LMFDB - Embedded newform 560.2.t.a.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36029 + 0.386778i) q^{2} +1.62010i q^{3} +(1.70080 - 1.05227i) q^{4} +(-2.19508 - 0.426188i) q^{5} +(-0.626621 - 2.20382i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.90660 + 2.08923i) q^{8} +0.375266 q^{9} +O(q^{10})$	\(q+(-1.36029 + 0.386778i) q^{2} +1.62010i q^{3} +(1.70080 - 1.05227i) q^{4} +(-2.19508 - 0.426188i) q^{5} +(-0.626621 - 2.20382i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.90660 + 2.08923i) q^{8} +0.375266 q^{9} +(3.15079 - 0.269268i) q^{10} +(-0.211993 + 0.211993i) q^{11} +(1.70478 + 2.75548i) q^{12} +5.00506 q^{13} +(-0.688380 + 1.23537i) q^{14} +(0.690468 - 3.55625i) q^{15} +(1.78547 - 3.57940i) q^{16} +(-5.14025 + 5.14025i) q^{17} +(-0.510472 + 0.145145i) q^{18} +(-3.34023 + 3.34023i) q^{19} +(-4.18186 + 1.58494i) q^{20} +(1.14559 + 1.14559i) q^{21} +(0.206379 - 0.370367i) q^{22} +(4.61932 + 4.61932i) q^{23} +(-3.38476 - 3.08889i) q^{24} +(4.63673 + 1.87103i) q^{25} +(-6.80836 + 1.93585i) q^{26} +5.46828i q^{27} +(0.458587 - 1.94671i) q^{28} +(-5.59017 - 5.59017i) q^{29} +(0.436241 + 5.10461i) q^{30} +4.67854i q^{31} +(-1.04434 + 5.55962i) q^{32} +(-0.343451 - 0.343451i) q^{33} +(5.00412 - 8.98039i) q^{34} +(-1.85351 + 1.25079i) q^{35} +(0.638254 - 0.394879i) q^{36} -0.816234 q^{37} +(3.25177 - 5.83562i) q^{38} +8.10871i q^{39} +(5.07554 - 3.77344i) q^{40} -8.72292i q^{41} +(-2.00142 - 1.11525i) q^{42} -7.71883 q^{43} +(-0.137486 + 0.583632i) q^{44} +(-0.823737 - 0.159934i) q^{45} +(-8.07030 - 4.49699i) q^{46} +(1.04599 + 1.04599i) q^{47} +(5.79899 + 2.89265i) q^{48} -1.00000i q^{49} +(-7.03099 - 0.751766i) q^{50} +(-8.32774 - 8.32774i) q^{51} +(8.51263 - 5.26665i) q^{52} +11.9617i q^{53} +(-2.11501 - 7.43847i) q^{54} +(0.555690 - 0.374992i) q^{55} +(0.129134 + 2.82548i) q^{56} +(-5.41151 - 5.41151i) q^{57} +(9.76644 + 5.44212i) q^{58} +(3.63917 + 3.63917i) q^{59} +(-2.56777 - 6.77505i) q^{60} +(-10.3396 + 10.3396i) q^{61} +(-1.80956 - 6.36420i) q^{62} +(0.265353 - 0.265353i) q^{63} +(-0.729731 - 7.96665i) q^{64} +(-10.9865 - 2.13309i) q^{65} +(0.600033 + 0.334355i) q^{66} -2.96152 q^{67} +(-3.33366 + 14.1515i) q^{68} +(-7.48378 + 7.48378i) q^{69} +(2.03755 - 2.41835i) q^{70} +11.0620 q^{71} +(-0.715483 + 0.784015i) q^{72} +(-3.80786 + 3.80786i) q^{73} +(1.11032 - 0.315702i) q^{74} +(-3.03126 + 7.51198i) q^{75} +(-2.16627 + 9.19588i) q^{76} +0.299803i q^{77} +(-3.13627 - 11.0302i) q^{78} +8.41143 q^{79} +(-5.44475 + 7.09610i) q^{80} -7.73338 q^{81} +(3.37384 + 11.8657i) q^{82} +8.16875i q^{83} +(3.15388 + 0.742958i) q^{84} +(13.4740 - 9.09253i) q^{85} +(10.4999 - 2.98548i) q^{86} +(9.05665 - 9.05665i) q^{87} +(-0.0387149 - 0.847088i) q^{88} -1.65050 q^{89} +(1.18238 - 0.101047i) q^{90} +(3.53911 - 3.53911i) q^{91} +(12.7173 + 2.99581i) q^{92} -7.57972 q^{93} +(-1.82743 - 1.01829i) q^{94} +(8.75562 - 5.90849i) q^{95} +(-9.00716 - 1.69194i) q^{96} +(7.98515 - 7.98515i) q^{97} +(0.386778 + 1.36029i) q^{98} +(-0.0795537 + 0.0795537i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.36029	+	0.386778i	−0.961874	+	0.273494i
$2$	−1.36029	+	0.386778i	−0.961874	+	0.273494i
$3$			1.62010i			0.935367i	0.883896	+	0.467684i	$0.154911\pi$
$3$			1.62010i			0.935367i	−0.883896	+	0.467684i	$0.845089\pi$
$4$	1.70080	−	1.05227i	0.850402	−	0.526133i
$5$	−2.19508	−	0.426188i	−0.981668	−	0.190597i
$5$	−2.19508	−	0.426188i	−0.981668	−	0.190597i
$6$	−0.626621	−	2.20382i	−0.255817	−	0.899705i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−1.90660	+	2.08923i	−0.674086	+	0.738653i
$9$	0.375266			0.125089
$10$	3.15079	−	0.269268i	0.996368	−	0.0851499i
$11$	−0.211993	+	0.211993i	−0.0639183	+	0.0639183i	−0.738343	−	0.674425i	$-0.764392\pi$
$11$	−0.211993	+	0.211993i	−0.0639183	+	0.0639183i	0.674425	+	0.738343i	$0.264392\pi$
$12$	1.70478	+	2.75548i	0.492127	+	0.795438i
$13$	5.00506			1.38815			0.694077	−	0.719901i	$-0.255813\pi$
$13$	5.00506			1.38815			0.694077	+	0.719901i	$0.255813\pi$
$14$	−0.688380	+	1.23537i	−0.183977	+	0.330166i
$15$	0.690468	−	3.55625i	0.178278	−	0.918220i
$16$	1.78547	−	3.57940i	0.446369	−	0.894849i
$17$	−5.14025	+	5.14025i	−1.24669	+	1.24669i	−0.289523	+	0.957171i	$0.593497\pi$
$17$	−5.14025	+	5.14025i	−1.24669	+	1.24669i	−0.957171	+	0.289523i	$0.906503\pi$
$18$	−0.510472	+	0.145145i	−0.120319	+	0.0342109i
$19$	−3.34023	+	3.34023i	−0.766301	+	0.766301i	−0.977453	−	0.211152i	$-0.932278\pi$
$19$	−3.34023	+	3.34023i	−0.766301	+	0.766301i	0.211152	+	0.977453i	$0.432278\pi$
$20$	−4.18186	+	1.58494i	−0.935092	+	0.354404i
$21$	1.14559	+	1.14559i	0.249987	+	0.249987i
$22$	0.206379	−	0.370367i	0.0440001	−	0.0789626i
$23$	4.61932	+	4.61932i	0.963195	+	0.963195i	0.999346	−	0.0361509i	$-0.0115097\pi$
$23$	4.61932	+	4.61932i	0.963195	+	0.963195i	−0.0361509	+	0.999346i	$0.511510\pi$
$24$	−3.38476	−	3.08889i	−0.690912	−	0.630518i
$25$	4.63673	+	1.87103i	0.927346	+	0.374206i
$26$	−6.80836	+	1.93585i	−1.33523	+	0.379651i
$27$			5.46828i			1.05237i
$28$	0.458587	−	1.94671i	0.0866647	−	0.367895i
$29$	−5.59017	−	5.59017i	−1.03807	−	1.03807i	−0.999246	−	0.0388223i	$-0.987639\pi$
$29$	−5.59017	−	5.59017i	−1.03807	−	1.03807i	−0.0388223	−	0.999246i	$-0.512361\pi$
$30$	0.436241	+	5.10461i	0.0796464	+	0.931970i
$31$			4.67854i			0.840291i	0.907457	+	0.420146i	$0.138021\pi$
$31$			4.67854i			0.840291i	−0.907457	+	0.420146i	$0.861979\pi$
$32$	−1.04434	+	5.55962i	−0.184615	+	0.982811i
$33$	−0.343451	−	0.343451i	−0.0597871	−	0.0597871i
$34$	5.00412	−	8.98039i	0.858199	−	1.54012i
$35$	−1.85351	+	1.25079i	−0.313301	+	0.211423i
$36$	0.638254	−	0.394879i	0.106376	−	0.0658132i
$37$	−0.816234			−0.134188			−0.0670940	−	0.997747i	$-0.521373\pi$
$37$	−0.816234			−0.134188			−0.0670940	+	0.997747i	$0.521373\pi$
$38$	3.25177	−	5.83562i	0.527506	−	0.946663i
$39$			8.10871i			1.29843i
$40$	5.07554	−	3.77344i	0.802514	−	0.596634i
$41$		−	8.72292i		−	1.36229i	−0.732148	−	0.681145i	$-0.761482\pi$
$41$		−	8.72292i		−	1.36229i	0.732148	−	0.681145i	$-0.238518\pi$
$42$	−2.00142	−	1.11525i	−0.308826	−	0.172086i
$43$	−7.71883			−1.17711			−0.588555	−	0.808457i	$-0.700303\pi$
$43$	−7.71883			−1.17711			−0.588555	+	0.808457i	$0.700303\pi$
$44$	−0.137486	+	0.583632i	−0.0207268	+	0.0879858i
$45$	−0.823737	−	0.159934i	−0.122795	−	0.0238415i
$46$	−8.07030	−	4.49699i	−1.18990	−	0.663045i
$47$	1.04599	+	1.04599i	0.152574	+	0.152574i	0.779267	−	0.626693i	$-0.215592\pi$
$47$	1.04599	+	1.04599i	0.152574	+	0.152574i	−0.626693	+	0.779267i	$0.715592\pi$
$48$	5.79899	+	2.89265i	0.837012	+	0.417519i
$49$		−	1.00000i		−	0.142857i
$50$	−7.03099	−	0.751766i	−0.994332	−	0.106316i
$51$	−8.32774	−	8.32774i	−1.16612	−	1.16612i
$52$	8.51263	−	5.26665i	1.18049	−	0.730353i
$53$			11.9617i			1.64307i	0.570158	+	0.821535i	$0.306882\pi$
$53$			11.9617i			1.64307i	−0.570158	+	0.821535i	$0.693118\pi$
$54$	−2.11501	−	7.43847i	−0.287817	−	1.01225i
$55$	0.555690	−	0.374992i	0.0749292	−	0.0505640i
$56$	0.129134	+	2.82548i	0.0172563	+	0.377570i
$57$	−5.41151	−	5.41151i	−0.716773	−	0.716773i
$58$	9.76644	+	5.44212i	1.28240	+	0.714586i
$59$	3.63917	+	3.63917i	0.473780	+	0.473780i	0.903136	−	0.429356i	$-0.141259\pi$
$59$	3.63917	+	3.63917i	0.473780	+	0.473780i	−0.429356	+	0.903136i	$0.641259\pi$
$60$	−2.56777	−	6.77505i	−0.331498	−	0.874655i
$61$	−10.3396	+	10.3396i	−1.32385	+	1.32385i	−0.413210	+	0.910636i	$0.635592\pi$
$61$	−10.3396	+	10.3396i	−1.32385	+	1.32385i	−0.910636	+	0.413210i	$0.864408\pi$
$62$	−1.80956	−	6.36420i	−0.229814	−	0.808254i
$63$	0.265353	−	0.265353i	0.0334313	−	0.0334313i
$64$	−0.729731	−	7.96665i	−0.0912164	−	0.995831i
$65$	−10.9865	−	2.13309i	−1.36271	−	0.264578i
$66$	0.600033	+	0.334355i	0.0738590	+	0.0411562i
$67$	−2.96152			−0.361808			−0.180904	−	0.983501i	$-0.557902\pi$
$67$	−2.96152			−0.361808			−0.180904	+	0.983501i	$0.557902\pi$
$68$	−3.33366	+	14.1515i	−0.404265	+	1.71612i
$69$	−7.48378	+	7.48378i	−0.900941	+	0.900941i
$70$	2.03755	−	2.41835i	0.243533	−	0.289048i
$71$	11.0620			1.31282			0.656411	−	0.754404i	$-0.272074\pi$
$71$	11.0620			1.31282			0.656411	+	0.754404i	$0.272074\pi$
$72$	−0.715483	+	0.784015i	−0.0843204	+	0.0923970i
$73$	−3.80786	+	3.80786i	−0.445677	+	0.445677i	−0.893914	−	0.448238i	$-0.852052\pi$
$73$	−3.80786	+	3.80786i	−0.445677	+	0.445677i	0.448238	+	0.893914i	$0.352052\pi$
$74$	1.11032	−	0.315702i	0.129072	−	0.0366996i
$75$	−3.03126	+	7.51198i	−0.350020	+	0.867409i
$76$	−2.16627	+	9.19588i	−0.248488	+	1.05484i
$77$			0.299803i			0.0341658i
$78$	−3.13627	−	11.0302i	−0.355113	−	1.24893i
$79$	8.41143			0.946360			0.473180	−	0.880966i	$-0.343106\pi$
$79$	8.41143			0.946360			0.473180	+	0.880966i	$0.343106\pi$
$80$	−5.44475	+	7.09610i	−0.608742	+	0.793369i
$81$	−7.73338			−0.859264
$82$	3.37384	+	11.8657i	0.372578	+	1.31035i
$83$			8.16875i			0.896637i	0.893874	+	0.448319i	$0.147977\pi$
$83$			8.16875i			0.896637i	−0.893874	+	0.448319i	$0.852023\pi$
$84$	3.15388	+	0.742958i	0.344116	+	0.0810633i
$85$	13.4740	−	9.09253i	1.46146	−	0.986224i
$86$	10.4999	−	2.98548i	1.13223	−	0.321932i
$87$	9.05665	−	9.05665i	0.970975	−	0.970975i
$88$	−0.0387149	−	0.847088i	−0.00412702	−	0.0902999i
$89$	−1.65050			−0.174953			−0.0874765	−	0.996167i	$-0.527880\pi$
$89$	−1.65050			−0.174953			−0.0874765	+	0.996167i	$0.527880\pi$
$90$	1.18238	−	0.101047i	0.124634	−	0.0106513i
$91$	3.53911	−	3.53911i	0.371000	−	0.371000i
$92$	12.7173	+	2.99581i	1.32587	+	0.312335i
$93$	−7.57972			−0.785981
$94$	−1.82743	−	1.01829i	−0.188485	−	0.105029i
$95$	8.75562	−	5.90849i	0.898308	−	0.606199i
$96$	−9.00716	−	1.69194i	−0.919289	−	0.172683i
$97$	7.98515	−	7.98515i	0.810769	−	0.810769i	−0.173980	−	0.984749i	$-0.555663\pi$
$97$	7.98515	−	7.98515i	0.810769	−	0.810769i	0.984749	+	0.173980i	$0.0556628\pi$
$98$	0.386778	+	1.36029i	0.0390705	+	0.137411i
$99$	−0.0795537	+	0.0795537i	−0.00799545	+	0.00799545i
$100$	9.85499	−	1.69681i	0.985499	−	0.169681i
$101$	0.0913874	+	0.0913874i	0.00909338	+	0.00909338i	0.711639	−	0.702545i	$-0.247953\pi$
$101$	0.0913874	+	0.0913874i	0.00909338	+	0.00909338i	−0.702545	+	0.711639i	$0.747953\pi$
$102$	14.5492	+	8.10719i	1.44058	+	0.802731i
$103$	4.83438	+	4.83438i	0.476346	+	0.476346i	0.903961	−	0.427615i	$-0.140646\pi$
$103$	4.83438	+	4.83438i	0.476346	+	0.476346i	−0.427615	+	0.903961i	$0.640646\pi$
$104$	−9.54266	+	10.4567i	−0.935735	+	1.02536i
$105$	−2.02642	−	3.00288i	−0.197758	−	0.293051i
$106$	−4.62654	−	16.2715i	−0.449369	−	1.58043i
$107$		−	6.40771i		−	0.619456i	−0.950825	−	0.309728i	$-0.899762\pi$
$107$		−	6.40771i		−	0.619456i	0.950825	−	0.309728i	$-0.100238\pi$
$108$	5.75408	+	9.30048i	0.553687	+	0.894939i
$109$	−3.70138	−	3.70138i	−0.354528	−	0.354528i	0.507263	−	0.861791i	$-0.330657\pi$
$109$	−3.70138	−	3.70138i	−0.354528	−	0.354528i	−0.861791	+	0.507263i	$0.830657\pi$
$110$	−0.610863	+	0.725029i	−0.0582435	+	0.0691288i
$111$		−	1.32238i		−	0.125515i
$112$	−1.26849	−	3.79354i	−0.119861	−	0.358456i
$113$	−1.33734	−	1.33734i	−0.125806	−	0.125806i	0.641400	−	0.767207i	$-0.278354\pi$
$113$	−1.33734	−	1.33734i	−0.125806	−	0.125806i	−0.767207	+	0.641400i	$0.778354\pi$
$114$	9.45431	+	5.26820i	0.885477	+	0.493412i
$115$	−8.17107	−	12.1085i	−0.761956	−	1.12912i
$116$	−15.3901	−	3.62545i	−1.42894	−	0.336614i
$117$	1.87823			0.173642
$118$	−6.35790	−	3.54280i	−0.585292	−	0.326141i
$119$			7.26941i			0.666386i
$120$	6.11337	+	8.22290i	0.558071	+	0.750645i
$121$			10.9101i			0.991829i
$122$	10.0657	−	18.0640i	0.911309	−	1.63544i
$123$	14.1320			1.27424
$124$	4.92307	+	7.95729i	0.442105	+	0.714586i
$125$	−9.38057	−	6.08317i	−0.839023	−	0.544095i
$126$	−0.258325	+	0.463591i	−0.0230135	+	0.0413000i
$127$	−2.44066	−	2.44066i	−0.216573	−	0.216573i	0.590479	−	0.807053i	$-0.298939\pi$
$127$	−2.44066	−	2.44066i	−0.216573	−	0.216573i	−0.807053	+	0.590479i	$0.798939\pi$
$128$	4.07398	+	10.5547i	0.360092	+	0.932917i
$129$		−	12.5053i		−	1.10103i
$130$	15.7699	−	1.34770i	1.38311	−	0.118201i
$131$	3.76840	+	3.76840i	0.329246	+	0.329246i	0.852300	−	0.523053i	$-0.175207\pi$
$131$	3.76840	+	3.76840i	0.329246	+	0.329246i	−0.523053	+	0.852300i	$0.675207\pi$
$132$	−0.945544	−	0.222741i	−0.0822990	−	0.0193871i
$133$			4.72380i			0.409605i
$134$	4.02854	−	1.14545i	0.348013	−	0.0989521i
$135$	2.33051	−	12.0033i	0.200579	−	1.03308i
$136$	−0.938729	−	20.5396i	−0.0804954	−	1.76125i
$137$	−4.01824	−	4.01824i	−0.343301	−	0.343301i	0.514306	−	0.857607i	$-0.328050\pi$
$137$	−4.01824	−	4.01824i	−0.343301	−	0.343301i	−0.857607	+	0.514306i	$0.828050\pi$
$138$	7.28558	−	13.0747i	0.620190	−	1.11299i
$139$	12.7170	+	12.7170i	1.07864	+	1.07864i	0.996632	+	0.0820074i	$0.0261331\pi$
$139$	12.7170	+	12.7170i	1.07864	+	1.07864i	0.0820074	+	0.996632i	$0.473867\pi$
$140$	−1.83630	+	4.07775i	−0.155196	+	0.344632i
$141$	−1.69462	+	1.69462i	−0.142713	+	0.142713i
$142$	−15.0476	+	4.27856i	−1.26277	+	0.359048i
$143$	−1.06104	+	1.06104i	−0.0887284	+	0.0887284i
$144$	0.670027	−	1.34322i	0.0558356	−	0.111935i
$145$	9.88839	+	14.6533i	0.821186	+	1.21689i
$146$	3.70702	−	6.65262i	0.306795	−	0.550574i
$147$	1.62010			0.133624
$148$	−1.38825	+	0.858895i	−0.114114	+	0.0706007i
$149$	5.46757	−	5.46757i	0.447921	−	0.447921i	−0.446742	−	0.894663i	$-0.647416\pi$
$149$	5.46757	−	5.46757i	0.447921	−	0.447921i	0.894663	+	0.446742i	$0.147416\pi$
$150$	1.21794	−	11.3909i	0.0994443	−	0.930066i
$151$	22.9583			1.86832			0.934159	−	0.356857i	$-0.116152\pi$
$151$	22.9583			1.86832			0.934159	+	0.356857i	$0.116152\pi$
$152$	−0.610003	−	13.3470i	−0.0494778	−	1.08258i
$153$	−1.92896	+	1.92896i	−0.155947	+	0.155947i
$154$	−0.115958	−	0.407821i	−0.00934412	−	0.0328632i
$155$	1.99394	−	10.2698i	0.160157	−	0.824887i
$156$	8.53252	+	13.7913i	0.683148	+	1.10419i
$157$		−	22.0012i		−	1.75589i	−0.478764	−	0.877944i	$-0.658915\pi$
$157$		−	22.0012i		−	1.75589i	0.478764	−	0.877944i	$-0.341085\pi$
$158$	−11.4420	+	3.25336i	−0.910279	+	0.258823i
$159$	−19.3792			−1.53687
$160$	4.66185	−	11.7587i	0.368551	−	0.929607i
$161$	6.53271			0.514850
$162$	10.5197	−	2.99110i	0.826504	−	0.235003i
$163$		−	9.51089i		−	0.744950i	−0.928042	−	0.372475i	$-0.878509\pi$
$163$		−	9.51089i		−	0.744950i	0.928042	−	0.372475i	$-0.121491\pi$
$164$	−9.17882	−	14.8360i	−0.716746	−	1.15850i
$165$	0.607526	+	0.900275i	0.0472959	+	0.0700863i
$166$	−3.15950	−	11.1119i	−0.245225	−	0.862452i
$167$	2.93902	−	2.93902i	0.227428	−	0.227428i	−0.584189	−	0.811618i	$-0.698587\pi$
$167$	2.93902	−	2.93902i	0.227428	−	0.227428i	0.811618	+	0.584189i	$0.198587\pi$
$168$	−4.57757	+	0.209211i	−0.353167	+	0.0161410i
$169$	12.0506			0.926970
$170$	−14.8118	+	17.5800i	−1.13601	+	1.34832i
$171$	−1.25347	+	1.25347i	−0.0958555	+	0.0958555i
$172$	−13.1282	+	8.12226i	−1.00102	+	0.619316i
$173$	14.1070			1.07253			0.536266	−	0.844049i	$-0.319834\pi$
$173$	14.1070			1.07253			0.536266	+	0.844049i	$0.319834\pi$
$174$	−8.81680	+	15.8226i	−0.668400	+	1.19951i
$175$	4.60168	−	1.95564i	0.347854	−	0.147833i
$176$	0.380299	+	1.13732i	0.0286661	+	0.0857284i
$177$	−5.89584	+	5.89584i	−0.443158	+	0.443158i
$178$	2.24517	−	0.638379i	0.168283	−	0.0478485i
$179$	5.75972	−	5.75972i	0.430501	−	0.430501i	−0.458298	−	0.888799i	$-0.651541\pi$
$179$	5.75972	−	5.75972i	0.430501	−	0.430501i	0.888799	+	0.458298i	$0.151541\pi$
$180$	−1.56931	+	0.594774i	−0.116969	+	0.0443319i
$181$	−3.09925	−	3.09925i	−0.230366	−	0.230366i	0.582480	−	0.812845i	$-0.302083\pi$
$181$	−3.09925	−	3.09925i	−0.230366	−	0.230366i	−0.812845	+	0.582480i	$0.802083\pi$
$182$	−3.44538	+	6.18309i	−0.255389	+	0.458321i
$183$	−16.7512	−	16.7512i	−1.23828	−	1.23828i
$184$	−18.4580	+	0.843596i	−1.36074	+	0.0621907i
$185$	1.79170	+	0.347869i	0.131728	+	0.0255758i
$186$	10.3107	−	2.93167i	0.756014	−	0.214961i
$187$		−	2.17939i		−	0.159373i
$188$	2.87970	+	0.678369i	0.210024	+	0.0494751i
$189$	3.86666	+	3.86666i	0.281258	+	0.281258i
$190$	−9.62495	+	11.4238i	−0.698267	+	0.828768i
$191$		−	10.9353i		−	0.791252i	−0.918412	−	0.395626i	$-0.870528\pi$
$191$		−	10.9353i		−	0.791252i	0.918412	−	0.395626i	$-0.129472\pi$
$192$	12.9068	−	1.18224i	0.931468	−	0.0853208i
$193$	−7.73794	−	7.73794i	−0.556989	−	0.556989i	0.371460	−	0.928449i	$-0.378857\pi$
$193$	−7.73794	−	7.73794i	−0.556989	−	0.556989i	−0.928449	+	0.371460i	$0.878857\pi$
$194$	−7.77368	+	13.9506i	−0.558117	+	1.00160i
$195$	3.45583	−	17.7992i	0.247477	−	1.27463i
$196$	−1.05227	−	1.70080i	−0.0751618	−	0.121486i
$197$	20.3909			1.45279			0.726397	−	0.687275i	$-0.241193\pi$
$197$	20.3909			1.45279			0.726397	+	0.687275i	$0.241193\pi$
$198$	0.0774469	−	0.138986i	0.00550391	−	0.00987732i
$199$			18.3780i			1.30278i	0.758743	+	0.651390i	$0.225814\pi$
$199$			18.3780i			1.30278i	−0.758743	+	0.651390i	$0.774186\pi$
$200$	−12.7494	+	6.11986i	−0.901519	+	0.432740i
$201$		−	4.79797i		−	0.338423i
$202$	−0.159660	−	0.0889671i	−0.0112337	−	0.00625971i
$203$	−7.90569			−0.554871
$204$	−22.9268	−	5.40087i	−1.60520	−	0.378136i
$205$	−3.71760	+	19.1475i	−0.259648	+	1.33732i
$206$	−8.44601	−	4.70635i	−0.588462	−	0.327907i
$207$	1.73347	+	1.73347i	0.120485	+	0.120485i
$208$	8.93640	−	17.9151i	0.619628	−	1.24219i
$209$		−	1.41621i		−	0.0979613i
$210$	3.91797	+	3.30103i	0.270366	+	0.227793i
$211$	6.47138	+	6.47138i	0.445508	+	0.445508i	0.893858	−	0.448350i	$-0.147988\pi$
$211$	6.47138	+	6.47138i	0.445508	+	0.445508i	−0.448350	+	0.893858i	$0.647988\pi$
$212$	12.5869	+	20.3446i	0.864473	+	1.39727i
$213$			17.9216i			1.22797i
$214$	2.47836	+	8.71637i	0.169417	+	0.595839i
$215$	16.9434	+	3.28967i	1.15553	+	0.224354i
$216$	−11.4245	−	10.4258i	−0.777337	−	0.709388i
$217$	3.30823	+	3.30823i	0.224577	+	0.224577i
$218$	6.46658	+	3.60335i	0.437972	+	0.244050i
$219$	−6.16913	−	6.16913i	−0.416871	−	0.416871i
$220$	0.550529	−	1.22252i	0.0371166	−	0.0824224i
$221$	−25.7272	+	25.7272i	−1.73060	+	1.73060i
$222$	0.511469	+	1.79883i	0.0343276	+	0.120730i
$223$	−3.73945	+	3.73945i	−0.250412	+	0.250412i	−0.821140	−	0.570728i	$-0.806661\pi$
$223$	−3.73945	+	3.73945i	−0.250412	+	0.250412i	0.570728	+	0.821140i	$0.306661\pi$
$224$	3.19278	+	4.66970i	0.213327	+	0.312008i
$225$	1.74000	+	0.702133i	0.116000	+	0.0468089i
$226$	2.33643	+	1.30192i	0.155417	+	0.0866026i
$227$	−17.2671			−1.14606			−0.573030	−	0.819534i	$-0.694232\pi$
$227$	−17.2671			−1.14606			−0.573030	+	0.819534i	$0.694232\pi$
$228$	−14.8983	−	3.50958i	−0.986663	−	0.232428i
$229$	15.3363	−	15.3363i	1.01345	−	1.01345i	0.0135409	−	0.999908i	$-0.495690\pi$
$229$	15.3363	−	15.3363i	1.01345	−	1.01345i	0.999908	−	0.0135409i	$-0.00431032\pi$
$230$	15.7984	+	13.3107i	1.04171	+	0.877681i
$231$	−0.485713			−0.0319575
$232$	22.3374	−	1.02089i	1.46652	−	0.0670250i
$233$	3.23734	−	3.23734i	0.212085	−	0.212085i	−0.593068	−	0.805153i	$-0.702083\pi$
$233$	3.23734	−	3.23734i	0.212085	−	0.212085i	0.805153	+	0.593068i	$0.202083\pi$
$234$	−2.55494	+	0.726457i	−0.167022	+	0.0474900i
$235$	−1.85025	−	2.74183i	−0.120697	−	0.178857i
$236$	10.0189	+	2.36015i	0.652175	+	0.153632i
$237$			13.6274i			0.885194i
$238$	−2.81165	−	9.88854i	−0.182252	−	0.640979i
$239$	−5.22844			−0.338199			−0.169100	−	0.985599i	$-0.554086\pi$
$239$	−5.22844			−0.338199			−0.169100	+	0.985599i	$0.554086\pi$
$240$	−11.4964	−	8.82106i	−0.742091	−	0.569397i
$241$	−3.76103			−0.242269			−0.121135	−	0.992636i	$-0.538653\pi$
$241$	−3.76103			−0.242269			−0.121135	+	0.992636i	$0.538653\pi$
$242$	−4.21980	−	14.8410i	−0.271259	−	0.954014i
$243$			3.87596i			0.248643i
$244$	−6.70562	+	28.4656i	−0.429283	+	1.82232i
$245$	−0.426188	+	2.19508i	−0.0272281	+	0.140238i
$246$	−19.2237	+	5.46596i	−1.22566	+	0.348497i
$247$	−16.7180	+	16.7180i	−1.06374	+	1.06374i
$248$	−9.77454	−	8.92012i	−0.620684	−	0.566428i
$249$	−13.2342			−0.838685
$250$	15.1132	+	4.64671i	0.955841	+	0.293884i
$251$	−15.9909	+	15.9909i	−1.00934	+	1.00934i	−0.00937937	+	0.999956i	$0.502986\pi$
$251$	−15.9909	+	15.9909i	−1.00934	+	1.00934i	−0.999956	+	0.00937937i	$0.997014\pi$
$252$	0.172092	−	0.730535i	0.0108408	−	0.0460194i
$253$	−1.95853			−0.123132
$254$	4.26401	+	2.37602i	0.267548	+	0.149085i
$255$	14.7308	+	21.8292i	0.922481	+	1.36700i
$256$	−9.62416	−	12.7818i	−0.601510	−	0.798865i
$257$	−12.1502	+	12.1502i	−0.757911	+	0.757911i	−0.975942	−	0.218031i	$-0.930037\pi$
$257$	−12.1502	+	12.1502i	−0.757911	+	0.757911i	0.218031	+	0.975942i	$0.430037\pi$
$258$	4.83678	+	17.0109i	0.301125	+	1.05905i
$259$	−0.577165	+	0.577165i	−0.0358633	+	0.0358633i
$260$	−20.9305	+	7.93273i	−1.29805	+	0.491967i
$261$	−2.09780	−	2.09780i	−0.129850	−	0.129850i
$262$	−6.58367	−	3.66860i	−0.406740	−	0.226647i
$263$	−1.85061	−	1.85061i	−0.114114	−	0.114114i	0.647744	−	0.761858i	$-0.275713\pi$
$263$	−1.85061	−	1.85061i	−0.114114	−	0.114114i	−0.761858	+	0.647744i	$0.775713\pi$
$264$	1.37237	−	0.0627221i	0.0844635	−	0.00386028i
$265$	5.09794	−	26.2569i	0.313164	−	1.61295i
$266$	−1.82706	−	6.42576i	−0.112024	−	0.393988i
$267$		−	2.67399i		−	0.163645i
$268$	−5.03697	+	3.11631i	−0.307682	+	0.190359i
$269$	−0.254079	−	0.254079i	−0.0154914	−	0.0154914i	0.699319	−	0.714810i	$-0.253487\pi$
$269$	−0.254079	−	0.254079i	−0.0154914	−	0.0154914i	−0.714810	+	0.699319i	$0.753487\pi$
$270$	1.47243	+	17.2294i	0.0896092	+	1.04855i
$271$		−	25.0075i		−	1.51910i	−0.650449	−	0.759550i	$-0.725419\pi$
$271$		−	25.0075i		−	1.51910i	0.650449	−	0.759550i	$-0.274581\pi$
$272$	9.22121	+	27.5768i	0.559118	+	1.67209i
$273$	5.73372	+	5.73372i	0.347021	+	0.347021i
$274$	7.02015	+	3.91182i	0.424103	+	0.236322i
$275$	−1.37960	+	0.586309i	−0.0831930	+	0.0353558i
$276$	−4.85353	+	20.6034i	−0.292148	+	1.24018i
$277$	−16.6970			−1.00322			−0.501612	−	0.865093i	$-0.667259\pi$
$277$	−16.6970			−1.00322			−0.501612	+	0.865093i	$0.667259\pi$
$278$	−22.2175	−	12.3802i	−1.33252	−	0.742514i
$279$			1.75570i			0.105111i
$280$	0.920724	−	6.25718i	0.0550238	−	0.373938i
$281$		−	23.0317i		−	1.37396i	−0.726677	−	0.686979i	$-0.758936\pi$
$281$		−	23.0317i		−	1.37396i	0.726677	−	0.686979i	$-0.241064\pi$
$282$	1.64974	−	2.96062i	0.0982406	−	0.176303i
$283$	−23.8870			−1.41993			−0.709967	−	0.704235i	$-0.751290\pi$
$283$	−23.8870			−1.41993			−0.709967	+	0.704235i	$0.751290\pi$
$284$	18.8144	−	11.6402i	1.11643	−	0.690719i
$285$	9.57237	+	14.1850i	0.567018	+	0.840248i
$286$	1.03294	−	1.85371i	0.0610789	−	0.109612i
$287$	−6.16803	−	6.16803i	−0.364087	−	0.364087i
$288$	−0.391905	+	2.08633i	−0.0230932	+	0.122938i
$289$		−	35.8443i		−	2.10849i
$290$	−19.1187	−	16.1082i	−1.12269	−	0.945907i
$291$	12.9368	+	12.9368i	0.758367	+	0.758367i
$292$	−2.46955	+	10.4833i	−0.144519	+	0.613490i
$293$		−	15.5355i		−	0.907592i	−0.891106	−	0.453796i	$-0.850069\pi$
$293$		−	15.5355i		−	0.907592i	0.891106	−	0.453796i	$-0.149931\pi$
$294$	−2.20382	+	0.626621i	−0.128529	+	0.0365453i
$295$	−6.43730	−	9.53924i	−0.374794	−	0.555396i
$296$	1.55623	−	1.70530i	0.0904543	−	0.0991184i
$297$	−1.15924	−	1.15924i	−0.0672658	−	0.0672658i
$298$	−5.32277	+	9.55225i	−0.308340	+	0.553347i
$299$	23.1200	+	23.1200i	1.33706	+	1.33706i
$300$	2.74901	+	15.9661i	0.158714	+	0.921803i
$301$	−5.45804	+	5.45804i	−0.314596	+	0.314596i
$302$	−31.2300	+	8.87976i	−1.79709	+	0.510973i
$303$	−0.148057	+	0.148057i	−0.00850565	+	0.00850565i
$304$	5.99211	+	17.9199i	0.343671	+	1.02778i
$305$	27.1027	−	18.2896i	1.55190	−	1.04726i
$306$	1.87787	−	3.37003i	0.107351	−	0.192652i
$307$	19.3889			1.10658			0.553291	−	0.832988i	$-0.313372\pi$
$307$	19.3889			1.10658			0.553291	+	0.832988i	$0.313372\pi$
$308$	0.315473	+	0.509907i	0.0179757	+	0.0290547i
$309$	−7.83219	+	7.83219i	−0.445558	+	0.445558i
$310$	1.25978	+	14.7411i	0.0715507	+	0.837239i
$311$	9.92859			0.562999			0.281499	−	0.959561i	$-0.409168\pi$
$311$	9.92859			0.562999			0.281499	+	0.959561i	$0.409168\pi$
$312$	−16.9409	−	15.4601i	−0.959091	−	0.875255i
$313$	0.519996	−	0.519996i	0.0293919	−	0.0293919i	−0.692258	−	0.721650i	$-0.743384\pi$
$313$	0.519996	−	0.519996i	0.0293919	−	0.0293919i	0.721650	+	0.692258i	$0.243384\pi$
$314$	8.50959	+	29.9281i	0.480224	+	1.68894i
$315$	−0.695560	+	0.469380i	−0.0391904	+	0.0264466i
$316$	14.3062	−	8.85106i	0.804787	−	0.497911i
$317$			1.81624i			0.102010i	0.998698	+	0.0510051i	$0.0162425\pi$
$317$			1.81624i			0.102010i	−0.998698	+	0.0510051i	$0.983758\pi$
$318$	26.3615	−	7.49547i	1.47828	−	0.420325i
$319$	2.37015			0.132703
$320$	−1.79347	+	17.7984i	−0.100258	+	0.994961i
$321$	10.3811			0.579419
$322$	−8.88641	+	2.52671i	−0.495220	+	0.140808i
$323$		−	34.3392i		−	1.91069i
$324$	−13.1530	+	8.13757i	−0.730720	+	0.452087i
$325$	23.2071	+	9.36461i	1.28730	+	0.519455i
$326$	3.67861	+	12.9376i	0.203739	+	0.716548i
$327$	5.99662	−	5.99662i	0.331614	−	0.331614i
$328$	18.2241	+	16.6311i	1.00626	+	0.918301i
$329$	1.47926			0.0815542
$330$	−1.17462	−	0.989662i	−0.0646608	−	0.0544791i
$331$	−15.6031	+	15.6031i	−0.857626	+	0.857626i	−0.991058	−	0.133432i	$-0.957400\pi$
$331$	−15.6031	+	15.6031i	−0.857626	+	0.857626i	0.133432	+	0.991058i	$0.457400\pi$
$332$	8.59570	+	13.8935i	0.471750	+	0.762503i
$333$	−0.306305			−0.0167854
$334$	−2.86119	+	5.13469i	−0.156557	+	0.280958i
$335$	6.50077	+	1.26216i	0.355175	+	0.0689594i
$336$	6.14592	−	2.05509i	0.335287	−	0.112114i
$337$	−13.1760	+	13.1760i	−0.717745	+	0.717745i	−0.968143	−	0.250398i	$-0.919438\pi$
$337$	−13.1760	+	13.1760i	−0.717745	+	0.717745i	0.250398	+	0.968143i	$0.419438\pi$
$338$	−16.3924	+	4.66091i	−0.891628	+	0.253520i
$339$	2.16663	−	2.16663i	0.117675	−	0.117675i
$340$	13.3488	−	29.6428i	0.723941	−	1.60761i
$341$	−0.991819	−	0.991819i	−0.0537100	−	0.0537100i
$342$	1.22028	−	2.18991i	0.0659850	−	0.118417i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	14.7167	−	16.1264i	0.793474	−	0.869476i
$345$	19.6170	−	13.2380i	1.05614	−	0.712709i
$346$	−19.1896	+	5.45627i	−1.03164	+	0.293331i
$347$		−	21.1963i		−	1.13788i	−0.822380	−	0.568939i	$-0.807354\pi$
$347$		−	21.1963i		−	1.13788i	0.822380	−	0.568939i	$-0.192646\pi$
$348$	5.87360	−	24.9336i	0.314858	−	1.33658i
$349$	−4.47772	−	4.47772i	−0.239687	−	0.239687i	0.577034	−	0.816720i	$-0.304210\pi$
$349$	−4.47772	−	4.47772i	−0.239687	−	0.239687i	−0.816720	+	0.577034i	$0.804210\pi$
$350$	−5.50324	+	4.44008i	−0.294161	+	0.237332i
$351$			27.3691i			1.46085i
$352$	−0.957208	−	1.39999i	−0.0510194	−	0.0746199i
$353$	9.13608	+	9.13608i	0.486264	+	0.486264i	0.907125	−	0.420861i	$-0.138272\pi$
$353$	9.13608	+	9.13608i	0.486264	+	0.486264i	−0.420861	+	0.907125i	$0.638272\pi$
$354$	5.73969	−	10.3005i	0.305061	−	0.547463i
$355$	−24.2820	−	4.71450i	−1.28876	−	0.250220i
$356$	−2.80718	+	1.73677i	−0.148780	+	0.0920485i
$357$	−11.7772			−0.623315
$358$	−5.60718	+	10.0626i	−0.296349	+	0.531827i
$359$		−	13.2861i		−	0.701214i	−0.936523	−	0.350607i	$-0.885975\pi$
$359$		−	13.2861i		−	0.701214i	0.936523	−	0.350607i	$-0.114025\pi$
$360$	1.90468	−	1.41604i	0.100385	−	0.0746320i
$361$		−	3.31425i		−	0.174434i
$362$	5.41462	+	3.01717i	0.284586	+	0.158579i
$363$	−17.6755			−0.927724
$364$	2.29525	−	9.74342i	0.120304	−	0.510694i
$365$	9.98142	−	6.73569i	0.522451	−	0.352562i
$366$	29.2655	+	16.3075i	1.52973	+	0.852409i
$367$	−1.11745	−	1.11745i	−0.0583306	−	0.0583306i	0.677340	−	0.735670i	$-0.263133\pi$
$367$	−1.11745	−	1.11745i	−0.0583306	−	0.0583306i	−0.735670	+	0.677340i	$0.763133\pi$
$368$	24.7821	−	8.28670i	1.29185	−	0.431974i
$369$		−	3.27341i		−	0.170407i
$370$	−2.57178	+	0.219785i	−0.133701	+	0.0114261i
$371$	8.45822	+	8.45822i	0.439129	+	0.439129i
$372$	−12.8916	+	7.97588i	−0.668400	+	0.413530i
$373$		−	0.569661i		−	0.0294959i	−0.999891	−	0.0147480i	$-0.995305\pi$
$373$		−	0.569661i		−	0.0294959i	0.999891	−	0.0147480i	$-0.00469460\pi$
$374$	0.842943	+	2.96462i	0.0435875	+	0.153297i
$375$	9.85537	−	15.1975i	0.508929	−	0.784795i
$376$	−4.17962	+	0.191023i	−0.215547	+	0.00985126i
$377$	−27.9791	−	27.9791i	−1.44100	−	1.44100i
$378$	−6.75533	−	3.76425i	−0.347457	−	0.193612i
$379$	4.16293	+	4.16293i	0.213835	+	0.213835i	0.805894	−	0.592059i	$-0.201685\pi$
$379$	4.16293	+	4.16293i	0.213835	+	0.213835i	−0.592059	+	0.805894i	$0.701685\pi$
$380$	8.67430	−	19.2624i	0.444982	−	0.988142i
$381$	3.95412	−	3.95412i	0.202576	−	0.202576i
$382$	4.22955	+	14.8753i	0.216402	+	0.761085i
$383$	−22.2951	+	22.2951i	−1.13923	+	1.13923i	−0.150637	+	0.988589i	$0.548132\pi$
$383$	−22.2951	+	22.2951i	−1.13923	+	1.13923i	−0.988589	+	0.150637i	$0.951868\pi$
$384$	−17.0998	+	6.60026i	−0.872620	+	0.336818i
$385$	0.127773	−	0.658092i	0.00651189	−	0.0335395i
$386$	13.5187	+	7.53301i	0.688086	+	0.383420i
$387$	−2.89661			−0.147243
$388$	5.17869	−	21.9837i	0.262908	−	1.11605i
$389$	11.9055	−	11.9055i	0.603635	−	0.603635i	−0.337640	−	0.941275i	$-0.609629\pi$
$389$	11.9055	−	11.9055i	0.603635	−	0.603635i	0.941275	+	0.337640i	$0.109629\pi$
$390$	2.18341	+	25.5489i	0.110561	+	1.29372i
$391$	−47.4890			−2.40162
$392$	2.08923	+	1.90660i	0.105522	+	0.0962980i
$393$	−6.10519	+	6.10519i	−0.307966	+	0.307966i
$394$	−27.7377	+	7.88677i	−1.39740	+	0.397330i
$395$	−18.4637	−	3.58485i	−0.929011	−	0.180373i
$396$	−0.0515937	+	0.219017i	−0.00259268	+	0.0110060i
$397$		−	11.1581i		−	0.560010i	−0.959998	−	0.280005i	$-0.909664\pi$
$397$		−	11.1581i		−	0.560010i	0.959998	−	0.280005i	$-0.0903362\pi$
$398$	−7.10821	−	24.9995i	−0.356302	−	1.25311i
$399$	−7.65304			−0.383131
$400$	14.9759	−	13.2560i	0.748796	−	0.662801i
$401$	9.19590			0.459221			0.229611	−	0.973283i	$-0.426255\pi$
$401$	9.19590			0.459221			0.229611	+	0.973283i	$0.426255\pi$
$402$	1.85575	+	6.52666i	0.0925565	+	0.325520i
$403$			23.4164i			1.16645i
$404$	0.251596	+	0.0592683i	0.0125174	+	0.00294871i
$405$	16.9754	+	3.29587i	0.843513	+	0.163773i
$406$	10.7541	−	3.05775i	0.533716	−	0.151754i
$407$	0.173036	−	0.173036i	0.00857707	−	0.00857707i
$408$	33.2762	−	1.52084i	1.64742	−	0.0752927i
$409$	20.5208			1.01469			0.507344	−	0.861743i	$-0.330627\pi$
$409$	20.5208			1.01469			0.507344	+	0.861743i	$0.330627\pi$
$410$	−2.34880	−	27.4841i	−0.115999	−	1.35734i
$411$	6.50996	−	6.50996i	0.321112	−	0.321112i
$412$	13.3094	+	3.13529i	0.655706	+	0.154464i
$413$	5.14657			0.253246
$414$	−3.02851	−	1.68757i	−0.148843	−	0.0829393i
$415$	3.48142	−	17.9310i	0.170896	−	0.880200i
$416$	−5.22698	+	27.8262i	−0.256274	+	1.36429i
$417$	−20.6028	+	20.6028i	−1.00892	+	1.00892i
$418$	0.547760	+	1.92646i	0.0267918	+	0.0942264i
$419$	9.03807	−	9.03807i	0.441538	−	0.441538i	−0.450990	−	0.892529i	$-0.648929\pi$
$419$	9.03807	−	9.03807i	0.441538	−	0.441538i	0.892529	+	0.450990i	$0.148929\pi$
$420$	−6.60637	−	2.97499i	−0.322358	−	0.145165i
$421$	10.2225	+	10.2225i	0.498216	+	0.498216i	0.910882	−	0.412666i	$-0.135402\pi$
$421$	10.2225	+	10.2225i	0.498216	+	0.498216i	−0.412666	+	0.910882i	$0.635402\pi$
$422$	−11.3060	−	6.30000i	−0.550366	−	0.306679i
$423$	0.392526	+	0.392526i	0.0190853	+	0.0190853i
$424$	−24.9908	−	22.8063i	−1.21366	−	1.10757i
$425$	−33.4515	+	14.2164i	−1.62264	+	0.689596i
$426$	−6.93170	−	24.3787i	−0.335842	−	1.18115i
$427$			14.6224i			0.707625i
$428$	−6.74261	−	10.8983i	−0.325916	−	0.526787i
$429$	−1.71899	−	1.71899i	−0.0829936	−	0.0829936i
$430$	−24.3204	+	2.07843i	−1.17284	+	0.100231i
$431$		−	18.1270i		−	0.873148i	−0.899668	−	0.436574i	$-0.856192\pi$
$431$		−	18.1270i		−	0.873148i	0.899668	−	0.436574i	$-0.143808\pi$
$432$	19.5731	+	9.76347i	0.941713	+	0.469745i
$433$	4.25449	+	4.25449i	0.204458	+	0.204458i	0.801907	−	0.597449i	$-0.203819\pi$
$433$	4.25449	+	4.25449i	0.204458	+	0.204458i	−0.597449	+	0.801907i	$0.703819\pi$
$434$	−5.77972	−	3.22062i	−0.277435	−	0.154595i
$435$	−23.7399	+	16.0202i	−1.13824	+	0.768111i
$436$	−10.1902	−	2.40049i	−0.488020	−	0.114963i
$437$	−30.8592			−1.47619
$438$	10.7779	+	6.00575i	0.514989	+	0.286966i
$439$		−	5.93580i		−	0.283300i	−0.989917	−	0.141650i	$-0.954759\pi$
$439$		−	5.93580i		−	0.283300i	0.989917	−	0.141650i	$-0.0452408\pi$
$440$	−0.276036	+	1.87592i	−0.0131595	+	0.0894311i
$441$		−	0.375266i		−	0.0178698i
$442$	25.0459	−	44.9474i	1.19131	−	2.13793i
$443$	−1.03957			−0.0493913			−0.0246957	−	0.999695i	$-0.507862\pi$
$443$	−1.03957			−0.0493913			−0.0246957	+	0.999695i	$0.507862\pi$
$444$	−1.39150	−	2.24912i	−0.0660376	−	0.106738i
$445$	3.62298	+	0.703424i	0.171746	+	0.0333455i
$446$	3.64042	−	6.53309i	0.172379	−	0.309351i
$447$	8.85803	+	8.85803i	0.418971	+	0.418971i
$448$	−6.14927	−	5.11727i	−0.290526	−	0.241768i
$449$			10.9688i			0.517648i	0.965925	+	0.258824i	$0.0833349\pi$
$449$			10.9688i			0.517648i	−0.965925	+	0.258824i	$0.916665\pi$
$450$	−2.63849	−	0.282112i	−0.124380	−	0.0132989i
$451$	1.84920	+	1.84920i	0.0870753	+	0.0870753i
$452$	−3.68179	−	0.867317i	−0.173177	−	0.0407952i
$453$			37.1948i			1.74756i
$454$	23.4884	−	6.67855i	1.10236	−	0.313440i
$455$	−9.27695	+	6.26030i	−0.434910	+	0.293487i
$456$	21.6235	−	0.988268i	1.01261	−	0.0462799i
$457$	1.17462	+	1.17462i	0.0549462	+	0.0549462i	0.734046	−	0.679100i	$-0.237630\pi$
$457$	1.17462	+	1.17462i	0.0549462	+	0.0549462i	−0.679100	+	0.734046i	$0.737630\pi$
$458$	−14.9301	+	26.7936i	−0.697638	+	1.25198i
$459$	−28.1083	−	28.1083i	−1.31198	−	1.31198i
$460$	−26.6387	−	11.9960i	−1.24204	−	0.559317i
$461$	13.3525	−	13.3525i	0.621890	−	0.621890i	−0.324124	−	0.946014i	$-0.605070\pi$
$461$	13.3525	−	13.3525i	0.621890	−	0.621890i	0.946014	+	0.324124i	$0.105070\pi$
$462$	0.660712	−	0.187863i	0.0307391	−	0.00874018i
$463$	11.8084	−	11.8084i	0.548784	−	0.548784i	−0.377305	−	0.926089i	$-0.623149\pi$
$463$	11.8084	−	11.8084i	0.548784	−	0.548784i	0.926089	+	0.377305i	$0.123149\pi$
$464$	−29.9905	+	10.0283i	−1.39228	+	0.465553i
$465$	16.6381	+	3.23038i	0.771572	+	0.149806i
$466$	−3.15160	+	5.65587i	−0.145995	+	0.262003i
$467$	39.4654			1.82624			0.913120	−	0.407690i	$-0.133666\pi$
$467$	39.4654			1.82624			0.913120	+	0.407690i	$0.133666\pi$
$468$	3.19450	−	1.97639i	0.147666	−	0.0913588i
$469$	−2.09411	+	2.09411i	−0.0966971	+	0.0966971i
$470$	3.57737	+	3.01406i	0.165012	+	0.139028i
$471$	35.6442			1.64240
$472$	−14.5415	+	0.664598i	−0.669327	+	0.0305906i
$473$	1.63634	−	1.63634i	0.0752389	−	0.0752389i
$474$	−5.27078	−	18.5373i	−0.242095	−	0.851444i
$475$	−21.7374	+	9.23806i	−0.997380	+	0.423871i
$476$	7.64935	+	12.3639i	0.350607	+	0.566696i
$477$			4.48883i			0.205529i
$478$	7.11222	−	2.02225i	0.325305	−	0.0924954i
$479$	15.3186			0.699926			0.349963	−	0.936764i	$-0.386194\pi$
$479$	15.3186			0.699926			0.349963	+	0.936764i	$0.386194\pi$
$480$	19.0503	+	7.55267i	0.869524	+	0.344731i
$481$	−4.08530			−0.186274
$482$	5.11611	−	1.45468i	0.233032	−	0.0662591i
$483$			10.5837i			0.481573i
$484$	11.4803	+	18.5560i	0.521834	+	0.843454i
$485$	−20.9312	+	14.1249i	−0.950437	+	0.641376i
$486$	−1.49914	−	5.27246i	−0.0680023	−	0.239163i
$487$	−7.83260	+	7.83260i	−0.354929	+	0.354929i	−0.861940	−	0.507011i	$-0.830750\pi$
$487$	−7.83260	+	7.83260i	−0.354929	+	0.354929i	0.507011	+	0.861940i	$0.330750\pi$
$488$	−1.88825	−	41.3151i	−0.0854768	−	1.87025i
$489$	15.4086			0.696802
$490$	−0.269268	−	3.15079i	−0.0121643	−	0.142338i
$491$	−4.71527	+	4.71527i	−0.212797	+	0.212797i	−0.805455	−	0.592658i	$-0.798079\pi$
$491$	−4.71527	+	4.71527i	−0.212797	+	0.212797i	0.592658	+	0.805455i	$0.298079\pi$
$492$	24.0358	−	14.8706i	1.08362	−	0.670420i
$493$	57.4697			2.58831
$494$	16.2753	−	29.2076i	0.732260	−	1.31411i
$495$	0.208531	−	0.140722i	0.00937279	−	0.00632497i
$496$	16.7464	+	8.35342i	0.751934	+	0.375080i
$497$	7.82204	−	7.82204i	0.350866	−	0.350866i
$498$	18.0024	−	5.11871i	0.806709	−	0.229375i
$499$	17.4382	−	17.4382i	0.780641	−	0.780641i	−0.199298	−	0.979939i	$-0.563866\pi$
$499$	17.4382	−	17.4382i	0.780641	−	0.780641i	0.979939	+	0.199298i	$0.0638661\pi$
$500$	−22.3556	−	0.475441i	−0.999774	−	0.0212624i
$501$	4.76152	+	4.76152i	0.212729	+	0.212729i
$502$	15.5674	−	27.9372i	0.694806	−	1.24690i
$503$	4.10368	+	4.10368i	0.182974	+	0.182974i	0.792650	−	0.609676i	$-0.208701\pi$
$503$	4.10368	+	4.10368i	0.182974	+	0.182974i	−0.609676	+	0.792650i	$0.708701\pi$
$504$	0.0484596	+	1.06030i	0.00215856	+	0.0472297i
$505$	−0.161654	−	0.239551i	−0.00719352	−	0.0106599i
$506$	2.66418	−	0.757517i	0.118437	−	0.0336757i
$507$			19.5232i			0.867057i
$508$	−6.71930	−	1.58286i	−0.298121	−	0.0702282i
$509$	−0.362811	−	0.362811i	−0.0160813	−	0.0160813i	0.699020	−	0.715102i	$-0.253620\pi$
$509$	−0.362811	−	0.362811i	−0.0160813	−	0.0160813i	−0.715102	+	0.699020i	$0.753620\pi$
$510$	−28.4814	−	23.9966i	−1.26118	−	1.06259i
$511$			5.38513i			0.238224i
$512$	18.0354	+	13.6647i	0.797061	+	0.603898i
$513$	−18.2653	−	18.2653i	−0.806433	−	0.806433i
$514$	11.8285	−	21.2274i	0.521731	−	0.936299i
$515$	−8.55148	−	12.6722i	−0.376823	−	0.558403i
$516$	−13.1589	−	21.2691i	−0.579288	−	0.936319i
$517$	−0.443487			−0.0195045
$518$	0.561879	−	1.00835i	0.0246876	−	0.0443043i
$519$			22.8547i			1.00321i
$520$	25.4034	−	18.8863i	1.11401	−	0.828219i
$521$		−	18.6292i		−	0.816162i	−0.912946	−	0.408081i	$-0.866198\pi$
$521$		−	18.6292i		−	0.816162i	0.912946	−	0.408081i	$-0.133802\pi$
$522$	3.66501	+	2.04224i	0.160413	+	0.0893865i
$523$	34.9631			1.52883			0.764416	−	0.644724i	$-0.223028\pi$
$523$	34.9631			1.52883			0.764416	+	0.644724i	$0.223028\pi$
$524$	10.3747	+	2.44395i	0.453219	+	0.106765i
$525$	3.16835	+	7.45520i	0.138278	+	0.325371i
$526$	3.23315	+	1.80160i	0.140972	+	0.0785535i
$527$	−24.0489	−	24.0489i	−1.04759	−	1.04759i
$528$	−1.84257	+	0.616124i	−0.0801875	+	0.0268133i
$529$			19.6763i			0.855491i
$530$	3.22090	+	37.6889i	0.139907	+	1.63710i
$531$	1.36566	+	1.36566i	0.0592645	+	0.0592645i
$532$	4.97069	+	8.03425i	0.215507	+	0.348329i
$533$		−	43.6587i		−	1.89107i
$534$	1.03424	+	3.63741i	0.0447559	+	0.157406i
$535$	−2.73089	+	14.0654i	−0.118066	+	0.608101i
$536$	5.64645	−	6.18729i	0.243889	−	0.267250i
$537$	9.33133	+	9.33133i	0.402677	+	0.402677i
$538$	0.443894	+	0.247350i	0.0191376	+	0.0106640i
$539$	0.211993	+	0.211993i	0.00913119	+	0.00913119i
$540$	−8.66690	−	22.8676i	−0.372964	−	0.984064i
$541$	0.0280185	−	0.0280185i	0.00120461	−	0.00120461i	−0.706504	−	0.707709i	$-0.749729\pi$
$541$	0.0280185	−	0.0280185i	0.00120461	−	0.00120461i	0.707709	+	0.706504i	$0.249729\pi$
$542$	9.67238	+	34.0176i	0.415464	+	1.46118i
$543$	5.02111	−	5.02111i	0.215476	−	0.215476i
$544$	−23.2097	−	33.9460i	−0.995106	−	1.45542i
$545$	6.54733	+	9.70230i	0.280457	+	0.415601i
$546$	−10.0172	−	5.58188i	−0.428698	−	0.238882i
$547$	−30.6197			−1.30920			−0.654602	−	0.755974i	$-0.727164\pi$
$547$	−30.6197			−1.30920			−0.654602	+	0.755974i	$0.727164\pi$
$548$	−11.0625	−	2.60598i	−0.472566	−	0.111322i
$549$	−3.88008	+	3.88008i	−0.165598	+	0.165598i
$550$	1.64989	−	1.33115i	0.0703516	−	0.0567605i
$551$	37.3449			1.59095
$552$	−1.36671	−	29.9039i	−0.0581711	−	1.27279i
$553$	5.94778	−	5.94778i	0.252925	−	0.252925i
$554$	22.7128	−	6.45803i	0.964975	−	0.274375i
$555$	−0.563583	+	2.90273i	−0.0239228	+	0.123214i
$556$	35.0107	+	8.24746i	1.48478	+	0.349770i
$557$			8.55813i			0.362619i	0.983426	+	0.181310i	$0.0580336\pi$
$557$			8.55813i			0.362619i	−0.983426	+	0.181310i	$0.941966\pi$
$558$	−0.679066	−	2.38827i	−0.0287471	−	0.101103i
$559$	−38.6332			−1.63401
$560$	1.16768	+	8.86772i	0.0493437	+	0.374730i
$561$	3.53084			0.149072
$562$	8.90818	+	31.3299i	0.375769	+	1.32157i
$563$			22.0505i			0.929319i	0.885489	+	0.464660i	$0.153823\pi$
$563$			22.0505i			0.929319i	−0.885489	+	0.464660i	$0.846177\pi$
$564$	−1.09903	+	4.66541i	−0.0462774	+	0.196449i
$565$	2.36561	+	3.50552i	0.0995218	+	0.147478i
$566$	32.4934	−	9.23897i	1.36580	−	0.388343i
$567$	−5.46832	+	5.46832i	−0.229648	+	0.229648i
$568$	−21.0909	+	23.1111i	−0.884955	+	0.969720i
$569$	35.1693			1.47437			0.737187	−	0.675689i	$-0.236154\pi$
$569$	35.1693			1.47437			0.737187	+	0.675689i	$0.236154\pi$
$570$	−18.5077	−	15.5934i	−0.775202	−	0.653136i
$571$	6.52717	−	6.52717i	0.273154	−	0.273154i	−0.557215	−	0.830368i	$-0.688130\pi$
$571$	6.52717	−	6.52717i	0.273154	−	0.273154i	0.830368	+	0.557215i	$0.188130\pi$
$572$	−0.688125	+	2.92111i	−0.0287719	+	0.122138i
$573$	17.7164			0.740111
$574$	10.7760	+	6.00468i	0.449782	+	0.250631i
$575$	12.7757	+	30.0614i	0.532782	+	1.25365i
$576$	−0.273843	−	2.98961i	−0.0114101	−	0.124567i
$577$	−2.39703	+	2.39703i	−0.0997896	+	0.0997896i	−0.755239	−	0.655449i	$-0.772479\pi$
$577$	−2.39703	+	2.39703i	−0.0997896	+	0.0997896i	0.655449	+	0.755239i	$0.272479\pi$
$578$	13.8638	+	48.7589i	0.576659	+	2.02810i
$579$	12.5363	−	12.5363i	0.520989	−	0.520989i
$580$	32.2374	+	14.5172i	1.33859	+	0.602795i
$581$	5.77618	+	5.77618i	0.239636	+	0.239636i
$582$	−22.6015	−	12.5942i	−0.936862	−	0.522045i
$583$	−2.53580	−	2.53580i	−0.105022	−	0.105022i
$584$	−0.695404	−	15.2156i	−0.0287760	−	0.629625i
$585$	−4.12285	−	0.800477i	−0.170459	−	0.0330956i
$586$	6.00879	+	21.1328i	0.248221	+	0.872989i
$587$		−	1.14968i		−	0.0474525i	−0.999718	−	0.0237263i	$-0.992447\pi$
$587$		−	1.14968i		−	0.0474525i	0.999718	−	0.0237263i	$-0.00755301\pi$
$588$	2.75548	−	1.70478i	0.113634	−	0.0703039i
$589$	−15.6274	−	15.6274i	−0.643916	−	0.643916i
$590$	12.4462	+	10.4864i	0.512402	+	0.431717i
$591$			33.0354i			1.35890i
$592$	−1.45737	+	2.92163i	−0.0598973	+	0.120078i
$593$	0.963591	+	0.963591i	0.0395699	+	0.0395699i	0.726615	−	0.687045i	$-0.241092\pi$
$593$	0.963591	+	0.963591i	0.0395699	+	0.0395699i	−0.687045	+	0.726615i	$0.741092\pi$
$594$	2.02527	+	1.12854i	0.0830979	+	0.0463044i
$595$	3.09813	−	15.9569i	0.127011	−	0.654170i
$596$	3.54594	−	15.0526i	0.145247	−	0.616579i
$597$	−29.7742			−1.21858
$598$	−40.3923	−	22.5077i	−1.65176	−	0.920408i
$599$			36.5665i			1.49407i	0.664786	+	0.747034i	$0.268523\pi$
$599$			36.5665i			1.49407i	−0.664786	+	0.747034i	$0.731477\pi$
$600$	−9.91481	−	20.6553i	−0.404770	−	0.843251i
$601$			25.6145i			1.04484i	0.852689	+	0.522419i	$0.174970\pi$
$601$			25.6145i			1.04484i	−0.852689	+	0.522419i	$0.825030\pi$
$602$	5.31349	−	9.53559i	0.216562	−	0.388642i
$603$	−1.11136			−0.0452580
$604$	39.0475	−	24.1582i	1.58882	−	0.982983i
$605$	4.64976	−	23.9486i	0.189040	−	0.973647i
$606$	0.144136	−	0.258666i	0.00585512	−	0.0105076i
$607$	−27.5588	−	27.5588i	−1.11858	−	1.11858i	−0.991950	−	0.126627i	$-0.959585\pi$
$607$	−27.5588	−	27.5588i	−1.11858	−	1.11858i	−0.126627	−	0.991950i	$-0.540415\pi$
$608$	−15.0821	−	22.0587i	−0.611658	−	0.894599i
$609$		−	12.8080i		−	0.519008i
$610$	−29.7937	+	35.3619i	−1.20631	+	1.43176i
$611$	5.23526	+	5.23526i	0.211796	+	0.211796i
$612$	−1.25101	+	5.31056i	−0.0505689	+	0.214667i
$613$			37.9938i			1.53456i	0.641315	+	0.767278i	$0.278389\pi$
$613$			37.9938i			1.53456i	−0.641315	+	0.767278i	$0.721611\pi$
$614$	−26.3746	+	7.49921i	−1.06439	+	0.302643i
$615$	−31.0209	−	6.02289i	−1.25088	−	0.242867i
$616$	−0.626357	−	0.571606i	−0.0252367	−	0.0230307i
$617$	13.6206	+	13.6206i	0.548344	+	0.548344i	0.925961	−	0.377618i	$-0.123257\pi$
$617$	13.6206	+	13.6206i	0.548344	+	0.548344i	−0.377618	+	0.925961i	$0.623257\pi$
$618$	7.62477	−	13.6834i	0.306713	−	0.550428i
$619$	−21.4007	−	21.4007i	−0.860166	−	0.860166i	0.131191	−	0.991357i	$-0.458120\pi$
$619$	−21.4007	−	21.4007i	−0.860166	−	0.860166i	−0.991357	+	0.131191i	$0.958120\pi$
$620$	−7.41522	−	19.5650i	−0.297802	−	0.785750i
$621$	−25.2597	+	25.2597i	−1.01364	+	1.01364i
$622$	−13.5058	+	3.84017i	−0.541534	+	0.153977i
$623$	−1.16708	+	1.16708i	−0.0467582	+	0.0467582i
$624$	29.0243	+	14.4779i	1.16190	+	0.579580i
$625$	17.9985	+	17.3509i	0.719940	+	0.694037i
$626$	−0.506225	+	0.908471i	−0.0202328	+	0.0363098i
$627$	2.29441			0.0916298
$628$	−23.1511	−	37.4198i	−0.923830	−	1.49321i
$629$	4.19565	−	4.19565i	0.167291	−	0.167291i
$630$	0.764621	−	0.907523i	0.0304632	−	0.0361566i
$631$	−3.42688			−0.136422			−0.0682110	−	0.997671i	$-0.521729\pi$
$631$	−3.42688			−0.136422			−0.0682110	+	0.997671i	$0.521729\pi$
$632$	−16.0373	+	17.5734i	−0.637928	+	0.699031i
$633$	−10.4843	+	10.4843i	−0.416714	+	0.416714i
$634$	−0.702483	−	2.47062i	−0.0278992	−	0.0981210i
$635$	4.31725	+	6.39761i	0.171325	+	0.253881i
$636$	−32.9603	+	20.3921i	−1.30696	+	0.808599i
$637$		−	5.00506i		−	0.198308i
$638$	−3.22411	+	0.916725i	−0.127644	+	0.0362935i
$639$	4.15120			0.164219
$640$	−4.44439	−	24.9048i	−0.175680	−	0.984447i
$641$	−5.53773			−0.218727			−0.109364	−	0.994002i	$-0.534881\pi$
$641$	−5.53773			−0.218727			−0.109364	+	0.994002i	$0.534881\pi$
$642$	−14.1214	+	4.01520i	−0.557328	+	0.158467i
$643$			12.5190i			0.493703i	0.969053	+	0.246851i	$0.0793959\pi$
$643$			12.5190i			0.493703i	−0.969053	+	0.246851i	$0.920604\pi$
$644$	11.1109	−	6.87414i	0.437829	−	0.270879i
$645$	−5.32961	+	27.4501i	−0.209853	+	1.08085i
$646$	13.2817	+	46.7115i	0.522560	+	1.83784i
$647$	2.10285	−	2.10285i	0.0826717	−	0.0826717i	−0.664562	−	0.747233i	$-0.731382\pi$
$647$	2.10285	−	2.10285i	0.0826717	−	0.0826717i	0.747233	+	0.664562i	$0.231382\pi$
$648$	14.7445	−	16.1568i	0.579218	−	0.634698i
$649$	−1.54296			−0.0605664
$650$	−35.1905	−	3.76263i	−1.38029	−	0.147583i
$651$	−5.35967	+	5.35967i	−0.210062	+	0.210062i
$652$	−10.0080	−	16.1762i	−0.391943	−	0.633507i
$653$	21.3805			0.836684			0.418342	−	0.908290i	$-0.362611\pi$
$653$	21.3805			0.836684			0.418342	+	0.908290i	$0.362611\pi$
$654$	−5.83781	+	10.4765i	−0.228276	+	0.409665i
$655$	−6.66588	−	9.87797i	−0.260457	−	0.385964i
$656$	−31.2228	−	15.5745i	−1.21904	−	0.608084i
$657$	−1.42896	+	1.42896i	−0.0557490	+	0.0557490i
$658$	−2.01223	+	0.572146i	−0.0784449	+	0.0223046i
$659$	−15.9608	+	15.9608i	−0.621746	+	0.621746i	−0.945978	−	0.324232i	$-0.894894\pi$
$659$	−15.9608	+	15.9608i	−0.621746	+	0.621746i	0.324232	+	0.945978i	$0.394894\pi$
$660$	1.98061	+	0.891913i	0.0770952	+	0.0347177i
$661$	10.9185	+	10.9185i	0.424681	+	0.424681i	0.886812	−	0.462131i	$-0.152915\pi$
$661$	10.9185	+	10.9185i	0.424681	+	0.424681i	−0.462131	+	0.886812i	$0.652915\pi$
$662$	15.1899	−	27.2598i	0.590373	−	1.05948i
$663$	−41.6808	−	41.6808i	−1.61875	−	1.61875i
$664$	−17.0664	−	15.5746i	−0.662304	−	0.604411i
$665$	2.01322	−	10.3691i	0.0780695	−	0.402096i
$666$	0.416665	−	0.118472i	0.0161454	−	0.00459070i
$667$		−	51.6456i		−	1.99973i
$668$	1.90607	−	8.09133i	0.0737481	−	0.313063i
$669$	−6.05829	−	6.05829i	−0.234227	−	0.234227i
$670$	−9.33114	+	0.797442i	−0.360493	+	0.0308079i
$671$		−	4.38383i		−	0.169236i
$672$	−7.56540	+	5.17264i	−0.291842	+	0.199539i
$673$	−6.57684	−	6.57684i	−0.253519	−	0.253519i	0.568893	−	0.822412i	$-0.307372\pi$
$673$	−6.57684	−	6.57684i	−0.253519	−	0.253519i	−0.822412	+	0.568893i	$0.807372\pi$
$674$	12.8271	−	23.0195i	0.494081	−	0.886678i
$675$	−10.2313	+	25.3549i	−0.393803	+	0.975911i
$676$	20.4957	−	12.6804i	0.788297	−	0.487709i
$677$	5.72946			0.220201			0.110101	−	0.993920i	$-0.464883\pi$
$677$	5.72946			0.220201			0.110101	+	0.993920i	$0.464883\pi$
$678$	−2.10925	+	3.78526i	−0.0810052	+	0.145372i
$679$		−	11.2927i		−	0.433374i
$680$	−6.69312	+	45.4860i	−0.256670	+	1.74431i
$681$		−	27.9745i		−	1.07199i
$682$	1.73278	+	0.965552i	0.0663516	+	0.0369729i
$683$	4.08274			0.156222			0.0781108	−	0.996945i	$-0.475111\pi$
$683$	4.08274			0.156222			0.0781108	+	0.996945i	$0.475111\pi$
$684$	−0.812927	+	3.45090i	−0.0310830	+	0.131948i
$685$	7.10781	+	10.5329i	0.271576	+	0.402440i
$686$	1.23537	+	0.688380i	0.0471665	+	0.0262825i
$687$	24.8463	+	24.8463i	0.947947	+	0.947947i
$688$	−13.7818	+	27.6288i	−0.525425	+	1.05334i
$689$			59.8691i			2.28083i
$690$	−21.5647	+	25.5950i	−0.820954	+	0.974384i
$691$	−5.04155	−	5.04155i	−0.191789	−	0.191789i	0.604679	−	0.796469i	$-0.293301\pi$
$691$	−5.04155	−	5.04155i	−0.191789	−	0.191789i	−0.796469	+	0.604679i	$0.793301\pi$
$692$	23.9932	−	14.8443i	0.912085	−	0.564295i
$693$			0.112506i			0.00427375i
$694$	8.19827	+	28.8332i	0.311202	+	1.09449i
$695$	−22.4949	−	33.3345i	−0.853281	−	1.26445i
$696$	1.65396	+	36.1888i	0.0626930	+	1.37173i
$697$	44.8380	+	44.8380i	1.69836	+	1.69836i
$698$	7.82290	+	4.35913i	0.296101	+	0.164996i
$699$	5.24482	+	5.24482i	0.198377	+	0.198377i
$700$	5.76870	−	8.16836i	0.218036	−	0.308735i
$701$	11.7523	−	11.7523i	0.443878	−	0.443878i	−0.449435	−	0.893313i	$-0.648375\pi$
$701$	11.7523	−	11.7523i	0.443878	−	0.443878i	0.893313	+	0.449435i	$0.148375\pi$
$702$	−10.5858	−	37.2300i	−0.399534	−	1.40516i
$703$	2.72641	−	2.72641i	0.102828	−	0.102828i
$704$	1.84357	+	1.53418i	0.0694822	+	0.0578214i
$705$	4.44205	−	2.99759i	0.167297	−	0.112896i
$706$	−15.9614	−	8.89412i	−0.600715	−	0.334735i
$707$	0.129241			0.00486062
$708$	−3.82368	+	16.2317i	−0.143703	+	0.610023i
$709$	26.2965	−	26.2965i	0.987585	−	0.987585i	−0.0123390	−	0.999924i	$-0.503928\pi$
$709$	26.2965	−	26.2965i	0.987585	−	0.987585i	0.999924	+	0.0123390i	$0.00392774\pi$
$710$	34.8542	−	2.97865i	1.30805	−	0.111787i
$711$	3.15652			0.118379
$712$	3.14685	−	3.44827i	0.117933	−	0.129230i
$713$	−21.6117	+	21.6117i	−0.809365	+	0.809365i
$714$	16.0205	−	4.55517i	0.599551	−	0.170473i
$715$	2.78126	−	1.87686i	0.104013	−	0.0701905i
$716$	3.73540	−	15.8569i	0.139599	−	0.592600i
$717$		−	8.47061i		−	0.316341i
$718$	5.13878	+	18.0730i	0.191778	+	0.674480i
$719$	−25.4828			−0.950350			−0.475175	−	0.879891i	$-0.657615\pi$
$719$	−25.4828			−0.950350			−0.475175	+	0.879891i	$0.657615\pi$
$720$	−2.04323	+	2.66292i	−0.0761466	+	0.0992413i
$721$	6.83684			0.254617
$722$	1.28188	+	4.50835i	0.0477066	+	0.167783i
$723$		−	6.09325i		−	0.226611i
$724$	−8.53246	−	2.00999i	−0.317106	−	0.0747006i
$725$	−15.4607	−	36.3795i	−0.574197	−	1.35110i
$726$	24.0439	−	6.83651i	0.892353	−	0.253727i
$727$	23.6578	−	23.6578i	0.877420	−	0.877420i	−0.115847	−	0.993267i	$-0.536958\pi$
$727$	23.6578	−	23.6578i	0.877420	−	0.877420i	0.993267	+	0.115847i	$0.0369582\pi$
$728$	0.646324	+	14.1417i	0.0239544	+	0.524126i
$729$	−29.4796			−1.09184
$730$	−10.9725	+	13.0231i	−0.406109	+	0.482007i
$731$	39.6767	−	39.6767i	1.46750	−	1.46750i
$732$	−46.1171	−	10.8638i	−1.70454	−	0.401537i
$733$	−26.9268			−0.994565			−0.497283	−	0.867589i	$-0.665669\pi$
$733$	−26.9268			−0.994565			−0.497283	+	0.867589i	$0.665669\pi$
$734$	1.95227	+	1.08786i	0.0720597	+	0.0401536i
$735$	−3.55625	−	0.690468i	−0.131174	−	0.0254683i
$736$	−30.5058	+	20.8575i	−1.12446	+	0.768819i
$737$	0.627822	−	0.627822i	0.0231261	−	0.0231261i
$738$	1.26608	+	4.45280i	0.0466052	+	0.163910i
$739$	−21.9807	+	21.9807i	−0.808574	+	0.808574i	−0.984418	−	0.175844i	$-0.943734\pi$
$739$	−21.9807	+	21.9807i	−0.808574	+	0.808574i	0.175844	+	0.984418i	$0.443734\pi$
$740$	3.41338	−	1.29368i	0.125478	−	0.0475568i
$741$	−27.0849	−	27.0849i	−0.994990	−	0.994990i
$742$	−14.7771	−	8.23422i	−0.542485	−	0.302288i
$743$	−31.7682	−	31.7682i	−1.16546	−	1.16546i	−0.983261	−	0.182203i	$-0.941677\pi$
$743$	−31.7682	−	31.7682i	−1.16546	−	1.16546i	−0.182203	−	0.983261i	$-0.558323\pi$
$744$	14.4515	−	15.8358i	0.529818	−	0.580567i
$745$	−14.3320	+	9.67153i	−0.525082	+	0.354338i
$746$	0.220333	+	0.774908i	0.00806695	+	0.0283714i
$747$			3.06545i			0.112159i
$748$	−2.29330	−	3.70673i	−0.0838514	−	0.135531i
$749$	−4.53093	−	4.53093i	−0.165557	−	0.165557i
$750$	−7.52814	+	24.4849i	−0.274889	+	0.894062i
$751$			41.8892i			1.52856i	0.644886	+	0.764279i	$0.276905\pi$
$751$			41.8892i			1.52856i	−0.644886	+	0.764279i	$0.723095\pi$
$752$	5.61163	−	1.87643i	0.204635	−	0.0684265i
$753$	−25.9069	−	25.9069i	−0.944099	−	0.944099i
$754$	48.8816	+	27.2381i	1.78016	+	0.991955i
$755$	−50.3952	−	9.78453i	−1.83407	−	0.356096i
$756$	10.6452	+	2.50768i	0.387161	+	0.0912034i
$757$	28.6389			1.04090			0.520450	−	0.853892i	$-0.325764\pi$
$757$	28.6389			1.04090			0.520450	+	0.853892i	$0.325764\pi$
$758$	−7.27294	−	4.05268i	−0.264165	−	0.147200i
$759$		−	3.17302i		−	0.115173i
$760$	−4.34931	+	29.5576i	−0.157766	+	1.07217i
$761$			23.8459i			0.864413i	0.901775	+	0.432206i	$0.142265\pi$
$761$			23.8459i			0.864413i	−0.901775	+	0.432206i	$0.857735\pi$
$762$	−3.84940	+	6.90813i	−0.139449	+	0.250255i
$763$	−5.23454			−0.189503
$764$	−11.5069	−	18.5988i	−0.416304	−	0.672883i
$765$	5.05631	−	3.41212i	0.182811	−	0.123365i
$766$	21.7046	−	38.9512i	0.784221	−	1.40736i
$767$	18.2143	+	18.2143i	0.657679	+	0.657679i
$768$	20.7079	−	15.5921i	0.747232	−	0.562633i
$769$		−	12.3328i		−	0.444731i	−0.974963	−	0.222366i	$-0.928622\pi$
$769$		−	12.3328i		−	0.444731i	0.974963	−	0.222366i	$-0.0713779\pi$
$770$	0.0807273	+	0.944619i	0.00290921	+	0.0340417i
$771$	−19.6846	−	19.6846i	−0.708925	−	0.708925i
$772$	−21.3031	−	5.01836i	−0.766715	−	0.180615i
$773$		−	14.2244i		−	0.511616i	−0.966728	−	0.255808i	$-0.917659\pi$
$773$		−	14.2244i		−	0.511616i	0.966728	−	0.255808i	$-0.0823414\pi$
$774$	3.94025	−	1.12035i	0.141629	−	0.0402700i
$775$	−8.75369	+	21.6931i	−0.314442	+	0.779240i
$776$	1.45827	+	31.9073i	0.0523490	+	1.14541i
$777$	−0.935066	−	0.935066i	−0.0335453	−	0.0335453i
$778$	−11.5902	+	20.7998i	−0.415530	+	0.745711i
$779$	29.1365	+	29.1365i	1.04392	+	1.04392i
$780$	−12.8518	−	33.9095i	−0.460169	−	1.21415i
$781$	−2.34507	+	2.34507i	−0.0839134	+	0.0839134i
$782$	64.5990	−	18.3677i	2.31005	−	0.656828i
$783$	30.5686	−	30.5686i	1.09243	−	1.09243i
$784$	−3.57940	−	1.78547i	−0.127836	−	0.0637670i
$785$	−9.37664	+	48.2943i	−0.334667	+	1.72370i
$786$	5.94351	−	10.6662i	0.211998	−	0.380451i
$787$	−33.2196			−1.18415			−0.592075	−	0.805883i	$-0.701691\pi$
$787$	−33.2196			−1.18415			−0.592075	+	0.805883i	$0.701691\pi$
$788$	34.6810	−	21.4567i	1.23546	−	0.764362i
$789$	2.99818	−	2.99818i	0.106738	−	0.106738i
$790$	26.5027	−	2.26492i	0.942923	−	0.0805824i
$791$	−1.89128			−0.0672463
$792$	−0.0145284	−	0.317883i	−0.000516243	−	0.0112955i
$793$	−51.7501	+	51.7501i	−1.83770	+	1.83770i
$794$	4.31572	+	15.1783i	0.153159	+	0.538659i
$795$	42.5389	+	8.25919i	1.50870	+	0.292923i
$796$	19.3385	+	31.2574i	0.685435	+	1.10789i
$797$		−	5.38083i		−	0.190599i	−0.995449	−	0.0952994i	$-0.969619\pi$
$797$		−	5.38083i		−	0.190599i	0.995449	−	0.0952994i	$-0.0303808\pi$
$798$	10.4104	−	2.96003i	0.368524	−	0.104784i
$799$	−10.7533			−0.380426
$800$	−15.2445	+	23.8244i	−0.538975	+	0.842321i
$801$	−0.619377			−0.0218846
$802$	−12.5091	+	3.55678i	−0.441713	+	0.125594i
$803$		−	1.61448i		−	0.0569738i
$804$	−5.04874	−	8.16041i	−0.178055	−	0.287796i
$805$	−14.3398	−	2.78416i	−0.505412	−	0.0981288i
$806$	−9.05695	−	31.8532i	−0.319017	−	1.12198i
$807$	0.411633	−	0.411633i	0.0144902	−	0.0144902i
$808$	−0.365168	+	0.0166895i	−0.0128466	+	0.000587133i
$809$	21.0131			0.738780			0.369390	−	0.929275i	$-0.379567\pi$
$809$	21.0131			0.738780			0.369390	+	0.929275i	$0.379567\pi$
$810$	−24.3663	+	2.08235i	−0.856144	+	0.0731662i
$811$	−16.8314	+	16.8314i	−0.591032	+	0.591032i	−0.937910	−	0.346878i	$-0.887242\pi$
$811$	−16.8314	+	16.8314i	−0.591032	+	0.591032i	0.346878	+	0.937910i	$0.387242\pi$
$812$	−13.4460	+	8.31889i	−0.471864	+	0.291936i
$813$	40.5148			1.42092
$814$	−0.168453	+	0.302306i	−0.00590429	+	0.0105958i
$815$	−4.05342	+	20.8771i	−0.141985	+	0.731294i
$816$	−44.6772	+	14.9393i	−1.56402	+	0.522980i
$817$	25.7827	−	25.7827i	0.902021	−	0.902021i
$818$	−27.9144	+	7.93701i	−0.976003	+	0.277511i
$819$	1.32811	−	1.32811i	0.0464078	−	0.0464078i
$820$	13.8253	+	36.4780i	0.482801	+	1.27387i
$821$	−26.4360	−	26.4360i	−0.922624	−	0.922624i	0.0745903	−	0.997214i	$-0.476235\pi$
$821$	−26.4360	−	26.4360i	−0.922624	−	0.922624i	−0.997214	+	0.0745903i	$0.976235\pi$
$822$	−6.33755	+	11.3734i	−0.221047	+	0.396692i
$823$	23.7746	+	23.7746i	0.828732	+	0.828732i	0.987341	−	0.158610i	$-0.0507012\pi$
$823$	23.7746	+	23.7746i	0.828732	+	0.828732i	−0.158610	+	0.987341i	$0.550701\pi$
$824$	−19.3174	+	0.882870i	−0.672952	+	0.0307562i
$825$	−0.949881	−	2.23509i	−0.0330706	−	0.0778160i
$826$	−7.00085	+	1.99058i	−0.243591	+	0.0692612i
$827$			7.80115i			0.271272i	0.990759	+	0.135636i	$0.0433078\pi$
$827$			7.80115i			0.271272i	−0.990759	+	0.135636i	$0.956692\pi$
$828$	4.77237	+	1.12423i	0.165851	+	0.0390695i
$829$	−5.64805	−	5.64805i	−0.196165	−	0.196165i	0.602189	−	0.798354i	$-0.294295\pi$
$829$	−5.64805	−	5.64805i	−0.196165	−	0.196165i	−0.798354	+	0.602189i	$0.794295\pi$
$830$	2.19958	+	25.7381i	0.0763485	+	0.893381i
$831$		−	27.0508i		−	0.938383i
$832$	−3.65235	−	39.8735i	−0.126622	−	1.38237i
$833$	5.14025	+	5.14025i	0.178099	+	0.178099i
$834$	20.0572	−	35.9946i	0.694523	−	1.24639i
$835$	−7.70395	+	5.19880i	−0.266606	+	0.179912i
$836$	−1.49023	−	2.40870i	−0.0515407	−	0.0833065i
$837$	−25.5836			−0.884298
$838$	−8.79871	+	15.7902i	−0.303946	+	0.545462i
$839$			10.6167i			0.366530i	0.983064	+	0.183265i	$0.0586667\pi$
$839$			10.6167i			0.366530i	−0.983064	+	0.183265i	$0.941333\pi$
$840$	10.1373	+	1.49167i	0.349769	+	0.0514675i
$841$			33.5000i			1.15517i
$842$	−17.8595	−	9.95181i	−0.615480	−	0.342962i
$843$	37.3138			1.28515
$844$	17.8162	+	4.19694i	0.613258	+	0.144465i
$845$	−26.4520	−	5.13582i	−0.909977	−	0.176678i
$846$	−0.685772	−	0.382131i	−0.0235773	−	0.0131379i
$847$	7.71462	+	7.71462i	0.265077	+	0.265077i
$848$	42.8158	+	21.3574i	1.47030	+	0.733415i
$849$		−	38.6994i		−	1.32816i
$850$	40.0053	−	32.2768i	1.37217	−	1.10708i
$851$	−3.77045	−	3.77045i	−0.129249	−	0.129249i
$852$	18.8583	+	30.4812i	0.646075	+	1.04427i
$853$		−	18.0392i		−	0.617651i	−0.951119	−	0.308825i	$-0.900064\pi$
$853$		−	18.0392i		−	0.617651i	0.951119	−	0.308825i	$-0.0999358\pi$
$854$	−5.65561	−	19.8907i	−0.193531	−	0.680646i
$855$	3.28568	−	2.21726i	0.112368	−	0.0758285i
$856$	13.3871	+	12.2170i	0.457563	+	0.417567i
$857$	−15.1507	−	15.1507i	−0.517538	−	0.517538i	0.399288	−	0.916826i	$-0.369257\pi$
$857$	−15.1507	−	15.1507i	−0.517538	−	0.517538i	−0.916826	+	0.399288i	$0.869257\pi$
$858$	3.00320	+	1.67347i	0.102528	+	0.0571312i
$859$	−7.80905	−	7.80905i	−0.266441	−	0.266441i	0.561223	−	0.827665i	$-0.310331\pi$
$859$	−7.80905	−	7.80905i	−0.266441	−	0.266441i	−0.827665	+	0.561223i	$0.810331\pi$
$860$	32.2791	−	12.2339i	1.10071	−	0.417172i
$861$	9.99285	−	9.99285i	0.340555	−	0.340555i
$862$	7.01114	+	24.6581i	0.238801	+	0.839858i
$863$	16.4861	−	16.4861i	0.561192	−	0.561192i	−0.368454	−	0.929646i	$-0.620113\pi$
$863$	16.4861	−	16.4861i	0.561192	−	0.561192i	0.929646	+	0.368454i	$0.120113\pi$
$864$	−30.4015	−	5.71074i	−1.03428	−	0.194283i
$865$	−30.9659	−	6.01222i	−1.05287	−	0.204421i
$866$	−7.43292	−	4.14182i	−0.252581	−	0.140745i
$867$	58.0715			1.97221
$868$	9.10779	+	2.14552i	0.309139	+	0.0728236i
$869$	−1.78316	+	1.78316i	−0.0604897	+	0.0604897i
$870$	26.0970	−	30.9743i	0.884770	−	1.05013i
$871$	−14.8226			−0.502244
$872$	14.7901	−	0.675958i	0.500855	−	0.0228908i
$873$	2.99655	−	2.99655i	0.101418	−	0.101418i
$874$	41.9776	−	11.9357i	1.41991	−	0.403730i
$875$	−10.9345	+	2.33161i	−0.369654	+	0.0788228i
$876$	−16.9841	−	4.00092i	−0.573838	−	0.135179i
$877$			20.3744i			0.687996i	0.938970	+	0.343998i	$0.111781\pi$
$877$			20.3744i			0.687996i	−0.938970	+	0.343998i	$0.888219\pi$
$878$	2.29584	+	8.07444i	0.0774808	+	0.272499i
$879$	25.1691			0.848932
$880$	−0.350076	−	2.65857i	−0.0118011	−	0.0896205i
$881$	41.4472			1.39639			0.698196	−	0.715906i	$-0.253986\pi$
$881$	41.4472			1.39639			0.698196	+	0.715906i	$0.253986\pi$
$882$	0.145145	+	0.510472i	0.00488727	+	0.0171885i
$883$			29.4714i			0.991793i	0.868382	+	0.495896i	$0.165160\pi$
$883$			29.4714i			0.991793i	−0.868382	+	0.495896i	$0.834840\pi$
$884$	−16.6851	+	70.8289i	−0.561182	+	2.38223i
$885$	15.4545	−	10.4291i	0.519499	−	0.350570i
$886$	1.41412	−	0.402082i	0.0475082	−	0.0135082i
$887$	3.19131	−	3.19131i	0.107154	−	0.107154i	−0.651497	−	0.758651i	$-0.725859\pi$
$887$	3.19131	−	3.19131i	0.107154	−	0.107154i	0.758651	+	0.651497i	$0.225859\pi$
$888$	2.76276	+	2.52126i	0.0927121	+	0.0846079i
$889$	−3.45161			−0.115763
$890$	−5.20039	+	0.444427i	−0.174318	+	0.0148972i
$891$	1.63942	−	1.63942i	0.0549227	−	0.0549227i
$892$	−2.42518	+	10.2950i	−0.0812010	+	0.344701i
$893$	−6.98772			−0.233835
$894$	−15.4756	−	8.62344i	−0.517583	−	0.288411i
$895$	−15.0977	+	10.1883i	−0.504662	+	0.340557i
$896$	10.3441	+	4.58260i	0.345571	+	0.153094i
$897$	−37.4568	+	37.4568i	−1.25064	+	1.25064i
$898$	−4.24248	−	14.9208i	−0.141573	−	0.497912i
$899$	26.1539	−	26.1539i	0.872280	−	0.872280i
$900$	3.69824	−	0.636755i	0.123275	−	0.0212252i
$901$	−61.4863	−	61.4863i	−2.04840	−	2.04840i
$902$	−3.23068	−	1.80022i	−0.107570	−	0.0599409i
$903$	−8.84258	−	8.84258i	−0.294263	−	0.294263i
$904$	5.34378	−	0.244229i	0.177731	−	0.00812295i
$905$	5.48224	+	8.12396i	0.182236	+	0.270050i
$906$	−14.3861	−	50.5959i	−0.477947	−	1.68093i
$907$		−	52.5522i		−	1.74497i	−0.488643	−	0.872484i	$-0.662508\pi$
$907$		−	52.5522i		−	1.74497i	0.488643	−	0.872484i	$-0.337492\pi$
$908$	−29.3680	+	18.1696i	−0.974612	+	0.602980i
$909$	0.0342945	+	0.0342945i	0.00113748	+	0.00113748i
$910$	10.1980	−	12.1040i	0.338062	−	0.401243i
$911$			3.94102i			0.130572i	0.997867	+	0.0652860i	$0.0207960\pi$
$911$			3.94102i			0.130572i	−0.997867	+	0.0652860i	$0.979204\pi$
$912$	−29.0321	+	9.70783i	−0.961348	+	0.321458i
$913$	−1.73172	−	1.73172i	−0.0573115	−	0.0573115i
$914$	−2.05214	−	1.14351i	−0.0678788	−	0.0378239i
$915$	29.6310	+	43.9092i	0.979569	+	1.45159i
$916$	9.94618	−	42.2218i	0.328631	−	1.39505i
$917$	5.32932			0.175990
$918$	49.1073	+	27.3639i	1.62078	+	0.903144i
$919$			42.7653i			1.41070i	0.708861	+	0.705349i	$0.249209\pi$
$919$			42.7653i			1.41070i	−0.708861	+	0.705349i	$0.750791\pi$
$920$	40.8763	+	6.01482i	1.34765	+	0.198303i
$921$			31.4120i			1.03506i
$922$	−12.9989	+	23.3279i	−0.428097	+	0.768263i
$923$	55.3661			1.82240
$924$	−0.826102	+	0.511099i	−0.0271768	+	0.0168139i
$925$	−3.78466	−	1.52720i	−0.124439	−	0.0502140i
$926$	−11.4957	+	20.6302i	−0.377772	+	0.677950i
$927$	1.81418	+	1.81418i	0.0595854	+	0.0595854i
$928$	36.9172	−	25.2412i	1.21187	−	0.828582i
$929$		−	2.31824i		−	0.0760591i	−0.999277	−	0.0380295i	$-0.987892\pi$
$929$		−	2.31824i		−	0.0760591i	0.999277	−	0.0380295i	$-0.0121081\pi$
$930$	−23.8821	+	2.04097i	−0.783126	+	0.0669261i
$931$	3.34023	+	3.34023i	0.109472	+	0.109472i
$932$	2.09954	−	8.91262i	0.0687728	−	0.291943i
$933$			16.0853i			0.526611i
$934$	−53.6846	+	15.2644i	−1.75661	+	0.499465i
$935$	−0.928831	+	4.78394i	−0.0303760	+	0.156452i
$936$	−3.58103	+	3.92404i	−0.117050	+	0.128261i
$937$	39.7344	+	39.7344i	1.29807	+	1.29807i	0.929668	+	0.368398i	$0.120094\pi$
$937$	39.7344	+	39.7344i	1.29807	+	1.29807i	0.368398	+	0.929668i	$0.379906\pi$
$938$	2.03865	−	3.65857i	0.0665644	−	0.119456i
$939$	0.842447	+	0.842447i	0.0274922	+	0.0274922i
$940$	−6.03205	−	2.71636i	−0.196744	−	0.0885980i
$941$	19.5718	−	19.5718i	0.638022	−	0.638022i	−0.312046	−	0.950067i	$-0.601014\pi$
$941$	19.5718	−	19.5718i	0.638022	−	0.638022i	0.950067	+	0.312046i	$0.101014\pi$
$942$	−48.4867	+	13.7864i	−1.57978	+	0.449186i
$943$	40.2940	−	40.2940i	1.31215	−	1.31215i
$944$	19.5237	−	6.52839i	0.635442	−	0.212481i
$945$	−6.83969	−	10.1355i	−0.222495	−	0.329709i
$946$	−1.59300	+	2.85880i	−0.0517930	+	0.0929477i
$947$	52.2029			1.69637			0.848183	−	0.529703i	$-0.177697\pi$
$947$	52.2029			1.69637			0.848183	+	0.529703i	$0.177697\pi$
$948$	14.3396	+	23.1775i	0.465729	+	0.752771i
$949$	−19.0586	+	19.0586i	−0.618667	+	0.618667i
$950$	25.9962	−	20.9740i	0.843428	−	0.680488i
$951$	−2.94250			−0.0954170
$952$	−15.1874	−	13.8599i	−0.492228	−	0.449201i
$953$	−0.368291	+	0.368291i	−0.0119301	+	0.0119301i	−0.713047	−	0.701117i	$-0.752685\pi$
$953$	−0.368291	+	0.368291i	−0.0119301	+	0.0119301i	0.701117	+	0.713047i	$0.252685\pi$
$954$	−1.73618	−	6.10613i	−0.0562109	−	0.197693i
$955$	−4.66050	+	24.0039i	−0.150810	+	0.776747i
$956$	−8.89255	+	5.50170i	−0.287606	+	0.177938i
$957$			3.83989i			0.124126i
$958$	−20.8379	+	5.92492i	−0.673241	+	0.191425i
$959$	−5.68264			−0.183502
$960$	−28.8353	−	2.90561i	−0.930654	−	0.0937781i
$961$	9.11123			0.293911
$962$	5.55721	−	1.58011i	0.179172	−	0.0509446i
$963$		−	2.40459i		−	0.0774869i
$964$	−6.39677	+	3.95760i	−0.206026	+	0.127466i
$965$	13.6876	+	20.2832i	0.440618	+	0.652939i
$966$	−4.09353	−	14.3969i	−0.131707	−	0.463213i
$967$	−2.50955	+	2.50955i	−0.0807017	+	0.0807017i	−0.746305	−	0.665604i	$-0.768174\pi$
$967$	−2.50955	+	2.50955i	−0.0807017	+	0.0807017i	0.665604	+	0.746305i	$0.268174\pi$
$968$	−22.7937	−	20.8013i	−0.732617	−	0.668578i
$969$	55.6331			1.78719
$970$	23.0094	−	27.3097i	0.738788	−	0.876862i
$971$	−6.06047	+	6.06047i	−0.194490	+	0.194490i	−0.797633	−	0.603143i	$-0.793915\pi$
$971$	−6.06047	+	6.06047i	−0.194490	+	0.194490i	0.603143	+	0.797633i	$0.293915\pi$
$972$	4.07854	+	6.59226i	0.130819	+	0.211447i
$973$	17.9845			0.576557
$974$	7.62516	−	13.6841i	0.244326	−	0.438468i
$975$	−15.1716	+	37.5979i	−0.485881	+	1.20410i
$976$	18.5484	+	55.4704i	0.593719	+	1.77557i
$977$	−39.5330	+	39.5330i	−1.26477	+	1.26477i	−0.316020	+	0.948753i	$0.602347\pi$
$977$	−39.5330	+	39.5330i	−1.26477	+	1.26477i	−0.948753	+	0.316020i	$0.897653\pi$
$978$	−20.9603	+	5.95972i	−0.670235	+	0.190571i
$979$	0.349895	−	0.349895i	0.0111827	−	0.0111827i
$980$	1.58494	+	4.18186i	0.0506291	+	0.133585i
$981$	−1.38900	−	1.38900i	−0.0443474	−	0.0443474i
$982$	4.59039	−	8.23791i	0.146485	−	0.262882i
$983$	−42.3328	−	42.3328i	−1.35021	−	1.35021i	−0.885424	−	0.464783i	$-0.846132\pi$
$983$	−42.3328	−	42.3328i	−1.35021	−	1.35021i	−0.464783	−	0.885424i	$-0.653868\pi$
$984$	−26.9442	+	29.5250i	−0.858948	+	0.941222i
$985$	−44.7597	−	8.69036i	−1.42616	−	0.276898i
$986$	−78.1758	+	22.2281i	−2.48962	+	0.707886i
$987$			2.39655i			0.0762831i
$988$	−10.8423	+	46.0259i	−0.344940	+	1.46428i
$989$	−35.6558	−	35.6558i	−1.13379	−	1.13379i
$990$	−0.229236	+	0.272079i	−0.00728560	+	0.00864722i
$991$			44.1499i			1.40247i	0.712931	+	0.701234i	$0.247367\pi$
$991$			44.1499i			1.40247i	−0.712931	+	0.701234i	$0.752633\pi$
$992$	−26.0109	−	4.88599i	−0.825847	−	0.155130i
$993$	−25.2787	−	25.2787i	−0.802195	−	0.802195i
$994$	−7.61488	+	13.6657i	−0.241529	+	0.433449i
$995$	7.83247	−	40.3411i	0.248306	−	1.27890i
$996$	−22.5088	+	13.9259i	−0.713220	+	0.441260i
$997$	3.03274			0.0960479			0.0480240	−	0.998846i	$-0.484708\pi$
$997$	3.03274			0.0960479			0.0480240	+	0.998846i	$0.484708\pi$
$998$	−16.9764	+	30.4658i	−0.537378	+	0.964379i
$999$		−	4.46340i		−	0.141216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.9	✓	144
5.2	odd	4		560.2.bl.a.267.30	yes	144
16.3	odd	4		560.2.bl.a.323.30	yes	144
80.67	even	4	inner	560.2.t.a.547.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.9	✓	144	1.1	even	1	trivial
560.2.t.a.547.9	yes	144	80.67	even	4	inner
560.2.bl.a.267.30	yes	144	5.2	odd	4
560.2.bl.a.323.30	yes	144	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.36029 + 0.386778i) q^{2} +1.62010i q^{3} +(1.70080 - 1.05227i) q^{4} +(-2.19508 - 0.426188i) q^{5} +(-0.626621 - 2.20382i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.90660 + 2.08923i) q^{8} +0.375266 q^{9} +O(q^{10})\)	\(q+(-1.36029 + 0.386778i) q^{2} +1.62010i q^{3} +(1.70080 - 1.05227i) q^{4} +(-2.19508 - 0.426188i) q^{5} +(-0.626621 - 2.20382i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.90660 + 2.08923i) q^{8} +0.375266 q^{9} +(3.15079 - 0.269268i) q^{10} +(-0.211993 + 0.211993i) q^{11} +(1.70478 + 2.75548i) q^{12} +5.00506 q^{13} +(-0.688380 + 1.23537i) q^{14} +(0.690468 - 3.55625i) q^{15} +(1.78547 - 3.57940i) q^{16} +(-5.14025 + 5.14025i) q^{17} +(-0.510472 + 0.145145i) q^{18} +(-3.34023 + 3.34023i) q^{19} +(-4.18186 + 1.58494i) q^{20} +(1.14559 + 1.14559i) q^{21} +(0.206379 - 0.370367i) q^{22} +(4.61932 + 4.61932i) q^{23} +(-3.38476 - 3.08889i) q^{24} +(4.63673 + 1.87103i) q^{25} +(-6.80836 + 1.93585i) q^{26} +5.46828i q^{27} +(0.458587 - 1.94671i) q^{28} +(-5.59017 - 5.59017i) q^{29} +(0.436241 + 5.10461i) q^{30} +4.67854i q^{31} +(-1.04434 + 5.55962i) q^{32} +(-0.343451 - 0.343451i) q^{33} +(5.00412 - 8.98039i) q^{34} +(-1.85351 + 1.25079i) q^{35} +(0.638254 - 0.394879i) q^{36} -0.816234 q^{37} +(3.25177 - 5.83562i) q^{38} +8.10871i q^{39} +(5.07554 - 3.77344i) q^{40} -8.72292i q^{41} +(-2.00142 - 1.11525i) q^{42} -7.71883 q^{43} +(-0.137486 + 0.583632i) q^{44} +(-0.823737 - 0.159934i) q^{45} +(-8.07030 - 4.49699i) q^{46} +(1.04599 + 1.04599i) q^{47} +(5.79899 + 2.89265i) q^{48} -1.00000i q^{49} +(-7.03099 - 0.751766i) q^{50} +(-8.32774 - 8.32774i) q^{51} +(8.51263 - 5.26665i) q^{52} +11.9617i q^{53} +(-2.11501 - 7.43847i) q^{54} +(0.555690 - 0.374992i) q^{55} +(0.129134 + 2.82548i) q^{56} +(-5.41151 - 5.41151i) q^{57} +(9.76644 + 5.44212i) q^{58} +(3.63917 + 3.63917i) q^{59} +(-2.56777 - 6.77505i) q^{60} +(-10.3396 + 10.3396i) q^{61} +(-1.80956 - 6.36420i) q^{62} +(0.265353 - 0.265353i) q^{63} +(-0.729731 - 7.96665i) q^{64} +(-10.9865 - 2.13309i) q^{65} +(0.600033 + 0.334355i) q^{66} -2.96152 q^{67} +(-3.33366 + 14.1515i) q^{68} +(-7.48378 + 7.48378i) q^{69} +(2.03755 - 2.41835i) q^{70} +11.0620 q^{71} +(-0.715483 + 0.784015i) q^{72} +(-3.80786 + 3.80786i) q^{73} +(1.11032 - 0.315702i) q^{74} +(-3.03126 + 7.51198i) q^{75} +(-2.16627 + 9.19588i) q^{76} +0.299803i q^{77} +(-3.13627 - 11.0302i) q^{78} +8.41143 q^{79} +(-5.44475 + 7.09610i) q^{80} -7.73338 q^{81} +(3.37384 + 11.8657i) q^{82} +8.16875i q^{83} +(3.15388 + 0.742958i) q^{84} +(13.4740 - 9.09253i) q^{85} +(10.4999 - 2.98548i) q^{86} +(9.05665 - 9.05665i) q^{87} +(-0.0387149 - 0.847088i) q^{88} -1.65050 q^{89} +(1.18238 - 0.101047i) q^{90} +(3.53911 - 3.53911i) q^{91} +(12.7173 + 2.99581i) q^{92} -7.57972 q^{93} +(-1.82743 - 1.01829i) q^{94} +(8.75562 - 5.90849i) q^{95} +(-9.00716 - 1.69194i) q^{96} +(7.98515 - 7.98515i) q^{97} +(0.386778 + 1.36029i) q^{98} +(-0.0795537 + 0.0795537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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