LMFDB - Embedded newform 185.2.u.a.23.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(8,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("185.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.u (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			23.12
Character	$\chi$	$=$	185.23
Dual form			185.2.u.a.177.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.983757 + 0.567972i) q^{2} +(1.02118 + 0.273625i) q^{3} +(-0.354815 - 0.614557i) q^{4} +(0.885178 + 2.05340i) q^{5} +(0.849185 + 0.849185i) q^{6} +(1.57806 + 0.422839i) q^{7} -3.07799i q^{8} +(-1.63013 - 0.941157i) q^{9} +(-0.295475 + 2.52281i) q^{10} +1.92257i q^{11} +(-0.194173 - 0.724662i) q^{12} +(-1.32247 + 0.763528i) q^{13} +(1.31226 + 1.31226i) q^{14} +(0.342067 + 2.33911i) q^{15} +(1.03858 - 1.79888i) q^{16} +(0.660110 - 1.14334i) q^{17} +(-1.06910 - 1.85174i) q^{18} +(-2.17790 - 0.583566i) q^{19} +(0.947859 - 1.27257i) q^{20} +(1.49579 + 0.863592i) q^{21} +(-1.09196 + 1.89134i) q^{22} -4.57925i q^{23} +(0.842216 - 3.14319i) q^{24} +(-3.43292 + 3.63525i) q^{25} -1.73465 q^{26} +(-3.64981 - 3.64981i) q^{27} +(-0.300059 - 1.11984i) q^{28} +(-0.241089 - 0.241089i) q^{29} +(-0.992038 + 2.49540i) q^{30} +(-1.00617 + 1.00617i) q^{31} +(-3.28781 + 1.89822i) q^{32} +(-0.526063 + 1.96329i) q^{33} +(1.29878 - 0.749849i) q^{34} +(0.528603 + 3.61467i) q^{35} +1.33575i q^{36} +(-5.83510 - 1.71804i) q^{37} +(-1.81107 - 1.81107i) q^{38} +(-1.55940 + 0.417841i) q^{39} +(6.32035 - 2.72457i) q^{40} +(6.76304 - 3.90464i) q^{41} +(0.980993 + 1.69913i) q^{42} +5.46568i q^{43} +(1.18153 - 0.682155i) q^{44} +(0.489616 - 4.18041i) 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} +(-5.44188 + 1.62640i) q^{50} +(0.986942 - 0.986942i) q^{51} +(0.938463 + 0.541822i) q^{52} +(3.24893 - 0.870548i) q^{53} +(-1.51754 - 5.66352i) q^{54} +(-3.94780 + 1.70181i) q^{55} +(1.30149 - 4.85724i) q^{56} +(-2.06436 - 1.19186i) q^{57} +(-0.100241 - 0.374105i) q^{58} +(1.40987 + 5.26170i) q^{59} +(1.31614 - 1.04017i) q^{60} +(10.4583 + 2.80230i) q^{61} +(-1.56131 + 0.418352i) q^{62} +(-2.17448 - 2.17448i) q^{63} -8.46687 q^{64} +(-2.73845 - 2.03970i) q^{65} +(-1.63261 + 1.63261i) q^{66} +(-2.53340 + 9.45477i) q^{67} -0.936868 q^{68} +(1.25300 - 4.67625i) q^{69} +(-1.53302 + 3.85619i) q^{70} +(1.65295 + 2.86299i) q^{71} +(-2.89687 + 5.01753i) 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} +(-0.812936 + 3.03392i) q^{77} +(-1.77140 - 0.474644i) q^{78} +(12.3408 + 3.30670i) q^{79} +(4.61315 + 0.540301i) q^{80} +(0.0950223 + 0.164583i) q^{81} +8.87092 q^{82} +(-8.57952 + 2.29888i) q^{83} -1.22566i q^{84} +(2.93206 + 0.343408i) q^{85} +(-3.10436 + 5.37690i) q^{86} +(-0.180228 - 0.312164i) q^{87} +5.91764 q^{88} +(16.4223 - 4.40035i) q^{89} +(2.85602 - 3.83442i) q^{90} +(-2.40978 + 0.645698i) q^{91} +(-2.81421 + 1.62479i) q^{92} +(-1.30280 + 0.752174i) q^{93} +(2.77976 - 0.744835i) q^{94} +(-0.729532 - 4.98866i) q^{95} +(-3.87685 + 1.03880i) q^{96} +15.4196 q^{97} +(-2.45986 - 4.26060i) q^{98} +(1.80944 - 3.13404i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) $ 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

Character values

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

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.983757	+	0.567972i	0.695621	+	0.401617i	0.805714	−	0.592304i	$-0.201782\pi$
$2$	0.983757	+	0.567972i	0.695621	+	0.401617i	−0.110093	+	0.993921i	$0.535115\pi$
$3$	1.02118	+	0.273625i	0.589581	+	0.157978i	0.541262	−	0.840854i	$-0.317947\pi$
$3$	1.02118	+	0.273625i	0.589581	+	0.157978i	0.0483191	+	0.998832i	$0.484614\pi$
$4$	−0.354815	−	0.614557i	−0.177407	−	0.307279i
$5$	0.885178	+	2.05340i	0.395864	+	0.918309i
$5$	0.885178	+	2.05340i	0.395864	+	0.918309i
$6$	0.849185	+	0.849185i	0.346678	+	0.346678i
$7$	1.57806	+	0.422839i	0.596449	+	0.159818i	0.544399	−	0.838826i	$-0.316758\pi$
$7$	1.57806	+	0.422839i	0.596449	+	0.159818i	0.0520501	+	0.998644i	$0.483424\pi$
$8$		−	3.07799i		−	1.08823i
$9$	−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	$0.0936014\pi$
$11$			1.92257i			0.579676i	−0.957076	+	0.289838i	$0.906399\pi$
$12$	−0.194173	−	0.724662i	−0.0560528	−	0.209192i
$13$	−1.32247	+	0.763528i	−0.366787	+	0.211764i	−0.672054	−	0.740502i	$-0.734588\pi$
$13$	−1.32247	+	0.763528i	−0.366787	+	0.211764i	0.305267	+	0.952267i	$0.401254\pi$
$14$	1.31226	+	1.31226i	0.350717	+	0.350717i
$15$	0.342067	+	2.33911i	0.0883212	+	0.603955i
$16$	1.03858	−	1.79888i	0.259646	−	0.449720i
$17$	0.660110	−	1.14334i	0.160100	−	0.277302i	−0.774804	−	0.632201i	$-0.782152\pi$
$17$	0.660110	−	1.14334i	0.160100	−	0.277302i	0.934904	+	0.354899i	$0.115485\pi$
$18$	−1.06910	−	1.85174i	−0.251990	−	0.436459i
$19$	−2.17790	−	0.583566i	−0.499644	−	0.133879i	0.000190628	−	1.00000i	$-0.499939\pi$
$19$	−2.17790	−	0.583566i	−0.499644	−	0.133879i	−0.499835	+	0.866121i	$0.666606\pi$
$20$	0.947859	−	1.27257i	0.211948	−	0.284555i
$21$	1.49579	+	0.863592i	0.326407	+	0.188451i
$22$	−1.09196	+	1.89134i	−0.232808	+	0.403235i
$23$		−	4.57925i		−	0.954839i	−0.878675	−	0.477420i	$-0.841572\pi$
$23$		−	4.57925i		−	0.954839i	0.878675	−	0.477420i	$-0.158428\pi$
$24$	0.842216	−	3.14319i	0.171917	−	0.641601i
$25$	−3.43292	+	3.63525i	−0.686584	+	0.727051i
$26$	−1.73465			−0.340193
$27$	−3.64981	−	3.64981i	−0.702407	−	0.702407i
$28$	−0.300059	−	1.11984i	−0.0567058	−	0.211629i
$29$	−0.241089	−	0.241089i	−0.0447691	−	0.0447691i	0.684368	−	0.729137i	$-0.260078\pi$
$29$	−0.241089	−	0.241089i	−0.0447691	−	0.0447691i	−0.729137	+	0.684368i	$0.760078\pi$
$30$	−0.992038	+	2.49540i	−0.181121	+	0.455595i
$31$	−1.00617	+	1.00617i	−0.180714	+	0.180714i	−0.791667	−	0.610953i	$-0.790787\pi$
$31$	−1.00617	+	1.00617i	−0.180714	+	0.180714i	0.610953	+	0.791667i	$0.290787\pi$
$32$	−3.28781	+	1.89822i	−0.581208	+	0.335560i
$33$	−0.526063	+	1.96329i	−0.0915758	+	0.341766i
$34$	1.29878	−	0.749849i	0.222738	−	0.128598i
$35$	0.528603	+	3.61467i	0.0893502	+	0.610991i
$36$			1.33575i			0.222624i
$37$	−5.83510	−	1.71804i	−0.959284	−	0.282443i
$37$	−5.83510	−	1.71804i	−0.959284	−	0.282443i
$38$	−1.81107	−	1.81107i	−0.293795	−	0.293795i
$39$	−1.55940	+	0.417841i	−0.249704	+	0.0669081i
$40$	6.32035	−	2.72457i	0.999335	−	0.430792i
$41$	6.76304	−	3.90464i	1.05621	−	0.609803i	0.131828	−	0.991273i	$-0.457915\pi$
$41$	6.76304	−	3.90464i	1.05621	−	0.609803i	0.924381	+	0.381470i	$0.124582\pi$
$42$	0.980993	+	1.69913i	0.151370	+	0.262181i
$43$			5.46568i			0.833509i	0.909019	+	0.416754i	$0.136832\pi$
$43$			5.46568i			0.833509i	−0.909019	+	0.416754i	$0.863168\pi$
$44$	1.18153	−	0.682155i	0.178122	−	0.102839i
$45$	0.489616	−	4.18041i	0.0729877	−	0.623178i
$46$	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
$50$	−5.44188	+	1.62640i	−0.769598	+	0.230008i
$51$	0.986942	−	0.986942i	0.138200	−	0.138200i
$52$	0.938463	+	0.541822i	0.130141	+	0.0751372i
$53$	3.24893	−	0.870548i	0.446275	−	0.119579i	−0.0286809	−	0.999589i	$-0.509131\pi$
$53$	3.24893	−	0.870548i	0.446275	−	0.119579i	0.474956	+	0.880010i	$0.342464\pi$
$54$	−1.51754	−	5.66352i	−0.206511	−	0.770708i
$55$	−3.94780	+	1.70181i	−0.532322	+	0.229473i
$56$	1.30149	−	4.85724i	0.173919	−	0.649076i
$57$	−2.06436	−	1.19186i	−0.273431	−	0.157865i
$58$	−0.100241	−	0.374105i	−0.0131623	−	0.0491223i
$59$	1.40987	+	5.26170i	0.183549	+	0.685016i	0.994936	+	0.100506i	$0.0320463\pi$
$59$	1.40987	+	5.26170i	0.183549	+	0.685016i	−0.811387	+	0.584509i	$0.801287\pi$
$60$	1.31614	−	1.04017i	0.169914	−	0.134285i
$61$	10.4583	+	2.80230i	1.33905	+	0.358797i	0.856081	−	0.516841i	$-0.172892\pi$
$61$	10.4583	+	2.80230i	1.33905	+	0.358797i	0.482968	+	0.875638i	$0.339559\pi$
$62$	−1.56131	+	0.418352i	−0.198287	+	0.0531307i
$63$	−2.17448	−	2.17448i	−0.273959	−	0.273959i
$64$	−8.46687			−1.05836
$65$	−2.73845	−	2.03970i	−0.339663	−	0.252994i
$66$	−1.63261	+	1.63261i	−0.200961	+	0.200961i
$67$	−2.53340	+	9.45477i	−0.309504	+	1.15508i	0.619495	+	0.785001i	$0.287338\pi$
$67$	−2.53340	+	9.45477i	−0.309504	+	1.15508i	−0.928999	+	0.370083i	$0.879329\pi$
$68$	−0.936868			−0.113612
$69$	1.25300	−	4.67625i	0.150843	−	0.562955i
$70$	−1.53302	+	3.85619i	−0.183231	+	0.460903i
$71$	1.65295	+	2.86299i	0.196169	+	0.339774i	0.947283	−	0.320398i	$-0.103817\pi$
$71$	1.65295	+	2.86299i	0.196169	+	0.339774i	−0.751114	+	0.660172i	$0.770483\pi$
$72$	−2.89687	+	5.01753i	−0.341399	+	0.591321i
$73$	−1.78634	+	1.78634i	−0.209075	+	0.209075i	−0.803874	−	0.594799i	$-0.797232\pi$
$73$	−1.78634	+	1.78634i	−0.209075	+	0.209075i	0.594799	+	0.803874i	$0.297232\pi$
$74$	−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
$77$	−0.812936	+	3.03392i	−0.0926427	+	0.345747i
$78$	−1.77140	−	0.474644i	−0.200571	−	0.0537429i
$79$	12.3408	+	3.30670i	1.38844	+	0.372032i	0.874181	−	0.485600i	$-0.161399\pi$
$79$	12.3408	+	3.30670i	1.38844	+	0.372032i	0.514263	+	0.857633i	$0.328066\pi$
$80$	4.61315	+	0.540301i	0.515766	+	0.0604074i
$81$	0.0950223	+	0.164583i	0.0105580	+	0.0182871i
$82$	8.87092			0.979629
$83$	−8.57952	+	2.29888i	−0.941725	+	0.252334i	−0.696847	−	0.717220i	$-0.745414\pi$
$83$	−8.57952	+	2.29888i	−0.941725	+	0.252334i	−0.244878	+	0.969554i	$0.578748\pi$
$84$		−	1.22566i		−	0.133731i
$85$	2.93206	+	0.343408i	0.318027	+	0.0372479i
$86$	−3.10436	+	5.37690i	−0.334751	+	0.579806i
$87$	−0.180228	−	0.312164i	−0.0193225	−	0.0334675i
$88$	5.91764			0.630823
$89$	16.4223	−	4.40035i	1.74076	−	0.466436i	0.758146	−	0.652085i	$-0.226106\pi$
$89$	16.4223	−	4.40035i	1.74076	−	0.466436i	0.982616	+	0.185650i	$0.0594390\pi$
$90$	2.85602	−	3.83442i	0.301051	−	0.404183i
$91$	−2.40978	+	0.645698i	−0.252613	+	0.0676876i
$92$	−2.81421	+	1.62479i	−0.293402	+	0.169396i
$93$	−1.30280	+	0.752174i	−0.135094	+	0.0779968i
$94$	2.77976	−	0.744835i	0.286711	−	0.0768239i
$95$	−0.729532	−	4.98866i	−0.0748485	−	0.511826i
$96$	−3.87685	+	1.03880i	−0.395680	+	0.106022i
$97$	15.4196			1.56563			0.782814	−	0.622256i	$-0.213784\pi$
$97$	15.4196			1.56563			0.782814	+	0.622256i	$0.213784\pi$
$98$	−2.45986	−	4.26060i	−0.248483	−	0.430385i
$99$	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	$-0.987847\pi$
$101$		−	0.767212i		−	0.0763405i	0.999271	−	0.0381702i	$-0.0121529\pi$
$102$	1.53147	−	0.410355i	0.151638	−	0.0406312i
$103$	−4.78539			−0.471518			−0.235759	−	0.971812i	$-0.575758\pi$
$103$	−4.78539			−0.471518			−0.235759	+	0.971812i	$0.575758\pi$
$104$	2.35013	+	4.07054i	0.230449	+	0.399150i
$105$	−0.449265	+	3.83588i	−0.0438438	+	0.374344i
$106$	3.69061	+	0.988895i	0.358463	+	0.0960500i
$107$	−12.5674	−	3.36743i	−1.21494	−	0.325542i	−0.406240	−	0.913766i	$-0.633160\pi$
$107$	−12.5674	−	3.36743i	−1.21494	−	0.325542i	−0.808698	+	0.588225i	$0.799827\pi$
$108$	−0.948011	+	3.53803i	−0.0912224	+	0.340447i
$109$	3.42875	+	12.7963i	0.328414	+	1.22566i	0.910835	+	0.412771i	$0.135439\pi$
$109$	3.42875	+	12.7963i	0.328414	+	1.22566i	−0.582421	+	0.812888i	$0.697894\pi$
$110$	−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
$113$	−7.28470	+	12.6175i	−0.685287	+	1.18695i	0.288060	+	0.957612i	$0.406990\pi$
$113$	−7.28470	+	12.6175i	−0.685287	+	1.18695i	−0.973347	+	0.229339i	$0.926343\pi$
$114$	−1.35388	−	2.34499i	−0.126803	−	0.219629i
$115$	9.40304	−	4.05345i	0.876838	−	0.377986i
$116$	−0.0626210	+	0.233705i	−0.00581421	+	0.0216989i
$117$	2.87440			0.265738
$118$	−1.60153	+	5.97701i	−0.147433	+	0.550228i
$119$	1.52514	−	1.52514i	0.139810	−	0.139810i
$120$	7.19975	−	1.05288i	0.657244	−	0.0961141i
$121$	7.30374			0.663976
$122$	8.69681	+	8.69681i	0.787372	+	0.787372i
$123$	7.97471	−	2.13682i	0.719056	−	0.192670i
$124$	0.975357	+	0.261346i	0.0875896	+	0.0234696i
$125$	−10.5034	−	3.83132i	−0.939451	−	0.342683i
$126$	−0.904116	−	3.37421i	−0.0805450	−	0.300598i
$127$	−1.32394	−	4.94102i	−0.117481	−	0.438445i	0.881980	−	0.471288i	$-0.156211\pi$
$127$	−1.32394	−	4.94102i	−0.117481	−	0.438445i	−0.999461	+	0.0328428i	$0.989544\pi$
$128$	−1.75373	−	1.01252i	−0.155009	−	0.0894947i
$129$	−1.49555	+	5.58146i	−0.131676	+	0.491421i
$130$	−1.53547	−	3.56193i	−0.134670	−	0.312402i
$131$	−0.824339	−	3.07647i	−0.0720228	−	0.268793i	0.920519	−	0.390698i	$-0.127766\pi$
$131$	−0.824339	−	3.07647i	−0.0720228	−	0.268793i	−0.992542	+	0.121905i	$0.961100\pi$
$132$	1.39321	−	0.373310i	0.121263	−	0.0324924i
$133$	−3.19009	−	1.84180i	−0.276616	−	0.159704i
$134$	−7.86230	+	7.86230i	−0.679199	+	0.679199i
$135$	4.26380	−	10.7253i	0.366969	−	0.923084i
$136$	−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	0.180910	+	0.983500i	$0.442096\pi$
$139$	−8.97537	+	15.5458i	−0.761281	+	1.31858i	−0.942191	+	0.335077i	$0.891238\pi$
$140$	2.03387	−	1.60740i	0.171893	−	0.135850i
$141$	2.31952	−	1.33917i	0.195339	−	0.112779i
$142$			3.75532i			0.315139i
$143$	−1.46793	−	2.54253i	−0.122755	−	0.212617i
$144$	−3.38605	+	1.95494i	−0.282171	+	0.162912i
$145$	0.281646	−	0.708459i	0.0233894	−	0.0588343i
$146$	−2.77191	+	0.742732i	−0.229405	+	0.0614689i
$147$	−3.23763	−	3.23763i	−0.267036	−	0.267036i
$148$	1.01455	+	4.19559i	0.0833952	+	0.344875i
$149$		−	16.8891i		−	1.38361i	−0.722084	−	0.691805i	$-0.756816\pi$
$149$		−	16.8891i		−	1.38361i	0.722084	−	0.691805i	$-0.243184\pi$
$150$	−6.00218	+	0.171819i	−0.490076	+	0.0140290i
$151$	−19.2569	+	11.1180i	−1.56711	+	0.904770i	−0.570603	+	0.821226i	$0.693290\pi$
$151$	−19.2569	+	11.1180i	−1.56711	+	0.904770i	−0.996504	+	0.0835434i	$0.973376\pi$
$152$	−1.79621	+	6.70355i	−0.145692	+	0.543730i
$153$	−2.15213	+	1.24253i	−0.173990	+	0.100453i
$154$	−2.52291	+	2.52291i	−0.203302	+	0.203302i
$155$	−2.95672	−	1.17544i	−0.237490	−	0.0944133i
$156$	0.810087	+	0.810087i	0.0648588	+	0.0648588i
$157$	1.34884	+	5.03393i	0.107649	+	0.401751i	0.998632	−	0.0522849i	$-0.0166504\pi$
$157$	1.34884	+	5.03393i	0.107649	+	0.401751i	−0.890983	+	0.454036i	$0.849984\pi$
$158$	10.2622	+	10.2622i	0.816417	+	0.816417i
$159$	3.55596			0.282006
$160$	−6.80809	−	5.07093i	−0.538227	−	0.400892i
$161$	1.93628	−	7.22631i	0.152601	−	0.569513i
$162$			0.215880i			0.0169611i
$163$	7.33603	−	12.7064i	0.574603	−	0.995241i	−0.421482	−	0.906837i	$-0.638490\pi$
$163$	7.33603	−	12.7064i	0.574603	−	0.995241i	0.996085	−	0.0884042i	$-0.0281767\pi$
$164$	−4.79925	−	2.77085i	−0.374759	−	0.216367i
$165$	−4.49709	+	0.657646i	−0.350098	+	0.0511977i
$166$	−9.74586	−	2.61140i	−0.756426	−	0.202684i
$167$	−10.7921	−	18.6925i	−0.835120	−	1.44647i	−0.893933	−	0.448201i	$-0.852065\pi$
$167$	−10.7921	−	18.6925i	−0.835120	−	1.44647i	0.0588131	−	0.998269i	$-0.481268\pi$
$168$	2.65813	−	4.60401i	0.205079	−	0.355207i
$169$	−5.33405	+	9.23885i	−0.410312	+	0.710681i
$170$	2.68939	+	2.00316i	0.206267	+	0.153635i
$171$	3.00103	+	3.00103i	0.229495	+	0.229495i
$172$	3.35897	−	1.93930i	0.256119	−	0.147871i
$173$	−0.213654	−	0.797367i	−0.0162438	−	0.0606227i	0.957328	−	0.289003i	$-0.0933237\pi$
$173$	−0.213654	−	0.797367i	−0.0162438	−	0.0606227i	−0.973572	+	0.228380i	$0.926657\pi$
$174$		−	0.409458i		−	0.0310409i
$175$	−6.95447	+	4.28506i	−0.525708	+	0.323920i
$176$	3.45847	+	1.99675i	0.260692	+	0.150510i
$177$			5.75894i			0.432869i
$178$	18.6548	+	4.99855i	1.39824	+	0.374657i
$179$	16.5150	+	16.5150i	1.23439	+	1.23439i	0.962262	+	0.272124i	$0.0877261\pi$
$179$	16.5150	+	16.5150i	1.23439	+	1.23439i	0.272124	+	0.962262i	$0.412274\pi$
$180$	−2.74282	+	1.18237i	−0.204438	+	0.0881288i
$181$	−10.0502	−	17.4074i	−0.747024	−	1.29388i	−0.949243	−	0.314544i	$-0.898148\pi$
$181$	−10.0502	−	17.4074i	−0.747024	−	1.29388i	0.202219	−	0.979340i	$-0.435185\pi$
$182$	−2.73738	−	0.733478i	−0.202908	−	0.0543690i
$183$	9.91307	+	5.72332i	0.732796	+	0.423080i
$184$	−14.0949			−1.03909
$185$	−1.63728	−	13.5026i	−0.120375	−	0.992728i
$186$	−1.70886			−0.125299
$187$	2.19816	+	1.26911i	0.160745	+	0.0928063i
$188$	−1.73653	−	0.465302i	−0.126649	−	0.0339356i
$189$	−4.21633	−	7.30289i	−0.306693	−	0.531207i
$190$	2.11574	−	5.32199i	0.153492	−	0.386097i
$191$	−12.5389	−	12.5389i	−0.907285	−	0.907285i	0.0887670	−	0.996052i	$-0.471707\pi$
$191$	−12.5389	−	12.5389i	−0.907285	−	0.907285i	−0.996052	+	0.0887670i	$0.971707\pi$
$192$	−8.64623	−	2.31675i	−0.623988	−	0.167197i
$193$		−	17.1943i		−	1.23767i	−0.785519	−	0.618837i	$-0.787604\pi$
$193$		−	17.1943i		−	1.23767i	0.785519	−	0.618837i	$-0.212396\pi$
$194$	15.1692	+	8.75793i	1.08908	+	0.628783i
$195$	−2.23835	−	2.83222i	−0.160291	−	0.202819i
$196$			3.07337i			0.219526i
$197$	−2.30767	−	8.61235i	−0.164415	−	0.613604i	−0.998114	−	0.0613857i	$-0.980448\pi$
$197$	−2.30767	−	8.61235i	−0.164415	−	0.613604i	0.833699	−	0.552219i	$-0.186219\pi$
$198$	3.56009	−	2.05542i	0.253005	−	0.146072i
$199$	−7.61077	−	7.61077i	−0.539513	−	0.539513i	0.383873	−	0.923386i	$-0.374590\pi$
$199$	−7.61077	−	7.61077i	−0.539513	−	0.539513i	−0.923386	+	0.383873i	$0.874590\pi$
$200$	11.1893	+	10.5665i	0.791201	+	0.747164i
$201$	−5.17413	+	8.96186i	−0.364955	+	0.632121i
$202$	0.435755	−	0.754750i	0.0306596	−	0.0531041i
$203$	−0.278510	−	0.482393i	−0.0195476	−	0.0338574i
$204$	−0.956714	−	0.256351i	−0.0669834	−	0.0179481i
$205$	14.0043	+	10.4309i	0.978102	+	0.728528i
$206$	−4.70766	−	2.71797i	−0.327998	−	0.189370i
$207$	−4.30979	+	7.46478i	−0.299551	+	0.518838i
$208$			3.17195i			0.219935i
$209$	1.12195	−	4.18716i	0.0776066	−	0.289632i
$210$	−2.62064	+	3.51841i	−0.180842	+	0.242793i
$211$	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
$213$	0.904577	+	3.37593i	0.0619806	+	0.231315i
$214$	−10.4507	−	10.4507i	−0.714393	−	0.714393i
$215$	−11.2232	+	4.83810i	−0.765419	+	0.329956i
$216$	−11.2341	+	11.2341i	−0.764383	+	0.764383i
$217$	−2.01325	+	1.16235i	−0.136668	+	0.0789054i
$218$	−3.89487	+	14.5358i	−0.263794	+	0.984491i
$219$	−2.31297	+	1.33539i	−0.156296	+	0.0902374i
$220$	2.44660	+	1.82232i	0.164950	+	0.122861i
$221$			2.01605i			0.135614i
$222$	−3.49615	−	6.41401i	−0.234646	−	0.430480i
$223$	−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
$225$	9.01745	−	2.69502i	0.601163	−	0.179668i
$226$	−14.3327	+	8.27502i	−0.953400	+	0.550446i
$227$	−10.6242	−	18.4016i	−0.705151	−	1.22136i	−0.966637	−	0.256150i	$-0.917546\pi$
$227$	−10.6242	−	18.4016i	−0.705151	−	1.22136i	0.261487	−	0.965207i	$-0.415787\pi$
$228$			1.69155i			0.112026i
$229$	3.48912	−	2.01445i	0.230568	−	0.133118i	−0.380266	−	0.924877i	$-0.624168\pi$
$229$	3.48912	−	2.01445i	0.230568	−	0.133118i	0.610834	+	0.791759i	$0.290834\pi$
$230$	11.5526	+	1.35306i	0.761753	+	0.0892178i
$231$	−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	−0.777021	−	0.629475i	$-0.783270\pi$
$233$	−2.25220	+	2.25220i	−0.147547	+	0.147547i	0.629475	+	0.777021i	$0.283270\pi$
$234$	2.82771	+	1.63258i	0.184853	+	0.106725i
$235$	5.26416	+	2.09275i	0.343396	+	0.136516i
$236$	2.73338	−	2.73338i	0.177928	−	0.177928i
$237$	11.6974	+	6.75349i	0.759827	+	0.438686i
$238$	2.36661	−	0.634131i	0.153404	−	0.0411046i
$239$	5.13865	+	19.1777i	0.332392	+	1.24050i	0.906669	+	0.421843i	$0.138617\pi$
$239$	5.13865	+	19.1777i	0.332392	+	1.24050i	−0.574277	+	0.818661i	$0.694717\pi$
$240$	4.56304	+	1.81402i	0.294543	+	0.117095i
$241$	2.89066	−	10.7881i	0.186204	−	0.694922i	−0.808166	−	0.588955i	$-0.799539\pi$
$241$	2.89066	−	10.7881i	0.186204	−	0.694922i	0.994370	−	0.105967i	$-0.0337939\pi$
$242$	7.18510	+	4.14832i	0.461876	+	0.266664i
$243$	4.05977	+	15.1513i	0.260435	+	0.971955i
$244$	−1.98859	−	7.42153i	−0.127307	−	0.475114i
$245$	1.12654	−	9.61854i	0.0719720	−	0.614506i
$246$	9.05883	+	2.42731i	0.577570	+	0.154759i
$247$	3.32577	−	0.891138i	0.211614	−	0.0567017i
$248$	3.09699	+	3.09699i	0.196659	+	0.196659i
$249$	−9.39030			−0.595086
$250$	−8.15669	−	9.73471i	−0.515875	−	0.615677i
$251$	−6.77562	+	6.77562i	−0.427673	+	0.427673i	−0.887835	−	0.460162i	$-0.847791\pi$
$251$	−6.77562	+	6.77562i	−0.427673	+	0.427673i	0.460162	+	0.887835i	$0.347791\pi$
$252$	−0.564805	+	2.10788i	−0.0355794	+	0.132784i
$253$	8.80391			0.553497
$254$	1.50393	−	5.61273i	0.0943647	−	0.352174i
$255$	2.90021	+	1.15297i	0.181618	+	0.0722017i
$256$	7.31671	+	12.6729i	0.457294	+	0.792057i
$257$	0.176949	−	0.306484i	0.0110378	−	0.0191180i	−0.860454	−	0.509529i	$-0.829820\pi$
$257$	0.176949	−	0.306484i	0.0110378	−	0.0191180i	0.871492	+	0.490411i	$0.163153\pi$
$258$	−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
$262$	0.936403	−	3.49470i	0.0578512	−	0.215904i
$263$	19.4898	+	5.22227i	1.20179	+	0.322019i	0.803536	−	0.595256i	$-0.202949\pi$
$263$	19.4898	+	5.22227i	1.20179	+	0.322019i	0.398255	+	0.917275i	$0.369616\pi$
$264$	6.04300	+	1.61922i	0.371921	+	0.0996559i
$265$	4.66347	+	5.90077i	0.286475	+	0.362481i
$266$	−2.09218	−	3.62377i	−0.128280	−	0.222187i
$267$	17.9742			1.10001
$268$	6.70939	−	1.79777i	0.409841	−	0.109817i
$269$			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	−0.923425	−	0.383779i	$-0.874622\pi$
$271$	−2.12937	+	3.68817i	−0.129350	+	0.224040i	0.794075	+	0.607820i	$0.207956\pi$
$272$	−1.37116	−	2.37492i	−0.0831388	−	0.144001i
$273$	−2.63751			−0.159629
$274$	23.7091	−	6.35282i	1.43232	−	0.383788i
$275$	−6.98902	−	6.60002i	−0.421454	−	0.397996i
$276$	−3.31841	+	0.889165i	−0.199745	+	0.0535214i
$277$	0.494657	−	0.285590i	0.0297211	−	0.0171595i	−0.485066	−	0.874478i	$-0.661204\pi$
$277$	0.494657	−	0.285590i	0.0297211	−	0.0171595i	0.514787	+	0.857318i	$0.327871\pi$
$278$	−17.6592	+	10.1955i	−1.05913	+	0.611487i
$279$	2.58716	−	0.693228i	0.154889	−	0.0415025i
$280$	11.1259	−	1.62703i	0.664901	−	0.0972338i
$281$	30.2609	−	8.10837i	1.80521	−	0.483705i	0.810439	−	0.585823i	$-0.199229\pi$
$281$	30.2609	−	8.10837i	1.80521	−	0.483705i	0.994772	+	0.102118i	$0.0325620\pi$
$282$	3.04245			0.181176
$283$	0.308111	+	0.533664i	0.0183153	+	0.0317230i	0.875038	−	0.484055i	$-0.160836\pi$
$283$	0.308111	+	0.533664i	0.0183153	+	0.0317230i	−0.856722	+	0.515778i	$0.827503\pi$
$284$	1.17298	−	2.03166i	0.0696036	−	0.120557i
$285$	0.620038	−	5.29396i	0.0367279	−	0.313587i
$286$		−	3.33498i		−	0.197202i
$287$	12.3235	−	3.30207i	0.727433	−	0.194915i
$288$	7.14608			0.421087
$289$	7.62851	+	13.2130i	0.448736	+	0.777233i
$290$	0.679456	−	0.536984i	0.0398990	−	0.0315328i
$291$	15.7463	+	4.21920i	0.923063	+	0.247334i
$292$	1.73163	+	0.463988i	0.101336	+	0.0271528i
$293$	2.55888	−	9.54988i	0.149492	−	0.557910i	−0.850023	−	0.526746i	$-0.823412\pi$
$293$	2.55888	−	9.54988i	0.149492	−	0.557910i	0.999514	−	0.0311641i	$-0.00992144\pi$
$294$	−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
$298$	9.59255	−	16.6148i	0.555682	−	0.962469i
$299$	3.49638	+	6.05591i	0.202201	+	0.350222i
$300$	3.30091	+	1.78184i	0.190578	+	0.102875i
$301$	−2.31110	+	8.62515i	−0.133210	+	0.497146i
$302$	−25.2589			−1.45348
$303$	0.209929	−	0.783464i	0.0120601	−	0.0450089i
$304$	−3.31170	+	3.31170i	−0.189939	+	0.189939i
$305$	3.50323	+	23.9556i	0.200594	+	1.37170i
$306$	−2.82290			−0.161375
$307$	12.7533	+	12.7533i	0.727869	+	0.727869i	0.970195	−	0.242326i	$-0.0779104\pi$
$307$	12.7533	+	12.7533i	0.727869	+	0.727869i	−0.242326	+	0.970195i	$0.577910\pi$
$308$	2.15296	−	0.576883i	0.122676	−	0.0328710i
$309$	−4.88676	−	1.30940i	−0.277998	−	0.0744893i
$310$	−2.24108	−	2.83568i	−0.127285	−	0.161056i
$311$	6.30945	+	23.5472i	0.357776	+	1.33524i	0.876955	+	0.480572i	$0.159571\pi$
$311$	6.30945	+	23.5472i	0.357776	+	1.33524i	−0.519179	+	0.854665i	$0.673762\pi$
$312$	1.28611	+	4.79983i	0.0728116	+	0.271737i
$313$	0.801929	+	0.462994i	0.0453277	+	0.0261700i	0.522493	−	0.852644i	$-0.325002\pi$
$313$	0.801929	+	0.462994i	0.0453277	+	0.0261700i	−0.477165	+	0.878814i	$0.658336\pi$
$314$	−1.53220	+	5.71826i	−0.0864673	+	0.322700i
$315$	2.54028	−	6.38989i	0.143129	−	0.360029i
$316$	−2.34653	−	8.75737i	−0.132003	−	0.492640i
$317$	−25.5685	+	6.85107i	−1.43607	+	0.384794i	−0.891156	−	0.453696i	$-0.850105\pi$
$317$	−25.5685	+	6.85107i	−1.43607	+	0.384794i	−0.544916	+	0.838491i	$0.683438\pi$
$318$	3.49820	+	2.01969i	0.196169	+	0.113258i
$319$	0.463509	−	0.463509i	0.0259515	−	0.0259515i
$320$	−7.49469	−	17.3859i	−0.418966	−	0.971901i
$321$	−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
$325$	1.76431	−	7.42864i	0.0978664	−	0.412067i
$326$	14.4338	−	8.33333i	0.799412	−	0.461540i
$327$			14.0055i			0.774507i
$328$	−12.0184	−	20.8166i	−0.663608	−	1.14940i
$329$	3.58440	−	2.06945i	0.197614	−	0.114093i
$330$	−4.79757	−	1.90726i	−0.264097	−	0.104991i
$331$	−9.40727	+	2.52067i	−0.517070	+	0.138549i	−0.507911	−	0.861410i	$-0.669582\pi$
$331$	−9.40727	+	2.52067i	−0.517070	+	0.138549i	−0.00915915	+	0.999958i	$0.502915\pi$
$332$	4.45693	+	4.45693i	0.244606	+	0.244606i
$333$	7.89503	+	8.29237i	0.432645	+	0.454419i
$334$		−	24.5185i		−	1.34159i
$335$	−21.6570	+	3.16707i	−1.18325	+	0.173036i
$336$	3.10700	−	1.79382i	0.169501	−	0.0978612i
$337$	−5.14226	+	19.1912i	−0.280117	+	1.04541i	0.672217	+	0.740354i	$0.265342\pi$
$337$	−5.14226	+	19.1912i	−0.280117	+	1.04541i	−0.952334	+	0.305057i	$0.901325\pi$
$338$	−10.4948	+	6.05919i	−0.570843	+	0.329576i
$339$	−10.8915	+	10.8915i	−0.591544	+	0.591544i
$340$	−0.829295	−	1.92377i	−0.0449748	−	0.104331i
$341$	−1.93444	−	1.93444i	−0.104756	−	0.104756i
$342$	1.24778	+	4.65679i	0.0674724	+	0.251810i
$343$	−13.0897	−	13.0897i	−0.706778	−	0.706778i
$344$	16.8233			0.907052
$345$	10.7114	−	1.56641i	0.576680	−	0.0843326i
$346$	0.242699	−	0.905765i	0.0130476	−	0.0486942i
$347$			10.3295i			0.554517i	0.960795	+	0.277258i	$0.0894258\pi$
$347$			10.3295i			0.554517i	−0.960795	+	0.277258i	$0.910574\pi$
$348$	−0.127895	+	0.221521i	−0.00685589	+	0.0118748i
$349$	−13.7141	−	7.91783i	−0.734098	−	0.423832i	0.0858212	−	0.996311i	$-0.472649\pi$
$349$	−13.7141	−	7.91783i	−0.734098	−	0.423832i	−0.819920	+	0.572479i	$0.805982\pi$
$350$	−9.27530	+	0.265515i	−0.495786	+	0.0141924i
$351$	7.61350	+	2.04003i	0.406378	+	0.108889i
$352$	−3.64945	−	6.32103i	−0.194516	−	0.336912i
$353$	−4.35227	+	7.53835i	−0.231648	+	0.401226i	−0.958293	−	0.285787i	$-0.907745\pi$
$353$	−4.35227	+	7.53835i	−0.231648	+	0.401226i	0.726645	+	0.687013i	$0.241078\pi$
$354$	−3.27092	+	5.66540i	−0.173847	+	0.301113i
$355$	−4.41572	+	5.92842i	−0.234362	+	0.314648i
$356$	−8.53114	−	8.53114i	−0.452150	−	0.452150i
$357$	1.97477	−	1.14013i	0.104516	−	0.0603422i
$358$	6.86667	+	25.6268i	0.362915	+	1.35442i
$359$		−	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
$362$		−	22.8329i		−	1.20007i
$363$	7.45845	+	1.99849i	0.391467	+	0.104893i
$364$	1.25184	+	1.25184i	0.0656144	+	0.0656144i
$365$	−5.24930	−	2.08684i	−0.274761	−	0.109230i
$366$	6.50137	+	11.2607i	0.339832	+	0.588606i
$367$	−19.5857	−	5.24797i	−1.02236	−	0.273942i	−0.291577	−	0.956547i	$-0.594180\pi$
$367$	−19.5857	−	5.24797i	−1.02236	−	0.273942i	−0.730787	+	0.682606i	$0.760847\pi$
$368$	−8.23752	−	4.75593i	−0.429410	−	0.247920i
$369$	−14.6995			−0.765227
$370$	6.05840	−	14.2132i	0.314961	−	0.738908i
$371$	5.49510			0.285291
$372$	0.924507	+	0.533765i	0.0479335	+	0.0276744i
$373$	−2.29926	−	0.616084i	−0.119051	−	0.0318996i	0.198802	−	0.980040i	$-0.436295\pi$
$373$	−2.29926	−	0.616084i	−0.119051	−	0.0318996i	−0.317853	+	0.948140i	$0.602962\pi$
$374$	1.44163	+	2.49698i	0.0745452	+	0.129116i
$375$	−9.67753	−	6.78647i	−0.499746	−	0.350452i
$376$	−5.51390	−	5.51390i	−0.284358	−	0.284358i
$377$	0.502910	+	0.134754i	0.0259012	+	0.00694021i
$378$		−	9.57903i		−	0.492692i
$379$	14.3987	+	8.31312i	0.739614	+	0.427016i	0.821929	−	0.569590i	$-0.192898\pi$
$379$	14.3987	+	8.31312i	0.739614	+	0.427016i	−0.0823151	+	0.996606i	$0.526231\pi$
$380$	−2.80697	+	2.21839i	−0.143994	+	0.113801i
$381$		−	5.40795i		−	0.277058i
$382$	−5.21350	−	19.4570i	−0.266746	−	0.995508i
$383$	−7.80032	+	4.50352i	−0.398578	+	0.230119i	−0.685870	−	0.727724i	$-0.740578\pi$
$383$	−7.80032	+	4.50352i	−0.398578	+	0.230119i	0.287292	+	0.957843i	$0.407245\pi$
$384$	−1.51383	−	1.51383i	−0.0772523	−	0.0772523i
$385$	−6.94945	+	1.01627i	−0.354177	+	0.0517941i
$386$	9.76590	−	16.9150i	0.497071	−	0.860953i
$387$	5.14406	−	8.90978i	0.261487	−	0.452910i
$388$	−5.47112	−	9.47625i	−0.277754	−	0.481084i
$389$	−11.4603	−	3.07078i	−0.581061	−	0.155695i	−0.0436964	−	0.999045i	$-0.513913\pi$
$389$	−11.4603	−	3.07078i	−0.581061	−	0.155695i	−0.537365	+	0.843350i	$0.680580\pi$
$390$	−0.593366	−	4.05753i	−0.0300463	−	0.205461i
$391$	−5.23566	−	3.02281i	−0.264779	−	0.152870i
$392$	−6.66530	+	11.5446i	−0.336649	+	0.583093i
$393$		−	3.36720i		−	0.169853i
$394$	2.62139	−	9.78315i	0.132064	−	0.492868i
$395$	4.13379	+	28.2676i	0.207994	+	1.42230i
$396$	−2.56806			−0.129050
$397$	−1.62569	−	1.62569i	−0.0815913	−	0.0815913i	0.665133	−	0.746725i	$-0.268375\pi$
$397$	−1.62569	−	1.62569i	−0.0815913	−	0.0815913i	−0.746725	+	0.665133i	$0.768375\pi$
$398$	−3.16444	−	11.8099i	−0.158619	−	0.591974i
$399$	−2.75371	−	2.75371i	−0.137858	−	0.137858i
$400$	2.97401	+	9.95092i	0.148700	+	0.497546i
$401$	16.9699	−	16.9699i	0.847436	−	0.847436i	−0.142377	−	0.989813i	$-0.545474\pi$
$401$	16.9699	−	16.9699i	0.847436	−	0.847436i	0.989813	+	0.142377i	$0.0454744\pi$
$402$	−10.1802	+	5.87753i	−0.507741	+	0.293144i
$403$	0.562392	−	2.09888i	0.0280147	−	0.104552i
$404$	−0.471496	+	0.272218i	−0.0234578	+	0.0135434i
$405$	−0.253844	+	0.340805i	−0.0126136	+	0.0169347i
$406$		−	0.632744i		−	0.0314026i
$407$	3.30304	−	11.2184i	0.163726	−	0.556074i
$408$	−3.03780	−	3.03780i	−0.150393	−	0.150393i
$409$	−24.9023	+	6.67256i	−1.23134	+	0.329937i	−0.815102	−	0.579318i	$-0.803319\pi$
$409$	−24.9023	+	6.67256i	−1.23134	+	0.329937i	−0.416240	+	0.909255i	$0.636652\pi$
$410$	7.85234	+	18.2156i	0.387800	+	0.899602i
$411$	19.7835	−	11.4220i	0.975850	−	0.563407i
$412$	1.69793	+	2.94089i	0.0836508	+	0.144887i
$413$			8.89941i			0.437911i
$414$	−8.47957	+	4.89568i	−0.416748	+	0.240610i
$415$	−12.3149	−	15.5823i	−0.604516	−	0.764905i
$416$	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	$-0.0278874\pi$
$419$	29.0354	+	16.7636i	1.41847	+	0.818955i	0.422306	+	0.906453i	$0.361221\pi$
$420$	2.51677	−	1.08493i	0.122806	−	0.0529391i
$421$	−0.954366	+	0.954366i	−0.0465130	+	0.0465130i	−0.729981	−	0.683468i	$-0.760471\pi$
$421$	−0.954366	+	0.954366i	−0.0465130	+	0.0465130i	0.683468	+	0.729981i	$0.260471\pi$
$422$	1.61656	+	0.933319i	0.0786927	+	0.0454333i
$423$	−4.60620	+	1.23423i	−0.223961	+	0.0600102i
$424$	−2.67954	−	10.0002i	−0.130130	−	0.485651i
$425$	1.89024	+	6.32468i	0.0916902	+	0.306792i
$426$	−1.02755	+	3.83487i	−0.0497849	+	0.185800i
$427$	15.3189	+	8.84436i	0.741333	+	0.428009i
$428$	2.38963	+	8.91821i	0.115507	+	0.431078i
$429$	−0.803327	−	2.99806i	−0.0387850	−	0.144748i
$430$	−13.7889	−	1.61497i	−0.664957	−	0.0778810i
$431$	−12.1677	−	3.26032i	−0.586097	−	0.157044i	−0.0464282	−	0.998922i	$-0.514784\pi$
$431$	−12.1677	−	3.26032i	−0.586097	−	0.157044i	−0.539669	+	0.841877i	$0.681451\pi$
$432$	−10.3562	+	2.77494i	−0.498263	+	0.133509i
$433$	−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
$435$	0.481464	−	0.646401i	0.0230844	−	0.0309926i
$436$	6.64746	−	6.64746i	0.318356	−	0.318356i
$437$	−2.67230	+	9.97314i	−0.127833	+	0.477080i
$438$	−3.03386			−0.144963
$439$	8.00818	−	29.8869i	0.382210	−	1.42643i	−0.460309	−	0.887759i	$-0.652261\pi$
$439$	8.00818	−	29.8869i	0.382210	−	1.42643i	0.842519	−	0.538667i	$-0.181072\pi$
$440$	5.23817	+	12.1513i	0.249720	+	0.579290i
$441$	4.07610	+	7.06001i	0.194100	+	0.336191i
$442$	−1.14506	+	1.98330i	−0.0544650	+	0.0943361i
$443$	13.3025	−	13.3025i	0.632023	−	0.632023i	−0.316552	−	0.948575i	$-0.602525\pi$
$443$	13.3025	−	13.3025i	0.632023	−	0.632023i	0.948575	+	0.316552i	$0.102525\pi$
$444$	−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
$447$	4.62129	−	17.2469i	0.218580	−	0.815750i
$448$	−13.3612	−	3.58012i	−0.631257	−	0.169145i
$449$	28.3423	+	7.59430i	1.33756	+	0.358397i	0.855527	−	0.517758i	$-0.173233\pi$
$449$	28.3423	+	7.59430i	1.33756	+	0.358397i	0.482029	+	0.876155i	$0.339900\pi$
$450$	10.4017	+	2.47041i	0.490340	+	0.116456i
$451$	7.50694	+	13.0024i	0.353488	+	0.612259i
$452$	10.3389			0.486300
$453$	−22.7070	+	6.08433i	−1.06687	+	0.285867i
$454$		−	24.1369i		−	1.13280i
$455$	−3.45896	−	4.37669i	−0.162159	−	0.205182i
$456$	−3.66852	+	6.35407i	−0.171794	+	0.297556i
$457$	3.20861	+	5.55747i	0.150092	+	0.259968i	0.931261	−	0.364352i	$-0.118710\pi$
$457$	3.20861	+	5.55747i	0.150092	+	0.259968i	−0.781169	+	0.624320i	$0.785376\pi$
$458$	4.57660			0.213850
$459$	−6.58228	+	1.76372i	−0.307234	+	0.0823232i
$460$	−5.82741	−	4.34048i	−0.271705	−	0.202376i
$461$	25.3037	−	6.78010i	1.17851	−	0.315781i	0.384175	−	0.923260i	$-0.374486\pi$
$461$	25.3037	−	6.78010i	1.17851	−	0.315781i	0.794335	+	0.607479i	$0.207819\pi$
$462$	−3.26669	+	1.88602i	−0.151980	+	0.0877458i
$463$	−33.0936	+	19.1066i	−1.53799	+	0.887960i	−0.539035	+	0.842283i	$0.681211\pi$
$463$	−33.0936	+	19.1066i	−1.53799	+	0.887960i	−0.998956	+	0.0456763i	$0.985456\pi$
$464$	−0.684081	+	0.183299i	−0.0317576	+	0.00850944i
$465$	−2.69773	−	2.00937i	−0.125104	−	0.0931823i
$466$	−3.49481	+	0.936431i	−0.161894	+	0.0433793i
$467$	13.5181			0.625544			0.312772	−	0.949828i	$-0.398742\pi$
$467$	13.5181			0.625544			0.312772	+	0.949828i	$0.398742\pi$
$468$	−1.01988	−	1.76648i	−0.0471439	−	0.0816556i
$469$	−7.99569	+	13.8489i	−0.369207	+	0.639485i
$470$	3.99003	+	5.04866i	0.184046	+	0.232877i
$471$			5.50964i			0.253871i
$472$	16.1955	−	4.33956i	0.745457	−	0.199745i
$473$	−10.5081			−0.483165
$474$	7.67159	+	13.2876i	0.352368	+	0.610319i
$475$	9.59796	−	5.91388i	0.440385	−	0.271347i
$476$	−1.47843	−	0.396144i	−0.0677637	−	0.0181572i
$477$	−6.11551	−	1.63865i	−0.280010	−	0.0750284i
$478$	−5.83723	+	21.7848i	−0.266989	+	0.996415i
$479$	0.466920	+	1.74257i	0.0213341	+	0.0796200i	0.975772	−	0.218789i	$-0.0702107\pi$
$479$	0.466920	+	1.74257i	0.0213341	+	0.0796200i	−0.954438	+	0.298409i	$0.903544\pi$
$480$	−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
$483$	3.95460	−	6.84957i	0.179941	−	0.311666i
$484$	−2.59147	−	4.48856i	−0.117794	−	0.204026i
$485$	13.6491	+	31.6627i	0.619775	+	1.43773i
$486$	−4.61168	+	17.2110i	−0.209190	+	0.780708i
$487$	4.70678			0.213285			0.106642	−	0.994297i	$-0.465990\pi$
$487$	4.70678			0.213285			0.106642	+	0.994297i	$0.465990\pi$
$488$	8.62544	−	32.1906i	0.390455	−	1.45720i
$489$	10.9682	−	10.9682i	0.496000	−	0.496000i
$490$	6.57131	−	8.82247i	0.296862	−	0.398558i
$491$	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
$493$	−0.434793	+	0.116502i	−0.0195821	+	0.00524700i
$494$	3.77789	+	1.01228i	0.169975	+	0.0455448i
$495$	8.03711	+	0.941320i	0.361241	+	0.0423092i
$496$	0.764990	+	2.85498i	0.0343491	+	0.128192i
$497$	1.39786	+	5.21689i	0.0627026	+	0.234009i
$498$	−9.23777	−	5.33343i	−0.413954	−	0.238997i
$499$	4.04934	−	15.1123i	0.181273	−	0.676521i	−0.814124	−	0.580691i	$-0.802783\pi$
$499$	4.04934	−	15.1123i	0.181273	−	0.676521i	0.995398	−	0.0958307i	$-0.0305507\pi$
$500$	1.37219	+	7.81434i	0.0613663	+	0.349468i
$501$	−5.90600	−	22.0415i	−0.263860	−	0.984741i
$502$	−10.5139	+	2.81720i	−0.469260	+	0.125738i
$503$	8.84970	+	5.10938i	0.394589	+	0.227816i	0.684146	−	0.729345i	$-0.260175\pi$
$503$	8.84970	+	5.10938i	0.394589	+	0.227816i	−0.289558	+	0.957161i	$0.593508\pi$
$504$	−6.69303	+	6.69303i	−0.298131	+	0.298131i
$505$	1.57540	−	0.679120i	0.0701042	−	0.0302204i
$506$	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	$-0.784665\pi$
$509$	3.43610	−	5.95149i	0.152302	−	0.263795i	0.932073	+	0.362269i	$0.117998\pi$
$510$	2.19825	+	2.78148i	0.0973399	+	0.123166i
$511$	−3.57427	+	2.06361i	−0.158117	+	0.0912886i
$512$			20.6728i			0.913618i
$513$	5.81902	+	10.0788i	0.256916	+	0.444991i
$514$	0.348149	−	0.201004i	0.0153562	−	0.00886591i
$515$	−4.23592	−	9.82632i	−0.186657	−	0.433000i
$516$	3.96077	−	1.06129i	0.174363	−	0.0467205i
$517$	3.44408	+	3.44408i	0.151471	+	0.151471i
$518$	−5.40267	−	9.91170i	−0.237379	−	0.435495i
$519$		−	0.872719i		−	0.0383081i
$520$	−6.27818	+	8.42892i	−0.275316	+	0.369633i
$521$	−19.6337	+	11.3355i	−0.860166	+	0.496617i	−0.864068	−	0.503375i	$-0.832091\pi$
$521$	−19.6337	+	11.3355i	−0.860166	+	0.496617i	0.00390182	+	0.999992i	$0.498758\pi$
$522$	−0.188685	+	0.704182i	−0.00825852	+	0.0308212i
$523$	7.34396	−	4.24004i	0.321129	−	0.185404i	−0.330767	−	0.943713i	$-0.607307\pi$
$523$	7.34396	−	4.24004i	0.321129	−	0.185404i	0.651896	+	0.758309i	$0.273974\pi$
$524$	−1.59818	+	1.59818i	−0.0698169	+	0.0698169i
$525$	−8.27429	+	2.47292i	−0.361119	+	0.107927i
$526$	16.2071	+	16.2071i	0.706663	+	0.706663i
$527$	0.486218	+	1.81459i	0.0211800	+	0.0790448i
$528$	2.98537	+	2.98537i	0.129921	+	0.129921i
$529$	2.03048			0.0882817
$530$	1.23625	+	8.45365i	0.0536991	+	0.367203i
$531$	2.65382	−	9.90418i	0.115166	−	0.429805i
$532$			2.61399i			0.113331i
$533$	−5.96260	+	10.3275i	−0.258269	+	0.447335i
$534$	17.6823	+	10.2089i	0.765187	+	0.441781i
$535$	−4.20972	−	28.7867i	−0.182002	−	1.24456i
$536$	29.1017	+	7.79777i	1.25700	+	0.336813i
$537$	12.3459	+	21.3837i	0.532765	+	0.922776i
$538$	−3.69142	+	6.39373i	−0.159148	+	0.275653i
$539$	4.16327	−	7.21099i	0.179325	−	0.310599i
$540$	−8.10415	+	1.18514i	−0.348747	+	0.0510001i
$541$	−9.87420	−	9.87420i	−0.424525	−	0.424525i	0.462233	−	0.886758i	$-0.347048\pi$
$541$	−9.87420	−	9.87420i	−0.424525	−	0.424525i	−0.886758	+	0.462233i	$0.847048\pi$
$542$	−4.18956	+	2.41884i	−0.179957	+	0.103898i
$543$	−5.49997	−	20.5262i	−0.236026	−	0.880862i
$544$			5.01213i			0.214893i
$545$	−23.2408	+	18.3676i	−0.995527	+	0.786780i
$546$	−2.59466	−	1.49803i	−0.111041	−	0.0641098i
$547$		−	16.2777i		−	0.695983i	−0.937498	−	0.347992i	$-0.886864\pi$
$547$		−	16.2777i		−	0.695983i	0.937498	−	0.347992i	$-0.113136\pi$
$548$	−14.8112	−	3.96864i	−0.632701	−	0.169532i
$549$	−14.4110	−	14.4110i	−0.615047	−	0.615047i
$550$	−3.12687	−	10.4624i	−0.133330	−	0.446117i
$551$	0.384376	+	0.665758i	0.0163750	+	0.0283623i
$552$	−14.3935	−	3.85672i	−0.612626	−	0.164153i
$553$	18.0762	+	10.4363i	0.768679	+	0.443797i
$554$	0.648830			0.0275661
$555$	2.02268	−	14.2366i	0.0858580	−	0.604310i
$556$	12.7384			0.540227
$557$	11.0303	+	6.36833i	0.467368	+	0.269835i	0.715137	−	0.698984i	$-0.246364\pi$
$557$	11.0303	+	6.36833i	0.467368	+	0.269835i	−0.247769	+	0.968819i	$0.579698\pi$
$558$	2.93887	+	0.787469i	0.124412	+	0.0333362i
$559$	−4.17320	−	7.22819i	−0.176508	−	0.305720i
$560$	7.05136	+	2.80325i	0.297974	+	0.118459i
$561$	1.89746	+	1.89746i	0.0801109	+	0.0801109i
$562$	34.3747	+	9.21066i	1.45001	+	0.388528i
$563$		−	9.88042i		−	0.416410i	−0.978085	−	0.208205i	$-0.933238\pi$
$563$		−	9.88042i		−	0.416410i	0.978085	−	0.208205i	$-0.0667622\pi$
$564$	−1.64600	−	0.950317i	−0.0693090	−	0.0400156i
$565$	−32.3570	−	3.78971i	−1.36127	−	0.159434i
$566$			0.699994i			0.0294229i
$567$	0.0803582	+	0.299901i	0.00337473	+	0.0125947i
$568$	8.81225	−	5.08776i	0.369754	−	0.213478i
$569$	−28.2430	−	28.2430i	−1.18401	−	1.18401i	−0.978697	−	0.205312i	$-0.934179\pi$
$569$	−28.2430	−	28.2430i	−1.18401	−	1.18401i	−0.205312	−	0.978697i	$-0.565821\pi$
$570$	3.61679	−	4.85580i	0.151491	−	0.203387i
$571$	−18.9395	+	32.8041i	−0.792592	+	1.37281i	0.131765	+	0.991281i	$0.457936\pi$
$571$	−18.9395	+	32.8041i	−0.792592	+	1.37281i	−0.924357	+	0.381529i	$0.875398\pi$
$572$	−1.04169	+	1.80426i	−0.0435552	+	0.0754398i
$573$	−9.37358	−	16.2355i	−0.391587	−	0.678249i
$574$	13.9988	+	3.75097i	0.584299	+	0.156562i
$575$	16.6467	+	15.7202i	0.694217	+	0.655577i
$576$	13.8021	+	7.96865i	0.575088	+	0.332027i
$577$	−13.6089	+	23.5713i	−0.566547	+	0.981288i	0.430357	+	0.902659i	$0.358388\pi$
$577$	−13.6089	+	23.5713i	−0.566547	+	0.981288i	−0.996904	+	0.0786291i	$0.974946\pi$
$578$			17.3311i			0.720880i
$579$	4.70480	−	17.5586i	0.195525	−	0.729709i
$580$	−0.535321	+	0.0782843i	−0.0222280	+	0.00325058i
$581$	−14.5110			−0.602019
$582$	13.0941	+	13.0941i	0.542769	+	0.542769i
$583$	1.67369	+	6.24629i	0.0693171	+	0.258695i
$584$	5.49833	+	5.49833i	0.227522	+	0.227522i
$585$	2.54435	+	5.90229i	0.105196	+	0.244030i
$586$	7.94139	−	7.94139i	0.328056	−	0.328056i
$587$	10.5112	−	6.06864i	0.433843	−	0.250480i	−0.267139	−	0.963658i	$-0.586078\pi$
$587$	10.5112	−	6.06864i	0.433843	−	0.250480i	0.700983	+	0.713178i	$0.252745\pi$
$588$	−0.840951	+	3.13847i	−0.0346802	+	0.129428i
$589$	2.77851	−	1.60418i	0.114487	−	0.0660989i
$590$	−13.6908	+	2.00212i	−0.563643	+	0.0824261i
$591$		−	9.42622i		−	0.387743i
$592$	−9.15077	+	8.71231i	−0.376095	+	0.358074i
$593$	−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
$595$	4.48175	+	1.78171i	0.183734	+	0.0730429i
$596$	−10.3793	+	5.99251i	−0.425154	+	0.245463i
$597$	−5.68949	−	9.85449i	−0.232855	−	0.403317i
$598$			7.94340i			0.324830i
$599$	2.59862	−	1.50032i	0.106177	−	0.0613013i	−0.445971	−	0.895047i	$-0.647142\pi$
$599$	2.59862	−	1.50032i	0.106177	−	0.0613013i	0.552148	+	0.833746i	$0.313808\pi$
$600$	8.53504	+	13.8520i	0.348442	+	0.565505i
$601$	7.76062	−	13.4418i	0.316562	−	0.548302i	−0.663206	−	0.748437i	$-0.730805\pi$
$601$	7.76062	−	13.4418i	0.316562	−	0.548302i	0.979768	+	0.200135i	$0.0641380\pi$
$602$	−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
$605$	6.46511	+	14.9975i	0.262844	+	0.609735i
$606$	0.651505	−	0.651505i	0.0264656	−	0.0264656i
$607$	−32.0701	−	18.5157i	−1.30169	−	0.751529i	−0.320994	−	0.947081i	$-0.604017\pi$
$607$	−32.0701	−	18.5157i	−1.30169	−	0.751529i	−0.980693	+	0.195552i	$0.937350\pi$
$608$	8.26824	−	2.21547i	0.335322	−	0.0898492i
$609$	−0.152415	−	0.568820i	−0.00617616	−	0.0230497i
$610$	−10.1598	+	25.5563i	−0.411359	+	1.03474i
$611$	−1.00129	+	3.73685i	−0.0405077	+	0.151177i
$612$	1.52722	+	0.881739i	0.0617341	+	0.0356422i
$613$	4.51123	+	16.8361i	0.182207	+	0.680005i	0.995211	+	0.0977478i	$0.0311638\pi$
$613$	4.51123	+	16.8361i	0.182207	+	0.680005i	−0.813004	+	0.582258i	$0.802169\pi$
$614$	5.30262	+	19.7897i	0.213996	+	0.798645i
$615$	11.4468	+	14.4838i	0.461579	+	0.584044i
$616$	9.33837	+	2.50221i	0.376254	+	0.100817i
$617$	−23.0967	+	6.18875i	−0.929839	+	0.249150i	−0.691786	−	0.722103i	$-0.743176\pi$
$617$	−23.0967	+	6.18875i	−0.929839	+	0.249150i	−0.238053	+	0.971252i	$0.576509\pi$
$618$	−4.06368	−	4.06368i	−0.163465	−	0.163465i
$619$	6.37727			0.256324			0.128162	−	0.991753i	$-0.459092\pi$
$619$	6.37727			0.256324			0.128162	+	0.991753i	$0.459092\pi$
$620$	0.326716	+	2.23414i	0.0131212	+	0.0897251i
$621$	−16.7134	+	16.7134i	−0.670686	+	0.670686i
$622$	−7.16718	+	26.7483i	−0.287378	+	1.07251i
$623$	27.7760			1.11282
$624$	−0.867925	+	3.23914i	−0.0347448	+	0.129669i
$625$	−1.43013	−	24.9591i	−0.0572052	−	0.998362i
$626$	0.525936	+	0.910947i	0.0210206	+	0.0364088i
$627$	2.29142	−	3.96886i	0.0915107	−	0.158501i
$628$	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	−0.978288	−	0.207249i	$-0.933549\pi$
$631$	−5.89535	−	22.0017i	−0.234690	−	0.875876i	0.743598	−	0.668627i	$-0.233118\pi$
$632$	10.1780	−	37.9847i	0.404858	−	1.51095i
$633$	1.67806	+	0.449634i	0.0666968	+	0.0178714i
$634$	−29.0445	−	7.78244i	−1.15350	−	0.309080i
$635$	8.97398	−	7.09227i	0.356121	−	0.281448i
$636$	−1.26171	−	2.18534i	−0.0500299	−	0.0866544i
$637$	6.61359			0.262040
$638$	0.719241	−	0.192720i	0.0284750	−	0.00762986i
$639$		−	6.22273i		−	0.246168i
$640$	0.526740	−	4.49737i	0.0208212	−	0.177774i
$641$	−11.7520	+	20.3550i	−0.464175	+	0.803976i	−0.999164	−	0.0408839i	$-0.986983\pi$
$641$	−11.7520	+	20.3550i	−0.464175	+	0.803976i	0.534988	+	0.844859i	$0.320316\pi$
$642$	−7.81249	−	13.5316i	−0.308334	−	0.534051i
$643$	24.3699			0.961055			0.480527	−	0.876980i	$-0.340445\pi$
$643$	24.3699			0.961055			0.480527	+	0.876980i	$0.340445\pi$
$644$	−5.12800	+	1.37404i	−0.202072	+	0.0541449i
$645$	−12.7848	+	1.86963i	−0.503402	+	0.0736165i
$646$	−3.26619	+	0.875173i	−0.128507	+	0.0344332i
$647$	35.9680	−	20.7661i	1.41405	−	0.816400i	0.418280	−	0.908318i	$-0.362633\pi$
$647$	35.9680	−	20.7661i	1.41405	−	0.816400i	0.995767	+	0.0919177i	$0.0292997\pi$
$648$	0.506586	−	0.292478i	0.0199006	−	0.0114896i
$649$	−10.1160	+	2.71057i	−0.397087	+	0.106399i
$650$	5.95491	−	6.30589i	0.233571	−	0.247337i
$651$	−2.37394	+	0.636096i	−0.0930422	+	0.0249306i
$652$	−10.4117			−0.407755
$653$	0.370684	+	0.642043i	0.0145060	+	0.0251251i	0.873187	−	0.487385i	$-0.162049\pi$
$653$	0.370684	+	0.642043i	0.0145060	+	0.0251251i	−0.858681	+	0.512510i	$0.828716\pi$
$654$	−7.95475	+	13.7780i	−0.311055	+	0.538763i
$655$	5.58755	−	4.41593i	0.218324	−	0.172545i
$656$		−	16.2212i		−	0.633331i
$657$	4.59319	−	1.23074i	0.179197	−	0.0480158i
$658$	4.70157			0.183286
$659$	−15.9185	−	27.5717i	−0.620098	−	1.07404i	−0.989467	−	0.144759i	$-0.953759\pi$
$659$	−15.9185	−	27.5717i	−0.620098	−	1.07404i	0.369369	−	0.929283i	$-0.379574\pi$
$660$	1.99980	+	2.53038i	0.0778419	+	0.0984948i
$661$	46.6955	+	12.5120i	1.81624	+	0.486661i	0.996312	−	0.0858000i	$-0.0273446\pi$
$661$	46.6955	+	12.5120i	1.81624	+	0.486661i	0.819932	+	0.572461i	$0.194011\pi$
$662$	−10.6861	−	2.86334i	−0.415329	−	0.111287i
$663$	−0.551642	+	2.05876i	−0.0214240	+	0.0799555i
$664$	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
$668$	−7.65841	+	13.2648i	−0.296313	+	0.513229i
$669$	−10.3302	−	17.8925i	−0.399390	−	0.691764i
$670$	−23.1040	−	9.18492i	−0.892585	−	0.354845i
$671$	−5.38760	+	20.1068i	−0.207986	+	0.776214i
$672$	−6.55714			−0.252947
$673$	4.43056	−	16.5351i	0.170785	−	0.637380i	−0.826446	−	0.563016i	$-0.809641\pi$
$673$	4.43056	−	16.5351i	0.170785	−	0.637380i	0.997231	−	0.0743635i	$-0.0236925\pi$
$674$	−15.9588	+	15.9588i	−0.614710	+	0.614710i
$675$	25.7975	−	0.738481i	0.992947	−	0.0284241i
$676$	7.57040			0.291169
$677$	−31.1728	−	31.1728i	−1.19807	−	1.19807i	−0.974745	−	0.223322i	$-0.928310\pi$
$677$	−31.1728	−	31.1728i	−1.19807	−	1.19807i	−0.223322	−	0.974745i	$-0.571690\pi$
$678$	−16.9006	+	4.52851i	−0.649064	+	0.173916i
$679$	24.3331	+	6.52002i	0.933817	+	0.250216i
$680$	1.05701	−	9.02486i	0.0405344	−	0.346087i
$681$	−5.81408	−	21.6984i	−0.222796	−	0.831486i
$682$	−0.804309	−	3.00172i	−0.0307986	−	0.114942i
$683$	31.9387	+	18.4398i	1.22210	+	0.705580i	0.965365	−	0.260901i	$-0.0840197\pi$
$683$	31.9387	+	18.4398i	1.22210	+	0.705580i	0.256736	+	0.966482i	$0.417353\pi$
$684$	0.779496	−	2.90912i	0.0298048	−	0.111233i
$685$	44.8989	+	17.8494i	1.71550	+	0.681992i
$686$	−5.44250	−	20.3117i	−0.207796	−	0.775503i
$687$	4.11424	−	1.10241i	0.156968	−	0.0420595i
$688$	9.83210	+	5.67657i	0.374845	+	0.216417i
$689$	−3.63192	+	3.63192i	−0.138365	+	0.138365i
$690$	11.4270	+	4.54279i	0.435020	+	0.172941i
$691$	−0.520289	−	0.300389i	−0.0197927	−	0.0114273i	0.490071	−	0.871683i	$-0.336971\pi$
$691$	−0.520289	−	0.300389i	−0.0197927	−	0.0114273i	−0.509864	+	0.860255i	$0.670304\pi$
$692$	−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
$695$	−39.8666	−	4.66924i	−1.51222	−	0.177114i
$696$	−0.960837	+	0.554740i	−0.0364204	+	0.0210274i
$697$		−	10.3100i		−	0.390518i
$698$	−8.99422	−	15.5785i	−0.340436	−	0.589653i
$699$	−2.91617	+	1.68365i	−0.110300	+	0.0636816i
$700$	5.10096	+	2.75351i	0.192798	+	0.104073i
$701$	−6.15868	+	1.65021i	−0.232610	+	0.0623277i	−0.373241	−	0.927734i	$-0.621754\pi$
$701$	−6.15868	+	1.65021i	−0.232610	+	0.0623277i	0.140631	+	0.990062i	$0.455087\pi$
$702$	6.33115	+	6.33115i	0.238954	+	0.238954i
$703$	11.7057	+	7.14687i	0.441487	+	0.269549i
$704$		−	16.2781i		−	0.613505i
$705$	4.80305	+	3.57749i	0.180893	+	0.134736i
$706$	−8.56315	+	4.94394i	−0.322278	+	0.186067i
$707$	0.324407	−	1.21070i	0.0122006	−	0.0455332i
$708$	3.53920	−	2.04336i	0.133011	−	0.0767941i
$709$	0.102970	−	0.102970i	0.00386711	−	0.00386711i	−0.705171	−	0.709038i	$-0.749130\pi$
$709$	0.102970	−	0.102970i	0.00386711	−	0.00386711i	0.709038	+	0.705171i	$0.249130\pi$
$710$	−7.71117	+	3.32412i	−0.289395	+	0.124752i
$711$	−17.0049	−	17.0049i	−0.637735	−	0.637735i
$712$	−13.5442	−	50.5477i	−0.507591	−	1.89436i
$713$	4.60752	+	4.60752i	0.172553	+	0.172553i
$714$	2.59025			0.0969378
$715$	3.92146	−	5.26485i	0.146654	−	0.196894i
$716$	4.28964	−	16.0091i	0.160311	−	0.598290i
$717$			20.9900i			0.783887i
$718$	5.60003	−	9.69954i	0.208991	−	0.361984i
$719$	15.6399	+	9.02972i	0.583271	+	0.336752i	0.762432	−	0.647068i	$-0.224005\pi$
$719$	15.6399	+	9.02972i	0.583271	+	0.336752i	−0.179161	+	0.983820i	$0.557338\pi$
$720$	−7.01154	−	5.22246i	−0.261305	−	0.194630i
$721$	−7.55161	−	2.02345i	−0.281237	−	0.0753571i
$722$	−7.90402	−	13.6902i	−0.294157	−	0.509495i
$723$	5.90379	−	10.2257i	0.219564	−	0.380297i
$724$	−7.13191	+	12.3528i	−0.265055	+	0.459089i
$725$	1.70406	−	0.0487804i	0.0632871	−	0.00181166i
$726$	6.20222	+	6.20222i	0.230186	+	0.230186i
$727$	−16.9712	+	9.79831i	−0.629426	+	0.363399i	−0.780530	−	0.625119i	$-0.785051\pi$
$727$	−16.9712	+	9.79831i	−0.629426	+	0.363399i	0.151104	+	0.988518i	$0.451717\pi$
$728$	1.98745	+	7.41727i	0.0736599	+	0.274902i
$729$			16.0130i			0.593073i
$730$	−3.97876	−	5.03440i	−0.147261	−	0.186332i
$731$	6.24916	+	3.60795i	0.231134	+	0.133445i
$732$		−	8.12287i		−	0.300230i
$733$	29.4663	+	7.89548i	1.08836	+	0.291626i	0.758018	−	0.652234i	$-0.226168\pi$
$733$	29.4663	+	7.89548i	1.08836	+	0.291626i	0.330346	+	0.943860i	$0.392835\pi$
$734$	−16.2868	−	16.2868i	−0.601158	−	0.601158i
$735$	3.78228	−	9.51405i	0.139512	−	0.350931i
$736$	8.69240	+	15.0557i	0.320406	+	0.554960i
$737$	−18.1774	−	4.87063i	−0.669574	−	0.179412i
$738$	−14.4608	−	8.34892i	−0.532308	−	0.307328i
$739$	−52.1459			−1.91822			−0.959110	−	0.283035i	$-0.908659\pi$
$739$	−52.1459			−1.91822			−0.959110	+	0.283035i	$0.908659\pi$
$740$	−7.71717	+	5.79711i	−0.283689	+	0.213106i
$741$	3.64006			0.133721
$742$	5.40584	+	3.12106i	0.198455	+	0.114578i
$743$	−25.3141	−	6.78290i	−0.928686	−	0.248841i	−0.237392	−	0.971414i	$-0.576292\pi$
$743$	−25.3141	−	6.78290i	−0.928686	−	0.248841i	−0.691294	+	0.722573i	$0.742959\pi$
$744$	2.31518	+	4.01001i	0.0848787	+	0.147014i
$745$	34.6801	−	14.9499i	1.27058	−	0.547721i
$746$	−1.91199	−	1.91199i	−0.0700030	−	0.0700030i
$747$	16.1494	+	4.32721i	0.590874	+	0.158324i
$748$		−	1.80119i		−	0.0658581i
$749$	−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	$0.420855\pi$
$751$			53.1233i			1.93850i	−0.246087	+	0.969248i	$0.579145\pi$
$752$	−1.36199	−	5.08302i	−0.0496667	−	0.185359i
$753$	−8.77313	+	5.06517i	−0.319711	+	0.184585i
$754$	0.418205	+	0.418205i	0.0152301	+	0.0152301i
$755$	−39.8755	−	29.7008i	−1.45122	−	1.08092i
$756$	−2.99203	+	5.18235i	−0.108819	+	0.188480i
$757$	−7.47044	+	12.9392i	−0.271518	+	0.470282i	−0.969251	−	0.246075i	$-0.920859\pi$
$757$	−7.47044	+	12.9392i	−0.271518	+	0.470282i	0.697733	+	0.716358i	$0.254192\pi$
$758$	9.44324	+	16.3562i	0.342994	+	0.594083i
$759$	8.99041	+	2.40897i	0.326331	+	0.0874402i
$760$	−15.3550	+	2.24549i	−0.556986	+	0.0814526i
$761$	−33.1931	−	19.1641i	−1.20325	−	0.694697i	−0.241974	−	0.970283i	$-0.577795\pi$
$761$	−33.1931	−	19.1641i	−1.20325	−	0.694697i	−0.961277	+	0.275586i	$0.911128\pi$
$762$	3.07157	−	5.32011i	0.111271	−	0.192727i
$763$			21.6430i			0.783530i
$764$	−3.25689	+	12.1549i	−0.117830	+	0.439749i
$765$	−4.45644	−	3.31933i	−0.161123	−	0.120011i
$766$	−10.2315			−0.369679
$767$	−5.88197	−	5.88197i	−0.212385	−	0.212385i
$768$	4.00407	+	14.9434i	0.144485	+	0.539224i
$769$	22.4800	+	22.4800i	0.810650	+	0.810650i	0.984731	−	0.174081i	$-0.0556955\pi$
$769$	22.4800	+	22.4800i	0.810650	+	0.810650i	−0.174081	+	0.984731i	$0.555696\pi$
$770$	−7.41378	−	2.94733i	−0.267174	−	0.106214i
$771$	0.264559	−	0.264559i	0.00952786	−	0.00952786i
$772$	−10.5669	+	6.10080i	−0.380311	+	0.219573i
$773$	7.93815	−	29.6256i	0.285515	−	1.06556i	−0.662947	−	0.748667i	$-0.730694\pi$
$773$	7.93815	−	29.6256i	0.285515	−	1.06556i	0.948462	−	0.316891i	$-0.102639\pi$
$774$	10.1210	−	5.84337i	0.363792	−	0.210036i
$775$	−0.203583	−	7.11181i	−0.00731292	−	0.255464i
$776$		−	47.4615i		−	1.70377i
$777$	−7.24437	−	7.60896i	−0.259890	−	0.272970i
$778$	−9.53005	−	9.53005i	−0.341669	−	0.341669i
$779$	−17.0078	+	4.55724i	−0.609369	+	0.163280i
$780$	−0.946362	+	2.38050i	−0.0338852	+	0.0852357i
$781$	−5.50429	+	3.17790i	−0.196959	+	0.113714i
$782$	−3.43375	−	5.94742i	−0.122790	−	0.212679i
$783$			1.75986i			0.0628922i
$784$	−7.79085	+	4.49805i	−0.278245	+	0.160645i
$785$	−9.14272	+	7.22563i	−0.326318	+	0.257894i
$786$	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
$790$	−11.9885	+	30.1563i	−0.426533	+	1.07291i
$791$	−16.8308	+	16.8308i	−0.598435	+	0.598435i
$792$	−9.64653	−	5.56943i	−0.342775	−	0.197901i
$793$	−15.9704	+	4.27926i	−0.567126	+	0.151961i
$794$	−0.675939	−	2.52264i	−0.0239882	−	0.0895251i
$795$	3.14766	+	7.30181i	0.111636	+	0.258969i
$796$	−1.97684	+	7.37767i	−0.0700672	+	0.261494i
$797$	24.4236	+	14.1009i	0.865127	+	0.499481i	0.865726	−	0.500519i	$-0.166857\pi$
$797$	24.4236	+	14.1009i	0.865127	+	0.499481i	−0.000599033		1.00000i	$0.500191\pi$
$798$	−1.14495	−	4.27301i	−0.0405307	−	0.151263i
$799$	−0.865665	−	3.23070i	−0.0306250	−	0.114294i
$800$	4.38628	−	18.4684i	0.155078	−	0.652958i
$801$	−30.9119	−	8.28283i	−1.09222	−	0.292659i
$802$	26.3327	−	7.05582i	0.929839	−	0.249150i
$803$	−3.43435	−	3.43435i	−0.121196	−	0.121196i
$804$	7.34343			0.258983
$805$	16.5525	−	2.42060i	0.583398	−	0.0853150i
$806$	1.74536	−	1.74536i	0.0614777	−	0.0614777i
$807$	−1.77837	+	6.63697i	−0.0626017	+	0.233633i
$808$	−2.36147			−0.0830763
$809$	−0.812619	+	3.03273i	−0.0285701	+	0.106625i	−0.978739	−	0.205112i	$-0.934244\pi$
$809$	−0.812619	+	3.03273i	−0.0285701	+	0.106625i	0.950168	+	0.311737i	$0.100911\pi$
$810$	−0.443289	+	0.191092i	−0.0155756	+	0.00671430i
$811$	−10.5095	−	18.2030i	−0.369038	−	0.639192i	0.620377	−	0.784303i	$-0.286979\pi$
$811$	−10.5095	−	18.2030i	−0.369038	−	0.639192i	−0.989415	+	0.145111i	$0.953646\pi$
$812$	−0.197639	+	0.342321i	−0.00693577	+	0.0120131i
$813$	−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
$817$	3.18959	−	11.9037i	0.111590	−	0.416458i
$818$	−28.2877	−	7.57966i	−0.989056	−	0.265017i
$819$	4.53596	+	1.21541i	0.158499	+	0.0424697i
$820$	1.44147	−	12.3075i	0.0503385	−	0.429796i
$821$	2.11926	+	3.67067i	0.0739627	+	0.128107i	0.900635	−	0.434577i	$-0.143102\pi$
$821$	2.11926	+	3.67067i	0.0739627	+	0.128107i	−0.826672	+	0.562684i	$0.809769\pi$
$822$	25.9496			0.905096
$823$	0.912687	−	0.244554i	0.0318143	−	0.00852461i	−0.242877	−	0.970057i	$-0.578091\pi$
$823$	0.912687	−	0.244554i	0.0318143	−	0.00852461i	0.274691	+	0.961533i	$0.411424\pi$
$824$			14.7294i			0.513122i
$825$	−5.33114	−	8.65220i	−0.185606	−	0.301231i
$826$	−5.05462	+	8.75486i	−0.175873	+	0.304621i
$827$	11.9529	+	20.7030i	0.415642	+	0.719912i	0.995496	−	0.0948080i	$-0.0302237\pi$
$827$	11.9529	+	20.7030i	0.415642	+	0.719912i	−0.579854	+	0.814720i	$0.696890\pi$
$828$	6.11671			0.212570
$829$	2.51032	−	0.672639i	0.0871871	−	0.0233617i	−0.214962	−	0.976622i	$-0.568963\pi$
$829$	2.51032	−	0.672639i	0.0871871	−	0.0233617i	0.302149	+	0.953261i	$0.402296\pi$
$830$	−3.26458	−	22.3237i	−0.113315	−	0.774868i
$831$	0.583280	−	0.156289i	0.0202338	−	0.00542162i
$832$	11.1972	−	6.46469i	0.388192	−	0.224123i
$833$	−4.95177	+	2.85890i	−0.171569	+	0.0990551i
$834$	−20.8230	+	5.57951i	−0.721041	+	0.193202i
$835$	28.8303	−	38.7068i	0.997713	−	1.33950i
$836$	−2.97133	+	0.796165i	−0.102766	+	0.0275360i
$837$	7.34470			0.253870
$838$	19.0425	+	32.9826i	0.657812	+	1.13936i
$839$	18.2196	−	31.5573i	0.629012	−	1.08948i	−0.358739	−	0.933438i	$-0.616793\pi$
$839$	18.2196	−	31.5573i	0.629012	−	1.08948i	0.987750	−	0.156042i	$-0.0498736\pi$
$840$	11.8068	+	1.38283i	0.407373	+	0.0477123i
$841$		−	28.8838i		−	0.995991i
$842$	−1.48092	+	0.396811i	−0.0510358	+	0.0136750i
$843$	33.1205			1.14073
$844$	−0.583049	−	1.00987i	−0.0200694	−	0.0347611i
$845$	−23.6927	−	2.77493i	−0.815052	−	0.0954603i
$846$	−5.23239	−	1.40201i	−0.179893	−	0.0482022i
$847$	11.5257	+	3.08830i	0.396028	+	0.106115i
$848$	1.80827	−	6.74857i	0.0620964	−	0.231747i
$849$	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
$853$	12.9804	−	22.4827i	0.444440	−	0.769792i	−0.553573	−	0.832800i	$-0.686736\pi$
$853$	12.9804	−	22.4827i	0.444440	−	0.769792i	0.998013	+	0.0630083i	$0.0200695\pi$
$854$	10.0467	+	17.4014i	0.343791	+	0.595464i
$855$	−3.50588	+	8.81878i	−0.119899	+	0.301596i
$856$	−10.3649	+	38.6824i	−0.354265	+	1.32214i
$857$	40.2792			1.37591			0.687955	−	0.725753i	$-0.258509\pi$
$857$	40.2792			1.37591			0.687955	+	0.725753i	$0.258509\pi$
$858$	0.912535	−	3.40563i	0.0311534	−	0.116266i
$859$	−3.69657	+	3.69657i	−0.126125	+	0.126125i	−0.767352	−	0.641226i	$-0.778426\pi$
$859$	−3.69657	+	3.69657i	−0.126125	+	0.126125i	0.641226	+	0.767352i	$0.278426\pi$
$860$	6.95546	+	5.18069i	0.237179	+	0.176660i
$861$	13.4881			0.459672
$862$	−10.1183	−	10.1183i	−0.344630	−	0.344630i
$863$	6.85933	−	1.83795i	0.233494	−	0.0625646i	−0.140174	−	0.990127i	$-0.544766\pi$
$863$	6.85933	−	1.83795i	0.233494	−	0.0625646i	0.373669	+	0.927562i	$0.378100\pi$
$864$	18.9280	+	5.07175i	0.643944	+	0.172544i
$865$	1.44819	−	1.14453i	0.0492401	−	0.0389152i
$866$	−5.70964	−	21.3087i	−0.194021	−	0.724098i
$867$	4.17471	+	15.5802i	0.141780	+	0.529132i
$868$	1.42866	+	0.824838i	0.0484919	+	0.0279968i
$869$	−6.35735	+	23.7259i	−0.215658	+	0.804847i
$870$	0.840782	−	0.362443i	0.0285052	−	0.0122880i
$871$	−3.86864	−	14.4380i	−0.131084	−	0.489212i
$872$	39.3867	−	10.5536i	1.33380	−	0.357391i
$873$	−25.1360	−	14.5123i	−0.850726	−	0.491167i
$874$	−8.29336	+	8.29336i	−0.280527	+	0.280527i
$875$	−14.9549	−	10.4873i	−0.505568	−	0.354534i
$876$	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
$880$	−1.03876	+	8.86910i	−0.0350167	+	0.298977i
$881$	−3.79357	+	2.19022i	−0.127809	+	0.0737904i	−0.562541	−	0.826769i	$-0.690176\pi$
$881$	−3.79357	+	2.19022i	−0.127809	+	0.0737904i	0.434733	+	0.900560i	$0.356843\pi$
$882$			9.26045i			0.311815i
$883$	29.2518	+	50.6657i	0.984402	+	1.70504i	0.644562	+	0.764552i	$0.277040\pi$
$883$	29.2518	+	50.6657i	0.984402	+	1.70504i	0.339840	+	0.940483i	$0.389627\pi$
$884$	1.23898	−	0.715324i	0.0416713	−	0.0240590i
$885$	−11.8254	+	5.09769i	−0.397507	+	0.171357i
$886$	20.6420	−	5.53099i	0.693480	−	0.185817i
$887$	−2.53298	−	2.53298i	−0.0850491	−	0.0850491i	0.663302	−	0.748351i	$-0.269154\pi$
$887$	−2.53298	−	2.53298i	−0.0850491	−	0.0850491i	−0.748351	+	0.663302i	$0.769154\pi$
$888$	−10.3145	+	16.8939i	−0.346133	+	0.566921i
$889$		−	8.35702i		−	0.280286i
$890$	6.24883	+	42.7305i	0.209461	+	1.43233i
$891$	−0.316423	+	0.182687i	−0.0106006	+	0.00612024i
$892$	−3.58929	+	13.3954i	−0.120178	+	0.448511i
$893$	−4.94688	+	2.85608i	−0.165541	+	0.0955752i
$894$	14.3420	−	14.3420i	0.479668	−	0.479668i
$895$	−19.2932	+	48.5305i	−0.644900	+	1.62220i
$896$	−2.33935	−	2.33935i	−0.0781523	−	0.0781523i
$897$	1.91340	+	7.14090i	0.0638865	+	0.238428i
$898$	23.5686	+	23.5686i	0.786494	+	0.786494i
$899$	0.485155			0.0161808
$900$	−4.85577	−	4.58551i	−0.161859	−	0.152850i
$901$	1.14932	−	4.28931i	0.0382893	−	0.142898i
$902$			17.0549i			0.567867i
$903$	−4.72012	+	8.17549i	−0.157076	+	0.272063i
$904$	38.8364	+	22.4222i	1.29168	+	0.745752i
$905$	26.8483	−	36.0457i	0.892466	−	1.19820i
$906$	−25.7939	−	6.91146i	−0.856946	−	0.229618i
$907$	6.14134	+	10.6371i	0.203920	+	0.353200i	0.949788	−	0.312894i	$-0.101298\pi$
$907$	6.14134	+	10.6371i	0.203920	+	0.353200i	−0.745868	+	0.666094i	$0.767965\pi$
$908$	−7.53922	+	13.0583i	−0.250198	+	0.433355i
$909$	−0.722067	+	1.25066i	−0.0239495	+	0.0414817i
$910$	−0.916941	−	6.27019i	−0.0303963	−	0.207855i
$911$	−8.69751	−	8.69751i	−0.288161	−	0.288161i	0.548191	−	0.836353i	$-0.315317\pi$
$911$	−8.69751	−	8.69751i	−0.288161	−	0.288161i	−0.836353	+	0.548191i	$0.815317\pi$
$912$	−4.28801	+	2.47568i	−0.141990	+	0.0819781i
$913$	−4.41974	−	16.4947i	−0.146272	−	0.545895i
$914$			7.28961i			0.241119i
$915$	−2.97743	+	25.4217i	−0.0984309	+	0.840415i
$916$	−2.47599	−	1.42951i	−0.0818089	−	0.0472324i
$917$		−	5.20341i		−	0.171832i
$918$	−7.47710	−	2.00348i	−0.246781	−	0.0661248i
$919$	−25.2847	−	25.2847i	−0.834065	−	0.834065i	0.154005	−	0.988070i	$-0.450783\pi$
$919$	−25.2847	−	25.2847i	−0.834065	−	0.834065i	−0.988070	+	0.154005i	$0.950783\pi$
$920$	−12.4765	−	28.9425i	−0.411337	−	0.954204i
$921$	9.53382	+	16.5131i	0.314150	+	0.544124i
$922$	28.7436	+	7.70182i	0.946620	+	0.253646i
$923$	−4.37194	−	2.52414i	−0.143904	−	0.0830832i
$924$	2.35642			0.0775204
$925$	26.2769	−	15.3142i	0.863980	−	0.503527i
$926$	−43.4081			−1.42648
$927$	7.80081	+	4.50380i	0.256212	+	0.147924i
$928$	1.25029	+	0.335015i	0.0410428	+	0.0109974i
$929$	6.26098	+	10.8443i	0.205416	+	0.355791i	0.950265	−	0.311442i	$-0.100812\pi$
$929$	6.26098	+	10.8443i	0.205416	+	0.355791i	−0.744849	+	0.667233i	$0.767479\pi$
$930$	−1.51264	−	3.50897i	−0.0496015	−	0.115064i
$931$	6.90497	+	6.90497i	0.226301	+	0.226301i
$932$	2.18322	+	0.584992i	0.0715138	+	0.0191621i
$933$			25.7724i			0.843751i
$934$	13.2985	+	7.67791i	0.435141	+	0.251229i
$935$	−0.660225	+	5.63709i	−0.0215917	+	0.184352i
$936$		−	8.84736i		−	0.289185i
$937$	−3.17302	−	11.8419i	−0.103658	−	0.386857i	0.894531	−	0.447005i	$-0.147509\pi$
$937$	−3.17302	−	11.8419i	−0.103658	−	0.386857i	−0.998189	+	0.0601478i	$0.980843\pi$
$938$	−15.7316	+	9.08266i	−0.513656	+	0.296559i
$939$	0.692230	+	0.692230i	0.0225901	+	0.0225901i
$940$	−0.581687	−	3.97767i	−0.0189725	−	0.129737i
$941$	−13.7869	+	23.8796i	−0.449440	+	0.778452i	−0.998350	−	0.0574293i	$-0.981710\pi$
$941$	−13.7869	+	23.8796i	−0.449440	+	0.778452i	0.548910	+	0.835881i	$0.315043\pi$
$942$	−3.12932	+	5.42015i	−0.101959	+	0.176598i
$943$	−17.8803	−	30.9696i	−0.582264	−	1.00851i
$944$	10.9294	+	2.92853i	0.355723	+	0.0953157i
$945$	11.2636	−	15.1222i	0.366404	−	0.491924i
$946$	−10.3375	−	5.96833i	−0.336100	−	0.194047i
$947$	4.48370	−	7.76600i	0.145701	−	0.252361i	−0.783933	−	0.620845i	$-0.786790\pi$
$947$	4.48370	−	7.76600i	0.145701	−	0.252361i	0.929634	+	0.368484i	$0.120123\pi$
$948$		−	9.58495i		−	0.311305i
$949$	0.998457	−	3.72629i	0.0324113	−	0.120961i
$950$	12.8010	−	0.366442i	0.415319	−	0.0118889i
$951$	−27.9848			−0.907469
$952$	−4.69437	−	4.69437i	−0.152145	−	0.152145i
$953$	9.63231	+	35.9483i	0.312021	+	1.16448i	0.926731	+	0.375725i	$0.122606\pi$
$953$	9.63231	+	35.9483i	0.312021	+	1.16448i	−0.614710	+	0.788753i	$0.710727\pi$
$954$	−5.08547	−	5.08547i	−0.164648	−	0.164648i
$955$	14.6483	−	36.8467i	0.474007	−	1.19233i
$956$	9.96253	−	9.96253i	0.322211	−	0.322211i
$957$	0.600156	−	0.346500i	0.0194003	−	0.0112008i
$958$	−0.530395	+	1.97946i	−0.0171363	+	0.0639535i
$959$	30.5719	−	17.6507i	0.987219	−	0.569971i
$960$	−2.89623	−	19.8049i	−0.0934755	−	0.639201i
$961$			28.9752i			0.934685i
$962$	10.1219	+	2.98019i	0.326342	+	0.0960852i
$963$	17.3173	+	17.3173i	0.558041	+	0.558041i
$964$	−7.65555	+	2.05130i	−0.246569	+	0.0660679i
$965$	35.3069	−	15.2200i	1.13657	−	0.489951i
$966$	7.78074	−	4.49221i	0.250341	−	0.144535i
$967$	−28.0830	−	48.6411i	−0.903087	−	1.56419i	−0.823464	−	0.567368i	$-0.807962\pi$
$967$	−28.0830	−	48.6411i	−0.903087	−	1.56419i	−0.0796228	−	0.996825i	$-0.525372\pi$
$968$		−	22.4808i		−	0.722561i
$969$	−2.72541	+	1.57351i	−0.0875526	+	0.0505485i
$970$	−4.55612	+	38.9007i	−0.146288	+	1.24903i
$971$	−19.7612	+	34.2274i	−0.634167	+	1.09841i	0.352523	+	0.935803i	$0.385324\pi$
$971$	−19.7612	+	34.2274i	−0.634167	+	1.09841i	−0.986691	+	0.162607i	$0.948010\pi$
$972$	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
$975$	3.83435	−	7.10324i	0.122797	−	0.227486i
$976$	15.9028	−	15.9028i	0.509037	−	0.509037i
$977$	5.20188	+	3.00331i	0.166423	+	0.0960843i	0.580898	−	0.813976i	$-0.302702\pi$
$977$	5.20188	+	3.00331i	0.166423	+	0.0960843i	−0.414475	+	0.910061i	$0.636035\pi$
$978$	17.0197	−	4.56042i	0.544231	−	0.145826i
$979$	8.45996	+	31.5730i	0.270381	+	1.00908i
$980$	−6.31086	+	2.72048i	−0.201593	+	0.0869025i
$981$	6.45397	−	24.0866i	0.206060	−	0.769025i
$982$	22.0038	+	12.7039i	0.702169	+	0.405398i
$983$	6.19133	+	23.1064i	0.197473	+	0.736979i	0.991613	+	0.129244i	$0.0412550\pi$
$983$	6.19133	+	23.1064i	0.197473	+	0.736979i	−0.794140	+	0.607735i	$0.792078\pi$
$984$	−6.57710	−	24.5461i	−0.209670	−	0.782501i
$985$	15.6419	−	12.3620i	0.498393	−	0.393887i
$986$	−0.493901	−	0.132340i	−0.0157290	−	0.00421457i
$987$	4.22658	−	1.13251i	0.134534	−	0.0360482i
$988$	−1.72769	−	1.72769i	−0.0549651	−	0.0549651i
$989$	25.0287			0.795867
$990$	7.37192	+	5.49089i	0.234295	+	0.174512i
$991$	18.5888	−	18.5888i	0.590492	−	0.590492i	−0.347272	−	0.937764i	$-0.612892\pi$
$991$	18.5888	−	18.5888i	0.590492	−	0.590492i	0.937764	+	0.347272i	$0.112892\pi$
$992$	1.39817	−	5.21804i	0.0443919	−	0.165673i
$993$	−10.2963			−0.326742
$994$	−1.58789	+	5.92610i	−0.0503649	+	0.187964i
$995$	8.89108	−	22.3649i	0.281866	−	0.709013i
$996$	3.33182	+	5.77087i	0.105573	+	0.182857i
$997$	25.8150	−	44.7129i	0.817569	−	1.41607i	−0.0898999	−	0.995951i	$-0.528655\pi$
$997$	25.8150	−	44.7129i	0.817569	−	1.41607i	0.907469	−	0.420120i	$-0.138012\pi$
$998$	12.5670	−	12.5670i	0.397800	−	0.397800i
$999$	15.0265	+	27.5675i	0.475417	+	0.872198i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.p.a.97.6	✓	68	5.2	odd	4
185.2.p.a.103.6	yes	68	37.29	odd	12
185.2.u.a.23.12	yes	68	1.1	even	1	trivial
185.2.u.a.177.12	yes	68	185.177	even	12	inner
925.2.t.b.282.12		68	5.3	odd	4
925.2.t.b.843.12		68	185.29	odd	12
925.2.y.b.393.6		68	5.4	even	2
925.2.y.b.732.6		68	185.103	even	12

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

\(f(q)\)	\(=\)	\(q+(0.983757 + 0.567972i) q^{2} +(1.02118 + 0.273625i) q^{3} +(-0.354815 - 0.614557i) q^{4} +(0.885178 + 2.05340i) q^{5} +(0.849185 + 0.849185i) q^{6} +(1.57806 + 0.422839i) q^{7} -3.07799i q^{8} +(-1.63013 - 0.941157i) q^{9} +(-0.295475 + 2.52281i) q^{10} +1.92257i q^{11} +(-0.194173 - 0.724662i) q^{12} +(-1.32247 + 0.763528i) q^{13} +(1.31226 + 1.31226i) q^{14} +(0.342067 + 2.33911i) q^{15} +(1.03858 - 1.79888i) q^{16} +(0.660110 - 1.14334i) q^{17} +(-1.06910 - 1.85174i) q^{18} +(-2.17790 - 0.583566i) q^{19} +(0.947859 - 1.27257i) q^{20} +(1.49579 + 0.863592i) q^{21} +(-1.09196 + 1.89134i) q^{22} -4.57925i q^{23} +(0.842216 - 3.14319i) q^{24} +(-3.43292 + 3.63525i) q^{25} -1.73465 q^{26} +(-3.64981 - 3.64981i) q^{27} +(-0.300059 - 1.11984i) q^{28} +(-0.241089 - 0.241089i) q^{29} +(-0.992038 + 2.49540i) q^{30} +(-1.00617 + 1.00617i) q^{31} +(-3.28781 + 1.89822i) q^{32} +(-0.526063 + 1.96329i) q^{33} +(1.29878 - 0.749849i) q^{34} +(0.528603 + 3.61467i) q^{35} +1.33575i q^{36} +(-5.83510 - 1.71804i) q^{37} +(-1.81107 - 1.81107i) q^{38} +(-1.55940 + 0.417841i) q^{39} +(6.32035 - 2.72457i) q^{40} +(6.76304 - 3.90464i) q^{41} +(0.980993 + 1.69913i) q^{42} +5.46568i q^{43} +(1.18153 - 0.682155i) q^{44} +(0.489616 - 4.18041i) 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} +(-5.44188 + 1.62640i) q^{50} +(0.986942 - 0.986942i) q^{51} +(0.938463 + 0.541822i) q^{52} +(3.24893 - 0.870548i) q^{53} +(-1.51754 - 5.66352i) q^{54} +(-3.94780 + 1.70181i) q^{55} +(1.30149 - 4.85724i) q^{56} +(-2.06436 - 1.19186i) q^{57} +(-0.100241 - 0.374105i) q^{58} +(1.40987 + 5.26170i) q^{59} +(1.31614 - 1.04017i) q^{60} +(10.4583 + 2.80230i) q^{61} +(-1.56131 + 0.418352i) q^{62} +(-2.17448 - 2.17448i) q^{63} -8.46687 q^{64} +(-2.73845 - 2.03970i) q^{65} +(-1.63261 + 1.63261i) q^{66} +(-2.53340 + 9.45477i) q^{67} -0.936868 q^{68} +(1.25300 - 4.67625i) q^{69} +(-1.53302 + 3.85619i) q^{70} +(1.65295 + 2.86299i) q^{71} +(-2.89687 + 5.01753i) 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} +(-0.812936 + 3.03392i) q^{77} +(-1.77140 - 0.474644i) q^{78} +(12.3408 + 3.30670i) q^{79} +(4.61315 + 0.540301i) q^{80} +(0.0950223 + 0.164583i) q^{81} +8.87092 q^{82} +(-8.57952 + 2.29888i) q^{83} -1.22566i q^{84} +(2.93206 + 0.343408i) q^{85} +(-3.10436 + 5.37690i) q^{86} +(-0.180228 - 0.312164i) q^{87} +5.91764 q^{88} +(16.4223 - 4.40035i) q^{89} +(2.85602 - 3.83442i) q^{90} +(-2.40978 + 0.645698i) q^{91} +(-2.81421 + 1.62479i) q^{92} +(-1.30280 + 0.752174i) q^{93} +(2.77976 - 0.744835i) q^{94} +(-0.729532 - 4.98866i) q^{95} +(-3.87685 + 1.03880i) q^{96} +15.4196 q^{97} +(-2.45986 - 4.26060i) q^{98} +(1.80944 - 3.13404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{2} - 4 q^{3} + 30 q^{4} - 8 q^{6} - 2 q^{7} - 6 q^{10} - 10 q^{12} - 6 q^{13} - 16 q^{15} - 26 q^{16} - 10 q^{17} - 8 q^{18} - 4 q^{19} - 28 q^{20} - 12 q^{21} - 14 q^{22} + 20 q^{25} - 24 q^{26}+ \cdots - 32 q^{99}+O(q^{100}) \) 68 * q - 6 * q^2 - 4 * q^3 + 30 * q^4 - 8 * q^6 - 2 * q^7 - 6 * q^10 - 10 * q^12 - 6 * q^13 - 16 * q^15 - 26 * q^16 - 10 * q^17 - 8 * q^18 - 4 * q^19 - 28 * q^20 - 12 * q^21 - 14 * q^22 + 20 * q^25 - 24 * q^26 + 68 * q^27 + 14 * q^28 - 14 * q^29 + 26 * q^30 - 24 * q^31 + 18 * q^32 + 10 * q^33 - 22 * q^35 - 18 * q^37 - 36 * q^38 - 52 * q^39 + 84 * q^40 - 18 * q^41 - 40 * q^42 + 36 * q^44 - 66 * q^45 - 52 * q^46 - 24 * q^47 + 60 * q^48 + 36 * q^49 - 12 * q^50 - 8 * q^51 - 78 * q^52 - 38 * q^53 - 40 * q^54 + 6 * q^55 + 16 * q^56 + 90 * q^57 + 16 * q^58 + 8 * q^59 - 52 * q^60 + 4 * q^61 - 22 * q^62 - 48 * q^63 + 20 * q^64 - 20 * q^65 + 80 * q^66 - 56 * q^67 - 20 * q^68 - 8 * q^69 + 62 * q^70 + 4 * q^71 + 32 * q^72 + 60 * q^73 + 44 * q^74 + 64 * q^75 + 72 * q^76 + 6 * q^77 - 24 * q^78 - 56 * q^79 - 76 * q^80 - 6 * q^81 - 8 * q^82 + 12 * q^83 + 20 * q^85 - 4 * q^86 - 32 * q^87 - 36 * q^88 + 22 * q^89 - 74 * q^90 + 44 * q^91 + 156 * q^92 - 30 * q^93 + 20 * q^94 + 28 * q^95 - 8 * q^96 + 16 * q^97 + 48 * q^98 - 32 * q^99

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