LMFDB - Embedded newform 280.2.bj.f.171.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			171.11
Character	$\chi$	$=$	280.171
Dual form			280.2.bj.f.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37350 + 0.336893i) q^{2} +(1.75472 + 1.01309i) q^{3} +(1.77301 + 0.925446i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.06881 + 1.98263i) q^{6} +(-1.63843 - 2.07739i) q^{7} +(2.12345 + 1.86841i) q^{8} +(0.552704 + 0.957311i) q^{9} +O(q^{10})$	\(q+(1.37350 + 0.336893i) q^{2} +(1.75472 + 1.01309i) q^{3} +(1.77301 + 0.925446i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.06881 + 1.98263i) q^{6} +(-1.63843 - 2.07739i) q^{7} +(2.12345 + 1.86841i) q^{8} +(0.552704 + 0.957311i) q^{9} +(-0.394992 - 1.35793i) q^{10} +(-0.572544 + 0.991675i) q^{11} +(2.17358 + 3.42012i) q^{12} -0.714654 q^{13} +(-1.55053 - 3.40527i) q^{14} -2.02618i q^{15} +(2.28710 + 3.28164i) q^{16} +(-1.98251 - 1.14460i) q^{17} +(0.436627 + 1.50107i) q^{18} +(-3.36692 + 1.94389i) q^{19} +(-0.0850431 - 1.99819i) q^{20} +(-0.770420 - 5.30512i) q^{21} +(-1.12048 + 1.16918i) q^{22} +(-4.00399 + 2.31171i) q^{23} +(1.83319 + 5.42979i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.981578 - 0.240762i) q^{26} -3.83879i q^{27} +(-0.982445 - 5.19950i) q^{28} +1.54366i q^{29} +(0.682607 - 2.78296i) q^{30} +(-0.590584 + 1.02292i) q^{31} +(2.03577 + 5.27785i) q^{32} +(-2.00931 + 1.16008i) q^{33} +(-2.33737 - 2.24000i) q^{34} +(-0.979852 + 2.45762i) q^{35} +(0.0940073 + 2.20882i) q^{36} +(5.72305 - 3.30420i) q^{37} +(-5.27936 + 1.53565i) q^{38} +(-1.25402 - 0.724009i) q^{39} +(0.556370 - 2.77317i) q^{40} -10.9848i q^{41} +(0.729087 - 7.54613i) q^{42} +10.8452 q^{43} +(-1.93286 + 1.22839i) q^{44} +(0.552704 - 0.957311i) q^{45} +(-6.27829 + 1.82621i) q^{46} +(2.60440 + 4.51095i) q^{47} +(0.688627 + 8.07541i) q^{48} +(-1.63107 + 6.80732i) q^{49} +(-0.978508 + 1.02104i) q^{50} +(-2.31917 - 4.01692i) q^{51} +(-1.26709 - 0.661374i) q^{52} +(2.25895 + 1.30420i) q^{53} +(1.29326 - 5.27257i) q^{54} +1.14509 q^{55} +(0.402288 - 7.47249i) q^{56} -7.87736 q^{57} +(-0.520048 + 2.12021i) q^{58} +(10.5249 + 6.07655i) q^{59} +(1.87512 - 3.59243i) q^{60} +(-7.13513 - 12.3584i) q^{61} +(-1.15578 + 1.20602i) q^{62} +(1.08314 - 2.71667i) q^{63} +(1.01806 + 7.93496i) q^{64} +(0.357327 + 0.618909i) q^{65} +(-3.15061 + 0.916442i) q^{66} +(4.08800 - 7.08062i) q^{67} +(-2.45573 - 3.86409i) q^{68} -9.36787 q^{69} +(-2.17378 + 3.04543i) q^{70} +15.8551i q^{71} +(-0.615016 + 3.06548i) q^{72} +(-4.71396 - 2.72160i) q^{73} +(8.97377 - 2.61027i) q^{74} +(-1.75472 + 1.01309i) q^{75} +(-7.76854 + 0.330630i) q^{76} +(2.99817 - 0.435400i) q^{77} +(-1.47848 - 1.41690i) q^{78} +(-8.20023 + 4.73440i) q^{79} +(1.69844 - 3.62151i) q^{80} +(5.54715 - 9.60794i) q^{81} +(3.70072 - 15.0877i) q^{82} +2.78987i q^{83} +(3.54364 - 10.1190i) q^{84} +2.28920i q^{85} +(14.8958 + 3.65366i) q^{86} +(-1.56386 + 2.70869i) q^{87} +(-3.06862 + 1.03602i) q^{88} +(-11.0522 + 6.38097i) q^{89} +(1.08165 - 1.12866i) q^{90} +(1.17091 + 1.48461i) q^{91} +(-9.23847 + 0.393190i) q^{92} +(-2.07262 + 1.19663i) q^{93} +(2.05743 + 7.07319i) q^{94} +(3.36692 + 1.94389i) q^{95} +(-1.77472 + 11.3236i) q^{96} -5.18530i q^{97} +(-4.53361 + 8.80036i) q^{98} -1.26579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	$ 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) $ 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.37350	+	0.336893i	0.971211	+	0.238220i
$2$	1.37350	+	0.336893i	0.971211	+	0.238220i
$3$	1.75472	+	1.01309i	1.01309	+	0.584908i	0.912095	−	0.409979i	$-0.134464\pi$
$3$	1.75472	+	1.01309i	1.01309	+	0.584908i	0.100995	+	0.994887i	$0.467797\pi$
$4$	1.77301	+	0.925446i	0.886503	+	0.462723i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.06881	+	1.98263i	0.844588	+	0.809407i
$7$	−1.63843	−	2.07739i	−0.619270	−	0.785178i
$7$	−1.63843	−	2.07739i	−0.619270	−	0.785178i
$8$	2.12345	+	1.86841i	0.750752	+	0.660584i
$9$	0.552704	+	0.957311i	0.184235	+	0.319104i
$10$	−0.394992	−	1.35793i	−0.124907	−	0.429416i
$11$	−0.572544	+	0.991675i	−0.172628	+	0.299001i	−0.939338	−	0.342993i	$-0.888559\pi$
$11$	−0.572544	+	0.991675i	−0.172628	+	0.299001i	0.766710	+	0.641994i	$0.221893\pi$
$12$	2.17358	+	3.42012i	0.627457	+	0.987303i
$13$	−0.714654			−0.198209			−0.0991047	−	0.995077i	$-0.531598\pi$
$13$	−0.714654			−0.198209			−0.0991047	+	0.995077i	$0.531598\pi$
$14$	−1.55053	−	3.40527i	−0.414397	−	0.910096i
$15$		−	2.02618i		−	0.523158i
$16$	2.28710	+	3.28164i	0.571775	+	0.820411i
$17$	−1.98251	−	1.14460i	−0.480829	−	0.277607i	0.239933	−	0.970789i	$-0.422875\pi$
$17$	−1.98251	−	1.14460i	−0.480829	−	0.277607i	−0.720762	+	0.693183i	$0.756208\pi$
$18$	0.436627	+	1.50107i	0.102914	+	0.353805i
$19$	−3.36692	+	1.94389i	−0.772425	+	0.445960i	−0.833739	−	0.552159i	$-0.813804\pi$
$19$	−3.36692	+	1.94389i	−0.772425	+	0.445960i	0.0613139	+	0.998119i	$0.480471\pi$
$20$	−0.0850431	−	1.99819i	−0.0190162	−	0.446809i
$21$	−0.770420	−	5.30512i	−0.168119	−	1.15767i
$22$	−1.12048	+	1.16918i	−0.238887	+	0.249270i
$23$	−4.00399	+	2.31171i	−0.834891	+	0.482024i	−0.855524	−	0.517763i	$-0.826765\pi$
$23$	−4.00399	+	2.31171i	−0.834891	+	0.482024i	0.0206336	+	0.999787i	$0.493432\pi$
$24$	1.83319	+	5.42979i	0.374199	+	1.10835i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.981578	−	0.240762i	−0.192503	−	0.0472174i
$27$		−	3.83879i		−	0.738775i
$28$	−0.982445	−	5.19950i	−0.185665	−	0.982613i
$29$			1.54366i			0.286650i	0.989676	+	0.143325i	$0.0457794\pi$
$29$			1.54366i			0.286650i	−0.989676	+	0.143325i	$0.954221\pi$
$30$	0.682607	−	2.78296i	0.124626	−	0.508097i
$31$	−0.590584	+	1.02292i	−0.106072	+	0.183722i	−0.914176	−	0.405318i	$-0.867161\pi$
$31$	−0.590584	+	1.02292i	−0.106072	+	0.183722i	0.808104	+	0.589040i	$0.200494\pi$
$32$	2.03577	+	5.27785i	0.359876	+	0.933000i
$33$	−2.00931	+	1.16008i	−0.349776	+	0.201943i
$34$	−2.33737	−	2.24000i	−0.400855	−	0.384158i
$35$	−0.979852	+	2.45762i	−0.165625	+	0.415413i
$36$	0.0940073	+	2.20882i	0.0156679	+	0.368136i
$37$	5.72305	−	3.30420i	0.940864	−	0.543208i	0.0506326	−	0.998717i	$-0.483876\pi$
$37$	5.72305	−	3.30420i	0.940864	−	0.543208i	0.890231	+	0.455510i	$0.150543\pi$
$38$	−5.27936	+	1.53565i	−0.856424	+	0.249115i
$39$	−1.25402	−	0.724009i	−0.200804	−	0.115934i
$40$	0.556370	−	2.77317i	0.0879699	−	0.438476i
$41$		−	10.9848i		−	1.71555i	−0.514029	−	0.857773i	$-0.671848\pi$
$41$		−	10.9848i		−	1.71555i	0.514029	−	0.857773i	$-0.328152\pi$
$42$	0.729087	−	7.54613i	0.112501	−	1.16439i
$43$	10.8452			1.65387			0.826935	−	0.562297i	$-0.190082\pi$
$43$	10.8452			1.65387			0.826935	+	0.562297i	$0.190082\pi$
$44$	−1.93286	+	1.22839i	−0.291390	+	0.185186i
$45$	0.552704	−	0.957311i	0.0823922	−	0.142708i
$46$	−6.27829	+	1.82621i	−0.925683	+	0.269260i
$47$	2.60440	+	4.51095i	0.379890	+	0.657989i	0.991046	−	0.133521i	$-0.0426285\pi$
$47$	2.60440	+	4.51095i	0.379890	+	0.657989i	−0.611156	+	0.791510i	$0.709295\pi$
$48$	0.688627	+	8.07541i	0.0993948	+	1.16559i
$49$	−1.63107	+	6.80732i	−0.233009	+	0.972474i
$50$	−0.978508	+	1.02104i	−0.138382	+	0.144397i
$51$	−2.31917	−	4.01692i	−0.324749	−	0.562481i
$52$	−1.26709	−	0.661374i	−0.175713	−	0.0917161i
$53$	2.25895	+	1.30420i	0.310290	+	0.179146i	0.647056	−	0.762442i	$-0.276000\pi$
$53$	2.25895	+	1.30420i	0.310290	+	0.179146i	−0.336766	+	0.941588i	$0.609333\pi$
$54$	1.29326	−	5.27257i	0.175991	−	0.717506i
$55$	1.14509			0.154404
$56$	0.402288	−	7.47249i	0.0537580	−	0.998554i
$57$	−7.87736			−1.04338
$58$	−0.520048	+	2.12021i	−0.0682856	+	0.278398i
$59$	10.5249	+	6.07655i	1.37023	+	0.791100i	0.990956	−	0.134187i	$-0.0428422\pi$
$59$	10.5249	+	6.07655i	1.37023	+	0.791100i	0.379269	+	0.925286i	$0.376176\pi$
$60$	1.87512	−	3.59243i	0.242077	−	0.463781i
$61$	−7.13513	−	12.3584i	−0.913559	−	1.58233i	−0.808997	−	0.587813i	$-0.799989\pi$
$61$	−7.13513	−	12.3584i	−0.913559	−	1.58233i	−0.104563	−	0.994518i	$-0.533344\pi$
$62$	−1.15578	+	1.20602i	−0.146784	+	0.153165i
$63$	1.08314	−	2.71667i	0.136462	−	0.342268i
$64$	1.01806	+	7.93496i	0.127257	+	0.991870i
$65$	0.357327	+	0.618909i	0.0443210	+	0.0767662i
$66$	−3.15061	+	0.916442i	−0.387814	+	0.112806i
$67$	4.08800	−	7.08062i	0.499429	−	0.865036i	−0.500571	−	0.865695i	$-0.666877\pi$
$67$	4.08800	−	7.08062i	0.499429	−	0.865036i	1.00000		0.000659524i	$0.000209933\pi$
$68$	−2.45573	−	3.86409i	−0.297801	−	0.468590i
$69$	−9.36787			−1.12776
$70$	−2.17378	+	3.04543i	−0.259817	+	0.363999i
$71$			15.8551i			1.88166i	0.338881	+	0.940829i	$0.389952\pi$
$71$			15.8551i			1.88166i	−0.338881	+	0.940829i	$0.610048\pi$
$72$	−0.615016	+	3.06548i	−0.0724804	+	0.361270i
$73$	−4.71396	−	2.72160i	−0.551727	−	0.318540i	0.198091	−	0.980184i	$-0.436526\pi$
$73$	−4.71396	−	2.72160i	−0.551727	−	0.318540i	−0.749818	+	0.661644i	$0.769859\pi$
$74$	8.97377	−	2.61027i	1.04318	−	0.303438i
$75$	−1.75472	+	1.01309i	−0.202618	+	0.116982i
$76$	−7.76854	+	0.330630i	−0.891113	+	0.0379258i
$77$	2.99817	−	0.435400i	0.341673	−	0.0496184i
$78$	−1.47848	−	1.41690i	−0.167405	−	0.160432i
$79$	−8.20023	+	4.73440i	−0.922598	+	0.532662i	−0.884463	−	0.466611i	$-0.845475\pi$
$79$	−8.20023	+	4.73440i	−0.922598	+	0.532662i	−0.0381347	+	0.999273i	$0.512142\pi$
$80$	1.69844	−	3.62151i	0.189891	−	0.404897i
$81$	5.54715	−	9.60794i	0.616350	−	1.06755i
$82$	3.70072	−	15.0877i	0.408676	−	1.66616i
$83$			2.78987i			0.306229i	0.988208	+	0.153114i	$0.0489303\pi$
$83$			2.78987i			0.306229i	−0.988208	+	0.153114i	$0.951070\pi$
$84$	3.54364	−	10.1190i	0.386643	−	1.10407i
$85$			2.28920i			0.248299i
$86$	14.8958	+	3.65366i	1.60626	+	0.393984i
$87$	−1.56386	+	2.70869i	−0.167664	+	0.290402i
$88$	−3.06862	+	1.03602i	−0.327117	+	0.110440i
$89$	−11.0522	+	6.38097i	−1.17153	+	0.676382i	−0.954039	−	0.299681i	$-0.903120\pi$
$89$	−11.0522	+	6.38097i	−1.17153	+	0.676382i	−0.217488	+	0.976063i	$0.569786\pi$
$90$	1.08165	−	1.12866i	0.114016	−	0.118972i
$91$	1.17091	+	1.48461i	0.122745	+	0.155630i
$92$	−9.23847	+	0.393190i	−0.963177	+	0.0409928i
$93$	−2.07262	+	1.19663i	−0.214921	+	0.124085i
$94$	2.05743	+	7.07319i	0.212208	+	0.729544i
$95$	3.36692	+	1.94389i	0.345439	+	0.199439i
$96$	−1.77472	+	11.3236i	−0.181132	+	1.15571i
$97$		−	5.18530i		−	0.526487i	−0.964729	−	0.263244i	$-0.915208\pi$
$97$		−	5.18530i		−	0.526487i	0.964729	−	0.263244i	$-0.0847923\pi$
$98$	−4.53361	+	8.80036i	−0.457964	+	0.888971i
$99$	−1.26579			−0.127216
$100$	−1.68796	+	1.07275i	−0.168796	+	0.107275i
$101$	0.506008	−	0.876431i	0.0503497	−	0.0872082i	−0.839752	−	0.542970i	$-0.817300\pi$
$101$	0.506008	−	0.876431i	0.0503497	−	0.0872082i	0.890102	+	0.455762i	$0.150633\pi$
$102$	−1.83211	−	6.29855i	−0.181406	−	0.623650i
$103$	−1.22006	−	2.11321i	−0.120217	−	0.208221i	0.799636	−	0.600484i	$-0.205026\pi$
$103$	−1.22006	−	2.11321i	−0.120217	−	0.208221i	−0.919853	+	0.392263i	$0.871692\pi$
$104$	−1.51753	−	1.33527i	−0.148806	−	0.130934i
$105$	−4.20916	+	3.31976i	−0.410772	+	0.323976i
$106$	2.66329	+	2.55235i	0.258681	+	0.247906i
$107$	−0.680251	−	1.17823i	−0.0657623	−	0.113904i	0.831270	−	0.555869i	$-0.187615\pi$
$107$	−0.680251	−	1.17823i	−0.0657623	−	0.113904i	−0.897032	+	0.441966i	$0.854281\pi$
$108$	3.55259	−	6.80619i	0.341848	−	0.654926i
$109$	9.05255	+	5.22649i	0.867077	+	0.500607i	0.866376	−	0.499393i	$-0.166444\pi$
$109$	9.05255	+	5.22649i	0.867077	+	0.500607i	0.000700983		1.00000i	$0.499777\pi$
$110$	1.57278	+	0.385772i	0.149958	+	0.0367819i
$111$	13.3898			1.27091
$112$	3.06998	−	10.1279i	0.290085	−	0.957001i
$113$	−7.83586			−0.737135			−0.368568	−	0.929601i	$-0.620152\pi$
$113$	−7.83586			−0.737135			−0.368568	+	0.929601i	$0.620152\pi$
$114$	−10.8196	−	2.65383i	−1.01334	−	0.248554i
$115$	4.00399	+	2.31171i	0.373374	+	0.215568i
$116$	−1.42857	+	2.73691i	−0.132640	+	0.254116i
$117$	−0.394992	−	0.684146i	−0.0365170	−	0.0632494i
$118$	12.4088	+	11.8919i	1.14232	+	1.09474i
$119$	0.870430	+	5.99379i	0.0797922	+	0.549450i
$120$	3.78574	−	4.30249i	0.345590	−	0.392762i
$121$	4.84439	+	8.39073i	0.440399	+	0.762793i
$122$	−5.63664	−	19.3780i	−0.510317	−	1.75441i
$123$	11.1286	−	19.2754i	1.00344	−	1.73800i
$124$	−1.99377	+	1.26709i	−0.179046	+	0.113788i
$125$	1.00000			0.0894427
$126$	2.40292	−	3.36645i	0.214069	−	0.299907i
$127$		−	12.0344i		−	1.06788i	−0.845522	−	0.533940i	$-0.820711\pi$
$127$		−	12.0344i		−	1.06788i	0.845522	−	0.533940i	$-0.179289\pi$
$128$	−1.27493	+	11.2416i	−0.112689	+	0.993630i
$129$	19.0302	+	10.9871i	1.67552	+	0.967362i
$130$	0.282283	+	0.970452i	0.0247578	+	0.0851143i
$131$	−17.9090	+	10.3397i	−1.56471	+	0.903387i	−0.567943	+	0.823068i	$0.692261\pi$
$131$	−17.9090	+	10.3397i	−1.56471	+	0.903387i	−0.996769	+	0.0803195i	$0.974406\pi$
$132$	−4.63611	+	0.197313i	−0.403522	+	0.0171739i
$133$	9.55470	+	3.80946i	0.828498	+	0.330322i
$134$	8.00028	−	8.34802i	0.691119	−	0.721159i
$135$	−3.32449	+	1.91939i	−0.286126	+	0.165195i
$136$	−2.07116	−	6.13465i	−0.177601	−	0.526042i
$137$	2.37459	−	4.11290i	0.202875	−	0.351389i	−0.746579	−	0.665297i	$-0.768305\pi$
$137$	2.37459	−	4.11290i	0.202875	−	0.351389i	0.949453	+	0.313908i	$0.101638\pi$
$138$	−12.8668	−	3.15597i	−1.09529	−	0.268654i
$139$			10.9812i			0.931416i	0.884938	+	0.465708i	$0.154200\pi$
$139$			10.9812i			0.931416i	−0.884938	+	0.465708i	$0.845800\pi$
$140$	−4.01168	+	3.45057i	−0.339049	+	0.291627i
$141$			10.5540i			0.888803i
$142$	−5.34149	+	21.7770i	−0.448248	+	1.82749i
$143$	0.409171	−	0.708704i	0.0342166	−	0.0592648i
$144$	−1.87746	+	4.00324i	−0.156455	+	0.333603i
$145$	1.33685	−	0.771829i	0.111019	−	0.0640969i
$146$	−5.55773	−	5.32622i	−0.459961	−	0.440801i
$147$	−9.75850	+	10.2926i	−0.804868	+	0.848915i
$148$	13.2049	−	0.562000i	1.08543	−	0.0461961i
$149$	13.4757	−	7.78020i	1.10397	−	0.637379i	0.166711	−	0.986006i	$-0.446685\pi$
$149$	13.4757	−	7.78020i	1.10397	−	0.637379i	0.937261	+	0.348627i	$0.113352\pi$
$150$	−2.75142	+	0.800325i	−0.224652	+	0.0653463i
$151$	10.8679	+	6.27460i	0.884419	+	0.510620i	0.872113	−	0.489305i	$-0.162749\pi$
$151$	10.8679	+	6.27460i	0.884419	+	0.510620i	0.0123061	+	0.999924i	$0.496083\pi$
$152$	−10.7815	−	2.16305i	−0.874494	−	0.175447i
$153$		−	2.53050i		−	0.204579i
$154$	4.26466	+	0.412040i	0.343656	+	0.0332032i
$155$	1.18117			0.0948737
$156$	−1.55335	−	2.44420i	−0.124368	−	0.195693i
$157$	3.83150	−	6.63634i	0.305787	−	0.529638i	−0.671650	−	0.740869i	$-0.734414\pi$
$157$	3.83150	−	6.63634i	0.305787	−	0.529638i	0.977436	+	0.211231i	$0.0677473\pi$
$158$	−12.8580	+	3.74010i	−1.02293	+	0.297547i
$159$	2.64255	+	4.57704i	0.209568	+	0.362983i
$160$	3.55286	−	4.40195i	0.280879	−	0.348005i
$161$	11.3626	+	4.53026i	0.895498	+	0.357035i
$162$	10.8559	−	11.3277i	0.852917	−	0.889989i
$163$	−10.0482	−	17.4040i	−0.787037	−	1.36319i	−0.927775	−	0.373141i	$-0.878281\pi$
$163$	−10.0482	−	17.4040i	−0.787037	−	1.36319i	0.140738	−	0.990047i	$-0.455053\pi$
$164$	10.1659	−	19.4762i	0.793822	−	1.52084i
$165$	2.00931	+	1.16008i	0.156425	+	0.0903118i
$166$	−0.939890	+	3.83189i	−0.0729496	+	0.297413i
$167$	6.77446			0.524224			0.262112	−	0.965037i	$-0.415581\pi$
$167$	6.77446			0.524224			0.262112	+	0.965037i	$0.415581\pi$
$168$	8.27622	−	12.7046i	0.638524	−	0.980182i
$169$	−12.4893			−0.960713
$170$	−0.771217	+	3.14422i	−0.0591497	+	0.241151i
$171$	−3.72182	−	2.14880i	−0.284615	−	0.164322i
$172$	19.2285	+	10.0366i	1.46616	+	0.765284i
$173$	8.70160	+	15.0716i	0.661570	+	1.14587i	0.980203	+	0.197995i	$0.0634429\pi$
$173$	8.70160	+	15.0716i	0.661570	+	1.14587i	−0.318633	+	0.947878i	$0.603224\pi$
$174$	−3.06051	+	3.19354i	−0.232017	+	0.242101i
$175$	2.61829	−	0.380233i	0.197924	−	0.0287429i
$176$	−4.56379	+	0.389175i	−0.344008	+	0.0293352i
$177$	12.3122	+	21.3253i	0.925441	+	1.60291i
$178$	−17.3299	+	5.04087i	−1.29893	+	0.377829i
$179$	−7.66373	+	13.2740i	−0.572814	+	0.992143i	0.423461	+	0.905914i	$0.360815\pi$
$179$	−7.66373	+	13.2740i	−0.572814	+	0.992143i	−0.996275	+	0.0862291i	$0.972518\pi$
$180$	1.86589	−	1.18582i	0.139075	−	0.0883858i
$181$	3.10021			0.230437			0.115218	−	0.993340i	$-0.463243\pi$
$181$	3.10021			0.230437			0.115218	+	0.993340i	$0.463243\pi$
$182$	1.10809	+	2.43359i	0.0821374	+	0.180390i
$183$		−	28.9141i		−	2.13739i
$184$	−12.8215	−	2.57233i	−0.945213	−	0.189635i
$185$	−5.72305	−	3.30420i	−0.420767	−	0.242930i
$186$	−3.24988	+	0.945318i	−0.238293	+	0.0693141i
$187$	2.27014	−	1.31067i	0.166009	−	0.0958456i
$188$	0.442972	+	10.4082i	0.0323070	+	0.759093i
$189$	−7.97464	+	6.28960i	−0.580070	+	0.457501i
$190$	3.96959	+	3.80423i	0.287984	+	0.275988i
$191$	−12.6460	+	7.30118i	−0.915034	+	0.528295i	−0.882047	−	0.471161i	$-0.843835\pi$
$191$	−12.6460	+	7.30118i	−0.915034	+	0.528295i	−0.0329865	+	0.999456i	$0.510502\pi$
$192$	−6.25242	+	14.9550i	−0.451230	+	1.07929i
$193$	8.50498	−	14.7311i	0.612202	−	1.06037i	−0.378666	−	0.925533i	$-0.623617\pi$
$193$	8.50498	−	14.7311i	0.612202	−	1.06037i	0.990868	−	0.134832i	$-0.0430494\pi$
$194$	1.74689	−	7.12201i	0.125420	−	0.511331i
$195$			1.44802i			0.103695i
$196$	−9.19170	+	10.5600i	−0.656550	+	0.754283i
$197$			15.2341i			1.08538i	0.839932	+	0.542692i	$0.182595\pi$
$197$			15.2341i			1.08538i	−0.839932	+	0.542692i	$0.817405\pi$
$198$	−1.73856	−	0.426436i	−0.123554	−	0.0303055i
$199$	8.02143	−	13.8935i	0.568624	−	0.984886i	−0.428078	−	0.903742i	$-0.640809\pi$
$199$	8.02143	−	13.8935i	0.568624	−	0.984886i	0.996702	−	0.0811444i	$-0.0258575\pi$
$200$	−2.67982	+	0.904752i	−0.189492	+	0.0639756i
$201$	14.3466	−	8.28303i	1.01193	−	0.584240i
$202$	0.990266	−	1.03331i	0.0696748	−	0.0727033i
$203$	3.20677	−	2.52918i	0.225071	−	0.177514i
$204$	−0.394459	−	9.26829i	−0.0276176	−	0.648910i
$205$	−9.51316	+	5.49242i	−0.664428	+	0.383608i
$206$	−0.963831	−	3.31353i	−0.0671533	−	0.230865i
$207$	−4.42605	−	2.55538i	−0.307632	−	0.177611i
$208$	−1.63449	−	2.34524i	−0.113331	−	0.162613i
$209$		−	4.45186i		−	0.307941i
$210$	−6.89969	+	3.14166i	−0.476124	+	0.216795i
$211$	−5.85788			−0.403273			−0.201637	−	0.979460i	$-0.564626\pi$
$211$	−5.85788			−0.403273			−0.201637	+	0.979460i	$0.564626\pi$
$212$	2.79816	+	4.40290i	0.192178	+	0.302392i
$213$	−16.0627	+	27.8214i	−1.10060	+	1.90629i
$214$	−0.537387	−	1.84747i	−0.0367350	−	0.126290i
$215$	−5.42258	−	9.39218i	−0.369817	−	0.640541i
$216$	7.17244	−	8.15146i	0.488023	−	0.554637i
$217$	3.09263	−	0.449119i	0.209942	−	0.0304882i
$218$	10.6729	+	10.2283i	0.722860	+	0.692750i
$219$	−5.51446	−	9.55132i	−0.372633	−	0.645419i
$220$	2.03025	+	1.05972i	0.136879	+	0.0714461i
$221$	1.41681	+	0.817994i	0.0953048	+	0.0550243i
$222$	18.3909	+	4.51094i	1.23432	+	0.302755i
$223$	12.3268			0.825465			0.412732	−	0.910852i	$-0.364574\pi$
$223$	12.3268			0.825465			0.412732	+	0.910852i	$0.364574\pi$
$224$	7.62865	−	12.8765i	0.509711	−	0.860346i
$225$	−1.10541			−0.0736938
$226$	−10.7625	−	2.63985i	−0.715914	−	0.175600i
$227$	6.79256	+	3.92168i	0.450838	+	0.260291i	0.708184	−	0.706028i	$-0.249515\pi$
$227$	6.79256	+	3.92168i	0.450838	+	0.260291i	−0.257346	+	0.966319i	$0.582848\pi$
$228$	−13.9666	−	7.29007i	−0.924961	−	0.482797i
$229$	−7.70634	−	13.3478i	−0.509249	−	0.882046i	−0.999943	−	0.0107133i	$-0.996590\pi$
$229$	−7.70634	−	13.3478i	−0.509249	−	0.882046i	0.490693	−	0.871332i	$-0.336744\pi$
$230$	4.72069	+	4.52405i	0.311273	+	0.298307i
$231$	5.70205	+	2.27341i	0.375168	+	0.149579i
$232$	−2.88419	+	3.27788i	−0.189356	+	0.215203i
$233$	−5.62905	−	9.74980i	−0.368771	−	0.638731i	0.620602	−	0.784126i	$-0.286888\pi$
$233$	−5.62905	−	9.74980i	−0.368771	−	0.638731i	−0.989374	+	0.145395i	$0.953555\pi$
$234$	−0.312037	−	1.07275i	−0.0203985	−	0.0701276i
$235$	2.60440	−	4.51095i	0.169892	−	0.294262i
$236$	13.0372	+	20.5140i	0.848648	+	1.33535i
$237$	−19.1855			−1.24623
$238$	−0.823732	+	8.52571i	−0.0533946	+	0.552640i
$239$		−	14.1518i		−	0.915404i	−0.889106	−	0.457702i	$-0.848673\pi$
$239$		−	14.1518i		−	0.915404i	0.889106	−	0.457702i	$-0.151327\pi$
$240$	6.64920	−	4.63408i	0.429204	−	0.299128i
$241$	17.9056	+	10.3378i	1.15340	+	0.665915i	0.949713	−	0.313121i	$-0.101375\pi$
$241$	17.9056	+	10.3378i	1.15340	+	0.665915i	0.203685	+	0.979036i	$0.434708\pi$
$242$	3.82699	+	13.1567i	0.246008	+	0.845745i
$243$	9.49397	−	5.48135i	0.609038	−	0.351628i
$244$	−1.21359	−	28.5147i	−0.0776919	−	1.82547i
$245$	6.71085	−	1.99112i	0.428740	−	0.127208i
$246$	21.7789	−	22.7256i	1.38857	−	1.44893i
$247$	2.40619	−	1.38921i	0.153102	−	0.0883935i
$248$	−3.16531	+	1.06866i	−0.200998	+	0.0678602i
$249$	−2.82640	+	4.89546i	−0.179116	+	0.310237i
$250$	1.37350	+	0.336893i	0.0868678	+	0.0213070i
$251$			13.1277i			0.828616i	0.910137	+	0.414308i	$0.135976\pi$
$251$			13.1277i			0.828616i	−0.910137	+	0.414308i	$0.864024\pi$
$252$	4.43454	−	3.81429i	0.279350	−	0.240278i
$253$		−	5.29421i		−	0.332844i
$254$	4.05431	−	16.5293i	0.254390	−	1.03714i
$255$	−2.31917	+	4.01692i	−0.145232	+	0.251549i
$256$	−5.53835	+	15.0109i	−0.346147	+	0.938180i
$257$	17.6932	−	10.2152i	1.10367	−	0.637205i	0.166488	−	0.986043i	$-0.446757\pi$
$257$	17.6932	−	10.2152i	1.10367	−	0.637205i	0.937183	+	0.348839i	$0.113424\pi$
$258$	22.4366	+	21.5020i	1.39684	+	1.33865i
$259$	−16.2409	−	6.47526i	−1.00916	−	0.402353i
$260$	0.0607764	+	1.42802i	0.00376919	+	0.0885618i
$261$	−1.47776	+	0.853186i	−0.0914711	+	0.0528109i
$262$	−28.0813	+	8.16823i	−1.73487	+	0.504635i
$263$	−27.1210	−	15.6583i	−1.67235	−	0.965532i	−0.966317	−	0.257355i	$-0.917149\pi$
$263$	−27.1210	−	15.6583i	−1.67235	−	0.965532i	−0.706034	−	0.708178i	$-0.749517\pi$
$264$	−6.43417	−	1.29086i	−0.395996	−	0.0794472i
$265$		−	2.60841i		−	0.160233i
$266$	11.8400	+	8.45120i	0.725957	+	0.518177i
$267$	−25.8580			−1.58248
$268$	13.8008	−	8.77076i	0.843017	−	0.535760i
$269$	−0.435079	+	0.753580i	−0.0265273	+	0.0459466i	−0.878984	−	0.476851i	$-0.841778\pi$
$269$	−0.435079	+	0.753580i	−0.0265273	+	0.0459466i	0.852457	+	0.522797i	$0.175112\pi$
$270$	−5.21281	+	1.51629i	−0.317242	+	0.0922785i
$271$	−15.6655	−	27.1335i	−0.951614	−	1.64824i	−0.741932	−	0.670475i	$-0.766090\pi$
$271$	−15.6655	−	27.1335i	−0.951614	−	1.64824i	−0.209682	−	0.977770i	$-0.567243\pi$
$272$	−0.778020	−	9.12370i	−0.0471744	−	0.553206i
$273$	0.550584	+	3.79133i	0.0333229	+	0.229462i
$274$	4.64710	−	4.84909i	0.280742	−	0.292944i
$275$	−0.572544	−	0.991675i	−0.0345257	−	0.0598002i
$276$	−16.6093	−	8.66946i	−0.999762	−	0.521840i
$277$	−24.3707	−	14.0705i	−1.46430	−	0.845412i	−0.465091	−	0.885263i	$-0.653978\pi$
$277$	−24.3707	−	14.0705i	−1.46430	−	0.845412i	−0.999206	+	0.0398511i	$0.987312\pi$
$278$	−3.69950	+	15.0827i	−0.221881	+	0.904602i
$279$	−1.30567			−0.0781685
$280$	−6.67251	+	3.38785i	−0.398759	+	0.202463i
$281$	−22.1338			−1.32039			−0.660195	−	0.751094i	$-0.729527\pi$
$281$	−22.1338			−1.32039			−0.660195	+	0.751094i	$0.729527\pi$
$282$	−3.55556	+	14.4959i	−0.211730	+	0.863216i
$283$	−2.28363	−	1.31845i	−0.135748	−	0.0783739i	0.430588	−	0.902548i	$-0.358306\pi$
$283$	−2.28363	−	1.31845i	−0.135748	−	0.0783739i	−0.566336	+	0.824175i	$0.691639\pi$
$284$	−14.6731	+	28.1113i	−0.870687	+	1.66810i
$285$	3.93868	+	6.82199i	0.233307	+	0.404100i
$286$	0.800754	−	0.835559i	0.0473496	−	0.0494076i
$287$	−22.8198	+	17.9980i	−1.34701	+	1.06239i
$288$	−3.92736	+	4.86595i	−0.231422	+	0.286729i
$289$	−5.87977	−	10.1841i	−0.345869	−	0.599063i
$290$	2.09618	−	0.609732i	0.123092	−	0.0358047i
$291$	5.25318	−	9.09877i	0.307947	−	0.533379i
$292$	−5.83917	−	9.18793i	−0.341712	−	0.537683i
$293$	−9.78791			−0.571816			−0.285908	−	0.958257i	$-0.592295\pi$
$293$	−9.78791			−0.571816			−0.285908	+	0.958257i	$0.592295\pi$
$294$	−16.8708	+	10.8492i	−0.983925	+	0.632741i
$295$		−	12.1531i		−	0.707581i
$296$	18.3262	+	3.67672i	1.06519	+	0.213705i
$297$	3.80683	+	2.19787i	0.220894	+	0.127533i
$298$	21.1300	−	6.14623i	1.22403	−	0.356042i
$299$	2.86147	−	1.65207i	0.165483	−	0.0955418i
$300$	−4.04870	+	0.172313i	−0.233752	+	0.00994848i
$301$	−17.7691	−	22.5296i	−1.02419	−	1.29858i
$302$	12.8132	+	12.2795i	0.737318	+	0.706605i
$303$	1.77581	−	1.02526i	0.102017	−	0.0588998i
$304$	−14.0797	−	6.60316i	−0.807524	−	0.378717i
$305$	−7.13513	+	12.3584i	−0.408556	+	0.707640i
$306$	0.852509	−	3.47565i	0.0487347	−	0.198689i
$307$			10.6770i			0.609367i	0.952454	+	0.304683i	$0.0985506\pi$
$307$			10.6770i			0.609367i	−0.952454	+	0.304683i	$0.901449\pi$
$308$	5.71870	+	2.00267i	0.325853	+	0.114113i
$309$		−	4.94414i		−	0.281262i
$310$	1.62233	+	0.397927i	0.0921424	+	0.0226008i
$311$	−4.23321	+	7.33214i	−0.240043	+	0.415767i	−0.960726	−	0.277497i	$-0.910495\pi$
$311$	−4.23321	+	7.33214i	−0.240043	+	0.415767i	0.720683	+	0.693265i	$0.243828\pi$
$312$	−1.31010	−	3.88043i	−0.0741697	−	0.219686i
$313$	−20.2436	+	11.6877i	−1.14424	+	0.660626i	−0.947476	−	0.319826i	$-0.896376\pi$
$313$	−20.2436	+	11.6877i	−1.14424	+	0.660626i	−0.196761	+	0.980452i	$0.563042\pi$
$314$	7.49830	−	7.82422i	0.423154	−	0.441546i
$315$	−2.89427	+	0.420312i	−0.163074	+	0.0236819i
$316$	−18.9205	+	0.805257i	−1.06436	+	0.0452992i
$317$	11.0950	−	6.40571i	0.623158	−	0.359780i	−0.154940	−	0.987924i	$-0.549518\pi$
$317$	11.0950	−	6.40571i	0.623158	−	0.359780i	0.778097	+	0.628144i	$0.216185\pi$
$318$	2.08757	+	7.17682i	0.117065	+	0.402456i
$319$	−1.53081	−	0.883811i	−0.0857087	−	0.0494839i
$320$	6.36285	−	4.84914i	0.355694	−	0.271075i
$321$		−	2.75662i		−	0.153860i
$322$	14.0803	+	10.0503i	0.784665	+	0.560081i
$323$	8.89994			0.495206
$324$	18.7268	−	11.9014i	1.04038	−	0.661186i
$325$	0.357327	−	0.618909i	0.0198209	−	0.0343309i
$326$	−7.93793	−	27.2896i	−0.439641	−	1.51143i
$327$	10.5898	+	18.3421i	0.585618	+	1.01432i
$328$	20.5242	−	23.3257i	1.13326	−	1.28795i
$329$	5.10384	−	12.8012i	0.281384	−	0.705754i
$330$	2.36897	+	2.27029i	0.130407	+	0.124975i
$331$	−11.1099	−	19.2429i	−0.610656	−	1.05769i	−0.991130	−	0.132896i	$-0.957573\pi$
$331$	−11.1099	−	19.2429i	−0.610656	−	1.05769i	0.380474	−	0.924792i	$-0.375761\pi$
$332$	−2.58188	+	4.94646i	−0.141699	+	0.271472i
$333$	6.32630	+	3.65249i	0.346679	+	0.200155i
$334$	9.30473	+	2.28227i	0.509132	+	0.124880i
$335$	−8.17600			−0.446703
$336$	15.6475	−	14.6616i	0.853640	−	0.799855i
$337$	14.9570			0.814761			0.407381	−	0.913258i	$-0.366442\pi$
$337$	14.9570			0.814761			0.407381	+	0.913258i	$0.366442\pi$
$338$	−17.1540	−	4.20755i	−0.933055	−	0.228861i
$339$	−13.7498	−	7.93843i	−0.746785	−	0.431156i
$340$	−2.11853	+	4.05877i	−0.114894	+	0.220118i
$341$	−0.676270	−	1.17133i	−0.0366221	−	0.0634313i
$342$	−4.38801	−	4.20523i	−0.237276	−	0.227393i
$343$	16.8138	−	7.76500i	0.907861	−	0.419270i
$344$	23.0291	+	20.2632i	1.24165	+	1.09252i
$345$	4.68394	+	8.11282i	0.252175	+	0.436779i
$346$	6.87412	+	23.6324i	0.369555	+	1.27048i
$347$	8.51734	−	14.7525i	0.457235	−	0.791954i	−0.541579	−	0.840650i	$-0.682173\pi$
$347$	8.51734	−	14.7525i	0.457235	−	0.791954i	0.998814	+	0.0486962i	$0.0155066\pi$
$348$	−5.27949	+	3.35526i	−0.283010	+	0.179861i
$349$	1.40440			0.0751760			0.0375880	−	0.999293i	$-0.488033\pi$
$349$	1.40440			0.0751760			0.0375880	+	0.999293i	$0.488033\pi$
$350$	3.72431	+	0.359833i	0.199073	+	0.0192339i
$351$			2.74340i			0.146432i
$352$	−6.39947	−	1.00298i	−0.341093	−	0.0534589i
$353$	11.0830	+	6.39876i	0.589887	+	0.340572i	0.765053	−	0.643967i	$-0.222713\pi$
$353$	11.0830	+	6.39876i	0.589887	+	0.340572i	−0.175166	+	0.984539i	$0.556046\pi$
$354$	9.72643	+	33.4383i	0.516954	+	1.77722i
$355$	13.7310	−	7.92757i	0.728763	−	0.420752i
$356$	−25.5008	+	1.08532i	−1.35154	+	0.0575216i
$357$	−4.54489	+	11.3993i	−0.240541	+	0.603313i
$358$	−14.9981	+	15.6499i	−0.792672	+	0.827125i
$359$	5.28987	−	3.05411i	0.279189	−	0.161190i	−0.353867	−	0.935296i	$-0.615134\pi$
$359$	5.28987	−	3.05411i	0.279189	−	0.161190i	0.633056	+	0.774106i	$0.281800\pi$
$360$	2.96229	−	1.00012i	0.156126	−	0.0527110i
$361$	−1.94255	+	3.36460i	−0.102240	+	0.177084i
$362$	4.25814	+	1.04444i	0.223803	+	0.0548945i
$363$			19.6312i			1.03037i
$364$	0.702108	+	3.71584i	0.0368005	+	0.194763i
$365$			5.44321i			0.284910i
$366$	9.74097	−	39.7135i	0.509169	−	2.07586i
$367$	−4.55727	+	7.89342i	−0.237888	+	0.412033i	−0.960108	−	0.279630i	$-0.909788\pi$
$367$	−4.55727	+	7.89342i	−0.237888	+	0.412033i	0.722220	+	0.691663i	$0.243122\pi$
$368$	−16.7437	−	7.85258i	−0.872827	−	0.409344i
$369$	10.5159	−	6.07137i	0.547437	−	0.316063i
$370$	−6.74745	−	6.46638i	−0.350783	−	0.336171i
$371$	−0.991802	−	6.82956i	−0.0514918	−	0.354573i
$372$	−4.78219	+	0.203530i	−0.247945	+	0.0105525i
$373$	19.9065	−	11.4930i	1.03072	−	0.595086i	0.113529	−	0.993535i	$-0.463785\pi$
$373$	19.9065	−	11.4930i	1.03072	−	0.595086i	0.917191	+	0.398448i	$0.130451\pi$
$374$	3.55960	−	1.03541i	0.184063	−	0.0535396i
$375$	1.75472	+	1.01309i	0.0906135	+	0.0523158i
$376$	−2.89802	+	14.4448i	−0.149454	+	0.744936i
$377$		−	1.10318i		−	0.0568167i
$378$	−13.0721	+	5.95216i	−0.672356	+	0.306146i
$379$	18.0966			0.929562			0.464781	−	0.885426i	$-0.346133\pi$
$379$	18.0966			0.929562			0.464781	+	0.885426i	$0.346133\pi$
$380$	4.17061	+	6.56244i	0.213948	+	0.336646i
$381$	12.1919	−	21.1170i	0.624612	−	1.08186i
$382$	−19.8290	+	5.76782i	−1.01454	+	0.295107i
$383$	10.7474	+	18.6150i	0.549165	+	0.951182i	0.998332	+	0.0577341i	$0.0183876\pi$
$383$	10.7474	+	18.6150i	0.549165	+	0.951182i	−0.449167	+	0.893448i	$0.648279\pi$
$384$	−13.6260	+	18.4344i	−0.695347	+	0.940724i
$385$	−1.87615	−	2.37879i	−0.0956175	−	0.121234i
$386$	16.6444	−	17.3678i	0.847177	−	0.884000i
$387$	5.99416	+	10.3822i	0.304700	+	0.527756i
$388$	4.79872	−	9.19357i	0.243618	−	0.466733i
$389$	2.38186	+	1.37517i	0.120765	+	0.0697238i	0.559166	−	0.829056i	$-0.311122\pi$
$389$	2.38186	+	1.37517i	0.120765	+	0.0697238i	−0.438401	+	0.898780i	$0.644455\pi$
$390$	−0.487828	+	1.98885i	−0.0247021	+	0.100710i
$391$	10.5839			0.535253
$392$	−16.1824	+	11.4075i	−0.817333	+	0.576165i
$393$	−41.9004			−2.11359
$394$	−5.13226	+	20.9240i	−0.258560	+	1.05414i
$395$	8.20023	+	4.73440i	0.412598	+	0.238214i
$396$	−2.24425	−	1.17142i	−0.112778	−	0.0588660i
$397$	7.62990	+	13.2154i	0.382934	+	0.663260i	0.991480	−	0.130258i	$-0.0415805\pi$
$397$	7.62990	+	13.2154i	0.382934	+	0.663260i	−0.608547	+	0.793518i	$0.708247\pi$
$398$	15.6981	−	16.3804i	0.786874	−	0.821075i
$399$	12.9065	+	16.3643i	0.646135	+	0.819241i
$400$	−3.98554	+	0.339865i	−0.199277	+	0.0169932i
$401$	4.15899	+	7.20358i	0.207690	+	0.359729i	0.950986	−	0.309233i	$-0.100072\pi$
$401$	4.15899	+	7.20358i	0.207690	+	0.359729i	−0.743297	+	0.668962i	$0.766739\pi$
$402$	22.4956	−	6.54346i	1.12198	−	0.326358i
$403$	0.422063	−	0.731035i	0.0210245	−	0.0364154i
$404$	1.70824	−	1.08563i	0.0849883	−	0.0540123i
$405$	−11.0943			−0.551280
$406$	5.25657	−	2.39349i	0.260879	−	0.118787i
$407$			7.56720i			0.375092i
$408$	2.58063	−	12.8629i	0.127760	−	0.636808i
$409$	23.3269	+	13.4678i	1.15344	+	0.665941i	0.949724	−	0.313089i	$-0.101364\pi$
$409$	23.3269	+	13.4678i	1.15344	+	0.665941i	0.203719	+	0.979029i	$0.434697\pi$
$410$	−14.9167	+	4.33893i	−0.736683	+	0.214284i
$411$	8.33349	−	4.81134i	0.411061	−	0.237326i
$412$	−0.207516	−	4.87584i	−0.0102236	−	0.240216i
$413$	−4.62101	−	31.8203i	−0.227385	−	1.56578i
$414$	−5.21829	−	5.00092i	−0.256465	−	0.245782i
$415$	2.41610	−	1.39494i	0.118602	−	0.0684748i
$416$	−1.45487	−	3.77183i	−0.0713309	−	0.184929i
$417$	−11.1250	+	19.2690i	−0.544793	+	0.943608i
$418$	1.49980	−	6.11463i	0.0733576	−	0.299076i
$419$		−	8.97603i		−	0.438508i	−0.975668	−	0.219254i	$-0.929638\pi$
$419$		−	8.97603i		−	0.438508i	0.975668	−	0.219254i	$-0.0703623\pi$
$420$	−10.5351	+	1.99061i	−0.514062	+	0.0971319i
$421$			13.4720i			0.656583i	0.944576	+	0.328292i	$0.106473\pi$
$421$			13.4720i			0.656583i	−0.944576	+	0.328292i	$0.893527\pi$
$422$	−8.04581	−	1.97348i	−0.391664	−	0.0960676i
$423$	−2.87892	+	4.98643i	−0.139978	+	0.242449i
$424$	2.35996	+	6.99006i	0.114610	+	0.339467i
$425$	1.98251	−	1.14460i	0.0961658	−	0.0555213i
$426$	−31.4349	+	32.8013i	−1.52303	+	1.58923i
$427$	−13.9827	+	35.0708i	−0.676672	+	1.69720i
$428$	−0.115701	−	2.71854i	−0.00559263	−	0.131406i
$429$	1.43596	−	0.829054i	0.0693290	−	0.0400271i
$430$	−4.28375	−	14.7270i	−0.206581	−	0.710198i
$431$	−20.5363	−	11.8567i	−0.989200	−	0.571115i	−0.0841648	−	0.996452i	$-0.526822\pi$
$431$	−20.5363	−	11.8567i	−0.989200	−	0.571115i	−0.905035	+	0.425337i	$0.860156\pi$
$432$	12.5975	−	8.77968i	0.606099	−	0.422413i
$433$			18.5650i			0.892178i	0.894989	+	0.446089i	$0.147183\pi$
$433$			18.5650i			0.892178i	−0.894989	+	0.446089i	$0.852817\pi$
$434$	4.39904	+	0.425023i	0.211161	+	0.0204018i
$435$	3.12773			0.149963
$436$	11.2134	+	17.6442i	0.537024	+	0.845006i
$437$	8.98743	−	15.5667i	0.429927	−	0.744656i
$438$	−4.35633	−	14.9765i	−0.208154	−	0.715606i
$439$	3.44704	+	5.97045i	0.164518	+	0.284954i	0.936484	−	0.350710i	$-0.114060\pi$
$439$	3.44704	+	5.97045i	0.164518	+	0.284954i	−0.771966	+	0.635664i	$0.780726\pi$
$440$	2.43153	+	2.13950i	0.115919	+	0.101997i
$441$	−7.41822	+	2.20100i	−0.353249	+	0.104809i
$442$	1.67041	+	1.60083i	0.0794533	+	0.0761437i
$443$	14.1129	+	24.4443i	0.670525	+	1.16138i	0.977755	+	0.209749i	$0.0672646\pi$
$443$	14.1129	+	24.4443i	0.670525	+	1.16138i	−0.307230	+	0.951635i	$0.599402\pi$
$444$	23.7402	+	12.3916i	1.12666	+	0.588078i
$445$	11.0522	+	6.38097i	0.523923	+	0.302487i
$446$	16.9309	+	4.15282i	0.801701	+	0.196642i
$447$	31.5282			1.49123
$448$	14.8160	−	15.1158i	0.699988	−	0.714155i
$449$	1.93651			0.0913896			0.0456948	−	0.998955i	$-0.485450\pi$
$449$	1.93651			0.0913896			0.0456948	+	0.998955i	$0.485450\pi$
$450$	−1.51828	−	0.372404i	−0.0715723	−	0.0175553i
$451$	10.8934	+	6.28930i	0.512950	+	0.296152i
$452$	−13.8930	−	7.25166i	−0.653473	−	0.341089i
$453$	12.7135	+	22.0204i	0.597331	+	1.03461i
$454$	8.00839	+	7.67480i	0.375852	+	0.360196i
$455$	0.700255	−	1.75635i	0.0328285	−	0.0823389i
$456$	−16.7272	−	14.7182i	−0.783321	−	0.689242i
$457$	−17.3752	−	30.0948i	−0.812779	−	1.40777i	−0.910912	−	0.412601i	$-0.864621\pi$
$457$	−17.3752	−	30.0948i	−0.812779	−	1.40777i	0.0981335	−	0.995173i	$-0.468713\pi$
$458$	−6.08789	−	20.9294i	−0.284468	−	0.977966i
$459$	−4.39388	+	7.61043i	−0.205089	+	0.355224i
$460$	4.95975	+	7.80415i	0.231249	+	0.363870i
$461$	29.3117			1.36518			0.682590	−	0.730802i	$-0.260854\pi$
$461$	29.3117			1.36518			0.682590	+	0.730802i	$0.260854\pi$
$462$	7.06587	+	5.04351i	0.328734	+	0.234645i
$463$		−	9.47208i		−	0.440205i	−0.975477	−	0.220102i	$-0.929361\pi$
$463$		−	9.47208i		−	0.440205i	0.975477	−	0.220102i	$-0.0706391\pi$
$464$	−5.06573	+	3.53050i	−0.235171	+	0.163899i
$465$	2.07262	+	1.19663i	0.0961156	+	0.0554924i
$466$	−4.44686	−	15.2877i	−0.205997	−	0.708191i
$467$	11.2422	−	6.49066i	0.520225	−	0.300352i	−0.216802	−	0.976216i	$-0.569563\pi$
$467$	11.2422	−	6.49066i	0.520225	−	0.300352i	0.737027	+	0.675864i	$0.236229\pi$
$468$	−0.0671827	−	1.57854i	−0.00310552	−	0.0729680i
$469$	−21.4071	+	3.10878i	−0.988489	+	0.143550i
$470$	5.09685	−	5.31838i	0.235100	−	0.245319i
$471$	13.4464	−	7.76330i	0.619579	−	0.357714i
$472$	10.9955	+	32.5681i	0.506111	+	1.49907i
$473$	−6.20932	+	10.7549i	−0.285505	+	0.494509i
$474$	−26.3513	−	6.46347i	−1.21036	−	0.296877i
$475$		−	3.88779i		−	0.178384i
$476$	−4.00365	+	11.4326i	−0.183507	+	0.524011i
$477$			2.88335i			0.132020i
$478$	4.76764	−	19.4375i	0.218067	−	0.889050i
$479$	9.96246	−	17.2555i	0.455197	−	0.788424i	−0.543503	−	0.839407i	$-0.682902\pi$
$479$	9.96246	−	17.2555i	0.455197	−	0.788424i	0.998699	+	0.0509837i	$0.0162357\pi$
$480$	10.6939	−	4.12483i	0.488106	−	0.188272i
$481$	−4.09000	+	2.36136i	−0.186488	+	0.107669i
$482$	21.1106	+	20.2312i	0.961560	+	0.921506i
$483$	15.3486	+	19.4607i	0.698388	+	0.885492i
$484$	0.823964	+	19.3600i	0.0374529	+	0.880001i
$485$	−4.49060	+	2.59265i	−0.203908	+	0.117726i
$486$	14.8866	−	4.33017i	0.675270	−	0.196421i
$487$	23.4025	+	13.5114i	1.06047	+	0.612261i	0.925562	−	0.378597i	$-0.123593\pi$
$487$	23.4025	+	13.5114i	1.06047	+	0.612261i	0.134906	+	0.990858i	$0.456927\pi$
$488$	7.93955	−	39.5738i	0.359406	−	1.79142i
$489$		−	40.7190i		−	1.84138i
$490$	9.88814	−	0.473960i	0.446701	−	0.0214113i
$491$	0.454409			0.0205072			0.0102536	−	0.999947i	$-0.496736\pi$
$491$	0.454409			0.0205072			0.0102536	+	0.999947i	$0.496736\pi$
$492$	37.5695	−	23.8764i	1.69376	−	1.07643i
$493$	1.76687	−	3.06031i	0.0795760	−	0.137830i
$494$	3.77291	−	1.09746i	0.169751	−	0.0493768i
$495$	0.632894	+	1.09620i	0.0284465	+	0.0492707i
$496$	−4.70759	+	0.401437i	−0.211377	+	0.0180251i
$497$	32.9372	−	25.9776i	1.47744	−	1.16525i
$498$	−5.53130	+	5.77172i	−0.247864	+	0.258637i
$499$	−4.29223	−	7.43436i	−0.192147	−	0.332808i	0.753815	−	0.657087i	$-0.228212\pi$
$499$	−4.29223	−	7.43436i	−0.192147	−	0.332808i	−0.945961	+	0.324279i	$0.894878\pi$
$500$	1.77301	+	0.925446i	0.0792912	+	0.0413872i
$501$	11.8873	+	6.86314i	0.531086	+	0.306623i
$502$	−4.42265	+	18.0310i	−0.197392	+	0.804761i
$503$	−43.3946			−1.93487			−0.967434	−	0.253123i	$-0.918542\pi$
$503$	−43.3946			−1.93487			−0.967434	+	0.253123i	$0.918542\pi$
$504$	7.37585	−	3.74496i	0.328546	−	0.166814i
$505$	−1.01202			−0.0450341
$506$	1.78358	−	7.27160i	0.0792900	−	0.323262i
$507$	−21.9152	−	12.6528i	−0.973289	−	0.561929i
$508$	11.1372	−	21.3371i	0.494133	−	0.946679i
$509$	11.5209	+	19.9548i	0.510654	+	0.884479i	0.999924	+	0.0123465i	$0.00393010\pi$
$509$	11.5209	+	19.9548i	0.510654	+	0.884479i	−0.489270	+	0.872133i	$0.662737\pi$
$510$	−4.53865	+	4.73593i	−0.200975	+	0.209710i
$511$	2.06969	+	14.2519i	0.0915575	+	0.630466i
$512$	−12.6640	+	18.7516i	−0.559675	+	0.828712i
$513$	7.46219	+	12.9249i	0.329464	+	0.570648i
$514$	27.7430	−	8.06982i	1.22369	−	0.355944i
$515$	−1.22006	+	2.11321i	−0.0537625	+	0.0931193i
$516$	23.5728	+	37.0917i	1.03773	+	1.63287i
$517$	−5.96452			−0.262319
$518$	−20.1255	−	14.3652i	−0.884263	−	0.631172i
$519$			35.2620i			1.54783i
$520$	−0.397613	+	1.98186i	−0.0174365	+	0.0869101i
$521$	−36.5041	−	21.0756i	−1.59927	−	0.923340i	−0.991628	−	0.129130i	$-0.958781\pi$
$521$	−36.5041	−	21.0756i	−1.59927	−	0.923340i	−0.607644	−	0.794209i	$-0.707885\pi$
$522$	−2.31714	+	0.674003i	−0.101418	+	0.0295003i
$523$	−9.61525	+	5.55137i	−0.420445	+	0.242744i	−0.695268	−	0.718751i	$-0.744714\pi$
$523$	−9.61525	+	5.55137i	−0.420445	+	0.242744i	0.274822	+	0.961495i	$0.411381\pi$
$524$	−41.3215	+	1.75865i	−1.80514	+	0.0768269i
$525$	4.97958	+	1.98536i	0.217327	+	0.0866481i
$526$	−31.9755	−	30.6436i	−1.39420	−	1.33612i
$527$	2.34167	−	1.35197i	0.102005	−	0.0588926i
$528$	−8.40245	−	3.94063i	−0.365670	−	0.171494i
$529$	−0.812016	+	1.40645i	−0.0353051	+	0.0611501i
$530$	0.878755	−	3.58265i	0.0381707	−	0.155620i
$531$			13.4341i			0.582992i
$532$	13.4151	+	15.5965i	0.581618	+	0.676196i
$533$			7.85037i			0.340037i
$534$	−35.5160	−	8.71139i	−1.53693	−	0.376979i
$535$	−0.680251	+	1.17823i	−0.0294098	+	0.0509393i
$536$	21.9102	−	7.39725i	0.946376	−	0.319513i
$537$	−26.8955	+	15.5281i	−1.16063	+	0.670087i
$538$	−0.851458	+	0.888467i	−0.0367089	+	0.0383045i
$539$	−5.81679	−	5.51497i	−0.250547	−	0.237547i
$540$	−7.67063	+	0.326462i	−0.330091	+	0.0140487i
$541$	−21.7744	+	12.5715i	−0.936156	+	0.540490i	−0.888753	−	0.458386i	$-0.848428\pi$
$541$	−21.7744	+	12.5715i	−0.936156	+	0.540490i	−0.0474025	+	0.998876i	$0.515094\pi$
$542$	−12.3755	−	42.5455i	−0.531575	−	1.82749i
$543$	5.44001	+	3.14079i	0.233453	+	0.134784i
$544$	2.00510	−	12.7935i	0.0859681	−	0.548517i
$545$		−	10.4530i		−	0.447756i
$546$	−0.521045	+	5.39288i	−0.0222987	+	0.230794i
$547$	4.35086			0.186030			0.0930148	−	0.995665i	$-0.470350\pi$
$547$	4.35086			0.186030			0.0930148	+	0.995665i	$0.470350\pi$
$548$	8.01643	−	5.09465i	0.342445	−	0.217633i
$549$	7.88722	−	13.6611i	0.336619	−	0.583040i
$550$	−0.452300	−	1.55495i	−0.0192861	−	0.0663033i
$551$	−3.00071	−	5.19738i	−0.127834	−	0.221416i
$552$	−19.8922	−	17.5031i	−0.846668	−	0.744980i
$553$	23.2707	+	9.27803i	0.989571	+	0.394542i
$554$	−28.7330	−	27.5361i	−1.22075	−	1.16990i
$555$	−6.69491	−	11.5959i	−0.284183	−	0.492220i
$556$	−10.1625	+	19.4698i	−0.430988	+	0.825703i
$557$	−22.5821	−	13.0378i	−0.956833	−	0.552428i	−0.0616365	−	0.998099i	$-0.519632\pi$
$557$	−22.5821	−	13.0378i	−0.956833	−	0.552428i	−0.895197	+	0.445671i	$0.852965\pi$
$558$	−1.79334	−	0.439872i	−0.0759182	−	0.0186213i
$559$	−7.75053			−0.327813
$560$	−10.3060	+	2.40529i	−0.435510	+	0.101642i
$561$	5.31130			0.224243
$562$	−30.4008	−	7.45672i	−1.28238	−	0.314543i
$563$	−15.6768	−	9.05099i	−0.660697	−	0.381454i	0.131845	−	0.991270i	$-0.457910\pi$
$563$	−15.6768	−	9.05099i	−0.660697	−	0.381454i	−0.792542	+	0.609817i	$0.791243\pi$
$564$	−9.76711	+	18.7122i	−0.411270	+	0.787926i
$565$	3.91793	+	6.78605i	0.164828	+	0.285491i
$566$	−2.69239	−	2.58023i	−0.113169	−	0.108455i
$567$	−29.0480	+	4.21842i	−1.21990	+	0.177157i
$568$	−29.6240	+	33.6676i	−1.24299	+	1.41266i
$569$	−12.4224	−	21.5163i	−0.520776	−	0.902010i	−0.999708	−	0.0241585i	$-0.992309\pi$
$569$	−12.4224	−	21.5163i	−0.520776	−	0.902010i	0.478932	−	0.877852i	$-0.341024\pi$
$570$	3.11149	+	10.6969i	0.130326	+	0.448045i
$571$	−2.25668	+	3.90869i	−0.0944392	+	0.163574i	−0.909374	−	0.415979i	$-0.863439\pi$
$571$	−2.25668	+	3.90869i	−0.0944392	+	0.163574i	0.814935	+	0.579552i	$0.196772\pi$
$572$	1.38133	−	0.877872i	0.0577563	−	0.0367057i
$573$	−29.5870			−1.23602
$574$	−37.4064	+	17.0324i	−1.56131	+	0.710917i
$575$		−	4.62342i		−	0.192810i
$576$	−7.03354	+	5.36028i	−0.293064	+	0.223345i
$577$	−20.3993	−	11.7776i	−0.849235	−	0.490306i	0.0111579	−	0.999938i	$-0.496448\pi$
$577$	−20.3993	−	11.7776i	−0.849235	−	0.490306i	−0.860393	+	0.509632i	$0.829782\pi$
$578$	−4.64493	−	15.9687i	−0.193203	−	0.664209i
$579$	29.8478	−	17.2326i	1.24043	−	0.716164i
$580$	3.08452	−	0.131277i	0.128078	−	0.00545100i
$581$	5.79565	−	4.57103i	0.240444	−	0.189638i
$582$	10.2806	−	10.7274i	0.426143	−	0.444665i
$583$	−2.58669	+	1.49343i	−0.107130	+	0.0618514i
$584$	−4.92475	−	14.5868i	−0.203788	−	0.603606i
$585$	−0.394992	+	0.684146i	−0.0163309	+	0.0282860i
$586$	−13.4437	−	3.29748i	−0.555354	−	0.136218i
$587$		−	3.48482i		−	0.143834i	−0.997411	−	0.0719170i	$-0.977088\pi$
$587$		−	3.48482i		−	0.143834i	0.997411	−	0.0719170i	$-0.0229117\pi$
$588$	−26.8271	+	9.21779i	−1.10633	+	0.380135i
$589$		−	4.59213i		−	0.189215i
$590$	4.09430	−	16.6923i	0.168560	−	0.687211i
$591$	−15.4335	+	26.7316i	−0.634850	+	1.09959i
$592$	23.9324	+	11.2240i	0.983616	+	0.461302i
$593$	−11.4527	+	6.61223i	−0.470307	+	0.271532i	−0.716368	−	0.697722i	$-0.754197\pi$
$593$	−11.4527	+	6.61223i	−0.470307	+	0.271532i	0.246061	+	0.969254i	$0.420864\pi$
$594$	4.48823	+	4.30127i	0.184154	+	0.176483i
$595$	4.75556	−	3.75071i	0.194959	−	0.153764i
$596$	31.0926	−	1.32330i	1.27360	−	0.0542047i
$597$	28.1508	−	16.2529i	1.15214	−	0.665186i
$598$	4.48680	−	1.30511i	0.183479	−	0.0533699i
$599$	−12.0329	−	6.94719i	−0.491650	−	0.283855i	0.233608	−	0.972331i	$-0.424947\pi$
$599$	−12.0329	−	6.94719i	−0.491650	−	0.283855i	−0.725259	+	0.688476i	$0.758280\pi$
$600$	−5.61894	−	1.12731i	−0.229392	−	0.0460221i
$601$			18.8327i			0.768200i	0.923291	+	0.384100i	$0.125488\pi$
$601$			18.8327i			0.768200i	−0.923291	+	0.384100i	$0.874512\pi$
$602$	−16.8158	−	36.9306i	−0.685359	−	1.50518i
$603$	9.03781			0.368048
$604$	13.4621	+	21.1826i	0.547765	+	0.861907i
$605$	4.84439	−	8.39073i	0.196952	−	0.341132i
$606$	2.78448	−	0.809941i	0.113112	−	0.0329016i
$607$	−12.1505	−	21.0453i	−0.493175	−	0.854204i	0.506794	−	0.862067i	$-0.330830\pi$
$607$	−12.1505	−	21.0453i	−0.493175	−	0.854204i	−0.999969	+	0.00786319i	$0.997497\pi$
$608$	−17.1138	−	13.8128i	−0.694058	−	0.560182i
$609$	8.18929	−	1.18927i	0.331847	−	0.0481915i
$610$	−13.9636	+	14.5705i	−0.565368	+	0.589942i
$611$	−1.86124	−	3.22377i	−0.0752978	−	0.130420i
$612$	2.34184	−	4.48660i	0.0946634	−	0.181360i
$613$	16.2648	+	9.39048i	0.656929	+	0.379278i	0.791106	−	0.611679i	$-0.209506\pi$
$613$	16.2648	+	9.39048i	0.656929	+	0.379278i	−0.134177	+	0.990957i	$0.542839\pi$
$614$	−3.59700	+	14.6648i	−0.145163	+	0.591824i
$615$	−22.2573			−0.897500
$616$	7.17995	+	4.67727i	0.289289	+	0.188452i
$617$	26.0641			1.04930			0.524651	−	0.851317i	$-0.324196\pi$
$617$	26.0641			1.04930			0.524651	+	0.851317i	$0.324196\pi$
$618$	1.66565	−	6.79078i	0.0670022	−	0.273165i
$619$	−20.7007	−	11.9515i	−0.832030	−	0.480373i	0.0225171	−	0.999746i	$-0.492832\pi$
$619$	−20.7007	−	11.9515i	−0.832030	−	0.480373i	−0.854547	+	0.519374i	$0.826165\pi$
$620$	2.09422	+	1.09311i	0.0841058	+	0.0439002i
$621$	8.87415	+	15.3705i	0.356107	+	0.616796i
$622$	−8.28447	+	8.64455i	−0.332177	+	0.346615i
$623$	31.3640	+	12.5048i	1.25657	+	0.500995i
$624$	−0.492130	−	5.77113i	−0.0197010	−	0.231030i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−31.7421	+	9.23306i	−1.26867	+	0.369027i
$627$	4.51013	−	7.81178i	0.180117	−	0.311972i
$628$	12.9348	−	8.22043i	0.516156	−	0.328031i
$629$	−15.1280			−0.603192
$630$	−4.11689	−	0.397762i	−0.164021	−	0.0158472i
$631$			29.3239i			1.16736i	0.811982	+	0.583682i	$0.198389\pi$
$631$			29.3239i			1.16736i	−0.811982	+	0.583682i	$0.801611\pi$
$632$	−26.2586	−	5.26816i	−1.04451	−	0.209556i
$633$	−10.2790	−	5.93457i	−0.408552	−	0.235878i
$634$	17.3970	−	5.06041i	0.690925	−	0.200974i
$635$	−10.4221	+	6.01720i	−0.413588	+	0.238785i
$636$	0.449462	+	10.5607i	0.0178223	+	0.418757i
$637$	1.16565	−	4.86488i	0.0461847	−	0.192754i
$638$	−1.80481	−	1.72963i	−0.0714532	−	0.0684768i
$639$	−15.1783	+	8.76320i	−0.600444	+	0.346667i
$640$	10.3730	−	4.51670i	0.410029	−	0.178538i
$641$	2.35512	−	4.07919i	0.0930217	−	0.161118i	−0.815760	−	0.578391i	$-0.803681\pi$
$641$	2.35512	−	4.07919i	0.0930217	−	0.161118i	0.908781	+	0.417273i	$0.137014\pi$
$642$	0.928687	−	3.78622i	0.0366524	−	0.149430i
$643$		−	3.22266i		−	0.127089i	−0.997979	−	0.0635446i	$-0.979759\pi$
$643$		−	3.22266i		−	0.127089i	0.997979	−	0.0635446i	$-0.0202405\pi$
$644$	15.9534	+	18.5476i	0.628653	+	0.730880i
$645$		−	21.9742i		−	0.865235i
$646$	12.2241	+	2.99833i	0.480949	+	0.117968i
$647$	0.242759	−	0.420471i	0.00954385	−	0.0165304i	−0.861214	−	0.508242i	$-0.830295\pi$
$647$	0.242759	−	0.420471i	0.00954385	−	0.0165304i	0.870758	+	0.491712i	$0.163629\pi$
$648$	29.7307	−	10.0376i	1.16793	−	0.394314i
$649$	−12.0519	+	6.95818i	−0.473079	+	0.273133i
$650$	0.699295	−	0.729690i	0.0274286	−	0.0286208i
$651$	5.88172	+	2.34504i	0.230523	+	0.0919093i
$652$	−1.70906	−	40.1565i	−0.0669321	−	1.57265i
$653$	−4.25225	+	2.45504i	−0.166403	+	0.0960730i	−0.580889	−	0.813983i	$-0.697295\pi$
$653$	−4.25225	+	2.45504i	−0.166403	+	0.0960730i	0.414485	+	0.910056i	$0.363962\pi$
$654$	8.36578	+	28.7605i	0.327128	+	1.12462i
$655$	17.9090	+	10.3397i	0.699761	+	0.404007i
$656$	36.0483	−	25.1234i	1.40745	−	0.980905i
$657$		−	6.01696i		−	0.234744i
$658$	11.3228	−	15.8630i	0.441408	−	0.618405i
$659$	50.3794			1.96250			0.981252	−	0.192729i	$-0.0617337\pi$
$659$	50.3794			1.96250			0.981252	+	0.192729i	$0.0617337\pi$
$660$	2.48893	+	3.91633i	0.0968816	+	0.152443i
$661$	−2.39100	+	4.14133i	−0.0929991	+	0.161079i	−0.908772	−	0.417294i	$-0.862979\pi$
$661$	−2.39100	+	4.14133i	−0.0929991	+	0.161079i	0.815773	+	0.578373i	$0.196312\pi$
$662$	−8.77665	−	30.1730i	−0.341114	−	1.17271i
$663$	1.65740	+	2.87071i	0.0643683	+	0.111489i
$664$	−5.21264	+	5.92415i	−0.202290	+	0.229902i
$665$	−1.47826	−	10.1793i	−0.0573246	−	0.394738i
$666$	7.45868	+	7.14799i	0.289018	+	0.276979i
$667$	−3.56849	−	6.18080i	−0.138172	−	0.239321i
$668$	12.0112	+	6.26940i	0.464726	+	0.242570i
$669$	21.6302	+	12.4882i	0.836270	+	0.482821i
$670$	−11.2297	−	2.75444i	−0.433843	−	0.106413i
$671$	16.3407			0.630825
$672$	26.4312	−	14.8662i	1.01961	−	0.573474i
$673$	27.2854			1.05177			0.525887	−	0.850555i	$-0.323734\pi$
$673$	27.2854			1.05177			0.525887	+	0.850555i	$0.323734\pi$
$674$	20.5435	+	5.03892i	0.791305	+	0.194092i
$675$	3.32449	+	1.91939i	0.127960	+	0.0738775i
$676$	−22.1435	−	11.5581i	−0.851675	−	0.444544i
$677$	−21.2029	−	36.7245i	−0.814893	−	1.41144i	−0.909405	−	0.415913i	$-0.863462\pi$
$677$	−21.2029	−	36.7245i	−0.814893	−	1.41144i	0.0945112	−	0.995524i	$-0.469871\pi$
$678$	−16.2109	−	15.5356i	−0.622576	−	0.596643i
$679$	−10.7719	+	8.49577i	−0.413386	+	0.326038i
$680$	−4.27718	+	4.86100i	−0.164022	+	0.186411i
$681$	7.94604	+	13.7629i	0.304493	+	0.527397i
$682$	−0.534242	−	1.83666i	−0.0204572	−	0.0703293i
$683$	−22.2969	+	38.6193i	−0.853165	+	1.47773i	0.0251714	+	0.999683i	$0.491987\pi$
$683$	−22.2969	+	38.6193i	−0.853165	+	1.47773i	−0.878337	+	0.478042i	$0.841347\pi$
$684$	−4.61022	−	7.25417i	−0.176276	−	0.277370i
$685$	−4.74917			−0.181457
$686$	25.7098	−	5.00076i	0.981604	−	0.190930i
$687$		−	31.2289i		−	1.19146i
$688$	24.8039	+	35.5899i	0.945641	+	1.35685i
$689$	−1.61437	−	0.932055i	−0.0615025	−	0.0355085i
$690$	3.70023	+	12.7209i	0.140866	+	0.484278i
$691$	2.71156	−	1.56552i	0.103152	−	0.0595551i	−0.447536	−	0.894266i	$-0.647698\pi$
$691$	2.71156	−	1.56552i	0.103152	−	0.0595551i	0.550689	+	0.834711i	$0.314365\pi$
$692$	1.48002	+	34.7749i	0.0562620	+	1.32194i
$693$	2.07391	+	2.62953i	0.0787814	+	0.0998876i
$694$	16.6686	−	17.3931i	0.632730	−	0.660232i
$695$	9.51003	−	5.49062i	0.360736	−	0.208271i
$696$	−8.38175	+	2.82982i	−0.317709	+	0.107264i
$697$	−12.5733	+	21.7776i	−0.476247	+	0.824884i
$698$	1.92895	+	0.473134i	0.0730117	+	0.0179084i
$699$		−	22.8110i		−	0.862789i
$700$	4.99412	+	1.74893i	0.188760	+	0.0661033i
$701$		−	0.816220i		−	0.0308282i	−0.999881	−	0.0154141i	$-0.995093\pi$
$701$		−	0.816220i		−	0.0308282i	0.999881	−	0.0154141i	$-0.00490665\pi$
$702$	−0.924235	+	3.76807i	−0.0348830	+	0.142217i
$703$	−12.8460	+	22.2500i	−0.484498	+	0.839175i
$704$	−8.45178	−	3.53353i	−0.318538	−	0.133175i
$705$	9.13999	−	5.27698i	0.344232	−	0.198742i
$706$	13.0668	+	12.5225i	0.491775	+	0.471290i
$707$	−2.64975	+	0.384801i	−0.0996540	+	0.0144719i
$708$	2.09413	+	49.2042i	0.0787024	+	1.84921i
$709$	25.7963	−	14.8935i	0.968799	−	0.559336i	0.0699290	−	0.997552i	$-0.477723\pi$
$709$	25.7963	−	14.8935i	0.968799	−	0.559336i	0.898870	+	0.438216i	$0.144389\pi$
$710$	21.5302	−	6.26265i	0.808014	−	0.235033i
$711$	−9.06459	−	5.23345i	−0.339949	−	0.196270i
$712$	−35.3910	−	7.10037i	−1.32633	−	0.266098i
$713$		−	5.46103i		−	0.204517i
$714$	−10.0827	+	14.1258i	−0.377337	+	0.528643i
$715$	−0.818341			−0.0306042
$716$	−25.8722	+	16.4425i	−0.966889	+	0.614484i
$717$	14.3370	−	24.8325i	0.535427	−	0.927386i
$718$	8.29455	−	2.41270i	0.309550	−	0.0900411i
$719$	2.37920	+	4.12090i	0.0887293	+	0.153684i	0.906974	−	0.421186i	$-0.138386\pi$
$719$	2.37920	+	4.12090i	0.0887293	+	0.153684i	−0.818245	+	0.574870i	$0.805053\pi$
$720$	4.40564	−	0.375689i	0.164189	−	0.0140011i
$721$	−2.39096	+	5.99691i	−0.0890442	+	0.223336i
$722$	−3.80160	+	3.96684i	−0.141481	+	0.147631i
$723$	20.9462	+	36.2799i	0.778998	+	1.34926i
$724$	5.49669	+	2.86908i	0.204283	+	0.106628i
$725$	−1.33685	−	0.771829i	−0.0496492	−	0.0286650i
$726$	−6.61362	+	26.9635i	−0.245455	+	1.00071i
$727$	14.0543			0.521246			0.260623	−	0.965441i	$-0.416072\pi$
$727$	14.0543			0.521246			0.260623	+	0.965441i	$0.416072\pi$
$728$	−0.287497	+	5.34025i	−0.0106554	+	0.197923i
$729$	−11.0705			−0.410019
$730$	−1.83378	+	7.47625i	−0.0678712	+	0.276708i
$731$	−21.5006	−	12.4134i	−0.795229	−	0.459125i
$732$	26.7585	−	51.2649i	0.989021	−	1.89480i
$733$	0.785118	+	1.35986i	0.0289990	+	0.0502277i	0.880161	−	0.474676i	$-0.157435\pi$
$733$	0.785118	+	1.35986i	0.0289990	+	0.0502277i	−0.851162	+	0.524904i	$0.824101\pi$
$734$	−8.91865	+	9.30630i	−0.329193	+	0.343502i
$735$	13.7929	+	3.30483i	0.508757	+	0.121901i
$736$	−20.3520	−	16.4264i	−0.750186	−	0.605484i
$737$	4.68112	+	8.10793i	0.172431	+	0.298660i
$738$	16.4890	−	4.79628i	0.606969	−	0.176554i
$739$	−3.63252	+	6.29171i	−0.133625	+	0.231444i	−0.925071	−	0.379794i	$-0.875995\pi$
$739$	−3.63252	+	6.29171i	−0.133625	+	0.231444i	0.791447	+	0.611238i	$0.209328\pi$
$740$	−7.08914	−	11.1547i	−0.260602	−	0.410057i
$741$	5.62959			0.206808
$742$	0.938592	−	9.71453i	0.0344568	−	0.356632i
$743$			0.694046i			0.0254621i	0.999919	+	0.0127310i	$0.00405253\pi$
$743$			0.694046i			0.0254621i	−0.999919	+	0.0127310i	$0.995947\pi$
$744$	−6.63690	−	1.33154i	−0.243321	−	0.0488166i
$745$	−13.4757	−	7.78020i	−0.493711	−	0.285044i
$746$	31.2135	−	9.07930i	1.14281	−	0.332417i
$747$	−2.67078	+	1.54197i	−0.0977187	+	0.0564179i
$748$	5.23793	−	0.222927i	0.191518	−	0.00815101i
$749$	−1.33309	+	3.34359i	−0.0487100	+	0.122172i
$750$	2.06881	+	1.98263i	0.0755423	+	0.0723956i
$751$	14.2883	−	8.24935i	0.521387	−	0.301023i	−0.216115	−	0.976368i	$-0.569339\pi$
$751$	14.2883	−	8.24935i	0.521387	−	0.301023i	0.737502	+	0.675345i	$0.236005\pi$
$752$	−8.84680	+	18.8637i	−0.322610	+	0.687887i
$753$	−13.2996	+	23.0356i	−0.484664	+	0.839463i
$754$	0.371654	−	1.51522i	0.0135349	−	0.0551811i
$755$		−	12.5492i		−	0.456712i
$756$	−19.9598	+	3.77140i	−0.725930	+	0.137164i
$757$			45.3048i			1.64663i	0.567583	+	0.823316i	$0.307879\pi$
$757$			45.3048i			1.64663i	−0.567583	+	0.823316i	$0.692121\pi$
$758$	24.8558	+	6.09664i	0.902802	+	0.221440i
$759$	5.36352	−	9.28988i	0.194683	−	0.337201i
$760$	3.51749	+	10.4186i	0.127593	+	0.377921i
$761$	4.16297	−	2.40349i	0.150907	−	0.0871265i	−0.422645	−	0.906295i	$-0.638898\pi$
$761$	4.16297	−	2.40349i	0.150907	−	0.0871265i	0.573552	+	0.819169i	$0.305565\pi$
$762$	23.8598	−	24.8969i	0.864350	−	0.901919i
$763$	−3.97457	−	27.3689i	−0.143889	−	0.990820i
$764$	−29.1783	+	1.24183i	−1.05563	+	0.0449279i
$765$	−2.19148	+	1.26525i	−0.0792331	+	0.0457453i
$766$	8.49025	+	29.1884i	0.306765	+	1.05462i
$767$	−7.52166	−	4.34263i	−0.271592	−	0.156803i
$768$	−24.9257	+	20.7291i	−0.899427	+	0.747997i
$769$			5.47427i			0.197407i	0.995117	+	0.0987035i	$0.0314695\pi$
$769$			5.47427i			0.197407i	−0.995117	+	0.0987035i	$0.968530\pi$
$770$	−1.77549	−	3.89933i	−0.0639844	−	0.140522i
$771$	41.3955			1.49082
$772$	28.7122	−	18.2474i	1.03337	−	0.656737i
$773$	−7.14164	+	12.3697i	−0.256867	+	0.444906i	−0.965401	−	0.260770i	$-0.916024\pi$
$773$	−7.14164	+	12.3697i	−0.256867	+	0.444906i	0.708534	+	0.705677i	$0.249357\pi$
$774$	4.73529	+	16.2793i	0.170206	+	0.585148i
$775$	−0.590584	−	1.02292i	−0.0212144	−	0.0367444i
$776$	9.68829	−	11.0107i	0.347789	−	0.395262i
$777$	−21.9384	−	27.8158i	−0.787034	−	0.997888i
$778$	2.80820	+	2.69123i	0.100679	+	0.0964851i
$779$	21.3534	+	36.9851i	0.765064	+	1.32513i
$780$	−1.34006	+	2.56735i	−0.0479820	+	0.0919257i
$781$	−15.7231	−	9.07776i	−0.562618	−	0.324828i
$782$	14.5370	+	3.56566i	0.519844	+	0.127508i
$783$	5.92577			0.211770
$784$	−26.0696	+	10.2164i	−0.931057	+	0.364873i
$785$	−7.66299			−0.273504
$786$	−57.5501	−	14.1159i	−2.05275	−	0.503499i
$787$	10.3383	+	5.96882i	0.368521	+	0.212765i	0.672812	−	0.739814i	$-0.265086\pi$
$787$	10.3383	+	5.96882i	0.368521	+	0.212765i	−0.304291	+	0.952579i	$0.598420\pi$
$788$	−14.0983	+	27.0101i	−0.502232	+	0.962196i
$789$	−31.7266	−	54.9520i	−1.12950	−	1.95634i
$790$	9.66802	+	9.26530i	0.343973	+	0.329645i
$791$	12.8385	+	16.2781i	0.456486	+	0.578783i
$792$	−2.68783	−	2.36502i	−0.0955080	−	0.0840372i
$793$	5.09915	+	8.83199i	0.181076	+	0.313633i
$794$	6.02750	+	20.7218i	0.213908	+	0.735388i
$795$	2.64255	−	4.57704i	0.0937217	−	0.162331i
$796$	27.0798	−	17.2099i	0.959817	−	0.609989i
$797$	44.5344			1.57749			0.788745	−	0.614720i	$-0.210731\pi$
$797$	44.5344			1.57749			0.788745	+	0.614720i	$0.210731\pi$
$798$	12.2141	+	26.8245i	0.432375	+	0.949578i
$799$		−	11.9240i		−	0.421840i
$800$	−5.58863	−	0.875896i	−0.197588	−	0.0309676i
$801$	−12.2172	−	7.05358i	−0.431672	−	0.249226i
$802$	3.28553	+	11.2952i	0.116016	+	0.398849i
$803$	5.39789	−	3.11647i	0.190487	−	0.109978i
$804$	33.1021	−	1.40883i	1.16742	−	0.0496856i
$805$	−1.75797	−	12.1054i	−0.0619604	−	0.426660i
$806$	0.825985	−	0.861886i	0.0290941	−	0.0303587i
$807$	−1.52689	+	0.881550i	−0.0537490	+	0.0310320i
$808$	2.71202	−	0.915623i	0.0954084	−	0.0322115i
$809$	8.90901	−	15.4309i	0.313224	−	0.542520i	−0.665834	−	0.746100i	$-0.731924\pi$
$809$	8.90901	−	15.4309i	0.313224	−	0.542520i	0.979058	+	0.203579i	$0.0652575\pi$
$810$	−15.2380	−	3.73759i	−0.535409	−	0.131326i
$811$			38.8733i			1.36503i	0.730873	+	0.682513i	$0.239113\pi$
$811$			38.8733i			1.36503i	−0.730873	+	0.682513i	$0.760887\pi$
$812$	8.02625	−	1.51656i	0.281666	−	0.0532208i
$813$		−	63.4825i		−	2.22643i
$814$	−2.54934	+	10.3936i	−0.0893543	+	0.364294i
$815$	−10.0482	+	17.4040i	−0.351974	+	0.609636i
$816$	7.87792	−	16.7978i	0.275782	−	0.588040i
$817$	−36.5148	+	21.0818i	−1.27749	+	0.737560i
$818$	27.5023	+	26.3567i	0.961597	+	0.921542i
$819$	−0.774068	+	1.94148i	−0.0270481	+	0.0678408i
$820$	−21.9498	+	0.934186i	−0.766521	+	0.0326232i
$821$	−12.4121	+	7.16612i	−0.433185	+	0.250099i	−0.700703	−	0.713454i	$-0.747130\pi$
$821$	−12.4121	+	7.16612i	−0.433185	+	0.250099i	0.267518	+	0.963553i	$0.413797\pi$
$822$	13.0670	−	3.80088i	0.455762	−	0.132571i
$823$	8.71650	+	5.03248i	0.303838	+	0.175421i	0.644166	−	0.764886i	$-0.277205\pi$
$823$	8.71650	+	5.03248i	0.303838	+	0.175421i	−0.340328	+	0.940307i	$0.610538\pi$
$824$	1.35762	−	6.76688i	0.0472948	−	0.235736i
$825$		−	2.32015i		−	0.0807774i
$826$	4.37309	−	45.2620i	0.152159	−	1.57487i
$827$	33.0985			1.15095			0.575475	−	0.817820i	$-0.304817\pi$
$827$	33.0985			1.15095			0.575475	+	0.817820i	$0.304817\pi$
$828$	−5.48254	−	8.62677i	−0.190531	−	0.299801i
$829$	−19.9412	+	34.5392i	−0.692586	+	1.19959i	0.278401	+	0.960465i	$0.410196\pi$
$829$	−19.9412	+	34.5392i	−0.692586	+	1.19959i	−0.970988	+	0.239130i	$0.923138\pi$
$830$	3.78846	−	1.10198i	0.131499	−	0.0382502i
$831$	−28.5093	−	49.3795i	−0.988976	−	1.71296i
$832$	−0.727559	−	5.67075i	−0.0252236	−	0.196598i
$833$	11.0253	−	11.6287i	0.382003	−	0.402909i
$834$	−21.7718	+	22.7181i	−0.753895	+	0.786663i
$835$	−3.38723	−	5.86686i	−0.117220	−	0.203031i
$836$	4.11995	−	7.89317i	0.142492	−	0.272991i
$837$	3.92678	+	2.26712i	0.135729	+	0.0783633i
$838$	3.02396	−	12.3286i	0.104461	−	0.425884i
$839$	9.19183			0.317337			0.158669	−	0.987332i	$-0.449280\pi$
$839$	9.19183			0.317337			0.158669	+	0.987332i	$0.449280\pi$
$840$	−15.1406	−	0.815109i	−0.522401	−	0.0281239i
$841$	26.6171			0.917832
$842$	−4.53861	+	18.5037i	−0.156411	+	0.637681i
$843$	−38.8387	−	22.4235i	−1.33768	−	0.772307i
$844$	−10.3861	−	5.42116i	−0.357503	−	0.186604i
$845$	6.24463	+	10.8160i	0.214822	+	0.372083i
$846$	−5.63409	+	5.87898i	−0.193704	+	0.202123i
$847$	9.49356	−	23.8113i	0.326203	−	0.818167i
$848$	0.886506	+	10.3959i	0.0304427	+	0.356997i
$849$	−2.67142	−	4.62704i	−0.0916830	−	0.158800i
$850$	3.10858	−	0.904217i	0.106624	−	0.0310144i
$851$	−15.2767	+	26.4600i	−0.523679	+	0.907038i
$852$	−54.2264	+	34.4623i	−1.85777	+	1.18066i
$853$	−22.3596			−0.765577			−0.382788	−	0.923836i	$-0.625036\pi$
$853$	−22.3596			−0.765577			−0.382788	+	0.923836i	$0.625036\pi$
$854$	−31.0204	+	43.4591i	−1.06150	+	1.48714i
$855$			4.29759i			0.146975i
$856$	0.756943	−	3.77290i	0.0258718	−	0.128955i
$857$	2.08869	+	1.20591i	0.0713485	+	0.0411930i	0.535250	−	0.844694i	$-0.320217\pi$
$857$	2.08869	+	1.20591i	0.0713485	+	0.0411930i	−0.463901	+	0.885887i	$0.653551\pi$
$858$	2.25160	−	0.654939i	0.0768683	−	0.0223593i
$859$	30.5635	−	17.6459i	1.04281	−	0.602069i	0.122185	−	0.992507i	$-0.461010\pi$
$859$	30.5635	−	17.6459i	1.04281	−	0.602069i	0.920629	+	0.390438i	$0.127676\pi$
$860$	−0.922305	−	21.6707i	−0.0314504	−	0.738964i
$861$	−58.2759	+	8.46295i	−1.98604	+	0.288417i
$862$	−24.2122	−	23.2037i	−0.824671	−	0.790320i
$863$	−19.8260	+	11.4466i	−0.674886	+	0.389645i	−0.797925	−	0.602756i	$-0.794069\pi$
$863$	−19.8260	+	11.4466i	−0.674886	+	0.389645i	0.123040	+	0.992402i	$0.460736\pi$
$864$	20.2605	−	7.81488i	0.689277	−	0.265868i
$865$	8.70160	−	15.0716i	0.295863	−	0.512450i
$866$	−6.25443	+	25.4991i	−0.212534	+	0.866493i
$867$		−	23.8270i		−	0.809206i
$868$	5.89889	+	2.06578i	0.200222	+	0.0701170i
$869$		−	10.8426i		−	0.367810i
$870$	4.29594	+	1.05371i	0.145646	+	0.0357242i
$871$	−2.92151	+	5.06020i	−0.0989915	+	0.171458i
$872$	9.45736	+	28.0121i	0.320267	+	0.948609i
$873$	4.96395	−	2.86594i	0.168004	−	0.0969972i
$874$	17.5885	−	18.3530i	0.594942	−	0.620801i
$875$	−1.63843	−	2.07739i	−0.0553892	−	0.0702285i
$876$	−0.937934	−	22.0379i	−0.0316898	−	0.744591i
$877$	−37.7590	+	21.8002i	−1.27503	+	0.736140i	−0.975931	−	0.218082i	$-0.930020\pi$
$877$	−37.7590	+	21.8002i	−1.27503	+	0.736140i	−0.299101	+	0.954221i	$0.596687\pi$
$878$	2.72311	+	9.36170i	0.0919004	+	0.315942i
$879$	−17.1751	−	9.91604i	−0.579301	−	0.334460i
$880$	2.61893	+	3.75777i	0.0882840	+	0.126674i
$881$			5.79085i			0.195099i	0.995231	+	0.0975494i	$0.0311004\pi$
$881$			5.79085i			0.195099i	−0.995231	+	0.0975494i	$0.968900\pi$
$882$	−10.9304	+	0.523919i	−0.368047	+	0.0176413i
$883$	−20.0070			−0.673288			−0.336644	−	0.941632i	$-0.609292\pi$
$883$	−20.0070			−0.673288			−0.336644	+	0.941632i	$0.609292\pi$
$884$	1.75500	+	2.76149i	0.0590270	+	0.0928789i
$885$	12.3122	−	21.3253i	0.413870	−	0.716844i
$886$	11.1490	+	38.3288i	0.374558	+	1.28768i
$887$	−6.86765	−	11.8951i	−0.230593	−	0.399399i	0.727390	−	0.686225i	$-0.240733\pi$
$887$	−6.86765	−	11.8951i	−0.230593	−	0.399399i	−0.957983	+	0.286826i	$0.907400\pi$
$888$	28.4326	+	25.0177i	0.954135	+	0.839541i
$889$	−25.0001	+	19.7176i	−0.838476	+	0.661306i
$890$	13.0305	+	12.4877i	0.436782	+	0.418588i
$891$	6.35197	+	11.0019i	0.212799	+	0.368579i
$892$	21.8555	+	11.4078i	0.731777	+	0.381962i
$893$	−17.5376	−	10.1253i	−0.586873	−	0.338832i
$894$	43.3040	+	10.6216i	1.44830	+	0.355240i
$895$	15.3275			0.512341
$896$	25.4421	−	15.7702i	0.849962	−	0.526844i
$897$	6.69479			0.223533
$898$	2.65980	+	0.652397i	0.0887586	+	0.0217708i
$899$	−1.57904	−	0.911659i	−0.0526639	−	0.0304055i
$900$	−1.95989	−	1.02300i	−0.0653298	−	0.0340998i
$901$	−2.98559	−	5.17119i	−0.0994644	−	0.172277i
$902$	12.8433	+	12.3083i	0.427634	+	0.409821i
$903$	−8.35533	−	57.5348i	−0.278048	−	1.91464i
$904$	−16.6390	−	14.6406i	−0.553406	−	0.486940i
$905$	−1.55010	−	2.68486i	−0.0515272	−	0.0892478i
$906$	10.0434	+	34.5281i	0.333671	+	1.14712i
$907$	−3.55400	+	6.15571i	−0.118009	+	0.204397i	−0.918978	−	0.394308i	$-0.870984\pi$
$907$	−3.55400	+	6.15571i	−0.118009	+	0.204397i	0.800970	+	0.598705i	$0.204318\pi$
$908$	8.41394	+	13.2393i	0.279226	+	0.439362i
$909$	1.11869			0.0371046
$910$	1.55350	−	2.17643i	0.0514981	−	0.0721480i
$911$		−	13.1201i		−	0.434690i	−0.976095	−	0.217345i	$-0.930260\pi$
$911$		−	13.1201i		−	0.434690i	0.976095	−	0.217345i	$-0.0697397\pi$
$912$	−18.0163	−	25.8507i	−0.596580	−	0.856002i
$913$	−2.76665	−	1.59732i	−0.0915627	−	0.0528637i
$914$	−13.7261	−	47.1888i	−0.454021	−	1.56087i
$915$	−25.0404	+	14.4571i	−0.827809	+	0.477936i
$916$	−1.31074	−	30.7975i	−0.0433081	−	1.01758i
$917$	50.8223	+	20.2628i	1.67830	+	0.669137i
$918$	−8.59890	+	8.97265i	−0.283806	+	0.296142i
$919$	−23.7519	+	13.7132i	−0.783502	+	0.452355i	−0.837670	−	0.546176i	$-0.816083\pi$
$919$	−23.7519	+	13.7132i	−0.783502	+	0.452355i	0.0541677	+	0.998532i	$0.482749\pi$
$920$	4.18305	+	12.3899i	0.137911	+	0.408483i
$921$	−10.8167	+	18.7351i	−0.356423	+	0.617343i
$922$	40.2596	+	9.87490i	1.32588	+	0.325213i
$923$		−	11.3309i		−	0.372963i
$924$	8.00586	+	9.30771i	0.263373	+	0.306201i
$925$			6.60841i			0.217283i
$926$	3.19108	−	13.0099i	0.104865	−	0.427532i
$927$	1.34867	−	2.33596i	0.0442961	−	0.0767231i
$928$	−8.14719	+	3.14253i	−0.267445	+	0.103159i
$929$	10.4779	−	6.04939i	0.343767	−	0.198474i	−0.318169	−	0.948034i	$-0.603068\pi$
$929$	10.4779	−	6.04939i	0.343767	−	0.198474i	0.661937	+	0.749560i	$0.269735\pi$
$930$	2.44361	+	2.34182i	0.0801292	+	0.0767914i
$931$	−7.74104	−	26.0903i	−0.253702	−	0.855077i
$932$	−0.957424	−	22.4958i	−0.0313615	−	0.736876i
$933$	−14.8562	+	8.57725i	−0.486371	+	0.280807i
$934$	17.6278	−	5.12752i	0.576798	−	0.167778i
$935$	−2.27014	−	1.31067i	−0.0742417	−	0.0428634i
$936$	0.439524	−	2.19076i	0.0143663	−	0.0716072i
$937$			50.1666i			1.63887i	0.573171	+	0.819435i	$0.305713\pi$
$937$			50.1666i			1.63887i	−0.573171	+	0.819435i	$0.694287\pi$
$938$	−30.4500	−	2.94200i	−0.994228	−	0.0960596i
$939$	−47.3626			−1.54562
$940$	8.79225	−	5.58771i	0.286771	−	0.182251i
$941$	21.2678	−	36.8369i	0.693311	−	1.20085i	−0.277436	−	0.960744i	$-0.589485\pi$
$941$	21.2678	−	36.8369i	0.693311	−	1.20085i	0.970747	−	0.240106i	$-0.0771820\pi$
$942$	21.0841	−	6.13288i	0.686956	−	0.199820i
$943$	25.3938	+	43.9833i	0.826935	+	1.43229i
$944$	4.13041	+	48.4366i	0.134433	+	1.57648i
$945$	9.43427	+	3.76144i	0.306897	+	0.122360i
$946$	−12.1517	+	12.6799i	−0.395087	+	0.412260i
$947$	−7.96280	−	13.7920i	−0.258756	−	0.448179i	0.707153	−	0.707061i	$-0.249979\pi$
$947$	−7.96280	−	13.7920i	−0.258756	−	0.448179i	−0.965909	+	0.258882i	$0.916646\pi$
$948$	−34.0160	−	17.7552i	−1.10479	−	0.576661i
$949$	3.36885	+	1.94501i	0.109357	+	0.0631375i
$950$	1.30977	−	5.33988i	0.0424945	−	0.173249i
$951$	25.9582			0.841754
$952$	−9.35057	+	14.3538i	−0.303054	+	0.465210i
$953$	31.6348			1.02475			0.512375	−	0.858762i	$-0.328766\pi$
$953$	31.6348			1.02475			0.512375	+	0.858762i	$0.328766\pi$
$954$	−0.971383	+	3.96029i	−0.0314497	+	0.128219i
$955$	12.6460	+	7.30118i	0.409216	+	0.236261i
$956$	13.0967	−	25.0912i	0.423578	−	0.811508i
$957$	−1.79076	−	3.10169i	−0.0578871	−	0.100263i
$958$	19.4967	−	20.3441i	0.629910	−	0.657289i
$959$	−12.4347	+	1.80579i	−0.401537	+	0.0583120i
$960$	16.0777	−	2.06277i	0.518904	−	0.0665755i
$961$	14.8024	+	25.6385i	0.477497	+	0.827050i
$962$	−6.41315	+	1.86544i	−0.206768	+	0.0601442i
$963$	0.751954	−	1.30242i	0.0242314	−	0.0419700i
$964$	22.1796	+	34.8996i	0.714357	+	1.12404i
$965$	−17.0100			−0.547570
$966$	14.5252	+	31.9001i	0.467340	+	1.02637i
$967$		−	9.06338i		−	0.291459i	−0.989324	−	0.145729i	$-0.953447\pi$
$967$		−	9.06338i		−	0.291459i	0.989324	−	0.145729i	$-0.0465529\pi$
$968$	−5.39055	+	26.8686i	−0.173259	+	0.863589i
$969$	15.6169	+	9.01644i	0.501688	+	0.289650i
$970$	−7.04129	+	2.04815i	−0.226082	+	0.0657622i
$971$	−42.3233	+	24.4354i	−1.35822	+	0.784168i	−0.989384	−	0.145327i	$-0.953577\pi$
$971$	−42.3233	+	24.4354i	−1.35822	+	0.784168i	−0.368835	+	0.929495i	$0.620243\pi$
$972$	21.9056	−	0.932301i	0.702621	−	0.0299036i
$973$	22.8123	−	17.9920i	0.731327	−	0.576798i
$974$	27.5914	+	26.4421i	0.884086	+	0.847259i
$975$	1.25402	−	0.724009i	0.0401608	−	0.0231869i
$976$	24.2371	−	51.6798i	0.775811	−	1.65423i
$977$	−15.3107	+	26.5188i	−0.489831	+	0.848413i	−0.999932	−	0.0117023i	$-0.996275\pi$
$977$	−15.3107	+	26.5188i	−0.489831	+	0.848413i	0.510100	+	0.860115i	$0.329608\pi$
$978$	13.7180	−	55.9275i	0.438652	−	1.78837i
$979$		−	14.6135i		−	0.467051i
$980$	13.7410	+	2.68026i	0.438941	+	0.0856179i
$981$			11.5548i			0.368917i
$982$	0.624131	+	0.153087i	0.0199168	+	0.00488522i
$983$	9.15271	−	15.8530i	0.291926	−	0.505631i	−0.682339	−	0.731036i	$-0.739037\pi$
$983$	9.15271	−	15.8530i	0.291926	−	0.505631i	0.974265	+	0.225405i	$0.0723705\pi$
$984$	59.6455	−	20.1373i	1.90143	−	0.641955i
$985$	13.1931	−	7.61705i	0.420367	−	0.242699i
$986$	3.45780	−	3.60809i	0.110119	−	0.114905i
$987$	21.9246	−	17.2920i	0.697869	−	0.550409i
$988$	5.55182	−	0.236286i	0.176627	−	0.00751725i
$989$	−43.4239	+	25.0708i	−1.38080	+	0.797206i
$990$	0.499976	+	1.71886i	0.0158903	+	0.0546288i
$991$	−33.4098	−	19.2891i	−1.06130	−	0.612740i	−0.135506	−	0.990777i	$-0.543266\pi$
$991$	−33.4098	−	19.2891i	−1.06130	−	0.612740i	−0.925791	+	0.378037i	$0.876599\pi$
$992$	−6.60111	−	1.03458i	−0.209585	−	0.0328479i
$993$		−	45.0214i		−	1.42871i
$994$	53.9910	−	24.5839i	1.71249	−	0.779754i
$995$	−16.0429			−0.508593
$996$	−9.54170	+	6.06400i	−0.302340	+	0.192145i
$997$	−27.5501	+	47.7182i	−0.872522	+	1.51125i	−0.0131423	+	0.999914i	$0.504183\pi$
$997$	−27.5501	+	47.7182i	−0.872522	+	1.51125i	−0.859379	+	0.511338i	$0.829150\pi$
$998$	−3.39079	−	11.6571i	−0.107334	−	0.369000i
$999$	−12.6841	−	21.9696i	−0.401308	−	0.695086i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.f.171.11	yes	24
4.3	odd	2		1120.2.bz.e.591.5		24
7.5	odd	6		280.2.bj.e.131.7	✓	24
8.3	odd	2		280.2.bj.e.171.7	yes	24
8.5	even	2		1120.2.bz.f.591.5		24
28.19	even	6		1120.2.bz.f.271.5		24
56.5	odd	6		1120.2.bz.e.271.5		24
56.19	even	6	inner	280.2.bj.f.131.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.7	✓	24	7.5	odd	6
280.2.bj.e.171.7	yes	24	8.3	odd	2
280.2.bj.f.131.11	yes	24	56.19	even	6	inner
280.2.bj.f.171.11	yes	24	1.1	even	1	trivial
1120.2.bz.e.271.5		24	56.5	odd	6
1120.2.bz.e.591.5		24	4.3	odd	2
1120.2.bz.f.271.5		24	28.19	even	6
1120.2.bz.f.591.5		24	8.5	even	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37350 + 0.336893i) q^{2} +(1.75472 + 1.01309i) q^{3} +(1.77301 + 0.925446i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.06881 + 1.98263i) q^{6} +(-1.63843 - 2.07739i) q^{7} +(2.12345 + 1.86841i) q^{8} +(0.552704 + 0.957311i) q^{9} +O(q^{10})\)	\(q+(1.37350 + 0.336893i) q^{2} +(1.75472 + 1.01309i) q^{3} +(1.77301 + 0.925446i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.06881 + 1.98263i) q^{6} +(-1.63843 - 2.07739i) q^{7} +(2.12345 + 1.86841i) q^{8} +(0.552704 + 0.957311i) q^{9} +(-0.394992 - 1.35793i) q^{10} +(-0.572544 + 0.991675i) q^{11} +(2.17358 + 3.42012i) q^{12} -0.714654 q^{13} +(-1.55053 - 3.40527i) q^{14} -2.02618i q^{15} +(2.28710 + 3.28164i) q^{16} +(-1.98251 - 1.14460i) q^{17} +(0.436627 + 1.50107i) q^{18} +(-3.36692 + 1.94389i) q^{19} +(-0.0850431 - 1.99819i) q^{20} +(-0.770420 - 5.30512i) q^{21} +(-1.12048 + 1.16918i) q^{22} +(-4.00399 + 2.31171i) q^{23} +(1.83319 + 5.42979i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.981578 - 0.240762i) q^{26} -3.83879i q^{27} +(-0.982445 - 5.19950i) q^{28} +1.54366i q^{29} +(0.682607 - 2.78296i) q^{30} +(-0.590584 + 1.02292i) q^{31} +(2.03577 + 5.27785i) q^{32} +(-2.00931 + 1.16008i) q^{33} +(-2.33737 - 2.24000i) q^{34} +(-0.979852 + 2.45762i) q^{35} +(0.0940073 + 2.20882i) q^{36} +(5.72305 - 3.30420i) q^{37} +(-5.27936 + 1.53565i) q^{38} +(-1.25402 - 0.724009i) q^{39} +(0.556370 - 2.77317i) q^{40} -10.9848i q^{41} +(0.729087 - 7.54613i) q^{42} +10.8452 q^{43} +(-1.93286 + 1.22839i) q^{44} +(0.552704 - 0.957311i) q^{45} +(-6.27829 + 1.82621i) q^{46} +(2.60440 + 4.51095i) q^{47} +(0.688627 + 8.07541i) q^{48} +(-1.63107 + 6.80732i) q^{49} +(-0.978508 + 1.02104i) q^{50} +(-2.31917 - 4.01692i) q^{51} +(-1.26709 - 0.661374i) q^{52} +(2.25895 + 1.30420i) q^{53} +(1.29326 - 5.27257i) q^{54} +1.14509 q^{55} +(0.402288 - 7.47249i) q^{56} -7.87736 q^{57} +(-0.520048 + 2.12021i) q^{58} +(10.5249 + 6.07655i) q^{59} +(1.87512 - 3.59243i) q^{60} +(-7.13513 - 12.3584i) q^{61} +(-1.15578 + 1.20602i) q^{62} +(1.08314 - 2.71667i) q^{63} +(1.01806 + 7.93496i) q^{64} +(0.357327 + 0.618909i) q^{65} +(-3.15061 + 0.916442i) q^{66} +(4.08800 - 7.08062i) q^{67} +(-2.45573 - 3.86409i) q^{68} -9.36787 q^{69} +(-2.17378 + 3.04543i) q^{70} +15.8551i q^{71} +(-0.615016 + 3.06548i) q^{72} +(-4.71396 - 2.72160i) q^{73} +(8.97377 - 2.61027i) q^{74} +(-1.75472 + 1.01309i) q^{75} +(-7.76854 + 0.330630i) q^{76} +(2.99817 - 0.435400i) q^{77} +(-1.47848 - 1.41690i) q^{78} +(-8.20023 + 4.73440i) q^{79} +(1.69844 - 3.62151i) q^{80} +(5.54715 - 9.60794i) q^{81} +(3.70072 - 15.0877i) q^{82} +2.78987i q^{83} +(3.54364 - 10.1190i) q^{84} +2.28920i q^{85} +(14.8958 + 3.65366i) q^{86} +(-1.56386 + 2.70869i) q^{87} +(-3.06862 + 1.03602i) q^{88} +(-11.0522 + 6.38097i) q^{89} +(1.08165 - 1.12866i) q^{90} +(1.17091 + 1.48461i) q^{91} +(-9.23847 + 0.393190i) q^{92} +(-2.07262 + 1.19663i) q^{93} +(2.05743 + 7.07319i) q^{94} +(3.36692 + 1.94389i) q^{95} +(-1.77472 + 11.3236i) q^{96} -5.18530i q^{97} +(-4.53361 + 8.80036i) q^{98} -1.26579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 + 12 * q^3 + q^4 - 12 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

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