LMFDB - Embedded newform 44.2.g.a.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [44,2,Mod(7,44)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(44, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

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

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

chi := DirichletCharacter("44.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$44 = 2^{2} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	44.g (of order $10$ , degree $4$ , 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:	$0.351341768894$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256$ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			19.3
Root			$-0.544389 - 1.30524i$ of defining polynomial
Character	$\chi$	$=$	44.19
Dual form			44.2.g.a.7.3

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.544389 - 1.30524i) q^{2} +(-0.704424 + 0.228881i) q^{3} +(-1.40728 - 1.42111i) q^{4} +(1.09089 + 0.792578i) q^{5} +(-0.0847364 + 1.04404i) q^{6} +(-0.503194 + 1.54867i) q^{7} +(-2.62099 + 1.06320i) q^{8} +(-1.98322 + 1.44090i) q^{9} +(1.62837 - 0.992398i) q^{10} +(3.29726 - 0.357912i) q^{11} +(1.31659 + 0.678965i) q^{12} +(-2.09089 - 2.87786i) q^{13} +(1.74745 + 1.49987i) q^{14} +(-0.949856 - 0.308627i) q^{15} +(-0.0391135 + 3.99981i) q^{16} +(-0.0411247 + 0.0566033i) q^{17} +(0.801066 + 3.37298i) q^{18} +(-2.45716 - 7.56236i) q^{19} +(-0.408849 - 2.66566i) q^{20} -1.20609i q^{21} +(1.32783 - 4.49854i) q^{22} +5.30988i q^{23} +(1.60295 - 1.34884i) q^{24} +(-0.983224 - 3.02605i) q^{25} +(-4.89455 + 1.16243i) q^{26} +(2.37331 - 3.26658i) q^{27} +(2.90897 - 1.46432i) q^{28} +(3.74364 + 1.21638i) q^{29} +(-0.919921 + 1.07177i) q^{30} +(2.17121 + 2.98842i) q^{31} +(5.19940 + 2.22850i) q^{32} +(-2.24075 + 1.00680i) q^{33} +(0.0514928 + 0.0844916i) q^{34} +(-1.77637 + 1.29061i) q^{35} +(4.83863 + 0.790633i) q^{36} +(-2.12561 + 6.54194i) q^{37} +(-11.2083 - 0.909689i) q^{38} +(2.13156 + 1.54867i) q^{39} +(-3.70188 - 0.917509i) q^{40} +(5.50305 - 1.78805i) q^{41} +(-1.57424 - 0.656583i) q^{42} -1.89516 q^{43} +(-5.14880 - 4.18208i) q^{44} -3.30550 q^{45} +(6.93064 + 2.89064i) q^{46} +(-9.32545 + 3.03002i) q^{47} +(-0.887929 - 2.82652i) q^{48} +(3.51794 + 2.55593i) q^{49} +(-4.48497 - 0.364009i) q^{50} +(0.0160138 - 0.0492854i) q^{51} +(-1.14729 + 7.02135i) q^{52} +(3.14518 - 2.28511i) q^{53} +(-2.97166 - 4.87602i) q^{54} +(3.88062 + 2.22289i) q^{55} +(-0.327678 - 4.59405i) q^{56} +(3.46177 + 4.76471i) q^{57} +(3.62566 - 4.22415i) q^{58} +(4.62366 + 1.50232i) q^{59} +(0.898122 + 1.78418i) q^{60} +(0.791173 - 1.08896i) q^{61} +(5.08257 - 1.20708i) q^{62} +(-1.23353 - 3.79641i) q^{63} +(5.73922 - 5.57328i) q^{64} -4.79662i q^{65} +(0.0942773 + 3.47280i) q^{66} -4.91303i q^{67} +(0.138314 - 0.0212140i) q^{68} +(-1.21533 - 3.74041i) q^{69} +(0.717514 + 3.02118i) q^{70} +(4.10014 - 5.64335i) q^{71} +(3.66606 - 5.88514i) q^{72} +(-9.62677 - 3.12793i) q^{73} +(7.38163 + 6.33578i) q^{74} +(1.38521 + 1.90658i) q^{75} +(-7.28904 + 14.1343i) q^{76} +(-1.10487 + 5.28646i) q^{77} +(3.18178 - 1.93911i) q^{78} +(-4.85779 + 3.52939i) q^{79} +(-3.21283 + 4.33235i) q^{80} +(1.34841 - 4.14999i) q^{81} +(0.661971 - 8.15617i) q^{82} +(-2.92211 - 2.12304i) q^{83} +(-1.71399 + 1.69731i) q^{84} +(-0.0897250 + 0.0291534i) q^{85} +(-1.03170 + 2.47363i) q^{86} -2.91552 q^{87} +(-8.26156 + 4.44372i) q^{88} -5.39711 q^{89} +(-1.79948 + 4.31446i) q^{90} +(5.50899 - 1.78998i) q^{91} +(7.54592 - 7.47249i) q^{92} +(-2.21345 - 1.60816i) q^{93} +(-1.12177 + 13.8214i) q^{94} +(3.31327 - 10.1972i) q^{95} +(-4.17265 - 0.379765i) q^{96} +(-5.92705 + 4.30625i) q^{97} +(5.25122 - 3.20032i) q^{98} +(-6.02348 + 5.46083i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q - 5 q^{2} - q^{4} - 6 q^{5} - 5 q^{6} - 5 q^{8} - 10 q^{9} - 22 q^{12} - 10 q^{13} + 8 q^{14} + 23 q^{16} - 10 q^{17} + 20 q^{18} + 16 q^{20} + 17 q^{22} + 25 q^{24} + 6 q^{25} - 4 q^{26} + 20 q^{28}+ \cdots - 68 q^{97}+O(q^{100})$ 16 * q - 5 * q^2 - q^4 - 6 * q^5 - 5 * q^6 - 5 * q^8 - 10 * q^9 - 22 * q^12 - 10 * q^13 + 8 * q^14 + 23 * q^16 - 10 * q^17 + 20 * q^18 + 16 * q^20 + 17 * q^22 + 25 * q^24 + 6 * q^25 - 4 * q^26 + 20 * q^28 - 10 * q^29 - 12 * q^33 - 6 * q^34 - 30 * q^36 + 18 * q^37 - 38 * q^38 - 40 * q^40 + 10 * q^41 - 26 * q^42 - 28 * q^44 + 40 * q^45 - 30 * q^46 - 36 * q^48 + 6 * q^49 - 15 * q^50 - 10 * q^52 + 38 * q^53 - 12 * q^56 + 30 * q^58 + 52 * q^60 - 10 * q^61 + 70 * q^62 + 23 * q^64 + 36 * q^66 + 60 * q^68 - 16 * q^69 + 12 * q^70 + 45 * q^72 - 30 * q^73 + 40 * q^74 + 2 * q^77 + 4 * q^78 - 28 * q^80 - 4 * q^81 - 59 * q^82 - 10 * q^84 - 50 * q^85 - 39 * q^86 - 53 * q^88 - 36 * q^89 - 50 * q^90 + 36 * q^92 - 38 * q^93 - 30 * q^94 - 68 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$ .

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$

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

)

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

$2$	0.544389	−	1.30524i	0.384941	−	0.922941i
$2$	0.544389	−	1.30524i	0.384941	−	0.922941i
$3$	−0.704424	+	0.228881i	−0.406700	+	0.132145i	−0.505221	−	0.862990i	$-0.668589\pi$
$3$	−0.704424	+	0.228881i	−0.406700	+	0.132145i	0.0985210	+	0.995135i	$0.468589\pi$
$4$	−1.40728	−	1.42111i	−0.703641	−	0.710556i
$5$	1.09089	+	0.792578i	0.487861	+	0.354452i	0.804361	−	0.594141i	$-0.202508\pi$
$5$	1.09089	+	0.792578i	0.487861	+	0.354452i	−0.316500	+	0.948592i	$0.602508\pi$
$6$	−0.0847364	+	1.04404i	−0.0345935	+	0.426228i
$7$	−0.503194	+	1.54867i	−0.190189	+	0.585343i	−0.999999	−	0.00134995i	$-0.999570\pi$
$7$	−0.503194	+	1.54867i	−0.190189	+	0.585343i	0.809810	+	0.586693i	$0.199570\pi$
$8$	−2.62099	+	1.06320i	−0.926661	+	0.375898i
$9$	−1.98322	+	1.44090i	−0.661075	+	0.480299i
$10$	1.62837	−	0.992398i	0.514936	−	0.313824i
$11$	3.29726	−	0.357912i	0.994160	−	0.107915i
$11$	3.29726	−	0.357912i	0.994160	−	0.107915i
$12$	1.31659	+	0.678965i	0.380067	+	0.196000i
$13$	−2.09089	−	2.87786i	−0.579909	−	0.798176i	0.413777	−	0.910378i	$-0.364209\pi$
$13$	−2.09089	−	2.87786i	−0.579909	−	0.798176i	−0.993685	+	0.112203i	$0.964209\pi$
$14$	1.74745	+	1.49987i	0.467025	+	0.400856i
$15$	−0.949856	−	0.308627i	−0.245252	−	0.0796871i
$16$	−0.0391135	+	3.99981i	−0.00977837	+	0.999952i
$17$	−0.0411247	+	0.0566033i	−0.00997420	+	0.0137283i	−0.813975	−	0.580900i	$-0.802701\pi$
$17$	−0.0411247	+	0.0566033i	−0.00997420	+	0.0137283i	0.804001	+	0.594628i	$0.202701\pi$
$18$	0.801066	+	3.37298i	0.188813	+	0.795020i
$19$	−2.45716	−	7.56236i	−0.563711	−	1.73493i	−0.671749	−	0.740778i	$-0.734457\pi$
$19$	−2.45716	−	7.56236i	−0.563711	−	1.73493i	0.108038	−	0.994147i	$-0.465543\pi$
$20$	−0.408849	−	2.66566i	−0.0914213	−	0.596059i
$21$		−	1.20609i		−	0.263191i
$22$	1.32783	−	4.49854i	0.283094	−	0.959092i
$23$			5.30988i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$23$			5.30988i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$24$	1.60295	−	1.34884i	0.327200	−	0.275331i
$25$	−0.983224	−	3.02605i	−0.196645	−	0.605210i
$26$	−4.89455	+	1.16243i	−0.959900	+	0.227971i
$27$	2.37331	−	3.26658i	0.456744	−	0.628654i
$28$	2.90897	−	1.46432i	0.549744	−	0.276731i
$29$	3.74364	+	1.21638i	0.695177	+	0.225877i	0.635228	−	0.772325i	$-0.280906\pi$
$29$	3.74364	+	1.21638i	0.695177	+	0.225877i	0.0599489	+	0.998201i	$0.480906\pi$
$30$	−0.919921	+	1.07177i	−0.167954	+	0.195678i
$31$	2.17121	+	2.98842i	0.389961	+	0.536735i	0.958189	−	0.286136i	$-0.0923708\pi$
$31$	2.17121	+	2.98842i	0.389961	+	0.536735i	−0.568228	+	0.822871i	$0.692371\pi$
$32$	5.19940	+	2.22850i	0.919133	+	0.393947i
$33$	−2.24075	+	1.00680i	−0.390064	+	0.175262i
$34$	0.0514928	+	0.0844916i	0.00883095	+	0.0144902i
$35$	−1.77637	+	1.29061i	−0.300262	+	0.218153i
$36$	4.83863	+	0.790633i	0.806438	+	0.131772i
$37$	−2.12561	+	6.54194i	−0.349448	+	1.07549i	0.609712	+	0.792623i	$0.291285\pi$
$37$	−2.12561	+	6.54194i	−0.349448	+	1.07549i	−0.959159	+	0.282866i	$0.908715\pi$
$38$	−11.2083	−	0.909689i	−1.81823	−	0.147571i
$39$	2.13156	+	1.54867i	0.341323	+	0.247986i
$40$	−3.70188	−	0.917509i	−0.585319	−	0.145071i
$41$	5.50305	−	1.78805i	0.859432	−	0.279246i	0.154041	−	0.988065i	$-0.450771\pi$
$41$	5.50305	−	1.78805i	0.859432	−	0.279246i	0.705391	+	0.708818i	$0.250771\pi$
$42$	−1.57424	−	0.656583i	−0.242910	−	0.101313i
$43$	−1.89516			−0.289009			−0.144505	−	0.989504i	$-0.546159\pi$
$43$	−1.89516			−0.289009			−0.144505	+	0.989504i	$0.546159\pi$
$44$	−5.14880	−	4.18208i	−0.776211	−	0.630473i
$45$	−3.30550			−0.492755
$46$	6.93064	+	2.89064i	1.02187	+	0.426201i
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.896129	−	0.443794i	$-0.853632\pi$
$47$	−9.32545	+	3.03002i	−1.36026	+	0.441974i	−0.464128	+	0.885768i	$0.653632\pi$
$48$	−0.887929	−	2.82652i	−0.128162	−	0.407972i
$49$	3.51794	+	2.55593i	0.502563	+	0.365133i
$50$	−4.48497	−	0.364009i	−0.634270	−	0.0514786i
$51$	0.0160138	−	0.0492854i	0.00224238	−	0.00690134i
$52$	−1.14729	+	7.02135i	−0.159101	+	0.973686i
$53$	3.14518	−	2.28511i	0.432023	−	0.313883i	−0.350434	−	0.936587i	$-0.613966\pi$
$53$	3.14518	−	2.28511i	0.432023	−	0.313883i	0.782457	+	0.622704i	$0.213966\pi$
$54$	−2.97166	−	4.87602i	−0.404391	−	0.663543i
$55$	3.88062	+	2.22289i	0.523262	+	0.299734i
$56$	−0.327678	−	4.59405i	−0.0437878	−	0.613906i
$57$	3.46177	+	4.76471i	0.458522	+	0.631102i
$58$	3.62566	−	4.22415i	0.476073	−	0.554658i
$59$	4.62366	+	1.50232i	0.601950	+	0.195585i	0.594110	−	0.804384i	$-0.297504\pi$
$59$	4.62366	+	1.50232i	0.601950	+	0.195585i	0.00783982	+	0.999969i	$0.497504\pi$
$60$	0.898122	+	1.78418i	0.115947	+	0.230336i
$61$	0.791173	−	1.08896i	0.101299	−	0.139427i	−0.755358	−	0.655312i	$-0.772537\pi$
$61$	0.791173	−	1.08896i	0.101299	−	0.139427i	0.856657	+	0.515886i	$0.172537\pi$
$62$	5.08257	−	1.20708i	0.645487	−	0.153300i
$63$	−1.23353	−	3.79641i	−0.155410	−	0.478303i
$64$	5.73922	−	5.57328i	0.717402	−	0.696659i
$65$		−	4.79662i		−	0.594948i
$66$	0.0942773	+	3.47280i	0.0116047	+	0.427472i
$67$		−	4.91303i		−	0.600223i	−0.953904	−	0.300111i	$-0.902976\pi$
$67$		−	4.91303i		−	0.600223i	0.953904	−	0.300111i	$-0.0970238\pi$
$68$	0.138314	−	0.0212140i	0.0167730	−	0.00257258i
$69$	−1.21533	−	3.74041i	−0.146309	−	0.450292i
$70$	0.717514	+	3.02118i	0.0857593	+	0.361100i
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	−0.493159	−	0.869939i	$-0.664158\pi$
$71$	4.10014	−	5.64335i	0.486597	−	0.669743i	0.979756	+	0.200196i	$0.0641580\pi$
$72$	3.66606	−	5.88514i	0.432049	−	0.693571i
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.314397	−	0.949292i	$-0.601802\pi$
$73$	−9.62677	−	3.12793i	−1.12673	−	0.366096i	−0.812332	+	0.583195i	$0.801802\pi$
$74$	7.38163	+	6.33578i	0.858097	+	0.736519i
$75$	1.38521	+	1.90658i	0.159951	+	0.220153i
$76$	−7.28904	+	14.1343i	−0.836110	+	1.62131i
$77$	−1.10487	+	5.28646i	−0.125912	+	0.602449i
$78$	3.18178	−	1.93911i	0.360266	−	0.219561i
$79$	−4.85779	+	3.52939i	−0.546544	+	0.397088i	−0.826510	−	0.562923i	$-0.809677\pi$
$79$	−4.85779	+	3.52939i	−0.546544	+	0.397088i	0.279966	+	0.960010i	$0.409677\pi$
$80$	−3.21283	+	4.33235i	−0.359205	+	0.484371i
$81$	1.34841	−	4.14999i	0.149824	−	0.461110i
$82$	0.661971	−	8.15617i	0.0731025	−	0.900699i
$83$	−2.92211	−	2.12304i	−0.320744	−	0.233034i	0.415749	−	0.909479i	$-0.363519\pi$
$83$	−2.92211	−	2.12304i	−0.320744	−	0.233034i	−0.736493	+	0.676446i	$0.763519\pi$
$84$	−1.71399	+	1.69731i	−0.187012	+	0.185192i
$85$	−0.0897250	+	0.0291534i	−0.00973205	+	0.00316213i
$86$	−1.03170	+	2.47363i	−0.111251	+	0.266738i
$87$	−2.91552			−0.312576
$88$	−8.26156	+	4.44372i	−0.880685	+	0.473703i
$89$	−5.39711			−0.572093			−0.286046	−	0.958216i	$-0.592341\pi$
$89$	−5.39711			−0.572093			−0.286046	+	0.958216i	$0.592341\pi$
$90$	−1.79948	+	4.31446i	−0.189682	+	0.454784i
$91$	5.50899	−	1.78998i	0.577499	−	0.187641i
$92$	7.54592	−	7.47249i	0.786717	−	0.779061i
$93$	−2.21345	−	1.60816i	−0.229524	−	0.166759i
$94$	−1.12177	+	13.8214i	−0.115702	+	1.42557i
$95$	3.31327	−	10.1972i	0.339934	−	1.04621i
$96$	−4.17265	−	0.379765i	−0.425869	−	0.0387596i
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	−0.846518	−	0.532361i	$-0.821305\pi$
$97$	−5.92705	+	4.30625i	−0.601801	+	0.437234i	0.244717	+	0.969595i	$0.421305\pi$
$98$	5.25122	−	3.20032i	0.530454	−	0.323281i
$99$	−6.02348	+	5.46083i	−0.605383	+	0.548834i
$100$	−2.91668	+	5.65578i	−0.291668	+	0.565578i
$101$	−5.62667	−	7.74445i	−0.559875	−	0.770602i	0.431436	−	0.902144i	$-0.358007\pi$
$101$	−5.62667	−	7.74445i	−0.559875	−	0.770602i	−0.991311	+	0.131542i	$0.958007\pi$
$102$	−0.0556114	−	0.0477322i	−0.00550635	−	0.00472619i
$103$	9.81631	+	3.18951i	0.967230	+	0.314272i	0.749697	−	0.661781i	$-0.230199\pi$
$103$	9.81631	+	3.18951i	0.967230	+	0.314272i	0.217533	+	0.976053i	$0.430199\pi$
$104$	8.53995	+	5.31983i	0.837411	+	0.521652i
$105$	0.955923	−	1.31571i	0.0932885	−	0.128401i
$106$	−1.27040	−	5.34919i	−0.123392	−	0.519559i
$107$	3.42303	+	10.5350i	0.330917	+	1.01846i	0.968699	+	0.248240i	$0.0798522\pi$
$107$	3.42303	+	10.5350i	0.330917	+	1.01846i	−0.637782	+	0.770217i	$0.720148\pi$
$108$	−7.98210	+	1.22426i	−0.768078	+	0.117805i
$109$			8.95933i			0.858149i	0.903269	+	0.429074i	$0.141160\pi$
$109$			8.95933i			0.858149i	−0.903269	+	0.429074i	$0.858840\pi$
$110$	5.01396	−	3.85501i	0.478062	−	0.367560i
$111$		−	5.09482i		−	0.483579i
$112$	−6.17471	−	2.07325i	−0.583455	−	0.195904i
$113$	3.40631	+	10.4836i	0.320439	+	0.986210i	0.973457	+	0.228868i	$0.0735025\pi$
$113$	3.40631	+	10.4836i	0.320439	+	0.986210i	−0.653018	+	0.757342i	$0.726498\pi$
$114$	8.10362	−	1.92457i	0.758974	−	0.180252i
$115$	−4.20849	+	5.79249i	−0.392444	+	0.540153i
$116$	−3.53974	−	7.03192i	−0.328657	−	0.652898i
$117$	8.29341	+	2.69469i	0.766726	+	0.249124i
$118$	4.47795	−	5.21713i	0.412229	−	0.480275i
$119$	−0.0669662	−	0.0921710i	−0.00613878	−	0.00844931i
$120$	2.81770	−	0.200977i	0.257219	−	0.0183466i
$121$	10.7438	−	2.36026i	0.976709	−	0.214569i
$122$	−0.990640	−	1.62548i	−0.0896883	−	0.147164i
$123$	−3.46723	+	2.51909i	−0.312630	+	0.227139i
$124$	1.19136	−	7.29108i	0.106988	−	0.654758i
$125$	3.40921	−	10.4925i	0.304929	−	0.938474i
$126$	−5.62673	−	0.456677i	−0.501269	−	0.0406840i
$127$	−8.32668	−	6.04969i	−0.738874	−	0.536823i	0.153485	−	0.988151i	$-0.450950\pi$
$127$	−8.32668	−	6.04969i	−0.738874	−	0.536823i	−0.892358	+	0.451328i	$0.850950\pi$
$128$	−4.15008	−	10.5251i	−0.366818	−	0.930293i
$129$	1.33500	−	0.433767i	0.117540	−	0.0381910i
$130$	−6.26073	−	2.61123i	−0.549102	−	0.229020i
$131$	−1.86768			−0.163180			−0.0815901	−	0.996666i	$-0.526000\pi$
$131$	−1.86768			−0.163180			−0.0815901	+	0.996666i	$0.526000\pi$
$132$	4.58414	+	1.76750i	0.398998	+	0.153841i
$133$	12.9480			1.12274
$134$	−6.41267	−	2.67460i	−0.553970	−	0.231050i
$135$	5.17804	−	1.68245i	0.445655	−	0.144802i
$136$	0.0476070	−	0.192081i	0.00408227	−	0.0164708i
$137$	1.01489	+	0.737362i	0.0867080	+	0.0629971i	0.630295	−	0.776356i	$-0.282934\pi$
$137$	1.01489	+	0.737362i	0.0867080	+	0.0629971i	−0.543587	+	0.839353i	$0.682934\pi$
$138$	−5.54373	−	0.449940i	−0.471913	−	0.0383014i
$139$	−1.94407	+	5.98323i	−0.164894	+	0.507491i	−0.999028	−	0.0440698i	$-0.985968\pi$
$139$	−1.94407	+	5.98323i	−0.164894	+	0.507491i	0.834135	+	0.551561i	$0.185968\pi$
$140$	4.33396	+	0.708169i	0.366286	+	0.0598512i
$141$	5.87556	−	4.26884i	0.494811	−	0.359501i
$142$	−5.13384	−	8.42382i	−0.430822	−	0.706912i
$143$	−7.92422	−	8.74070i	−0.662657	−	0.730934i
$144$	−5.68574	−	7.98888i	−0.473812	−	0.665740i
$145$	3.11982	+	4.29407i	0.259087	+	0.356603i
$146$	−9.32339	+	10.8624i	−0.771609	+	0.898979i
$147$	−3.06313	−	0.995271i	−0.252643	−	0.0820886i
$148$	12.2882	−	6.18564i	1.01008	−	0.508456i
$149$	−10.0839	+	13.8792i	−0.826102	+	1.13703i	0.162534	+	0.986703i	$0.448033\pi$
$149$	−10.0839	+	13.8792i	−0.826102	+	1.13703i	−0.988636	+	0.150329i	$0.951967\pi$
$150$	3.24264	−	0.770109i	0.264760	−	0.0628791i
$151$	3.75712	+	11.5632i	0.305750	+	0.941002i	0.979396	+	0.201948i	$0.0647271\pi$
$151$	3.75712	+	11.5632i	0.305750	+	0.941002i	−0.673646	+	0.739054i	$0.735273\pi$
$152$	14.4805	+	17.2085i	1.17452	+	1.39579i
$153$		−	0.171513i		−	0.0138660i
$154$	6.29861	+	4.32001i	0.507556	+	0.348116i
$155$			4.98089i			0.400074i
$156$	−0.798877	−	5.20860i	−0.0639613	−	0.417022i
$157$	−1.63833	−	5.04225i	−0.130753	−	0.402415i	0.864153	−	0.503230i	$-0.167855\pi$
$157$	−1.63833	−	5.04225i	−0.130753	−	0.402415i	−0.994905	+	0.100815i	$0.967855\pi$
$158$	1.96216	+	8.26192i	0.156101	+	0.657283i
$159$	−1.69252	+	2.32956i	−0.134226	+	0.184746i
$160$	3.90571	+	6.55198i	0.308774	+	0.517980i
$161$	−8.22325	−	2.67190i	−0.648083	−	0.210575i
$162$	−4.68266	−	4.01921i	−0.367904	−	0.315779i
$163$	−5.91168	−	8.13673i	−0.463039	−	0.637318i	0.512097	−	0.858928i	$-0.328869\pi$
$163$	−5.91168	−	8.13673i	−0.463039	−	0.637318i	−0.975135	+	0.221610i	$0.928869\pi$
$164$	−10.2854	−	5.30415i	−0.803152	−	0.414185i
$165$	−3.24238	−	0.677657i	−0.252419	−	0.0527555i
$166$	−4.36183	+	2.65829i	−0.338544	+	0.206323i
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.373879	−	0.927478i	$-0.378028\pi$
$167$	17.7237	−	12.8770i	1.37150	−	0.996451i	0.997618	−	0.0689735i	$-0.0219724\pi$
$168$	1.28232	+	3.16116i	0.0989329	+	0.243889i
$169$	0.106946	−	0.329146i	0.00822661	−	0.0253189i
$170$	−0.0107932	+	0.132983i	−0.000827798	+	0.0101993i
$171$	15.7697	+	11.4573i	1.20594	+	0.876165i
$172$	2.66702	+	2.69323i	0.203359	+	0.205357i
$173$	−11.2531	+	3.65635i	−0.855557	+	0.277987i	−0.703772	−	0.710426i	$-0.748502\pi$
$173$	−11.2531	+	3.65635i	−0.855557	+	0.277987i	−0.151785	+	0.988413i	$0.548502\pi$
$174$	−1.58718	+	3.80544i	−0.120323	+	0.288490i
$175$	5.18111			0.391655
$176$	1.30261	+	13.2024i	0.0981882	+	0.995168i
$177$	−3.60087			−0.270658
$178$	−2.93813	+	7.04450i	−0.220222	+	0.528008i
$179$	−0.887979	+	0.288522i	−0.0663707	+	0.0215651i	−0.342014	−	0.939695i	$-0.611109\pi$
$179$	−0.887979	+	0.288522i	−0.0663707	+	0.0215651i	0.275643	+	0.961260i	$0.411109\pi$
$180$	4.65177	+	4.69749i	0.346723	+	0.350130i
$181$	−15.2414	−	11.0736i	−1.13289	−	0.823091i	−0.146775	−	0.989170i	$-0.546889\pi$
$181$	−15.2414	−	11.0736i	−1.13289	−	0.823091i	−0.986113	+	0.166079i	$0.946889\pi$
$182$	0.662685	−	8.16497i	0.0491215	−	0.605228i
$183$	−0.308080	+	0.948172i	−0.0227739	+	0.0700909i
$184$	−5.64545	−	13.9172i	−0.416188	−	1.02599i
$185$	−7.50380	+	5.45183i	−0.551691	+	0.400827i
$186$	−3.30401	+	2.01361i	−0.242262	+	0.147645i
$187$	−0.115340	+	0.201355i	−0.00843447	+	0.0147245i
$188$	17.4295	+	8.98840i	1.27118	+	0.655547i
$189$	3.86463	+	5.31920i	0.281110	+	0.386915i
$190$	−11.5060	−	9.87584i	−0.834736	−	0.716468i
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.495472	−	0.868624i	$-0.665005\pi$
$191$	−19.4435	−	6.31757i	−1.40688	−	0.457124i	−0.911410	+	0.411500i	$0.865005\pi$
$192$	−2.76722	+	5.23955i	−0.199707	+	0.378132i
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	−0.265267	−	0.964175i	$-0.585460\pi$
$193$	10.1927	−	14.0291i	0.733690	−	1.00984i	0.998957	−	0.0456628i	$-0.0145400\pi$
$194$	2.39406	+	10.0805i	0.171883	+	0.723736i
$195$	1.09786	+	3.37886i	0.0786192	+	0.241965i
$196$	−1.31847	−	8.59630i	−0.0941764	−	0.614022i
$197$			3.49133i			0.248747i	0.992235	+	0.124374i	$0.0396921\pi$
$197$			3.49133i			0.248747i	−0.992235	+	0.124374i	$0.960308\pi$
$198$	3.84855	+	10.8349i	0.273505	+	0.770001i
$199$		−	11.2660i		−	0.798625i	−0.916815	−	0.399313i	$-0.869249\pi$
$199$		−	11.2660i		−	0.798625i	0.916815	−	0.399313i	$-0.130751\pi$
$200$	5.79432	+	6.88590i	0.409720	+	0.486907i
$201$	1.12450	+	3.46086i	0.0793162	+	0.244110i
$202$	−13.1714	+	3.12815i	−0.926739	+	0.220096i
$203$	−3.76755	+	5.18559i	−0.264430	+	0.363957i
$204$	−0.0925760	+	0.0466011i	−0.00648161	+	0.00326273i
$205$	7.42039	+	2.41103i	0.518262	+	0.168394i
$206$	9.50696	−	11.0763i	0.662381	−	0.771720i
$207$	−7.65098	−	10.5307i	−0.531780	−	0.731932i
$208$	11.5927	−	8.25060i	0.803808	−	0.572076i
$209$	−10.8086	−	24.0556i	−0.747643	−	1.66396i
$210$	−1.19693	−	1.96397i	−0.0825957	−	0.135526i
$211$	2.21909	−	1.61227i	0.152769	−	0.110993i	−0.508775	−	0.860899i	$-0.669902\pi$
$211$	2.21909	−	1.61227i	0.152769	−	0.110993i	0.661544	+	0.749906i	$0.269902\pi$
$212$	−7.67354	−	1.25386i	−0.527021	−	0.0861154i
$213$	−1.59658	+	4.91376i	−0.109396	+	0.336685i
$214$	15.6141	+	1.26727i	1.06736	+	0.0866290i
$215$	−2.06741	−	1.50206i	−0.140996	−	0.102440i
$216$	−2.74741	+	11.0850i	−0.186937	+	0.754238i
$217$	−5.72061	+	1.85874i	−0.388341	+	0.126180i
$218$	11.6940	+	4.87736i	0.792021	+	0.330336i
$219$	7.49726			0.506618
$220$	−2.30215	−	8.64302i	−0.155211	−	0.582712i
$221$	0.248884			0.0167417
$222$	−6.64994	−	2.77356i	−0.446315	−	0.186149i
$223$	22.5646	−	7.33167i	1.51103	−	0.490965i	0.567821	−	0.823152i	$-0.307787\pi$
$223$	22.5646	−	7.33167i	1.51103	−	0.490965i	0.943213	+	0.332187i	$0.107787\pi$
$224$	−6.06752	+	6.93079i	−0.405403	+	0.463083i
$225$	6.31018	+	4.58462i	0.420679	+	0.305641i
$226$	15.5379	+	1.26108i	1.03356	+	0.0838861i
$227$	−0.247473	+	0.761643i	−0.0164254	+	0.0505520i	−0.958933	−	0.283632i	$-0.908461\pi$
$227$	−0.247473	+	0.761643i	−0.0164254	+	0.0505520i	0.942508	+	0.334184i	$0.108461\pi$
$228$	1.89950	−	11.6249i	0.125798	−	0.769875i
$229$	19.0839	−	13.8652i	1.26110	−	0.916241i	0.262286	−	0.964990i	$-0.415524\pi$
$229$	19.0839	−	13.8652i	1.26110	−	0.916241i	0.998811	+	0.0487497i	$0.0155237\pi$
$230$	5.26951	+	8.64644i	0.347461	+	0.570129i
$231$	−0.431676	−	3.97680i	−0.0284022	−	0.261654i
$232$	−11.1053	+	0.792103i	−0.729100	+	0.0520041i
$233$	10.2812	+	14.1509i	0.673547	+	0.927058i	0.999834	−	0.0182127i	$-0.00579761\pi$
$233$	10.2812	+	14.1509i	0.673547	+	0.927058i	−0.326287	+	0.945271i	$0.605798\pi$
$234$	8.03204	−	9.35789i	0.525071	−	0.611745i
$235$	−12.5746	−	4.08572i	−0.820274	−	0.266523i
$236$	−4.37184	−	8.68492i	−0.284582	−	0.565340i
$237$	2.61413	−	3.59805i	0.169806	−	0.233718i
$238$	−0.156761	+	0.0372298i	−0.0101613	+	0.00241325i
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	0.995373	−	0.0960826i	$-0.0306313\pi$
$239$	2.06577	+	6.35778i	0.133623	+	0.411251i	−0.861750	+	0.507333i	$0.830631\pi$
$240$	1.27160	−	3.78717i	0.0820815	−	0.244461i
$241$		−	4.28655i		−	0.276121i	−0.990424	−	0.138061i	$-0.955913\pi$
$241$		−	4.28655i		−	0.276121i	0.990424	−	0.138061i	$-0.0440868\pi$
$242$	2.76811	−	15.3081i	0.177941	−	0.984041i
$243$			15.3451i			0.984391i
$244$	−2.66093	+	0.408124i	−0.170349	+	0.0261275i
$245$	1.81191	+	5.57648i	0.115759	+	0.356268i
$246$	1.40049	+	5.89692i	0.0892918	+	0.375974i
$247$	−16.6258	+	22.8834i	−1.05787	+	1.45604i
$248$	−8.86801	−	5.52419i	−0.563119	−	0.350786i
$249$	2.54433	+	0.826703i	0.161240	+	0.0523902i
$250$	−11.8392	−	10.1618i	−0.748777	−	0.642688i
$251$	2.87878	+	3.96230i	0.181707	+	0.250098i	0.890148	−	0.455672i	$-0.150601\pi$
$251$	2.87878	+	3.96230i	0.181707	+	0.250098i	−0.708441	+	0.705770i	$0.750601\pi$
$252$	−3.65920	+	7.09560i	−0.230508	+	0.446981i
$253$	1.90047	+	17.5080i	0.119482	+	1.10072i
$254$	−12.4292	+	7.57491i	−0.779879	+	0.475292i
$255$	0.0565318	−	0.0410728i	0.00354016	−	0.00257208i
$256$	−15.9969	−	0.312893i	−0.999809	−	0.0195558i
$257$	−3.82696	+	11.7782i	−0.238719	+	0.734702i	0.757887	+	0.652386i	$0.226232\pi$
$257$	−3.82696	+	11.7782i	−0.238719	+	0.734702i	−0.996606	+	0.0823161i	$0.973768\pi$
$258$	0.160589	−	1.97862i	0.00999783	−	0.123184i
$259$	−9.06173	−	6.58373i	−0.563068	−	0.409093i
$260$	−6.81654	+	6.75020i	−0.422744	+	0.418630i
$261$	−9.17716	+	2.98184i	−0.568052	+	0.184571i
$262$	−1.01675	+	2.43777i	−0.0628148	+	0.150606i
$263$	16.9489			1.04511			0.522556	−	0.852605i	$-0.324979\pi$
$263$	16.9489			1.04511			0.522556	+	0.852605i	$0.324979\pi$
$264$	4.80256	−	5.02118i	0.295577	−	0.309033i
$265$	5.24217			0.322024
$266$	7.04877	−	16.9003i	0.432188	−	1.03622i
$267$	3.80186	−	1.23530i	0.232670	−	0.0755990i
$268$	−6.98197	+	6.91403i	−0.426492	+	0.422341i
$269$	−3.19947	−	2.32455i	−0.195075	−	0.141730i	0.485960	−	0.873981i	$-0.338470\pi$
$269$	−3.19947	−	2.32455i	−0.195075	−	0.141730i	−0.681035	+	0.732251i	$0.738470\pi$
$270$	0.622875	−	7.67447i	0.0379070	−	0.467054i
$271$	−7.33528	+	22.5757i	−0.445587	+	1.37137i	0.436252	+	0.899824i	$0.356305\pi$
$271$	−7.33528	+	22.5757i	−0.445587	+	1.37137i	−0.881839	+	0.471550i	$0.843695\pi$
$272$	−0.224794	−	0.166705i	−0.0136301	−	0.0101080i
$273$	−3.47097	+	2.52181i	−0.210073	+	0.152627i
$274$	1.51493	−	0.923261i	0.0915200	−	0.0557763i
$275$	−4.32500	−	9.62576i	−0.260807	−	0.580455i
$276$	−3.60522	+	6.99093i	−0.217009	+	0.420804i
$277$	−8.82329	−	12.1442i	−0.530140	−	0.729675i	0.457012	−	0.889461i	$-0.348920\pi$
$277$	−8.82329	−	12.1442i	−0.530140	−	0.729675i	−0.987152	+	0.159786i	$0.948920\pi$
$278$	6.75120	+	5.79467i	0.404910	+	0.347541i
$279$	−8.61200	−	2.79821i	−0.515587	−	0.167524i
$280$	3.28368	−	5.27131i	0.196238	−	0.315021i
$281$	3.37468	−	4.64485i	0.201317	−	0.277089i	−0.696408	−	0.717647i	$-0.745219\pi$
$281$	3.37468	−	4.64485i	0.201317	−	0.277089i	0.897724	+	0.440558i	$0.145219\pi$
$282$	−2.37326	−	9.99290i	−0.141326	−	0.595068i
$283$	−3.45938	−	10.6469i	−0.205639	−	0.632890i	−0.999687	−	0.0250353i	$-0.992030\pi$
$283$	−3.45938	−	10.6469i	−0.205639	−	0.632890i	0.794048	−	0.607855i	$-0.207970\pi$
$284$	−13.7899	+	2.11504i	−0.818279	+	0.125505i
$285$			7.94150i			0.470414i
$286$	−15.7225	+	5.58464i	−0.929693	+	0.330227i
$287$			9.42215i			0.556172i
$288$	−13.5226	+	3.07218i	−0.796828	+	0.181030i
$289$	5.25178	+	16.1633i	0.308928	+	0.950783i
$290$	7.30317	−	1.73446i	0.428857	−	0.101851i
$291$	3.18954	−	4.39002i	0.186974	−	0.257348i
$292$	9.10245	+	18.0826i	0.532681	+	1.05820i
$293$	5.04336	+	1.63869i	0.294636	+	0.0957331i	0.452605	−	0.891711i	$-0.350495\pi$
$293$	5.04336	+	1.63869i	0.294636	+	0.0957331i	−0.157969	+	0.987444i	$0.550495\pi$
$294$	−2.96660	+	3.45629i	−0.173015	+	0.201575i
$295$	3.85320	+	5.30348i	0.224342	+	0.308780i
$296$	−1.38419	−	19.4063i	−0.0804542	−	1.12797i
$297$	6.65627	−	11.6202i	0.386236	−	0.674272i
$298$	12.6261	+	20.7175i	0.731413	+	1.20013i
$299$	15.2811	−	11.1024i	0.883729	−	0.642066i
$300$	0.760080	−	4.65164i	0.0438832	−	0.268563i
$301$	0.953632	−	2.93498i	0.0549664	−	0.169169i
$302$	17.1381	+	1.39096i	0.986185	+	0.0800407i
$303$	5.73613	+	4.16754i	0.329532	+	0.239419i
$304$	30.3441	−	9.53238i	1.74035	−	0.546720i
$305$	1.72617	−	0.560865i	0.0988400	−	0.0321150i
$306$	−0.223866	−	0.0933699i	−0.0127975	−	0.00533760i
$307$	2.27014			0.129564			0.0647820	−	0.997899i	$-0.479365\pi$
$307$	2.27014			0.129564			0.0647820	+	0.997899i	$0.479365\pi$
$308$	9.06752	−	5.86940i	0.516670	−	0.334440i
$309$	−7.64487			−0.434901
$310$	6.50123	+	2.71154i	0.369245	+	0.154005i
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.797307	−	0.603574i	$-0.793743\pi$
$311$	−19.1795	+	6.23180i	−1.08757	+	0.353373i	−0.290263	+	0.956947i	$0.593743\pi$
$312$	−7.23336	−	1.79278i	−0.409508	−	0.101496i
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	0.551973	−	0.833862i	$-0.313875\pi$
$313$	−1.24741	−	0.906296i	−0.0705078	−	0.0512269i	−0.622481	+	0.782635i	$0.713875\pi$
$314$	−7.47321	−	0.606540i	−0.421738	−	0.0342290i
$315$	1.66331	−	5.11913i	0.0937168	−	0.288431i
$316$	11.8519	+	1.93661i	0.666724	+	0.108943i
$317$	13.6418	−	9.91136i	0.766201	−	0.556678i	−0.134605	−	0.990899i	$-0.542977\pi$
$317$	13.6418	−	9.91136i	0.766201	−	0.556678i	0.900806	+	0.434222i	$0.142977\pi$
$318$	2.11923	+	3.47732i	0.118841	+	0.194999i
$319$	12.7791	+	2.67083i	0.715492	+	0.149538i
$320$	10.6781	−	1.53105i	0.596924	−	0.0855885i
$321$	−4.82253	−	6.63765i	−0.269167	−	0.370477i
$322$	−7.96410	+	9.27874i	−0.443822	+	0.517084i
$323$	0.529105	+	0.171917i	0.0294402	+	0.00956569i
$324$	−7.79520	+	3.92396i	−0.433067	+	0.217998i
$325$	−6.65275	+	9.15673i	−0.369028	+	0.507924i
$326$	−13.8386	+	3.28660i	−0.766450	+	0.182028i
$327$	−2.05062	−	6.31117i	−0.113400	−	0.349009i
$328$	−12.5224	+	10.5373i	−0.691434	+	0.581825i
$329$		−	15.9667i		−	0.880275i
$330$	−2.64962	+	3.86316i	−0.145857	+	0.212660i
$331$		−	33.9735i		−	1.86735i	−0.358115	−	0.933677i	$-0.616581\pi$
$331$		−	33.9735i		−	1.86735i	0.358115	−	0.933677i	$-0.383419\pi$
$332$	1.09516	+	7.14036i	0.0601049	+	0.391878i
$333$	−5.21071	−	16.0369i	−0.285545	−	0.878818i
$334$	−7.15895	−	30.1436i	−0.391721	−	1.64939i
$335$	3.89396	−	5.35958i	0.212750	−	0.292825i
$336$	4.82414	+	0.0471745i	0.263179	+	0.00257358i
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.169368	−	0.985553i	$-0.554173\pi$
$337$	−16.2590	−	5.28286i	−0.885683	−	0.287776i	−0.716315	+	0.697777i	$0.754173\pi$
$338$	−0.371393	−	0.318773i	−0.0202011	−	0.0173390i
$339$	−4.79898	−	6.60523i	−0.260645	−	0.358747i
$340$	0.167699	+	0.0864821i	0.00909474	+	0.00469015i
$341$	8.22863	+	9.07647i	0.445605	+	0.491518i
$342$	23.5394	−	14.3459i	1.27286	−	0.775738i
$343$	−14.9502	+	10.8619i	−0.807232	+	0.586489i
$344$	4.96720	−	2.01493i	0.267814	−	0.108638i
$345$	1.63877	−	5.04362i	0.0882284	−	0.271539i
$346$	−1.35365	+	16.6784i	−0.0727729	+	0.896638i
$347$	2.02180	+	1.46893i	0.108536	+	0.0788561i	0.640729	−	0.767767i	$-0.278632\pi$
$347$	2.02180	+	1.46893i	0.108536	+	0.0788561i	−0.532193	+	0.846623i	$0.678632\pi$
$348$	4.10296	+	4.14328i	0.219942	+	0.222103i
$349$	−6.66811	+	2.16660i	−0.356936	+	0.115975i	−0.481995	−	0.876174i	$-0.660088\pi$
$349$	−6.66811	+	2.16660i	−0.356936	+	0.115975i	0.125060	+	0.992149i	$0.460088\pi$
$350$	2.82054	−	6.76257i	0.150764	−	0.361475i
$351$	−14.3631			−0.766646
$352$	17.9414	+	5.48701i	0.956278	+	0.292459i
$353$	17.9431			0.955017			0.477509	−	0.878627i	$-0.341540\pi$
$353$	17.9431			0.955017			0.477509	+	0.878627i	$0.341540\pi$
$354$	−1.96027	+	4.69999i	−0.104187	+	0.249802i
$355$	8.94560	−	2.90660i	0.474783	−	0.154266i
$356$	7.59526	+	7.66989i	0.402548	+	0.406504i
$357$	0.0682688	+	0.0496002i	0.00361317	+	0.00262512i
$358$	−0.106816	+	1.31609i	−0.00564542	+	0.0695575i
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	−0.840575	−	0.541696i	$-0.817783\pi$
$359$	2.99112	−	9.20572i	0.157865	−	0.485859i	0.998440	+	0.0558363i	$0.0177825\pi$
$360$	8.66370	−	3.51441i	0.456617	−	0.185225i
$361$	−35.7804	+	25.9960i	−1.88318	+	1.36821i
$362$	−22.7509	+	13.8654i	−1.19576	+	0.728748i
$363$	−7.02797	+	4.12168i	−0.368873	+	0.216332i
$364$	−10.2965	−	5.30988i	−0.539681	−	0.278313i
$365$	−8.02262	−	11.0422i	−0.419923	−	0.577975i
$366$	1.06987	+	0.918291i	0.0559232	+	0.0479998i
$367$	29.4325	+	9.56319i	1.53636	+	0.499194i	0.950370	−	0.311122i	$-0.100705\pi$
$367$	29.4325	+	9.56319i	1.53636	+	0.499194i	0.585992	+	0.810317i	$0.300705\pi$
$368$	−21.2385	−	0.207688i	−1.10713	−	0.0108265i
$369$	−8.33739	+	11.4754i	−0.434027	+	0.597387i
$370$	3.03094	+	12.7621i	0.157571	+	0.663473i
$371$	1.95624	+	6.02070i	0.101563	+	0.312579i
$372$	0.829566	+	5.40869i	0.0430110	+	0.280428i
$373$		−	4.92658i		−	0.255088i	−0.991833	−	0.127544i	$-0.959291\pi$
$373$		−	4.92658i		−	0.255088i	0.991833	−	0.127544i	$-0.0407095\pi$
$374$	0.200026	+	0.260161i	0.0103431	+	0.0134526i
$375$			8.17145i			0.421972i
$376$	21.2204	−	17.8565i	1.09436	−	0.920877i
$377$	−4.32696	−	13.3170i	−0.222850	−	0.685861i
$378$	9.04667	−	2.14854i	0.465311	−	0.110509i
$379$	2.36592	−	3.25642i	0.121529	−	0.167271i	−0.743918	−	0.668271i	$-0.767035\pi$
$379$	2.36592	−	3.25642i	0.121529	−	0.167271i	0.865447	+	0.501000i	$0.167035\pi$
$380$	−19.1541	+	9.64181i	−0.982582	+	0.494614i
$381$	7.25018	+	2.35573i	0.371438	+	0.120688i
$382$	−18.8307	+	21.9391i	−0.963464	+	1.12250i
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	0.950171	−	0.311729i	$-0.100908\pi$
$383$	7.04690	+	9.69922i	0.360080	+	0.495607i	−0.590091	+	0.807337i	$0.700908\pi$
$384$	5.33240	+	6.46423i	0.272118	+	0.329877i
$385$	−5.39523	+	4.89125i	−0.274966	+	0.249281i
$386$	−12.7625	−	20.9412i	−0.649594	−	1.06588i
$387$	3.75853	−	2.73073i	0.191057	−	0.138811i
$388$	14.4607	+	2.36288i	0.734131	+	0.119957i
$389$	4.24498	−	13.0647i	0.215229	−	0.662407i	−0.783908	−	0.620877i	$-0.786777\pi$
$389$	4.24498	−	13.0647i	0.215229	−	0.662407i	0.999137	−	0.0415304i	$-0.0132233\pi$
$390$	5.00787	+	0.406449i	0.253583	+	0.0205813i
$391$	−0.300556	−	0.218367i	−0.0151998	−	0.0110433i
$392$	−11.9380	−	2.95882i	−0.602958	−	0.149443i
$393$	1.31564	−	0.427478i	0.0663654	−	0.0215634i
$394$	4.55701	+	1.90064i	0.229579	+	0.0957529i
$395$	−8.09663			−0.407386
$396$	16.2372	+	0.875116i	0.815949	+	0.0439763i
$397$	−12.1547			−0.610027			−0.305014	−	0.952348i	$-0.598661\pi$
$397$	−12.1547			−0.610027			−0.305014	+	0.952348i	$0.598661\pi$
$398$	−14.7048	−	6.13308i	−0.737084	−	0.307424i
$399$	−9.12092	+	2.96357i	−0.456617	+	0.148364i
$400$	12.1421	−	3.81435i	0.607104	−	0.190717i
$401$	23.2839	+	16.9167i	1.16274	+	0.844782i	0.990122	−	0.140207i	$-0.0447768\pi$
$401$	23.2839	+	16.9167i	1.16274	+	0.844782i	0.172620	+	0.984989i	$0.444777\pi$
$402$	5.12941	+	0.416313i	0.255832	+	0.0207638i
$403$	4.06049	−	12.4969i	0.202267	−	0.622515i
$404$	−3.08741	+	18.8948i	−0.153604	+	0.940049i
$405$	4.76016	−	3.45846i	0.236534	−	0.171852i
$406$	4.71741	+	7.74052i	0.234121	+	0.384156i
$407$	−4.66723	+	22.3312i	−0.231346	+	1.10692i
$408$	0.0104281	+	0.146203i	0.000516269	+	0.00723811i
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	0.990136	−	0.140108i	$-0.0447449\pi$
$409$	11.1416	+	15.3351i	0.550917	+	0.758272i	−0.439219	+	0.898380i	$0.644745\pi$
$410$	7.18654	−	8.37282i	0.354918	−	0.413504i
$411$	−0.883682	−	0.287126i	−0.0435888	−	0.0141629i
$412$	−9.28167	−	18.4386i	−0.457275	−	0.908405i
$413$	−4.65320	+	6.40457i	−0.228969	+	0.315149i
$414$	−17.9101	+	4.25356i	−0.880235	+	0.209051i
$415$	−1.50503	−	4.63200i	−0.0738790	−	0.227376i
$416$	−4.45805	−	19.6227i	−0.218574	−	0.962083i
$417$		−	4.65970i		−	0.228186i
$418$	−37.2823	+	1.01212i	−1.82354	+	0.0495042i
$419$			15.3705i			0.750898i	0.926843	+	0.375449i	$0.122512\pi$
$419$			15.3705i			0.750898i	−0.926843	+	0.375449i	$0.877488\pi$
$420$	−3.21503	+	0.493110i	−0.156877	+	0.0240613i
$421$	5.97047	+	18.3752i	0.290983	+	0.895553i	0.984541	+	0.175153i	$0.0560419\pi$
$421$	5.97047	+	18.3752i	0.290983	+	0.895553i	−0.693558	+	0.720400i	$0.743958\pi$
$422$	−0.896339	−	3.77414i	−0.0436331	−	0.183722i
$423$	14.1285	−	19.4462i	0.686952	−	0.945508i
$424$	−5.81397	+	9.33320i	−0.282351	+	0.453260i
$425$	0.211719	+	0.0687918i	0.0102699	+	0.00333689i
$426$	5.54446	+	4.75891i	0.268630	+	0.230570i
$427$	1.28832	+	1.77322i	0.0623463	+	0.0858123i
$428$	10.1542	−	19.6902i	0.490824	−	0.951763i
$429$	7.58260	+	4.34345i	0.366091	+	0.209704i
$430$	−3.08602	+	1.88075i	−0.148821	+	0.0906980i
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.973384	−	0.229179i	$-0.926396\pi$
$431$	−21.9276	+	15.9313i	−1.05621	+	0.767385i	−0.0828305	+	0.996564i	$0.526396\pi$
$432$	12.9729	+	9.62056i	0.624158	+	0.462869i
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	−0.913487	−	0.406868i	$-0.866621\pi$
$433$	1.34612	−	4.14294i	0.0646905	−	0.199097i	0.978177	+	0.207771i	$0.0666209\pi$
$434$	−0.688142	+	8.47863i	−0.0330319	+	0.406987i
$435$	−3.18051	−	2.31078i	−0.152494	−	0.110793i
$436$	12.7322	−	12.6083i	0.609762	−	0.603829i
$437$	40.1552	−	13.0472i	1.92088	−	0.624133i
$438$	4.08142	−	9.78569i	0.195018	−	0.467578i
$439$	−24.0996			−1.15021			−0.575105	−	0.818080i	$-0.695039\pi$
$439$	−24.0996			−1.15021			−0.575105	+	0.818080i	$0.695039\pi$
$440$	−12.5344	−	1.70031i	−0.597556	−	0.0810592i
$441$	−10.6597			−0.507605
$442$	0.135489	−	0.324852i	0.00644458	−	0.0154516i
$443$	−21.9169	+	7.12124i	−1.04130	+	0.338340i	−0.779250	−	0.626713i	$-0.784400\pi$
$443$	−21.9169	+	7.12124i	−1.04130	+	0.338340i	−0.262054	+	0.965053i	$0.584400\pi$
$444$	−7.24030	+	7.16985i	−0.343609	+	0.340266i
$445$	−5.88765	−	4.27763i	−0.279102	−	0.202779i
$446$	2.71433	−	33.4434i	0.128527	−	1.58359i
$447$	3.92662	−	12.0849i	0.185723	−	0.571595i
$448$	5.74323	+	11.6926i	0.271342	+	0.552423i
$449$	3.05281	−	2.21800i	0.144071	−	0.104674i	−0.513415	−	0.858140i	$-0.671620\pi$
$449$	3.05281	−	2.21800i	0.144071	−	0.104674i	0.657486	+	0.753467i	$0.271620\pi$
$450$	9.41920	−	5.74046i	0.444025	−	0.270608i
$451$	17.5050	−	7.86527i	0.824278	−	0.370361i
$452$	10.1047	−	19.5941i	0.475283	−	0.921628i
$453$	−5.29321	−	7.28548i	−0.248697	−	0.342302i
$454$	0.859403	+	0.737640i	0.0403338	+	0.0346192i
$455$	7.42839	+	2.41363i	0.348248	+	0.113153i
$456$	−14.1391	−	8.80774i	−0.662125	−	0.412460i
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.0270646	−	0.999634i	$-0.491384\pi$
$457$	20.7236	−	28.5236i	0.969409	−	1.33428i	0.942345	−	0.334644i	$-0.108616\pi$
$458$	−7.70837	−	32.4570i	−0.360188	−	1.51662i
$459$	0.0872976	+	0.268674i	0.00407470	+	0.0125406i
$460$	14.1543	−	2.17094i	0.659948	−	0.101220i
$461$			38.5074i			1.79347i	0.442571	+	0.896734i	$0.354067\pi$
$461$			38.5074i			1.79347i	−0.442571	+	0.896734i	$0.645933\pi$
$462$	−5.42566	−	1.60149i	−0.252425	−	0.0745078i
$463$			10.7672i			0.500394i	0.968195	+	0.250197i	$0.0804954\pi$
$463$			10.7672i			0.500394i	−0.968195	+	0.250197i	$0.919505\pi$
$464$	−5.01172	+	14.9263i	−0.232663	+	0.692935i
$465$	−1.14003	−	3.50866i	−0.0528677	−	0.162710i
$466$	24.0673	−	5.71586i	1.11490	−	0.264782i
$467$	12.1553	−	16.7304i	0.562481	−	0.774189i	−0.429158	−	0.903229i	$-0.641190\pi$
$467$	12.1553	−	16.7304i	0.562481	−	0.774189i	0.991639	+	0.129040i	$0.0411897\pi$
$468$	−7.84171	−	15.5780i	−0.362483	−	0.720095i
$469$	7.60867	+	2.47221i	0.351336	+	0.114156i
$470$	−12.1783	+	14.1886i	−0.561742	+	0.654469i
$471$	2.30815	+	3.17690i	0.106354	+	0.146384i
$472$	−13.7159	+	0.978304i	−0.631323	+	0.0450301i
$473$	−6.24883	+	0.678301i	−0.287321	+	0.0311883i
$474$	−3.27320	−	5.37080i	−0.150343	−	0.246689i
$475$	−20.4682	+	14.8710i	−0.939144	+	0.682328i
$476$	−0.0367450	+	0.224877i	−0.00168420	+	0.0103072i
$477$	−2.94499	+	9.06375i	−0.134842	+	0.415001i
$478$	9.42299	+	0.764788i	0.430997	+	0.0349806i
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	0.778406	−	0.627761i	$-0.216028\pi$
$479$	9.23398	+	6.70888i	0.421911	+	0.306536i	−0.356495	+	0.934297i	$0.616028\pi$
$480$	−4.25091	−	3.72143i	−0.194026	−	0.169859i
$481$	23.2712	−	7.56128i	1.06108	−	0.344765i
$482$	−5.59496	−	2.33355i	−0.254843	−	0.106290i
$483$	6.40421			0.291401
$484$	−18.4737	−	11.9466i	−0.839716	−	0.543026i
$485$	−9.87880			−0.448573
$486$	20.0290	+	8.35372i	0.908535	+	0.378932i
$487$	−3.80894	+	1.23760i	−0.172600	+	0.0560810i	−0.394042	−	0.919092i	$-0.628924\pi$
$487$	−3.80894	+	1.23760i	−0.172600	+	0.0560810i	0.221442	+	0.975173i	$0.428924\pi$
$488$	−0.915883	+	3.69532i	−0.0414601	+	0.167279i
$489$	6.02668	+	4.37864i	0.272536	+	0.198009i
$490$	8.26501	+	0.670804i	0.373375	+	0.0303039i
$491$	3.45914	−	10.6461i	0.156109	−	0.480454i	−0.842163	−	0.539223i	$-0.818718\pi$
$491$	3.45914	−	10.6461i	0.156109	−	0.480454i	0.998272	+	0.0587698i	$0.0187178\pi$
$492$	8.45928	+	1.38225i	0.381374	+	0.0623166i
$493$	−0.222807	+	0.161879i	−0.0100347	+	0.00729066i
$494$	20.8174	+	34.1581i	0.936619	+	1.53684i
$495$	−10.8991	+	1.18308i	−0.489877	+	0.0531755i
$496$	−12.0380	+	8.56754i	−0.540523	+	0.384694i
$497$	6.67654	+	9.18946i	0.299484	+	0.412204i
$498$	2.46415	−	2.87091i	0.110421	−	0.128648i
$499$	37.4389	+	12.1646i	1.67599	+	0.544564i	0.984128	−	0.177462i	$-0.0567886\pi$
$499$	37.4389	+	12.1646i	1.67599	+	0.544564i	0.691867	+	0.722025i	$0.256789\pi$
$500$	−19.7087	+	9.92099i	−0.881398	+	0.443680i
$501$	−9.53767	+	13.1275i	−0.426112	+	0.586492i
$502$	6.73892	−	1.60046i	0.300773	−	0.0714319i
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	−0.991360	−	0.131168i	$-0.958127\pi$
$503$	−5.97544	−	18.3905i	−0.266432	−	0.819993i	0.724928	−	0.688824i	$-0.241873\pi$
$504$	7.26941	+	8.63888i	0.323805	+	0.384807i
$505$		−	12.9079i		−	0.574395i
$506$	23.8867	+	7.05061i	1.06189	+	0.313438i
$507$			0.256336i			0.0113843i
$508$	3.12071	+	20.3468i	0.138459	+	0.902742i
$509$	−13.2867	−	40.8921i	−0.588920	−	1.81251i	−0.582921	−	0.812529i	$-0.698090\pi$
$509$	−13.2867	−	40.8921i	−0.588920	−	1.81251i	−0.00599915	−	0.999982i	$-0.501910\pi$
$510$	−0.0228344	−	0.0961469i	−0.00101112	−	0.00425746i
$511$	9.68826	−	13.3347i	0.428583	−	0.589895i
$512$	−9.11695	+	20.7094i	−0.402916	+	0.915237i
$513$	−30.5347	−	9.92132i	−1.34814	−	0.438037i
$514$	13.2899	+	11.4070i	0.586194	+	0.503140i
$515$	8.18058	+	11.2596i	0.360479	+	0.496157i
$516$	−2.49515	−	1.28675i	−0.109843	−	0.0566458i
$517$	−29.6639	+	13.3285i	−1.30462	+	0.586185i
$518$	−13.5264	+	8.24359i	−0.594317	+	0.362202i
$519$	7.09009	−	5.15125i	0.311220	−	0.226115i
$520$	5.09977	+	12.5719i	0.223640	+	0.551315i
$521$	−4.55221	+	14.0103i	−0.199436	+	0.613801i	0.800460	+	0.599386i	$0.204589\pi$
$521$	−4.55221	+	14.0103i	−0.199436	+	0.613801i	−0.999896	+	0.0144150i	$0.995411\pi$
$522$	−1.10394	+	13.6016i	−0.0483180	+	0.595328i
$523$	−32.7270	−	23.7776i	−1.43105	−	1.03972i	−0.989819	−	0.142329i	$-0.954541\pi$
$523$	−32.7270	−	23.7776i	−1.43105	−	1.03972i	−0.441234	−	0.897392i	$-0.645459\pi$
$524$	2.62836	+	2.65419i	0.114820	+	0.115949i
$525$	−3.64970	+	1.18586i	−0.159286	+	0.0517552i
$526$	9.22676	−	22.1223i	0.402306	−	0.964576i
$527$	−0.258445			−0.0112580
$528$	−3.93937	−	9.00194i	−0.171439	−	0.391759i
$529$	−5.19479			−0.225860
$530$	2.85378	−	6.84227i	0.123960	−	0.297209i
$531$	−11.3344	+	3.68278i	−0.491873	+	0.159819i
$532$	−18.2215	−	18.4006i	−0.790004	−	0.797767i
$533$	−16.6520	−	12.0984i	−0.721280	−	0.524040i
$534$	0.457332	−	5.63480i	0.0197907	−	0.243842i
$535$	−4.61566	+	14.2055i	−0.199552	+	0.614159i
$536$	5.22353	+	12.8770i	0.225622	+	0.556203i
$537$	0.559477	−	0.406484i	0.0241432	−	0.0175411i
$538$	−4.77584	+	2.91060i	−0.205901	+	0.125485i
$539$	12.5144	+	7.16845i	0.539031	+	0.308767i
$540$	−9.67791	−	4.99089i	−0.416471	−	0.214774i
$541$	−9.83661	−	13.5389i	−0.422909	−	0.582084i	0.543399	−	0.839475i	$-0.317137\pi$
$541$	−9.83661	−	13.5389i	−0.422909	−	0.582084i	−0.966307	+	0.257391i	$0.917137\pi$
$542$	25.4733	+	21.8642i	1.09417	+	0.939148i
$543$	13.2710	+	4.31200i	0.569512	+	0.185046i
$544$	−0.339964	+	0.202657i	−0.0145759	+	0.00868884i
$545$	−7.10097	+	9.77365i	−0.304172	+	0.418657i
$546$	1.40200	+	5.90328i	0.0600000	+	0.252637i
$547$	−2.87078	−	8.83536i	−0.122746	−	0.377773i	0.870738	−	0.491747i	$-0.163642\pi$
$547$	−2.87078	−	8.83536i	−0.122746	−	0.377773i	−0.993484	+	0.113975i	$0.963642\pi$
$548$	−0.380366	−	2.47995i	−0.0162484	−	0.105938i
$549$			3.29964i			0.140825i
$550$	−14.9184	+	0.404995i	−0.636122	+	0.0172690i
$551$		−	31.2996i		−	1.33341i
$552$	7.16217	+	8.51144i	0.304842	+	0.362271i
$553$	−3.02146	−	9.29909i	−0.128485	−	0.395437i
$554$	−20.6544	+	4.90530i	−0.877520	+	0.208406i
$555$	4.03804	−	5.55788i	0.171405	−	0.235919i
$556$	11.2387	−	5.65736i	0.476627	−	0.239925i
$557$	12.6129	+	4.09818i	0.534425	+	0.173645i	0.563782	−	0.825924i	$-0.309346\pi$
$557$	12.6129	+	4.09818i	0.534425	+	0.173645i	−0.0293567	+	0.999569i	$0.509346\pi$
$558$	−8.34059	+	9.71738i	−0.353086	+	0.411369i
$559$	3.96257	+	5.45401i	0.167599	+	0.230680i
$560$	−5.09271	−	7.15563i	−0.215206	−	0.302380i
$561$	0.0351618	−	0.168238i	0.00148453	−	0.00710302i
$562$	−4.22549	−	6.93336i	−0.178241	−	0.292466i
$563$	−19.0155	+	13.8156i	−0.801408	+	0.582257i	−0.911327	−	0.411684i	$-0.864941\pi$
$563$	−19.0155	+	13.8156i	−0.801408	+	0.582257i	0.109919	+	0.993941i	$0.464941\pi$
$564$	−14.3351	−	2.34235i	−0.603615	−	0.0986309i
$565$	−4.59312	+	14.1362i	−0.193234	+	0.594713i
$566$	−15.7799	−	1.28073i	−0.663279	−	0.0538330i
$567$	5.74846	+	4.17650i	0.241413	+	0.175396i
$568$	−4.74643	+	19.1505i	−0.199156	+	0.803535i
$569$	−12.2494	+	3.98008i	−0.513523	+	0.166854i	−0.554304	−	0.832315i	$-0.687015\pi$
$569$	−12.2494	+	3.98008i	−0.513523	+	0.166854i	0.0407811	+	0.999168i	$0.487015\pi$
$570$	10.3655	+	4.32326i	0.434164	+	0.181081i
$571$	−20.4261			−0.854806			−0.427403	−	0.904061i	$-0.640571\pi$
$571$	−20.4261			−0.854806			−0.427403	+	0.904061i	$0.640571\pi$
$572$	−1.26988	+	23.5618i	−0.0530965	+	0.985169i
$573$	15.1424			0.632585
$574$	12.2981	+	5.12931i	0.513314	+	0.214093i
$575$	16.0680	−	5.22080i	0.670080	−	0.217722i
$576$	−3.35164	+	19.3227i	−0.139652	+	0.805111i
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	0.466518	−	0.884512i	$-0.345508\pi$
$577$	−5.53777	−	4.02342i	−0.230540	−	0.167497i	−0.697058	+	0.717014i	$0.745508\pi$
$578$	23.9559	+	1.94431i	0.996436	+	0.0808727i
$579$	−3.96902	+	12.2154i	−0.164947	+	0.507654i
$580$	1.71188	−	10.4766i	0.0710818	−	0.435016i
$581$	4.75828	−	3.45709i	0.197407	−	0.143424i
$582$	−3.99367	−	6.55298i	−0.165543	−	0.271630i
$583$	9.55259	−	8.66028i	0.395628	−	0.358672i
$584$	28.5573	−	2.03689i	1.18171	−	0.0842873i
$585$	6.91144	+	9.51278i	0.285753	+	0.393305i
$586$	4.88442	−	5.69069i	0.201773	−	0.235080i
$587$	0.607533	+	0.197399i	0.0250756	+	0.00814754i	0.321528	−	0.946900i	$-0.395804\pi$
$587$	0.607533	+	0.197399i	0.0250756	+	0.00814754i	−0.296452	+	0.955048i	$0.595804\pi$
$588$	2.89630	+	5.75367i	0.119441	+	0.237277i
$589$	17.2645	−	23.7625i	0.711370	−	0.979117i
$590$	9.01993	−	2.14219i	0.371345	−	0.0881924i
$591$	−0.799100	−	2.45938i	−0.0328706	−	0.101165i
$592$	−26.0834	−	8.75790i	−1.07202	−	0.359947i
$593$		−	17.0480i		−	0.700077i	−0.936735	−	0.350039i	$-0.886168\pi$
$593$		−	17.0480i		−	0.700077i	0.936735	−	0.350039i	$-0.113832\pi$
$594$	−11.5435	−	15.0139i	−0.473636	−	0.616028i
$595$		−	0.153624i		−	0.00629799i
$596$	33.9148	−	5.20173i	1.38920	−	0.213071i
$597$	2.57858	+	7.93604i	0.105534	+	0.324801i
$598$	−6.17236	−	25.9894i	−0.252406	−	1.06279i
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	−0.784519	−	0.620104i	$-0.787090\pi$
$599$	1.16656	−	1.60564i	0.0476645	−	0.0656045i	0.832184	+	0.554500i	$0.187090\pi$
$600$	−5.65771	−	3.52439i	−0.230975	−	0.143882i
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.610410	−	0.792086i	$-0.291005\pi$
$601$	15.6571	+	5.08729i	0.638665	+	0.207515i	0.0282553	+	0.999601i	$0.491005\pi$
$602$	−3.31169	−	2.84248i	−0.134975	−	0.115851i
$603$	7.07917	+	9.74365i	0.288286	+	0.396792i
$604$	11.1453	−	21.6120i	0.453496	−	0.879380i
$605$	13.5910	+	5.94052i	0.552552	+	0.241516i
$606$	8.56231	−	5.21824i	0.347820	−	0.211976i
$607$	23.2353	−	16.8814i	0.943091	−	0.685196i	−0.00607141	−	0.999982i	$-0.501933\pi$
$607$	23.2353	−	16.8814i	0.943091	−	0.685196i	0.949163	+	0.314786i	$0.101933\pi$
$608$	4.07698	−	44.7956i	0.165343	−	1.81670i
$609$	1.46707	−	4.51518i	0.0594487	−	0.182964i
$610$	0.207643	−	2.55838i	0.00840723	−	0.103586i
$611$	28.2185	+	20.5019i	1.14160	+	0.829419i
$612$	−0.243740	+	0.241368i	−0.00985259	+	0.00975671i
$613$	6.32812	−	2.05613i	0.255590	−	0.0830464i	−0.178419	−	0.983955i	$-0.557098\pi$
$613$	6.32812	−	2.05613i	0.255590	−	0.0830464i	0.434010	+	0.900908i	$0.357098\pi$
$614$	1.23584	−	2.96307i	0.0498745	−	0.119580i
$615$	−5.77894			−0.233029
$616$	−2.72470	−	15.0305i	−0.109781	−	0.605596i
$617$	−17.8948			−0.720416			−0.360208	−	0.932872i	$-0.617294\pi$
$617$	−17.8948			−0.720416			−0.360208	+	0.932872i	$0.617294\pi$
$618$	−4.16178	+	9.97836i	−0.167411	+	0.401388i
$619$	−22.1005	+	7.18088i	−0.888293	+	0.288624i	−0.717397	−	0.696665i	$-0.754666\pi$
$619$	−22.1005	+	7.18088i	−0.888293	+	0.288624i	−0.170897	+	0.985289i	$0.554666\pi$
$620$	7.07839	−	7.00951i	0.284275	−	0.281509i
$621$	17.3452	+	12.6020i	0.696037	+	0.505700i
$622$	−2.30714	+	28.4263i	−0.0925077	+	1.13979i
$623$	2.71579	−	8.35835i	0.108806	−	0.334870i
$624$	−6.27776	+	8.46527i	−0.251312	+	0.338882i
$625$	−0.835407	+	0.606959i	−0.0334163	+	0.0242784i
$626$	−1.86201	+	1.13479i	−0.0744208	+	0.0453552i
$627$	13.1197	+	14.4715i	0.523950	+	0.577935i
$628$	−4.86001	+	9.42411i	−0.193935	+	0.376063i
$629$	−0.282881	−	0.389352i	−0.0112792	−	0.0155245i
$630$	−5.77619	−	4.95781i	−0.230129	−	0.197524i
$631$	−44.0545	−	14.3142i	−1.75378	−	0.569838i	−0.757255	−	0.653119i	$-0.773460\pi$
$631$	−44.0545	−	14.3142i	−1.75378	−	0.569838i	−0.996526	+	0.0832806i	$0.973460\pi$
$632$	8.97979	−	14.4153i	0.357197	−	0.573410i
$633$	−1.19417	+	1.64363i	−0.0474639	+	0.0653284i
$634$	−5.51022	−	23.2014i	−0.218839	−	0.921446i
$635$	−4.28864	−	13.1991i	−0.170190	−	0.523790i
$636$	5.69241	−	0.873082i	0.225719	−	0.0346199i
$637$		−	15.4683i		−	0.612877i
$638$	10.4429	−	15.2258i	0.413437	−	0.602794i
$639$			17.0999i			0.676462i
$640$	3.81465	−	14.7709i	0.150787	−	0.583873i
$641$	8.39773	+	25.8456i	0.331691	+	1.02084i	0.968329	+	0.249676i	$0.0803242\pi$
$641$	8.39773	+	25.8456i	0.331691	+	1.02084i	−0.636639	+	0.771162i	$0.719676\pi$
$642$	−11.2890	+	2.68108i	−0.445542	+	0.105814i
$643$	−18.2352	+	25.0987i	−0.719128	+	0.989794i	0.280425	+	0.959876i	$0.409525\pi$
$643$	−18.2352	+	25.0987i	−0.719128	+	0.989794i	−0.999552	+	0.0299182i	$0.990475\pi$
$644$	7.77537	+	15.4463i	0.306393	+	0.608668i
$645$	1.80013	+	0.584897i	0.0708800	+	0.0230303i
$646$	0.512430	−	0.597017i	0.0201613	−	0.0234893i
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.939738	−	0.341895i	$-0.888931\pi$
$647$	−24.7877	−	34.1173i	−0.974505	−	1.34129i	−0.0347664	−	0.999395i	$-0.511069\pi$
$648$	0.878082	+	12.3107i	0.0344943	+	0.483611i
$649$	15.7831	+	3.29867i	0.619541	+	0.129484i
$650$	8.33001	+	13.6682i	0.326730	+	0.536112i
$651$	3.60431	−	2.61868i	0.141264	−	0.102634i
$652$	−3.24380	+	19.8518i	−0.127037	+	0.777458i
$653$	−1.25077	+	3.84947i	−0.0489464	+	0.150641i	−0.972542	−	0.232726i	$-0.925236\pi$
$653$	−1.25077	+	3.84947i	−0.0489464	+	0.150641i	0.923596	+	0.383367i	$0.125236\pi$
$654$	−9.35391	−	0.759181i	−0.365767	−	0.0296863i
$655$	−2.03744	−	1.48028i	−0.0796093	−	0.0578395i
$656$	6.93661	+	22.0811i	0.270829	+	0.862121i
$657$	23.5991	−	7.66780i	0.920687	−	0.299149i
$658$	−20.8404	−	8.69211i	−0.812442	−	0.338854i
$659$	6.46292			0.251760			0.125880	−	0.992045i	$-0.459825\pi$
$659$	6.46292			0.251760			0.125880	+	0.992045i	$0.459825\pi$
$660$	3.59992	+	5.56143i	0.140127	+	0.216479i
$661$	26.6232			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$661$	26.6232			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$662$	−44.3435	−	18.4948i	−1.72346	−	0.718821i
$663$	−0.175320	+	0.0569648i	−0.00680885	+	0.00221233i
$664$	9.91605	+	2.45769i	0.384817	+	0.0953767i
$665$	14.1249	+	10.2623i	0.547740	+	0.397956i
$666$	−23.7686	−	1.92911i	−0.921015	−	0.0747514i
$667$	−6.45884	+	19.8783i	−0.250087	+	0.769690i
$668$	−43.2418	−	7.06572i	−1.67308	−	0.273381i
$669$	−14.2169	+	10.3292i	−0.549659	+	0.399350i
$670$	−4.87569	−	8.00023i	−0.188364	−	0.309076i
$671$	2.21895	−	3.87374i	0.0856616	−	0.149544i
$672$	2.68778	−	6.27096i	0.103683	−	0.241908i
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	0.704294	−	0.709909i	$-0.251264\pi$
$673$	−4.89033	−	6.73096i	−0.188508	−	0.259460i	−0.892802	+	0.450449i	$0.851264\pi$
$674$	−15.7466	+	18.3459i	−0.606536	+	0.706657i
$675$	−12.2183	−	3.96998i	−0.470284	−	0.152805i
$676$	−0.618256	+	0.311219i	−0.0237791	+	0.0119700i
$677$	−8.97132	+	12.3480i	−0.344796	+	0.474571i	−0.945834	−	0.324649i	$-0.894754\pi$
$677$	−8.97132	+	12.3480i	−0.344796	+	0.474571i	0.601039	+	0.799220i	$0.294754\pi$
$678$	−11.2339	+	2.66799i	−0.431435	+	0.102464i
$679$	−3.68652	−	11.3459i	−0.141476	−	0.435417i
$680$	0.204173	−	0.171806i	0.00782967	−	0.00658848i
$681$		−	0.593162i		−	0.0227300i
$682$	16.3265	−	5.79918i	0.625174	−	0.222062i
$683$			32.9156i			1.25948i	0.776806	+	0.629740i	$0.216839\pi$
$683$			32.9156i			1.25948i	−0.776806	+	0.629740i	$0.783161\pi$
$684$	−5.91023	−	38.5342i	−0.225983	−	1.47339i
$685$	0.522718	+	1.60876i	0.0199720	+	0.0614676i
$686$	6.03868	+	25.4266i	0.230558	+	0.970792i
$687$	−10.2696	+	14.1349i	−0.391811	+	0.539282i
$688$	0.0741263	−	7.58027i	0.00282604	−	0.288995i
$689$	−13.1524	−	4.27349i	−0.501068	−	0.162807i
$690$	−5.69098	−	4.88467i	−0.216652	−	0.185956i
$691$	26.7545	+	36.8244i	1.01779	+	1.40087i	0.913742	+	0.406294i	$0.133179\pi$
$691$	26.7545	+	36.8244i	1.01779	+	1.40087i	0.104047	+	0.994572i	$0.466821\pi$
$692$	21.0324	+	10.8464i	0.799531	+	0.412318i
$693$	−5.42604	−	12.0762i	−0.206118	−	0.458739i
$694$	3.01794	−	1.83926i	0.114559	−	0.0698175i
$695$	−6.86294	+	4.98622i	−0.260326	+	0.189138i
$696$	7.64156	−	3.09978i	0.289652	−	0.117497i
$697$	−0.125102	+	0.385024i	−0.00473857	+	0.0145838i
$698$	−0.802118	+	9.88293i	−0.0303606	+	0.374074i
$699$	−10.4812	−	7.61507i	−0.396437	−	0.288028i
$700$	−7.29129	−	7.36294i	−0.275585	−	0.278293i
$701$	−47.6330	+	15.4769i	−1.79907	+	0.584555i	−0.999864	−	0.0164975i	$-0.994748\pi$
$701$	−47.6330	+	15.4769i	−1.79907	+	0.584555i	−0.799210	+	0.601052i	$0.794748\pi$
$702$	−7.81911	+	18.7473i	−0.295113	+	0.707569i
$703$	54.6955			2.06288
$704$	16.9289	−	20.4307i	0.638033	−	0.770009i
$705$	9.79298			0.368825
$706$	9.76804	−	23.4200i	0.367625	−	0.881425i
$707$	14.8249	−	4.81691i	0.557548	−	0.181158i
$708$	5.06744	+	5.11724i	0.190446	+	0.192318i
$709$	6.87556	+	4.99539i	0.258217	+	0.187606i	0.709361	−	0.704846i	$-0.248984\pi$
$709$	6.87556	+	4.99539i	0.258217	+	0.187606i	−0.451144	+	0.892451i	$0.648984\pi$
$710$	1.07608	−	13.2584i	0.0403846	−	0.497580i
$711$	4.54860	−	13.9991i	0.170586	−	0.525009i
$712$	14.1458	−	5.73820i	0.530136	−	0.215048i
$713$	−15.8681	+	11.5289i	−0.594266	+	0.431759i
$714$	0.101905	−	0.0621052i	0.00381369	−	0.00232423i
$715$	−1.71677	−	15.8157i	−0.0642036	−	0.591474i
$716$	1.65966	+	0.855885i	0.0620243	+	0.0319859i
$717$	−2.91036	−	4.00576i	−0.108689	−	0.149598i
$718$	−10.3873	−	8.91561i	−0.387651	−	0.332728i
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	0.176730	−	0.984259i	$-0.443448\pi$
$719$	−6.94019	−	2.25500i	−0.258825	−	0.0840974i	−0.435555	+	0.900162i	$0.643448\pi$
$720$	0.129290	−	13.2214i	0.00481834	−	0.492732i
$721$	−9.87901	+	13.5973i	−0.367914	+	0.506390i
$722$	14.4524	+	60.8537i	0.537864	+	2.26474i
$723$	0.981112	+	3.01955i	0.0364879	+	0.112298i
$724$	5.71226	+	37.2434i	0.212294	+	1.38414i
$725$		−	12.5244i		−	0.465146i
$726$	1.55381	+	11.4170i	0.0576674	+	0.423723i
$727$			1.85004i			0.0686140i	0.999411	+	0.0343070i	$0.0109224\pi$
$727$			1.85004i			0.0686140i	−0.999411	+	0.0343070i	$0.989078\pi$
$728$	−12.5359	+	10.5487i	−0.464612	+	0.390960i
$729$	0.533026	+	1.64049i	0.0197417	+	0.0607587i
$730$	−18.7801	+	4.46017i	−0.695082	+	0.165078i
$731$	0.0779378	−	0.107272i	0.00288264	−	0.00396761i
$732$	1.78101	−	0.896530i	0.0658282	−	0.0331367i
$733$	17.9690	+	5.83849i	0.663701	+	0.215650i	0.621446	−	0.783457i	$-0.286546\pi$
$733$	17.9690	+	5.83849i	0.663701	+	0.215650i	0.0422555	+	0.999107i	$0.486546\pi$
$734$	28.5049	−	33.2102i	1.05214	−	1.22581i
$735$	−2.55271	−	3.51350i	−0.0941580	−	0.129597i
$736$	−11.8331	+	27.6082i	−0.436173	+	1.01765i
$737$	−1.75843	−	16.1995i	−0.0647728	−	0.596717i
$738$	10.4394	+	17.1293i	0.384278	+	0.630540i
$739$	12.7166	−	9.23916i	0.467788	−	0.339868i	−0.328791	−	0.944403i	$-0.606641\pi$
$739$	12.7166	−	9.23916i	0.467788	−	0.339868i	0.796579	+	0.604535i	$0.206641\pi$
$740$	18.3076	+	2.99147i	0.673002	+	0.109969i
$741$	6.47402	−	19.9250i	0.237829	−	0.731963i
$742$	8.92339	+	0.724240i	0.327588	+	0.0265877i
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	0.670608	−	0.741812i	$-0.266033\pi$
$743$	4.69746	+	3.41290i	0.172333	+	0.125207i	−0.498275	+	0.867019i	$0.666033\pi$
$744$	7.51123	+	1.86165i	0.275375	+	0.0682515i
$745$	−22.0008	+	7.14848i	−0.806045	+	0.261900i
$746$	−6.43034	−	2.68197i	−0.235432	−	0.0981940i
$747$	8.85428			0.323961
$748$	0.448463	−	0.119452i	0.0163974	−	0.00436761i
$749$	−18.0377			−0.659083
$750$	10.6657	+	4.44844i	0.389455	+	0.162434i
$751$	2.85643	−	0.928110i	0.104233	−	0.0338672i	−0.256436	−	0.966561i	$-0.582548\pi$
$751$	2.85643	−	0.928110i	0.104233	−	0.0338672i	0.360669	+	0.932694i	$0.382548\pi$
$752$	−11.7548	−	37.4185i	−0.428652	−	1.36451i
$753$	−2.93478	−	2.13224i	−0.106949	−	0.0777033i
$754$	−19.7374	−	1.60192i	−0.718793	−	0.0583387i
$755$	−5.06615	+	15.5920i	−0.184376	+	0.567451i
$756$	2.12056	−	12.9777i	0.0771239	−	0.471994i
$757$	21.1049	−	15.3336i	0.767071	−	0.557310i	−0.134000	−	0.990981i	$-0.542782\pi$
$757$	21.1049	−	15.3336i	0.767071	−	0.557310i	0.901071	+	0.433672i	$0.142782\pi$
$758$	−2.96241	−	4.86085i	−0.107600	−	0.176554i
$759$	−5.34600	−	11.8981i	−0.194047	−	0.431874i
$760$	2.15759	+	30.2495i	0.0782639	+	1.09726i
$761$	−18.7813	−	25.8502i	−0.680820	−	0.937068i	0.319123	−	0.947713i	$-0.396612\pi$
$761$	−18.7813	−	25.8502i	−0.680820	−	0.937068i	−0.999943	+	0.0106450i	$0.996612\pi$
$762$	7.02169	−	8.18077i	0.254369	−	0.296358i
$763$	−13.8751	−	4.50828i	−0.502311	−	0.163211i
$764$	18.3845	+	36.5220i	0.665128	+	1.32132i
$765$	0.135938	−	0.187102i	0.00491484	−	0.00676470i
$766$	16.4960	−	3.91772i	0.596026	−	0.141553i
$767$	−5.34410	−	16.4474i	−0.192964	−	0.593883i
$768$	11.3402	−	3.44099i	0.409206	−	0.124166i
$769$			22.3560i			0.806176i	0.915161	+	0.403088i	$0.132063\pi$
$769$			22.3560i			0.806176i	−0.915161	+	0.403088i	$0.867937\pi$
$770$	3.44714	+	9.70479i	0.124226	+	0.349736i
$771$		−	9.17275i		−	0.330348i
$772$	−34.2810	+	5.25790i	−1.23380	+	0.189236i
$773$	1.56889	+	4.82855i	0.0564291	+	0.173671i	0.975299	−	0.220891i	$-0.0708964\pi$
$773$	1.56889	+	4.82855i	0.0564291	+	0.173671i	−0.918869	+	0.394562i	$0.870896\pi$
$774$	−1.51815	−	6.39234i	−0.0545687	−	0.229768i
$775$	6.90832	−	9.50848i	0.248154	−	0.341555i
$776$	10.9564	−	17.5883i	0.393310	−	0.631383i
$777$	7.89020	+	2.56368i	0.283059	+	0.0919715i
$778$	−14.7416	−	12.6530i	−0.528513	−	0.453632i
$779$	−27.0438	−	37.2225i	−0.968943	−	1.33364i
$780$	3.25674	−	6.31519i	0.116610	−	0.226120i
$781$	11.4994	−	20.0751i	0.411480	−	0.718343i
$782$	−0.448640	+	0.273421i	−0.0160433	+	0.00977750i
$783$	12.8582	−	9.34206i	0.459516	−	0.333858i
$784$	−10.3608	+	13.9711i	−0.370030	+	0.498969i
$785$	2.20914	−	6.79904i	0.0788476	−	0.242668i
$786$	0.158261	−	1.94994i	0.00564497	−	0.0695520i
$787$	2.38155	+	1.73029i	0.0848930	+	0.0616783i	0.629422	−	0.777064i	$-0.283292\pi$
$787$	2.38155	+	1.73029i	0.0848930	+	0.0616783i	−0.544529	+	0.838742i	$0.683292\pi$
$788$	4.96157	−	4.91329i	0.176749	−	0.175029i
$789$	−11.9392	+	3.87928i	−0.425046	+	0.138106i
$790$	−4.40771	+	10.5680i	−0.156819	+	0.375993i
$791$	−17.9496			−0.638215
$792$	9.98157	−	20.7169i	0.354680	−	0.736145i
$793$	−4.78812			−0.170031
$794$	−6.61688	+	15.8648i	−0.234824	+	0.563019i
$795$	−3.69271	+	1.19983i	−0.130967	+	0.0425537i
$796$	−16.0102	+	15.8544i	−0.567468	+	0.561946i
$797$	−6.06111	−	4.40365i	−0.214695	−	0.155985i	0.475240	−	0.879856i	$-0.342361\pi$
$797$	−6.06111	−	4.40365i	−0.214695	−	0.155985i	−0.689936	+	0.723871i	$0.742361\pi$
$798$	−1.09717	+	13.5183i	−0.0388394	+	0.478542i
$799$	0.211997	−	0.652460i	0.00749992	−	0.0230824i
$800$	1.63139	−	17.9248i	0.0576783	−	0.633737i
$801$	10.7037	−	7.77668i	0.378196	−	0.274775i
$802$	34.7558	−	21.1817i	1.22727	−	0.747952i
$803$	−32.8615	−	6.86804i	−1.15966	−	0.242368i
$804$	3.33578	−	6.46845i	0.117644	−	0.228125i
$805$	−6.85298	−	9.43231i	−0.241536	−	0.332445i
$806$	−14.1009	−	12.1031i	−0.496684	−	0.426312i
$807$	2.78583	+	0.905170i	0.0980658	+	0.0318635i
$808$	22.9814	+	14.3159i	0.808482	+	0.503631i
$809$	23.4091	−	32.2199i	0.823022	−	1.13279i	−0.166160	−	0.986099i	$-0.553137\pi$
$809$	23.4091	−	32.2199i	0.823022	−	1.13279i	0.989182	−	0.146694i	$-0.0468631\pi$
$810$	−1.92273	−	8.09588i	−0.0675578	−	0.284460i
$811$	13.1790	+	40.5607i	0.462777	+	1.42428i	0.861757	+	0.507321i	$0.169364\pi$
$811$	13.1790	+	40.5607i	0.462777	+	1.42428i	−0.398981	+	0.916959i	$0.630636\pi$
$812$	12.6713	−	1.94348i	0.444676	−	0.0682028i
$813$		−	17.5818i		−	0.616619i
$814$	26.6068	+	18.2487i	0.932567	+	0.639617i
$815$		−	13.5617i		−	0.475047i
$816$	0.196506	+	0.0659799i	0.00687908	+	0.00230976i
$817$	4.65671	+	14.3319i	0.162918	+	0.501409i
$818$	26.0813	−	6.19417i	0.911911	−	0.216574i
$819$	−8.34638	+	11.4878i	−0.291646	+	0.401416i
$820$	−7.01624	−	13.9382i	−0.245018	−	0.486743i
$821$	−18.3658	−	5.96742i	−0.640972	−	0.208264i	−0.0295426	−	0.999564i	$-0.509405\pi$
$821$	−18.3658	−	5.96742i	−0.640972	−	0.208264i	−0.611429	+	0.791299i	$0.709405\pi$
$822$	−0.855834	+	0.997106i	−0.0298506	+	0.0347781i
$823$	−5.83041	−	8.02487i	−0.203235	−	0.279729i	0.695218	−	0.718799i	$-0.255308\pi$
$823$	−5.83041	−	8.02487i	−0.203235	−	0.279729i	−0.898453	+	0.439070i	$0.855308\pi$
$824$	−29.1196	+	2.07700i	−1.01443	+	0.0723557i
$825$	5.24979	+	5.79071i	0.182774	+	0.201607i
$826$	5.82633	+	9.56010i	0.202724	+	0.332638i
$827$	35.2981	−	25.6455i	1.22743	−	0.891783i	0.230738	−	0.973016i	$-0.425886\pi$
$827$	35.2981	−	25.6455i	1.22743	−	0.891783i	0.996695	+	0.0812332i	$0.0258859\pi$
$828$	−4.19817	+	25.6925i	−0.145896	+	0.892877i
$829$	−8.69871	+	26.7719i	−0.302119	+	0.929826i	0.678618	+	0.734491i	$0.262579\pi$
$829$	−8.69871	+	26.7719i	−0.302119	+	0.929826i	−0.980737	+	0.195335i	$0.937421\pi$
$830$	−6.86518	−	0.557191i	−0.238294	−	0.0193404i
$831$	8.99492	+	6.53519i	0.312030	+	0.226703i
$832$	−28.0392	−	4.86357i	−0.972084	−	0.168614i
$833$	−0.289348	+	0.0940150i	−0.0100253	+	0.00325743i
$834$	−6.08200	−	2.53669i	−0.210603	−	0.0878382i
$835$	29.5406			1.02229
$836$	−18.9750	+	49.2132i	−0.656264	+	1.70207i
$837$	14.9149			0.515533
$838$	20.0621	+	8.36753i	0.693035	+	0.289051i
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.327388	−	0.944890i	$-0.393831\pi$
$839$	33.2421	−	10.8010i	1.14764	−	0.372892i	0.820255	+	0.571998i	$0.193831\pi$
$840$	−1.10660	+	4.46482i	−0.0381814	+	0.154051i
$841$	−10.9262	−	7.93837i	−0.376767	−	0.273737i
$842$	27.2342	+	2.21038i	0.938554	+	0.0761749i
$843$	−1.31409	+	4.04435i	−0.0452596	+	0.139295i
$844$	−5.41410	−	0.884666i	−0.186361	−	0.0304515i
$845$	0.377540	−	0.274299i	0.0129878	−	0.00943617i
$846$	−17.6905	−	29.0273i	−0.608212	−	0.997980i
$847$	−1.75095	+	17.8263i	−0.0601634	+	0.612518i
$848$	9.01697	+	12.6695i	0.309644	+	0.435072i
$849$	4.87374	+	6.70812i	0.167266	+	0.230222i
$850$	0.205047	−	0.238894i	0.00703306	−	0.00819400i
$851$	−34.7369	−	11.2867i	−1.19077	−	0.386903i
$852$	9.22984	−	4.64613i	0.316209	−	0.159174i
$853$	−15.9973	+	22.0183i	−0.547736	+	0.753894i	−0.989703	−	0.143138i	$-0.954281\pi$
$853$	−15.9973	+	22.0183i	−0.547736	+	0.753894i	0.441967	+	0.897031i	$0.354281\pi$
$854$	3.01582	−	0.716242i	0.103199	−	0.0245093i
$855$	8.12215	+	24.9974i	0.277772	+	0.854893i
$856$	−20.1725	−	23.9728i	−0.689483	−	0.819374i
$857$			37.5541i			1.28282i	0.767197	+	0.641412i	$0.221651\pi$
$857$			37.5541i			1.28282i	−0.767197	+	0.641412i	$0.778349\pi$
$858$	9.79711	−	7.53255i	0.334468	−	0.257157i
$859$		−	4.50293i		−	0.153638i	−0.997045	−	0.0768190i	$-0.975524\pi$
$859$		−	4.50293i		−	0.153638i	0.997045	−	0.0768190i	$-0.0244764\pi$
$860$	0.774833	+	5.05184i	0.0264216	+	0.172266i
$861$	−2.15655	−	6.63719i	−0.0734952	−	0.226195i
$862$	8.85701	+	37.2935i	0.301671	+	1.27022i
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	−0.950392	−	0.311054i	$-0.899318\pi$
$863$	−10.6014	+	14.5915i	−0.360875	+	0.496702i	0.589517	+	0.807756i	$0.299318\pi$
$864$	19.6194	−	11.6953i	0.667465	−	0.397884i
$865$	−15.1738	−	4.93028i	−0.515926	−	0.167634i
$866$	−4.67470	−	4.01237i	−0.158853	−	0.136346i
$867$	−7.39896	−	10.1838i	−0.251282	−	0.345860i
$868$	10.6920	+	5.51386i	0.362910	+	0.187152i
$869$	−14.7542	+	13.3760i	−0.500501	+	0.453749i
$870$	−4.74754	+	2.89336i	−0.160957	+	0.0980940i
$871$	−14.1390	+	10.2726i	−0.479083	+	0.348074i
$872$	−9.52555	−	23.4824i	−0.322576	−	0.795213i
$873$	5.54980	−	17.0805i	0.187832	−	0.578089i
$874$	4.83034	−	59.5148i	0.163389	−	2.01312i
$875$	14.5339	+	10.5595i	0.491335	+	0.356976i
$876$	−10.5508	−	10.6544i	−0.356477	−	0.359980i
$877$	−12.9541	+	4.20903i	−0.437428	+	0.142129i	−0.519449	−	0.854502i	$-0.673863\pi$
$877$	−12.9541	+	4.20903i	−0.437428	+	0.142129i	0.0820206	+	0.996631i	$0.473863\pi$
$878$	−13.1195	+	31.4556i	−0.442762	+	1.06158i
$879$	−3.92773			−0.132479
$880$	−9.04292	+	15.4348i	−0.304837	+	0.520306i
$881$	5.44549			0.183463			0.0917317	−	0.995784i	$-0.470760\pi$
$881$	5.44549			0.183463			0.0917317	+	0.995784i	$0.470760\pi$
$882$	−5.80302	+	13.9134i	−0.195398	+	0.468489i
$883$	26.8480	−	8.72345i	0.903508	−	0.293568i	0.179824	−	0.983699i	$-0.442447\pi$
$883$	26.8480	−	8.72345i	0.903508	−	0.293568i	0.723684	+	0.690131i	$0.242447\pi$
$884$	−0.350250	−	0.353691i	−0.0117802	−	0.0118959i
$885$	−3.92816	−	2.85397i	−0.132044	−	0.0959352i
$886$	−2.63642	+	32.4835i	−0.0885723	+	1.09130i
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	0.447171	+	0.894449i	$0.352432\pi$
$887$	−13.1145	+	40.3623i	−0.440342	+	1.35523i	−0.887512	+	0.460784i	$0.847568\pi$
$888$	5.41680	+	13.3535i	0.181776	+	0.448114i
$889$	13.5589	−	9.85113i	0.454751	−	0.330396i
$890$	−8.78849	+	5.35608i	−0.294591	+	0.179536i
$891$	2.96073	−	14.1662i	0.0991883	−	0.474586i
$892$	−42.1738	−	21.7490i	−1.41208	−	0.728211i
$893$	45.8283	+	63.0772i	1.53358	+	2.11080i
$894$	−13.6360	−	11.7040i	−0.456057	−	0.391441i
$895$	−1.19736	−	0.389047i	−0.0400234	−	0.0130044i
$896$	18.3881	−	1.13096i	0.614305	−	0.0377827i
$897$	−8.22325	+	11.3183i	−0.274566	+	0.377908i
$898$	−1.23310	−	5.19210i	−0.0411489	−	0.173263i
$899$	4.49318	+	13.8286i	0.149856	+	0.461209i
$900$	−2.36496	−	15.4193i	−0.0788320	−	0.513977i
$901$			0.272002i			0.00906169i
$902$	−0.736506	−	27.1299i	−0.0245230	−	0.903327i
$903$			2.28574i			0.0760646i
$904$	−20.0740	−	23.8558i	−0.667653	−	0.793430i
$905$	−7.85008	−	24.1601i	−0.260946	−	0.803108i
$906$	−12.3908	+	2.94276i	−0.411658	+	0.0977666i
$907$	−20.3902	+	28.0647i	−0.677046	+	0.931873i	−0.999894	−	0.0145776i	$-0.995360\pi$
$907$	−20.3902	+	28.0647i	−0.677046	+	0.931873i	0.322848	+	0.946451i	$0.395360\pi$
$908$	1.43064	−	0.720161i	0.0474776	−	0.0238994i
$909$	22.3179	+	7.25153i	0.740238	+	0.240518i
$910$	7.19429	−	8.38185i	0.238488	−	0.277856i
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	0.993446	−	0.114300i	$-0.0364627\pi$
$911$	17.4380	+	24.0014i	0.577748	+	0.795202i	−0.415698	+	0.909503i	$0.636463\pi$
$912$	−19.1933	+	13.6600i	−0.635555	+	0.452329i
$913$	−10.3948	−	5.95434i	−0.344018	−	0.197060i
$914$	−25.9483	−	42.5771i	−0.858294	−	1.40833i
$915$	−1.08758	+	0.790174i	−0.0359543	+	0.0261224i
$916$	−46.5604	−	7.60798i	−1.53840	−	0.251375i
$917$	0.939807	−	2.89243i	0.0310352	−	0.0955164i
$918$	0.398207	+	0.0323193i	0.0131428	+	0.00106670i
$919$	−17.4823	−	12.7016i	−0.576687	−	0.418988i	0.260841	−	0.965382i	$-0.416000\pi$
$919$	−17.4823	−	12.7016i	−0.576687	−	0.418988i	−0.837528	+	0.546394i	$0.816000\pi$
$920$	4.87186	−	19.6565i	0.160620	−	0.648057i
$921$	−1.59915	+	0.519594i	−0.0526936	+	0.0171212i
$922$	50.2612	+	20.9630i	1.65527	+	0.690379i
$923$	−24.8137			−0.816754
$924$	−5.04398	+	6.20994i	−0.165935	+	0.204292i
$925$	21.8862			0.719614
$926$	14.0537	+	5.86154i	0.461834	+	0.192622i
$927$	−24.0637	+	7.81877i	−0.790356	+	0.256802i
$928$	16.7540	+	14.6672i	0.549976	+	0.481474i
$929$	−38.2024	−	27.7557i	−1.25338	−	0.910635i	−0.254968	−	0.966949i	$-0.582065\pi$
$929$	−38.2024	−	27.7557i	−1.25338	−	0.910635i	−0.998413	+	0.0563145i	$0.982065\pi$
$930$	−5.20025	−	0.422062i	−0.170523	−	0.0138400i
$931$	10.6848	−	32.8843i	0.350179	−	1.07774i
$932$	5.64142	−	34.5251i	0.184791	−	1.13091i
$933$	12.0842	−	8.77967i	0.395618	−	0.287433i
$934$	−15.2199	−	24.9734i	−0.498009	−	0.817154i
$935$	−0.285412	+	0.128240i	−0.00933397	+	0.00419390i
$936$	−24.6020	+	1.75477i	−0.804140	+	0.0573565i
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	0.973329	+	0.229412i	$0.0736804\pi$
$937$	27.2659	+	37.5283i	0.890738	+	1.22600i	−0.0825914	+	0.996583i	$0.526320\pi$
$938$	7.36889	−	8.58527i	0.240603	−	0.280319i
$939$	1.08614	+	0.352908i	0.0354449	+	0.0115167i
$940$	11.8897	+	23.6196i	0.387799	+	0.770387i
$941$	23.1708	−	31.8919i	0.755347	−	1.03965i	−0.242240	−	0.970216i	$-0.577882\pi$
$941$	23.1708	−	31.8919i	0.755347	−	1.03965i	0.997587	−	0.0694293i	$-0.0221178\pi$
$942$	5.40314	−	1.28322i	0.176044	−	0.0418094i
$943$	9.49432	+	29.2205i	0.309178	+	0.951551i
$944$	−6.18984	+	18.4350i	−0.201462	+	0.600008i
$945$			8.86568i			0.288401i
$946$	−2.51645	+	8.52545i	−0.0818167	+	0.277186i
$947$		−	24.9488i		−	0.810725i	−0.914156	−	0.405363i	$-0.867145\pi$
$947$		−	24.9488i		−	0.810725i	0.914156	−	0.405363i	$-0.132855\pi$
$948$	−8.79205	+	1.34849i	−0.285552	+	0.0437970i
$949$	11.1268	+	34.2447i	0.361190	+	1.11163i
$950$	8.26752	+	34.8114i	0.268234	+	1.12943i
$951$	−7.34110	+	10.1042i	−0.238052	+	0.327650i
$952$	0.273514	+	0.170381i	0.00886464	+	0.00552209i
$953$	38.9090	+	12.6423i	1.26039	+	0.409524i	0.861632	−	0.507534i	$-0.169443\pi$
$953$	38.9090	+	12.6423i	1.26039	+	0.409524i	0.398754	+	0.917058i	$0.369443\pi$
$954$	10.2271	+	8.77811i	0.331115	+	0.284202i
$955$	−16.2035	−	22.3023i	−0.524334	−	0.721684i
$956$	6.12800	−	11.8829i	0.198194	−	0.384320i
$957$	−9.61321	+	1.04350i	−0.310751	+	0.0337316i
$958$	13.7835	−	8.40029i	0.445326	−	0.271401i
$959$	−1.65262	+	1.20070i	−0.0533658	+	0.0387725i
$960$	−7.17149	+	3.52253i	−0.231459	+	0.113689i
$961$	5.36305	−	16.5058i	0.173002	−	0.532445i
$962$	2.79933	−	34.4907i	0.0902542	−	1.11203i
$963$	−21.9685	−	15.9610i	−0.707925	−	0.514337i
$964$	−6.09167	+	6.03239i	−0.196199	+	0.194290i
$965$	22.2383	−	7.22567i	0.715877	−	0.232603i
$966$	3.48638	−	8.35900i	0.112172	−	0.268946i
$967$	−23.6696			−0.761164			−0.380582	−	0.924747i	$-0.624276\pi$
$967$	−23.6696			−0.761164			−0.380582	+	0.924747i	$0.624276\pi$
$968$	−25.6500	+	17.6090i	−0.824422	+	0.565975i
$969$	−0.412063			−0.0132374
$970$	−5.37791	+	12.8942i	−0.172674	+	0.414007i
$971$	51.2925	−	16.6659i	1.64606	−	0.534836i	0.668176	−	0.744004i	$-0.267076\pi$
$971$	51.2925	−	16.6659i	1.64606	−	0.534836i	0.977880	+	0.209168i	$0.0670755\pi$
$972$	21.8071	−	21.5949i	0.699465	−	0.692658i
$973$	−8.28781	−	6.02145i	−0.265695	−	0.193039i
$974$	−0.458184	+	5.64530i	−0.0146812	+	0.180887i
$975$	2.59056	−	7.97291i	0.0829642	−	0.255338i
$976$	4.32467	+	3.20713i	0.138429	+	0.102658i
$977$	7.76321	−	5.64030i	0.248367	−	0.180449i	−0.456636	−	0.889654i	$-0.650946\pi$
$977$	7.76321	−	5.64030i	0.248367	−	0.180449i	0.705003	+	0.709204i	$0.250946\pi$
$978$	8.99601	−	5.48256i	0.287661	−	0.175313i
$979$	−17.7957	+	1.93169i	−0.568752	+	0.0617371i
$980$	5.37494	−	10.4226i	0.171696	−	0.332938i
$981$	−12.9095	−	17.7684i	−0.412168	−	0.567300i
$982$	−12.0126	−	10.3106i	−0.383338	−	0.329026i
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.790824	−	0.612043i	$-0.209652\pi$
$983$	33.5747	+	10.9091i	1.07087	+	0.347945i	0.280041	+	0.959988i	$0.409652\pi$
$984$	6.40930	−	10.2889i	0.204321	−	0.327997i
$985$	−2.76715	+	3.80866i	−0.0881688	+	0.121354i
$986$	0.0899965	+	0.378941i	0.00286607	+	0.0120679i
$987$	3.65449	+	11.2474i	0.116324	+	0.358007i
$988$	55.9171	−	8.57636i	1.77896	−	0.272850i
$989$		−	10.0631i		−	0.319987i
$990$	−4.38914	+	14.8699i	−0.139496	+	0.472598i
$991$		−	17.8021i		−	0.565502i	−0.959193	−	0.282751i	$-0.908753\pi$
$991$		−	17.8021i		−	0.565502i	0.959193	−	0.282751i	$-0.0912471\pi$
$992$	4.62931	+	20.3765i	0.146981	+	0.646955i
$993$	7.77591	+	23.9318i	0.246761	+	0.759452i
$994$	15.6291	−	3.71182i	0.495723	−	0.117732i
$995$	8.92918	−	12.2900i	0.283074	−	0.389618i
$996$	−2.40575	−	4.77918i	−0.0762293	−	0.151434i
$997$	−59.8586	−	19.4492i	−1.89574	−	0.615963i	−0.973144	−	0.230197i	$-0.926063\pi$
$997$	−59.8586	−	19.4492i	−1.89574	−	0.615963i	−0.922596	−	0.385766i	$-0.873937\pi$
$998$	36.2590	−	42.2443i	1.14776	−	1.33722i
$999$	16.3251	+	22.4695i	0.516503	+	0.710905i

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	44.2.g.a.19.3	yes	16
3.2	odd	2		396.2.r.a.19.2		16
4.3	odd	2	inner	44.2.g.a.19.1	yes	16
8.3	odd	2		704.2.u.c.63.2		16
8.5	even	2		704.2.u.c.63.3		16
11.2	odd	10		484.2.c.d.483.13		16
11.3	even	5		484.2.g.j.215.1		16
11.4	even	5		484.2.g.i.403.4		16
11.5	even	5		484.2.g.f.475.3		16
11.6	odd	10		484.2.g.j.475.2		16
11.7	odd	10	inner	44.2.g.a.7.1	✓	16
11.8	odd	10		484.2.g.f.215.4		16
11.9	even	5		484.2.c.d.483.4		16
11.10	odd	2		484.2.g.i.239.2		16
12.11	even	2		396.2.r.a.19.4		16
33.29	even	10		396.2.r.a.271.4		16
44.3	odd	10		484.2.g.j.215.2		16
44.7	even	10	inner	44.2.g.a.7.3	yes	16
44.15	odd	10		484.2.g.i.403.2		16
44.19	even	10		484.2.g.f.215.3		16
44.27	odd	10		484.2.g.f.475.4		16
44.31	odd	10		484.2.c.d.483.14		16
44.35	even	10		484.2.c.d.483.3		16
44.39	even	10		484.2.g.j.475.1		16
44.43	even	2		484.2.g.i.239.4		16
88.29	odd	10		704.2.u.c.447.2		16
88.51	even	10		704.2.u.c.447.3		16
132.95	odd	10		396.2.r.a.271.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	11.7	odd	10	inner
44.2.g.a.7.3	yes	16	44.7	even	10	inner
44.2.g.a.19.1	yes	16	4.3	odd	2	inner
44.2.g.a.19.3	yes	16	1.1	even	1	trivial
396.2.r.a.19.2		16	3.2	odd	2
396.2.r.a.19.4		16	12.11	even	2
396.2.r.a.271.2		16	132.95	odd	10
396.2.r.a.271.4		16	33.29	even	10
484.2.c.d.483.3		16	44.35	even	10
484.2.c.d.483.4		16	11.9	even	5
484.2.c.d.483.13		16	11.2	odd	10
484.2.c.d.483.14		16	44.31	odd	10
484.2.g.f.215.3		16	44.19	even	10
484.2.g.f.215.4		16	11.8	odd	10
484.2.g.f.475.3		16	11.5	even	5
484.2.g.f.475.4		16	44.27	odd	10
484.2.g.i.239.2		16	11.10	odd	2
484.2.g.i.239.4		16	44.43	even	2
484.2.g.i.403.2		16	44.15	odd	10
484.2.g.i.403.4		16	11.4	even	5
484.2.g.j.215.1		16	11.3	even	5
484.2.g.j.215.2		16	44.3	odd	10
484.2.g.j.475.1		16	44.39	even	10
484.2.g.j.475.2		16	11.6	odd	10
704.2.u.c.63.2		16	8.3	odd	2
704.2.u.c.63.3		16	8.5	even	2
704.2.u.c.447.2		16	88.29	odd	10
704.2.u.c.447.3		16	88.51	even	10

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

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Modular forms

Varieties

Fields

Representations

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Database

Properties

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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	44.2.g.a.19.3

Level	$44$
Weight	$2$
Character	44.19
Analytic conductor	$0.351$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$