LMFDB - Embedded newform 270.2.r.a.257.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(23,270)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("270.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$270 = 2 \cdot 3^{3} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	270.r (of order $36$ , degree $12$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			257.5
Character	$\chi$	$=$	270.257
Dual form			270.2.r.a.83.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.243179 + 1.71489i) q^{3} +(0.342020 + 0.939693i) q^{4} +(1.53369 + 1.62720i) q^{5} +(0.784422 - 1.54424i) q^{6} +(-0.164138 - 0.351996i) q^{7} +(0.258819 - 0.965926i) q^{8} +(-2.88173 + 0.834054i) q^{9} +(-0.323002 - 2.21262i) q^{10} +(3.24179 + 3.86341i) q^{11} +(-1.52830 + 0.815042i) q^{12} +(-2.12398 - 3.03335i) q^{13} +(-0.0674422 + 0.382484i) q^{14} +(-2.41752 + 3.02582i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-0.0721973 - 0.269444i) q^{17} +(2.83897 + 0.969674i) q^{18} +(-5.80783 + 3.35315i) q^{19} +(-1.00452 + 1.99774i) q^{20} +(0.563720 - 0.367078i) q^{21} +(-0.439555 - 5.02414i) q^{22} +(4.00940 + 1.86961i) q^{23} +(1.71940 + 0.208954i) q^{24} +(-0.295578 + 4.99126i) q^{25} +3.70304i q^{26} +(-2.13109 - 4.73903i) q^{27} +(0.274629 - 0.274629i) q^{28} +(0.711596 + 4.03566i) q^{29} +(3.71586 - 1.09198i) q^{30} +(8.64856 - 3.14782i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(-5.83701 + 6.49883i) q^{33} +(-0.0954062 + 0.262126i) q^{34} +(0.321031 - 0.806939i) q^{35} +(-1.76936 - 2.42267i) q^{36} +(1.02954 - 0.275865i) q^{37} +(6.68078 + 0.584493i) q^{38} +(4.68538 - 4.38005i) q^{39} +(1.96871 - 1.06028i) q^{40} +(1.25495 + 0.221281i) q^{41} +(-0.672320 - 0.0226441i) q^{42} +(0.614870 - 7.02799i) q^{43} +(-2.52166 + 4.36765i) q^{44} +(-5.77686 - 3.40997i) q^{45} +(-2.21194 - 3.83119i) q^{46} +(0.552133 - 0.257464i) q^{47} +(-1.28860 - 1.15737i) q^{48} +(4.40255 - 5.24676i) q^{49} +(3.10499 - 3.91906i) q^{50} +(0.444511 - 0.189334i) q^{51} +(2.12398 - 3.03335i) q^{52} +(-7.96395 - 7.96395i) q^{53} +(-0.972510 + 5.10433i) q^{54} +(-1.31465 + 11.2003i) q^{55} +(-0.382484 + 0.0674422i) q^{56} +(-7.16264 - 9.14439i) q^{57} +(1.73186 - 3.71398i) q^{58} +(3.03423 + 2.54602i) q^{59} +(-3.67018 - 1.23683i) q^{60} +(-9.72912 - 3.54111i) q^{61} +(-8.89000 - 2.38207i) q^{62} +(0.766585 + 0.877455i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(1.67836 - 8.10837i) q^{65} +(8.50898 - 1.97556i) q^{66} +(-3.80051 + 2.66114i) q^{67} +(0.228502 - 0.159999i) q^{68} +(-2.23119 + 7.33034i) q^{69} +(-0.725814 + 0.476870i) q^{70} +(9.02280 + 5.20932i) q^{71} +(0.0597886 + 2.99940i) q^{72} +(-2.01255 - 0.539261i) q^{73} +(-1.00158 - 0.364546i) q^{74} +(-8.63136 + 0.706886i) q^{75} +(-5.13732 - 4.31073i) q^{76} +(0.827803 - 1.77523i) q^{77} +(-6.35033 + 0.900504i) q^{78} +(14.3854 - 2.53654i) q^{79} +(-2.22082 - 0.260671i) q^{80} +(7.60871 - 4.80703i) q^{81} +(-0.901072 - 0.901072i) q^{82} +(4.36450 - 6.23316i) q^{83} +(0.537744 + 0.404176i) q^{84} +(0.327712 - 0.530724i) q^{85} +(-4.53476 + 5.40432i) q^{86} +(-6.74769 + 2.20170i) q^{87} +(4.57081 - 2.13140i) q^{88} +(-5.24263 - 9.08050i) q^{89} +(2.77624 + 6.10676i) q^{90} +(-0.719102 + 1.24552i) q^{91} +(-0.385567 + 4.40705i) q^{92} +(7.50133 + 14.0659i) q^{93} +(-0.599956 - 0.105789i) q^{94} +(-14.3637 - 4.30781i) q^{95} +(0.391717 + 1.68717i) q^{96} +(7.74535 + 0.677631i) q^{97} +(-6.61578 + 1.77269i) q^{98} +(-12.5643 - 8.42948i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100})$ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	0.243179	+	1.71489i	0.140400	+	0.990095i
$3$	0.243179	+	1.71489i	0.140400	+	0.990095i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	1.53369	+	1.62720i	0.685888	+	0.727707i
$5$	1.53369	+	1.62720i	0.685888	+	0.727707i
$6$	0.784422	−	1.54424i	0.320239	−	0.630434i
$7$	−0.164138	−	0.351996i	−0.0620384	−	0.133042i	0.872844	−	0.487999i	$-0.162273\pi$
$7$	−0.164138	−	0.351996i	−0.0620384	−	0.133042i	−0.934882	+	0.354957i	$0.884495\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	−2.88173	+	0.834054i	−0.960576	+	0.278018i
$10$	−0.323002	−	2.21262i	−0.102142	−	0.699691i
$11$	3.24179	+	3.86341i	0.977436	+	1.16486i	0.986310	+	0.164903i	$0.0527310\pi$
$11$	3.24179	+	3.86341i	0.977436	+	1.16486i	−0.00887352	+	0.999961i	$0.502825\pi$
$12$	−1.52830	+	0.815042i	−0.441183	+	0.235282i
$13$	−2.12398	−	3.03335i	−0.589085	−	0.841301i	0.408354	−	0.912824i	$-0.366103\pi$
$13$	−2.12398	−	3.03335i	−0.589085	−	0.841301i	−0.997439	+	0.0715227i	$0.977214\pi$
$14$	−0.0674422	+	0.382484i	−0.0180247	+	0.102223i
$15$	−2.41752	+	3.02582i	−0.624201	+	0.781264i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.0721973	−	0.269444i	−0.0175104	−	0.0653498i	0.956618	−	0.291346i	$-0.0941030\pi$
$17$	−0.0721973	−	0.269444i	−0.0175104	−	0.0653498i	−0.974128	+	0.225996i	$0.927436\pi$
$18$	2.83897	+	0.969674i	0.669151	+	0.228554i
$19$	−5.80783	+	3.35315i	−1.33241	+	0.769265i	−0.985668	−	0.168697i	$-0.946044\pi$
$19$	−5.80783	+	3.35315i	−1.33241	+	0.769265i	−0.346739	+	0.937962i	$0.612711\pi$
$20$	−1.00452	+	1.99774i	−0.224617	+	0.446707i
$21$	0.563720	−	0.367078i	0.123014	−	0.0801030i
$22$	−0.439555	−	5.02414i	−0.0937135	−	1.07115i
$23$	4.00940	+	1.86961i	0.836017	+	0.389841i	0.792991	−	0.609233i	$-0.208523\pi$
$23$	4.00940	+	1.86961i	0.836017	+	0.389841i	0.0430256	+	0.999074i	$0.486300\pi$
$24$	1.71940	+	0.208954i	0.350971	+	0.0426526i
$25$	−0.295578	+	4.99126i	−0.0591156	+	0.998251i
$26$			3.70304i			0.726226i
$27$	−2.13109	−	4.73903i	−0.410129	−	0.912028i
$28$	0.274629	−	0.274629i	0.0519000	−	0.0519000i
$29$	0.711596	+	4.03566i	0.132140	+	0.749404i	0.976809	+	0.214114i	$0.0686865\pi$
$29$	0.711596	+	4.03566i	0.132140	+	0.749404i	−0.844668	+	0.535290i	$0.820202\pi$
$30$	3.71586	−	1.09198i	0.678419	−	0.199367i
$31$	8.64856	−	3.14782i	1.55333	−	0.565365i	0.584132	−	0.811659i	$-0.301435\pi$
$31$	8.64856	−	3.14782i	1.55333	−	0.565365i	0.969195	+	0.246294i	$0.0792128\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	−5.83701	+	6.49883i	−1.01609	+	1.13130i
$34$	−0.0954062	+	0.262126i	−0.0163620	+	0.0449543i
$35$	0.321031	−	0.806939i	0.0542641	−	0.136398i
$36$	−1.76936	−	2.42267i	−0.294894	−	0.403779i
$37$	1.02954	−	0.275865i	0.169256	−	0.0453520i	−0.173196	−	0.984887i	$-0.555409\pi$
$37$	1.02954	−	0.275865i	0.169256	−	0.0453520i	0.342452	+	0.939535i	$0.388743\pi$
$38$	6.68078	+	0.584493i	1.08377	+	0.0948172i
$39$	4.68538	−	4.38005i	0.750261	−	0.701369i
$40$	1.96871	−	1.06028i	0.311280	−	0.167645i
$41$	1.25495	+	0.221281i	0.195990	+	0.0345583i	0.270781	−	0.962641i	$-0.412718\pi$
$41$	1.25495	+	0.221281i	0.195990	+	0.0345583i	−0.0747914	+	0.997199i	$0.523829\pi$
$42$	−0.672320	−	0.0226441i	−0.103741	−	0.00349406i
$43$	0.614870	−	7.02799i	0.0937667	−	1.07176i	−0.792901	−	0.609351i	$-0.791430\pi$
$43$	0.614870	−	7.02799i	0.0937667	−	1.07176i	0.886667	−	0.462408i	$-0.153014\pi$
$44$	−2.52166	+	4.36765i	−0.380155	+	0.658448i
$45$	−5.77686	−	3.40997i	−0.861163	−	0.508329i
$46$	−2.21194	−	3.83119i	−0.326133	−	0.564879i
$47$	0.552133	−	0.257464i	0.0805369	−	0.0375550i	−0.381932	−	0.924190i	$-0.624741\pi$
$47$	0.552133	−	0.257464i	0.0805369	−	0.0375550i	0.462469	+	0.886635i	$0.346964\pi$
$48$	−1.28860	−	1.15737i	−0.185993	−	0.167052i
$49$	4.40255	−	5.24676i	0.628936	−	0.749537i
$50$	3.10499	−	3.91906i	0.439112	−	0.554239i
$51$	0.444511	−	0.189334i	0.0622440	−	0.0265121i
$52$	2.12398	−	3.03335i	0.294543	−	0.420651i
$53$	−7.96395	−	7.96395i	−1.09393	−	1.09393i	−0.995105	−	0.0988282i	$-0.968491\pi$
$53$	−7.96395	−	7.96395i	−1.09393	−	1.09393i	−0.0988282	−	0.995105i	$-0.531509\pi$
$54$	−0.972510	+	5.10433i	−0.132342	+	0.694612i
$55$	−1.31465	+	11.2003i	−0.177268	+	1.51025i
$56$	−0.382484	+	0.0674422i	−0.0511115	+	0.00901234i
$57$	−7.16264	−	9.14439i	−0.948715	−	1.21120i
$58$	1.73186	−	3.71398i	0.227404	−	0.487669i
$59$	3.03423	+	2.54602i	0.395024	+	0.331464i	0.818566	−	0.574412i	$-0.194769\pi$
$59$	3.03423	+	2.54602i	0.395024	+	0.331464i	−0.423543	+	0.905876i	$0.639214\pi$
$60$	−3.67018	−	1.23683i	−0.473819	−	0.159674i
$61$	−9.72912	−	3.54111i	−1.24569	−	0.453393i	−0.366745	−	0.930322i	$-0.619528\pi$
$61$	−9.72912	−	3.54111i	−1.24569	−	0.453393i	−0.878942	+	0.476929i	$0.841750\pi$
$62$	−8.89000	−	2.38207i	−1.12903	−	0.302523i
$63$	0.766585	+	0.877455i	0.0965807	+	0.110549i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	1.67836	−	8.10837i	0.208174	−	1.00572i
$66$	8.50898	−	1.97556i	1.04738	−	0.243174i
$67$	−3.80051	+	2.66114i	−0.464306	+	0.325110i	−0.782213	−	0.623012i	$-0.785909\pi$
$67$	−3.80051	+	2.66114i	−0.464306	+	0.325110i	0.317907	+	0.948122i	$0.397020\pi$
$68$	0.228502	−	0.159999i	0.0277099	−	0.0194027i
$69$	−2.23119	+	7.33034i	−0.268603	+	0.882470i
$70$	−0.725814	+	0.476870i	−0.0867514	+	0.0569969i
$71$	9.02280	+	5.20932i	1.07081	+	0.618232i	0.928403	−	0.371576i	$-0.121182\pi$
$71$	9.02280	+	5.20932i	1.07081	+	0.618232i	0.142407	+	0.989808i	$0.454516\pi$
$72$	0.0597886	+	2.99940i	0.00704616	+	0.353483i
$73$	−2.01255	−	0.539261i	−0.235551	−	0.0631157i	0.139112	−	0.990277i	$-0.455575\pi$
$73$	−2.01255	−	0.539261i	−0.235551	−	0.0631157i	−0.374663	+	0.927161i	$0.622242\pi$
$74$	−1.00158	−	0.364546i	−0.116432	−	0.0423776i
$75$	−8.63136	+	0.706886i	−0.996663	+	0.0816241i
$76$	−5.13732	−	4.31073i	−0.589291	−	0.494474i
$77$	0.827803	−	1.77523i	0.0943369	−	0.202306i
$78$	−6.35033	+	0.900504i	−0.719033	+	0.101962i
$79$	14.3854	−	2.53654i	1.61849	−	0.285383i	0.710286	−	0.703913i	$-0.248566\pi$
$79$	14.3854	−	2.53654i	1.61849	−	0.285383i	0.908203	+	0.418530i	$0.137454\pi$
$80$	−2.22082	−	0.260671i	−0.248295	−	0.0291440i
$81$	7.60871	−	4.80703i	0.845412	−	0.534115i
$82$	−0.901072	−	0.901072i	−0.0995067	−	0.0995067i
$83$	4.36450	−	6.23316i	0.479067	−	0.684178i	−0.504769	−	0.863255i	$-0.668422\pi$
$83$	4.36450	−	6.23316i	0.479067	−	0.684178i	0.983835	+	0.179077i	$0.0573111\pi$
$84$	0.537744	+	0.404176i	0.0586727	+	0.0440992i
$85$	0.327712	−	0.530724i	0.0355453	−	0.0575651i
$86$	−4.53476	+	5.40432i	−0.488996	+	0.582763i
$87$	−6.74769	+	2.20170i	−0.723429	+	0.236047i
$88$	4.57081	−	2.13140i	0.487250	−	0.227208i
$89$	−5.24263	−	9.08050i	−0.555718	−	0.962531i	−0.997847	−	0.0655803i	$-0.979110\pi$
$89$	−5.24263	−	9.08050i	−0.555718	−	0.962531i	0.442129	−	0.896951i	$-0.354223\pi$
$90$	2.77624	+	6.10676i	0.292642	+	0.643709i
$91$	−0.719102	+	1.24552i	−0.0753823	+	0.130566i
$92$	−0.385567	+	4.40705i	−0.0401981	+	0.459466i
$93$	7.50133	+	14.0659i	0.777852	+	1.45856i
$94$	−0.599956	−	0.105789i	−0.0618808	−	0.0109113i
$95$	−14.3637	−	4.30781i	−1.47368	−	0.441972i
$96$	0.391717	+	1.68717i	0.0399794	+	0.172197i
$97$	7.74535	+	0.677631i	0.786421	+	0.0688030i	0.473290	−	0.880907i	$-0.343066\pi$
$97$	7.74535	+	0.677631i	0.786421	+	0.0688030i	0.313132	+	0.949710i	$0.398622\pi$
$98$	−6.61578	+	1.77269i	−0.668295	+	0.179069i
$99$	−12.5643	−	8.42948i	−1.26275	−	0.847195i
$100$	−4.79134	+	1.42936i	−0.479134	+	0.142936i
$101$	4.56235	−	12.5349i	0.453970	−	1.24727i	−0.475937	−	0.879480i	$-0.657891\pi$
$101$	4.56235	−	12.5349i	0.453970	−	1.24727i	0.929907	−	0.367794i	$-0.119887\pi$
$102$	−0.472720	−	0.0998678i	−0.0468062	−	0.00988839i
$103$	12.6574	−	1.10738i	1.24717	−	0.109113i	0.555616	−	0.831439i	$-0.312482\pi$
$103$	12.6574	−	1.10738i	1.24717	−	0.109113i	0.691553	+	0.722326i	$0.256927\pi$
$104$	−3.47972	+	1.26651i	−0.341215	+	0.124192i
$105$	1.46188	+	0.354303i	0.142665	+	0.0345764i
$106$	1.95575	+	11.0916i	0.189959	+	1.07731i
$107$	5.18640	−	5.18640i	0.501388	−	0.501388i	−0.410481	−	0.911869i	$-0.634639\pi$
$107$	5.18640	−	5.18640i	0.501388	−	0.501388i	0.911869	+	0.410481i	$0.134639\pi$
$108$	3.72436	−	3.62342i	0.358377	−	0.348663i
$109$		−	7.81263i		−	0.748314i	−0.927365	−	0.374157i	$-0.877932\pi$
$109$		−	7.81263i		−	0.748314i	0.927365	−	0.374157i	$-0.122068\pi$
$110$	7.50115	−	8.42073i	0.715207	−	0.802885i
$111$	0.723444	+	1.69847i	0.0686662	+	0.161212i
$112$	0.351996	+	0.164138i	0.0332605	+	0.0155096i
$113$	0.731549	+	8.36164i	0.0688183	+	0.786597i	0.949680	+	0.313223i	$0.101409\pi$
$113$	0.731549	+	8.36164i	0.0688183	+	0.786597i	−0.880861	+	0.473374i	$0.843036\pi$
$114$	0.622285	+	11.5990i	0.0582824	+	1.08634i
$115$	3.10694	+	9.39151i	0.289724	+	0.875763i
$116$	−3.54890	+	2.04896i	−0.329507	+	0.190241i
$117$	8.65071	+	6.96979i	0.799758	+	0.644357i
$118$	−1.02516	−	3.82595i	−0.0943735	−	0.352207i
$119$	−0.0829928	+	0.0696392i	−0.00760794	+	0.00638382i
$120$	2.29702	+	3.11828i	0.209688	+	0.284659i
$121$	−2.50664	+	14.2159i	−0.227876	+	1.29235i
$122$	5.93853	+	8.48111i	0.537650	+	0.767843i
$123$	−0.0742964	+	2.20591i	−0.00669908	+	0.198901i
$124$	5.91596	+	7.05037i	0.531269	+	0.633142i
$125$	−8.57511	+	7.17408i	−0.766981	+	0.641670i
$126$	−0.124662	−	1.15846i	−0.0111058	−	0.103204i
$127$	−1.71823	+	6.41254i	−0.152469	+	0.569021i	0.846840	+	0.531848i	$0.178502\pi$
$127$	−1.71823	+	6.41254i	−0.152469	+	0.569021i	−0.999309	+	0.0371734i	$0.988165\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	12.2018	−	0.654627i	1.07431	−	0.0576367i
$130$	−6.02560	+	5.67933i	−0.528480	+	0.498110i
$131$	3.89427	+	10.6994i	0.340244	+	0.934812i	0.985324	+	0.170697i	$0.0546018\pi$
$131$	3.89427	+	10.6994i	0.340244	+	0.934812i	−0.645080	+	0.764115i	$0.723176\pi$
$132$	−8.10328	−	3.26227i	−0.705300	−	0.283944i
$133$	2.13358	+	1.49395i	0.185005	+	0.129542i
$134$	4.63956			0.400797
$135$	4.44293	−	10.7359i	0.382387	−	0.924002i
$136$	−0.278949			−0.0239197
$137$	−7.66910	−	5.36996i	−0.655215	−	0.458787i	0.198100	−	0.980182i	$-0.436523\pi$
$137$	−7.66910	−	5.36996i	−0.655215	−	0.458787i	−0.853315	+	0.521395i	$0.825412\pi$
$138$	6.03219	−	4.72491i	0.513494	−	0.402211i
$139$	−4.31624	−	11.8588i	−0.366099	−	1.00585i	−0.976831	−	0.214012i	$-0.931347\pi$
$139$	−4.31624	−	11.8588i	−0.366099	−	1.00585i	0.610732	−	0.791837i	$-0.290875\pi$
$140$	0.868074	+	0.0256808i	0.0733656	+	0.00217042i
$141$	0.575791	+	0.884241i	0.0484904	+	0.0744665i
$142$	−4.40311	−	9.44249i	−0.369500	−	0.792396i
$143$	4.83362	−	18.0393i	0.404207	−	1.50852i
$144$	1.67141	−	2.49126i	0.139284	−	0.207605i
$145$	−5.47547	+	7.34738i	−0.454713	+	0.610166i
$146$	1.33928	+	1.59609i	0.110839	+	0.132093i
$147$	10.0683	+	6.27401i	0.830415	+	0.517472i
$148$	0.611353	+	0.873103i	0.0502529	+	0.0717686i
$149$	−1.83013	+	10.3792i	−0.149930	+	0.850294i	0.813346	+	0.581780i	$0.197644\pi$
$149$	−1.83013	+	10.3792i	−0.149930	+	0.850294i	−0.963276	+	0.268514i	$0.913468\pi$
$150$	7.47585	+	4.37170i	0.610400	+	0.356947i
$151$	−10.3005	+	8.64311i	−0.838239	+	0.703366i	−0.957167	−	0.289537i	$-0.906499\pi$
$151$	−10.3005	+	8.64311i	−0.838239	+	0.703366i	0.118928	+	0.992903i	$0.462054\pi$
$152$	1.73572	+	6.47779i	0.140785	+	0.525418i
$153$	0.432784	+	0.716248i	0.0349885	+	0.0579052i
$154$	−1.69633	+	0.979375i	−0.136694	+	0.0789203i
$155$	18.3864	+	9.24518i	1.47683	+	0.742591i
$156$	5.71839	+	2.90475i	0.457838	+	0.232566i
$157$	1.23326	+	14.0962i	0.0984247	+	1.12500i	0.871403	+	0.490567i	$0.163210\pi$
$157$	1.23326	+	14.0962i	0.0984247	+	1.12500i	−0.772979	+	0.634432i	$0.781234\pi$
$158$	−13.2388	−	6.17334i	−1.05322	−	0.491125i
$159$	11.7207	−	15.5940i	0.929509	−	1.23669i
$160$	1.66968	+	1.48734i	0.131999	+	0.117585i
$161$		−	1.71817i		−	0.135410i
$162$	−8.98989	−	0.426483i	−0.706312	−	0.0335077i
$163$	−13.0322	+	13.0322i	−1.02076	+	1.02076i	−0.0209823	+	0.999780i	$0.506679\pi$
$163$	−13.0322	+	13.0322i	−1.02076	+	1.02076i	−0.999780	+	0.0209823i	$0.993321\pi$
$164$	0.221281	+	1.25495i	0.0172792	+	0.0979950i
$165$	−19.5271	+	0.469202i	−1.52018	+	0.0365273i
$166$	−7.15038	+	2.60253i	−0.554977	+	0.201995i
$167$	14.9103	−	1.30448i	1.15380	−	0.100944i	0.505843	−	0.862625i	$-0.331181\pi$
$167$	14.9103	−	1.30448i	1.15380	−	0.100944i	0.647952	+	0.761681i	$0.275626\pi$
$168$	−0.208668	−	0.639519i	−0.0160991	−	0.0493400i
$169$	−0.243696	+	0.669550i	−0.0187459	+	0.0515039i
$170$	−0.572856	+	0.246776i	−0.0439361	+	0.0189268i
$171$	13.9399	−	14.5069i	1.06601	−	1.10937i
$172$	6.81445	−	1.82593i	0.519597	−	0.139226i
$173$	−4.98566	−	0.436189i	−0.379053	−	0.0331628i	−0.103962	−	0.994581i	$-0.533152\pi$
$173$	−4.98566	−	0.436189i	−0.379053	−	0.0331628i	−0.275090	+	0.961418i	$0.588708\pi$
$174$	6.79023	+	2.06679i	0.514766	+	0.156683i
$175$	1.80542	−	0.715214i	0.136477	−	0.0540651i
$176$	−4.96671	−	0.875765i	−0.374380	−	0.0660133i
$177$	−3.62830	+	5.82253i	−0.272720	+	0.437648i
$178$	−0.913851	+	10.4454i	−0.0684960	+	0.782913i
$179$	−10.2631	+	17.7763i	−0.767102	+	1.32866i	0.172026	+	0.985092i	$0.444969\pi$
$179$	−10.2631	+	17.7763i	−0.767102	+	1.32866i	−0.939128	+	0.343567i	$0.888365\pi$
$180$	1.22852	−	6.59475i	0.0915688	−	0.491544i
$181$	−1.26767	−	2.19566i	−0.0942248	−	0.163202i	0.815060	−	0.579377i	$-0.196704\pi$
$181$	−1.26767	−	2.19566i	−0.0942248	−	0.163202i	−0.909285	+	0.416174i	$0.863371\pi$
$182$	1.30345	−	0.607811i	0.0966185	−	0.0450539i
$183$	3.70671	−	17.5455i	0.274008	−	1.29700i
$184$	2.84362	−	3.38889i	0.209634	−	0.249832i
$185$	2.02789	+	1.25218i	0.149093	+	0.0920623i
$186$	1.92313	−	15.8247i	0.141011	−	1.16032i
$187$	0.806925	−	1.15241i	0.0590082	−	0.0842725i
$188$	0.430778	+	0.430778i	0.0314177	+	0.0314177i
$189$	−1.31833	+	1.52799i	−0.0958941	+	0.111145i
$190$	9.29517	+	11.7674i	0.674343	+	0.853698i
$191$	−17.3951	+	3.06722i	−1.25866	+	0.221936i	−0.762897	−	0.646520i	$-0.776224\pi$
$191$	−17.3951	+	3.06722i	−1.25866	+	0.221936i	−0.495766	+	0.868456i	$0.665113\pi$
$192$	0.646848	−	1.60673i	0.0466822	−	0.115956i
$193$	7.93758	−	17.0222i	0.571360	−	1.22528i	−0.382200	−	0.924080i	$-0.624833\pi$
$193$	7.93758	−	17.0222i	0.571360	−	1.22528i	0.953559	−	0.301205i	$-0.0973889\pi$
$194$	−5.95595	−	4.99763i	−0.427612	−	0.358809i
$195$	14.3131	+	0.906413i	1.02499	+	0.0649096i
$196$	6.43610	+	2.34255i	0.459722	+	0.167325i
$197$	−12.0914	−	3.23987i	−0.861474	−	0.230831i	−0.199076	−	0.979984i	$-0.563794\pi$
$197$	−12.0914	−	3.23987i	−0.861474	−	0.230831i	−0.662397	+	0.749153i	$0.730461\pi$
$198$	5.45708	+	14.1116i	0.387818	+	1.00287i
$199$	−8.02540	−	4.63347i	−0.568906	−	0.328458i	0.187806	−	0.982206i	$-0.439862\pi$
$199$	−8.02540	−	4.63347i	−0.568906	−	0.328458i	−0.756712	+	0.653748i	$0.773196\pi$
$200$	4.74468	+	1.57734i	0.335500	+	0.111535i
$201$	−5.48779	−	5.87033i	−0.387079	−	0.414061i
$202$	−10.9270	+	7.65117i	−0.768821	+	0.538335i
$203$	1.30374	−	0.912886i	0.0915043	−	0.0640720i
$204$	0.329948	+	0.352948i	0.0231010	+	0.0247113i
$205$	1.56463	+	2.38143i	0.109279	+	0.166326i
$206$	−11.0035	−	6.35287i	−0.766650	−	0.442625i
$207$	−13.1133	−	2.04366i	−0.911441	−	0.142044i
$208$	3.57686	+	0.958418i	0.248011	+	0.0664543i
$209$	−31.7824	−	11.5678i	−2.19843	−	0.800164i
$210$	−0.994285	−	1.12873i	−0.0686122	−	0.0778898i
$211$	−16.2813	−	13.6616i	−1.12085	−	0.940503i	−0.122201	−	0.992505i	$-0.538995\pi$
$211$	−16.2813	−	13.6616i	−1.12085	−	0.940503i	−0.998647	+	0.0520025i	$0.983440\pi$
$212$	4.75983	−	10.2075i	0.326907	−	0.701054i
$213$	−6.73927	+	16.7400i	−0.461767	+	1.14700i
$214$	−7.22324	+	1.27365i	−0.493771	+	0.0870651i
$215$	12.3790	−	9.77826i	0.844240	−	0.666872i
$216$	−5.12912	+	0.831925i	−0.348993	+	0.0566053i
$217$	−2.52758	−	2.52758i	−0.171583	−	0.171583i
$218$	−4.48114	+	6.39973i	−0.303501	+	0.433444i
$219$	0.435365	−	3.58245i	0.0294192	−	0.242079i
$220$	−10.9745	+	2.59537i	−0.739901	+	0.174980i
$221$	−0.663974	+	0.791293i	−0.0446637	+	0.0532281i
$222$	0.381594	−	1.80626i	0.0256109	−	0.121228i
$223$	−9.50424	+	4.43190i	−0.636451	+	0.296782i	−0.713935	−	0.700212i	$-0.753089\pi$
$223$	−9.50424	+	4.43190i	−0.636451	+	0.296782i	0.0774845	+	0.996994i	$0.475311\pi$
$224$	−0.194192	−	0.336351i	−0.0129750	−	0.0224734i
$225$	−3.31120	−	14.6300i	−0.220747	−	0.975331i
$226$	4.19679	−	7.26905i	0.279166	−	0.483530i
$227$	1.68877	−	19.3027i	0.112087	−	1.28117i	−0.706883	−	0.707330i	$-0.749899\pi$
$227$	1.68877	−	19.3027i	0.112087	−	1.28117i	0.818971	−	0.573835i	$-0.194545\pi$
$228$	6.14315	−	9.85825i	0.406840	−	0.652878i
$229$	8.06691	+	1.42241i	0.533076	+	0.0939958i	0.433705	−	0.901055i	$-0.357206\pi$
$229$	8.06691	+	1.42241i	0.533076	+	0.0939958i	0.0993710	+	0.995050i	$0.468317\pi$
$230$	2.84169	−	9.47514i	0.187376	−	0.624772i
$231$	3.24564	+	0.987896i	0.213547	+	0.0649988i
$232$	4.08233	+	0.357157i	0.268018	+	0.0234485i
$233$	−21.7774	+	5.83523i	−1.42668	+	0.382279i	−0.887850	−	0.460133i	$-0.847802\pi$
$233$	−21.7774	+	5.83523i	−1.42668	+	0.382279i	−0.538834	+	0.842412i	$0.681135\pi$
$234$	−3.08854	−	10.6712i	−0.201904	−	0.697595i
$235$	1.26575	+	0.503562i	0.0825683	+	0.0328488i
$236$	−1.35471	+	3.72204i	−0.0881842	+	0.242284i
$237$	7.84815	+	24.0527i	0.509792	+	1.56239i
$238$	0.107927	−	0.00944240i	0.00699588	−	0.000612060i
$239$	−1.42470	+	0.518549i	−0.0921563	+	0.0335421i	−0.387687	−	0.921791i	$-0.626726\pi$
$239$	−1.42470	+	0.518549i	−0.0921563	+	0.0335421i	0.295531	+	0.955333i	$0.404504\pi$
$240$	−0.0930341	−	3.87187i	−0.00600533	−	0.249928i
$241$	−3.03894	−	17.2347i	−0.195755	−	1.11018i	−0.911339	−	0.411657i	$-0.864950\pi$
$241$	−3.03894	−	17.2347i	−0.195755	−	1.11018i	0.715583	−	0.698527i	$-0.246161\pi$
$242$	10.2072	−	10.2072i	0.656144	−	0.656144i
$243$	10.0938	+	11.8792i	0.647520	+	0.762048i
$244$		−	10.3535i		−	0.662816i
$245$	15.2897	−	0.883065i	0.976823	−	0.0564169i
$246$	1.32612	−	1.76436i	0.0845504	−	0.112492i
$247$	22.5070	+	10.4952i	1.43209	+	0.667792i
$248$	−0.802147	−	9.16858i	−0.0509364	−	0.582206i
$249$	11.7506	+	5.96889i	0.744662	+	0.378263i
$250$	11.1392	−	0.958183i	0.704505	−	0.0606008i
$251$	−1.50125	+	0.866749i	−0.0947583	+	0.0547087i	−0.546630	−	0.837374i	$-0.684090\pi$
$251$	−1.50125	+	0.866749i	−0.0947583	+	0.0547087i	0.451872	+	0.892083i	$0.350756\pi$
$252$	−0.562351	+	1.02046i	−0.0354248	+	0.0642831i
$253$	5.77453	+	21.5509i	0.363042	+	1.35489i
$254$	5.08558	−	4.26731i	0.319098	−	0.267755i
$255$	0.989828	+	0.432930i	0.0619854	+	0.0271111i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	8.76192	+	12.5133i	0.546554	+	0.780560i	0.993479	−	0.114011i	$-0.0363701\pi$
$257$	8.76192	+	12.5133i	0.546554	+	0.780560i	−0.446926	+	0.894571i	$0.647481\pi$
$258$	−10.3706	−	6.46242i	−0.645645	−	0.402333i
$259$	−0.266091	−	0.317115i	−0.0165341	−	0.0197045i
$260$	8.19341	−	1.19609i	0.508134	−	0.0741783i
$261$	−5.41659	−	11.0362i	−0.335279	−	0.683122i
$262$	2.94693	−	10.9981i	0.182062	−	0.679465i
$263$	4.41206	+	9.46170i	0.272059	+	0.583433i	0.994106	−	0.108411i	$-0.0345762\pi$
$263$	4.41206	+	9.46170i	0.272059	+	0.583433i	−0.722047	+	0.691844i	$0.756798\pi$
$264$	4.76666	+	7.32014i	0.293368	+	0.450524i
$265$	0.744716	−	25.1732i	0.0457475	−	1.54638i
$266$	−0.890833	−	2.44754i	−0.0546205	−	0.150068i
$267$	14.2972	−	11.1988i	0.874975	−	0.685353i
$268$	−3.80051	−	2.66114i	−0.232153	−	0.162555i
$269$	27.1077			1.65278			0.826392	−	0.563096i	$-0.190390\pi$
$269$	27.1077			1.65278			0.826392	+	0.563096i	$0.190390\pi$
$270$	−9.79732	+	6.24600i	−0.596246	+	0.380120i
$271$	−15.2642			−0.927235			−0.463617	−	0.886036i	$-0.653449\pi$
$271$	−15.2642			−0.927235			−0.463617	+	0.886036i	$0.653449\pi$
$272$	0.228502	+	0.159999i	0.0138549	+	0.00970134i
$273$	−2.31081	−	0.930298i	−0.139856	−	0.0563042i
$274$	3.20207	+	8.79763i	0.193444	+	0.531484i
$275$	−20.2415	+	15.0387i	−1.22061	+	0.906865i
$276$	−7.65138	+	0.410497i	−0.460559	+	0.0247090i
$277$	7.46727	+	16.0136i	0.448665	+	0.962165i	0.992417	+	0.122919i	$0.0392255\pi$
$277$	7.46727	+	16.0136i	0.448665	+	0.962165i	−0.543752	+	0.839246i	$0.682997\pi$
$278$	−3.26626	+	12.1898i	−0.195897	+	0.731098i
$279$	−22.2973	+	16.2845i	−1.33491	+	0.974929i
$280$	−0.696354	−	0.518943i	−0.0416151	−	0.0310128i
$281$	4.53958	+	5.41006i	0.270808	+	0.322737i	0.884260	−	0.466996i	$-0.154664\pi$
$281$	4.53958	+	5.41006i	0.270808	+	0.322737i	−0.613451	+	0.789733i	$0.710219\pi$
$282$	0.0355191	−	1.05459i	0.00211513	−	0.0627998i
$283$	−6.52905	−	9.32445i	−0.388112	−	0.554281i	0.576790	−	0.816893i	$-0.304305\pi$
$283$	−6.52905	−	9.32445i	−0.388112	−	0.554281i	−0.964902	+	0.262612i	$0.915416\pi$
$284$	−1.80918	+	10.2604i	−0.107355	+	0.608840i
$285$	3.89449	−	25.6798i	0.230690	−	1.52114i
$286$	−14.3064	+	12.0045i	−0.845954	+	0.709840i
$287$	−0.128095	−	0.478057i	−0.00756121	−	0.0282188i
$288$	−2.79807	+	1.08204i	−0.164878	+	0.0637598i
$289$	14.6550	−	8.46109i	0.862061	−	0.497711i
$290$	8.69953	−	2.87802i	0.510854	−	0.169003i
$291$	0.721446	+	13.4473i	0.0422919	+	0.788292i
$292$	−0.181593	−	2.07561i	−0.0106269	−	0.121466i
$293$	−1.01372	−	0.472706i	−0.0592223	−	0.0276158i	0.392781	−	0.919632i	$-0.371513\pi$
$293$	−1.01372	−	0.472706i	−0.0592223	−	0.0276158i	−0.452004	+	0.892016i	$0.649291\pi$
$294$	−4.64880	−	10.9143i	−0.271124	−	0.636534i
$295$	0.510682	+	8.84213i	0.0297330	+	0.514809i
$296$		−	1.06586i		−	0.0619519i
$297$	11.4003	−	23.5962i	0.661513	−	1.36919i
$298$	7.45239	−	7.45239i	0.431705	−	0.431705i
$299$	−2.84467	−	16.1329i	−0.164512	−	0.932992i
$300$	−3.61635	−	7.86905i	−0.208790	−	0.454320i
$301$	−2.57475	+	0.937131i	−0.148406	+	0.0540153i
$302$	13.3951	−	1.17192i	0.770802	−	0.0674365i
$303$	22.6056	+	4.77570i	1.29866	+	0.274357i
$304$	2.29369	−	6.30186i	0.131552	−	0.361436i
$305$	−9.15937	−	21.2622i	−0.524464	−	1.21747i
$306$	0.0563070	−	0.834951i	0.00321886	−	0.0477309i
$307$	−7.58934	+	2.03356i	−0.433147	+	0.116061i	−0.468803	−	0.883303i	$-0.655315\pi$
$307$	−7.58934	+	2.03356i	−0.433147	+	0.116061i	0.0356562	+	0.999364i	$0.488648\pi$
$308$	1.95130	+	0.170716i	0.111185	+	0.00972746i
$309$	4.97705	+	21.4368i	0.283135	+	1.21950i
$310$	−9.75841	−	18.1192i	−0.554241	−	1.02910i
$311$	−0.704251	−	0.124178i	−0.0399344	−	0.00704151i	0.153645	−	0.988126i	$-0.450899\pi$
$311$	−0.704251	−	0.124178i	−0.0399344	−	0.00704151i	−0.193580	+	0.981085i	$0.562010\pi$
$312$	−3.01814	−	5.65937i	−0.170868	−	0.320398i
$313$	1.07717	−	12.3121i	0.0608850	−	0.695918i	−0.903007	−	0.429625i	$-0.858646\pi$
$313$	1.07717	−	12.3121i	0.0608850	−	0.695918i	0.963892	−	0.266293i	$-0.0857989\pi$
$314$	7.07502	−	12.2543i	0.399267	−	0.691550i
$315$	−0.252092	+	2.59314i	−0.0142038	+	0.146107i
$316$	7.30368	+	12.6504i	0.410864	+	0.711638i
$317$	−17.4277	+	8.12667i	−0.978837	+	0.456439i	−0.845118	−	0.534580i	$-0.820470\pi$
$317$	−17.4277	+	8.12667i	−0.978837	+	0.456439i	−0.133719	+	0.991019i	$0.542692\pi$
$318$	−18.5454	+	6.05116i	−1.03997	+	0.339332i
$319$	−13.2846	+	15.8320i	−0.743795	+	0.886420i
$320$	−0.514615	−	2.17604i	−0.0287678	−	0.121645i
$321$	10.1554	+	7.63290i	0.566816	+	0.426027i
$322$	−0.985499	+	1.40744i	−0.0549197	+	0.0784335i
$323$	1.32280	+	1.32280i	0.0736023	+	0.0736023i
$324$	7.11947	+	5.50574i	0.395526	+	0.305875i
$325$	15.7680	−	9.70472i	0.874654	−	0.538321i
$326$	18.1503	−	3.20039i	1.00525	−	0.177253i
$327$	13.3978	−	1.89987i	0.740902	−	0.105063i
$328$	0.538546	−	1.15491i	0.0297362	−	0.0637695i
$329$	−0.181252	−	0.152089i	−0.00999277	−	0.00838493i
$330$	16.2648	+	10.8159i	0.895347	+	0.595398i
$331$	−15.4902	−	5.63799i	−0.851421	−	0.309892i	−0.120801	−	0.992677i	$-0.538546\pi$
$331$	−15.4902	−	5.63799i	−0.851421	−	0.309892i	−0.730619	+	0.682785i	$0.760769\pi$
$332$	7.35000	+	1.96943i	0.403384	+	0.108086i
$333$	−2.73678	+	1.65366i	−0.149974	+	0.0906202i
$334$	−12.9620	−	7.48364i	−0.709251	−	0.409486i
$335$	−10.1590	−	2.10282i	−0.555047	−	0.114889i
$336$	−0.195882	+	0.643551i	−0.0106862	+	0.0351086i
$337$	−26.9096	+	18.8423i	−1.46586	+	1.02641i	−0.476780	+	0.879022i	$0.658196\pi$
$337$	−26.9096	+	18.8423i	−1.46586	+	1.02641i	−0.989079	+	0.147384i	$0.952915\pi$
$338$	0.583663	−	0.408685i	0.0317471	−	0.0222295i
$339$	−14.1614	+	3.28791i	−0.769144	+	0.178575i
$340$	0.610801	+	0.126430i	0.0331253	+	0.00685663i
$341$	40.1981	+	23.2084i	2.17685	+	1.25681i
$342$	−19.7397	+	3.88779i	−1.06740	+	0.210227i
$343$	−5.19552	−	1.39213i	−0.280532	−	0.0751682i
$344$	−6.62938	−	2.41290i	−0.357432	−	0.130095i
$345$	−15.3499	+	7.61190i	−0.826411	+	0.409811i
$346$	3.83383	+	3.21696i	0.206108	+	0.172945i
$347$	−7.96319	+	17.0771i	−0.427486	+	0.916747i	0.568106	+	0.822956i	$0.307677\pi$
$347$	−7.96319	+	17.0771i	−0.427486	+	0.916747i	−0.995592	+	0.0937917i	$0.970101\pi$
$348$	−4.37677	−	5.58773i	−0.234620	−	0.299534i
$349$	5.35585	−	0.944381i	0.286692	−	0.0505515i	−0.0284528	−	0.999595i	$-0.509058\pi$
$349$	5.35585	−	0.944381i	0.286692	−	0.0505515i	0.315145	+	0.949044i	$0.397947\pi$
$350$	−1.88914	−	0.449675i	−0.100979	−	0.0240361i
$351$	−9.84878	+	16.5300i	−0.525689	+	0.882304i
$352$	3.56617	+	3.56617i	0.190078	+	0.190078i
$353$	−15.5096	+	22.1500i	−0.825492	+	1.17892i	0.156064	+	0.987747i	$0.450119\pi$
$353$	−15.5096	+	22.1500i	−0.825492	+	1.17892i	−0.981555	+	0.191177i	$0.938769\pi$
$354$	6.31180	−	2.68843i	0.335468	−	0.142888i
$355$	5.36158	+	22.6714i	0.284563	+	1.20327i
$356$	6.73980	−	8.03218i	0.357209	−	0.425705i
$357$	−0.139606	−	0.125389i	−0.00738874	−	0.00663629i
$358$	18.6031	−	8.67477i	0.983204	−	0.458476i
$359$	4.12972	+	7.15289i	0.217958	+	0.377515i	0.954184	−	0.299221i	$-0.0967269\pi$
$359$	4.12972	+	7.15289i	0.217958	+	0.377515i	−0.736225	+	0.676737i	$0.763394\pi$
$360$	−4.78894	+	4.69745i	−0.252399	+	0.247577i
$361$	12.9872	−	22.4945i	0.683538	−	1.18392i
$362$	−0.220969	+	2.52568i	−0.0116139	+	0.132747i
$363$	−24.9883	−	0.841618i	−1.31154	−	0.0441735i
$364$	−1.41635	−	0.249741i	−0.0742371	−	0.0130900i
$365$	−2.20914	−	4.10188i	−0.115632	−	0.214702i
$366$	−13.1001	+	12.2464i	−0.684752	+	0.640129i
$367$	−3.08947	−	0.270294i	−0.161269	−	0.0141092i	0.00623524	−	0.999981i	$-0.498015\pi$
$367$	−3.08947	−	0.270294i	−0.161269	−	0.0141092i	−0.167504	+	0.985871i	$0.553571\pi$
$368$	−4.27314	+	1.14498i	−0.222753	+	0.0596864i
$369$	−3.80098	+	0.409023i	−0.197871	+	0.0212929i
$370$	−0.942928	−	2.18888i	−0.0490205	−	0.113794i
$371$	−1.49609	+	4.11046i	−0.0776730	+	0.213405i
$372$	−10.6520	+	11.8598i	−0.552281	+	0.614900i
$373$	24.4364	−	2.13791i	1.26527	−	0.110697i	0.565309	−	0.824880i	$-0.308757\pi$
$373$	24.4364	−	2.13791i	1.26527	−	0.110697i	0.699959	+	0.714183i	$0.253202\pi$
$374$	−1.32199	+	0.481165i	−0.0683584	+	0.0248804i
$375$	−14.3881	−	12.9608i	−0.742998	−	0.669294i
$376$	−0.105789	−	0.599956i	−0.00545563	−	0.0309404i
$377$	10.7302	−	10.7302i	0.552633	−	0.552633i
$378$	1.95633	−	0.495497i	0.100623	−	0.0254856i
$379$		−	25.9577i		−	1.33336i	−0.745346	−	0.666678i	$-0.767716\pi$
$379$		−	25.9577i		−	1.33336i	0.745346	−	0.666678i	$-0.232284\pi$
$380$	−0.864646	−	14.9708i	−0.0443554	−	0.767985i
$381$	−11.4147	−	1.38719i	−0.584791	−	0.0710681i
$382$	16.0085	+	7.46489i	0.819066	+	0.381937i
$383$	−1.78641	−	20.4187i	−0.0912812	−	1.04335i	−0.894322	−	0.447425i	$-0.852341\pi$
$383$	−1.78641	−	20.4187i	−0.0912812	−	1.04335i	0.803040	−	0.595925i	$-0.203214\pi$
$384$	−1.45145	+	0.945141i	−0.0740690	+	0.0482315i
$385$	4.15825	−	1.37565i	0.211924	−	0.0701097i
$386$	−16.2656	+	9.39096i	−0.827898	+	0.477987i
$387$	4.08984	+	20.7656i	0.207898	+	1.05557i
$388$	2.01230	+	7.51001i	0.102159	+	0.381263i
$389$	−28.6831	+	24.0680i	−1.45429	+	1.22030i	−0.524922	+	0.851150i	$0.675906\pi$
$389$	−28.6831	+	24.0680i	−1.45429	+	1.22030i	−0.929371	+	0.369147i	$0.879650\pi$
$390$	−11.2047	−	8.95217i	−0.567374	−	0.453311i
$391$	0.214288	−	1.21529i	0.0108370	−	0.0614598i
$392$	−3.92852	−	5.61050i	−0.198420	−	0.283373i
$393$	−17.4014	+	9.28013i	−0.877782	+	0.468121i
$394$	8.04635	+	9.58926i	0.405369	+	0.483100i
$395$	26.1903	+	19.5178i	1.31778	+	0.982045i
$396$	3.62389	−	14.6896i	0.182107	−	0.738179i
$397$	4.83281	−	18.0363i	0.242552	−	0.905215i	−0.732047	−	0.681254i	$-0.761435\pi$
$397$	4.83281	−	18.0363i	0.242552	−	0.905215i	0.974598	−	0.223960i	$-0.0718986\pi$
$398$	3.91638	+	8.39870i	0.196310	+	0.420989i
$399$	−2.04312	+	4.02216i	−0.102284	+	0.201360i
$400$	−2.98189	−	4.01352i	−0.149095	−	0.200676i
$401$	0.245045	+	0.673257i	0.0122370	+	0.0336208i	0.945661	−	0.325155i	$-0.105416\pi$
$401$	0.245045	+	0.673257i	0.0122370	+	0.0336208i	−0.933424	+	0.358776i	$0.883194\pi$
$402$	1.12825	+	7.95636i	0.0562718	+	0.396827i
$403$	−27.9178	−	19.5483i	−1.39068	−	0.973768i
$404$	13.3394			0.663660
$405$	19.4914	+	5.00840i	0.968537	+	0.248869i
$406$	−1.59157			−0.0789882
$407$	4.40334	+	3.08325i	0.218266	+	0.152831i
$408$	−0.0678347	−	0.478368i	−0.00335832	−	0.0236828i
$409$	−4.47728	−	12.3012i	−0.221387	−	0.608257i	0.778423	−	0.627740i	$-0.216020\pi$
$409$	−4.47728	−	12.3012i	−0.221387	−	0.608257i	−0.999810	+	0.0194834i	$0.993798\pi$
$410$	0.0842600	−	2.84819i	0.00416130	−	0.140662i
$411$	7.34395	−	14.4576i	0.362250	−	0.713139i
$412$	5.36968	+	11.5153i	0.264545	+	0.567319i
$413$	0.398156	−	1.48594i	0.0195920	−	0.0731182i
$414$	9.56963	+	9.19557i	0.470322	+	0.451938i
$415$	16.8364	−	2.45781i	0.826467	−	0.120649i
$416$	−2.38027	−	2.83669i	−0.116702	−	0.139080i
$417$	19.2869	−	10.2857i	0.944486	−	0.503694i
$418$	19.3995	+	27.7054i	0.948863	+	1.35512i
$419$	3.97998	−	22.5716i	0.194435	−	1.10269i	−0.718787	−	0.695231i	$-0.755302\pi$
$419$	3.97998	−	22.5716i	0.194435	−	1.10269i	0.913221	−	0.407464i	$-0.133587\pi$
$420$	0.167058	+	1.49490i	0.00815159	+	0.0729437i
$421$	17.5962	−	14.7650i	0.857585	−	0.719600i	−0.103861	−	0.994592i	$-0.533120\pi$
$421$	17.5962	−	14.7650i	0.857585	−	0.719600i	0.961446	+	0.274992i	$0.0886753\pi$
$422$	5.50085	+	20.5295i	0.267777	+	0.999359i
$423$	−1.37636	+	1.20245i	−0.0669209	+	0.0584651i
$424$	−9.75381	+	5.63136i	−0.473687	+	0.273483i
$425$	1.36620	−	0.280714i	0.0662706	−	0.0136166i
$426$	15.1221	−	9.84708i	0.732670	−	0.477093i
$427$	0.350466	+	4.00584i	0.0169602	+	0.193856i
$428$	6.64747	+	3.09977i	0.321318	+	0.149833i
$429$	32.1109	+	3.90236i	1.55033	+	0.188408i
$430$	−15.7489	+	0.909583i	−0.759477	+	0.0438640i
$431$			27.7440i			1.33638i	0.743990	+	0.668191i	$0.232931\pi$
$431$			27.7440i			1.33638i	−0.743990	+	0.668191i	$0.767069\pi$
$432$	4.67870	+	2.26047i	0.225104	+	0.108757i
$433$	−3.84591	+	3.84591i	−0.184822	+	0.184822i	−0.793453	−	0.608631i	$-0.791719\pi$
$433$	−3.84591	+	3.84591i	−0.184822	+	0.184822i	0.608631	+	0.793453i	$0.291719\pi$
$434$	0.620712	+	3.52023i	0.0297951	+	0.168976i
$435$	−13.9315	−	7.60313i	−0.667964	−	0.364542i
$436$	7.34147	−	2.67208i	0.351593	−	0.127969i
$437$	−29.5550	+	2.58572i	−1.41381	+	0.123692i
$438$	−2.41144	+	2.68485i	−0.115223	+	0.128287i
$439$	−2.54594	+	6.99491i	−0.121511	+	0.333849i	−0.985503	−	0.169656i	$-0.945734\pi$
$439$	−2.54594	+	6.99491i	−0.121511	+	0.333849i	0.863992	+	0.503505i	$0.167956\pi$
$440$	10.4784	+	4.16872i	0.499540	+	0.198736i
$441$	−8.31088	+	18.7917i	−0.395756	+	0.894843i
$442$	0.997763	−	0.267350i	0.0474587	−	0.0127165i
$443$	15.9484	+	1.39531i	0.757733	+	0.0662931i	0.459473	−	0.888192i	$-0.348038\pi$
$443$	15.9484	+	1.39531i	0.757733	+	0.0662931i	0.298260	+	0.954485i	$0.403594\pi$
$444$	−1.34861	+	1.26073i	−0.0640022	+	0.0598314i
$445$	6.73524	−	22.4575i	0.319281	−	1.06459i
$446$	10.3274	+	1.82101i	0.489019	+	0.0862272i
$447$	−18.2442	−	0.614475i	−0.862922	−	0.0290637i
$448$	−0.0338499	+	0.386906i	−0.00159926	+	0.0182796i
$449$	10.5760	−	18.3182i	0.499114	−	0.864490i	−0.500886	−	0.865513i	$-0.666992\pi$
$449$	10.5760	−	18.3182i	0.499114	−	0.864490i	0.999999	+	0.00102332i	$0.000325732\pi$
$450$	−5.67903	+	13.8834i	−0.267712	+	0.654470i
$451$	3.21338	+	5.56573i	0.151312	+	0.262080i
$452$	−7.60717	+	3.54728i	−0.357811	+	0.166850i
$453$	−17.3269	−	15.5624i	−0.814088	−	0.731184i
$454$	−12.4549	+	14.8432i	−0.584539	+	0.696626i
$455$	−3.12959	+	0.740121i	−0.146718	+	0.0346974i
$456$	−10.6866	+	4.55184i	−0.500447	+	0.213159i
$457$	12.7430	−	18.1989i	0.596094	−	0.851310i	−0.401830	−	0.915714i	$-0.631626\pi$
$457$	12.7430	−	18.1989i	0.596094	−	0.851310i	0.997924	+	0.0644039i	$0.0205146\pi$
$458$	−5.79216	−	5.79216i	−0.270650	−	0.270650i
$459$	−1.12305	+	0.916356i	−0.0524193	+	0.0427718i
$460$	−7.76250	+	6.13166i	−0.361928	+	0.285890i
$461$	−1.53025	+	0.269825i	−0.0712711	+	0.0125670i	−0.209170	−	0.977879i	$-0.567076\pi$
$461$	−1.53025	+	0.269825i	−0.0712711	+	0.0125670i	0.137899	+	0.990446i	$0.455965\pi$
$462$	−2.09204	−	2.67086i	−0.0973303	−	0.124260i
$463$	−8.64666	+	18.5428i	−0.401845	+	0.861758i	0.596409	+	0.802681i	$0.296594\pi$
$463$	−8.64666	+	18.5428i	−0.401845	+	0.861758i	−0.998253	+	0.0590777i	$0.981184\pi$
$464$	−3.13919	−	2.63409i	−0.145733	−	0.122285i
$465$	−11.3833	+	33.7789i	−0.527889	+	1.56646i
$466$	21.1859	+	7.71105i	0.981419	+	0.357207i
$467$	−22.6931	−	6.08060i	−1.05011	−	0.281377i	−0.307814	−	0.951447i	$-0.599597\pi$
$467$	−22.6931	−	6.08060i	−1.05011	−	0.281377i	−0.742298	+	0.670070i	$0.766264\pi$
$468$	−3.59074	+	10.5128i	−0.165982	+	0.485955i
$469$	1.56052	+	0.900966i	0.0720581	+	0.0416028i
$470$	−0.748009	−	1.13850i	−0.0345031	−	0.0525150i
$471$	−23.8736	+	5.54281i	−1.10004	+	0.255399i
$472$	3.24459	−	2.27188i	0.149344	−	0.104572i
$473$	29.1453	−	20.4078i	1.34010	−	0.938350i
$474$	7.36723	−	24.2043i	0.338388	−	1.11174i
$475$	−15.0198	−	29.9795i	−0.689154	−	1.37555i
$476$	−0.0938247	−	0.0541697i	−0.00430045	−	0.00248286i
$477$	29.5923	+	16.3076i	1.35494	+	0.746672i
$478$	1.46447	+	0.392405i	0.0669835	+	0.0179482i
$479$	36.8277	+	13.4042i	1.68270	+	0.612453i	0.993676	−	0.112283i	$-0.0358164\pi$
$479$	36.8277	+	13.4042i	1.68270	+	0.612453i	0.689026	+	0.724737i	$0.258039\pi$
$480$	−2.14460	+	3.22501i	−0.0978872	+	0.147201i
$481$	−3.02352	−	2.53704i	−0.137861	−	0.115679i
$482$	−7.39606	+	15.8609i	−0.336881	+	0.722444i
$483$	2.94647	−	0.417822i	0.134069	−	0.0190116i
$484$	−14.2159	+	2.50664i	−0.646176	+	0.113938i
$485$	10.7763	+	13.6425i	0.489329	+	0.619476i
$486$	−1.45478	−	15.5204i	−0.0659903	−	0.704021i
$487$	5.43345	+	5.43345i	0.246213	+	0.246213i	0.819415	−	0.573201i	$-0.194299\pi$
$487$	5.43345	+	5.43345i	0.246213	+	0.246213i	−0.573201	+	0.819415i	$0.694299\pi$
$488$	−5.93853	+	8.48111i	−0.268825	+	0.383922i
$489$	−25.5180	−	19.1797i	−1.15397	−	0.867337i
$490$	−13.0311	−	8.04645i	−0.588685	−	0.363502i
$491$	−4.04270	+	4.81790i	−0.182444	+	0.217429i	−0.849513	−	0.527567i	$-0.823104\pi$
$491$	−4.04270	+	4.81790i	−0.182444	+	0.217429i	0.667069	+	0.744996i	$0.267549\pi$
$492$	−2.09829	+	0.684652i	−0.0945983	+	0.0308665i
$493$	1.03601	−	0.483100i	0.0466596	−	0.0217577i
$494$	−12.4169	−	21.5066i	−0.558661	−	0.967629i
$495$	−5.55322	−	33.3728i	−0.249599	−	1.50000i
$496$	−4.60180	+	7.97056i	−0.206627	+	0.357889i
$497$	0.352670	−	4.03104i	0.0158194	−	0.180817i
$498$	−6.20189	−	11.6293i	−0.277913	−	0.521120i
$499$	29.6109	+	5.22120i	1.32556	+	0.233733i	0.791219	−	0.611533i	$-0.209447\pi$
$499$	29.6109	+	5.22120i	1.32556	+	0.233733i	0.534346	+	0.845266i	$0.320558\pi$
$500$	−9.67429	−	5.60429i	−0.432648	−	0.250631i
$501$	5.86294	+	25.2524i	0.261937	+	1.12819i
$502$	1.72690	+	0.151084i	0.0770754	+	0.00674323i
$503$	−32.4378	+	8.69169i	−1.44633	+	0.387543i	−0.894746	−	0.446576i	$-0.852643\pi$
$503$	−32.4378	+	8.69169i	−1.44633	+	0.387543i	−0.551585	+	0.834119i	$0.685977\pi$
$504$	1.04596	−	0.513362i	0.0465909	−	0.0228670i
$505$	27.3941	−	11.8009i	1.21902	−	0.525132i
$506$	7.63084	−	20.9656i	0.339232	−	0.932033i
$507$	−1.20747	−	0.255093i	−0.0536256	−	0.0113291i
$508$	−6.61349	+	0.578605i	−0.293426	+	0.0256715i
$509$	6.29400	−	2.29083i	0.278977	−	0.101539i	−0.198743	−	0.980052i	$-0.563686\pi$
$509$	6.29400	−	2.29083i	0.278977	−	0.101539i	0.477719	+	0.878513i	$0.341464\pi$
$510$	−0.562501	−	0.922378i	−0.0249080	−	0.0408436i
$511$	0.140519	+	0.796922i	0.00621618	+	0.0352537i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	28.2677	+	20.3776i	1.24805	+	0.899694i
$514$		−	15.2759i		−	0.673793i
$515$	21.2145	+	18.8978i	0.934821	+	0.832735i
$516$	4.78841	+	11.2420i	0.210798	+	0.494903i
$517$	2.78459	+	1.29848i	0.122466	+	0.0571069i
$518$	0.0360793	+	0.412389i	0.00158523	+	0.0181193i
$519$	−0.464392	−	8.65595i	−0.0203846	−	0.379954i
$520$	−7.39770	−	3.71977i	−0.324410	−	0.163123i
$521$	4.66305	−	2.69221i	0.204292	−	0.117948i	−0.394364	−	0.918954i	$-0.629035\pi$
$521$	4.66305	−	2.69221i	0.204292	−	0.117948i	0.598656	+	0.801006i	$0.295702\pi$
$522$	−1.89308	+	12.1471i	−0.0828578	+	0.531666i
$523$	6.38478	+	23.8283i	0.279187	+	1.04194i	0.952983	+	0.303023i	$0.0979959\pi$
$523$	6.38478	+	23.8283i	0.279187	+	1.04194i	−0.673796	+	0.738917i	$0.735337\pi$
$524$	−8.72224	+	7.31883i	−0.381033	+	0.319724i
$525$	1.66556	+	2.92217i	0.0726908	+	0.127534i
$526$	1.81286	−	10.2812i	0.0790443	−	0.448283i
$527$	−1.47256	−	2.10304i	−0.0641459	−	0.0916098i
$528$	0.294043	−	8.73035i	0.0127966	−	0.379940i
$529$	−2.20430	−	2.62699i	−0.0958393	−	0.114217i
$530$	−15.0488	+	20.1935i	−0.653678	+	0.877151i
$531$	−10.8674	−	4.80623i	−0.471603	−	0.208573i
$532$	−0.674125	+	2.51587i	−0.0292270	+	0.109077i
$533$	−1.99426	−	4.27670i	−0.0863809	−	0.185244i
$534$	−18.1349	+	0.972940i	−0.784775	+	0.0421032i
$535$	16.3937	+	0.484985i	0.708760	+	0.0209677i
$536$	1.58682	+	4.35976i	0.0685403	+	0.188313i
$537$	−32.9802	−	13.2774i	−1.42320	−	0.572960i
$538$	−22.2053	−	15.5483i	−0.957339	−	0.670336i
$539$	34.5426			1.48785
$540$	11.6081	+	0.503083i	0.499531	+	0.0216492i
$541$	22.9118			0.985056			0.492528	−	0.870297i	$-0.336073\pi$
$541$	22.9118			0.985056			0.492528	+	0.870297i	$0.336073\pi$
$542$	12.5037	+	8.75519i	0.537080	+	0.376068i
$543$	3.45706	−	2.70785i	0.148357	−	0.116205i
$544$	−0.0954062	−	0.262126i	−0.00409051	−	0.0112386i
$545$	12.7127	−	11.9822i	0.544553	−	0.513259i
$546$	1.35931	+	2.08748i	0.0581729	+	0.0893359i
$547$	−16.9708	−	36.3939i	−0.725617	−	1.55609i	−0.827609	−	0.561305i	$-0.810299\pi$
$547$	−16.9708	−	36.3939i	−0.725617	−	1.55609i	0.101992	−	0.994785i	$-0.467478\pi$
$548$	2.42313	−	9.04323i	0.103511	−	0.386308i
$549$	30.9902	+	2.08990i	1.32263	+	0.0891948i
$550$	25.2067	−	0.708907i	1.07482	−	0.0302279i
$551$	−17.6650	−	21.0523i	−0.752555	−	0.896860i
$552$	6.50310	+	4.05239i	0.276790	+	0.172481i
$553$	−3.25405	−	4.64727i	−0.138376	−	0.197622i
$554$	3.06820	−	17.4006i	0.130355	−	0.739282i
$555$	−1.65422	+	3.78212i	−0.0702178	+	0.160542i
$556$	9.66737	−	8.11189i	0.409988	−	0.344021i
$557$	−9.15095	−	34.1518i	−0.387738	−	1.44706i	−0.833805	−	0.552059i	$-0.813842\pi$
$557$	−9.15095	−	34.1518i	−0.387738	−	1.44706i	0.446067	−	0.895000i	$-0.352824\pi$
$558$	27.6053	−	0.550271i	1.16863	−	0.0232948i
$559$	−22.6244	+	13.0622i	−0.956908	+	0.552471i
$560$	0.272767	+	0.824506i	0.0115265	+	0.0348417i
$561$	2.17249	+	1.10355i	0.0917225	+	0.0465919i
$562$	−0.615522	−	7.03545i	−0.0259642	−	0.296773i
$563$	19.2425	+	8.97292i	0.810975	+	0.378164i	0.783448	−	0.621457i	$-0.213459\pi$
$563$	19.2425	+	8.97292i	0.810975	+	0.378164i	0.0275267	+	0.999621i	$0.491237\pi$
$564$	−0.633982	+	0.843495i	−0.0266955	+	0.0355175i
$565$	−12.4841	+	14.0146i	−0.525211	+	0.589597i
$566$			11.3831i			0.478465i
$567$	−2.94094	−	1.88921i	−0.123508	−	0.0793395i
$568$	7.36709	−	7.36709i	0.309116	−	0.309116i
$569$	−0.985438	−	5.58870i	−0.0413117	−	0.234290i	0.957160	−	0.289560i	$-0.0935091\pi$
$569$	−0.985438	−	5.58870i	−0.0413117	−	0.234290i	−0.998471	+	0.0552701i	$0.982398\pi$
$570$	−17.9195	+	18.8018i	−0.750565	+	0.787522i
$571$	−29.9272	+	10.8926i	−1.25241	+	0.455842i	−0.881217	−	0.472712i	$-0.843275\pi$
$571$	−29.9272	+	10.8926i	−1.25241	+	0.455842i	−0.371198	+	0.928554i	$0.621053\pi$
$572$	18.6046	−	1.62769i	0.777897	−	0.0680572i
$573$	−9.49009	−	29.0848i	−0.396454	−	1.21504i
$574$	−0.169273	+	0.465074i	−0.00706532	+	0.0194118i
$575$	−10.5168	+	19.4593i	−0.438581	+	0.811509i
$576$	2.91268	+	0.718552i	0.121362	+	0.0299396i
$577$	−40.9020	+	10.9597i	−1.70277	+	0.456257i	−0.973636	−	0.228109i	$-0.926746\pi$
$577$	−40.9020	+	10.9597i	−1.70277	+	0.456257i	−0.729139	+	0.684366i	$0.760079\pi$
$578$	−16.8578	−	1.47487i	−0.701192	−	0.0613463i
$579$	31.1215	+	9.47267i	1.29337	+	0.393671i
$580$	−8.77700	−	2.63231i	−0.364445	−	0.109301i
$581$	−2.91043	−	0.513187i	−0.120745	−	0.0212906i
$582$	7.12205	−	11.4291i	0.295219	−	0.473753i
$583$	4.95059	−	56.5855i	0.205032	−	2.34353i
$584$	−1.04177	+	1.80440i	−0.0431088	+	0.0746667i
$585$	1.92626	+	24.7660i	0.0796411	+	1.02395i
$586$	0.559259	+	0.968666i	0.0231028	+	0.0400152i
$587$	−11.2268	+	5.23515i	−0.463380	+	0.216078i	−0.640265	−	0.768154i	$-0.721176\pi$
$587$	−11.2268	+	5.23515i	−0.463380	+	0.216078i	0.176885	+	0.984231i	$0.443398\pi$
$588$	−2.45210	+	11.6069i	−0.101123	+	0.478660i
$589$	−39.6742	+	47.2819i	−1.63475	+	1.94822i
$590$	4.65331	−	7.53596i	0.191574	−	0.310251i
$591$	2.61567	−	21.5233i	0.107594	−	0.885349i
$592$	−0.611353	+	0.873103i	−0.0251265	+	0.0358843i
$593$	2.66985	+	2.66985i	0.109638	+	0.109638i	0.759798	−	0.650160i	$-0.225298\pi$
$593$	2.66985	+	2.66985i	0.109638	+	0.109638i	−0.650160	+	0.759798i	$0.725298\pi$
$594$	−22.8728	+	12.7900i	−0.938484	+	0.524779i
$595$	−0.240602	−	0.0282410i	−0.00986374	−	0.00115777i
$596$	−10.3792	+	1.83013i	−0.425147	+	0.0749649i
$597$	5.99430	−	14.8895i	0.245330	−	0.609386i
$598$	−6.92325	+	14.8470i	−0.283113	+	0.607138i
$599$	−8.11321	−	6.80779i	−0.331497	−	0.278159i	0.461813	−	0.886978i	$-0.347199\pi$
$599$	−8.11321	−	6.80779i	−0.331497	−	0.278159i	−0.793309	+	0.608819i	$0.791644\pi$
$600$	−1.55116	+	8.52021i	−0.0633259	+	0.347836i
$601$	−10.3384	−	3.76287i	−0.421712	−	0.153491i	0.122442	−	0.992476i	$-0.460927\pi$
$601$	−10.3384	−	3.76287i	−0.421712	−	0.153491i	−0.544155	+	0.838985i	$0.683150\pi$
$602$	2.64662	+	0.709161i	0.107868	+	0.0289032i
$603$	8.73249	−	10.8385i	0.355614	−	0.441379i
$604$	−11.6448	−	6.72314i	−0.473821	−	0.273561i
$605$	−26.9765	+	17.7239i	−1.09675	+	0.720581i
$606$	−15.7782	−	16.8781i	−0.640945	−	0.685624i
$607$	21.0411	−	14.7331i	0.854031	−	0.597999i	−0.0624634	−	0.998047i	$-0.519896\pi$
$607$	21.0411	−	14.7331i	0.854031	−	0.597999i	0.916494	+	0.400049i	$0.131007\pi$
$608$	−5.49348	+	3.84658i	−0.222790	+	0.155999i
$609$	1.88254	+	2.01377i	0.0762846	+	0.0816023i
$610$	−4.69260	+	22.6706i	−0.189998	+	0.917906i
$611$	−1.95370	−	1.12797i	−0.0790382	−	0.0456327i
$612$	−0.525032	+	0.651655i	−0.0212232	+	0.0263416i
$613$	15.4298	+	4.13440i	0.623203	+	0.166987i	0.556584	−	0.830792i	$-0.312112\pi$
$613$	15.4298	+	4.13440i	0.623203	+	0.166987i	0.0666198	+	0.997778i	$0.478779\pi$
$614$	7.38323	+	2.68727i	0.297963	+	0.108450i
$615$	−3.70342	+	3.26230i	−0.149336	+	0.131549i
$616$	−1.50049	−	1.25906i	−0.0604564	−	0.0507290i
$617$	10.9672	−	23.5193i	0.441524	−	0.946852i	−0.552065	−	0.833801i	$-0.686160\pi$
$617$	10.9672	−	23.5193i	0.441524	−	0.946852i	0.993589	−	0.113051i	$-0.0360623\pi$
$618$	8.21868	−	20.4147i	0.330604	−	0.821200i
$619$	24.1933	−	4.26594i	0.972413	−	0.171463i	0.335197	−	0.942148i	$-0.391197\pi$
$619$	24.1933	−	4.26594i	0.972413	−	0.171463i	0.637216	+	0.770686i	$0.280086\pi$
$620$	−2.39912	+	20.4396i	−0.0963509	+	0.820873i
$621$	0.315763	−	22.9850i	0.0126711	−	0.922356i
$622$	0.505663	+	0.505663i	0.0202752	+	0.0202752i
$623$	−2.33578	+	3.33584i	−0.0935811	+	0.133648i
$624$	−0.773766	+	6.36701i	−0.0309754	+	0.254884i
$625$	−24.8253	−	2.95061i	−0.993011	−	0.118024i
$626$	−7.94427	+	9.46761i	−0.317517	+	0.378402i
$627$	12.1088	−	57.3165i	0.483579	−	2.28900i
$628$	−12.8243	+	5.98007i	−0.511745	+	0.238631i
$629$	−0.148661	−	0.257488i	−0.00592748	−	0.0102667i
$630$	1.69386	−	1.97958i	0.0674851	−	0.0788683i
$631$	15.5861	−	26.9960i	0.620474	−	1.07469i	−0.368923	−	0.929460i	$-0.620274\pi$
$631$	15.5861	−	26.9960i	0.620474	−	1.07469i	0.989398	−	0.145233i	$-0.0463931\pi$
$632$	1.27312	−	14.5518i	0.0506418	−	0.578839i
$633$	19.4689	−	31.2429i	0.773820	−	1.24179i
$634$	18.9372	+	3.33914i	0.752092	+	0.132614i
$635$	−13.0697	+	7.03894i	−0.518657	+	0.279332i
$636$	18.6623	+	5.68036i	0.740007	+	0.225241i
$637$	−25.2662	−	2.21051i	−1.00108	−	0.0875835i
$638$	19.9629	−	5.34906i	0.790341	−	0.211771i
$639$	−30.3461	−	7.48633i	−1.20047	−	0.296154i
$640$	−0.826580	+	2.07768i	−0.0326735	+	0.0821276i
$641$	2.53679	−	6.96976i	0.100197	−	0.275289i	−0.879459	−	0.475976i	$-0.842095\pi$
$641$	2.53679	−	6.96976i	0.100197	−	0.275289i	0.979655	+	0.200687i	$0.0643173\pi$
$642$	−3.94072	−	12.0774i	−0.155528	−	0.476656i
$643$	−13.2278	+	1.15728i	−0.521653	+	0.0456387i	−0.344942	−	0.938624i	$-0.612101\pi$
$643$	−13.2278	+	1.15728i	−0.521653	+	0.0456387i	−0.176711	+	0.984263i	$0.556546\pi$
$644$	1.61455	−	0.587647i	0.0636221	−	0.0231565i
$645$	19.7790	+	18.8508i	0.778797	+	0.742249i
$646$	−0.324846	−	1.84230i	−0.0127809	−	0.0724841i
$647$	10.8696	−	10.8696i	0.427327	−	0.427327i	−0.460390	−	0.887717i	$-0.652290\pi$
$647$	10.8696	−	10.8696i	0.427327	−	0.427327i	0.887717	+	0.460390i	$0.152290\pi$
$648$	−2.67396	−	8.59360i	−0.105043	−	0.337588i
$649$			19.9762i			0.784133i
$650$	−18.4828	−	1.09454i	−0.724956	−	0.0429313i
$651$	3.71988	−	4.94919i	0.145793	−	0.193974i
$652$	−16.7036	−	7.78900i	−0.654162	−	0.305041i
$653$	−0.530158	−	6.05974i	−0.0207467	−	0.237136i	−0.999487	−	0.0320317i	$-0.989802\pi$
$653$	−0.530158	−	6.05974i	−0.0207467	−	0.237136i	0.978740	−	0.205104i	$-0.0657533\pi$
$654$	−12.0646	−	6.12840i	−0.471762	−	0.239639i
$655$	−11.4375	+	22.7464i	−0.446900	+	0.888774i
$656$	−1.10358	+	0.637154i	−0.0430877	+	0.0248767i
$657$	6.24939	−	0.124572i	0.243812	−	0.00486002i
$658$	0.0612387	+	0.228546i	0.00238733	+	0.00890965i
$659$	−27.3442	+	22.9445i	−1.06518	+	0.893793i	−0.994607	−	0.103714i	$-0.966927\pi$
$659$	−27.3442	+	22.9445i	−1.06518	+	0.893793i	−0.0705735	+	0.997507i	$0.522483\pi$
$660$	−7.11956	−	18.1890i	−0.277129	−	0.708005i
$661$	−1.92171	+	10.8986i	−0.0747460	+	0.423906i	0.924356	+	0.381532i	$0.124603\pi$
$661$	−1.92171	+	10.8986i	−0.0747460	+	0.423906i	−0.999102	+	0.0423742i	$0.986508\pi$
$662$	9.45505	+	13.5032i	0.367481	+	0.524817i
$663$	−1.51845	−	0.946219i	−0.0589717	−	0.0367481i
$664$	−4.89115	−	5.82905i	−0.189813	−	0.226211i
$665$	0.841297	+	5.76303i	0.0326241	+	0.223481i
$666$	3.19034	+	0.215149i	0.123623	+	0.00833684i
$667$	−4.69206	+	17.5110i	−0.181677	+	0.678028i
$668$	6.32544	+	13.5650i	0.244739	+	0.524844i
$669$	−9.91148	−	15.2210i	−0.383200	−	0.588479i
$670$	7.11566	+	7.54951i	0.274902	+	0.291663i
$671$	−17.8590	−	49.0672i	−0.689439	−	1.89422i
$672$	0.529582	−	0.414813i	0.0204291	−	0.0160017i
$673$	27.6429	+	19.3557i	1.06555	+	0.746109i	0.968461	−	0.249166i	$-0.0801565\pi$
$673$	27.6429	+	19.3557i	1.06555	+	0.746109i	0.0970935	+	0.995275i	$0.469045\pi$
$674$	32.8506			1.26536
$675$	24.2836	−	9.23607i	0.934678	−	0.355497i
$676$	−0.712520			−0.0274046
$677$	23.6658	+	16.5710i	0.909551	+	0.636875i	0.931837	−	0.362877i	$-0.118206\pi$
$677$	23.6658	+	16.5710i	0.909551	+	0.636875i	−0.0222859	+	0.999752i	$0.507094\pi$
$678$	13.4862	+	5.42937i	0.517936	+	0.208514i
$679$	−1.03279	−	2.83756i	−0.0396347	−	0.108895i
$680$	−0.427822	−	0.453907i	−0.0164062	−	0.0174065i
$681$	33.5128	−	1.79796i	1.28421	−	0.0688980i
$682$	−19.6166	−	42.0679i	−0.751158	−	1.61086i
$683$	−2.26449	+	8.45117i	−0.0866481	+	0.323375i	−0.995621	−	0.0934796i	$-0.970201\pi$
$683$	−2.26449	+	8.45117i	−0.0866481	+	0.323375i	0.908973	+	0.416855i	$0.136868\pi$
$684$	18.3997	+	8.13753i	0.703532	+	0.311146i
$685$	−3.02402	−	20.7150i	−0.115542	−	0.791481i
$686$	3.45742	+	4.12040i	0.132005	+	0.157317i
$687$	−0.477583	+	14.1798i	−0.0182209	+	0.540993i
$688$	4.04649	+	5.77898i	0.154271	+	0.220322i
$689$	−7.24223	+	41.0727i	−0.275907	+	1.56475i
$690$	16.9399	+	2.56904i	0.644892	+	0.0978018i
$691$	−19.4470	+	16.3179i	−0.739797	+	0.620763i	−0.932783	−	0.360438i	$-0.882627\pi$
$691$	−19.4470	+	16.3179i	−0.739797	+	0.620763i	0.192986	+	0.981202i	$0.438183\pi$
$692$	−1.29531	−	4.83417i	−0.0492404	−	0.183768i
$693$	−0.904865	+	5.80616i	−0.0343730	+	0.220558i
$694$	16.3181	−	9.42125i	0.619426	−	0.357626i
$695$	12.6769	−	25.2111i	0.480861	−	0.956313i
$696$	0.380251	+	7.08761i	0.0144134	+	0.268655i
$697$	−0.0309810	−	0.354114i	−0.00117349	−	0.0134130i
$698$	−4.92893	−	2.29840i	−0.186563	−	0.0869956i
$699$	−15.3026	−	35.9269i	−0.578798	−	1.35888i
$700$	1.28957	+	1.45192i	0.0487412	+	0.0548774i
$701$		−	24.6781i		−	0.932080i	−0.884764	−	0.466040i	$-0.845680\pi$
$701$		−	24.6781i		−	0.932080i	0.884764	−	0.466040i	$-0.154320\pi$
$702$	17.5488	−	7.89152i	0.662338	−	0.297846i
$703$	−5.05439	+	5.05439i	−0.190630	+	0.190630i
$704$	−0.875765	−	4.96671i	−0.0330066	−	0.187190i
$705$	−0.555753	+	2.29308i	−0.0209309	+	0.0863625i
$706$	25.4094	−	9.24827i	0.956296	−	0.348063i
$707$	−5.16110	+	0.451538i	−0.194103	+	0.0169818i
$708$	−6.71234	−	1.41806i	−0.252265	−	0.0532941i
$709$	−11.9992	+	32.9676i	−0.450641	+	1.23813i	0.481633	+	0.876373i	$0.340044\pi$
$709$	−11.9992	+	32.9676i	−0.450641	+	1.23813i	−0.932274	+	0.361753i	$0.882178\pi$
$710$	8.61184	−	21.6466i	0.323197	−	0.812383i
$711$	−39.3393	+	19.3079i	−1.47534	+	0.724102i
$712$	−10.1280	+	2.71379i	−0.379562	+	0.101703i
$713$	40.5607	+	3.54860i	1.51901	+	0.132896i
$714$	0.0424384	+	0.182787i	0.00158822	+	0.00684065i
$715$	36.7669	−	19.8015i	1.37500	−	0.740533i
$716$	−20.2144	−	3.56435i	−0.755448	−	0.133206i
$717$	−1.23572	−	2.31711i	−0.0461486	−	0.0865342i
$718$	0.719858	−	8.22802i	0.0268649	−	0.307067i
$719$	−0.0178442	+	0.0309071i	−0.000665478	+	0.00115264i	−0.866358	−	0.499424i	$-0.833545\pi$
$719$	−0.0178442	+	0.0309071i	−0.000665478	+	0.00115264i	0.865692	+	0.500576i	$0.166878\pi$
$720$	6.61722	−	1.10110i	0.246609	−	0.0410356i
$721$	−2.46735	−	4.27358i	−0.0918891	−	0.159157i
$722$	−23.5408	+	10.9773i	−0.876100	+	0.408532i
$723$	28.8167	−	9.40259i	1.07170	−	0.349686i
$724$	1.62968	−	1.94218i	0.0605666	−	0.0721804i
$725$	−20.3534	+	2.35891i	−0.755905	+	0.0876076i
$726$	19.9865	+	15.0221i	0.741767	+	0.557522i
$727$	−12.4958	+	17.8458i	−0.463442	+	0.661864i	−0.981050	−	0.193754i	$-0.937934\pi$
$727$	−12.4958	+	17.8458i	−0.463442	+	0.661864i	0.517608	+	0.855618i	$0.326823\pi$
$728$	1.01696	+	1.01696i	0.0376912	+	0.0376912i
$729$	−17.9169	+	20.1986i	−0.663589	+	0.748098i
$730$	−0.543120	+	4.62718i	−0.0201018	+	0.171260i
$731$	−1.93804	+	0.341729i	−0.0716811	+	0.0126393i
$732$	17.7552	−	2.51776i	0.656251	−	0.0930592i
$733$	−8.71758	+	18.6949i	−0.321991	+	0.690512i	−0.998965	−	0.0454951i	$-0.985513\pi$
$733$	−8.71758	+	18.6949i	−0.321991	+	0.690512i	0.676973	+	0.736008i	$0.263291\pi$
$734$	2.37571	+	1.99346i	0.0876891	+	0.0735799i
$735$	5.23250	+	26.0055i	0.193004	+	0.959227i
$736$	4.15709	+	1.51306i	0.153232	+	0.0557720i
$737$	−22.6015	−	6.05606i	−0.832538	−	0.223078i
$738$	3.34819	+	1.84510i	0.123248	+	0.0679191i
$739$	11.5469	+	6.66660i	0.424759	+	0.245235i	0.697111	−	0.716963i	$-0.254468\pi$
$739$	11.5469	+	6.66660i	0.424759	+	0.245235i	−0.272352	+	0.962198i	$0.587802\pi$
$740$	−0.483088	+	2.33387i	−0.0177587	+	0.0857946i
$741$	−12.5249	+	41.1493i	−0.460113	+	1.51166i
$742$	3.58319	−	2.50898i	0.131543	−	0.0921074i
$743$	36.9100	−	25.8447i	1.35410	−	0.948150i	0.354182	−	0.935176i	$-0.384759\pi$
$743$	36.9100	−	25.8447i	1.35410	−	0.948150i	0.999916	−	0.0129733i	$-0.00412965\pi$
$744$	15.5281	−	3.60521i	0.569287	−	0.132173i
$745$	−19.6958	+	12.9404i	−0.721600	+	0.474101i
$746$	−21.2434	−	12.2649i	−0.777775	−	0.449048i
$747$	−7.37852	+	21.6025i	−0.269966	+	0.790394i
$748$	1.35890	+	0.364115i	0.0496861	+	0.0133134i
$749$	−2.67688	−	0.974303i	−0.0978109	−	0.0356003i
$750$	4.35201	+	18.8696i	0.158913	+	0.689019i
$751$	16.6006	+	13.9295i	0.605764	+	0.508296i	0.893293	−	0.449476i	$-0.148389\pi$
$751$	16.6006	+	13.9295i	0.605764	+	0.508296i	−0.287528	+	0.957772i	$0.592834\pi$
$752$	−0.257464	+	0.552133i	−0.00938875	+	0.0201342i
$753$	−1.85146	−	2.36372i	−0.0674709	−	0.0861386i
$754$	−14.9442	+	2.63507i	−0.544237	+	0.0959637i
$755$	−29.8618	−	3.50506i	−1.08678	−	0.127562i
$756$	−1.88674	−	0.716217i	−0.0686200	−	0.0260486i
$757$	−14.2927	−	14.2927i	−0.519479	−	0.519479i	0.397935	−	0.917414i	$-0.369727\pi$
$757$	−14.2927	−	14.2927i	−0.519479	−	0.519479i	−0.917414	+	0.397935i	$0.869727\pi$
$758$	−14.8887	+	21.2633i	−0.540782	+	0.772317i
$759$	−35.5532	+	15.1434i	−1.29050	+	0.549672i
$760$	−7.87862	+	12.7593i	−0.285788	+	0.462828i
$761$	32.6847	−	38.9521i	1.18482	−	1.41201i	0.295123	−	0.955459i	$-0.404639\pi$
$761$	32.6847	−	38.9521i	1.18482	−	1.41201i	0.889696	−	0.456553i	$-0.150916\pi$
$762$	8.55469	+	7.68351i	0.309904	+	0.278344i
$763$	−2.75001	+	1.28235i	−0.0995571	+	0.0464242i
$764$	−8.83171	−	15.2970i	−0.319520	−	0.553425i
$765$	−0.501723	+	1.80273i	−0.0181398	+	0.0651779i
$766$	−10.2484	+	17.7507i	−0.370289	+	0.641359i
$767$	1.27835	−	14.6116i	0.0461585	−	0.527594i
$768$	1.73107	+	0.0583033i	0.0624646	+	0.00210384i
$769$	2.08506	+	0.367651i	0.0751890	+	0.0132579i	0.211116	−	0.977461i	$-0.432290\pi$
$769$	2.08506	+	0.367651i	0.0751890	+	0.0132579i	−0.135927	+	0.990719i	$0.543401\pi$
$770$	−4.19528	−	1.25821i	−0.151188	−	0.0453427i
$771$	−19.3283	+	18.0688i	−0.696092	+	0.650730i
$772$	18.7105	+	1.63695i	0.673404	+	0.0589152i
$773$	−8.12377	+	2.17676i	−0.292192	+	0.0782925i	−0.401937	−	0.915667i	$-0.631663\pi$
$773$	−8.12377	+	2.17676i	−0.292192	+	0.0782925i	0.109746	+	0.993960i	$0.464996\pi$
$774$	8.56045	−	19.3560i	0.307699	−	0.695738i
$775$	13.1552	+	44.0976i	0.472550	+	1.58403i
$776$	2.65919	−	7.30605i	0.0954592	−	0.262272i
$777$	0.479110	−	0.533433i	0.0171880	−	0.0191368i
$778$	37.3007	−	3.26339i	1.33730	−	0.116998i
$779$	−8.03051	+	2.92287i	−0.287723	+	0.104723i
$780$	4.04364	+	13.7600i	0.144785	+	0.492686i
$781$	9.12427	+	51.7463i	0.326492	+	1.85163i
$782$	−0.872596	+	0.872596i	−0.0312040	+	0.0312040i
$783$	17.6087	−	11.9727i	0.629283	−	0.427868i
$784$			6.84916i			0.244613i
$785$	−21.0459	+	23.6260i	−0.751162	+	0.843248i
$786$	19.5772	+	2.37917i	0.698296	+	0.0848621i
$787$	11.4357	+	5.33254i	0.407638	+	0.190085i	0.615612	−	0.788050i	$-0.288909\pi$
$787$	11.4357	+	5.33254i	0.407638	+	0.190085i	−0.207974	+	0.978134i	$0.566687\pi$
$788$	−1.09101	−	12.4703i	−0.0388655	−	0.444235i
$789$	−15.1529	+	9.86711i	−0.539457	+	0.351279i
$790$	−10.2589	−	31.0102i	−0.364996	−	1.10329i
$791$	2.82319	−	1.62997i	0.100381	−	0.0579550i
$792$	−11.3941	+	9.95443i	−0.404872	+	0.353715i
$793$	9.92300	+	37.0331i	0.352376	+	1.31508i
$794$	−14.3040	+	12.0025i	−0.507629	+	0.425952i
$795$	43.3505	−	4.84450i	1.53748	−	0.171817i
$796$	1.60919	−	9.12615i	0.0570361	−	0.323468i
$797$	−8.01826	−	11.4513i	−0.284021	−	0.405625i	0.651637	−	0.758531i	$-0.274082\pi$
$797$	−8.01826	−	11.4513i	−0.284021	−	0.405625i	−0.935659	+	0.352906i	$0.885194\pi$
$798$	3.98065	−	2.12288i	0.140913	−	0.0751490i
$799$	−0.109235	−	0.130181i	−0.00386445	−	0.00460547i
$800$	0.140563	+	4.99802i	0.00496966	+	0.176707i
$801$	22.6815	+	21.7949i	0.801410	+	0.770085i
$802$	0.185435	−	0.692052i	0.00654793	−	0.0244372i
$803$	−4.44087	−	9.52348i	−0.156715	−	0.336076i
$804$	3.63938	−	7.16460i	0.128351	−	0.252676i
$805$	2.79580	−	2.63514i	0.0985391	−	0.0928763i
$806$	11.6565	+	32.0260i	0.410583	+	1.12807i
$807$	6.59203	+	46.4868i	0.232050	+	1.63641i
$808$	−10.9270	−	7.65117i	−0.384411	−	0.269167i
$809$	−38.2878			−1.34613			−0.673064	−	0.739584i	$-0.735022\pi$
$809$	−38.2878			−1.34613			−0.673064	+	0.739584i	$0.735022\pi$
$810$	−13.0937	−	15.2825i	−0.460067	−	0.536971i
$811$	48.3569			1.69804			0.849020	−	0.528360i	$-0.177193\pi$
$811$	48.3569			1.69804			0.849020	+	0.528360i	$0.177193\pi$
$812$	1.30374	+	0.912886i	0.0457522	+	0.0320360i
$813$	−3.71194	−	26.1765i	−0.130183	−	0.918050i
$814$	−1.83853	−	5.05131i	−0.0644403	−	0.177048i
$815$	−41.1935	−	1.21865i	−1.44294	−	0.0426876i
$816$	−0.218814	+	0.430765i	−0.00766001	+	0.0150798i
$817$	19.9949	+	42.8791i	0.699531	+	1.50015i
$818$	−3.38812	+	12.6446i	−0.118463	+	0.442110i
$819$	1.03342	−	4.18902i	0.0361107	−	0.146376i
$820$	−1.70268	+	2.28477i	−0.0594601	+	0.0797877i
$821$	8.88139	+	10.5844i	0.309963	+	0.369399i	0.898426	−	0.439125i	$-0.144711\pi$
$821$	8.88139	+	10.5844i	0.309963	+	0.369399i	−0.588464	+	0.808524i	$0.700267\pi$
$822$	−14.3083	+	7.63062i	−0.499060	+	0.266149i
$823$	1.30209	+	1.85958i	0.0453880	+	0.0648208i	0.841205	−	0.540717i	$-0.181847\pi$
$823$	1.30209	+	1.85958i	0.0453880	+	0.0648208i	−0.795817	+	0.605538i	$0.792958\pi$
$824$	2.20633	−	12.5127i	0.0768611	−	0.435901i
$825$	−30.7120	−	31.0549i	−1.06926	−	1.08119i
$826$	−1.17845	+	0.988836i	−0.0410035	+	0.0344060i
$827$	6.78467	+	25.3207i	0.235926	+	0.880488i	0.977729	+	0.209870i	$0.0673042\pi$
$827$	6.78467	+	25.3207i	0.235926	+	0.880488i	−0.741803	+	0.670618i	$0.766029\pi$
$828$	−2.56462	−	13.0215i	−0.0891266	−	0.452528i
$829$	22.5791	−	13.0361i	0.784206	−	0.452762i	−0.0537128	−	0.998556i	$-0.517106\pi$
$829$	22.5791	−	13.0361i	0.784206	−	0.452762i	0.837919	+	0.545795i	$0.183772\pi$
$830$	−15.2013	−	7.64365i	−0.527646	−	0.265315i
$831$	−25.6458	+	16.6998i	−0.889642	+	0.579309i
$832$	0.322741	+	3.68895i	0.0111890	+	0.127891i
$833$	−1.73156	−	0.807440i	−0.0599950	−	0.0279761i
$834$	−21.6986	−	2.63697i	−0.751361	−	0.0913108i
$835$	24.9905	+	22.2614i	0.864832	+	0.770389i
$836$		−	33.8221i		−	1.16976i
$837$	−33.3485	−	34.2775i	−1.15269	−	1.18480i
$838$	−16.2067	+	16.2067i	−0.559853	+	0.559853i
$839$	−3.31873	−	18.8214i	−0.114575	−	0.649788i	−0.986960	−	0.160968i	$-0.948538\pi$
$839$	−3.31873	−	18.8214i	−0.114575	−	0.649788i	0.872384	−	0.488820i	$-0.162573\pi$
$840$	0.720594	−	1.32037i	0.0248628	−	0.0455571i
$841$	11.4709	−	4.17506i	0.395547	−	0.143967i
$842$	−22.8828	+	2.00198i	−0.788593	+	0.0689929i
$843$	−8.17375	+	9.10051i	−0.281519	+	0.313438i
$844$	7.26918	−	19.9719i	0.250216	−	0.687462i
$845$	−1.46325	+	0.630340i	−0.0503373	+	0.0216844i
$846$	1.81714	−	0.195543i	0.0624747	−	0.00672289i
$847$	5.41536	−	1.45104i	0.186074	−	0.0498584i
$848$	11.2199	+	0.981611i	0.385292	+	0.0337087i
$849$	14.4027	−	13.4641i	0.494300	−	0.462088i
$850$	−1.28014	−	0.553675i	−0.0439084	−	0.0189909i
$851$	4.64361	+	0.818793i	0.159181	+	0.0280679i
$852$	−18.0354	−	0.607441i	−0.617882	−	0.0208106i
$853$	0.0952619	−	1.08885i	0.00326171	−	0.0372815i	−0.994389	−	0.105781i	$-0.966266\pi$
$853$	0.0952619	−	1.08885i	0.00326171	−	0.0372815i	0.997651	+	0.0684998i	$0.0218212\pi$
$854$	2.01057	−	3.48241i	0.0688003	−	0.119166i
$855$	44.9851	+	0.433859i	1.53846	+	0.0148376i
$856$	−3.66734	−	6.35201i	−0.125347	−	0.217107i
$857$	−42.8556	+	19.9839i	−1.46392	+	0.682638i	−0.981175	−	0.193123i	$-0.938138\pi$
$857$	−42.8556	+	19.9839i	−1.46392	+	0.682638i	−0.482746	+	0.875760i	$0.660361\pi$
$858$	−24.0654	−	21.6147i	−0.821581	−	0.737914i
$859$	−5.03971	+	6.00609i	−0.171953	+	0.204925i	−0.845137	−	0.534549i	$-0.820481\pi$
$859$	−5.03971	+	6.00609i	−0.171953	+	0.204925i	0.673185	+	0.739474i	$0.264926\pi$
$860$	13.4224	+	8.28808i	0.457701	+	0.282621i
$861$	0.788667	−	0.335923i	0.0268777	−	0.0114482i
$862$	15.9133	−	22.7266i	0.542009	−	0.774069i
$863$	−8.19948	−	8.19948i	−0.279113	−	0.279113i	0.553642	−	0.832755i	$-0.313238\pi$
$863$	−8.19948	−	8.19948i	−0.279113	−	0.279113i	−0.832755	+	0.553642i	$0.813238\pi$
$864$	−2.53602	−	4.53526i	−0.0862770	−	0.154293i
$865$	−6.93670	−	8.78166i	−0.235855	−	0.298585i
$866$	5.35630	−	0.944461i	0.182015	−	0.0320941i
$867$	18.0737	+	23.0743i	0.613815	+	0.783644i
$868$	1.51066	−	3.23963i	0.0512753	−	0.109960i
$869$	56.4343	+	47.3540i	1.91440	+	1.60637i
$870$	7.05104	+	14.2189i	0.239053	+	0.482066i
$871$	16.1444	+	5.87607i	0.547031	+	0.199103i
$872$	−7.54642	−	2.02206i	−0.255554	−	0.0684755i
$873$	−22.8852	+	4.50730i	−0.774546	+	0.152549i
$874$	25.6931	+	14.8339i	0.869083	+	0.501765i
$875$	3.93275	+	1.84086i	0.132951	+	0.0622324i
$876$	3.51530	−	0.816159i	0.118771	−	0.0275755i
$877$	−10.4734	+	7.33359i	−0.353663	+	0.247638i	−0.736884	−	0.676019i	$-0.763704\pi$
$877$	−10.4734	+	7.33359i	−0.353663	+	0.247638i	0.383221	+	0.923657i	$0.374815\pi$
$878$	6.09763	−	4.26960i	0.205785	−	0.144092i
$879$	0.564125	−	1.85338i	0.0190275	−	0.0625129i
$880$	−6.19236	−	9.42500i	−0.208744	−	0.317717i
$881$	−17.3133	−	9.99582i	−0.583299	−	0.336768i	0.179144	−	0.983823i	$-0.442667\pi$
$881$	−17.3133	−	9.99582i	−0.583299	−	0.336768i	−0.762443	+	0.647055i	$0.776000\pi$
$882$	17.5863	−	10.6263i	0.592163	−	0.357807i
$883$	−50.0441	−	13.4093i	−1.68412	−	0.451258i	−0.715257	−	0.698861i	$-0.753690\pi$
$883$	−50.0441	−	13.4093i	−1.68412	−	0.451258i	−0.968862	+	0.247603i	$0.920357\pi$
$884$	−0.970665	−	0.353293i	−0.0326470	−	0.0118825i
$885$	−15.0391	+	3.02599i	−0.505535	+	0.101718i
$886$	−12.2639	−	10.2906i	−0.412013	−	0.345720i
$887$	−3.62978	+	7.78409i	−0.121876	+	0.261364i	−0.957775	−	0.287520i	$-0.907169\pi$
$887$	−3.62978	+	7.78409i	−0.121876	+	0.261364i	0.835899	+	0.548884i	$0.184947\pi$
$888$	1.82784	−	0.259196i	0.0613383	−	0.00869804i
$889$	2.53921	−	0.447732i	0.0851625	−	0.0150164i
$890$	−18.3983	+	14.5329i	−0.616712	+	0.487146i
$891$	43.2374	+	13.8122i	1.44851	+	0.462726i
$892$	−7.41526	−	7.41526i	−0.248281	−	0.248281i
$893$	−2.34338	+	3.34669i	−0.0784182	+	0.111993i
$894$	14.5923	+	10.9678i	0.488041	+	0.366818i
$895$	−44.6660	+	10.5631i	−1.49302	+	0.353086i
$896$	0.249649	−	0.297520i	0.00834017	−	0.00993943i
$897$	26.9745	−	8.80151i	0.900653	−	0.293874i
$898$	−19.1703	+	8.93924i	−0.639720	+	0.298306i
$899$	18.8578	+	32.6627i	0.628944	+	1.08936i
$900$	12.6152	−	8.11526i	0.420506	−	0.270509i
$901$	−1.57086	+	2.72081i	−0.0523330	+	0.0906435i
$902$	0.560128	−	6.40230i	0.0186502	−	0.213173i
$903$	−2.23321	−	4.18753i	−0.0743164	−	0.139352i
$904$	8.26606	+	1.45753i	0.274925	+	0.0484767i
$905$	1.62858	−	5.43022i	0.0541358	−	0.180507i
$906$	5.26714	+	22.6862i	0.174989	+	0.753700i
$907$	3.64420	+	0.318826i	0.121004	+	0.0105864i	0.147497	−	0.989063i	$-0.452878\pi$
$907$	3.64420	+	0.318826i	0.121004	+	0.0105864i	−0.0264931	+	0.999649i	$0.508434\pi$
$908$	18.7162	−	5.01499i	0.621119	−	0.166428i
$909$	−2.69262	+	39.9275i	−0.0893084	+	1.32431i
$910$	2.98813	+	1.18879i	0.0990555	+	0.0394080i
$911$	6.68311	−	18.3617i	0.221421	−	0.608350i	−0.778390	−	0.627781i	$-0.783963\pi$
$911$	6.68311	−	18.3617i	0.221421	−	0.608350i	0.999811	+	0.0194313i	$0.00618555\pi$
$912$	11.3648	+	2.40095i	0.376326	+	0.0795035i
$913$	38.2301	−	3.34470i	1.26523	−	0.110693i
$914$	−20.8770	+	7.59859i	−0.690549	+	0.251339i
$915$	34.2351	−	20.8779i	1.13178	−	0.690202i
$916$	1.42241	+	8.06691i	0.0469979	+	0.266538i
$917$	3.12695	−	3.12695i	0.103261	−	0.103261i
$918$	1.44554	−	0.106482i	0.0477101	−	0.00351444i
$919$			16.5010i			0.544319i	0.962252	+	0.272159i	$0.0877378\pi$
$919$			16.5010i			0.544319i	−0.962252	+	0.272159i	$0.912262\pi$
$920$	9.87564	−	0.570373i	0.325590	−	0.0188046i
$921$	−5.33291	−	12.5204i	−0.175725	−	0.412561i
$922$	1.40828	+	0.656690i	0.0463791	+	0.0216269i
$923$	−3.36252	−	38.4338i	−0.110679	−	1.26506i
$924$	0.181755	+	3.38778i	0.00597929	+	0.111450i
$925$	1.07260	+	5.22025i	0.0352670	+	0.171641i
$926$	17.7187	−	10.2299i	0.582271	−	0.336175i
$927$	−35.5515	+	13.7481i	−1.16767	+	0.451547i
$928$	1.06062	+	3.95829i	0.0348166	+	0.129937i
$929$	41.6431	−	34.9427i	1.36627	−	1.14643i	0.392274	−	0.919849i	$-0.371689\pi$
$929$	41.6431	−	34.9427i	1.36627	−	1.14643i	0.973992	−	0.226584i	$-0.0727558\pi$
$930$	28.6995	−	21.1409i	0.941092	−	0.693236i
$931$	−7.97610	+	45.2347i	−0.261406	+	1.48251i
$932$	−12.9316	−	18.4683i	−0.423589	−	0.604948i
$933$	0.0416936	−	1.23791i	0.00136499	−	0.0405275i
$934$	15.1014	+	17.9972i	0.494134	+	0.588885i
$935$	3.11278	−	0.454409i	0.101799	−	0.0148608i
$936$	8.97127	−	6.55203i	0.293235	−	0.214160i
$937$	3.70883	−	13.8416i	0.121162	−	0.452184i	−0.878512	−	0.477721i	$-0.841463\pi$
$937$	3.70883	−	13.8416i	0.121162	−	0.452184i	0.999674	+	0.0255372i	$0.00812963\pi$
$938$	−0.761530	−	1.63311i	−0.0248648	−	0.0533228i
$939$	21.3758	−	1.14681i	0.697574	−	0.0374249i
$940$	−0.0402824	+	1.36164i	−0.00131387	+	0.0444119i
$941$	−15.5867	−	42.8242i	−0.508113	−	1.39603i	−0.883181	−	0.469032i	$-0.844603\pi$
$941$	−15.5867	−	42.8242i	−0.508113	−	1.39603i	0.375068	−	0.926997i	$-0.377619\pi$
$942$	22.7353	+	9.15292i	0.740757	+	0.298218i
$943$	4.61787	+	3.23347i	0.150379	+	0.105296i
$944$	−3.96091			−0.128917
$945$	−4.50826	+	0.198286i	−0.146654	+	0.00645024i
$946$	−35.5799			−1.15680
$947$	1.04390	+	0.730946i	0.0339221	+	0.0237525i	0.590415	−	0.807100i	$-0.298964\pi$
$947$	1.04390	+	0.730946i	0.0339221	+	0.0237525i	−0.556492	+	0.830853i	$0.687853\pi$
$948$	−19.9179	+	15.6014i	−0.646904	+	0.506708i
$949$	2.63884	+	7.25015i	0.0856603	+	0.235350i
$950$	−4.89204	+	33.1727i	−0.158719	+	1.07627i
$951$	−18.1744	−	27.9104i	−0.589346	−	0.905057i
$952$	0.0457862	+	0.0981888i	0.00148394	+	0.00318232i
$953$	−2.58541	+	9.64890i	−0.0837498	+	0.312558i	−0.995075	−	0.0991298i	$-0.968394\pi$
$953$	−2.58541	+	9.64890i	−0.0837498	+	0.312558i	0.911325	+	0.411688i	$0.135061\pi$
$954$	−14.8870	−	30.3318i	−0.481983	−	0.982029i
$955$	−31.6697	−	23.6011i	−1.02481	−	0.763715i
$956$	−0.974553	−	1.16143i	−0.0315193	−	0.0375633i
$957$	−30.3807	−	18.9317i	−0.982068	−	0.611974i
$958$	−22.4792	−	32.1036i	−0.726269	−	1.03722i
$959$	−0.631410	+	3.58091i	−0.0203893	+	0.115633i
$960$	3.60654	−	1.41168i	0.116401	−	0.0455618i
$961$	41.1415	−	34.5218i	1.32714	−	1.11361i
$962$	1.02154	+	3.81244i	0.0329358	+	0.122918i
$963$	−10.6200	+	19.2715i	−0.342226	+	0.621016i
$964$	15.1559	−	8.75028i	0.488140	−	0.281828i
$965$	39.8724	−	13.1908i	1.28354	−	0.424625i
$966$	−2.65326	−	1.34777i	−0.0853673	−	0.0433637i
$967$	−2.73726	−	31.2870i	−0.0880244	−	1.00612i	−0.903857	−	0.427835i	$-0.859276\pi$
$967$	−2.73726	−	31.2870i	−0.0880244	−	1.00612i	0.815832	−	0.578288i	$-0.196279\pi$
$968$	13.0827	+	6.10057i	0.420494	+	0.196080i
$969$	−1.94678	+	2.59013i	−0.0625395	+	0.0832070i
$970$	−1.00243	−	17.3564i	−0.0321860	−	0.557279i
$971$			0.690575i			0.0221616i	0.999939	+	0.0110808i	$0.00352720\pi$
$971$			0.690575i			0.0221616i	−0.999939	+	0.0110808i	$0.996473\pi$
$972$	−7.71046	+	13.5480i	−0.247313	+	0.434553i
$973$	−3.46578	+	3.46578i	−0.111108	+	0.111108i
$974$	−1.33432	−	7.56733i	−0.0427545	−	0.242473i
$975$	20.4770	+	24.6806i	0.655790	+	0.790410i
$976$	9.72912	−	3.54111i	0.311422	−	0.113348i
$977$	22.7266	−	1.98832i	0.727087	−	0.0636119i	0.282399	−	0.959297i	$-0.408870\pi$
$977$	22.7266	−	1.98832i	0.727087	−	0.0636119i	0.444689	+	0.895685i	$0.353314\pi$
$978$	9.90213	+	30.3477i	0.316635	+	0.970411i
$979$	18.0862	−	49.6915i	0.578039	−	1.58815i
$980$	6.05920	+	14.0656i	0.193554	+	0.449309i
$981$	6.51615	+	22.5139i	0.208045	+	0.718812i
$982$	6.07502	−	1.62780i	0.193862	−	0.0519450i
$983$	24.4864	+	2.14228i	0.780995	+	0.0683282i	0.470678	−	0.882305i	$-0.344009\pi$
$983$	24.4864	+	2.14228i	0.780995	+	0.0683282i	0.310317	+	0.950633i	$0.399565\pi$
$984$	2.11152	+	0.642698i	0.0673128	+	0.0204884i
$985$	−13.2725	−	24.6441i	−0.422897	−	0.785225i
$986$	−1.12574	−	0.198499i	−0.0358510	−	0.00632150i
$987$	0.216739	−	0.347814i	0.00689889	−	0.0110710i
$988$	−2.16440	+	24.7392i	−0.0688587	+	0.787059i
$989$	15.6049	−	27.0284i	0.496206	−	0.859454i
$990$	−14.5929	+	30.5226i	−0.463794	+	0.970072i
$991$	31.2578	+	54.1401i	0.992936	+	1.71982i	0.599222	+	0.800583i	$0.295477\pi$
$991$	31.2578	+	54.1401i	0.992936	+	1.71982i	0.393714	+	0.919233i	$0.371190\pi$
$992$	8.34130	−	3.88961i	0.264837	−	0.123495i
$993$	5.90164	−	27.9352i	0.187283	−	0.886496i
$994$	−2.60100	+	3.09975i	−0.0824986	+	0.0983180i
$995$	−4.76890	−	20.1653i	−0.151184	−	0.639282i
$996$	−1.58999	+	13.0834i	−0.0503808	+	0.414563i
$997$	4.51464	−	6.44757i	0.142980	−	0.204197i	−0.741274	−	0.671202i	$-0.765778\pi$
$997$	4.51464	−	6.44757i	0.142980	−	0.204197i	0.884254	+	0.467005i	$0.154667\pi$
$998$	−21.2611	−	21.2611i	−0.673007	−	0.673007i
$999$	−3.50139	−	4.29115i	−0.110779	−	0.135766i

Display

a_p

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p

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a_n

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a_n

instead) (See

a_n

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a_n

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n

up to: 50 250 1000 (See only

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.257.5	yes	216
3.2	odd	2		810.2.s.a.557.12		216
5.3	odd	4	inner	270.2.r.a.203.2	yes	216
15.8	even	4		810.2.s.a.233.18		216
27.2	odd	18	inner	270.2.r.a.137.2	yes	216
27.25	even	9		810.2.s.a.737.18		216
135.83	even	36	inner	270.2.r.a.83.5	✓	216
135.133	odd	36		810.2.s.a.413.12		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.5	✓	216	135.83	even	36	inner
270.2.r.a.137.2	yes	216	27.2	odd	18	inner
270.2.r.a.203.2	yes	216	5.3	odd	4	inner
270.2.r.a.257.5	yes	216	1.1	even	1	trivial
810.2.s.a.233.18		216	15.8	even	4
810.2.s.a.413.12		216	135.133	odd	36
810.2.s.a.557.12		216	3.2	odd	2
810.2.s.a.737.18		216	27.25	even	9

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Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	270.2.r.a.257.5

Level	$270$
Weight	$2$
Character	270.257
Analytic conductor	$2.156$
Analytic rank	$0$
Dimension	$216$
Inner twists	$4$