LMFDB - Embedded newform 273.2.bj.c.142.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 $ x^16 - 11x^14 + 88x^12 - 303x^10 + 758x^8 - 968x^6 + 867x^4 - 30*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.3
Root			$-1.14630 + 0.661815i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.c.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14630 - 0.661815i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.124000 - 0.214775i) q^{4} +(-1.98394 - 1.14543i) q^{5} +1.32363i q^{6} +(-1.14630 - 2.38453i) q^{7} +2.97552i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.14630 - 0.661815i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.124000 - 0.214775i) q^{4} +(-1.98394 - 1.14543i) q^{5} +1.32363i q^{6} +(-1.14630 - 2.38453i) q^{7} +2.97552i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.51612 + 2.62600i) q^{10} +(-1.08496 + 0.626403i) q^{11} +(-0.124000 + 0.214775i) q^{12} +(2.78424 + 2.29085i) q^{13} +(-0.264122 + 3.49202i) q^{14} +2.29085i q^{15} +(1.72125 - 2.98129i) q^{16} +(-0.418875 - 0.725512i) q^{17} +(1.14630 - 0.661815i) q^{18} +(-0.837638 - 0.483610i) q^{19} +0.568133i q^{20} +(-1.49192 + 2.18499i) q^{21} +1.65825 q^{22} +(-4.11337 + 7.12456i) q^{23} +(2.57688 - 1.48776i) q^{24} +(0.124000 + 0.214775i) q^{25} +(-1.67545 - 4.46865i) q^{26} +1.00000 q^{27} +(-0.369997 + 0.541880i) q^{28} -4.78424 q^{29} +(1.51612 - 2.62600i) q^{30} +(0.553355 - 0.319479i) q^{31} +(1.20763 - 0.697228i) q^{32} +(1.08496 + 0.626403i) q^{33} +1.10887i q^{34} +(-0.457125 + 6.04376i) q^{35} +0.248001 q^{36} +(5.21509 + 3.01094i) q^{37} +(0.640122 + 1.10872i) q^{38} +(0.591815 - 3.55665i) q^{39} +(3.40824 - 5.90325i) q^{40} -0.497308i q^{41} +(3.15624 - 1.51728i) q^{42} -12.2912 q^{43} +(0.269072 + 0.155349i) q^{44} +(1.98394 - 1.14543i) q^{45} +(9.43029 - 5.44458i) q^{46} +(-7.83745 - 4.52495i) q^{47} -3.44249 q^{48} +(-4.37200 + 5.46677i) q^{49} -0.328262i q^{50} +(-0.418875 + 0.725512i) q^{51} +(0.146771 - 0.882053i) q^{52} +(-3.04836 - 5.27992i) q^{53} +(-1.14630 - 0.661815i) q^{54} +2.86999 q^{55} +(7.09524 - 3.41084i) q^{56} +0.967221i q^{57} +(5.48417 + 3.16628i) q^{58} +(7.97598 - 4.60494i) q^{59} +(0.492018 - 0.284067i) q^{60} +(3.36537 - 5.82899i) q^{61} -0.845746 q^{62} +(2.63822 + 0.199544i) q^{63} -8.73073 q^{64} +(-2.89975 - 7.73404i) q^{65} +(-0.829126 - 1.43609i) q^{66} +(-10.3293 + 5.96360i) q^{67} +(-0.103881 + 0.179928i) q^{68} +8.22673 q^{69} +(4.52386 - 6.62542i) q^{70} -10.9173i q^{71} +(-2.57688 - 1.48776i) q^{72} +(-3.04780 + 1.75965i) q^{73} +(-3.98537 - 6.90286i) q^{74} +(0.124000 - 0.214775i) q^{75} +0.239872i q^{76} +(2.73737 + 1.86908i) q^{77} +(-3.03224 + 3.68531i) q^{78} +(6.71524 - 11.6311i) q^{79} +(-6.82969 + 3.94312i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.329126 + 0.570063i) q^{82} +1.79658i q^{83} +(0.654280 + 0.0494870i) q^{84} +1.91916i q^{85} +(14.0894 + 8.13452i) q^{86} +(2.39212 + 4.14327i) q^{87} +(-1.86388 - 3.22833i) q^{88} +(-3.47585 - 2.00678i) q^{89} -3.03224 q^{90} +(2.27104 - 9.26512i) q^{91} +2.04024 q^{92} +(-0.553355 - 0.319479i) q^{93} +(5.98937 + 10.3739i) q^{94} +(1.10788 + 1.91890i) q^{95} +(-1.20763 - 0.697228i) q^{96} +2.57644i q^{97} +(8.62961 - 3.37309i) q^{98} -1.25281i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	$ 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) $ 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.14630	−	0.661815i	−0.810555	−	0.467974i	0.0365935	−	0.999330i	$-0.488349\pi$
$2$	−1.14630	−	0.661815i	−0.810555	−	0.467974i	−0.847149	+	0.531356i	$0.821683\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.124000	−	0.214775i	−0.0620002	−	0.107388i
$5$	−1.98394	−	1.14543i	−0.887243	−	0.512250i	−0.0142033	−	0.999899i	$-0.504521\pi$
$5$	−1.98394	−	1.14543i	−0.887243	−	0.512250i	−0.873040	+	0.487649i	$0.837855\pi$
$6$			1.32363i			0.540370i
$7$	−1.14630	−	2.38453i	−0.433260	−	0.901269i
$7$	−1.14630	−	2.38453i	−0.433260	−	0.901269i
$8$			2.97552i			1.05201i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.51612	+	2.62600i	0.479440	+	0.830414i
$11$	−1.08496	+	0.626403i	−0.327128	+	0.188868i	−0.654565	−	0.756005i	$-0.727148\pi$
$11$	−1.08496	+	0.626403i	−0.327128	+	0.188868i	0.327437	+	0.944873i	$0.393815\pi$
$12$	−0.124000	+	0.214775i	−0.0357959	+	0.0620002i
$13$	2.78424	+	2.29085i	0.772210	+	0.635368i
$13$	2.78424	+	2.29085i	0.772210	+	0.635368i
$14$	−0.264122	+	3.49202i	−0.0705896	+	0.933283i
$15$			2.29085i			0.591495i
$16$	1.72125	−	2.98129i	0.430312	−	0.745322i
$17$	−0.418875	−	0.725512i	−0.101592	−	0.175963i	0.810749	−	0.585394i	$-0.199060\pi$
$17$	−0.418875	−	0.725512i	−0.101592	−	0.175963i	−0.912341	+	0.409432i	$0.865727\pi$
$18$	1.14630	−	0.661815i	0.270185	−	0.155991i
$19$	−0.837638	−	0.483610i	−0.192167	−	0.110948i	0.400829	−	0.916153i	$-0.368722\pi$
$19$	−0.837638	−	0.483610i	−0.192167	−	0.110948i	−0.592997	+	0.805205i	$0.702055\pi$
$20$			0.568133i			0.127038i
$21$	−1.49192	+	2.18499i	−0.325563	+	0.476804i
$22$	1.65825			0.353541
$23$	−4.11337	+	7.12456i	−0.857696	+	1.48557i	0.0164244	+	0.999865i	$0.494772\pi$
$23$	−4.11337	+	7.12456i	−0.857696	+	1.48557i	−0.874121	+	0.485709i	$0.838562\pi$
$24$	2.57688	−	1.48776i	0.526003	−	0.303688i
$25$	0.124000	+	0.214775i	0.0248001	+	0.0429550i
$26$	−1.67545	−	4.46865i	−0.328583	−	0.876375i
$27$	1.00000			0.192450
$28$	−0.369997	+	0.541880i	−0.0699229	+	0.102406i
$29$	−4.78424			−0.888411			−0.444206	−	0.895925i	$-0.646514\pi$
$29$	−4.78424			−0.888411			−0.444206	+	0.895925i	$0.646514\pi$
$30$	1.51612	−	2.62600i	0.276805	−	0.479440i
$31$	0.553355	−	0.319479i	0.0993854	−	0.0573802i	−0.449483	−	0.893289i	$-0.648392\pi$
$31$	0.553355	−	0.319479i	0.0993854	−	0.0573802i	0.548869	+	0.835908i	$0.315059\pi$
$32$	1.20763	−	0.697228i	0.213482	−	0.123254i
$33$	1.08496	+	0.626403i	0.188868	+	0.109043i
$34$			1.10887i			0.190170i
$35$	−0.457125	+	6.04376i	−0.0772682	+	1.02158i
$36$	0.248001			0.0413335
$37$	5.21509	+	3.01094i	0.857356	+	0.494995i	0.863126	−	0.504988i	$-0.168503\pi$
$37$	5.21509	+	3.01094i	0.857356	+	0.494995i	−0.00576977	+	0.999983i	$0.501837\pi$
$38$	0.640122	+	1.10872i	0.103841	+	0.179859i
$39$	0.591815	−	3.55665i	0.0947663	−	0.569520i
$40$	3.40824	−	5.90325i	0.538890	−	0.933385i
$41$		−	0.497308i		−	0.0776665i	−0.999246	−	0.0388332i	$-0.987636\pi$
$41$		−	0.497308i		−	0.0776665i	0.999246	−	0.0388332i	$-0.0123641\pi$
$42$	3.15624	−	1.51728i	0.487019	−	0.234121i
$43$	−12.2912			−1.87439			−0.937197	−	0.348801i	$-0.886589\pi$
$43$	−12.2912			−1.87439			−0.937197	+	0.348801i	$0.886589\pi$
$44$	0.269072	+	0.155349i	0.0405641	+	0.0234197i
$45$	1.98394	−	1.14543i	0.295748	−	0.170750i
$46$	9.43029	−	5.44458i	1.39042	−	0.802760i
$47$	−7.83745	−	4.52495i	−1.14321	−	0.660032i	−0.195986	−	0.980607i	$-0.562791\pi$
$47$	−7.83745	−	4.52495i	−1.14321	−	0.660032i	−0.947223	+	0.320575i	$0.896124\pi$
$48$	−3.44249			−0.496881
$49$	−4.37200	+	5.46677i	−0.624572	+	0.780968i
$50$		−	0.328262i		−	0.0464232i
$51$	−0.418875	+	0.725512i	−0.0586542	+	0.101592i
$52$	0.146771	−	0.882053i	0.0203534	−	0.122319i
$53$	−3.04836	−	5.27992i	−0.418725	−	0.725253i	0.577087	−	0.816683i	$-0.304190\pi$
$53$	−3.04836	−	5.27992i	−0.418725	−	0.725253i	−0.995811	+	0.0914302i	$0.970856\pi$
$54$	−1.14630	−	0.661815i	−0.155991	−	0.0900617i
$55$	2.86999			0.386990
$56$	7.09524	−	3.41084i	0.948141	−	0.455792i
$57$			0.967221i			0.128111i
$58$	5.48417	+	3.16628i	0.720106	+	0.415754i
$59$	7.97598	−	4.60494i	1.03838	−	0.599512i	0.119009	−	0.992893i	$-0.462028\pi$
$59$	7.97598	−	4.60494i	1.03838	−	0.599512i	0.919375	+	0.393381i	$0.128695\pi$
$60$	0.492018	−	0.284067i	0.0635192	−	0.0366729i
$61$	3.36537	−	5.82899i	0.430891	−	0.746325i	−0.566059	−	0.824365i	$-0.691533\pi$
$61$	3.36537	−	5.82899i	0.430891	−	0.746325i	0.996950	+	0.0780394i	$0.0248660\pi$
$62$	−0.845746			−0.107410
$63$	2.63822	+	0.199544i	0.332384	+	0.0251401i
$64$	−8.73073			−1.09134
$65$	−2.89975	−	7.73404i	−0.359670	−	0.959290i
$66$	−0.829126	−	1.43609i	−0.102058	−	0.176770i
$67$	−10.3293	+	5.96360i	−1.26192	+	0.728570i	−0.973446	−	0.228917i	$-0.926481\pi$
$67$	−10.3293	+	5.96360i	−1.26192	+	0.728570i	−0.288475	+	0.957488i	$0.593148\pi$
$68$	−0.103881	+	0.179928i	−0.0125975	+	0.0218194i
$69$	8.22673			0.990382
$70$	4.52386	−	6.62542i	0.540704	−	0.791889i
$71$		−	10.9173i		−	1.29565i	−0.761791	−	0.647823i	$-0.775680\pi$
$71$		−	10.9173i		−	1.29565i	0.761791	−	0.647823i	$-0.224320\pi$
$72$	−2.57688	−	1.48776i	−0.303688	−	0.175334i
$73$	−3.04780	+	1.75965i	−0.356718	+	0.205951i	−0.667640	−	0.744484i	$-0.732696\pi$
$73$	−3.04780	+	1.75965i	−0.356718	+	0.205951i	0.310922	+	0.950435i	$0.399362\pi$
$74$	−3.98537	−	6.90286i	−0.463290	−	0.802441i
$75$	0.124000	−	0.214775i	0.0143183	−	0.0248001i
$76$			0.239872i			0.0275152i
$77$	2.73737	+	1.86908i	0.311952	+	0.213002i
$78$	−3.03224	+	3.68531i	−0.343334	+	0.417279i
$79$	6.71524	−	11.6311i	0.755523	−	1.30860i	−0.189590	−	0.981863i	$-0.560716\pi$
$79$	6.71524	−	11.6311i	0.755523	−	1.30860i	0.945114	−	0.326742i	$-0.105951\pi$
$80$	−6.82969	+	3.94312i	−0.763582	+	0.440854i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.329126	+	0.570063i	−0.0363459	+	0.0629530i
$83$			1.79658i			0.197200i	0.995127	+	0.0986001i	$0.0314365\pi$
$83$			1.79658i			0.197200i	−0.995127	+	0.0986001i	$0.968564\pi$
$84$	0.654280	+	0.0494870i	0.0713878	+	0.00539947i
$85$			1.91916i			0.208162i
$86$	14.0894	+	8.13452i	1.51930	+	0.877168i
$87$	2.39212	+	4.14327i	0.256462	+	0.444206i
$88$	−1.86388	−	3.22833i	−0.198690	−	0.344141i
$89$	−3.47585	−	2.00678i	−0.368440	−	0.212719i	0.304337	−	0.952564i	$-0.401565\pi$
$89$	−3.47585	−	2.00678i	−0.368440	−	0.212719i	−0.672777	+	0.739846i	$0.734898\pi$
$90$	−3.03224			−0.319626
$91$	2.27104	−	9.26512i	0.238070	−	0.971248i
$92$	2.04024			0.212710
$93$	−0.553355	−	0.319479i	−0.0573802	−	0.0331285i
$94$	5.98937	+	10.3739i	0.617756	+	1.06998i
$95$	1.10788	+	1.91890i	0.113666	+	0.196875i
$96$	−1.20763	−	0.697228i	−0.123254	−	0.0711606i
$97$			2.57644i			0.261598i	0.991409	+	0.130799i	$0.0417542\pi$
$97$			2.57644i			0.261598i	−0.991409	+	0.130799i	$0.958246\pi$
$98$	8.62961	−	3.37309i	0.871722	−	0.340734i
$99$		−	1.25281i		−	0.125912i
$100$	0.0307522	−	0.0532644i	0.00307522	−	0.00532644i
$101$	−0.302372	−	0.523724i	−0.0300871	−	0.0521125i	0.850590	−	0.525830i	$-0.176245\pi$
$101$	−0.302372	−	0.523724i	−0.0300871	−	0.0521125i	−0.880677	+	0.473717i	$0.842912\pi$
$102$	0.960311	−	0.554436i	0.0950849	−	0.0548973i
$103$	−1.45712	+	2.52381i	−0.143575	+	0.248679i	−0.928840	−	0.370480i	$-0.879193\pi$
$103$	−1.45712	+	2.52381i	−0.143575	+	0.248679i	0.785266	+	0.619159i	$0.212526\pi$
$104$	−6.81648	+	8.28458i	−0.668411	+	0.812370i
$105$	5.46261	−	2.62600i	0.533096	−	0.256271i
$106$			8.06982i			0.783810i
$107$	−9.17785	+	15.8965i	−0.887256	+	1.53677i	−0.0441510	+	0.999025i	$0.514058\pi$
$107$	−9.17785	+	15.8965i	−0.887256	+	1.53677i	−0.843105	+	0.537748i	$0.819275\pi$
$108$	−0.124000	−	0.214775i	−0.0119320	−	0.0206667i
$109$	−10.8430	+	6.26023i	−1.03857	+	0.599621i	−0.919429	−	0.393256i	$-0.871349\pi$
$109$	−10.8430	+	6.26023i	−1.03857	+	0.599621i	−0.119145	+	0.992877i	$0.538015\pi$
$110$	−3.28987	−	1.89941i	−0.313676	−	0.181101i
$111$		−	6.02187i		−	0.571571i
$112$	−9.08204	−	0.686927i	−0.858172	−	0.0649085i
$113$	8.31249			0.781973			0.390986	−	0.920396i	$-0.372134\pi$
$113$	8.31249			0.781973			0.390986	+	0.920396i	$0.372134\pi$
$114$	0.640122	−	1.10872i	0.0599529	−	0.103841i
$115$	16.3213	−	9.42311i	1.52197	−	0.878710i
$116$	0.593248	+	1.02754i	0.0550817	+	0.0954043i
$117$	−3.37606	+	1.26580i	−0.312117	+	0.117023i
$118$	−12.1905			−1.12222
$119$	−1.24985	+	1.83047i	−0.114574	+	0.167799i
$120$	−6.81648			−0.622257
$121$	−4.71524	+	8.16703i	−0.428658	+	0.742458i
$122$	−7.71543	+	4.45450i	−0.698522	+	0.403292i
$123$	−0.430681	+	0.248654i	−0.0388332	+	0.0224204i
$124$	−0.137232	−	0.0792312i	−0.0123238	−	0.00711517i
$125$			10.8861i			0.973685i
$126$	−2.89212	−	1.97475i	−0.257651	−	0.175925i
$127$	−7.68648			−0.682064			−0.341032	−	0.940052i	$-0.610777\pi$
$127$	−7.68648			−0.682064			−0.341032	+	0.940052i	$0.610777\pi$
$128$	7.59275	+	4.38368i	0.671111	+	0.387466i
$129$	6.14561	+	10.6445i	0.541091	+	0.937197i
$130$	−1.79453	+	10.7846i	−0.157390	+	0.945874i
$131$	1.90424	−	3.29825i	0.166375	−	0.288169i	−0.770768	−	0.637116i	$-0.780127\pi$
$131$	1.90424	−	3.29825i	0.166375	−	0.288169i	0.937143	+	0.348947i	$0.113461\pi$
$132$		−	0.310697i		−	0.0270427i
$133$	−0.193003	+	2.55174i	−0.0167355	+	0.221264i
$134$	15.7872			1.36381
$135$	−1.98394	−	1.14543i	−0.170750	−	0.0985826i
$136$	2.15878	−	1.24637i	0.185114	−	0.106876i
$137$	10.3695	−	5.98684i	0.885927	−	0.511490i	0.0133187	−	0.999911i	$-0.495760\pi$
$137$	10.3695	−	5.98684i	0.885927	−	0.511490i	0.872608	+	0.488421i	$0.162427\pi$
$138$	−9.43029	−	5.44458i	−0.802760	−	0.463473i
$139$	−1.79751			−0.152463			−0.0762315	−	0.997090i	$-0.524289\pi$
$139$	−1.79751			−0.152463			−0.0762315	+	0.997090i	$0.524289\pi$
$140$	1.35473	−	0.651250i	0.114496	−	0.0550407i
$141$			9.04990i			0.762139i
$142$	−7.22524	+	12.5145i	−0.606329	+	1.05019i
$143$	−4.45579	−	0.741429i	−0.372612	−	0.0620014i
$144$	1.72125	+	2.98129i	0.143437	+	0.248441i
$145$	9.49163	+	5.47999i	0.788237	+	0.455089i
$146$	4.65825			0.385520
$147$	6.92036	+	1.05288i	0.570782	+	0.0868399i
$148$		−	1.49343i		−	0.122759i
$149$	−1.43123	−	0.826323i	−0.117251	−	0.0676950i	0.440227	−	0.897886i	$-0.354898\pi$
$149$	−1.43123	−	0.826323i	−0.117251	−	0.0676950i	−0.557479	+	0.830191i	$0.688231\pi$
$150$	−0.284283	+	0.164131i	−0.0232116	+	0.0134012i
$151$	−11.9597	+	6.90495i	−0.973268	+	0.561917i	−0.900231	−	0.435413i	$-0.856602\pi$
$151$	−11.9597	+	6.90495i	−0.973268	+	0.561917i	−0.0730371	+	0.997329i	$0.523269\pi$
$152$	1.43899	−	2.49241i	0.116718	−	0.202161i
$153$	0.837750			0.0677280
$154$	−1.90085	−	3.95416i	−0.153175	−	0.318635i
$155$	−1.46376			−0.117572
$156$	−0.837265	+	0.313919i	−0.0670349	+	0.0251336i
$157$	3.38549	+	5.86383i	0.270191	+	0.467985i	0.968911	−	0.247411i	$-0.0795798\pi$
$157$	3.38549	+	5.86383i	0.270191	+	0.467985i	−0.698719	+	0.715396i	$0.746246\pi$
$158$	−15.3953	+	8.88850i	−1.22479	+	0.707131i
$159$	−3.04836	+	5.27992i	−0.241751	+	0.418725i
$160$	−3.19449			−0.252547
$161$	21.7039	+	1.64159i	1.71051	+	0.129376i
$162$			1.32363i			0.103994i
$163$	−6.54475	−	3.77861i	−0.512624	−	0.295964i	0.221287	−	0.975209i	$-0.428974\pi$
$163$	−6.54475	−	3.77861i	−0.512624	−	0.295964i	−0.733912	+	0.679245i	$0.762307\pi$
$164$	−0.106809	+	0.0616664i	−0.00834041	+	0.00481534i
$165$	−1.43500	−	2.48549i	−0.111714	−	0.193495i
$166$	1.18900	−	2.05942i	0.0922847	−	0.159842i
$167$		−	23.6854i		−	1.83283i	−0.400231	−	0.916414i	$-0.631070\pi$
$167$		−	23.6854i		−	1.83283i	0.400231	−	0.916414i	$-0.368930\pi$
$168$	−6.50149	−	4.43924i	−0.501601	−	0.342495i
$169$	2.50400	+	12.7566i	0.192615	+	0.981274i
$170$	1.27013	−	2.19993i	0.0974145	−	0.168727i
$171$	0.837638	−	0.483610i	0.0640557	−	0.0369826i
$172$	1.52412	+	2.63985i	0.116213	+	0.201287i
$173$	6.23073	−	10.7919i	0.473714	−	0.820496i	−0.525833	−	0.850588i	$-0.676246\pi$
$173$	6.23073	−	10.7919i	0.473714	−	0.820496i	0.999547	+	0.0300912i	$0.00957977\pi$
$174$		−	6.33257i		−	0.480071i
$175$	0.369997	−	0.541880i	0.0279691	−	0.0409623i
$176$			4.31278i			0.325088i
$177$	−7.97598	−	4.60494i	−0.599512	−	0.346128i
$178$	2.65624	+	4.60075i	0.199094	+	0.344841i
$179$	−2.02012	−	3.49895i	−0.150991	−	0.261524i	0.780601	−	0.625029i	$-0.214913\pi$
$179$	−2.02012	−	3.49895i	−0.150991	−	0.261524i	−0.931592	+	0.363506i	$0.881580\pi$
$180$	−0.492018	−	0.284067i	−0.0366729	−	0.0211731i
$181$	21.5070			1.59860			0.799301	−	0.600931i	$-0.205204\pi$
$181$	21.5070			1.59860			0.799301	+	0.600931i	$0.205204\pi$
$182$	−8.73509	+	9.11757i	−0.647488	+	0.675839i
$183$	−6.73073			−0.497550
$184$	−21.1993	−	12.2394i	−1.56283	−	0.902302i
$185$	−6.89761	−	11.9470i	−0.507122	−	0.878362i
$186$	0.422873	+	0.732437i	0.0310065	+	0.0537049i
$187$	0.908926	+	0.524769i	0.0664673	+	0.0383749i
$188$			2.24439i			0.163689i
$189$	−1.14630	−	2.38453i	−0.0833809	−	0.173449i
$190$		−	2.93285i		−	0.212771i
$191$	7.58262	−	13.1335i	0.548659	−	0.950305i	−0.449708	−	0.893176i	$-0.648472\pi$
$191$	7.58262	−	13.1335i	0.548659	−	0.950305i	0.998367	−	0.0571292i	$-0.0181947\pi$
$192$	4.36537	+	7.56104i	0.315043	+	0.545671i
$193$	−6.55063	+	3.78201i	−0.471525	+	0.272235i	−0.716878	−	0.697199i	$-0.754430\pi$
$193$	−6.55063	+	3.78201i	−0.471525	+	0.272235i	0.245353	+	0.969434i	$0.421096\pi$
$194$	1.70513	−	2.95336i	0.122421	−	0.212039i
$195$	−5.24800	+	6.37828i	−0.375817	+	0.456758i
$196$	1.71626	+	0.261115i	0.122590	+	0.0186511i
$197$			8.95547i			0.638051i	0.947746	+	0.319026i	$0.103356\pi$
$197$			8.95547i			0.638051i	−0.947746	+	0.319026i	$0.896644\pi$
$198$	−0.829126	+	1.43609i	−0.0589234	+	0.102058i
$199$	−13.4626	−	23.3179i	−0.954339	−	1.65296i	−0.735873	−	0.677120i	$-0.763228\pi$
$199$	−13.4626	−	23.3179i	−0.954339	−	1.65296i	−0.218466	−	0.975844i	$-0.570105\pi$
$200$	−0.639069	+	0.368966i	−0.0451890	+	0.0260899i
$201$	10.3293	+	5.96360i	0.728570	+	0.420640i
$202$			0.800458i			0.0563200i
$203$	5.48417	+	11.4082i	0.384913	+	0.800698i
$204$	0.207763			0.0145463
$205$	−0.569629	+	0.986627i	−0.0397846	+	0.0689090i
$206$	3.34060	−	1.92870i	0.232751	−	0.134379i
$207$	−4.11337	−	7.12456i	−0.285899	−	0.495191i
$208$	11.6221	−	4.35750i	0.805844	−	0.302138i
$209$	1.21174			0.0838178
$210$	−7.99971	−	0.605064i	−0.552032	−	0.0417534i
$211$	10.4667			0.720560			0.360280	−	0.932844i	$-0.382681\pi$
$211$	10.4667			0.720560			0.360280	+	0.932844i	$0.382681\pi$
$212$	−0.755997	+	1.30943i	−0.0519221	+	0.0899317i
$213$	−9.45467	+	5.45865i	−0.647823	+	0.374021i
$214$	21.0411	−	12.1481i	1.43834	−	0.830426i
$215$	24.3850	+	14.0787i	1.66304	+	0.960158i
$216$			2.97552i			0.202459i
$217$	−1.39612	−	0.953274i	−0.0947747	−	0.0647125i
$218$	16.5725			1.12243
$219$	3.04780	+	1.75965i	0.205951	+	0.118906i
$220$	−0.355880	−	0.616403i	−0.0239935	−	0.0415579i
$221$	0.495793	−	2.97958i	0.0333506	−	0.200428i
$222$	−3.98537	+	6.90286i	−0.267480	+	0.463290i
$223$		−	24.6617i		−	1.65147i	−0.564060	−	0.825734i	$-0.690761\pi$
$223$		−	24.6617i		−	1.65147i	0.564060	−	0.825734i	$-0.309239\pi$
$224$	−3.04687	−	2.08041i	−0.203578	−	0.139004i
$225$	−0.248001			−0.0165334
$226$	−9.52859	−	5.50133i	−0.633832	−	0.365943i
$227$	−16.8133	+	9.70718i	−1.11594	+	0.644288i	−0.940361	−	0.340177i	$-0.889513\pi$
$227$	−16.8133	+	9.70718i	−1.11594	+	0.644288i	−0.175579	+	0.984465i	$0.556180\pi$
$228$	0.207735	−	0.119936i	0.0137576	−	0.00794294i
$229$	−12.1061	−	6.98947i	−0.799995	−	0.461877i	0.0434746	−	0.999055i	$-0.486157\pi$
$229$	−12.1061	−	6.98947i	−0.799995	−	0.461877i	−0.843469	+	0.537177i	$0.819491\pi$
$230$	−24.9455			−1.64485
$231$	0.249989	−	3.30517i	0.0164481	−	0.217464i
$232$		−	14.2356i		−	0.934614i
$233$	−7.07713	+	12.2579i	−0.463638	+	0.803045i	−0.999139	−	0.0414901i	$-0.986790\pi$
$233$	−7.07713	+	12.2579i	−0.463638	+	0.803045i	0.535501	+	0.844535i	$0.320123\pi$
$234$	4.70769	+	0.783345i	0.307751	+	0.0512088i
$235$	10.3660	+	17.9544i	0.676203	+	1.17122i
$236$	−1.97805	−	1.14203i	−0.128760	−	0.0743397i
$237$	−13.4305			−0.872403
$238$	2.64414	−	1.27110i	0.171394	−	0.0823930i
$239$		−	2.46293i		−	0.159314i	−0.996822	−	0.0796570i	$-0.974617\pi$
$239$		−	2.46293i		−	0.159314i	0.996822	−	0.0796570i	$-0.0253825\pi$
$240$	6.82969	+	3.94312i	0.440854	+	0.254527i
$241$	24.8611	−	14.3536i	1.60145	−	0.924596i	0.610249	−	0.792210i	$-0.291070\pi$
$241$	24.8611	−	14.3536i	1.60145	−	0.924596i	0.991198	−	0.132386i	$-0.0422638\pi$
$242$	10.8101	−	6.24124i	0.694902	−	0.401202i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.66923			−0.106861
$245$	14.9356	−	5.83792i	0.954197	−	0.372971i
$246$	0.658252			0.0419686
$247$	−1.22431	−	3.26539i	−0.0779007	−	0.207772i
$248$	0.950619	+	1.64652i	0.0603643	+	0.104554i
$249$	1.55588	−	0.898290i	0.0986001	−	0.0569268i
$250$	7.20461	−	12.4787i	0.455659	−	0.789225i
$251$	−15.5967			−0.984458			−0.492229	−	0.870466i	$-0.663818\pi$
$251$	−15.5967			−0.984458			−0.492229	+	0.870466i	$0.663818\pi$
$252$	−0.284283	−	0.591367i	−0.0179081	−	0.0372526i
$253$		−	10.3065i		−	0.647964i
$254$	8.81099	+	5.08703i	0.552851	+	0.319189i
$255$	1.66204	−	0.959580i	0.104081	−	0.0600912i
$256$	2.92836	+	5.07207i	0.183023	+	0.317004i
$257$	8.88211	−	15.3843i	0.554051	−	0.959645i	−0.443926	−	0.896064i	$-0.646415\pi$
$257$	8.88211	−	15.3843i	0.554051	−	0.959645i	0.997977	−	0.0635810i	$-0.0202521\pi$
$258$		−	16.2690i		−	1.01287i
$259$	1.20163	−	15.8870i	0.0746654	−	0.987170i
$260$	−1.30151	+	1.58182i	−0.0807162	+	0.0981003i
$261$	2.39212	−	4.14327i	0.148069	−	0.256462i
$262$	−4.36566	+	2.52052i	−0.269711	+	0.155718i
$263$	−9.90424	−	17.1547i	−0.610722	−	1.05780i	−0.991119	−	0.132978i	$-0.957546\pi$
$263$	−9.90424	−	17.1547i	−0.610722	−	1.05780i	0.380397	−	0.924823i	$-0.375787\pi$
$264$	−1.86388	+	3.22833i	−0.114714	+	0.198690i
$265$			13.9667i			0.857967i
$266$	1.91002	−	2.79732i	0.117111	−	0.171515i
$267$			4.01357i			0.245626i
$268$	2.56167	+	1.47898i	0.156479	+	0.0903431i
$269$	6.97588	+	12.0826i	0.425327	+	0.736688i	0.996451	−	0.0841758i	$-0.0268257\pi$
$269$	6.97588	+	12.0826i	0.425327	+	0.736688i	−0.571124	+	0.820864i	$0.693492\pi$
$270$	1.51612	+	2.62600i	0.0922682	+	0.159813i
$271$	20.1111	+	11.6111i	1.22166	+	0.705326i	0.965272	−	0.261248i	$-0.0841341\pi$
$271$	20.1111	+	11.6111i	1.22166	+	0.705326i	0.256388	+	0.966574i	$0.417467\pi$
$272$	−2.88395			−0.174865
$273$	−9.15935	+	2.66578i	−0.554349	+	0.161340i
$274$	−15.8487			−0.957457
$275$	−0.269072	−	0.155349i	−0.0162256	−	0.00936787i
$276$	−1.02012	−	1.76690i	−0.0614040	−	0.106355i
$277$	0.566494	+	0.981196i	0.0340373	+	0.0589544i	0.882542	−	0.470233i	$-0.155830\pi$
$277$	0.566494	+	0.981196i	0.0340373	+	0.0589544i	−0.848505	+	0.529187i	$0.822497\pi$
$278$	2.06048	+	1.18962i	0.123580	+	0.0713487i
$279$			0.638959i			0.0382535i
$280$	−17.9834	−	1.36019i	−1.07471	−	0.0812866i
$281$		−	17.3169i		−	1.03304i	−0.856275	−	0.516520i	$-0.827227\pi$
$281$		−	17.3169i		−	1.03304i	0.856275	−	0.516520i	$-0.172773\pi$
$282$	5.98937	−	10.3739i	0.356662	−	0.617756i
$283$	4.38350	+	7.59244i	0.260572	+	0.451324i	0.966394	−	0.257065i	$-0.0827556\pi$
$283$	4.38350	+	7.59244i	0.260572	+	0.451324i	−0.705822	+	0.708389i	$0.749422\pi$
$284$	−2.34477	+	1.35375i	−0.139136	+	0.0803304i
$285$	1.10788	−	1.91890i	0.0656251	−	0.113666i
$286$	4.61697	+	3.79881i	0.273007	+	0.224628i
$287$	−1.18585	+	0.570063i	−0.0699984	+	0.0336498i
$288$			1.39446i			0.0821691i
$289$	8.14909	−	14.1146i	0.479358	−	0.830273i
$290$	−7.25349	−	12.5634i	−0.425940	−	0.737749i
$291$	2.23126	−	1.28822i	0.130799	−	0.0755167i
$292$	0.755858	+	0.436395i	0.0442332	+	0.0255381i
$293$		−	2.80648i		−	0.163956i	−0.996634	−	0.0819781i	$-0.973876\pi$
$293$		−	2.80648i		−	0.163956i	0.996634	−	0.0819781i	$-0.0261238\pi$
$294$	−7.23599	−	5.78692i	−0.422011	−	0.337500i
$295$	−21.0985			−1.22840
$296$	−8.95911	+	15.5176i	−0.520738	+	0.901944i
$297$	−1.08496	+	0.626403i	−0.0629559	+	0.0363476i
$298$	1.09375	+	1.89442i	0.0633590	+	0.109741i
$299$	−27.7739	+	10.4134i	−1.60621	+	0.602221i
$300$	−0.0615045			−0.00355096
$301$	14.0894	+	29.3088i	0.812100	+	1.68933i
$302$	18.2792			1.05185
$303$	−0.302372	+	0.523724i	−0.0173708	+	0.0300871i
$304$	−2.88356	+	1.66483i	−0.165384	+	0.0954843i
$305$	−13.3533	+	7.70955i	−0.764610	+	0.441448i
$306$	−0.960311	−	0.554436i	−0.0548973	−	0.0316950i
$307$		−	15.3612i		−	0.876707i	−0.898803	−	0.438354i	$-0.855562\pi$
$307$		−	15.3612i		−	0.876707i	0.898803	−	0.438354i	$-0.144438\pi$
$308$	0.0619976	−	0.819686i	0.00353264	−	0.0467059i
$309$	2.91425			0.165786
$310$	1.67791	+	0.968739i	0.0952986	+	0.0550207i
$311$	−15.5916	−	27.0054i	−0.884117	−	1.53134i	−0.846722	−	0.532036i	$-0.821427\pi$
$311$	−15.5916	−	27.0054i	−0.884117	−	1.53134i	−0.0373956	−	0.999301i	$-0.511906\pi$
$312$	10.5829	+	1.76096i	0.599138	+	0.0996947i
$313$	−15.5196	+	26.8807i	−0.877220	+	1.51939i	−0.0228403	+	0.999739i	$0.507271\pi$
$313$	−15.5196	+	26.8807i	−0.877220	+	1.51939i	−0.854379	+	0.519650i	$0.826062\pi$
$314$		−	8.96227i		−	0.505770i
$315$	−5.00549	−	3.41776i	−0.282027	−	0.192569i
$316$	−3.33077			−0.187371
$317$	14.7100	+	8.49282i	0.826196	+	0.477005i	0.852548	−	0.522648i	$-0.175056\pi$
$317$	14.7100	+	8.49282i	0.826196	+	0.477005i	−0.0263524	+	0.999653i	$0.508389\pi$
$318$	6.98867	−	4.03491i	0.391905	−	0.226266i
$319$	5.19072	−	2.99686i	0.290624	−	0.167792i
$320$	17.3212	+	10.0004i	0.968285	+	0.559040i
$321$	18.3557			1.02452
$322$	−23.7927	−	16.2457i	−1.32592	−	0.905339i
$323$			0.810289i			0.0450857i
$324$	−0.124000	+	0.214775i	−0.00688892	+	0.0119320i
$325$	−0.146771	+	0.882053i	−0.00814137	+	0.0489275i
$326$	5.00149	+	8.66283i	0.277007	+	0.479790i
$327$	10.8430	+	6.26023i	0.599621	+	0.346191i
$328$	1.47975			0.0817056
$329$	−1.80585	+	23.8756i	−0.0995597	+	1.31630i
$330$			3.79881i			0.209118i
$331$	16.0020	+	9.23879i	0.879552	+	0.507810i	0.870511	−	0.492149i	$-0.163789\pi$
$331$	16.0020	+	9.23879i	0.879552	+	0.507810i	0.00904140	+	0.999959i	$0.497122\pi$
$332$	0.385861	−	0.222777i	0.0211769	−	0.0122265i
$333$	−5.21509	+	3.01094i	−0.285785	+	0.164998i
$334$	−15.6753	+	27.1505i	−0.857717	+	1.48561i
$335$	27.3235			1.49284
$336$	3.94612	+	8.20874i	0.215279	+	0.447824i
$337$	22.1520			1.20669			0.603347	−	0.797479i	$-0.293833\pi$
$337$	22.1520			1.20669			0.603347	+	0.797479i	$0.293833\pi$
$338$	5.57217	−	16.2800i	0.303086	−	0.885516i
$339$	−4.15624	−	7.19882i	−0.225736	−	0.390986i
$340$	0.412188	−	0.237977i	0.0223540	−	0.0129061i
$341$	−0.400246	+	0.693246i	−0.0216745	+	0.0375414i
$342$	−1.28024			−0.0692276
$343$	18.0473	+	4.15863i	0.974464	+	0.224545i
$344$		−	36.5728i		−	1.97187i
$345$	−16.3213	−	9.42311i	−0.878710	−	0.507323i
$346$	−14.2846	+	8.24719i	−0.767942	+	0.443372i
$347$	11.2402	+	19.4686i	0.603407	+	1.04513i	0.992301	+	0.123849i	$0.0395237\pi$
$347$	11.2402	+	19.4686i	0.603407	+	1.04513i	−0.388895	+	0.921282i	$0.627143\pi$
$348$	0.593248	−	1.02754i	0.0318014	−	0.0550817i
$349$			11.9051i			0.637267i	0.947878	+	0.318634i	$0.103224\pi$
$349$			11.9051i			0.637267i	−0.947878	+	0.318634i	$0.896776\pi$
$350$	−0.782751	+	0.376286i	−0.0418398	+	0.0201133i
$351$	2.78424	+	2.29085i	0.148612	+	0.122277i
$352$	−0.873491	+	1.51293i	−0.0465572	+	0.0806395i
$353$	−7.79786	+	4.50210i	−0.415038	+	0.239622i	−0.692952	−	0.720984i	$-0.743690\pi$
$353$	−7.79786	+	4.50210i	−0.415038	+	0.239622i	0.277914	+	0.960606i	$0.410357\pi$
$354$	6.09524	+	10.5573i	0.323958	+	0.561112i
$355$	−12.5050	+	21.6592i	−0.663695	+	1.14955i
$356$			0.995369i			0.0527545i
$357$	2.21016	+	0.167168i	0.116974	+	0.00884744i
$358$			5.34778i			0.282639i
$359$	3.10914	+	1.79506i	0.164094	+	0.0947397i	0.579798	−	0.814760i	$-0.303131\pi$
$359$	3.10914	+	1.79506i	0.164094	+	0.0947397i	−0.415704	+	0.909500i	$0.636465\pi$
$360$	3.40824	+	5.90325i	0.179630	+	0.311128i
$361$	−9.03224	−	15.6443i	−0.475381	−	0.823384i
$362$	−24.6534	−	14.2337i	−1.29575	−	0.748104i
$363$	9.43048			0.494972
$364$	−2.27153	+	0.661115i	−0.119060	+	0.0346519i
$365$	8.06219			0.421994
$366$	7.71543	+	4.45450i	0.403292	+	0.232841i
$367$	3.19363	+	5.53153i	0.166706	+	0.288743i	0.937260	−	0.348632i	$-0.113354\pi$
$367$	3.19363	+	5.53153i	0.166706	+	0.288743i	−0.770554	+	0.637375i	$0.780020\pi$
$368$	14.1602	+	24.5263i	0.738154	+	1.27852i
$369$	0.430681	+	0.248654i	0.0224204	+	0.0129444i
$370$			18.2598i			0.949281i
$371$	−9.09581	+	13.3213i	−0.472231	+	0.691607i
$372$			0.158462i			0.00821589i
$373$	4.58575	−	7.94275i	0.237441	−	0.411260i	−0.722538	−	0.691331i	$-0.757025\pi$
$373$	4.58575	−	7.94275i	0.237441	−	0.411260i	0.959979	+	0.280071i	$0.0903580\pi$
$374$	−0.694600	−	1.20308i	−0.0359169	−	0.0622099i
$375$	9.42766	−	5.44306i	0.486842	−	0.281079i
$376$	13.4641	−	23.3205i	0.694358	−	1.20266i
$377$	−13.3205	−	10.9600i	−0.686040	−	0.564468i
$378$	−0.264122	+	3.49202i	−0.0135850	+	0.179610i
$379$			22.1872i			1.13968i	0.821755	+	0.569841i	$0.192995\pi$
$379$			22.1872i			1.13968i	−0.821755	+	0.569841i	$0.807005\pi$
$380$	0.274755	−	0.475890i	0.0140946	−	0.0244126i
$381$	3.84324	+	6.65668i	0.196895	+	0.341032i
$382$	−17.3839	+	10.0366i	−0.889436	+	0.513516i
$383$	−25.2622	−	14.5851i	−1.29084	−	0.745266i	−0.312036	−	0.950070i	$-0.601011\pi$
$383$	−25.2622	−	14.5851i	−1.29084	−	0.745266i	−0.978803	+	0.204804i	$0.934344\pi$
$384$		−	8.76736i		−	0.447407i
$385$	−3.28987	−	6.84359i	−0.167667	−	0.348782i
$386$	10.0120			0.509596
$387$	6.14561	−	10.6445i	0.312399	−	0.541091i
$388$	0.553355	−	0.319479i	0.0280923	−	0.0162191i
$389$	−4.02276	−	6.96762i	−0.203962	−	0.353272i	0.745840	−	0.666126i	$-0.232049\pi$
$389$	−4.02276	−	6.96762i	−0.203962	−	0.353272i	−0.949801	+	0.312853i	$0.898715\pi$
$390$	10.2370	−	3.83821i	0.518372	−	0.194355i
$391$	6.89194			0.348541
$392$	−16.2665	−	13.0090i	−0.821583	−	0.657053i
$393$	−3.80849			−0.192113
$394$	5.92687	−	10.2656i	0.298591	−	0.517176i
$395$	−26.6452	+	15.3836i	−1.34067	+	0.774034i
$396$	−0.269072	+	0.155349i	−0.0135214	+	0.00780656i
$397$	−11.5528	−	6.66999i	−0.579817	−	0.334757i	0.181244	−	0.983438i	$-0.441988\pi$
$397$	−11.5528	−	6.66999i	−0.579817	−	0.334757i	−0.761060	+	0.648681i	$0.775321\pi$
$398$			35.6391i			1.78642i
$399$	2.30637	−	1.10872i	0.115463	−	0.0555056i
$400$	0.853742			0.0426871
$401$	−25.6903	−	14.8323i	−1.28291	−	0.740689i	−0.305531	−	0.952182i	$-0.598834\pi$
$401$	−25.6903	−	14.8323i	−1.28291	−	0.740689i	−0.977379	+	0.211493i	$0.932167\pi$
$402$	−7.89361	−	13.6721i	−0.393698	−	0.681904i
$403$	2.27255	+	0.378145i	0.113204	+	0.0188368i
$404$	−0.0749885	+	0.129884i	−0.00373082	+	0.00646197i
$405$			2.29085i			0.113833i
$406$	1.26362	−	16.7067i	0.0627126	−	0.829139i
$407$	−7.54424			−0.373954
$408$	−2.15878	−	1.24637i	−0.106876	−	0.0617046i
$409$	−32.1822	+	18.5804i	−1.59131	+	0.918742i	−0.598224	+	0.801329i	$0.704127\pi$
$409$	−32.1822	+	18.5804i	−1.59131	+	0.918742i	−0.993083	+	0.117413i	$0.962540\pi$
$410$	1.30593	−	0.753979i	0.0644953	−	0.0372364i
$411$	−10.3695	−	5.98684i	−0.511490	−	0.295309i
$412$	0.722737			0.0356067
$413$	−20.1235	−	13.7404i	−0.990212	−	0.676120i
$414$			10.8892i			0.535173i
$415$	2.05785	−	3.56430i	0.101016	−	0.174965i
$416$	4.95959	+	0.825260i	0.243164	+	0.0404617i
$417$	0.898756	+	1.55669i	0.0440123	+	0.0762315i
$418$	−1.38901	−	0.801948i	−0.0679389	−	0.0392246i
$419$	32.1157			1.56895			0.784477	−	0.620158i	$-0.212931\pi$
$419$	32.1157			1.56895			0.784477	+	0.620158i	$0.212931\pi$
$420$	−1.24137	−	0.847608i	−0.0605725	−	0.0413591i
$421$		−	28.2099i		−	1.37486i	−0.726248	−	0.687432i	$-0.758738\pi$
$421$		−	28.2099i		−	1.37486i	0.726248	−	0.687432i	$-0.241262\pi$
$422$	−11.9980	−	6.92705i	−0.584054	−	0.337204i
$423$	7.83745	−	4.52495i	0.381070	−	0.220011i
$424$	15.7105	−	9.07048i	0.762971	−	0.440501i
$425$	0.103881	−	0.179928i	0.00503899	−	0.00872778i
$426$	14.4505			0.700129
$427$	−17.7571	−	1.34307i	−0.859328	−	0.0649959i
$428$	4.55223			0.220040
$429$	1.58580	+	4.22954i	0.0765631	+	0.204204i
$430$	−18.6350	−	32.2767i	−0.898658	−	1.55652i
$431$	12.6166	−	7.28421i	0.607722	−	0.350868i	−0.164352	−	0.986402i	$-0.552553\pi$
$431$	12.6166	−	7.28421i	0.607722	−	0.350868i	0.772073	+	0.635534i	$0.219220\pi$
$432$	1.72125	−	2.98129i	0.0828135	−	0.143437i
$433$	−7.98798			−0.383878			−0.191939	−	0.981407i	$-0.561478\pi$
$433$	−7.98798			−0.383878			−0.191939	+	0.981407i	$0.561478\pi$
$434$	0.969477	+	2.01671i	0.0465364	+	0.0968051i
$435$		−	10.9600i		−	0.525491i
$436$	2.68908	+	1.55254i	0.128784	+	0.0743533i
$437$	6.89102	−	3.97853i	0.329642	−	0.190319i
$438$	−2.32913	−	4.03416i	−0.111290	−	0.192760i
$439$	−4.75085	+	8.22872i	−0.226746	+	0.392735i	−0.956842	−	0.290609i	$-0.906142\pi$
$439$	−4.75085	+	8.22872i	−0.226746	+	0.392735i	0.730096	+	0.683345i	$0.239475\pi$
$440$			8.53973i			0.407116i
$441$	−2.54836	−	6.51965i	−0.121351	−	0.310460i
$442$	−2.54026	+	3.08737i	−0.120828	+	0.146851i
$443$	−3.36485	+	5.82809i	−0.159869	+	0.276901i	−0.934821	−	0.355119i	$-0.884440\pi$
$443$	−3.36485	+	5.82809i	−0.159869	+	0.276901i	0.774952	+	0.632019i	$0.217774\pi$
$444$	−1.29335	+	0.746715i	−0.0613796	+	0.0354375i
$445$	4.59725	+	7.96266i	0.217930	+	0.377466i
$446$	−16.3215	+	28.2696i	−0.772844	+	1.33861i
$447$			1.65265i			0.0781675i
$448$	10.0080	+	20.8187i	0.472835	+	0.983592i
$449$			8.46045i			0.399273i	0.979870	+	0.199637i	$0.0639762\pi$
$449$			8.46045i			0.399273i	−0.979870	+	0.199637i	$0.936024\pi$
$450$	0.284283	+	0.164131i	0.0134012	+	0.00773720i
$451$	0.311515	+	0.539560i	0.0146687	+	0.0254069i
$452$	−1.03075	−	1.78532i	−0.0484825	−	0.0839742i
$453$	11.9597	+	6.90495i	0.561917	+	0.324423i
$454$	25.6975			1.20604
$455$	−15.1181	+	15.7801i	−0.708748	+	0.739782i
$456$	−2.87799			−0.134774
$457$	−15.3715	−	8.87474i	−0.719048	−	0.415143i	0.0953541	−	0.995443i	$-0.469602\pi$
$457$	−15.3715	−	8.87474i	−0.719048	−	0.415143i	−0.814402	+	0.580301i	$0.802935\pi$
$458$	9.25148	+	16.0240i	0.432293	+	0.748754i
$459$	−0.418875	−	0.725512i	−0.0195514	−	0.0338640i
$460$	−4.04770	−	2.33694i	−0.188725	−	0.108960i
$461$			7.60141i			0.354033i	0.984208	+	0.177016i	$0.0566446\pi$
$461$			7.60141i			0.354033i	−0.984208	+	0.177016i	$0.943355\pi$
$462$	−2.47398	+	3.62326i	−0.115100	+	0.168570i
$463$		−	8.29441i		−	0.385474i	−0.981250	−	0.192737i	$-0.938264\pi$
$463$		−	8.29441i		−	0.385474i	0.981250	−	0.192737i	$-0.0617364\pi$
$464$	−8.23486	+	14.2632i	−0.382294	+	0.662152i
$465$	0.731880	+	1.26765i	0.0339401	+	0.0587860i
$466$	16.2250	−	9.36750i	0.751608	−	0.433941i
$467$	−8.83861	+	15.3089i	−0.409002	+	0.708413i	−0.994778	−	0.102060i	$-0.967456\pi$
$467$	−8.83861	+	15.3089i	−0.409002	+	0.708413i	0.585776	+	0.810473i	$0.300790\pi$
$468$	0.690495	+	0.568133i	0.0319181	+	0.0262620i
$469$	26.0608	+	17.7944i	1.20338	+	0.821670i
$470$		−	27.4415i		−	1.26578i
$471$	3.38549	−	5.86383i	0.155995	−	0.270191i
$472$	13.7021	+	23.7327i	0.630690	+	1.09239i
$473$	13.3355	−	7.69925i	0.613167	−	0.354012i
$474$	15.3953	+	8.88850i	0.707131	+	0.408262i
$475$		−	0.239872i		−	0.0110061i
$476$	0.548123	+	0.0414577i	0.0251232	+	0.00190021i
$477$	6.09673			0.279150
$478$	−1.63001	+	2.82326i	−0.0745548	+	0.129133i
$479$	−20.6163	+	11.9028i	−0.941983	+	0.543854i	−0.890581	−	0.454824i	$-0.849702\pi$
$479$	−20.6163	+	11.9028i	−0.941983	+	0.543854i	−0.0514018	+	0.998678i	$0.516369\pi$
$480$	1.59725	+	2.76651i	0.0729040	+	0.126273i
$481$	7.62247	+	20.3302i	0.347555	+	0.926977i
$482$	−37.9977			−1.73075
$483$	−9.43029	−	19.6169i	−0.429093	−	0.892601i
$484$	2.33877			0.106308
$485$	2.95112	−	5.11148i	0.134003	−	0.232101i
$486$	1.14630	−	0.661815i	0.0519971	−	0.0300206i
$487$	27.5548	−	15.9088i	1.24863	−	0.720895i	0.277791	−	0.960642i	$-0.410398\pi$
$487$	27.5548	−	15.9088i	1.24863	−	0.720895i	0.970835	+	0.239747i	$0.0770644\pi$
$488$	17.3443	+	10.0137i	0.785139	+	0.453300i
$489$			7.55723i			0.341750i
$490$	−20.9842	−	3.19258i	−0.947971	−	0.144226i
$491$	11.2923			0.509612			0.254806	−	0.966992i	$-0.417988\pi$
$491$	11.2923			0.509612			0.254806	+	0.966992i	$0.417988\pi$
$492$	0.106809	+	0.0616664i	0.00481534	+	0.00278014i
$493$	2.00400	+	3.47103i	0.0902555	+	0.156327i
$494$	−0.757667	+	4.55338i	−0.0340891	+	0.204866i
$495$	−1.43500	+	2.48549i	−0.0644983	+	0.111714i
$496$		−	2.19961i		−	0.0987655i
$497$	−26.0327	+	12.5145i	−1.16773	+	0.561352i
$498$	−2.37801			−0.106561
$499$	10.4789	+	6.05002i	0.469102	+	0.270836i	0.715864	−	0.698240i	$-0.246033\pi$
$499$	10.4789	+	6.05002i	0.469102	+	0.270836i	−0.246762	+	0.969076i	$0.579367\pi$
$500$	2.33807	−	1.34988i	0.104562	−	0.0603687i
$501$	−20.5121	+	11.8427i	−0.916414	+	0.529092i
$502$	17.8785	+	10.3222i	0.797957	+	0.460701i
$503$	13.0259			0.580797			0.290399	−	0.956906i	$-0.406212\pi$
$503$	13.0259			0.580797			0.290399	+	0.956906i	$0.406212\pi$
$504$	−0.593747	+	7.85007i	−0.0264476	+	0.349670i
$505$			1.38538i			0.0616485i
$506$	−6.82100	+	11.8143i	−0.303230	+	0.525211i
$507$	9.79551	−	8.54681i	0.435034	−	0.379577i
$508$	0.953127	+	1.65086i	0.0422882	+	0.0732452i
$509$	25.8869	+	14.9458i	1.14741	+	0.662460i	0.948256	−	0.317507i	$-0.102846\pi$
$509$	25.8869	+	14.9458i	1.14741	+	0.662460i	0.199159	+	0.979967i	$0.436179\pi$
$510$	−2.54026			−0.112485
$511$	7.68963	+	5.25050i	0.340169	+	0.232269i
$512$		−	25.2868i		−	1.11753i
$513$	−0.837638	−	0.483610i	−0.0369826	−	0.0213519i
$514$	−20.3631	+	11.7566i	−0.898178	+	0.518563i
$515$	5.78168	−	3.33806i	0.254771	−	0.147092i
$516$	1.52412	−	2.63985i	0.0670955	−	0.116213i
$517$	11.3378			0.498635
$518$	−11.8917	+	17.4160i	−0.522491	+	0.765214i
$519$	−12.4615			−0.546998
$520$	23.0128	−	8.62829i	1.00918	−	0.378376i
$521$	−17.9152	−	31.0301i	−0.784880	−	1.35945i	−0.929071	−	0.369902i	$-0.879391\pi$
$521$	−17.9152	−	31.0301i	−0.784880	−	1.35945i	0.144191	−	0.989550i	$-0.453942\pi$
$522$	−5.48417	+	3.16628i	−0.240035	+	0.138585i
$523$	−5.13696	+	8.89748i	−0.224624	+	0.389060i	−0.956207	−	0.292693i	$-0.905449\pi$
$523$	−5.13696	+	8.89748i	−0.224624	+	0.389060i	0.731583	+	0.681753i	$0.238782\pi$
$524$	−0.944509			−0.0412610
$525$	−0.654280	−	0.0494870i	−0.0285551	−	0.00215979i
$526$			26.2191i			1.14321i
$527$	−0.463573	−	0.267644i	−0.0201935	−	0.0116587i
$528$	3.73497	−	2.15639i	0.162544	−	0.0938447i
$529$	−22.3396	−	38.6933i	−0.971286	−	1.68232i
$530$	9.24338	−	16.0100i	0.401507	−	0.695430i
$531$			9.20987i			0.399674i
$532$	0.571982	−	0.274964i	0.0247986	−	0.0119212i
$533$	1.13926	−	1.38463i	0.0493468	−	0.0599748i
$534$	2.65624	−	4.60075i	0.114947	−	0.199094i
$535$	36.4165	−	21.0251i	1.57442	−	0.908994i
$536$	−17.7448	−	30.7350i	−0.766461	−	1.32755i
$537$	−2.02012	+	3.49895i	−0.0871746	+	0.150991i
$538$		−	18.4670i		−	0.796168i
$539$	1.31905	−	8.66987i	0.0568156	−	0.373438i
$540$			0.568133i			0.0244486i
$541$	−7.59484	−	4.38488i	−0.326528	−	0.188521i	0.327771	−	0.944757i	$-0.393703\pi$
$541$	−7.59484	−	4.38488i	−0.326528	−	0.188521i	−0.654298	+	0.756236i	$0.727036\pi$
$542$	−15.3688	−	26.6196i	−0.660148	−	1.14341i
$543$	−10.7535	−	18.6256i	−0.461476	−	0.799301i
$544$	−1.01170	−	0.584103i	−0.0433761	−	0.0250432i
$545$	28.6825			1.22862
$546$	12.2636	+	3.00602i	0.524833	+	0.128646i
$547$	11.0675			0.473211			0.236605	−	0.971606i	$-0.423965\pi$
$547$	11.0675			0.473211			0.236605	+	0.971606i	$0.423965\pi$
$548$	−2.57165	−	1.48474i	−0.109855	−	0.0634250i
$549$	3.36537	+	5.82899i	0.143630	+	0.248775i
$550$	0.205624	+	0.356151i	0.00876784	+	0.0151863i
$551$	4.00746	+	2.31371i	0.170724	+	0.0985673i
$552$			24.4788i			1.04189i
$553$	−35.4325	−	2.67997i	−1.50674	−	0.113964i
$554$		−	1.49966i		−	0.0637144i
$555$	−6.89761	+	11.9470i	−0.292787	+	0.507122i
$556$	0.222892	+	0.386061i	0.00945274	+	0.0163726i
$557$	−3.92633	+	2.26687i	−0.166364	+	0.0960503i	−0.580870	−	0.813996i	$-0.697288\pi$
$557$	−3.92633	+	2.26687i	−0.166364	+	0.0960503i	0.414506	+	0.910046i	$0.363954\pi$
$558$	0.422873	−	0.732437i	0.0179016	−	0.0310065i
$559$	−34.2217	−	28.1574i	−1.44742	−	1.19093i
$560$	17.2314	+	11.7656i	0.728158	+	0.497188i
$561$		−	1.04954i		−	0.0443115i
$562$	−11.4606	+	19.8503i	−0.483436	+	0.837336i
$563$	0.462613	+	0.801269i	0.0194968	+	0.0337694i	0.875609	−	0.483020i	$-0.160460\pi$
$563$	0.462613	+	0.801269i	0.0194968	+	0.0337694i	−0.856112	+	0.516790i	$0.827127\pi$
$564$	1.94369	−	1.12219i	0.0818443	−	0.0472528i
$565$	−16.4914	−	9.52134i	−0.693800	−	0.400566i
$566$		−	11.6043i		−	0.487764i
$567$	−1.49192	+	2.18499i	−0.0626547	+	0.0917610i
$568$	32.4847			1.36303
$569$	−0.456283	+	0.790306i	−0.0191284	+	0.0331314i	−0.875431	−	0.483343i	$-0.839422\pi$
$569$	−0.456283	+	0.790306i	−0.0191284	+	0.0331314i	0.856303	+	0.516474i	$0.172756\pi$
$570$	−2.53992	+	1.46642i	−0.106386	+	0.0614217i
$571$	−6.76211	−	11.7123i	−0.282986	−	0.490145i	0.689133	−	0.724635i	$-0.257992\pi$
$571$	−6.76211	−	11.7123i	−0.282986	−	0.490145i	−0.972119	+	0.234489i	$0.924658\pi$
$572$	0.393280	+	1.04893i	0.0164438	+	0.0438580i
$573$	−15.1652			−0.633537
$574$	1.73661	+	0.131350i	0.0724848	+	0.00548244i
$575$	−2.04024			−0.0850838
$576$	4.36537	−	7.56104i	0.181890	−	0.315043i
$577$	11.0442	−	6.37639i	0.459777	−	0.265453i	−0.252173	−	0.967682i	$-0.581145\pi$
$577$	11.0442	−	6.37639i	0.459777	−	0.265453i	0.711951	+	0.702230i	$0.247812\pi$
$578$	−18.6826	+	10.7864i	−0.777092	+	0.448654i
$579$	6.55063	+	3.78201i	0.272235	+	0.157175i
$580$		−	2.71809i		−	0.112862i
$581$	4.28401	−	2.05942i	0.177731	−	0.0854390i
$582$	−3.41025			−0.141359
$583$	6.61471	+	3.81901i	0.273953	+	0.158167i
$584$	−5.23588	−	9.06881i	−0.216662	−	0.375270i
$585$	8.14776	+	1.35576i	0.336868	+	0.0560538i
$586$	−1.85737	+	3.21706i	−0.0767273	+	0.132896i
$587$			10.9311i			0.451174i	0.974223	+	0.225587i	$0.0724300\pi$
$587$			10.9311i			0.451174i	−0.974223	+	0.225587i	$0.927570\pi$
$588$	−0.631997	−	1.61688i	−0.0260631	−	0.0666790i
$589$	−0.618014			−0.0254648
$590$	24.1851	+	13.9633i	0.995685	+	0.574859i
$591$	7.75567	−	4.47774i	0.319026	−	0.184189i
$592$	17.9529	−	10.3651i	0.737861	−	0.426004i
$593$	6.69180	+	3.86351i	0.274799	+	0.158655i	0.631067	−	0.775729i	$-0.282617\pi$
$593$	6.69180	+	3.86351i	0.274799	+	0.158655i	−0.356267	+	0.934384i	$0.615951\pi$
$594$	1.65825			0.0680389
$595$	4.57630	−	2.19993i	0.187610	−	0.0901883i
$596$			0.409858i			0.0167884i
$597$	−13.4626	+	23.3179i	−0.550988	+	0.954339i
$598$	38.7289	+	6.44437i	1.58374	+	0.263530i
$599$	15.2192	+	26.3605i	0.621841	+	1.07706i	0.989143	+	0.146959i	$0.0469484\pi$
$599$	15.2192	+	26.3605i	0.621841	+	1.07706i	−0.367301	+	0.930102i	$0.619718\pi$
$600$	0.639069	+	0.368966i	0.0260899	+	0.0150630i
$601$	−7.58975			−0.309592			−0.154796	−	0.987946i	$-0.549472\pi$
$601$	−7.58975			−0.309592			−0.154796	+	0.987946i	$0.549472\pi$
$602$	3.24638	−	42.9212i	0.132313	−	1.74934i
$603$		−	11.9272i		−	0.485713i
$604$	2.96602	+	1.71243i	0.120686	+	0.0696779i
$605$	18.7095	−	10.8019i	0.760648	−	0.439160i
$606$	0.693217	−	0.400229i	0.0281600	−	0.0162582i
$607$	7.89761	−	13.6791i	0.320554	−	0.555216i	−0.660048	−	0.751223i	$-0.729464\pi$
$607$	7.89761	−	13.6791i	0.320554	−	0.555216i	0.980602	+	0.196007i	$0.0627976\pi$
$608$	−1.34875			−0.0546989
$609$	7.13769	−	10.4535i	0.289234	−	0.423598i
$610$	20.4092			0.826345
$611$	−11.4553	−	30.5530i	−0.463434	−	1.23604i
$612$	−0.103881	−	0.179928i	−0.00419916	−	0.00727315i
$613$	27.1776	−	15.6910i	1.09769	−	0.633753i	0.162078	−	0.986778i	$-0.448180\pi$
$613$	27.1776	−	15.6910i	1.09769	−	0.633753i	0.935614	+	0.353025i	$0.114847\pi$
$614$	−10.1662	+	17.6085i	−0.410276	+	0.710620i
$615$	1.13926			0.0459394
$616$	−5.56150	+	8.14510i	−0.224079	+	0.328176i
$617$		−	5.98827i		−	0.241079i	−0.992709	−	0.120539i	$-0.961538\pi$
$617$		−	5.98827i		−	0.241079i	0.992709	−	0.120539i	$-0.0384624\pi$
$618$	−3.34060	−	1.92870i	−0.134379	−	0.0775835i
$619$	−38.6478	+	22.3133i	−1.55339	+	0.896848i	−0.555523	+	0.831501i	$0.687482\pi$
$619$	−38.6478	+	22.3133i	−1.55339	+	0.896848i	−0.997863	+	0.0653469i	$0.979185\pi$
$620$	0.181507	+	0.314379i	0.00728949	+	0.0126258i
$621$	−4.11337	+	7.12456i	−0.165064	+	0.285899i
$622$			41.2750i			1.65498i
$623$	−0.800882	+	10.5887i	−0.0320867	+	0.424226i
$624$	−9.58473	−	7.88624i	−0.383696	−	0.315702i
$625$	13.0893	−	22.6712i	0.523570	−	0.906850i
$626$	35.5802	−	20.5422i	1.42207	−	0.821032i
$627$	−0.605870	−	1.04940i	−0.0241961	−	0.0419089i
$628$	0.839604	−	1.45424i	0.0335038	−	0.0580303i
$629$		−	5.04482i		−	0.201150i
$630$	3.47585	+	7.23048i	0.138481	+	0.288069i
$631$			28.8824i			1.14979i	0.818227	+	0.574896i	$0.194957\pi$
$631$			28.8824i			1.14979i	−0.818227	+	0.574896i	$0.805043\pi$
$632$	34.6087	+	19.9814i	1.37666	+	0.794816i
$633$	−5.23337	−	9.06446i	−0.208008	−	0.360280i
$634$	−11.2414	−	19.4706i	−0.446452	−	0.773277i
$635$	15.2495	+	8.80429i	0.605157	+	0.349387i
$636$	1.51199			0.0599545
$637$	−24.6963	+	5.20521i	−0.978502	+	0.206238i
$638$	−7.93348			−0.314089
$639$	9.45467	+	5.45865i	0.374021	+	0.215941i
$640$	−10.0424	−	17.3939i	−0.396959	−	0.687553i
$641$	2.76326	+	4.78611i	0.109142	+	0.189040i	0.915423	−	0.402493i	$-0.131856\pi$
$641$	2.76326	+	4.78611i	0.109142	+	0.189040i	−0.806281	+	0.591533i	$0.798523\pi$
$642$	−21.0411	−	12.1481i	−0.830426	−	0.479447i
$643$		−	43.5581i		−	1.71776i	−0.512173	−	0.858882i	$-0.671159\pi$
$643$		−	43.5581i		−	1.71776i	0.512173	−	0.858882i	$-0.328841\pi$
$644$	−2.33872	−	4.86502i	−0.0921585	−	0.191709i
$645$		−	28.1574i		−	1.10869i
$646$	0.536262	−	0.928832i	0.0210989	−	0.0365444i
$647$	14.5237	+	25.1558i	0.570987	+	0.988978i	0.996465	+	0.0840092i	$0.0267725\pi$
$647$	14.5237	+	25.1558i	0.570987	+	0.988978i	−0.425478	+	0.904969i	$0.639894\pi$
$648$	2.57688	−	1.48776i	0.101229	−	0.0584448i
$649$	−5.76909	+	9.99236i	−0.226457	+	0.392234i
$650$	0.751999	−	0.913960i	0.0294958	−	0.0358485i
$651$	−0.127500	+	1.68571i	−0.00499712	+	0.0660682i
$652$			1.87420i			0.0733993i
$653$	5.49023	−	9.50936i	0.214849	−	0.372130i	−0.738377	−	0.674389i	$-0.764407\pi$
$653$	5.49023	−	9.50936i	0.214849	−	0.372130i	0.953226	+	0.302259i	$0.0977406\pi$
$654$	−8.28623	−	14.3522i	−0.324017	−	0.561214i
$655$	−7.55579	+	4.36234i	−0.295229	+	0.170451i
$656$	−1.48262	−	0.855990i	−0.0578865	−	0.0334208i
$657$		−	3.51930i		−	0.137301i
$658$	17.8713	−	26.1734i	0.696695	−	1.02035i
$659$	−12.5950			−0.490631			−0.245315	−	0.969443i	$-0.578892\pi$
$659$	−12.5950			−0.490631			−0.245315	+	0.969443i	$0.578892\pi$
$660$	−0.355880	+	0.616403i	−0.0138526	+	0.0239935i
$661$	−8.26553	+	4.77210i	−0.321492	+	0.185613i	−0.652057	−	0.758170i	$-0.726094\pi$
$661$	−8.26553	+	4.77210i	−0.321492	+	0.185613i	0.330566	+	0.943783i	$0.392761\pi$
$662$	−12.2287	−	21.1808i	−0.475284	−	0.823215i
$663$	−2.82829	+	1.06042i	−0.109842	+	0.0411834i
$664$	−5.34577			−0.207456
$665$	3.30573	−	4.84141i	0.128191	−	0.187742i
$666$	7.97074			0.308860
$667$	19.6793	−	34.0856i	0.761987	−	1.31980i
$668$	−5.08703	+	2.93700i	−0.196823	+	0.113636i
$669$	−21.3576	+	12.3308i	−0.825734	+	0.476738i
$670$	−31.3208	−	18.0831i	−1.21003	−	0.698611i
$671$			8.43230i			0.325525i
$672$	−0.278255	+	3.67888i	−0.0107339	+	0.141916i
$673$	16.3942			0.631951			0.315975	−	0.948767i	$-0.397668\pi$
$673$	16.3942			0.631951			0.315975	+	0.948767i	$0.397668\pi$
$674$	−25.3927	−	14.6605i	−0.978092	−	0.564702i
$675$	0.124000	+	0.214775i	0.00477278	+	0.00826670i
$676$	2.42930	−	2.11962i	0.0934345	−	0.0815237i
$677$	−8.39413	+	14.5391i	−0.322613	+	0.558781i	−0.981026	−	0.193875i	$-0.937894\pi$
$677$	−8.39413	+	14.5391i	−0.322613	+	0.558781i	0.658414	+	0.752656i	$0.271228\pi$
$678$			11.0027i			0.422555i
$679$	6.14360	−	2.95336i	0.235770	−	0.113340i
$680$	−5.71051			−0.218988
$681$	16.8133	+	9.70718i	0.644288	+	0.371980i
$682$	0.917602	−	0.529777i	0.0351368	−	0.0202862i
$683$	−36.3526	+	20.9882i	−1.39099	+	0.803090i	−0.993425	−	0.114483i	$-0.963479\pi$
$683$	−36.3526	+	20.9882i	−1.39099	+	0.803090i	−0.397567	+	0.917573i	$0.630145\pi$
$684$	−0.207735	−	0.119936i	−0.00794294	−	0.00458586i
$685$	−27.4299			−1.04804
$686$	−17.9354	−	16.7110i	−0.684775	−	0.638030i
$687$			13.9789i			0.533330i
$688$	−21.1562	+	36.6437i	−0.806573	+	1.39703i
$689$	3.60813	−	21.6839i	0.137459	−	0.826092i
$690$	12.4727	+	21.6034i	0.474829	+	0.822427i
$691$	−9.37221	−	5.41105i	−0.356536	−	0.205846i	0.311024	−	0.950402i	$-0.399328\pi$
$691$	−9.37221	−	5.41105i	−0.356536	−	0.205846i	−0.667560	+	0.744556i	$0.732661\pi$
$692$	−3.09046			−0.117481
$693$	−2.98736	+	1.43609i	−0.113480	+	0.0545525i
$694$		−	29.7558i		−	1.12951i
$695$	3.56615	+	2.05892i	0.135272	+	0.0780991i
$696$	−12.3284	+	7.11781i	−0.467307	+	0.269800i
$697$	−0.360803	+	0.208310i	−0.0136664	+	0.00789030i
$698$	7.87900	−	13.6468i	0.298225	−	0.516540i
$699$	14.1543			0.535363
$700$	−0.162262	−	0.0122728i	−0.00613293	−	0.000463869i
$701$	−11.3970			−0.430458			−0.215229	−	0.976564i	$-0.569050\pi$
$701$	−11.3970			−0.430458			−0.215229	+	0.976564i	$0.569050\pi$
$702$	−1.67545	−	4.46865i	−0.0632358	−	0.168658i
$703$	−2.91224	−	5.04415i	−0.109837	−	0.190244i
$704$	9.47251	−	5.46896i	0.357009	−	0.206119i
$705$	10.3660	−	17.9544i	0.390406	−	0.676203i
$706$	11.9182			0.448548
$707$	−0.902228	+	1.32136i	−0.0339318	+	0.0496948i
$708$			2.28406i			0.0858401i
$709$	−25.2537	−	14.5802i	−0.948422	−	0.547571i	−0.0558313	−	0.998440i	$-0.517781\pi$
$709$	−25.2537	−	14.5802i	−0.948422	−	0.547571i	−0.892590	+	0.450869i	$0.851114\pi$
$710$	28.6688	−	16.5520i	1.07592	−	0.621184i
$711$	6.71524	+	11.6311i	0.251841	+	0.436202i
$712$	5.97124	−	10.3425i	0.223782	−	0.387601i
$713$			5.25654i			0.196859i
$714$	−2.42287	−	1.65434i	−0.0906737	−	0.0619123i
$715$	7.99075	+	6.57473i	0.298837	+	0.245881i
$716$	−0.500992	+	0.867743i	−0.0187229	+	0.0324291i
$717$	−2.13296	+	1.23147i	−0.0796570	+	0.0459900i
$718$	−2.37600	−	4.11535i	−0.0886715	−	0.153584i
$719$	22.9555	−	39.7600i	0.856094	−	1.48280i	−0.0195321	−	0.999809i	$-0.506218\pi$
$719$	22.9555	−	39.7600i	0.856094	−	1.48280i	0.875626	−	0.482989i	$-0.160449\pi$
$720$		−	7.88624i		−	0.293903i
$721$	7.68842	+	0.581520i	0.286332	+	0.0216569i
$722$			23.9107i			0.889865i
$723$	−24.8611	−	14.3536i	−0.924596	−	0.533816i
$724$	−2.66688	−	4.61916i	−0.0991137	−	0.171670i
$725$	−0.593248	−	1.02754i	−0.0220327	−	0.0381617i
$726$	−10.8101	−	6.24124i	−0.401202	−	0.231634i
$727$	−29.2517			−1.08488			−0.542442	−	0.840093i	$-0.682500\pi$
$727$	−29.2517			−1.08488			−0.542442	+	0.840093i	$0.682500\pi$
$728$	27.5686	+	6.75754i	1.02176	+	0.250451i
$729$	1.00000			0.0370370
$730$	−9.24167	−	5.33568i	−0.342050	−	0.197482i
$731$	5.14848	+	8.91743i	0.190423	+	0.329823i
$732$	0.834614	+	1.44559i	0.0308482	+	0.0534307i
$733$	−12.5203	−	7.22859i	−0.462447	−	0.266994i	0.250625	−	0.968084i	$-0.419364\pi$
$733$	−12.5203	−	7.22859i	−0.462447	−	0.266994i	−0.713073	+	0.701090i	$0.752697\pi$
$734$		−	8.45438i		−	0.312057i
$735$	−12.5236	−	10.0156i	−0.461939	−	0.369431i
$736$			11.4718i			0.422857i
$737$	7.47124	−	12.9406i	0.275207	−	0.476672i
$738$	−0.329126	−	0.570063i	−0.0121153	−	0.0209843i
$739$	−26.7818	+	15.4625i	−0.985183	+	0.568796i	−0.903831	−	0.427890i	$-0.859257\pi$
$739$	−26.7818	+	15.4625i	−0.985183	+	0.568796i	−0.0813521	+	0.996685i	$0.525924\pi$
$740$	−1.71061	+	2.96287i	−0.0628834	+	0.108917i
$741$	−2.21576	+	2.69298i	−0.0813979	+	0.0989289i
$742$	19.2427	−	9.25041i	0.706424	−	0.339593i
$743$			43.9023i			1.61062i	0.592855	+	0.805309i	$0.298001\pi$
$743$			43.9023i			1.61062i	−0.592855	+	0.805309i	$0.701999\pi$
$744$	0.950619	−	1.64652i	0.0348514	−	0.0603643i
$745$	1.89298	+	3.27874i	0.0693535	+	0.120124i
$746$	−10.5133	+	6.06984i	−0.384918	+	0.222233i
$747$	−1.55588	−	0.898290i	−0.0569268	−	0.0328667i
$748$		−	0.260286i		−	0.00951701i
$749$	48.4263	+	3.66276i	1.76946	+	0.133834i
$750$	−14.4092			−0.526150
$751$	−26.7806	+	46.3853i	−0.977237	+	1.69262i	−0.304893	+	0.952387i	$0.598621\pi$
$751$	−26.7806	+	46.3853i	−0.977237	+	1.69262i	−0.672345	+	0.740238i	$0.734713\pi$
$752$	−26.9804	+	15.5771i	−0.983873	+	0.568039i
$753$	7.79837	+	13.5072i	0.284189	+	0.492229i
$754$	8.01575	+	21.3791i	0.291917	+	0.778581i
$755$	31.6364			1.15137
$756$	−0.369997	+	0.541880i	−0.0134567	+	0.0197080i
$757$	−1.27329			−0.0462784			−0.0231392	−	0.999732i	$-0.507366\pi$
$757$	−1.27329			−0.0462784			−0.0231392	+	0.999732i	$0.507366\pi$
$758$	14.6839	−	25.4332i	0.533342	−	0.923775i
$759$	−8.92569	+	5.15325i	−0.323982	+	0.187051i
$760$	−5.70974	+	3.29652i	−0.207114	+	0.119577i
$761$	1.90804	+	1.10161i	0.0691664	+	0.0399332i	0.534184	−	0.845368i	$-0.320619\pi$
$761$	1.90804	+	1.10161i	0.0691664	+	0.0399332i	−0.465018	+	0.885301i	$0.653952\pi$
$762$		−	10.1741i		−	0.368567i
$763$	27.3571	+	18.6795i	0.990392	+	0.676243i
$764$	−3.76099			−0.136068
$765$	−1.66204	−	0.959580i	−0.0600912	−	0.0346937i
$766$	19.3054	+	33.4379i	0.697531	+	1.20816i
$767$	32.7563	+	5.45054i	1.18276	+	0.196808i
$768$	2.92836	−	5.07207i	0.105668	−	0.183023i
$769$		−	0.955106i		−	0.0344420i	−0.999852	−	0.0172210i	$-0.994518\pi$
$769$		−	0.955106i		−	0.0344420i	0.999852	−	0.0172210i	$-0.00548189\pi$
$770$	−0.758028	+	10.0221i	−0.0273174	+	0.361171i
$771$	−17.7642			−0.639763
$772$	1.62456	+	0.937942i	0.0584693	+	0.0337573i
$773$	−18.5051	+	10.6839i	−0.665583	+	0.384275i	−0.794401	−	0.607394i	$-0.792215\pi$
$773$	−18.5051	+	10.6839i	−0.665583	+	0.384275i	0.128818	+	0.991668i	$0.458882\pi$
$774$	−14.0894	+	8.13452i	−0.506433	+	0.292389i
$775$	0.137232	+	0.0792312i	0.00492954	+	0.00284607i
$776$	−7.66625			−0.275202
$777$	−14.3594	+	6.90286i	−0.515139	+	0.247639i
$778$			10.6493i			0.381796i
$779$	−0.240503	+	0.416564i	−0.00861692	+	0.0149250i
$780$	2.02065	+	0.336230i	0.0723509	+	0.0120390i
$781$	6.83863	+	11.8449i	0.244706	+	0.423842i
$782$	−7.90022	−	4.56120i	−0.282511	−	0.163108i
$783$	−4.78424			−0.170975
$784$	8.77272	+	22.4439i	0.313312	+	0.801566i
$785$		−	15.5113i		−	0.553622i
$786$	4.36566	+	2.52052i	0.155718	+	0.0899038i
$787$	−10.2660	+	5.92705i	−0.365942	+	0.211276i	−0.671684	−	0.740838i	$-0.734429\pi$
$787$	−10.2660	+	5.92705i	−0.365942	+	0.211276i	0.305742	+	0.952114i	$0.401095\pi$
$788$	1.92341	−	1.11048i	0.0685188	−	0.0395593i
$789$	−9.90424	+	17.1547i	−0.352600	+	0.610722i
$790$	40.7245			1.44891
$791$	−9.52859	−	19.8214i	−0.338798	−	0.704768i
$792$	3.72775			0.132460
$793$	22.7233	−	8.51975i	0.806929	−	0.302545i
$794$	8.82861	+	15.2916i	0.313316	+	0.542678i
$795$	12.0955	−	6.98335i	0.428984	−	0.247674i
$796$	−3.33874	+	5.78287i	−0.118339	+	0.204968i
$797$	−41.6422			−1.47504			−0.737522	−	0.675324i	$-0.764004\pi$
$797$	−41.6422			−1.47504			−0.737522	+	0.675324i	$0.764004\pi$
$798$	−3.37756	−	0.255464i	−0.119564	−	0.00904334i
$799$			7.58155i			0.268216i
$800$	0.299495	+	0.172913i	0.0105887	+	0.00611341i
$801$	3.47585	−	2.00678i	0.122813	−	0.0709063i
$802$	19.6325	+	34.0044i	0.693247	+	1.20074i
$803$	2.20450	−	3.81830i	0.0777951	−	0.134745i
$804$		−	2.95796i		−	0.104319i
$805$	−41.1788	−	28.1170i	−1.45136	−	0.990995i
$806$	−2.35476	−	1.93748i	−0.0829429	−	0.0682447i
$807$	6.97588	−	12.0826i	0.245563	−	0.425327i
$808$	1.55835	−	0.899715i	0.0548226	−	0.0316519i
$809$	7.24085	+	12.5415i	0.254575	+	0.440936i	0.964780	−	0.263059i	$-0.0847312\pi$
$809$	7.24085	+	12.5415i	0.254575	+	0.440936i	−0.710205	+	0.703995i	$0.751398\pi$
$810$	1.51612	−	2.62600i	0.0532711	−	0.0922682i
$811$			50.6606i			1.77893i	0.457000	+	0.889467i	$0.348924\pi$
$811$			50.6606i			1.77893i	−0.457000	+	0.889467i	$0.651076\pi$
$812$	1.77016	−	2.59248i	0.0621203	−	0.0909783i
$813$		−	23.2222i		−	0.814440i
$814$	8.64794	+	4.99289i	0.303110	+	0.175001i
$815$	8.65624	+	14.9931i	0.303215	+	0.525184i
$816$	1.44197	+	2.49757i	0.0504792	+	0.0874325i
$817$	10.2956	+	5.94416i	0.360197	+	0.207960i
$818$	49.1872			1.71979
$819$	6.88830	+	6.59934i	0.240697	+	0.230600i
$820$	0.282537			0.00986663
$821$	26.4488	+	15.2702i	0.923068	+	0.532933i	0.884613	−	0.466327i	$-0.154423\pi$
$821$	26.4488	+	15.2702i	0.923068	+	0.532933i	0.0384554	+	0.999260i	$0.487756\pi$
$822$	7.92436	+	13.7254i	0.276394	+	0.478728i
$823$	−7.69946	−	13.3359i	−0.268386	−	0.464859i	0.700059	−	0.714085i	$-0.253157\pi$
$823$	−7.69946	−	13.3359i	−0.268386	−	0.464859i	−0.968445	+	0.249226i	$0.919824\pi$
$824$	−7.50967	−	4.33571i	−0.261612	−	0.151042i
$825$			0.310697i			0.0108171i
$826$	13.9739	+	29.0686i	0.486215	+	1.01143i
$827$			29.3134i			1.01933i	0.860373	+	0.509664i	$0.170230\pi$
$827$			29.3134i			1.01933i	−0.860373	+	0.509664i	$0.829770\pi$
$828$	−1.02012	+	1.76690i	−0.0354516	+	0.0614040i
$829$	12.4144	+	21.5023i	0.431168	+	0.746806i	0.996974	−	0.0777329i	$-0.0247681\pi$
$829$	12.4144	+	21.5023i	0.431168	+	0.746806i	−0.565806	+	0.824539i	$0.691435\pi$
$830$	−4.71782	+	2.72383i	−0.163758	+	0.0945456i
$831$	0.566494	−	0.981196i	0.0196515	−	0.0340373i
$832$	−24.3085	−	20.0008i	−0.842744	−	0.693403i
$833$	5.79753	+	0.882048i	0.200873	+	0.0305612i
$834$		−	2.37924i		−	0.0823864i
$835$	−27.1298	+	46.9902i	−0.938867	+	1.62616i
$836$	−0.150256	−	0.260252i	−0.00519672	−	0.00900099i
$837$	0.553355	−	0.319479i	0.0191267	−	0.0110428i
$838$	−36.8142	−	21.2547i	−1.27172	−	0.734230i
$839$			27.9921i			0.966395i	0.875511	+	0.483197i	$0.160525\pi$
$839$			27.9921i			0.966395i	−0.875511	+	0.483197i	$0.839475\pi$
$840$	7.81372	+	16.2541i	0.269599	+	0.560821i
$841$	−6.11104			−0.210725
$842$	−18.6697	+	32.3369i	−0.643401	+	1.11440i
$843$	−14.9969	+	8.65846i	−0.516520	+	0.298213i
$844$	−1.29788	−	2.24800i	−0.0446749	−	0.0773792i
$845$	9.64393	−	28.1764i	0.331761	−	0.969296i
$846$	−11.9787			−0.411837
$847$	24.8796	+	1.88179i	0.854874	+	0.0646591i
$848$	−20.9879			−0.720729
$849$	4.38350	−	7.59244i	0.150441	−	0.260572i
$850$	−0.238158	+	0.137501i	−0.00816875	+	0.00471623i
$851$	−42.9032	+	24.7702i	−1.47070	+	0.849111i
$852$	2.34477	+	1.35375i	0.0803304	+	0.0463788i
$853$		−	47.8337i		−	1.63779i	−0.573941	−	0.818897i	$-0.694586\pi$
$853$		−	47.8337i		−	1.63779i	0.573941	−	0.818897i	$-0.305414\pi$
$854$	19.4661	+	13.2915i	0.666116	+	0.454826i
$855$	−2.21576			−0.0757774
$856$	−47.3004	−	27.3089i	−1.61670	−	0.933400i
$857$	27.6742	+	47.9331i	0.945333	+	1.63736i	0.755084	+	0.655628i	$0.227596\pi$
$857$	27.6742	+	47.9331i	0.945333	+	1.63736i	0.190249	+	0.981736i	$0.439071\pi$
$858$	0.981379	−	5.89782i	0.0335037	−	0.201348i
$859$	10.1960	−	17.6599i	0.347882	−	0.602549i	−0.637991	−	0.770044i	$-0.720234\pi$
$859$	10.1960	−	17.6599i	0.347882	−	0.602549i	0.985873	+	0.167495i	$0.0535677\pi$
$860$		−	6.98305i		−	0.238120i
$861$	1.08661	+	0.741943i	0.0370317	+	0.0252853i
$862$	−19.2832			−0.656789
$863$	42.6737	+	24.6377i	1.45263	+	0.838677i	0.998630	−	0.0523251i	$-0.0166632\pi$
$863$	42.6737	+	24.6377i	1.45263	+	0.838677i	0.454000	+	0.891002i	$0.349997\pi$
$864$	1.20763	−	0.697228i	0.0410846	−	0.0237202i
$865$	−24.7227	+	14.2737i	−0.840599	+	0.485320i
$866$	9.15661	+	5.28657i	0.311154	+	0.179645i
$867$	−16.2982			−0.553515
$868$	−0.0316202	+	0.418058i	−0.00107326	+	0.0141898i
$869$			16.8258i			0.570775i
$870$	−7.25349	+	12.5634i	−0.245916	+	0.425940i
$871$	−42.4209	−	7.05870i	−1.43738	−	0.239175i
$872$	−18.6275	−	32.2637i	−0.630805	−	1.09259i
$873$	−2.23126	−	1.28822i	−0.0755167	−	0.0435996i
$874$	−10.5322			−0.356258
$875$	25.9583	−	12.4787i	0.877552	−	0.421859i
$876$		−	0.872789i		−	0.0294888i
$877$	35.7681	+	20.6507i	1.20780	+	0.697326i	0.962279	−	0.272064i	$-0.0877063\pi$
$877$	35.7681	+	20.6507i	1.20780	+	0.697326i	0.245525	+	0.969390i	$0.421040\pi$
$878$	10.8918	−	6.28837i	0.367580	−	0.212222i
$879$	−2.43048	+	1.40324i	−0.0819781	+	0.0473301i
$880$	4.93996	−	8.55627i	0.166526	−	0.288432i
$881$	−44.2487			−1.49078			−0.745388	−	0.666631i	$-0.767736\pi$
$881$	−44.2487			−1.49078			−0.745388	+	0.666631i	$0.767736\pi$
$882$	−1.39362	+	9.16001i	−0.0469257	+	0.308434i
$883$	−34.0974			−1.14747			−0.573735	−	0.819041i	$-0.694506\pi$
$883$	−34.0974			−1.14747			−0.573735	+	0.819041i	$0.694506\pi$
$884$	−0.701419	+	0.262986i	−0.0235913	+	0.00884516i
$885$	10.5492	+	18.2718i	0.354608	+	0.614200i
$886$	7.71423	−	4.45382i	0.259165	−	0.149629i
$887$	17.5803	−	30.4500i	0.590289	−	1.02241i	−0.403904	−	0.914801i	$-0.632347\pi$
$887$	17.5803	−	30.4500i	0.590289	−	1.02241i	0.994193	−	0.107610i	$-0.0343197\pi$
$888$	17.9182			0.601296
$889$	8.81099	+	18.3287i	0.295511	+	0.614723i
$890$		−	12.1701i		−	0.407943i
$891$	1.08496	+	0.626403i	0.0363476	+	0.0209853i
$892$	−5.29671	+	3.05806i	−0.177347	+	0.102391i
$893$	4.37663	+	7.58054i	0.146458	+	0.253673i
$894$	1.09375	−	1.89442i	0.0365804	−	0.0633590i
$895$			9.25559i			0.309380i
$896$	1.74947	−	23.1302i	0.0584457	−	0.772725i
$897$	22.9052	+	18.8462i	0.764783	+	0.629257i
$898$	5.59926	−	9.69820i	0.186850	−	0.323633i
$899$	−2.64738	+	1.52847i	−0.0882951	+	0.0509772i
$900$	0.0307522	+	0.0532644i	0.00102507	+	0.00177548i
$901$	−2.55377	+	4.42325i	−0.0850782	+	0.147360i
$902$		−	0.824662i		−	0.0274583i
$903$	18.3375	−	26.8562i	0.610233	−	0.893718i
$904$			24.7340i			0.822641i
$905$	−42.6685	−	24.6346i	−1.41835	−	0.818883i
$906$	−9.13960	−	15.8303i	−0.303643	−	0.525925i
$907$	−1.31015	−	2.26925i	−0.0435030	−	0.0753493i	0.843454	−	0.537201i	$-0.180518\pi$
$907$	−1.31015	−	2.26925i	−0.0435030	−	0.0753493i	−0.886957	+	0.461852i	$0.847185\pi$
$908$	4.16972	+	2.40739i	0.138377	+	0.0798921i
$909$	0.604744			0.0200581
$910$	27.7734	−	8.08328i	0.920678	−	0.267958i
$911$	−54.3726			−1.80145			−0.900723	−	0.434394i	$-0.856963\pi$
$911$	−54.3726			−1.80145			−0.900723	+	0.434394i	$0.856963\pi$
$912$	2.88356	+	1.66483i	0.0954843	+	0.0551279i
$913$	−1.12538	−	1.94922i	−0.0372447	−	0.0645098i
$914$	11.7469	+	20.3462i	0.388552	+	0.672992i
$915$	13.3533	+	7.70955i	0.441448	+	0.254870i
$916$			3.46679i			0.114546i
$917$	−10.0476	−	0.759959i	−0.331801	−	0.0250961i
$918$			1.10887i			0.0365982i
$919$	6.25686	−	10.8372i	0.206395	−	0.357486i	−0.744181	−	0.667978i	$-0.767160\pi$
$919$	6.25686	−	10.8372i	0.206395	−	0.357486i	0.950576	+	0.310491i	$0.100494\pi$
$920$	28.0387	+	48.5645i	0.924409	+	1.60112i
$921$	−13.3031	+	7.68058i	−0.438354	+	0.253084i
$922$	5.03073	−	8.71348i	0.165678	−	0.286963i
$923$	25.0099	−	30.3964i	0.823212	−	1.00051i
$924$	−0.740868	+	0.356151i	−0.0243728	+	0.0117165i
$925$			1.49343i			0.0491037i
$926$	−5.48937	+	9.50786i	−0.180392	+	0.312448i
$927$	−1.45712	−	2.52381i	−0.0478583	−	0.0828929i
$928$	−5.77762	+	3.33571i	−0.189660	+	0.109500i
$929$	7.02497	+	4.05587i	0.230482	+	0.133069i	0.610794	−	0.791789i	$-0.290850\pi$
$929$	7.02497	+	4.05587i	0.230482	+	0.133069i	−0.380312	+	0.924858i	$0.624184\pi$
$930$		−	1.93748i		−	0.0635324i
$931$	6.30594	−	2.46483i	0.206669	−	0.0807815i
$932$	3.51027			0.114983
$933$	−15.5916	+	27.0054i	−0.510445	+	0.884117i
$934$	20.2634	−	11.6991i	0.663038	−	0.382805i
$935$	−1.20217	−	2.08221i	−0.0393151	−	0.0680957i
$936$	−3.76641	−	10.0455i	−0.123109	−	0.328349i
$937$	−34.3454			−1.12202			−0.561008	−	0.827810i	$-0.689586\pi$
$937$	−34.3454			−1.12202			−0.561008	+	0.827810i	$0.689586\pi$
$938$	−18.0969	−	37.6452i	−0.590883	−	1.22916i
$939$	31.0392			1.01293
$940$	2.57078	−	4.45272i	0.0838495	−	0.145232i
$941$	35.6780	−	20.5987i	1.16307	−	0.671498i	0.211031	−	0.977479i	$-0.432318\pi$
$941$	35.6780	−	20.5987i	1.16307	−	0.671498i	0.952037	+	0.305982i	$0.0989847\pi$
$942$	−7.76155	+	4.48113i	−0.252885	+	0.146003i
$943$	3.54310	+	2.04561i	0.115379	+	0.0666143i
$944$		−	31.7049i		−	1.03191i
$945$	−0.457125	+	6.04376i	−0.0148703	+	0.196604i
$946$	−20.3819			−0.662674
$947$	13.8215	+	7.97984i	0.449138	+	0.259310i	0.707466	−	0.706747i	$-0.249838\pi$
$947$	13.8215	+	7.97984i	0.449138	+	0.259310i	−0.258328	+	0.966057i	$0.583172\pi$
$948$	1.66539	+	2.88453i	0.0540892	+	0.0936853i
$949$	−12.5169	−	2.08277i	−0.406316	−	0.0676097i
$950$	−0.158751	+	0.274964i	−0.00515056	+	0.00892102i
$951$		−	16.9856i		−	0.550797i
$952$	−5.44662	−	3.71897i	−0.176526	−	0.120532i
$953$	20.4528			0.662531			0.331265	−	0.943538i	$-0.392524\pi$
$953$	20.4528			0.662531			0.331265	+	0.943538i	$0.392524\pi$
$954$	−6.98867	−	4.03491i	−0.226266	−	0.130635i
$955$	−30.0868	+	17.3706i	−0.973587	+	0.562101i
$956$	−0.528977	+	0.305405i	−0.0171083	+	0.00987751i
$957$	−5.19072	−	2.99686i	−0.167792	−	0.0968748i
$958$	31.5099			1.01804
$959$	−26.1624	−	17.8637i	−0.844827	−	0.576850i
$960$		−	20.0008i		−	0.645523i
$961$	−15.2959	+	26.4932i	−0.493415	+	0.854620i
$962$	4.71720	−	28.3491i	0.152089	−	0.914012i
$963$	−9.17785	−	15.8965i	−0.295752	−	0.512258i
$964$	−6.16559	−	3.55970i	−0.198580	−	0.114650i
$965$	17.3280			0.557810
$966$	−2.17286	+	28.7280i	−0.0699107	+	0.924307i
$967$		−	33.3886i		−	1.07371i	−0.843676	−	0.536853i	$-0.819613\pi$
$967$		−	33.3886i		−	1.07371i	0.843676	−	0.536853i	$-0.180387\pi$
$968$	−24.3012	−	14.0303i	−0.781070	−	0.450951i
$969$	0.701731	−	0.405144i	0.0225428	−	0.0130151i
$970$	−6.76572	+	3.90619i	−0.217234	+	0.125420i
$971$	−1.85411	+	3.21141i	−0.0595011	+	0.103059i	−0.894242	−	0.447585i	$-0.852284\pi$
$971$	−1.85411	+	3.21141i	−0.0595011	+	0.103059i	0.834740	+	0.550644i	$0.185618\pi$
$972$	0.248001			0.00795464
$973$	2.06048	+	4.28623i	0.0660561	+	0.137410i
$974$	−42.1147			−1.34944
$975$	0.837265	−	0.313919i	0.0268139	−	0.0100535i
$976$	−11.5853	−	20.0662i	−0.370835	−	0.642305i
$977$	39.0033	−	22.5186i	1.24783	−	0.720433i	0.277152	−	0.960826i	$-0.410610\pi$
$977$	39.0033	−	22.5186i	1.24783	−	0.720433i	0.970676	+	0.240393i	$0.0772762\pi$
$978$	5.00149	−	8.66283i	0.159930	−	0.277007i
$979$	5.02822			0.160703
$980$	−3.10586	−	2.48388i	−0.0992129	−	0.0793446i
$981$		−	12.5205i		−	0.399747i
$982$	−12.9443	−	7.47339i	−0.413069	−	0.238486i
$983$	11.8258	−	6.82762i	0.377184	−	0.217767i	−0.299408	−	0.954125i	$-0.596789\pi$
$983$	11.8258	−	6.82762i	0.377184	−	0.217767i	0.676592	+	0.736358i	$0.263456\pi$
$984$	−0.739876	−	1.28150i	−0.0235864	−	0.0408528i
$985$	10.2578	−	17.7671i	0.326842	−	0.566106i
$986$		−	5.30511i		−	0.168949i
$987$	21.5798	−	10.3739i	0.686893	−	0.330204i
$988$	−0.549510	+	0.667861i	−0.0174823	+	0.0212475i
$989$	50.5583	−	87.5695i	1.60766	−	2.78455i
$990$	3.28987	−	1.89941i	0.104559	−	0.0603671i
$991$	0.235985	+	0.408739i	0.00749633	+	0.0129840i	0.869749	−	0.493494i	$-0.164280\pi$
$991$	0.235985	+	0.408739i	0.00749633	+	0.0129840i	−0.862253	+	0.506478i	$0.830947\pi$
$992$	0.445500	−	0.771629i	0.0141446	−	0.0244992i
$993$		−	18.4776i		−	0.586368i
$994$	38.1235	+	2.88350i	1.20920	+	0.0914591i
$995$			61.6817i			1.95544i
$996$	−0.385861	−	0.222777i	−0.0122265	−	0.00705895i
$997$	17.7705	+	30.7793i	0.562796	+	0.974791i	0.997251	+	0.0740975i	$0.0236076\pi$
$997$	17.7705	+	30.7793i	0.562796	+	0.974791i	−0.434455	+	0.900693i	$0.643059\pi$
$998$	−8.00800	−	13.8703i	−0.253489	−	0.439055i
$999$	5.21509	+	3.01094i	0.164998	+	0.0952618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.c.142.3	yes	16
3.2	odd	2		819.2.dl.f.415.6		16
7.2	even	3		1911.2.c.n.883.6		8
7.4	even	3	inner	273.2.bj.c.25.6	yes	16
7.5	odd	6		1911.2.c.k.883.6		8
13.12	even	2	inner	273.2.bj.c.142.6	yes	16
21.11	odd	6		819.2.dl.f.298.3		16
39.38	odd	2		819.2.dl.f.415.3		16
91.12	odd	6		1911.2.c.k.883.3		8
91.25	even	6	inner	273.2.bj.c.25.3	✓	16
91.51	even	6		1911.2.c.n.883.3		8
273.116	odd	6		819.2.dl.f.298.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.c.25.3	✓	16	91.25	even	6	inner
273.2.bj.c.25.6	yes	16	7.4	even	3	inner
273.2.bj.c.142.3	yes	16	1.1	even	1	trivial
273.2.bj.c.142.6	yes	16	13.12	even	2	inner
819.2.dl.f.298.3		16	21.11	odd	6
819.2.dl.f.298.6		16	273.116	odd	6
819.2.dl.f.415.3		16	39.38	odd	2
819.2.dl.f.415.6		16	3.2	odd	2
1911.2.c.k.883.3		8	91.12	odd	6
1911.2.c.k.883.6		8	7.5	odd	6
1911.2.c.n.883.3		8	91.51	even	6
1911.2.c.n.883.6		8	7.2	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14630 - 0.661815i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.124000 - 0.214775i) q^{4} +(-1.98394 - 1.14543i) q^{5} +1.32363i q^{6} +(-1.14630 - 2.38453i) q^{7} +2.97552i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.14630 - 0.661815i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.124000 - 0.214775i) q^{4} +(-1.98394 - 1.14543i) q^{5} +1.32363i q^{6} +(-1.14630 - 2.38453i) q^{7} +2.97552i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.51612 + 2.62600i) q^{10} +(-1.08496 + 0.626403i) q^{11} +(-0.124000 + 0.214775i) q^{12} +(2.78424 + 2.29085i) q^{13} +(-0.264122 + 3.49202i) q^{14} +2.29085i q^{15} +(1.72125 - 2.98129i) q^{16} +(-0.418875 - 0.725512i) q^{17} +(1.14630 - 0.661815i) q^{18} +(-0.837638 - 0.483610i) q^{19} +0.568133i q^{20} +(-1.49192 + 2.18499i) q^{21} +1.65825 q^{22} +(-4.11337 + 7.12456i) q^{23} +(2.57688 - 1.48776i) q^{24} +(0.124000 + 0.214775i) q^{25} +(-1.67545 - 4.46865i) q^{26} +1.00000 q^{27} +(-0.369997 + 0.541880i) q^{28} -4.78424 q^{29} +(1.51612 - 2.62600i) q^{30} +(0.553355 - 0.319479i) q^{31} +(1.20763 - 0.697228i) q^{32} +(1.08496 + 0.626403i) q^{33} +1.10887i q^{34} +(-0.457125 + 6.04376i) q^{35} +0.248001 q^{36} +(5.21509 + 3.01094i) q^{37} +(0.640122 + 1.10872i) q^{38} +(0.591815 - 3.55665i) q^{39} +(3.40824 - 5.90325i) q^{40} -0.497308i q^{41} +(3.15624 - 1.51728i) q^{42} -12.2912 q^{43} +(0.269072 + 0.155349i) q^{44} +(1.98394 - 1.14543i) q^{45} +(9.43029 - 5.44458i) q^{46} +(-7.83745 - 4.52495i) q^{47} -3.44249 q^{48} +(-4.37200 + 5.46677i) q^{49} -0.328262i q^{50} +(-0.418875 + 0.725512i) q^{51} +(0.146771 - 0.882053i) q^{52} +(-3.04836 - 5.27992i) q^{53} +(-1.14630 - 0.661815i) q^{54} +2.86999 q^{55} +(7.09524 - 3.41084i) q^{56} +0.967221i q^{57} +(5.48417 + 3.16628i) q^{58} +(7.97598 - 4.60494i) q^{59} +(0.492018 - 0.284067i) q^{60} +(3.36537 - 5.82899i) q^{61} -0.845746 q^{62} +(2.63822 + 0.199544i) q^{63} -8.73073 q^{64} +(-2.89975 - 7.73404i) q^{65} +(-0.829126 - 1.43609i) q^{66} +(-10.3293 + 5.96360i) q^{67} +(-0.103881 + 0.179928i) q^{68} +8.22673 q^{69} +(4.52386 - 6.62542i) q^{70} -10.9173i q^{71} +(-2.57688 - 1.48776i) q^{72} +(-3.04780 + 1.75965i) q^{73} +(-3.98537 - 6.90286i) q^{74} +(0.124000 - 0.214775i) q^{75} +0.239872i q^{76} +(2.73737 + 1.86908i) q^{77} +(-3.03224 + 3.68531i) q^{78} +(6.71524 - 11.6311i) q^{79} +(-6.82969 + 3.94312i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.329126 + 0.570063i) q^{82} +1.79658i q^{83} +(0.654280 + 0.0494870i) q^{84} +1.91916i q^{85} +(14.0894 + 8.13452i) q^{86} +(2.39212 + 4.14327i) q^{87} +(-1.86388 - 3.22833i) q^{88} +(-3.47585 - 2.00678i) q^{89} -3.03224 q^{90} +(2.27104 - 9.26512i) q^{91} +2.04024 q^{92} +(-0.553355 - 0.319479i) q^{93} +(5.98937 + 10.3739i) q^{94} +(1.10788 + 1.91890i) q^{95} +(-1.20763 - 0.697228i) q^{96} +2.57644i q^{97} +(8.62961 - 3.37309i) q^{98} -1.25281i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9	\( 16 q - 8 q^{3} + 6 q^{4} - 8 q^{9} - 4 q^{10} + 6 q^{12} + 4 q^{13} + 40 q^{14} - 10 q^{16} - 8 q^{17} - 8 q^{22} - 8 q^{23} - 6 q^{25} - 4 q^{26} + 16 q^{27} - 36 q^{29} - 4 q^{30} - 14 q^{35} - 12 q^{36} - 26 q^{38} - 2 q^{39} + 6 q^{40} - 14 q^{42} + 32 q^{43} + 20 q^{48} - 46 q^{49} - 8 q^{51} + 40 q^{52} + 36 q^{53} - 8 q^{55} + 54 q^{56} + 12 q^{61} - 80 q^{62} - 56 q^{64} + 34 q^{65} + 4 q^{66} + 10 q^{68} + 16 q^{69} + 18 q^{74} - 6 q^{75} - 22 q^{77} + 8 q^{78} + 8 q^{79} - 8 q^{81} + 12 q^{82} + 18 q^{87} - 98 q^{88} + 8 q^{90} + 16 q^{91} + 40 q^{92} + 46 q^{94} + 38 q^{95}+O(q^{100}) \) 16 * q - 8 * q^3 + 6 * q^4 - 8 * q^9 - 4 * q^10 + 6 * q^12 + 4 * q^13 + 40 * q^14 - 10 * q^16 - 8 * q^17 - 8 * q^22 - 8 * q^23 - 6 * q^25 - 4 * q^26 + 16 * q^27 - 36 * q^29 - 4 * q^30 - 14 * q^35 - 12 * q^36 - 26 * q^38 - 2 * q^39 + 6 * q^40 - 14 * q^42 + 32 * q^43 + 20 * q^48 - 46 * q^49 - 8 * q^51 + 40 * q^52 + 36 * q^53 - 8 * q^55 + 54 * q^56 + 12 * q^61 - 80 * q^62 - 56 * q^64 + 34 * q^65 + 4 * q^66 + 10 * q^68 + 16 * q^69 + 18 * q^74 - 6 * q^75 - 22 * q^77 + 8 * q^78 + 8 * q^79 - 8 * q^81 + 12 * q^82 + 18 * q^87 - 98 * q^88 + 8 * q^90 + 16 * q^91 + 40 * q^92 + 46 * q^94 + 38 * q^95

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