LMFDB - Embedded newform 185.2.p.a.103.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(82,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.p (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.6
Character	$\chi$	$=$	185.103
Dual form			185.2.p.a.97.6

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.567972 - 0.983757i) q^{2} +(0.273625 + 1.02118i) q^{3} +(0.354815 - 0.614557i) q^{4} +(-1.79329 - 1.33571i) q^{5} +(0.849185 - 0.849185i) q^{6} +(-0.422839 - 1.57806i) q^{7} -3.07799 q^{8} +(1.63013 - 0.941157i) q^{9} +(-0.295475 + 2.52281i) q^{10} -1.92257i q^{11} +(0.724662 + 0.194173i) q^{12} +(0.763528 - 1.32247i) q^{13} +(-1.31226 + 1.31226i) q^{14} +(0.873315 - 2.19676i) q^{15} +(1.03858 + 1.79888i) q^{16} +(1.14334 - 0.660110i) q^{17} +(-1.85174 - 1.06910i) q^{18} +(2.17790 - 0.583566i) q^{19} +(-1.45715 + 0.628149i) q^{20} +(1.49579 - 0.863592i) q^{21} +(-1.89134 + 1.09196i) q^{22} -4.57925 q^{23} +(-0.842216 - 3.14319i) q^{24} +(1.43176 + 4.79062i) q^{25} -1.73465 q^{26} +(3.64981 + 3.64981i) q^{27} +(-1.11984 - 0.300059i) q^{28} +(0.241089 - 0.241089i) q^{29} +(-2.65710 + 0.388569i) q^{30} +(-1.00617 - 1.00617i) q^{31} +(-1.89822 + 3.28781i) q^{32} +(1.96329 - 0.526063i) q^{33} +(-1.29878 - 0.749849i) q^{34} +(-1.34955 + 3.39470i) q^{35} -1.33575i q^{36} +(1.71804 + 5.83510i) q^{37} +(-1.81107 - 1.81107i) q^{38} +(1.55940 + 0.417841i) q^{39} +(5.51972 + 4.11130i) q^{40} +(6.76304 + 3.90464i) q^{41} +(-1.69913 - 0.980993i) q^{42} +5.46568 q^{43} +(-1.18153 - 0.682155i) q^{44} +(-4.18041 - 0.489616i) q^{45} +(2.60089 + 4.50487i) q^{46} +(1.79140 - 1.79140i) q^{47} +(-1.55280 + 1.55280i) q^{48} +(3.75071 - 2.16547i) q^{49} +(3.89961 - 4.12945i) q^{50} +(0.986942 + 0.986942i) q^{51} +(-0.541822 - 0.938463i) q^{52} +(-0.870548 + 3.24893i) q^{53} +(1.51754 - 5.66352i) q^{54} +(-2.56799 + 3.44772i) q^{55} +(1.30149 + 4.85724i) q^{56} +(1.19186 + 2.06436i) q^{57} +(-0.374105 - 0.100241i) q^{58} +(-1.40987 + 5.26170i) q^{59} +(-1.04017 - 1.31614i) q^{60} +(10.4583 - 2.80230i) q^{61} +(-0.418352 + 1.56131i) q^{62} +(-2.17448 - 2.17448i) q^{63} +8.46687 q^{64} +(-3.13566 + 1.35172i) q^{65} +(-1.63261 - 1.63261i) q^{66} +(-9.45477 + 2.53340i) q^{67} -0.936868i q^{68} +(-1.25300 - 4.67625i) q^{69} +(4.10607 - 0.600463i) q^{70} +(1.65295 - 2.86299i) q^{71} +(-5.01753 + 2.89687i) q^{72} +(1.78634 - 1.78634i) q^{73} +(4.76452 - 5.00430i) q^{74} +(-4.50034 + 2.77293i) q^{75} +(0.414116 - 1.54550i) q^{76} +(-3.03392 + 0.812936i) q^{77} +(-0.474644 - 1.77140i) q^{78} +(-12.3408 + 3.30670i) q^{79} +(0.540301 - 4.61315i) q^{80} +(0.0950223 - 0.164583i) q^{81} -8.87092i q^{82} +(2.29888 - 8.57952i) q^{83} -1.22566i q^{84} +(-2.93206 - 0.343408i) q^{85} +(-3.10436 - 5.37690i) q^{86} +(0.312164 + 0.180228i) q^{87} +5.91764i q^{88} +(-16.4223 - 4.40035i) q^{89} +(1.89269 + 4.39059i) q^{90} +(-2.40978 - 0.645698i) q^{91} +(-1.62479 + 2.81421i) q^{92} +(0.752174 - 1.30280i) q^{93} +(-2.77976 - 0.744835i) q^{94} +(-4.68507 - 1.86254i) q^{95} +(-3.87685 - 1.03880i) q^{96} -15.4196i q^{97} +(-4.26060 - 2.45986i) q^{98} +(-1.80944 - 3.13404i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100})$ 68 * q - 4 * q^2 - 8 * q^3 - 30 * q^4 - 10 * q^5 - 8 * q^6 - 2 * q^7 + 12 * q^8 - 6 * q^10 + 14 * q^12 - 6 * q^13 - 8 * q^15 - 26 * q^16 + 12 * q^17 + 18 * q^18 + 4 * q^19 + 48 * q^20 - 12 * q^21 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 68 * q^27 - 26 * q^28 + 14 * q^29 + 10 * q^30 - 24 * q^31 - 16 * q^32 - 2 * q^33 - 10 * q^35 - 16 * q^37 - 36 * q^38 + 52 * q^39 + 42 * q^40 - 18 * q^41 + 132 * q^42 + 8 * q^43 - 36 * q^44 - 32 * q^45 - 52 * q^46 - 24 * q^47 - 60 * q^48 - 36 * q^49 - 8 * q^50 - 8 * q^51 - 26 * q^52 + 82 * q^53 + 40 * q^54 + 18 * q^55 + 16 * q^56 - 6 * q^57 + 86 * q^58 - 8 * q^59 + 36 * q^60 + 4 * q^61 + 10 * q^62 - 48 * q^63 - 20 * q^64 + 8 * q^65 + 80 * q^66 - 40 * q^67 + 8 * q^69 - 82 * q^70 + 4 * q^71 - 90 * q^72 - 60 * q^73 - 44 * q^74 + 64 * q^75 + 72 * q^76 + 66 * q^77 - 24 * q^78 + 56 * q^79 + 34 * q^80 - 6 * q^81 + 24 * q^83 - 20 * q^85 - 4 * q^86 - 84 * q^87 - 22 * q^89 - 50 * q^90 + 44 * q^91 + 44 * q^92 - 34 * q^93 - 20 * q^94 - 28 * q^95 - 8 * q^96 + 42 * q^98 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$ .

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.567972	−	0.983757i	−0.401617	−	0.695621i	0.592304	−	0.805714i	$-0.298218\pi$
$2$	−0.567972	−	0.983757i	−0.401617	−	0.695621i	−0.993921	+	0.110093i	$0.964885\pi$
$3$	0.273625	+	1.02118i	0.157978	+	0.589581i	0.998832	+	0.0483191i	$0.0153864\pi$
$3$	0.273625	+	1.02118i	0.157978	+	0.589581i	−0.840854	+	0.541262i	$0.817947\pi$
$4$	0.354815	−	0.614557i	0.177407	−	0.307279i
$5$	−1.79329	−	1.33571i	−0.801983	−	0.597347i
$5$	−1.79329	−	1.33571i	−0.801983	−	0.597347i
$6$	0.849185	−	0.849185i	0.346678	−	0.346678i
$7$	−0.422839	−	1.57806i	−0.159818	−	0.596449i	−0.998644	−	0.0520501i	$-0.983424\pi$
$7$	−0.422839	−	1.57806i	−0.159818	−	0.596449i	0.838826	−	0.544399i	$-0.183242\pi$
$8$	−3.07799			−1.08823
$9$	1.63013	−	0.941157i	0.543377	−	0.313719i
$10$	−0.295475	+	2.52281i	−0.0934375	+	0.797781i
$11$		−	1.92257i		−	0.579676i	−0.957076	−	0.289838i	$-0.906399\pi$
$11$		−	1.92257i		−	0.579676i	0.957076	−	0.289838i	$-0.0936014\pi$
$12$	0.724662	+	0.194173i	0.209192	+	0.0560528i
$13$	0.763528	−	1.32247i	0.211764	−	0.366787i	−0.740502	−	0.672054i	$-0.765412\pi$
$13$	0.763528	−	1.32247i	0.211764	−	0.366787i	0.952267	+	0.305267i	$0.0987457\pi$
$14$	−1.31226	+	1.31226i	−0.350717	+	0.350717i
$15$	0.873315	−	2.19676i	0.225489	−	0.567201i
$16$	1.03858	+	1.79888i	0.259646	+	0.449720i
$17$	1.14334	−	0.660110i	0.277302	−	0.160100i	−0.354899	−	0.934904i	$-0.615485\pi$
$17$	1.14334	−	0.660110i	0.277302	−	0.160100i	0.632201	+	0.774804i	$0.282152\pi$
$18$	−1.85174	−	1.06910i	−0.436459	−	0.251990i
$19$	2.17790	−	0.583566i	0.499644	−	0.133879i	−0.000190628	−	1.00000i	$-0.500061\pi$
$19$	2.17790	−	0.583566i	0.499644	−	0.133879i	0.499835	+	0.866121i	$0.333394\pi$
$20$	−1.45715	+	0.628149i	−0.325830	+	0.140458i
$21$	1.49579	−	0.863592i	0.326407	−	0.188451i
$22$	−1.89134	+	1.09196i	−0.403235	+	0.232808i
$23$	−4.57925			−0.954839			−0.477420	−	0.878675i	$-0.658428\pi$
$23$	−4.57925			−0.954839			−0.477420	+	0.878675i	$0.658428\pi$
$24$	−0.842216	−	3.14319i	−0.171917	−	0.641601i
$25$	1.43176	+	4.79062i	0.286352	+	0.958124i
$26$	−1.73465			−0.340193
$27$	3.64981	+	3.64981i	0.702407	+	0.702407i
$28$	−1.11984	−	0.300059i	−0.211629	−	0.0567058i
$29$	0.241089	−	0.241089i	0.0447691	−	0.0447691i	−0.684368	−	0.729137i	$-0.739922\pi$
$29$	0.241089	−	0.241089i	0.0447691	−	0.0447691i	0.729137	+	0.684368i	$0.239922\pi$
$30$	−2.65710	+	0.388569i	−0.485117	+	0.0709426i
$31$	−1.00617	−	1.00617i	−0.180714	−	0.180714i	0.610953	−	0.791667i	$-0.290787\pi$
$31$	−1.00617	−	1.00617i	−0.180714	−	0.180714i	−0.791667	+	0.610953i	$0.790787\pi$
$32$	−1.89822	+	3.28781i	−0.335560	+	0.581208i
$33$	1.96329	−	0.526063i	0.341766	−	0.0915758i
$34$	−1.29878	−	0.749849i	−0.222738	−	0.128598i
$35$	−1.34955	+	3.39470i	−0.228116	+	0.573809i
$36$		−	1.33575i		−	0.222624i
$37$	1.71804	+	5.83510i	0.282443	+	0.959284i
$37$	1.71804	+	5.83510i	0.282443	+	0.959284i
$38$	−1.81107	−	1.81107i	−0.293795	−	0.293795i
$39$	1.55940	+	0.417841i	0.249704	+	0.0669081i
$40$	5.51972	+	4.11130i	0.872744	+	0.650053i
$41$	6.76304	+	3.90464i	1.05621	+	0.609803i	0.924381	−	0.381470i	$-0.124582\pi$
$41$	6.76304	+	3.90464i	1.05621	+	0.609803i	0.131828	+	0.991273i	$0.457915\pi$
$42$	−1.69913	−	0.980993i	−0.262181	−	0.151370i
$43$	5.46568			0.833509			0.416754	−	0.909019i	$-0.363168\pi$
$43$	5.46568			0.833509			0.416754	+	0.909019i	$0.363168\pi$
$44$	−1.18153	−	0.682155i	−0.178122	−	0.102839i
$45$	−4.18041	−	0.489616i	−0.623178	−	0.0729877i
$46$	2.60089	+	4.50487i	0.383480	+	0.664207i
$47$	1.79140	−	1.79140i	0.261302	−	0.261302i	−0.564281	−	0.825583i	$-0.690846\pi$
$47$	1.79140	−	1.79140i	0.261302	−	0.261302i	0.825583	+	0.564281i	$0.190846\pi$
$48$	−1.55280	+	1.55280i	−0.224128	+	0.224128i
$49$	3.75071	−	2.16547i	0.535816	−	0.309353i
$50$	3.89961	−	4.12945i	0.551488	−	0.583992i
$51$	0.986942	+	0.986942i	0.138200	+	0.138200i
$52$	−0.541822	−	0.938463i	−0.0751372	−	0.130141i
$53$	−0.870548	+	3.24893i	−0.119579	+	0.446275i	−0.999589	−	0.0286809i	$-0.990869\pi$
$53$	−0.870548	+	3.24893i	−0.119579	+	0.446275i	0.880010	+	0.474956i	$0.157536\pi$
$54$	1.51754	−	5.66352i	0.206511	−	0.770708i
$55$	−2.56799	+	3.44772i	−0.346268	+	0.464890i
$56$	1.30149	+	4.85724i	0.173919	+	0.649076i
$57$	1.19186	+	2.06436i	0.157865	+	0.273431i
$58$	−0.374105	−	0.100241i	−0.0491223	−	0.0131623i
$59$	−1.40987	+	5.26170i	−0.183549	+	0.685016i	0.811387	+	0.584509i	$0.198713\pi$
$59$	−1.40987	+	5.26170i	−0.183549	+	0.685016i	−0.994936	+	0.100506i	$0.967954\pi$
$60$	−1.04017	−	1.31614i	−0.134285	−	0.169914i
$61$	10.4583	−	2.80230i	1.33905	−	0.358797i	0.482968	−	0.875638i	$-0.339559\pi$
$61$	10.4583	−	2.80230i	1.33905	−	0.358797i	0.856081	+	0.516841i	$0.172892\pi$
$62$	−0.418352	+	1.56131i	−0.0531307	+	0.198287i
$63$	−2.17448	−	2.17448i	−0.273959	−	0.273959i
$64$	8.46687			1.05836
$65$	−3.13566	+	1.35172i	−0.388931	+	0.167660i
$66$	−1.63261	−	1.63261i	−0.200961	−	0.200961i
$67$	−9.45477	+	2.53340i	−1.15508	+	0.309504i	−0.785001	−	0.619495i	$-0.787338\pi$
$67$	−9.45477	+	2.53340i	−1.15508	+	0.309504i	−0.370083	+	0.928999i	$0.620671\pi$
$68$		−	0.936868i		−	0.113612i
$69$	−1.25300	−	4.67625i	−0.150843	−	0.562955i
$70$	4.10607	−	0.600463i	0.490769	−	0.0717691i
$71$	1.65295	−	2.86299i	0.196169	−	0.339774i	−0.751114	−	0.660172i	$-0.770483\pi$
$71$	1.65295	−	2.86299i	0.196169	−	0.339774i	0.947283	+	0.320398i	$0.103817\pi$
$72$	−5.01753	+	2.89687i	−0.591321	+	0.341399i
$73$	1.78634	−	1.78634i	0.209075	−	0.209075i	−0.594799	−	0.803874i	$-0.702768\pi$
$73$	1.78634	−	1.78634i	0.209075	−	0.209075i	0.803874	+	0.594799i	$0.202768\pi$
$74$	4.76452	−	5.00430i	0.553864	−	0.581739i
$75$	−4.50034	+	2.77293i	−0.519654	+	0.320190i
$76$	0.414116	−	1.54550i	0.0475023	−	0.177281i
$77$	−3.03392	+	0.812936i	−0.345747	+	0.0926427i
$78$	−0.474644	−	1.77140i	−0.0537429	−	0.200571i
$79$	−12.3408	+	3.30670i	−1.38844	+	0.372032i	−0.874181	−	0.485600i	$-0.838601\pi$
$79$	−12.3408	+	3.30670i	−1.38844	+	0.372032i	−0.514263	+	0.857633i	$0.671934\pi$
$80$	0.540301	−	4.61315i	0.0604074	−	0.515766i
$81$	0.0950223	−	0.164583i	0.0105580	−	0.0182871i
$82$		−	8.87092i		−	0.979629i
$83$	2.29888	−	8.57952i	0.252334	−	0.941725i	−0.717220	−	0.696847i	$-0.754586\pi$
$83$	2.29888	−	8.57952i	0.252334	−	0.941725i	0.969554	−	0.244878i	$-0.0787478\pi$
$84$		−	1.22566i		−	0.133731i
$85$	−2.93206	−	0.343408i	−0.318027	−	0.0372479i
$86$	−3.10436	−	5.37690i	−0.334751	−	0.579806i
$87$	0.312164	+	0.180228i	0.0334675	+	0.0193225i
$88$			5.91764i			0.630823i
$89$	−16.4223	−	4.40035i	−1.74076	−	0.466436i	−0.758146	−	0.652085i	$-0.773894\pi$
$89$	−16.4223	−	4.40035i	−1.74076	−	0.466436i	−0.982616	+	0.185650i	$0.940561\pi$
$90$	1.89269	+	4.39059i	0.199507	+	0.462809i
$91$	−2.40978	−	0.645698i	−0.252613	−	0.0676876i
$92$	−1.62479	+	2.81421i	−0.169396	+	0.293402i
$93$	0.752174	−	1.30280i	0.0779968	−	0.135094i
$94$	−2.77976	−	0.744835i	−0.286711	−	0.0768239i
$95$	−4.68507	−	1.86254i	−0.480678	−	0.191092i
$96$	−3.87685	−	1.03880i	−0.395680	−	0.106022i
$97$		−	15.4196i		−	1.56563i	−0.622256	−	0.782814i	$-0.713784\pi$
$97$		−	15.4196i		−	1.56563i	0.622256	−	0.782814i	$-0.286216\pi$
$98$	−4.26060	−	2.45986i	−0.430385	−	0.248483i
$99$	−1.80944	−	3.13404i	−0.181855	−	0.314983i
$100$	3.45212	+	0.819884i	0.345212	+	0.0819884i
$101$			0.767212i			0.0763405i	0.999271	+	0.0381702i	$0.0121529\pi$
$101$			0.767212i			0.0763405i	−0.999271	+	0.0381702i	$0.987847\pi$
$102$	0.410355	−	1.53147i	0.0406312	−	0.151638i
$103$		−	4.78539i		−	0.471518i	−0.971812	−	0.235759i	$-0.924242\pi$
$103$		−	4.78539i		−	0.471518i	0.971812	−	0.235759i	$-0.0757576\pi$
$104$	−2.35013	+	4.07054i	−0.230449	+	0.399150i
$105$	−3.83588	−	0.449265i	−0.374344	−	0.0438438i
$106$	3.69061	−	0.988895i	0.358463	−	0.0960500i
$107$	3.36743	+	12.5674i	0.325542	+	1.21494i	0.913766	+	0.406240i	$0.133160\pi$
$107$	3.36743	+	12.5674i	0.325542	+	1.21494i	−0.588225	+	0.808698i	$0.700173\pi$
$108$	3.53803	−	0.948011i	0.340447	−	0.0912224i
$109$	−3.42875	+	12.7963i	−0.328414	+	1.22566i	0.582421	+	0.812888i	$0.302106\pi$
$109$	−3.42875	+	12.7963i	−0.328414	+	1.22566i	−0.910835	+	0.412771i	$0.864561\pi$
$110$	4.85026	+	0.568071i	0.462454	+	0.0541635i
$111$	−5.48861	+	3.35106i	−0.520955	+	0.318069i
$112$	2.39958	−	2.39958i	0.226739	−	0.226739i
$113$	12.6175	−	7.28470i	1.18695	−	0.685287i	0.229339	−	0.973347i	$-0.426343\pi$
$113$	12.6175	−	7.28470i	1.18695	−	0.685287i	0.957612	+	0.288060i	$0.0930102\pi$
$114$	1.35388	−	2.34499i	0.126803	−	0.219629i
$115$	8.21191	+	6.11655i	0.765765	+	0.570371i
$116$	−0.0626210	−	0.233705i	−0.00581421	−	0.0216989i
$117$		−	2.87440i		−	0.265738i
$118$	5.97701	−	1.60153i	0.550228	−	0.147433i
$119$	−1.52514	−	1.52514i	−0.139810	−	0.139810i
$120$	−2.68806	+	6.76160i	−0.245385	+	0.617247i
$121$	7.30374			0.663976
$122$	−8.69681	−	8.69681i	−0.787372	−	0.787372i
$123$	−2.13682	+	7.97471i	−0.192670	+	0.719056i
$124$	−0.975357	+	0.261346i	−0.0875896	+	0.0234696i
$125$	3.83132	−	10.5034i	0.342683	−	0.939451i
$126$	−0.904116	+	3.37421i	−0.0805450	+	0.300598i
$127$	4.94102	+	1.32394i	0.438445	+	0.117481i	0.471288	−	0.881980i	$-0.343789\pi$
$127$	4.94102	+	1.32394i	0.438445	+	0.117481i	−0.0328428	+	0.999461i	$0.510456\pi$
$128$	−1.01252	−	1.75373i	−0.0894947	−	0.155009i
$129$	1.49555	+	5.58146i	0.131676	+	0.491421i
$130$	3.11073	+	2.31699i	0.272829	+	0.203213i
$131$	−0.824339	+	3.07647i	−0.0720228	+	0.268793i	−0.992542	−	0.121905i	$-0.961100\pi$
$131$	−0.824339	+	3.07647i	−0.0720228	+	0.268793i	0.920519	+	0.390698i	$0.127766\pi$
$132$	0.373310	−	1.39321i	0.0324924	−	0.121263i
$133$	−1.84180	−	3.19009i	−0.159704	−	0.276616i
$134$	7.86230	+	7.86230i	0.679199	+	0.679199i
$135$	−1.67008	−	11.4203i	−0.143737	−	0.982899i
$136$	−3.51920	+	2.03181i	−0.301769	+	0.174227i
$137$	15.2791	−	15.2791i	1.30538	−	1.30538i	0.380674	−	0.924709i	$-0.375692\pi$
$137$	15.2791	−	15.2791i	1.30538	−	1.30538i	0.924709	−	0.380674i	$-0.124308\pi$
$138$	−3.88863	+	3.88863i	−0.331022	+	0.331022i
$139$	8.97537	+	15.5458i	0.761281	+	1.31858i	0.942191	+	0.335077i	$0.108762\pi$
$139$	8.97537	+	15.5458i	0.761281	+	1.31858i	−0.180910	+	0.983500i	$0.557904\pi$
$140$	1.60740	+	2.03387i	0.135850	+	0.171893i
$141$	2.31952	+	1.33917i	0.195339	+	0.112779i
$142$	−3.75532			−0.315139
$143$	−2.54253	−	1.46793i	−0.212617	−	0.122755i
$144$	3.38605	+	1.95494i	0.282171	+	0.162912i
$145$	−0.754366	+	0.110317i	−0.0626467	+	0.00916133i
$146$	−2.77191	−	0.742732i	−0.229405	−	0.0614689i
$147$	3.23763	+	3.23763i	0.267036	+	0.267036i
$148$	4.19559	+	1.01455i	0.344875	+	0.0833952i
$149$		−	16.8891i		−	1.38361i	−0.722084	−	0.691805i	$-0.756816\pi$
$149$		−	16.8891i		−	1.38361i	0.722084	−	0.691805i	$-0.243184\pi$
$150$	5.28395	+	2.85229i	0.431433	+	0.232889i
$151$	−19.2569	−	11.1180i	−1.56711	−	0.904770i	−0.996504	−	0.0835434i	$-0.973376\pi$
$151$	−19.2569	−	11.1180i	−1.56711	−	0.904770i	−0.570603	−	0.821226i	$-0.693290\pi$
$152$	−6.70355	+	1.79621i	−0.543730	+	0.145692i
$153$	1.24253	−	2.15213i	0.100453	−	0.173990i
$154$	2.52291	+	2.52291i	0.203302	+	0.203302i
$155$	0.460404	+	3.14832i	0.0369805	+	0.252879i
$156$	0.810087	−	0.810087i	0.0648588	−	0.0648588i
$157$	−5.03393	−	1.34884i	−0.401751	−	0.107649i	0.0522849	−	0.998632i	$-0.483350\pi$
$157$	−5.03393	−	1.34884i	−0.401751	−	0.107649i	−0.454036	+	0.890983i	$0.650016\pi$
$158$	10.2622	+	10.2622i	0.816417	+	0.816417i
$159$	−3.55596			−0.282006
$160$	7.79560	−	3.36052i	0.616296	−	0.265672i
$161$	1.93628	+	7.22631i	0.152601	+	0.569513i
$162$	−0.215880			−0.0169611
$163$	−12.7064	+	7.33603i	−0.995241	+	0.574603i	−0.906837	−	0.421482i	$-0.861510\pi$
$163$	−12.7064	+	7.33603i	−0.995241	+	0.574603i	−0.0884042	+	0.996085i	$0.528177\pi$
$164$	4.79925	−	2.77085i	0.374759	−	0.216367i
$165$	−4.22342	−	1.67901i	−0.328793	−	0.130711i
$166$	−9.74586	+	2.61140i	−0.756426	+	0.202684i
$167$	18.6925	+	10.7921i	1.44647	+	0.835120i	0.998269	−	0.0588131i	$-0.0187316\pi$
$167$	18.6925	+	10.7921i	1.44647	+	0.835120i	0.448201	+	0.893933i	$0.352065\pi$
$168$	−4.60401	+	2.65813i	−0.355207	+	0.205079i
$169$	5.33405	+	9.23885i	0.410312	+	0.710681i
$170$	1.32750	+	3.07948i	0.101815	+	0.236186i
$171$	3.00103	−	3.00103i	0.229495	−	0.229495i
$172$	1.93930	−	3.35897i	0.147871	−	0.256119i
$173$	−0.797367	−	0.213654i	−0.0606227	−	0.0162438i	0.228380	−	0.973572i	$-0.426657\pi$
$173$	−0.797367	−	0.213654i	−0.0606227	−	0.0162438i	−0.289003	+	0.957328i	$0.593324\pi$
$174$		−	0.409458i		−	0.0310409i
$175$	6.95447	−	4.28506i	0.525708	−	0.323920i
$176$	3.45847	−	1.99675i	0.260692	−	0.150510i
$177$	−5.75894			−0.432869
$178$	4.99855	+	18.6548i	0.374657	+	1.39824i
$179$	−16.5150	+	16.5150i	−1.23439	+	1.23439i	−0.272124	+	0.962262i	$0.587726\pi$
$179$	−16.5150	+	16.5150i	−1.23439	+	1.23439i	−0.962262	+	0.272124i	$0.912274\pi$
$180$	−1.78417	+	2.39538i	−0.132984	+	0.178541i
$181$	−10.0502	+	17.4074i	−0.747024	+	1.29388i	0.202219	+	0.979340i	$0.435185\pi$
$181$	−10.0502	+	17.4074i	−0.747024	+	1.29388i	−0.949243	+	0.314544i	$0.898148\pi$
$182$	0.733478	+	2.73738i	0.0543690	+	0.202908i
$183$	5.72332	+	9.91307i	0.423080	+	0.732796i
$184$	14.0949			1.03909
$185$	4.71306	−	12.7588i	0.346511	−	0.938046i
$186$	−1.70886			−0.125299
$187$	−1.26911	−	2.19816i	−0.0928063	−	0.160745i
$188$	−0.465302	−	1.73653i	−0.0339356	−	0.126649i
$189$	4.21633	−	7.30289i	0.306693	−	0.531207i
$190$	0.828709	+	5.66684i	0.0601208	+	0.411116i
$191$	−12.5389	+	12.5389i	−0.907285	+	0.907285i	−0.996052	−	0.0887670i	$-0.971707\pi$
$191$	−12.5389	+	12.5389i	−0.907285	+	0.907285i	0.0887670	+	0.996052i	$0.471707\pi$
$192$	2.31675	+	8.64623i	0.167197	+	0.623988i
$193$	−17.1943			−1.23767			−0.618837	−	0.785519i	$-0.712396\pi$
$193$	−17.1943			−1.23767			−0.618837	+	0.785519i	$0.712396\pi$
$194$	−15.1692	+	8.75793i	−1.08908	+	0.628783i
$195$	−2.23835	−	2.83222i	−0.160291	−	0.202819i
$196$		−	3.07337i		−	0.219526i
$197$	8.61235	+	2.30767i	0.613604	+	0.164415i	0.552219	−	0.833699i	$-0.313781\pi$
$197$	8.61235	+	2.30767i	0.613604	+	0.164415i	0.0613857	+	0.998114i	$0.480448\pi$
$198$	−2.05542	+	3.56009i	−0.146072	+	0.253005i
$199$	7.61077	−	7.61077i	0.539513	−	0.539513i	−0.383873	−	0.923386i	$-0.625410\pi$
$199$	7.61077	−	7.61077i	0.539513	−	0.539513i	0.923386	+	0.383873i	$0.125410\pi$
$200$	−4.40695	−	14.7455i	−0.311618	−	1.04266i
$201$	−5.17413	−	8.96186i	−0.364955	−	0.632121i
$202$	0.754750	−	0.435755i	0.0531041	−	0.0306596i
$203$	−0.482393	−	0.278510i	−0.0338574	−	0.0195476i
$204$	0.956714	−	0.256351i	0.0669834	−	0.0179481i
$205$	−6.91261	−	16.0356i	−0.482798	−	1.11997i
$206$	−4.70766	+	2.71797i	−0.327998	+	0.189370i
$207$	−7.46478	+	4.30979i	−0.518838	+	0.299551i
$208$	3.17195			0.219935
$209$	−1.12195	−	4.18716i	−0.0776066	−	0.289632i
$210$	1.73671	+	4.02875i	0.119844	+	0.278010i
$211$	1.64325			0.113126			0.0565629	−	0.998399i	$-0.481986\pi$
$211$	1.64325			0.113126			0.0565629	+	0.998399i	$0.481986\pi$
$212$	1.68777	+	1.68777i	0.115917	+	0.115917i
$213$	3.37593	+	0.904577i	0.231315	+	0.0619806i
$214$	10.4507	−	10.4507i	0.714393	−	0.714393i
$215$	−9.80154	−	7.30056i	−0.668460	−	0.497894i
$216$	−11.2341	−	11.2341i	−0.764383	−	0.764383i
$217$	−1.16235	+	2.01325i	−0.0789054	+	0.136668i
$218$	14.5358	−	3.89487i	0.984491	−	0.263794i
$219$	2.31297	+	1.33539i	0.156296	+	0.0902374i
$220$	1.20766	+	2.80148i	0.0814203	+	0.188876i
$221$		−	2.01605i		−	0.135614i
$222$	6.41401	+	3.49615i	0.430480	+	0.234646i
$223$	−13.8186	−	13.8186i	−0.925365	−	0.925365i	0.0720369	−	0.997402i	$-0.477050\pi$
$223$	−13.8186	−	13.8186i	−0.925365	−	0.925365i	−0.997402	+	0.0720369i	$0.977050\pi$
$224$	5.99098	+	1.60528i	0.400289	+	0.107257i
$225$	6.84269	+	6.46183i	0.456179	+	0.430789i
$226$	−14.3327	−	8.27502i	−0.953400	−	0.550446i
$227$	18.4016	+	10.6242i	1.22136	+	0.705151i	0.965207	−	0.261487i	$-0.0842127\pi$
$227$	18.4016	+	10.6242i	1.22136	+	0.705151i	0.256150	+	0.966637i	$0.417546\pi$
$228$	1.69155			0.112026
$229$	−3.48912	−	2.01445i	−0.230568	−	0.133118i	0.380266	−	0.924877i	$-0.375832\pi$
$229$	−3.48912	−	2.01445i	−0.230568	−	0.133118i	−0.610834	+	0.791759i	$0.709166\pi$
$230$	1.35306	−	11.5526i	0.0892178	−	0.761753i
$231$	−1.66031	−	2.87575i	−0.109241	−	0.189210i
$232$	−0.742069	+	0.742069i	−0.0487192	+	0.0487192i
$233$	2.25220	−	2.25220i	0.147547	−	0.147547i	−0.629475	−	0.777021i	$-0.716730\pi$
$233$	2.25220	−	2.25220i	0.147547	−	0.147547i	0.777021	+	0.629475i	$0.216730\pi$
$234$	−2.82771	+	1.63258i	−0.184853	+	0.106725i
$235$	−5.60528	+	0.819705i	−0.365648	+	0.0534717i
$236$	2.73338	+	2.73338i	0.177928	+	0.177928i
$237$	−6.75349	−	11.6974i	−0.438686	−	0.759827i
$238$	−0.634131	+	2.36661i	−0.0411046	+	0.153404i
$239$	−5.13865	+	19.1777i	−0.332392	+	1.24050i	0.574277	+	0.818661i	$0.305283\pi$
$239$	−5.13865	+	19.1777i	−0.332392	+	1.24050i	−0.906669	+	0.421843i	$0.861383\pi$
$240$	4.85872	−	0.710529i	0.313629	−	0.0458645i
$241$	2.89066	+	10.7881i	0.186204	+	0.694922i	0.994370	+	0.105967i	$0.0337939\pi$
$241$	2.89066	+	10.7881i	0.186204	+	0.694922i	−0.808166	+	0.588955i	$0.799539\pi$
$242$	−4.14832	−	7.18510i	−0.266664	−	0.461876i
$243$	15.1513	+	4.05977i	0.971955	+	0.260435i
$244$	1.98859	−	7.42153i	0.127307	−	0.475114i
$245$	−9.61854	−	1.12654i	−0.614506	−	0.0719720i
$246$	9.05883	−	2.42731i	0.577570	−	0.154759i
$247$	0.891138	−	3.32577i	0.0567017	−	0.211614i
$248$	3.09699	+	3.09699i	0.196659	+	0.196659i
$249$	9.39030			0.595086
$250$	−12.5089	+	2.19655i	−0.791130	+	0.138922i
$251$	−6.77562	−	6.77562i	−0.427673	−	0.427673i	0.460162	−	0.887835i	$-0.347791\pi$
$251$	−6.77562	−	6.77562i	−0.427673	−	0.427673i	−0.887835	+	0.460162i	$0.847791\pi$
$252$	−2.10788	+	0.564805i	−0.132784	+	0.0355794i
$253$			8.80391i			0.553497i
$254$	−1.50393	−	5.61273i	−0.0943647	−	0.352174i
$255$	−0.451603	−	3.08814i	−0.0282805	−	0.193387i
$256$	7.31671	−	12.6729i	0.457294	−	0.792057i
$257$	0.306484	−	0.176949i	0.0191180	−	0.0110378i	−0.490411	−	0.871492i	$-0.663153\pi$
$257$	0.306484	−	0.176949i	0.0191180	−	0.0110378i	0.509529	+	0.860454i	$0.329820\pi$
$258$	4.64137	−	4.64137i	0.288959	−	0.288959i
$259$	8.48166	−	5.17846i	0.527025	−	0.321774i
$260$	−0.281871	+	2.40665i	−0.0174809	+	0.149254i
$261$	0.166104	−	0.619909i	0.0102816	−	0.0383714i
$262$	3.49470	−	0.936403i	0.215904	−	0.0578512i
$263$	5.22227	+	19.4898i	0.322019	+	1.20179i	0.917275	+	0.398255i	$0.130384\pi$
$263$	5.22227	+	19.4898i	0.322019	+	1.20179i	−0.595256	+	0.803536i	$0.702949\pi$
$264$	−6.04300	+	1.61922i	−0.371921	+	0.0996559i
$265$	5.90077	−	4.66347i	0.362481	−	0.286475i
$266$	−2.09218	+	3.62377i	−0.128280	+	0.222187i
$267$		−	17.9742i		−	1.10001i
$268$	−1.79777	+	6.70939i	−0.109817	+	0.409841i
$269$			6.49930i			0.396269i	0.980175	+	0.198135i	$0.0634883\pi$
$269$			6.49930i			0.396269i	−0.980175	+	0.198135i	$0.936512\pi$
$270$	−10.2862	+	8.12934i	−0.625998	+	0.494736i
$271$	−2.12937	−	3.68817i	−0.129350	−	0.224040i	0.794075	−	0.607820i	$-0.207956\pi$
$271$	−2.12937	−	3.68817i	−0.129350	−	0.224040i	−0.923425	+	0.383779i	$0.874622\pi$
$272$	2.37492	+	1.37116i	0.144001	+	0.0831388i
$273$		−	2.63751i		−	0.159629i
$274$	−23.7091	−	6.35282i	−1.43232	−	0.383788i
$275$	9.21029	−	2.75266i	0.555401	−	0.165992i
$276$	−3.31841	−	0.889165i	−0.199745	−	0.0535214i
$277$	0.285590	−	0.494657i	0.0171595	−	0.0297211i	−0.857318	−	0.514787i	$-0.827871\pi$
$277$	0.285590	−	0.494657i	0.0171595	−	0.0297211i	0.874478	+	0.485066i	$0.161204\pi$
$278$	10.1955	−	17.6592i	0.611487	−	1.05913i
$279$	−2.58716	−	0.693228i	−0.154889	−	0.0415025i
$280$	4.15391	−	10.4488i	0.248243	−	0.624438i
$281$	30.2609	+	8.10837i	1.80521	+	0.483705i	0.994772	−	0.102118i	$-0.0325620\pi$
$281$	30.2609	+	8.10837i	1.80521	+	0.483705i	0.810439	+	0.585823i	$0.199229\pi$
$282$		−	3.04245i		−	0.181176i
$283$	0.533664	+	0.308111i	0.0317230	+	0.0183153i	0.515778	−	0.856722i	$-0.327503\pi$
$283$	0.533664	+	0.308111i	0.0317230	+	0.0183153i	−0.484055	+	0.875038i	$0.660836\pi$
$284$	−1.17298	−	2.03166i	−0.0696036	−	0.120557i
$285$	0.620038	−	5.29396i	0.0367279	−	0.313587i
$286$			3.33498i			0.197202i
$287$	3.30207	−	12.3235i	0.194915	−	0.727433i
$288$			7.14608i			0.421087i
$289$	−7.62851	+	13.2130i	−0.448736	+	0.777233i
$290$	0.536984	+	0.679456i	0.0315328	+	0.0398990i
$291$	15.7463	−	4.21920i	0.923063	−	0.247334i
$292$	−0.463988	−	1.73163i	−0.0271528	−	0.101336i
$293$	−9.54988	+	2.55888i	−0.557910	+	0.149492i	−0.526746	−	0.850023i	$-0.676588\pi$
$293$	−9.54988	+	2.55888i	−0.557910	+	0.149492i	−0.0311641	+	0.999514i	$0.509921\pi$
$294$	1.34616	−	5.02393i	0.0785096	−	0.293002i
$295$	9.55641	−	7.55258i	0.556396	−	0.439728i
$296$	−5.28810	−	17.9604i	−0.307364	−	1.04393i
$297$	7.01701	−	7.01701i	0.407168	−	0.407168i
$298$	−16.6148	+	9.59255i	−0.962469	+	0.555682i
$299$	−3.49638	+	6.05591i	−0.202201	+	0.350222i
$300$	0.107336	+	3.74959i	0.00619705	+	0.216483i
$301$	−2.31110	−	8.62515i	−0.133210	−	0.497146i
$302$			25.2589i			1.45348i
$303$	−0.783464	+	0.209929i	−0.0450089	+	0.0120601i
$304$	3.31170	+	3.31170i	0.189939	+	0.189939i
$305$	−22.4978	−	8.94394i	−1.28822	−	0.512128i
$306$	−2.82290			−0.161375
$307$	−12.7533	−	12.7533i	−0.727869	−	0.727869i	0.242326	−	0.970195i	$-0.422090\pi$
$307$	−12.7533	−	12.7533i	−0.727869	−	0.727869i	−0.970195	+	0.242326i	$0.922090\pi$
$308$	−0.576883	+	2.15296i	−0.0328710	+	0.122676i
$309$	4.88676	−	1.30940i	0.277998	−	0.0744893i
$310$	2.83568	−	2.24108i	0.161056	−	0.127285i
$311$	6.30945	−	23.5472i	0.357776	−	1.33524i	−0.519179	−	0.854665i	$-0.673762\pi$
$311$	6.30945	−	23.5472i	0.357776	−	1.33524i	0.876955	−	0.480572i	$-0.159571\pi$
$312$	−4.79983	−	1.28611i	−0.271737	−	0.0728116i
$313$	0.462994	+	0.801929i	0.0261700	+	0.0453277i	0.878814	−	0.477165i	$-0.158336\pi$
$313$	0.462994	+	0.801929i	0.0261700	+	0.0453277i	−0.852644	+	0.522493i	$0.825002\pi$
$314$	1.53220	+	5.71826i	0.0864673	+	0.322700i
$315$	0.994996	+	6.80394i	0.0560617	+	0.383359i
$316$	−2.34653	+	8.75737i	−0.132003	+	0.492640i
$317$	−6.85107	+	25.5685i	−0.384794	+	1.43607i	0.453696	+	0.891156i	$0.350105\pi$
$317$	−6.85107	+	25.5685i	−0.384794	+	1.43607i	−0.838491	+	0.544916i	$0.816562\pi$
$318$	2.01969	+	3.49820i	0.113258	+	0.196169i
$319$	−0.463509	−	0.463509i	−0.0259515	−	0.0259515i
$320$	−15.1835	−	11.3093i	−0.848785	−	0.632208i
$321$	−11.9122	+	6.87752i	−0.664875	+	0.383866i
$322$	6.00918	−	6.00918i	0.334878	−	0.334878i
$323$	2.10487	−	2.10487i	0.117118	−	0.117118i
$324$	−0.0674306	−	0.116793i	−0.00374615	−	0.00648852i
$325$	7.42864	+	1.76431i	0.412067	+	0.0978664i
$326$	14.4338	+	8.33333i	0.799412	+	0.461540i
$327$	−14.0055			−0.774507
$328$	−20.8166	−	12.0184i	−1.14940	−	0.663608i
$329$	−3.58440	−	2.06945i	−0.197614	−	0.114093i
$330$	0.747049	+	5.10845i	0.0411237	+	0.281211i
$331$	−9.40727	−	2.52067i	−0.517070	−	0.138549i	−0.00915915	−	0.999958i	$-0.502915\pi$
$331$	−9.40727	−	2.52067i	−0.517070	−	0.138549i	−0.507911	+	0.861410i	$0.669582\pi$
$332$	−4.45693	−	4.45693i	−0.244606	−	0.244606i
$333$	8.29237	+	7.89503i	0.454419	+	0.432645i
$334$		−	24.5185i		−	1.34159i
$335$	20.3390	+	8.08571i	1.11124	+	0.441770i
$336$	3.10700	+	1.79382i	0.169501	+	0.0978612i
$337$	−19.1912	+	5.14226i	−1.04541	+	0.280117i	−0.740354	−	0.672217i	$-0.765342\pi$
$337$	−19.1912	+	5.14226i	−1.04541	+	0.280117i	−0.305057	+	0.952334i	$0.598675\pi$
$338$	6.05919	−	10.4948i	0.329576	−	0.570843i
$339$	10.8915	+	10.8915i	0.591544	+	0.591544i
$340$	−1.25138	+	1.68007i	−0.0678658	+	0.0911148i
$341$	−1.93444	+	1.93444i	−0.104756	+	0.104756i
$342$	−4.65679	−	1.24778i	−0.251810	−	0.0674724i
$343$	−13.0897	−	13.0897i	−0.706778	−	0.706778i
$344$	−16.8233			−0.907052
$345$	−3.99913	+	10.0595i	−0.215306	+	0.541586i
$346$	0.242699	+	0.905765i	0.0130476	+	0.0486942i
$347$	−10.3295			−0.554517			−0.277258	−	0.960795i	$-0.589426\pi$
$347$	−10.3295			−0.554517			−0.277258	+	0.960795i	$0.589426\pi$
$348$	0.221521	−	0.127895i	0.0118748	−	0.00685589i
$349$	13.7141	−	7.91783i	0.734098	−	0.423832i	−0.0858212	−	0.996311i	$-0.527351\pi$
$349$	13.7141	−	7.91783i	0.734098	−	0.423832i	0.819920	+	0.572479i	$0.194018\pi$
$350$	−8.16540	−	4.40771i	−0.436459	−	0.235602i
$351$	7.61350	−	2.04003i	0.406378	−	0.108889i
$352$	6.32103	+	3.64945i	0.336912	+	0.194516i
$353$	7.53835	−	4.35227i	0.401226	−	0.231648i	−0.285787	−	0.958293i	$-0.592255\pi$
$353$	7.53835	−	4.35227i	0.401226	−	0.231648i	0.687013	+	0.726645i	$0.258922\pi$
$354$	3.27092	+	5.66540i	0.173847	+	0.301113i
$355$	−6.78833	+	2.92631i	−0.360287	+	0.155312i
$356$	−8.53114	+	8.53114i	−0.452150	+	0.452150i
$357$	1.14013	−	1.97477i	0.0603422	−	0.104516i
$358$	25.6268	+	6.86667i	1.35442	+	0.362915i
$359$		−	9.85969i		−	0.520375i	−0.965558	−	0.260187i	$-0.916216\pi$
$359$		−	9.85969i		−	0.520375i	0.965558	−	0.260187i	$-0.0837843\pi$
$360$	12.8672	+	1.50703i	0.678163	+	0.0794277i
$361$	−12.0518	+	6.95810i	−0.634305	+	0.366216i
$362$	22.8329			1.20007
$363$	1.99849	+	7.45845i	0.104893	+	0.391467i
$364$	−1.25184	+	1.25184i	−0.0656144	+	0.0656144i
$365$	−5.58944	+	0.817390i	−0.292565	+	0.0427841i
$366$	6.50137	−	11.2607i	0.339832	−	0.588606i
$367$	5.24797	+	19.5857i	0.273942	+	1.02236i	0.956547	+	0.291577i	$0.0941800\pi$
$367$	5.24797	+	19.5857i	0.273942	+	1.02236i	−0.682606	+	0.730787i	$0.739153\pi$
$368$	−4.75593	−	8.23752i	−0.247920	−	0.429410i
$369$	14.6995			0.765227
$370$	−15.2285	+	2.61014i	−0.791689	+	0.135695i
$371$	5.49510			0.285291
$372$	−0.533765	−	0.924507i	−0.0276744	−	0.0479335i
$373$	−0.616084	−	2.29926i	−0.0318996	−	0.119051i	0.948140	−	0.317853i	$-0.102962\pi$
$373$	−0.616084	−	2.29926i	−0.0318996	−	0.119051i	−0.980040	+	0.198802i	$0.936295\pi$
$374$	−1.44163	+	2.49698i	−0.0745452	+	0.129116i
$375$	11.7742	+	1.03849i	0.608018	+	0.0536272i
$376$	−5.51390	+	5.51390i	−0.284358	+	0.284358i
$377$	−0.134754	−	0.502910i	−0.00694021	−	0.0259012i
$378$	−9.57903			−0.492692
$379$	−14.3987	+	8.31312i	−0.739614	+	0.427016i	−0.821929	−	0.569590i	$-0.807102\pi$
$379$	−14.3987	+	8.31312i	−0.739614	+	0.427016i	0.0823151	+	0.996606i	$0.473769\pi$
$380$	−2.80697	+	2.21839i	−0.143994	+	0.113801i
$381$			5.40795i			0.277058i
$382$	19.4570	+	5.21350i	0.995508	+	0.266746i
$383$	4.50352	−	7.80032i	0.230119	−	0.398578i	−0.727724	−	0.685870i	$-0.759422\pi$
$383$	4.50352	−	7.80032i	0.230119	−	0.398578i	0.957843	+	0.287292i	$0.0927551\pi$
$384$	1.51383	−	1.51383i	0.0772523	−	0.0772523i
$385$	6.52653	+	2.59460i	0.332623	+	0.132233i
$386$	9.76590	+	16.9150i	0.497071	+	0.860953i
$387$	8.90978	−	5.14406i	0.452910	−	0.261487i
$388$	−9.47625	−	5.47112i	−0.481084	−	0.277754i
$389$	11.4603	−	3.07078i	0.581061	−	0.155695i	0.0436964	−	0.999045i	$-0.486087\pi$
$389$	11.4603	−	3.07078i	0.581061	−	0.155695i	0.537365	+	0.843350i	$0.319420\pi$
$390$	−1.51490	+	3.81061i	−0.0767098	+	0.192958i
$391$	−5.23566	+	3.02281i	−0.264779	+	0.152870i
$392$	−11.5446	+	6.66530i	−0.583093	+	0.336649i
$393$	−3.36720			−0.169853
$394$	−2.62139	−	9.78315i	−0.132064	−	0.492868i
$395$	26.5473	+	10.5538i	1.33574	+	0.531020i
$396$	−2.56806			−0.129050
$397$	1.62569	+	1.62569i	0.0815913	+	0.0815913i	0.746725	−	0.665133i	$-0.231625\pi$
$397$	1.62569	+	1.62569i	0.0815913	+	0.0815913i	−0.665133	+	0.746725i	$0.731625\pi$
$398$	−11.8099	−	3.16444i	−0.591974	−	0.158619i
$399$	2.75371	−	2.75371i	0.137858	−	0.137858i
$400$	−7.13075	+	7.55103i	−0.356537	+	0.377551i
$401$	16.9699	+	16.9699i	0.847436	+	0.847436i	0.989813	−	0.142377i	$-0.0454744\pi$
$401$	16.9699	+	16.9699i	0.847436	+	0.847436i	−0.142377	+	0.989813i	$0.545474\pi$
$402$	−5.87753	+	10.1802i	−0.293144	+	0.507741i
$403$	−2.09888	+	0.562392i	−0.104552	+	0.0280147i
$404$	0.471496	+	0.272218i	0.0234578	+	0.0135434i
$405$	−0.390238	+	0.168223i	−0.0193911	+	0.00835909i
$406$			0.632744i			0.0314026i
$407$	11.2184	−	3.30304i	0.556074	−	0.163726i
$408$	−3.03780	−	3.03780i	−0.150393	−	0.150393i
$409$	24.9023	+	6.67256i	1.23134	+	0.329937i	0.815102	−	0.579318i	$-0.196681\pi$
$409$	24.9023	+	6.67256i	1.23134	+	0.329937i	0.416240	+	0.909255i	$0.363348\pi$
$410$	−11.8490	+	15.9081i	−0.585179	+	0.785645i
$411$	19.7835	+	11.4220i	0.975850	+	0.563407i
$412$	−2.94089	−	1.69793i	−0.144887	−	0.0836508i
$413$	8.89941			0.437911
$414$	8.47957	+	4.89568i	0.416748	+	0.240610i
$415$	−15.5823	+	12.3149i	−0.764905	+	0.604516i
$416$	2.89868	+	5.02066i	0.142120	+	0.246158i
$417$	−13.4192	+	13.4192i	−0.657142	+	0.657142i
$418$	−3.48191	+	3.48191i	−0.170306	+	0.170306i
$419$	−29.0354	+	16.7636i	−1.41847	+	0.818955i	−0.996165	−	0.0874987i	$-0.972113\pi$
$419$	−29.0354	+	16.7636i	−1.41847	+	0.818955i	−0.422306	+	0.906453i	$0.638779\pi$
$420$	−1.63713	+	2.19796i	−0.0798836	+	0.107250i
$421$	−0.954366	−	0.954366i	−0.0465130	−	0.0465130i	0.683468	−	0.729981i	$-0.260471\pi$
$421$	−0.954366	−	0.954366i	−0.0465130	−	0.0465130i	−0.729981	+	0.683468i	$0.760471\pi$
$422$	−0.933319	−	1.61656i	−0.0454333	−	0.0786927i
$423$	1.23423	−	4.60620i	0.0600102	−	0.223961i
$424$	2.67954	−	10.0002i	0.130130	−	0.485651i
$425$	4.79934	+	4.53221i	0.232802	+	0.219845i
$426$	−1.02755	−	3.83487i	−0.0497849	−	0.185800i
$427$	−8.84436	−	15.3189i	−0.428009	−	0.741333i
$428$	8.91821	+	2.38963i	0.431078	+	0.115507i
$429$	0.803327	−	2.99806i	0.0387850	−	0.144748i
$430$	−1.61497	+	13.7889i	−0.0778810	+	0.664957i
$431$	−12.1677	+	3.26032i	−0.586097	+	0.157044i	−0.539669	−	0.841877i	$-0.681451\pi$
$431$	−12.1677	+	3.26032i	−0.586097	+	0.157044i	−0.0464282	+	0.998922i	$0.514784\pi$
$432$	−2.77494	+	10.3562i	−0.133509	+	0.498263i
$433$	−13.7322	−	13.7322i	−0.659928	−	0.659928i	0.295435	−	0.955363i	$-0.404535\pi$
$433$	−13.7322	−	13.7322i	−0.659928	−	0.659928i	−0.955363	+	0.295435i	$0.904535\pi$
$434$	2.64073			0.126759
$435$	−0.319068	−	0.740161i	−0.0152981	−	0.0354880i
$436$	6.64746	+	6.64746i	0.318356	+	0.318356i
$437$	−9.97314	+	2.67230i	−0.477080	+	0.127833i
$438$		−	3.03386i		−	0.144963i
$439$	−8.00818	−	29.8869i	−0.382210	−	1.42643i	−0.842519	−	0.538667i	$-0.818928\pi$
$439$	−8.00818	−	29.8869i	−0.382210	−	1.42643i	0.460309	−	0.887759i	$-0.347739\pi$
$440$	7.90425	−	10.6120i	0.376820	−	0.505909i
$441$	4.07610	−	7.06001i	0.194100	−	0.336191i
$442$	−1.98330	+	1.14506i	−0.0943361	+	0.0544650i
$443$	−13.3025	+	13.3025i	−0.632023	+	0.632023i	−0.948575	−	0.316552i	$-0.897475\pi$
$443$	−13.3025	+	13.3025i	−0.632023	+	0.632023i	0.316552	+	0.948575i	$0.397475\pi$
$444$	0.111980	+	4.56207i	0.00531432	+	0.216506i
$445$	23.5723	+	29.8265i	1.11744	+	1.41391i
$446$	−5.74558	+	21.4428i	−0.272061	+	1.01535i
$447$	17.2469	−	4.62129i	0.815750	−	0.218580i
$448$	−3.58012	−	13.3612i	−0.169145	−	0.631257i
$449$	−28.3423	+	7.59430i	−1.33756	+	0.358397i	−0.855527	−	0.517758i	$-0.826767\pi$
$449$	−28.3423	+	7.59430i	−1.33756	+	0.358397i	−0.482029	+	0.876155i	$0.660100\pi$
$450$	2.47041	−	10.4017i	0.116456	−	0.490340i
$451$	7.50694	−	13.0024i	0.353488	−	0.612259i
$452$		−	10.3389i		−	0.486300i
$453$	6.08433	−	22.7070i	0.285867	−	1.06687i
$454$		−	24.1369i		−	1.13280i
$455$	3.45896	+	4.37669i	0.162159	+	0.205182i
$456$	−3.66852	−	6.35407i	−0.171794	−	0.297556i
$457$	−5.55747	−	3.20861i	−0.259968	−	0.150092i	0.364352	−	0.931261i	$-0.381290\pi$
$457$	−5.55747	−	3.20861i	−0.259968	−	0.150092i	−0.624320	+	0.781169i	$0.714624\pi$
$458$			4.57660i			0.213850i
$459$	6.58228	+	1.76372i	0.307234	+	0.0823232i
$460$	6.67267	−	2.87645i	0.311115	−	0.134115i
$461$	25.3037	+	6.78010i	1.17851	+	0.315781i	0.794335	−	0.607479i	$-0.207819\pi$
$461$	25.3037	+	6.78010i	1.17851	+	0.315781i	0.384175	+	0.923260i	$0.374486\pi$
$462$	−1.88602	+	3.26669i	−0.0877458	+	0.151980i
$463$	19.1066	−	33.0936i	0.887960	−	1.53799i	0.0456763	−	0.998956i	$-0.485456\pi$
$463$	19.1066	−	33.0936i	0.887960	−	1.53799i	0.842283	−	0.539035i	$-0.181211\pi$
$464$	0.684081	+	0.183299i	0.0317576	+	0.00850944i
$465$	−3.08903	+	1.33162i	−0.143250	+	0.0617522i
$466$	−3.49481	−	0.936431i	−0.161894	−	0.0433793i
$467$		−	13.5181i		−	0.625544i	−0.949828	−	0.312772i	$-0.898742\pi$
$467$		−	13.5181i		−	0.625544i	0.949828	−	0.312772i	$-0.101258\pi$
$468$	−1.76648	−	1.01988i	−0.0816556	−	0.0471439i
$469$	7.99569	+	13.8489i	0.369207	+	0.639485i
$470$	3.99003	+	5.04866i	0.184046	+	0.232877i
$471$		−	5.50964i		−	0.253871i
$472$	4.33956	−	16.1955i	0.199745	−	0.745457i
$473$		−	10.5081i		−	0.483165i
$474$	−7.67159	+	13.2876i	−0.352368	+	0.610319i
$475$	5.91388	+	9.59796i	0.271347	+	0.440385i
$476$	−1.47843	+	0.396144i	−0.0677637	+	0.0181572i
$477$	1.63865	+	6.11551i	0.0750284	+	0.280010i
$478$	21.7848	−	5.83723i	0.996415	−	0.266989i
$479$	−0.466920	+	1.74257i	−0.0213341	+	0.0796200i	−0.975772	−	0.218789i	$-0.929789\pi$
$479$	−0.466920	+	1.74257i	−0.0213341	+	0.0796200i	0.954438	+	0.298409i	$0.0964560\pi$
$480$	5.56478	+	7.04122i	0.253996	+	0.321386i
$481$	9.02850	+	2.18321i	0.411664	+	0.0995457i
$482$	8.97105	−	8.97105i	0.408620	−	0.408620i
$483$	−6.84957	+	3.95460i	−0.311666	+	0.179941i
$484$	2.59147	−	4.48856i	0.117794	−	0.204026i
$485$	−20.5962	+	27.6519i	−0.935223	+	1.25561i
$486$	−4.61168	−	17.2110i	−0.209190	−	0.780708i
$487$		−	4.70678i		−	0.213285i	−0.994297	−	0.106642i	$-0.965990\pi$
$487$		−	4.70678i		−	0.213285i	0.994297	−	0.106642i	$-0.0340100\pi$
$488$	−32.1906	+	8.62544i	−1.45720	+	0.390455i
$489$	−10.9682	−	10.9682i	−0.496000	−	0.496000i
$490$	4.35483	+	10.1022i	0.196731	+	0.456369i
$491$	22.3671			1.00941			0.504707	−	0.863291i	$-0.331601\pi$
$491$	22.3671			1.00941			0.504707	+	0.863291i	$0.331601\pi$
$492$	4.14274	+	4.14274i	0.186769	+	0.186769i
$493$	0.116502	−	0.434793i	0.00524700	−	0.0195821i
$494$	−3.77789	+	1.01228i	−0.169975	+	0.0455448i
$495$	−0.941320	+	8.03711i	−0.0423092	+	0.361241i
$496$	0.764990	−	2.85498i	0.0343491	−	0.128192i
$497$	−5.21689	−	1.39786i	−0.234009	−	0.0627026i
$498$	−5.33343	−	9.23777i	−0.238997	−	0.413954i
$499$	−4.04934	−	15.1123i	−0.181273	−	0.676521i	−0.995398	−	0.0958307i	$-0.969449\pi$
$499$	−4.04934	−	15.1123i	−0.181273	−	0.676521i	0.814124	−	0.580691i	$-0.197217\pi$
$500$	−5.09552	−	6.08132i	−0.227879	−	0.271965i
$501$	−5.90600	+	22.0415i	−0.263860	+	0.984741i
$502$	−2.81720	+	10.5139i	−0.125738	+	0.469260i
$503$	5.10938	+	8.84970i	0.227816	+	0.394589i	0.957161	−	0.289558i	$-0.0935083\pi$
$503$	5.10938	+	8.84970i	0.227816	+	0.394589i	−0.729345	+	0.684146i	$0.760175\pi$
$504$	6.69303	+	6.69303i	0.298131	+	0.298131i
$505$	1.02477	−	1.37583i	0.0456018	−	0.0612237i
$506$	8.66091	−	5.00038i	0.385024	−	0.222294i
$507$	−7.97503	+	7.97503i	−0.354183	+	0.354183i
$508$	2.56679	−	2.56679i	0.113883	−	0.113883i
$509$	−3.43610	−	5.95149i	−0.152302	−	0.263795i	0.779771	−	0.626065i	$-0.215335\pi$
$509$	−3.43610	−	5.95149i	−0.152302	−	0.263795i	−0.932073	+	0.362269i	$0.882002\pi$
$510$	−2.78148	+	2.19825i	−0.123166	+	0.0973399i
$511$	−3.57427	−	2.06361i	−0.158117	−	0.0912886i
$512$	−20.6728			−0.913618
$513$	10.0788	+	5.81902i	0.444991	+	0.256916i
$514$	−0.348149	−	0.201004i	−0.0153562	−	0.00886591i
$515$	−6.39189	+	8.58158i	−0.281660	+	0.378149i
$516$	3.96077	+	1.06129i	0.174363	+	0.0467205i
$517$	−3.44408	−	3.44408i	−0.151471	−	0.151471i
$518$	−9.91170	−	5.40267i	−0.435495	−	0.237379i
$519$		−	0.872719i		−	0.0383081i
$520$	9.65152	−	4.16057i	0.423247	−	0.182453i
$521$	−19.6337	−	11.3355i	−0.860166	−	0.496617i	0.00390182	−	0.999992i	$-0.498758\pi$
$521$	−19.6337	−	11.3355i	−0.860166	−	0.496617i	−0.864068	+	0.503375i	$0.832091\pi$
$522$	−0.704182	+	0.188685i	−0.0308212	+	0.00825852i
$523$	−4.24004	+	7.34396i	−0.185404	+	0.321129i	−0.943713	−	0.330767i	$-0.892693\pi$
$523$	−4.24004	+	7.34396i	−0.185404	+	0.321129i	0.758309	+	0.651896i	$0.226026\pi$
$524$	1.59818	+	1.59818i	0.0698169	+	0.0698169i
$525$	6.27875	+	5.92928i	0.274027	+	0.258775i
$526$	16.2071	−	16.2071i	0.706663	−	0.706663i
$527$	−1.81459	−	0.486218i	−0.0790448	−	0.0211800i
$528$	2.98537	+	2.98537i	0.129921	+	0.129921i
$529$	−2.03048			−0.0882817
$530$	−7.93919	−	3.15620i	−0.344857	−	0.137097i
$531$	2.65382	+	9.90418i	0.115166	+	0.429805i
$532$	−2.61399			−0.113331
$533$	10.3275	−	5.96260i	0.447335	−	0.258269i
$534$	−17.6823	+	10.2089i	−0.765187	+	0.441781i
$535$	10.7476	−	27.0349i	0.464661	−	1.16882i
$536$	29.1017	−	7.79777i	1.25700	−	0.336813i
$537$	−21.3837	−	12.3459i	−0.922776	−	0.532765i
$538$	6.39373	−	3.69142i	0.275653	−	0.159148i
$539$	−4.16327	−	7.21099i	−0.179325	−	0.310599i
$540$	−7.61097	−	3.02572i	−0.327524	−	0.130206i
$541$	−9.87420	+	9.87420i	−0.424525	+	0.424525i	−0.886758	−	0.462233i	$-0.847048\pi$
$541$	−9.87420	+	9.87420i	−0.424525	+	0.424525i	0.462233	+	0.886758i	$0.347048\pi$
$542$	−2.41884	+	4.18956i	−0.103898	+	0.179957i
$543$	−20.5262	−	5.49997i	−0.880862	−	0.236026i
$544$			5.01213i			0.214893i
$545$	23.2408	−	18.3676i	0.995527	−	0.786780i
$546$	−2.59466	+	1.49803i	−0.111041	+	0.0641098i
$547$	16.2777			0.695983			0.347992	−	0.937498i	$-0.386864\pi$
$547$	16.2777			0.695983			0.347992	+	0.937498i	$0.386864\pi$
$548$	−3.96864	−	14.8112i	−0.169532	−	0.632701i
$549$	14.4110	−	14.4110i	0.615047	−	0.615047i
$550$	−7.93914	−	7.49725i	−0.338526	−	0.319684i
$551$	0.384376	−	0.665758i	0.0163750	−	0.0283623i
$552$	3.85672	+	14.3935i	0.164153	+	0.612626i
$553$	10.4363	+	18.0762i	0.443797	+	0.768679i
$554$	−0.648830			−0.0275661
$555$	14.3187	+	1.32177i	0.607795	+	0.0561059i
$556$	12.7384			0.540227
$557$	−6.36833	−	11.0303i	−0.269835	−	0.467368i	0.698984	−	0.715137i	$-0.253636\pi$
$557$	−6.36833	−	11.0303i	−0.269835	−	0.467368i	−0.968819	+	0.247769i	$0.920302\pi$
$558$	0.787469	+	2.93887i	0.0333362	+	0.124412i
$559$	4.17320	−	7.22819i	0.176508	−	0.305720i
$560$	−7.50828	+	1.09800i	−0.317283	+	0.0463988i
$561$	1.89746	−	1.89746i	0.0801109	−	0.0801109i
$562$	−9.21066	−	34.3747i	−0.388528	−	1.45001i
$563$	−9.88042			−0.416410			−0.208205	−	0.978085i	$-0.566762\pi$
$563$	−9.88042			−0.416410			−0.208205	+	0.978085i	$0.566762\pi$
$564$	1.64600	−	0.950317i	0.0693090	−	0.0400156i
$565$	−32.3570	−	3.78971i	−1.36127	−	0.159434i
$566$		−	0.699994i		−	0.0294229i
$567$	−0.299901	−	0.0803582i	−0.0125947	−	0.00337473i
$568$	−5.08776	+	8.81225i	−0.213478	+	0.369754i
$569$	28.2430	−	28.2430i	1.18401	−	1.18401i	0.205312	−	0.978697i	$-0.434179\pi$
$569$	28.2430	−	28.2430i	1.18401	−	1.18401i	0.978697	−	0.205312i	$-0.0658210\pi$
$570$	−5.56013	+	2.39686i	−0.232888	+	0.100393i
$571$	−18.9395	−	32.8041i	−0.792592	−	1.37281i	−0.924357	−	0.381529i	$-0.875398\pi$
$571$	−18.9395	−	32.8041i	−0.792592	−	1.37281i	0.131765	−	0.991281i	$-0.457936\pi$
$572$	−1.80426	+	1.04169i	−0.0754398	+	0.0435552i
$573$	−16.2355	−	9.37358i	−0.678249	−	0.391587i
$574$	−13.9988	+	3.75097i	−0.584299	+	0.156562i
$575$	−6.55639	−	21.9375i	−0.273421	−	0.914855i
$576$	13.8021	−	7.96865i	0.575088	−	0.332027i
$577$	−23.5713	+	13.6089i	−0.981288	+	0.566547i	−0.902659	−	0.430357i	$-0.858388\pi$
$577$	−23.5713	+	13.6089i	−0.981288	+	0.566547i	−0.0786291	+	0.996904i	$0.525054\pi$
$578$	17.3311			0.720880
$579$	−4.70480	−	17.5586i	−0.195525	−	0.729709i
$580$	−0.199864	+	0.502743i	−0.00829891	+	0.0208753i
$581$	−14.5110			−0.602019
$582$	−13.0941	−	13.0941i	−0.542769	−	0.542769i
$583$	6.24629	+	1.67369i	0.258695	+	0.0693171i
$584$	−5.49833	+	5.49833i	−0.227522	+	0.227522i
$585$	−3.83936	+	5.15462i	−0.158738	+	0.213117i
$586$	7.94139	+	7.94139i	0.328056	+	0.328056i
$587$	6.06864	−	10.5112i	0.250480	−	0.433843i	−0.713178	−	0.700983i	$-0.752745\pi$
$587$	6.06864	−	10.5112i	0.250480	−	0.433843i	0.963658	+	0.267139i	$0.0860784\pi$
$588$	3.13847	−	0.840951i	0.129428	−	0.0346802i
$589$	−2.77851	−	1.60418i	−0.114487	−	0.0660989i
$590$	−12.8577	−	5.11153i	−0.529342	−	0.210438i
$591$			9.42622i			0.387743i
$592$	−8.71231	+	9.15077i	−0.358074	+	0.376095i
$593$	−22.9652	−	22.9652i	−0.943070	−	0.943070i	0.0553950	−	0.998465i	$-0.482358\pi$
$593$	−22.9652	−	22.9652i	−0.943070	−	0.943070i	−0.998465	+	0.0553950i	$0.982358\pi$
$594$	−10.8885	−	2.91757i	−0.446761	−	0.119709i
$595$	0.697872	+	4.77216i	0.0286100	+	0.195640i
$596$	−10.3793	−	5.99251i	−0.425154	−	0.245463i
$597$	9.85449	+	5.68949i	0.403317	+	0.232855i
$598$	7.94340			0.324830
$599$	−2.59862	−	1.50032i	−0.106177	−	0.0613013i	0.445971	−	0.895047i	$-0.352858\pi$
$599$	−2.59862	−	1.50032i	−0.106177	−	0.0613013i	−0.552148	+	0.833746i	$0.686192\pi$
$600$	13.8520	−	8.53504i	0.565505	−	0.348442i
$601$	7.76062	+	13.4418i	0.316562	+	0.548302i	0.979768	−	0.200135i	$-0.0641380\pi$
$601$	7.76062	+	13.4418i	0.316562	+	0.548302i	−0.663206	+	0.748437i	$0.730805\pi$
$602$	−7.17241	+	7.17241i	−0.292326	+	0.292326i
$603$	−13.0282	+	13.0282i	−0.530549	+	0.530549i
$604$	−13.6653	+	7.88966i	−0.556033	+	0.321026i
$605$	−13.0977	−	9.75567i	−0.532497	−	0.396624i
$606$	0.651505	+	0.651505i	0.0264656	+	0.0264656i
$607$	18.5157	+	32.0701i	0.751529	+	1.30169i	0.947081	+	0.320994i	$0.104017\pi$
$607$	18.5157	+	32.0701i	0.751529	+	1.30169i	−0.195552	+	0.980693i	$0.562650\pi$
$608$	−2.21547	+	8.26824i	−0.0898492	+	0.335322i
$609$	0.152415	−	0.568820i	0.00617616	−	0.0230497i
$610$	3.97947	+	27.2123i	0.161124	+	1.10179i
$611$	−1.00129	−	3.73685i	−0.0405077	−	0.151177i
$612$	−0.881739	−	1.52722i	−0.0356422	−	0.0617341i
$613$	16.8361	+	4.51123i	0.680005	+	0.182207i	0.582258	−	0.813004i	$-0.302169\pi$
$613$	16.8361	+	4.51123i	0.680005	+	0.182207i	0.0977478	+	0.995211i	$0.468836\pi$
$614$	−5.30262	+	19.7897i	−0.213996	+	0.798645i
$615$	14.4838	−	11.4468i	0.584044	−	0.461579i
$616$	9.33837	−	2.50221i	0.376254	−	0.100817i
$617$	−6.18875	+	23.0967i	−0.249150	+	0.929839i	0.722103	+	0.691786i	$0.243176\pi$
$617$	−6.18875	+	23.0967i	−0.249150	+	0.929839i	−0.971252	+	0.238053i	$0.923491\pi$
$618$	−4.06368	−	4.06368i	−0.163465	−	0.163465i
$619$	−6.37727			−0.256324			−0.128162	−	0.991753i	$-0.540908\pi$
$619$	−6.37727			−0.256324			−0.128162	+	0.991753i	$0.540908\pi$
$620$	2.09818	+	0.834124i	0.0842649	+	0.0334992i
$621$	−16.7134	−	16.7134i	−0.670686	−	0.670686i
$622$	−26.7483	+	7.16718i	−1.07251	+	0.287378i
$623$			27.7760i			1.11282i
$624$	0.867925	+	3.23914i	0.0347448	+	0.129669i
$625$	−20.9001	+	13.7181i	−0.836005	+	0.548722i
$626$	0.525936	−	0.910947i	0.0210206	−	0.0364088i
$627$	3.96886	−	2.29142i	0.158501	−	0.0915107i
$628$	−2.61505	+	2.61505i	−0.104352	+	0.104352i
$629$	5.81612	+	5.53743i	0.231904	+	0.220792i
$630$	6.12830	−	4.84329i	0.244157	−	0.192961i
$631$	−5.89535	+	22.0017i	−0.234690	+	0.875876i	0.743598	+	0.668627i	$0.233118\pi$
$631$	−5.89535	+	22.0017i	−0.234690	+	0.875876i	−0.978288	+	0.207249i	$0.933549\pi$
$632$	37.9847	−	10.1780i	1.51095	−	0.404858i
$633$	0.449634	+	1.67806i	0.0178714	+	0.0666968i
$634$	29.0445	−	7.78244i	1.15350	−	0.309080i
$635$	−7.09227	−	8.97398i	−0.281448	−	0.356121i
$636$	−1.26171	+	2.18534i	−0.0500299	+	0.0866544i
$637$		−	6.61359i		−	0.262040i
$638$	−0.192720	+	0.719241i	−0.00762986	+	0.0284750i
$639$		−	6.22273i		−	0.246168i
$640$	−0.526740	+	4.49737i	−0.0208212	+	0.177774i
$641$	−11.7520	−	20.3550i	−0.464175	−	0.803976i	0.534988	−	0.844859i	$-0.320316\pi$
$641$	−11.7520	−	20.3550i	−0.464175	−	0.803976i	−0.999164	+	0.0408839i	$0.986983\pi$
$642$	13.5316	+	7.81249i	0.534051	+	0.308334i
$643$			24.3699i			0.961055i	0.876980	+	0.480527i	$0.159555\pi$
$643$			24.3699i			0.961055i	−0.876980	+	0.480527i	$0.840445\pi$
$644$	5.12800	+	1.37404i	0.202072	+	0.0541449i
$645$	4.77326	−	12.0068i	0.187947	−	0.472767i
$646$	−3.26619	−	0.875173i	−0.128507	−	0.0344332i
$647$	20.7661	−	35.9680i	0.816400	−	1.41405i	−0.0919177	−	0.995767i	$-0.529300\pi$
$647$	20.7661	−	35.9680i	0.816400	−	1.41405i	0.908318	−	0.418280i	$-0.137367\pi$
$648$	−0.292478	+	0.506586i	−0.0114896	+	0.0199006i
$649$	10.1160	+	2.71057i	0.397087	+	0.106399i
$650$	−2.48361	−	8.31005i	−0.0974151	−	0.325947i
$651$	−2.37394	−	0.636096i	−0.0930422	−	0.0249306i
$652$			10.4117i			0.407755i
$653$	0.642043	+	0.370684i	0.0251251	+	0.0145060i	0.512510	−	0.858681i	$-0.328716\pi$
$653$	0.642043	+	0.370684i	0.0251251	+	0.0145060i	−0.487385	+	0.873187i	$0.662049\pi$
$654$	7.95475	+	13.7780i	0.311055	+	0.538763i
$655$	5.58755	−	4.41593i	0.218324	−	0.172545i
$656$			16.2212i			0.633331i
$657$	1.23074	−	4.59319i	0.0480158	−	0.179197i
$658$			4.70157i			0.183286i
$659$	15.9185	−	27.5717i	0.620098	−	1.07404i	−0.369369	−	0.929283i	$-0.620426\pi$
$659$	15.9185	−	27.5717i	0.620098	−	1.07404i	0.989467	−	0.144759i	$-0.0462406\pi$
$660$	−2.53038	+	1.99980i	−0.0984948	+	0.0778419i
$661$	46.6955	−	12.5120i	1.81624	−	0.486661i	0.819932	−	0.572461i	$-0.194011\pi$
$661$	46.6955	−	12.5120i	1.81624	−	0.486661i	0.996312	+	0.0858000i	$0.0273446\pi$
$662$	2.86334	+	10.6861i	0.111287	+	0.415329i
$663$	2.05876	−	0.551642i	0.0799555	−	0.0214240i
$664$	−7.07592	+	26.4077i	−0.274599	+	1.02482i
$665$	−0.958157	+	8.18086i	−0.0371557	+	0.317240i
$666$	3.05696	−	12.6418i	0.118455	−	0.489861i
$667$	−1.10401	+	1.10401i	−0.0427473	+	0.0427473i
$668$	13.2648	−	7.65841i	0.513229	−	0.296313i
$669$	10.3302	−	17.8925i	0.399390	−	0.691764i
$670$	−3.59762	−	24.6011i	−0.138988	−	0.950424i
$671$	−5.38760	−	20.1068i	−0.207986	−	0.776214i
$672$			6.55714i			0.252947i
$673$	−16.5351	+	4.43056i	−0.637380	+	0.170785i	−0.563016	−	0.826446i	$-0.690359\pi$
$673$	−16.5351	+	4.43056i	−0.637380	+	0.170785i	−0.0743635	+	0.997231i	$0.523693\pi$
$674$	15.9588	+	15.9588i	0.614710	+	0.614710i
$675$	−12.2592	+	22.7105i	−0.471857	+	0.874129i
$676$	7.57040			0.291169
$677$	31.1728	+	31.1728i	1.19807	+	1.19807i	0.974745	+	0.223322i	$0.0716902\pi$
$677$	31.1728	+	31.1728i	1.19807	+	1.19807i	0.223322	+	0.974745i	$0.428310\pi$
$678$	4.52851	−	16.9006i	0.173916	−	0.649064i
$679$	−24.3331	+	6.52002i	−0.933817	+	0.250216i
$680$	9.02486	+	1.05701i	0.346087	+	0.0405344i
$681$	−5.81408	+	21.6984i	−0.222796	+	0.831486i
$682$	3.00172	+	0.804309i	0.114942	+	0.0307986i
$683$	18.4398	+	31.9387i	0.705580	+	1.22210i	0.966482	+	0.256736i	$0.0826469\pi$
$683$	18.4398	+	31.9387i	0.705580	+	1.22210i	−0.260901	+	0.965365i	$0.584020\pi$
$684$	−0.779496	−	2.90912i	−0.0298048	−	0.111233i
$685$	−47.8083	+	6.99140i	−1.82666	+	0.267128i
$686$	−5.44250	+	20.3117i	−0.207796	+	0.775503i
$687$	1.10241	−	4.11424i	0.0420595	−	0.156968i
$688$	5.67657	+	9.83210i	0.216417	+	0.374845i
$689$	3.63192	+	3.63192i	0.138365	+	0.138365i
$690$	12.1675	−	1.77935i	0.463209	−	0.0677388i
$691$	−0.520289	+	0.300389i	−0.0197927	+	0.0114273i	−0.509864	−	0.860255i	$-0.670304\pi$
$691$	−0.520289	+	0.300389i	−0.0197927	+	0.0114273i	0.490071	+	0.871683i	$0.336971\pi$
$692$	−0.414220	+	0.414220i	−0.0157463	+	0.0157463i
$693$	−4.18059	+	4.18059i	−0.158807	+	0.158807i
$694$	5.86687	+	10.1617i	0.222703	+	0.385734i
$695$	4.66924	−	39.8666i	0.177114	−	1.51222i
$696$	−0.960837	−	0.554740i	−0.0364204	−	0.0210274i
$697$	10.3100			0.390518
$698$	−15.5785	−	8.99422i	−0.589653	−	0.340436i
$699$	2.91617	+	1.68365i	0.110300	+	0.0636816i
$700$	−0.165869	−	5.79432i	−0.00626924	−	0.219005i
$701$	−6.15868	−	1.65021i	−0.232610	−	0.0623277i	0.140631	−	0.990062i	$-0.455087\pi$
$701$	−6.15868	−	1.65021i	−0.232610	−	0.0623277i	−0.373241	+	0.927734i	$0.621754\pi$
$702$	−6.33115	−	6.33115i	−0.238954	−	0.238954i
$703$	7.14687	+	11.7057i	0.269549	+	0.441487i
$704$		−	16.2781i		−	0.613505i
$705$	−2.37081	−	5.49972i	−0.0892900	−	0.207132i
$706$	−8.56315	−	4.94394i	−0.322278	−	0.186067i
$707$	1.21070	−	0.324407i	0.0455332	−	0.0122006i
$708$	−2.04336	+	3.53920i	−0.0767941	+	0.133011i
$709$	−0.102970	−	0.102970i	−0.00386711	−	0.00386711i	0.705171	−	0.709038i	$-0.250870\pi$
$709$	−0.102970	−	0.102970i	−0.00386711	−	0.00386711i	−0.709038	+	0.705171i	$0.750870\pi$
$710$	6.73436	+	5.01601i	0.252736	+	0.188247i
$711$	−17.0049	+	17.0049i	−0.637735	+	0.637735i
$712$	50.5477	+	13.5442i	1.89436	+	0.507591i
$713$	4.60752	+	4.60752i	0.172553	+	0.172553i
$714$	−2.59025			−0.0969378
$715$	2.59876	+	6.02851i	0.0971883	+	0.225454i
$716$	4.28964	+	16.0091i	0.160311	+	0.598290i
$717$	−20.9900			−0.783887
$718$	−9.69954	+	5.60003i	−0.361984	+	0.208991i
$719$	−15.6399	+	9.02972i	−0.583271	+	0.336752i	−0.762432	−	0.647068i	$-0.775995\pi$
$719$	−15.6399	+	9.02972i	−0.583271	+	0.336752i	0.179161	+	0.983820i	$0.442662\pi$
$720$	−3.46094	−	8.02855i	−0.128982	−	0.299207i
$721$	−7.55161	+	2.02345i	−0.281237	+	0.0753571i
$722$	13.6902	+	7.90402i	0.509495	+	0.294157i
$723$	−10.2257	+	5.90379i	−0.380297	+	0.219564i
$724$	7.13191	+	12.3528i	0.265055	+	0.459089i
$725$	1.50015	+	0.809784i	0.0557141	+	0.0300746i
$726$	6.20222	−	6.20222i	0.230186	−	0.230186i
$727$	−9.79831	+	16.9712i	−0.363399	+	0.629426i	−0.988518	−	0.151104i	$-0.951717\pi$
$727$	−9.79831	+	16.9712i	−0.363399	+	0.629426i	0.625119	+	0.780530i	$0.285051\pi$
$728$	7.41727	+	1.98745i	0.274902	+	0.0736599i
$729$			16.0130i			0.593073i
$730$	3.97876	+	5.03440i	0.147261	+	0.186332i
$731$	6.24916	−	3.60795i	0.231134	−	0.133445i
$732$	8.12287			0.300230
$733$	7.89548	+	29.4663i	0.291626	+	1.08836i	0.943860	+	0.330346i	$0.107165\pi$
$733$	7.89548	+	29.4663i	0.291626	+	1.08836i	−0.652234	+	0.758018i	$0.726168\pi$
$734$	16.2868	−	16.2868i	0.601158	−	0.601158i
$735$	−1.48147	−	10.1305i	−0.0546449	−	0.373671i
$736$	8.69240	−	15.0557i	0.320406	−	0.554960i
$737$	4.87063	+	18.1774i	0.179412	+	0.669574i
$738$	−8.34892	−	14.4608i	−0.307328	−	0.532308i
$739$	52.1459			1.91822			0.959110	−	0.283035i	$-0.0913412\pi$
$739$	52.1459			1.91822			0.959110	+	0.283035i	$0.0913412\pi$
$740$	−6.16875	−	7.42346i	−0.226768	−	0.272892i
$741$	3.64006			0.133721
$742$	−3.12106	−	5.40584i	−0.114578	−	0.198455i
$743$	−6.78290	−	25.3141i	−0.248841	−	0.928686i	−0.971414	−	0.237392i	$-0.923708\pi$
$743$	−6.78290	−	25.3141i	−0.248841	−	0.928686i	0.722573	−	0.691294i	$-0.242959\pi$
$744$	−2.31518	+	4.01001i	−0.0848787	+	0.147014i
$745$	−22.5590	+	30.2870i	−0.826496	+	1.10963i
$746$	−1.91199	+	1.91199i	−0.0700030	+	0.0700030i
$747$	−4.32721	−	16.1494i	−0.158324	−	0.590874i
$748$	−1.80119			−0.0658581
$749$	18.4082	−	10.6280i	0.672621	−	0.388338i
$750$	−5.66582	−	12.1728i	−0.206886	−	0.444488i
$751$		−	53.1233i		−	1.93850i	−0.246087	−	0.969248i	$-0.579145\pi$
$751$		−	53.1233i		−	1.93850i	0.246087	−	0.969248i	$-0.420855\pi$
$752$	5.08302	+	1.36199i	0.185359	+	0.0496667i
$753$	5.06517	−	8.77313i	0.184585	−	0.319711i
$754$	−0.418205	+	0.418205i	−0.0152301	+	0.0152301i
$755$	19.6828	+	45.6594i	0.716331	+	1.66172i
$756$	−2.99203	−	5.18235i	−0.108819	−	0.188480i
$757$	−12.9392	+	7.47044i	−0.470282	+	0.271518i	−0.716358	−	0.697733i	$-0.754192\pi$
$757$	−12.9392	+	7.47044i	−0.470282	+	0.271518i	0.246075	+	0.969251i	$0.420859\pi$
$758$	16.3562	+	9.44324i	0.594083	+	0.342994i
$759$	−8.99041	+	2.40897i	−0.326331	+	0.0874402i
$760$	14.4206	+	5.73287i	0.523090	+	0.207953i
$761$	−33.1931	+	19.1641i	−1.20325	+	0.694697i	−0.961277	−	0.275586i	$-0.911128\pi$
$761$	−33.1931	+	19.1641i	−1.20325	+	0.694697i	−0.241974	+	0.970283i	$0.577795\pi$
$762$	5.32011	−	3.07157i	0.192727	−	0.111271i
$763$	21.6430			0.783530
$764$	3.25689	+	12.1549i	0.117830	+	0.439749i
$765$	−5.10285	+	2.19973i	−0.184494	+	0.0795314i
$766$	−10.2315			−0.369679
$767$	5.88197	+	5.88197i	0.212385	+	0.212385i
$768$	14.9434	+	4.00407i	0.539224	+	0.144485i
$769$	−22.4800	+	22.4800i	−0.810650	+	0.810650i	−0.984731	−	0.174081i	$-0.944304\pi$
$769$	−22.4800	+	22.4800i	−0.810650	+	0.810650i	0.174081	+	0.984731i	$0.444304\pi$
$770$	−1.15443	−	7.89419i	−0.0416028	−	0.284487i
$771$	0.264559	+	0.264559i	0.00952786	+	0.00952786i
$772$	−6.10080	+	10.5669i	−0.219573	+	0.380311i
$773$	−29.6256	+	7.93815i	−1.06556	+	0.285515i	−0.748667	−	0.662947i	$-0.769306\pi$
$773$	−29.6256	+	7.93815i	−1.06556	+	0.285515i	−0.316891	+	0.948462i	$0.602639\pi$
$774$	−10.1210	−	5.84337i	−0.363792	−	0.210036i
$775$	3.37960	−	6.26080i	0.121399	−	0.224895i
$776$			47.4615i			1.70377i
$777$	7.60896	+	7.24437i	0.272970	+	0.259890i
$778$	−9.53005	−	9.53005i	−0.341669	−	0.341669i
$779$	17.0078	+	4.55724i	0.609369	+	0.163280i
$780$	−2.53476	+	0.370678i	−0.0907589	+	0.0132724i
$781$	−5.50429	−	3.17790i	−0.196959	−	0.113714i
$782$	5.94742	+	3.43375i	0.212679	+	0.122790i
$783$	1.75986			0.0628922
$784$	7.79085	+	4.49805i	0.278245	+	0.160645i
$785$	7.22563	+	9.14272i	0.257894	+	0.326318i
$786$	1.91248	+	3.31251i	0.0682159	+	0.118153i
$787$	−17.9843	+	17.9843i	−0.641072	+	0.641072i	−0.950819	−	0.309747i	$-0.899756\pi$
$787$	−17.9843	+	17.9843i	−0.641072	+	0.641072i	0.309747	+	0.950819i	$0.399756\pi$
$788$	4.47398	−	4.47398i	0.159379	−	0.159379i
$789$	−18.4737	+	10.6658i	−0.657681	+	0.379712i
$790$	−4.69576	−	32.1104i	−0.167068	−	1.14244i
$791$	−16.8308	−	16.8308i	−0.598435	−	0.598435i
$792$	5.56943	+	9.64653i	0.197901	+	0.342775i
$793$	4.27926	−	15.9704i	0.151961	−	0.567126i
$794$	0.675939	−	2.52264i	0.0239882	−	0.0895251i
$795$	6.37686	+	4.74973i	0.226164	+	0.168455i
$796$	−1.97684	−	7.37767i	−0.0700672	−	0.261494i
$797$	−14.1009	−	24.4236i	−0.499481	−	0.865127i	0.500519	−	0.865726i	$-0.333143\pi$
$797$	−14.1009	−	24.4236i	−0.499481	−	0.865127i	−1.00000		0.000599033i	$0.999809\pi$
$798$	−4.27301	−	1.14495i	−0.151263	−	0.0405307i
$799$	0.865665	−	3.23070i	0.0306250	−	0.114294i
$800$	−18.4684	−	4.38628i	−0.652958	−	0.155078i
$801$	−30.9119	+	8.28283i	−1.09222	+	0.292659i
$802$	7.05582	−	26.3327i	0.249150	−	0.929839i
$803$	−3.43435	−	3.43435i	−0.121196	−	0.121196i
$804$	−7.34343			−0.258983
$805$	6.17994	−	15.5452i	0.217814	−	0.547895i
$806$	1.74536	+	1.74536i	0.0614777	+	0.0614777i
$807$	−6.63697	+	1.77837i	−0.233633	+	0.0626017i
$808$		−	2.36147i		−	0.0830763i
$809$	0.812619	+	3.03273i	0.0285701	+	0.106625i	0.978739	−	0.205112i	$-0.0657558\pi$
$809$	0.812619	+	3.03273i	0.0285701	+	0.106625i	−0.950168	+	0.311737i	$0.899089\pi$
$810$	0.387135	+	0.288353i	0.0136025	+	0.0101317i
$811$	−10.5095	+	18.2030i	−0.369038	+	0.639192i	−0.989415	−	0.145111i	$-0.953646\pi$
$811$	−10.5095	+	18.2030i	−0.369038	+	0.639192i	0.620377	+	0.784303i	$0.286979\pi$
$812$	−0.342321	+	0.197639i	−0.0120131	+	0.00693577i
$813$	3.18365	−	3.18365i	0.111655	−	0.111655i
$814$	−9.62111	−	9.16011i	−0.337220	−	0.321062i
$815$	32.5850	+	3.81641i	1.14140	+	0.133683i
$816$	−0.750368	+	2.80041i	−0.0262681	+	0.0980340i
$817$	11.9037	−	3.18959i	0.416458	−	0.111590i
$818$	−7.57966	−	28.2877i	−0.265017	−	0.989056i
$819$	−4.53596	+	1.21541i	−0.158499	+	0.0424697i
$820$	−12.3075	−	1.44147i	−0.429796	−	0.0503385i
$821$	2.11926	−	3.67067i	0.0739627	−	0.128107i	−0.826672	−	0.562684i	$-0.809769\pi$
$821$	2.11926	−	3.67067i	0.0739627	−	0.128107i	0.900635	+	0.434577i	$0.143102\pi$
$822$		−	25.9496i		−	0.905096i
$823$	−0.244554	+	0.912687i	−0.00852461	+	0.0318143i	−0.970057	−	0.242877i	$-0.921909\pi$
$823$	−0.244554	+	0.912687i	−0.00852461	+	0.0318143i	0.961533	+	0.274691i	$0.0885756\pi$
$824$			14.7294i			0.513122i
$825$	5.33114	+	8.65220i	0.185606	+	0.301231i
$826$	−5.05462	−	8.75486i	−0.175873	−	0.304621i
$827$	−20.7030	−	11.9529i	−0.719912	−	0.415642i	0.0948080	−	0.995496i	$-0.469776\pi$
$827$	−20.7030	−	11.9529i	−0.719912	−	0.415642i	−0.814720	+	0.579854i	$0.803110\pi$
$828$			6.11671i			0.212570i
$829$	−2.51032	−	0.672639i	−0.0871871	−	0.0233617i	0.214962	−	0.976622i	$-0.431037\pi$
$829$	−2.51032	−	0.672639i	−0.0871871	−	0.0233617i	−0.302149	+	0.953261i	$0.597704\pi$
$830$	20.9652	+	8.33466i	0.727713	+	0.289300i
$831$	0.583280	+	0.156289i	0.0202338	+	0.00542162i
$832$	6.46469	−	11.1972i	0.224123	−	0.388192i
$833$	2.85890	−	4.95177i	0.0990551	−	0.171569i
$834$	20.8230	+	5.57951i	0.721041	+	0.193202i
$835$	−19.1059	−	44.3211i	−0.661187	−	1.53380i
$836$	−2.97133	−	0.796165i	−0.102766	−	0.0275360i
$837$		−	7.34470i		−	0.253870i
$838$	32.9826	+	19.0425i	1.13936	+	0.657812i
$839$	−18.2196	−	31.5573i	−0.629012	−	1.08948i	−0.987750	−	0.156042i	$-0.950126\pi$
$839$	−18.2196	−	31.5573i	−0.629012	−	1.08948i	0.358739	−	0.933438i	$-0.383207\pi$
$840$	11.8068	+	1.38283i	0.407373	+	0.0477123i
$841$			28.8838i			0.995991i
$842$	−0.396811	+	1.48092i	−0.0136750	+	0.0510358i
$843$			33.1205i			1.14073i
$844$	0.583049	−	1.00987i	0.0200694	−	0.0347611i
$845$	2.77493	−	23.6927i	0.0954603	−	0.815052i
$846$	−5.23239	+	1.40201i	−0.179893	+	0.0482022i
$847$	−3.08830	−	11.5257i	−0.106115	−	0.396028i
$848$	−6.74857	+	1.80827i	−0.231747	+	0.0620964i
$849$	−0.168614	+	0.629276i	−0.00578681	+	0.0215967i
$850$	1.73270	−	7.29555i	0.0594313	−	0.250235i
$851$	−7.86732	−	26.7204i	−0.269688	−	0.915962i
$852$	1.75374	−	1.75374i	0.0600822	−	0.0600822i
$853$	−22.4827	+	12.9804i	−0.769792	+	0.444440i	−0.832800	−	0.553573i	$-0.813264\pi$
$853$	−22.4827	+	12.9804i	−0.769792	+	0.444440i	0.0630083	+	0.998013i	$0.479931\pi$
$854$	−10.0467	+	17.4014i	−0.343791	+	0.595464i
$855$	−9.39023	+	1.37321i	−0.321139	+	0.0469627i
$856$	−10.3649	−	38.6824i	−0.354265	−	1.32214i
$857$		−	40.2792i		−	1.37591i	−0.725753	−	0.687955i	$-0.758509\pi$
$857$		−	40.2792i		−	1.37591i	0.725753	−	0.687955i	$-0.241491\pi$
$858$	−3.40563	+	0.912535i	−0.116266	+	0.0311534i
$859$	3.69657	+	3.69657i	0.126125	+	0.126125i	0.767352	−	0.641226i	$-0.221574\pi$
$859$	3.69657	+	3.69657i	0.126125	+	0.126125i	−0.641226	+	0.767352i	$0.721574\pi$
$860$	−7.96434	+	3.43326i	−0.271582	+	0.117073i
$861$	13.4881			0.459672
$862$	10.1183	+	10.1183i	0.344630	+	0.344630i
$863$	−1.83795	+	6.85933i	−0.0625646	+	0.233494i	−0.990127	−	0.140174i	$-0.955234\pi$
$863$	−1.83795	+	6.85933i	−0.0625646	+	0.233494i	0.927562	+	0.373669i	$0.121900\pi$
$864$	−18.9280	+	5.07175i	−0.643944	+	0.172544i
$865$	1.14453	+	1.44819i	0.0389152	+	0.0492401i
$866$	−5.70964	+	21.3087i	−0.194021	+	0.724098i
$867$	−15.5802	−	4.17471i	−0.529132	−	0.141780i
$868$	0.824838	+	1.42866i	0.0279968	+	0.0484919i
$869$	6.35735	+	23.7259i	0.215658	+	0.804847i
$870$	−0.546917	+	0.734276i	−0.0185422	+	0.0248943i
$871$	−3.86864	+	14.4380i	−0.131084	+	0.489212i
$872$	10.5536	−	39.3867i	0.357391	−	1.33380i
$873$	−14.5123	−	25.1360i	−0.491167	−	0.850726i
$874$	8.29336	+	8.29336i	0.280527	+	0.280527i
$875$	−18.1950	−	1.60479i	−0.615102	−	0.0542520i
$876$	1.64135	−	0.947633i	0.0554560	−	0.0320176i
$877$	−26.8398	+	26.8398i	−0.906315	+	0.906315i	−0.995973	−	0.0896576i	$-0.971423\pi$
$877$	−26.8398	+	26.8398i	−0.906315	+	0.906315i	0.0896576	+	0.995973i	$0.471423\pi$
$878$	−24.8531	+	24.8531i	−0.838750	+	0.838750i
$879$	−5.22618	−	9.05201i	−0.176275	−	0.305317i
$880$	−8.86910	−	1.03876i	−0.298977	−	0.0350167i
$881$	−3.79357	−	2.19022i	−0.127809	−	0.0737904i	0.434733	−	0.900560i	$-0.356843\pi$
$881$	−3.79357	−	2.19022i	−0.127809	−	0.0737904i	−0.562541	+	0.826769i	$0.690176\pi$
$882$	−9.26045			−0.311815
$883$	50.6657	+	29.2518i	1.70504	+	0.984402i	0.940483	+	0.339840i	$0.110373\pi$
$883$	50.6657	+	29.2518i	1.70504	+	0.984402i	0.764552	+	0.644562i	$0.222960\pi$
$884$	−1.23898	−	0.715324i	−0.0416713	−	0.0240590i
$885$	10.3274	+	7.69227i	0.347153	+	0.258573i
$886$	20.6420	+	5.53099i	0.693480	+	0.185817i
$887$	2.53298	+	2.53298i	0.0850491	+	0.0850491i	0.748351	−	0.663302i	$-0.230846\pi$
$887$	2.53298	+	2.53298i	0.0850491	+	0.0850491i	−0.663302	+	0.748351i	$0.730846\pi$
$888$	16.8939	−	10.3145i	0.566921	−	0.346133i
$889$		−	8.35702i		−	0.280286i
$890$	15.9536	−	40.1301i	0.534766	−	1.34516i
$891$	−0.316423	−	0.182687i	−0.0106006	−	0.00612024i
$892$	−13.3954	+	3.58929i	−0.448511	+	0.120178i
$893$	2.85608	−	4.94688i	0.0955752	−	0.165541i
$894$	−14.3420	−	14.3420i	−0.479668	−	0.479668i
$895$	51.6753	−	7.55689i	1.72731	−	0.252599i
$896$	−2.33935	+	2.33935i	−0.0781523	+	0.0781523i
$897$	−7.14090	−	1.91340i	−0.238428	−	0.0638865i
$898$	23.5686	+	23.5686i	0.786494	+	0.786494i
$899$	−0.485155			−0.0161808
$900$	6.39905	−	1.91247i	0.213302	−	0.0637490i
$901$	1.14932	+	4.28931i	0.0382893	+	0.142898i
$902$	−17.0549			−0.567867
$903$	8.17549	−	4.72012i	0.272063	−	0.157076i
$904$	−38.8364	+	22.4222i	−1.29168	+	0.745752i
$905$	41.2741	−	17.7924i	1.37200	−	0.591440i
$906$	−25.7939	+	6.91146i	−0.856946	+	0.229618i
$907$	−10.6371	−	6.14134i	−0.353200	−	0.203920i	0.312894	−	0.949788i	$-0.398702\pi$
$907$	−10.6371	−	6.14134i	−0.353200	−	0.203920i	−0.666094	+	0.745868i	$0.732035\pi$
$908$	13.0583	−	7.53922i	0.433355	−	0.250198i
$909$	0.722067	+	1.25066i	0.0239495	+	0.0414817i
$910$	2.34100	−	5.88861i	0.0776034	−	0.195206i
$911$	−8.69751	+	8.69751i	−0.288161	+	0.288161i	−0.836353	−	0.548191i	$-0.815317\pi$
$911$	−8.69751	+	8.69751i	−0.288161	+	0.288161i	0.548191	+	0.836353i	$0.315317\pi$
$912$	−2.47568	+	4.28801i	−0.0819781	+	0.141990i
$913$	−16.4947	−	4.41974i	−0.545895	−	0.146272i
$914$			7.28961i			0.241119i
$915$	2.97743	−	25.4217i	0.0984309	−	0.840415i
$916$	−2.47599	+	1.42951i	−0.0818089	+	0.0472324i
$917$	5.20341			0.171832
$918$	−2.00348	−	7.47710i	−0.0661248	−	0.246781i
$919$	25.2847	−	25.2847i	0.834065	−	0.834065i	−0.154005	−	0.988070i	$-0.549217\pi$
$919$	25.2847	−	25.2847i	0.834065	−	0.834065i	0.988070	+	0.154005i	$0.0492173\pi$
$920$	−25.2762	−	18.8267i	−0.833331	−	0.620697i
$921$	9.53382	−	16.5131i	0.314150	−	0.544124i
$922$	−7.70182	−	28.7436i	−0.253646	−	0.946620i
$923$	−2.52414	−	4.37194i	−0.0830832	−	0.143904i
$924$	−2.35642			−0.0775204
$925$	−25.4939	+	16.5849i	−0.838235	+	0.545309i
$926$	−43.4081			−1.42648
$927$	−4.50380	−	7.80081i	−0.147924	−	0.256212i
$928$	0.335015	+	1.25029i	0.0109974	+	0.0410428i
$929$	−6.26098	+	10.8443i	−0.205416	+	0.355791i	−0.950265	−	0.311442i	$-0.899188\pi$
$929$	−6.26098	+	10.8443i	−0.205416	+	0.355791i	0.744849	+	0.667233i	$0.232521\pi$
$930$	3.06447	+	2.28253i	0.100488	+	0.0748472i
$931$	6.90497	−	6.90497i	0.226301	−	0.226301i
$932$	−0.584992	−	2.18322i	−0.0191621	−	0.0715138i
$933$	25.7724			0.843751
$934$	−13.2985	+	7.67791i	−0.435141	+	0.251229i
$935$	−0.660225	+	5.63709i	−0.0215917	+	0.184352i
$936$			8.84736i			0.289185i
$937$	11.8419	+	3.17302i	0.386857	+	0.103658i	0.447005	−	0.894531i	$-0.352491\pi$
$937$	11.8419	+	3.17302i	0.386857	+	0.103658i	−0.0601478	+	0.998189i	$0.519157\pi$
$938$	9.08266	−	15.7316i	0.296559	−	0.513656i
$939$	−0.692230	+	0.692230i	−0.0225901	+	0.0225901i
$940$	−1.48508	+	3.73561i	−0.0484379	+	0.121842i
$941$	−13.7869	−	23.8796i	−0.449440	−	0.778452i	0.548910	−	0.835881i	$-0.315043\pi$
$941$	−13.7869	−	23.8796i	−0.449440	−	0.778452i	−0.998350	+	0.0574293i	$0.981710\pi$
$942$	−5.42015	+	3.12932i	−0.176598	+	0.101959i
$943$	−30.9696	−	17.8803i	−1.00851	−	0.582264i
$944$	−10.9294	+	2.92853i	−0.355723	+	0.0953157i
$945$	−17.3156	+	7.46440i	−0.563277	+	0.242817i
$946$	−10.3375	+	5.96833i	−0.336100	+	0.194047i
$947$	7.76600	−	4.48370i	0.252361	−	0.145701i	−0.368484	−	0.929634i	$-0.620123\pi$
$947$	7.76600	−	4.48370i	0.252361	−	0.145701i	0.620845	+	0.783933i	$0.286790\pi$
$948$	−9.58495			−0.311305
$949$	−0.998457	−	3.72629i	−0.0324113	−	0.120961i
$950$	6.08314	−	11.2692i	0.197363	−	0.365621i
$951$	−27.9848			−0.907469
$952$	4.69437	+	4.69437i	0.152145	+	0.152145i
$953$	35.9483	+	9.63231i	1.16448	+	0.312021i	0.788753	−	0.614710i	$-0.210727\pi$
$953$	35.9483	+	9.63231i	1.16448	+	0.312021i	0.375725	+	0.926731i	$0.377394\pi$
$954$	5.08547	−	5.08547i	0.164648	−	0.164648i
$955$	39.2343	−	5.73755i	1.26959	−	0.185663i
$956$	9.96253	+	9.96253i	0.322211	+	0.322211i
$957$	0.346500	−	0.600156i	0.0112008	−	0.0194003i
$958$	1.97946	−	0.530395i	0.0639535	−	0.0171363i
$959$	−30.5719	−	17.6507i	−0.987219	−	0.569971i
$960$	7.39425	−	18.5997i	0.238648	−	0.600302i
$961$		−	28.9752i		−	0.934685i
$962$	−2.98019	−	10.1219i	−0.0960852	−	0.326342i
$963$	17.3173	+	17.3173i	0.558041	+	0.558041i
$964$	7.65555	+	2.05130i	0.246569	+	0.0660679i
$965$	30.8344	+	22.9666i	0.992594	+	0.739322i
$966$	7.78074	+	4.49221i	0.250341	+	0.144535i
$967$	48.6411	+	28.0830i	1.56419	+	0.903087i	0.996825	+	0.0796228i	$0.0253716\pi$
$967$	48.6411	+	28.0830i	1.56419	+	0.903087i	0.567368	+	0.823464i	$0.307962\pi$
$968$	−22.4808			−0.722561
$969$	2.72541	+	1.57351i	0.0875526	+	0.0505485i
$970$	38.9007	+	4.55612i	1.24903	+	0.146288i
$971$	−19.7612	−	34.2274i	−0.634167	−	1.09841i	−0.986691	−	0.162607i	$-0.948010\pi$
$971$	−19.7612	−	34.2274i	−0.634167	−	1.09841i	0.352523	−	0.935803i	$-0.385324\pi$
$972$	7.87086	−	7.87086i	0.252458	−	0.252458i
$973$	20.7370	−	20.7370i	0.664798	−	0.664798i
$974$	−4.63033	+	2.67332i	−0.148365	+	0.0856588i
$975$	0.230977	+	8.06876i	0.00739718	+	0.258407i
$976$	15.9028	+	15.9028i	0.509037	+	0.509037i
$977$	−3.00331	−	5.20188i	−0.0960843	−	0.166423i	0.813976	−	0.580898i	$-0.197298\pi$
$977$	−3.00331	−	5.20188i	−0.0960843	−	0.166423i	−0.910061	+	0.414475i	$0.863965\pi$
$978$	−4.56042	+	17.0197i	−0.145826	+	0.544231i
$979$	−8.45996	+	31.5730i	−0.270381	+	1.00908i
$980$	−4.10513	+	5.51143i	−0.131133	+	0.176056i
$981$	6.45397	+	24.0866i	0.206060	+	0.769025i
$982$	−12.7039	−	22.0038i	−0.405398	−	0.702169i
$983$	23.1064	+	6.19133i	0.736979	+	0.197473i	0.607735	−	0.794140i	$-0.292078\pi$
$983$	23.1064	+	6.19133i	0.736979	+	0.197473i	0.129244	+	0.991613i	$0.458745\pi$
$984$	6.57710	−	24.5461i	0.209670	−	0.782501i
$985$	−12.3620	−	15.6419i	−0.393887	−	0.498393i
$986$	−0.493901	+	0.132340i	−0.0157290	+	0.00421457i
$987$	1.13251	−	4.22658i	0.0360482	−	0.134534i
$988$	−1.72769	−	1.72769i	−0.0549651	−	0.0549651i
$989$	−25.0287			−0.795867
$990$	8.44121	−	3.63883i	0.268279	−	0.115649i
$991$	18.5888	+	18.5888i	0.590492	+	0.590492i	0.937764	−	0.347272i	$-0.112892\pi$
$991$	18.5888	+	18.5888i	0.590492	+	0.590492i	−0.347272	+	0.937764i	$0.612892\pi$
$992$	5.21804	−	1.39817i	0.165673	−	0.0443919i
$993$		−	10.2963i		−	0.326742i
$994$	1.58789	+	5.92610i	0.0503649	+	0.187964i
$995$	−23.8141	+	3.48252i	−0.754957	+	0.110403i
$996$	3.33182	−	5.77087i	0.105573	−	0.182857i
$997$	44.7129	−	25.8150i	1.41607	−	0.817569i	0.420120	−	0.907469i	$-0.361988\pi$
$997$	44.7129	−	25.8150i	1.41607	−	0.817569i	0.995951	+	0.0898999i	$0.0286547\pi$
$998$	−12.5670	+	12.5670i	−0.397800	+	0.397800i
$999$	−15.0265	+	27.5675i	−0.475417	+	0.872198i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.p.a.103.6	yes	68
5.2	odd	4		185.2.u.a.177.12	yes	68
5.3	odd	4		925.2.y.b.732.6		68
5.4	even	2		925.2.t.b.843.12		68
37.23	odd	12		185.2.u.a.23.12	yes	68
185.23	even	12		925.2.t.b.282.12		68
185.97	even	12	inner	185.2.p.a.97.6	✓	68
185.134	odd	12		925.2.y.b.393.6		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.6	✓	68	185.97	even	12	inner
185.2.p.a.103.6	yes	68	1.1	even	1	trivial
185.2.u.a.23.12	yes	68	37.23	odd	12
185.2.u.a.177.12	yes	68	5.2	odd	4
925.2.t.b.282.12		68	185.23	even	12
925.2.t.b.843.12		68	5.4	even	2
925.2.y.b.393.6		68	185.134	odd	12
925.2.y.b.732.6		68	5.3	odd	4

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
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Newspace parameters

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.p.a.103.6

Level	$185$
Weight	$2$
Character	185.103
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$68$
Inner twists	$2$