LMFDB - Embedded newform 504.2.be.a.139.9

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			139.9
Character	$\chi$	$=$	504.139
Dual form			504.2.be.a.475.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37416 - 0.334195i) q^{2} +(-0.522528 - 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(-0.649625 + 1.12518i) q^{5} +(0.166162 + 2.44385i) q^{6} +(-0.237312 + 2.63509i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +O(q^{10})$	\(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} +(-0.237312 + 2.63509i) 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} +(1.20674 - 3.54172i) 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} +(4.47546 - 0.985021i) 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} +(-2.84188 + 4.46360i) 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} +(-6.47918 - 0.142102i) 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} +(-6.88737 - 1.25067i) 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} +(5.39691 - 5.18396i) 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} +(-3.96517 - 6.87586i) 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} +(3.20116 + 3.65859i) 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} +(0.782874 - 0.362633i) 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} +(8.85594 + 2.36058i) 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} +(9.04637 + 4.02035i) 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	−0.973933	−	0.226836i	$-0.927162\pi$
$5$	−0.649625	+	1.12518i	−0.290521	+	0.503197i	0.683412	+	0.730033i	$0.260495\pi$
$6$	0.166162	+	2.44385i	0.0678354	+	0.997697i
$7$	−0.237312	+	2.63509i	−0.0896954	+	0.995969i
$7$	−0.237312	+	2.63509i	−0.0896954	+	0.995969i
$8$	−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	$-0.649200\pi$
$13$	1.97132	−	3.41442i	0.546745	−	0.946989i	0.998495	−	0.0548450i	$-0.0174665\pi$
$14$	1.20674	−	3.54172i	0.322514	−	0.946565i
$15$	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	$-0.793368\pi$
$17$		−	4.98494i		−	1.20903i	0.796595	−	0.604513i	$-0.206632\pi$
$18$	3.94883	−	1.55137i	0.930748	−	0.365661i
$19$		−	7.44404i		−	1.70778i	−0.520453	−	0.853890i	$-0.674237\pi$
$19$		−	7.44404i		−	1.70778i	0.520453	−	0.853890i	$-0.325763\pi$
$20$	−2.18760	+	1.40237i	−0.489161	+	0.313579i
$21$	4.47546	−	0.985021i	0.976625	−	0.214949i
$22$	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
$28$	−2.84188	+	4.46360i	−0.537064	+	0.843541i
$29$	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	−0.549158	−	0.835718i	$-0.685052\pi$
$31$	2.50090	−	4.33168i	0.449174	−	0.777992i	0.998332	+	0.0577260i	$0.0183850\pi$
$32$	−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	0.493335	−	0.869839i	$-0.335778\pi$
$41$	−0.0851599	−	0.0491671i	−0.0132997	−	0.00767861i	−0.506635	+	0.862161i	$0.669111\pi$
$42$	−6.47918	−	0.142102i	−0.999760	−	0.0219268i
$43$	−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	0.500666	−	0.865640i	$-0.333088\pi$
$47$	−3.42326	−	5.92926i	−0.499333	−	0.864871i	−1.00000		0.000769517i	$0.999755\pi$
$48$	4.18081	−	5.52457i	0.603448	−	0.797403i
$49$	−6.88737	−	1.25067i	−0.983909	−	0.178668i
$50$	−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
$56$	5.39691	−	5.18396i	0.721192	−	0.692735i
$57$	−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	0.598112	−	0.801412i	$-0.295918\pi$
$59$	1.56024	+	0.900803i	0.203125	+	0.117275i	−0.394987	+	0.918687i	$0.629251\pi$
$60$	3.45888	+	2.87971i	0.446540	+	0.371770i
$61$	2.25943	+	3.91345i	0.289291	+	0.501066i	0.973641	−	0.228088i	$-0.0732473\pi$
$61$	2.25943	+	3.91345i	0.289291	+	0.501066i	−0.684350	+	0.729154i	$0.739914\pi$
$62$	−4.88425	+	5.11663i	−0.620301	+	0.649812i
$63$	−3.96517	−	6.87586i	−0.499564	−	0.866277i
$64$	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
$70$	3.20116	+	3.65859i	0.382612	+	0.437285i
$71$			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	$-0.923039\pi$
$73$		−	4.09140i		−	0.478862i	0.970913	−	0.239431i	$-0.0769608\pi$
$74$	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
$77$	0.782874	−	0.362633i	0.0892168	−	0.0413259i
$78$	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	−0.277746	−	0.960654i	$-0.589587\pi$
$83$	3.78385	−	2.18461i	0.415332	−	0.239792i	0.693078	+	0.720863i	$0.256254\pi$
$84$	8.85594	+	2.36058i	0.966262	+	0.257561i
$85$	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	$0.0549970\pi$
$89$			3.24378i			0.343840i	−0.985111	+	0.171920i	$0.945003\pi$
$90$	−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	−0.662292	−	0.749246i	$-0.730416\pi$
$97$	−3.39365	+	1.95932i	−0.344572	+	0.198939i	0.317720	+	0.948185i	$0.397083\pi$
$98$	9.04637	+	4.02035i	0.913821	+	0.406117i
$99$	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	0.942977	−	0.332859i	$-0.108013\pi$
$101$	1.84138	+	3.18937i	0.183224	+	0.317354i	−0.759752	+	0.650212i	$0.774680\pi$
$102$	12.1824	−	0.828309i	1.20624	−	0.0820148i
$103$	−3.76237	+	6.51662i	−0.370718	+	0.642102i	−0.989676	−	0.143322i	$-0.954222\pi$
$103$	−3.76237	+	6.51662i	−0.370718	+	0.642102i	0.618958	+	0.785424i	$0.287555\pi$
$104$	−10.5443	+	3.62929i	−1.03396	+	0.355881i
$105$	−1.79904	+	5.67561i	−0.175568	+	0.553883i
$106$	−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
$112$	−9.14866	+	5.31996i	−0.864467	+	0.502689i
$113$	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
$119$	13.1358	+	1.18299i	1.20415	+	0.108444i
$120$	−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
$126$	3.15089	+	10.7737i	0.280704	+	0.959794i
$127$		−	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	0.967553	−	0.252668i	$-0.0813079\pi$
$131$	14.1068	+	8.14454i	1.23251	+	0.711592i	0.264960	+	0.964259i	$0.414641\pi$
$132$	−1.06003	+	0.390449i	−0.0922634	+	0.0339842i
$133$	19.6157	+	1.76656i	1.70090	+	0.153180i
$134$	−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	$-0.955322\pi$
$139$	−18.9392	−	10.9346i	−1.60640	−	0.927458i	−0.616239	−	0.787559i	$-0.711344\pi$
$140$	−3.17622	−	6.09730i	−0.268439	−	0.515316i
$141$	−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
$147$	1.53354	+	12.0270i	0.126484	+	0.991969i
$148$	−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
$154$	−1.19698	+	0.236683i	−0.0964557	+	0.0190724i
$155$	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	−0.516166	−	0.856489i	$-0.672641\pi$
$157$	6.06022	−	10.4966i	0.483658	−	0.837720i	0.999824	+	0.0187685i	$0.00597455\pi$
$158$	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	$-0.552207\pi$
$167$	9.98632	−	17.2968i	0.772765	−	1.33847i	0.936042	−	0.351888i	$-0.114460\pi$
$168$	−11.3806	−	6.20343i	−0.878030	−	0.478605i
$169$	−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	0.928719	−	0.370785i	$-0.120911\pi$
$173$	1.88417	+	3.26347i	0.143251	+	0.248117i	−0.785468	+	0.618902i	$0.787578\pi$
$174$	7.56751	+	11.2660i	0.573692	+	0.854076i
$175$	−7.95102	+	3.68297i	−0.601041	+	0.278406i
$176$	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	$-0.719956\pi$
$181$	−17.1485			−1.27463			−0.637317	+	0.770601i	$0.719956\pi$
$182$	−9.71406	−	11.1022i	−0.720054	−	0.822947i
$183$	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
$189$	−9.28256	+	10.1407i	−0.675207	+	0.737629i
$190$	−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
$196$	−11.0876	−	8.54786i	−0.791969	−	0.610561i
$197$		−	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	$-0.676761\pi$
$199$	−14.8744			−1.05442			−0.527208	+	0.849736i	$0.676761\pi$
$200$	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
$203$	6.16131	+	13.3014i	0.432439	+	0.933576i
$204$	−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
$210$	4.36893	−	7.19796i	0.301485	−	0.496706i
$211$	−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	$-0.947261\pi$
$223$	−9.49725	−	16.4497i	−0.635983	−	1.10156i	0.350323	−	0.936629i	$-0.386072\pi$
$224$	14.3496	−	4.25303i	0.958775	−	0.284168i
$225$	−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	−0.811796	−	0.583942i	$-0.801510\pi$
$227$	−10.7271	+	6.19331i	−0.711985	+	0.411065i	0.0998107	+	0.995006i	$0.468176\pi$
$228$	−25.4122	−	4.38000i	−1.68297	−	0.290072i
$229$	1.41581	−	2.45225i	0.0935593	−	0.162049i	−0.815447	−	0.578832i	$-0.803509\pi$
$229$	1.41581	−	2.45225i	0.0935593	−	0.162049i	0.909006	+	0.416782i	$0.136842\pi$
$230$	−12.5603	+	3.68028i	−0.828203	+	0.242671i
$231$	−1.00791	−	1.10332i	−0.0663155	−	0.0725928i
$232$	−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
$238$	−17.6553	−	6.01552i	−1.14442	−	0.389928i
$239$	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	−0.231791	−	0.972766i	$-0.574459\pi$
$241$	7.68063	−	4.43441i	0.494753	−	0.285646i	0.726544	+	0.687120i	$0.241125\pi$
$242$	−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
$245$	5.88144	−	6.93708i	0.375752	−	0.443194i
$246$	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	$-0.882552\pi$
$251$		−	11.4278i		−	0.721314i	0.932698	−	0.360657i	$-0.117448\pi$
$252$	−0.729319	−	15.8577i	−0.0459428	−	0.998944i
$253$			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	0.961229	−	0.275750i	$-0.0889263\pi$
$257$	19.2862	+	11.1349i	1.20304	+	0.694574i	0.241808	+	0.970324i	$0.422260\pi$
$258$	21.2254	−	14.2573i	1.32144	−	0.887622i
$259$	−21.6497	−	1.94974i	−1.34525	−	0.121151i
$260$	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
$266$	−26.3647	−	8.98301i	−1.61653	−	0.550784i
$267$	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	$-0.564284\pi$
$269$	−6.57969			−0.401171			−0.200585	+	0.979676i	$0.564284\pi$
$270$	9.42977	−	1.49470i	0.573878	−	0.0909645i
$271$	19.4818			1.18343			0.591716	−	0.806146i	$-0.298451\pi$
$271$	19.4818			1.18343			0.591716	+	0.806146i	$0.298451\pi$
$272$	16.2687	−	11.5292i	0.986438	−	0.699061i
$273$	5.45927	−	17.2229i	0.330410	−	1.04238i
$274$	−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
$280$	2.32694	+	9.44014i	0.139061	+	0.564156i
$281$	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	0.348113	−	0.937453i	$-0.386823\pi$
$283$	−4.87331	−	2.81361i	−0.289688	−	0.167252i	−0.637801	+	0.770201i	$0.720156\pi$
$284$	−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	−0.715037	−	0.699087i	$-0.753590\pi$
$293$	4.24352	−	7.34998i	0.247909	−	0.429391i	0.962945	+	0.269696i	$0.0869233\pi$
$294$	1.91204	−	17.0395i	0.111512	−	0.993763i
$295$	−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
$301$	25.0601	−	11.6080i	1.44444	−	0.669075i
$302$	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	$0.227393\pi$
$307$			22.9582i			1.31029i	−0.755502	+	0.655147i	$0.772607\pi$
$308$	1.72395	+	0.0747869i	0.0982309	+	0.00426138i
$309$	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	$0.444778\pi$
$311$	−13.5212	+	23.4195i	−0.766718	+	1.32800i	−0.939333	+	0.343006i	$0.888555\pi$
$312$	11.5029	+	15.5160i	0.651226	+	0.878421i
$313$	0.515228	−	0.297467i	0.0291224	−	0.0168138i	−0.485368	−	0.874310i	$-0.661314\pi$
$313$	0.515228	−	0.297467i	0.0291224	−	0.0168138i	0.514491	+	0.857496i	$0.327981\pi$
$314$	−11.8356	+	12.3987i	−0.667923	+	0.699699i
$315$	10.3125	+	0.00518757i	0.581042	+	0.000292287i
$316$	−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
$322$	−20.0586	+	17.5506i	−1.11782	+	0.978059i
$323$	−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
$329$	16.4365	−	7.61350i	0.906173	−	0.419746i
$330$	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
$336$	13.5656	+	12.3278i	0.740062	+	0.672539i
$337$	−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	0.835349	−	0.549719i	$-0.185265\pi$
$349$	−1.09093	−	1.88955i	−0.0583963	−	0.101145i	−0.893746	+	0.448574i	$0.851932\pi$
$350$	12.1568	−	2.40379i	0.649808	−	0.128488i
$351$	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	−0.427345	−	0.904089i	$-0.640551\pi$
$353$	2.66693	−	1.53975i	0.141946	−	0.0819527i	0.569291	+	0.822136i	$0.307218\pi$
$354$	−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
$357$	−4.91028	−	22.3099i	−0.259879	−	1.18077i
$358$	−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
$364$	9.63837	+	18.5025i	0.505188	+	0.969796i
$365$	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	$0.0103995\pi$
$367$	10.1154	+	17.5205i	0.528022	+	0.914561i	−0.471444	+	0.881896i	$0.656267\pi$
$368$	−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
$371$	14.1452	+	1.27390i	0.734384	+	0.0661374i
$372$	−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
$378$	16.1447	−	10.8328i	0.830393	−	0.557178i
$379$	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	−0.738676	−	0.674061i	$-0.764549\pi$
$383$	4.19619	−	7.26802i	0.214415	−	0.371378i	0.953092	+	0.302682i	$0.0978820\pi$
$384$	−19.1765	+	4.03269i	−0.978596	+	0.205792i
$385$	−0.100546	+	1.11645i	−0.00512430	+	0.0568997i
$386$	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
$392$	12.3794	+	15.4515i	0.625256	+	0.780420i
$393$	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	$-0.824641\pi$
$397$	−33.9539			−1.70410			−0.852050	+	0.523461i	$0.824641\pi$
$398$	20.4397	+	4.97094i	1.02455	+	0.249171i
$399$	−7.33254	−	33.3155i	−0.367086	−	1.66786i
$400$	−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
$406$	−4.02135	−	20.3373i	−0.199576	−	1.00933i
$407$	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	0.980665	−	0.195696i	$-0.0626965\pi$
$409$	26.3216	+	15.1968i	1.30152	+	0.751433i	0.320855	+	0.947128i	$0.396030\pi$
$410$	−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	0.337579	−	0.941297i	$-0.390392\pi$
$419$	−6.32138	−	3.64965i	−0.308819	−	0.178297i	−0.646398	+	0.763000i	$0.723725\pi$
$420$	−8.40913	+	8.43106i	−0.410324	+	0.411394i
$421$	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
$427$	−10.8485	+	5.02509i	−0.524994	+	0.243181i
$428$	−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	$-0.886765\pi$
$433$		−	14.4945i		−	0.696563i	0.937390	−	0.348282i	$-0.113235\pi$
$434$	−12.3237	−	14.0847i	−0.591555	−	0.676086i
$435$	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	0.938182	−	0.346143i	$-0.112509\pi$
$439$	3.54769	+	6.14478i	0.169322	+	0.293275i	−0.768860	+	0.639418i	$0.779176\pi$
$440$	−0.904326	−	0.786309i	−0.0431120	−	0.0374858i
$441$	19.0595	−	8.81684i	0.907594	−	0.419850i
$442$	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
$448$	−21.1400	+	1.04877i	−0.998772	+	0.0495496i
$449$	−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
$455$	−12.2975	+	5.69631i	−0.576518	+	0.267047i
$456$	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	$-0.777527\pi$
$461$	−20.1818	−	34.9560i	−0.939962	−	1.62806i	−0.174425	−	0.984670i	$-0.555807\pi$
$462$	1.01630	+	1.85297i	0.0472827	+	0.0862079i
$463$	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	$0.143369\pi$
$467$			18.8152i			0.870662i	−0.900270	+	0.435331i	$0.856631\pi$
$468$	−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
$476$	22.2508	+	14.1666i	1.01986	+	0.649325i
$477$	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	$0.000649596\pi$
$479$	10.9817	+	19.0208i	0.501766	+	0.869085i	−0.498232	+	0.867044i	$0.666017\pi$
$480$	−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
$483$	−31.1170	−	9.86341i	−1.41587	−	0.448800i
$484$	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
$490$	−10.4004	+	7.56711i	−0.469841	+	0.341847i
$491$	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
$497$	−30.5399	−	2.75038i	−1.36990	−	0.123371i
$498$	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	$-0.201982\pi$
$503$	36.1238			1.61068			0.805341	+	0.592812i	$0.201982\pi$
$504$	−4.29738	+	22.0348i	−0.191421	+	0.981508i
$505$	−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	$-0.566563\pi$
$509$	16.7710	−	29.0482i	0.743362	−	1.28754i	0.950956	−	0.309326i	$-0.100103\pi$
$510$	−6.98202	+	14.2456i	−0.309169	+	0.630805i
$511$	10.7812	+	0.970936i	0.476931	+	0.0429517i
$512$	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
$518$	29.0986	+	9.91448i	1.27852	+	0.435617i
$519$	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	$-0.958319\pi$
$521$		−	5.96073i		−	0.261144i	0.991439	−	0.130572i	$-0.0416814\pi$
$522$	14.6500	−	18.3835i	0.641211	−	0.804622i
$523$		−	8.95062i		−	0.391383i	−0.980665	−	0.195692i	$-0.937305\pi$
$523$		−	8.95062i		−	0.391383i	0.980665	−	0.195692i	$-0.0626952\pi$
$524$	17.5819	+	27.4265i	0.768068	+	1.19813i
$525$	10.2365	+	11.2055i	0.446758	+	0.489047i
$526$	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
$532$	33.2272	+	21.1551i	1.44058	+	0.917188i
$533$	−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
$546$	−13.2577	+	21.8425i	−0.567378	+	0.934773i
$547$	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
$553$	−4.88966	−	10.5561i	−0.207929	−	0.448891i
$554$	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
$560$	−0.0427334	−	13.7499i	−0.00180582	−	0.581040i
$561$	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	0.402773	−	0.915300i	$-0.368046\pi$
$563$	−4.47297	−	2.58247i	−0.188513	−	0.108838i	−0.591286	+	0.806462i	$0.701380\pi$
$564$	−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
$567$	21.5963	+	10.0300i	0.906959	+	0.421219i
$568$	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
$574$	−0.276902	+	0.242281i	−0.0115577	+	0.0101126i
$575$		−	23.5919i		−	0.983849i
$576$	−16.3996	−	17.5229i	−0.683318	−	0.730121i
$577$		−	24.1119i		−	1.00379i	−0.864928	−	0.501897i	$-0.832636\pi$
$577$		−	24.1119i		−	1.00379i	0.864928	−	0.501897i	$-0.167364\pi$
$578$	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
$581$	4.85868	+	10.4892i	0.201572	+	0.435166i
$582$	−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	−0.625168	−	0.780490i	$-0.714969\pi$
$587$	−6.34357	+	3.66246i	−0.261827	+	0.151166i	0.363341	+	0.931656i	$0.381636\pi$
$588$	−8.32196	+	22.7760i	−0.343192	+	0.939265i
$589$	−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	$-0.785909\pi$
$593$		−	30.3427i		−	1.24602i	0.782212	−	0.623012i	$-0.214091\pi$
$594$	−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	−0.532168	−	0.846639i	$-0.678622\pi$
$601$	−1.59450	+	0.920586i	−0.0650410	+	0.0375515i	0.467127	+	0.884190i	$0.345289\pi$
$602$	−38.3159	+	7.57629i	−1.56164	+	0.308787i
$603$	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	−0.920174	−	0.391510i	$-0.871953\pi$
$607$	−2.98185	+	5.16472i	−0.121030	+	0.209629i	0.799144	+	0.601139i	$0.205286\pi$
$608$	−39.1378	+	15.5394i	−1.58725	+	0.630205i
$609$	18.7459	−	17.1249i	0.759621	−	0.693934i
$610$	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
$616$	−2.34398	−	0.678904i	−0.0944417	−	0.0273538i
$617$	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	−0.00524975	−	0.999986i	$-0.501671\pi$
$619$	21.3502	−	12.3266i	0.858139	−	0.495447i	0.863389	+	0.504540i	$0.168338\pi$
$620$	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
$623$	−8.54764	−	0.769786i	−0.342454	−	0.0308408i
$624$	−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
$630$	−14.1693	−	3.45351i	−0.564517	−	0.137591i
$631$		−	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
$637$	−17.8475	+	21.0509i	−0.707144	+	0.834066i
$638$	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	0.656648	−	0.754197i	$-0.271974\pi$
$643$	8.41406	+	4.85786i	0.331818	+	0.191575i	−0.324830	+	0.945772i	$0.605307\pi$
$644$	33.4290	−	17.4139i	1.31729	−	0.686204i
$645$	−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	$-0.725280\pi$
$647$	−33.0729			−1.30023			−0.650116	+	0.759835i	$0.725280\pi$
$648$	−22.2150	+	12.4296i	−0.872687	+	0.488281i
$649$		−	0.587506i		−	0.0230616i
$650$	−17.9435	−	4.36385i	−0.703801	−	0.171164i
$651$	6.92586	−	21.8497i	0.271446	−	0.856356i
$652$	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
$658$	−25.1307	+	4.96916i	−0.979698	+	0.193718i
$659$	−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	−0.852867	−	0.522128i	$-0.825138\pi$
$661$	0.661849	−	1.14636i	0.0257430	−	0.0445881i	0.878610	+	0.477540i	$0.158472\pi$
$662$	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
$672$	−14.5213	−	21.4740i	−0.560173	−	0.828376i
$673$	−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	0.990245	−	0.139334i	$-0.0444962\pi$
$677$	9.74305	+	16.8755i	0.374456	+	0.648576i	−0.615790	+	0.787911i	$0.711163\pi$
$678$	10.6998	+	5.24419i	0.410925	+	0.201402i
$679$	−4.35763	−	9.40752i	−0.167231	−	0.361028i
$680$	−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
$686$	−12.7408	+	22.8839i	−0.486445	+	0.873711i
$687$	−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	−0.292023	−	0.956411i	$-0.594328\pi$
$691$	10.2582	−	5.92260i	0.390242	−	0.225306i	0.682265	+	0.731105i	$0.260995\pi$
$692$	0.350043	+	7.52854i	0.0133066	+	0.286192i
$693$	−1.29530	+	2.24093i	−0.0492045	+	0.0851257i
$694$	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
$700$	−17.5087	−	0.759550i	−0.661767	−	0.0287083i
$701$		−	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
$707$	−8.84124	+	4.09533i	−0.332509	+	0.154021i
$708$	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
$714$	−0.708370	+	32.2984i	−0.0265101	+	1.20874i
$715$	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	$-0.524858\pi$
$719$	−4.18381			−0.156030			−0.0780149	+	0.996952i	$0.524858\pi$
$720$	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	0.644445	−	0.764651i	$-0.277089\pi$
$727$	−9.16698	−	15.8777i	−0.339985	−	0.588871i	−0.984429	+	0.175780i	$0.943755\pi$
$728$	−7.06120	−	28.6465i	−0.261705	−	1.06171i
$729$	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	−0.856476	−	0.516187i	$-0.827351\pi$
$733$	0.508814	−	0.881292i	0.0187935	−	0.0325513i	0.875269	+	0.483636i	$0.160684\pi$
$734$	−8.04498	−	27.4565i	−0.296945	−	1.01344i
$735$	−14.5288	−	6.08752i	−0.535902	−	0.224541i
$736$	−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
$742$	−19.0121	−	6.47780i	−0.697955	−	0.237808i
$743$	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
$749$	2.53845	−	28.1867i	0.0927530	−	1.02992i
$750$	−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
$756$	−25.8056	+	9.49048i	−0.938542	+	0.345165i
$757$		−	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	0.652964	−	0.757389i	$-0.273525\pi$
$761$	8.92489	+	5.15279i	0.323527	+	0.186788i	−0.329437	+	0.944178i	$0.606859\pi$
$762$	2.23213	−	0.151767i	0.0808617	−	0.00549795i
$763$	7.44899	+	0.670844i	0.269672	+	0.0242862i
$764$	−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	0.913679	−	0.406436i	$-0.133229\pi$
$769$	28.2448	+	16.3072i	1.01853	+	0.588051i	0.104856	+	0.994487i	$0.466562\pi$
$770$	0.511280	−	1.50058i	0.0184252	−	0.0540772i
$771$	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	$-0.527696\pi$
$773$	−4.83211			−0.173799			−0.0868994	+	0.996217i	$0.527696\pi$
$774$	−34.6347	−	27.6008i	−1.24492	−	0.992089i
$775$	16.5657			0.595057
$776$	10.8797	+	2.11616i	0.390559	+	0.0759657i
$777$	8.09287	+	36.7701i	0.290330	+	1.31912i
$778$	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
$784$	−11.8475	−	25.3700i	−0.423124	−	0.906072i
$785$	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	0.414622	−	0.909994i	$-0.363914\pi$
$787$	−4.66095	−	2.69100i	−0.166145	−	0.0959239i	−0.580767	+	0.814070i	$0.697247\pi$
$788$	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	$-0.586469\pi$
$797$	19.7648	−	34.2337i	0.700106	−	1.21262i	0.968429	−	0.249291i	$-0.0801974\pi$
$798$	−1.05781	+	48.2313i	−0.0374462	+	1.70737i
$799$	−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
$805$	10.2917	+	22.2183i	0.362734	+	0.783092i
$806$	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	$0.187721\pi$
$811$			31.6761i			1.11230i	−0.831083	+	0.556149i	$0.812279\pi$
$812$	−1.27067	+	29.2907i	−0.0445916	+	1.02790i
$813$	−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
$819$	−31.2937	−	0.0157419i	−1.09349	−	0.000550067i
$820$	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
$826$	5.07319	−	4.43889i	0.176519	−	0.154449i
$827$	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	$-0.443496\pi$
$829$	10.1684			0.353163			0.176582	+	0.984286i	$0.443496\pi$
$830$	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
$833$	−6.23454	+	34.3331i	−0.216014	+	1.18957i
$834$	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	$-0.960545\pi$
$839$	−17.4730	−	30.2641i	−0.603234	−	1.04483i	0.389094	−	0.921198i	$-0.372788\pi$
$840$	14.3731	−	8.77533i	0.495919	−	0.302778i
$841$	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	0.987347	−	0.158573i	$-0.0506893\pi$
$853$	10.4075	+	18.0263i	0.356345	+	0.617208i	−0.631002	+	0.775781i	$0.717356\pi$
$854$	16.5869	−	3.27977i	0.567592	−	0.112231i
$855$	−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	−0.885234	−	0.465146i	$-0.846002\pi$
$857$	−27.0797	+	15.6344i	−0.925023	+	0.534062i	−0.0397892	+	0.999208i	$0.512669\pi$
$858$	−0.213634	−	3.14205i	−0.00729335	−	0.107268i
$859$	−5.48681	−	3.16781i	−0.187208	−	0.108084i	0.403467	−	0.914994i	$-0.367805\pi$
$859$	−5.48681	−	3.16781i	−0.187208	−	0.108084i	−0.590675	+	0.806910i	$0.701138\pi$
$860$	24.0953	+	12.4567i	0.821643	+	0.424770i
$861$	−0.429560	−	0.136161i	−0.0146394	−	0.00464035i
$862$	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
$868$	12.2276	+	23.4731i	0.415033	+	0.796729i
$869$	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
$875$	2.56280	−	28.4571i	0.0866385	−	0.962026i
$876$	−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	$0.313108\pi$
$881$			49.4216i			1.66506i	−0.553982	+	0.832529i	$0.686892\pi$
$882$	−29.1373	+	5.74616i	−0.981104	+	0.193483i
$883$	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	$-0.482672\pi$
$887$	26.5645	−	46.0110i	0.891948	−	1.54490i	0.837537	−	0.546380i	$-0.183995\pi$
$888$	−36.9259	−	16.0162i	−1.23915	−	0.537468i
$889$	2.40681	+	0.216753i	0.0807217	+	0.00726967i
$890$	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
$896$	29.4002	+	5.62372i	0.982193	+	0.187875i
$897$	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
$903$	−32.2635	−	35.3175i	−1.07366	−	1.17529i
$904$	−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
$910$	18.8025	−	3.71786i	0.623296	−	0.123246i
$911$	−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
$924$	−0.777310	−	2.88592i	−0.0255716	−	0.0949398i
$925$	−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	−0.423563	−	0.905867i	$-0.639221\pi$
$929$	4.54629	−	2.62480i	0.149159	−	0.0861170i	0.572722	+	0.819750i	$0.305887\pi$
$930$	−13.2139	+	8.87592i	−0.433301	+	0.291053i
$931$	−9.31007	+	51.2699i	−0.305125	+	1.68030i
$932$	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	$-0.602104\pi$
$937$		−	58.0982i		−	1.89799i	0.315296	−	0.948993i	$-0.397896\pi$
$938$	−35.0134	−	40.0167i	−1.14323	−	1.30659i
$939$	−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	−0.946022	−	0.324101i	$-0.894938\pi$
$941$	−5.89990	+	10.2189i	−0.192331	+	0.333128i	0.753691	+	0.657229i	$0.228271\pi$
$942$	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
$945$	−5.37999	−	17.0322i	−0.175011	−	0.554059i
$946$	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
$952$	−25.8417	−	26.9033i	−0.837536	−	0.871940i
$953$	−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
$959$	−41.3407	+	19.1493i	−1.33496	+	0.618364i
$960$	−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
$966$	39.4635	+	23.9531i	1.26972	+	0.770677i
$967$	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	$0.0196990\pi$
$971$			3.85440i			0.123694i	−0.998086	+	0.0618468i	$0.980301\pi$
$972$	−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
$980$	16.8207	−	6.92265i	0.537317	−	0.221136i
$981$	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	0.963836	−	0.266494i	$-0.0858654\pi$
$983$	7.87355	+	13.6374i	0.251127	+	0.434965i	−0.712709	+	0.701460i	$0.752532\pi$
$984$	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
$987$	−21.1611	−	23.1642i	−0.673565	−	0.737323i
$988$	−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
$994$	41.0475	+	13.9858i	1.30195	+	0.443601i
$995$	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	$0.0850067\pi$
$997$	22.4442	+	38.8745i	0.710814	+	1.23117i	−0.253738	+	0.967273i	$0.581660\pi$
$998$	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.139.9	✓	184
7.6	odd	2	inner	504.2.be.a.139.10	yes	184
8.3	odd	2	inner	504.2.be.a.139.53	yes	184
9.7	even	3	inner	504.2.be.a.475.54	yes	184
56.27	even	2	inner	504.2.be.a.139.54	yes	184
63.34	odd	6	inner	504.2.be.a.475.53	yes	184
72.43	odd	6	inner	504.2.be.a.475.10	yes	184
504.475	even	6	inner	504.2.be.a.475.9	yes	184

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

\(f(q)\)	\(=\)	\(q+(-1.37416 - 0.334195i) q^{2} +(-0.522528 - 1.65135i) q^{3} +(1.77663 + 0.918475i) q^{4} +(-0.649625 + 1.12518i) q^{5} +(0.166162 + 2.44385i) q^{6} +(-0.237312 + 2.63509i) q^{7} +(-2.13442 - 1.85587i) q^{8} +(-2.45393 + 1.72576i) q^{9} +O(q^{10})\)	\(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} +(-0.237312 + 2.63509i) 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} +(1.20674 - 3.54172i) 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} +(4.47546 - 0.985021i) 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} +(-2.84188 + 4.46360i) 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} +(-6.47918 - 0.142102i) 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} +(-6.88737 - 1.25067i) 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} +(5.39691 - 5.18396i) 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} +(-3.96517 - 6.87586i) 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} +(3.20116 + 3.65859i) 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} +(0.782874 - 0.362633i) 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} +(8.85594 + 2.36058i) 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} +(9.04637 + 4.02035i) 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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