LMFDB - Embedded newform 504.2.be.a.139.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(139,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 2, 3]))

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

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

chi := DirichletCharacter("504.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.be (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.10
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37416 - 0.334195i) q^{2} +(0.522528 + 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(0.649625 - 1.12518i) q^{5} +(-0.166162 - 2.44385i) q^{6} +(-2.40071 - 1.11203i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +O(q^{10})$	\(q+(-1.37416 - 0.334195i) q^{2} +(0.522528 + 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(0.649625 - 1.12518i) q^{5} +(-0.166162 - 2.44385i) q^{6} +(-2.40071 - 1.11203i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +(-1.26872 + 1.32908i) q^{10} +(-0.163051 - 0.282412i) q^{11} +(-0.588389 + 3.41377i) q^{12} +(-1.97132 + 3.41442i) q^{13} +(2.92732 + 2.33041i) q^{14} +(2.19752 + 0.484820i) q^{15} +(2.31281 + 3.26358i) q^{16} +4.98494i q^{17} +(3.94883 - 1.55137i) q^{18} +7.44404i q^{19} +(2.18760 - 1.40237i) q^{20} +(0.581909 - 4.54548i) q^{21} +(0.129677 + 0.442570i) q^{22} +(-6.16892 - 3.56163i) q^{23} +(1.94941 - 4.49442i) q^{24} +(1.65597 + 2.86823i) q^{25} +(3.84998 - 4.03315i) q^{26} +(-4.13208 - 3.15055i) q^{27} +(-3.24379 - 4.18065i) q^{28} +(4.79832 - 2.77031i) q^{29} +(-2.85772 - 1.40062i) q^{30} +(-2.50090 + 4.33168i) q^{31} +(-2.08749 - 5.25760i) q^{32} +(0.381163 - 0.416822i) q^{33} +(1.66595 - 6.85011i) q^{34} +(-2.81079 + 1.97884i) q^{35} +(-5.94478 + 0.812149i) q^{36} +8.21594i q^{37} +(2.48777 - 10.2293i) q^{38} +(-6.66848 - 1.47121i) q^{39} +(-3.47477 + 1.19599i) q^{40} +(0.0851599 + 0.0491671i) q^{41} +(-2.31871 + 6.05174i) q^{42} +(-5.21931 - 9.04011i) q^{43} +(-0.0302917 - 0.651499i) q^{44} +(0.347657 + 3.88222i) q^{45} +(7.28680 + 6.95587i) q^{46} +(3.42326 + 5.92926i) q^{47} +(-4.18081 + 5.52457i) q^{48} +(4.52680 + 5.33930i) q^{49} +(-1.31702 - 4.49483i) q^{50} +(-8.23190 + 2.60477i) q^{51} +(-6.63835 + 4.25554i) q^{52} -5.36803i q^{53} +(4.62523 + 5.71027i) q^{54} -0.423687 q^{55} +(3.06034 + 6.82893i) q^{56} +(-12.2927 + 3.88972i) q^{57} +(-7.51948 + 2.20327i) q^{58} +(-1.56024 - 0.900803i) q^{59} +(3.45888 + 2.87971i) q^{60} +(-2.25943 - 3.91345i) q^{61} +(4.88425 - 5.11663i) q^{62} +(7.81025 - 1.41420i) q^{63} +(1.11148 + 7.92241i) q^{64} +(2.56123 + 4.43618i) q^{65} +(-0.663079 + 0.445397i) q^{66} +(7.10542 - 12.3069i) q^{67} +(-4.57855 + 8.85639i) q^{68} +(2.65807 - 12.0481i) q^{69} +(4.52380 - 1.77988i) q^{70} +11.5897i q^{71} +(8.44049 + 0.870695i) q^{72} +4.09140i q^{73} +(2.74573 - 11.2900i) q^{74} +(-3.87117 + 4.23333i) q^{75} +(-6.83717 + 13.2253i) q^{76} +(0.0773877 + 0.859306i) q^{77} +(8.67188 + 4.25025i) q^{78} +(-3.80798 + 2.19854i) q^{79} +(5.17458 - 0.482231i) q^{80} +(3.04354 - 8.46976i) q^{81} +(-0.100592 - 0.0960235i) q^{82} +(-3.78385 + 2.18461i) q^{83} +(5.20875 - 7.54115i) q^{84} +(5.60898 + 3.23835i) q^{85} +(4.15100 + 14.1668i) q^{86} +(7.08201 + 6.47615i) q^{87} +(-0.176102 + 0.905387i) q^{88} -3.24378i q^{89} +(0.819682 - 5.45097i) q^{90} +(8.52947 - 6.00487i) q^{91} +(-7.68860 - 11.9937i) q^{92} +(-8.45991 - 1.86644i) q^{93} +(-2.72257 - 9.29178i) q^{94} +(8.37592 + 4.83584i) q^{95} +(7.59138 - 6.19443i) q^{96} +(3.39365 - 1.95932i) q^{97} +(-4.43617 - 8.84988i) q^{98} +(0.887489 + 0.411634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	$ 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) $ 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.37416	−	0.334195i	−0.971677	−	0.236312i
$2$	−1.37416	−	0.334195i	−0.971677	−	0.236312i
$3$	0.522528	+	1.65135i	0.301682	+	0.953409i
$3$	0.522528	+	1.65135i	0.301682	+	0.953409i
$4$	1.77663	+	0.918475i	0.888313	+	0.459238i
$5$	0.649625	−	1.12518i	0.290521	−	0.503197i	−0.683412	−	0.730033i	$-0.739505\pi$
$5$	0.649625	−	1.12518i	0.290521	−	0.503197i	0.973933	+	0.226836i	$0.0728380\pi$
$6$	−0.166162	−	2.44385i	−0.0678354	−	0.997697i
$7$	−2.40071	−	1.11203i	−0.907382	−	0.420306i
$7$	−2.40071	−	1.11203i	−0.907382	−	0.420306i
$8$	−2.13442	−	1.85587i	−0.754631	−	0.656150i
$9$	−2.45393	+	1.72576i	−0.817976	+	0.575252i
$10$	−1.26872	+	1.32908i	−0.401204	+	0.420292i
$11$	−0.163051	−	0.282412i	−0.0491616	−	0.0851505i	0.840397	−	0.541971i	$-0.182322\pi$
$11$	−0.163051	−	0.282412i	−0.0491616	−	0.0851505i	−0.889559	+	0.456820i	$0.848988\pi$
$12$	−0.588389	+	3.41377i	−0.169853	+	0.985469i
$13$	−1.97132	+	3.41442i	−0.546745	+	0.946989i	0.451750	+	0.892144i	$0.350800\pi$
$13$	−1.97132	+	3.41442i	−0.546745	+	0.946989i	−0.998495	+	0.0548450i	$0.982534\pi$
$14$	2.92732	+	2.33041i	0.782360	+	0.622827i
$15$	2.19752	+	0.484820i	0.567398	+	0.125180i
$16$	2.31281	+	3.26358i	0.578202	+	0.815894i
$17$			4.98494i			1.20903i	0.796595	+	0.604513i	$0.206632\pi$
$17$			4.98494i			1.20903i	−0.796595	+	0.604513i	$0.793368\pi$
$18$	3.94883	−	1.55137i	0.930748	−	0.365661i
$19$			7.44404i			1.70778i	0.520453	+	0.853890i	$0.325763\pi$
$19$			7.44404i			1.70778i	−0.520453	+	0.853890i	$0.674237\pi$
$20$	2.18760	−	1.40237i	0.489161	−	0.313579i
$21$	0.581909	−	4.54548i	0.126983	−	0.991905i
$22$	0.129677	+	0.442570i	0.0276472	+	0.0943562i
$23$	−6.16892	−	3.56163i	−1.28631	−	0.742651i	−0.308315	−	0.951284i	$-0.599765\pi$
$23$	−6.16892	−	3.56163i	−1.28631	−	0.742651i	−0.977994	+	0.208633i	$0.933098\pi$
$24$	1.94941	−	4.49442i	0.397921	−	0.917420i
$25$	1.65597	+	2.86823i	0.331195	+	0.573646i
$26$	3.84998	−	4.03315i	0.755044	−	0.790966i
$27$	−4.13208	−	3.15055i	−0.795218	−	0.606323i
$28$	−3.24379	−	4.18065i	−0.613020	−	0.790068i
$29$	4.79832	−	2.77031i	0.891025	−	0.514434i	0.0167476	−	0.999860i	$-0.494669\pi$
$29$	4.79832	−	2.77031i	0.891025	−	0.514434i	0.874278	+	0.485426i	$0.161335\pi$
$30$	−2.85772	−	1.40062i	−0.521746	−	0.255717i
$31$	−2.50090	+	4.33168i	−0.449174	+	0.777992i	−0.998332	−	0.0577260i	$-0.981615\pi$
$31$	−2.50090	+	4.33168i	−0.449174	+	0.777992i	0.549158	+	0.835718i	$0.314948\pi$
$32$	−2.08749	−	5.25760i	−0.369020	−	0.929421i
$33$	0.381163	−	0.416822i	0.0663520	−	0.0725595i
$34$	1.66595	−	6.85011i	0.285707	−	1.17478i
$35$	−2.81079	+	1.97884i	−0.475111	+	0.334485i
$36$	−5.94478	+	0.812149i	−0.990797	+	0.135358i
$37$			8.21594i			1.35069i	0.737501	+	0.675346i	$0.236006\pi$
$37$			8.21594i			1.35069i	−0.737501	+	0.675346i	$0.763994\pi$
$38$	2.48777	−	10.2293i	0.403569	−	1.65941i
$39$	−6.66848	−	1.47121i	−1.06781	−	0.235582i
$40$	−3.47477	+	1.19599i	−0.549409	+	0.189103i
$41$	0.0851599	+	0.0491671i	0.0132997	+	0.00767861i	0.506635	−	0.862161i	$-0.330889\pi$
$41$	0.0851599	+	0.0491671i	0.0132997	+	0.00767861i	−0.493335	+	0.869839i	$0.664222\pi$
$42$	−2.31871	+	6.05174i	−0.357785	+	0.933804i
$43$	−5.21931	−	9.04011i	−0.795937	−	1.37860i	−0.922242	−	0.386612i	$-0.873645\pi$
$43$	−5.21931	−	9.04011i	−0.795937	−	1.37860i	0.126305	−	0.991991i	$-0.459688\pi$
$44$	−0.0302917	−	0.651499i	−0.00456665	−	0.0982172i
$45$	0.347657	+	3.88222i	0.0518257	+	0.578727i
$46$	7.28680	+	6.95587i	1.07438	+	1.02559i
$47$	3.42326	+	5.92926i	0.499333	+	0.864871i	1.00000		0.000769517i	$-0.000244945\pi$
$47$	3.42326	+	5.92926i	0.499333	+	0.864871i	−0.500666	+	0.865640i	$0.666912\pi$
$48$	−4.18081	+	5.52457i	−0.603448	+	0.797403i
$49$	4.52680	+	5.33930i	0.646685	+	0.762757i
$50$	−1.31702	−	4.49483i	−0.186255	−	0.635664i
$51$	−8.23190	+	2.60477i	−1.15270	+	0.364741i
$52$	−6.63835	+	4.25554i	−0.920574	+	0.590138i
$53$		−	5.36803i		−	0.737356i	−0.929557	−	0.368678i	$-0.879811\pi$
$53$		−	5.36803i		−	0.737356i	0.929557	−	0.368678i	$-0.120189\pi$
$54$	4.62523	+	5.71027i	0.629414	+	0.777070i
$55$	−0.423687			−0.0571300
$56$	3.06034	+	6.82893i	0.408955	+	0.912555i
$57$	−12.2927	+	3.88972i	−1.62821	+	0.515206i
$58$	−7.51948	+	2.20327i	−0.987356	+	0.289304i
$59$	−1.56024	−	0.900803i	−0.203125	−	0.117275i	0.394987	−	0.918687i	$-0.370749\pi$
$59$	−1.56024	−	0.900803i	−0.203125	−	0.117275i	−0.598112	+	0.801412i	$0.704082\pi$
$60$	3.45888	+	2.87971i	0.446540	+	0.371770i
$61$	−2.25943	−	3.91345i	−0.289291	−	0.501066i	0.684350	−	0.729154i	$-0.260086\pi$
$61$	−2.25943	−	3.91345i	−0.289291	−	0.501066i	−0.973641	+	0.228088i	$0.926753\pi$
$62$	4.88425	−	5.11663i	0.620301	−	0.649812i
$63$	7.81025	−	1.41420i	0.983999	−	0.178173i
$64$	1.11148	+	7.92241i	0.138935	+	0.990301i
$65$	2.56123	+	4.43618i	0.317682	+	0.550241i
$66$	−0.663079	+	0.445397i	−0.0816194	+	0.0548246i
$67$	7.10542	−	12.3069i	0.868065	−	1.50353i	0.00409390	−	0.999992i	$-0.498697\pi$
$67$	7.10542	−	12.3069i	0.868065	−	1.50353i	0.863971	−	0.503541i	$-0.167970\pi$
$68$	−4.57855	+	8.85639i	−0.555231	+	1.07399i
$69$	2.65807	−	12.0481i	0.319994	−	1.45042i
$70$	4.52380	−	1.77988i	0.540697	−	0.212737i
$71$			11.5897i			1.37545i	0.725973	+	0.687723i	$0.241390\pi$
$71$			11.5897i			1.37545i	−0.725973	+	0.687723i	$0.758610\pi$
$72$	8.44049	+	0.870695i	0.994721	+	0.102612i
$73$			4.09140i			0.478862i	0.970913	+	0.239431i	$0.0769608\pi$
$73$			4.09140i			0.478862i	−0.970913	+	0.239431i	$0.923039\pi$
$74$	2.74573	−	11.2900i	0.319184	−	1.31244i
$75$	−3.87117	+	4.23333i	−0.447004	+	0.488823i
$76$	−6.83717	+	13.2253i	−0.784277	+	1.51704i
$77$	0.0773877	+	0.859306i	0.00881914	+	0.0979270i
$78$	8.67188	+	4.25025i	0.981897	+	0.481246i
$79$	−3.80798	+	2.19854i	−0.428431	+	0.247355i	−0.698678	−	0.715436i	$-0.746228\pi$
$79$	−3.80798	+	2.19854i	−0.428431	+	0.247355i	0.270247	+	0.962791i	$0.412895\pi$
$80$	5.17458	−	0.482231i	0.578536	−	0.0539151i
$81$	3.04354	−	8.46976i	0.338171	−	0.941085i
$82$	−0.100592	−	0.0960235i	−0.0111085	−	0.0106040i
$83$	−3.78385	+	2.18461i	−0.415332	+	0.239792i	−0.693078	−	0.720863i	$-0.743746\pi$
$83$	−3.78385	+	2.18461i	−0.415332	+	0.239792i	0.277746	+	0.960654i	$0.410413\pi$
$84$	5.20875	−	7.54115i	0.568321	−	0.822807i
$85$	5.60898	+	3.23835i	0.608379	+	0.351248i
$86$	4.15100	+	14.1668i	0.447614	+	1.52765i
$87$	7.08201	+	6.47615i	0.759272	+	0.694316i
$88$	−0.176102	+	0.905387i	−0.0187726	+	0.0965145i
$89$		−	3.24378i		−	0.343840i	−0.985111	−	0.171920i	$-0.945003\pi$
$89$		−	3.24378i		−	0.343840i	0.985111	−	0.171920i	$-0.0549970\pi$
$90$	0.819682	−	5.45097i	0.0864021	−	0.574582i
$91$	8.52947	−	6.00487i	0.894132	−	0.629481i
$92$	−7.68860	−	11.9937i	−0.801592	−	1.25043i
$93$	−8.45991	−	1.86644i	−0.877252	−	0.193541i
$94$	−2.72257	−	9.29178i	−0.280812	−	0.958374i
$95$	8.37592	+	4.83584i	0.859351	+	0.496147i
$96$	7.59138	−	6.19443i	0.774792	−	0.632216i
$97$	3.39365	−	1.95932i	0.344572	−	0.198939i	−0.317720	−	0.948185i	$-0.602917\pi$
$97$	3.39365	−	1.95932i	0.344572	−	0.198939i	0.662292	+	0.749246i	$0.269584\pi$
$98$	−4.43617	−	8.84988i	−0.448121	−	0.893973i
$99$	0.887489	+	0.411634i	0.0891960	+	0.0413708i
$100$	0.307649	+	6.61675i	0.0307649	+	0.661675i
$101$	−1.84138	−	3.18937i	−0.183224	−	0.317354i	0.759752	−	0.650212i	$-0.225320\pi$
$101$	−1.84138	−	3.18937i	−0.183224	−	0.317354i	−0.942977	+	0.332859i	$0.891987\pi$
$102$	12.1824	−	0.828309i	1.20624	−	0.0820148i
$103$	3.76237	−	6.51662i	0.370718	−	0.642102i	−0.618958	−	0.785424i	$-0.712445\pi$
$103$	3.76237	−	6.51662i	0.370718	−	0.642102i	0.989676	+	0.143322i	$0.0457784\pi$
$104$	10.5443	−	3.62929i	1.03396	−	0.355881i
$105$	−4.73648	−	3.60761i	−0.462233	−	0.352067i
$106$	−1.79397	+	7.37653i	−0.174246	+	0.716472i
$107$	−10.6967			−1.03409			−0.517045	−	0.855958i	$-0.672968\pi$
$107$	−10.6967			−1.03409			−0.517045	+	0.855958i	$0.672968\pi$
$108$	−4.44746	−	9.39256i	−0.427957	−	0.903799i
$109$		−	2.82685i		−	0.270763i	−0.990794	−	0.135381i	$-0.956774\pi$
$109$		−	2.82685i		−	0.270763i	0.990794	−	0.135381i	$-0.0432260\pi$
$110$	0.582214	+	0.141594i	0.0555119	+	0.0135005i
$111$	−13.5674	+	4.29306i	−1.28776	+	0.407479i
$112$	−1.92319	−	10.4068i	−0.181725	−	0.983349i
$113$	2.43232	−	4.21290i	0.228813	−	0.396316i	−0.728644	−	0.684893i	$-0.759849\pi$
$113$	2.43232	−	4.21290i	0.228813	−	0.396316i	0.957457	+	0.288577i	$0.0931822\pi$
$114$	18.1921	−	1.23692i	1.70385	−	0.115848i
$115$	−8.01497	+	4.62745i	−0.747400	+	0.431512i
$116$	11.0693	−	0.514671i	1.02776	−	0.0477860i
$117$	−1.05498	−	11.7808i	−0.0975331	−	1.08913i
$118$	1.84297	+	1.75927i	0.169659	+	0.161954i
$119$	5.54339	−	11.9674i	0.508161	−	1.09705i
$120$	−3.79067	−	5.11313i	−0.346039	−	0.466763i
$121$	5.44683	−	9.43418i	0.495166	−	0.857653i
$122$	1.79696	+	6.13279i	0.162689	+	0.555237i
$123$	−0.0366938	+	0.166320i	−0.00330857	+	0.0149966i
$124$	−8.42170	+	5.39876i	−0.756291	+	0.484823i
$125$	10.7993			0.965919
$126$	−11.2051	−	0.666811i	−0.998234	−	0.0594043i
$127$		−	0.913369i		−	0.0810484i	−0.999179	−	0.0405242i	$-0.987097\pi$
$127$		−	0.913369i		−	0.0810484i	0.999179	−	0.0405242i	$-0.0129028\pi$
$128$	1.12028	−	11.2581i	0.0990199	−	0.995085i
$129$	12.2012	−	13.3426i	1.07425	−	1.17475i
$130$	−2.03699	−	6.95198i	−0.178656	−	0.609729i
$131$	−14.1068	−	8.14454i	−1.23251	−	0.711592i	−0.264960	−	0.964259i	$-0.585359\pi$
$131$	−14.1068	−	8.14454i	−1.23251	−	0.711592i	−0.967553	+	0.252668i	$0.918692\pi$
$132$	1.06003	−	0.390449i	0.0922634	−	0.0339842i
$133$	8.27797	−	17.8710i	0.717791	−	1.54961i
$134$	−13.8769	+	14.5371i	−1.19878	+	1.25581i
$135$	−6.22925	+	2.60267i	−0.536128	+	0.224002i
$136$	9.25142	−	10.6400i	0.793303	−	0.912369i
$137$	8.61011	+	14.9131i	0.735611	+	1.27412i	0.954455	+	0.298356i	$0.0964383\pi$
$137$	8.61011	+	14.9131i	0.735611	+	1.27412i	−0.218843	+	0.975760i	$0.570228\pi$
$138$	−7.67904	+	15.6677i	−0.653683	+	1.33372i
$139$	18.9392	+	10.9346i	1.60640	+	0.927458i	0.990166	+	0.139899i	$0.0446777\pi$
$139$	18.9392	+	10.9346i	1.60640	+	0.927458i	0.616239	+	0.787559i	$0.288656\pi$
$140$	−6.81125	+	0.934013i	−0.575655	+	0.0789385i
$141$	−8.00254	+	8.75121i	−0.673936	+	0.736984i
$142$	3.87323	−	15.9261i	0.325034	−	1.33649i
$143$	1.28570			0.107515
$144$	−11.3076	−	4.01725i	−0.942300	−	0.334771i
$145$		−	7.19865i		−	0.597816i
$146$	1.36733	−	5.62223i	0.113161	−	0.465299i
$147$	−6.45168	+	10.2653i	−0.532126	+	0.846665i
$148$	−7.54614	+	14.5967i	−0.620289	+	1.19984i
$149$	4.24162	+	2.44890i	0.347487	+	0.200622i	0.663578	−	0.748107i	$-0.269037\pi$
$149$	4.24162	+	2.44890i	0.347487	+	0.200622i	−0.316091	+	0.948729i	$0.602370\pi$
$150$	6.73436	−	4.52354i	0.549858	−	0.369345i
$151$	−0.770548	+	0.444876i	−0.0627063	+	0.0362035i	−0.531025	−	0.847356i	$-0.678193\pi$
$151$	−0.770548	+	0.444876i	−0.0627063	+	0.0362035i	0.468319	+	0.883559i	$0.344860\pi$
$152$	13.8152	−	15.8887i	1.12056	−	1.28874i
$153$	−8.60279	−	12.2327i	−0.695495	−	0.988955i
$154$	0.180833	−	1.20669i	0.0145719	−	0.0972375i
$155$	3.24929	+	5.62793i	0.260989	+	0.452046i
$156$	−10.4961	−	8.73862i	−0.840363	−	0.699649i
$157$	−6.06022	+	10.4966i	−0.483658	+	0.837720i	−0.999824	−	0.0187685i	$-0.994025\pi$
$157$	−6.06022	+	10.4966i	−0.483658	+	0.837720i	0.516166	+	0.856489i	$0.327359\pi$
$158$	5.96751	−	1.74853i	0.474750	−	0.139106i
$159$	8.86451	−	2.80494i	0.703001	−	0.222447i
$160$	−7.27186	−	1.06666i	−0.574891	−	0.0843267i
$161$	10.8492	+	15.4104i	0.855033	+	1.21451i
$162$	−7.01286	+	10.6217i	−0.550982	+	0.834517i
$163$	9.09164			0.712112			0.356056	−	0.934465i	$-0.384121\pi$
$163$	9.09164			0.712112			0.356056	+	0.934465i	$0.384121\pi$
$164$	0.106139	+	0.165569i	0.00828803	+	0.0129288i
$165$	−0.221388	−	0.699657i	−0.0172351	−	0.0544682i
$166$	5.92970	−	1.73745i	0.460234	−	0.134852i
$167$	−9.98632	+	17.2968i	−0.772765	+	1.33847i	0.163278	+	0.986580i	$0.447793\pi$
$167$	−9.98632	+	17.2968i	−0.772765	+	1.33847i	−0.936042	+	0.351888i	$0.885540\pi$
$168$	−9.67786	+	8.62200i	−0.746663	+	0.665202i
$169$	−1.27217	−	2.20346i	−0.0978593	−	0.169497i
$170$	−6.62539	−	6.32450i	−0.508144	−	0.485067i
$171$	−12.8466	−	18.2672i	−0.982404	−	1.39692i
$172$	−0.969649	−	20.8547i	−0.0739351	−	1.59016i
$173$	−1.88417	−	3.26347i	−0.143251	−	0.248117i	0.785468	−	0.618902i	$-0.212422\pi$
$173$	−1.88417	−	3.26347i	−0.143251	−	0.248117i	−0.928719	+	0.370785i	$0.879089\pi$
$174$	−7.56751	−	11.2660i	−0.573692	−	0.854076i
$175$	−0.785964	−	8.72727i	−0.0594133	−	0.659720i
$176$	0.544569	−	1.18529i	0.0410484	−	0.0893448i
$177$	0.672276	−	3.04719i	0.0505314	−	0.229041i
$178$	−1.08406	+	4.45747i	−0.0812534	+	0.334101i
$179$	17.5715			1.31335			0.656677	−	0.754172i	$-0.271961\pi$
$179$	17.5715			1.31335			0.656677	+	0.754172i	$0.271961\pi$
$180$	−2.94806	+	7.21656i	−0.219736	+	0.537891i
$181$	17.1485			1.27463			0.637317	−	0.770601i	$-0.280044\pi$
$181$	17.1485			1.27463			0.637317	+	0.770601i	$0.280044\pi$
$182$	−13.7277	+	5.40114i	−1.01756	+	0.400359i
$183$	5.28187	−	5.77600i	0.390447	−	0.426974i
$184$	6.55713	+	19.0507i	0.483398	+	1.40444i
$185$	9.24444	+	5.33728i	0.679665	+	0.392405i
$186$	11.0015	+	5.39205i	0.806670	+	0.395364i
$187$	1.40781	−	0.812799i	0.102949	−	0.0594377i
$188$	0.635976	+	13.6783i	0.0463834	+	0.997589i
$189$	6.41642	+	12.1585i	0.466726	+	0.884402i
$190$	−9.89373	−	9.44441i	−0.717767	−	0.685169i
$191$	−12.8375	+	7.41172i	−0.928887	+	0.536293i	−0.886459	−	0.462806i	$-0.846843\pi$
$191$	−12.8375	+	7.41172i	−0.928887	+	0.536293i	−0.0424276	+	0.999100i	$0.513509\pi$
$192$	−12.5019	+	5.97513i	−0.902248	+	0.431218i
$193$	−5.42038	+	9.38838i	−0.390168	+	0.675790i	−0.992471	−	0.122477i	$-0.960916\pi$
$193$	−5.42038	+	9.38838i	−0.390168	+	0.675790i	0.602304	+	0.798267i	$0.294250\pi$
$194$	−5.31821	+	1.55828i	−0.381825	+	0.111878i
$195$	−5.98739	+	6.54753i	−0.428766	+	0.468878i
$196$	3.13842	+	13.6437i	0.224173	+	0.974549i
$197$		−	11.1390i		−	0.793620i	−0.917901	−	0.396810i	$-0.870117\pi$
$197$		−	11.1390i		−	0.793620i	0.917901	−	0.396810i	$-0.129883\pi$
$198$	−1.08199	−	0.862245i	−0.0768933	−	0.0612771i
$199$	14.8744			1.05442			0.527208	−	0.849736i	$-0.323239\pi$
$199$	14.8744			1.05442			0.527208	+	0.849736i	$0.323239\pi$
$200$	1.78853	−	9.19528i	0.126468	−	0.650205i
$201$	24.0359	+	5.30283i	1.69536	+	0.374033i
$202$	1.46448	+	4.99808i	0.103040	+	0.351664i
$203$	−14.6000	+	1.31485i	−1.02472	+	0.0922846i
$204$	−17.0174	−	2.93309i	−1.19146	−	0.205357i
$205$	0.110644	−	0.0638804i	0.00772771	−	0.00446160i
$206$	−7.34792	+	7.69751i	−0.511954	+	0.536311i
$207$	21.2846	−	1.90606i	1.47938	−	0.132481i
$208$	−15.7025	+	1.46335i	−1.08877	+	0.101465i
$209$	2.10229	−	1.21376i	0.145418	−	0.0839573i
$210$	5.30303	+	6.54034i	0.365944	+	0.451327i
$211$	−0.299601	+	0.518924i	−0.0206254	+	0.0357242i	−0.876154	−	0.482032i	$-0.839899\pi$
$211$	−0.299601	+	0.518924i	−0.0206254	+	0.0357242i	0.855528	+	0.517756i	$0.173232\pi$
$212$	4.93040	−	9.53699i	0.338621	−	0.655003i
$213$	−19.1387	+	6.05595i	−1.31136	+	0.414947i
$214$	14.6990	+	3.57479i	1.00480	+	0.244368i
$215$	−13.5624			−0.924947
$216$	2.97257	+	14.3932i	0.202258	+	0.979332i
$217$	10.8209	−	7.61803i	0.734568	−	0.517146i
$218$	−0.944719	+	3.88454i	−0.0639845	+	0.263094i
$219$	−6.75633	+	2.13787i	−0.456551	+	0.144464i
$220$	−0.752734	−	0.389146i	−0.0507493	−	0.0262362i
$221$	−17.0207	−	9.82690i	−1.14494	−	0.661029i
$222$	20.0785	−	1.36518i	1.34758	−	0.0916247i
$223$	9.49725	+	16.4497i	0.635983	+	1.10156i	0.986306	+	0.164926i	$0.0527386\pi$
$223$	9.49725	+	16.4497i	0.635983	+	1.10156i	−0.350323	+	0.936629i	$0.613928\pi$
$224$	−0.835128	+	14.9433i	−0.0557993	+	0.998442i
$225$	−9.01351	−	4.18063i	−0.600901	−	0.278709i
$226$	−4.75032	+	4.97632i	−0.315987	+	0.331020i
$227$	10.7271	−	6.19331i	0.711985	−	0.411065i	−0.0998107	−	0.995006i	$-0.531824\pi$
$227$	10.7271	−	6.19331i	0.711985	−	0.411065i	0.811796	+	0.583942i	$0.198490\pi$
$228$	−25.4122	−	4.38000i	−1.68297	−	0.290072i
$229$	−1.41581	+	2.45225i	−0.0935593	+	0.162049i	−0.909006	−	0.416782i	$-0.863158\pi$
$229$	−1.41581	+	2.45225i	−0.0935593	+	0.162049i	0.815447	+	0.578832i	$0.196491\pi$
$230$	12.5603	−	3.68028i	0.828203	−	0.242671i
$231$	−1.37858	+	0.576805i	−0.0907038	+	0.0379510i
$232$	−15.3830	−	2.99206i	−1.00994	−	0.196439i
$233$	8.19004			0.536548			0.268274	−	0.963343i	$-0.413547\pi$
$233$	8.19004			0.536548			0.268274	+	0.963343i	$0.413547\pi$
$234$	−2.48736	+	16.5412i	−0.162604	+	1.08133i
$235$	8.89534			0.580268
$236$	−1.94459	−	3.03343i	−0.126582	−	0.197459i
$237$	−5.62033	−	5.13952i	−0.365080	−	0.333848i
$238$	−11.6169	+	14.5925i	−0.753015	+	0.945893i
$239$	6.39226	+	3.69058i	0.413481	+	0.238723i	0.692284	−	0.721625i	$-0.256604\pi$
$239$	6.39226	+	3.69058i	0.413481	+	0.238723i	−0.278803	+	0.960348i	$0.589938\pi$
$240$	3.50020	+	8.29308i	0.225937	+	0.535316i
$241$	−7.68063	+	4.43441i	−0.494753	+	0.285646i	−0.726544	−	0.687120i	$-0.758875\pi$
$241$	−7.68063	+	4.43441i	−0.494753	+	0.285646i	0.231791	+	0.972766i	$0.425541\pi$
$242$	−10.6377	+	11.1438i	−0.683815	+	0.716348i
$243$	15.5769	+	0.600269i	0.999258	+	0.0385073i
$244$	−0.419760	−	9.02797i	−0.0268724	−	0.577957i
$245$	8.94841	−	1.62494i	0.571693	−	0.103813i
$246$	0.106007	−	0.216288i	0.00675873	−	0.0137900i
$247$	−25.4171	−	14.6746i	−1.61725	−	0.933720i
$248$	13.3770	−	4.60427i	0.849440	−	0.292371i
$249$	−5.58472	−	5.10695i	−0.353917	−	0.323640i
$250$	−14.8400	−	3.60908i	−0.938561	−	0.228258i
$251$			11.4278i			0.721314i	0.932698	+	0.360657i	$0.117448\pi$
$251$			11.4278i			0.721314i	−0.932698	+	0.360657i	$0.882552\pi$
$252$	15.1748	+	4.66101i	0.955923	+	0.293616i
$253$			2.32290i			0.146040i
$254$	−0.305244	+	1.25511i	−0.0191527	+	0.0787529i
$255$	−2.41680	+	10.9545i	−0.151346	+	0.685999i
$256$	−5.30185	+	15.0960i	−0.331366	+	0.943502i
$257$	−19.2862	−	11.1349i	−1.20304	−	0.694574i	−0.241808	−	0.970324i	$-0.577740\pi$
$257$	−19.2862	−	11.1349i	−1.20304	−	0.694574i	−0.961229	+	0.275750i	$0.911074\pi$
$258$	−21.2254	+	14.2573i	−1.32144	+	0.887622i
$259$	9.13633	−	19.7241i	0.567704	−	1.22559i
$260$	0.475829	+	10.2339i	0.0295096	+	0.634678i
$261$	−6.99386	+	15.0789i	−0.432909	+	0.933359i
$262$	16.6631	+	15.9063i	1.02945	+	0.982695i
$263$	−10.7186	+	6.18839i	−0.660937	+	0.381592i	−0.792634	−	0.609698i	$-0.791291\pi$
$263$	−10.7186	+	6.18839i	−0.660937	+	0.381592i	0.131697	+	0.991290i	$0.457957\pi$
$264$	−1.58713	+	0.182283i	−0.0976812	+	0.0112187i
$265$	−6.04002	−	3.48721i	−0.371035	−	0.214217i
$266$	−17.3476	+	21.7911i	−1.06365	+	1.33610i
$267$	5.35662	−	1.69496i	0.327820	−	0.103730i
$268$	23.9273	−	15.3387i	1.46159	−	0.936960i
$269$	6.57969			0.401171			0.200585	−	0.979676i	$-0.435716\pi$
$269$	6.57969			0.401171			0.200585	+	0.979676i	$0.435716\pi$
$270$	9.42977	−	1.49470i	0.573878	−	0.0909645i
$271$	−19.4818			−1.18343			−0.591716	−	0.806146i	$-0.701549\pi$
$271$	−19.4818			−1.18343			−0.591716	+	0.806146i	$0.701549\pi$
$272$	−16.2687	+	11.5292i	−0.986438	+	0.699061i
$273$	14.3730	+	10.9475i	0.869896	+	0.662570i
$274$	−6.84776	−	23.3705i	−0.413688	−	1.41186i
$275$	0.540016	−	0.935334i	0.0325642	−	0.0564028i
$276$	15.7883	−	18.9636i	0.950344	−	1.14148i
$277$	−2.56121	+	1.47871i	−0.153888	+	0.0888473i	−0.574967	−	0.818177i	$-0.694985\pi$
$277$	−2.56121	+	1.47871i	−0.153888	+	0.0888473i	0.421079	+	0.907024i	$0.361652\pi$
$278$	−22.3712	−	21.3552i	−1.34174	−	1.28080i
$279$	−1.33839	−	14.9456i	−0.0801276	−	0.894767i
$280$	9.67188	+	0.992805i	0.578005	+	0.0593314i
$281$	12.0868	+	20.9350i	0.721040	+	1.24888i	0.960583	+	0.277992i	$0.0896688\pi$
$281$	12.0868	+	20.9350i	0.721040	+	1.24888i	−0.239544	+	0.970886i	$0.576998\pi$
$282$	13.9214	−	9.35114i	0.829006	−	0.556852i
$283$	4.87331	+	2.81361i	0.289688	+	0.167252i	0.637801	−	0.770201i	$-0.279844\pi$
$283$	4.87331	+	2.81361i	0.289688	+	0.167252i	−0.348113	+	0.937453i	$0.613177\pi$
$284$	−10.6449	+	20.5906i	−0.631657	+	1.22183i
$285$	−3.60902	+	16.3585i	−0.213780	+	0.968991i
$286$	−1.76675	−	0.429674i	−0.104470	−	0.0254072i
$287$	−0.149769	−	0.212736i	−0.00884058	−	0.0125574i
$288$	14.1959	+	9.29928i	0.836501	+	0.547966i
$289$	−7.84967			−0.461745
$290$	−2.40576	+	9.89210i	−0.141271	+	0.580884i
$291$	5.00881	+	4.58030i	0.293621	+	0.268502i
$292$	−3.75785	+	7.26888i	−0.219911	+	0.425379i
$293$	−4.24352	+	7.34998i	−0.247909	+	0.429391i	−0.962945	−	0.269696i	$-0.913077\pi$
$293$	−4.24352	+	7.34998i	−0.247909	+	0.429391i	0.715037	+	0.699087i	$0.246410\pi$
$294$	12.2962	−	11.9500i	0.717132	−	0.696938i
$295$	−2.02714	+	1.17037i	−0.118025	+	0.0681415i
$296$	15.2477	−	17.5362i	0.886256	−	1.01927i
$297$	−0.216015	+	1.68065i	−0.0125344	+	0.0975210i
$298$	−5.01025	−	4.78271i	−0.290236	−	0.277055i
$299$	24.3218	−	14.0422i	1.40657	−	0.812081i
$300$	−10.7658	+	3.96547i	−0.621565	+	0.228947i
$301$	2.47721	+	27.5067i	0.142784	+	1.58546i
$302$	1.20753	−	0.353817i	0.0694856	−	0.0203599i
$303$	4.30459	−	4.70730i	0.247292	−	0.270427i
$304$	−24.2942	+	17.2166i	−1.39337	+	0.987442i
$305$	−5.87113			−0.336180
$306$	7.73350	+	19.6847i	0.442094	+	1.12530i
$307$		−	22.9582i		−	1.31029i	−0.755502	−	0.655147i	$-0.772607\pi$
$307$		−	22.9582i		−	1.31029i	0.755502	−	0.655147i	$-0.227393\pi$
$308$	−0.651762	+	1.59774i	−0.0371376	+	0.0910399i
$309$	12.7272	+	2.80789i	0.724024	+	0.159735i
$310$	−2.58421	−	8.81957i	−0.146773	−	0.500918i
$311$	13.5212	−	23.4195i	0.766718	−	1.32800i	−0.172615	−	0.984989i	$-0.555222\pi$
$311$	13.5212	−	23.4195i	0.766718	−	1.32800i	0.939333	−	0.343006i	$-0.111445\pi$
$312$	11.5029	+	15.5160i	0.651226	+	0.878421i
$313$	−0.515228	+	0.297467i	−0.0291224	+	0.0168138i	−0.514491	−	0.857496i	$-0.672019\pi$
$313$	−0.515228	+	0.297467i	−0.0291224	+	0.0168138i	0.485368	+	0.874310i	$0.338686\pi$
$314$	11.8356	−	12.3987i	0.667923	−	0.699699i
$315$	3.48250	−	9.70667i	0.196217	−	0.546909i
$316$	−8.78466	+	0.408447i	−0.494176	+	0.0229769i
$317$	−14.4119	+	8.32072i	−0.809453	+	0.467338i	−0.846766	−	0.531966i	$-0.821454\pi$
$317$	−14.4119	+	8.32072i	−0.809453	+	0.467338i	0.0373126	+	0.999304i	$0.488120\pi$
$318$	−13.1186	+	0.891963i	−0.735657	+	0.0500188i
$319$	−1.56474	−	0.903402i	−0.0876085	−	0.0505808i
$320$	9.63622	+	3.89598i	0.538681	+	0.217792i
$321$	−5.58932	−	17.6640i	−0.311966	−	0.985910i
$322$	−9.75838	−	24.8021i	−0.543813	−	1.38217i
$323$	−37.1082			−2.06475
$324$	13.1865	−	12.2522i	0.732583	−	0.680677i
$325$	−13.0578			−0.724316
$326$	−12.4934	−	3.03839i	−0.691944	−	0.168281i
$327$	4.66812	−	1.47711i	0.258148	−	0.0816842i
$328$	−0.0905190	−	0.262989i	−0.00499808	−	0.0145211i
$329$	−1.62476	−	18.0412i	−0.0895758	−	0.994641i
$330$	0.0704008	+	1.03543i	0.00387543	+	0.0569984i
$331$	−3.55671	−	6.16040i	−0.195494	−	0.338606i	0.751568	−	0.659656i	$-0.229298\pi$
$331$	−3.55671	−	6.16040i	−0.195494	−	0.338606i	−0.947063	+	0.321049i	$0.895964\pi$
$332$	−8.72900	+	0.405859i	−0.479066	+	0.0222744i
$333$	−14.1787	−	20.1613i	−0.776988	−	1.10483i
$334$	19.5033	−	20.4312i	1.06717	−	1.11795i
$335$	−9.23172	−	15.9898i	−0.504383	−	0.873616i
$336$	16.1804	−	8.61371i	0.882711	−	0.469916i
$337$	−6.63837	+	11.4980i	−0.361615	+	0.626336i	−0.988227	−	0.152996i	$-0.951108\pi$
$337$	−6.63837	+	11.4980i	−0.361615	+	0.626336i	0.626612	+	0.779332i	$0.284441\pi$
$338$	1.01178	+	3.45306i	0.0550334	+	0.187822i
$339$	8.22793	+	1.81526i	0.446880	+	0.0985912i
$340$	6.99072	+	10.9050i	0.379125	+	0.591409i
$341$	1.63109			0.0883285
$342$	11.5485	+	29.3953i	0.624470	+	1.58951i
$343$	−4.93009	−	17.8520i	−0.266200	−	0.963918i
$344$	−5.63710	+	28.9817i	−0.303932	+	1.56259i
$345$	−11.8296	−	10.8176i	−0.636884	−	0.582399i
$346$	1.49851	+	5.11421i	0.0805603	+	0.274942i
$347$	−6.25897	+	10.8409i	−0.335999	+	0.581968i	−0.983676	−	0.179947i	$-0.942407\pi$
$347$	−6.25897	+	10.8409i	−0.335999	+	0.581968i	0.647677	+	0.761915i	$0.275741\pi$
$348$	6.63391	+	18.0104i	0.355615	+	0.965457i
$349$	1.09093	+	1.88955i	0.0583963	+	0.101145i	0.893746	−	0.448574i	$-0.148068\pi$
$349$	1.09093	+	1.88955i	0.0583963	+	0.101145i	−0.835349	+	0.549719i	$0.814735\pi$
$350$	−1.83657	+	12.2553i	−0.0981690	+	0.655075i
$351$	18.9029	−	7.89792i	1.00896	−	0.421560i
$352$	−1.14444	+	1.44679i	−0.0609990	+	0.0771141i
$353$	−2.66693	+	1.53975i	−0.141946	+	0.0819527i	−0.569291	−	0.822136i	$-0.692782\pi$
$353$	−2.66693	+	1.53975i	−0.141946	+	0.0819527i	0.427345	+	0.904089i	$0.359449\pi$
$354$	−1.94217	+	3.96266i	−0.103225	+	0.210613i
$355$	13.0406	+	7.52897i	0.692121	+	0.399596i
$356$	2.97933	−	5.76298i	0.157904	−	0.305438i
$357$	22.6590	+	2.90079i	1.19924	+	0.153526i
$358$	−24.1460	−	5.87231i	−1.27616	−	0.310361i
$359$			18.2103i			0.961104i	0.876966	+	0.480552i	$0.159564\pi$
$359$			18.2103i			0.961104i	−0.876966	+	0.480552i	$0.840436\pi$
$360$	6.46285	−	8.93148i	0.340622	−	0.470730i
$361$	−36.4138			−1.91652
$362$	−23.5647	−	5.73094i	−1.23853	−	0.301211i
$363$	18.4253	+	4.06501i	0.967077	+	0.213358i
$364$	20.6690	−	2.83430i	1.08335	−	0.148558i
$365$	4.60357	+	2.65787i	0.240962	+	0.139119i
$366$	−9.18844	+	6.17197i	−0.480288	+	0.322614i
$367$	−10.1154	−	17.5205i	−0.528022	−	0.914561i	−0.999466	−	0.0326653i	$-0.989600\pi$
$367$	−10.1154	−	17.5205i	−0.528022	−	0.914561i	0.471444	−	0.881896i	$-0.343733\pi$
$368$	−2.64388	−	28.3701i	−0.137822	−	1.47889i
$369$	−0.293827	+	0.0263126i	−0.0152960	+	0.00136978i
$370$	−10.9196	−	10.4237i	−0.567685	−	0.541903i
$371$	−5.96939	+	12.8871i	−0.309915	+	0.669063i
$372$	−13.3158	−	11.0862i	−0.690394	−	0.574792i
$373$	−14.3768	−	8.30043i	−0.744400	−	0.429780i	0.0792667	−	0.996853i	$-0.474742\pi$
$373$	−14.3768	−	8.30043i	−0.744400	−	0.429780i	−0.823667	+	0.567074i	$0.808075\pi$
$374$	−2.20619	+	0.646432i	−0.114079	+	0.0334262i
$375$	5.64294	+	17.8335i	0.291400	+	0.920916i
$376$	3.69728	−	19.0086i	0.190672	−	0.980296i
$377$			21.8446i			1.12506i
$378$	−4.75386	−	18.8521i	−0.244512	−	0.969646i
$379$	4.54685			0.233556			0.116778	−	0.993158i	$-0.462743\pi$
$379$	4.54685			0.233556			0.116778	+	0.993158i	$0.462743\pi$
$380$	10.4393	+	16.2846i	0.535524	+	0.835380i
$381$	1.50829	−	0.477261i	0.0772723	−	0.0244508i
$382$	20.1177	−	5.89466i	1.02931	−	0.301597i
$383$	−4.19619	+	7.26802i	−0.214415	+	0.371378i	−0.953092	−	0.302682i	$-0.902118\pi$
$383$	−4.19619	+	7.26802i	−0.214415	+	0.371378i	0.738676	+	0.674061i	$0.235451\pi$
$384$	19.1765	−	4.03269i	0.978596	−	0.205792i
$385$	1.01715	+	0.471151i	0.0518387	+	0.0240121i
$386$	10.5860	−	11.0897i	0.538814	−	0.564449i
$387$	28.4088	+	13.1765i	1.44410	+	0.669801i
$388$	7.82883	−	0.364005i	0.397449	−	0.0184796i
$389$	−6.08750	+	3.51462i	−0.308649	+	0.178198i	−0.646322	−	0.763065i	$-0.723694\pi$
$389$	−6.08750	+	3.51462i	−0.308649	+	0.178198i	0.337673	+	0.941264i	$0.390360\pi$
$390$	10.4158	−	6.99639i	0.527423	−	0.354276i
$391$	17.7545	−	30.7517i	0.897885	−	1.55518i
$392$	0.246971	−	19.7974i	0.0124739	−	0.999922i
$393$	6.07833	−	27.5510i	0.306611	−	1.38976i
$394$	−3.72260	+	15.3068i	−0.187542	+	0.771143i
$395$			5.71290i			0.287447i
$396$	1.19866	+	1.54646i	0.0602350	+	0.0777124i
$397$	33.9539			1.70410			0.852050	−	0.523461i	$-0.175359\pi$
$397$	33.9539			1.70410			0.852050	+	0.523461i	$0.175359\pi$
$398$	−20.4397	−	4.97094i	−1.02455	−	0.249171i
$399$	33.8368	+	4.33176i	1.69396	+	0.216859i
$400$	−5.53074	+	12.0381i	−0.276537	+	0.601903i
$401$	10.9071	−	18.8917i	0.544676	−	0.943407i	−0.453951	−	0.891027i	$-0.649986\pi$
$401$	10.9071	−	18.8917i	0.544676	−	0.943407i	0.998627	−	0.0523802i	$-0.0166808\pi$
$402$	−31.2570	−	15.3196i	−1.55896	−	0.764073i
$403$	−9.86011	−	17.0782i	−0.491167	−	0.850726i
$404$	−0.342094	−	7.35758i	−0.0170198	−	0.366053i
$405$	−7.55288	−	8.92671i	−0.375306	−	0.443572i
$406$	20.5022	+	3.07244i	1.01751	+	0.152483i
$407$	2.32028	−	1.33961i	0.115012	−	0.0664022i
$408$	22.4044	+	9.71768i	1.10918	+	0.481097i
$409$	−26.3216	−	15.1968i	−1.30152	−	0.751433i	−0.320855	−	0.947128i	$-0.603970\pi$
$409$	−26.3216	−	15.1968i	−1.30152	−	0.751433i	−0.980665	+	0.195696i	$0.937304\pi$
$410$	−0.173391	+	0.0508051i	−0.00856317	+	0.00250908i
$411$	−20.1278	+	22.0109i	−0.992833	+	1.08572i
$412$	12.6697	−	8.12196i	0.624191	−	0.400140i
$413$	2.74396	+	3.89759i	0.135021	+	0.191788i
$414$	−29.8854	−	4.49398i	−1.46879	−	0.220867i
$415$			5.67670i			0.278658i
$416$	22.0668	+	3.23682i	1.08191	+	0.158698i
$417$	−8.16055	+	36.9890i	−0.399624	+	1.81136i
$418$	−3.29451	+	0.965320i	−0.161140	+	0.0472153i
$419$	6.32138	+	3.64965i	0.308819	+	0.178297i	0.646398	−	0.763000i	$-0.276275\pi$
$419$	6.32138	+	3.64965i	0.308819	+	0.178297i	−0.337579	+	0.941297i	$0.609608\pi$
$420$	−5.10145	−	10.7597i	−0.248925	−	0.525020i
$421$	20.5331	−	11.8548i	1.00072	−	0.577767i	0.0922596	−	0.995735i	$-0.470591\pi$
$421$	20.5331	−	11.8548i	1.00072	−	0.577767i	0.908462	+	0.417968i	$0.137258\pi$
$422$	0.585121	−	0.612959i	0.0284833	−	0.0298384i
$423$	−18.6329	−	8.64227i	−0.905961	−	0.420202i
$424$	−9.96237	+	11.4576i	−0.483816	+	0.556431i
$425$	−14.2980	+	8.25494i	−0.693554	+	0.400423i
$426$	28.3235	−	1.92577i	1.37228	−	0.0933039i
$427$	1.07238	+	11.9076i	0.0518960	+	0.576249i
$428$	−19.0041	−	9.82466i	−0.918595	−	0.474893i
$429$	0.671813	+	2.12314i	0.0324354	+	0.102506i
$430$	18.6369	+	4.53249i	0.898750	+	0.218576i
$431$			1.32902i			0.0640164i	0.999488	+	0.0320082i	$0.0101903\pi$
$431$			1.32902i			0.0640164i	−0.999488	+	0.0320082i	$0.989810\pi$
$432$	0.725357	−	20.7719i	0.0348988	−	0.999391i
$433$			14.4945i			0.696563i	0.937390	+	0.348282i	$0.113235\pi$
$433$			14.4945i			0.696563i	−0.937390	+	0.348282i	$0.886765\pi$
$434$	−17.4155	+	6.85211i	−0.835970	+	0.328912i
$435$	11.8875	−	3.76150i	0.569963	−	0.180350i
$436$	2.59639	−	5.02225i	0.124345	−	0.240522i
$437$	26.5129	−	45.9217i	1.26829	−	2.19673i
$438$	9.99875	−	0.679835i	0.477759	−	0.0324838i
$439$	−3.54769	−	6.14478i	−0.169322	−	0.293275i	0.768860	−	0.639418i	$-0.220824\pi$
$439$	−3.54769	−	6.14478i	−0.169322	−	0.293275i	−0.938182	+	0.346143i	$0.887491\pi$
$440$	0.904326	+	0.786309i	0.0431120	+	0.0374858i
$441$	−20.3228	−	5.29011i	−0.967751	−	0.251910i
$442$	20.1050	+	19.1920i	0.956299	+	0.912868i
$443$	3.50391	+	6.06894i	0.166476	+	0.288344i	0.937178	−	0.348851i	$-0.113428\pi$
$443$	3.50391	+	6.06894i	0.166476	+	0.288344i	−0.770703	+	0.637195i	$0.780095\pi$
$444$	−28.0473	−	4.83417i	−1.33107	−	0.229420i
$445$	−3.64985	−	2.10724i	−0.173019	−	0.0998928i
$446$	−7.55332	−	25.7785i	−0.357660	−	1.22065i
$447$	−1.82763	+	8.28403i	−0.0864441	+	0.391821i
$448$	6.14158	−	20.2554i	0.290163	−	0.956977i
$449$	−10.2649			−0.484431			−0.242216	−	0.970222i	$-0.577874\pi$
$449$	−10.2649			−0.484431			−0.242216	+	0.970222i	$0.577874\pi$
$450$	10.9888	+	8.75713i	0.518019	+	0.412815i
$451$		−	0.0320669i		−	0.00150997i
$452$	8.19076	−	5.25072i	0.385261	−	0.246973i
$453$	−1.13728	−	1.03999i	−0.0534341	−	0.0488628i
$454$	−16.8106	+	4.92564i	−0.788959	+	0.231172i
$455$	−1.21562	−	13.4981i	−0.0569892	−	0.632803i
$456$	33.4567	+	14.5115i	1.56675	+	0.679561i
$457$	7.12149	+	12.3348i	0.333129	+	0.576997i	0.983124	−	0.182942i	$-0.0585621\pi$
$457$	7.12149	+	12.3348i	0.333129	+	0.576997i	−0.649994	+	0.759939i	$0.725229\pi$
$458$	2.76508	−	2.89663i	0.129204	−	0.135351i
$459$	15.7053	−	20.5982i	0.733061	−	0.961440i
$460$	−18.4898	+	0.859692i	−0.862092	+	0.0400834i
$461$	20.1818	+	34.9560i	0.939962	+	1.62806i	0.765537	+	0.643392i	$0.222473\pi$
$461$	20.1818	+	34.9560i	0.939962	+	1.62806i	0.174425	+	0.984670i	$0.444193\pi$
$462$	2.08715	−	0.331908i	0.0971031	−	0.0154417i
$463$	36.0521	+	20.8147i	1.67548	+	0.967339i	0.964483	+	0.264145i	$0.0850899\pi$
$463$	36.0521	+	20.8147i	1.67548	+	0.967339i	0.710998	+	0.703194i	$0.248243\pi$
$464$	20.1387	+	9.25248i	0.934916	+	0.429536i
$465$	−7.59586	+	8.30647i	−0.352249	+	0.385203i
$466$	−11.2544	−	2.73707i	−0.521351	−	0.126793i
$467$		−	18.8152i		−	0.870662i	−0.900270	−	0.435331i	$-0.856631\pi$
$467$		−	18.8152i		−	0.870662i	0.900270	−	0.435331i	$-0.143369\pi$
$468$	8.94602	−	21.8990i	0.413530	−	1.01228i
$469$	−30.7437	+	21.6440i	−1.41961	+	0.999426i
$470$	−12.2236	−	2.97278i	−0.563833	−	0.137124i
$471$	−20.5002	−	4.52279i	−0.944600	−	0.208399i
$472$	1.65842	+	4.81829i	0.0763351	+	0.221780i
$473$	−1.70202	+	2.94799i	−0.0782592	+	0.135549i
$474$	6.00563	+	8.94080i	0.275848	+	0.410665i
$475$	−21.3512	+	12.3271i	−0.979662	+	0.565608i
$476$	20.8403	−	16.1701i	0.955213	−	0.741157i
$477$	9.26390	+	13.1728i	0.424165	+	0.603140i
$478$	−7.55061	−	7.20770i	−0.345357	−	0.329673i
$479$	−10.9817	−	19.0208i	−0.501766	−	0.869085i	−0.999998	−	0.00204077i	$-0.999350\pi$
$479$	−10.9817	−	19.0208i	−0.501766	−	0.869085i	0.498232	−	0.867044i	$-0.333983\pi$
$480$	−2.03832	−	12.5658i	−0.0930361	−	0.573546i
$481$	−28.0527	−	16.1962i	−1.27909	−	0.738483i
$482$	12.0364	−	3.52676i	0.548242	−	0.160639i
$483$	−19.7791	+	25.9682i	−0.899978	+	1.18159i
$484$	18.3420	−	11.7582i	0.833729	−	0.534466i
$485$		−	5.09130i		−	0.231184i
$486$	−21.2045	−	6.03059i	−0.961857	−	0.273553i
$487$		−	2.85903i		−	0.129555i	−0.997900	−	0.0647775i	$-0.979366\pi$
$487$		−	2.85903i		−	0.129555i	0.997900	−	0.0647775i	$-0.0206338\pi$
$488$	−2.44029	+	12.5462i	−0.110467	+	0.567938i
$489$	4.75064	+	15.0135i	0.214831	+	0.678934i
$490$	−12.8396	−	0.757595i	−0.580034	−	0.0342246i
$491$	15.2503	−	26.4143i	0.688237	−	1.19206i	−0.284170	−	0.958774i	$-0.591718\pi$
$491$	15.2503	−	26.4143i	0.688237	−	1.19206i	0.972408	−	0.233288i	$-0.0749485\pi$
$492$	−0.217952	+	0.261787i	−0.00982604	+	0.0118023i
$493$	13.8098	+	23.9194i	0.621964	+	1.07727i
$494$	30.0230	+	28.6595i	1.35080	+	1.28945i
$495$	1.03970	−	0.731181i	0.0467310	−	0.0328641i
$496$	−19.9208	+	1.85647i	−0.894472	+	0.0833580i
$497$	12.8881	−	27.8235i	0.578109	−	1.24806i
$498$	5.96758	+	8.88415i	0.267414	+	0.398108i
$499$	−5.82556	+	10.0902i	−0.260788	+	0.451698i	−0.966452	−	0.256849i	$-0.917316\pi$
$499$	−5.82556	+	10.0902i	−0.260788	+	0.451698i	0.705664	+	0.708547i	$0.250649\pi$
$500$	19.1863	+	9.91889i	0.858039	+	0.443586i
$501$	−33.7813	−	7.45287i	−1.50924	−	0.332970i
$502$	3.81911	−	15.7036i	0.170455	−	0.700885i
$503$	−36.1238			−1.61068			−0.805341	−	0.592812i	$-0.798018\pi$
$503$	−36.1238			−1.61068			−0.805341	+	0.592812i	$0.798018\pi$
$504$	−19.2949	−	11.4763i	−0.859464	−	0.511196i
$505$	−4.78483			−0.212922
$506$	0.776304	−	3.19204i	0.0345109	−	0.141903i
$507$	2.97395	−	3.25217i	0.132078	−	0.144434i
$508$	0.838907	−	1.62272i	0.0372205	−	0.0719964i
$509$	−16.7710	+	29.0482i	−0.743362	+	1.28754i	0.207594	+	0.978215i	$0.433437\pi$
$509$	−16.7710	+	29.0482i	−0.743362	+	1.28754i	−0.950956	+	0.309326i	$0.899897\pi$
$510$	6.98202	−	14.2456i	0.309169	−	0.630805i
$511$	4.54974	−	9.82224i	0.201268	−	0.434511i
$512$	12.3306	−	18.9725i	0.544941	−	0.838474i
$513$	23.4528	−	30.7594i	1.03547	−	1.35806i
$514$	22.7810	+	21.7464i	1.00483	+	0.959194i
$515$	−4.88826	−	8.46672i	−0.215403	−	0.373088i
$516$	33.9318	−	12.4984i	1.49376	−	0.550211i
$517$	1.11633	−	1.93354i	0.0490961	−	0.0850369i
$518$	−19.1465	+	24.0507i	−0.841247	+	1.05673i
$519$	4.40462	−	4.81668i	0.193341	−	0.211429i
$520$	2.76625	−	14.2220i	0.121308	−	0.623676i
$521$			5.96073i			0.261144i	0.991439	+	0.130572i	$0.0416814\pi$
$521$			5.96073i			0.261144i	−0.991439	+	0.130572i	$0.958319\pi$
$522$	14.6500	−	18.3835i	0.641211	−	0.804622i
$523$			8.95062i			0.391383i	0.980665	+	0.195692i	$0.0626952\pi$
$523$			8.95062i			0.391383i	−0.980665	+	0.195692i	$0.937305\pi$
$524$	−17.5819	−	27.4265i	−0.768068	−	1.19813i
$525$	14.0011	−	5.85815i	0.611059	−	0.255670i
$526$	16.7972	−	4.92172i	0.732393	−	0.214597i
$527$	−21.5932	−	12.4668i	−0.940613	−	0.543063i
$528$	2.24189	+	0.279926i	0.0975657	+	0.0121822i
$529$	13.8704	+	24.0242i	0.603061	+	1.04453i
$530$	7.13454	+	6.81052i	0.309905	+	0.295830i
$531$	5.38327	−	0.482079i	0.233614	−	0.0209205i
$532$	31.1209	−	24.1470i	1.34926	−	1.04690i
$533$	−0.335754	+	0.193848i	−0.0145431	+	0.00839648i
$534$	−7.92730	+	0.538993i	−0.343048	+	0.0233245i
$535$	−6.94885	+	12.0358i	−0.300425	+	0.520351i
$536$	−38.0060	+	13.0814i	−1.64161	+	0.565031i
$537$	9.18159	+	29.0167i	0.396215	+	1.25216i
$538$	−9.04154	−	2.19890i	−0.389808	−	0.0948014i
$539$	0.769785	−	2.14900i	0.0331570	−	0.0925639i
$540$	−13.4575	−	1.09743i	−0.579120	−	0.0472260i
$541$			33.9933i			1.46149i	0.682652	+	0.730743i	$0.260826\pi$
$541$			33.9933i			1.46149i	−0.682652	+	0.730743i	$0.739174\pi$
$542$	26.7710	+	6.51071i	1.14991	+	0.279659i
$543$	8.96055	+	28.3181i	0.384534	+	1.21525i
$544$	26.2089	−	10.4060i	1.12370	−	0.446155i
$545$	−3.18072	−	1.83639i	−0.136247	−	0.0786624i
$546$	−16.0923	−	19.8470i	−0.688685	−	0.849371i
$547$	16.1616	+	27.9927i	0.691021	+	1.19688i	0.971504	+	0.237024i	$0.0761719\pi$
$547$	16.1616	+	27.9927i	0.691021	+	1.19688i	−0.280483	+	0.959859i	$0.590495\pi$
$548$	1.59960	+	34.4033i	0.0683313	+	1.46963i
$549$	12.2981	+	5.70410i	0.524872	+	0.243445i
$550$	−1.05465	+	1.10483i	−0.0449705	+	0.0471100i
$551$	20.6223	+	35.7189i	0.878540	+	1.52168i
$552$	−28.0332	+	20.7827i	−1.19317	+	0.884569i
$553$	11.5867	−	1.04348i	0.492715	−	0.0443732i
$554$	4.01369	−	1.17604i	0.170525	−	0.0499653i
$555$	−3.98325	+	18.0547i	−0.169080	+	0.766380i
$556$	23.6048	+	36.8219i	1.00107	+	1.56159i
$557$		−	15.0439i		−	0.637432i	−0.947850	−	0.318716i	$-0.896748\pi$
$557$		−	15.0439i		−	0.637432i	0.947850	−	0.318716i	$-0.103252\pi$
$558$	−3.15557	+	20.9849i	−0.133586	+	0.888360i
$559$	41.1556			1.74070
$560$	−12.9589	−	4.59657i	−0.547614	−	0.194240i
$561$	2.07784	+	1.90008i	0.0877263	+	0.0802214i
$562$	−9.61285	−	32.8074i	−0.405493	−	1.38390i
$563$	4.47297	+	2.58247i	0.188513	+	0.108838i	0.591286	−	0.806462i	$-0.298620\pi$
$563$	4.47297	+	2.58247i	0.188513	+	0.108838i	−0.402773	+	0.915300i	$0.631954\pi$
$564$	−22.2553	+	8.19749i	−0.937117	+	0.345177i
$565$	−3.16019	−	5.47361i	−0.132950	−	0.230276i
$566$	−5.75641	−	5.49498i	−0.241960	−	0.230971i
$567$	−16.7252	+	16.9489i	−0.702394	+	0.711788i
$568$	21.5090	−	24.7373i	0.902499	−	1.03795i
$569$	−6.90418	−	11.9584i	−0.289438	−	0.501322i	0.684237	−	0.729259i	$-0.260135\pi$
$569$	−6.90418	−	11.9584i	−0.289438	−	0.501322i	−0.973676	+	0.227937i	$0.926802\pi$
$570$	10.4263	−	21.2730i	0.436709	−	0.891028i
$571$	−6.03708	+	10.4565i	−0.252644	+	0.437592i	−0.964253	−	0.264984i	$-0.914633\pi$
$571$	−6.03708	+	10.4565i	−0.252644	+	0.437592i	0.711609	+	0.702576i	$0.247967\pi$
$572$	2.28421	+	1.18088i	0.0955074	+	0.0493751i
$573$	−18.9473	−	17.3264i	−0.791535	−	0.723819i
$574$	0.134711	+	0.342385i	0.00562273	+	0.0142909i
$575$		−	23.5919i		−	0.983849i
$576$	−16.3996	−	17.5229i	−0.683318	−	0.730121i
$577$			24.1119i			1.00379i	0.864928	+	0.501897i	$0.167364\pi$
$577$			24.1119i			1.00379i	−0.864928	+	0.501897i	$0.832636\pi$
$578$	10.7867	+	2.62332i	0.448668	+	0.109116i
$579$	−18.3358	−	4.04527i	−0.762011	−	0.168116i
$580$	6.61179	−	12.7893i	0.274539	−	0.531048i
$581$	11.5133	−	1.03687i	0.477650	−	0.0430164i
$582$	−5.35218	−	7.96799i	−0.221855	−	0.330284i
$583$	−1.51600	+	0.875261i	−0.0627862	+	0.0362496i
$584$	7.59310	−	8.73275i	0.314205	−	0.361364i
$585$	−13.9409	−	6.46602i	−0.576383	−	0.267337i
$586$	8.28760	−	8.68189i	0.342357	−	0.358645i
$587$	6.34357	−	3.66246i	0.261827	−	0.151166i	−0.363341	−	0.931656i	$-0.618364\pi$
$587$	6.34357	−	3.66246i	0.261827	−	0.151166i	0.625168	+	0.780490i	$0.285031\pi$
$588$	−20.8906	+	12.3118i	−0.861515	+	0.507732i
$589$	−32.2452	−	18.6168i	−1.32864	−	0.767091i
$590$	3.17674	−	0.930812i	0.130784	−	0.0383209i
$591$	18.3944	−	5.82043i	0.756645	−	0.239421i
$592$	−26.8133	+	19.0019i	−1.10202	+	0.780972i
$593$			30.3427i			1.24602i	0.782212	+	0.623012i	$0.214091\pi$
$593$			30.3427i			1.24602i	−0.782212	+	0.623012i	$0.785909\pi$
$594$	0.858503	−	2.23729i	0.0352248	−	0.0917969i
$595$	−9.86440	−	14.0116i	−0.404401	−	0.574422i
$596$	5.28652	+	8.24661i	0.216544	+	0.337794i
$597$	7.77227	+	24.5628i	0.318098	+	1.00529i
$598$	−38.1148	+	11.1680i	−1.55863	+	0.456692i
$599$	40.4470	+	23.3521i	1.65262	+	0.954140i	0.975990	+	0.217815i	$0.0698931\pi$
$599$	40.4470	+	23.3521i	1.65262	+	0.954140i	0.676629	+	0.736324i	$0.263440\pi$
$600$	16.1192	−	1.85130i	0.658064	−	0.0755790i
$601$	1.59450	−	0.920586i	0.0650410	−	0.0375515i	−0.467127	−	0.884190i	$-0.654711\pi$
$601$	1.59450	−	0.920586i	0.0650410	−	0.0375515i	0.532168	+	0.846639i	$0.321378\pi$
$602$	5.78853	−	38.6264i	0.235923	−	1.57430i
$603$	3.80258	+	42.4626i	0.154853	+	1.72921i
$604$	−1.77758	+	0.0826496i	−0.0723289	+	0.00336296i
$605$	−7.07679	−	12.2574i	−0.287713	−	0.498333i
$606$	−7.48836	+	5.03001i	−0.304194	+	0.204330i
$607$	2.98185	−	5.16472i	0.121030	−	0.209629i	−0.799144	−	0.601139i	$-0.794714\pi$
$607$	2.98185	−	5.16472i	0.121030	−	0.209629i	0.920174	+	0.391510i	$0.128047\pi$
$608$	39.1378	−	15.5394i	1.58725	−	0.630205i
$609$	−9.80020	−	23.4227i	−0.397124	−	0.949137i
$610$	8.06787	+	1.96211i	0.326659	+	0.0794433i
$611$	−26.9933			−1.09203
$612$	−4.04852	−	29.6344i	−0.163652	−	1.19790i
$613$		−	9.66261i		−	0.390269i	−0.980776	−	0.195135i	$-0.937486\pi$
$613$		−	9.66261i		−	0.390269i	0.980776	−	0.195135i	$-0.0625144\pi$
$614$	−7.67252	+	31.5482i	−0.309638	+	1.27318i
$615$	0.163304	+	0.149333i	0.00658504	+	0.00602169i
$616$	1.42958	−	1.97774i	0.0575996	−	0.0796854i
$617$	5.04300	−	8.73472i	0.203023	−	0.351647i	−0.746478	−	0.665410i	$-0.768257\pi$
$617$	5.04300	−	8.73472i	0.203023	−	0.351647i	0.949501	+	0.313764i	$0.101590\pi$
$618$	−16.5508	−	8.11185i	−0.665771	−	0.326306i
$619$	−21.3502	+	12.3266i	−0.858139	+	0.495447i	−0.863389	−	0.504540i	$-0.831662\pi$
$619$	−21.3502	+	12.3266i	−0.858139	+	0.495447i	0.00524975	+	0.999986i	$0.498329\pi$
$620$	0.603656	+	12.9831i	0.0242434	+	0.521415i
$621$	14.2694	+	34.1524i	0.572610	+	1.37049i
$622$	−26.4070	+	27.6633i	−1.05882	+	1.10920i
$623$	−3.60717	+	7.78737i	−0.144518	+	0.311994i
$624$	−10.6215	−	25.1657i	−0.425200	−	1.00743i
$625$	−1.26437	+	2.18996i	−0.0505749	+	0.0875984i
$626$	0.807417	−	0.236580i	0.0322709	−	0.00945564i
$627$	3.10284	+	2.83740i	0.123916	+	0.113315i
$628$	−20.4076	+	13.0824i	−0.814352	+	0.522044i
$629$	−40.9560			−1.63302
$630$	−8.02943	+	12.1747i	−0.319900	+	0.485051i
$631$		−	34.4547i		−	1.37162i	−0.727781	−	0.685809i	$-0.759448\pi$
$631$		−	34.4547i		−	1.37162i	0.727781	−	0.685809i	$-0.240552\pi$
$632$	12.2080	+	2.37452i	0.485609	+	0.0944534i
$633$	−1.01348	−	0.223594i	−0.0402821	−	0.00888708i
$634$	22.5850	−	6.61760i	0.896965	−	0.262818i
$635$	−1.02771	−	0.593348i	−0.0407834	−	0.0235463i
$636$	18.3252	+	3.15849i	0.726641	+	0.125242i
$637$	−27.1543	+	4.93094i	−1.07589	+	0.195371i
$638$	1.84829	+	1.76435i	0.0731744	+	0.0698512i
$639$	−20.0010	−	28.4404i	−0.791228	−	1.12508i
$640$	−11.9397	−	8.57407i	−0.471957	−	0.338920i
$641$	−24.3099	−	42.1059i	−0.960182	−	1.66308i	−0.722037	−	0.691855i	$-0.756794\pi$
$641$	−24.3099	−	42.1059i	−0.960182	−	1.66308i	−0.238146	−	0.971229i	$-0.576540\pi$
$642$	1.77739	+	26.1411i	0.0701478	+	1.03171i
$643$	−8.41406	−	4.85786i	−0.331818	−	0.191575i	0.324830	−	0.945772i	$-0.394693\pi$
$643$	−8.41406	−	4.85786i	−0.331818	−	0.191575i	−0.656648	+	0.754197i	$0.728026\pi$
$644$	5.12081	+	37.3433i	0.201788	+	1.47153i
$645$	−7.08672	−	22.3963i	−0.279039	−	0.881852i
$646$	50.9925	+	12.4014i	2.00627	+	0.487925i
$647$	33.0729			1.30023			0.650116	−	0.759835i	$-0.274720\pi$
$647$	33.0729			1.30023			0.650116	+	0.759835i	$0.274720\pi$
$648$	−22.2150	+	12.4296i	−0.872687	+	0.488281i
$649$			0.587506i			0.0230616i
$650$	17.9435	+	4.36385i	0.703801	+	0.171164i
$651$	18.2343	+	13.8884i	0.714657	+	0.544330i
$652$	16.1525	+	8.35045i	0.632579	+	0.327029i
$653$	−20.1944	−	11.6592i	−0.790267	−	0.456261i	0.0497898	−	0.998760i	$-0.484145\pi$
$653$	−20.1944	−	11.6592i	−0.790267	−	0.456261i	−0.840056	+	0.542499i	$0.817478\pi$
$654$	−6.90838	+	0.469715i	−0.270139	+	0.0183673i
$655$	−18.3282	+	10.5818i	−0.716142	+	0.413465i
$656$	0.0364978	+	0.391640i	0.00142500	+	0.0152910i
$657$	−7.06075	−	10.0400i	−0.275466	−	0.391697i
$658$	−3.79660	+	25.3344i	−0.148007	+	0.987638i
$659$	−5.88459	−	10.1924i	−0.229231	−	0.397040i	0.728349	−	0.685206i	$-0.240288\pi$
$659$	−5.88459	−	10.1924i	−0.229231	−	0.397040i	−0.957580	+	0.288166i	$0.906954\pi$
$660$	0.249293	−	1.44637i	0.00970372	−	0.0562999i
$661$	−0.661849	+	1.14636i	−0.0257430	+	0.0445881i	−0.878610	−	0.477540i	$-0.841528\pi$
$661$	−0.661849	+	1.14636i	−0.0257430	+	0.0445881i	0.852867	+	0.522128i	$0.174862\pi$
$662$	2.82871	+	9.65401i	0.109941	+	0.375214i
$663$	7.33389	−	33.2420i	0.284825	−	1.29101i
$664$	12.1307	+	2.35948i	0.470761	+	0.0915654i
$665$	−14.7306	−	20.9237i	−0.571227	−	0.811385i
$666$	12.7460	+	32.4433i	0.493896	+	1.25715i
$667$	−39.4673			−1.52818
$668$	−33.6287	+	21.5578i	−1.30113	+	0.834096i
$669$	−22.2017	+	24.2788i	−0.858368	+	0.938671i
$670$	7.34213	+	25.0577i	0.283651	+	0.968065i
$671$	−0.736804	+	1.27618i	−0.0284440	+	0.0492664i
$672$	−25.1131	+	6.42920i	−0.968757	+	0.248012i
$673$	−5.17124	−	8.95685i	−0.199337	−	0.345261i	0.748977	−	0.662596i	$-0.230545\pi$
$673$	−5.17124	−	8.95685i	−0.199337	−	0.345261i	−0.948314	+	0.317335i	$0.897212\pi$
$674$	12.9648	−	13.5816i	0.499384	−	0.523143i
$675$	2.19389	−	17.0690i	0.0844428	−	0.656985i
$676$	−0.236345	−	5.08319i	−0.00909020	−	0.195507i
$677$	−9.74305	−	16.8755i	−0.374456	−	0.648576i	0.615790	−	0.787911i	$-0.288837\pi$
$677$	−9.74305	−	16.8755i	−0.374456	−	0.648576i	−0.990245	+	0.139334i	$0.955504\pi$
$678$	−10.6998	−	5.24419i	−0.410925	−	0.201402i
$679$	−10.3260	+	0.929940i	−0.396274	+	0.0356878i
$680$	−5.96195	−	17.3215i	−0.228630	−	0.664250i
$681$	15.8326	+	14.4781i	0.606705	+	0.554802i
$682$	−2.24138	−	0.545103i	−0.0858268	−	0.0208731i
$683$	−23.7061			−0.907087			−0.453544	−	0.891234i	$-0.649840\pi$
$683$	−23.7061			−0.907087			−0.453544	+	0.891234i	$0.649840\pi$
$684$	−6.04568	−	44.2532i	−0.231162	−	1.69206i
$685$	22.3734			0.854843
$686$	0.808664	+	26.1791i	0.0308749	+	0.999523i
$687$	−4.78933	−	1.05663i	−0.182725	−	0.0403129i
$688$	17.4318	−	37.9416i	0.664582	−	1.44651i
$689$	18.3287	+	10.5821i	0.698268	+	0.403145i
$690$	12.6406	+	18.8185i	0.481218	+	0.716407i
$691$	−10.2582	+	5.92260i	−0.390242	+	0.225306i	−0.682265	−	0.731105i	$-0.739005\pi$
$691$	−10.2582	+	5.92260i	−0.390242	+	0.225306i	0.292023	+	0.956411i	$0.405672\pi$
$692$	−0.350043	−	7.52854i	−0.0133066	−	0.286192i
$693$	−1.67285	−	1.97512i	−0.0635465	−	0.0750287i
$694$	12.2238	−	12.8053i	0.464009	−	0.486084i
$695$	24.6068	−	14.2067i	0.933389	−	0.538892i
$696$	−3.09707	−	26.9661i	−0.117394	−	1.02215i
$697$	−0.245095	+	0.424517i	−0.00928364	+	0.0160797i
$698$	−0.867636	−	2.96113i	−0.0328405	−	0.112080i
$699$	4.27953	+	13.5246i	0.161867	+	0.511549i
$700$	6.61942	−	16.2270i	0.250191	−	0.613323i
$701$		−	10.4649i		−	0.395253i	−0.980277	−	0.197627i	$-0.936677\pi$
$701$		−	10.4649i		−	0.395253i	0.980277	−	0.197627i	$-0.0633233\pi$
$702$	−28.6151	+	4.53573i	−1.08001	+	0.171190i
$703$	−61.1598			−2.30669
$704$	2.05616	−	1.60565i	0.0774943	−	0.0605152i
$705$	4.64806	+	14.6893i	0.175056	+	0.553232i
$706$	4.17936	−	1.22459i	0.157292	−	0.0460880i
$707$	0.873962	+	9.70440i	0.0328687	+	0.364972i
$708$	3.99316	−	4.79626i	0.150072	−	0.180254i
$709$	26.4576	−	15.2753i	0.993637	−	0.573677i	0.0872776	−	0.996184i	$-0.472183\pi$
$709$	26.4576	−	15.2753i	0.993637	−	0.573677i	0.906359	+	0.422507i	$0.138850\pi$
$710$	−15.4037	−	14.7041i	−0.578089	−	0.551835i
$711$	5.55037	−	11.9667i	0.208155	−	0.448786i
$712$	−6.02004	+	6.92358i	−0.225610	+	0.259472i
$713$	30.8557	−	17.8145i	1.15555	−	0.667159i
$714$	−30.1676	−	11.5587i	−1.12899	−	0.432572i
$715$	0.835222	−	1.44665i	0.0312355	−	0.0541015i
$716$	31.2180	+	16.1390i	1.16667	+	0.603142i
$717$	−2.75430	+	12.4843i	−0.102861	+	0.466235i
$718$	6.08580	−	25.0239i	0.227120	−	0.933883i
$719$	4.18381			0.156030			0.0780149	−	0.996952i	$-0.475142\pi$
$719$	4.18381			0.156030			0.0780149	+	0.996952i	$0.475142\pi$
$720$	−11.8658	+	10.1134i	−0.442214	+	0.376905i
$721$	−16.2790	+	11.4607i	−0.606262	+	0.426817i
$722$	50.0384	+	12.1693i	1.86223	+	0.452895i
$723$	−11.3361	−	10.3663i	−0.421595	−	0.385528i
$724$	30.4664	+	15.7504i	1.13228	+	0.585360i
$725$	15.8918	+	9.17513i	0.590206	+	0.340756i
$726$	−23.9608	−	11.7436i	−0.889267	−	0.435846i
$727$	9.16698	+	15.8777i	0.339985	+	0.588871i	0.984429	−	0.175780i	$-0.0562448\pi$
$727$	9.16698	+	15.8777i	0.339985	+	0.588871i	−0.644445	+	0.764651i	$0.722911\pi$
$728$	−29.3497	−	3.01271i	−1.08777	−	0.111658i
$729$	7.14811	+	26.0366i	0.264745	+	0.964319i
$730$	−5.43779	−	5.19083i	−0.201262	−	0.192121i
$731$	45.0645	−	26.0180i	1.66677	−	0.962309i
$732$	14.6890	−	5.41054i	0.542922	−	0.199979i
$733$	−0.508814	+	0.881292i	−0.0187935	+	0.0325513i	−0.875269	−	0.483636i	$-0.839316\pi$
$733$	−0.508814	+	0.881292i	−0.0187935	+	0.0325513i	0.856476	+	0.516187i	$0.172649\pi$
$734$	8.04498	+	27.4565i	0.296945	+	1.01344i
$735$	7.35914	+	13.9279i	0.271446	+	0.513739i
$736$	−5.84805	+	39.8686i	−0.215562	+	1.46958i
$737$	−4.63417			−0.170702
$738$	0.412558	+	0.0620379i	0.0151865	+	0.00228365i
$739$	28.5079			1.04868			0.524340	−	0.851509i	$-0.324312\pi$
$739$	28.5079			1.04868			0.524340	+	0.851509i	$0.324312\pi$
$740$	11.5218	+	17.9731i	0.423548	+	0.660706i
$741$	10.9517	−	49.6404i	0.402322	−	1.82359i
$742$	12.5097	−	15.7139i	0.459245	−	0.576877i
$743$	24.4419	+	14.1116i	0.896687	+	0.517703i	0.876124	−	0.482086i	$-0.160121\pi$
$743$	24.4419	+	14.1116i	0.896687	+	0.517703i	0.0205634	+	0.999789i	$0.493454\pi$
$744$	14.5931	+	19.6843i	0.535010	+	0.721660i
$745$	5.51093	−	3.18174i	0.201905	−	0.116570i
$746$	16.9820	+	16.2108i	0.621755	+	0.593518i
$747$	5.51520	−	11.8909i	0.201791	−	0.435064i
$748$	3.24769	−	0.151003i	0.118747	−	0.00552120i
$749$	25.6797	+	11.8950i	0.938314	+	0.434634i
$750$	−1.79443	−	26.3918i	−0.0655235	−	0.963694i
$751$	4.32718	+	2.49830i	0.157901	+	0.0911642i	0.576868	−	0.816837i	$-0.304275\pi$
$751$	4.32718	+	2.49830i	0.157901	+	0.0911642i	−0.418967	+	0.908001i	$0.637608\pi$
$752$	−11.4332	+	24.8853i	−0.416928	+	0.907473i
$753$	−18.8713	+	5.97133i	−0.687707	+	0.217607i
$754$	7.30037	−	30.0180i	0.265864	−	1.09319i
$755$			1.15601i			0.0420715i
$756$	0.232285	+	27.4945i	0.00844813	+	0.999964i
$757$		−	8.22743i		−	0.299031i	−0.988759	−	0.149516i	$-0.952229\pi$
$757$		−	8.22743i		−	0.299031i	0.988759	−	0.149516i	$-0.0477714\pi$
$758$	−6.24809	−	1.51954i	−0.226941	−	0.0551920i
$759$	−3.83593	+	1.21378i	−0.139236	+	0.0440575i
$760$	−8.90301	−	25.8663i	−0.322946	−	0.938270i
$761$	−8.92489	−	5.15279i	−0.323527	−	0.186788i	0.329437	−	0.944178i	$-0.393141\pi$
$761$	−8.92489	−	5.15279i	−0.323527	−	0.186788i	−0.652964	+	0.757389i	$0.726475\pi$
$762$	−2.23213	+	0.151767i	−0.0808617	+	0.00549795i
$763$	−3.14353	+	6.78644i	−0.113803	+	0.245685i
$764$	−29.6149	+	1.37696i	−1.07143	+	0.0498166i
$765$	−19.3526	+	1.73305i	−0.699696	+	0.0626587i
$766$	8.19518	−	8.58507i	0.296104	−	0.310191i
$767$	6.15144	−	3.55153i	0.222115	−	0.128238i
$768$	−27.6992	−	0.867129i	−0.999510	−	0.0312898i
$769$	−28.2448	−	16.3072i	−1.01853	−	0.588051i	−0.104856	−	0.994487i	$-0.533438\pi$
$769$	−28.2448	−	16.3072i	−1.01853	−	0.588051i	−0.913679	+	0.406436i	$0.866771\pi$
$770$	−1.24027	−	0.987363i	−0.0446962	−	0.0355821i
$771$	8.31004	−	37.6665i	0.299279	−	1.35653i
$772$	−18.2530	+	11.7012i	−0.656939	+	0.421134i
$773$	4.83211			0.173799			0.0868994	−	0.996217i	$-0.472304\pi$
$773$	4.83211			0.173799			0.0868994	+	0.996217i	$0.472304\pi$
$774$	−34.6347	−	27.6008i	−1.24492	−	0.992089i
$775$	−16.5657			−0.595057
$776$	−10.8797	−	2.11616i	−0.390559	−	0.0759657i
$777$	37.3454	+	4.78093i	1.33976	+	0.171515i
$778$	9.53977	−	2.79523i	0.342017	−	0.100214i
$779$	−0.366002	+	0.633934i	−0.0131134	+	0.0227130i
$780$	−16.6511	+	6.13324i	−0.596205	+	0.219605i
$781$	3.27308	−	1.88971i	0.117120	−	0.0676192i
$782$	−34.6746	+	36.3243i	−1.23996	+	1.29895i
$783$	−28.5550	−	3.67019i	−1.02047	−	0.131162i
$784$	−6.95559	+	27.1223i	−0.248414	+	0.968654i
$785$	7.87374	+	13.6377i	0.281026	+	0.486751i
$786$	−17.5600	+	35.8281i	−0.626345	+	1.27795i
$787$	4.66095	+	2.69100i	0.166145	+	0.0959239i	0.580767	−	0.814070i	$-0.302753\pi$
$787$	4.66095	+	2.69100i	0.166145	+	0.0959239i	−0.414622	+	0.909994i	$0.636086\pi$
$788$	10.2309	−	19.7898i	0.364460	−	0.704984i
$789$	−15.8200	−	14.4666i	−0.563206	−	0.515024i
$790$	1.90922	−	7.85043i	0.0679272	−	0.279306i
$791$	−10.5241	+	7.40914i	−0.374195	+	0.263439i
$792$	−1.13033	−	2.52566i	−0.0401646	−	0.0897456i
$793$	17.8162			0.632672
$794$	−46.6581	−	11.3472i	−1.65583	−	0.402699i
$795$	2.60253	−	11.7964i	0.0923022	−	0.418374i
$796$	26.4262	+	13.6617i	0.936651	+	0.484227i
$797$	−19.7648	+	34.2337i	−0.700106	+	1.21262i	0.268322	+	0.963329i	$0.413531\pi$
$797$	−19.7648	+	34.2337i	−0.700106	+	1.21262i	−0.968429	+	0.249291i	$0.919803\pi$
$798$	−45.0494	−	17.2606i	−1.59473	−	0.611019i
$799$	−29.5570	+	17.0647i	−1.04565	+	0.603707i
$800$	11.6232	−	14.6939i	0.410942	−	0.519507i
$801$	5.59797	+	7.96000i	0.197794	+	0.281253i
$802$	−21.3017	+	22.3151i	−0.752188	+	0.787974i
$803$	1.15546	−	0.667105i	0.0407753	−	0.0235416i
$804$	37.8323	+	31.4975i	1.33424	+	1.11083i
$805$	24.3875	−	2.19629i	0.859545	−	0.0774092i
$806$	7.84190	+	26.7634i	0.276219	+	0.942700i
$807$	3.43807	+	10.8654i	0.121026	+	0.382480i
$808$	−1.98878	+	10.2248i	−0.0699649	+	0.359707i
$809$	−11.8608			−0.417004			−0.208502	−	0.978022i	$-0.566859\pi$
$809$	−11.8608			−0.417004			−0.208502	+	0.978022i	$0.566859\pi$
$810$	7.39559	+	14.7909i	0.259855	+	0.519698i
$811$		−	31.6761i		−	1.11230i	−0.831083	−	0.556149i	$-0.812279\pi$
$811$		−	31.6761i		−	1.11230i	0.831083	−	0.556149i	$-0.187721\pi$
$812$	−27.1464	−	11.0738i	−0.952653	−	0.388612i
$813$	−10.1798	−	32.1712i	−0.357020	−	1.12829i
$814$	−3.63613	+	1.06542i	−0.127446	+	0.0373428i
$815$	5.90616	−	10.2298i	0.206884	−	0.358333i
$816$	−27.5397	−	20.8411i	−0.964081	−	0.729584i
$817$	67.2950	−	38.8528i	2.35435	−	1.35929i
$818$	31.0914	+	29.6794i	1.08708	+	1.03771i
$819$	−10.5678	+	29.4553i	−0.369269	+	1.02925i
$820$	0.255246	−	0.0118678i	0.00891357	−	0.000414440i
$821$	46.8366	−	27.0411i	1.63461	−	0.943742i	0.651963	−	0.758251i	$-0.273946\pi$
$821$	46.8366	−	27.0411i	1.63461	−	0.943742i	0.982646	−	0.185491i	$-0.0593875\pi$
$822$	35.0148	−	23.5198i	1.22128	−	0.820347i
$823$	28.2891	+	16.3327i	0.986097	+	0.569323i	0.904105	−	0.427310i	$-0.140539\pi$
$823$	28.2891	+	16.3327i	0.986097	+	0.569323i	0.0819917	+	0.996633i	$0.473872\pi$
$824$	−20.1245	+	6.92671i	−0.701070	+	0.241303i
$825$	1.82674	+	0.403018i	0.0635989	+	0.0140313i
$826$	−2.46808	−	6.27292i	−0.0858754	−	0.218263i
$827$	42.6757			1.48398			0.741989	−	0.670412i	$-0.233883\pi$
$827$	42.6757			1.48398			0.741989	+	0.670412i	$0.233883\pi$
$828$	39.5655	+	16.1630i	1.37499	+	0.561704i
$829$	−10.1684			−0.353163			−0.176582	−	0.984286i	$-0.556504\pi$
$829$	−10.1684			−0.353163			−0.176582	+	0.984286i	$0.556504\pi$
$830$	1.89713	−	7.80069i	0.0658503	−	0.270766i
$831$	−3.78018	−	3.45679i	−0.131133	−	0.119915i
$832$	−29.2415	−	11.8225i	−1.01377	−	0.409872i
$833$	−26.6161	+	22.5658i	−0.922193	+	0.781860i
$834$	23.5754	−	48.1015i	0.816351	−	1.66562i
$835$	12.9747	+	22.4729i	0.449009	+	0.777707i
$836$	4.84979	−	0.225493i	0.167733	−	0.00779884i
$837$	23.9810	−	10.0196i	0.828906	−	0.346329i
$838$	−7.46688	−	7.12777i	−0.257939	−	0.246225i
$839$	17.4730	+	30.2641i	0.603234	+	1.04483i	0.992328	+	0.123634i	$0.0394548\pi$
$839$	17.4730	+	30.2641i	0.603234	+	1.04483i	−0.389094	+	0.921198i	$0.627212\pi$
$840$	3.41435	+	16.4904i	0.117806	+	0.568974i
$841$	0.849240	−	1.47093i	0.0292842	−	0.0507216i
$842$	−32.1775	+	9.42830i	−1.10891	+	0.324921i
$843$	−28.2554	+	30.8987i	−0.973166	+	1.06421i
$844$	−1.00890	+	0.646758i	−0.0347277	+	0.0222623i
$845$	−3.30574			−0.113721
$846$	22.7163	+	18.1029i	0.781004	+	0.622390i
$847$	−23.5673	+	16.5917i	−0.809782	+	0.570098i
$848$	17.5190	−	12.4152i	0.601604	−	0.426340i
$849$	−2.09982	+	9.51774i	−0.0720655	+	0.326648i
$850$	22.4065	−	6.56528i	0.768535	−	0.225187i
$851$	29.2621	−	50.6835i	1.00309	−	1.73741i
$852$	−39.5646	−	6.81927i	−1.35546	−	0.233624i
$853$	−10.4075	−	18.0263i	−0.356345	−	0.617208i	0.631002	−	0.775781i	$-0.282644\pi$
$853$	−10.4075	−	18.0263i	−0.356345	−	0.617208i	−0.987347	+	0.158573i	$0.949311\pi$
$854$	2.50584	−	16.7213i	0.0857482	−	0.572192i
$855$	−28.8994	+	2.58798i	−0.988338	+	0.0885069i
$856$	22.8312	+	19.8517i	0.780356	+	0.678517i
$857$	27.0797	−	15.6344i	0.925023	−	0.534062i	0.0397892	−	0.999208i	$-0.487331\pi$
$857$	27.0797	−	15.6344i	0.925023	−	0.534062i	0.885234	+	0.465146i	$0.153998\pi$
$858$	−0.213634	−	3.14205i	−0.00729335	−	0.107268i
$859$	5.48681	+	3.16781i	0.187208	+	0.108084i	0.590675	−	0.806910i	$-0.298862\pi$
$859$	5.48681	+	3.16781i	0.187208	+	0.108084i	−0.403467	+	0.914994i	$0.632195\pi$
$860$	−24.0953	−	12.4567i	−0.821643	−	0.424770i
$861$	0.273043	−	0.358482i	0.00930529	−	0.0122170i
$862$	0.444151	−	1.82628i	0.0151278	−	0.0622033i
$863$		−	20.2434i		−	0.689093i	−0.938769	−	0.344547i	$-0.888033\pi$
$863$		−	20.2434i		−	0.689093i	0.938769	−	0.344547i	$-0.111967\pi$
$864$	−7.93865	+	28.3016i	−0.270078	+	0.962838i
$865$	−4.89601			−0.166469
$866$	4.84401	−	19.9178i	0.164606	−	0.676834i
$867$	−4.10167	−	12.9626i	−0.139300	−	0.440232i
$868$	26.2216	−	3.59572i	0.890019	−	0.122047i
$869$	1.24179	+	0.716946i	0.0421247	+	0.0243207i
$870$	−17.5924	+	1.19614i	−0.596439	+	0.0405531i
$871$	28.0140	+	48.5218i	0.949220	+	1.64410i
$872$	−5.24627	+	6.03367i	−0.177661	+	0.204326i
$873$	−4.94646	+	10.6646i	−0.167412	+	0.360943i
$874$	−51.7798	+	54.2433i	−1.75148	+	1.83481i
$875$	−25.9260	−	12.0091i	−0.876458	−	0.405982i
$876$	−13.9671	−	2.40733i	−0.471903	−	0.0813363i
$877$	9.52550	+	5.49955i	0.321653	+	0.185707i	0.652129	−	0.758108i	$-0.273876\pi$
$877$	9.52550	+	5.49955i	0.321653	+	0.185707i	−0.330476	+	0.943814i	$0.607209\pi$
$878$	2.82154	+	9.62953i	0.0952222	+	0.324981i
$879$	−14.3548	−	3.16697i	−0.484174	−	0.106819i
$880$	−0.979907	−	1.38274i	−0.0330327	−	0.0466120i
$881$		−	49.4216i		−	1.66506i	−0.553982	−	0.832529i	$-0.686892\pi$
$881$		−	49.4216i		−	1.66506i	0.553982	−	0.832529i	$-0.313108\pi$
$882$	26.1588	+	14.0612i	0.880812	+	0.473466i
$883$	20.7194			0.697264			0.348632	−	0.937260i	$-0.386646\pi$
$883$	20.7194			0.697264			0.348632	+	0.937260i	$0.386646\pi$
$884$	−21.2136	−	33.0918i	−0.713492	−	1.11300i
$885$	−2.99193	−	2.73597i	−0.100572	−	0.0919686i
$886$	−2.78671	−	9.51068i	−0.0936214	−	0.319518i
$887$	−26.5645	+	46.0110i	−0.891948	+	1.54490i	−0.0544101	+	0.998519i	$0.517328\pi$
$887$	−26.5645	+	46.0110i	−0.891948	+	1.54490i	−0.837537	+	0.546380i	$0.816005\pi$
$888$	36.9259	+	16.0162i	1.23915	+	0.537468i
$889$	−1.01569	+	2.19273i	−0.0340651	+	0.0735419i
$890$	4.31124	+	4.11545i	0.144513	+	0.137950i
$891$	−2.88821	+	0.521468i	−0.0967588	+	0.0174699i
$892$	1.76441	+	37.9480i	0.0590768	+	1.27059i
$893$	−44.1376	+	25.4829i	−1.47701	+	0.852752i
$894$	5.27995	−	10.7728i	0.176588	−	0.360296i
$895$	11.4149	−	19.7712i	0.381557	−	0.660877i
$896$	−15.2088	+	25.7816i	−0.508089	+	0.861304i
$897$	35.8974	+	32.8264i	1.19858	+	1.09604i
$898$	14.1056	+	3.43049i	0.470711	+	0.114477i
$899$			27.7130i			0.924281i
$900$	−12.1738	−	15.7061i	−0.405795	−	0.523537i
$901$	26.7593			0.891483
$902$	−0.0107166	+	0.0440650i	−0.000356824	+	0.00146721i
$903$	−44.1288	+	18.4637i	−1.46851	+	0.614435i
$904$	−13.0102	+	4.47801i	−0.432712	+	0.148937i
$905$	11.1401	−	19.2952i	0.370308	−	0.641393i
$906$	1.21525	+	1.80918i	0.0403738	+	0.0601060i
$907$	4.85783	+	8.41401i	0.161302	+	0.279382i	0.935336	−	0.353761i	$-0.115097\pi$
$907$	4.85783	+	8.41401i	0.161302	+	0.279382i	−0.774034	+	0.633144i	$0.781764\pi$
$908$	24.7465	−	1.15060i	0.821242	−	0.0381840i
$909$	10.0227	+	4.64871i	0.332431	+	0.154188i
$910$	−2.84056	+	18.9548i	−0.0941636	+	0.628347i
$911$	−26.8845	+	15.5218i	−0.890724	+	0.514259i	−0.874179	−	0.485604i	$-0.838600\pi$
$911$	−26.8845	+	15.5218i	−0.890724	+	0.514259i	−0.0165445	+	0.999863i	$0.505267\pi$
$912$	−41.1251	−	31.1221i	−1.36179	−	1.03056i
$913$	1.23392	+	0.712403i	0.0408368	+	0.0235771i
$914$	−5.66383	−	19.3299i	−0.187343	−	0.639377i
$915$	−3.06783	−	9.69531i	−0.101419	−	0.320517i
$916$	−4.76770	+	3.05635i	−0.157529	+	0.100985i
$917$	24.8093	+	35.2397i	0.819274	+	1.16372i
$918$	−28.4654	+	23.0565i	−0.939498	+	0.760979i
$919$		−	26.3950i		−	0.870692i	−0.900263	−	0.435346i	$-0.856626\pi$
$919$		−	26.3950i		−	0.870692i	0.900263	−	0.435346i	$-0.143374\pi$
$920$	25.6953	+	4.99786i	0.847147	+	0.164774i
$921$	37.9121	−	11.9963i	1.24925	−	0.395291i
$922$	−16.0509	−	54.7798i	−0.528610	−	1.80408i
$923$	−39.5722	−	22.8470i	−1.30253	−	0.752018i
$924$	−2.97900	−	0.241423i	−0.0980020	−	0.00794223i
$925$	−23.5652	+	13.6054i	−0.774819	+	0.447342i
$926$	−42.5851	−	40.6511i	−1.39943	−	1.33588i
$927$	2.01349	+	22.4843i	0.0661318	+	0.738480i
$928$	−24.5816	−	19.4446i	−0.806932	−	0.638302i
$929$	−4.54629	+	2.62480i	−0.149159	+	0.0861170i	−0.572722	−	0.819750i	$-0.694113\pi$
$929$	−4.54629	+	2.62480i	−0.149159	+	0.0861170i	0.423563	+	0.905867i	$0.360779\pi$
$930$	13.2139	−	8.87592i	0.433301	−	0.291053i
$931$	−39.7460	+	33.6977i	−1.30262	+	1.10440i
$932$	14.5507	+	7.52235i	0.476622	+	0.246403i
$933$	45.7390	+	10.0910i	1.49743	+	0.330364i
$934$	−6.28794	+	25.8550i	−0.205748	+	0.846003i
$935$		−	2.11206i		−	0.0690717i
$936$	−19.6118	+	27.1030i	−0.641031	+	0.885888i
$937$			58.0982i			1.89799i	0.315296	+	0.948993i	$0.397896\pi$
$937$			58.0982i			1.89799i	−0.315296	+	0.948993i	$0.602104\pi$
$938$	49.4800	−	19.4679i	1.61558	−	0.635649i
$939$	−0.760443	−	0.695388i	−0.0248161	−	0.0226931i
$940$	15.8037	+	8.17015i	0.515460	+	0.266481i
$941$	5.89990	−	10.2189i	0.192331	−	0.333128i	−0.753691	−	0.657229i	$-0.771729\pi$
$941$	5.89990	−	10.2189i	0.192331	−	0.333128i	0.946022	+	0.324101i	$0.105062\pi$
$942$	26.6591	+	13.0661i	0.868600	+	0.425717i
$943$	−0.350230	−	0.606616i	−0.0114051	−	0.0197541i
$944$	−0.668686	−	7.17533i	−0.0217639	−	0.233537i
$945$	17.8488	+	0.678828i	0.580623	+	0.0220823i
$946$	3.32406	−	3.48220i	0.108074	−	0.113216i
$947$	7.57377	+	13.1182i	0.246114	+	0.426283i	0.962444	−	0.271479i	$-0.0875127\pi$
$947$	7.57377	+	13.1182i	0.246114	+	0.426283i	−0.716330	+	0.697762i	$0.754179\pi$
$948$	−5.26472	−	14.2931i	−0.170990	−	0.464220i
$949$	−13.9697	−	8.06543i	−0.453477	−	0.261815i
$950$	33.4597	−	9.80397i	1.08558	−	0.318083i
$951$	−21.2711	−	19.4513i	−0.689761	−	0.630753i
$952$	−34.0419	+	15.2556i	−1.10330	+	0.494437i
$953$	−17.2489			−0.558745			−0.279373	−	0.960183i	$-0.590127\pi$
$953$	−17.2489			−0.558745			−0.279373	+	0.960183i	$0.590127\pi$
$954$	−8.32780	−	21.1974i	−0.269623	−	0.686292i
$955$			19.2594i			0.623218i
$956$	7.96697	+	12.4279i	0.257670	+	0.401947i
$957$	0.674216	−	3.05599i	0.0217943	−	0.0987860i
$958$	8.73391	+	29.8077i	0.282180	+	0.963043i
$959$	−4.08656	−	45.3768i	−0.131962	−	1.46529i
$960$	−1.39844	+	17.9485i	−0.0451345	+	0.579287i
$961$	2.99105	+	5.18065i	0.0964854	+	0.167118i
$962$	33.1361	+	31.6312i	1.06835	+	1.01983i
$963$	26.2490	−	18.4599i	0.845861	−	0.594862i
$964$	−17.7185	+	0.823830i	−0.570675	+	0.0265338i
$965$	7.04243	+	12.1978i	0.226704	+	0.392663i
$966$	35.8580	−	29.0743i	1.15371	−	0.935451i
$967$	17.7574	+	10.2522i	0.571038	+	0.329689i	0.757564	−	0.652761i	$-0.226389\pi$
$967$	17.7574	+	10.2522i	0.571038	+	0.329689i	−0.186526	+	0.982450i	$0.559723\pi$
$968$	−29.1344	+	10.0279i	−0.936417	+	0.322308i
$969$	−19.3900	−	61.2786i	−0.622898	−	1.96855i
$970$	−1.70149	+	6.99626i	−0.0546315	+	0.224636i
$971$		−	3.85440i		−	0.123694i	−0.998086	−	0.0618468i	$-0.980301\pi$
$971$		−	3.85440i		−	0.123694i	0.998086	−	0.0618468i	$-0.0196990\pi$
$972$	27.1230	+	15.3734i	0.869971	+	0.493104i
$973$	−33.3080	−	47.3116i	−1.06781	−	1.51674i
$974$	−0.955475	+	3.92876i	−0.0306154	+	0.125886i
$975$	−6.82306	−	21.5630i	−0.218513	−	0.690569i
$976$	7.54621	−	16.4249i	0.241548	−	0.525748i
$977$	−20.1938	+	34.9766i	−0.646056	+	1.11900i	0.338000	+	0.941146i	$0.390249\pi$
$977$	−20.1938	+	34.9766i	−0.646056	+	1.11900i	−0.984057	+	0.177856i	$0.943084\pi$
$978$	−1.51069	−	22.2186i	−0.0483064	−	0.710472i
$979$	−0.916082	+	0.528900i	−0.0292781	+	0.0169037i
$980$	17.3905	+	5.33199i	0.555518	+	0.170324i
$981$	4.87845	+	6.93688i	0.155757	+	0.221478i
$982$	−29.7839	+	31.2009i	−0.950443	+	0.995661i
$983$	−7.87355	−	13.6374i	−0.251127	−	0.434965i	0.712709	−	0.701460i	$-0.247468\pi$
$983$	−7.87355	−	13.6374i	−0.251127	−	0.434965i	−0.963836	+	0.266494i	$0.914135\pi$
$984$	0.386989	−	0.286898i	0.0123368	−	0.00914597i
$985$	−12.5334	−	7.23617i	−0.399348	−	0.230564i
$986$	−10.9832	−	37.4842i	−0.349776	−	1.19374i
$987$	28.9433	−	12.1101i	0.921277	−	0.385467i
$988$	−31.6785	−	49.4162i	−1.00783	−	1.57214i
$989$			74.3570i			2.36441i
$990$	−1.67307	+	0.657296i	−0.0531736	+	0.0208902i
$991$			50.4938i			1.60399i	0.597333	+	0.801994i	$0.296227\pi$
$991$			50.4938i			1.60399i	−0.597333	+	0.801994i	$0.703773\pi$
$992$	27.9948	+	4.10637i	0.888837	+	0.130377i
$993$	8.31451	−	9.09236i	0.263853	−	0.288537i
$994$	−27.0087	+	33.9268i	−0.856665	+	1.07609i
$995$	9.66276	−	16.7364i	0.306330	−	0.530579i
$996$	−5.23136	−	14.2026i	−0.165762	−	0.450026i
$997$	−22.4442	−	38.8745i	−0.710814	−	1.23117i	−0.964552	−	0.263893i	$-0.914993\pi$
$997$	−22.4442	−	38.8745i	−0.710814	−	1.23117i	0.253738	−	0.967273i	$-0.418340\pi$
$998$	11.3773	−	11.9186i	0.360143	−	0.377277i
$999$	25.8847	−	33.9489i	0.818956	−	1.07409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.be.a.139.10	yes	184
7.6	odd	2	inner	504.2.be.a.139.9	✓	184
8.3	odd	2	inner	504.2.be.a.139.54	yes	184
9.7	even	3	inner	504.2.be.a.475.53	yes	184
56.27	even	2	inner	504.2.be.a.139.53	yes	184
63.34	odd	6	inner	504.2.be.a.475.54	yes	184
72.43	odd	6	inner	504.2.be.a.475.9	yes	184
504.475	even	6	inner	504.2.be.a.475.10	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.be.a.139.9	✓	184	7.6	odd	2	inner
504.2.be.a.139.10	yes	184	1.1	even	1	trivial
504.2.be.a.139.53	yes	184	56.27	even	2	inner
504.2.be.a.139.54	yes	184	8.3	odd	2	inner
504.2.be.a.475.9	yes	184	72.43	odd	6	inner
504.2.be.a.475.10	yes	184	504.475	even	6	inner
504.2.be.a.475.53	yes	184	9.7	even	3	inner
504.2.be.a.475.54	yes	184	63.34	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37416 - 0.334195i) q^{2} +(0.522528 + 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(0.649625 - 1.12518i) q^{5} +(-0.166162 - 2.44385i) q^{6} +(-2.40071 - 1.11203i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +O(q^{10})\)	\(q+(-1.37416 - 0.334195i) q^{2} +(0.522528 + 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(0.649625 - 1.12518i) q^{5} +(-0.166162 - 2.44385i) q^{6} +(-2.40071 - 1.11203i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +(-1.26872 + 1.32908i) q^{10} +(-0.163051 - 0.282412i) q^{11} +(-0.588389 + 3.41377i) q^{12} +(-1.97132 + 3.41442i) q^{13} +(2.92732 + 2.33041i) q^{14} +(2.19752 + 0.484820i) q^{15} +(2.31281 + 3.26358i) q^{16} +4.98494i q^{17} +(3.94883 - 1.55137i) q^{18} +7.44404i q^{19} +(2.18760 - 1.40237i) q^{20} +(0.581909 - 4.54548i) q^{21} +(0.129677 + 0.442570i) q^{22} +(-6.16892 - 3.56163i) q^{23} +(1.94941 - 4.49442i) q^{24} +(1.65597 + 2.86823i) q^{25} +(3.84998 - 4.03315i) q^{26} +(-4.13208 - 3.15055i) q^{27} +(-3.24379 - 4.18065i) q^{28} +(4.79832 - 2.77031i) q^{29} +(-2.85772 - 1.40062i) q^{30} +(-2.50090 + 4.33168i) q^{31} +(-2.08749 - 5.25760i) q^{32} +(0.381163 - 0.416822i) q^{33} +(1.66595 - 6.85011i) q^{34} +(-2.81079 + 1.97884i) q^{35} +(-5.94478 + 0.812149i) q^{36} +8.21594i q^{37} +(2.48777 - 10.2293i) q^{38} +(-6.66848 - 1.47121i) q^{39} +(-3.47477 + 1.19599i) q^{40} +(0.0851599 + 0.0491671i) q^{41} +(-2.31871 + 6.05174i) q^{42} +(-5.21931 - 9.04011i) q^{43} +(-0.0302917 - 0.651499i) q^{44} +(0.347657 + 3.88222i) q^{45} +(7.28680 + 6.95587i) q^{46} +(3.42326 + 5.92926i) q^{47} +(-4.18081 + 5.52457i) q^{48} +(4.52680 + 5.33930i) q^{49} +(-1.31702 - 4.49483i) q^{50} +(-8.23190 + 2.60477i) q^{51} +(-6.63835 + 4.25554i) q^{52} -5.36803i q^{53} +(4.62523 + 5.71027i) q^{54} -0.423687 q^{55} +(3.06034 + 6.82893i) q^{56} +(-12.2927 + 3.88972i) q^{57} +(-7.51948 + 2.20327i) q^{58} +(-1.56024 - 0.900803i) q^{59} +(3.45888 + 2.87971i) q^{60} +(-2.25943 - 3.91345i) q^{61} +(4.88425 - 5.11663i) q^{62} +(7.81025 - 1.41420i) q^{63} +(1.11148 + 7.92241i) q^{64} +(2.56123 + 4.43618i) q^{65} +(-0.663079 + 0.445397i) q^{66} +(7.10542 - 12.3069i) q^{67} +(-4.57855 + 8.85639i) q^{68} +(2.65807 - 12.0481i) q^{69} +(4.52380 - 1.77988i) q^{70} +11.5897i q^{71} +(8.44049 + 0.870695i) q^{72} +4.09140i q^{73} +(2.74573 - 11.2900i) q^{74} +(-3.87117 + 4.23333i) q^{75} +(-6.83717 + 13.2253i) q^{76} +(0.0773877 + 0.859306i) q^{77} +(8.67188 + 4.25025i) q^{78} +(-3.80798 + 2.19854i) q^{79} +(5.17458 - 0.482231i) q^{80} +(3.04354 - 8.46976i) q^{81} +(-0.100592 - 0.0960235i) q^{82} +(-3.78385 + 2.18461i) q^{83} +(5.20875 - 7.54115i) q^{84} +(5.60898 + 3.23835i) q^{85} +(4.15100 + 14.1668i) q^{86} +(7.08201 + 6.47615i) q^{87} +(-0.176102 + 0.905387i) q^{88} -3.24378i q^{89} +(0.819682 - 5.45097i) q^{90} +(8.52947 - 6.00487i) q^{91} +(-7.68860 - 11.9937i) q^{92} +(-8.45991 - 1.86644i) q^{93} +(-2.72257 - 9.29178i) q^{94} +(8.37592 + 4.83584i) q^{95} +(7.59138 - 6.19443i) q^{96} +(3.39365 - 1.95932i) q^{97} +(-4.43617 - 8.84988i) q^{98} +(0.887489 + 0.411634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9	\( 184 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} - 4 q^{11} - 10 q^{14} - 2 q^{16} - 10 q^{18} + 6 q^{22} - 80 q^{25} - 12 q^{28} + 4 q^{30} - 12 q^{32} + 12 q^{35} - 46 q^{36} + 10 q^{42} - 4 q^{43} - 36 q^{44} - 16 q^{46} - 2 q^{49} + 16 q^{50} - 24 q^{51} + 40 q^{56} + 16 q^{57} - 10 q^{58} + 40 q^{60} - 8 q^{64} + 36 q^{65} - 4 q^{67} - 76 q^{72} - 40 q^{74} + 60 q^{78} + 8 q^{81} + 40 q^{84} + 32 q^{86} - 18 q^{88} + 20 q^{91} - 26 q^{92} - 132 q^{98} + 28 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 2 * q^4 - 8 * q^8 - 8 * q^9 - 4 * q^11 - 10 * q^14 - 2 * q^16 - 10 * q^18 + 6 * q^22 - 80 * q^25 - 12 * q^28 + 4 * q^30 - 12 * q^32 + 12 * q^35 - 46 * q^36 + 10 * q^42 - 4 * q^43 - 36 * q^44 - 16 * q^46 - 2 * q^49 + 16 * q^50 - 24 * q^51 + 40 * q^56 + 16 * q^57 - 10 * q^58 + 40 * q^60 - 8 * q^64 + 36 * q^65 - 4 * q^67 - 76 * q^72 - 40 * q^74 + 60 * q^78 + 8 * q^81 + 40 * q^84 + 32 * q^86 - 18 * q^88 + 20 * q^91 - 26 * q^92 - 132 * q^98 + 28 * q^99

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