.34556i	−0.876943	−	0.585955i
$56$	−0.182858	+	0.112095i	−0.0244354	+	0.0149794i
$57$	−2.85442	−	4.27194i	−0.378077	−	0.565832i
$58$	−2.10304	−	9.58271i	−0.276143	−	1.25827i
$59$	−2.05527	−	2.50436i	−0.267574	−	0.326040i	0.621839	−	0.783145i	$-0.286386\pi$
$59$	−2.05527	−	2.50436i	−0.267574	−	0.326040i	−0.889412	+	0.457106i	$0.848886\pi$
$60$	−3.60682	+	2.62109i	−0.465638	+	0.338381i
$61$	7.68834	−	4.10951i	0.984392	−	0.526168i	0.101042	−	0.994882i	$-0.467782\pi$
$61$	7.68834	−	4.10951i	0.984392	−	0.526168i	0.883350	+	0.468714i	$0.155282\pi$
$62$	3.41084	−	12.0964i	0.433177	−	1.53624i
$63$		−	0.0758307i		−	0.00955377i
$64$	7.97554	+	0.625148i	0.996942	+	0.0781435i
$65$			15.0588i			1.86781i
$66$	−4.77572	−	1.34662i	−0.587850	−	0.165757i
$67$	−3.37931	+	1.80628i	−0.412849	+	0.220672i	−0.664727	−	0.747087i	$-0.731452\pi$
$67$	−3.37931	+	1.80628i	−0.412849	+	0.220672i	0.251878	+	0.967759i	$0.418952\pi$
$68$	−0.883512	+	5.58209i	−0.107142	+	0.676928i
$69$	3.34832	+	4.07993i	0.403090	+	0.491166i
$70$	−0.233515	+	0.0512478i	−0.0279104	+	0.00612528i
$71$	−0.353091	−	0.528437i	−0.0419041	−	0.0627140i	0.809926	−	0.586532i	$-0.199507\pi$
$71$	−0.353091	−	0.528437i	−0.0419041	−	0.0627140i	−0.851830	+	0.523818i	$0.824507\pi$
$72$	−1.66215	+	2.28851i	−0.195886	+	0.269703i
$73$	12.9362	+	8.64371i	1.51407	+	1.01167i	0.986795	+	0.161975i	$0.0517862\pi$
$73$	12.9362	+	8.64371i	1.51407	+	1.01167i	0.527275	+	0.849695i	$0.323214\pi$
$74$	−14.7220	+	6.44045i	−1.71139	+	0.748687i
$75$	0.0288960	−	0.00876552i	0.00333663	−	0.00101215i
$76$	−4.48340	+	9.24595i	−0.514282	+	1.06058i
$77$	−0.205668	−	0.168788i	−0.0234381	−	0.0192351i
$78$	2.95249	+	9.08520i	0.334304	+	1.02870i
$79$	0.108585	−	0.262147i	0.0122167	−	0.0294938i	−0.917653	−	0.397382i	$-0.869919\pi$
$79$	0.108585	−	0.262147i	0.0122167	−	0.0294938i	0.929870	+	0.367888i	$0.119919\pi$
$80$	8.17061	+	3.57184i	0.913502	+	0.399344i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	6.27824	−	5.36269i	0.693315	−	0.592210i
$83$	0.880145	+	8.93626i	0.0966084	+	0.980882i	0.914249	+	0.405153i	$0.132782\pi$
$83$	0.880145	+	8.93626i	0.0966084	+	0.980882i	−0.817641	+	0.575729i	$0.804718\pi$
$84$	−0.130835	+	0.0767025i	−0.0142753	+	0.00836893i
$85$	−2.96959	+	5.55570i	−0.322097	+	0.602601i
$86$	4.36859	−	0.0860187i	0.471078	−	0.00927564i
$87$	−1.35339	−	6.80396i	−0.145099	−	0.729461i
$88$	2.50722	+	9.60195i	0.267270	+	1.02357i
$89$	4.54759	+	0.904572i	0.482043	+	0.0958844i	0.430130	−	0.902767i	$-0.358468\pi$
$89$	4.54759	+	0.904572i	0.482043	+	0.0958844i	0.0519139	+	0.998652i	$0.483468\pi$
$90$	−2.58640	+	1.80282i	−0.272630	+	0.190034i
$91$	−0.0502074	+	0.509764i	−0.00526316	+	0.0534378i
$92$	3.65255	−	9.90390i	0.380805	−	1.03255i
$93$	2.57974	−	8.50428i	0.267507	−	0.881852i
$94$	−5.81714	+	7.37981i	−0.599992	+	0.761169i
$95$	−8.09903	+	8.09903i	−0.830943	+	0.830943i
$96$	5.62976	+	0.552983i	0.574585	+	0.0564386i
$97$	−7.86360	−	7.86360i	−0.798428	−	0.798428i	0.184420	−	0.982848i	$-0.440959\pi$
$97$	−7.86360	−	7.86360i	−0.798428	−	0.798428i	−0.982848	+	0.184420i	$0.940959\pi$
$98$	9.82274	−	1.16312i	0.992246	−	0.117493i
$99$	−3.35754	−	1.01850i	−0.337446	−	0.102363i
$100$	−0.0443519	−	0.0409898i	−0.00443519	−	0.00409898i
$101$	−11.9325	−	1.17525i	−1.18733	−	0.116942i	−0.514998	−	0.857192i	$-0.672207\pi$
$101$	−11.9325	−	1.17525i	−1.18733	−	0.116942i	−0.672332	+	0.740250i	$0.734707\pi$
$102$	−0.702321	+	3.93407i	−0.0695402	+	0.389531i
$103$	−2.54265	+	12.7827i	−0.250534	+	1.25952i	0.626625	+	0.779321i	$0.284436\pi$
$103$	−2.54265	+	12.7827i	−0.250534	+	1.25952i	−0.877159	+	0.480200i	$0.840564\pi$
$104$	12.6888	−	14.2838i	1.24424	−	1.40064i
$105$	−0.165802	+	0.0329800i	−0.0161806	+	0.00321852i
$106$	−7.03883	−	6.76699i	−0.683672	−	0.657268i
$107$	2.52066	+	1.34732i	0.243681	+	0.130250i	0.588717	−	0.808339i	$-0.299633\pi$
$107$	2.52066	+	1.34732i	0.243681	+	0.130250i	−0.345036	+	0.938589i	$0.612133\pi$
$108$	−1.20694	+	1.59477i	−0.116138	+	0.153457i
$109$	−10.9966	+	1.08307i	−1.05328	+	0.103739i	−0.609808	−	0.792549i	$-0.708753\pi$
$109$	−10.9966	+	1.08307i	−1.05328	+	0.103739i	−0.443472	+	0.896288i	$0.646253\pi$
$110$	−0.867308	+	11.0276i	−0.0826946	+	1.05144i
$111$	−10.4976	+	4.34826i	−0.996392	+	0.412719i
$112$	0.264679	+	0.148154i	0.0250098	+	0.0139992i
$113$	2.01890	+	0.836257i	0.189922	+	0.0786684i	0.475618	−	0.879652i	$-0.342225\pi$
$113$	2.01890	+	0.836257i	0.189922	+	0.0786684i	−0.285695	+	0.958320i	$0.592225\pi$
$114$	−3.29834	+	6.47420i	−0.308918	+	0.606364i
$115$	7.46442	−	9.09542i	0.696061	−	0.848152i
$116$	−10.3703	+	9.21727i	−0.962862	+	0.855802i
$117$	1.96085	+	6.46406i	0.181281	+	0.597602i
$118$	−1.66967	+	4.26663i	−0.153705	+	0.392775i
$119$	−0.119048	+	0.178169i	−0.0109132	+	0.0163327i
$120$	5.72665	+	2.63892i	0.522769	+	0.240900i
$121$	−1.08959	+	0.728041i	−0.0990536	+	0.0661855i
$122$	−10.3838	−	6.64634i	−0.940106	−	0.601731i
$123$	4.51317	−	3.70387i	0.406939	−	0.333966i
$124$	−17.2824	+	4.15106i	−1.55200	+	0.372776i
$125$	−5.28617	−	9.88973i	−0.472809	−	0.884564i
$126$	−0.0935644	+	0.0524051i	−0.00833538	+	0.00466862i
$127$	−5.66558			−0.502739			−0.251369	−	0.967891i	$-0.580881\pi$
$127$	−5.66558			−0.502739			−0.251369	+	0.967891i	$0.580881\pi$
$128$	−4.74039	−	10.2727i	−0.418995	−	0.907988i
$129$	3.08966			0.272029
$130$	18.5804	−	10.4068i	1.62961	−	0.912739i
$131$	−7.18241	−	13.4373i	−0.627530	−	1.17403i	−0.971945	−	0.235208i	$-0.924423\pi$
$131$	−7.18241	−	13.4373i	−0.627530	−	1.17403i	0.344415	−	0.938817i	$-0.388077\pi$
$132$	1.63886	+	6.82319i	0.142645	+	0.593882i
$133$	−0.301168	+	0.247162i	−0.0261146	+	0.0214317i
$134$	4.56407	+	2.92131i	0.394276	+	0.252363i
$135$	−1.85360	+	1.23854i	−0.159532	+	0.106596i
$136$	7.49809	−	2.76754i	0.642956	−	0.237315i
$137$	3.26384	−	4.88468i	0.278848	−	0.417326i	−0.665437	−	0.746454i	$-0.731755\pi$
$137$	3.26384	−	4.88468i	0.278848	−	0.417326i	0.944285	+	0.329128i	$0.106755\pi$
$138$	2.72011	−	6.95091i	0.231551	−	0.591701i
$139$	1.56513	+	5.15955i	0.132753	+	0.437628i	0.997964	−	0.0637802i	$-0.0203156\pi$
$139$	1.56513	+	5.15955i	0.132753	+	0.437628i	−0.865211	+	0.501408i	$0.832816\pi$
$140$	0.224610	+	0.252709i	0.0189830	+	0.0213578i
$141$	−4.21527	+	5.13632i	−0.354990	+	0.432557i
$142$	−0.408003	+	0.800856i	−0.0342389	+	0.0672064i
$143$	21.8964	+	9.06978i	1.83107	+	0.758453i
$144$	3.97237	+	0.469311i	0.331031	+	0.0391093i
$145$	−14.2880	+	5.91830i	−1.18656	+	0.491488i
$146$	1.72515	−	21.9350i	0.142775	−	1.81535i
$147$	6.96057	−	0.685556i	0.574098	−	0.0565437i
$148$	18.1207	+	13.7140i	1.48951	+	1.12728i
$149$	4.83147	+	2.58248i	0.395810	+	0.211565i	0.657279	−	0.753647i	$-0.271707\pi$
$149$	4.83147	+	2.58248i	0.395810	+	0.211565i	−0.261470	+	0.965212i	$0.584207\pi$
$150$	−0.0307849	−	0.0295960i	−0.00251358	−	0.00241650i
$151$	−2.52306	+	0.501868i	−0.205324	+	0.0408414i	−0.296680	−	0.954977i	$-0.595880\pi$
$151$	−2.52306	+	0.501868i	−0.205324	+	0.0408414i	0.0913568	+	0.995818i	$0.470880\pi$
$152$	14.5066	−	0.857803i	1.17664	−	0.0695770i
$153$	−0.551284	+	2.77149i	−0.0445687	+	0.224062i
$154$	−0.0661269	+	0.370411i	−0.00532866	+	0.0298486i
$155$	−19.7163	−	1.94189i	−1.58365	−	0.155976i
$156$	9.16945	−	9.92155i	0.734143	−	0.794360i
$157$	−3.63854	−	1.10374i	−0.290387	−	0.0880879i	0.141730	−	0.989905i	$-0.454733\pi$
$157$	−3.63854	−	1.10374i	−0.290387	−	0.0880879i	−0.432117	+	0.901817i	$0.642233\pi$
$158$	−0.398493	+	0.0471861i	−0.0317024	+	0.00375392i
$159$	−4.88204	−	4.88204i	−0.387171	−	0.387171i
$160$	−1.23939	−	12.5498i	−0.0979825	−	0.992149i
$161$	0.283008	−	0.283008i	0.0223041	−	0.0223041i
$162$	−0.875472	+	1.11065i	−0.0687836	+	0.0872611i
$163$	1.55676	−	5.13196i	0.121935	−	0.401966i	−0.874629	−	0.484793i	$-0.838895\pi$
$163$	1.55676	−	5.13196i	0.121935	−	0.401966i	0.996564	+	0.0828269i	$0.0263949\pi$
$164$	−10.9556	−	4.04041i	−0.855487	−	0.315503i
$165$	−0.766670	+	7.78413i	−0.0596852	+	0.605994i
$166$	10.4178	−	7.26164i	0.808581	−	0.563613i
$167$	−7.16513	−	1.42523i	−0.554455	−	0.110288i	−0.0900927	−	0.995933i	$-0.528716\pi$
$167$	−7.16513	−	1.42523i	−0.554455	−	0.110288i	−0.464362	+	0.885645i	$0.653716\pi$
$168$	0.185058	+	0.108425i	0.0142775	+	0.00836517i
$169$	−6.36560	−	32.0020i	−0.489662	−	2.46169i
$170$	8.90718	−	0.175385i	0.683149	−	0.0134514i
$171$	−2.42195	+	4.53115i	−0.185211	+	0.346505i
$172$	−3.12518	−	5.33078i	−0.238293	−	0.406468i
$173$	−0.0963916	−	0.978680i	−0.00732852	−	0.0744077i	0.990825	−	0.135152i	$-0.0431524\pi$
$173$	−0.0963916	−	0.978680i	−0.00732852	−	0.0744077i	−0.998153	+	0.0607448i	$0.980652\pi$
$174$	−7.45982	+	6.37197i	−0.565528	+	0.483058i
$175$	−0.000876271	−	0.00211550i	−6.62398e−5	−	0.000159917i
$176$	10.1148	−	9.72927i	0.762429	−	0.733371i
$177$	−1.23980	+	2.99313i	−0.0931888	+	0.224978i
$178$	−2.02663	−	6.23622i	−0.151903	−	0.467424i
$179$	10.3278	+	8.47580i	0.771936	+	0.633511i	0.935623	−	0.353001i	$-0.114839\pi$
$179$	10.3278	+	8.47580i	0.771936	+	0.633511i	−0.163687	+	0.986512i	$0.552339\pi$
$180$	4.01183	+	1.94536i	0.299024	+	0.144998i
$181$	5.37751	−	1.63125i	0.399707	−	0.121250i	−0.0840300	−	0.996463i	$-0.526779\pi$
$181$	5.37751	−	1.63125i	0.399707	−	0.121250i	0.483737	+	0.875213i	$0.339279\pi$
$182$	0.663674	−	0.290339i	0.0491948	−	0.0215213i
$183$	−7.24852	−	4.84331i	−0.535826	−	0.358028i
$184$	−14.7442	+	2.33765i	−1.08696	+	0.172334i
$185$	14.0729	+	21.0616i	1.03466	+	1.54848i
$186$	−12.2759	+	2.69409i	−0.900112	+	0.197540i
$187$	6.28977	+	7.66411i	0.459954	+	0.560455i
$188$	13.1258	+	2.07750i	0.957294	+	0.151517i
$189$	−0.0668767	+	0.0357463i	−0.00486457	+	0.00260016i
$190$	15.5901	+	4.39599i	1.13103	+	0.318918i
$191$		−	16.6333i		−	1.20354i	−0.798668	−	0.601772i	$-0.794461\pi$
$191$		−	16.6333i		−	1.20354i	0.798668	−	0.601772i	$-0.205539\pi$
$192$	−3.20831	−	7.32849i	−0.231540	−	0.528888i
$193$		−	16.0620i		−	1.15617i	−0.815976	−	0.578085i	$-0.803800\pi$
$193$		−	16.0620i		−	1.15617i	0.815976	−	0.578085i	$-0.196200\pi$
$194$	−4.26820	+	15.1370i	−0.306439	+	1.08677i
$195$	13.2807	−	7.09866i	0.951048	−	0.508346i
$196$	−8.22343	−	11.3161i	−0.587388	−	0.808290i
$197$	−1.29630	−	1.57954i	−0.0923573	−	0.112538i	0.724781	−	0.688979i	$-0.241941\pi$
$197$	−1.29630	−	1.57954i	−0.0923573	−	0.112538i	−0.817138	+	0.576441i	$0.804441\pi$
$198$	1.06365	+	4.84660i	0.0755900	+	0.344433i
$199$	−9.53649	−	14.2724i	−0.676024	−	1.01174i	−0.997888	−	0.0649553i	$-0.979310\pi$
$199$	−9.53649	−	14.2724i	−0.676024	−	1.01174i	0.321864	−	0.946786i	$-0.395690\pi$
$200$	−0.0199250	+	0.0830513i	−0.00140891	+	0.00587261i
$201$	3.18599	+	2.12881i	0.224723	+	0.150155i
$202$	6.79623	+	15.5352i	0.478181	+	1.09306i
$203$	−0.503405	+	0.152706i	−0.0353321	+	0.0107179i
$204$	5.33945	−	1.85219i	0.373836	−	0.129679i
$205$	−10.0612	−	8.25705i	−0.702708	−	0.576697i
$206$	17.5293	−	5.69663i	1.22132	−	0.396903i
$207$	2.01980	−	4.87622i	0.140386	−	0.338921i
$208$	−26.3931	−	5.78500i	−1.83003	−	0.401117i
$209$	6.89850	+	16.6545i	0.477179	+	1.15201i
$210$	0.155275	+	0.181784i	0.0107150	+	0.0125443i
$211$	0.0624934	+	0.634506i	0.00430222	+	0.0436812i	0.997096	−	0.0761529i	$-0.0242637\pi$
$211$	0.0624934	+	0.634506i	0.00430222	+	0.0436812i	−0.992794	+	0.119834i	$0.961764\pi$
$212$	−3.48512	+	13.3615i	−0.239359	+	0.917669i
$213$	−0.299594	+	0.560502i	−0.0205279	+	0.0384049i
$214$	−0.0795730	−	4.04124i	−0.00543950	−	0.276253i
$215$	−1.34374	−	6.75545i	−0.0916425	−	0.460718i
$216$	2.80181	+	0.387086i	0.190639	+	0.0263379i
$217$	−0.660954	−	0.131472i	−0.0448685	−	0.00892490i
$218$	8.93586	+	12.8197i	0.605213	+	0.868261i
$219$	1.52498	−	15.4833i	0.103048	−	1.04627i
$220$	14.2059	−	6.55084i	0.957763	−	0.441658i
$221$	5.54095	−	18.2661i	0.372725	−	1.22871i
$222$	12.6199	+	9.94761i	0.846989	+	0.667640i
$223$	−18.3464	+	18.3464i	−1.22857	+	1.22857i	−0.264064	+	0.964505i	$0.585063\pi$
$223$	−18.3464	+	18.3464i	−1.22857	+	1.22857i	−0.964505	+	0.264064i	$0.914937\pi$
$224$	−0.000113167	−	0.428963i	−7.56128e−6	−	0.0286613i
$225$	−0.0213520	−	0.0213520i	−0.00142347	−	0.00142347i
$226$	−0.363400	−	3.06896i	−0.0241730	−	0.204144i
$227$	21.3099	+	6.46430i	1.41439	+	0.429051i	0.902756	−	0.430153i	$-0.141540\pi$
$227$	21.3099	+	6.46430i	1.41439	+	0.429051i	0.511634	+	0.859203i	$0.329040\pi$
$228$	10.2677	−	0.404503i	0.679993	−	0.0267888i
$229$	−19.6190	−	1.93230i	−1.29646	−	0.127690i	−0.573859	−	0.818954i	$-0.694554\pi$
$229$	−19.6190	−	1.93230i	−1.29646	−	0.127690i	−0.722602	+	0.691264i	$0.757054\pi$
$230$	−16.3810	−	2.92438i	−1.08013	−	0.192828i
$231$	−0.0519060	+	0.260949i	−0.00341516	+	0.0171692i
$232$	18.5395	+	6.42567i	1.21718	+	0.421866i
$233$	−4.85273	+	0.965269i	−0.317913	+	0.0632368i	−0.351468	−	0.936200i	$-0.614317\pi$
$233$	−4.85273	+	0.965269i	−0.317913	+	0.0632368i	0.0335545	+	0.999437i	$0.489317\pi$
$234$	6.62063	−	6.88659i	0.432804	−	0.450191i
$235$	13.0637	+	6.98270i	0.852183	+	0.455501i
$236$	6.41829	−	0.888447i	0.417795	−	0.0578330i
$237$	−0.282379	+	0.0278119i	−0.0183425	+	0.00180658i
$238$	0.302107	+	0.0237603i	0.0195827	+	0.00154015i
$239$	9.99554	−	4.14029i	0.646558	−	0.267813i	−0.0352121	−	0.999380i	$-0.511211\pi$
$239$	9.99554	−	4.14029i	0.646558	−	0.267813i	0.681770	+	0.731567i	$0.261211\pi$
$240$	−0.701513	−	8.88959i	−0.0452825	−	0.573820i
$241$	−7.31045	−	3.02809i	−0.470908	−	0.195056i	0.134593	−	0.990901i	$-0.457027\pi$
$241$	−7.31045	−	3.02809i	−0.470908	−	0.195056i	−0.605501	+	0.795845i	$0.707027\pi$
$242$	1.65129	+	0.841266i	0.106149	+	0.0540786i
$243$	−0.634393	+	0.773010i	−0.0406963	+	0.0495886i
$244$	−1.02460	+	17.4053i	−0.0655934	+	1.11426i
$245$	−4.52621	−	14.9209i	−0.289169	−	0.953263i
$246$	−7.68901	−	3.00895i	−0.490234	−	0.191844i
$247$	19.2814	−	28.8566i	1.22684	−	1.83610i
$248$	17.0653	+	18.4553i	1.08365	+	1.17191i
$249$	7.46618	−	4.98874i	0.473150	−	0.316149i
$250$	−8.54937	+	13.3570i	−0.540709	+	0.844770i
$251$	−9.05126	+	7.42818i	−0.571311	+	0.468862i	−0.875144	−	0.483863i	$-0.839233\pi$
$251$	−9.05126	+	7.42818i	−0.571311	+	0.468862i	0.303833	+	0.952725i	$0.401733\pi$
$252$	0.129321	+	0.0792292i	0.00814646	+	0.00499097i
$253$	−8.72954	−	16.3318i	−0.548821	−	1.02677i
$254$	3.91537	+	6.99053i	0.245672	+	0.438625i
$255$	6.29955			0.394493
$256$	−9.39910	+	12.9482i	−0.587444	+	0.809265i
$257$	−24.1719			−1.50780			−0.753900	−	0.656990i	$-0.771830\pi$
$257$	−24.1719			−1.50780			−0.753900	+	0.656990i	$0.771830\pi$
$258$	−2.13520	−	3.81221i	−0.132932	−	0.237338i
$259$	0.406170	+	0.759891i	0.0252382	+	0.0472173i
$260$	−25.6811	−	15.7337i	−1.59268	−	0.975761i
$261$	−5.36257	+	4.40095i	−0.331935	+	0.272412i
$262$	−11.6162	+	18.1484i	−0.717649	+	1.12121i
$263$	−22.5603	+	15.0743i	−1.39113	+	0.929522i	−0.391170	+	0.920319i	$0.627929\pi$
$263$	−22.5603	+	15.0743i	−1.39113	+	0.929522i	−0.999958	+	0.00920306i	$0.997071\pi$
$264$	7.28627	−	6.73749i	0.448439	−	0.414664i
$265$	−8.55116	+	12.7977i	−0.525293	+	0.786157i
$266$	0.513095	+	0.200790i	0.0314598	+	0.0123112i
$267$	−1.34596	−	4.43703i	−0.0823713	−	0.271542i
$268$	0.450351	−	7.65028i	0.0275095	−	0.467315i
$269$	7.15539	−	8.71886i	0.436272	−	0.531599i	−0.507740	−	0.861510i	$-0.669519\pi$
$269$	7.15539	−	8.71886i	0.436272	−	0.531599i	0.944012	+	0.329912i	$0.107019\pi$
$270$	2.80916	+	1.43115i	0.170960	+	0.0870973i
$271$	10.9341	+	4.52903i	0.664196	+	0.275119i	0.689203	−	0.724568i	$-0.257961\pi$
$271$	10.9341	+	4.52903i	0.664196	+	0.275119i	−0.0250069	+	0.999687i	$0.507961\pi$
$272$	−8.59653	−	7.33900i	−0.521241	−	0.444992i
$273$	0.473239	−	0.196022i	0.0286418	−	0.0118638i
$274$	−8.28258	−	0.651413i	−0.500369	−	0.0393533i
$275$	−0.105437	+	0.0103847i	−0.00635810	+	0.000626218i
$276$	−10.4563	+	1.44740i	−0.629393	+	0.0871233i
$277$	26.1385	+	13.9713i	1.57051	+	0.839456i	0.999833	+	0.0182836i	$0.00582019\pi$
$277$	26.1385	+	13.9713i	1.57051	+	0.839456i	0.570680	+	0.821173i	$0.306680\pi$
$278$	5.28453	−	5.49682i	0.316945	−	0.329677i
$279$	−8.71618	+	1.73376i	−0.521824	+	0.103797i
$280$	0.156583	−	0.451779i	0.00935764	−	0.0269990i
$281$	0.588498	−	2.95858i	0.0351068	−	0.176494i	−0.959254	−	0.282546i	$-0.908821\pi$
$281$	0.588498	−	2.95858i	0.0351068	−	0.176494i	0.994361	+	0.106052i	$0.0338210\pi$
$282$	9.25059	+	1.65144i	0.550865	+	0.0983420i
$283$	29.7091	+	2.92609i	1.76602	+	0.173938i	0.928220	−	0.372033i	$-0.121339\pi$
$283$	29.7091	+	2.92609i	1.76602	+	0.173938i	0.837804	+	0.545971i	$0.183839\pi$
$284$	1.27011	−	0.0500369i	0.0753670	−	0.00296914i
$285$	10.9606	+	3.32485i	0.649248	+	0.196947i
$286$	−3.94132	−	33.2850i	−0.233055	−	1.96818i
$287$	−0.313060	−	0.313060i	−0.0184793	−	0.0184793i
$288$	−2.16616	−	5.22568i	−0.127642	−	0.307926i
$289$	−6.37451	+	6.37451i	−0.374971	+	0.374971i
$290$	17.1765	+	13.5394i	1.00864	+	0.795062i
$291$	−3.22820	+	10.6420i	−0.189241	+	0.623842i
$292$	−28.2569	+	13.0302i	−1.65361	+	0.762536i
$293$	−0.705454	+	7.16260i	−0.0412131	+	0.418443i	0.952337	+	0.305048i	$0.0986726\pi$
$293$	−0.705454	+	7.16260i	−0.0412131	+	0.418443i	−0.993550	+	0.113395i	$0.963827\pi$
$294$	−5.65619	−	8.11459i	−0.329876	−	0.473252i
$295$	7.08361	+	1.40902i	0.412424	+	0.0820361i
$296$	4.39829	−	31.8358i	0.255645	−	1.85042i
$297$	0.684498	+	3.44121i	0.0397186	+	0.199679i
$298$	−0.152522	−	7.74606i	−0.00883535	−	0.448717i
$299$	−16.8064	+	31.4426i	−0.971939	+	1.81837i
$300$	−0.0152424	+	0.0584374i	−0.000880023	+	0.00337388i
$301$	−0.0229646	−	0.233163i	−0.00132365	−	0.0134393i
$302$	2.36287	+	2.76627i	0.135968	+	0.159181i
$303$	4.58847	+	11.0775i	0.263601	+	0.636388i
$304$	−11.0836	−	17.3063i	−0.635689	−	0.992583i
$305$	−7.43725	+	17.9551i	−0.425856	+	1.02811i
$306$	3.80061	−	1.23512i	0.217266	−	0.0706068i
$307$	−19.0327	−	15.6198i	−1.08626	−	0.891467i	−0.0917114	−	0.995786i	$-0.529234\pi$
$307$	−19.0327	−	15.6198i	−1.08626	−	0.891467i	−0.994544	+	0.104319i	$0.966734\pi$
$308$	0.502734	−	0.174393i	0.0286460	−	0.00993694i
$309$	12.4720	−	3.78333i	0.709505	−	0.215226i
$310$	11.2295	+	25.6692i	0.637795	+	1.45791i
$311$	−0.287924	−	0.192385i	−0.0163267	−	0.0109091i	0.547380	−	0.836884i	$-0.315625\pi$
$311$	−0.287924	−	0.192385i	−0.0163267	−	0.0109091i	−0.563707	+	0.825975i	$0.690625\pi$
$312$	−18.5786	−	4.45722i	−1.05181	−	0.252340i
$313$	5.46818	+	8.18370i	0.309080	+	0.462570i	0.953194	−	0.302359i	$-0.0977740\pi$
$313$	5.46818	+	8.18370i	0.309080	+	0.462570i	−0.644115	+	0.764929i	$0.722774\pi$
$314$	1.15266	+	5.25221i	0.0650485	+	0.296400i
$315$	0.107244	+	0.130677i	0.00604252	+	0.00736283i
$316$	0.333611	+	0.459075i	0.0187671	+	0.0258250i
$317$	12.7923	−	6.83763i	0.718487	−	0.384039i	−0.0712716	−	0.997457i	$-0.522706\pi$
$317$	12.7923	−	6.83763i	0.718487	−	0.384039i	0.789759	+	0.613418i	$0.210206\pi$
$318$	−2.64987	+	9.39763i	−0.148597	+	0.526993i
$319$			24.3402i			1.36279i
$320$	−14.6282	+	10.2022i	−0.817740	+	0.570318i
$321$		−	2.85814i		−	0.159526i
$322$	−0.544772	−	0.153611i	−0.0303590	−	0.00856039i
$323$	12.8041	−	6.84391i	0.712437	−	0.380806i
$324$	1.97541	+	0.312660i	0.109745	+	0.0173700i
$325$	0.129399	+	0.157674i	0.00717779	+	0.00874616i
$326$	−7.40797	+	1.62577i	−0.410289	+	0.0900430i
$327$	6.13892	+	9.18755i	0.339483	+	0.508073i
$328$	2.58588	+	16.3099i	0.142781	+	0.900563i
$329$	0.418947	+	0.279931i	0.0230973	+	0.0154331i
$330$	10.1344	−	4.43349i	0.557878	−	0.244056i
$331$	10.6859	−	3.24153i	0.587350	−	0.178171i	0.0173978	−	0.999849i	$-0.494462\pi$
$331$	10.6859	−	3.24153i	0.587350	−	0.178171i	0.569952	+	0.821678i	$0.306962\pi$
$332$	−16.1594	−	7.83576i	−0.886862	−	0.430043i
$333$	8.78338	+	7.20833i	0.481326	+	0.395014i
$334$	3.19314	+	9.82572i	0.174721	+	0.537639i
$335$	3.26895	−	7.89194i	0.178602	−	0.431183i
$336$	0.00589134	−	0.303266i	0.000321399	−	0.0165445i
$337$	−2.41648	−	5.83389i	−0.131634	−	0.317792i	0.844296	−	0.535877i	$-0.180019\pi$
$337$	−2.41648	−	5.83389i	−0.131634	−	0.317792i	−0.975930	+	0.218085i	$0.930019\pi$
$338$	−35.0869	+	29.9702i	−1.90847	+	1.63016i
$339$	−0.214191	−	2.17472i	−0.0116333	−	0.118115i
$340$	−6.37197	−	10.8690i	−0.345569	−	0.589454i
$341$	−14.6986	+	27.4991i	−0.795973	+	1.48916i
$342$	7.26456	−	0.143041i	0.392822	−	0.00773477i
$343$	−0.207029	−	1.04080i	−0.0111785	−	0.0561981i
$344$	−4.41769	+	7.54003i	−0.238186	+	0.406531i
$345$	−11.5401	−	2.29548i	−0.621301	−	0.123584i
$346$	−1.14094	+	0.795280i	−0.0613373	+	0.0427545i
$347$	2.74825	−	27.9035i	0.147534	−	1.49794i	−0.581550	−	0.813511i	$-0.697553\pi$
$347$	2.74825	−	27.9035i	0.147534	−	1.49794i	0.729083	−	0.684425i	$-0.239947\pi$
$348$	13.0175	+	4.80083i	0.697809	+	0.257352i
$349$	−4.47754	+	14.7605i	−0.239677	+	0.790109i	0.751750	+	0.659448i	$0.229210\pi$
$349$	−4.47754	+	14.7605i	−0.239677	+	0.790109i	−0.991427	+	0.130661i	$0.958290\pi$
$350$	−0.00200466	+	0.00254318i	−0.000107154	+	0.000135939i
$351$	4.77645	−	4.77645i	0.254948	−	0.254948i
$352$	−18.9947	−	5.75649i	−1.01242	−	0.306822i
$353$	6.40061	+	6.40061i	0.340670	+	0.340670i	0.856619	−	0.515949i	$-0.172561\pi$
$353$	6.40061	+	6.40061i	0.340670	+	0.340670i	−0.515949	+	0.856619i	$0.672561\pi$
$354$	4.54991	−	0.538760i	0.241825	−	0.0286348i
$355$	1.35582	+	0.411283i	0.0719594	+	0.0218286i
$356$	−6.29405	+	6.81030i	−0.333584	+	0.360945i
$357$	0.213250	+	0.0210033i	0.0112864	+	0.00111161i
$358$	3.32062	−	18.6005i	0.175500	−	0.983067i
$359$	4.48001	−	22.5225i	0.236446	−	1.18869i	−0.661964	−	0.749536i	$-0.730277\pi$
$359$	4.48001	−	22.5225i	0.236446	−	1.18869i	0.898410	−	0.439158i	$-0.144723\pi$
$360$	−0.372202	−	6.29443i	−0.0196168	−	0.331746i
$361$	7.25499	−	1.44311i	0.381842	−	0.0759531i
$362$	−5.72902	−	5.50776i	−0.301110	−	0.289482i
$363$	1.15570	+	0.617736i	0.0606587	+	0.0324228i
$364$	−0.816889	−	0.618233i	−0.0428166	−	0.0324042i
$365$	−34.5171	+	3.39964i	−1.80671	+	0.177945i
$366$	−0.966652	+	12.2908i	−0.0505277	+	0.642449i
$367$	−8.93298	+	3.70016i	−0.466298	+	0.193147i	−0.603446	−	0.797404i	$-0.706206\pi$
$367$	−8.93298	+	3.70016i	−0.466298	+	0.193147i	0.137148	+	0.990551i	$0.456206\pi$
$368$	13.0738	+	16.5768i	0.681517	+	0.864125i
$369$	−5.39401	−	2.23427i	−0.280801	−	0.116312i
$370$	16.2616	−	31.9193i	0.845399	−	1.65941i
$371$	−0.332139	+	0.404713i	−0.0172438	+	0.0210116i
$372$	11.8078	+	13.2849i	0.612203	+	0.688789i
$373$	0.939360	+	3.09665i	0.0486382	+	0.160339i	0.977895	−	0.209095i	$-0.0670517\pi$
$373$	0.939360	+	3.09665i	0.0486382	+	0.160339i	−0.929257	+	0.369434i	$0.879552\pi$
$374$	5.10970	−	13.0572i	0.264216	−	0.675172i
$375$	−6.23008	+	9.32397i	−0.321720	+	0.481488i
$376$	−6.50761	−	17.6310i	−0.335604	−	0.909252i
$377$	38.9632	−	26.0344i	2.00671	−	1.34084i
$378$	0.0903231	+	0.0578129i	0.00464572	+	0.00297357i
$379$	−22.6197	+	18.5635i	−1.16190	+	0.953545i	−0.999450	−	0.0331718i	$-0.989439\pi$
$379$	−22.6197	+	18.5635i	−1.16190	+	0.953545i	−0.162449	+	0.986717i	$0.551939\pi$
$380$	−5.35000	−	22.2740i	−0.274449	−	1.14263i
$381$	2.67074	+	4.99660i	0.136826	+	0.255983i
$382$	−20.5232	+	11.4950i	−1.05006	+	0.588133i
$383$	20.7869			1.06216			0.531081	−	0.847321i	$-0.321786\pi$
$383$	20.7869			1.06216			0.531081	+	0.847321i	$0.321786\pi$
$384$	−6.82512	+	9.02317i	−0.348293	+	0.460462i
$385$	0.593132			0.0302288
$386$	−19.8183	+	11.1002i	−1.00872	+	0.564983i
$387$	−1.45646	−	2.72484i	−0.0740358	−	0.138511i
$388$	21.6265	−	5.19449i	1.09792	−	0.263710i
$389$	6.38859	−	5.24298i	0.323914	−	0.265830i	−0.458356	−	0.888769i	$-0.651562\pi$
$389$	6.38859	−	5.24298i	0.323914	−	0.265830i	0.782270	+	0.622939i	$0.214062\pi$
$390$	−17.9368	−	11.4807i	−0.908263	−	0.581349i
$391$	−12.4009	+	8.28603i	−0.627141	+	0.419042i
$392$	−8.27939	+	17.9669i	−0.418172	+	0.907463i
$393$	−8.46491	+	12.6686i	−0.426998	+	0.639048i
$394$	−1.05309	+	2.69104i	−0.0530538	+	0.135573i
$395$	0.183621	+	0.605318i	0.00923899	+	0.0304569i
$396$	5.24496	−	4.66178i	0.263569	−	0.234263i
$397$	−17.5948	+	21.4394i	−0.883059	+	1.07601i	0.113534	+	0.993534i	$0.463783\pi$
$397$	−17.5948	+	21.4394i	−0.883059	+	1.07601i	−0.996593	+	0.0824768i	$0.973717\pi$
$398$	−11.0196	+	21.6300i	−0.552363	+	1.08422i
$399$	0.359947	+	0.149095i	0.0180199	+	0.00746409i
$400$	0.116243	−	0.0328105i	0.00581217	−	0.00164053i
$401$	−14.0017	+	5.79970i	−0.699212	+	0.289623i	−0.703832	−	0.710366i	$-0.748529\pi$
$401$	−14.0017	+	5.79970i	−0.699212	+	0.289623i	0.00462040	+	0.999989i	$0.498529\pi$
$402$	0.424879	−	5.40225i	0.0211911	−	0.269440i
$403$	59.7416	−	5.88403i	2.97594	−	0.293104i
$404$	14.4716	−	19.1217i	0.719987	−	0.951339i
$405$	1.96607	+	1.05089i	0.0976949	+	0.0522190i
$406$	0.536311	+	0.515599i	0.0266167	+	0.0255887i
$407$	39.1009	−	7.77766i	1.93816	−	0.385524i
$408$	−5.97533	−	5.30812i	−0.295823	−	0.262791i
$409$	−0.426183	+	2.14257i	−0.0210734	+	0.105943i	−0.989890	−	0.141834i	$-0.954700\pi$
$409$	−0.426183	+	2.14257i	−0.0210734	+	0.105943i	0.968817	+	0.247777i	$0.0797001\pi$
$410$	−3.23491	+	18.1204i	−0.159761	+	0.894905i
$411$	−5.84646	−	0.575826i	−0.288385	−	0.0284034i
$412$	−19.1430	−	17.6918i	−0.943106	−	0.871614i
$413$	0.235094	+	0.0713149i	0.0115682	+	0.00350918i
$414$	−7.41241	+	0.877713i	−0.364300	+	0.0431372i
$415$	−14.1549	−	14.1549i	−0.694836	−	0.694836i
$416$	11.1019	+	36.5633i	0.544315	+	1.79266i
$417$	3.81252	−	3.81252i	0.186700	−	0.186700i
$418$	15.7818	−	20.0213i	0.771915	−	0.979276i
$419$	−8.26545	+	27.2476i	−0.403794	+	1.33113i	0.485677	+	0.874138i	$0.338573\pi$
$419$	−8.26545	+	27.2476i	−0.403794	+	1.33113i	−0.889471	+	0.456992i	$0.848927\pi$
$420$	0.116989	−	0.317215i	0.00570846	−	0.0154785i
$421$	−0.761530	+	7.73195i	−0.0371147	+	0.376832i	0.958628	+	0.284660i	$0.0918809\pi$
$421$	−0.761530	+	7.73195i	−0.0371147	+	0.376832i	−0.995743	+	0.0921717i	$0.970619\pi$
$422$	0.739703	−	0.515602i	0.0360082	−	0.0250991i
$423$	6.51690	+	1.29629i	0.316863	+	0.0630279i
$424$	18.8947	−	4.93369i	0.917605	−	0.239601i
$425$	0.0166467	+	0.0836887i	0.000807485	+	0.00405950i
$426$	0.898624	−	0.0176941i	0.0435385	−	0.000857284i
$427$	−0.311627	+	0.583013i	−0.0150807	+	0.0282140i
$428$	−4.93133	+	2.89100i	−0.238365	+	0.139742i
$429$	−2.32305	−	23.5864i	−0.112158	−	1.13876i
$430$	−7.40664	+	6.32655i	−0.357180	+	0.305093i
$431$	−3.31696	−	8.00784i	−0.159772	−	0.385724i	0.823639	−	0.567114i	$-0.191940\pi$
$431$	−3.31696	−	8.00784i	−0.159772	−	0.385724i	−0.983411	+	0.181390i	$0.941940\pi$
$432$	−1.45867	−	3.72455i	−0.0701802	−	0.179198i
$433$	−5.21842	+	12.5984i	−0.250781	+	0.605439i	−0.998268	−	0.0588378i	$-0.981261\pi$
$433$	−5.21842	+	12.5984i	−0.250781	+	0.605439i	0.747486	+	0.664277i	$0.231261\pi$
$434$	0.294554	+	0.906382i	0.0141391	+	0.0435077i
$435$	11.9548	+	9.81106i	0.573189	+	0.470404i
$436$	9.64235	−	19.8850i	0.461785	−	0.952321i
$437$	−25.9496	+	7.87173i	−1.24134	+	0.376556i
$438$	−20.1581	+	8.81862i	−0.963193	+	0.421370i
$439$	25.7965	+	17.2366i	1.23120	+	0.822660i	0.989050	−	0.147580i	$-0.0471483\pi$
$439$	25.7965	+	17.2366i	1.23120	+	0.822660i	0.242147	+	0.970239i	$0.422148\pi$
$440$	−17.9002	−	13.0010i	−0.853361	−	0.619796i
$441$	−3.88580	−	5.81551i	−0.185038	−	0.276929i
$442$	−26.3670	+	5.78656i	−1.25415	+	0.275238i
$443$	−16.9076	−	20.6019i	−0.803303	−	0.978827i	0.196696	−	0.980465i	$-0.436979\pi$
$443$	−16.9076	−	20.6019i	−0.803303	−	0.978827i	−0.999999	+	0.00163746i	$0.999479\pi$
$444$	3.55262	−	22.4457i	0.168600	−	1.06523i
$445$	−9.11605	+	4.87263i	−0.432142	+	0.230985i
$446$	35.3158	+	9.95807i	1.67225	+	0.471528i
$447$		−	5.47835i		−	0.259117i
$448$	−0.529202	+	0.296588i	−0.0250024	+	0.0140124i
$449$		−	12.6945i		−	0.599093i	−0.954082	−	0.299546i	$-0.903165\pi$
$449$		−	12.6945i		−	0.599093i	0.954082	−	0.299546i	$-0.0968353\pi$
$450$	−0.0115894	+	0.0411013i	−0.000546331	+	0.00193753i
$451$	−18.0661	+	9.65651i	−0.850697	+	0.454707i
$452$	−3.53553	+	2.56928i	−0.166297	+	0.120849i
$453$	1.63197	+	1.98856i	0.0766766	+	0.0934307i
$454$	−6.75083	−	30.7608i	−0.316832	−	1.44368i
$455$	−0.634416	−	0.949471i	−0.0297419	−	0.0445119i
$456$	−7.59487	−	12.3893i	−0.355663	−	0.580182i
$457$	9.87472	+	6.59808i	0.461920	+	0.308645i	0.764667	−	0.644426i	$-0.222904\pi$
$457$	9.87472	+	6.59808i	0.461920	+	0.308645i	−0.302747	+	0.953071i	$0.597904\pi$
$458$	11.1741	+	25.5425i	0.522132	+	1.19352i
$459$	2.70411	−	0.820283i	0.126217	−	0.0382875i
$460$	7.71229	+	22.2328i	0.359587	+	1.03661i
$461$	−8.39685	−	6.89111i	−0.391080	−	0.320951i	0.418221	−	0.908345i	$-0.362654\pi$
$461$	−8.39685	−	6.89111i	−0.391080	−	0.320951i	−0.809301	+	0.587394i	$0.800154\pi$
$462$	0.357846	−	0.116292i	0.0166485	−	0.00541039i
$463$	−6.19506	+	14.9562i	−0.287909	+	0.695073i	−0.999975	−	0.00703887i	$-0.997759\pi$
$463$	−6.19506	+	14.9562i	−0.287909	+	0.695073i	0.712066	+	0.702112i	$0.247759\pi$
$464$	−4.88394	−	27.3158i	−0.226731	−	1.26811i
$465$	7.58161	+	18.3036i	0.351589	+	0.848811i
$466$	4.54463	+	5.32051i	0.210526	+	0.246468i
$467$	−3.37994	−	34.3171i	−0.156405	−	1.58801i	−0.678162	−	0.734912i	$-0.737223\pi$
$467$	−3.37994	−	34.3171i	−0.156405	−	1.58801i	0.521757	−	0.853094i	$-0.325277\pi$
$468$	−13.0725	−	3.40974i	−0.604275	−	0.157615i
$469$	0.136972	−	0.256256i	0.00632476	−	0.0118328i
$470$	−0.412400	−	20.9444i	−0.0190226	−	0.966092i
$471$	0.741784	+	3.72920i	0.0341796	+	0.171833i
$472$	−5.53177	−	7.30528i	−0.254620	−	0.336253i
$473$	−10.6322	−	2.11487i	−0.488867	−	0.0972417i
$474$	0.229463	+	0.329196i	0.0105396	+	0.0151205i
$475$	−0.0152067	+	0.154396i	−0.000697729	+	0.00708417i
$476$	−0.179463	−	0.389178i	−0.00822568	−	0.0178379i
$477$	−2.00420	+	6.60695i	−0.0917659	+	0.302512i
$478$	−12.0162	−	9.47182i	−0.549610	−	0.433231i
$479$	15.6968	−	15.6968i	0.717204	−	0.717204i	−0.250828	−	0.968032i	$-0.580703\pi$
$479$	15.6968	−	15.6968i	0.717204	−	0.717204i	0.968032	+	0.250828i	$0.0807027\pi$
$480$	−10.4837	+	7.00898i	−0.478513	+	0.319915i
$481$	−54.2727	−	54.2727i	−2.47462	−	2.47462i
$482$	1.31587	+	11.1127i	0.0599363	+	0.506171i
$483$	−0.382999	−	0.116182i	−0.0174271	−	0.00528644i
$484$	−0.103172	−	2.61885i	−0.00468961	−	0.119038i
$485$	24.6723	+	2.43001i	1.12031	+	0.110341i
$486$	1.39220	+	0.248540i	0.0631516	+	0.0112740i
$487$	3.51434	−	17.6678i	0.159250	−	0.800603i	−0.815751	−	0.578403i	$-0.803676\pi$
$487$	3.51434	−	17.6678i	0.159250	−	0.800603i	0.975001	−	0.222200i	$-0.0713238\pi$
$488$	22.1838	−	10.7642i	1.00421	−	0.487275i
$489$	−5.25984	+	1.04625i	−0.237858	+	0.0473129i
$490$	−15.2823	+	15.8963i	−0.690386	+	0.718120i
$491$	21.8952	+	11.7032i	0.988114	+	0.528158i	0.884540	−	0.466464i	$-0.154472\pi$
$491$	21.8952	+	11.7032i	0.988114	+	0.528158i	0.103574	+	0.994622i	$0.466972\pi$
$492$	1.60110	+	11.5666i	0.0721830	+	0.521462i
$493$	19.5088	−	1.92145i	0.878633	−	0.0865378i
$494$	−48.9299	−	3.84827i	−2.20146	−	0.173142i
$495$	7.22640	−	2.99327i	0.324802	−	0.134538i
$496$	10.9777	−	33.8103i	0.492915	−	1.51813i
$497$	0.0445254	+	0.0184430i	0.00199724	+	0.000827282i
$498$	−11.3151	−	5.76459i	−0.507043	−	0.258318i
$499$	14.0013	−	17.0607i	0.626786	−	0.763741i	−0.358708	−	0.933450i	$-0.616783\pi$
$499$	14.0013	−	17.0607i	0.626786	−	0.763741i	0.985494	+	0.169709i	$0.0542827\pi$
$500$	22.3889	+	1.31797i	1.00126	+	0.0589416i
$501$	2.12068	+	6.99093i	0.0947449	+	0.312332i
$502$	15.4205	+	6.03452i	0.688249	+	0.269334i
$503$	7.60851	−	11.3869i	0.339247	−	0.507718i	−0.622145	−	0.782902i	$-0.713739\pi$
$503$	7.60851	−	11.3869i	0.339247	−	0.507718i	0.961392	+	0.275184i	$0.0887386\pi$
$504$	0.00838659	−	0.214318i	0.000373568	−	0.00954647i
$505$	22.2251	−	14.8504i	0.989005	−	0.660832i
$506$	−14.1184	+	22.0576i	−0.627637	+	0.980580i
$507$	−25.2225	+	20.6996i	−1.12017	+	0.919302i
$508$	5.91950	−	9.66203i	0.262635	−	0.428683i
$509$	−17.5778	−	32.8858i	−0.779124	−	1.45764i	−0.886158	−	0.463384i	$-0.846635\pi$
$509$	−17.5778	−	32.8858i	−0.779124	−	1.45764i	0.107033	−	0.994255i	$-0.465865\pi$
$510$	−4.35349	−	7.77275i	−0.192776	−	0.344183i
$511$	−1.17979			−0.0521910
$512$	22.4718	+	2.64890i	0.993124	+	0.117066i
$513$	5.13781			0.226840
$514$	16.7047	+	29.8247i	0.736812	+	1.31551i
$515$	−13.6964	−	25.6242i	−0.603535	−	1.12914i
$516$	−3.22813	+	5.26908i	−0.142111	+	0.231958i
$517$	18.0214	−	14.7898i	0.792582	−	0.650455i
$518$	0.656902	−	1.02630i	0.0288626	−	0.0450931i
$519$	−0.817680	+	0.546357i	−0.0358922	+	0.0239824i
$520$	−1.66544	+	42.5601i	−0.0730346	+	1.86638i
$521$	−16.9459	+	25.3613i	−0.742412	+	1.11110i	0.247428	+	0.968906i	$0.420415\pi$
$521$	−16.9459	+	25.3613i	−0.742412	+	1.11110i	−0.989839	+	0.142191i	$0.954585\pi$
$522$	9.13612	+	3.57525i	0.399877	+	0.156484i
$523$	4.97237	+	16.3917i	0.217427	+	0.716760i	0.996012	+	0.0892208i	$0.0284377\pi$
$523$	4.97237	+	16.3917i	0.217427	+	0.716760i	−0.778585	+	0.627539i	$0.784062\pi$
$524$	30.4202	+	1.79075i	1.32891	+	0.0782294i
$525$	−0.00145264	+	0.00177004i	−6.33983e−5	+	7.72510e-5i
$526$	34.1905	+	17.4187i	1.49078	+	0.759490i
$527$	23.2010	+	9.61018i	1.01065	+	0.418626i
$528$	−13.3485	−	4.33408i	−0.580919	−	0.188617i
$529$	4.48736	−	1.85873i	0.195103	−	0.0808141i
$530$	21.7001	+	1.70668i	0.942593	+	0.0741336i
$531$	3.22415	−	0.317551i	0.139916	−	0.0137805i
$532$	−0.106843	−	0.771848i	−0.00463221	−	0.0334639i
$533$	34.7814	+	18.5910i	1.50655	+	0.805267i
$534$	−4.54450	+	4.72706i	−0.196660	+	0.204560i
$535$	−6.24924	+	1.24305i	−0.270178	+	0.0537418i
$536$	−9.75060	+	4.73129i	−0.421162	+	0.204360i
$537$	2.60650	−	13.1038i	0.112479	−	0.565469i
$538$	−15.7028	−	2.80331i	−0.676996	−	0.120859i
$539$	−24.4220	−	2.40536i	−1.05193	−	0.103606i
$540$	−0.175514	−	4.45516i	−0.00755294	−	0.191719i
$541$	6.83742	+	2.07411i	0.293963	+	0.0891728i	0.433822	−	0.900999i	$-0.357165\pi$
$541$	6.83742	+	2.07411i	0.293963	+	0.0891728i	−0.139858	+	0.990172i	$0.544665\pi$
$542$	−1.96811	−	16.6210i	−0.0845378	−	0.713933i
$543$	−3.97357	−	3.97357i	−0.170522	−	0.170522i
$544$	−3.11440	+	15.6787i	−0.133529	+	0.672221i
$545$	17.4184	−	17.4184i	0.746122	−	0.746122i
$546$	−0.568910	−	0.448444i	−0.0243471	−	0.0191916i
$547$	−0.699697	+	2.30659i	−0.0299169	+	0.0986228i	−0.970627	−	0.240588i	$-0.922660\pi$
$547$	−0.699697	+	2.30659i	−0.0299169	+	0.0986228i	0.940711	+	0.339210i	$0.110160\pi$
$548$	4.92017	+	10.6697i	0.210179	+	0.455788i
$549$	−0.854486	+	8.67574i	−0.0364686	+	0.370272i
$550$	0.0856787	+	0.122918i	0.00365335	+	0.00524124i
$551$	34.9575	+	6.95347i	1.48924	+	0.296228i
$552$	9.01200	+	11.9013i	0.383576	+	0.506552i
$553$	0.00419769	+	0.0211032i	0.000178504	+	0.000897399i
$554$	−0.825152	−	41.9066i	−0.0350573	−	1.78044i
$555$	11.9408	−	22.3396i	0.506858	−	0.948264i
$556$	−10.4343	−	2.72163i	−0.442514	−	0.115423i
$557$	−1.02809	−	10.4384i	−0.0435618	−	0.442290i	−0.992084	−	0.125579i	$-0.959921\pi$
$557$	−1.02809	−	10.4384i	−0.0435618	−	0.442290i	0.948522	−	0.316712i	$-0.102579\pi$
$558$	8.16279	+	9.55638i	0.345559	+	0.404554i
$559$	7.98676	+	19.2818i	0.337804	+	0.815531i
$560$	−0.665643	+	0.119014i	−0.0281286	+	0.00502925i
$561$	3.79416	−	9.15992i	0.160190	−	0.386732i
$562$	−4.05717	+	1.31849i	−0.171141	+	0.0556172i
$563$	−8.15656	−	6.69391i	−0.343758	−	0.282115i	0.446633	−	0.894717i	$-0.352623\pi$
$563$	−8.15656	−	6.69391i	−0.343758	−	0.282115i	−0.790391	+	0.612602i	$0.790123\pi$
$564$	−4.35525	−	12.5552i	−0.183389	−	0.528670i
$565$	−4.66181	+	1.41414i	−0.196124	+	0.0594935i
$566$	−16.9210	−	38.6790i	−0.711242	−	1.62580i
$567$	0.0630509	+	0.0421293i	0.00264789	+	0.00176926i
$568$	−0.939484	−	1.53255i	−0.0394199	−	0.0643045i
$569$	20.1477	+	30.1532i	0.844636	+	1.26409i	0.962561	+	0.271065i	$0.0873759\pi$
$569$	20.1477	+	30.1532i	0.844636	+	1.26409i	−0.117925	+	0.993023i	$0.537624\pi$
$570$	−3.47223	−	15.8215i	−0.145436	−	0.662691i
$571$	9.57181	+	11.6633i	0.400568	+	0.488093i	0.933759	−	0.357901i	$-0.116508\pi$
$571$	9.57181	+	11.6633i	0.400568	+	0.488093i	−0.533192	+	0.845994i	$0.679008\pi$
$572$	−38.3452	+	27.8656i	−1.60330	+	1.16512i
$573$	−14.6693	+	7.84089i	−0.612818	+	0.327558i
$574$	−0.169922	+	0.602621i	−0.00709242	+	0.0251529i
$575$		−	0.159375i		−	0.00664641i
$576$	−4.95076	+	6.28410i	−0.206282	+	0.261838i
$577$		−	0.500470i		−	0.0208348i	−0.999946	−	0.0104174i	$-0.996684\pi$
$577$		−	0.500470i		−	0.0208348i	0.999946	−	0.0104174i	$-0.00331603\pi$
$578$	12.2705	+	3.45995i	0.510387	+	0.143915i
$579$	−14.1655	+	7.57159i	−0.588696	+	0.314665i
$580$	4.83538	−	30.5502i	0.200778	−	1.26853i
$581$	−0.431972	−	0.526359i	−0.0179212	−	0.0218371i
$582$	15.3616	−	3.37129i	0.636760	−	0.139745i
$583$	13.4584	+	20.1419i	0.557388	+	0.834190i
$584$	35.6052	+	25.8601i	1.47335	+	1.07010i
$585$	−12.5209	−	8.36621i	−0.517677	−	0.345900i
$586$	9.32516	−	4.07950i	0.385219	−	0.168522i
$587$	−46.1858	+	14.0103i	−1.90629	+	0.578268i	−0.927325	+	0.374258i	$0.877897\pi$
$587$	−46.1858	+	14.0103i	−1.90629	+	0.578268i	−0.978969	+	0.204010i	$0.934603\pi$
$588$	−6.10338	+	12.5868i	−0.251699	+	0.519070i
$589$	35.2952	+	28.9661i	1.45432	+	1.19353i
$590$	−3.15681	−	9.71392i	−0.129964	−	0.399916i
$591$	−0.781962	+	1.88782i	−0.0321656	+	0.0776546i
$592$	−42.3205	+	16.5742i	−1.73936	+	0.681196i
$593$	−2.62342	−	6.33350i	−0.107731	−	0.260086i	0.860816	−	0.508916i	$-0.169954\pi$
$593$	−2.62342	−	6.33350i	−0.107731	−	0.260086i	−0.968547	+	0.248831i	$0.919954\pi$
$594$	3.77292	−	3.22272i	0.154805	−	0.132230i
$595$	−0.0468227	−	0.475399i	−0.00191954	−	0.0194894i
$596$	−9.45214	+	5.54133i	−0.387175	+	0.226982i
$597$	−8.09163	+	15.1384i	−0.331168	+	0.619573i
$598$	50.4103	−	0.992591i	2.06143	−	0.0405901i
$599$	−5.42946	−	27.2957i	−0.221842	−	1.11527i	−0.917755	−	0.397147i	$-0.870000\pi$
$599$	−5.42946	−	27.2957i	−0.221842	−	1.11527i	0.695913	−	0.718126i	$-0.255000\pi$
$600$	0.0826373	−	0.0215779i	0.00337365	−	0.000880913i
$601$	29.9860	+	5.96459i	1.22316	+	0.243301i	0.764095	−	0.645104i	$-0.223186\pi$
$601$	29.9860	+	5.96459i	1.22316	+	0.243301i	0.459061	+	0.888405i	$0.348186\pi$
$602$	−0.271820	+	0.189469i	−0.0110786	+	0.00772219i
$603$	0.375578	−	3.81331i	0.0152947	−	0.155290i
$604$	1.78026	−	4.82716i	0.0724376	−	0.196414i
$605$	0.848028	−	2.79557i	0.0344773	−	0.113656i
$606$	10.4971	−	13.3170i	0.426417	−	0.540966i
$607$	4.61066	−	4.61066i	0.187141	−	0.187141i	−0.607318	−	0.794459i	$-0.707755\pi$
$607$	4.61066	−	4.61066i	0.187141	−	0.187141i	0.794459	+	0.607318i	$0.207755\pi$
$608$	−13.6938	+	25.6357i	−0.555359	+	1.03966i
$609$	0.371978	+	0.371978i	0.0150733	+	0.0150733i
$610$	27.2938	−	3.23190i	1.10509	−	0.130856i
$611$	−42.9509	−	13.0290i	−1.73761	−	0.527098i
$612$	−4.15048	−	3.83586i	−0.167773	−	0.155055i
$613$	−20.4217	−	2.01136i	−0.824824	−	0.0812381i	−0.323207	−	0.946328i	$-0.604761\pi$
$613$	−20.4217	−	2.01136i	−0.824824	−	0.0812381i	−0.501617	+	0.865090i	$0.667261\pi$
$614$	−6.11945	+	34.2782i	−0.246961	+	1.38336i
$615$	−2.53923	+	12.7656i	−0.102392	+	0.514758i
$616$	−0.562606	−	0.499784i	−0.0226680	−	0.0201369i
$617$	−23.2638	+	4.62746i	−0.936566	+	0.186295i	−0.639700	−	0.768625i	$-0.720941\pi$
$617$	−23.2638	+	4.62746i	−0.936566	+	0.186295i	−0.296866	+	0.954919i	$0.595941\pi$
$618$	−13.2872	−	12.7741i	−0.534490	−	0.513848i
$619$	14.3111	+	7.64942i	0.575210	+	0.307456i	0.733231	−	0.679980i	$-0.238011\pi$
$619$	14.3111	+	7.64942i	0.575210	+	0.307456i	−0.158021	+	0.987436i	$0.550511\pi$
$620$	23.9116	−	31.5951i	0.960314	−	1.26889i
$621$	−5.25257	+	0.517333i	−0.210778	+	0.0207598i
$622$	−0.0383971	+	0.488211i	−0.00153958	+	0.0195755i
$623$	−0.324839	+	0.134553i	−0.0130144	+	0.00539074i
$624$	7.33973	+	26.0037i	0.293824	+	1.04098i
$625$	22.9567	+	9.50896i	0.918266	+	0.380358i
$626$	6.31859	−	12.4026i	0.252542	−	0.495706i
$627$	11.4360	−	13.9348i	0.456709	−	0.556502i
$628$	5.68391	−	5.05192i	0.226813	−	0.201594i
$629$	−9.32052	−	30.7256i	−0.371633	−	1.22511i
$630$	0.0871232	−	0.222633i	0.00347107	−	0.00886989i
$631$	−5.15750	+	7.71874i	−0.205317	+	0.307278i	−0.919810	−	0.392364i	$-0.871657\pi$
$631$	−5.15750	+	7.71874i	−0.205317	+	0.307278i	0.714493	+	0.699642i	$0.246657\pi$
$632$	0.335882	−	0.728887i	0.0133607	−	0.0289936i
$633$	0.530125	−	0.354218i	0.0210706	−	0.0140789i
$634$	−17.2772	−	11.0586i	−0.686164	−	0.439191i
$635$	9.76336	−	8.01258i	0.387447	−	0.317970i
$636$	13.4266	−	3.22495i	0.532400	−	0.127877i
$637$	22.2714	+	41.6669i	0.882426	+	1.65090i
$638$	30.0324	−	16.8210i	1.18899	−	0.665951i
$639$	0.635546			0.0251418
$640$	22.6973	+	10.9986i	0.897188	+	0.434758i
$641$	38.1516			1.50690			0.753448	−	0.657507i	$-0.228389\pi$
$641$	38.1516			1.50690			0.753448	+	0.657507i	$0.228389\pi$
$642$	−3.52654	+	1.97520i	−0.139182	+	0.0779551i
$643$	−13.4797	−	25.2187i	−0.531587	−	0.994529i	−0.994157	−	0.107946i	$-0.965573\pi$
$643$	−13.4797	−	25.2187i	−0.531587	−	0.994529i	0.462570	−	0.886583i	$-0.346927\pi$
$644$	0.186947	+	0.778329i	0.00736675	+	0.0306705i
$645$	−5.32434	+	4.36957i	−0.209646	+	0.172052i
$646$	−17.2931	−	11.0687i	−0.680386	−	0.435493i
$647$	−37.9660	+	25.3681i	−1.49260	+	0.997322i	−0.501360	+	0.865239i	$0.667167\pi$
$647$	−37.9660	+	25.3681i	−1.49260	+	0.997322i	−0.991239	+	0.132084i	$0.957833\pi$
$648$	−0.979387	−	2.65345i	−0.0384740	−	0.104237i
$649$	6.31519	−	9.45135i	0.247893	−	0.370998i
$650$	0.105122	−	0.268626i	0.00412322	−	0.0105364i
$651$	0.195624	+	0.644885i	0.00766710	+	0.0252750i
$652$	7.12547	+	8.01685i	0.279055	+	0.313964i
$653$	−20.8339	+	25.3862i	−0.815293	+	0.993437i	0.184651	+	0.982804i	$0.440885\pi$
$653$	−20.8339	+	25.3862i	−0.815293	+	0.993437i	−0.999943	+	0.0106327i	$0.996615\pi$
$654$	7.09366	−	13.9239i	0.277384	−	0.544468i
$655$	31.3811	+	12.9985i	1.22616	+	0.507893i
$656$	18.3370	−	14.4620i	0.715941	−	0.564648i
$657$	−14.3740	+	5.95389i	−0.560781	+	0.232283i
$658$	0.0558701	−	0.710376i	0.00217804	−	0.0276933i
$659$	−35.9819	+	3.54390i	−1.40165	+	0.138051i	−0.770418	−	0.637540i	$-0.779952\pi$
$659$	−35.9819	+	3.54390i	−1.40165	+	0.138051i	−0.631236	+	0.775590i	$0.717452\pi$
$660$	−12.4740	−	9.44046i	−0.485548	−	0.367470i
$661$	1.21464	+	0.649238i	0.0472440	+	0.0252524i	0.494850	−	0.868979i	$-0.335223\pi$
$661$	1.21464	+	0.649238i	0.0472440	+	0.0252524i	−0.447606	+	0.894231i	$0.647723\pi$
$662$	−11.3844	−	10.9447i	−0.442467	−	0.425379i
$663$	−18.7212	+	3.72388i	−0.727072	+	0.144624i
$664$	1.49921	+	25.3536i	0.0581804	+	0.983909i
$665$	0.169445	−	0.851858i	0.00657080	−	0.0330336i
$666$	2.82405	−	15.8190i	0.109430	−	0.612973i
$667$	−36.4384	−	3.58887i	−1.41090	−	0.138962i
$668$	9.91684	−	10.7302i	0.383694	−	0.415166i
$669$	24.8286	+	7.53167i	0.959928	+	0.291191i
$670$	−11.9966	+	1.42054i	−0.463471	+	0.0548802i
$671$	21.6284	+	21.6284i	0.834956	+	0.834956i
$672$	−0.378258	+	0.202312i	−0.0145916	+	0.00780434i
$673$	9.40336	−	9.40336i	0.362473	−	0.362473i	−0.502250	−	0.864723i	$-0.667494\pi$
$673$	9.40336	−	9.40336i	0.362473	−	0.362473i	0.864723	+	0.502250i	$0.167494\pi$
$674$	−5.52822	+	7.01328i	−0.212939	+	0.270141i
$675$	−0.00876552	+	0.0288960i	−0.000337385	+	0.00111221i
$676$	61.2269	+	22.5804i	2.35488	+	0.868478i
$677$	3.59548	−	36.5056i	0.138186	−	1.40302i	−0.636793	−	0.771035i	$-0.719739\pi$
$677$	3.59548	−	36.5056i	0.138186	−	1.40302i	0.774979	−	0.631987i	$-0.217761\pi$
$678$	−2.53528	+	1.76719i	−0.0973668	+	0.0678685i
$679$	0.827095	+	0.164519i	0.0317410	+	0.00631368i
$680$	−9.00727	+	15.3735i	−0.345413	+	0.589545i
$681$	−4.34443	−	21.8409i	−0.166479	−	0.836946i
$682$	44.0880	−	0.868103i	1.68822	−	0.0332414i
$683$	8.82810	−	16.5162i	0.337798	−	0.631975i	−0.654470	−	0.756088i	$-0.727108\pi$
$683$	8.82810	−	16.5162i	0.337798	−	0.631975i	0.992268	+	0.124113i	$0.0396084\pi$
$684$	−5.19688	−	8.86459i	−0.198708	−	0.338946i
$685$	1.28369	+	13.0336i	0.0490474	+	0.497986i
$686$	−1.14113	+	0.974722i	−0.0435686	+	0.0372151i
$687$	7.54420	+	18.2133i	0.287829	+	0.694881i
$688$	12.3563	+	0.240038i	0.471080	+	0.00915136i
$689$	17.8475	−	43.0876i	0.679934	−	1.64151i
$690$	5.14287	+	15.8253i	0.195786	+	0.602458i
$691$	−27.2082	−	22.3292i	−1.03505	−	0.849442i	−0.0462844	−	0.998928i	$-0.514738\pi$
$691$	−27.2082	−	22.3292i	−1.03505	−	0.849442i	−0.988764	+	0.149486i	$0.952238\pi$
$692$	1.76974	+	0.858157i	0.0672756	+	0.0326222i
$693$	0.254605	−	0.0772336i	0.00967164	−	0.00293386i
$694$	−36.3282	+	15.8926i	−1.37900	+	0.603273i
$695$	−9.99409	−	6.67784i	−0.379097	−	0.253305i
$696$	−3.07255	−	19.3795i	−0.116465	−	0.734577i
$697$	9.16590	+	13.7177i	0.347183	+	0.519597i
$698$	21.3067	−	4.67601i	0.806469	−	0.176989i
$699$	3.13885	+	3.82470i	0.118722	+	0.144664i
$700$	0.00452330		0.000715932i	0.000170965		2.70597e-5i
$701$	45.4882	−	24.3139i	1.71806	−	0.918325i	0.752332	−	0.658784i	$-0.228929\pi$
$701$	45.4882	−	24.3139i	1.71806	−	0.918325i	0.965732	−	0.259541i	$-0.0835712\pi$
$702$	−9.19438	−	2.59256i	−0.347019	−	0.0978499i
$703$		−	58.3787i		−	2.20180i
$704$	6.02412	+	27.4149i	0.227043	+	1.03324i
$705$		−	14.8128i		−	0.557882i
$706$	3.47412	−	12.3208i	0.130750	−	0.463699i
$707$	0.801868	−	0.428608i	0.0301574	−	0.0161194i
$708$	−3.80910	−	5.24162i	−0.143155	−	0.196992i
$709$	−12.8182	−	15.6190i	−0.481398	−	0.586585i	0.474511	−	0.880250i	$-0.342625\pi$
$709$	−12.8182	−	15.6190i	−0.481398	−	0.586585i	−0.955908	+	0.293665i	$0.905125\pi$
$710$	−0.429514	−	1.95712i	−0.0161194	−	0.0734494i
$711$	0.157641	+	0.235926i	0.00591198	+	0.00884791i
$712$	12.7526	+	3.05950i	0.477926	+	0.114660i
$713$	−39.0002	−	26.0591i	−1.46057	−	0.975921i
$714$	−0.121458	−	0.277635i	−0.00454543	−	0.0103902i
$715$	−50.5605	+	15.3374i	−1.89086	+	0.573585i
$716$	−25.2452	+	8.75726i	−0.943458	+	0.327274i
$717$	−8.36327	−	6.86356i	−0.312332	−	0.256324i
$718$	−30.8857	+	10.0372i	−1.15264	+	0.374584i
$719$	8.01713	−	19.3551i	0.298988	−	0.721822i	−0.700974	−	0.713187i	$-0.747251\pi$
$719$	8.01713	−	19.3551i	0.298988	−	0.721822i	0.999963	−	0.00863533i	$-0.00274874\pi$
$720$	−7.50922	+	4.80920i	−0.279852	+	0.179228i
$721$	−0.378212	−	0.913084i	−0.0140853	−	0.0340050i
$722$	−6.79437	−	7.95434i	−0.252860	−	0.296030i
$723$	0.775588	+	7.87467i	0.0288444	+	0.292862i
$724$	−2.83659	+	10.8751i	−0.105421	+	0.404170i
$725$	−0.0987479	+	0.184744i	−0.00366740	+	0.00686123i
$726$	−0.0364837	−	1.85288i	−0.00135404	−	0.0687669i
$727$	−8.67438	−	43.6090i	−0.321715	−	1.61737i	−0.715807	−	0.698299i	$-0.753941\pi$
$727$	−8.67438	−	43.6090i	−0.321715	−	1.61737i	0.394092	−	0.919071i	$-0.371059\pi$
$728$	−0.198277	+	1.43518i	−0.00734864	+	0.0531911i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	28.0487	+	40.2398i	1.03813	+	1.48934i
$731$	−0.855761	+	8.68869i	−0.0316515	+	0.321363i
$732$	15.8331	−	7.30119i	0.585209	−	0.269860i
$733$	−11.4509	+	37.7484i	−0.422947	+	1.39427i	0.444071	+	0.895992i	$0.353534\pi$
$733$	−11.4509	+	37.7484i	−0.422947	+	1.39427i	−0.867018	+	0.498278i	$0.833966\pi$
$734$	10.7389	+	8.46494i	0.396379	+	0.312446i
$735$	−11.0254	+	11.0254i	−0.406679	+	0.406679i
$736$	11.4184	−	27.5871i	0.420888	−	1.01687i
$737$	−9.50649	−	9.50649i	−0.350176	−	0.350176i
$738$	0.970915	+	8.19952i	0.0357399	+	0.301828i
$739$	−47.9887	−	14.5572i	−1.76529	−	0.535496i	−0.770502	−	0.637437i	$-0.779994\pi$
$739$	−47.9887	−	14.5572i	−1.76529	−	0.535496i	−0.994790	+	0.101942i	$0.967494\pi$
$740$	−50.6220	+	1.99429i	−1.86090	+	0.0733117i
$741$	−34.5384	−	3.40174i	−1.26880	−	0.124966i
$742$	0.728893	+	0.130124i	0.0267585	+	0.00477701i
$743$	−4.60756	+	23.1638i	−0.169035	+	0.849796i	0.799452	+	0.600730i	$0.205123\pi$
$743$	−4.60756	+	23.1638i	−0.169035	+	0.849796i	−0.968487	+	0.249065i	$0.919877\pi$
$744$	8.23158	−	23.7500i	0.301784	−	0.870718i
$745$	−11.9782	+	2.38262i	−0.438849	+	0.0872925i
$746$	3.17166	−	3.29907i	0.116123	−	0.120788i
$747$	−7.91921	−	4.23291i	−0.289749	−	0.154874i
$748$	−19.6420	+	2.71893i	−0.718181	+	0.0994137i
$749$	−0.215691	+	0.0212437i	−0.00788119	+	0.000776229i
$750$	15.8100	+	1.24343i	0.577298	+	0.0454037i
$751$	−27.7653	+	11.5008i	−1.01317	+	0.419669i	−0.826610	−	0.562774i	$-0.809734\pi$
$751$	−27.7653	+	11.5008i	−1.01317	+	0.419669i	−0.186560	+	0.982444i	$0.559734\pi$
$752$	−17.2570	+	20.2139i	−0.629296	+	0.737126i
$753$	10.8178	+	4.48088i	0.394223	+	0.163292i
$754$	−59.0494	−	30.0833i	−2.15045	−	1.09557i
$755$	3.63816	−	4.43311i	0.132406	−	0.161337i
$756$	0.00891245	−	0.151399i	0.000324143	−	0.00550634i
$757$	1.67476	+	5.52093i	0.0608700	+	0.200662i	0.982101	−	0.188354i	$-0.0603152\pi$
$757$	1.67476	+	5.52093i	0.0608700	+	0.200662i	−0.921231	+	0.389016i	$0.872815\pi$
$758$	38.5369	+	15.0807i	1.39972	+	0.547755i
$759$	−10.2883	+	15.3975i	−0.373442	+	0.558895i
$760$	−23.7857	+	21.9943i	−0.862799	+	0.797816i
$761$	−25.2801	+	16.8916i	−0.916403	+	0.612321i	−0.921801	−	0.387665i	$-0.873282\pi$
$761$	−25.2801	+	16.8916i	−0.916403	+	0.612321i	0.00539756	+	0.999985i	$0.498282\pi$
$762$	4.31940	−	6.74836i	0.156475	−	0.244467i
$763$	0.647715	−	0.531566i	0.0234488	−	0.0192440i
$764$	28.3663	+	17.3788i	1.02626	+	0.628742i
$765$	−2.96959	−	5.55570i	−0.107366	−	0.200867i
$766$	−14.3654	−	25.6481i	−0.519044	−	0.926705i
$767$	−21.8842			−0.790194
$768$	15.8500	+	2.18551i	0.571939	+	0.0788627i
$769$	−1.27916			−0.0461276			−0.0230638	−	0.999734i	$-0.507342\pi$
$769$	−1.27916			−0.0461276			−0.0230638	+	0.999734i	$0.507342\pi$
$770$	−0.409902	−	0.731842i	−0.0147718	−	0.0263737i
$771$	11.3945	+	21.3177i	0.410364	+	0.767737i
$772$	27.3921	+	16.7819i	0.985862	+	0.603994i
$773$	−11.5914	+	9.51279i	−0.416913	+	0.342151i	−0.819347	−	0.573297i	$-0.805664\pi$
$773$	−11.5914	+	9.51279i	−0.416913	+	0.342151i	0.402435	+	0.915449i	$0.368164\pi$
$774$	−2.35554	+	3.68014i	−0.0846681	+	0.132280i
$775$	−0.223127	+	0.149089i	−0.00801496	+	0.00535543i
$776$	−21.3549	−	23.0943i	−0.766597	−	0.829037i
$777$	0.478697	−	0.716420i	0.0171731	−	0.0257014i
$778$	−10.8841	−	4.25930i	−0.390215	−	0.152703i
$779$	8.70762	+	28.7052i	0.311983	+	1.02847i
$780$	−1.76987	+	30.0655i	−0.0633716	+	1.07652i
$781$	1.41463	−	1.72373i	0.0506194	−	0.0616799i
$782$	18.7938	+	9.57468i	0.672065	+	0.342390i
$783$	6.40919	+	2.65477i	0.229046	+	0.0948738i
$784$	27.8903	−	2.20094i	0.996082	−	0.0786049i
$785$	7.83117	−	3.24378i	0.279507	−	0.115775i
$786$	21.4812	+	1.68947i	0.766211	+	0.0602614i
$787$	−9.33934	+	0.919845i	−0.332912	+	0.0327889i	−0.263092	−	0.964771i	$-0.584742\pi$
$787$	−9.33934	+	0.919845i	−0.332912	+	0.0327889i	−0.0698195	+	0.997560i	$0.522242\pi$
$788$	4.04813	−	0.560360i	0.144209	−	0.0199620i
$789$	23.9292	+	12.7904i	0.851902	+	0.455351i
$790$	0.619980	−	0.644886i	0.0220579	−	0.0229440i
$791$	−0.162525	+	0.0323282i	−0.00577871	+	0.00114946i
$792$	−9.37666	−	3.24988i	−0.333185	−	0.115479i
$793$	11.4884	−	57.7560i	0.407965	−	2.05098i
$794$	38.6126	+	6.89323i	1.37031	+	0.244632i
$795$	15.3176	+	1.50865i	0.543258	+	0.0535062i
$796$	34.3038	−	1.35143i	1.21587	−	0.0479001i
$797$	−39.0766	−	11.8538i	−1.38417	−	0.419882i	−0.491608	−	0.870816i	$-0.663591\pi$
$797$	−39.0766	−	11.8538i	−1.38417	−	0.419882i	−0.892557	+	0.450934i	$0.851091\pi$
$798$	−0.0647900	−	0.547161i	−0.00229354	−	0.0193693i
$799$	−13.2767	−	13.2767i	−0.469698	−	0.469698i
$800$	−0.120817	−	0.120753i	−0.00427153	−	0.00426927i
$801$	−3.27863	+	3.27863i	−0.115845	+	0.115845i
$802$	16.8323	+	13.2681i	0.594369	+	0.468512i
$803$	−15.8461	+	52.2375i	−0.559196	+	1.84342i
$804$	−6.95924	+	3.20914i	−0.245433	+	0.113178i
$805$	−0.0874550	+	0.887945i	−0.00308238	+	0.0312960i
$806$	−48.5463	−	69.6463i	−1.70997	−	2.45319i
$807$	−11.0624	−	2.20044i	−0.389414	−	0.0774593i
$808$	−33.5945	−	4.64126i	−1.18185	−	0.163279i
$809$	−7.25257	−	36.4611i	−0.254987	−	1.28190i	−0.869868	−	0.493285i	$-0.835796\pi$
$809$	−7.25257	−	36.4611i	−0.254987	−	1.28190i	0.614881	−	0.788620i	$-0.289204\pi$
$810$	−0.0620657	−	3.15210i	−0.00218077	−	0.110754i
$811$	3.02345	−	5.65647i	0.106168	−	0.198626i	−0.823228	−	0.567711i	$-0.807829\pi$
$811$	3.02345	−	5.65647i	0.106168	−	0.198626i	0.929395	+	0.369086i	$0.120329\pi$
$812$	0.265542	−	1.01805i	0.00931871	−	0.0357266i
$813$	−1.16003	−	11.7779i	−0.0406839	−	0.413070i
$814$	−36.6184	−	42.8701i	−1.28347	−	1.50259i
$815$	4.57518	+	11.0455i	0.160261	+	0.386905i
$816$	−2.42004	+	11.0410i	−0.0847183	+	0.386514i
$817$	−6.07476	+	14.6658i	−0.212529	+	0.513090i
$818$	2.93815	−	0.954834i	0.102730	−	0.0333850i
$819$	−0.395960	−	0.324956i	−0.0138359	−	0.0113549i
$820$	24.5937	−	8.53125i	0.858848	−	0.297924i
$821$	−52.9223	+	16.0538i	−1.84700	+	0.560282i	−0.847434	+	0.530900i	$0.821854\pi$
$821$	−52.9223	+	16.0538i	−1.84700	+	0.560282i	−0.999568	+	0.0293816i	$0.990646\pi$
$822$	3.32988	+	7.61165i	0.116143	+	0.265487i
$823$	26.3314	+	17.5941i	0.917855	+	0.613291i	0.922206	−	0.386699i	$-0.126385\pi$
$823$	26.3314	+	17.5941i	0.917855	+	0.613291i	−0.00435058	+	0.999991i	$0.501385\pi$
$824$	−8.59991	+	35.8462i	−0.299592	+	1.24876i
$825$	0.0588612	+	0.0880920i	0.00204928	+	0.00306697i
$826$	−0.0744760	−	0.339357i	−0.00259135	−	0.0118077i
$827$	3.30225	+	4.02380i	0.114830	+	0.139921i	0.827253	−	0.561829i	$-0.189902\pi$
$827$	3.30225	+	4.02380i	0.114830	+	0.139921i	−0.712423	+	0.701750i	$0.752402\pi$
$828$	6.20554	+	8.53930i	0.215657	+	0.296761i
$829$	9.75505	−	5.21418i	0.338807	−	0.181096i	−0.293215	−	0.956047i	$-0.594725\pi$
$829$	9.75505	−	5.21418i	0.338807	−	0.181096i	0.632022	+	0.774950i	$0.282225\pi$
$830$	−7.68298	+	27.2473i	−0.266680	+	0.945768i
$831$		−	29.6382i		−	1.02814i
$832$	37.4417	−	38.9663i	1.29806	−	1.35091i
$833$			19.7643i			0.684791i
$834$	−7.33887	−	2.06936i	−0.254124	−	0.0716560i
$835$	14.3632	−	7.67727i	0.497057	−	0.265683i
$836$	−35.6100	−	5.63622i	−1.23160	−	0.194933i
$837$	5.63782	+	6.86970i	0.194871	+	0.237452i
$838$	39.3317	−	8.63183i	1.35869	−	0.298182i
$839$	−6.95323	−	10.4062i	−0.240052	−	0.359263i	0.691808	−	0.722082i	$-0.256815\pi$
$839$	−6.95323	−	10.4062i	−0.240052	−	0.359263i	−0.931860	+	0.362818i	$0.881815\pi$
$840$	−0.472247	+	0.0748731i	−0.0162941	+	0.00258337i
$841$	15.9023	+	10.6256i	0.548354	+	0.366399i
$842$	10.0664	−	4.40377i	0.346912	−	0.151764i
$843$	−2.88665	+	0.875655i	−0.0994215	+	0.0301592i
$844$	−1.14737	−	0.556367i	−0.0394943	−	0.0191509i
$845$	56.2288	+	46.1458i	1.93433	+	1.58746i
$846$	−2.90426	−	8.93678i	−0.0998504	−	0.307253i
$847$	0.0380278	−	0.0918073i	0.00130665	−	0.00315454i
$848$	−19.1452	−	19.9038i	−0.657448	−	0.683498i
$849$	−11.4242	−	27.5804i	−0.392077	−	0.946559i
$850$	0.0917559	−	0.0783753i	0.00314720	−	0.00268825i
$851$	5.87822	+	59.6826i	0.201503	+	2.04589i
$852$	−0.642853	−	1.09655i	−0.0220238	−	0.0375671i
$853$	−0.485278	+	0.907891i	−0.0166156	+	0.0310856i	−0.890092	−	0.455781i	$-0.849360\pi$
$853$	−0.485278	+	0.907891i	−0.0166156	+	0.0310856i	0.873476	+	0.486866i	$0.161860\pi$
$854$	0.934715	−	0.0184048i	0.0319853	−	0.000629798i
$855$	−2.23452	−	11.2337i	−0.0764189	−	0.384184i
$856$	6.97503	+	4.08665i	0.238402	+	0.139679i
$857$	−11.1595	−	2.21976i	−0.381201	−	0.0758256i	0.000770360	−	1.00000i	$-0.499755\pi$
$857$	−11.1595	−	2.21976i	−0.381201	−	0.0758256i	−0.381972	+	0.924174i	$0.624755\pi$
$858$	−27.4968	+	19.1664i	−0.938726	+	0.654329i
$859$	4.10215	−	41.6498i	0.139963	−	1.42107i	−0.626819	−	0.779165i	$-0.715643\pi$
$859$	4.10215	−	41.6498i	0.139963	−	1.42107i	0.766782	−	0.641907i	$-0.221857\pi$
$860$	12.9246	+	4.76661i	0.440727	+	0.162540i
$861$	−0.128519	+	0.423669i	−0.00437990	+	0.0144386i
$862$	−7.58827	+	9.62672i	−0.258457	+	0.327887i
$863$	−37.4722	+	37.4722i	−1.27557	+	1.27557i	−0.332445	+	0.943123i	$0.607874\pi$
$863$	−37.4722	+	37.4722i	−1.27557	+	1.27557i	−0.943123	+	0.332445i	$0.892126\pi$
$864$	−3.58752	+	4.37375i	−0.122050	+	0.148798i
$865$	1.55021	+	1.55021i	0.0527089	+	0.0527089i
$866$	19.1510	−	2.26769i	0.650776	−	0.0770593i
$867$	8.62674	+	2.61689i	0.292980	+	0.0888744i
$868$	0.914788	−	0.989821i	0.0310499	−	0.0335967i
$869$	0.990762	+	0.0975816i	0.0336093	+	0.00331023i
$870$	3.84374	−	21.5308i	0.130315	−	0.729962i
$871$	−5.04957	+	25.3859i	−0.171098	+	0.860169i
$872$	−31.1990	+	1.84486i	−1.05653	+	0.0624747i
$873$	10.9071	−	2.16956i	0.369150	−	0.0734286i
$874$	27.6459	+	26.5782i	0.935135	+	0.899020i
$875$	0.749945	+	0.400854i	0.0253528	+	0.0135513i
$876$	24.8118	+	18.7779i	0.838314	+	0.634448i
$877$	−20.6711	+	2.03592i	−0.698013	+	0.0687483i	−0.440799	−	0.897606i	$-0.645305\pi$
$877$	−20.6711	+	2.03592i	−0.698013	+	0.0687483i	−0.257214	+	0.966354i	$0.582805\pi$
$878$	3.44018	−	43.7411i	0.116100	−	1.47619i
$879$	6.64940	−	2.75427i	0.224279	−	0.0928992i
$880$	−3.67086	+	31.0711i	−0.123745	+	1.04741i
$881$	31.7765	+	13.1622i	1.07058	+	0.443447i	0.847194	−	0.531284i	$-0.178290\pi$
$881$	31.7765	+	13.1622i	1.07058	+	0.443447i	0.223382	+	0.974731i	$0.428290\pi$
$882$	−4.49012	+	8.81351i	−0.151190	+	0.296766i
$883$	−1.17453	+	1.43117i	−0.0395262	+	0.0481628i	−0.792398	−	0.610004i	$-0.791168\pi$
$883$	−1.17453	+	1.43117i	−0.0395262	+	0.0481628i	0.752872	+	0.658167i	$0.228668\pi$
$884$	25.3615	+	28.5342i	0.852999	+	0.959708i
$885$	−2.09655	−	6.91139i	−0.0704747	−	0.232324i
$886$	−13.7354	+	35.0991i	−0.461450	+	1.17918i
$887$	12.5739	−	18.8181i	0.422189	−	0.631851i	−0.558017	−	0.829829i	$-0.688438\pi$
$887$	12.5739	−	18.8181i	0.422189	−	0.631851i	0.980206	+	0.197979i	$0.0634377\pi$
$888$	−30.1500	+	11.1283i	−1.01177	+	0.373443i
$889$	0.357220	−	0.238687i	0.0119808	−	0.00800530i
$890$	12.3121	+	7.88055i	0.412701	+	0.264156i
$891$	2.71220	−	2.22585i	0.0908622	−	0.0745687i
$892$	−12.1192	−	50.4565i	−0.405780	−	1.68941i
$893$	−16.0928	−	30.1075i	−0.538526	−	1.00751i
$894$	−6.75951	+	3.78598i	−0.226072	+	0.126622i
$895$	−29.7846			−0.995590
$896$	0.731668	+	0.447995i	0.0244433	+	0.0149665i
$897$	35.6524			1.19040
$898$	−15.6633	+	8.77294i	−0.522690	+	0.292757i
$899$	29.0621	+	54.3713i	0.969275	+	1.81339i
$900$	0.0587224	−	0.0141046i	0.00195741	−	0.000470152i
$901$	15.0814	−	12.3770i	0.502434	−	0.412337i
$902$	24.3999	+	15.6176i	0.812426	+	0.520008i
$903$	−0.194806	+	0.130165i	−0.00648274	+	0.00433163i
$904$	5.61347	+	2.58677i	0.186701	+	0.0860346i
$905$	−6.95993	+	10.4163i	−0.231356	+	0.346248i
$906$	1.32578	−	3.38788i	0.0440462	−	0.112555i
$907$	−5.62076	−	18.5292i	−0.186634	−	0.615251i	−0.999464	−	0.0327489i	$-0.989574\pi$
$907$	−5.62076	−	18.5292i	−0.186634	−	0.615251i	0.812829	−	0.582502i	$-0.197926\pi$
$908$	−33.2891	+	29.5878i	−1.10474	+	0.981904i
$909$	7.60653	−	9.26859i	0.252293	−	0.307420i
$910$	−0.733081	+	1.43894i	−0.0243014	+	0.0477004i
$911$	−2.61936	−	1.08497i	−0.0867832	−	0.0359468i	0.338870	−	0.940833i	$-0.389955\pi$
$911$	−2.61936	−	1.08497i	−0.0867832	−	0.0359468i	−0.425653	+	0.904887i	$0.639955\pi$
$912$	−10.0380	+	17.9330i	−0.332391	+	0.593821i
$913$	−29.1074	+	12.0567i	−0.963316	+	0.399018i
$914$	1.31688	−	16.7438i	0.0435584	−	0.553836i
$915$	19.3409	−	1.90491i	0.639390	−	0.0629744i
$916$	23.7936	−	31.4392i	0.786163	−	1.03878i
$917$	1.01896	+	0.544647i	0.0336491	+	0.0179858i
$918$	−2.88087	−	2.76961i	−0.0950829	−	0.0914108i
$919$	−14.9026	+	2.96431i	−0.491591	+	0.0977836i	−0.434660	−	0.900595i	$-0.643132\pi$
$919$	−14.9026	+	2.96431i	−0.491591	+	0.0977836i	−0.0569311	+	0.998378i	$0.518132\pi$
$920$	22.1023	−	24.8805i	0.728693	−	0.820287i
$921$	−4.80343	+	24.1485i	−0.158278	+	0.795719i
$922$	−2.69977	+	15.1228i	−0.0889123	+	0.498044i
$923$	−4.27239	−	0.420794i	−0.140628	−	0.0138506i
$924$	−0.390788	−	0.361164i	−0.0128560	−	0.0118814i
$925$	0.328333	+	0.0995987i	0.0107955	+	0.00327479i
$926$	22.7351	−	2.69209i	0.747122	−	0.0884677i
$927$	−9.21584	−	9.21584i	−0.302688	−	0.302688i
$928$	−30.3287	+	24.9035i	−0.995589	+	0.817498i
$929$	15.4618	−	15.4618i	0.507285	−	0.507285i	−0.406407	−	0.913692i	$-0.633219\pi$
$929$	15.4618	−	15.4618i	0.507285	−	0.507285i	0.913692	+	0.406407i	$0.133219\pi$
$930$	17.3446	−	22.0039i	0.568752	−	0.721537i
$931$	−10.4314	+	34.3878i	−0.341876	+	1.12701i
$932$	3.42406	−	9.28433i	0.112159	−	0.304118i
$933$	−0.0339417	+	0.344616i	−0.00111120	+	0.0112822i
$934$	−40.0067	+	27.8862i	−1.30906	+	0.912465i
$935$	−21.6780	−	4.31203i	−0.708948	−	0.141018i
$936$	4.82698	+	18.4860i	0.157775	+	0.604234i
$937$	2.65616	+	13.3534i	0.0867729	+	0.436237i	0.999610	+	0.0279136i	$0.00888632\pi$
$937$	2.65616	+	13.3534i	0.0867729	+	0.436237i	−0.912837	+	0.408323i	$0.866114\pi$
$938$	−0.410842	+	0.00808958i	−0.0134145	+	0.000264134i
$939$	4.63970	−	8.68027i	0.151411	−	0.283270i
$940$	−25.5574	+	14.9831i	−0.833591	+	0.488694i
$941$	3.15934	+	32.0773i	0.102992	+	1.04569i	0.898269	+	0.439445i	$0.144825\pi$
$941$	3.15934	+	32.0773i	0.102992	+	1.04569i	−0.795278	+	0.606245i	$0.792675\pi$
$942$	4.08868	−	3.49243i	0.133216	−	0.113790i
$943$	−11.7925	−	28.4695i	−0.384015	−	0.927095i
$944$	−5.19079	+	11.8740i	−0.168946	+	0.386464i
$945$	0.0646926	−	0.156182i	0.00210445	−	0.00508059i
$946$	4.73822	+	14.5801i	0.154053	+	0.474041i
$947$	−30.7861	−	25.2655i	−1.00041	−	0.821019i	−0.0165375	−	0.999863i	$-0.505264\pi$
$947$	−30.7861	−	25.2655i	−1.00041	−	0.821019i	−0.983877	+	0.178844i	$0.942764\pi$
$948$	0.247604	−	0.510625i	0.00804182	−	0.0165843i
$949$	100.569	−	30.5074i	3.26462	−	0.990313i
$950$	0.201012	−	0.0879370i	0.00652168	−	0.00285305i
$951$	−12.0605	−	8.05857i	−0.391088	−	0.261317i
$952$	−0.356167	+	0.490385i	−0.0115434	+	0.0158935i
$953$	−18.1247	−	27.1255i	−0.587116	−	0.878681i	0.412361	−	0.911021i	$-0.364704\pi$
$953$	−18.1247	−	27.1255i	−0.587116	−	0.878681i	−0.999477	+	0.0323394i	$0.989704\pi$
$954$	9.53711	−	2.09304i	0.308775	−	0.0677645i
$955$	23.5238	+	28.6638i	0.761212	+	0.927539i
$956$	−3.38270	+	21.3721i	−0.109404	+	0.691224i
$957$	21.4662	−	11.4739i	0.693902	−	0.370898i
$958$	−30.2153	−	8.51989i	−0.976213	−	0.275265i
$959$			0.445487i			0.0143855i
$960$	15.8932	+	8.09164i	0.512950	+	0.261156i
$961$			47.9778i			1.54767i
$962$	−29.4581	+	104.472i	−0.949768	+	3.36830i
$963$	−2.52066	+	1.34732i	−0.0812270	+	0.0434167i
$964$	12.8022	−	9.30338i	0.412330	−	0.299642i
$965$	22.7158	+	27.6793i	0.731249	+	0.891029i
$966$	0.121331	+	0.552858i	0.00390377	+	0.0177879i
$967$	−11.7879	−	17.6419i	−0.379074	−	0.567325i	0.592049	−	0.805902i	$-0.298319\pi$
$967$	−11.7879	−	17.6419i	−0.379074	−	0.567325i	−0.971124	+	0.238577i	$0.923319\pi$
$968$	−3.15999	+	1.93713i	−0.101566	+	0.0622617i
$969$	−12.0716	−	8.06598i	−0.387795	−	0.259116i
$970$	−14.0522	−	32.1215i	−0.451190	−	1.03136i
$971$	40.1196	−	12.1702i	1.28750	−	0.390559i	0.428969	−	0.903319i	$-0.358877\pi$
$971$	40.1196	−	12.1702i	1.28750	−	0.390559i	0.858532	+	0.512760i	$0.171377\pi$
$972$	−0.655460	−	1.88954i	−0.0210239	−	0.0606071i
$973$	−0.316051	−	0.259377i	−0.0101321	−	0.00831524i
$974$	−24.2282	+	7.87364i	−0.776323	+	0.252288i
$975$	0.0780573	−	0.188447i	0.00249983	−	0.00603513i
$976$	−28.6123	−	19.9327i	−0.915859	−	0.638031i
$977$	16.2700	+	39.2794i	0.520525	+	1.25666i	0.937578	+	0.347776i	$0.113063\pi$
$977$	16.2700	+	39.2794i	0.520525	+	1.25666i	−0.417053	+	0.908882i	$0.636937\pi$
$978$	4.92589	+	5.76686i	0.157513	+	0.184404i
$979$	1.59458	+	16.1900i	0.0509630	+	0.517436i
$980$	30.1751	+	7.87067i	0.963907	+	0.251419i
$981$	5.20883	−	9.74503i	0.166305	−	0.311135i
$982$	−0.691195	−	35.1034i	−0.0220569	−	1.12019i
$983$	9.37751	+	47.1439i	0.299096	+	1.50366i	0.779384	+	0.626547i	$0.215532\pi$
$983$	9.37751	+	47.1439i	0.299096	+	1.50366i	−0.480287	+	0.877111i	$0.659468\pi$
$984$	13.1651	−	9.96897i	0.419687	−	0.317799i
$985$	4.46776	+	0.888692i	0.142355	+	0.0283161i
$986$	−15.8530	−	22.7433i	−0.504861	−	0.724293i
$987$	0.0493872	−	0.501437i	0.00157201	−	0.0159609i
$988$	29.0663	+	63.0321i	0.924721	+	2.00532i
$989$	4.73372	−	15.6050i	0.150524	−	0.496210i
$990$	−8.68729	−	6.84777i	−0.276100	−	0.217636i
$991$	−6.62128	+	6.62128i	−0.210332	+	0.210332i	−0.804408	−	0.594077i	$-0.797518\pi$
$991$	−6.62128	+	6.62128i	−0.210332	+	0.210332i	0.594077	+	0.804408i	$0.297518\pi$
$992$	−49.3036	+	9.82062i	−1.56539	+	0.311805i
$993$	−7.89607	−	7.89607i	−0.250574	−	0.250574i
$994$	−0.00801451	−	0.0676836i	−0.000254205	−	0.00214679i
$995$	36.6188	+	11.1082i	1.16089	+	0.352153i
$996$	0.706960	+	17.9451i	0.0224009	+	0.568611i
$997$	−3.88026	−	0.382172i	−0.122889	−	0.0121035i	0.0363856	−	0.999338i	$-0.488416\pi$
$997$	−3.88026	−	0.382172i	−0.122889	−	0.0121035i	−0.159275	+	0.987234i	$0.550916\pi$
$998$	−30.7265	−	5.48539i	−0.972631	−	0.173637i
$999$	2.21673	−	11.1442i	0.0701341	−	0.352588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.13	✓	512
128.45	even	32	inner	384.2.v.a.301.13	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.13	✓	512	1.1	even	1	trivial
384.2.v.a.301.13	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)

\(f(q)\)	\(=\)	\(q+(-0.691080 - 1.23386i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.04482 + 1.70539i) q^{4} +(-1.72328 + 1.41426i) q^{5} +(-0.762394 + 1.19112i) q^{6} +(-0.0630509 + 0.0421293i) q^{7} +(2.82626 + 0.110596i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-0.691080 - 1.23386i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.04482 + 1.70539i) q^{4} +(-1.72328 + 1.41426i) q^{5} +(-0.762394 + 1.19112i) q^{6} +(-0.0630509 + 0.0421293i) q^{7} +(2.82626 + 0.110596i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(2.93592 + 1.14892i) q^{10} +(1.01850 + 3.35754i) q^{11} +(1.99654 + 0.117531i) q^{12} +(4.28528 - 5.22163i) q^{13} +(0.0955548 + 0.0486813i) q^{14} +(2.05961 + 0.853118i) q^{15} +(-1.81671 - 3.56364i) q^{16} +(2.61069 - 1.08138i) q^{17} +(1.40986 + 0.110884i) q^{18} +(5.11307 - 0.503594i) q^{19} +(-0.611351 - 4.41650i) q^{20} +(0.0668767 + 0.0357463i) q^{21} +(3.43887 - 3.57702i) q^{22} +(-5.17657 + 1.02968i) q^{23} +(-1.23475 - 2.54468i) q^{24} +(-0.00589100 + 0.0296161i) q^{25} +(-9.40422 - 1.67887i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-0.00597019 - 0.151544i) q^{28} +(6.63854 + 2.01378i) q^{29} +(-0.370727 - 3.13084i) q^{30} +(6.28402 + 6.28402i) q^{31} +(-3.14154 + 4.70433i) q^{32} +(2.48097 - 2.48097i) q^{33} +(-3.13847 - 2.47390i) q^{34} +(0.0490726 - 0.161771i) q^{35} +(-0.837511 - 1.81620i) q^{36} +(1.11373 - 11.3078i) q^{37} +(-4.15491 - 5.96079i) q^{38} +(-6.62513 - 1.31782i) q^{39} +(-5.02685 + 3.80647i) q^{40} +(1.13902 + 5.72626i) q^{41} +(-0.00211119 - 0.107220i) q^{42} +(-1.45646 + 2.72484i) q^{43} +(-6.79007 - 1.77108i) q^{44} +(-0.218510 - 2.21857i) q^{45} +(4.84790 + 5.67556i) q^{46} +(-2.54277 - 6.13879i) q^{47} +(-2.28646 + 3.28209i) q^{48} +(-2.67658 + 6.46184i) q^{49} +(0.0406132 - 0.0131984i) q^{50} +(-2.18436 - 1.79266i) q^{51} +(4.42758 + 12.7637i) q^{52} +(6.60695 - 2.00420i) q^{53} +(-0.566813 - 1.29566i) q^{54} +(-6.50358 - 4.34556i) q^{55} +(-0.182858 + 0.112095i) q^{56} +(-2.85442 - 4.27194i) q^{57} +(-2.10304 - 9.58271i) q^{58} +(-2.05527 - 2.50436i) q^{59} +(-3.60682 + 2.62109i) q^{60} +(7.68834 - 4.10951i) q^{61} +(3.41084 - 12.0964i) q^{62} -0.0758307i q^{63} +(7.97554 + 0.625148i) q^{64} +15.0588i q^{65} +(-4.77572 - 1.34662i) q^{66} +(-3.37931 + 1.80628i) q^{67} +(-0.883512 + 5.58209i) q^{68} +(3.34832 + 4.07993i) q^{69} +(-0.233515 + 0.0512478i) q^{70} +(-0.353091 - 0.528437i) q^{71} +(-1.66215 + 2.28851i) q^{72} +(12.9362 + 8.64371i) q^{73} +(-14.7220 + 6.44045i) q^{74} +(0.0288960 - 0.00876552i) q^{75} +(-4.48340 + 9.24595i) q^{76} +(-0.205668 - 0.168788i) q^{77} +(2.95249 + 9.08520i) q^{78} +(0.108585 - 0.262147i) q^{79} +(8.17061 + 3.57184i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(6.27824 - 5.36269i) q^{82} +(0.880145 + 8.93626i) q^{83} +(-0.130835 + 0.0767025i) q^{84} +(-2.96959 + 5.55570i) q^{85} +(4.36859 - 0.0860187i) q^{86} +(-1.35339 - 6.80396i) q^{87} +(2.50722 + 9.60195i) q^{88} +(4.54759 + 0.904572i) q^{89} +(-2.58640 + 1.80282i) q^{90} +(-0.0502074 + 0.509764i) q^{91} +(3.65255 - 9.90390i) q^{92} +(2.57974 - 8.50428i) q^{93} +(-5.81714 + 7.37981i) q^{94} +(-8.09903 + 8.09903i) q^{95} +(5.62976 + 0.552983i) q^{96} +(-7.86360 - 7.86360i) q^{97} +(9.82274 - 1.16312i) q^{98} +(-3.35754 - 1.01850i) 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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