LMFDB - Embedded newform 384.2.v.a.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			325.1
Character	$\chi$	$=$	384.325
Dual form			384.2.v.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40051 + 0.196427i) q^{2} +(0.290285 - 0.956940i) q^{3} +(1.92283 - 0.550195i) q^{4} +(0.0502132 - 0.509823i) q^{5} +(-0.218576 + 1.39722i) q^{6} +(-1.66106 - 2.48595i) q^{7} +(-2.58487 + 1.14825i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.40051 + 0.196427i) q^{2} +(0.290285 - 0.956940i) q^{3} +(1.92283 - 0.550195i) q^{4} +(0.0502132 - 0.509823i) q^{5} +(-0.218576 + 1.39722i) q^{6} +(-1.66106 - 2.48595i) q^{7} +(-2.58487 + 1.14825i) q^{8} +(-0.831470 - 0.555570i) q^{9} +(0.0298193 + 0.723874i) q^{10} +(-2.39179 - 1.27844i) q^{11} +(0.0316653 - 1.99975i) q^{12} +(-0.147254 + 0.0145033i) q^{13} +(2.81463 + 3.15532i) q^{14} +(-0.473294 - 0.196045i) q^{15} +(3.39457 - 2.11586i) q^{16} +(-5.02760 + 2.08250i) q^{17} +(1.27361 + 0.614756i) q^{18} +(-0.869829 - 0.713850i) q^{19} +(-0.183951 - 1.00793i) q^{20} +(-2.86109 + 0.867902i) q^{21} +(3.60084 + 1.32065i) q^{22} +(-0.0792843 - 0.398589i) q^{23} +(0.348458 + 2.80688i) q^{24} +(4.64653 + 0.924252i) q^{25} +(0.203382 - 0.0492367i) q^{26} +(-0.773010 + 0.634393i) q^{27} +(-4.56170 - 3.86617i) q^{28} +(1.28926 + 2.41204i) q^{29} +(0.701360 + 0.181594i) q^{30} +(-3.00006 - 3.00006i) q^{31} +(-4.33850 + 3.63007i) q^{32} +(-1.91769 + 1.91769i) q^{33} +(6.63212 - 3.90411i) q^{34} +(-1.35080 + 0.722020i) q^{35} +(-1.90445 - 0.610798i) q^{36} +(-5.49304 - 6.69329i) q^{37} +(1.35842 + 0.828893i) q^{38} +(-0.0288669 + 0.145124i) q^{39} +(0.455609 + 1.37548i) q^{40} +(-7.61357 + 1.51443i) q^{41} +(3.83649 - 1.77750i) q^{42} +(-1.01220 - 3.33679i) q^{43} +(-5.30241 - 1.14227i) q^{44} +(-0.324993 + 0.396006i) q^{45} +(0.189332 + 0.542652i) q^{46} +(-3.94790 - 9.53108i) q^{47} +(-1.03936 - 3.86261i) q^{48} +(-0.742058 + 1.79149i) q^{49} +(-6.68904 - 0.381716i) q^{50} +(0.533393 + 5.41563i) q^{51} +(-0.275166 + 0.108906i) q^{52} +(4.05063 - 7.57820i) q^{53} +(0.957994 - 1.04031i) q^{54} +(-0.771878 + 1.15520i) q^{55} +(7.14811 + 4.51855i) q^{56} +(-0.935610 + 0.625154i) q^{57} +(-2.27941 - 3.12483i) q^{58} +(6.40642 + 0.630977i) q^{59} +(-1.01793 - 0.116558i) q^{60} +(9.35612 + 2.83815i) q^{61} +(4.79090 + 3.61231i) q^{62} +2.98983i q^{63} +(5.36306 - 5.93613i) q^{64} +0.0758019i q^{65} +(2.30905 - 3.06243i) q^{66} +(-0.0861833 - 0.0261434i) q^{67} +(-8.52145 + 6.77046i) q^{68} +(-0.404441 - 0.0398339i) q^{69} +(1.74999 - 1.27653i) q^{70} +(8.16418 - 5.45513i) q^{71} +(2.78717 + 0.481341i) q^{72} +(-9.01176 + 13.4871i) q^{73} +(9.00778 + 8.29501i) q^{74} +(2.23327 - 4.17815i) q^{75} +(-2.06529 - 0.894039i) q^{76} +(0.794772 + 8.06946i) q^{77} +(0.0119220 - 0.208917i) q^{78} +(1.41245 - 3.40995i) q^{79} +(-0.908265 - 1.83688i) q^{80} +(0.382683 + 0.923880i) q^{81} +(10.3654 - 3.61648i) q^{82} +(2.88556 - 3.51607i) q^{83} +(-5.02388 + 3.24299i) q^{84} +(0.809255 + 2.66776i) q^{85} +(2.07303 + 4.47437i) q^{86} +(2.68243 - 0.533569i) q^{87} +(7.65043 + 0.558225i) q^{88} +(-0.951785 + 4.78495i) q^{89} +(0.377369 - 0.618446i) q^{90} +(0.280653 + 0.341977i) q^{91} +(-0.371752 - 0.722798i) q^{92} +(-3.74175 + 2.00001i) q^{93} +(7.40122 + 12.5729i) q^{94} +(-0.407614 + 0.407614i) q^{95} +(2.21436 + 5.20544i) q^{96} +(8.57980 + 8.57980i) q^{97} +(0.687360 - 2.65475i) q^{98} +(1.27844 + 2.39179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.40051	+	0.196427i	−0.990307	+	0.138895i
$2$	−1.40051	+	0.196427i	−0.990307	+	0.138895i
$3$	0.290285	−	0.956940i	0.167596	−	0.552490i
$3$	0.290285	−	0.956940i	0.167596	−	0.552490i
$4$	1.92283	−	0.550195i	0.961416	−	0.275097i
$5$	0.0502132	−	0.509823i	0.0224560	−	0.228000i	−0.977406	−	0.211372i	$-0.932207\pi$
$5$	0.0502132	−	0.509823i	0.0224560	−	0.228000i	0.999862	−	0.0166280i	$-0.00529312\pi$
$6$	−0.218576	+	1.39722i	−0.0892334	+	0.570413i
$7$	−1.66106	−	2.48595i	−0.627822	−	0.939602i	−0.999935	−	0.0114147i	$-0.996367\pi$
$7$	−1.66106	−	2.48595i	−0.627822	−	0.939602i	0.372113	−	0.928188i	$-0.378633\pi$
$8$	−2.58487	+	1.14825i	−0.913888	+	0.405967i
$9$	−0.831470	−	0.555570i	−0.277157	−	0.185190i
$10$	0.0298193	+	0.723874i	0.00942968	+	0.228909i
$11$	−2.39179	−	1.27844i	−0.721153	−	0.385464i	0.0696203	−	0.997574i	$-0.477821\pi$
$11$	−2.39179	−	1.27844i	−0.721153	−	0.385464i	−0.790773	+	0.612109i	$0.790321\pi$
$12$	0.0316653	−	1.99975i	0.00914100	−	0.577278i
$13$	−0.147254	+	0.0145033i	−0.0408410	+	0.00402249i	−0.118417	−	0.992964i	$-0.537782\pi$
$13$	−0.147254	+	0.0145033i	−0.0408410	+	0.00402249i	0.0775760	+	0.996986i	$0.475282\pi$
$14$	2.81463	+	3.15532i	0.752243	+	0.843293i
$15$	−0.473294	−	0.196045i	−0.122204	−	0.0506186i
$16$	3.39457	−	2.11586i	0.848643	−	0.528966i
$17$	−5.02760	+	2.08250i	−1.21937	+	0.505080i	−0.897210	−	0.441604i	$-0.854409\pi$
$17$	−5.02760	+	2.08250i	−1.21937	+	0.505080i	−0.322162	+	0.946685i	$0.604409\pi$
$18$	1.27361	+	0.614756i	0.300192	+	0.144899i
$19$	−0.869829	−	0.713850i	−0.199552	−	0.163768i	0.529310	−	0.848428i	$-0.322451\pi$
$19$	−0.869829	−	0.713850i	−0.199552	−	0.163768i	−0.728863	+	0.684660i	$0.759951\pi$
$20$	−0.183951	−	1.00793i	−0.0411326	−	0.225380i
$21$	−2.86109	+	0.867902i	−0.624341	+	0.189392i
$22$	3.60084	+	1.32065i	0.767702	+	0.281563i
$23$	−0.0792843	−	0.398589i	−0.0165319	−	0.0831115i	0.971639	−	0.236471i	$-0.0759908\pi$
$23$	−0.0792843	−	0.398589i	−0.0165319	−	0.0831115i	−0.988170	+	0.153359i	$0.950991\pi$
$24$	0.348458	+	2.80688i	0.0711286	+	0.572952i
$25$	4.64653	+	0.924252i	0.929306	+	0.184850i
$26$	0.203382	−	0.0492367i	0.0398864	−	0.00965611i
$27$	−0.773010	+	0.634393i	−0.148766	+	0.122089i
$28$	−4.56170	−	3.86617i	−0.862081	−	0.730637i
$29$	1.28926	+	2.41204i	0.239410	+	0.447905i	0.972718	−	0.231992i	$-0.0745244\pi$
$29$	1.28926	+	2.41204i	0.239410	+	0.447905i	−0.733307	+	0.679897i	$0.762024\pi$
$30$	0.701360	+	0.181594i	0.128050	+	0.0331544i
$31$	−3.00006	−	3.00006i	−0.538827	−	0.538827i	0.384358	−	0.923184i	$-0.374423\pi$
$31$	−3.00006	−	3.00006i	−0.538827	−	0.538827i	−0.923184	+	0.384358i	$0.874423\pi$
$32$	−4.33850	+	3.63007i	−0.766946	+	0.641711i
$33$	−1.91769	+	1.91769i	−0.333827	+	0.333827i
$34$	6.63212	−	3.90411i	1.13740	−	0.669549i
$35$	−1.35080	+	0.722020i	−0.228328	+	0.122044i
$36$	−1.90445	−	0.610798i	−0.317408	−	0.101800i
$37$	−5.49304	−	6.69329i	−0.903051	−	1.10037i	−0.994518	−	0.104563i	$-0.966656\pi$
$37$	−5.49304	−	6.69329i	−0.903051	−	1.10037i	0.0914675	−	0.995808i	$-0.470844\pi$
$38$	1.35842	+	0.828893i	0.220365	+	0.134464i
$39$	−0.0288669	+	0.145124i	−0.00462240	+	0.0232384i
$40$	0.455609	+	1.37548i	0.0720381	+	0.217483i
$41$	−7.61357	+	1.51443i	−1.18904	+	0.236515i	−0.749682	−	0.661798i	$-0.769794\pi$
$41$	−7.61357	+	1.51443i	−1.18904	+	0.236515i	−0.439357	+	0.898312i	$0.644794\pi$
$42$	3.83649	−	1.77750i	0.591984	−	0.274274i
$43$	−1.01220	−	3.33679i	−0.154360	−	0.508855i	0.845318	−	0.534264i	$-0.179411\pi$
$43$	−1.01220	−	3.33679i	−0.154360	−	0.508855i	−0.999677	+	0.0254088i	$0.991911\pi$
$44$	−5.30241	−	1.14227i	−0.799368	−	0.172204i
$45$	−0.324993	+	0.396006i	−0.0484472	+	0.0590330i
$46$	0.189332	+	0.542652i	0.0279154	+	0.0800097i
$47$	−3.94790	−	9.53108i	−0.575861	−	1.39025i	−0.896498	−	0.443048i	$-0.853897\pi$
$47$	−3.94790	−	9.53108i	−0.575861	−	1.39025i	0.320637	−	0.947202i	$-0.396103\pi$
$48$	−1.03936	−	3.86261i	−0.150019	−	0.557519i
$49$	−0.742058	+	1.79149i	−0.106008	+	0.255927i
$50$	−6.68904	−	0.381716i	−0.945973	−	0.0539828i
$51$	0.533393	+	5.41563i	0.0746899	+	0.758340i
$52$	−0.275166	+	0.108906i	−0.0381586	+	0.0151025i
$53$	4.05063	−	7.57820i	0.556397	−	1.04095i	−0.433766	−	0.901026i	$-0.642815\pi$
$53$	4.05063	−	7.57820i	0.556397	−	1.04095i	0.990163	−	0.139920i	$-0.0446845\pi$
$54$	0.957994	−	1.04031i	0.130366	−	0.141568i
$55$	−0.771878	+	1.15520i	−0.104080	+	0.155767i
$56$	7.14811	+	4.51855i	0.955206	+	0.603816i
$57$	−0.935610	+	0.625154i	−0.123925	+	0.0828037i
$58$	−2.27941	−	3.12483i	−0.299301	−	0.410311i
$59$	6.40642	+	0.630977i	0.834045	+	0.0821463i	0.506019	−	0.862522i	$-0.331117\pi$
$59$	6.40642	+	0.630977i	0.834045	+	0.0821463i	0.328026	+	0.944669i	$0.393617\pi$
$60$	−1.01793	−	0.116558i	−0.131414	−	0.0150475i
$61$	9.35612	+	2.83815i	1.19793	+	0.363388i	0.825354	−	0.564615i	$-0.190975\pi$
$61$	9.35612	+	2.83815i	1.19793	+	0.363388i	0.372574	+	0.928003i	$0.378475\pi$
$62$	4.79090	+	3.61231i	0.608444	+	0.458764i
$63$			2.98983i			0.376683i
$64$	5.36306	−	5.93613i	0.670382	−	0.742016i
$65$			0.0758019i			0.00940207i
$66$	2.30905	−	3.06243i	0.284225	−	0.376958i
$67$	−0.0861833	−	0.0261434i	−0.0105290	−	0.00319393i	0.285016	−	0.958523i	$-0.408001\pi$
$67$	−0.0861833	−	0.0261434i	−0.0105290	−	0.00319393i	−0.295545	+	0.955329i	$0.595501\pi$
$68$	−8.52145	+	6.77046i	−1.03338	+	0.821038i
$69$	−0.404441	−	0.0398339i	−0.0486889	−	0.00479544i
$70$	1.74999	−	1.27653i	0.209163	−	0.152574i
$71$	8.16418	−	5.45513i	0.968910	−	0.647405i	0.0329301	−	0.999458i	$-0.489516\pi$
$71$	8.16418	−	5.45513i	0.968910	−	0.647405i	0.935980	+	0.352052i	$0.114516\pi$
$72$	2.78717	+	0.481341i	0.328471	+	0.0567266i
$73$	−9.01176	+	13.4871i	−1.05475	+	1.57854i	−0.265851	+	0.964014i	$0.585653\pi$
$73$	−9.01176	+	13.4871i	−1.05475	+	1.57854i	−0.788896	+	0.614527i	$0.789347\pi$
$74$	9.00778	+	8.29501i	1.04713	+	0.964276i
$75$	2.23327	−	4.17815i	0.257876	−	0.482452i
$76$	−2.06529	−	0.894039i	−0.236905	−	0.102553i
$77$	0.794772	+	8.06946i	0.0905727	+	0.919600i
$78$	0.0119220	−	0.208917i	0.00134990	−	0.0236552i
$79$	1.41245	−	3.40995i	0.158913	−	0.383650i	−0.824289	−	0.566169i	$-0.808425\pi$
$79$	1.41245	−	3.40995i	0.158913	−	0.383650i	0.983202	+	0.182519i	$0.0584251\pi$
$80$	−0.908265	−	1.83688i	−0.101547	−	0.205369i
$81$	0.382683	+	0.923880i	0.0425204	+	0.102653i
$82$	10.3654	−	3.61648i	1.14466	−	0.399374i
$83$	2.88556	−	3.51607i	0.316732	−	0.385939i	−0.590171	−	0.807278i	$-0.700940\pi$
$83$	2.88556	−	3.51607i	0.316732	−	0.385939i	0.906903	+	0.421339i	$0.138440\pi$
$84$	−5.02388	+	3.24299i	−0.548151	+	0.353839i
$85$	0.809255	+	2.66776i	0.0877760	+	0.289359i
$86$	2.07303	+	4.47437i	0.223541	+	0.482483i
$87$	2.68243	−	0.533569i	0.287587	−	0.0572046i
$88$	7.65043	+	0.558225i	0.815538	+	0.0595070i
$89$	−0.951785	+	4.78495i	−0.100889	+	0.507203i	0.896987	+	0.442058i	$0.145751\pi$
$89$	−0.951785	+	4.78495i	−0.100889	+	0.507203i	−0.997876	+	0.0651459i	$0.979249\pi$
$90$	0.377369	−	0.618446i	0.0397782	−	0.0651899i
$91$	0.280653	+	0.341977i	0.0294204	+	0.0358489i
$92$	−0.371752	−	0.722798i	−0.0387578	−	0.0753569i
$93$	−3.74175	+	2.00001i	−0.388001	+	0.207391i
$94$	7.40122	+	12.5729i	0.763378	+	1.29679i
$95$	−0.407614	+	0.407614i	−0.0418203	+	0.0418203i
$96$	2.21436	+	5.20544i	0.226002	+	0.531278i
$97$	8.57980	+	8.57980i	0.871146	+	0.871146i	0.992597	−	0.121451i	$-0.0387547\pi$
$97$	8.57980	+	8.57980i	0.871146	+	0.871146i	−0.121451	+	0.992597i	$0.538755\pi$
$98$	0.687360	−	2.65475i	0.0694338	−	0.268170i
$99$	1.27844	+	2.39179i	0.128488	+	0.240384i
$100$	9.44301	−	0.779313i	0.944301	−	0.0779313i
$101$	9.89529	−	8.12085i	0.984618	−	0.808055i	0.00321143	−	0.999995i	$-0.498978\pi$
$101$	9.89529	−	8.12085i	0.984618	−	0.808055i	0.981407	+	0.191940i	$0.0614778\pi$
$102$	−1.81080	−	7.47985i	−0.179296	−	0.740615i
$103$	−3.61428	−	0.718924i	−0.356125	−	0.0708377i	0.0137856	−	0.999905i	$-0.495612\pi$
$103$	−3.61428	−	0.718924i	−0.356125	−	0.0708377i	−0.369911	+	0.929067i	$0.620612\pi$
$104$	0.363979	−	0.206573i	0.0356911	−	0.0202562i
$105$	0.298812	+	1.50223i	0.0291611	+	0.146603i
$106$	−4.18437	+	11.4090i	−0.406422	+	1.10814i
$107$	11.1233	−	3.37423i	1.07533	−	0.326199i	0.297534	−	0.954711i	$-0.403836\pi$
$107$	11.1233	−	3.37423i	1.07533	−	0.326199i	0.777799	+	0.628513i	$0.216336\pi$
$108$	−1.13733	+	1.64514i	−0.109440	+	0.158304i
$109$	10.2267	+	8.39283i	0.979539	+	0.803887i	0.980581	−	0.196112i	$-0.0628317\pi$
$109$	10.2267	+	8.39283i	0.979539	+	0.803887i	−0.00104218	+	0.999999i	$0.500332\pi$
$110$	0.854108	−	1.76948i	0.0814360	−	0.168713i
$111$	−7.99963	+	3.31355i	−0.759291	+	0.314509i
$112$	−10.8985	−	4.92417i	−1.02981	−	0.465290i
$113$	−8.86196	−	3.67075i	−0.833663	−	0.345315i	−0.0753116	−	0.997160i	$-0.523995\pi$
$113$	−8.86196	−	3.67075i	−0.833663	−	0.345315i	−0.758352	+	0.651845i	$0.773995\pi$
$114$	1.18753	−	1.05931i	0.111222	−	0.0992136i
$115$	−0.207191	+	0.0204065i	−0.0193207	+	0.00190292i
$116$	3.80613	+	3.92861i	0.353390	+	0.364762i
$117$	0.130495	+	0.0697511i	0.0120643	+	0.00644849i
$118$	−9.09617	+	0.374708i	−0.837370	+	0.0344946i
$119$	13.5281	+	9.03922i	1.24012	+	0.828624i
$120$	1.44851	−	0.0367093i	0.132230	−	0.00335109i
$121$	−2.02501	−	3.03064i	−0.184092	−	0.275512i
$122$	−13.6608	−	2.13705i	−1.23679	−	0.193479i
$123$	−0.760880	+	7.72535i	−0.0686063	+	0.696571i
$124$	−7.41923	−	4.11800i	−0.666267	−	0.369807i
$125$	1.44807	−	4.77365i	0.129520	−	0.426969i
$126$	−0.587284	−	4.18728i	−0.0523194	−	0.373032i
$127$	−2.07680			−0.184287			−0.0921433	−	0.995746i	$-0.529372\pi$
$127$	−2.07680			−0.184287			−0.0921433	+	0.995746i	$0.529372\pi$
$128$	−6.34497	+	9.36703i	−0.560822	+	0.827937i
$129$	−3.48693			−0.307007
$130$	−0.0148896	−	0.106161i	−0.00130590	−	0.00931094i
$131$	1.75926	−	5.79951i	0.153707	−	0.506705i	−0.845940	−	0.533279i	$-0.820960\pi$
$131$	1.75926	−	5.79951i	0.153707	−	0.506705i	0.999647	+	0.0265737i	$0.00845965\pi$
$132$	−2.63230	+	4.74250i	−0.229112	+	0.412782i
$133$	−0.329759	+	3.34810i	−0.0285938	+	0.290317i
$134$	0.125835	+	0.0196853i	0.0108705	+	0.00170055i
$135$	0.284613	+	0.425954i	0.0244956	+	0.0366603i
$136$	10.6044	−	11.1559i	0.909323	−	0.956611i
$137$	−1.13927	−	0.761238i	−0.0973346	−	0.0650369i	0.505950	−	0.862563i	$-0.331142\pi$
$137$	−1.13927	−	0.761238i	−0.0973346	−	0.0650369i	−0.603285	+	0.797526i	$0.706142\pi$
$138$	0.574246	−	0.0236555i	0.0488831	−	0.00201369i
$139$	3.06940	+	1.64063i	0.260343	+	0.139156i	0.596405	−	0.802683i	$-0.296595\pi$
$139$	3.06940	+	1.64063i	0.260343	+	0.139156i	−0.336062	+	0.941840i	$0.609095\pi$
$140$	−2.20012	+	2.13153i	−0.185944	+	0.180147i
$141$	−10.2667	+	1.01118i	−0.864611	+	0.0851567i
$142$	−10.3625	+	9.24361i	−0.869597	+	0.775707i
$143$	0.370743	+	0.153567i	0.0310031	+	0.0128419i
$144$	−3.99799	−	0.126645i	−0.333166	−	0.0105538i
$145$	1.29445	−	0.536180i	0.107499	−	0.0445274i
$146$	9.97180	−	20.6589i	0.825272	−	1.70974i
$147$	1.49894	+	1.23015i	0.123630	+	0.101461i
$148$	−14.2448	−	9.84784i	−1.17092	−	0.809487i
$149$	17.2561	−	5.23459i	1.41368	−	0.428835i	0.511160	−	0.859486i	$-0.329216\pi$
$149$	17.2561	−	5.23459i	1.41368	−	0.428835i	0.902518	+	0.430651i	$0.141716\pi$
$150$	−2.30700	+	6.29020i	−0.188366	+	0.513593i
$151$	−3.05808	−	15.3740i	−0.248863	−	1.25112i	−0.879822	−	0.475303i	$-0.842338\pi$
$151$	−3.05808	−	15.3740i	−0.248863	−	1.25112i	0.630959	−	0.775816i	$-0.282662\pi$
$152$	3.06807	+	0.846427i	0.248853	+	0.0686543i
$153$	5.33727	+	1.06165i	0.431493	+	0.0858292i
$154$	−2.69814	−	11.1452i	−0.217423	−	0.898106i
$155$	−1.68014	+	1.37886i	−0.134952	+	0.110753i
$156$	0.0243401	+	0.294931i	0.00194877	+	0.0236134i
$157$	−1.35779	−	2.54024i	−0.108363	−	0.202733i	0.821895	−	0.569639i	$-0.192917\pi$
$157$	−1.35779	−	2.54024i	−0.108363	−	0.202733i	−0.930258	+	0.366906i	$0.880417\pi$
$158$	−1.30833	+	5.05310i	−0.104086	+	0.402003i
$159$	−6.07605	−	6.07605i	−0.481862	−	0.481862i
$160$	1.63284	+	2.39415i	0.129088	+	0.189274i
$161$	−0.859178	+	0.859178i	−0.0677127	+	0.0677127i
$162$	−0.717425	−	1.21873i	−0.0563663	−	0.0957524i
$163$	2.67403	−	1.42930i	0.209446	−	0.111951i	−0.363338	−	0.931657i	$-0.618363\pi$
$163$	2.67403	−	1.42930i	0.209446	−	0.111951i	0.572785	+	0.819706i	$0.305863\pi$
$164$	−13.8064	+	7.10095i	−1.07810	+	0.554491i
$165$	0.881391	+	1.07398i	0.0686162	+	0.0836090i
$166$	−3.35060	+	5.49108i	−0.260057	+	0.426190i
$167$	1.53457	−	7.71479i	0.118748	−	0.596988i	−0.874885	−	0.484330i	$-0.839063\pi$
$167$	1.53457	−	7.71479i	0.118748	−	0.596988i	0.993634	−	0.112658i	$-0.0359366\pi$
$168$	6.39897	−	5.52865i	0.493691	−	0.426545i
$169$	−12.7287	+	2.53190i	−0.979133	+	0.194762i
$170$	−1.65739	−	3.57725i	−0.127116	−	0.274362i
$171$	0.326642	+	1.07680i	0.0249790	+	0.0823446i
$172$	−3.78218	−	5.85918i	−0.288389	−	0.446758i
$173$	6.79195	−	8.27601i	0.516382	−	0.629214i	−0.447902	−	0.894083i	$-0.647829\pi$
$173$	6.79195	−	8.27601i	0.516382	−	0.629214i	0.964284	+	0.264869i	$0.0853287\pi$
$174$	−3.65196	+	1.27417i	−0.276854	+	0.0965946i
$175$	−5.42052	−	13.0863i	−0.409753	−	0.989231i
$176$	−10.8241	+	0.720955i	−0.815899	+	0.0543440i
$177$	2.46349	−	5.94740i	0.185168	−	0.447034i
$178$	0.393087	−	6.88830i	0.0294631	−	0.516300i
$179$	1.95098	+	19.8086i	0.145823	+	1.48057i	0.738023	+	0.674776i	$0.235760\pi$
$179$	1.95098	+	19.8086i	0.145823	+	1.48057i	−0.592200	+	0.805791i	$0.701740\pi$
$180$	−0.407028	+	0.940262i	−0.0303381	+	0.0700830i
$181$	−4.04506	+	7.56777i	−0.300667	+	0.562508i	−0.986205	−	0.165529i	$-0.947067\pi$
$181$	−4.04506	+	7.56777i	−0.300667	+	0.562508i	0.685538	+	0.728037i	$0.259567\pi$
$182$	−0.460230	−	0.423812i	−0.0341145	−	0.0314151i
$183$	5.43188	−	8.12938i	0.401536	−	0.600941i
$184$	0.662618	+	0.939261i	0.0488488	+	0.0692432i
$185$	−3.68822	+	2.46439i	−0.271163	+	0.181186i
$186$	4.84749	−	3.53600i	0.355435	−	0.259272i
$187$	14.6873	+	1.44658i	1.07404	+	0.105784i
$188$	−12.8351	−	16.1545i	−0.936096	−	1.17819i
$189$	2.86109	+	0.867902i	0.208114	+	0.0631306i
$190$	0.490800	−	0.650933i	0.0356063	−	0.0472236i
$191$			6.28243i			0.454580i	0.973827	+	0.227290i	$0.0729866\pi$
$191$			6.28243i			0.454580i	−0.973827	+	0.227290i	$0.927013\pi$
$192$	−4.12371	−	6.85529i	−0.297603	−	0.494738i
$193$		−	18.0651i		−	1.30035i	−0.759783	−	0.650177i	$-0.774695\pi$
$193$		−	18.0651i		−	1.30035i	0.759783	−	0.650177i	$-0.225305\pi$
$194$	−13.7014	−	10.3307i	−0.983700	−	0.741705i
$195$	0.0725379	+	0.0220041i	0.00519455	+	0.00157575i
$196$	−0.441187	+	3.85301i	−0.0315134	+	0.275215i
$197$	−13.8191	−	1.36106i	−0.984569	−	0.0969716i	−0.407099	−	0.913384i	$-0.633460\pi$
$197$	−13.8191	−	1.36106i	−0.984569	−	0.0969716i	−0.577469	+	0.816412i	$0.695960\pi$
$198$	−2.26028	−	3.09860i	−0.160631	−	0.220208i
$199$	−8.82304	+	5.89537i	−0.625449	+	0.417912i	−0.827502	−	0.561463i	$-0.810239\pi$
$199$	−8.82304	+	5.89537i	−0.625449	+	0.417912i	0.202053	+	0.979375i	$0.435239\pi$
$200$	−13.0719	+	2.94630i	−0.924324	+	0.208335i
$201$	−0.0500354	+	0.0748832i	−0.00352922	+	0.00528185i
$202$	−12.2633	+	13.3170i	−0.862840	+	0.936981i
$203$	3.85468	−	7.21160i	0.270546	−	0.506155i
$204$	4.00528	+	10.1199i	0.280425	+	0.708533i
$205$	0.389792	+	3.95762i	0.0272242	+	0.276412i
$206$	5.20303	+	0.296916i	0.362512	+	0.0206871i
$207$	−0.155522	+	0.375463i	−0.0108095	+	0.0260964i
$208$	−0.469178	+	0.360803i	−0.0325317	+	0.0250172i
$209$	1.16784	+	2.81941i	0.0807809	+	0.195022i
$210$	−0.713567	−	2.04519i	−0.0492408	−	0.141131i
$211$	−15.2896	+	18.6304i	−1.05258	+	1.28257i	−0.0946664	+	0.995509i	$0.530178\pi$
$211$	−15.2896	+	18.6304i	−1.05258	+	1.28257i	−0.957912	+	0.287062i	$0.907322\pi$
$212$	3.61920	−	16.8002i	0.248568	−	1.15385i
$213$	−2.85030	−	9.39618i	−0.195299	−	0.643816i
$214$	−14.9155	+	6.91055i	−1.01960	+	0.472395i
$215$	−1.75200	+	0.348494i	−0.119485	+	0.0237671i
$216$	1.26969	−	2.52743i	0.0863913	−	0.171970i
$217$	−2.47473	+	12.4413i	−0.167995	+	0.844570i
$218$	−15.9711	−	9.74540i	−1.08170	−	0.660042i
$219$	10.2903	+	12.5388i	0.695356	+	0.847294i
$220$	−0.848609	+	2.64593i	−0.0572132	+	0.178389i
$221$	0.710132	−	0.379574i	0.0477687	−	0.0255329i
$222$	10.5527	−	6.21200i	0.708248	−	0.416922i
$223$	2.27947	−	2.27947i	0.152644	−	0.152644i	−0.626654	−	0.779298i	$-0.715576\pi$
$223$	2.27947	−	2.27947i	0.152644	−	0.152644i	0.779298	+	0.626654i	$0.215576\pi$
$224$	16.2307	+	4.75556i	1.08446	+	0.317744i
$225$	−3.34996	−	3.34996i	−0.223331	−	0.223331i
$226$	13.1323	+	3.40017i	0.873545	+	0.226176i
$227$	2.19377	+	4.10425i	0.145606	+	0.272409i	0.944143	−	0.329536i	$-0.106892\pi$
$227$	2.19377	+	4.10425i	0.145606	+	0.272409i	−0.798537	+	0.601945i	$0.794392\pi$
$228$	−1.45506	+	1.71683i	−0.0963640	+	0.113700i
$229$	7.22832	−	5.93213i	0.477661	−	0.392006i	−0.364525	−	0.931194i	$-0.618769\pi$
$229$	7.22832	−	5.93213i	0.477661	−	0.392006i	0.842186	+	0.539187i	$0.181269\pi$
$230$	0.286164	−	0.0692774i	0.0188691	−	0.00456802i
$231$	7.95270	+	1.58189i	0.523249	+	0.104081i
$232$	−6.10219	−	4.75441i	−0.400629	−	0.312142i
$233$	−2.22656	−	11.1937i	−0.145867	−	0.733321i	−0.982604	−	0.185716i	$-0.940540\pi$
$233$	−2.22656	−	11.1937i	−0.145867	−	0.733321i	0.836737	−	0.547605i	$-0.184460\pi$
$234$	−0.196460	−	0.0720540i	−0.0128430	−	0.00471032i
$235$	−5.05740	+	1.53415i	−0.329909	+	0.100077i
$236$	12.6656	−	2.31152i	0.824463	−	0.150467i
$237$	−2.85311	−	2.34149i	−0.185329	−	0.152096i
$238$	−20.7218	−	10.0022i	−1.34319	−	0.648345i
$239$	−27.4028	+	11.3506i	−1.77254	+	0.734211i	−0.778196	+	0.628021i	$0.783865\pi$
$239$	−27.4028	+	11.3506i	−1.77254	+	0.734211i	−0.994346	+	0.106190i	$0.966135\pi$
$240$	−2.02144	+	0.335938i	−0.130483	+	0.0216847i
$241$	27.3100	+	11.3122i	1.75919	+	0.728680i	0.996654	+	0.0817347i	$0.0260460\pi$
$241$	27.3100	+	11.3122i	1.75919	+	0.728680i	0.762536	+	0.646946i	$0.223954\pi$
$242$	3.43133	+	3.84666i	0.220574	+	0.247273i
$243$	0.995185	−	0.0980171i	0.0638411	−	0.00628780i
$244$	19.5518	+	0.309596i	1.25167	+	0.0198198i
$245$	0.876081	+	0.468275i	0.0559707	+	0.0299170i
$246$	−0.451851	−	10.9689i	−0.0288090	−	0.699348i
$247$	0.138439	+	0.0925021i	0.00880867	+	0.00588577i
$248$	11.1996	+	4.30994i	0.711173	+	0.273681i
$249$	−2.52703	−	3.78197i	−0.160144	−	0.239673i
$250$	−1.09036	+	6.96997i	−0.0689603	+	0.440820i
$251$	1.99883	−	20.2945i	0.126165	−	1.28098i	−0.698604	−	0.715508i	$-0.746195\pi$
$251$	1.99883	−	20.2945i	0.126165	−	1.28098i	0.824770	−	0.565469i	$-0.191305\pi$
$252$	1.64499	+	5.74895i	0.103625	+	0.362150i
$253$	−0.319940	+	1.05470i	−0.0201145	+	0.0663086i
$254$	2.90858	−	0.407941i	0.182500	−	0.0255965i
$255$	2.78780			0.174579
$256$	7.04623	−	14.3649i	0.440389	−	0.897807i
$257$	19.6514			1.22582			0.612912	−	0.790152i	$-0.289998\pi$
$257$	19.6514			1.22582			0.612912	+	0.790152i	$0.289998\pi$
$258$	4.88347	−	0.684929i	0.304032	−	0.0426418i
$259$	−7.51494	+	24.7734i	−0.466955	+	1.53935i
$260$	0.0417058	+	0.145754i	0.00258649	+	0.00903931i
$261$	0.268076	−	2.72182i	0.0165935	−	0.168476i
$262$	−1.32467	+	8.46781i	−0.0818387	+	0.523143i
$263$	2.51887	+	3.76975i	0.155320	+	0.232453i	0.900966	−	0.433889i	$-0.142859\pi$
$263$	2.51887	+	3.76975i	0.155320	+	0.232453i	−0.745646	+	0.666342i	$0.767859\pi$
$264$	2.75499	−	7.15896i	0.169558	−	0.440604i
$265$	−3.66015	−	2.44563i	−0.224841	−	0.150234i
$266$	−0.195828	−	4.75381i	−0.0120070	−	0.291475i
$267$	4.30262	+	2.29980i	0.263316	+	0.140745i
$268$	−0.180100	−	0.00285182i	−0.0110014	−	0.000174203i
$269$	7.60881	−	0.749403i	0.463917	−	0.0456919i	0.136641	−	0.990621i	$-0.456369\pi$
$269$	7.60881	−	0.749403i	0.463917	−	0.0456919i	0.327276	+	0.944929i	$0.393869\pi$
$270$	−0.482271	−	0.540645i	−0.0293501	−	0.0329026i
$271$	−16.4337	−	6.80706i	−0.998276	−	0.413500i	−0.177111	−	0.984191i	$-0.556675\pi$
$271$	−16.4337	−	6.80706i	−0.998276	−	0.413500i	−0.821165	+	0.570691i	$0.806675\pi$
$272$	−12.6603	+	17.7069i	−0.767641	+	1.07364i
$273$	0.408720	−	0.169298i	0.0247369	−	0.0102464i
$274$	1.74509	+	0.842334i	0.105424	+	0.0508872i
$275$	−9.93193	−	8.15093i	−0.598918	−	0.491519i
$276$	−0.799588	+	0.145927i	−0.0481296	+	0.00878378i
$277$	−8.22516	+	2.49508i	−0.494202	+	0.149915i	−0.527541	−	0.849530i	$-0.676886\pi$
$277$	−8.22516	+	2.49508i	−0.494202	+	0.149915i	0.0333390	+	0.999444i	$0.489386\pi$
$278$	−4.62098	−	1.69480i	−0.277148	−	0.101647i
$279$	0.827715	+	4.16120i	0.0495540	+	0.249125i
$280$	2.66259	−	3.41738i	0.159120	−	0.204228i
$281$	−0.485545	−	0.0965810i	−0.0289652	−	0.00576154i	0.180586	−	0.983559i	$-0.442200\pi$
$281$	−0.485545	−	0.0965810i	−0.0289652	−	0.00576154i	−0.209552	+	0.977798i	$0.567200\pi$
$282$	14.1799	−	3.43282i	0.844402	−	0.204421i
$283$	−21.2114	+	17.4078i	−1.26089	+	1.03479i	−0.263348	+	0.964701i	$0.584827\pi$
$283$	−21.2114	+	17.4078i	−1.26089	+	1.03479i	−0.997541	+	0.0700842i	$0.977673\pi$
$284$	12.6970	−	14.9812i	0.753427	−	0.888971i
$285$	0.271738	+	0.508387i	0.0160964	+	0.0301142i
$286$	−0.549393	−	0.142247i	−0.0324863	−	0.00841126i
$287$	16.4114	+	16.4114i	0.968735	+	0.968735i
$288$	5.62409	−	0.607947i	0.331403	−	0.0358236i
$289$	8.91912	−	8.91912i	0.524654	−	0.524654i
$290$	−1.70757	+	1.00519i	−0.100272	+	0.0590268i
$291$	10.7009	−	5.71977i	0.627300	−	0.335299i
$292$	−9.90761	+	30.8916i	−0.579799	+	1.80779i
$293$	−19.0785	−	23.2472i	−1.11458	−	1.35812i	−0.926646	−	0.375934i	$-0.877322\pi$
$293$	−19.0785	−	23.2472i	−1.11458	−	1.35812i	−0.187931	−	0.982182i	$-0.560178\pi$
$294$	−2.34091	−	1.42840i	−0.136524	−	0.0833057i
$295$	0.643374	−	3.23446i	0.0374587	−	0.188318i
$296$	21.8843	+	10.9939i	1.27200	+	0.639007i
$297$	2.65992	−	0.529090i	0.154344	−	0.0307009i
$298$	−23.1391	+	10.7207i	−1.34041	+	0.621031i
$299$	0.0174558	+	0.0575440i	0.00100949	+	0.00332786i
$300$	1.99541	−	9.26262i	0.115205	−	0.534778i
$301$	−6.61377	+	8.05890i	−0.381211	+	0.464507i
$302$	7.30273	+	20.9307i	0.420225	+	1.20443i
$303$	−4.89872	−	11.8266i	−0.281424	−	0.679418i
$304$	−4.46311	−	0.582775i	−0.255977	−	0.0334244i
$305$	1.91675	−	4.62746i	0.109753	−	0.264967i
$306$	−7.68341	−	0.438461i	−0.439231	−	0.0250651i
$307$	2.22751	+	22.6163i	0.127131	+	1.29078i	0.821103	+	0.570780i	$0.193359\pi$
$307$	2.22751	+	22.6163i	0.127131	+	1.29078i	−0.693972	+	0.720002i	$0.744141\pi$
$308$	5.96799	+	15.0789i	0.340058	+	0.859202i
$309$	−1.73714	+	3.24995i	−0.0988223	+	0.184883i
$310$	2.08221	−	2.26112i	0.118261	−	0.128423i
$311$	−14.7868	+	22.1300i	−0.838482	+	1.25488i	0.126344	+	0.991987i	$0.459676\pi$
$311$	−14.7868	+	22.1300i	−0.838482	+	1.25488i	−0.964826	+	0.262890i	$0.915324\pi$
$312$	−0.0920209	−	0.408271i	−0.00520966	−	0.0231138i
$313$	19.9198	−	13.3100i	1.12594	−	0.752326i	0.154116	−	0.988053i	$-0.450747\pi$
$313$	19.9198	−	13.3100i	1.12594	−	0.752326i	0.971819	+	0.235727i	$0.0757471\pi$
$314$	2.40056	+	3.29091i	0.135471	+	0.185717i
$315$	1.52429	+	0.150129i	0.0858838	+	0.00845881i
$316$	0.839764	−	7.33389i	0.0472404	−	0.412563i
$317$	2.65592	+	0.805665i	0.149171	+	0.0452506i	0.363987	−	0.931404i	$-0.381415\pi$
$317$	2.65592	+	0.805665i	0.149171	+	0.0452506i	−0.214816	+	0.976655i	$0.568915\pi$
$318$	9.70304	+	7.31604i	0.544120	+	0.410263i
$319$		−	7.41735i		−	0.415292i
$320$	−2.75708	−	3.03228i	−0.154126	−	0.169510i
$321$		−	11.6239i		−	0.648780i
$322$	1.03452	−	1.37205i	0.0576514	−	0.0764613i
$323$	5.85974	+	1.77753i	0.326045	+	0.0989046i
$324$	1.24415	+	1.56592i	0.0691194	+	0.0869953i
$325$	−0.697626	−	0.0687102i	−0.0386973	−	0.00381135i
$326$	−3.46424	+	2.52700i	−0.191867	+	0.139957i
$327$	11.0001	−	7.35002i	0.608306	−	0.406457i
$328$	17.9411	−	12.6569i	0.990632	−	0.698859i
$329$	−17.1361	+	25.6460i	−0.944744	+	1.41391i
$330$	−1.44535	−	1.33098i	−0.0795640	−	0.0732682i
$331$	15.0899	−	28.2312i	0.829415	−	1.55173i	−0.00460341	−	0.999989i	$-0.501465\pi$
$331$	15.0899	−	28.2312i	0.829415	−	1.55173i	0.834018	−	0.551737i	$-0.186035\pi$
$332$	3.61393	−	8.34844i	0.198340	−	0.458180i
$333$	0.848704	+	8.61704i	0.0465087	+	0.472211i
$334$	−0.633776	+	11.1060i	−0.0346787	+	0.607695i
$335$	−0.0176561	+	0.0426255i	−0.000964654	+	0.00232888i
$336$	−7.87581	+	8.99984i	−0.429661	+	0.490981i
$337$	7.80189	+	18.8354i	0.424996	+	1.02603i	0.980852	+	0.194753i	$0.0623906\pi$
$337$	7.80189	+	18.8354i	0.424996	+	1.02603i	−0.555856	+	0.831279i	$0.687609\pi$
$338$	17.3293	−	6.04621i	0.942591	−	0.328871i
$339$	−6.08518	+	7.41481i	−0.330501	+	0.402717i
$340$	3.02385	+	4.68440i	0.163991	+	0.254047i
$341$	3.34013	+	11.0109i	0.180878	+	0.596275i
$342$	−0.668976	−	1.44390i	−0.0361741	−	0.0780770i
$343$	−14.8405	+	2.95196i	−0.801313	+	0.159391i
$344$	6.44787	+	7.46289i	0.347646	+	0.402372i
$345$	−0.0406165	+	0.204193i	−0.00218672	+	0.0109934i
$346$	−7.88653	+	12.9247i	−0.423982	+	0.694838i
$347$	−2.14065	−	2.60839i	−0.114916	−	0.140026i	0.712375	−	0.701799i	$-0.247619\pi$
$347$	−2.14065	−	2.60839i	−0.114916	−	0.140026i	−0.827291	+	0.561773i	$0.810119\pi$
$348$	4.86431	−	2.50183i	0.260754	−	0.134112i
$349$	32.5854	−	17.4172i	1.74425	−	0.932323i	0.802069	−	0.597231i	$-0.203733\pi$
$349$	32.5854	−	17.4172i	1.74425	−	0.932323i	0.942185	−	0.335092i	$-0.108767\pi$
$350$	10.1620	+	17.2627i	0.543180	+	0.922730i
$351$	0.104628	−	0.104628i	0.00558465	−	0.00558465i
$352$	15.0176	−	3.13585i	0.800442	−	0.167142i
$353$	−15.2255	−	15.2255i	−0.810369	−	0.810369i	0.174320	−	0.984689i	$-0.444227\pi$
$353$	−15.2255	−	15.2255i	−0.810369	−	0.810369i	−0.984689	+	0.174320i	$0.944227\pi$
$354$	−2.28191	+	8.81326i	−0.121282	+	0.468420i
$355$	−2.37120	−	4.43621i	−0.125850	−	0.235450i
$356$	0.802529	+	9.72432i	0.0425340	+	0.515388i
$357$	12.5770	−	10.3217i	0.665646	−	0.546281i
$358$	−6.62331	−	27.3589i	−0.350053	−	1.44596i
$359$	19.6434	+	3.90731i	1.03674	+	0.206220i	0.683984	−	0.729497i	$-0.260246\pi$
$359$	19.6434	+	3.90731i	1.03674	+	0.206220i	0.352753	+	0.935717i	$0.385246\pi$
$360$	0.385352	−	1.39679i	0.0203098	−	0.0736175i
$361$	−3.45970	−	17.3931i	−0.182089	−	0.915425i
$362$	4.17861	−	11.3933i	0.219623	−	0.598817i
$363$	−3.48797	+	1.05806i	−0.183071	+	0.0555339i
$364$	0.727802	+	0.503150i	0.0381472	+	0.0263722i
$365$	6.42351	+	5.27164i	0.336222	+	0.275930i
$366$	−6.01054	+	12.4522i	−0.314176	+	0.650887i
$367$	−14.9745	+	6.20265i	−0.781663	+	0.323776i	−0.737587	−	0.675253i	$-0.764035\pi$
$367$	−14.9745	+	6.20265i	−0.781663	+	0.323776i	−0.0440769	+	0.999028i	$0.514035\pi$
$368$	−1.11250	−	1.18528i	−0.0579929	−	0.0617872i
$369$	7.17183	+	2.97067i	0.373350	+	0.154647i
$370$	4.68130	−	4.17586i	0.243369	−	0.217093i
$371$	−25.5674	+	2.51817i	−1.32739	+	0.130737i
$372$	−6.09437	+	5.90437i	−0.315978	+	0.306127i
$373$	9.22636	+	4.93159i	0.477723	+	0.255348i	0.692639	−	0.721284i	$-0.256448\pi$
$373$	9.22636	+	4.93159i	0.477723	+	0.255348i	−0.214916	+	0.976632i	$0.568948\pi$
$374$	−20.8538	+	0.859053i	−1.07833	+	0.0444206i
$375$	−4.14775	−	2.77144i	−0.214189	−	0.143116i
$376$	21.1488	+	20.1034i	1.09067	+	1.03675i
$377$	−0.224832	−	0.336485i	−0.0115794	−	0.0173299i
$378$	−4.17745	−	0.653506i	−0.214865	−	0.0336127i
$379$	1.56505	−	15.8902i	0.0803913	−	0.816227i	−0.867458	−	0.497510i	$-0.834248\pi$
$379$	1.56505	−	15.8902i	0.0803913	−	0.816227i	0.947850	−	0.318717i	$-0.103252\pi$
$380$	−0.559507	+	1.00804i	−0.0287021	+	0.0517114i
$381$	−0.602864	+	1.98738i	−0.0308857	+	0.101816i
$382$	−1.23404	−	8.79857i	−0.0631389	−	0.450174i
$383$	7.45038			0.380697			0.190348	−	0.981717i	$-0.439038\pi$
$383$	7.45038			0.380697			0.190348	+	0.981717i	$0.439038\pi$
$384$	7.12184	+	8.79087i	0.363435	+	0.448607i
$385$	4.15390			0.211703
$386$	3.54848	+	25.3003i	0.180613	+	1.28775i
$387$	−1.01220	+	3.33679i	−0.0514532	+	0.169618i
$388$	21.2181	+	11.7770i	1.07718	+	0.597884i
$389$	1.69928	−	17.2531i	0.0861571	−	0.874768i	−0.850839	−	0.525427i	$-0.823906\pi$
$389$	1.69928	−	17.2531i	0.0861571	−	0.874768i	0.936996	−	0.349341i	$-0.113594\pi$
$390$	−0.105912	−	0.0165685i	−0.00536306	−	0.000838979i
$391$	1.22867	+	1.83884i	0.0621365	+	0.0929939i
$392$	−0.138950	−	5.48282i	−0.00701804	−	0.276924i
$393$	−5.03909	−	3.36702i	−0.254189	−	0.169843i
$394$	19.6211	−	0.808270i	0.988494	−	0.0407200i
$395$	−1.66755	−	0.891324i	−0.0839035	−	0.0448474i
$396$	3.77418	+	3.89563i	0.189660	+	0.195763i
$397$	−7.21767	+	0.710878i	−0.362244	+	0.0356780i	−0.277502	−	0.960725i	$-0.589507\pi$
$397$	−7.21767	+	0.710878i	−0.362244	+	0.0356780i	−0.0847420	+	0.996403i	$0.527007\pi$
$398$	11.1987	−	9.98958i	0.561341	−	0.500733i
$399$	3.10821	+	1.28746i	0.155605	+	0.0644538i
$400$	17.7286	−	6.69399i	0.886428	−	0.334699i
$401$	−21.2668	+	8.80899i	−1.06201	+	0.439900i	−0.844165	−	0.536083i	$-0.819903\pi$
$401$	−21.2668	+	8.80899i	−1.06201	+	0.439900i	−0.217847	+	0.975983i	$0.569903\pi$
$402$	0.0553657	−	0.114703i	0.00276139	−	0.00572085i
$403$	0.485283	+	0.398261i	0.0241736	+	0.0198388i
$404$	14.5589	−	21.0594i	0.724334	−	1.04774i
$405$	0.490231	−	0.148710i	0.0243598	−	0.00738946i
$406$	−3.98195	+	10.8571i	−0.197621	+	0.538826i
$407$	4.58125	+	23.0315i	0.227084	+	1.14163i
$408$	−7.59723	−	13.3862i	−0.376119	−	0.662716i
$409$	−26.8970	−	5.35014i	−1.32997	−	0.264548i	−0.521584	−	0.853200i	$-0.674659\pi$
$409$	−26.8970	−	5.35014i	−1.32997	−	0.264548i	−0.808386	+	0.588652i	$0.799659\pi$
$410$	−1.32329	−	5.46610i	−0.0653526	−	0.269952i
$411$	−1.05917	+	0.869240i	−0.0522451	+	0.0428765i
$412$	−7.34520	+	0.606185i	−0.361872	+	0.0298646i
$413$	−9.07288	−	16.9742i	−0.446447	−	0.835244i
$414$	0.144058	−	0.556386i	0.00708006	−	0.0273449i
$415$	−1.64768	−	1.64768i	−0.0808815	−	0.0808815i
$416$	0.586215	−	0.597466i	0.0287416	−	0.0292932i
$417$	2.46099	−	2.46099i	0.120515	−	0.120515i
$418$	−2.18937	−	3.71920i	−0.107086	−	0.181912i
$419$	20.7454	−	11.0887i	1.01348	−	0.541716i	0.120928	−	0.992661i	$-0.461413\pi$
$419$	20.7454	−	11.0887i	1.01348	−	0.541716i	0.892552	+	0.450945i	$0.148913\pi$
$420$	1.40109	+	2.72413i	0.0683660	+	0.132924i
$421$	−19.0562	−	23.2201i	−0.928744	−	1.13168i	−0.991033	−	0.133619i	$-0.957340\pi$
$421$	−19.0562	−	23.2201i	−0.928744	−	1.13168i	0.0622891	−	0.998058i	$-0.480160\pi$
$422$	17.7536	−	29.0953i	0.864233	−	1.41634i
$423$	−2.01262	+	10.1181i	−0.0978570	+	0.491961i
$424$	−1.76869	+	24.2398i	−0.0858951	+	1.17719i
$425$	−25.2856	+	5.02962i	−1.22653	+	0.243973i
$426$	5.83753	+	12.5995i	0.282829	+	0.610449i
$427$	−8.48558	−	27.9732i	−0.410646	−	1.35372i
$428$	19.5318	−	12.6081i	0.944107	−	0.609434i
$429$	0.254576	−	0.310201i	0.0122910	−	0.0149767i
$430$	2.38523	−	0.832208i	0.115026	−	0.0401326i
$431$	−6.47070	−	15.6217i	−0.311683	−	0.752469i	−0.999643	−	0.0267203i	$-0.991494\pi$
$431$	−6.47070	−	15.6217i	−0.311683	−	0.752469i	0.687960	−	0.725748i	$-0.258506\pi$
$432$	−1.28175	+	3.78908i	−0.0616682	+	0.182302i
$433$	−0.102501	+	0.247460i	−0.00492590	+	0.0118922i	−0.926323	−	0.376729i	$-0.877049\pi$
$433$	−0.102501	+	0.247460i	−0.00492590	+	0.0118922i	0.921397	+	0.388622i	$0.127049\pi$
$434$	1.02206	−	17.9102i	0.0490605	−	0.859718i
$435$	−0.137332	−	1.39436i	−0.00658459	−	0.0668544i
$436$	24.2819	+	10.5113i	1.16289	+	0.503402i
$437$	−0.215569	+	0.403301i	−0.0103121	+	0.0192925i
$438$	−16.8746	−	15.5394i	−0.806301	−	0.742500i
$439$	−13.6537	+	20.4341i	−0.651653	+	0.975268i	0.347638	+	0.937629i	$0.386984\pi$
$439$	−13.6537	+	20.4341i	−0.651653	+	0.975268i	−0.999291	+	0.0376393i	$0.988016\pi$
$440$	0.668749	−	3.87234i	0.0318813	−	0.184606i
$441$	1.61230	−	1.07730i	0.0767760	−	0.0513001i
$442$	−0.919986	+	0.671084i	−0.0437593	+	0.0319202i
$443$	−14.2573	−	1.40423i	−0.677387	−	0.0667168i	−0.246527	−	0.969136i	$-0.579290\pi$
$443$	−14.2573	−	1.40423i	−0.677387	−	0.0667168i	−0.430860	+	0.902419i	$0.641790\pi$
$444$	−13.5588	+	10.7728i	−0.643474	+	0.511253i
$445$	2.39169	+	0.725510i	0.113377	+	0.0343925i
$446$	−2.74466	+	3.64015i	−0.129963	+	0.172366i
$447$		−	18.0326i		−	0.852914i
$448$	−23.6653	−	3.47203i	−1.11808	−	0.164038i
$449$		−	14.8920i		−	0.702796i	−0.936226	−	0.351398i	$-0.885706\pi$
$449$		−	14.8920i		−	0.702796i	0.936226	−	0.351398i	$-0.114294\pi$
$450$	5.34966	+	4.03362i	0.252185	+	0.190146i
$451$	20.1462	+	6.11128i	0.948647	+	0.287769i
$452$	−19.0597	−	2.18242i	−0.896493	−	0.102653i
$453$	−15.5997	−	1.53644i	−0.732939	−	0.0721882i
$454$	−3.87857	−	5.31712i	−0.182031	−	0.249545i
$455$	0.188440	−	0.125912i	0.00883421	−	0.00590283i
$456$	1.70059	−	2.69025i	0.0796376	−	0.125983i
$457$	17.5403	−	26.2509i	0.820499	−	1.22796i	−0.150436	−	0.988620i	$-0.548068\pi$
$457$	17.5403	−	26.2509i	0.820499	−	1.22796i	0.970935	−	0.239343i	$-0.0769322\pi$
$458$	−8.95808	+	9.72782i	−0.418583	+	0.454551i
$459$	2.56526	−	4.79927i	0.119736	−	0.224011i
$460$	−0.387166	+	0.153234i	−0.0180517	+	0.00714456i
$461$	3.05147	+	30.9821i	0.142121	+	1.44298i	0.756512	+	0.653980i	$0.226902\pi$
$461$	3.05147	+	30.9821i	0.142121	+	1.44298i	−0.614391	+	0.789002i	$0.710598\pi$
$462$	−11.4485	−	0.653320i	−0.532634	−	0.0303952i
$463$	−3.53033	+	8.52297i	−0.164068	+	0.396096i	−0.984437	−	0.175739i	$-0.943768\pi$
$463$	−3.53033	+	8.52297i	−0.164068	+	0.396096i	0.820368	+	0.571835i	$0.193768\pi$
$464$	9.48005	+	5.45994i	0.440100	+	0.253472i
$465$	0.831765	+	2.00806i	0.0385722	+	0.0931215i
$466$	5.31704	+	15.2394i	0.246307	+	0.705953i
$467$	−2.78337	+	3.39155i	−0.128799	+	0.156942i	−0.833417	−	0.552645i	$-0.813619\pi$
$467$	−2.78337	+	3.39155i	−0.128799	+	0.156942i	0.704618	+	0.709587i	$0.251119\pi$
$468$	0.289297	+	0.0623219i	0.0133728	+	0.00288083i
$469$	0.0781644	+	0.257673i	0.00360930	+	0.0118983i
$470$	6.78157	−	3.14199i	0.312811	−	0.144929i
$471$	−2.82500	+	0.561928i	−0.130169	+	0.0258923i
$472$	−17.2843	+	5.72517i	−0.795572	+	0.263522i
$473$	−1.84490	+	9.27495i	−0.0848287	+	0.426463i
$474$	4.45573	+	2.71884i	0.204658	+	0.124880i
$475$	−3.38191	−	4.12086i	−0.155172	−	0.189078i
$476$	30.9857	+	9.93779i	1.42023	+	0.455498i
$477$	−7.57820	+	4.05063i	−0.346982	+	0.185466i
$478$	36.1483	−	21.2793i	1.65338	−	0.973292i
$479$	−27.2972	+	27.2972i	−1.24724	+	1.24724i	−0.290309	+	0.956933i	$0.593758\pi$
$479$	−27.2972	+	27.2972i	−1.24724	+	1.24724i	−0.956933	+	0.290309i	$0.906242\pi$
$480$	2.76505	−	0.867549i	0.126207	−	0.0395980i
$481$	0.905949	+	0.905949i	0.0413077	+	0.0413077i
$482$	−40.4698	−	10.4783i	−1.84335	−	0.477275i
$483$	0.572776	+	1.07159i	0.0260622	+	0.0487589i
$484$	−5.56119	−	4.71326i	−0.252781	−	0.214239i
$485$	4.80500	−	3.94336i	0.218184	−	0.179059i
$486$	−1.37451	+	0.332755i	−0.0623490	+	0.0150941i
$487$	33.5974	+	6.68295i	1.52245	+	0.302833i	0.884240	−	0.467033i	$-0.154677\pi$
$487$	33.5974	+	6.68295i	1.52245	+	0.302833i	0.638205	+	0.769866i	$0.279677\pi$
$488$	−27.4432	+	3.40691i	−1.24230	+	0.154224i
$489$	−0.591524	−	2.97379i	−0.0267497	−	0.134480i
$490$	−1.31894	−	0.483736i	−0.0595835	−	0.0218529i
$491$	−37.5405	+	11.3878i	−1.69418	+	0.513923i	−0.982129	−	0.188207i	$-0.939732\pi$
$491$	−37.5405	+	11.3878i	−1.69418	+	0.513923i	−0.712048	+	0.702131i	$0.752232\pi$
$492$	2.78740	+	15.2732i	0.125666	+	0.688568i
$493$	−11.5050	−	9.44189i	−0.518158	−	0.425241i
$494$	−0.212055	−	0.102357i	−0.00954080	−	0.00460524i
$495$	1.28359	−	0.531679i	0.0576929	−	0.0238972i
$496$	−16.5316	−	3.83620i	−0.742293	−	0.172250i
$497$	−27.1224	−	11.2345i	−1.21661	−	0.503935i
$498$	4.28201	+	4.80030i	0.191881	+	0.215106i
$499$	−12.5653	+	1.23758i	−0.562502	+	0.0554016i	−0.375272	−	0.926915i	$-0.622451\pi$
$499$	−12.5653	+	1.23758i	−0.562502	+	0.0554016i	−0.187230	+	0.982316i	$0.559951\pi$
$500$	0.157961	−	9.97566i	0.00706424	−	0.446125i
$501$	−6.93713	−	3.70797i	−0.309928	−	0.165660i
$502$	1.18701	+	28.8152i	0.0529790	+	1.28608i
$503$	35.1846	+	23.5096i	1.56880	+	1.04824i	0.968673	+	0.248341i	$0.0798853\pi$
$503$	35.1846	+	23.5096i	1.56880	+	1.04824i	0.600132	+	0.799901i	$0.295115\pi$
$504$	−3.43307	−	7.72831i	−0.152921	−	0.344246i
$505$	−3.64333	−	5.45262i	−0.162126	−	0.242639i
$506$	0.240906	−	1.53996i	0.0107096	−	0.0684596i
$507$	−1.27208	+	12.9156i	−0.0564949	+	0.573602i
$508$	−3.99335	+	1.14265i	−0.177176	+	0.0506967i
$509$	−6.43329	+	21.2077i	−0.285150	+	0.940015i	0.690988	+	0.722866i	$0.257176\pi$
$509$	−6.43329	+	21.2077i	−0.285150	+	0.940015i	−0.976139	+	0.217149i	$0.930324\pi$
$510$	−3.90433	+	0.547599i	−0.172886	+	0.0242481i
$511$	48.4973			2.14539
$512$	−7.04663	+	21.5022i	−0.311420	+	0.950272i
$513$	1.12525			0.0496809
$514$	−27.5220	+	3.86008i	−1.21394	+	0.170261i
$515$	−0.548009	+	1.80654i	−0.0241482	+	0.0796058i
$516$	−6.70479	+	1.91849i	−0.295162	+	0.0844569i
$517$	−2.74235	+	27.8435i	−0.120608	+	1.22456i
$518$	5.65854	−	36.1715i	0.248622	−	1.58928i
$519$	−5.94805	−	8.90189i	−0.261090	−	0.390750i
$520$	−0.0870394	−	0.195938i	−0.00381693	−	0.00859244i
$521$	7.42745	+	4.96287i	0.325403	+	0.217427i	0.707531	−	0.706682i	$-0.249809\pi$
$521$	7.42745	+	4.96287i	0.325403	+	0.217427i	−0.382129	+	0.924109i	$0.624809\pi$
$522$	0.159197	+	3.86458i	0.00696788	+	0.169148i
$523$	−31.5529	−	16.8654i	−1.37971	−	0.737471i	−0.396173	−	0.918176i	$-0.629662\pi$
$523$	−31.5529	−	16.8654i	−1.37971	−	0.737471i	−0.983537	+	0.180705i	$0.942162\pi$
$524$	0.191907	−	12.1194i	0.00838348	−	0.529439i
$525$	−14.0963	+	1.38836i	−0.615213	+	0.0605932i
$526$	−4.26817	−	4.78478i	−0.186101	−	0.208626i
$527$	21.3307	+	8.83547i	0.929181	+	0.384879i
$528$	−2.45217	+	10.5673i	−0.106717	+	0.459884i
$529$	21.0966	−	8.73852i	0.917245	−	0.379935i
$530$	5.60645	+	2.70617i	0.243528	+	0.117549i
$531$	−4.97619	−	4.08386i	−0.215948	−	0.177224i
$532$	1.20804	+	6.61927i	0.0523750	+	0.286982i
$533$	1.09917	−	0.333429i	0.0476102	−	0.0144424i
$534$	−6.47759	−	2.37573i	−0.280313	−	0.102808i
$535$	−1.16172	−	5.84037i	−0.0502256	−	0.252501i
$536$	0.252791	−	0.0313825i	0.0109189	−	0.00135552i
$537$	19.5220	+	3.88317i	0.842437	+	0.167571i
$538$	−10.5090	+	2.54412i	−0.453074	+	0.109685i
$539$	4.06516	−	3.33619i	0.175099	−	0.143700i
$540$	0.781621	+	0.662445i	0.0336356	+	0.0285071i
$541$	−11.7277	−	21.9411i	−0.504215	−	0.943320i	−0.997307	−	0.0733427i	$-0.976633\pi$
$541$	−11.7277	−	21.9411i	−0.504215	−	0.943320i	0.493092	−	0.869977i	$-0.335867\pi$
$542$	24.3526	+	6.30530i	1.04603	+	0.270836i
$543$	6.06769	+	6.06769i	0.260389	+	0.260389i
$544$	14.2526	−	27.2854i	0.611077	−	1.16985i
$545$	4.79237	−	4.79237i	0.205283	−	0.205283i
$546$	−0.539161	+	0.317386i	−0.0230739	+	0.0135829i
$547$	28.8526	−	15.4220i	1.23365	−	0.659398i	0.279906	−	0.960027i	$-0.409697\pi$
$547$	28.8526	−	15.4220i	1.23365	−	0.659398i	0.953741	+	0.300629i	$0.0971967\pi$
$548$	−2.60946	−	0.836911i	−0.111471	−	0.0357511i
$549$	−6.20254	−	7.55782i	−0.264718	−	0.322560i
$550$	15.5108	+	9.46452i	0.661382	+	0.403568i
$551$	0.600398	−	3.01840i	0.0255778	−	0.128588i
$552$	1.09116	−	0.361433i	0.0464430	−	0.0153836i
$553$	−10.8231	+	2.15286i	−0.460247	+	0.0915488i
$554$	11.0293	−	5.11001i	0.468589	−	0.217104i
$555$	1.28764	+	4.24478i	0.0546573	+	0.180181i
$556$	6.80461	+	1.46589i	0.288580	+	0.0621675i
$557$	2.89015	−	3.52166i	0.122459	−	0.149217i	−0.708172	−	0.706040i	$-0.750480\pi$
$557$	2.89015	−	3.52166i	0.122459	−	0.149217i	0.830631	+	0.556823i	$0.187980\pi$
$558$	−1.97659	−	5.66520i	−0.0836758	−	0.239827i
$559$	0.197446	+	0.476676i	0.00835106	+	0.0201613i
$560$	−3.05771	+	5.30907i	−0.129212	+	0.224349i
$561$	5.64779	−	13.6350i	0.238450	−	0.575669i
$562$	0.698980	+	0.0398879i	0.0294847	+	0.00168257i
$563$	−3.33001	−	33.8102i	−0.140343	−	1.42493i	−0.765000	−	0.644030i	$-0.777261\pi$
$563$	−3.33001	−	33.8102i	−0.140343	−	1.42493i	0.624657	−	0.780899i	$-0.285239\pi$
$564$	−19.1848	+	7.59301i	−0.807825	+	0.319723i
$565$	−2.31642	+	4.33372i	−0.0974525	+	0.182321i
$566$	26.2874	−	28.5462i	1.10494	−	1.19989i
$567$	1.66106	−	2.48595i	0.0697580	−	0.104400i
$568$	−14.8395	+	23.4753i	−0.622650	+	0.985001i
$569$	18.1451	−	12.1242i	0.760683	−	0.508272i	−0.113696	−	0.993516i	$-0.536269\pi$
$569$	18.1451	−	12.1242i	0.760683	−	0.508272i	0.874379	+	0.485243i	$0.161269\pi$
$570$	−0.480432	−	0.658622i	−0.0201231	−	0.0275866i
$571$	11.5260	+	1.13522i	0.482350	+	0.0475073i	0.336270	−	0.941766i	$-0.390834\pi$
$571$	11.5260	+	1.13522i	0.482350	+	0.0475073i	0.146080	+	0.989273i	$0.453334\pi$
$572$	0.797369	+	0.0913025i	0.0333397	+	0.00381755i
$573$	6.01191	+	1.82369i	0.251151	+	0.0761858i
$574$	−26.2079	−	19.7606i	−1.09390	−	0.824793i
$575$		−	1.92533i		−	0.0802919i
$576$	−7.75715	+	1.95616i	−0.323215	+	0.0815066i
$577$		−	7.01568i		−	0.292067i	−0.989280	−	0.146033i	$-0.953349\pi$
$577$		−	7.01568i		−	0.292067i	0.989280	−	0.146033i	$-0.0466507\pi$
$578$	−10.7393	+	14.2432i	−0.446697	+	0.592440i
$579$	−17.2872	−	5.24402i	−0.718432	−	0.217934i
$580$	2.19401	−	1.74319i	0.0911015	−	0.0723819i
$581$	−13.5339	−	1.33297i	−0.561480	−	0.0553010i
$582$	−13.8632	+	10.1125i	−0.574648	+	0.419178i
$583$	−19.3765	+	12.9470i	−0.802495	+	0.536210i
$584$	7.80771	−	45.2100i	0.323086	−	1.87080i
$585$	0.0421133	−	0.0630270i	0.00174117	−	0.00260585i
$586$	31.2859	+	28.8103i	1.29241	+	1.19014i
$587$	−7.87283	+	14.7290i	−0.324947	+	0.607932i	−0.990356	−	0.138546i	$-0.955757\pi$
$587$	−7.87283	+	14.7290i	−0.324947	+	0.607932i	0.665409	+	0.746479i	$0.268257\pi$
$588$	3.55903	+	1.54066i	0.146772	+	0.0635357i
$589$	0.467946	+	4.75113i	0.0192814	+	0.195767i
$590$	−0.265713	+	4.65626i	−0.0109392	+	0.191695i
$591$	−5.31392	+	12.8289i	−0.218586	+	0.527712i
$592$	−32.8086	−	11.0983i	−1.34843	−	0.456138i
$593$	13.0568	+	31.5220i	0.536180	+	1.29445i	0.927371	+	0.374143i	$0.122063\pi$
$593$	13.0568	+	31.5220i	0.536180	+	1.29445i	−0.391192	+	0.920309i	$0.627937\pi$
$594$	−3.62130	+	1.26347i	−0.148584	+	0.0518409i
$595$	5.28770	−	6.44308i	0.216774	−	0.264140i
$596$	30.3006	−	19.5595i	1.24116	−	0.801188i
$597$	3.08032	+	10.1545i	0.126069	+	0.415594i
$598$	−0.0357502	−	0.0771620i	−0.00146193	−	0.00315539i
$599$	−6.28685	+	1.25053i	−0.256874	+	0.0510954i	−0.321847	−	0.946792i	$-0.604304\pi$
$599$	−6.28685	+	1.25053i	−0.256874	+	0.0510954i	0.0649733	+	0.997887i	$0.479304\pi$
$600$	−0.975146	+	13.3643i	−0.0398102	+	0.545596i
$601$	−3.50430	+	17.6173i	−0.142943	+	0.718625i	0.841126	+	0.540839i	$0.181893\pi$
$601$	−3.50430	+	17.6173i	−0.142943	+	0.718625i	−0.984069	+	0.177786i	$0.943107\pi$
$602$	7.67963	−	12.5857i	0.312999	−	0.512953i
$603$	0.0571343	+	0.0696183i	0.00232669	+	0.00283508i
$604$	−14.3389	−	27.8791i	−0.583441	−	1.13438i
$605$	−1.64677	+	0.880218i	−0.0669508	+	0.0357859i
$606$	9.18375	+	15.6009i	0.373064	+	0.633744i
$607$	23.6239	−	23.6239i	0.958864	−	0.958864i	−0.0403228	−	0.999187i	$-0.512839\pi$
$607$	23.6239	−	23.6239i	0.958864	−	0.958864i	0.999187	+	0.0403228i	$0.0128386\pi$
$608$	6.36508	−	0.0604959i	0.258138	−	0.00245343i
$609$	−5.78212	−	5.78212i	−0.234303	−	0.234303i
$610$	−1.77547	+	6.85728i	−0.0718866	+	0.277643i
$611$	0.719577	+	1.34623i	0.0291110	+	0.0544628i
$612$	10.8468	−	0.895164i	0.438455	−	0.0361849i
$613$	−19.5301	+	16.0280i	−0.788815	+	0.647364i	−0.940013	−	0.341140i	$-0.889187\pi$
$613$	−19.5301	+	16.0280i	−0.788815	+	0.647364i	0.151198	+	0.988504i	$0.451687\pi$
$614$	−7.56211	−	31.2368i	−0.305182	−	1.26061i
$615$	3.90036	+	0.775829i	0.157278	+	0.0312845i
$616$	−11.3201	−	19.9459i	−0.456100	−	0.803642i
$617$	6.11966	+	30.7656i	0.246368	+	1.23858i	0.883724	+	0.468008i	$0.155028\pi$
$617$	6.11966	+	30.7656i	0.246368	+	1.23858i	−0.637356	+	0.770569i	$0.719972\pi$
$618$	1.79449	−	4.89280i	0.0721850	−	0.196817i
$619$	24.3993	−	7.40144i	0.980690	−	0.297489i	0.241066	−	0.970509i	$-0.422503\pi$
$619$	24.3993	−	7.40144i	0.980690	−	0.297489i	0.739625	+	0.673020i	$0.235003\pi$
$620$	−2.47199	+	3.57572i	−0.0992777	+	0.143604i
$621$	0.314150	+	0.257816i	0.0126064	+	0.0103458i
$622$	16.3621	−	33.8977i	0.656059	−	1.35917i
$623$	13.4761	−	5.58200i	0.539910	−	0.223638i
$624$	0.209071	+	0.553711i	0.00836955	+	0.0221662i
$625$	19.5237	+	8.08696i	0.780946	+	0.323479i
$626$	−25.2834	+	22.5535i	−1.01053	+	0.901420i
$627$	3.03701	−	0.299119i	0.121286	−	0.0119457i
$628$	−4.00842	−	4.13741i	−0.159953	−	0.165100i
$629$	41.5556	+	22.2119i	1.65693	+	0.885647i
$630$	−2.16426	+	0.0891545i	−0.0862262	+	0.00355200i
$631$	0.781917	+	0.522460i	0.0311276	+	0.0207988i	0.571037	−	0.820925i	$-0.306541\pi$
$631$	0.781917	+	0.522460i	0.0311276	+	0.0207988i	−0.539909	+	0.841723i	$0.681541\pi$
$632$	0.264480	+	10.4361i	0.0105205	+	0.415126i
$633$	13.3899	+	20.0393i	0.532199	+	0.796493i
$634$	−3.87789	−	0.606643i	−0.154011	−	0.0240929i
$635$	−0.104283	+	1.05880i	−0.00413834	+	0.0420173i
$636$	−15.0262	−	8.34021i	−0.595829	−	0.330711i
$637$	0.0832888	−	0.274566i	0.00330002	−	0.0108787i
$638$	1.45697	+	10.3880i	0.0576820	+	0.411267i
$639$	−9.81898			−0.388433
$640$	4.45693	+	3.70516i	0.176176	+	0.146459i
$641$	16.5034			0.651846			0.325923	−	0.945396i	$-0.394325\pi$
$641$	16.5034			0.651846			0.325923	+	0.945396i	$0.394325\pi$
$642$	2.28324	+	16.2793i	0.0901123	+	0.642492i
$643$	−11.0405	+	36.3957i	−0.435396	+	1.43531i	0.415317	+	0.909677i	$0.363671\pi$
$643$	−11.0405	+	36.3957i	−0.435396	+	1.43531i	−0.850713	+	0.525631i	$0.823829\pi$
$644$	−1.17934	+	2.12477i	−0.0464725	+	0.0837277i
$645$	−0.175090	+	1.77772i	−0.00689417	+	0.0699977i
$646$	−8.55575	−	1.33843i	−0.336622	−	0.0526599i
$647$	−17.1620	−	25.6848i	−0.674708	−	1.00977i	−0.997984	−	0.0634675i	$-0.979784\pi$
$647$	−17.1620	−	25.6848i	−0.674708	−	1.00977i	0.323276	−	0.946305i	$-0.395216\pi$
$648$	−2.05003	−	1.94869i	−0.0805327	−	0.0765517i
$649$	−14.5162	−	9.69939i	−0.569809	−	0.380734i
$650$	0.990526	−	0.0408037i	0.0388516	−	0.00160045i
$651$	11.1872	+	5.97968i	0.438461	+	0.234362i
$652$	4.35532	−	4.21954i	0.170568	−	0.165250i
$653$	−7.91007	+	0.779074i	−0.309545	+	0.0304875i	−0.251597	−	0.967832i	$-0.580956\pi$
$653$	−7.91007	+	0.779074i	−0.309545	+	0.0304875i	−0.0579480	+	0.998320i	$0.518456\pi$
$654$	−13.9619	+	12.4545i	−0.545955	+	0.487008i
$655$	−2.86839	−	1.18812i	−0.112077	−	0.0464239i
$656$	−22.6405	+	21.2501i	−0.883962	+	0.829678i
$657$	14.9860	−	6.20741i	0.584660	−	0.242174i
$658$	18.9616	−	39.2834i	0.739202	−	1.53143i
$659$	−30.8615	−	25.3273i	−1.20219	−	0.986613i	−0.999974	−	0.00727271i	$-0.997685\pi$
$659$	−30.8615	−	25.3273i	−1.20219	−	0.986613i	−0.202218	−	0.979341i	$-0.564815\pi$
$660$	2.28566	+	1.58014i	0.0889693	+	0.0615070i
$661$	−46.3690	+	14.0659i	−1.80355	+	0.547100i	−0.998910	−	0.0466691i	$-0.985139\pi$
$661$	−46.3690	+	14.0659i	−1.80355	+	0.547100i	−0.804636	+	0.593769i	$0.797639\pi$
$662$	−15.5881	+	42.5020i	−0.605849	+	1.65189i
$663$	−0.157089	−	0.789739i	−0.00610082	−	0.0306709i
$664$	−3.42148	+	12.4019i	−0.132779	+	0.481287i
$665$	1.69038	+	0.336238i	0.0655502	+	0.0130387i
$666$	−2.88124	−	11.9015i	−0.111646	−	0.461174i
$667$	0.859195	−	0.705123i	0.0332682	−	0.0273025i
$668$	−1.29392	−	15.6786i	−0.0500633	−	0.606622i
$669$	−1.51962	−	2.84301i	−0.0587519	−	0.109917i
$670$	0.0163546	−	0.0631654i	0.000631834	−	0.00244029i
$671$	−18.7495	−	18.7495i	−0.723816	−	0.723816i
$672$	9.26231	−	14.1513i	0.357301	−	0.545900i
$673$	−17.1310	+	17.1310i	−0.660353	+	0.660353i	−0.955463	−	0.295110i	$-0.904644\pi$
$673$	−17.1310	+	17.1310i	−0.660353	+	0.660353i	0.295110	+	0.955463i	$0.404644\pi$
$674$	−14.6264	−	24.8466i	−0.563387	−	0.957057i
$675$	−4.17815	+	2.23327i	−0.160817	+	0.0859586i
$676$	−23.0822	+	11.8717i	−0.887777	+	0.456604i
$677$	−0.222557	−	0.271187i	−0.00855357	−	0.0104226i	0.768716	−	0.639590i	$-0.220896\pi$
$677$	−0.222557	−	0.271187i	−0.00855357	−	0.0104226i	−0.777270	+	0.629168i	$0.783396\pi$
$678$	7.06586	−	11.5798i	0.271363	−	0.444719i
$679$	7.07741	−	35.5805i	0.271606	−	1.36546i
$680$	−5.15506	−	5.96656i	−0.197687	−	0.228807i
$681$	4.56434	−	0.907905i	0.174906	−	0.0347910i
$682$	−6.84071	−	14.7648i	−0.261944	−	0.565372i
$683$	−3.25007	−	10.7140i	−0.124360	−	0.409961i	0.872549	−	0.488527i	$-0.162466\pi$
$683$	−3.25007	−	10.7140i	−0.124360	−	0.409961i	−0.996909	+	0.0785662i	$0.974966\pi$
$684$	1.22053	+	1.89078i	0.0466680	+	0.0722958i
$685$	−0.445303	+	0.542604i	−0.0170142	+	0.0207318i
$686$	20.2044	−	7.04932i	0.771407	−	0.269144i
$687$	−3.57842	−	8.63908i	−0.136525	−	0.329602i
$688$	−10.4962	−	9.18528i	−0.400163	−	0.350185i
$689$	−0.486564	+	1.17467i	−0.0185366	+	0.0447514i
$690$	0.0167746	−	0.293952i	0.000638599	−	0.0111906i
$691$	2.20589	+	22.3968i	0.0839160	+	0.852014i	0.941353	+	0.337424i	$0.109556\pi$
$691$	2.20589	+	22.3968i	0.0839160	+	0.852014i	−0.857437	+	0.514590i	$0.827944\pi$
$692$	8.50636	−	19.6503i	0.323363	−	0.746992i
$693$	3.82232	−	7.15106i	0.145198	−	0.271646i
$694$	3.51035	+	3.23258i	0.133251	+	0.122707i
$695$	0.990556	−	1.48247i	0.0375739	−	0.0562334i
$696$	−6.32106	+	4.45930i	−0.239599	+	0.169029i
$697$	35.1242	−	23.4692i	1.33042	−	0.888960i
$698$	−42.2148	+	30.7936i	−1.59785	+	1.16555i
$699$	−11.3580	−	1.11866i	−0.429599	−	0.0423118i
$700$	−17.6228	−	22.1804i	−0.666078	−	0.838341i
$701$	20.1709	+	6.11877i	0.761843	+	0.231103i	0.647217	−	0.762306i	$-0.275933\pi$
$701$	20.1709	+	6.11877i	0.761843	+	0.231103i	0.114627	+	0.993409i	$0.463433\pi$
$702$	−0.125981	+	0.167084i	−0.00475484	+	0.00630620i
$703$			9.74323i			0.367473i
$704$	−20.4163	+	7.34165i	−0.769469	+	0.276699i
$705$			5.28497i			0.199044i
$706$	24.3140	+	18.3326i	0.915071	+	0.689958i
$707$	−36.6248	−	11.1100i	−1.37742	−	0.417834i
$708$	1.46466	−	12.7913i	0.0550452	−	0.480725i
$709$	25.5081	+	2.51233i	0.957976	+	0.0943524i	0.564905	−	0.825156i	$-0.308913\pi$
$709$	25.5081	+	2.51233i	0.957976	+	0.0943524i	0.393071	+	0.919508i	$0.371413\pi$
$710$	4.19228	+	5.74717i	0.157333	+	0.215687i
$711$	−3.06888	+	2.05056i	−0.115092	+	0.0769019i
$712$	−3.03407	−	13.4613i	−0.113706	−	0.504485i
$713$	−0.957933	+	1.43365i	−0.0358749	+	0.0536906i
$714$	−15.5867	+	16.9260i	−0.583318	+	0.633441i
$715$	0.0969082	−	0.181303i	0.00362416	−	0.00678033i
$716$	14.6500	+	37.0153i	0.547497	+	1.38333i
$717$	2.90725	+	29.5178i	0.108573	+	1.10236i
$718$	−28.2781	−	1.61372i	−1.05533	−	0.0602234i
$719$	−5.26705	+	12.7158i	−0.196428	+	0.474218i	−0.991149	−	0.132757i	$-0.957617\pi$
$719$	−5.26705	+	12.7158i	−0.196428	+	0.474218i	0.794721	+	0.606975i	$0.207617\pi$
$720$	−0.265319	+	2.03191i	−0.00988786	+	0.0757249i
$721$	4.21632	+	10.1791i	0.157024	+	0.379090i
$722$	8.26179	+	23.6795i	0.307472	+	0.881260i
$723$	18.7527	−	22.8503i	0.697422	−	0.849811i
$724$	−3.61422	+	16.7771i	−0.134322	+	0.623517i
$725$	3.76126	+	12.3992i	0.139690	+	0.460496i
$726$	4.67709	−	2.16696i	0.173583	−	0.0804232i
$727$	18.2925	−	3.63861i	0.678432	−	0.134949i	0.156166	−	0.987731i	$-0.450087\pi$
$727$	18.2925	−	3.63861i	0.678432	−	0.134949i	0.522266	+	0.852782i	$0.325087\pi$
$728$	−1.11812	−	0.561704i	−0.0414404	−	0.0208181i
$729$	0.195090	−	0.980785i	0.00722557	−	0.0363254i
$730$	−10.0317	−	6.12121i	−0.371288	−	0.226556i
$731$	12.0378	+	14.6681i	0.445234	+	0.542520i
$732$	5.97185	−	18.6200i	0.220726	−	0.688216i
$733$	2.14762	−	1.14793i	0.0793242	−	0.0423997i	−0.431258	−	0.902229i	$-0.641930\pi$
$733$	2.14762	−	1.14793i	0.0793242	−	0.0423997i	0.510582	+	0.859829i	$0.329430\pi$
$734$	19.7535	−	11.6282i	0.729116	−	0.429206i
$735$	0.702424	−	0.702424i	0.0259093	−	0.0259093i
$736$	1.79088	+	1.44147i	0.0660127	+	0.0531334i
$737$	0.172710	+	0.172710i	0.00636185	+	0.00636185i
$738$	−10.6277	−	2.75170i	−0.391211	−	0.101291i
$739$	−8.67266	−	16.2254i	−0.319029	−	0.596861i	0.670380	−	0.742018i	$-0.266131\pi$
$739$	−8.67266	−	16.2254i	−0.319029	−	0.596861i	−0.989409	+	0.145157i	$0.953631\pi$
$740$	−5.73594	+	6.76785i	−0.210857	+	0.248791i
$741$	0.128706	−	0.105626i	0.00472812	−	0.00388027i
$742$	35.3127	−	8.54884i	1.29637	−	0.313838i
$743$	15.7285	+	3.12859i	0.577022	+	0.114777i	0.474970	−	0.880002i	$-0.342459\pi$
$743$	15.7285	+	3.12859i	0.577022	+	0.114777i	0.102053	+	0.994779i	$0.467459\pi$
$744$	7.37542	−	9.46620i	0.270396	−	0.347048i
$745$	−1.80223	−	9.06043i	−0.0660287	−	0.331948i
$746$	−13.8903	−	5.09442i	−0.508559	−	0.186520i
$747$	−4.35268	+	1.32037i	−0.159256	+	0.0483099i
$748$	29.0372	−	5.29937i	1.06170	−	0.193764i
$749$	−26.8647	−	22.0473i	−0.981615	−	0.805591i
$750$	6.35333	+	3.06668i	0.231991	+	0.111979i
$751$	38.6789	−	16.0213i	1.41141	−	0.584626i	0.458724	−	0.888579i	$-0.348307\pi$
$751$	38.6789	−	16.0213i	1.41141	−	0.584626i	0.952687	+	0.303953i	$0.0983066\pi$
$752$	−33.5679	−	24.0007i	−1.22410	−	0.875215i
$753$	−18.8404	−	7.80395i	−0.686582	−	0.284392i
$754$	0.380974	+	0.427086i	0.0138742	+	0.0155536i
$755$	−7.99159	+	0.787103i	−0.290844	+	0.0286456i
$756$	5.97891	+	0.0946740i	0.217451	+	0.00344326i
$757$	8.56154	+	4.57624i	0.311174	+	0.166326i	0.619590	−	0.784925i	$-0.287299\pi$
$757$	8.56154	+	4.57624i	0.311174	+	0.166326i	−0.308416	+	0.951252i	$0.599799\pi$
$758$	0.929411	+	22.5618i	0.0337577	+	0.819481i
$759$	0.916413	+	0.612328i	0.0332637	+	0.0222261i
$760$	0.585586	−	1.52167i	0.0212414	−	0.0551968i
$761$	−17.1543	−	25.6733i	−0.621844	−	0.930655i	−0.999988	−	0.00490799i	$-0.998438\pi$
$761$	−17.1543	−	25.6733i	−0.621844	−	0.930655i	0.378144	−	0.925747i	$-0.376562\pi$
$762$	0.453940	−	2.90175i	0.0164445	−	0.105119i
$763$	3.87702	−	39.3641i	0.140358	−	1.42508i
$764$	3.45656	+	12.0801i	0.125054	+	0.437041i
$765$	0.809255	−	2.66776i	0.0292587	−	0.0964529i
$766$	−10.4343	+	1.46346i	−0.377007	+	0.0528769i
$767$	−0.952524			−0.0343937
$768$	−11.7009	−	10.9127i	−0.422222	−	0.393779i
$769$	44.8350			1.61679			0.808396	−	0.588639i	$-0.200336\pi$
$769$	44.8350			1.61679			0.808396	+	0.588639i	$0.200336\pi$
$770$	−5.81757	+	0.815940i	−0.209651	+	0.0294044i
$771$	5.70451	−	18.8053i	0.205443	−	0.677255i
$772$	−9.93932	−	34.7362i	−0.357724	−	1.25018i
$773$	−0.0512533	+	0.520383i	−0.00184345	+	0.0187169i	−0.996062	−	0.0886544i	$-0.971743\pi$
$773$	−0.0512533	+	0.520383i	−0.00184345	+	0.0187169i	0.994219	+	0.107371i	$0.0342433\pi$
$774$	0.762161	−	4.87201i	0.0273953	−	0.175121i
$775$	−11.1671	−	16.7127i	−0.401132	−	0.600337i
$776$	−32.0293	−	12.3259i	−1.14979	−	0.442474i
$777$	21.5252	+	14.3827i	0.772213	+	0.515976i
$778$	1.00912	+	24.4969i	0.0361789	+	0.878256i
$779$	7.70358	+	4.11765i	0.276009	+	0.147530i
$780$	0.151585	+	0.00240029i	0.00542761	+	8.59443e-5i
$781$	−26.5011	+	2.61013i	−0.948284	+	0.0933978i
$782$	−2.08196	−	2.33395i	−0.0744506	−	0.0834621i
$783$	−2.52680	−	1.04663i	−0.0903004	−	0.0374036i
$784$	1.27157	+	7.65142i	0.0454134	+	0.273265i
$785$	−1.36325	+	0.564677i	−0.0486565	+	0.0201542i
$786$	7.71865	+	3.72571i	0.275315	+	0.132892i
$787$	25.8347	+	21.2020i	0.920908	+	0.755770i	0.970020	−	0.243024i	$-0.0781393\pi$
$787$	25.8347	+	21.2020i	0.920908	+	0.755770i	−0.0491124	+	0.998793i	$0.515639\pi$
$788$	−27.3206	+	4.98609i	−0.973257	+	0.177622i
$789$	4.33861	−	1.31610i	0.154459	−	0.0468545i
$790$	2.51049	+	0.920752i	0.0893193	+	0.0327589i
$791$	5.59496	+	28.1278i	0.198934	+	1.00011i
$792$	−6.05097	−	4.71450i	−0.215012	−	0.167522i
$793$	−1.41889	−	0.282235i	−0.0503863	−	0.0100225i
$794$	9.96875	−	2.41333i	0.353778	−	0.0856461i
$795$	−3.40281	+	2.79261i	−0.120685	+	0.0990438i
$796$	−13.7216	+	16.1902i	−0.486350	+	0.573846i
$797$	21.6919	+	40.5827i	0.768367	+	1.43751i	0.895235	+	0.445595i	$0.147008\pi$
$797$	21.6919	+	40.5827i	0.768367	+	1.43751i	−0.126867	+	0.991920i	$0.540492\pi$
$798$	−4.60596	−	1.19256i	−0.163049	−	0.0422162i
$799$	39.6969	+	39.6969i	1.40438	+	1.40438i
$800$	−23.5141	+	12.8573i	−0.831348	+	0.454576i
$801$	3.44976	−	3.44976i	0.121891	−	0.121891i
$802$	28.0539	−	16.5144i	0.990618	−	0.583144i
$803$	38.7967	−	20.7373i	1.36910	−	0.731802i
$804$	−0.0550093	+	0.171517i	−0.00194003	+	0.00604894i
$805$	0.394887	+	0.481171i	0.0139179	+	0.0169590i
$806$	−0.757870	−	0.462444i	−0.0266948	−	0.0162889i
$807$	1.49159	−	7.49872i	0.0525064	−	0.263967i
$808$	−16.2532	+	32.3536i	−0.571787	+	1.13819i
$809$	−2.65529	+	0.528170i	−0.0933550	+	0.0185695i	−0.241547	−	0.970389i	$-0.577655\pi$
$809$	−2.65529	+	0.528170i	−0.0933550	+	0.0185695i	0.148192	+	0.988959i	$0.452655\pi$
$810$	−0.657361	+	0.304564i	−0.0230973	+	0.0107013i
$811$	−11.8501	−	39.0646i	−0.416114	−	1.37174i	−0.875376	−	0.483443i	$-0.839386\pi$
$811$	−11.8501	−	39.0646i	−0.416114	−	1.37174i	0.459262	−	0.888301i	$-0.348114\pi$
$812$	3.44412	−	15.9875i	0.120865	−	0.561052i
$813$	−11.2844	+	13.7501i	−0.395761	+	0.482237i
$814$	−10.9401	−	31.3559i	−0.383450	−	1.09902i
$815$	−0.594419	−	1.43505i	−0.0208216	−	0.0502678i
$816$	13.2694	+	17.2552i	0.464521	+	0.604051i
$817$	−1.50152	+	3.62499i	−0.0525316	+	0.126823i
$818$	38.7203	+	2.20961i	1.35382	+	0.0772571i
$819$	−0.0433624	−	0.440266i	−0.00151520	−	0.0153841i
$820$	2.92697	+	7.39538i	0.102214	+	0.258258i
$821$	4.81586	−	9.00983i	0.168075	−	0.314445i	−0.783757	−	0.621068i	$-0.786699\pi$
$821$	4.81586	−	9.00983i	0.168075	−	0.314445i	0.951831	+	0.306623i	$0.0991990\pi$
$822$	1.31263	−	1.42543i	0.0457834	−	0.0497175i
$823$	−14.6622	+	21.9435i	−0.511092	+	0.764903i	−0.993836	−	0.110858i	$-0.964640\pi$
$823$	−14.6622	+	21.9435i	−0.511092	+	0.764903i	0.482744	+	0.875761i	$0.339640\pi$
$824$	10.1679	−	2.29176i	0.354216	−	0.0798373i
$825$	−10.6830	+	7.13818i	−0.371936	+	0.248519i
$826$	16.0408	+	21.9902i	0.558131	+	0.765139i
$827$	39.4247	+	3.88300i	1.37093	+	0.135025i	0.756525	−	0.653964i	$-0.226895\pi$
$827$	39.4247	+	3.88300i	1.37093	+	0.135025i	0.614407	+	0.788989i	$0.289395\pi$
$828$	−0.0924646	+	0.807519i	−0.00321337	+	0.0280632i
$829$	16.0416	+	4.86616i	0.557147	+	0.169009i	0.556286	−	0.830991i	$-0.312226\pi$
$829$	16.0416	+	4.86616i	0.557147	+	0.169009i	0.000860943		1.00000i	$0.499726\pi$
$830$	2.63124	+	1.98394i	0.0913315	+	0.0688635i
$831$			8.59527i			0.298167i
$832$	−0.703640	+	0.951903i	−0.0243943	+	0.0330013i
$833$		−	10.5522i		−	0.365612i
$834$	−2.96322	+	3.93003i	−0.102608	+	0.136086i
$835$	−3.85612	−	1.16974i	−0.133447	−	0.0404806i
$836$	3.79677	+	4.77871i	0.131314	+	0.165275i
$837$	4.22230	+	0.415860i	0.145944	+	0.0143742i
$838$	−26.8760	+	19.6047i	−0.928415	+	0.677233i
$839$	11.0199	−	7.36327i	0.380449	−	0.254208i	−0.350611	−	0.936521i	$-0.614026\pi$
$839$	11.0199	−	7.36327i	0.380449	−	0.254208i	0.731060	+	0.682313i	$0.239026\pi$
$840$	−2.49732	−	3.53995i	−0.0861658	−	0.122140i
$841$	11.9558	−	17.8931i	0.412269	−	0.617003i
$842$	31.2494	+	28.7767i	1.07693	+	0.991710i
$843$	−0.233369	+	0.436602i	−0.00803764	+	0.0150374i
$844$	−19.1490	+	44.2354i	−0.659134	+	1.52265i
$845$	0.651672	+	6.61654i	0.0224182	+	0.227616i
$846$	0.831212	−	14.5658i	0.0285777	−	0.500784i
$847$	−4.17036	+	10.0681i	−0.143295	+	0.345946i
$848$	−2.28429	−	34.2953i	−0.0784427	−	1.17771i
$849$	10.5008	+	25.3513i	0.360388	+	0.870054i
$850$	34.4247	−	12.0108i	1.18076	−	0.411967i
$851$	−2.23236	+	2.72014i	−0.0765243	+	0.0932452i
$852$	−10.6504	−	16.4991i	−0.364876	−	0.565248i
$853$	1.01809	+	3.35618i	0.0348586	+	0.114913i	0.972643	−	0.232304i	$-0.0746265\pi$
$853$	1.01809	+	3.35618i	0.0348586	+	0.114913i	−0.937785	+	0.347218i	$0.887127\pi$
$854$	17.3788	+	37.5099i	0.594691	+	1.28356i
$855$	0.565377	−	0.112461i	0.0193355	−	0.00384607i
$856$	−24.8779	+	21.4943i	−0.850308	+	0.734659i
$857$	−5.86180	+	29.4693i	−0.200235	+	1.00665i	0.741668	+	0.670767i	$0.234035\pi$
$857$	−5.86180	+	29.4693i	−0.200235	+	1.00665i	−0.941904	+	0.335884i	$0.890965\pi$
$858$	−0.295603	+	0.484444i	−0.0100917	+	0.0165387i
$859$	27.2746	+	33.2342i	0.930598	+	1.13394i	0.990744	+	0.135747i	$0.0433435\pi$
$859$	27.2746	+	33.2342i	0.930598	+	1.13394i	−0.0601456	+	0.998190i	$0.519157\pi$
$860$	−3.17706	+	1.63404i	−0.108337	+	0.0557202i
$861$	20.4687	−	10.9408i	0.697572	−	0.372860i
$862$	12.1308	+	20.6072i	0.413176	+	0.701884i
$863$	−12.1495	+	12.1495i	−0.413575	+	0.413575i	−0.882982	−	0.469407i	$-0.844468\pi$
$863$	−12.1495	+	12.1495i	−0.413575	+	0.413575i	0.469407	+	0.882982i	$0.344468\pi$
$864$	1.05082	−	5.55840i	0.0357496	−	0.189101i
$865$	−3.87826	−	3.87826i	−0.131865	−	0.131865i
$866$	0.0949457	−	0.366703i	0.00322639	−	0.0124611i
$867$	−5.94598	−	11.1241i	−0.201936	−	0.377796i
$868$	2.08665	+	25.2841i	0.0708255	+	0.858199i
$869$	−7.73770	+	6.35017i	−0.262484	+	0.215415i
$870$	0.466225	+	1.92583i	0.0158065	+	0.0652919i
$871$	0.0130700	+	0.00259979i	0.000442861	+	8.80905e-5i
$872$	−36.0717	−	9.95156i	−1.22154	−	0.337002i
$873$	−2.36716	−	11.9005i	−0.0801162	−	0.402772i
$874$	0.222686	−	0.607169i	0.00753247	−	0.0205378i
$875$	−14.2724	+	4.32949i	−0.482496	+	0.146364i
$876$	26.6854	+	18.4483i	0.901615	+	0.623312i
$877$	−6.69286	−	5.49269i	−0.226002	−	0.185475i	0.514577	−	0.857444i	$-0.327949\pi$
$877$	−6.69286	−	5.49269i	−0.226002	−	0.185475i	−0.740579	+	0.671969i	$0.765449\pi$
$878$	15.1082	−	31.3001i	0.509877	−	1.05633i
$879$	−27.7844	+	11.5087i	−0.937144	+	0.388178i
$880$	−0.175954	+	5.55459i	−0.00593141	+	0.187245i
$881$	−18.4327	−	7.63506i	−0.621013	−	0.257232i	0.0499164	−	0.998753i	$-0.484105\pi$
$881$	−18.4327	−	7.63506i	−0.621013	−	0.257232i	−0.670929	+	0.741522i	$0.734105\pi$
$882$	−2.04642	+	1.82547i	−0.0689065	+	0.0614666i
$883$	−11.9420	+	1.17618i	−0.401880	+	0.0395817i	−0.296938	−	0.954897i	$-0.595966\pi$
$883$	−11.9420	+	1.17618i	−0.401880	+	0.0395817i	−0.104942	+	0.994478i	$0.533466\pi$
$884$	1.15663	−	1.12057i	0.0389016	−	0.0376888i
$885$	−2.90842	−	1.55458i	−0.0977656	−	0.0522568i
$886$	20.2433	−	0.833903i	0.680088	−	0.0280155i
$887$	−12.2180	−	8.16383i	−0.410241	−	0.274115i	0.333278	−	0.942828i	$-0.391845\pi$
$887$	−12.2180	−	8.16383i	−0.410241	−	0.274115i	−0.743520	+	0.668714i	$0.766845\pi$
$888$	16.8732	−	17.7506i	0.566227	−	0.595673i
$889$	3.44970	+	5.16284i	0.115699	+	0.173156i
$890$	−3.49208	−	0.546289i	−0.117055	−	0.0183116i
$891$	0.265825	−	2.69897i	0.00890547	−	0.0904188i
$892$	3.12888	−	5.63718i	0.104763	−	0.188747i
$893$	−3.36976	+	11.1086i	−0.112765	+	0.371735i
$894$	3.54210	+	25.2548i	0.118465	+	0.844646i
$895$	10.1969			0.340844
$896$	33.8254	+	0.214093i	1.13003	+	0.00715234i
$897$	0.0601334			0.00200779
$898$	2.92519	+	20.8563i	0.0976148	+	0.695984i
$899$	3.36841	−	11.1041i	0.112343	−	0.370344i
$900$	−8.28454	−	4.59828i	−0.276151	−	0.153276i
$901$	−4.58335	+	46.5356i	−0.152694	+	1.55032i
$902$	−29.4153	−	4.60163i	−0.979422	−	0.153217i
$903$	5.79201	+	8.66836i	0.192746	+	0.288465i
$904$	27.1219	−	0.687345i	0.902061	−	0.0228608i
$905$	3.65511	+	2.44227i	0.121500	+	0.0811837i
$906$	22.1493	−	0.912418i	0.735861	−	0.0303131i
$907$	22.5951	+	12.0773i	0.750258	+	0.401021i	0.801756	−	0.597652i	$-0.203900\pi$
$907$	22.5951	+	12.0773i	0.750258	+	0.401021i	−0.0514980	+	0.998673i	$0.516400\pi$
$908$	6.47639	+	6.68479i	0.214927	+	0.221843i
$909$	−12.7393	+	1.25472i	−0.422537	+	0.0416163i
$910$	−0.239179	+	0.213355i	−0.00792871	+	0.00707264i
$911$	37.6555	+	15.5974i	1.24758	+	0.516766i	0.906077	−	0.423114i	$-0.139063\pi$
$911$	37.6555	+	15.5974i	1.24758	+	0.516766i	0.341506	+	0.939879i	$0.389063\pi$
$912$	−1.85325	+	4.10175i	−0.0613673	+	0.135823i
$913$	−11.3968	+	4.72069i	−0.377178	+	0.156232i
$914$	−19.4089	+	40.2099i	−0.641988	+	1.33002i
$915$	−3.87179	−	3.17750i	−0.127998	−	0.105045i
$916$	10.6350	−	15.3835i	0.351391	−	0.508285i
$917$	−17.3395	+	5.25989i	−0.572602	+	0.173697i
$918$	−2.64996	+	7.22529i	−0.0874616	+	0.238470i
$919$	−0.994780	−	5.00110i	−0.0328148	−	0.164971i	0.960903	−	0.276885i	$-0.0893020\pi$
$919$	−0.994780	−	5.00110i	−0.0328148	−	0.164971i	−0.993718	+	0.111914i	$0.964302\pi$
$920$	0.512129	−	0.290655i	0.0168844	−	0.00958260i
$921$	22.2891	+	4.43358i	0.734451	+	0.146091i
$922$	−10.3593	−	42.7913i	−0.341167	−	1.40926i
$923$	−1.12309	+	0.921699i	−0.0369671	+	0.0303381i
$924$	16.1621	−	1.33382i	0.531693	−	0.0438795i
$925$	−19.3373	−	36.1775i	−0.635806	−	1.18951i
$926$	3.27010	−	12.6299i	0.107462	−	0.415045i
$927$	2.60575	+	2.60575i	0.0855840	+	0.0855840i
$928$	−14.3494	−	5.78454i	−0.471041	−	0.189887i
$929$	10.5910	−	10.5910i	0.347478	−	0.347478i	−0.511691	−	0.859169i	$-0.670981\pi$
$929$	10.5910	−	10.5910i	0.347478	−	0.347478i	0.859169	+	0.511691i	$0.170981\pi$
$930$	−1.55933	−	2.64892i	−0.0511324	−	0.0868614i
$931$	1.92432	−	1.02857i	0.0630669	−	0.0337100i
$932$	−10.4400	−	20.2985i	−0.341973	−	0.664899i
$933$	16.8847	+	20.5741i	0.552781	+	0.673565i
$934$	3.23194	−	5.29661i	0.105752	−	0.173310i
$935$	1.47500	−	7.41530i	0.0482375	−	0.242506i
$936$	−0.417404	−	0.0304565i	−0.0136433	−	0.000995501i
$937$	−35.4996	+	7.06131i	−1.15972	+	0.230683i	−0.737203	−	0.675671i	$-0.763854\pi$
$937$	−35.4996	+	7.06131i	−1.15972	+	0.230683i	−0.422518	+	0.906354i	$0.638854\pi$
$938$	−0.160084	−	0.345520i	−0.00522692	−	0.0112816i
$939$	−6.95446	−	22.9258i	−0.226950	−	0.748154i
$940$	−8.88046	+	5.73246i	−0.289649	+	0.186972i
$941$	12.1992	−	14.8648i	0.397683	−	0.484578i	−0.535216	−	0.844715i	$-0.679770\pi$
$941$	12.1992	−	14.8648i	0.397683	−	0.484578i	0.932900	+	0.360137i	$0.117270\pi$
$942$	3.84605	−	1.34189i	0.125311	−	0.0437211i
$943$	1.20727	+	2.91461i	0.0393142	+	0.0949129i
$944$	23.0821	−	11.4132i	0.751259	−	0.371469i
$945$	0.586141	−	1.41507i	0.0190672	−	0.0460322i
$946$	0.761944	−	13.3520i	0.0247729	−	0.434111i
$947$	−1.16732	−	11.8520i	−0.0379329	−	0.385139i	−0.995342	−	0.0964051i	$-0.969266\pi$
$947$	−1.16732	−	11.8520i	−0.0379329	−	0.385139i	0.957409	−	0.288734i	$-0.0932344\pi$
$948$	−6.77432	−	2.93252i	−0.220020	−	0.0952438i
$949$	1.13141	−	2.11673i	0.0367273	−	0.0687119i
$950$	5.54583	+	5.10700i	0.179930	+	0.165693i
$951$	1.54195	−	2.30768i	0.0500010	−	0.0748318i
$952$	−45.3477	−	7.83150i	−1.46973	−	0.253820i
$953$	43.2227	−	28.8805i	1.40012	−	0.935530i	0.400303	−	0.916383i	$-0.368905\pi$
$953$	43.2227	−	28.8805i	1.40012	−	0.935530i	0.999817	−	0.0191476i	$-0.00609525\pi$
$954$	9.81766	−	7.16150i	0.317858	−	0.231862i
$955$	3.20293	+	0.315461i	0.103644	+	0.0102081i
$956$	−46.4460	+	36.9023i	−1.50217	+	1.19350i
$957$	−7.09797	−	2.15314i	−0.229445	−	0.0696013i
$958$	32.8680	−	43.5918i	1.06192	−	1.40839i
$959$			4.09664i			0.132287i
$960$	−3.70205	+	1.75814i	−0.119483	+	0.0567436i
$961$		−	12.9993i		−	0.419331i
$962$	−1.44674	−	1.09083i	−0.0466448	−	0.0351699i
$963$	−11.1233	−	3.37423i	−0.358444	−	0.108733i
$964$	58.7364	+	6.72559i	1.89177	+	0.216617i
$965$	−9.21001	−	0.907107i	−0.296481	−	0.0292008i
$966$	−1.01266	−	1.38826i	−0.0325819	−	0.0446664i
$967$	7.44218	−	4.97270i	0.239324	−	0.159911i	−0.430125	−	0.902770i	$-0.641530\pi$
$967$	7.44218	−	4.97270i	0.239324	−	0.159911i	0.669449	+	0.742858i	$0.266530\pi$
$968$	8.71429	+	5.50858i	0.280088	+	0.177052i
$969$	3.40199	−	5.09143i	0.109288	−	0.163560i
$970$	−5.95485	+	6.46653i	−0.191199	+	0.207628i
$971$	7.76714	−	14.5313i	0.249259	−	0.466331i	−0.725911	−	0.687789i	$-0.758581\pi$
$971$	7.76714	−	14.5313i	0.249259	−	0.466331i	0.975170	+	0.221458i	$0.0710814\pi$
$972$	1.85965	−	0.736016i	0.0596481	−	0.0236077i
$973$	−1.01994	−	10.3556i	−0.0326976	−	0.331985i
$974$	−48.3661	−	2.76005i	−1.54975	−	0.0884379i
$975$	−0.268262	+	0.647641i	−0.00859125	+	0.0207411i
$976$	37.7652	−	10.1620i	1.20883	−	0.325277i
$977$	20.1035	+	48.5342i	0.643168	+	1.55275i	0.822382	+	0.568935i	$0.192645\pi$
$977$	20.1035	+	48.5342i	0.643168	+	1.55275i	−0.179214	+	0.983810i	$0.557355\pi$
$978$	1.41257	+	4.04862i	0.0451689	+	0.129461i
$979$	8.39374	−	10.2278i	0.268265	−	0.326882i
$980$	1.94220	+	0.418399i	0.0620413	+	0.0133653i
$981$	−3.84038	−	12.6600i	−0.122614	−	0.404204i
$982$	50.3388	−	23.3226i	1.60637	−	0.744255i
$983$	6.13810	−	1.22094i	0.195775	−	0.0389421i	−0.0962287	−	0.995359i	$-0.530678\pi$
$983$	6.13810	−	1.22094i	0.195775	−	0.0389421i	0.292004	+	0.956417i	$0.405678\pi$
$984$	−6.90384	−	20.8427i	−0.220086	−	0.664440i
$985$	−1.38780	+	6.97695i	−0.0442190	+	0.222304i
$986$	17.9674	+	10.9635i	0.572199	+	0.349150i
$987$	19.5673	+	23.8429i	0.622835	+	0.758927i
$988$	0.317090	+	0.101698i	0.0100880	+	0.00323543i
$989$	−1.24975	+	0.668008i	−0.0397399	+	0.0212414i
$990$	−1.69323	+	0.996751i	−0.0538145	+	0.0316788i
$991$	−40.3165	+	40.3165i	−1.28070	+	1.28070i	−0.340425	+	0.940272i	$0.610571\pi$
$991$	−40.3165	+	40.3165i	−1.28070	+	1.28070i	−0.940272	+	0.340425i	$0.889429\pi$
$992$	23.9062	+	2.12535i	0.759022	+	0.0674800i
$993$	−22.6352	−	22.6352i	−0.718306	−	0.718306i
$994$	40.1919	+	10.4064i	1.27481	+	0.330070i
$995$	2.56256	+	4.79422i	0.0812387	+	0.151987i
$996$	−6.93989	−	5.88174i	−0.219899	−	0.186370i
$997$	−15.2943	+	12.5517i	−0.484374	+	0.397516i	−0.844641	−	0.535334i	$-0.820186\pi$
$997$	−15.2943	+	12.5517i	−0.484374	+	0.397516i	0.360266	+	0.932849i	$0.382686\pi$
$998$	17.3547	−	4.20141i	0.549355	−	0.132993i
$999$	8.49236	+	1.68924i	0.268686	+	0.0534450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.325.1	yes	512
128.13	even	32	inner	384.2.v.a.13.1	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.1	✓	512	128.13	even	32	inner
384.2.v.a.325.1	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.40051 + 0.196427i) q^{2} +(0.290285 - 0.956940i) q^{3} +(1.92283 - 0.550195i) q^{4} +(0.0502132 - 0.509823i) q^{5} +(-0.218576 + 1.39722i) q^{6} +(-1.66106 - 2.48595i) q^{7} +(-2.58487 + 1.14825i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.40051 + 0.196427i) q^{2} +(0.290285 - 0.956940i) q^{3} +(1.92283 - 0.550195i) q^{4} +(0.0502132 - 0.509823i) q^{5} +(-0.218576 + 1.39722i) q^{6} +(-1.66106 - 2.48595i) q^{7} +(-2.58487 + 1.14825i) q^{8} +(-0.831470 - 0.555570i) q^{9} +(0.0298193 + 0.723874i) q^{10} +(-2.39179 - 1.27844i) q^{11} +(0.0316653 - 1.99975i) q^{12} +(-0.147254 + 0.0145033i) q^{13} +(2.81463 + 3.15532i) q^{14} +(-0.473294 - 0.196045i) q^{15} +(3.39457 - 2.11586i) q^{16} +(-5.02760 + 2.08250i) q^{17} +(1.27361 + 0.614756i) q^{18} +(-0.869829 - 0.713850i) q^{19} +(-0.183951 - 1.00793i) q^{20} +(-2.86109 + 0.867902i) q^{21} +(3.60084 + 1.32065i) q^{22} +(-0.0792843 - 0.398589i) q^{23} +(0.348458 + 2.80688i) q^{24} +(4.64653 + 0.924252i) q^{25} +(0.203382 - 0.0492367i) q^{26} +(-0.773010 + 0.634393i) q^{27} +(-4.56170 - 3.86617i) q^{28} +(1.28926 + 2.41204i) q^{29} +(0.701360 + 0.181594i) q^{30} +(-3.00006 - 3.00006i) q^{31} +(-4.33850 + 3.63007i) q^{32} +(-1.91769 + 1.91769i) q^{33} +(6.63212 - 3.90411i) q^{34} +(-1.35080 + 0.722020i) q^{35} +(-1.90445 - 0.610798i) q^{36} +(-5.49304 - 6.69329i) q^{37} +(1.35842 + 0.828893i) q^{38} +(-0.0288669 + 0.145124i) q^{39} +(0.455609 + 1.37548i) q^{40} +(-7.61357 + 1.51443i) q^{41} +(3.83649 - 1.77750i) q^{42} +(-1.01220 - 3.33679i) q^{43} +(-5.30241 - 1.14227i) q^{44} +(-0.324993 + 0.396006i) q^{45} +(0.189332 + 0.542652i) q^{46} +(-3.94790 - 9.53108i) q^{47} +(-1.03936 - 3.86261i) q^{48} +(-0.742058 + 1.79149i) q^{49} +(-6.68904 - 0.381716i) q^{50} +(0.533393 + 5.41563i) q^{51} +(-0.275166 + 0.108906i) q^{52} +(4.05063 - 7.57820i) q^{53} +(0.957994 - 1.04031i) q^{54} +(-0.771878 + 1.15520i) q^{55} +(7.14811 + 4.51855i) q^{56} +(-0.935610 + 0.625154i) q^{57} +(-2.27941 - 3.12483i) q^{58} +(6.40642 + 0.630977i) q^{59} +(-1.01793 - 0.116558i) q^{60} +(9.35612 + 2.83815i) q^{61} +(4.79090 + 3.61231i) q^{62} +2.98983i q^{63} +(5.36306 - 5.93613i) q^{64} +0.0758019i q^{65} +(2.30905 - 3.06243i) q^{66} +(-0.0861833 - 0.0261434i) q^{67} +(-8.52145 + 6.77046i) q^{68} +(-0.404441 - 0.0398339i) q^{69} +(1.74999 - 1.27653i) q^{70} +(8.16418 - 5.45513i) q^{71} +(2.78717 + 0.481341i) q^{72} +(-9.01176 + 13.4871i) q^{73} +(9.00778 + 8.29501i) q^{74} +(2.23327 - 4.17815i) q^{75} +(-2.06529 - 0.894039i) q^{76} +(0.794772 + 8.06946i) q^{77} +(0.0119220 - 0.208917i) q^{78} +(1.41245 - 3.40995i) q^{79} +(-0.908265 - 1.83688i) q^{80} +(0.382683 + 0.923880i) q^{81} +(10.3654 - 3.61648i) q^{82} +(2.88556 - 3.51607i) q^{83} +(-5.02388 + 3.24299i) q^{84} +(0.809255 + 2.66776i) q^{85} +(2.07303 + 4.47437i) q^{86} +(2.68243 - 0.533569i) q^{87} +(7.65043 + 0.558225i) q^{88} +(-0.951785 + 4.78495i) q^{89} +(0.377369 - 0.618446i) q^{90} +(0.280653 + 0.341977i) q^{91} +(-0.371752 - 0.722798i) q^{92} +(-3.74175 + 2.00001i) q^{93} +(7.40122 + 12.5729i) q^{94} +(-0.407614 + 0.407614i) q^{95} +(2.21436 + 5.20544i) q^{96} +(8.57980 + 8.57980i) q^{97} +(0.687360 - 2.65475i) q^{98} +(1.27844 + 2.39179i) 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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