LMFDB - Embedded newform 840.2.bj.b.517.52

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			517.52
Character	$\chi$	$=$	840.517
Dual form			840.2.bj.b.13.52

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.228667 - 1.39560i) 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} +(-1.32417 + 2.49931i) q^{8} -1.00000i q^{9} +(-1.91062 - 2.51983i) q^{10} -1.17840i q^{11} +(-1.79158 + 0.888951i) q^{12} +(-2.75196 + 2.75196i) q^{13} +(-3.57165 - 1.11506i) q^{14} +(-0.0575851 - 2.23533i) q^{15} +(3.18526 + 2.41953i) q^{16} +(-2.48718 + 2.48718i) q^{17} +(-1.39560 - 0.228667i) q^{18} -7.80855i q^{19} +(-3.95358 + 2.09026i) q^{20} +(-1.59103 - 2.11391i) q^{21} +(-1.64458 - 0.269461i) 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} +(-2.37289 + 4.72963i) q^{28} -0.471378 q^{29} +(-3.13280 - 0.430779i) q^{30} +10.8187i q^{31} +(4.10507 - 3.89209i) 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} +(-10.8976 - 1.78556i) q^{38} +3.89186i q^{39} +(2.01313 + 5.99561i) q^{40} -1.37639i q^{41} +(-3.31400 + 1.73707i) 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} +(3.96318 - 0.541449i) q^{48} +(-6.72660 - 1.93723i) q^{49} +(-7.02763 - 0.782529i) q^{50} +3.51740i q^{51} +(6.97258 - 3.45967i) q^{52} +(-4.32457 - 4.32457i) q^{53} +(-1.14853 + 0.825150i) q^{54} +(-1.91058 - 1.81462i) q^{55} +(6.05809 + 4.39313i) q^{56} +(-5.52148 - 5.52148i) q^{57} +(-0.107788 + 0.657857i) q^{58} -0.533140i q^{59} +(-1.31756 + 4.27364i) q^{60} -5.79323 q^{61} +(15.0986 + 2.47388i) 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} +(6.30172 - 3.12680i) q^{68} -3.91592i q^{69} +(-7.30784 + 4.07376i) q^{70} -10.7753 q^{71} +(2.49931 + 1.32417i) 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} +(5.43149 + 0.889938i) q^{78} +12.6470i q^{79} +(8.82783 - 1.43854i) q^{80} -1.00000 q^{81} +(-1.92089 - 0.314734i) q^{82} +(9.82093 - 9.82093i) q^{83} +(1.66646 + 5.02224i) q^{84} +(0.202550 + 7.86254i) q^{85} +(14.0563 - 10.0986i) q^{86} +(-0.333314 + 0.333314i) q^{87} +(2.94519 + 1.56041i) q^{88} -2.61406 q^{89} +(-2.51983 + 1.91062i) q^{90} +(6.19207 + 8.22703i) q^{91} +(-7.01568 + 3.48106i) 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} +(-4.24176 + 8.94469i) 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.228667	−	1.39560i	0.161692	−	0.986841i
$2$	0.228667	−	1.39560i	0.161692	−	0.986841i
$3$	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
$8$	−1.32417	+	2.49931i	−0.468166	+	0.883640i
$9$		−	1.00000i		−	0.333333i
$10$	−1.91062	−	2.51983i	−0.604190	−	0.796840i
$11$		−	1.17840i		−	0.355301i	−0.984094	−	0.177651i	$-0.943150\pi$
$11$		−	1.17840i		−	0.355301i	0.984094	−	0.177651i	$-0.0568497\pi$
$12$	−1.79158	+	0.888951i	−0.517185	+	0.256618i
$13$	−2.75196	+	2.75196i	−0.763256	+	0.763256i	−0.976909	−	0.213654i	$-0.931464\pi$
$13$	−2.75196	+	2.75196i	−0.763256	+	0.763256i	0.213654	+	0.976909i	$0.431464\pi$
$14$	−3.57165	−	1.11506i	−0.954562	−	0.298011i
$15$	−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	−0.941168	−	0.337939i	$-0.890270\pi$
$17$	−2.48718	+	2.48718i	−0.603230	+	0.603230i	0.337939	+	0.941168i	$0.390270\pi$
$18$	−1.39560	−	0.228667i	−0.328947	−	0.0538973i
$19$		−	7.80855i		−	1.79140i	−0.444655	−	0.895702i	$-0.646674\pi$
$19$		−	7.80855i		−	1.79140i	0.444655	−	0.895702i	$-0.353326\pi$
$20$	−3.95358	+	2.09026i	−0.884047	+	0.467397i
$21$	−1.59103	−	2.11391i	−0.347192	−	0.461293i
$22$	−1.64458	−	0.269461i	−0.350626	−	0.0574493i
$23$	2.76897	−	2.76897i	0.577370	−	0.577370i	−0.356808	−	0.934178i	$-0.616135\pi$
$23$	2.76897	−	2.76897i	0.577370	−	0.577370i	0.934178	+	0.356808i	$0.116135\pi$
$24$	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
$28$	−2.37289	+	4.72963i	−0.448435	+	0.893816i
$29$	−0.471378			−0.0875327			−0.0437663	−	0.999042i	$-0.513936\pi$
$29$	−0.471378			−0.0875327			−0.0437663	+	0.999042i	$0.513936\pi$
$30$	−3.13280	−	0.430779i	−0.571968	−	0.0786491i
$31$			10.8187i			1.94310i	0.236841	+	0.971548i	$0.423888\pi$
$31$			10.8187i			1.94310i	−0.236841	+	0.971548i	$0.576112\pi$
$32$	4.10507	−	3.89209i	0.725681	−	0.688031i
$33$	−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	$-0.561430\pi$
$37$	4.80321	−	4.80321i	0.789643	−	0.789643i	0.981436	+	0.191792i	$0.0614300\pi$
$38$	−10.8976	−	1.78556i	−1.76783	−	0.289655i
$39$			3.89186i			0.623196i
$40$	2.01313	+	5.99561i	0.318304	+	0.947989i
$41$		−	1.37639i		−	0.214956i	−0.994207	−	0.107478i	$-0.965723\pi$
$41$		−	1.37639i		−	0.214956i	0.994207	−	0.107478i	$-0.0342775\pi$
$42$	−3.31400	+	1.73707i	−0.511361	+	0.268036i
$43$	8.65392	+	8.65392i	1.31971	+	1.31971i	0.914003	+	0.405707i	$0.132975\pi$
$43$	8.65392	+	8.65392i	1.31971	+	1.31971i	0.405707	+	0.914003i	$0.367025\pi$
$44$	−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	−0.815268	−	0.579084i	$-0.803410\pi$
$47$	−1.61919	+	1.61919i	−0.236183	+	0.236183i	0.579084	+	0.815268i	$0.303410\pi$
$48$	3.96318	−	0.541449i	0.572036	−	0.0781514i
$49$	−6.72660	−	1.93723i	−0.960943	−	0.276748i
$50$	−7.02763	−	0.782529i	−0.993858	−	0.110666i
$51$			3.51740i			0.492535i
$52$	6.97258	−	3.45967i	0.966923	−	0.479770i
$53$	−4.32457	−	4.32457i	−0.594025	−	0.594025i	0.344691	−	0.938716i	$-0.387984\pi$
$53$	−4.32457	−	4.32457i	−0.594025	−	0.594025i	−0.938716	+	0.344691i	$0.887984\pi$
$54$	−1.14853	+	0.825150i	−0.156296	+	0.112289i
$55$	−1.91058	−	1.81462i	−0.257623	−	0.244683i
$56$	6.05809	+	4.39313i	0.809546	+	0.587057i
$57$	−5.52148	−	5.52148i	−0.731338	−	0.731338i
$58$	−0.107788	+	0.657857i	−0.0141533	+	0.0863808i
$59$		−	0.533140i		−	0.0694090i	−0.999398	−	0.0347045i	$-0.988951\pi$
$59$		−	0.533140i		−	0.0694090i	0.999398	−	0.0347045i	$-0.0110490\pi$
$60$	−1.31756	+	4.27364i	−0.170097	+	0.551725i
$61$	−5.79323			−0.741748			−0.370874	−	0.928683i	$-0.620942\pi$
$61$	−5.79323			−0.741748			−0.370874	+	0.928683i	$0.620942\pi$
$62$	15.0986	+	2.47388i	1.91753	+	0.314183i
$63$	−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	$-0.551440\pi$
$67$	6.76168	−	6.76168i	0.826070	−	0.826070i	0.986971	+	0.160900i	$0.0514398\pi$
$68$	6.30172	−	3.12680i	0.764195	−	0.379180i
$69$		−	3.91592i		−	0.471421i
$70$	−7.30784	+	4.07376i	−0.873454	+	0.486907i
$71$	−10.7753			−1.27879			−0.639395	−	0.768879i	$-0.720815\pi$
$71$	−10.7753			−1.27879			−0.639395	+	0.768879i	$0.720815\pi$
$72$	2.49931	+	1.32417i	0.294547	+	0.156055i
$73$	−0.365295	−	0.365295i	−0.0427545	−	0.0427545i	0.685406	−	0.728161i	$-0.259625\pi$
$73$	−0.365295	−	0.365295i	−0.0427545	−	0.0427545i	−0.728161	+	0.685406i	$0.759625\pi$
$74$	−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
$78$	5.43149	+	0.889938i	0.614995	+	0.100766i
$79$			12.6470i			1.42290i	0.702739	+	0.711448i	$0.251960\pi$
$79$			12.6470i			1.42290i	−0.702739	+	0.711448i	$0.748040\pi$
$80$	8.82783	−	1.43854i	0.986982	−	0.160833i
$81$	−1.00000			−0.111111
$82$	−1.92089	−	0.314734i	−0.212127	−	0.0347566i
$83$	9.82093	−	9.82093i	1.07799	−	1.07799i	0.0812973	−	0.996690i	$-0.474094\pi$
$83$	9.82093	−	9.82093i	1.07799	−	1.07799i	0.996690	−	0.0812973i	$-0.0259063\pi$
$84$	1.66646	+	5.02224i	0.181826	+	0.547971i
$85$	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
$88$	2.94519	+	1.56041i	0.313959	+	0.166340i
$89$	−2.61406			−0.277089			−0.138545	−	0.990356i	$-0.544242\pi$
$89$	−2.61406			−0.277089			−0.138545	+	0.990356i	$0.544242\pi$
$90$	−2.51983	+	1.91062i	−0.265613	+	0.201397i
$91$	6.19207	+	8.22703i	0.649105	+	0.862427i
$92$	−7.01568	+	3.48106i	−0.731436	+	0.362925i
$93$	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	−0.975407	−	0.220410i	$-0.929260\pi$
$97$	−7.43586	+	7.43586i	−0.754997	+	0.754997i	0.220410	+	0.975407i	$0.429260\pi$
$98$	−4.24176	+	8.94469i	−0.428482	+	0.903550i
$99$	−1.17840			−0.118434
$100$	−2.69909	+	9.62886i	−0.269909	+	0.962886i
$101$	6.36620			0.633461			0.316730	−	0.948516i	$-0.397415\pi$
$101$	6.36620			0.633461			0.316730	+	0.948516i	$0.397415\pi$
$102$	4.90890	+	0.804313i	0.486054	+	0.0796388i
$103$	3.68459	+	3.68459i	0.363053	+	0.363053i	0.864936	−	0.501882i	$-0.167359\pi$
$103$	3.68459	+	3.68459i	0.363053	+	0.363053i	−0.501882	+	0.864936i	$0.667359\pi$
$104$	−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	0.330974	−	0.943640i	$-0.392623\pi$
$107$	13.1847	−	13.1847i	1.27461	−	1.27461i	0.943640	−	0.330974i	$-0.107377\pi$
$108$	0.888951	+	1.79158i	0.0855393	+	0.172395i
$109$	7.38166			0.707035			0.353517	−	0.935428i	$-0.384985\pi$
$109$	7.38166			0.707035			0.353517	+	0.935428i	$0.384985\pi$
$110$	−2.96937	+	2.25147i	−0.283118	+	0.214670i
$111$		−	6.79277i		−	0.644741i
$112$	7.51635	−	7.45013i	0.710229	−	0.703971i
$113$	13.2590	−	13.2590i	1.24730	−	1.24730i	0.290389	−	0.956909i	$-0.406215\pi$
$113$	13.2590	−	13.2590i	1.24730	−	1.24730i	0.956909	−	0.290389i	$-0.0937847\pi$
$114$	−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
$118$	−0.744053	−	0.121911i	−0.0684956	−	0.0112229i
$119$	5.59630	+	7.43547i	0.513012	+	0.681609i
$120$	5.66303	+	2.81604i	0.516962	+	0.257068i
$121$	9.61137			0.873761
$122$	−1.32472	+	8.08506i	−0.119934	+	0.731987i
$123$	−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
$126$	−1.11506	+	3.57165i	−0.0993371	+	0.318187i
$127$	5.12310	+	5.12310i	0.454602	+	0.454602i	0.896879	−	0.442277i	$-0.145829\pi$
$127$	5.12310	+	5.12310i	0.454602	+	0.454602i	−0.442277	+	0.896879i	$0.645829\pi$
$128$	−10.2650	+	4.75707i	−0.907307	+	0.420470i
$129$	12.2385			1.07754
$130$	12.1924	+	1.67653i	1.06934	+	0.147041i
$131$	17.3109			1.51246			0.756230	−	0.654306i	$-0.227039\pi$
$131$	17.3109			1.51246			0.756230	+	0.654306i	$0.227039\pi$
$132$	1.04754	+	2.11120i	0.0911767	+	0.183757i
$133$	−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	0.793409	−	0.608689i	$-0.208304\pi$
$137$	2.16208	+	2.16208i	0.184719	+	0.184719i	−0.608689	+	0.793409i	$0.708304\pi$
$138$	−5.46507	−	0.895440i	−0.465218	−	0.0762249i
$139$		−	2.95060i		−	0.250267i	−0.992140	−	0.125133i	$-0.960064\pi$
$139$		−	2.95060i		−	0.250267i	0.992140	−	0.125133i	$-0.0399359\pi$
$140$	4.01429	+	11.1304i	0.339270	+	0.940689i
$141$			2.28988i			0.192843i
$142$	−2.46395	+	15.0380i	−0.206770	+	1.26196i
$143$	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
$148$	−12.1698	+	6.03844i	−1.00035	+	0.496356i
$149$	−15.9170			−1.30397			−0.651984	−	0.758233i	$-0.726063\pi$
$149$	−15.9170			−1.30397			−0.651984	+	0.758233i	$0.726063\pi$
$150$	−5.52262	+	4.41596i	−0.450920	+	0.360561i
$151$	9.89080			0.804902			0.402451	−	0.915441i	$-0.368158\pi$
$151$	9.89080			0.804902			0.402451	+	0.915441i	$0.368158\pi$
$152$	19.5160	+	10.3399i	1.58296	+	0.838675i
$153$	2.48718	+	2.48718i	0.201077	+	0.201077i
$154$	−1.31398	+	4.20883i	−0.105884	+	0.339157i
$155$	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	$-0.0999484\pi$
$157$	8.04729	+	8.04729i	0.642244	+	0.642244i	−0.308863	+	0.951107i	$0.599948\pi$
$158$	17.6502	+	2.89194i	1.40417	+	0.230070i
$159$	−6.11586			−0.485019
$160$	0.0110049	−	12.6491i	0.000870015	−	1.00000i
$161$	−6.23035	−	8.27789i	−0.491020	−	0.652389i
$162$	−0.228667	+	1.39560i	−0.0179658	+	0.109649i
$163$	−2.56160	−	2.56160i	−0.200640	−	0.200640i	0.599634	−	0.800274i	$-0.295313\pi$
$163$	−2.56160	−	2.56160i	−0.200640	−	0.200640i	−0.800274	+	0.599634i	$0.795313\pi$
$164$	−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	−0.220998	−	0.975274i	$-0.570931\pi$
$167$	9.74741	−	9.74741i	0.754277	−	0.754277i	0.975274	+	0.220998i	$0.0709313\pi$
$168$	7.39013	−	1.17730i	0.570161	−	0.0908308i
$169$		−	2.14654i		−	0.165118i
$170$	11.0193	+	1.51522i	0.845143	+	0.116212i
$171$	−7.80855			−0.597135
$172$	−10.8794	−	21.9263i	−0.829548	−	1.67186i
$173$	−5.30008	+	5.30008i	−0.402958	+	0.402958i	−0.879274	−	0.476316i	$-0.841972\pi$
$173$	−5.30008	+	5.30008i	−0.402958	+	0.402958i	0.476316	+	0.879274i	$0.341972\pi$
$174$	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
$178$	−0.597747	+	3.64819i	−0.0448031	+	0.273443i
$179$	−11.1254			−0.831548			−0.415774	−	0.909468i	$-0.636489\pi$
$179$	−11.1254			−0.831548			−0.415774	+	0.909468i	$0.636489\pi$
$180$	2.09026	+	3.95358i	0.155799	+	0.294682i
$181$	−7.93167			−0.589556			−0.294778	−	0.955566i	$-0.595246\pi$
$181$	−7.93167			−0.589556			−0.294778	+	0.955566i	$0.595246\pi$
$182$	12.8976	−	6.76043i	0.956034	−	0.501116i
$183$	−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
$188$	4.10251	−	2.03559i	0.299206	−	0.148461i
$189$	−2.11391	+	1.59103i	−0.153764	+	0.115731i
$190$	−19.6762	+	14.9191i	−1.42746	+	1.08235i
$191$	12.8338			0.928624			0.464312	−	0.885672i	$-0.346302\pi$
$191$	12.8338			0.928624			0.464312	+	0.885672i	$0.346302\pi$
$192$	−7.85750	−	1.50325i	−0.567066	−	0.108488i
$193$	10.6329	−	10.6329i	0.765369	−	0.765369i	−0.211918	−	0.977287i	$-0.567971\pi$
$193$	10.6329	−	10.6329i	0.765369	−	0.765369i	0.977287	+	0.211918i	$0.0679710\pi$
$194$	8.67719	+	12.0779i	0.622986	+	0.867140i
$195$	6.30999	+	5.99305i	0.451868	+	0.429171i
$196$	11.5133	+	7.96517i	0.822378	+	0.568941i
$197$	10.3779	−	10.3779i	0.739397	−	0.739397i	−0.233064	−	0.972461i	$-0.574875\pi$
$197$	10.3779	−	10.3779i	0.739397	−	0.739397i	0.972461	+	0.233064i	$0.0748752\pi$
$198$	−0.269461	+	1.64458i	−0.0191498	+	0.116875i
$199$	−13.1354			−0.931144			−0.465572	−	0.885010i	$-0.654151\pi$
$199$	−13.1354			−0.931144			−0.465572	+	0.885010i	$0.654151\pi$
$200$	12.8209	+	5.96866i	0.906574	+	0.422048i
$201$		−	9.56245i		−	0.674483i
$202$	1.45574	−	8.88470i	0.102425	−	0.625125i
$203$	−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
$208$	−15.4241	+	2.10724i	−1.06947	+	0.146111i
$209$	−9.20160			−0.636488
$210$	−2.28684	+	8.04800i	−0.157807	+	0.555365i
$211$		−	7.68962i		−	0.529375i	−0.964334	−	0.264688i	$-0.914731\pi$
$211$		−	7.68962i		−	0.529375i	0.964334	−	0.264688i	$-0.0852689\pi$
$212$	5.43670	+	10.9571i	0.373394	+	0.752534i
$213$	−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
$218$	1.68794	−	10.3019i	0.114322	−	0.697731i
$219$	−0.516605			−0.0349089
$220$	2.46317	+	4.65890i	0.166067	+	0.314103i
$221$		−	13.6892i		−	0.920837i
$222$	−9.48002	−	1.55328i	−0.636257	−	0.104249i
$223$	15.4672	+	15.4672i	1.03576	+	1.03576i	0.999336	+	0.0364244i	$0.0115968\pi$
$223$	15.4672	+	15.4672i	1.03576	+	1.03576i	0.0364244	+	0.999336i	$0.488403\pi$
$224$	−8.67869	−	12.1935i	−0.579870	−	0.814709i
$225$	−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	$-0.400853\pi$
$227$	−9.72415	−	9.72415i	−0.645415	−	0.645415i	−0.951881	+	0.306467i	$0.900853\pi$
$228$	6.94142	+	13.9897i	0.459707	+	0.926488i
$229$			1.70188i			0.112463i	0.998418	+	0.0562317i	$0.0179085\pi$
$229$			1.70188i			0.112463i	−0.998418	+	0.0562317i	$0.982091\pi$
$230$	−12.2678	−	1.68689i	−0.808913	−	0.111230i
$231$	−2.49103	+	1.87487i	−0.163898	+	0.123358i
$232$	0.624186	−	1.17812i	0.0409798	−	0.0773474i
$233$	−8.21746	+	8.21746i	−0.538343	+	0.538343i	−0.923042	−	0.384699i	$-0.874305\pi$
$233$	−8.21746	+	8.21746i	−0.538343	+	0.538343i	0.384699	+	0.923042i	$0.374305\pi$
$234$	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
$238$	11.6567	−	6.10998i	0.755589	−	0.396051i
$239$		−	20.1255i		−	1.30181i	−0.759159	−	0.650906i	$-0.774389\pi$
$239$		−	20.1255i		−	1.30181i	0.759159	−	0.650906i	$-0.225611\pi$
$240$	5.22502	−	7.25942i	0.337274	−	0.468593i
$241$		−	12.2565i		−	0.789512i	−0.918786	−	0.394756i	$-0.870829\pi$
$241$		−	12.2565i		−	0.789512i	0.918786	−	0.394756i	$-0.129171\pi$
$242$	2.19780	−	13.4137i	0.141280	−	0.862263i
$243$	−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
$248$	−27.0393	−	14.3258i	−1.71700	−	0.909692i
$249$		−	13.8889i		−	0.880173i
$250$	−12.0906	+	10.1891i	−0.764674	+	0.644417i
$251$	−10.5836			−0.668031			−0.334016	−	0.942568i	$-0.608404\pi$
$251$	−10.5836			−0.668031			−0.334016	+	0.942568i	$0.608404\pi$
$252$	4.72963	+	2.37289i	0.297939	+	0.149478i
$253$	−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	−0.218936	+	0.975739i	$0.570259\pi$
$257$	−19.1521	+	19.1521i	−1.19468	+	1.19468i	−0.975739	+	0.218936i	$0.929741\pi$
$258$	2.79854	−	17.0801i	0.174229	−	1.06336i
$259$	−10.8075	−	14.3593i	−0.671546	−	0.892243i
$260$	5.12777	−	16.6324i	0.318011	−	1.03150i
$261$			0.471378i			0.0291776i
$262$	3.95842	−	24.1591i	0.244552	−	1.49256i
$263$	8.48263	−	8.48263i	0.523062	−	0.523062i	−0.395433	−	0.918495i	$-0.629405\pi$
$263$	8.48263	−	8.48263i	0.523062	−	0.523062i	0.918495	+	0.395433i	$0.129405\pi$
$264$	3.18594	−	0.979191i	0.196081	−	0.0602650i
$265$	−13.6709	+	0.352182i	−0.839800	+	0.0216344i
$266$	−8.70697	+	27.8894i	−0.533859	+	1.71001i
$267$	−1.84842	+	1.84842i	−0.113121	+	0.113121i
$268$	−17.1319	+	8.50055i	−1.04650	+	0.519254i
$269$			16.0595i			0.979164i	0.871957	+	0.489582i	$0.162851\pi$
$269$			16.0595i			0.979164i	−0.871957	+	0.489582i	$0.837149\pi$
$270$	−0.430779	+	3.13280i	−0.0262164	+	0.190656i
$271$		−	6.71295i		−	0.407782i	−0.978994	−	0.203891i	$-0.934641\pi$
$271$		−	6.71295i		−	0.407782i	0.978994	−	0.203891i	$-0.0653589\pi$
$272$	−13.9401	+	1.90449i	−0.845244	+	0.115477i
$273$	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	$-0.864149\pi$
$277$	−8.26095	+	8.26095i	−0.496352	+	0.496352i	0.413948	+	0.910300i	$0.364149\pi$
$278$	−4.11787	−	0.674705i	−0.246974	−	0.0404661i
$279$	10.8187			0.647699
$280$	16.4515	−	3.05722i	0.983168	−	0.182704i
$281$	−3.53880			−0.211107			−0.105554	−	0.994414i	$-0.533661\pi$
$281$	−3.53880			−0.211107			−0.105554	+	0.994414i	$0.533661\pi$
$282$	3.19577	+	0.523620i	0.190305	+	0.0311811i
$283$	2.89630	−	2.89630i	0.172167	−	0.172167i	−0.615764	−	0.787931i	$-0.711152\pi$
$283$	2.89630	−	2.89630i	0.172167	−	0.172167i	0.787931	+	0.615764i	$0.211152\pi$
$284$	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
$288$	−3.89209	−	4.10507i	−0.229344	−	0.241894i
$289$			4.62788i			0.272228i
$290$	0.900622	+	1.18779i	0.0528864	+	0.0697495i
$291$			10.5159i			0.616453i
$292$	0.459237	+	0.925541i	0.0268748	+	0.0541632i
$293$	5.06929	−	5.06929i	0.296151	−	0.296151i	−0.543353	−	0.839504i	$-0.682846\pi$
$293$	5.06929	−	5.06929i	0.296151	−	0.296151i	0.839504	+	0.543353i	$0.182846\pi$
$294$	3.32547	+	9.32423i	0.193946	+	0.543800i
$295$	−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
$298$	−3.63968	+	22.2138i	−0.210841	+	1.28681i
$299$			15.2402i			0.881362i
$300$	4.90009	+	8.71717i	0.282907	+	0.503286i
$301$	25.8711	−	19.4718i	1.49118	−	1.12234i
$302$	2.26170	−	13.8036i	0.130146	−	0.794311i
$303$	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	$-0.0118237\pi$
$307$	16.8586	+	16.8586i	0.962174	+	0.962174i	−0.0371367	+	0.999310i	$0.511824\pi$
$308$	5.57340	+	2.79622i	0.317574	+	0.159330i
$309$	5.21080			0.296432
$310$	27.2613	−	20.6704i	1.54834	−	1.17400i
$311$			17.6305i			0.999733i	0.866102	+	0.499867i	$0.166618\pi$
$311$			17.6305i			0.999733i	−0.866102	+	0.499867i	$0.833382\pi$
$312$	−9.72696	−	5.15349i	−0.550681	−	0.291759i
$313$	8.32589	+	8.32589i	0.470607	+	0.470607i	0.902111	−	0.431504i	$-0.142017\pi$
$313$	8.32589	+	8.32589i	0.470607	+	0.470607i	−0.431504	+	0.902111i	$0.642017\pi$
$314$	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	$-0.902172\pi$
$317$	−11.5840	+	11.5840i	−0.650621	+	0.650621i	0.302521	+	0.953143i	$0.402172\pi$
$318$	−1.39849	+	8.53532i	−0.0784237	+	0.478637i
$319$			0.555472i			0.0311005i
$320$	−17.6506	−	2.90779i	−0.986700	−	0.162550i
$321$		−	18.6460i		−	1.04072i
$322$	−12.9773	+	6.80222i	−0.723199	+	0.379073i
$323$	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
$328$	3.44002	+	1.82258i	0.189944	+	0.100635i
$329$	3.64328	+	4.84060i	0.200860	+	0.266871i
$330$	−0.507630	+	3.69169i	−0.0279441	+	0.203221i
$331$			8.52163i			0.468391i	0.972190	+	0.234195i	$0.0752456\pi$
$331$			8.52163i			0.468391i	−0.972190	+	0.234195i	$0.924754\pi$
$332$	−24.8831	+	12.3465i	−1.36564	+	0.677605i
$333$	−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
$336$	0.0468280	−	10.5829i	0.00255468	−	0.577345i
$337$	6.75033	+	6.75033i	0.367714	+	0.367714i	0.866643	−	0.498929i	$-0.166273\pi$
$337$	6.75033	+	6.75033i	0.367714	+	0.367714i	−0.498929	+	0.866643i	$0.666273\pi$
$338$	−2.99572	−	0.490842i	−0.162946	−	0.0266983i
$339$		−	18.7510i		−	1.01841i
$340$	4.63440	−	15.0321i	0.251336	−	0.815231i
$341$	12.7488			0.690385
$342$	−1.78556	+	10.8976i	−0.0965518	+	0.589277i
$343$	−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	$-0.678715\pi$
$347$	5.85047	−	5.85047i	0.314070	−	0.314070i	0.846484	+	0.532414i	$0.178715\pi$
$348$	0.844512	−	0.419032i	0.0452706	−	0.0224625i
$349$			13.6236i			0.729256i	0.931153	+	0.364628i	$0.118804\pi$
$349$			13.6236i			0.729256i	−0.931153	+	0.364628i	$0.881196\pi$
$350$	−4.64839	+	18.1216i	−0.248467	+	0.968640i
$351$	3.89186			0.207732
$352$	−4.58645	−	4.83742i	−0.244458	−	0.257836i
$353$	−5.55745	−	5.55745i	−0.295793	−	0.295793i	0.543570	−	0.839364i	$-0.317072\pi$
$353$	−5.55745	−	5.55745i	−0.295793	−	0.295793i	−0.839364	+	0.543570i	$0.817072\pi$
$354$	−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
$358$	−2.54400	+	15.5266i	−0.134455	+	0.820606i
$359$			17.8417i			0.941647i	0.882227	+	0.470823i	$0.156043\pi$
$359$			17.8417i			0.941647i	−0.882227	+	0.470823i	$0.843957\pi$
$360$	5.99561	−	2.01313i	0.315996	−	0.106101i
$361$	−41.9734			−2.20913
$362$	−1.81371	+	11.0695i	−0.0953265	+	0.581799i
$363$	6.79627	−	6.79627i	0.356711	−	0.356711i
$364$	−6.48563	−	19.5458i	−0.339939	−	1.02448i
$365$	−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	−0.254808	+	0.966992i	$0.582012\pi$
$367$	−23.4063	+	23.4063i	−1.22180	+	1.22180i	−0.966992	+	0.254808i	$0.917988\pi$
$368$	15.5195	−	2.12027i	0.809010	−	0.110527i
$369$	−1.37639			−0.0716519
$370$	−21.2804	−	2.92618i	−1.10631	−	0.152125i
$371$	−12.9284	+	9.73053i	−0.671208	+	0.505184i
$372$	−9.61730	−	19.3826i	−0.498634	−	1.00494i
$373$	17.6625	+	17.6625i	0.914531	+	0.914531i	0.996625	−	0.0820940i	$-0.0261608\pi$
$373$	17.6625	+	17.6625i	0.914531	+	0.914531i	−0.0820940	+	0.996625i	$0.526161\pi$
$374$	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
$378$	1.73707	+	3.31400i	0.0893453	+	0.170454i
$379$	1.32887			0.0682593			0.0341296	−	0.999417i	$-0.489134\pi$
$379$	1.32887			0.0682593			0.0341296	+	0.999417i	$0.489134\pi$
$380$	16.3219	+	30.8717i	0.837297	+	1.58369i
$381$	7.24516			0.371181
$382$	2.93467	−	17.9110i	0.150151	−	0.916404i
$383$	−6.97935	−	6.97935i	−0.356628	−	0.356628i	0.505940	−	0.862569i	$-0.331146\pi$
$383$	−6.97935	−	6.97935i	−0.356628	−	0.356628i	−0.862569	+	0.505940i	$0.831146\pi$
$384$	−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
$388$	18.8401	−	9.34812i	0.956461	−	0.474579i
$389$	−12.6704			−0.642417			−0.321209	−	0.947008i	$-0.604089\pi$
$389$	−12.6704			−0.642417			−0.321209	+	0.947008i	$0.604089\pi$
$390$	9.80681	−	7.43584i	0.496587	−	0.376529i
$391$			13.7739i			0.696574i
$392$	13.7489	−	14.2466i	0.694426	−	0.719564i
$393$	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	$-0.292949\pi$
$397$	−3.79046	−	3.79046i	−0.190238	−	0.190238i	−0.795799	+	0.605561i	$0.792949\pi$
$398$	−3.00363	+	18.3318i	−0.150558	+	0.918891i
$399$	−16.5066	+	12.4237i	−0.826362	+	0.621961i
$400$	11.2616	−	16.5281i	0.563080	−	0.826403i
$401$	−15.8951			−0.793764			−0.396882	−	0.917870i	$-0.629908\pi$
$401$	−15.8951			−0.793764			−0.396882	+	0.917870i	$0.629908\pi$
$402$	−13.3454	−	2.18661i	−0.665608	−	0.109058i
$403$	−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
$406$	1.68359	+	0.525613i	0.0835554	+	0.0260857i
$407$	−5.66011	−	5.66011i	−0.280561	−	0.280561i
$408$	−8.79109	−	4.65765i	−0.435224	−	0.230588i
$409$	1.12314			0.0555358			0.0277679	−	0.999614i	$-0.491160\pi$
$409$	1.12314			0.0555358			0.0277679	+	0.999614i	$0.491160\pi$
$410$	−3.46826	+	2.62975i	−0.171285	+	0.129874i
$411$	3.05765			0.150823
$412$	−4.63214	−	9.33557i	−0.228209	−	0.459931i
$413$	−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
$418$	−2.10410	+	12.8418i	−0.102915	+	0.628113i
$419$			25.5925i			1.25027i	0.780515	+	0.625137i	$0.214957\pi$
$419$			25.5925i			1.25027i	−0.780515	+	0.625137i	$0.785043\pi$
$420$	10.7089	+	5.03184i	0.522541	+	0.245528i
$421$		−	17.5467i		−	0.855173i	−0.903974	−	0.427587i	$-0.859364\pi$
$421$		−	17.5467i		−	0.855173i	0.903974	−	0.427587i	$-0.140636\pi$
$422$	−10.7317	−	1.75836i	−0.522410	−	0.0855957i
$423$	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
$428$	−33.4058	+	16.5754i	−1.61473	+	0.801201i
$429$	4.58617			0.221422
$430$	5.27208	−	38.3407i	0.254242	−	1.84895i
$431$	−8.10696			−0.390498			−0.195249	−	0.980754i	$-0.562552\pi$
$431$	−8.10696			−0.390498			−0.195249	+	0.980754i	$0.562552\pi$
$432$	−0.541449	−	3.96318i	−0.0260505	−	0.190679i
$433$	16.9355	+	16.9355i	0.813868	+	0.813868i	0.985211	−	0.171343i	$-0.0548108\pi$
$433$	16.9355	+	16.9355i	0.813868	+	0.813868i	−0.171343	+	0.985211i	$0.554811\pi$
$434$	12.0635	−	38.6406i	0.579065	−	1.85481i
$435$	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
$438$	−0.118130	+	0.720976i	−0.00564449	+	0.0344496i
$439$	−4.82760			−0.230409			−0.115204	−	0.993342i	$-0.536752\pi$
$439$	−4.82760			−0.230409			−0.115204	+	0.993342i	$0.536752\pi$
$440$	7.06523	−	2.37227i	0.336822	−	0.113094i
$441$	−1.93723	+	6.72660i	−0.0922492	+	0.320314i
$442$	−19.1047	−	3.13027i	−0.908720	−	0.148892i
$443$	−27.6716	−	27.6716i	−1.31472	−	1.31472i	−0.917896	−	0.396821i	$-0.870113\pi$
$443$	−27.6716	−	27.6716i	−1.31472	−	1.31472i	−0.396821	−	0.917896i	$-0.629887\pi$
$444$	−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
$448$	−19.0018	+	9.32378i	−0.897749	+	0.440507i
$449$			6.52588i			0.307975i	0.988073	+	0.153988i	$0.0492116\pi$
$449$			6.52588i			0.307975i	−0.988073	+	0.153988i	$0.950788\pi$
$450$	−0.782529	+	7.02763i	−0.0368888	+	0.331286i
$451$	−1.62194			−0.0763740
$452$	−33.5939	+	16.6687i	−1.58013	+	0.784030i
$453$	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	0.715598	−	0.698512i	$-0.246154\pi$
$457$	0.365261	+	0.365261i	0.0170862	+	0.0170862i	−0.698512	+	0.715598i	$0.746154\pi$
$458$	2.37515	+	0.389163i	0.110983	+	0.0181844i
$459$	3.51740			0.164178
$460$	−5.15947	+	16.7352i	−0.240561	+	0.780284i
$461$	−19.0291			−0.886274			−0.443137	−	0.896454i	$-0.646135\pi$
$461$	−19.0291			−0.886274			−0.443137	+	0.896454i	$0.646135\pi$
$462$	2.04697	+	3.90522i	0.0952335	+	0.181687i
$463$	−2.25269	+	2.25269i	−0.104691	+	0.104691i	−0.757512	−	0.652821i	$-0.773585\pi$
$463$	−2.25269	+	2.25269i	−0.104691	+	0.104691i	0.652821	+	0.757512i	$0.273585\pi$
$464$	−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	$-0.106209\pi$
$467$	13.3408	+	13.3408i	0.617340	+	0.617340i	−0.327508	+	0.944848i	$0.606209\pi$
$468$	−3.45967	−	6.97258i	−0.159923	−	0.322308i
$469$	−15.2142	−	20.2142i	−0.702525	−	0.933404i
$470$	7.17374	+	0.986433i	0.330900	+	0.0455007i
$471$	11.3806			0.524390
$472$	1.33248	+	0.705971i	0.0613326	+	0.0324949i
$473$	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
$476$	−5.86162	−	17.6652i	−0.268667	−	0.809685i
$477$	−4.32457	+	4.32457i	−0.198008	+	0.198008i
$478$	−28.0873	−	4.60204i	−1.28468	−	0.210492i
$479$	18.0254			0.823599			0.411800	−	0.911274i	$-0.364900\pi$
$479$	18.0254			0.823599			0.411800	+	0.911274i	$0.364900\pi$
$480$	−8.93649	−	8.95205i	−0.407893	−	0.408603i
$481$			26.4365i			1.20540i
$482$	−17.1052	−	2.80266i	−0.779123	−	0.127658i
$483$	−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	0.838119	−	0.545488i	$-0.183656\pi$
$487$	6.45780	+	6.45780i	0.292631	+	0.292631i	−0.545488	+	0.838119i	$0.683656\pi$
$488$	7.67125	−	14.4791i	0.347261	−	0.655438i
$489$	−3.62266			−0.163822
$490$	7.97045	+	20.6512i	0.360068	+	0.932926i
$491$			35.0523i			1.58189i	0.611888	+	0.790944i	$0.290410\pi$
$491$			35.0523i			1.58189i	−0.611888	+	0.790944i	$0.709590\pi$
$492$	1.22354	+	2.46591i	0.0551615	+	0.111172i
$493$	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
$498$	−19.3834	−	3.17593i	−0.868591	−	0.142317i
$499$	6.99167			0.312990			0.156495	−	0.987679i	$-0.449980\pi$
$499$	6.99167			0.312990			0.156495	+	0.987679i	$0.449980\pi$
$500$	11.4553	+	19.2036i	0.512296	+	0.858809i
$501$		−	13.7849i		−	0.615864i
$502$	−2.42012	+	14.7705i	−0.108015	+	0.659241i
$503$	−13.5873	−	13.5873i	−0.605827	−	0.605827i	0.336026	−	0.941853i	$-0.390917\pi$
$503$	−13.5873	−	13.5873i	−0.605827	−	0.605827i	−0.941853	+	0.336026i	$0.890917\pi$
$504$	4.39313	−	6.05809i	0.195686	−	0.269849i
$505$	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
$508$	−6.44059	−	12.9803i	−0.285755	−	0.575907i
$509$			2.58072i			0.114389i	0.998363	+	0.0571943i	$0.0182154\pi$
$509$			2.58072i			0.114389i	−0.998363	+	0.0571943i	$0.981785\pi$
$510$	8.86326	−	6.72041i	0.392472	−	0.297585i
$511$	−1.09206	+	0.821935i	−0.0483098	+	0.0363603i
$512$	22.4928	−	2.46496i	0.994049	−	0.108937i
$513$	−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
$518$	−22.5112	+	11.7995i	−0.989086	+	0.518441i
$519$			7.49545i			0.329014i
$520$	−22.0397	−	10.9596i	−0.966505	−	0.480611i
$521$		−	11.0924i		−	0.485966i	−0.970030	−	0.242983i	$-0.921874\pi$
$521$		−	11.0924i		−	0.485966i	0.970030	−	0.242983i	$-0.0781260\pi$
$522$	0.657857	+	0.107788i	0.0287936	+	0.00471777i
$523$	14.8259	−	14.8259i	0.648290	−	0.648290i	−0.304289	−	0.952580i	$-0.598419\pi$
$523$	14.8259	−	14.8259i	0.648290	−	0.648290i	0.952580	+	0.304289i	$0.0984189\pi$
$524$	−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
$528$	−0.638044	−	4.67022i	−0.0277673	−	0.203245i
$529$			7.66561i			0.333287i
$530$	−2.63458	+	19.1598i	−0.114439	+	0.832247i
$531$	−0.533140			−0.0231363
$532$	36.9315	+	18.5289i	1.60118	+	0.803328i
$533$	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
$538$	22.4127	+	3.67227i	0.966279	+	0.158323i
$539$	−2.28284	+	7.92663i	−0.0983288	+	0.341424i
$540$	4.27364	+	1.31756i	0.183908	+	0.0566989i
$541$			28.8656i			1.24103i	0.784195	+	0.620515i	$0.213076\pi$
$541$			28.8656i			1.24103i	−0.784195	+	0.620515i	$0.786924\pi$
$542$	−9.36862	−	1.53503i	−0.402417	−	0.0659351i
$543$	−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
$546$	4.33964	−	13.9003i	0.185719	−	0.594879i
$547$	−10.2013	+	10.2013i	−0.436175	+	0.436175i	−0.890723	−	0.454547i	$-0.849801\pi$
$547$	−10.2013	+	10.2013i	−0.436175	+	0.436175i	0.454547	+	0.890723i	$0.349801\pi$
$548$	−2.71810	−	5.47803i	−0.116111	−	0.234010i
$549$			5.79323i			0.247249i
$550$	−0.922133	+	8.28137i	−0.0393199	+	0.353119i
$551$			3.68078i			0.156806i
$552$	9.78710	+	5.18535i	0.416567	+	0.220703i
$553$	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	−0.0449831	+	0.998988i	$0.514323\pi$
$557$	−24.6386	+	24.6386i	−1.04397	+	1.04397i	−0.998988	+	0.0449831i	$0.985677\pi$
$558$	2.47388	−	15.0986i	0.104728	−	0.639176i
$559$	−47.6304			−2.01455
$560$	−0.504741	−	23.6589i	−0.0213292	−	0.999773i
$561$	4.14491			0.174998
$562$	−0.809206	+	4.93877i	−0.0341343	+	0.208329i
$563$	−18.6930	+	18.6930i	−0.787814	+	0.787814i	−0.981135	−	0.193321i	$-0.938074\pi$
$563$	−18.6930	+	18.6930i	−0.787814	+	0.787814i	0.193321	+	0.981135i	$0.438074\pi$
$564$	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
$568$	14.2683	−	26.9308i	0.598686	−	1.12999i
$569$			15.0539i			0.631094i	0.948910	+	0.315547i	$0.102188\pi$
$569$			15.0539i			0.631094i	−0.948910	+	0.315547i	$0.897812\pi$
$570$	−3.36376	+	24.4626i	−0.140892	+	1.02463i
$571$		−	29.2344i		−	1.22342i	−0.791082	−	0.611710i	$-0.790482\pi$
$571$		−	29.2344i		−	1.22342i	0.791082	−	0.611710i	$-0.209518\pi$
$572$	−4.07688	−	8.21650i	−0.170463	−	0.343549i
$573$	9.07489	−	9.07489i	0.379109	−	0.379109i
$574$	−1.53475	+	4.91597i	−0.0640592	+	0.205189i
$575$	−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	−0.731444	−	0.681902i	$-0.761153\pi$
$577$	−1.19004	+	1.19004i	−0.0495418	+	0.0495418i	0.681902	+	0.731444i	$0.261153\pi$
$578$	6.45869	+	1.05824i	0.268646	+	0.0440171i
$579$		−	15.0371i		−	0.624921i
$580$	1.86363	−	0.985304i	0.0773830	−	0.0409125i
$581$	−22.0977	−	29.3599i	−0.916766	−	1.21805i
$582$	14.6760	+	2.40464i	0.608341	+	0.0996754i
$583$	−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	$-0.440289\pi$
$587$	−19.2848	−	19.2848i	−0.795969	−	0.795969i	−0.982457	+	0.186489i	$0.940289\pi$
$588$	13.7734	−	2.50890i	0.568004	−	0.103465i
$589$	84.4784			3.48087
$590$	−1.34342	+	1.01863i	−0.0553079	+	0.0419362i
$591$		−	14.6766i		−	0.603715i
$592$	26.9210	−	3.67794i	1.10645	−	0.151162i
$593$	−14.5029	−	14.5029i	−0.595564	−	0.595564i	0.343565	−	0.939129i	$-0.388366\pi$
$593$	−14.5029	−	14.5029i	−0.595564	−	0.595564i	−0.939129	+	0.343565i	$0.888366\pi$
$594$	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
$598$	21.2693	+	3.48492i	0.869765	+	0.142509i
$599$			1.34016i			0.0547576i	0.999625	+	0.0273788i	$0.00871603\pi$
$599$			1.34016i			0.0547576i	−0.999625	+	0.0273788i	$0.991284\pi$
$600$	13.2862	−	4.84526i	0.542407	−	0.197807i
$601$		−	23.9818i		−	0.978239i	−0.872217	−	0.489119i	$-0.837318\pi$
$601$		−	23.9818i		−	0.978239i	0.872217	−	0.489119i	$-0.162682\pi$
$602$	−21.2591	−	40.5583i	−0.866457	−	1.65303i
$603$	−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	−0.605056	−	0.796183i	$-0.706849\pi$
$607$	4.70885	−	4.70885i	0.191126	−	0.191126i	0.796183	+	0.605056i	$0.206849\pi$
$608$	−30.3916	−	32.0547i	−1.23254	−	1.29999i
$609$	0.749977	+	0.996450i	0.0303906	+	0.0403782i
$610$	11.0686	+	14.5980i	0.448156	+	0.591054i
$611$		−	8.91189i		−	0.360536i
$612$	−3.12680	−	6.30172i	−0.126393	−	0.254732i
$613$	−2.34915	−	2.34915i	−0.0948813	−	0.0948813i	0.658073	−	0.752954i	$-0.271372\pi$
$613$	−2.34915	−	2.34915i	−0.0948813	−	0.0948813i	−0.752954	+	0.658073i	$0.771372\pi$
$614$	27.3830	−	19.6730i	1.10509	−	0.793937i
$615$	−3.07668	+	0.0792594i	−0.124064	+	0.00319605i
$616$	5.17687	−	7.13886i	0.208582	−	0.287633i
$617$	24.9442	+	24.9442i	1.00421	+	1.00421i	0.999991	+	0.00422348i	$0.00134438\pi$
$617$	24.9442	+	24.9442i	1.00421	+	1.00421i	0.00422348	+	0.999991i	$0.498656\pi$
$618$	1.19154	−	7.27221i	0.0479306	−	0.292531i
$619$			20.8085i			0.836362i	0.908364	+	0.418181i	$0.137332\pi$
$619$			20.8085i			0.836362i	−0.908364	+	0.418181i	$0.862668\pi$
$620$	−22.6139	−	42.7726i	−0.908198	−	1.71779i
$621$	−3.91592			−0.157140
$622$	24.6052	+	4.03151i	0.986578	+	0.161649i
$623$	−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
$628$	−10.1168	−	20.3893i	−0.403704	−	0.813620i
$629$			23.8929i			0.952672i
$630$	4.07376	+	7.30784i	0.162302	+	0.291151i
$631$	9.10899			0.362623			0.181312	−	0.983426i	$-0.441966\pi$
$631$	9.10899			0.362623			0.181312	+	0.983426i	$0.441966\pi$
$632$	−31.6087	−	16.7468i	−1.25733	−	0.666151i
$633$	−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
$638$	0.775219	+	0.127018i	0.0306912	+	0.00502869i
$639$			10.7753i			0.426263i
$640$	−8.09423	+	23.9684i	−0.319953	+	0.947434i
$641$	−15.6571			−0.618417			−0.309209	−	0.950994i	$-0.600064\pi$
$641$	−15.6571			−0.618417			−0.309209	+	0.950994i	$0.600064\pi$
$642$	−26.0224	−	4.26372i	−1.02702	−	0.168276i
$643$	6.87547	−	6.87547i	0.271142	−	0.271142i	−0.558418	−	0.829560i	$-0.688591\pi$
$643$	6.87547	−	6.87547i	0.271142	−	0.271142i	0.829560	+	0.558418i	$0.188591\pi$
$644$	6.52572	+	19.6667i	0.257150	+	0.774975i
$645$	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	0.0734252	−	0.997301i	$-0.476607\pi$
$647$	27.2352	−	27.2352i	1.07073	−	1.07073i	0.997301	−	0.0734252i	$-0.0233930\pi$
$648$	1.32417	−	2.49931i	0.0520185	−	0.0981823i
$649$	−0.628253			−0.0246611
$650$	21.4932	−	17.1863i	0.843034	−	0.674101i
$651$	22.8698	−	17.2129i	0.896337	−	0.674627i
$652$	3.22036	+	6.49029i	0.126119	+	0.254179i
$653$	26.4122	+	26.4122i	1.03359	+	1.03359i	0.999416	+	0.0341742i	$0.0108801\pi$
$653$	26.4122	+	26.4122i	1.03359	+	1.03359i	0.0341742	+	0.999416i	$0.489120\pi$
$654$	−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
$658$	7.58867	−	3.97769i	0.295837	−	0.155066i
$659$	27.7274			1.08011			0.540053	−	0.841631i	$-0.318404\pi$
$659$	27.7274			1.08011			0.540053	+	0.841631i	$0.318404\pi$
$660$	5.03607	+	1.55262i	0.196029	+	0.0604356i
$661$	−0.497810			−0.0193626			−0.00968128	−	0.999953i	$-0.503082\pi$
$661$	−0.497810			−0.0193626			−0.00968128	+	0.999953i	$0.503082\pi$
$662$	11.8928	+	1.94861i	0.462227	+	0.0757350i
$663$	−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
$668$	−24.6968	+	12.2541i	−0.955548	+	0.474126i
$669$	21.8739			0.845695
$670$	−29.9572	−	4.11930i	−1.15735	−	0.159143i
$671$			6.82675i			0.263544i
$672$	−14.7588	−	2.48531i	−0.569334	−	0.0958729i
$673$	24.8228	−	24.8228i	0.956850	−	0.956850i	−0.0422568	−	0.999107i	$-0.513455\pi$
$673$	24.8228	−	24.8228i	0.956850	−	0.956850i	0.999107	+	0.0422568i	$0.0134548\pi$
$674$	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	$-0.0339123\pi$
$677$	23.1049	+	23.1049i	0.887993	+	0.887993i	−0.106337	+	0.994330i	$0.533912\pi$
$678$	−26.1690	−	4.28773i	−1.00501	−	0.164669i
$679$	16.7311	+	22.2297i	0.642082	+	0.853096i
$680$	−19.9192	−	9.90514i	−0.763865	−	0.379845i
$681$	−13.7520			−0.526979
$682$	2.91522	−	17.7922i	0.111630	−	0.681300i
$683$	−7.96194	−	7.96194i	−0.304655	−	0.304655i	0.538177	−	0.842832i	$-0.319113\pi$
$683$	−7.96194	−	7.96194i	−0.304655	−	0.304655i	−0.842832	+	0.538177i	$0.819113\pi$
$684$	14.8005	+	4.98386i	0.565911	+	0.190563i
$685$	6.83484	−	0.176075i	0.261146	−	0.00672748i
$686$	21.8649	+	14.4196i	0.834806	+	0.550545i
$687$	1.20341	+	1.20341i	0.0459130	+	0.0459130i
$688$	6.62652	+	48.5034i	0.252634	+	1.84917i
$689$	23.8020			0.906786
$690$	−9.86744	+	7.48181i	−0.375647	+	0.284828i
$691$	−23.0214			−0.875777			−0.437889	−	0.899029i	$-0.644274\pi$
$691$	−23.0214			−0.875777			−0.437889	+	0.899029i	$0.644274\pi$
$692$	13.4287	−	6.66309i	0.510483	−	0.253293i
$693$	−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
$698$	19.0132	+	3.11527i	0.719660	+	0.117915i
$699$			11.6212i			0.439556i
$700$	24.2277	+	10.6311i	0.915719	+	0.401819i
$701$			21.6777i			0.818757i	0.912365	+	0.409379i	$0.134254\pi$
$701$			21.6777i			0.818757i	−0.912365	+	0.409379i	$0.865746\pi$
$702$	0.889938	−	5.43149i	0.0335885	−	0.204998i
$703$	−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
$708$	0.473936	+	0.955165i	0.0178116	+	0.0358973i
$709$	21.7250			0.815899			0.407950	−	0.913004i	$-0.366244\pi$
$709$	21.7250			0.815899			0.407950	+	0.913004i	$0.366244\pi$
$710$	20.5874	+	27.1518i	0.772632	+	1.01899i
$711$	12.6470			0.474298
$712$	3.46146	−	6.53334i	0.129724	−	0.244847i
$713$	29.9567	+	29.9567i	1.12189	+	1.12189i
$714$	3.92210	−	12.5629i	0.146781	−	0.470155i
$715$	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
$718$	24.8999	+	4.07979i	0.929256	+	0.152257i
$719$	−49.1382			−1.83255			−0.916273	−	0.400555i	$-0.868817\pi$
$719$	−49.1382			−1.83255			−0.916273	+	0.400555i	$0.868817\pi$
$720$	−1.43854	−	8.82783i	−0.0536111	−	0.328994i
$721$	11.0152	−	8.29055i	0.410226	−	0.308756i
$722$	−9.59793	+	58.5783i	−0.357198	+	2.18006i
$723$	−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	−0.305770	−	0.952105i	$-0.598914\pi$
$727$	17.4271	−	17.4271i	0.646335	−	0.646335i	0.952105	+	0.305770i	$0.0989139\pi$
$728$	−28.7613	+	4.58189i	−1.06596	+	0.169816i
$729$			1.00000i			0.0370370i
$730$	−0.222543	+	1.61842i	−0.00823667	+	0.0599004i
$731$	−43.0477			−1.59218
$732$	10.3791	−	5.14990i	0.383621	−	0.190346i
$733$	−24.6426	+	24.6426i	−0.910193	+	0.910193i	−0.996287	−	0.0860936i	$-0.972562\pi$
$733$	−24.6426	+	24.6426i	−0.910193	+	0.910193i	0.0860936	+	0.996287i	$0.472562\pi$
$734$	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
$738$	−0.314734	+	1.92089i	−0.0115855	+	0.0707090i
$739$	−36.3996			−1.33898			−0.669490	−	0.742821i	$-0.733487\pi$
$739$	−36.3996			−1.33898			−0.669490	+	0.742821i	$0.733487\pi$
$740$	−8.94990	+	29.0299i	−0.329005	+	1.06716i
$741$	30.3897			1.11640
$742$	10.6237	+	20.2680i	0.390008	+	0.744060i
$743$	3.09843	−	3.09843i	0.113670	−	0.113670i	−0.647984	−	0.761654i	$-0.724388\pi$
$743$	3.09843	−	3.09843i	0.113670	−	0.113670i	0.761654	+	0.647984i	$0.224388\pi$
$744$	−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
$748$	−3.68462	−	7.42595i	−0.134723	−	0.271520i
$749$	−29.6664	−	39.4160i	−1.08399	−	1.44023i
$750$	−1.34452	+	15.7541i	−0.0490949	+	0.575259i
$751$	16.4075			0.598719			0.299359	−	0.954140i	$-0.403227\pi$
$751$	16.4075			0.598719			0.299359	+	0.954140i	$0.403227\pi$
$752$	−9.07522	+	1.23985i	−0.330939	+	0.0452128i
$753$	−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
$756$	5.02224	−	1.66646i	0.182657	−	0.0606086i
$757$	−23.8496	+	23.8496i	−0.866827	+	0.866827i	−0.992120	−	0.125292i	$-0.960013\pi$
$757$	−23.8496	+	23.8496i	−0.866827	+	0.866827i	0.125292	+	0.992120i	$0.460013\pi$
$758$	0.303867	−	1.85457i	0.0110370	−	0.0673610i
$759$	−4.61452			−0.167496
$760$	46.8170	−	15.7196i	1.69823	−	0.570210i
$761$			0.391527i			0.0141929i	0.999975	+	0.00709643i	$0.00225888\pi$
$761$			0.391527i			0.0141929i	−0.999975	+	0.00709643i	$0.997741\pi$
$762$	1.65673	−	10.1114i	0.0600169	−	0.366296i
$763$	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
$768$	13.9338	+	7.86440i	0.502793	+	0.283782i
$769$	28.1457			1.01496			0.507481	−	0.861663i	$-0.330577\pi$
$769$	28.1457			1.01496			0.507481	+	0.861663i	$0.330577\pi$
$770$	4.80052	+	8.61157i	0.172999	+	0.310339i
$771$			27.0852i			0.975448i
$772$	−26.9402	+	13.3673i	−0.969600	+	0.481098i
$773$	34.2060	−	34.2060i	1.23030	−	1.23030i	0.266456	−	0.963847i	$-0.414147\pi$
$773$	34.2060	−	34.2060i	1.23030	−	1.23030i	0.963847	−	0.266456i	$-0.0858528\pi$
$774$	−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
$778$	−2.89731	+	17.6829i	−0.103874	+	0.633964i
$779$	−10.7476			−0.385072
$780$	−8.13500	−	15.3868i	−0.291280	−	0.550935i
$781$			12.6976i			0.454356i
$782$	19.2228	+	3.14962i	0.687408	+	0.112630i
$783$	0.333314	+	0.333314i	0.0119117	+	0.0119117i
$784$	−16.7387	−	22.4458i	−0.597812	−	0.801636i
$785$	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	$-0.186593\pi$
$787$	7.85073	+	7.85073i	0.279848	+	0.279848i	−0.553200	+	0.833048i	$0.686593\pi$
$788$	−26.2944	+	13.0468i	−0.936698	+	0.464773i
$789$		−	11.9963i		−	0.427078i
$790$	31.8682	−	24.1635i	1.13382	−	0.859699i
$791$	−29.8334	−	39.6379i	−1.06075	−	1.40936i
$792$	1.56041	−	2.94519i	0.0554467	−	0.104653i
$793$	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	$-0.362846\pi$
$797$	−13.8594	−	13.8594i	−0.490926	−	0.490926i	−0.908598	+	0.417672i	$0.862846\pi$
$798$	13.5640	+	25.8775i	0.480160	+	0.916054i
$799$		−	8.05444i		−	0.284945i
$800$	−20.4915	−	19.4961i	−0.724483	−	0.689293i
$801$			2.61406i			0.0923631i
$802$	−3.63468	+	22.1833i	−0.128345	+	0.783319i
$803$	−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
$808$	−8.42996	+	15.9111i	−0.296565	+	0.559751i
$809$			25.3224i			0.890289i	0.895459	+	0.445144i	$0.146848\pi$
$809$			25.3224i			0.890289i	−0.895459	+	0.445144i	$0.853152\pi$
$810$	1.91062	+	2.51983i	0.0671322	+	0.0885378i
$811$	−28.3941			−0.997051			−0.498525	−	0.866875i	$-0.666125\pi$
$811$	−28.3941			−0.997051			−0.498525	+	0.866875i	$0.666125\pi$
$812$	1.11853	−	2.22944i	0.0392527	−	0.0782380i
$813$	−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
$818$	0.256825	−	1.56746i	0.00897969	−	0.0548051i
$819$	8.22703	−	6.19207i	0.287476	−	0.216368i
$820$	2.87701	+	5.44166i	0.100470	+	0.190031i
$821$			15.6094i			0.544771i	0.962188	+	0.272385i	$0.0878126\pi$
$821$			15.6094i			0.544771i	−0.962188	+	0.272385i	$0.912187\pi$
$822$	0.699183	−	4.26727i	0.0243868	−	0.148838i
$823$	−26.3199	+	26.3199i	−0.917453	+	0.917453i	−0.996844	−	0.0793908i	$-0.974703\pi$
$823$	−26.3199	+	26.3199i	−0.917453	+	0.917453i	0.0793908	+	0.996844i	$0.474703\pi$
$824$	−14.0880	+	4.32990i	−0.490778	+	0.150839i
$825$	−3.94624	+	4.37527i	−0.137390	+	0.152327i
$826$	−0.594482	+	1.90419i	−0.0206847	+	0.0662552i
$827$	30.0471	−	30.0471i	1.04484	−	1.04484i	0.0458943	−	0.998946i	$-0.485386\pi$
$827$	30.0471	−	30.0471i	1.04484	−	1.04484i	0.998946	−	0.0458943i	$-0.0146138\pi$
$828$	3.48106	+	7.01568i	0.120975	+	0.243812i
$829$		−	5.99665i		−	0.208272i	−0.994563	−	0.104136i	$-0.966792\pi$
$829$		−	5.99665i		−	0.208272i	0.994563	−	0.104136i	$-0.0332078\pi$
$830$	−43.5111	−	5.98304i	−1.51029	−	0.207674i
$831$			11.6827i			0.405270i
$832$	30.5802	+	5.85045i	1.06018	+	0.202828i
$833$	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
$838$	35.7170	+	5.85215i	1.23382	+	0.202159i
$839$	7.63941			0.263742			0.131871	−	0.991267i	$-0.457902\pi$
$839$	7.63941			0.263742			0.131871	+	0.991267i	$0.457902\pi$
$840$	9.47122	−	13.7948i	0.326788	−	0.475965i
$841$	−28.7778			−0.992338
$842$	−24.4882	−	4.01234i	−0.843920	−	0.138275i
$843$	−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
$848$	−3.31143	−	24.2383i	−0.113715	−	0.832346i
$849$		−	4.09599i		−	0.140574i
$850$	19.4253	−	15.5327i	0.666281	−	0.532767i
$851$		−	26.5999i		−	0.911833i
$852$	19.3048	−	9.57869i	0.661371	−	0.328160i
$853$	29.0765	−	29.0765i	0.995560	−	0.995560i	−0.00443003	−	0.999990i	$-0.501410\pi$
$853$	29.0765	−	29.0765i	0.995560	−	0.995560i	0.999990	+	0.00443003i	$0.00141013\pi$
$854$	20.6914	+	6.45978i	0.708044	+	0.221049i
$855$	−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	−0.989448	−	0.144890i	$-0.953717\pi$
$857$	−24.7241	+	24.7241i	−0.844558	+	0.844558i	0.144890	+	0.989448i	$0.453717\pi$
$858$	1.04870	−	6.40048i	0.0358022	−	0.218509i
$859$		−	3.66598i		−	0.125082i	−0.998042	−	0.0625409i	$-0.980080\pi$
$859$		−	3.66598i		−	0.125082i	0.998042	−	0.0625409i	$-0.0199204\pi$
$860$	−52.3029	−	16.1250i	−1.78352	−	0.549858i
$861$	−2.90956	+	2.18988i	−0.0991576	+	0.0746308i
$862$	−1.85379	+	11.3141i	−0.0631404	+	0.385360i
$863$	39.2591	−	39.2591i	1.33640	−	1.33640i	0.436873	−	0.899523i	$-0.356086\pi$
$863$	39.2591	−	39.2591i	1.33640	−	1.33640i	0.899523	−	0.436873i	$-0.143914\pi$
$864$	−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
$868$	−51.1684	−	25.6716i	−1.73677	−	0.871352i
$869$	14.9032			0.505557
$870$	1.47673	+	0.203060i	0.0500659	+	0.00688436i
$871$			37.2157i			1.26101i
$872$	−9.77460	+	18.4491i	−0.331010	+	0.624765i
$873$	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	$-0.790628\pi$
$877$	−5.33102	+	5.33102i	−0.180016	+	0.180016i	0.611347	+	0.791363i	$0.290628\pi$
$878$	−1.10391	+	6.73742i	−0.0372552	+	0.227377i
$879$		−	7.16905i		−	0.241806i
$880$	−1.69517	−	10.4027i	−0.0571442	−	0.350676i
$881$			0.259921i			0.00875697i	0.999990	+	0.00437848i	$0.00139372\pi$
$881$			0.259921i			0.00875697i	−0.999990	+	0.00437848i	$0.998606\pi$
$882$	8.94469	+	4.24176i	0.301183	+	0.142827i
$883$	39.1580	+	39.1580i	1.31777	+	1.31777i	0.915536	+	0.402237i	$0.131767\pi$
$883$	39.1580	+	39.1580i	1.31777	+	1.31777i	0.402237	+	0.915536i	$0.368233\pi$
$884$	−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	−0.888718	−	0.458455i	$-0.848403\pi$
$887$	−12.8143	+	12.8143i	−0.430263	+	0.430263i	0.458455	+	0.888718i	$0.348403\pi$
$888$	16.9772	+	8.99480i	0.569719	+	0.301846i
$889$	15.3156	−	11.5273i	0.513669	−	0.386612i
$890$	4.99446	+	6.58697i	0.167415	+	0.220796i
$891$			1.17840i			0.0394779i
$892$	−19.4449	−	39.1889i	−0.651062	−	1.31214i
$893$	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
$896$	8.66724	+	28.6510i	0.289552	+	0.957162i
$897$	10.7764	+	10.7764i	0.359815	+	0.359815i
$898$	9.10754	+	1.49225i	0.303923	+	0.0497971i
$899$		−	5.09970i		−	0.170084i
$900$	9.62886	+	2.69909i	0.320962	+	0.0899696i
$901$	21.5119			0.716667
$902$	−0.370883	+	2.26358i	−0.0123491	+	0.0753691i
$903$	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	$-0.929927\pi$
$907$	−22.8132	+	22.8132i	−0.757500	+	0.757500i	0.218367	+	0.975867i	$0.429927\pi$
$908$	12.2249	+	24.6379i	0.405697	+	0.817637i
$909$		−	6.36620i		−	0.211154i
$910$	8.90006	−	31.3217i	0.295034	−	1.03830i
$911$	32.5148			1.07726			0.538631	−	0.842542i	$-0.318942\pi$
$911$	32.5148			1.07726			0.538631	+	0.842542i	$0.318942\pi$
$912$	−4.22793	−	30.9467i	−0.140001	−	1.02475i
$913$	−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
$918$	0.804313	−	4.90890i	0.0265463	−	0.162018i
$919$		−	43.8704i		−	1.44715i	−0.690245	−	0.723576i	$-0.742497\pi$
$919$		−	43.8704i		−	1.44715i	0.690245	−	0.723576i	$-0.257503\pi$
$920$	22.1760	+	11.0274i	0.731120	+	0.363561i
$921$	23.8417			0.785611
$922$	−4.35133	+	26.5571i	−0.143303	+	0.874612i
$923$	29.6531	−	29.6531i	0.976043	−	0.976043i
$924$	5.91822	−	1.96376i	0.194695	−	0.0646030i
$925$	−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
$928$	−1.93504	+	1.83465i	−0.0635208	+	0.0602252i
$929$	−34.1044			−1.11893			−0.559464	−	0.828855i	$-0.688993\pi$
$929$	−34.1044			−1.11893			−0.559464	+	0.828855i	$0.688993\pi$
$930$	4.66047	−	33.8928i	0.152823	−	1.11139i
$931$	−15.1270	+	52.5250i	−0.495767	+	1.72144i
$932$	20.8204	−	10.3307i	0.681995	−	0.338394i
$933$	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	−0.0537927	+	0.998552i	$0.517131\pi$
$937$	−32.2128	+	32.2128i	−1.05234	+	1.05234i	−0.998552	+	0.0537927i	$0.982869\pi$
$938$	−31.6900	+	16.6107i	−1.03471	+	0.542357i
$939$	11.7746			0.384249
$940$	3.01707	−	9.78614i	0.0984058	−	0.319189i
$941$	4.64137			0.151304			0.0756522	−	0.997134i	$-0.475896\pi$
$941$	4.64137			0.151304			0.0756522	+	0.997134i	$0.475896\pi$
$942$	2.60236	−	15.8828i	0.0847895	−	0.517490i
$943$	−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	$-0.687180\pi$
$947$	8.53326	−	8.53326i	0.277294	−	0.277294i	0.832028	+	0.554734i	$0.187180\pi$
$948$	−11.2425	−	22.6581i	−0.365141	−	0.735900i
$949$	2.01055			0.0652653
$950$	−6.11041	+	54.8756i	−0.198248	+	1.78040i
$951$			16.3822i			0.531230i
$952$	−25.9940	+	4.14105i	−0.842472	+	0.134212i
$953$	−12.7175	+	12.7175i	−0.411960	+	0.411960i	−0.882421	−	0.470461i	$-0.844088\pi$
$953$	−12.7175	+	12.7175i	−0.411960	+	0.411960i	0.470461	+	0.882421i	$0.344088\pi$
$954$	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
$958$	4.12180	−	25.1563i	0.133169	−	0.812762i
$959$	6.46360	−	4.86482i	0.208720	−	0.157093i
$960$	−14.5370	+	10.4248i	−0.469180	+	0.336458i
$961$	−86.0444			−2.77562
$962$	36.8948	+	6.04514i	1.18954	+	0.194903i
$963$	−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
$966$	−4.36647	+	13.9863i	−0.140489	+	0.450001i
$967$	−19.2798	−	19.2798i	−0.619997	−	0.619997i	0.325533	−	0.945531i	$-0.394456\pi$
$967$	−19.2798	−	19.2798i	−0.619997	−	0.619997i	−0.945531	+	0.325533i	$0.894456\pi$
$968$	−12.7271	+	24.0218i	−0.409065	+	0.772090i
$969$	27.4658			0.882329
$970$	32.9442	+	4.53003i	1.05777	+	0.145450i
$971$	−13.2078			−0.423858			−0.211929	−	0.977285i	$-0.567975\pi$
$971$	−13.2078			−0.423858			−0.211929	+	0.977285i	$0.567975\pi$
$972$	1.79158	−	0.888951i	0.0574650	−	0.0285131i
$973$	−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	0.691428	−	0.722445i	$-0.256982\pi$
$977$	−0.969515	−	0.969515i	−0.0310175	−	0.0310175i	−0.722445	+	0.691428i	$0.756982\pi$
$978$	−0.828381	+	5.05580i	−0.0264887	+	0.161666i
$979$			3.08041i			0.0984502i
$980$	30.6435	−	6.40136i	0.978870	−	0.204484i
$981$		−	7.38166i		−	0.235678i
$982$	48.9192	+	8.01530i	1.56107	+	0.255778i
$983$	30.0600	+	30.0600i	0.958766	+	0.958766i	0.999183	−	0.0404171i	$-0.0128687\pi$
$983$	30.0600	+	30.0600i	0.958766	+	0.958766i	−0.0404171	+	0.999183i	$0.512869\pi$
$984$	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
$988$	−27.0150	−	54.4457i	−0.859461	−	1.73215i
$989$	47.9249			1.52392
$990$	2.25147	+	2.96937i	0.0715565	+	0.0943728i
$991$	12.3196			0.391345			0.195673	−	0.980669i	$-0.437311\pi$
$991$	12.3196			0.391345			0.195673	+	0.980669i	$0.437311\pi$
$992$	42.1074	+	44.4116i	1.33691	+	1.41007i
$993$	6.02570	+	6.02570i	0.191220	+	0.191220i
$994$	38.4854	+	12.0150i	1.22068	+	0.381094i
$995$	−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	−0.994572	−	0.104055i	$-0.966818\pi$
$997$	−34.6895	−	34.6895i	−1.09863	−	1.09863i	−0.104055	−	0.994572i	$-0.533182\pi$
$998$	1.59876	−	9.75760i	0.0506079	−	0.308872i
$999$	−6.79277			−0.214914

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.5	✓	184	35.13	even	4	inner
840.2.bj.b.13.6	yes	184	5.3	odd	4	inner
840.2.bj.b.13.51	yes	184	40.13	odd	4	inner
840.2.bj.b.13.52	yes	184	280.13	even	4	inner
840.2.bj.b.517.5	yes	184	8.5	even	2	inner
840.2.bj.b.517.6	yes	184	56.13	odd	2	inner
840.2.bj.b.517.51	yes	184	7.6	odd	2	inner
840.2.bj.b.517.52	yes	184	1.1	even	1	trivial

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+(0.228667 - 1.39560i) 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} +(-1.32417 + 2.49931i) q^{8} -1.00000i q^{9} +(-1.91062 - 2.51983i) q^{10} -1.17840i q^{11} +(-1.79158 + 0.888951i) q^{12} +(-2.75196 + 2.75196i) q^{13} +(-3.57165 - 1.11506i) q^{14} +(-0.0575851 - 2.23533i) q^{15} +(3.18526 + 2.41953i) q^{16} +(-2.48718 + 2.48718i) q^{17} +(-1.39560 - 0.228667i) q^{18} -7.80855i q^{19} +(-3.95358 + 2.09026i) q^{20} +(-1.59103 - 2.11391i) q^{21} +(-1.64458 - 0.269461i) 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} +(-2.37289 + 4.72963i) q^{28} -0.471378 q^{29} +(-3.13280 - 0.430779i) q^{30} +10.8187i q^{31} +(4.10507 - 3.89209i) 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} +(-10.8976 - 1.78556i) q^{38} +3.89186i q^{39} +(2.01313 + 5.99561i) q^{40} -1.37639i q^{41} +(-3.31400 + 1.73707i) 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} +(3.96318 - 0.541449i) q^{48} +(-6.72660 - 1.93723i) q^{49} +(-7.02763 - 0.782529i) q^{50} +3.51740i q^{51} +(6.97258 - 3.45967i) q^{52} +(-4.32457 - 4.32457i) q^{53} +(-1.14853 + 0.825150i) q^{54} +(-1.91058 - 1.81462i) q^{55} +(6.05809 + 4.39313i) q^{56} +(-5.52148 - 5.52148i) q^{57} +(-0.107788 + 0.657857i) q^{58} -0.533140i q^{59} +(-1.31756 + 4.27364i) q^{60} -5.79323 q^{61} +(15.0986 + 2.47388i) 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} +(6.30172 - 3.12680i) q^{68} -3.91592i q^{69} +(-7.30784 + 4.07376i) q^{70} -10.7753 q^{71} +(2.49931 + 1.32417i) 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} +(5.43149 + 0.889938i) q^{78} +12.6470i q^{79} +(8.82783 - 1.43854i) q^{80} -1.00000 q^{81} +(-1.92089 - 0.314734i) q^{82} +(9.82093 - 9.82093i) q^{83} +(1.66646 + 5.02224i) q^{84} +(0.202550 + 7.86254i) q^{85} +(14.0563 - 10.0986i) q^{86} +(-0.333314 + 0.333314i) q^{87} +(2.94519 + 1.56041i) q^{88} -2.61406 q^{89} +(-2.51983 + 1.91062i) q^{90} +(6.19207 + 8.22703i) q^{91} +(-7.01568 + 3.48106i) 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} +(-4.24176 + 8.94469i) 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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