LMFDB - Embedded newform 726.2.i.c.133.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [726,2,Mod(67,726)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(726, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 20])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("726.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.i (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.3
Character	$\chi$	$=$	726.133
Dual form			726.2.i.c.595.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841254 - 0.540641i) q^{2} -1.00000 q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.149872 + 1.04238i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.49653 + 1.72708i) q^{7} +(-0.142315 - 0.989821i) q^{8} +1.00000 q^{9} +(0.437474 + 0.957934i) q^{10} +(1.40051 - 3.00642i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.661261 - 1.44796i) q^{13} +(-0.325226 + 2.26200i) q^{14} +(0.149872 - 1.04238i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(4.69189 + 1.37766i) q^{17} +(0.841254 - 0.540641i) q^{18} +(6.04298 - 1.77438i) q^{19} +(0.885925 + 0.569349i) q^{20} +(1.49653 - 1.72708i) q^{21} +(-0.447205 - 3.28634i) q^{22} +(4.60421 + 5.31355i) q^{23} +(0.142315 + 0.989821i) q^{24} +(3.73337 + 1.09622i) q^{25} +(-0.226538 - 1.57561i) q^{26} -1.00000 q^{27} +(0.949330 + 2.07874i) q^{28} +(0.0196100 - 0.00575801i) q^{29} +(-0.437474 - 0.957934i) q^{30} +(-1.08953 - 2.38575i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.40051 + 3.00642i) q^{33} +(4.69189 - 1.37766i) q^{34} +(-1.57599 - 1.81879i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.73751 + 5.99431i) q^{37} +(4.12438 - 4.75979i) q^{38} +(-0.661261 + 1.44796i) q^{39} +1.05310 q^{40} +(-6.78363 + 4.35957i) q^{41} +(0.325226 - 2.26200i) q^{42} +(-1.52696 - 10.6202i) q^{43} +(-2.15294 - 2.52286i) q^{44} +(-0.149872 + 1.04238i) q^{45} +(6.74603 + 1.98081i) q^{46} +(2.09857 + 1.34867i) q^{47} +(0.654861 + 0.755750i) q^{48} +(0.252979 + 1.75951i) q^{49} +(3.73337 - 1.09622i) q^{50} +(-4.69189 - 1.37766i) q^{51} +(-1.04241 - 1.20301i) q^{52} +(8.34530 - 9.63099i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(2.92394 + 1.91045i) q^{55} +(1.92248 + 1.23550i) q^{56} +(-6.04298 + 1.77438i) q^{57} +(0.0133840 - 0.0154459i) q^{58} +(-10.5387 - 6.77284i) q^{59} +(-0.885925 - 0.569349i) q^{60} +(3.91621 + 2.51679i) q^{61} +(-2.20641 - 1.41797i) q^{62} +(-1.49653 + 1.72708i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.41022 + 0.906294i) q^{65} +(0.447205 + 3.28634i) q^{66} +(1.64883 - 1.05964i) q^{67} +(3.20225 - 3.69559i) q^{68} +(-4.60421 - 5.31355i) q^{69} +(-2.30912 - 0.678019i) q^{70} +(-10.6173 + 3.11753i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-0.0828815 - 0.0956504i) q^{73} +(5.54371 + 3.56272i) q^{74} +(-3.73337 - 1.09622i) q^{75} +(0.896313 - 6.23400i) q^{76} +(3.09643 + 6.91799i) q^{77} +(0.226538 + 1.57561i) q^{78} +(1.19217 - 8.29169i) q^{79} +(0.885925 - 0.569349i) q^{80} +1.00000 q^{81} +(-3.34979 + 7.33501i) q^{82} +(-7.82694 + 9.03277i) q^{83} +(-0.949330 - 2.07874i) q^{84} +(-2.13924 + 4.68427i) q^{85} +(-7.02630 - 8.10878i) q^{86} +(-0.0196100 + 0.00575801i) q^{87} +(-3.17513 - 0.958402i) q^{88} +(-14.6233 - 4.29379i) q^{89} +(0.437474 + 0.957934i) q^{90} +(1.51115 + 3.30896i) q^{91} +(6.74603 - 1.98081i) q^{92} +(1.08953 + 2.38575i) q^{93} +2.49457 q^{94} +(0.943908 + 6.56503i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.0583832 - 0.406064i) q^{97} +(1.16408 + 1.34342i) q^{98} +(1.40051 - 3.00642i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{2} - 60 q^{3} - 6 q^{4} - 2 q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 60 q^{9} - 13 q^{10} - 10 q^{11} + 6 q^{12} - 17 q^{13} - 6 q^{14} + 2 q^{15} - 6 q^{16} + 10 q^{17} - 6 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) $ 60 * q - 6 * q^2 - 60 * q^3 - 6 * q^4 - 2 * q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 60 * q^9 - 13 * q^10 - 10 * q^11 + 6 * q^12 - 17 * q^13 - 6 * q^14 + 2 * q^15 - 6 * q^16 + 10 * q^17 - 6 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 10 * q^22 - 26 * q^23 + 6 * q^24 - 2 * q^25 + 5 * q^26 - 60 * q^27 + 5 * q^28 - 6 * q^29 + 13 * q^30 - 52 * q^31 - 6 * q^32 + 10 * q^33 + 10 * q^34 + 63 * q^35 - 6 * q^36 - 47 * q^37 + 18 * q^38 + 17 * q^39 - 2 * q^40 + 27 * q^41 + 6 * q^42 + 84 * q^43 + q^44 - 2 * q^45 + 7 * q^46 + 10 * q^47 + 6 * q^48 - 33 * q^49 - 2 * q^50 - 10 * q^51 + 5 * q^52 + 42 * q^53 + 6 * q^54 + 13 * q^55 - 6 * q^56 + 4 * q^57 + 16 * q^58 - 11 * q^59 + 2 * q^60 - 24 * q^61 + 14 * q^62 + 5 * q^63 - 6 * q^64 - 80 * q^65 + 10 * q^66 - 2 * q^67 - q^68 + 26 * q^69 - 14 * q^70 - 30 * q^71 - 6 * q^72 - 51 * q^73 + 8 * q^74 + 2 * q^75 - 4 * q^76 + 73 * q^77 - 5 * q^78 - 30 * q^79 - 2 * q^80 + 60 * q^81 - 6 * q^82 + 4 * q^83 - 5 * q^84 + 45 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 44 * q^89 - 13 * q^90 - 90 * q^91 + 7 * q^92 + 52 * q^93 - 78 * q^94 - 65 * q^95 + 6 * q^96 - 41 * q^97 + 33 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/726\mathbb{Z}\right)^\times$.

$n$	$485$	$607$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.149872	+	1.04238i	−0.0670247	+	0.466167i	0.928474	+	0.371396i	$0.121121\pi$
$5$	−0.149872	+	1.04238i	−0.0670247	+	0.466167i	−0.995499	+	0.0947709i	$0.969788\pi$
$6$	−0.841254	+	0.540641i	−0.343440	+	0.220716i
$7$	−1.49653	+	1.72708i	−0.565633	+	0.652776i	−0.964453	−	0.264254i	$-0.914874\pi$
$7$	−1.49653	+	1.72708i	−0.565633	+	0.652776i	0.398820	+	0.917029i	$0.369420\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	1.00000			0.333333
$10$	0.437474	+	0.957934i	0.138341	+	0.302925i
$11$	1.40051	−	3.00642i	0.422271	−	0.906470i
$11$	1.40051	−	3.00642i	0.422271	−	0.906470i
$12$	−0.415415	+	0.909632i	−0.119920	+	0.262588i
$13$	0.661261	−	1.44796i	0.183401	−	0.401592i	−0.795493	−	0.605963i	$-0.792788\pi$
$13$	0.661261	−	1.44796i	0.183401	−	0.401592i	0.978893	+	0.204372i	$0.0655151\pi$
$14$	−0.325226	+	2.26200i	−0.0869203	+	0.604544i
$15$	0.149872	−	1.04238i	0.0386968	−	0.269142i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	4.69189	+	1.37766i	1.13795	+	0.334133i	0.795828	−	0.605522i	$-0.207036\pi$
$17$	4.69189	+	1.37766i	1.13795	+	0.334133i	0.342123	+	0.939655i	$0.388854\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	6.04298	−	1.77438i	1.38636	−	0.407071i	0.498379	−	0.866959i	$-0.333929\pi$
$19$	6.04298	−	1.77438i	1.38636	−	0.407071i	0.887977	+	0.459889i	$0.152111\pi$
$20$	0.885925	+	0.569349i	0.198099	+	0.127310i
$21$	1.49653	−	1.72708i	0.326569	−	0.376880i
$22$	−0.447205	−	3.28634i	−0.0953444	−	0.700649i
$23$	4.60421	+	5.31355i	0.960045	+	1.10795i	0.994093	+	0.108531i	$0.0346146\pi$
$23$	4.60421	+	5.31355i	0.960045	+	1.10795i	−0.0340480	+	0.999420i	$0.510840\pi$
$24$	0.142315	+	0.989821i	0.0290499	+	0.202046i
$25$	3.73337	+	1.09622i	0.746673	+	0.219243i
$26$	−0.226538	−	1.57561i	−0.0444277	−	0.309002i
$27$	−1.00000			−0.192450
$28$	0.949330	+	2.07874i	0.179407	+	0.392845i
$29$	0.0196100	−	0.00575801i	0.00364148	−	0.00106924i	−0.279911	−	0.960026i	$-0.590305\pi$
$29$	0.0196100	−	0.00575801i	0.00364148	−	0.00106924i	0.283553	+	0.958957i	$0.408487\pi$
$30$	−0.437474	−	0.957934i	−0.0798714	−	0.174894i
$31$	−1.08953	−	2.38575i	−0.195686	−	0.428493i	0.786198	−	0.617974i	$-0.212046\pi$
$31$	−1.08953	−	2.38575i	−0.195686	−	0.428493i	−0.981884	+	0.189482i	$0.939319\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−1.40051	+	3.00642i	−0.243798	+	0.523350i
$34$	4.69189	−	1.37766i	0.804653	−	0.236268i
$35$	−1.57599	−	1.81879i	−0.266391	−	0.307432i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	2.73751	+	5.99431i	0.450044	+	0.985458i	0.989645	+	0.143537i	$0.0458477\pi$
$37$	2.73751	+	5.99431i	0.450044	+	0.985458i	−0.539601	+	0.841921i	$0.681425\pi$
$38$	4.12438	−	4.75979i	0.669063	−	0.772139i
$39$	−0.661261	+	1.44796i	−0.105886	+	0.231859i
$40$	1.05310			0.166510
$41$	−6.78363	+	4.35957i	−1.05942	+	0.680851i	−0.949716	−	0.313113i	$-0.898628\pi$
$41$	−6.78363	+	4.35957i	−1.05942	+	0.680851i	−0.109709	+	0.993964i	$0.534992\pi$
$42$	0.325226	−	2.26200i	0.0501835	−	0.349034i
$43$	−1.52696	−	10.6202i	−0.232859	−	1.61957i	−0.685634	−	0.727947i	$-0.740475\pi$
$43$	−1.52696	−	10.6202i	−0.232859	−	1.61957i	0.452774	−	0.891625i	$-0.350434\pi$
$44$	−2.15294	−	2.52286i	−0.324568	−	0.380336i
$45$	−0.149872	+	1.04238i	−0.0223416	+	0.155389i
$46$	6.74603	+	1.98081i	0.994648	+	0.292055i
$47$	2.09857	+	1.34867i	0.306108	+	0.196723i	0.684672	−	0.728852i	$-0.259946\pi$
$47$	2.09857	+	1.34867i	0.306108	+	0.196723i	−0.378564	+	0.925575i	$0.623582\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	0.252979	+	1.75951i	0.0361398	+	0.251358i
$50$	3.73337	−	1.09622i	0.527978	−	0.155028i
$51$	−4.69189	−	1.37766i	−0.656997	−	0.192912i
$52$	−1.04241	−	1.20301i	−0.144557	−	0.166827i
$53$	8.34530	−	9.63099i	1.14631	−	1.32292i	0.207604	−	0.978213i	$-0.433433\pi$
$53$	8.34530	−	9.63099i	1.14631	−	1.32292i	0.938711	−	0.344705i	$-0.112021\pi$
$54$	−0.841254	+	0.540641i	−0.114480	+	0.0735719i
$55$	2.92394	+	1.91045i	0.394264	+	0.257605i
$56$	1.92248	+	1.23550i	0.256902	+	0.165101i
$57$	−6.04298	+	1.77438i	−0.800413	+	0.235022i
$58$	0.0133840	−	0.0154459i	0.00175740	−	0.00202815i
$59$	−10.5387	−	6.77284i	−1.37203	−	0.881749i	−0.373088	−	0.927796i	$-0.621701\pi$
$59$	−10.5387	−	6.77284i	−1.37203	−	0.881749i	−0.998939	+	0.0460472i	$0.985338\pi$
$60$	−0.885925	−	0.569349i	−0.114372	−	0.0735027i
$61$	3.91621	+	2.51679i	0.501419	+	0.322243i	0.766784	−	0.641906i	$-0.221856\pi$
$61$	3.91621	+	2.51679i	0.501419	+	0.322243i	−0.265364	+	0.964148i	$0.585492\pi$
$62$	−2.20641	−	1.41797i	−0.280214	−	0.180082i
$63$	−1.49653	+	1.72708i	−0.188544	+	0.217592i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	1.41022	+	0.906294i	0.174916	+	0.112412i
$66$	0.447205	+	3.28634i	0.0550471	+	0.404520i
$67$	1.64883	−	1.05964i	0.201437	−	0.129456i	−0.436034	−	0.899930i	$-0.643617\pi$
$67$	1.64883	−	1.05964i	0.201437	−	0.129456i	0.637470	+	0.770475i	$0.279981\pi$
$68$	3.20225	−	3.69559i	0.388330	−	0.448157i
$69$	−4.60421	−	5.31355i	−0.554282	−	0.639676i
$70$	−2.30912	−	0.678019i	−0.275993	−	0.0810388i
$71$	−10.6173	+	3.11753i	−1.26005	+	0.369983i	−0.842512	−	0.538678i	$-0.818924\pi$
$71$	−10.6173	+	3.11753i	−1.26005	+	0.369983i	−0.417535	+	0.908661i	$0.637106\pi$
$72$	−0.142315	−	0.989821i	−0.0167720	−	0.116652i
$73$	−0.0828815	−	0.0956504i	−0.00970055	−	0.0111950i	0.750879	−	0.660440i	$-0.229630\pi$
$73$	−0.0828815	−	0.0956504i	−0.00970055	−	0.0111950i	−0.760579	+	0.649245i	$0.775085\pi$
$74$	5.54371	+	3.56272i	0.644443	+	0.414158i
$75$	−3.73337	−	1.09622i	−0.431092	−	0.126580i
$76$	0.896313	−	6.23400i	0.102814	−	0.715088i
$77$	3.09643	+	6.91799i	0.352871	+	0.788378i
$78$	0.226538	+	1.57561i	0.0256504	+	0.178402i
$79$	1.19217	−	8.29169i	0.134129	−	0.932888i	−0.805963	−	0.591967i	$-0.798352\pi$
$79$	1.19217	−	8.29169i	0.134129	−	0.932888i	0.940092	−	0.340922i	$-0.110739\pi$
$80$	0.885925	−	0.569349i	0.0990494	−	0.0636552i
$81$	1.00000			0.111111
$82$	−3.34979	+	7.33501i	−0.369922	+	0.810016i
$83$	−7.82694	+	9.03277i	−0.859119	+	0.991476i	0.140880	+	0.990027i	$0.455007\pi$
$83$	−7.82694	+	9.03277i	−0.859119	+	0.991476i	−0.999999	+	0.00144900i	$0.999539\pi$
$84$	−0.949330	−	2.07874i	−0.103580	−	0.226809i
$85$	−2.13924	+	4.68427i	−0.232033	+	0.508081i
$86$	−7.02630	−	8.10878i	−0.757665	−	0.874392i
$87$	−0.0196100	+	0.00575801i	−0.00210241	+	0.000617324i
$88$	−3.17513	−	0.958402i	−0.338470	−	0.102166i
$89$	−14.6233	−	4.29379i	−1.55007	−	0.455140i	−0.608945	−	0.793212i	$-0.708407\pi$
$89$	−14.6233	−	4.29379i	−1.55007	−	0.455140i	−0.941120	+	0.338072i	$0.890225\pi$
$90$	0.437474	+	0.957934i	0.0461138	+	0.100975i
$91$	1.51115	+	3.30896i	0.158412	+	0.346873i
$92$	6.74603	−	1.98081i	0.703322	−	0.206514i
$93$	1.08953	+	2.38575i	0.112979	+	0.247390i
$94$	2.49457			0.257296
$95$	0.943908	+	6.56503i	0.0968429	+	0.673557i
$96$	0.959493	+	0.281733i	0.0979278	+	0.0287542i
$97$	−0.0583832	−	0.406064i	−0.00592792	−	0.0412296i	0.986643	−	0.162899i	$-0.0520844\pi$
$97$	−0.0583832	−	0.406064i	−0.00592792	−	0.0412296i	−0.992571	+	0.121669i	$0.961175\pi$
$98$	1.16408	+	1.34342i	0.117590	+	0.135706i
$99$	1.40051	−	3.00642i	0.140757	−	0.302157i
$100$	2.54805	−	2.94061i	0.254805	−	0.294061i
$101$	14.8668	+	9.55433i	1.47930	+	0.950691i	0.997216	+	0.0745689i	$0.0237581\pi$
$101$	14.8668	+	9.55433i	1.47930	+	0.950691i	0.482089	+	0.876122i	$0.339878\pi$
$102$	−4.69189	+	1.37766i	−0.464567	+	0.136409i
$103$	8.24360	−	5.29784i	0.812266	−	0.522011i	−0.0673316	−	0.997731i	$-0.521449\pi$
$103$	8.24360	−	5.29784i	0.812266	−	0.522011i	0.879597	+	0.475719i	$0.157812\pi$
$104$	−1.52733	−	0.448464i	−0.149767	−	0.0439755i
$105$	1.57599	+	1.81879i	0.153801	+	0.177496i
$106$	1.81361	−	12.6139i	0.176153	−	1.22517i
$107$	−1.26036	+	8.76600i	−0.121844	+	0.847441i	0.833621	+	0.552336i	$0.186264\pi$
$107$	−1.26036	+	8.76600i	−0.121844	+	0.847441i	−0.955465	+	0.295104i	$0.904646\pi$
$108$	−0.415415	+	0.909632i	−0.0399733	+	0.0875294i
$109$	−0.611305	+	1.33857i	−0.0585524	+	0.128212i	−0.936646	−	0.350276i	$-0.886088\pi$
$109$	−0.611305	+	1.33857i	−0.0585524	+	0.128212i	0.878094	+	0.478488i	$0.158815\pi$
$110$	3.49264	+	0.0263711i	0.333010	+	0.00251439i
$111$	−2.73751	−	5.99431i	−0.259833	−	0.568955i
$112$	2.28526			0.215936
$113$	2.77899	+	19.3283i	0.261425	+	1.81825i	0.522168	+	0.852842i	$0.325123\pi$
$113$	2.77899	+	19.3283i	0.261425	+	1.81825i	−0.260743	+	0.965408i	$0.583968\pi$
$114$	−4.12438	+	4.75979i	−0.386283	+	0.445795i
$115$	−6.22879	+	4.00300i	−0.580837	+	0.373282i
$116$	0.00290861	−	0.0202298i	0.000270058	−	0.00187829i
$117$	0.661261	−	1.44796i	0.0611336	−	0.133864i
$118$	−12.5274			−1.15324
$119$	−9.40088	+	6.04158i	−0.861777	+	0.553831i
$120$	−1.05310			−0.0961345
$121$	−7.07712	−	8.42107i	−0.643374	−	0.765552i
$122$	4.65521			0.421463
$123$	6.78363	−	4.35957i	0.611659	−	0.393089i
$124$	−2.62276			−0.235531
$125$	−3.88957	+	8.51697i	−0.347894	+	0.761781i
$126$	−0.325226	+	2.26200i	−0.0289734	+	0.201515i
$127$	15.3478	−	9.86344i	1.36190	−	0.875239i	0.363487	−	0.931599i	$-0.381586\pi$
$127$	15.3478	−	9.86344i	1.36190	−	0.875239i	0.998410	+	0.0563606i	$0.0179496\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	1.52696	+	10.6202i	0.134441	+	0.935060i
$130$	1.67633			0.147024
$131$	−0.587406	−	1.28624i	−0.0513219	−	0.112379i	0.882234	−	0.470811i	$-0.156039\pi$
$131$	−0.587406	−	1.28624i	−0.0513219	−	0.112379i	−0.933556	+	0.358432i	$0.883311\pi$
$132$	2.15294	+	2.52286i	0.187389	+	0.219587i
$133$	−5.97898	+	13.0921i	−0.518443	+	1.13523i
$134$	0.814200	−	1.78285i	0.0703362	−	0.154015i
$135$	0.149872	−	1.04238i	0.0128989	−	0.0897139i
$136$	0.695916	−	4.84020i	0.0596743	−	0.415044i
$137$	−14.6802	−	16.9418i	−1.25421	−	1.44744i	−0.844796	−	0.535088i	$-0.820279\pi$
$137$	−14.6802	−	16.9418i	−1.25421	−	1.44744i	−0.409414	−	0.912349i	$-0.634267\pi$
$138$	−6.74603	−	1.98081i	−0.574260	−	0.168618i
$139$	−13.8506	+	8.90121i	−1.17479	+	0.754991i	−0.974421	−	0.224730i	$-0.927850\pi$
$139$	−13.8506	+	8.90121i	−1.17479	+	0.754991i	−0.200368	+	0.979721i	$0.564214\pi$
$140$	−2.30912	+	0.678019i	−0.195156	+	0.0573031i
$141$	−2.09857	−	1.34867i	−0.176731	−	0.113578i
$142$	−7.24641	+	8.36280i	−0.608105	+	0.701791i
$143$	−3.42707	−	4.01592i	−0.286586	−	0.335828i
$144$	−0.654861	−	0.755750i	−0.0545717	−	0.0629791i
$145$	0.00306306	+	0.0213041i	0.000254373	+	0.00176921i
$146$	−0.121437	−	0.0356571i	−0.0100502	−	0.00295100i
$147$	−0.252979	−	1.75951i	−0.0208653	−	0.145122i
$148$	6.58982			0.541680
$149$	0.597305	+	1.30791i	0.0489331	+	0.107149i	0.932520	−	0.361120i	$-0.117605\pi$
$149$	0.597305	+	1.30791i	0.0489331	+	0.107149i	−0.883586	+	0.468268i	$0.844878\pi$
$150$	−3.73337	+	1.09622i	−0.304828	+	0.0895056i
$151$	−2.19907	−	4.81529i	−0.178958	−	0.391863i	0.798801	−	0.601595i	$-0.205468\pi$
$151$	−2.19907	−	4.81529i	−0.178958	−	0.391863i	−0.977759	+	0.209732i	$0.932741\pi$
$152$	−2.61633	−	5.72895i	−0.212212	−	0.464680i
$153$	4.69189	+	1.37766i	0.379317	+	0.111378i
$154$	6.34503	+	4.14573i	0.511297	+	0.334072i
$155$	2.65015	−	0.778154i	0.212865	−	0.0625028i
$156$	1.04241	+	1.20301i	0.0834598	+	0.0963177i
$157$	1.06409	−	2.33002i	0.0849232	−	0.185956i	−0.862406	−	0.506217i	$-0.831043\pi$
$157$	1.06409	−	2.33002i	0.0849232	−	0.185956i	0.947329	+	0.320261i	$0.103771\pi$
$158$	−3.47991	−	7.61995i	−0.276847	−	0.606211i
$159$	−8.34530	+	9.63099i	−0.661825	+	0.763787i
$160$	0.437474	−	0.957934i	0.0345854	−	0.0757314i
$161$	−16.0673			−1.26628
$162$	0.841254	−	0.540641i	0.0660951	−	0.0424768i
$163$	3.29557	−	22.9212i	0.258129	−	1.79533i	−0.288003	−	0.957629i	$-0.592991\pi$
$163$	3.29557	−	22.9212i	0.258129	−	1.79533i	0.546133	−	0.837699i	$-0.316099\pi$
$164$	1.14759	+	7.98163i	0.0896114	+	0.623261i
$165$	−2.92394	−	1.91045i	−0.227628	−	0.148728i
$166$	−1.70096	+	11.8304i	−0.132020	+	0.918218i
$167$	−10.0296	−	2.94495i	−0.776113	−	0.227887i	−0.130394	−	0.991462i	$-0.541624\pi$
$167$	−10.0296	−	2.94495i	−0.776113	−	0.227887i	−0.645719	+	0.763575i	$0.723442\pi$
$168$	−1.92248	−	1.23550i	−0.148323	−	0.0953211i
$169$	6.85387	+	7.90979i	0.527221	+	0.608445i
$170$	0.732869	+	5.09722i	0.0562085	+	0.390939i
$171$	6.04298	−	1.77438i	0.462118	−	0.135690i
$172$	−10.2948	−	3.02284i	−0.784974	−	0.230489i
$173$	2.59426	+	2.99394i	0.197238	+	0.227625i	0.845750	−	0.533580i	$-0.179154\pi$
$173$	2.59426	+	2.99394i	0.197238	+	0.227625i	−0.648512	+	0.761205i	$0.724608\pi$
$174$	−0.0133840	+	0.0154459i	−0.00101464	+	0.00117095i
$175$	−7.48033	+	4.80732i	−0.565460	+	0.363399i
$176$	−3.18924	+	0.910348i	−0.240398	+	0.0686200i
$177$	10.5387	+	6.77284i	0.792141	+	0.509078i
$178$	−14.6233	+	4.29379i	−1.09606	+	0.321833i
$179$	−12.7683	+	14.7354i	−0.954349	+	1.10138i	0.0404155	+	0.999183i	$0.487132\pi$
$179$	−12.7683	+	14.7354i	−0.954349	+	1.10138i	−0.994764	+	0.102194i	$0.967414\pi$
$180$	0.885925	+	0.569349i	0.0660329	+	0.0424368i
$181$	3.96273	+	2.54669i	0.294547	+	0.189294i	0.679565	−	0.733615i	$-0.262168\pi$
$181$	3.96273	+	2.54669i	0.294547	+	0.189294i	−0.385018	+	0.922909i	$0.625805\pi$
$182$	3.06022	+	1.96668i	0.226839	+	0.145780i
$183$	−3.91621	−	2.51679i	−0.289495	−	0.186047i
$184$	4.60421	−	5.31355i	0.339427	−	0.391720i
$185$	−6.65863	+	1.95515i	−0.489552	+	0.143746i
$186$	2.20641	+	1.41797i	0.161781	+	0.103971i
$187$	10.7129	−	12.1764i	0.783405	−	0.890424i
$188$	2.09857	−	1.34867i	0.153054	−	0.0983617i
$189$	1.49653	−	1.72708i	0.108856	−	0.125627i
$190$	4.34339	+	5.01254i	0.315102	+	0.363648i
$191$	11.0370	+	3.24076i	0.798611	+	0.234493i	0.655482	−	0.755211i	$-0.272465\pi$
$191$	11.0370	+	3.24076i	0.798611	+	0.234493i	0.143129	+	0.989704i	$0.454284\pi$
$192$	0.959493	−	0.281733i	0.0692454	−	0.0203323i
$193$	−0.373965	−	2.60099i	−0.0269186	−	0.187223i	0.971926	−	0.235289i	$-0.0756035\pi$
$193$	−0.373965	−	2.60099i	−0.0269186	−	0.187223i	−0.998844	+	0.0480654i	$0.984694\pi$
$194$	−0.268650	−	0.310039i	−0.0192879	−	0.0222595i
$195$	−1.41022	−	0.906294i	−0.100988	−	0.0649011i
$196$	1.70559	+	0.500808i	0.121828	+	0.0357720i
$197$	1.09043	−	7.58409i	0.0776897	−	0.540344i	−0.913391	−	0.407083i	$-0.866546\pi$
$197$	1.09043	−	7.58409i	0.0776897	−	0.540344i	0.991081	−	0.133261i	$-0.0425449\pi$
$198$	−0.447205	−	3.28634i	−0.0317815	−	0.233550i
$199$	1.99541	+	13.8784i	0.141451	+	0.983814i	0.929663	+	0.368410i	$0.120098\pi$
$199$	1.99541	+	13.8784i	0.141451	+	0.983814i	−0.788212	+	0.615404i	$0.788993\pi$
$200$	0.553744	−	3.85137i	0.0391556	−	0.272333i
$201$	−1.64883	+	1.05964i	−0.116300	+	0.0747412i
$202$	17.6722			1.24341
$203$	−0.0194023	+	0.0424851i	−0.00136177	+	0.00298187i
$204$	−3.20225	+	3.69559i	−0.224202	+	0.258743i
$205$	−3.52766	−	7.72451i	−0.246383	−	0.539503i
$206$	4.07073	−	8.91365i	0.283621	−	0.621043i
$207$	4.60421	+	5.31355i	0.320015	+	0.369317i
$208$	−1.52733	+	0.448464i	−0.105901	+	0.0310954i
$209$	3.12876	−	20.6528i	0.216421	−	1.42858i
$210$	2.30912	+	0.678019i	0.159345	+	0.0467878i
$211$	−6.35534	−	13.9162i	−0.437519	−	0.958034i	−0.992047	−	0.125868i	$-0.959828\pi$
$211$	−6.35534	−	13.9162i	−0.437519	−	0.958034i	0.554528	−	0.832165i	$-0.312899\pi$
$212$	−5.29389	−	11.5920i	−0.363586	−	0.796142i
$213$	10.6173	−	3.11753i	0.727488	−	0.213610i
$214$	3.67897	+	8.05583i	0.251489	+	0.550685i
$215$	11.2992			0.770599
$216$	0.142315	+	0.989821i	0.00968330	+	0.0673488i
$217$	5.75089	+	1.68861i	0.390396	+	0.114631i
$218$	0.209424	+	1.45657i	0.0141840	+	0.0986516i
$219$	0.0828815	+	0.0956504i	0.00560062	+	0.00646346i
$220$	2.95245	−	1.86608i	0.199054	−	0.125811i
$221$	5.09737	−	5.88268i	0.342886	−	0.395712i
$222$	−5.54371	−	3.56272i	−0.372069	−	0.239114i
$223$	−10.6464	+	3.12607i	−0.712936	+	0.209337i	−0.618036	−	0.786150i	$-0.712071\pi$
$223$	−10.6464	+	3.12607i	−0.712936	+	0.209337i	−0.0949000	+	0.995487i	$0.530253\pi$
$224$	1.92248	−	1.23550i	0.128451	−	0.0825505i
$225$	3.73337	+	1.09622i	0.248891	+	0.0730810i
$226$	12.7875	+	14.7575i	0.850611	+	0.981657i
$227$	0.288099	−	2.00377i	0.0191218	−	0.132995i	−0.978024	−	0.208491i	$-0.933145\pi$
$227$	0.288099	−	2.00377i	0.0191218	−	0.132995i	0.997146	+	0.0754958i	$0.0240539\pi$
$228$	−0.896313	+	6.23400i	−0.0593598	+	0.412856i
$229$	−5.15274	+	11.2829i	−0.340503	+	0.745597i	−0.999981	−	0.00612618i	$-0.998050\pi$
$229$	−5.15274	+	11.2829i	−0.340503	+	0.745597i	0.659478	+	0.751724i	$0.270777\pi$
$230$	−3.07580	+	6.73507i	−0.202813	+	0.444098i
$231$	−3.09643	−	6.91799i	−0.203730	−	0.455170i
$232$	−0.00849020	−	0.0185909i	−0.000557409	−	0.00122055i
$233$	5.31038			0.347895			0.173947	−	0.984755i	$-0.444348\pi$
$233$	5.31038			0.347895			0.173947	+	0.984755i	$0.444348\pi$
$234$	−0.226538	−	1.57561i	−0.0148092	−	0.103001i
$235$	−1.72034	+	1.98538i	−0.112223	+	0.129512i
$236$	−10.5387	+	6.77284i	−0.686014	+	0.440874i
$237$	−1.19217	+	8.29169i	−0.0774395	+	0.538603i
$238$	−4.64220	+	10.1650i	−0.300909	+	0.658899i
$239$	−18.0354			−1.16662			−0.583308	−	0.812251i	$-0.698242\pi$
$239$	−18.0354			−1.16662			−0.583308	+	0.812251i	$0.698242\pi$
$240$	−0.885925	+	0.569349i	−0.0571862	+	0.0367513i
$241$	17.9946			1.15913			0.579566	−	0.814925i	$-0.303222\pi$
$241$	17.9946			1.15913			0.579566	+	0.814925i	$0.303222\pi$
$242$	−10.5064	−	3.25808i	−0.675378	−	0.209437i
$243$	−1.00000			−0.0641500
$244$	3.91621	−	2.51679i	0.250710	−	0.161121i
$245$	−1.87199			−0.119597
$246$	3.34979	−	7.33501i	0.213575	−	0.467663i
$247$	1.42676	−	9.92332i	0.0907824	−	0.631406i
$248$	−2.20641	+	1.41797i	−0.140107	+	0.0900412i
$249$	7.82694	−	9.03277i	0.496012	−	0.572429i
$250$	1.33251	+	9.26779i	0.0842752	+	0.586147i
$251$	3.45930			0.218349			0.109174	−	0.994023i	$-0.465179\pi$
$251$	3.45930			0.218349			0.109174	+	0.994023i	$0.465179\pi$
$252$	0.949330	+	2.07874i	0.0598022	+	0.130948i
$253$	22.4230	−	6.40050i	1.40972	−	0.402396i
$254$	7.57882	−	16.5953i	0.475538	−	1.04128i
$255$	2.13924	−	4.68427i	0.133964	−	0.293341i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−0.801722	+	5.57610i	−0.0500100	+	0.347827i	0.949418	+	0.314015i	$0.101674\pi$
$257$	−0.801722	+	5.57610i	−0.0500100	+	0.347827i	−0.999428	+	0.0338128i	$0.989235\pi$
$258$	7.02630	+	8.10878i	0.437438	+	0.504831i
$259$	−14.4494	−	4.24273i	−0.897843	−	0.263630i
$260$	1.41022	−	0.906294i	0.0874582	−	0.0562060i
$261$	0.0196100	−	0.00575801i	0.00121383	−	0.000356412i
$262$	−1.18955	−	0.764478i	−0.0734907	−	0.0472296i
$263$	−4.35839	+	5.02984i	−0.268750	+	0.310154i	−0.874043	−	0.485849i	$-0.838510\pi$
$263$	−4.35839	+	5.02984i	−0.268750	+	0.310154i	0.605293	+	0.796003i	$0.293056\pi$
$264$	3.17513	+	0.958402i	0.195416	+	0.0589855i
$265$	8.78844	+	10.1424i	0.539870	+	0.623043i
$266$	2.04831	+	14.2463i	0.125590	+	0.873496i
$267$	14.6233	+	4.29379i	0.894931	+	0.262775i
$268$	−0.278933	−	1.94002i	−0.0170385	−	0.118506i
$269$	−14.2934			−0.871484			−0.435742	−	0.900071i	$-0.643514\pi$
$269$	−14.2934			−0.871484			−0.435742	+	0.900071i	$0.643514\pi$
$270$	−0.437474	−	0.957934i	−0.0266238	−	0.0582980i
$271$	−8.30251	+	2.43784i	−0.504341	+	0.148088i	−0.523999	−	0.851719i	$-0.675561\pi$
$271$	−8.30251	+	2.43784i	−0.504341	+	0.148088i	0.0196578	+	0.999807i	$0.493742\pi$
$272$	−2.03137	−	4.44808i	−0.123170	−	0.269704i
$273$	−1.51115	−	3.30896i	−0.0914590	−	0.200267i
$274$	−21.5092	−	6.31566i	−1.29942	−	0.381543i
$275$	8.52432	−	9.68880i	0.514036	−	0.584257i
$276$	−6.74603	+	1.98081i	−0.406063	+	0.119231i
$277$	11.1896	+	12.9135i	0.672316	+	0.775894i	0.984737	−	0.174050i	$-0.0556853\pi$
$277$	11.1896	+	12.9135i	0.672316	+	0.775894i	−0.312421	+	0.949944i	$0.601140\pi$
$278$	−6.83947	+	14.9764i	−0.410204	+	0.898222i
$279$	−1.08953	−	2.38575i	−0.0652287	−	0.142831i
$280$	−1.57599	+	1.81879i	−0.0941835	+	0.108694i
$281$	3.66141	−	8.01738i	0.218422	−	0.478277i	−0.768424	−	0.639941i	$-0.778959\pi$
$281$	3.66141	−	8.01738i	0.218422	−	0.478277i	0.986846	+	0.161664i	$0.0516861\pi$
$282$	−2.49457			−0.148550
$283$	15.4676	−	9.94043i	0.919454	−	0.590897i	0.00695485	−	0.999976i	$-0.497786\pi$
$283$	15.4676	−	9.94043i	0.919454	−	0.590897i	0.912499	+	0.409079i	$0.134150\pi$
$284$	−1.57480	+	10.9529i	−0.0934469	+	0.649938i
$285$	−0.943908	−	6.56503i	−0.0559123	−	0.388879i
$286$	−5.05420	−	1.52559i	−0.298861	−	0.0902101i
$287$	2.62253	−	18.2401i	0.154803	−	1.07668i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	5.81461	+	3.73682i	0.342036	+	0.219813i
$290$	0.0140947	+	0.0162661i	0.000827667	+	0.000955178i
$291$	0.0583832	+	0.406064i	0.00342248	+	0.0238039i
$292$	−0.121437	+	0.0356571i	−0.00710656	+	0.00208667i
$293$	14.7637	+	4.33502i	0.862506	+	0.253255i	0.682925	−	0.730489i	$-0.260708\pi$
$293$	14.7637	+	4.33502i	0.862506	+	0.253255i	0.179581	+	0.983743i	$0.442526\pi$
$294$	−1.16408	−	1.34342i	−0.0678906	−	0.0783499i
$295$	8.63935	−	9.97034i	0.503002	−	0.580495i
$296$	5.54371	−	3.56272i	0.322221	−	0.207079i
$297$	−1.40051	+	3.00642i	−0.0812661	+	0.174450i
$298$	1.20960	+	0.777361i	0.0700701	+	0.0450313i
$299$	10.7384	−	3.15307i	0.621017	−	0.182347i
$300$	−2.54805	+	2.94061i	−0.147112	+	0.169776i
$301$	20.6272	+	13.2563i	1.18893	+	0.764079i
$302$	−4.45332	−	2.86197i	−0.256260	−	0.164688i
$303$	−14.8668	−	9.55433i	−0.854077	−	0.548882i
$304$	−5.29830	−	3.40501i	−0.303878	−	0.195291i
$305$	−3.21039	+	3.70499i	−0.183826	+	0.212147i
$306$	4.69189	−	1.37766i	0.268218	−	0.0787558i
$307$	17.9566	+	11.5400i	1.02483	+	0.658621i	0.941191	−	0.337875i	$-0.109708\pi$
$307$	17.9566	+	11.5400i	1.02483	+	0.658621i	0.0836434	+	0.996496i	$0.473344\pi$
$308$	7.57912	+	0.0572260i	0.431861	+	0.00326076i
$309$	−8.24360	+	5.29784i	−0.468962	+	0.301383i
$310$	1.80875	−	2.08740i	0.102730	−	0.118557i
$311$	11.3406	+	13.0878i	0.643068	+	0.742140i	0.979914	−	0.199420i	$-0.0639057\pi$
$311$	11.3406	+	13.0878i	0.643068	+	0.742140i	−0.336846	+	0.941560i	$0.609360\pi$
$312$	1.52733	+	0.448464i	0.0864679	+	0.0253893i
$313$	−29.3850	+	8.62821i	−1.66094	+	0.487695i	−0.971577	−	0.236723i	$-0.923927\pi$
$313$	−29.3850	+	8.62821i	−1.66094	+	0.487695i	−0.689361	+	0.724418i	$0.742108\pi$
$314$	−0.364539	−	2.53543i	−0.0205721	−	0.143082i
$315$	−1.57599	−	1.81879i	−0.0887971	−	0.102477i
$316$	−7.04715	−	4.52893i	−0.396433	−	0.254772i
$317$	−27.3806	−	8.03966i	−1.53785	−	0.451552i	−0.600405	−	0.799696i	$-0.704994\pi$
$317$	−27.3806	−	8.03966i	−1.53785	−	0.451552i	−0.937441	+	0.348144i	$0.886812\pi$
$318$	−1.81361	+	12.6139i	−0.101702	+	0.707353i
$319$	0.0101531	−	0.0670200i	0.000568464	−	0.00375240i
$320$	−0.149872	−	1.04238i	−0.00837809	−	0.0582709i
$321$	1.26036	−	8.76600i	0.0703464	−	0.489270i
$322$	−13.5166	+	8.68661i	−0.753253	+	0.484086i
$323$	30.7975			1.71362
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	4.05600	−	4.68088i	0.224987	−	0.259648i
$326$	−9.61973	−	21.0643i	−0.532788	−	1.16664i
$327$	0.611305	−	1.33857i	0.0338052	−	0.0740231i
$328$	5.28061	+	6.09415i	0.291573	+	0.336493i
$329$	−5.46982	+	1.60608i	−0.301561	+	0.0885463i
$330$	−3.49264	−	0.0263711i	−0.192264	−	0.00145168i
$331$	−14.1418	−	4.15241i	−0.777305	−	0.228237i	−0.131067	−	0.991373i	$-0.541840\pi$
$331$	−14.1418	−	4.15241i	−0.777305	−	0.228237i	−0.646238	+	0.763136i	$0.723659\pi$
$332$	4.96507	+	10.8720i	0.272494	+	0.596678i
$333$	2.73751	+	5.99431i	0.150015	+	0.328486i
$334$	−10.0296	+	2.94495i	−0.548794	+	0.161141i
$335$	0.857435	+	1.87752i	0.0468467	+	0.102580i
$336$	−2.28526			−0.124671
$337$	−4.86734	−	33.8531i	−0.265141	−	1.84409i	−0.492537	−	0.870291i	$-0.663930\pi$
$337$	−4.86734	−	33.8531i	−0.265141	−	1.84409i	0.227397	−	0.973802i	$-0.426979\pi$
$338$	10.0422	+	2.94866i	0.546223	+	0.160386i
$339$	−2.77899	−	19.3283i	−0.150934	−	1.04977i
$340$	3.37229	+	3.89183i	0.182888	+	0.211064i
$341$	−8.69846	−	0.0656775i	−0.471048	−	0.00355664i
$342$	4.12438	−	4.75979i	0.223021	−	0.257380i
$343$	−16.8748	−	10.8448i	−0.911152	−	0.585562i
$344$	−10.2948	+	3.02284i	−0.555060	+	0.162980i
$345$	6.22879	−	4.00300i	0.335347	−	0.215514i
$346$	3.80108	+	1.11610i	0.204347	+	0.0600017i
$347$	−6.78023	−	7.82481i	−0.363982	−	0.420058i	0.543988	−	0.839093i	$-0.316914\pi$
$347$	−6.78023	−	7.82481i	−0.363982	−	0.420058i	−0.907970	+	0.419035i	$0.862368\pi$
$348$	−0.00290861	+	0.0202298i	−0.000155918	+	0.00108443i
$349$	−0.0575225	+	0.400078i	−0.00307911	+	0.0214157i	−0.991303	−	0.131599i	$-0.957989\pi$
$349$	−0.0575225	+	0.400078i	−0.00307911	+	0.0214157i	0.988224	+	0.153014i	$0.0488981\pi$
$350$	−3.69382	+	8.08834i	−0.197443	+	0.432340i
$351$	−0.661261	+	1.44796i	−0.0352955	+	0.0772863i
$352$	−2.19079	+	2.49007i	−0.116770	+	0.132721i
$353$	6.57234	+	14.3914i	0.349810	+	0.765978i	0.999981	+	0.00618951i	$0.00197020\pi$
$353$	6.57234	+	14.3914i	0.349810	+	0.765978i	−0.650170	+	0.759788i	$0.725303\pi$
$354$	12.5274			0.665825
$355$	−1.65842	−	11.5346i	−0.0880197	−	0.612191i
$356$	−9.98050	+	11.5181i	−0.528965	+	0.610459i
$357$	9.40088	−	6.04158i	0.497547	−	0.319754i
$358$	−2.77482	+	19.2993i	−0.146654	+	1.02000i
$359$	6.90212	−	15.1135i	0.364280	−	0.797662i	−0.635396	−	0.772187i	$-0.719163\pi$
$359$	6.90212	−	15.1135i	0.364280	−	0.797662i	0.999675	−	0.0254750i	$-0.00810981\pi$
$360$	1.05310			0.0555033
$361$	17.3854	−	11.1729i	0.915021	−	0.588049i
$362$	4.71050			0.247579
$363$	7.07712	+	8.42107i	0.371452	+	0.441992i
$364$	3.63769			0.190667
$365$	0.112126	−	0.0720589i	0.00586894	−	0.00377174i
$366$	−4.65521			−0.243332
$367$	0.628885	−	1.37707i	0.0328275	−	0.0718823i	−0.892508	−	0.451032i	$-0.851056\pi$
$367$	0.628885	−	1.37707i	0.0328275	−	0.0718823i	0.925335	+	0.379149i	$0.123783\pi$
$368$	1.00059	−	6.95927i	0.0521594	−	0.362777i
$369$	−6.78363	+	4.35957i	−0.353141	+	0.226950i
$370$	−4.54456	+	5.24471i	−0.236261	+	0.272659i
$371$	4.14456	+	28.8260i	0.215175	+	1.49657i
$372$	2.62276			0.135984
$373$	6.47808	+	14.1850i	0.335422	+	0.734472i	0.999918	−	0.0128202i	$-0.00408092\pi$
$373$	6.47808	+	14.1850i	0.335422	+	0.734472i	−0.664496	+	0.747292i	$0.731354\pi$
$374$	2.42923	−	16.0352i	0.125613	−	0.829163i
$375$	3.88957	−	8.51697i	0.200857	−	0.439815i
$376$	1.03628	−	2.26914i	0.0534422	−	0.117022i
$377$	0.00462995	−	0.0322020i	0.000238455	−	0.00165849i
$378$	0.325226	−	2.26200i	0.0167278	−	0.116345i
$379$	−10.4783	−	12.0926i	−0.538236	−	0.621157i	0.419866	−	0.907586i	$-0.362077\pi$
$379$	−10.4783	−	12.0926i	−0.538236	−	0.621157i	−0.958101	+	0.286429i	$0.907532\pi$
$380$	6.36387	+	1.86860i	0.326460	+	0.0958572i
$381$	−15.3478	+	9.86344i	−0.786292	+	0.505319i
$382$	11.0370	−	3.24076i	0.564703	−	0.165812i
$383$	−27.4365	−	17.6324i	−1.40194	−	0.900972i	−0.402047	−	0.915619i	$-0.631701\pi$
$383$	−27.4365	−	17.6324i	−1.40194	−	0.900972i	−0.999893	+	0.0146471i	$0.995338\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−7.67525	+	2.19085i	−0.391167	+	0.111656i
$386$	−1.72080	−	1.98591i	−0.0875864	−	0.101080i
$387$	−1.52696	−	10.6202i	−0.0776198	−	0.539857i
$388$	−0.393622	−	0.115578i	−0.0199831	−	0.00586758i
$389$	−2.58066	−	17.9489i	−0.130845	−	0.910046i	−0.944456	−	0.328637i	$-0.893411\pi$
$389$	−2.58066	−	17.9489i	−0.130845	−	0.910046i	0.813611	−	0.581409i	$-0.197498\pi$
$390$	−1.67633			−0.0848845
$391$	14.2822	+	31.2737i	0.722282	+	1.58158i
$392$	1.70559	−	0.500808i	0.0861455	−	0.0252946i
$393$	0.587406	+	1.28624i	0.0296307	+	0.0648822i
$394$	−3.18294	−	6.96967i	−0.160354	−	0.351127i
$395$	8.46444	+	2.48538i	0.425892	+	0.125053i
$396$	−2.15294	−	2.52286i	−0.108189	−	0.126779i
$397$	−30.9562	+	9.08955i	−1.55364	+	0.456191i	−0.942188	−	0.335086i	$-0.891235\pi$
$397$	−30.9562	+	9.08955i	−1.55364	+	0.456191i	−0.611457	+	0.791277i	$0.709416\pi$
$398$	9.18188	+	10.5965i	0.460246	+	0.531152i
$399$	5.97898	−	13.0921i	0.299323	−	0.655426i
$400$	−1.61637	−	3.53936i	−0.0808185	−	0.176968i
$401$	−3.42858	+	3.95680i	−0.171215	+	0.197593i	−0.834872	−	0.550445i	$-0.814458\pi$
$401$	−3.42858	+	3.95680i	−0.171215	+	0.197593i	0.663656	+	0.748038i	$0.269004\pi$
$402$	−0.814200	+	1.78285i	−0.0406086	+	0.0889205i
$403$	−4.17493			−0.207968
$404$	14.8668	−	9.55433i	0.739652	−	0.475346i
$405$	−0.149872	+	1.04238i	−0.00744719	+	0.0517964i
$406$	0.00664693	+	0.0462304i	0.000329881	+	0.00229438i
$407$	21.8553	+	0.165018i	1.08333	+	0.00817965i
$408$	−0.695916	+	4.84020i	−0.0344530	+	0.239626i
$409$	−28.1012	−	8.25126i	−1.38952	−	0.407999i	−0.500445	−	0.865768i	$-0.666830\pi$
$409$	−28.1012	−	8.25126i	−1.38952	−	0.407999i	−0.889071	+	0.457770i	$0.848648\pi$
$410$	−7.14384	−	4.59107i	−0.352809	−	0.226737i
$411$	14.6802	+	16.9418i	0.724119	+	0.835678i
$412$	−1.39457	−	9.69944i	−0.0687055	−	0.477857i
$413$	27.4687	−	8.06555i	1.35165	−	0.396880i
$414$	6.74603	+	1.98081i	0.331549	+	0.0973517i
$415$	−8.24256	−	9.51242i	−0.404611	−	0.466946i
$416$	−1.04241	+	1.20301i	−0.0511085	+	0.0589823i
$417$	13.8506	−	8.90121i	0.678265	−	0.435894i
$418$	−8.53366	−	19.0658i	−0.417395	−	0.932537i
$419$	−4.36452	−	2.80491i	−0.213221	−	0.137029i	0.429671	−	0.902985i	$-0.358629\pi$
$419$	−4.36452	−	2.80491i	−0.213221	−	0.137029i	−0.642892	+	0.765957i	$0.722266\pi$
$420$	2.30912	−	0.678019i	0.112674	−	0.0330840i
$421$	13.9424	−	16.0904i	0.679511	−	0.784197i	−0.306322	−	0.951928i	$-0.599098\pi$
$421$	13.9424	−	16.0904i	0.679511	−	0.784197i	0.985833	+	0.167730i	$0.0536438\pi$
$422$	−12.8701	−	8.27114i	−0.626509	−	0.402633i
$423$	2.09857	+	1.34867i	0.102036	+	0.0655745i
$424$	−10.7206	−	6.88972i	−0.520639	−	0.334595i
$425$	16.0063	+	10.2867i	0.776422	+	0.498976i
$426$	7.24641	−	8.36280i	0.351090	−	0.405179i
$427$	−10.2074	+	2.99717i	−0.493972	+	0.145043i
$428$	7.45026	+	4.78799i	0.360122	+	0.231436i
$429$	3.42707	+	4.01592i	0.165460	+	0.193890i
$430$	9.50549	−	6.10881i	0.458395	−	0.294593i
$431$	20.0185	−	23.1025i	0.964256	−	1.11281i	−0.0293117	−	0.999570i	$-0.509332\pi$
$431$	20.0185	−	23.1025i	0.964256	−	1.11281i	0.993568	−	0.113240i	$-0.0361230\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	−10.7818	−	3.16581i	−0.518139	−	0.152139i	0.0121991	−	0.999926i	$-0.496117\pi$
$433$	−10.7818	−	3.16581i	−0.518139	−	0.152139i	−0.530338	+	0.847786i	$0.677935\pi$
$434$	5.75089	−	1.68861i	0.276052	−	0.0810561i
$435$	−0.00306306	−	0.0213041i	−0.000146863	−	0.00102145i
$436$	0.963662	+	1.11212i	0.0461510	+	0.0532611i
$437$	37.2514	+	23.9400i	1.78198	+	1.14521i
$438$	0.121437	+	0.0356571i	0.00580248	+	0.00170376i
$439$	0.419740	−	2.91935i	0.0200331	−	0.139333i	−0.977350	−	0.211628i	$-0.932123\pi$
$439$	0.419740	−	2.91935i	0.0200331	−	0.139333i	0.997383	+	0.0722953i	$0.0230324\pi$
$440$	1.47488	−	3.16606i	0.0703123	−	0.150936i
$441$	0.252979	+	1.75951i	0.0120466	+	0.0837860i
$442$	1.10776	−	7.70467i	0.0526909	−	0.366474i
$443$	1.27497	−	0.819373i	0.0605756	−	0.0389296i	−0.510003	−	0.860173i	$-0.670356\pi$
$443$	1.27497	−	0.819373i	0.0605756	−	0.0389296i	0.570578	+	0.821243i	$0.306719\pi$
$444$	−6.58982			−0.312739
$445$	6.66738	−	14.5995i	0.316064	−	0.692084i
$446$	−7.26624	+	8.38569i	−0.344067	+	0.397074i
$447$	−0.597305	−	1.30791i	−0.0282515	−	0.0618622i
$448$	0.949330	−	2.07874i	0.0448516	−	0.0982114i
$449$	−8.79025	−	10.1445i	−0.414837	−	0.478748i	0.509420	−	0.860518i	$-0.329860\pi$
$449$	−8.79025	−	10.1445i	−0.414837	−	0.478748i	−0.924257	+	0.381770i	$0.875315\pi$
$450$	3.73337	−	1.09622i	0.175993	−	0.0516761i
$451$	3.60613	+	26.5001i	0.169806	+	1.24784i
$452$	18.7360	+	5.50140i	0.881269	+	0.258764i
$453$	2.19907	+	4.81529i	0.103321	+	0.226242i
$454$	−0.840957	−	1.84144i	−0.0394681	−	0.0864230i
$455$	−3.67568	+	1.07928i	−0.172318	+	0.0505972i
$456$	2.61633	+	5.72895i	0.122521	+	0.268283i
$457$	−9.62970			−0.450458			−0.225229	−	0.974306i	$-0.572313\pi$
$457$	−9.62970			−0.450458			−0.225229	+	0.974306i	$0.572313\pi$
$458$	1.76525	+	12.2776i	0.0824848	+	0.573694i
$459$	−4.69189	−	1.37766i	−0.218999	−	0.0643039i
$460$	1.05372	+	7.32881i	0.0491301	+	0.341708i
$461$	12.7656	+	14.7323i	0.594552	+	0.686150i	0.970668	−	0.240423i	$-0.0772861\pi$
$461$	12.7656	+	14.7323i	0.594552	+	0.686150i	−0.376116	+	0.926573i	$0.622741\pi$
$462$	−6.34503	−	4.14573i	−0.295197	−	0.192877i
$463$	−23.5757	+	27.2078i	−1.09565	+	1.26445i	−0.133766	+	0.991013i	$0.542707\pi$
$463$	−23.5757	+	27.2078i	−1.09565	+	1.26445i	−0.961889	+	0.273440i	$0.911839\pi$
$464$	−0.0171934	−	0.0110495i	−0.000798185	−	0.000512962i
$465$	−2.65015	+	0.778154i	−0.122898	+	0.0360860i
$466$	4.46738	−	2.87101i	0.206947	−	0.132997i
$467$	0.176766	+	0.0519033i	0.00817977	+	0.00240180i	0.285820	−	0.958283i	$-0.407734\pi$
$467$	0.176766	+	0.0519033i	0.00817977	+	0.00240180i	−0.277640	+	0.960685i	$0.589552\pi$
$468$	−1.04241	−	1.20301i	−0.0481855	−	0.0556091i
$469$	−0.637433	+	4.43344i	−0.0294339	+	0.204717i
$470$	−0.373866	+	2.60030i	−0.0172452	+	0.119943i
$471$	−1.06409	+	2.33002i	−0.0490305	+	0.107362i
$472$	−5.20408	+	11.3954i	−0.239537	+	0.524514i
$473$	−34.0674	−	10.2831i	−1.56642	−	0.472819i
$474$	3.47991	+	7.61995i	0.159838	+	0.349996i
$475$	24.5058			1.12440
$476$	1.59035	+	11.0611i	0.0728934	+	0.506985i
$477$	8.34530	−	9.63099i	0.382105	−	0.440973i
$478$	−15.1724	+	9.75070i	−0.693969	+	0.445987i
$479$	0.988380	−	6.87433i	0.0451602	−	0.314096i	−0.954703	−	0.297560i	$-0.903827\pi$
$479$	0.988380	−	6.87433i	0.0451602	−	0.314096i	0.999863	−	0.0165360i	$-0.00526381\pi$
$480$	−0.437474	+	0.957934i	−0.0199679	+	0.0437235i
$481$	10.4897			0.478290
$482$	15.1380	−	9.72860i	0.689517	−	0.443126i
$483$	16.0673			0.731085
$484$	−10.6000	+	2.93933i	−0.481819	+	0.133606i
$485$	0.432024			0.0196172
$486$	−0.841254	+	0.540641i	−0.0381600	+	0.0245240i
$487$	−4.80661			−0.217808			−0.108904	−	0.994052i	$-0.534734\pi$
$487$	−4.80661			−0.217808			−0.108904	+	0.994052i	$0.534734\pi$
$488$	1.93384	−	4.23453i	0.0875410	−	0.191688i
$489$	−3.29557	+	22.9212i	−0.149031	+	1.03653i
$490$	−1.57482	+	1.01208i	−0.0711431	+	0.0457209i
$491$	−6.47179	+	7.46884i	−0.292068	+	0.337064i	−0.882752	−	0.469838i	$-0.844312\pi$
$491$	−6.47179	+	7.46884i	−0.292068	+	0.337064i	0.590685	+	0.806902i	$0.298858\pi$
$492$	−1.14759	−	7.98163i	−0.0517372	−	0.359840i
$493$	0.0999406			0.00450110
$494$	−4.16469	−	9.11939i	−0.187378	−	0.410301i
$495$	2.92394	+	1.91045i	0.131421	+	0.0858683i
$496$	−1.08953	+	2.38575i	−0.0489215	+	0.107123i
$497$	10.5049	−	23.0025i	0.471208	−	1.03180i
$498$	1.70096	−	11.8304i	0.0762217	−	0.530134i
$499$	−4.10619	+	28.5592i	−0.183818	+	1.27848i	0.663813	+	0.747899i	$0.268937\pi$
$499$	−4.10619	+	28.5592i	−0.183818	+	1.27848i	−0.847631	+	0.530586i	$0.821972\pi$
$500$	6.13152	+	7.07616i	0.274210	+	0.316455i
$501$	10.0296	+	2.94495i	0.448089	+	0.131571i
$502$	2.91015	−	1.87024i	0.129886	−	0.0834728i
$503$	13.2472	−	3.88972i	0.590662	−	0.173434i	0.0272759	−	0.999628i	$-0.491317\pi$
$503$	13.2472	−	3.88972i	0.590662	−	0.173434i	0.563386	+	0.826194i	$0.309499\pi$
$504$	1.92248	+	1.23550i	0.0856341	+	0.0550337i
$505$	−12.1874	+	14.0650i	−0.542331	+	0.625884i
$506$	15.4031	−	17.5072i	0.684750	−	0.778292i
$507$	−6.85387	−	7.90979i	−0.304391	−	0.351286i
$508$	−2.59639	−	18.0583i	−0.115196	−	0.801207i
$509$	1.52835	+	0.448764i	0.0677429	+	0.0198911i	0.315428	−	0.948949i	$-0.397852\pi$
$509$	1.52835	+	0.448764i	0.0677429	+	0.0198911i	−0.247686	+	0.968840i	$0.579670\pi$
$510$	−0.732869	−	5.09722i	−0.0324520	−	0.225709i
$511$	0.289230			0.0127948
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−6.04298	+	1.77438i	−0.266804	+	0.0783408i
$514$	2.34021	+	5.12435i	0.103222	+	0.226026i
$515$	4.28689	+	9.38697i	0.188903	+	0.413639i
$516$	10.2948	+	3.02284i	0.453205	+	0.133073i
$517$	6.99374	−	4.42035i	0.307584	−	0.194407i
$518$	−14.4494	+	4.24273i	−0.634871	+	0.186415i
$519$	−2.59426	−	2.99394i	−0.113875	−	0.131419i
$520$	0.696374	−	1.52485i	0.0305380	−	0.0668690i
$521$	−2.17817	−	4.76954i	−0.0954276	−	0.208957i	0.855898	−	0.517144i	$-0.173005\pi$
$521$	−2.17817	−	4.76954i	−0.0954276	−	0.208957i	−0.951326	+	0.308187i	$0.900278\pi$
$522$	0.0133840	−	0.0154459i	0.000585800	−	0.000676049i
$523$	17.9660	−	39.3400i	0.785597	−	1.72022i	0.0967525	−	0.995308i	$-0.469154\pi$
$523$	17.9660	−	39.3400i	0.785597	−	1.72022i	0.688845	−	0.724909i	$-0.258118\pi$
$524$	−1.41402			−0.0617718
$525$	7.48033	−	4.80732i	0.326468	−	0.209808i
$526$	−0.947168	+	6.58770i	−0.0412985	+	0.287237i
$527$	−1.82522	−	12.6947i	−0.0795078	−	0.552989i
$528$	3.18924	−	0.910348i	0.138794	−	0.0396178i
$529$	−3.76175	+	26.1635i	−0.163554	+	1.13754i
$530$	12.8767	+	3.78094i	0.559328	+	0.164234i
$531$	−10.5387	−	6.77284i	−0.457343	−	0.293916i
$532$	9.42527	+	10.8773i	0.408637	+	0.471592i
$533$	1.82674	+	12.7052i	0.0791247	+	0.550324i
$534$	14.6233	−	4.29379i	0.632812	−	0.185810i
$535$	−8.94862	−	2.62755i	−0.386883	−	0.113599i
$536$	−1.28351	−	1.48125i	−0.0554390	−	0.0639801i
$537$	12.7683	−	14.7354i	0.550994	−	0.635881i
$538$	−12.0244	+	7.72760i	−0.518408	+	0.333160i
$539$	5.64412	+	1.70365i	0.243109	+	0.0733816i
$540$	−0.885925	−	0.569349i	−0.0381241	−	0.0245009i
$541$	31.2456	−	9.17455i	1.34335	−	0.394445i	0.470489	−	0.882406i	$-0.344077\pi$
$541$	31.2456	−	9.17455i	1.34335	−	0.394445i	0.872865	+	0.487961i	$0.162259\pi$
$542$	−5.66652	+	6.53951i	−0.243398	+	0.280896i
$543$	−3.96273	−	2.54669i	−0.170057	−	0.109289i
$544$	−4.11371	−	2.64372i	−0.176374	−	0.113349i
$545$	−1.30368	−	0.837827i	−0.0558437	−	0.0358886i
$546$	−3.06022	−	1.96668i	−0.130965	−	0.0841663i
$547$	−2.24778	+	2.59407i	−0.0961081	+	0.110915i	−0.801766	−	0.597638i	$-0.796106\pi$
$547$	−2.24778	+	2.59407i	−0.0961081	+	0.110915i	0.705658	+	0.708553i	$0.250651\pi$
$548$	−21.5092	+	6.31566i	−0.918826	+	0.269792i
$549$	3.91621	+	2.51679i	0.167140	+	0.107414i
$550$	1.93295	−	12.7593i	0.0824214	−	0.544060i
$551$	0.108286	−	0.0695912i	0.00461314	−	0.00296468i
$552$	−4.60421	+	5.31355i	−0.195968	+	0.226160i
$553$	12.5363	+	14.4677i	0.533099	+	0.615229i
$554$	16.3948	+	4.81395i	0.696549	+	0.204525i
$555$	6.65863	−	1.95515i	0.282643	−	0.0829915i
$556$	2.34310	+	16.2966i	0.0993695	+	0.691130i
$557$	26.6535	+	30.7597i	1.12934	+	1.30333i	0.947410	+	0.320021i	$0.103690\pi$
$557$	26.6535	+	30.7597i	1.12934	+	1.30333i	0.181933	+	0.983311i	$0.441765\pi$
$558$	−2.20641	−	1.41797i	−0.0934046	−	0.0600275i
$559$	−16.3874	−	4.81177i	−0.693113	−	0.203516i
$560$	−0.342496	+	2.38211i	−0.0144731	+	0.100663i
$561$	−10.7129	+	12.1764i	−0.452299	+	0.514086i
$562$	−1.25434	−	8.72416i	−0.0529113	−	0.368006i
$563$	0.127279	−	0.885248i	0.00536419	−	0.0373087i	−0.986964	−	0.160944i	$-0.948546\pi$
$563$	0.127279	−	0.885248i	0.00536419	−	0.0373087i	0.992328	+	0.123635i	$0.0394553\pi$
$564$	−2.09857	+	1.34867i	−0.0883657	+	0.0567892i
$565$	−20.5639			−0.865131
$566$	7.63798	−	16.7248i	0.321048	−	0.702998i
$567$	−1.49653	+	1.72708i	−0.0628481	+	0.0725306i
$568$	4.59681	+	10.0656i	0.192878	+	0.422343i
$569$	−3.55445	+	7.78317i	−0.149010	+	0.326287i	−0.969388	−	0.245535i	$-0.921036\pi$
$569$	−3.55445	+	7.78317i	−0.149010	+	0.326287i	0.820377	+	0.571823i	$0.193764\pi$
$570$	−4.34339	−	5.01254i	−0.181924	−	0.209952i
$571$	−28.4857	+	8.36416i	−1.19209	+	0.350029i	−0.816823	−	0.576888i	$-0.804267\pi$
$571$	−28.4857	+	8.36416i	−1.19209	+	0.350029i	−0.375266	+	0.926917i	$0.622449\pi$
$572$	−5.07666	+	1.44910i	−0.212266	+	0.0605898i
$573$	−11.0370	−	3.24076i	−0.461078	−	0.135385i
$574$	−7.65512	−	16.7624i	−0.319519	−	0.699648i
$575$	11.3644	+	24.8846i	0.473929	+	1.03776i
$576$	−0.959493	+	0.281733i	−0.0399789	+	0.0117389i
$577$	−3.44023	−	7.53306i	−0.143219	−	0.313605i	0.824406	−	0.565999i	$-0.191509\pi$
$577$	−3.44023	−	7.53306i	−0.143219	−	0.313605i	−0.967625	+	0.252394i	$0.918782\pi$
$578$	6.91184			0.287494
$579$	0.373965	+	2.60099i	0.0155415	+	0.108093i
$580$	0.0206513	+	0.00606377i	0.000857499	+	0.000251784i
$581$	−3.88712	−	27.0355i	−0.161265	−	1.12162i
$582$	0.268650	+	0.310039i	0.0111359	+	0.0128515i
$583$	−17.2671	−	38.5778i	−0.715129	−	1.59773i
$584$	−0.0828815	+	0.0956504i	−0.00342966	+	0.00395804i
$585$	1.41022	+	0.906294i	0.0583055	+	0.0374707i
$586$	14.7637	−	4.33502i	0.609884	−	0.179078i
$587$	28.4396	−	18.2770i	1.17383	−	0.754373i	0.199586	−	0.979880i	$-0.436040\pi$
$587$	28.4396	−	18.2770i	1.17383	−	0.754373i	0.974242	+	0.225507i	$0.0724038\pi$
$588$	−1.70559	−	0.500808i	−0.0703375	−	0.0206530i
$589$	−10.8173	−	12.4838i	−0.445717	−	0.514385i
$590$	1.87751	−	13.0584i	0.0772958	−	0.537604i
$591$	−1.09043	+	7.58409i	−0.0448542	+	0.311968i
$592$	2.73751	−	5.99431i	0.112511	−	0.246365i
$593$	−5.89123	+	12.9000i	−0.241924	+	0.529739i	−0.991177	−	0.132544i	$-0.957685\pi$
$593$	−5.89123	+	12.9000i	−0.241924	+	0.529739i	0.749253	+	0.662283i	$0.230413\pi$
$594$	0.447205	+	3.28634i	0.0183490	+	0.134840i
$595$	−4.88870	−	10.7048i	−0.200417	−	0.438853i
$596$	1.43785			0.0588967
$597$	−1.99541	−	13.8784i	−0.0816668	−	0.568005i
$598$	7.32902	−	8.45814i	0.299706	−	0.345879i
$599$	−23.1253	+	14.8617i	−0.944874	+	0.607234i	−0.919773	−	0.392451i	$-0.871627\pi$
$599$	−23.1253	+	14.8617i	−0.944874	+	0.607234i	−0.0251012	+	0.999685i	$0.507991\pi$
$600$	−0.553744	+	3.85137i	−0.0226065	+	0.157232i
$601$	−6.88286	+	15.0714i	−0.280758	+	0.614774i	−0.996500	−	0.0835906i	$-0.973361\pi$
$601$	−6.88286	+	15.0714i	−0.280758	+	0.614774i	0.715742	+	0.698364i	$0.246088\pi$
$602$	24.5196			0.999343
$603$	1.64883	−	1.05964i	0.0671456	−	0.0431518i
$604$	−5.29367			−0.215396
$605$	9.83863	−	6.11498i	0.399997	−	0.248609i
$606$	−17.6722			−0.717885
$607$	−30.3670	+	19.5157i	−1.23256	+	0.792118i	−0.984288	−	0.176572i	$-0.943499\pi$
$607$	−30.3670	+	19.5157i	−1.23256	+	0.792118i	−0.248272	+	0.968690i	$0.579863\pi$
$608$	−6.29810			−0.255422
$609$	0.0194023	−	0.0424851i	0.000786220	−	0.00172158i
$610$	−0.697685	+	4.85250i	−0.0282484	+	0.196472i
$611$	3.34052	−	2.14682i	0.135143	−	0.0868510i
$612$	3.20225	−	3.69559i	0.129443	−	0.149386i
$613$	−2.71433	−	18.8786i	−0.109631	−	0.762498i	−0.968268	−	0.249914i	$-0.919597\pi$
$613$	−2.71433	−	18.8786i	−0.109631	−	0.762498i	0.858637	−	0.512584i	$-0.171312\pi$
$614$	21.3450			0.861414
$615$	3.52766	+	7.72451i	0.142249	+	0.311482i
$616$	6.40690	−	4.04944i	0.258142	−	0.163157i
$617$	−15.9600	+	34.9476i	−0.642527	+	1.40694i	0.255419	+	0.966830i	$0.417787\pi$
$617$	−15.9600	+	34.9476i	−0.642527	+	1.40694i	−0.897946	+	0.440107i	$0.854941\pi$
$618$	−4.07073	+	8.91365i	−0.163749	+	0.358560i
$619$	−2.98289	+	20.7464i	−0.119892	+	0.833869i	0.837780	+	0.546008i	$0.183853\pi$
$619$	−2.98289	+	20.7464i	−0.119892	+	0.833869i	−0.957672	+	0.287861i	$0.907056\pi$
$620$	0.393078	−	2.73392i	0.0157864	−	0.109797i
$621$	−4.60421	−	5.31355i	−0.184761	−	0.213225i
$622$	16.6161	+	4.87894i	0.666246	+	0.195628i
$623$	29.2998	−	18.8299i	1.17387	−	0.754403i
$624$	1.52733	−	0.448464i	0.0611421	−	0.0179529i
$625$	8.07150	+	5.18724i	0.322860	+	0.207489i
$626$	−20.0555	+	23.1452i	−0.801578	+	0.925070i
$627$	−3.12876	+	20.6528i	−0.124951	+	0.824793i
$628$	−1.67743	−	1.93585i	−0.0669365	−	0.0772489i
$629$	4.58596	+	31.8960i	0.182854	+	1.27178i
$630$	−2.30912	−	0.678019i	−0.0919976	−	0.0270129i
$631$	2.73329	+	19.0104i	0.108810	+	0.756794i	0.969043	+	0.246892i	$0.0794092\pi$
$631$	2.73329	+	19.0104i	0.108810	+	0.756794i	−0.860233	+	0.509902i	$0.829682\pi$
$632$	−8.37696			−0.333218
$633$	6.35534	+	13.9162i	0.252602	+	0.553121i
$634$	−27.3806	+	8.03966i	−1.08742	+	0.319296i
$635$	7.98126	+	17.4765i	0.316727	+	0.693535i
$636$	5.29389	+	11.5920i	0.209917	+	0.459653i
$637$	2.71498	+	0.797190i	0.107571	+	0.0315858i
$638$	−0.0276925	−	0.0618700i	−0.00109635	−	0.00244946i
$639$	−10.6173	+	3.11753i	−0.420015	+	0.123328i
$640$	−0.689634	−	0.795881i	−0.0272602	−	0.0314599i
$641$	10.4891	−	22.9680i	0.414296	−	0.907182i	−0.581322	−	0.813673i	$-0.697465\pi$
$641$	10.4891	−	22.9680i	0.414296	−	0.907182i	0.995618	−	0.0935085i	$-0.0298082\pi$
$642$	−3.67897	−	8.05583i	−0.145197	−	0.317938i
$643$	3.51974	−	4.06199i	0.138805	−	0.160189i	−0.682091	−	0.731267i	$-0.738929\pi$
$643$	3.51974	−	4.06199i	0.138805	−	0.160189i	0.820896	+	0.571078i	$0.193475\pi$
$644$	−6.67458	+	14.6153i	−0.263015	+	0.575923i
$645$	−11.2992			−0.444905
$646$	25.9085	−	16.6504i	1.01936	−	0.655102i
$647$	−5.98711	+	41.6413i	−0.235378	+	1.63709i	0.438848	+	0.898562i	$0.355387\pi$
$647$	−5.98711	+	41.6413i	−0.235378	+	1.63709i	−0.674225	+	0.738526i	$0.735522\pi$
$648$	−0.142315	−	0.989821i	−0.00559065	−	0.0388839i
$649$	−35.1217	+	22.1984i	−1.37865	+	0.871364i
$650$	0.881454	−	6.13065i	0.0345735	−	0.240464i
$651$	−5.75089	−	1.68861i	−0.225395	−	0.0661820i
$652$	−19.4808	−	12.5196i	−0.762929	−	0.490304i
$653$	−27.3715	−	31.5884i	−1.07113	−	1.23615i	−0.970468	−	0.241229i	$-0.922450\pi$
$653$	−27.3715	−	31.5884i	−1.07113	−	1.23615i	−0.100661	−	0.994921i	$-0.532096\pi$
$654$	−0.209424	−	1.45657i	−0.00818911	−	0.0569565i
$655$	1.42879	−	0.419530i	0.0558274	−	0.0163924i
$656$	7.73707	+	2.27181i	0.302082	+	0.0886993i
$657$	−0.0828815	−	0.0956504i	−0.00323352	−	0.00373168i
$658$	−3.73319	+	4.30833i	−0.145535	+	0.167956i
$659$	−17.1363	+	11.0128i	−0.667535	+	0.428999i	−0.830036	−	0.557709i	$-0.811680\pi$
$659$	−17.1363	+	11.0128i	−0.667535	+	0.428999i	0.162501	+	0.986708i	$0.448044\pi$
$660$	−2.95245	+	1.86608i	−0.114924	+	0.0726370i
$661$	19.5969	+	12.5942i	0.762233	+	0.489857i	0.863094	−	0.505043i	$-0.168524\pi$
$661$	19.5969	+	12.5942i	0.762233	+	0.489857i	−0.100861	+	0.994900i	$0.532160\pi$
$662$	−14.1418	+	4.15241i	−0.549637	+	0.161388i
$663$	−5.09737	+	5.88268i	−0.197965	+	0.228464i
$664$	10.0547	+	6.46178i	0.390199	+	0.250766i
$665$	−12.7509	−	8.19452i	−0.494460	−	0.317770i
$666$	5.54371	+	3.56272i	0.214814	+	0.138053i
$667$	0.120884	+	0.0776875i	0.00468065	+	0.00300807i
$668$	−6.84526	+	7.89985i	−0.264851	+	0.305655i
$669$	10.6464	−	3.12607i	0.411614	−	0.120861i
$670$	1.73638	+	1.11591i	0.0670824	+	0.0431112i
$671$	13.0513	−	8.24896i	0.503838	−	0.318448i
$672$	−1.92248	+	1.23550i	−0.0741613	+	0.0476606i
$673$	−2.68972	+	3.10410i	−0.103681	+	0.119654i	−0.805218	−	0.592979i	$-0.797952\pi$
$673$	−2.68972	+	3.10410i	−0.103681	+	0.119654i	0.701537	+	0.712633i	$0.252497\pi$
$674$	−22.3970	−	25.8475i	−0.862701	−	0.995609i
$675$	−3.73337	−	1.09622i	−0.143697	−	0.0421933i
$676$	10.0422	−	2.94866i	0.386238	−	0.113410i
$677$	−4.62963	−	32.1998i	−0.177931	−	1.23754i	−0.861540	−	0.507690i	$-0.830500\pi$
$677$	−4.62963	−	32.1998i	−0.177931	−	1.23754i	0.683609	−	0.729849i	$-0.260409\pi$
$678$	−12.7875	−	14.7575i	−0.491100	−	0.566760i
$679$	0.788678	+	0.506853i	0.0302667	+	0.0194512i
$680$	4.94104	+	1.45082i	0.189480	+	0.0556364i
$681$	−0.288099	+	2.00377i	−0.0110400	+	0.0767847i
$682$	−7.35312	+	4.64749i	−0.281565	+	0.177962i
$683$	1.29835	+	9.03024i	0.0496801	+	0.345532i	0.999467	+	0.0326360i	$0.0103902\pi$
$683$	1.29835	+	9.03024i	0.0496801	+	0.345532i	−0.949787	+	0.312896i	$0.898701\pi$
$684$	0.896313	−	6.23400i	0.0342714	−	0.238363i
$685$	19.8600	−	12.7632i	0.758811	−	0.487658i
$686$	−20.0591			−0.765859
$687$	5.15274	−	11.2829i	0.196589	−	0.430471i
$688$	−7.02630	+	8.10878i	−0.267875	+	0.309144i
$689$	−8.42686	−	18.4522i	−0.321038	−	0.702975i
$690$	3.07580	−	6.73507i	0.117094	−	0.256400i
$691$	−2.53943	−	2.93066i	−0.0966044	−	0.111487i	0.705389	−	0.708821i	$-0.250772\pi$
$691$	−2.53943	−	2.93066i	−0.0966044	−	0.111487i	−0.801993	+	0.597333i	$0.796227\pi$
$692$	3.80108	−	1.11610i	0.144495	−	0.0424276i
$693$	3.09643	+	6.91799i	0.117624	+	0.262793i
$694$	−9.93431	−	2.91698i	−0.377101	−	0.110727i
$695$	−7.20265	−	15.7716i	−0.273212	−	0.598251i
$696$	0.00849020	+	0.0185909i	0.000321820	+	0.000704688i
$697$	−37.8341	+	11.1091i	−1.43307	+	0.420787i
$698$	0.167907	+	0.367666i	0.00635539	+	0.0139164i
$699$	−5.31038			−0.200857
$700$	1.26545	+	8.80138i	0.0478294	+	0.332661i
$701$	−12.0943	−	3.55121i	−0.456796	−	0.134127i	0.0452364	−	0.998976i	$-0.485596\pi$
$701$	−12.0943	−	3.55121i	−0.456796	−	0.134127i	−0.502032	+	0.864849i	$0.667414\pi$
$702$	0.226538	+	1.57561i	0.00855012	+	0.0594674i
$703$	27.1789	+	31.3661i	1.02507	+	1.18300i
$704$	−0.496778	+	3.27921i	−0.0187230	+	0.123590i
$705$	1.72034	−	1.98538i	0.0647919	−	0.0747738i
$706$	13.3096	+	8.55356i	0.500913	+	0.321917i
$707$	−38.7497	+	11.3779i	−1.45733	+	0.427911i
$708$	10.5387	−	6.77284i	0.396070	−	0.254539i
$709$	−41.8143	−	12.2778i	−1.57037	−	0.461102i	−0.623260	−	0.782014i	$-0.714192\pi$
$709$	−41.8143	−	12.2778i	−1.57037	−	0.461102i	−0.947109	+	0.320912i	$0.896011\pi$
$710$	−7.63120	−	8.80687i	−0.286394	−	0.330516i
$711$	1.19217	−	8.29169i	0.0447097	−	0.310963i
$712$	−2.16897	+	15.0855i	−0.0812856	+	0.565354i
$713$	7.66033	−	16.7738i	0.286881	−	0.628183i
$714$	4.64220	−	10.1650i	0.173730	−	0.380415i
$715$	4.69974	−	2.97044i	0.175760	−	0.111088i
$716$	8.09966	+	17.7358i	0.302699	+	0.662818i
$717$	18.0354			0.673546
$718$	−2.36456	−	16.4459i	−0.0882446	−	0.613755i
$719$	−13.6316	+	15.7317i	−0.508374	+	0.586695i	−0.950682	−	0.310168i	$-0.899615\pi$
$719$	−13.6316	+	15.7317i	−0.508374	+	0.586695i	0.442307	+	0.896863i	$0.354160\pi$
$720$	0.885925	−	0.569349i	0.0330165	−	0.0212184i
$721$	−3.18695	+	22.1657i	−0.118688	+	0.825494i
$722$	8.58500	−	18.7985i	0.319500	−	0.699608i
$723$	−17.9946			−0.669225
$724$	3.96273	−	2.54669i	0.147274	−	0.0946470i
$725$	0.0795233			0.00295342
$726$	10.5064	+	3.25808i	0.389930	+	0.120919i
$727$	−42.0043			−1.55785			−0.778926	−	0.627116i	$-0.784235\pi$
$727$	−42.0043			−1.55785			−0.778926	+	0.627116i	$0.784235\pi$
$728$	3.06022	−	1.96668i	0.113419	−	0.0728901i
$729$	1.00000			0.0370370
$730$	0.0553683	−	0.121240i	0.00204927	−	0.00448728i
$731$	7.46680	−	51.9327i	0.276169	−	1.92080i
$732$	−3.91621	+	2.51679i	−0.144747	+	0.0930234i
$733$	−19.2241	+	22.1858i	−0.710058	+	0.819450i	−0.990074	−	0.140545i	$-0.955115\pi$
$733$	−19.2241	+	22.1858i	−0.710058	+	0.819450i	0.280017	+	0.959995i	$0.409660\pi$
$734$	−0.215446	−	1.49846i	−0.00795227	−	0.0553093i
$735$	1.87199			0.0690495
$736$	−2.92071	−	6.39547i	−0.107659	−	0.235740i
$737$	−0.876508	−	6.44112i	−0.0322866	−	0.237262i
$738$	−3.34979	+	7.33501i	−0.123307	+	0.270005i
$739$	−4.05843	+	8.88672i	−0.149292	+	0.326903i	−0.969472	−	0.245202i	$-0.921146\pi$
$739$	−4.05843	+	8.88672i	−0.149292	+	0.326903i	0.820180	+	0.572105i	$0.193873\pi$
$740$	−0.987628	+	6.86911i	−0.0363059	+	0.252513i
$741$	−1.42676	+	9.92332i	−0.0524133	+	0.364542i
$742$	19.0712	+	22.0093i	0.700124	+	0.807986i
$743$	−5.79387	−	1.70124i	−0.212557	−	0.0624123i	0.173721	−	0.984795i	$-0.444421\pi$
$743$	−5.79387	−	1.70124i	−0.212557	−	0.0624123i	−0.386277	+	0.922383i	$0.626239\pi$
$744$	2.20641	−	1.41797i	0.0808907	−	0.0519853i
$745$	−1.45287	+	0.426600i	−0.0532289	+	0.0156294i
$746$	13.1187	+	8.43087i	0.480310	+	0.308676i
$747$	−7.82694	+	9.03277i	−0.286373	+	0.330492i
$748$	−6.62571	−	14.8030i	−0.242260	−	0.541253i
$749$	−13.2534	−	15.2953i	−0.484270	−	0.558877i
$750$	−1.33251	−	9.26779i	−0.0486563	−	0.338412i
$751$	−6.97149	−	2.04701i	−0.254393	−	0.0746966i	0.152049	−	0.988373i	$-0.451413\pi$
$751$	−6.97149	−	2.04701i	−0.254393	−	0.0746966i	−0.406443	+	0.913676i	$0.633231\pi$
$752$	−0.355015	−	2.46918i	−0.0129461	−	0.0900418i
$753$	−3.45930			−0.126064
$754$	−0.0135148	−	0.0295932i	−0.000492178	−	0.00107772i
$755$	5.34895	−	1.57059i	0.194668	−	0.0571597i
$756$	−0.949330	−	2.07874i	−0.0345268	−	0.0756032i
$757$	1.41135	+	3.09043i	0.0512964	+	0.112323i	0.933545	−	0.358461i	$-0.116698\pi$
$757$	1.41135	+	3.09043i	0.0512964	+	0.112323i	−0.882248	+	0.470784i	$0.843971\pi$
$758$	−15.3527	−	4.50796i	−0.557635	−	0.163736i
$759$	−22.4230	+	6.40050i	−0.813904	+	0.232323i
$760$	6.36387	−	1.86860i	0.230842	−	0.0677813i
$761$	−16.2400	−	18.7419i	−0.588698	−	0.679394i	0.380754	−	0.924677i	$-0.375665\pi$
$761$	−16.2400	−	18.7419i	−0.588698	−	0.679394i	−0.969452	+	0.245283i	$0.921119\pi$
$762$	−7.57882	+	16.5953i	−0.274552	+	0.601184i
$763$	−1.39699	−	3.05898i	−0.0505744	−	0.110742i
$764$	7.53285	−	8.69337i	0.272529	−	0.314515i
$765$	−2.13924	+	4.68427i	−0.0773442	+	0.169360i
$766$	−32.6138			−1.17839
$767$	−16.7757	+	10.7811i	−0.605734	+	0.389281i
$768$	0.142315	−	0.989821i	0.00513534	−	0.0357171i
$769$	−1.27374	−	8.85909i	−0.0459324	−	0.319467i	−0.999814	−	0.0192839i	$-0.993861\pi$
$769$	−1.27374	−	8.85909i	−0.0459324	−	0.319467i	0.953882	−	0.300183i	$-0.0970477\pi$
$770$	−5.27237	+	5.99261i	−0.190003	+	0.215959i
$771$	0.801722	−	5.57610i	0.0288733	−	0.200818i
$772$	−2.52129	−	0.740318i	−0.0907433	−	0.0266446i
$773$	−30.2146	−	19.4177i	−1.08674	−	0.698407i	−0.130638	−	0.991430i	$-0.541702\pi$
$773$	−30.2146	−	19.4177i	−1.08674	−	0.698407i	−0.956105	+	0.293023i	$0.905339\pi$
$774$	−7.02630	−	8.10878i	−0.252555	−	0.291464i
$775$	−1.45234	−	10.1012i	−0.0521695	−	0.362847i
$776$	−0.393622	+	0.115578i	−0.0141302	+	0.00414900i
$777$	14.4494	+	4.24273i	0.518370	+	0.152207i
$778$	−11.8749	−	13.7044i	−0.425736	−	0.491326i
$779$	−33.2578	+	38.3815i	−1.19158	+	1.37516i
$780$	−1.41022	+	0.906294i	−0.0504940	+	0.0324505i
$781$	−5.49713	+	36.2863i	−0.196703	+	1.29843i
$782$	28.9228	+	18.5875i	1.03428	+	0.664689i
$783$	−0.0196100	+	0.00575801i	−0.000700804	+	0.000205775i
$784$	1.16408	−	1.34342i	0.0415743	−	0.0479793i
$785$	2.26930	+	1.45839i	0.0809946	+	0.0520521i
$786$	1.18955	+	0.764478i	0.0424299	+	0.0272680i
$787$	41.8919	+	26.9223i	1.49329	+	0.959677i	0.995737	+	0.0922413i	$0.0294031\pi$
$787$	41.8919	+	26.9223i	1.49329	+	0.959677i	0.497550	+	0.867436i	$0.334233\pi$
$788$	−6.44575	−	4.14243i	−0.229620	−	0.147568i
$789$	4.35839	−	5.02984i	0.155163	−	0.179067i
$790$	8.46444	−	2.48538i	0.301151	−	0.0884260i
$791$	−37.5403	−	24.1257i	−1.33478	−	0.857811i
$792$	−3.17513	−	0.958402i	−0.112823	−	0.0340553i
$793$	6.23385	−	4.00625i	0.221371	−	0.142266i
$794$	−21.1278	+	24.3828i	−0.749797	+	0.865312i
$795$	−8.78844	−	10.1424i	−0.311694	−	0.359714i
$796$	13.4532	+	3.95020i	0.476835	+	0.140011i
$797$	−2.92012	+	0.857425i	−0.103436	+	0.0303716i	−0.333041	−	0.942912i	$-0.608075\pi$
$797$	−2.92012	+	0.857425i	−0.103436	+	0.0303716i	0.229605	+	0.973284i	$0.426257\pi$
$798$	−2.04831	−	14.2463i	−0.0725092	−	0.504313i
$799$	7.98825	+	9.21893i	0.282604	+	0.326142i
$800$	−3.27330	−	2.10362i	−0.115729	−	0.0743743i
$801$	−14.6233	−	4.29379i	−0.516689	−	0.151713i
$802$	−0.745102	+	5.18230i	−0.0263105	+	0.182993i
$803$	−0.403642	+	0.115217i	−0.0142442	+	0.00406592i
$804$	0.278933	+	1.94002i	0.00983719	+	0.0684192i
$805$	2.40803	−	16.7482i	0.0848719	−	0.590297i
$806$	−3.51217	+	2.25714i	−0.123711	+	0.0795042i
$807$	14.2934			0.503152
$808$	7.34131	−	16.0752i	0.258266	−	0.565525i
$809$	10.8060	−	12.4708i	0.379920	−	0.438451i	−0.533295	−	0.845929i	$-0.679046\pi$
$809$	10.8060	−	12.4708i	0.379920	−	0.438451i	0.913215	+	0.407478i	$0.133592\pi$
$810$	0.437474	+	0.957934i	0.0153713	+	0.0336584i
$811$	−2.34662	+	5.13839i	−0.0824011	+	0.180433i	−0.946348	−	0.323150i	$-0.895258\pi$
$811$	−2.34662	+	5.13839i	−0.0824011	+	0.180433i	0.863947	+	0.503583i	$0.167985\pi$
$812$	0.0305858	+	0.0352979i	0.00107335	+	0.00123871i
$813$	8.30251	−	2.43784i	0.291182	−	0.0854986i
$814$	18.4751	−	11.6771i	0.647551	−	0.409281i
$815$	23.3987	+	6.87049i	0.819622	+	0.240663i
$816$	2.03137	+	4.44808i	0.0711121	+	0.155714i
$817$	−28.0717	−	61.4685i	−0.982106	−	2.15051i
$818$	−28.1012	+	8.25126i	−0.982536	+	0.288499i
$819$	1.51115	+	3.30896i	0.0528039	+	0.115624i
$820$	−8.49190			−0.296550
$821$	1.69537	+	11.7915i	0.0591687	+	0.411527i	0.997783	+	0.0665578i	$0.0212017\pi$
$821$	1.69537	+	11.7915i	0.0591687	+	0.411527i	−0.938614	+	0.344970i	$0.887889\pi$
$822$	21.5092	+	6.31566i	0.750218	+	0.220284i
$823$	−3.05640	−	21.2577i	−0.106539	−	0.740998i	−0.971135	−	0.238530i	$-0.923335\pi$
$823$	−3.05640	−	21.2577i	−0.106539	−	0.740998i	0.864596	−	0.502468i	$-0.167575\pi$
$824$	−6.41710	−	7.40573i	−0.223550	−	0.257991i
$825$	−8.52432	+	9.68880i	−0.296779	+	0.337321i
$826$	18.7476	−	21.6359i	0.652313	−	0.752809i
$827$	24.4973	+	15.7435i	0.851856	+	0.547454i	0.892153	−	0.451733i	$-0.149194\pi$
$827$	24.4973	+	15.7435i	0.851856	+	0.547454i	−0.0402973	+	0.999188i	$0.512831\pi$
$828$	6.74603	−	1.98081i	0.234441	−	0.0688380i
$829$	38.8735	−	24.9825i	1.35013	−	0.867677i	0.352457	−	0.935828i	$-0.385346\pi$
$829$	38.8735	−	24.9825i	1.35013	−	0.867677i	0.997675	+	0.0681514i	$0.0217101\pi$
$830$	−12.0769	−	3.54609i	−0.419195	−	0.123087i
$831$	−11.1896	−	12.9135i	−0.388162	−	0.447963i
$832$	−0.226538	+	1.57561i	−0.00785379	+	0.0546243i
$833$	−1.23706	+	8.60394i	−0.0428616	+	0.298109i
$834$	6.83947	−	14.9764i	0.236831	−	0.518589i
$835$	4.57292	−	10.0133i	0.158252	−	0.346524i
$836$	−17.4867	−	11.4255i	−0.604790	−	0.395159i
$837$	1.08953	+	2.38575i	0.0376598	+	0.0824634i
$838$	−5.18812			−0.179221
$839$	6.39475	+	44.4765i	0.220771	+	1.53550i	0.735132	+	0.677924i	$0.237120\pi$
$839$	6.39475	+	44.4765i	0.220771	+	1.53550i	−0.514360	+	0.857574i	$0.671971\pi$
$840$	1.57599	−	1.81879i	0.0543769	−	0.0627543i
$841$	−24.3960	+	15.6784i	−0.841241	+	0.540633i
$842$	3.02997	−	21.0739i	0.104420	−	0.726255i
$843$	−3.66141	+	8.01738i	−0.126106	+	0.276133i
$844$	−15.2988			−0.526605
$845$	−9.27222	+	5.95890i	−0.318974	+	0.204992i
$846$	2.49457			0.0857652
$847$	25.1350	+	0.379584i	0.863648	+	0.0130427i
$848$	−12.7436			−0.437618
$849$	−15.4676	+	9.94043i	−0.530847	+	0.341155i
$850$	19.0268			0.652613
$851$	−19.2470	+	42.1450i	−0.659777	+	1.44471i
$852$	1.57480	−	10.9529i	0.0539516	−	0.375242i
$853$	−10.6564	+	6.84848i	−0.364870	+	0.234488i	−0.710210	−	0.703990i	$-0.751400\pi$
$853$	−10.6564	+	6.84848i	−0.364870	+	0.234488i	0.345340	+	0.938478i	$0.387764\pi$
$854$	−6.96663	+	8.03992i	−0.238393	+	0.275121i
$855$	0.943908	+	6.56503i	0.0322810	+	0.224519i
$856$	8.85614			0.302697
$857$	−0.393282	−	0.861167i	−0.0134343	−	0.0294169i	0.902796	−	0.430069i	$-0.141511\pi$
$857$	−0.393282	−	0.861167i	−0.0134343	−	0.0294169i	−0.916230	+	0.400652i	$0.868784\pi$
$858$	5.05420	+	1.52559i	0.172548	+	0.0520828i
$859$	−0.495851	+	1.08576i	−0.0169182	+	0.0370458i	−0.917902	−	0.396806i	$-0.870119\pi$
$859$	−0.495851	+	1.08576i	−0.0169182	+	0.0370458i	0.900984	+	0.433852i	$0.142846\pi$
$860$	4.69386	−	10.2781i	0.160059	−	0.350481i
$861$	−2.62253	+	18.2401i	−0.0893755	+	0.621621i
$862$	4.35043	−	30.2579i	0.148176	−	1.03059i
$863$	36.0722	+	41.6296i	1.22791	+	1.41709i	0.876869	+	0.480729i	$0.159628\pi$
$863$	36.0722	+	41.6296i	1.22791	+	1.41709i	0.351044	+	0.936359i	$0.385827\pi$
$864$	0.959493	+	0.281733i	0.0326426	+	0.00958474i
$865$	−3.50963	+	2.25550i	−0.119331	+	0.0766894i
$866$	−10.7818	+	3.16581i	−0.366380	+	0.107579i
$867$	−5.81461	−	3.73682i	−0.197474	−	0.126909i
$868$	3.92503	−	4.52972i	0.133224	−	0.153749i
$869$	−23.2587	−	15.1968i	−0.788996	−	0.515516i
$870$	−0.0140947	−	0.0162661i	−0.000477854	−	0.000551473i
$871$	−0.444007	−	3.08814i	−0.0150446	−	0.104638i
$872$	1.41194	+	0.414584i	0.0478144	+	0.0140396i
$873$	−0.0583832	−	0.406064i	−0.00197597	−	0.0137432i
$874$	44.2809			1.49782
$875$	−8.88867	−	19.4635i	−0.300492	−	0.657985i
$876$	0.121437	−	0.0356571i	0.00410297	−	0.00120474i
$877$	17.9846	+	39.3808i	0.607297	+	1.32979i	0.924408	+	0.381406i	$0.124560\pi$
$877$	17.9846	+	39.3808i	0.607297	+	1.32979i	−0.317111	+	0.948388i	$0.602713\pi$
$878$	−1.22521	−	2.68285i	−0.0413490	−	0.0905417i
$879$	−14.7637	−	4.33502i	−0.497968	−	0.146217i
$880$	−0.470952	−	3.46084i	−0.0158758	−	0.116665i
$881$	17.6656	−	5.18708i	0.595168	−	0.174757i	0.0297440	−	0.999558i	$-0.490531\pi$
$881$	17.6656	−	5.18708i	0.595168	−	0.174757i	0.565424	+	0.824800i	$0.308713\pi$
$882$	1.16408	+	1.34342i	0.0391966	+	0.0452353i
$883$	2.85737	−	6.25677i	0.0961582	−	0.210557i	−0.855440	−	0.517902i	$-0.826713\pi$
$883$	2.85737	−	6.25677i	0.0961582	−	0.210557i	0.951598	+	0.307345i	$0.0994405\pi$
$884$	−3.23355	−	7.08048i	−0.108756	−	0.238142i
$885$	−8.63935	+	9.97034i	−0.290408	+	0.335149i
$886$	0.629586	−	1.37860i	0.0211513	−	0.0463150i
$887$	49.3513			1.65706			0.828528	−	0.559948i	$-0.189179\pi$
$887$	49.3513			1.65706			0.828528	+	0.559948i	$0.189179\pi$
$888$	−5.54371	+	3.56272i	−0.186035	+	0.119557i
$889$	−5.93341	+	41.2678i	−0.199000	+	1.38408i
$890$	−2.28414	−	15.8866i	−0.0765647	−	0.532519i
$891$	1.40051	−	3.00642i	0.0469190	−	0.100719i
$892$	−1.57911	+	10.9829i	−0.0528724	+	0.367735i
$893$	15.0747	+	4.42632i	0.504454	+	0.148121i
$894$	−1.20960	−	0.777361i	−0.0404550	−	0.0259988i
$895$	−13.4463	−	15.5179i	−0.449461	−	0.518706i
$896$	−0.325226	−	2.26200i	−0.0108650	−	0.0755680i
$897$	−10.7384	+	3.15307i	−0.358544	+	0.105278i
$898$	−12.8794	−	3.78172i	−0.429790	−	0.126198i
$899$	−0.0351029	−	0.0405109i	−0.00117075	−	0.00135111i
$900$	2.54805	−	2.94061i	0.0849350	−	0.0980202i
$901$	52.4235	−	33.6906i	1.74648	−	1.12240i
$902$	17.3607	+	20.3437i	0.578048	+	0.677370i
$903$	−20.6272	−	13.2563i	−0.686429	−	0.441141i
$904$	18.7360	−	5.50140i	0.623152	−	0.182974i
$905$	−3.24852	+	3.74900i	−0.107985	+	0.124621i
$906$	4.45332	+	2.86197i	0.147952	+	0.0950827i
$907$	44.8376	+	28.8154i	1.48881	+	0.956799i	0.996250	+	0.0865185i	$0.0275742\pi$
$907$	44.8376	+	28.8154i	1.48881	+	0.956799i	0.492557	+	0.870280i	$0.336062\pi$
$908$	−1.70301	−	1.09446i	−0.0565165	−	0.0363210i
$909$	14.8668	+	9.55433i	0.493102	+	0.316897i
$910$	−2.50868	+	2.89517i	−0.0831618	+	0.0959738i
$911$	−9.46094	+	2.77798i	−0.313455	+	0.0920386i	−0.434676	−	0.900587i	$-0.643137\pi$
$911$	−9.46094	+	2.77798i	−0.313455	+	0.0920386i	0.121221	+	0.992626i	$0.461319\pi$
$912$	5.29830	+	3.40501i	0.175444	+	0.112751i
$913$	16.1946	+	36.1816i	0.535962	+	1.19744i
$914$	−8.10102	+	5.20621i	−0.267958	+	0.172206i
$915$	3.21039	−	3.70499i	0.106132	−	0.122483i
$916$	8.12279	+	9.37420i	0.268385	+	0.309732i
$917$	3.10051	+	0.910392i	0.102388	+	0.0300638i
$918$	−4.69189	+	1.37766i	−0.154856	+	0.0454697i
$919$	−1.82545	−	12.6963i	−0.0602161	−	0.418812i	−0.997525	−	0.0703126i	$-0.977600\pi$
$919$	−1.82545	−	12.6963i	−0.0602161	−	0.418812i	0.937309	−	0.348500i	$-0.113309\pi$
$920$	4.84870	+	5.59570i	0.159857	+	0.184485i
$921$	−17.9566	−	11.5400i	−0.591689	−	0.380255i
$922$	18.7039	+	5.49197i	0.615982	+	0.180869i
$923$	−2.50677	+	17.4350i	−0.0825114	+	0.573879i
$924$	−7.57912	−	0.0572260i	−0.249335	−	0.00188260i
$925$	3.64907	+	25.3798i	0.119981	+	0.834484i
$926$	−5.12348	+	35.6346i	−0.168368	+	1.17103i
$927$	8.24360	−	5.29784i	0.270755	−	0.174004i
$928$	−0.0204379			−0.000670906
$929$	20.4470	−	44.7727i	0.670844	−	1.46894i	−0.201217	−	0.979547i	$-0.564490\pi$
$929$	20.4470	−	44.7727i	0.670844	−	1.46894i	0.872061	−	0.489397i	$-0.162783\pi$
$930$	−1.80875	+	2.08740i	−0.0593111	+	0.0684486i
$931$	4.65078	+	10.1838i	0.152423	+	0.333760i
$932$	2.20601	−	4.83050i	0.0722604	−	0.158228i
$933$	−11.3406	−	13.0878i	−0.371276	−	0.428475i
$934$	0.176766	−	0.0519033i	0.00578397	−	0.00169833i
$935$	11.0869	+	12.9918i	0.362579	+	0.424878i
$936$	−1.52733	−	0.448464i	−0.0499223	−	0.0146585i
$937$	−0.288257	−	0.631194i	−0.00941694	−	0.0206202i	0.904865	−	0.425698i	$-0.139972\pi$
$937$	−0.288257	−	0.631194i	−0.00941694	−	0.0206202i	−0.914282	+	0.405078i	$0.867244\pi$
$938$	1.86066	+	4.07427i	0.0607526	+	0.133030i
$939$	29.3850	−	8.62821i	0.958943	−	0.281571i
$940$	1.09131	+	2.38964i	0.0355946	+	0.0779414i
$941$	11.1084			0.362123			0.181062	−	0.983472i	$-0.442047\pi$
$941$	11.1084			0.362123			0.181062	+	0.983472i	$0.442047\pi$
$942$	0.364539	+	2.53543i	0.0118773	+	0.0826087i
$943$	−54.3981	−	15.9727i	−1.77144	−	0.520143i
$944$	1.78284	+	12.3999i	0.0580265	+	0.403583i
$945$	1.57599	+	1.81879i	0.0512670	+	0.0591653i
$946$	−34.2188	+	9.76753i	−1.11255	+	0.317570i
$947$	11.7873	−	13.6033i	0.383037	−	0.442048i	−0.531189	−	0.847254i	$-0.678254\pi$
$947$	11.7873	−	13.6033i	0.383037	−	0.442048i	0.914226	+	0.405205i	$0.132800\pi$
$948$	7.04715	+	4.52893i	0.228881	+	0.147093i
$949$	−0.193304	+	0.0567592i	−0.00627492	+	0.00184248i
$950$	20.6156	−	13.2488i	0.668857	−	0.429849i
$951$	27.3806	+	8.03966i	0.887876	+	0.260704i
$952$	7.31797	+	8.44538i	0.237177	+	0.273716i
$953$	4.26847	−	29.6878i	0.138269	−	0.961684i	−0.796046	−	0.605236i	$-0.793079\pi$
$953$	4.26847	−	29.6878i	0.138269	−	0.961684i	0.934315	−	0.356448i	$-0.116012\pi$
$954$	1.81361	−	12.6139i	0.0587177	−	0.408390i
$955$	−5.03225	+	11.0191i	−0.162840	+	0.356570i
$956$	−7.49220	+	16.4056i	−0.242315	+	0.530596i
$957$	−0.0101531	+	0.0670200i	−0.000328203	+	0.00216645i
$958$	−2.88507	−	6.31741i	−0.0932123	−	0.204106i
$959$	51.2291			1.65427
$960$	0.149872	+	1.04238i	0.00483709	+	0.0336427i
$961$	15.7960	−	18.2295i	0.509548	−	0.588050i
$962$	8.82451	−	5.67117i	0.284514	−	0.182846i
$963$	−1.26036	+	8.76600i	−0.0406145	+	0.282480i
$964$	7.47522	−	16.3684i	0.240761	−	0.527192i
$965$	2.76727			0.0890815
$966$	13.5166	−	8.68661i	0.434891	−	0.279487i
$967$	48.4718			1.55875			0.779374	−	0.626559i	$-0.215537\pi$
$967$	48.4718			1.55875			0.779374	+	0.626559i	$0.215537\pi$
$968$	−7.32818	+	8.20352i	−0.235537	+	0.263671i
$969$	−30.7975			−0.989360
$970$	0.363442	−	0.233570i	0.0116694	−	0.00749947i
$971$	−31.9511			−1.02536			−0.512680	−	0.858580i	$-0.671347\pi$
$971$	−31.9511			−1.02536			−0.512680	+	0.858580i	$0.671347\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	5.35458	−	37.2419i	0.171660	−	1.19392i
$974$	−4.04358	+	2.59865i	−0.129565	+	0.0832661i
$975$	−4.05600	+	4.68088i	−0.129896	+	0.149908i
$976$	−0.662505	−	4.60782i	−0.0212063	−	0.147493i
$977$	−7.59066			−0.242847			−0.121423	−	0.992601i	$-0.538746\pi$
$977$	−7.59066			−0.242847			−0.121423	+	0.992601i	$0.538746\pi$
$978$	9.61973	+	21.0643i	0.307605	+	0.673561i
$979$	−33.3891	+	37.9502i	−1.06712	+	1.21289i
$980$	−0.777654	+	1.70282i	−0.0248412	+	0.0543947i
$981$	−0.611305	+	1.33857i	−0.0195175	+	0.0427373i
$982$	−1.40645	+	9.78210i	−0.0448817	+	0.312159i
$983$	−5.07523	+	35.2990i	−0.161875	+	1.12586i	0.733221	+	0.679990i	$0.238016\pi$
$983$	−5.07523	+	35.2990i	−0.161875	+	1.12586i	−0.895096	+	0.445873i	$0.852893\pi$
$984$	−5.28061	−	6.09415i	−0.168340	−	0.194274i
$985$	7.74209	+	2.27328i	0.246683	+	0.0724328i
$986$	0.0840754	−	0.0540320i	0.00267751	−	0.00172073i
$987$	5.46982	−	1.60608i	0.174106	−	0.0511222i
$988$	−8.43387	−	5.42012i	−0.268317	−	0.172437i
$989$	49.4007	−	57.0115i	1.57085	−	1.81286i
$990$	3.49264	+	0.0263711i	0.111003	+	0.000838129i
$991$	0.906011	+	1.04559i	0.0287804	+	0.0332143i	0.769957	−	0.638095i	$-0.220277\pi$
$991$	0.906011	+	1.04559i	0.0287804	+	0.0332143i	−0.741177	+	0.671310i	$0.765732\pi$
$992$	0.373258	+	2.59606i	0.0118509	+	0.0824251i
$993$	14.1418	+	4.15241i	0.448777	+	0.131773i
$994$	−3.59881	−	25.0303i	−0.114147	−	0.793913i
$995$	−14.7657			−0.468103
$996$	−4.96507	−	10.8720i	−0.157324	−	0.344492i
$997$	50.8222	−	14.9228i	1.60956	−	0.472608i	0.651372	−	0.758759i	$-0.274194\pi$
$997$	50.8222	−	14.9228i	1.60956	−	0.472608i	0.958185	+	0.286150i	$0.0923757\pi$
$998$	11.9859	+	26.2455i	0.379407	+	0.830786i
$999$	−2.73751	−	5.99431i	−0.0866109	−	0.189652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.i.c.133.3	✓	60
121.111	even	11	inner	726.2.i.c.595.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
726.2.i.c.133.3	✓	60	1.1	even	1	trivial
726.2.i.c.595.3	yes	60	121.111	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} -1.00000 q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.149872 + 1.04238i) q^{5} +(-0.841254 + 0.540641i) q^{6} +(-1.49653 + 1.72708i) q^{7} +(-0.142315 - 0.989821i) q^{8} +1.00000 q^{9} +(0.437474 + 0.957934i) q^{10} +(1.40051 - 3.00642i) q^{11} +(-0.415415 + 0.909632i) q^{12} +(0.661261 - 1.44796i) q^{13} +(-0.325226 + 2.26200i) q^{14} +(0.149872 - 1.04238i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(4.69189 + 1.37766i) q^{17} +(0.841254 - 0.540641i) q^{18} +(6.04298 - 1.77438i) q^{19} +(0.885925 + 0.569349i) q^{20} +(1.49653 - 1.72708i) q^{21} +(-0.447205 - 3.28634i) q^{22} +(4.60421 + 5.31355i) q^{23} +(0.142315 + 0.989821i) q^{24} +(3.73337 + 1.09622i) q^{25} +(-0.226538 - 1.57561i) q^{26} -1.00000 q^{27} +(0.949330 + 2.07874i) q^{28} +(0.0196100 - 0.00575801i) q^{29} +(-0.437474 - 0.957934i) q^{30} +(-1.08953 - 2.38575i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.40051 + 3.00642i) q^{33} +(4.69189 - 1.37766i) q^{34} +(-1.57599 - 1.81879i) q^{35} +(0.415415 - 0.909632i) q^{36} +(2.73751 + 5.99431i) q^{37} +(4.12438 - 4.75979i) q^{38} +(-0.661261 + 1.44796i) q^{39} +1.05310 q^{40} +(-6.78363 + 4.35957i) q^{41} +(0.325226 - 2.26200i) q^{42} +(-1.52696 - 10.6202i) q^{43} +(-2.15294 - 2.52286i) q^{44} +(-0.149872 + 1.04238i) q^{45} +(6.74603 + 1.98081i) q^{46} +(2.09857 + 1.34867i) q^{47} +(0.654861 + 0.755750i) q^{48} +(0.252979 + 1.75951i) q^{49} +(3.73337 - 1.09622i) q^{50} +(-4.69189 - 1.37766i) q^{51} +(-1.04241 - 1.20301i) q^{52} +(8.34530 - 9.63099i) q^{53} +(-0.841254 + 0.540641i) q^{54} +(2.92394 + 1.91045i) q^{55} +(1.92248 + 1.23550i) q^{56} +(-6.04298 + 1.77438i) q^{57} +(0.0133840 - 0.0154459i) q^{58} +(-10.5387 - 6.77284i) q^{59} +(-0.885925 - 0.569349i) q^{60} +(3.91621 + 2.51679i) q^{61} +(-2.20641 - 1.41797i) q^{62} +(-1.49653 + 1.72708i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(1.41022 + 0.906294i) q^{65} +(0.447205 + 3.28634i) q^{66} +(1.64883 - 1.05964i) q^{67} +(3.20225 - 3.69559i) q^{68} +(-4.60421 - 5.31355i) q^{69} +(-2.30912 - 0.678019i) q^{70} +(-10.6173 + 3.11753i) q^{71} +(-0.142315 - 0.989821i) q^{72} +(-0.0828815 - 0.0956504i) q^{73} +(5.54371 + 3.56272i) q^{74} +(-3.73337 - 1.09622i) q^{75} +(0.896313 - 6.23400i) q^{76} +(3.09643 + 6.91799i) q^{77} +(0.226538 + 1.57561i) q^{78} +(1.19217 - 8.29169i) q^{79} +(0.885925 - 0.569349i) q^{80} +1.00000 q^{81} +(-3.34979 + 7.33501i) q^{82} +(-7.82694 + 9.03277i) q^{83} +(-0.949330 - 2.07874i) q^{84} +(-2.13924 + 4.68427i) q^{85} +(-7.02630 - 8.10878i) q^{86} +(-0.0196100 + 0.00575801i) q^{87} +(-3.17513 - 0.958402i) q^{88} +(-14.6233 - 4.29379i) q^{89} +(0.437474 + 0.957934i) q^{90} +(1.51115 + 3.30896i) q^{91} +(6.74603 - 1.98081i) q^{92} +(1.08953 + 2.38575i) q^{93} +2.49457 q^{94} +(0.943908 + 6.56503i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.0583832 - 0.406064i) q^{97} +(1.16408 + 1.34342i) q^{98} +(1.40051 - 3.00642i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{2} - 60 q^{3} - 6 q^{4} - 2 q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 60 q^{9} - 13 q^{10} - 10 q^{11} + 6 q^{12} - 17 q^{13} - 6 q^{14} + 2 q^{15} - 6 q^{16} + 10 q^{17} - 6 q^{18} - 4 q^{19} - 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) \) 60 * q - 6 * q^2 - 60 * q^3 - 6 * q^4 - 2 * q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 60 * q^9 - 13 * q^10 - 10 * q^11 + 6 * q^12 - 17 * q^13 - 6 * q^14 + 2 * q^15 - 6 * q^16 + 10 * q^17 - 6 * q^18 - 4 * q^19 - 2 * q^20 - 5 * q^21 - 10 * q^22 - 26 * q^23 + 6 * q^24 - 2 * q^25 + 5 * q^26 - 60 * q^27 + 5 * q^28 - 6 * q^29 + 13 * q^30 - 52 * q^31 - 6 * q^32 + 10 * q^33 + 10 * q^34 + 63 * q^35 - 6 * q^36 - 47 * q^37 + 18 * q^38 + 17 * q^39 - 2 * q^40 + 27 * q^41 + 6 * q^42 + 84 * q^43 + q^44 - 2 * q^45 + 7 * q^46 + 10 * q^47 + 6 * q^48 - 33 * q^49 - 2 * q^50 - 10 * q^51 + 5 * q^52 + 42 * q^53 + 6 * q^54 + 13 * q^55 - 6 * q^56 + 4 * q^57 + 16 * q^58 - 11 * q^59 + 2 * q^60 - 24 * q^61 + 14 * q^62 + 5 * q^63 - 6 * q^64 - 80 * q^65 + 10 * q^66 - 2 * q^67 - q^68 + 26 * q^69 - 14 * q^70 - 30 * q^71 - 6 * q^72 - 51 * q^73 + 8 * q^74 + 2 * q^75 - 4 * q^76 + 73 * q^77 - 5 * q^78 - 30 * q^79 - 2 * q^80 + 60 * q^81 - 6 * q^82 + 4 * q^83 - 5 * q^84 + 45 * q^85 - 4 * q^86 + 6 * q^87 + 12 * q^88 - 44 * q^89 - 13 * q^90 - 90 * q^91 + 7 * q^92 + 52 * q^93 - 78 * q^94 - 65 * q^95 + 6 * q^96 - 41 * q^97 + 33 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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