LMFDB - Embedded newform 650.2.p.a.571.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(181,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("650.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.p (of order $10$, degree $4$, 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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			571.8
Character	$\chi$	$=$	650.571
Dual form			650.2.p.a.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 - 0.309017i) q^{2} +(-0.454733 - 0.330383i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02575 + 0.946747i) q^{5} +(0.330383 + 0.454733i) q^{6} -3.59180i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.829422 - 2.55270i) q^{9} +O(q^{10})$	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.454733 - 0.330383i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02575 + 0.946747i) q^{5} +(0.330383 + 0.454733i) q^{6} -3.59180i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.829422 - 2.55270i) q^{9} +(-1.63404 - 1.52640i) q^{10} +(-3.90463 - 1.26869i) q^{11} +(-0.173693 - 0.534571i) q^{12} +(0.643204 + 3.54772i) q^{13} +(-1.10993 + 3.41600i) q^{14} +(-0.608388 - 1.09979i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.477217 + 0.346718i) q^{17} +2.68406i q^{18} +(-4.56943 - 6.28928i) q^{19} +(1.08238 + 1.95664i) q^{20} +(-1.18667 + 1.63331i) q^{21} +(3.32147 + 2.41319i) q^{22} +(0.238776 - 0.734876i) q^{23} +0.562081i q^{24} +(3.20734 + 3.83575i) q^{25} +(0.484581 - 3.57284i) q^{26} +(-0.987280 + 3.03854i) q^{27} +(2.11121 - 2.90582i) q^{28} +(-2.30028 - 1.67125i) q^{29} +(0.238757 + 1.23397i) q^{30} +(-1.23637 - 1.70172i) q^{31} -1.00000i q^{32} +(1.35641 + 1.86694i) q^{33} +(0.561002 - 0.182281i) q^{34} +(3.40052 - 7.27609i) q^{35} +(0.829422 - 2.55270i) q^{36} +(6.46545 - 2.10075i) q^{37} +(2.40229 + 7.39349i) q^{38} +(0.879619 - 1.82577i) q^{39} +(-0.424773 - 2.19535i) q^{40} +(-7.00845 + 2.27718i) q^{41} +(1.63331 - 1.18667i) q^{42} +2.01123 q^{43} +(-2.41319 - 3.32147i) q^{44} +(0.736555 - 5.95638i) q^{45} +(-0.454178 + 0.625122i) q^{46} +(2.01990 - 2.78015i) q^{47} +(0.173693 - 0.534571i) q^{48} -5.90101 q^{49} +(-1.86505 - 4.63914i) q^{50} +0.331556 q^{51} +(-1.56493 + 3.24823i) q^{52} +(-6.24449 - 4.53689i) q^{53} +(1.87792 - 2.58473i) q^{54} +(-6.70868 - 6.26674i) q^{55} +(-2.90582 + 2.11121i) q^{56} +4.36961i q^{57} +(1.67125 + 2.30028i) q^{58} +(-4.82429 + 1.56751i) q^{59} +(0.154245 - 1.24735i) q^{60} +(4.02092 - 12.3751i) q^{61} +(0.650000 + 2.00049i) q^{62} +(-9.16877 + 2.97911i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.05582 + 7.79574i) q^{65} +(-0.713107 - 2.19472i) q^{66} +(3.99722 + 5.50170i) q^{67} -0.589873 q^{68} +(-0.351370 + 0.255285i) q^{69} +(-5.48252 + 5.86915i) q^{70} +(3.16005 - 4.34944i) q^{71} +(-1.57765 + 2.17145i) q^{72} +(-15.0226 - 4.88114i) q^{73} -6.79817 q^{74} +(-0.191219 - 2.80389i) q^{75} -7.77398i q^{76} +(-4.55688 + 14.0246i) q^{77} +(-1.40076 + 1.46459i) q^{78} +(-9.97122 - 7.24451i) q^{79} +(-0.274418 + 2.21917i) q^{80} +(-5.06153 + 3.67742i) q^{81} +7.36912 q^{82} +(3.41474 + 4.69998i) q^{83} +(-1.92007 + 0.623869i) q^{84} +(-1.29498 + 0.250562i) q^{85} +(-1.91279 - 0.621504i) q^{86} +(0.493861 + 1.51995i) q^{87} +(1.26869 + 3.90463i) q^{88} +(11.9736 + 3.89045i) q^{89} +(-2.54113 + 5.43725i) q^{90} +(12.7427 - 2.31026i) q^{91} +(0.625122 - 0.454178i) q^{92} +1.18231i q^{93} +(-2.78015 + 2.01990i) q^{94} +(-3.30218 - 17.0666i) q^{95} +(-0.330383 + 0.454733i) q^{96} +(9.53929 - 13.1297i) q^{97} +(5.61219 + 1.82351i) q^{98} +11.0196i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) $ 136 * q + 34 * q^4 - 30 * q^9	$ 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) $ 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$

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 $

$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$2$	−0.951057	−	0.309017i	−0.672499	−	0.218508i
$3$	−0.454733	−	0.330383i	−0.262540	−	0.190747i	0.448726	−	0.893669i	$-0.351878\pi$
$3$	−0.454733	−	0.330383i	−0.262540	−	0.190747i	−0.711266	+	0.702923i	$0.751878\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	2.02575	+	0.946747i	0.905944	+	0.423398i
$5$	2.02575	+	0.946747i	0.905944	+	0.423398i
$6$	0.330383	+	0.454733i	0.134878	+	0.185644i
$7$		−	3.59180i		−	1.35757i	−0.734336	−	0.678786i	$-0.762506\pi$
$7$		−	3.59180i		−	1.35757i	0.734336	−	0.678786i	$-0.237494\pi$
$8$	−0.587785	−	0.809017i	−0.207813	−	0.286031i
$9$	−0.829422	−	2.55270i	−0.276474	−	0.850899i
$10$	−1.63404	−	1.52640i	−0.516730	−	0.482691i
$11$	−3.90463	−	1.26869i	−1.17729	−	0.382525i	−0.345930	−	0.938260i	$-0.612437\pi$
$11$	−3.90463	−	1.26869i	−1.17729	−	0.382525i	−0.831359	+	0.555736i	$0.812437\pi$
$12$	−0.173693	−	0.534571i	−0.0501407	−	0.154317i
$13$	0.643204	+	3.54772i	0.178393	+	0.983959i
$13$	0.643204	+	3.54772i	0.178393	+	0.983959i
$14$	−1.10993	+	3.41600i	−0.296640	+	0.912965i
$15$	−0.608388	−	1.09979i	−0.157085	−	0.283965i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.477217	+	0.346718i	−0.115742	+	0.0840916i	−0.644151	−	0.764899i	$-0.722789\pi$
$17$	−0.477217	+	0.346718i	−0.115742	+	0.0840916i	0.528408	+	0.848990i	$0.322789\pi$
$18$			2.68406i			0.632640i
$19$	−4.56943	−	6.28928i	−1.04830	−	1.44286i	−0.890274	−	0.455425i	$-0.849487\pi$
$19$	−4.56943	−	6.28928i	−1.04830	−	1.44286i	−0.158025	−	0.987435i	$-0.550513\pi$
$20$	1.08238	+	1.95664i	0.242028	+	0.437518i
$21$	−1.18667	+	1.63331i	−0.258952	+	0.356417i
$22$	3.32147	+	2.41319i	0.708141	+	0.514494i
$23$	0.238776	−	0.734876i	0.0497881	−	0.153232i	−0.923071	−	0.384629i	$-0.874329\pi$
$23$	0.238776	−	0.734876i	0.0497881	−	0.153232i	0.972860	+	0.231397i	$0.0743295\pi$
$24$			0.562081i			0.114734i
$25$	3.20734	+	3.83575i	0.641468	+	0.767150i
$26$	0.484581	−	3.57284i	0.0950341	−	0.700691i
$27$	−0.987280	+	3.03854i	−0.190002	+	0.584766i
$28$	2.11121	−	2.90582i	0.398980	−	0.549149i
$29$	−2.30028	−	1.67125i	−0.427152	−	0.310344i	0.353357	−	0.935488i	$-0.385040\pi$
$29$	−2.30028	−	1.67125i	−0.427152	−	0.310344i	−0.780509	+	0.625145i	$0.785040\pi$
$30$	0.238757	+	1.23397i	0.0435908	+	0.225290i
$31$	−1.23637	−	1.70172i	−0.222059	−	0.305638i	0.683423	−	0.730023i	$-0.260490\pi$
$31$	−1.23637	−	1.70172i	−0.222059	−	0.305638i	−0.905482	+	0.424385i	$0.860490\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.35641	+	1.86694i	0.236121	+	0.324992i
$34$	0.561002	−	0.182281i	0.0962111	−	0.0312609i
$35$	3.40052	−	7.27609i	0.574793	−	1.22988i
$36$	0.829422	−	2.55270i	0.138237	−	0.425450i
$37$	6.46545	−	2.10075i	1.06291	−	0.345361i	0.275189	−	0.961390i	$-0.411259\pi$
$37$	6.46545	−	2.10075i	1.06291	−	0.345361i	0.787724	+	0.616029i	$0.211259\pi$
$38$	2.40229	+	7.39349i	0.389703	+	1.19938i
$39$	0.879619	−	1.82577i	0.140852	−	0.292357i
$40$	−0.424773	−	2.19535i	−0.0671625	−	0.347116i
$41$	−7.00845	+	2.27718i	−1.09454	+	0.355636i	−0.799998	−	0.600003i	$-0.795166\pi$
$41$	−7.00845	+	2.27718i	−1.09454	+	0.355636i	−0.294539	+	0.955640i	$0.595166\pi$
$42$	1.63331	−	1.18667i	0.252025	−	0.183107i
$43$	2.01123			0.306710			0.153355	−	0.988171i	$-0.450992\pi$
$43$	2.01123			0.306710			0.153355	+	0.988171i	$0.450992\pi$
$44$	−2.41319	−	3.32147i	−0.363802	−	0.500731i
$45$	0.736555	−	5.95638i	0.109799	−	0.887925i
$46$	−0.454178	+	0.625122i	−0.0669649	+	0.0921693i
$47$	2.01990	−	2.78015i	0.294632	−	0.405526i	−0.635880	−	0.771788i	$-0.719363\pi$
$47$	2.01990	−	2.78015i	0.294632	−	0.405526i	0.930512	+	0.366262i	$0.119363\pi$
$48$	0.173693	−	0.534571i	0.0250704	−	0.0771587i
$49$	−5.90101			−0.843001
$50$	−1.86505	−	4.63914i	−0.263758	−	0.656073i
$51$	0.331556			0.0464272
$52$	−1.56493	+	3.24823i	−0.217017	+	0.450448i
$53$	−6.24449	−	4.53689i	−0.857746	−	0.623189i	0.0695247	−	0.997580i	$-0.477852\pi$
$53$	−6.24449	−	4.53689i	−0.857746	−	0.623189i	−0.927271	+	0.374391i	$0.877852\pi$
$54$	1.87792	−	2.58473i	0.255552	−	0.351738i
$55$	−6.70868	−	6.26674i	−0.904598	−	0.845008i
$56$	−2.90582	+	2.11121i	−0.388307	+	0.282122i
$57$			4.36961i			0.578769i
$58$	1.67125	+	2.30028i	0.219446	+	0.302042i
$59$	−4.82429	+	1.56751i	−0.628069	+	0.204072i	−0.605719	−	0.795678i	$-0.707115\pi$
$59$	−4.82429	+	1.56751i	−0.628069	+	0.204072i	−0.0223494	+	0.999750i	$0.507115\pi$
$60$	0.154245	−	1.24735i	0.0199130	−	0.161032i
$61$	4.02092	−	12.3751i	0.514826	−	1.58447i	−0.268772	−	0.963204i	$-0.586618\pi$
$61$	4.02092	−	12.3751i	0.514826	−	1.58447i	0.783598	−	0.621268i	$-0.213382\pi$
$62$	0.650000	+	2.00049i	0.0825500	+	0.254063i
$63$	−9.16877	+	2.97911i	−1.15516	+	0.375333i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.05582	+	7.79574i	−0.254993	+	0.966943i
$66$	−0.713107	−	2.19472i	−0.0877774	−	0.270151i
$67$	3.99722	+	5.50170i	0.488338	+	0.672140i	0.980080	−	0.198601i	$-0.0636398\pi$
$67$	3.99722	+	5.50170i	0.488338	+	0.672140i	−0.491742	+	0.870741i	$0.663640\pi$
$68$	−0.589873			−0.0715326
$69$	−0.351370	+	0.255285i	−0.0422999	+	0.0307327i
$70$	−5.48252	+	5.86915i	−0.655287	+	0.701498i
$71$	3.16005	−	4.34944i	0.375029	−	0.516183i	−0.579230	−	0.815164i	$-0.696647\pi$
$71$	3.16005	−	4.34944i	0.375029	−	0.516183i	0.954259	+	0.298981i	$0.0966467\pi$
$72$	−1.57765	+	2.17145i	−0.185928	+	0.255908i
$73$	−15.0226	−	4.88114i	−1.75826	−	0.571294i	−0.761245	−	0.648465i	$-0.775411\pi$
$73$	−15.0226	−	4.88114i	−1.75826	−	0.571294i	−0.997018	+	0.0771703i	$0.975411\pi$
$74$	−6.79817			−0.790272
$75$	−0.191219	−	2.80389i	−0.0220800	−	0.323766i
$76$		−	7.77398i		−	0.891737i
$77$	−4.55688	+	14.0246i	−0.519304	+	1.59825i
$78$	−1.40076	+	1.46459i	−0.158605	+	0.165832i
$79$	−9.97122	−	7.24451i	−1.12185	−	0.815072i	−0.137361	−	0.990521i	$-0.543862\pi$
$79$	−9.97122	−	7.24451i	−1.12185	−	0.815072i	−0.984488	+	0.175449i	$0.943862\pi$
$80$	−0.274418	+	2.21917i	−0.0306809	+	0.248110i
$81$	−5.06153	+	3.67742i	−0.562393	+	0.408602i
$82$	7.36912			0.813784
$83$	3.41474	+	4.69998i	0.374816	+	0.515890i	0.954202	−	0.299163i	$-0.0967075\pi$
$83$	3.41474	+	4.69998i	0.374816	+	0.515890i	−0.579386	+	0.815053i	$0.696708\pi$
$84$	−1.92007	+	0.623869i	−0.209497	+	0.0680696i
$85$	−1.29498	+	0.250562i	−0.140460	+	0.0271773i
$86$	−1.91279	−	0.621504i	−0.206262	−	0.0670185i
$87$	0.493861	+	1.51995i	0.0529475	+	0.162956i
$88$	1.26869	+	3.90463i	0.135243	+	0.416235i
$89$	11.9736	+	3.89045i	1.26920	+	0.412387i	0.864762	−	0.502181i	$-0.167469\pi$
$89$	11.9736	+	3.89045i	1.26920	+	0.412387i	0.404433	+	0.914568i	$0.367469\pi$
$90$	−2.54113	+	5.43725i	−0.267859	+	0.573136i
$91$	12.7427	−	2.31026i	1.33580	−	0.242181i
$92$	0.625122	−	0.454178i	0.0651735	−	0.0473513i
$93$			1.18231i			0.122599i
$94$	−2.78015	+	2.01990i	−0.286750	+	0.208336i
$95$	−3.30218	−	17.0666i	−0.338796	−	1.75100i
$96$	−0.330383	+	0.454733i	−0.0337196	+	0.0464110i
$97$	9.53929	−	13.1297i	0.968568	−	1.33312i	0.0258012	−	0.999667i	$-0.491786\pi$
$97$	9.53929	−	13.1297i	0.968568	−	1.33312i	0.942767	−	0.333452i	$-0.108214\pi$
$98$	5.61219	+	1.82351i	0.566917	+	0.184202i
$99$			11.0196i			1.10751i
$100$	0.340198	+	4.98841i	0.0340198	+	0.498841i
$101$	10.6269			1.05741			0.528707	−	0.848804i	$-0.322677\pi$
$101$	10.6269			1.05741			0.528707	+	0.848804i	$0.322677\pi$
$102$	−0.315329	−	0.102457i	−0.0312222	−	0.0101447i
$103$	4.36503	+	3.17138i	0.430099	+	0.312485i	0.781689	−	0.623669i	$-0.214359\pi$
$103$	4.36503	+	3.17138i	0.430099	+	0.312485i	−0.351589	+	0.936154i	$0.614359\pi$
$104$	2.49210	−	2.60566i	0.244370	−	0.255506i
$105$	−3.95023	+	2.18520i	−0.385503	+	0.213254i
$106$	4.53689	+	6.24449i	0.440661	+	0.606518i
$107$	9.93480			0.960433			0.480217	−	0.877150i	$-0.340558\pi$
$107$	9.93480			0.960433			0.480217	+	0.877150i	$0.340558\pi$
$108$	−2.58473	+	1.87792i	−0.248716	+	0.180703i
$109$	11.5462	−	3.75160i	1.10593	−	0.359338i	0.301547	−	0.953451i	$-0.402497\pi$
$109$	11.5462	−	3.75160i	1.10593	−	0.359338i	0.804381	+	0.594113i	$0.202497\pi$
$110$	4.44380	+	8.03312i	0.423700	+	0.765928i
$111$	−3.63411	−	1.18079i	−0.344934	−	0.112076i
$112$	3.41600	−	1.10993i	0.322782	−	0.104878i
$113$	1.38988	+	4.27761i	0.130749	+	0.402403i	0.994905	−	0.100821i	$-0.0321470\pi$
$113$	1.38988	+	4.27761i	0.130749	+	0.402403i	−0.864156	+	0.503224i	$0.832147\pi$
$114$	1.35028	−	4.15574i	0.126466	−	0.389221i
$115$	1.17944	−	1.26262i	0.109983	−	0.117740i
$116$	−0.878629	−	2.70414i	−0.0815787	−	0.251073i
$117$	8.52276	−	4.58446i	0.787929	−	0.423833i
$118$	5.07256			0.466967
$119$	1.24534	+	1.71407i	0.114160	+	0.157128i
$120$	−0.532148	+	1.13864i	−0.0485783	+	0.103943i
$121$	4.73735	+	3.44189i	0.430668	+	0.312899i
$122$	−7.64824	+	10.5269i	−0.692439	+	0.953061i
$123$	3.93932	+	1.27996i	0.355196	+	0.115410i
$124$		−	2.10344i		−	0.188895i
$125$	2.86580	+	10.8068i	0.256325	+	0.966591i
$126$	9.64062			0.858854
$127$	4.22820	−	13.0131i	0.375192	−	1.15472i	−0.568157	−	0.822920i	$-0.692343\pi$
$127$	4.22820	−	13.0131i	0.375192	−	1.15472i	0.943349	−	0.331802i	$-0.107657\pi$
$128$	0.587785	−	0.809017i	0.0519534	−	0.0715077i
$129$	−0.914573	−	0.664476i	−0.0805237	−	0.0585039i
$130$	4.36421	−	6.77891i	0.382767	−	0.594550i
$131$	3.29630	−	2.39490i	0.287999	−	0.209244i	−0.434400	−	0.900720i	$-0.643039\pi$
$131$	3.29630	−	2.39490i	0.287999	−	0.209244i	0.722399	+	0.691477i	$0.243039\pi$
$132$			2.30766i			0.200856i
$133$	−22.5898	+	16.4125i	−1.95879	+	1.42314i
$134$	−2.10146	−	6.46764i	−0.181539	−	0.558719i
$135$	−4.87671	+	5.22062i	−0.419720	+	0.449319i
$136$	0.561002	+	0.182281i	0.0481055	+	0.0156304i
$137$	−12.9227	+	4.19884i	−1.10406	+	0.358731i	−0.803664	−	0.595083i	$-0.797119\pi$
$137$	−12.9227	+	4.19884i	−1.10406	+	0.358731i	−0.300397	+	0.953814i	$0.597119\pi$
$138$	0.413060	−	0.134211i	0.0351620	−	0.0114248i
$139$	0.387414	−	1.19234i	0.0328600	−	0.101133i	−0.933281	−	0.359146i	$-0.883068\pi$
$139$	0.387414	−	1.19234i	0.0328600	−	0.101133i	0.966141	+	0.258014i	$0.0830679\pi$
$140$	7.02786	−	3.88770i	0.593962	−	0.328571i
$141$	−1.83703	+	0.596886i	−0.154706	+	0.0502669i
$142$	−4.34944	+	3.16005i	−0.364997	+	0.265186i
$143$	1.98948	−	14.6685i	0.166369	−	1.22664i
$144$	2.17145	−	1.57765i	0.180955	−	0.131471i
$145$	−3.07755	−	5.56333i	−0.255576	−	0.462009i
$146$	12.7790	+	9.28448i	1.05760	+	0.768389i
$147$	2.68338	+	1.94959i	0.221322	+	0.160800i
$148$	6.46545	+	2.10075i	0.531456	+	0.172681i
$149$			11.4068i			0.934484i	0.884130	+	0.467242i	$0.154752\pi$
$149$			11.4068i			0.934484i	−0.884130	+	0.467242i	$0.845248\pi$
$150$	−0.684591	+	2.72575i	−0.0558966	+	0.222557i
$151$			12.2867i			0.999877i	0.866061	+	0.499939i	$0.166644\pi$
$151$			12.2867i			0.999877i	−0.866061	+	0.499939i	$0.833356\pi$
$152$	−2.40229	+	7.39349i	−0.194852	+	0.599692i
$153$	1.28088	+	0.930615i	0.103553	+	0.0752358i
$154$	8.66770	−	11.9301i	0.698463	−	0.961352i
$155$	−0.893485	−	4.61780i	−0.0717665	−	0.370910i
$156$	1.78479	−	0.960050i	0.142897	−	0.0768655i
$157$	16.0813			1.28343			0.641715	−	0.766943i	$-0.278223\pi$
$157$	16.0813			1.28343			0.641715	+	0.766943i	$0.278223\pi$
$158$	7.24451	+	9.97122i	0.576343	+	0.793268i
$159$	1.34067	+	4.12614i	0.106322	+	0.327225i
$160$	0.946747	−	2.02575i	0.0748469	−	0.160150i
$161$	−2.63952	−	0.857633i	−0.208024	−	0.0675910i
$162$	5.95019	−	1.93333i	0.467491	−	0.151897i
$163$	−2.03218	+	0.660294i	−0.159172	+	0.0517182i	−0.387519	−	0.921862i	$-0.626668\pi$
$163$	−2.03218	+	0.660294i	−0.159172	+	0.0517182i	0.228347	+	0.973580i	$0.426668\pi$
$164$	−7.00845	−	2.27718i	−0.547268	−	0.177818i
$165$	0.980232	+	5.06613i	0.0763110	+	0.394398i
$166$	−1.79523	−	5.52516i	−0.139337	−	0.428836i
$167$	12.9962	+	17.8877i	1.00567	+	1.38419i	0.921778	+	0.387717i	$0.126736\pi$
$167$	12.9962	+	17.8877i	1.00567	+	1.38419i	0.0838958	+	0.996475i	$0.473264\pi$
$168$	2.01888			0.155760
$169$	−12.1726	+	4.56381i	−0.936352	+	0.351063i
$170$	1.30903	+	0.161872i	0.100398	+	0.0124150i
$171$	−12.2646	+	16.8808i	−0.937901	+	1.29091i
$172$	1.62712	+	1.18217i	0.124067	+	0.0901397i
$173$	−5.10554	+	15.7132i	−0.388167	+	1.19465i	0.545990	+	0.837792i	$0.316154\pi$
$173$	−5.10554	+	15.7132i	−0.388167	+	1.19465i	−0.934157	+	0.356863i	$0.883846\pi$
$174$		−	1.59817i		−	0.121157i
$175$	13.7772	−	11.5201i	1.04146	−	0.870839i
$176$		−	4.10557i		−	0.309469i
$177$	2.71164	+	0.881066i	0.203819	+	0.0662250i
$178$	−10.1853	−	7.40007i	−0.763422	−	0.554659i
$179$	−0.207882	−	0.151035i	−0.0155379	−	0.0112889i	0.579989	−	0.814624i	$-0.303057\pi$
$179$	−0.207882	−	0.151035i	−0.0155379	−	0.0112889i	−0.595527	+	0.803335i	$0.703057\pi$
$180$	4.09696	−	4.38588i	0.305369	−	0.326904i
$181$	17.6754	−	12.8420i	1.31381	−	0.954535i	0.313818	−	0.949483i	$-0.398392\pi$
$181$	17.6754	−	12.8420i	1.31381	−	0.954535i	0.999987	−	0.00505226i	$-0.00160819\pi$
$182$	−12.8329	−	1.74052i	−0.951239	−	0.129016i
$183$	−5.91697	+	4.29893i	−0.437395	+	0.317786i
$184$	−0.734876	+	0.238776i	−0.0541757	+	0.0176028i
$185$	15.0863	+	1.86554i	1.10916	+	0.137157i
$186$	0.365352	−	1.12444i	0.0267889	−	0.0824479i
$187$	2.30323	−	0.748366i	0.168429	−	0.0547259i
$188$	3.26826	−	1.06192i	0.238362	−	0.0774486i
$189$	10.9138	+	3.54611i	0.793862	+	0.257942i
$190$	−2.13332	+	17.2517i	−0.154767	+	1.25157i
$191$	−2.95099	−	9.08220i	−0.213526	−	0.657165i	−0.999255	−	0.0385942i	$-0.987712\pi$
$191$	−2.95099	−	9.08220i	−0.213526	−	0.657165i	0.785729	−	0.618571i	$-0.212288\pi$
$192$	0.454733	−	0.330383i	0.0328175	−	0.0238433i
$193$		−	10.7836i		−	0.776217i	−0.921614	−	0.388109i	$-0.873129\pi$
$193$		−	10.7836i		−	0.776217i	0.921614	−	0.388109i	$-0.126871\pi$
$194$	−13.1297	+	9.53929i	−0.942658	+	0.684881i
$195$	3.51043	−	2.86578i	0.251387	−	0.205223i
$196$	−4.77402	−	3.46853i	−0.341001	−	0.247752i
$197$	4.80242	−	6.60997i	0.342158	−	0.470941i	−0.602912	−	0.797808i	$-0.705993\pi$
$197$	4.80242	−	6.60997i	0.342158	−	0.470941i	0.945070	+	0.326867i	$0.105993\pi$
$198$	3.40525	−	10.4803i	0.242000	−	0.744801i
$199$	−6.47550			−0.459036			−0.229518	−	0.973304i	$-0.573715\pi$
$199$	−6.47550			−0.459036			−0.229518	+	0.973304i	$0.573715\pi$
$200$	1.21796	−	4.84939i	0.0861226	−	0.342904i
$201$		−	3.82242i		−	0.269613i
$202$	−10.1068	−	3.28389i	−0.711109	−	0.231053i
$203$	−6.00280	+	8.26215i	−0.421314	+	0.579889i
$204$	0.268235	+	0.194884i	0.0187802	+	0.0136446i
$205$	−16.3533	−	2.02222i	−1.14216	−	0.141238i
$206$	−3.17138	−	4.36503i	−0.220961	−	0.304126i
$207$	−2.07396			−0.144150
$208$	−3.17532	+	1.70803i	−0.220169	+	0.118430i
$209$	9.86277	+	30.3545i	0.682222	+	2.09966i
$210$	4.43215	−	0.857566i	0.305848	−	0.0591777i
$211$	−2.12358	+	6.53571i	−0.146193	+	0.449937i	−0.997163	−	0.0752790i	$-0.976015\pi$
$211$	−2.12358	+	6.53571i	−0.146193	+	0.449937i	0.850969	+	0.525215i	$0.176015\pi$
$212$	−2.38518	−	7.34083i	−0.163815	−	0.504171i
$213$	−2.87396	+	0.933806i	−0.196921	+	0.0639834i
$214$	−9.44855	−	3.07002i	−0.645890	−	0.209862i
$215$	4.07425	+	1.90413i	0.277862	+	0.129860i
$216$	3.03854	−	0.987280i	0.206746	−	0.0671759i
$217$	−6.11224	+	4.44080i	−0.414926	+	0.301461i
$218$	−12.1404			−0.822253
$219$	5.21863	+	7.18283i	0.352642	+	0.485371i
$220$	−1.74393	−	9.01316i	−0.117576	−	0.607667i
$221$	−1.53701	−	1.47002i	−0.103390	−	0.0988842i
$222$	3.09135	+	2.24600i	0.207478	+	0.150742i
$223$	23.1749	+	7.52997i	1.55190	+	0.504244i	0.954630	−	0.297794i	$-0.0962509\pi$
$223$	23.1749	+	7.52997i	1.55190	+	0.504244i	0.597273	+	0.802038i	$0.296251\pi$
$224$	−3.59180			−0.239987
$225$	7.13127	−	11.3688i	0.475418	−	0.757922i
$226$		−	4.49774i		−	0.299185i
$227$	−18.0480	−	5.86414i	−1.19789	−	0.389217i	−0.358904	−	0.933375i	$-0.616849\pi$
$227$	−18.0480	−	5.86414i	−1.19789	−	0.389217i	−0.838983	+	0.544158i	$0.816849\pi$
$228$	−2.56839	+	3.53509i	−0.170096	+	0.234117i
$229$	−9.55746	+	13.1547i	−0.631575	+	0.869288i	−0.998131	−	0.0611075i	$-0.980537\pi$
$229$	−9.55746	+	13.1547i	−0.631575	+	0.869288i	0.366556	+	0.930396i	$0.380537\pi$
$230$	−1.51188	+	0.836351i	−0.0996907	+	0.0551474i
$231$	6.70566	−	4.87195i	0.441200	−	0.320551i
$232$			2.84330i			0.186672i
$233$	−9.62635	+	6.99396i	−0.630643	+	0.458189i	−0.856623	−	0.515943i	$-0.827442\pi$
$233$	−9.62635	+	6.99396i	−0.630643	+	0.458189i	0.225980	+	0.974132i	$0.427442\pi$
$234$	−9.52230	+	1.72640i	−0.622492	+	0.112858i
$235$	6.72391	−	3.71956i	0.438619	−	0.242637i
$236$	−4.82429	−	1.56751i	−0.314034	−	0.102036i
$237$	2.14078	+	6.58864i	0.139059	+	0.427978i
$238$	−0.654715	−	2.01501i	−0.0424389	−	0.130613i
$239$	−20.3654	−	6.61711i	−1.31733	−	0.428025i	−0.435750	−	0.900068i	$-0.643517\pi$
$239$	−20.3654	−	6.61711i	−1.31733	−	0.428025i	−0.881576	+	0.472042i	$0.843517\pi$
$240$	0.857961	−	0.918465i	0.0553812	−	0.0592867i
$241$	−4.96839	+	1.61433i	−0.320042	+	0.103988i	−0.464633	−	0.885504i	$-0.653814\pi$
$241$	−4.96839	+	1.61433i	−0.320042	+	0.103988i	0.144590	+	0.989492i	$0.453814\pi$
$242$	−3.44189	−	4.73735i	−0.221253	−	0.304529i
$243$	13.1013			0.840450
$244$	10.5269	−	7.64824i	0.673916	−	0.489629i
$245$	−11.9540	−	5.58676i	−0.763712	−	0.356925i
$246$	−3.35098	−	2.43463i	−0.213651	−	0.155227i
$247$	19.3735	−	20.2563i	1.23271	−	1.28888i
$248$	−0.650000	+	2.00049i	−0.0412750	+	0.127031i
$249$		−	3.26541i		−	0.206937i
$250$	0.613955	−	11.1635i	0.0388299	−	0.706040i
$251$	14.8502			0.937336			0.468668	−	0.883374i	$-0.344734\pi$
$251$	14.8502			0.937336			0.468668	+	0.883374i	$0.344734\pi$
$252$	−9.16877	−	2.97911i	−0.577578	−	0.187667i
$253$	−1.86466	+	2.56648i	−0.117230	+	0.161353i
$254$	−8.04251	+	11.0696i	−0.504632	+	0.694566i
$255$	0.671651	+	0.313900i	0.0420604	+	0.0196572i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.90310			−0.368225			−0.184113	−	0.982905i	$-0.558941\pi$
$257$	−5.90310			−0.368225			−0.184113	+	0.982905i	$0.558941\pi$
$258$	0.664476	+	0.914573i	0.0413685	+	0.0569388i
$259$	−7.54547	−	23.2226i	−0.468853	−	1.44298i
$260$	−6.24541	+	5.09851i	−0.387324	+	0.316196i
$261$	−2.35830	+	7.25810i	−0.145975	+	0.449265i
$262$	−3.87503	+	1.25908i	−0.239400	+	0.0777859i
$263$	7.00163	+	21.5488i	0.431739	+	1.32876i	0.896391	+	0.443263i	$0.146179\pi$
$263$	7.00163	+	21.5488i	0.431739	+	1.32876i	−0.464652	+	0.885493i	$0.653821\pi$
$264$	0.713107	−	2.19472i	0.0438887	−	0.135076i
$265$	−8.35450	−	15.1026i	−0.513213	−	0.927742i
$266$	26.5559	−	8.62855i	1.62825	−	0.529050i
$267$	−4.15944	−	5.72498i	−0.254554	−	0.350363i
$268$			6.80048i			0.415405i
$269$	−3.03099	+	2.20214i	−0.184803	+	0.134267i	−0.676340	−	0.736589i	$-0.736435\pi$
$269$	−3.03099	+	2.20214i	−0.184803	+	0.134267i	0.491537	+	0.870856i	$0.336435\pi$
$270$	6.25128	−	3.45811i	0.380441	−	0.210454i
$271$	4.05813	−	5.58554i	0.246514	−	0.339297i	−0.667773	−	0.744365i	$-0.732752\pi$
$271$	4.05813	−	5.58554i	0.246514	−	0.339297i	0.914287	+	0.405068i	$0.132752\pi$
$272$	−0.477217	−	0.346718i	−0.0289355	−	0.0210229i
$273$	−6.55779	−	3.15941i	−0.396895	−	0.191216i
$274$	13.5877			0.820865
$275$	−7.65710	−	19.0463i	−0.461740	−	1.14853i
$276$	−0.434317			−0.0261428
$277$	4.48369	−	13.7994i	0.269399	−	0.829125i	−0.721248	−	0.692677i	$-0.756431\pi$
$277$	4.48369	−	13.7994i	0.269399	−	0.829125i	0.990647	−	0.136448i	$-0.0435688\pi$
$278$	−0.736905	+	1.01426i	−0.0441966	+	0.0608314i
$279$	−3.31850	+	4.56753i	−0.198674	+	0.273451i
$280$	−7.88526	+	1.52570i	−0.471234	+	0.0911779i
$281$	5.62072	+	7.73626i	0.335304	+	0.461507i	0.943063	−	0.332615i	$-0.107931\pi$
$281$	5.62072	+	7.73626i	0.335304	+	0.461507i	−0.607758	+	0.794122i	$0.707931\pi$
$282$	1.93157			0.115023
$283$	16.3963	−	11.9126i	0.974657	−	0.708130i	0.0181489	−	0.999835i	$-0.494223\pi$
$283$	16.3963	−	11.9126i	0.974657	−	0.708130i	0.956508	+	0.291706i	$0.0942227\pi$
$284$	5.11307	−	1.66134i	0.303405	−	0.0985822i
$285$	−4.13691	+	8.85174i	−0.245049	+	0.524332i
$286$	−6.42493	+	13.3358i	−0.379914	+	0.788564i
$287$	8.17918	+	25.1729i	0.482802	+	1.48591i
$288$	−2.55270	+	0.829422i	−0.150419	+	0.0488741i
$289$	−5.14577	+	15.8370i	−0.302692	+	0.931591i
$290$	1.20776	+	6.24205i	0.0709220	+	0.366546i
$291$	−8.67566	+	2.81889i	−0.508576	+	0.165246i
$292$	−9.28448	−	12.7790i	−0.543333	−	0.747834i
$293$			7.57993i			0.442824i	0.975180	+	0.221412i	$0.0710666\pi$
$293$			7.57993i			0.442824i	−0.975180	+	0.221412i	$0.928933\pi$
$294$	−1.94959	−	2.68338i	−0.113703	−	0.156498i
$295$	−11.2568	−	1.39200i	−0.655399	−	0.0810454i
$296$	−5.49984	−	3.99587i	−0.319672	−	0.232255i
$297$	7.70992	−	10.6118i	0.447375	−	0.615759i
$298$	3.52490	−	10.8485i	0.204192	−	0.628439i
$299$	2.76071	+	0.374433i	0.159656	+	0.0216540i
$300$	1.49339	−	2.38079i	0.0862208	−	0.137455i
$301$		−	7.22393i		−	0.416381i
$302$	3.79680	−	11.6853i	0.218481	−	0.672416i
$303$	−4.83239	−	3.51094i	−0.277614	−	0.201698i
$304$	4.56943	−	6.28928i	0.262075	−	0.360715i
$305$	19.8615	−	21.2621i	1.13727	−	1.21747i
$306$	−0.930615	−	1.28088i	−0.0531997	−	0.0732231i
$307$			4.68581i			0.267434i	0.991020	+	0.133717i	$0.0426912\pi$
$307$			4.68581i			0.267434i	−0.991020	+	0.133717i	$0.957309\pi$
$308$	−11.9301	+	8.66770i	−0.679778	+	0.493888i
$309$	−0.937154	−	2.88426i	−0.0533128	−	0.164080i
$310$	−0.577222	+	4.66789i	−0.0327840	+	0.265118i
$311$	3.63982	−	11.2022i	0.206395	−	0.635220i	−0.793258	−	0.608886i	$-0.791617\pi$
$311$	3.63982	−	11.2022i	0.206395	−	0.635220i	0.999653	−	0.0263338i	$-0.00838327\pi$
$312$	−1.99410	+	0.361533i	−0.112894	+	0.0204678i
$313$	−5.12768	−	15.7814i	−0.289834	−	0.892016i	−0.984908	−	0.173078i	$-0.944629\pi$
$313$	−5.12768	−	15.7814i	−0.289834	−	0.892016i	0.695074	−	0.718938i	$-0.255371\pi$
$314$	−15.2943	−	4.96941i	−0.863105	−	0.280440i
$315$	−21.3941	−	2.64556i	−1.20542	−	0.149060i
$316$	−3.80867	−	11.7219i	−0.214254	−	0.659407i
$317$	18.7018	+	25.7408i	1.05040	+	1.44575i	0.888465	+	0.458945i	$0.151772\pi$
$317$	18.7018	+	25.7408i	1.05040	+	1.44575i	0.161932	+	0.986802i	$0.448228\pi$
$318$		−	4.33848i		−	0.243290i
$319$	6.86144	+	9.44396i	0.384167	+	0.528760i
$320$	−1.52640	+	1.63404i	−0.0853284	+	0.0913458i
$321$	−4.51768	−	3.28229i	−0.252152	−	0.183199i
$322$	2.24531	+	1.63132i	0.125126	+	0.0909097i
$323$	4.36122	+	1.41705i	0.242665	+	0.0788466i
$324$	−6.25640			−0.347578
$325$	−11.5452	+	13.8459i	−0.640411	+	0.768033i
$326$	2.13676			0.118344
$327$	−6.48992	−	2.10870i	−0.358893	−	0.116612i
$328$	5.96175	+	4.33146i	0.329182	+	0.239165i
$329$	−9.98573	−	7.25506i	−0.550531	−	0.399984i
$330$	0.633264	−	5.12108i	0.0348600	−	0.281906i
$331$	6.05604	+	8.33542i	0.332870	+	0.458156i	0.942342	−	0.334651i	$-0.108619\pi$
$331$	6.05604	+	8.33542i	0.332870	+	0.458156i	−0.609472	+	0.792808i	$0.708619\pi$
$332$			5.80950i			0.318838i
$333$	−10.7252	−	14.7619i	−0.587735	−	0.808948i
$334$	−6.83249	−	21.0283i	−0.373857	−	1.15061i
$335$	2.88866	+	14.9294i	0.157824	+	0.815682i
$336$	−1.92007	−	0.623869i	−0.104748	−	0.0340348i
$337$	−0.137204	−	0.422271i	−0.00747400	−	0.0230026i	0.947250	−	0.320496i	$-0.103849\pi$
$337$	−0.137204	−	0.422271i	−0.00747400	−	0.0230026i	−0.954724	+	0.297493i	$0.903849\pi$
$338$	12.9871	−	0.578911i	0.706405	−	0.0314886i
$339$	0.781224	−	2.40436i	0.0424303	−	0.130587i
$340$	−1.19494	−	0.558460i	−0.0648045	−	0.0302867i
$341$	2.66862	+	8.21316i	0.144514	+	0.444768i
$342$	16.8808	−	12.2646i	0.912811	−	0.663196i
$343$		−	3.94736i		−	0.213137i
$344$	−1.18217	−	1.62712i	−0.0637384	−	0.0877284i
$345$	−0.953478	+	0.184486i	−0.0513335	+	0.00993239i
$346$	9.71131	−	13.3665i	0.522083	−	0.718586i
$347$	7.08654	+	5.14867i	0.380425	+	0.276395i	0.761521	−	0.648141i	$-0.224453\pi$
$347$	7.08654	+	5.14867i	0.380425	+	0.276395i	−0.381095	+	0.924536i	$0.624453\pi$
$348$	−0.493861	+	1.51995i	−0.0264737	+	0.0814778i
$349$		−	19.4630i		−	1.04183i	−0.853608	−	0.520916i	$-0.825590\pi$
$349$		−	19.4630i		−	1.04183i	0.853608	−	0.520916i	$-0.174410\pi$
$350$	−16.6628	+	6.69889i	−0.890666	+	0.358071i
$351$	−11.4149	−	1.54819i	−0.609281	−	0.0826363i
$352$	−1.26869	+	3.90463i	−0.0676214	+	0.208117i
$353$	6.49700	−	8.94236i	0.345800	−	0.475954i	−0.600324	−	0.799757i	$-0.704962\pi$
$353$	6.49700	−	8.94236i	0.345800	−	0.475954i	0.946124	+	0.323803i	$0.104962\pi$
$354$	−2.30666	−	1.67589i	−0.122598	−	0.0890724i
$355$	10.5193	−	5.81911i	0.558306	−	0.308846i
$356$	7.40007	+	10.1853i	0.392203	+	0.539821i
$357$		−	1.19088i		−	0.0630282i
$358$	0.151035	+	0.207882i	0.00798247	+	0.0109869i
$359$	−23.8172	+	7.73869i	−1.25703	+	0.408432i	−0.860434	−	0.509562i	$-0.829807\pi$
$359$	−23.8172	+	7.73869i	−1.25703	+	0.408432i	−0.396592	+	0.917995i	$0.629807\pi$
$360$	−5.25175	+	2.90519i	−0.276792	+	0.153117i
$361$	−12.8040	+	39.4068i	−0.673897	+	2.07404i
$362$	−20.7787	+	6.75142i	−1.09211	+	0.354847i
$363$	−1.01709	−	3.13028i	−0.0533834	−	0.164297i
$364$	11.6670	+	5.62092i	0.611516	+	0.294616i
$365$	−25.8109	−	24.1106i	−1.35100	−	1.26201i
$366$	6.95582	−	2.26008i	0.363587	−	0.118136i
$367$	−16.0962	+	11.6946i	−0.840216	+	0.610453i	−0.922431	−	0.386162i	$-0.873801\pi$
$367$	−16.0962	+	11.6946i	−0.840216	+	0.610453i	0.0822149	+	0.996615i	$0.473801\pi$
$368$	0.772694			0.0402795
$369$	11.6259	+	16.0017i	0.605222	+	0.833016i
$370$	−13.7714	−	6.43615i	−0.715942	−	0.334599i
$371$	−16.2956	+	22.4289i	−0.846024	+	1.16445i
$372$	−0.694942	+	0.956505i	−0.0360310	+	0.0495925i
$373$	1.03331	−	3.18020i	0.0535027	−	0.164665i	−0.920735	−	0.390189i	$-0.872410\pi$
$373$	1.03331	−	3.18020i	0.0535027	−	0.164665i	0.974237	+	0.225525i	$0.0724096\pi$
$374$	−2.42176			−0.125226
$375$	2.26721	−	5.86103i	0.117078	−	0.302662i
$376$	−3.43645			−0.177222
$377$	4.44958	−	9.23570i	0.229165	−	0.475663i
$378$	−9.28384	−	6.74510i	−0.477509	−	0.346931i
$379$	10.3711	−	14.2746i	0.532728	−	0.733237i	−0.454815	−	0.890586i	$-0.650295\pi$
$379$	10.3711	−	14.2746i	0.532728	−	0.733237i	0.987543	+	0.157349i	$0.0502947\pi$
$380$	7.35999	−	15.7482i	0.377560	−	0.807863i
$381$	−6.22199	+	4.52054i	−0.318762	+	0.231594i
$382$			9.54959i			0.488600i
$383$	−18.4796	−	25.4350i	−0.944265	−	1.29967i	−0.954028	−	0.299717i	$-0.903108\pi$
$383$	−18.4796	−	25.4350i	−0.944265	−	1.29967i	0.00976327	−	0.999952i	$-0.496892\pi$
$384$	−0.534571	+	0.173693i	−0.0272797	+	0.00886371i
$385$	−22.5089	+	24.0962i	−1.14716	+	1.22806i
$386$	−3.33230	+	10.2558i	−0.169610	+	0.522005i
$387$	−1.66816	−	5.13406i	−0.0847972	−	0.260979i
$388$	15.4349	−	5.01510i	0.783588	−	0.254603i
$389$	7.78645	−	23.9642i	0.394789	−	1.21503i	−0.534337	−	0.845271i	$-0.679439\pi$
$389$	7.78645	−	23.9642i	0.394789	−	1.21503i	0.929126	−	0.369763i	$-0.120561\pi$
$390$	−4.22419	+	1.64073i	−0.213900	+	0.0830818i
$391$	0.140847	+	0.433483i	0.00712295	+	0.0219222i
$392$	3.46853	+	4.77402i	0.175187	+	0.241124i
$393$	−2.29017			−0.115524
$394$	−6.60997	+	4.80242i	−0.333005	+	0.241943i
$395$	−13.3405	−	24.1158i	−0.671233	−	1.21340i
$396$	−6.47716	+	8.91505i	−0.325490	+	0.447998i
$397$	−1.53138	+	2.10777i	−0.0768580	+	0.105786i	−0.845715	−	0.533635i	$-0.820826\pi$
$397$	−1.53138	+	2.10777i	−0.0768580	+	0.105786i	0.768857	+	0.639421i	$0.220826\pi$
$398$	6.15856	+	2.00104i	0.308701	+	0.100303i
$399$	15.6947			0.785720
$400$	−2.65689	+	4.23567i	−0.132845	+	0.211784i
$401$		−	30.8112i		−	1.53864i	−0.638866	−	0.769318i	$-0.720596\pi$
$401$		−	30.8112i		−	1.53864i	0.638866	−	0.769318i	$-0.279404\pi$
$402$	−1.18119	+	3.63534i	−0.0589125	+	0.181314i
$403$	5.24198	−	5.48085i	0.261122	−	0.273021i
$404$	8.59733	+	6.24632i	0.427733	+	0.310766i
$405$	−13.7350	+	2.65755i	−0.682497	+	0.132055i
$406$	8.26215	−	6.00280i	0.410043	−	0.297914i
$407$	−27.9104			−1.38347
$408$	−0.194884	−	0.268235i	−0.00964819	−	0.0132796i
$409$	26.0222	−	8.45513i	1.28672	−	0.418079i	0.415775	−	0.909468i	$-0.363510\pi$
$409$	26.0222	−	8.45513i	1.28672	−	0.418079i	0.870940	+	0.491389i	$0.163510\pi$
$410$	14.9280	+	6.97669i	0.737242	+	0.344554i
$411$	7.26360	+	2.36009i	0.358287	+	0.116415i
$412$	1.66729	+	5.13140i	0.0821416	+	0.252806i
$413$	5.63017	+	17.3279i	0.277042	+	0.852649i
$414$	1.97245	+	0.640889i	0.0969408	+	0.0314980i
$415$	2.46772	+	12.7539i	0.121135	+	0.626064i
$416$	3.54772	−	0.643204i	0.173941	−	0.0315357i
$417$	−0.570098	+	0.414200i	−0.0279178	+	0.0202835i
$418$		−	31.9166i		−	1.56109i
$419$	29.6299	−	21.5274i	1.44752	−	1.05168i	0.461113	−	0.887341i	$-0.347450\pi$
$419$	29.6299	−	21.5274i	1.44752	−	1.05168i	0.986404	−	0.164341i	$-0.0525499\pi$
$420$	−4.48023	−	0.554017i	−0.218613	−	0.0270333i
$421$	−7.05513	+	9.71055i	−0.343846	+	0.473263i	−0.945560	−	0.325448i	$-0.894485\pi$
$421$	−7.05513	+	9.71055i	−0.343846	+	0.473263i	0.601714	+	0.798712i	$0.294485\pi$
$422$	4.03929	−	5.55960i	0.196629	−	0.270637i
$423$	−8.77222	−	2.85027i	−0.426520	−	0.138585i
$424$			7.71861i			0.374849i
$425$	−2.86052	−	0.718440i	−0.138756	−	0.0348494i
$426$	3.02186			0.146410
$427$	−44.4489	−	14.4423i	−2.15103	−	0.698913i
$428$	8.03742	+	5.83953i	0.388503	+	0.282264i
$429$	−5.75092	+	6.01298i	−0.277657	+	0.290309i
$430$	−3.28644	−	3.06995i	−0.158486	−	0.148046i
$431$	−3.72383	−	5.12541i	−0.179371	−	0.246882i	0.709859	−	0.704344i	$-0.248759\pi$
$431$	−3.72383	−	5.12541i	−0.179371	−	0.246882i	−0.889229	+	0.457462i	$0.848759\pi$
$432$	−3.19491			−0.153715
$433$	28.0021	−	20.3447i	1.34569	−	0.977703i	0.346479	−	0.938058i	$-0.387377\pi$
$433$	28.0021	−	20.3447i	1.34569	−	0.977703i	0.999214	−	0.0396452i	$-0.0126228\pi$
$434$	7.18536	−	2.33467i	0.344909	−	0.112068i
$435$	−0.438566	+	3.54660i	−0.0210276	+	0.170046i
$436$	11.5462	+	3.75160i	0.552964	+	0.179669i
$437$	−5.71291	+	1.85624i	−0.273285	+	0.0887958i
$438$	−2.74360	−	8.44392i	−0.131094	−	0.403466i
$439$	−9.62784	+	29.6315i	−0.459512	+	1.41423i	0.406243	+	0.913765i	$0.366839\pi$
$439$	−9.62784	+	29.6315i	−0.459512	+	1.41423i	−0.865755	+	0.500467i	$0.833161\pi$
$440$	−1.12664	+	9.11093i	−0.0537105	+	0.434347i
$441$	4.89442	+	15.0635i	0.233068	+	0.717309i
$442$	1.00752	+	1.87303i	0.0479228	+	0.0890911i
$443$	−15.7404			−0.747851			−0.373926	−	0.927459i	$-0.621988\pi$
$443$	−15.7404			−0.747851			−0.373926	+	0.927459i	$0.621988\pi$
$444$	−2.24600	−	3.09135i	−0.106590	−	0.146709i
$445$	20.5722	+	19.2170i	0.975216	+	0.910974i
$446$	−19.7137	−	14.3228i	−0.933471	−	0.678206i
$447$	3.76862	−	5.18706i	0.178250	−	0.245340i
$448$	3.41600	+	1.10993i	0.161391	+	0.0524391i
$449$			19.7152i			0.930420i	0.885200	+	0.465210i	$0.154021\pi$
$449$			19.7152i			0.930420i	−0.885200	+	0.465210i	$0.845979\pi$
$450$	−10.2954	+	8.60871i	−0.485330	+	0.405819i
$451$	30.2544			1.42463
$452$	−1.38988	+	4.27761i	−0.0653744	+	0.201202i
$453$	4.05932	−	5.58717i	0.190723	−	0.262508i
$454$	15.3525	+	11.1543i	0.720530	+	0.523496i
$455$	28.0007	+	7.38407i	1.31269	+	0.346171i
$456$	3.53509	−	2.56839i	0.165546	−	0.120276i
$457$			17.6787i			0.826977i	0.910509	+	0.413488i	$0.135690\pi$
$457$			17.6787i			0.826977i	−0.910509	+	0.413488i	$0.864310\pi$
$458$	13.1547	−	9.55746i	0.614680	−	0.446591i
$459$	−0.582370	−	1.79235i	−0.0271827	−	0.0836597i
$460$	1.69633	−	0.328219i	0.0790920	−	0.0153033i
$461$	−3.69334	−	1.20004i	−0.172016	−	0.0558915i	0.221743	−	0.975105i	$-0.428826\pi$
$461$	−3.69334	−	1.20004i	−0.172016	−	0.0558915i	−0.393759	+	0.919214i	$0.628826\pi$
$462$	−7.88298	+	2.56134i	−0.366749	+	0.119164i
$463$	−13.9300	+	4.52614i	−0.647383	+	0.210348i	−0.614260	−	0.789104i	$-0.710545\pi$
$463$	−13.9300	+	4.52614i	−0.647383	+	0.210348i	−0.0331233	+	0.999451i	$0.510545\pi$
$464$	0.878629	−	2.70414i	0.0407893	−	0.125537i
$465$	−1.11934	+	2.39506i	−0.0519083	+	0.111068i
$466$	11.3165	−	3.67694i	0.524225	−	0.170331i
$467$	19.1387	−	13.9051i	0.885633	−	0.643450i	−0.0491029	−	0.998794i	$-0.515636\pi$
$467$	19.1387	−	13.9051i	0.885633	−	0.643450i	0.934736	+	0.355344i	$0.115636\pi$
$468$	9.58973	+	1.30065i	0.443286	+	0.0601224i
$469$	19.7610	−	14.3572i	0.912478	−	0.662954i
$470$	−7.54422	+	1.45971i	−0.347989	+	0.0673315i
$471$	−7.31272	−	5.31300i	−0.336952	−	0.244810i
$472$	4.10379	+	2.98157i	0.188892	+	0.137238i
$473$	−7.85311	−	2.55163i	−0.361086	−	0.117324i
$474$		−	6.92771i		−	0.318200i
$475$	9.46838	−	37.6991i	0.434439	−	1.72975i
$476$			2.11870i			0.0971106i
$477$	−6.40198	+	19.7033i	−0.293127	+	0.902151i
$478$	17.3238	+	12.5865i	0.792373	+	0.575693i
$479$	6.35461	−	8.74637i	0.290350	−	0.399632i	−0.638778	−	0.769391i	$-0.720560\pi$
$479$	6.35461	−	8.74637i	0.290350	−	0.399632i	0.929128	+	0.369759i	$0.120560\pi$
$480$	−1.09979	+	0.608388i	−0.0501984	+	0.0277690i
$481$	11.6115	+	21.5864i	0.529438	+	0.984253i
$482$	5.22408			0.237950
$483$	0.916932	+	1.26205i	0.0417218	+	0.0574252i
$484$	1.80951	+	5.56909i	0.0822503	+	0.253141i
$485$	31.7547	−	17.5662i	1.44191	−	0.797642i
$486$	−12.4601	−	4.04853i	−0.565201	−	0.183645i
$487$	1.79855	−	0.584385i	0.0815002	−	0.0264810i	−0.267983	−	0.963424i	$-0.586357\pi$
$487$	1.79855	−	0.584385i	0.0815002	−	0.0264810i	0.349483	+	0.936943i	$0.386357\pi$
$488$	−12.3751	+	4.02092i	−0.560195	+	0.182018i
$489$	1.14225	+	0.371139i	0.0516542	+	0.0167835i
$490$	9.64250	+	9.00731i	0.435604	+	0.406909i
$491$	−13.0581	−	40.1886i	−0.589302	−	1.81368i	−0.581262	−	0.813717i	$-0.697441\pi$
$491$	−13.0581	−	40.1886i	−0.589302	−	1.81368i	−0.00803997	−	0.999968i	$-0.502559\pi$
$492$	2.43463	+	3.35098i	0.109762	+	0.151074i
$493$	1.67719			0.0755367
$494$	−24.6849	+	13.2782i	−1.11062	+	0.597413i
$495$	−10.4328	+	22.3230i	−0.468919	+	1.00334i
$496$	1.23637	−	1.70172i	0.0555148	−	0.0764095i
$497$	−15.6223	−	11.3503i	−0.700756	−	0.509129i
$498$	−1.00907	+	3.10559i	−0.0452174	+	0.139165i
$499$			32.1726i			1.44024i	0.693848	+	0.720122i	$0.255914\pi$
$499$			32.1726i			1.44024i	−0.693848	+	0.720122i	$0.744086\pi$
$500$	−4.03361	+	10.4274i	−0.180388	+	0.466326i
$501$		−	12.4278i		−	0.555235i
$502$	−14.1234	−	4.58896i	−0.630357	−	0.204815i
$503$	−15.8917	−	11.5460i	−0.708576	−	0.514811i	0.174138	−	0.984721i	$-0.444286\pi$
$503$	−15.8917	−	11.5460i	−0.708576	−	0.514811i	−0.882714	+	0.469911i	$0.844286\pi$
$504$	7.79942	+	5.66661i	0.347414	+	0.252411i
$505$	21.5274	+	10.0610i	0.957958	+	0.447707i
$506$	2.56648	−	1.86466i	0.114094	−	0.0828942i
$507$	7.04308	+	1.94629i	0.312794	+	0.0864380i
$508$	11.0696	−	8.04251i	0.491133	−	0.356829i
$509$	6.39328	−	2.07730i	0.283377	−	0.0920748i	−0.163880	−	0.986480i	$-0.552401\pi$
$509$	6.39328	−	2.07730i	0.283377	−	0.0920748i	0.447257	+	0.894405i	$0.352401\pi$
$510$	−0.541777	−	0.506088i	−0.0239903	−	0.0224100i
$511$	−17.5321	+	53.9581i	−0.775573	+	2.38697i
$512$	0.951057	−	0.309017i	0.0420312	−	0.0136568i
$513$	23.6215	−	7.67510i	1.04292	−	0.338864i
$514$	5.61418	+	1.82416i	0.247631	+	0.0804602i
$515$	5.83997	+	10.5570i	0.257340	+	0.465197i
$516$	−0.349336	−	1.07515i	−0.0153787	−	0.0473306i
$517$	−11.4141	+	8.29282i	−0.501991	+	0.364718i
$518$			24.4177i			1.07285i
$519$	7.51304	−	5.45854i	0.329786	−	0.239603i
$520$	7.51527	−	2.91903i	0.329566	−	0.128008i
$521$	−29.2771	−	21.2711i	−1.28266	−	0.931903i	−0.283025	−	0.959112i	$-0.591338\pi$
$521$	−29.2771	−	21.2711i	−1.28266	−	0.931903i	−0.999630	+	0.0272089i	$0.991338\pi$
$522$	4.48575	−	6.17411i	0.196336	−	0.270233i
$523$	−0.751286	+	2.31222i	−0.0328514	+	0.101106i	−0.966138	−	0.258027i	$-0.916928\pi$
$523$	−0.751286	+	2.31222i	−0.0328514	+	0.101106i	0.933286	+	0.359133i	$0.116928\pi$
$524$	4.07445			0.177993
$525$	−10.0710	+	0.686819i	−0.439535	+	0.0299752i
$526$		−	22.6578i		−	0.987925i
$527$	1.18004	+	0.383417i	0.0514032	+	0.0167019i
$528$	−1.35641	+	1.86694i	−0.0590302	+	0.0812480i
$529$	18.1244	+	13.1681i	0.788016	+	0.572527i
$530$	3.27866	+	16.9451i	0.142416	+	0.736046i
$531$	8.00274	+	11.0148i	0.347289	+	0.478003i
$532$	−27.9226			−1.21060
$533$	−12.5867	−	23.3993i	−0.545189	−	1.01354i
$534$	2.18675	+	6.73011i	0.0946298	+	0.291241i
$535$	20.1254	+	9.40574i	0.870098	+	0.406646i
$536$	2.10146	−	6.46764i	0.0907694	−	0.279359i
$537$	0.0446315	+	0.137362i	0.00192599	+	0.00592759i
$538$	3.56314	−	1.15774i	0.153618	−	0.0499135i
$539$	23.0412	+	7.48655i	0.992456	+	0.322469i
$540$	−7.01394	+	1.35711i	−0.301832	+	0.0584007i
$541$	22.5315	−	7.32094i	0.968706	−	0.314752i	0.218413	−	0.975857i	$-0.429912\pi$
$541$	22.5315	−	7.32094i	0.968706	−	0.314752i	0.750294	+	0.661105i	$0.229912\pi$
$542$	−5.58554	+	4.05813i	−0.239919	+	0.174312i
$543$	−12.2804			−0.527001
$544$	0.346718	+	0.477217i	0.0148654	+	0.0204605i
$545$	26.9416	+	3.33155i	1.15405	+	0.142708i
$546$	5.26052	+	5.03125i	0.225129	+	0.215317i
$547$	−24.4699	−	17.7784i	−1.04626	−	0.760149i	−0.0747590	−	0.997202i	$-0.523819\pi$
$547$	−24.4699	−	17.7784i	−1.04626	−	0.760149i	−0.971497	+	0.237052i	$0.923819\pi$
$548$	−12.9227	−	4.19884i	−0.552030	−	0.179366i
$549$	−34.9250			−1.49056
$550$	1.39670	+	20.4803i	0.0595557	+	0.873282i
$551$			22.1038i			0.941653i
$552$	0.413060	+	0.134211i	0.0175810	+	0.00571241i
$553$	−26.0208	+	35.8146i	−1.10652	+	1.52299i
$554$	−8.52849	+	11.7385i	−0.362341	+	0.498720i
$555$	−6.24388	−	5.83257i	−0.265038	−	0.247579i
$556$	1.01426	−	0.736905i	0.0430143	−	0.0312517i
$557$		−	5.82972i		−	0.247013i	−0.992344	−	0.123507i	$-0.960586\pi$
$557$		−	5.82972i		−	0.247013i	0.992344	−	0.123507i	$-0.0394140\pi$
$558$	4.56753	−	3.31850i	0.193359	−	0.140483i
$559$	1.29363	+	7.13527i	0.0547148	+	0.301790i
$560$	7.97079	+	0.985653i	0.336827	+	0.0416515i
$561$	−1.29460	−	0.420642i	−0.0546582	−	0.0177595i
$562$	−2.95499	−	9.09452i	−0.124649	−	0.383629i
$563$	−4.95024	−	15.2353i	−0.208628	−	0.642091i	−0.999545	−	0.0301672i	$-0.990396\pi$
$563$	−4.95024	−	15.2353i	−0.208628	−	0.642091i	0.790917	−	0.611923i	$-0.209604\pi$
$564$	−1.83703	−	0.596886i	−0.0773528	−	0.0251335i
$565$	−1.23426	+	9.98123i	−0.0519257	+	0.419913i
$566$	−19.2750	+	6.26282i	−0.810187	+	0.263246i
$567$	13.2085	+	18.1800i	0.554707	+	0.763488i
$568$	−5.37620			−0.225580
$569$	17.9526	−	13.0433i	0.752612	−	0.546805i	−0.144023	−	0.989574i	$-0.546004\pi$
$569$	17.9526	−	13.0433i	0.752612	−	0.546805i	0.896635	+	0.442770i	$0.146004\pi$
$570$	6.66977	−	7.14013i	0.279366	−	0.299067i
$571$	−14.8864	−	10.8156i	−0.622975	−	0.452618i	0.230984	−	0.972957i	$-0.425805\pi$
$571$	−14.8864	−	10.8156i	−0.622975	−	0.452618i	−0.853959	+	0.520339i	$0.825805\pi$
$572$	10.2315	−	10.6977i	0.427799	−	0.447294i
$573$	−1.65869	+	5.10493i	−0.0692929	+	0.213262i
$574$		−	26.4684i		−	1.10477i
$575$	3.58463	−	1.44111i	0.149489	−	0.0600986i
$576$	2.68406			0.111836
$577$	−14.3885	−	4.67511i	−0.599002	−	0.194628i	−0.00620677	−	0.999981i	$-0.501976\pi$
$577$	−14.3885	−	4.67511i	−0.599002	−	0.194628i	−0.592795	+	0.805353i	$0.701976\pi$
$578$	9.78783	−	13.4718i	0.407120	−	0.560353i
$579$	−3.56270	+	4.90364i	−0.148061	+	0.203788i
$580$	0.780254	−	6.30976i	0.0323983	−	0.261999i
$581$	16.8814	−	12.2650i	0.700358	−	0.508840i
$582$	9.12213			0.378125
$583$	18.6265	+	25.6372i	0.771430	+	1.06178i
$584$	4.88114	+	15.0226i	0.201983	+	0.621640i
$585$	21.6053	−	1.21808i	0.893270	−	0.0503615i
$586$	2.34233	−	7.20895i	0.0967607	−	0.297799i
$587$	30.7837	−	10.0022i	1.27058	−	0.412836i	0.405326	−	0.914172i	$-0.367158\pi$
$587$	30.7837	−	10.0022i	1.27058	−	0.412836i	0.865252	+	0.501336i	$0.167158\pi$
$588$	1.02496	+	3.15451i	0.0422687	+	0.130090i
$589$	−5.05308	+	15.5518i	−0.208209	+	0.640800i
$590$	10.2757	+	4.80243i	0.423046	+	0.197713i
$591$	−4.36764	+	1.41913i	−0.179661	+	0.0583753i
$592$	3.99587	+	5.49984i	0.164229	+	0.226042i
$593$			4.16492i			0.171033i	0.996337	+	0.0855163i	$0.0272540\pi$
$593$			4.16492i			0.171033i	−0.996337	+	0.0855163i	$0.972746\pi$
$594$	−10.6118	+	7.70992i	−0.435407	+	0.316342i
$595$	0.899968	+	4.65130i	0.0368951	+	0.190685i
$596$	−6.70477	+	9.22832i	−0.274638	+	0.378007i
$597$	2.94462	+	2.13939i	0.120515	+	0.0875596i
$598$	−2.50989	−	1.20921i	−0.102637	−	0.0494484i
$599$	33.0094			1.34873			0.674364	−	0.738399i	$-0.264418\pi$
$599$	33.0094			1.34873			0.674364	+	0.738399i	$0.264418\pi$
$600$	−2.15600	+	1.80279i	−0.0880184	+	0.0735984i
$601$	−40.1843			−1.63915			−0.819576	−	0.572971i	$-0.805791\pi$
$601$	−40.1843			−1.63915			−0.819576	+	0.572971i	$0.805791\pi$
$602$	−2.23232	+	6.87037i	−0.0909825	+	0.280015i
$603$	10.7288	−	14.7669i	0.436910	−	0.601356i
$604$	−7.22194	+	9.94015i	−0.293857	+	0.404459i
$605$	6.33810	+	11.4575i	0.257681	+	0.465813i
$606$	3.51094	+	4.83239i	0.142622	+	0.196303i
$607$	26.8574			1.09011			0.545054	−	0.838401i	$-0.316509\pi$
$607$	26.8574			1.09011			0.545054	+	0.838401i	$0.316509\pi$
$608$	−6.28928	+	4.56943i	−0.255064	+	0.185315i
$609$	5.45934	−	1.77385i	0.221224	−	0.0718800i
$610$	−25.4598	+	14.0839i	−1.03084	+	0.570242i
$611$	11.1624	+	5.37781i	0.451582	+	0.217563i
$612$	0.489253	+	1.50577i	0.0197769	+	0.0608670i
$613$	16.4724	−	5.35219i	0.665312	−	0.216173i	0.0431586	−	0.999068i	$-0.486258\pi$
$613$	16.4724	−	5.35219i	0.665312	−	0.216173i	0.622154	+	0.782895i	$0.286258\pi$
$614$	1.44800	−	4.45647i	0.0584364	−	0.179849i
$615$	6.76828	+	6.32242i	0.272924	+	0.254945i
$616$	14.0246	−	4.55688i	0.565068	−	0.183602i
$617$	28.5397	+	39.2816i	1.14897	+	1.58142i	0.745624	+	0.666367i	$0.232152\pi$
$617$	28.5397	+	39.2816i	1.14897	+	1.58142i	0.403342	+	0.915049i	$0.367848\pi$
$618$			3.03269i			0.121993i
$619$	−16.1131	−	22.1778i	−0.647640	−	0.891400i	0.351354	−	0.936243i	$-0.385721\pi$
$619$	−16.1131	−	22.1778i	−0.647640	−	0.891400i	−0.998994	+	0.0448424i	$0.985721\pi$
$620$	1.99143	−	4.26105i	0.0799776	−	0.171128i
$621$	1.99721	+	1.45106i	0.0801452	+	0.0582289i
$622$	−6.92335	+	9.52918i	−0.277601	+	0.382085i
$623$	13.9737	−	43.0066i	0.559844	−	1.72302i
$624$	2.00823	+	0.272374i	0.0803934	+	0.0109037i
$625$	−4.42592	+	24.6051i	−0.177037	+	0.984204i
$626$			16.5935i			0.663211i
$627$	5.54368	−	17.0617i	0.221393	−	0.681378i
$628$	13.0101	+	9.45237i	0.519158	+	0.377191i
$629$	−2.35705	+	3.24420i	−0.0939818	+	0.129355i
$630$	19.5295	+	9.12722i	0.778074	+	0.363637i
$631$	−2.26580	−	3.11861i	−0.0902001	−	0.124150i	0.761532	−	0.648127i	$-0.224448\pi$
$631$	−2.26580	−	3.11861i	−0.0902001	−	0.124150i	−0.851732	+	0.523978i	$0.824448\pi$
$632$			12.3251i			0.490266i
$633$	3.12495	−	2.27041i	0.124206	−	0.0902406i
$634$	−9.83211	−	30.2601i	−0.390483	−	1.20178i
$635$	20.8853	−	22.3582i	0.828810	−	0.887258i
$636$	−1.34067	+	4.12614i	−0.0531608	+	0.163612i
$637$	−3.79555	−	20.9351i	−0.150385	−	0.829479i
$638$	−3.60727	−	11.1020i	−0.142813	−	0.439534i
$639$	−13.7238	−	4.45914i	−0.542906	−	0.176401i
$640$	1.95664	−	1.08238i	0.0773430	−	0.0427850i
$641$	0.945030	+	2.90850i	0.0373264	+	0.114879i	0.967984	−	0.251013i	$-0.0807638\pi$
$641$	0.945030	+	2.90850i	0.0373264	+	0.114879i	−0.930657	+	0.365892i	$0.880764\pi$
$642$	3.28229	+	4.51768i	0.129542	+	0.178299i
$643$			34.9230i			1.37723i	0.725128	+	0.688614i	$0.241781\pi$
$643$			34.9230i			1.37723i	−0.725128	+	0.688614i	$0.758219\pi$
$644$	−1.63132	−	2.24531i	−0.0642828	−	0.0884777i
$645$	−1.22361	−	2.21193i	−0.0481795	−	0.0870948i
$646$	−3.70988	−	2.69538i	−0.145963	−	0.106048i
$647$	−39.7177	−	28.8566i	−1.56146	−	1.13447i	−0.934797	−	0.355183i	$-0.884418\pi$
$647$	−39.7177	−	28.8566i	−1.56146	−	1.13447i	−0.626667	−	0.779287i	$-0.715582\pi$
$648$	5.95019	+	1.93333i	0.233745	+	0.0759485i
$649$	20.8257			0.817481
$650$	15.2587	−	9.60059i	0.598497	−	0.376566i
$651$	4.24660			0.166437
$652$	−2.03218	−	0.660294i	−0.0795861	−	0.0258591i
$653$	2.37158	+	1.72306i	0.0928072	+	0.0674284i	0.633221	−	0.773971i	$-0.281732\pi$
$653$	2.37158	+	1.72306i	0.0928072	+	0.0674284i	−0.540414	+	0.841399i	$0.681732\pi$
$654$	5.52065	+	4.01099i	0.215875	+	0.156842i
$655$	8.94486	−	1.73072i	0.349504	−	0.0676247i
$656$	−4.33146	−	5.96175i	−0.169115	−	0.232767i
$657$			42.3967i			1.65405i
$658$	7.25506	+	9.98573i	0.282832	+	0.389284i
$659$	8.30066	+	25.5468i	0.323348	+	0.995162i	0.972181	+	0.234231i	$0.0752573\pi$
$659$	8.30066	+	25.5468i	0.323348	+	0.995162i	−0.648833	+	0.760931i	$0.724743\pi$
$660$	−2.18477	+	4.67475i	−0.0850421	+	0.181964i
$661$	−29.9782	−	9.74051i	−1.16602	−	0.378862i	−0.338862	−	0.940836i	$-0.610042\pi$
$661$	−29.9782	−	9.74051i	−1.16602	−	0.378862i	−0.827155	+	0.561974i	$0.810042\pi$
$662$	−3.18385	−	9.79888i	−0.123744	−	0.380844i
$663$	0.213258	+	1.17627i	0.00828227	+	0.0456824i
$664$	1.79523	−	5.52516i	0.0696686	−	0.214418i
$665$	−61.2998	+	11.8607i	−2.37711	+	0.459940i
$666$	5.63855	+	17.3537i	0.218489	+	0.672441i
$667$	−1.77741	+	1.29137i	−0.0688217	+	0.0500019i
$668$			22.1104i			0.855478i
$669$	−8.05060	−	11.0807i	−0.311254	−	0.428405i
$670$	1.86617	−	15.0914i	0.0720965	−	0.583031i
$671$	−31.4004	+	43.2189i	−1.21220	+	1.66845i
$672$	1.63331	+	1.18667i	0.0630063	+	0.0457767i
$673$	14.0691	−	43.3001i	0.542323	−	1.66910i	−0.184949	−	0.982748i	$-0.559212\pi$
$673$	14.0691	−	43.3001i	0.542323	−	1.66910i	0.727272	−	0.686350i	$-0.240788\pi$
$674$			0.444003i			0.0171023i
$675$	−14.8216	+	5.95866i	−0.570484	+	0.229349i
$676$	−12.5304	−	3.46266i	−0.481937	−	0.133179i
$677$	0.551320	−	1.69679i	0.0211890	−	0.0652129i	−0.939903	−	0.341442i	$-0.889085\pi$
$677$	0.551320	−	1.69679i	0.0211890	−	0.0652129i	0.961092	+	0.276229i	$0.0890848\pi$
$678$	−1.48598	+	2.04527i	−0.0570686	+	0.0785482i
$679$	−47.1592	−	34.2632i	−1.80981	−	1.31490i
$680$	0.963878	+	0.900383i	0.0369630	+	0.0345281i
$681$	6.26960	+	8.62937i	0.240252	+	0.330678i
$682$		−	8.63583i		−	0.330683i
$683$	22.4277	+	30.8691i	0.858172	+	1.18117i	0.982002	+	0.188870i	$0.0604823\pi$
$683$	22.4277	+	30.8691i	0.858172	+	1.18117i	−0.123830	+	0.992303i	$0.539518\pi$
$684$	−19.8446	+	6.44791i	−0.758778	+	0.246542i
$685$	−30.1534	−	3.72872i	−1.15210	−	0.142467i
$686$	−1.21980	+	3.75416i	−0.0465722	+	0.143335i
$687$	8.69219	−	2.82426i	0.331628	−	0.107752i
$688$	0.621504	+	1.91279i	0.0236946	+	0.0729246i
$689$	12.0791	−	25.0718i	0.460177	−	0.955160i
$690$	0.963820	+	0.119184i	0.0366920	+	0.00453727i
$691$	22.5678	−	7.33272i	0.858520	−	0.278950i	0.153509	−	0.988147i	$-0.450942\pi$
$691$	22.5678	−	7.33272i	0.858520	−	0.278950i	0.705010	+	0.709197i	$0.250942\pi$
$692$	−13.3665	+	9.71131i	−0.508117	+	0.369169i
$693$	39.5802			1.50353
$694$	−5.14867	−	7.08654i	−0.195441	−	0.269001i
$695$	1.91365	−	2.04860i	0.0725887	−	0.0777077i
$696$	0.939379	−	1.29294i	0.0356071	−	0.0490090i
$697$	2.55501	−	3.51667i	0.0967780	−	0.133203i
$698$	−6.01441	+	18.5105i	−0.227649	+	0.700631i
$699$	6.68811			0.252967
$700$	17.9174	−	1.22192i	0.677213	−	0.0461843i
$701$	14.5127			0.548137			0.274068	−	0.961710i	$-0.411630\pi$
$701$	14.5127			0.548137			0.274068	+	0.961710i	$0.411630\pi$
$702$	10.3778	+	4.99981i	0.391684	+	0.188706i
$703$	−42.7556	−	31.0638i	−1.61256	−	1.17159i
$704$	2.41319	−	3.32147i	0.0909506	−	0.125183i
$705$	−4.28646	−	0.530056i	−0.161438	−	0.0199631i
$706$	−8.94236	+	6.49700i	−0.336550	+	0.244518i
$707$		−	38.1696i		−	1.43552i
$708$	1.67589	+	2.30666i	0.0629837	+	0.0866896i
$709$	−0.124149	+	0.0403385i	−0.00466251	+	0.00151494i	−0.311347	−	0.950296i	$-0.600780\pi$
$709$	−0.124149	+	0.0403385i	−0.00466251	+	0.00151494i	0.306685	+	0.951811i	$0.400780\pi$
$710$	−11.8027	+	2.28366i	−0.442946	+	0.0857044i
$711$	−10.2227	+	31.4623i	−0.383381	+	1.17993i
$712$	−3.89045	−	11.9736i	−0.145801	−	0.448728i
$713$	−1.54577	+	0.502251i	−0.0578895	+	0.0188094i
$714$	−0.368003	+	1.13260i	−0.0137722	+	0.0423864i
$715$	17.9176	−	27.8313i	0.670079	−	1.04083i
$716$	−0.0794040	−	0.244380i	−0.00296747	−	0.00913292i
$717$	7.07463	+	9.73739i	0.264207	+	0.363650i
$718$	25.0429			0.934594
$719$	−32.4092	+	23.5467i	−1.20866	+	0.878144i	−0.995109	−	0.0987880i	$-0.968503\pi$
$719$	−32.4092	+	23.5467i	−1.20866	+	0.878144i	−0.213552	+	0.976932i	$0.568503\pi$
$720$	5.89247	−	1.14012i	0.219599	−	0.0424897i
$721$	11.3910	−	15.6783i	0.424221	−	0.583890i
$722$	24.3547	−	33.5214i	0.906390	−	1.24754i
$723$	2.79264	+	0.907384i	0.103859	+	0.0337460i
$724$	21.8480			0.811976
$725$	−0.967285	−	14.1836i	−0.0359241	−	0.526765i
$726$			3.29137i			0.122154i
$727$	0.340587	−	1.04822i	0.0126317	−	0.0388763i	−0.944542	−	0.328391i	$-0.893494\pi$
$727$	0.340587	−	1.04822i	0.0126317	−	0.0388763i	0.957174	+	0.289514i	$0.0934938\pi$
$728$	−9.35900	−	8.95110i	−0.346867	−	0.331750i
$729$	9.22699	+	6.70380i	0.341741	+	0.248289i
$730$	17.0970	+	30.9065i	0.632789	+	1.14390i
$731$	−0.959793	+	0.697331i	−0.0354992	+	0.0257917i
$732$	−7.31378			−0.270325
$733$	1.90532	+	2.62244i	0.0703745	+	0.0968621i	0.842753	−	0.538300i	$-0.180933\pi$
$733$	1.90532	+	2.62244i	0.0703745	+	0.0968621i	−0.772379	+	0.635162i	$0.780933\pi$
$734$	18.9222	−	6.14821i	0.698433	−	0.226935i
$735$	3.59010	+	6.48988i	0.132423	+	0.239383i
$736$	−0.734876	−	0.238776i	−0.0270879	−	0.00880138i
$737$	−8.62770	−	26.5533i	−0.317805	−	0.978104i
$738$	−6.11211	−	18.8111i	−0.224990	−	0.692448i
$739$	−28.6081	−	9.29534i	−1.05237	−	0.341935i	−0.268770	−	0.963204i	$-0.586617\pi$
$739$	−28.6081	−	9.29534i	−1.05237	−	0.341935i	−0.783597	+	0.621270i	$0.786617\pi$
$740$	11.1085	+	10.3767i	0.408357	+	0.381457i
$741$	−15.5021	+	2.81055i	−0.569485	+	0.103248i
$742$	22.4289	−	16.2956i	0.823392	−	0.598229i
$743$		−	10.4367i		−	0.382885i	−0.981504	−	0.191443i	$-0.938683\pi$
$743$		−	10.4367i		−	0.382885i	0.981504	−	0.191443i	$-0.0613166\pi$
$744$	0.956505	−	0.694942i	0.0350672	−	0.0254778i
$745$	−10.7994	+	23.1074i	−0.395659	+	0.846590i
$746$	−1.96547	+	2.70524i	−0.0719610	+	0.0990459i
$747$	9.16538	−	12.6151i	0.335344	−	0.461561i
$748$	2.30323	+	0.748366i	0.0842145	+	0.0273630i
$749$		−	35.6838i		−	1.30386i
$750$	−3.96741	+	4.87356i	−0.144869	+	0.177957i
$751$	11.6006			0.423312			0.211656	−	0.977344i	$-0.432114\pi$
$751$	11.6006			0.423312			0.211656	+	0.977344i	$0.432114\pi$
$752$	3.26826	+	1.06192i	0.119181	+	0.0387243i
$753$	−6.75287	−	4.90625i	−0.246088	−	0.178794i
$754$	−7.08579	+	7.40868i	−0.258049	+	0.269808i
$755$	−11.6324	+	24.8898i	−0.423346	+	0.905833i
$756$	6.74510	+	9.28384i	0.245317	+	0.337650i
$757$	2.80617			0.101992			0.0509959	−	0.998699i	$-0.483760\pi$
$757$	2.80617			0.101992			0.0509959	+	0.998699i	$0.483760\pi$
$758$	−14.2746	+	10.3711i	−0.518477	+	0.376696i
$759$	1.69584	−	0.551013i	0.0615553	−	0.0200005i
$760$	−11.8662	+	12.7030i	−0.430433	+	0.460787i
$761$	−25.7293	−	8.35996i	−0.932687	−	0.303048i	−0.197026	−	0.980398i	$-0.563128\pi$
$761$	−25.7293	−	8.35996i	−0.932687	−	0.303048i	−0.735661	+	0.677350i	$0.763128\pi$
$762$	7.31439	−	2.37659i	0.264973	−	0.0860948i
$763$	−13.4750	−	41.4717i	−0.487827	−	1.50138i
$764$	2.95099	−	9.08220i	0.106763	−	0.328582i
$765$	1.71369	+	3.09787i	0.0619586	+	0.112004i
$766$	9.71532	+	29.9007i	0.351029	+	1.08036i
$767$	−8.66407	−	16.1070i	−0.312841	−	0.581589i
$768$	0.562081			0.0202824
$769$	5.56063	+	7.65355i	0.200522	+	0.275994i	0.897422	−	0.441174i	$-0.145438\pi$
$769$	5.56063	+	7.65355i	0.200522	+	0.275994i	−0.696900	+	0.717168i	$0.745438\pi$
$770$	28.8534	−	15.9612i	1.03980	−	0.575203i
$771$	2.68434	+	1.95028i	0.0966740	+	0.0702378i
$772$	6.33841	−	8.72408i	0.228124	−	0.313986i
$773$	−30.7770	−	10.0001i	−1.10697	−	0.359677i	−0.302190	−	0.953248i	$-0.597718\pi$
$773$	−30.7770	−	10.0001i	−1.10697	−	0.359677i	−0.804782	+	0.593570i	$0.797718\pi$
$774$			5.39827i			0.194037i
$775$	2.56190	−	10.2004i	0.0920263	−	0.366410i
$776$	−16.2292			−0.582595
$777$	−4.24117	+	13.0530i	−0.152151	+	0.468273i
$778$	−14.8107	+	20.3852i	−0.530990	+	0.730844i
$779$	46.3465	+	33.6727i	1.66054	+	1.20645i
$780$	4.52446	−	0.255084i	0.162002	−	0.00913346i
$781$	−17.8569	+	12.9738i	−0.638971	+	0.464239i
$782$		−	0.455791i		−	0.0162991i
$783$	7.34918	−	5.33949i	0.262638	−	0.190818i
$784$	−1.82351	−	5.61219i	−0.0651254	−	0.200435i
$785$	32.5768	+	15.2249i	1.16272	+	0.543402i
$786$	2.17808	+	0.707702i	0.0776897	+	0.0252429i
$787$	−36.2978	+	11.7939i	−1.29388	+	0.420406i	−0.873447	−	0.486920i	$-0.838120\pi$
$787$	−36.2978	+	11.7939i	−1.29388	+	0.420406i	−0.420429	+	0.907325i	$0.638120\pi$
$788$	7.77048	−	2.52478i	0.276812	−	0.0899417i
$789$	3.93549	−	12.1122i	0.140107	−	0.431205i
$790$	5.23537	+	27.0579i	0.186266	+	0.962678i
$791$	15.3643	−	4.99216i	0.546291	−	0.177501i
$792$	8.91505	−	6.47716i	0.316783	−	0.230156i
$793$	46.4897	+	6.30535i	1.65090	+	0.223910i
$794$	2.10777	−	1.53138i	0.0748020	−	0.0543468i
$795$	−1.19056	+	9.62781i	−0.0422247	+	0.341463i
$796$	−5.23879	−	3.80620i	−0.185684	−	0.134907i
$797$	−39.9663	−	29.0372i	−1.41568	−	1.02855i	−0.992466	−	0.122522i	$-0.960902\pi$
$797$	−39.9663	−	29.0372i	−1.41568	−	1.02855i	−0.423214	−	0.906030i	$-0.639098\pi$
$798$	−14.9266	−	4.84994i	−0.528395	−	0.171686i
$799$			2.02707i			0.0717126i
$800$	3.83575	−	3.20734i	0.135614	−	0.113397i
$801$		−	33.7917i		−	1.19397i
$802$	−9.52117	+	29.3032i	−0.336204	+	1.03473i
$803$	52.4650	+	38.1181i	1.85145	+	1.34516i
$804$	2.24676	−	3.09240i	0.0792372	−	0.109061i
$805$	−4.53506	−	4.23631i	−0.159840	−	0.149310i
$806$	−6.67910	+	3.59274i	−0.235261	+	0.126549i
$807$	2.10584			0.0741292
$808$	−6.24632	−	8.59733i	−0.219745	−	0.302453i
$809$	−2.20986	−	6.80124i	−0.0776945	−	0.239119i	0.904664	−	0.426125i	$-0.140122\pi$
$809$	−2.20986	−	6.80124i	−0.0776945	−	0.239119i	−0.982359	+	0.187006i	$0.940122\pi$
$810$	13.8840	+	1.71687i	0.487833	+	0.0603246i
$811$	−46.6523	−	15.1583i	−1.63818	−	0.532278i	−0.662052	−	0.749458i	$-0.730314\pi$
$811$	−46.6523	−	15.1583i	−1.63818	−	0.532278i	−0.976132	+	0.217180i	$0.930314\pi$
$812$	−9.71273	+	3.15586i	−0.340850	+	0.110749i
$813$	−3.69073	+	1.19919i	−0.129440	+	0.0420575i
$814$	26.5443	+	8.62478i	0.930378	+	0.302298i
$815$	−4.74181	−	0.586364i	−0.166099	−	0.0205394i
$816$	0.102457	+	0.315329i	0.00358670	+	0.0110387i
$817$	−9.19018	−	12.6492i	−0.321524	−	0.442539i
$818$	−27.3614			−0.956668
$819$	−16.4664	−	30.6120i	−0.575384	−	1.06967i
$820$	−12.0415	−	11.2482i	−0.420506	−	0.392806i
$821$	−3.96258	+	5.45403i	−0.138295	+	0.190347i	−0.872547	−	0.488530i	$-0.837533\pi$
$821$	−3.96258	+	5.45403i	−0.138295	+	0.190347i	0.734252	+	0.678877i	$0.237533\pi$
$822$	−6.17879	−	4.48915i	−0.215510	−	0.156577i
$823$	−15.6933	+	48.2990i	−0.547034	+	1.68360i	0.169071	+	0.985604i	$0.445923\pi$
$823$	−15.6933	+	48.2990i	−0.547034	+	1.68360i	−0.716104	+	0.697993i	$0.754077\pi$
$824$		−	5.39547i		−	0.187960i
$825$	−2.81063	+	11.1908i	−0.0978537	+	0.389612i
$826$		−	18.2196i		−	0.633941i
$827$	−10.3572	−	3.36526i	−0.360155	−	0.117021i	0.123350	−	0.992363i	$-0.460636\pi$
$827$	−10.3572	−	3.36526i	−0.360155	−	0.117021i	−0.483505	+	0.875342i	$0.660636\pi$
$828$	−1.67787	−	1.21904i	−0.0583100	−	0.0423647i
$829$	−18.2199	−	13.2375i	−0.632802	−	0.459758i	0.224568	−	0.974458i	$-0.427903\pi$
$829$	−18.2199	−	13.2375i	−0.632802	−	0.459758i	−0.857370	+	0.514701i	$0.827903\pi$
$830$	1.59423	−	12.8922i	0.0553365	−	0.447496i
$831$	−6.59797	+	4.79371i	−0.228881	+	0.166292i
$832$	−3.57284	−	0.484581i	−0.123866	−	0.0167998i
$833$	2.81606	−	2.04599i	0.0975707	−	0.0708893i
$834$	0.670190	−	0.217758i	0.0232068	−	0.00754034i
$835$	9.39190	+	48.5401i	0.325020	+	1.67980i
$836$	−9.86277	+	30.3545i	−0.341111	+	1.04983i
$837$	6.39139	−	2.07669i	0.220919	−	0.0717808i
$838$	−34.8321	+	11.3176i	−1.20325	+	0.390961i
$839$	33.7375	+	10.9620i	1.16475	+	0.378449i	0.826680	−	0.562673i	$-0.190227\pi$
$839$	33.7375	+	10.9620i	1.16475	+	0.378449i	0.338067	+	0.941122i	$0.390227\pi$
$840$	4.08975	+	1.91137i	0.141110	+	0.0659485i
$841$	−6.46328	−	19.8919i	−0.222872	−	0.685929i
$842$	9.71055	−	7.05513i	0.334648	−	0.243136i
$843$		−	5.37493i		−	0.185122i
$844$	−5.55960	+	4.03929i	−0.191369	+	0.139038i
$845$	−28.9794	−	2.27919i	−0.996921	−	0.0784067i
$846$	7.46210	+	5.42153i	0.256552	+	0.186396i
$847$	12.3626	−	17.0156i	0.424783	−	0.584663i
$848$	2.38518	−	7.34083i	0.0819075	−	0.252085i
$849$	−11.3916			−0.390960
$850$	2.49851	+	1.56723i	0.0856981	+	0.0537554i
$851$		−	5.25291i		−	0.180067i
$852$	−2.87396	−	0.933806i	−0.0984603	−	0.0319917i
$853$	12.3986	−	17.0652i	0.424519	−	0.584300i	−0.542165	−	0.840272i	$-0.682395\pi$
$853$	12.3986	−	17.0652i	0.424519	−	0.584300i	0.966684	+	0.255972i	$0.0823954\pi$
$854$	37.8105	+	27.4709i	1.29385	+	0.940036i
$855$	−40.8270	+	22.5849i	−1.39625	+	0.772387i
$856$	−5.83953	−	8.03742i	−0.199591	−	0.274713i
$857$	1.67189			0.0571107			0.0285554	−	0.999592i	$-0.490909\pi$
$857$	1.67189			0.0571107			0.0285554	+	0.999592i	$0.490909\pi$
$858$	7.32756	−	3.94155i	0.250159	−	0.134562i
$859$	11.6002	+	35.7018i	0.395794	+	1.21813i	0.928342	+	0.371728i	$0.121235\pi$
$859$	11.6002	+	35.7018i	0.395794	+	1.21813i	−0.532548	+	0.846400i	$0.678765\pi$
$860$	2.17692	+	3.93526i	0.0742325	+	0.134191i
$861$	4.59737	−	14.1492i	0.156678	−	0.482205i
$862$	1.95773	+	6.02528i	0.0666807	+	0.205222i
$863$	−17.1527	+	5.57325i	−0.583885	+	0.189716i	−0.586040	−	0.810282i	$-0.699314\pi$
$863$	−17.1527	+	5.57325i	−0.583885	+	0.189716i	0.00215548	+	0.999998i	$0.499314\pi$
$864$	3.03854	+	0.987280i	0.103373	+	0.0335879i
$865$	−25.2190	+	26.9975i	−0.857472	+	0.917941i
$866$	−32.9184	+	10.6958i	−1.11861	+	0.363459i
$867$	7.57224	−	5.50155i	0.257167	−	0.186843i
$868$	−7.55514			−0.256438
$869$	29.7428	+	40.9375i	1.00896	+	1.38871i
$870$	1.51306	−	3.23749i	0.0512975	−	0.109761i
$871$	−16.9474	+	17.7197i	−0.574242	+	0.600410i
$872$	−9.82181	−	7.13596i	−0.332609	−	0.241654i
$873$	−41.4283	−	13.4609i	−1.40213	−	0.455581i
$874$	6.00691			0.203187
$875$	38.8159	−	10.2934i	1.31222	−	0.347979i
$876$			8.87846i			0.299976i
$877$	−22.7778	−	7.40095i	−0.769152	−	0.249912i	−0.101950	−	0.994790i	$-0.532508\pi$
$877$	−22.7778	−	7.40095i	−0.769152	−	0.249912i	−0.667202	+	0.744877i	$0.732508\pi$
$878$	18.3132	−	25.2060i	0.618042	−	0.850662i
$879$	2.50428	−	3.44685i	0.0844673	−	0.116259i
$880$	3.88693	−	8.31686i	0.131028	−	0.280361i
$881$	−26.1901	+	19.0282i	−0.882368	+	0.641078i	−0.933877	−	0.357595i	$-0.883597\pi$
$881$	−26.1901	+	19.0282i	−0.882368	+	0.641078i	0.0515092	+	0.998673i	$0.483597\pi$
$882$		−	15.8387i		−	0.533316i
$883$	−22.3376	+	16.2292i	−0.751722	+	0.546158i	−0.896360	−	0.443327i	$-0.853798\pi$
$883$	−22.3376	+	16.2292i	−0.751722	+	0.546158i	0.144638	+	0.989485i	$0.453798\pi$
$884$	−0.379409	−	2.09270i	−0.0127609	−	0.0703851i
$885$	4.65897	+	4.35206i	0.156609	+	0.146293i
$886$	14.9701	+	4.86407i	0.502929	+	0.163411i
$887$	−1.66209	−	5.11540i	−0.0558077	−	0.171758i	0.919267	−	0.393634i	$-0.128782\pi$
$887$	−1.66209	−	5.11540i	−0.0558077	−	0.171758i	−0.975075	+	0.221875i	$0.928782\pi$
$888$	1.18079	+	3.63411i	0.0396248	+	0.121953i
$889$	−46.7403	−	15.1868i	−1.56762	−	0.509350i
$890$	−13.6269	−	24.6336i	−0.456776	−	0.825721i
$891$	24.4289	−	7.93743i	0.818399	−	0.265914i
$892$	14.3228	+	19.7137i	0.479564	+	0.660064i
$893$	−26.7149			−0.893981
$894$	−5.18706	+	3.76862i	−0.173481	+	0.126042i
$895$	−0.278126	−	0.502772i	−0.00929672	−	0.0168058i
$896$	−2.90582	−	2.11121i	−0.0970768	−	0.0705304i
$897$	−1.13168	−	1.08236i	−0.0377857	−	0.0361389i
$898$	6.09234	−	18.7503i	0.203304	−	0.625706i
$899$			5.98073i			0.199468i
$900$	12.4517	−	5.00592i	0.415058	−	0.166864i
$901$	4.55300			0.151682
$902$	−28.7737	−	9.34914i	−0.958059	−	0.311292i
$903$	−2.38666	+	3.28496i	−0.0794232	+	0.109317i
$904$	2.64371	−	3.63875i	0.0879283	−	0.121023i
$905$	47.9641	−	9.28046i	1.59438	−	0.308493i
$906$	−5.58717	+	4.05932i	−0.185621	+	0.134862i
$907$	−12.2279			−0.406022			−0.203011	−	0.979176i	$-0.565073\pi$
$907$	−12.2279			−0.406022			−0.203011	+	0.979176i	$0.565073\pi$
$908$	−11.1543	−	15.3525i	−0.370167	−	0.509492i
$909$	−8.81416	−	27.1272i	−0.292347	−	0.899753i
$910$	−24.3485	−	15.6754i	−0.807144	−	0.519634i
$911$	17.5632	−	54.0539i	0.581895	−	1.79089i	−0.0295044	−	0.999565i	$-0.509393\pi$
$911$	17.5632	−	54.0539i	0.581895	−	1.79089i	0.611399	−	0.791323i	$-0.290607\pi$
$912$	−4.15574	+	1.35028i	−0.137610	+	0.0447123i
$913$	−7.37045	−	22.6839i	−0.243926	−	0.750728i
$914$	5.46303	−	16.8135i	0.180701	−	0.556141i
$915$	−16.0563	+	3.10670i	−0.530806	+	0.102704i
$916$	−15.4643	+	5.02466i	−0.510955	+	0.166019i
$917$	−8.60201	−	11.8396i	−0.284063	−	0.390980i
$918$			1.88459i			0.0622007i
$919$	34.3086	−	24.9267i	1.13174	−	0.822255i	0.145790	−	0.989316i	$-0.453428\pi$
$919$	34.3086	−	24.9267i	1.13174	−	0.822255i	0.985947	+	0.167061i	$0.0534276\pi$
$920$	−1.71474	−	0.212041i	−0.0565332	−	0.00699079i
$921$	1.54811	−	2.13079i	0.0510121	−	0.0702121i
$922$	3.14175	+	2.28261i	0.103468	+	0.0751738i
$923$	17.4631	+	8.41339i	0.574806	+	0.276930i
$924$	8.28865			0.272677
$925$	28.7948	+	18.0620i	0.946769	+	0.593875i
$926$	14.6469			0.481327
$927$	4.47512	−	13.7730i	0.146982	−	0.452365i
$928$	−1.67125	+	2.30028i	−0.0548616	+	0.0755104i
$929$	31.4389	−	43.2719i	1.03148	−	1.41971i	0.127644	−	0.991820i	$-0.459259\pi$
$929$	31.4389	−	43.2719i	1.03148	−	1.41971i	0.903833	−	0.427886i	$-0.140741\pi$
$930$	1.80467	−	1.93194i	0.0591775	−	0.0633508i
$931$	26.9642	+	37.1131i	0.883717	+	1.21633i
$932$	−11.8988			−0.389759
$933$	−5.35617	+	3.89149i	−0.175353	+	0.127402i
$934$	−22.4989	+	7.31033i	−0.736186	+	0.239201i
$935$	5.37429	+	0.664575i	0.175758	+	0.0217339i
$936$	−8.71846	−	4.20038i	−0.284972	−	0.137294i
$937$	8.10809	+	24.9541i	0.264880	+	0.815216i	0.991721	+	0.128410i	$0.0409875\pi$
$937$	8.10809	+	24.9541i	0.264880	+	0.815216i	−0.726841	+	0.686805i	$0.759013\pi$
$938$	−23.2304	+	7.54803i	−0.758501	+	0.246452i
$939$	−2.88217	+	8.87041i	−0.0940561	+	0.289475i
$940$	7.62606	+	0.943024i	0.248735	+	0.0307581i
$941$	45.4028	−	14.7523i	1.48009	−	0.480910i	0.545949	−	0.837818i	$-0.316169\pi$
$941$	45.4028	−	14.7523i	1.48009	−	0.480910i	0.934139	+	0.356908i	$0.116169\pi$
$942$	5.31300	+	7.31272i	0.173107	+	0.238261i
$943$			5.69408i			0.185425i
$944$	−2.98157	−	4.10379i	−0.0970420	−	0.133567i
$945$	18.7514	+	17.5161i	0.609983	+	0.569800i
$946$	6.68025	+	4.85349i	0.217194	+	0.157800i
$947$	9.98757	−	13.7467i	0.324552	−	0.446708i	−0.615298	−	0.788295i	$-0.710964\pi$
$947$	9.98757	−	13.7467i	0.324552	−	0.446708i	0.939850	+	0.341587i	$0.110964\pi$
$948$	−2.14078	+	6.58864i	−0.0695293	+	0.213989i
$949$	7.65429	−	56.4355i	0.248469	−	1.83197i
$950$	−20.6546	+	32.9280i	−0.670124	+	1.06833i
$951$		−	17.8839i		−	0.579926i
$952$	0.654715	−	2.01501i	0.0212194	−	0.0653067i
$953$	11.1768	+	8.12043i	0.362053	+	0.263047i	0.753908	−	0.656980i	$-0.228167\pi$
$953$	11.1768	+	8.12043i	0.362053	+	0.263047i	−0.391855	+	0.920027i	$0.628167\pi$
$954$	12.1773	−	16.7606i	0.394254	−	0.542645i
$955$	2.62058	−	21.1921i	0.0847999	−	0.685761i
$956$	−12.5865	−	17.3238i	−0.407076	−	0.560292i
$957$		−	6.56139i		−	0.212100i
$958$	−8.74637	+	6.35461i	−0.282582	+	0.205308i
$959$	15.0814	+	46.4157i	0.487003	+	1.49884i
$960$	1.23397	−	0.238757i	0.0398261	−	0.00770584i
$961$	8.21229	−	25.2748i	0.264913	−	0.815317i
$962$	−4.37262	−	24.1180i	−0.140979	−	0.777595i
$963$	−8.24014	−	25.3605i	−0.265535	−	0.817232i
$964$	−4.96839	−	1.61433i	−0.160021	−	0.0519940i
$965$	10.2093	−	21.8448i	0.328649	−	0.703209i
$966$	−0.482059	−	1.48363i	−0.0155100	−	0.0477349i
$967$	4.84945	+	6.67470i	0.155948	+	0.214644i	0.879841	−	0.475269i	$-0.157649\pi$
$967$	4.84945	+	6.67470i	0.155948	+	0.214644i	−0.723893	+	0.689912i	$0.757649\pi$
$968$		−	5.85569i		−	0.188209i
$969$	−1.51502	−	2.08525i	−0.0486696	−	0.0669879i
$970$	−35.6288	+	6.89373i	−1.14397	+	0.221344i
$971$	7.24888	+	5.26662i	0.232628	+	0.169014i	0.697993	−	0.716105i	$-0.254077\pi$
$971$	7.24888	+	5.26662i	0.232628	+	0.169014i	−0.465365	+	0.885119i	$0.654077\pi$
$972$	10.5992	+	7.70076i	0.339969	+	0.247002i
$973$	−4.28263	−	1.39151i	−0.137295	−	0.0446098i
$974$	−1.89111			−0.0605951
$975$	9.82442	−	2.48187i	0.314633	−	0.0794833i
$976$	13.0120			0.416503
$977$	−5.05994	−	1.64407i	−0.161882	−	0.0525986i	0.226955	−	0.973905i	$-0.427123\pi$
$977$	−5.05994	−	1.64407i	−0.161882	−	0.0525986i	−0.388837	+	0.921307i	$0.627123\pi$
$978$	−0.971654	−	0.705948i	−0.0310701	−	0.0225737i
$979$	−41.8165	−	30.3815i	−1.33646	−	0.970997i
$980$	−6.38716	−	11.5462i	−0.204030	−	0.368828i
$981$	−19.1534	−	26.3624i	−0.611521	−	0.841686i
$982$			42.2568i			1.34847i
$983$	−5.21987	−	7.18454i	−0.166488	−	0.229151i	0.717619	−	0.696436i	$-0.245232\pi$
$983$	−5.21987	−	7.18454i	−0.166488	−	0.229151i	−0.884107	+	0.467285i	$0.845232\pi$
$984$	−1.27996	−	3.93932i	−0.0408037	−	0.125581i
$985$	15.9865	−	8.84348i	0.509372	−	0.281777i
$986$	−1.59510	−	0.518280i	−0.0507983	−	0.0165054i
$987$	2.14390	+	6.59823i	0.0682409	+	0.210024i
$988$	27.5799	−	5.00026i	0.877433	−	0.159079i
$989$	0.480233	−	1.47800i	0.0152705	−	0.0469978i
$990$	16.8203	−	18.0065i	0.534586	−	0.572285i
$991$	5.70485	+	17.5577i	0.181220	+	0.557739i	0.999863	−	0.0165644i	$-0.00527286\pi$
$991$	5.70485	+	17.5577i	0.181220	+	0.557739i	−0.818642	+	0.574304i	$0.805273\pi$
$992$	−1.70172	+	1.23637i	−0.0540297	+	0.0392549i
$993$		−	5.79121i		−	0.183778i
$994$	11.3503	+	15.6223i	0.360009	+	0.495509i
$995$	−13.1178	−	6.13066i	−0.415861	−	0.194355i
$996$	1.91936	−	2.64177i	0.0608172	−	0.0837077i
$997$	15.1543	+	11.0102i	0.479941	+	0.348698i	0.801303	−	0.598259i	$-0.204141\pi$
$997$	15.1543	+	11.0102i	0.479941	+	0.348698i	−0.321362	+	0.946956i	$0.604141\pi$
$998$	9.94188	−	30.5980i	0.314705	−	0.968561i
$999$			21.7195i			0.687175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.p.a.571.8	yes	136
13.12	even	2	inner	650.2.p.a.571.25	yes	136
25.6	even	5	inner	650.2.p.a.181.25	yes	136
325.181	even	10	inner	650.2.p.a.181.8	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.p.a.181.8	✓	136	325.181	even	10	inner
650.2.p.a.181.25	yes	136	25.6	even	5	inner
650.2.p.a.571.8	yes	136	1.1	even	1	trivial
650.2.p.a.571.25	yes	136	13.12	even	2	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.454733 - 0.330383i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02575 + 0.946747i) q^{5} +(0.330383 + 0.454733i) q^{6} -3.59180i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.829422 - 2.55270i) q^{9} +O(q^{10})\)	\(q+(-0.951057 - 0.309017i) q^{2} +(-0.454733 - 0.330383i) q^{3} +(0.809017 + 0.587785i) q^{4} +(2.02575 + 0.946747i) q^{5} +(0.330383 + 0.454733i) q^{6} -3.59180i q^{7} +(-0.587785 - 0.809017i) q^{8} +(-0.829422 - 2.55270i) q^{9} +(-1.63404 - 1.52640i) q^{10} +(-3.90463 - 1.26869i) q^{11} +(-0.173693 - 0.534571i) q^{12} +(0.643204 + 3.54772i) q^{13} +(-1.10993 + 3.41600i) q^{14} +(-0.608388 - 1.09979i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.477217 + 0.346718i) q^{17} +2.68406i q^{18} +(-4.56943 - 6.28928i) q^{19} +(1.08238 + 1.95664i) q^{20} +(-1.18667 + 1.63331i) q^{21} +(3.32147 + 2.41319i) q^{22} +(0.238776 - 0.734876i) q^{23} +0.562081i q^{24} +(3.20734 + 3.83575i) q^{25} +(0.484581 - 3.57284i) q^{26} +(-0.987280 + 3.03854i) q^{27} +(2.11121 - 2.90582i) q^{28} +(-2.30028 - 1.67125i) q^{29} +(0.238757 + 1.23397i) q^{30} +(-1.23637 - 1.70172i) q^{31} -1.00000i q^{32} +(1.35641 + 1.86694i) q^{33} +(0.561002 - 0.182281i) q^{34} +(3.40052 - 7.27609i) q^{35} +(0.829422 - 2.55270i) q^{36} +(6.46545 - 2.10075i) q^{37} +(2.40229 + 7.39349i) q^{38} +(0.879619 - 1.82577i) q^{39} +(-0.424773 - 2.19535i) q^{40} +(-7.00845 + 2.27718i) q^{41} +(1.63331 - 1.18667i) q^{42} +2.01123 q^{43} +(-2.41319 - 3.32147i) q^{44} +(0.736555 - 5.95638i) q^{45} +(-0.454178 + 0.625122i) q^{46} +(2.01990 - 2.78015i) q^{47} +(0.173693 - 0.534571i) q^{48} -5.90101 q^{49} +(-1.86505 - 4.63914i) q^{50} +0.331556 q^{51} +(-1.56493 + 3.24823i) q^{52} +(-6.24449 - 4.53689i) q^{53} +(1.87792 - 2.58473i) q^{54} +(-6.70868 - 6.26674i) q^{55} +(-2.90582 + 2.11121i) q^{56} +4.36961i q^{57} +(1.67125 + 2.30028i) q^{58} +(-4.82429 + 1.56751i) q^{59} +(0.154245 - 1.24735i) q^{60} +(4.02092 - 12.3751i) q^{61} +(0.650000 + 2.00049i) q^{62} +(-9.16877 + 2.97911i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.05582 + 7.79574i) q^{65} +(-0.713107 - 2.19472i) q^{66} +(3.99722 + 5.50170i) q^{67} -0.589873 q^{68} +(-0.351370 + 0.255285i) q^{69} +(-5.48252 + 5.86915i) q^{70} +(3.16005 - 4.34944i) q^{71} +(-1.57765 + 2.17145i) q^{72} +(-15.0226 - 4.88114i) q^{73} -6.79817 q^{74} +(-0.191219 - 2.80389i) q^{75} -7.77398i q^{76} +(-4.55688 + 14.0246i) q^{77} +(-1.40076 + 1.46459i) q^{78} +(-9.97122 - 7.24451i) q^{79} +(-0.274418 + 2.21917i) q^{80} +(-5.06153 + 3.67742i) q^{81} +7.36912 q^{82} +(3.41474 + 4.69998i) q^{83} +(-1.92007 + 0.623869i) q^{84} +(-1.29498 + 0.250562i) q^{85} +(-1.91279 - 0.621504i) q^{86} +(0.493861 + 1.51995i) q^{87} +(1.26869 + 3.90463i) q^{88} +(11.9736 + 3.89045i) q^{89} +(-2.54113 + 5.43725i) q^{90} +(12.7427 - 2.31026i) q^{91} +(0.625122 - 0.454178i) q^{92} +1.18231i q^{93} +(-2.78015 + 2.01990i) q^{94} +(-3.30218 - 17.0666i) q^{95} +(-0.330383 + 0.454733i) q^{96} +(9.53929 - 13.1297i) q^{97} +(5.61219 + 1.82351i) q^{98} +11.0196i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) \) 136 * q + 34 * q^4 - 30 * q^9	\( 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) \) 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more