LMFDB - Embedded newform 560.2.bb.d.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (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:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.2
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40611 - 0.151214i) q^{2} +(-1.45780 + 1.45780i) q^{3} +(1.95427 + 0.425246i) q^{4} +(-2.23574 + 0.0381166i) q^{5} +(2.27026 - 1.82938i) q^{6} +1.00000 q^{7} +(-2.68361 - 0.893453i) q^{8} -1.25035i q^{9} +O(q^{10})$	\(q+(-1.40611 - 0.151214i) q^{2} +(-1.45780 + 1.45780i) q^{3} +(1.95427 + 0.425246i) q^{4} +(-2.23574 + 0.0381166i) q^{5} +(2.27026 - 1.82938i) q^{6} +1.00000 q^{7} +(-2.68361 - 0.893453i) q^{8} -1.25035i q^{9} +(3.14946 + 0.284479i) q^{10} +(2.74817 - 2.74817i) q^{11} +(-3.46885 + 2.22901i) q^{12} +(3.71588 - 3.71588i) q^{13} +(-1.40611 - 0.151214i) q^{14} +(3.20370 - 3.31483i) q^{15} +(3.63833 + 1.66209i) q^{16} +7.56673i q^{17} +(-0.189071 + 1.75813i) q^{18} +(1.29353 + 1.29353i) q^{19} +(-4.38545 - 0.876250i) q^{20} +(-1.45780 + 1.45780i) q^{21} +(-4.27978 + 3.44866i) q^{22} -0.243636 q^{23} +(5.21463 - 2.60968i) q^{24} +(4.99709 - 0.170438i) q^{25} +(-5.78681 + 4.66302i) q^{26} +(-2.55063 - 2.55063i) q^{27} +(1.95427 + 0.425246i) q^{28} +(-1.36116 - 1.36116i) q^{29} +(-5.00599 + 4.17656i) q^{30} -8.02856 q^{31} +(-4.86455 - 2.88724i) q^{32} +8.01255i q^{33} +(1.14419 - 10.6396i) q^{34} +(-2.23574 + 0.0381166i) q^{35} +(0.531708 - 2.44353i) q^{36} +(5.39030 + 5.39030i) q^{37} +(-1.62324 - 2.01444i) q^{38} +10.8340i q^{39} +(6.03391 + 1.89524i) q^{40} +7.47606i q^{41} +(2.27026 - 1.82938i) q^{42} +(1.85872 + 1.85872i) q^{43} +(6.53931 - 4.20201i) q^{44} +(0.0476593 + 2.79547i) q^{45} +(0.342578 + 0.0368411i) q^{46} +6.05197i q^{47} +(-7.72695 + 2.88097i) q^{48} +1.00000 q^{49} +(-7.05222 - 0.515976i) q^{50} +(-11.0308 - 11.0308i) q^{51} +(8.84198 - 5.68166i) q^{52} +(2.07180 + 2.07180i) q^{53} +(3.20077 + 3.97215i) q^{54} +(-6.03945 + 6.24895i) q^{55} +(-2.68361 - 0.893453i) q^{56} -3.77141 q^{57} +(1.70811 + 2.11976i) q^{58} +(-4.18816 + 4.18816i) q^{59} +(7.67050 - 5.11571i) q^{60} +(1.46095 + 1.46095i) q^{61} +(11.2890 + 1.21403i) q^{62} -1.25035i q^{63} +(6.40348 + 4.79535i) q^{64} +(-8.16611 + 8.44938i) q^{65} +(1.21161 - 11.2665i) q^{66} +(-7.82426 + 7.82426i) q^{67} +(-3.21772 + 14.7874i) q^{68} +(0.355172 - 0.355172i) q^{69} +(3.14946 + 0.284479i) q^{70} +2.24130i q^{71} +(-1.11713 + 3.35546i) q^{72} +6.84723 q^{73} +(-6.76425 - 8.39443i) q^{74} +(-7.03629 + 7.53322i) q^{75} +(1.97783 + 3.07797i) q^{76} +(2.74817 - 2.74817i) q^{77} +(1.63825 - 15.2338i) q^{78} +7.06875 q^{79} +(-8.19773 - 3.57732i) q^{80} +11.1877 q^{81} +(1.13048 - 10.5121i) q^{82} +(11.1631 - 11.1631i) q^{83} +(-3.46885 + 2.22901i) q^{84} +(-0.288418 - 16.9173i) q^{85} +(-2.33250 - 2.89463i) q^{86} +3.96859 q^{87} +(-9.83036 + 4.91964i) q^{88} +13.8506i q^{89} +(0.355700 - 3.93794i) q^{90} +(3.71588 - 3.71588i) q^{91} +(-0.476130 - 0.103605i) q^{92} +(11.7040 - 11.7040i) q^{93} +(0.915142 - 8.50971i) q^{94} +(-2.94130 - 2.84269i) q^{95} +(11.3005 - 2.88252i) q^{96} +16.3214i q^{97} +(-1.40611 - 0.151214i) q^{98} +(-3.43619 - 3.43619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.40611	−	0.151214i	−0.994267	−	0.106924i
$2$	−1.40611	−	0.151214i	−0.994267	−	0.106924i
$3$	−1.45780	+	1.45780i	−0.841661	+	0.841661i	−0.989075	−	0.147414i	$-0.952905\pi$
$3$	−1.45780	+	1.45780i	−0.841661	+	0.841661i	0.147414	+	0.989075i	$0.452905\pi$
$4$	1.95427	+	0.425246i	0.977134	+	0.212623i
$5$	−2.23574	+	0.0381166i	−0.999855	+	0.0170463i
$5$	−2.23574	+	0.0381166i	−0.999855	+	0.0170463i
$6$	2.27026	−	1.82938i	0.926829	−	0.746841i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−2.68361	−	0.893453i	−0.948798	−	0.315883i
$9$		−	1.25035i		−	0.416785i
$10$	3.14946	+	0.284479i	0.995945	+	0.0899603i
$11$	2.74817	−	2.74817i	0.828604	−	0.828604i	−0.158720	−	0.987324i	$-0.550737\pi$
$11$	2.74817	−	2.74817i	0.828604	−	0.828604i	0.987324	+	0.158720i	$0.0507366\pi$
$12$	−3.46885	+	2.22901i	−1.00137	+	0.643459i
$13$	3.71588	−	3.71588i	1.03060	−	1.03060i	0.0310817	−	0.999517i	$-0.490105\pi$
$13$	3.71588	−	3.71588i	1.03060	−	1.03060i	0.999517	−	0.0310817i	$-0.00989521\pi$
$14$	−1.40611	−	0.151214i	−0.375798	−	0.0404136i
$15$	3.20370	−	3.31483i	0.827191	−	0.855885i
$16$	3.63833	+	1.66209i	0.909583	+	0.415522i
$17$			7.56673i			1.83520i	0.397504	+	0.917601i	$0.369877\pi$
$17$			7.56673i			1.83520i	−0.397504	+	0.917601i	$0.630123\pi$
$18$	−0.189071	+	1.75813i	−0.0445645	+	0.414396i
$19$	1.29353	+	1.29353i	0.296756	+	0.296756i	0.839742	−	0.542986i	$-0.182706\pi$
$19$	1.29353	+	1.29353i	0.296756	+	0.296756i	−0.542986	+	0.839742i	$0.682706\pi$
$20$	−4.38545	−	0.876250i	−0.980617	−	0.195935i
$21$	−1.45780	+	1.45780i	−0.318118	+	0.318118i
$22$	−4.27978	+	3.44866i	−0.912452	+	0.735256i
$23$	−0.243636			−0.0508016			−0.0254008	−	0.999677i	$-0.508086\pi$
$23$	−0.243636			−0.0508016			−0.0254008	+	0.999677i	$0.508086\pi$
$24$	5.21463	−	2.60968i	1.06443	−	0.532699i
$25$	4.99709	−	0.170438i	0.999419	−	0.0340876i
$26$	−5.78681	+	4.66302i	−1.13489	+	0.914494i
$27$	−2.55063	−	2.55063i	−0.490869	−	0.490869i
$28$	1.95427	+	0.425246i	0.369322	+	0.0803639i
$29$	−1.36116	−	1.36116i	−0.252761	−	0.252761i	0.569341	−	0.822102i	$-0.307198\pi$
$29$	−1.36116	−	1.36116i	−0.252761	−	0.252761i	−0.822102	+	0.569341i	$0.807198\pi$
$30$	−5.00599	+	4.17656i	−0.913964	+	0.762532i
$31$	−8.02856			−1.44197			−0.720986	−	0.692950i	$-0.756311\pi$
$31$	−8.02856			−1.44197			−0.720986	+	0.692950i	$0.756311\pi$
$32$	−4.86455	−	2.88724i	−0.859939	−	0.510397i
$33$			8.01255i			1.39481i
$34$	1.14419	−	10.6396i	0.196228	−	1.82468i
$35$	−2.23574	+	0.0381166i	−0.377910	+	0.00644288i
$36$	0.531708	−	2.44353i	0.0886180	−	0.407255i
$37$	5.39030	+	5.39030i	0.886161	+	0.886161i	0.994152	−	0.107991i	$-0.0344419\pi$
$37$	5.39030	+	5.39030i	0.886161	+	0.886161i	−0.107991	+	0.994152i	$0.534442\pi$
$38$	−1.62324	−	2.01444i	−0.263324	−	0.326785i
$39$			10.8340i			1.73483i
$40$	6.03391	+	1.89524i	0.954045	+	0.299664i
$41$			7.47606i			1.16756i	0.811910	+	0.583782i	$0.198428\pi$
$41$			7.47606i			1.16756i	−0.811910	+	0.583782i	$0.801572\pi$
$42$	2.27026	−	1.82938i	0.350309	−	0.282280i
$43$	1.85872	+	1.85872i	0.283453	+	0.283453i	0.834484	−	0.551032i	$-0.185766\pi$
$43$	1.85872	+	1.85872i	0.283453	+	0.283453i	−0.551032	+	0.834484i	$0.685766\pi$
$44$	6.53931	−	4.20201i	0.985838	−	0.633477i
$45$	0.0476593	+	2.79547i	0.00710463	+	0.416724i
$46$	0.342578	+	0.0368411i	0.0505103	+	0.00543193i
$47$			6.05197i			0.882771i	0.897318	+	0.441385i	$0.145513\pi$
$47$			6.05197i			0.882771i	−0.897318	+	0.441385i	$0.854487\pi$
$48$	−7.72695	+	2.88097i	−1.11529	+	0.415832i
$49$	1.00000			0.142857
$50$	−7.05222	−	0.515976i	−0.997334	−	0.0729701i
$51$	−11.0308	−	11.0308i	−1.54462	−	1.54462i
$52$	8.84198	−	5.68166i	1.22616	−	0.787905i
$53$	2.07180	+	2.07180i	0.284584	+	0.284584i	0.834934	−	0.550350i	$-0.185506\pi$
$53$	2.07180	+	2.07180i	0.284584	+	0.284584i	−0.550350	+	0.834934i	$0.685506\pi$
$54$	3.20077	+	3.97215i	0.435569	+	0.540541i
$55$	−6.03945	+	6.24895i	−0.814359	+	0.842608i
$56$	−2.68361	−	0.893453i	−0.358612	−	0.119393i
$57$	−3.77141			−0.499535
$58$	1.70811	+	2.11976i	0.224285	+	0.278338i
$59$	−4.18816	+	4.18816i	−0.545252	+	0.545252i	−0.925064	−	0.379812i	$-0.875989\pi$
$59$	−4.18816	+	4.18816i	−0.545252	+	0.545252i	0.379812	+	0.925064i	$0.375989\pi$
$60$	7.67050	−	5.11571i	0.990258	−	0.660435i
$61$	1.46095	+	1.46095i	0.187056	+	0.187056i	0.794422	−	0.607366i	$-0.207774\pi$
$61$	1.46095	+	1.46095i	0.187056	+	0.187056i	−0.607366	+	0.794422i	$0.707774\pi$
$62$	11.2890	+	1.21403i	1.43371	+	0.154182i
$63$		−	1.25035i		−	0.157530i
$64$	6.40348	+	4.79535i	0.800435	+	0.599419i
$65$	−8.16611	+	8.44938i	−1.01288	+	1.04802i
$66$	1.21161	−	11.2665i	0.149139	−	1.38681i
$67$	−7.82426	+	7.82426i	−0.955886	+	0.955886i	−0.999067	−	0.0431814i	$-0.986251\pi$
$67$	−7.82426	+	7.82426i	−0.955886	+	0.955886i	0.0431814	+	0.999067i	$0.486251\pi$
$68$	−3.21772	+	14.7874i	−0.390206	+	1.79324i
$69$	0.355172	−	0.355172i	0.0427577	−	0.0427577i
$70$	3.14946	+	0.284479i	0.376432	+	0.0340018i
$71$			2.24130i			0.265993i	0.991116	+	0.132997i	$0.0424600\pi$
$71$			2.24130i			0.265993i	−0.991116	+	0.132997i	$0.957540\pi$
$72$	−1.11713	+	3.35546i	−0.131655	+	0.395445i
$73$	6.84723			0.801408			0.400704	−	0.916208i	$-0.368766\pi$
$73$	6.84723			0.801408			0.400704	+	0.916208i	$0.368766\pi$
$74$	−6.76425	−	8.39443i	−0.786328	−	0.975832i
$75$	−7.03629	+	7.53322i	−0.812481	+	0.869862i
$76$	1.97783	+	3.07797i	0.226873	+	0.353067i
$77$	2.74817	−	2.74817i	0.313183	−	0.313183i
$78$	1.63825	−	15.2338i	0.185495	−	1.72488i
$79$	7.06875			0.795296			0.397648	−	0.917538i	$-0.369826\pi$
$79$	7.06875			0.795296			0.397648	+	0.917538i	$0.369826\pi$
$80$	−8.19773	−	3.57732i	−0.916534	−	0.399957i
$81$	11.1877			1.24308
$82$	1.13048	−	10.5121i	0.124841	−	1.16087i
$83$	11.1631	−	11.1631i	1.22531	−	1.22531i	0.259598	−	0.965717i	$-0.416410\pi$
$83$	11.1631	−	11.1631i	1.22531	−	1.22531i	0.965717	−	0.259598i	$-0.0835899\pi$
$84$	−3.46885	+	2.22901i	−0.378483	+	0.243205i
$85$	−0.288418	−	16.9173i	−0.0312833	−	1.83493i
$86$	−2.33250	−	2.89463i	−0.251520	−	0.312136i
$87$	3.96859			0.425477
$88$	−9.83036	+	4.91964i	−1.04792	+	0.524436i
$89$			13.8506i			1.46816i	0.679063	+	0.734080i	$0.262386\pi$
$89$			13.8506i			1.46816i	−0.679063	+	0.734080i	$0.737614\pi$
$90$	0.355700	−	3.93794i	0.0374941	−	0.415095i
$91$	3.71588	−	3.71588i	0.389530	−	0.389530i
$92$	−0.476130	−	0.103605i	−0.0496400	−	0.0108016i
$93$	11.7040	−	11.7040i	1.21365	−	1.21365i
$94$	0.915142	−	8.50971i	0.0943897	−	0.877710i
$95$	−2.94130	−	2.84269i	−0.301771	−	0.291654i
$96$	11.3005	−	2.88252i	1.15336	−	0.294196i
$97$			16.3214i			1.65719i	0.559848	+	0.828595i	$0.310859\pi$
$97$			16.3214i			1.65719i	−0.559848	+	0.828595i	$0.689141\pi$
$98$	−1.40611	−	0.151214i	−0.142038	−	0.0152749i
$99$	−3.43619	−	3.43619i	−0.345350	−	0.345350i
$100$	9.83814	+	1.79191i	0.983814	+	0.179191i
$101$	6.59068	−	6.59068i	0.655798	−	0.655798i	−0.298585	−	0.954383i	$-0.596515\pi$
$101$	6.59068	−	6.59068i	0.655798	−	0.655798i	0.954383	+	0.298585i	$0.0965147\pi$
$102$	13.8424	+	17.1784i	1.37060	+	1.70092i
$103$	−4.37713			−0.431291			−0.215646	−	0.976472i	$-0.569186\pi$
$103$	−4.37713			−0.431291			−0.215646	+	0.976472i	$0.569186\pi$
$104$	−13.2919	+	6.65199i	−1.30338	+	0.652281i
$105$	3.20370	−	3.31483i	0.312649	−	0.323494i
$106$	−2.59989	−	3.22646i	−0.252524	−	0.313382i
$107$	−4.80653	−	4.80653i	−0.464665	−	0.464665i	0.435516	−	0.900181i	$-0.356566\pi$
$107$	−4.80653	−	4.80653i	−0.464665	−	0.464665i	−0.900181	+	0.435516i	$0.856566\pi$
$108$	−3.89997	−	6.06926i	−0.375275	−	0.584015i
$109$	3.22824	+	3.22824i	0.309210	+	0.309210i	0.844603	−	0.535393i	$-0.179837\pi$
$109$	3.22824	+	3.22824i	0.309210	+	0.309210i	−0.535393	+	0.844603i	$0.679837\pi$
$110$	9.43703	−	7.87344i	0.899786	−	0.750703i
$111$	−15.7160			−1.49169
$112$	3.63833	+	1.66209i	0.343790	+	0.157053i
$113$		−	13.2683i		−	1.24818i	−0.781353	−	0.624089i	$-0.785470\pi$
$113$		−	13.2683i		−	1.24818i	0.781353	−	0.624089i	$-0.214530\pi$
$114$	5.30300	+	0.570289i	0.496671	+	0.0534125i
$115$	0.544707	−	0.00928657i	0.0507942	−	0.000865977i
$116$	−2.08124	−	3.23889i	−0.193238	−	0.300724i
$117$	−4.64616	−	4.64616i	−0.429538	−	0.429538i
$118$	6.52230	−	5.25569i	0.600426	−	0.483825i
$119$			7.56673i			0.693641i
$120$	−11.5591	+	6.03335i	−1.05520	+	0.550767i
$121$		−	4.10486i		−	0.373169i
$122$	−1.83334	−	2.27517i	−0.165983	−	0.205985i
$123$	−10.8986	−	10.8986i	−0.982693	−	0.982693i
$124$	−15.6900	−	3.41411i	−1.40900	−	0.306596i
$125$	−11.1657	+	0.571528i	−0.998693	+	0.0511190i
$126$	−0.189071	+	1.75813i	−0.0168438	+	0.156627i
$127$		−	14.7925i		−	1.31262i	−0.754490	−	0.656312i	$-0.772116\pi$
$127$		−	14.7925i		−	1.31262i	0.754490	−	0.656312i	$-0.227884\pi$
$128$	−8.27885	−	7.71107i	−0.731754	−	0.681569i
$129$	−5.41929			−0.477142
$130$	12.7601	−	10.6459i	1.11913	−	0.933707i
$131$	1.63795	+	1.63795i	0.143109	+	0.143109i	0.775031	−	0.631923i	$-0.217734\pi$
$131$	1.63795	+	1.63795i	0.143109	+	0.143109i	−0.631923	+	0.775031i	$0.717734\pi$
$132$	−3.40730	+	15.6587i	−0.296568	+	1.36291i
$133$	1.29353	+	1.29353i	0.112163	+	0.112163i
$134$	12.1849	−	9.81861i	1.05261	−	0.848198i
$135$	5.79978	+	5.60533i	0.499165	+	0.482430i
$136$	6.76052	−	20.3061i	0.579709	−	1.74124i
$137$	3.34707			0.285960			0.142980	−	0.989726i	$-0.454332\pi$
$137$	3.34707			0.285960			0.142980	+	0.989726i	$0.454332\pi$
$138$	−0.553116	+	0.445703i	−0.0470844	+	0.0379407i
$139$	−4.17282	+	4.17282i	−0.353934	+	0.353934i	−0.861571	−	0.507637i	$-0.830519\pi$
$139$	−4.17282	+	4.17282i	−0.353934	+	0.353934i	0.507637	+	0.861571i	$0.330519\pi$
$140$	−4.38545	−	0.876250i	−0.370638	−	0.0740566i
$141$	−8.82256	−	8.82256i	−0.742993	−	0.742993i
$142$	0.338916	−	3.15150i	0.0284412	−	0.264468i
$143$		−	20.4237i		−	1.70792i
$144$	2.07820	−	4.54921i	0.173183	−	0.379101i
$145$	3.09508	+	2.99132i	0.257032	+	0.248415i
$146$	−9.62794	−	1.03540i	−0.796814	−	0.0856901i
$147$	−1.45780	+	1.45780i	−0.120237	+	0.120237i
$148$	8.24190	+	12.8263i	0.677480	+	1.05432i
$149$	1.81895	−	1.81895i	0.149014	−	0.149014i	−0.628663	−	0.777678i	$-0.716398\pi$
$149$	1.81895	−	1.81895i	0.149014	−	0.149014i	0.777678	+	0.628663i	$0.216398\pi$
$150$	11.0329	−	9.52852i	0.900833	−	0.778001i
$151$		−	5.22041i		−	0.424831i	−0.977179	−	0.212416i	$-0.931867\pi$
$151$		−	5.22041i		−	0.424831i	0.977179	−	0.212416i	$-0.0681330\pi$
$152$	−2.31561	−	4.62703i	−0.187821	−	0.375301i
$153$	9.46110			0.764884
$154$	−4.27978	+	3.44866i	−0.344874	+	0.277901i
$155$	17.9498	−	0.306021i	1.44176	−	0.0245802i
$156$	−4.60711	+	21.1725i	−0.368864	+	1.69516i
$157$	−8.82423	+	8.82423i	−0.704250	+	0.704250i	−0.965320	−	0.261070i	$-0.915925\pi$
$157$	−8.82423	+	8.82423i	−0.704250	+	0.704250i	0.261070	+	0.965320i	$0.415925\pi$
$158$	−9.93941	−	1.06889i	−0.790737	−	0.0850366i
$159$	−6.04054			−0.479046
$160$	10.9859	+	6.26970i	0.868515	+	0.495664i
$161$	−0.243636			−0.0192012
$162$	−15.7311	−	1.69173i	−1.23595	−	0.132915i
$163$	−11.4386	+	11.4386i	−0.895942	+	0.895942i	−0.995074	−	0.0991326i	$-0.968393\pi$
$163$	−11.4386	+	11.4386i	−0.895942	+	0.895942i	0.0991326	+	0.995074i	$0.468393\pi$
$164$	−3.17916	+	14.6102i	−0.248251	+	1.14087i
$165$	−0.305411	−	17.9140i	−0.0237763	−	1.39460i
$166$	−17.3846	+	14.0085i	−1.34931	+	1.08727i
$167$	23.6496			1.83006			0.915032	−	0.403381i	$-0.132165\pi$
$167$	23.6496			1.83006			0.915032	+	0.403381i	$0.132165\pi$
$168$	5.21463	−	2.60968i	0.402318	−	0.201341i
$169$		−	14.6155i		−	1.12427i
$170$	−2.15258	+	23.8311i	−0.165095	+	1.82776i
$171$	1.61737	−	1.61737i	0.123683	−	0.123683i
$172$	2.84203	+	4.42286i	0.216703	+	0.337240i
$173$	−9.11187	+	9.11187i	−0.692763	+	0.692763i	−0.962839	−	0.270076i	$-0.912951\pi$
$173$	−9.11187	+	9.11187i	−0.692763	+	0.692763i	0.270076	+	0.962839i	$0.412951\pi$
$174$	−5.58025	−	0.600106i	−0.423038	−	0.0454939i
$175$	4.99709	−	0.170438i	0.377745	−	0.0128839i
$176$	14.5665	−	5.43105i	1.09799	−	0.409381i
$177$		−	12.2110i		−	0.917834i
$178$	2.09440	−	19.4754i	0.156982	−	1.45974i
$179$	−4.34687	−	4.34687i	−0.324900	−	0.324900i	0.525743	−	0.850643i	$-0.323787\pi$
$179$	−4.34687	−	4.34687i	−0.324900	−	0.324900i	−0.850643	+	0.525743i	$0.823787\pi$
$180$	−1.09562	+	5.48337i	−0.0816629	+	0.408706i
$181$	12.2383	−	12.2383i	0.909662	−	0.909662i	−0.0865823	−	0.996245i	$-0.527595\pi$
$181$	12.2383	−	12.2383i	0.909662	−	0.909662i	0.996245	+	0.0865823i	$0.0275945\pi$
$182$	−5.78681	+	4.66302i	−0.428947	+	0.345646i
$183$	−4.25956			−0.314876
$184$	0.653823	+	0.217677i	0.0482004	+	0.0160474i
$185$	−12.2568	−	11.8459i	−0.901137	−	0.870926i
$186$	−18.2269	+	14.6873i	−1.33646	+	1.07692i
$187$	20.7946	+	20.7946i	1.52066	+	1.52066i
$188$	−2.57357	+	11.8272i	−0.187697	+	0.862586i
$189$	−2.55063	−	2.55063i	−0.185531	−	0.185531i
$190$	3.70593	+	4.44189i	0.268856	+	0.322249i
$191$	0.487357			0.0352639			0.0176319	−	0.999845i	$-0.494387\pi$
$191$	0.487357			0.0352639			0.0176319	+	0.999845i	$0.494387\pi$
$192$	−16.3256	+	2.34433i	−1.17820	+	0.169188i
$193$			18.4361i			1.32706i	0.748150	+	0.663529i	$0.230942\pi$
$193$			18.4361i			1.32706i	−0.748150	+	0.663529i	$0.769058\pi$
$194$	2.46803	−	22.9497i	0.177194	−	1.64769i
$195$	−0.412955	−	24.2220i	−0.0295724	−	1.73458i
$196$	1.95427	+	0.425246i	0.139591	+	0.0303747i
$197$	7.54607	+	7.54607i	0.537635	+	0.537635i	0.922834	−	0.385199i	$-0.125867\pi$
$197$	7.54607	+	7.54607i	0.537635	+	0.537635i	−0.385199	+	0.922834i	$0.625867\pi$
$198$	4.31204	+	5.35124i	0.306444	+	0.380296i
$199$			8.42779i			0.597430i	0.954342	+	0.298715i	$0.0965581\pi$
$199$			8.42779i			0.597430i	−0.954342	+	0.298715i	$0.903442\pi$
$200$	−13.5625	−	4.00728i	−0.959014	−	0.283358i
$201$		−	22.8124i		−	1.60906i
$202$	−10.2638	+	8.27060i	−0.722159	+	0.581917i
$203$	−1.36116	−	1.36116i	−0.0955345	−	0.0955345i
$204$	−16.8663	−	26.2479i	−1.18088	−	1.83772i
$205$	−0.284962	−	16.7146i	−0.0199026	−	1.16740i
$206$	6.15471	+	0.661883i	0.428819	+	0.0461156i
$207$			0.304631i			0.0211733i
$208$	19.6957	−	7.34348i	1.36565	−	0.509179i
$209$	7.10967			0.491786
$210$	−5.00599	+	4.17656i	−0.345446	+	0.288210i
$211$	13.9551	+	13.9551i	0.960711	+	0.960711i	0.999257	−	0.0385460i	$-0.0122726\pi$
$211$	13.9551	+	13.9551i	0.960711	+	0.960711i	−0.0385460	+	0.999257i	$0.512273\pi$
$212$	3.16783	+	4.92988i	0.217568	+	0.338586i
$213$	−3.26736	−	3.26736i	−0.223876	−	0.223876i
$214$	6.03168	+	7.48530i	0.412317	+	0.511685i
$215$	−4.22648	−	4.08478i	−0.288243	−	0.278580i
$216$	4.56602	+	9.12376i	0.310678	+	0.620793i
$217$	−8.02856			−0.545014
$218$	−4.05110	−	5.02741i	−0.274375	−	0.340499i
$219$	−9.98189	+	9.98189i	−0.674514	+	0.674514i
$220$	−14.4600	+	9.64388i	−0.974896	+	0.650190i
$221$	28.1170	+	28.1170i	1.89136	+	1.89136i
$222$	22.0983	+	2.37647i	1.48314	+	0.159498i
$223$		−	14.5798i		−	0.976336i	−0.872750	−	0.488168i	$-0.837665\pi$
$223$		−	14.5798i		−	0.976336i	0.872750	−	0.488168i	$-0.162335\pi$
$224$	−4.86455	−	2.88724i	−0.325026	−	0.192912i
$225$	−0.213108	−	6.24814i	−0.0142072	−	0.416543i
$226$	−2.00635	+	18.6567i	−0.133461	+	1.24102i
$227$	−19.1319	+	19.1319i	−1.26983	+	1.26983i	−0.323650	+	0.946177i	$0.604910\pi$
$227$	−19.1319	+	19.1319i	−1.26983	+	1.26983i	−0.946177	+	0.323650i	$0.895090\pi$
$228$	−7.37034	−	1.60377i	−0.488113	−	0.106213i
$229$	−0.0929897	+	0.0929897i	−0.00614494	+	0.00614494i	−0.710173	−	0.704028i	$-0.751383\pi$
$229$	−0.0929897	+	0.0929897i	−0.00614494	+	0.00614494i	0.704028	+	0.710173i	$0.251383\pi$
$230$	−0.767320	−	0.0693094i	−0.0505956	−	0.00457012i
$231$			8.01255i			0.527187i
$232$	2.43668	+	4.86894i	0.159976	+	0.319662i
$233$	15.6694			1.02653			0.513267	−	0.858229i	$-0.328435\pi$
$233$	15.6694			1.02653			0.513267	+	0.858229i	$0.328435\pi$
$234$	5.83043	+	7.23556i	0.381147	+	0.473004i
$235$	−0.230681	−	13.5307i	−0.0150479	−	0.882642i
$236$	−9.96578	+	6.40379i	−0.648717	+	0.416851i
$237$	−10.3048	+	10.3048i	−0.669369	+	0.669369i
$238$	1.14419	−	10.6396i	0.0741671	−	0.689664i
$239$	19.5612			1.26531			0.632653	−	0.774435i	$-0.281966\pi$
$239$	19.5612			1.26531			0.632653	+	0.774435i	$0.281966\pi$
$240$	17.1657	−	6.73563i	1.10804	−	0.434783i
$241$	−25.3137			−1.63060			−0.815299	−	0.579040i	$-0.803427\pi$
$241$	−25.3137			−1.63060			−0.815299	+	0.579040i	$0.803427\pi$
$242$	−0.620713	+	5.77187i	−0.0399009	+	0.371030i
$243$	−8.65749	+	8.65749i	−0.555378	+	0.555378i
$244$	2.23383	+	3.47636i	0.143007	+	0.222551i
$245$	−2.23574	+	0.0381166i	−0.142836	+	0.00243518i
$246$	13.6766	+	16.9726i	0.871986	+	1.08213i
$247$	9.61318			0.611672
$248$	21.5455	+	7.17314i	1.36814	+	0.455495i
$249$			32.5472i			2.06260i
$250$	15.7866	+	0.884784i	0.998433	+	0.0559586i
$251$	2.16272	−	2.16272i	0.136510	−	0.136510i	−0.635550	−	0.772060i	$-0.719227\pi$
$251$	2.16272	−	2.16272i	0.136510	−	0.136510i	0.772060	+	0.635550i	$0.219227\pi$
$252$	0.531708	−	2.44353i	0.0334944	−	0.153928i
$253$	−0.669552	+	0.669552i	−0.0420944	+	0.0420944i
$254$	−2.23683	+	20.7998i	−0.140351	+	1.30510i
$255$	25.0824	+	24.2415i	1.57072	+	1.51806i
$256$	10.4749	+	12.0945i	0.654683	+	0.755904i
$257$		−	30.7171i		−	1.91608i	−0.286639	−	0.958039i	$-0.592538\pi$
$257$		−	30.7171i		−	1.91608i	0.286639	−	0.958039i	$-0.407462\pi$
$258$	7.62010	+	0.819472i	0.474407	+	0.0510181i
$259$	5.39030	+	5.39030i	0.334937	+	0.334937i
$260$	−19.5518	+	13.0398i	−1.21255	+	0.808692i
$261$	−1.70193	+	1.70193i	−0.105347	+	0.105347i
$262$	−2.05545	−	2.55082i	−0.126986	−	0.157590i
$263$	−17.1536			−1.05774			−0.528869	−	0.848704i	$-0.677384\pi$
$263$	−17.1536			−1.05774			−0.528869	+	0.848704i	$0.677384\pi$
$264$	7.15884	−	21.5025i	0.440596	−	1.32339i
$265$	−4.71099	−	4.55305i	−0.289394	−	0.279692i
$266$	−1.62324	−	2.01444i	−0.0995271	−	0.123513i
$267$	−20.1914	−	20.1914i	−1.23569	−	1.23569i
$268$	−18.6179	+	11.9635i	−1.13727	+	0.730786i
$269$	10.8618	+	10.8618i	0.662256	+	0.662256i	0.955911	−	0.293655i	$-0.0948718\pi$
$269$	10.8618	+	10.8618i	0.662256	+	0.662256i	−0.293655	+	0.955911i	$0.594872\pi$
$270$	−7.30750	−	8.75870i	−0.444720	−	0.533038i
$271$	28.5524			1.73443			0.867217	−	0.497931i	$-0.165907\pi$
$271$	28.5524			1.73443			0.867217	+	0.497931i	$0.165907\pi$
$272$	−12.5766	+	27.5303i	−0.762567	+	1.66927i
$273$			10.8340i			0.655703i
$274$	−4.70634	−	0.506124i	−0.284320	−	0.0305761i
$275$	13.2645	−	14.2013i	0.799877	−	0.856368i
$276$	0.845137	−	0.543066i	0.0508713	−	0.0326887i
$277$	4.33914	+	4.33914i	0.260714	+	0.260714i	0.825344	−	0.564630i	$-0.190981\pi$
$277$	4.33914	+	4.33914i	0.260714	+	0.260714i	−0.564630	+	0.825344i	$0.690981\pi$
$278$	6.49841	−	5.23643i	0.389749	−	0.314060i
$279$			10.0385i			0.600992i
$280$	6.03391	+	1.89524i	0.360595	+	0.113262i
$281$			21.2809i			1.26951i	0.772712	+	0.634756i	$0.218900\pi$
$281$			21.2809i			1.26951i	−0.772712	+	0.634756i	$0.781100\pi$
$282$	11.0714	+	13.7395i	0.659290	+	0.818178i
$283$	−15.4361	−	15.4361i	−0.917584	−	0.917584i	0.0792696	−	0.996853i	$-0.474741\pi$
$283$	−15.4361	−	15.4361i	−0.917584	−	0.917584i	−0.996853	+	0.0792696i	$0.974741\pi$
$284$	−0.953103	+	4.38010i	−0.0565562	+	0.259911i
$285$	8.43190	−	0.143753i	0.499463	−	0.00851521i
$286$	−3.08835	+	28.7179i	−0.182618	+	1.69813i
$287$			7.47606i			0.441298i
$288$	−3.61007	+	6.08241i	−0.212726	+	0.358410i
$289$	−40.2554			−2.36796
$290$	−3.89968	−	4.67413i	−0.228997	−	0.274474i
$291$	−23.7934	−	23.7934i	−1.39479	−	1.39479i
$292$	13.3813	+	2.91176i	0.783083	+	0.170398i
$293$	−0.0702219	−	0.0702219i	−0.00410241	−	0.00410241i	0.705053	−	0.709155i	$-0.250923\pi$
$293$	−0.0702219	−	0.0702219i	−0.00410241	−	0.00410241i	−0.709155	+	0.705053i	$0.750923\pi$
$294$	2.27026	−	1.82938i	0.132404	−	0.106692i
$295$	9.20401	−	9.52328i	0.535878	−	0.554467i
$296$	−9.64947	−	19.2814i	−0.560864	−	1.12071i
$297$	−14.0191			−0.813472
$298$	−2.83269	+	2.28259i	−0.164094	+	0.132227i
$299$	−0.905320	+	0.905320i	−0.0523560	+	0.0523560i
$300$	−16.9543	+	11.7298i	−0.978856	+	0.677220i
$301$	1.85872	+	1.85872i	0.107135	+	0.107135i
$302$	−0.789399	+	7.34045i	−0.0454248	+	0.422396i
$303$			19.2158i			1.10392i
$304$	2.55633	+	6.85624i	0.146615	+	0.393233i
$305$	−3.32201	−	3.21063i	−0.190218	−	0.183840i
$306$	−13.3033	−	1.43065i	−0.760499	−	0.0817848i
$307$	−2.27398	+	2.27398i	−0.129783	+	0.129783i	−0.769014	−	0.639232i	$-0.779253\pi$
$307$	−2.27398	+	2.27398i	−0.129783	+	0.129783i	0.639232	+	0.769014i	$0.279253\pi$
$308$	6.53931	−	4.20201i	0.372612	−	0.239432i
$309$	6.38097	−	6.38097i	0.363001	−	0.363001i
$310$	−25.2856	−	2.28396i	−1.43613	−	0.129720i
$311$		−	19.9119i		−	1.12910i	−0.825399	−	0.564550i	$-0.809050\pi$
$311$		−	19.9119i		−	1.12910i	0.825399	−	0.564550i	$-0.190950\pi$
$312$	9.67967	−	29.0742i	0.548003	−	1.64600i
$313$	17.4529			0.986498			0.493249	−	0.869888i	$-0.335809\pi$
$313$	17.4529			0.986498			0.493249	+	0.869888i	$0.335809\pi$
$314$	13.7422	−	11.0735i	0.775515	−	0.624911i
$315$	0.0476593	+	2.79547i	0.00268530	+	0.157507i
$316$	13.8142	+	3.00595i	0.777111	+	0.169098i
$317$	5.35444	−	5.35444i	0.300735	−	0.300735i	−0.540566	−	0.841302i	$-0.681790\pi$
$317$	5.35444	−	5.35444i	0.300735	−	0.300735i	0.841302	+	0.540566i	$0.181790\pi$
$318$	8.49365	+	0.913414i	0.476300	+	0.0512217i
$319$	−7.48138			−0.418877
$320$	−14.4993	−	10.4771i	−0.810537	−	0.585687i
$321$	14.0139			0.782180
$322$	0.342578	+	0.0368411i	0.0190911	+	0.00205308i
$323$	−9.78778	+	9.78778i	−0.544607	+	0.544607i
$324$	21.8637	+	4.75751i	1.21465	+	0.264306i
$325$	17.9353	−	19.2019i	0.994869	−	1.06513i
$326$	17.8136	−	14.3542i	0.986603	−	0.795007i
$327$	−9.41226			−0.520499
$328$	6.67951	−	20.0628i	0.368814	−	1.10778i
$329$			6.05197i			0.333656i
$330$	−2.27941	+	25.2352i	−0.125477	+	1.38915i
$331$	16.1687	−	16.1687i	0.888710	−	0.888710i	−0.105689	−	0.994399i	$-0.533705\pi$
$331$	16.1687	−	16.1687i	0.888710	−	0.888710i	0.994399	+	0.105689i	$0.0337049\pi$
$332$	26.5629	−	17.0687i	1.45783	−	0.936767i
$333$	6.73979	−	6.73979i	0.369338	−	0.369338i
$334$	−33.2539	−	3.57615i	−1.81957	−	0.195678i
$335$	17.1948	−	17.7913i	0.939453	−	0.972041i
$336$	−7.72695	+	2.88097i	−0.421540	+	0.157170i
$337$		−	11.8555i		−	0.645812i	−0.946431	−	0.322906i	$-0.895340\pi$
$337$		−	11.8555i		−	0.645812i	0.946431	−	0.322906i	$-0.104660\pi$
$338$	−2.21006	+	20.5509i	−0.120212	+	1.11782i
$339$	19.3425	+	19.3425i	1.05054	+	1.05054i
$340$	6.63034	−	33.1835i	0.359581	−	1.79963i
$341$	−22.0638	+	22.0638i	−1.19482	+	1.19482i
$342$	−2.51876	+	2.02962i	−0.136199	+	0.109750i
$343$	1.00000			0.0539949
$344$	−3.32740	−	6.64876i	−0.179401	−	0.358477i
$345$	−0.780535	+	0.807611i	−0.0420226	+	0.0434803i
$346$	14.1901	−	11.4344i	0.762864	−	0.614718i
$347$	−5.56147	−	5.56147i	−0.298555	−	0.298555i	0.541893	−	0.840448i	$-0.317708\pi$
$347$	−5.56147	−	5.56147i	−0.298555	−	0.298555i	−0.840448	+	0.541893i	$0.817708\pi$
$348$	7.75569	+	1.68762i	0.415748	+	0.0904662i
$349$	−10.0973	−	10.0973i	−0.540498	−	0.540498i	0.383177	−	0.923675i	$-0.374830\pi$
$349$	−10.0973	−	10.0973i	−0.540498	−	0.540498i	−0.923675	+	0.383177i	$0.874830\pi$
$350$	−7.05222	−	0.515976i	−0.376957	−	0.0275801i
$351$	−18.9557			−1.01178
$352$	−21.3032	+	5.43399i	−1.13547	+	0.289632i
$353$			12.3353i			0.656541i	0.944584	+	0.328270i	$0.106466\pi$
$353$			12.3353i			0.656541i	−0.944584	+	0.328270i	$0.893534\pi$
$354$	−1.84647	+	17.1699i	−0.0981388	+	0.912572i
$355$	−0.0854307	−	5.01097i	−0.00453419	−	0.265955i
$356$	−5.88990	+	27.0678i	−0.312164	+	1.43459i
$357$	−11.0308	−	11.0308i	−0.583810	−	0.583810i
$358$	5.45485	+	6.76947i	0.288298	+	0.357777i
$359$			6.36954i			0.336171i	0.985772	+	0.168086i	$0.0537585\pi$
$359$			6.36954i			0.336171i	−0.985772	+	0.168086i	$0.946241\pi$
$360$	2.36972	−	7.54453i	0.124895	−	0.397632i
$361$		−	15.6536i		−	0.823872i
$362$	−19.0589	+	15.3577i	−1.00171	+	0.807182i
$363$	5.98407	+	5.98407i	0.314082	+	0.314082i
$364$	8.84198	−	5.68166i	0.463446	−	0.297800i
$365$	−15.3087	+	0.260993i	−0.801292	+	0.0136610i
$366$	5.98939	+	0.644104i	0.313070	+	0.0336679i
$367$		−	9.67176i		−	0.504862i	−0.967615	−	0.252431i	$-0.918770\pi$
$367$		−	9.67176i		−	0.504862i	0.967615	−	0.252431i	$-0.0812301\pi$
$368$	−0.886428	−	0.404944i	−0.0462083	−	0.0211092i
$369$	9.34773			0.486624
$370$	15.4431	+	18.5100i	0.802848	+	0.962287i
$371$	2.07180	+	2.07180i	0.107563	+	0.107563i
$372$	27.8499	−	17.8957i	1.44395	−	0.927850i
$373$	−20.4843	−	20.4843i	−1.06063	−	1.06063i	−0.998039	−	0.0625960i	$-0.980062\pi$
$373$	−20.4843	−	20.4843i	−1.06063	−	1.06063i	−0.0625960	−	0.998039i	$-0.519938\pi$
$374$	−26.0950	−	32.3839i	−1.34934	−	1.67453i
$375$	15.4442	−	17.1105i	0.797535	−	0.883585i
$376$	5.40715	−	16.2411i	0.278853	−	0.837571i
$377$	−10.1158			−0.520989
$378$	3.20077	+	3.97215i	0.164630	+	0.204305i
$379$	−2.49354	+	2.49354i	−0.128084	+	0.128084i	−0.768243	−	0.640159i	$-0.778869\pi$
$379$	−2.49354	+	2.49354i	−0.128084	+	0.128084i	0.640159	+	0.768243i	$0.278869\pi$
$380$	−4.53925	−	6.80616i	−0.232859	−	0.349149i
$381$	21.5645	+	21.5645i	1.10478	+	1.10478i
$382$	−0.685275	−	0.0736951i	−0.0350617	−	0.00377057i
$383$			0.0325674i			0.00166412i	1.00000		0.000832059i	$0.000264853\pi$
$383$			0.0325674i			0.00166412i	−1.00000		0.000832059i	$0.999735\pi$
$384$	23.3101	−	0.827716i	1.18954	−	0.0422392i
$385$	−6.03945	+	6.24895i	−0.307799	+	0.318476i
$386$	2.78779	−	25.9231i	0.141895	−	1.31945i
$387$	2.32406	−	2.32406i	0.118139	−	0.118139i
$388$	−6.94062	+	31.8965i	−0.352356	+	1.61930i
$389$	18.1676	−	18.1676i	0.921136	−	0.921136i	−0.0759738	−	0.997110i	$-0.524207\pi$
$389$	18.1676	−	18.1676i	0.921136	−	0.921136i	0.997110	+	0.0759738i	$0.0242065\pi$
$390$	−3.08205	+	34.1212i	−0.156066	+	1.72779i
$391$		−	1.84353i		−	0.0932311i
$392$	−2.68361	−	0.893453i	−0.135543	−	0.0451262i
$393$	−4.77561			−0.240898
$394$	−9.46950	−	11.7516i	−0.477067	−	0.592039i
$395$	−15.8039	+	0.269437i	−0.795181	+	0.0135568i
$396$	−5.25401	−	8.17645i	−0.264024	−	0.410882i
$397$	−12.0000	+	12.0000i	−0.602263	+	0.602263i	−0.940913	−	0.338649i	$-0.890030\pi$
$397$	−12.0000	+	12.0000i	−0.602263	+	0.602263i	0.338649	+	0.940913i	$0.390030\pi$
$398$	1.27440	−	11.8504i	0.0638799	−	0.594005i
$399$	−3.77141			−0.188807
$400$	18.4644	+	7.68550i	0.923219	+	0.384275i
$401$	−6.52550			−0.325868			−0.162934	−	0.986637i	$-0.552096\pi$
$401$	−6.52550			−0.325868			−0.162934	+	0.986637i	$0.552096\pi$
$402$	−3.44955	+	32.0767i	−0.172048	+	1.59984i
$403$	−29.8331	+	29.8331i	−1.48609	+	1.48609i
$404$	15.6826	−	10.0773i	0.780240	−	0.501365i
$405$	−25.0128	+	0.426436i	−1.24289	+	0.0211898i
$406$	1.70811	+	2.11976i	0.0847719	+	0.105202i
$407$	29.6269			1.46855
$408$	19.7468	+	39.4577i	0.977611	+	1.95345i
$409$			23.9194i			1.18274i	0.806401	+	0.591370i	$0.201413\pi$
$409$			23.9194i			1.18274i	−0.806401	+	0.591370i	$0.798587\pi$
$410$	−2.12679	+	23.5455i	−0.105034	+	1.16283i
$411$	−4.87936	+	4.87936i	−0.240681	+	0.240681i
$412$	−8.55409	−	1.86135i	−0.421430	−	0.0917024i
$413$	−4.18816	+	4.18816i	−0.206086	+	0.206086i
$414$	0.0460645	−	0.428344i	0.00226395	−	0.0210520i
$415$	−24.5324	+	25.3834i	−1.20425	+	1.24602i
$416$	−28.8047	+	7.34745i	−1.41227	+	0.360238i
$417$		−	12.1663i		−	0.595784i
$418$	−9.99695	−	1.07508i	−0.488967	−	0.0525839i
$419$	−10.5211	−	10.5211i	−0.513988	−	0.513988i	0.401758	−	0.915746i	$-0.368399\pi$
$419$	−10.5211	−	10.5211i	−0.513988	−	0.513988i	−0.915746	+	0.401758i	$0.868399\pi$
$420$	7.67050	−	5.11571i	0.374282	−	0.249621i
$421$	−13.5916	+	13.5916i	−0.662413	+	0.662413i	−0.955948	−	0.293536i	$-0.905168\pi$
$421$	−13.5916	+	13.5916i	−0.662413	+	0.662413i	0.293536	+	0.955948i	$0.405168\pi$
$422$	−17.5122	−	21.7326i	−0.852480	−	1.05793i
$423$	7.56711			0.367926
$424$	−3.70884	−	7.41096i	−0.180117	−	0.359908i
$425$	1.28966	+	37.8117i	0.0625576	+	1.83413i
$426$	4.10019	+	5.08833i	0.198655	+	0.246530i
$427$	1.46095	+	1.46095i	0.0707006	+	0.0707006i
$428$	−7.34930	−	11.4372i	−0.355242	−	0.552838i
$429$	29.7737	+	29.7737i	1.43749	+	1.43749i
$430$	5.32520	+	6.38274i	0.256804	+	0.307803i
$431$	−19.0402			−0.917136			−0.458568	−	0.888659i	$-0.651638\pi$
$431$	−19.0402			−0.917136			−0.458568	+	0.888659i	$0.651638\pi$
$432$	−5.04067	−	13.5194i	−0.242519	−	0.650453i
$433$			12.1367i			0.583252i	0.956532	+	0.291626i	$0.0941963\pi$
$433$			12.1367i			0.583252i	−0.956532	+	0.291626i	$0.905804\pi$
$434$	11.2890	+	1.21403i	0.541890	+	0.0582753i
$435$	−8.87274	+	0.151269i	−0.425415	+	0.00725280i
$436$	4.93606	+	7.68165i	0.236394	+	0.367884i
$437$	−0.315150	−	0.315150i	−0.0150757	−	0.0150757i
$438$	15.5450	−	12.5262i	0.742769	−	0.598525i
$439$		−	10.6307i		−	0.507374i	−0.967286	−	0.253687i	$-0.918357\pi$
$439$		−	10.6307i		−	0.507374i	0.967286	−	0.253687i	$-0.0816434\pi$
$440$	21.7906	−	11.3738i	1.03883	−	0.542223i
$441$		−	1.25035i		−	0.0595407i
$442$	−35.2838	−	43.7872i	−1.67828	−	2.08275i
$443$	−3.78890	−	3.78890i	−0.180016	−	0.180016i	0.611347	−	0.791363i	$-0.290628\pi$
$443$	−3.78890	−	3.78890i	−0.180016	−	0.180016i	−0.791363	+	0.611347i	$0.790628\pi$
$444$	−30.7132	−	6.68314i	−1.45758	−	0.317168i
$445$	−0.527938	−	30.9664i	−0.0250267	−	1.46795i
$446$	−2.20467	+	20.5008i	−0.104394	+	0.970739i
$447$			5.30334i			0.250839i
$448$	6.40348	+	4.79535i	0.302536	+	0.226559i
$449$	10.4074			0.491156			0.245578	−	0.969377i	$-0.421022\pi$
$449$	10.4074			0.491156			0.245578	+	0.969377i	$0.421022\pi$
$450$	−0.645153	+	8.81777i	−0.0304128	+	0.415674i
$451$	20.5455	+	20.5455i	0.967449	+	0.967449i
$452$	5.64230	−	25.9299i	0.265391	−	1.21964i
$453$	7.61031	+	7.61031i	0.357564	+	0.357564i
$454$	29.7944	−	24.0084i	1.39832	−	1.12677i
$455$	−8.16611	+	8.44938i	−0.382833	+	0.396113i
$456$	10.1210	+	3.36958i	0.473958	+	0.157795i
$457$	25.0310			1.17090			0.585449	−	0.810709i	$-0.300918\pi$
$457$	25.0310			1.17090			0.585449	+	0.810709i	$0.300918\pi$
$458$	0.144815	−	0.116692i	0.00676675	−	0.00545266i
$459$	19.2999	−	19.2999i	0.900844	−	0.900844i
$460$	1.06845	+	0.213486i	0.0498169	+	0.00995383i
$461$	−7.73196	−	7.73196i	−0.360113	−	0.360113i	0.503741	−	0.863854i	$-0.331956\pi$
$461$	−7.73196	−	7.73196i	−0.360113	−	0.360113i	−0.863854	+	0.503741i	$0.831956\pi$
$462$	1.21161	−	11.2665i	0.0563692	−	0.524165i
$463$			16.0759i			0.747111i	0.927608	+	0.373555i	$0.121861\pi$
$463$			16.0759i			0.747111i	−0.927608	+	0.373555i	$0.878139\pi$
$464$	−2.68998	−	7.21471i	−0.124879	−	0.334934i
$465$	−25.7211	+	26.6133i	−1.19279	+	1.23416i
$466$	−22.0328	−	2.36943i	−1.02065	−	0.109762i
$467$	3.34560	−	3.34560i	0.154816	−	0.154816i	−0.625449	−	0.780265i	$-0.715084\pi$
$467$	3.34560	−	3.34560i	0.154816	−	0.154816i	0.780265	+	0.625449i	$0.215084\pi$
$468$	−7.10409	−	11.0556i	−0.328387	−	0.511046i
$469$	−7.82426	+	7.82426i	−0.361291	+	0.361291i
$470$	−1.72166	+	19.0604i	−0.0794143	+	0.879191i
$471$		−	25.7279i		−	1.18548i
$472$	14.9813	−	7.49744i	0.689570	−	0.345098i
$473$	10.2162			0.469740
$474$	16.0479	−	12.9314i	0.737104	−	0.593960i
$475$	6.68435	+	6.24342i	0.306699	+	0.286468i
$476$	−3.21772	+	14.7874i	−0.147484	+	0.677780i
$477$	2.59049	−	2.59049i	0.118610	−	0.118610i
$478$	−27.5051	−	2.95792i	−1.25805	−	0.135292i
$479$	17.5284			0.800895			0.400448	−	0.916320i	$-0.368855\pi$
$479$	17.5284			0.800895			0.400448	+	0.916320i	$0.368855\pi$
$480$	−25.1553	+	6.87532i	−1.14817	+	0.313814i
$481$	40.0594			1.82655
$482$	35.5937	+	3.82778i	1.62125	+	0.174351i
$483$	0.355172	−	0.355172i	0.0161609	−	0.0161609i
$484$	1.74558	−	8.02201i	0.0793443	−	0.364637i
$485$	−0.622118	−	36.4905i	−0.0282489	−	1.65695i
$486$	13.4825	−	10.8642i	0.611578	−	0.492811i
$487$	21.2601			0.963386			0.481693	−	0.876340i	$-0.340022\pi$
$487$	21.2601			0.963386			0.481693	+	0.876340i	$0.340022\pi$
$488$	−2.61533	−	5.22592i	−0.118391	−	0.236566i
$489$		−	33.3504i		−	1.50816i
$490$	3.14946	+	0.284479i	0.142278	+	0.0128515i
$491$	−3.53688	+	3.53688i	−0.159617	+	0.159617i	−0.782397	−	0.622780i	$-0.786003\pi$
$491$	−3.53688	+	3.53688i	−0.159617	+	0.159617i	0.622780	+	0.782397i	$0.286003\pi$
$492$	−16.6642	−	25.9334i	−0.751280	−	1.16917i
$493$	10.2995	−	10.2995i	0.463867	−	0.463867i
$494$	−13.5172	−	1.45365i	−0.608165	−	0.0654027i
$495$	7.81341	+	7.55145i	0.351186	+	0.339413i
$496$	−29.2106	−	13.3442i	−1.31159	−	0.599171i
$497$			2.24130i			0.100536i
$498$	4.92160	−	45.7649i	0.220542	−	2.05077i
$499$	−20.2630	−	20.2630i	−0.907096	−	0.907096i	0.0889408	−	0.996037i	$-0.471652\pi$
$499$	−20.2630	−	20.2630i	−0.907096	−	0.907096i	−0.996037	+	0.0889408i	$0.971652\pi$
$500$	−22.0639	−	3.63126i	−0.986726	−	0.162395i
$501$	−34.4764	+	34.4764i	−1.54029	+	1.54029i
$502$	−3.36805	+	2.71398i	−0.150323	+	0.121131i
$503$	−17.1305			−0.763809			−0.381905	−	0.924202i	$-0.624732\pi$
$503$	−17.1305			−0.763809			−0.381905	+	0.924202i	$0.624732\pi$
$504$	−1.11713	+	3.35546i	−0.0497611	+	0.149464i
$505$	−14.4839	+	14.9863i	−0.644523	+	0.666881i
$506$	1.04271	−	0.840216i	0.0463540	−	0.0373522i
$507$	21.3064	+	21.3064i	0.946251	+	0.946251i
$508$	6.29045	−	28.9086i	0.279094	−	1.28261i
$509$	−26.9775	−	26.9775i	−1.19576	−	1.19576i	−0.975425	−	0.220330i	$-0.929286\pi$
$509$	−26.9775	−	26.9775i	−1.19576	−	1.19576i	−0.220330	−	0.975425i	$-0.570714\pi$
$510$	−31.6029	−	37.8789i	−1.39940	−	1.67731i
$511$	6.84723			0.302904
$512$	−12.9000	−	18.5900i	−0.570105	−	0.821572i
$513$		−	6.59863i		−	0.291336i
$514$	−4.64485	+	43.1914i	−0.204875	+	1.90509i
$515$	9.78614	−	0.166841i	0.431229	−	0.00735191i
$516$	−10.5908	−	2.30453i	−0.466232	−	0.101451i
$517$	16.6318	+	16.6318i	0.731467	+	0.731467i
$518$	−6.76425	−	8.39443i	−0.297204	−	0.368830i
$519$		−	26.5665i		−	1.16614i
$520$	29.4637	−	15.3788i	1.29207	−	0.674404i
$521$		−	9.18168i		−	0.402257i	−0.979565	−	0.201128i	$-0.935539\pi$
$521$		−	9.18168i		−	0.402257i	0.979565	−	0.201128i	$-0.0644608\pi$
$522$	2.65045	−	2.13574i	0.116007	−	0.0934787i
$523$	−12.2389	−	12.2389i	−0.535171	−	0.535171i	0.386936	−	0.922107i	$-0.373534\pi$
$523$	−12.2389	−	12.2389i	−0.535171	−	0.535171i	−0.922107	+	0.386936i	$0.873534\pi$
$524$	2.50447	+	3.89753i	0.109408	+	0.170264i
$525$	−7.03629	+	7.53322i	−0.307089	+	0.328777i
$526$	24.1198	+	2.59386i	1.05167	+	0.113098i
$527$		−	60.7499i		−	2.64631i
$528$	−13.3176	+	29.1523i	−0.579573	+	1.26869i
$529$	−22.9406			−0.997419
$530$	5.93567	+	7.11444i	0.257829	+	0.309031i
$531$	5.23668	+	5.23668i	0.227253	+	0.227253i
$532$	1.97783	+	3.07797i	0.0857500	+	0.133447i
$533$	27.7801	+	27.7801i	1.20329	+	1.20329i
$534$	25.3380	+	31.4444i	1.09648	+	1.36073i
$535$	10.9294	+	10.5630i	0.472518	+	0.456676i
$536$	27.9879	−	14.0066i	1.20889	−	0.604994i
$537$	12.6737			0.546911
$538$	−13.6304	−	16.9153i	−0.587648	−	0.729271i
$539$	2.74817	−	2.74817i	0.118372	−	0.118372i
$540$	8.95068	+	13.4207i	0.385176	+	0.577533i
$541$	−12.1320	−	12.1320i	−0.521596	−	0.521596i	0.396457	−	0.918053i	$-0.370240\pi$
$541$	−12.1320	−	12.1320i	−0.521596	−	0.521596i	−0.918053	+	0.396457i	$0.870240\pi$
$542$	−40.1477	−	4.31752i	−1.72449	−	0.185453i
$543$			35.6818i			1.53125i
$544$	21.8470	−	36.8087i	0.936680	−	1.57816i
$545$	−7.34057	−	7.09447i	−0.314436	−	0.303894i
$546$	1.63825	−	15.2338i	0.0701107	−	0.651944i
$547$	−2.03213	+	2.03213i	−0.0868876	+	0.0868876i	−0.749215	−	0.662327i	$-0.769569\pi$
$547$	−2.03213	+	2.03213i	−0.0868876	+	0.0868876i	0.662327	+	0.749215i	$0.269569\pi$
$548$	6.54108	+	1.42333i	0.279421	+	0.0608015i
$549$	1.82671	−	1.82671i	0.0779622	−	0.0779622i
$550$	−20.7987	+	17.9627i	−0.886858	+	0.765932i
$551$		−	3.52139i		−	0.150016i
$552$	−1.27047	+	0.635812i	−0.0540748	+	0.0270620i
$553$	7.06875			0.300594
$554$	−5.44515	−	6.75743i	−0.231342	−	0.287096i
$555$	35.1368	−	0.599039i	1.49148	−	0.0254278i
$556$	−9.92928	+	6.38033i	−0.421095	+	0.270586i
$557$	21.4933	−	21.4933i	0.910701	−	0.910701i	−0.0856265	−	0.996327i	$-0.527289\pi$
$557$	21.4933	−	21.4933i	0.910701	−	0.910701i	0.996327	+	0.0856265i	$0.0272892\pi$
$558$	1.51797	−	14.1153i	0.0642607	−	0.597547i
$559$	13.8136			0.584252
$560$	−8.19773	−	3.57732i	−0.346417	−	0.151169i
$561$	−60.6288			−2.55975
$562$	3.21797	−	29.9232i	0.135742	−	1.26224i
$563$	29.2941	−	29.2941i	1.23460	−	1.23460i	0.272422	−	0.962178i	$-0.412175\pi$
$563$	29.2941	−	29.2941i	1.23460	−	1.23460i	0.962178	−	0.272422i	$-0.0878247\pi$
$564$	−13.4899	−	20.9934i	−0.568027	−	0.883982i
$565$	0.505744	+	29.6646i	0.0212768	+	1.24800i
$566$	19.3707	+	24.0390i	0.814211	+	1.01044i
$567$	11.1877			0.469838
$568$	2.00250	−	6.01476i	0.0840228	−	0.252374i
$569$			4.90009i			0.205422i	0.994711	+	0.102711i	$0.0327517\pi$
$569$			4.90009i			0.205422i	−0.994711	+	0.102711i	$0.967248\pi$
$570$	−11.8779	−	1.07289i	−0.497510	−	0.0449383i
$571$	−13.2450	+	13.2450i	−0.554286	+	0.554286i	−0.927675	−	0.373389i	$-0.878196\pi$
$571$	−13.2450	+	13.2450i	−0.554286	+	0.554286i	0.373389	+	0.927675i	$0.378196\pi$
$572$	8.68509	−	39.9134i	0.363142	−	1.66886i
$573$	−0.710468	+	0.710468i	−0.0296802	+	0.0296802i
$574$	1.13048	−	10.5121i	0.0471855	−	0.438768i
$575$	−1.21747	+	0.0415248i	−0.0507721	+	0.00173170i
$576$	5.99589	−	8.00663i	0.249829	−	0.333609i
$577$		−	35.7709i		−	1.48916i	−0.667533	−	0.744580i	$-0.732650\pi$
$577$		−	35.7709i		−	1.48916i	0.667533	−	0.744580i	$-0.267350\pi$
$578$	56.6033	+	6.08717i	2.35439	+	0.253193i
$579$	−26.8761	−	26.8761i	−1.11693	−	1.11693i
$580$	4.77658	+	7.16200i	0.198337	+	0.297386i
$581$	11.1631	−	11.1631i	0.463125	−	0.463125i
$582$	29.8581	+	37.0539i	1.23766	+	1.53593i
$583$	11.3873			0.471615
$584$	−18.3753	−	6.11768i	−0.760375	−	0.253151i
$585$	10.5647	+	10.2105i	0.436798	+	0.422154i
$586$	0.0881210	+	0.109358i	0.00364024	+	0.00451754i
$587$	12.3485	+	12.3485i	0.509675	+	0.509675i	0.914427	−	0.404751i	$-0.132642\pi$
$587$	12.3485	+	12.3485i	0.509675	+	0.509675i	−0.404751	+	0.914427i	$0.632642\pi$
$588$	−3.46885	+	2.22901i	−0.143053	+	0.0919227i
$589$	−10.3852	−	10.3852i	−0.427913	−	0.427913i
$590$	−14.3819	+	11.9990i	−0.592092	+	0.493990i
$591$	−22.0013			−0.905013
$592$	10.6526	+	28.5709i	0.437817	+	1.17426i
$593$		−	19.9203i		−	0.818030i	−0.912528	−	0.409015i	$-0.865872\pi$
$593$		−	19.9203i		−	0.818030i	0.912528	−	0.409015i	$-0.134128\pi$
$594$	19.7124	+	2.11989i	0.808809	+	0.0869800i
$595$	−0.288418	−	16.9173i	−0.0118240	−	0.693540i
$596$	4.32823	−	2.78122i	0.177291	−	0.113923i
$597$	−12.2860	−	12.2860i	−0.502834	−	0.502834i
$598$	1.40987	−	1.13608i	0.0576540	−	0.0464577i
$599$			30.8658i			1.26114i	0.776131	+	0.630572i	$0.217180\pi$
$599$			30.8658i			1.26114i	−0.776131	+	0.630572i	$0.782820\pi$
$600$	25.6132	−	13.9296i	1.04566	−	0.568674i
$601$		−	37.6973i		−	1.53771i	−0.639426	−	0.768853i	$-0.720828\pi$
$601$		−	37.6973i		−	1.53771i	0.639426	−	0.768853i	$-0.279172\pi$
$602$	−2.33250	−	2.89463i	−0.0950655	−	0.117976i
$603$	9.78311	+	9.78311i	0.398399	+	0.398399i
$604$	2.21996	−	10.2021i	0.0903288	−	0.415117i
$605$	0.156464	+	9.17742i	0.00636115	+	0.373115i
$606$	2.90569	−	27.0194i	0.118036	−	1.09759i
$607$			13.3037i			0.539982i	0.962863	+	0.269991i	$0.0870207\pi$
$607$			13.3037i			0.539982i	−0.962863	+	0.269991i	$0.912979\pi$
$608$	−2.55771	−	10.0272i	−0.103729	−	0.406655i
$609$	3.96859			0.160815
$610$	4.18560	+	5.01682i	0.169470	+	0.203125i
$611$	22.4884	+	22.4884i	0.909782	+	0.909782i
$612$	18.4895	+	4.02329i	0.747395	+	0.162632i
$613$	8.50922	+	8.50922i	0.343684	+	0.343684i	0.857750	−	0.514066i	$-0.171861\pi$
$613$	8.50922	+	8.50922i	0.343684	+	0.343684i	−0.514066	+	0.857750i	$0.671861\pi$
$614$	3.54131	−	2.85360i	0.142916	−	0.115162i
$615$	24.7819	+	23.9510i	0.999302	+	0.965799i
$616$	−9.83036	+	4.91964i	−0.396077	+	0.198218i
$617$	−9.59464			−0.386266			−0.193133	−	0.981173i	$-0.561865\pi$
$617$	−9.59464			−0.386266			−0.193133	+	0.981173i	$0.561865\pi$
$618$	−9.93722	+	8.00744i	−0.399734	+	0.322106i
$619$	12.3932	−	12.3932i	0.498123	−	0.498123i	−0.412730	−	0.910853i	$-0.635425\pi$
$619$	12.3932	−	12.3932i	0.498123	−	0.498123i	0.910853	+	0.412730i	$0.135425\pi$
$620$	35.2089	+	7.03502i	1.41402	+	0.282533i
$621$	0.621425	+	0.621425i	0.0249369	+	0.0249369i
$622$	−3.01095	+	27.9982i	−0.120728	+	1.12263i
$623$			13.8506i			0.554912i
$624$	−18.0071	+	39.4177i	−0.720859	+	1.57797i
$625$	24.9419	−	1.70339i	0.997676	−	0.0681355i
$626$	−24.5407	−	2.63913i	−0.980842	−	0.105481i
$627$	−10.3645	+	10.3645i	−0.413917	+	0.413917i
$628$	−20.9974	+	13.4925i	−0.837887	+	0.538408i
$629$	−40.7870	+	40.7870i	−1.62628	+	1.62628i
$630$	0.355700	−	3.93794i	0.0141714	−	0.156891i
$631$			9.15487i			0.364449i	0.983257	+	0.182225i	$0.0583298\pi$
$631$			9.15487i			0.364449i	−0.983257	+	0.182225i	$0.941670\pi$
$632$	−18.9697	−	6.31559i	−0.754576	−	0.251221i
$633$	−40.6875			−1.61718
$634$	−8.33858	+	6.71925i	−0.331167	+	0.266855i
$635$	0.563841	+	33.0723i	0.0223753	+	1.31243i
$636$	−11.8048	−	2.56871i	−0.468093	−	0.101856i
$637$	3.71588	−	3.71588i	0.147228	−	0.147228i
$638$	10.5196	+	1.13129i	0.416476	+	0.0447881i
$639$	2.80242			0.110862
$640$	18.8033	+	16.9244i	0.743266	+	0.668996i
$641$	1.57740			0.0623037			0.0311518	−	0.999515i	$-0.490082\pi$
$641$	1.57740			0.0623037			0.0311518	+	0.999515i	$0.490082\pi$
$642$	−19.7050	−	2.11910i	−0.777696	−	0.0836341i
$643$	−6.37511	+	6.37511i	−0.251410	+	0.251410i	−0.821548	−	0.570139i	$-0.806889\pi$
$643$	−6.37511	+	6.37511i	−0.251410	+	0.251410i	0.570139	+	0.821548i	$0.306889\pi$
$644$	−0.476130	−	0.103605i	−0.0187621	−	0.00408261i
$645$	12.1161	−	0.206565i	0.477073	−	0.00813349i
$646$	15.2427	−	12.2826i	0.599716	−	0.483253i
$647$	40.0913			1.57615			0.788076	−	0.615578i	$-0.211077\pi$
$647$	40.0913			1.57615			0.788076	+	0.615578i	$0.211077\pi$
$648$	−30.0233	−	9.99566i	−1.17943	−	0.392667i
$649$			23.0195i			0.903595i
$650$	−28.1225	+	24.2879i	−1.10305	+	0.952648i
$651$	11.7040	−	11.7040i	0.458717	−	0.458717i
$652$	−27.2184	+	17.4899i	−1.06595	+	0.684958i
$653$	18.5775	−	18.5775i	0.726992	−	0.726992i	−0.243027	−	0.970020i	$-0.578140\pi$
$653$	18.5775	−	18.5775i	0.726992	−	0.726992i	0.970020	+	0.243027i	$0.0781404\pi$
$654$	13.2346	+	1.42326i	0.517515	+	0.0556540i
$655$	−3.72447	−	3.59961i	−0.145527	−	0.140648i
$656$	−12.4259	+	27.2004i	−0.485149	+	1.06200i
$657$		−	8.56147i		−	0.334015i
$658$	0.915142	−	8.50971i	0.0356760	−	0.331743i
$659$	28.2153	+	28.2153i	1.09911	+	1.09911i	0.994515	+	0.104597i	$0.0333552\pi$
$659$	28.2153	+	28.2153i	1.09911	+	1.09911i	0.104597	+	0.994515i	$0.466645\pi$
$660$	7.02100	−	35.1387i	0.273292	−	1.36777i
$661$	10.0649	−	10.0649i	0.391479	−	0.391479i	−0.483735	−	0.875214i	$-0.660720\pi$
$661$	10.0649	−	10.0649i	0.391479	−	0.391479i	0.875214	+	0.483735i	$0.160720\pi$
$662$	−25.1798	+	20.2899i	−0.978640	+	0.788590i
$663$	−81.9779			−3.18376
$664$	−39.9312	+	19.9837i	−1.54963	+	0.775520i
$665$	−2.94130	−	2.84269i	−0.114059	−	0.110235i
$666$	−10.4960	+	8.45771i	−0.406712	+	0.327730i
$667$	0.331627	+	0.331627i	0.0128406	+	0.0128406i
$668$	46.2178	+	10.0569i	1.78822	+	0.389113i
$669$	21.2544	+	21.2544i	0.821744	+	0.821744i
$670$	−26.8680	+	22.4163i	−1.03800	+	0.866018i
$671$	8.02990			0.309991
$672$	11.3005	−	2.88252i	0.435928	−	0.111196i
$673$		−	0.980897i		−	0.0378108i	−0.999821	−	0.0189054i	$-0.993982\pi$
$673$		−	0.980897i		−	0.0378108i	0.999821	−	0.0189054i	$-0.00601814\pi$
$674$	−1.79272	+	16.6701i	−0.0690530	+	0.642109i
$675$	−13.1805	−	12.3110i	−0.507316	−	0.473851i
$676$	6.21516	−	28.5626i	0.239045	−	1.09856i
$677$	−26.4000	−	26.4000i	−1.01463	−	1.01463i	−0.999891	−	0.0147420i	$-0.995307\pi$
$677$	−26.4000	−	26.4000i	−1.01463	−	1.01463i	−0.0147420	−	0.999891i	$-0.504693\pi$
$678$	−24.2728	−	30.1225i	−0.932192	−	1.15685i
$679$			16.3214i			0.626359i
$680$	−14.3408	+	45.6570i	−0.549944	+	1.75086i
$681$		−	55.7808i		−	2.13753i
$682$	34.3605	−	27.6877i	1.31573	−	1.06022i
$683$	24.3082	+	24.3082i	0.930127	+	0.930127i	0.997713	−	0.0675865i	$-0.0215299\pi$
$683$	24.3082	+	24.3082i	0.930127	+	0.930127i	−0.0675865	+	0.997713i	$0.521530\pi$
$684$	3.84855	−	2.47300i	0.147153	−	0.0945573i
$685$	−7.48319	+	0.127579i	−0.285918	+	0.00487455i
$686$	−1.40611	−	0.151214i	−0.0536854	−	0.00577337i
$687$		−	0.271121i		−	0.0103439i
$688$	3.67329	+	9.85202i	0.140043	+	0.375605i
$689$	15.3971			0.586584
$690$	1.21964	−	1.01756i	0.0464308	−	0.0387378i
$691$	23.7450	+	23.7450i	0.903301	+	0.903301i	0.995720	−	0.0924188i	$-0.0294598\pi$
$691$	23.7450	+	23.7450i	0.903301	+	0.903301i	−0.0924188	+	0.995720i	$0.529460\pi$
$692$	−21.6818	+	13.9323i	−0.824219	+	0.529625i
$693$	−3.43619	−	3.43619i	−0.130530	−	0.130530i
$694$	6.97904	+	8.66098i	0.264921	+	0.328766i
$695$	9.17029	−	9.48840i	0.347849	−	0.359915i
$696$	−10.6501	−	3.54575i	−0.403692	−	0.134401i
$697$	−56.5693			−2.14272
$698$	12.6711	+	15.7248i	0.479607	+	0.595192i
$699$	−22.8428	+	22.8428i	−0.863994	+	0.863994i
$700$	9.83814	+	1.79191i	0.371847	+	0.0677279i
$701$	−17.4462	−	17.4462i	−0.658932	−	0.658932i	0.296195	−	0.955127i	$-0.404282\pi$
$701$	−17.4462	−	17.4462i	−0.658932	−	0.658932i	−0.955127	+	0.296195i	$0.904282\pi$
$702$	26.6537	+	2.86636i	1.00598	+	0.108184i
$703$			13.9450i			0.525946i
$704$	30.7763	−	4.41942i	1.15993	−	0.166563i
$705$	20.0613	+	19.3887i	0.755551	+	0.730220i
$706$	1.86527	−	17.3447i	0.0702002	−	0.652777i
$707$	6.59068	−	6.59068i	0.247868	−	0.247868i
$708$	5.19267	−	23.8635i	0.195152	−	0.896847i
$709$	−20.7239	+	20.7239i	−0.778304	+	0.778304i	−0.979542	−	0.201239i	$-0.935503\pi$
$709$	−20.7239	+	20.7239i	−0.778304	+	0.778304i	0.201239	+	0.979542i	$0.435503\pi$
$710$	−0.637604	+	7.05887i	−0.0239288	+	0.264915i
$711$		−	8.83844i		−	0.331468i
$712$	12.3749	−	37.1695i	0.463767	−	1.39299i
$713$	1.95604			0.0732544
$714$	13.8424	+	17.1784i	0.518040	+	0.642887i
$715$	0.778483	+	45.6622i	0.0291136	+	1.70767i
$716$	−6.64646	−	10.3434i	−0.248390	−	0.386552i
$717$	−28.5162	+	28.5162i	−1.06496	+	1.06496i
$718$	0.963163	−	8.95625i	0.0359449	−	0.334244i
$719$	8.77286			0.327172			0.163586	−	0.986529i	$-0.447694\pi$
$719$	8.77286			0.327172			0.163586	+	0.986529i	$0.447694\pi$
$720$	−4.47292	+	10.2501i	−0.166696	+	0.381998i
$721$	−4.37713			−0.163013
$722$	−2.36704	+	22.0106i	−0.0880920	+	0.819149i
$723$	36.9023	−	36.9023i	1.37241	−	1.37241i
$724$	29.1211	−	18.7126i	1.08228	−	0.695447i
$725$	−7.03382	−	6.56984i	−0.261230	−	0.243998i
$726$	−7.50936	−	9.31911i	−0.278698	−	0.345864i
$727$	−43.6867			−1.62025			−0.810126	−	0.586256i	$-0.800601\pi$
$727$	−43.6867			−1.62025			−0.810126	+	0.586256i	$0.800601\pi$
$728$	−13.2919	+	6.65199i	−0.492631	+	0.246539i
$729$			8.32127i			0.308195i
$730$	21.5651	+	1.94790i	0.798159	+	0.0720949i
$731$	−14.0645	+	14.0645i	−0.520193	+	0.520193i
$732$	−8.32432	−	1.81136i	−0.307676	−	0.0669497i
$733$	25.6677	−	25.6677i	0.948059	−	0.948059i	−0.0506576	−	0.998716i	$-0.516132\pi$
$733$	25.6677	−	25.6677i	0.948059	−	0.948059i	0.998716	+	0.0506576i	$0.0161317\pi$
$734$	−1.46250	+	13.5995i	−0.0539820	+	0.501968i
$735$	3.20370	−	3.31483i	0.118170	−	0.122269i
$736$	1.18518	+	0.703435i	0.0436863	+	0.0259289i
$737$			43.0048i			1.58410i
$738$	−13.1439	−	1.41351i	−0.483834	−	0.0520319i
$739$	−13.8755	−	13.8755i	−0.510417	−	0.510417i	0.404237	−	0.914654i	$-0.367537\pi$
$739$	−13.8755	−	13.8755i	−0.510417	−	0.510417i	−0.914654	+	0.404237i	$0.867537\pi$
$740$	−18.9157	−	28.3622i	−0.695354	−	1.04261i
$741$	−14.0141	+	14.0141i	−0.514820	+	0.514820i
$742$	−2.59989	−	3.22646i	−0.0954449	−	0.118447i
$743$	23.8830			0.876184			0.438092	−	0.898930i	$-0.355654\pi$
$743$	23.8830			0.876184			0.438092	+	0.898930i	$0.355654\pi$
$744$	−41.8660	+	20.9520i	−1.53488	+	0.768137i
$745$	−3.99738	+	4.13605i	−0.146453	+	0.151533i
$746$	25.7055	+	31.9006i	0.941147	+	1.16796i
$747$	−13.9579	−	13.9579i	−0.510693	−	0.510693i
$748$	31.7955	+	49.4812i	1.16256	+	1.80921i
$749$	−4.80653	−	4.80653i	−0.175627	−	0.175627i
$750$	−24.3035	+	21.7239i	−0.887440	+	0.793244i
$751$	−12.9285			−0.471766			−0.235883	−	0.971781i	$-0.575798\pi$
$751$	−12.9285			−0.471766			−0.235883	+	0.971781i	$0.575798\pi$
$752$	−10.0589	+	22.0191i	−0.366811	+	0.802953i
$753$			6.30563i			0.229790i
$754$	14.2239	+	1.52965i	0.518003	+	0.0557065i
$755$	0.198984	+	11.6715i	0.00724178	+	0.424769i
$756$	−3.89997	−	6.06926i	−0.141841	−	0.220737i
$757$	9.22570	+	9.22570i	0.335314	+	0.335314i	0.854600	−	0.519286i	$-0.173802\pi$
$757$	9.22570	+	9.22570i	0.335314	+	0.335314i	−0.519286	+	0.854600i	$0.673802\pi$
$758$	3.88323	−	3.12912i	0.141045	−	0.113655i
$759$		−	1.95215i		−	0.0708584i
$760$	5.35348	+	10.2566i	0.194191	+	0.372045i
$761$		−	7.94628i		−	0.288053i	−0.989574	−	0.144026i	$-0.953995\pi$
$761$		−	7.94628i		−	0.288053i	0.989574	−	0.144026i	$-0.0460050\pi$
$762$	−27.0611	−	33.5828i	−0.980322	−	1.21658i
$763$	3.22824	+	3.22824i	0.116870	+	0.116870i
$764$	0.952426	+	0.207246i	0.0344576	+	0.00749791i
$765$	−21.1526	+	0.360625i	−0.764773	+	0.0130384i
$766$	0.00492465	−	0.0457933i	0.000177935	−	0.00165458i
$767$			31.1253i			1.12387i
$768$	−32.9016	−	2.36095i	−1.18724	−	0.0851936i
$769$	−12.4465			−0.448834			−0.224417	−	0.974493i	$-0.572048\pi$
$769$	−12.4465			−0.448834			−0.224417	+	0.974493i	$0.572048\pi$
$770$	9.43703	−	7.87344i	0.340087	−	0.283739i
$771$	44.7793	+	44.7793i	1.61269	+	1.61269i
$772$	−7.83986	+	36.0291i	−0.282163	+	1.29671i
$773$	16.4977	+	16.4977i	0.593382	+	0.593382i	0.938543	−	0.345161i	$-0.112176\pi$
$773$	16.4977	+	16.4977i	0.593382	+	0.593382i	−0.345161	+	0.938543i	$0.612176\pi$
$774$	−3.61931	+	2.91645i	−0.130093	+	0.104830i
$775$	−40.1195	+	1.36837i	−1.44113	+	0.0491533i
$776$	14.5824	−	43.8003i	0.523479	−	1.57234i
$777$	−15.7160			−0.563807
$778$	−28.2928	+	22.7984i	−1.01435	+	0.817363i
$779$	−9.67050	+	9.67050i	−0.346482	+	0.346482i
$780$	9.49329	−	47.5120i	0.339914	−	1.70120i
$781$	6.15947	+	6.15947i	0.220403	+	0.220403i
$782$	−0.278767	+	2.59219i	−0.00996868	+	0.0926966i
$783$			6.94362i			0.248145i
$784$	3.63833	+	1.66209i	0.129940	+	0.0593603i
$785$	19.3924	−	20.0651i	0.692143	−	0.716153i
$786$	6.71501	+	0.722139i	0.239517	+	0.0257578i
$787$	1.81553	−	1.81553i	0.0647166	−	0.0647166i	−0.674008	−	0.738724i	$-0.735429\pi$
$787$	1.81553	−	1.81553i	0.0647166	−	0.0647166i	0.738724	+	0.674008i	$0.235429\pi$
$788$	11.5381	+	17.9560i	0.411028	+	0.639655i
$789$	25.0065	−	25.0065i	0.890256	−	0.890256i
$790$	22.2627	+	2.01091i	0.792072	+	0.0715451i
$791$		−	13.2683i		−	0.471767i
$792$	6.15130	+	12.2914i	0.218577	+	0.436757i
$793$	10.8575			0.385560
$794$	18.6879	−	15.0587i	0.663207	−	0.534414i
$795$	13.5051	−	0.230245i	0.478977	−	0.00816595i
$796$	−3.58388	+	16.4702i	−0.127027	+	0.583770i
$797$	2.48217	−	2.48217i	0.0879229	−	0.0879229i	−0.661777	−	0.749700i	$-0.730198\pi$
$797$	2.48217	−	2.48217i	0.0879229	−	0.0879229i	0.749700	+	0.661777i	$0.230198\pi$
$798$	5.30300	+	0.570289i	0.187724	+	0.0201880i
$799$	−45.7936			−1.62006
$800$	−24.8007	−	13.5987i	−0.876838	−	0.480787i
$801$	17.3182			0.611907
$802$	9.17555	+	0.986747i	0.324000	+	0.0348432i
$803$	18.8174	−	18.8174i	0.664050	−	0.664050i
$804$	9.70087	−	44.5816i	0.342123	−	1.57227i
$805$	0.544707	−	0.00928657i	0.0191984	−	0.000327309i
$806$	46.4597	−	37.4374i	1.63647	−	1.31867i
$807$	−31.6687			−1.11479
$808$	−23.5753	+	11.7983i	−0.829375	+	0.415064i
$809$			44.3893i			1.56065i	0.625377	+	0.780323i	$0.284945\pi$
$809$			44.3893i			1.56065i	−0.625377	+	0.780323i	$0.715055\pi$
$810$	35.2351	+	3.18266i	1.23804	+	0.111827i
$811$	29.9343	−	29.9343i	1.05114	−	1.05114i	0.0525165	−	0.998620i	$-0.483276\pi$
$811$	29.9343	−	29.9343i	1.05114	−	1.05114i	0.998620	−	0.0525165i	$-0.0167242\pi$
$812$	−2.08124	−	3.23889i	−0.0730372	−	0.113663i
$813$	−41.6236	+	41.6236i	−1.45980	+	1.45980i
$814$	−41.6586	−	4.48000i	−1.46013	−	0.157024i
$815$	25.1378	−	26.0098i	0.880539	−	0.911084i
$816$	−21.7995	−	58.4677i	−0.763135	−	2.04678i
$817$			4.80862i			0.168232i
$818$	3.61695	−	33.6332i	0.126464	−	1.17596i
$819$	−4.64616	−	4.64616i	−0.162350	−	0.162350i
$820$	6.55090	−	32.7859i	0.228767	−	1.14493i
$821$	−21.9174	+	21.9174i	−0.764922	+	0.764922i	−0.977208	−	0.212286i	$-0.931909\pi$
$821$	−21.9174	+	21.9174i	−0.764922	+	0.764922i	0.212286	+	0.977208i	$0.431909\pi$
$822$	7.59872	−	6.12307i	0.265036	−	0.213567i
$823$	−27.0226			−0.941949			−0.470975	−	0.882147i	$-0.656098\pi$
$823$	−27.0226			−0.941949			−0.470975	+	0.882147i	$0.656098\pi$
$824$	11.7465	+	3.91076i	0.409208	+	0.136238i
$825$	1.36564	+	40.0395i	0.0475456	+	1.39400i
$826$	6.52230	−	5.25569i	0.226940	−	0.182869i
$827$	−1.24215	−	1.24215i	−0.0431939	−	0.0431939i	0.685180	−	0.728374i	$-0.259724\pi$
$827$	−1.24215	−	1.24215i	−0.0431939	−	0.0431939i	−0.728374	+	0.685180i	$0.759724\pi$
$828$	−0.129543	+	0.595331i	−0.00450193	+	0.0206892i
$829$	−31.8232	−	31.8232i	−1.10527	−	1.10527i	−0.993764	−	0.111503i	$-0.964434\pi$
$829$	−31.8232	−	31.8232i	−1.10527	−	1.10527i	−0.111503	−	0.993764i	$-0.535566\pi$
$830$	38.3335	−	31.9821i	1.33058	−	1.11012i
$831$	−12.6512			−0.438865
$832$	41.6135	−	5.97562i	1.44269	−	0.207167i
$833$			7.56673i			0.262172i
$834$	−1.83971	+	17.1070i	−0.0637038	+	0.592368i
$835$	−52.8745	+	0.901444i	−1.82980	+	0.0311958i
$836$	13.8942	+	3.02336i	0.480541	+	0.104565i
$837$	20.4779	+	20.4779i	0.707819	+	0.707819i
$838$	13.2028	+	16.3847i	0.456083	+	0.565999i
$839$		−	27.1270i		−	0.936529i	−0.883588	−	0.468264i	$-0.844880\pi$
$839$		−	27.1270i		−	0.936529i	0.883588	−	0.468264i	$-0.155120\pi$
$840$	−11.5591	+	6.03335i	−0.398827	+	0.208170i
$841$		−	25.2945i		−	0.872224i
$842$	21.1664	−	17.0560i	0.729443	−	0.587787i
$843$	−31.0233	−	31.0233i	−1.06850	−	1.06850i
$844$	21.3377	+	33.2064i	0.734475	+	1.14301i
$845$	0.557092	+	32.6764i	0.0191646	+	1.12410i
$846$	−10.6402	−	1.14425i	−0.365816	−	0.0393402i
$847$		−	4.10486i		−	0.141045i
$848$	4.09439	+	10.9814i	0.140602	+	0.377104i
$849$	45.0056			1.54459
$850$	3.90425	−	53.3622i	0.133915	−	1.83031i
$851$	−1.31327	−	1.31327i	−0.0450184	−	0.0450184i
$852$	−4.99587	−	7.77474i	−0.171156	−	0.266358i
$853$	−25.5010	−	25.5010i	−0.873136	−	0.873136i	0.119677	−	0.992813i	$-0.461814\pi$
$853$	−25.5010	−	25.5010i	−0.873136	−	0.873136i	−0.992813	+	0.119677i	$0.961814\pi$
$854$	−1.83334	−	2.27517i	−0.0627356	−	0.0778549i
$855$	−3.55437	+	3.67767i	−0.121557	+	0.125774i
$856$	8.60442	+	17.1932i	0.294093	+	0.587653i
$857$	−11.0434			−0.377234			−0.188617	−	0.982051i	$-0.560401\pi$
$857$	−11.0434			−0.377234			−0.188617	+	0.982051i	$0.560401\pi$
$858$	−37.3627	−	46.3671i	−1.27554	−	1.58295i
$859$	34.1780	−	34.1780i	1.16614	−	1.16614i	0.183030	−	0.983107i	$-0.441409\pi$
$859$	34.1780	−	34.1780i	1.16614	−	1.16614i	0.983107	−	0.183030i	$-0.0585907\pi$
$860$	−6.52264	−	9.78005i	−0.222420	−	0.333497i
$861$	−10.8986	−	10.8986i	−0.371423	−	0.371423i
$862$	26.7726	+	2.87915i	0.911879	+	0.0980642i
$863$		−	28.3852i		−	0.966244i	−0.875553	−	0.483122i	$-0.839503\pi$
$863$		−	28.3852i		−	0.966244i	0.875553	−	0.483122i	$-0.160497\pi$
$864$	5.04339	+	19.7720i	0.171580	+	0.672655i
$865$	20.0245	−	20.7191i	0.680853	−	0.704471i
$866$	1.83524	−	17.0655i	0.0623639	−	0.579908i
$867$	58.6843	−	58.6843i	1.99302	−	1.99302i
$868$	−15.6900	−	3.41411i	−0.532552	−	0.115882i
$869$	19.4261	−	19.4261i	0.658986	−	0.658986i
$870$	12.4989	+	1.12898i	0.423752	+	0.0382761i
$871$			58.1480i			1.97027i
$872$	−5.77905	−	11.5476i	−0.195703	−	0.391052i
$873$	20.4076			0.690692
$874$	0.395479	+	0.490789i	0.0133773	+	0.0166012i
$875$	−11.1657	+	0.571528i	−0.377470	+	0.0193212i
$876$	−23.7521	+	15.2625i	−0.802507	+	0.515674i
$877$	9.53407	−	9.53407i	0.321943	−	0.321943i	−0.527569	−	0.849512i	$-0.676896\pi$
$877$	9.53407	−	9.53407i	0.321943	−	0.321943i	0.849512	+	0.527569i	$0.176896\pi$
$878$	−1.60751	+	14.9478i	−0.0542507	+	0.504465i
$879$	0.204739			0.00690567
$880$	−32.3598	+	12.6977i	−1.09085	+	0.428038i
$881$	50.6000			1.70476			0.852379	−	0.522925i	$-0.175159\pi$
$881$	50.6000			1.70476			0.852379	+	0.522925i	$0.175159\pi$
$882$	−0.189071	+	1.75813i	−0.00636635	+	0.0591994i
$883$	−9.14029	+	9.14029i	−0.307595	+	0.307595i	−0.843976	−	0.536381i	$-0.819791\pi$
$883$	−9.14029	+	9.14029i	−0.307595	+	0.307595i	0.536381	+	0.843976i	$0.319791\pi$
$884$	42.9916	+	66.9049i	1.44596	+	2.25025i
$885$	0.465441	+	27.3006i	0.0156456	+	0.917700i
$886$	4.75466	+	5.90053i	0.159736	+	0.198232i
$887$	−48.3398			−1.62309			−0.811546	−	0.584289i	$-0.801374\pi$
$887$	−48.3398			−1.62309			−0.811546	+	0.584289i	$0.801374\pi$
$888$	42.1754	+	14.0415i	1.41532	+	0.471201i
$889$		−	14.7925i		−	0.496125i
$890$	−3.94021	+	43.6218i	−0.132076	+	1.46221i
$891$	30.7456	−	30.7456i	1.03002	−	1.03002i
$892$	6.20000	−	28.4929i	0.207591	−	0.954012i
$893$	−7.82840	+	7.82840i	−0.261967	+	0.261967i
$894$	0.801938	−	7.45705i	0.0268208	−	0.249401i
$895$	9.88417	+	9.55279i	0.330391	+	0.319315i
$896$	−8.27885	−	7.71107i	−0.276577	−	0.257609i
$897$		−	2.63955i		−	0.0881320i
$898$	−14.6339	−	1.57374i	−0.488340	−	0.0525165i
$899$	10.9281	+	10.9281i	0.364474	+	0.364474i
$900$	2.24052	−	12.3012i	0.0746841	−	0.410039i
$901$	−15.6768	+	15.6768i	−0.522269	+	0.522269i
$902$	−25.7824	−	31.9959i	−0.858459	−	1.06535i
$903$	−5.41929			−0.180343
$904$	−11.8546	+	35.6070i	−0.394279	+	1.18427i
$905$	−26.8951	+	27.8281i	−0.894024	+	0.925037i
$906$	−9.55012	−	11.8517i	−0.317281	−	0.393746i
$907$	−0.898656	−	0.898656i	−0.0298394	−	0.0298394i	0.692030	−	0.721869i	$-0.256717\pi$
$907$	−0.898656	−	0.898656i	−0.0298394	−	0.0298394i	−0.721869	+	0.692030i	$0.756717\pi$
$908$	−45.5245	+	29.2531i	−1.51079	+	0.970797i
$909$	−8.24069	−	8.24069i	−0.273327	−	0.273327i
$910$	12.7601	−	10.6459i	0.422992	−	0.352908i
$911$	−38.6623			−1.28094			−0.640469	−	0.767984i	$-0.721260\pi$
$911$	−38.6623			−1.28094			−0.640469	+	0.767984i	$0.721260\pi$
$912$	−13.7216	−	6.26841i	−0.454369	−	0.207568i
$913$		−	61.3564i		−	2.03060i
$914$	−35.1962	−	3.78503i	−1.16419	−	0.125198i
$915$	9.52327	−	0.162360i	0.314830	−	0.00536745i
$916$	−0.221270	+	0.142183i	−0.00731098	+	0.00469787i
$917$	1.63795	+	1.63795i	0.0540899	+	0.0540899i
$918$	−30.0562	+	24.2193i	−0.992001	+	0.799357i
$919$			13.6628i			0.450693i	0.974279	+	0.225347i	$0.0723515\pi$
$919$			13.6628i			0.450693i	−0.974279	+	0.225347i	$0.927649\pi$
$920$	−1.47008	−	0.461749i	−0.0484670	−	0.0152234i
$921$		−	6.63001i		−	0.218466i
$922$	9.70277	+	12.0411i	0.319544	+	0.396553i
$923$	8.32839	+	8.32839i	0.274132	+	0.274132i
$924$	−3.40730	+	15.6587i	−0.112092	+	0.515133i
$925$	27.8546	+	26.0171i	0.915853	+	0.855438i
$926$	2.43090	−	22.6044i	0.0798844	−	0.742828i
$927$			5.47297i			0.179756i
$928$	2.69143	+	10.5514i	0.0883506	+	0.346367i
$929$	49.5925			1.62708			0.813539	−	0.581510i	$-0.197538\pi$
$929$	49.5925			1.62708			0.813539	+	0.581510i	$0.197538\pi$
$930$	40.1909	−	33.5318i	1.31791	−	1.09955i
$931$	1.29353	+	1.29353i	0.0423937	+	0.0423937i
$932$	30.6222	+	6.66333i	1.00306	+	0.218265i
$933$	29.0275	+	29.0275i	0.950319	+	0.950319i
$934$	−5.21017	+	4.19837i	−0.170482	+	0.137375i
$935$	−47.2841	−	45.6989i	−1.54636	−	1.49451i
$936$	8.31734	+	16.6196i	0.271861	+	0.543229i
$937$	8.51572			0.278197			0.139098	−	0.990279i	$-0.455580\pi$
$937$	8.51572			0.278197			0.139098	+	0.990279i	$0.455580\pi$
$938$	12.1849	−	9.81861i	0.397850	−	0.320589i
$939$	−25.4429	+	25.4429i	−0.830296	+	0.830296i
$940$	5.30304	−	26.5406i	0.172966	−	0.865660i
$941$	−25.5821	−	25.5821i	−0.833954	−	0.833954i	0.154101	−	0.988055i	$-0.450752\pi$
$941$	−25.5821	−	25.5821i	−0.833954	−	0.833954i	−0.988055	+	0.154101i	$0.950752\pi$
$942$	−3.89042	+	36.1762i	−0.126757	+	1.17868i
$943$		−	1.82144i		−	0.0593141i
$944$	−22.1990	+	8.27682i	−0.722516	+	0.269388i
$945$	5.79978	+	5.60533i	0.188667	+	0.182342i
$946$	−14.3650	−	1.54483i	−0.467047	−	0.0502267i
$947$	−8.22283	+	8.22283i	−0.267206	+	0.267206i	−0.827973	−	0.560767i	$-0.810506\pi$
$947$	−8.22283	+	8.22283i	−0.267206	+	0.267206i	0.560767	+	0.827973i	$0.310506\pi$
$948$	−24.5204	+	15.7563i	−0.796387	+	0.511741i
$949$	25.4435	−	25.4435i	0.825930	−	0.825930i
$950$	−8.45481	−	9.78967i	−0.274310	−	0.317619i
$951$			15.6114i			0.506234i
$952$	6.76052	−	20.3061i	0.219110	−	0.658125i
$953$	38.1372			1.23539			0.617693	−	0.786419i	$-0.288067\pi$
$953$	38.1372			1.23539			0.617693	+	0.786419i	$0.288067\pi$
$954$	−4.03422	+	3.25078i	−0.130613	+	0.105248i
$955$	−1.08960	+	0.0185764i	−0.0352588	+	0.000601118i
$956$	38.2278	+	8.31830i	1.23637	+	0.269033i
$957$	10.9063	−	10.9063i	0.352552	−	0.352552i
$958$	−24.6469	−	2.65055i	−0.796304	−	0.0856352i
$959$	3.34707			0.108083
$960$	36.4106	−	5.86360i	1.17515	−	0.189247i
$961$	33.4578			1.07928
$962$	−56.3278	−	6.05754i	−1.81608	−	0.195303i
$963$	−6.00987	+	6.00987i	−0.193665	+	0.193665i
$964$	−49.4697	−	10.7645i	−1.59331	−	0.346702i
$965$	−0.702721	−	41.2184i	−0.0226214	−	1.32687i
$966$	−0.553116	+	0.445703i	−0.0177962	+	0.0143402i
$967$	−26.1182			−0.839906			−0.419953	−	0.907546i	$-0.637953\pi$
$967$	−26.1182			−0.839906			−0.419953	+	0.907546i	$0.637953\pi$
$968$	−3.66750	+	11.0158i	−0.117878	+	0.354062i
$969$		−	28.5372i		−	0.916748i
$970$	−4.64311	+	51.4036i	−0.149081	+	1.65047i
$971$	8.26209	−	8.26209i	0.265143	−	0.265143i	−0.561997	−	0.827140i	$-0.689967\pi$
$971$	8.26209	−	8.26209i	0.265143	−	0.265143i	0.827140	+	0.561997i	$0.189967\pi$
$972$	−20.6006	+	13.2375i	−0.660765	+	0.424593i
$973$	−4.17282	+	4.17282i	−0.133774	+	0.133774i
$974$	−29.8939	−	3.21482i	−0.957863	−	0.103009i
$975$	1.84652	+	54.1385i	0.0591361	+	1.73382i
$976$	2.88720	+	7.74368i	0.0924171	+	0.247869i
$977$		−	25.0211i		−	0.800495i	−0.916407	−	0.400248i	$-0.868924\pi$
$977$		−	25.0211i		−	0.800495i	0.916407	−	0.400248i	$-0.131076\pi$
$978$	−5.04304	+	46.8942i	−0.161259	+	1.49951i
$979$	38.0638	+	38.0638i	1.21652	+	1.21652i
$980$	−4.38545	−	0.876250i	−0.140088	−	0.0279908i
$981$	4.03645	−	4.03645i	0.128874	−	0.128874i
$982$	5.50806	−	4.43840i	0.175769	−	0.141635i
$983$	−3.94276			−0.125755			−0.0628773	−	0.998021i	$-0.520028\pi$
$983$	−3.94276			−0.125755			−0.0628773	+	0.998021i	$0.520028\pi$
$984$	19.5102	+	38.9849i	0.621961	+	1.24279i
$985$	−17.1587	−	16.5834i	−0.546722	−	0.528392i
$986$	−16.0396	+	12.9248i	−0.510806	+	0.411609i
$987$	−8.82256	−	8.82256i	−0.280825	−	0.280825i
$988$	18.7867	+	4.08796i	0.597686	+	0.130055i
$989$	−0.452852	−	0.452852i	−0.0143998	−	0.0143998i
$990$	−9.84459	−	11.7996i	−0.312882	−	0.375017i
$991$	−32.0511			−1.01814			−0.509068	−	0.860726i	$-0.670010\pi$
$991$	−32.0511			−1.01814			−0.509068	+	0.860726i	$0.670010\pi$
$992$	39.0553	+	23.1804i	1.24001	+	0.735977i
$993$			47.1413i			1.49598i
$994$	0.338916	−	3.15150i	0.0107498	−	0.0999597i
$995$	−0.321239	−	18.8424i	−0.0101840	−	0.597344i
$996$	−13.8406	+	63.6061i	−0.438555	+	2.01544i
$997$	−1.89485	−	1.89485i	−0.0600106	−	0.0600106i	0.676465	−	0.736475i	$-0.263511\pi$
$997$	−1.89485	−	1.89485i	−0.0600106	−	0.0600106i	−0.736475	+	0.676465i	$0.763511\pi$
$998$	25.4279	+	31.5560i	0.804905	+	0.998887i
$999$		−	27.4973i		−	0.869978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.2	yes	70
5.4	even	2		560.2.bb.c.29.34	✓	70
16.5	even	4		560.2.bb.c.309.34	yes	70
80.69	even	4	inner	560.2.bb.d.309.2	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.34	✓	70	5.4	even	2
560.2.bb.c.309.34	yes	70	16.5	even	4
560.2.bb.d.29.2	yes	70	1.1	even	1	trivial
560.2.bb.d.309.2	yes	70	80.69	even	4	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40611 - 0.151214i) q^{2} +(-1.45780 + 1.45780i) q^{3} +(1.95427 + 0.425246i) q^{4} +(-2.23574 + 0.0381166i) q^{5} +(2.27026 - 1.82938i) q^{6} +1.00000 q^{7} +(-2.68361 - 0.893453i) q^{8} -1.25035i q^{9} +O(q^{10})\)	\(q+(-1.40611 - 0.151214i) q^{2} +(-1.45780 + 1.45780i) q^{3} +(1.95427 + 0.425246i) q^{4} +(-2.23574 + 0.0381166i) q^{5} +(2.27026 - 1.82938i) q^{6} +1.00000 q^{7} +(-2.68361 - 0.893453i) q^{8} -1.25035i q^{9} +(3.14946 + 0.284479i) q^{10} +(2.74817 - 2.74817i) q^{11} +(-3.46885 + 2.22901i) q^{12} +(3.71588 - 3.71588i) q^{13} +(-1.40611 - 0.151214i) q^{14} +(3.20370 - 3.31483i) q^{15} +(3.63833 + 1.66209i) q^{16} +7.56673i q^{17} +(-0.189071 + 1.75813i) q^{18} +(1.29353 + 1.29353i) q^{19} +(-4.38545 - 0.876250i) q^{20} +(-1.45780 + 1.45780i) q^{21} +(-4.27978 + 3.44866i) q^{22} -0.243636 q^{23} +(5.21463 - 2.60968i) q^{24} +(4.99709 - 0.170438i) q^{25} +(-5.78681 + 4.66302i) q^{26} +(-2.55063 - 2.55063i) q^{27} +(1.95427 + 0.425246i) q^{28} +(-1.36116 - 1.36116i) q^{29} +(-5.00599 + 4.17656i) q^{30} -8.02856 q^{31} +(-4.86455 - 2.88724i) q^{32} +8.01255i q^{33} +(1.14419 - 10.6396i) q^{34} +(-2.23574 + 0.0381166i) q^{35} +(0.531708 - 2.44353i) q^{36} +(5.39030 + 5.39030i) q^{37} +(-1.62324 - 2.01444i) q^{38} +10.8340i q^{39} +(6.03391 + 1.89524i) q^{40} +7.47606i q^{41} +(2.27026 - 1.82938i) q^{42} +(1.85872 + 1.85872i) q^{43} +(6.53931 - 4.20201i) q^{44} +(0.0476593 + 2.79547i) q^{45} +(0.342578 + 0.0368411i) q^{46} +6.05197i q^{47} +(-7.72695 + 2.88097i) q^{48} +1.00000 q^{49} +(-7.05222 - 0.515976i) q^{50} +(-11.0308 - 11.0308i) q^{51} +(8.84198 - 5.68166i) q^{52} +(2.07180 + 2.07180i) q^{53} +(3.20077 + 3.97215i) q^{54} +(-6.03945 + 6.24895i) q^{55} +(-2.68361 - 0.893453i) q^{56} -3.77141 q^{57} +(1.70811 + 2.11976i) q^{58} +(-4.18816 + 4.18816i) q^{59} +(7.67050 - 5.11571i) q^{60} +(1.46095 + 1.46095i) q^{61} +(11.2890 + 1.21403i) q^{62} -1.25035i q^{63} +(6.40348 + 4.79535i) q^{64} +(-8.16611 + 8.44938i) q^{65} +(1.21161 - 11.2665i) q^{66} +(-7.82426 + 7.82426i) q^{67} +(-3.21772 + 14.7874i) q^{68} +(0.355172 - 0.355172i) q^{69} +(3.14946 + 0.284479i) q^{70} +2.24130i q^{71} +(-1.11713 + 3.35546i) q^{72} +6.84723 q^{73} +(-6.76425 - 8.39443i) q^{74} +(-7.03629 + 7.53322i) q^{75} +(1.97783 + 3.07797i) q^{76} +(2.74817 - 2.74817i) q^{77} +(1.63825 - 15.2338i) q^{78} +7.06875 q^{79} +(-8.19773 - 3.57732i) q^{80} +11.1877 q^{81} +(1.13048 - 10.5121i) q^{82} +(11.1631 - 11.1631i) q^{83} +(-3.46885 + 2.22901i) q^{84} +(-0.288418 - 16.9173i) q^{85} +(-2.33250 - 2.89463i) q^{86} +3.96859 q^{87} +(-9.83036 + 4.91964i) q^{88} +13.8506i q^{89} +(0.355700 - 3.93794i) q^{90} +(3.71588 - 3.71588i) q^{91} +(-0.476130 - 0.103605i) q^{92} +(11.7040 - 11.7040i) q^{93} +(0.915142 - 8.50971i) q^{94} +(-2.94130 - 2.84269i) q^{95} +(11.3005 - 2.88252i) q^{96} +16.3214i q^{97} +(-1.40611 - 0.151214i) q^{98} +(-3.43619 - 3.43619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

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