LMFDB - Embedded newform 770.2.o.a.439.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.6
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.781614 - 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.438635 - 2.19262i) q^{5} +1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.781614 - 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.438635 - 2.19262i) q^{5} +1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +(2.11819 + 0.716443i) q^{10} +(-2.06350 - 2.59653i) q^{11} +(-0.781614 + 1.35379i) q^{12} -2.41576i q^{13} +(-1.84086 - 1.90033i) q^{14} +(-2.62552 + 2.30761i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.35472 + 3.66890i) q^{17} +(0.278160 + 0.481787i) q^{18} +(2.89975 - 5.02252i) q^{19} +(-1.67955 + 1.47618i) q^{20} +(4.01149 - 1.00682i) q^{21} +(3.28041 - 0.488782i) q^{22} +(7.48569 + 4.32187i) q^{23} +(-0.781614 - 1.35379i) q^{24} +(-4.61520 + 1.92352i) q^{25} +(2.09211 + 1.20788i) q^{26} -5.55934 q^{27} +(2.56616 - 0.644067i) q^{28} +4.47156i q^{29} +(-0.685686 - 3.42757i) q^{30} +(-0.862051 + 0.497705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.90230 + 4.82304i) q^{33} -7.33780i q^{34} +(5.89704 + 0.474255i) q^{35} -0.556319 q^{36} +(-3.20955 - 1.85303i) q^{37} +(2.89975 + 5.02252i) q^{38} +(-3.27044 + 1.88819i) q^{39} +(-0.438635 - 2.19262i) q^{40} -6.97297 q^{41} +(-1.13381 + 3.97747i) q^{42} -6.18781 q^{43} +(-1.21691 + 3.08531i) q^{44} +(-1.17839 - 0.398571i) q^{45} +(-7.48569 + 4.32187i) q^{46} +(-5.29717 + 9.17496i) q^{47} +1.56323 q^{48} +(-5.94787 - 3.69091i) q^{49} +(0.641780 - 4.95864i) q^{50} +(9.93388 + 5.73533i) q^{51} +(-2.09211 + 1.20788i) q^{52} +(-1.54044 + 0.889372i) q^{53} +(2.77967 - 4.81453i) q^{54} +(-4.78808 + 5.66341i) q^{55} +(-0.725302 + 2.54439i) q^{56} -9.06595 q^{57} +(-3.87248 - 2.23578i) q^{58} +(-7.38314 + 4.26266i) q^{59} +(3.31121 + 1.11996i) q^{60} +(1.71192 - 2.96514i) q^{61} -0.995411i q^{62} +(1.02411 + 1.05719i) q^{63} +1.00000 q^{64} +(-5.29684 + 1.05963i) q^{65} +(-3.22572 - 4.05896i) q^{66} +(9.76197 - 5.63608i) q^{67} +(6.35472 + 3.66890i) q^{68} -13.5121i q^{69} +(-3.35924 + 4.86986i) q^{70} +0.788593 q^{71} +(0.278160 - 0.481787i) q^{72} +(-8.04910 + 4.64715i) q^{73} +(3.20955 - 1.85303i) q^{74} +(6.21136 + 4.74458i) q^{75} -5.79951 q^{76} +(8.10325 - 3.36710i) q^{77} -3.77638i q^{78} +(2.68359 + 1.54937i) q^{79} +(2.11819 + 0.716443i) q^{80} +(3.51078 + 6.08084i) q^{81} +(3.48649 - 6.03877i) q^{82} -11.1034i q^{83} +(-2.87768 - 2.97064i) q^{84} +(10.8319 + 12.3242i) q^{85} +(3.09391 - 5.35880i) q^{86} +(6.05357 - 3.49503i) q^{87} +(-2.06350 - 2.59653i) q^{88} +(-3.28611 - 1.89724i) q^{89} +(0.934366 - 0.821228i) q^{90} +(6.14663 + 1.75215i) q^{91} -8.64373i q^{92} +(1.34758 + 0.778027i) q^{93} +(-5.29717 - 9.17496i) q^{94} +(-12.2844 - 4.15502i) q^{95} +(-0.781614 + 1.35379i) q^{96} -1.37580 q^{97} +(6.17036 - 3.30556i) q^{98} +(-1.82496 + 0.271919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	$ 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.781614	−	1.35379i	−0.451265	−	0.781614i	0.547200	−	0.837002i	$-0.315694\pi$
$3$	−0.781614	−	1.35379i	−0.451265	−	0.781614i	−0.998465	+	0.0553881i	$0.982360\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.438635	−	2.19262i	−0.196163	−	0.980571i
$5$	−0.438635	−	2.19262i	−0.196163	−	0.980571i
$6$	1.56323			0.638185
$7$	−0.725302	+	2.54439i	−0.274138	+	0.961690i
$7$	−0.725302	+	2.54439i	−0.274138	+	0.961690i
$8$	1.00000			0.353553
$9$	0.278160	−	0.481787i	0.0927199	−	0.160596i
$10$	2.11819	+	0.716443i	0.669829	+	0.226559i
$11$	−2.06350	−	2.59653i	−0.622169	−	0.782883i
$11$	−2.06350	−	2.59653i	−0.622169	−	0.782883i
$12$	−0.781614	+	1.35379i	−0.225632	+	0.390807i
$13$		−	2.41576i		−	0.670010i	−0.942216	−	0.335005i	$-0.891262\pi$
$13$		−	2.41576i		−	0.670010i	0.942216	−	0.335005i	$-0.108738\pi$
$14$	−1.84086	−	1.90033i	−0.491990	−	0.507884i
$15$	−2.62552	+	2.30761i	−0.677906	+	0.595821i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.35472	+	3.66890i	−1.54125	+	0.889839i	−0.542486	+	0.840065i	$0.682517\pi$
$17$	−6.35472	+	3.66890i	−1.54125	+	0.889839i	−0.998760	+	0.0497746i	$0.984150\pi$
$18$	0.278160	+	0.481787i	0.0655629	+	0.113558i
$19$	2.89975	−	5.02252i	0.665249	−	1.15225i	−0.313968	−	0.949433i	$-0.601659\pi$
$19$	2.89975	−	5.02252i	0.665249	−	1.15225i	0.979218	−	0.202812i	$-0.0650081\pi$
$20$	−1.67955	+	1.47618i	−0.375559	+	0.330084i
$21$	4.01149	−	1.00682i	0.875379	−	0.219707i
$22$	3.28041	−	0.488782i	0.699386	−	0.104209i
$23$	7.48569	+	4.32187i	1.56087	+	0.901171i	0.997169	+	0.0751954i	$0.0239580\pi$
$23$	7.48569	+	4.32187i	1.56087	+	0.901171i	0.563705	+	0.825976i	$0.309375\pi$
$24$	−0.781614	−	1.35379i	−0.159546	−	0.276342i
$25$	−4.61520	+	1.92352i	−0.923040	+	0.384704i
$26$	2.09211	+	1.20788i	0.410296	+	0.236884i
$27$	−5.55934			−1.06989
$28$	2.56616	−	0.644067i	0.484959	−	0.121717i
$29$			4.47156i			0.830347i	0.909742	+	0.415174i	$0.136279\pi$
$29$			4.47156i			0.830347i	−0.909742	+	0.415174i	$0.863721\pi$
$30$	−0.685686	−	3.42757i	−0.125189	−	0.625786i
$31$	−0.862051	+	0.497705i	−0.154829	+	0.0893905i	−0.575413	−	0.817863i	$-0.695159\pi$
$31$	−0.862051	+	0.497705i	−0.154829	+	0.0893905i	0.420584	+	0.907254i	$0.361825\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.90230	+	4.82304i	−0.331149	+	0.839584i
$34$		−	7.33780i		−	1.25842i
$35$	5.89704	+	0.474255i	0.996782	+	0.0801638i
$36$	−0.556319			−0.0927199
$37$	−3.20955	−	1.85303i	−0.527646	−	0.304637i	0.212411	−	0.977180i	$-0.431868\pi$
$37$	−3.20955	−	1.85303i	−0.527646	−	0.304637i	−0.740057	+	0.672544i	$0.765202\pi$
$38$	2.89975	+	5.02252i	0.470402	+	0.814761i
$39$	−3.27044	+	1.88819i	−0.523689	+	0.302352i
$40$	−0.438635	−	2.19262i	−0.0693542	−	0.346684i
$41$	−6.97297			−1.08900			−0.544498	−	0.838762i	$-0.683280\pi$
$41$	−6.97297			−1.08900			−0.544498	+	0.838762i	$0.683280\pi$
$42$	−1.13381	+	3.97747i	−0.174951	+	0.613736i
$43$	−6.18781			−0.943632			−0.471816	−	0.881697i	$-0.656401\pi$
$43$	−6.18781			−0.943632			−0.471816	+	0.881697i	$0.656401\pi$
$44$	−1.21691	+	3.08531i	−0.183456	+	0.465128i
$45$	−1.17839	−	0.398571i	−0.175664	−	0.0594155i
$46$	−7.48569	+	4.32187i	−1.10370	+	0.637224i
$47$	−5.29717	+	9.17496i	−0.772671	+	1.33831i	0.163423	+	0.986556i	$0.447746\pi$
$47$	−5.29717	+	9.17496i	−0.772671	+	1.33831i	−0.936094	+	0.351750i	$0.885587\pi$
$48$	1.56323			0.225632
$49$	−5.94787	−	3.69091i	−0.849696	−	0.527272i
$50$	0.641780	−	4.95864i	0.0907615	−	0.701258i
$51$	9.93388	+	5.73533i	1.39102	+	0.803107i
$52$	−2.09211	+	1.20788i	−0.290123	+	0.167502i
$53$	−1.54044	+	0.889372i	−0.211595	+	0.122165i	−0.602053	−	0.798456i	$-0.705650\pi$
$53$	−1.54044	+	0.889372i	−0.211595	+	0.122165i	0.390457	+	0.920621i	$0.372317\pi$
$54$	2.77967	−	4.81453i	0.378265	−	0.655174i
$55$	−4.78808	+	5.66341i	−0.645625	+	0.763654i
$56$	−0.725302	+	2.54439i	−0.0969226	+	0.340009i
$57$	−9.06595			−1.20081
$58$	−3.87248	−	2.23578i	−0.508482	−	0.293572i
$59$	−7.38314	+	4.26266i	−0.961203	+	0.554951i	−0.896543	−	0.442957i	$-0.853930\pi$
$59$	−7.38314	+	4.26266i	−0.961203	+	0.554951i	−0.0646597	+	0.997907i	$0.520596\pi$
$60$	3.31121	+	1.11996i	0.427475	+	0.144587i
$61$	1.71192	−	2.96514i	0.219189	−	0.379647i	−0.735371	−	0.677665i	$-0.762992\pi$
$61$	1.71192	−	2.96514i	0.219189	−	0.379647i	0.954560	+	0.298018i	$0.0963254\pi$
$62$		−	0.995411i		−	0.126417i
$63$	1.02411	+	1.05719i	0.129025	+	0.133193i
$64$	1.00000			0.125000
$65$	−5.29684	+	1.05963i	−0.656992	+	0.131431i
$66$	−3.22572	−	4.05896i	−0.397059	−	0.499624i
$67$	9.76197	−	5.63608i	1.19261	−	0.688556i	0.233716	−	0.972305i	$-0.424911\pi$
$67$	9.76197	−	5.63608i	1.19261	−	0.688556i	0.958899	+	0.283749i	$0.0915781\pi$
$68$	6.35472	+	3.66890i	0.770623	+	0.444920i
$69$		−	13.5121i		−	1.62667i
$70$	−3.35924	+	4.86986i	−0.401506	+	0.582059i
$71$	0.788593			0.0935888			0.0467944	−	0.998905i	$-0.485099\pi$
$71$	0.788593			0.0935888			0.0467944	+	0.998905i	$0.485099\pi$
$72$	0.278160	−	0.481787i	0.0327814	−	0.0567791i
$73$	−8.04910	+	4.64715i	−0.942076	+	0.543908i	−0.890611	−	0.454767i	$-0.849723\pi$
$73$	−8.04910	+	4.64715i	−0.942076	+	0.543908i	−0.0514657	+	0.998675i	$0.516389\pi$
$74$	3.20955	−	1.85303i	0.373102	−	0.215411i
$75$	6.21136	+	4.74458i	0.717226	+	0.547857i
$76$	−5.79951			−0.665249
$77$	8.10325	−	3.36710i	0.923451	−	0.383716i
$78$		−	3.77638i		−	0.427590i
$79$	2.68359	+	1.54937i	0.301927	+	0.174318i	0.643308	−	0.765607i	$-0.277561\pi$
$79$	2.68359	+	1.54937i	0.301927	+	0.174318i	−0.341381	+	0.939925i	$0.610895\pi$
$80$	2.11819	+	0.716443i	0.236820	+	0.0801008i
$81$	3.51078	+	6.08084i	0.390086	+	0.675649i
$82$	3.48649	−	6.03877i	0.385018	−	0.666871i
$83$		−	11.1034i		−	1.21875i	−0.792881	−	0.609376i	$-0.791420\pi$
$83$		−	11.1034i		−	1.21875i	0.792881	−	0.609376i	$-0.208580\pi$
$84$	−2.87768	−	2.97064i	−0.313981	−	0.324124i
$85$	10.8319	+	12.3242i	1.17489	+	1.33675i
$86$	3.09391	−	5.35880i	0.333624	−	0.577854i
$87$	6.05357	−	3.49503i	0.649011	−	0.374707i
$88$	−2.06350	−	2.59653i	−0.219970	−	0.276791i
$89$	−3.28611	−	1.89724i	−0.348327	−	0.201107i	0.315621	−	0.948885i	$-0.397787\pi$
$89$	−3.28611	−	1.89724i	−0.348327	−	0.201107i	−0.663948	+	0.747779i	$0.731120\pi$
$90$	0.934366	−	0.821228i	0.0984909	−	0.0865650i
$91$	6.14663	+	1.75215i	0.644342	+	0.183675i
$92$		−	8.64373i		−	0.901171i
$93$	1.34758	+	0.778027i	0.139738	+	0.0806776i
$94$	−5.29717	−	9.17496i	−0.546361	−	0.946325i
$95$	−12.2844	−	4.15502i	−1.26036	−	0.426296i
$96$	−0.781614	+	1.35379i	−0.0797731	+	0.138171i
$97$	−1.37580			−0.139691			−0.0698455	−	0.997558i	$-0.522251\pi$
$97$	−1.37580			−0.139691			−0.0698455	+	0.997558i	$0.522251\pi$
$98$	6.17036	−	3.30556i	0.623300	−	0.333912i
$99$	−1.82496	+	0.271919i	−0.183415	+	0.0273289i
$100$	3.97342	+	3.03512i	0.397342	+	0.303512i
$101$	−1.36011	−	2.35579i	−0.135336	−	0.234409i	0.790390	−	0.612605i	$-0.209878\pi$
$101$	−1.36011	−	2.35579i	−0.135336	−	0.234409i	−0.925726	+	0.378195i	$0.876545\pi$
$102$	−9.93388	+	5.73533i	−0.983601	+	0.567882i
$103$	9.62535	−	16.6716i	0.948414	−	1.64270i	0.199647	−	0.979868i	$-0.436020\pi$
$103$	9.62535	−	16.6716i	0.948414	−	1.64270i	0.748767	−	0.662833i	$-0.230646\pi$
$104$		−	2.41576i		−	0.236884i
$105$	−3.96716	−	8.35407i	−0.387156	−	0.815273i
$106$		−	1.77874i		−	0.172767i
$107$	−8.42442	+	14.5915i	−0.814420	+	1.41062i	0.0953239	+	0.995446i	$0.469611\pi$
$107$	−8.42442	+	14.5915i	−0.814420	+	1.41062i	−0.909744	+	0.415170i	$0.863722\pi$
$108$	2.77967	+	4.81453i	0.267474	+	0.463278i
$109$	−13.4790	+	7.78209i	−1.29105	+	0.745389i	−0.978841	−	0.204624i	$-0.934403\pi$
$109$	−13.4790	+	7.78209i	−1.29105	+	0.745389i	−0.312211	+	0.950013i	$0.601070\pi$
$110$	−2.51062	−	6.97831i	−0.239378	−	0.665356i
$111$			5.79343i			0.549888i
$112$	−1.84086	−	1.90033i	−0.173945	−	0.179564i
$113$		−	7.70432i		−	0.724762i	−0.932030	−	0.362381i	$-0.881964\pi$
$113$		−	7.70432i		−	0.724762i	0.932030	−	0.362381i	$-0.118036\pi$
$114$	4.53298	−	7.85134i	0.424552	−	0.735346i
$115$	6.19274	−	18.3090i	0.577476	−	1.70733i
$116$	3.87248	−	2.23578i	0.359551	−	0.207587i
$117$	−1.16388	−	0.671966i	−0.107601	−	0.0621232i
$118$		−	8.52531i		−	0.784819i
$119$	−4.72603	−	18.8300i	−0.433235	−	1.72614i
$120$	−2.62552	+	2.30761i	−0.239676	+	0.210655i
$121$	−2.48391	+	10.7159i	−0.225810	+	0.974171i
$122$	1.71192	+	2.96514i	0.154990	+	0.268451i
$123$	5.45017	+	9.43998i	0.491426	+	0.851174i
$124$	0.862051	+	0.497705i	0.0774145	+	0.0446953i
$125$	6.24195	+	9.27567i	0.558297	+	0.829641i
$126$	−1.42760	+	0.358307i	−0.127181	+	0.0319205i
$127$	7.79433			0.691635			0.345818	−	0.938302i	$-0.387602\pi$
$127$	7.79433			0.691635			0.345818	+	0.938302i	$0.387602\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.83648	+	8.37703i	0.425828	+	0.737556i
$130$	1.73075	−	5.11702i	0.151797	−	0.448792i
$131$	5.54331	−	9.60129i	0.484321	−	0.838869i	−0.515517	−	0.856880i	$-0.672400\pi$
$131$	5.54331	−	9.60129i	0.484321	−	0.838869i	0.999838	+	0.0180106i	$0.00573328\pi$
$132$	5.12803	−	0.764077i	0.446338	−	0.0665044i
$133$	10.6761	+	11.0210i	0.925733	+	0.955638i
$134$			11.2722i			0.973766i
$135$	2.43852	+	12.1895i	0.209874	+	1.04911i
$136$	−6.35472	+	3.66890i	−0.544913	+	0.314606i
$137$	7.71390	−	4.45362i	0.659043	−	0.380499i	−0.132869	−	0.991134i	$-0.542419\pi$
$137$	7.71390	−	4.45362i	0.659043	−	0.380499i	0.791912	+	0.610635i	$0.209086\pi$
$138$	11.7018	+	6.75606i	0.996127	+	0.575114i
$139$	18.4038			1.56099			0.780496	−	0.625161i	$-0.214967\pi$
$139$	18.4038			1.56099			0.780496	+	0.625161i	$0.214967\pi$
$140$	−2.53780	−	5.34411i	−0.214483	−	0.451660i
$141$	16.5614			1.39472
$142$	−0.394297	+	0.682942i	−0.0330886	+	0.0573112i
$143$	−6.27258	+	4.98492i	−0.524539	+	0.416860i
$144$	0.278160	+	0.481787i	0.0231800	+	0.0401489i
$145$	9.80444	−	1.96138i	0.814215	−	0.162884i
$146$		−	9.29430i		−	0.769202i
$147$	−0.347791	+	10.9371i	−0.0286853	+	0.902074i
$148$			3.70607i			0.304637i
$149$	2.89183	+	1.66960i	0.236908	+	0.136779i	0.613755	−	0.789497i	$-0.289658\pi$
$149$	2.89183	+	1.66960i	0.236908	+	0.136779i	−0.376847	+	0.926276i	$0.622992\pi$
$150$	−7.21461	+	3.00690i	−0.589070	+	0.245513i
$151$	0.298524	−	0.172353i	0.0242935	−	0.0140259i	−0.487804	−	0.872953i	$-0.662202\pi$
$151$	0.298524	−	0.172353i	0.0242935	−	0.0140259i	0.512098	+	0.858927i	$0.328869\pi$
$152$	2.89975	−	5.02252i	0.235201	−	0.407380i
$153$			4.08216i			0.330023i
$154$	−1.13564	+	8.70117i	−0.0915121	+	0.701160i
$155$	1.46941	+	1.67184i	0.118026	+	0.134286i
$156$	3.27044	+	1.88819i	0.261845	+	0.151176i
$157$	−9.08338	−	15.7329i	−0.724933	−	1.25562i	−0.959002	−	0.283401i	$-0.908537\pi$
$157$	−9.08338	−	15.7329i	−0.724933	−	1.25562i	0.234069	−	0.972220i	$-0.424796\pi$
$158$	−2.68359	+	1.54937i	−0.213495	+	0.123261i
$159$	2.40806	+	1.39029i	0.190971	+	0.110257i
$160$	−1.67955	+	1.47618i	−0.132780	+	0.116702i
$161$	−16.4259	+	15.9119i	−1.29454	+	1.25403i
$162$	−7.02155			−0.551665
$163$	−5.32629	−	3.07513i	−0.417187	−	0.240863i	0.276686	−	0.960960i	$-0.410764\pi$
$163$	−5.32629	−	3.07513i	−0.417187	−	0.240863i	−0.693873	+	0.720097i	$0.744097\pi$
$164$	3.48649	+	6.03877i	0.272249	+	0.471549i
$165$	11.4095	+	2.05548i	0.888231	+	0.160019i
$166$	9.61579	+	5.55168i	0.746330	+	0.430894i
$167$		−	1.94657i		−	0.150630i	−0.997160	−	0.0753152i	$-0.976004\pi$
$167$		−	1.94657i		−	0.150630i	0.997160	−	0.0753152i	$-0.0239963\pi$
$168$	4.01149	−	1.00682i	0.309493	−	0.0776781i
$169$	7.16413			0.551087
$170$	−16.0890	+	3.21862i	−1.23397	+	0.246857i
$171$	−1.61319	−	2.79413i	−0.123364	−	0.213672i
$172$	3.09391	+	5.35880i	0.235908	+	0.408605i
$173$	−11.4230	−	6.59506i	−0.868474	−	0.501413i	−0.00163288	−	0.999999i	$-0.500520\pi$
$173$	−11.4230	−	6.59506i	−0.868474	−	0.501413i	−0.866841	+	0.498585i	$0.833853\pi$
$174$			6.99006i			0.529915i
$175$	−1.54678	−	13.1380i	−0.116926	−	0.993141i
$176$	3.28041	−	0.488782i	0.247270	−	0.0368433i
$177$	11.5415	+	6.66350i	0.867514	+	0.500860i
$178$	3.28611	−	1.89724i	0.246304	−	0.142204i
$179$	−5.38578	−	9.32844i	−0.402552	−	0.697241i	0.591481	−	0.806319i	$-0.298543\pi$
$179$	−5.38578	−	9.32844i	−0.402552	−	0.697241i	−0.994033	+	0.109078i	$0.965210\pi$
$180$	0.244021	+	1.21980i	0.0181883	+	0.0909185i
$181$		−	4.72166i		−	0.350958i	−0.984483	−	0.175479i	$-0.943853\pi$
$181$		−	4.72166i		−	0.350958i	0.984483	−	0.175479i	$-0.0561474\pi$
$182$	−4.59072	+	4.44706i	−0.340287	+	0.329638i
$183$	−5.35225			−0.395650
$184$	7.48569	+	4.32187i	0.551852	+	0.318612i
$185$	−2.65519	+	7.85014i	−0.195213	+	0.577153i
$186$	−1.34758	+	0.778027i	−0.0988095	+	0.0570477i
$187$	22.6394	+	8.92943i	1.65556	+	0.652984i
$188$	10.5943			0.772671
$189$	4.03220	−	14.1451i	0.293299	−	1.02891i
$190$	9.74057	−	8.56112i	0.706655	−	0.621089i
$191$	−7.80888	+	13.5254i	−0.565031	+	0.978662i	0.432016	+	0.901866i	$0.357802\pi$
$191$	−7.80888	+	13.5254i	−0.565031	+	0.978662i	−0.997047	+	0.0767959i	$0.975531\pi$
$192$	−0.781614	−	1.35379i	−0.0564081	−	0.0977017i
$193$	−0.956755	−	1.65715i	−0.0688687	−	0.119284i	0.829535	−	0.558455i	$-0.188606\pi$
$193$	−0.956755	−	1.65715i	−0.0688687	−	0.119284i	−0.898404	+	0.439171i	$0.855272\pi$
$194$	0.687898	−	1.19147i	0.0493882	−	0.0855429i
$195$	5.57461	+	6.34261i	0.399206	+	0.454204i
$196$	−0.222483	+	6.99646i	−0.0158916	+	0.499747i
$197$	−14.8366			−1.05706			−0.528531	−	0.848914i	$-0.677257\pi$
$197$	−14.8366			−1.05706			−0.528531	+	0.848914i	$0.677257\pi$
$198$	0.676989	−	1.71642i	0.0481115	−	0.121980i
$199$	18.8792	−	10.8999i	1.33831	−	0.772675i	0.351755	−	0.936092i	$-0.385585\pi$
$199$	18.8792	−	10.8999i	1.33831	−	0.772675i	0.986557	+	0.163417i	$0.0522517\pi$
$200$	−4.61520	+	1.92352i	−0.326344	+	0.136014i
$201$	−15.2602	−	8.81047i	−1.07637	−	0.621443i
$202$	2.72023			0.191394
$203$	−11.3774	−	3.24323i	−0.798537	−	0.227630i
$204$		−	11.4707i		−	0.803107i
$205$	3.05859	+	15.2891i	0.213621	+	1.06784i
$206$	9.62535	+	16.6716i	0.670630	+	1.16157i
$207$	4.16443	−	2.40434i	0.289448	−	0.167113i
$208$	2.09211	+	1.20788i	0.145061	+	0.0837512i
$209$	−19.0248	+	2.83469i	−1.31597	+	0.196080i
$210$	9.21842	+	0.741369i	0.636131	+	0.0511593i
$211$		−	22.3531i		−	1.53885i	−0.638738	−	0.769425i	$-0.720543\pi$
$211$		−	22.3531i		−	1.53885i	0.638738	−	0.769425i	$-0.279457\pi$
$212$	1.54044	+	0.889372i	0.105798	+	0.0610823i
$213$	−0.616375	−	1.06759i	−0.0422334	−	0.0731503i
$214$	−8.42442	−	14.5915i	−0.575882	−	0.997456i
$215$	2.71419	+	13.5675i	0.185106	+	0.925299i
$216$	−5.55934			−0.378265
$217$	−0.641111	−	2.55438i	−0.0435214	−	0.173403i
$218$		−	15.5642i		−	1.05414i
$219$	12.5826	+	7.26456i	0.850252	+	0.490893i
$220$	7.29870	+	1.31490i	0.492078	+	0.0886503i
$221$	8.86317	+	15.3515i	0.596201	+	1.03265i
$222$	−5.01725	−	2.89671i	−0.336736	−	0.194415i
$223$	−20.8452			−1.39590			−0.697949	−	0.716147i	$-0.745904\pi$
$223$	−20.8452			−1.39590			−0.697949	+	0.716147i	$0.745904\pi$
$224$	2.56616	−	0.644067i	0.171459	−	0.0430335i
$225$	−0.357035	+	2.75859i	−0.0238023	+	0.183906i
$226$	6.67214	+	3.85216i	0.443824	+	0.256242i
$227$	10.3977	−	6.00313i	0.690122	−	0.398442i	−0.113536	−	0.993534i	$-0.536218\pi$
$227$	10.3977	−	6.00313i	0.690122	−	0.398442i	0.803658	+	0.595092i	$0.202884\pi$
$228$	4.53298	+	7.85134i	0.300204	+	0.519968i
$229$	0.995628	+	0.574826i	0.0657930	+	0.0379856i	0.532536	−	0.846408i	$-0.321239\pi$
$229$	0.995628	+	0.574826i	0.0657930	+	0.0379856i	−0.466743	+	0.884393i	$0.654573\pi$
$230$	12.7597	+	14.5176i	0.841350	+	0.957261i
$231$	−10.8920	−	8.33837i	−0.716639	−	0.548625i
$232$			4.47156i			0.293572i
$233$	−0.0103605	+	0.0179449i	−0.000678740	+	0.00117561i	−0.866365	−	0.499412i	$-0.833549\pi$
$233$	−0.0103605	+	0.0179449i	−0.000678740	+	0.00117561i	0.865686	+	0.500588i	$0.166883\pi$
$234$	1.16388	−	0.671966i	0.0760851	−	0.0439278i
$235$	22.4408	+	7.59024i	1.46387	+	0.495132i
$236$	7.38314	+	4.26266i	0.480601	+	0.277475i
$237$		−	4.84404i		−	0.314654i
$238$	18.6703	+	5.32212i	1.21021	+	0.344982i
$239$		−	3.74980i		−	0.242554i	−0.992619	−	0.121277i	$-0.961301\pi$
$239$		−	3.74980i		−	0.242554i	0.992619	−	0.121277i	$-0.0386990\pi$
$240$	−0.685686	−	3.42757i	−0.0442608	−	0.221249i
$241$	9.64709	+	16.7093i	0.621424	+	1.07634i	0.989221	+	0.146432i	$0.0467789\pi$
$241$	9.64709	+	16.7093i	0.621424	+	1.07634i	−0.367797	+	0.929906i	$0.619888\pi$
$242$	−8.03827	−	7.50907i	−0.516720	−	0.482702i
$243$	−2.85086	+	4.93784i	−0.182883	+	0.316763i
$244$	−3.42385			−0.219189
$245$	−5.48383	+	14.6604i	−0.350349	+	0.936619i
$246$	−10.9003			−0.694981
$247$	−12.1332	−	7.00510i	−0.772016	−	0.445724i
$248$	−0.862051	+	0.497705i	−0.0547403	+	0.0316043i
$249$	−15.0317	+	8.67854i	−0.952593	+	0.549980i
$250$	−11.1539	+	0.767849i	−0.705437	+	0.0485631i
$251$			1.86262i			0.117567i	0.998271	+	0.0587836i	$0.0187222\pi$
$251$			1.86262i			0.117567i	−0.998271	+	0.0587836i	$0.981278\pi$
$252$	0.403500	−	1.41550i	0.0254181	−	0.0891678i
$253$	−4.22490	−	28.3550i	−0.265617	−	1.78266i
$254$	−3.89717	+	6.75009i	−0.244530	+	0.423538i
$255$	8.21807	−	24.2970i	0.514636	−	1.52154i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.56618	−	4.44475i	0.160074	−	0.277256i	−0.774821	−	0.632180i	$-0.782160\pi$
$257$	2.56618	−	4.44475i	0.160074	−	0.277256i	0.934895	+	0.354925i	$0.115494\pi$
$258$	−9.67296			−0.602212
$259$	7.04274	−	6.82234i	0.437614	−	0.423920i
$260$	3.56609	+	4.05738i	0.221160	+	0.251628i
$261$	2.15434	+	1.24381i	0.133350	+	0.0769897i
$262$	5.54331	+	9.60129i	0.342467	+	0.593170i
$263$	−5.97415	−	10.3475i	−0.368382	−	0.638056i	0.620931	−	0.783865i	$-0.286755\pi$
$263$	−5.97415	−	10.3475i	−0.368382	−	0.638056i	−0.989313	+	0.145809i	$0.953421\pi$
$264$	−1.90230	+	4.82304i	−0.117079	+	0.296838i
$265$	2.62575	+	2.98749i	0.161298	+	0.183520i
$266$	−14.8825	+	3.73527i	−0.912503	+	0.229024i
$267$			5.93163i			0.363010i
$268$	−9.76197	−	5.63608i	−0.596307	−	0.344278i
$269$	−9.49594	+	5.48248i	−0.578978	+	0.334273i	−0.760727	−	0.649072i	$-0.775157\pi$
$269$	−9.49594	+	5.48248i	−0.578978	+	0.334273i	0.181749	+	0.983345i	$0.441824\pi$
$270$	−11.7757	−	3.98295i	−0.716647	−	0.242395i
$271$	11.6342	−	20.1511i	0.706730	−	1.22409i	−0.259333	−	0.965788i	$-0.583503\pi$
$271$	11.6342	−	20.1511i	0.706730	−	1.22409i	0.966063	−	0.258305i	$-0.0831639\pi$
$272$		−	7.33780i		−	0.444920i
$273$	−2.43224	−	9.69078i	−0.147206	−	0.586513i
$274$			8.90724i			0.538106i
$275$	14.5180	+	8.01430i	0.875466	+	0.483280i
$276$	−11.7018	+	6.75606i	−0.704368	+	0.406667i
$277$	−10.2915	−	17.8254i	−0.618356	−	1.07102i	−0.989786	−	0.142564i	$-0.954465\pi$
$277$	−10.2915	−	17.8254i	−0.618356	−	1.07102i	0.371429	−	0.928461i	$-0.378868\pi$
$278$	−9.20191	+	15.9382i	−0.551894	+	0.955909i
$279$			0.553766i			0.0331531i
$280$	5.89704	+	0.474255i	0.352416	+	0.0283422i
$281$			6.50399i			0.387995i	0.981002	+	0.193998i	$0.0621454\pi$
$281$			6.50399i			0.387995i	−0.981002	+	0.193998i	$0.937855\pi$
$282$	−8.28068	+	14.3426i	−0.493107	+	0.854087i
$283$	−12.5405	+	7.24027i	−0.745456	+	0.430389i	−0.824050	−	0.566518i	$-0.808290\pi$
$283$	−12.5405	+	7.24027i	−0.745456	+	0.430389i	0.0785938	+	0.996907i	$0.474957\pi$
$284$	−0.394297	−	0.682942i	−0.0233972	−	0.0405251i
$285$	3.97664	+	19.8782i	0.235556	+	1.17748i
$286$	−1.18078	−	7.92467i	−0.0698208	−	0.468595i
$287$	5.05751	−	17.7420i	0.298536	−	1.04728i
$288$	−0.556319			−0.0327814
$289$	18.4217	−	31.9073i	1.08363	−	1.87690i
$290$	−3.20362	+	9.47159i	−0.188123	+	0.556191i
$291$	1.07534	+	1.86255i	0.0630376	+	0.109184i
$292$	8.04910	+	4.64715i	0.471038	+	0.271954i
$293$		−	19.4674i		−	1.13730i	−0.822580	−	0.568650i	$-0.807466\pi$
$293$		−	19.4674i		−	1.13730i	0.822580	−	0.568650i	$-0.192534\pi$
$294$	−9.29788	−	5.76973i	−0.542263	−	0.336497i
$295$	12.5849	+	14.3187i	0.732721	+	0.833667i
$296$	−3.20955	−	1.85303i	−0.186551	−	0.107705i
$297$	11.4717	+	14.4350i	0.665656	+	0.837602i
$298$	−2.89183	+	1.66960i	−0.167519	+	0.0967172i
$299$	10.4406	−	18.0836i	0.603794	−	1.04580i
$300$	1.00325	−	7.75148i	0.0579226	−	0.447532i
$301$	4.48803	−	15.7442i	0.258686	−	0.907482i
$302$			0.344706i			0.0198356i
$303$	−2.12617	+	3.68263i	−0.122145	+	0.211562i
$304$	2.89975	+	5.02252i	0.166312	+	0.288061i
$305$	−7.25235	−	2.45299i	−0.415268	−	0.140458i
$306$	−3.53526	−	2.04108i	−0.202097	−	0.116681i
$307$			7.39584i			0.422103i	0.977475	+	0.211052i	$0.0676888\pi$
$307$			7.39584i			0.422103i	−0.977475	+	0.211052i	$0.932311\pi$
$308$	−6.96762	−	5.33407i	−0.397017	−	0.303937i
$309$	−30.0932			−1.71194
$310$	−2.18256	+	0.436622i	−0.123961	+	0.0247984i
$311$	10.5980	−	6.11878i	0.600960	−	0.346964i	−0.168459	−	0.985709i	$-0.553879\pi$
$311$	10.5980	−	6.11878i	0.600960	−	0.346964i	0.769419	+	0.638744i	$0.220546\pi$
$312$	−3.27044	+	1.88819i	−0.185152	+	0.106898i
$313$	−10.3410	+	17.9111i	−0.584507	+	1.01240i	0.410430	+	0.911892i	$0.365379\pi$
$313$	−10.3410	+	17.9111i	−0.584507	+	1.01240i	−0.994937	+	0.100504i	$0.967955\pi$
$314$	18.1668			1.02521
$315$	1.86881	−	2.70920i	0.105295	−	0.152646i
$316$		−	3.09874i		−	0.174318i
$317$	6.76443	+	3.90544i	0.379928	+	0.219352i	0.677787	−	0.735258i	$-0.262939\pi$
$317$	6.76443	+	3.90544i	0.379928	+	0.219352i	−0.297859	+	0.954610i	$0.596272\pi$
$318$	−2.40806	+	1.39029i	−0.135037	+	0.0779637i
$319$	11.6105	−	9.22707i	0.650064	−	0.516617i
$320$	−0.438635	−	2.19262i	−0.0245204	−	0.122571i
$321$	26.3386			1.47008
$322$	−5.56714	−	22.1812i	−0.310244	−	1.23611i
$323$			42.5556i			2.36786i
$324$	3.51078	−	6.08084i	0.195043	−	0.337825i
$325$	4.64676	+	11.1492i	0.257756	+	0.618446i
$326$	5.32629	−	3.07513i	0.294996	−	0.170316i
$327$	21.0707	+	12.1652i	1.16521	+	0.672736i
$328$	−6.97297			−0.385018
$329$	−19.5027	−	20.1327i	−1.07522	−	1.10995i
$330$	−7.48487	+	8.85320i	−0.412028	+	0.487353i
$331$	−9.35906	+	16.2104i	−0.514421	+	0.891002i	0.485440	+	0.874270i	$0.338660\pi$
$331$	−9.35906	+	16.2104i	−0.514421	+	0.891002i	−0.999860	+	0.0167322i	$0.994674\pi$
$332$	−9.61579	+	5.55168i	−0.527735	+	0.304688i
$333$	−1.78553	+	1.03088i	−0.0978466	+	0.0564918i
$334$	1.68578	+	0.973287i	0.0922419	+	0.0532559i
$335$	−16.6397	−	18.9322i	−0.909126	−	1.03437i
$336$	−1.13381	+	3.97747i	−0.0618545	+	0.216989i
$337$	−3.10399			−0.169085			−0.0845426	−	0.996420i	$-0.526943\pi$
$337$	−3.10399			−0.169085			−0.0845426	+	0.996420i	$0.526943\pi$
$338$	−3.58206	+	6.20432i	−0.194839	+	0.337470i
$339$	−10.4301	+	6.02181i	−0.566484	+	0.327060i
$340$	5.25712	−	15.5428i	0.285107	−	0.842928i
$341$	3.07115	+	1.21132i	0.166312	+	0.0655968i
$342$	3.22638			0.174463
$343$	13.7051	−	12.4567i	0.740007	−	0.672599i
$344$	−6.18781			−0.333624
$345$	−29.6270	+	5.92689i	−1.59506	+	0.319093i
$346$	11.4230	−	6.59506i	0.614104	−	0.354553i
$347$	7.01443	+	12.1493i	0.376554	+	0.652211i	0.990558	−	0.137092i	$-0.0437755\pi$
$347$	7.01443	+	12.1493i	0.376554	+	0.652211i	−0.614004	+	0.789303i	$0.710442\pi$
$348$	−6.05357	−	3.49503i	−0.324505	−	0.187353i
$349$	−10.9124			−0.584125			−0.292063	−	0.956399i	$-0.594342\pi$
$349$	−10.9124			−0.584125			−0.292063	+	0.956399i	$0.594342\pi$
$350$	12.1512	+	5.22945i	0.649511	+	0.279526i
$351$			13.4300i			0.716840i
$352$	−1.21691	+	3.08531i	−0.0648614	+	0.164448i
$353$	−1.95844	−	3.39212i	−0.104237	−	0.180544i	0.809189	−	0.587548i	$-0.199907\pi$
$353$	−1.95844	−	3.39212i	−0.104237	−	0.180544i	−0.913426	+	0.407004i	$0.866573\pi$
$354$	−11.5415	+	6.66350i	−0.613425	+	0.354161i
$355$	−0.345904	−	1.72909i	−0.0183587	−	0.0917705i
$356$			3.79448i			0.201107i
$357$	−21.7980	+	21.1158i	−1.15367	+	1.11757i
$358$	10.7716			0.569295
$359$	−11.8456	−	6.83908i	−0.625188	−	0.360953i	0.153698	−	0.988118i	$-0.450882\pi$
$359$	−11.8456	−	6.83908i	−0.625188	−	0.360953i	−0.778886	+	0.627165i	$0.784215\pi$
$360$	−1.17839	−	0.398571i	−0.0621065	−	0.0210065i
$361$	−7.31715	−	12.6737i	−0.385113	−	0.667036i
$362$	4.08908	+	2.36083i	0.214917	+	0.124082i
$363$	16.4486	−	5.01297i	0.863326	−	0.263113i
$364$	−1.55591	−	6.19921i	−0.0815517	−	0.324927i
$365$	13.7201	+	15.6103i	0.718141	+	0.817078i
$366$	2.67613	−	4.63519i	0.139883	−	0.242285i
$367$	−0.190067	−	0.329206i	−0.00992143	−	0.0171844i	0.861022	−	0.508568i	$-0.169825\pi$
$367$	−0.190067	−	0.329206i	−0.00992143	−	0.0171844i	−0.870943	+	0.491383i	$0.836491\pi$
$368$	−7.48569	+	4.32187i	−0.390219	+	0.225293i
$369$	−1.93960	+	3.35949i	−0.100972	+	0.174888i
$370$	−5.47082	−	6.22453i	−0.284415	−	0.323598i
$371$	−1.14563	−	4.56454i	−0.0594782	−	0.236979i
$372$		−	1.55605i		−	0.0806776i
$373$	−3.71164	+	6.42875i	−0.192182	+	0.332868i	−0.945973	−	0.324246i	$-0.894890\pi$
$373$	−3.71164	+	6.42875i	−0.192182	+	0.332868i	0.753791	+	0.657114i	$0.228223\pi$
$374$	−19.0528	+	15.1416i	−0.985197	+	0.782952i
$375$	7.67856	−	15.7003i	0.396519	−	0.810761i
$376$	−5.29717	+	9.17496i	−0.273181	+	0.473163i
$377$	10.8022			0.556341
$378$	10.2340	+	10.5646i	0.526378	+	0.543382i
$379$	−12.0907			−0.621059			−0.310529	−	0.950564i	$-0.600506\pi$
$379$	−12.0907			−0.621059			−0.310529	+	0.950564i	$0.600506\pi$
$380$	2.54387	+	12.7161i	0.130498	+	0.652324i
$381$	−6.09216	−	10.5519i	−0.312111	−	0.540592i
$382$	−7.80888	−	13.5254i	−0.399537	−	0.692018i
$383$	7.34126	−	12.7154i	0.375121	−	0.649729i	−0.615224	−	0.788352i	$-0.710934\pi$
$383$	7.34126	−	12.7154i	0.375121	−	0.649729i	0.990345	+	0.138624i	$0.0442678\pi$
$384$	1.56323			0.0797731
$385$	−10.9371	−	16.2905i	−0.557408	−	0.830239i
$386$	1.91351			0.0973951
$387$	−1.72120	+	2.98121i	−0.0874935	+	0.151543i
$388$	0.687898	+	1.19147i	0.0349227	+	0.0604880i
$389$	−12.3561	−	21.4013i	−0.626478	−	1.08509i	−0.988253	−	0.152826i	$-0.951163\pi$
$389$	−12.3561	−	21.4013i	−0.626478	−	1.08509i	0.361776	−	0.932265i	$-0.382171\pi$
$390$	−8.28017	+	1.65645i	−0.419283	+	0.0838776i
$391$	−63.4260			−3.20759
$392$	−5.94787	−	3.69091i	−0.300413	−	0.186419i
$393$	−17.3309			−0.874229
$394$	7.41829	−	12.8489i	0.373728	−	0.647316i
$395$	2.22007	−	6.56371i	0.111704	−	0.330256i
$396$	1.14797	+	1.44450i	0.0576875	+	0.0725888i
$397$	−9.10381	+	15.7683i	−0.456907	+	0.791386i	−0.998796	−	0.0490641i	$-0.984376\pi$
$397$	−9.10381	+	15.7683i	−0.456907	+	0.791386i	0.541889	+	0.840450i	$0.317709\pi$
$398$			21.7998i			1.09273i
$399$	6.57555	−	23.0673i	0.329189	−	1.15481i
$400$	0.641780	−	4.95864i	0.0320890	−	0.247932i
$401$	11.0903	−	19.2090i	0.553825	−	0.959252i	−0.444169	−	0.895943i	$-0.646501\pi$
$401$	11.0903	−	19.2090i	0.553825	−	0.959252i	0.997994	−	0.0633096i	$-0.0201656\pi$
$402$	15.2602	−	8.81047i	0.761109	−	0.439426i
$403$	1.20233	+	2.08250i	0.0598925	+	0.103737i
$404$	−1.36011	+	2.35579i	−0.0676682	+	0.117205i
$405$	11.7930	−	10.3651i	0.586001	−	0.515045i
$406$	8.49742	−	8.23150i	0.421720	−	0.408523i
$407$	1.81146	+	12.1574i	0.0897906	+	0.602621i
$408$	9.93388	+	5.73533i	0.491800	+	0.283941i
$409$	−11.3050	−	19.5808i	−0.558995	−	0.968207i	−0.997581	−	0.0695178i	$-0.977854\pi$
$409$	−11.3050	−	19.5808i	−0.558995	−	0.968207i	0.438586	−	0.898689i	$-0.355479\pi$
$410$	−14.7701	−	4.99574i	−0.729441	−	0.246722i
$411$	−12.0586	−	6.96202i	−0.594806	−	0.343411i
$412$	−19.2507			−0.948414
$413$	−5.49087	−	21.8773i	−0.270188	−	1.07651i
$414$			4.80867i			0.236333i
$415$	−24.3455	+	4.87032i	−1.19507	+	0.239075i
$416$	−2.09211	+	1.20788i	−0.102574	+	0.0592211i
$417$	−14.3847	−	24.9150i	−0.704421	−	1.22009i
$418$	7.05747	−	17.8933i	0.345192	−	0.875189i
$419$			22.1700i			1.08307i	0.840677	+	0.541537i	$0.182157\pi$
$419$			22.1700i			1.08307i	−0.840677	+	0.541537i	$0.817843\pi$
$420$	−5.25125	+	7.61270i	−0.256235	+	0.371462i
$421$	−5.06729			−0.246964			−0.123482	−	0.992347i	$-0.539406\pi$
$421$	−5.06729			−0.246964			−0.123482	+	0.992347i	$0.539406\pi$
$422$	19.3583	+	11.1765i	0.942349	+	0.544065i
$423$	2.94692	+	5.10421i	0.143284	+	0.248175i
$424$	−1.54044	+	0.889372i	−0.0748103	+	0.0431917i
$425$	22.2711	−	29.1562i	1.08031	−	1.41428i
$426$	1.23275			0.0597270
$427$	6.30282	+	6.50643i	0.305015	+	0.314868i
$428$	16.8488			0.814420
$429$	11.6513	+	4.59550i	0.562529	+	0.221873i
$430$	−13.1069	−	4.43321i	−0.632072	−	0.213789i
$431$	−1.49673	+	0.864138i	−0.0720950	+	0.0416241i	−0.535614	−	0.844463i	$-0.679920\pi$
$431$	−1.49673	+	0.864138i	−0.0720950	+	0.0416241i	0.463519	+	0.886087i	$0.346587\pi$
$432$	2.77967	−	4.81453i	0.133737	−	0.231639i
$433$	1.16651			0.0560588			0.0280294	−	0.999607i	$-0.491077\pi$
$433$	1.16651			0.0560588			0.0280294	+	0.999607i	$0.491077\pi$
$434$	2.53272	+	0.721973i	0.121574	+	0.0346558i
$435$	−10.3186	−	11.7402i	−0.494739	−	0.562898i
$436$	13.4790	+	7.78209i	0.645526	+	0.372695i
$437$	43.4133	−	25.0647i	2.07674	−	1.19901i
$438$	−12.5826	+	7.26456i	−0.601219	+	0.347114i
$439$	−7.42466	+	12.8599i	−0.354360	+	0.613769i	−0.987008	−	0.160670i	$-0.948634\pi$
$439$	−7.42466	+	12.8599i	−0.354360	+	0.613769i	0.632649	+	0.774439i	$0.281968\pi$
$440$	−4.78808	+	5.66341i	−0.228263	+	0.269993i
$441$	−3.43269	+	1.83894i	−0.163461	+	0.0875688i
$442$	−17.7263			−0.843156
$443$	−27.9784	−	16.1533i	−1.32929	−	0.767468i	−0.344104	−	0.938932i	$-0.611817\pi$
$443$	−27.9784	−	16.1533i	−1.32929	−	0.767468i	−0.985191	+	0.171463i	$0.945151\pi$
$444$	5.01725	−	2.89671i	0.238108	−	0.137472i
$445$	−2.71853	+	8.03740i	−0.128870	+	0.381009i
$446$	10.4226	−	18.0525i	0.493525	−	0.854810i
$447$		−	5.21992i		−	0.246894i
$448$	−0.725302	+	2.54439i	−0.0342673	+	0.120211i
$449$	−31.2597			−1.47524			−0.737618	−	0.675218i	$-0.764049\pi$
$449$	−31.2597			−1.47524			−0.737618	+	0.675218i	$0.764049\pi$
$450$	−2.21049	−	1.68850i	−0.104203	−	0.0795964i
$451$	14.3888	+	18.1055i	0.677540	+	0.852556i
$452$	−6.67214	+	3.85216i	−0.313831	+	0.181190i
$453$	−0.466661	−	0.269427i	−0.0219257	−	0.0126588i
$454$			12.0063i			0.563482i
$455$	1.14568	−	14.2458i	0.0537105	−	0.667854i
$456$	−9.06595			−0.424552
$457$	20.0531	−	34.7330i	0.938044	−	1.62474i	0.168930	−	0.985628i	$-0.445969\pi$
$457$	20.0531	−	34.7330i	0.938044	−	1.62474i	0.769114	−	0.639112i	$-0.220698\pi$
$458$	−0.995628	+	0.574826i	−0.0465227	+	0.0268599i
$459$	35.3280	−	20.3967i	1.64897	−	0.952034i
$460$	−18.9525	+	3.79144i	−0.883663	+	0.176777i
$461$	−21.3818			−0.995848			−0.497924	−	0.867221i	$-0.665904\pi$
$461$	−21.3818			−0.995848			−0.497924	+	0.867221i	$0.665904\pi$
$462$	12.6672	−	5.26354i	0.589333	−	0.244882i
$463$			20.7517i			0.964415i	0.876057	+	0.482207i	$0.160165\pi$
$463$			20.7517i			0.964415i	−0.876057	+	0.482207i	$0.839835\pi$
$464$	−3.87248	−	2.23578i	−0.179775	−	0.103793i
$465$	1.11482	−	3.29601i	0.0516987	−	0.152849i
$466$	−0.0103605	−	0.0179449i	−0.000479942	−	0.000831283i
$467$	0.436949	−	0.756818i	0.0202196	−	0.0350213i	−0.855739	−	0.517408i	$-0.826897\pi$
$467$	0.436949	−	0.756818i	0.0202196	−	0.0350213i	0.875958	+	0.482387i	$0.160230\pi$
$468$			1.34393i			0.0621232i
$469$	7.26002	+	28.9261i	0.335236	+	1.33569i
$470$	−17.7937	+	15.6392i	−0.820763	+	0.721380i
$471$	−14.1994	+	24.5941i	−0.654274	+	1.13324i
$472$	−7.38314	+	4.26266i	−0.339836	+	0.196205i
$473$	12.7686	+	16.0668i	0.587099	+	0.738753i
$474$	4.19506	+	2.42202i	0.192686	+	0.111247i
$475$	−3.72201	+	28.7577i	−0.170778	+	1.31949i
$476$	−13.9442	+	13.5079i	−0.639132	+	0.619131i
$477$			0.989550i			0.0453084i
$478$	3.24742	+	1.87490i	0.148534	+	0.0857559i
$479$	−2.01746	−	3.49434i	−0.0921801	−	0.159661i	0.816248	−	0.577702i	$-0.196050\pi$
$479$	−2.01746	−	3.49434i	−0.0921801	−	0.159661i	−0.908428	+	0.418041i	$0.862717\pi$
$480$	3.31121	+	1.11996i	0.151135	+	0.0511191i
$481$	−4.47647	+	7.75348i	−0.204110	+	0.353528i
$482$	−19.2942			−0.878826
$483$	34.3801	+	9.80037i	1.56435	+	0.445932i
$484$	10.5222	−	3.20681i	0.478281	−	0.145764i
$485$	0.603472	+	3.01660i	0.0274023	+	0.136977i
$486$	−2.85086	−	4.93784i	−0.129318	−	0.223985i
$487$	−10.6366	+	6.14105i	−0.481991	+	0.278277i	−0.721246	−	0.692679i	$-0.756430\pi$
$487$	−10.6366	+	6.14105i	−0.481991	+	0.278277i	0.239255	+	0.970957i	$0.423097\pi$
$488$	1.71192	−	2.96514i	0.0774952	−	0.134226i
$489$			9.61427i			0.434772i
$490$	−9.95437	−	12.0793i	−0.449693	−	0.545689i
$491$			6.98569i			0.315260i	0.987498	+	0.157630i	$0.0503853\pi$
$491$			6.98569i			0.315260i	−0.987498	+	0.157630i	$0.949615\pi$
$492$	5.45017	−	9.43998i	0.245713	−	0.425587i
$493$	−16.4057	−	28.4155i	−0.738876	−	1.27977i
$494$	12.1332	−	7.00510i	0.545898	−	0.315174i
$495$	1.39670	+	3.88217i	0.0627772	+	0.174491i
$496$		−	0.995411i		−	0.0446953i
$497$	−0.571968	+	2.00649i	−0.0256563	+	0.0900034i
$498$		−	17.3571i		−	0.777789i
$499$	15.3366	−	26.5638i	0.686561	−	1.18916i	−0.286383	−	0.958115i	$-0.592453\pi$
$499$	15.3366	−	26.5638i	0.686561	−	1.18916i	0.972944	−	0.231043i	$-0.0742137\pi$
$500$	4.91199	−	10.0435i	0.219671	−	0.449160i
$501$	−2.63526	+	1.52147i	−0.117735	+	0.0679742i
$502$	−1.61307	−	0.931308i	−0.0719950	−	0.0415663i
$503$			15.2089i			0.678133i	0.940762	+	0.339067i	$0.110111\pi$
$503$			15.2089i			0.678133i	−0.940762	+	0.339067i	$0.889889\pi$
$504$	1.02411	+	1.05719i	0.0456173	+	0.0470909i
$505$	−4.56876	+	4.01555i	−0.203307	+	0.178689i
$506$	26.6686	+	10.5186i	1.18556	+	0.467610i
$507$	−5.59958	−	9.69876i	−0.248686	−	0.430737i
$508$	−3.89717	−	6.75009i	−0.172909	−	0.299487i
$509$	15.7863	+	9.11423i	0.699716	+	0.403981i	0.807242	−	0.590221i	$-0.200959\pi$
$509$	15.7863	+	9.11423i	0.699716	+	0.403981i	−0.107526	+	0.994202i	$0.534293\pi$
$510$	16.9328	+	19.2655i	0.749795	+	0.853093i
$511$	−5.98615	−	23.8507i	−0.264812	−	1.05509i
$512$	1.00000			0.0441942
$513$	−16.1207	+	27.9219i	−0.711747	+	1.23278i
$514$	2.56618	+	4.44475i	0.113189	+	0.196049i
$515$	−40.7766	−	13.7920i	−1.79683	−	0.607750i
$516$	4.83648	−	8.37703i	0.212914	−	0.368778i
$517$	34.7538	−	5.17832i	1.52847	−	0.227742i
$518$	2.38695	+	9.51036i	0.104877	+	0.417861i
$519$			20.6192i			0.905081i
$520$	−5.29684	+	1.05963i	−0.232282	+	0.0464680i
$521$	20.3030	−	11.7220i	0.889492	−	0.513549i	0.0157158	−	0.999876i	$-0.494997\pi$
$521$	20.3030	−	11.7220i	0.889492	−	0.513549i	0.873776	+	0.486328i	$0.161664\pi$
$522$	−2.15434	+	1.24381i	−0.0942927	+	0.0544399i
$523$	−20.7215	−	11.9635i	−0.906086	−	0.523129i	−0.0269161	−	0.999638i	$-0.508569\pi$
$523$	−20.7215	−	11.9635i	−0.906086	−	0.523129i	−0.879170	+	0.476509i	$0.841902\pi$
$524$	−11.0866			−0.484321
$525$	−16.5772	+	12.3629i	−0.723488	+	0.539560i
$526$	11.9483			0.520971
$527$	3.65206	−	6.32556i	0.159086	−	0.275546i
$528$	−3.22572	−	4.05896i	−0.140382	−	0.176644i
$529$	25.8570	+	44.7857i	1.12422	+	1.94720i
$530$	−3.90012	+	0.780219i	−0.169410	+	0.0338906i
$531$			4.74280i			0.205820i
$532$	4.20640	−	14.7562i	0.182370	−	0.639764i
$533$			16.8450i			0.729638i
$534$	−5.13694	−	2.96581i	−0.222297	−	0.128343i
$535$	35.6890	+	12.0712i	1.54297	+	0.521885i
$536$	9.76197	−	5.63608i	0.421653	−	0.243441i
$537$	−8.41920	+	14.5825i	−0.363315	+	0.629281i
$538$		−	10.9650i		−	0.472733i
$539$	2.68991	+	23.0600i	0.115863	+	0.993265i
$540$	9.33719	−	8.20659i	0.401809	−	0.353155i
$541$	31.8171	+	18.3696i	1.36792	+	0.789770i	0.990662	−	0.136337i	$-0.0435331\pi$
$541$	31.8171	+	18.3696i	1.36792	+	0.789770i	0.377260	+	0.926107i	$0.376866\pi$
$542$	11.6342	+	20.1511i	0.499734	+	0.865564i
$543$	−6.39216	+	3.69051i	−0.274314	+	0.158375i
$544$	6.35472	+	3.66890i	0.272457	+	0.157303i
$545$	22.9755	+	26.1408i	0.984164	+	1.11975i
$546$	9.60858	+	2.73901i	0.411209	+	0.117219i
$547$	33.9176			1.45021			0.725106	−	0.688637i	$-0.241791\pi$
$547$	33.9176			1.45021			0.725106	+	0.688637i	$0.241791\pi$
$548$	−7.71390	−	4.45362i	−0.329521	−	0.190249i
$549$	−0.952377	−	1.64956i	−0.0406464	−	0.0704017i
$550$	−14.1996	+	8.56577i	−0.605471	+	0.365246i
$551$	22.4585	+	12.9664i	0.956764	+	0.552388i
$552$		−	13.5121i		−	0.575114i
$553$	−5.88862	+	5.70434i	−0.250410	+	0.242573i
$554$	20.5830			0.874488
$555$	12.7028	−	2.54120i	0.539204	−	0.107868i
$556$	−9.20191	−	15.9382i	−0.390248	−	0.675929i
$557$	−7.99756	−	13.8522i	−0.338868	−	0.586936i	0.645352	−	0.763885i	$-0.276711\pi$
$557$	−7.99756	−	13.8522i	−0.338868	−	0.586936i	−0.984220	+	0.176949i	$0.943377\pi$
$558$	−0.479576	−	0.276883i	−0.0203021	−	0.0117214i
$559$			14.9482i			0.632243i
$560$	−3.35924	+	4.86986i	−0.141954	+	0.205789i
$561$	−5.60665	−	37.6285i	−0.236713	−	1.58867i
$562$	−5.63262	−	3.25199i	−0.237598	−	0.137177i
$563$	−39.3395	+	22.7127i	−1.65796	+	0.957226i	−0.684310	+	0.729191i	$0.739897\pi$
$563$	−39.3395	+	22.7127i	−1.65796	+	0.957226i	−0.973653	+	0.228035i	$0.926770\pi$
$564$	−8.28068	−	14.3426i	−0.348679	−	0.603930i
$565$	−16.8927	+	3.37938i	−0.710680	+	0.142172i
$566$		−	14.4805i		−	0.608662i
$567$	−18.0184	+	4.52235i	−0.756703	+	0.189921i
$568$	0.788593			0.0330886
$569$	−22.2683	−	12.8566i	−0.933537	−	0.538978i	−0.0456086	−	0.998959i	$-0.514523\pi$
$569$	−22.2683	−	12.8566i	−0.933537	−	0.538978i	−0.887929	+	0.459981i	$0.847856\pi$
$570$	−19.2034	−	6.49524i	−0.804341	−	0.272056i
$571$	1.28028	−	0.739171i	0.0535781	−	0.0309333i	−0.472972	−	0.881078i	$-0.656819\pi$
$571$	1.28028	−	0.739171i	0.0535781	−	0.0309333i	0.526550	+	0.850144i	$0.323485\pi$
$572$	7.45335	+	2.93975i	0.311640	+	0.122917i
$573$	24.4141			1.01991
$574$	12.8363	+	13.2509i	0.535775	+	0.553083i
$575$	−42.8612	−	5.54738i	−1.78743	−	0.231342i
$576$	0.278160	−	0.481787i	0.0115900	−	0.0200744i
$577$	−20.1440	−	34.8905i	−0.838608	−	1.45251i	−0.891059	−	0.453888i	$-0.850037\pi$
$577$	−20.1440	−	34.8905i	−0.838608	−	1.45251i	0.0524512	−	0.998623i	$-0.483297\pi$
$578$	18.4217	+	31.9073i	0.766241	+	1.32717i
$579$	−1.49563	+	2.59050i	−0.0621561	+	0.107658i
$580$	−6.60083	−	7.51021i	−0.274084	−	0.311844i
$581$	28.2513	+	8.05329i	1.17206	+	0.334107i
$582$	−2.15068			−0.0891487
$583$	5.48798	+	2.16457i	0.227289	+	0.0896473i
$584$	−8.04910	+	4.64715i	−0.333074	+	0.192301i
$585$	−0.962850	+	2.84670i	−0.0398090	+	0.117696i
$586$	16.8593	+	9.73371i	0.696451	+	0.402096i
$587$	−15.4414			−0.637335			−0.318667	−	0.947867i	$-0.603235\pi$
$587$	−15.4414			−0.637335			−0.318667	+	0.947867i	$0.603235\pi$
$588$	9.64567	−	5.16734i	0.397781	−	0.213097i
$589$			5.77289i			0.237868i
$590$	−18.6928	+	3.73950i	−0.769571	+	0.153953i
$591$	11.5965	+	20.0857i	0.477015	+	0.826215i
$592$	3.20955	−	1.85303i	0.131912	−	0.0761592i
$593$	−12.7767	−	7.37664i	−0.524677	−	0.302922i	0.214169	−	0.976797i	$-0.431296\pi$
$593$	−12.7767	−	7.37664i	−0.524677	−	0.302922i	−0.738846	+	0.673874i	$0.764629\pi$
$594$	−18.2369	+	2.71730i	−0.748269	+	0.111492i
$595$	−39.2141	+	18.6219i	−1.60762	+	0.763423i
$596$		−	3.33920i		−	0.136779i
$597$	−29.5125	−	17.0391i	−1.20787	−	0.697362i
$598$	10.4406	+	18.0836i	0.426947	+	0.739493i
$599$	17.6585	+	30.5853i	0.721505	+	1.24968i	0.960397	+	0.278637i	$0.0898826\pi$
$599$	17.6585	+	30.5853i	0.721505	+	1.24968i	−0.238892	+	0.971046i	$0.576784\pi$
$600$	6.21136	+	4.74458i	0.253578	+	0.193697i
$601$	−17.7029			−0.722115			−0.361057	−	0.932544i	$-0.617584\pi$
$601$	−17.7029			−0.722115			−0.361057	+	0.932544i	$0.617584\pi$
$602$	11.3909	+	11.7589i	0.464258	+	0.479255i
$603$		−	6.27092i		−	0.255371i
$604$	−0.298524	−	0.172353i	−0.0121468	−	0.00701294i
$605$	24.5854	+	0.745929i	0.999540	+	0.0303263i
$606$	−2.12617	−	3.68263i	−0.0863696	−	0.149597i
$607$	8.30150	+	4.79288i	0.336948	+	0.194537i	0.658921	−	0.752212i	$-0.271013\pi$
$607$	8.30150	+	4.79288i	0.336948	+	0.194537i	−0.321974	+	0.946749i	$0.604346\pi$
$608$	−5.79951			−0.235201
$609$	4.50207	+	17.9376i	0.182433	+	0.726869i
$610$	5.75053	−	5.05422i	0.232832	−	0.204639i
$611$	22.1645	+	12.7967i	0.896678	+	0.517697i
$612$	3.53526	−	2.04108i	0.142904	−	0.0825058i
$613$	−1.69971	−	2.94399i	−0.0686508	−	0.118907i	0.829657	−	0.558274i	$-0.188536\pi$
$613$	−1.69971	−	2.94399i	−0.0686508	−	0.118907i	−0.898308	+	0.439367i	$0.855203\pi$
$614$	−6.40499	−	3.69792i	−0.258484	−	0.149236i
$615$	18.3077	−	16.0909i	0.738237	−	0.648847i
$616$	8.10325	−	3.36710i	0.326489	−	0.135664i
$617$		−	2.52801i		−	0.101774i	−0.998704	−	0.0508870i	$-0.983795\pi$
$617$		−	2.52801i		−	0.101774i	0.998704	−	0.0508870i	$-0.0162048\pi$
$618$	15.0466	−	26.0615i	0.605264	−	1.04835i
$619$	10.7041	−	6.18003i	0.430235	−	0.248396i	−0.269212	−	0.963081i	$-0.586763\pi$
$619$	10.7041	−	6.18003i	0.430235	−	0.248396i	0.699447	+	0.714685i	$0.253430\pi$
$620$	0.713155	−	2.10846i	0.0286410	−	0.0846780i
$621$	−41.6155	−	24.0267i	−1.66997	−	0.964158i
$622$			12.2376i			0.490682i
$623$	7.21074	−	6.98509i	0.288892	−	0.279852i
$624$		−	3.77638i		−	0.151176i
$625$	17.6001	−	17.7549i	0.704005	−	0.710195i
$626$	−10.3410	−	17.9111i	−0.413309	−	0.715872i
$627$	18.7076	+	23.5400i	0.747110	+	0.940097i
$628$	−9.08338	+	15.7329i	−0.362466	+	0.627810i
$629$	27.1944			1.08431
$630$	1.41183	+	2.97303i	0.0562486	+	0.118449i
$631$	−3.86853			−0.154004			−0.0770018	−	0.997031i	$-0.524535\pi$
$631$	−3.86853			−0.154004			−0.0770018	+	0.997031i	$0.524535\pi$
$632$	2.68359	+	1.54937i	0.106747	+	0.0616307i
$633$	−30.2615	+	17.4715i	−1.20279	+	0.694429i
$634$	−6.76443	+	3.90544i	−0.268650	+	0.155105i
$635$	−3.41887	−	17.0900i	−0.135674	−	0.678198i
$636$		−	2.78058i		−	0.110257i
$637$	−8.91633	+	14.3686i	−0.353278	+	0.569305i
$638$	2.18562	+	14.6685i	0.0865293	+	0.580733i
$639$	0.219355	−	0.379934i	0.00867754	−	0.0150299i
$640$	2.11819	+	0.716443i	0.0837286	+	0.0283199i
$641$	4.08934	+	7.08294i	0.161519	+	0.279760i	0.935414	−	0.353555i	$-0.115027\pi$
$641$	4.08934	+	7.08294i	0.161519	+	0.279760i	−0.773895	+	0.633315i	$0.781694\pi$
$642$	−13.1693	+	22.8099i	−0.519751	+	0.900234i
$643$	28.2230			1.11301			0.556504	−	0.830845i	$-0.312142\pi$
$643$	28.2230			1.11301			0.556504	+	0.830845i	$0.312142\pi$
$644$	21.9930	+	6.26932i	0.866648	+	0.247046i
$645$	16.2462	−	14.2790i	0.639694	−	0.562236i
$646$	−36.8543	−	21.2778i	−1.45001	−	0.837165i
$647$	8.01674	+	13.8854i	0.315171	+	0.545892i	0.979474	−	0.201572i	$-0.0646049\pi$
$647$	8.01674	+	13.8854i	0.315171	+	0.545892i	−0.664303	+	0.747463i	$0.731272\pi$
$648$	3.51078	+	6.08084i	0.137916	+	0.238878i
$649$	26.3032	+	10.3745i	1.03249	+	0.407236i
$650$	−11.9789	−	1.55038i	−0.469850	−	0.0608111i
$651$	−2.95701	+	2.86447i	−0.115894	+	0.112268i
$652$			6.15027i			0.240863i
$653$	39.3535	+	22.7208i	1.54002	+	0.889132i	0.998836	+	0.0482281i	$0.0153574\pi$
$653$	39.3535	+	22.7208i	1.54002	+	0.889132i	0.541185	+	0.840904i	$0.317976\pi$
$654$	−21.0707	+	12.1652i	−0.823930	+	0.475696i
$655$	−23.4835	−	7.94293i	−0.917577	−	0.310356i
$656$	3.48649	−	6.03877i	0.136124	−	0.235774i
$657$			5.17060i			0.201724i
$658$	27.1868	−	6.82346i	1.05985	−	0.266006i
$659$			48.4979i			1.88921i	0.328212	+	0.944604i	$0.393554\pi$
$659$			48.4979i			1.88921i	−0.328212	+	0.944604i	$0.606446\pi$
$660$	−3.92467	−	10.9087i	−0.152767	−	0.424620i
$661$	−17.2004	+	9.93066i	−0.669018	+	0.386258i	−0.795705	−	0.605685i	$-0.792899\pi$
$661$	−17.2004	+	9.93066i	−0.669018	+	0.386258i	0.126686	+	0.991943i	$0.459566\pi$
$662$	−9.35906	−	16.2104i	−0.363750	−	0.630034i
$663$	13.8551	−	23.9978i	0.538089	−	0.931998i
$664$		−	11.1034i		−	0.430894i
$665$	19.4819	−	28.2428i	0.755477	−	1.09521i
$666$		−	2.06176i		−	0.0798914i
$667$	−19.3255	+	33.4727i	−0.748285	+	1.29607i
$668$	−1.68578	+	0.973287i	−0.0652249	+	0.0376576i
$669$	16.2929	+	28.2201i	0.629920	+	1.09105i
$670$	24.7156	−	4.94436i	0.954847	−	0.191017i
$671$	−11.2316	+	1.67351i	−0.433592	+	0.0646053i
$672$	−2.87768	−	2.97064i	−0.111009	−	0.114595i
$673$	15.0386			0.579695			0.289848	−	0.957073i	$-0.406395\pi$
$673$	15.0386			0.579695			0.289848	+	0.957073i	$0.406395\pi$
$674$	1.55200	−	2.68814i	0.0597806	−	0.103543i
$675$	25.6574	−	10.6935i	0.987556	−	0.411593i
$676$	−3.58206	−	6.20432i	−0.137772	−	0.238628i
$677$	−3.39917	−	1.96251i	−0.130641	−	0.0754254i	0.433255	−	0.901271i	$-0.357365\pi$
$677$	−3.39917	−	1.96251i	−0.130641	−	0.0754254i	−0.563896	+	0.825846i	$0.690698\pi$
$678$		−	12.0436i		−	0.462532i
$679$	0.997868	−	3.50057i	0.0382947	−	0.134339i
$680$	10.8319	+	12.3242i	0.415385	+	0.472612i
$681$	−16.2540	−	9.38426i	−0.622855	−	0.359606i
$682$	−2.58461	+	2.05403i	−0.0989699	+	0.0786530i
$683$	38.8580	−	22.4347i	1.48686	−	0.858440i	0.486974	−	0.873417i	$-0.338101\pi$
$683$	38.8580	−	22.4347i	1.48686	−	0.858440i	0.999888	+	0.0149766i	$0.00476738\pi$
$684$	−1.61319	+	2.79413i	−0.0616818	+	0.106836i
$685$	−13.1487	−	14.9602i	−0.502386	−	0.571599i
$686$	3.93526	+	18.0973i	0.150249	+	0.690960i
$687$		−	1.79717i		−	0.0685663i
$688$	3.09391	−	5.35880i	0.117954	−	0.204302i
$689$	2.14851	+	3.72132i	0.0818516	+	0.141771i
$690$	9.68066	−	28.6212i	0.368537	−	1.08959i
$691$	−16.0707	−	9.27845i	−0.611360	−	0.352969i	0.162137	−	0.986768i	$-0.448161\pi$
$691$	−16.0707	−	9.27845i	−0.611360	−	0.352969i	−0.773498	+	0.633799i	$0.781495\pi$
$692$			13.1901i			0.501413i
$693$	0.631776	−	4.84063i	0.0239992	−	0.183880i
$694$	−14.0289			−0.532528
$695$	−8.07256	−	40.3527i	−0.306210	−	1.53066i
$696$	6.05357	−	3.49503i	0.229460	−	0.132479i
$697$	44.3113	−	25.5832i	1.67841	−	0.969031i
$698$	5.45618	−	9.45038i	0.206520	−	0.357702i
$699$	0.0323917			0.00122517
$700$	−10.6045	+	7.90856i	−0.400811	+	0.298916i
$701$		−	20.4291i		−	0.771598i	−0.922583	−	0.385799i	$-0.873926\pi$
$701$		−	20.4291i		−	0.771598i	0.922583	−	0.385799i	$-0.126074\pi$
$702$	−11.6307	−	6.71500i	−0.438973	−	0.253441i
$703$	−18.6138	+	10.7467i	−0.702033	+	0.405319i
$704$	−2.06350	−	2.59653i	−0.0777712	−	0.0978603i
$705$	−7.26439	−	36.3128i	−0.273593	−	1.36762i
$706$	3.91688			0.147414
$707$	6.98054	−	1.75201i	0.262530	−	0.0658910i
$708$		−	13.3270i		−	0.500860i
$709$	−13.1689	+	22.8093i	−0.494570	+	0.856620i	−0.999980	−	0.00625917i	$-0.998008\pi$
$709$	−13.1689	+	22.8093i	−0.494570	+	0.856620i	0.505411	+	0.862879i	$0.331341\pi$
$710$	1.67039	+	0.564982i	0.0626885	+	0.0212034i
$711$	1.49293	−	0.861945i	0.0559893	−	0.0323255i
$712$	−3.28611	−	1.89724i	−0.123152	−	0.0711020i
$713$	−8.60406			−0.322225
$714$	−7.38787	−	29.4355i	−0.276484	−	1.10160i
$715$	13.6814	+	11.5668i	0.511656	+	0.432575i
$716$	−5.38578	+	9.32844i	−0.201276	+	0.348620i
$717$	−5.07646	+	2.93089i	−0.189584	+	0.109456i
$718$	11.8456	−	6.83908i	0.442075	−	0.255232i
$719$	39.2384	+	22.6543i	1.46335	+	0.844863i	0.999164	−	0.0408772i	$-0.0130152\pi$
$719$	39.2384	+	22.6543i	1.46335	+	0.844863i	0.464181	+	0.885740i	$0.346349\pi$
$720$	0.934366	−	0.821228i	0.0348218	−	0.0306054i
$721$	35.4378	+	36.5826i	1.31977	+	1.36241i
$722$	14.6343			0.544632
$723$	15.0806	−	26.1204i	0.560854	−	0.971427i
$724$	−4.08908	+	2.36083i	−0.151969	+	0.0877395i
$725$	−8.60114	−	20.6371i	−0.319438	−	0.766444i
$726$	−3.88292	+	16.7514i	−0.144109	+	0.621702i
$727$	18.1010			0.671329			0.335665	−	0.941982i	$-0.391039\pi$
$727$	18.1010			0.671329			0.335665	+	0.941982i	$0.391039\pi$
$728$	6.14663	+	1.75215i	0.227809	+	0.0649391i
$729$	29.9778			1.11029
$730$	−20.3789	+	4.07680i	−0.754257	+	0.150889i
$731$	39.3218	−	22.7025i	1.45437	−	0.839681i
$732$	2.67613	+	4.63519i	0.0989125	+	0.171321i
$733$	−9.66386	−	5.57943i	−0.356943	−	0.206081i	0.310796	−	0.950477i	$-0.399404\pi$
$733$	−9.66386	−	5.57943i	−0.356943	−	0.206081i	−0.667739	+	0.744396i	$0.732738\pi$
$734$	0.380135			0.0140310
$735$	24.1334	−	4.03480i	0.890175	−	0.148826i
$736$		−	8.64373i		−	0.318612i
$737$	−34.7781	−	13.7172i	−1.28107	−	0.505278i
$738$	−1.93960	−	3.35949i	−0.0713977	−	0.123664i
$739$	−39.9416	+	23.0603i	−1.46928	+	0.848287i	−0.999406	−	0.0344480i	$-0.989033\pi$
$739$	−39.9416	+	23.0603i	−1.46928	+	0.848287i	−0.469870	+	0.882735i	$0.655699\pi$
$740$	8.12601	−	1.62561i	0.298718	−	0.0597586i
$741$			21.9011i			0.804558i
$742$	4.52583	+	1.29013i	0.166148	+	0.0473621i
$743$	−17.7370			−0.650706			−0.325353	−	0.945593i	$-0.605483\pi$
$743$	−17.7370			−0.650706			−0.325353	+	0.945593i	$0.605483\pi$
$744$	1.34758	+	0.778027i	0.0494047	+	0.0285238i
$745$	2.39234	−	7.07304i	0.0876487	−	0.259136i
$746$	−3.71164	−	6.42875i	−0.135893	−	0.235373i
$747$	−5.34945	−	3.08851i	−0.195726	−	0.113003i
$748$	−3.58658	−	24.0710i	−0.131138	−	0.880123i
$749$	−31.0163	−	32.0183i	−1.13331	−	1.16992i
$750$	9.75759	+	14.5000i	0.356297	+	0.529465i
$751$	15.9123	−	27.5609i	0.580648	−	1.00571i	−0.414754	−	0.909933i	$-0.636132\pi$
$751$	15.9123	−	27.5609i	0.580648	−	1.00571i	0.995403	−	0.0957789i	$-0.0305342\pi$
$752$	−5.29717	−	9.17496i	−0.193168	−	0.334576i
$753$	2.52160	−	1.45585i	0.0918922	−	0.0530540i
$754$	−5.40109	+	9.35497i	−0.196696	+	0.340688i
$755$	−0.508848	−	0.578951i	−0.0185189	−	0.0210702i
$756$	−14.2661	+	3.58058i	−0.518855	+	0.130225i
$757$		−	30.9859i		−	1.12620i	−0.826388	−	0.563101i	$-0.809608\pi$
$757$		−	30.9859i		−	1.12620i	0.826388	−	0.563101i	$-0.190392\pi$
$758$	6.04536	−	10.4709i	0.219577	−	0.380319i
$759$	−35.0846	+	27.8823i	−1.27349	+	1.01206i
$760$	−12.2844	−	4.15502i	−0.445603	−	0.150718i
$761$	−12.4190	+	21.5103i	−0.450187	+	0.779747i	−0.998397	−	0.0565938i	$-0.981976\pi$
$761$	−12.4190	+	21.5103i	−0.450187	+	0.779747i	0.548210	+	0.836341i	$0.315309\pi$
$762$	12.1843			0.441391
$763$	−10.0244	−	39.9402i	−0.362907	−	1.44593i
$764$	15.6178			0.565031
$765$	8.95064	−	1.79058i	0.323611	−	0.0647385i
$766$	7.34126	+	12.7154i	0.265251	+	0.459428i
$767$	10.2975	+	17.8359i	0.371822	+	0.644015i
$768$	−0.781614	+	1.35379i	−0.0282041	+	0.0488509i
$769$	16.6967			0.602099			0.301049	−	0.953609i	$-0.402663\pi$
$769$	16.6967			0.602099			0.301049	+	0.953609i	$0.402663\pi$
$770$	19.5765	−	1.32661i	0.705489	−	0.0478078i
$771$	−8.02303			−0.288942
$772$	−0.956755	+	1.65715i	−0.0344344	+	0.0596421i
$773$	−1.87123	−	3.24107i	−0.0673036	−	0.116573i	0.830410	−	0.557153i	$-0.188106\pi$
$773$	−1.87123	−	3.24107i	−0.0673036	−	0.116573i	−0.897714	+	0.440580i	$0.854773\pi$
$774$	−1.72120	−	2.98121i	−0.0618672	−	0.107157i
$775$	3.02119	−	3.95518i	0.108524	−	0.142074i
$776$	−1.37580			−0.0493882
$777$	−14.7408	−	4.20198i	−0.528822	−	0.150745i
$778$	24.7121			0.885973
$779$	−20.2199	+	35.0219i	−0.724454	+	1.25479i
$780$	2.70556	−	7.99906i	0.0968745	−	0.286412i
$781$	−1.62726	−	2.04760i	−0.0582281	−	0.0732691i
$782$	31.7130	−	54.9285i	1.13405	−	1.96424i
$783$		−	24.8589i		−	0.888384i
$784$	6.17036	−	3.30556i	0.220370	−	0.118056i
$785$	−30.5120	+	26.8174i	−1.08902	+	0.957155i
$786$	8.66545	−	15.0090i	0.309087	−	0.535354i
$787$	−29.5678	+	17.0710i	−1.05398	+	0.608514i	−0.923760	−	0.382971i	$-0.874901\pi$
$787$	−29.5678	+	17.0710i	−1.05398	+	0.608514i	−0.130218	+	0.991485i	$0.541568\pi$
$788$	7.41829	+	12.8489i	0.264266	+	0.457722i
$789$	−9.33896	+	16.1756i	−0.332476	+	0.575865i
$790$	4.57430	+	5.20449i	0.162746	+	0.185168i
$791$	19.6028	+	5.58796i	0.696996	+	0.198685i
$792$	−1.82496	+	0.271919i	−0.0648470	+	0.00966221i
$793$	−7.16305	−	4.13559i	−0.254367	−	0.146859i
$794$	−9.10381	−	15.7683i	−0.323082	−	0.559595i
$795$	1.99213	−	5.88979i	0.0706535	−	0.208889i
$796$	−18.8792	−	10.8999i	−0.669156	−	0.386337i
$797$	48.7853			1.72806			0.864032	−	0.503438i	$-0.167932\pi$
$797$	48.7853			1.72806			0.864032	+	0.503438i	$0.167932\pi$
$798$	16.6891	+	17.2283i	0.590789	+	0.609874i
$799$		−	77.7391i		−	2.75021i
$800$	3.97342	+	3.03512i	0.140482	+	0.107308i
$801$	−1.82813	+	1.05547i	−0.0645937	+	0.0372932i
$802$	11.0903	+	19.2090i	0.391613	+	0.678294i
$803$	28.6758	+	11.3103i	1.01195	+	0.399132i
$804$			17.6209i			0.621443i
$805$	42.0937	+	29.0363i	1.48361	+	1.02340i
$806$	−2.40467			−0.0847008
$807$	14.8443	+	8.57037i	0.522545	+	0.301691i
$808$	−1.36011	−	2.35579i	−0.0478486	−	0.0828762i
$809$	2.38177	−	1.37512i	0.0837386	−	0.0483465i	−0.457546	−	0.889186i	$-0.651271\pi$
$809$	2.38177	−	1.37512i	0.0837386	−	0.0483465i	0.541285	+	0.840839i	$0.317938\pi$
$810$	3.07990	+	15.3956i	0.108217	+	0.540947i
$811$	30.7840			1.08097			0.540486	−	0.841353i	$-0.318240\pi$
$811$	30.7840			1.08097			0.540486	+	0.841353i	$0.318240\pi$
$812$	2.87998	+	11.4747i	0.101068	+	0.402684i
$813$	−36.3740			−1.27569
$814$	−11.4344	−	4.50994i	−0.400774	−	0.158073i
$815$	−4.40632	+	13.0274i	−0.154346	+	0.456330i
$816$	−9.93388	+	5.73533i	−0.347755	+	0.200777i
$817$	−17.9431	+	31.0784i	−0.627751	+	1.08730i
$818$	22.6099			0.790538
$819$	2.55391	−	2.47399i	0.0892408	−	0.0864481i
$820$	11.7115	−	10.2934i	0.408982	−	0.359460i
$821$	−21.9663	−	12.6823i	−0.766630	−	0.442614i	0.0650411	−	0.997883i	$-0.479282\pi$
$821$	−21.9663	−	12.6823i	−0.766630	−	0.442614i	−0.831671	+	0.555269i	$0.812615\pi$
$822$	12.0586	−	6.96202i	0.420591	−	0.242828i
$823$	−8.96688	+	5.17703i	−0.312566	+	0.180460i	−0.648074	−	0.761577i	$-0.724425\pi$
$823$	−8.96688	+	5.17703i	−0.312566	+	0.180460i	0.335508	+	0.942037i	$0.391092\pi$
$824$	9.62535	−	16.6716i	0.335315	−	0.580783i
$825$	−0.497716	−	25.9184i	−0.0173283	−	0.902364i
$826$	21.6918	+	6.18343i	0.754753	+	0.215149i
$827$	−42.0465			−1.46210			−0.731049	−	0.682325i	$-0.760969\pi$
$827$	−42.0465			−1.46210			−0.731049	+	0.682325i	$0.760969\pi$
$828$	−4.16443	−	2.40434i	−0.144724	−	0.0835565i
$829$	4.88779	−	2.82197i	0.169760	−	0.0980109i	−0.412713	−	0.910861i	$-0.635419\pi$
$829$	4.88779	−	2.82197i	0.169760	−	0.0980109i	0.582473	+	0.812850i	$0.302085\pi$
$830$	7.95493	−	23.5190i	0.276119	−	0.816356i
$831$	−16.0880	+	27.8652i	−0.558085	+	0.966632i
$832$		−	2.41576i		−	0.0837512i
$833$	51.3387	+	1.63253i	1.77878	+	0.0565639i
$834$	28.7694			0.996202
$835$	−4.26810	+	0.853835i	−0.147704	+	0.0295482i
$836$	11.9673	+	15.0586i	0.413898	+	0.520812i
$837$	4.79243	−	2.76691i	0.165651	−	0.0956384i
$838$	−19.1998	−	11.0850i	−0.663245	−	0.382924i
$839$		−	18.9602i		−	0.654579i	−0.944924	−	0.327290i	$-0.893865\pi$
$839$		−	18.9602i		−	0.654579i	0.944924	−	0.327290i	$-0.106135\pi$
$840$	−3.96716	−	8.35407i	−0.136880	−	0.288243i
$841$	9.00518			0.310523
$842$	2.53364	−	4.38840i	0.0873151	−	0.151234i
$843$	8.80507	−	5.08361i	0.303263	−	0.175089i
$844$	−19.3583	+	11.1765i	−0.666341	+	0.384712i
$845$	−3.14244	−	15.7082i	−0.108103	−	0.540380i
$846$	−5.89383			−0.202634
$847$	−25.4638	−	14.0923i	−0.874948	−	0.484217i
$848$		−	1.77874i		−	0.0610823i
$849$	19.6037	+	11.3182i	0.672796	+	0.388439i
$850$	14.1144	+	33.8654i	0.484121	+	1.16157i
$851$	−16.0171	−	27.7425i	−0.549060	−	0.950999i
$852$	−0.616375	+	1.06759i	−0.0211167	+	0.0365752i
$853$		−	27.6201i		−	0.945693i	−0.881145	−	0.472846i	$-0.843227\pi$
$853$		−	27.6201i		−	0.945693i	0.881145	−	0.472846i	$-0.156773\pi$
$854$	−8.78614	+	2.20519i	−0.300656	+	0.0754599i
$855$	−5.41887	+	4.76272i	−0.185321	+	0.162882i
$856$	−8.42442	+	14.5915i	−0.287941	+	0.498728i
$857$	17.2917	−	9.98337i	0.590673	−	0.341025i	−0.174690	−	0.984623i	$-0.555892\pi$
$857$	17.2917	−	9.98337i	0.590673	−	0.341025i	0.765364	+	0.643598i	$0.222559\pi$
$858$	−9.80546	+	7.79256i	−0.334753	+	0.266034i
$859$	13.2809	+	7.66771i	0.453137	+	0.261619i	0.709154	−	0.705053i	$-0.249077\pi$
$859$	13.2809	+	7.66771i	0.453137	+	0.261619i	−0.256017	+	0.966672i	$0.582410\pi$
$860$	10.3927	−	9.13433i	0.354390	−	0.311478i
$861$	−27.9720	+	7.02055i	−0.953284	+	0.239260i
$862$		−	1.72828i		−	0.0588653i
$863$	43.9294	+	25.3627i	1.49538	+	0.863355i	0.999986	−	0.00531596i	$-0.00169213\pi$
$863$	43.9294	+	25.3627i	1.49538	+	0.863355i	0.495389	+	0.868671i	$0.335025\pi$
$864$	2.77967	+	4.81453i	0.0945662	+	0.163794i
$865$	−9.44998	+	27.9391i	−0.321309	+	0.949959i
$866$	−0.583254	+	1.01023i	−0.0198198	+	0.0343289i
$867$	−57.5945			−1.95601
$868$	−1.89161	+	1.83241i	−0.0642053	+	0.0621960i
$869$	−1.51461	−	10.1651i	−0.0513796	−	0.344829i
$870$	15.3266	−	3.06608i	0.519620	−	0.103950i
$871$	−13.6154	−	23.5825i	−0.461340	−	0.799064i
$872$	−13.4790	+	7.78209i	−0.456456	+	0.263535i
$873$	−0.382691	+	0.662840i	−0.0129521	+	0.0224337i
$874$			50.1294i			1.69565i
$875$	−28.1283	+	9.15431i	−0.950909	+	0.309472i
$876$		−	14.5291i		−	0.490893i
$877$	12.0867	−	20.9347i	0.408137	−	0.706915i	−0.586544	−	0.809918i	$-0.699512\pi$
$877$	12.0867	−	20.9347i	0.408137	−	0.706915i	0.994681	+	0.103003i	$0.0328451\pi$
$878$	−7.42466	−	12.8599i	−0.250570	−	0.434000i
$879$	−26.3549	+	15.2160i	−0.888929	+	0.513223i
$880$	−2.51062	−	6.97831i	−0.0846329	−	0.235239i
$881$			36.0228i			1.21364i	0.794840	+	0.606819i	$0.207555\pi$
$881$			36.0228i			1.21364i	−0.794840	+	0.606819i	$0.792445\pi$
$882$	0.123771	−	3.89227i	0.00416760	−	0.131059i
$883$		−	1.47027i		−	0.0494785i	−0.999694	−	0.0247393i	$-0.992124\pi$
$883$		−	1.47027i		−	0.0494785i	0.999694	−	0.0247393i	$-0.00787556\pi$
$884$	8.86317	−	15.3515i	0.298101	−	0.516325i
$885$	9.54804	−	28.2291i	0.320954	−	0.948910i
$886$	27.9784	−	16.1533i	0.939953	−	0.542682i
$887$	−23.8127	−	13.7483i	−0.799552	−	0.461622i	0.0437623	−	0.999042i	$-0.486066\pi$
$887$	−23.8127	−	13.7483i	−0.799552	−	0.461622i	−0.843315	+	0.537420i	$0.819399\pi$
$888$			5.79343i			0.194415i
$889$	−5.65325	+	19.8319i	−0.189604	+	0.665139i
$890$	−5.60133	−	6.37301i	−0.187757	−	0.213624i
$891$	8.54458	−	21.6637i	0.286254	−	0.725760i
$892$	10.4226	+	18.0525i	0.348975	+	0.604442i
$893$	30.7210	+	53.2103i	1.02804	+	1.78061i
$894$	4.52059	+	2.60996i	0.151191	+	0.0872902i
$895$	−18.0914	+	15.9008i	−0.604728	+	0.531504i
$896$	−1.84086	−	1.90033i	−0.0614988	−	0.0634855i
$897$	−32.6420			−1.08988
$898$	15.6298	−	27.0717i	0.521575	−	0.903394i
$899$	−2.22552	−	3.85471i	−0.0742252	−	0.128562i
$900$	2.56752	−	1.07009i	0.0855842	−	0.0356698i
$901$	6.52604	−	11.3034i	0.217414	−	0.376572i
$902$	−22.8742	+	3.40826i	−0.761628	+	0.113483i
$903$	−24.8224	+	6.23003i	−0.826036	+	0.207322i
$904$		−	7.70432i		−	0.256242i
$905$	−10.3528	+	2.07108i	−0.344139	+	0.0688452i
$906$	0.466661	−	0.269427i	0.0155038	−	0.00895111i
$907$	−1.99949	+	1.15440i	−0.0663918	+	0.0383313i	−0.532828	−	0.846223i	$-0.678871\pi$
$907$	−1.99949	+	1.15440i	−0.0663918	+	0.0383313i	0.466437	+	0.884555i	$0.345538\pi$
$908$	−10.3977	−	6.00313i	−0.345061	−	0.199221i
$909$	−1.51331			−0.0501935
$910$	11.7644	+	8.11509i	0.389986	+	0.269013i
$911$	15.2046			0.503752			0.251876	−	0.967760i	$-0.418953\pi$
$911$	15.2046			0.503752			0.251876	+	0.967760i	$0.418953\pi$
$912$	4.53298	−	7.85134i	0.150102	−	0.259984i
$913$	−28.8302	+	22.9118i	−0.954140	+	0.758270i
$914$	20.0531	+	34.7330i	0.663297	+	1.14886i
$915$	2.34768	+	11.7355i	0.0776121	+	0.387963i
$916$		−	1.14965i		−	0.0379856i
$917$	20.4089	+	21.0682i	0.673961	+	0.695733i
$918$			40.7933i			1.34638i
$919$	−1.33444	−	0.770439i	−0.0440191	−	0.0254144i	0.477829	−	0.878453i	$-0.341424\pi$
$919$	−1.33444	−	0.770439i	−0.0440191	−	0.0254144i	−0.521848	+	0.853038i	$0.674757\pi$
$920$	6.19274	−	18.3090i	0.204169	−	0.603631i
$921$	10.0125	−	5.78069i	0.329922	−	0.190480i
$922$	10.6909	−	18.5171i	0.352085	−	0.609830i
$923$		−	1.90505i		−	0.0627054i
$924$	−1.77526	+	13.6019i	−0.0584017	+	0.447470i
$925$	18.3771	+	2.37848i	0.604234	+	0.0782040i
$926$	−17.9715	−	10.3759i	−0.590581	−	0.340972i
$927$	−5.35477	−	9.27473i	−0.175874	−	0.304622i
$928$	3.87248	−	2.23578i	0.127120	−	0.0733930i
$929$	−4.87979	−	2.81735i	−0.160101	−	0.0924342i	0.417809	−	0.908535i	$-0.362798\pi$
$929$	−4.87979	−	2.81735i	−0.160101	−	0.0924342i	−0.577910	+	0.816101i	$0.696131\pi$
$930$	2.29702	+	2.61347i	0.0753221	+	0.0856991i
$931$	−35.7850	+	19.1706i	−1.17281	+	0.628291i
$932$	0.0207210			0.000678740
$933$	−16.5671	−	9.56505i	−0.542384	−	0.313146i
$934$	0.436949	+	0.756818i	0.0142974	+	0.0247638i
$935$	9.64845	−	53.5564i	0.315538	−	1.75148i
$936$	−1.16388	−	0.671966i	−0.0380426	−	0.0219639i
$937$			53.8656i			1.75971i	0.475241	+	0.879855i	$0.342361\pi$
$937$			53.8656i			1.75971i	−0.475241	+	0.879855i	$0.657639\pi$
$938$	−28.6808	−	8.17572i	−0.936461	−	0.266947i
$939$	32.3306			1.05507
$940$	−4.64704	−	23.2294i	−0.151570	−	0.757659i
$941$	−9.19669	−	15.9291i	−0.299804	−	0.519275i	0.676287	−	0.736638i	$-0.263588\pi$
$941$	−9.19669	−	15.9291i	−0.299804	−	0.519275i	−0.976091	+	0.217363i	$0.930254\pi$
$942$	−14.1994	−	24.5941i	−0.462641	−	0.801318i
$943$	−52.1975	−	30.1363i	−1.69979	−	0.981372i
$944$		−	8.52531i		−	0.277475i
$945$	−32.7836	−	2.63654i	−1.06645	−	0.0857668i
$946$	−20.2986	+	3.02449i	−0.659963	+	0.0983346i
$947$	−19.5459	−	11.2848i	−0.635156	−	0.366707i	0.147590	−	0.989049i	$-0.452848\pi$
$947$	−19.5459	−	11.2848i	−0.635156	−	0.366707i	−0.782746	+	0.622341i	$0.786182\pi$
$948$	−4.19506	+	2.42202i	−0.136249	+	0.0786635i
$949$	11.2264	+	19.4447i	0.364424	+	0.631200i
$950$	−23.0439	−	17.6022i	−0.747642	−	0.571091i
$951$		−	12.2102i		−	0.395943i
$952$	−4.72603	−	18.8300i	−0.153172	−	0.610283i
$953$	48.0685			1.55709			0.778546	−	0.627587i	$-0.215957\pi$
$953$	48.0685			1.55709			0.778546	+	0.627587i	$0.215957\pi$
$954$	−0.856976	−	0.494775i	−0.0277456	−	0.0160189i
$955$	33.0813	+	11.1892i	1.07049	+	0.362075i
$956$	−3.24742	+	1.87490i	−0.105029	+	0.0606386i
$957$	−21.5665	−	8.50626i	−0.697146	−	0.274968i
$958$	4.03492			0.130362
$959$	5.73686	+	22.8574i	0.185253	+	0.738104i
$960$	−2.62552	+	2.30761i	−0.0847383	+	0.0744777i
$961$	−15.0046	+	25.9887i	−0.484019	+	0.838345i
$962$	−4.47647	−	7.75348i	−0.144327	−	0.249982i
$963$	4.68667	+	8.11755i	0.151026	+	0.261584i
$964$	9.64709	−	16.7093i	0.310712	−	0.538169i
$965$	−3.21384	+	2.82469i	−0.103457	+	0.0909299i
$966$	−25.6774	+	24.8739i	−0.826158	+	0.800304i
$967$	33.6784			1.08302			0.541512	−	0.840693i	$-0.317852\pi$
$967$	33.6784			1.08302			0.541512	+	0.840693i	$0.317852\pi$
$968$	−2.48391	+	10.7159i	−0.0798360	+	0.344422i
$969$	57.6116	−	33.2621i	1.85075	−	1.06853i
$970$	−2.91419	−	0.985680i	−0.0935691	−	0.0316483i
$971$	4.09133	+	2.36213i	0.131297	+	0.0758043i	0.564210	−	0.825631i	$-0.309181\pi$
$971$	4.09133	+	2.36213i	0.131297	+	0.0758043i	−0.432913	+	0.901436i	$0.642514\pi$
$972$	5.70173			0.182883
$973$	−13.3483	+	46.8266i	−0.427928	+	1.50119i
$974$		−	12.2821i		−	0.393544i
$975$	11.4617	−	15.0051i	0.367070	−	0.480548i
$976$	1.71192	+	2.96514i	0.0547974	+	0.0949118i
$977$	−23.7125	+	13.6904i	−0.758629	+	0.437995i	−0.828803	−	0.559540i	$-0.810978\pi$
$977$	−23.7125	+	13.6904i	−0.758629	+	0.437995i	0.0701744	+	0.997535i	$0.477644\pi$
$978$	−8.32620	−	4.80713i	−0.266242	−	0.153715i
$979$	1.85467	+	12.4474i	0.0592755	+	0.397822i
$980$	15.4382	−	2.58107i	0.493155	−	0.0824493i
$981$			8.65866i			0.276450i
$982$	−6.04979	−	3.49285i	−0.193057	−	0.111461i
$983$	−19.8353	−	34.3557i	−0.632646	−	1.09578i	−0.987009	−	0.160668i	$-0.948635\pi$
$983$	−19.8353	−	34.3557i	−0.632646	−	1.09578i	0.354362	−	0.935108i	$-0.384698\pi$
$984$	5.45017	+	9.43998i	0.173745	+	0.300935i
$985$	6.50784	+	32.5310i	0.207357	+	1.03653i
$986$	32.8114			1.04493
$987$	−12.0120	+	42.1386i	−0.382346	+	1.34129i
$988$			14.0102i			0.445724i
$989$	−46.3200	−	26.7429i	−1.47289	−	0.850374i
$990$	−4.06041	−	0.731503i	−0.129048	−	0.0232487i
$991$	−29.7219	−	51.4798i	−0.944147	−	1.63531i	−0.757450	−	0.652893i	$-0.773555\pi$
$991$	−29.7219	−	51.4798i	−0.944147	−	1.63531i	−0.186697	−	0.982418i	$-0.559778\pi$
$992$	0.862051	+	0.497705i	0.0273701	+	0.0158022i
$993$	29.2607			0.928560
$994$	−1.45169	−	1.49858i	−0.0460448	−	0.0475322i
$995$	−32.1805	−	36.6139i	−1.02019	−	1.16074i
$996$	15.0317	+	8.67854i	0.476297	+	0.274990i
$997$	−16.6501	+	9.61297i	−0.527315	+	0.304446i	−0.739923	−	0.672692i	$-0.765138\pi$
$997$	−16.6501	+	9.61297i	−0.527315	+	0.304446i	0.212607	+	0.977138i	$0.431805\pi$
$998$	15.3366	+	26.5638i	0.485472	+	0.840862i
$999$	17.8430	+	10.3016i	0.564526	+	0.325929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.a.439.6	✓	48
5.4	even	2		770.2.o.b.439.19	yes	48
7.3	odd	6	inner	770.2.o.a.549.19	yes	48
11.10	odd	2		770.2.o.b.439.6	yes	48
35.24	odd	6		770.2.o.b.549.6	yes	48
55.54	odd	2	inner	770.2.o.a.439.19	yes	48
77.10	even	6		770.2.o.b.549.19	yes	48
385.164	even	6	inner	770.2.o.a.549.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.6	✓	48	1.1	even	1	trivial
770.2.o.a.439.19	yes	48	55.54	odd	2	inner
770.2.o.a.549.6	yes	48	385.164	even	6	inner
770.2.o.a.549.19	yes	48	7.3	odd	6	inner
770.2.o.b.439.6	yes	48	11.10	odd	2
770.2.o.b.439.19	yes	48	5.4	even	2
770.2.o.b.549.6	yes	48	35.24	odd	6
770.2.o.b.549.19	yes	48	77.10	even	6

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.781614 - 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.438635 - 2.19262i) q^{5} +1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.781614 - 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.438635 - 2.19262i) q^{5} +1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +(2.11819 + 0.716443i) q^{10} +(-2.06350 - 2.59653i) q^{11} +(-0.781614 + 1.35379i) q^{12} -2.41576i q^{13} +(-1.84086 - 1.90033i) q^{14} +(-2.62552 + 2.30761i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-6.35472 + 3.66890i) q^{17} +(0.278160 + 0.481787i) q^{18} +(2.89975 - 5.02252i) q^{19} +(-1.67955 + 1.47618i) q^{20} +(4.01149 - 1.00682i) q^{21} +(3.28041 - 0.488782i) q^{22} +(7.48569 + 4.32187i) q^{23} +(-0.781614 - 1.35379i) q^{24} +(-4.61520 + 1.92352i) q^{25} +(2.09211 + 1.20788i) q^{26} -5.55934 q^{27} +(2.56616 - 0.644067i) q^{28} +4.47156i q^{29} +(-0.685686 - 3.42757i) q^{30} +(-0.862051 + 0.497705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.90230 + 4.82304i) q^{33} -7.33780i q^{34} +(5.89704 + 0.474255i) q^{35} -0.556319 q^{36} +(-3.20955 - 1.85303i) q^{37} +(2.89975 + 5.02252i) q^{38} +(-3.27044 + 1.88819i) q^{39} +(-0.438635 - 2.19262i) q^{40} -6.97297 q^{41} +(-1.13381 + 3.97747i) q^{42} -6.18781 q^{43} +(-1.21691 + 3.08531i) q^{44} +(-1.17839 - 0.398571i) q^{45} +(-7.48569 + 4.32187i) q^{46} +(-5.29717 + 9.17496i) q^{47} +1.56323 q^{48} +(-5.94787 - 3.69091i) q^{49} +(0.641780 - 4.95864i) q^{50} +(9.93388 + 5.73533i) q^{51} +(-2.09211 + 1.20788i) q^{52} +(-1.54044 + 0.889372i) q^{53} +(2.77967 - 4.81453i) q^{54} +(-4.78808 + 5.66341i) q^{55} +(-0.725302 + 2.54439i) q^{56} -9.06595 q^{57} +(-3.87248 - 2.23578i) q^{58} +(-7.38314 + 4.26266i) q^{59} +(3.31121 + 1.11996i) q^{60} +(1.71192 - 2.96514i) q^{61} -0.995411i q^{62} +(1.02411 + 1.05719i) q^{63} +1.00000 q^{64} +(-5.29684 + 1.05963i) q^{65} +(-3.22572 - 4.05896i) q^{66} +(9.76197 - 5.63608i) q^{67} +(6.35472 + 3.66890i) q^{68} -13.5121i q^{69} +(-3.35924 + 4.86986i) q^{70} +0.788593 q^{71} +(0.278160 - 0.481787i) q^{72} +(-8.04910 + 4.64715i) q^{73} +(3.20955 - 1.85303i) q^{74} +(6.21136 + 4.74458i) q^{75} -5.79951 q^{76} +(8.10325 - 3.36710i) q^{77} -3.77638i q^{78} +(2.68359 + 1.54937i) q^{79} +(2.11819 + 0.716443i) q^{80} +(3.51078 + 6.08084i) q^{81} +(3.48649 - 6.03877i) q^{82} -11.1034i q^{83} +(-2.87768 - 2.97064i) q^{84} +(10.8319 + 12.3242i) q^{85} +(3.09391 - 5.35880i) q^{86} +(6.05357 - 3.49503i) q^{87} +(-2.06350 - 2.59653i) q^{88} +(-3.28611 - 1.89724i) q^{89} +(0.934366 - 0.821228i) q^{90} +(6.14663 + 1.75215i) q^{91} -8.64373i q^{92} +(1.34758 + 0.778027i) q^{93} +(-5.29717 - 9.17496i) q^{94} +(-12.2844 - 4.15502i) q^{95} +(-0.781614 + 1.35379i) q^{96} -1.37580 q^{97} +(6.17036 - 3.30556i) q^{98} +(-1.82496 + 0.271919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9	\( 48 q - 24 q^{2} - 24 q^{4} - 6 q^{5} - 4 q^{7} + 48 q^{8} - 28 q^{9} + 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} - 28 q^{18} - 2 q^{22} - 6 q^{26} + 2 q^{28} - 2 q^{30} + 12 q^{31} - 24 q^{32} + 24 q^{33} - 8 q^{35} + 56 q^{36} - 6 q^{40} + 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} + 6 q^{52} - 4 q^{56} - 4 q^{57} - 2 q^{60} - 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} - 28 q^{72} + 42 q^{73} + 90 q^{75} + 19 q^{77} + 6 q^{80} - 72 q^{81} - 40 q^{85} - 12 q^{86} + 18 q^{87} + q^{88} + 60 q^{89} - 56 q^{91} + 24 q^{95} + 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 24 * q^4 - 6 * q^5 - 4 * q^7 + 48 * q^8 - 28 * q^9 + 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 - 28 * q^18 - 2 * q^22 - 6 * q^26 + 2 * q^28 - 2 * q^30 + 12 * q^31 - 24 * q^32 + 24 * q^33 - 8 * q^35 + 56 * q^36 - 6 * q^40 + 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 + 6 * q^52 - 4 * q^56 - 4 * q^57 - 2 * q^60 - 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 - 28 * q^72 + 42 * q^73 + 90 * q^75 + 19 * q^77 + 6 * q^80 - 72 * q^81 - 40 * q^85 - 12 * q^86 + 18 * q^87 + q^88 + 60 * q^89 - 56 * q^91 + 24 * q^95 + 42 * q^98 - 58 * q^99

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