LMFDB - Embedded newform 384.2.v.a.13.1

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			13.1
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.1

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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	0.999862	+	0.0166280i	$0.00529312\pi$
$5$	0.0502132	+	0.509823i	0.0224560	+	0.228000i	−0.977406	+	0.211372i	$0.932207\pi$
$6$	−0.218576	−	1.39722i	−0.0892334	−	0.570413i
$7$	−1.66106	+	2.48595i	−0.627822	+	0.939602i	0.372113	+	0.928188i	$0.378633\pi$
$7$	−1.66106	+	2.48595i	−0.627822	+	0.939602i	−0.999935	+	0.0114147i	$0.996367\pi$
$8$	−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	−0.790773	−	0.612109i	$-0.790321\pi$
$11$	−2.39179	+	1.27844i	−0.721153	+	0.385464i	0.0696203	+	0.997574i	$0.477821\pi$
$12$	0.0316653	+	1.99975i	0.00914100	+	0.577278i
$13$	−0.147254	−	0.0145033i	−0.0408410	−	0.00402249i	0.0775760	−	0.996986i	$-0.475282\pi$
$13$	−0.147254	−	0.0145033i	−0.0408410	−	0.00402249i	−0.118417	+	0.992964i	$0.537782\pi$
$14$	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	−0.322162	−	0.946685i	$-0.604409\pi$
$17$	−5.02760	−	2.08250i	−1.21937	−	0.505080i	−0.897210	+	0.441604i	$0.854409\pi$
$18$	1.27361	−	0.614756i	0.300192	−	0.144899i
$19$	−0.869829	+	0.713850i	−0.199552	+	0.163768i	−0.728863	−	0.684660i	$-0.759951\pi$
$19$	−0.869829	+	0.713850i	−0.199552	+	0.163768i	0.529310	+	0.848428i	$0.322451\pi$
$20$	−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	−0.988170	−	0.153359i	$-0.950991\pi$
$23$	−0.0792843	+	0.398589i	−0.0165319	+	0.0831115i	0.971639	+	0.236471i	$0.0759908\pi$
$24$	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	−0.733307	−	0.679897i	$-0.762024\pi$
$29$	1.28926	−	2.41204i	0.239410	−	0.447905i	0.972718	+	0.231992i	$0.0745244\pi$
$30$	0.701360	−	0.181594i	0.128050	−	0.0331544i
$31$	−3.00006	+	3.00006i	−0.538827	+	0.538827i	−0.923184	−	0.384358i	$-0.874423\pi$
$31$	−3.00006	+	3.00006i	−0.538827	+	0.538827i	0.384358	+	0.923184i	$0.374423\pi$
$32$	−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	0.0914675	+	0.995808i	$0.470844\pi$
$37$	−5.49304	+	6.69329i	−0.903051	+	1.10037i	−0.994518	+	0.104563i	$0.966656\pi$
$38$	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	−0.439357	−	0.898312i	$-0.644794\pi$
$41$	−7.61357	−	1.51443i	−1.18904	−	0.236515i	−0.749682	+	0.661798i	$0.769794\pi$
$42$	3.83649	+	1.77750i	0.591984	+	0.274274i
$43$	−1.01220	+	3.33679i	−0.154360	+	0.508855i	−0.999677	−	0.0254088i	$-0.991911\pi$
$43$	−1.01220	+	3.33679i	−0.154360	+	0.508855i	0.845318	+	0.534264i	$0.179411\pi$
$44$	−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	0.320637	+	0.947202i	$0.396103\pi$
$47$	−3.94790	+	9.53108i	−0.575861	+	1.39025i	−0.896498	+	0.443048i	$0.853897\pi$
$48$	−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	0.990163	+	0.139920i	$0.0446845\pi$
$53$	4.05063	+	7.57820i	0.556397	+	1.04095i	−0.433766	+	0.901026i	$0.642815\pi$
$54$	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	0.328026	−	0.944669i	$-0.393617\pi$
$59$	6.40642	−	0.630977i	0.834045	−	0.0821463i	0.506019	+	0.862522i	$0.331117\pi$
$60$	−1.01793	+	0.116558i	−0.131414	+	0.0150475i
$61$	9.35612	−	2.83815i	1.19793	−	0.363388i	0.372574	−	0.928003i	$-0.378475\pi$
$61$	9.35612	−	2.83815i	1.19793	−	0.363388i	0.825354	+	0.564615i	$0.190975\pi$
$62$	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	−0.295545	−	0.955329i	$-0.595501\pi$
$67$	−0.0861833	+	0.0261434i	−0.0105290	+	0.00319393i	0.285016	+	0.958523i	$0.408001\pi$
$68$	−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	0.935980	−	0.352052i	$-0.114516\pi$
$71$	8.16418	+	5.45513i	0.968910	+	0.647405i	0.0329301	+	0.999458i	$0.489516\pi$
$72$	2.78717	−	0.481341i	0.328471	−	0.0567266i
$73$	−9.01176	−	13.4871i	−1.05475	−	1.57854i	−0.788896	−	0.614527i	$-0.789347\pi$
$73$	−9.01176	−	13.4871i	−1.05475	−	1.57854i	−0.265851	−	0.964014i	$-0.585653\pi$
$74$	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	0.983202	−	0.182519i	$-0.0584251\pi$
$79$	1.41245	+	3.40995i	0.158913	+	0.383650i	−0.824289	+	0.566169i	$0.808425\pi$
$80$	−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	0.906903	−	0.421339i	$-0.138440\pi$
$83$	2.88556	+	3.51607i	0.316732	+	0.385939i	−0.590171	+	0.807278i	$0.700940\pi$
$84$	−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	−0.997876	−	0.0651459i	$-0.979249\pi$
$89$	−0.951785	−	4.78495i	−0.100889	−	0.507203i	0.896987	−	0.442058i	$-0.145751\pi$
$90$	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	−0.121451	−	0.992597i	$-0.538755\pi$
$97$	8.57980	−	8.57980i	0.871146	−	0.871146i	0.992597	+	0.121451i	$0.0387547\pi$
$98$	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	0.981407	−	0.191940i	$-0.0614778\pi$
$101$	9.89529	+	8.12085i	0.984618	+	0.808055i	0.00321143	+	0.999995i	$0.498978\pi$
$102$	−1.81080	+	7.47985i	−0.179296	+	0.740615i
$103$	−3.61428	+	0.718924i	−0.356125	+	0.0708377i	−0.369911	−	0.929067i	$-0.620612\pi$
$103$	−3.61428	+	0.718924i	−0.356125	+	0.0708377i	0.0137856	+	0.999905i	$0.495612\pi$
$104$	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	0.777799	−	0.628513i	$-0.216336\pi$
$107$	11.1233	+	3.37423i	1.07533	+	0.326199i	0.297534	+	0.954711i	$0.403836\pi$
$108$	−1.13733	−	1.64514i	−0.109440	−	0.158304i
$109$	10.2267	−	8.39283i	0.979539	−	0.803887i	−0.00104218	−	0.999999i	$-0.500332\pi$
$109$	10.2267	−	8.39283i	0.979539	−	0.803887i	0.980581	+	0.196112i	$0.0628317\pi$
$110$	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	−0.758352	−	0.651845i	$-0.773995\pi$
$113$	−8.86196	+	3.67075i	−0.833663	+	0.345315i	−0.0753116	+	0.997160i	$0.523995\pi$
$114$	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	0.999647	−	0.0265737i	$-0.00845965\pi$
$131$	1.75926	+	5.79951i	0.153707	+	0.506705i	−0.845940	+	0.533279i	$0.820960\pi$
$132$	−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	−0.603285	−	0.797526i	$-0.706142\pi$
$137$	−1.13927	+	0.761238i	−0.0973346	+	0.0650369i	0.505950	+	0.862563i	$0.331142\pi$
$138$	0.574246	+	0.0236555i	0.0488831	+	0.00201369i
$139$	3.06940	−	1.64063i	0.260343	−	0.139156i	−0.336062	−	0.941840i	$-0.609095\pi$
$139$	3.06940	−	1.64063i	0.260343	−	0.139156i	0.596405	+	0.802683i	$0.296595\pi$
$140$	−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	0.902518	−	0.430651i	$-0.141716\pi$
$149$	17.2561	+	5.23459i	1.41368	+	0.428835i	0.511160	+	0.859486i	$0.329216\pi$
$150$	−2.30700	−	6.29020i	−0.188366	−	0.513593i
$151$	−3.05808	+	15.3740i	−0.248863	+	1.25112i	0.630959	+	0.775816i	$0.282662\pi$
$151$	−3.05808	+	15.3740i	−0.248863	+	1.25112i	−0.879822	+	0.475303i	$0.842338\pi$
$152$	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	−0.930258	−	0.366906i	$-0.880417\pi$
$157$	−1.35779	+	2.54024i	−0.108363	+	0.202733i	0.821895	+	0.569639i	$0.192917\pi$
$158$	−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	0.572785	−	0.819706i	$-0.305863\pi$
$163$	2.67403	+	1.42930i	0.209446	+	0.111951i	−0.363338	+	0.931657i	$0.618363\pi$
$164$	−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	0.993634	+	0.112658i	$0.0359366\pi$
$167$	1.53457	+	7.71479i	0.118748	+	0.596988i	−0.874885	+	0.484330i	$0.839063\pi$
$168$	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	0.964284	−	0.264869i	$-0.0853287\pi$
$173$	6.79195	+	8.27601i	0.516382	+	0.629214i	−0.447902	+	0.894083i	$0.647829\pi$
$174$	−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	−0.592200	−	0.805791i	$-0.701740\pi$
$179$	1.95098	−	19.8086i	0.145823	−	1.48057i	0.738023	−	0.674776i	$-0.235760\pi$
$180$	−0.407028	−	0.940262i	−0.0303381	−	0.0700830i
$181$	−4.04506	−	7.56777i	−0.300667	−	0.562508i	0.685538	−	0.728037i	$-0.259567\pi$
$181$	−4.04506	−	7.56777i	−0.300667	−	0.562508i	−0.986205	+	0.165529i	$0.947067\pi$
$182$	−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	$-0.927013\pi$
$191$		−	6.28243i		−	0.454580i	0.973827	−	0.227290i	$-0.0729866\pi$
$192$	−4.12371	+	6.85529i	−0.297603	+	0.494738i
$193$			18.0651i			1.30035i	0.759783	+	0.650177i	$0.225305\pi$
$193$			18.0651i			1.30035i	−0.759783	+	0.650177i	$0.774695\pi$
$194$	−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	−0.577469	−	0.816412i	$-0.695960\pi$
$197$	−13.8191	+	1.36106i	−0.984569	+	0.0969716i	−0.407099	+	0.913384i	$0.633460\pi$
$198$	−2.26028	+	3.09860i	−0.160631	+	0.220208i
$199$	−8.82304	−	5.89537i	−0.625449	−	0.417912i	0.202053	−	0.979375i	$-0.435239\pi$
$199$	−8.82304	−	5.89537i	−0.625449	−	0.417912i	−0.827502	+	0.561463i	$0.810239\pi$
$200$	−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	−0.957912	−	0.287062i	$-0.907322\pi$
$211$	−15.2896	−	18.6304i	−1.05258	−	1.28257i	−0.0946664	−	0.995509i	$-0.530178\pi$
$212$	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	0.779298	−	0.626654i	$-0.215576\pi$
$223$	2.27947	+	2.27947i	0.152644	+	0.152644i	−0.626654	+	0.779298i	$0.715576\pi$
$224$	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	−0.798537	−	0.601945i	$-0.794392\pi$
$227$	2.19377	−	4.10425i	0.145606	−	0.272409i	0.944143	+	0.329536i	$0.106892\pi$
$228$	−1.45506	−	1.71683i	−0.0963640	−	0.113700i
$229$	7.22832	+	5.93213i	0.477661	+	0.392006i	0.842186	−	0.539187i	$-0.181269\pi$
$229$	7.22832	+	5.93213i	0.477661	+	0.392006i	−0.364525	+	0.931194i	$0.618769\pi$
$230$	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	0.836737	+	0.547605i	$0.184460\pi$
$233$	−2.22656	+	11.1937i	−0.145867	+	0.733321i	−0.982604	+	0.185716i	$0.940540\pi$
$234$	−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	−0.994346	−	0.106190i	$-0.966135\pi$
$239$	−27.4028	−	11.3506i	−1.77254	−	0.734211i	−0.778196	−	0.628021i	$-0.783865\pi$
$240$	−2.02144	−	0.335938i	−0.130483	−	0.0216847i
$241$	27.3100	−	11.3122i	1.75919	−	0.728680i	0.762536	−	0.646946i	$-0.223954\pi$
$241$	27.3100	−	11.3122i	1.75919	−	0.728680i	0.996654	−	0.0817347i	$-0.0260460\pi$
$242$	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	0.824770	+	0.565469i	$0.191305\pi$
$251$	1.99883	+	20.2945i	0.126165	+	1.28098i	−0.698604	+	0.715508i	$0.746195\pi$
$252$	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	−0.745646	−	0.666342i	$-0.767859\pi$
$263$	2.51887	−	3.76975i	0.155320	−	0.232453i	0.900966	+	0.433889i	$0.142859\pi$
$264$	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	0.327276	−	0.944929i	$-0.393869\pi$
$269$	7.60881	+	0.749403i	0.463917	+	0.0456919i	0.136641	+	0.990621i	$0.456369\pi$
$270$	−0.482271	+	0.540645i	−0.0293501	+	0.0329026i
$271$	−16.4337	+	6.80706i	−0.998276	+	0.413500i	−0.821165	−	0.570691i	$-0.806675\pi$
$271$	−16.4337	+	6.80706i	−0.998276	+	0.413500i	−0.177111	+	0.984191i	$0.556675\pi$
$272$	−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	0.0333390	−	0.999444i	$-0.489386\pi$
$277$	−8.22516	−	2.49508i	−0.494202	−	0.149915i	−0.527541	+	0.849530i	$0.676886\pi$
$278$	−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	−0.209552	−	0.977798i	$-0.567200\pi$
$281$	−0.485545	+	0.0965810i	−0.0289652	+	0.00576154i	0.180586	+	0.983559i	$0.442200\pi$
$282$	14.1799	+	3.43282i	0.844402	+	0.204421i
$283$	−21.2114	−	17.4078i	−1.26089	−	1.03479i	−0.997541	−	0.0700842i	$-0.977673\pi$
$283$	−21.2114	−	17.4078i	−1.26089	−	1.03479i	−0.263348	−	0.964701i	$-0.584827\pi$
$284$	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	−0.187931	+	0.982182i	$0.560178\pi$
$293$	−19.0785	+	23.2472i	−1.11458	+	1.35812i	−0.926646	+	0.375934i	$0.877322\pi$
$294$	−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	−0.693972	−	0.720002i	$-0.744141\pi$
$307$	2.22751	−	22.6163i	0.127131	−	1.29078i	0.821103	−	0.570780i	$-0.193359\pi$
$308$	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	−0.964826	−	0.262890i	$-0.915324\pi$
$311$	−14.7868	−	22.1300i	−0.838482	−	1.25488i	0.126344	−	0.991987i	$-0.459676\pi$
$312$	−0.0920209	+	0.408271i	−0.00520966	+	0.0231138i
$313$	19.9198	+	13.3100i	1.12594	+	0.752326i	0.971819	−	0.235727i	$-0.0757471\pi$
$313$	19.9198	+	13.3100i	1.12594	+	0.752326i	0.154116	+	0.988053i	$0.450747\pi$
$314$	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	−0.214816	−	0.976655i	$-0.568915\pi$
$317$	2.65592	−	0.805665i	0.149171	−	0.0452506i	0.363987	+	0.931404i	$0.381415\pi$
$318$	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	0.834018	+	0.551737i	$0.186035\pi$
$331$	15.0899	+	28.2312i	0.829415	+	1.55173i	−0.00460341	+	0.999989i	$0.501465\pi$
$332$	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	−0.555856	−	0.831279i	$-0.687609\pi$
$337$	7.80189	−	18.8354i	0.424996	−	1.02603i	0.980852	−	0.194753i	$-0.0623906\pi$
$338$	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	−0.827291	−	0.561773i	$-0.810119\pi$
$347$	−2.14065	+	2.60839i	−0.114916	+	0.140026i	0.712375	+	0.701799i	$0.247619\pi$
$348$	4.86431	+	2.50183i	0.260754	+	0.134112i
$349$	32.5854	+	17.4172i	1.74425	+	0.932323i	0.942185	+	0.335092i	$0.108767\pi$
$349$	32.5854	+	17.4172i	1.74425	+	0.932323i	0.802069	+	0.597231i	$0.203733\pi$
$350$	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	−0.984689	−	0.174320i	$-0.944227\pi$
$353$	−15.2255	+	15.2255i	−0.810369	+	0.810369i	0.174320	+	0.984689i	$0.444227\pi$
$354$	−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	0.352753	−	0.935717i	$-0.385246\pi$
$359$	19.6434	−	3.90731i	1.03674	−	0.206220i	0.683984	+	0.729497i	$0.260246\pi$
$360$	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	−0.0440769	−	0.999028i	$-0.514035\pi$
$367$	−14.9745	−	6.20265i	−0.781663	−	0.323776i	−0.737587	+	0.675253i	$0.764035\pi$
$368$	−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	−0.214916	−	0.976632i	$-0.568948\pi$
$373$	9.22636	−	4.93159i	0.477723	−	0.255348i	0.692639	+	0.721284i	$0.256448\pi$
$374$	−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	0.947850	+	0.318717i	$0.103252\pi$
$379$	1.56505	+	15.8902i	0.0803913	+	0.816227i	−0.867458	+	0.497510i	$0.834248\pi$
$380$	−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	0.936996	+	0.349341i	$0.113594\pi$
$389$	1.69928	+	17.2531i	0.0861571	+	0.874768i	−0.850839	+	0.525427i	$0.823906\pi$
$390$	−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	−0.0847420	−	0.996403i	$-0.527007\pi$
$397$	−7.21767	−	0.710878i	−0.362244	−	0.0356780i	−0.277502	+	0.960725i	$0.589507\pi$
$398$	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	−0.217847	−	0.975983i	$-0.569903\pi$
$401$	−21.2668	−	8.80899i	−1.06201	−	0.439900i	−0.844165	+	0.536083i	$0.819903\pi$
$402$	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	−0.808386	−	0.588652i	$-0.799659\pi$
$409$	−26.8970	+	5.35014i	−1.32997	+	0.264548i	−0.521584	+	0.853200i	$0.674659\pi$
$410$	−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	0.892552	−	0.450945i	$-0.148913\pi$
$419$	20.7454	+	11.0887i	1.01348	+	0.541716i	0.120928	+	0.992661i	$0.461413\pi$
$420$	1.40109	−	2.72413i	0.0683660	−	0.132924i
$421$	−19.0562	+	23.2201i	−0.928744	+	1.13168i	0.0622891	+	0.998058i	$0.480160\pi$
$421$	−19.0562	+	23.2201i	−0.928744	+	1.13168i	−0.991033	+	0.133619i	$0.957340\pi$
$422$	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	0.687960	+	0.725748i	$0.258506\pi$
$431$	−6.47070	+	15.6217i	−0.311683	+	0.752469i	−0.999643	+	0.0267203i	$0.991494\pi$
$432$	−1.28175	−	3.78908i	−0.0616682	−	0.182302i
$433$	−0.102501	−	0.247460i	−0.00492590	−	0.0118922i	0.921397	−	0.388622i	$-0.127049\pi$
$433$	−0.102501	−	0.247460i	−0.00492590	−	0.0118922i	−0.926323	+	0.376729i	$0.877049\pi$
$434$	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	−0.999291	−	0.0376393i	$-0.988016\pi$
$439$	−13.6537	−	20.4341i	−0.651653	−	0.975268i	0.347638	−	0.937629i	$-0.386984\pi$
$440$	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	−0.430860	−	0.902419i	$-0.641790\pi$
$443$	−14.2573	+	1.40423i	−0.677387	+	0.0667168i	−0.246527	+	0.969136i	$0.579290\pi$
$444$	−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	$0.114294\pi$
$449$			14.8920i			0.702796i	−0.936226	+	0.351398i	$0.885706\pi$
$450$	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	0.970935	+	0.239343i	$0.0769322\pi$
$457$	17.5403	+	26.2509i	0.820499	+	1.22796i	−0.150436	+	0.988620i	$0.548068\pi$
$458$	−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	−0.614391	−	0.789002i	$-0.710598\pi$
$461$	3.05147	−	30.9821i	0.142121	−	1.44298i	0.756512	−	0.653980i	$-0.226902\pi$
$462$	−11.4485	+	0.653320i	−0.532634	+	0.0303952i
$463$	−3.53033	−	8.52297i	−0.164068	−	0.396096i	0.820368	−	0.571835i	$-0.193768\pi$
$463$	−3.53033	−	8.52297i	−0.164068	−	0.396096i	−0.984437	+	0.175739i	$0.943768\pi$
$464$	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	0.704618	−	0.709587i	$-0.251119\pi$
$467$	−2.78337	−	3.39155i	−0.128799	−	0.156942i	−0.833417	+	0.552645i	$0.813619\pi$
$468$	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	−0.956933	−	0.290309i	$-0.906242\pi$
$479$	−27.2972	−	27.2972i	−1.24724	−	1.24724i	−0.290309	−	0.956933i	$-0.593758\pi$
$480$	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	0.638205	−	0.769866i	$-0.279677\pi$
$487$	33.5974	−	6.68295i	1.52245	−	0.302833i	0.884240	+	0.467033i	$0.154677\pi$
$488$	−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	−0.712048	−	0.702131i	$-0.752232\pi$
$491$	−37.5405	−	11.3878i	−1.69418	−	0.513923i	−0.982129	+	0.188207i	$0.939732\pi$
$492$	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	−0.187230	−	0.982316i	$-0.559951\pi$
$499$	−12.5653	−	1.23758i	−0.562502	−	0.0554016i	−0.375272	+	0.926915i	$0.622451\pi$
$500$	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	0.600132	−	0.799901i	$-0.295115\pi$
$503$	35.1846	−	23.5096i	1.56880	−	1.04824i	0.968673	−	0.248341i	$-0.0798853\pi$
$504$	−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	−0.976139	−	0.217149i	$-0.930324\pi$
$509$	−6.43329	−	21.2077i	−0.285150	−	0.940015i	0.690988	−	0.722866i	$-0.257176\pi$
$510$	−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	−0.382129	−	0.924109i	$-0.624809\pi$
$521$	7.42745	−	4.96287i	0.325403	−	0.217427i	0.707531	+	0.706682i	$0.249809\pi$
$522$	0.159197	−	3.86458i	0.00696788	−	0.169148i
$523$	−31.5529	+	16.8654i	−1.37971	+	0.737471i	−0.983537	−	0.180705i	$-0.942162\pi$
$523$	−31.5529	+	16.8654i	−1.37971	+	0.737471i	−0.396173	+	0.918176i	$0.629662\pi$
$524$	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	0.493092	+	0.869977i	$0.335867\pi$
$541$	−11.7277	+	21.9411i	−0.504215	+	0.943320i	−0.997307	+	0.0733427i	$0.976633\pi$
$542$	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	0.953741	−	0.300629i	$-0.0971967\pi$
$547$	28.8526	+	15.4220i	1.23365	+	0.659398i	0.279906	+	0.960027i	$0.409697\pi$
$548$	−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	0.830631	−	0.556823i	$-0.187980\pi$
$557$	2.89015	+	3.52166i	0.122459	+	0.149217i	−0.708172	+	0.706040i	$0.750480\pi$
$558$	−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	0.624657	+	0.780899i	$0.285239\pi$
$563$	−3.33001	+	33.8102i	−0.140343	+	1.42493i	−0.765000	+	0.644030i	$0.777261\pi$
$564$	−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	0.874379	−	0.485243i	$-0.161269\pi$
$569$	18.1451	+	12.1242i	0.760683	+	0.508272i	−0.113696	+	0.993516i	$0.536269\pi$
$570$	−0.480432	+	0.658622i	−0.0201231	+	0.0275866i
$571$	11.5260	−	1.13522i	0.482350	−	0.0475073i	0.146080	−	0.989273i	$-0.453334\pi$
$571$	11.5260	−	1.13522i	0.482350	−	0.0475073i	0.336270	+	0.941766i	$0.390834\pi$
$572$	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	$0.0466507\pi$
$577$			7.01568i			0.292067i	−0.989280	+	0.146033i	$0.953349\pi$
$578$	−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	0.665409	−	0.746479i	$-0.268257\pi$
$587$	−7.87283	−	14.7290i	−0.324947	−	0.607932i	−0.990356	+	0.138546i	$0.955757\pi$
$588$	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	−0.391192	−	0.920309i	$-0.627937\pi$
$593$	13.0568	−	31.5220i	0.536180	−	1.29445i	0.927371	−	0.374143i	$-0.122063\pi$
$594$	−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	0.0649733	−	0.997887i	$-0.479304\pi$
$599$	−6.28685	−	1.25053i	−0.256874	−	0.0510954i	−0.321847	+	0.946792i	$0.604304\pi$
$600$	−0.975146	−	13.3643i	−0.0398102	−	0.545596i
$601$	−3.50430	−	17.6173i	−0.142943	−	0.718625i	−0.984069	−	0.177786i	$-0.943107\pi$
$601$	−3.50430	−	17.6173i	−0.142943	−	0.718625i	0.841126	−	0.540839i	$-0.181893\pi$
$602$	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	0.999187	−	0.0403228i	$-0.0128386\pi$
$607$	23.6239	+	23.6239i	0.958864	+	0.958864i	−0.0403228	+	0.999187i	$0.512839\pi$
$608$	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	0.151198	−	0.988504i	$-0.451687\pi$
$613$	−19.5301	−	16.0280i	−0.788815	−	0.647364i	−0.940013	+	0.341140i	$0.889187\pi$
$614$	−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	−0.637356	−	0.770569i	$-0.719972\pi$
$617$	6.11966	−	30.7656i	0.246368	−	1.23858i	0.883724	−	0.468008i	$-0.155028\pi$
$618$	1.79449	+	4.89280i	0.0721850	+	0.196817i
$619$	24.3993	+	7.40144i	0.980690	+	0.297489i	0.739625	−	0.673020i	$-0.235003\pi$
$619$	24.3993	+	7.40144i	0.980690	+	0.297489i	0.241066	+	0.970509i	$0.422503\pi$
$620$	−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	−0.539909	−	0.841723i	$-0.681541\pi$
$631$	0.781917	−	0.522460i	0.0311276	−	0.0207988i	0.571037	+	0.820925i	$0.306541\pi$
$632$	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	−0.850713	−	0.525631i	$-0.823829\pi$
$643$	−11.0405	−	36.3957i	−0.435396	−	1.43531i	0.415317	−	0.909677i	$-0.363671\pi$
$644$	−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	0.323276	+	0.946305i	$0.395216\pi$
$647$	−17.1620	+	25.6848i	−0.674708	+	1.00977i	−0.997984	+	0.0634675i	$0.979784\pi$
$648$	−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	−0.0579480	−	0.998320i	$-0.518456\pi$
$653$	−7.91007	−	0.779074i	−0.309545	−	0.0304875i	−0.251597	+	0.967832i	$0.580956\pi$
$654$	−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	−0.202218	+	0.979341i	$0.564815\pi$
$659$	−30.8615	+	25.3273i	−1.20219	+	0.986613i	−0.999974	+	0.00727271i	$0.997685\pi$
$660$	2.28566	−	1.58014i	0.0889693	−	0.0615070i
$661$	−46.3690	−	14.0659i	−1.80355	−	0.547100i	−0.804636	−	0.593769i	$-0.797639\pi$
$661$	−46.3690	−	14.0659i	−1.80355	−	0.547100i	−0.998910	+	0.0466691i	$0.985139\pi$
$662$	−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	0.295110	−	0.955463i	$-0.404644\pi$
$673$	−17.1310	−	17.1310i	−0.660353	−	0.660353i	−0.955463	+	0.295110i	$0.904644\pi$
$674$	−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	−0.777270	−	0.629168i	$-0.783396\pi$
$677$	−0.222557	+	0.271187i	−0.00855357	+	0.0104226i	0.768716	+	0.639590i	$0.220896\pi$
$678$	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	−0.996909	−	0.0785662i	$-0.974966\pi$
$683$	−3.25007	+	10.7140i	−0.124360	+	0.409961i	0.872549	+	0.488527i	$0.162466\pi$
$684$	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	−0.857437	−	0.514590i	$-0.827944\pi$
$691$	2.20589	−	22.3968i	0.0839160	−	0.852014i	0.941353	−	0.337424i	$-0.109556\pi$
$692$	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	0.114627	−	0.993409i	$-0.463433\pi$
$701$	20.1709	−	6.11877i	0.761843	−	0.231103i	0.647217	+	0.762306i	$0.275933\pi$
$702$	−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	0.393071	−	0.919508i	$-0.371413\pi$
$709$	25.5081	−	2.51233i	0.957976	−	0.0943524i	0.564905	+	0.825156i	$0.308913\pi$
$710$	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	0.794721	−	0.606975i	$-0.207617\pi$
$719$	−5.26705	−	12.7158i	−0.196428	−	0.474218i	−0.991149	+	0.132757i	$0.957617\pi$
$720$	−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	0.522266	−	0.852782i	$-0.325087\pi$
$727$	18.2925	+	3.63861i	0.678432	+	0.134949i	0.156166	+	0.987731i	$0.450087\pi$
$728$	−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	0.510582	−	0.859829i	$-0.329430\pi$
$733$	2.14762	+	1.14793i	0.0793242	+	0.0423997i	−0.431258	+	0.902229i	$0.641930\pi$
$734$	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	−0.989409	−	0.145157i	$-0.953631\pi$
$739$	−8.67266	+	16.2254i	−0.319029	+	0.596861i	0.670380	+	0.742018i	$0.266131\pi$
$740$	−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	0.102053	−	0.994779i	$-0.467459\pi$
$743$	15.7285	−	3.12859i	0.577022	−	0.114777i	0.474970	+	0.880002i	$0.342459\pi$
$744$	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	0.952687	−	0.303953i	$-0.0983066\pi$
$751$	38.6789	+	16.0213i	1.41141	+	0.584626i	0.458724	+	0.888579i	$0.348307\pi$
$752$	−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	−0.308416	−	0.951252i	$-0.599799\pi$
$757$	8.56154	−	4.57624i	0.311174	−	0.166326i	0.619590	+	0.784925i	$0.287299\pi$
$758$	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	0.378144	+	0.925747i	$0.376562\pi$
$761$	−17.1543	+	25.6733i	−0.621844	+	0.930655i	−0.999988	+	0.00490799i	$0.998438\pi$
$762$	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	0.994219	−	0.107371i	$-0.0342433\pi$
$773$	−0.0512533	−	0.520383i	−0.00184345	−	0.0187169i	−0.996062	+	0.0886544i	$0.971743\pi$
$774$	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	−0.0491124	−	0.998793i	$-0.515639\pi$
$787$	25.8347	−	21.2020i	0.920908	−	0.755770i	0.970020	+	0.243024i	$0.0781393\pi$
$788$	−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	−0.126867	−	0.991920i	$-0.540492\pi$
$797$	21.6919	−	40.5827i	0.768367	−	1.43751i	0.895235	−	0.445595i	$-0.147008\pi$
$798$	−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	0.148192	−	0.988959i	$-0.452655\pi$
$809$	−2.65529	−	0.528170i	−0.0933550	−	0.0185695i	−0.241547	+	0.970389i	$0.577655\pi$
$810$	−0.657361	−	0.304564i	−0.0230973	−	0.0107013i
$811$	−11.8501	+	39.0646i	−0.416114	+	1.37174i	0.459262	+	0.888301i	$0.348114\pi$
$811$	−11.8501	+	39.0646i	−0.416114	+	1.37174i	−0.875376	+	0.483443i	$0.839386\pi$
$812$	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	0.951831	−	0.306623i	$-0.0991990\pi$
$821$	4.81586	+	9.00983i	0.168075	+	0.314445i	−0.783757	+	0.621068i	$0.786699\pi$
$822$	1.31263	+	1.42543i	0.0457834	+	0.0497175i
$823$	−14.6622	−	21.9435i	−0.511092	−	0.764903i	0.482744	−	0.875761i	$-0.339640\pi$
$823$	−14.6622	−	21.9435i	−0.511092	−	0.764903i	−0.993836	+	0.110858i	$0.964640\pi$
$824$	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	0.614407	−	0.788989i	$-0.289395\pi$
$827$	39.4247	−	3.88300i	1.37093	−	0.135025i	0.756525	+	0.653964i	$0.226895\pi$
$828$	−0.0924646	−	0.807519i	−0.00321337	−	0.0280632i
$829$	16.0416	−	4.86616i	0.557147	−	0.169009i	0.000860943	−	1.00000i	$-0.499726\pi$
$829$	16.0416	−	4.86616i	0.557147	−	0.169009i	0.556286	+	0.830991i	$0.312226\pi$
$830$	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	0.731060	−	0.682313i	$-0.239026\pi$
$839$	11.0199	+	7.36327i	0.380449	+	0.254208i	−0.350611	+	0.936521i	$0.614026\pi$
$840$	−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	−0.937785	−	0.347218i	$-0.887127\pi$
$853$	1.01809	−	3.35618i	0.0348586	−	0.114913i	0.972643	+	0.232304i	$0.0746265\pi$
$854$	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	−0.941904	−	0.335884i	$-0.890965\pi$
$857$	−5.86180	−	29.4693i	−0.200235	−	1.00665i	0.741668	−	0.670767i	$-0.234035\pi$
$858$	−0.295603	−	0.484444i	−0.0100917	−	0.0165387i
$859$	27.2746	−	33.2342i	0.930598	−	1.13394i	−0.0601456	−	0.998190i	$-0.519157\pi$
$859$	27.2746	−	33.2342i	0.930598	−	1.13394i	0.990744	−	0.135747i	$-0.0433435\pi$
$860$	−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	0.469407	−	0.882982i	$-0.344468\pi$
$863$	−12.1495	−	12.1495i	−0.413575	−	0.413575i	−0.882982	+	0.469407i	$0.844468\pi$
$864$	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	−0.740579	−	0.671969i	$-0.765449\pi$
$877$	−6.69286	+	5.49269i	−0.226002	+	0.185475i	0.514577	+	0.857444i	$0.327949\pi$
$878$	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	−0.670929	−	0.741522i	$-0.734105\pi$
$881$	−18.4327	+	7.63506i	−0.621013	+	0.257232i	0.0499164	+	0.998753i	$0.484105\pi$
$882$	−2.04642	−	1.82547i	−0.0689065	−	0.0614666i
$883$	−11.9420	−	1.17618i	−0.401880	−	0.0395817i	−0.104942	−	0.994478i	$-0.533466\pi$
$883$	−11.9420	−	1.17618i	−0.401880	−	0.0395817i	−0.296938	+	0.954897i	$0.595966\pi$
$884$	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	−0.743520	−	0.668714i	$-0.766845\pi$
$887$	−12.2180	+	8.16383i	−0.410241	+	0.274115i	0.333278	+	0.942828i	$0.391845\pi$
$888$	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	−0.0514980	−	0.998673i	$-0.516400\pi$
$907$	22.5951	−	12.0773i	0.750258	−	0.401021i	0.801756	+	0.597652i	$0.203900\pi$
$908$	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	0.341506	−	0.939879i	$-0.389063\pi$
$911$	37.6555	−	15.5974i	1.24758	−	0.516766i	0.906077	+	0.423114i	$0.139063\pi$
$912$	−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	−0.993718	−	0.111914i	$-0.964302\pi$
$919$	−0.994780	+	5.00110i	−0.0328148	+	0.164971i	0.960903	+	0.276885i	$0.0893020\pi$
$920$	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	0.859169	−	0.511691i	$-0.170981\pi$
$929$	10.5910	+	10.5910i	0.347478	+	0.347478i	−0.511691	+	0.859169i	$0.670981\pi$
$930$	−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	−0.422518	−	0.906354i	$-0.638854\pi$
$937$	−35.4996	−	7.06131i	−1.15972	−	0.230683i	−0.737203	+	0.675671i	$0.763854\pi$
$938$	−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	0.932900	−	0.360137i	$-0.117270\pi$
$941$	12.1992	+	14.8648i	0.397683	+	0.484578i	−0.535216	+	0.844715i	$0.679770\pi$
$942$	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	0.957409	+	0.288734i	$0.0932344\pi$
$947$	−1.16732	+	11.8520i	−0.0379329	+	0.385139i	−0.995342	+	0.0964051i	$0.969266\pi$
$948$	−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	0.999817	+	0.0191476i	$0.00609525\pi$
$953$	43.2227	+	28.8805i	1.40012	+	0.935530i	0.400303	+	0.916383i	$0.368905\pi$
$954$	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	0.669449	−	0.742858i	$-0.266530\pi$
$967$	7.44218	+	4.97270i	0.239324	+	0.159911i	−0.430125	+	0.902770i	$0.641530\pi$
$968$	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	0.975170	−	0.221458i	$-0.0710814\pi$
$971$	7.76714	+	14.5313i	0.249259	+	0.466331i	−0.725911	+	0.687789i	$0.758581\pi$
$972$	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	−0.179214	−	0.983810i	$-0.557355\pi$
$977$	20.1035	−	48.5342i	0.643168	−	1.55275i	0.822382	−	0.568935i	$-0.192645\pi$
$978$	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	0.292004	−	0.956417i	$-0.405678\pi$
$983$	6.13810	+	1.22094i	0.195775	+	0.0389421i	−0.0962287	+	0.995359i	$0.530678\pi$
$984$	−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	−0.940272	−	0.340425i	$-0.889429\pi$
$991$	−40.3165	−	40.3165i	−1.28070	−	1.28070i	−0.340425	−	0.940272i	$-0.610571\pi$
$992$	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	0.360266	−	0.932849i	$-0.382686\pi$
$997$	−15.2943	−	12.5517i	−0.484374	−	0.397516i	−0.844641	+	0.535334i	$0.820186\pi$
$998$	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.13.1	✓	512
128.69	even	32	inner	384.2.v.a.325.1	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.1	✓	512	1.1	even	1	trivial
384.2.v.a.325.1	yes	512	128.69	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.40051 - 0.196427i) q^{2} +(0.290285 + 0.956940i) q^{3} +(1.92283 + 0.550195i) q^{4} +(0.0502132 + 0.509823i) q^{5} +(-0.218576 - 1.39722i) q^{6} +(-1.66106 + 2.48595i) q^{7} +(-2.58487 - 1.14825i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(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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