LMFDB - Embedded newform 560.2.bb.c.29.15

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			29.15
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.c.309.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.525764 - 1.31285i) q^{2} +(1.37854 - 1.37854i) q^{3} +(-1.44714 + 1.38050i) q^{4} +(-1.88536 + 1.20226i) q^{5} +(-2.53459 - 1.08502i) q^{6} -1.00000 q^{7} +(2.57324 + 1.17407i) q^{8} -0.800723i q^{9} +O(q^{10})$	\(q+(-0.525764 - 1.31285i) q^{2} +(1.37854 - 1.37854i) q^{3} +(-1.44714 + 1.38050i) q^{4} +(-1.88536 + 1.20226i) q^{5} +(-2.53459 - 1.08502i) q^{6} -1.00000 q^{7} +(2.57324 + 1.17407i) q^{8} -0.800723i q^{9} +(2.56964 + 1.84308i) q^{10} +(-3.37209 + 3.37209i) q^{11} +(-0.0918757 + 3.89801i) q^{12} +(-1.61037 + 1.61037i) q^{13} +(0.525764 + 1.31285i) q^{14} +(-0.941670 + 4.25639i) q^{15} +(0.188455 - 3.99556i) q^{16} +1.57967i q^{17} +(-1.05123 + 0.420991i) q^{18} +(1.26169 + 1.26169i) q^{19} +(1.06866 - 4.34258i) q^{20} +(-1.37854 + 1.37854i) q^{21} +(6.19996 + 2.65412i) q^{22} -4.70941 q^{23} +(5.16580 - 1.92881i) q^{24} +(2.10913 - 4.53338i) q^{25} +(2.96085 + 1.26750i) q^{26} +(3.03178 + 3.03178i) q^{27} +(1.44714 - 1.38050i) q^{28} +(6.25506 + 6.25506i) q^{29} +(6.08310 - 1.00159i) q^{30} -9.70431 q^{31} +(-5.34465 + 1.85331i) q^{32} +9.29709i q^{33} +(2.07387 - 0.830536i) q^{34} +(1.88536 - 1.20226i) q^{35} +(1.10540 + 1.15876i) q^{36} +(1.26570 + 1.26570i) q^{37} +(0.993060 - 2.31977i) q^{38} +4.43992i q^{39} +(-6.26301 + 0.880176i) q^{40} -3.36899i q^{41} +(2.53459 + 1.08502i) q^{42} +(-2.94390 - 2.94390i) q^{43} +(0.224741 - 9.53506i) q^{44} +(0.962678 + 1.50965i) q^{45} +(2.47604 + 6.18274i) q^{46} +0.678032i q^{47} +(-5.24823 - 5.76781i) q^{48} +1.00000 q^{49} +(-7.06055 - 0.385484i) q^{50} +(2.17764 + 2.17764i) q^{51} +(0.107327 - 4.55356i) q^{52} +(0.573591 + 0.573591i) q^{53} +(2.38627 - 5.57427i) q^{54} +(2.30345 - 10.4117i) q^{55} +(-2.57324 - 1.17407i) q^{56} +3.47858 q^{57} +(4.92326 - 11.5006i) q^{58} +(-1.31915 + 1.31915i) q^{59} +(-4.51321 - 7.45959i) q^{60} +(-5.88041 - 5.88041i) q^{61} +(5.10217 + 12.7403i) q^{62} +0.800723i q^{63} +(5.24314 + 6.04231i) q^{64} +(1.10004 - 4.97222i) q^{65} +(12.2057 - 4.88807i) q^{66} +(7.79753 - 7.79753i) q^{67} +(-2.18074 - 2.28602i) q^{68} +(-6.49209 + 6.49209i) q^{69} +(-2.56964 - 1.84308i) q^{70} +13.7406i q^{71} +(0.940102 - 2.06045i) q^{72} -3.52533 q^{73} +(0.996215 - 2.32714i) q^{74} +(-3.34192 - 9.15695i) q^{75} +(-3.56762 - 0.0840885i) q^{76} +(3.37209 - 3.37209i) q^{77} +(5.82894 - 2.33435i) q^{78} -14.9949 q^{79} +(4.44840 + 7.75962i) q^{80} +10.7610 q^{81} +(-4.42297 + 1.77129i) q^{82} +(12.2463 - 12.2463i) q^{83} +(0.0918757 - 3.89801i) q^{84} +(-1.89918 - 2.97825i) q^{85} +(-2.31710 + 5.41269i) q^{86} +17.2456 q^{87} +(-12.6363 + 4.71814i) q^{88} +7.61855i q^{89} +(1.47580 - 2.05757i) q^{90} +(1.61037 - 1.61037i) q^{91} +(6.81519 - 6.50132i) q^{92} +(-13.3777 + 13.3777i) q^{93} +(0.890153 - 0.356485i) q^{94} +(-3.89563 - 0.861855i) q^{95} +(-4.81294 + 9.92264i) q^{96} +11.2937i q^{97} +(-0.525764 - 1.31285i) q^{98} +(2.70011 + 2.70011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) $ 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	$ 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 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} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 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} - 64 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} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 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} + 158 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 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * 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 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * 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 - 64 * 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 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * 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 + 158 * 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 $

$2$	−0.525764	−	1.31285i	−0.371771	−	0.928324i
$2$	−0.525764	−	1.31285i	−0.371771	−	0.928324i
$3$	1.37854	−	1.37854i	0.795898	−	0.795898i	−0.186548	−	0.982446i	$-0.559730\pi$
$3$	1.37854	−	1.37854i	0.795898	−	0.795898i	0.982446	+	0.186548i	$0.0597299\pi$
$4$	−1.44714	+	1.38050i	−0.723572	+	0.690249i
$5$	−1.88536	+	1.20226i	−0.843157	+	0.537668i
$5$	−1.88536	+	1.20226i	−0.843157	+	0.537668i
$6$	−2.53459	−	1.08502i	−1.03474	−	0.442960i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.57324	+	1.17407i	0.909778	+	0.415095i
$9$		−	0.800723i		−	0.266908i
$10$	2.56964	+	1.84308i	0.812592	+	0.582834i
$11$	−3.37209	+	3.37209i	−1.01672	+	1.01672i	−0.0168651	+	0.999858i	$0.505369\pi$
$11$	−3.37209	+	3.37209i	−1.01672	+	1.01672i	−0.999858	+	0.0168651i	$0.994631\pi$
$12$	−0.0918757	+	3.89801i	−0.0265222	+	1.12526i
$13$	−1.61037	+	1.61037i	−0.446637	+	0.446637i	−0.894235	−	0.447598i	$-0.852280\pi$
$13$	−1.61037	+	1.61037i	−0.446637	+	0.446637i	0.447598	+	0.894235i	$0.352280\pi$
$14$	0.525764	+	1.31285i	0.140516	+	0.350874i
$15$	−0.941670	+	4.25639i	−0.243138	+	1.09900i
$16$	0.188455	−	3.99556i	0.0471137	−	0.998890i
$17$			1.57967i			0.383127i	0.981480	+	0.191564i	$0.0613558\pi$
$17$			1.57967i			0.383127i	−0.981480	+	0.191564i	$0.938644\pi$
$18$	−1.05123	+	0.420991i	−0.247777	+	0.0992286i
$19$	1.26169	+	1.26169i	0.289452	+	0.289452i	0.836864	−	0.547411i	$-0.184387\pi$
$19$	1.26169	+	1.26169i	0.289452	+	0.289452i	−0.547411	+	0.836864i	$0.684387\pi$
$20$	1.06866	−	4.34258i	0.238960	−	0.971029i
$21$	−1.37854	+	1.37854i	−0.300821	+	0.300821i
$22$	6.19996	+	2.65412i	1.32184	+	0.565860i
$23$	−4.70941			−0.981979			−0.490990	−	0.871165i	$-0.663365\pi$
$23$	−4.70941			−0.981979			−0.490990	+	0.871165i	$0.663365\pi$
$24$	5.16580	−	1.92881i	1.05446	−	0.393717i
$25$	2.10913	−	4.53338i	0.421827	−	0.906677i
$26$	2.96085	+	1.26750i	0.580671	+	0.248577i
$27$	3.03178	+	3.03178i	0.583467	+	0.583467i
$28$	1.44714	−	1.38050i	0.273485	−	0.260889i
$29$	6.25506	+	6.25506i	1.16154	+	1.16154i	0.984140	+	0.177395i	$0.0567672\pi$
$29$	6.25506	+	6.25506i	1.16154	+	1.16154i	0.177395	+	0.984140i	$0.443233\pi$
$30$	6.08310	−	1.00159i	1.11062	−	0.182864i
$31$	−9.70431			−1.74294			−0.871472	−	0.490444i	$-0.836834\pi$
$31$	−9.70431			−1.74294			−0.871472	+	0.490444i	$0.836834\pi$
$32$	−5.34465	+	1.85331i	−0.944809	+	0.327622i
$33$			9.29709i			1.61842i
$34$	2.07387	−	0.830536i	0.355666	−	0.142436i
$35$	1.88536	−	1.20226i	0.318683	−	0.203219i
$36$	1.10540	+	1.15876i	0.184233	+	0.193127i
$37$	1.26570	+	1.26570i	0.208080	+	0.208080i	0.803451	−	0.595371i	$-0.202995\pi$
$37$	1.26570	+	1.26570i	0.208080	+	0.208080i	−0.595371	+	0.803451i	$0.702995\pi$
$38$	0.993060	−	2.31977i	0.161096	−	0.376316i
$39$			4.43992i			0.710956i
$40$	−6.26301	+	0.880176i	−0.990269	+	0.139168i
$41$		−	3.36899i		−	0.526147i	−0.964776	−	0.263074i	$-0.915264\pi$
$41$		−	3.36899i		−	0.526147i	0.964776	−	0.263074i	$-0.0847362\pi$
$42$	2.53459	+	1.08502i	0.391096	+	0.167423i
$43$	−2.94390	−	2.94390i	−0.448941	−	0.448941i	0.446062	−	0.895002i	$-0.352826\pi$
$43$	−2.94390	−	2.94390i	−0.448941	−	0.448941i	−0.895002	+	0.446062i	$0.852826\pi$
$44$	0.224741	−	9.53506i	0.0338809	−	1.43746i
$45$	0.962678	+	1.50965i	0.143508	+	0.225045i
$46$	2.47604	+	6.18274i	0.365072	+	0.911595i
$47$			0.678032i			0.0989011i	0.998777	+	0.0494505i	$0.0157470\pi$
$47$			0.678032i			0.0989011i	−0.998777	+	0.0494505i	$0.984253\pi$
$48$	−5.24823	−	5.76781i	−0.757517	−	0.832512i
$49$	1.00000			0.142857
$50$	−7.06055	−	0.385484i	−0.998513	−	0.0545156i
$51$	2.17764	+	2.17764i	0.304930	+	0.304930i
$52$	0.107327	−	4.55356i	0.0148836	−	0.631465i
$53$	0.573591	+	0.573591i	0.0787887	+	0.0787887i	0.745403	−	0.666614i	$-0.232257\pi$
$53$	0.573591	+	0.573591i	0.0787887	+	0.0787887i	−0.666614	+	0.745403i	$0.732257\pi$
$54$	2.38627	−	5.57427i	0.324730	−	0.758563i
$55$	2.30345	−	10.4117i	0.310598	−	1.40392i
$56$	−2.57324	−	1.17407i	−0.343864	−	0.156891i
$57$	3.47858			0.460749
$58$	4.92326	−	11.5006i	0.646456	−	1.51011i
$59$	−1.31915	+	1.31915i	−0.171739	+	0.171739i	−0.787743	−	0.616004i	$-0.788751\pi$
$59$	−1.31915	+	1.31915i	−0.171739	+	0.171739i	0.616004	+	0.787743i	$0.288751\pi$
$60$	−4.51321	−	7.45959i	−0.582652	−	0.963028i
$61$	−5.88041	−	5.88041i	−0.752910	−	0.752910i	0.222112	−	0.975021i	$-0.428705\pi$
$61$	−5.88041	−	5.88041i	−0.752910	−	0.752910i	−0.975021	+	0.222112i	$0.928705\pi$
$62$	5.10217	+	12.7403i	0.647977	+	1.61802i
$63$			0.800723i			0.100882i
$64$	5.24314	+	6.04231i	0.655392	+	0.755289i
$65$	1.10004	−	4.97222i	0.136443	−	0.616728i
$66$	12.2057	−	4.88807i	1.50241	−	0.601680i
$67$	7.79753	−	7.79753i	0.952620	−	0.952620i	−0.0463069	−	0.998927i	$-0.514745\pi$
$67$	7.79753	−	7.79753i	0.952620	−	0.952620i	0.998927	+	0.0463069i	$0.0147452\pi$
$68$	−2.18074	−	2.28602i	−0.264453	−	0.277220i
$69$	−6.49209	+	6.49209i	−0.781555	+	0.781555i
$70$	−2.56964	−	1.84308i	−0.307131	−	0.220290i
$71$			13.7406i			1.63071i	0.578963	+	0.815354i	$0.303457\pi$
$71$			13.7406i			1.63071i	−0.578963	+	0.815354i	$0.696543\pi$
$72$	0.940102	−	2.06045i	0.110792	−	0.242827i
$73$	−3.52533			−0.412608			−0.206304	−	0.978488i	$-0.566144\pi$
$73$	−3.52533			−0.412608			−0.206304	+	0.978488i	$0.566144\pi$
$74$	0.996215	−	2.32714i	0.115808	−	0.270524i
$75$	−3.34192	−	9.15695i	−0.385891	−	1.05735i
$76$	−3.56762	−	0.0840885i	−0.409234	−	0.00964561i
$77$	3.37209	−	3.37209i	0.384285	−	0.384285i
$78$	5.82894	−	2.33435i	0.659998	−	0.264313i
$79$	−14.9949			−1.68706			−0.843531	−	0.537080i	$-0.819527\pi$
$79$	−14.9949			−1.68706			−0.843531	+	0.537080i	$0.819527\pi$
$80$	4.44840	+	7.75962i	0.497347	+	0.867552i
$81$	10.7610			1.19567
$82$	−4.42297	+	1.77129i	−0.488435	+	0.195606i
$83$	12.2463	−	12.2463i	1.34421	−	1.34421i	0.452389	−	0.891821i	$-0.350572\pi$
$83$	12.2463	−	12.2463i	1.34421	−	1.34421i	0.891821	−	0.452389i	$-0.149428\pi$
$84$	0.0918757	−	3.89801i	0.0100245	−	0.425307i
$85$	−1.89918	−	2.97825i	−0.205995	−	0.323036i
$86$	−2.31710	+	5.41269i	−0.249859	+	0.583666i
$87$	17.2456			1.84893
$88$	−12.6363	+	4.71814i	−1.34703	+	0.502955i
$89$			7.61855i			0.807565i	0.914855	+	0.403782i	$0.132305\pi$
$89$			7.61855i			0.807565i	−0.914855	+	0.403782i	$0.867695\pi$
$90$	1.47580	−	2.05757i	0.155563	−	0.216887i
$91$	1.61037	−	1.61037i	0.168813	−	0.168813i
$92$	6.81519	−	6.50132i	0.710533	−	0.677810i
$93$	−13.3777	+	13.3777i	−1.38721	+	1.38721i
$94$	0.890153	−	0.356485i	0.0918123	−	0.0367686i
$95$	−3.89563	−	0.861855i	−0.399683	−	0.0884245i
$96$	−4.81294	+	9.92264i	−0.491218	+	1.01273i
$97$			11.2937i			1.14671i	0.819308	+	0.573353i	$0.194358\pi$
$97$			11.2937i			1.14671i	−0.819308	+	0.573353i	$0.805642\pi$
$98$	−0.525764	−	1.31285i	−0.0531102	−	0.132618i
$99$	2.70011	+	2.70011i	0.271371	+	0.271371i
$100$	3.20610	+	9.47211i	0.320610	+	0.947211i
$101$	−7.18556	+	7.18556i	−0.714989	+	0.714989i	−0.967575	−	0.252585i	$-0.918719\pi$
$101$	−7.18556	+	7.18556i	−0.714989	+	0.714989i	0.252585	+	0.967575i	$0.418719\pi$
$102$	1.71399	−	4.00383i	0.169710	−	0.396439i
$103$	−3.39877			−0.334891			−0.167445	−	0.985881i	$-0.553552\pi$
$103$	−3.39877			−0.334891			−0.167445	+	0.985881i	$0.553552\pi$
$104$	−6.03457	+	2.25319i	−0.591738	+	0.220944i
$105$	0.941670	−	4.25639i	0.0918975	−	0.415381i
$106$	0.451465	−	1.05461i	0.0438501	−	0.102433i
$107$	2.57292	+	2.57292i	0.248733	+	0.248733i	0.820451	−	0.571717i	$-0.193723\pi$
$107$	2.57292	+	2.57292i	0.248733	+	0.248733i	−0.571717	+	0.820451i	$0.693723\pi$
$108$	−8.57280	−	0.202060i	−0.824918	−	0.0194433i
$109$	7.29780	+	7.29780i	0.699003	+	0.699003i	0.964195	−	0.265193i	$-0.0854355\pi$
$109$	7.29780	+	7.29780i	0.699003	+	0.699003i	−0.265193	+	0.964195i	$0.585436\pi$
$110$	−14.8801	+	2.45002i	−1.41876	+	0.233600i
$111$	3.48963			0.331221
$112$	−0.188455	+	3.99556i	−0.0178073	+	0.377545i
$113$			9.16602i			0.862267i	0.902288	+	0.431133i	$0.141886\pi$
$113$			9.16602i			0.862267i	−0.902288	+	0.431133i	$0.858114\pi$
$114$	−1.82891	−	4.56685i	−0.171293	−	0.427725i
$115$	8.87891	−	5.66194i	0.827962	−	0.527979i
$116$	−17.6871	−	0.416883i	−1.64220	−	0.0387066i
$117$	1.28946	+	1.28946i	0.119211	+	0.119211i
$118$	2.42541	+	1.03829i	0.223277	+	0.0955820i
$119$		−	1.57967i		−	0.144809i
$120$	−7.42043	+	9.84714i	−0.677389	+	0.898917i
$121$		−	11.7420i		−	1.06745i
$122$	−4.62838	+	10.8118i	−0.419034	+	0.978854i
$123$	−4.64427	−	4.64427i	−0.418760	−	0.418760i
$124$	14.0435	−	13.3968i	1.26115	−	1.20307i
$125$	1.47385	+	11.0828i	0.131825	+	0.991273i
$126$	1.05123	−	0.420991i	0.0936508	−	0.0375049i
$127$		−	13.2074i		−	1.17197i	−0.810322	−	0.585985i	$-0.800708\pi$
$127$		−	13.2074i		−	1.17197i	0.810322	−	0.585985i	$-0.199292\pi$
$128$	5.17599	−	10.0603i	0.457497	−	0.889211i
$129$	−8.11654			−0.714622
$130$	−7.10613	+	1.17003i	−0.623249	+	0.102619i
$131$	−5.34433	−	5.34433i	−0.466937	−	0.466937i	0.433984	−	0.900921i	$-0.357107\pi$
$131$	−5.34433	−	5.34433i	−0.466937	−	0.466937i	−0.900921	+	0.433984i	$0.857107\pi$
$132$	−12.8346	−	13.4542i	−1.11711	−	1.17104i
$133$	−1.26169	−	1.26169i	−0.109403	−	0.109403i
$134$	−14.3366	−	6.13732i	−1.23850	−	0.530184i
$135$	−9.36099	−	2.07099i	−0.805665	−	0.178243i
$136$	−1.85464	+	4.06488i	−0.159034	+	0.348561i
$137$	−18.3961			−1.57168			−0.785842	−	0.618428i	$-0.787770\pi$
$137$	−18.3961			−1.57168			−0.785842	+	0.618428i	$0.787770\pi$
$138$	11.9364	+	5.10982i	1.01610	+	0.434977i
$139$	10.5274	−	10.5274i	0.892919	−	0.892919i	−0.101878	−	0.994797i	$-0.532485\pi$
$139$	10.5274	−	10.5274i	0.892919	−	0.892919i	0.994797	+	0.101878i	$0.0324852\pi$
$140$	−1.06866	+	4.34258i	−0.0903185	+	0.367015i
$141$	0.934691	+	0.934691i	0.0787152	+	0.0787152i
$142$	18.0393	−	7.22430i	1.51383	−	0.606250i
$143$		−	10.8606i		−	0.908213i
$144$	−3.19933	−	0.150900i	−0.266611	−	0.0125750i
$145$	−19.3132	−	4.27279i	−1.60388	−	0.354836i
$146$	1.85349	+	4.62822i	0.153396	+	0.383034i
$147$	1.37854	−	1.37854i	0.113700	−	0.113700i
$148$	−3.57895	−	0.0843556i	−0.294188	−	0.00693399i
$149$	−7.87250	+	7.87250i	−0.644941	+	0.644941i	−0.951766	−	0.306825i	$-0.900733\pi$
$149$	−7.87250	+	7.87250i	−0.644941	+	0.644941i	0.306825	+	0.951766i	$0.400733\pi$
$150$	−10.2646	+	9.20182i	−0.838103	+	0.751326i
$151$		−	1.42202i		−	0.115722i	−0.998325	−	0.0578611i	$-0.981572\pi$
$151$		−	1.42202i		−	0.115722i	0.998325	−	0.0578611i	$-0.0184280\pi$
$152$	1.76533	+	4.72795i	0.143187	+	0.383488i
$153$	1.26488			0.102260
$154$	−6.19996	−	2.65412i	−0.499607	−	0.213875i
$155$	18.2961	−	11.6671i	1.46958	−	0.937125i
$156$	−6.12929	−	6.42520i	−0.490736	−	0.514428i
$157$	15.6319	−	15.6319i	1.24756	−	1.24756i	0.290770	−	0.956793i	$-0.406089\pi$
$157$	15.6319	−	15.6319i	1.24756	−	1.24756i	0.956793	−	0.290770i	$-0.0939115\pi$
$158$	7.88380	+	19.6861i	0.627201	+	1.56614i
$159$	1.58143			0.125416
$160$	7.84840	−	9.91981i	0.620470	−	0.784230i
$161$	4.70941			0.371153
$162$	−5.65775	−	14.1276i	−0.444515	−	1.10997i
$163$	−14.0948	+	14.0948i	−1.10399	+	1.10399i	−0.110066	+	0.993924i	$0.535106\pi$
$163$	−14.0948	+	14.0948i	−1.10399	+	1.10399i	−0.993924	+	0.110066i	$0.964894\pi$
$164$	4.65088	+	4.87541i	0.363172	+	0.380706i
$165$	−11.1775	−	17.5283i	−0.870170	−	1.36458i
$166$	−22.5163	−	9.63890i	−1.74760	−	0.748124i
$167$	−4.33503			−0.335454			−0.167727	−	0.985833i	$-0.553643\pi$
$167$	−4.33503			−0.335454			−0.167727	+	0.985833i	$0.553643\pi$
$168$	−5.16580	+	1.92881i	−0.398550	+	0.148811i
$169$			7.81339i			0.601030i
$170$	−2.91147	+	4.05919i	−0.223299	+	0.311326i
$171$	1.01027	−	1.01027i	0.0772570	−	0.0772570i
$172$	8.32429	+	0.196203i	0.634722	+	0.0149603i
$173$	1.52580	−	1.52580i	0.116005	−	0.116005i	−0.646722	−	0.762726i	$-0.723860\pi$
$173$	1.52580	−	1.52580i	0.116005	−	0.116005i	0.762726	+	0.646722i	$0.223860\pi$
$174$	−9.06714	−	22.6409i	−0.687378	−	1.71640i
$175$	−2.10913	+	4.53338i	−0.159435	+	0.342692i
$176$	12.8379	+	14.1089i	0.967692	+	1.06350i
$177$			3.63700i			0.273374i
$178$	10.0020	−	4.00556i	0.749682	−	0.300229i
$179$	8.78665	+	8.78665i	0.656745	+	0.656745i	0.954609	−	0.297863i	$-0.0962740\pi$
$179$	8.78665	+	8.78665i	0.656745	+	0.656745i	−0.297863	+	0.954609i	$0.596274\pi$
$180$	−3.47720	−	0.855703i	−0.259175	−	0.0637803i
$181$	4.75968	−	4.75968i	0.353784	−	0.353784i	−0.507731	−	0.861516i	$-0.669516\pi$
$181$	4.75968	−	4.75968i	0.353784	−	0.353784i	0.861516	+	0.507731i	$0.169516\pi$
$182$	−2.96085	−	1.26750i	−0.219473	−	0.0939534i
$183$	−16.2127			−1.19848
$184$	−12.1184	−	5.52916i	−0.893383	−	0.407615i
$185$	−3.90800	−	0.864593i	−0.287322	−	0.0635662i
$186$	24.5965	+	10.5294i	1.80350	+	0.772054i
$187$	−5.32680	−	5.32680i	−0.389534	−	0.389534i
$188$	−0.936021	−	0.981210i	−0.0682663	−	0.0715621i
$189$	−3.03178	−	3.03178i	−0.220530	−	0.220530i
$190$	0.916694	+	5.56750i	0.0665040	+	0.403909i
$191$	−2.14240			−0.155018			−0.0775092	−	0.996992i	$-0.524697\pi$
$191$	−2.14240			−0.155018			−0.0775092	+	0.996992i	$0.524697\pi$
$192$	15.5574	+	1.10169i	1.12276	+	0.0795078i
$193$			6.09947i			0.439050i	0.975607	+	0.219525i	$0.0704507\pi$
$193$			6.09947i			0.439050i	−0.975607	+	0.219525i	$0.929549\pi$
$194$	14.8270	−	5.93784i	1.06452	−	0.426312i
$195$	−5.33794	−	8.37082i	−0.382258	−	0.599447i
$196$	−1.44714	+	1.38050i	−0.103367	+	0.0986069i
$197$	9.37356	+	9.37356i	0.667839	+	0.667839i	0.957215	−	0.289377i	$-0.0934480\pi$
$197$	9.37356	+	9.37356i	0.667839	+	0.667839i	−0.289377	+	0.957215i	$0.593448\pi$
$198$	2.12521	−	4.96445i	0.151032	−	0.352808i
$199$		−	3.85382i		−	0.273190i	−0.990627	−	0.136595i	$-0.956384\pi$
$199$		−	3.85382i		−	0.273190i	0.990627	−	0.136595i	$-0.0436159\pi$
$200$	10.7498	−	9.18922i	0.760126	−	0.649776i
$201$		−	21.4984i		−	1.51638i
$202$	13.2115	+	5.65564i	0.929555	+	0.397930i
$203$	−6.25506	−	6.25506i	−0.439019	−	0.439019i
$204$	−6.15758	−	0.145134i	−0.431117	−	0.0101614i
$205$	4.05040	+	6.35174i	0.282892	+	0.443625i
$206$	1.78695	+	4.46207i	0.124503	+	0.310887i
$207$			3.77093i			0.262098i
$208$	6.13086	+	6.73783i	0.425099	+	0.467184i
$209$	−8.50908			−0.588585
$210$	−6.08310	+	1.00159i	−0.419773	+	0.0691161i
$211$	3.00824	+	3.00824i	0.207096	+	0.207096i	0.803032	−	0.595936i	$-0.203219\pi$
$211$	3.00824	+	3.00824i	0.207096	+	0.207096i	−0.595936	+	0.803032i	$0.703219\pi$
$212$	−1.62191	−	0.0382283i	−0.111393	−	0.00262553i
$213$	18.9419	+	18.9419i	1.29788	+	1.29788i
$214$	2.02511	−	4.73060i	0.138433	−	0.323377i
$215$	9.08964	+	2.01096i	0.619908	+	0.137146i
$216$	4.24199	+	11.3610i	0.288631	+	0.773020i
$217$	9.70431			0.658771
$218$	5.74399	−	13.4178i	0.389032	−	0.908771i
$219$	−4.85979	+	4.85979i	−0.328394	+	0.328394i
$220$	11.0399	+	18.2472i	0.744311	+	1.23022i
$221$	−2.54387	−	2.54387i	−0.171119	−	0.171119i
$222$	−1.83472	−	4.58136i	−0.123139	−	0.307481i
$223$		−	10.4356i		−	0.698823i	−0.936969	−	0.349411i	$-0.886382\pi$
$223$		−	10.4356i		−	0.698823i	0.936969	−	0.349411i	$-0.113618\pi$
$224$	5.34465	−	1.85331i	0.357104	−	0.123829i
$225$	−3.62998	−	1.68883i	−0.241999	−	0.112589i
$226$	12.0336	−	4.81916i	0.800463	−	0.320566i
$227$	−19.1818	+	19.1818i	−1.27314	+	1.27314i	−0.328712	+	0.944430i	$0.606615\pi$
$227$	−19.1818	+	19.1818i	−1.27314	+	1.27314i	−0.944430	+	0.328712i	$0.893385\pi$
$228$	−5.03401	+	4.80217i	−0.333385	+	0.318031i
$229$	4.64322	−	4.64322i	0.306833	−	0.306833i	−0.536847	−	0.843680i	$-0.680385\pi$
$229$	4.64322	−	4.64322i	0.306833	−	0.306833i	0.843680	+	0.536847i	$0.180385\pi$
$230$	−12.1015	−	8.67982i	−0.797948	−	0.572330i
$231$		−	9.29709i		−	0.611704i
$232$	8.75192	+	23.4396i	0.574591	+	1.53889i
$233$	−0.717074			−0.0469770			−0.0234885	−	0.999724i	$-0.507477\pi$
$233$	−0.717074			−0.0469770			−0.0234885	+	0.999724i	$0.507477\pi$
$234$	1.01492	−	2.37082i	0.0663472	−	0.154986i
$235$	−0.815172	−	1.27833i	−0.0531759	−	0.0833891i
$236$	0.0879181	−	3.73009i	0.00572298	−	0.242808i
$237$	−20.6711	+	20.6711i	−1.34273	+	1.34273i
$238$	−2.07387	+	0.830536i	−0.134429	+	0.0538356i
$239$	25.2310			1.63206			0.816030	−	0.578009i	$-0.196170\pi$
$239$	25.2310			1.63206			0.816030	+	0.578009i	$0.196170\pi$
$240$	16.8292	+	4.56463i	1.08632	+	0.294646i
$241$	3.37206			0.217214			0.108607	−	0.994085i	$-0.465361\pi$
$241$	3.37206			0.217214			0.108607	+	0.994085i	$0.465361\pi$
$242$	−15.4154	+	6.17350i	−0.990941	+	0.396847i
$243$	5.73909	−	5.73909i	0.368163	−	0.368163i
$244$	16.6277	+	0.391914i	1.06448	+	0.0250897i
$245$	−1.88536	+	1.20226i	−0.120451	+	0.0768097i
$246$	−3.65543	+	8.53901i	−0.233062	+	0.544428i
$247$	−4.06360			−0.258560
$248$	−24.9715	−	11.3935i	−1.58569	−	0.723488i
$249$		−	33.7640i		−	2.13971i
$250$	13.7751	−	7.76186i	0.871214	−	0.490903i
$251$	1.29276	−	1.29276i	0.0815984	−	0.0815984i	−0.665130	−	0.746728i	$-0.731624\pi$
$251$	1.29276	−	1.29276i	0.0815984	−	0.0815984i	0.746728	+	0.665130i	$0.231624\pi$
$252$	−1.10540	−	1.15876i	−0.0696334	−	0.0729951i
$253$	15.8805	−	15.8805i	0.998401	−	0.998401i
$254$	−17.3394	+	6.94399i	−1.08797	+	0.435705i
$255$	−6.72371	−	1.48753i	−0.421055	−	0.0931528i
$256$	−15.9290	−	1.50596i	−0.995561	−	0.0941227i
$257$		−	27.3267i		−	1.70459i	−0.523060	−	0.852296i	$-0.675210\pi$
$257$		−	27.3267i		−	1.70459i	0.523060	−	0.852296i	$-0.324790\pi$
$258$	4.26739	+	10.6558i	0.265676	+	0.663401i
$259$	−1.26570	−	1.26570i	−0.0786469	−	0.0786469i
$260$	5.27222	+	8.71412i	0.326969	+	0.540427i
$261$	5.00857	−	5.00857i	0.310022	−	0.310022i
$262$	−4.20645	+	9.82616i	−0.259875	+	0.607062i
$263$	23.9076			1.47421			0.737103	−	0.675781i	$-0.236193\pi$
$263$	23.9076			1.47421			0.737103	+	0.675781i	$0.236193\pi$
$264$	−10.9154	+	23.9236i	−0.671797	+	1.47240i
$265$	−1.77103	−	0.391816i	−0.108793	−	0.0240691i
$266$	−0.993060	+	2.31977i	−0.0608884	+	0.142234i
$267$	10.5024	+	10.5024i	0.642739	+	0.642739i
$268$	−0.519685	+	22.0486i	−0.0317448	+	1.34683i
$269$	15.6432	+	15.6432i	0.953780	+	0.953780i	0.998978	−	0.0451982i	$-0.0143920\pi$
$269$	15.6432	+	15.6432i	0.953780	+	0.953780i	−0.0451982	+	0.998978i	$0.514392\pi$
$270$	2.20277	+	13.3784i	0.134056	+	0.814184i
$271$	6.96152			0.422882			0.211441	−	0.977391i	$-0.432184\pi$
$271$	6.96152			0.422882			0.211441	+	0.977391i	$0.432184\pi$
$272$	6.31168	+	0.297697i	0.382702	+	0.0180505i
$273$		−	4.43992i		−	0.268716i
$274$	9.67200	+	24.1513i	0.584307	+	1.45903i
$275$	8.17478	+	22.3991i	0.492958	+	1.35072i
$276$	0.432680	−	18.3573i	0.0260443	−	1.10498i
$277$	12.5713	+	12.5713i	0.755336	+	0.755336i	0.975470	−	0.220133i	$-0.0706493\pi$
$277$	12.5713	+	12.5713i	0.755336	+	0.755336i	−0.220133	+	0.975470i	$0.570649\pi$
$278$	−19.3557	−	8.28592i	−1.16088	−	0.496957i
$279$			7.77046i			0.465205i
$280$	6.26301	−	0.880176i	0.374286	−	0.0526006i
$281$			20.4465i			1.21973i	0.792504	+	0.609867i	$0.208777\pi$
$281$			20.4465i			1.21973i	−0.792504	+	0.609867i	$0.791223\pi$
$282$	0.735681	−	1.71853i	0.0438092	−	0.102337i
$283$	−4.70490	−	4.70490i	−0.279677	−	0.279677i	0.553303	−	0.832980i	$-0.313367\pi$
$283$	−4.70490	−	4.70490i	−0.279677	−	0.279677i	−0.832980	+	0.553303i	$0.813367\pi$
$284$	−18.9688	−	19.8846i	−1.12559	−	1.17993i
$285$	−6.55836	+	4.18216i	−0.388484	+	0.247730i
$286$	−14.2584	+	5.71014i	−0.843116	+	0.337647i
$287$			3.36899i			0.198865i
$288$	1.48399	+	4.27958i	0.0874447	+	0.252177i
$289$	14.5046			0.853213
$290$	4.54467	+	27.6018i	0.266872	+	1.62084i
$291$	15.5688	+	15.5688i	0.912661	+	0.912661i
$292$	5.10166	−	4.86671i	0.298552	−	0.284802i
$293$	−16.6450	−	16.6450i	−0.972413	−	0.972413i	0.0272170	−	0.999630i	$-0.491336\pi$
$293$	−16.6450	−	16.6450i	−0.972413	−	0.972413i	−0.999630	+	0.0272170i	$0.991336\pi$
$294$	−2.53459	−	1.08502i	−0.147821	−	0.0632799i
$295$	0.901106	−	4.07304i	0.0524644	−	0.237142i
$296$	1.77094	+	4.74297i	0.102934	+	0.275680i
$297$	−20.4469			−1.18645
$298$	14.4745	+	6.19633i	0.838484	+	0.358944i
$299$	7.58391	−	7.58391i	0.438589	−	0.438589i
$300$	17.4774	+	8.63792i	1.00906	+	0.498711i
$301$	2.94390	+	2.94390i	0.169684	+	0.169684i
$302$	−1.86689	+	0.747646i	−0.107428	+	0.0430222i
$303$			19.8111i			1.13812i
$304$	5.27894	−	4.80340i	0.302768	−	0.275494i
$305$	18.1565	+	4.01687i	1.03964	+	0.230006i
$306$	−0.665029	−	1.66060i	−0.0380172	−	0.0949301i
$307$	−8.88266	+	8.88266i	−0.506960	+	0.506960i	−0.913592	−	0.406632i	$-0.866703\pi$
$307$	−8.88266	+	8.88266i	−0.506960	+	0.506960i	0.406632	+	0.913592i	$0.366703\pi$
$308$	−0.224741	+	9.53506i	−0.0128058	+	0.543310i
$309$	−4.68533	+	4.68533i	−0.266539	+	0.266539i
$310$	−24.9366	−	17.8858i	−1.41630	−	1.01585i
$311$		−	28.0473i		−	1.59042i	−0.606336	−	0.795208i	$-0.707361\pi$
$311$		−	28.0473i		−	1.59042i	0.606336	−	0.795208i	$-0.292639\pi$
$312$	−5.21276	+	11.4250i	−0.295114	+	0.646812i
$313$	22.5991			1.27738			0.638690	−	0.769464i	$-0.279477\pi$
$313$	22.5991			1.27738			0.638690	+	0.769464i	$0.279477\pi$
$314$	−28.7411	−	12.3036i	−1.62195	−	0.694335i
$315$	−0.962678	−	1.50965i	−0.0542408	−	0.0850590i
$316$	21.6998	−	20.7005i	1.22071	−	1.16449i
$317$	5.95097	−	5.95097i	0.334240	−	0.334240i	−0.519954	−	0.854194i	$-0.674051\pi$
$317$	5.95097	−	5.95097i	0.334240	−	0.334240i	0.854194	+	0.519954i	$0.174051\pi$
$318$	−0.831459	−	2.07618i	−0.0466259	−	0.116426i
$319$	−42.1852			−2.36192
$320$	−17.1496	−	5.08828i	−0.958693	−	0.284444i
$321$	7.09372			0.395933
$322$	−2.47604	−	6.18274i	−0.137984	−	0.344551i
$323$	−1.99306	+	1.99306i	−0.110897	+	0.110897i
$324$	−15.5727	+	14.8555i	−0.865152	+	0.825308i
$325$	3.90395	+	10.6969i	0.216552	+	0.593359i
$326$	25.9149	+	11.0938i	1.43529	+	0.614429i
$327$	20.1206			1.11267
$328$	3.95541	−	8.66921i	0.218401	−	0.478677i
$329$		−	0.678032i		−	0.0373811i
$330$	−17.1353	+	23.8902i	−0.943267	+	1.31511i
$331$	7.88660	−	7.88660i	0.433487	−	0.433487i	−0.456326	−	0.889813i	$-0.650835\pi$
$331$	7.88660	−	7.88660i	0.433487	−	0.433487i	0.889813	+	0.456326i	$0.150835\pi$
$332$	−0.816185	+	34.6282i	−0.0447940	+	1.90047i
$333$	1.01348	−	1.01348i	0.0555382	−	0.0555382i
$334$	2.27920	+	5.69124i	0.124712	+	0.311411i
$335$	−5.32645	+	24.0758i	−0.291015	+	1.31540i
$336$	5.24823	+	5.76781i	0.286314	+	0.314660i
$337$		−	0.918064i		−	0.0500101i	−0.999687	−	0.0250051i	$-0.992040\pi$
$337$		−	0.918064i		−	0.0500101i	0.999687	−	0.0250051i	$-0.00796019\pi$
$338$	10.2578	−	4.10800i	0.557951	−	0.223446i
$339$	12.6357	+	12.6357i	0.686277	+	0.686277i
$340$	6.85985	+	1.68814i	0.372028	+	0.0915522i
$341$	32.7238	−	32.7238i	1.77209	−	1.77209i
$342$	−1.85749	−	0.795165i	−0.100441	−	0.0429976i
$343$	−1.00000			−0.0539949
$344$	−4.11903	−	11.0317i	−0.222083	−	0.594789i
$345$	4.43470	−	20.0451i	0.238756	−	1.07919i
$346$	−2.80536	−	1.20094i	−0.150817	−	0.0645627i
$347$	22.7391	+	22.7391i	1.22070	+	1.22070i	0.967384	+	0.253316i	$0.0815211\pi$
$347$	22.7391	+	22.7391i	1.22070	+	1.22070i	0.253316	+	0.967384i	$0.418479\pi$
$348$	−24.9569	+	23.8076i	−1.33783	+	1.27622i
$349$	14.1828	+	14.1828i	0.759190	+	0.759190i	0.976175	−	0.216985i	$-0.0696222\pi$
$349$	14.1828	+	14.1828i	0.759190	+	0.759190i	−0.216985	+	0.976175i	$0.569622\pi$
$350$	7.06055	+	0.385484i	0.377402	+	0.0206050i
$351$	−9.76461			−0.521196
$352$	11.7731	−	24.2721i	0.627509	−	1.29371i
$353$		−	17.1097i		−	0.910656i	−0.890324	−	0.455328i	$-0.849522\pi$
$353$		−	17.1097i		−	0.910656i	0.890324	−	0.455328i	$-0.150478\pi$
$354$	4.77483	−	1.91220i	0.253780	−	0.101633i
$355$	−16.5198	−	25.9059i	−0.876779	−	1.37494i
$356$	−10.5174	−	11.0251i	−0.557420	−	0.584331i
$357$	−2.17764	−	2.17764i	−0.115253	−	0.115253i
$358$	6.91584	−	16.1553i	0.365514	−	0.853832i
$359$			21.0842i			1.11278i	0.830921	+	0.556390i	$0.187814\pi$
$359$			21.0842i			1.11278i	−0.830921	+	0.556390i	$0.812186\pi$
$360$	0.704777	+	5.01493i	0.0371450	+	0.264310i
$361$		−	15.8163i		−	0.832435i
$362$	−8.75121	−	3.74627i	−0.459953	−	0.196900i
$363$	−16.1867	−	16.1867i	−0.849582	−	0.849582i
$364$	−0.107327	+	4.55356i	−0.00562547	+	0.238671i
$365$	6.64650	−	4.23837i	0.347894	−	0.221846i
$366$	8.52406	+	21.2848i	0.445560	+	1.11258i
$367$		−	27.9184i		−	1.45733i	−0.684870	−	0.728665i	$-0.740141\pi$
$367$		−	27.9184i		−	1.45733i	0.684870	−	0.728665i	$-0.259859\pi$
$368$	−0.887510	+	18.8167i	−0.0462647	+	0.980889i
$369$	−2.69762			−0.140433
$370$	0.919607	+	5.58519i	0.0478081	+	0.290360i
$371$	−0.573591	−	0.573591i	−0.0297793	−	0.0297793i
$372$	0.891590	−	37.8274i	0.0462268	−	1.96126i
$373$	23.2349	+	23.2349i	1.20306	+	1.20306i	0.973231	+	0.229829i	$0.0738167\pi$
$373$	23.2349	+	23.2349i	1.20306	+	1.20306i	0.229829	+	0.973231i	$0.426183\pi$
$374$	−4.19265	+	9.79393i	−0.216797	+	0.506432i
$375$	17.3097	+	13.2462i	0.893871	+	0.684033i
$376$	−0.796054	+	1.74474i	−0.0410534	+	0.0899780i
$377$	−20.1460			−1.03757
$378$	−2.38627	+	5.57427i	−0.122737	+	0.286710i
$379$	3.44834	−	3.44834i	0.177129	−	0.177129i	−0.612974	−	0.790103i	$-0.710027\pi$
$379$	3.44834	−	3.44834i	0.177129	−	0.177129i	0.790103	+	0.612974i	$0.210027\pi$
$380$	6.82732	−	4.13067i	0.350234	−	0.211899i
$381$	−18.2069	−	18.2069i	−0.932769	−	0.932769i
$382$	1.12640	+	2.81264i	0.0576314	+	0.143907i
$383$		−	6.05694i		−	0.309495i	−0.987954	−	0.154747i	$-0.950544\pi$
$383$		−	6.05694i		−	0.309495i	0.987954	−	0.154747i	$-0.0494564\pi$
$384$	−6.73316	−	21.0037i	−0.343600	−	1.07184i
$385$	−2.30345	+	10.4117i	−0.117395	+	0.530630i
$386$	8.00768	−	3.20688i	0.407580	−	0.163226i
$387$	−2.35725	+	2.35725i	−0.119826	+	0.119826i
$388$	−15.5910	−	16.3437i	−0.791512	−	0.829725i
$389$	−8.84075	+	8.84075i	−0.448244	+	0.448244i	−0.894770	−	0.446526i	$-0.852661\pi$
$389$	−8.84075	+	8.84075i	−0.448244	+	0.448244i	0.446526	+	0.894770i	$0.352661\pi$
$390$	−8.18313	+	11.4090i	−0.414369	+	0.577717i
$391$		−	7.43933i		−	0.376223i
$392$	2.57324	+	1.17407i	0.129968	+	0.0592993i
$393$	−14.7347			−0.743268
$394$	7.37779	−	17.2344i	0.371688	−	0.868254i
$395$	28.2708	−	18.0278i	1.42246	−	0.907079i
$396$	−7.63494	−	0.179955i	−0.383670	−	0.00904307i
$397$	23.3489	−	23.3489i	1.17185	−	1.17185i	0.190077	−	0.981769i	$-0.439126\pi$
$397$	23.3489	−	23.3489i	1.17185	−	1.17185i	0.981769	−	0.190077i	$-0.0608736\pi$
$398$	−5.05948	+	2.02620i	−0.253609	+	0.101564i
$399$	−3.47858			−0.174147
$400$	−17.7159	−	9.28150i	−0.885796	−	0.464075i
$401$	5.16139			0.257747			0.128874	−	0.991661i	$-0.458864\pi$
$401$	5.16139			0.257747			0.128874	+	0.991661i	$0.458864\pi$
$402$	−28.2241	+	11.3031i	−1.40769	+	0.563746i
$403$	15.6276	−	15.6276i	0.778464	−	0.778464i
$404$	0.478898	−	20.3182i	0.0238261	−	1.01087i
$405$	−20.2883	+	12.9376i	−1.00814	+	0.642872i
$406$	−4.92326	+	11.5006i	−0.244337	+	0.570767i
$407$	−8.53612			−0.423120
$408$	3.04689	+	8.16028i	0.150844	+	0.403994i
$409$			9.12250i			0.451079i	0.974234	+	0.225539i	$0.0724144\pi$
$409$			9.12250i			0.451079i	−0.974234	+	0.225539i	$0.927586\pi$
$410$	6.20932	−	8.65708i	0.306656	−	0.427543i
$411$	−25.3597	+	25.3597i	−1.25090	+	1.25090i
$412$	4.91851	−	4.69199i	0.242318	−	0.231158i
$413$	1.31915	−	1.31915i	0.0649113	−	0.0649113i
$414$	4.95066	−	1.98262i	0.243312	−	0.0974404i
$415$	−8.36540	+	37.8120i	−0.410641	+	1.85612i
$416$	5.62236	−	11.5914i	0.275659	−	0.568315i
$417$		−	29.0247i		−	1.42134i
$418$	4.47377	+	11.1711i	0.218819	+	0.546398i
$419$	−14.3409	−	14.3409i	−0.700598	−	0.700598i	0.263941	−	0.964539i	$-0.414978\pi$
$419$	−14.3409	−	14.3409i	−0.700598	−	0.700598i	−0.964539	+	0.263941i	$0.914978\pi$
$420$	4.51321	+	7.45959i	0.220222	+	0.363991i
$421$	−13.6418	+	13.6418i	−0.664861	+	0.664861i	−0.956522	−	0.291661i	$-0.905792\pi$
$421$	−13.6418	+	13.6418i	−0.664861	+	0.664861i	0.291661	+	0.956522i	$0.405792\pi$
$422$	2.36774	−	5.53098i	0.115260	−	0.269244i
$423$	0.542915			0.0263974
$424$	0.802553	+	2.14942i	0.0389754	+	0.104385i
$425$	7.16127	+	3.33174i	0.347373	+	0.161613i
$426$	14.9089	−	34.8268i	0.722337	−	1.68736i
$427$	5.88041	+	5.88041i	0.284573	+	0.284573i
$428$	−7.27529	−	0.171478i	−0.351665	−	0.00828871i
$429$	−14.9718	−	14.9718i	−0.722845	−	0.722845i
$430$	−2.13892	−	12.9906i	−0.103148	−	0.626463i
$431$	0.334064			0.0160913			0.00804565	−	0.999968i	$-0.497439\pi$
$431$	0.334064			0.0160913			0.00804565	+	0.999968i	$0.497439\pi$
$432$	12.6850	−	11.5423i	0.610308	−	0.555330i
$433$			17.0693i			0.820299i	0.912018	+	0.410149i	$0.134523\pi$
$433$			17.0693i			0.820299i	−0.912018	+	0.410149i	$0.865477\pi$
$434$	−5.10217	−	12.7403i	−0.244912	−	0.611553i
$435$	−32.5142	+	20.7338i	−1.55894	+	0.994109i
$436$	−20.6356	−	0.486379i	−0.988265	−	0.0232933i
$437$	−5.94183	−	5.94183i	−0.284236	−	0.284236i
$438$	8.93527	+	3.82507i	0.426944	+	0.182769i
$439$			37.2351i			1.77713i	0.458746	+	0.888567i	$0.348299\pi$
$439$			37.2351i			1.77713i	−0.458746	+	0.888567i	$0.651701\pi$
$440$	18.1514	−	24.0875i	0.865334	−	1.14832i
$441$		−	0.800723i		−	0.0381297i
$442$	−2.00224	+	4.67719i	−0.0952368	+	0.222471i
$443$	−5.92788	−	5.92788i	−0.281642	−	0.281642i	0.552122	−	0.833764i	$-0.313818\pi$
$443$	−5.92788	−	5.92788i	−0.281642	−	0.281642i	−0.833764	+	0.552122i	$0.813818\pi$
$444$	−5.05000	+	4.81743i	−0.239662	+	0.228625i
$445$	−9.15949	−	14.3637i	−0.434202	−	0.680904i
$446$	−13.7004	+	5.48669i	−0.648734	+	0.259802i
$447$			21.7051i			1.02661i
$448$	−5.24314	−	6.04231i	−0.247715	−	0.285472i
$449$	−2.94187			−0.138836			−0.0694178	−	0.997588i	$-0.522114\pi$
$449$	−2.94187			−0.138836			−0.0694178	+	0.997588i	$0.522114\pi$
$450$	−0.308666	+	5.65354i	−0.0145506	+	0.266511i
$451$	11.3605	+	11.3605i	0.534946	+	0.534946i
$452$	−12.6537	−	13.2646i	−0.595179	−	0.623912i
$453$	−1.96030	−	1.96030i	−0.0921031	−	0.0921031i
$454$	35.2679	+	15.0977i	1.65521	+	0.708571i
$455$	−1.10004	+	4.97222i	−0.0515705	+	0.233101i
$456$	8.95122	+	4.08408i	0.419179	+	0.191255i
$457$	−25.7535			−1.20470			−0.602350	−	0.798232i	$-0.705769\pi$
$457$	−25.7535			−1.20470			−0.602350	+	0.798232i	$0.705769\pi$
$458$	−8.53709	−	3.65461i	−0.398912	−	0.170769i
$459$	−4.78923	+	4.78923i	−0.223542	+	0.223542i
$460$	−5.03277	+	20.4510i	−0.234654	+	0.953531i
$461$	−13.1107	−	13.1107i	−0.610625	−	0.610625i	0.332484	−	0.943109i	$-0.392113\pi$
$461$	−13.1107	−	13.1107i	−0.610625	−	0.610625i	−0.943109	+	0.332484i	$0.892113\pi$
$462$	−12.2057	+	4.88807i	−0.567859	+	0.227414i
$463$		−	21.4954i		−	0.998978i	−0.866320	−	0.499489i	$-0.833521\pi$
$463$		−	21.4954i		−	0.998978i	0.866320	−	0.499489i	$-0.166479\pi$
$464$	26.1712	−	23.8137i	1.21497	−	1.10552i
$465$	9.13825	−	41.3053i	0.423776	−	1.91549i
$466$	0.377011	+	0.941409i	0.0174647	+	0.0436099i
$467$	−10.9831	+	10.9831i	−0.508239	+	0.508239i	−0.913985	−	0.405747i	$-0.867011\pi$
$467$	−10.9831	+	10.9831i	−0.508239	+	0.508239i	0.405747	+	0.913985i	$0.367011\pi$
$468$	−3.64614	−	0.0859393i	−0.168543	−	0.00397254i
$469$	−7.79753	+	7.79753i	−0.360057	+	0.360057i
$470$	−1.24967	+	1.74230i	−0.0576429	+	0.0803662i
$471$		−	43.0983i		−	1.98587i
$472$	−4.94327	+	1.84573i	−0.227533	+	0.0849564i
$473$	19.8542			0.912896
$474$	38.0061	+	16.2699i	1.74568	+	0.747300i
$475$	8.38082	−	3.05866i	0.384538	−	0.140341i
$476$	2.18074	+	2.28602i	0.0999539	+	0.104779i
$477$	0.459287	−	0.459287i	0.0210293	−	0.0210293i
$478$	−13.2656	−	33.1246i	−0.606753	−	1.51508i
$479$	−17.9884			−0.821912			−0.410956	−	0.911655i	$-0.634805\pi$
$479$	−17.9884			−0.821912			−0.410956	+	0.911655i	$0.634805\pi$
$480$	−2.85551	−	24.4941i	−0.130336	−	1.11800i
$481$	−4.07651			−0.185873
$482$	−1.77291	−	4.42701i	−0.0807538	−	0.201645i
$483$	6.49209	−	6.49209i	0.295400	−	0.295400i
$484$	16.2097	+	16.9923i	0.736806	+	0.772378i
$485$	−13.5780	−	21.2927i	−0.616547	−	0.966853i
$486$	−10.5520	−	4.51715i	−0.478647	−	0.204902i
$487$	−43.2870			−1.96152			−0.980760	−	0.195220i	$-0.937458\pi$
$487$	−43.2870			−1.96152			−0.980760	+	0.195220i	$0.937458\pi$
$488$	−8.22772	−	22.0357i	−0.372451	−	0.997510i
$489$			38.8604i			1.75733i
$490$	2.56964	+	1.84308i	0.116085	+	0.0832619i
$491$	−20.5055	+	20.5055i	−0.925401	+	0.925401i	−0.997404	−	0.0720030i	$-0.977061\pi$
$491$	−20.5055	+	20.5055i	−0.925401	+	0.925401i	0.0720030	+	0.997404i	$0.477061\pi$
$492$	13.1323	+	0.309528i	0.592051	+	0.0139546i
$493$	−9.88095	+	9.88095i	−0.445016	+	0.445016i
$494$	2.13649	+	5.33489i	0.0961253	+	0.240028i
$495$	−8.33690	−	1.84443i	−0.374716	−	0.0829008i
$496$	−1.82882	+	38.7741i	−0.0821166	+	1.74101i
$497$		−	13.7406i		−	0.616349i
$498$	−44.3271	+	17.7519i	−1.98634	+	0.795482i
$499$	18.0695	+	18.0695i	0.808902	+	0.808902i	0.984468	−	0.175566i	$-0.0561756\pi$
$499$	18.0695	+	18.0695i	0.808902	+	0.808902i	−0.175566	+	0.984468i	$0.556176\pi$
$500$	−17.4326	−	14.0037i	−0.779610	−	0.626266i
$501$	−5.97599	+	5.97599i	−0.266988	+	0.266988i
$502$	−2.37689	−	1.01751i	−0.106086	−	0.0454138i
$503$	−8.72663			−0.389101			−0.194551	−	0.980892i	$-0.562325\pi$
$503$	−8.72663			−0.389101			−0.194551	+	0.980892i	$0.562325\pi$
$504$	−0.940102	+	2.06045i	−0.0418755	+	0.0917798i
$505$	4.90841	−	22.1862i	0.218421	−	0.987275i
$506$	−29.1982	−	12.4993i	−1.29802	−	0.555663i
$507$	10.7710	+	10.7710i	0.478359	+	0.478359i
$508$	18.2328	+	19.1131i	0.808951	+	0.848005i
$509$	24.0440	+	24.0440i	1.06573	+	1.06573i	0.997682	+	0.0680492i	$0.0216775\pi$
$509$	24.0440	+	24.0440i	1.06573	+	1.06573i	0.0680492	+	0.997682i	$0.478323\pi$
$510$	1.58218	+	9.60931i	0.0700602	+	0.425507i
$511$	3.52533			0.155951
$512$	6.39778	+	21.7041i	0.282744	+	0.959195i
$513$			7.65036i			0.337772i
$514$	−35.8758	+	14.3674i	−1.58241	+	0.633718i
$515$	6.40789	−	4.08621i	0.282366	−	0.180060i
$516$	11.7458	−	11.2049i	0.517081	−	0.493267i
$517$	−2.28638	−	2.28638i	−0.100555	−	0.100555i
$518$	−0.996215	+	2.32714i	−0.0437712	+	0.102248i
$519$		−	4.20675i		−	0.184656i
$520$	8.66838	−	11.5032i	0.380133	−	0.504449i
$521$			30.4873i			1.33567i	0.744308	+	0.667837i	$0.232779\pi$
$521$			30.4873i			1.33567i	−0.744308	+	0.667837i	$0.767221\pi$
$522$	−9.20882	−	3.94217i	−0.403059	−	0.172544i
$523$	2.21016	+	2.21016i	0.0966435	+	0.0966435i	0.753776	−	0.657132i	$-0.228231\pi$
$523$	2.21016	+	2.21016i	0.0966435	+	0.0966435i	−0.657132	+	0.753776i	$0.728231\pi$
$524$	15.1119	+	0.356186i	0.660165	+	0.0155600i
$525$	3.34192	+	9.15695i	0.145853	+	0.399642i
$526$	−12.5698	−	31.3871i	−0.548067	−	1.36854i
$527$		−	15.3296i		−	0.667770i
$528$	37.1471	+	1.75208i	1.61662	+	0.0762495i
$529$	−0.821492			−0.0357170
$530$	0.416747	+	2.53110i	0.0181023	+	0.109944i
$531$	1.05628	+	1.05628i	0.0458385	+	0.0458385i
$532$	3.56762	+	0.0840885i	0.154676	+	0.00364570i
$533$	5.42533	+	5.42533i	0.234997	+	0.234997i
$534$	8.26632	−	19.3099i	0.357719	−	0.835622i
$535$	−7.94419	−	1.75755i	−0.343457	−	0.0759853i
$536$	29.2198	−	10.9101i	1.26210	−	0.471245i
$537$	24.2254			1.04540
$538$	12.3125	−	28.7617i	0.530829	−	1.24000i
$539$	−3.37209	+	3.37209i	−0.145246	+	0.145246i
$540$	16.4057	−	9.92579i	0.705989	−	0.427138i
$541$	18.3990	+	18.3990i	0.791036	+	0.791036i	0.981663	−	0.190626i	$-0.0610519\pi$
$541$	18.3990	+	18.3990i	0.791036	+	0.791036i	−0.190626	+	0.981663i	$0.561052\pi$
$542$	−3.66012	−	9.13943i	−0.157215	−	0.392572i
$543$		−	13.1228i		−	0.563152i
$544$	−2.92762	−	8.44280i	−0.125521	−	0.361982i
$545$	−22.5328	−	4.98509i	−0.965200	−	0.213538i
$546$	−5.82894	+	2.33435i	−0.249456	+	0.0999009i
$547$	−8.71598	+	8.71598i	−0.372668	+	0.372668i	−0.868448	−	0.495780i	$-0.834882\pi$
$547$	−8.71598	+	8.71598i	−0.372668	+	0.372668i	0.495780	+	0.868448i	$0.334882\pi$
$548$	26.6218	−	25.3957i	1.13723	−	1.08485i
$549$	−4.70858	+	4.70858i	−0.200957	+	0.200957i
$550$	25.1087	−	22.5089i	1.07064	−	0.959784i
$551$			15.7839i			0.672418i
$552$	−24.3278	+	9.08356i	−1.03546	+	0.386622i
$553$	14.9949			0.637650
$554$	9.89468	−	23.1138i	0.420385	−	0.982009i
$555$	−6.57920	+	4.19545i	−0.279271	+	0.178087i
$556$	−0.701620	+	29.7676i	−0.0297553	+	1.26243i
$557$	9.33106	−	9.33106i	0.395370	−	0.395370i	−0.481227	−	0.876596i	$-0.659809\pi$
$557$	9.33106	−	9.33106i	0.395370	−	0.395370i	0.876596	+	0.481227i	$0.159809\pi$
$558$	10.2014	−	4.08543i	0.431861	−	0.172950i
$559$	9.48156			0.401027
$560$	−4.44840	−	7.75962i	−0.187979	−	0.327904i
$561$	−14.6864			−0.620059
$562$	26.8431	−	10.7500i	1.13231	−	0.453462i
$563$	3.46184	−	3.46184i	0.145899	−	0.145899i	−0.630384	−	0.776283i	$-0.717103\pi$
$563$	3.46184	−	3.46184i	0.145899	−	0.145899i	0.776283	+	0.630384i	$0.217103\pi$
$564$	−2.64297	−	0.0622946i	−0.111289	−	0.00262308i
$565$	−11.0200	−	17.2812i	−0.463613	−	0.727026i
$566$	−3.70315	+	8.65048i	−0.155655	+	0.363607i
$567$	−10.7610			−0.451920
$568$	−16.1324	+	35.3578i	−0.676899	+	1.48358i
$569$		−	27.8708i		−	1.16840i	−0.811609	−	0.584201i	$-0.801408\pi$
$569$		−	27.8708i		−	1.16840i	0.811609	−	0.584201i	$-0.198592\pi$
$570$	8.93870	+	6.41130i	0.374401	+	0.268540i
$571$	−33.0411	+	33.0411i	−1.38273	+	1.38273i	−0.542990	+	0.839739i	$0.682708\pi$
$571$	−33.0411	+	33.0411i	−1.38273	+	1.38273i	−0.839739	+	0.542990i	$0.817292\pi$
$572$	14.9931	+	15.7169i	0.626893	+	0.657158i
$573$	−2.95337	+	2.95337i	−0.123379	+	0.123379i
$574$	4.42297	−	1.77129i	0.184611	−	0.0739323i
$575$	−9.93276	+	21.3495i	−0.414225	+	0.890337i
$576$	4.83822	−	4.19830i	0.201592	−	0.174929i
$577$			2.10205i			0.0875096i	0.999042	+	0.0437548i	$0.0139320\pi$
$577$			2.10205i			0.0875096i	−0.999042	+	0.0437548i	$0.986068\pi$
$578$	−7.62601	−	19.0424i	−0.317200	−	0.792059i
$579$	8.40834	+	8.40834i	0.349439	+	0.349439i
$580$	33.8476	−	20.4785i	1.40545	−	0.850324i
$581$	−12.2463	+	12.2463i	−0.508064	+	0.508064i
$582$	12.2540	−	28.6251i	0.507944	−	1.18655i
$583$	−3.86840			−0.160213
$584$	−9.07152	−	4.13897i	−0.375382	−	0.171272i
$585$	−3.98137	−	0.880824i	−0.164609	−	0.0364176i
$586$	−13.1010	+	30.6038i	−0.541199	+	1.26423i
$587$	−5.93582	−	5.93582i	−0.244998	−	0.244998i	0.573916	−	0.818914i	$-0.305423\pi$
$587$	−5.93582	−	5.93582i	−0.244998	−	0.244998i	−0.818914	+	0.573916i	$0.805423\pi$
$588$	−0.0918757	+	3.89801i	−0.00378889	+	0.160751i
$589$	−12.2439	−	12.2439i	−0.504499	−	0.504499i
$590$	−5.82106	+	0.958443i	−0.239649	+	0.0394585i
$591$	25.8436			1.06306
$592$	5.29571	−	4.81866i	0.217652	−	0.198046i
$593$			21.1605i			0.868959i	0.900682	+	0.434480i	$0.143068\pi$
$593$			21.1605i			0.868959i	−0.900682	+	0.434480i	$0.856932\pi$
$594$	10.7502	+	26.8437i	0.441087	+	1.10141i
$595$	1.89918	+	2.97825i	0.0778589	+	0.122096i
$596$	0.524681	−	22.2606i	0.0214918	−	0.911831i
$597$	−5.31263	−	5.31263i	−0.217431	−	0.217431i
$598$	−13.9439	−	5.96918i	−0.570207	−	0.244098i
$599$			11.5208i			0.470729i	0.971907	+	0.235364i	$0.0756283\pi$
$599$			11.5208i			0.470729i	−0.971907	+	0.235364i	$0.924372\pi$
$600$	2.15131	−	27.4867i	0.0878269	−	1.12214i
$601$			5.23109i			0.213380i	0.994292	+	0.106690i	$0.0340253\pi$
$601$			5.23109i			0.213380i	−0.994292	+	0.106690i	$0.965975\pi$
$602$	2.31710	−	5.41269i	0.0944379	−	0.220605i
$603$	−6.24366	−	6.24366i	−0.254262	−	0.254262i
$604$	1.96309	+	2.05787i	0.0798771	+	0.0837334i
$605$	14.1169	+	22.1378i	0.573934	+	0.900028i
$606$	26.0090	−	10.4160i	1.05654	−	0.423119i
$607$			33.7404i			1.36948i	0.728786	+	0.684741i	$0.240085\pi$
$607$			33.7404i			1.36948i	−0.728786	+	0.684741i	$0.759915\pi$
$608$	−9.08161	−	4.40500i	−0.368308	−	0.178646i
$609$	−17.2456			−0.698829
$610$	−4.27246	−	25.9486i	−0.172987	−	1.05063i
$611$	−1.09188	−	1.09188i	−0.0441729	−	0.0441729i
$612$	−1.83047	+	1.74616i	−0.0739922	+	0.0705845i
$613$	2.99624	+	2.99624i	0.121017	+	0.121017i	0.765022	−	0.644005i	$-0.222728\pi$
$613$	2.99624	+	2.99624i	0.121017	+	0.121017i	−0.644005	+	0.765022i	$0.722728\pi$
$614$	16.3318	+	6.99141i	0.659097	+	0.282150i
$615$	14.3397	+	3.17247i	0.578234	+	0.127926i
$616$	12.6363	−	4.71814i	0.509129	−	0.190099i
$617$	−41.0538			−1.65276			−0.826382	−	0.563110i	$-0.809605\pi$
$617$	−41.0538			−1.65276			−0.826382	+	0.563110i	$0.809605\pi$
$618$	8.61450	+	3.68775i	0.346526	+	0.148343i
$619$	6.91185	−	6.91185i	0.277811	−	0.277811i	−0.554424	−	0.832235i	$-0.687061\pi$
$619$	6.91185	−	6.91185i	0.277811	−	0.277811i	0.832235	+	0.554424i	$0.187061\pi$
$620$	−10.3706	+	42.1417i	−0.416495	+	1.69245i
$621$	−14.2779	−	14.2779i	−0.572952	−	0.572952i
$622$	−36.8219	+	14.7463i	−1.47642	+	0.591271i
$623$		−	7.61855i		−	0.305231i
$624$	17.7399	+	0.836723i	0.710166	+	0.0334957i
$625$	−16.1031	−	19.1230i	−0.644125	−	0.764921i
$626$	−11.8818	−	29.6693i	−0.474893	−	1.18582i
$627$	−11.7301	+	11.7301i	−0.468454	+	0.468454i
$628$	−1.04183	+	44.2015i	−0.0415734	+	1.76383i
$629$	−1.99940	+	1.99940i	−0.0797212	+	0.0797212i
$630$	−1.47580	+	2.05757i	−0.0587972	+	0.0819755i
$631$		−	23.3061i		−	0.927800i	−0.885888	−	0.463900i	$-0.846450\pi$
$631$		−	23.3061i		−	0.927800i	0.885888	−	0.463900i	$-0.153550\pi$
$632$	−38.5856	−	17.6051i	−1.53485	−	0.700291i
$633$	8.29392			0.329654
$634$	−10.9415	−	4.68392i	−0.434544	−	0.186022i
$635$	15.8788	+	24.9007i	0.630131	+	0.988155i
$636$	−2.28856	+	2.18316i	−0.0907472	+	0.0865679i
$637$	−1.61037	+	1.61037i	−0.0638053	+	0.0638053i
$638$	22.1795	+	55.3828i	0.878093	+	2.19263i
$639$	11.0024			0.435248
$640$	2.33650	+	25.1901i	0.0923583	+	0.995726i
$641$	3.93565			0.155449			0.0777244	−	0.996975i	$-0.475235\pi$
$641$	3.93565			0.155449			0.0777244	+	0.996975i	$0.475235\pi$
$642$	−3.72962	−	9.31298i	−0.147196	−	0.367554i
$643$	−6.55701	+	6.55701i	−0.258583	+	0.258583i	−0.824478	−	0.565895i	$-0.808531\pi$
$643$	−6.55701	+	6.55701i	−0.258583	+	0.258583i	0.565895	+	0.824478i	$0.308531\pi$
$644$	−6.81519	+	6.50132i	−0.268556	+	0.256188i
$645$	15.3026	−	9.75821i	0.602538	−	0.384229i
$646$	3.66447	+	1.56871i	0.144177	+	0.0617201i
$647$	−2.68542			−0.105575			−0.0527874	−	0.998606i	$-0.516811\pi$
$647$	−2.68542			−0.105575			−0.0527874	+	0.998606i	$0.516811\pi$
$648$	27.6907	+	12.6341i	1.08779	+	0.496316i
$649$		−	8.89661i		−	0.349222i
$650$	11.9909	−	10.7494i	0.470322	−	0.421625i
$651$	13.3777	−	13.3777i	0.524315	−	0.524315i
$652$	0.939381	−	39.8551i	0.0367890	−	1.56084i
$653$	2.62232	−	2.62232i	0.102619	−	0.102619i	−0.653933	−	0.756552i	$-0.726882\pi$
$653$	2.62232	−	2.62232i	0.102619	−	0.102619i	0.756552	+	0.653933i	$0.226882\pi$
$654$	−10.5787	−	26.4153i	−0.413659	−	1.03292i
$655$	16.5013	+	3.65068i	0.644758	+	0.142644i
$656$	−13.4610	−	0.634901i	−0.525563	−	0.0247887i
$657$			2.82281i			0.110128i
$658$	−0.890153	+	0.356485i	−0.0347018	+	0.0138972i
$659$	−10.4906	−	10.4906i	−0.408656	−	0.408656i	0.472613	−	0.881270i	$-0.343311\pi$
$659$	−10.4906	−	10.4906i	−0.408656	−	0.408656i	−0.881270	+	0.472613i	$0.843311\pi$
$660$	40.3733	+	9.93546i	1.57153	+	0.386737i
$661$	−15.2476	+	15.2476i	−0.593063	+	0.593063i	−0.938458	−	0.345395i	$-0.887745\pi$
$661$	−15.2476	+	15.2476i	−0.593063	+	0.593063i	0.345395	+	0.938458i	$0.387745\pi$
$662$	−14.5004	−	6.20743i	−0.563575	−	0.241259i
$663$	−7.01362			−0.272387
$664$	45.8908	−	17.1348i	1.78091	−	0.664957i
$665$	3.89563	+	0.861855i	0.151066	+	0.0334213i
$666$	−1.86339	−	0.797692i	−0.0722049	−	0.0309099i
$667$	−29.4576	−	29.4576i	−1.14060	−	1.14060i
$668$	6.27341	−	5.98449i	0.242726	−	0.231547i
$669$	−14.3859	−	14.3859i	−0.556192	−	0.556192i
$670$	34.4083	−	5.66537i	1.32931	−	0.218872i
$671$	39.6585			1.53100
$672$	4.81294	−	9.92264i	0.185663	−	0.382774i
$673$		−	16.7113i		−	0.644175i	−0.946710	−	0.322088i	$-0.895615\pi$
$673$		−	16.7113i		−	0.644175i	0.946710	−	0.322088i	$-0.104385\pi$
$674$	−1.20528	+	0.482685i	−0.0464256	+	0.0185923i
$675$	20.1387	−	7.34980i	0.775138	−	0.282894i
$676$	−10.7864	−	11.3071i	−0.414860	−	0.434889i
$677$	−33.0407	−	33.0407i	−1.26986	−	1.26986i	−0.946161	−	0.323695i	$-0.895075\pi$
$677$	−33.0407	−	33.0407i	−1.26986	−	1.26986i	−0.323695	−	0.946161i	$-0.604925\pi$
$678$	9.94536	−	23.2321i	0.381949	−	0.892225i
$679$		−	11.2937i		−	0.433414i
$680$	−1.39039	−	9.89352i	−0.0533191	−	0.379399i
$681$			52.8857i			2.02658i
$682$	−60.1664	−	25.7564i	−2.30389	−	0.986263i
$683$	0.608455	+	0.608455i	0.0232819	+	0.0232819i	0.718652	−	0.695370i	$-0.244759\pi$
$683$	0.608455	+	0.608455i	0.0232819	+	0.0232819i	−0.695370	+	0.718652i	$0.744759\pi$
$684$	−0.0673315	+	2.85667i	−0.00257449	+	0.109228i
$685$	34.6832	−	22.1169i	1.32518	−	0.845044i
$686$	0.525764	+	1.31285i	0.0200738	+	0.0501248i
$687$		−	12.8017i		−	0.488415i
$688$	−12.3173	+	11.2077i	−0.469593	+	0.427291i
$689$	−1.84739			−0.0703800
$690$	−28.6478	+	4.71688i	−1.09060	+	0.179569i
$691$	−24.0607	−	24.0607i	−0.915311	−	0.915311i	0.0813725	−	0.996684i	$-0.474070\pi$
$691$	−24.0607	−	24.0607i	−0.915311	−	0.915311i	−0.996684	+	0.0813725i	$0.974070\pi$
$692$	−0.101691	+	4.31442i	−0.00386570	+	0.164010i
$693$	−2.70011	−	2.70011i	−0.102569	−	0.102569i
$694$	17.8976	−	41.8084i	0.679384	−	1.58703i
$695$	−7.19117	+	32.5044i	−0.272777	+	1.23296i
$696$	44.3772	+	20.2475i	1.68211	+	0.767481i
$697$	5.32190			0.201581
$698$	11.1631	−	26.0768i	0.422530	−	0.987020i
$699$	−0.988512	+	0.988512i	−0.0373889	+	0.0373889i
$700$	−3.20610	−	9.47211i	−0.121179	−	0.358012i
$701$	−10.0017	−	10.0017i	−0.377760	−	0.377760i	0.492533	−	0.870294i	$-0.336071\pi$
$701$	−10.0017	−	10.0017i	−0.377760	−	0.377760i	−0.870294	+	0.492533i	$0.836071\pi$
$702$	5.13388	+	12.8195i	0.193766	+	0.483839i
$703$			3.19386i			0.120459i
$704$	−38.0555	−	2.69489i	−1.43427	−	0.101568i
$705$	−2.88597	−	0.638482i	−0.108692	−	0.0240466i
$706$	−22.4624	+	8.99565i	−0.845384	+	0.338556i
$707$	7.18556	−	7.18556i	0.270241	−	0.270241i
$708$	−5.02087	−	5.26327i	−0.188696	−	0.197806i
$709$	−7.62379	+	7.62379i	−0.286317	+	0.286317i	−0.835622	−	0.549305i	$-0.814893\pi$
$709$	−7.62379	+	7.62379i	−0.286317	+	0.286317i	0.549305	+	0.835622i	$0.314893\pi$
$710$	−25.3250	+	35.3084i	−0.950431	+	1.32510i
$711$			12.0068i			0.450290i
$712$	−8.94468	+	19.6044i	−0.335216	+	0.734705i
$713$	45.7015			1.71154
$714$	−1.71399	+	4.00383i	−0.0641443	+	0.149840i
$715$	13.0573	+	20.4762i	0.488317	+	0.765766i
$716$	−24.8455	−	0.585607i	−0.928520	−	0.0218852i
$717$	34.7819	−	34.7819i	1.29895	−	1.29895i
$718$	27.6803	−	11.0853i	1.03302	−	0.413700i
$719$	35.0242			1.30618			0.653091	−	0.757279i	$-0.273472\pi$
$719$	35.0242			1.30618			0.653091	+	0.757279i	$0.273472\pi$
$720$	6.21330	−	3.56194i	0.231556	−	0.132746i
$721$	3.39877			0.126577
$722$	−20.7644	+	8.31562i	−0.772769	+	0.309475i
$723$	4.64851	−	4.64851i	0.172880	−	0.172880i
$724$	−0.317220	+	13.4587i	−0.0117894	+	0.500188i
$725$	41.5493	−	15.1638i	1.54310	−	0.563170i
$726$	−12.7403	+	29.7611i	−0.472838	+	1.10454i
$727$	−3.80857			−0.141252			−0.0706260	−	0.997503i	$-0.522500\pi$
$727$	−3.80857			−0.141252			−0.0706260	+	0.997503i	$0.522500\pi$
$728$	6.03457	−	2.25319i	0.223656	−	0.0835089i
$729$			16.4599i			0.609628i
$730$	−9.05882	−	6.49747i	−0.335282	−	0.240482i
$731$	4.65040	−	4.65040i	0.172001	−	0.172001i
$732$	23.4621	−	22.3816i	0.867186	−	0.827248i
$733$	−31.1423	+	31.1423i	−1.15027	+	1.15027i	−0.163769	+	0.986499i	$0.552365\pi$
$733$	−31.1423	+	31.1423i	−1.15027	+	1.15027i	−0.986499	+	0.163769i	$0.947635\pi$
$734$	−36.6527	+	14.6785i	−1.35288	+	0.541794i
$735$	−0.941670	+	4.25639i	−0.0347340	+	0.156999i
$736$	25.1701	−	8.72798i	0.927783	−	0.321718i
$737$			52.5879i			1.93710i
$738$	1.41831	+	3.54157i	0.0522088	+	0.130367i
$739$	9.37252	+	9.37252i	0.344774	+	0.344774i	0.858159	−	0.513385i	$-0.171609\pi$
$739$	9.37252	+	9.37252i	0.344774	+	0.344774i	−0.513385	+	0.858159i	$0.671609\pi$
$740$	6.84902	−	4.14380i	0.251775	−	0.152329i
$741$	−5.60181	+	5.60181i	−0.205788	+	0.205788i
$742$	−0.451465	+	1.05461i	−0.0165738	+	0.0387160i
$743$	19.4164			0.712320			0.356160	−	0.934425i	$-0.384086\pi$
$743$	19.4164			0.712320			0.356160	+	0.934425i	$0.384086\pi$
$744$	−50.1305	+	18.7178i	−1.83787	+	0.686227i
$745$	5.37766	−	24.3073i	0.197022	−	0.890550i
$746$	18.2879	−	42.7201i	0.669567	−	1.56409i
$747$	−9.80592	−	9.80592i	−0.358780	−	0.358780i
$748$	15.0623	+	0.355017i	0.550732	+	0.0129807i
$749$	−2.57292	−	2.57292i	−0.0940124	−	0.0940124i
$750$	8.28948	−	29.6895i	0.302689	−	1.08411i
$751$	38.7782			1.41503			0.707517	−	0.706696i	$-0.249815\pi$
$751$	38.7782			1.41503			0.707517	+	0.706696i	$0.249815\pi$
$752$	2.70911	+	0.127778i	0.0987913	+	0.00465959i
$753$		−	3.56424i		−	0.129888i
$754$	10.5920	+	26.4486i	0.385739	+	0.963202i
$755$	1.70964	+	2.68101i	0.0622201	+	0.0975719i
$756$	8.57280	+	0.202060i	0.311790	+	0.00734886i
$757$	12.8720	+	12.8720i	0.467841	+	0.467841i	0.901215	−	0.433373i	$-0.142677\pi$
$757$	12.8720	+	12.8720i	0.467841	+	0.467841i	−0.433373	+	0.901215i	$0.642677\pi$
$758$	−6.34016	−	2.71413i	−0.230285	−	0.0985818i
$759$		−	43.7838i		−	1.58925i
$760$	−9.01251	−	6.79148i	−0.326918	−	0.246353i
$761$			46.0148i			1.66803i	0.551739	+	0.834017i	$0.313965\pi$
$761$			46.0148i			1.66803i	−0.551739	+	0.834017i	$0.686035\pi$
$762$	−14.3304	+	33.4755i	−0.519136	+	1.21269i
$763$	−7.29780	−	7.29780i	−0.264198	−	0.264198i
$764$	3.10036	−	2.95757i	0.112167	−	0.107001i
$765$	−2.38475	+	1.52072i	−0.0862209	+	0.0549817i
$766$	−7.95184	+	3.18452i	−0.287312	+	0.115061i
$767$		−	4.24866i		−	0.153410i
$768$	−24.0347	+	19.8826i	−0.867277	+	0.717453i
$769$	19.6835			0.709807			0.354903	−	0.934903i	$-0.384514\pi$
$769$	19.6835			0.709807			0.354903	+	0.934903i	$0.384514\pi$
$770$	14.8801	−	2.45002i	0.536241	−	0.0882926i
$771$	−37.6708	−	37.6708i	−1.35668	−	1.35668i
$772$	−8.42030	−	8.82682i	−0.303053	−	0.317684i
$773$	19.7419	+	19.7419i	0.710066	+	0.710066i	0.966549	−	0.256483i	$-0.0825637\pi$
$773$	19.7419	+	19.7419i	0.710066	+	0.710066i	−0.256483	+	0.966549i	$0.582564\pi$
$774$	4.33407	+	1.85535i	0.155785	+	0.0666893i
$775$	−20.4677	+	43.9933i	−0.735221	+	1.58029i
$776$	−13.2596	+	29.0615i	−0.475992	+	1.04325i
$777$	−3.48963			−0.125190
$778$	16.2547	+	6.95842i	0.582760	+	0.249472i
$779$	4.25063	−	4.25063i	0.152295	−	0.152295i
$780$	19.2807	+	4.74478i	0.690359	+	0.169890i
$781$	−46.3345	−	46.3345i	−1.65798	−	1.65798i
$782$	−9.76671	+	3.91133i	−0.349257	+	0.139869i
$783$			37.9280i			1.35543i
$784$	0.188455	−	3.99556i	0.00673053	−	0.142699i
$785$	−10.6781	+	48.2654i	−0.381117	+	1.72267i
$786$	7.74698	+	19.3445i	0.276326	+	0.689994i
$787$	−14.8949	+	14.8949i	−0.530944	+	0.530944i	−0.920853	−	0.389909i	$-0.872506\pi$
$787$	−14.8949	+	14.8949i	−0.530944	+	0.530944i	0.389909	+	0.920853i	$0.372506\pi$
$788$	−26.5051	−	0.624723i	−0.944204	−	0.0222548i
$789$	32.9575	−	32.9575i	1.17332	−	1.17332i
$790$	−38.5316	−	27.6369i	−1.37089	−	0.983276i
$791$		−	9.16602i		−	0.325906i
$792$	3.77792	+	10.1181i	0.134243	+	0.359532i
$793$	18.9393			0.672555
$794$	−42.9295	−	18.3775i	−1.52351	−	0.652194i
$795$	−2.98156	+	1.90129i	−0.105745	+	0.0674319i
$796$	5.32019	+	5.57703i	0.188569	+	0.197673i
$797$	−16.3003	+	16.3003i	−0.577385	+	0.577385i	−0.934182	−	0.356797i	$-0.883869\pi$
$797$	−16.3003	+	16.3003i	−0.577385	+	0.577385i	0.356797	+	0.934182i	$0.383869\pi$
$798$	1.82891	+	4.56685i	0.0647428	+	0.161665i
$799$	−1.07107			−0.0378917
$800$	−2.87082	+	28.1382i	−0.101499	+	0.994836i
$801$	6.10035			0.215545
$802$	−2.71367	−	6.77612i	−0.0958231	−	0.239273i
$803$	11.8877	−	11.8877i	0.419508	−	0.419508i
$804$	29.6784	+	31.1112i	1.04668	+	1.09721i
$805$	−8.87891	+	5.66194i	−0.312940	+	0.199557i
$806$	−28.7330	−	12.3002i	−1.01208	−	0.433257i
$807$	43.1293			1.51822
$808$	−26.9265	+	10.0538i	−0.947270	+	0.353693i
$809$		−	44.9718i		−	1.58112i	−0.612382	−	0.790562i	$-0.709788\pi$
$809$		−	44.9718i		−	1.58112i	0.612382	−	0.790562i	$-0.290212\pi$
$810$	27.6519	+	19.8334i	0.971590	+	0.696875i
$811$	4.55557	−	4.55557i	0.159968	−	0.159968i	−0.622585	−	0.782552i	$-0.713917\pi$
$811$	4.55557	−	4.55557i	0.159968	−	0.159968i	0.782552	+	0.622585i	$0.213917\pi$
$812$	17.6871	+	0.416883i	0.620694	+	0.0146297i
$813$	9.59671	−	9.59671i	0.336571	−	0.336571i
$814$	4.48798	+	11.2066i	0.157304	+	0.392792i
$815$	9.62808	−	43.5194i	0.337257	−	1.52442i
$816$	9.11127	−	8.29049i	0.318958	−	0.290225i
$817$		−	7.42860i		−	0.259894i
$818$	11.9765	−	4.79628i	0.418747	−	0.167698i
$819$	−1.28946	−	1.28946i	−0.0450575	−	0.0450575i
$820$	−14.6301	−	3.60031i	−0.510904	−	0.125728i
$821$	−21.6442	+	21.6442i	−0.755386	+	0.755386i	−0.975479	−	0.220093i	$-0.929364\pi$
$821$	−21.6442	+	21.6442i	−0.755386	+	0.755386i	0.220093	+	0.975479i	$0.429364\pi$
$822$	46.6266	+	19.9602i	1.62629	+	0.696192i
$823$	−29.7953			−1.03860			−0.519299	−	0.854593i	$-0.673807\pi$
$823$	−29.7953			−1.03860			−0.519299	+	0.854593i	$0.673807\pi$
$824$	−8.74586	−	3.99038i	−0.304676	−	0.139012i
$825$	42.1473	+	19.6088i	1.46738	+	0.682691i
$826$	−2.42541	−	1.03829i	−0.0843909	−	0.0361266i
$827$	25.4195	+	25.4195i	0.883922	+	0.883922i	0.993931	−	0.110009i	$-0.0350879\pi$
$827$	25.4195	+	25.4195i	0.883922	+	0.883922i	−0.110009	+	0.993931i	$0.535088\pi$
$828$	−5.20576	−	5.45708i	−0.180913	−	0.189647i
$829$	−35.7939	−	35.7939i	−1.24318	−	1.24318i	−0.958676	−	0.284499i	$-0.908173\pi$
$829$	−35.7939	−	35.7939i	−1.24318	−	1.24318i	−0.284499	−	0.958676i	$-0.591827\pi$
$830$	54.0397	−	8.89768i	1.87574	−	0.308843i
$831$	34.6600			1.20234
$832$	−18.1738	−	1.28697i	−0.630063	−	0.0446177i
$833$			1.57967i			0.0547325i
$834$	−38.1050	+	15.2601i	−1.31947	+	0.528415i
$835$	8.17307	−	5.21184i	0.282841	−	0.180363i
$836$	12.3139	−	11.7468i	0.425884	−	0.406270i
$837$	−29.4214	−	29.4214i	−1.01695	−	1.01695i
$838$	−11.2875	+	26.3673i	−0.389920	+	0.910844i
$839$		−	6.50969i		−	0.224739i	−0.993666	−	0.112370i	$-0.964156\pi$
$839$		−	6.50969i		−	0.224739i	0.993666	−	0.112370i	$-0.0358441\pi$
$840$	7.42043	−	9.84714i	0.256029	−	0.339759i
$841$			49.2515i			1.69833i
$842$	25.0820	+	10.7373i	0.864383	+	0.370030i
$843$	28.1862	+	28.1862i	0.970784	+	0.970784i
$844$	−8.50621	−	0.200491i	−0.292796	−	0.00690118i
$845$	−9.39374	−	14.7310i	−0.323155	−	0.506763i
$846$	−0.285445	−	0.712766i	−0.00981381	−	0.0245054i
$847$			11.7420i			0.403458i
$848$	2.39991	−	2.18372i	0.0824133	−	0.0749892i
$849$	−12.9717			−0.445189
$850$	0.608939	−	11.1534i	0.0208864	−	0.382558i
$851$	−5.96071	−	5.96071i	−0.204330	−	0.204330i
$852$	−53.5609	−	1.26243i	−1.83497	−	0.0432500i
$853$	8.69719	+	8.69719i	0.297786	+	0.297786i	0.840146	−	0.542360i	$-0.182469\pi$
$853$	8.69719	+	8.69719i	0.297786	+	0.297786i	−0.542360	+	0.840146i	$0.682469\pi$
$854$	4.62838	−	10.8118i	0.158380	−	0.369972i
$855$	−0.690107	+	3.11932i	−0.0236012	+	0.106678i
$856$	3.59996	+	9.64152i	0.123044	+	0.329540i
$857$	21.4359			0.732237			0.366118	−	0.930568i	$-0.380687\pi$
$857$	21.4359			0.732237			0.366118	+	0.930568i	$0.380687\pi$
$858$	−11.7841	+	27.5273i	−0.402302	+	0.939768i
$859$	−25.7552	+	25.7552i	−0.878755	+	0.878755i	−0.993406	−	0.114650i	$-0.963425\pi$
$859$	−25.7552	+	25.7552i	−0.878755	+	0.878755i	0.114650	+	0.993406i	$0.463425\pi$
$860$	−15.9301	+	9.63807i	−0.543213	+	0.328655i
$861$	4.64427	+	4.64427i	0.158276	+	0.158276i
$862$	−0.175639	−	0.438576i	−0.00598228	−	0.0149379i
$863$			28.7151i			0.977474i	0.872431	+	0.488737i	$0.162542\pi$
$863$			28.7151i			0.977474i	−0.872431	+	0.488737i	$0.837458\pi$
$864$	−21.8226	−	10.5850i	−0.742421	−	0.360108i
$865$	−1.04227	+	4.71109i	−0.0354381	+	0.160182i
$866$	22.4094	−	8.97443i	0.761503	−	0.304963i
$867$	19.9952	−	19.9952i	0.679071	−	0.679071i
$868$	−14.0435	+	13.3968i	−0.476669	+	0.454716i
$869$	50.5643	−	50.5643i	1.71527	−	1.71527i
$870$	44.3151	+	31.7851i	1.50242	+	1.07762i
$871$			25.1139i			0.850952i
$872$	10.2109	+	27.3471i	0.345785	+	0.926090i
$873$	9.04316			0.306065
$874$	−4.67672	+	10.9247i	−0.158192	+	0.369534i
$875$	−1.47385	−	11.0828i	−0.0498251	−	0.374666i
$876$	0.323892	−	13.7417i	0.0109433	−	0.464291i
$877$	−24.1367	+	24.1367i	−0.815040	+	0.815040i	−0.985385	−	0.170345i	$-0.945512\pi$
$877$	−24.1367	+	24.1367i	−0.815040	+	0.815040i	0.170345	+	0.985385i	$0.445512\pi$
$878$	48.8841	−	19.5769i	1.64976	−	0.660688i
$879$	−45.8915			−1.54788
$880$	−41.1665	−	11.1657i	−1.38772	−	0.376396i
$881$	−21.2074			−0.714494			−0.357247	−	0.934010i	$-0.616285\pi$
$881$	−21.2074			−0.714494			−0.357247	+	0.934010i	$0.616285\pi$
$882$	−1.05123	+	0.420991i	−0.0353967	+	0.0141755i
$883$	−25.8335	+	25.8335i	−0.869367	+	0.869367i	−0.992402	−	0.123035i	$-0.960737\pi$
$883$	−25.8335	+	25.8335i	−0.869367	+	0.869367i	0.123035	+	0.992402i	$0.460737\pi$
$884$	7.19314	+	0.169542i	0.241932	+	0.00570231i
$885$	−4.37263	−	6.85704i	−0.146984	−	0.230497i
$886$	−4.66574	+	10.8991i	−0.156749	+	0.366162i
$887$	5.50472			0.184830			0.0924152	−	0.995721i	$-0.470541\pi$
$887$	5.50472			0.184830			0.0924152	+	0.995721i	$0.470541\pi$
$888$	8.97966	+	4.09706i	0.301338	+	0.137488i
$889$			13.2074i			0.442963i
$890$	−14.0416	+	19.5769i	−0.470676	+	0.656220i
$891$	−36.2871	+	36.2871i	−1.21566	+	1.21566i
$892$	14.4064	+	15.1019i	0.482361	+	0.505649i
$893$	−0.855468	+	0.855468i	−0.0286271	+	0.0286271i
$894$	28.4955	−	11.4117i	0.953031	−	0.381666i
$895$	−27.1298	−	6.00211i	−0.906850	−	0.200628i
$896$	−5.17599	+	10.0603i	−0.172918	+	0.336090i
$897$		−	20.9094i		−	0.698144i
$898$	1.54673	+	3.86223i	0.0516150	+	0.128884i
$899$	−60.7010	−	60.7010i	−2.02449	−	2.02449i
$900$	7.58454	−	2.56720i	0.252818	−	0.0855733i
$901$	−0.906086	+	0.906086i	−0.0301861	+	0.0301861i
$902$	8.94169	−	20.8876i	0.297726	−	0.695481i
$903$	8.11654			0.270102
$904$	−10.7615	+	23.5864i	−0.357923	+	0.784471i
$905$	−3.25131	+	14.6961i	−0.108077	+	0.488514i
$906$	−1.54292	+	3.60424i	−0.0512602	+	0.119743i
$907$	19.3883	+	19.3883i	0.643779	+	0.643779i	0.951482	−	0.307703i	$-0.0995605\pi$
$907$	19.3883	+	19.3883i	0.643779	+	0.643779i	−0.307703	+	0.951482i	$0.599560\pi$
$908$	1.27842	−	54.2393i	0.0424258	−	1.80000i
$909$	5.75364	+	5.75364i	0.190836	+	0.190836i
$910$	7.10613	−	1.17003i	0.235566	−	0.0387862i
$911$	−26.5835			−0.880749			−0.440375	−	0.897814i	$-0.645154\pi$
$911$	−26.5835			−0.880749			−0.440375	+	0.897814i	$0.645154\pi$
$912$	0.655555	−	13.8989i	0.0217076	−	0.460237i
$913$			82.5914i			2.73338i
$914$	13.5403	+	33.8105i	0.447872	+	1.11835i
$915$	30.5667	−	19.4919i	1.01051	−	0.644383i
$916$	−0.309458	+	13.1294i	−0.0102248	+	0.433807i
$917$	5.34433	+	5.34433i	0.176485	+	0.176485i
$918$	8.80554	+	3.76953i	0.290626	+	0.124413i
$919$		−	16.7137i		−	0.551335i	−0.961253	−	0.275668i	$-0.911101\pi$
$919$		−	16.7137i		−	0.551335i	0.961253	−	0.275668i	$-0.0888989\pi$
$920$	29.4951	−	4.14511i	0.972423	−	0.136660i
$921$			24.4901i			0.806978i
$922$	−10.3192	+	24.1055i	−0.339845	+	0.793871i
$923$	−22.1275	−	22.1275i	−0.728335	−	0.728335i
$924$	12.8346	+	13.4542i	0.422228	+	0.442612i
$925$	8.40745	−	3.06838i	0.276435	−	0.100888i
$926$	−28.2203	+	11.3015i	−0.927375	+	0.371391i
$927$			2.72147i			0.0893849i
$928$	−45.0236	−	21.8385i	−1.47797	−	0.716885i
$929$	−9.13147			−0.299594			−0.149797	−	0.988717i	$-0.547862\pi$
$929$	−9.13147			−0.299594			−0.149797	+	0.988717i	$0.547862\pi$
$930$	−59.0322	+	9.71971i	−1.93574	+	0.318722i
$931$	1.26169	+	1.26169i	0.0413503	+	0.0413503i
$932$	1.03771	−	0.989918i	0.0339913	−	0.0324258i
$933$	−38.6642	−	38.6642i	−1.26581	−	1.26581i
$934$	20.1937	+	8.64466i	0.660759	+	0.282862i
$935$	16.4471	+	3.63871i	0.537879	+	0.118998i
$936$	1.80418	+	4.83201i	0.0589716	+	0.157939i
$937$	42.5194			1.38905			0.694523	−	0.719470i	$-0.255615\pi$
$937$	42.5194			1.38905			0.694523	+	0.719470i	$0.255615\pi$
$938$	14.3366	+	6.13732i	0.468108	+	0.200391i
$939$	31.1537	−	31.1537i	1.01666	−	1.01666i
$940$	2.94440	+	0.724587i	0.0960358	+	0.0236334i
$941$	20.6231	+	20.6231i	0.672294	+	0.672294i	0.958244	−	0.285950i	$-0.0923092\pi$
$941$	20.6231	+	20.6231i	0.672294	+	0.672294i	−0.285950	+	0.958244i	$0.592309\pi$
$942$	−56.5816	+	22.6595i	−1.84353	+	0.738288i
$943$			15.8659i			0.516666i
$944$	5.02216	+	5.51936i	0.163457	+	0.179640i
$945$	9.36099	+	2.07099i	0.304513	+	0.0673694i
$946$	−10.4386	−	26.0655i	−0.339389	−	0.847464i
$947$	37.7361	−	37.7361i	1.22626	−	1.22626i	0.260892	−	0.965368i	$-0.415983\pi$
$947$	37.7361	−	37.7361i	1.22626	−	1.22626i	0.965368	−	0.260892i	$-0.0840165\pi$
$948$	1.37767	−	58.4504i	0.0447447	−	1.89838i
$949$	5.67710	−	5.67710i	0.184286	−	0.184286i
$950$	−8.42189	−	9.39461i	−0.273242	−	0.304802i
$951$		−	16.4073i		−	0.532042i
$952$	1.85464	−	4.06488i	0.0601093	−	0.131744i
$953$	−42.3431			−1.37163			−0.685815	−	0.727776i	$-0.740554\pi$
$953$	−42.3431			−1.37163			−0.685815	+	0.727776i	$0.740554\pi$
$954$	−0.844451	−	0.361498i	−0.0273401	−	0.0117039i
$955$	4.03918	−	2.57572i	0.130705	−	0.0833484i
$956$	−36.5130	+	34.8314i	−1.18091	+	1.12653i
$957$	−58.1538	+	58.1538i	−1.87985	+	1.87985i
$958$	9.45766	+	23.6161i	0.305563	+	0.763001i
$959$	18.3961			0.594040
$960$	−30.6557	+	16.6270i	−0.989410	+	0.536633i
$961$	63.1736			2.03786
$962$	2.14328	+	5.35184i	0.0691021	+	0.172550i
$963$	2.06019	−	2.06019i	0.0663888	−	0.0663888i
$964$	−4.87986	+	4.65512i	−0.157170	+	0.149931i
$965$	−7.33316	−	11.4997i	−0.236063	−	0.370188i
$966$	−11.9364	−	5.10982i	−0.384048	−	0.164406i
$967$	−9.39650			−0.302171			−0.151086	−	0.988521i	$-0.548277\pi$
$967$	−9.39650			−0.302171			−0.151086	+	0.988521i	$0.548277\pi$
$968$	13.7858	−	30.2149i	0.443094	−	0.971143i
$969$			5.49502i			0.176526i
$970$	−20.8153	+	29.0209i	−0.668339	+	0.931804i
$971$	8.47992	−	8.47992i	0.272134	−	0.272134i	−0.557825	−	0.829959i	$-0.688364\pi$
$971$	8.47992	−	8.47992i	0.272134	−	0.272134i	0.829959	+	0.557825i	$0.188364\pi$
$972$	−0.382495	+	16.2281i	−0.0122685	+	0.520516i
$973$	−10.5274	+	10.5274i	−0.337492	+	0.337492i
$974$	22.7587	+	56.8292i	0.729236	+	1.82093i
$975$	20.1278	+	9.36438i	0.644607	+	0.299900i
$976$	−24.6037	+	22.3873i	−0.787546	+	0.716601i
$977$			29.6359i			0.948136i	0.880488	+	0.474068i	$0.157215\pi$
$977$			29.6359i			0.948136i	−0.880488	+	0.474068i	$0.842785\pi$
$978$	51.0178	−	20.4314i	1.63137	−	0.653324i
$979$	−25.6904	−	25.6904i	−0.821069	−	0.821069i
$980$	1.06866	−	4.34258i	0.0341372	−	0.138718i
$981$	5.84352	−	5.84352i	0.186569	−	0.186569i
$982$	37.7017	+	16.1396i	1.20311	+	0.515035i
$983$	−23.9791			−0.764813			−0.382407	−	0.923994i	$-0.624905\pi$
$983$	−23.9791			−0.764813			−0.382407	+	0.923994i	$0.624905\pi$
$984$	−6.49814	−	17.4035i	−0.207153	−	0.554803i
$985$	−28.9420	−	6.40302i	−0.922168	−	0.204017i
$986$	18.1673	+	7.77715i	0.578563	+	0.247675i
$987$	−0.934691	−	0.934691i	−0.0297515	−	0.0297515i
$988$	5.88061	−	5.60978i	0.187087	−	0.178471i
$989$	13.8640	+	13.8640i	0.440850	+	0.440850i
$990$	1.96179	+	11.9148i	0.0623497	+	0.378678i
$991$	47.9535			1.52329			0.761647	−	0.647992i	$-0.224391\pi$
$991$	47.9535			1.52329			0.761647	+	0.647992i	$0.224391\pi$
$992$	51.8661	−	17.9851i	1.64675	−	0.571026i
$993$		−	21.7439i		−	0.690023i
$994$	−18.0393	+	7.22430i	−0.572172	+	0.229141i
$995$	4.63330	+	7.26582i	0.146885	+	0.230342i
$996$	46.6111	+	48.8614i	1.47693	+	1.54823i
$997$	−16.9952	−	16.9952i	−0.538245	−	0.538245i	0.384768	−	0.923013i	$-0.374281\pi$
$997$	−16.9952	−	16.9952i	−0.538245	−	0.538245i	−0.923013	+	0.384768i	$0.874281\pi$
$998$	14.2222	−	33.2228i	0.450197	−	1.05165i
$999$			7.67467i			0.242816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.c.29.15	✓	70
5.4	even	2		560.2.bb.d.29.21	yes	70
16.5	even	4		560.2.bb.d.309.21	yes	70
80.69	even	4	inner	560.2.bb.c.309.15	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.15	✓	70	1.1	even	1	trivial
560.2.bb.c.309.15	yes	70	80.69	even	4	inner
560.2.bb.d.29.21	yes	70	5.4	even	2
560.2.bb.d.309.21	yes	70	16.5	even	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.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.525764 - 1.31285i) q^{2} +(1.37854 - 1.37854i) q^{3} +(-1.44714 + 1.38050i) q^{4} +(-1.88536 + 1.20226i) q^{5} +(-2.53459 - 1.08502i) q^{6} -1.00000 q^{7} +(2.57324 + 1.17407i) q^{8} -0.800723i q^{9} +O(q^{10})\)	\(q+(-0.525764 - 1.31285i) q^{2} +(1.37854 - 1.37854i) q^{3} +(-1.44714 + 1.38050i) q^{4} +(-1.88536 + 1.20226i) q^{5} +(-2.53459 - 1.08502i) q^{6} -1.00000 q^{7} +(2.57324 + 1.17407i) q^{8} -0.800723i q^{9} +(2.56964 + 1.84308i) q^{10} +(-3.37209 + 3.37209i) q^{11} +(-0.0918757 + 3.89801i) q^{12} +(-1.61037 + 1.61037i) q^{13} +(0.525764 + 1.31285i) q^{14} +(-0.941670 + 4.25639i) q^{15} +(0.188455 - 3.99556i) q^{16} +1.57967i q^{17} +(-1.05123 + 0.420991i) q^{18} +(1.26169 + 1.26169i) q^{19} +(1.06866 - 4.34258i) q^{20} +(-1.37854 + 1.37854i) q^{21} +(6.19996 + 2.65412i) q^{22} -4.70941 q^{23} +(5.16580 - 1.92881i) q^{24} +(2.10913 - 4.53338i) q^{25} +(2.96085 + 1.26750i) q^{26} +(3.03178 + 3.03178i) q^{27} +(1.44714 - 1.38050i) q^{28} +(6.25506 + 6.25506i) q^{29} +(6.08310 - 1.00159i) q^{30} -9.70431 q^{31} +(-5.34465 + 1.85331i) q^{32} +9.29709i q^{33} +(2.07387 - 0.830536i) q^{34} +(1.88536 - 1.20226i) q^{35} +(1.10540 + 1.15876i) q^{36} +(1.26570 + 1.26570i) q^{37} +(0.993060 - 2.31977i) q^{38} +4.43992i q^{39} +(-6.26301 + 0.880176i) q^{40} -3.36899i q^{41} +(2.53459 + 1.08502i) q^{42} +(-2.94390 - 2.94390i) q^{43} +(0.224741 - 9.53506i) q^{44} +(0.962678 + 1.50965i) q^{45} +(2.47604 + 6.18274i) q^{46} +0.678032i q^{47} +(-5.24823 - 5.76781i) q^{48} +1.00000 q^{49} +(-7.06055 - 0.385484i) q^{50} +(2.17764 + 2.17764i) q^{51} +(0.107327 - 4.55356i) q^{52} +(0.573591 + 0.573591i) q^{53} +(2.38627 - 5.57427i) q^{54} +(2.30345 - 10.4117i) q^{55} +(-2.57324 - 1.17407i) q^{56} +3.47858 q^{57} +(4.92326 - 11.5006i) q^{58} +(-1.31915 + 1.31915i) q^{59} +(-4.51321 - 7.45959i) q^{60} +(-5.88041 - 5.88041i) q^{61} +(5.10217 + 12.7403i) q^{62} +0.800723i q^{63} +(5.24314 + 6.04231i) q^{64} +(1.10004 - 4.97222i) q^{65} +(12.2057 - 4.88807i) q^{66} +(7.79753 - 7.79753i) q^{67} +(-2.18074 - 2.28602i) q^{68} +(-6.49209 + 6.49209i) q^{69} +(-2.56964 - 1.84308i) q^{70} +13.7406i q^{71} +(0.940102 - 2.06045i) q^{72} -3.52533 q^{73} +(0.996215 - 2.32714i) q^{74} +(-3.34192 - 9.15695i) q^{75} +(-3.56762 - 0.0840885i) q^{76} +(3.37209 - 3.37209i) q^{77} +(5.82894 - 2.33435i) q^{78} -14.9949 q^{79} +(4.44840 + 7.75962i) q^{80} +10.7610 q^{81} +(-4.42297 + 1.77129i) q^{82} +(12.2463 - 12.2463i) q^{83} +(0.0918757 - 3.89801i) q^{84} +(-1.89918 - 2.97825i) q^{85} +(-2.31710 + 5.41269i) q^{86} +17.2456 q^{87} +(-12.6363 + 4.71814i) q^{88} +7.61855i q^{89} +(1.47580 - 2.05757i) q^{90} +(1.61037 - 1.61037i) q^{91} +(6.81519 - 6.50132i) q^{92} +(-13.3777 + 13.3777i) q^{93} +(0.890153 - 0.356485i) q^{94} +(-3.89563 - 0.861855i) q^{95} +(-4.81294 + 9.92264i) q^{96} +11.2937i q^{97} +(-0.525764 - 1.31285i) q^{98} +(2.70011 + 2.70011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8}+O(q^{10}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8	\( 70 q - 2 q^{2} - 2 q^{3} - 4 q^{5} - 70 q^{7} - 8 q^{8} + 6 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} + 18 q^{18} + 14 q^{19} + 20 q^{20} + 2 q^{21} + 12 q^{22} + 20 q^{24} - 6 q^{25} - 36 q^{26} - 8 q^{27} + 2 q^{29} + 28 q^{30} + 16 q^{31} + 8 q^{32} + 4 q^{34} + 4 q^{35} - 40 q^{36} - 10 q^{37} + 12 q^{38} + 44 q^{40} - 2 q^{43} - 24 q^{44} + 22 q^{45} - 16 q^{46} + 44 q^{48} + 70 q^{49} - 74 q^{50} + 8 q^{51} - 28 q^{52} + 30 q^{53} - 32 q^{54} - 6 q^{55} + 8 q^{56} + 76 q^{57} - 56 q^{58} + 2 q^{59} - 64 q^{60} + 30 q^{61} - 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} - 6 q^{67} + 36 q^{68} - 16 q^{69} - 6 q^{70} - 4 q^{72} + 36 q^{73} - 32 q^{74} - 98 q^{75} + 44 q^{76} + 2 q^{77} + 84 q^{78} - 40 q^{79} - 24 q^{80} - 82 q^{81} - 24 q^{82} - 10 q^{83} - 4 q^{84} - 32 q^{85} + 32 q^{86} + 4 q^{87} - 32 q^{88} + 158 q^{90} + 6 q^{91} + 92 q^{92} + 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} - 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q - 2 * q^2 - 2 * q^3 - 4 * q^5 - 70 * q^7 - 8 * q^8 + 6 * 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 + 20 * q^20 + 2 * q^21 + 12 * q^22 + 20 * q^24 - 6 * q^25 - 36 * q^26 - 8 * q^27 + 2 * q^29 + 28 * q^30 + 16 * q^31 + 8 * q^32 + 4 * q^34 + 4 * q^35 - 40 * q^36 - 10 * q^37 + 12 * q^38 + 44 * q^40 - 2 * q^43 - 24 * q^44 + 22 * q^45 - 16 * q^46 + 44 * q^48 + 70 * q^49 - 74 * 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 - 64 * 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 - 6 * q^70 - 4 * q^72 + 36 * q^73 - 32 * q^74 - 98 * q^75 + 44 * q^76 + 2 * q^77 + 84 * q^78 - 40 * q^79 - 24 * 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 + 158 * 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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