LMFDB - Embedded newform 840.2.bj.b.13.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39560 - 0.228667i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.89542 + 0.638257i) q^{4} +(-1.53990 - 1.62133i) q^{5} +(0.825150 + 1.14853i) q^{6} +(0.369731 + 2.61979i) q^{7} +(-2.49931 - 1.32417i) q^{8} +1.00000i q^{9} +(1.77834 + 2.61486i) q^{10} -1.17840i q^{11} +(-0.888951 - 1.79158i) q^{12} +(2.75196 + 2.75196i) q^{13} +(0.0830611 - 3.74074i) q^{14} +(-0.0575851 + 2.23533i) q^{15} +(3.18526 + 2.41953i) q^{16} +(-2.48718 - 2.48718i) q^{17} +(0.228667 - 1.39560i) q^{18} -7.80855i q^{19} +(-1.88393 - 4.05596i) q^{20} +(1.59103 - 2.11391i) q^{21} +(-0.269461 + 1.64458i) q^{22} +(2.76897 + 2.76897i) q^{23} +(0.830949 + 2.70361i) q^{24} +(-0.257443 + 4.99337i) q^{25} +(-3.21136 - 4.46992i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.971302 + 5.20159i) q^{28} +0.471378 q^{29} +(0.591511 - 3.10646i) q^{30} -10.8187i q^{31} +(-3.89209 - 4.10507i) q^{32} +(-0.833256 + 0.833256i) q^{33} +(2.90238 + 4.03985i) q^{34} +(3.67821 - 4.63366i) q^{35} +(-0.638257 + 1.89542i) q^{36} +(-4.80321 - 4.80321i) q^{37} +(-1.78556 + 10.8976i) q^{38} -3.89186i q^{39} +(1.70175 + 6.09131i) q^{40} +1.37639i q^{41} +(-2.70383 + 2.58637i) q^{42} +(-8.65392 + 8.65392i) q^{43} +(0.752122 - 2.23357i) q^{44} +(1.62133 - 1.53990i) q^{45} +(-3.23122 - 4.49756i) q^{46} +(-1.61919 - 1.61919i) q^{47} +(-0.541449 - 3.96318i) q^{48} +(-6.72660 + 1.93723i) q^{49} +(1.50111 - 6.90990i) q^{50} +3.51740i q^{51} +(3.45967 + 6.97258i) q^{52} +(4.32457 - 4.32457i) q^{53} +(-1.14853 + 0.825150i) q^{54} +(-1.91058 + 1.81462i) q^{55} +(2.54498 - 7.03726i) q^{56} +(-5.52148 + 5.52148i) q^{57} +(-0.657857 - 0.107788i) q^{58} -0.533140i q^{59} +(-1.53586 + 4.20014i) q^{60} +5.79323 q^{61} +(-2.47388 + 15.0986i) q^{62} +(-2.61979 + 0.369731i) q^{63} +(4.49313 + 6.61905i) q^{64} +(0.224113 - 8.69957i) q^{65} +(1.35343 - 0.972357i) q^{66} +(-6.76168 - 6.76168i) q^{67} +(-3.12680 - 6.30172i) q^{68} -3.91592i q^{69} +(-6.19288 + 5.62567i) q^{70} -10.7753 q^{71} +(1.32417 - 2.49931i) q^{72} +(-0.365295 + 0.365295i) q^{73} +(5.60505 + 7.80172i) q^{74} +(3.71288 - 3.34880i) q^{75} +(4.98386 - 14.8005i) q^{76} +(3.08716 - 0.435691i) q^{77} +(-0.889938 + 5.43149i) q^{78} -12.6470i q^{79} +(-0.982095 - 8.89019i) q^{80} -1.00000 q^{81} +(0.314734 - 1.92089i) q^{82} +(-9.82093 - 9.82093i) q^{83} +(4.36490 - 2.99127i) q^{84} +(-0.202550 + 7.86254i) q^{85} +(14.0563 - 10.0986i) q^{86} +(-0.333314 - 0.333314i) q^{87} +(-1.56041 + 2.94519i) q^{88} -2.61406 q^{89} +(-2.61486 + 1.77834i) q^{90} +(-6.19207 + 8.22703i) q^{91} +(3.48106 + 7.01568i) q^{92} +(-7.64998 + 7.64998i) q^{93} +(1.88949 + 2.63001i) q^{94} +(-12.6603 + 12.0243i) q^{95} +(-0.150600 + 5.65485i) q^{96} +(-7.43586 - 7.43586i) q^{97} +(9.83065 - 1.16546i) q^{98} +1.17840 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.39560	−	0.228667i	−0.986841	−	0.161692i
$2$	−1.39560	−	0.228667i	−0.986841	−	0.161692i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.89542	+	0.638257i	0.947712	+	0.319128i
$5$	−1.53990	−	1.62133i	−0.688662	−	0.725082i
$5$	−1.53990	−	1.62133i	−0.688662	−	0.725082i
$6$	0.825150	+	1.14853i	0.336866	+	0.468887i
$7$	0.369731	+	2.61979i	0.139745	+	0.990188i
$7$	0.369731	+	2.61979i	0.139745	+	0.990188i
$8$	−2.49931	−	1.32417i	−0.883640	−	0.468166i
$9$			1.00000i			0.333333i
$10$	1.77834	+	2.61486i	0.562361	+	0.826892i
$11$		−	1.17840i		−	0.355301i	−0.984094	−	0.177651i	$-0.943150\pi$
$11$		−	1.17840i		−	0.355301i	0.984094	−	0.177651i	$-0.0568497\pi$
$12$	−0.888951	−	1.79158i	−0.256618	−	0.517185i
$13$	2.75196	+	2.75196i	0.763256	+	0.763256i	0.976909	−	0.213654i	$-0.0685364\pi$
$13$	2.75196	+	2.75196i	0.763256	+	0.763256i	−0.213654	+	0.976909i	$0.568536\pi$
$14$	0.0830611	−	3.74074i	0.0221990	−	0.999754i
$15$	−0.0575851	+	2.23533i	−0.0148684	+	0.577159i
$16$	3.18526	+	2.41953i	0.796314	+	0.604883i
$17$	−2.48718	−	2.48718i	−0.603230	−	0.603230i	0.337939	−	0.941168i	$-0.390270\pi$
$17$	−2.48718	−	2.48718i	−0.603230	−	0.603230i	−0.941168	+	0.337939i	$0.890270\pi$
$18$	0.228667	−	1.39560i	0.0538973	−	0.328947i
$19$		−	7.80855i		−	1.79140i	−0.444655	−	0.895702i	$-0.646674\pi$
$19$		−	7.80855i		−	1.79140i	0.444655	−	0.895702i	$-0.353326\pi$
$20$	−1.88393	−	4.05596i	−0.421259	−	0.906940i
$21$	1.59103	−	2.11391i	0.347192	−	0.461293i
$22$	−0.269461	+	1.64458i	−0.0574493	+	0.350626i
$23$	2.76897	+	2.76897i	0.577370	+	0.577370i	0.934178	−	0.356808i	$-0.116135\pi$
$23$	2.76897	+	2.76897i	0.577370	+	0.577370i	−0.356808	+	0.934178i	$0.616135\pi$
$24$	0.830949	+	2.70361i	0.169617	+	0.551873i
$25$	−0.257443	+	4.99337i	−0.0514886	+	0.998674i
$26$	−3.21136	−	4.46992i	−0.629800	−	0.876624i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−0.971302	+	5.20159i	−0.183559	+	0.983009i
$29$	0.471378			0.0875327			0.0437663	−	0.999042i	$-0.486064\pi$
$29$	0.471378			0.0875327			0.0437663	+	0.999042i	$0.486064\pi$
$30$	0.591511	−	3.10646i	0.107995	−	0.567160i
$31$		−	10.8187i		−	1.94310i	−0.236841	−	0.971548i	$-0.576112\pi$
$31$		−	10.8187i		−	1.94310i	0.236841	−	0.971548i	$-0.423888\pi$
$32$	−3.89209	−	4.10507i	−0.688031	−	0.725681i
$33$	−0.833256	+	0.833256i	−0.145051	+	0.145051i
$34$	2.90238	+	4.03985i	0.497755	+	0.692829i
$35$	3.67821	−	4.63366i	0.621730	−	0.783231i
$36$	−0.638257	+	1.89542i	−0.106376	+	0.315904i
$37$	−4.80321	−	4.80321i	−0.789643	−	0.789643i	0.191792	−	0.981436i	$-0.438570\pi$
$37$	−4.80321	−	4.80321i	−0.789643	−	0.789643i	−0.981436	+	0.191792i	$0.938570\pi$
$38$	−1.78556	+	10.8976i	−0.289655	+	1.76783i
$39$		−	3.89186i		−	0.623196i
$40$	1.70175	+	6.09131i	0.269071	+	0.963120i
$41$			1.37639i			0.214956i	0.994207	+	0.107478i	$0.0342775\pi$
$41$			1.37639i			0.214956i	−0.994207	+	0.107478i	$0.965723\pi$
$42$	−2.70383	+	2.58637i	−0.417210	+	0.399085i
$43$	−8.65392	+	8.65392i	−1.31971	+	1.31971i	−0.405707	+	0.914003i	$0.632975\pi$
$43$	−8.65392	+	8.65392i	−1.31971	+	1.31971i	−0.914003	+	0.405707i	$0.867025\pi$
$44$	0.752122	−	2.23357i	0.113387	−	0.336723i
$45$	1.62133	−	1.53990i	0.241694	−	0.229554i
$46$	−3.23122	−	4.49756i	−0.476417	−	0.663129i
$47$	−1.61919	−	1.61919i	−0.236183	−	0.236183i	0.579084	−	0.815268i	$-0.303410\pi$
$47$	−1.61919	−	1.61919i	−0.236183	−	0.236183i	−0.815268	+	0.579084i	$0.803410\pi$
$48$	−0.541449	−	3.96318i	−0.0781514	−	0.572036i
$49$	−6.72660	+	1.93723i	−0.960943	+	0.276748i
$50$	1.50111	−	6.90990i	0.212288	−	0.977207i
$51$			3.51740i			0.492535i
$52$	3.45967	+	6.97258i	0.479770	+	0.966923i
$53$	4.32457	−	4.32457i	0.594025	−	0.594025i	−0.344691	−	0.938716i	$-0.612016\pi$
$53$	4.32457	−	4.32457i	0.594025	−	0.594025i	0.938716	+	0.344691i	$0.112016\pi$
$54$	−1.14853	+	0.825150i	−0.156296	+	0.112289i
$55$	−1.91058	+	1.81462i	−0.257623	+	0.244683i
$56$	2.54498	−	7.03726i	0.340088	−	0.940394i
$57$	−5.52148	+	5.52148i	−0.731338	+	0.731338i
$58$	−0.657857	−	0.107788i	−0.0863808	−	0.0141533i
$59$		−	0.533140i		−	0.0694090i	−0.999398	−	0.0347045i	$-0.988951\pi$
$59$		−	0.533140i		−	0.0694090i	0.999398	−	0.0347045i	$-0.0110490\pi$
$60$	−1.53586	+	4.20014i	−0.198279	+	0.542235i
$61$	5.79323			0.741748			0.370874	−	0.928683i	$-0.379058\pi$
$61$	5.79323			0.741748			0.370874	+	0.928683i	$0.379058\pi$
$62$	−2.47388	+	15.0986i	−0.314183	+	1.91753i
$63$	−2.61979	+	0.369731i	−0.330063	+	0.0465817i
$64$	4.49313	+	6.61905i	0.561641	+	0.827381i
$65$	0.224113	−	8.69957i	0.0277978	−	1.07905i
$66$	1.35343	−	0.972357i	0.166596	−	0.119689i
$67$	−6.76168	−	6.76168i	−0.826070	−	0.826070i	0.160900	−	0.986971i	$-0.448560\pi$
$67$	−6.76168	−	6.76168i	−0.826070	−	0.826070i	−0.986971	+	0.160900i	$0.948560\pi$
$68$	−3.12680	−	6.30172i	−0.379180	−	0.764195i
$69$		−	3.91592i		−	0.471421i
$70$	−6.19288	+	5.62567i	−0.740191	+	0.672396i
$71$	−10.7753			−1.27879			−0.639395	−	0.768879i	$-0.720815\pi$
$71$	−10.7753			−1.27879			−0.639395	+	0.768879i	$0.720815\pi$
$72$	1.32417	−	2.49931i	0.156055	−	0.294547i
$73$	−0.365295	+	0.365295i	−0.0427545	+	0.0427545i	−0.728161	−	0.685406i	$-0.759625\pi$
$73$	−0.365295	+	0.365295i	−0.0427545	+	0.0427545i	0.685406	+	0.728161i	$0.259625\pi$
$74$	5.60505	+	7.80172i	0.651574	+	0.906931i
$75$	3.71288	−	3.34880i	0.428727	−	0.386687i
$76$	4.98386	−	14.8005i	0.571688	−	1.69773i
$77$	3.08716	−	0.435691i	0.351815	−	0.0496516i
$78$	−0.889938	+	5.43149i	−0.100766	+	0.614995i
$79$		−	12.6470i		−	1.42290i	−0.702739	−	0.711448i	$-0.748040\pi$
$79$		−	12.6470i		−	1.42290i	0.702739	−	0.711448i	$-0.251960\pi$
$80$	−0.982095	−	8.89019i	−0.109802	−	0.993954i
$81$	−1.00000			−0.111111
$82$	0.314734	−	1.92089i	0.0347566	−	0.212127i
$83$	−9.82093	−	9.82093i	−1.07799	−	1.07799i	−0.996690	−	0.0812973i	$-0.974094\pi$
$83$	−9.82093	−	9.82093i	−1.07799	−	1.07799i	−0.0812973	−	0.996690i	$-0.525906\pi$
$84$	4.36490	−	2.99127i	0.476249	−	0.326374i
$85$	−0.202550	+	7.86254i	−0.0219696	+	0.852812i
$86$	14.0563	−	10.0986i	1.51573	−	1.08896i
$87$	−0.333314	−	0.333314i	−0.0357351	−	0.0357351i
$88$	−1.56041	+	2.94519i	−0.166340	+	0.313959i
$89$	−2.61406			−0.277089			−0.138545	−	0.990356i	$-0.544242\pi$
$89$	−2.61406			−0.277089			−0.138545	+	0.990356i	$0.544242\pi$
$90$	−2.61486	+	1.77834i	−0.275631	+	0.187454i
$91$	−6.19207	+	8.22703i	−0.649105	+	0.862427i
$92$	3.48106	+	7.01568i	0.362925	+	0.731436i
$93$	−7.64998	+	7.64998i	−0.793266	+	0.793266i
$94$	1.88949	+	2.63001i	0.194887	+	0.271264i
$95$	−12.6603	+	12.0243i	−1.29892	+	1.23367i
$96$	−0.150600	+	5.65485i	−0.0153705	+	0.577146i
$97$	−7.43586	−	7.43586i	−0.754997	−	0.754997i	0.220410	−	0.975407i	$-0.429260\pi$
$97$	−7.43586	−	7.43586i	−0.754997	−	0.754997i	−0.975407	+	0.220410i	$0.929260\pi$
$98$	9.83065	−	1.16546i	0.993046	−	0.117729i
$99$	1.17840			0.118434
$100$	−3.67501	+	9.30023i	−0.367501	+	0.930023i
$101$	−6.36620			−0.633461			−0.316730	−	0.948516i	$-0.602585\pi$
$101$	−6.36620			−0.633461			−0.316730	+	0.948516i	$0.602585\pi$
$102$	0.804313	−	4.90890i	0.0796388	−	0.486054i
$103$	3.68459	−	3.68459i	0.363053	−	0.363053i	−0.501882	−	0.864936i	$-0.667359\pi$
$103$	3.68459	−	3.68459i	0.363053	−	0.363053i	0.864936	+	0.501882i	$0.167359\pi$
$104$	−3.23393	−	10.5221i	−0.317113	−	1.03177i
$105$	−5.87738	+	0.675608i	−0.573573	+	0.0659326i
$106$	−7.02427	+	5.04650i	−0.682257	+	0.490159i
$107$	−13.1847	−	13.1847i	−1.27461	−	1.27461i	−0.943640	−	0.330974i	$-0.892623\pi$
$107$	−13.1847	−	13.1847i	−1.27461	−	1.27461i	−0.330974	−	0.943640i	$-0.607377\pi$
$108$	1.79158	−	0.888951i	0.172395	−	0.0855393i
$109$	−7.38166			−0.707035			−0.353517	−	0.935428i	$-0.615015\pi$
$109$	−7.38166			−0.707035			−0.353517	+	0.935428i	$0.615015\pi$
$110$	3.08136	−	2.09560i	0.293796	−	0.199807i
$111$			6.79277i			0.644741i
$112$	−5.16098	+	9.23928i	−0.487667	+	0.873030i
$113$	13.2590	+	13.2590i	1.24730	+	1.24730i	0.956909	+	0.290389i	$0.0937847\pi$
$113$	13.2590	+	13.2590i	1.24730	+	1.24730i	0.290389	+	0.956909i	$0.406215\pi$
$114$	8.96838	−	6.44322i	0.839965	−	0.603463i
$115$	0.225498	−	8.75335i	0.0210278	−	0.816254i
$116$	0.893460	+	0.300860i	0.0829557	+	0.0279341i
$117$	−2.75196	+	2.75196i	−0.254419	+	0.254419i
$118$	−0.121911	+	0.744053i	−0.0112229	+	0.0684956i
$119$	5.59630	−	7.43547i	0.513012	−	0.681609i
$120$	3.10388	−	5.51053i	0.283345	−	0.503040i
$121$	9.61137			0.873761
$122$	−8.08506	−	1.32472i	−0.731987	−	0.119934i
$123$	0.973253	−	0.973253i	0.0877553	−	0.0877553i
$124$	6.90511	−	20.5060i	0.620097	−	1.84150i
$125$	8.49235	−	7.27186i	0.759579	−	0.650415i
$126$	3.74074	+	0.0830611i	0.333251	+	0.00739967i
$127$	5.12310	−	5.12310i	0.454602	−	0.454602i	−0.442277	−	0.896879i	$-0.645829\pi$
$127$	5.12310	−	5.12310i	0.454602	−	0.454602i	0.896879	+	0.442277i	$0.145829\pi$
$128$	−4.75707	−	10.2650i	−0.420470	−	0.907307i
$129$	12.2385			1.07754
$130$	−2.30207	+	12.0899i	−0.201905	+	1.06035i
$131$	−17.3109			−1.51246			−0.756230	−	0.654306i	$-0.772961\pi$
$131$	−17.3109			−1.51246			−0.756230	+	0.654306i	$0.772961\pi$
$132$	−2.11120	+	1.04754i	−0.183757	+	0.0911767i
$133$	20.4568	−	2.88706i	1.77383	−	0.250340i
$134$	7.89045	+	10.9828i	0.681631	+	0.948769i
$135$	−2.23533	−	0.0575851i	−0.192386	−	0.00495613i
$136$	2.92278	+	9.50970i	0.250626	+	0.815450i
$137$	2.16208	−	2.16208i	0.184719	−	0.184719i	−0.608689	−	0.793409i	$-0.708304\pi$
$137$	2.16208	−	2.16208i	0.184719	−	0.184719i	0.793409	+	0.608689i	$0.208304\pi$
$138$	−0.895440	+	5.46507i	−0.0762249	+	0.465218i
$139$		−	2.95060i		−	0.250267i	−0.992140	−	0.125133i	$-0.960064\pi$
$139$		−	2.95060i		−	0.250267i	0.992140	−	0.125133i	$-0.0399359\pi$
$140$	9.92922	−	6.43511i	0.839172	−	0.543866i
$141$			2.28988i			0.192843i
$142$	15.0380	+	2.46395i	1.26196	+	0.206770i
$143$	3.24291	−	3.24291i	0.271186	−	0.271186i
$144$	−2.41953	+	3.18526i	−0.201628	+	0.265438i
$145$	−0.725873	−	0.764260i	−0.0602804	−	0.0634684i
$146$	0.593338	−	0.426277i	0.0491050	−	0.0352789i
$147$	6.12625	+	3.38659i	0.505285	+	0.279321i
$148$	−6.03844	−	12.1698i	−0.496356	−	1.00035i
$149$	15.9170			1.30397			0.651984	−	0.758233i	$-0.273937\pi$
$149$	15.9170			1.30397			0.651984	+	0.758233i	$0.273937\pi$
$150$	−5.94748	+	3.82459i	−0.485609	+	0.312277i
$151$	9.89080			0.804902			0.402451	−	0.915441i	$-0.368158\pi$
$151$	9.89080			0.804902			0.402451	+	0.915441i	$0.368158\pi$
$152$	−10.3399	+	19.5160i	−0.838675	+	1.58296i
$153$	2.48718	−	2.48718i	0.201077	−	0.201077i
$154$	−4.40809	−	0.0978794i	−0.355214	−	0.00788734i
$155$	−17.5407	+	16.6597i	−1.40890	+	1.33814i
$156$	2.48400	−	7.37671i	0.198879	−	0.590610i
$157$	−8.04729	+	8.04729i	−0.642244	+	0.642244i	−0.951107	−	0.308863i	$-0.900052\pi$
$157$	−8.04729	+	8.04729i	−0.642244	+	0.642244i	0.308863	+	0.951107i	$0.400052\pi$
$158$	−2.89194	+	17.6502i	−0.230070	+	1.40417i
$159$	−6.11586			−0.485019
$160$	−0.662275	+	12.6318i	−0.0523574	+	0.998628i
$161$	−6.23035	+	8.27789i	−0.491020	+	0.652389i
$162$	1.39560	+	0.228667i	0.109649	+	0.0179658i
$163$	2.56160	−	2.56160i	0.200640	−	0.200640i	−0.599634	−	0.800274i	$-0.704687\pi$
$163$	2.56160	−	2.56160i	0.200640	−	0.200640i	0.800274	+	0.599634i	$0.204687\pi$
$164$	−0.878489	+	2.60884i	−0.0685984	+	0.203716i
$165$	2.63411	+	0.0678583i	0.205065	+	0.00528276i
$166$	11.4604	+	15.9519i	0.889501	+	1.23810i
$167$	9.74741	+	9.74741i	0.754277	+	0.754277i	0.975274	−	0.220998i	$-0.0709313\pi$
$167$	9.74741	+	9.74741i	0.754277	+	0.754277i	−0.220998	+	0.975274i	$0.570931\pi$
$168$	−6.77567	+	3.17652i	−0.522754	+	0.245074i
$169$			2.14654i			0.165118i
$170$	2.08058	−	10.9267i	0.159573	−	0.838038i
$171$	7.80855			0.597135
$172$	−21.9263	+	10.8794i	−1.67186	+	0.829548i
$173$	5.30008	+	5.30008i	0.402958	+	0.402958i	0.879274	−	0.476316i	$-0.158028\pi$
$173$	5.30008	+	5.30008i	0.402958	+	0.402958i	−0.476316	+	0.879274i	$0.658028\pi$
$174$	0.388957	+	0.541393i	0.0294868	+	0.0410429i
$175$	−13.1768	+	1.17175i	−0.996069	+	0.0885763i
$176$	2.85118	−	3.75351i	0.214916	−	0.282932i
$177$	−0.376987	+	0.376987i	−0.0283361	+	0.0283361i
$178$	3.64819	+	0.597747i	0.273443	+	0.0448031i
$179$	11.1254			0.831548			0.415774	−	0.909468i	$-0.363511\pi$
$179$	11.1254			0.831548			0.415774	+	0.909468i	$0.363511\pi$
$180$	4.05596	−	1.88393i	0.302313	−	0.140420i
$181$	7.93167			0.589556			0.294778	−	0.955566i	$-0.404754\pi$
$181$	7.93167			0.589556			0.294778	+	0.955566i	$0.404754\pi$
$182$	10.5229	−	10.0658i	0.780011	−	0.746124i
$183$	−4.09643	−	4.09643i	−0.302817	−	0.302817i
$184$	−3.25392	−	10.5871i	−0.239882	−	0.780493i
$185$	−0.391162	+	15.1841i	−0.0287588	+	1.11635i
$186$	12.4256	−	8.92705i	0.911092	−	0.654563i
$187$	−2.93090	+	2.93090i	−0.214328	+	0.214328i
$188$	−2.03559	−	4.10251i	−0.148461	−	0.299206i
$189$	2.11391	+	1.59103i	0.153764	+	0.115731i
$190$	20.4183	−	13.8863i	1.48130	−	1.00741i
$191$	12.8338			0.928624			0.464312	−	0.885672i	$-0.346302\pi$
$191$	12.8338			0.928624			0.464312	+	0.885672i	$0.346302\pi$
$192$	1.50325	−	7.85750i	0.108488	−	0.567066i
$193$	10.6329	+	10.6329i	0.765369	+	0.765369i	0.977287	−	0.211918i	$-0.0679710\pi$
$193$	10.6329	+	10.6329i	0.765369	+	0.765369i	−0.211918	+	0.977287i	$0.567971\pi$
$194$	8.67719	+	12.0779i	0.622986	+	0.867140i
$195$	−6.30999	+	5.99305i	−0.451868	+	0.429171i
$196$	−13.9862	−	0.621419i	−0.999014	−	0.0443871i
$197$	−10.3779	−	10.3779i	−0.739397	−	0.739397i	0.233064	−	0.972461i	$-0.425125\pi$
$197$	−10.3779	−	10.3779i	−0.739397	−	0.739397i	−0.972461	+	0.233064i	$0.925125\pi$
$198$	−1.64458	−	0.269461i	−0.116875	−	0.0191498i
$199$	−13.1354			−0.931144			−0.465572	−	0.885010i	$-0.654151\pi$
$199$	−13.1354			−0.931144			−0.465572	+	0.885010i	$0.654151\pi$
$200$	7.25552	−	12.1391i	0.513043	−	0.858363i
$201$			9.56245i			0.674483i
$202$	8.88470	+	1.45574i	0.625125	+	0.102425i
$203$	0.174283	+	1.23491i	0.0122323	+	0.0866737i
$204$	−2.24501	+	6.66697i	−0.157182	+	0.466781i
$205$	2.23158	−	2.11949i	0.155861	−	0.148032i
$206$	−5.98477	+	4.29969i	−0.416979	+	0.299573i
$207$	−2.76897	+	2.76897i	−0.192457	+	0.192457i
$208$	2.10724	+	15.4241i	0.146111	+	1.06947i
$209$	−9.20160			−0.636488
$210$	8.35698	+	0.401079i	0.576686	+	0.0276771i
$211$		−	7.68962i		−	0.529375i	−0.964334	−	0.264688i	$-0.914731\pi$
$211$		−	7.68962i		−	0.529375i	0.964334	−	0.264688i	$-0.0852689\pi$
$212$	10.9571	−	5.43670i	0.752534	−	0.373394i
$213$	7.61927	+	7.61927i	0.522063	+	0.522063i
$214$	15.3857	+	21.4155i	1.05175	+	1.46394i
$215$	27.3570	+	0.704754i	1.86573	+	0.0480638i
$216$	−2.70361	+	0.830949i	−0.183958	+	0.0565389i
$217$	28.3427	−	4.00001i	1.92403	−	0.271538i
$218$	10.3019	+	1.68794i	0.697731	+	0.114322i
$219$	0.516605			0.0349089
$220$	−4.77955	+	2.22002i	−0.322237	+	0.149674i
$221$		−	13.6892i		−	0.920837i
$222$	1.55328	−	9.48002i	0.104249	−	0.636257i
$223$	15.4672	−	15.4672i	1.03576	−	1.03576i	0.0364244	−	0.999336i	$-0.488403\pi$
$223$	15.4672	−	15.4672i	1.03576	−	1.03576i	0.999336	−	0.0364244i	$-0.0115968\pi$
$224$	9.31540	−	11.7142i	0.622411	−	0.782690i
$225$	−4.99337	−	0.257443i	−0.332891	−	0.0171629i
$226$	−15.4724	−	21.5361i	−1.02921	−	1.43256i
$227$	9.72415	−	9.72415i	0.645415	−	0.645415i	−0.306467	−	0.951881i	$-0.599147\pi$
$227$	9.72415	−	9.72415i	0.645415	−	0.645415i	0.951881	+	0.306467i	$0.0991468\pi$
$228$	−13.9897	+	6.94142i	−0.926488	+	0.459707i
$229$			1.70188i			0.112463i	0.998418	+	0.0562317i	$0.0179085\pi$
$229$			1.70188i			0.112463i	−0.998418	+	0.0562317i	$0.982091\pi$
$230$	−2.31631	+	12.1646i	−0.152733	+	0.802113i
$231$	−2.49103	−	1.87487i	−0.163898	−	0.123358i
$232$	−1.17812	−	0.624186i	−0.0773474	−	0.0409798i
$233$	−8.21746	−	8.21746i	−0.538343	−	0.538343i	0.384699	−	0.923042i	$-0.374305\pi$
$233$	−8.21746	−	8.21746i	−0.538343	−	0.538343i	−0.923042	+	0.384699i	$0.874305\pi$
$234$	4.46992	−	3.21136i	0.292208	−	0.209933i
$235$	−0.131863	+	5.11863i	−0.00860179	+	0.333903i
$236$	0.340280	−	1.01053i	0.0221504	−	0.0657797i
$237$	−8.94276	+	8.94276i	−0.580894	+	0.580894i
$238$	−9.51047	+	9.09729i	−0.616472	+	0.589690i
$239$			20.1255i			1.30181i	0.759159	+	0.650906i	$0.225611\pi$
$239$			20.1255i			1.30181i	−0.759159	+	0.650906i	$0.774389\pi$
$240$	−5.59187	+	6.98076i	−0.360954	+	0.450606i
$241$			12.2565i			0.789512i	0.918786	+	0.394756i	$0.129171\pi$
$241$			12.2565i			0.789512i	−0.918786	+	0.394756i	$0.870829\pi$
$242$	−13.4137	−	2.19780i	−0.862263	−	0.141280i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	10.9806	+	3.69757i	0.702963	+	0.236713i
$245$	13.4992	+	7.92292i	0.862430	+	0.506177i
$246$	−1.58083	+	1.13573i	−0.100790	+	0.0724112i
$247$	21.4888	−	21.4888i	1.36730	−	1.36730i
$248$	−14.3258	+	27.0393i	−0.909692	+	1.71700i
$249$			13.8889i			0.880173i
$250$	−13.5148	+	8.20673i	−0.854751	+	0.519039i
$251$	10.5836			0.668031			0.334016	−	0.942568i	$-0.391596\pi$
$251$	10.5836			0.668031			0.334016	+	0.942568i	$0.391596\pi$
$252$	−5.20159	−	0.971302i	−0.327670	−	0.0611863i
$253$	3.26296	−	3.26296i	0.205140	−	0.205140i
$254$	−8.32130	+	5.97834i	−0.522125	+	0.375114i
$255$	5.70288	−	5.41643i	0.357128	−	0.339190i
$256$	4.29173	+	15.4137i	0.268233	+	0.963354i
$257$	−19.1521	−	19.1521i	−1.19468	−	1.19468i	−0.975739	−	0.218936i	$-0.929741\pi$
$257$	−19.1521	−	19.1521i	−1.19468	−	1.19468i	−0.218936	−	0.975739i	$-0.570259\pi$
$258$	−17.0801	−	2.79854i	−1.06336	−	0.174229i
$259$	10.8075	−	14.3593i	0.671546	−	0.892243i
$260$	5.97734	−	16.3463i	0.370699	−	1.01376i
$261$			0.471378i			0.0291776i
$262$	24.1591	+	3.95842i	1.49256	+	0.244552i
$263$	8.48263	+	8.48263i	0.523062	+	0.523062i	0.918495	−	0.395433i	$-0.129405\pi$
$263$	8.48263	+	8.48263i	0.523062	+	0.523062i	−0.395433	+	0.918495i	$0.629405\pi$
$264$	3.18594	−	0.979191i	0.196081	−	0.0602650i
$265$	−13.6709	−	0.352182i	−0.839800	−	0.0216344i
$266$	−29.2097	−	0.648587i	−1.79096	−	0.0397674i
$267$	1.84842	+	1.84842i	0.113121	+	0.113121i
$268$	−8.50055	−	17.1319i	−0.519254	−	1.04650i
$269$			16.0595i			0.979164i	0.871957	+	0.489582i	$0.162851\pi$
$269$			16.0595i			0.979164i	−0.871957	+	0.489582i	$0.837149\pi$
$270$	3.10646	+	0.591511i	0.189053	+	0.0359982i
$271$			6.71295i			0.407782i	0.978994	+	0.203891i	$0.0653589\pi$
$271$			6.71295i			0.407782i	−0.978994	+	0.203891i	$0.934641\pi$
$272$	−1.90449	−	13.9401i	−0.115477	−	0.845244i
$273$	10.1958	−	1.43894i	0.617081	−	0.0870885i
$274$	−3.51181	+	2.52302i	−0.212156	+	0.152421i
$275$	5.88419	+	0.303371i	0.354830	+	0.0182940i
$276$	2.49936	−	7.42232i	0.150444	−	0.446771i
$277$	8.26095	+	8.26095i	0.496352	+	0.496352i	0.910300	−	0.413948i	$-0.135851\pi$
$277$	8.26095	+	8.26095i	0.496352	+	0.496352i	−0.413948	+	0.910300i	$0.635851\pi$
$278$	−0.674705	+	4.11787i	−0.0404661	+	0.246974i
$279$	10.8187			0.647699
$280$	−15.3288	+	6.71038i	−0.916068	+	0.401022i
$281$	−3.53880			−0.211107			−0.105554	−	0.994414i	$-0.533661\pi$
$281$	−3.53880			−0.211107			−0.105554	+	0.994414i	$0.533661\pi$
$282$	0.523620	−	3.19577i	0.0311811	−	0.190305i
$283$	−2.89630	−	2.89630i	−0.172167	−	0.172167i	0.615764	−	0.787931i	$-0.288848\pi$
$283$	−2.89630	−	2.89630i	−0.172167	−	0.172167i	−0.787931	+	0.615764i	$0.788848\pi$
$284$	−20.4237	−	6.87739i	−1.21192	−	0.408098i
$285$	17.4547	+	0.449656i	1.03392	+	0.0266353i
$286$	−5.26737	+	3.78427i	−0.311466	+	0.223769i
$287$	−3.60585	+	0.508893i	−0.212846	+	0.0300390i
$288$	4.10507	−	3.89209i	0.241894	−	0.229344i
$289$		−	4.62788i		−	0.272228i
$290$	0.838270	+	1.23259i	0.0492249	+	0.0723801i
$291$			10.5159i			0.616453i
$292$	−0.925541	+	0.459237i	−0.0541632	+	0.0268748i
$293$	−5.06929	−	5.06929i	−0.296151	−	0.296151i	0.543353	−	0.839504i	$-0.317154\pi$
$293$	−5.06929	−	5.06929i	−0.296151	−	0.296151i	−0.839504	+	0.543353i	$0.817154\pi$
$294$	−7.77543	−	6.12721i	−0.453472	−	0.357346i
$295$	−0.864398	+	0.820981i	−0.0503272	+	0.0477993i
$296$	5.64444	+	18.3650i	0.328076	+	1.06744i
$297$	−0.833256	−	0.833256i	−0.0483504	−	0.0483504i
$298$	−22.2138	−	3.63968i	−1.28681	−	0.210841i
$299$			15.2402i			0.881362i
$300$	9.17488	−	3.97763i	0.529712	−	0.229649i
$301$	−25.8711	−	19.4718i	−1.49118	−	1.12234i
$302$	−13.8036	−	2.26170i	−0.794311	−	0.130146i
$303$	4.50158	+	4.50158i	0.258609	+	0.258609i
$304$	18.8930	−	24.8722i	1.08359	−	1.42652i
$305$	−8.92097	−	9.39276i	−0.510814	−	0.537828i
$306$	−4.03985	+	2.90238i	−0.230943	+	0.165918i
$307$	−16.8586	+	16.8586i	−0.962174	+	0.962174i	−0.999310	−	0.0371367i	$-0.988176\pi$
$307$	−16.8586	+	16.8586i	−0.962174	+	0.962174i	0.0371367	+	0.999310i	$0.488176\pi$
$308$	6.12956	+	1.14458i	0.349264	+	0.0652187i
$309$	−5.21080			−0.296432
$310$	28.2894	−	19.2393i	1.60673	−	1.09272i
$311$		−	17.6305i		−	0.999733i	−0.866102	−	0.499867i	$-0.833382\pi$
$311$		−	17.6305i		−	0.999733i	0.866102	−	0.499867i	$-0.166618\pi$
$312$	−5.15349	+	9.72696i	−0.291759	+	0.550681i
$313$	8.32589	−	8.32589i	0.470607	−	0.470607i	−0.431504	−	0.902111i	$-0.642017\pi$
$313$	8.32589	−	8.32589i	0.470607	−	0.470607i	0.902111	+	0.431504i	$0.142017\pi$
$314$	13.0710	−	9.39069i	0.737638	−	0.529947i
$315$	4.63366	+	3.67821i	0.261077	+	0.207243i
$316$	8.07201	−	23.9714i	0.454086	−	1.34849i
$317$	11.5840	+	11.5840i	0.650621	+	0.650621i	0.953143	−	0.302521i	$-0.0978283\pi$
$317$	11.5840	+	11.5840i	0.650621	+	0.650621i	−0.302521	+	0.953143i	$0.597828\pi$
$318$	8.53532	+	1.39849i	0.478637	+	0.0784237i
$319$		−	0.555472i		−	0.0311005i
$320$	3.81274	−	17.4775i	0.213138	−	0.977022i
$321$			18.6460i			1.04072i
$322$	10.5880	−	10.1280i	0.590045	−	0.564411i
$323$	−19.4213	+	19.4213i	−1.08063	+	1.08063i
$324$	−1.89542	−	0.638257i	−0.105301	−	0.0354587i
$325$	−14.4500	+	13.0331i	−0.801542	+	0.722944i
$326$	−4.16074	+	2.98923i	−0.230442	+	0.165558i
$327$	5.21962	+	5.21962i	0.288646	+	0.288646i
$328$	1.82258	−	3.44002i	0.100635	−	0.189944i
$329$	3.64328	−	4.84060i	0.200860	−	0.266871i
$330$	−3.66066	−	0.697037i	−0.201513	−	0.0383706i
$331$			8.52163i			0.468391i	0.972190	+	0.234195i	$0.0752456\pi$
$331$			8.52163i			0.468391i	−0.972190	+	0.234195i	$0.924754\pi$
$332$	−12.3465	−	24.8831i	−0.677605	−	1.36564i
$333$	4.80321	−	4.80321i	0.263214	−	0.263214i
$334$	−11.3746	−	15.8324i	−0.622391	−	0.866312i
$335$	−0.550655	+	21.3752i	−0.0300855	+	1.16785i
$336$	10.1825	−	2.88379i	0.555502	−	0.157324i
$337$	6.75033	−	6.75033i	0.367714	−	0.367714i	−0.498929	−	0.866643i	$-0.666273\pi$
$337$	6.75033	−	6.75033i	0.367714	−	0.367714i	0.866643	+	0.498929i	$0.166273\pi$
$338$	0.490842	−	2.99572i	0.0266983	−	0.162946i
$339$		−	18.7510i		−	1.01841i
$340$	−5.40224	+	14.7736i	−0.292977	+	0.801209i
$341$	−12.7488			−0.690385
$342$	−10.8976	−	1.78556i	−0.589277	−	0.0965518i
$343$	−7.56217	−	16.9060i	−0.408319	−	0.912839i
$344$	33.0881	−	10.1696i	1.78399	−	0.548306i
$345$	−6.34900	+	6.03010i	−0.341819	+	0.324650i
$346$	−6.18487	−	8.60877i	−0.332500	−	0.462810i
$347$	−5.85047	−	5.85047i	−0.314070	−	0.314070i	0.532414	−	0.846484i	$-0.321285\pi$
$347$	−5.85047	−	5.85047i	−0.314070	−	0.314070i	−0.846484	+	0.532414i	$0.821285\pi$
$348$	−0.419032	−	0.844512i	−0.0224625	−	0.0452706i
$349$			13.6236i			0.729256i	0.931153	+	0.364628i	$0.118804\pi$
$349$			13.6236i			0.729256i	−0.931153	+	0.364628i	$0.881196\pi$
$350$	18.6575	+	1.37778i	0.997284	+	0.0736455i
$351$	3.89186			0.207732
$352$	−4.83742	+	4.58645i	−0.257836	+	0.244458i
$353$	−5.55745	+	5.55745i	−0.295793	+	0.295793i	−0.839364	−	0.543570i	$-0.817072\pi$
$353$	−5.55745	+	5.55745i	−0.295793	+	0.295793i	0.543570	+	0.839364i	$0.317072\pi$
$354$	0.612329	−	0.439921i	0.0325449	−	0.0233815i
$355$	16.5928	+	17.4703i	0.880654	+	0.927227i
$356$	−4.95474	−	1.66844i	−0.262601	−	0.0884270i
$357$	−9.21486	+	1.30049i	−0.487702	+	0.0688293i
$358$	−15.5266	−	2.54400i	−0.820606	−	0.134455i
$359$		−	17.8417i		−	0.941647i	−0.882227	−	0.470823i	$-0.843957\pi$
$359$		−	17.8417i		−	0.941647i	0.882227	−	0.470823i	$-0.156043\pi$
$360$	−6.09131	+	1.70175i	−0.321040	+	0.0896903i
$361$	−41.9734			−2.20913
$362$	−11.0695	−	1.81371i	−0.581799	−	0.0953265i
$363$	−6.79627	−	6.79627i	−0.356711	−	0.356711i
$364$	−16.9875	+	11.6416i	−0.890389	+	0.610185i
$365$	1.15478	+	0.0297487i	0.0604440	+	0.00155712i
$366$	4.78028	+	6.65372i	0.249869	+	0.347796i
$367$	−23.4063	−	23.4063i	−1.22180	−	1.22180i	−0.966992	−	0.254808i	$-0.917988\pi$
$367$	−23.4063	−	23.4063i	−1.22180	−	1.22180i	−0.254808	−	0.966992i	$-0.582012\pi$
$368$	2.12027	+	15.5195i	0.110527	+	0.809010i
$369$	−1.37639			−0.0716519
$370$	4.01799	−	21.1015i	0.208886	−	1.09701i
$371$	12.9284	+	9.73053i	0.671208	+	0.505184i
$372$	−19.3826	+	9.61730i	−1.00494	+	0.498634i
$373$	−17.6625	+	17.6625i	−0.914531	+	0.914531i	−0.996625	−	0.0820940i	$-0.973839\pi$
$373$	−17.6625	+	17.6625i	−0.914531	+	0.914531i	0.0820940	+	0.996625i	$0.473839\pi$
$374$	4.76057	−	3.42017i	0.246163	−	0.176853i
$375$	−11.1470	−	0.863012i	−0.575628	−	0.0445658i
$376$	1.90277	+	6.19095i	0.0981281	+	0.319274i
$377$	1.29721	+	1.29721i	0.0668098	+	0.0668098i
$378$	−2.58637	−	2.70383i	−0.133028	−	0.139070i
$379$	−1.32887			−0.0682593			−0.0341296	−	0.999417i	$-0.510866\pi$
$379$	−1.32887			−0.0682593			−0.0341296	+	0.999417i	$0.510866\pi$
$380$	−31.6712	+	14.7107i	−1.62470	+	0.754645i
$381$	−7.24516			−0.371181
$382$	−17.9110	−	2.93467i	−0.916404	−	0.150151i
$383$	−6.97935	+	6.97935i	−0.356628	+	0.356628i	−0.862569	−	0.505940i	$-0.831146\pi$
$383$	−6.97935	+	6.97935i	−0.356628	+	0.356628i	0.505940	+	0.862569i	$0.331146\pi$
$384$	−3.89470	+	10.6222i	−0.198750	+	0.542062i
$385$	−5.46031	−	4.33440i	−0.278283	−	0.220902i
$386$	−12.4079	−	17.2706i	−0.631544	−	0.879052i
$387$	−8.65392	−	8.65392i	−0.439903	−	0.439903i
$388$	−9.34812	−	18.8401i	−0.474579	−	0.956461i
$389$	12.6704			0.642417			0.321209	−	0.947008i	$-0.395911\pi$
$389$	12.6704			0.642417			0.321209	+	0.947008i	$0.395911\pi$
$390$	10.1767	−	6.92104i	0.515316	−	0.350461i
$391$		−	13.7739i		−	0.696574i
$392$	19.3771	+	4.06543i	0.978692	+	0.205335i
$393$	12.2406	+	12.2406i	0.617459	+	0.617459i
$394$	12.1104	+	16.8566i	0.610113	+	0.849222i
$395$	−20.5049	+	19.4750i	−1.03172	+	0.979894i
$396$	2.23357	+	0.752122i	0.112241	+	0.0377956i
$397$	3.79046	−	3.79046i	0.190238	−	0.190238i	−0.605561	−	0.795799i	$-0.707051\pi$
$397$	3.79046	−	3.79046i	0.190238	−	0.190238i	0.795799	+	0.605561i	$0.207051\pi$
$398$	18.3318	+	3.00363i	0.918891	+	0.150558i
$399$	−16.5066	−	12.4237i	−0.826362	−	0.621961i
$400$	−12.9016	+	15.2823i	−0.645082	+	0.764113i
$401$	−15.8951			−0.793764			−0.396882	−	0.917870i	$-0.629908\pi$
$401$	−15.8951			−0.793764			−0.396882	+	0.917870i	$0.629908\pi$
$402$	2.18661	−	13.3454i	0.109058	−	0.665608i
$403$	29.7726	−	29.7726i	1.48308	−	1.48308i
$404$	−12.0666	−	4.06327i	−0.600338	−	0.202155i
$405$	1.53990	+	1.62133i	0.0765180	+	0.0805647i
$406$	0.0391532	−	1.76330i	0.00194314	−	0.0875111i
$407$	−5.66011	+	5.66011i	−0.280561	+	0.280561i
$408$	4.65765	−	8.79109i	0.230588	−	0.435224i
$409$	1.12314			0.0555358			0.0277679	−	0.999614i	$-0.491160\pi$
$409$	1.12314			0.0555358			0.0277679	+	0.999614i	$0.491160\pi$
$410$	−3.59907	+	2.44769i	−0.177745	+	0.120883i
$411$	−3.05765			−0.150823
$412$	9.33557	−	4.63214i	0.459931	−	0.228209i
$413$	1.39672	−	0.197118i	0.0687279	−	0.00969956i
$414$	4.49756	−	3.23122i	0.221043	−	0.158806i
$415$	−0.799793	+	31.0462i	−0.0392603	+	1.52400i
$416$	0.586113	−	22.0079i	0.0287365	−	1.07902i
$417$	−2.08639	+	2.08639i	−0.102171	+	0.102171i
$418$	12.8418	+	2.10410i	0.628113	+	0.102915i
$419$			25.5925i			1.25027i	0.780515	+	0.625137i	$0.214957\pi$
$419$			25.5925i			1.25027i	−0.780515	+	0.625137i	$0.785043\pi$
$420$	−11.5713	−	2.47071i	−0.564623	−	0.120558i
$421$		−	17.5467i		−	0.855173i	−0.903974	−	0.427587i	$-0.859364\pi$
$421$		−	17.5467i		−	0.855173i	0.903974	−	0.427587i	$-0.140636\pi$
$422$	−1.75836	+	10.7317i	−0.0855957	+	0.522410i
$423$	1.61919	−	1.61919i	0.0787278	−	0.0787278i
$424$	−16.5349	+	5.08197i	−0.803007	+	0.246802i
$425$	13.0597	−	11.7791i	0.633489	−	0.571370i
$426$	−8.89121	−	12.3758i	−0.430780	−	0.599607i
$427$	2.14194	+	15.1771i	0.103656	+	0.734469i
$428$	−16.5754	−	33.4058i	−0.801201	−	1.61473i
$429$	−4.58617			−0.221422
$430$	−38.0184	−	7.23920i	−1.83341	−	0.349105i
$431$	−8.10696			−0.390498			−0.195249	−	0.980754i	$-0.562552\pi$
$431$	−8.10696			−0.390498			−0.195249	+	0.980754i	$0.562552\pi$
$432$	3.96318	−	0.541449i	0.190679	−	0.0260505i
$433$	16.9355	−	16.9355i	0.813868	−	0.813868i	−0.171343	−	0.985211i	$-0.554811\pi$
$433$	16.9355	−	16.9355i	0.813868	−	0.813868i	0.985211	+	0.171343i	$0.0548108\pi$
$434$	−40.4699	−	0.898614i	−1.94262	−	0.0431349i
$435$	−0.0271443	+	1.05368i	−0.00130147	+	0.0505202i
$436$	−13.9914	−	4.71139i	−0.670065	−	0.225635i
$437$	21.6216	−	21.6216i	1.03430	−	1.03430i
$438$	−0.720976	−	0.118130i	−0.0344496	−	0.00564449i
$439$	−4.82760			−0.230409			−0.115204	−	0.993342i	$-0.536752\pi$
$439$	−4.82760			−0.230409			−0.115204	+	0.993342i	$0.536752\pi$
$440$	7.17801	−	2.00535i	0.342198	−	0.0956012i
$441$	−1.93723	−	6.72660i	−0.0922492	−	0.320314i
$442$	−3.13027	+	19.1047i	−0.148892	+	0.908720i
$443$	27.6716	−	27.6716i	1.31472	−	1.31472i	0.396821	−	0.917896i	$-0.370113\pi$
$443$	27.6716	−	27.6716i	1.31472	−	1.31472i	0.917896	−	0.396821i	$-0.129887\pi$
$444$	−4.33553	+	12.8752i	−0.205755	+	0.611028i
$445$	4.02537	+	4.23825i	0.190821	+	0.200913i
$446$	−25.1229	+	18.0493i	−1.18961	+	0.854658i
$447$	−11.2550	−	11.2550i	−0.532343	−	0.532343i
$448$	−15.6793	+	14.2183i	−0.740776	+	0.671752i
$449$		−	6.52588i		−	0.307975i	−0.988073	−	0.153988i	$-0.950788\pi$
$449$		−	6.52588i		−	0.307975i	0.988073	−	0.153988i	$-0.0492116\pi$
$450$	6.90990	+	1.50111i	0.325736	+	0.0707628i
$451$	1.62194			0.0763740
$452$	16.6687	+	33.5939i	0.784030	+	1.58013i
$453$	−6.99385	−	6.99385i	−0.328600	−	0.328600i
$454$	−15.7947	+	11.3475i	−0.741280	+	0.532564i
$455$	22.8739	−	2.62937i	1.07234	−	0.123267i
$456$	21.1113	−	6.48850i	0.988627	−	0.303852i
$457$	0.365261	−	0.365261i	0.0170862	−	0.0170862i	−0.698512	−	0.715598i	$-0.746154\pi$
$457$	0.365261	−	0.365261i	0.0170862	−	0.0170862i	0.715598	+	0.698512i	$0.246154\pi$
$458$	0.389163	−	2.37515i	0.0181844	−	0.110983i
$459$	−3.51740			−0.164178
$460$	6.01430	−	16.4474i	0.280418	−	0.766863i
$461$	19.0291			0.886274			0.443137	−	0.896454i	$-0.353865\pi$
$461$	19.0291			0.886274			0.443137	+	0.896454i	$0.353865\pi$
$462$	3.04778	+	3.18620i	0.141795	+	0.148235i
$463$	−2.25269	−	2.25269i	−0.104691	−	0.104691i	0.652821	−	0.757512i	$-0.273585\pi$
$463$	−2.25269	−	2.25269i	−0.104691	−	0.104691i	−0.757512	+	0.652821i	$0.773585\pi$
$464$	1.50146	+	1.14051i	0.0697035	+	0.0529470i
$465$	24.1833	+	0.622996i	1.12148	+	0.0288907i
$466$	9.58926	+	13.3474i	0.444214	+	0.618305i
$467$	−13.3408	+	13.3408i	−0.617340	+	0.617340i	−0.944848	−	0.327508i	$-0.893791\pi$
$467$	−13.3408	+	13.3408i	−0.617340	+	0.617340i	0.327508	+	0.944848i	$0.393791\pi$
$468$	−6.97258	+	3.45967i	−0.322308	+	0.159923i
$469$	15.2142	−	20.2142i	0.702525	−	0.933404i
$470$	1.35449	−	7.11343i	0.0624780	−	0.328118i
$471$	11.3806			0.524390
$472$	−0.705971	+	1.33248i	−0.0324949	+	0.0613326i
$473$	10.1978	+	10.1978i	0.468895	+	0.468895i
$474$	14.5255	−	10.4356i	0.667177	−	0.479325i
$475$	38.9910	+	2.01025i	1.78903	+	0.0922368i
$476$	15.3531	−	10.5215i	0.703708	−	0.482252i
$477$	4.32457	+	4.32457i	0.198008	+	0.198008i
$478$	4.60204	−	28.0873i	0.210492	−	1.28468i
$479$	18.0254			0.823599			0.411800	−	0.911274i	$-0.364900\pi$
$479$	18.0254			0.823599			0.411800	+	0.911274i	$0.364900\pi$
$480$	9.40030	−	8.46371i	0.429063	−	0.386314i
$481$		−	26.4365i		−	1.20540i
$482$	2.80266	−	17.1052i	0.127658	−	0.779123i
$483$	10.2589	−	1.44783i	0.466795	−	0.0658787i
$484$	18.2176	+	6.13452i	0.828073	+	0.278842i
$485$	−0.605559	+	23.5065i	−0.0274970	+	1.06737i
$486$	−0.825150	−	1.14853i	−0.0374295	−	0.0520985i
$487$	6.45780	−	6.45780i	0.292631	−	0.292631i	−0.545488	−	0.838119i	$-0.683656\pi$
$487$	6.45780	−	6.45780i	0.292631	−	0.292631i	0.838119	+	0.545488i	$0.183656\pi$
$488$	−14.4791	−	7.67125i	−0.655438	−	0.347261i
$489$	−3.62266			−0.163822
$490$	−17.0278	−	14.1441i	−0.769237	−	0.638964i
$491$			35.0523i			1.58189i	0.611888	+	0.790944i	$0.290410\pi$
$491$			35.0523i			1.58189i	−0.611888	+	0.790944i	$0.709590\pi$
$492$	2.46591	−	1.22354i	0.111172	−	0.0551615i
$493$	−1.17240	−	1.17240i	−0.0528023	−	0.0528023i
$494$	−34.9036	+	25.0761i	−1.57039	+	1.12823i
$495$	−1.81462	−	1.91058i	−0.0815609	−	0.0858742i
$496$	26.1762	−	34.4604i	1.17535	−	1.54732i
$497$	−3.98395	−	28.2289i	−0.178704	−	1.26624i
$498$	3.17593	−	19.3834i	0.142317	−	0.868591i
$499$	−6.99167			−0.312990			−0.156495	−	0.987679i	$-0.550020\pi$
$499$	−6.99167			−0.312990			−0.156495	+	0.987679i	$0.550020\pi$
$500$	20.7379	−	8.36296i	0.927427	−	0.374003i
$501$		−	13.7849i		−	0.615864i
$502$	−14.7705	−	2.42012i	−0.659241	−	0.108015i
$503$	−13.5873	+	13.5873i	−0.605827	+	0.605827i	−0.941853	−	0.336026i	$-0.890917\pi$
$503$	−13.5873	+	13.5873i	−0.605827	+	0.605827i	0.336026	+	0.941853i	$0.390917\pi$
$504$	7.03726	+	2.54498i	0.313465	+	0.113363i
$505$	9.80328	+	10.3217i	0.436240	+	0.459311i
$506$	−5.29993	+	3.80767i	−0.235611	+	0.169272i
$507$	1.51783	−	1.51783i	0.0674093	−	0.0674093i
$508$	12.9803	−	6.44059i	0.575907	−	0.285755i
$509$			2.58072i			0.114389i	0.998363	+	0.0571943i	$0.0182154\pi$
$509$			2.58072i			0.114389i	−0.998363	+	0.0571943i	$0.981785\pi$
$510$	−9.19752	+	6.25514i	−0.407273	+	0.276982i
$511$	−1.09206	−	0.821935i	−0.0483098	−	0.0363603i
$512$	−2.46496	−	22.4928i	−0.108937	−	0.994049i
$513$	−5.52148	−	5.52148i	−0.243779	−	0.243779i
$514$	22.3493	+	31.1082i	0.985786	+	1.37212i
$515$	−11.6478	−	0.300064i	−0.513265	−	0.0132224i
$516$	23.1971	+	7.81130i	1.02120	+	0.343873i
$517$	−1.90806	+	1.90806i	−0.0839162	+	0.0839162i
$518$	−18.3665	+	17.5686i	−0.806978	+	0.771919i
$519$		−	7.49545i		−	0.329014i
$520$	−12.0799	+	21.4462i	−0.529737	+	0.940477i
$521$			11.0924i			0.485966i	0.970030	+	0.242983i	$0.0781260\pi$
$521$			11.0924i			0.485966i	−0.970030	+	0.242983i	$0.921874\pi$
$522$	0.107788	−	0.657857i	0.00471777	−	0.0287936i
$523$	−14.8259	−	14.8259i	−0.648290	−	0.648290i	0.304289	−	0.952580i	$-0.401581\pi$
$523$	−14.8259	−	14.8259i	−0.648290	−	0.648290i	−0.952580	+	0.304289i	$0.901581\pi$
$524$	−32.8114	−	11.0488i	−1.43337	−	0.482668i
$525$	10.1459	+	8.48882i	0.442805	+	0.370482i
$526$	−9.89871	−	13.7781i	−0.431604	−	0.600754i
$527$	−26.9081	+	26.9081i	−1.17213	+	1.17213i
$528$	−4.67022	+	0.638044i	−0.203245	+	0.0277673i
$529$		−	7.66561i		−	0.333287i
$530$	18.9987	+	3.61760i	0.825251	+	0.157138i
$531$	0.533140			0.0231363
$532$	40.6169	+	7.58446i	1.76097	+	0.328828i
$533$	−3.78776	+	3.78776i	−0.164066	+	0.164066i
$534$	−2.15699	−	3.00233i	−0.0933419	−	0.129923i
$535$	−1.07373	+	41.6799i	−0.0464214	+	1.80198i
$536$	7.94591	+	25.8532i	0.343211	+	1.11669i
$537$	−7.86682	−	7.86682i	−0.339478	−	0.339478i
$538$	3.67227	−	22.4127i	0.158323	−	0.966279i
$539$	2.28284	+	7.92663i	0.0983288	+	0.341424i
$540$	−4.20014	−	1.53586i	−0.180745	−	0.0660929i
$541$			28.8656i			1.24103i	0.784195	+	0.620515i	$0.213076\pi$
$541$			28.8656i			1.24103i	−0.784195	+	0.620515i	$0.786924\pi$
$542$	1.53503	−	9.36862i	0.0659351	−	0.402417i
$543$	−5.60854	−	5.60854i	−0.240685	−	0.240685i
$544$	−0.529720	+	19.8904i	−0.0227116	+	0.852793i
$545$	11.3670	+	11.9681i	0.486908	+	0.512659i
$546$	−14.5584	−	0.323262i	−0.623042	−	0.0138343i
$547$	10.2013	+	10.2013i	0.436175	+	0.436175i	0.890723	−	0.454547i	$-0.150199\pi$
$547$	10.2013	+	10.2013i	0.436175	+	0.436175i	−0.454547	+	0.890723i	$0.650199\pi$
$548$	5.47803	−	2.71810i	0.234010	−	0.116111i
$549$			5.79323i			0.247249i
$550$	−8.14263	−	1.76890i	−0.347203	−	0.0754264i
$551$		−	3.68078i		−	0.156806i
$552$	−5.18535	+	9.78710i	−0.220703	+	0.416567i
$553$	33.1324	−	4.67597i	1.40893	−	0.198843i
$554$	−9.64001	−	13.4180i	−0.409565	−	0.570077i
$555$	11.0133	−	10.4602i	0.467490	−	0.444009i
$556$	1.88324	−	5.59264i	0.0798672	−	0.237181i
$557$	24.6386	+	24.6386i	1.04397	+	1.04397i	0.998988	+	0.0449831i	$0.0143234\pi$
$557$	24.6386	+	24.6386i	1.04397	+	1.04397i	0.0449831	+	0.998988i	$0.485677\pi$
$558$	−15.0986	−	2.47388i	−0.639176	−	0.104728i
$559$	−47.6304			−2.01455
$560$	22.9273	−	5.85986i	0.968856	−	0.247624i
$561$	4.14491			0.174998
$562$	4.93877	+	0.809206i	0.208329	+	0.0341343i
$563$	18.6930	+	18.6930i	0.787814	+	0.787814i	0.981135	−	0.193321i	$-0.0619260\pi$
$563$	18.6930	+	18.6930i	0.787814	+	0.787814i	−0.193321	+	0.981135i	$0.561926\pi$
$564$	−1.46153	+	4.34029i	−0.0615416	+	0.182759i
$565$	1.07978	−	41.9146i	0.0454266	−	1.76336i
$566$	3.37981	+	4.70438i	0.142064	+	0.197740i
$567$	−0.369731	−	2.61979i	−0.0155272	−	0.110021i
$568$	26.9308	+	14.2683i	1.12999	+	0.598686i
$569$		−	15.0539i		−	0.631094i	−0.948910	−	0.315547i	$-0.897812\pi$
$569$		−	15.0539i		−	0.631094i	0.948910	−	0.315547i	$-0.102188\pi$
$570$	−24.2570	−	4.61884i	−1.01601	−	0.193462i
$571$		−	29.2344i		−	1.22342i	−0.791082	−	0.611710i	$-0.790482\pi$
$571$		−	29.2344i		−	1.22342i	0.791082	−	0.611710i	$-0.209518\pi$
$572$	8.21650	−	4.07688i	0.343549	−	0.170463i
$573$	−9.07489	−	9.07489i	−0.379109	−	0.379109i
$574$	5.14870	+	0.114324i	0.214903	+	0.00477181i
$575$	−14.5393	+	13.1136i	−0.606332	+	0.546876i
$576$	−6.61905	+	4.49313i	−0.275794	+	0.187214i
$577$	−1.19004	−	1.19004i	−0.0495418	−	0.0495418i	0.681902	−	0.731444i	$-0.261153\pi$
$577$	−1.19004	−	1.19004i	−0.0495418	−	0.0495418i	−0.731444	+	0.681902i	$0.761153\pi$
$578$	−1.05824	+	6.45869i	−0.0440171	+	0.268646i
$579$		−	15.0371i		−	0.624921i
$580$	−0.888041	−	1.91189i	−0.0368739	−	0.0793869i
$581$	22.0977	−	29.3599i	0.916766	−	1.21805i
$582$	2.40464	−	14.6760i	0.0996754	−	0.608341i
$583$	−5.09608	−	5.09608i	−0.211058	−	0.211058i
$584$	1.39670	−	0.429272i	0.0577959	−	0.0177634i
$585$	8.69957	+	0.224113i	0.359683	+	0.00926592i
$586$	5.91554	+	8.23389i	0.244369	+	0.340139i
$587$	19.2848	−	19.2848i	0.795969	−	0.795969i	−0.186489	−	0.982457i	$-0.559711\pi$
$587$	19.2848	−	19.2848i	0.795969	−	0.795969i	0.982457	+	0.186489i	$0.0597107\pi$
$588$	9.45033	+	10.3291i	0.389725	+	0.425967i
$589$	−84.4784			−3.48087
$590$	1.39409	−	0.948105i	0.0573937	−	0.0390329i
$591$			14.6766i			0.603715i
$592$	−3.67794	−	26.9210i	−0.151162	−	1.10645i
$593$	−14.5029	+	14.5029i	−0.595564	+	0.595564i	−0.939129	−	0.343565i	$-0.888366\pi$
$593$	−14.5029	+	14.5029i	−0.595564	+	0.595564i	0.343565	+	0.939129i	$0.388366\pi$
$594$	0.972357	+	1.35343i	0.0398963	+	0.0555320i
$595$	−20.6731	+	2.37638i	−0.847514	+	0.0974223i
$596$	30.1694	+	10.1591i	1.23579	+	0.416133i
$597$	9.28813	+	9.28813i	0.380138	+	0.380138i
$598$	3.48492	−	21.2693i	0.142509	−	0.869765i
$599$		−	1.34016i		−	0.0547576i	−0.999625	−	0.0273788i	$-0.991284\pi$
$599$		−	1.34016i		−	0.0547576i	0.999625	−	0.0273788i	$-0.00871603\pi$
$600$	−13.7141	+	3.45321i	−0.559874	+	0.140977i
$601$			23.9818i			0.978239i	0.872217	+	0.489119i	$0.162682\pi$
$601$			23.9818i			0.978239i	−0.872217	+	0.489119i	$0.837318\pi$
$602$	31.6532	+	33.0908i	1.29009	+	1.34868i
$603$	6.76168	−	6.76168i	0.275357	−	0.275357i
$604$	18.7473	+	6.31287i	0.762815	+	0.256867i
$605$	−14.8005	−	15.5832i	−0.601726	−	0.633549i
$606$	−5.25307	−	7.31179i	−0.213391	−	0.297021i
$607$	4.70885	+	4.70885i	0.191126	+	0.191126i	0.796183	−	0.605056i	$-0.206849\pi$
$607$	4.70885	+	4.70885i	0.191126	+	0.191126i	−0.605056	+	0.796183i	$0.706849\pi$
$608$	−32.0547	+	30.3916i	−1.29999	+	1.23254i
$609$	0.749977	−	0.996450i	0.0303906	−	0.0403782i
$610$	10.3023	+	15.1485i	0.417130	+	0.613345i
$611$		−	8.91189i		−	0.360536i
$612$	6.30172	−	3.12680i	0.254732	−	0.126393i
$613$	2.34915	−	2.34915i	0.0948813	−	0.0948813i	−0.658073	−	0.752954i	$-0.728628\pi$
$613$	2.34915	−	2.34915i	0.0948813	−	0.0948813i	0.752954	+	0.658073i	$0.228628\pi$
$614$	27.3830	−	19.6730i	1.10509	−	0.793937i
$615$	−3.07668	−	0.0792594i	−0.124064	−	0.00319605i
$616$	−8.29272	−	2.99901i	−0.334123	−	0.120834i
$617$	24.9442	−	24.9442i	1.00421	−	1.00421i	0.00422348	−	0.999991i	$-0.498656\pi$
$617$	24.9442	−	24.9442i	1.00421	−	1.00421i	0.999991	−	0.00422348i	$-0.00134438\pi$
$618$	7.27221	+	1.19154i	0.292531	+	0.0479306i
$619$			20.8085i			0.836362i	0.908364	+	0.418181i	$0.137332\pi$
$619$			20.8085i			0.836362i	−0.908364	+	0.418181i	$0.862668\pi$
$620$	−43.8802	+	20.3817i	−1.76227	+	0.818547i
$621$	3.91592			0.157140
$622$	−4.03151	+	24.6052i	−0.161649	+	0.986578i
$623$	−0.966496	−	6.84828i	−0.0387219	−	0.274370i
$624$	9.41647	−	12.3966i	0.376961	−	0.496260i
$625$	−24.8674	−	2.57101i	−0.994698	−	0.102841i
$626$	−13.5235	+	9.71579i	−0.540508	+	0.388321i
$627$	6.50652	+	6.50652i	0.259845	+	0.259845i
$628$	−20.3893	+	10.1168i	−0.813620	+	0.403704i
$629$			23.8929i			0.952672i
$630$	−5.62567	−	6.19288i	−0.224132	−	0.246730i
$631$	9.10899			0.362623			0.181312	−	0.983426i	$-0.441966\pi$
$631$	9.10899			0.362623			0.181312	+	0.983426i	$0.441966\pi$
$632$	−16.7468	+	31.6087i	−0.666151	+	1.25733i
$633$	−5.43738	+	5.43738i	−0.216117	+	0.216117i
$634$	−13.5178	−	18.8155i	−0.536860	−	0.747260i
$635$	−16.1953	−	0.417213i	−0.642690	−	0.0165566i
$636$	−11.5921	−	3.90349i	−0.459658	−	0.154783i
$637$	−23.8425	−	13.1801i	−0.944674	−	0.522216i
$638$	−0.127018	+	0.775219i	−0.00502869	+	0.0306912i
$639$		−	10.7753i		−	0.426263i
$640$	−9.31760	+	23.5198i	−0.368310	+	0.929703i
$641$	−15.6571			−0.618417			−0.309209	−	0.950994i	$-0.600064\pi$
$641$	−15.6571			−0.618417			−0.309209	+	0.950994i	$0.600064\pi$
$642$	4.26372	−	26.0224i	0.168276	−	1.02702i
$643$	−6.87547	−	6.87547i	−0.271142	−	0.271142i	0.558418	−	0.829560i	$-0.311409\pi$
$643$	−6.87547	−	6.87547i	−0.271142	−	0.271142i	−0.829560	+	0.558418i	$0.811409\pi$
$644$	−17.0926	+	11.7136i	−0.673541	+	0.461579i
$645$	−18.8460	−	19.8427i	−0.742060	−	0.781304i
$646$	31.5454	−	22.6634i	1.24114	−	0.891679i
$647$	27.2352	+	27.2352i	1.07073	+	1.07073i	0.997301	+	0.0734252i	$0.0233930\pi$
$647$	27.2352	+	27.2352i	1.07073	+	1.07073i	0.0734252	+	0.997301i	$0.476607\pi$
$648$	2.49931	+	1.32417i	0.0981823	+	0.0520185i
$649$	−0.628253			−0.0246611
$650$	23.1467	−	14.8848i	0.907889	−	0.583829i
$651$	−22.8698	−	17.2129i	−0.896337	−	0.674627i
$652$	6.49029	−	3.22036i	0.254179	−	0.126119i
$653$	−26.4122	+	26.4122i	−1.03359	+	1.03359i	−0.0341742	+	0.999416i	$0.510880\pi$
$653$	−26.4122	+	26.4122i	−1.03359	+	1.03359i	−0.999416	+	0.0341742i	$0.989120\pi$
$654$	−6.09097	−	8.47808i	−0.238176	−	0.331519i
$655$	26.6570	+	28.0667i	1.04157	+	1.09666i
$656$	−3.33022	+	4.38415i	−0.130023	+	0.171172i
$657$	−0.365295	−	0.365295i	−0.0142515	−	0.0142515i
$658$	−6.19146	+	5.92247i	−0.241368	+	0.230882i
$659$	−27.7274			−1.08011			−0.540053	−	0.841631i	$-0.681596\pi$
$659$	−27.7274			−1.08011			−0.540053	+	0.841631i	$0.681596\pi$
$660$	4.94944	+	1.80986i	0.192657	+	0.0704487i
$661$	0.497810			0.0193626			0.00968128	−	0.999953i	$-0.496918\pi$
$661$	0.497810			0.0193626			0.00968128	+	0.999953i	$0.496918\pi$
$662$	1.94861	−	11.8928i	0.0757350	−	0.462227i
$663$	−9.67974	+	9.67974i	−0.375930	+	0.375930i
$664$	11.5410	+	37.5502i	0.447876	+	1.45723i
$665$	−36.1822	−	28.7214i	−1.40308	−	1.11377i
$666$	−7.80172	+	5.60505i	−0.302310	+	0.217191i
$667$	1.30523	+	1.30523i	0.0505388	+	0.0505388i
$668$	12.2541	+	24.6968i	0.474126	+	0.955548i
$669$	−21.8739			−0.845695
$670$	5.65629	−	29.7054i	0.218522	−	1.14762i
$671$		−	6.82675i		−	0.263544i
$672$	−14.8702	+	1.69623i	−0.573630	+	0.0654335i
$673$	24.8228	+	24.8228i	0.956850	+	0.956850i	0.999107	−	0.0422568i	$-0.0134548\pi$
$673$	24.8228	+	24.8228i	0.956850	+	0.956850i	−0.0422568	+	0.999107i	$0.513455\pi$
$674$	−10.9644	+	7.87722i	−0.422332	+	0.303419i
$675$	3.34880	+	3.71288i	0.128896	+	0.142909i
$676$	−1.37004	+	4.06860i	−0.0526940	+	0.156485i
$677$	−23.1049	+	23.1049i	−0.887993	+	0.887993i	−0.994330	−	0.106337i	$-0.966088\pi$
$677$	−23.1049	+	23.1049i	−0.887993	+	0.887993i	0.106337	+	0.994330i	$0.466088\pi$
$678$	−4.28773	+	26.1690i	−0.164669	+	1.00501i
$679$	16.7311	−	22.2297i	0.642082	−	0.853096i
$680$	10.9176	−	19.3827i	0.418671	−	0.743294i
$681$	−13.7520			−0.526979
$682$	17.7922	+	2.91522i	0.681300	+	0.111630i
$683$	7.96194	−	7.96194i	0.304655	−	0.304655i	−0.538177	−	0.842832i	$-0.680887\pi$
$683$	7.96194	−	7.96194i	0.304655	−	0.304655i	0.842832	+	0.538177i	$0.180887\pi$
$684$	14.8005	+	4.98386i	0.565911	+	0.190563i
$685$	−6.83484	−	0.176075i	−0.261146	−	0.00672748i
$686$	6.68796	+	25.3233i	0.255347	+	0.966849i
$687$	1.20341	−	1.20341i	0.0459130	−	0.0459130i
$688$	−48.5034	+	6.62652i	−1.84917	+	0.252634i
$689$	23.8020			0.906786
$690$	10.2396	−	6.96383i	0.389814	−	0.265108i
$691$	23.0214			0.875777			0.437889	−	0.899029i	$-0.355726\pi$
$691$	23.0214			0.875777			0.437889	+	0.899029i	$0.355726\pi$
$692$	6.66309	+	13.4287i	0.253293	+	0.510483i
$693$	0.435691	+	3.08716i	0.0165505	+	0.117272i
$694$	6.82713	+	9.50274i	0.259154	+	0.360719i
$695$	−4.78391	+	4.54362i	−0.181464	+	0.172349i
$696$	0.391691	+	1.27442i	0.0148470	+	0.0483069i
$697$	3.42332	−	3.42332i	0.129668	−	0.129668i
$698$	3.11527	−	19.0132i	0.117915	−	0.719660i
$699$			11.6212i			0.439556i
$700$	−25.7234	−	6.18918i	−0.972254	−	0.233929i
$701$			21.6777i			0.818757i	0.912365	+	0.409379i	$0.134254\pi$
$701$			21.6777i			0.818757i	−0.912365	+	0.409379i	$0.865746\pi$
$702$	−5.43149	−	0.889938i	−0.204998	−	0.0335885i
$703$	−37.5061	+	37.5061i	−1.41457	+	1.41457i
$704$	7.79990	−	5.29471i	0.293970	−	0.199552i
$705$	3.71266	−	3.52618i	0.139827	−	0.132804i
$706$	9.02681	−	6.48520i	0.339729	−	0.244074i
$707$	−2.35378	−	16.6781i	−0.0885230	−	0.627245i
$708$	−0.955165	+	0.473936i	−0.0358973	+	0.0178116i
$709$	−21.7250			−0.815899			−0.407950	−	0.913004i	$-0.633756\pi$
$709$	−21.7250			−0.815899			−0.407950	+	0.913004i	$0.633756\pi$
$710$	−19.1621	−	28.1758i	−0.719141	−	1.05742i
$711$	12.6470			0.474298
$712$	6.53334	+	3.46146i	0.244847	+	0.129724i
$713$	29.9567	−	29.9567i	1.12189	−	1.12189i
$714$	13.1577	+	0.292159i	0.492413	+	0.0109338i
$715$	−10.2516	−	0.264095i	−0.383387	−	0.00987659i
$716$	21.0873	+	7.10083i	0.788068	+	0.265371i
$717$	14.2309	−	14.2309i	0.531462	−	0.531462i
$718$	−4.07979	+	24.8999i	−0.152257	+	0.929256i
$719$	−49.1382			−1.83255			−0.916273	−	0.400555i	$-0.868817\pi$
$719$	−49.1382			−1.83255			−0.916273	+	0.400555i	$0.868817\pi$
$720$	8.89019	−	0.982095i	0.331318	−	0.0366005i
$721$	11.0152	+	8.29055i	0.410226	+	0.308756i
$722$	58.5783	+	9.59793i	2.18006	+	0.357198i
$723$	8.66667	−	8.66667i	0.322317	−	0.322317i
$724$	15.0339	+	5.06244i	0.558729	+	0.188144i
$725$	−0.121353	+	2.35376i	−0.00450693	+	0.0874166i
$726$	7.93082	+	11.0390i	0.294340	+	0.409695i
$727$	17.4271	+	17.4271i	0.646335	+	0.646335i	0.952105	−	0.305770i	$-0.0989139\pi$
$727$	17.4271	+	17.4271i	0.646335	+	0.646335i	−0.305770	+	0.952105i	$0.598914\pi$
$728$	26.3699	−	12.3626i	0.977335	−	0.458187i
$729$		−	1.00000i		−	0.0370370i
$730$	−1.60482	−	0.305578i	−0.0593969	−	0.0113099i
$731$	43.0477			1.59218
$732$	−5.14990	−	10.3791i	−0.190346	−	0.383621i
$733$	24.6426	+	24.6426i	0.910193	+	0.910193i	0.996287	−	0.0860936i	$-0.0274384\pi$
$733$	24.6426	+	24.6426i	0.910193	+	0.910193i	−0.0860936	+	0.996287i	$0.527438\pi$
$734$	27.3137	+	38.0182i	1.00817	+	1.40328i
$735$	−3.94300	−	15.1477i	−0.145440	−	0.558731i
$736$	0.589736	−	22.1439i	0.0217380	−	0.816235i
$737$	−7.96797	+	7.96797i	−0.293504	+	0.293504i
$738$	1.92089	+	0.314734i	0.0707090	+	0.0115855i
$739$	36.3996			1.33898			0.669490	−	0.742821i	$-0.266513\pi$
$739$	36.3996			1.33898			0.669490	+	0.742821i	$0.266513\pi$
$740$	−10.4327	+	28.5305i	−0.383515	+	1.04880i
$741$	−30.3897			−1.11640
$742$	−15.8179	−	16.5363i	−0.580692	−	0.607065i
$743$	3.09843	+	3.09843i	0.113670	+	0.113670i	0.761654	−	0.647984i	$-0.224388\pi$
$743$	3.09843	+	3.09843i	0.113670	+	0.113670i	−0.647984	+	0.761654i	$0.724388\pi$
$744$	29.2496	−	8.98979i	1.07234	−	0.329582i
$745$	−24.5104	−	25.8067i	−0.897993	−	0.945484i
$746$	28.6887	−	20.6111i	1.05037	−	0.754624i
$747$	9.82093	−	9.82093i	0.359329	−	0.359329i
$748$	−7.42595	+	3.68462i	−0.271520	+	0.134723i
$749$	29.6664	−	39.4160i	1.08399	−	1.44023i
$750$	15.3594	+	3.75337i	0.560847	+	0.137054i
$751$	16.4075			0.598719			0.299359	−	0.954140i	$-0.403227\pi$
$751$	16.4075			0.598719			0.299359	+	0.954140i	$0.403227\pi$
$752$	−1.23985	−	9.07522i	−0.0452128	−	0.330939i
$753$	−7.48374	−	7.48374i	−0.272723	−	0.272723i
$754$	−1.51377	−	2.10702i	−0.0551281	−	0.0767333i
$755$	−15.2308	−	16.0363i	−0.554306	−	0.583620i
$756$	2.99127	+	4.36490i	0.108791	+	0.158750i
$757$	23.8496	+	23.8496i	0.866827	+	0.866827i	0.992120	−	0.125292i	$-0.0399869\pi$
$757$	23.8496	+	23.8496i	0.866827	+	0.866827i	−0.125292	+	0.992120i	$0.539987\pi$
$758$	1.85457	+	0.303867i	0.0673610	+	0.0110370i
$759$	−4.61452			−0.167496
$760$	47.5643	−	13.2882i	1.72534	−	0.482015i
$761$		−	0.391527i		−	0.0141929i	−0.999975	−	0.00709643i	$-0.997741\pi$
$761$		−	0.391527i		−	0.0141929i	0.999975	−	0.00709643i	$-0.00225888\pi$
$762$	10.1114	+	1.65673i	0.366296	+	0.0600169i
$763$	−2.72923	−	19.3384i	−0.0988046	−	0.700097i
$764$	24.3256	+	8.19128i	0.880068	+	0.296350i
$765$	−7.86254	−	0.202550i	−0.284271	−	0.00732321i
$766$	11.3364	−	8.14447i	0.409599	−	0.294272i
$767$	1.46718	−	1.46718i	0.0529768	−	0.0529768i
$768$	7.86440	−	13.9338i	0.283782	−	0.502793i
$769$	28.1457			1.01496			0.507481	−	0.861663i	$-0.330577\pi$
$769$	28.1457			1.01496			0.507481	+	0.861663i	$0.330577\pi$
$770$	6.62930	+	7.29770i	0.238903	+	0.262991i
$771$			27.0852i			0.975448i
$772$	13.3673	+	26.9402i	0.481098	+	0.969600i
$773$	−34.2060	−	34.2060i	−1.23030	−	1.23030i	−0.963847	−	0.266456i	$-0.914147\pi$
$773$	−34.2060	−	34.2060i	−1.23030	−	1.23030i	−0.266456	−	0.963847i	$-0.585853\pi$
$774$	10.0986	+	14.0563i	0.362986	+	0.505244i
$775$	54.0218	+	2.78520i	1.94052	+	0.100047i
$776$	8.73817	+	28.4309i	0.313682	+	1.02061i
$777$	−17.7956	+	2.51149i	−0.638414	+	0.0900993i
$778$	−17.6829	−	2.89731i	−0.633964	−	0.103874i
$779$	10.7476			0.385072
$780$	−15.7852	+	7.33197i	−0.565201	+	0.262527i
$781$			12.6976i			0.454356i
$782$	−3.14962	+	19.2228i	−0.112630	+	0.687408i
$783$	0.333314	−	0.333314i	0.0119117	−	0.0119117i
$784$	−26.1131	−	10.1046i	−0.932612	−	0.360880i
$785$	25.4393	+	0.655352i	0.907969	+	0.0233905i
$786$	−14.2841	−	19.8821i	−0.509496	−	0.709172i
$787$	−7.85073	+	7.85073i	−0.279848	+	0.279848i	−0.833048	−	0.553200i	$-0.813407\pi$
$787$	−7.85073	+	7.85073i	−0.279848	+	0.279848i	0.553200	+	0.833048i	$0.313407\pi$
$788$	−13.0468	−	26.2944i	−0.464773	−	0.936698i
$789$		−	11.9963i		−	0.427078i
$790$	33.0701	−	22.4906i	1.17658	−	0.800180i
$791$	−29.8334	+	39.6379i	−1.06075	+	1.40936i
$792$	−2.94519	−	1.56041i	−0.104653	−	0.0554467i
$793$	15.9427	+	15.9427i	0.566143	+	0.566143i
$794$	−6.15674	+	4.42323i	−0.218494	+	0.156975i
$795$	9.41779	+	9.91585i	0.334015	+	0.351679i
$796$	−24.8971	−	8.38375i	−0.882456	−	0.297154i
$797$	13.8594	−	13.8594i	0.490926	−	0.490926i	−0.417672	−	0.908598i	$-0.637154\pi$
$797$	13.8594	−	13.8594i	0.490926	−	0.490926i	0.908598	+	0.417672i	$0.137154\pi$
$798$	20.1958	+	21.1130i	0.714922	+	0.747392i
$799$			8.05444i			0.284945i
$800$	21.5001	−	18.3778i	0.760144	−	0.649754i
$801$		−	2.61406i		−	0.0923631i
$802$	22.1833	+	3.63468i	0.783319	+	0.128345i
$803$	0.430464	+	0.430464i	0.0151908	+	0.0151908i
$804$	−6.10330	+	18.1249i	−0.215247	+	0.639216i
$805$	23.0153	−	2.64562i	0.811183	−	0.0932460i
$806$	−48.3588	+	34.7428i	−1.70337	+	1.22376i
$807$	11.3558	−	11.3558i	0.399742	−	0.399742i
$808$	15.9111	+	8.42996i	0.559751	+	0.296565i
$809$		−	25.3224i		−	0.890289i	−0.895459	−	0.445144i	$-0.853152\pi$
$809$		−	25.3224i		−	0.890289i	0.895459	−	0.445144i	$-0.146848\pi$
$810$	−1.77834	−	2.61486i	−0.0624845	−	0.0918769i
$811$	28.3941			0.997051			0.498525	−	0.866875i	$-0.333875\pi$
$811$	28.3941			0.997051			0.498525	+	0.866875i	$0.333875\pi$
$812$	−0.457850	+	2.45192i	−0.0160674	+	0.0860454i
$813$	4.74677	−	4.74677i	0.166476	−	0.166476i
$814$	9.19355	−	6.60500i	0.322234	−	0.231505i
$815$	−8.09782	−	0.208611i	−0.283654	−	0.00730732i
$816$	−8.51047	+	11.2038i	−0.297926	+	0.392213i
$817$	67.5745	+	67.5745i	2.36413	+	2.36413i
$818$	−1.56746	−	0.256825i	−0.0548051	−	0.00897969i
$819$	−8.22703	−	6.19207i	−0.287476	−	0.216368i
$820$	5.58258	−	2.59301i	0.194952	−	0.0905520i
$821$			15.6094i			0.544771i	0.962188	+	0.272385i	$0.0878126\pi$
$821$			15.6094i			0.544771i	−0.962188	+	0.272385i	$0.912187\pi$
$822$	4.26727	+	0.699183i	0.148838	+	0.0243868i
$823$	−26.3199	−	26.3199i	−0.917453	−	0.917453i	0.0793908	−	0.996844i	$-0.474703\pi$
$823$	−26.3199	−	26.3199i	−0.917453	−	0.917453i	−0.996844	+	0.0793908i	$0.974703\pi$
$824$	−14.0880	+	4.32990i	−0.490778	+	0.150839i
$825$	−3.94624	−	4.37527i	−0.137390	−	0.152327i
$826$	−1.99434	−	0.0442833i	−0.0693919	−	0.00154081i
$827$	−30.0471	−	30.0471i	−1.04484	−	1.04484i	−0.998946	−	0.0458943i	$-0.985386\pi$
$827$	−30.0471	−	30.0471i	−1.04484	−	1.04484i	−0.0458943	−	0.998946i	$-0.514614\pi$
$828$	−7.01568	+	3.48106i	−0.243812	+	0.120975i
$829$		−	5.99665i		−	0.208272i	−0.994563	−	0.104136i	$-0.966792\pi$
$829$		−	5.99665i		−	0.208272i	0.994563	−	0.104136i	$-0.0332078\pi$
$830$	8.21543	−	43.1453i	0.285162	−	1.49760i
$831$		−	11.6827i		−	0.405270i
$832$	−5.85045	+	30.5802i	−0.202828	+	1.06018i
$833$	21.5485	+	11.9120i	0.746611	+	0.412727i
$834$	3.38886	−	2.43469i	0.117347	−	0.0843064i
$835$	0.793805	−	30.8138i	0.0274708	−	1.06635i
$836$	−17.4409	−	5.87298i	−0.603207	−	0.203121i
$837$	−7.64998	−	7.64998i	−0.264422	−	0.264422i
$838$	5.85215	−	35.7170i	0.202159	−	1.23382i
$839$	7.63941			0.263742			0.131871	−	0.991267i	$-0.457902\pi$
$839$	7.63941			0.263742			0.131871	+	0.991267i	$0.457902\pi$
$840$	15.5840	+	6.09411i	0.537700	+	0.210267i
$841$	−28.7778			−0.992338
$842$	−4.01234	+	24.4882i	−0.138275	+	0.843920i
$843$	2.50231	+	2.50231i	0.0861842	+	0.0861842i
$844$	4.90795	−	14.5751i	0.168939	−	0.501695i
$845$	3.48026	−	3.30545i	0.119724	−	0.113711i
$846$	−2.63001	+	1.88949i	−0.0904214	+	0.0649622i
$847$	3.55362	+	25.1798i	0.122104	+	0.865187i
$848$	24.2383	−	3.31143i	0.832346	−	0.113715i
$849$			4.09599i			0.140574i
$850$	−20.9197	+	13.4526i	−0.717539	+	0.461422i
$851$		−	26.5999i		−	0.911833i
$852$	9.57869	+	19.3048i	0.328160	+	0.661371i
$853$	−29.0765	−	29.0765i	−0.995560	−	0.995560i	0.00443003	−	0.999990i	$-0.498590\pi$
$853$	−29.0765	−	29.0765i	−0.995560	−	0.995560i	−0.999990	+	0.00443003i	$0.998590\pi$
$854$	0.481193	−	21.6710i	0.0164661	−	0.741565i
$855$	−12.0243	−	12.6603i	−0.411224	−	0.432972i
$856$	15.4939	+	50.4116i	0.529569	+	1.72303i
$857$	−24.7241	−	24.7241i	−0.844558	−	0.844558i	0.144890	−	0.989448i	$-0.453717\pi$
$857$	−24.7241	−	24.7241i	−0.844558	−	0.844558i	−0.989448	+	0.144890i	$0.953717\pi$
$858$	6.40048	+	1.04870i	0.218509	+	0.0358022i
$859$		−	3.66598i		−	0.125082i	−0.998042	−	0.0625409i	$-0.980080\pi$
$859$		−	3.66598i		−	0.125082i	0.998042	−	0.0625409i	$-0.0199204\pi$
$860$	51.4033	+	18.7966i	1.75284	+	0.640959i
$861$	2.90956	+	2.18988i	0.0991576	+	0.0746308i
$862$	11.3141	+	1.85379i	0.385360	+	0.0631404i
$863$	39.2591	+	39.2591i	1.33640	+	1.33640i	0.899523	+	0.436873i	$0.143914\pi$
$863$	39.2591	+	39.2591i	1.33640	+	1.33640i	0.436873	+	0.899523i	$0.356086\pi$
$864$	−5.65485	−	0.150600i	−0.192382	−	0.00512351i
$865$	0.431626	−	16.7548i	0.0146757	−	0.569679i
$866$	−27.5078	+	19.7627i	−0.934754	+	0.671563i
$867$	−3.27241	+	3.27241i	−0.111137	+	0.111137i
$868$	56.2745	+	10.5082i	1.91008	+	0.356673i
$869$	−14.9032			−0.505557
$870$	0.278825	−	1.46432i	0.00945305	−	0.0496450i
$871$		−	37.2157i		−	1.26101i
$872$	18.4491	+	9.77460i	0.624765	+	0.331010i
$873$	7.43586	−	7.43586i	0.251666	−	0.251666i
$874$	−35.1194	+	25.2311i	−1.18793	+	0.853455i
$875$	22.1906	+	19.5595i	0.750181	+	0.661233i
$876$	0.979185	+	0.329727i	0.0330836	+	0.0111404i
$877$	5.33102	+	5.33102i	0.180016	+	0.180016i	0.791363	−	0.611347i	$-0.209372\pi$
$877$	5.33102	+	5.33102i	0.180016	+	0.180016i	−0.611347	+	0.791363i	$0.709372\pi$
$878$	6.73742	+	1.10391i	0.227377	+	0.0372552i
$879$			7.16905i			0.241806i
$880$	−10.4762	+	1.15730i	−0.353153	+	0.0390126i
$881$		−	0.259921i		−	0.00875697i	−0.999990	−	0.00437848i	$-0.998606\pi$
$881$		−	0.259921i		−	0.00875697i	0.999990	−	0.00437848i	$-0.00139372\pi$
$882$	1.16546	+	9.83065i	0.0392431	+	0.331015i
$883$	−39.1580	+	39.1580i	−1.31777	+	1.31777i	−0.402237	+	0.915536i	$0.631767\pi$
$883$	−39.1580	+	39.1580i	−1.31777	+	1.31777i	−0.915536	+	0.402237i	$0.868233\pi$
$884$	8.73724	−	25.9469i	0.293865	−	0.872688i
$885$	1.19174	+	0.0307009i	0.0400600	+	0.00103200i
$886$	−44.9462	+	32.2910i	−1.51000	+	1.08484i
$887$	−12.8143	−	12.8143i	−0.430263	−	0.430263i	0.458455	−	0.888718i	$-0.348403\pi$
$887$	−12.8143	−	12.8143i	−0.430263	−	0.430263i	−0.888718	+	0.458455i	$0.848403\pi$
$888$	8.99480	−	16.9772i	0.301846	−	0.569719i
$889$	15.3156	+	11.5273i	0.513669	+	0.386612i
$890$	−4.64868	−	6.83540i	−0.155824	−	0.229123i
$891$			1.17840i			0.0394779i
$892$	39.1889	−	19.4449i	1.31214	−	0.651062i
$893$	−12.6435	+	12.6435i	−0.423100	+	0.423100i
$894$	13.1339	+	18.2811i	0.439262	+	0.611413i
$895$	−17.1319	−	18.0379i	−0.572656	−	0.602941i
$896$	25.1333	−	16.2578i	0.839645	−	0.543135i
$897$	10.7764	−	10.7764i	0.359815	−	0.359815i
$898$	−1.49225	+	9.10754i	−0.0497971	+	0.303923i
$899$		−	5.09970i		−	0.170084i
$900$	−9.30023	−	3.67501i	−0.310008	−	0.122500i
$901$	−21.5119			−0.716667
$902$	−2.26358	−	0.370883i	−0.0753691	−	0.0123491i
$903$	4.52494	+	32.0623i	0.150581	+	1.06697i
$904$	−15.5811	−	50.6954i	−0.518220	−	1.68611i
$905$	−12.2139	−	12.8599i	−0.406005	−	0.427477i
$906$	8.16139	+	11.3599i	0.271144	+	0.377408i
$907$	22.8132	+	22.8132i	0.757500	+	0.757500i	0.975867	−	0.218367i	$-0.0700729\pi$
$907$	22.8132	+	22.8132i	0.757500	+	0.757500i	−0.218367	+	0.975867i	$0.570073\pi$
$908$	24.6379	−	12.2249i	0.817637	−	0.405697i
$909$		−	6.36620i		−	0.211154i
$910$	−32.5242	−	1.56094i	−1.07817	−	0.0517447i
$911$	32.5148			1.07726			0.538631	−	0.842542i	$-0.318942\pi$
$911$	32.5148			1.07726			0.538631	+	0.842542i	$0.318942\pi$
$912$	−30.9467	+	4.22793i	−1.02475	+	0.140001i
$913$	−11.5730	+	11.5730i	−0.383010	+	0.383010i
$914$	−0.593283	+	0.426237i	−0.0196241	+	0.0140987i
$915$	−0.333604	+	12.9498i	−0.0110286	+	0.428106i
$916$	−1.08624	+	3.22578i	−0.0358902	+	0.106583i
$917$	−6.40036	−	45.3509i	−0.211359	−	1.49762i
$918$	4.90890	+	0.804313i	0.162018	+	0.0265463i
$919$			43.8704i			1.44715i	0.690245	+	0.723576i	$0.257503\pi$
$919$			43.8704i			1.44715i	−0.690245	+	0.723576i	$0.742497\pi$
$920$	−12.1545	+	21.5788i	−0.400724	+	0.711431i
$921$	23.8417			0.785611
$922$	−26.5571	−	4.35133i	−0.874612	−	0.143303i
$923$	−29.6531	−	29.6531i	−0.976043	−	0.976043i
$924$	−3.52491	−	5.14360i	−0.115961	−	0.169212i
$925$	25.2208	−	22.7476i	0.829253	−	0.747938i
$926$	2.62875	+	3.65898i	0.0863861	+	0.120242i
$927$	3.68459	+	3.68459i	0.121018	+	0.121018i
$928$	−1.83465	−	1.93504i	−0.0602252	−	0.0635208i
$929$	−34.1044			−1.11893			−0.559464	−	0.828855i	$-0.688993\pi$
$929$	−34.1044			−1.11893			−0.559464	+	0.828855i	$0.688993\pi$
$930$	−33.6079	−	6.39938i	−1.10205	−	0.209844i
$931$	15.1270	+	52.5250i	0.495767	+	1.72144i
$932$	−10.3307	−	20.8204i	−0.338394	−	0.681995i
$933$	−12.4666	+	12.4666i	−0.408139	+	0.408139i
$934$	21.6691	−	15.5679i	0.709035	−	0.509398i
$935$	9.26523	+	0.238685i	0.303005	+	0.00780584i
$936$	10.5221	−	3.23393i	0.343925	−	0.105704i
$937$	−32.2128	−	32.2128i	−1.05234	−	1.05234i	−0.998552	−	0.0537927i	$-0.982869\pi$
$937$	−32.2128	−	32.2128i	−1.05234	−	1.05234i	−0.0537927	−	0.998552i	$-0.517131\pi$
$938$	−25.8553	+	24.7320i	−0.844205	+	0.807529i
$939$	−11.7746			−0.384249
$940$	−3.51694	+	9.61781i	−0.114710	+	0.313698i
$941$	−4.64137			−0.151304			−0.0756522	−	0.997134i	$-0.524104\pi$
$941$	−4.64137			−0.151304			−0.0756522	+	0.997134i	$0.524104\pi$
$942$	−15.8828	−	2.60236i	−0.517490	−	0.0847895i
$943$	−3.81118	+	3.81118i	−0.124109	+	0.124109i
$944$	1.28995	−	1.69819i	0.0419843	−	0.0552714i
$945$	−0.675608	−	5.87738i	−0.0219775	−	0.191191i
$946$	−11.9002	−	16.5640i	−0.386908	−	0.538541i
$947$	−8.53326	−	8.53326i	−0.277294	−	0.277294i	0.554734	−	0.832028i	$-0.312820\pi$
$947$	−8.53326	−	8.53326i	−0.277294	−	0.277294i	−0.832028	+	0.554734i	$0.812820\pi$
$948$	−22.6581	+	11.2425i	−0.735900	+	0.365141i
$949$	−2.01055			−0.0652653
$950$	−53.9563	−	11.7215i	−1.75057	−	0.380294i
$951$		−	16.3822i		−	0.531230i
$952$	−23.8328	+	11.1731i	−0.772424	+	0.362122i
$953$	−12.7175	−	12.7175i	−0.411960	−	0.411960i	0.470461	−	0.882421i	$-0.344088\pi$
$953$	−12.7175	−	12.7175i	−0.411960	−	0.411960i	−0.882421	+	0.470461i	$0.844088\pi$
$954$	−5.04650	−	7.02427i	−0.163386	−	0.227419i
$955$	−19.7628	−	20.8079i	−0.639508	−	0.673329i
$956$	−12.8452	+	38.1464i	−0.415445	+	1.23374i
$957$	−0.392778	+	0.392778i	−0.0126967	+	0.0126967i
$958$	−25.1563	−	4.12180i	−0.812762	−	0.133169i
$959$	6.46360	+	4.86482i	0.208720	+	0.157093i
$960$	−15.0545	+	9.66245i	−0.485881	+	0.311854i
$961$	−86.0444			−2.77562
$962$	−6.04514	+	36.8948i	−0.194903	+	1.18954i
$963$	13.1847	−	13.1847i	0.424871	−	0.424871i
$964$	−7.82280	+	23.2313i	−0.251956	+	0.748229i
$965$	0.865914	−	33.6129i	0.0278747	−	1.08204i
$966$	−14.6484	−	0.325260i	−0.471305	−	0.0104651i
$967$	−19.2798	+	19.2798i	−0.619997	+	0.619997i	−0.945531	−	0.325533i	$-0.894456\pi$
$967$	−19.2798	+	19.2798i	−0.619997	+	0.619997i	0.325533	+	0.945531i	$0.394456\pi$
$968$	−24.0218	−	12.7271i	−0.772090	−	0.409065i
$969$	27.4658			0.882329
$970$	6.22027	−	32.6672i	0.199721	−	1.04888i
$971$	13.2078			0.423858			0.211929	−	0.977285i	$-0.432025\pi$
$971$	13.2078			0.423858			0.211929	+	0.977285i	$0.432025\pi$
$972$	0.888951	+	1.79158i	0.0285131	+	0.0574650i
$973$	7.72996	−	1.09093i	0.247811	−	0.0349735i
$974$	−10.4892	+	7.53586i	−0.336096	+	0.241464i
$975$	19.4335	+	1.00193i	0.622369	+	0.0320875i
$976$	18.4529	+	14.0169i	0.590664	+	0.448671i
$977$	−0.969515	+	0.969515i	−0.0310175	+	0.0310175i	−0.722445	−	0.691428i	$-0.756982\pi$
$977$	−0.969515	+	0.969515i	−0.0310175	+	0.0310175i	0.691428	+	0.722445i	$0.256982\pi$
$978$	5.05580	+	0.828381i	0.161666	+	0.0264887i
$979$			3.08041i			0.0984502i
$980$	20.5298	+	23.6332i	0.655799	+	0.754935i
$981$		−	7.38166i		−	0.235678i
$982$	8.01530	−	48.9192i	0.255778	−	1.56107i
$983$	30.0600	−	30.0600i	0.958766	−	0.958766i	−0.0404171	−	0.999183i	$-0.512869\pi$
$983$	30.0600	−	30.0600i	0.958766	−	0.958766i	0.999183	+	0.0404171i	$0.0128687\pi$
$984$	−3.72122	+	1.14371i	−0.118628	+	0.0364601i
$985$	−0.845154	+	32.8070i	−0.0269288	+	1.04532i
$986$	1.36812	+	1.90430i	0.0435698	+	0.0606452i
$987$	−5.99901	+	0.846639i	−0.190951	+	0.0269488i
$988$	54.4457	−	27.0150i	1.73215	−	0.859461i
$989$	−47.9249			−1.52392
$990$	2.09560	+	3.08136i	0.0666025	+	0.0979320i
$991$	12.3196			0.391345			0.195673	−	0.980669i	$-0.437311\pi$
$991$	12.3196			0.391345			0.195673	+	0.980669i	$0.437311\pi$
$992$	−44.4116	+	42.1074i	−1.41007	+	1.33691i
$993$	6.02570	−	6.02570i	0.191220	−	0.191220i
$994$	−0.895006	+	40.3074i	−0.0283879	+	1.27847i
$995$	20.2271	+	21.2969i	0.641244	+	0.675156i
$996$	−8.86468	+	26.3253i	−0.280888	+	0.834150i
$997$	34.6895	−	34.6895i	1.09863	−	1.09863i	0.104055	−	0.994572i	$-0.466818\pi$
$997$	34.6895	−	34.6895i	1.09863	−	1.09863i	0.994572	−	0.104055i	$-0.0331817\pi$
$998$	9.75760	+	1.59876i	0.308872	+	0.0506079i
$999$	−6.79277			−0.214914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.13.5	✓	184
5.2	odd	4	inner	840.2.bj.b.517.51	yes	184
7.6	odd	2	inner	840.2.bj.b.13.6	yes	184
8.5	even	2	inner	840.2.bj.b.13.52	yes	184
35.27	even	4	inner	840.2.bj.b.517.52	yes	184
40.37	odd	4	inner	840.2.bj.b.517.6	yes	184
56.13	odd	2	inner	840.2.bj.b.13.51	yes	184
280.237	even	4	inner	840.2.bj.b.517.5	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.5	✓	184	1.1	even	1	trivial
840.2.bj.b.13.6	yes	184	7.6	odd	2	inner
840.2.bj.b.13.51	yes	184	56.13	odd	2	inner
840.2.bj.b.13.52	yes	184	8.5	even	2	inner
840.2.bj.b.517.5	yes	184	280.237	even	4	inner
840.2.bj.b.517.6	yes	184	40.37	odd	4	inner
840.2.bj.b.517.51	yes	184	5.2	odd	4	inner
840.2.bj.b.517.52	yes	184	35.27	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39560 - 0.228667i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.89542 + 0.638257i) q^{4} +(-1.53990 - 1.62133i) q^{5} +(0.825150 + 1.14853i) q^{6} +(0.369731 + 2.61979i) q^{7} +(-2.49931 - 1.32417i) q^{8} +1.00000i q^{9} +(1.77834 + 2.61486i) q^{10} -1.17840i q^{11} +(-0.888951 - 1.79158i) q^{12} +(2.75196 + 2.75196i) q^{13} +(0.0830611 - 3.74074i) q^{14} +(-0.0575851 + 2.23533i) q^{15} +(3.18526 + 2.41953i) q^{16} +(-2.48718 - 2.48718i) q^{17} +(0.228667 - 1.39560i) q^{18} -7.80855i q^{19} +(-1.88393 - 4.05596i) q^{20} +(1.59103 - 2.11391i) q^{21} +(-0.269461 + 1.64458i) q^{22} +(2.76897 + 2.76897i) q^{23} +(0.830949 + 2.70361i) q^{24} +(-0.257443 + 4.99337i) q^{25} +(-3.21136 - 4.46992i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.971302 + 5.20159i) q^{28} +0.471378 q^{29} +(0.591511 - 3.10646i) q^{30} -10.8187i q^{31} +(-3.89209 - 4.10507i) q^{32} +(-0.833256 + 0.833256i) q^{33} +(2.90238 + 4.03985i) q^{34} +(3.67821 - 4.63366i) q^{35} +(-0.638257 + 1.89542i) q^{36} +(-4.80321 - 4.80321i) q^{37} +(-1.78556 + 10.8976i) q^{38} -3.89186i q^{39} +(1.70175 + 6.09131i) q^{40} +1.37639i q^{41} +(-2.70383 + 2.58637i) q^{42} +(-8.65392 + 8.65392i) q^{43} +(0.752122 - 2.23357i) q^{44} +(1.62133 - 1.53990i) q^{45} +(-3.23122 - 4.49756i) q^{46} +(-1.61919 - 1.61919i) q^{47} +(-0.541449 - 3.96318i) q^{48} +(-6.72660 + 1.93723i) q^{49} +(1.50111 - 6.90990i) q^{50} +3.51740i q^{51} +(3.45967 + 6.97258i) q^{52} +(4.32457 - 4.32457i) q^{53} +(-1.14853 + 0.825150i) q^{54} +(-1.91058 + 1.81462i) q^{55} +(2.54498 - 7.03726i) q^{56} +(-5.52148 + 5.52148i) q^{57} +(-0.657857 - 0.107788i) q^{58} -0.533140i q^{59} +(-1.53586 + 4.20014i) q^{60} +5.79323 q^{61} +(-2.47388 + 15.0986i) q^{62} +(-2.61979 + 0.369731i) q^{63} +(4.49313 + 6.61905i) q^{64} +(0.224113 - 8.69957i) q^{65} +(1.35343 - 0.972357i) q^{66} +(-6.76168 - 6.76168i) q^{67} +(-3.12680 - 6.30172i) q^{68} -3.91592i q^{69} +(-6.19288 + 5.62567i) q^{70} -10.7753 q^{71} +(1.32417 - 2.49931i) q^{72} +(-0.365295 + 0.365295i) q^{73} +(5.60505 + 7.80172i) q^{74} +(3.71288 - 3.34880i) q^{75} +(4.98386 - 14.8005i) q^{76} +(3.08716 - 0.435691i) q^{77} +(-0.889938 + 5.43149i) q^{78} -12.6470i q^{79} +(-0.982095 - 8.89019i) q^{80} -1.00000 q^{81} +(0.314734 - 1.92089i) q^{82} +(-9.82093 - 9.82093i) q^{83} +(4.36490 - 2.99127i) q^{84} +(-0.202550 + 7.86254i) q^{85} +(14.0563 - 10.0986i) q^{86} +(-0.333314 - 0.333314i) q^{87} +(-1.56041 + 2.94519i) q^{88} -2.61406 q^{89} +(-2.61486 + 1.77834i) q^{90} +(-6.19207 + 8.22703i) q^{91} +(3.48106 + 7.01568i) q^{92} +(-7.64998 + 7.64998i) q^{93} +(1.88949 + 2.63001i) q^{94} +(-12.6603 + 12.0243i) q^{95} +(-0.150600 + 5.65485i) q^{96} +(-7.43586 - 7.43586i) q^{97} +(9.83065 - 1.16546i) q^{98} +1.17840 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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