LMFDB - Embedded newform 560.2.t.a.43.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

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

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

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36754 - 0.360316i) q^{2} +3.13969i q^{3} +(1.74034 + 0.985496i) q^{4} +(1.64497 + 1.51462i) q^{5} +(1.13128 - 4.29365i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.02490 - 1.97478i) q^{8} -6.85762 q^{9} +O(q^{10})$	\(q+(-1.36754 - 0.360316i) q^{2} +3.13969i q^{3} +(1.74034 + 0.985496i) q^{4} +(1.64497 + 1.51462i) q^{5} +(1.13128 - 4.29365i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.02490 - 1.97478i) q^{8} -6.85762 q^{9} +(-1.70383 - 2.66401i) q^{10} +(-3.65075 + 3.65075i) q^{11} +(-3.09415 + 5.46413i) q^{12} +6.00313 q^{13} +(-1.22178 + 0.712216i) q^{14} +(-4.75542 + 5.16470i) q^{15} +(2.05760 + 3.43020i) q^{16} +(-0.665139 + 0.665139i) q^{17} +(9.37809 + 2.47091i) q^{18} +(-2.61268 + 2.61268i) q^{19} +(1.37017 + 4.25707i) q^{20} +(2.22009 + 2.22009i) q^{21} +(6.30798 - 3.67713i) q^{22} +(-3.49520 - 3.49520i) q^{23} +(6.20019 - 6.35756i) q^{24} +(0.411870 + 4.98301i) q^{25} +(-8.20954 - 2.16303i) q^{26} -12.1117i q^{27} +(1.92746 - 0.533758i) q^{28} +(4.94803 + 4.94803i) q^{29} +(8.36416 - 5.34948i) q^{30} -6.72187i q^{31} +(-1.57789 - 5.43234i) q^{32} +(-11.4622 - 11.4622i) q^{33} +(1.14927 - 0.669945i) q^{34} +(2.23417 - 0.0921753i) q^{35} +(-11.9346 - 6.75816i) q^{36} -0.0770166 q^{37} +(4.51434 - 2.63156i) q^{38} +18.8479i q^{39} +(-0.339873 - 6.31542i) q^{40} +2.66162i q^{41} +(-2.23613 - 3.83601i) q^{42} -3.14240 q^{43} +(-9.95137 + 2.75576i) q^{44} +(-11.2806 - 10.3867i) q^{45} +(3.52046 + 6.03921i) q^{46} +(2.78700 + 2.78700i) q^{47} +(-10.7698 + 6.46020i) q^{48} -1.00000i q^{49} +(1.23221 - 6.96288i) q^{50} +(-2.08833 - 2.08833i) q^{51} +(10.4475 + 5.91606i) q^{52} -8.82864i q^{53} +(-4.36405 + 16.5633i) q^{54} +(-11.5349 + 0.475896i) q^{55} +(-2.82821 + 0.0354414i) q^{56} +(-8.20299 - 8.20299i) q^{57} +(-4.98379 - 8.54950i) q^{58} +(1.45278 + 1.45278i) q^{59} +(-13.3659 + 4.30190i) q^{60} +(-1.61792 + 1.61792i) q^{61} +(-2.42200 + 9.19244i) q^{62} +(-4.84907 + 4.84907i) q^{63} +(0.200471 + 7.99749i) q^{64} +(9.87499 + 9.09244i) q^{65} +(11.5450 + 19.8051i) q^{66} +6.93826 q^{67} +(-1.81306 + 0.502079i) q^{68} +(10.9738 - 10.9738i) q^{69} +(-3.08853 - 0.678954i) q^{70} -2.95077 q^{71} +(13.8860 + 13.5423i) q^{72} +(7.73163 - 7.73163i) q^{73} +(0.105323 + 0.0277503i) q^{74} +(-15.6451 + 1.29314i) q^{75} +(-7.12174 + 1.97217i) q^{76} +5.16294i q^{77} +(6.79122 - 25.7754i) q^{78} -3.01216 q^{79} +(-1.81076 + 8.75906i) q^{80} +17.4541 q^{81} +(0.959024 - 3.63987i) q^{82} +8.33044i q^{83} +(1.67583 + 6.05162i) q^{84} +(-2.10157 + 0.0867046i) q^{85} +(4.29737 + 1.13226i) q^{86} +(-15.5353 + 15.5353i) q^{87} +(14.6019 - 0.182982i) q^{88} -5.82692 q^{89} +(11.6842 + 18.2688i) q^{90} +(4.24485 - 4.24485i) q^{91} +(-2.63835 - 9.52736i) q^{92} +21.1046 q^{93} +(-2.80714 - 4.81555i) q^{94} +(-8.25499 + 0.340577i) q^{95} +(17.0558 - 4.95408i) q^{96} +(1.48367 - 1.48367i) q^{97} +(-0.360316 + 1.36754i) q^{98} +(25.0355 - 25.0355i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.36754	−	0.360316i	−0.966998	−	0.254782i
$2$	−1.36754	−	0.360316i	−0.966998	−	0.254782i
$3$			3.13969i			1.81270i	0.422530	+	0.906349i	$0.361142\pi$
$3$			3.13969i			1.81270i	−0.422530	+	0.906349i	$0.638858\pi$
$4$	1.74034	+	0.985496i	0.870172	+	0.492748i
$5$	1.64497	+	1.51462i	0.735654	+	0.677357i
$5$	1.64497	+	1.51462i	0.735654	+	0.677357i
$6$	1.13128	−	4.29365i	0.461843	−	1.75288i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−2.02490	−	1.97478i	−0.715912	−	0.698191i
$9$	−6.85762			−2.28587
$10$	−1.70383	−	2.66401i	−0.538798	−	0.842435i
$11$	−3.65075	+	3.65075i	−1.10074	+	1.10074i	−0.106422	+	0.994321i	$0.533940\pi$
$11$	−3.65075	+	3.65075i	−1.10074	+	1.10074i	−0.994321	+	0.106422i	$0.966060\pi$
$12$	−3.09415	+	5.46413i	−0.893203	+	1.57736i
$13$	6.00313			1.66497			0.832484	−	0.554048i	$-0.186918\pi$
$13$	6.00313			1.66497			0.832484	+	0.554048i	$0.186918\pi$
$14$	−1.22178	+	0.712216i	−0.326535	+	0.190348i
$15$	−4.75542	+	5.16470i	−1.22784	+	1.33352i
$16$	2.05760	+	3.43020i	0.514399	+	0.857551i
$17$	−0.665139	+	0.665139i	−0.161320	+	0.161320i	−0.783151	−	0.621831i	$-0.786389\pi$
$17$	−0.665139	+	0.665139i	−0.161320	+	0.161320i	0.621831	+	0.783151i	$0.286389\pi$
$18$	9.37809	+	2.47091i	2.21044	+	0.582400i
$19$	−2.61268	+	2.61268i	−0.599389	+	0.599389i	−0.940150	−	0.340761i	$-0.889315\pi$
$19$	−2.61268	+	2.61268i	−0.599389	+	0.599389i	0.340761	+	0.940150i	$0.389315\pi$
$20$	1.37017	+	4.25707i	0.306379	+	0.951910i
$21$	2.22009	+	2.22009i	0.484464	+	0.484464i
$22$	6.30798	−	3.67713i	1.34487	−	0.783967i
$23$	−3.49520	−	3.49520i	−0.728800	−	0.728800i	0.241581	−	0.970381i	$-0.422334\pi$
$23$	−3.49520	−	3.49520i	−0.728800	−	0.728800i	−0.970381	+	0.241581i	$0.922334\pi$
$24$	6.20019	−	6.35756i	1.26561	−	1.29773i
$25$	0.411870	+	4.98301i	0.0823740	+	0.996601i
$26$	−8.20954	−	2.16303i	−1.61002	−	0.424204i
$27$		−	12.1117i		−	2.33090i
$28$	1.92746	−	0.533758i	0.364256	−	0.100871i
$29$	4.94803	+	4.94803i	0.918827	+	0.918827i	0.996944	−	0.0781174i	$-0.0248909\pi$
$29$	4.94803	+	4.94803i	0.918827	+	0.918827i	−0.0781174	+	0.996944i	$0.524891\pi$
$30$	8.36416	−	5.34948i	1.52708	−	0.976678i
$31$		−	6.72187i		−	1.20728i	−0.797256	−	0.603642i	$-0.793716\pi$
$31$		−	6.72187i		−	1.20728i	0.797256	−	0.603642i	$-0.206284\pi$
$32$	−1.57789	−	5.43234i	−0.278934	−	0.960310i
$33$	−11.4622	−	11.4622i	−1.99532	−	1.99532i
$34$	1.14927	−	0.669945i	0.197098	−	0.114895i
$35$	2.23417	−	0.0921753i	0.377643	−	0.0155805i
$36$	−11.9346	−	6.75816i	−1.98910	−	1.12636i
$37$	−0.0770166			−0.0126615			−0.00633073	−	0.999980i	$-0.502015\pi$
$37$	−0.0770166			−0.0126615			−0.00633073	+	0.999980i	$0.502015\pi$
$38$	4.51434	−	2.63156i	0.732322	−	0.426895i
$39$			18.8479i			3.01809i
$40$	−0.339873	−	6.31542i	−0.0537386	−	0.998555i
$41$			2.66162i			0.415675i	0.978163	+	0.207837i	$0.0666425\pi$
$41$			2.66162i			0.415675i	−0.978163	+	0.207837i	$0.933358\pi$
$42$	−2.23613	−	3.83601i	−0.345043	−	0.591909i
$43$	−3.14240			−0.479212			−0.239606	−	0.970870i	$-0.577018\pi$
$43$	−3.14240			−0.479212			−0.239606	+	0.970870i	$0.577018\pi$
$44$	−9.95137	+	2.75576i	−1.50022	+	0.415447i
$45$	−11.2806	−	10.3867i	−1.68161	−	1.54835i
$46$	3.52046	+	6.03921i	0.519063	+	0.890433i
$47$	2.78700	+	2.78700i	0.406526	+	0.406526i	0.880525	−	0.473999i	$-0.157190\pi$
$47$	2.78700	+	2.78700i	0.406526	+	0.406526i	−0.473999	+	0.880525i	$0.657190\pi$
$48$	−10.7698	+	6.46020i	−1.55448	+	0.932450i
$49$		−	1.00000i		−	0.142857i
$50$	1.23221	−	6.96288i	0.174261	−	0.984700i
$51$	−2.08833	−	2.08833i	−0.292424	−	0.292424i
$52$	10.4475	+	5.91606i	1.44881	+	0.820410i
$53$		−	8.82864i		−	1.21271i	−0.795195	−	0.606354i	$-0.792632\pi$
$53$		−	8.82864i		−	1.21271i	0.795195	−	0.606354i	$-0.207368\pi$
$54$	−4.36405	+	16.5633i	−0.593873	+	2.25398i
$55$	−11.5349	+	0.475896i	−1.55536	+	0.0641698i
$56$	−2.82821	+	0.0354414i	−0.377935	+	0.00473606i
$57$	−8.20299	−	8.20299i	−1.08651	−	1.08651i
$58$	−4.98379	−	8.54950i	−0.654403	−	1.12260i
$59$	1.45278	+	1.45278i	0.189136	+	0.189136i	0.795323	−	0.606186i	$-0.207301\pi$
$59$	1.45278	+	1.45278i	0.189136	+	0.189136i	−0.606186	+	0.795323i	$0.707301\pi$
$60$	−13.3659	+	4.30190i	−1.72552	+	0.555373i
$61$	−1.61792	+	1.61792i	−0.207153	+	0.207153i	−0.803056	−	0.595903i	$-0.796794\pi$
$61$	−1.61792	+	1.61792i	−0.207153	+	0.207153i	0.595903	+	0.803056i	$0.296794\pi$
$62$	−2.42200	+	9.19244i	−0.307594	+	1.16744i
$63$	−4.84907	+	4.84907i	−0.610926	+	0.610926i
$64$	0.200471	+	7.99749i	0.0250589	+	0.999686i
$65$	9.87499	+	9.09244i	1.22484	+	1.12778i
$66$	11.5450	+	19.8051i	1.42110	+	2.43784i
$67$	6.93826			0.847643			0.423822	−	0.905746i	$-0.360688\pi$
$67$	6.93826			0.847643			0.423822	+	0.905746i	$0.360688\pi$
$68$	−1.81306	+	0.502079i	−0.219866	+	0.0608860i
$69$	10.9738	−	10.9738i	1.32109	−	1.32109i
$70$	−3.08853	−	0.678954i	−0.369150	−	0.0811505i
$71$	−2.95077			−0.350192			−0.175096	−	0.984551i	$-0.556024\pi$
$71$	−2.95077			−0.350192			−0.175096	+	0.984551i	$0.556024\pi$
$72$	13.8860	+	13.5423i	1.63648	+	1.59598i
$73$	7.73163	−	7.73163i	0.904919	−	0.904919i	−0.0909373	−	0.995857i	$-0.528986\pi$
$73$	7.73163	−	7.73163i	0.904919	−	0.904919i	0.995857	+	0.0909373i	$0.0289863\pi$
$74$	0.105323	+	0.0277503i	0.0122436	+	0.00322591i
$75$	−15.6451	+	1.29314i	−1.80654	+	0.149319i
$76$	−7.12174	+	1.97217i	−0.816920	+	0.226224i
$77$			5.16294i			0.588372i
$78$	6.79122	−	25.7754i	0.768955	−	2.91848i
$79$	−3.01216			−0.338894			−0.169447	−	0.985539i	$-0.554198\pi$
$79$	−3.01216			−0.338894			−0.169447	+	0.985539i	$0.554198\pi$
$80$	−1.81076	+	8.75906i	−0.202449	+	0.979293i
$81$	17.4541			1.93935
$82$	0.959024	−	3.63987i	0.105907	−	0.401957i
$83$			8.33044i			0.914385i	0.889368	+	0.457192i	$0.151145\pi$
$83$			8.33044i			0.914385i	−0.889368	+	0.457192i	$0.848855\pi$
$84$	1.67583	+	6.05162i	0.182848	+	0.660286i
$85$	−2.10157	+	0.0867046i	−0.227947	+	0.00940443i
$86$	4.29737	+	1.13226i	0.463397	+	0.122095i
$87$	−15.5353	+	15.5353i	−1.66556	+	1.66556i
$88$	14.6019	−	0.182982i	1.55656	−	0.0195060i
$89$	−5.82692			−0.617652			−0.308826	−	0.951118i	$-0.599936\pi$
$89$	−5.82692			−0.617652			−0.308826	+	0.951118i	$0.599936\pi$
$90$	11.6842	+	18.2688i	1.23162	+	1.92570i
$91$	4.24485	−	4.24485i	0.444982	−	0.444982i
$92$	−2.63835	−	9.52736i	−0.275067	−	0.993296i
$93$	21.1046			2.18844
$94$	−2.80714	−	4.81555i	−0.289535	−	0.496686i
$95$	−8.25499	+	0.340577i	−0.846944	+	0.0349425i
$96$	17.0558	−	4.95408i	1.74075	−	0.505623i
$97$	1.48367	−	1.48367i	0.150643	−	0.150643i	−0.627762	−	0.778405i	$-0.716029\pi$
$97$	1.48367	−	1.48367i	0.150643	−	0.150643i	0.778405	+	0.627762i	$0.216029\pi$
$98$	−0.360316	+	1.36754i	−0.0363975	+	0.138143i
$99$	25.0355	−	25.0355i	2.51616	−	2.51616i
$100$	−4.19394	+	9.07804i	−0.419394	+	0.907804i
$101$	−5.22374	−	5.22374i	−0.519782	−	0.519782i	0.397723	−	0.917505i	$-0.369800\pi$
$101$	−5.22374	−	5.22374i	−0.519782	−	0.519782i	−0.917505	+	0.397723i	$0.869800\pi$
$102$	2.10342	+	3.60833i	0.208269	+	0.357278i
$103$	8.54548	+	8.54548i	0.842011	+	0.842011i	0.989120	−	0.147109i	$-0.0469969\pi$
$103$	8.54548	+	8.54548i	0.842011	+	0.842011i	−0.147109	+	0.989120i	$0.546997\pi$
$104$	−12.1558	−	11.8549i	−1.19197	−	1.16247i
$105$	0.289401	+	7.01458i	0.0282427	+	0.684553i
$106$	−3.18111	+	12.0735i	−0.308976	+	1.17269i
$107$		−	7.60152i		−	0.734867i	−0.930050	−	0.367433i	$-0.880237\pi$
$107$		−	7.60152i		−	0.734867i	0.930050	−	0.367433i	$-0.119763\pi$
$108$	11.9361	−	21.0786i	1.14855	−	2.02829i
$109$	−4.70458	−	4.70458i	−0.450617	−	0.450617i	0.444942	−	0.895559i	$-0.353224\pi$
$109$	−4.70458	−	4.70458i	−0.450617	−	0.450617i	−0.895559	+	0.444942i	$0.853224\pi$
$110$	15.9459	+	3.50540i	1.52038	+	0.334227i
$111$		−	0.241808i		−	0.0229514i
$112$	3.88046	+	0.970581i	0.366669	+	0.0917113i
$113$	−1.60641	−	1.60641i	−0.151118	−	0.151118i	0.627499	−	0.778617i	$-0.284079\pi$
$113$	−1.60641	−	1.60641i	−0.151118	−	0.151118i	−0.778617	+	0.627499i	$0.784079\pi$
$114$	8.26226	+	14.1736i	0.773831	+	1.32748i
$115$	−0.455619	−	11.0434i	−0.0424867	−	1.02980i
$116$	3.73501	+	13.4875i	0.346787	+	1.25229i
$117$	−41.1672			−3.80591
$118$	−1.46328	−	2.51021i	−0.134706	−	0.231083i
$119$			0.940649i			0.0862291i
$120$	19.8284	−	1.06709i	1.81008	−	0.0974118i
$121$		−	15.6560i		−	1.42327i
$122$	2.79553	−	1.62961i	0.253096	−	0.147538i
$123$	−8.35664			−0.753493
$124$	6.62438	−	11.6984i	0.594887	−	1.05054i
$125$	−6.86983	+	8.82074i	−0.614457	+	0.788951i
$126$	8.37851	−	4.88411i	0.746417	−	0.435111i
$127$	11.6812	+	11.6812i	1.03654	+	1.03654i	0.999307	+	0.0372340i	$0.0118547\pi$
$127$	11.6812	+	11.6812i	1.03654	+	1.03654i	0.0372340	+	0.999307i	$0.488145\pi$
$128$	2.60747	−	11.0091i	0.230470	−	0.973079i
$129$		−	9.86615i		−	0.868666i
$130$	−10.2283	−	15.9924i	−0.897082	−	1.40263i
$131$	15.1174	+	15.1174i	1.32081	+	1.32081i	0.913118	+	0.407694i	$0.133667\pi$
$131$	15.1174	+	15.1174i	1.32081	+	1.32081i	0.407694	+	0.913118i	$0.366333\pi$
$132$	−8.65223	−	31.2442i	−0.753080	−	2.71946i
$133$			3.69488i			0.320387i
$134$	−9.48836	−	2.49997i	−0.819670	−	0.215964i
$135$	18.3446	−	19.9235i	1.57885	−	1.71474i
$136$	2.66035	−	0.0333379i	0.228123	−	0.00285870i
$137$	8.75700	+	8.75700i	0.748161	+	0.748161i	0.974134	−	0.225972i	$-0.0725559\pi$
$137$	8.75700	+	8.75700i	0.748161	+	0.748161i	−0.225972	+	0.974134i	$0.572556\pi$
$138$	−18.9612	+	11.0531i	−1.61409	+	0.940905i
$139$	−1.86754	−	1.86754i	−0.158403	−	0.158403i	0.623456	−	0.781859i	$-0.285728\pi$
$139$	−1.86754	−	1.86754i	−0.158403	−	0.158403i	−0.781859	+	0.623456i	$0.785728\pi$
$140$	3.97906	+	2.04135i	0.336292	+	0.172525i
$141$	−8.75031	+	8.75031i	−0.736909	+	0.736909i
$142$	4.03530	+	1.06321i	0.338635	+	0.0892226i
$143$	−21.9159	+	21.9159i	−1.83270	+	1.83270i
$144$	−14.1102	−	23.5231i	−1.17585	−	1.96025i
$145$	0.645004	+	15.6338i	0.0535646	+	1.29831i
$146$	−13.3592	+	7.78750i	−1.10561	+	0.644498i
$147$	3.13969			0.258957
$148$	−0.134035	−	0.0758996i	−0.0110176	−	0.00623890i
$149$	−12.2998	+	12.2998i	−1.00764	+	1.00764i	−0.00766932	+	0.999971i	$0.502441\pi$
$149$	−12.2998	+	12.2998i	−1.00764	+	1.00764i	−0.999971	+	0.00766932i	$0.997559\pi$
$150$	21.8612	+	3.86875i	1.78496	+	0.315882i
$151$	7.16666			0.583215			0.291607	−	0.956538i	$-0.405810\pi$
$151$	7.16666			0.583215			0.291607	+	0.956538i	$0.405810\pi$
$152$	10.4499	−	0.130952i	0.847598	−	0.0106216i
$153$	4.56127	−	4.56127i	0.368757	−	0.368757i
$154$	1.86029	−	7.06054i	0.149907	−	0.568955i
$155$	10.1811	−	11.0573i	0.817762	−	0.888143i
$156$	−18.5746	+	32.8019i	−1.48716	+	2.62625i
$157$		−	4.81448i		−	0.384237i	−0.981372	−	0.192119i	$-0.938464\pi$
$157$		−	4.81448i		−	0.384237i	0.981372	−	0.192119i	$-0.0615358\pi$
$158$	4.11925	+	1.08533i	0.327710	+	0.0863443i
$159$	27.7192			2.19827
$160$	5.63232	−	11.3259i	0.445274	−	0.895394i
$161$	−4.94296			−0.389560
$162$	−23.8693	−	6.28901i	−1.87535	−	0.494111i
$163$			0.165186i			0.0129384i	0.999979	+	0.00646918i	$0.00205922\pi$
$163$			0.165186i			0.0129384i	−0.999979	+	0.00646918i	$0.997941\pi$
$164$	−2.62301	+	4.63213i	−0.204823	+	0.361709i
$165$	−1.49416	−	36.2159i	−0.116320	−	2.81940i
$166$	3.00159	−	11.3922i	0.232969	−	0.884209i
$167$	5.05451	−	5.05451i	0.391130	−	0.391130i	−0.483960	−	0.875090i	$-0.660802\pi$
$167$	5.05451	−	5.05451i	0.391130	−	0.391130i	0.875090	+	0.483960i	$0.160802\pi$
$168$	−0.111275	−	8.87967i	−0.00858505	−	0.685082i
$169$	23.0376			1.77212
$170$	2.90522	+	0.638657i	0.222820	+	0.0489827i
$171$	17.9168	−	17.9168i	1.37013	−	1.37013i
$172$	−5.46886	−	3.09682i	−0.416997	−	0.236131i
$173$	18.1739			1.38174			0.690868	−	0.722981i	$-0.257229\pi$
$173$	18.1739			1.38174			0.690868	+	0.722981i	$0.257229\pi$
$174$	26.8428	−	15.6475i	2.03494	−	1.18624i
$175$	3.81475	+	3.23228i	0.288368	+	0.244338i
$176$	−20.0346	−	5.01106i	−1.51016	−	0.377723i
$177$	−4.56129	+	4.56129i	−0.342847	+	0.342847i
$178$	7.96856	+	2.09954i	0.597269	+	0.157367i
$179$	4.08501	−	4.08501i	0.305328	−	0.305328i	−0.537766	−	0.843094i	$-0.680732\pi$
$179$	4.08501	−	4.08501i	0.305328	−	0.305328i	0.843094	+	0.537766i	$0.180732\pi$
$180$	−9.39611	−	29.1934i	−0.700344	−	2.17595i
$181$	13.4717	+	13.4717i	1.00135	+	1.00135i	0.999999	+	0.00134700i	$0.000428763\pi$
$181$	13.4717	+	13.4717i	1.00135	+	1.00135i	0.00134700	+	0.999999i	$0.499571\pi$
$182$	−7.33451	+	4.27553i	−0.543670	+	0.316923i
$183$	−5.07976	−	5.07976i	−0.375506	−	0.375506i
$184$	0.175186	+	13.9797i	0.0129148	+	1.03060i
$185$	−0.126690	−	0.116651i	−0.00931445	−	0.00857633i
$186$	−28.8614	−	7.60432i	−2.11622	−	0.557576i
$187$		−	4.85652i		−	0.355144i
$188$	2.10376	+	7.59692i	0.153433	+	0.554063i
$189$	−8.56428	−	8.56428i	−0.622960	−	0.622960i
$190$	11.4118	+	2.50865i	0.827896	+	0.181997i
$191$			6.65829i			0.481777i	0.970553	+	0.240889i	$0.0774388\pi$
$191$			6.65829i			0.481777i	−0.970553	+	0.240889i	$0.922561\pi$
$192$	−25.1096	+	0.629417i	−1.81213	+	0.0454242i
$193$	9.75912	+	9.75912i	0.702477	+	0.702477i	0.964942	−	0.262465i	$-0.0845353\pi$
$193$	9.75912	+	9.75912i	0.702477	+	0.702477i	−0.262465	+	0.964942i	$0.584535\pi$
$194$	−2.56357	+	1.49439i	−0.184053	+	0.107291i
$195$	−28.5474	+	31.0043i	−2.04432	+	2.22027i
$196$	0.985496	−	1.74034i	0.0703926	−	0.124310i
$197$	10.2262			0.728583			0.364292	−	0.931285i	$-0.381311\pi$
$197$	10.2262			0.728583			0.364292	+	0.931285i	$0.381311\pi$
$198$	−43.2578	+	25.2164i	−3.07420	+	1.79205i
$199$		−	20.4462i		−	1.44939i	−0.689069	−	0.724696i	$-0.741980\pi$
$199$		−	20.4462i		−	1.44939i	0.689069	−	0.724696i	$-0.258020\pi$
$200$	9.00636	−	10.9035i	0.636846	−	0.770991i
$201$			21.7840i			1.53652i
$202$	5.26149	+	9.02589i	0.370197	+	0.635060i
$203$	6.99758			0.491134
$204$	−1.57637	−	5.69245i	−0.110368	−	0.398551i
$205$	−4.03133	+	4.37829i	−0.281560	+	0.305793i
$206$	−8.60723	−	14.7654i	−0.599694	−	1.02875i
$207$	23.9688	+	23.9688i	1.66594	+	1.66594i
$208$	12.3520	+	20.5920i	0.856458	+	1.42780i
$209$		−	19.0765i		−	1.31955i
$210$	2.13170	−	9.69701i	0.147101	−	0.669158i
$211$	15.0405	+	15.0405i	1.03543	+	1.03543i	0.999349	+	0.0360852i	$0.0114888\pi$
$211$	15.0405	+	15.0405i	1.03543	+	1.03543i	0.0360852	+	0.999349i	$0.488511\pi$
$212$	8.70059	−	15.3649i	0.597559	−	1.05526i
$213$		−	9.26448i		−	0.634792i
$214$	−2.73895	+	10.3954i	−0.187231	+	0.710615i
$215$	−5.16916	−	4.75953i	−0.352534	−	0.324598i
$216$	−23.9180	+	24.5251i	−1.62742	+	1.66872i
$217$	−4.75308	−	4.75308i	−0.322660	−	0.322660i
$218$	4.73858	+	8.12886i	0.320937	+	0.550556i
$219$	24.2749	+	24.2749i	1.64035	+	1.64035i
$220$	−20.5437	−	10.5394i	−1.38505	−	0.710563i
$221$	−3.99292	+	3.99292i	−0.268593	+	0.268593i
$222$	−0.0871274	+	0.330683i	−0.00584761	+	0.0221940i
$223$	5.30253	−	5.30253i	0.355083	−	0.355083i	−0.506913	−	0.861997i	$-0.669214\pi$
$223$	5.30253	−	5.30253i	0.355083	−	0.355083i	0.861997	+	0.506913i	$0.169214\pi$
$224$	−4.95698	−	2.72550i	−0.331202	−	0.182105i
$225$	−2.82445	−	34.1716i	−0.188297	−	2.27811i
$226$	1.61802	+	2.77565i	0.107629	+	0.184633i
$227$	−25.4872			−1.69165			−0.845823	−	0.533463i	$-0.820890\pi$
$227$	−25.4872			−1.69165			−0.845823	+	0.533463i	$0.820890\pi$
$228$	−6.19201	−	22.3600i	−0.410076	−	1.48083i
$229$	−16.7828	+	16.7828i	−1.10904	+	1.10904i	−0.115763	+	0.993277i	$0.536931\pi$
$229$	−16.7828	+	16.7828i	−1.10904	+	1.10904i	−0.993277	+	0.115763i	$0.963069\pi$
$230$	−3.35604	+	15.2665i	−0.221291	+	1.00664i
$231$	−16.2100			−1.06654
$232$	−0.248004	−	19.7906i	−0.0162823	−	1.29932i
$233$	−12.5020	+	12.5020i	−0.819031	+	0.819031i	−0.985968	−	0.166937i	$-0.946612\pi$
$233$	−12.5020	+	12.5020i	−0.819031	+	0.819031i	0.166937	+	0.985968i	$0.446612\pi$
$234$	56.2979	+	14.8332i	3.68031	+	0.969678i
$235$	0.363301	+	8.80579i	0.0236992	+	0.574426i
$236$	1.09663	+	3.96006i	0.0713846	+	0.257778i
$237$		−	9.45723i		−	0.614313i
$238$	0.338931	−	1.28638i	0.0219696	−	0.0833834i
$239$	14.7465			0.953875			0.476937	−	0.878937i	$-0.341747\pi$
$239$	14.7465			0.953875			0.476937	+	0.878937i	$0.341747\pi$
$240$	−27.5007	−	5.68521i	−1.77516	−	0.366979i
$241$	−6.47584			−0.417146			−0.208573	−	0.978007i	$-0.566882\pi$
$241$	−6.47584			−0.417146			−0.208573	+	0.978007i	$0.566882\pi$
$242$	−5.64111	+	21.4102i	−0.362624	+	1.37630i
$243$			18.4653i			1.18455i
$244$	−4.41019	+	1.22128i	−0.282333	+	0.0781846i
$245$	1.51462	−	1.64497i	0.0967653	−	0.105093i
$246$	11.4281	+	3.01103i	0.728626	+	0.191977i
$247$	−15.6842	+	15.6842i	−0.997965	+	0.997965i
$248$	−13.2742	+	13.6111i	−0.842914	+	0.864308i
$249$	−26.1550			−1.65750
$250$	12.5730	−	9.58742i	0.795189	−	0.606361i
$251$	−4.82159	+	4.82159i	−0.304336	+	0.304336i	−0.842708	−	0.538371i	$-0.819040\pi$
$251$	−4.82159	+	4.82159i	−0.304336	+	0.304336i	0.538371	+	0.842708i	$0.319040\pi$
$252$	−13.2178	+	3.66031i	−0.832643	+	0.230578i
$253$	25.5202			1.60444
$254$	−11.7656	−	20.1835i	−0.738241	−	1.26643i
$255$	−0.272225	−	6.59826i	−0.0170474	−	0.413199i
$256$	−7.53260	+	14.1159i	−0.470788	+	0.882247i
$257$	0.707413	−	0.707413i	0.0441272	−	0.0441272i	−0.684699	−	0.728826i	$-0.740066\pi$
$257$	0.707413	−	0.707413i	0.0441272	−	0.0441272i	0.728826	+	0.684699i	$0.240066\pi$
$258$	−3.55494	+	13.4924i	−0.221321	+	0.839999i
$259$	−0.0544590	+	0.0544590i	−0.00338392	+	0.00338392i
$260$	8.22531	+	25.5557i	0.510112	+	1.58490i
$261$	−33.9318	−	33.9318i	−2.10032	−	2.10032i
$262$	−15.2266	−	26.1207i	−0.940704	−	1.61374i
$263$	0.160119	+	0.160119i	0.00987334	+	0.00987334i	0.712026	−	0.702153i	$-0.247778\pi$
$263$	0.160119	+	0.160119i	0.00987334	+	0.00987334i	−0.702153	+	0.712026i	$0.747778\pi$
$264$	0.574506	+	45.8453i	0.0353584	+	2.82158i
$265$	13.3720	−	14.5229i	0.821436	−	0.892133i
$266$	1.33133	−	5.05291i	0.0816289	−	0.309814i
$267$		−	18.2947i		−	1.11962i
$268$	12.0750	+	6.83763i	0.737596	+	0.417675i
$269$	10.5890	+	10.5890i	0.645620	+	0.645620i	0.951931	−	0.306312i	$-0.0990949\pi$
$269$	10.5890	+	10.5890i	0.645620	+	0.645620i	−0.306312	+	0.951931i	$0.599095\pi$
$270$	−32.2658	+	20.6363i	−1.96363	+	1.25589i
$271$			8.67514i			0.526977i	0.964663	+	0.263489i	$0.0848731\pi$
$271$			8.67514i			0.526977i	−0.964663	+	0.263489i	$0.915127\pi$
$272$	−3.65015	−	0.912976i	−0.221323	−	0.0553573i
$273$	13.3275	+	13.3275i	0.806617	+	0.806617i
$274$	−8.82028	−	15.1309i	−0.532853	−	0.914089i
$275$	−19.6954	−	16.6881i	−1.18767	−	1.00633i
$276$	29.9129	−	8.28357i	1.80055	−	0.498613i
$277$	−15.0297			−0.903049			−0.451524	−	0.892259i	$-0.649120\pi$
$277$	−15.0297			−0.903049			−0.451524	+	0.892259i	$0.649120\pi$
$278$	1.88104	+	3.22685i	0.112817	+	0.193534i
$279$			46.0961i			2.75970i
$280$	−4.70600	−	4.22535i	−0.281237	−	0.252513i
$281$		−	15.9203i		−	0.949728i	−0.880059	−	0.474864i	$-0.842497\pi$
$281$		−	15.9203i		−	0.949728i	0.880059	−	0.474864i	$-0.157503\pi$
$282$	15.1193	−	8.81354i	0.900341	−	0.524839i
$283$	−0.604522			−0.0359351			−0.0179675	−	0.999839i	$-0.505720\pi$
$283$	−0.604522			−0.0359351			−0.0179675	+	0.999839i	$0.505720\pi$
$284$	−5.13535	−	2.90797i	−0.304727	−	0.172556i
$285$	−1.06930	−	25.9181i	−0.0633401	−	1.53525i
$286$	37.8677	−	22.0743i	2.23916	−	1.30528i
$287$	1.88205	+	1.88205i	0.111094	+	0.111094i
$288$	10.8206	+	37.2529i	0.637608	+	2.19515i
$289$			16.1152i			0.947952i
$290$	4.75103	−	21.6122i	0.278990	−	1.26911i
$291$	4.65824	+	4.65824i	0.273071	+	0.273071i
$292$	21.0752	−	5.83621i	1.23333	−	0.341538i
$293$		−	5.98116i		−	0.349423i	−0.984620	−	0.174712i	$-0.944101\pi$
$293$		−	5.98116i		−	0.349423i	0.984620	−	0.174712i	$-0.0558993\pi$
$294$	−4.29365	−	1.13128i	−0.250411	−	0.0659776i
$295$	0.189378	+	4.59020i	0.0110260	+	0.267252i
$296$	0.155951	+	0.152091i	0.00906448	+	0.00884011i
$297$	44.2169	+	44.2169i	2.56573	+	2.56573i
$298$	21.2523	−	12.3887i	1.23111	−	0.717658i
$299$	−20.9821	−	20.9821i	−1.21343	−	1.21343i
$300$	−28.5022	−	13.1676i	−1.64558	−	0.760234i
$301$	−2.22201	+	2.22201i	−0.128075	+	0.128075i
$302$	−9.80071	−	2.58227i	−0.563968	−	0.148593i
$303$	16.4009	−	16.4009i	0.942208	−	0.942208i
$304$	−14.3379	−	3.58618i	−0.822332	−	0.205682i
$305$	−5.11196	+	0.210905i	−0.292710	+	0.0120764i
$306$	−7.88124	+	4.59423i	−0.450540	+	0.262635i
$307$	−34.9658			−1.99560			−0.997800	−	0.0662887i	$-0.978884\pi$
$307$	−34.9658			−1.99560			−0.997800	+	0.0662887i	$0.978884\pi$
$308$	−5.08806	+	8.98530i	−0.289919	+	0.511985i
$309$	−26.8301	+	26.8301i	−1.52631	+	1.52631i
$310$	−17.9072	+	11.4529i	−1.01706	+	0.650482i
$311$	0.604147			0.0342581			0.0171290	−	0.999853i	$-0.494547\pi$
$311$	0.604147			0.0342581			0.0171290	+	0.999853i	$0.494547\pi$
$312$	37.2206	−	38.1653i	2.10720	−	2.16068i
$313$	17.4883	−	17.4883i	0.988495	−	0.988495i	−0.0114396	−	0.999935i	$-0.503641\pi$
$313$	17.4883	−	17.4883i	0.988495	−	0.988495i	0.999935	+	0.0114396i	$0.00364140\pi$
$314$	−1.73474	+	6.58400i	−0.0978968	+	0.371557i
$315$	−15.3211	+	0.632103i	−0.863245	+	0.0356150i
$316$	−5.24219	−	2.96847i	−0.294896	−	0.166990i
$317$		−	19.6255i		−	1.10228i	−0.834413	−	0.551139i	$-0.814193\pi$
$317$		−	19.6255i		−	1.10228i	0.834413	−	0.551139i	$-0.185807\pi$
$318$	−37.9071	−	9.98767i	−2.12573	−	0.560081i
$319$	−36.1281			−2.02278
$320$	−11.7834	+	13.4593i	−0.658710	+	0.752397i
$321$	23.8664			1.33209
$322$	6.75971	+	1.78103i	0.376704	+	0.0992529i
$323$		−	3.47559i		−	0.193387i
$324$	30.3762	+	17.2010i	1.68757	+	0.955610i
$325$	2.47251	+	29.9136i	0.137150	+	1.65931i
$326$	0.0595192	−	0.225899i	0.00329646	−	0.0125114i
$327$	14.7709	−	14.7709i	0.816833	−	0.816833i
$328$	5.25611	−	5.38952i	0.290220	−	0.297586i
$329$	3.94142			0.217297
$330$	−11.0059	+	50.0651i	−0.605852	+	2.75600i
$331$	18.2634	−	18.2634i	1.00385	−	1.00385i	0.00385604	−	0.999993i	$-0.498773\pi$
$331$	18.2634	−	18.2634i	1.00385	−	1.00385i	0.999993	−	0.00385604i	$-0.00122742\pi$
$332$	−8.20962	+	14.4978i	−0.450561	+	0.795672i
$333$	0.528151			0.0289425
$334$	−8.73348	+	5.09103i	−0.477875	+	0.278569i
$335$	11.4132	+	10.5088i	0.623572	+	0.574157i
$336$	−3.04732	+	12.1834i	−0.166245	+	0.664660i
$337$	−19.1932	+	19.1932i	−1.04552	+	1.04552i	−0.0466046	+	0.998913i	$0.514840\pi$
$337$	−19.1932	+	19.1932i	−1.04552	+	1.04552i	−0.998913	+	0.0466046i	$0.985160\pi$
$338$	−31.5049	−	8.30082i	−1.71364	−	0.451505i
$339$	5.04362	−	5.04362i	0.273932	−	0.273932i
$340$	−3.74290	−	1.92019i	−0.202987	−	0.104137i
$341$	24.5399	+	24.5399i	1.32891	+	1.32891i
$342$	−30.9576	+	18.0462i	−1.67400	+	0.975828i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	6.36306	+	6.20556i	0.343073	+	0.334581i
$345$	34.6728	−	1.43050i	1.86672	−	0.0770155i
$346$	−24.8536	−	6.54835i	−1.33614	−	0.352042i
$347$			19.0184i			1.02096i	0.859890	+	0.510479i	$0.170532\pi$
$347$			19.0184i			1.02096i	−0.859890	+	0.510479i	$0.829468\pi$
$348$	−42.3467	+	11.7268i	−2.27002	+	0.628621i
$349$	−1.74349	−	1.74349i	−0.0933269	−	0.0933269i	0.658902	−	0.752229i	$-0.271021\pi$
$349$	−1.74349	−	1.74349i	−0.0933269	−	0.0933269i	−0.752229	+	0.658902i	$0.771021\pi$
$350$	−4.05219	−	5.79480i	−0.216599	−	0.309745i
$351$		−	72.7083i		−	3.88088i
$352$	25.5926	+	14.0716i	1.36409	+	0.750020i
$353$	3.39254	+	3.39254i	0.180567	+	0.180567i	0.791603	−	0.611036i	$-0.209247\pi$
$353$	3.39254	+	3.39254i	0.180567	+	0.180567i	−0.611036	+	0.791603i	$0.709247\pi$
$354$	7.88126	−	4.59425i	0.418884	−	0.244181i
$355$	−4.85393	−	4.46928i	−0.257620	−	0.237205i
$356$	−10.1408	−	5.74241i	−0.537464	−	0.304347i
$357$	−2.95334			−0.156307
$358$	−7.05833	+	4.11453i	−0.373044	+	0.217460i
$359$		−	26.5366i		−	1.40055i	−0.713873	−	0.700275i	$-0.753061\pi$
$359$		−	26.5366i		−	1.40055i	0.713873	−	0.700275i	$-0.246939\pi$
$360$	2.33072	+	43.3088i	0.122840	+	2.28257i
$361$			5.34783i			0.281465i
$362$	−13.5691	−	23.2773i	−0.713175	−	1.22343i
$363$	49.1549			2.57996
$364$	11.5708	−	3.20422i	0.606474	−	0.167947i
$365$	24.4288	−	1.00786i	1.27866	−	0.0527539i
$366$	5.11646	+	8.77710i	0.267442	+	0.458786i
$367$	−10.5526	−	10.5526i	−0.550840	−	0.550840i	0.375843	−	0.926683i	$-0.377353\pi$
$367$	−10.5526	−	10.5526i	−0.550840	−	0.550840i	−0.926683	+	0.375843i	$0.877353\pi$
$368$	4.79754	−	19.1810i	0.250089	−	0.999877i
$369$		−	18.2524i		−	0.950180i
$370$	0.131223	+	0.205173i	0.00682196	+	0.0106665i
$371$	−6.24279	−	6.24279i	−0.324110	−	0.324110i
$372$	36.7292	+	20.7985i	1.90432	+	1.07835i
$373$		−	25.6355i		−	1.32736i	−0.748018	−	0.663679i	$-0.768994\pi$
$373$		−	25.6355i		−	1.32736i	0.748018	−	0.663679i	$-0.231006\pi$
$374$	−1.74988	+	6.64149i	−0.0904843	+	0.343423i
$375$	−27.6943	−	21.5691i	−1.43013	−	1.11382i
$376$	−0.139689	−	11.1471i	−0.00720393	−	0.574870i
$377$	29.7037	+	29.7037i	1.52982	+	1.52982i
$378$	8.62617	+	14.7979i	0.443682	+	0.761120i
$379$	3.05925	+	3.05925i	0.157143	+	0.157143i	0.781300	−	0.624156i	$-0.214557\pi$
$379$	3.05925	+	3.05925i	0.157143	+	0.157143i	−0.624156	+	0.781300i	$0.714557\pi$
$380$	−14.7022	−	7.54254i	−0.754205	−	0.386924i
$381$	−36.6754	+	36.6754i	−1.87894	+	1.87894i
$382$	2.39909	−	9.10550i	0.122748	−	0.465878i
$383$	2.86738	−	2.86738i	0.146516	−	0.146516i	−0.630044	−	0.776560i	$-0.716963\pi$
$383$	2.86738	−	2.86738i	0.146516	−	0.146516i	0.776560	+	0.630044i	$0.216963\pi$
$384$	34.5652	+	8.18665i	1.76390	+	0.417773i
$385$	−7.81988	+	8.49290i	−0.398538	+	0.432838i
$386$	−9.82964	−	16.8624i	−0.500316	−	0.858273i
$387$	21.5494			1.09542
$388$	4.04424	−	1.11994i	0.205315	−	0.0568565i
$389$	8.04864	−	8.04864i	0.408082	−	0.408082i	−0.472987	−	0.881069i	$-0.656824\pi$
$389$	8.04864	−	8.04864i	0.408082	−	0.408082i	0.881069	+	0.472987i	$0.156824\pi$
$390$	50.2112	−	32.1137i	2.54254	−	1.62614i
$391$	4.64959			0.235140
$392$	−1.97478	+	2.02490i	−0.0997416	+	0.102273i
$393$	−47.4639	+	47.4639i	−2.39424	+	2.39424i
$394$	−13.9847	−	3.68465i	−0.704539	−	0.185630i
$395$	−4.95492	−	4.56227i	−0.249309	−	0.229553i
$396$	68.2427	−	18.8980i	3.42933	−	0.949660i
$397$		−	4.62006i		−	0.231874i	−0.993257	−	0.115937i	$-0.963013\pi$
$397$		−	4.62006i		−	0.231874i	0.993257	−	0.115937i	$-0.0369871\pi$
$398$	−7.36710	+	27.9610i	−0.369279	+	1.40156i
$399$	−11.6008			−0.580765
$400$	−16.2453	+	11.6658i	−0.812264	+	0.583291i
$401$	20.0084			0.999173			0.499587	−	0.866264i	$-0.333485\pi$
$401$	20.0084			0.999173			0.499587	+	0.866264i	$0.333485\pi$
$402$	7.84912	−	29.7905i	0.391478	−	1.48581i
$403$		−	40.3523i		−	2.01009i
$404$	−3.94313	−	14.2391i	−0.196178	−	0.708421i
$405$	28.7116	+	26.4363i	1.42669	+	1.31363i
$406$	−9.56948	−	2.52134i	−0.474925	−	0.125132i
$407$	0.281169	−	0.281169i	0.0139370	−	0.0139370i
$408$	0.104671	+	8.35265i	0.00518197	+	0.413518i
$409$	−7.62908			−0.377234			−0.188617	−	0.982051i	$-0.560400\pi$
$409$	−7.62908			−0.377234			−0.188617	+	0.982051i	$0.560400\pi$
$410$	7.09058	−	4.53494i	0.350179	−	0.223965i
$411$	−27.4942	+	27.4942i	−1.35619	+	1.35619i
$412$	6.45054	+	23.2936i	0.317795	+	1.14759i
$413$	2.05455			0.101098
$414$	−24.1420	−	41.4147i	−1.18651	−	2.03542i
$415$	−12.6174	+	13.7033i	−0.619365	+	0.672671i
$416$	−9.47228	−	32.6110i	−0.464417	−	1.59889i
$417$	5.86350	−	5.86350i	0.287137	−	0.287137i
$418$	−6.87357	+	26.0879i	−0.336197	+	1.27600i
$419$	19.2419	−	19.2419i	0.940027	−	0.940027i	−0.0582732	−	0.998301i	$-0.518559\pi$
$419$	19.2419	−	19.2419i	0.940027	−	0.940027i	0.998301	+	0.0582732i	$0.0185595\pi$
$420$	−6.40918	+	12.4930i	−0.312736	+	0.609596i
$421$	−7.04225	−	7.04225i	−0.343218	−	0.343218i	0.514357	−	0.857576i	$-0.328030\pi$
$421$	−7.04225	−	7.04225i	−0.343218	−	0.343218i	−0.857576	+	0.514357i	$0.828030\pi$
$422$	−15.1492	−	25.9879i	−0.737453	−	1.26507i
$423$	−19.1122	−	19.1122i	−0.929268	−	0.929268i
$424$	−17.4346	+	17.8772i	−0.846701	+	0.868191i
$425$	−3.58834	−	3.04044i	−0.174060	−	0.147483i
$426$	−3.33815	+	12.6696i	−0.161734	+	0.613843i
$427$			2.28808i			0.110728i
$428$	7.49127	−	13.2293i	0.362104	−	0.639460i
$429$	−68.8092	−	68.8092i	−3.32214	−	3.32214i
$430$	5.35411	+	8.37140i	0.258198	+	0.403705i
$431$		−	13.6478i		−	0.657391i	−0.944436	−	0.328695i	$-0.893391\pi$
$431$		−	13.6478i		−	0.657391i	0.944436	−	0.328695i	$-0.106609\pi$
$432$	41.5457	−	24.9210i	1.99887	−	1.19901i
$433$	−18.0001	−	18.0001i	−0.865031	−	0.865031i	0.126886	−	0.991917i	$-0.459502\pi$
$433$	−18.0001	−	18.0001i	−0.865031	−	0.865031i	−0.991917	+	0.126886i	$0.959502\pi$
$434$	4.78743	+	8.21265i	0.229804	+	0.394220i
$435$	−49.0851	+	2.02511i	−2.35345	+	0.0970965i
$436$	−3.55125	−	12.8239i	−0.170074	−	0.614155i
$437$	18.2637			0.873669
$438$	−24.4503	−	41.9436i	−1.16828	−	2.00414i
$439$		−	19.9427i		−	0.951812i	−0.879496	−	0.475906i	$-0.842120\pi$
$439$		−	19.9427i		−	0.951812i	0.879496	−	0.475906i	$-0.157880\pi$
$440$	24.2968	+	21.8152i	1.15831	+	1.04000i
$441$			6.85762i			0.326554i
$442$	6.89920	−	4.02177i	0.328161	−	0.191296i
$443$	21.6006			1.02627			0.513137	−	0.858306i	$-0.328483\pi$
$443$	21.6006			1.02627			0.513137	+	0.858306i	$0.328483\pi$
$444$	0.238301	−	0.420829i	0.0113093	−	0.0199717i
$445$	−9.58513	−	8.82556i	−0.454379	−	0.418371i
$446$	−9.16202	+	5.34084i	−0.433834	+	0.252896i
$447$	−38.6175	−	38.6175i	−1.82655	−	1.82655i
$448$	5.79683	+	5.51332i	0.273875	+	0.260480i
$449$		−	38.4618i		−	1.81512i	−0.419920	−	0.907561i	$-0.637942\pi$
$449$		−	38.4618i		−	1.81512i	0.419920	−	0.907561i	$-0.362058\pi$
$450$	−8.45003	+	47.7488i	−0.398338	+	2.25090i
$451$	−9.71690	−	9.71690i	−0.457551	−	0.457551i
$452$	−1.21260	−	4.37882i	−0.0570357	−	0.205962i
$453$			22.5011i			1.05719i
$454$	34.8549	+	9.18347i	1.63582	+	0.431001i
$455$	13.4120	−	0.553340i	0.628764	−	0.0259410i
$456$	0.411148	+	32.8094i	0.0192538	+	1.53644i
$457$	6.96238	+	6.96238i	0.325686	+	0.325686i	0.850944	−	0.525257i	$-0.176031\pi$
$457$	6.96238	+	6.96238i	0.325686	+	0.325686i	−0.525257	+	0.850944i	$0.676031\pi$
$458$	28.9983	−	16.9041i	1.35500	−	0.789876i
$459$	8.05598	+	8.05598i	0.376021	+	0.376021i
$460$	10.0903	−	19.6683i	0.470462	−	0.917040i
$461$	18.7413	−	18.7413i	0.872868	−	0.872868i	−0.119916	−	0.992784i	$-0.538263\pi$
$461$	18.7413	−	18.7413i	0.872868	−	0.872868i	0.992784	+	0.119916i	$0.0382626\pi$
$462$	22.1679	+	5.84074i	1.03134	+	0.271736i
$463$	−9.85257	+	9.85257i	−0.457888	+	0.457888i	−0.897962	−	0.440074i	$-0.854952\pi$
$463$	−9.85257	+	9.85257i	−0.457888	+	0.457888i	0.440074	+	0.897962i	$0.354952\pi$
$464$	−6.79172	+	27.1538i	−0.315297	+	1.26058i
$465$	34.7164	+	31.9653i	1.60994	+	1.48236i
$466$	21.6016	−	12.5923i	1.00068	−	0.583327i
$467$	−5.91589			−0.273755			−0.136877	−	0.990588i	$-0.543707\pi$
$467$	−5.91589			−0.273755			−0.136877	+	0.990588i	$0.543707\pi$
$468$	−71.6451	−	40.5701i	−3.31180	−	1.87535i
$469$	4.90609	−	4.90609i	0.226542	−	0.226542i
$470$	2.67604	−	12.1732i	0.123436	−	0.561507i
$471$	15.1159			0.696506
$472$	−0.0728161	−	5.81068i	−0.00335163	−	0.267458i
$473$	11.4721	−	11.4721i	0.527489	−	0.527489i
$474$	−3.40760	+	12.9332i	−0.156516	+	0.594040i
$475$	−14.0951	−	11.9429i	−0.646726	−	0.547978i
$476$	−0.927005	+	1.63705i	−0.0424892	+	0.0750342i
$477$			60.5435i			2.77210i
$478$	−20.1665	−	5.31342i	−0.922395	−	0.243030i
$479$	−1.13821			−0.0520060			−0.0260030	−	0.999662i	$-0.508278\pi$
$479$	−1.13821			−0.0520060			−0.0260030	+	0.999662i	$0.508278\pi$
$480$	35.5599	+	17.6837i	1.62308	+	0.807148i
$481$	−0.462341			−0.0210809
$482$	8.85599	+	2.33335i	0.403379	+	0.106281i
$483$		−	15.5193i		−	0.706154i
$484$	15.4289	−	27.2468i	0.701314	−	1.23849i
$485$	4.68778	−	0.193404i	0.212861	−	0.00878203i
$486$	6.65336	−	25.2521i	0.301802	−	1.14546i
$487$	−0.819677	+	0.819677i	−0.0371431	+	0.0371431i	−0.725434	−	0.688291i	$-0.758361\pi$
$487$	−0.819677	+	0.819677i	−0.0371431	+	0.0371431i	0.688291	+	0.725434i	$0.258361\pi$
$488$	6.47117	−	0.0810929i	0.292936	−	0.00367090i
$489$	−0.518632			−0.0234533
$490$	−2.66401	+	1.70383i	−0.120348	+	0.0769711i
$491$	8.54221	−	8.54221i	0.385504	−	0.385504i	−0.487576	−	0.873080i	$-0.662119\pi$
$491$	8.54221	−	8.54221i	0.385504	−	0.385504i	0.873080	+	0.487576i	$0.162119\pi$
$492$	−14.5434	−	8.23543i	−0.655668	−	0.371282i
$493$	−6.58226			−0.296450
$494$	27.1002	−	15.7976i	1.21929	−	0.710767i
$495$	79.1019	−	3.26351i	3.55536	−	0.146684i
$496$	23.0574	−	13.8309i	1.03531	−	0.621025i
$497$	−2.08651	+	2.08651i	−0.0935927	+	0.0935927i
$498$	35.7680	+	9.42406i	1.60280	+	0.422302i
$499$	8.58677	−	8.58677i	0.384396	−	0.384396i	−0.488287	−	0.872683i	$-0.662378\pi$
$499$	8.58677	−	8.58677i	0.384396	−	0.384396i	0.872683	+	0.488287i	$0.162378\pi$
$500$	−20.6487	+	8.58092i	−0.923437	+	0.383751i
$501$	15.8696	+	15.8696i	0.709000	+	0.709000i
$502$	8.33103	−	4.85643i	0.371832	−	0.216753i
$503$	0.282617	+	0.282617i	0.0126012	+	0.0126012i	0.713379	−	0.700778i	$-0.247164\pi$
$503$	0.282617	+	0.282617i	0.0126012	+	0.0126012i	−0.700778	+	0.713379i	$0.747164\pi$
$504$	19.3948	−	0.243044i	0.863912	−	0.0108260i
$505$	−0.680944	−	16.5049i	−0.0303016	−	0.734458i
$506$	−34.9000	−	9.19536i	−1.55149	−	0.408783i
$507$			72.3307i			3.21232i
$508$	8.81755	+	31.8411i	0.391215	+	1.41272i
$509$	−6.27329	−	6.27329i	−0.278059	−	0.278059i	0.554275	−	0.832334i	$-0.312996\pi$
$509$	−6.27329	−	6.27329i	−0.278059	−	0.278059i	−0.832334	+	0.554275i	$0.812996\pi$
$510$	−2.00518	+	9.12148i	−0.0887909	+	0.403906i
$511$		−	10.9342i		−	0.483700i
$512$	15.3874	−	16.5900i	0.680032	−	0.733183i
$513$	31.6440	+	31.6440i	1.39712	+	1.39712i
$514$	−1.22231	+	0.712525i	−0.0539138	+	0.0314281i
$515$	1.11395	+	27.0002i	0.0490865	+	1.18977i
$516$	9.72305	−	17.1705i	0.428034	−	0.755889i
$517$	−20.3493			−0.894962
$518$	0.0940974	−	0.0548525i	0.00413440	−	0.00241008i
$519$			57.0603i			2.50467i
$520$	−2.04030	−	37.9123i	−0.0894731	−	1.66256i
$521$			10.6698i			0.467452i	0.972302	+	0.233726i	$0.0750919\pi$
$521$			10.6698i			0.467452i	−0.972302	+	0.233726i	$0.924908\pi$
$522$	34.1769	+	58.6293i	1.49588	+	2.56613i
$523$	−18.0981			−0.791374			−0.395687	−	0.918385i	$-0.629493\pi$
$523$	−18.0981			−0.791374			−0.395687	+	0.918385i	$0.629493\pi$
$524$	11.4113	+	41.2076i	0.498507	+	1.80016i
$525$	−10.1483	+	11.9771i	−0.442910	+	0.522725i
$526$	−0.161276	−	0.276663i	−0.00703196	−	0.0120631i
$527$	4.47098	+	4.47098i	0.194759	+	0.194759i
$528$	15.7331	−	62.9023i	0.684697	−	2.73747i
$529$			1.43285i			0.0622979i
$530$	−23.5196	+	15.0425i	−1.02163	+	0.653404i
$531$	−9.96265	−	9.96265i	−0.432342	−	0.432342i
$532$	−3.64129	+	6.43037i	−0.157870	+	0.278792i
$533$			15.9780i			0.692085i
$534$	−6.59188	+	25.0188i	−0.285259	+	1.08267i
$535$	11.5134	−	12.5043i	0.497767	−	0.540608i
$536$	−14.0493	−	13.7016i	−0.606838	−	0.591817i
$537$	12.8257	+	12.8257i	0.553468	+	0.553468i
$538$	−10.6655	−	18.2962i	−0.459821	−	0.788806i
$539$	3.65075	+	3.65075i	0.157249	+	0.157249i
$540$	51.5605	−	16.5951i	2.21881	−	0.714140i
$541$	−15.2932	+	15.2932i	−0.657504	+	0.657504i	−0.954789	−	0.297285i	$-0.903919\pi$
$541$	−15.2932	+	15.2932i	−0.657504	+	0.657504i	0.297285	+	0.954789i	$0.403919\pi$
$542$	3.12580	−	11.8636i	0.134264	−	0.509586i
$543$	−42.2970	+	42.2970i	−1.81514	+	1.81514i
$544$	4.66277	+	2.56374i	0.199915	+	0.109920i
$545$	−0.613269	−	14.8646i	−0.0262695	−	0.636728i
$546$	−13.4238	−	23.0280i	−0.574486	−	0.985510i
$547$	40.3084			1.72346			0.861731	−	0.507366i	$-0.169381\pi$
$547$	40.3084			1.72346			0.861731	+	0.507366i	$0.169381\pi$
$548$	6.61021	+	23.8702i	0.282374	+	1.01968i
$549$	11.0951	−	11.0951i	0.473526	−	0.473526i
$550$	20.9212	+	29.9182i	0.892085	+	1.27572i
$551$	−25.8552			−1.10147
$552$	−43.8919	+	0.550027i	−1.86816	+	0.0234107i
$553$	−2.12992	+	2.12992i	−0.0905733	+	0.0905733i
$554$	20.5538	+	5.41546i	0.873247	+	0.230081i
$555$	0.366246	−	0.397767i	0.0155463	−	0.0168843i
$556$	−1.40971	−	5.09063i	−0.0597851	−	0.215891i
$557$		−	25.9253i		−	1.09849i	−0.835662	−	0.549245i	$-0.814915\pi$
$557$		−	25.9253i		−	1.09849i	0.835662	−	0.549245i	$-0.185085\pi$
$558$	16.6092	−	63.0383i	0.703122	−	2.66862i
$559$	−18.8642			−0.797873
$560$	4.91319	+	7.47399i	0.207620	+	0.315834i
$561$	15.2479			0.643768
$562$	−5.73636	+	21.7717i	−0.241974	+	0.918386i
$563$			38.0231i			1.60248i	0.598342	+	0.801241i	$0.295827\pi$
$563$			38.0231i			1.60248i	−0.598342	+	0.801241i	$0.704173\pi$
$564$	−23.8520	+	6.60516i	−1.00435	+	0.278127i
$565$	−0.209404	−	5.07560i	−0.00880971	−	0.213532i
$566$	0.826709	+	0.217819i	0.0347492	+	0.00915562i
$567$	12.3419	−	12.3419i	0.518313	−	0.518313i
$568$	5.97502	+	5.82712i	0.250706	+	0.244501i
$569$	3.89605			0.163331			0.0816654	−	0.996660i	$-0.473976\pi$
$569$	3.89605			0.163331			0.0816654	+	0.996660i	$0.473976\pi$
$570$	−7.87639	+	35.8293i	−0.329906	+	1.50073i
$571$	29.3718	−	29.3718i	1.22917	−	1.22917i	0.264895	−	0.964277i	$-0.414663\pi$
$571$	29.3718	−	29.3718i	1.22917	−	1.22917i	0.964277	−	0.264895i	$-0.0853372\pi$
$572$	−59.7394	+	16.5432i	−2.49783	+	0.691706i
$573$	−20.9049			−0.873317
$574$	−1.89565	−	3.25191i	−0.0791228	−	0.135732i
$575$	15.9770	−	18.8562i	0.666289	−	0.786357i
$576$	−1.37476	−	54.8438i	−0.0572815	−	2.28516i
$577$	−9.02944	+	9.02944i	−0.375901	+	0.375901i	−0.869621	−	0.493720i	$-0.835637\pi$
$577$	−9.02944	+	9.02944i	−0.375901	+	0.375901i	0.493720	+	0.869621i	$0.335637\pi$
$578$	5.80656	−	22.0382i	0.241521	−	0.916668i
$579$	−30.6406	+	30.6406i	−1.27338	+	1.27338i
$580$	−14.2845	+	27.8438i	−0.593131	+	1.15615i
$581$	5.89051	+	5.89051i	0.244380	+	0.244380i
$582$	−4.69190	−	8.04879i	−0.194486	−	0.333633i
$583$	32.2312	+	32.2312i	1.33488	+	1.33488i
$584$	−30.9241	+	0.387523i	−1.27965	+	0.0160358i
$585$	−67.7189	−	62.3526i	−2.79983	−	2.57796i
$586$	−2.15511	+	8.17949i	−0.0890268	+	0.337892i
$587$		−	19.2844i		−	0.795954i	−0.917395	−	0.397977i	$-0.869712\pi$
$587$		−	19.2844i		−	0.795954i	0.917395	−	0.397977i	$-0.130288\pi$
$588$	5.46413	+	3.09415i	0.225337	+	0.127600i
$589$	17.5621	+	17.5621i	0.723633	+	0.723633i
$590$	1.39494	−	6.34553i	0.0574289	−	0.261241i
$591$			32.1069i			1.32070i
$592$	−0.158469	−	0.264183i	−0.00651304	−	0.0108578i
$593$	−34.0800	−	34.0800i	−1.39950	−	1.39950i	−0.801495	−	0.598002i	$-0.795962\pi$
$593$	−34.0800	−	34.0800i	−1.39950	−	1.39950i	−0.598002	−	0.801495i	$-0.704038\pi$
$594$	−44.5364	−	76.4006i	−1.82735	−	3.13475i
$595$	−1.42472	+	1.54734i	−0.0584079	+	0.0634348i
$596$	−33.5273	+	9.28449i	−1.37333	+	0.380308i
$597$	64.1946			2.62731
$598$	21.1338	+	36.2542i	0.864224	+	1.48254i
$599$			23.4927i			0.959884i	0.877300	+	0.479942i	$0.159342\pi$
$599$			23.4927i			0.959884i	−0.877300	+	0.479942i	$0.840658\pi$
$600$	34.2334	+	28.2771i	1.39757	+	1.15441i
$601$			44.0527i			1.79695i	0.439026	+	0.898474i	$0.355324\pi$
$601$			44.0527i			1.79695i	−0.439026	+	0.898474i	$0.644676\pi$
$602$	3.83933	−	2.23807i	0.156479	−	0.0912169i
$603$	−47.5800			−1.93761
$604$	12.4725	+	7.06272i	0.507497	+	0.287378i
$605$	23.7128	−	25.7537i	0.964063	−	1.04704i
$606$	−28.3385	+	16.5194i	−1.15117	+	0.671056i
$607$	11.2601	+	11.2601i	0.457035	+	0.457035i	0.897681	−	0.440646i	$-0.145251\pi$
$607$	11.2601	+	11.2601i	0.457035	+	0.457035i	−0.440646	+	0.897681i	$0.645251\pi$
$608$	18.3155	+	10.0704i	0.742790	+	0.408410i
$609$			21.9702i			0.890277i
$610$	7.06681	+	1.55350i	0.286127	+	0.0628995i
$611$	16.7307	+	16.7307i	0.676853	+	0.676853i
$612$	12.4333	−	3.44307i	0.502586	−	0.139178i
$613$			11.8456i			0.478438i	0.970966	+	0.239219i	$0.0768914\pi$
$613$			11.8456i			0.478438i	−0.970966	+	0.239219i	$0.923109\pi$
$614$	47.8171	+	12.5987i	1.92974	+	0.508444i
$615$	−13.7464	−	12.6571i	−0.554310	−	0.510384i
$616$	10.1957	−	10.4545i	0.410796	−	0.421222i
$617$	−23.4550	−	23.4550i	−0.944265	−	0.944265i	0.0542621	−	0.998527i	$-0.482719\pi$
$617$	−23.4550	−	23.4550i	−0.944265	−	0.944265i	−0.998527	+	0.0542621i	$0.982719\pi$
$618$	46.3586	−	27.0240i	1.86482	−	1.08706i
$619$	−12.6797	−	12.6797i	−0.509641	−	0.509641i	0.404775	−	0.914416i	$-0.367350\pi$
$619$	−12.6797	−	12.6797i	−0.509641	−	0.509641i	−0.914416	+	0.404775i	$0.867350\pi$
$620$	28.6155	−	9.21010i	1.14922	−	0.369887i
$621$	−42.3329	+	42.3329i	−1.69876	+	1.69876i
$622$	−0.826197	−	0.217684i	−0.0331275	−	0.00872834i
$623$	−4.12026	+	4.12026i	−0.165075	+	0.165075i
$624$	−64.6523	+	38.7814i	−2.58816	+	1.55250i
$625$	−24.6607	+	4.10470i	−0.986429	+	0.164188i
$626$	−30.2172	+	17.6146i	−1.20772	+	0.704022i
$627$	59.8941			2.39194
$628$	4.74465	−	8.37885i	0.189332	−	0.334352i
$629$	0.0512267	−	0.0512267i	0.00204254	−	0.00204254i
$630$	21.1800	+	4.65601i	0.843831	+	0.185500i
$631$	−17.7621			−0.707098			−0.353549	−	0.935416i	$-0.615025\pi$
$631$	−17.7621			−0.707098			−0.353549	+	0.935416i	$0.615025\pi$
$632$	6.09933	+	5.94836i	0.242618	+	0.236613i
$633$	−47.2226	+	47.2226i	−1.87693	+	1.87693i
$634$	−7.07139	+	26.8387i	−0.280841	+	1.06590i
$635$	1.52271	+	36.9079i	0.0604270	+	1.46464i
$636$	48.2409	+	27.3171i	1.91288	+	1.08319i
$637$		−	6.00313i		−	0.237853i
$638$	49.4067	+	13.0175i	1.95603	+	0.515370i
$639$	20.2353			0.800494
$640$	20.9638	−	14.1604i	0.828669	−	0.559739i
$641$	−48.1232			−1.90075			−0.950376	−	0.311105i	$-0.899301\pi$
$641$	−48.1232			−1.90075			−0.950376	+	0.311105i	$0.899301\pi$
$642$	−32.6383	−	8.59945i	−1.28813	−	0.339393i
$643$		−	40.0755i		−	1.58042i	−0.612834	−	0.790211i	$-0.709971\pi$
$643$		−	40.0755i		−	1.58042i	0.612834	−	0.790211i	$-0.290029\pi$
$644$	−8.60245	−	4.87127i	−0.338984	−	0.191955i
$645$	14.9434	−	16.2295i	0.588397	−	0.639038i
$646$	−1.25231	+	4.75301i	−0.0492715	+	0.187005i
$647$	26.6352	−	26.6352i	1.04714	−	1.04714i	0.0483057	−	0.998833i	$-0.484618\pi$
$647$	26.6352	−	26.6352i	1.04714	−	1.04714i	0.998833	−	0.0483057i	$-0.0153822\pi$
$648$	−35.3429	−	34.4681i	−1.38840	−	1.35404i
$649$	−10.6075			−0.416381
$650$	7.39712	−	41.7991i	0.290139	−	1.63949i
$651$	14.9232	−	14.9232i	0.584885	−	0.584885i
$652$	−0.162790	+	0.287480i	−0.00637535	+	0.0112586i
$653$	34.8879			1.36527			0.682634	−	0.730761i	$-0.260834\pi$
$653$	34.8879			1.36527			0.682634	+	0.730761i	$0.260834\pi$
$654$	−25.5221	+	14.8776i	−0.997991	+	0.581762i
$655$	1.97064	+	47.7648i	0.0769991	+	1.86632i
$656$	−9.12989	+	5.47653i	−0.356462	+	0.213823i
$657$	−53.0206	+	53.0206i	−2.06853	+	2.06853i
$658$	−5.39005	−	1.42016i	−0.210126	−	0.0553635i
$659$	−17.2577	+	17.2577i	−0.672265	+	0.672265i	−0.958238	−	0.285973i	$-0.907683\pi$
$659$	−17.2577	+	17.2577i	−0.672265	+	0.672265i	0.285973	+	0.958238i	$0.407683\pi$
$660$	33.0903	−	64.5006i	1.28804	−	2.51068i
$661$	7.86683	+	7.86683i	0.305984	+	0.305984i	0.843350	−	0.537365i	$-0.180580\pi$
$661$	7.86683	+	7.86683i	0.305984	+	0.305984i	−0.537365	+	0.843350i	$0.680580\pi$
$662$	−31.5566	+	18.3954i	−1.22648	+	0.714957i
$663$	−12.5365	−	12.5365i	−0.486877	−	0.486877i
$664$	16.4508	−	16.8683i	0.638415	−	0.654619i
$665$	−5.59633	+	6.07798i	−0.217017	+	0.235694i
$666$	−0.722269	−	0.190301i	−0.0279873	−	0.00737403i
$667$		−	34.5887i		−	1.33928i
$668$	13.7778	−	3.81539i	0.533078	−	0.147622i
$669$	16.6483	+	16.6483i	0.643659	+	0.643659i
$670$	−11.8216	−	18.4836i	−0.456708	−	0.714085i
$671$		−	11.8132i		−	0.456045i
$672$	8.55723	−	15.5633i	0.330102	−	0.600369i
$673$	3.08851	+	3.08851i	0.119053	+	0.119053i	0.764123	−	0.645070i	$-0.223172\pi$
$673$	3.08851	+	3.08851i	0.119053	+	0.119053i	−0.645070	+	0.764123i	$0.723172\pi$
$674$	33.1631	−	19.3318i	1.27739	−	0.744635i
$675$	60.3528	−	4.98846i	2.32298	−	0.192006i
$676$	40.0933	+	22.7034i	1.54205	+	0.873209i
$677$	37.4795			1.44045			0.720227	−	0.693738i	$-0.244038\pi$
$677$	37.4795			1.44045			0.720227	+	0.693738i	$0.244038\pi$
$678$	−8.71466	+	5.08007i	−0.334685	+	0.195099i
$679$		−	2.09822i		−	0.0805223i
$680$	4.42669	+	3.97457i	0.169756	+	0.152418i
$681$		−	80.0219i		−	3.06644i
$682$	−24.7172	−	42.4015i	−0.946471	−	1.62364i
$683$	14.2079			0.543651			0.271825	−	0.962347i	$-0.412373\pi$
$683$	14.2079			0.543651			0.271825	+	0.962347i	$0.412373\pi$
$684$	48.8382	−	13.5244i	1.86738	−	0.517120i
$685$	1.14152	+	27.6685i	0.0436154	+	1.05716i
$686$	0.712216	+	1.22178i	0.0271925	+	0.0466478i
$687$	−52.6928	−	52.6928i	−2.01035	−	2.01035i
$688$	−6.46579	−	10.7791i	−0.246506	−	0.410949i
$689$		−	52.9995i		−	2.01912i
$690$	−47.9320	−	10.5369i	−1.82474	−	0.401133i
$691$	−19.7608	−	19.7608i	−0.751738	−	0.751738i	0.223066	−	0.974803i	$-0.428394\pi$
$691$	−19.7608	−	19.7608i	−0.751738	−	0.751738i	−0.974803	+	0.223066i	$0.928394\pi$
$692$	31.6288	+	17.9103i	1.20235	+	0.680847i
$693$		−	35.4055i		−	1.34494i
$694$	6.85263	−	26.0084i	0.260122	−	0.987266i
$695$	−0.243445	−	5.90067i	−0.00923438	−	0.223825i
$696$	62.1362	−	0.778655i	2.35527	−	0.0295148i
$697$	−1.77035	−	1.77035i	−0.0670566	−	0.0670566i
$698$	1.75609	+	3.01250i	0.0664689	+	0.114025i
$699$	−39.2522	−	39.2522i	−1.48466	−	1.48466i
$700$	3.45358	+	9.38471i	0.130533	+	0.354709i
$701$	11.3939	−	11.3939i	0.430343	−	0.430343i	−0.458402	−	0.888745i	$-0.651578\pi$
$701$	11.3939	−	11.3939i	0.430343	−	0.430343i	0.888745	+	0.458402i	$0.151578\pi$
$702$	−26.1980	+	99.4316i	−0.988779	+	3.75281i
$703$	0.201220	−	0.201220i	0.00758914	−	0.00758914i
$704$	−29.9287	−	28.4650i	−1.12798	−	1.07281i
$705$	−27.6474	+	1.14065i	−1.04126	+	0.0429594i
$706$	−3.41706	−	5.86184i	−0.128603	−	0.220613i
$707$	−7.38749			−0.277835
$708$	−12.4333	+	3.44308i	−0.467273	+	0.129399i
$709$	−27.9535	+	27.9535i	−1.04982	+	1.04982i	−0.0511228	+	0.998692i	$0.516280\pi$
$709$	−27.9535	+	27.9535i	−1.04982	+	1.04982i	−0.998692	+	0.0511228i	$0.983720\pi$
$710$	5.02760	+	7.86089i	0.188683	+	0.295014i
$711$	20.6563			0.774670
$712$	11.7990	+	11.5069i	0.442185	+	0.431239i
$713$	−23.4943	+	23.4943i	−0.879868	+	0.879868i
$714$	4.03882	+	1.06414i	0.151149	+	0.0398243i
$715$	−69.2454	+	2.85686i	−2.58963	+	0.106841i
$716$	11.1351	−	3.08357i	0.416138	−	0.115238i
$717$			46.2995i			1.72909i
$718$	−9.56159	+	36.2900i	−0.356835	+	1.35433i
$719$	−11.0115			−0.410659			−0.205329	−	0.978693i	$-0.565827\pi$
$719$	−11.0115			−0.410659			−0.205329	+	0.978693i	$0.565827\pi$
$720$	12.4175	−	60.0664i	0.462773	−	2.23854i
$721$	12.0851			0.450074
$722$	1.92691	−	7.31339i	0.0717122	−	0.272176i
$723$		−	20.3321i		−	0.756159i
$724$	10.1691	+	36.7218i	0.377932	+	1.36475i
$725$	−22.6181	+	26.6940i	−0.840017	+	0.991392i
$726$	−67.2214	−	17.7113i	−2.49482	−	0.657328i
$727$	5.41254	−	5.41254i	0.200740	−	0.200740i	−0.599577	−	0.800317i	$-0.704664\pi$
$727$	5.41254	−	5.41254i	0.200740	−	0.200740i	0.800317	+	0.599577i	$0.204664\pi$
$728$	−16.9781	+	0.212759i	−0.629250	+	0.00788539i
$729$	−5.61288			−0.207884
$730$	−33.7706	−	7.42380i	−1.24990	−	0.274767i
$731$	2.09013	−	2.09013i	0.0773064	−	0.0773064i
$732$	−3.83444	−	13.8466i	−0.141725	−	0.511785i
$733$	29.5794			1.09254			0.546270	−	0.837609i	$-0.316047\pi$
$733$	29.5794			1.09254			0.546270	+	0.837609i	$0.316047\pi$
$734$	10.6288	+	18.2334i	0.392317	+	0.673005i
$735$	5.16470	+	4.75542i	0.190503	+	0.175406i
$736$	−13.4721	+	24.5021i	−0.496587	+	0.903161i
$737$	−25.3299	+	25.3299i	−0.933038	+	0.933038i
$738$	−6.57663	+	24.9609i	−0.242089	+	0.918823i
$739$	20.0027	−	20.0027i	0.735813	−	0.735813i	−0.235952	−	0.971765i	$-0.575821\pi$
$739$	20.0027	−	20.0027i	0.735813	−	0.735813i	0.971765	+	0.235952i	$0.0758208\pi$
$740$	−0.105526	−	0.327865i	−0.00387921	−	0.0120526i
$741$	−49.2436	−	49.2436i	−1.80901	−	1.80901i
$742$	6.28790	+	10.7867i	0.230836	+	0.395991i
$743$	−9.38871	−	9.38871i	−0.344438	−	0.344438i	0.513595	−	0.858033i	$-0.328314\pi$
$743$	−9.38871	−	9.38871i	−0.344438	−	0.344438i	−0.858033	+	0.513595i	$0.828314\pi$
$744$	−42.7347	−	41.6769i	−1.56673	−	1.52795i
$745$	−38.8624	+	1.60335i	−1.42381	+	0.0587421i
$746$	−9.23691	+	35.0577i	−0.338187	+	1.28355i
$747$		−	57.1270i		−	2.09017i
$748$	4.78608	−	8.45201i	0.174996	−	0.309036i
$749$	−5.37509	−	5.37509i	−0.196401	−	0.196401i
$750$	30.1015	+	39.4754i	1.09915	+	1.44144i
$751$			31.4432i			1.14738i	0.819073	+	0.573689i	$0.194488\pi$
$751$			31.4432i			1.14738i	−0.819073	+	0.573689i	$0.805512\pi$
$752$	−3.82547	+	15.2945i	−0.139500	+	0.557733i
$753$	−15.1383	−	15.1383i	−0.551670	−	0.551670i
$754$	−29.9183	−	51.3238i	−1.08956	−	1.86910i
$755$	11.7890	+	10.8547i	0.429044	+	0.395045i
$756$	−6.46473	−	23.3449i	−0.235120	−	0.849045i
$757$	−0.0968547			−0.00352024			−0.00176012	−	0.999998i	$-0.500560\pi$
$757$	−0.0968547			−0.00352024			−0.00176012	+	0.999998i	$0.500560\pi$
$758$	−3.08136	−	5.28596i	−0.111920	−	0.191995i
$759$			80.1255i			2.90837i
$760$	17.3881	+	15.6122i	0.630734	+	0.566313i
$761$		−	50.1015i		−	1.81618i	−0.418779	−	0.908088i	$-0.637542\pi$
$761$		−	50.1015i		−	1.81618i	0.418779	−	0.908088i	$-0.362458\pi$
$762$	63.3698	−	36.9404i	2.29565	−	1.33821i
$763$	−6.65329			−0.240865
$764$	−6.56172	+	11.5877i	−0.237395	+	0.419229i
$765$	14.4118	−	0.594587i	0.521058	−	0.0214973i
$766$	−4.95443	+	2.88810i	−0.179011	+	0.104351i
$767$	8.72125	+	8.72125i	0.314906	+	0.314906i
$768$	−44.3196	−	23.6500i	−1.59925	−	0.853396i
$769$			10.8794i			0.392321i	0.980572	+	0.196161i	$0.0628474\pi$
$769$			10.8794i			0.392321i	−0.980572	+	0.196161i	$0.937153\pi$
$770$	13.7542	−	8.79677i	0.495665	−	0.317014i
$771$	2.22105	+	2.22105i	0.0799893	+	0.0799893i
$772$	7.36666	+	26.6018i	0.265132	+	0.957420i
$773$		−	35.0953i		−	1.26229i	−0.775664	−	0.631146i	$-0.782585\pi$
$773$		−	35.0953i		−	1.26229i	0.775664	−	0.631146i	$-0.217415\pi$
$774$	−29.4697	−	7.76461i	−1.05927	−	0.279093i
$775$	33.4951	−	2.76854i	1.20318	−	0.0994488i
$776$	−5.93420	+	0.0743639i	−0.213025	+	0.00266951i
$777$	−0.170984	−	0.170984i	−0.00613402	−	0.00613402i
$778$	−13.9069	+	8.10680i	−0.498587	+	0.290643i
$779$	−6.95395	−	6.95395i	−0.249151	−	0.249151i
$780$	−80.2370	+	25.8249i	−2.87294	+	0.924679i
$781$	10.7725	−	10.7725i	0.385471	−	0.385471i
$782$	−6.35851	−	1.67532i	−0.227380	−	0.0599094i
$783$	59.9292	−	59.9292i	2.14170	−	2.14170i
$784$	3.43020	−	2.05760i	0.122507	−	0.0734855i
$785$	7.29209	−	7.91968i	0.260266	−	0.282666i
$786$	82.0108	−	47.8068i	2.92523	−	1.70521i
$787$	9.70628			0.345991			0.172996	−	0.984923i	$-0.444655\pi$
$787$	9.70628			0.345991			0.172996	+	0.984923i	$0.444655\pi$
$788$	17.7970	+	10.0778i	0.633993	+	0.359008i
$789$	−0.502722	+	0.502722i	−0.0178974	+	0.0178974i
$790$	5.13220	+	8.02443i	0.182596	+	0.285497i
$791$	−2.27181			−0.0807761
$792$	−100.134	+	1.25482i	−3.55811	+	0.0445882i
$793$	−9.71258	+	9.71258i	−0.344904	+	0.344904i
$794$	−1.66468	+	6.31812i	−0.0590774	+	0.224222i
$795$	45.5973	+	41.9839i	1.61717	+	1.48902i
$796$	20.1496	−	35.5834i	0.714185	−	1.26122i
$797$		−	26.6828i		−	0.945154i	−0.881289	−	0.472577i	$-0.843324\pi$
$797$		−	26.6828i		−	0.945154i	0.881289	−	0.472577i	$-0.156676\pi$
$798$	15.8645	+	4.17995i	0.561599	+	0.147969i
$799$	−3.70749			−0.131162
$800$	26.4195	−	10.1001i	0.934070	−	0.357091i
$801$	39.9588			1.41188
$802$	−27.3624	−	7.20937i	−0.966199	−	0.254572i
$803$			56.4526i			1.99217i
$804$	−21.4680	+	37.9116i	−0.757118	+	1.33704i
$805$	−8.13103	−	7.48669i	−0.286581	−	0.263871i
$806$	−14.5396	+	55.1834i	−0.512135	+	1.94375i
$807$	−33.2460	+	33.2460i	−1.17031	+	1.17031i
$808$	0.261823	+	20.8933i	0.00921091	+	0.735025i
$809$	−0.0398409			−0.00140073			−0.000700366	−	1.00000i	$-0.500223\pi$
$809$	−0.0398409			−0.00140073			−0.000700366		1.00000i	$0.500223\pi$
$810$	−29.7389	−	46.4981i	−1.04492	−	1.63378i
$811$	−15.7313	+	15.7313i	−0.552399	+	0.552399i	−0.927133	−	0.374733i	$-0.877734\pi$
$811$	−15.7313	+	15.7313i	−0.552399	+	0.552399i	0.374733	+	0.927133i	$0.377734\pi$
$812$	12.1782	+	6.89608i	0.427371	+	0.242005i
$813$	−27.2372			−0.955251
$814$	−0.485820	+	0.283200i	−0.0170280	+	0.00992616i
$815$	−0.250193	+	0.271726i	−0.00876389	+	0.00951815i
$816$	2.86646	−	11.4603i	0.100346	−	0.401192i
$817$	8.21008	−	8.21008i	0.287234	−	0.287234i
$818$	10.4331	+	2.74888i	0.364784	+	0.0961124i
$819$	−29.1096	+	29.1096i	−1.01717	+	1.01717i
$820$	−11.3307	+	3.64687i	−0.395685	+	0.127354i
$821$	15.7584	+	15.7584i	0.549971	+	0.549971i	0.926432	−	0.376461i	$-0.122859\pi$
$821$	15.7584	+	15.7584i	0.549971	+	0.549971i	−0.376461	+	0.926432i	$0.622859\pi$
$822$	47.5062	−	27.6929i	1.65697	−	0.965901i
$823$	−32.9590	−	32.9590i	−1.14888	−	1.14888i	−0.986774	−	0.162103i	$-0.948172\pi$
$823$	−32.9590	−	32.9590i	−1.14888	−	1.14888i	−0.162103	−	0.986774i	$-0.551828\pi$
$824$	−0.428314	−	34.1792i	−0.0149210	−	1.19069i
$825$	52.3954	−	61.8372i	1.82417	−	2.15290i
$826$	−2.80968	−	0.740287i	−0.0977613	−	0.0257579i
$827$			5.33499i			0.185516i	0.995689	+	0.0927578i	$0.0295682\pi$
$827$			5.33499i			0.185516i	−0.995689	+	0.0927578i	$0.970432\pi$
$828$	18.0928	+	65.3350i	0.628768	+	2.27055i
$829$	3.49514	+	3.49514i	0.121391	+	0.121391i	0.765193	−	0.643801i	$-0.222644\pi$
$829$	3.49514	+	3.49514i	0.121391	+	0.121391i	−0.643801	+	0.765193i	$0.722644\pi$
$830$	22.1924	−	14.1936i	0.770310	−	0.492668i
$831$		−	47.1886i		−	1.63696i
$832$	1.20345	+	48.0100i	0.0417223	+	1.66445i
$833$	0.665139	+	0.665139i	0.0230457	+	0.0230457i
$834$	−10.1313	+	5.90587i	−0.350818	+	0.204504i
$835$	15.9702	−	0.658883i	0.552671	−	0.0228016i
$836$	18.7998	−	33.1996i	0.650204	−	1.14823i
$837$	−81.4135			−2.81406
$838$	−33.2473	+	19.3809i	−1.14851	+	0.669503i
$839$		−	39.8454i		−	1.37562i	−0.725892	−	0.687809i	$-0.758573\pi$
$839$		−	39.8454i		−	1.37562i	0.725892	−	0.687809i	$-0.241427\pi$
$840$	13.2663	−	14.7754i	0.457730	−	0.509798i
$841$			19.9661i			0.688485i
$842$	7.09314	+	12.1680i	0.244446	+	0.419338i
$843$	49.9849			1.72157
$844$	11.3533	+	40.9981i	0.390798	+	1.41121i
$845$	37.8962	+	34.8931i	1.30367	+	1.20036i
$846$	19.2503	+	33.0232i	0.661840	+	1.13536i
$847$	−11.0705	−	11.0705i	−0.380385	−	0.380385i
$848$	30.2841	−	18.1658i	1.03996	−	0.623815i
$849$		−	1.89801i		−	0.0651395i
$850$	3.81169	+	5.45087i	0.130740	+	0.186963i
$851$	0.269188	+	0.269188i	0.00922766	+	0.00922766i
$852$	9.13011	−	16.1234i	0.312792	−	0.552378i
$853$			1.97903i			0.0677607i	0.999426	+	0.0338803i	$0.0107865\pi$
$853$			1.97903i			0.0677607i	−0.999426	+	0.0338803i	$0.989213\pi$
$854$	0.824434	−	3.12905i	0.0282115	−	0.107074i
$855$	56.6096	−	2.33555i	1.93601	−	0.0798741i
$856$	−15.0113	+	15.3923i	−0.513077	+	0.526100i
$857$	−26.1525	−	26.1525i	−0.893353	−	0.893353i	0.101484	−	0.994837i	$-0.467641\pi$
$857$	−26.1525	−	26.1525i	−0.893353	−	0.893353i	−0.994837	+	0.101484i	$0.967641\pi$
$858$	69.3064	+	118.893i	2.36608	+	4.05892i
$859$	19.2645	+	19.2645i	0.657296	+	0.657296i	0.954739	−	0.297443i	$-0.0961339\pi$
$859$	19.2645	+	19.2645i	0.657296	+	0.657296i	−0.297443	+	0.954739i	$0.596134\pi$
$860$	−4.30562	−	13.3774i	−0.146820	−	0.456166i
$861$	−5.90904	+	5.90904i	−0.201379	+	0.201379i
$862$	−4.91752	+	18.6639i	−0.167491	+	0.635696i
$863$	21.0838	−	21.0838i	0.717701	−	0.717701i	−0.250433	−	0.968134i	$-0.580573\pi$
$863$	21.0838	−	21.0838i	0.717701	−	0.717701i	0.968134	+	0.250433i	$0.0805730\pi$
$864$	−65.7950	+	19.1110i	−2.23839	+	0.650168i
$865$	29.8956	+	27.5265i	1.01648	+	0.935929i
$866$	18.1302	+	31.1017i	0.616089	+	1.05688i
$867$	−50.5966			−1.71835
$868$	−3.58785	−	12.9561i	−0.121780	−	0.439760i
$869$	10.9966	−	10.9966i	0.373036	−	0.373036i
$870$	67.8556	+	14.9167i	2.30052	+	0.505725i
$871$	41.6513			1.41130
$872$	0.235802	+	18.8169i	0.00798526	+	0.637219i
$873$	−10.1744	+	10.1744i	−0.344352	+	0.344352i
$874$	−24.9763	−	6.58070i	−0.844837	−	0.222595i
$875$	1.37950	+	11.0949i	0.0466355	+	0.375076i
$876$	18.3239	+	66.1695i	0.619106	+	2.23566i
$877$			45.4706i			1.53543i	0.640790	+	0.767716i	$0.278607\pi$
$877$			45.4706i			1.53543i	−0.640790	+	0.767716i	$0.721393\pi$
$878$	−7.18568	+	27.2725i	−0.242505	+	0.920401i
$879$	18.7790			0.633399
$880$	−25.3665	−	38.5878i	−0.855106	−	1.30079i
$881$	18.6312			0.627701			0.313850	−	0.949472i	$-0.398381\pi$
$881$	18.6312			0.627701			0.313850	+	0.949472i	$0.398381\pi$
$882$	2.47091	−	9.37809i	0.0832000	−	0.315777i
$883$		−	36.3569i		−	1.22351i	−0.791049	−	0.611753i	$-0.790465\pi$
$883$		−	36.3569i		−	1.22351i	0.791049	−	0.611753i	$-0.209535\pi$
$884$	−10.8841	+	3.01405i	−0.366070	+	0.101373i
$885$	−14.4118	+	0.594589i	−0.484447	+	0.0199869i
$886$	−29.5397	−	7.78305i	−0.992406	−	0.261477i
$887$	−36.5722	+	36.5722i	−1.22798	+	1.22798i	−0.263247	+	0.964729i	$0.584793\pi$
$887$	−36.5722	+	36.5722i	−1.22798	+	1.22798i	−0.964729	+	0.263247i	$0.915207\pi$
$888$	−0.477518	+	0.489638i	−0.0160245	+	0.0164312i
$889$	16.5197			0.554054
$890$	9.92807	+	15.5230i	0.332790	+	0.520332i
$891$	−63.7207	+	63.7207i	−2.13472	+	2.13472i
$892$	14.4538	−	4.00260i	0.483950	−	0.134017i
$893$	−14.5631			−0.487335
$894$	38.8966	+	66.7257i	1.30090	+	2.23164i
$895$	12.9070	−	0.532504i	0.431432	−	0.0177997i
$896$	−5.94087	−	9.62840i	−0.198471	−	0.321662i
$897$	65.8773	−	65.8773i	2.19958	−	2.19958i
$898$	−13.8584	+	52.5981i	−0.462461	+	1.75522i
$899$	33.2600	−	33.2600i	1.10928	−	1.10928i
$900$	28.7605	−	62.2538i	0.958682	−	2.07513i
$901$	5.87228	+	5.87228i	0.195634	+	0.195634i
$902$	9.78712	+	16.7894i	0.325875	+	0.559027i
$903$	−6.97642	−	6.97642i	−0.232161	−	0.232161i
$904$	0.0805160	+	6.42513i	0.00267792	+	0.213697i
$905$	1.75612	+	42.5652i	0.0583752	+	1.41491i
$906$	8.10750	−	30.7712i	0.269354	−	1.02230i
$907$		−	58.4296i		−	1.94012i	−0.242859	−	0.970062i	$-0.578085\pi$
$907$		−	58.4296i		−	1.94012i	0.242859	−	0.970062i	$-0.421915\pi$
$908$	−44.3565	−	25.1176i	−1.47202	−	0.833555i
$909$	35.8225	+	35.8225i	1.18816	+	1.18816i
$910$	−18.5409	−	4.07585i	−0.614623	−	0.135113i
$911$			39.6362i			1.31321i	0.754237	+	0.656603i	$0.228007\pi$
$911$			39.6362i			1.31321i	−0.754237	+	0.656603i	$0.771993\pi$
$912$	11.2595	−	45.0163i	0.372839	−	1.49064i
$913$	−30.4124	−	30.4124i	−1.00650	−	1.00650i
$914$	−7.01269	−	12.0300i	−0.231959	−	0.397917i
$915$	−0.662174	−	16.0499i	−0.0218908	−	0.530595i
$916$	−45.7473	+	12.6685i	−1.51153	+	0.418578i
$917$	21.3792			0.706004
$918$	−8.11419	−	13.9196i	−0.267808	−	0.459415i
$919$		−	15.3971i		−	0.507903i	−0.967217	−	0.253951i	$-0.918270\pi$
$919$		−	15.3971i		−	0.507903i	0.967217	−	0.253951i	$-0.0817303\pi$
$920$	−20.8857	+	23.2616i	−0.688582	+	0.766911i
$921$		−	109.781i		−	3.61742i
$922$	−32.3823	+	18.8767i	−1.06645	+	0.621671i
$923$	−17.7138			−0.583058
$924$	−28.2110	−	15.9749i	−0.928074	−	0.525536i
$925$	−0.0317208	−	0.383774i	−0.00104297	−	0.0126184i
$926$	17.0238	−	9.92376i	0.559438	−	0.326115i
$927$	−58.6017	−	58.6017i	−1.92473	−	1.92473i
$928$	19.0719	−	34.6868i	0.626067	−	1.13865i
$929$		−	8.47766i		−	0.278143i	−0.990282	−	0.139071i	$-0.955588\pi$
$929$		−	8.47766i		−	0.278143i	0.990282	−	0.139071i	$-0.0444118\pi$
$930$	−35.9585	−	56.2228i	−1.17913	−	1.84362i
$931$	2.61268	+	2.61268i	0.0856270	+	0.0856270i
$932$	−34.0783	+	9.43708i	−1.11627	+	0.309122i
$933$			1.89683i			0.0620995i
$934$	8.09023	+	2.13159i	0.264720	+	0.0697478i
$935$	7.35576	−	7.98884i	0.240559	−	0.261263i
$936$	83.3596	+	81.2963i	2.72470	+	2.65725i
$937$	−17.1494	−	17.1494i	−0.560246	−	0.560246i	0.369131	−	0.929377i	$-0.379655\pi$
$937$	−17.1494	−	17.1494i	−0.560246	−	0.560246i	−0.929377	+	0.369131i	$0.879655\pi$
$938$	−8.47703	+	4.94154i	−0.276785	+	0.161347i
$939$	54.9076	+	54.9076i	1.79184	+	1.79184i
$940$	−8.04580	+	15.6831i	−0.262425	+	0.511527i
$941$	−29.5469	+	29.5469i	−0.963203	+	0.963203i	−0.999347	−	0.0361437i	$-0.988493\pi$
$941$	−29.5469	+	29.5469i	−0.963203	+	0.963203i	0.0361437	+	0.999347i	$0.488493\pi$
$942$	−20.6717	−	5.44652i	−0.673520	−	0.177457i
$943$	9.30288	−	9.30288i	0.302944	−	0.302944i
$944$	−1.99410	+	7.97259i	−0.0649026	+	0.259486i
$945$	−1.11640	−	27.0596i	−0.0363166	−	0.880250i
$946$	−19.8222	+	11.5550i	−0.644476	+	0.375686i
$947$	−30.9661			−1.00626			−0.503131	−	0.864210i	$-0.667819\pi$
$947$	−30.9661			−1.00626			−0.503131	+	0.864210i	$0.667819\pi$
$948$	9.32006	−	16.4588i	0.302702	−	0.534558i
$949$	46.4140	−	46.4140i	1.50666	−	1.50666i
$950$	14.9724	+	21.4111i	0.485768	+	0.694668i
$951$	61.6179			1.99810
$952$	1.85758	−	1.90472i	0.0602044	−	0.0617324i
$953$	−15.0414	+	15.0414i	−0.487238	+	0.487238i	−0.907434	−	0.420195i	$-0.861962\pi$
$953$	−15.0414	+	15.0414i	−0.487238	+	0.487238i	0.420195	+	0.907434i	$0.361962\pi$
$954$	21.8148	−	82.7958i	0.706281	−	2.68061i
$955$	−10.0848	+	10.9527i	−0.326335	+	0.354421i
$956$	25.6641	+	14.5327i	0.830035	+	0.470020i
$957$		−	113.431i		−	3.66670i
$958$	1.55655	+	0.410115i	0.0502897	+	0.0132502i
$959$	12.3843			0.399909
$960$	−42.2579	−	36.9960i	−1.36387	−	1.19404i
$961$	−14.1835			−0.457534
$962$	0.632271	+	0.166589i	0.0203852	+	0.00537104i
$963$			52.1284i			1.67981i
$964$	−11.2702	−	6.38192i	−0.362989	−	0.205548i
$965$	1.27216	+	30.8348i	0.0409521	+	0.992608i
$966$	−5.59187	+	21.2234i	−0.179916	+	0.682850i
$967$	−37.2466	+	37.2466i	−1.19777	+	1.19777i	−0.222938	+	0.974833i	$0.571565\pi$
$967$	−37.2466	+	37.2466i	−1.19777	+	1.19777i	−0.974833	+	0.222938i	$0.928435\pi$
$968$	−30.9172	+	31.7019i	−0.993715	+	1.01894i
$969$	10.9123			0.350552
$970$	−6.48042	−	1.42459i	−0.208074	−	0.0457410i
$971$	8.42881	−	8.42881i	0.270494	−	0.270494i	−0.558805	−	0.829299i	$-0.688740\pi$
$971$	8.42881	−	8.42881i	0.270494	−	0.270494i	0.829299	+	0.558805i	$0.188740\pi$
$972$	−18.1975	+	32.1360i	−0.583685	+	1.03076i
$973$	−2.64111			−0.0846700
$974$	1.41629	−	0.825600i	0.0453807	−	0.0264539i
$975$	−93.9194	+	7.76290i	−3.00783	+	0.248612i
$976$	−8.87881	−	2.22077i	−0.284204	−	0.0710851i
$977$	4.86048	−	4.86048i	0.155501	−	0.155501i	−0.625069	−	0.780570i	$-0.714929\pi$
$977$	4.86048	−	4.86048i	0.155501	−	0.155501i	0.780570	+	0.625069i	$0.214929\pi$
$978$	0.709251	+	0.186872i	0.0226793	+	0.00597549i
$979$	21.2726	−	21.2726i	0.679877	−	0.679877i
$980$	4.25707	−	1.37017i	0.135987	−	0.0437685i
$981$	32.2623	+	32.2623i	1.03005	+	1.03005i
$982$	−14.7597	+	8.60393i	−0.471002	+	0.274562i
$983$	−1.57962	−	1.57962i	−0.0503820	−	0.0503820i	0.681467	−	0.731849i	$-0.261342\pi$
$983$	−1.57962	−	1.57962i	−0.0503820	−	0.0503820i	−0.731849	+	0.681467i	$0.761342\pi$
$984$	16.9214	+	16.5025i	0.539434	+	0.526082i
$985$	16.8217	+	15.4887i	0.535985	+	0.493511i
$986$	9.00152	+	2.37170i	0.286667	+	0.0755302i
$987$			12.3748i			0.393895i
$988$	−42.7527	+	11.8392i	−1.36015	+	0.376656i
$989$	10.9833	+	10.9833i	0.349249	+	0.349249i
$990$	−109.351	−	24.0387i	−3.47540	−	0.764000i
$991$			35.4695i			1.12673i	0.826209	+	0.563364i	$0.190493\pi$
$991$			35.4695i			1.12673i	−0.826209	+	0.563364i	$0.809507\pi$
$992$	−36.5155	+	10.6064i	−1.15937	+	0.336753i
$993$	57.3414	+	57.3414i	1.81967	+	1.81967i
$994$	3.60519	−	2.10158i	0.114350	−	0.0666582i
$995$	30.9681	−	33.6334i	0.981756	−	1.06625i
$996$	−45.5186	−	25.7756i	−1.44231	−	0.816731i
$997$	30.6605			0.971028			0.485514	−	0.874229i	$-0.338633\pi$
$997$	30.6605			0.971028			0.485514	+	0.874229i	$0.338633\pi$
$998$	−14.8367	+	8.64881i	−0.469648	+	0.273773i
$999$			0.932804i			0.0295126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.8	✓	144
5.2	odd	4		560.2.bl.a.267.44	yes	144
16.3	odd	4		560.2.bl.a.323.44	yes	144
80.67	even	4	inner	560.2.t.a.547.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.8	✓	144	1.1	even	1	trivial
560.2.t.a.547.8	yes	144	80.67	even	4	inner
560.2.bl.a.267.44	yes	144	5.2	odd	4
560.2.bl.a.323.44	yes	144	16.3	odd	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36754 - 0.360316i) q^{2} +3.13969i q^{3} +(1.74034 + 0.985496i) q^{4} +(1.64497 + 1.51462i) q^{5} +(1.13128 - 4.29365i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.02490 - 1.97478i) q^{8} -6.85762 q^{9} +O(q^{10})\)	\(q+(-1.36754 - 0.360316i) q^{2} +3.13969i q^{3} +(1.74034 + 0.985496i) q^{4} +(1.64497 + 1.51462i) q^{5} +(1.13128 - 4.29365i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-2.02490 - 1.97478i) q^{8} -6.85762 q^{9} +(-1.70383 - 2.66401i) q^{10} +(-3.65075 + 3.65075i) q^{11} +(-3.09415 + 5.46413i) q^{12} +6.00313 q^{13} +(-1.22178 + 0.712216i) q^{14} +(-4.75542 + 5.16470i) q^{15} +(2.05760 + 3.43020i) q^{16} +(-0.665139 + 0.665139i) q^{17} +(9.37809 + 2.47091i) q^{18} +(-2.61268 + 2.61268i) q^{19} +(1.37017 + 4.25707i) q^{20} +(2.22009 + 2.22009i) q^{21} +(6.30798 - 3.67713i) q^{22} +(-3.49520 - 3.49520i) q^{23} +(6.20019 - 6.35756i) q^{24} +(0.411870 + 4.98301i) q^{25} +(-8.20954 - 2.16303i) q^{26} -12.1117i q^{27} +(1.92746 - 0.533758i) q^{28} +(4.94803 + 4.94803i) q^{29} +(8.36416 - 5.34948i) q^{30} -6.72187i q^{31} +(-1.57789 - 5.43234i) q^{32} +(-11.4622 - 11.4622i) q^{33} +(1.14927 - 0.669945i) q^{34} +(2.23417 - 0.0921753i) q^{35} +(-11.9346 - 6.75816i) q^{36} -0.0770166 q^{37} +(4.51434 - 2.63156i) q^{38} +18.8479i q^{39} +(-0.339873 - 6.31542i) q^{40} +2.66162i q^{41} +(-2.23613 - 3.83601i) q^{42} -3.14240 q^{43} +(-9.95137 + 2.75576i) q^{44} +(-11.2806 - 10.3867i) q^{45} +(3.52046 + 6.03921i) q^{46} +(2.78700 + 2.78700i) q^{47} +(-10.7698 + 6.46020i) q^{48} -1.00000i q^{49} +(1.23221 - 6.96288i) q^{50} +(-2.08833 - 2.08833i) q^{51} +(10.4475 + 5.91606i) q^{52} -8.82864i q^{53} +(-4.36405 + 16.5633i) q^{54} +(-11.5349 + 0.475896i) q^{55} +(-2.82821 + 0.0354414i) q^{56} +(-8.20299 - 8.20299i) q^{57} +(-4.98379 - 8.54950i) q^{58} +(1.45278 + 1.45278i) q^{59} +(-13.3659 + 4.30190i) q^{60} +(-1.61792 + 1.61792i) q^{61} +(-2.42200 + 9.19244i) q^{62} +(-4.84907 + 4.84907i) q^{63} +(0.200471 + 7.99749i) q^{64} +(9.87499 + 9.09244i) q^{65} +(11.5450 + 19.8051i) q^{66} +6.93826 q^{67} +(-1.81306 + 0.502079i) q^{68} +(10.9738 - 10.9738i) q^{69} +(-3.08853 - 0.678954i) q^{70} -2.95077 q^{71} +(13.8860 + 13.5423i) q^{72} +(7.73163 - 7.73163i) q^{73} +(0.105323 + 0.0277503i) q^{74} +(-15.6451 + 1.29314i) q^{75} +(-7.12174 + 1.97217i) q^{76} +5.16294i q^{77} +(6.79122 - 25.7754i) q^{78} -3.01216 q^{79} +(-1.81076 + 8.75906i) q^{80} +17.4541 q^{81} +(0.959024 - 3.63987i) q^{82} +8.33044i q^{83} +(1.67583 + 6.05162i) q^{84} +(-2.10157 + 0.0867046i) q^{85} +(4.29737 + 1.13226i) q^{86} +(-15.5353 + 15.5353i) q^{87} +(14.6019 - 0.182982i) q^{88} -5.82692 q^{89} +(11.6842 + 18.2688i) q^{90} +(4.24485 - 4.24485i) q^{91} +(-2.63835 - 9.52736i) q^{92} +21.1046 q^{93} +(-2.80714 - 4.81555i) q^{94} +(-8.25499 + 0.340577i) q^{95} +(17.0558 - 4.95408i) q^{96} +(1.48367 - 1.48367i) q^{97} +(-0.360316 + 1.36754i) q^{98} +(25.0355 - 25.0355i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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