LMFDB - Embedded newform 560.2.t.a.43.1

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			43.1
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41270 - 0.0654069i) q^{2} +1.49919i q^{3} +(1.99144 + 0.184801i) q^{4} +(1.45710 - 1.69613i) q^{5} +(0.0980575 - 2.11791i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.80123 - 0.391322i) q^{8} +0.752424 q^{9} +O(q^{10})$	\(q+(-1.41270 - 0.0654069i) q^{2} +1.49919i q^{3} +(1.99144 + 0.184801i) q^{4} +(1.45710 - 1.69613i) q^{5} +(0.0980575 - 2.11791i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.80123 - 0.391322i) q^{8} +0.752424 q^{9} +(-2.16939 + 2.30082i) q^{10} +(-4.60762 + 4.60762i) q^{11} +(-0.277052 + 2.98556i) q^{12} -4.52764 q^{13} +(1.04518 - 0.952680i) q^{14} +(2.54282 + 2.18447i) q^{15} +(3.93170 + 0.736041i) q^{16} +(-2.86073 + 2.86073i) q^{17} +(-1.06295 - 0.0492138i) q^{18} +(2.16518 - 2.16518i) q^{19} +(3.21518 - 3.10847i) q^{20} +(-1.06009 - 1.06009i) q^{21} +(6.81055 - 6.20781i) q^{22} +(6.64158 + 6.64158i) q^{23} +(0.586667 - 4.19957i) q^{24} +(-0.753713 - 4.94287i) q^{25} +(6.39619 + 0.296139i) q^{26} +5.62560i q^{27} +(-1.53884 + 1.27749i) q^{28} +(3.21005 + 3.21005i) q^{29} +(-3.44937 - 3.25232i) q^{30} +3.09664i q^{31} +(-5.50617 - 1.29696i) q^{32} +(-6.90770 - 6.90770i) q^{33} +(4.22847 - 3.85424i) q^{34} +(0.169019 + 2.22967i) q^{35} +(1.49841 + 0.139049i) q^{36} -0.0568512 q^{37} +(-3.20037 + 2.91713i) q^{38} -6.78779i q^{39} +(-4.74540 + 4.18105i) q^{40} +6.15567i q^{41} +(1.42825 + 1.56692i) q^{42} -9.31921 q^{43} +(-10.0273 + 8.32432i) q^{44} +(1.09636 - 1.27621i) q^{45} +(-8.94815 - 9.81696i) q^{46} +(-1.01939 - 1.01939i) q^{47} +(-1.10347 + 5.89437i) q^{48} -1.00000i q^{49} +(0.741474 + 7.03208i) q^{50} +(-4.28878 - 4.28878i) q^{51} +(-9.01653 - 0.836710i) q^{52} +2.02505i q^{53} +(0.367953 - 7.94729i) q^{54} +(1.10135 + 14.5289i) q^{55} +(2.25747 - 1.70406i) q^{56} +(3.24602 + 3.24602i) q^{57} +(-4.32487 - 4.74479i) q^{58} +(0.419674 + 0.419674i) q^{59} +(4.66020 + 4.82017i) q^{60} +(5.84049 - 5.84049i) q^{61} +(0.202542 - 4.37462i) q^{62} +(-0.532044 + 0.532044i) q^{63} +(7.69373 + 2.19236i) q^{64} +(-6.59722 + 7.67946i) q^{65} +(9.30670 + 10.2103i) q^{66} +2.41650 q^{67} +(-6.22565 + 5.16832i) q^{68} +(-9.95700 + 9.95700i) q^{69} +(-0.0929372 - 3.16091i) q^{70} -4.61260 q^{71} +(-2.10771 - 0.294440i) q^{72} +(-6.05340 + 6.05340i) q^{73} +(0.0803137 + 0.00371846i) q^{74} +(7.41030 - 1.12996i) q^{75} +(4.71196 - 3.91171i) q^{76} -6.51615i q^{77} +(-0.443969 + 9.58912i) q^{78} +5.36998 q^{79} +(6.97730 - 5.59618i) q^{80} -6.17658 q^{81} +(0.402624 - 8.69612i) q^{82} -11.4409i q^{83} +(-1.91520 - 2.30701i) q^{84} +(0.683797 + 9.02054i) q^{85} +(13.1653 + 0.609541i) q^{86} +(-4.81247 + 4.81247i) q^{87} +(14.7100 - 11.1039i) q^{88} -0.661410 q^{89} +(-1.63230 + 1.73119i) q^{90} +(3.20152 - 3.20152i) q^{91} +(11.9990 + 14.4537i) q^{92} -4.64246 q^{93} +(1.37341 + 1.50676i) q^{94} +(-0.517541 - 6.82731i) q^{95} +(1.94440 - 8.25480i) q^{96} +(11.8269 - 11.8269i) q^{97} +(-0.0654069 + 1.41270i) q^{98} +(-3.46688 + 3.46688i) 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 $

$2$	−1.41270	−	0.0654069i	−0.998930	−	0.0462497i
$2$	−1.41270	−	0.0654069i	−0.998930	−	0.0462497i
$3$			1.49919i			0.865559i	0.901500	+	0.432779i	$0.142467\pi$
$3$			1.49919i			0.865559i	−0.901500	+	0.432779i	$0.857533\pi$
$4$	1.99144	+	0.184801i	0.995722	+	0.0924004i
$5$	1.45710	−	1.69613i	0.651635	−	0.758532i
$5$	1.45710	−	1.69613i	0.651635	−	0.758532i
$6$	0.0980575	−	2.11791i	0.0400318	−	0.864632i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.80123	−	0.391322i	−0.990383	−	0.138353i
$9$	0.752424			0.250808
$10$	−2.16939	+	2.30082i	−0.686020	+	0.727583i
$11$	−4.60762	+	4.60762i	−1.38925	+	1.38925i	−0.562347	+	0.826901i	$0.690102\pi$
$11$	−4.60762	+	4.60762i	−1.38925	+	1.38925i	−0.826901	+	0.562347i	$0.809898\pi$
$12$	−0.277052	+	2.98556i	−0.0799779	+	0.861856i
$13$	−4.52764			−1.25574			−0.627870	−	0.778318i	$-0.716073\pi$
$13$	−4.52764			−1.25574			−0.627870	+	0.778318i	$0.716073\pi$
$14$	1.04518	−	0.952680i	0.279336	−	0.254615i
$15$	2.54282	+	2.18447i	0.656554	+	0.564029i
$16$	3.93170	+	0.736041i	0.982924	+	0.184010i
$17$	−2.86073	+	2.86073i	−0.693829	+	0.693829i	−0.963072	−	0.269243i	$-0.913226\pi$
$17$	−2.86073	+	2.86073i	−0.693829	+	0.693829i	0.269243	+	0.963072i	$0.413226\pi$
$18$	−1.06295	−	0.0492138i	−0.250540	−	0.0115998i
$19$	2.16518	−	2.16518i	0.496726	−	0.496726i	−0.413691	−	0.910417i	$-0.635761\pi$
$19$	2.16518	−	2.16518i	0.496726	−	0.496726i	0.910417	+	0.413691i	$0.135761\pi$
$20$	3.21518	−	3.10847i	0.718936	−	0.695076i
$21$	−1.06009	−	1.06009i	−0.231330	−	0.231330i
$22$	6.81055	−	6.20781i	1.45201	−	1.32351i
$23$	6.64158	+	6.64158i	1.38486	+	1.38486i	0.835741	+	0.549123i	$0.185038\pi$
$23$	6.64158	+	6.64158i	1.38486	+	1.38486i	0.549123	+	0.835741i	$0.314962\pi$
$24$	0.586667	−	4.19957i	0.119753	−	0.857235i
$25$	−0.753713	−	4.94287i	−0.150743	−	0.988573i
$26$	6.39619	+	0.296139i	1.25440	+	0.0580776i
$27$			5.62560i			1.08265i
$28$	−1.53884	+	1.27749i	−0.290813	+	0.241423i
$29$	3.21005	+	3.21005i	0.596091	+	0.596091i	0.939270	−	0.343179i	$-0.111504\pi$
$29$	3.21005	+	3.21005i	0.596091	+	0.596091i	−0.343179	+	0.939270i	$0.611504\pi$
$30$	−3.44937	−	3.25232i	−0.629766	−	0.593791i
$31$			3.09664i			0.556173i	0.960556	+	0.278086i	$0.0897001\pi$
$31$			3.09664i			0.556173i	−0.960556	+	0.278086i	$0.910300\pi$
$32$	−5.50617	−	1.29696i	−0.973362	−	0.229273i
$33$	−6.90770	−	6.90770i	−1.20248	−	1.20248i
$34$	4.22847	−	3.85424i	0.725176	−	0.660997i
$35$	0.169019	+	2.22967i	0.0285694	+	0.376883i
$36$	1.49841	+	0.139049i	0.249735	+	0.0231748i
$37$	−0.0568512			−0.00934628			−0.00467314	−	0.999989i	$-0.501488\pi$
$37$	−0.0568512			−0.00934628			−0.00467314	+	0.999989i	$0.501488\pi$
$38$	−3.20037	+	2.91713i	−0.519168	+	0.473221i
$39$		−	6.78779i		−	1.08692i
$40$	−4.74540	+	4.18105i	−0.750314	+	0.661082i
$41$			6.15567i			0.961355i	0.876898	+	0.480677i	$0.159609\pi$
$41$			6.15567i			0.961355i	−0.876898	+	0.480677i	$0.840391\pi$
$42$	1.42825	+	1.56692i	0.220384	+	0.241782i
$43$	−9.31921			−1.42117			−0.710583	−	0.703613i	$-0.751569\pi$
$43$	−9.31921			−1.42117			−0.710583	+	0.703613i	$0.751569\pi$
$44$	−10.0273	+	8.32432i	−1.51167	+	1.25494i
$45$	1.09636	−	1.27621i	0.163435	−	0.190246i
$46$	−8.94815	−	9.81696i	−1.31933	−	1.44743i
$47$	−1.01939	−	1.01939i	−0.148693	−	0.148693i	0.628841	−	0.777534i	$-0.283530\pi$
$47$	−1.01939	−	1.01939i	−0.148693	−	0.148693i	−0.777534	+	0.628841i	$0.783530\pi$
$48$	−1.10347	+	5.89437i	−0.159272	+	0.850779i
$49$		−	1.00000i		−	0.142857i
$50$	0.741474	+	7.03208i	0.104860	+	0.994487i
$51$	−4.28878	−	4.28878i	−0.600550	−	0.600550i
$52$	−9.01653	−	0.836710i	−1.25037	−	0.116031i
$53$			2.02505i			0.278162i	0.990281	+	0.139081i	$0.0444149\pi$
$53$			2.02505i			0.278162i	−0.990281	+	0.139081i	$0.955585\pi$
$54$	0.367953	−	7.94729i	0.0500721	−	1.08149i
$55$	1.10135	+	14.5289i	0.148506	+	1.95907i
$56$	2.25747	−	1.70406i	0.301667	−	0.227714i
$57$	3.24602	+	3.24602i	0.429946	+	0.429946i
$58$	−4.32487	−	4.74479i	−0.567884	−	0.623022i
$59$	0.419674	+	0.419674i	0.0546369	+	0.0546369i	0.733897	−	0.679260i	$-0.237699\pi$
$59$	0.419674	+	0.419674i	0.0546369	+	0.0546369i	−0.679260	+	0.733897i	$0.737699\pi$
$60$	4.66020	+	4.82017i	0.601629	+	0.622282i
$61$	5.84049	−	5.84049i	0.747798	−	0.747798i	−0.226267	−	0.974065i	$-0.572652\pi$
$61$	5.84049	−	5.84049i	0.747798	−	0.747798i	0.974065	+	0.226267i	$0.0726522\pi$
$62$	0.202542	−	4.37462i	0.0257228	−	0.555578i
$63$	−0.532044	+	0.532044i	−0.0670313	+	0.0670313i
$64$	7.69373	+	2.19236i	0.961717	+	0.274046i
$65$	−6.59722	+	7.67946i	−0.818285	+	0.952520i
$66$	9.30670	+	10.2103i	1.14558	+	1.25680i
$67$	2.41650			0.295223			0.147611	−	0.989045i	$-0.452842\pi$
$67$	2.41650			0.295223			0.147611	+	0.989045i	$0.452842\pi$
$68$	−6.22565	+	5.16832i	−0.754971	+	0.626751i
$69$	−9.95700	+	9.95700i	−1.19868	+	1.19868i
$70$	−0.0929372	−	3.16091i	−0.0111081	−	0.377801i
$71$	−4.61260			−0.547415			−0.273707	−	0.961813i	$-0.588250\pi$
$71$	−4.61260			−0.547415			−0.273707	+	0.961813i	$0.588250\pi$
$72$	−2.10771	−	0.294440i	−0.248396	−	0.0347001i
$73$	−6.05340	+	6.05340i	−0.708496	+	0.708496i	−0.966219	−	0.257723i	$-0.917028\pi$
$73$	−6.05340	+	6.05340i	−0.708496	+	0.708496i	0.257723	+	0.966219i	$0.417028\pi$
$74$	0.0803137	+	0.00371846i	0.00933628	+	0.000432262i
$75$	7.41030	−	1.12996i	0.855668	−	0.130477i
$76$	4.71196	−	3.91171i	0.540499	−	0.448704i
$77$		−	6.51615i		−	0.742585i
$78$	−0.443969	+	9.58912i	−0.0502696	+	1.08575i
$79$	5.36998			0.604169			0.302085	−	0.953281i	$-0.402317\pi$
$79$	5.36998			0.604169			0.302085	+	0.953281i	$0.402317\pi$
$80$	6.97730	−	5.59618i	0.780086	−	0.625672i
$81$	−6.17658			−0.686287
$82$	0.402624	−	8.69612i	0.0444623	−	0.960326i
$83$		−	11.4409i		−	1.25580i	−0.778294	−	0.627900i	$-0.783915\pi$
$83$		−	11.4409i		−	1.25580i	0.778294	−	0.627900i	$-0.216085\pi$
$84$	−1.91520	−	2.30701i	−0.208966	−	0.251716i
$85$	0.683797	+	9.02054i	0.0741682	+	0.978415i
$86$	13.1653	+	0.609541i	1.41965	+	0.0657285i
$87$	−4.81247	+	4.81247i	−0.515951	+	0.515951i
$88$	14.7100	−	11.1039i	1.56810	−	1.18368i
$89$	−0.661410			−0.0701093			−0.0350546	−	0.999385i	$-0.511161\pi$
$89$	−0.661410			−0.0701093			−0.0350546	+	0.999385i	$0.511161\pi$
$90$	−1.63230	+	1.73119i	−0.172059	+	0.182484i
$91$	3.20152	−	3.20152i	0.335611	−	0.335611i
$92$	11.9990	+	14.4537i	1.25098	+	1.50690i
$93$	−4.64246			−0.481400
$94$	1.37341	+	1.50676i	0.141657	+	0.155411i
$95$	−0.517541	−	6.82731i	−0.0530986	−	0.700468i
$96$	1.94440	−	8.25480i	0.198449	−	0.842502i
$97$	11.8269	−	11.8269i	1.20084	−	1.20084i	0.226928	−	0.973912i	$-0.427132\pi$
$97$	11.8269	−	11.8269i	1.20084	−	1.20084i	0.973912	−	0.226928i	$-0.0728682\pi$
$98$	−0.0654069	+	1.41270i	−0.00660710	+	0.142704i
$99$	−3.46688	+	3.46688i	−0.348435	+	0.348435i
$100$	−0.587533	−	9.98273i	−0.0587533	−	0.998273i
$101$	1.86050	+	1.86050i	0.185127	+	0.185127i	0.793586	−	0.608459i	$-0.208212\pi$
$101$	1.86050	+	1.86050i	0.185127	+	0.185127i	−0.608459	+	0.793586i	$0.708212\pi$
$102$	5.77825	+	6.33928i	0.572132	+	0.627682i
$103$	1.29916	+	1.29916i	0.128010	+	0.128010i	0.768209	−	0.640199i	$-0.221148\pi$
$103$	1.29916	+	1.29916i	0.128010	+	0.128010i	−0.640199	+	0.768209i	$0.721148\pi$
$104$	12.6829	+	1.77176i	1.24366	+	0.173736i
$105$	−3.34270	+	0.253392i	−0.326215	+	0.0247285i
$106$	0.132452	−	2.86079i	0.0128649	−	0.277865i
$107$			14.8446i			1.43508i	0.696518	+	0.717540i	$0.254732\pi$
$107$			14.8446i			1.43508i	−0.696518	+	0.717540i	$0.745268\pi$
$108$	−1.03962	+	11.2031i	−0.100037	+	1.07802i
$109$	−4.93038	−	4.93038i	−0.472245	−	0.472245i	0.430396	−	0.902640i	$-0.358374\pi$
$109$	−4.93038	−	4.93038i	−0.472245	−	0.472245i	−0.902640	+	0.430396i	$0.858374\pi$
$110$	−0.605593	−	20.5970i	−0.0577411	−	1.96385i
$111$		−	0.0852308i		−	0.00808975i
$112$	−3.30059	+	2.25967i	−0.311876	+	0.213519i
$113$	0.202593	+	0.202593i	0.0190584	+	0.0190584i	0.716572	−	0.697513i	$-0.245710\pi$
$113$	0.202593	+	0.202593i	0.0190584	+	0.0190584i	−0.697513	+	0.716572i	$0.745710\pi$
$114$	−4.37334	−	4.79797i	−0.409601	−	0.449371i
$115$	20.9424	−	1.58753i	1.95289	−	0.148038i
$116$	5.79941	+	6.98585i	0.538462	+	0.648620i
$117$	−3.40670			−0.314950
$118$	−0.565424	−	0.620323i	−0.0520515	−	0.0571054i
$119$		−	4.04568i		−	0.370867i
$120$	−6.26819	−	7.11427i	−0.572205	−	0.649441i
$121$		−	31.4602i		−	2.86002i
$122$	−8.63287	+	7.86885i	−0.781583	+	0.712412i
$123$	−9.22853			−0.832109
$124$	−0.572261	+	6.16678i	−0.0513906	+	0.553793i
$125$	−9.48198	−	5.92386i	−0.848094	−	0.529846i
$126$	0.786419	−	0.716820i	0.0700597	−	0.0638594i
$127$	11.3495	+	11.3495i	1.00711	+	1.00711i	0.999975	+	0.00713318i	$0.00227058\pi$
$127$	11.3495	+	11.3495i	1.00711	+	1.00711i	0.00713318	+	0.999975i	$0.497729\pi$
$128$	−10.7255	−	3.60038i	−0.948013	−	0.318231i
$129$		−	13.9713i		−	1.23010i
$130$	9.82219	−	10.4173i	0.861463	−	0.913655i
$131$	−11.6475	−	11.6475i	−1.01765	−	1.01765i	−0.999841	−	0.0178064i	$-0.994332\pi$
$131$	−11.6475	−	11.6475i	−1.01765	−	1.01765i	−0.0178064	−	0.999841i	$-0.505668\pi$
$132$	−12.4797	−	15.0328i	−1.08622	−	1.30844i
$133$			3.06203i			0.265511i
$134$	−3.41379	−	0.158056i	−0.294907	−	0.0136540i
$135$	9.54175	+	8.19707i	0.821223	+	0.705492i
$136$	9.13302	−	6.89408i	0.783150	−	0.591163i
$137$	6.15852	+	6.15852i	0.526158	+	0.526158i	0.919425	−	0.393266i	$-0.128655\pi$
$137$	6.15852	+	6.15852i	0.526158	+	0.526158i	−0.393266	+	0.919425i	$0.628655\pi$
$138$	14.7175	−	13.4150i	1.25284	−	1.14196i
$139$	−3.92488	−	3.92488i	−0.332904	−	0.332904i	0.520785	−	0.853688i	$-0.325639\pi$
$139$	−3.92488	−	3.92488i	−0.332904	−	0.332904i	−0.853688	+	0.520785i	$0.825639\pi$
$140$	−0.0754530	+	4.47150i	−0.00637694	+	0.377911i
$141$	1.52826	−	1.52826i	0.128702	−	0.128702i
$142$	6.51622	+	0.301696i	0.546829	+	0.0253178i
$143$	20.8616	−	20.8616i	1.74454	−	1.74454i
$144$	2.95830	+	0.553815i	0.246525	+	0.0461512i
$145$	10.1220	−	0.767294i	0.840588	−	0.0637203i
$146$	8.94757	−	8.15570i	0.740506	−	0.674970i
$147$	1.49919			0.123651
$148$	−0.113216	−	0.0105061i	−0.00930629	−	0.000863599i
$149$	−0.116837	+	0.116837i	−0.00957163	+	0.00957163i	−0.711876	−	0.702305i	$-0.752154\pi$
$149$	−0.116837	+	0.116837i	−0.00957163	+	0.00957163i	0.702305	+	0.711876i	$0.252154\pi$
$150$	−10.5424	+	1.11161i	−0.860787	+	0.0907627i
$151$	1.05136			0.0855588			0.0427794	−	0.999085i	$-0.486379\pi$
$151$	1.05136			0.0855588			0.0427794	+	0.999085i	$0.486379\pi$
$152$	−6.91244	+	5.21788i	−0.560673	+	0.423226i
$153$	−2.15248	+	2.15248i	−0.174018	+	0.174018i
$154$	−0.426201	+	9.20537i	−0.0343443	+	0.741790i
$155$	5.25230	+	4.51212i	0.421875	+	0.362422i
$156$	1.25439	−	13.5175i	0.100432	−	1.08227i
$157$			2.00501i			0.160017i	0.996794	+	0.0800084i	$0.0254947\pi$
$157$			2.00501i			0.160017i	−0.996794	+	0.0800084i	$0.974505\pi$
$158$	−7.58616	−	0.351234i	−0.603523	−	0.0279426i
$159$	−3.03594			−0.240766
$160$	−10.2229	+	7.44937i	−0.808188	+	0.588924i
$161$	−9.39261			−0.740241
$162$	8.72566	+	0.403991i	0.685553	+	0.0317406i
$163$		−	16.3705i		−	1.28224i	−0.767441	−	0.641120i	$-0.778470\pi$
$163$		−	16.3705i		−	1.28224i	0.767441	−	0.641120i	$-0.221530\pi$
$164$	−1.13757	+	12.2587i	−0.0888295	+	0.957242i
$165$	−21.7816	+	1.65114i	−1.69569	+	0.128541i
$166$	−0.748313	+	16.1625i	−0.0580804	+	1.25446i
$167$	15.0511	−	15.0511i	1.16469	−	1.16469i	0.181250	−	0.983437i	$-0.441986\pi$
$167$	15.0511	−	15.0511i	1.16469	−	1.16469i	0.983437	−	0.181250i	$-0.0580144\pi$
$168$	2.55471	+	3.38438i	0.197100	+	0.261111i
$169$	7.49948			0.576883
$170$	−0.375995	−	12.7880i	−0.0288375	−	0.980799i
$171$	1.62913	−	1.62913i	0.124583	−	0.124583i
$172$	−18.5587	−	1.72220i	−1.41509	−	0.131316i
$173$	−0.996397			−0.0757546			−0.0378773	−	0.999282i	$-0.512060\pi$
$173$	−0.996397			−0.0757546			−0.0378773	+	0.999282i	$0.512060\pi$
$174$	7.11335	−	6.48382i	0.539262	−	0.491537i
$175$	4.02809	+	2.96218i	0.304495	+	0.223920i
$176$	−21.5071	+	14.7244i	−1.62116	+	1.10989i
$177$	−0.629172	+	0.629172i	−0.0472914	+	0.0472914i
$178$	0.934374	+	0.0432608i	0.0700343	+	0.00324253i
$179$	−9.78533	+	9.78533i	−0.731390	+	0.731390i	−0.970895	−	0.239505i	$-0.923015\pi$
$179$	−9.78533	+	9.78533i	−0.731390	+	0.731390i	0.239505	+	0.970895i	$0.423015\pi$
$180$	2.41918	−	2.33889i	0.180315	−	0.174331i
$181$	9.35061	+	9.35061i	0.695025	+	0.695025i	0.963333	−	0.268308i	$-0.0864645\pi$
$181$	9.35061	+	9.35061i	0.695025	+	0.695025i	−0.268308	+	0.963333i	$0.586465\pi$
$182$	−4.73219	+	4.31339i	−0.350773	+	0.319730i
$183$	8.75601	+	8.75601i	0.647263	+	0.647263i
$184$	−16.0056	−	21.2036i	−1.17995	−	1.56315i
$185$	−0.0828379	+	0.0964270i	−0.00609037	+	0.00708945i
$186$	6.55840	+	0.303649i	0.480885	+	0.0222646i
$187$		−	26.3623i		−	1.92780i
$188$	−1.84167	−	2.21844i	−0.134318	−	0.161796i
$189$	−3.97790	−	3.97790i	−0.289350	−	0.289350i
$190$	0.284576	+	9.67880i	0.0206453	+	0.702174i
$191$			17.6610i			1.27791i	0.769245	+	0.638954i	$0.220633\pi$
$191$			17.6610i			1.27791i	−0.769245	+	0.638954i	$0.779367\pi$
$192$	−3.28677	+	11.5344i	−0.237202	+	0.832422i
$193$	6.18790	+	6.18790i	0.445415	+	0.445415i	0.893827	−	0.448412i	$-0.148010\pi$
$193$	6.18790	+	6.18790i	0.445415	+	0.445415i	−0.448412	+	0.893827i	$0.648010\pi$
$194$	−17.4814	+	15.9343i	−1.25509	+	1.14402i
$195$	−11.5130	−	9.89050i	−0.824462	−	0.708273i
$196$	0.184801	−	1.99144i	0.0132001	−	0.142246i
$197$	−7.40653			−0.527693			−0.263847	−	0.964565i	$-0.584991\pi$
$197$	−7.40653			−0.527693			−0.263847	+	0.964565i	$0.584991\pi$
$198$	5.12442	−	4.67091i	0.364177	−	0.331947i
$199$			4.57306i			0.324176i	0.986776	+	0.162088i	$0.0518228\pi$
$199$			4.57306i			0.324176i	−0.986776	+	0.162088i	$0.948177\pi$
$200$	0.177068	+	14.1410i	0.0125206	+	0.999922i
$201$			3.62280i			0.255533i
$202$	−2.50664	−	2.75002i	−0.176367	−	0.193491i
$203$	−4.53969			−0.318624
$204$	−7.74830	−	9.33344i	−0.542490	−	0.653472i
$205$	10.4408	+	8.96944i	0.729219	+	0.626453i
$206$	−1.75035	−	1.92029i	−0.121952	−	0.133793i
$207$	4.99728	+	4.99728i	0.347335	+	0.347335i
$208$	−17.8013	−	3.33252i	−1.23430	−	0.231069i
$209$			19.9526i			1.38015i
$210$	4.73881	−	0.139331i	0.327009	−	0.00961473i
$211$	3.92687	+	3.92687i	0.270337	+	0.270337i	0.829236	−	0.558899i	$-0.188776\pi$
$211$	3.92687	+	3.92687i	0.270337	+	0.270337i	−0.558899	+	0.829236i	$0.688776\pi$
$212$	−0.374231	+	4.03278i	−0.0257023	+	0.276972i
$213$		−	6.91517i		−	0.473820i
$214$	0.970938	−	20.9709i	0.0663720	−	1.43354i
$215$	−13.5790	+	15.8066i	−0.926082	+	1.07800i
$216$	2.20142	−	15.7586i	0.149788	−	1.07224i
$217$	−2.18965	−	2.18965i	−0.148643	−	0.148643i
$218$	6.64266	+	7.28763i	0.449898	+	0.493580i
$219$	−9.07520	−	9.07520i	−0.613245	−	0.613245i
$220$	−0.491663	+	29.1370i	−0.0331479	+	1.96441i
$221$	12.9523	−	12.9523i	0.871269	−	0.871269i
$222$	−0.00557469	+	0.120406i	−0.000374148	+	0.00808110i
$223$	14.7194	−	14.7194i	0.985681	−	0.985681i	−0.0142179	−	0.999899i	$-0.504526\pi$
$223$	14.7194	−	14.7194i	0.985681	−	0.985681i	0.999899	+	0.0142179i	$0.00452586\pi$
$224$	4.81054	−	2.97636i	0.321418	−	0.198866i
$225$	−0.567112	−	3.71913i	−0.0378075	−	0.247942i
$226$	−0.272953	−	0.299455i	−0.0181565	−	0.0199194i
$227$	16.4085			1.08907			0.544537	−	0.838737i	$-0.316705\pi$
$227$	16.4085			1.08907			0.544537	+	0.838737i	$0.316705\pi$
$228$	5.86440	+	7.06413i	0.388379	+	0.467834i
$229$	−6.27177	+	6.27177i	−0.414450	+	0.414450i	−0.883286	−	0.468835i	$-0.844674\pi$
$229$	−6.27177	+	6.27177i	−0.414450	+	0.414450i	0.468835	+	0.883286i	$0.344674\pi$
$230$	−29.6892	+	0.872923i	−1.95765	+	0.0575589i
$231$	9.76896			0.642751
$232$	−7.73590	−	10.2482i	−0.507887	−	0.672829i
$233$	15.8565	−	15.8565i	1.03880	−	1.03880i	0.0395804	−	0.999216i	$-0.487398\pi$
$233$	15.8565	−	15.8565i	1.03880	−	1.03880i	0.999216	−	0.0395804i	$-0.0126021\pi$
$234$	4.81265	+	0.222822i	0.314613	+	0.0145663i
$235$	−3.21436	+	0.243663i	−0.209682	+	0.0158948i
$236$	0.758201	+	0.913313i	0.0493547	+	0.0594516i
$237$			8.05062i			0.522944i
$238$	−0.264616	+	5.71534i	−0.0171525	+	0.370470i
$239$	9.46576			0.612289			0.306144	−	0.951985i	$-0.400961\pi$
$239$	9.46576			0.612289			0.306144	+	0.951985i	$0.400961\pi$
$240$	8.38975	+	10.4603i	0.541556	+	0.675210i
$241$	20.6573			1.33065			0.665326	−	0.746553i	$-0.268293\pi$
$241$	20.6573			1.33065			0.665326	+	0.746553i	$0.268293\pi$
$242$	−2.05772	+	44.4439i	−0.132275	+	2.85696i
$243$			7.61693i			0.488626i
$244$	12.7103	−	10.5517i	0.813696	−	0.675502i
$245$	−1.69613	−	1.45710i	−0.108362	−	0.0930908i
$246$	13.0372	+	0.603610i	0.831219	+	0.0384848i
$247$	−9.80315	+	9.80315i	−0.623759	+	0.623759i
$248$	1.21178	−	8.67439i	0.0769483	−	0.550824i
$249$	17.1521			1.08697
$250$	13.0077	+	8.98882i	0.822681	+	0.568503i
$251$	2.18738	−	2.18738i	0.138066	−	0.138066i	−0.634696	−	0.772762i	$-0.718875\pi$
$251$	2.18738	−	2.18738i	0.138066	−	0.138066i	0.772762	+	0.634696i	$0.218875\pi$
$252$	−1.15786	+	0.961214i	−0.0729382	+	0.0605508i
$253$	−61.2037			−3.84784
$254$	−15.2911	−	16.7758i	−0.959452	−	1.05261i
$255$	−13.5235	+	1.02514i	−0.846876	+	0.0641970i
$256$	14.9165	+	5.78778i	0.932281	+	0.361736i
$257$	16.4270	−	16.4270i	1.02469	−	1.02469i	0.0250030	−	0.999687i	$-0.492040\pi$
$257$	16.4270	−	16.4270i	1.02469	−	1.02469i	0.999687	−	0.0250030i	$-0.00795954\pi$
$258$	−0.913818	+	19.7372i	−0.0568919	+	1.22879i
$259$	0.0401999	−	0.0401999i	0.00249790	−	0.00249790i
$260$	−14.5572	+	14.0740i	−0.902797	+	0.872835i
$261$	2.41532	+	2.41532i	0.149504	+	0.149504i
$262$	15.6926	+	17.2163i	0.969493	+	1.06362i
$263$	−3.00845	−	3.00845i	−0.185509	−	0.185509i	0.608242	−	0.793751i	$-0.291875\pi$
$263$	−3.00845	−	3.00845i	−0.185509	−	0.185509i	−0.793751	+	0.608242i	$0.791875\pi$
$264$	16.6469	+	22.0532i	1.02455	+	1.35728i
$265$	3.43475	+	2.95071i	0.210995	+	0.181260i
$266$	0.200278	−	4.32573i	0.0122798	−	0.265227i
$267$		−	0.991580i		−	0.0606837i
$268$	4.81233	+	0.446571i	0.293960	+	0.0272787i
$269$	0.662450	+	0.662450i	0.0403903	+	0.0403903i	0.727013	−	0.686623i	$-0.240908\pi$
$269$	0.662450	+	0.662450i	0.0403903	+	0.0403903i	−0.686623	+	0.727013i	$0.740908\pi$
$270$	−12.9435	−	12.2041i	−0.787716	−	0.742718i
$271$			10.7048i			0.650268i	0.945668	+	0.325134i	$0.105409\pi$
$271$			10.7048i			0.650268i	−0.945668	+	0.325134i	$0.894591\pi$
$272$	−13.3531	+	9.14191i	−0.809653	+	0.554310i
$273$	4.79969	+	4.79969i	0.290491	+	0.290491i
$274$	−8.29734	−	9.10296i	−0.501261	−	0.549930i
$275$	26.2476	+	19.3020i	1.58279	+	1.16395i
$276$	−21.6689	+	17.9887i	−1.30431	+	1.08280i
$277$	25.8430			1.55275			0.776377	−	0.630269i	$-0.217055\pi$
$277$	25.8430			1.55275			0.776377	+	0.630269i	$0.217055\pi$
$278$	5.28796	+	5.80139i	0.317151	+	0.347944i
$279$			2.32999i			0.139493i
$280$	0.399059	−	6.31195i	0.0238484	−	0.377211i
$281$			5.20123i			0.310280i	0.987893	+	0.155140i	$0.0495828\pi$
$281$			5.20123i			0.310280i	−0.987893	+	0.155140i	$0.950417\pi$
$282$	−2.25893	+	2.05901i	−0.134517	+	0.122612i
$283$	−18.9019			−1.12360			−0.561800	−	0.827273i	$-0.689891\pi$
$283$	−18.9019			−1.12360			−0.561800	+	0.827273i	$0.689891\pi$
$284$	−9.18573	−	0.852412i	−0.545073	−	0.0505813i
$285$	10.2355	−	0.775893i	0.606296	−	0.0459599i
$286$	−30.8357	+	28.1067i	−1.82335	+	1.66198i
$287$	−4.35272	−	4.35272i	−0.256933	−	0.256933i
$288$	−4.14297	−	0.975868i	−0.244127	−	0.0575036i
$289$			0.632446i			0.0372027i
$290$	−14.3496	+	0.421906i	−0.842635	+	0.0247752i
$291$	17.7308	+	17.7308i	1.03940	+	1.03940i
$292$	−13.1737	+	10.9363i	−0.770931	+	0.640000i
$293$			4.94966i			0.289162i	0.989493	+	0.144581i	$0.0461834\pi$
$293$			4.94966i			0.289162i	−0.989493	+	0.144581i	$0.953817\pi$
$294$	−2.11791	−	0.0980575i	−0.123519	−	0.00571883i
$295$	1.32333	−	0.100314i	0.0770472	−	0.00584052i
$296$	0.159253	+	0.0222471i	0.00925639	+	0.00129309i
$297$	−25.9206	−	25.9206i	−1.50407	−	1.50407i
$298$	0.172697	−	0.157413i	0.0100041	−	0.00911871i
$299$	−30.0706	−	30.0706i	−1.73903	−	1.73903i
$300$	14.9660	−	0.880824i	0.864063	−	0.0508544i
$301$	6.58968	−	6.58968i	0.379823	−	0.379823i
$302$	−1.48526	−	0.0687665i	−0.0854673	−	0.00395707i
$303$	−2.78925	+	2.78925i	−0.160238	+	0.160238i
$304$	10.1065	−	6.91917i	0.579647	−	0.396842i
$305$	−1.39605	−	18.4164i	−0.0799374	−	1.05452i
$306$	3.18160	−	2.90003i	0.181880	−	0.165783i
$307$	−26.8194			−1.53066			−0.765332	−	0.643635i	$-0.777425\pi$
$307$	−26.8194			−1.53066			−0.765332	+	0.643635i	$0.777425\pi$
$308$	1.20419	−	12.9766i	0.0686151	−	0.739408i
$309$	−1.94769	+	1.94769i	−0.110800	+	0.110800i
$310$	−7.12480	−	6.71780i	−0.404662	−	0.381546i
$311$	−1.67923			−0.0952203			−0.0476102	−	0.998866i	$-0.515161\pi$
$311$	−1.67923			−0.0952203			−0.0476102	+	0.998866i	$0.515161\pi$
$312$	−2.65621	+	19.0141i	−0.150379	+	1.07646i
$313$	12.0341	−	12.0341i	0.680205	−	0.680205i	−0.279841	−	0.960046i	$-0.590282\pi$
$313$	12.0341	−	12.0341i	0.680205	−	0.680205i	0.960046	+	0.279841i	$0.0902819\pi$
$314$	0.131141	−	2.83247i	0.00740073	−	0.159846i
$315$	0.127174	+	1.67766i	0.00716544	+	0.0945254i
$316$	10.6940	+	0.992375i	0.601585	+	0.0558255i
$317$			0.438578i			0.0246330i	0.999924	+	0.0123165i	$0.00392056\pi$
$317$			0.438578i			0.0246330i	−0.999924	+	0.0123165i	$0.996079\pi$
$318$	4.28888	+	0.198572i	0.240508	+	0.0111353i
$319$	−29.5813			−1.65624
$320$	14.9291	−	9.85508i	0.834561	−	0.550916i
$321$	−22.2549			−1.24215
$322$	13.2689	+	0.614342i	0.739449	+	0.0342359i
$323$			12.3880i			0.689286i
$324$	−12.3003	−	1.14144i	−0.683351	−	0.0634132i
$325$	3.41254	+	22.3795i	0.189294	+	1.24139i
$326$	−1.07075	+	23.1267i	−0.0593032	+	1.28087i
$327$	7.39158	−	7.39158i	0.408755	−	0.408755i
$328$	2.40885	−	17.2434i	0.133007	−	0.952109i
$329$	1.44163			0.0794797
$330$	30.8788	−	0.907900i	1.69982	−	0.0499783i
$331$	−6.87097	+	6.87097i	−0.377663	+	0.377663i	−0.870258	−	0.492596i	$-0.836048\pi$
$331$	−6.87097	+	6.87097i	−0.377663	+	0.377663i	0.492596	+	0.870258i	$0.336048\pi$
$332$	2.11428	−	22.7839i	0.116036	−	1.25043i
$333$	−0.0427762			−0.00234412
$334$	−22.2471	+	20.2782i	−1.21731	+	1.10957i
$335$	3.52109	−	4.09870i	0.192378	−	0.223936i
$336$	−3.38768	−	4.94822i	−0.184813	−	0.269947i
$337$	10.4485	−	10.4485i	0.569165	−	0.569165i	−0.362729	−	0.931895i	$-0.618155\pi$
$337$	10.4485	−	10.4485i	0.569165	−	0.569165i	0.931895	+	0.362729i	$0.118155\pi$
$338$	−10.5945	−	0.490518i	−0.576266	−	0.0266807i
$339$	−0.303726	+	0.303726i	−0.0164961	+	0.0164961i
$340$	−0.305259	+	18.0903i	−0.0165550	+	0.981083i
$341$	−14.2681	−	14.2681i	−0.772662	−	0.772662i
$342$	−2.40804	+	2.19492i	−0.130212	+	0.118688i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	26.1052	+	3.64681i	1.40750	+	0.196623i
$345$	2.38001	+	31.3967i	0.128135	+	1.69034i
$346$	1.40761	+	0.0651712i	0.0756736	+	0.00350363i
$347$		−	8.10704i		−	0.435209i	−0.976037	−	0.217604i	$-0.930176\pi$
$347$		−	8.10704i		−	0.435209i	0.976037	−	0.217604i	$-0.0698243\pi$
$348$	−10.4731	+	8.69442i	−0.561418	+	0.466070i
$349$	8.68107	+	8.68107i	0.464687	+	0.464687i	0.900188	−	0.435501i	$-0.143429\pi$
$349$	8.68107	+	8.68107i	0.464687	+	0.464687i	−0.435501	+	0.900188i	$0.643429\pi$
$350$	−5.49674	−	4.44813i	−0.293813	−	0.237763i
$351$		−	25.4707i		−	1.35952i
$352$	31.3462	−	19.3944i	1.67076	−	1.03372i
$353$	−13.0485	−	13.0485i	−0.694503	−	0.694503i	0.268717	−	0.963219i	$-0.413400\pi$
$353$	−13.0485	−	13.0485i	−0.694503	−	0.694503i	−0.963219	+	0.268717i	$0.913400\pi$
$354$	0.929983	−	0.847679i	0.0494280	−	0.0450536i
$355$	−6.72102	+	7.82357i	−0.356715	+	0.415232i
$356$	−1.31716	−	0.122229i	−0.0698094	−	0.00647812i
$357$	6.06525			0.321007
$358$	14.4638	−	13.1837i	0.764433	−	0.696780i
$359$			9.35451i			0.493712i	0.969052	+	0.246856i	$0.0793975\pi$
$359$			9.35451i			0.493712i	−0.969052	+	0.246856i	$0.920603\pi$
$360$	−3.57056	+	3.14592i	−0.188185	+	0.165805i
$361$			9.62399i			0.506526i
$362$	−12.5980	−	13.8212i	−0.662137	−	0.726426i
$363$	47.1649			2.47552
$364$	6.96729	−	5.78401i	0.365185	−	0.303164i
$365$	1.44694	+	19.0878i	0.0757361	+	0.999099i
$366$	−11.7969	−	12.9423i	−0.616635	−	0.676506i
$367$	−13.9948	−	13.9948i	−0.730523	−	0.730523i	0.240200	−	0.970723i	$-0.422787\pi$
$367$	−13.9948	−	13.9948i	−0.730523	−	0.730523i	−0.970723	+	0.240200i	$0.922787\pi$
$368$	21.2242	+	31.0011i	1.10639	+	1.61605i
$369$			4.63168i			0.241116i
$370$	0.123332	−	0.130804i	0.00641173	−	0.00680019i
$371$	−1.43193	−	1.43193i	−0.0743420	−	0.0743420i
$372$	−9.24519	−	0.857929i	−0.479341	−	0.0444816i
$373$			35.5178i			1.83904i	0.393041	+	0.919521i	$0.371423\pi$
$373$			35.5178i			1.83904i	−0.393041	+	0.919521i	$0.628577\pi$
$374$	−1.72428	+	37.2420i	−0.0891602	+	1.92574i
$375$	8.88100	−	14.2153i	0.458613	−	0.734075i
$376$	2.45663	+	3.25444i	0.126691	+	0.167835i
$377$	−14.5339	−	14.5339i	−0.748535	−	0.748535i
$378$	5.35940	+	5.87977i	0.275658	+	0.302423i
$379$	17.8245	+	17.8245i	0.915581	+	0.915581i	0.996704	−	0.0811232i	$-0.0258507\pi$
$379$	17.8245	+	17.8245i	0.915581	+	0.915581i	−0.0811232	+	0.996704i	$0.525851\pi$
$380$	0.231039	−	13.6919i	0.0118521	−	0.702377i
$381$	−17.0151	+	17.0151i	−0.871711	+	0.871711i
$382$	1.15515	−	24.9498i	0.0591028	−	1.27654i
$383$	−23.9041	+	23.9041i	−1.22144	+	1.22144i	−0.254325	+	0.967119i	$0.581853\pi$
$383$	−23.9041	+	23.9041i	−1.22144	+	1.22144i	−0.967119	+	0.254325i	$0.918147\pi$
$384$	5.39765	−	16.0796i	0.275448	−	0.820561i
$385$	−11.0522	−	9.49469i	−0.563274	−	0.483894i
$386$	−8.33691	−	9.14637i	−0.424338	−	0.465538i
$387$	−7.01200			−0.356440
$388$	25.7382	−	21.3670i	1.30666	−	1.08474i
$389$	13.1717	−	13.1717i	0.667833	−	0.667833i	−0.289381	−	0.957214i	$-0.593449\pi$
$389$	13.1717	−	13.1717i	0.667833	−	0.667833i	0.957214	+	0.289381i	$0.0934495\pi$
$390$	15.6175	+	14.7253i	0.790822	+	0.745647i
$391$	−37.9995			−1.92172
$392$	−0.391322	+	2.80123i	−0.0197648	+	0.141483i
$393$	17.4619	−	17.4619i	0.880834	−	0.880834i
$394$	10.4632	+	0.484438i	0.527129	+	0.0244057i
$395$	7.82460	−	9.10818i	0.393698	−	0.458282i
$396$	−7.54478	+	6.26342i	−0.379140	+	0.314749i
$397$		−	18.1799i		−	0.912422i	−0.889872	−	0.456211i	$-0.849206\pi$
$397$		−	18.1799i		−	0.912422i	0.889872	−	0.456211i	$-0.150794\pi$
$398$	0.299110	−	6.46037i	0.0149930	−	0.323829i
$399$	−4.59057			−0.229816
$400$	0.674776	−	19.9886i	0.0337388	−	0.999431i
$401$	−30.8199			−1.53907			−0.769537	−	0.638602i	$-0.779513\pi$
$401$	−30.8199			−1.53907			−0.769537	+	0.638602i	$0.779513\pi$
$402$	0.236956	−	5.11793i	0.0118183	−	0.255259i
$403$		−	14.0205i		−	0.698408i
$404$	3.36126	+	4.04891i	0.167229	+	0.201441i
$405$	−8.99991	+	10.4763i	−0.447209	+	0.520571i
$406$	6.41322	+	0.296927i	0.318283	+	0.0147362i
$407$	0.261948	−	0.261948i	0.0129843	−	0.0129843i
$408$	10.3356	+	13.6921i	0.511686	+	0.677862i
$409$	−1.80173			−0.0890896			−0.0445448	−	0.999007i	$-0.514184\pi$
$409$	−1.80173			−0.0890896			−0.0445448	+	0.999007i	$0.514184\pi$
$410$	−14.1631	−	13.3540i	−0.699465	−	0.659508i
$411$	−9.23281	+	9.23281i	−0.455421	+	0.455421i
$412$	2.34711	+	2.82728i	0.115634	+	0.139290i
$413$	−0.593509			−0.0292046
$414$	−6.73281	−	7.38652i	−0.330899	−	0.363028i
$415$	−19.4052	−	16.6705i	−0.952565	−	0.818324i
$416$	24.9299	+	5.87218i	1.22229	+	0.287908i
$417$	5.88414	−	5.88414i	0.288148	−	0.288148i
$418$	1.30504	−	28.1871i	0.0638316	−	1.37868i
$419$	14.9957	−	14.9957i	0.732590	−	0.732590i	−0.238542	−	0.971132i	$-0.576670\pi$
$419$	14.9957	−	14.9957i	0.732590	−	0.732590i	0.971132	+	0.238542i	$0.0766696\pi$
$420$	−6.70363	−	0.113119i	−0.327104	−	0.00551962i
$421$	−10.6008	−	10.6008i	−0.516651	−	0.516651i	0.399905	−	0.916556i	$-0.369043\pi$
$421$	−10.6008	−	10.6008i	−0.516651	−	0.516651i	−0.916556	+	0.399905i	$0.869043\pi$
$422$	−5.29065	−	5.80434i	−0.257545	−	0.282551i
$423$	−0.767012	−	0.767012i	−0.0372934	−	0.0372934i
$424$	0.792448	−	5.67263i	0.0384847	−	0.275487i
$425$	16.2964	+	11.9840i	0.790490	+	0.581311i
$426$	−0.452300	+	9.76906i	−0.0219140	+	0.473313i
$427$			8.25970i			0.399715i
$428$	−2.74329	+	29.5621i	−0.132602	+	1.42894i
$429$	31.2755	+	31.2755i	1.51000	+	1.51000i
$430$	20.2170	−	21.4418i	0.974948	−	1.03402i
$431$		−	15.8901i		−	0.765398i	−0.923873	−	0.382699i	$-0.874995\pi$
$431$		−	15.8901i		−	0.765398i	0.923873	−	0.382699i	$-0.125005\pi$
$432$	−4.14067	+	22.1182i	−0.199218	+	1.06416i
$433$	−7.08471	−	7.08471i	−0.340470	−	0.340470i	0.516074	−	0.856544i	$-0.327393\pi$
$433$	−7.08471	−	7.08471i	−0.340470	−	0.340470i	−0.856544	+	0.516074i	$0.827393\pi$
$434$	2.95011	+	3.23654i	0.141610	+	0.155359i
$435$	1.15032	+	15.1748i	0.0551537	+	0.727578i
$436$	−8.90743	−	10.7297i	−0.426589	−	0.513860i
$437$	28.7604			1.37580
$438$	12.2270	+	13.4141i	0.584227	+	0.640951i
$439$		−	32.0379i		−	1.52909i	−0.644572	−	0.764543i	$-0.722965\pi$
$439$		−	32.0379i		−	1.52909i	0.644572	−	0.764543i	$-0.277035\pi$
$440$	2.60033	−	41.1297i	0.123966	−	1.96078i
$441$		−	0.752424i		−	0.0358297i
$442$	−19.1450	+	17.4506i	−0.910633	+	0.830041i
$443$	7.75382			0.368395			0.184198	−	0.982889i	$-0.441031\pi$
$443$	7.75382			0.368395			0.184198	+	0.982889i	$0.441031\pi$
$444$	0.0157507	−	0.169732i	0.000747496	−	0.00805514i
$445$	−0.963741	+	1.12184i	−0.0456857	+	0.0531802i
$446$	−21.7568	+	19.8313i	−1.03021	+	0.939039i
$447$	−0.175161	−	0.175161i	−0.00828481	−	0.00828481i
$448$	−6.99053	+	3.89006i	−0.330271	+	0.183788i
$449$			34.9777i			1.65070i	0.564623	+	0.825349i	$0.309022\pi$
$449$			34.9777i			1.65070i	−0.564623	+	0.825349i	$0.690978\pi$
$450$	0.557903	+	5.29111i	0.0262998	+	0.249425i
$451$	−28.3630	−	28.3630i	−1.33556	−	1.33556i
$452$	0.366014	+	0.440893i	0.0172158	+	0.0207378i
$453$			1.57620i			0.0740562i
$454$	−23.1804	−	1.07323i	−1.08791	−	0.0503693i
$455$	−0.765256	−	10.0951i	−0.0358758	−	0.473267i
$456$	−7.82260	−	10.3631i	−0.366327	−	0.485296i
$457$	23.9008	+	23.9008i	1.11803	+	1.11803i	0.992030	+	0.126005i	$0.0402155\pi$
$457$	23.9008	+	23.9008i	1.11803	+	1.11803i	0.126005	+	0.992030i	$0.459784\pi$
$458$	9.27035	−	8.44992i	0.433175	−	0.394839i
$459$	−16.0933	−	16.0933i	−0.751172	−	0.751172i
$460$	41.9990	+	0.708701i	1.95822	+	0.0330433i
$461$	27.8359	−	27.8359i	1.29645	−	1.29645i	0.365727	−	0.930722i	$-0.380820\pi$
$461$	27.8359	−	27.8359i	1.29645	−	1.29645i	0.930722	−	0.365727i	$-0.119180\pi$
$462$	−13.8006	−	0.638958i	−0.642063	−	0.0297270i
$463$	−4.60941	+	4.60941i	−0.214217	+	0.214217i	−0.806056	−	0.591839i	$-0.798402\pi$
$463$	−4.60941	+	4.60941i	−0.214217	+	0.214217i	0.591839	+	0.806056i	$0.298402\pi$
$464$	10.2582	+	14.9837i	0.476225	+	0.695599i
$465$	−6.76453	+	7.87421i	−0.313697	+	0.365158i
$466$	−23.4377	+	21.3634i	−1.08573	+	0.989641i
$467$	11.1586			0.516357			0.258179	−	0.966097i	$-0.416878\pi$
$467$	11.1586			0.516357			0.258179	+	0.966097i	$0.416878\pi$
$468$	−6.78426	−	0.629561i	−0.313602	−	0.0291015i
$469$	−1.70872	+	1.70872i	−0.0789016	+	0.0789016i
$470$	4.55687	−	0.133981i	0.210193	−	0.00618009i
$471$	−3.00589			−0.138504
$472$	−1.01137	−	1.33983i	−0.0465522	−	0.0616706i
$473$	42.9393	−	42.9393i	1.97435	−	1.97435i
$474$	0.526566	−	11.3731i	0.0241860	−	0.522384i
$475$	−12.3341	−	9.07027i	−0.565928	−	0.416173i
$476$	0.747645	−	8.05675i	0.0342683	−	0.369281i
$477$			1.52370i			0.0697654i
$478$	−13.3723	−	0.619126i	−0.611634	−	0.0283182i
$479$	9.53476			0.435654			0.217827	−	0.975987i	$-0.430103\pi$
$479$	9.53476			0.435654			0.217827	+	0.975987i	$0.430103\pi$
$480$	−11.1680	−	15.3260i	−0.509748	−	0.699534i
$481$	0.257401			0.0117365
$482$	−29.1825	−	1.35113i	−1.32923	−	0.0615422i
$483$		−	14.0813i		−	0.640722i
$484$	5.81388	−	62.6513i	0.264267	−	2.84779i
$485$	−2.82697	−	37.2929i	−0.128366	−	1.69339i
$486$	0.498200	−	10.7604i	0.0225988	−	0.488103i
$487$	−2.45779	+	2.45779i	−0.111373	+	0.111373i	−0.760597	−	0.649224i	$-0.775094\pi$
$487$	−2.45779	+	2.45779i	−0.111373	+	0.111373i	0.649224	+	0.760597i	$0.275094\pi$
$488$	−18.6460	+	14.0750i	−0.844067	+	0.637146i
$489$	24.5426			1.10985
$490$	2.30082	+	2.16939i	0.103940	+	0.0980028i
$491$	−13.1528	+	13.1528i	−0.593578	+	0.593578i	−0.938596	−	0.345018i	$-0.887873\pi$
$491$	−13.1528	+	13.1528i	−0.593578	+	0.593578i	0.345018	+	0.938596i	$0.387873\pi$
$492$	−18.3781	−	1.70544i	−0.828549	−	0.0768872i
$493$	−18.3662			−0.827170
$494$	14.4901	−	13.2077i	0.651941	−	0.594243i
$495$	0.828685	+	10.9319i	0.0372466	+	0.491351i
$496$	−2.27925	+	12.1750i	−0.102341	+	0.546676i
$497$	3.26160	−	3.26160i	0.146303	−	0.146303i
$498$	−24.2307	−	1.12186i	−1.08581	−	0.0502720i
$499$	−17.7630	+	17.7630i	−0.795182	+	0.795182i	−0.982331	−	0.187149i	$-0.940075\pi$
$499$	−17.7630	+	17.7630i	−0.795182	+	0.795182i	0.187149	+	0.982331i	$0.440075\pi$
$500$	−17.7881	−	13.5493i	−0.795508	−	0.605943i
$501$	22.5644	+	22.5644i	1.00811	+	1.00811i
$502$	−3.23319	+	2.94705i	−0.144304	+	0.131533i
$503$	20.5073	+	20.5073i	0.914374	+	0.914374i	0.996613	−	0.0822385i	$-0.0262069\pi$
$503$	20.5073	+	20.5073i	0.914374	+	0.914374i	−0.0822385	+	0.996613i	$0.526207\pi$
$504$	1.69858	−	1.28218i	0.0756606	−	0.0571126i
$505$	5.86660	−	0.444714i	0.261060	−	0.0197895i
$506$	86.4624	+	4.00314i	3.84372	+	0.177961i
$507$			11.2432i			0.499327i
$508$	20.5045	+	24.6993i	0.909742	+	1.09586i
$509$	22.7398	+	22.7398i	1.00793	+	1.00793i	0.999968	+	0.00795736i	$0.00253293\pi$
$509$	22.7398	+	22.7398i	1.00793	+	1.00793i	0.00795736	+	0.999968i	$0.497467\pi$
$510$	19.1717	−	0.563688i	0.848939	−	0.0249605i
$511$		−	8.56079i		−	0.378707i
$512$	−20.6940	−	9.15204i	−0.914553	−	0.404467i
$513$	12.1804	+	12.1804i	0.537780	+	0.537780i
$514$	−24.2809	+	22.1320i	−1.07099	+	0.976202i
$515$	4.09654	−	0.310536i	0.180515	−	0.0136839i
$516$	2.58190	−	27.8230i	0.113662	−	1.22484i
$517$	9.39389			0.413143
$518$	−0.0594197	+	0.0541610i	−0.00261075	+	0.00237970i
$519$		−	1.49379i		−	0.0655701i
$520$	21.4855	−	18.9303i	0.942199	−	0.830147i
$521$			6.98989i			0.306233i	0.988208	+	0.153116i	$0.0489309\pi$
$521$			6.98989i			0.306233i	−0.988208	+	0.153116i	$0.951069\pi$
$522$	−3.25414	−	3.57010i	−0.142430	−	0.156259i
$523$	−15.1506			−0.662488			−0.331244	−	0.943545i	$-0.607468\pi$
$523$	−15.1506			−0.662488			−0.331244	+	0.943545i	$0.607468\pi$
$524$	−21.0429	−	25.3478i	−0.919263	−	1.10733i
$525$	−4.44087	+	6.03888i	−0.193816	+	0.263558i
$526$	4.05326	+	4.44681i	0.176731	+	0.193890i
$527$	−8.85865	−	8.85865i	−0.385889	−	0.385889i
$528$	−22.0746	−	32.2433i	−0.960675	−	1.40321i
$529$			65.2211i			2.83570i
$530$	−4.65928	−	4.39312i	−0.202386	−	0.190825i
$531$	0.315773	+	0.315773i	0.0137034	+	0.0137034i
$532$	−0.565865	+	6.09786i	−0.0245334	+	0.264376i
$533$		−	27.8706i		−	1.20721i
$534$	−0.0648562	+	1.40081i	−0.00280660	+	0.0606188i
$535$	25.1783	+	21.6300i	1.08855	+	0.935149i
$536$	−6.76917	−	0.945631i	−0.292384	−	0.0408450i
$537$	−14.6701	−	14.6701i	−0.633061	−	0.633061i
$538$	−0.892515	−	0.979173i	−0.0384791	−	0.0422151i
$539$	4.60762	+	4.60762i	0.198464	+	0.198464i
$540$	17.4870	+	18.0873i	0.752523	+	0.778355i
$541$	15.5236	−	15.5236i	0.667411	−	0.667411i	−0.289705	−	0.957116i	$-0.593557\pi$
$541$	15.5236	−	15.5236i	0.667411	−	0.667411i	0.957116	+	0.289705i	$0.0935571\pi$
$542$	0.700166	−	15.1226i	0.0300747	−	0.649573i
$543$	−14.0184	+	14.0184i	−0.601585	+	0.601585i
$544$	19.4619	−	12.0414i	0.834423	−	0.516270i
$545$	−15.5466	+	1.17850i	−0.665944	+	0.0504815i
$546$	−6.46660	−	7.09446i	−0.276745	−	0.303615i
$547$	16.4945			0.705255			0.352628	−	0.935764i	$-0.385288\pi$
$547$	16.4945			0.705255			0.352628	+	0.935764i	$0.385288\pi$
$548$	11.1263	+	13.4025i	0.475290	+	0.572524i
$549$	4.39453	−	4.39453i	0.187554	−	0.187554i
$550$	−35.8176	−	28.9847i	−1.52727	−	1.23591i
$551$	13.9007			0.592188
$552$	31.7882	−	23.9954i	1.35300	−	1.02131i
$553$	−3.79715	+	3.79715i	−0.161471	+	0.161471i
$554$	−36.5084	−	1.69031i	−1.55109	−	0.0718144i
$555$	−0.144563	−	0.124190i	−0.00613634	−	0.00527157i
$556$	−7.09085	−	8.54149i	−0.300719	−	0.362240i
$557$			23.1857i			0.982408i	0.871045	+	0.491204i	$0.163443\pi$
$557$			23.1857i			0.982408i	−0.871045	+	0.491204i	$0.836557\pi$
$558$	0.152397	−	3.29157i	0.00645149	−	0.139343i
$559$	42.1940			1.78462
$560$	−0.976597	+	8.89080i	−0.0412687	+	0.375705i
$561$	39.5221			1.66863
$562$	0.340197	−	7.34778i	0.0143503	−	0.309948i
$563$			13.8217i			0.582514i	0.956645	+	0.291257i	$0.0940735\pi$
$563$			13.8217i			0.582514i	−0.956645	+	0.291257i	$0.905926\pi$
$564$	3.32586	−	2.76102i	0.140044	−	0.116260i
$565$	0.638823	−	0.0484257i	0.0268755	−	0.00203728i
$566$	26.7027	+	1.23631i	1.12240	+	0.0519662i
$567$	4.36750	−	4.36750i	0.183418	−	0.183418i
$568$	12.9209	+	1.80501i	0.542150	+	0.0757366i
$569$	−42.5836			−1.78520			−0.892599	−	0.450851i	$-0.851121\pi$
$569$	−42.5836			−1.78520			−0.892599	+	0.450851i	$0.851121\pi$
$570$	−14.5104	+	0.426635i	−0.607773	+	0.0178698i
$571$	−20.0975	+	20.0975i	−0.841055	+	0.841055i	−0.988996	−	0.147941i	$-0.952735\pi$
$571$	−20.0975	+	20.0975i	−0.841055	+	0.841055i	0.147941	+	0.988996i	$0.452735\pi$
$572$	45.4000	−	37.6895i	1.89827	−	1.57588i
$573$	−26.4773			−1.10610
$574$	5.86439	+	6.43378i	0.244775	+	0.268541i
$575$	27.8226	−	37.8343i	1.16028	−	1.57780i
$576$	5.78895	+	1.64959i	0.241206	+	0.0687328i
$577$	1.63064	−	1.63064i	0.0678843	−	0.0678843i	−0.672350	−	0.740234i	$-0.734715\pi$
$577$	1.63064	−	1.63064i	0.0678843	−	0.0678843i	0.740234	+	0.672350i	$0.234715\pi$
$578$	0.0413663	−	0.893456i	0.00172061	−	0.0371629i
$579$	−9.27684	+	9.27684i	−0.385532	+	0.385532i
$580$	20.2992	+	0.342533i	0.842879	+	0.0142229i
$581$	8.08993	+	8.08993i	0.335627	+	0.335627i
$582$	−23.8886	−	26.2080i	−0.990213	−	1.08636i
$583$	−9.33067	−	9.33067i	−0.386437	−	0.386437i
$584$	19.3258	−	14.5881i	0.799706	−	0.603660i
$585$	−4.96391	+	5.77821i	−0.205232	+	0.238900i
$586$	0.323742	−	6.99238i	0.0133736	−	0.288853i
$587$		−	4.84652i		−	0.200037i	−0.994986	−	0.100019i	$-0.968110\pi$
$587$		−	4.84652i		−	0.200037i	0.994986	−	0.100019i	$-0.0318903\pi$
$588$	2.98556	+	0.277052i	0.123122	+	0.0114254i
$589$	6.70478	+	6.70478i	0.276266	+	0.276266i
$590$	−1.87603	+	0.0551590i	−0.0772348	+	0.00227086i
$591$		−	11.1038i		−	0.456750i
$592$	−0.223522	−	0.0418448i	−0.00918668	−	0.00171981i
$593$	−15.1360	−	15.1360i	−0.621562	−	0.621562i	0.324369	−	0.945931i	$-0.394848\pi$
$593$	−15.1360	−	15.1360i	−0.621562	−	0.621562i	−0.945931	+	0.324369i	$0.894848\pi$
$594$	34.9227	+	38.3135i	1.43289	+	1.57202i
$595$	−6.86200	−	5.89497i	−0.281315	−	0.241670i
$596$	−0.254265	+	0.211082i	−0.0104151	+	0.00864626i
$597$	−6.85590			−0.280593
$598$	40.5140	+	44.4476i	1.65674	+	1.81760i
$599$		−	13.8402i		−	0.565493i	−0.959195	−	0.282747i	$-0.908754\pi$
$599$		−	13.8402i		−	0.565493i	0.959195	−	0.282747i	$-0.0912456\pi$
$600$	−21.2001	+	0.265460i	−0.865491	+	0.0108373i
$601$			43.8765i			1.78976i	0.446308	+	0.894880i	$0.352739\pi$
$601$			43.8765i			1.78976i	−0.446308	+	0.894880i	$0.647261\pi$
$602$	−9.74025	+	8.87823i	−0.396983	+	0.361850i
$603$	1.81823			0.0740442
$604$	2.09373	+	0.194293i	0.0851928	+	0.00790567i
$605$	−53.3607	−	45.8408i	−2.16942	−	1.86369i
$606$	4.12281	−	3.75794i	0.167478	−	0.152656i
$607$	24.1522	+	24.1522i	0.980306	+	0.980306i	0.999810	−	0.0195041i	$-0.00620873\pi$
$607$	24.1522	+	24.1522i	0.980306	+	0.980306i	−0.0195041	+	0.999810i	$0.506209\pi$
$608$	−14.7300	+	9.11368i	−0.597381	+	0.369609i
$609$		−	6.80587i		−	0.275788i
$610$	0.767634	+	26.1082i	0.0310806	+	1.05709i
$611$	4.61542	+	4.61542i	0.186720	+	0.186720i
$612$	−4.68433	+	3.88877i	−0.189353	+	0.157194i
$613$		−	5.96484i		−	0.240918i	−0.992718	−	0.120459i	$-0.961563\pi$
$613$		−	5.96484i		−	0.240918i	0.992718	−	0.120459i	$-0.0384366\pi$
$614$	37.8878	+	1.75417i	1.52903	+	0.0707927i
$615$	−13.4469	+	15.6528i	−0.542232	+	0.631182i
$616$	−2.54992	+	18.2532i	−0.102739	+	0.735443i
$617$	3.07621	+	3.07621i	0.123844	+	0.123844i	0.766312	−	0.642468i	$-0.222090\pi$
$617$	3.07621	+	3.07621i	0.123844	+	0.123844i	−0.642468	+	0.766312i	$0.722090\pi$
$618$	2.87889	−	2.62410i	0.115806	−	0.105557i
$619$	−15.6071	−	15.6071i	−0.627303	−	0.627303i	0.320085	−	0.947389i	$-0.396288\pi$
$619$	−15.6071	−	15.6071i	−0.627303	−	0.627303i	−0.947389	+	0.320085i	$0.896288\pi$
$620$	9.62582	+	9.95625i	0.386582	+	0.399853i
$621$	−37.3629	+	37.3629i	−1.49932	+	1.49932i
$622$	2.37225	+	0.109833i	0.0951184	+	0.00440391i
$623$	0.467687	−	0.467687i	0.0187375	−	0.0187375i
$624$	4.99609	−	26.6876i	0.200004	−	1.06836i
$625$	−23.8638	+	7.45101i	−0.954553	+	0.298040i
$626$	−17.7876	+	16.2134i	−0.710936	+	0.648018i
$627$	−29.9128			−1.19460
$628$	−0.370526	+	3.99285i	−0.0147856	+	0.159332i
$629$	0.162636	−	0.162636i	0.00648472	−	0.00648472i
$630$	−0.0699282	−	2.37835i	−0.00278601	−	0.0947556i
$631$	−37.5365			−1.49431			−0.747153	−	0.664652i	$-0.768580\pi$
$631$	−37.5365			−1.49431			−0.747153	+	0.664652i	$0.768580\pi$
$632$	−15.0425	−	2.10139i	−0.598359	−	0.0835888i
$633$	−5.88714	+	5.88714i	−0.233993	+	0.233993i
$634$	0.0286860	−	0.619579i	0.00113927	−	0.0246066i
$635$	35.7877	−	2.71287i	1.42019	−	0.107657i
$636$	−6.04591	−	0.561044i	−0.239736	−	0.0222469i
$637$			4.52764i			0.179391i
$638$	41.7895	+	1.93482i	1.65446	+	0.0766004i
$639$	−3.47063			−0.137296
$640$	−21.7349	+	12.9458i	−0.859148	+	0.511728i
$641$	−4.04175			−0.159639			−0.0798197	−	0.996809i	$-0.525434\pi$
$641$	−4.04175			−0.159639			−0.0798197	+	0.996809i	$0.525434\pi$
$642$	31.4395	+	1.45562i	1.24082	+	0.0574488i
$643$		−	1.46953i		−	0.0579527i	−0.999580	−	0.0289764i	$-0.990775\pi$
$643$		−	1.46953i		−	0.0579527i	0.999580	−	0.0289764i	$-0.00922476\pi$
$644$	−18.7049	−	1.73576i	−0.737075	−	0.0683986i
$645$	−23.6971	−	20.3576i	−0.933073	−	0.801579i
$646$	0.810260	−	17.5005i	0.0318793	−	0.688549i
$647$	−19.4003	+	19.4003i	−0.762704	+	0.762704i	−0.976810	−	0.214106i	$-0.931316\pi$
$647$	−19.4003	+	19.4003i	−0.762704	+	0.762704i	0.214106	+	0.976810i	$0.431316\pi$
$648$	17.3020	+	2.41703i	0.679687	+	0.0949501i
$649$	−3.86739			−0.151808
$650$	−3.35712	−	31.8387i	−0.131677	−	1.24882i
$651$	3.28271	−	3.28271i	0.128660	−	0.128660i
$652$	3.02529	−	32.6010i	0.118479	−	1.27675i
$653$	39.0943			1.52988			0.764938	−	0.644104i	$-0.222769\pi$
$653$	39.0943			1.52988			0.764938	+	0.644104i	$0.222769\pi$
$654$	−10.9255	+	9.95863i	−0.427223	+	0.389413i
$655$	−36.7273	+	2.78409i	−1.43505	+	0.108783i
$656$	−4.53083	+	24.2022i	−0.176899	+	0.944939i
$657$	−4.55472	+	4.55472i	−0.177697	+	0.177697i
$658$	−2.03659	−	0.0942927i	−0.0793947	−	0.00367591i
$659$	−9.77637	+	9.77637i	−0.380833	+	0.380833i	−0.871402	−	0.490569i	$-0.836789\pi$
$659$	−9.77637	+	9.77637i	−0.380833	+	0.380833i	0.490569	+	0.871402i	$0.336789\pi$
$660$	−43.6819	−	0.737098i	−1.70032	−	0.0286915i
$661$	−21.1413	−	21.1413i	−0.822301	−	0.822301i	0.164137	−	0.986438i	$-0.447516\pi$
$661$	−21.1413	−	21.1413i	−0.822301	−	0.822301i	−0.986438	+	0.164137i	$0.947516\pi$
$662$	10.1560	−	9.25721i	0.394725	−	0.359792i
$663$	19.4180	+	19.4180i	0.754134	+	0.754134i
$664$	−4.47707	+	32.0485i	−0.173744	+	1.24372i
$665$	5.19360	+	4.46168i	0.201399	+	0.173017i
$666$	0.0604300	+	0.00279786i	0.00234161	+	0.000108415i
$667$			42.6395i			1.65101i
$668$	32.7548	−	27.1919i	1.26732	−	1.05209i
$669$	22.0671	+	22.0671i	0.853165	+	0.853165i
$670$	−5.24232	+	5.55993i	−0.202529	+	0.214799i
$671$			53.8215i			2.07775i
$672$	4.46213	+	7.21192i	0.172130	+	0.278206i
$673$	18.4068	+	18.4068i	0.709529	+	0.709529i	0.966436	−	0.256907i	$-0.0827035\pi$
$673$	18.4068	+	18.4068i	0.709529	+	0.709529i	−0.256907	+	0.966436i	$0.582704\pi$
$674$	−15.4440	+	14.0772i	−0.594880	+	0.542232i
$675$	27.8066	−	4.24009i	1.07028	−	0.163201i
$676$	14.9348	+	1.38591i	0.574416	+	0.0533042i
$677$	2.02158			0.0776957			0.0388478	−	0.999245i	$-0.487631\pi$
$677$	2.02158			0.0776957			0.0388478	+	0.999245i	$0.487631\pi$
$678$	0.448940	−	0.409208i	0.0172414	−	0.0157155i
$679$			16.7258i			0.641876i
$680$	1.61447	−	25.5362i	0.0619120	−	0.979267i
$681$			24.5996i			0.942657i
$682$	19.2233	+	21.0898i	0.736100	+	0.807571i
$683$	−25.5458			−0.977484			−0.488742	−	0.872428i	$-0.662544\pi$
$683$	−25.5458			−0.977484			−0.488742	+	0.872428i	$0.662544\pi$
$684$	3.54540	−	2.94326i	0.135562	−	0.112539i
$685$	19.4192	−	1.47207i	0.741971	−	0.0562447i
$686$	−0.952680	−	1.04518i	−0.0363735	−	0.0399051i
$687$	−9.40259	−	9.40259i	−0.358731	−	0.358731i
$688$	−36.6403	−	6.85932i	−1.39690	−	0.261509i
$689$		−	9.16870i		−	0.349300i
$690$	−1.30868	−	44.5098i	−0.0498206	−	1.69446i
$691$	−19.3712	−	19.3712i	−0.736914	−	0.736914i	0.235066	−	0.971980i	$-0.424469\pi$
$691$	−19.3712	−	19.3712i	−0.736914	−	0.736914i	−0.971980	+	0.235066i	$0.924469\pi$
$692$	−1.98427	−	0.184135i	−0.0754306	−	0.00699976i
$693$		−	4.90291i		−	0.186246i
$694$	−0.530257	+	11.4528i	−0.0201283	+	0.434743i
$695$	−12.3760	+	0.938159i	−0.469450	+	0.0355864i
$696$	15.3641	−	11.5976i	0.582373	−	0.439606i
$697$	−17.6097	−	17.6097i	−0.667016	−	0.667016i
$698$	−11.6959	−	12.8316i	−0.442698	−	0.485681i
$699$	23.7720	+	23.7720i	0.899140	+	0.899140i
$700$	7.47430	+	6.64340i	0.282502	+	0.251097i
$701$	16.0114	−	16.0114i	0.604743	−	0.604743i	−0.336824	−	0.941567i	$-0.609353\pi$
$701$	16.0114	−	16.0114i	0.604743	−	0.604743i	0.941567	+	0.336824i	$0.109353\pi$
$702$	−1.66596	+	35.9824i	−0.0628776	+	1.35807i
$703$	−0.123093	+	0.123093i	−0.00464254	+	0.00464254i
$704$	−45.5513	+	25.3482i	−1.71678	+	0.955346i
$705$	−0.365298	−	4.81895i	−0.0137579	−	0.181492i
$706$	17.5802	+	19.2871i	0.661639	+	0.725880i
$707$	−2.63115			−0.0989545
$708$	−1.36923	+	1.13669i	−0.0514589	+	0.0427194i
$709$	25.7852	−	25.7852i	0.968382	−	0.968382i	−0.0311331	−	0.999515i	$-0.509912\pi$
$709$	25.7852	−	25.7852i	0.968382	−	0.968382i	0.999515	+	0.0311331i	$0.00991158\pi$
$710$	10.0065	−	10.6128i	0.375537	−	0.398290i
$711$	4.04050			0.151531
$712$	1.85276	+	0.258824i	0.0694351	+	0.00969985i
$713$	−20.5666	+	20.5666i	−0.770224	+	0.770224i
$714$	−8.56839	−	0.396710i	−0.320664	−	0.0148465i
$715$	−4.98653	−	65.7815i	−0.186486	−	2.46009i
$716$	−21.2953	+	17.6786i	−0.795841	+	0.660680i
$717$			14.1910i			0.529972i
$718$	0.611850	−	13.2151i	0.0228340	−	0.493184i
$719$	−8.83171			−0.329367			−0.164684	−	0.986346i	$-0.552660\pi$
$719$	−8.83171			−0.329367			−0.164684	+	0.986346i	$0.552660\pi$
$720$	5.24989	−	4.21071i	0.195652	−	0.156924i
$721$	−1.83729			−0.0684241
$722$	0.629475	−	13.5958i	0.0234266	−	0.505984i
$723$			30.9692i			1.15176i
$724$	16.8932	+	20.3492i	0.627831	+	0.756272i
$725$	13.4474	−	18.2863i	0.499423	−	0.679135i
$726$	−66.6299	−	3.08491i	−2.47287	−	0.114492i
$727$	20.2766	−	20.2766i	0.752019	−	0.752019i	−0.222837	−	0.974856i	$-0.571532\pi$
$727$	20.2766	−	20.2766i	0.752019	−	0.752019i	0.974856	+	0.222837i	$0.0715317\pi$
$728$	−10.2210	+	7.71536i	−0.378816	+	0.285950i
$729$	−29.9490			−1.10922
$730$	−0.795617	−	27.0599i	−0.0294471	−	1.00153i
$731$	26.6597	−	26.6597i	0.986046	−	0.986046i
$732$	15.8190	+	19.0552i	0.584687	+	0.704301i
$733$	29.7000			1.09700			0.548498	−	0.836152i	$-0.315200\pi$
$733$	29.7000			1.09700			0.548498	+	0.836152i	$0.315200\pi$
$734$	18.8551	+	20.6858i	0.695955	+	0.763528i
$735$	2.18447	−	2.54282i	0.0805755	−	0.0937935i
$736$	−27.9557	−	45.1835i	−1.03046	−	1.66549i
$737$	−11.1343	+	11.1343i	−0.410138	+	0.410138i
$738$	0.302944	−	6.54317i	0.0111515	−	0.240858i
$739$	−16.4057	+	16.4057i	−0.603492	+	0.603492i	−0.941237	−	0.337746i	$-0.890336\pi$
$739$	−16.4057	+	16.4057i	−0.603492	+	0.603492i	0.337746	+	0.941237i	$0.390336\pi$
$740$	−0.182787	+	0.176720i	−0.00671938	+	0.00649637i
$741$	−14.6968	−	14.6968i	−0.539900	−	0.539900i
$742$	1.92923	+	2.11654i	0.0708242	+	0.0777008i
$743$	−31.6104	−	31.6104i	−1.15967	−	1.15967i	−0.984546	−	0.175127i	$-0.943966\pi$
$743$	−31.6104	−	31.6104i	−1.15967	−	1.15967i	−0.175127	−	0.984546i	$-0.556034\pi$
$744$	13.0046	+	1.81670i	0.476771	+	0.0666033i
$745$	0.0279273	+	0.368413i	0.00102318	+	0.0134976i
$746$	2.32311	−	50.1760i	0.0850551	−	1.83707i
$747$		−	8.60840i		−	0.314965i
$748$	4.87177	−	52.4990i	0.178130	−	1.91955i
$749$	−10.4967	−	10.4967i	−0.383541	−	0.383541i
$750$	−13.4760	+	19.5011i	−0.492073	+	0.712079i
$751$			15.5494i			0.567406i	0.958912	+	0.283703i	$0.0915630\pi$
$751$			15.5494i			0.567406i	−0.958912	+	0.283703i	$0.908437\pi$
$752$	−3.25761	−	4.75823i	−0.118793	−	0.173515i
$753$	3.27931	+	3.27931i	0.119505	+	0.119505i
$754$	19.5815	+	21.4827i	0.713114	+	0.782353i
$755$	1.53194	−	1.78325i	0.0557532	−	0.0648991i
$756$	−7.18665	−	8.65689i	−0.261376	−	0.314848i
$757$	−9.99591			−0.363307			−0.181654	−	0.983363i	$-0.558145\pi$
$757$	−9.99591			−0.363307			−0.181654	+	0.983363i	$0.558145\pi$
$758$	−24.0148	−	26.3465i	−0.872256	−	0.956946i
$759$		−	91.7560i		−	3.33053i
$760$	−1.22193	+	19.3274i	−0.0443241	+	0.701078i
$761$			22.3436i			0.809954i	0.914327	+	0.404977i	$0.132721\pi$
$761$			22.3436i			0.809954i	−0.914327	+	0.404977i	$0.867279\pi$
$762$	25.1502	−	22.9244i	0.911094	−	0.830462i
$763$	6.97261			0.252425
$764$	−3.26377	+	35.1710i	−0.118079	+	1.27244i
$765$	0.514506	+	6.78728i	0.0186020	+	0.245394i
$766$	35.3329	−	32.2059i	1.27663	−	1.16365i
$767$	−1.90013	−	1.90013i	−0.0686097	−	0.0686097i
$768$	−8.67699	+	22.3627i	−0.313104	+	0.806944i
$769$		−	21.0383i		−	0.758661i	−0.925261	−	0.379331i	$-0.876154\pi$
$769$		−	21.0383i		−	0.758661i	0.925261	−	0.379331i	$-0.123846\pi$
$770$	14.9925	+	14.1360i	0.540292	+	0.509428i
$771$	24.6273	+	24.6273i	0.886930	+	0.886930i
$772$	11.1793	+	13.4664i	0.402353	+	0.484666i
$773$			28.7945i			1.03567i	0.855482	+	0.517833i	$0.173261\pi$
$773$			28.7945i			1.03567i	−0.855482	+	0.517833i	$0.826739\pi$
$774$	9.90585	+	0.458633i	0.356059	+	0.0164852i
$775$	15.3063	−	2.33398i	0.549817	−	0.0838390i
$776$	−37.7579	+	28.5017i	−1.35543	+	1.02315i
$777$	0.0602673	+	0.0602673i	0.00216208	+	0.00216208i
$778$	−19.4692	+	17.7462i	−0.698005	+	0.636231i
$779$	13.3281	+	13.3281i	0.477530	+	0.477530i
$780$	−21.0997	−	21.8240i	−0.755490	−	0.781424i
$781$	21.2531	−	21.2531i	0.760495	−	0.760495i
$782$	53.6819	+	2.48543i	1.91966	+	0.0888789i
$783$	−18.0584	+	18.0584i	−0.645356	+	0.645356i
$784$	0.736041	−	3.93170i	0.0262872	−	0.140418i
$785$	3.40075	+	2.92149i	0.121378	+	0.104273i
$786$	−25.8105	+	23.5262i	−0.920630	+	0.839153i
$787$	−8.49013			−0.302641			−0.151320	−	0.988485i	$-0.548352\pi$
$787$	−8.49013			−0.302641			−0.151320	+	0.988485i	$0.548352\pi$
$788$	−14.7497	−	1.36873i	−0.525436	−	0.0487591i
$789$	4.51024	−	4.51024i	0.160569	−	0.160569i
$790$	−11.6495	+	12.3553i	−0.414472	+	0.439583i
$791$	−0.286510			−0.0101871
$792$	11.0682	−	8.35485i	0.393291	−	0.296877i
$793$	−26.4436	+	26.4436i	−0.939040	+	0.939040i
$794$	−1.18909	+	25.6827i	−0.0421992	+	0.911446i
$795$	−4.42368	+	5.14935i	−0.156892	+	0.182629i
$796$	−0.845106	+	9.10700i	−0.0299540	+	0.322789i
$797$		−	0.638385i		−	0.0226127i	−0.999936	−	0.0113064i	$-0.996401\pi$
$797$		−	0.638385i		−	0.0226127i	0.999936	−	0.0113064i	$-0.00359901\pi$
$798$	6.48509	+	0.300255i	0.229570	+	0.0106289i
$799$	5.83239			0.206335
$800$	−2.26065	+	28.1938i	−0.0799261	+	0.996801i
$801$	−0.497661			−0.0175840
$802$	43.5393	+	2.01584i	1.53743	+	0.0711817i
$803$		−	55.7834i		−	1.96855i
$804$	−0.669496	+	7.21460i	−0.0236113	+	0.254439i
$805$	−13.6860	+	15.9311i	−0.482367	+	0.561497i
$806$	−0.917035	+	19.8067i	−0.0323012	+	0.697661i
$807$	−0.993140	+	0.993140i	−0.0349602	+	0.0349602i
$808$	−4.48363	−	5.93975i	−0.157734	−	0.208960i
$809$	6.48957			0.228161			0.114081	−	0.993472i	$-0.463608\pi$
$809$	6.48957			0.228161			0.114081	+	0.993472i	$0.463608\pi$
$810$	13.3994	−	14.2112i	0.470807	−	0.499331i
$811$	−2.81055	+	2.81055i	−0.0986917	+	0.0986917i	−0.754729	−	0.656037i	$-0.772232\pi$
$811$	−2.81055	+	2.81055i	−0.0986917	+	0.0986917i	0.656037	+	0.754729i	$0.272232\pi$
$812$	−9.04054	−	0.838938i	−0.317261	−	0.0294410i
$813$	−16.0485			−0.562845
$814$	−0.387188	+	0.352921i	−0.0135709	+	0.0123699i
$815$	−27.7666	−	23.8535i	−0.972620	−	0.835553i
$816$	−13.7055	−	20.0189i	−0.479788	−	0.700802i
$817$	−20.1778	+	20.1778i	−0.705931	+	0.705931i
$818$	2.54530	+	0.117845i	0.0889943	+	0.00412037i
$819$	2.40890	−	2.40890i	0.0841739	−	0.0841739i
$820$	19.1348	+	19.7916i	0.668215	+	0.691153i
$821$	5.43611	+	5.43611i	0.189722	+	0.189722i	0.795576	−	0.605854i	$-0.207168\pi$
$821$	5.43611	+	5.43611i	0.189722	+	0.189722i	−0.605854	+	0.795576i	$0.707168\pi$
$822$	13.6471	−	12.4393i	0.475997	−	0.433870i
$823$	23.6739	+	23.6739i	0.825220	+	0.825220i	0.986851	−	0.161631i	$-0.0516754\pi$
$823$	23.6739	+	23.6739i	0.825220	+	0.825220i	−0.161631	+	0.986851i	$0.551675\pi$
$824$	−3.13084	−	4.14762i	−0.109068	−	0.144489i
$825$	−28.9374	+	39.3503i	−1.00747	+	1.37000i
$826$	0.838450	+	0.0388196i	0.0291734	+	0.00135071i
$827$			22.9305i			0.797372i	0.917087	+	0.398686i	$0.130534\pi$
$827$			22.9305i			0.797372i	−0.917087	+	0.398686i	$0.869466\pi$
$828$	9.02831	+	10.8753i	0.313755	+	0.377943i
$829$	16.4609	+	16.4609i	0.571710	+	0.571710i	0.932606	−	0.360896i	$-0.117529\pi$
$829$	16.4609	+	16.4609i	0.571710	+	0.571710i	−0.360896	+	0.932606i	$0.617529\pi$
$830$	26.3234	+	24.8197i	0.913699	+	0.861504i
$831$			38.7436i			1.34400i
$832$	−34.8344	−	9.92623i	−1.20767	−	0.344130i
$833$	2.86073	+	2.86073i	0.0991184	+	0.0991184i
$834$	−8.69739	+	7.92766i	−0.301166	+	0.274513i
$835$	−3.59764	−	47.4595i	−0.124502	−	1.64240i
$836$	−3.68726	+	39.7346i	−0.127527	+	1.37425i
$837$	−17.4205			−0.602139
$838$	−22.1653	+	20.2037i	−0.765688	+	0.697924i
$839$		−	7.58620i		−	0.261905i	−0.991389	−	0.130952i	$-0.958196\pi$
$839$		−	7.58620i		−	0.261905i	0.991389	−	0.130952i	$-0.0418035\pi$
$840$	9.46283	+	0.598267i	0.326499	+	0.0206422i
$841$		−	8.39120i		−	0.289352i
$842$	14.2824	+	15.6691i	0.492203	+	0.539993i
$843$	−7.79765			−0.268565
$844$	7.09446	+	8.54584i	0.244201	+	0.294160i
$845$	10.9275	−	12.7201i	0.375918	−	0.437585i
$846$	1.03339	+	1.13373i	0.0355287	+	0.0389783i
$847$	22.2458	+	22.2458i	0.764373	+	0.764373i
$848$	−1.49052	+	7.96190i	−0.0511847	+	0.273413i
$849$		−	28.3376i		−	0.972543i
$850$	−22.2381	−	17.9957i	−0.762759	−	0.617249i
$851$	−0.377582	−	0.377582i	−0.0129433	−	0.0129433i
$852$	1.27793	−	13.7712i	0.0437811	−	0.471793i
$853$		−	20.7591i		−	0.710779i	−0.934718	−	0.355390i	$-0.884348\pi$
$853$		−	20.7591i		−	0.710779i	0.934718	−	0.355390i	$-0.115652\pi$
$854$	0.540242	−	11.6685i	0.0184867	−	0.399287i
$855$	−0.389410	−	5.13704i	−0.0133175	−	0.175683i
$856$	5.80901	−	41.5830i	0.198548	−	1.42128i
$857$	−1.67934	−	1.67934i	−0.0573651	−	0.0573651i	0.677842	−	0.735207i	$-0.262915\pi$
$857$	−1.67934	−	1.67934i	−0.0573651	−	0.0573651i	−0.735207	+	0.677842i	$0.762915\pi$
$858$	−42.1373	−	46.2286i	−1.43854	−	1.57822i
$859$	27.2997	+	27.2997i	0.931455	+	0.931455i	0.997797	−	0.0663419i	$-0.0211328\pi$
$859$	27.2997	+	27.2997i	0.931455	+	0.931455i	−0.0663419	+	0.997797i	$0.521133\pi$
$860$	−29.9629	+	28.9685i	−1.02173	+	0.987818i
$861$	6.52556	−	6.52556i	0.222390	−	0.222390i
$862$	−1.03932	+	22.4479i	−0.0353994	+	0.764579i
$863$	22.4493	−	22.4493i	0.764182	−	0.764182i	−0.212893	−	0.977075i	$-0.568289\pi$
$863$	22.4493	−	22.4493i	0.764182	−	0.764182i	0.977075	+	0.212893i	$0.0682887\pi$
$864$	7.29621	−	30.9755i	0.248222	−	1.05381i
$865$	−1.45185	+	1.69002i	−0.0493644	+	0.0574623i
$866$	9.54519	+	10.4720i	0.324359	+	0.355852i
$867$	−0.948157			−0.0322011
$868$	−3.95592	−	4.76522i	−0.134273	−	0.161742i
$869$	−24.7428	+	24.7428i	−0.839341	+	0.839341i
$870$	−0.632519	−	21.5127i	−0.0214444	−	0.729350i
$871$	−10.9410			−0.370723
$872$	11.8817	+	15.7405i	0.402366	+	0.533039i
$873$	8.89885	−	8.89885i	0.301180	−	0.301180i
$874$	−40.6299	−	1.88113i	−1.37433	−	0.0636302i
$875$	10.8936	−	2.51597i	0.368270	−	0.0850553i
$876$	−16.3956	−	19.7499i	−0.553958	−	0.667286i
$877$			0.119947i			0.00405033i	0.999998	+	0.00202517i	$0.000644631\pi$
$877$			0.119947i			0.00405033i	−0.999998	+	0.00202517i	$0.999355\pi$
$878$	−2.09550	+	45.2600i	−0.0707198	+	1.52745i
$879$	−7.42048			−0.250287
$880$	−6.36365	+	57.9338i	−0.214519	+	1.95295i
$881$	−11.2764			−0.379910			−0.189955	−	0.981793i	$-0.560834\pi$
$881$	−11.2764			−0.379910			−0.189955	+	0.981793i	$0.560834\pi$
$882$	−0.0492138	+	1.06295i	−0.00165711	+	0.0357914i
$883$		−	33.6385i		−	1.13203i	−0.824397	−	0.566013i	$-0.808485\pi$
$883$		−	33.6385i		−	1.13203i	0.824397	−	0.566013i	$-0.191515\pi$
$884$	28.1875	−	23.4003i	0.948047	−	0.787036i
$885$	0.150390	+	1.98392i	0.00505531	+	0.0666889i
$886$	−10.9538	−	0.507153i	−0.368001	−	0.0170382i
$887$	−9.14070	+	9.14070i	−0.306915	+	0.306915i	−0.843711	−	0.536797i	$-0.819634\pi$
$887$	−9.14070	+	9.14070i	−0.306915	+	0.306915i	0.536797	+	0.843711i	$0.319634\pi$
$888$	−0.0333527	+	0.238751i	−0.00111924	+	0.00801195i
$889$	−16.0507			−0.538322
$890$	1.43485	−	1.52178i	0.0480964	−	0.0510103i
$891$	28.4593	−	28.4593i	0.953423	−	0.953423i
$892$	32.0329	−	26.5926i	1.07254	−	0.890387i
$893$	−4.41432			−0.147719
$894$	0.235993	+	0.258906i	0.00789278	+	0.00865912i
$895$	2.33898	+	30.8554i	0.0781833	+	1.03138i
$896$	10.1300	−	5.03825i	0.338418	−	0.168316i
$897$	45.0817	−	45.0817i	1.50523	−	1.50523i
$898$	2.28778	−	49.4129i	0.0763442	−	1.64893i
$899$	−9.94035	+	9.94035i	−0.331529	+	0.331529i
$900$	−0.442074	−	7.51125i	−0.0147358	−	0.250375i
$901$	−5.79313	−	5.79313i	−0.192997	−	0.192997i
$902$	38.2133	+	41.9235i	1.27236	+	1.39590i
$903$	9.87919	+	9.87919i	0.328759	+	0.328759i
$904$	−0.488230	−	0.646789i	−0.0162383	−	0.0215119i
$905$	29.4846	−	2.23507i	0.980102	−	0.0742961i
$906$	0.103094	−	2.22669i	0.00342507	−	0.0739769i
$907$			3.21386i			0.106715i	0.998575	+	0.0533573i	$0.0169922\pi$
$907$			3.21386i			0.106715i	−0.998575	+	0.0533573i	$0.983008\pi$
$908$	32.6767	+	3.03231i	1.08441	+	0.100631i
$909$	1.39989	+	1.39989i	0.0464313	+	0.0464313i
$910$	0.420786	+	14.3115i	0.0139489	+	0.474420i
$911$		−	14.8814i		−	0.493044i	−0.969137	−	0.246522i	$-0.920712\pi$
$911$		−	14.8814i		−	0.493044i	0.969137	−	0.246522i	$-0.0792878\pi$
$912$	10.3732	+	15.1516i	0.343490	+	0.501719i
$913$	52.7152	+	52.7152i	1.74462	+	1.74462i
$914$	−32.2015	−	35.3280i	−1.06513	−	1.16855i
$915$	27.6097	−	2.09294i	0.912750	−	0.0691905i
$916$	−13.6489	+	11.3309i	−0.450973	+	0.374382i
$917$	16.4721			0.543956
$918$	21.6824	+	23.7877i	0.715627	+	0.785110i
$919$		−	38.7160i		−	1.27712i	−0.769571	−	0.638561i	$-0.779530\pi$
$919$		−	38.7160i		−	1.27712i	0.769571	−	0.638561i	$-0.220470\pi$
$920$	−59.2857	−	3.74821i	−1.95459	−	0.123575i
$921$		−	40.2074i		−	1.32488i
$922$	−41.1445	+	37.5032i	−1.35502	+	1.23510i
$923$	20.8842			0.687411
$924$	19.4543	+	1.80531i	0.640001	+	0.0593904i
$925$	0.0428495	+	0.281008i	0.00140888	+	0.00923948i
$926$	6.81320	−	6.21023i	0.223896	−	0.204081i
$927$	0.977518	+	0.977518i	0.0321059	+	0.0321059i
$928$	−13.5117	−	21.8384i	−0.443544	−	0.716880i
$929$		−	49.3741i		−	1.61991i	−0.586491	−	0.809956i	$-0.699491\pi$
$929$		−	49.3741i		−	1.61991i	0.586491	−	0.809956i	$-0.300509\pi$
$930$	10.0713	−	10.6814i	0.330250	−	0.350258i
$931$	−2.16518	−	2.16518i	−0.0709609	−	0.0709609i
$932$	34.5077	−	28.6471i	1.13034	−	0.938368i
$933$		−	2.51749i		−	0.0824188i
$934$	−15.7637	−	0.729848i	−0.515805	−	0.0238813i
$935$	−44.7139	−	38.4125i	−1.46230	−	1.25622i
$936$	9.54295	+	1.33312i	0.311921	+	0.0435743i
$937$	3.16703	+	3.16703i	0.103462	+	0.103462i	0.756943	−	0.653481i	$-0.226692\pi$
$937$	3.16703	+	3.16703i	0.103462	+	0.103462i	−0.653481	+	0.756943i	$0.726692\pi$
$938$	2.52568	−	2.30215i	0.0824663	−	0.0751680i
$939$	18.0414	+	18.0414i	0.588757	+	0.588757i
$940$	−6.44625	−	0.108775i	−0.210254	−	0.00354786i
$941$	−21.3053	+	21.3053i	−0.694533	+	0.694533i	−0.963226	−	0.268693i	$-0.913408\pi$
$941$	−21.3053	+	21.3053i	−0.694533	+	0.694533i	0.268693	+	0.963226i	$0.413408\pi$
$942$	4.24642	+	0.196606i	0.138356	+	0.00640576i
$943$	−40.8834	+	40.8834i	−1.33135	+	1.33135i
$944$	1.34113	+	1.95893i	0.0436502	+	0.0637577i
$945$	−12.5432	+	0.950834i	−0.408032	+	0.0309306i
$946$	−63.4689	+	57.8519i	−2.06355	+	1.88093i
$947$	−17.8040			−0.578551			−0.289276	−	0.957246i	$-0.593414\pi$
$947$	−17.8040			−0.578551			−0.289276	+	0.957246i	$0.593414\pi$
$948$	−1.48776	+	16.0324i	−0.0483202	+	0.520707i
$949$	27.4076	−	27.4076i	0.889687	−	0.889687i
$950$	16.8312	+	13.6203i	0.546075	+	0.441901i
$951$	−0.657513			−0.0213213
$952$	−1.58317	+	11.3329i	−0.0513107	+	0.367301i
$953$	−12.3661	+	12.3661i	−0.400578	+	0.400578i	−0.878437	−	0.477859i	$-0.841413\pi$
$953$	−12.3661	+	12.3661i	−0.400578	+	0.400578i	0.477859	+	0.878437i	$0.341413\pi$
$954$	0.0996605	−	2.15253i	0.00322663	−	0.0696907i
$955$	29.9554	+	25.7339i	0.969334	+	0.832730i
$956$	18.8505	+	1.74928i	0.609669	+	0.0565757i
$957$		−	44.3481i		−	1.43357i
$958$	−13.4698	−	0.623639i	−0.435188	−	0.0201489i
$959$	−8.70947			−0.281243
$960$	14.7746	+	22.3816i	0.476850	+	0.722362i
$961$	21.4108			0.690672
$962$	−0.363631	−	0.0168358i	−0.0117239	−	0.000542809i
$963$			11.1694i			0.359930i
$964$	41.1378	+	3.81748i	1.32496	+	0.122953i
$965$	19.5119	−	1.47909i	0.628109	−	0.0476135i
$966$	−0.921016	+	19.8927i	−0.0296332	+	0.640037i
$967$	24.9169	−	24.9169i	0.801274	−	0.801274i	−0.182021	−	0.983295i	$-0.558264\pi$
$967$	24.9169	−	24.9169i	0.801274	−	0.801274i	0.983295	+	0.182021i	$0.0582637\pi$
$968$	−12.3111	+	88.1273i	−0.395694	+	2.83252i
$969$	−18.5720			−0.596618
$970$	1.55445	+	52.8686i	0.0499102	+	1.69751i
$971$	−6.29760	+	6.29760i	−0.202100	+	0.202100i	−0.800899	−	0.598799i	$-0.795645\pi$
$971$	−6.29760	+	6.29760i	−0.202100	+	0.202100i	0.598799	+	0.800899i	$0.295645\pi$
$972$	−1.40761	+	15.1687i	−0.0451492	+	0.486536i
$973$	5.55061			0.177944
$974$	3.63288	−	3.31137i	0.116405	−	0.106103i
$975$	−33.5511	+	5.11605i	−1.07450	+	0.163845i
$976$	27.2619	−	18.6642i	0.872631	−	0.597427i
$977$	9.95163	−	9.95163i	0.318381	−	0.318381i	−0.529764	−	0.848145i	$-0.677720\pi$
$977$	9.95163	−	9.95163i	0.318381	−	0.318381i	0.848145	+	0.529764i	$0.177720\pi$
$978$	−34.6713	−	1.60525i	−1.10867	−	0.0513304i
$979$	3.04752	−	3.04752i	0.0973992	−	0.0973992i
$980$	−3.10847	−	3.21518i	−0.0992966	−	0.102705i
$981$	−3.70974	−	3.70974i	−0.118443	−	0.118443i
$982$	19.4413	−	17.7207i	0.620396	−	0.565490i
$983$	32.6745	+	32.6745i	1.04216	+	1.04216i	0.999071	+	0.0430848i	$0.0137186\pi$
$983$	32.6745	+	32.6745i	1.04216	+	1.04216i	0.0430848	+	0.999071i	$0.486281\pi$
$984$	25.8512	+	3.61133i	0.824106	+	0.115125i
$985$	−10.7921	+	12.5624i	−0.343864	+	0.400273i
$986$	25.9459	+	1.20127i	0.826285	+	0.0382563i
$987$			2.16128i			0.0687944i
$988$	−21.3340	+	17.7108i	−0.678726	+	0.563455i
$989$	−61.8943	−	61.8943i	−1.96812	−	1.96812i
$990$	−0.455663	−	15.4977i	−0.0144819	−	0.492548i
$991$		−	16.5711i		−	0.526397i	−0.964742	−	0.263199i	$-0.915223\pi$
$991$		−	16.5711i		−	0.526397i	0.964742	−	0.263199i	$-0.0847775\pi$
$992$	4.01623	−	17.0506i	0.127515	−	0.541357i
$993$	−10.3009	−	10.3009i	−0.326889	−	0.326889i
$994$	−4.82099	+	4.39433i	−0.152913	+	0.139380i
$995$	7.75651	+	6.66342i	0.245898	+	0.211244i
$996$	34.1574	+	3.16972i	1.08232	+	0.100436i
$997$	−59.4554			−1.88297			−0.941486	−	0.337053i	$-0.890570\pi$
$997$	−59.4554			−1.88297			−0.941486	+	0.337053i	$0.890570\pi$
$998$	26.2556	−	23.9320i	0.831108	−	0.757554i
$999$		−	0.319822i		−	0.0101187i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.1	✓	144
5.2	odd	4		560.2.bl.a.267.38	yes	144
16.3	odd	4		560.2.bl.a.323.38	yes	144
80.67	even	4	inner	560.2.t.a.547.1	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.1	✓	144	1.1	even	1	trivial
560.2.t.a.547.1	yes	144	80.67	even	4	inner
560.2.bl.a.267.38	yes	144	5.2	odd	4
560.2.bl.a.323.38	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)

\(f(q)\)	\(=\)	\(q+(-1.41270 - 0.0654069i) q^{2} +1.49919i q^{3} +(1.99144 + 0.184801i) q^{4} +(1.45710 - 1.69613i) q^{5} +(0.0980575 - 2.11791i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.80123 - 0.391322i) q^{8} +0.752424 q^{9} +O(q^{10})\)	\(q+(-1.41270 - 0.0654069i) q^{2} +1.49919i q^{3} +(1.99144 + 0.184801i) q^{4} +(1.45710 - 1.69613i) q^{5} +(0.0980575 - 2.11791i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.80123 - 0.391322i) q^{8} +0.752424 q^{9} +(-2.16939 + 2.30082i) q^{10} +(-4.60762 + 4.60762i) q^{11} +(-0.277052 + 2.98556i) q^{12} -4.52764 q^{13} +(1.04518 - 0.952680i) q^{14} +(2.54282 + 2.18447i) q^{15} +(3.93170 + 0.736041i) q^{16} +(-2.86073 + 2.86073i) q^{17} +(-1.06295 - 0.0492138i) q^{18} +(2.16518 - 2.16518i) q^{19} +(3.21518 - 3.10847i) q^{20} +(-1.06009 - 1.06009i) q^{21} +(6.81055 - 6.20781i) q^{22} +(6.64158 + 6.64158i) q^{23} +(0.586667 - 4.19957i) q^{24} +(-0.753713 - 4.94287i) q^{25} +(6.39619 + 0.296139i) q^{26} +5.62560i q^{27} +(-1.53884 + 1.27749i) q^{28} +(3.21005 + 3.21005i) q^{29} +(-3.44937 - 3.25232i) q^{30} +3.09664i q^{31} +(-5.50617 - 1.29696i) q^{32} +(-6.90770 - 6.90770i) q^{33} +(4.22847 - 3.85424i) q^{34} +(0.169019 + 2.22967i) q^{35} +(1.49841 + 0.139049i) q^{36} -0.0568512 q^{37} +(-3.20037 + 2.91713i) q^{38} -6.78779i q^{39} +(-4.74540 + 4.18105i) q^{40} +6.15567i q^{41} +(1.42825 + 1.56692i) q^{42} -9.31921 q^{43} +(-10.0273 + 8.32432i) q^{44} +(1.09636 - 1.27621i) q^{45} +(-8.94815 - 9.81696i) q^{46} +(-1.01939 - 1.01939i) q^{47} +(-1.10347 + 5.89437i) q^{48} -1.00000i q^{49} +(0.741474 + 7.03208i) q^{50} +(-4.28878 - 4.28878i) q^{51} +(-9.01653 - 0.836710i) q^{52} +2.02505i q^{53} +(0.367953 - 7.94729i) q^{54} +(1.10135 + 14.5289i) q^{55} +(2.25747 - 1.70406i) q^{56} +(3.24602 + 3.24602i) q^{57} +(-4.32487 - 4.74479i) q^{58} +(0.419674 + 0.419674i) q^{59} +(4.66020 + 4.82017i) q^{60} +(5.84049 - 5.84049i) q^{61} +(0.202542 - 4.37462i) q^{62} +(-0.532044 + 0.532044i) q^{63} +(7.69373 + 2.19236i) q^{64} +(-6.59722 + 7.67946i) q^{65} +(9.30670 + 10.2103i) q^{66} +2.41650 q^{67} +(-6.22565 + 5.16832i) q^{68} +(-9.95700 + 9.95700i) q^{69} +(-0.0929372 - 3.16091i) q^{70} -4.61260 q^{71} +(-2.10771 - 0.294440i) q^{72} +(-6.05340 + 6.05340i) q^{73} +(0.0803137 + 0.00371846i) q^{74} +(7.41030 - 1.12996i) q^{75} +(4.71196 - 3.91171i) q^{76} -6.51615i q^{77} +(-0.443969 + 9.58912i) q^{78} +5.36998 q^{79} +(6.97730 - 5.59618i) q^{80} -6.17658 q^{81} +(0.402624 - 8.69612i) q^{82} -11.4409i q^{83} +(-1.91520 - 2.30701i) q^{84} +(0.683797 + 9.02054i) q^{85} +(13.1653 + 0.609541i) q^{86} +(-4.81247 + 4.81247i) q^{87} +(14.7100 - 11.1039i) q^{88} -0.661410 q^{89} +(-1.63230 + 1.73119i) q^{90} +(3.20152 - 3.20152i) q^{91} +(11.9990 + 14.4537i) q^{92} -4.64246 q^{93} +(1.37341 + 1.50676i) q^{94} +(-0.517541 - 6.82731i) q^{95} +(1.94440 - 8.25480i) q^{96} +(11.8269 - 11.8269i) q^{97} +(-0.0654069 + 1.41270i) q^{98} +(-3.46688 + 3.46688i) 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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