LMFDB - Embedded newform 384.2.v.a.205.3

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			205.3
Character	$\chi$	$=$	384.205
Dual form			384.2.v.a.133.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37277 + 0.339837i) q^{2} +(0.956940 - 0.290285i) q^{3} +(1.76902 - 0.933039i) q^{4} +(-1.86055 + 0.183248i) q^{5} +(-1.21501 + 0.723699i) q^{6} +(-2.89290 + 4.32953i) q^{7} +(-2.11139 + 1.88203i) q^{8} +(0.831470 - 0.555570i) q^{9} +O(q^{10})$	\(q+(-1.37277 + 0.339837i) q^{2} +(0.956940 - 0.290285i) q^{3} +(1.76902 - 0.933039i) q^{4} +(-1.86055 + 0.183248i) q^{5} +(-1.21501 + 0.723699i) q^{6} +(-2.89290 + 4.32953i) q^{7} +(-2.11139 + 1.88203i) q^{8} +(0.831470 - 0.555570i) q^{9} +(2.49184 - 0.883840i) q^{10} +(-2.66065 - 4.97772i) q^{11} +(1.42200 - 1.40638i) q^{12} +(0.437495 - 4.44197i) q^{13} +(2.49996 - 6.92658i) q^{14} +(-1.72724 + 0.715445i) q^{15} +(2.25888 - 3.30113i) q^{16} +(-2.49948 - 1.03532i) q^{17} +(-0.952617 + 1.04524i) q^{18} +(-1.16679 - 1.42174i) q^{19} +(-3.12037 + 2.06013i) q^{20} +(-1.51153 + 4.98286i) q^{21} +(5.34408 + 5.92911i) q^{22} +(-0.0337176 + 0.169510i) q^{23} +(-1.47415 + 2.41390i) q^{24} +(-1.47587 + 0.293569i) q^{25} +(0.908961 + 6.24650i) q^{26} +(0.634393 - 0.773010i) q^{27} +(-1.07798 + 10.3582i) q^{28} +(-7.60402 - 4.06443i) q^{29} +(2.12797 - 1.56912i) q^{30} +(-3.50040 + 3.50040i) q^{31} +(-1.97908 + 5.29936i) q^{32} +(-3.99104 - 3.99104i) q^{33} +(3.78307 + 0.571845i) q^{34} +(4.58899 - 8.58540i) q^{35} +(0.952519 - 1.75861i) q^{36} +(7.26929 + 5.96576i) q^{37} +(2.08490 + 1.55520i) q^{38} +(-0.870778 - 4.37769i) q^{39} +(3.58346 - 3.88851i) q^{40} +(4.23481 + 0.842356i) q^{41} +(0.381637 - 7.35402i) q^{42} +(-2.31910 - 0.703493i) q^{43} +(-9.35115 - 6.32321i) q^{44} +(-1.44518 + 1.18603i) q^{45} +(-0.0113190 - 0.244157i) q^{46} +(-1.11734 + 2.69751i) q^{47} +(1.20334 - 3.81470i) q^{48} +(-7.69716 - 18.5826i) q^{49} +(1.92627 - 0.904560i) q^{50} +(-2.69240 - 0.265178i) q^{51} +(-3.37059 - 8.26613i) q^{52} +(-4.51829 + 2.41507i) q^{53} +(-0.608182 + 1.27676i) q^{54} +(5.86242 + 8.77373i) q^{55} +(-2.04028 - 14.5858i) q^{56} +(-1.52925 - 1.02182i) q^{57} +(11.8199 + 2.99543i) q^{58} +(1.36261 + 13.8348i) q^{59} +(-2.38798 + 2.87722i) q^{60} +(-1.33545 - 4.40238i) q^{61} +(3.61570 - 5.99483i) q^{62} +5.20708i q^{63} +(0.915916 - 7.94740i) q^{64} +8.34465i q^{65} +(6.83510 + 4.12250i) q^{66} +(1.08137 + 3.56479i) q^{67} +(-5.38764 + 0.500612i) q^{68} +(0.0169404 + 0.171998i) q^{69} +(-3.38202 + 13.3453i) q^{70} +(2.70548 + 1.80775i) q^{71} +(-0.709954 + 2.73788i) q^{72} +(-4.12329 - 6.17093i) q^{73} +(-12.0065 - 5.71927i) q^{74} +(-1.32710 + 0.709351i) q^{75} +(-3.39061 - 1.42642i) q^{76} +(29.2482 + 2.88069i) q^{77} +(2.68308 + 5.71367i) q^{78} +(0.120031 + 0.289780i) q^{79} +(-3.59782 + 6.55585i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-6.09970 + 0.282779i) q^{82} +(-2.32164 + 1.90532i) q^{83} +(1.97527 + 10.2251i) q^{84} +(4.84013 + 1.46824i) q^{85} +(3.42268 + 0.177620i) q^{86} +(-8.45644 - 1.68209i) q^{87} +(14.9859 + 5.50248i) q^{88} +(-0.508114 - 2.55446i) q^{89} +(1.58085 - 2.11928i) q^{90} +(17.9660 + 14.7443i) q^{91} +(0.0985120 + 0.331326i) q^{92} +(-2.33356 + 4.36579i) q^{93} +(0.617150 - 4.08279i) q^{94} +(2.43139 + 2.43139i) q^{95} +(-0.355540 + 5.64567i) q^{96} +(2.97039 - 2.97039i) q^{97} +(16.8815 + 22.8939i) q^{98} +(-4.97772 - 2.66065i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{31}{32}\right)$	$1$

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 $

$2$	−1.37277	+	0.339837i	−0.970698	+	0.240301i
$2$	−1.37277	+	0.339837i	−0.970698	+	0.240301i
$3$	0.956940	−	0.290285i	0.552490	−	0.167596i
$3$	0.956940	−	0.290285i	0.552490	−	0.167596i
$4$	1.76902	−	0.933039i	0.884511	−	0.466519i
$5$	−1.86055	+	0.183248i	−0.832062	+	0.0819509i	−0.505072	−	0.863077i	$-0.668534\pi$
$5$	−1.86055	+	0.183248i	−0.832062	+	0.0819509i	−0.326989	+	0.945028i	$0.606034\pi$
$6$	−1.21501	+	0.723699i	−0.496027	+	0.295449i
$7$	−2.89290	+	4.32953i	−1.09341	+	1.63641i	−0.398772	+	0.917050i	$0.630564\pi$
$7$	−2.89290	+	4.32953i	−1.09341	+	1.63641i	−0.694640	+	0.719357i	$0.744436\pi$
$8$	−2.11139	+	1.88203i	−0.746488	+	0.665399i
$9$	0.831470	−	0.555570i	0.277157	−	0.185190i
$10$	2.49184	−	0.883840i	0.787988	−	0.279495i
$11$	−2.66065	−	4.97772i	−0.802216	−	1.50084i	−0.864417	−	0.502776i	$-0.832312\pi$
$11$	−2.66065	−	4.97772i	−0.802216	−	1.50084i	0.0622010	−	0.998064i	$-0.480188\pi$
$12$	1.42200	−	1.40638i	0.410496	−	0.405988i
$13$	0.437495	−	4.44197i	0.121339	−	1.23198i	−0.720963	−	0.692974i	$-0.756300\pi$
$13$	0.437495	−	4.44197i	0.121339	−	1.23198i	0.842302	−	0.539006i	$-0.181200\pi$
$14$	2.49996	−	6.92658i	0.668144	−	1.85121i
$15$	−1.72724	+	0.715445i	−0.445971	+	0.184727i
$16$	2.25888	−	3.30113i	0.564719	−	0.825283i
$17$	−2.49948	−	1.03532i	−0.606214	−	0.251102i	0.0583947	−	0.998294i	$-0.481402\pi$
$17$	−2.49948	−	1.03532i	−0.606214	−	0.251102i	−0.664609	+	0.747191i	$0.731402\pi$
$18$	−0.952617	+	1.04524i	−0.224534	+	0.246365i
$19$	−1.16679	−	1.42174i	−0.267680	−	0.326168i	0.621772	−	0.783199i	$-0.286413\pi$
$19$	−1.16679	−	1.42174i	−0.267680	−	0.326168i	−0.889451	+	0.457030i	$0.848913\pi$
$20$	−3.12037	+	2.06013i	−0.697736	+	0.460660i
$21$	−1.51153	+	4.98286i	−0.329844	+	1.08735i
$22$	5.34408	+	5.92911i	1.13936	+	1.26409i
$23$	−0.0337176	+	0.169510i	−0.00703060	+	0.0353452i	−0.984141	−	0.177386i	$-0.943236\pi$
$23$	−0.0337176	+	0.169510i	−0.00703060	+	0.0353452i	0.977111	+	0.212731i	$0.0682359\pi$
$24$	−1.47415	+	2.41390i	−0.300909	+	0.492734i
$25$	−1.47587	+	0.293569i	−0.295174	+	0.0587138i
$26$	0.908961	+	6.24650i	0.178262	+	1.22504i
$27$	0.634393	−	0.773010i	0.122089	−	0.148766i
$28$	−1.07798	+	10.3582i	−0.203719	+	1.95752i
$29$	−7.60402	−	4.06443i	−1.41203	−	0.754747i	−0.423519	−	0.905887i	$-0.639205\pi$
$29$	−7.60402	−	4.06443i	−1.41203	−	0.754747i	−0.988512	+	0.151140i	$0.951705\pi$
$30$	2.12797	−	1.56912i	0.388513	−	0.286482i
$31$	−3.50040	+	3.50040i	−0.628691	+	0.628691i	−0.947739	−	0.319048i	$-0.896637\pi$
$31$	−3.50040	+	3.50040i	−0.628691	+	0.628691i	0.319048	+	0.947739i	$0.396637\pi$
$32$	−1.97908	+	5.29936i	−0.349856	+	0.936804i
$33$	−3.99104	−	3.99104i	−0.694751	−	0.694751i
$34$	3.78307	+	0.571845i	0.648791	+	0.0980706i
$35$	4.58899	−	8.58540i	0.775682	−	1.45120i
$36$	0.952519	−	1.75861i	0.158753	−	0.293102i
$37$	7.26929	+	5.96576i	1.19506	+	0.980764i	1.00000		2.61897e-5i	$-8.33643e-6\pi$
$37$	7.26929	+	5.96576i	1.19506	+	0.980764i	0.195065	+	0.980790i	$0.437508\pi$
$38$	2.08490	+	1.55520i	0.338215	+	0.252288i
$39$	−0.870778	−	4.37769i	−0.139436	−	0.700992i
$40$	3.58346	−	3.88851i	0.566594	−	0.614828i
$41$	4.23481	+	0.842356i	0.661366	+	0.131554i	0.514350	−	0.857580i	$-0.328033\pi$
$41$	4.23481	+	0.842356i	0.661366	+	0.131554i	0.147016	+	0.989134i	$0.453033\pi$
$42$	0.381637	−	7.35402i	0.0588878	−	1.13475i
$43$	−2.31910	−	0.703493i	−0.353660	−	0.107282i	0.108456	−	0.994101i	$-0.465409\pi$
$43$	−2.31910	−	0.703493i	−0.353660	−	0.107282i	−0.462116	+	0.886820i	$0.652909\pi$
$44$	−9.35115	−	6.32321i	−1.40974	−	0.953260i
$45$	−1.44518	+	1.18603i	−0.215435	+	0.176803i
$46$	−0.0113190	−	0.244157i	−0.00166890	−	0.0359990i
$47$	−1.11734	+	2.69751i	−0.162981	+	0.393472i	−0.984180	−	0.177170i	$-0.943306\pi$
$47$	−1.11734	+	2.69751i	−0.162981	+	0.393472i	0.821199	+	0.570642i	$0.193306\pi$
$48$	1.20334	−	3.81470i	0.173687	−	0.550605i
$49$	−7.69716	−	18.5826i	−1.09959	−	2.65466i
$50$	1.92627	−	0.904560i	0.272416	−	0.127924i
$51$	−2.69240	−	0.265178i	−0.377011	−	0.0371323i
$52$	−3.37059	−	8.26613i	−0.467416	−	1.14631i
$53$	−4.51829	+	2.41507i	−0.620634	+	0.331736i	−0.751568	−	0.659655i	$-0.770702\pi$
$53$	−4.51829	+	2.41507i	−0.620634	+	0.331736i	0.130934	+	0.991391i	$0.458202\pi$
$54$	−0.608182	+	1.27676i	−0.0827631	+	0.173745i
$55$	5.86242	+	8.77373i	0.790488	+	1.18305i
$56$	−2.04028	−	14.5858i	−0.272644	−	1.94911i
$57$	−1.52925	−	1.02182i	−0.202555	−	0.135343i
$58$	11.8199	+	2.99543i	1.55202	+	0.393319i
$59$	1.36261	+	13.8348i	0.177397	+	1.80114i	0.512217	+	0.858856i	$0.328824\pi$
$59$	1.36261	+	13.8348i	0.177397	+	1.80114i	−0.334820	+	0.942282i	$0.608676\pi$
$60$	−2.38798	+	2.87722i	−0.308287	+	0.371447i
$61$	−1.33545	−	4.40238i	−0.170986	−	0.563667i	−0.999990	−	0.00442367i	$-0.998592\pi$
$61$	−1.33545	−	4.40238i	−0.170986	−	0.563667i	0.829004	−	0.559243i	$-0.188908\pi$
$62$	3.61570	−	5.99483i	0.459194	−	0.761344i
$63$			5.20708i			0.656030i
$64$	0.915916	−	7.94740i	0.114490	−	0.993424i
$65$			8.34465i			1.03503i
$66$	6.83510	+	4.12250i	0.841343	+	0.507444i
$67$	1.08137	+	3.56479i	0.132110	+	0.435508i	0.997891	−	0.0649153i	$-0.0206777\pi$
$67$	1.08137	+	3.56479i	0.132110	+	0.435508i	−0.865781	+	0.500423i	$0.833178\pi$
$68$	−5.38764	+	0.500612i	−0.653347	+	0.0607081i
$69$	0.0169404	+	0.171998i	0.00203938	+	0.0207062i
$70$	−3.38202	+	13.3453i	−0.404229	+	1.59507i
$71$	2.70548	+	1.80775i	0.321082	+	0.214540i	0.705657	−	0.708554i	$-0.250652\pi$
$71$	2.70548	+	1.80775i	0.321082	+	0.214540i	−0.384575	+	0.923094i	$0.625652\pi$
$72$	−0.709954	+	2.73788i	−0.0836689	+	0.322662i
$73$	−4.12329	−	6.17093i	−0.482594	−	0.722253i	0.507655	−	0.861560i	$-0.330512\pi$
$73$	−4.12329	−	6.17093i	−0.482594	−	0.722253i	−0.990249	+	0.139307i	$0.955512\pi$
$74$	−12.0065	−	5.71927i	−1.39573	−	0.664851i
$75$	−1.32710	+	0.709351i	−0.153241	+	0.0819088i
$76$	−3.39061	−	1.42642i	−0.388929	−	0.163622i
$77$	29.2482	+	2.88069i	3.33314	+	0.328285i
$78$	2.68308	+	5.71367i	0.303799	+	0.646945i
$79$	0.120031	+	0.289780i	0.0135045	+	0.0326028i	0.930488	−	0.366322i	$-0.119383\pi$
$79$	0.120031	+	0.289780i	0.0135045	+	0.0326028i	−0.916983	+	0.398925i	$0.869383\pi$
$80$	−3.59782	+	6.55585i	−0.402248	+	0.732966i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−6.09970	+	0.282779i	−0.673599	+	0.0312277i
$83$	−2.32164	+	1.90532i	−0.254833	+	0.209136i	−0.753133	−	0.657869i	$-0.771458\pi$
$83$	−2.32164	+	1.90532i	−0.254833	+	0.209136i	0.498299	+	0.867005i	$0.333958\pi$
$84$	1.97527	+	10.2251i	0.215519	+	1.11565i
$85$	4.84013	+	1.46824i	0.524986	+	0.159253i
$86$	3.42268	+	0.177620i	0.369077	+	0.0191532i
$87$	−8.45644	−	1.68209i	−0.906625	−	0.180339i
$88$	14.9859	+	5.50248i	1.59750	+	0.586566i
$89$	−0.508114	−	2.55446i	−0.0538600	−	0.270773i	0.944466	−	0.328609i	$-0.106580\pi$
$89$	−0.508114	−	2.55446i	−0.0538600	−	0.270773i	−0.998326	+	0.0578364i	$0.981580\pi$
$90$	1.58085	−	2.11928i	0.166636	−	0.223391i
$91$	17.9660	+	14.7443i	1.88335	+	1.54562i
$92$	0.0985120	+	0.331326i	0.0102706	+	0.0345431i
$93$	−2.33356	+	4.36579i	−0.241979	+	0.452711i
$94$	0.617150	−	4.08279i	0.0636542	−	0.421107i
$95$	2.43139	+	2.43139i	0.249456	+	0.249456i
$96$	−0.355540	+	5.64567i	−0.0362872	+	0.576209i
$97$	2.97039	−	2.97039i	0.301597	−	0.301597i	−0.540041	−	0.841639i	$-0.681591\pi$
$97$	2.97039	−	2.97039i	0.301597	−	0.301597i	0.841639	+	0.540041i	$0.181591\pi$
$98$	16.8815	+	22.8939i	1.70529	+	2.31264i
$99$	−4.97772	−	2.66065i	−0.500280	−	0.267405i
$100$	−2.33694	+	1.89638i	−0.233694	+	0.189638i
$101$	5.23777	−	6.38224i	0.521177	−	0.635056i	−0.444196	−	0.895930i	$-0.646511\pi$
$101$	5.23777	−	6.38224i	0.521177	−	0.635056i	0.965373	+	0.260874i	$0.0840106\pi$
$102$	3.78617	−	0.550946i	0.374887	−	0.0545518i
$103$	−2.55075	+	0.507375i	−0.251333	+	0.0499932i	−0.319149	−	0.947705i	$-0.603397\pi$
$103$	−2.55075	+	0.507375i	−0.251333	+	0.0499932i	0.0678160	+	0.997698i	$0.478397\pi$
$104$	7.43620	+	10.2021i	0.729179	+	1.00040i
$105$	1.89918	−	9.54783i	0.185341	−	0.931773i
$106$	5.38186	−	4.85083i	0.522732	−	0.471155i
$107$	−1.69487	+	5.58724i	−0.163849	+	0.540139i	−0.999965	−	0.00841476i	$-0.997321\pi$
$107$	−1.69487	+	5.58724i	−0.163849	+	0.540139i	0.836115	+	0.548554i	$0.184821\pi$
$108$	0.401007	−	1.95939i	0.0385869	−	0.188542i
$109$	−10.3683	−	12.6338i	−0.993100	−	1.21010i	−0.977655	−	0.210215i	$-0.932584\pi$
$109$	−10.3683	−	12.6338i	−0.993100	−	1.21010i	−0.0154446	−	0.999881i	$-0.504916\pi$
$110$	−11.0294	−	10.0521i	−1.05161	−	0.958429i
$111$	8.68805	+	3.59871i	0.824633	+	0.341574i
$112$	7.75765	+	19.3297i	0.733029	+	1.82649i
$113$	15.0858	−	6.24874i	1.41915	−	0.587832i	0.464505	−	0.885571i	$-0.346232\pi$
$113$	15.0858	−	6.24874i	1.41915	−	0.587832i	0.954648	+	0.297738i	$0.0962323\pi$
$114$	2.44657	+	0.883025i	0.229143	+	0.0827029i
$115$	0.0316708	−	0.321559i	0.00295332	−	0.0299856i
$116$	−17.2440	−	0.0952242i	−1.60106	−	0.00884134i
$117$	−2.10406	−	3.93642i	−0.194520	−	0.363922i
$118$	−6.57213	−	18.5290i	−0.605014	−	1.70573i
$119$	11.7132	−	7.82651i	1.07375	−	0.717455i
$120$	2.30038	−	4.76130i	0.209995	−	0.434645i
$121$	−11.5874	+	17.3418i	−1.05340	+	1.57652i
$122$	3.32936	+	5.58964i	0.301426	+	0.506062i
$123$	4.29698	−	0.423216i	0.387446	−	0.0381601i
$124$	−2.92628	+	9.45830i	−0.262787	+	0.849380i
$125$	11.6374	−	3.53016i	1.04088	−	0.315747i
$126$	−1.76956	−	7.14815i	−0.157645	−	0.636807i
$127$	−4.48530			−0.398006			−0.199003	−	0.979999i	$-0.563770\pi$
$127$	−4.48530			−0.398006			−0.199003	+	0.979999i	$0.563770\pi$
$128$	1.44347	+	11.2212i	0.127586	+	0.991828i
$129$	−2.42346			−0.213374
$130$	−2.83582	−	11.4553i	−0.248718	−	1.00470i
$131$	−5.51294	+	1.67233i	−0.481668	+	0.146112i	−0.521775	−	0.853083i	$-0.674730\pi$
$131$	−5.51294	+	1.67233i	−0.481668	+	0.146112i	0.0401072	+	0.999195i	$0.487230\pi$
$132$	−10.7840	−	3.33644i	−0.938629	−	0.290400i
$133$	9.53084	−	0.938706i	0.826429	−	0.0813961i
$134$	−2.69592	−	4.52616i	−0.232892	−	0.391001i
$135$	−1.03867	+	1.55447i	−0.0893941	+	0.133788i
$136$	7.22589	−	2.51815i	0.619615	−	0.215929i
$137$	−11.4469	+	7.64860i	−0.977979	+	0.653464i	−0.938327	−	0.345749i	$-0.887625\pi$
$137$	−11.4469	+	7.64860i	−0.977979	+	0.653464i	−0.0396516	+	0.999214i	$0.512625\pi$
$138$	−0.0817067	−	0.230358i	−0.00695533	−	0.0196094i
$139$	−4.90566	−	9.17784i	−0.416092	−	0.778454i	0.583337	−	0.812230i	$-0.301747\pi$
$139$	−4.90566	−	9.17784i	−0.416092	−	0.778454i	−0.999429	+	0.0337761i	$0.989247\pi$
$140$	0.107514	−	19.4695i	0.00908658	−	1.64547i
$141$	−0.286187	+	2.90570i	−0.0241013	+	0.244704i
$142$	−4.32836	−	1.56221i	−0.363228	−	0.131097i
$143$	−23.2749	+	9.64078i	−1.94634	+	0.806202i
$144$	0.0441761	−	3.99976i	0.00368134	−	0.333313i
$145$	14.8924	+	6.16865i	1.23675	+	0.512279i
$146$	7.75746	+	7.07006i	0.642012	+	0.585122i
$147$	−12.7600	−	15.5481i	−1.05242	−	1.28238i
$148$	18.4258	+	3.77102i	1.51459	+	0.309976i
$149$	−0.145001	+	0.478005i	−0.0118790	+	0.0391597i	−0.962679	−	0.270644i	$-0.912763\pi$
$149$	−0.145001	+	0.478005i	−0.0118790	+	0.0391597i	0.950801	+	0.309804i	$0.100263\pi$
$150$	1.58075	−	1.42478i	0.129068	−	0.116333i
$151$	−3.34620	+	16.8225i	−0.272310	+	1.36899i	0.566272	+	0.824219i	$0.308385\pi$
$151$	−3.34620	+	16.8225i	−0.272310	+	1.36899i	−0.838582	+	0.544776i	$0.816615\pi$
$152$	5.13929	+	0.805903i	0.416852	+	0.0653674i
$153$	−2.65344	+	0.527802i	−0.214518	+	0.0426702i
$154$	−41.1301	+	5.98506i	−3.31436	+	0.482290i
$155$	5.87122	−	7.15410i	0.471588	−	0.574631i
$156$	−5.62498	−	6.93177i	−0.450359	−	0.554986i
$157$	6.24095	+	3.33586i	0.498082	+	0.266231i	0.701253	−	0.712913i	$-0.252625\pi$
$157$	6.24095	+	3.33586i	0.498082	+	0.266231i	−0.203170	+	0.979143i	$0.565125\pi$
$158$	−0.263254	−	0.357012i	−0.0209433	−	0.0284024i
$159$	−3.62267	+	3.62267i	−0.287297	+	0.287297i
$160$	2.71108	−	10.2224i	0.214330	−	0.808150i
$161$	−0.636355	−	0.636355i	−0.0501518	−	0.0501518i
$162$	−0.211370	+	1.39833i	−0.0166068	+	0.109863i
$163$	4.73698	−	8.86226i	0.371029	−	0.694146i	−0.625242	−	0.780431i	$-0.715000\pi$
$163$	4.73698	−	8.86226i	0.371029	−	0.694146i	0.996270	+	0.0862854i	$0.0274997\pi$
$164$	8.27742	−	2.46110i	0.646358	−	0.192179i
$165$	8.15686	+	6.69416i	0.635011	+	0.521140i
$166$	2.53959	−	3.40456i	0.197111	−	0.264245i
$167$	−1.63005	−	8.19482i	−0.126137	−	0.634134i	−0.991189	−	0.132453i	$-0.957715\pi$
$167$	−1.63005	−	8.19482i	−0.126137	−	0.634134i	0.865052	−	0.501682i	$-0.167285\pi$
$168$	−6.18647	−	13.3655i	−0.477296	−	1.03117i
$169$	−6.78945	−	1.35050i	−0.522265	−	0.103885i
$170$	−7.14337	−	0.370705i	−0.547871	−	0.0284318i
$171$	−1.76002	−	0.533897i	−0.134592	−	0.0408281i
$172$	−4.75893	+	0.919321i	−0.362865	+	0.0700976i
$173$	−1.31354	+	1.07799i	−0.0998664	+	0.0819582i	−0.683002	−	0.730417i	$-0.739326\pi$
$173$	−1.31354	+	1.07799i	−0.0998664	+	0.0819582i	0.583135	+	0.812375i	$0.301826\pi$
$174$	12.1804	−	0.564678i	0.923396	−	0.0428082i
$175$	2.99853	−	7.23909i	0.226668	−	0.547224i
$176$	−22.4422	−	2.46091i	−1.69164	−	0.185498i
$177$	5.31997	+	12.8435i	0.399873	+	0.965379i
$178$	1.56563	+	3.33403i	0.117349	+	0.249896i
$179$	12.6999	+	1.25084i	0.949238	+	0.0934918i	0.560771	−	0.827971i	$-0.310505\pi$
$179$	12.6999	+	1.25084i	0.949238	+	0.0934918i	0.388467	+	0.921463i	$0.373005\pi$
$180$	−1.44995	+	3.44652i	−0.108073	+	0.256889i
$181$	−19.9819	+	10.6805i	−1.48524	+	0.793878i	−0.996893	−	0.0787698i	$-0.974901\pi$
$181$	−19.9819	+	10.6805i	−1.48524	+	0.793878i	−0.488349	+	0.872648i	$0.662401\pi$
$182$	−29.6739	−	14.1351i	−2.19958	−	1.04776i
$183$	−2.55589	−	3.82515i	−0.188936	−	0.282763i
$184$	−0.247832	−	0.421358i	−0.0182704	−	0.0310629i
$185$	−14.6181	−	9.76748i	−1.07474	−	0.718120i
$186$	1.71980	−	6.78628i	0.126102	−	0.497594i
$187$	1.49671	+	15.1964i	0.109450	+	1.11127i
$188$	0.540274	+	5.81448i	0.0394035	+	0.424064i
$189$	1.51153	+	4.98286i	0.109948	+	0.362450i
$190$	−4.16403	−	2.51148i	−0.302091	−	0.182202i
$191$		−	3.68369i		−	0.266543i	−0.991080	−	0.133271i	$-0.957452\pi$
$191$		−	3.68369i		−	0.266543i	0.991080	−	0.133271i	$-0.0425482\pi$
$192$	−1.43053	−	7.87106i	−0.103240	−	0.568045i
$193$		−	12.5724i		−	0.904979i	−0.891770	−	0.452489i	$-0.850536\pi$
$193$		−	12.5724i		−	0.904979i	0.891770	−	0.452489i	$-0.149464\pi$
$194$	−3.06823	+	5.08713i	−0.220286	+	0.365234i
$195$	2.42233	+	7.98534i	0.173466	+	0.571842i
$196$	−30.9547	−	25.6913i	−2.21105	−	1.83509i
$197$	−2.04664	−	20.7799i	−0.145817	−	1.48051i	−0.738053	−	0.674743i	$-0.764254\pi$
$197$	−2.04664	−	20.7799i	−0.145817	−	1.48051i	0.592235	−	0.805765i	$-0.298246\pi$
$198$	7.73748	+	1.96086i	0.549879	+	0.139352i
$199$	5.98478	+	3.99891i	0.424250	+	0.283475i	0.749311	−	0.662218i	$-0.230385\pi$
$199$	5.98478	+	3.99891i	0.424250	+	0.283475i	−0.325061	+	0.945693i	$0.605385\pi$
$200$	2.56363	−	3.39748i	0.181276	−	0.240238i
$201$	2.06961	+	3.09738i	0.145979	+	0.218473i
$202$	−5.02135	+	10.5414i	−0.353301	+	0.741687i
$203$	39.5947	−	21.1638i	2.77901	−	1.48541i
$204$	−5.01033	+	2.04300i	−0.350793	+	0.143039i
$205$	−8.03342	−	0.791223i	−0.561078	−	0.0552614i
$206$	3.32918	−	1.56335i	0.231955	−	0.108924i
$207$	0.0661394	+	0.159675i	0.00459701	+	0.0110982i
$208$	−13.6753	−	11.4781i	−0.948209	−	0.795862i
$209$	−3.97259	+	9.59068i	−0.274790	+	0.663401i
$210$	0.637556	+	13.7524i	0.0439956	+	0.949009i
$211$	13.9105	−	11.4160i	0.957635	−	0.785911i	−0.0192196	−	0.999815i	$-0.506118\pi$
$211$	13.9105	−	11.4160i	0.957635	−	0.785911i	0.976855	+	0.213905i	$0.0686182\pi$
$212$	−5.73959	+	8.48806i	−0.394197	+	0.582962i
$213$	3.11375	+	0.944545i	0.213350	+	0.0647192i
$214$	0.427926	−	8.24601i	0.0292524	−	0.563685i
$215$	4.44372	+	0.883910i	0.303059	+	0.0602822i
$216$	0.115380	+	2.82607i	0.00785059	+	0.192290i
$217$	−5.02878	−	25.2814i	−0.341376	−	1.71621i
$218$	18.5267	+	13.8198i	1.25479	+	0.935995i
$219$	−5.73707	−	4.70829i	−0.387675	−	0.318157i
$220$	18.5570	+	10.0511i	1.25111	+	0.677642i
$221$	−5.69237	+	10.6497i	−0.382910	+	0.716375i
$222$	−13.1497	−	1.98770i	−0.882551	−	0.133405i
$223$	−15.2283	−	15.2283i	−1.01976	−	1.01976i	−0.999801	−	0.0199597i	$-0.993646\pi$
$223$	−15.2283	−	15.2283i	−1.01976	−	1.01976i	−0.0199597	−	0.999801i	$-0.506354\pi$
$224$	−17.2184	−	23.8990i	−1.15046	−	1.59682i
$225$	−1.06404	+	1.06404i	−0.0709363	+	0.0709363i
$226$	−18.5859	+	13.7048i	−1.23631	+	0.911631i
$227$	−2.84630	−	1.52138i	−0.188915	−	0.100977i	0.374228	−	0.927337i	$-0.377908\pi$
$227$	−2.84630	−	1.52138i	−0.188915	−	0.100977i	−0.563143	+	0.826360i	$0.690408\pi$
$228$	−3.65868	−	0.380759i	−0.242302	−	0.0252164i
$229$	−7.90465	+	9.63184i	−0.522354	+	0.636490i	−0.965638	−	0.259891i	$-0.916313\pi$
$229$	−7.90465	+	9.63184i	−0.522354	+	0.636490i	0.443284	+	0.896381i	$0.353813\pi$
$230$	0.0658008	+	0.452191i	0.00433878	+	0.0298166i
$231$	28.8250	−	5.73364i	1.89654	−	0.377246i
$232$	23.7044	−	5.72941i	1.55627	−	0.376154i
$233$	−3.19287	+	16.0517i	−0.209172	+	1.05158i	0.723354	+	0.690477i	$0.242599\pi$
$233$	−3.19287	+	16.0517i	−0.209172	+	1.05158i	−0.932526	+	0.361102i	$0.882401\pi$
$234$	4.22614	+	4.68878i	0.276271	+	0.306515i
$235$	1.58456	−	5.22359i	0.103365	−	0.340750i
$236$	15.3189	+	23.2027i	0.997175	+	1.51037i
$237$	0.198981	+	0.242459i	0.0129252	+	0.0157494i
$238$	−13.4199	+	14.7246i	−0.869880	+	0.954455i
$239$	2.43846	+	1.01004i	0.157731	+	0.0653343i	0.460152	−	0.887840i	$-0.347795\pi$
$239$	2.43846	+	1.01004i	0.157731	+	0.0653343i	−0.302421	+	0.953174i	$0.597795\pi$
$240$	−1.53984	+	7.31795i	−0.0993961	+	0.472371i
$241$	3.25803	−	1.34952i	0.209868	−	0.0869302i	−0.275273	−	0.961366i	$-0.588768\pi$
$241$	3.25803	−	1.34952i	0.209868	−	0.0869302i	0.485141	+	0.874436i	$0.338768\pi$
$242$	10.0135	−	27.7442i	0.643694	−	1.78346i
$243$	0.0980171	−	0.995185i	0.00628780	−	0.0638411i
$244$	−6.47002	−	6.54188i	−0.414201	−	0.418801i
$245$	17.7262	+	33.1633i	1.13248	+	2.11873i
$246$	−5.75496	+	2.04125i	−0.366923	+	0.130146i
$247$	−6.82576	+	4.56083i	−0.434313	+	0.290199i
$248$	0.802840	−	13.9786i	0.0509804	−	0.887640i
$249$	−1.66859	+	2.49722i	−0.105742	+	0.158255i
$250$	−14.7758	+	8.80092i	−0.934504	+	0.556619i
$251$	15.3624	−	1.51307i	0.969667	−	0.0955039i	0.399235	−	0.916849i	$-0.369276\pi$
$251$	15.3624	−	1.51307i	0.969667	−	0.0955039i	0.570432	+	0.821345i	$0.306776\pi$
$252$	4.85841	+	9.21143i	0.306051	+	0.580266i
$253$	0.933483	−	0.283169i	0.0586876	−	0.0178027i
$254$	6.15731	−	1.52427i	0.386344	−	0.0956413i
$255$	5.05792			0.316739
$256$	−5.79495	−	14.9137i	−0.362185	−	0.932106i
$257$	6.42102			0.400532			0.200266	−	0.979742i	$-0.435819\pi$
$257$	6.42102			0.400532			0.200266	+	0.979742i	$0.435819\pi$
$258$	3.32686	−	0.823580i	0.207121	−	0.0512739i
$259$	−46.8582	+	14.2143i	−2.91163	+	0.883233i
$260$	7.78589	+	14.7619i	0.482860	+	0.915493i
$261$	−8.58059	+	0.845115i	−0.531125	+	0.0523113i
$262$	6.99971	−	4.16924i	0.432444	−	0.257576i
$263$	−9.49372	+	14.2084i	−0.585408	+	0.876125i	−0.999417	−	0.0341482i	$-0.989128\pi$
$263$	−9.49372	+	14.2084i	−0.585408	+	0.876125i	0.414009	+	0.910273i	$0.364128\pi$
$264$	15.9379	+	0.915370i	0.980909	+	0.0563371i
$265$	7.96393	−	5.32132i	0.489220	−	0.326886i
$266$	−12.7647	+	4.52756i	−0.782653	+	0.277603i
$267$	−1.22776	−	2.29697i	−0.0751375	−	0.140572i
$268$	5.23904	+	5.29723i	0.320026	+	0.323580i
$269$	0.922757	−	9.36891i	0.0562615	−	0.571232i	−0.925188	−	0.379510i	$-0.876093\pi$
$269$	0.922757	−	9.36891i	0.0562615	−	0.571232i	0.981449	−	0.191723i	$-0.0614074\pi$
$270$	0.897587	−	2.48692i	0.0546254	−	0.151349i
$271$	8.86701	−	3.67284i	0.538633	−	0.223109i	−0.0967468	−	0.995309i	$-0.530844\pi$
$271$	8.86701	−	3.67284i	0.538633	−	0.223109i	0.635379	+	0.772200i	$0.280844\pi$
$272$	−9.06376	+	5.91247i	−0.549571	+	0.358496i
$273$	21.4724	+	8.89417i	1.29957	+	0.538299i
$274$	13.1148	−	14.3899i	0.792294	−	0.869326i
$275$	5.38808	+	6.56540i	0.324914	+	0.395908i
$276$	0.190449	+	0.288463i	0.0114637	+	0.0173634i
$277$	−3.57547	+	11.7868i	−0.214829	+	0.708198i	0.781601	+	0.623779i	$0.214403\pi$
$277$	−3.57547	+	11.7868i	−0.214829	+	0.708198i	−0.996430	+	0.0844188i	$0.973097\pi$
$278$	9.85333	+	10.9320i	0.590963	+	0.655657i
$279$	−0.965759	+	4.85520i	−0.0578185	+	0.290673i
$280$	6.46885	+	26.7637i	0.386588	+	1.59944i
$281$	−6.85388	+	1.36332i	−0.408868	+	0.0813289i	−0.395239	−	0.918578i	$-0.629338\pi$
$281$	−6.85388	+	1.36332i	−0.408868	+	0.0813289i	−0.0136288	+	0.999907i	$0.504338\pi$
$282$	−0.594595	−	4.08613i	−0.0354076	−	0.243326i
$283$	16.2480	−	19.7982i	0.965843	−	1.17688i	−0.0183587	−	0.999831i	$-0.505844\pi$
$283$	16.2480	−	19.7982i	0.965843	−	1.17688i	0.984202	−	0.177052i	$-0.0566559\pi$
$284$	6.47276	+	0.673621i	0.384088	+	0.0399721i
$285$	3.03249	+	1.62090i	0.179629	+	0.0960140i
$286$	28.6749	−	21.1443i	1.69558	−	1.25029i
$287$	−15.8979	+	15.8979i	−0.938421	+	0.938421i
$288$	1.29862	+	5.50578i	0.0765220	+	0.324431i
$289$	−6.84528	−	6.84528i	−0.402664	−	0.402664i
$290$	−22.5403	−	3.40717i	−1.32361	−	0.200076i
$291$	1.98023	−	3.70475i	0.116083	−	0.217176i
$292$	−13.0519	−	7.06933i	−0.763805	−	0.413701i
$293$	−5.03123	−	4.12903i	−0.293928	−	0.241220i	0.475859	−	0.879522i	$-0.342137\pi$
$293$	−5.03123	−	4.12903i	−0.293928	−	0.241220i	−0.769786	+	0.638301i	$0.779637\pi$
$294$	22.8004	+	17.0077i	1.32974	+	0.991909i
$295$	−5.07040	−	25.4906i	−0.295210	−	1.48412i
$296$	−26.5760	+	1.08502i	−1.54470	+	0.0630653i
$297$	−5.53573	−	1.10112i	−0.321216	−	0.0638938i
$298$	0.0366103	−	0.705469i	0.00212078	−	0.0408668i
$299$	0.738205	+	0.223932i	0.0426915	+	0.0129503i
$300$	−1.68582	+	2.49310i	−0.0973309	+	0.143939i
$301$	9.75472	−	8.00549i	0.562253	−	0.461429i
$302$	−1.12332	−	24.2306i	−0.0646398	−	1.39432i
$303$	3.15956	−	7.62786i	0.181512	−	0.438209i
$304$	−7.32897	+	0.640198i	−0.420345	+	0.0367179i
$305$	3.29139	+	7.94611i	0.188464	+	0.454993i
$306$	3.46321	−	1.62629i	0.197978	−	0.0929688i
$307$	−20.8220	−	2.05079i	−1.18837	−	0.117045i	−0.515558	−	0.856854i	$-0.672415\pi$
$307$	−20.8220	−	2.05079i	−1.18837	−	0.117045i	−0.672816	+	0.739810i	$0.734915\pi$
$308$	54.4284	−	22.1937i	3.10135	−	1.26460i
$309$	−2.29363	+	1.22597i	−0.130480	+	0.0697431i
$310$	−5.62864	+	11.8162i	−0.319685	+	0.671117i
$311$	−17.5344	−	26.2422i	−0.994287	−	1.48806i	−0.868309	−	0.496023i	$-0.834793\pi$
$311$	−17.5344	−	26.2422i	−0.994287	−	1.48806i	−0.125978	−	0.992033i	$-0.540207\pi$
$312$	10.0775	+	7.60418i	0.570526	+	0.430502i
$313$	9.56939	+	6.39406i	0.540894	+	0.361414i	0.795807	−	0.605550i	$-0.207047\pi$
$313$	9.56939	+	6.39406i	0.540894	+	0.361414i	−0.254913	+	0.966964i	$0.582047\pi$
$314$	−9.70107	−	2.45848i	−0.547463	−	0.138740i
$315$	−0.954186	−	9.68801i	−0.0537623	−	0.545858i
$316$	0.482714	+	0.400634i	0.0271548	+	0.0225374i
$317$	1.21207	+	3.99567i	0.0680769	+	0.224419i	0.984377	−	0.176072i	$-0.0563393\pi$
$317$	1.21207	+	3.99567i	0.0680769	+	0.224419i	−0.916300	+	0.400492i	$0.868839\pi$
$318$	3.74199	−	6.20423i	0.209841	−	0.347916i
$319$			48.6647i			2.72470i
$320$	−0.247762	+	14.9543i	−0.0138503	+	0.835973i
$321$			5.83865i			0.325882i
$322$	1.08983	+	0.657315i	0.0607338	+	0.0366308i
$323$	1.44442	+	4.76160i	0.0803695	+	0.264943i
$324$	−0.185040	−	1.99142i	−0.0102800	−	0.110635i
$325$	0.658337	+	6.68421i	0.0365180	+	0.370773i
$326$	−3.49108	+	13.7757i	−0.193353	+	0.762965i
$327$	−13.5892	−	9.08001i	−0.751485	−	0.502126i
$328$	−10.5267	+	6.19150i	−0.581238	+	0.341869i
$329$	−8.44657	−	12.6412i	−0.465675	−	0.696931i
$330$	−13.4725	−	6.41758i	−0.741634	−	0.353276i
$331$	−27.9405	+	14.9345i	−1.53575	+	0.820875i	−0.999728	−	0.0233295i	$-0.992573\pi$
$331$	−27.9405	+	14.9345i	−1.53575	+	0.820875i	−0.536021	+	0.844205i	$0.680073\pi$
$332$	−2.32930	+	5.53674i	−0.127837	+	0.303868i
$333$	9.35859	+	0.921741i	0.512848	+	0.0505111i
$334$	5.02260	+	10.6957i	0.274824	+	0.585242i
$335$	−2.66517	−	6.43429i	−0.145614	−	0.351543i
$336$	13.0347	+	16.2454i	0.711102	+	0.886262i
$337$	−7.78737	+	18.8004i	−0.424205	+	1.02412i	0.556888	+	0.830587i	$0.311995\pi$
$337$	−7.78737	+	18.8004i	−0.424205	+	1.02412i	−0.981093	+	0.193535i	$0.938005\pi$
$338$	9.77933	−	0.453365i	0.531926	−	0.0246598i
$339$	12.6223	−	10.3588i	0.685549	−	0.562615i
$340$	9.93222	−	1.91869i	0.538650	−	0.104055i
$341$	26.7374	+	8.11069i	1.44791	+	0.439219i
$342$	2.59755	+	0.134800i	0.140460	+	0.00728914i
$343$	66.9718	+	13.3215i	3.61614	+	0.719294i
$344$	6.22052	−	2.87928i	0.335388	−	0.155240i
$345$	−0.0630367	−	0.316907i	−0.00339378	−	0.0170617i
$346$	1.43685	−	1.92623i	0.0772455	−	0.103555i
$347$	−8.70591	−	7.14475i	−0.467358	−	0.383550i	0.371034	−	0.928619i	$-0.379003\pi$
$347$	−8.70591	−	7.14475i	−0.467358	−	0.383550i	−0.838391	+	0.545069i	$0.816503\pi$
$348$	−16.5291	+	4.91453i	−0.886052	+	0.263447i
$349$	13.7576	−	25.7386i	0.736426	−	1.37776i	−0.182453	−	0.983215i	$-0.558404\pi$
$349$	13.7576	−	25.7386i	0.736426	−	1.37776i	0.918878	−	0.394541i	$-0.129096\pi$
$350$	−1.65620	+	10.9567i	−0.0885274	+	0.585658i
$351$	−3.15614	−	3.15614i	−0.168462	−	0.168462i
$352$	31.6444	−	4.24841i	1.68665	−	0.226441i
$353$	−3.70948	+	3.70948i	−0.197436	+	0.197436i	−0.798900	−	0.601464i	$-0.794584\pi$
$353$	−3.70948	+	3.70948i	−0.197436	+	0.197436i	0.601464	+	0.798900i	$0.294584\pi$
$354$	−11.6678	−	15.8234i	−0.620138	−	0.841002i
$355$	−5.36495	−	2.86762i	−0.284742	−	0.152198i
$356$	−3.28228	−	4.04481i	−0.173960	−	0.214375i
$357$	8.93692	−	10.8897i	0.472992	−	0.576342i
$358$	−17.8592	+	2.59879i	−0.943890	+	0.137351i
$359$	−25.7321	+	5.11844i	−1.35809	+	0.270141i	−0.819815	−	0.572628i	$-0.805924\pi$
$359$	−25.7321	+	5.11844i	−1.35809	+	0.270141i	−0.538275	+	0.842769i	$0.680924\pi$
$360$	0.819193	−	5.22404i	0.0431753	−	0.275331i
$361$	3.04678	−	15.3172i	0.160357	−	0.806168i
$362$	23.8010	−	21.4526i	1.25095	−	1.12752i
$363$	−6.05440	+	19.9587i	−0.317774	+	1.04756i
$364$	45.5392	+	9.32003i	2.38690	+	0.488502i
$365$	8.80238	+	10.7257i	0.460738	+	0.561410i
$366$	4.80858	+	4.38249i	0.251349	+	0.229076i
$367$	0.126612	+	0.0524443i	0.00660908	+	0.00273757i	0.385986	−	0.922505i	$-0.373861\pi$
$367$	0.126612	+	0.0524443i	0.00660908	+	0.00273757i	−0.379376	+	0.925242i	$0.623861\pi$
$368$	0.483410	+	0.494208i	0.0251995	+	0.0257623i
$369$	3.98910	−	1.65234i	0.207664	−	0.0860174i
$370$	23.3867	+	8.44080i	1.21582	+	0.438816i
$371$	2.61481	−	26.5486i	0.135754	−	1.37833i
$372$	−0.0546722	+	9.90048i	−0.00283462	+	0.513316i
$373$	16.2061	+	30.3194i	0.839119	+	1.56988i	0.821621	+	0.570034i	$0.193070\pi$
$373$	16.2061	+	30.3194i	0.839119	+	1.56988i	0.0174972	+	0.999847i	$0.494430\pi$
$374$	−7.21893	−	20.3526i	−0.373282	−	1.05241i
$375$	10.1115	−	6.75630i	0.522156	−	0.348894i
$376$	−2.71765	−	7.79836i	−0.140152	−	0.402170i
$377$	−21.3808	+	31.9986i	−1.10117	+	1.64801i
$378$	−3.76836	−	6.32667i	−0.193823	−	0.325409i
$379$	−8.62151	+	0.849145i	−0.442857	+	0.0436176i	−0.316989	−	0.948429i	$-0.602672\pi$
$379$	−8.62151	+	0.849145i	−0.442857	+	0.0436176i	−0.125869	+	0.992047i	$0.540172\pi$
$380$	6.56977	+	2.03260i	0.337022	+	0.104270i
$381$	−4.29217	+	1.30201i	−0.219894	+	0.0667042i
$382$	1.25185	+	5.05688i	0.0640505	+	0.258733i
$383$	−37.2550			−1.90364			−0.951820	−	0.306656i	$-0.900790\pi$
$383$	−37.2550			−1.90364			−0.951820	+	0.306656i	$0.900790\pi$
$384$	4.63867	+	10.3190i	0.236716	+	0.526592i
$385$	−54.9455			−2.80028
$386$	4.27255	+	17.2590i	0.217467	+	0.878462i
$387$	−2.31910	+	0.703493i	−0.117887	+	0.0357605i
$388$	2.48320	−	8.02618i	0.126065	−	0.407467i
$389$	−10.6995	+	1.05381i	−0.542485	+	0.0534301i	−0.365549	−	0.930792i	$-0.619119\pi$
$389$	−10.6995	+	1.05381i	−0.542485	+	0.0534301i	−0.176936	+	0.984222i	$0.556619\pi$
$390$	−6.03902	−	10.1389i	−0.305798	−	0.513402i
$391$	0.259773	−	0.388778i	0.0131373	−	0.0196614i
$392$	51.2247	+	24.7488i	2.58724	+	1.25000i
$393$	−4.79011	+	3.20065i	−0.241629	+	0.161451i
$394$	9.87137	+	27.8306i	0.497312	+	1.40209i
$395$	−0.276425	−	0.517155i	−0.0139084	−	0.0260209i
$396$	−11.2882	−	0.0623354i	−0.567253	−	0.00313247i
$397$	2.13542	−	21.6813i	0.107174	−	1.08815i	−0.779703	−	0.626149i	$-0.784630\pi$
$397$	2.13542	−	21.6813i	0.107174	−	1.08815i	0.886877	−	0.462005i	$-0.152870\pi$
$398$	−9.57474	−	3.45575i	−0.479938	−	0.173221i
$399$	8.84795	−	3.66494i	0.442952	−	0.183477i
$400$	−2.36470	+	5.53519i	−0.118235	+	0.276759i
$401$	11.5091	+	4.76723i	0.574737	+	0.238064i	0.651069	−	0.759019i	$-0.274321\pi$
$401$	11.5091	+	4.76723i	0.574737	+	0.238064i	−0.0763318	+	0.997082i	$0.524321\pi$
$402$	−3.89371	−	3.54868i	−0.194200	−	0.176992i
$403$	14.0173	+	17.0801i	0.698249	+	0.850819i
$404$	3.31085	−	16.1774i	0.164721	−	0.804853i
$405$	−0.542701	+	1.78905i	−0.0269671	+	0.0888985i
$406$	−47.1624	+	42.5089i	−2.34063	+	2.10968i
$407$	10.3548	−	52.0573i	0.513270	−	2.58039i
$408$	6.18376	−	4.50728i	0.306142	−	0.223144i
$409$	28.5667	−	5.68227i	1.41253	−	0.280970i	0.570900	−	0.821020i	$-0.306594\pi$
$409$	28.5667	−	5.68227i	1.41253	−	0.280970i	0.841633	+	0.540049i	$0.181594\pi$
$410$	11.2970	−	1.64388i	0.557917	−	0.0811855i
$411$	−8.73377	+	10.6421i	−0.430805	+	0.524938i
$412$	−4.03893	+	3.27751i	−0.198984	+	0.161471i
$413$	−63.8400	−	34.1232i	−3.14136	−	1.67909i
$414$	−0.145058	−	0.196721i	−0.00712920	−	0.00966829i
$415$	3.97038	−	3.97038i	0.194898	−	0.194898i
$416$	22.6737	+	11.1095i	1.11167	+	0.544686i
$417$	−7.35861	−	7.35861i	−0.360353	−	0.360353i
$418$	2.19421	−	14.5159i	0.107322	−	0.709995i
$419$	3.41782	−	6.39430i	0.166972	−	0.312382i	−0.784494	−	0.620136i	$-0.787077\pi$
$419$	3.41782	−	6.39430i	0.166972	−	0.312382i	0.951466	+	0.307754i	$0.0995774\pi$
$420$	−5.54881	−	18.6623i	−0.270754	−	0.910629i
$421$	−26.1582	−	21.4675i	−1.27487	−	1.04626i	−0.996309	−	0.0858442i	$-0.972641\pi$
$421$	−26.1582	−	21.4675i	−1.27487	−	1.04626i	−0.278565	−	0.960417i	$-0.589859\pi$
$422$	−15.2163	+	20.3989i	−0.740720	+	0.993003i
$423$	0.569617	+	2.86366i	0.0276957	+	0.139236i
$424$	4.99461	−	13.6027i	0.242560	−	0.660606i
$425$	3.99286	+	0.794229i	0.193682	+	0.0385258i
$426$	−4.59547	−	0.238482i	−0.222651	−	0.0115545i
$427$	22.9235	+	6.95377i	1.10935	+	0.336517i
$428$	2.21485	+	11.4653i	0.107059	+	0.554198i
$429$	−19.4741	+	15.9820i	−0.940219	+	0.771618i
$430$	−6.40061	+	0.296729i	−0.308665	+	0.0143095i
$431$	5.49761	−	13.2724i	0.264811	−	0.639309i	−0.734413	−	0.678703i	$-0.762543\pi$
$431$	5.49761	−	13.2724i	0.264811	−	0.639309i	0.999224	+	0.0393934i	$0.0125425\pi$
$432$	−1.11879	−	3.84035i	−0.0538280	−	0.184769i
$433$	4.79576	+	11.5780i	0.230469	+	0.556402i	0.996233	−	0.0867201i	$-0.0276386\pi$
$433$	4.79576	+	11.5780i	0.230469	+	0.556402i	−0.765763	+	0.643123i	$0.777639\pi$
$434$	15.4949	+	32.9967i	0.743781	+	1.58389i
$435$	16.0418	+	1.57998i	0.769147	+	0.0757544i
$436$	−30.1295	−	12.6754i	−1.44294	−	0.607042i
$437$	0.280339	−	0.149844i	0.0134104	−	0.00716803i
$438$	9.47575	+	4.51375i	0.452769	+	0.215676i
$439$	−16.7436	−	25.0586i	−0.799129	−	1.19598i	−0.977275	−	0.211977i	$-0.932010\pi$
$439$	−16.7436	−	25.0586i	−0.799129	−	1.19598i	0.178146	−	0.984004i	$-0.442990\pi$
$440$	−28.8903	−	7.49149i	−1.37729	−	0.357143i
$441$	−16.7239	−	11.1746i	−0.796376	−	0.532121i
$442$	4.19519	−	16.5541i	0.199545	−	0.787398i
$443$	1.75056	+	17.7737i	0.0831715	+	0.844454i	0.942761	+	0.333469i	$0.108219\pi$
$443$	1.75056	+	17.7737i	0.0831715	+	0.844454i	−0.859590	+	0.510985i	$0.829281\pi$
$444$	18.7271	−	1.74010i	0.888748	−	0.0825813i
$445$	1.41347	+	4.65959i	0.0670049	+	0.220886i
$446$	26.0801	+	15.7299i	1.23493	+	0.744830i
$447$			0.499514i			0.0236262i
$448$	31.7588	+	26.9565i	1.50046	+	1.27357i
$449$		−	1.14418i		−	0.0539974i	−0.999635	−	0.0269987i	$-0.991405\pi$
$449$		−	1.14418i		−	0.0539974i	0.999635	−	0.0269987i	$-0.00859500\pi$
$450$	1.09909	−	1.82229i	0.0518117	−	0.0859038i
$451$	−7.07432	−	23.3209i	−0.333117	−	1.09814i
$452$	20.8568	−	25.1298i	0.981021	−	1.18201i
$453$	1.68120	+	17.0695i	0.0789895	+	0.801993i
$454$	4.42434	+	1.12123i	0.207645	+	0.0526220i
$455$	−36.1284	−	24.1402i	−1.69373	−	1.13171i
$456$	5.15194	−	0.720657i	0.241262	−	0.0337478i
$457$	7.82366	+	11.7089i	0.365976	+	0.547721i	0.968062	−	0.250709i	$-0.0806639\pi$
$457$	7.82366	+	11.7089i	0.365976	+	0.547721i	−0.602087	+	0.798431i	$0.705664\pi$
$458$	7.57805	−	15.9086i	0.354099	−	0.743362i
$459$	−2.38597	+	1.27533i	−0.111368	+	0.0595272i
$460$	−0.244001	−	0.598396i	−0.0113766	−	0.0279003i
$461$	−5.23033	−	0.515143i	−0.243601	−	0.0239926i	−0.0245201	−	0.999699i	$-0.507806\pi$
$461$	−5.23033	−	0.515143i	−0.243601	−	0.0239926i	−0.219081	+	0.975707i	$0.570306\pi$
$462$	−37.6217	+	17.6668i	−1.75032	+	0.821933i
$463$	1.63154	+	3.93889i	0.0758242	+	0.183056i	0.957247	−	0.289273i	$-0.0934135\pi$
$463$	1.63154	+	3.93889i	0.0758242	+	0.183056i	−0.881422	+	0.472329i	$0.843414\pi$
$464$	−30.5938	+	15.9208i	−1.42028	+	0.739106i
$465$	3.54168	−	8.55037i	0.164242	−	0.396514i
$466$	−1.07185	−	23.1204i	−0.0496524	−	1.07103i
$467$	3.10764	−	2.55037i	0.143804	−	0.118017i	−0.559741	−	0.828668i	$-0.689099\pi$
$467$	3.10764	−	2.55037i	0.143804	−	0.118017i	0.703545	+	0.710651i	$0.251599\pi$
$468$	−7.39496	−	5.00044i	−0.341832	−	0.231145i
$469$	−18.5621	−	5.63076i	−0.857119	−	0.260004i
$470$	−0.400074	+	7.70931i	−0.0184540	+	0.355604i
$471$	6.94057	+	1.38056i	0.319805	+	0.0636131i
$472$	−28.9145	−	26.6462i	−1.33090	−	1.22649i
$473$	2.66853	+	13.4156i	0.122699	+	0.616850i
$474$	−0.355553	−	0.265221i	−0.0163311	−	0.0121820i
$475$	2.13941	+	1.75577i	0.0981627	+	0.0805601i
$476$	13.4185	−	24.7741i	0.615035	−	1.13552i
$477$	−2.41507	+	4.51829i	−0.110579	+	0.206878i
$478$	−3.69071	−	0.557883i	−0.168809	−	0.0255170i
$479$	14.1730	+	14.1730i	0.647580	+	0.647580i	0.952408	−	0.304828i	$-0.0985989\pi$
$479$	14.1730	+	14.1730i	0.647580	+	0.647580i	−0.304828	+	0.952408i	$0.598599\pi$
$480$	−0.373058	−	10.5692i	−0.0170277	−	0.482415i
$481$	29.6800	−	29.6800i	1.35329	−	1.35329i
$482$	−4.01392	+	2.95979i	−0.182829	+	0.134815i
$483$	−0.793678	−	0.424230i	−0.0361136	−	0.0193031i
$484$	−4.31782	+	41.4895i	−0.196264	+	1.88589i
$485$	−4.98223	+	6.07087i	−0.226232	+	0.275664i
$486$	0.203645	+	1.39947i	0.00923752	+	0.0634815i
$487$	−6.09103	+	1.21158i	−0.276011	+	0.0549020i	−0.331155	−	0.943576i	$-0.607438\pi$
$487$	−6.09103	+	1.21158i	−0.276011	+	0.0549020i	0.0551438	+	0.998478i	$0.482438\pi$
$488$	11.1051	+	6.78177i	0.502702	+	0.306996i
$489$	1.96043	−	9.85572i	0.0886535	−	0.445691i
$490$	−35.6041	−	39.5018i	−1.60843	−	1.78451i
$491$	6.83611	−	22.5356i	0.308509	−	1.01702i	−0.656395	−	0.754417i	$-0.727919\pi$
$491$	6.83611	−	22.5356i	0.308509	−	1.01702i	0.964904	−	0.262602i	$-0.0845805\pi$
$492$	7.20658	−	4.75793i	0.324898	−	0.214504i
$493$	14.7981	+	18.0316i	0.666475	+	0.812102i
$494$	7.82030	−	8.58064i	0.351852	−	0.386061i
$495$	9.74884	+	4.03810i	0.438178	+	0.181499i
$496$	3.64832	+	19.4623i	0.163814	+	0.873882i
$497$	−15.6534	+	6.48384i	−0.702150	+	0.290840i
$498$	1.44195	−	3.99516i	0.0646152	−	0.179028i
$499$	1.53081	−	15.5426i	0.0685285	−	0.695782i	−0.898133	−	0.439724i	$-0.855076\pi$
$499$	1.53081	−	15.5426i	0.0685285	−	0.695782i	0.966661	−	0.256058i	$-0.0824238\pi$
$500$	17.2930	−	17.1030i	0.773366	−	0.764871i
$501$	−3.93869	−	7.36878i	−0.175968	−	0.329213i
$502$	−20.5749	+	7.29781i	−0.918305	+	0.325717i
$503$	0.147698	−	0.0986888i	0.00658554	−	0.00440032i	−0.552273	−	0.833663i	$-0.686239\pi$
$503$	0.147698	−	0.0986888i	0.00658554	−	0.00440032i	0.558859	+	0.829263i	$0.311239\pi$
$504$	−9.79988	−	10.9942i	−0.436522	−	0.489719i
$505$	−8.57558	+	12.8343i	−0.381608	+	0.571117i
$506$	−1.18523	+	0.705959i	−0.0526899	+	0.0313837i
$507$	−6.88913	+	0.678520i	−0.305957	+	0.0301341i
$508$	−7.93460	+	4.18496i	−0.352041	+	0.185678i
$509$	1.13882	−	0.345457i	0.0504773	−	0.0153121i	−0.264945	−	0.964264i	$-0.585354\pi$
$509$	1.13882	−	0.345457i	0.0504773	−	0.0153121i	0.315422	+	0.948951i	$0.397854\pi$
$510$	−6.94339	+	1.71887i	−0.307458	+	0.0761128i
$511$	38.6455			1.70958
$512$	13.0234	+	18.5038i	0.575558	+	0.817761i
$513$	−1.83922			−0.0812035
$514$	−8.81461	+	2.18210i	−0.388796	+	0.0962482i
$515$	4.65281	−	1.41141i	0.205027	−	0.0621944i
$516$	−4.28715	+	2.26118i	−0.188731	+	0.0995429i
$517$	16.4003	−	1.61529i	0.721285	−	0.0710404i
$518$	59.4953	−	35.4372i	2.61407	−	1.55702i
$519$	−0.944052	+	1.41287i	−0.0414393	+	0.0620183i
$520$	−15.7049	−	17.6188i	−0.688705	−	0.772636i
$521$	−10.2408	+	6.84269i	−0.448658	+	0.299784i	−0.759297	−	0.650744i	$-0.774457\pi$
$521$	−10.2408	+	6.84269i	−0.448658	+	0.299784i	0.310639	+	0.950528i	$0.399457\pi$
$522$	11.4920	−	4.07615i	0.502992	−	0.178408i
$523$	6.24640	+	11.6862i	0.273136	+	0.511001i	0.980668	−	0.195680i	$-0.0626914\pi$
$523$	6.24640	+	11.6862i	0.273136	+	0.511001i	−0.707532	+	0.706681i	$0.750191\pi$
$524$	−8.19216	+	8.10218i	−0.357876	+	0.353946i
$525$	0.768017	−	7.79781i	0.0335190	−	0.340324i
$526$	8.20422	−	22.7312i	0.357721	−	0.991127i
$527$	12.3732	−	5.12516i	0.538987	−	0.223256i
$528$	−22.1902	+	4.15968i	−0.965705	+	0.181027i
$529$	21.2216	+	8.79029i	0.922680	+	0.382186i
$530$	−9.12429	+	10.0114i	−0.396334	+	0.434868i
$531$	8.81917	+	10.7462i	0.382720	+	0.466345i
$532$	15.9844	−	10.5532i	0.693012	−	0.457541i
$533$	5.59442	−	18.4423i	0.242321	−	0.798827i
$534$	2.46603	+	2.73599i	0.106715	+	0.118398i
$535$	2.12954	−	10.7059i	0.0920679	−	0.462857i
$536$	−8.99222	−	5.49148i	−0.388405	−	0.237196i
$537$	12.5162	−	2.48962i	0.540113	−	0.107435i
$538$	1.91716	+	13.1750i	0.0826547	+	0.568014i
$539$	−72.0196	+	87.7561i	−3.10210	+	3.77992i
$540$	−0.387038	+	3.71901i	−0.0166555	+	0.160041i
$541$	24.4395	+	13.0632i	1.05074	+	0.561630i	0.903994	−	0.427545i	$-0.140621\pi$
$541$	24.4395	+	13.0632i	1.05074	+	0.561630i	0.146742	+	0.989175i	$0.453121\pi$
$542$	−10.9242	+	8.05531i	−0.469237	+	0.346005i
$543$	−16.0211	+	16.0211i	−0.687530	+	0.687530i
$544$	10.4332	−	11.1967i	0.447321	−	0.480054i
$545$	21.6058	+	21.6058i	0.925489	+	0.925489i
$546$	−32.4994	−	4.91257i	−1.39084	−	0.210239i
$547$	−0.284362	+	0.532004i	−0.0121584	+	0.0227469i	−0.887927	−	0.459984i	$-0.847855\pi$
$547$	−0.284362	+	0.532004i	−0.0121584	+	0.0227469i	0.875769	+	0.482731i	$0.160355\pi$
$548$	−13.1135	+	24.2110i	−0.560179	+	1.03424i
$549$	−3.55621	−	2.91851i	−0.151775	−	0.124559i
$550$	−9.62779	−	7.18174i	−0.410530	−	0.306231i
$551$	3.09373	+	15.5532i	0.131797	+	0.662590i
$552$	−0.359474	−	0.331273i	−0.0153002	−	0.0140999i
$553$	−1.60185	−	0.318628i	−0.0681176	−	0.0135494i
$554$	0.902746	−	17.3956i	0.0383540	−	0.739070i
$555$	−16.8240	−	5.10350i	−0.714138	−	0.216631i
$556$	−17.2415	−	11.6586i	−0.731202	−	0.494436i
$557$	−20.6165	+	16.9195i	−0.873550	+	0.716904i	−0.960194	−	0.279335i	$-0.909886\pi$
$557$	−20.6165	+	16.9195i	−0.873550	+	0.716904i	0.0866434	+	0.996239i	$0.472386\pi$
$558$	−0.324206	−	6.99329i	−0.0137247	−	0.296050i
$559$	−4.13949	+	9.99361i	−0.175082	+	0.422685i
$560$	−17.9756	−	34.5422i	−0.759607	−	1.45968i
$561$	5.84354	+	14.1075i	0.246714	+	0.595621i
$562$	8.94552	−	4.20073i	0.377344	−	0.177197i
$563$	−0.358401	−	0.0352995i	−0.0151048	−	0.00148769i	0.0904619	−	0.995900i	$-0.471166\pi$
$563$	−0.358401	−	0.0352995i	−0.0151048	−	0.00148769i	−0.105567	+	0.994412i	$0.533666\pi$
$564$	2.20486	+	5.40728i	0.0928415	+	0.227687i
$565$	−26.9228	+	14.3905i	−1.13265	+	0.605414i
$566$	−15.5767	+	32.7002i	−0.654736	+	1.37449i
$567$	2.89290	+	4.32953i	0.121490	+	0.181823i
$568$	−9.11456	+	1.27495i	−0.382439	+	0.0534958i
$569$	6.80401	+	4.54629i	0.285239	+	0.190591i	0.689956	−	0.723851i	$-0.257630\pi$
$569$	6.80401	+	4.54629i	0.285239	+	0.190591i	−0.404717	+	0.914442i	$0.632630\pi$
$570$	−4.71377	−	1.19458i	−0.197438	−	0.0500355i
$571$	−2.79711	−	28.3995i	−0.117055	−	1.18848i	−0.856820	−	0.515616i	$-0.827563\pi$
$571$	−2.79711	−	28.3995i	−0.117055	−	1.18848i	0.739765	−	0.672866i	$-0.234937\pi$
$572$	−32.1786	+	38.7711i	−1.34545	+	1.62110i
$573$	−1.06932	−	3.52507i	−0.0446715	−	0.147262i
$574$	16.4215	−	27.2269i	0.685421	−	1.13643i
$575$		−	0.260073i		−	0.0108458i
$576$	−3.65378	−	7.11687i	−0.152241	−	0.296536i
$577$		−	23.1331i		−	0.963042i	−0.876435	−	0.481521i	$-0.840085\pi$
$577$		−	23.1331i		−	0.963042i	0.876435	−	0.481521i	$-0.159915\pi$
$578$	11.7233	+	7.07075i	0.487625	+	0.294104i
$579$	−3.64957	−	12.0310i	−0.151671	−	0.499992i
$580$	32.1006	−	2.98275i	1.33291	−	0.123852i
$581$	−1.53287	−	15.5635i	−0.0635943	−	0.645683i
$582$	−1.45940	+	5.75874i	−0.0604940	+	0.238707i
$583$	24.0431	+	16.0651i	0.995765	+	0.665349i
$584$	20.3197	+	5.26908i	0.840837	+	0.218036i
$585$	4.63604	+	6.93833i	0.191677	+	0.286864i
$586$	8.30994	+	3.95842i	0.343281	+	0.163521i
$587$	−12.3381	+	6.59484i	−0.509247	+	0.272198i	−0.705946	−	0.708266i	$-0.749478\pi$
$587$	−12.3381	+	6.59484i	−0.509247	+	0.272198i	0.196699	+	0.980464i	$0.436978\pi$
$588$	−37.0796	−	15.5993i	−1.52914	−	0.643305i
$589$	9.06087	+	0.892418i	0.373347	+	0.0367714i
$590$	15.6232	+	33.2698i	0.643195	+	1.36969i
$591$	−7.99061	−	19.2910i	−0.328690	−	0.793527i
$592$	36.1142	−	10.5210i	1.48428	−	0.432410i
$593$	5.75974	−	13.9052i	0.236524	−	0.571020i	−0.760395	−	0.649461i	$-0.774994\pi$
$593$	5.75974	−	13.9052i	0.236524	−	0.571020i	0.996919	+	0.0784416i	$0.0249944\pi$
$594$	7.97351	−	0.369648i	0.327157	−	0.0151668i
$595$	−20.3588	+	16.7080i	−0.834628	+	0.684962i
$596$	0.189487	+	0.980892i	0.00776168	+	0.0401789i
$597$	6.88790	+	2.08942i	0.281903	+	0.0855144i
$598$	−1.08949	−	0.0565390i	−0.0445525	−	0.00231205i
$599$	37.9879	+	7.55627i	1.55214	+	0.308741i	0.895362	−	0.445340i	$-0.146917\pi$
$599$	37.9879	+	7.55627i	1.55214	+	0.308741i	0.656782	+	0.754080i	$0.271917\pi$
$600$	1.46701	−	3.99536i	0.0598903	−	0.163110i
$601$	6.51223	+	32.7392i	0.265639	+	1.33546i	0.851205	+	0.524834i	$0.175873\pi$
$601$	6.51223	+	32.7392i	0.265639	+	1.33546i	−0.585565	+	0.810625i	$0.699127\pi$
$602$	−10.6705	+	14.3048i	−0.434896	+	0.583018i
$603$	2.87961	+	2.36324i	0.117267	+	0.0962384i
$604$	9.77653	+	32.8815i	0.397802	+	1.33793i
$605$	18.3811	−	34.3885i	0.747296	−	1.39809i
$606$	−1.74514	+	11.5451i	−0.0708915	+	0.468987i
$607$	−19.4135	−	19.4135i	−0.787970	−	0.787970i	0.193191	−	0.981161i	$-0.438116\pi$
$607$	−19.4135	−	19.4135i	−0.787970	−	0.787970i	−0.981161	+	0.193191i	$0.938116\pi$
$608$	9.84346	−	3.36950i	0.399205	−	0.136651i
$609$	31.7463	−	31.7463i	1.28642	−	1.28642i
$610$	−7.21871	−	9.78969i	−0.292277	−	0.396373i
$611$	11.4934	+	6.14335i	0.464974	+	0.248534i
$612$	−4.20153	+	3.40945i	−0.169837	+	0.137819i
$613$	−11.8624	+	14.4544i	−0.479119	+	0.583808i	−0.955337	−	0.295520i	$-0.904507\pi$
$613$	−11.8624	+	14.4544i	−0.479119	+	0.583808i	0.476218	+	0.879327i	$0.342007\pi$
$614$	29.2809	−	4.26081i	1.18168	−	0.171952i
$615$	−7.91718	+	1.57483i	−0.319252	+	0.0635031i
$616$	−67.1758	+	48.9637i	−2.70659	+	1.97280i
$617$	5.53099	−	27.8062i	0.222669	−	1.11943i	−0.694058	−	0.719919i	$-0.744179\pi$
$617$	5.53099	−	27.8062i	0.222669	−	1.11943i	0.916727	−	0.399515i	$-0.130821\pi$
$618$	2.73201	−	2.46244i	0.109897	−	0.0990540i
$619$	−3.34252	+	11.0188i	−0.134347	+	0.442884i	−0.998140	−	0.0609636i	$-0.980583\pi$
$619$	−3.34252	+	11.0188i	−0.134347	+	0.442884i	0.863793	+	0.503848i	$0.168083\pi$
$620$	3.71126	−	18.1338i	0.149048	−	0.728273i
$621$	0.109643	+	0.133600i	0.00439980	+	0.00536118i
$622$	32.9889	+	30.0657i	1.32273	+	1.20553i
$623$	12.5295	+	5.18990i	0.501985	+	0.207929i
$624$	−16.4183	−	7.01412i	−0.657259	−	0.280789i
$625$	−14.0538	+	5.82126i	−0.562151	+	0.232850i
$626$	−15.3096	−	5.52558i	−0.611893	−	0.220847i
$627$	−1.01750	+	10.3309i	−0.0406352	+	0.412576i
$628$	14.1529	+	0.0781546i	0.564761	+	0.00311871i
$629$	−11.9930	−	22.4374i	−0.478193	−	0.894636i
$630$	4.60223	+	12.9752i	0.183357	+	0.516944i
$631$	0.753695	−	0.503603i	0.0300041	−	0.0200481i	−0.540478	−	0.841358i	$-0.681756\pi$
$631$	0.753695	−	0.503603i	0.0300041	−	0.0200481i	0.570482	+	0.821310i	$0.306756\pi$
$632$	−0.798808	−	0.385937i	−0.0317749	−	0.0153517i
$633$	9.99758	−	14.9624i	0.397368	−	0.594703i
$634$	−3.02178	−	5.07325i	−0.120010	−	0.201485i
$635$	8.34511	−	0.821922i	0.331166	−	0.0326170i
$636$	−3.02849	+	9.78868i	−0.120087	+	0.388146i
$637$	−85.9107	+	26.0607i	−3.40391	+	1.03256i
$638$	−16.5381	−	66.8057i	−0.654749	−	2.64486i
$639$	3.25386			0.128721
$640$	−4.74192	−	20.6131i	−0.187441	−	0.814806i
$641$	13.4468			0.531115			0.265557	−	0.964095i	$-0.414444\pi$
$641$	13.4468			0.531115			0.265557	+	0.964095i	$0.414444\pi$
$642$	−1.98419	−	8.01516i	−0.0783097	−	0.316333i
$643$	−29.7903	+	9.03678i	−1.17481	+	0.356376i	−0.816566	−	0.577251i	$-0.804125\pi$
$643$	−29.7903	+	9.03678i	−1.17481	+	0.356376i	−0.358247	+	0.933627i	$0.616625\pi$
$644$	−1.71947	−	0.531982i	−0.0677566	−	0.0209630i
$645$	4.50896	−	0.444093i	0.177540	−	0.0174862i
$646$	−3.60103	−	6.04575i	−0.141681	−	0.237867i
$647$	13.8875	−	20.7841i	0.545975	−	0.817109i	−0.451185	−	0.892431i	$-0.648998\pi$
$647$	13.8875	−	20.7841i	0.545975	−	0.817109i	0.997159	+	0.0753218i	$0.0239984\pi$
$648$	0.930777	+	2.67089i	0.0365644	+	0.104922i
$649$	65.2404	−	43.5922i	2.56091	−	1.71115i
$650$	−3.17529	−	8.95219i	−0.124545	−	0.351134i
$651$	−12.1510	−	22.7330i	−0.476237	−	0.890977i
$652$	0.110981	−	20.0973i	0.00434635	−	0.787072i
$653$	1.53531	−	15.5882i	0.0600812	−	0.610015i	−0.917252	−	0.398307i	$-0.869598\pi$
$653$	1.53531	−	15.5882i	0.0600812	−	0.610015i	0.977333	−	0.211707i	$-0.0679023\pi$
$654$	21.7406	+	7.84670i	0.850126	+	0.306830i
$655$	9.95064	−	4.12169i	0.388804	−	0.161048i
$656$	12.3466	−	12.0769i	0.482055	−	0.471523i
$657$	−6.85678	−	2.84017i	−0.267508	−	0.110806i
$658$	15.8912	+	14.4831i	0.619503	+	0.564608i
$659$	5.02436	+	6.12219i	0.195721	+	0.238487i	0.861618	−	0.507557i	$-0.169451\pi$
$659$	5.02436	+	6.12219i	0.195721	+	0.238487i	−0.665897	+	0.746043i	$0.731951\pi$
$660$	20.6756	+	4.23145i	0.804796	+	0.164709i
$661$	5.77248	−	19.0293i	0.224524	−	0.740155i	−0.770222	−	0.637776i	$-0.779855\pi$
$661$	5.77248	−	19.0293i	0.224524	−	0.740155i	0.994745	−	0.102379i	$-0.0326454\pi$
$662$	33.2807	−	29.9969i	1.29349	−	1.16586i
$663$	−2.35582	+	11.8435i	−0.0914925	+	0.459964i
$664$	1.31601	−	8.39228i	0.0510711	−	0.325684i
$665$	−17.5606	+	3.49301i	−0.680969	+	0.135453i
$666$	−13.1605	+	1.91505i	−0.509958	+	0.0742068i
$667$	0.945350	−	1.15191i	0.0366041	−	0.0446022i
$668$	−10.5297	−	12.9759i	−0.407406	−	0.502053i
$669$	−18.9931	−	10.1520i	−0.734315	−	0.392500i
$670$	5.84529	+	7.92711i	0.225823	+	0.306251i
$671$	−18.3607	+	18.3607i	−0.708805	+	0.708805i
$672$	−23.4145	−	17.8717i	−0.903235	−	0.689414i
$673$	32.9891	+	32.9891i	1.27164	+	1.27164i	0.945229	+	0.326408i	$0.105838\pi$
$673$	32.9891	+	32.9891i	1.27164	+	1.27164i	0.326408	+	0.945229i	$0.394162\pi$
$674$	4.30125	−	28.4551i	0.165678	−	1.09605i
$675$	−0.709351	+	1.32710i	−0.0273029	+	0.0510802i
$676$	−13.2708	+	3.94575i	−0.510414	+	0.151759i
$677$	−36.0818	−	29.6115i	−1.38673	−	1.13806i	−0.973827	−	0.227291i	$-0.927013\pi$
$677$	−36.0818	−	29.6115i	−1.38673	−	1.13806i	−0.412908	−	0.910773i	$-0.635487\pi$
$678$	−13.8072	+	18.5099i	−0.530264	+	0.710868i
$679$	4.26735	+	21.4534i	0.163766	+	0.823307i
$680$	−12.9827	+	6.00926i	−0.497862	+	0.230444i
$681$	−3.16537	−	0.629631i	−0.121297	−	0.0241275i
$682$	−39.4607	−	2.04781i	−1.51103	−	0.0784147i
$683$	−36.0935	−	10.9488i	−1.38108	−	0.418946i	−0.489576	−	0.871961i	$-0.662848\pi$
$683$	−36.0935	−	10.9488i	−1.38108	−	0.418946i	−0.891503	+	0.453015i	$0.850348\pi$
$684$	−3.61166	+	0.697694i	−0.138095	+	0.0266770i
$685$	19.8960	−	16.3282i	0.760187	−	0.623869i
$686$	−96.4643	+	4.47204i	−3.68303	+	0.170743i
$687$	−4.76830	+	11.5117i	−0.181922	+	0.439199i
$688$	−7.56089	+	6.06657i	−0.288256	+	0.231286i
$689$	8.75095	+	21.1267i	0.333385	+	0.804861i
$690$	0.194232	+	0.413619i	0.00739427	+	0.0157462i
$691$	−35.7196	−	3.51808i	−1.35884	−	0.133834i	−0.607799	−	0.794091i	$-0.707947\pi$
$691$	−35.7196	−	3.51808i	−1.35884	−	0.133834i	−0.751040	+	0.660257i	$0.770447\pi$
$692$	−1.31787	+	3.13257i	−0.0500978	+	0.119083i
$693$	25.9194	−	13.8542i	0.984596	−	0.526278i
$694$	14.3793	+	6.84955i	0.545831	+	0.260005i
$695$	10.8090	+	16.1768i	0.410010	+	0.613623i
$696$	21.0206	−	12.3637i	0.796783	−	0.468646i
$697$	−9.71273	−	6.48984i	−0.367896	−	0.245820i
$698$	−10.1391	+	40.0086i	−0.383771	+	1.51435i
$699$	1.60416	+	16.2873i	0.0606749	+	0.616043i
$700$	−1.44989	−	15.6039i	−0.0548007	−	0.589770i
$701$	−4.58811	−	15.1250i	−0.173291	−	0.571263i	−0.999963	−	0.00857942i	$-0.997269\pi$
$701$	−4.58811	−	15.1250i	−0.173291	−	0.571263i	0.826673	−	0.562683i	$-0.190231\pi$
$702$	5.40525	+	3.26010i	0.204008	+	0.123044i
$703$		−	17.2958i		−	0.652323i
$704$	−41.9969	+	16.5860i	−1.58282	+	0.625110i
$705$		−	5.45864i		−	0.205584i
$706$	3.83166	−	6.35290i	0.144206	−	0.239094i
$707$	12.4797	+	41.1402i	0.469349	+	1.54724i
$708$	21.3947	+	17.7568i	0.804061	+	0.667340i
$709$	−0.257349	−	2.61290i	−0.00966493	−	0.0981297i	0.989142	−	0.146963i	$-0.0469498\pi$
$709$	−0.257349	−	2.61290i	−0.00966493	−	0.0981297i	−0.998807	+	0.0488331i	$0.984450\pi$
$710$	8.33939	+	2.11339i	0.312972	+	0.0793143i
$711$	0.260795	+	0.174258i	0.00978059	+	0.00653518i
$712$	5.88041	+	4.43717i	0.220378	+	0.166290i
$713$	−0.475327	−	0.711377i	−0.0178011	−	0.0266413i
$714$	−8.56767	+	17.9862i	−0.320637	+	0.673115i
$715$	41.5374	−	22.2022i	1.55341	−	0.830315i
$716$	23.6336	−	9.63679i	0.883228	−	0.360144i
$717$	2.62666	+	0.258704i	0.0980945	+	0.00966146i
$718$	33.5850	−	15.7712i	1.25338	−	0.588576i
$719$	−12.0541	−	29.1013i	−0.449544	−	1.08529i	−0.972493	−	0.232931i	$-0.925168\pi$
$719$	−12.0541	−	29.1013i	−0.449544	−	1.08529i	0.522949	−	0.852364i	$-0.324832\pi$
$720$	0.650755	+	7.44983i	0.0242522	+	0.277639i
$721$	5.18236	−	12.5113i	0.193001	−	0.465946i
$722$	1.02280	+	22.0625i	0.0380649	+	0.821080i
$723$	2.72600	−	2.23717i	0.101381	−	0.0832011i
$724$	−25.3830	+	37.5380i	−0.943353	+	1.39509i
$725$	12.4158	+	3.76628i	0.461110	+	0.139876i
$726$	1.52863	−	29.4563i	0.0567329	−	1.09323i
$727$	18.8774	+	3.75494i	0.700122	+	0.139263i	0.532302	−	0.846555i	$-0.321327\pi$
$727$	18.8774	+	3.75494i	0.700122	+	0.139263i	0.167820	+	0.985818i	$0.446327\pi$
$728$	−65.6824	+	2.68161i	−2.43435	+	0.0993869i
$729$	−0.195090	−	0.980785i	−0.00722557	−	0.0363254i
$730$	−15.7287	−	11.7326i	−0.582145	−	0.434244i
$731$	5.06823	+	4.15939i	0.187455	+	0.153840i
$732$	−8.09043	−	4.38204i	−0.299031	−	0.161965i
$733$	−2.58275	+	4.83198i	−0.0953960	+	0.178473i	−0.925093	−	0.379741i	$-0.876013\pi$
$733$	−2.58275	+	4.83198i	−0.0953960	+	0.178473i	0.829697	+	0.558214i	$0.188513\pi$
$734$	−0.191632	−	0.0289669i	−0.00707326	−	0.00106919i
$735$	26.5897	+	26.5897i	0.980775	+	0.980775i
$736$	−0.831563	−	0.514155i	−0.0306518	−	0.0189520i
$737$	14.8674	−	14.8674i	0.547647	−	0.547647i
$738$	−4.91461	+	3.62393i	−0.180909	+	0.133399i
$739$	−5.04416	−	2.69616i	−0.185553	−	0.0991799i	0.376005	−	0.926618i	$-0.377298\pi$
$739$	−5.04416	−	2.69616i	−0.185553	−	0.0991799i	−0.561557	+	0.827438i	$0.689798\pi$
$740$	−34.9731	−	3.63966i	−1.28564	−	0.133797i
$741$	−5.20791	+	6.34586i	−0.191317	+	0.233121i
$742$	5.43265	+	37.3339i	0.199439	+	1.37057i
$743$	−0.897544	+	0.178533i	−0.0329277	+	0.00654972i	−0.211527	−	0.977372i	$-0.567844\pi$
$743$	−0.897544	+	0.178533i	−0.0329277	+	0.00654972i	0.178599	+	0.983922i	$0.442844\pi$
$744$	−3.28950	−	13.6097i	−0.120599	−	0.498956i
$745$	0.182188	−	0.915921i	0.00667485	−	0.0335568i
$746$	−32.5509	−	36.1143i	−1.19177	−	1.32224i
$747$	−0.871834	+	2.87405i	−0.0318988	+	0.105156i
$748$	16.8265	+	25.4862i	0.615238	+	0.931868i
$749$	−19.2870	−	23.5013i	−0.704733	−	0.858719i
$750$	−11.5848	+	12.7111i	−0.423017	+	0.464145i
$751$	−16.5277	−	6.84600i	−0.603104	−	0.249814i	0.0601726	−	0.998188i	$-0.480835\pi$
$751$	−16.5277	−	6.84600i	−0.603104	−	0.249814i	−0.663277	+	0.748374i	$0.730835\pi$
$752$	6.38089	+	9.78184i	0.232687	+	0.356707i
$753$	14.2617	−	5.90739i	0.519725	−	0.215277i
$754$	18.4767	−	51.1929i	0.672882	−	1.86434i
$755$	3.14308	−	31.9122i	0.114388	−	1.16140i
$756$	7.32314	+	7.40447i	0.266340	+	0.269298i
$757$	11.4246	+	21.3740i	0.415235	+	0.776851i	0.999395	−	0.0347881i	$-0.0110756\pi$
$757$	11.4246	+	21.3740i	0.415235	+	0.776851i	−0.584159	+	0.811639i	$0.698576\pi$
$758$	11.5468	−	4.09559i	0.419399	−	0.148759i
$759$	0.811088	−	0.541951i	0.0294406	−	0.0196716i
$760$	−9.70957	−	0.557656i	−0.352203	−	0.0202283i
$761$	−17.8753	+	26.7523i	−0.647979	+	0.969770i	0.351457	+	0.936204i	$0.385686\pi$
$761$	−17.8753	+	26.7523i	−0.647979	+	0.969770i	−0.999437	+	0.0335656i	$0.989314\pi$
$762$	5.44971	−	3.24601i	0.197422	−	0.117590i
$763$	84.6926	−	8.34149i	3.06608	−	0.301982i
$764$	−3.43703	−	6.51653i	−0.124347	−	0.235760i
$765$	4.84013	−	1.46824i	0.174995	−	0.0530842i
$766$	51.1427	−	12.6606i	1.84786	−	0.457447i
$767$	62.0499			2.24049
$768$	−9.87464	−	12.5893i	−0.356321	−	0.454279i
$769$	−33.6537			−1.21358			−0.606792	−	0.794861i	$-0.707544\pi$
$769$	−33.6537			−1.21358			−0.606792	+	0.794861i	$0.707544\pi$
$770$	75.4278	−	18.6725i	2.71823	−	0.672910i
$771$	6.14453	−	1.86392i	0.221290	−	0.0671275i
$772$	−11.7305	−	22.2408i	−0.422190	−	0.800464i
$773$	41.5754	−	4.09482i	1.49536	−	0.147280i	0.682993	−	0.730425i	$-0.260678\pi$
$773$	41.5754	−	4.09482i	1.49536	−	0.147280i	0.812368	+	0.583145i	$0.198178\pi$
$774$	2.94454	−	1.75385i	0.105839	−	0.0630410i
$775$	4.13853	−	6.19376i	0.148661	−	0.222486i
$776$	−0.681278	+	11.8620i	−0.0244565	+	0.425822i
$777$	−40.7143	+	27.2044i	−1.46062	+	0.975954i
$778$	14.3298	−	5.08271i	0.513750	−	0.182224i
$779$	−3.74352	−	7.00363i	−0.134125	−	0.250931i
$780$	11.7358	+	11.8661i	0.420208	+	0.424875i
$781$	1.80012	−	18.2769i	0.0644134	−	0.654000i
$782$	−0.224489	+	0.621986i	−0.00802772	+	0.0222422i
$783$	−7.96579	+	3.29954i	−0.284674	+	0.117916i
$784$	−78.7306	−	16.5664i	−2.81181	−	0.591658i
$785$	−12.2229	−	5.06288i	−0.436253	−	0.180702i
$786$	5.48804	−	6.02162i	0.195752	−	0.214784i
$787$	28.1889	+	34.3482i	1.00482	+	1.22438i	0.974395	+	0.224845i	$0.0721875\pi$
$787$	28.1889	+	34.3482i	1.00482	+	1.22438i	0.0304294	+	0.999537i	$0.490313\pi$
$788$	−23.0090	−	34.8505i	−0.819663	−	1.24150i
$789$	−4.96045	+	16.3524i	−0.176597	+	0.582162i
$790$	0.555217	+	0.615997i	0.0197537	+	0.0219162i
$791$	−16.5876	+	83.3913i	−0.589786	+	2.96505i
$792$	15.5173	−	3.75057i	0.551384	−	0.133271i
$793$	−20.1395	+	4.00599i	−0.715173	+	0.142257i
$794$	4.43666	+	30.4893i	0.157451	+	1.08202i
$795$	6.07630	−	7.40400i	0.215504	−	0.262593i
$796$	14.3183	+	1.49011i	0.507500	+	0.0528157i
$797$	8.63836	+	4.61730i	0.305986	+	0.163553i	0.617243	−	0.786773i	$-0.288250\pi$
$797$	8.63836	+	4.61730i	0.305986	+	0.163553i	−0.311256	+	0.950326i	$0.600750\pi$
$798$	−10.9008	+	8.03800i	−0.385883	+	0.284542i
$799$	5.58557	−	5.58557i	0.197603	−	0.197603i
$800$	1.36514	−	8.40218i	0.0482651	−	0.297062i
$801$	−1.84167	−	1.84167i	−0.0650720	−	0.0650720i
$802$	−17.4195	−	2.63311i	−0.615104	−	0.0929784i
$803$	−19.7466	+	36.9433i	−0.696842	+	1.30370i
$804$	6.55116	+	3.54832i	0.231041	+	0.125139i
$805$	1.30058	+	1.06736i	0.0458394	+	0.0376194i
$806$	−25.0470	−	18.6835i	−0.882242	−	0.658099i
$807$	−1.83663	−	9.23335i	−0.0646523	−	0.325029i
$808$	0.952614	+	23.3330i	0.0335128	+	0.820853i
$809$	38.8104	+	7.71988i	1.36450	+	0.271416i	0.822406	−	0.568900i	$-0.192631\pi$
$809$	38.8104	+	7.71988i	1.36450	+	0.271416i	0.542096	+	0.840317i	$0.317631\pi$
$810$	0.137023	−	2.64039i	0.00481449	−	0.0927738i
$811$	−3.21496	−	0.975247i	−0.112892	−	0.0342455i	0.233333	−	0.972397i	$-0.425037\pi$
$811$	−3.21496	−	0.975247i	−0.112892	−	0.0342455i	−0.346225	+	0.938151i	$0.612537\pi$
$812$	50.2973	−	74.3827i	1.76509	−	2.61032i
$813$	7.41903	−	6.08864i	0.260197	−	0.213538i
$814$	3.47612	+	74.9819i	0.121838	+	2.62812i
$815$	−7.18938	+	17.3567i	−0.251833	+	0.607978i
$816$	−6.95718	+	8.28895i	−0.243550	+	0.290171i
$817$	1.70572	+	4.11798i	0.0596757	+	0.144070i
$818$	−37.2846	+	17.5085i	−1.30363	+	0.612170i
$819$	23.1297	+	2.27807i	0.808216	+	0.0796023i
$820$	−14.9495	+	6.09580i	−0.522060	+	0.212875i
$821$	16.1811	−	8.64897i	0.564724	−	0.301851i	−0.164221	−	0.986424i	$-0.552511\pi$
$821$	16.1811	−	8.64897i	0.564724	−	0.301851i	0.728945	+	0.684572i	$0.240011\pi$
$822$	8.37291	−	17.5773i	0.292039	−	0.613079i
$823$	10.8343	+	16.2146i	0.377658	+	0.565206i	0.970799	−	0.239893i	$-0.0771123\pi$
$823$	10.8343	+	16.2146i	0.377658	+	0.565206i	−0.593141	+	0.805099i	$0.702112\pi$
$824$	4.43072	−	5.87185i	0.154352	−	0.204556i
$825$	7.06191	+	4.71862i	0.245864	+	0.164281i
$826$	99.2343	+	25.1483i	3.45280	+	0.875021i
$827$	0.604459	+	6.13717i	0.0210191	+	0.213410i	0.999957	+	0.00925315i	$0.00294541\pi$
$827$	0.604459	+	6.13717i	0.0210191	+	0.213410i	−0.978938	+	0.204157i	$0.934555\pi$
$828$	0.265985	+	0.220757i	0.00924361	+	0.00767184i
$829$	2.94210	+	9.69880i	0.102183	+	0.336853i	0.993093	−	0.117326i	$-0.0374324\pi$
$829$	2.94210	+	9.69880i	0.102183	+	0.336853i	−0.890910	+	0.454180i	$0.849932\pi$
$830$	−4.10115	+	6.79971i	−0.142353	+	0.236022i
$831$			12.3171i			0.427276i
$832$	−34.9013	−	7.54542i	−1.20999	−	0.261590i
$833$			54.4160i			1.88540i
$834$	12.6024	+	7.60098i	0.436387	+	0.263201i
$835$	4.53447	+	14.9481i	0.156922	+	0.517302i
$836$	1.92088	+	20.6727i	0.0664351	+	0.714981i
$837$	0.485216	+	4.92648i	0.0167715	+	0.170284i
$838$	−2.51888	+	9.93943i	−0.0870134	+	0.343352i
$839$	−13.4844	−	9.00999i	−0.465533	−	0.311060i	0.300589	−	0.953754i	$-0.402817\pi$
$839$	−13.4844	−	9.00999i	−0.465533	−	0.311060i	−0.766123	+	0.642694i	$0.777817\pi$
$840$	13.9594	+	23.7335i	0.481646	+	0.818884i
$841$	25.1900	+	37.6995i	0.868621	+	1.29998i
$842$	43.2048	+	20.5805i	1.48894	+	0.709251i
$843$	−6.16300	+	3.29419i	−0.212265	+	0.113458i
$844$	13.9563	−	33.1742i	0.480396	−	1.14190i
$845$	12.8796	+	1.26853i	0.443070	+	0.0436386i
$846$	−1.75513	−	3.73758i	−0.0603427	−	0.128501i
$847$	−41.5605	−	100.336i	−1.42804	−	3.44758i
$848$	−2.23377	+	20.3708i	−0.0767080	+	0.699537i
$849$	9.80123	−	23.6623i	0.336378	−	0.812087i
$850$	−5.75120	+	0.266623i	−0.197265	+	0.00914509i
$851$	−1.25636	+	1.03106i	−0.0430673	+	0.0353444i
$852$	6.38959	−	1.23433i	0.218904	−	0.0422874i
$853$	−15.8726	−	4.81489i	−0.543467	−	0.164859i	0.00660198	−	0.999978i	$-0.497899\pi$
$853$	−15.8726	−	4.81489i	−0.543467	−	0.164859i	−0.550069	+	0.835119i	$0.685399\pi$
$854$	−33.8320	−	1.75571i	−1.15771	−	0.0600791i
$855$	3.37244	+	0.670820i	0.115335	+	0.0229416i
$856$	−6.93684	−	14.9866i	−0.237096	−	0.512233i
$857$	5.85165	+	29.4182i	0.199888	+	1.00491i	0.942251	+	0.334908i	$0.108705\pi$
$857$	5.85165	+	29.4182i	0.199888	+	1.00491i	−0.742362	+	0.669999i	$0.766295\pi$
$858$	21.3023	−	28.5577i	0.727249	−	0.974944i
$859$	−1.33945	−	1.09926i	−0.0457014	−	0.0375062i	0.611265	−	0.791426i	$-0.290661\pi$
$859$	−1.33945	−	1.09926i	−0.0457014	−	0.0375062i	−0.656967	+	0.753920i	$0.728161\pi$
$860$	8.68575	−	2.58250i	0.296182	−	0.0880627i
$861$	−10.5984	+	19.8282i	−0.361193	+	0.675744i
$862$	−3.03653	+	20.0883i	−0.103425	+	0.684211i
$863$	−19.9729	−	19.9729i	−0.679886	−	0.679886i	0.280088	−	0.959974i	$-0.409636\pi$
$863$	−19.9729	−	19.9729i	−0.679886	−	0.679886i	−0.959974	+	0.280088i	$0.909636\pi$
$864$	2.84095	+	4.89173i	0.0966509	+	0.166420i
$865$	2.24636	−	2.24636i	0.0763785	−	0.0763785i
$866$	−10.5181	−	14.2642i	−0.357420	−	0.484717i
$867$	−8.53760	−	4.56344i	−0.289952	−	0.154983i
$868$	−32.4845	−	40.0313i	−1.10260	−	1.35875i
$869$	1.12309	−	1.36848i	0.0380981	−	0.0464227i
$870$	−22.5588	+	3.28265i	−0.764814	+	0.111292i
$871$	16.3077	−	3.24381i	0.552567	−	0.109912i
$872$	45.6686	+	7.16138i	1.54653	+	0.242515i
$873$	0.819529	−	4.12005i	0.0277369	−	0.139443i
$874$	−0.333920	+	0.300972i	−0.0112950	+	0.0101805i
$875$	−18.3818	+	60.5967i	−0.621418	+	2.04854i
$876$	−14.5420	−	2.97616i	−0.491329	−	0.100555i
$877$	19.8880	+	24.2337i	0.671572	+	0.818312i	0.991634	−	0.129084i	$-0.0412038\pi$
$877$	19.8880	+	24.2337i	0.671572	+	0.818312i	−0.320062	+	0.947397i	$0.603704\pi$
$878$	31.5010	+	28.7097i	1.06311	+	0.968905i
$879$	−6.01318	−	2.49074i	−0.202820	−	0.0840106i
$880$	42.2057	+	0.466149i	1.42275	+	0.0157139i
$881$	−3.73490	+	1.54705i	−0.125832	+	0.0521214i	−0.444711	−	0.895674i	$-0.646694\pi$
$881$	−3.73490	+	1.54705i	−0.125832	+	0.0521214i	0.318879	+	0.947795i	$0.396694\pi$
$882$	26.7557	+	9.65675i	0.900910	+	0.325160i
$883$	−1.68964	+	17.1552i	−0.0568611	+	0.577320i	0.923971	+	0.382463i	$0.124924\pi$
$883$	−1.68964	+	17.1552i	−0.0568611	+	0.577320i	−0.980832	+	0.194857i	$0.937576\pi$
$884$	−0.133365	+	24.1507i	−0.00448553	+	0.812276i
$885$	−12.2516	−	22.9211i	−0.411833	−	0.770485i
$886$	−8.44328	−	23.8044i	−0.283658	−	0.799724i
$887$	−6.83661	+	4.56808i	−0.229551	+	0.153381i	−0.665027	−	0.746819i	$-0.731580\pi$
$887$	−6.83661	+	4.56808i	−0.229551	+	0.153381i	0.435476	+	0.900200i	$0.356580\pi$
$888$	−25.1167	+	8.75291i	−0.842862	+	0.293729i
$889$	12.9755	−	19.4192i	0.435185	−	0.651300i
$890$	−3.52388	−	5.91621i	−0.118121	−	0.198312i
$891$	−5.61700	+	0.553226i	−0.188177	+	0.0185338i
$892$	−41.1477	−	12.7306i	−1.37773	−	0.426251i
$893$	5.13885	−	1.55885i	0.171965	−	0.0521650i
$894$	−0.169753	−	0.685720i	−0.00567739	−	0.0229339i
$895$	−23.8581			−0.797487
$896$	−52.7585	−	26.2124i	−1.76254	−	0.875694i
$897$	0.771422			0.0257570
$898$	0.388836	+	1.57071i	0.0129756	+	0.0524152i
$899$	40.8443	−	12.3900i	1.36223	−	0.413229i
$900$	−0.889523	+	2.87511i	−0.0296508	+	0.0958371i
$901$	13.7938	−	1.35857i	0.459537	−	0.0452604i
$902$	17.6368	+	29.6102i	0.587240	+	0.985913i
$903$	7.01081	−	10.4924i	0.233305	−	0.349166i
$904$	−20.0916	+	41.5855i	−0.668238	+	1.38311i
$905$	35.2201	−	23.5333i	1.17075	−	0.782273i
$906$	−8.10874	−	22.8612i	−0.269395	−	0.759513i
$907$	−8.16782	−	15.2809i	−0.271208	−	0.507394i	0.709040	−	0.705169i	$-0.249129\pi$
$907$	−8.16782	−	15.2809i	−0.271208	−	0.507394i	−0.980248	+	0.197774i	$0.936629\pi$
$908$	−6.45466	−	0.0356438i	−0.214206	−	0.00118288i
$909$	0.809263	−	8.21658i	0.0268415	−	0.272527i
$910$	57.7999	+	20.8613i	1.91605	+	0.691547i
$911$	40.4469	−	16.7536i	1.34006	−	0.555073i	0.406555	−	0.913626i	$-0.366730\pi$
$911$	40.4469	−	16.7536i	1.34006	−	0.555073i	0.933509	+	0.358553i	$0.116730\pi$
$912$	−6.82754	+	2.74012i	−0.226083	+	0.0907344i
$913$	15.6612	+	6.48710i	0.518311	+	0.214692i
$914$	−14.7193	−	13.4150i	−0.486870	−	0.443728i
$915$	5.45629	+	6.64851i	0.180380	+	0.219793i
$916$	−4.99661	+	24.4143i	−0.165093	+	0.806671i
$917$	8.70797	−	28.7063i	0.287562	−	0.947966i
$918$	2.84200	−	2.56158i	0.0937999	−	0.0845447i
$919$	−2.37379	+	11.9338i	−0.0783040	+	0.393661i	0.921680	+	0.387952i	$0.126817\pi$
$919$	−2.37379	+	11.9338i	−0.0783040	+	0.393661i	−0.999984	+	0.00570902i	$0.998183\pi$
$920$	0.538315	+	0.738542i	0.0177477	+	0.0243490i
$921$	−20.5207	+	4.08183i	−0.676181	+	0.134501i
$922$	7.35513	−	1.07028i	0.242228	−	0.0352479i
$923$	9.21359	−	11.2268i	0.303269	−	0.369534i
$924$	45.6423	−	37.0378i	1.50152	−	1.21845i
$925$	−12.4799	−	6.67065i	−0.410337	−	0.219330i
$926$	−3.57832	−	4.85275i	−0.117591	−	0.159471i
$927$	−1.83899	+	1.83899i	−0.0604003	+	0.0604003i
$928$	36.5879	−	32.2526i	1.20106	−	1.05874i
$929$	−36.1212	−	36.1212i	−1.18510	−	1.18510i	−0.978406	−	0.206691i	$-0.933731\pi$
$929$	−36.1212	−	36.1212i	−1.18510	−	1.18510i	−0.206691	−	0.978406i	$-0.566269\pi$
$930$	−1.95620	+	12.9413i	−0.0641463	+	0.424363i
$931$	−17.4386	+	32.6253i	−0.571526	+	1.06925i
$932$	9.32856	+	31.3748i	0.305567	+	1.02772i
$933$	−24.3971	−	20.0222i	−0.798726	−	0.655497i
$934$	−3.39938	+	4.55718i	−0.111231	+	0.149115i
$935$	−5.56940	−	27.9993i	−0.182139	−	0.915674i
$936$	11.8509	+	4.35140i	0.387360	+	0.142230i
$937$	2.48575	+	0.494446i	0.0812058	+	0.0161528i	0.235526	−	0.971868i	$-0.424319\pi$
$937$	2.48575	+	0.494446i	0.0812058	+	0.0161528i	−0.154320	+	0.988021i	$0.549319\pi$
$938$	27.3951	+	1.42167i	0.894483	+	0.0464192i
$939$	11.0134	+	3.34089i	0.359410	+	0.109026i
$940$	−2.07070	−	10.7191i	−0.0675386	−	0.349619i
$941$	−25.3601	+	20.8125i	−0.826715	+	0.678468i	−0.949432	−	0.313974i	$-0.898339\pi$
$941$	−25.3601	+	20.8125i	−0.826715	+	0.678468i	0.122716	+	0.992442i	$0.460839\pi$
$942$	−9.99701	+	0.463456i	−0.325720	+	0.0151002i
$943$	−0.285575	+	0.689439i	−0.00929960	+	0.0224512i
$944$	48.7485	+	26.7530i	1.58663	+	0.870735i
$945$	−3.72538	−	8.99386i	−0.121187	−	0.292570i
$946$	−8.22241	−	17.5097i	−0.267334	−	0.569291i
$947$	−22.7014	−	2.23589i	−0.737697	−	0.0726568i	−0.277812	−	0.960635i	$-0.589609\pi$
$947$	−22.7014	−	2.23589i	−0.737697	−	0.0726568i	−0.459885	+	0.887979i	$0.652109\pi$
$948$	0.578226	+	0.243259i	0.0187799	+	0.00790067i
$949$	−29.2150	+	15.6157i	−0.948359	+	0.506908i
$950$	−3.53360	−	1.68322i	−0.114645	−	0.0546109i
$951$	2.31977	+	3.47178i	0.0752236	+	0.112580i
$952$	−10.0014	+	38.5694i	−0.324146	+	1.25004i
$953$	−50.6759	−	33.8606i	−1.64155	−	1.09685i	−0.909590	−	0.415507i	$-0.863604\pi$
$953$	−50.6759	−	33.8606i	−1.64155	−	1.09685i	−0.731963	−	0.681344i	$-0.761396\pi$
$954$	1.77987	−	7.02332i	0.0576255	−	0.227388i
$955$	0.675029	+	6.85368i	0.0218434	+	0.221780i
$956$	5.25610	−	0.488390i	0.169994	−	0.0157957i
$957$	14.1266	+	46.5693i	0.456649	+	1.50537i
$958$	−24.2728	−	14.6398i	−0.784219	−	0.472991i
$959$		−	71.6865i		−	2.31488i
$960$	4.10392	+	14.3823i	0.132454	+	0.464188i
$961$			6.49437i			0.209496i
$962$	−30.6576	+	50.8303i	−0.988440	+	1.63883i
$963$	1.69487	+	5.58724i	0.0546165	+	0.180046i
$964$	4.50437	−	5.42720i	0.145076	−	0.174798i
$965$	2.30386	+	23.3915i	0.0741639	+	0.752998i
$966$	1.23371	+	0.312651i	0.0396940	+	0.0100594i
$967$	−25.1012	−	16.7721i	−0.807200	−	0.539354i	0.0821291	−	0.996622i	$-0.473828\pi$
$967$	−25.1012	−	16.7721i	−0.807200	−	0.539354i	−0.889329	+	0.457268i	$0.848828\pi$
$968$	−8.17226	−	58.4231i	−0.262666	−	1.87779i
$969$	2.76444	+	4.13728i	0.0888067	+	0.132909i
$970$	4.77638	−	10.0271i	0.153360	−	0.321950i
$971$	37.2349	−	19.9025i	1.19493	−	0.638701i	0.250721	−	0.968059i	$-0.419332\pi$
$971$	37.2349	−	19.9025i	1.19493	−	0.638701i	0.944205	+	0.329358i	$0.106832\pi$
$972$	−0.755152	−	1.85196i	−0.0242215	−	0.0594016i
$973$	53.9273	+	5.31137i	1.72883	+	0.170275i
$974$	7.94988	−	3.73319i	0.254731	−	0.119619i
$975$	2.57031	+	6.20528i	0.0823159	+	0.198728i
$976$	−17.5494	−	5.53594i	−0.561744	−	0.177201i
$977$	−20.7533	+	50.1029i	−0.663956	+	1.60293i	0.127592	+	0.991827i	$0.459275\pi$
$977$	−20.7533	+	50.1029i	−0.663956	+	1.60293i	−0.791549	+	0.611106i	$0.790725\pi$
$978$	0.658115	+	14.1959i	0.0210442	+	0.453935i
$979$	−11.3635	+	9.32578i	−0.363179	+	0.298053i
$980$	62.3006	+	42.1274i	1.99012	+	1.34571i
$981$	−15.6398	−	4.74429i	−0.499342	−	0.151474i
$982$	−1.72600	+	33.2595i	−0.0550789	+	1.06135i
$983$	17.3142	+	3.44400i	0.552236	+	0.109847i	0.463317	−	0.886192i	$-0.346659\pi$
$983$	17.3142	+	3.44400i	0.552236	+	0.109847i	0.0889184	+	0.996039i	$0.471659\pi$
$984$	−8.27609	+	8.98063i	−0.263832	+	0.286292i
$985$	7.61575	+	38.2870i	0.242658	+	1.21992i
$986$	−26.4423	−	19.7244i	−0.842095	−	0.628152i
$987$	−11.7524	−	9.64495i	−0.374083	−	0.307002i
$988$	−7.81949	+	14.4369i	−0.248771	+	0.459299i
$989$	0.197443	−	0.369391i	0.00627833	−	0.0117459i
$990$	−14.7553	−	2.23039i	−0.468953	−	0.0708865i
$991$	24.8418	+	24.8418i	0.789126	+	0.789126i	0.981351	−	0.192225i	$-0.0615702\pi$
$991$	24.8418	+	24.8418i	0.789126	+	0.789126i	−0.192225	+	0.981351i	$0.561570\pi$
$992$	−11.6223	−	25.4775i	−0.369009	−	0.808911i
$993$	−22.4021	+	22.4021i	−0.710910	+	0.710910i
$994$	19.2851	−	14.2204i	0.611687	−	0.451045i
$995$	−11.8678	−	6.34345i	−0.376233	−	0.201101i
$996$	−0.621766	+	5.97449i	−0.0197014	+	0.189309i
$997$	18.3715	−	22.3858i	0.581832	−	0.708964i	−0.396025	−	0.918240i	$-0.629611\pi$
$997$	18.3715	−	22.3858i	0.581832	−	0.708964i	0.977857	+	0.209276i	$0.0671106\pi$
$998$	3.18049	+	21.8567i	0.100677	+	0.691862i
$999$	9.22318	−	1.83461i	0.291809	−	0.0580443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.205.3	yes	512
128.5	even	32	inner	384.2.v.a.133.3	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.133.3	✓	512	128.5	even	32	inner
384.2.v.a.205.3	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)

\(f(q)\)	\(=\)	\(q+(-1.37277 + 0.339837i) q^{2} +(0.956940 - 0.290285i) q^{3} +(1.76902 - 0.933039i) q^{4} +(-1.86055 + 0.183248i) q^{5} +(-1.21501 + 0.723699i) q^{6} +(-2.89290 + 4.32953i) q^{7} +(-2.11139 + 1.88203i) q^{8} +(0.831470 - 0.555570i) q^{9} +O(q^{10})\)	\(q+(-1.37277 + 0.339837i) q^{2} +(0.956940 - 0.290285i) q^{3} +(1.76902 - 0.933039i) q^{4} +(-1.86055 + 0.183248i) q^{5} +(-1.21501 + 0.723699i) q^{6} +(-2.89290 + 4.32953i) q^{7} +(-2.11139 + 1.88203i) q^{8} +(0.831470 - 0.555570i) q^{9} +(2.49184 - 0.883840i) q^{10} +(-2.66065 - 4.97772i) q^{11} +(1.42200 - 1.40638i) q^{12} +(0.437495 - 4.44197i) q^{13} +(2.49996 - 6.92658i) q^{14} +(-1.72724 + 0.715445i) q^{15} +(2.25888 - 3.30113i) q^{16} +(-2.49948 - 1.03532i) q^{17} +(-0.952617 + 1.04524i) q^{18} +(-1.16679 - 1.42174i) q^{19} +(-3.12037 + 2.06013i) q^{20} +(-1.51153 + 4.98286i) q^{21} +(5.34408 + 5.92911i) q^{22} +(-0.0337176 + 0.169510i) q^{23} +(-1.47415 + 2.41390i) q^{24} +(-1.47587 + 0.293569i) q^{25} +(0.908961 + 6.24650i) q^{26} +(0.634393 - 0.773010i) q^{27} +(-1.07798 + 10.3582i) q^{28} +(-7.60402 - 4.06443i) q^{29} +(2.12797 - 1.56912i) q^{30} +(-3.50040 + 3.50040i) q^{31} +(-1.97908 + 5.29936i) q^{32} +(-3.99104 - 3.99104i) q^{33} +(3.78307 + 0.571845i) q^{34} +(4.58899 - 8.58540i) q^{35} +(0.952519 - 1.75861i) q^{36} +(7.26929 + 5.96576i) q^{37} +(2.08490 + 1.55520i) q^{38} +(-0.870778 - 4.37769i) q^{39} +(3.58346 - 3.88851i) q^{40} +(4.23481 + 0.842356i) q^{41} +(0.381637 - 7.35402i) q^{42} +(-2.31910 - 0.703493i) q^{43} +(-9.35115 - 6.32321i) q^{44} +(-1.44518 + 1.18603i) q^{45} +(-0.0113190 - 0.244157i) q^{46} +(-1.11734 + 2.69751i) q^{47} +(1.20334 - 3.81470i) q^{48} +(-7.69716 - 18.5826i) q^{49} +(1.92627 - 0.904560i) q^{50} +(-2.69240 - 0.265178i) q^{51} +(-3.37059 - 8.26613i) q^{52} +(-4.51829 + 2.41507i) q^{53} +(-0.608182 + 1.27676i) q^{54} +(5.86242 + 8.77373i) q^{55} +(-2.04028 - 14.5858i) q^{56} +(-1.52925 - 1.02182i) q^{57} +(11.8199 + 2.99543i) q^{58} +(1.36261 + 13.8348i) q^{59} +(-2.38798 + 2.87722i) q^{60} +(-1.33545 - 4.40238i) q^{61} +(3.61570 - 5.99483i) q^{62} +5.20708i q^{63} +(0.915916 - 7.94740i) q^{64} +8.34465i q^{65} +(6.83510 + 4.12250i) q^{66} +(1.08137 + 3.56479i) q^{67} +(-5.38764 + 0.500612i) q^{68} +(0.0169404 + 0.171998i) q^{69} +(-3.38202 + 13.3453i) q^{70} +(2.70548 + 1.80775i) q^{71} +(-0.709954 + 2.73788i) q^{72} +(-4.12329 - 6.17093i) q^{73} +(-12.0065 - 5.71927i) q^{74} +(-1.32710 + 0.709351i) q^{75} +(-3.39061 - 1.42642i) q^{76} +(29.2482 + 2.88069i) q^{77} +(2.68308 + 5.71367i) q^{78} +(0.120031 + 0.289780i) q^{79} +(-3.59782 + 6.55585i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-6.09970 + 0.282779i) q^{82} +(-2.32164 + 1.90532i) q^{83} +(1.97527 + 10.2251i) q^{84} +(4.84013 + 1.46824i) q^{85} +(3.42268 + 0.177620i) q^{86} +(-8.45644 - 1.68209i) q^{87} +(14.9859 + 5.50248i) q^{88} +(-0.508114 - 2.55446i) q^{89} +(1.58085 - 2.11928i) q^{90} +(17.9660 + 14.7443i) q^{91} +(0.0985120 + 0.331326i) q^{92} +(-2.33356 + 4.36579i) q^{93} +(0.617150 - 4.08279i) q^{94} +(2.43139 + 2.43139i) q^{95} +(-0.355540 + 5.64567i) q^{96} +(2.97039 - 2.97039i) q^{97} +(16.8815 + 22.8939i) q^{98} +(-4.97772 - 2.66065i) 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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