LMFDB - Embedded newform 384.2.v.a.157.31

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			157.31
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37680 - 0.323159i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.79114 - 0.889849i) q^{4} +(-3.05895 + 1.63504i) q^{5} +(0.186654 + 1.40184i) q^{6} +(0.897509 + 4.51208i) q^{7} +(2.17847 - 1.80396i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(1.37680 - 0.323159i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.79114 - 0.889849i) q^{4} +(-3.05895 + 1.63504i) q^{5} +(0.186654 + 1.40184i) q^{6} +(0.897509 + 4.51208i) q^{7} +(2.17847 - 1.80396i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-3.68317 + 3.23965i) q^{10} +(-1.49441 + 1.82094i) q^{11} +(0.710002 + 1.86973i) q^{12} +(2.64959 - 4.95704i) q^{13} +(2.69381 + 5.92218i) q^{14} +(-1.32734 - 3.20448i) q^{15} +(2.41634 - 3.18768i) q^{16} +(-2.71873 + 6.56358i) q^{17} +(-1.41339 + 0.0483504i) q^{18} +(0.494439 + 1.62995i) q^{19} +(-4.02405 + 5.65059i) q^{20} +(-4.57833 + 0.450926i) q^{21} +(-1.46904 + 2.99000i) q^{22} +(4.60673 - 3.07812i) q^{23} +(1.58175 + 2.34480i) q^{24} +(3.90596 - 5.84568i) q^{25} +(2.04603 - 7.68107i) q^{26} +(0.290285 - 0.956940i) q^{27} +(5.62264 + 7.28311i) q^{28} +(2.72288 - 2.23461i) q^{29} +(-2.86304 - 3.98298i) q^{30} +(2.98553 - 2.98553i) q^{31} +(2.29667 - 5.16965i) q^{32} +(-1.66570 - 1.66570i) q^{33} +(-1.62205 + 9.91530i) q^{34} +(-10.1229 - 12.3348i) q^{35} +(-1.93032 + 0.523318i) q^{36} +(2.73216 + 0.828790i) q^{37} +(1.20748 + 2.08432i) q^{38} +(4.67346 + 3.12271i) q^{39} +(-3.71426 + 9.08012i) q^{40} +(1.02226 + 1.52992i) q^{41} +(-6.15770 + 2.10036i) q^{42} +(-0.649456 - 6.59404i) q^{43} +(-1.05632 + 4.59135i) q^{44} +(3.31915 - 1.00685i) q^{45} +(5.34781 - 5.72665i) q^{46} +(3.79591 + 1.57232i) q^{47} +(2.93549 + 2.71715i) q^{48} +(-13.0862 + 5.42049i) q^{49} +(3.48862 - 9.31056i) q^{50} +(-6.26550 - 3.34898i) q^{51} +(0.334762 - 11.2365i) q^{52} +(-7.75287 - 6.36262i) q^{53} +(0.0904186 - 1.41132i) q^{54} +(1.59400 - 8.01359i) q^{55} +(10.0948 + 8.21035i) q^{56} +(-1.67056 + 0.332296i) q^{57} +(3.02671 - 3.95652i) q^{58} +(-1.13136 - 2.11662i) q^{59} +(-5.22895 - 4.55853i) q^{60} +(-7.50183 - 0.738865i) q^{61} +(3.14566 - 5.07526i) q^{62} -4.60048i q^{63} +(1.49143 - 7.85975i) q^{64} +19.4955i q^{65} +(-2.83161 - 1.75504i) q^{66} +(10.1357 + 0.998275i) q^{67} +(0.970994 + 14.1755i) q^{68} +(2.61176 + 4.88626i) q^{69} +(-17.9233 - 13.7112i) q^{70} +(10.0974 - 2.00850i) q^{71} +(-2.48854 + 1.34430i) q^{72} +(-2.68574 + 13.5021i) q^{73} +(4.02945 + 0.258154i) q^{74} +(5.43468 + 4.46013i) q^{75} +(2.33602 + 2.47948i) q^{76} +(-9.55749 - 5.10858i) q^{77} +(7.44354 + 2.78906i) q^{78} +(-6.59080 + 2.73000i) q^{79} +(-2.17945 + 13.7018i) q^{80} +(0.923880 + 0.382683i) q^{81} +(1.90186 + 1.77604i) q^{82} +(-1.58732 + 0.481509i) q^{83} +(-7.79915 + 4.88169i) q^{84} +(-2.41530 - 24.5229i) q^{85} +(-3.02510 - 8.86877i) q^{86} +(1.95696 + 2.92880i) q^{87} +(0.0293952 + 6.66272i) q^{88} +(-3.98123 - 2.66017i) q^{89} +(4.24443 - 2.45885i) q^{90} +(24.7446 + 7.50619i) q^{91} +(5.51222 - 9.61263i) q^{92} +(2.67852 + 3.26378i) q^{93} +(5.73430 + 0.938076i) q^{94} +(-4.17750 - 4.17750i) q^{95} +(4.91964 + 2.79233i) q^{96} +(8.26790 - 8.26790i) q^{97} +(-16.2654 + 11.6918i) q^{98} +(1.82094 - 1.49441i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	1.37680	−	0.323159i	0.973542	−	0.228508i
$2$	1.37680	−	0.323159i	0.973542	−	0.228508i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	1.79114	−	0.889849i	0.895568	−	0.444925i
$5$	−3.05895	+	1.63504i	−1.36800	+	0.731213i	−0.981570	−	0.191103i	$-0.938793\pi$
$5$	−3.05895	+	1.63504i	−1.36800	+	0.731213i	−0.386434	+	0.922317i	$0.626293\pi$
$6$	0.186654	+	1.40184i	0.0762010	+	0.572300i
$7$	0.897509	+	4.51208i	0.339227	+	1.70541i	0.654212	+	0.756311i	$0.273000\pi$
$7$	0.897509	+	4.51208i	0.339227	+	1.70541i	−0.314986	+	0.949096i	$0.602000\pi$
$8$	2.17847	−	1.80396i	0.770204	−	0.637798i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−3.68317	+	3.23965i	−1.16472	+	1.02447i
$11$	−1.49441	+	1.82094i	−0.450581	+	0.549035i	−0.947915	−	0.318525i	$-0.896813\pi$
$11$	−1.49441	+	1.82094i	−0.450581	+	0.549035i	0.497333	+	0.867560i	$0.334313\pi$
$12$	0.710002	+	1.86973i	0.204960	+	0.539745i
$13$	2.64959	−	4.95704i	0.734864	−	1.37483i	−0.185056	−	0.982728i	$-0.559247\pi$
$13$	2.64959	−	4.95704i	0.734864	−	1.37483i	0.919920	−	0.392106i	$-0.128253\pi$
$14$	2.69381	+	5.92218i	0.719951	+	1.58277i
$15$	−1.32734	−	3.20448i	−0.342718	−	0.827394i
$16$	2.41634	−	3.18768i	0.604084	−	0.796921i
$17$	−2.71873	+	6.56358i	−0.659388	+	1.59190i	0.139363	+	0.990241i	$0.455494\pi$
$17$	−2.71873	+	6.56358i	−0.659388	+	1.59190i	−0.798751	+	0.601662i	$0.794506\pi$
$18$	−1.41339	+	0.0483504i	−0.333138	+	0.0113963i
$19$	0.494439	+	1.62995i	0.113432	+	0.373936i	0.995214	−	0.0977223i	$-0.0311557\pi$
$19$	0.494439	+	1.62995i	0.113432	+	0.373936i	−0.881782	+	0.471658i	$0.843656\pi$
$20$	−4.02405	+	5.65059i	−0.899806	+	1.26351i
$21$	−4.57833	+	0.450926i	−0.999073	+	0.0984001i
$22$	−1.46904	+	2.99000i	−0.313201	+	0.637470i
$23$	4.60673	−	3.07812i	0.960570	−	0.641832i	0.0267754	−	0.999641i	$-0.491476\pi$
$23$	4.60673	−	3.07812i	0.960570	−	0.641832i	0.933795	+	0.357809i	$0.116476\pi$
$24$	1.58175	+	2.34480i	0.322873	+	0.478629i
$25$	3.90596	−	5.84568i	0.781192	−	1.16914i
$26$	2.04603	−	7.68107i	0.401260	−	1.50638i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	5.62264	+	7.28311i	1.06258	+	1.37638i
$29$	2.72288	−	2.23461i	0.505626	−	0.414956i	−0.346693	−	0.937979i	$-0.612696\pi$
$29$	2.72288	−	2.23461i	0.505626	−	0.414956i	0.852319	+	0.523022i	$0.175196\pi$
$30$	−2.86304	−	3.98298i	−0.522716	−	0.727189i
$31$	2.98553	−	2.98553i	0.536216	−	0.536216i	−0.386199	−	0.922415i	$-0.626212\pi$
$31$	2.98553	−	2.98553i	0.536216	−	0.536216i	0.922415	+	0.386199i	$0.126212\pi$
$32$	2.29667	−	5.16965i	0.405998	−	0.913874i
$33$	−1.66570	−	1.66570i	−0.289960	−	0.289960i
$34$	−1.62205	+	9.91530i	−0.278179	+	1.70046i
$35$	−10.1229	−	12.3348i	−1.71108	−	2.08496i
$36$	−1.93032	+	0.523318i	−0.321720	+	0.0872196i
$37$	2.73216	+	0.828790i	0.449164	+	0.136252i	0.506759	−	0.862088i	$-0.330843\pi$
$37$	2.73216	+	0.828790i	0.449164	+	0.136252i	−0.0575955	+	0.998340i	$0.518343\pi$
$38$	1.20748	+	2.08432i	0.195878	+	0.338122i
$39$	4.67346	+	3.12271i	0.748353	+	0.500033i
$40$	−3.71426	+	9.08012i	−0.587276	+	1.43569i
$41$	1.02226	+	1.52992i	0.159651	+	0.238934i	0.902668	−	0.430339i	$-0.141606\pi$
$41$	1.02226	+	1.52992i	0.159651	+	0.238934i	−0.743017	+	0.669273i	$0.766606\pi$
$42$	−6.15770	+	2.10036i	−0.950154	+	0.324093i
$43$	−0.649456	−	6.59404i	−0.0990412	−	1.00558i	−0.908353	−	0.418203i	$-0.862660\pi$
$43$	−0.649456	−	6.59404i	−0.0990412	−	1.00558i	0.809312	−	0.587379i	$-0.199840\pi$
$44$	−1.05632	+	4.59135i	−0.159247	+	0.692173i
$45$	3.31915	−	1.00685i	0.494790	−	0.150093i
$46$	5.34781	−	5.72665i	0.788491	−	0.844349i
$47$	3.79591	+	1.57232i	0.553690	+	0.229346i	0.641943	−	0.766752i	$-0.278129\pi$
$47$	3.79591	+	1.57232i	0.553690	+	0.229346i	−0.0882533	+	0.996098i	$0.528129\pi$
$48$	2.93549	+	2.71715i	0.423702	+	0.392187i
$49$	−13.0862	+	5.42049i	−1.86946	+	0.774355i
$50$	3.48862	−	9.31056i	0.493366	−	1.31671i
$51$	−6.26550	−	3.34898i	−0.877345	−	0.468951i
$52$	0.334762	−	11.2365i	0.0464232	−	1.55822i
$53$	−7.75287	−	6.36262i	−1.06494	−	0.873973i	−0.0725806	−	0.997363i	$-0.523123\pi$
$53$	−7.75287	−	6.36262i	−1.06494	−	0.873973i	−0.992358	+	0.123390i	$0.960623\pi$
$54$	0.0904186	−	1.41132i	0.0123044	−	0.192056i
$55$	1.59400	−	8.01359i	0.214935	−	1.08055i
$56$	10.0948	+	8.21035i	1.34898	+	1.09715i
$57$	−1.67056	+	0.332296i	−0.221271	+	0.0440136i
$58$	3.02671	−	3.95652i	0.397427	−	0.519517i
$59$	−1.13136	−	2.11662i	−0.147290	−	0.275560i	0.797447	−	0.603389i	$-0.206183\pi$
$59$	−1.13136	−	2.11662i	−0.147290	−	0.275560i	−0.944737	+	0.327828i	$0.893683\pi$
$60$	−5.22895	−	4.55853i	−0.675055	−	0.588504i
$61$	−7.50183	−	0.738865i	−0.960511	−	0.0946020i	−0.394407	−	0.918936i	$-0.629050\pi$
$61$	−7.50183	−	0.738865i	−0.960511	−	0.0946020i	−0.566104	+	0.824334i	$0.691550\pi$
$62$	3.14566	−	5.07526i	0.399499	−	0.644559i
$63$		−	4.60048i		−	0.579606i
$64$	1.49143	−	7.85975i	0.186429	−	0.982469i
$65$			19.4955i			2.41812i
$66$	−2.83161	−	1.75504i	−0.348547	−	0.216030i
$67$	10.1357	+	0.998275i	1.23827	+	0.121959i	0.695873	−	0.718165i	$-0.255018\pi$
$67$	10.1357	+	0.998275i	1.23827	+	0.121959i	0.542395	+	0.840124i	$0.317518\pi$
$68$	0.970994	+	14.1755i	0.117750	+	1.71904i
$69$	2.61176	+	4.88626i	0.314419	+	0.588236i
$70$	−17.9233	−	13.7112i	−2.14224	−	1.63880i
$71$	10.0974	−	2.00850i	1.19834	−	0.238365i	0.444717	−	0.895671i	$-0.353304\pi$
$71$	10.0974	−	2.00850i	1.19834	−	0.238365i	0.753623	+	0.657307i	$0.228304\pi$
$72$	−2.48854	+	1.34430i	−0.293278	+	0.158428i
$73$	−2.68574	+	13.5021i	−0.314342	+	1.58030i	0.423863	+	0.905726i	$0.360674\pi$
$73$	−2.68574	+	13.5021i	−0.314342	+	1.58030i	−0.738205	+	0.674577i	$0.764326\pi$
$74$	4.02945	+	0.258154i	0.468414	+	0.0300097i
$75$	5.43468	+	4.46013i	0.627543	+	0.515011i
$76$	2.33602	+	2.47948i	0.267959	+	0.284416i
$77$	−9.55749	−	5.10858i	−1.08918	−	0.582177i
$78$	7.44354	+	2.78906i	0.842814	+	0.315799i
$79$	−6.59080	+	2.73000i	−0.741522	+	0.307149i	−0.721277	−	0.692646i	$-0.756445\pi$
$79$	−6.59080	+	2.73000i	−0.741522	+	0.307149i	−0.0202451	+	0.999795i	$0.506445\pi$
$80$	−2.17945	+	13.7018i	−0.243670	+	1.53191i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	1.90186	+	1.77604i	0.210025	+	0.196131i
$83$	−1.58732	+	0.481509i	−0.174231	+	0.0528524i	−0.376195	−	0.926541i	$-0.622768\pi$
$83$	−1.58732	+	0.481509i	−0.174231	+	0.0528524i	0.201964	+	0.979393i	$0.435268\pi$
$84$	−7.79915	+	4.88169i	−0.850957	+	0.532636i
$85$	−2.41530	−	24.5229i	−0.261976	−	2.65988i
$86$	−3.02510	−	8.86877i	−0.326204	−	0.956344i
$87$	1.95696	+	2.92880i	0.209808	+	0.314000i
$88$	0.0293952	+	6.66272i	0.00313354	+	0.710248i
$89$	−3.98123	−	2.66017i	−0.422010	−	0.281978i	0.326378	−	0.945239i	$-0.394172\pi$
$89$	−3.98123	−	2.66017i	−0.422010	−	0.281978i	−0.748388	+	0.663261i	$0.769172\pi$
$90$	4.24443	−	2.45885i	0.447402	−	0.259186i
$91$	24.7446	+	7.50619i	2.59394	+	0.786862i
$92$	5.51222	−	9.61263i	0.574689	−	1.00219i
$93$	2.67852	+	3.26378i	0.277749	+	0.338439i
$94$	5.73430	+	0.938076i	0.591448	+	0.0967551i
$95$	−4.17750	−	4.17750i	−0.428602	−	0.428602i
$96$	4.91964	+	2.79233i	0.502109	+	0.284991i
$97$	8.26790	−	8.26790i	0.839478	−	0.839478i	−0.149312	−	0.988790i	$-0.547706\pi$
$97$	8.26790	−	8.26790i	0.839478	−	0.839478i	0.988790	+	0.149312i	$0.0477060\pi$
$98$	−16.2654	+	11.6918i	−1.64305	+	1.18105i
$99$	1.82094	−	1.49441i	0.183012	−	0.150194i
$100$	1.79433	−	13.9461i	0.179433	−	1.39461i
$101$	−0.908878	+	2.99617i	−0.0904367	+	0.298130i	−0.990477	−	0.137676i	$-0.956037\pi$
$101$	−0.908878	+	2.99617i	−0.0904367	+	0.298130i	0.900041	+	0.435806i	$0.143537\pi$
$102$	−9.70857	−	2.58611i	−0.961291	−	0.256063i
$103$	7.36673	−	11.0251i	0.725865	−	1.08633i	−0.266600	−	0.963807i	$-0.585900\pi$
$103$	7.36673	−	11.0251i	0.725865	−	1.08633i	0.992465	−	0.122527i	$-0.0390997\pi$
$104$	−3.17027	−	15.5785i	−0.310870	−	1.52760i
$105$	13.2676	−	8.86512i	1.29478	−	0.865147i
$106$	−12.7303	−	6.25461i	−1.23647	−	0.607502i
$107$	−5.15598	+	0.507819i	−0.498447	+	0.0490927i	−0.344117	−	0.938927i	$-0.611822\pi$
$107$	−5.15598	+	0.507819i	−0.498447	+	0.0490927i	−0.154330	+	0.988019i	$0.549322\pi$
$108$	−0.331593	−	1.97232i	−0.0319076	−	0.189787i
$109$	2.61289	+	8.61356i	0.250270	+	0.825029i	0.988597	+	0.150586i	$0.0481161\pi$
$109$	2.61289	+	8.61356i	0.250270	+	0.825029i	−0.738327	+	0.674443i	$0.764384\pi$
$110$	−0.395051	−	11.5482i	−0.0376666	−	1.10108i
$111$	−1.09260	+	2.63776i	−0.103705	+	0.250365i
$112$	16.5518	+	8.04174i	1.56400	+	0.759873i
$113$	0.838254	+	2.02372i	0.0788563	+	0.190376i	0.958391	−	0.285459i	$-0.0921460\pi$
$113$	0.838254	+	2.02372i	0.0788563	+	0.190376i	−0.879535	+	0.475835i	$0.842146\pi$
$114$	−2.19264	+	0.997361i	−0.205360	+	0.0934115i
$115$	−9.05891	+	16.9480i	−0.844748	+	1.58041i
$116$	2.88858	−	6.42544i	0.268198	−	0.596587i
$117$	−3.56575	+	4.34488i	−0.329654	+	0.401684i
$118$	−2.24165	−	2.54854i	−0.206361	−	0.234612i
$119$	−32.0555	−	6.37624i	−2.93852	−	0.584509i
$120$	−8.67234	−	4.58638i	−0.791672	−	0.418678i
$121$	1.06342	+	5.34618i	0.0966746	+	0.486016i
$122$	−10.5673	+	1.40702i	−0.956715	+	0.127386i
$123$	−1.62276	+	0.867381i	−0.146319	+	0.0782091i
$124$	2.69082	−	8.00415i	0.241642	−	0.718794i
$125$	−0.690330	+	7.00904i	−0.0617450	+	0.626908i
$126$	−1.48669	−	6.33392i	−0.132445	−	0.564271i
$127$	2.07094			0.183766			0.0918831	−	0.995770i	$-0.470711\pi$
$127$	2.07094			0.183766			0.0918831	+	0.995770i	$0.470711\pi$
$128$	−0.486557	−	11.3032i	−0.0430060	−	0.999075i
$129$	6.62595			0.583382
$130$	6.30016	+	26.8414i	0.552561	+	2.35414i
$131$	0.341950	−	3.47188i	0.0298763	−	0.303340i	−0.968621	−	0.248542i	$-0.920049\pi$
$131$	0.341950	−	3.47188i	0.0298763	−	0.303340i	0.998497	−	0.0547977i	$-0.0174514\pi$
$132$	−4.46571	−	1.50127i	−0.388690	−	0.130669i
$133$	−6.91070	+	3.69384i	−0.599233	+	0.320297i
$134$	14.2773	−	1.90101i	1.23337	−	0.164222i
$135$	0.676672	+	3.40186i	0.0582387	+	0.292786i
$136$	5.91782	+	19.2030i	0.507449	+	1.64665i
$137$	−4.36371	−	0.867996i	−0.372817	−	0.0741579i	0.00512587	−	0.999987i	$-0.498368\pi$
$137$	−4.36371	−	0.867996i	−0.372817	−	0.0741579i	−0.377943	+	0.925829i	$0.623368\pi$
$138$	5.17490	+	5.88337i	0.440517	+	0.500826i
$139$	−1.22685	+	1.49492i	−0.104060	+	0.126797i	−0.822436	−	0.568857i	$-0.807386\pi$
$139$	−1.22685	+	1.49492i	−0.104060	+	0.126797i	0.718376	+	0.695655i	$0.244886\pi$
$140$	−29.1076	−	13.0854i	−2.46004	−	1.10592i
$141$	−1.93681	+	3.62351i	−0.163109	+	0.305155i
$142$	13.2530	−	6.02836i	1.11217	−	0.505889i
$143$	5.06690	+	12.2326i	0.423716	+	1.02294i
$144$	−2.99179	+	2.65503i	−0.249316	+	0.221252i
$145$	−4.67547	+	11.2876i	−0.388277	+	0.937382i
$146$	0.665622	+	19.4576i	0.0550873	+	1.61032i
$147$	−4.11171	−	13.5545i	−0.339128	−	1.11796i
$148$	5.63116	−	0.946731i	0.462879	−	0.0778208i
$149$	9.04205	−	0.890564i	0.740754	−	0.0729579i	0.279401	−	0.960175i	$-0.409864\pi$
$149$	9.04205	−	0.890564i	0.740754	−	0.0729579i	0.461353	+	0.887217i	$0.347364\pi$
$150$	8.92378	+	4.38442i	0.728624	+	0.357986i
$151$	−7.62452	+	5.09454i	−0.620475	+	0.414588i	−0.825686	−	0.564130i	$-0.809212\pi$
$151$	−7.62452	+	5.09454i	−0.620475	+	0.414588i	0.205211	+	0.978718i	$0.434212\pi$
$152$	4.01749	+	2.65884i	0.325861	+	0.215660i
$153$	3.94698	−	5.90707i	0.319094	−	0.477558i
$154$	−14.8096	−	3.94489i	−1.19339	−	0.317888i
$155$	−4.25111	+	14.0140i	−0.341458	+	1.12564i
$156$	11.1495	+	1.43452i	0.892678	+	0.114853i
$157$	2.97734	−	2.44344i	0.237618	−	0.195008i	−0.508047	−	0.861330i	$-0.669632\pi$
$157$	2.97734	−	2.44344i	0.237618	−	0.195008i	0.745664	+	0.666322i	$0.232132\pi$
$158$	−8.19196	+	5.88853i	−0.651717	+	0.468466i
$159$	7.09189	−	7.09189i	0.562424	−	0.562424i
$160$	1.42719	+	19.5689i	0.112830	+	1.54705i
$161$	18.0233	+	18.0233i	1.42044	+	1.42044i
$162$	1.39566	+	0.228317i	0.109654	+	0.0179383i
$163$	−4.06035	−	4.94755i	−0.318031	−	0.387522i	0.589317	−	0.807902i	$-0.299397\pi$
$163$	−4.06035	−	4.94755i	−0.318031	−	0.387522i	−0.907348	+	0.420380i	$0.861897\pi$
$164$	3.19241	+	1.83064i	0.249285	+	0.142949i
$165$	7.81877	+	2.37180i	0.608690	+	0.184644i
$166$	−2.02981	+	1.17590i	−0.157544	+	0.0912673i
$167$	−5.83810	−	3.90090i	−0.451766	−	0.301860i	0.308793	−	0.951129i	$-0.400075\pi$
$167$	−5.83810	−	3.90090i	−0.451766	−	0.301860i	−0.760559	+	0.649269i	$0.775075\pi$
$168$	−9.16028	+	9.24146i	−0.706731	+	0.712994i
$169$	−10.3295	−	15.4591i	−0.794574	−	1.18916i
$170$	−11.2502	−	32.9825i	−0.862850	−	2.52964i
$171$	−0.166952	−	1.69509i	−0.0127671	−	0.129627i
$172$	−7.03097	−	11.2329i	−0.536106	−	0.856501i
$173$	0.211856	−	0.0642658i	0.0161071	−	0.00488604i	−0.282221	−	0.959349i	$-0.591071\pi$
$173$	0.211856	−	0.0642658i	0.0161071	−	0.00488604i	0.298328	+	0.954463i	$0.403571\pi$
$174$	3.64080	+	3.39995i	0.276009	+	0.257749i
$175$	29.8818	+	12.3775i	2.25886	+	0.935648i
$176$	2.19359	+	9.16371i	0.165348	+	0.690740i
$177$	2.21732	−	0.918443i	0.166664	−	0.0690344i
$178$	−6.34100	−	2.37594i	−0.475278	−	0.178085i
$179$	15.8807	+	8.48843i	1.18698	+	0.634455i	0.942176	−	0.335117i	$-0.108776\pi$
$179$	15.8807	+	8.48843i	1.18698	+	0.634455i	0.244805	+	0.969572i	$0.421276\pi$
$180$	5.04911	−	4.75696i	0.376338	−	0.354563i
$181$	6.13761	+	5.03701i	0.456205	+	0.374398i	0.834247	−	0.551391i	$-0.185903\pi$
$181$	6.13761	+	5.03701i	0.456205	+	0.374398i	−0.378042	+	0.925788i	$0.623403\pi$
$182$	36.4940	+	2.33805i	2.70511	+	0.173308i
$183$	1.47062	−	7.39328i	0.108711	−	0.546527i
$184$	4.48279	−	15.0160i	0.330476	−	1.10699i
$185$	−9.71264	+	1.93196i	−0.714087	+	0.142041i
$186$	4.74250	+	3.62798i	0.347737	+	0.266016i
$187$	−7.88902	−	14.7593i	−0.576902	−	1.07931i
$188$	8.19811	−	0.561553i	0.597909	−	0.0409555i
$189$	4.57833	+	0.450926i	0.333024	+	0.0328000i
$190$	−7.10157	−	4.40157i	−0.515202	−	0.319323i
$191$			5.07503i			0.367216i	0.983000	+	0.183608i	$0.0587778\pi$
$191$			5.07503i			0.367216i	−0.983000	+	0.183608i	$0.941222\pi$
$192$	7.67572	+	2.25464i	0.553947	+	0.162714i
$193$		−	10.7756i		−	0.775646i	−0.921734	−	0.387823i	$-0.873227\pi$
$193$		−	10.7756i		−	0.775646i	0.921734	−	0.387823i	$-0.126773\pi$
$194$	8.71136	−	14.0551i	0.625439	−	1.00909i
$195$	−19.4016	−	1.91090i	−1.38938	−	0.136842i
$196$	−18.6158	+	21.3536i	−1.32970	+	1.52526i
$197$	−11.1189	−	20.8020i	−0.792189	−	1.48208i	−0.874262	−	0.485455i	$-0.838654\pi$
$197$	−11.1189	−	20.8020i	−0.792189	−	1.48208i	0.0820728	−	0.996626i	$-0.473846\pi$
$198$	2.02413	−	2.64595i	0.143849	−	0.188040i
$199$	14.1412	−	2.81286i	1.00244	−	0.199398i	0.333531	−	0.942739i	$-0.391760\pi$
$199$	14.1412	−	2.81286i	1.00244	−	0.199398i	0.668913	+	0.743341i	$0.266760\pi$
$200$	−2.03640	−	19.7808i	−0.143995	−	1.39872i
$201$	−1.98694	+	9.98900i	−0.140148	+	0.704570i
$202$	−0.283099	+	4.41883i	−0.0199188	+	0.310908i
$203$	12.5265	+	10.2803i	0.879191	+	0.721534i
$204$	−14.2024	−	0.423126i	−0.994370	−	0.0296248i
$205$	−5.62854	−	3.00852i	−0.393114	−	0.210124i
$206$	6.57962	−	17.5599i	0.458424	−	1.22346i
$207$	−5.11873	+	2.12025i	−0.355776	+	0.147367i
$208$	−9.39915	−	20.4239i	−0.651714	−	1.41614i
$209$	−3.70694	−	1.53546i	−0.256414	−	0.106210i
$210$	15.4019	−	16.4930i	1.06283	−	1.13813i
$211$	−22.6591	+	6.87356i	−1.55992	+	0.473195i	−0.948144	−	0.317840i	$-0.897043\pi$
$211$	−22.6591	+	6.87356i	−1.55992	+	0.473195i	−0.611771	+	0.791035i	$0.709543\pi$
$212$	−19.5482	−	4.49742i	−1.34258	−	0.308884i
$213$	1.00911	+	10.2456i	0.0691429	+	0.702020i
$214$	−6.93462	+	2.36537i	−0.474041	+	0.161693i
$215$	12.7682	+	19.1090i	0.870784	+	1.30322i
$216$	−1.09391	−	2.60833i	−0.0744312	−	0.177474i
$217$	16.1505	+	10.7914i	1.09637	+	0.732569i
$218$	6.38098	+	11.0147i	0.432174	+	0.746012i
$219$	−13.1739	−	3.99624i	−0.890206	−	0.270041i
$220$	−4.27582	−	15.7719i	−0.288275	−	1.06334i
$221$	25.3324	+	30.8676i	1.70404	+	2.07638i
$222$	−0.651866	+	3.98475i	−0.0437504	+	0.267439i
$223$	9.35994	+	9.35994i	0.626788	+	0.626788i	0.947259	−	0.320470i	$-0.103841\pi$
$223$	9.35994	+	9.35994i	0.626788	+	0.626788i	−0.320470	+	0.947259i	$0.603841\pi$
$224$	25.3872	+	5.72297i	1.69625	+	0.382382i
$225$	−4.97134	+	4.97134i	−0.331423	+	0.331423i
$226$	1.80809	+	2.51536i	0.120272	+	0.167320i
$227$	−7.89662	+	6.48059i	−0.524117	+	0.430132i	−0.858885	−	0.512169i	$-0.828842\pi$
$227$	−7.89662	+	6.48059i	−0.524117	+	0.430132i	0.334768	+	0.942301i	$0.391342\pi$
$228$	−2.69651	+	2.08174i	−0.178581	+	0.137866i
$229$	−2.82024	+	9.29709i	−0.186367	+	0.614369i	0.813113	+	0.582106i	$0.197771\pi$
$229$	−2.82024	+	9.29709i	−0.186367	+	0.614369i	−0.999479	+	0.0322624i	$0.989729\pi$
$230$	−6.99536	+	26.2614i	−0.461260	+	1.73163i
$231$	6.02078	−	9.01074i	0.396138	−	0.592863i
$232$	1.90055	−	9.77999i	0.124777	−	0.642088i
$233$	9.80903	−	6.55418i	0.642611	−	0.429379i	−0.191107	−	0.981569i	$-0.561208\pi$
$233$	9.80903	−	6.55418i	0.642611	−	0.429379i	0.833718	+	0.552190i	$0.186208\pi$
$234$	−3.50522	+	7.13432i	−0.229144	+	0.466385i
$235$	−14.1823	+	1.39683i	−0.925151	+	0.0911194i
$236$	−3.90988	−	2.78441i	−0.254512	−	0.181250i
$237$	−2.07084	−	6.82665i	−0.134516	−	0.443438i
$238$	−46.1945	+	1.58026i	−2.99434	+	0.102433i
$239$	−3.48044	+	8.40252i	−0.225131	+	0.543514i	−0.995573	−	0.0939966i	$-0.970036\pi$
$239$	−3.48044	+	8.40252i	−0.225131	+	0.543514i	0.770442	+	0.637510i	$0.220036\pi$
$240$	−13.4222	−	3.51197i	−0.866398	−	0.226697i
$241$	−5.08306	−	12.2716i	−0.327429	−	0.790482i	−0.998782	−	0.0493449i	$-0.984287\pi$
$241$	−5.08306	−	12.2716i	−0.327429	−	0.790482i	0.671353	−	0.741138i	$-0.265713\pi$
$242$	3.19178	+	7.01694i	0.205175	+	0.451066i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	−14.0943	+	5.35209i	−0.902293	+	0.342632i
$245$	31.1674	−	37.9775i	1.99121	−	2.42630i
$246$	−1.95390	+	1.71862i	−0.124576	+	0.109575i
$247$	9.38977	+	1.86774i	0.597457	+	0.118842i
$248$	1.11809	−	11.8897i	0.0709986	−	0.754994i
$249$	−0.323605	−	1.62687i	−0.0205077	−	0.103099i
$250$	1.31459	+	9.87311i	0.0831422	+	0.624430i
$251$	−0.402128	+	0.214942i	−0.0253821	+	0.0135670i	−0.484039	−	0.875046i	$-0.660831\pi$
$251$	−0.402128	+	0.214942i	−0.0253821	+	0.0135670i	0.458657	+	0.888613i	$0.348331\pi$
$252$	−4.09373	−	8.24009i	−0.257881	−	0.519077i
$253$	−1.27926	+	12.9886i	−0.0804265	+	0.816584i
$254$	2.85126	−	0.669244i	0.178904	−	0.0419921i
$255$	24.6416			1.54311
$256$	−4.32264	−	15.4050i	−0.270165	−	0.962814i
$257$	−13.3237			−0.831109			−0.415554	−	0.909568i	$-0.636412\pi$
$257$	−13.3237			−0.831109			−0.415554	+	0.909568i	$0.636412\pi$
$258$	9.12258	−	2.14124i	0.567947	−	0.133308i
$259$	−1.28744	+	13.0716i	−0.0799974	+	0.812227i
$260$	17.3481	+	34.9191i	1.07588	+	2.16559i
$261$	−3.10651	+	1.66046i	−0.192288	+	0.102780i
$262$	−0.651175	−	4.89058i	−0.0402297	−	0.302141i
$263$	−6.25675	−	31.4548i	−0.385808	−	1.93959i	−0.339329	−	0.940668i	$-0.610200\pi$
$263$	−6.25675	−	31.4548i	−0.385808	−	1.93959i	−0.0464785	−	0.998919i	$-0.514800\pi$
$264$	−6.63352	−	0.623807i	−0.408265	−	0.0383927i
$265$	34.1188	+	6.78665i	2.09590	+	0.416901i
$266$	−8.32092	+	7.31893i	−0.510188	+	0.448752i
$267$	3.03759	−	3.70132i	0.185898	−	0.226517i
$268$	19.0426	−	7.23116i	1.16321	−	0.441713i
$269$	−4.01002	+	7.50222i	−0.244495	+	0.457419i	−0.973997	−	0.226560i	$-0.927252\pi$
$269$	−4.01002	+	7.50222i	−0.244495	+	0.457419i	0.729502	+	0.683979i	$0.239752\pi$
$270$	2.03098	+	4.46500i	0.123602	+	0.271731i
$271$	1.96349	+	4.74028i	0.119273	+	0.287951i	0.972229	−	0.234032i	$-0.0751922\pi$
$271$	1.96349	+	4.74028i	0.119273	+	0.287951i	−0.852955	+	0.521984i	$0.825192\pi$
$272$	14.3533	+	24.5263i	0.870295	+	1.48712i
$273$	−9.89544	+	23.8897i	−0.598899	+	1.44587i
$274$	−6.28844	+	0.215120i	−0.379899	+	0.0129959i
$275$	4.80755	+	15.8484i	0.289906	+	0.955692i
$276$	9.02605	+	6.42788i	0.543304	+	0.386913i
$277$	−28.8272	+	2.83924i	−1.73206	+	0.170593i	−0.914320	−	0.404993i	$-0.867274\pi$
$277$	−28.8272	+	2.83924i	−1.73206	+	0.170593i	−0.817741	+	0.575586i	$0.804774\pi$
$278$	−1.20602	+	2.45467i	−0.0723324	+	0.147221i
$279$	−3.51061	+	2.34571i	−0.210175	+	0.140434i
$280$	−44.3038	−	8.60956i	−2.64766	−	0.514520i
$281$	12.8248	−	19.1936i	0.765061	−	1.14499i	−0.220453	−	0.975398i	$-0.570754\pi$
$281$	12.8248	−	19.1936i	0.765061	−	1.14499i	0.985514	−	0.169597i	$-0.0542465\pi$
$282$	−1.49562	+	5.61474i	−0.0890628	+	0.334353i
$283$	−2.27121	+	7.48717i	−0.135009	+	0.445066i	−0.998211	−	0.0597936i	$-0.980956\pi$
$283$	−2.27121	+	7.48717i	−0.135009	+	0.445066i	0.863201	+	0.504860i	$0.168456\pi$
$284$	16.2985	−	12.5826i	0.967141	−	0.746643i
$285$	4.56685	−	3.74792i	0.270517	−	0.222007i
$286$	10.9292	+	15.2044i	0.646255	+	0.899053i
$287$	−5.98565	+	5.98565i	−0.353322	+	0.353322i
$288$	−3.26109	+	4.62226i	−0.192162	+	0.272369i
$289$	−23.6684	−	23.6684i	−1.39226	−	1.39226i
$290$	−2.78948	+	17.0516i	−0.163804	+	1.00131i
$291$	7.41769	+	9.03848i	0.434833	+	0.529845i
$292$	7.20433	+	26.5740i	0.421601	+	1.55513i
$293$	−15.6995	−	4.76240i	−0.917176	−	0.278222i	−0.203807	−	0.979011i	$-0.565332\pi$
$293$	−15.6995	−	4.76240i	−0.917176	−	0.278222i	−0.713369	+	0.700789i	$0.752832\pi$
$294$	−10.0413	−	17.3331i	−0.585618	−	1.01088i
$295$	6.92152	+	4.62481i	0.402987	+	0.269267i
$296$	7.44702	−	3.12322i	0.432849	−	0.181533i
$297$	1.30873	+	1.95865i	0.0759402	+	0.113652i
$298$	12.1613	−	4.14815i	0.704483	−	0.240296i
$299$	−3.05240	−	30.9915i	−0.176525	−	1.79228i
$300$	13.7031	+	3.15265i	0.791149	+	0.182018i
$301$	29.1700	−	8.84861i	1.68133	−	0.510026i
$302$	−8.85107	+	9.47809i	−0.509322	+	0.545403i
$303$	−2.89266	−	1.19818i	−0.166179	−	0.0688335i
$304$	6.39049	+	2.36239i	0.366520	+	0.135492i
$305$	24.1558	−	10.0057i	1.38316	−	0.572922i
$306$	3.52526	−	9.40834i	0.201526	−	0.537839i
$307$	−4.34771	−	2.32390i	−0.248137	−	0.132632i	0.342640	−	0.939467i	$-0.388679\pi$
$307$	−4.34771	−	2.32390i	−0.248137	−	0.132632i	−0.590777	+	0.806835i	$0.701179\pi$
$308$	−21.6646	−	0.645443i	−1.23446	−	0.0367775i
$309$	10.2499	+	8.41190i	0.583098	+	0.478536i
$310$	−1.32415	+	20.6683i	−0.0752065	+	1.17388i
$311$	1.40471	−	7.06196i	0.0796539	−	0.400447i	−0.920303	−	0.391205i	$-0.872058\pi$
$311$	1.40471	−	7.06196i	0.0796539	−	0.400447i	0.999957	−	0.00924180i	$-0.00294180\pi$
$312$	15.8142	−	1.62804i	0.895304	−	0.0921698i
$313$	−30.1712	+	6.00142i	−1.70538	+	0.339221i	−0.949086	−	0.315016i	$-0.897990\pi$
$313$	−30.1712	+	6.00142i	−1.70538	+	0.339221i	−0.756290	+	0.654236i	$0.772990\pi$
$314$	3.30958	−	4.32628i	0.186770	−	0.244146i
$315$	7.52198	+	14.0726i	0.423816	+	0.792903i
$316$	−9.37573	+	10.7546i	−0.527426	+	0.604994i
$317$	−31.5789	−	3.11025i	−1.77365	−	0.174689i	−0.842346	−	0.538938i	$-0.818826\pi$
$317$	−31.5789	−	3.11025i	−1.77365	−	0.174689i	−0.931302	+	0.364249i	$0.881326\pi$
$318$	7.47228	−	12.0559i	0.419025	−	0.676062i
$319$			8.29762i			0.464578i
$320$	8.28882	+	26.4811i	0.463359	+	1.48034i
$321$		−	5.18092i		−	0.289171i
$322$	30.6388	+	18.9900i	1.70744	+	1.05827i
$323$	−12.0425	−	1.18609i	−0.670065	−	0.0659957i
$324$	1.99532	−	0.136676i	0.110851	−	0.00759309i
$325$	−18.6281	−	34.8507i	−1.03330	−	1.93317i
$326$	−7.18913	−	5.49963i	−0.398169	−	0.304596i
$327$	−8.82819	+	1.75604i	−0.488200	+	0.0971090i
$328$	4.98689	+	1.48876i	0.275355	+	0.0822032i
$329$	−3.68756	+	18.5386i	−0.203302	+	1.02207i
$330$	11.5313	+	0.738773i	0.634778	+	0.0406681i
$331$	−2.67600	−	2.19614i	−0.147086	−	0.120711i	0.557972	−	0.829859i	$-0.311579\pi$
$331$	−2.67600	−	2.19614i	−0.147086	−	0.120711i	−0.705059	+	0.709149i	$0.749079\pi$
$332$	−2.41464	+	2.27492i	−0.132521	+	0.124853i
$333$	−2.51797	−	1.34588i	−0.137984	−	0.0737539i
$334$	−9.29849	−	3.48410i	−0.508791	−	0.190642i
$335$	−32.6367	+	13.5186i	−1.78313	+	0.738598i
$336$	−9.62537	+	15.6838i	−0.525107	+	0.855624i
$337$	−27.0696	−	11.2126i	−1.47458	−	0.610789i	−0.506679	−	0.862135i	$-0.669127\pi$
$337$	−27.0696	−	11.2126i	−1.47458	−	0.610789i	−0.967897	+	0.251346i	$0.919127\pi$
$338$	−19.2173	−	17.9460i	−1.04528	−	0.976134i
$339$	−2.09614	+	0.635858i	−0.113847	+	0.0345350i
$340$	−26.1478	−	41.7746i	−1.41806	−	2.26555i
$341$	0.974875	+	9.89807i	0.0527924	+	0.536010i
$342$	−0.777643	−	2.27984i	−0.0420501	−	0.123280i
$343$	−18.3115	−	27.4050i	−0.988726	−	1.47973i
$344$	−13.3102	−	13.1933i	−0.717639	−	0.711335i
$345$	−15.9785	−	10.6765i	−0.860253	−	0.574803i
$346$	0.270915	−	0.156944i	0.0145645	−	0.00843738i
$347$	31.0513	+	9.41932i	1.66692	+	0.505655i	0.976091	−	0.217361i	$-0.0697449\pi$
$347$	31.0513	+	9.41932i	1.66692	+	0.505655i	0.690831	+	0.723016i	$0.257245\pi$
$348$	6.11137	+	3.50447i	0.327604	+	0.187860i
$349$	3.98504	+	4.85579i	0.213314	+	0.259924i	0.868664	−	0.495401i	$-0.164979\pi$
$349$	3.98504	+	4.85579i	0.213314	+	0.259924i	−0.655350	+	0.755325i	$0.727479\pi$
$350$	45.1411	+	7.38465i	2.41289	+	0.394726i
$351$	−3.97445	−	3.97445i	−0.212141	−	0.212141i
$352$	5.98147	+	11.9077i	0.318813	+	0.634681i
$353$	−16.0585	+	16.0585i	−0.854705	+	0.854705i	−0.990708	−	0.136003i	$-0.956574\pi$
$353$	−16.0585	+	16.0585i	−0.854705	+	0.854705i	0.136003	+	0.990708i	$0.456574\pi$
$354$	2.75599	−	1.98106i	0.146479	−	0.105292i
$355$	−27.6034	+	22.6536i	−1.46504	+	1.20233i
$356$	−9.49808	−	1.22204i	−0.503397	−	0.0647678i
$357$	9.48753	−	31.2762i	0.502133	−	1.65531i
$358$	24.6077	+	6.55483i	1.30055	+	0.346433i
$359$	14.2807	−	21.3725i	0.753704	−	1.12800i	−0.234087	−	0.972216i	$-0.575210\pi$
$359$	14.2807	−	21.3725i	0.753704	−	1.12800i	0.987791	−	0.155783i	$-0.0497900\pi$
$360$	5.41434	−	8.18103i	0.285361	−	0.431178i
$361$	13.3857	−	8.94401i	0.704509	−	0.470738i
$362$	10.0780	+	4.95150i	0.529688	+	0.260245i
$363$	−5.42467	+	0.534283i	−0.284721	+	0.0280426i
$364$	51.0003	−	8.57435i	2.67314	−	0.449418i
$365$	−13.8610	−	45.6936i	−0.725518	−	2.39171i
$366$	−0.364471	−	10.6543i	−0.0190512	−	0.556908i
$367$	−7.70704	+	18.6064i	−0.402304	+	0.971248i	0.584801	+	0.811177i	$0.301172\pi$
$367$	−7.70704	+	18.6064i	−0.402304	+	0.971248i	−0.987105	+	0.160072i	$0.948828\pi$
$368$	1.31934	−	22.1226i	0.0687756	−	1.15322i
$369$	−0.704146	−	1.69996i	−0.0366564	−	0.0884964i
$370$	−12.7480	+	5.79865i	−0.662736	+	0.301457i
$371$	21.7504	−	40.6921i	1.12922	−	2.11263i
$372$	7.70187	+	3.46240i	0.399323	+	0.179517i
$373$	0.291859	−	0.355631i	0.0151119	−	0.0184139i	−0.765400	−	0.643555i	$-0.777459\pi$
$373$	0.291859	−	0.355631i	0.0151119	−	0.0184139i	0.780512	+	0.625141i	$0.214959\pi$
$374$	−15.6312	−	17.7712i	−0.808269	−	0.918925i
$375$	−6.90763	−	1.37401i	−0.356708	−	0.0709537i
$376$	11.1057	−	3.42244i	0.572730	−	0.176499i
$377$	−3.86252	−	19.4182i	−0.198930	−	1.00009i
$378$	6.44915	−	0.858697i	0.331708	−	0.0441666i
$379$	−15.7077	+	8.39593i	−0.806849	+	0.431270i	−0.822610	−	0.568606i	$-0.807483\pi$
$379$	−15.7077	+	8.39593i	−0.806849	+	0.431270i	0.0157609	+	0.999876i	$0.494983\pi$
$380$	−11.1998	−	3.76513i	−0.574539	−	0.193147i
$381$	−0.202988	+	2.06097i	−0.0103994	+	0.105587i
$382$	1.64004	+	6.98729i	0.0839120	+	0.357501i
$383$	31.7794			1.62385			0.811926	−	0.583760i	$-0.198419\pi$
$383$	31.7794			1.62385			0.811926	+	0.583760i	$0.198419\pi$
$384$	11.2965	+	0.623697i	0.576472	+	0.0318279i
$385$	37.5886			1.91569
$386$	−3.48224	−	14.8358i	−0.177242	−	0.755124i
$387$	−0.649456	+	6.59404i	−0.0330137	+	0.335194i
$388$	7.45174	−	22.1661i	0.378305	−	1.12531i
$389$	21.0795	−	11.2672i	1.06877	−	0.571270i	0.159382	−	0.987217i	$-0.449050\pi$
$389$	21.0795	−	11.2672i	1.06877	−	0.571270i	0.909389	+	0.415947i	$0.136550\pi$
$390$	−27.3296	+	3.63891i	−1.38389	+	0.184263i
$391$	7.67906	+	38.6052i	0.388347	+	1.95235i
$392$	−18.7295	+	35.4154i	−0.945983	+	1.78875i
$393$	3.42165	+	0.680608i	0.172599	+	0.0343321i
$394$	−22.0308	−	25.0469i	−1.10990	−	1.26185i
$395$	15.6973	−	19.1272i	0.789815	−	0.962392i
$396$	1.93176	−	4.29705i	0.0970744	−	0.215935i
$397$	13.8729	−	25.9544i	0.696262	−	1.30261i	−0.246498	−	0.969143i	$-0.579280\pi$
$397$	13.8729	−	25.9544i	0.696262	−	1.30261i	0.942760	−	0.333471i	$-0.108220\pi$
$398$	18.5606	−	8.44260i	0.930356	−	0.423189i
$399$	−2.99869	−	7.23948i	−0.150122	−	0.362427i
$400$	−9.19607	−	26.5761i	−0.459803	−	1.32880i
$401$	4.53061	−	10.9379i	0.226248	−	0.546211i	−0.769467	−	0.638687i	$-0.779478\pi$
$401$	4.53061	−	10.9379i	0.226248	−	0.546211i	0.995715	+	0.0924755i	$0.0294780\pi$
$402$	0.492434	+	14.3949i	0.0245604	+	0.717953i
$403$	−6.88894	−	22.7098i	−0.343162	−	1.13126i
$404$	1.03822	+	6.17531i	0.0516531	+	0.307233i
$405$	−3.45181	+	0.339973i	−0.171522	+	0.0168934i
$406$	20.5687	+	10.1058i	1.02081	+	0.501541i
$407$	−5.59214	+	3.73655i	−0.277192	+	0.185214i
$408$	−19.6906	+	4.00709i	−0.974830	+	0.198381i
$409$	4.05998	−	6.07619i	0.200753	−	0.300448i	−0.717410	−	0.696651i	$-0.754672\pi$
$409$	4.05998	−	6.07619i	0.200753	−	0.300448i	0.918163	+	0.396203i	$0.129672\pi$
$410$	−8.72158	−	2.32320i	−0.430728	−	0.114735i
$411$	1.29153	−	4.25762i	0.0637067	−	0.210013i
$412$	3.38414	−	26.3027i	0.166725	−	1.29584i
$413$	8.53495	−	7.00446i	0.419978	−	0.344667i
$414$	−6.36227	+	4.57331i	−0.312688	+	0.224766i
$415$	4.06825	−	4.06825i	0.199703	−	0.199703i
$416$	−19.5409	−	25.0822i	−0.958072	−	1.22975i
$417$	−1.36747	−	1.36747i	−0.0669652	−	0.0669652i
$418$	−5.59989	−	0.916088i	−0.273900	−	0.0448074i
$419$	−9.35831	−	11.4031i	−0.457183	−	0.557079i	0.492491	−	0.870317i	$-0.336086\pi$
$419$	−9.35831	−	11.4031i	−0.457183	−	0.557079i	−0.949675	+	0.313238i	$0.898586\pi$
$420$	15.8754	−	27.6848i	0.774642	−	1.35088i
$421$	−19.2586	−	5.84203i	−0.938607	−	0.284723i	−0.216325	−	0.976322i	$-0.569407\pi$
$421$	−19.2586	−	5.84203i	−0.938607	−	0.284723i	−0.722282	+	0.691598i	$0.756907\pi$
$422$	−28.9757	+	16.7860i	−1.41051	+	0.817129i
$423$	−3.41623	−	2.28265i	−0.166103	−	0.110986i
$424$	−28.3673	+	0.125153i	−1.37764	+	0.00607799i
$425$	27.7494	+	41.5299i	1.34604	+	2.01450i
$426$	4.70031	+	13.7801i	0.227731	+	0.667646i
$427$	−3.39914	−	34.5120i	−0.164496	−	1.67015i
$428$	−8.78317	+	5.49761i	−0.424551	+	0.265737i
$429$	−12.6703	+	3.84350i	−0.611729	+	0.185566i
$430$	23.7544	+	22.1830i	1.14554	+	1.06976i
$431$	−14.1609	−	5.86565i	−0.682108	−	0.282538i	0.0145998	−	0.999893i	$-0.495353\pi$
$431$	−14.1609	−	5.86565i	−0.682108	−	0.282538i	−0.696708	+	0.717355i	$0.745353\pi$
$432$	−2.34900	−	3.23762i	−0.113016	−	0.155770i
$433$	−17.5018	+	7.24950i	−0.841085	+	0.348389i	−0.761281	−	0.648422i	$-0.775429\pi$
$433$	−17.5018	+	7.24950i	−0.841085	+	0.348389i	−0.0798037	+	0.996811i	$0.525429\pi$
$434$	25.7233	+	9.63839i	1.23476	+	0.462658i
$435$	−10.7750	−	5.75933i	−0.516619	−	0.276139i
$436$	12.3448	+	13.1030i	0.591210	+	0.627519i
$437$	7.29493	+	5.98679i	0.348964	+	0.286387i
$438$	−19.4291	−	1.24476i	−0.928360	−	0.0594769i
$439$	3.80364	−	19.1222i	0.181538	−	0.912653i	−0.777393	−	0.629015i	$-0.783458\pi$
$439$	3.80364	−	19.1222i	0.181538	−	0.912653i	0.958931	−	0.283638i	$-0.0915415\pi$
$440$	−10.9838	−	20.3329i	−0.523630	−	0.969331i
$441$	13.8923	−	2.76334i	0.661536	−	0.131588i
$442$	44.8527	+	34.3120i	2.13343	+	1.63206i
$443$	7.23367	+	13.5332i	0.343682	+	0.642984i	0.993077	−	0.117468i	$-0.0374777\pi$
$443$	7.23367	+	13.5332i	0.343682	+	0.642984i	−0.649395	+	0.760451i	$0.724978\pi$
$444$	0.390222	+	5.69684i	0.0185191	+	0.270360i
$445$	16.5279	+	1.62785i	0.783497	+	0.0771677i
$446$	15.9115	+	9.86198i	0.753431	+	0.466978i
$447$			9.08580i			0.429744i
$448$	36.8024	−	0.324743i	1.73875	−	0.0153427i
$449$		−	0.709298i		−	0.0334738i	−0.999860	−	0.0167369i	$-0.994672\pi$
$449$		−	0.709298i		−	0.0334738i	0.999860	−	0.0167369i	$-0.00532777\pi$
$450$	−5.23799	+	8.45107i	−0.246921	+	0.398387i
$451$	−4.31358	−	0.424850i	−0.203119	−	0.0200054i
$452$	3.30223	+	2.87884i	0.155324	+	0.135409i
$453$	−4.32268	−	8.08716i	−0.203097	−	0.379968i
$454$	−8.77778	+	11.4743i	−0.411961	+	0.538516i
$455$	−87.9654	+	17.4974i	−4.12388	+	0.820291i
$456$	−3.03982	+	3.73753i	−0.142352	+	0.175026i
$457$	2.86137	−	14.3851i	0.133849	−	0.672906i	−0.854346	−	0.519705i	$-0.826042\pi$
$457$	2.86137	−	14.3851i	0.133849	−	0.672906i	0.988195	−	0.153201i	$-0.0489582\pi$
$458$	−0.878455	+	13.7116i	−0.0410475	+	0.640700i
$459$	5.49175	+	4.50697i	0.256333	+	0.210367i
$460$	−1.14455	+	38.4173i	−0.0533648	+	1.79121i
$461$	30.7497	+	16.4361i	1.43216	+	0.765503i	0.991243	−	0.132047i	$-0.0421549\pi$
$461$	30.7497	+	16.4361i	1.43216	+	0.765503i	0.440913	+	0.897550i	$0.354655\pi$
$462$	5.37749	−	14.3516i	0.250183	−	0.667698i
$463$	−20.6299	+	8.54516i	−0.958751	+	0.397127i	−0.806513	−	0.591216i	$-0.798648\pi$
$463$	−20.6299	+	8.54516i	−0.958751	+	0.397127i	−0.152238	+	0.988344i	$0.548648\pi$
$464$	−0.543833	−	14.0792i	−0.0252468	−	0.653612i
$465$	−13.5299	−	5.60426i	−0.627433	−	0.259891i
$466$	11.3870	−	12.1937i	0.527492	−	0.564860i
$467$	18.9417	−	5.74591i	0.876518	−	0.265889i	0.180207	−	0.983629i	$-0.442323\pi$
$467$	18.9417	−	5.74591i	0.876518	−	0.265889i	0.696311	+	0.717740i	$0.254823\pi$
$468$	−2.52045	+	10.9552i	−0.116508	+	0.506406i
$469$	4.59254	+	46.6289i	0.212064	+	2.15312i
$470$	−19.0747	+	6.50630i	−0.879852	+	0.300113i
$471$	2.13985	+	3.20251i	0.0985989	+	0.147564i
$472$	−6.28292	−	2.57006i	−0.289195	−	0.118296i
$473$	12.9779	+	8.67157i	0.596725	+	0.398719i
$474$	−5.05722	−	8.72969i	−0.232286	−	0.400968i
$475$	11.4594	+	3.47618i	0.525794	+	0.159498i
$476$	−63.0897	+	17.1039i	−2.89171	+	0.783955i
$477$	6.36262	+	7.75287i	0.291324	+	0.354980i
$478$	−2.07650	+	12.6933i	−0.0949769	+	0.580578i
$479$	−29.5655	−	29.5655i	−1.35088	−	1.35088i	−0.884678	−	0.466203i	$-0.845621\pi$
$479$	−29.5655	−	29.5655i	−1.35088	−	1.35088i	−0.466203	−	0.884678i	$-0.654379\pi$
$480$	−19.6145	−	0.497763i	−0.895277	−	0.0227197i
$481$	11.3474	−	11.3474i	0.517399	−	0.517399i
$482$	−10.9640	−	15.2528i	−0.499397	−	0.694748i
$483$	−19.7031	+	16.1699i	−0.896523	+	0.735758i
$484$	6.66202	+	8.62944i	0.302819	+	0.392247i
$485$	−11.7727	+	38.8095i	−0.534572	+	1.76225i
$486$	−0.364016	+	1.36656i	−0.0165121	+	0.0619885i
$487$	5.64653	−	8.45063i	0.255869	−	0.382934i	−0.681190	−	0.732107i	$-0.738537\pi$
$487$	5.64653	−	8.45063i	0.255869	−	0.382934i	0.937059	+	0.349172i	$0.113537\pi$
$488$	−17.6754	+	11.9234i	−0.800126	+	0.539748i
$489$	5.32171	−	3.55585i	0.240656	−	0.160801i
$490$	30.6383	−	62.3593i	1.38410	−	2.81711i
$491$	11.7196	−	1.15428i	0.528896	−	0.0520917i	0.169955	−	0.985452i	$-0.445638\pi$
$491$	11.7196	−	1.15428i	0.528896	−	0.0520917i	0.358941	+	0.933360i	$0.383138\pi$
$492$	−2.13474	+	2.99761i	−0.0962414	+	0.135142i
$493$	7.26428	+	23.9471i	0.327167	+	1.07852i
$494$	13.5314	−	0.462893i	0.608806	−	0.0208266i
$495$	−3.12675	+	7.54864i	−0.140537	+	0.339286i
$496$	−2.30288	−	16.7309i	−0.103402	−	0.751242i
$497$	18.1250	+	43.7576i	0.813018	+	1.96280i
$498$	−0.971278	−	2.13530i	−0.0435240	−	0.0956850i
$499$	−7.41237	+	13.8676i	−0.331823	+	0.620797i	−0.991404	−	0.130836i	$-0.958234\pi$
$499$	−7.41237	+	13.8676i	−0.331823	+	0.620797i	0.659581	+	0.751634i	$0.270734\pi$
$500$	5.00051	+	13.1684i	0.223630	+	0.588910i
$501$	4.45435	−	5.42764i	0.199006	−	0.242489i
$502$	−0.484188	+	0.425883i	−0.0216104	+	0.0190081i
$503$	7.83481	+	1.55844i	0.349337	+	0.0694875i	0.366640	−	0.930363i	$-0.380508\pi$
$503$	7.83481	+	1.55844i	0.349337	+	0.0694875i	−0.0173031	+	0.999850i	$0.505508\pi$
$504$	−8.29910	−	10.0220i	−0.369671	−	0.446415i
$505$	−2.11865	−	10.6512i	−0.0942788	−	0.473972i
$506$	2.43609	+	18.2960i	0.108298	+	0.813357i
$507$	16.3972	−	8.76446i	0.728223	−	0.389243i
$508$	3.70934	−	1.84283i	0.164575	−	0.0817622i
$509$	1.88210	−	19.1093i	0.0834225	−	0.847003i	−0.858866	−	0.512201i	$-0.828830\pi$
$509$	1.88210	−	19.1093i	0.0834225	−	0.847003i	0.942288	−	0.334802i	$-0.108670\pi$
$510$	33.9264	−	7.96316i	1.50229	−	0.352614i
$511$	−63.3332			−2.80169
$512$	−10.9297	−	19.8127i	−0.483028	−	0.875605i
$513$	1.70329			0.0752021
$514$	−18.3440	+	4.30567i	−0.809119	+	0.189915i
$515$	−4.50796	+	45.7701i	−0.198645	+	2.01687i
$516$	11.8680	−	5.89609i	0.522458	−	0.259561i
$517$	−8.53573	+	4.56244i	−0.375401	+	0.200656i
$518$	2.45166	+	18.4129i	0.107720	+	0.809017i
$519$	0.0431909	+	0.217135i	0.00189587	+	0.00953117i
$520$	35.1692	+	42.4703i	1.54227	+	1.86245i
$521$	9.80137	+	1.94961i	0.429406	+	0.0854141i	0.405061	−	0.914290i	$-0.367250\pi$
$521$	9.80137	+	1.94961i	0.429406	+	0.0854141i	0.0243444	+	0.999704i	$0.492250\pi$
$522$	−3.74044	+	3.29002i	−0.163714	+	0.144000i
$523$	−2.65025	+	3.22934i	−0.115888	+	0.141209i	−0.827723	−	0.561137i	$-0.810364\pi$
$523$	−2.65025	+	3.22934i	−0.115888	+	0.141209i	0.711836	+	0.702346i	$0.247864\pi$
$524$	−2.47697	−	6.52289i	−0.108207	−	0.284954i
$525$	−15.2468	+	28.5248i	−0.665425	+	1.24492i
$526$	−18.7792	−	41.2849i	−0.818812	−	1.80011i
$527$	11.4789	+	27.7126i	0.500030	+	1.20718i
$528$	−9.33459	+	1.28483i	−0.406236	+	0.0559150i
$529$	2.94544	−	7.11093i	0.128063	−	0.309171i
$530$	49.1678	−	1.68198i	2.13571	−	0.0730604i
$531$	0.696686	+	2.29666i	0.0302336	+	0.0996667i
$532$	−9.09103	+	12.7657i	−0.394146	+	0.553461i
$533$	10.2925	−	1.01372i	0.445816	−	0.0439090i
$534$	2.98603	−	6.07759i	0.129218	−	0.263003i
$535$	14.9416	−	9.98364i	0.645980	−	0.431630i
$536$	23.8810	−	16.1096i	1.03150	−	0.695831i
$537$	−10.0041	+	14.9723i	−0.431710	+	0.646100i
$538$	−3.09657	+	11.6249i	−0.133503	+	0.501185i
$539$	9.68576	−	31.9297i	0.417195	−	1.37531i
$540$	4.23916	+	5.49106i	0.182424	+	0.236298i
$541$	13.9169	−	11.4213i	0.598335	−	0.491040i	−0.285790	−	0.958292i	$-0.592256\pi$
$541$	13.9169	−	11.4213i	0.598335	−	0.491040i	0.884124	+	0.467252i	$0.154756\pi$
$542$	4.23519	+	5.89188i	0.181917	+	0.253078i
$543$	−5.61434	+	5.61434i	−0.240934	+	0.240934i
$544$	27.6874	+	29.1293i	1.18709	+	1.24891i
$545$	−22.0763	−	22.0763i	−0.945643	−	0.945643i
$546$	−5.90382	+	36.0891i	−0.252660	+	1.54447i
$547$	11.3122	+	13.7839i	0.483673	+	0.589358i	0.956476	−	0.291811i	$-0.0942577\pi$
$547$	11.3122	+	13.7839i	0.483673	+	0.589358i	−0.472803	+	0.881168i	$0.656758\pi$
$548$	−8.58838	+	2.32835i	−0.366878	+	0.0994620i
$549$	7.21354	+	2.18820i	0.307866	+	0.0933902i
$550$	11.7406	+	20.2664i	0.500619	+	0.864161i
$551$	4.98859	+	3.33327i	0.212521	+	0.142002i
$552$	14.5043	+	5.93303i	0.617342	+	0.252526i
$553$	−18.2333	−	27.2880i	−0.775358	−	1.16040i
$554$	−38.7717	+	13.2248i	−1.64725	+	0.561870i
$555$	−0.970656	−	9.85523i	−0.0412020	−	0.418331i
$556$	−0.867199	+	3.76931i	−0.0367774	+	0.159854i
$557$	5.41335	−	1.64212i	0.229371	−	0.0695789i	−0.173507	−	0.984833i	$-0.555510\pi$
$557$	5.41335	−	1.64212i	0.229371	−	0.0695789i	0.402878	+	0.915254i	$0.368010\pi$
$558$	−4.07535	+	4.36406i	−0.172523	+	0.184745i
$559$	−34.4077	−	14.2521i	−1.45529	−	0.602801i
$560$	−63.7796	+	2.46359i	−2.69518	+	0.104106i
$561$	15.4615	−	6.40437i	0.652785	−	0.270393i
$562$	11.4545	−	30.5701i	0.483178	−	1.28952i
$563$	−19.4876	−	10.4163i	−0.821304	−	0.438996i	0.00652367	−	0.999979i	$-0.497923\pi$
$563$	−19.4876	−	10.4163i	−0.821304	−	0.438996i	−0.827828	+	0.560983i	$0.810423\pi$
$564$	−0.244706	+	8.21367i	−0.0103040	+	0.345858i
$565$	−5.87305	−	4.81989i	−0.247081	−	0.202774i
$566$	−0.707441	+	11.0423i	−0.0297360	+	0.464141i
$567$	−0.897509	+	4.51208i	−0.0376918	+	0.189490i
$568$	18.3736	−	22.5908i	0.770938	−	0.947888i
$569$	−27.4633	+	5.46279i	−1.15132	+	0.229012i	−0.733612	−	0.679568i	$-0.762167\pi$
$569$	−27.4633	+	5.46279i	−1.15132	+	0.229012i	−0.417710	+	0.908580i	$0.637167\pi$
$570$	5.07645	−	6.63594i	0.212629	−	0.277949i
$571$	20.0201	+	37.4550i	0.837817	+	1.56744i	0.823339	+	0.567549i	$0.192108\pi$
$571$	20.0201	+	37.4550i	0.837817	+	1.56744i	0.0144772	+	0.999895i	$0.495392\pi$
$572$	19.9607	+	17.4014i	0.834598	+	0.727591i
$573$	−5.05059	−	0.497440i	−0.210992	−	0.0207809i
$574$	−6.30670	+	10.1753i	−0.263237	+	0.424711i
$575$		−	38.9525i		−	1.62443i
$576$	−2.99613	+	7.41776i	−0.124839	+	0.309073i
$577$		−	24.6876i		−	1.02776i	−0.857863	−	0.513878i	$-0.828208\pi$
$577$		−	24.6876i		−	1.02776i	0.857863	−	0.513878i	$-0.171792\pi$
$578$	−40.2352	−	24.9379i	−1.67356	−	1.03728i
$579$	10.7237	+	1.05620i	0.445663	+	0.0438940i
$580$	1.66985	+	24.3781i	0.0693366	+	1.01224i
$581$	−3.59724	−	6.72997i	−0.149239	−	0.279206i
$582$	13.1335	+	10.0470i	0.544402	+	0.416464i
$583$	23.1719	−	4.60918i	0.959683	−	0.190893i
$584$	18.5065	+	34.2589i	0.765806	+	1.41764i
$585$	3.80339	−	19.1209i	0.157251	−	0.790553i
$586$	−23.1541	−	1.48340i	−0.956486	−	0.0612788i
$587$	10.1761	+	8.35127i	0.420011	+	0.344694i	0.820539	−	0.571591i	$-0.193673\pi$
$587$	10.1761	+	8.35127i	0.420011	+	0.344694i	−0.400528	+	0.916284i	$0.631173\pi$
$588$	−19.4261	−	20.6192i	−0.801119	−	0.850320i
$589$	6.34242	+	3.39009i	0.261335	+	0.139686i
$590$	11.0241	+	4.13067i	0.453854	+	0.170057i
$591$	21.7917	−	9.02641i	0.896390	−	0.371297i
$592$	9.24373	−	6.70661i	0.379915	−	0.275640i
$593$	−1.74379	−	0.722303i	−0.0716090	−	0.0296614i	0.346591	−	0.938016i	$-0.387339\pi$
$593$	−1.74379	−	0.722303i	−0.0716090	−	0.0296614i	−0.418200	+	0.908355i	$0.637339\pi$
$594$	2.43481	+	2.27374i	0.0999015	+	0.0932925i
$595$	108.482	−	32.9076i	4.44732	−	1.34908i
$596$	15.4031	−	9.64119i	0.630935	−	0.394918i
$597$	1.41324	+	14.3488i	0.0578399	+	0.587258i
$598$	−14.2177	−	41.6826i	−0.581406	−	1.70453i
$599$	17.2256	+	25.7799i	0.703819	+	1.05334i	0.995307	+	0.0967649i	$0.0308495\pi$
$599$	17.2256	+	25.7799i	0.703819	+	1.05334i	−0.291488	+	0.956574i	$0.594150\pi$
$600$	19.8852	−	0.0877313i	0.811809	−	0.00358161i
$601$	−20.5506	−	13.7314i	−0.838275	−	0.560117i	0.0606808	−	0.998157i	$-0.480673\pi$
$601$	−20.5506	−	13.7314i	−0.838275	−	0.560117i	−0.898956	+	0.438040i	$0.855673\pi$
$602$	37.3016	−	21.6093i	1.52030	−	0.880729i
$603$	−9.74615	−	2.95646i	−0.396894	−	0.120396i
$604$	−9.12318	+	15.9097i	−0.371217	+	0.647356i
$605$	−11.9942	−	14.6149i	−0.487633	−	0.594182i
$606$	−4.36980	−	0.714857i	−0.177511	−	0.0290391i
$607$	22.4508	+	22.4508i	0.911250	+	0.911250i	0.996371	−	0.0851210i	$-0.0271277\pi$
$607$	22.4508	+	22.4508i	0.911250	+	0.911250i	−0.0851210	+	0.996371i	$0.527128\pi$
$608$	9.56183	+	1.18738i	0.387783	+	0.0481546i
$609$	−11.4586	+	11.4586i	−0.464325	+	0.464325i
$610$	30.0242	−	21.5819i	1.21564	−	0.873827i
$611$	17.8516	−	14.6504i	0.722199	−	0.592694i
$612$	1.81317	−	14.0926i	0.0732931	−	0.569659i
$613$	−13.5467	+	44.6576i	−0.547147	+	1.80370i	0.0464262	+	0.998922i	$0.485217\pi$
$613$	−13.5467	+	44.6576i	−0.547147	+	1.80370i	−0.593573	+	0.804780i	$0.702283\pi$
$614$	−6.73691	−	1.79453i	−0.271879	−	0.0724215i
$615$	3.54572	−	5.30655i	0.142977	−	0.213981i
$616$	−30.0364	+	6.11249i	−1.21020	+	0.246279i
$617$	16.8322	−	11.2469i	0.677640	−	0.452784i	−0.168531	−	0.985696i	$-0.553902\pi$
$617$	16.8322	−	11.2469i	0.677640	−	0.452784i	0.846171	+	0.532912i	$0.178902\pi$
$618$	16.8305	+	8.26911i	0.677020	+	0.332632i
$619$	1.75627	−	0.172978i	0.0705905	−	0.00695256i	−0.0626602	−	0.998035i	$-0.519958\pi$
$619$	1.75627	−	0.172978i	0.0705905	−	0.00695256i	0.133251	+	0.991082i	$0.457458\pi$
$620$	4.85607	+	28.8839i	0.195024	+	1.16001i
$621$	−1.60831	−	5.30190i	−0.0645394	−	0.212758i
$622$	−0.348138	−	10.1768i	−0.0139591	−	0.408054i
$623$	8.42973	−	20.3512i	0.337730	−	0.815353i
$624$	21.2469	−	7.35200i	0.850555	−	0.294316i
$625$	4.10397	+	9.90785i	0.164159	+	0.396314i
$626$	−39.6002	+	18.0128i	−1.58274	+	0.719938i
$627$	1.89141	−	3.53858i	0.0755357	−	0.141317i
$628$	3.15853	−	7.02593i	0.126039	−	0.280365i
$629$	−12.8678	+	15.6795i	−0.513073	+	0.625182i
$630$	14.9039	+	16.9444i	0.593787	+	0.675079i
$631$	19.4064	+	3.86017i	0.772557	+	0.153671i	0.565601	−	0.824679i	$-0.308644\pi$
$631$	19.4064	+	3.86017i	0.772557	+	0.153671i	0.206956	+	0.978350i	$0.433644\pi$
$632$	−9.43301	+	17.8368i	−0.375225	+	0.709508i
$633$	−4.61948	−	23.2237i	−0.183608	−	0.923059i
$634$	−44.4828	+	5.92284i	−1.76664	+	0.235226i
$635$	−6.33491	+	3.38608i	−0.251393	+	0.134372i
$636$	6.39183	−	19.0133i	0.253453	−	0.753925i
$637$	−7.80356	+	79.2309i	−0.309188	+	3.13924i
$638$	2.68145	+	11.4241i	0.106160	+	0.452286i
$639$	−10.2952			−0.407272
$640$	19.9696	+	33.7805i	0.789369	+	1.33529i
$641$	−13.5502			−0.535201			−0.267601	−	0.963530i	$-0.586231\pi$
$641$	−13.5502			−0.535201			−0.267601	+	0.963530i	$0.586231\pi$
$642$	−1.67426	−	7.13308i	−0.0660779	−	0.281520i
$643$	1.40200	−	14.2348i	0.0552895	−	0.561364i	−0.927138	−	0.374720i	$-0.877739\pi$
$643$	1.40200	−	14.2348i	0.0552895	−	0.561364i	0.982428	−	0.186644i	$-0.0597611\pi$
$644$	48.3203	+	16.2442i	1.90408	+	0.640110i
$645$	−20.2684	+	10.8337i	−0.798069	+	0.426577i
$646$	−16.9634	+	2.25866i	−0.667417	+	0.0888659i
$647$	3.75797	+	18.8926i	0.147741	+	0.742745i	0.981627	+	0.190808i	$0.0611109\pi$
$647$	3.75797	+	18.8926i	0.147741	+	0.742745i	−0.833886	+	0.551936i	$0.813889\pi$
$648$	2.70299	−	0.832982i	0.106183	−	0.0327226i
$649$	5.54495	+	1.10296i	0.217658	+	0.0432949i
$650$	−36.9094	−	41.9624i	−1.44770	−	1.64590i
$651$	−12.3225	+	15.0150i	−0.482956	+	0.588483i
$652$	−11.6752	−	5.24864i	−0.457237	−	0.205553i
$653$	7.79614	−	14.5856i	0.305087	−	0.570777i	−0.681926	−	0.731422i	$-0.738857\pi$
$653$	7.79614	−	14.5856i	0.305087	−	0.570777i	0.987012	+	0.160644i	$0.0513572\pi$
$654$	−11.5871	+	5.27062i	−0.453093	+	0.206097i
$655$	4.63066	+	11.1794i	0.180935	+	0.436816i
$656$	7.34704	+	0.438162i	0.286854	+	0.0171074i
$657$	5.26826	−	12.7187i	0.205535	−	0.496204i
$658$	0.913909	+	26.7156i	0.0356279	+	1.04148i
$659$	6.56845	+	21.6533i	0.255871	+	0.843492i	0.986926	+	0.161174i	$0.0515281\pi$
$659$	6.56845	+	21.6533i	0.255871	+	0.843492i	−0.731055	+	0.682318i	$0.760972\pi$
$660$	16.1150	−	2.70931i	0.627276	−	0.105460i
$661$	−17.4906	+	1.72267i	−0.680305	+	0.0670042i	−0.432266	−	0.901746i	$-0.642286\pi$
$661$	−17.4906	+	1.72267i	−0.680305	+	0.0670042i	−0.248038	+	0.968750i	$0.579786\pi$
$662$	−4.39401	−	2.15886i	−0.170778	−	0.0839065i
$663$	−33.2020	+	22.1849i	−1.28946	+	0.861589i
$664$	−2.58930	+	3.91242i	−0.100484	+	0.151831i
$665$	15.0999	−	22.5986i	0.585548	−	0.876335i
$666$	−3.90166	−	1.03930i	−0.151186	−	0.0402721i
$667$	5.66518	−	18.6756i	0.219357	−	0.723122i
$668$	−13.9280	−	1.79200i	−0.538892	−	0.0693347i
$669$	−10.2323	+	8.39744i	−0.395604	+	0.324664i
$670$	−40.5654	+	29.1592i	−1.56718	+	1.12652i
$671$	12.5562	−	12.5562i	0.484728	−	0.484728i
$672$	−8.18379	+	24.7040i	−0.315697	+	0.952977i
$673$	17.5725	+	17.5725i	0.677371	+	0.677371i	0.959404	−	0.282034i	$-0.0910091\pi$
$673$	17.5725	+	17.5725i	0.677371	+	0.677371i	−0.282034	+	0.959404i	$0.591009\pi$
$674$	−40.8928	−	6.68967i	−1.57513	−	0.257676i
$675$	−4.46013	−	5.43468i	−0.171670	−	0.209181i
$676$	−32.2578	−	18.4977i	−1.24068	−	0.711451i
$677$	−10.5818	−	3.20996i	−0.406692	−	0.123369i	0.0803092	−	0.996770i	$-0.474409\pi$
$677$	−10.5818	−	3.20996i	−0.406692	−	0.123369i	−0.487001	+	0.873401i	$0.661909\pi$
$678$	−2.68048	+	1.55283i	−0.102943	+	0.0596362i
$679$	44.7259	+	29.8849i	1.71642	+	1.14688i
$680$	−49.5001	−	49.0652i	−1.89824	−	1.88157i
$681$	−5.67538	−	8.49381i	−0.217481	−	0.325483i
$682$	4.54086	+	13.3126i	0.173878	+	0.509765i
$683$	4.59241	+	46.6275i	0.175724	+	1.78415i	0.528988	+	0.848630i	$0.322572\pi$
$683$	4.59241	+	46.6275i	0.175724	+	1.78415i	−0.353264	+	0.935524i	$0.614928\pi$
$684$	−1.80741	−	2.88757i	−0.0691079	−	0.110409i
$685$	14.7676	−	4.47970i	0.564240	−	0.171160i
$686$	−34.0674	−	31.8136i	−1.30070	−	1.21465i
$687$	−8.97589	−	3.71793i	−0.342451	−	0.141848i
$688$	−22.5890	−	13.8632i	−0.861198	−	0.528528i
$689$	−52.0817	+	21.5729i	−1.98415	+	0.821863i
$690$	−25.4493	−	9.53574i	−0.968839	−	0.363020i
$691$	13.9181	+	7.43940i	0.529471	+	0.283008i	0.714392	−	0.699745i	$-0.246703\pi$
$691$	13.9181	+	7.43940i	0.529471	+	0.283008i	−0.184922	+	0.982753i	$0.559203\pi$
$692$	0.322276	−	0.303629i	0.0122511	−	0.0115422i
$693$	8.37721	+	6.87500i	0.318224	+	0.261160i
$694$	45.7953	+	2.93395i	1.73837	+	0.111371i
$695$	1.30861	−	6.57883i	0.0496384	−	0.249549i
$696$	9.54661	+	2.85000i	0.361863	+	0.108029i
$697$	−12.8210	+	2.55026i	−0.485631	+	0.0965981i
$698$	7.05578	+	5.39762i	0.267065	+	0.204303i
$699$	5.56117	+	10.4042i	0.210343	+	0.393524i
$700$	64.5365	−	4.42062i	2.43925	−	0.167084i
$701$	5.45302	+	0.537075i	0.205958	+	0.0202851i	0.200470	−	0.979700i	$-0.435753\pi$
$701$	5.45302	+	0.537075i	0.205958	+	0.0202851i	0.00548782	+	0.999985i	$0.498253\pi$
$702$	−6.75639	−	4.18763i	−0.255004	−	0.158052i
$703$			4.86306i			0.183414i
$704$	12.0833	+	14.4615i	0.455408	+	0.545038i
$705$		−	14.2509i		−	0.536721i
$706$	−16.9198	+	27.2987i	−0.636784	+	1.02740i
$707$	−14.3347	−	1.41184i	−0.539112	−	0.0530979i
$708$	3.15424	−	3.61814i	0.118544	−	0.135978i
$709$	23.2925	+	43.5771i	0.874766	+	1.63657i	0.766309	+	0.642472i	$0.222091\pi$
$709$	23.2925	+	43.5771i	0.874766	+	1.63657i	0.108457	+	0.994101i	$0.465409\pi$
$710$	−30.6836	+	40.1097i	−1.15154	+	1.50529i
$711$	6.99675	−	1.39174i	0.262399	−	0.0521943i
$712$	−13.4718	+	1.38690i	−0.504878	+	0.0519762i
$713$	4.56371	−	22.9433i	0.170912	−	0.859235i
$714$	2.95520	−	46.1269i	0.110595	−	1.72626i
$715$	−35.5002	−	29.1343i	−1.32763	−	1.08956i
$716$	35.9980	+	1.07247i	1.34531	+	0.0400801i
$717$	−8.02092	−	4.28727i	−0.299547	−	0.160111i
$718$	12.7548	−	34.0405i	0.476006	−	1.27038i
$719$	−3.14865	+	1.30421i	−0.117425	+	0.0486390i	−0.440622	−	0.897693i	$-0.645242\pi$
$719$	−3.14865	+	1.30421i	−0.117425	+	0.0486390i	0.323197	+	0.946332i	$0.395242\pi$
$720$	4.81066	−	13.0133i	0.179283	−	0.484977i
$721$	56.3578	+	23.3442i	2.09887	+	0.869382i
$722$	15.5390	−	16.6398i	0.578301	−	0.619269i
$723$	12.7107	−	3.85576i	0.472717	−	0.143397i
$724$	15.4755	+	3.56041i	0.575141	+	0.132322i
$725$	−2.42736	−	24.6454i	−0.0901498	−	0.915306i
$726$	−7.29600	+	2.48863i	−0.270780	+	0.0923617i
$727$	−22.2125	−	33.2433i	−0.823815	−	1.23293i	−0.969864	−	0.243648i	$-0.921656\pi$
$727$	−22.2125	−	33.2433i	−0.823815	−	1.23293i	0.146049	−	0.989277i	$-0.453344\pi$
$728$	67.4461	−	28.2864i	2.49972	−	1.04836i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−33.8501	−	58.4315i	−1.25285	−	2.16265i
$731$	45.0462	+	13.6646i	1.66610	+	0.505404i
$732$	−3.94484	−	14.5510i	−0.145805	−	0.537820i
$733$	10.6746	+	13.0071i	0.394276	+	0.480426i	0.931878	−	0.362772i	$-0.118170\pi$
$733$	10.6746	+	13.0071i	0.394276	+	0.480426i	−0.537602	+	0.843199i	$0.680670\pi$
$734$	−4.59818	+	28.1079i	−0.169722	+	1.03748i
$735$	34.7397	+	34.7397i	1.28139	+	1.28139i
$736$	−5.33265	−	30.8846i	−0.196564	−	1.13842i
$737$	−16.9646	+	16.9646i	−0.624899	+	0.624899i
$738$	−1.51882	−	2.11295i	−0.0559087	−	0.0777786i
$739$	23.4368	−	19.2341i	0.862138	−	0.707539i	−0.0955257	−	0.995427i	$-0.530453\pi$
$739$	23.4368	−	19.2341i	0.862138	−	0.707539i	0.957664	+	0.287888i	$0.0929532\pi$
$740$	−15.6775	+	12.1032i	−0.576316	+	0.444922i
$741$	−2.77911	+	9.16149i	−0.102093	+	0.336556i
$742$	16.7958	−	63.0536i	0.616594	−	2.31477i
$743$	−12.5770	+	18.8228i	−0.461406	+	0.690542i	−0.987095	−	0.160134i	$-0.948807\pi$
$743$	−12.5770	+	18.8228i	−0.461406	+	0.690542i	0.525690	+	0.850676i	$0.323807\pi$
$744$	11.7228	+	2.27809i	0.429779	+	0.0835189i
$745$	−26.2031	+	17.5083i	−0.960007	+	0.641456i
$746$	0.286905	−	0.583948i	0.0105043	−	0.0213799i
$747$	1.65076	−	0.162586i	0.0603981	−	0.00594870i
$748$	−27.2639	−	19.4159i	−0.996866	−	0.709916i
$749$	−6.91886	−	22.8084i	−0.252810	−	0.833401i
$750$	−9.95442	+	0.340529i	−0.363484	+	0.0124344i
$751$	20.4182	−	49.2940i	0.745072	−	1.79876i	0.161192	−	0.986923i	$-0.448466\pi$
$751$	20.4182	−	49.2940i	0.745072	−	1.79876i	0.583880	−	0.811840i	$-0.301534\pi$
$752$	14.1842	−	8.30090i	0.517246	−	0.302703i
$753$	−0.174491	−	0.421260i	−0.00635882	−	0.0153516i
$754$	−11.5931	−	25.4867i	−0.422195	−	0.928171i
$755$	14.9932	−	28.0504i	0.545660	−	1.02086i
$756$	8.60166	−	3.26635i	0.312839	−	0.118796i
$757$	11.0739	−	13.4936i	0.402487	−	0.490432i	−0.531842	−	0.846844i	$-0.678500\pi$
$757$	11.0739	−	13.4936i	0.402487	−	0.490432i	0.934329	+	0.356412i	$0.116000\pi$
$758$	−18.9130	+	16.6356i	−0.686953	+	0.604231i
$759$	−12.8006	−	2.54620i	−0.464633	−	0.0924213i
$760$	−16.6366	−	1.56448i	−0.603473	−	0.0567498i
$761$	1.24994	+	6.28386i	0.0453102	+	0.227790i	0.996805	−	0.0798756i	$-0.0254523\pi$
$761$	1.24994	+	6.28386i	0.0453102	+	0.227790i	−0.951495	+	0.307665i	$0.900452\pi$
$762$	0.386549	+	2.90313i	0.0140032	+	0.105169i
$763$	−36.5200	+	19.5203i	−1.32211	+	0.706684i
$764$	4.51601	+	9.09007i	0.163384	+	0.328867i
$765$	−2.41530	+	24.5229i	−0.0873252	+	0.886628i
$766$	43.7538	−	10.2698i	1.58089	−	0.371064i
$767$	−13.4898			−0.487088
$768$	15.7545	−	2.79187i	0.568493	−	0.100743i
$769$	0.784880			0.0283035			0.0141517	−	0.999900i	$-0.495495\pi$
$769$	0.784880			0.0283035			0.0141517	+	0.999900i	$0.495495\pi$
$770$	51.7519	−	12.1471i	1.86501	−	0.437752i
$771$	1.30595	−	13.2595i	0.0470326	−	0.477530i
$772$	−9.58868	−	19.3006i	−0.345104	−	0.694644i
$773$	−16.4873	+	8.81265i	−0.593007	+	0.316969i	−0.740460	−	0.672100i	$-0.765392\pi$
$773$	−16.4873	+	8.81265i	−0.593007	+	0.316969i	0.147453	+	0.989069i	$0.452892\pi$
$774$	1.23676	+	9.28853i	0.0444543	+	0.333869i
$775$	−5.79109	−	29.1138i	−0.208022	−	1.04580i
$776$	3.09635	−	32.9263i	0.111152	−	1.18199i
$777$	−12.8824	−	2.56247i	−0.462154	−	0.0919282i
$778$	25.3810	−	22.3247i	0.909954	−	0.800379i
$779$	−1.98825	+	2.42269i	−0.0712364	+	0.0868018i
$780$	−36.4514	+	13.8419i	−1.30517	+	0.495618i
$781$	−11.4323	+	21.3883i	−0.409079	+	0.765333i
$782$	23.0482	+	50.6700i	0.824200	+	1.81196i
$783$	−1.34798	−	3.25430i	−0.0481728	−	0.116299i
$784$	−14.3419	+	54.8124i	−0.512211	+	1.95759i
$785$	−5.11241	+	12.3425i	−0.182470	+	0.440521i
$786$	4.93085	−	0.168679i	0.175878	−	0.00601658i
$787$	3.25582	+	10.7330i	0.116057	+	0.382590i	0.995654	−	0.0931303i	$-0.0296873\pi$
$787$	3.25582	+	10.7330i	0.116057	+	0.382590i	−0.879596	+	0.475721i	$0.842187\pi$
$788$	−38.4261	−	27.3651i	−1.36887	−	0.974840i
$789$	31.9166	−	3.14351i	1.13626	−	0.111912i
$790$	15.4308	−	31.4069i	0.549003	−	1.11741i
$791$	−8.37887	+	5.59858i	−0.297918	+	0.199063i
$792$	1.27100	−	6.54043i	0.0451631	−	0.232404i
$793$	−23.5394	+	35.2291i	−0.835907	+	1.25102i
$794$	10.7128	−	40.2171i	0.380182	−	1.42725i
$795$	−10.0982	+	33.2893i	−0.358146	+	1.18065i
$796$	22.8258	−	17.6218i	0.809039	−	0.624587i
$797$	−32.5579	+	26.7196i	−1.15326	+	0.946455i	−0.999134	−	0.0415963i	$-0.986756\pi$
$797$	−32.5579	+	26.7196i	−1.15326	+	0.946455i	−0.154124	+	0.988051i	$0.549256\pi$
$798$	−6.46809	−	8.99823i	−0.228968	−	0.318534i
$799$	−20.6401	+	20.6401i	−0.730193	+	0.730193i
$800$	−21.2494	−	33.6181i	−0.751281	−	1.18858i
$801$	3.38576	+	3.38576i	0.119630	+	0.119630i
$802$	2.70306	−	16.5233i	0.0954483	−	0.583459i
$803$	−20.5730	−	25.0683i	−0.726005	−	0.884639i
$804$	5.32983	+	19.6597i	0.187969	+	0.693345i
$805$	−84.6014	−	25.6635i	−2.98181	−	0.904521i
$806$	−16.8235	−	29.0405i	−0.592584	−	1.02291i
$807$	−7.07305	−	4.72606i	−0.248983	−	0.166365i
$808$	3.42502	+	8.16664i	0.120492	+	0.287301i
$809$	9.50064	+	14.2187i	0.334025	+	0.499903i	0.960023	−	0.279921i	$-0.0903084\pi$
$809$	9.50064	+	14.2187i	0.334025	+	0.499903i	−0.625998	+	0.779824i	$0.715308\pi$
$810$	−4.64257	+	1.58356i	−0.163123	+	0.0556405i
$811$	−3.31121	−	33.6193i	−0.116272	−	1.18053i	−0.859371	−	0.511352i	$-0.829145\pi$
$811$	−3.31121	−	33.6193i	−0.116272	−	1.18053i	0.743099	−	0.669182i	$-0.233355\pi$
$812$	31.5846	+	7.26662i	1.10840	+	0.255009i
$813$	−4.90991	+	1.48940i	−0.172198	+	0.0522357i
$814$	−6.49173	+	6.95161i	−0.227535	+	0.243654i
$815$	20.5099	+	8.49547i	0.718430	+	0.297583i
$816$	−25.8150	+	11.8802i	−0.903707	+	0.415889i
$817$	10.4268	−	4.31893i	0.364788	−	0.151100i
$818$	3.62619	−	9.67770i	0.126787	−	0.338373i
$819$	−22.8047	−	12.1894i	−0.796862	−	0.425932i
$820$	−12.7586	−	0.380111i	−0.445550	−	0.0132740i
$821$	6.45623	+	5.29849i	0.225324	+	0.184919i	0.740281	−	0.672297i	$-0.234692\pi$
$821$	6.45623	+	5.29849i	0.225324	+	0.184919i	−0.514957	+	0.857216i	$0.672192\pi$
$822$	0.402290	−	6.27924i	0.0140315	−	0.219014i
$823$	2.14748	−	10.7961i	0.0748564	−	0.376328i	−0.925138	−	0.379631i	$-0.876051\pi$
$823$	2.14748	−	10.7961i	0.0748564	−	0.376328i	0.999995	+	0.00330220i	$0.00105113\pi$
$824$	−3.84069	−	37.3071i	−0.133797	−	1.29965i
$825$	−16.2433	+	3.23099i	−0.565518	+	0.112489i
$826$	9.48734	−	12.4019i	0.330107	−	0.431516i
$827$	13.2008	+	24.6970i	0.459038	+	0.858799i	0.999844	+	0.0176523i	$0.00561919\pi$
$827$	13.2008	+	24.6970i	0.459038	+	0.858799i	−0.540806	+	0.841147i	$0.681881\pi$
$828$	−7.28164	+	8.35255i	−0.253054	+	0.290271i
$829$	10.2420	+	1.00875i	0.355721	+	0.0350354i	0.274299	−	0.961644i	$-0.411554\pi$
$829$	10.2420	+	1.00875i	0.355721	+	0.0350354i	0.0814214	+	0.996680i	$0.474054\pi$
$830$	4.28646	−	6.91585i	0.148785	−	0.240052i
$831$		−	28.9667i		−	1.00484i
$832$	−35.0094	−	28.2182i	−1.21373	−	0.978290i
$833$		−	100.629i		−	3.48660i
$834$	−2.32463	−	1.44081i	−0.0804955	−	0.0498913i
$835$	24.2366	+	2.38710i	0.838742	+	0.0826089i
$836$	−8.00596	+	0.548391i	−0.276892	+	0.0189665i
$837$	−1.99032	−	3.72362i	−0.0687955	−	0.128707i
$838$	−16.5695	−	12.6756i	−0.572384	−	0.437870i
$839$	18.9110	−	3.76164i	0.652882	−	0.129866i	0.142474	−	0.989799i	$-0.454494\pi$
$839$	18.9110	−	3.76164i	0.652882	−	0.129866i	0.510408	+	0.859932i	$0.329494\pi$
$840$	12.9106	−	43.2466i	0.445460	−	1.49215i
$841$	−3.23703	+	16.2736i	−0.111622	+	0.561160i
$842$	−28.4031	−	1.81969i	−0.978835	−	0.0627107i
$843$	17.8441	+	14.6443i	0.614585	+	0.504377i
$844$	−34.4691	+	32.4746i	−1.18647	+	1.11782i
$845$	56.8736	+	30.3996i	1.95651	+	1.04578i
$846$	−5.44111	−	2.03876i	−0.187069	−	0.0700939i
$847$	−23.1680	+	9.59648i	−0.796061	+	0.329739i
$848$	−39.0155	+	9.33947i	−1.33980	+	0.320719i
$849$	−7.22850	−	2.99414i	−0.248081	−	0.102759i
$850$	51.6261	+	48.2107i	1.77076	+	1.65361i
$851$	15.1374	−	4.59189i	0.518904	−	0.157408i
$852$	10.9245	+	17.4534i	0.374268	+	0.597943i
$853$	−4.93756	−	50.1319i	−0.169059	−	1.71648i	−0.588329	−	0.808622i	$-0.700214\pi$
$853$	−4.93756	−	50.1319i	−0.169059	−	1.71648i	0.419270	−	0.907862i	$-0.362286\pi$
$854$	−15.8328	−	46.4175i	−0.541787	−	1.58838i
$855$	3.28224	+	4.91222i	0.112250	+	0.167994i
$856$	−10.3160	+	10.4075i	−0.352595	+	0.355720i
$857$	4.43344	+	2.96233i	0.151443	+	0.101191i	0.628983	−	0.777419i	$-0.283471\pi$
$857$	4.43344	+	2.96233i	0.151443	+	0.101191i	−0.477540	+	0.878610i	$0.658471\pi$
$858$	−16.2024	+	9.38626i	−0.553141	+	0.320441i
$859$	−35.5199	−	10.7749i	−1.21192	−	0.367633i	−0.381292	−	0.924455i	$-0.624521\pi$
$859$	−35.5199	−	10.7749i	−1.21192	−	0.367633i	−0.830632	+	0.556821i	$0.812021\pi$
$860$	39.8737	+	22.8650i	1.35968	+	0.779689i
$861$	−5.37013	−	6.54353i	−0.183014	−	0.223003i
$862$	−21.3923	−	3.49957i	−0.728623	−	0.119196i
$863$	16.4702	+	16.4702i	0.560653	+	0.560653i	0.929493	−	0.368840i	$-0.120245\pi$
$863$	16.4702	+	16.4702i	0.560653	+	0.560653i	−0.368840	+	0.929493i	$0.620245\pi$
$864$	−4.28036	−	3.69845i	−0.145621	−	0.125824i
$865$	−0.542980	+	0.542980i	−0.0184619	+	0.0184619i
$866$	−21.7537	+	15.6370i	−0.739222	+	0.531366i
$867$	25.8743	−	21.2345i	0.878737	−	0.721161i
$868$	38.5304	+	4.95738i	1.30781	+	0.168264i
$869$	4.87818	−	16.0812i	0.165481	−	0.545517i
$870$	−16.6961	−	4.44740i	−0.566051	−	0.150781i
$871$	31.8038	−	47.5978i	1.07763	−	1.61279i
$872$	21.2306	+	14.0508i	0.718960	+	0.475819i
$873$	−9.72202	+	6.49604i	−0.329040	+	0.219858i
$874$	11.9783	+	5.88517i	0.405173	+	0.199069i
$875$	−32.2450	+	3.17585i	−1.09008	+	0.107363i
$876$	−27.1522	+	4.56493i	−0.917388	+	0.154235i
$877$	−4.74995	−	15.6585i	−0.160394	−	0.528749i	0.839499	−	0.543361i	$-0.182849\pi$
$877$	−4.74995	−	15.6585i	−0.160394	−	0.528749i	−0.999893	+	0.0146122i	$0.995349\pi$
$878$	−0.942679	−	27.5566i	−0.0318139	−	0.929989i
$879$	6.27829	−	15.1571i	0.211761	−	0.511237i
$880$	−21.6931	−	24.4447i	−0.731276	−	0.824031i
$881$	3.82070	+	9.22399i	0.128723	+	0.310764i	0.975081	−	0.221850i	$-0.0712096\pi$
$881$	3.82070	+	9.22399i	0.128723	+	0.310764i	−0.846358	+	0.532614i	$0.821210\pi$
$882$	18.2338	−	8.29397i	0.613964	−	0.279273i
$883$	−2.27327	+	4.25299i	−0.0765016	+	0.143124i	−0.917264	−	0.398280i	$-0.869607\pi$
$883$	−2.27327	+	4.25299i	−0.0765016	+	0.143124i	0.840762	+	0.541405i	$0.182107\pi$
$884$	72.8413	+	32.7461i	2.44992	+	1.10137i
$885$	−5.28097	+	6.43488i	−0.177518	+	0.216306i
$886$	14.3327	+	16.2949i	0.481516	+	0.547437i
$887$	−14.0493	−	2.79457i	−0.471728	−	0.0938325i	−0.0464989	−	0.998918i	$-0.514806\pi$
$887$	−14.0493	−	2.79457i	−0.471728	−	0.0938325i	−0.425229	+	0.905086i	$0.639806\pi$
$888$	2.37824	+	7.71728i	0.0798086	+	0.258975i
$889$	1.85869	+	9.34426i	0.0623384	+	0.313396i
$890$	23.2816	−	3.09992i	0.780401	−	0.103909i
$891$	−2.07750	+	1.11045i	−0.0695988	+	0.0372013i
$892$	25.0939	+	8.43599i	0.840205	+	0.282458i
$893$	−0.685948	+	6.96454i	−0.0229544	+	0.233060i
$894$	2.93616	+	12.5093i	0.0982000	+	0.418374i
$895$	−62.4573			−2.08772
$896$	50.5645	−	12.3402i	1.68924	−	0.412255i
$897$	31.1415			1.03978
$898$	−0.229216	−	0.976558i	−0.00764904	−	0.0325882i
$899$	1.45774	−	14.8007i	0.0486184	−	0.493631i
$900$	−4.48061	+	13.3281i	−0.149354	+	0.444270i
$901$	62.8395	−	33.5884i	2.09349	−	1.11899i
$902$	−6.07621	+	0.809041i	−0.202316	+	0.0269381i
$903$	5.94685	+	29.8968i	0.197899	+	0.994904i
$904$	5.47683	+	2.89643i	0.182157	+	0.0963339i
$905$	−27.0104	−	5.37270i	−0.897855	−	0.178594i
$906$	−8.56489	−	9.73746i	−0.284549	−	0.323505i
$907$	−13.7675	+	16.7757i	−0.457142	+	0.557029i	−0.949664	−	0.313271i	$-0.898575\pi$
$907$	−13.7675	+	16.7757i	−0.457142	+	0.557029i	0.492522	+	0.870300i	$0.336075\pi$
$908$	−8.37717	+	18.6344i	−0.278006	+	0.618405i
$909$	1.47594	−	2.76129i	0.0489538	−	0.0915860i
$910$	−115.456	+	52.5172i	−3.82733	+	1.74093i
$911$	18.0541	+	43.5866i	0.598161	+	1.44409i	0.875454	+	0.483302i	$0.160563\pi$
$911$	18.0541	+	43.5866i	0.598161	+	1.44409i	−0.277293	+	0.960785i	$0.589437\pi$
$912$	−2.97739	+	6.12816i	−0.0985912	+	0.202924i
$913$	1.49531	−	3.60999i	0.0494875	−	0.119473i
$914$	−0.709151	−	20.7300i	−0.0234566	−	0.685688i
$915$	7.58980	+	25.0202i	0.250911	+	0.827142i
$916$	3.22157	+	19.1619i	0.106444	+	0.633128i
$917$	15.9723	−	1.57314i	0.527452	−	0.0519495i
$918$	9.01750	+	4.43046i	0.297622	+	0.146227i
$919$	−14.2589	+	9.52747i	−0.470357	+	0.314282i	−0.768062	−	0.640376i	$-0.778779\pi$
$919$	−14.2589	+	9.52747i	−0.470357	+	0.314282i	0.297705	+	0.954658i	$0.403779\pi$
$920$	10.8391	+	53.2626i	0.357355	+	1.75602i
$921$	2.73886	−	4.09900i	0.0902486	−	0.135067i
$922$	47.6475	+	12.6920i	1.56919	+	0.417990i
$923$	16.7978	−	55.3748i	0.552905	−	1.82268i
$924$	2.76584	−	21.4970i	0.0909895	−	0.707201i
$925$	15.5165	−	12.7341i	0.510181	−	0.418694i
$926$	−25.6417	+	18.4317i	−0.842637	+	0.605703i
$927$	−9.37606	+	9.37606i	−0.307950	+	0.307950i
$928$	−5.29859	−	19.2085i	−0.173935	−	0.630550i
$929$	28.4298	+	28.4298i	0.932751	+	0.932751i	0.997877	−	0.0651256i	$-0.0207448\pi$
$929$	28.4298	+	28.4298i	0.932751	+	0.932751i	−0.0651256	+	0.997877i	$0.520745\pi$
$930$	−20.4390	−	3.34362i	−0.670220	−	0.109641i
$931$	−15.3055	−	18.6497i	−0.501616	−	0.611221i
$932$	11.7371	−	20.4680i	0.384461	−	0.670451i
$933$	6.89027	+	2.09014i	0.225577	+	0.0684282i
$934$	24.2220	−	14.0321i	0.792569	−	0.459145i
$935$	48.2642	+	32.2491i	1.57841	+	1.05466i
$936$	0.0701387	+	15.8977i	0.00229256	+	0.519631i
$937$	−7.32533	−	10.9631i	−0.239308	−	0.358150i	0.692303	−	0.721607i	$-0.256596\pi$
$937$	−7.32533	−	10.9631i	−0.239308	−	0.358150i	−0.931611	+	0.363457i	$0.881596\pi$
$938$	21.3916	+	62.7143i	0.698459	+	2.04770i
$939$	−3.01523	−	30.6142i	−0.0983983	−	0.999055i
$940$	−24.1594	+	15.1220i	−0.787994	+	0.493226i
$941$	−47.1239	+	14.2949i	−1.53620	+	0.466000i	−0.941234	−	0.337755i	$-0.890333\pi$
$941$	−47.1239	+	14.2949i	−1.53620	+	0.466000i	−0.594961	+	0.803754i	$0.702833\pi$
$942$	3.98105	+	3.71769i	0.129710	+	0.121129i
$943$	9.41858	+	3.90130i	0.306711	+	0.127044i
$944$	−9.48084	−	1.50806i	−0.308575	−	0.0490831i
$945$	−14.7422	+	6.10640i	−0.479563	+	0.198641i
$946$	20.6702	+	7.74505i	0.672048	+	0.251813i
$947$	−2.79269	−	1.49272i	−0.0907502	−	0.0485070i	0.425397	−	0.905007i	$-0.360134\pi$
$947$	−2.79269	−	1.49272i	−0.0907502	−	0.0485070i	−0.516148	+	0.856500i	$0.672634\pi$
$948$	−9.78384	−	10.3847i	−0.317764	−	0.337280i
$949$	59.8144	+	49.0884i	1.94166	+	1.59348i
$950$	16.9006	+	1.08277i	0.548329	+	0.0351296i
$951$	6.19055	−	31.1220i	0.200742	−	1.00920i
$952$	−81.3344	+	43.9366i	−2.63606	+	1.42399i
$953$	−31.7617	+	6.31779i	−1.02886	+	0.204653i	−0.680532	−	0.732719i	$-0.738251\pi$
$953$	−31.7617	+	6.31779i	−1.02886	+	0.204653i	−0.348330	+	0.937372i	$0.613251\pi$
$954$	11.2654	+	8.61799i	0.364732	+	0.279018i
$955$	−8.29790	−	15.5243i	−0.268514	−	0.502354i
$956$	1.24304	+	18.1471i	0.0402028	+	0.586920i
$957$	−8.25767	−	0.813309i	−0.266932	−	0.0262906i
$958$	−50.2600	−	31.1513i	−1.62383	−	1.00645i
$959$		−	20.4685i		−	0.660961i
$960$	−27.1661	+	5.65330i	−0.876781	+	0.182459i
$961$			13.1733i			0.424944i
$962$	11.9561	−	19.2901i	0.385479	−	0.621939i
$963$	5.15598	+	0.507819i	0.166149	+	0.0163642i
$964$	−20.0243	−	17.4569i	−0.644940	−	0.562250i
$965$	17.6186	+	32.9621i	0.567163	+	1.06109i
$966$	−21.9017	+	28.6300i	−0.704676	+	0.921154i
$967$	−51.5027	+	10.2445i	−1.65622	+	0.329442i	−0.932642	−	0.360804i	$-0.882502\pi$
$967$	−51.5027	+	10.2445i	−1.65622	+	0.329442i	−0.723575	+	0.690246i	$0.757502\pi$
$968$	11.9609	+	9.72809i	0.384439	+	0.312673i
$969$	2.36075	−	11.8683i	0.0758383	−	0.381265i
$970$	−3.66699	+	57.2372i	−0.117740	+	1.83777i
$971$	−12.2856	−	10.0825i	−0.394264	−	0.323564i	0.416286	−	0.909234i	$-0.363332\pi$
$971$	−12.2856	−	10.0825i	−0.394264	−	0.323564i	−0.810550	+	0.585670i	$0.800832\pi$
$972$	−0.0595586	+	1.99911i	−0.00191034	+	0.0641216i
$973$	−7.84630	−	4.19394i	−0.251541	−	0.134451i
$974$	5.04322	−	13.4595i	0.161595	−	0.431271i
$975$	36.5087	−	15.1224i	1.16921	−	0.484304i
$976$	−20.4822	+	22.1281i	−0.655619	+	0.708303i
$977$	21.9662	+	9.09870i	0.702762	+	0.291093i	0.705306	−	0.708903i	$-0.250810\pi$
$977$	21.9662	+	9.09870i	0.702762	+	0.291093i	−0.00254406	+	0.999997i	$0.500810\pi$
$978$	6.17781	−	6.61545i	0.197544	−	0.211539i
$979$	10.7936	−	3.27421i	0.344965	−	0.104644i
$980$	22.0307	−	95.7572i	0.703744	−	3.05885i
$981$	−0.882266	−	8.95780i	−0.0281686	−	0.286001i
$982$	15.7624	−	5.37649i	0.502999	−	0.171571i
$983$	−22.2329	−	33.2739i	−0.709119	−	1.06127i	−0.994690	−	0.102914i	$-0.967183\pi$
$983$	−22.2329	−	33.2739i	−0.709119	−	1.06127i	0.285572	−	0.958357i	$-0.407817\pi$
$984$	−1.97039	+	4.81695i	−0.0628139	+	0.153559i
$985$	68.0243	+	45.4524i	2.16744	+	1.44823i
$986$	17.7402	+	30.6228i	0.564962	+	0.975229i
$987$	−18.0879	−	5.48690i	−0.575744	−	0.174650i
$988$	18.4804	−	5.01010i	0.587939	−	0.159393i
$989$	−23.2891	−	28.3779i	−0.740551	−	0.902364i
$990$	−1.86548	+	11.4034i	−0.0592889	+	0.362423i
$991$	17.6800	+	17.6800i	0.561623	+	0.561623i	0.929768	−	0.368146i	$-0.120007\pi$
$991$	17.6800	+	17.6800i	0.561623	+	0.561623i	−0.368146	+	0.929768i	$0.620007\pi$
$992$	−8.57735	−	22.2909i	−0.272331	−	0.707737i
$993$	2.44786	−	2.44786i	0.0776804	−	0.0776804i
$994$	39.0951	+	54.3881i	1.24002	+	1.72509i
$995$	−38.6581	+	31.7259i	−1.22554	+	1.00578i
$996$	−2.02729	−	2.62599i	−0.0642373	−	0.0832078i
$997$	1.34120	−	4.42134i	0.0424762	−	0.140025i	−0.933138	−	0.359519i	$-0.882941\pi$
$997$	1.34120	−	4.42134i	0.0424762	−	0.140025i	0.975614	+	0.219494i	$0.0704406\pi$
$998$	−5.72388	+	21.4882i	−0.181186	+	0.680197i
$999$	1.58621	−	2.37392i	0.0501853	−	0.0751076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.31	✓	512
128.53	even	32	inner	384.2.v.a.181.31	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.31	✓	512	1.1	even	1	trivial
384.2.v.a.181.31	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(1.37680 - 0.323159i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.79114 - 0.889849i) q^{4} +(-3.05895 + 1.63504i) q^{5} +(0.186654 + 1.40184i) q^{6} +(0.897509 + 4.51208i) q^{7} +(2.17847 - 1.80396i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.37680 - 0.323159i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.79114 - 0.889849i) q^{4} +(-3.05895 + 1.63504i) q^{5} +(0.186654 + 1.40184i) q^{6} +(0.897509 + 4.51208i) q^{7} +(2.17847 - 1.80396i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-3.68317 + 3.23965i) q^{10} +(-1.49441 + 1.82094i) q^{11} +(0.710002 + 1.86973i) q^{12} +(2.64959 - 4.95704i) q^{13} +(2.69381 + 5.92218i) q^{14} +(-1.32734 - 3.20448i) q^{15} +(2.41634 - 3.18768i) q^{16} +(-2.71873 + 6.56358i) q^{17} +(-1.41339 + 0.0483504i) q^{18} +(0.494439 + 1.62995i) q^{19} +(-4.02405 + 5.65059i) q^{20} +(-4.57833 + 0.450926i) q^{21} +(-1.46904 + 2.99000i) q^{22} +(4.60673 - 3.07812i) q^{23} +(1.58175 + 2.34480i) q^{24} +(3.90596 - 5.84568i) q^{25} +(2.04603 - 7.68107i) q^{26} +(0.290285 - 0.956940i) q^{27} +(5.62264 + 7.28311i) q^{28} +(2.72288 - 2.23461i) q^{29} +(-2.86304 - 3.98298i) q^{30} +(2.98553 - 2.98553i) q^{31} +(2.29667 - 5.16965i) q^{32} +(-1.66570 - 1.66570i) q^{33} +(-1.62205 + 9.91530i) q^{34} +(-10.1229 - 12.3348i) q^{35} +(-1.93032 + 0.523318i) q^{36} +(2.73216 + 0.828790i) q^{37} +(1.20748 + 2.08432i) q^{38} +(4.67346 + 3.12271i) q^{39} +(-3.71426 + 9.08012i) q^{40} +(1.02226 + 1.52992i) q^{41} +(-6.15770 + 2.10036i) q^{42} +(-0.649456 - 6.59404i) q^{43} +(-1.05632 + 4.59135i) q^{44} +(3.31915 - 1.00685i) q^{45} +(5.34781 - 5.72665i) q^{46} +(3.79591 + 1.57232i) q^{47} +(2.93549 + 2.71715i) q^{48} +(-13.0862 + 5.42049i) q^{49} +(3.48862 - 9.31056i) q^{50} +(-6.26550 - 3.34898i) q^{51} +(0.334762 - 11.2365i) q^{52} +(-7.75287 - 6.36262i) q^{53} +(0.0904186 - 1.41132i) q^{54} +(1.59400 - 8.01359i) q^{55} +(10.0948 + 8.21035i) q^{56} +(-1.67056 + 0.332296i) q^{57} +(3.02671 - 3.95652i) q^{58} +(-1.13136 - 2.11662i) q^{59} +(-5.22895 - 4.55853i) q^{60} +(-7.50183 - 0.738865i) q^{61} +(3.14566 - 5.07526i) q^{62} -4.60048i q^{63} +(1.49143 - 7.85975i) q^{64} +19.4955i q^{65} +(-2.83161 - 1.75504i) q^{66} +(10.1357 + 0.998275i) q^{67} +(0.970994 + 14.1755i) q^{68} +(2.61176 + 4.88626i) q^{69} +(-17.9233 - 13.7112i) q^{70} +(10.0974 - 2.00850i) q^{71} +(-2.48854 + 1.34430i) q^{72} +(-2.68574 + 13.5021i) q^{73} +(4.02945 + 0.258154i) q^{74} +(5.43468 + 4.46013i) q^{75} +(2.33602 + 2.47948i) q^{76} +(-9.55749 - 5.10858i) q^{77} +(7.44354 + 2.78906i) q^{78} +(-6.59080 + 2.73000i) q^{79} +(-2.17945 + 13.7018i) q^{80} +(0.923880 + 0.382683i) q^{81} +(1.90186 + 1.77604i) q^{82} +(-1.58732 + 0.481509i) q^{83} +(-7.79915 + 4.88169i) q^{84} +(-2.41530 - 24.5229i) q^{85} +(-3.02510 - 8.86877i) q^{86} +(1.95696 + 2.92880i) q^{87} +(0.0293952 + 6.66272i) q^{88} +(-3.98123 - 2.66017i) q^{89} +(4.24443 - 2.45885i) q^{90} +(24.7446 + 7.50619i) q^{91} +(5.51222 - 9.61263i) q^{92} +(2.67852 + 3.26378i) q^{93} +(5.73430 + 0.938076i) q^{94} +(-4.17750 - 4.17750i) q^{95} +(4.91964 + 2.79233i) q^{96} +(8.26790 - 8.26790i) q^{97} +(-16.2654 + 11.6918i) q^{98} +(1.82094 - 1.49441i) 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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