LMFDB - Embedded newform 768.2.z.a.637.52

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			637.52
Character	$\chi$	$=$	768.637
Dual form			768.2.z.a.469.52

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.14588 - 0.828823i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.626104 - 1.89947i) q^{4} +(-0.424127 - 0.0629133i) q^{5} +(-0.259318 - 1.39024i) q^{6} +(-0.156537 - 1.58935i) q^{7} +(-0.856883 - 2.69551i) q^{8} +(-0.634393 - 0.773010i) q^{9} +O(q^{10})$	\(q+(1.14588 - 0.828823i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.626104 - 1.89947i) q^{4} +(-0.424127 - 0.0629133i) q^{5} +(-0.259318 - 1.39024i) q^{6} +(-0.156537 - 1.58935i) q^{7} +(-0.856883 - 2.69551i) q^{8} +(-0.634393 - 0.773010i) q^{9} +(-0.538144 + 0.279435i) q^{10} +(3.45376 - 0.169672i) q^{11} +(-1.44941 - 1.37812i) q^{12} +(2.42973 + 1.80201i) q^{13} +(-1.49666 - 1.69147i) q^{14} +(-0.238210 + 0.356507i) q^{15} +(-3.21599 - 2.37853i) q^{16} +(-1.15252 - 1.72487i) q^{17} +(-1.36763 - 0.359981i) q^{18} +(-1.75225 - 0.438917i) q^{19} +(-0.385050 + 0.766227i) q^{20} +(-1.50368 - 0.538026i) q^{21} +(3.81698 - 3.05698i) q^{22} +(1.13418 - 2.12190i) q^{23} +(-2.80307 - 0.377864i) q^{24} +(-4.60878 - 1.39806i) q^{25} +(4.27774 + 0.0510800i) q^{26} +(-0.970031 + 0.242980i) q^{27} +(-3.11693 - 0.697760i) q^{28} +(-2.42587 + 2.19868i) q^{29} +(0.0225196 + 0.605951i) q^{30} +(1.78490 + 4.30913i) q^{31} +(-5.65654 - 0.0600423i) q^{32} +(1.32329 - 3.19471i) q^{33} +(-2.75027 - 1.02127i) q^{34} +(-0.0335995 + 0.683933i) q^{35} +(-1.86551 + 0.721027i) q^{36} +(-3.69070 - 2.21212i) q^{37} +(-2.37167 + 0.949361i) q^{38} +(2.66784 - 1.42599i) q^{39} +(0.193844 + 1.19715i) q^{40} +(-0.109976 + 0.0333609i) q^{41} +(-2.16897 + 0.629771i) q^{42} +(-4.29096 + 2.02947i) q^{43} +(1.84013 - 6.66655i) q^{44} +(0.220431 + 0.367766i) q^{45} +(-0.459041 - 3.37149i) q^{46} +(5.15618 + 1.02563i) q^{47} +(-3.52518 + 1.89026i) q^{48} +(4.36397 - 0.868048i) q^{49} +(-6.43987 + 2.21785i) q^{50} +(-2.05203 + 0.304391i) q^{51} +(4.94413 - 3.48696i) q^{52} +(5.92124 + 5.36670i) q^{53} +(-0.910157 + 1.08241i) q^{54} +(-1.47551 - 0.145325i) q^{55} +(-4.14996 + 1.78383i) q^{56} +(-1.14596 + 1.39636i) q^{57} +(-0.957451 + 4.53006i) q^{58} +(9.53576 - 7.07220i) q^{59} +(0.528031 + 0.675685i) q^{60} +(11.3779 - 4.07108i) q^{61} +(5.61680 + 3.45840i) q^{62} +(-1.12928 + 1.12928i) q^{63} +(-6.53150 + 4.61947i) q^{64} +(-0.917143 - 0.917143i) q^{65} +(-1.13151 - 4.75754i) q^{66} +(1.49308 + 4.17288i) q^{67} +(-3.99795 + 1.10924i) q^{68} +(-1.43325 - 1.93252i) q^{69} +(0.528359 + 0.811557i) q^{70} +(10.2243 + 8.39088i) q^{71} +(-1.54005 + 2.37239i) q^{72} +(-0.446705 + 4.53547i) q^{73} +(-6.06257 + 0.524102i) q^{74} +(-3.23433 + 3.56854i) q^{75} +(-1.93080 + 3.05355i) q^{76} +(-0.810310 - 5.46267i) q^{77} +(1.87514 - 3.84519i) q^{78} +(2.16072 + 10.8627i) q^{79} +(1.21434 + 1.21113i) q^{80} +(-0.195090 + 0.980785i) q^{81} +(-0.0983698 + 0.129379i) q^{82} +(6.25422 - 3.74863i) q^{83} +(-1.96343 + 2.51934i) q^{84} +(0.380299 + 0.804074i) q^{85} +(-3.23487 + 5.88199i) q^{86} +(0.950392 + 3.13302i) q^{87} +(-3.41682 - 9.16424i) q^{88} +(-4.72586 - 8.84147i) q^{89} +(0.557401 + 0.238720i) q^{90} +(2.48368 - 4.14377i) q^{91} +(-3.32038 - 3.48287i) q^{92} +(4.65855 + 0.228860i) q^{93} +(6.75846 - 3.09831i) q^{94} +(0.715564 + 0.296396i) q^{95} +(-2.47276 + 5.08778i) q^{96} +(-10.8238 + 4.48338i) q^{97} +(4.28115 - 4.61165i) q^{98} +(-2.32220 - 2.56215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{64}\right)$

Coefficient data

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

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

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

$2$	1.14588	−	0.828823i	0.810263	−	0.586067i
$2$	1.14588	−	0.828823i	0.810263	−	0.586067i
$3$	0.427555	−	0.903989i	0.246849	−	0.521918i
$3$	0.427555	−	0.903989i	0.246849	−	0.521918i
$4$	0.626104	−	1.89947i	0.313052	−	0.949736i
$5$	−0.424127	−	0.0629133i	−0.189675	−	0.0281357i	0.0512169	−	0.998688i	$-0.483690\pi$
$5$	−0.424127	−	0.0629133i	−0.189675	−	0.0281357i	−0.240892	+	0.970552i	$0.577440\pi$
$6$	−0.259318	−	1.39024i	−0.105866	−	0.567561i
$7$	−0.156537	−	1.58935i	−0.0591655	−	0.600717i	−0.978360	−	0.206912i	$-0.933659\pi$
$7$	−0.156537	−	1.58935i	−0.0591655	−	0.600717i	0.919194	−	0.393805i	$-0.128841\pi$
$8$	−0.856883	−	2.69551i	−0.302954	−	0.953005i
$9$	−0.634393	−	0.773010i	−0.211464	−	0.257670i
$10$	−0.538144	+	0.279435i	−0.170176	+	0.0883650i
$11$	3.45376	−	0.169672i	1.04135	−	0.0511581i	0.478801	−	0.877924i	$-0.341072\pi$
$11$	3.45376	−	0.169672i	1.04135	−	0.0511581i	0.562547	+	0.826765i	$0.309822\pi$
$12$	−1.44941	−	1.37812i	−0.418408	−	0.397829i
$13$	2.42973	+	1.80201i	0.673885	+	0.499788i	0.877693	−	0.479223i	$-0.159082\pi$
$13$	2.42973	+	1.80201i	0.673885	+	0.499788i	−0.203807	+	0.979011i	$0.565332\pi$
$14$	−1.49666	−	1.69147i	−0.400000	−	0.452064i
$15$	−0.238210	+	0.356507i	−0.0615057	+	0.0920498i
$16$	−3.21599	−	2.37853i	−0.803997	−	0.594634i
$17$	−1.15252	−	1.72487i	−0.279528	−	0.418343i	0.664965	−	0.746874i	$-0.268446\pi$
$17$	−1.15252	−	1.72487i	−0.279528	−	0.418343i	−0.944493	+	0.328531i	$0.893446\pi$
$18$	−1.36763	−	0.359981i	−0.322354	−	0.0848484i
$19$	−1.75225	−	0.438917i	−0.401995	−	0.100694i	0.0367095	−	0.999326i	$-0.488312\pi$
$19$	−1.75225	−	0.438917i	−0.401995	−	0.100694i	−0.438704	+	0.898632i	$0.644562\pi$
$20$	−0.385050	+	0.766227i	−0.0860997	+	0.171333i
$21$	−1.50368	−	0.538026i	−0.328130	−	0.117407i
$22$	3.81698	−	3.05698i	0.813783	−	0.651751i
$23$	1.13418	−	2.12190i	0.236493	−	0.442447i	−0.735478	−	0.677549i	$-0.763042\pi$
$23$	1.13418	−	2.12190i	0.236493	−	0.442447i	0.971971	+	0.235102i	$0.0755423\pi$
$24$	−2.80307	−	0.377864i	−0.572175	−	0.0771312i
$25$	−4.60878	−	1.39806i	−0.921755	−	0.279611i
$26$	4.27774	+	0.0510800i	0.838933	+	0.0100176i
$27$	−0.970031	+	0.242980i	−0.186683	+	0.0467616i
$28$	−3.11693	−	0.697760i	−0.589044	−	0.131864i
$29$	−2.42587	+	2.19868i	−0.450473	+	0.408285i	−0.865016	−	0.501745i	$-0.832692\pi$
$29$	−2.42587	+	2.19868i	−0.450473	+	0.408285i	0.414542	+	0.910030i	$0.363942\pi$
$30$	0.0225196	+	0.605951i	0.00411150	+	0.110631i
$31$	1.78490	+	4.30913i	0.320577	+	0.773942i	0.999221	+	0.0394743i	$0.0125683\pi$
$31$	1.78490	+	4.30913i	0.320577	+	0.773942i	−0.678643	+	0.734468i	$0.737432\pi$
$32$	−5.65654	−	0.0600423i	−0.999944	−	0.0106141i
$33$	1.32329	−	3.19471i	0.230355	−	0.556127i
$34$	−2.75027	−	1.02127i	−0.471668	−	0.175146i
$35$	−0.0335995	+	0.683933i	−0.00567935	+	0.115606i
$36$	−1.86551	+	0.721027i	−0.310918	+	0.120171i
$37$	−3.69070	−	2.21212i	−0.606747	−	0.363670i	0.177498	−	0.984121i	$-0.443200\pi$
$37$	−3.69070	−	2.21212i	−0.606747	−	0.363670i	−0.784245	+	0.620451i	$0.786950\pi$
$38$	−2.37167	+	0.949361i	−0.384735	+	0.154007i
$39$	2.66784	−	1.42599i	0.427196	−	0.228341i
$40$	0.193844	+	1.19715i	0.0306494	+	0.189285i
$41$	−0.109976	+	0.0333609i	−0.0171754	+	0.00521010i	−0.298861	−	0.954297i	$-0.596607\pi$
$41$	−0.109976	+	0.0333609i	−0.0171754	+	0.00521010i	0.281685	+	0.959507i	$0.409107\pi$
$42$	−2.16897	+	0.629771i	−0.334680	+	0.0971757i
$43$	−4.29096	+	2.02947i	−0.654365	+	0.309492i	−0.725751	−	0.687957i	$-0.758508\pi$
$43$	−4.29096	+	2.02947i	−0.654365	+	0.309492i	0.0713861	+	0.997449i	$0.477258\pi$
$44$	1.84013	−	6.66655i	0.277409	−	1.00502i
$45$	0.220431	+	0.367766i	0.0328598	+	0.0548233i
$46$	−0.459041	−	3.37149i	−0.0676820	−	0.497099i
$47$	5.15618	+	1.02563i	0.752106	+	0.149603i	0.556234	−	0.831026i	$-0.312246\pi$
$47$	5.15618	+	1.02563i	0.752106	+	0.149603i	0.195873	+	0.980629i	$0.437246\pi$
$48$	−3.52518	+	1.89026i	−0.508816	+	0.272836i
$49$	4.36397	−	0.868048i	0.623425	−	0.124007i
$50$	−6.43987	+	2.21785i	−0.910735	+	0.313651i
$51$	−2.05203	+	0.304391i	−0.287342	+	0.0426232i
$52$	4.94413	−	3.48696i	0.685627	−	0.483554i
$53$	5.92124	+	5.36670i	0.813345	+	0.737173i	0.968042	−	0.250789i	$-0.0806900\pi$
$53$	5.92124	+	5.36670i	0.813345	+	0.737173i	−0.154696	+	0.987962i	$0.549440\pi$
$54$	−0.910157	+	1.08241i	−0.123857	+	0.147298i
$55$	−1.47551	−	0.145325i	−0.198957	−	0.0195956i
$56$	−4.14996	+	1.78383i	−0.554562	+	0.238375i
$57$	−1.14596	+	1.39636i	−0.151786	+	0.184952i
$58$	−0.957451	+	4.53006i	−0.125720	+	0.594826i
$59$	9.53576	−	7.07220i	1.24145	−	0.920722i	0.242670	−	0.970109i	$-0.421977\pi$
$59$	9.53576	−	7.07220i	1.24145	−	0.920722i	0.998780	+	0.0493871i	$0.0157268\pi$
$60$	0.528031	+	0.675685i	0.0681685	+	0.0872305i
$61$	11.3779	−	4.07108i	1.45679	−	0.521248i	0.514924	−	0.857236i	$-0.327820\pi$
$61$	11.3779	−	4.07108i	1.45679	−	0.521248i	0.941866	+	0.335988i	$0.109070\pi$
$62$	5.61680	+	3.45840i	0.713334	+	0.439217i
$63$	−1.12928	+	1.12928i	−0.142275	+	0.142275i
$64$	−6.53150	+	4.61947i	−0.816438	+	0.577433i
$65$	−0.917143	−	0.917143i	−0.113758	−	0.113758i
$66$	−1.13151	−	4.75754i	−0.139279	−	0.585613i
$67$	1.49308	+	4.17288i	0.182409	+	0.509798i	0.997588	−	0.0694104i	$-0.0221118\pi$
$67$	1.49308	+	4.17288i	0.182409	+	0.509798i	−0.815180	+	0.579208i	$0.803362\pi$
$68$	−3.99795	+	1.10924i	−0.484822	+	0.134515i
$69$	−1.43325	−	1.93252i	−0.172543	−	0.232648i
$70$	0.528359	+	0.811557i	0.0631509	+	0.0969996i
$71$	10.2243	+	8.39088i	1.21340	+	0.995814i	0.999822	+	0.0188887i	$0.00601282\pi$
$71$	10.2243	+	8.39088i	1.21340	+	0.995814i	0.213581	+	0.976925i	$0.431487\pi$
$72$	−1.54005	+	2.37239i	−0.181497	+	0.279589i
$73$	−0.446705	+	4.53547i	−0.0522828	+	0.530837i	0.932997	+	0.359885i	$0.117184\pi$
$73$	−0.446705	+	4.53547i	−0.0522828	+	0.530837i	−0.985279	+	0.170951i	$0.945316\pi$
$74$	−6.06257	+	0.524102i	−0.704759	+	0.0609256i
$75$	−3.23433	+	3.56854i	−0.373469	+	0.412059i
$76$	−1.93080	+	3.05355i	−0.221478	+	0.350266i
$77$	−0.810310	−	5.46267i	−0.0923434	−	0.622529i
$78$	1.87514	−	3.84519i	0.212318	−	0.435382i
$79$	2.16072	+	10.8627i	0.243100	+	1.22215i	0.888707	+	0.458476i	$0.151604\pi$
$79$	2.16072	+	10.8627i	0.243100	+	1.22215i	−0.645607	+	0.763670i	$0.723396\pi$
$80$	1.21434	+	1.21113i	0.135768	+	0.135408i
$81$	−0.195090	+	0.980785i	−0.0216767	+	0.108976i
$82$	−0.0983698	+	0.129379i	−0.0108631	+	0.0142875i
$83$	6.25422	−	3.74863i	0.686490	−	0.411466i	−0.127898	−	0.991787i	$-0.540823\pi$
$83$	6.25422	−	3.74863i	0.686490	−	0.411466i	0.814388	+	0.580321i	$0.197073\pi$
$84$	−1.96343	+	2.51934i	−0.214227	+	0.274883i
$85$	0.380299	+	0.804074i	0.0412492	+	0.0872141i
$86$	−3.23487	+	5.88199i	−0.348825	+	0.634271i
$87$	0.950392	+	3.13302i	0.101893	+	0.335895i
$88$	−3.41682	−	9.16424i	−0.364234	−	0.976911i
$89$	−4.72586	−	8.84147i	−0.500941	−	0.937194i	−0.997599	−	0.0692481i	$-0.977940\pi$
$89$	−4.72586	−	8.84147i	−0.500941	−	0.937194i	0.496659	−	0.867946i	$-0.334560\pi$
$90$	0.557401	+	0.238720i	0.0587552	+	0.0251633i
$91$	2.48368	−	4.14377i	0.260360	−	0.434385i
$92$	−3.32038	−	3.48287i	−0.346173	−	0.363115i
$93$	4.65855	+	0.228860i	0.483069	+	0.0237317i
$94$	6.75846	−	3.09831i	0.697081	−	0.319566i
$95$	0.715564	+	0.296396i	0.0734153	+	0.0304096i
$96$	−2.47276	+	5.08778i	−0.252375	+	0.519269i
$97$	−10.8238	+	4.48338i	−1.09899	+	0.455219i	−0.857135	−	0.515093i	$-0.827758\pi$
$97$	−10.8238	+	4.48338i	−1.09899	+	0.455219i	−0.241860	+	0.970311i	$0.577758\pi$
$98$	4.28115	−	4.61165i	0.432462	−	0.465847i
$99$	−2.32220	−	2.56215i	−0.233390	−	0.257506i
$100$	−5.54114	+	7.87891i	−0.554114	+	0.787891i
$101$	−2.80942	−	11.2158i	−0.279547	−	1.11602i	−0.933239	−	0.359255i	$-0.883031\pi$
$101$	−2.80942	−	11.2158i	−0.279547	−	1.11602i	0.653692	−	0.756761i	$-0.273219\pi$
$102$	−2.09911	+	2.04957i	−0.207843	+	0.202938i
$103$	−2.37698	+	7.83586i	−0.234211	+	0.772090i	0.758511	+	0.651661i	$0.225927\pi$
$103$	−2.37698	+	7.83586i	−0.234211	+	0.772090i	−0.992722	+	0.120430i	$0.961573\pi$
$104$	2.77533	−	8.09346i	0.272144	−	0.793629i
$105$	0.603903	+	0.322793i	0.0589349	+	0.0315013i
$106$	11.2331	+	1.24196i	1.09106	+	0.120630i
$107$	−1.59901	+	4.46893i	−0.154582	+	0.432028i	−0.993721	−	0.111890i	$-0.964310\pi$
$107$	−1.59901	+	4.46893i	−0.154582	+	0.432028i	0.839138	+	0.543918i	$0.183060\pi$
$108$	−0.145807	+	1.99468i	−0.0140303	+	0.191938i
$109$	0.151574	−	0.605117i	0.0145181	−	0.0579597i	−0.962339	−	0.271852i	$-0.912364\pi$
$109$	0.151574	−	0.605117i	0.0145181	−	0.0579597i	0.976857	+	0.213892i	$0.0686140\pi$
$110$	−1.81121	+	1.05641i	−0.172692	+	0.100725i
$111$	−3.57771	+	2.39055i	−0.339581	+	0.226901i
$112$	−3.27690	+	5.48365i	−0.309638	+	0.518156i
$113$	3.51102	+	2.34599i	0.330289	+	0.220692i	0.709646	−	0.704558i	$-0.248855\pi$
$113$	3.51102	+	2.34599i	0.330289	+	0.220692i	−0.379357	+	0.925250i	$0.623855\pi$
$114$	−0.155806	+	2.54986i	−0.0145926	+	0.238817i
$115$	−0.614532	+	0.828600i	−0.0573054	+	0.0772674i
$116$	2.65749	+	5.98448i	0.246741	+	0.555645i
$117$	−0.148431	−	3.02139i	−0.0137225	−	0.279327i
$118$	5.06528	−	16.0074i	0.466296	−	1.47360i
$119$	−2.56101	+	2.10177i	−0.234768	+	0.192669i
$120$	1.16509	+	0.336613i	0.106357	+	0.0307284i
$121$	0.952636	−	0.0938264i	0.0866032	−	0.00852968i
$122$	9.66356	−	14.0952i	0.874897	−	1.27612i
$123$	−0.0168630	+	0.113681i	−0.00152048	+	0.0102503i
$124$	9.30260	−	0.692403i	0.835398	−	0.0621796i
$125$	3.80476	+	1.79952i	0.340308	+	0.160954i
$126$	−0.358050	+	2.22999i	−0.0318977	+	0.198663i
$127$			14.5139i			1.28790i	0.765067	+	0.643950i	$0.222706\pi$
$127$			14.5139i			1.28790i	−0.765067	+	0.643950i	$0.777294\pi$
$128$	−3.65563	+	10.7068i	−0.323115	+	0.946360i
$129$			4.74669i			0.417923i
$130$	−1.81109	−	0.290791i	−0.158843	−	0.0255040i
$131$	−2.14474	−	1.01439i	−0.187387	−	0.0886274i	0.331559	−	0.943434i	$-0.392425\pi$
$131$	−2.14474	−	1.01439i	−0.187387	−	0.0886274i	−0.518946	+	0.854807i	$0.673675\pi$
$132$	−5.23974	−	4.51377i	−0.456061	−	0.392873i
$133$	−0.423299	+	2.85365i	−0.0367046	+	0.247443i
$134$	5.16947	+	3.54414i	0.446574	+	0.306167i
$135$	0.426703	−	0.0420266i	0.0367247	−	0.00361707i
$136$	−3.66183	+	4.58465i	−0.313999	+	0.393130i
$137$	9.69193	−	7.95396i	0.828038	−	0.679553i	−0.121711	−	0.992566i	$-0.538838\pi$
$137$	9.69193	−	7.95396i	0.828038	−	0.679553i	0.949749	+	0.313012i	$0.101338\pi$
$138$	−3.24406	−	1.02653i	−0.276152	−	0.0873839i
$139$	−0.315789	−	6.42803i	−0.0267849	−	0.545219i	−0.974265	−	0.225405i	$-0.927630\pi$
$139$	−0.315789	−	6.42803i	−0.0267849	−	0.545219i	0.947480	−	0.319814i	$-0.103620\pi$
$140$	1.27808	+	0.492035i	0.108017	+	0.0415845i
$141$	3.13171	−	4.22262i	0.263737	−	0.355609i
$142$	18.6704	+	1.14083i	1.56679	+	0.0957364i
$143$	8.69745	+	5.81145i	0.727317	+	0.485978i
$144$	0.201568	+	3.99492i	0.0167974	+	0.332910i
$145$	1.16720	−	0.779901i	0.0969310	−	0.0647672i
$146$	3.24723	+	5.56737i	0.268743	+	0.460759i
$147$	1.08113	−	4.31612i	0.0891703	−	0.355988i
$148$	−6.51262	+	5.62536i	−0.535334	+	0.462402i
$149$	2.00464	−	5.60258i	0.164226	−	0.458981i	−0.831035	−	0.556220i	$-0.812251\pi$
$149$	2.00464	−	5.60258i	0.164226	−	0.458981i	0.995261	+	0.0972389i	$0.0310011\pi$
$150$	−0.748488	+	6.76982i	−0.0611138	+	0.552754i
$151$	4.87548	+	2.60600i	0.396761	+	0.212073i	0.657696	−	0.753283i	$-0.271531\pi$
$151$	4.87548	+	2.60600i	0.396761	+	0.212073i	−0.260936	+	0.965356i	$0.584031\pi$
$152$	0.318374	+	5.09931i	0.0258235	+	0.413609i
$153$	−0.602192	+	1.98516i	−0.0486843	+	0.160491i
$154$	−5.45611	−	5.58798i	−0.439666	−	0.450292i
$155$	−0.485922	−	1.93991i	−0.0390302	−	0.155817i
$156$	−1.03828	−	5.96031i	−0.0831291	−	0.477206i
$157$	−1.93171	−	2.13131i	−0.154167	−	0.170097i	0.658970	−	0.752169i	$-0.270992\pi$
$157$	−1.93171	−	2.13131i	−0.154167	−	0.170097i	−0.813137	+	0.582072i	$0.802242\pi$
$158$	11.4792	+	10.6565i	0.913233	+	0.847787i
$159$	7.38310	−	3.05818i	0.585518	−	0.242529i
$160$	2.39531	+	0.381337i	0.189366	+	0.0301473i
$161$	−3.54998	−	1.47045i	−0.279778	−	0.115888i
$162$	0.589347	+	1.28556i	0.0463034	+	0.101003i
$163$	8.80533	+	0.432578i	0.689687	+	0.0338821i	0.390894	−	0.920436i	$-0.372166\pi$
$163$	8.80533	+	0.432578i	0.689687	+	0.0338821i	0.298793	+	0.954318i	$0.403416\pi$
$164$	−0.00548844	+	0.229784i	−0.000428575	+	0.0179431i
$165$	−0.762232	+	1.27171i	−0.0593397	+	0.0990023i
$166$	4.05966	−	9.47914i	0.315091	−	0.735724i
$167$	−8.64524	−	16.1741i	−0.668989	−	1.25159i	−0.955917	−	0.293638i	$-0.905134\pi$
$167$	−8.64524	−	16.1741i	−0.668989	−	1.25159i	0.286928	−	0.957952i	$-0.407366\pi$
$168$	−0.161773	+	4.51421i	−0.0124810	+	0.348279i
$169$	−1.11736	−	3.68344i	−0.0859506	−	0.283341i
$170$	1.10221	+	0.606176i	0.0845359	+	0.0464916i
$171$	0.772331	+	1.63296i	0.0590616	+	0.124875i
$172$	1.16834	+	9.42122i	0.0890850	+	0.718361i
$173$	6.49202	−	3.89117i	0.493579	−	0.295840i	−0.245573	−	0.969378i	$-0.578976\pi$
$173$	6.49202	−	3.89117i	0.493579	−	0.295840i	0.739153	+	0.673538i	$0.235226\pi$
$174$	3.68576	+	2.80237i	0.279417	+	0.212447i
$175$	−1.50055	+	7.54380i	−0.113431	+	0.570257i
$176$	−11.5108	−	7.66922i	−0.867661	−	0.578089i
$177$	−2.31613	−	11.6440i	−0.174091	−	0.875215i
$178$	−12.7433	−	6.21440i	−0.955152	−	0.465789i
$179$	1.95899	+	13.2065i	0.146422	+	0.987098i	0.930462	+	0.366388i	$0.119406\pi$
$179$	1.95899	+	13.2065i	0.146422	+	0.987098i	−0.784040	+	0.620710i	$0.786844\pi$
$180$	0.836574	−	0.188442i	0.0623545	−	0.0140456i
$181$	−6.05671	+	6.68255i	−0.450192	+	0.496710i	−0.923185	−	0.384356i	$-0.874424\pi$
$181$	−6.05671	+	6.68255i	−0.450192	+	0.496710i	0.472993	+	0.881066i	$0.343174\pi$
$182$	−0.588441	−	6.80681i	−0.0436181	−	0.504554i
$183$	1.18447	−	12.0261i	0.0875584	−	0.888995i
$184$	−6.69146	−	1.23897i	−0.493301	−	0.0913379i
$185$	1.42615	+	1.17041i	0.104853	+	0.0860504i
$186$	5.52785	−	3.59887i	0.405321	−	0.263882i
$187$	−4.27320	−	5.76175i	−0.312488	−	0.421341i
$188$	5.17646	−	9.15187i	0.377532	−	0.667469i
$189$	0.538026	+	1.50368i	0.0391356	+	0.109377i
$190$	1.06561	−	0.253440i	0.0773078	−	0.0183865i
$191$	12.9143	+	12.9143i	0.934447	+	0.934447i	0.997980	−	0.0635330i	$-0.0202368\pi$
$191$	12.9143	+	12.9143i	0.934447	+	0.934447i	−0.0635330	+	0.997980i	$0.520237\pi$
$192$	1.38337	+	7.87949i	0.0998362	+	0.568653i
$193$	−10.8497	+	10.8497i	−0.780981	+	0.780981i	−0.979996	−	0.199016i	$-0.936226\pi$
$193$	−10.8497	+	10.8497i	−0.780981	+	0.780981i	0.199016	+	0.979996i	$0.436226\pi$
$194$	−8.68695	+	14.1085i	−0.623686	+	1.01293i
$195$	−1.22122	+	0.436958i	−0.0874531	+	0.0312912i
$196$	1.08347	−	8.83273i	0.0773906	−	0.630910i
$197$	−0.627315	+	0.465249i	−0.0446943	+	0.0331476i	−0.617816	−	0.786323i	$-0.711982\pi$
$197$	−0.627315	+	0.465249i	−0.0446943	+	0.0331476i	0.573122	+	0.819470i	$0.305732\pi$
$198$	−4.78455	−	1.01124i	−0.340023	−	0.0718656i
$199$	−16.0242	+	19.5255i	−1.13592	+	1.38413i	−0.223590	+	0.974683i	$0.571778\pi$
$199$	−16.0242	+	19.5255i	−1.13592	+	1.38413i	−0.912335	+	0.409445i	$0.865722\pi$
$200$	0.180711	+	13.6210i	0.0127782	+	0.963147i
$201$	4.41061	+	0.434407i	0.311100	+	0.0306407i
$202$	−12.5152	−	10.5235i	−0.880566	−	0.740433i
$203$	3.87421	+	3.51138i	0.271916	+	0.246451i
$204$	−0.706606	+	4.08836i	−0.0494723	+	0.286243i
$205$	0.0487427	−	0.00723030i	0.00340434	−	0.000504986i
$206$	3.77080	+	10.9491i	0.262724	+	0.762860i
$207$	−2.35977	+	0.469387i	−0.164015	+	0.0326247i
$208$	−3.52783	−	11.5744i	−0.244611	−	0.802543i
$209$	−6.12634	−	1.21860i	−0.423767	−	0.0842926i
$210$	0.959541	−	0.130645i	0.0662146	−	0.00901538i
$211$	−11.4598	−	19.1195i	−0.788925	−	1.31624i	−0.944531	−	0.328423i	$-0.893483\pi$
$211$	−11.4598	−	19.1195i	−0.788925	−	1.31624i	0.155605	−	0.987819i	$-0.450267\pi$
$212$	13.9012	−	7.88712i	0.954739	−	0.541690i
$213$	11.9567	−	5.65511i	0.819261	−	0.387482i
$214$	1.87167	+	6.44618i	0.127945	+	0.440652i
$215$	1.94759	−	0.590796i	0.132825	−	0.0402919i
$216$	1.48616	+	2.40652i	0.101120	+	0.163743i
$217$	6.56930	−	3.51137i	0.445953	−	0.238367i
$218$	−0.327849	−	0.819022i	−0.0222047	−	0.0554712i
$219$	3.90903	+	2.34298i	0.264147	+	0.158324i
$220$	−1.19986	+	2.71169i	−0.0808946	+	0.182822i
$221$	0.307919	−	6.26783i	0.0207129	−	0.421620i
$222$	−2.11830	+	5.70458i	−0.142171	+	0.382866i
$223$	−4.99186	+	12.0514i	−0.334280	+	0.807023i	0.663963	+	0.747766i	$0.268873\pi$
$223$	−4.99186	+	12.0514i	−0.334280	+	0.807023i	−0.998243	+	0.0592576i	$0.981127\pi$
$224$	0.790030	+	8.99960i	0.0527861	+	0.601311i
$225$	1.84306	+	4.44955i	0.122871	+	0.296637i
$226$	5.96764	−	0.221782i	0.396961	−	0.0147527i
$227$	4.93456	−	4.47243i	0.327519	−	0.296846i	−0.491193	−	0.871051i	$-0.663439\pi$
$227$	4.93456	−	4.47243i	0.327519	−	0.296846i	0.818711	+	0.574205i	$0.194689\pi$
$228$	1.93485	+	3.05099i	0.128139	+	0.202056i
$229$	−12.4362	+	3.11509i	−0.821804	+	0.205851i	−0.631006	−	0.775778i	$-0.717358\pi$
$229$	−12.4362	+	3.11509i	−0.821804	+	0.205851i	−0.190798	+	0.981629i	$0.561108\pi$
$230$	−0.0174196	+	1.45882i	−0.00114861	+	0.0961916i
$231$	−5.28464	−	1.60308i	−0.347704	−	0.105475i
$232$	8.00525	+	4.65494i	0.525571	+	0.305612i
$233$	0.882558	−	1.65115i	0.0578183	−	0.108170i	−0.851352	−	0.524595i	$-0.824217\pi$
$233$	0.882558	−	1.65115i	0.0578183	−	0.108170i	0.909170	+	0.416424i	$0.136717\pi$
$234$	−2.67428	−	3.33914i	−0.174823	−	0.218286i
$235$	−2.12235	−	0.759389i	−0.138447	−	0.0495371i
$236$	−7.46307	−	22.5408i	−0.485804	−	1.46728i
$237$	10.7436	+	2.69112i	0.697869	+	0.174807i
$238$	−1.19263	+	4.53101i	−0.0773067	+	0.293702i
$239$	9.34094	+	13.9797i	0.604215	+	0.904271i	0.999900	−	0.0141146i	$-0.00449297\pi$
$239$	9.34094	+	13.9797i	0.604215	+	0.904271i	−0.395686	+	0.918386i	$0.629493\pi$
$240$	1.61405	−	0.579931i	0.104186	−	0.0374344i
$241$	−2.09233	+	3.13140i	−0.134779	+	0.201711i	−0.892720	−	0.450612i	$-0.851206\pi$
$241$	−2.09233	+	3.13140i	−0.134779	+	0.201711i	0.757941	+	0.652324i	$0.226206\pi$
$242$	1.01385	−	0.897081i	0.0651724	−	0.0576665i
$243$	0.803208	+	0.595699i	0.0515258	+	0.0382141i
$244$	−0.609146	−	24.1609i	−0.0389966	−	1.54674i
$245$	−1.90549	+	0.0936107i	−0.121737	+	0.00598057i
$246$	0.0748984	+	0.144242i	0.00477535	+	0.00919652i
$247$	−3.46657	−	4.22403i	−0.220572	−	0.268768i
$248$	10.0858	−	8.50363i	0.640451	−	0.539981i
$249$	−0.714702	−	7.25649i	−0.0452924	−	0.459862i
$250$	5.85129	−	1.09143i	0.370068	−	0.0690282i
$251$	2.81683	+	0.417837i	0.177796	+	0.0263736i	0.235035	−	0.971987i	$-0.424480\pi$
$251$	2.81683	+	0.417837i	0.177796	+	0.0263736i	−0.0572385	+	0.998361i	$0.518230\pi$
$252$	1.43798	+	2.85207i	0.0905845	+	0.179664i
$253$	3.55716	−	7.52098i	0.223637	−	0.472840i
$254$	12.0295	+	16.6313i	0.754795	+	1.04354i
$255$	0.889473			0.0557010
$256$	4.68514	+	15.2987i	0.292822	+	0.956167i
$257$	−27.2768			−1.70148			−0.850739	−	0.525588i	$-0.823846\pi$
$257$	−27.2768			−1.70148			−0.850739	+	0.525588i	$0.823846\pi$
$258$	3.93417	+	5.43916i	0.244931	+	0.338628i
$259$	−2.93810	+	6.21208i	−0.182564	+	0.386000i
$260$	−2.31631	+	1.16786i	−0.143652	+	0.0724276i
$261$	3.23856	+	0.480395i	0.200462	+	0.0297357i
$262$	−3.29837	+	0.615241i	−0.203774	+	0.0380097i
$263$	1.41606	+	14.3775i	0.0873179	+	0.886553i	0.934669	+	0.355520i	$0.115696\pi$
$263$	1.41606	+	14.3775i	0.0873179	+	0.886553i	−0.847351	+	0.531033i	$0.821804\pi$
$264$	−9.74525	−	0.829448i	−0.599779	−	0.0510490i
$265$	−2.17372	−	2.64869i	−0.133531	−	0.162708i
$266$	1.88012	+	3.62079i	0.115277	+	0.222005i
$267$	−10.0132	+	0.491915i	−0.612796	+	0.0301047i
$268$	8.86108	−	0.223406i	0.541277	−	0.0136467i
$269$	7.85721	+	5.82730i	0.479062	+	0.355297i	0.808125	−	0.589011i	$-0.200483\pi$
$269$	7.85721	+	5.82730i	0.479062	+	0.355297i	−0.329062	+	0.944308i	$0.606733\pi$
$270$	0.454120	−	0.401819i	0.0276369	−	0.0244539i
$271$	3.29285	−	4.92810i	0.200026	−	0.299361i	−0.717873	−	0.696174i	$-0.754884\pi$
$271$	3.29285	−	4.92810i	0.200026	−	0.299361i	0.917899	+	0.396814i	$0.129884\pi$
$272$	−0.396171	+	8.28849i	−0.0240214	+	0.502563i
$273$	−2.68401	−	4.01691i	−0.162444	−	0.243114i
$274$	4.51341	−	17.1472i	0.272665	−	1.03590i
$275$	−16.1548	−	4.04657i	−0.974172	−	0.244017i
$276$	−4.56812	+	1.51246i	−0.274969	+	0.0910397i
$277$	−17.3456	−	6.20637i	−1.04220	−	0.372904i	−0.240510	−	0.970647i	$-0.577315\pi$
$277$	−17.3456	−	6.20637i	−1.04220	−	0.372904i	−0.801688	+	0.597742i	$0.796065\pi$
$278$	−5.68956	−	7.10405i	−0.341237	−	0.426073i
$279$	2.19867	−	4.11343i	0.131631	−	0.246265i
$280$	1.87234	−	0.495483i	0.111894	−	0.0296108i
$281$	−11.7394	−	3.56111i	−0.700315	−	0.212438i	−0.0800042	−	0.996795i	$-0.525493\pi$
$281$	−11.7394	−	3.56111i	−0.700315	−	0.212438i	−0.620310	+	0.784356i	$0.712993\pi$
$282$	0.0887719	−	7.43427i	0.00528629	−	0.442704i
$283$	−5.59541	+	1.40158i	−0.332613	+	0.0833151i	−0.405689	−	0.914011i	$-0.632968\pi$
$283$	−5.59541	+	1.40158i	−0.332613	+	0.0833151i	0.0730762	+	0.997326i	$0.476718\pi$
$284$	22.3397	−	14.1672i	1.32562	−	0.840671i
$285$	0.573882	−	0.520136i	0.0339938	−	0.0308102i
$286$	14.7829	−	0.549395i	0.874134	−	0.0324864i
$287$	0.0702375	+	0.169568i	0.00414599	+	0.0100093i
$288$	3.54205	+	4.41065i	0.208718	+	0.259900i
$289$	4.85874	−	11.7300i	0.285808	−	0.690002i
$290$	0.691081	−	1.86108i	0.0405817	−	0.109287i
$291$	−0.574859	+	11.7015i	−0.0336989	+	0.685956i
$292$	8.33531	+	3.68818i	0.487787	+	0.215834i
$293$	−2.92821	−	1.75510i	−0.171068	−	0.102534i	0.426006	−	0.904720i	$-0.359920\pi$
$293$	−2.92821	−	1.75510i	−0.171068	−	0.102534i	−0.597074	+	0.802186i	$0.703670\pi$
$294$	−2.33845	−	5.84185i	−0.136381	−	0.340704i
$295$	−4.48930	+	2.39958i	−0.261377	+	0.139709i
$296$	−2.80028	+	11.8438i	−0.162763	+	0.688408i
$297$	−3.30903	+	1.00378i	−0.192009	+	0.0582454i
$298$	−2.34647	−	8.08140i	−0.135927	−	0.468143i
$299$	6.57943	−	3.11184i	0.380499	−	0.179962i
$300$	4.75331	+	8.37780i	0.274432	+	0.483693i
$301$	3.89723	+	6.50214i	0.224633	+	0.374777i
$302$	7.74664	−	1.05474i	0.445769	−	0.0606932i
$303$	−11.3402	−	2.25570i	−0.651475	−	0.129586i
$304$	4.59125	+	5.57935i	0.263326	+	0.319997i
$305$	−5.08180	+	1.01083i	−0.290983	+	0.0578801i
$306$	0.955305	+	2.77388i	0.0546111	+	0.158572i
$307$	−21.4553	+	3.18259i	−1.22452	+	0.181640i	−0.727504	−	0.686104i	$-0.759320\pi$
$307$	−21.4553	+	3.18259i	−1.22452	+	0.181640i	−0.497012	+	0.867743i	$0.665570\pi$
$308$	−10.8835	−	1.88104i	−0.620146	−	0.107182i
$309$	6.06724	+	5.49903i	0.345153	+	0.312829i
$310$	−2.16465	−	1.82017i	−0.122944	−	0.103379i
$311$	15.8259	+	1.55872i	0.897406	+	0.0883868i	0.536192	−	0.844096i	$-0.319862\pi$
$311$	15.8259	+	1.55872i	0.897406	+	0.0883868i	0.361214	+	0.932483i	$0.382362\pi$
$312$	−6.12979	−	5.96927i	−0.347031	−	0.337943i
$313$	14.5899	−	17.7779i	0.824670	−	1.00486i	−0.175123	−	0.984546i	$-0.556032\pi$
$313$	14.5899	−	17.7779i	0.824670	−	1.00486i	0.999794	−	0.0203170i	$-0.00646755\pi$
$314$	−3.97999	−	0.841192i	−0.224604	−	0.0474712i
$315$	0.550003	−	0.407910i	0.0309891	−	0.0229831i
$316$	21.9862	+	2.69694i	1.23682	+	0.151715i
$317$	−13.3178	+	4.76520i	−0.748005	+	0.267640i	−0.683174	−	0.730256i	$-0.739401\pi$
$317$	−13.3178	+	4.76520i	−0.748005	+	0.267640i	−0.0648311	+	0.997896i	$0.520651\pi$
$318$	5.92549	−	9.62361i	0.332285	−	0.539665i
$319$	−8.00533	+	8.00533i	−0.448212	+	0.448212i
$320$	3.06081	−	1.54832i	0.171105	−	0.0865538i
$321$	3.35620	+	3.35620i	0.187325	+	0.187325i
$322$	−5.28661	+	1.25734i	−0.294611	+	0.0700688i
$323$	1.26244	+	3.52828i	0.0702439	+	0.196319i
$324$	1.74083	+	0.984642i	0.0967126	+	0.0547024i
$325$	−8.67876	−	11.7020i	−0.481411	−	0.649108i
$326$	10.4484	−	6.80238i	0.578685	−	0.376749i
$327$	−0.482213	−	0.395742i	−0.0266664	−	0.0218846i
$328$	0.184161	+	0.267855i	0.0101686	+	0.0147898i
$329$	0.822946	−	8.35552i	0.0453705	−	0.460654i
$330$	0.180590	+	2.08899i	0.00994118	+	0.114995i
$331$	9.22947	−	10.1832i	0.507298	−	0.559717i	−0.432418	−	0.901673i	$-0.642340\pi$
$331$	9.22947	−	10.1832i	0.507298	−	0.559717i	0.939716	+	0.341957i	$0.111090\pi$
$332$	−3.20463	−	14.2267i	−0.175877	−	0.780794i
$333$	0.631363	+	4.25630i	0.0345985	+	0.233244i
$334$	−23.3119	−	11.3683i	−1.27557	−	0.622045i
$335$	−0.370725	−	1.86376i	−0.0202549	−	0.101828i
$336$	3.55611	+	5.30684i	0.194002	+	0.289512i
$337$	−0.818264	+	4.11369i	−0.0445737	+	0.224087i	−0.996651	−	0.0817697i	$-0.973943\pi$
$337$	−0.818264	+	4.11369i	−0.0445737	+	0.224087i	0.952078	+	0.305857i	$0.0989428\pi$
$338$	−4.33328	−	3.29470i	−0.235699	−	0.179208i
$339$	3.62191	−	2.17089i	0.196715	−	0.117906i
$340$	1.76542	−	0.218933i	0.0957435	−	0.0118733i
$341$	6.89575	+	14.5798i	0.373426	+	0.789543i
$342$	2.23843	+	1.23105i	0.121041	+	0.0665678i
$343$	−5.30792	−	17.4979i	−0.286601	−	0.944797i
$344$	9.14731	+	9.82729i	0.493190	+	0.529852i
$345$	0.486299	+	0.909802i	0.0261815	+	0.0489821i
$346$	4.21402	−	9.83957i	0.226547	−	0.528979i
$347$	0.694408	−	1.15855i	0.0372778	−	0.0621942i	−0.838526	−	0.544862i	$-0.816582\pi$
$347$	0.694408	−	1.15855i	0.0372778	−	0.0621942i	0.875804	+	0.482668i	$0.160332\pi$
$348$	6.54613	+	0.156356i	0.350909	+	0.00838154i
$349$	6.72390	+	0.330324i	0.359922	+	0.0176818i	0.228226	−	0.973608i	$-0.426708\pi$
$349$	6.72390	+	0.330324i	0.359922	+	0.0176818i	0.131696	+	0.991290i	$0.457958\pi$
$350$	4.53301	+	9.88802i	0.242300	+	0.528537i
$351$	−2.79477	−	1.15763i	−0.149174	−	0.0617897i
$352$	−19.5465	+	0.752386i	−1.04183	+	0.0401023i
$353$	−18.4268	+	7.63262i	−0.980758	+	0.406243i	−0.814706	−	0.579874i	$-0.803102\pi$
$353$	−18.4268	+	7.63262i	−0.980758	+	0.406243i	−0.166052	+	0.986117i	$0.553102\pi$
$354$	−12.3048	−	11.4230i	−0.653994	−	0.607125i
$355$	−3.80851	−	4.20204i	−0.202135	−	0.223021i
$356$	−19.7530	+	3.44096i	−1.04691	+	0.182371i
$357$	0.805002	+	3.21375i	0.0426052	+	0.170090i
$358$	13.1906	+	13.5094i	0.697145	+	0.713996i
$359$	1.61854	−	5.33562i	0.0854234	−	0.281603i	−0.903813	−	0.427927i	$-0.859244\pi$
$359$	1.61854	−	5.33562i	0.0854234	−	0.281603i	0.989237	+	0.146324i	$0.0467441\pi$
$360$	0.802433	−	0.909304i	0.0422919	−	0.0479246i
$361$	−13.8788	−	7.41835i	−0.730461	−	0.390440i
$362$	−1.40164	+	12.6774i	−0.0736686	+	0.666308i
$363$	0.322486	−	0.901288i	0.0169261	−	0.0473054i
$364$	−6.31593	−	7.31210i	−0.331044	−	0.383258i
$365$	0.474801	−	1.89551i	0.0248522	−	0.0992156i
$366$	−8.61025	−	14.7622i	−0.450065	−	0.771635i
$367$	−9.45348	+	6.31661i	−0.493467	+	0.329724i	−0.777279	−	0.629156i	$-0.783401\pi$
$367$	−9.45348	+	6.31661i	−0.493467	+	0.329724i	0.283812	+	0.958880i	$0.408401\pi$
$368$	−8.69452	+	4.12632i	−0.453233	+	0.215099i
$369$	0.0955565	+	0.0638488i	0.00497447	+	0.00332384i
$370$	2.60427	+	0.159130i	0.135390	+	0.00827279i
$371$	7.60266	−	10.2510i	0.394711	−	0.532206i
$372$	3.35145	−	8.70549i	0.173765	−	0.451359i
$373$	0.892695	+	18.1712i	0.0462220	+	0.940871i	0.904180	+	0.427151i	$0.140483\pi$
$373$	0.892695	+	18.1712i	0.0462220	+	0.940871i	−0.857958	+	0.513720i	$0.828267\pi$
$374$	−9.67207	−	3.06057i	−0.500131	−	0.158258i
$375$	3.25348	−	2.67007i	0.168009	−	0.137882i
$376$	−1.65366	−	14.7774i	−0.0852809	−	0.762084i
$377$	−9.85626	+	0.970757i	−0.507623	+	0.0499965i
$378$	1.86280	+	1.27712i	0.0958122	+	0.0656879i
$379$	1.08769	−	7.33258i	0.0558706	−	0.376649i	−0.943149	−	0.332371i	$-0.892151\pi$
$379$	1.08769	−	7.33258i	0.0558706	−	0.376649i	0.999019	−	0.0442779i	$-0.0140987\pi$
$380$	1.01101	−	1.17362i	0.0518639	−	0.0602054i
$381$	13.1204	+	6.20549i	0.672179	+	0.317917i
$382$	25.5020	+	4.09463i	1.30480	+	0.209500i
$383$		−	16.6144i		−	0.848956i	−0.905438	−	0.424478i	$-0.860458\pi$
$383$		−	16.6144i		−	0.848956i	0.905438	−	0.424478i	$-0.139542\pi$
$384$	8.11588	+	7.88241i	0.414162	+	0.402248i
$385$			2.36784i			0.120676i
$386$	−3.44003	+	21.4250i	−0.175093	+	1.09051i
$387$	4.29096	+	2.02947i	0.218122	+	0.103164i
$388$	1.73921	+	23.3667i	0.0882948	+	1.18626i
$389$	4.90226	−	33.0483i	0.248554	−	1.67562i	−0.401600	−	0.915815i	$-0.631546\pi$
$389$	4.90226	−	33.0483i	0.248554	−	1.67562i	0.650154	−	0.759802i	$-0.274704\pi$
$390$	−1.03721	+	1.51288i	−0.0525213	+	0.0766074i
$391$	−4.96718	+	0.489225i	−0.251201	+	0.0247411i
$392$	−6.07924	−	11.0193i	−0.307048	−	0.556559i
$393$	−1.83399	+	1.50512i	−0.0925126	+	0.0759231i
$394$	−0.333222	+	1.05305i	−0.0167875	+	0.0530521i
$395$	−0.233013	−	4.74309i	−0.0117242	−	0.238651i
$396$	−6.32068	+	2.80678i	−0.317626	+	0.141046i
$397$	10.2788	−	13.8593i	0.515877	−	0.695579i	−0.466068	−	0.884749i	$-0.654330\pi$
$397$	10.2788	−	13.8593i	0.515877	−	0.695579i	0.981944	+	0.189170i	$0.0605796\pi$
$398$	−2.17866	+	35.6552i	−0.109207	+	1.78724i
$399$	2.39868	+	1.60275i	0.120084	+	0.0802378i
$400$	11.4964	+	15.4583i	0.574822	+	0.772913i
$401$	−22.5366	+	15.0585i	−1.12543	+	0.751985i	−0.971721	−	0.236132i	$-0.924120\pi$
$401$	−22.5366	+	15.0585i	−1.12543	+	0.751985i	−0.153704	+	0.988117i	$0.549120\pi$
$402$	5.41410	−	3.15783i	0.270031	−	0.157498i
$403$	−3.42827	+	13.6864i	−0.170774	+	0.681769i
$404$	−23.0631	−	1.68586i	−1.14743	−	0.0838749i
$405$	0.144447	−	0.403704i	0.00717765	−	0.0200602i
$406$	7.34971	+	0.812601i	0.364760	+	0.0403287i
$407$	−13.1221	−	7.01392i	−0.650439	−	0.347667i
$408$	2.57884	+	5.27044i	0.127672	+	0.260926i
$409$	−10.2810	+	33.8920i	−0.508364	+	1.67585i	0.208004	+	0.978128i	$0.433303\pi$
$409$	−10.2810	+	33.8920i	−0.508364	+	1.67585i	−0.716368	+	0.697723i	$0.754197\pi$
$410$	0.0498609	−	0.0486842i	0.00246245	−	0.00240434i
$411$	−3.04646	−	12.1622i	−0.150271	−	0.599915i
$412$	13.3958	+	9.42108i	0.659962	+	0.464143i
$413$	−12.7329	−	14.0486i	−0.626544	−	0.691285i
$414$	−2.31498	+	2.49369i	−0.113775	+	0.122558i
$415$	−2.88842	+	1.19642i	−0.141787	+	0.0587301i
$416$	−13.6356	−	10.3390i	−0.668543	−	0.506912i
$417$	−5.94589	−	2.46287i	−0.291172	−	0.120607i
$418$	−8.03008	+	3.68127i	−0.392764	+	0.180057i
$419$	−13.3755	−	0.657095i	−0.653435	−	0.0321012i	−0.280349	−	0.959898i	$-0.590450\pi$
$419$	−13.3755	−	0.657095i	−0.653435	−	0.0321012i	−0.373086	+	0.927797i	$0.621700\pi$
$420$	0.991242	−	0.944994i	0.0483676	−	0.0461110i
$421$	1.00497	−	1.67668i	0.0489790	−	0.0817166i	−0.832265	−	0.554377i	$-0.812956\pi$
$421$	1.00497	−	1.67668i	0.0489790	−	0.0817166i	0.881244	+	0.472661i	$0.156706\pi$
$422$	−28.9783	−	12.4106i	−1.41064	−	0.604140i
$423$	−2.47823	−	4.63643i	−0.120495	−	0.225431i
$424$	9.39216	−	20.5594i	0.456124	−	0.998452i
$425$	2.90025	+	9.56085i	0.140683	+	0.463769i
$426$	9.01394	−	16.3901i	0.436727	−	0.794103i
$427$	−8.25142	−	17.4462i	−0.399314	−	0.844279i
$428$	7.48747	+	5.83529i	0.361920	+	0.282060i
$429$	8.97213	−	5.37769i	0.433178	−	0.259637i
$430$	1.74205	−	2.29119i	0.0840092	−	0.110491i
$431$	−2.57711	+	12.9560i	−0.124135	+	0.624069i	0.867757	+	0.496988i	$0.165561\pi$
$431$	−2.57711	+	12.9560i	−0.124135	+	0.624069i	−0.991892	+	0.127081i	$0.959439\pi$
$432$	3.69754	+	1.52583i	0.177898	+	0.0734116i
$433$	5.08451	+	25.5615i	0.244346	+	1.22841i	0.886825	+	0.462106i	$0.152906\pi$
$433$	5.08451	+	25.5615i	0.244346	+	1.22841i	−0.642479	+	0.766303i	$0.722094\pi$
$434$	4.61736	−	9.46841i	0.221641	−	0.454498i
$435$	−0.205978	−	1.38859i	−0.00987589	−	0.0665778i
$436$	−1.05450	−	0.666776i	−0.0505014	−	0.0319328i
$437$	−2.91871	+	3.22030i	−0.139621	+	0.154048i
$438$	6.42121	−	0.555106i	0.306817	−	0.0265240i
$439$	1.84950	−	18.7783i	0.0882720	−	0.896241i	−0.844447	−	0.535638i	$-0.820071\pi$
$439$	1.84950	−	18.7783i	0.0882720	−	0.896241i	0.932720	−	0.360603i	$-0.117429\pi$
$440$	0.872613	+	4.10176i	0.0416002	+	0.195544i
$441$	−3.43949	−	2.82271i	−0.163785	−	0.134415i
$442$	−4.84209	−	7.43743i	−0.230315	−	0.353762i
$443$	6.84405	+	9.22814i	0.325171	+	0.438442i	0.935298	−	0.353862i	$-0.115132\pi$
$443$	6.84405	+	9.22814i	0.325171	+	0.438442i	−0.610127	+	0.792304i	$0.708882\pi$
$444$	2.30076	+	8.29249i	0.109189	+	0.393544i
$445$	1.44812	+	4.04722i	0.0686475	+	0.191857i
$446$	4.26840	+	17.9469i	0.202115	+	0.849811i
$447$	−4.20758	−	4.20758i	−0.199012	−	0.199012i
$448$	8.36436	+	9.65771i	0.395179	+	0.456284i
$449$	−16.1090	+	16.1090i	−0.760231	+	0.760231i	−0.976364	−	0.216133i	$-0.930656\pi$
$449$	−16.1090	+	16.1090i	−0.760231	+	0.760231i	0.216133	+	0.976364i	$0.430656\pi$
$450$	5.79983	+	3.57110i	0.273407	+	0.168343i
$451$	−0.374171	+	0.133881i	−0.0176190	+	0.00630419i
$452$	6.65441	−	5.20025i	0.312997	−	0.244599i
$453$	4.44033	−	3.29317i	0.208625	−	0.154727i
$454$	1.94759	−	9.21477i	0.0914049	−	0.432471i
$455$	−1.31409	+	1.60123i	−0.0616056	+	0.0750666i
$456$	4.74584	+	1.89243i	0.222245	+	0.0886211i
$457$	14.7103	+	1.44884i	0.688120	+	0.0677739i	0.436033	−	0.899931i	$-0.356383\pi$
$457$	14.7103	+	1.44884i	0.688120	+	0.0677739i	0.252087	+	0.967705i	$0.418883\pi$
$458$	−11.6685	+	13.8769i	−0.545235	+	0.648426i
$459$	1.53709	+	1.39314i	0.0717454	+	0.0650262i
$460$	1.18914	+	1.68608i	0.0554440	+	0.0786137i
$461$	17.9050	−	2.65595i	0.833918	−	0.123700i	0.283901	−	0.958854i	$-0.408371\pi$
$461$	17.9050	−	2.65595i	0.833918	−	0.123700i	0.550017	+	0.835153i	$0.314621\pi$
$462$	−7.38426	+	2.54309i	−0.343547	+	0.118315i
$463$	−22.4640	+	4.46837i	−1.04399	+	0.207663i	−0.687160	−	0.726506i	$-0.741143\pi$
$463$	−22.4640	+	4.46837i	−1.04399	+	0.207663i	−0.356831	+	0.934169i	$0.616143\pi$
$464$	13.0312	−	1.30091i	0.604959	−	0.0603934i
$465$	−1.96142	−	0.390150i	−0.0909585	−	0.0180928i
$466$	−0.357202	−	2.62351i	−0.0165470	−	0.121532i
$467$	−7.88030	−	13.1475i	−0.364657	−	0.608393i	0.619646	−	0.784882i	$-0.287276\pi$
$467$	−7.88030	−	13.1475i	−0.364657	−	0.608393i	−0.984303	+	0.176488i	$0.943526\pi$
$468$	−5.83198	−	1.60976i	−0.269583	−	0.0744113i
$469$	6.39843	−	3.02623i	0.295452	−	0.139738i
$470$	−3.06137	+	0.888880i	−0.141210	+	0.0410010i
$471$	−2.75259	+	0.834989i	−0.126833	+	0.0384743i
$472$	−27.2342	−	19.6436i	−1.25355	−	0.904172i
$473$	−14.4756	+	7.73737i	−0.665589	+	0.355765i
$474$	14.5413	−	5.82080i	0.667906	−	0.267358i
$475$	7.46212	+	4.47262i	0.342385	+	0.205218i
$476$	2.38879	+	6.18049i	0.109490	+	0.283283i
$477$	0.392120	−	7.98178i	0.0179539	−	0.365461i
$478$	22.2903	+	8.27714i	1.01954	+	0.378588i
$479$	8.09466	−	19.5422i	0.369855	−	0.892908i	−0.623919	−	0.781489i	$-0.714460\pi$
$479$	8.09466	−	19.5422i	0.369855	−	0.892908i	0.993774	−	0.111419i	$-0.0355395\pi$
$480$	1.36885	−	2.00229i	0.0624792	−	0.0913917i
$481$	−4.98113	−	12.0255i	−0.227120	−	0.548317i
$482$	0.197802	+	5.32239i	0.00900965	+	0.242428i
$483$	−2.84708	+	2.58045i	−0.129547	+	0.117414i
$484$	0.418229	−	1.86825i	0.0190104	−	0.0849205i
$485$	4.87275	−	1.22056i	0.221260	−	0.0554227i
$486$	1.41411	+	0.0168858i	0.0641455	+	0.000765955i
$487$	5.66329	+	1.71794i	0.256628	+	0.0778473i	0.415977	−	0.909375i	$-0.363440\pi$
$487$	5.66329	+	1.71794i	0.256628	+	0.0778473i	−0.159349	+	0.987222i	$0.550940\pi$
$488$	−20.7231	−	27.1807i	−0.938092	−	1.23041i
$489$	4.15581	−	7.77498i	0.187932	−	0.351597i
$490$	−2.10589	+	1.68658i	−0.0951342	+	0.0761920i
$491$	−5.06737	−	1.81314i	−0.228687	−	0.0818256i	0.220053	−	0.975488i	$-0.429377\pi$
$491$	−5.06737	−	1.81314i	−0.228687	−	0.0818256i	−0.448740	+	0.893662i	$0.648127\pi$
$492$	0.205376	+	0.103207i	0.00925906	+	0.00465293i
$493$	6.58833	+	1.65029i	0.296723	+	0.0743253i
$494$	−7.47326	−	1.96708i	−0.336238	−	0.0885029i
$495$	0.823714	+	1.23278i	0.0370232	+	0.0554091i
$496$	4.50920	−	18.1035i	0.202469	−	0.812873i
$497$	11.7355	−	17.5635i	0.526411	−	0.787830i
$498$	−6.83332	−	7.72275i	−0.306208	−	0.346064i
$499$	−16.6362	−	12.3382i	−0.744739	−	0.552336i	0.155446	−	0.987844i	$-0.450319\pi$
$499$	−16.6362	−	12.3382i	−0.744739	−	0.552336i	−0.900185	+	0.435509i	$0.856569\pi$
$500$	5.80030	−	6.10034i	0.259397	−	0.272816i
$501$	−18.3175	+	0.899883i	−0.818367	+	0.0402038i
$502$	3.57407	−	1.85586i	0.159519	−	0.0828310i
$503$	−14.7010	−	17.9133i	−0.655487	−	0.798713i	0.334117	−	0.942532i	$-0.391562\pi$
$503$	−14.7010	−	17.9133i	−0.655487	−	0.798713i	−0.989604	+	0.143818i	$0.954062\pi$
$504$	4.01163	+	2.07631i	0.178692	+	0.0924864i
$505$	0.485925	+	4.93368i	0.0216234	+	0.219546i
$506$	−2.15747	−	11.5664i	−0.0959111	−	0.514190i
$507$	−3.80752	−	0.564792i	−0.169098	−	0.0250833i
$508$	27.5687	+	9.08721i	1.22317	+	0.403180i
$509$	−0.330864	+	0.699554i	−0.0146653	+	0.0310072i	−0.911189	−	0.411989i	$-0.864834\pi$
$509$	−0.330864	+	0.699554i	−0.0146653	+	0.0310072i	0.896524	+	0.442996i	$0.146084\pi$
$510$	1.01923	−	0.737216i	0.0451324	−	0.0326445i
$511$	7.27837			0.321976
$512$	18.0485	+	13.6474i	0.797640	+	0.603134i
$513$	1.80639			0.0797540
$514$	−31.2561	+	22.6076i	−1.37865	+	0.997180i
$515$	1.50112	−	3.17386i	0.0661473	−	0.139857i
$516$	9.01621	+	2.97192i	0.396917	+	0.130832i
$517$	17.9822	+	2.66741i	0.790858	+	0.117313i
$518$	1.78200	+	9.55349i	0.0782965	+	0.419756i
$519$	−0.741877	−	7.53241i	−0.0325648	−	0.330636i
$520$	−1.68628	+	3.25805i	−0.0739482	+	0.142875i
$521$	−26.4200	−	32.1929i	−1.15748	−	1.41040i	−0.895349	−	0.445366i	$-0.853074\pi$
$521$	−26.4200	−	32.1929i	−1.15748	−	1.41040i	−0.262135	−	0.965031i	$-0.584426\pi$
$522$	4.10918	−	2.13372i	0.179854	−	0.0933903i
$523$	10.6728	−	0.524323i	0.466690	−	0.0229270i	0.185635	−	0.982619i	$-0.440566\pi$
$523$	10.6728	−	0.524323i	0.466690	−	0.0229270i	0.281055	+	0.959692i	$0.409316\pi$
$524$	−3.26963	+	3.43876i	−0.142835	+	0.150223i
$525$	6.17794	+	4.58187i	0.269627	+	0.199969i
$526$	13.5390	+	15.3013i	0.590330	+	0.667167i
$527$	5.37556	−	8.04510i	0.234163	−	0.350450i
$528$	−11.8544	+	7.12664i	−0.515897	+	0.310147i
$529$	9.56201	+	14.3106i	0.415740	+	0.622199i
$530$	−4.68613	−	1.23346i	−0.203552	−	0.0535781i
$531$	−11.5163	−	2.88468i	−0.499765	−	0.125185i
$532$	5.15539	+	2.59072i	0.223515	+	0.112322i
$533$	−0.327329	−	0.117120i	−0.0141782	−	0.00507304i
$534$	−11.0662	+	8.86282i	−0.478882	+	0.383532i
$535$	0.959338	−	1.79480i	0.0414758	−	0.0775958i
$536$	9.96862	−	7.60027i	0.430579	−	0.328282i
$537$	12.7761	+	3.87558i	0.551329	+	0.167244i
$538$	13.8333	+	0.165182i	0.596394	+	0.00712148i
$539$	14.9248	−	3.73848i	0.642858	−	0.161028i
$540$	0.187332	−	0.836823i	0.00806149	−	0.0360111i
$541$	−18.5513	+	16.8139i	−0.797584	+	0.722888i	−0.964786	−	0.263035i	$-0.915277\pi$
$541$	−18.5513	+	16.8139i	−0.797584	+	0.722888i	0.167203	+	0.985923i	$0.446527\pi$
$542$	−0.311295	−	8.37623i	−0.0133713	−	0.359790i
$543$	3.45138	+	8.33236i	0.148113	+	0.357576i
$544$	6.41573	+	9.82601i	0.275072	+	0.421287i
$545$	−0.102356	+	0.247110i	−0.00438447	+	0.0105850i
$546$	−6.40487	−	2.37834i	−0.274103	−	0.101784i
$547$	1.47215	−	29.9663i	0.0629446	−	1.28127i	−0.734805	−	0.678279i	$-0.762726\pi$
$547$	1.47215	−	29.9663i	0.0629446	−	1.28127i	0.797750	−	0.602989i	$-0.206024\pi$
$548$	−9.04017	−	23.3896i	−0.386177	−	0.999153i
$549$	−10.3650	−	6.21257i	−0.442369	−	0.265146i
$550$	−21.8655	+	8.75258i	−0.932346	+	0.373211i
$551$	5.21578	−	2.78789i	0.222200	−	0.118768i
$552$	−3.98098	+	5.51928i	−0.169442	+	0.234916i
$553$	16.9263	−	5.13455i	0.719781	−	0.218343i
$554$	−25.0201	+	7.26468i	−1.06300	+	0.308647i
$555$	1.66780	−	0.788810i	0.0707941	−	0.0334831i
$556$	−12.4076	−	3.42479i	−0.526199	−	0.145243i
$557$	9.79090	+	16.3351i	0.414854	+	0.692142i	0.992241	−	0.124329i	$-0.0396777\pi$
$557$	9.79090	+	16.3351i	0.414854	+	0.692142i	−0.577387	+	0.816470i	$0.695928\pi$
$558$	−0.889879	−	6.53583i	−0.0376716	−	0.276684i
$559$	−14.0830	−	2.80128i	−0.595647	−	0.118482i
$560$	1.73481	−	2.11960i	0.0733093	−	0.0895696i
$561$	−7.03559	+	1.39947i	−0.297043	+	0.0590855i
$562$	−16.4035	+	5.64927i	−0.691942	+	0.238300i
$563$	−33.8764	+	5.02509i	−1.42772	+	0.211782i	−0.815433	−	0.578852i	$-0.803501\pi$
$563$	−33.8764	+	5.02509i	−1.42772	+	0.211782i	−0.612289	+	0.790634i	$0.709751\pi$
$564$	−6.05997	−	8.59239i	−0.255171	−	0.361805i
$565$	−1.34152	−	1.21589i	−0.0564384	−	0.0511527i
$566$	−5.25004	+	6.24365i	−0.220676	+	0.262440i
$567$	1.58935	+	0.156537i	0.0667463	+	0.00657394i
$568$	13.8566	−	34.7497i	0.581411	−	1.45807i
$569$	−11.7196	+	14.2804i	−0.491312	+	0.598665i	−0.958359	−	0.285568i	$-0.907818\pi$
$569$	−11.7196	+	14.2804i	−0.491312	+	0.598665i	0.467047	+	0.884232i	$0.345318\pi$
$570$	0.226502	−	1.07166i	0.00948711	−	0.0448870i
$571$	30.5343	−	22.6458i	1.27782	−	0.947697i	0.277905	−	0.960609i	$-0.410360\pi$
$571$	30.5343	−	22.6458i	1.27782	−	0.947697i	0.999917	+	0.0129114i	$0.00410995\pi$
$572$	16.4842	−	12.8820i	0.689239	−	0.538623i
$573$	17.1960	−	6.15282i	0.718372	−	0.257038i
$574$	0.221026	+	0.136091i	0.00922545	+	0.00568034i
$575$	−8.19372	+	8.19372i	−0.341702	+	0.341702i
$576$	7.71444	+	2.11836i	0.321435	+	0.0882651i
$577$	−3.98358	−	3.98358i	−0.165839	−	0.165839i	0.619309	−	0.785147i	$-0.287413\pi$
$577$	−3.98358	−	3.98358i	−0.165839	−	0.165839i	−0.785147	+	0.619309i	$0.787413\pi$
$578$	−4.15457	−	17.4683i	−0.172807	−	0.726586i
$579$	5.16918	+	14.4469i	0.214824	+	0.600393i
$580$	−0.750608	−	2.70537i	−0.0311673	−	0.112334i
$581$	−6.93690	−	9.35333i	−0.287791	−	0.388041i
$582$	9.03978	+	13.8851i	0.374711	+	0.575554i
$583$	21.3611	+	17.5306i	0.884688	+	0.726045i
$584$	12.6082	−	2.68227i	0.521729	−	0.110993i
$585$	−0.127132	+	1.29079i	−0.00525625	+	0.0533676i
$586$	−4.81005	+	0.415824i	−0.198701	+	0.0171775i
$587$	15.7434	−	17.3702i	0.649799	−	0.716943i	−0.323565	−	0.946206i	$-0.604882\pi$
$587$	15.7434	−	17.3702i	0.649799	−	0.716943i	0.973365	+	0.229263i	$0.0736315\pi$
$588$	−7.52145	−	4.75593i	−0.310180	−	0.196131i
$589$	−1.23625	−	8.33411i	−0.0509387	−	0.343401i
$590$	−3.15540	+	6.47049i	−0.129906	+	0.266386i
$591$	0.152368	+	0.766006i	0.00626758	+	0.0315093i
$592$	6.60763	+	15.8926i	0.271572	+	0.653182i
$593$	−3.62427	+	18.2205i	−0.148831	+	0.748225i	0.832215	+	0.554452i	$0.187072\pi$
$593$	−3.62427	+	18.2205i	−0.148831	+	0.748225i	−0.981047	+	0.193772i	$0.937928\pi$
$594$	−2.95981	+	3.89282i	−0.121442	+	0.159724i
$595$	1.21842	−	0.730294i	0.0499505	−	0.0299392i
$596$	−9.38683	−	7.31555i	−0.384500	−	0.299657i
$597$	10.7996	+	22.8339i	0.442000	+	0.934531i
$598$	4.96011	−	9.01900i	0.202834	−	0.368814i
$599$	−2.98667	−	9.84572i	−0.122032	−	0.402285i	0.874546	−	0.484942i	$-0.161159\pi$
$599$	−2.98667	−	9.84572i	−0.122032	−	0.402285i	−0.996578	+	0.0826572i	$0.973659\pi$
$600$	12.3905	+	5.66035i	0.505838	+	0.231083i
$601$	13.2950	+	24.8731i	0.542313	+	1.01460i	0.992567	+	0.121696i	$0.0388333\pi$
$601$	13.2950	+	24.8731i	0.542313	+	1.01460i	−0.450254	+	0.892900i	$0.648667\pi$
$602$	9.85491	+	4.22059i	0.401656	+	0.172018i
$603$	2.27848	−	3.80141i	0.0927868	−	0.154805i
$604$	8.00257	−	7.62920i	0.325620	−	0.310428i
$605$	−0.409941	−	0.0201391i	−0.0166665	−	0.000818772i
$606$	−14.8641	+	6.81422i	−0.603812	+	0.276809i
$607$	10.5529	+	4.37116i	0.428329	+	0.177420i	0.586424	−	0.810004i	$-0.300535\pi$
$607$	10.5529	+	4.37116i	0.428329	+	0.177420i	−0.158095	+	0.987424i	$0.550535\pi$
$608$	9.88533	+	2.58796i	0.400903	+	0.104956i
$609$	4.83069	−	2.00094i	0.195749	−	0.0810821i
$610$	−4.98535	+	5.37021i	−0.201851	+	0.217433i
$611$	10.6799	+	11.7835i	0.432064	+	0.476709i
$612$	3.39372	+	2.38676i	0.137183	+	0.0964792i
$613$	−5.18870	−	20.7145i	−0.209570	−	0.836649i	−0.979979	−	0.199100i	$-0.936198\pi$
$613$	−5.18870	−	20.7145i	−0.209570	−	0.836649i	0.770409	−	0.637549i	$-0.220052\pi$
$614$	−21.9475	+	21.4295i	−0.885727	+	0.864824i
$615$	0.0143041	−	0.0471542i	0.000576796	−	0.00190144i
$616$	−14.0303	+	6.86506i	−0.565297	+	0.276601i
$617$	−27.1447	−	14.5091i	−1.09280	−	0.584115i	−0.176378	−	0.984322i	$-0.556438\pi$
$617$	−27.1447	−	14.5091i	−1.09280	−	0.584115i	−0.916425	+	0.400207i	$0.868938\pi$
$618$	11.5101	+	1.27258i	0.463004	+	0.0511908i
$619$	10.9542	−	30.6148i	0.440285	−	1.23051i	−0.492574	−	0.870271i	$-0.663944\pi$
$619$	10.9542	−	30.6148i	0.440285	−	1.23051i	0.932859	−	0.360243i	$-0.117306\pi$
$620$	−3.98904	−	0.291590i	−0.160204	−	0.0117106i
$621$	−0.584610	+	2.33389i	−0.0234596	+	0.0936559i
$622$	19.4266	−	11.3308i	0.778936	−	0.454323i
$623$	−13.3124	+	8.89506i	−0.533350	+	0.356373i
$624$	−11.9715	−	1.75958i	−0.479244	−	0.0704397i
$625$	18.5220	+	12.3760i	0.740878	+	0.495039i
$626$	1.98366	−	32.4638i	0.0792828	−	1.29752i
$627$	−3.72095	+	5.01712i	−0.148600	+	0.200365i
$628$	−5.25781	+	2.33480i	−0.209810	+	0.0931686i
$629$	0.437991	+	8.91551i	0.0174638	+	0.355484i
$630$	0.292155	−	0.923273i	0.0116397	−	0.0367841i
$631$	5.40194	−	4.43326i	0.215048	−	0.176485i	−0.520702	−	0.853738i	$-0.674330\pi$
$631$	5.40194	−	4.43326i	0.215048	−	0.176485i	0.735750	+	0.677253i	$0.236830\pi$
$632$	27.4289	−	15.1323i	1.09106	−	0.601929i
$633$	−22.1835	+	2.18489i	−0.881717	+	0.0868415i
$634$	−11.3112	+	16.4985i	−0.449226	+	0.655240i
$635$	0.913117	−	6.15573i	0.0362359	−	0.244283i
$636$	−1.18634	−	15.9387i	−0.0470413	−	0.632012i
$637$	12.1675	+	5.75480i	0.482094	+	0.228014i
$638$	−2.53818	+	15.8082i	−0.100488	+	0.625852i
$639$		−	13.2266i		−	0.523237i
$640$	2.22405	−	4.31107i	0.0879134	−	0.170410i
$641$			24.6976i			0.975498i	0.872984	+	0.487749i	$0.162182\pi$
$641$			24.6976i			0.975498i	−0.872984	+	0.487749i	$0.837818\pi$
$642$	6.62752	+	1.06412i	0.261567	+	0.0419976i
$643$	25.5101	+	12.0654i	1.00602	+	0.475812i	0.858262	−	0.513211i	$-0.171544\pi$
$643$	25.5101	+	12.0654i	1.00602	+	0.475812i	0.147758	+	0.989024i	$0.452794\pi$
$644$	−5.01574	+	5.82243i	−0.197648	+	0.229436i
$645$	0.298630	−	2.01320i	0.0117585	−	0.0792697i
$646$	4.37093	+	2.99666i	0.171972	+	0.117902i
$647$	−25.7412	+	2.53529i	−1.01199	+	0.0996726i	−0.590398	−	0.807112i	$-0.701029\pi$
$647$	−25.7412	+	2.53529i	−1.01199	+	0.0996726i	−0.421594	+	0.906785i	$0.638529\pi$
$648$	2.81088	−	0.314551i	0.110422	−	0.0123567i
$649$	31.7343	−	26.0436i	1.24568	−	1.02230i
$650$	−19.6437	−	6.21594i	−0.770490	−	0.243809i
$651$	−0.365498	−	7.43988i	−0.0143250	−	0.291592i
$652$	6.33473	−	16.4546i	0.248087	−	0.644414i
$653$	−17.8923	+	24.1250i	−0.700180	+	0.944084i	−0.999951	−	0.00992763i	$-0.996840\pi$
$653$	−17.8923	+	24.1250i	−0.700180	+	0.944084i	0.299771	+	0.954011i	$0.403090\pi$
$654$	−0.880560	−	0.0538054i	−0.0344326	−	0.00210396i
$655$	0.845824	+	0.565161i	0.0330491	+	0.0220827i
$656$	0.433032	+	0.154294i	0.0169071	+	0.00602417i
$657$	3.78935	−	2.53196i	0.147837	−	0.0987813i
$658$	−5.98224	−	10.2565i	−0.233212	−	0.399841i
$659$	−1.59991	+	6.38720i	−0.0623237	+	0.248810i	−0.993183	−	0.116569i	$-0.962810\pi$
$659$	−1.59991	+	6.38720i	−0.0623237	+	0.248810i	0.930859	+	0.365379i	$0.119060\pi$
$660$	1.93834	+	2.24406i	0.0754496	+	0.0873499i
$661$	11.2273	−	31.3783i	0.436693	−	1.22047i	−0.498672	−	0.866791i	$-0.666179\pi$
$661$	11.2273	−	31.3783i	0.436693	−	1.22047i	0.935365	−	0.353684i	$-0.115071\pi$
$662$	2.13588	−	19.3183i	0.0830133	−	0.750828i
$663$	−5.53440	−	2.95820i	−0.214938	−	0.114887i
$664$	−15.4636	−	13.6461i	−0.600104	−	0.529573i
$665$	0.359065	−	1.18368i	0.0139239	−	0.0459010i
$666$	4.25119	+	4.35394i	0.164730	+	0.168712i
$667$	1.91401	+	7.64116i	0.0741108	+	0.295867i
$668$	−36.1351	+	6.29471i	−1.39811	+	0.243550i
$669$	8.76006	+	9.66524i	0.338684	+	0.373680i
$670$	−1.96954	−	1.82839i	−0.0760899	−	0.0706369i
$671$	38.6058	−	15.9910i	1.49036	−	0.617327i
$672$	8.47333	+	3.13365i	0.326866	+	0.120883i
$673$	41.0924	+	17.0210i	1.58400	+	0.656112i	0.989040	−	0.147646i	$-0.0471697\pi$
$673$	41.0924	+	17.0210i	1.58400	+	0.656112i	0.594955	+	0.803759i	$0.297170\pi$
$674$	2.47189	+	5.39201i	0.0952135	+	0.207692i
$675$	4.81036	+	0.236318i	0.185151	+	0.00909587i
$676$	−7.69617	−	0.183825i	−0.296006	−	0.00707018i
$677$	−6.08139	+	10.1462i	−0.233727	+	0.389950i	−0.952138	−	0.305669i	$-0.901120\pi$
$677$	−6.08139	+	10.1462i	−0.233727	+	0.389950i	0.718411	+	0.695619i	$0.244870\pi$
$678$	2.35101	−	5.48950i	0.0902898	−	0.210823i
$679$	8.81999	+	16.5010i	0.338480	+	0.633252i
$680$	1.84151	−	1.71409i	0.0706189	−	0.0657325i
$681$	−1.93323	−	6.37300i	−0.0740815	−	0.244214i
$682$	19.9859	+	10.9915i	0.765298	+	0.420885i
$683$	18.4302	+	38.9674i	0.705212	+	1.49105i	0.863871	+	0.503713i	$0.168033\pi$
$683$	18.4302	+	38.9674i	0.705212	+	1.49105i	−0.158659	+	0.987333i	$0.550717\pi$
$684$	3.58531	−	0.444620i	0.137088	−	0.0170005i
$685$	−4.61102	+	2.76374i	−0.176178	+	0.105597i
$686$	−20.5849	−	15.6512i	−0.785936	−	0.597567i
$687$	−2.50113	+	12.5740i	−0.0954240	+	0.479729i
$688$	18.6268	+	3.67944i	0.710142	+	0.140277i
$689$	4.71617	+	23.7098i	0.179672	+	0.903270i
$690$	1.31131	+	0.639472i	0.0499207	+	0.0243443i
$691$	5.98706	+	40.3615i	0.227758	+	1.53542i	0.737650	+	0.675184i	$0.235936\pi$
$691$	5.98706	+	40.3615i	0.227758	+	1.53542i	−0.509891	+	0.860239i	$0.670314\pi$
$692$	−3.32648	−	14.7677i	−0.126454	−	0.561383i
$693$	−3.70864	+	4.09186i	−0.140880	+	0.155437i
$694$	−0.164521	−	1.90311i	−0.00624514	−	0.0722409i
$695$	−0.270474	+	2.74617i	−0.0102597	+	0.104168i
$696$	7.63070	−	5.24642i	0.289241	−	0.198865i
$697$	0.184294	+	0.151246i	0.00698062	+	0.00572884i
$698$	7.97860	−	5.19441i	0.301994	−	0.196611i
$699$	−1.11528	−	1.50378i	−0.0421838	−	0.0568782i
$700$	13.3897	+	7.57346i	0.506084	+	0.286250i
$701$	14.1020	+	39.4125i	0.532626	+	1.48859i	0.842967	+	0.537965i	$0.180807\pi$
$701$	14.1020	+	39.4125i	0.532626	+	1.48859i	−0.310341	+	0.950625i	$0.600443\pi$
$702$	−4.16195	+	0.989856i	−0.157083	+	0.0373597i
$703$	5.49610	+	5.49610i	0.207289	+	0.207289i
$704$	−21.7744	+	17.0627i	−0.820655	+	0.643076i
$705$	−1.59390	+	1.59390i	−0.0600298	+	0.0600298i
$706$	−14.7889	+	24.0186i	−0.556586	+	0.903953i
$707$	−17.3861	+	6.22083i	−0.653870	+	0.233958i
$708$	−23.5675	−	2.89092i	−0.885723	−	0.108647i
$709$	−17.1971	+	12.7543i	−0.645852	+	0.478997i	−0.868360	−	0.495934i	$-0.834826\pi$
$709$	−17.1971	+	12.7543i	−0.645852	+	0.478997i	0.222508	+	0.974931i	$0.428576\pi$
$710$	−7.84686	−	1.65848i	−0.294487	−	0.0622415i
$711$	7.02621	−	8.56146i	0.263503	−	0.321080i
$712$	−19.7827	+	20.3147i	−0.741389	+	0.761326i
$713$	11.1679	+	1.09995i	0.418243	+	0.0411933i
$714$	3.58607	+	3.01538i	0.134205	+	0.112848i
$715$	−3.32320	−	3.01198i	−0.124281	−	0.112642i
$716$	26.3118	+	4.54757i	0.983320	+	0.169951i
$717$	16.6313	−	2.46701i	0.621106	−	0.0921323i
$718$	−2.56762	−	7.45549i	−0.0958228	−	0.278236i
$719$	37.8414	−	7.52712i	1.41125	−	0.280714i	0.570124	−	0.821559i	$-0.306895\pi$
$719$	37.8414	−	7.52712i	1.41125	−	0.280714i	0.841123	+	0.540845i	$0.181895\pi$
$720$	0.165843	−	1.70703i	0.00618060	−	0.0636174i
$721$	12.8260	+	2.55125i	0.477665	+	0.0950135i
$722$	−22.0520	+	3.00246i	−0.820689	+	0.111740i
$723$	1.93616	+	3.23029i	0.0720066	+	0.120136i
$724$	8.90119	+	15.6885i	0.330810	+	0.583059i
$725$	14.2542	−	6.74173i	0.529387	−	0.250382i
$726$	−0.377477	−	1.30006i	−0.0140095	−	0.0482496i
$727$	13.7697	−	4.17700i	0.510691	−	0.154916i	−0.0244141	−	0.999702i	$-0.507772\pi$
$727$	13.7697	−	4.17700i	0.510691	−	0.154916i	0.535105	+	0.844786i	$0.320272\pi$
$728$	−13.2978	−	3.14404i	−0.492848	−	0.116526i
$729$	0.881921	−	0.471397i	0.0326638	−	0.0174591i
$730$	−1.02698	−	2.56556i	−0.0380101	−	0.0949557i
$731$	8.44602	+	5.06235i	0.312387	+	0.187238i
$732$	−22.1017	−	9.77946i	−0.816901	−	0.361459i
$733$	−1.04975	+	21.3681i	−0.0387733	+	0.789249i	0.898145	+	0.439700i	$0.144915\pi$
$733$	−1.04975	+	21.3681i	−0.0387733	+	0.789249i	−0.936918	+	0.349549i	$0.886335\pi$
$734$	−5.59724	+	15.0734i	−0.206598	+	0.556368i
$735$	−0.730079	+	1.76257i	−0.0269294	+	0.0650132i
$736$	−6.54293	+	11.9345i	−0.241176	+	0.439912i
$737$	5.86476	+	14.1588i	0.216031	+	0.521545i
$738$	0.162416	−	0.00603606i	0.00597862	−	0.000222190i
$739$	32.2701	−	29.2479i	1.18708	−	1.07590i	0.191542	−	0.981484i	$-0.438651\pi$
$739$	32.2701	−	29.2479i	1.18708	−	1.07590i	0.995533	−	0.0944178i	$-0.0300989\pi$
$740$	3.11609	−	1.97614i	0.114550	−	0.0726442i
$741$	−5.30062	+	1.32774i	−0.194723	+	0.0487756i
$742$	0.215506	−	18.0477i	0.00791148	−	0.662553i
$743$	−45.1910	−	13.7085i	−1.65790	−	0.502918i	−0.683919	−	0.729558i	$-0.739726\pi$
$743$	−45.1910	−	13.7085i	−1.65790	−	0.502918i	−0.973979	+	0.226640i	$0.927226\pi$
$744$	−3.37494	−	12.7533i	−0.123731	−	0.467557i
$745$	−1.20270	+	2.25009i	−0.0440634	+	0.0824368i
$746$	16.0837	+	20.0823i	0.588865	+	0.735264i
$747$	−6.86537	−	2.45647i	−0.251191	−	0.0898775i
$748$	−13.6197	+	4.50937i	−0.497987	+	0.164879i
$749$	7.35300	+	1.84183i	0.268673	+	0.0672990i
$750$	1.51511	−	5.75615i	0.0553239	−	0.210185i
$751$	17.4449	+	26.1082i	0.636575	+	0.952702i	0.999780	+	0.0209924i	$0.00668258\pi$
$751$	17.4449	+	26.1082i	0.636575	+	0.952702i	−0.363205	+	0.931709i	$0.618317\pi$
$752$	−14.1427	−	15.5626i	−0.515732	−	0.567508i
$753$	1.58207	−	2.36773i	0.0576538	−	0.0862850i
$754$	−10.4896	+	9.28147i	−0.382007	+	0.338011i
$755$	−1.90387	−	1.41200i	−0.0692889	−	0.0513881i
$756$	3.19306	−	0.0805037i	0.116131	−	0.00292789i
$757$	−46.0055	+	2.26011i	−1.67210	+	0.0821450i	−0.862895	−	0.505383i	$-0.831351\pi$
$757$	−46.0055	+	2.26011i	−1.67210	+	0.0821450i	−0.809204	+	0.587528i	$0.800101\pi$
$758$	−4.83105	−	9.30379i	−0.175472	−	0.337929i
$759$	−5.27800	−	6.43126i	−0.191579	−	0.233440i
$760$	0.185783	−	2.18278i	0.00673907	−	0.0791779i
$761$	−3.52764	−	35.8167i	−0.127877	−	1.29836i	−0.818234	−	0.574886i	$-0.805046\pi$
$761$	−3.52764	−	35.8167i	−0.127877	−	1.29836i	0.690357	−	0.723469i	$-0.257454\pi$
$762$	20.1777	−	3.76372i	0.730962	−	0.136345i
$763$	−0.985468	−	0.146180i	−0.0356763	−	0.00529208i
$764$	32.6161	−	16.4447i	1.18001	−	0.594947i
$765$	0.380299	−	0.804074i	0.0137497	−	0.0290714i
$766$	−13.7704	−	19.0382i	−0.497545	−	0.687877i
$767$	35.9135			1.29676
$768$	15.8330	+	2.30571i	0.571324	+	0.0832000i
$769$	−35.4983			−1.28010			−0.640051	−	0.768332i	$-0.721087\pi$
$769$	−35.4983			−1.28010			−0.640051	+	0.768332i	$0.721087\pi$
$770$	1.96252	+	2.71327i	0.0707244	+	0.0977796i
$771$	−11.6623	+	24.6579i	−0.420008	+	0.888033i
$772$	13.8157	+	27.4018i	0.497238	+	0.986213i
$773$	−32.5515	−	4.82856i	−1.17080	−	0.173671i	−0.467121	−	0.884193i	$-0.654709\pi$
$773$	−32.5515	−	4.82856i	−1.17080	−	0.173671i	−0.703675	+	0.710522i	$0.748459\pi$
$774$	6.59902	−	1.23090i	0.237197	−	0.0442440i
$775$	−2.20180	−	22.3552i	−0.0790908	−	0.803023i
$776$	21.3598	+	25.3340i	0.766770	+	0.909438i
$777$	4.35946	+	5.31201i	0.156395	+	0.190567i
$778$	−21.7738	−	41.9327i	−0.780629	−	1.50336i
$779$	0.207349	−	0.0101864i	0.00742905	−	0.000364966i
$780$	0.0653811	+	2.59325i	0.00234102	+	0.0928531i
$781$	36.7360	+	27.2453i	1.31452	+	0.974913i
$782$	−5.28634	+	4.67751i	−0.189039	+	0.167267i
$783$	1.81894	−	2.72223i	0.0650035	−	0.0972846i
$784$	−16.0992	−	7.58823i	−0.574970	−	0.271008i
$785$	0.685201	+	1.02548i	0.0244559	+	0.0366008i
$786$	−0.854066	+	3.24474i	−0.0304635	+	0.115736i
$787$	−30.5104	−	7.64246i	−1.08758	−	0.272424i	−0.342579	−	0.939489i	$-0.611300\pi$
$787$	−30.5104	−	7.64246i	−1.08758	−	0.272424i	−0.745000	+	0.667065i	$0.767550\pi$
$788$	0.490962	+	1.48286i	0.0174898	+	0.0528248i
$789$	13.6025	+	4.86706i	0.484263	+	0.173272i
$790$	−4.19819	−	5.24190i	−0.149365	−	0.186499i
$791$	3.17899	−	5.94747i	0.113032	−	0.211468i
$792$	−4.91645	+	8.45497i	−0.174698	+	0.300434i
$793$	34.9813	+	10.6115i	1.24222	+	0.376824i
$794$	0.291364	−	24.4005i	0.0103401	−	0.865940i
$795$	−3.32377	+	0.832561i	−0.117882	+	0.0295279i
$796$	27.0554	+	42.6625i	0.958953	+	1.51213i
$797$	−11.7313	+	10.6327i	−0.415545	+	0.376628i	−0.852388	−	0.522910i	$-0.824846\pi$
$797$	−11.7313	+	10.6327i	−0.415545	+	0.376628i	0.436843	+	0.899538i	$0.356096\pi$
$798$	4.07701	−	0.151519i	0.144325	−	0.00536370i
$799$	−4.17354	−	10.0758i	−0.147649	−	0.356457i
$800$	25.9858	+	8.18488i	0.918736	+	0.289379i
$801$	−3.83649	+	9.26211i	−0.135556	+	0.327261i
$802$	−13.3436	+	35.9342i	−0.471177	+	1.26888i
$803$	−0.773267	+	15.7402i	−0.0272880	+	0.555460i
$804$	3.58664	−	8.10584i	0.126491	−	0.285871i
$805$	1.41313	+	0.846998i	0.0498063	+	0.0298528i
$806$	7.41522	+	18.5245i	0.261190	+	0.652497i
$807$	8.62721	−	4.61134i	0.303692	−	0.162327i
$808$	−27.8250	+	17.1834i	−0.978879	+	0.604511i
$809$	44.0144	−	13.3516i	1.54746	−	0.469418i	0.602920	−	0.797801i	$-0.294004\pi$
$809$	44.0144	−	13.3516i	1.54746	−	0.469418i	0.944545	+	0.328383i	$0.106504\pi$
$810$	−0.169079	−	0.582319i	−0.00594082	−	0.0204606i
$811$	−43.6367	+	20.6386i	−1.53229	+	0.724719i	−0.993079	−	0.117451i	$-0.962528\pi$
$811$	−43.6367	+	20.6386i	−1.53229	+	0.724719i	−0.539212	+	0.842170i	$0.681278\pi$
$812$	9.09543	−	5.16047i	0.319187	−	0.181097i
$813$	−3.04707	−	5.08374i	−0.106866	−	0.178294i
$814$	−20.8497	+	2.83877i	−0.730783	+	0.0994989i
$815$	−3.70736	−	0.737440i	−0.129863	−	0.0258314i
$816$	7.32332	+	3.90192i	0.256367	+	0.136594i
$817$	8.40962	−	1.67278i	0.294215	−	0.0585231i
$818$	16.3096	+	47.3575i	0.570252	+	1.65581i
$819$	−4.77880	+	0.708868i	−0.166985	+	0.0247699i
$820$	0.0167843	−	0.0971123i	0.000586132	−	0.00339131i
$821$	34.1759	+	30.9752i	1.19275	+	1.08104i	0.994906	+	0.100810i	$0.0321433\pi$
$821$	34.1759	+	30.9752i	1.19275	+	1.08104i	0.197842	+	0.980234i	$0.436607\pi$
$822$	−13.5712	−	11.4115i	−0.473349	−	0.398020i
$823$	6.13792	+	0.604532i	0.213954	+	0.0210727i	0.204426	−	0.978882i	$-0.434467\pi$
$823$	6.13792	+	0.604532i	0.213954	+	0.0210727i	0.00952802	+	0.999955i	$0.496967\pi$
$824$	23.1584	−	0.307246i	0.806761	−	0.0107034i
$825$	−10.5651	+	12.8736i	−0.367831	+	0.448203i
$826$	−26.2342	−	5.54474i	−0.912805	−	0.192926i
$827$	18.7780	−	13.9267i	0.652976	−	0.484280i	−0.217779	−	0.975998i	$-0.569881\pi$
$827$	18.7780	−	13.9267i	0.652976	−	0.484280i	0.870754	+	0.491718i	$0.163631\pi$
$828$	−0.585873	+	4.77620i	−0.0203605	+	0.165984i
$829$	−16.8058	+	6.01322i	−0.583690	+	0.208848i	−0.612142	−	0.790748i	$-0.709692\pi$
$829$	−16.8058	+	6.01322i	−0.583690	+	0.208848i	0.0284524	+	0.999595i	$0.490942\pi$
$830$	−2.31817	+	3.76495i	−0.0804650	+	0.130683i
$831$	−13.0267	+	13.0267i	−0.451891	+	0.451891i
$832$	−24.1941	−	0.545781i	−0.838780	−	0.0189216i
$833$	−6.52686	−	6.52686i	−0.226142	−	0.226142i
$834$	−8.85459	+	2.10593i	−0.306609	+	0.0729223i
$835$	2.64911	+	7.40377i	0.0916763	+	0.256218i
$836$	−6.15043	+	10.8738i	−0.212717	+	0.376079i
$837$	−2.77844	−	3.74629i	−0.0960370	−	0.129491i
$838$	−15.8714	+	10.3330i	−0.548267	+	0.356946i
$839$	22.7693	+	18.6862i	0.786082	+	0.645121i	0.939310	−	0.343070i	$-0.111467\pi$
$839$	22.7693	+	18.6862i	0.786082	+	0.645121i	−0.153228	+	0.988191i	$0.548967\pi$
$840$	0.352616	−	1.90442i	0.0121664	−	0.0657087i
$841$	−1.79184	+	18.1929i	−0.0617878	+	0.627342i
$842$	−0.238100	−	2.75423i	−0.00820545	−	0.0949169i
$843$	−8.23845	+	9.08973i	−0.283747	+	0.313067i
$844$	−43.4920	+	9.79676i	−1.49706	+	0.337218i
$845$	0.242165	+	1.63254i	0.00833071	+	0.0561611i
$846$	−6.68255	−	3.25881i	−0.229751	−	0.112040i
$847$	−0.298246	−	1.49938i	−0.0102478	−	0.0515194i
$848$	−6.27775	−	31.3431i	−0.215579	−	1.07633i
$849$	−1.12534	+	5.65744i	−0.0386214	+	0.194163i
$850$	11.2476	+	8.55184i	0.385790	+	0.293326i
$851$	−8.87981	+	5.32235i	−0.304396	+	0.182448i
$852$	−3.25557	−	26.2521i	−0.111534	−	0.899384i
$853$	−0.458565	−	0.969555i	−0.0157010	−	0.0331969i	0.895986	−	0.444081i	$-0.146470\pi$
$853$	−0.458565	−	0.969555i	−0.0157010	−	0.0331969i	−0.911687	+	0.410885i	$0.865220\pi$
$854$	−23.9150	−	13.1523i	−0.818353	−	0.450063i
$855$	−0.224832	−	0.741170i	−0.00768908	−	0.0253475i
$856$	13.4162	+	0.480787i	0.458556	+	0.0164330i
$857$	6.81554	+	12.7510i	0.232814	+	0.435565i	0.971016	−	0.239015i	$-0.0768246\pi$
$857$	6.81554	+	12.7510i	0.232814	+	0.435565i	−0.738201	+	0.674580i	$0.764325\pi$
$858$	5.82387	−	13.5985i	0.198824	−	0.464246i
$859$	25.6977	−	42.8740i	0.876794	−	1.46284i	−0.00962320	−	0.999954i	$-0.503063\pi$
$859$	25.6977	−	42.8740i	0.876794	−	1.46284i	0.886417	−	0.462888i	$-0.153187\pi$
$860$	0.0971960	−	4.06930i	0.00331436	−	0.138762i
$861$	0.183318	+	0.00900585i	0.00624747	+	0.000306919i
$862$	7.78517	+	16.9821i	0.265164	+	0.578411i
$863$	25.2984	+	10.4789i	0.861166	+	0.356707i	0.769163	−	0.639052i	$-0.220673\pi$
$863$	25.2984	+	10.4789i	0.861166	+	0.356707i	0.0920026	+	0.995759i	$0.470673\pi$
$864$	5.50161	−	1.31618i	0.187168	−	0.0447775i
$865$	−2.99825	+	1.24191i	−0.101943	+	0.0422264i
$866$	27.0123	+	25.0764i	0.917914	+	0.852132i
$867$	−8.52645	−	9.40749i	−0.289573	−	0.319495i
$868$	−2.55667	−	14.6767i	−0.0867791	−	0.498159i
$869$	9.30570	+	37.1504i	0.315674	+	1.26024i
$870$	−1.38692	−	1.42045i	−0.0470211	−	0.0481576i
$871$	−3.89178	+	12.8295i	−0.131868	+	0.434711i
$872$	−1.76098	+	0.109946i	−0.0596342	+	0.00372324i
$873$	10.3323	+	5.52272i	0.349695	+	0.186916i
$874$	−0.675446	+	6.10918i	−0.0228473	+	0.206646i
$875$	2.26447	−	6.32877i	0.0765531	−	0.213952i
$876$	6.89788	−	5.95814i	0.233058	−	0.201307i
$877$	12.2302	−	48.8256i	0.412983	−	1.64872i	−0.304771	−	0.952426i	$-0.598580\pi$
$877$	12.2302	−	48.8256i	0.412983	−	1.64872i	0.717754	−	0.696296i	$-0.245170\pi$
$878$	−13.4446	−	23.0507i	−0.453733	−	0.777924i
$879$	−2.83856	+	1.89667i	−0.0957423	+	0.0639729i
$880$	4.39955	+	3.97691i	0.148309	+	0.134061i
$881$	31.4734	+	21.0298i	1.06036	+	0.708513i	0.958155	−	0.286250i	$-0.0924087\pi$
$881$	31.4734	+	21.0298i	1.06036	+	0.708513i	0.102210	+	0.994763i	$0.467409\pi$
$882$	−6.28079	−	0.383779i	−0.211485	−	0.0129225i
$883$	9.73273	−	13.1231i	0.327532	−	0.441626i	−0.608493	−	0.793559i	$-0.708226\pi$
$883$	9.73273	−	13.1231i	0.327532	−	0.441626i	0.936025	+	0.351933i	$0.114476\pi$
$884$	−11.7128	−	4.50920i	−0.393944	−	0.151661i
$885$	0.249773	+	5.08424i	0.00839601	+	0.170905i
$886$	15.4910	+	4.90187i	0.520430	+	0.164682i
$887$	−17.5531	+	14.4055i	−0.589377	+	0.483689i	−0.881175	−	0.472791i	$-0.843247\pi$
$887$	−17.5531	+	14.4055i	−0.589377	+	0.483689i	0.291798	+	0.956480i	$0.405747\pi$
$888$	9.50941	+	7.59531i	0.319115	+	0.254882i
$889$	23.0676	−	2.27196i	0.773664	−	0.0761992i
$890$	5.01381	+	3.43742i	0.168063	+	0.115222i
$891$	−0.507383	+	3.42050i	−0.0169980	+	0.114591i
$892$	19.7659	+	17.0274i	0.661812	+	0.570118i
$893$	−8.58477	−	4.06030i	−0.287278	−	0.135873i
$894$	−8.30874	−	1.33406i	−0.277886	−	0.0446177i
$895$		−	5.72446i		−	0.191348i
$896$	17.5891	+	4.13405i	0.587612	+	0.138109i
$897$		−	7.27822i		−	0.243013i
$898$	−5.10755	+	31.8106i	−0.170441	+	1.06153i
$899$	−13.8043	−	6.52897i	−0.460401	−	0.217753i
$900$	9.60575	−	0.714966i	0.320192	−	0.0238322i
$901$	2.43251	−	16.3986i	0.0810386	−	0.546318i
$902$	−0.317794	+	0.463533i	−0.0105814	+	0.0154340i
$903$	7.54415	−	0.743034i	0.251054	−	0.0247266i
$904$	3.31509	−	11.4742i	0.110258	−	0.381627i
$905$	2.98923	−	2.45320i	0.0993655	−	0.0815472i
$906$	2.35865	−	7.45384i	0.0783608	−	0.247637i
$907$	0.992926	+	20.2115i	0.0329696	+	0.671111i	0.957227	+	0.289340i	$0.0934357\pi$
$907$	0.992926	+	20.2115i	0.0329696	+	0.671111i	−0.924257	+	0.381771i	$0.875314\pi$
$908$	−5.40570	−	12.1733i	−0.179394	−	0.403984i
$909$	−6.88767	+	9.28695i	−0.228450	+	0.308029i
$910$	−0.178665	+	2.92397i	−0.00592269	+	0.0969287i
$911$	−40.4809	−	27.0485i	−1.34119	−	0.896155i	−0.342137	−	0.939650i	$-0.611151\pi$
$911$	−40.4809	−	27.0485i	−1.34119	−	0.896155i	−0.999054	+	0.0434946i	$0.986151\pi$
$912$	7.00668	−	1.76496i	0.232014	−	0.0584437i
$913$	20.9645	−	14.0081i	0.693825	−	0.463599i
$914$	18.0572	−	10.5321i	0.597278	−	0.348369i
$915$	−1.25897	+	5.02607i	−0.0416201	+	0.166157i
$916$	−1.86929	+	25.5725i	−0.0617632	+	0.844939i
$917$	−1.27648	+	3.56753i	−0.0421532	+	0.117810i
$918$	2.91600	+	0.322400i	0.0962423	+	0.0106408i
$919$	−29.7393	−	15.8960i	−0.981010	−	0.524361i	−0.0987447	−	0.995113i	$-0.531483\pi$
$919$	−29.7393	−	15.8960i	−0.981010	−	0.524361i	−0.882266	+	0.470752i	$0.843983\pi$
$920$	2.76008	+	0.946460i	0.0909971	+	0.0312039i
$921$	−6.29628	+	20.7561i	−0.207470	+	0.683935i
$922$	18.3157	−	17.8835i	0.603197	−	0.588961i
$923$	9.72187	+	38.8119i	0.319999	+	1.27751i
$924$	−6.35374	+	9.03434i	−0.209023	+	0.297208i
$925$	13.9169	+	15.3550i	0.457586	+	0.504868i
$926$	−22.0377	+	23.7389i	−0.724203	+	0.780110i
$927$	7.56515	−	3.13359i	0.248472	−	0.102920i
$928$	13.8540	−	12.2913i	0.454781	−	0.403481i
$929$	35.7766	+	14.8191i	1.17379	+	0.486200i	0.882444	−	0.470417i	$-0.155896\pi$
$929$	35.7766	+	14.8191i	1.17379	+	0.486200i	0.291347	+	0.956617i	$0.405896\pi$
$930$	−2.57092	+	1.17860i	−0.0843039	+	0.0386478i
$931$	−8.02779	−	0.394380i	−0.263100	−	0.0129253i
$932$	−2.58374	−	2.71019i	−0.0846332	−	0.0887751i
$933$	8.17552	−	13.6400i	0.267655	−	0.446555i
$934$	−19.9269	−	8.53414i	−0.652027	−	0.279245i
$935$	1.44989	+	2.71255i	0.0474165	+	0.0887099i
$936$	−8.01698	+	2.98907i	−0.262043	+	0.0977009i
$937$	−13.3475	−	44.0007i	−0.436043	−	1.43744i	−0.849825	−	0.527064i	$-0.823293\pi$
$937$	−13.3475	−	44.0007i	−0.436043	−	1.43744i	0.413783	−	0.910376i	$-0.364207\pi$
$938$	4.82365	−	8.77088i	0.157498	−	0.286379i
$939$	−9.83300	−	20.7901i	−0.320888	−	0.678460i
$940$	−2.77125	+	3.55589i	−0.0903882	+	0.115980i
$941$	19.0703	−	11.4303i	0.621673	−	0.372617i	−0.168320	−	0.985732i	$-0.553834\pi$
$941$	19.0703	−	11.4303i	0.621673	−	0.372617i	0.789993	+	0.613116i	$0.210084\pi$
$942$	−2.46209	+	3.23821i	−0.0802194	+	0.105507i
$943$	−0.0539442	+	0.271196i	−0.00175667	+	0.00883136i
$944$	−47.4883	+	0.0629719i	−1.54561	+	0.00204956i
$945$	−0.133590	−	0.671601i	−0.00434567	−	0.0218472i
$946$	−10.1745	+	20.8638i	−0.330800	+	0.678342i
$947$	−8.69318	−	58.6047i	−0.282490	−	1.90440i	−0.409180	−	0.912454i	$-0.634185\pi$
$947$	−8.69318	−	58.6047i	−0.282490	−	1.90440i	0.126689	−	0.991942i	$-0.459565\pi$
$948$	11.8383	−	18.7222i	0.384490	−	0.608068i
$949$	−9.25833	+	10.2150i	−0.300538	+	0.331593i
$950$	12.2577	−	1.05967i	0.397693	−	0.0343801i
$951$	−1.38642	+	14.0766i	−0.0449578	+	0.456464i
$952$	7.85981	+	5.10225i	0.254738	+	0.165365i
$953$	−26.7408	−	21.9456i	−0.866218	−	0.710887i	0.0923570	−	0.995726i	$-0.470560\pi$
$953$	−26.7408	−	21.9456i	−0.866218	−	0.710887i	−0.958575	+	0.284839i	$0.908060\pi$
$954$	−6.16616	−	9.47120i	−0.199637	−	0.306642i
$955$	−4.66482	−	6.28979i	−0.150950	−	0.203533i
$956$	32.4024	−	8.99010i	1.04797	−	0.290760i
$957$	3.81401	+	10.6594i	0.123289	+	0.344571i
$958$	−6.92151	−	29.1022i	−0.223624	−	0.940250i
$959$	−14.1588	−	14.1588i	−0.457210	−	0.457210i
$960$	−0.0910004	−	3.42893i	−0.00293703	−	0.110668i
$961$	6.53758	−	6.53758i	0.210890	−	0.210890i
$962$	−15.6748	−	9.65138i	−0.505377	−	0.311173i
$963$	4.46893	−	1.59901i	0.144009	−	0.0515274i
$964$	4.63798	+	5.93491i	0.149379	+	0.191151i
$965$	5.28425	−	3.91907i	0.170106	−	0.126159i
$966$	−1.12370	+	5.31662i	−0.0361543	+	0.171060i
$967$	10.4508	−	12.7343i	0.336075	−	0.409508i	−0.577363	−	0.816488i	$-0.695918\pi$
$967$	10.4508	−	12.7343i	0.336075	−	0.409508i	0.913437	+	0.406980i	$0.133418\pi$
$968$	−1.06921	−	2.48744i	−0.0343656	−	0.0799492i
$969$	3.72929	+	0.367303i	0.119802	+	0.0117995i
$970$	4.57198	−	5.43727i	0.146797	−	0.174580i
$971$	38.5208	+	34.9132i	1.23619	+	1.12042i	0.988443	+	0.151595i	$0.0484410\pi$
$971$	38.5208	+	34.9132i	1.23619	+	1.12042i	0.247750	+	0.968824i	$0.420309\pi$
$972$	1.63441	−	1.15270i	0.0524236	−	0.0369729i
$973$	−10.1669	+	1.50812i	−0.325937	+	0.0483482i
$974$	7.91334	−	2.72530i	0.253560	−	0.0873243i
$975$	−14.2891	+	2.84228i	−0.457617	+	0.0910257i
$976$	−46.2744	−	13.9702i	−1.48121	−	0.447175i
$977$	19.0164	+	3.78259i	0.608387	+	0.121016i	0.489663	−	0.871912i	$-0.337120\pi$
$977$	19.0164	+	3.78259i	0.608387	+	0.121016i	0.118724	+	0.992927i	$0.462120\pi$
$978$	−1.68200	−	12.3537i	−0.0537844	−	0.395027i
$979$	−17.8222	−	29.7345i	−0.569598	−	0.950318i
$980$	−1.01522	+	3.67803i	−0.0324302	+	0.117491i
$981$	−0.563919	+	0.266714i	−0.0180045	+	0.00851552i
$982$	−7.30939	+	2.12231i	−0.233252	+	0.0677257i
$983$	−0.969605	+	0.294127i	−0.0309256	+	0.00938118i	−0.305710	−	0.952125i	$-0.598894\pi$
$983$	−0.969605	+	0.294127i	−0.0309256	+	0.00938118i	0.274784	+	0.961506i	$0.411394\pi$
$984$	0.320877	−	0.0519570i	0.0102292	−	0.00165633i
$985$	0.295331	−	0.157858i	0.00941004	−	0.00502977i
$986$	8.91726	−	3.56952i	0.283983	−	0.113677i
$987$	−7.20144	−	4.31638i	−0.229224	−	0.137392i
$988$	−10.1939	+	3.93997i	−0.324310	+	0.125347i
$989$	−0.560379	+	11.4068i	−0.0178190	+	0.362715i
$990$	1.96563	+	0.729905i	0.0624719	+	0.0231979i
$991$	−8.57773	+	20.7085i	−0.272481	+	0.657826i	−0.999588	−	0.0286973i	$-0.990864\pi$
$991$	−8.57773	+	20.7085i	−0.272481	+	0.657826i	0.727108	+	0.686524i	$0.240864\pi$
$992$	−9.83762	−	24.4819i	−0.312345	−	0.777301i
$993$	−5.25935	−	12.6972i	−0.166900	−	0.402933i
$994$	−1.10944	−	29.8524i	−0.0351893	−	0.946861i
$995$	8.02470	−	7.27317i	0.254400	−	0.230575i
$996$	−14.2310	−	3.18576i	−0.450926	−	0.100945i
$997$	9.98850	−	2.50199i	0.316339	−	0.0792387i	−0.0815589	−	0.996669i	$-0.525990\pi$
$997$	9.98850	−	2.50199i	0.316339	−	0.0792387i	0.397898	+	0.917430i	$0.369740\pi$
$998$	−29.2894	−	0.349742i	−0.927140	−	0.0110709i
$999$	4.11759	+	1.24906i	0.130275	+	0.0395185i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.637.52	yes	2048
256.213	even	64	inner	768.2.z.a.469.52	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.469.52	✓	2048	256.213	even	64	inner
768.2.z.a.637.52	yes	2048	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14588 - 0.828823i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.626104 - 1.89947i) q^{4} +(-0.424127 - 0.0629133i) q^{5} +(-0.259318 - 1.39024i) q^{6} +(-0.156537 - 1.58935i) q^{7} +(-0.856883 - 2.69551i) q^{8} +(-0.634393 - 0.773010i) q^{9} +O(q^{10})\)	\(q+(1.14588 - 0.828823i) q^{2} +(0.427555 - 0.903989i) q^{3} +(0.626104 - 1.89947i) q^{4} +(-0.424127 - 0.0629133i) q^{5} +(-0.259318 - 1.39024i) q^{6} +(-0.156537 - 1.58935i) q^{7} +(-0.856883 - 2.69551i) q^{8} +(-0.634393 - 0.773010i) q^{9} +(-0.538144 + 0.279435i) q^{10} +(3.45376 - 0.169672i) q^{11} +(-1.44941 - 1.37812i) q^{12} +(2.42973 + 1.80201i) q^{13} +(-1.49666 - 1.69147i) q^{14} +(-0.238210 + 0.356507i) q^{15} +(-3.21599 - 2.37853i) q^{16} +(-1.15252 - 1.72487i) q^{17} +(-1.36763 - 0.359981i) q^{18} +(-1.75225 - 0.438917i) q^{19} +(-0.385050 + 0.766227i) q^{20} +(-1.50368 - 0.538026i) q^{21} +(3.81698 - 3.05698i) q^{22} +(1.13418 - 2.12190i) q^{23} +(-2.80307 - 0.377864i) q^{24} +(-4.60878 - 1.39806i) q^{25} +(4.27774 + 0.0510800i) q^{26} +(-0.970031 + 0.242980i) q^{27} +(-3.11693 - 0.697760i) q^{28} +(-2.42587 + 2.19868i) q^{29} +(0.0225196 + 0.605951i) q^{30} +(1.78490 + 4.30913i) q^{31} +(-5.65654 - 0.0600423i) q^{32} +(1.32329 - 3.19471i) q^{33} +(-2.75027 - 1.02127i) q^{34} +(-0.0335995 + 0.683933i) q^{35} +(-1.86551 + 0.721027i) q^{36} +(-3.69070 - 2.21212i) q^{37} +(-2.37167 + 0.949361i) q^{38} +(2.66784 - 1.42599i) q^{39} +(0.193844 + 1.19715i) q^{40} +(-0.109976 + 0.0333609i) q^{41} +(-2.16897 + 0.629771i) q^{42} +(-4.29096 + 2.02947i) q^{43} +(1.84013 - 6.66655i) q^{44} +(0.220431 + 0.367766i) q^{45} +(-0.459041 - 3.37149i) q^{46} +(5.15618 + 1.02563i) q^{47} +(-3.52518 + 1.89026i) q^{48} +(4.36397 - 0.868048i) q^{49} +(-6.43987 + 2.21785i) q^{50} +(-2.05203 + 0.304391i) q^{51} +(4.94413 - 3.48696i) q^{52} +(5.92124 + 5.36670i) q^{53} +(-0.910157 + 1.08241i) q^{54} +(-1.47551 - 0.145325i) q^{55} +(-4.14996 + 1.78383i) q^{56} +(-1.14596 + 1.39636i) q^{57} +(-0.957451 + 4.53006i) q^{58} +(9.53576 - 7.07220i) q^{59} +(0.528031 + 0.675685i) q^{60} +(11.3779 - 4.07108i) q^{61} +(5.61680 + 3.45840i) q^{62} +(-1.12928 + 1.12928i) q^{63} +(-6.53150 + 4.61947i) q^{64} +(-0.917143 - 0.917143i) q^{65} +(-1.13151 - 4.75754i) q^{66} +(1.49308 + 4.17288i) q^{67} +(-3.99795 + 1.10924i) q^{68} +(-1.43325 - 1.93252i) q^{69} +(0.528359 + 0.811557i) q^{70} +(10.2243 + 8.39088i) q^{71} +(-1.54005 + 2.37239i) q^{72} +(-0.446705 + 4.53547i) q^{73} +(-6.06257 + 0.524102i) q^{74} +(-3.23433 + 3.56854i) q^{75} +(-1.93080 + 3.05355i) q^{76} +(-0.810310 - 5.46267i) q^{77} +(1.87514 - 3.84519i) q^{78} +(2.16072 + 10.8627i) q^{79} +(1.21434 + 1.21113i) q^{80} +(-0.195090 + 0.980785i) q^{81} +(-0.0983698 + 0.129379i) q^{82} +(6.25422 - 3.74863i) q^{83} +(-1.96343 + 2.51934i) q^{84} +(0.380299 + 0.804074i) q^{85} +(-3.23487 + 5.88199i) q^{86} +(0.950392 + 3.13302i) q^{87} +(-3.41682 - 9.16424i) q^{88} +(-4.72586 - 8.84147i) q^{89} +(0.557401 + 0.238720i) q^{90} +(2.48368 - 4.14377i) q^{91} +(-3.32038 - 3.48287i) q^{92} +(4.65855 + 0.228860i) q^{93} +(6.75846 - 3.09831i) q^{94} +(0.715564 + 0.296396i) q^{95} +(-2.47276 + 5.08778i) q^{96} +(-10.8238 + 4.48338i) q^{97} +(4.28115 - 4.61165i) q^{98} +(-2.32220 - 2.56215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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