LMFDB - Embedded newform 560.2.bb.d.29.14

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			29.14
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.332249 + 1.37463i) q^{2} +(-1.50237 + 1.50237i) q^{3} +(-1.77922 - 0.913441i) q^{4} +(2.16429 + 0.562013i) q^{5} +(-1.56605 - 2.56437i) q^{6} +1.00000 q^{7} +(1.84679 - 2.14228i) q^{8} -1.51426i q^{9} +O(q^{10})$	\(q+(-0.332249 + 1.37463i) q^{2} +(-1.50237 + 1.50237i) q^{3} +(-1.77922 - 0.913441i) q^{4} +(2.16429 + 0.562013i) q^{5} +(-1.56605 - 2.56437i) q^{6} +1.00000 q^{7} +(1.84679 - 2.14228i) q^{8} -1.51426i q^{9} +(-1.49164 + 2.78837i) q^{10} +(-2.92887 + 2.92887i) q^{11} +(4.04539 - 1.30073i) q^{12} +(-2.02453 + 2.02453i) q^{13} +(-0.332249 + 1.37463i) q^{14} +(-4.09592 + 2.40722i) q^{15} +(2.33125 + 3.25043i) q^{16} +4.96537i q^{17} +(2.08155 + 0.503111i) q^{18} +(-5.51854 - 5.51854i) q^{19} +(-3.33738 - 2.97689i) q^{20} +(-1.50237 + 1.50237i) q^{21} +(-3.05300 - 4.99923i) q^{22} -5.25399 q^{23} +(0.443941 + 5.99308i) q^{24} +(4.36828 + 2.43272i) q^{25} +(-2.11033 - 3.45563i) q^{26} +(-2.23214 - 2.23214i) q^{27} +(-1.77922 - 0.913441i) q^{28} +(1.35682 + 1.35682i) q^{29} +(-1.94817 - 6.43018i) q^{30} +8.13059 q^{31} +(-5.24269 + 2.12466i) q^{32} -8.80052i q^{33} +(-6.82555 - 1.64974i) q^{34} +(2.16429 + 0.562013i) q^{35} +(-1.38318 + 2.69420i) q^{36} +(0.869503 + 0.869503i) q^{37} +(9.41949 - 5.75243i) q^{38} -6.08321i q^{39} +(5.20097 - 3.59859i) q^{40} -7.00115i q^{41} +(-1.56605 - 2.56437i) q^{42} +(-2.50309 - 2.50309i) q^{43} +(7.88645 - 2.53576i) q^{44} +(0.851032 - 3.27729i) q^{45} +(1.74564 - 7.22230i) q^{46} +8.48514i q^{47} +(-8.38577 - 1.38094i) q^{48} +1.00000 q^{49} +(-4.79545 + 5.19651i) q^{50} +(-7.45984 - 7.45984i) q^{51} +(5.45138 - 1.75280i) q^{52} +(-0.474781 - 0.474781i) q^{53} +(3.81000 - 2.32674i) q^{54} +(-7.98498 + 4.69285i) q^{55} +(1.84679 - 2.14228i) q^{56} +16.5818 q^{57} +(-2.31592 + 1.41432i) q^{58} +(-8.46993 + 8.46993i) q^{59} +(9.48640 - 0.541586i) q^{60} +(-6.66865 - 6.66865i) q^{61} +(-2.70138 + 11.1766i) q^{62} -1.51426i q^{63} +(-1.17874 - 7.91268i) q^{64} +(-5.51948 + 3.24386i) q^{65} +(12.0975 + 2.92397i) q^{66} +(-3.42923 + 3.42923i) q^{67} +(4.53557 - 8.83449i) q^{68} +(7.89346 - 7.89346i) q^{69} +(-1.49164 + 2.78837i) q^{70} +6.99090i q^{71} +(-3.24397 - 2.79651i) q^{72} -10.5753 q^{73} +(-1.48414 + 0.906354i) q^{74} +(-10.2176 + 2.90795i) q^{75} +(4.77784 + 14.8596i) q^{76} +(-2.92887 + 2.92887i) q^{77} +(8.36217 + 2.02114i) q^{78} +12.2244 q^{79} +(3.21872 + 8.34505i) q^{80} +11.2498 q^{81} +(9.62400 + 2.32613i) q^{82} +(8.65699 - 8.65699i) q^{83} +(4.04539 - 1.30073i) q^{84} +(-2.79060 + 10.7465i) q^{85} +(4.27248 - 2.60918i) q^{86} -4.07689 q^{87} +(0.865460 + 11.6835i) q^{88} -6.38032i q^{89} +(4.22231 + 2.25873i) q^{90} +(-2.02453 + 2.02453i) q^{91} +(9.34801 + 4.79921i) q^{92} +(-12.2152 + 12.2152i) q^{93} +(-11.6639 - 2.81918i) q^{94} +(-8.84222 - 15.0452i) q^{95} +(4.68445 - 11.0685i) q^{96} +6.64084i q^{97} +(-0.332249 + 1.37463i) q^{98} +(4.43506 + 4.43506i) 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 $

$2$	−0.332249	+	1.37463i	−0.234936	+	0.972011i
$2$	−0.332249	+	1.37463i	−0.234936	+	0.972011i
$3$	−1.50237	+	1.50237i	−0.867396	+	0.867396i	−0.992184	−	0.124787i	$-0.960175\pi$
$3$	−1.50237	+	1.50237i	−0.867396	+	0.867396i	0.124787	+	0.992184i	$0.460175\pi$
$4$	−1.77922	−	0.913441i	−0.889610	−	0.456720i
$5$	2.16429	+	0.562013i	0.967899	+	0.251340i
$5$	2.16429	+	0.562013i	0.967899	+	0.251340i
$6$	−1.56605	−	2.56437i	−0.639336	−	1.04690i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.84679	−	2.14228i	0.652938	−	0.757411i
$9$		−	1.51426i		−	0.504753i
$10$	−1.49164	+	2.78837i	−0.471699	+	0.881760i
$11$	−2.92887	+	2.92887i	−0.883087	+	0.883087i	−0.993847	−	0.110760i	$-0.964672\pi$
$11$	−2.92887	+	2.92887i	−0.883087	+	0.883087i	0.110760	+	0.993847i	$0.464672\pi$
$12$	4.04539	−	1.30073i	1.16780	−	0.375487i
$13$	−2.02453	+	2.02453i	−0.561504	+	0.561504i	−0.929735	−	0.368230i	$-0.879964\pi$
$13$	−2.02453	+	2.02453i	−0.561504	+	0.561504i	0.368230	+	0.929735i	$0.379964\pi$
$14$	−0.332249	+	1.37463i	−0.0887974	+	0.367386i
$15$	−4.09592	+	2.40722i	−1.05756	+	0.621541i
$16$	2.33125	+	3.25043i	0.582813	+	0.812606i
$17$			4.96537i			1.20428i	0.798391	+	0.602139i	$0.205685\pi$
$17$			4.96537i			1.20428i	−0.798391	+	0.602139i	$0.794315\pi$
$18$	2.08155	+	0.503111i	0.490625	+	0.118584i
$19$	−5.51854	−	5.51854i	−1.26604	−	1.26604i	−0.948116	−	0.317925i	$-0.897014\pi$
$19$	−5.51854	−	5.51854i	−1.26604	−	1.26604i	−0.317925	−	0.948116i	$-0.602986\pi$
$20$	−3.33738	−	2.97689i	−0.746261	−	0.665654i
$21$	−1.50237	+	1.50237i	−0.327845	+	0.327845i
$22$	−3.05300	−	4.99923i	−0.650902	−	1.06584i
$23$	−5.25399			−1.09553			−0.547766	−	0.836631i	$-0.684522\pi$
$23$	−5.25399			−1.09553			−0.547766	+	0.836631i	$0.684522\pi$
$24$	0.443941	+	5.99308i	0.0906190	+	1.22333i
$25$	4.36828	+	2.43272i	0.873657	+	0.486543i
$26$	−2.11033	−	3.45563i	−0.413871	−	0.677706i
$27$	−2.23214	−	2.23214i	−0.429576	−	0.429576i
$28$	−1.77922	−	0.913441i	−0.336241	−	0.172624i
$29$	1.35682	+	1.35682i	0.251955	+	0.251955i	0.821772	−	0.569817i	$-0.192986\pi$
$29$	1.35682	+	1.35682i	0.251955	+	0.251955i	−0.569817	+	0.821772i	$0.692986\pi$
$30$	−1.94817	−	6.43018i	−0.355685	−	1.17399i
$31$	8.13059			1.46030			0.730148	−	0.683289i	$-0.239451\pi$
$31$	8.13059			1.46030			0.730148	+	0.683289i	$0.239451\pi$
$32$	−5.24269	+	2.12466i	−0.926786	+	0.375590i
$33$		−	8.80052i		−	1.53197i
$34$	−6.82555	−	1.64974i	−1.17057	−	0.282928i
$35$	2.16429	+	0.562013i	0.365831	+	0.0949975i
$36$	−1.38318	+	2.69420i	−0.230531	+	0.449033i
$37$	0.869503	+	0.869503i	0.142945	+	0.142945i	0.774958	−	0.632013i	$-0.217771\pi$
$37$	0.869503	+	0.869503i	0.142945	+	0.142945i	−0.632013	+	0.774958i	$0.717771\pi$
$38$	9.41949	−	5.75243i	1.52804	−	0.933167i
$39$		−	6.08321i		−	0.974093i
$40$	5.20097	−	3.59859i	0.822346	−	0.568988i
$41$		−	7.00115i		−	1.09340i	−0.837330	−	0.546698i	$-0.815884\pi$
$41$		−	7.00115i		−	1.09340i	0.837330	−	0.546698i	$-0.184116\pi$
$42$	−1.56605	−	2.56437i	−0.241646	−	0.395691i
$43$	−2.50309	−	2.50309i	−0.381718	−	0.381718i	0.490003	−	0.871721i	$-0.336996\pi$
$43$	−2.50309	−	2.50309i	−0.381718	−	0.381718i	−0.871721	+	0.490003i	$0.836996\pi$
$44$	7.88645	−	2.53576i	1.18893	−	0.382280i
$45$	0.851032	−	3.27729i	0.126864	−	0.488549i
$46$	1.74564	−	7.22230i	0.257380	−	1.06487i
$47$			8.48514i			1.23768i	0.785515	+	0.618842i	$0.212398\pi$
$47$			8.48514i			1.23768i	−0.785515	+	0.618842i	$0.787602\pi$
$48$	−8.38577	−	1.38094i	−1.21038	−	0.199322i
$49$	1.00000			0.142857
$50$	−4.79545	+	5.19651i	−0.678178	+	0.734897i
$51$	−7.45984	−	7.45984i	−1.04459	−	1.04459i
$52$	5.45138	−	1.75280i	0.755970	−	0.243070i
$53$	−0.474781	−	0.474781i	−0.0652162	−	0.0652162i	0.673746	−	0.738963i	$-0.264684\pi$
$53$	−0.474781	−	0.474781i	−0.0652162	−	0.0652162i	−0.738963	+	0.673746i	$0.764684\pi$
$54$	3.81000	−	2.32674i	0.518475	−	0.316630i
$55$	−7.98498	+	4.69285i	−1.07669	+	0.632784i
$56$	1.84679	−	2.14228i	0.246788	−	0.286274i
$57$	16.5818			2.19632
$58$	−2.31592	+	1.41432i	−0.304096	+	0.185709i
$59$	−8.46993	+	8.46993i	−1.10269	+	1.10269i	−0.108606	+	0.994085i	$0.534639\pi$
$59$	−8.46993	+	8.46993i	−1.10269	+	1.10269i	−0.994085	+	0.108606i	$0.965361\pi$
$60$	9.48640	−	0.541586i	1.22469	−	0.0699185i
$61$	−6.66865	−	6.66865i	−0.853833	−	0.853833i	0.136770	−	0.990603i	$-0.456328\pi$
$61$	−6.66865	−	6.66865i	−0.853833	−	0.853833i	−0.990603	+	0.136770i	$0.956328\pi$
$62$	−2.70138	+	11.1766i	−0.343076	+	1.41942i
$63$		−	1.51426i		−	0.190779i
$64$	−1.17874	−	7.91268i	−0.147343	−	0.989085i
$65$	−5.51948	+	3.24386i	−0.684608	+	0.402351i
$66$	12.0975	+	2.92397i	1.48909	+	0.359915i
$67$	−3.42923	+	3.42923i	−0.418947	+	0.418947i	−0.884841	−	0.465894i	$-0.845733\pi$
$67$	−3.42923	+	3.42923i	−0.418947	+	0.418947i	0.465894	+	0.884841i	$0.345733\pi$
$68$	4.53557	−	8.83449i	0.550019	−	1.07134i
$69$	7.89346	−	7.89346i	0.950261	−	0.950261i
$70$	−1.49164	+	2.78837i	−0.178286	+	0.333274i
$71$			6.99090i			0.829667i	0.909897	+	0.414833i	$0.136160\pi$
$71$			6.99090i			0.829667i	−0.909897	+	0.414833i	$0.863840\pi$
$72$	−3.24397	−	2.79651i	−0.382305	−	0.329572i
$73$	−10.5753			−1.23774			−0.618871	−	0.785492i	$-0.712410\pi$
$73$	−10.5753			−1.23774			−0.618871	+	0.785492i	$0.712410\pi$
$74$	−1.48414	+	0.906354i	−0.172528	+	0.105362i
$75$	−10.2176	+	2.90795i	−1.17983	+	0.335781i
$76$	4.77784	+	14.8596i	0.548056	+	1.70451i
$77$	−2.92887	+	2.92887i	−0.333776	+	0.333776i
$78$	8.36217	+	2.02114i	0.946829	+	0.228849i
$79$	12.2244			1.37536			0.687678	−	0.726016i	$-0.258630\pi$
$79$	12.2244			1.37536			0.687678	+	0.726016i	$0.258630\pi$
$80$	3.21872	+	8.34505i	0.359864	+	0.933005i
$81$	11.2498			1.24998
$82$	9.62400	+	2.32613i	1.06279	+	0.256878i
$83$	8.65699	−	8.65699i	0.950229	−	0.950229i	−0.0485902	−	0.998819i	$-0.515473\pi$
$83$	8.65699	−	8.65699i	0.950229	−	0.950229i	0.998819	+	0.0485902i	$0.0154728\pi$
$84$	4.04539	−	1.30073i	0.441388	−	0.141921i
$85$	−2.79060	+	10.7465i	−0.302683	+	1.16562i
$86$	4.27248	−	2.60918i	0.460714	−	0.281355i
$87$	−4.07689			−0.437089
$88$	0.865460	+	11.6835i	0.0922583	+	1.24546i
$89$		−	6.38032i		−	0.676312i	−0.941090	−	0.338156i	$-0.890197\pi$
$89$		−	6.38032i		−	0.676312i	0.941090	−	0.338156i	$-0.109803\pi$
$90$	4.22231	+	2.25873i	0.445070	+	0.238091i
$91$	−2.02453	+	2.02453i	−0.212229	+	0.212229i
$92$	9.34801	+	4.79921i	0.974597	+	0.500352i
$93$	−12.2152	+	12.2152i	−1.26666	+	1.26666i
$94$	−11.6639	−	2.81918i	−1.20304	−	0.290776i
$95$	−8.84222	−	15.0452i	−0.907193	−	1.54361i
$96$	4.68445	−	11.0685i	0.478105	−	1.12968i
$97$			6.64084i			0.674275i	0.941455	+	0.337138i	$0.109459\pi$
$97$			6.64084i			0.674275i	−0.941455	+	0.337138i	$0.890541\pi$
$98$	−0.332249	+	1.37463i	−0.0335623	+	0.138859i
$99$	4.43506	+	4.43506i	0.445741	+	0.445741i
$100$	−5.55000	−	8.31850i	−0.555000	−	0.831850i
$101$	−5.79516	+	5.79516i	−0.576640	+	0.576640i	−0.933976	−	0.357336i	$-0.883685\pi$
$101$	−5.79516	+	5.79516i	−0.576640	+	0.576640i	0.357336	+	0.933976i	$0.383685\pi$
$102$	12.7331	−	7.77600i	1.26076	−	0.769939i
$103$	−10.1822			−1.00328			−0.501641	−	0.865076i	$-0.667270\pi$
$103$	−10.1822			−1.00328			−0.501641	+	0.865076i	$0.667270\pi$
$104$	0.598235	+	8.07600i	0.0586617	+	0.791917i
$105$	−4.09592	+	2.40722i	−0.399721	+	0.234920i
$106$	0.810395	−	0.494903i	0.0787125	−	0.0480692i
$107$	11.2130	+	11.2130i	1.08400	+	1.08400i	0.996132	+	0.0878732i	$0.0280070\pi$
$107$	11.2130	+	11.2130i	1.08400	+	1.08400i	0.0878732	+	0.996132i	$0.471993\pi$
$108$	1.93254	+	6.01040i	0.185959	+	0.578351i
$109$	6.71938	+	6.71938i	0.643600	+	0.643600i	0.951439	−	0.307839i	$-0.0996057\pi$
$109$	6.71938	+	6.71938i	0.643600	+	0.643600i	−0.307839	+	0.951439i	$0.599606\pi$
$110$	−3.79794	−	12.5356i	−0.362119	−	1.19522i
$111$	−2.61264			−0.247981
$112$	2.33125	+	3.25043i	0.220283	+	0.307136i
$113$			3.81671i			0.359046i	0.983754	+	0.179523i	$0.0574555\pi$
$113$			3.81671i			0.359046i	−0.983754	+	0.179523i	$0.942545\pi$
$114$	−5.50931	+	22.7939i	−0.515994	+	2.13485i
$115$	−11.3711	−	2.95281i	−1.06036	−	0.275351i
$116$	−1.17470	−	3.65345i	−0.109069	−	0.339214i
$117$	3.06566	+	3.06566i	0.283421	+	0.283421i
$118$	−8.82890	−	14.4572i	−0.812766	−	1.33089i
$119$			4.96537i			0.455175i
$120$	−2.40737	+	13.2202i	−0.219762	+	1.20684i
$121$		−	6.15655i		−	0.559686i
$122$	11.3826	−	6.95127i	1.03053	−	0.629339i
$123$	10.5184	+	10.5184i	0.948408	+	0.948408i
$124$	−14.4661	−	7.42681i	−1.29910	−	0.666947i
$125$	8.08700	+	7.72013i	0.723324	+	0.690509i
$126$	2.08155	+	0.503111i	0.185439	+	0.0448207i
$127$		−	5.36723i		−	0.476264i	−0.971233	−	0.238132i	$-0.923465\pi$
$127$		−	5.36723i		−	0.476264i	0.971233	−	0.238132i	$-0.0765352\pi$
$128$	11.2687	+	1.00865i	0.996018	+	0.0891529i
$129$	7.52117			0.662202
$130$	−2.62526	−	8.66502i	−0.230251	−	0.759973i
$131$	14.5779	+	14.5779i	1.27367	+	1.27367i	0.944145	+	0.329529i	$0.106890\pi$
$131$	14.5779	+	14.5779i	1.27367	+	1.27367i	0.329529	+	0.944145i	$0.393110\pi$
$132$	−8.03875	+	15.6581i	−0.699683	+	1.36286i
$133$	−5.51854	−	5.51854i	−0.478518	−	0.478518i
$134$	−3.57457	−	5.85328i	−0.308795	−	0.505647i
$135$	−3.57650	−	6.08549i	−0.307816	−	0.523755i
$136$	10.6372	+	9.16999i	0.912134	+	0.786320i
$137$	15.2183			1.30018			0.650092	−	0.759856i	$-0.274730\pi$
$137$	15.2183			1.30018			0.650092	+	0.759856i	$0.274730\pi$
$138$	8.22800	+	13.4732i	0.700414	+	1.14691i
$139$	−3.39093	+	3.39093i	−0.287615	+	0.287615i	−0.836136	−	0.548522i	$-0.815191\pi$
$139$	−3.39093	+	3.39093i	−0.287615	+	0.287615i	0.548522	+	0.836136i	$0.315191\pi$
$140$	−3.33738	−	2.97689i	−0.282060	−	0.251593i
$141$	−12.7479	−	12.7479i	−1.07356	−	1.07356i
$142$	−9.60990	−	2.32272i	−0.806445	−	0.194918i
$143$		−	11.8592i		−	0.991714i
$144$	4.92198	−	3.53012i	0.410165	−	0.294176i
$145$	2.17399	+	3.69909i	0.180540	+	0.307193i
$146$	3.51363	−	14.5371i	0.290790	−	1.20310i
$147$	−1.50237	+	1.50237i	−0.123914	+	0.123914i
$148$	−0.752798	−	2.34128i	−0.0618797	−	0.192452i
$149$	10.4463	−	10.4463i	0.855796	−	0.855796i	−0.135044	−	0.990840i	$-0.543118\pi$
$149$	10.4463	−	10.4463i	0.855796	−	0.855796i	0.990840	+	0.135044i	$0.0431175\pi$
$150$	−0.602548	−	15.0117i	−0.0491979	−	1.22570i
$151$			1.38811i			0.112963i	0.998404	+	0.0564814i	$0.0179882\pi$
$151$			1.38811i			0.112963i	−0.998404	+	0.0564814i	$0.982012\pi$
$152$	−22.0139	+	1.63069i	−1.78556	+	0.132266i
$153$	7.51885			0.607863
$154$	−3.05300	−	4.99923i	−0.246018	−	0.402849i
$155$	17.5969	+	4.56950i	1.41342	+	0.367031i
$156$	−5.55665	+	10.8234i	−0.444888	+	0.866563i
$157$	−14.3749	+	14.3749i	−1.14724	+	1.14724i	−0.160151	+	0.987093i	$0.551198\pi$
$157$	−14.3749	+	14.3749i	−1.14724	+	1.14724i	−0.987093	+	0.160151i	$0.948802\pi$
$158$	−4.06156	+	16.8041i	−0.323120	+	1.33686i
$159$	1.42660			0.113137
$160$	−12.5408	+	1.65191i	−0.991436	+	0.130595i
$161$	−5.25399			−0.414072
$162$	−3.73774	+	15.4643i	−0.293664	+	1.21499i
$163$	−3.29809	+	3.29809i	−0.258326	+	0.258326i	−0.824373	−	0.566047i	$-0.808472\pi$
$163$	−3.29809	+	3.29809i	−0.258326	+	0.258326i	0.566047	+	0.824373i	$0.308472\pi$
$164$	−6.39514	+	12.4566i	−0.499376	+	0.972697i
$165$	4.94600	−	19.0468i	0.385046	−	1.48280i
$166$	9.02389	+	14.7765i	0.700390	+	1.14688i
$167$	1.06759			0.0826124			0.0413062	−	0.999147i	$-0.486848\pi$
$167$	1.06759			0.0826124			0.0413062	+	0.999147i	$0.486848\pi$
$168$	0.443941	+	5.99308i	0.0342508	+	0.462376i
$169$			4.80254i			0.369426i
$170$	−13.8453	−	7.40656i	−1.06188	−	0.568057i
$171$	−8.35650	+	8.35650i	−0.639037	+	0.639037i
$172$	2.16713	+	6.73999i	0.165242	+	0.513919i
$173$	−5.55294	+	5.55294i	−0.422182	+	0.422182i	−0.885954	−	0.463772i	$-0.846496\pi$
$173$	−5.55294	+	5.55294i	−0.422182	+	0.422182i	0.463772	+	0.885954i	$0.346496\pi$
$174$	1.35455	−	5.60422i	0.102688	−	0.424855i
$175$	4.36828	+	2.43272i	0.330211	+	0.183896i
$176$	−16.3480	−	2.69214i	−1.23228	−	0.202927i
$177$		−	25.4500i		−	1.91294i
$178$	8.77058	+	2.11986i	0.657383	+	0.158890i
$179$	2.65008	+	2.65008i	0.198076	+	0.198076i	0.799175	−	0.601099i	$-0.205270\pi$
$179$	2.65008	+	2.65008i	0.198076	+	0.198076i	−0.601099	+	0.799175i	$0.705270\pi$
$180$	−4.50778	+	5.05365i	−0.335990	+	0.376677i
$181$	3.40764	−	3.40764i	0.253288	−	0.253288i	−0.569029	−	0.822317i	$-0.692681\pi$
$181$	3.40764	−	3.40764i	0.253288	−	0.253288i	0.822317	+	0.569029i	$0.192681\pi$
$182$	−2.11033	−	3.45563i	−0.156428	−	0.256149i
$183$	20.0376			1.48122
$184$	−9.70301	+	11.2555i	−0.715315	+	0.829768i
$185$	1.39318	+	2.37053i	0.102429	+	0.174285i
$186$	−12.7329	−	20.8499i	−0.933621	−	1.52879i
$187$	−14.5429	−	14.5429i	−1.06348	−	1.06348i
$188$	7.75067	−	15.0969i	0.565276	−	1.10106i
$189$	−2.23214	−	2.23214i	−0.162364	−	0.162364i
$190$	23.6194	−	7.15603i	1.71353	−	0.519153i
$191$	9.89168			0.715737			0.357869	−	0.933772i	$-0.383504\pi$
$191$	9.89168			0.715737			0.357869	+	0.933772i	$0.383504\pi$
$192$	13.6587	+	10.1169i	0.985734	+	0.730125i
$193$			3.20311i			0.230565i	0.993333	+	0.115282i	$0.0367773\pi$
$193$			3.20311i			0.230565i	−0.993333	+	0.115282i	$0.963223\pi$
$194$	−9.12870	−	2.20641i	−0.655403	−	0.158411i
$195$	3.41884	−	13.1658i	0.244828	−	0.942824i
$196$	−1.77922	−	0.913441i	−0.127087	−	0.0652458i
$197$	2.06335	+	2.06335i	0.147008	+	0.147008i	0.776780	−	0.629772i	$-0.216852\pi$
$197$	2.06335	+	2.06335i	0.147008	+	0.147008i	−0.629772	+	0.776780i	$0.716852\pi$
$198$	−7.57012	+	4.62303i	−0.537985	+	0.328544i
$199$			12.1674i			0.862527i	0.902226	+	0.431264i	$0.141932\pi$
$199$			12.1674i			0.862527i	−0.902226	+	0.431264i	$0.858068\pi$
$200$	13.2789	−	4.86538i	0.938957	−	0.344034i
$201$		−	10.3040i		−	0.726786i
$202$	−6.04077	−	9.89165i	−0.425027	−	0.695974i
$203$	1.35682	+	1.35682i	0.0952299	+	0.0952299i
$204$	6.45858	+	20.0868i	0.452191	+	1.40636i
$205$	3.93474	−	15.1525i	0.274814	−	1.05830i
$206$	3.38303	−	13.9968i	0.235707	−	0.975201i
$207$			7.95589i			0.552973i
$208$	−11.3003	−	1.86089i	−0.783534	−	0.129030i
$209$	32.3262			2.23605
$210$	−1.94817	−	6.43018i	−0.134436	−	0.443725i
$211$	17.8479	+	17.8479i	1.22870	+	1.22870i	0.964457	+	0.264240i	$0.0851211\pi$
$211$	17.8479	+	17.8479i	1.22870	+	1.22870i	0.264240	+	0.964457i	$0.414879\pi$
$212$	0.411056	+	1.27842i	0.0282314	+	0.0878026i
$213$	−10.5029	−	10.5029i	−0.719650	−	0.719650i
$214$	−19.1393	+	11.6883i	−1.30834	+	0.798993i
$215$	−4.01065	−	6.82419i	−0.273524	−	0.465406i
$216$	−8.90417	+	0.659582i	−0.605852	+	0.0448789i
$217$	8.13059			0.551940
$218$	−11.4692	+	7.00416i	−0.776791	+	0.474382i
$219$	15.8880	−	15.8880i	1.07361	−	1.07361i
$220$	18.4937	−	1.05582i	1.24684	−	0.0711833i
$221$	−10.0525	−	10.0525i	−0.676208	−	0.676208i
$222$	0.868048	−	3.59141i	0.0582595	−	0.241040i
$223$		−	26.2737i		−	1.75942i	−0.475514	−	0.879708i	$-0.657738\pi$
$223$		−	26.2737i		−	1.75942i	0.475514	−	0.879708i	$-0.342262\pi$
$224$	−5.24269	+	2.12466i	−0.350292	+	0.141960i
$225$	3.68376	−	6.61471i	0.245584	−	0.440980i
$226$	−5.24657	−	1.26810i	−0.348997	−	0.0843528i
$227$	4.33323	−	4.33323i	0.287607	−	0.287607i	−0.548526	−	0.836133i	$-0.684811\pi$
$227$	4.33323	−	4.33323i	0.287607	−	0.287607i	0.836133	+	0.548526i	$0.184811\pi$
$228$	−29.5027	−	15.1465i	−1.95387	−	1.00310i
$229$	−5.89007	+	5.89007i	−0.389227	+	0.389227i	−0.874412	−	0.485185i	$-0.838752\pi$
$229$	−5.89007	+	5.89007i	−0.389227	+	0.389227i	0.485185	+	0.874412i	$0.338752\pi$
$230$	7.83708	−	14.6501i	0.516762	−	0.965996i
$231$		−	8.80052i		−	0.579031i
$232$	5.41244	−	0.400930i	0.355344	−	0.0263223i
$233$	10.5422			0.690643			0.345322	−	0.938484i	$-0.387770\pi$
$233$	10.5422			0.690643			0.345322	+	0.938484i	$0.387770\pi$
$234$	−5.23272	+	3.19559i	−0.342074	+	0.208902i
$235$	−4.76876	+	18.3643i	−0.311079	+	1.19795i
$236$	22.8066	−	7.33309i	1.48459	−	0.477344i
$237$	−18.3657	+	18.3657i	−1.19298	+	1.19298i
$238$	−6.82555	−	1.64974i	−0.442435	−	0.106937i
$239$	−7.21958			−0.466996			−0.233498	−	0.972357i	$-0.575017\pi$
$239$	−7.21958			−0.466996			−0.233498	+	0.972357i	$0.575017\pi$
$240$	−17.3731	−	7.70167i	−1.12143	−	0.497140i
$241$	9.18389			0.591586			0.295793	−	0.955252i	$-0.404416\pi$
$241$	9.18389			0.591586			0.295793	+	0.955252i	$0.404416\pi$
$242$	8.46298	+	2.04551i	0.544021	+	0.131490i
$243$	−10.2050	+	10.2050i	−0.654650	+	0.654650i
$244$	5.77358	+	17.9564i	0.369616	+	1.14954i
$245$	2.16429	+	0.562013i	0.138271	+	0.0359057i
$246$	−17.9536	+	10.9641i	−1.14468	+	0.699048i
$247$	22.3449			1.42177
$248$	15.0155	−	17.4180i	0.953484	−	1.10604i
$249$			26.0121i			1.64845i
$250$	−13.2992	+	8.55164i	−0.841117	+	0.540853i
$251$	−8.36861	+	8.36861i	−0.528222	+	0.528222i	−0.920042	−	0.391820i	$-0.871846\pi$
$251$	−8.36861	+	8.36861i	−0.528222	+	0.528222i	0.391820	+	0.920042i	$0.371846\pi$
$252$	−1.38318	+	2.69420i	−0.0871324	+	0.169719i
$253$	15.3882	−	15.3882i	0.967451	−	0.967451i
$254$	7.37796	+	1.78326i	0.462934	+	0.111892i
$255$	−11.9527	−	20.3378i	−0.748508	−	1.27360i
$256$	−5.13053	+	15.1551i	−0.320658	+	0.947195i
$257$		−	18.1146i		−	1.12996i	−0.825105	−	0.564979i	$-0.808884\pi$
$257$		−	18.1146i		−	1.12996i	0.825105	−	0.564979i	$-0.191116\pi$
$258$	−2.49890	+	10.3388i	−0.155575	+	0.643668i
$259$	0.869503	+	0.869503i	0.0540283	+	0.0540283i
$260$	12.7834	−	0.729817i	0.792796	−	0.0452613i
$261$	2.05457	−	2.05457i	0.127175	−	0.127175i
$262$	−24.8827	+	15.1957i	−1.53726	+	0.938794i
$263$	6.91489			0.426390			0.213195	−	0.977010i	$-0.431613\pi$
$263$	6.91489			0.426390			0.213195	+	0.977010i	$0.431613\pi$
$264$	−18.8532	−	16.2527i	−1.16033	−	1.00028i
$265$	−0.760730	−	1.29440i	−0.0467313	−	0.0795141i
$266$	9.41949	−	5.75243i	0.577546	−	0.352704i
$267$	9.58562	+	9.58562i	0.586631	+	0.586631i
$268$	9.23375	−	2.96896i	0.564041	−	0.181358i
$269$	−9.37532	−	9.37532i	−0.571623	−	0.571623i	0.360958	−	0.932582i	$-0.382450\pi$
$269$	−9.37532	−	9.37532i	−0.571623	−	0.571623i	−0.932582	+	0.360958i	$0.882450\pi$
$270$	9.55359	−	2.89447i	0.581413	−	0.176152i
$271$	−3.79646			−0.230618			−0.115309	−	0.993330i	$-0.536786\pi$
$271$	−3.79646			−0.230618			−0.115309	+	0.993330i	$0.536786\pi$
$272$	−16.1396	+	11.5755i	−0.978605	+	0.701869i
$273$		−	6.08321i		−	0.368173i
$274$	−5.05626	+	20.9195i	−0.305460	+	1.26379i
$275$	−19.9192	+	5.66902i	−1.20117	+	0.341855i
$276$	−21.2544	+	6.83400i	−1.27937	+	0.411358i
$277$	−1.04385	−	1.04385i	−0.0627189	−	0.0627189i	0.675052	−	0.737770i	$-0.264121\pi$
$277$	−1.04385	−	1.04385i	−0.0627189	−	0.0627189i	−0.737770	+	0.675052i	$0.764121\pi$
$278$	−3.53464	−	5.78791i	−0.211994	−	0.347136i
$279$		−	12.3118i		−	0.737089i
$280$	5.20097	−	3.59859i	0.310818	−	0.215057i
$281$			18.8305i			1.12334i	0.827363	+	0.561668i	$0.189840\pi$
$281$			18.8305i			1.12334i	−0.827363	+	0.561668i	$0.810160\pi$
$282$	21.7591	−	13.2881i	1.29573	−	0.791296i
$283$	10.6476	+	10.6476i	0.632934	+	0.632934i	0.948803	−	0.315869i	$-0.102296\pi$
$283$	10.6476	+	10.6476i	0.632934	+	0.632934i	−0.315869	+	0.948803i	$0.602296\pi$
$284$	6.38577	−	12.4383i	0.378926	−	0.738080i
$285$	35.8879	+	9.31921i	2.12581	+	0.552022i
$286$	16.3020	+	3.94020i	0.963957	+	0.232989i
$287$		−	7.00115i		−	0.413265i
$288$	3.21728	+	7.93879i	0.189580	+	0.467798i
$289$	−7.65489			−0.450287
$290$	−5.80719	+	1.75942i	−0.341010	+	0.103317i
$291$	−9.97703	−	9.97703i	−0.584864	−	0.584864i
$292$	18.8157	+	9.65989i	1.10111	+	0.565302i
$293$	11.5095	+	11.5095i	0.672391	+	0.672391i	0.958267	−	0.285876i	$-0.0922845\pi$
$293$	11.5095	+	11.5095i	0.672391	+	0.672391i	−0.285876	+	0.958267i	$0.592284\pi$
$294$	−1.56605	−	2.56437i	−0.0913337	−	0.149557i
$295$	−23.0916	+	13.5712i	−1.34444	+	0.790143i
$296$	3.46851	−	0.256932i	0.201603	−	0.0149339i
$297$	13.0753			0.758706
$298$	10.8890	+	17.8306i	0.630786	+	1.03290i
$299$	10.6369	−	10.6369i	0.615146	−	0.615146i
$300$	20.8357	+	4.15933i	1.20295	+	0.240139i
$301$	−2.50309	−	2.50309i	−0.144276	−	0.144276i
$302$	−1.90814	−	0.461199i	−0.109801	−	0.0265390i
$303$		−	17.4130i		−	1.00035i
$304$	5.07250	−	30.8027i	0.290928	−	1.76666i
$305$	−10.6850	−	18.1807i	−0.611821	−	1.04103i
$306$	−2.49813	+	10.3356i	−0.142809	+	0.590849i
$307$	−6.14667	+	6.14667i	−0.350809	+	0.350809i	−0.860411	−	0.509601i	$-0.829793\pi$
$307$	−6.14667	+	6.14667i	−0.350809	+	0.350809i	0.509601	+	0.860411i	$0.329793\pi$
$308$	7.88645	−	2.53576i	0.449372	−	0.144488i
$309$	15.2975	−	15.2975i	0.870243	−	0.870243i
$310$	−12.1279	+	22.6711i	−0.688821	+	1.28763i
$311$		−	1.08604i		−	0.0615837i	−0.999526	−	0.0307919i	$-0.990197\pi$
$311$		−	1.08604i		−	0.0615837i	0.999526	−	0.0307919i	$-0.00980291\pi$
$312$	−13.0319	−	11.2344i	−0.737789	−	0.636023i
$313$	−18.3061			−1.03472			−0.517361	−	0.855767i	$-0.673086\pi$
$313$	−18.3061			−1.03472			−0.517361	+	0.855767i	$0.673086\pi$
$314$	−14.9841	−	24.5363i	−0.845604	−	1.38466i
$315$	0.851032	−	3.27729i	0.0479502	−	0.184654i
$316$	−21.7500	−	11.1663i	−1.22353	−	0.628153i
$317$	−1.69600	+	1.69600i	−0.0952567	+	0.0952567i	−0.753129	−	0.657873i	$-0.771457\pi$
$317$	−1.69600	+	1.69600i	−0.0952567	+	0.0952567i	0.657873	+	0.753129i	$0.271457\pi$
$318$	−0.473986	+	1.96105i	−0.0265798	+	0.109970i
$319$	−7.94788			−0.444996
$320$	1.89589	−	17.7878i	0.105984	−	0.994368i
$321$	−33.6923			−1.88052
$322$	1.74564	−	7.22230i	0.0972804	−	0.402483i
$323$	27.4016	−	27.4016i	1.52467	−	1.52467i
$324$	−20.0159	−	10.2760i	−1.11199	−	0.570890i
$325$	−13.7688	+	3.91862i	−0.763758	+	0.217366i
$326$	−3.43787	−	5.62945i	−0.190406	−	0.311786i
$327$	−20.1901			−1.11651
$328$	−14.9984	−	12.9297i	−0.828150	−	0.713921i
$329$			8.48514i			0.467801i
$330$	24.5391	+	13.1272i	1.35083	+	0.722630i
$331$	−5.68839	+	5.68839i	−0.312662	+	0.312662i	−0.845940	−	0.533278i	$-0.820960\pi$
$331$	−5.68839	+	5.68839i	−0.312662	+	0.312662i	0.533278	+	0.845940i	$0.320960\pi$
$332$	−23.3104	+	7.49505i	−1.27932	+	0.411344i
$333$	1.31665	−	1.31665i	0.0721521	−	0.0721521i
$334$	−0.354705	+	1.46754i	−0.0194086	+	0.0803001i
$335$	−9.34911	+	5.49457i	−0.510796	+	0.300200i
$336$	−8.38577	−	1.38094i	−0.457481	−	0.0753365i
$337$			2.83036i			0.154180i	0.997024	+	0.0770898i	$0.0245628\pi$
$337$			2.83036i			0.154180i	−0.997024	+	0.0770898i	$0.975437\pi$
$338$	−6.60172	−	1.59564i	−0.359086	−	0.0867914i
$339$	−5.73413	−	5.73413i	−0.311435	−	0.311435i
$340$	14.7814	−	16.5713i	0.801633	−	0.898706i
$341$	−23.8134	+	23.8134i	−1.28957	+	1.28957i
$342$	−8.71066	−	14.2635i	−0.471019	−	0.771284i
$343$	1.00000			0.0539949
$344$	−9.98502	+	0.739646i	−0.538356	+	0.0398791i
$345$	21.5199	−	12.6475i	1.15859	−	0.680918i
$346$	−5.78828	−	9.47821i	−0.311180	−	0.509552i
$347$	−20.6932	−	20.6932i	−1.11087	−	1.11087i	−0.993033	−	0.117838i	$-0.962404\pi$
$347$	−20.6932	−	20.6932i	−1.11087	−	1.11087i	−0.117838	−	0.993033i	$-0.537596\pi$
$348$	7.25369	+	3.72400i	0.388839	+	0.199627i
$349$	−6.86051	−	6.86051i	−0.367235	−	0.367235i	0.499233	−	0.866468i	$-0.333615\pi$
$349$	−6.86051	−	6.86051i	−0.367235	−	0.367235i	−0.866468	+	0.499233i	$0.833615\pi$
$350$	−4.79545	+	5.19651i	−0.256327	+	0.277765i
$351$	9.03808			0.482417
$352$	9.13231	−	21.5780i	0.486754	−	1.15011i
$353$			5.77946i			0.307610i	0.988101	+	0.153805i	$0.0491527\pi$
$353$			5.77946i			0.307610i	−0.988101	+	0.153805i	$0.950847\pi$
$354$	34.9844	+	8.45575i	1.85940	+	0.449418i
$355$	−3.92897	+	15.1303i	−0.208528	+	0.803034i
$356$	−5.82804	+	11.3520i	−0.308886	+	0.601654i
$357$	−7.45984	−	7.45984i	−0.394817	−	0.394817i
$358$	−4.52337	+	2.76239i	−0.239067	+	0.145997i
$359$		−	9.64690i		−	0.509144i	−0.967054	−	0.254572i	$-0.918065\pi$
$359$		−	9.64690i		−	0.509144i	0.967054	−	0.254572i	$-0.0819345\pi$
$360$	−5.44920	−	7.87561i	−0.287198	−	0.415081i
$361$			41.9087i			2.20572i
$362$	3.55206	+	5.81643i	0.186692	+	0.305705i
$363$	9.24944	+	9.24944i	0.485470	+	0.485470i
$364$	5.45138	−	1.75280i	0.285730	−	0.0918716i
$365$	−22.8879	−	5.94344i	−1.19801	−	0.311094i
$366$	−6.65748	+	27.5443i	−0.347992	+	1.43976i
$367$		−	23.6835i		−	1.23627i	−0.786073	−	0.618134i	$-0.787889\pi$
$367$		−	23.6835i		−	1.23627i	0.786073	−	0.618134i	$-0.212111\pi$
$368$	−12.2484	−	17.0777i	−0.638491	−	0.890237i
$369$	−10.6016			−0.551895
$370$	−3.72148	+	1.12751i	−0.193471	+	0.0586163i
$371$	−0.474781	−	0.474781i	−0.0246494	−	0.0246494i
$372$	32.8914	−	10.5757i	1.70534	−	0.548323i
$373$	−9.30159	−	9.30159i	−0.481618	−	0.481618i	0.424030	−	0.905648i	$-0.360615\pi$
$373$	−9.30159	−	9.30159i	−0.481618	−	0.481618i	−0.905648	+	0.424030i	$0.860615\pi$
$374$	24.8230	−	15.1593i	1.28357	−	0.783867i
$375$	−23.7482	+	0.551188i	−1.22635	+	0.0284632i
$376$	18.1776	+	15.6703i	0.937436	+	0.808132i
$377$	−5.49384			−0.282947
$378$	3.81000	−	2.32674i	0.195965	−	0.119675i
$379$	20.3601	−	20.3601i	1.04583	−	1.04583i	0.0469287	−	0.998898i	$-0.485057\pi$
$379$	20.3601	−	20.3601i	1.04583	−	1.04583i	0.998898	−	0.0469287i	$-0.0149433\pi$
$380$	1.98936	+	34.8456i	0.102052	+	1.78754i
$381$	8.06358	+	8.06358i	0.413110	+	0.413110i
$382$	−3.28651	+	13.5974i	−0.168152	+	0.695704i
$383$			21.8114i			1.11451i	0.830341	+	0.557256i	$0.188146\pi$
$383$			21.8114i			1.11451i	−0.830341	+	0.557256i	$0.811854\pi$
$384$	−18.4451	+	15.4144i	−0.941273	+	0.786611i
$385$	−7.98498	+	4.69285i	−0.406952	+	0.239170i
$386$	−4.40309	−	1.06423i	−0.224111	−	0.0541679i
$387$	−3.79033	+	3.79033i	−0.192673	+	0.192673i
$388$	6.06601	−	11.8155i	0.307955	−	0.599842i
$389$	−1.28341	+	1.28341i	−0.0650715	+	0.0650715i	−0.738894	−	0.673822i	$-0.764651\pi$
$389$	−1.28341	+	1.28341i	−0.0650715	+	0.0650715i	0.673822	+	0.738894i	$0.264651\pi$
$390$	16.9622	+	9.07398i	0.858916	+	0.459479i
$391$		−	26.0880i		−	1.31933i
$392$	1.84679	−	2.14228i	0.0932769	−	0.108202i
$393$	−43.8028			−2.20956
$394$	−3.52190	+	2.15080i	−0.177431	+	0.108356i
$395$	26.4572	+	6.87029i	1.33121	+	0.345682i
$396$	−3.83979	−	11.9421i	−0.192957	−	0.600114i
$397$	21.0987	−	21.0987i	1.05891	−	1.05891i	0.0607588	−	0.998152i	$-0.480648\pi$
$397$	21.0987	−	21.0987i	1.05891	−	1.05891i	0.998152	−	0.0607588i	$-0.0193521\pi$
$398$	−16.7257	−	4.04263i	−0.838386	−	0.202639i
$399$	16.5818			0.830130
$400$	2.27621	+	19.8700i	0.113811	+	0.993502i
$401$	20.3655			1.01700			0.508502	−	0.861061i	$-0.330200\pi$
$401$	20.3655			1.01700			0.508502	+	0.861061i	$0.330200\pi$
$402$	14.1642	+	3.42349i	0.706444	+	0.170748i
$403$	−16.4606	+	16.4606i	−0.819963	+	0.819963i
$404$	15.6044	−	5.01733i	0.776348	−	0.249622i
$405$	24.3478	+	6.32253i	1.20985	+	0.314169i
$406$	−2.31592	+	1.41432i	−0.114937	+	0.0701916i
$407$	−5.09332			−0.252467
$408$	−29.7578	+	2.20433i	−1.47323	+	0.109131i
$409$		−	9.31544i		−	0.460619i	−0.973117	−	0.230309i	$-0.926026\pi$
$409$		−	9.31544i		−	0.460619i	0.973117	−	0.230309i	$-0.0739738\pi$
$410$	19.5218	+	10.4432i	0.964113	+	0.515754i
$411$	−22.8635	+	22.8635i	−1.12777	+	1.12777i
$412$	18.1164	+	9.30084i	0.892530	+	0.458219i
$413$	−8.46993	+	8.46993i	−0.416778	+	0.416778i
$414$	−10.9364	−	2.64334i	−0.537496	−	0.129913i
$415$	23.6016	−	13.8709i	1.15856	−	0.680895i
$416$	6.31256	−	14.9154i	0.309499	−	0.731290i
$417$		−	10.1889i		−	0.498952i
$418$	−10.7404	+	44.4366i	−0.525328	+	2.17346i
$419$	−1.38793	−	1.38793i	−0.0678047	−	0.0678047i	0.672391	−	0.740196i	$-0.265267\pi$
$419$	−1.38793	−	1.38793i	−0.0678047	−	0.0678047i	−0.740196	+	0.672391i	$0.765267\pi$
$420$	9.48640	−	0.541586i	0.462889	−	0.0264267i
$421$	1.75596	−	1.75596i	0.0855801	−	0.0855801i	−0.663021	−	0.748601i	$-0.730726\pi$
$421$	1.75596	−	1.75596i	0.0855801	−	0.0855801i	0.748601	+	0.663021i	$0.230726\pi$
$422$	−30.4642	+	18.6043i	−1.48297	+	0.905642i
$423$	12.8487			0.624724
$424$	−1.89394	+	0.140294i	−0.0919776	+	0.00681330i
$425$	−12.0793	+	21.6901i	−0.585933	+	1.05213i
$426$	17.9273	−	10.9481i	0.868579	−	0.530436i
$427$	−6.66865	−	6.66865i	−0.322718	−	0.322718i
$428$	−9.70802	−	30.1929i	−0.469255	−	1.45943i
$429$	17.8169	+	17.8169i	0.860209	+	0.860209i
$430$	10.7133	−	3.24582i	0.516640	−	0.156528i
$431$	−22.5174			−1.08462			−0.542312	−	0.840177i	$-0.682451\pi$
$431$	−22.5174			−1.08462			−0.542312	+	0.840177i	$0.682451\pi$
$432$	2.05172	−	12.4591i	0.0987136	−	0.599438i
$433$		−	4.37198i		−	0.210104i	−0.994467	−	0.105052i	$-0.966499\pi$
$433$		−	4.37198i		−	0.210104i	0.994467	−	0.105052i	$-0.0335009\pi$
$434$	−2.70138	+	11.1766i	−0.129671	+	0.536492i
$435$	−8.82357	−	2.29127i	−0.423058	−	0.109858i
$436$	−5.81751	−	18.0930i	−0.278608	−	0.866499i
$437$	28.9944	+	28.9944i	1.38699	+	1.38699i
$438$	16.5614	+	27.1190i	0.791333	+	1.29579i
$439$		−	5.59276i		−	0.266928i	−0.991054	−	0.133464i	$-0.957390\pi$
$439$		−	5.59276i		−	0.266928i	0.991054	−	0.133464i	$-0.0426100\pi$
$440$	−4.69315	+	25.7728i	−0.223737	+	1.22867i
$441$		−	1.51426i		−	0.0721075i
$442$	17.1585	−	10.4786i	0.816146	−	0.498416i
$443$	19.7575	+	19.7575i	0.938707	+	0.938707i	0.998227	−	0.0595203i	$-0.0189571\pi$
$443$	19.7575	+	19.7575i	0.938707	+	0.938707i	−0.0595203	+	0.998227i	$0.518957\pi$
$444$	4.64846	+	2.38649i	0.220606	+	0.113258i
$445$	3.58582	−	13.8088i	0.169984	−	0.654602i
$446$	36.1166	+	8.72942i	1.71017	+	0.413350i
$447$			31.3886i			1.48463i
$448$	−1.17874	−	7.91268i	−0.0556903	−	0.373839i
$449$	−24.2209			−1.14305			−0.571527	−	0.820583i	$-0.693649\pi$
$449$	−24.2209			−1.14305			−0.571527	+	0.820583i	$0.693649\pi$
$450$	7.86885	+	7.26154i	0.370941	+	0.342312i
$451$	20.5055	+	20.5055i	0.965564	+	0.965564i
$452$	3.48634	−	6.79078i	0.163984	−	0.319411i
$453$	−2.08546	−	2.08546i	−0.0979836	−	0.0979836i
$454$	4.51688	+	7.39631i	0.211988	+	0.347126i
$455$	−5.51948	+	3.24386i	−0.258757	+	0.152074i
$456$	30.6232	−	35.5230i	1.43406	−	1.66352i
$457$	11.6669			0.545752			0.272876	−	0.962049i	$-0.412025\pi$
$457$	11.6669			0.545752			0.272876	+	0.962049i	$0.412025\pi$
$458$	−6.13970	−	10.0537i	−0.286890	−	0.469776i
$459$	11.0834	−	11.0834i	0.517329	−	0.517329i
$460$	17.5346	+	15.6406i	0.817553	+	0.729245i
$461$	−16.1694	−	16.1694i	−0.753082	−	0.753082i	0.221971	−	0.975053i	$-0.428751\pi$
$461$	−16.1694	−	16.1694i	−0.753082	−	0.753082i	−0.975053	+	0.221971i	$0.928751\pi$
$462$	12.0975	+	2.92397i	0.562825	+	0.136035i
$463$			31.8411i			1.47978i	0.672726	+	0.739891i	$0.265123\pi$
$463$			31.8411i			1.47978i	−0.672726	+	0.739891i	$0.734877\pi$
$464$	−1.24715	+	7.57331i	−0.0578974	+	0.351582i
$465$	−33.3023	+	19.5721i	−1.54436	+	0.907634i
$466$	−3.50264	+	14.4917i	−0.162257	+	0.671313i
$467$	29.4921	−	29.4921i	1.36473	−	1.36473i	0.496959	−	0.867774i	$-0.334450\pi$
$467$	29.4921	−	29.4921i	1.36473	−	1.36473i	0.867774	−	0.496959i	$-0.165550\pi$
$468$	−2.65419	−	8.25479i	−0.122690	−	0.381578i
$469$	−3.42923	+	3.42923i	−0.158347	+	0.158347i
$470$	−23.6597	−	12.6568i	−1.09134	−	0.583815i
$471$		−	43.1930i		−	1.99023i
$472$	2.50280	+	33.7871i	0.115201	+	1.55518i
$473$	14.6625			0.674181
$474$	−19.1440	−	31.3480i	−0.879315	−	1.43986i
$475$	−10.6815	−	37.5316i	−0.490102	−	1.72207i
$476$	4.53557	−	8.83449i	0.207888	−	0.404928i
$477$	−0.718941	+	0.718941i	−0.0329181	+	0.0329181i
$478$	2.39870	−	9.92426i	0.109714	−	0.453925i
$479$	31.5811			1.44298			0.721489	−	0.692426i	$-0.243458\pi$
$479$	31.5811			1.44298			0.721489	+	0.692426i	$0.243458\pi$
$480$	16.3592	−	21.3227i	0.746690	−	0.973246i
$481$	−3.52067			−0.160529
$482$	−3.05134	+	12.6245i	−0.138985	+	0.575028i
$483$	7.89346	−	7.89346i	0.359165	−	0.359165i
$484$	−5.62364	+	10.9539i	−0.255620	+	0.497902i
$485$	−3.73224	+	14.3727i	−0.169472	+	0.652630i
$486$	−10.6375	−	17.4187i	−0.482526	−	0.790128i
$487$	−26.3403			−1.19359			−0.596796	−	0.802393i	$-0.703560\pi$
$487$	−26.3403			−1.19359			−0.596796	+	0.802393i	$0.703560\pi$
$488$	−26.6017	+	1.97054i	−1.20420	+	0.0892020i
$489$		−	9.90993i		−	0.448143i
$490$	−1.49164	+	2.78837i	−0.0673856	+	0.125966i
$491$	17.0861	−	17.0861i	0.771085	−	0.771085i	−0.207211	−	0.978296i	$-0.566439\pi$
$491$	17.0861	−	17.0861i	0.771085	−	0.771085i	0.978296	+	0.207211i	$0.0664387\pi$
$492$	−9.10658	−	28.3224i	−0.410556	−	1.27687i
$493$	−6.73710	+	6.73710i	−0.303424	+	0.303424i
$494$	−7.42409	+	30.7160i	−0.334026	+	1.38198i
$495$	7.10619	+	12.0913i	0.319399	+	0.543464i
$496$	18.9545	+	26.4279i	0.851080	+	1.18665i
$497$			6.99090i			0.313585i
$498$	−35.7570	−	8.64250i	−1.60231	−	0.387280i
$499$	17.4457	+	17.4457i	0.780975	+	0.780975i	0.979995	−	0.199020i	$-0.0637759\pi$
$499$	17.4457	+	17.4457i	0.780975	+	0.780975i	−0.199020	+	0.979995i	$0.563776\pi$
$500$	−7.33669	−	21.1228i	−0.328107	−	0.944641i
$501$	−1.60392	+	1.60392i	−0.0716577	+	0.0716577i
$502$	−8.72329	−	14.2842i	−0.389339	−	0.637536i
$503$	34.6776			1.54620			0.773099	−	0.634286i	$-0.218706\pi$
$503$	34.6776			1.54620			0.773099	+	0.634286i	$0.218706\pi$
$504$	−3.24397	−	2.79651i	−0.144498	−	0.124567i
$505$	−15.7994	+	9.28544i	−0.703062	+	0.413197i
$506$	16.0404	+	26.2659i	0.713084	+	1.16766i
$507$	−7.21521	−	7.21521i	−0.320439	−	0.320439i
$508$	−4.90264	+	9.54948i	−0.217520	+	0.423690i
$509$	29.3647	+	29.3647i	1.30157	+	1.30157i	0.927335	+	0.374233i	$0.122094\pi$
$509$	29.3647	+	29.3647i	1.30157	+	1.30157i	0.374233	+	0.927335i	$0.377906\pi$
$510$	31.9282	−	9.67336i	1.41381	−	0.428344i
$511$	−10.5753			−0.467823
$512$	−19.1281	−	12.0879i	−0.845350	−	0.534213i
$513$			24.6363i			1.08772i
$514$	24.9009	+	6.01857i	1.09833	+	0.265468i
$515$	−22.0372	−	5.72253i	−0.971076	−	0.252165i
$516$	−13.3818	−	6.87014i	−0.589102	−	0.302441i
$517$	−24.8519	−	24.8519i	−1.09298	−	1.09298i
$518$	−1.48414	+	0.906354i	−0.0652093	+	0.0398229i
$519$		−	16.6852i		−	0.732399i
$520$	−3.24406	+	17.8150i	−0.142262	+	0.781240i
$521$			31.2494i			1.36906i	0.728985	+	0.684530i	$0.239993\pi$
$521$			31.2494i			1.36906i	−0.728985	+	0.684530i	$0.760007\pi$
$522$	2.14165	+	3.50691i	0.0937373	+	0.153493i
$523$	15.3960	+	15.3960i	0.673221	+	0.673221i	0.958457	−	0.285236i	$-0.0920720\pi$
$523$	15.3960	+	15.3960i	0.673221	+	0.673221i	−0.285236	+	0.958457i	$0.592072\pi$
$524$	−12.6212	−	39.2533i	−0.551361	−	1.71479i
$525$	−10.2176	+	2.90795i	−0.445935	+	0.126913i
$526$	−2.29747	+	9.50542i	−0.100174	+	0.414456i
$527$			40.3714i			1.75860i
$528$	28.6054	−	20.5162i	1.24489	−	0.892854i
$529$	4.60441			0.200192
$530$	2.03207	−	0.615661i	0.0882675	−	0.0267426i
$531$	12.8257	+	12.8257i	0.556586	+	0.556586i
$532$	4.77784	+	14.8596i	0.207146	+	0.644244i
$533$	14.1741	+	14.1741i	0.613947	+	0.613947i
$534$	−16.3615	+	9.99188i	−0.708032	+	0.432391i
$535$	17.9664	+	30.5701i	0.776754	+	1.32166i
$536$	1.01331	+	13.6794i	0.0437684	+	0.590862i
$537$	−7.96282			−0.343621
$538$	16.0026	−	9.77266i	0.689919	−	0.421329i
$539$	−2.92887	+	2.92887i	−0.126155	+	0.126155i
$540$	0.804657	+	14.0943i	0.0346269	+	0.606524i
$541$	−22.0240	−	22.0240i	−0.946886	−	0.946886i	0.0517732	−	0.998659i	$-0.483513\pi$
$541$	−22.0240	−	22.0240i	−0.946886	−	0.946886i	−0.998659	+	0.0517732i	$0.983513\pi$
$542$	1.26137	−	5.21873i	0.0541805	−	0.224164i
$543$			10.2391i			0.439402i
$544$	−10.5497	−	26.0319i	−0.452315	−	1.11611i
$545$	10.7663	+	18.3191i	0.461178	+	0.784702i
$546$	8.36217	+	2.02114i	0.357868	+	0.0864969i
$547$	2.30334	−	2.30334i	0.0984838	−	0.0984838i	−0.656148	−	0.754632i	$-0.727815\pi$
$547$	2.30334	−	2.30334i	0.0984838	−	0.0984838i	0.754632	+	0.656148i	$0.227815\pi$
$548$	−27.0766	−	13.9010i	−1.15666	−	0.593820i
$549$	−10.0980	+	10.0980i	−0.430974	+	0.430974i
$550$	−1.17466	−	29.2651i	−0.0500878	−	1.24787i
$551$		−	14.9753i		−	0.637970i
$552$	−2.33246	−	31.4876i	−0.0992761	−	1.34020i
$553$	12.2244			0.519836
$554$	1.78173	−	1.08809i	0.0756983	−	0.0462285i
$555$	−5.65450	−	1.46834i	−0.240020	−	0.0623274i
$556$	9.13062	−	2.93580i	0.387224	−	0.124506i
$557$	−11.8854	+	11.8854i	−0.503603	+	0.503603i	−0.912555	−	0.408953i	$-0.865894\pi$
$557$	−11.8854	+	11.8854i	−0.503603	+	0.503603i	0.408953	+	0.912555i	$0.365894\pi$
$558$	16.9242	+	4.09059i	0.716458	+	0.173169i
$559$	10.1352			0.428673
$560$	3.21872	+	8.34505i	0.136016	+	0.352643i
$561$	43.6978			1.84492
$562$	−25.8850	−	6.25644i	−1.09189	−	0.263912i
$563$	0.811392	−	0.811392i	0.0341961	−	0.0341961i	−0.689802	−	0.723998i	$-0.742302\pi$
$563$	0.811392	−	0.811392i	0.0341961	−	0.0341961i	0.723998	+	0.689802i	$0.242302\pi$
$564$	11.0368	+	34.3256i	0.464735	+	1.44537i
$565$	−2.14504	+	8.26047i	−0.0902426	+	0.347521i
$566$	−18.1742	+	11.0989i	−0.763918	+	0.466520i
$567$	11.2498			0.472447
$568$	14.9765	+	12.9107i	0.628399	+	0.541721i
$569$		−	7.33173i		−	0.307362i	−0.988121	−	0.153681i	$-0.950887\pi$
$569$		−	7.33173i		−	0.307362i	0.988121	−	0.153681i	$-0.0491128\pi$
$570$	−24.7342	+	46.2363i	−1.03600	+	1.93662i
$571$	2.84498	−	2.84498i	0.119059	−	0.119059i	−0.645067	−	0.764126i	$-0.723171\pi$
$571$	2.84498	−	2.84498i	0.119059	−	0.119059i	0.764126	+	0.645067i	$0.223171\pi$
$572$	−10.8327	+	21.1001i	−0.452936	+	0.882239i
$573$	−14.8610	+	14.8610i	−0.620828	+	0.620828i
$574$	9.62400	+	2.32613i	0.401698	+	0.0970908i
$575$	−22.9509	−	12.7815i	−0.957119	−	0.533024i
$576$	−11.9818	+	1.78492i	−0.499243	+	0.0743716i
$577$		−	37.8586i		−	1.57608i	−0.615627	−	0.788038i	$-0.711097\pi$
$577$		−	37.8586i		−	1.57608i	0.615627	−	0.788038i	$-0.288903\pi$
$578$	2.54333	−	10.5226i	0.105789	−	0.437684i
$579$	−4.81227	−	4.81227i	−0.199991	−	0.199991i
$580$	−0.489115	−	8.56731i	−0.0203094	−	0.355738i
$581$	8.65699	−	8.65699i	0.359153	−	0.359153i
$582$	17.0296	−	10.3999i	0.705899	−	0.431088i
$583$	2.78114			0.115183
$584$	−19.5303	+	22.6552i	−0.808170	+	0.937480i
$585$	4.91204	+	8.35792i	0.203088	+	0.345557i
$586$	−19.6453	+	11.9973i	−0.811540	+	0.495603i
$587$	−4.20131	−	4.20131i	−0.173407	−	0.173407i	0.615068	−	0.788474i	$-0.289129\pi$
$587$	−4.20131	−	4.20131i	−0.173407	−	0.173407i	−0.788474	+	0.615068i	$0.789129\pi$
$588$	4.04539	−	1.30073i	0.166829	−	0.0536410i
$589$	−44.8690	−	44.8690i	−1.84880	−	1.84880i
$590$	−10.9832	−	36.2514i	−0.452170	−	1.49245i
$591$	−6.19986			−0.255028
$592$	−0.799224	+	4.85329i	−0.0328479	+	0.199469i
$593$		−	6.12929i		−	0.251700i	−0.992049	−	0.125850i	$-0.959834\pi$
$593$		−	6.12929i		−	0.251700i	0.992049	−	0.125850i	$-0.0401658\pi$
$594$	−4.34426	+	17.9737i	−0.178247	+	0.737470i
$595$	−2.79060	+	10.7465i	−0.114403	+	0.440563i
$596$	−28.1284	+	9.04421i	−1.15218	+	0.370465i
$597$	−18.2801	−	18.2801i	−0.748153	−	0.748153i
$598$	11.0877	+	18.1559i	0.453409	+	0.742449i
$599$			36.8375i			1.50514i	0.658512	+	0.752571i	$0.271186\pi$
$599$			36.8375i			1.50514i	−0.658512	+	0.752571i	$0.728814\pi$
$600$	−12.6402	+	27.2594i	−0.516034	+	1.11286i
$601$		−	27.2740i		−	1.11253i	−0.831005	−	0.556266i	$-0.812234\pi$
$601$		−	27.2740i		−	1.11253i	0.831005	−	0.556266i	$-0.187766\pi$
$602$	4.27248	−	2.60918i	0.174133	−	0.106342i
$603$	5.19274	+	5.19274i	0.211465	+	0.211465i
$604$	1.26796	−	2.46976i	0.0515924	−	0.100493i
$605$	3.46006	−	13.3245i	0.140671	−	0.541719i
$606$	23.9365	+	5.78546i	0.972352	+	0.235018i
$607$			23.1634i			0.940174i	0.882620	+	0.470087i	$0.155777\pi$
$607$			23.1634i			0.940174i	−0.882620	+	0.470087i	$0.844223\pi$
$608$	40.6571	+	17.2070i	1.64886	+	0.697836i
$609$	−4.07689			−0.165204
$610$	28.5419	−	8.64740i	1.15563	−	0.350123i
$611$	−17.1784	−	17.1784i	−0.694965	−	0.694965i
$612$	−13.3777	−	6.86802i	−0.540761	−	0.277623i
$613$	−20.1147	−	20.1147i	−0.812427	−	0.812427i	0.172570	−	0.984997i	$-0.444793\pi$
$613$	−20.1147	−	20.1147i	−0.812427	−	0.812427i	−0.984997	+	0.172570i	$0.944793\pi$
$614$	−6.40718	−	10.4916i	−0.258573	−	0.423408i
$615$	16.8533	+	28.6762i	0.679590	+	1.15634i
$616$	0.865460	+	11.6835i	0.0348704	+	0.470740i
$617$	−39.0883			−1.57364			−0.786818	−	0.617185i	$-0.788273\pi$
$617$	−39.0883			−1.57364			−0.786818	+	0.617185i	$0.788273\pi$
$618$	15.9458	+	26.1110i	0.641435	+	1.05034i
$619$	2.61578	−	2.61578i	0.105137	−	0.105137i	−0.652581	−	0.757719i	$-0.726314\pi$
$619$	2.61578	−	2.61578i	0.105137	−	0.105137i	0.757719	+	0.652581i	$0.226314\pi$
$620$	−27.1349	−	24.2039i	−1.08976	−	0.972052i
$621$	11.7276	+	11.7276i	0.470614	+	0.470614i
$622$	1.49291	+	0.360837i	0.0598601	+	0.0144682i
$623$		−	6.38032i		−	0.255622i
$624$	19.7730	−	14.1815i	0.791554	−	0.567714i
$625$	13.1638	+	21.2536i	0.526552	+	0.850143i
$626$	6.08219	−	25.1641i	0.243093	−	1.00576i
$627$	−48.5660	+	48.5660i	−1.93954	+	1.93954i
$628$	38.7068	−	12.4455i	1.54457	−	0.496630i
$629$	−4.31740	+	4.31740i	−0.172146	+	0.172146i
$630$	4.22231	+	2.25873i	0.168221	+	0.0899901i
$631$		−	10.8503i		−	0.431944i	−0.976400	−	0.215972i	$-0.930708\pi$
$631$		−	10.8503i		−	0.431944i	0.976400	−	0.215972i	$-0.0692920\pi$
$632$	22.5759	−	26.1882i	0.898023	−	1.04171i
$633$	−53.6283			−2.13153
$634$	−1.76788	−	2.89487i	−0.0702114	−	0.114970i
$635$	3.01645	−	11.6162i	0.119704	−	0.460976i
$636$	−2.53823	−	1.30311i	−0.100647	−	0.0516718i
$637$	−2.02453	+	2.02453i	−0.0802149	+	0.0802149i
$638$	2.64068	−	10.9254i	0.104545	−	0.432541i
$639$	10.5860			0.418776
$640$	23.8217	+	8.51614i	0.941637	+	0.336630i
$641$	43.9293			1.73510			0.867551	−	0.497348i	$-0.165693\pi$
$641$	43.9293			1.73510			0.867551	+	0.497348i	$0.165693\pi$
$642$	11.1943	−	46.3145i	0.441802	−	1.82789i
$643$	27.4408	−	27.4408i	1.08216	−	1.08216i	0.0858531	−	0.996308i	$-0.472638\pi$
$643$	27.4408	−	27.4408i	1.08216	−	1.08216i	0.996308	−	0.0858531i	$-0.0273616\pi$
$644$	9.34801	+	4.79921i	0.368363	+	0.189115i
$645$	16.2780	+	4.22699i	0.640945	+	0.166438i
$646$	28.5629	+	46.7713i	1.12379	+	1.84019i
$647$	−23.4510			−0.921952			−0.460976	−	0.887412i	$-0.652501\pi$
$647$	−23.4510			−0.921952			−0.460976	+	0.887412i	$0.652501\pi$
$648$	20.7760	−	24.1002i	0.816158	−	0.946747i
$649$		−	49.6146i		−	1.94754i
$650$	−0.811967	−	20.2290i	−0.0318480	−	0.793448i
$651$	−12.2152	+	12.2152i	−0.478751	+	0.478751i
$652$	8.88064	−	2.85542i	0.347793	−	0.111827i
$653$	5.52578	−	5.52578i	0.216240	−	0.216240i	−0.590672	−	0.806912i	$-0.701137\pi$
$653$	5.52578	−	5.52578i	0.216240	−	0.216240i	0.806912	+	0.590672i	$0.201137\pi$
$654$	6.70813	−	27.7539i	0.262309	−	1.08526i
$655$	23.3578	+	39.7437i	0.912663	+	1.55291i
$656$	22.7567	−	16.3215i	0.888501	−	0.637246i
$657$			16.0137i			0.624754i
$658$	−11.6639	−	2.81918i	−0.454707	−	0.109903i
$659$	−21.7749	−	21.7749i	−0.848230	−	0.848230i	0.141682	−	0.989912i	$-0.454749\pi$
$659$	−21.7749	−	21.7749i	−0.848230	−	0.848230i	−0.989912	+	0.141682i	$0.954749\pi$
$660$	−26.1982	+	29.3707i	−1.01976	+	1.14325i
$661$	3.85504	−	3.85504i	0.149944	−	0.149944i	−0.628149	−	0.778093i	$-0.716187\pi$
$661$	3.85504	−	3.85504i	0.149944	−	0.149944i	0.778093	+	0.628149i	$0.216187\pi$
$662$	−5.92947	−	9.70940i	−0.230456	−	0.377367i
$663$	30.2054			1.17308
$664$	−2.55808	−	34.5334i	−0.0992727	−	1.34015i
$665$	−8.84222	−	15.0452i	−0.342887	−	0.583428i
$666$	1.37245	+	2.24737i	0.0531815	+	0.0870837i
$667$	−7.12870	−	7.12870i	−0.276024	−	0.276024i
$668$	−1.89947	−	0.975178i	−0.0734928	−	0.0377308i
$669$	39.4729	+	39.4729i	1.52611	+	1.52611i
$670$	−4.44677	−	14.6771i	−0.171794	−	0.567028i
$671$	39.0632			1.50802
$672$	4.68445	−	11.0685i	0.180707	−	0.426977i
$673$			23.7636i			0.916019i	0.888947	+	0.458010i	$0.151437\pi$
$673$			23.7636i			0.916019i	−0.888947	+	0.458010i	$0.848563\pi$
$674$	−3.89070	−	0.940386i	−0.149864	−	0.0362223i
$675$	−4.32046	−	15.1808i	−0.166295	−	0.584309i
$676$	4.38684	−	8.54478i	0.168724	−	0.328645i
$677$	16.9035	+	16.9035i	0.649655	+	0.649655i	0.952909	−	0.303255i	$-0.0980733\pi$
$677$	16.9035	+	16.9035i	0.649655	+	0.649655i	−0.303255	+	0.952909i	$0.598073\pi$
$678$	9.78748	−	5.97716i	0.375886	−	0.229551i
$679$			6.64084i			0.254852i
$680$	17.8684	+	25.8247i	0.685220	+	0.990334i
$681$			13.0203i			0.498938i
$682$	−24.8227	−	40.6467i	−0.950509	−	1.55644i
$683$	15.9058	+	15.9058i	0.608617	+	0.608617i	0.942585	−	0.333967i	$-0.108388\pi$
$683$	15.9058	+	15.9058i	0.608617	+	0.608617i	−0.333967	+	0.942585i	$0.608388\pi$
$684$	22.5012	−	7.23489i	0.860356	−	0.276633i
$685$	32.9367	+	8.55286i	1.25845	+	0.326788i
$686$	−0.332249	+	1.37463i	−0.0126853	+	0.0524837i
$687$		−	17.6982i		−	0.675228i
$688$	2.30078	−	13.9715i	0.0877163	−	0.532657i
$689$	1.92242			0.0732383
$690$	10.2356	+	33.7841i	0.389664	+	1.28614i
$691$	−33.2066	−	33.2066i	−1.26324	−	1.26324i	−0.949514	−	0.313726i	$-0.898423\pi$
$691$	−33.2066	−	33.2066i	−1.26324	−	1.26324i	−0.313726	−	0.949514i	$-0.601577\pi$
$692$	14.9522	−	4.80763i	0.568397	−	0.182759i
$693$	4.43506	+	4.43506i	0.168474	+	0.168474i
$694$	35.3209	−	21.5702i	1.34076	−	0.818795i
$695$	−9.24469	+	5.43320i	−0.350671	+	0.206093i
$696$	−7.52916	+	8.73386i	−0.285392	+	0.331056i
$697$	34.7633			1.31675
$698$	11.7101	−	7.15127i	0.443233	−	0.270679i
$699$	−15.8384	+	15.8384i	−0.599061	+	0.599061i
$700$	−5.55000	−	8.31850i	−0.209770	−	0.314410i
$701$	26.2448	+	26.2448i	0.991252	+	0.991252i	0.999962	−	0.00871030i	$-0.00277261\pi$
$701$	26.2448	+	26.2448i	0.991252	+	0.991252i	−0.00871030	+	0.999962i	$0.502773\pi$
$702$	−3.00290	+	12.4240i	−0.113337	+	0.468915i
$703$		−	9.59678i		−	0.361950i
$704$	26.6276	+	19.7228i	1.00357	+	0.743332i
$705$	−20.4256	−	34.7545i	−0.769271	−	1.30893i
$706$	−7.94463	−	1.92022i	−0.299000	−	0.0722686i
$707$	−5.79516	+	5.79516i	−0.217949	+	0.217949i
$708$	−23.2471	+	45.2812i	−0.873678	+	1.70177i
$709$	−0.320056	+	0.320056i	−0.0120200	+	0.0120200i	−0.713091	−	0.701071i	$-0.752705\pi$
$709$	−0.320056	+	0.320056i	−0.0120200	+	0.0120200i	0.701071	+	0.713091i	$0.252705\pi$
$710$	−19.4932	−	10.4279i	−0.731567	−	0.391353i
$711$		−	18.5109i		−	0.694214i
$712$	−13.6684	−	11.7831i	−0.512246	−	0.441590i
$713$	−42.7180			−1.59980
$714$	12.7331	−	7.77600i	0.476523	−	0.291010i
$715$	6.66501	−	25.6667i	0.249257	−	0.959879i
$716$	−2.29439	−	7.13577i	−0.0857452	−	0.266676i
$717$	10.8465	−	10.8465i	0.405071	−	0.405071i
$718$	13.2609	+	3.20518i	0.494893	+	0.119616i
$719$	−32.2268			−1.20186			−0.600929	−	0.799302i	$-0.705203\pi$
$719$	−32.2268			−1.20186			−0.600929	+	0.799302i	$0.705203\pi$
$720$	12.6366	−	4.87397i	0.470937	−	0.181642i
$721$	−10.1822			−0.379205
$722$	−57.6089	−	13.9241i	−2.14398	−	0.518202i
$723$	−13.7976	+	13.7976i	−0.513140	+	0.513140i
$724$	−9.17561	+	2.95026i	−0.341009	+	0.109646i
$725$	2.62621	+	9.22771i	0.0975350	+	0.342709i
$726$	−15.7877	+	9.64144i	−0.585936	+	0.357828i
$727$	37.8987			1.40558			0.702792	−	0.711395i	$-0.251936\pi$
$727$	37.8987			1.40558			0.702792	+	0.711395i	$0.251936\pi$
$728$	0.598235	+	8.07600i	0.0221721	+	0.299317i
$729$			3.08598i			0.114296i
$730$	15.7745	−	29.4878i	0.583842	−	1.09139i
$731$	12.4288	−	12.4288i	0.459695	−	0.459695i
$732$	−35.6513	−	18.3032i	−1.31771	−	0.676504i
$733$	−23.1291	+	23.1291i	−0.854292	+	0.854292i	−0.990658	−	0.136367i	$-0.956457\pi$
$733$	−23.1291	+	23.1291i	−0.854292	+	0.854292i	0.136367	+	0.990658i	$0.456457\pi$
$734$	32.5560	+	7.86882i	1.20167	+	0.290443i
$735$	−4.09592	+	2.40722i	−0.151080	+	0.0887915i
$736$	27.5451	−	11.1629i	1.01532	−	0.411471i
$737$		−	20.0875i		−	0.739934i
$738$	3.52236	−	14.5732i	0.129660	−	0.536448i
$739$	−14.2675	−	14.2675i	−0.524839	−	0.524839i	0.394190	−	0.919029i	$-0.371025\pi$
$739$	−14.2675	−	14.2675i	−0.524839	−	0.524839i	−0.919029	+	0.394190i	$0.871025\pi$
$740$	−0.313444	−	5.49028i	−0.0115224	−	0.201827i
$741$	−33.5705	+	33.5705i	−1.23324	+	1.23324i
$742$	0.810395	−	0.494903i	0.0297505	−	0.0181685i
$743$	−22.3384			−0.819516			−0.409758	−	0.912194i	$-0.634387\pi$
$743$	−22.3384			−0.819516			−0.409758	+	0.912194i	$0.634387\pi$
$744$	3.60950	+	48.7272i	0.132331	+	1.78643i
$745$	28.4798	−	16.7379i	1.04342	−	0.613228i
$746$	15.8767	−	9.69580i	0.581287	−	0.354989i
$747$	−13.1089	−	13.1089i	−0.479630	−	0.479630i
$748$	12.5910	+	39.1591i	0.460371	+	1.43180i
$749$	11.2130	+	11.2130i	0.409715	+	0.409715i
$750$	7.13266	−	32.8282i	0.260448	−	1.19872i
$751$	−3.78051			−0.137953			−0.0689765	−	0.997618i	$-0.521973\pi$
$751$	−3.78051			−0.137953			−0.0689765	+	0.997618i	$0.521973\pi$
$752$	−27.5803	+	19.7810i	−1.00575	+	0.721339i
$753$		−	25.1456i		−	0.916356i
$754$	1.82532	−	7.55200i	0.0664744	−	0.275028i
$755$	−0.780136	+	3.00427i	−0.0283921	+	0.109337i
$756$	1.93254	+	6.01040i	0.0702859	+	0.218596i
$757$	−31.3761	−	31.3761i	−1.14038	−	1.14038i	−0.988380	−	0.152005i	$-0.951427\pi$
$757$	−31.3761	−	31.3761i	−1.14038	−	1.14038i	−0.152005	−	0.988380i	$-0.548573\pi$
$758$	21.2230	+	34.7522i	0.770853	+	1.26226i
$759$			46.2378i			1.67833i
$760$	−48.5608	−	8.84279i	−1.76149	−	0.320762i
$761$		−	5.51805i		−	0.200029i	−0.994986	−	0.100015i	$-0.968111\pi$
$761$		−	5.51805i		−	0.200029i	0.994986	−	0.100015i	$-0.0318889\pi$
$762$	−13.7636	+	8.40533i	−0.498602	+	0.304493i
$763$	6.71938	+	6.71938i	0.243258	+	0.243258i
$764$	−17.5995	−	9.03547i	−0.636727	−	0.326892i
$765$	16.2730	+	4.22569i	0.588350	+	0.152780i
$766$	−29.9826	−	7.24683i	−1.08332	−	0.261839i
$767$		−	34.2953i		−	1.23833i
$768$	−15.0607	−	30.4766i	−0.543456	−	1.09973i
$769$	−54.5915			−1.96862			−0.984309	−	0.176453i	$-0.943538\pi$
$769$	−54.5915			−1.96862			−0.984309	+	0.176453i	$0.943538\pi$
$770$	−3.79794	−	12.5356i	−0.136868	−	0.451751i
$771$	27.2149	+	27.2149i	0.980122	+	0.980122i
$772$	2.92585	−	5.69904i	0.105304	−	0.205113i
$773$	−22.3582	−	22.3582i	−0.804170	−	0.804170i	0.179574	−	0.983744i	$-0.442528\pi$
$773$	−22.3582	−	22.3582i	−0.804170	−	0.804170i	−0.983744	+	0.179574i	$0.942528\pi$
$774$	−3.95097	−	6.46964i	−0.142015	−	0.232546i
$775$	35.5167	+	19.7794i	1.27580	+	0.710497i
$776$	14.2265	+	12.2642i	0.510703	+	0.440260i
$777$	−2.61264			−0.0937279
$778$	−1.33780	−	2.19063i	−0.0479626	−	0.0785379i
$779$	−38.6362	+	38.6362i	−1.38428	+	1.38428i
$780$	−18.1091	+	20.3020i	−0.648409	+	0.726928i
$781$	−20.4754	−	20.4754i	−0.732668	−	0.732668i
$782$	35.8614	+	8.66772i	1.28240	+	0.309957i
$783$		−	6.05721i		−	0.216467i
$784$	2.33125	+	3.25043i	0.0832590	+	0.116087i
$785$	−39.1903	+	23.0326i	−1.39876	+	0.822068i
$786$	14.5535	−	60.2128i	0.519105	−	2.14772i
$787$	12.4401	−	12.4401i	0.443440	−	0.443440i	−0.449726	−	0.893166i	$-0.648478\pi$
$787$	12.4401	−	12.4401i	0.443440	−	0.443440i	0.893166	+	0.449726i	$0.148478\pi$
$788$	−1.78641	−	5.55591i	−0.0636382	−	0.197921i
$789$	−10.3887	+	10.3887i	−0.369849	+	0.369849i
$790$	−18.2345	+	34.0862i	−0.648754	+	1.21273i
$791$			3.81671i			0.135707i
$792$	17.6918	−	1.31053i	0.628650	−	0.0465676i
$793$	27.0018			0.958861
$794$	21.9929	+	36.0129i	0.780497	+	1.27805i
$795$	3.08757	+	0.801767i	0.109505	+	0.0284357i
$796$	11.1142	−	21.6486i	0.393934	−	0.767313i
$797$	−17.5525	+	17.5525i	−0.621740	+	0.621740i	−0.945976	−	0.324236i	$-0.894893\pi$
$797$	−17.5525	+	17.5525i	−0.621740	+	0.621740i	0.324236	+	0.945976i	$0.394893\pi$
$798$	−5.50931	+	22.7939i	−0.195027	+	0.806896i
$799$	−42.1318			−1.49052
$800$	−28.0703	−	3.47286i	−0.992433	−	0.122784i
$801$	−9.66144			−0.341370
$802$	−6.76642	+	27.9950i	−0.238930	+	0.988538i
$803$	30.9736	−	30.9736i	1.09303	−	1.09303i
$804$	−9.41207	+	18.3330i	−0.331938	+	0.646557i
$805$	−11.3711	−	2.95281i	−0.400780	−	0.104073i
$806$	−17.1583	−	28.0963i	−0.604374	−	0.989651i
$807$	28.1705			0.991648
$808$	1.71243	+	23.1173i	0.0602430	+	0.813264i
$809$		−	49.7748i		−	1.74999i	−0.484134	−	0.874994i	$-0.660865\pi$
$809$		−	49.7748i		−	1.74999i	0.484134	−	0.874994i	$-0.339135\pi$
$810$	−16.7807	+	31.3686i	−0.589613	+	1.10218i
$811$	12.5186	−	12.5186i	0.439587	−	0.439587i	−0.452286	−	0.891873i	$-0.649391\pi$
$811$	12.5186	−	12.5186i	0.439587	−	0.439587i	0.891873	+	0.452286i	$0.149391\pi$
$812$	−1.17470	−	3.65345i	−0.0412241	−	0.128211i
$813$	5.70370	−	5.70370i	0.200038	−	0.200038i
$814$	1.69225	−	7.00144i	0.0593134	−	0.245400i
$815$	−8.99159	+	5.28445i	−0.314962	+	0.185106i
$816$	6.85688	−	41.6384i	0.240039	−	1.45764i
$817$			27.6269i			0.966542i
$818$	12.8053	+	3.09505i	0.447727	+	0.108216i
$819$	3.06566	+	3.06566i	0.107123	+	0.107123i
$820$	−20.8417	+	23.3655i	−0.727823	+	0.815959i
$821$	−2.83075	+	2.83075i	−0.0987938	+	0.0987938i	−0.754776	−	0.655982i	$-0.772255\pi$
$821$	−2.83075	+	2.83075i	−0.0987938	+	0.0987938i	0.655982	+	0.754776i	$0.272255\pi$
$822$	−23.8325	−	39.0253i	−0.831254	−	1.36116i
$823$	−26.5464			−0.925351			−0.462675	−	0.886528i	$-0.653110\pi$
$823$	−26.5464			−0.925351			−0.462675	+	0.886528i	$0.653110\pi$
$824$	−18.8044	+	21.8131i	−0.655082	+	0.759897i
$825$	21.4091	−	38.4431i	0.745371	−	1.33842i
$826$	−8.82890	−	14.4572i	−0.307197	−	0.503029i
$827$	−18.0782	−	18.0782i	−0.628639	−	0.628639i	0.319087	−	0.947726i	$-0.396624\pi$
$827$	−18.0782	−	18.0782i	−0.628639	−	0.628639i	−0.947726	+	0.319087i	$0.896624\pi$
$828$	7.26724	−	14.1553i	0.252554	−	0.491930i
$829$	−11.4748	−	11.4748i	−0.398536	−	0.398536i	0.479181	−	0.877716i	$-0.340934\pi$
$829$	−11.4748	−	11.4748i	−0.398536	−	0.398536i	−0.877716	+	0.479181i	$0.840934\pi$
$830$	11.2257	+	37.0520i	0.389651	+	1.28610i
$831$	3.13651			0.108804
$832$	18.4059	+	13.6331i	0.638109	+	0.472642i
$833$			4.96537i			0.172040i
$834$	14.0060	+	3.38525i	0.484987	+	0.117222i
$835$	2.31057	+	0.599998i	0.0799604	+	0.0207638i
$836$	−57.5154	−	29.5281i	−1.98921	−	1.02125i
$837$	−18.1486	−	18.1486i	−0.627308	−	0.627308i
$838$	2.36903	−	1.44675i	0.0818367	−	0.0499772i
$839$		−	34.1333i		−	1.17841i	−0.807982	−	0.589207i	$-0.799440\pi$
$839$		−	34.1333i		−	1.17841i	0.807982	−	0.589207i	$-0.200560\pi$
$840$	−2.40737	+	13.2202i	−0.0830622	+	0.456142i
$841$		−	25.3181i		−	0.873038i
$842$	1.83038	+	2.99721i	0.0630790	+	0.103291i
$843$	−28.2905	−	28.2905i	−0.974377	−	0.974377i
$844$	−15.4523	−	48.0582i	−0.531891	−	1.65423i
$845$	−2.69909	+	10.3941i	−0.0928515	+	0.357567i
$846$	−4.26897	+	17.6622i	−0.146770	+	0.607239i
$847$		−	6.15655i		−	0.211541i
$848$	0.436406	−	2.65008i	0.0149862	−	0.0910040i
$849$	−31.9934			−1.09801
$850$	−25.8026	−	23.8112i	−0.885021	−	0.816716i
$851$	−4.56836	−	4.56836i	−0.156601	−	0.156601i
$852$	9.09324	+	28.2809i	0.311529	+	0.968887i
$853$	−2.40301	−	2.40301i	−0.0822774	−	0.0822774i	0.664770	−	0.747048i	$-0.268529\pi$
$853$	−2.40301	−	2.40301i	−0.0822774	−	0.0822774i	−0.747048	+	0.664770i	$0.768529\pi$
$854$	11.3826	−	6.95127i	0.389504	−	0.237868i
$855$	−22.7823	+	13.3894i	−0.779139	+	0.457908i
$856$	44.7296	−	3.31337i	1.52883	−	0.113249i
$857$	−8.07430			−0.275813			−0.137906	−	0.990445i	$-0.544037\pi$
$857$	−8.07430			−0.275813			−0.137906	+	0.990445i	$0.544037\pi$
$858$	−30.4114	+	18.5720i	−1.03823	+	0.634039i
$859$	1.46059	−	1.46059i	0.0498345	−	0.0498345i	−0.681750	−	0.731585i	$-0.738781\pi$
$859$	1.46059	−	1.46059i	0.0498345	−	0.0498345i	0.731585	+	0.681750i	$0.238781\pi$
$860$	0.902332	+	15.8052i	0.0307693	+	0.538954i
$861$	10.5184	+	10.5184i	0.358465	+	0.358465i
$862$	7.48139	−	30.9531i	0.254817	−	1.05427i
$863$			36.3699i			1.23805i	0.785372	+	0.619024i	$0.212472\pi$
$863$			36.3699i			1.23805i	−0.785372	+	0.619024i	$0.787528\pi$
$864$	16.4450	+	6.95989i	0.559469	+	0.236780i
$865$	−15.1390	+	8.89734i	−0.514741	+	0.302519i
$866$	6.00985	+	1.45259i	0.204223	+	0.0493609i
$867$	11.5005	−	11.5005i	0.390578	−	0.390578i
$868$	−14.4661	−	7.42681i	−0.491012	−	0.252082i
$869$	−35.8038	+	35.8038i	−1.21456	+	1.21456i
$870$	6.08127	−	11.3679i	0.206174	−	0.385407i
$871$		−	13.8852i		−	0.470481i
$872$	26.8041	−	1.98553i	0.907701	−	0.0672385i
$873$	10.0559			0.340342
$874$	−49.4899	+	30.2232i	−1.67402	+	1.02231i
$875$	8.08700	+	7.72013i	0.273391	+	0.260988i
$876$	−42.7811	+	13.7555i	−1.44544	+	0.464756i
$877$	17.2976	−	17.2976i	0.584100	−	0.584100i	−0.351927	−	0.936027i	$-0.614474\pi$
$877$	17.2976	−	17.2976i	0.584100	−	0.584100i	0.936027	+	0.351927i	$0.114474\pi$
$878$	7.68798	+	1.85819i	0.259457	+	0.0627109i
$879$	−34.5831			−1.16646
$880$	−33.8688	−	15.0143i	−1.14172	−	0.506133i
$881$	12.6207			0.425201			0.212600	−	0.977139i	$-0.431807\pi$
$881$	12.6207			0.425201			0.212600	+	0.977139i	$0.431807\pi$
$882$	2.08155	+	0.503111i	0.0700893	+	0.0169406i
$883$	0.749189	−	0.749189i	0.0252122	−	0.0252122i	−0.694388	−	0.719601i	$-0.744325\pi$
$883$	0.749189	−	0.749189i	0.0252122	−	0.0252122i	0.719601	+	0.694388i	$0.244325\pi$
$884$	8.70329	+	27.0681i	0.292723	+	0.910399i
$885$	14.3032	−	55.0811i	0.480798	−	1.85153i
$886$	−33.7237	+	20.5948i	−1.13297	+	0.691897i
$887$	−6.48030			−0.217587			−0.108794	−	0.994064i	$-0.534699\pi$
$887$	−6.48030			−0.217587			−0.108794	+	0.994064i	$0.534699\pi$
$888$	−4.82499	+	5.59701i	−0.161916	+	0.187823i
$889$		−	5.36723i		−	0.180011i
$890$	17.7907	+	9.51716i	0.596345	+	0.319016i
$891$	−32.9492	+	32.9492i	−1.10384	+	1.10384i
$892$	−23.9995	+	46.7467i	−0.803561	+	1.56520i
$893$	46.8256	−	46.8256i	1.56696	−	1.56696i
$894$	−43.1477	−	10.4288i	−1.44307	−	0.348792i
$895$	4.24616	+	7.22491i	0.141933	+	0.241502i
$896$	11.2687	+	1.00865i	0.376459	+	0.0336966i
$897$			31.9611i			1.06715i
$898$	8.04738	−	33.2948i	0.268545	−	1.11106i
$899$	11.0317	+	11.0317i	0.367928	+	0.367928i
$900$	−12.5964	+	8.40413i	−0.419879	+	0.280138i
$901$	2.35746	−	2.35746i	0.0785385	−	0.0785385i
$902$	−35.0004	+	21.3745i	−1.16538	+	0.711693i
$903$	7.52117			0.250289
$904$	8.17648	+	7.04867i	0.271946	+	0.234435i
$905$	9.29024	−	5.45997i	0.308818	−	0.181496i
$906$	3.55964	−	2.17385i	0.118261	−	0.0722213i
$907$	11.9651	+	11.9651i	0.397295	+	0.397295i	0.877278	−	0.479983i	$-0.159357\pi$
$907$	11.9651	+	11.9651i	0.397295	+	0.397295i	−0.479983	+	0.877278i	$0.659357\pi$
$908$	−11.6679	+	3.75163i	−0.387214	+	0.124502i
$909$	8.77537	+	8.77537i	0.291061	+	0.291061i
$910$	−2.62526	−	8.66502i	−0.0870266	−	0.287243i
$911$	−50.8980			−1.68633			−0.843163	−	0.537657i	$-0.819309\pi$
$911$	−50.8980			−1.68633			−0.843163	+	0.537657i	$0.819309\pi$
$912$	38.6564	+	53.8980i	1.28004	+	1.78474i
$913$			50.7104i			1.67827i
$914$	−3.87630	+	16.0376i	−0.128217	+	0.530477i
$915$	43.3671	+	11.2614i	1.43367	+	0.372290i
$916$	15.8600	−	5.09951i	0.524028	−	0.168492i
$917$	14.5779	+	14.5779i	0.481404	+	0.481404i
$918$	11.5531	+	18.9180i	0.381310	+	0.624389i
$919$			36.6746i			1.20978i	0.796308	+	0.604891i	$0.206783\pi$
$919$			36.6746i			1.20978i	−0.796308	+	0.604891i	$0.793217\pi$
$920$	−27.3259	+	18.9070i	−0.900907	+	0.623345i
$921$		−	18.4692i		−	0.608581i
$922$	27.5992	−	16.8546i	0.908930	−	0.555078i
$923$	−14.1533	−	14.1533i	−0.465861	−	0.465861i
$924$	−8.03875	+	15.6581i	−0.264455	+	0.515112i
$925$	1.68298	+	5.91349i	0.0553361	+	0.194434i
$926$	−43.7698	−	10.5792i	−1.43836	−	0.347654i
$927$			15.4185i			0.506409i
$928$	−9.99615	−	4.23060i	−0.328140	−	0.138876i
$929$	−32.9401			−1.08073			−0.540364	−	0.841431i	$-0.681714\pi$
$929$	−32.9401			−1.08073			−0.540364	+	0.841431i	$0.681714\pi$
$930$	−15.8397	−	52.2812i	−0.519406	−	1.71437i
$931$	−5.51854	−	5.51854i	−0.180863	−	0.180863i
$932$	−18.7569	−	9.62969i	−0.614403	−	0.315431i
$933$	1.63164	+	1.63164i	0.0534175	+	0.0534175i
$934$	30.7421	+	50.3395i	1.00591	+	1.64716i
$935$	−23.3017	−	39.6484i	−0.762049	−	1.29664i
$936$	12.2291	−	0.905882i	0.399722	−	0.0296097i
$937$	−3.34269			−0.109201			−0.0546004	−	0.998508i	$-0.517388\pi$
$937$	−3.34269			−0.109201			−0.0546004	+	0.998508i	$0.517388\pi$
$938$	−3.57457	−	5.85328i	−0.116714	−	0.191117i
$939$	27.5026	−	27.5026i	0.897514	−	0.897514i
$940$	25.2593	−	28.3181i	0.823869	−	0.923635i
$941$	−27.1784	−	27.1784i	−0.885991	−	0.885991i	0.108144	−	0.994135i	$-0.465509\pi$
$941$	−27.1784	−	27.1784i	−0.885991	−	0.885991i	−0.994135	+	0.108144i	$0.965509\pi$
$942$	59.3744	+	14.3509i	1.93452	+	0.467576i
$943$			36.7840i			1.19785i
$944$	−47.2764	−	7.78533i	−1.53872	−	0.253391i
$945$	−3.57650	−	6.08549i	−0.116344	−	0.197961i
$946$	−4.87160	+	20.1555i	−0.158389	+	0.655311i
$947$	31.7759	−	31.7759i	1.03258	−	1.03258i	0.0331273	−	0.999451i	$-0.489453\pi$
$947$	31.7759	−	31.7759i	1.03258	−	1.03258i	0.999451	−	0.0331273i	$-0.0105467\pi$
$948$	49.4525	−	15.9006i	1.60614	−	0.516428i
$949$	21.4100	−	21.4100i	0.694997	−	0.694997i
$950$	55.1410	−	2.21329i	1.78901	−	0.0718086i
$951$		−	5.09605i		−	0.165251i
$952$	10.6372	+	9.16999i	0.344754	+	0.297201i
$953$	24.3418			0.788509			0.394255	−	0.919001i	$-0.371003\pi$
$953$	24.3418			0.788509			0.394255	+	0.919001i	$0.371003\pi$
$954$	−0.749411	−	1.22715i	−0.0242631	−	0.0397303i
$955$	21.4084	+	5.55925i	0.692761	+	0.179893i
$956$	12.8452	+	6.59466i	0.415445	+	0.213287i
$957$	11.9407	−	11.9407i	0.385988	−	0.385988i
$958$	−10.4928	+	43.4124i	−0.339007	+	1.40259i
$959$	15.2183			0.491423
$960$	23.8756	+	29.5723i	0.770581	+	0.954441i
$961$	35.1065			1.13247
$962$	1.16974	−	4.83963i	0.0377140	−	0.156036i
$963$	16.9794	−	16.9794i	0.547154	−	0.547154i
$964$	−16.3402	−	8.38893i	−0.526281	−	0.270189i
$965$	−1.80019	+	6.93245i	−0.0579501	+	0.223163i
$966$	8.22800	+	13.4732i	0.264731	+	0.433493i
$967$	32.4025			1.04199			0.520997	−	0.853558i	$-0.325560\pi$
$967$	32.4025			1.04199			0.520997	+	0.853558i	$0.325560\pi$
$968$	−13.1891	−	11.3698i	−0.423912	−	0.365441i
$969$			82.3349i			2.64498i
$970$	−18.5171	−	9.90577i	−0.594548	−	0.318055i
$971$	−19.9278	+	19.9278i	−0.639515	+	0.639515i	−0.950436	−	0.310921i	$-0.899362\pi$
$971$	−19.9278	+	19.9278i	−0.639515	+	0.639515i	0.310921	+	0.950436i	$0.399362\pi$
$972$	27.4786	−	8.83527i	0.881375	−	0.283391i
$973$	−3.39093	+	3.39093i	−0.108708	+	0.108708i
$974$	8.75154	−	36.2082i	0.280417	−	1.16018i
$975$	14.7987	−	26.5732i	0.473938	−	0.851023i
$976$	6.12964	−	37.2222i	0.196205	−	1.19145i
$977$			9.34265i			0.298898i	0.988769	+	0.149449i	$0.0477500\pi$
$977$			9.34265i			0.298898i	−0.988769	+	0.149449i	$0.952250\pi$
$978$	13.6225	+	3.29257i	0.435600	+	0.105285i
$979$	18.6871	+	18.6871i	0.597243	+	0.597243i
$980$	−3.33738	−	2.97689i	−0.106609	−	0.0950934i
$981$	10.1749	−	10.1749i	0.324859	−	0.324859i
$982$	17.8102	+	29.1639i	0.568348	+	0.930659i
$983$	−16.1756			−0.515921			−0.257960	−	0.966155i	$-0.583050\pi$
$983$	−16.1756			−0.515921			−0.257960	+	0.966155i	$0.583050\pi$
$984$	41.9585	−	3.10810i	1.33759	−	0.0990825i
$985$	3.30606	+	5.62532i	0.105340	+	0.179238i
$986$	−7.02263	−	11.4994i	−0.223646	−	0.366216i
$987$	−12.7479	−	12.7479i	−0.405769	−	0.405769i
$988$	−39.7566	−	20.4108i	−1.26483	−	0.649353i
$989$	13.1512	+	13.1512i	0.418185	+	0.418185i
$990$	−18.9821	+	5.75106i	−0.603291	+	0.182781i
$991$	54.0757			1.71777			0.858886	−	0.512167i	$-0.171157\pi$
$991$	54.0757			1.71777			0.858886	+	0.512167i	$0.171157\pi$
$992$	−42.6262	+	17.2747i	−1.35338	+	0.548473i
$993$		−	17.0922i		−	0.542404i
$994$	−9.60990	−	2.32272i	−0.304808	−	0.0736722i
$995$	−6.83826	+	26.3338i	−0.216787	+	0.834839i
$996$	23.7605	−	46.2813i	0.752880	−	1.46648i
$997$	25.4471	+	25.4471i	0.805917	+	0.805917i	0.984013	−	0.178096i	$-0.0569937\pi$
$997$	25.4471	+	25.4471i	0.805917	+	0.805917i	−0.178096	+	0.984013i	$0.556994\pi$
$998$	−29.7777	+	18.1850i	−0.942596	+	0.575638i
$999$		−	3.88171i		−	0.122812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.14	yes	70
5.4	even	2		560.2.bb.c.29.22	✓	70
16.5	even	4		560.2.bb.c.309.22	yes	70
80.69	even	4	inner	560.2.bb.d.309.14	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.22	✓	70	5.4	even	2
560.2.bb.c.309.22	yes	70	16.5	even	4
560.2.bb.d.29.14	yes	70	1.1	even	1	trivial
560.2.bb.d.309.14	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)

\(f(q)\)	\(=\)	\(q+(-0.332249 + 1.37463i) q^{2} +(-1.50237 + 1.50237i) q^{3} +(-1.77922 - 0.913441i) q^{4} +(2.16429 + 0.562013i) q^{5} +(-1.56605 - 2.56437i) q^{6} +1.00000 q^{7} +(1.84679 - 2.14228i) q^{8} -1.51426i q^{9} +O(q^{10})\)	\(q+(-0.332249 + 1.37463i) q^{2} +(-1.50237 + 1.50237i) q^{3} +(-1.77922 - 0.913441i) q^{4} +(2.16429 + 0.562013i) q^{5} +(-1.56605 - 2.56437i) q^{6} +1.00000 q^{7} +(1.84679 - 2.14228i) q^{8} -1.51426i q^{9} +(-1.49164 + 2.78837i) q^{10} +(-2.92887 + 2.92887i) q^{11} +(4.04539 - 1.30073i) q^{12} +(-2.02453 + 2.02453i) q^{13} +(-0.332249 + 1.37463i) q^{14} +(-4.09592 + 2.40722i) q^{15} +(2.33125 + 3.25043i) q^{16} +4.96537i q^{17} +(2.08155 + 0.503111i) q^{18} +(-5.51854 - 5.51854i) q^{19} +(-3.33738 - 2.97689i) q^{20} +(-1.50237 + 1.50237i) q^{21} +(-3.05300 - 4.99923i) q^{22} -5.25399 q^{23} +(0.443941 + 5.99308i) q^{24} +(4.36828 + 2.43272i) q^{25} +(-2.11033 - 3.45563i) q^{26} +(-2.23214 - 2.23214i) q^{27} +(-1.77922 - 0.913441i) q^{28} +(1.35682 + 1.35682i) q^{29} +(-1.94817 - 6.43018i) q^{30} +8.13059 q^{31} +(-5.24269 + 2.12466i) q^{32} -8.80052i q^{33} +(-6.82555 - 1.64974i) q^{34} +(2.16429 + 0.562013i) q^{35} +(-1.38318 + 2.69420i) q^{36} +(0.869503 + 0.869503i) q^{37} +(9.41949 - 5.75243i) q^{38} -6.08321i q^{39} +(5.20097 - 3.59859i) q^{40} -7.00115i q^{41} +(-1.56605 - 2.56437i) q^{42} +(-2.50309 - 2.50309i) q^{43} +(7.88645 - 2.53576i) q^{44} +(0.851032 - 3.27729i) q^{45} +(1.74564 - 7.22230i) q^{46} +8.48514i q^{47} +(-8.38577 - 1.38094i) q^{48} +1.00000 q^{49} +(-4.79545 + 5.19651i) q^{50} +(-7.45984 - 7.45984i) q^{51} +(5.45138 - 1.75280i) q^{52} +(-0.474781 - 0.474781i) q^{53} +(3.81000 - 2.32674i) q^{54} +(-7.98498 + 4.69285i) q^{55} +(1.84679 - 2.14228i) q^{56} +16.5818 q^{57} +(-2.31592 + 1.41432i) q^{58} +(-8.46993 + 8.46993i) q^{59} +(9.48640 - 0.541586i) q^{60} +(-6.66865 - 6.66865i) q^{61} +(-2.70138 + 11.1766i) q^{62} -1.51426i q^{63} +(-1.17874 - 7.91268i) q^{64} +(-5.51948 + 3.24386i) q^{65} +(12.0975 + 2.92397i) q^{66} +(-3.42923 + 3.42923i) q^{67} +(4.53557 - 8.83449i) q^{68} +(7.89346 - 7.89346i) q^{69} +(-1.49164 + 2.78837i) q^{70} +6.99090i q^{71} +(-3.24397 - 2.79651i) q^{72} -10.5753 q^{73} +(-1.48414 + 0.906354i) q^{74} +(-10.2176 + 2.90795i) q^{75} +(4.77784 + 14.8596i) q^{76} +(-2.92887 + 2.92887i) q^{77} +(8.36217 + 2.02114i) q^{78} +12.2244 q^{79} +(3.21872 + 8.34505i) q^{80} +11.2498 q^{81} +(9.62400 + 2.32613i) q^{82} +(8.65699 - 8.65699i) q^{83} +(4.04539 - 1.30073i) q^{84} +(-2.79060 + 10.7465i) q^{85} +(4.27248 - 2.60918i) q^{86} -4.07689 q^{87} +(0.865460 + 11.6835i) q^{88} -6.38032i q^{89} +(4.22231 + 2.25873i) q^{90} +(-2.02453 + 2.02453i) q^{91} +(9.34801 + 4.79921i) q^{92} +(-12.2152 + 12.2152i) q^{93} +(-11.6639 - 2.81918i) q^{94} +(-8.84222 - 15.0452i) q^{95} +(4.68445 - 11.0685i) q^{96} +6.64084i q^{97} +(-0.332249 + 1.37463i) q^{98} +(4.43506 + 4.43506i) 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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