LMFDB - Embedded newform 435.2.u.a.16.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,2,Mod(16,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$435 = 3 \cdot 5 \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	435.u (of order $7$ , degree $6$ , minimal)

Newform invariants

comment:select newform

sage:traces = [30,1,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			16.4
Character	$\chi$	$=$	435.16
Dual form			435.2.u.a.136.4

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52210 + 0.733005i) q^{2} +(0.623490 - 0.781831i) q^{3} +(0.532514 + 0.667752i) q^{4} +(0.900969 + 0.433884i) q^{5} +(1.52210 - 0.733005i) q^{6} +(1.30031 - 1.63054i) q^{7} +(-0.430781 - 1.88737i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(1.05333 + 1.32083i) q^{10} +(-0.0905464 + 0.396710i) q^{11} +0.854086 q^{12} +(-0.545743 + 2.39106i) q^{13} +(3.17440 - 1.52871i) q^{14} +(0.900969 - 0.433884i) q^{15} +(1.10787 - 4.85388i) q^{16} +3.42230 q^{17} +(0.375928 - 1.64705i) q^{18} +(2.33281 + 2.92525i) q^{19} +(0.190052 + 0.832673i) q^{20} +(-0.464076 - 2.03325i) q^{21} +(-0.428611 + 0.537461i) q^{22} +(-6.04165 + 2.90951i) q^{23} +(-1.74420 - 0.839960i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-2.58333 + 3.23940i) q^{26} +(-0.900969 - 0.433884i) q^{27} +1.78123 q^{28} +(-5.30345 - 0.934582i) q^{29} +1.68940 q^{30} +(-2.02553 - 0.975444i) q^{31} +(2.83016 - 3.54891i) q^{32} +(0.253705 + 0.318137i) q^{33} +(5.20909 + 2.50857i) q^{34} +(1.87900 - 0.904881i) q^{35} +(0.532514 - 0.667752i) q^{36} +(1.97953 + 8.67287i) q^{37} +(1.40655 + 6.16249i) q^{38} +(1.52914 + 1.91748i) q^{39} +(0.430781 - 1.88737i) q^{40} +2.69792 q^{41} +(0.784011 - 3.43498i) q^{42} +(-2.61215 + 1.25795i) q^{43} +(-0.313121 + 0.150791i) q^{44} +(0.222521 - 0.974928i) q^{45} -11.3287 q^{46} +(0.287810 - 1.26098i) q^{47} +(-3.10417 - 3.89251i) q^{48} +(0.589800 + 2.58408i) q^{49} +(0.375928 + 1.64705i) q^{50} +(2.13377 - 2.67566i) q^{51} +(-1.88725 + 0.908851i) q^{52} +(-5.30014 - 2.55241i) q^{53} +(-1.05333 - 1.32083i) q^{54} +(-0.253705 + 0.318137i) q^{55} +(-3.63758 - 1.75177i) q^{56} +3.74154 q^{57} +(-7.38733 - 5.30998i) q^{58} -5.74518 q^{59} +(0.769505 + 0.370574i) q^{60} +(6.77203 - 8.49186i) q^{61} +(-2.36805 - 2.96945i) q^{62} +(-1.87900 - 0.904881i) q^{63} +(-2.06216 + 0.993084i) q^{64} +(-1.52914 + 1.91748i) q^{65} +(0.152970 + 0.670203i) q^{66} +(-1.52478 - 6.68048i) q^{67} +(1.82243 + 2.28525i) q^{68} +(-1.49217 + 6.53760i) q^{69} +3.52331 q^{70} +(-3.53964 + 15.5082i) q^{71} +(-1.74420 + 0.839960i) q^{72} +(-1.82409 + 0.878435i) q^{73} +(-3.34422 + 14.6520i) q^{74} +1.00000 q^{75} +(-0.711088 + 3.11548i) q^{76} +(0.529112 + 0.663486i) q^{77} +(0.921981 + 4.03946i) q^{78} +(-1.89199 - 8.28936i) q^{79} +(3.10417 - 3.89251i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(4.10651 + 1.97759i) q^{82} +(-5.77329 - 7.23947i) q^{83} +(1.11058 - 1.39262i) q^{84} +(3.08339 + 1.48488i) q^{85} -4.89804 q^{86} +(-4.03733 + 3.56370i) q^{87} +0.787745 q^{88} +(4.72139 + 2.27370i) q^{89} +(1.05333 - 1.32083i) q^{90} +(3.18907 + 3.99897i) q^{91} +(-5.16009 - 2.48497i) q^{92} +(-2.02553 + 0.975444i) q^{93} +(1.36238 - 1.70837i) q^{94} +(0.832571 + 3.64773i) q^{95} +(-1.01007 - 4.42542i) q^{96} +(4.28577 + 5.37418i) q^{97} +(-0.996410 + 4.36556i) q^{98} +0.406912 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$30 q + q^{2} - 5 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} - 5 q^{9} + 6 q^{10} - 18 q^{11} + 32 q^{12} - 5 q^{13} + 18 q^{14} + 5 q^{15} - 13 q^{16} + 44 q^{17} + q^{18} - 8 q^{19} + 10 q^{20} + 7 q^{21} - 19 q^{22}+ \cdots + 10 q^{99}+O(q^{100})$ 30 * q + q^2 - 5 * q^3 - 3 * q^4 + 5 * q^5 + q^6 - 5 * q^9 + 6 * q^10 - 18 * q^11 + 32 * q^12 - 5 * q^13 + 18 * q^14 + 5 * q^15 - 13 * q^16 + 44 * q^17 + q^18 - 8 * q^19 + 10 * q^20 + 7 * q^21 - 19 * q^22 + 8 * q^23 + 14 * q^24 - 5 * q^25 - 34 * q^26 - 5 * q^27 - 102 * q^28 - 27 * q^29 - 8 * q^30 + 5 * q^31 - 2 * q^32 + 10 * q^33 - 5 * q^34 - 3 * q^36 + 9 * q^37 + 7 * q^38 + 2 * q^39 + 6 * q^41 - 17 * q^42 + 33 * q^43 + 5 * q^45 + 98 * q^46 - 30 * q^47 + q^48 - 9 * q^49 + q^50 - 26 * q^51 - 45 * q^52 + 38 * q^53 - 6 * q^54 - 10 * q^55 - 70 * q^56 - 8 * q^57 - 27 * q^58 + 102 * q^59 + 3 * q^60 + 8 * q^61 - 22 * q^62 + 30 * q^64 - 2 * q^65 - 40 * q^66 - 2 * q^67 + 23 * q^68 - 13 * q^69 + 24 * q^70 - 12 * q^71 + 14 * q^72 - 28 * q^73 - 65 * q^74 + 30 * q^75 - 41 * q^76 + 24 * q^77 + 71 * q^78 + 31 * q^79 - q^80 - 5 * q^81 - 39 * q^82 - 17 * q^83 - 11 * q^84 - 2 * q^85 + 38 * q^86 - 27 * q^87 + 22 * q^88 + 25 * q^89 + 6 * q^90 + 90 * q^91 + 39 * q^92 + 5 * q^93 + 11 * q^94 + 8 * q^95 - 16 * q^96 - 27 * q^97 - 47 * q^98 + 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$ .

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{1}{7}\right)$	$1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	1.52210	+	0.733005i	1.07629	+	0.518313i	0.886128	−	0.463440i	$-0.153385\pi$
$2$	1.52210	+	0.733005i	1.07629	+	0.518313i	0.190160	+	0.981753i	$0.439099\pi$
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$3$	0.623490	−	0.781831i	0.359972	−	0.451391i
$4$	0.532514	+	0.667752i	0.266257	+	0.333876i
$5$	0.900969	+	0.433884i	0.402926	+	0.194039i
$5$	0.900969	+	0.433884i	0.402926	+	0.194039i
$6$	1.52210	−	0.733005i	0.621395	−	0.299248i
$7$	1.30031	−	1.63054i	0.491471	−	0.616286i	−0.472810	−	0.881164i	$-0.656760\pi$
$7$	1.30031	−	1.63054i	0.491471	−	0.616286i	0.964282	+	0.264879i	$0.0853319\pi$
$8$	−0.430781	−	1.88737i	−0.152304	−	0.667287i
$9$	−0.222521	−	0.974928i	−0.0741736	−	0.324976i
$10$	1.05333	+	1.32083i	0.333091	+	0.417683i
$11$	−0.0905464	+	0.396710i	−0.0273008	+	0.119613i	−0.986742	−	0.162296i	$-0.948110\pi$
$11$	−0.0905464	+	0.396710i	−0.0273008	+	0.119613i	0.959441	+	0.281908i	$0.0909673\pi$
$12$	0.854086			0.246554
$13$	−0.545743	+	2.39106i	−0.151362	+	0.663160i	0.841128	+	0.540836i	$0.181892\pi$
$13$	−0.545743	+	2.39106i	−0.151362	+	0.663160i	−0.992490	+	0.122324i	$0.960965\pi$
$14$	3.17440	−	1.52871i	0.848393	−	0.408565i
$15$	0.900969	−	0.433884i	0.232629	−	0.112028i
$16$	1.10787	−	4.85388i	0.276967	−	1.21347i
$17$	3.42230			0.830030			0.415015	−	0.909814i	$-0.363776\pi$
$17$	3.42230			0.830030			0.415015	+	0.909814i	$0.363776\pi$
$18$	0.375928	−	1.64705i	0.0886070	−	0.388213i
$19$	2.33281	+	2.92525i	0.535184	+	0.671099i	0.973755	−	0.227597i	$-0.0730869\pi$
$19$	2.33281	+	2.92525i	0.535184	+	0.671099i	−0.438572	+	0.898696i	$0.644515\pi$
$20$	0.190052	+	0.832673i	0.0424969	+	0.186191i
$21$	−0.464076	−	2.03325i	−0.101270	−	0.443691i
$22$	−0.428611	+	0.537461i	−0.0913802	+	0.114587i
$23$	−6.04165	+	2.90951i	−1.25977	+	0.606674i	−0.940114	−	0.340859i	$-0.889282\pi$
$23$	−6.04165	+	2.90951i	−1.25977	+	0.606674i	−0.319657	+	0.947533i	$0.603568\pi$
$24$	−1.74420	−	0.839960i	−0.356032	−	0.171456i
$25$	0.623490	+	0.781831i	0.124698	+	0.156366i
$26$	−2.58333	+	3.23940i	−0.506633	+	0.635298i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	1.78123			0.336621
$29$	−5.30345	−	0.934582i	−0.984825	−	0.173548i
$29$	−5.30345	−	0.934582i	−0.984825	−	0.173548i
$30$	1.68940			0.308442
$31$	−2.02553	−	0.975444i	−0.363796	−	0.175195i	0.243051	−	0.970013i	$-0.421852\pi$
$31$	−2.02553	−	0.975444i	−0.363796	−	0.175195i	−0.606847	+	0.794819i	$0.707566\pi$
$32$	2.83016	−	3.54891i	0.500307	−	0.627365i
$33$	0.253705	+	0.318137i	0.0441644	+	0.0553805i
$34$	5.20909	+	2.50857i	0.893352	+	0.430215i
$35$	1.87900	−	0.904881i	0.317610	−	0.152953i
$36$	0.532514	−	0.667752i	0.0887524	−	0.111292i
$37$	1.97953	+	8.67287i	0.325432	+	1.42581i	0.827735	+	0.561120i	$0.189629\pi$
$37$	1.97953	+	8.67287i	0.325432	+	1.42581i	−0.502303	+	0.864692i	$0.667514\pi$
$38$	1.40655	+	6.16249i	0.228172	+	0.999689i
$39$	1.52914	+	1.91748i	0.244858	+	0.307042i
$40$	0.430781	−	1.88737i	0.0681124	−	0.298420i
$41$	2.69792			0.421345			0.210672	−	0.977557i	$-0.432435\pi$
$41$	2.69792			0.421345			0.210672	+	0.977557i	$0.432435\pi$
$42$	0.784011	−	3.43498i	0.120976	−	0.530029i
$43$	−2.61215	+	1.25795i	−0.398349	+	0.191835i	−0.622323	−	0.782760i	$-0.713811\pi$
$43$	−2.61215	+	1.25795i	−0.398349	+	0.191835i	0.223974	+	0.974595i	$0.428097\pi$
$44$	−0.313121	+	0.150791i	−0.0472048	+	0.0227326i
$45$	0.222521	−	0.974928i	0.0331715	−	0.145334i
$46$	−11.3287			−1.67032
$47$	0.287810	−	1.26098i	0.0419814	−	0.183932i	−0.949590	−	0.313495i	$-0.898500\pi$
$47$	0.287810	−	1.26098i	0.0419814	−	0.183932i	0.991571	+	0.129562i	$0.0413573\pi$
$48$	−3.10417	−	3.89251i	−0.448049	−	0.561836i
$49$	0.589800	+	2.58408i	0.0842571	+	0.369154i
$50$	0.375928	+	1.64705i	0.0531642	+	0.232928i
$51$	2.13377	−	2.67566i	0.298788	−	0.374668i
$52$	−1.88725	+	0.908851i	−0.261714	+	0.126035i
$53$	−5.30014	−	2.55241i	−0.728030	−	0.350601i	0.0328792	−	0.999459i	$-0.489532\pi$
$53$	−5.30014	−	2.55241i	−0.728030	−	0.350601i	−0.760909	+	0.648859i	$0.775247\pi$
$54$	−1.05333	−	1.32083i	−0.143340	−	0.179742i
$55$	−0.253705	+	0.318137i	−0.0342096	+	0.0428975i
$56$	−3.63758	−	1.75177i	−0.486093	−	0.234090i
$57$	3.74154			0.495579
$58$	−7.38733	−	5.30998i	−0.970004	−	0.697235i
$59$	−5.74518			−0.747959			−0.373980	−	0.927437i	$-0.622007\pi$
$59$	−5.74518			−0.747959			−0.373980	+	0.927437i	$0.622007\pi$
$60$	0.769505	+	0.370574i	0.0993427	+	0.0478409i
$61$	6.77203	−	8.49186i	0.867070	−	1.08727i	−0.128355	−	0.991728i	$-0.540970\pi$
$61$	6.77203	−	8.49186i	0.867070	−	1.08727i	0.995425	−	0.0955431i	$-0.0304588\pi$
$62$	−2.36805	−	2.96945i	−0.300743	−	0.377120i
$63$	−1.87900	−	0.904881i	−0.236732	−	0.114004i
$64$	−2.06216	+	0.993084i	−0.257770	+	0.124135i
$65$	−1.52914	+	1.91748i	−0.189666	+	0.237834i
$66$	0.152970	+	0.670203i	0.0188292	+	0.0824963i
$67$	−1.52478	−	6.68048i	−0.186281	−	0.816150i	−0.978555	−	0.205985i	$-0.933960\pi$
$67$	−1.52478	−	6.68048i	−0.186281	−	0.816150i	0.792274	−	0.610165i	$-0.208897\pi$
$68$	1.82243	+	2.28525i	0.221002	+	0.277127i
$69$	−1.49217	+	6.53760i	−0.179636	+	0.787035i
$70$	3.52331			0.421117
$71$	−3.53964	+	15.5082i	−0.420078	+	1.84048i	0.111894	+	0.993720i	$0.464308\pi$
$71$	−3.53964	+	15.5082i	−0.420078	+	1.84048i	−0.531972	+	0.846762i	$0.678549\pi$
$72$	−1.74420	+	0.839960i	−0.205555	+	0.0989903i
$73$	−1.82409	+	0.878435i	−0.213493	+	0.102813i	−0.537574	−	0.843216i	$-0.680659\pi$
$73$	−1.82409	+	0.878435i	−0.213493	+	0.102813i	0.324081	+	0.946029i	$0.394945\pi$
$74$	−3.34422	+	14.6520i	−0.388758	+	1.70326i
$75$	1.00000			0.115470
$76$	−0.711088	+	3.11548i	−0.0815674	+	0.357370i
$77$	0.529112	+	0.663486i	0.0602979	+	0.0756112i
$78$	0.921981	+	4.03946i	0.104394	+	0.457379i
$79$	−1.89199	−	8.28936i	−0.212866	−	0.932626i	−0.962608	−	0.270897i	$-0.912680\pi$
$79$	−1.89199	−	8.28936i	−0.212866	−	0.932626i	0.749743	−	0.661730i	$-0.230177\pi$
$80$	3.10417	−	3.89251i	0.347057	−	0.435196i
$81$	−0.900969	+	0.433884i	−0.100108	+	0.0482093i
$82$	4.10651	+	1.97759i	0.453488	+	0.218388i
$83$	−5.77329	−	7.23947i	−0.633700	−	0.794635i	0.356499	−	0.934296i	$-0.383970\pi$
$83$	−5.77329	−	7.23947i	−0.633700	−	0.794635i	−0.990199	+	0.139661i	$0.955399\pi$
$84$	1.11058	−	1.39262i	0.121174	−	0.151947i
$85$	3.08339	+	1.48488i	0.334440	+	0.161058i
$86$	−4.89804			−0.528169
$87$	−4.03733	+	3.56370i	−0.432847	+	0.382069i
$88$	0.787745			0.0839739
$89$	4.72139	+	2.27370i	0.500466	+	0.241012i	0.667047	−	0.745016i	$-0.267558\pi$
$89$	4.72139	+	2.27370i	0.500466	+	0.241012i	−0.166580	+	0.986028i	$0.553272\pi$
$90$	1.05333	−	1.32083i	0.111030	−	0.139228i
$91$	3.18907	+	3.99897i	0.334306	+	0.419206i
$92$	−5.16009	−	2.48497i	−0.537977	−	0.259076i
$93$	−2.02553	+	0.975444i	−0.210038	+	0.101149i
$94$	1.36238	−	1.70837i	0.140519	−	0.176205i
$95$	0.832571	+	3.64773i	0.0854200	+	0.374249i
$96$	−1.01007	−	4.42542i	−0.103090	−	0.451668i
$97$	4.28577	+	5.37418i	0.435154	+	0.545666i	0.950259	−	0.311462i	$-0.100819\pi$
$97$	4.28577	+	5.37418i	0.435154	+	0.545666i	−0.515105	+	0.857127i	$0.672247\pi$
$98$	−0.996410	+	4.36556i	−0.100653	+	0.440988i
$99$	0.406912			0.0408962
$100$	−0.190052	+	0.832673i	−0.0190052	+	0.0832673i
$101$	−15.0386	+	7.24220i	−1.49639	+	0.720626i	−0.989920	−	0.141629i	$-0.954766\pi$
$101$	−15.0386	+	7.24220i	−1.49639	+	0.720626i	−0.506475	+	0.862255i	$0.669052\pi$
$102$	5.20909	−	2.50857i	0.515777	−	0.248385i
$103$	0.942869	−	4.13098i	0.0929036	−	0.407037i	−0.906997	−	0.421137i	$-0.861631\pi$
$103$	0.942869	−	4.13098i	0.0929036	−	0.407037i	0.999901	+	0.0140998i	$0.00448827\pi$
$104$	4.74791			0.465571
$105$	0.464076	−	2.03325i	0.0452891	−	0.198425i
$106$	−6.19641	−	7.77005i	−0.601849	−	0.754694i
$107$	−0.107615	−	0.471492i	−0.0104035	−	0.0455809i	0.969460	−	0.245251i	$-0.0788702\pi$
$107$	−0.107615	−	0.471492i	−0.0104035	−	0.0455809i	−0.979863	+	0.199670i	$0.936013\pi$
$108$	−0.190052	−	0.832673i	−0.0182878	−	0.0801240i
$109$	6.42482	−	8.05647i	0.615386	−	0.771670i	−0.372301	−	0.928112i	$-0.621431\pi$
$109$	6.42482	−	8.05647i	0.615386	−	0.771670i	0.987687	+	0.156442i	$0.0500026\pi$
$110$	−0.619361	+	0.298268i	−0.0590537	+	0.0284388i
$111$	8.01494	+	3.85979i	0.760744	+	0.366355i
$112$	−6.47387	−	8.11798i	−0.611723	−	0.767077i
$113$	3.65299	−	4.58070i	0.343644	−	0.430916i	−0.579735	−	0.814805i	$-0.696844\pi$
$113$	3.65299	−	4.58070i	0.343644	−	0.430916i	0.923379	+	0.383889i	$0.125415\pi$
$114$	5.69500	+	2.74257i	0.533386	+	0.256865i
$115$	−6.70573			−0.625313
$116$	−2.20009	−	4.03906i	−0.204273	−	0.375018i
$117$	2.45255			0.226738
$118$	−8.74475	−	4.21125i	−0.805019	−	0.387677i
$119$	4.45006	−	5.58020i	0.407936	−	0.511536i
$120$	−1.20702	−	1.51356i	−0.110185	−	0.138168i
$121$	9.76148	+	4.70088i	0.887407	+	0.427353i
$122$	16.5323	−	7.96153i	1.49676	−	0.720803i
$123$	1.68213	−	2.10932i	0.151672	−	0.190191i
$124$	−0.427269	−	1.87199i	−0.0383699	−	0.168110i
$125$	0.222521	+	0.974928i	0.0199029	+	0.0872002i
$126$	−2.19675	−	2.75464i	−0.195702	−	0.245403i
$127$	0.604087	−	2.64668i	0.0536041	−	0.234855i	−0.941028	−	0.338328i	$-0.890139\pi$
$127$	0.604087	−	2.64668i	0.0536041	−	0.234855i	0.994632	+	0.103474i	$0.0329957\pi$
$128$	−12.9452			−1.14421
$129$	−0.645148	+	2.82658i	−0.0568021	+	0.248866i
$130$	−3.73302	+	1.79773i	−0.327408	+	0.157671i
$131$	−9.80238	+	4.72058i	−0.856438	+	0.412439i	−0.809963	−	0.586481i	$-0.800513\pi$
$131$	−9.80238	+	4.72058i	−0.856438	+	0.412439i	−0.0464745	+	0.998919i	$0.514799\pi$
$132$	−0.0773345	+	0.338824i	−0.00673110	+	0.0294909i
$133$	7.80312			0.676616
$134$	2.57596	−	11.2860i	0.222529	−	0.974964i
$135$	−0.623490	−	0.781831i	−0.0536615	−	0.0672893i
$136$	−1.47426	−	6.45917i	−0.126417	−	0.553869i
$137$	0.686178	+	3.00634i	0.0586241	+	0.256849i	0.995744	−	0.0921573i	$-0.0293763\pi$
$137$	0.686178	+	3.00634i	0.0586241	+	0.256849i	−0.937120	+	0.349006i	$0.886519\pi$
$138$	−7.06332	+	8.85712i	−0.601270	+	0.753969i
$139$	17.9210	−	8.63032i	1.52004	−	0.732014i	0.527011	−	0.849858i	$-0.323313\pi$
$139$	17.9210	−	8.63032i	1.52004	−	0.732014i	0.993032	+	0.117844i	$0.0375982\pi$
$140$	1.60483	+	0.772846i	0.135633	+	0.0653174i
$141$	−0.806425	−	1.01122i	−0.0679132	−	0.0851605i
$142$	−16.7553	+	21.0104i	−1.40607	+	1.76316i
$143$	−0.899141	−	0.433003i	−0.0751899	−	0.0362096i
$144$	−4.97871			−0.414892
$145$	−4.37274	−	3.14311i	−0.363136	−	0.261021i
$146$	−3.42034			−0.283070
$147$	2.38805	+	1.15002i	0.196963	+	0.0948524i
$148$	−4.73720	+	5.94026i	−0.389395	+	0.488286i
$149$	7.93923	+	9.95548i	0.650407	+	0.815585i	0.992261	−	0.124168i	$-0.0396263\pi$
$149$	7.93923	+	9.95548i	0.650407	+	0.815585i	−0.341854	+	0.939753i	$0.611055\pi$
$150$	1.52210	+	0.733005i	0.124279	+	0.0598496i
$151$	12.8020	−	6.16513i	1.04181	−	0.501712i	0.166893	−	0.985975i	$-0.446627\pi$
$151$	12.8020	−	6.16513i	1.04181	−	0.501712i	0.874922	+	0.484264i	$0.160912\pi$
$152$	4.51612	−	5.66303i	0.366305	−	0.459333i
$153$	−0.761534	−	3.33650i	−0.0615664	−	0.269740i
$154$	0.319024	+	1.39773i	0.0257077	+	0.112633i
$155$	−1.40171	−	1.75769i	−0.112588	−	0.141181i
$156$	−0.466112	+	2.04217i	−0.0373188	+	0.163504i
$157$	−15.9977			−1.27675			−0.638376	−	0.769725i	$-0.720393\pi$
$157$	−15.9977			−1.27675			−0.638376	+	0.769725i	$0.720393\pi$
$158$	3.19634	−	14.0041i	0.254287	−	1.11411i
$159$	−5.30014	+	2.55241i	−0.420328	+	0.202419i
$160$	4.08970	−	1.96950i	0.323320	−	0.155702i
$161$	−3.11197	+	13.6344i	−0.245257	+	1.07454i
$162$	−1.68940			−0.132732
$163$	3.17435	−	13.9077i	0.248634	−	1.08934i	−0.684274	−	0.729225i	$-0.739881\pi$
$163$	3.17435	−	13.9077i	0.248634	−	1.08934i	0.932908	−	0.360114i	$-0.117262\pi$
$164$	1.43668	+	1.80154i	0.112186	+	0.140677i
$165$	0.0905464	+	0.396710i	0.00704903	+	0.0308838i
$166$	−3.48095	−	15.2510i	−0.270174	−	1.18371i
$167$	3.56903	−	4.47542i	0.276179	−	0.346318i	−0.624325	−	0.781165i	$-0.714626\pi$
$167$	3.56903	−	4.47542i	0.276179	−	0.346318i	0.900505	+	0.434847i	$0.143197\pi$
$168$	−3.63758	+	1.75177i	−0.280646	+	0.135152i
$169$	6.29328	+	3.03068i	0.484098	+	0.233129i
$170$	3.60480	+	4.52028i	0.276476	+	0.346690i
$171$	2.33281	−	2.92525i	0.178395	−	0.223700i
$172$	−2.23100	−	1.07439i	−0.170112	−	0.0819218i
$173$	−11.5217			−0.875976			−0.437988	−	0.898981i	$-0.644309\pi$
$173$	−11.5217			−0.875976			−0.437988	+	0.898981i	$0.644309\pi$
$174$	−8.75743	+	2.46493i	−0.663899	+	0.186866i
$175$	2.08554			0.157652
$176$	1.82527	+	0.879003i	0.137585	+	0.0662574i
$177$	−3.58206	+	4.49177i	−0.269244	+	0.337622i
$178$	5.51979	+	6.92160i	0.413726	+	0.518796i
$179$	14.4212	+	6.94489i	1.07789	+	0.519086i	0.886642	−	0.462456i	$-0.153032\pi$
$179$	14.4212	+	6.94489i	1.07789	+	0.519086i	0.191250	+	0.981541i	$0.438746\pi$
$180$	0.769505	−	0.370574i	0.0573555	−	0.0276210i
$181$	2.79297	−	3.50227i	0.207600	−	0.260322i	−0.667121	−	0.744950i	$-0.732473\pi$
$181$	2.79297	−	3.50227i	0.207600	−	0.260322i	0.874721	+	0.484628i	$0.161045\pi$
$182$	1.92283	+	8.42445i	0.142529	+	0.624462i
$183$	−2.41691	−	10.5892i	−0.178663	−	0.782774i
$184$	8.09396	+	10.1495i	0.596694	+	0.748231i
$185$	−1.97953	+	8.67287i	−0.145538	+	0.637642i
$186$	−3.79806			−0.278488
$187$	−0.309877	+	1.35766i	−0.0226605	+	0.0992820i
$188$	0.995282	−	0.479303i	0.0725884	−	0.0349567i
$189$	−1.87900	+	0.904881i	−0.136677	+	0.0658204i
$190$	−1.40655	+	6.16249i	−0.102042	+	0.447074i
$191$	15.8959			1.15018			0.575092	−	0.818088i	$-0.304966\pi$
$191$	15.8959			1.15018			0.575092	+	0.818088i	$0.304966\pi$
$192$	−0.509311	+	2.23144i	−0.0367564	+	0.161040i
$193$	−5.15989	−	6.47030i	−0.371417	−	0.465742i	0.560637	−	0.828062i	$-0.310556\pi$
$193$	−5.15989	−	6.47030i	−0.371417	−	0.465742i	−0.932054	+	0.362319i	$0.881985\pi$
$194$	2.58407	+	11.3215i	0.185525	+	0.812839i
$195$	0.545743	+	2.39106i	0.0390815	+	0.171227i
$196$	−1.41145	+	1.76990i	−0.100818	+	0.126421i
$197$	11.7277	−	5.64775i	0.835562	−	0.402386i	0.0333640	−	0.999443i	$-0.489378\pi$
$197$	11.7277	−	5.64775i	0.835562	−	0.402386i	0.802198	+	0.597058i	$0.203664\pi$
$198$	0.619361	+	0.298268i	0.0440161	+	0.0211970i
$199$	−0.0298772	−	0.0374648i	−0.00211794	−	0.00265581i	0.780771	−	0.624817i	$-0.214826\pi$
$199$	−0.0298772	−	0.0374648i	−0.00211794	−	0.00265581i	−0.782889	+	0.622161i	$0.786255\pi$
$200$	1.20702	−	1.51356i	0.0853493	−	0.107025i
$201$	−6.17369	−	2.97309i	−0.435458	−	0.209706i
$202$	−28.1988			−1.98406
$203$	−8.42000	+	7.43223i	−0.590968	+	0.521640i
$204$	2.92294			0.204647
$205$	2.43075	+	1.17059i	0.169771	+	0.0817572i
$206$	4.46317	−	5.59663i	0.310964	−	0.389936i
$207$	4.18095	+	5.24275i	0.290596	+	0.364396i
$208$	11.0013	+	5.29795i	0.762803	+	0.367347i
$209$	−1.37170	+	0.660578i	−0.0948828	+	0.0456932i
$210$	2.19675	−	2.75464i	0.151590	−	0.190088i
$211$	2.30234	+	10.0872i	0.158500	+	0.694433i	0.990252	+	0.139286i	$0.0444807\pi$
$211$	2.30234	+	10.0872i	0.158500	+	0.694433i	−0.831752	+	0.555147i	$0.812662\pi$
$212$	−1.11802	−	4.89837i	−0.0767860	−	0.336421i
$213$	9.91785	+	12.4366i	0.679560	+	0.852141i
$214$	0.181805	−	0.796541i	0.0124279	−	0.0544504i
$215$	−2.89927			−0.197728
$216$	−0.430781	+	1.88737i	−0.0293109	+	0.128420i
$217$	−4.22432	+	2.03432i	−0.286765	+	0.138099i
$218$	15.6846	−	7.55333i	1.06230	−	0.511576i
$219$	−0.450513	+	1.97382i	−0.0304428	+	0.133379i
$220$	−0.347538			−0.0234310
$221$	−1.86770	+	8.18292i	−0.125635	+	0.550443i
$222$	9.37030	+	11.7500i	0.628893	+	0.788607i
$223$	−1.83008	−	8.01809i	−0.122551	−	0.536931i	−0.998511	−	0.0545476i	$-0.982628\pi$
$223$	−1.83008	−	8.01809i	−0.122551	−	0.536931i	0.875960	−	0.482383i	$-0.160229\pi$
$224$	−2.10655	−	9.22938i	−0.140750	−	0.616664i
$225$	0.623490	−	0.781831i	0.0415660	−	0.0521221i
$226$	8.91789	−	4.29463i	0.593210	−	0.285675i
$227$	−13.5083	−	6.50525i	−0.896577	−	0.431769i	−0.0719255	−	0.997410i	$-0.522914\pi$
$227$	−13.5083	−	6.50525i	−0.896577	−	0.431769i	−0.824651	+	0.565641i	$0.808629\pi$
$228$	1.99242	+	2.49842i	0.131951	+	0.165462i
$229$	5.14009	−	6.44547i	0.339667	−	0.425929i	−0.582434	−	0.812878i	$-0.697900\pi$
$229$	5.14009	−	6.44547i	0.339667	−	0.425929i	0.922101	+	0.386949i	$0.126471\pi$
$230$	−10.2068	−	4.91533i	−0.673016	−	0.324107i
$231$	0.848630			0.0558357
$232$	0.520717	+	10.4122i	0.0341868	+	0.683594i
$233$	18.2159			1.19336			0.596681	−	0.802479i	$-0.296486\pi$
$233$	18.2159			1.19336			0.596681	+	0.802479i	$0.296486\pi$
$234$	3.73302	+	1.79773i	0.244035	+	0.117521i
$235$	0.806425	−	1.01122i	0.0526054	−	0.0659650i
$236$	−3.05939	−	3.83636i	−0.199149	−	0.249726i
$237$	−7.66052	−	3.68911i	−0.497604	−	0.239634i
$238$	10.8637	−	5.23171i	0.704192	−	0.339121i
$239$	12.3322	−	15.4641i	0.797705	−	1.00029i	−0.202076	−	0.979370i	$-0.564769\pi$
$239$	12.3322	−	15.4641i	0.797705	−	1.00029i	0.999781	−	0.0209209i	$-0.00665982\pi$
$240$	−1.10787	−	4.85388i	−0.0715125	−	0.313317i
$241$	5.55013	+	24.3167i	0.357515	+	1.56638i	0.759361	+	0.650670i	$0.225512\pi$
$241$	5.55013	+	24.3167i	0.357515	+	1.56638i	−0.401845	+	0.915708i	$0.631631\pi$
$242$	11.4122	+	14.3104i	0.733603	+	0.919909i
$243$	−0.222521	+	0.974928i	−0.0142747	+	0.0625417i
$244$	9.27666			0.593877
$245$	−0.589800	+	2.58408i	−0.0376809	+	0.165091i
$246$	4.10651	−	1.97759i	0.261822	−	0.126087i
$247$	−8.26757	+	3.98145i	−0.526053	+	0.253334i
$248$	−0.968467	+	4.24313i	−0.0614977	+	0.269439i
$249$	−9.25963			−0.586805
$250$	−0.375928	+	1.64705i	−0.0237758	+	0.104168i
$251$	−10.1335	−	12.7071i	−0.639624	−	0.802063i	0.351332	−	0.936251i	$-0.385729\pi$
$251$	−10.1335	−	12.7071i	−0.639624	−	0.802063i	−0.990956	+	0.134188i	$0.957157\pi$
$252$	−0.396361	−	1.73657i	−0.0249684	−	0.109394i
$253$	−0.607180	−	2.66023i	−0.0381731	−	0.167247i
$254$	2.85951	−	3.58571i	0.179422	−	0.224988i
$255$	3.08339	−	1.48488i	0.193089	−	0.0929869i
$256$	−15.5796	−	7.50274i	−0.973724	−	0.468921i
$257$	−12.6025	−	15.8031i	−0.786125	−	0.985769i	−0.999960	−	0.00889976i	$-0.997167\pi$
$257$	−12.6025	−	15.8031i	−0.786125	−	0.985769i	0.213835	−	0.976870i	$-0.431404\pi$
$258$	−3.05388	+	3.82944i	−0.190126	+	0.238410i
$259$	16.7155	+	8.04974i	1.03865	+	0.500186i
$260$	−2.09469			−0.129907
$261$	0.268978	+	5.37844i	0.0166493	+	0.332917i
$262$	−18.3804			−1.13555
$263$	−26.4307	−	12.7284i	−1.62979	−	0.784865i	−0.999967	−	0.00812489i	$-0.997414\pi$
$263$	−26.4307	−	12.7284i	−1.62979	−	0.784865i	−0.629822	−	0.776740i	$-0.716872\pi$
$264$	0.491151	−	0.615884i	0.0302283	−	0.0379050i
$265$	−3.66781	−	4.59929i	−0.225312	−	0.282532i
$266$	11.8771	+	5.71973i	0.728234	+	0.350699i
$267$	4.72139	−	2.27370i	0.288944	−	0.139148i
$268$	3.64894	−	4.57562i	0.222894	−	0.279500i
$269$	2.16053	+	9.46589i	0.131730	+	0.577145i	0.997106	+	0.0760229i	$0.0242222\pi$
$269$	2.16053	+	9.46589i	0.131730	+	0.577145i	−0.865376	+	0.501122i	$0.832921\pi$
$270$	−0.375928	−	1.64705i	−0.0228782	−	0.100236i
$271$	14.4684	+	18.1428i	0.878893	+	1.10210i	0.994069	+	0.108752i	$0.0346853\pi$
$271$	14.4684	+	18.1428i	0.878893	+	1.10210i	−0.115176	+	0.993345i	$0.536743\pi$
$272$	3.79146	−	16.6115i	0.229891	−	1.00722i
$273$	5.11488			0.309567
$274$	−1.15923	+	5.07893i	−0.0700318	+	0.306829i
$275$	−0.366615	+	0.176552i	−0.0221077	+	0.0106465i
$276$	−5.16009	+	2.48497i	−0.310601	+	0.149578i
$277$	−0.529197	+	2.31856i	−0.0317964	+	0.139309i	−0.988335	−	0.152298i	$-0.951333\pi$
$277$	−0.529197	+	2.31856i	−0.0317964	+	0.139309i	0.956538	+	0.291607i	$0.0941899\pi$
$278$	33.6037			2.01542
$279$	−0.500264	+	2.19180i	−0.0299500	+	0.131220i
$280$	−2.51729	−	3.15658i	−0.150437	−	0.188642i
$281$	4.07500	+	17.8537i	0.243094	+	1.06506i	0.938183	+	0.346141i	$0.112508\pi$
$281$	4.07500	+	17.8537i	0.243094	+	1.06506i	−0.695089	+	0.718924i	$0.744635\pi$
$282$	−0.486227	−	2.13030i	−0.0289544	−	0.126857i
$283$	−4.13872	+	5.18979i	−0.246021	+	0.308501i	−0.889475	−	0.456984i	$-0.848930\pi$
$283$	−4.13872	+	5.18979i	−0.246021	+	0.308501i	0.643454	+	0.765485i	$0.277501\pi$
$284$	−12.2405	+	5.89472i	−0.726341	+	0.349788i
$285$	3.37101	+	1.62339i	0.199681	+	0.0961615i
$286$	−1.05119	−	1.31815i	−0.0621581	−	0.0779438i
$287$	3.50814	−	4.39907i	0.207079	−	0.259669i
$288$	−4.08970	−	1.96950i	−0.240988	−	0.116054i
$289$	−5.28784			−0.311049
$290$	−4.35184	−	7.98937i	−0.255549	−	0.469152i
$291$	6.87384			0.402951
$292$	−1.55793	−	0.750259i	−0.0911709	−	0.0439056i
$293$	10.3504	−	12.9790i	0.604677	−	0.758241i	−0.381422	−	0.924401i	$-0.624565\pi$
$293$	10.3504	−	12.9790i	0.604677	−	0.758241i	0.986099	+	0.166160i	$0.0531368\pi$
$294$	2.79188	+	3.50091i	0.162826	+	0.204177i
$295$	−5.17623	−	2.49274i	−0.301372	−	0.145133i
$296$	15.5162	−	7.47221i	0.901861	−	0.434314i
$297$	0.253705	−	0.318137i	0.0147215	−	0.0184602i
$298$	4.78689	+	20.9727i	0.277297	+	1.21492i
$299$	−3.65961	−	16.0338i	−0.211640	−	0.927258i
$300$	0.532514	+	0.667752i	0.0307447	+	0.0385527i
$301$	−1.34548	+	5.89493i	−0.0775522	+	0.339778i
$302$	24.0051			1.38134
$303$	−3.71422	+	16.2731i	−0.213377	+	0.934864i
$304$	16.7833	−	8.08240i	0.962588	−	0.463558i
$305$	9.78587	−	4.71263i	0.560337	−	0.269844i
$306$	1.28654	−	5.63670i	0.0735465	−	0.322228i
$307$	−19.4590			−1.11058			−0.555292	−	0.831655i	$-0.687394\pi$
$307$	−19.4590			−1.11058			−0.555292	+	0.831655i	$0.687394\pi$
$308$	−0.161284	+	0.706631i	−0.00919000	+	0.0402640i
$309$	−2.64186	−	3.31279i	−0.150290	−	0.188458i
$310$	−0.845149	−	3.70284i	−0.0480012	−	0.210307i
$311$	−7.01942	−	30.7541i	−0.398035	−	1.74390i	−0.635119	−	0.772415i	$-0.719049\pi$
$311$	−7.01942	−	30.7541i	−0.398035	−	1.74390i	0.237084	−	0.971489i	$-0.423808\pi$
$312$	2.96028	−	3.71207i	0.167593	−	0.210155i
$313$	7.44324	−	3.58448i	0.420717	−	0.202607i	−0.211533	−	0.977371i	$-0.567846\pi$
$313$	7.44324	−	3.58448i	0.420717	−	0.202607i	0.632250	+	0.774764i	$0.282131\pi$
$314$	−24.3500	−	11.7264i	−1.37415	−	0.661757i
$315$	−1.30031	−	1.63054i	−0.0732642	−	0.0918704i
$316$	4.52772	−	5.67759i	0.254704	−	0.319389i
$317$	−2.49258	−	1.20036i	−0.139997	−	0.0674190i	0.362574	−	0.931955i	$-0.381898\pi$
$317$	−2.49258	−	1.20036i	−0.139997	−	0.0674190i	−0.502571	+	0.864536i	$0.667612\pi$
$318$	−9.93827			−0.557311
$319$	0.850966	−	2.01931i	0.0476450	−	0.113059i
$320$	−2.28882			−0.127949
$321$	−0.435724	−	0.209834i	−0.0243197	−	0.0117118i
$322$	−14.7308	+	18.4719i	−0.820916	+	1.02940i
$323$	7.98359	+	10.0111i	0.444219	+	0.557033i
$324$	−0.769505	−	0.370574i	−0.0427503	−	0.0205875i
$325$	−2.20967	+	1.06412i	−0.122570	+	0.0590268i
$326$	15.0261	−	18.8422i	0.832220	−	1.04357i
$327$	−2.29299	−	10.0463i	−0.126803	−	0.555559i
$328$	−1.16221	−	5.09199i	−0.0641725	−	0.281158i
$329$	−1.68183	−	2.10895i	−0.0927222	−	0.116270i
$330$	−0.152970	+	0.670203i	−0.00842069	+	0.0368935i
$331$	24.7576			1.36080			0.680401	−	0.732840i	$-0.261806\pi$
$331$	24.7576			1.36080			0.680401	+	0.732840i	$0.261806\pi$
$332$	1.75981	−	7.71024i	0.0965823	−	0.423155i
$333$	8.01494	−	3.85979i	0.439216	−	0.211515i
$334$	8.71292	−	4.19592i	0.476750	−	0.229591i
$335$	1.52478	−	6.68048i	0.0833074	−	0.364993i
$336$	−10.3833			−0.566454
$337$	0.334694	−	1.46639i	0.0182319	−	0.0798794i	−0.964993	−	0.262274i	$-0.915528\pi$
$337$	0.334694	−	1.46639i	0.0182319	−	0.0798794i	0.983225	+	0.182394i	$0.0583848\pi$
$338$	7.35749	+	9.22601i	0.400195	+	0.501829i
$339$	−1.30374	−	5.71204i	−0.0708093	−	0.310236i
$340$	0.650416	+	2.84966i	0.0352738	+	0.154544i
$341$	0.570372	−	0.715224i	0.0308874	−	0.0387316i
$342$	5.69500	−	2.74257i	0.307950	−	0.148301i
$343$	18.1334	+	8.73258i	0.979111	+	0.471515i
$344$	3.49948	+	4.38821i	0.188679	+	0.236596i
$345$	−4.18095	+	5.24275i	−0.225095	+	0.282260i
$346$	−17.5371	−	8.44544i	−0.942803	−	0.454030i
$347$	−21.5136			−1.15491			−0.577456	−	0.816422i	$-0.695954\pi$
$347$	−21.5136			−1.15491			−0.577456	+	0.816422i	$0.695954\pi$
$348$	−4.52960	−	0.798214i	−0.242812	−	0.0427888i
$349$	−29.3357			−1.57031			−0.785153	−	0.619302i	$-0.787416\pi$
$349$	−29.3357			−1.57031			−0.785153	+	0.619302i	$0.787416\pi$
$350$	3.17440	+	1.52871i	0.169679	+	0.0817129i
$351$	1.52914	−	1.91748i	0.0816194	−	0.102347i
$352$	1.15163	+	1.44410i	0.0613819	+	0.0769705i
$353$	−6.71470	−	3.23363i	−0.357387	−	0.172109i	0.246571	−	0.969125i	$-0.420696\pi$
$353$	−6.71470	−	3.23363i	−0.357387	−	0.172109i	−0.603958	+	0.797016i	$0.706411\pi$
$354$	−8.74475	+	4.21125i	−0.464778	+	0.223825i
$355$	−9.91785	+	12.4366i	−0.526385	+	0.660066i
$356$	0.995939	+	4.36349i	0.0527847	+	0.231265i
$357$	−1.58821	−	6.95839i	−0.0840569	−	0.368277i
$358$	16.8599	+	21.1416i	0.891074	+	1.11737i
$359$	5.11645	−	22.4166i	0.270036	−	1.18310i	−0.639934	−	0.768430i	$-0.721038\pi$
$359$	5.11645	−	22.4166i	0.270036	−	1.18310i	0.909970	−	0.414675i	$-0.136105\pi$
$360$	−1.93591			−0.102031
$361$	1.11280	−	4.87549i	0.0585684	−	0.256605i
$362$	6.81837	−	3.28355i	0.358365	−	0.172580i
$363$	9.76148	−	4.70088i	0.512345	−	0.246732i
$364$	−0.972094	+	4.25902i	−0.0509515	+	0.223233i
$365$	−2.02458			−0.105972
$366$	4.08314	−	17.8894i	0.213429	−	0.935094i
$367$	11.4249	+	14.3264i	0.596376	+	0.747832i	0.984808	−	0.173646i	$-0.0555547\pi$
$367$	11.4249	+	14.3264i	0.596376	+	0.747832i	−0.388432	+	0.921477i	$0.626983\pi$
$368$	7.42906	+	32.5488i	0.387266	+	1.69672i
$369$	−0.600345	−	2.63028i	−0.0312527	−	0.136927i
$370$	−9.37030	+	11.7500i	−0.487139	+	0.610852i
$371$	−11.0536	+	5.32315i	−0.573876	+	0.276364i
$372$	−1.72998	−	0.833113i	−0.0896951	−	0.0431949i
$373$	−8.30711	−	10.4168i	−0.430126	−	0.539361i	0.518785	−	0.854905i	$-0.326384\pi$
$373$	−8.30711	−	10.4168i	−0.430126	−	0.539361i	−0.948911	+	0.315544i	$0.897813\pi$
$374$	−1.46684	+	1.83936i	−0.0758483	+	0.0951108i
$375$	0.900969	+	0.433884i	0.0465258	+	0.0224057i
$376$	−2.50392			−0.129130
$377$	5.12896	−	12.1708i	0.264155	−	0.626828i
$378$	−3.52331			−0.181220
$379$	−30.4188	−	14.6489i	−1.56251	−	0.752465i	−0.565143	−	0.824993i	$-0.691179\pi$
$379$	−30.4188	−	14.6489i	−1.56251	−	0.752465i	−0.997366	+	0.0725281i	$0.976893\pi$
$380$	−1.99242	+	2.49842i	−0.102209	+	0.128166i
$381$	−1.69261	−	2.12247i	−0.0867153	−	0.108737i
$382$	24.1951	+	11.6518i	1.23793	+	0.596156i
$383$	−7.49918	+	3.61141i	−0.383190	+	0.184535i	−0.615555	−	0.788094i	$-0.711068\pi$
$383$	−7.49918	+	3.61141i	−0.383190	+	0.184535i	0.232365	+	0.972629i	$0.425354\pi$
$384$	−8.07121	+	10.1210i	−0.411882	+	0.516484i
$385$	0.188838	+	0.827353i	0.00962407	+	0.0421658i
$386$	−3.11111	−	13.6307i	−0.158351	−	0.693783i
$387$	1.80766	+	2.26674i	0.0918887	+	0.115225i
$388$	−1.30639	+	5.72366i	−0.0663218	+	0.290575i
$389$	−25.1648			−1.27591			−0.637953	−	0.770075i	$-0.720219\pi$
$389$	−25.1648			−1.27591			−0.637953	+	0.770075i	$0.720219\pi$
$390$	−0.921981	+	4.03946i	−0.0466863	+	0.204546i
$391$	−20.6764	+	9.95722i	−1.04565	+	0.503558i
$392$	4.62305	−	2.22635i	0.233499	−	0.112447i
$393$	−2.42099	+	10.6070i	−0.122123	+	0.535054i
$394$	21.9905			1.10787
$395$	1.89199	−	8.28936i	0.0951965	−	0.417083i
$396$	0.216686	+	0.271716i	0.0108889	+	0.0136542i
$397$	6.12692	+	26.8438i	0.307501	+	1.34725i	0.858530	+	0.512764i	$0.171378\pi$
$397$	6.12692	+	26.8438i	0.307501	+	1.34725i	−0.551029	+	0.834486i	$0.685764\pi$
$398$	−0.0180142	−	0.0789253i	−0.000902970	−	0.00395617i
$399$	4.86517	−	6.10073i	0.243563	−	0.305418i
$400$	4.48566	−	2.16018i	0.224283	−	0.108009i
$401$	−1.89422	−	0.912211i	−0.0945931	−	0.0455536i	0.385989	−	0.922503i	$-0.373860\pi$
$401$	−1.89422	−	0.912211i	−0.0945931	−	0.0455536i	−0.480582	+	0.876950i	$0.659575\pi$
$402$	−7.21768	−	9.05069i	−0.359985	−	0.451407i
$403$	3.43776	−	4.31081i	0.171247	−	0.214737i
$404$	−12.8442	−	6.18546i	−0.639025	−	0.307738i
$405$	−1.00000			−0.0496904
$406$	−18.2640	+	5.14069i	−0.906425	+	0.255128i
$407$	−3.61985			−0.179429
$408$	−5.96917	−	2.87460i	−0.295518	−	0.142314i
$409$	−20.2670	+	25.4140i	−1.00214	+	1.25664i	−0.0358010	+	0.999359i	$0.511398\pi$
$409$	−20.2670	+	25.4140i	−1.00214	+	1.25664i	−0.966336	+	0.257282i	$0.917173\pi$
$410$	2.84179	+	3.56350i	0.140346	+	0.175989i
$411$	2.77828	+	1.33795i	0.137042	+	0.0659961i
$412$	3.26056	−	1.57020i	0.160636	−	0.0773583i
$413$	−7.47053	+	9.36774i	−0.367601	+	0.460957i
$414$	2.52087	+	11.0447i	0.123894	+	0.542815i
$415$	−2.06046	−	9.02747i	−0.101144	−	0.443141i
$416$	6.94111	+	8.70388i	0.340316	+	0.426743i
$417$	4.42613	−	19.3922i	0.216749	−	0.949638i
$418$	−2.57208			−0.125805
$419$	4.05522	−	17.7671i	0.198111	−	0.867979i	−0.773950	−	0.633247i	$-0.781722\pi$
$419$	4.05522	−	17.7671i	0.198111	−	0.867979i	0.972060	−	0.234732i	$-0.0754212\pi$
$420$	1.60483	−	0.772846i	0.0783078	−	0.0377110i
$421$	−8.60365	+	4.14330i	−0.419316	+	0.201932i	−0.631631	−	0.775269i	$-0.717614\pi$
$421$	−8.60365	+	4.14330i	−0.419316	+	0.201932i	0.212315	+	0.977201i	$0.431900\pi$
$422$	−3.88959	+	17.0414i	−0.189342	+	0.829562i
$423$	−1.29341			−0.0628875
$424$	−2.53416	+	11.1029i	−0.123070	+	0.539203i
$425$	2.13377	+	2.67566i	0.103503	+	0.129789i
$426$	5.97988	+	26.1996i	0.289726	+	1.26937i
$427$	−5.04056	−	22.0841i	−0.243930	−	1.06873i
$428$	0.257533	−	0.322936i	0.0124483	−	0.0156097i
$429$	−0.899141	+	0.433003i	−0.0434109	+	0.0209056i
$430$	−4.41298	−	2.12518i	−0.212813	−	0.102485i
$431$	0.274387	+	0.344070i	0.0132168	+	0.0165733i	0.788396	−	0.615168i	$-0.210912\pi$
$431$	0.274387	+	0.344070i	0.0132168	+	0.0165733i	−0.775179	+	0.631741i	$0.782340\pi$
$432$	−3.10417	+	3.89251i	−0.149350	+	0.187279i
$433$	−7.77473	−	3.74411i	−0.373630	−	0.179931i	0.237639	−	0.971353i	$-0.423626\pi$
$433$	−7.77473	−	3.74411i	−0.373630	−	0.179931i	−0.611269	+	0.791423i	$0.709341\pi$
$434$	−7.92100			−0.380220
$435$	−5.18374	+	1.45905i	−0.248541	+	0.0699561i
$436$	8.80103			0.421493
$437$	−22.6051	−	10.8860i	−1.08135	−	0.520750i
$438$	−2.13255	+	2.67413i	−0.101897	+	0.127775i
$439$	−13.7559	−	17.2494i	−0.656535	−	0.823269i	0.336426	−	0.941710i	$-0.390782\pi$
$439$	−13.7559	−	17.2494i	−0.656535	−	0.823269i	−0.992961	+	0.118441i	$0.962210\pi$
$440$	0.709734	+	0.341790i	0.0338352	+	0.0162942i
$441$	2.38805	−	1.15002i	0.113717	−	0.0547631i
$442$	−8.84095	+	11.0862i	−0.420521	+	0.527317i
$443$	4.72187	+	20.6879i	0.224343	+	0.982910i	0.954167	+	0.299275i	$0.0967448\pi$
$443$	4.72187	+	20.6879i	0.224343	+	0.982910i	−0.729824	+	0.683635i	$0.760398\pi$
$444$	1.69069	+	7.40738i	0.0802364	+	0.351539i
$445$	3.26730	+	4.09707i	0.154885	+	0.194220i
$446$	3.09174	−	13.5458i	0.146398	−	0.641412i
$447$	12.7335			0.602276
$448$	−1.06219	+	4.65375i	−0.0501836	+	0.219869i
$449$	−2.05100	+	0.987708i	−0.0967926	+	0.0466128i	−0.481654	−	0.876362i	$-0.659964\pi$
$449$	−2.05100	+	0.987708i	−0.0967926	+	0.0466128i	0.384861	+	0.922975i	$0.374249\pi$
$450$	1.52210	−	0.733005i	0.0717525	−	0.0345542i
$451$	−0.244287	+	1.07029i	−0.0115030	+	0.0503981i
$452$	5.00404			0.235370
$453$	3.16184	−	13.8529i	0.148556	−	0.650868i
$454$	−15.7926	−	19.8033i	−0.741183	−	0.929415i
$455$	1.13817	+	4.98664i	0.0533581	+	0.233777i
$456$	−1.61178	−	7.06169i	−0.0754787	−	0.330694i
$457$	4.65659	−	5.83918i	0.217826	−	0.273145i	−0.660897	−	0.750476i	$-0.729824\pi$
$457$	4.65659	−	5.83918i	0.217826	−	0.273145i	0.878724	+	0.477331i	$0.158396\pi$
$458$	12.5483	−	6.04295i	0.586344	−	0.282368i
$459$	−3.08339	−	1.48488i	−0.143920	−	0.0693083i
$460$	−3.57090	−	4.47776i	−0.166494	−	0.208777i
$461$	−13.5144	+	16.9466i	−0.629430	+	0.789280i	−0.989637	−	0.143592i	$-0.954135\pi$
$461$	−13.5144	+	16.9466i	−0.629430	+	0.789280i	0.360207	+	0.932872i	$0.382706\pi$
$462$	1.29170	+	0.622050i	0.0600953	+	0.0289404i
$463$	−27.7149			−1.28802			−0.644011	−	0.765017i	$-0.722731\pi$
$463$	−27.7149			−1.28802			−0.644011	+	0.765017i	$0.722731\pi$
$464$	−10.4119	+	24.7069i	−0.483359	+	1.14699i
$465$	−2.24817			−0.104256
$466$	27.7264	+	13.3523i	1.28440	+	0.618534i
$467$	14.2936	−	17.9236i	0.661429	−	0.829406i	−0.332069	−	0.943255i	$-0.607747\pi$
$467$	14.2936	−	17.9236i	0.661429	−	0.829406i	0.993498	+	0.113849i	$0.0363180\pi$
$468$	1.30602	+	1.63769i	0.0603706	+	0.0757024i
$469$	−12.8755	−	6.20049i	−0.594533	−	0.286312i
$470$	1.96869	−	0.948072i	0.0908090	−	0.0437313i
$471$	−9.97437	+	12.5075i	−0.459595	+	0.576314i
$472$	2.47491	+	10.8433i	0.113917	+	0.499104i
$473$	−0.262518	−	1.15017i	−0.0120706	−	0.0528848i
$474$	−8.95595	−	11.2304i	−0.411360	−	0.515830i
$475$	−0.832571	+	3.64773i	−0.0382010	+	0.167369i
$476$	6.09591			0.279405
$477$	−1.30903	+	5.73522i	−0.0599362	+	0.262598i
$478$	30.1062	−	14.4984i	1.37702	−	0.663140i
$479$	−16.9688	+	8.17175i	−0.775324	+	0.373377i	−0.779329	−	0.626615i	$-0.784440\pi$
$479$	−16.9688	+	8.17175i	−0.775324	+	0.373377i	0.00400419	+	0.999992i	$0.498725\pi$
$480$	1.01007	−	4.42542i	0.0461033	−	0.201992i
$481$	−21.8176			−0.994799
$482$	−9.37642	+	41.0808i	−0.427084	+	1.87118i
$483$	8.71953	+	10.9339i	0.396753	+	0.497512i
$484$	2.05911	+	9.02153i	0.0935957	+	0.410069i
$485$	1.52957	+	6.70150i	0.0694543	+	0.304299i
$486$	−1.05333	+	1.32083i	−0.0477799	+	0.0599140i
$487$	16.2589	−	7.82988i	0.736761	−	0.354806i	−0.0275781	−	0.999620i	$-0.508779\pi$
$487$	16.2589	−	7.82988i	0.736761	−	0.354806i	0.764339	+	0.644814i	$0.223065\pi$
$488$	−18.9446	−	9.12323i	−0.857581	−	0.412989i
$489$	−8.89434	−	11.1531i	−0.402216	−	0.504363i
$490$	−2.79188	+	3.50091i	−0.126124	+	0.158155i
$491$	33.2962	+	16.0346i	1.50264	+	0.723632i	0.990785	−	0.135441i	$-0.0432452\pi$
$491$	33.2962	+	16.0346i	1.50264	+	0.723632i	0.511852	+	0.859073i	$0.328959\pi$
$492$	2.30426			0.103884
$493$	−18.1500	−	3.19842i	−0.817435	−	0.144050i
$494$	−15.5025			−0.697490
$495$	0.366615	+	0.176552i	0.0164781	+	0.00793544i
$496$	−6.97871	+	8.75102i	−0.313353	+	0.392932i
$497$	20.6840	+	25.9370i	0.927806	+	1.16343i
$498$	−14.0941	−	6.78736i	−0.631571	−	0.304149i
$499$	0.201946	−	0.0972521i	0.00904035	−	0.00435360i	−0.429358	−	0.903134i	$-0.641260\pi$
$499$	0.201946	−	0.0972521i	0.00904035	−	0.00435360i	0.438398	+	0.898781i	$0.355546\pi$
$500$	−0.532514	+	0.667752i	−0.0238148	+	0.0298628i
$501$	−1.27377	−	5.58075i	−0.0569079	−	0.249330i
$502$	−6.10993	−	26.7694i	−0.272700	−	1.19478i
$503$	−24.4571	−	30.6682i	−1.09049	−	1.36743i	−0.924448	−	0.381308i	$-0.875474\pi$
$503$	−24.4571	−	30.6682i	−1.09049	−	1.36743i	−0.166039	−	0.986119i	$-0.553098\pi$
$504$	−0.898409	+	3.93619i	−0.0400183	+	0.175332i
$505$	−16.6916			−0.742765
$506$	1.02577	−	4.49420i	0.0456011	−	0.199792i
$507$	6.29328	−	3.03068i	0.279494	−	0.134597i
$508$	2.08901	−	1.00601i	0.0926848	−	0.0446346i
$509$	−4.95127	+	21.6929i	−0.219461	+	0.961522i	0.738416	+	0.674345i	$0.235574\pi$
$509$	−4.95127	+	21.6929i	−0.219461	+	0.961522i	−0.957877	+	0.287177i	$0.907283\pi$
$510$	5.78165			0.256016
$511$	−0.939561	+	4.11648i	−0.0415637	+	0.182103i
$512$	−2.07175	−	2.59789i	−0.0915593	−	0.114812i
$513$	−0.832571	−	3.64773i	−0.0367589	−	0.161051i
$514$	−7.59859	−	33.2916i	−0.335160	−	1.46843i
$515$	2.64186	−	3.31279i	0.116414	−	0.145979i
$516$	−2.23100	+	1.07439i	−0.0982144	+	0.0472976i
$517$	0.474182	+	0.228354i	0.0208545	+	0.0100430i
$518$	19.5421	+	24.5050i	0.858631	+	1.07669i
$519$	−7.18364	+	9.00801i	−0.315327	+	0.395408i
$520$	4.27772	+	2.06004i	0.187591	+	0.0903389i
$521$	2.14413			0.0939360			0.0469680	−	0.998896i	$-0.485044\pi$
$521$	2.14413			0.0939360			0.0469680	+	0.998896i	$0.485044\pi$
$522$	−3.53301	+	8.38369i	−0.154636	+	0.366944i
$523$	35.1915			1.53882			0.769409	−	0.638756i	$-0.220551\pi$
$523$	35.1915			1.53882			0.769409	+	0.638756i	$0.220551\pi$
$524$	−8.37208	−	4.03178i	−0.365736	−	0.176129i
$525$	1.30031	−	1.63054i	0.0567502	−	0.0711625i
$526$	−30.9003	−	38.7477i	−1.34732	−	1.68948i
$527$	−6.93198	−	3.33826i	−0.301962	−	0.145417i
$528$	1.82527	−	0.879003i	0.0794347	−	0.0382537i
$529$	13.6961	−	17.1743i	0.595482	−	0.746711i
$530$	−2.21147	−	9.68910i	−0.0960603	−	0.420868i
$531$	1.27842	+	5.60114i	0.0554789	+	0.243069i
$532$	4.15527	+	5.21055i	0.180154	+	0.225906i
$533$	−1.47237	+	6.45089i	−0.0637756	+	0.279419i
$534$	8.85306			0.383110
$535$	0.107615	−	0.471492i	0.00465260	−	0.0203844i
$536$	−11.9517	+	5.75564i	−0.516235	+	0.248606i
$537$	14.4212	−	6.94489i	0.622321	−	0.299694i
$538$	−3.65000	+	15.9917i	−0.157363	+	0.689451i
$539$	−1.07853			−0.0464558
$540$	0.190052	−	0.832673i	0.00817854	−	0.0358325i
$541$	14.5698	+	18.2700i	0.626407	+	0.785489i	0.989230	−	0.146369i	$-0.0467586\pi$
$541$	14.5698	+	18.2700i	0.626407	+	0.785489i	−0.362823	+	0.931858i	$0.618187\pi$
$542$	8.72360	+	38.2206i	0.374711	+	1.64171i
$543$	−0.996800	−	4.36726i	−0.0427768	−	0.187417i
$544$	9.68568	−	12.1455i	0.415270	−	0.520732i
$545$	9.28413	−	4.47100i	0.397688	−	0.191517i
$546$	7.78536	+	3.74923i	0.333183	+	0.160452i
$547$	−14.2362	−	17.8516i	−0.608695	−	0.763280i	0.378010	−	0.925802i	$-0.376609\pi$
$547$	−14.2362	−	17.8516i	−0.608695	−	0.763280i	−0.986705	+	0.162522i	$0.948037\pi$
$548$	−1.64209	+	2.05912i	−0.0701466	+	0.0879611i
$549$	−9.78587	−	4.71263i	−0.417651	−	0.201130i
$550$	−0.687439			−0.0293125
$551$	−9.63806	−	17.6941i	−0.410595	−	0.753796i
$552$	12.9817			0.552538
$553$	−15.9763	−	7.69378i	−0.679382	−	0.327173i
$554$	−2.50501	+	3.14118i	−0.106428	+	0.133456i
$555$	5.54651	+	6.95510i	0.235436	+	0.295228i
$556$	15.3061	+	7.37104i	0.649124	+	0.312602i
$557$	−0.0178269	+	0.00858500i	−0.000755351	+	0.000363758i	−0.434261	−	0.900787i	$-0.642991\pi$
$557$	−0.0178269	+	0.00858500i	−0.000755351	+	0.000363758i	0.433506	+	0.901151i	$0.357276\pi$
$558$	−2.36805	+	2.96945i	−0.100248	+	0.125707i
$559$	−1.58226	−	6.93232i	−0.0669223	−	0.293206i
$560$	−2.31050	−	10.1230i	−0.0976363	−	0.427773i
$561$	0.868257	+	1.08876i	0.0366578	+	0.0459675i
$562$	−6.88432	+	30.1622i	−0.290398	+	1.27231i
$563$	7.69885			0.324468			0.162234	−	0.986752i	$-0.448130\pi$
$563$	7.69885			0.324468			0.162234	+	0.986752i	$0.448130\pi$
$564$	0.245814	−	1.07698i	0.0103507	−	0.0453492i
$565$	5.27872	−	2.54210i	0.222077	−	0.106947i
$566$	−10.1037	+	4.86568i	−0.424689	+	0.204520i
$567$	−0.464076	+	2.03325i	−0.0194893	+	0.0853884i
$568$	30.7945			1.29211
$569$	−7.24251	+	31.7315i	−0.303622	+	1.33025i	0.560993	+	0.827820i	$0.310419\pi$
$569$	−7.24251	+	31.7315i	−0.303622	+	1.33025i	−0.864615	+	0.502435i	$0.832438\pi$
$570$	3.94106	+	4.94194i	0.165073	+	0.206995i
$571$	−3.52734	−	15.4543i	−0.147615	−	0.646741i	−0.993544	−	0.113447i	$-0.963811\pi$
$571$	−3.52734	−	15.4543i	−0.147615	−	0.646741i	0.845930	−	0.533295i	$-0.179046\pi$
$572$	−0.189666	−	0.830983i	−0.00793035	−	0.0347452i
$573$	9.91091	−	12.4279i	0.414034	−	0.519183i
$574$	8.56428	−	4.12434i	0.357466	−	0.172147i
$575$	−6.04165	−	2.90951i	−0.251954	−	0.121335i
$576$	1.42706	+	1.78947i	0.0594608	+	0.0745615i
$577$	23.2614	−	29.1689i	0.968386	−	1.21432i	−0.00836997	−	0.999965i	$-0.502664\pi$
$577$	23.2614	−	29.1689i	0.968386	−	1.21432i	0.976756	−	0.214353i	$-0.0687643\pi$
$578$	−8.04862	−	3.87601i	−0.334779	−	0.161221i
$579$	−8.27582			−0.343932
$580$	−0.229730	−	4.59366i	−0.00953904	−	0.190741i
$581$	−19.3113			−0.801168
$582$	10.4627	+	5.03856i	0.433692	+	0.208855i
$583$	1.49247	−	1.87150i	0.0618120	−	0.0775098i
$584$	2.44372	+	3.06432i	0.101122	+	0.126803i
$585$	2.20967	+	1.06412i	0.0913586	+	0.0439960i
$586$	25.2680	−	12.1684i	1.04381	−	0.502674i
$587$	25.5733	−	32.0679i	1.05552	−	1.32358i	0.111478	−	0.993767i	$-0.464441\pi$
$587$	25.5733	−	32.0679i	1.05552	−	1.32358i	0.944045	−	0.329817i	$-0.106987\pi$
$588$	0.503740	+	2.20703i	0.0207739	+	0.0910163i
$589$	−1.87176	−	8.20072i	−0.0771245	−	0.337905i
$590$	−6.05155	−	7.58841i	−0.249139	−	0.312410i
$591$	2.89650	−	12.6904i	0.119146	−	0.522013i
$592$	44.2902			1.82031
$593$	−5.12462	+	22.4524i	−0.210443	+	0.922010i	0.753824	+	0.657077i	$0.228207\pi$
$593$	−5.12462	+	22.4524i	−0.210443	+	0.922010i	−0.964267	+	0.264934i	$0.914650\pi$
$594$	0.619361	−	0.298268i	0.0254127	−	0.0122381i
$595$	6.43052	−	3.09678i	0.263626	−	0.126955i
$596$	−2.42004	+	10.6029i	−0.0991285	+	0.434310i
$597$	−0.0479193			−0.00196121
$598$	6.18255	−	27.0875i	0.252823	−	1.10769i
$599$	−18.0511	−	22.6353i	−0.737547	−	0.924855i	0.261640	−	0.965166i	$-0.415737\pi$
$599$	−18.0511	−	22.6353i	−0.737547	−	0.924855i	−0.999187	+	0.0403107i	$0.987165\pi$
$600$	−0.430781	−	1.88737i	−0.0175866	−	0.0770517i
$601$	−5.01584	−	21.9758i	−0.204600	−	0.896413i	−0.968092	−	0.250595i	$-0.919374\pi$
$601$	−5.01584	−	21.9758i	−0.204600	−	0.896413i	0.763492	−	0.645818i	$-0.223483\pi$
$602$	−6.36897	+	7.98644i	−0.259580	+	0.325503i
$603$	−6.17369	+	2.97309i	−0.251412	+	0.121074i
$604$	10.9340	+	5.26556i	0.444900	+	0.214253i
$605$	6.75515	+	8.47069i	0.274636	+	0.344383i
$606$	−17.5817	+	22.0467i	−0.714206	+	0.895586i
$607$	−0.226839	−	0.109240i	−0.00920711	−	0.00443391i	0.429275	−	0.903174i	$-0.358769\pi$
$607$	−0.226839	−	0.109240i	−0.00920711	−	0.00443391i	−0.438482	+	0.898740i	$0.644484\pi$
$608$	16.9837			0.688781
$609$	0.560964	+	11.2169i	0.0227314	+	0.454533i
$610$	18.3495			0.742948
$611$	2.85800	+	1.37634i	0.115622	+	0.0556807i
$612$	1.82243	−	2.28525i	0.0736672	−	0.0923757i
$613$	14.4199	+	18.0819i	0.582413	+	0.730322i	0.982522	−	0.186145i	$-0.0595994\pi$
$613$	14.4199	+	18.0819i	0.582413	+	0.730322i	−0.400110	+	0.916467i	$0.631028\pi$
$614$	−29.6186	−	14.2636i	−1.19531	−	0.575630i
$615$	2.43075	−	1.17059i	0.0980171	−	0.0472026i
$616$	1.02431	−	1.28445i	0.0412708	−	0.0517519i
$617$	−4.46965	−	19.5828i	−0.179941	−	0.788374i	−0.981655	−	0.190666i	$-0.938935\pi$
$617$	−4.46965	−	19.5828i	−0.179941	−	0.788374i	0.801714	−	0.597708i	$-0.203922\pi$
$618$	−1.59289	−	6.97889i	−0.0640753	−	0.280732i
$619$	20.6801	+	25.9320i	0.831204	+	1.04230i	0.998410	+	0.0563743i	$0.0179540\pi$
$619$	20.6801	+	25.9320i	0.831204	+	1.04230i	−0.167206	+	0.985922i	$0.553475\pi$
$620$	0.427269	−	1.87199i	0.0171595	−	0.0751809i
$621$	6.70573			0.269092
$622$	11.8586	−	51.9561i	0.475488	−	2.08325i
$623$	9.84663	−	4.74189i	0.394497	−	0.189980i
$624$	11.0013	−	5.29795i	0.440404	−	0.212088i
$625$	−0.222521	+	0.974928i	−0.00890084	+	0.0389971i
$626$	13.9568			0.557826
$627$	−0.338783	+	1.48431i	−0.0135297	+	0.0592775i
$628$	−8.51898	−	10.6825i	−0.339944	−	0.426277i
$629$	6.77454	+	29.6812i	0.270119	+	1.18347i
$630$	−0.784011	−	3.43498i	−0.0312358	−	0.136853i
$631$	−7.73022	+	9.69339i	−0.307735	+	0.385888i	−0.911517	−	0.411262i	$-0.865088\pi$
$631$	−7.73022	+	9.69339i	−0.307735	+	0.385888i	0.603782	+	0.797149i	$0.293660\pi$
$632$	−14.8301	+	7.14180i	−0.589909	+	0.284085i
$633$	9.32199	+	4.48923i	0.370516	+	0.178431i
$634$	−2.91408	−	3.65414i	−0.115733	−	0.145125i
$635$	1.69261	−	2.12247i	0.0671693	−	0.0842277i
$636$	−4.52678	−	2.17998i	−0.179498	−	0.0864418i
$637$	−6.50057			−0.257562
$638$	2.77542	−	2.44983i	0.109880	−	0.0969895i
$639$	15.9070			0.629271
$640$	−11.6632	−	5.61672i	−0.461030	−	0.222020i
$641$	18.9502	−	23.7628i	0.748488	−	0.938575i	−0.251080	−	0.967966i	$-0.580786\pi$
$641$	18.9502	−	23.7628i	0.748488	−	0.938575i	0.999568	+	0.0293918i	$0.00935703\pi$
$642$	−0.509407	−	0.638776i	−0.0201047	−	0.0252105i
$643$	−21.4296	−	10.3199i	−0.845101	−	0.406979i	−0.0393440	−	0.999226i	$-0.512527\pi$
$643$	−21.4296	−	10.3199i	−0.845101	−	0.406979i	−0.805757	+	0.592247i	$0.798241\pi$
$644$	−10.7616	+	5.18250i	−0.424065	+	0.204219i
$645$	−1.80766	+	2.26674i	−0.0711767	+	0.0892528i
$646$	4.81364	+	21.0899i	0.189390	+	0.829772i
$647$	8.81707	+	38.6301i	0.346635	+	1.51871i	0.784764	+	0.619795i	$0.212784\pi$
$647$	8.81707	+	38.6301i	0.346635	+	1.51871i	−0.438129	+	0.898912i	$0.644359\pi$
$648$	1.20702	+	1.51356i	0.0474163	+	0.0594581i
$649$	0.520206	−	2.27917i	0.0204199	−	0.0894653i
$650$	−4.14334			−0.162515
$651$	−1.04332	+	4.57108i	−0.0408909	+	0.179155i
$652$	10.9773	−	5.28639i	0.429904	−	0.207031i
$653$	10.0051	−	4.81821i	0.391531	−	0.188551i	−0.227752	−	0.973719i	$-0.573138\pi$
$653$	10.0051	−	4.81821i	0.391531	−	0.188551i	0.619283	+	0.785168i	$0.287423\pi$
$654$	3.87379	−	16.9722i	0.151477	−	0.663665i
$655$	−10.8798			−0.425110
$656$	2.98894	−	13.0954i	0.116699	−	0.511290i
$657$	1.26231	+	1.58288i	0.0492473	+	0.0617542i
$658$	−1.01404	−	4.44282i	−0.0395316	−	0.173199i
$659$	1.13856	+	4.98835i	0.0443519	+	0.194318i	0.992250	−	0.124254i	$-0.0396538\pi$
$659$	1.13856	+	4.98835i	0.0443519	+	0.194318i	−0.947899	+	0.318572i	$0.896797\pi$
$660$	−0.216686	+	0.271716i	−0.00843451	+	0.0105765i
$661$	39.7909	−	19.1623i	1.54769	−	0.745326i	0.551633	−	0.834087i	$-0.314005\pi$
$661$	39.7909	−	19.1623i	1.54769	−	0.745326i	0.996053	+	0.0887611i	$0.0282908\pi$
$662$	37.6836	+	18.1475i	1.46461	+	0.705321i
$663$	5.23318	+	6.56219i	0.203240	+	0.254855i
$664$	−11.1766	+	14.0150i	−0.433735	+	0.543886i
$665$	7.03037	+	3.38565i	0.272626	+	0.131290i
$666$	15.0288			0.582354
$667$	34.7608	−	9.78400i	1.34594	−	0.378838i
$668$	4.88902			0.189162
$669$	−7.40983	−	3.56839i	−0.286481	−	0.137962i
$670$	7.21768	−	9.05069i	0.278843	−	0.349659i
$671$	2.75562	+	3.45544i	0.106380	+	0.133396i
$672$	−8.52923	−	4.10746i	−0.329022	−	0.158449i
$673$	36.1188	−	17.3939i	1.39228	−	0.670486i	0.420700	−	0.907200i	$-0.361785\pi$
$673$	36.1188	−	17.3939i	1.39228	−	0.670486i	0.971579	+	0.236714i	$0.0760703\pi$
$674$	1.58431	−	1.98666i	0.0610253	−	0.0765233i
$675$	−0.222521	−	0.974928i	−0.00856483	−	0.0375250i
$676$	1.32752	+	5.81623i	0.0510583	+	0.223701i
$677$	9.54432	+	11.9682i	0.366818	+	0.459975i	0.930648	−	0.365916i	$-0.119244\pi$
$677$	9.54432	+	11.9682i	0.366818	+	0.459975i	−0.563830	+	0.825891i	$0.690673\pi$
$678$	2.20254	−	9.64995i	0.0845880	−	0.370604i
$679$	14.3356			0.550151
$680$	1.47426	−	6.45917i	0.0565354	−	0.247698i
$681$	−13.5083	+	6.50525i	−0.517639	+	0.249282i
$682$	1.39243	−	0.670558i	0.0533188	−	0.0256770i
$683$	−7.54141	+	33.0411i	−0.288564	+	1.26428i	0.597933	+	0.801546i	$0.295989\pi$
$683$	−7.54141	+	33.0411i	−0.288564	+	1.26428i	−0.886497	+	0.462735i	$0.846868\pi$
$684$	3.19560			0.122187
$685$	−0.686178	+	3.00634i	−0.0262175	+	0.114866i
$686$	21.1998	+	26.5837i	0.809413	+	1.01497i
$687$	−1.83448	−	8.03738i	−0.0699897	−	0.306645i
$688$	3.21200	+	14.0727i	0.122456	+	0.536517i
$689$	8.99547	−	11.2800i	0.342700	−	0.429733i
$690$	−10.2068	+	4.91533i	−0.388566	+	0.187124i
$691$	−1.62590	−	0.782993i	−0.0618522	−	0.0297865i	0.402702	−	0.915331i	$-0.368071\pi$
$691$	−1.62590	−	0.782993i	−0.0618522	−	0.0297865i	−0.464554	+	0.885545i	$0.653785\pi$
$692$	−6.13545	−	7.69362i	−0.233235	−	0.292467i
$693$	0.529112	−	0.663486i	0.0200993	−	0.0252037i
$694$	−32.7459	−	15.7696i	−1.24302	−	0.598606i
$695$	19.8909			0.754503
$696$	8.46524	+	6.08478i	0.320874	+	0.230643i
$697$	9.23311			0.349729
$698$	−44.6519	−	21.5032i	−1.69010	−	0.813909i
$699$	11.3574	−	14.2417i	0.429577	−	0.538672i
$700$	1.11058	+	1.39262i	0.0419759	+	0.0526361i
$701$	36.9174	+	17.7785i	1.39435	+	0.671484i	0.972007	−	0.234951i	$-0.0754931\pi$
$701$	36.9174	+	17.7785i	1.39435	+	0.671484i	0.422344	+	0.906436i	$0.361207\pi$
$702$	3.73302	−	1.79773i	0.140894	−	0.0678509i
$703$	−20.7525	+	26.0228i	−0.782695	+	0.981469i
$704$	−0.207245	−	0.907999i	−0.00781083	−	0.0342215i
$705$	−0.287810	−	1.26098i	−0.0108395	−	0.0474911i
$706$	−7.85018	−	9.84381i	−0.295445	−	0.370477i
$707$	−7.74615	+	33.9381i	−0.291324	+	1.27637i
$708$	−4.90688			−0.184412
$709$	−8.76548	+	38.4041i	−0.329195	+	1.44230i	0.491474	+	0.870892i	$0.336458\pi$
$709$	−8.76548	+	38.4041i	−0.329195	+	1.44230i	−0.820669	+	0.571404i	$0.806399\pi$
$710$	−24.2121	+	11.6599i	−0.908662	+	0.437589i
$711$	−7.66052	+	3.68911i	−0.287292	+	0.138353i
$712$	2.25744	−	9.89049i	0.0846012	−	0.370662i
$713$	15.0756			0.564586
$714$	2.68312	−	11.7555i	0.100413	−	0.439940i
$715$	−0.622225	−	0.780245i	−0.0232699	−	0.0291795i
$716$	3.04204	+	13.3280i	0.113686	+	0.498092i
$717$	−4.40132	−	19.2834i	−0.164370	−	0.720153i
$718$	24.2193	−	30.3700i	0.903855	−	1.13340i
$719$	11.0837	−	5.33764i	0.413353	−	0.199060i	−0.215637	−	0.976474i	$-0.569183\pi$
$719$	11.0837	−	5.33764i	0.413353	−	0.199060i	0.628990	+	0.777413i	$0.283469\pi$
$720$	−4.48566	−	2.16018i	−0.167171	−	0.0805052i
$721$	−5.50969	−	6.90894i	−0.205192	−	0.257302i
$722$	5.26755	−	6.60530i	0.196038	−	0.245824i
$723$	22.4720	+	10.8220i	0.835744	+	0.402473i
$724$	3.82595			0.142190
$725$	−2.57596	−	4.72910i	−0.0956687	−	0.175635i
$726$	18.3037			0.679315
$727$	−2.47567	−	1.19222i	−0.0918174	−	0.0442169i	0.387411	−	0.921907i	$-0.373369\pi$
$727$	−2.47567	−	1.19222i	−0.0918174	−	0.0442169i	−0.479229	+	0.877690i	$0.659084\pi$
$728$	6.17377	−	7.74166i	0.228815	−	0.286925i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	−3.08162	−	1.48403i	−0.114056	−	0.0549264i
$731$	−8.93957	+	4.30507i	−0.330642	+	0.159229i
$732$	5.78390	−	7.25278i	0.213779	−	0.268071i
$733$	−1.83237	−	8.02812i	−0.0676800	−	0.296525i	0.929748	−	0.368195i	$-0.120024\pi$
$733$	−1.83237	−	8.02812i	−0.0676800	−	0.296525i	−0.997428	+	0.0716701i	$0.977167\pi$
$734$	6.88856	+	30.1807i	0.254261	+	1.11399i
$735$	1.65258	+	2.07227i	0.0609564	+	0.0764369i
$736$	−6.77328	+	29.6757i	−0.249666	+	1.09386i
$737$	2.78827			0.102707
$738$	1.01422	−	4.44361i	0.0373341	−	0.163571i
$739$	6.55624	−	3.15732i	0.241175	−	0.116144i	−0.309392	−	0.950934i	$-0.600126\pi$
$739$	6.55624	−	3.15732i	0.241175	−	0.116144i	0.550568	+	0.834791i	$0.314411\pi$
$740$	−6.84545	+	3.29660i	−0.251644	+	0.121185i
$741$	−2.04192	+	8.94624i	−0.0750118	+	0.328648i
$742$	−20.7266			−0.760899
$743$	3.66227	−	16.0455i	0.134356	−	0.588651i	−0.862261	−	0.506464i	$-0.830952\pi$
$743$	3.66227	−	16.0455i	0.134356	−	0.588651i	0.996617	−	0.0821872i	$-0.0261905\pi$
$744$	2.71359	+	3.40273i	0.0994849	+	0.124750i
$745$	2.83348	+	12.4143i	0.103811	+	0.454824i
$746$	−5.00870	−	21.9446i	−0.183382	−	0.803447i
$747$	−5.77329	+	7.23947i	−0.211233	+	0.264878i
$748$	−1.07159	+	0.516053i	−0.0391814	+	0.0188688i
$749$	−0.908719	−	0.437616i	−0.0332039	−	0.0159901i
$750$	1.05333	+	1.32083i	0.0384620	+	0.0482299i
$751$	−24.9196	+	31.2481i	−0.909328	+	1.14026i	0.0803237	+	0.996769i	$0.474405\pi$
$751$	−24.9196	+	31.2481i	−0.909328	+	1.14026i	−0.989651	+	0.143492i	$0.954167\pi$
$752$	−5.80178	−	2.79399i	−0.211569	−	0.101886i
$753$	−16.2529			−0.592290
$754$	16.7281	−	14.7656i	0.609200	−	0.537733i
$755$	14.2092			0.517125
$756$	−1.60483	−	0.772846i	−0.0583672	−	0.0281081i
$757$	−22.1495	+	27.7746i	−0.805038	+	1.00949i	0.194553	+	0.980892i	$0.437674\pi$
$757$	−22.1495	+	27.7746i	−0.805038	+	1.00949i	−0.999591	+	0.0285938i	$0.990897\pi$
$758$	−35.5628	−	44.5943i	−1.29170	−	1.61974i
$759$	−2.45842	−	1.18391i	−0.0892350	−	0.0429733i
$760$	6.52598	−	3.14275i	0.236722	−	0.113999i
$761$	25.8308	−	32.3908i	0.936365	−	1.17416i	−0.0481459	−	0.998840i	$-0.515331\pi$
$761$	25.8308	−	32.3908i	0.936365	−	1.17416i	0.984511	−	0.175324i	$-0.0560973\pi$
$762$	−1.02055	−	4.47131i	−0.0369705	−	0.161978i
$763$	−4.78212	−	20.9518i	−0.173124	−	0.758507i
$764$	8.46478	+	10.6145i	0.306245	+	0.384019i
$765$	0.761534	−	3.33650i	0.0275333	−	0.120631i
$766$	−14.0617			−0.508069
$767$	3.13540	−	13.7371i	0.113213	−	0.496017i
$768$	−15.5796	+	7.50274i	−0.562180	+	0.270732i
$769$	18.6795	−	8.99559i	0.673601	−	0.324389i	−0.0656270	−	0.997844i	$-0.520905\pi$
$769$	18.6795	−	8.99559i	0.673601	−	0.324389i	0.739228	+	0.673455i	$0.235190\pi$
$770$	−0.319024	+	1.39773i	−0.0114968	+	0.0503708i
$771$	−20.2129			−0.727950
$772$	1.57284	−	6.89105i	0.0566077	−	0.248014i
$773$	31.1529	+	39.0644i	1.12049	+	1.40505i	0.903347	+	0.428911i	$0.141102\pi$
$773$	31.1529	+	39.0644i	1.12049	+	1.40505i	0.217143	+	0.976140i	$0.430326\pi$
$774$	1.08992	+	4.77523i	0.0391762	+	0.171642i
$775$	−0.500264	−	2.19180i	−0.0179700	−	0.0787318i
$776$	8.29686	−	10.4039i	0.297840	−	0.373480i
$777$	16.7155	−	8.04974i	0.599663	−	0.288783i
$778$	−38.3034	−	18.4459i	−1.37324	−	0.661319i
$779$	6.29375	+	7.89211i	0.225497	+	0.282764i
$780$	−1.30602	+	1.63769i	−0.0467629	+	0.0586388i
$781$	−5.83174	−	2.80842i	−0.208676	−	0.100493i
$782$	−38.7702			−1.38642
$783$	4.37274	+	3.14311i	0.156269	+	0.112326i
$784$	13.1962			0.471295
$785$	−14.4134	−	6.94112i	−0.514436	−	0.247739i
$786$	−11.4600	+	14.3704i	−0.408765	+	0.512575i
$787$	−10.1674	−	12.7495i	−0.362429	−	0.454472i	0.566866	−	0.823810i	$-0.308156\pi$
$787$	−10.1674	−	12.7495i	−0.362429	−	0.454472i	−0.929295	+	0.369338i	$0.879584\pi$
$788$	10.0164	+	4.82367i	0.356821	+	0.171836i
$789$	−26.4307	+	12.7284i	−0.940959	+	0.453142i
$790$	8.95595	−	11.2304i	0.318638	−	0.399560i
$791$	−2.71899	−	11.9127i	−0.0966762	−	0.423566i
$792$	−0.175290	−	0.767995i	−0.00622865	−	0.0272895i
$793$	16.6087	+	20.8267i	0.589793	+	0.739578i
$794$	−10.3508	+	45.3500i	−0.367337	+	1.60941i
$795$	−5.88271			−0.208638
$796$	0.00910716	−	0.0399011i	0.000322795	−	0.00141426i
$797$	−29.6886	+	14.2973i	−1.05163	+	0.506436i	−0.878142	−	0.478400i	$-0.841217\pi$
$797$	−29.6886	+	14.2973i	−1.05163	+	0.506436i	−0.173484	+	0.984837i	$0.555502\pi$
$798$	11.8771	−	5.71973i	0.420446	−	0.202476i
$799$	0.984972	−	4.31545i	0.0348458	−	0.152669i
$800$	4.53923			0.160486
$801$	1.16609	−	5.10896i	0.0412017	−	0.180516i
$802$	−2.21455	−	2.77695i	−0.0781983	−	0.0980576i
$803$	−0.183319	−	0.803173i	−0.00646918	−	0.0283433i
$804$	−1.30229	−	5.70571i	−0.0459282	−	0.201225i
$805$	−8.71953	+	10.9339i	−0.307323	+	0.385371i
$806$	8.39247	−	4.04160i	0.295612	−	0.142359i
$807$	8.74779	+	4.21272i	0.307937	+	0.148295i
$808$	20.1471	+	25.2636i	0.708771	+	0.888771i
$809$	8.77478	−	11.0032i	0.308505	−	0.386853i	−0.603274	−	0.797534i	$-0.706138\pi$
$809$	8.77478	−	11.0032i	0.308505	−	0.386853i	0.911779	+	0.410681i	$0.134709\pi$
$810$	−1.52210	−	0.733005i	−0.0534812	−	0.0257552i
$811$	36.1288			1.26865			0.634327	−	0.773065i	$-0.281277\pi$
$811$	36.1288			1.26865			0.634327	+	0.773065i	$0.281277\pi$
$812$	−9.44665	−	1.66470i	−0.331513	−	0.0584197i
$813$	23.2055			0.813853
$814$	−5.50978	−	2.65337i	−0.193118	−	0.0930006i
$815$	8.89434	−	11.1531i	0.311555	−	0.390678i
$816$	−10.6234	−	13.3214i	−0.371894	−	0.466341i
$817$	−9.77347	−	4.70665i	−0.341930	−	0.164665i
$818$	−49.4770	+	23.8268i	−1.72992	+	0.833086i
$819$	3.18907	−	3.99897i	0.111435	−	0.139735i
$820$	0.512746	+	2.24649i	0.0179059	+	0.0784508i
$821$	7.77242	+	34.0532i	0.271259	+	1.18847i	0.908528	+	0.417824i	$0.137207\pi$
$821$	7.77242	+	34.0532i	0.271259	+	1.18847i	−0.637269	+	0.770642i	$0.719936\pi$
$822$	3.24810	+	4.07298i	0.113290	+	0.142062i
$823$	−10.3496	+	45.3444i	−0.360763	+	1.58061i	0.390499	+	0.920603i	$0.372303\pi$
$823$	−10.3496	+	45.3444i	−0.360763	+	1.58061i	−0.751262	+	0.660004i	$0.770555\pi$
$824$	−8.20287			−0.285760
$825$	−0.0905464	+	0.396710i	−0.00315242	+	0.0138117i
$826$	−18.2375	+	8.78271i	−0.634564	+	0.305590i
$827$	−20.2820	+	9.76728i	−0.705273	+	0.339642i	−0.751906	−	0.659271i	$-0.770865\pi$
$827$	−20.2820	+	9.76728i	−0.705273	+	0.339642i	0.0466329	+	0.998912i	$0.485151\pi$
$828$	−1.27444	+	5.58368i	−0.0442898	+	0.194046i
$829$	−40.6697			−1.41252			−0.706258	−	0.707955i	$-0.749618\pi$
$829$	−40.6697			−1.41252			−0.706258	+	0.707955i	$0.749618\pi$
$830$	3.48095	−	15.2510i	0.120826	−	0.529372i
$831$	1.48278	+	1.85934i	0.0514370	+	0.0644999i
$832$	−1.24911	−	5.47271i	−0.0433051	−	0.189732i
$833$	2.01847	+	8.84351i	0.0699360	+	0.306409i
$834$	20.9516	−	26.2724i	0.725493	−	0.909740i
$835$	5.15739	−	2.48367i	0.178479	−	0.0859509i
$836$	−1.17155	−	0.564191i	−0.0405191	−	0.0195130i
$837$	1.40171	+	1.75769i	0.0484502	+	0.0607546i
$838$	19.1958	−	24.0708i	0.663109	−	0.831512i
$839$	−20.5423	−	9.89267i	−0.709200	−	0.341533i	0.0442656	−	0.999020i	$-0.485905\pi$
$839$	−20.5423	−	9.89267i	−0.709200	−	0.341533i	−0.753466	+	0.657487i	$0.771620\pi$
$840$	−4.03741			−0.139304
$841$	27.2531	+	9.91301i	0.939763	+	0.341828i
$842$	−16.1327			−0.555969
$843$	16.4993	+	7.94566i	0.568267	+	0.273663i
$844$	−5.50973	+	6.90898i	−0.189653	+	0.237817i
$845$	4.35508	+	5.46110i	0.149819	+	0.187868i
$846$	−1.96869	−	0.948072i	−0.0676851	−	0.0325954i
$847$	20.3579	−	9.80386i	0.699506	−	0.336865i
$848$	−18.2610	+	22.8985i	−0.627084	+	0.786338i
$849$	1.47709	+	6.47156i	0.0506936	+	0.222103i
$850$	1.28654	+	5.63670i	0.0441279	+	0.193337i
$851$	−37.1934	−	46.6390i	−1.27497	−	1.59877i
$852$	−3.02316	+	13.2453i	−0.103572	+	0.453777i
$853$	−47.5532			−1.62819			−0.814096	−	0.580731i	$-0.802767\pi$
$853$	−47.5532			−1.62819			−0.814096	+	0.580731i	$0.802767\pi$
$854$	8.51554	−	37.3090i	0.291396	−	1.27669i
$855$	3.37101	−	1.62339i	0.115286	−	0.0555189i
$856$	−0.843523	+	0.406219i	−0.0288310	+	0.0138843i
$857$	−3.88792	+	17.0341i	−0.132809	+	0.581874i	0.864101	+	0.503319i	$0.167888\pi$
$857$	−3.88792	+	17.0341i	−0.132809	+	0.581874i	−0.996910	+	0.0785551i	$0.974969\pi$
$858$	−1.68598			−0.0575583
$859$	1.88497	−	8.25858i	0.0643142	−	0.281779i	−0.932537	−	0.361075i	$-0.882410\pi$
$859$	1.88497	−	8.25858i	0.0643142	−	0.281779i	0.996851	+	0.0792956i	$0.0252671\pi$
$860$	−1.54390	−	1.93599i	−0.0526466	−	0.0660168i
$861$	−1.25204	−	5.48555i	−0.0426694	−	0.186947i
$862$	0.165439	+	0.724837i	0.00563488	+	0.0246880i
$863$	−11.2559	+	14.1145i	−0.383156	+	0.480462i	−0.935587	−	0.353096i	$-0.885129\pi$
$863$	−11.2559	+	14.1145i	−0.383156	+	0.480462i	0.552431	+	0.833559i	$0.313700\pi$
$864$	−4.08970	+	1.96950i	−0.139135	+	0.0670037i
$865$	−10.3807	−	4.99907i	−0.352953	−	0.169973i
$866$	−9.08947	−	11.3978i	−0.308873	−	0.387314i
$867$	−3.29691	+	4.13420i	−0.111969	+	0.140405i
$868$	−3.60793	−	1.73749i	−0.122461	−	0.0589742i
$869$	3.45978			0.117365
$870$	−8.95967	−	1.57889i	−0.303761	−	0.0535293i
$871$	16.8055			0.569434
$872$	−17.9733	−	8.65546i	−0.608651	−	0.293111i
$873$	4.28577	−	5.37418i	0.145051	−	0.181889i
$874$	−26.4277	−	33.1393i	−0.893930	−	1.12095i
$875$	1.87900	+	0.904881i	0.0635219	+	0.0305905i
$876$	−1.55793	+	0.750259i	−0.0526375	+	0.0253489i
$877$	−30.8343	+	38.6650i	−1.04120	+	1.30562i	−0.0903706	+	0.995908i	$0.528805\pi$
$877$	−30.8343	+	38.6650i	−1.04120	+	1.30562i	−0.950829	+	0.309715i	$0.899766\pi$
$878$	−8.29403	−	36.3385i	−0.279910	−	1.22637i
$879$	−3.69402	−	16.1845i	−0.124596	−	0.545891i
$880$	1.26313	+	1.58391i	0.0425800	+	0.0533936i
$881$	5.13480	−	22.4970i	0.172996	−	0.757943i	−0.811759	−	0.583993i	$-0.801490\pi$
$881$	5.13480	−	22.4970i	0.172996	−	0.757943i	0.984754	−	0.173951i	$-0.0556533\pi$
$882$	4.47783			0.150776
$883$	−6.94768	+	30.4398i	−0.233808	+	1.02438i	0.712642	+	0.701528i	$0.247499\pi$
$883$	−6.94768	+	30.4398i	−0.233808	+	1.02438i	−0.946450	+	0.322852i	$0.895359\pi$
$884$	−6.45874	+	3.11036i	−0.217231	+	0.104613i
$885$	−5.17623	+	2.49274i	−0.173997	+	0.0837926i
$886$	−7.97715	+	34.9502i	−0.267998	+	1.17417i
$887$	−41.4954			−1.39328			−0.696640	−	0.717421i	$-0.745323\pi$
$887$	−41.4954			−1.39328			−0.696640	+	0.717421i	$0.745323\pi$
$888$	3.83219	−	16.7899i	0.128600	−	0.563432i
$889$	−3.53001	−	4.42649i	−0.118393	−	0.148460i
$890$	1.96999	+	8.63110i	0.0660343	+	0.289315i
$891$	−0.0905464	−	0.396710i	−0.00303342	−	0.0132903i
$892$	4.37955	−	5.49178i	0.146638	−	0.183879i
$893$	4.36008	−	2.09971i	0.145905	−	0.0702640i
$894$	19.3817	+	9.33375i	0.648222	+	0.312167i
$895$	9.97979	+	12.5143i	0.333588	+	0.418306i
$896$	−16.8328	+	21.1077i	−0.562344	+	0.705157i
$897$	−14.8174	−	7.13570i	−0.494740	−	0.238254i
$898$	−3.84582			−0.128337
$899$	9.83066	+	7.06624i	0.327871	+	0.235672i
$900$	0.854086			0.0284695
$901$	−18.1387	−	8.73513i	−0.604287	−	0.291009i
$902$	−1.15636	+	1.45003i	−0.0385026	+	0.0482807i
$903$	3.76995	+	4.72737i	0.125456	+	0.157317i
$904$	−10.2191	−	4.92128i	−0.339883	−	0.163679i
$905$	4.03596	−	1.94362i	0.134160	−	0.0646080i
$906$	14.9669	−	18.7679i	0.497242	−	0.623522i
$907$	2.51353	+	11.0125i	0.0834603	+	0.365664i	0.999361	−	0.0357412i	$-0.0113792\pi$
$907$	2.51353	+	11.0125i	0.0834603	+	0.365664i	−0.915901	+	0.401405i	$0.868522\pi$
$908$	−2.84947	−	12.4843i	−0.0945628	−	0.414307i
$909$	10.4070	+	13.0500i	0.345179	+	0.432841i
$910$	−1.92283	+	8.42445i	−0.0637410	+	0.279268i
$911$	0.289346			0.00958647			0.00479323	−	0.999989i	$-0.498474\pi$
$911$	0.289346			0.00958647			0.00479323	+	0.999989i	$0.498474\pi$
$912$	4.14513	−	18.1610i	0.137259	−	0.601371i
$913$	3.39472	−	1.63481i	0.112349	−	0.0541043i
$914$	11.3680	−	5.47452i	0.376018	−	0.181081i
$915$	2.41691	−	10.5892i	0.0799006	−	0.350067i
$916$	7.04115			0.232646
$917$	−5.04906	+	22.1214i	−0.166735	+	0.730512i
$918$	−3.60480	−	4.52028i	−0.118976	−	0.149191i
$919$	3.82407	+	16.7543i	0.126144	+	0.552674i	0.998017	+	0.0629421i	$0.0200484\pi$
$919$	3.82407	+	16.7543i	0.126144	+	0.552674i	−0.871873	+	0.489732i	$0.837094\pi$
$920$	2.88870	+	12.6562i	0.0952376	+	0.417263i
$921$	−12.1325	+	15.2137i	−0.399779	+	0.501307i
$922$	−32.9923	+	15.8882i	−1.08654	+	0.523251i
$923$	−35.1492	−	16.9270i	−1.15695	−	0.557158i
$924$	0.451907	+	0.566674i	0.0148667	+	0.0186422i
$925$	−5.54651	+	6.95510i	−0.182368	+	0.228682i
$926$	−42.1849	−	20.3152i	−1.38628	−	0.667598i
$927$	−4.23721			−0.139168
$928$	−18.3264	+	16.1765i	−0.601593	+	0.531018i
$929$	41.7580			1.37003			0.685017	−	0.728527i	$-0.259795\pi$
$929$	41.7580			1.37003			0.685017	+	0.728527i	$0.259795\pi$
$930$	−3.42194	−	1.64792i	−0.112210	−	0.0540374i
$931$	−6.18320	+	7.75349i	−0.202646	+	0.254110i
$932$	9.70021	+	12.1637i	0.317741	+	0.398434i
$933$	−28.4210	−	13.6869i	−0.930463	−	0.448087i
$934$	34.8944	−	16.8043i	1.14178	−	0.549852i
$935$	−0.868257	+	1.08876i	−0.0283950	+	0.0356063i
$936$	−1.05651	−	4.62887i	−0.0345331	−	0.151299i
$937$	−1.69623	−	7.43166i	−0.0554134	−	0.242782i	0.939634	−	0.342180i	$-0.111165\pi$
$937$	−1.69623	−	7.43166i	−0.0554134	−	0.242782i	−0.995048	+	0.0993983i	$0.968308\pi$
$938$	−15.0527	−	18.8755i	−0.491490	−	0.616308i
$939$	1.83833	−	8.05424i	0.0599916	−	0.262840i
$940$	1.10468			0.0360307
$941$	4.78576	−	20.9678i	0.156011	−	0.683530i	−0.835056	−	0.550165i	$-0.814565\pi$
$941$	4.78576	−	20.9678i	0.156011	−	0.683530i	0.991067	−	0.133365i	$-0.0425782\pi$
$942$	−24.3500	+	11.7264i	−0.793367	+	0.382065i
$943$	−16.2999	+	7.84963i	−0.530798	+	0.255619i
$944$	−6.36490	+	27.8864i	−0.207160	+	0.907627i
$945$	−2.08554			−0.0678425
$946$	0.443500	−	1.94310i	0.0144194	−	0.0631756i
$947$	21.8406	+	27.3872i	0.709724	+	0.889965i	0.997708	−	0.0676700i	$-0.0215565\pi$
$947$	21.8406	+	27.3872i	0.709724	+	0.889965i	−0.287984	+	0.957635i	$0.592985\pi$
$948$	−1.61593	−	7.07983i	−0.0524828	−	0.229942i
$949$	−1.10490	−	4.84090i	−0.0358667	−	0.157142i
$950$	−3.94106	+	4.94194i	−0.127865	+	0.160338i
$951$	−2.49258	+	1.20036i	−0.0808273	+	0.0389244i
$952$	−12.4489	−	5.99508i	−0.403472	−	0.194302i
$953$	27.8684	+	34.9459i	0.902748	+	1.13201i	0.990724	+	0.135887i	$0.0433885\pi$
$953$	27.8684	+	34.9459i	0.902748	+	1.13201i	−0.0879767	+	0.996123i	$0.528040\pi$
$954$	−6.19641	+	7.77005i	−0.200616	+	0.251565i
$955$	14.3217	+	6.89696i	0.463439	+	0.223180i
$956$	16.8933			0.546368
$957$	−1.04819	−	1.92433i	−0.0338831	−	0.0622047i
$958$	−31.8182			−1.02800
$959$	5.79420	+	2.79034i	0.187104	+	0.0901048i
$960$	−1.42706	+	1.78947i	−0.0460581	+	0.0577551i
$961$	−16.1769	−	20.2852i	−0.521836	−	0.654361i
$962$	−33.2087	−	15.9924i	−1.07069	−	0.515617i
$963$	−0.435724	+	0.209834i	−0.0140410	+	0.00676180i
$964$	−13.2820	+	16.6551i	−0.427785	+	0.536425i
$965$	−1.84154	−	8.06833i	−0.0592814	−	0.259729i
$966$	5.25737	+	23.0340i	0.169153	+	0.741108i
$967$	3.31945	+	4.16246i	0.106746	+	0.133856i	0.832335	−	0.554273i	$-0.187004\pi$
$967$	3.31945	+	4.16246i	0.106746	+	0.133856i	−0.725588	+	0.688129i	$0.758432\pi$
$968$	4.66726	−	20.4486i	0.150011	−	0.657243i
$969$	12.8047			0.411346
$970$	−2.58407	+	11.3215i	−0.0829694	+	0.363513i
$971$	−0.0436551	+	0.0210232i	−0.00140096	+	0.000674666i	−0.434584	−	0.900631i	$-0.643105\pi$
$971$	−0.0436551	+	0.0210232i	−0.00140096	+	0.000674666i	0.433183	+	0.901306i	$0.357390\pi$
$972$	−0.769505	+	0.370574i	−0.0246819	+	0.0118862i
$973$	9.23086	−	40.4431i	0.295928	−	1.29654i
$974$	30.4870			0.976867
$975$	−0.545743	+	2.39106i	−0.0174778	+	0.0765751i
$976$	−33.7160	−	42.2785i	−1.07922	−	1.35330i
$977$	6.09294	+	26.6949i	0.194930	+	0.854045i	0.973899	+	0.226982i	$0.0728860\pi$
$977$	6.09294	+	26.6949i	0.194930	+	0.854045i	−0.778969	+	0.627063i	$0.784257\pi$
$978$	−5.36276	−	23.4958i	−0.171482	−	0.751313i
$979$	−1.32950	+	1.66715i	−0.0424911	+	0.0532822i
$980$	−2.03960	+	0.982220i	−0.0651527	+	0.0313759i
$981$	−9.28413	−	4.47100i	−0.296419	−	0.142748i
$982$	38.9268	+	48.8126i	1.24220	+	1.55767i
$983$	12.2392	−	15.3474i	0.390368	−	0.489507i	−0.547349	−	0.836904i	$-0.684363\pi$
$983$	12.2392	−	15.3474i	0.390368	−	0.489507i	0.937718	+	0.347398i	$0.112935\pi$
$984$	−4.70571	−	2.26615i	−0.150012	−	0.0722422i
$985$	13.0167			0.414748
$986$	−25.2817	−	18.1724i	−0.805133	−	0.578726i
$987$	−2.69744			−0.0858606
$988$	−7.06122	−	3.40050i	−0.224647	−	0.108184i
$989$	12.1217	−	15.2001i	0.385448	−	0.483336i
$990$	0.428611	+	0.537461i	0.0136222	+	0.0170816i
$991$	45.1726	+	21.7540i	1.43495	+	0.691037i	0.979911	−	0.199433i	$-0.0639100\pi$
$991$	45.1726	+	21.7540i	1.43495	+	0.691037i	0.455042	+	0.890470i	$0.349624\pi$
$992$	−9.19434	+	4.42776i	−0.291921	+	0.140582i
$993$	15.4361	−	19.3563i	0.489851	−	0.614253i
$994$	12.4713	+	54.6402i	0.395565	+	1.73308i
$995$	−0.0106630	−	0.0467178i	−0.000338041	−	0.00148106i
$996$	−4.93089	−	6.18313i	−0.156241	−	0.195920i
$997$	11.7536	−	51.4958i	0.372240	−	1.63089i	−0.348235	−	0.937407i	$-0.613219\pi$
$997$	11.7536	−	51.4958i	0.372240	−	1.63089i	0.720474	−	0.693482i	$-0.243924\pi$
$998$	0.378669			0.0119865
$999$	1.97953	−	8.67287i	0.0626294	−	0.274398i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.u.a.16.4	✓	30
29.20	even	7	inner	435.2.u.a.136.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.u.a.16.4	✓	30	1.1	even	1	trivial
435.2.u.a.136.4	yes	30	29.20	even	7	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

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	435.2.u.a.16.4

Level	$435$
Weight	$2$
Character	435.16
Analytic conductor	$3.473$
Analytic rank	$0$
Dimension	$30$
Inner twists	$2$