LMFDB - Embedded newform 770.2.o.a.439.19

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			439.19
Character	$\chi$	$=$	770.439
Dual form			770.2.o.a.549.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.781614 + 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.11819 + 0.716443i) q^{5} -1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.781614 + 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.11819 + 0.716443i) q^{5} -1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +(0.438635 - 2.19262i) q^{10} +(-1.21691 - 3.08531i) 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} +(3.97342 - 3.03512i) q^{25} +(2.09211 + 1.20788i) q^{26} +5.55934 q^{27} +(2.56616 - 0.644067i) q^{28} -4.47156i q^{29} +(3.31121 - 1.11996i) q^{30} +(-0.862051 + 0.497705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.22572 - 4.05896i) q^{33} -7.33780i q^{34} +(-0.286589 - 5.90913i) q^{35} -0.556319 q^{36} +(3.20955 + 1.85303i) q^{37} +(-2.89975 - 5.02252i) q^{38} +(3.27044 - 1.88819i) q^{39} +(-2.11819 + 0.716443i) q^{40} +6.97297 q^{41} +(1.13381 - 3.97747i) q^{42} -6.18781 q^{43} +(-2.06350 + 2.59653i) q^{44} +(-0.244021 + 1.21980i) 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} +(-0.685686 + 3.42757i) q^{60} +(-1.71192 + 2.96514i) q^{61} -0.995411i q^{62} +(1.02411 + 1.05719i) q^{63} +1.00000 q^{64} +(1.73075 + 5.11702i) q^{65} +(1.90230 + 4.82304i) q^{66} +(-9.76197 + 5.63608i) q^{67} +(6.35472 + 3.66890i) q^{68} -13.5121i q^{69} +(5.26075 + 2.70637i) q^{70} +0.788593 q^{71} +(0.278160 - 0.481787i) q^{72} +(-8.04910 + 4.64715i) q^{73} +(-3.20955 + 1.85303i) q^{74} +(7.21461 + 3.00690i) q^{75} +5.79951 q^{76} +(8.73287 - 0.858510i) q^{77} +3.77638i q^{78} +(-2.68359 - 1.54937i) q^{79} +(0.438635 - 2.19262i) 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} +(-1.21691 - 3.08531i) 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} +(2.54387 - 12.7161i) 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	0.998465	−	0.0553881i	$-0.0176396\pi$
$3$	0.781614	+	1.35379i	0.451265	+	0.781614i	−0.547200	+	0.837002i	$0.684306\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.11819	+	0.716443i	−0.947281	+	0.320403i
$5$	−2.11819	+	0.716443i	−0.947281	+	0.320403i
$6$	−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
$10$	0.438635	−	2.19262i	0.138708	−	0.693369i
$11$	−1.21691	−	3.08531i	−0.366911	−	0.930256i
$11$	−1.21691	−	3.08531i	−0.366911	−	0.930256i
$12$	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	$0.398341\pi$
$19$	−2.89975	+	5.02252i	−0.665249	+	1.15225i	−0.979218	+	0.202812i	$0.934992\pi$
$20$	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	$-0.976042\pi$
$23$	−7.48569	−	4.32187i	−1.56087	−	0.901171i	−0.563705	−	0.825976i	$-0.690625\pi$
$24$	0.781614	+	1.35379i	0.159546	+	0.276342i
$25$	3.97342	−	3.03512i	0.794684	−	0.607024i
$26$	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	$-0.863721\pi$
$29$		−	4.47156i		−	0.830347i	0.909742	−	0.415174i	$-0.136279\pi$
$30$	3.31121	−	1.11996i	0.604541	−	0.204476i
$31$	−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
$33$	3.22572	−	4.05896i	0.561527	−	0.706575i
$34$		−	7.33780i		−	1.25842i
$35$	−0.286589	−	5.90913i	−0.0484423	−	0.998826i
$36$	−0.556319			−0.0927199
$37$	3.20955	+	1.85303i	0.527646	+	0.304637i	0.740057	−	0.672544i	$-0.234798\pi$
$37$	3.20955	+	1.85303i	0.527646	+	0.304637i	−0.212411	+	0.977180i	$0.568132\pi$
$38$	−2.89975	−	5.02252i	−0.470402	−	0.814761i
$39$	3.27044	−	1.88819i	0.523689	−	0.302352i
$40$	−2.11819	+	0.716443i	−0.334915	+	0.113280i
$41$	6.97297			1.08900			0.544498	−	0.838762i	$-0.316720\pi$
$41$	6.97297			1.08900			0.544498	+	0.838762i	$0.316720\pi$
$42$	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	$0.656401\pi$
$44$	−2.06350	+	2.59653i	−0.311085	+	0.391441i
$45$	−0.244021	+	1.21980i	−0.0363765	+	0.181837i
$46$	7.48569	−	4.32187i	1.10370	−	0.637224i
$47$	5.29717	−	9.17496i	0.772671	−	1.33831i	−0.163423	−	0.986556i	$-0.552254\pi$
$47$	5.29717	−	9.17496i	0.772671	−	1.33831i	0.936094	−	0.351750i	$-0.114413\pi$
$48$	−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	−0.390457	−	0.920621i	$-0.627683\pi$
$53$	1.54044	−	0.889372i	0.211595	−	0.122165i	0.602053	+	0.798456i	$0.294350\pi$
$54$	−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	$0.520596\pi$
$60$	−0.685686	+	3.42757i	−0.0885217	+	0.442497i
$61$	−1.71192	+	2.96514i	−0.219189	+	0.379647i	−0.954560	−	0.298018i	$-0.903675\pi$
$61$	−1.71192	+	2.96514i	−0.219189	+	0.379647i	0.735371	+	0.677665i	$0.237008\pi$
$62$		−	0.995411i		−	0.126417i
$63$	1.02411	+	1.05719i	0.129025	+	0.133193i
$64$	1.00000			0.125000
$65$	1.73075	+	5.11702i	0.214673	+	0.634688i
$66$	1.90230	+	4.82304i	0.234157	+	0.593675i
$67$	−9.76197	+	5.63608i	−1.19261	+	0.688556i	−0.958899	−	0.283749i	$-0.908422\pi$
$67$	−9.76197	+	5.63608i	−1.19261	+	0.688556i	−0.233716	+	0.972305i	$0.575089\pi$
$68$	6.35472	+	3.66890i	0.770623	+	0.444920i
$69$		−	13.5121i		−	1.62667i
$70$	5.26075	+	2.70637i	0.628780	+	0.323474i
$71$	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
$75$	7.21461	+	3.00690i	0.833071	+	0.347207i
$76$	5.79951			0.665249
$77$	8.73287	−	0.858510i	0.995203	−	0.0978364i
$78$			3.77638i			0.427590i
$79$	−2.68359	−	1.54937i	−0.301927	−	0.174318i	0.341381	−	0.939925i	$-0.389105\pi$
$79$	−2.68359	−	1.54937i	−0.301927	−	0.174318i	−0.643308	+	0.765607i	$0.722439\pi$
$80$	0.438635	−	2.19262i	0.0490409	−	0.245143i
$81$	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
$88$	−1.21691	−	3.08531i	−0.129723	−	0.328895i
$89$	−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
$95$	2.54387	−	12.7161i	0.260995	−	1.30465i
$96$	0.781614	−	1.35379i	0.0797731	−	0.138171i
$97$	1.37580			0.139691			0.0698455	−	0.997558i	$-0.477749\pi$
$97$	1.37580			0.139691			0.0698455	+	0.997558i	$0.477749\pi$
$98$	6.17036	−	3.30556i	0.623300	−	0.333912i
$99$	−1.82496	−	0.271919i	−0.183415	−	0.0273289i
$100$	−4.61520	−	1.92352i	−0.461520	−	0.192352i
$101$	1.36011	+	2.35579i	0.135336	+	0.234409i	0.925726	−	0.378195i	$-0.123455\pi$
$101$	1.36011	+	2.35579i	0.135336	+	0.234409i	−0.790390	+	0.612605i	$0.790122\pi$
$102$	9.93388	−	5.73533i	0.983601	−	0.567882i
$103$	−9.62535	+	16.6716i	−0.948414	+	1.64270i	−0.199647	+	0.979868i	$0.563980\pi$
$103$	−9.62535	+	16.6716i	−0.948414	+	1.64270i	−0.748767	+	0.662833i	$0.769354\pi$
$104$		−	2.41576i		−	0.236884i
$105$	7.77575	−	5.00664i	0.758836	−	0.488598i
$106$			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	0.312211	−	0.950013i	$-0.398930\pi$
$109$	13.4790	−	7.78209i	1.29105	−	0.745389i	0.978841	+	0.204624i	$0.0655970\pi$
$110$	−7.29870	+	1.31490i	−0.695904	+	0.125371i
$111$			5.79343i			0.549888i
$112$	−1.84086	−	1.90033i	−0.173945	−	0.179564i
$113$			7.70432i			0.724762i	0.932030	+	0.362381i	$0.118036\pi$
$113$			7.70432i			0.724762i	−0.932030	+	0.362381i	$0.881964\pi$
$114$	4.53298	−	7.85134i	0.424552	−	0.735346i
$115$	18.9525	+	3.79144i	1.76733	+	0.353554i
$116$	−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
$121$	−8.03827	+	7.50907i	−0.730752	+	0.682643i
$122$	−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
$130$	−5.29684	−	1.05963i	−0.464564	−	0.0929361i
$131$	−5.54331	+	9.60129i	−0.484321	+	0.838869i	−0.999838	−	0.0180106i	$-0.994267\pi$
$131$	−5.54331	+	9.60129i	−0.484321	+	0.838869i	0.515517	+	0.856880i	$0.327600\pi$
$132$	−5.12803	−	0.764077i	−0.446338	−	0.0665044i
$133$	−10.6761	−	11.0210i	−0.925733	−	0.955638i
$134$		−	11.2722i		−	0.973766i
$135$	−11.7757	+	3.98295i	−1.01349	+	0.342798i
$136$	−6.35472	+	3.66890i	−0.544913	+	0.314606i
$137$	−7.71390	+	4.45362i	−0.659043	+	0.380499i	−0.791912	−	0.610635i	$-0.790914\pi$
$137$	−7.71390	+	4.45362i	−0.659043	+	0.380499i	0.132869	+	0.991134i	$0.457581\pi$
$138$	11.7018	+	6.75606i	0.996127	+	0.575114i
$139$	−18.4038			−1.56099			−0.780496	−	0.625161i	$-0.785033\pi$
$139$	−18.4038			−1.56099			−0.780496	+	0.625161i	$0.785033\pi$
$140$	−4.97417	+	3.20276i	−0.420394	+	0.270683i
$141$	16.5614			1.39472
$142$	−0.394297	+	0.682942i	−0.0330886	+	0.0573112i
$143$	−7.45335	+	2.93975i	−0.623281	+	0.245834i
$144$	0.278160	+	0.481787i	0.0231800	+	0.0401489i
$145$	3.20362	+	9.47159i	0.266046	+	0.786572i
$146$		−	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	0.376847	−	0.926276i	$-0.377008\pi$
$149$	−2.89183	−	1.66960i	−0.236908	−	0.136779i	−0.613755	+	0.789497i	$0.710342\pi$
$150$	−6.21136	+	4.74458i	−0.507155	+	0.387393i
$151$	−0.298524	+	0.172353i	−0.0242935	+	0.0140259i	−0.512098	−	0.858927i	$-0.671131\pi$
$151$	−0.298524	+	0.172353i	−0.0242935	+	0.0140259i	0.487804	+	0.872953i	$0.337798\pi$
$152$	−2.89975	+	5.02252i	−0.235201	+	0.407380i
$153$			4.08216i			0.330023i
$154$	−3.62294	+	7.99214i	−0.291945	+	0.644025i
$155$	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	$0.0914626\pi$
$157$	9.08338	+	15.7329i	0.724933	+	1.25562i	−0.234069	+	0.972220i	$0.575204\pi$
$158$	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	0.693873	−	0.720097i	$-0.255903\pi$
$163$	5.32629	+	3.07513i	0.417187	+	0.240863i	−0.276686	+	0.960960i	$0.589236\pi$
$164$	−3.48649	−	6.03877i	−0.272249	−	0.471549i
$165$	−3.92467	+	10.9087i	−0.305535	+	0.849240i
$166$	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
$170$	5.25712	+	15.5428i	0.403203	+	1.19208i
$171$	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
$175$	4.84061	+	12.3113i	0.365915	+	0.930648i
$176$	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	$0.965210\pi$
$180$	1.17839	−	0.398571i	0.0878318	−	0.0297077i
$181$		−	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
$185$	−8.12601	−	1.62561i	−0.597436	−	0.119517i
$186$	1.34758	−	0.778027i	0.0988095	−	0.0570477i
$187$	19.0528	+	15.1416i	1.39328	+	1.10726i
$188$	−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	$0.677257\pi$
$198$	1.14797	−	1.44450i	0.0815824	−	0.102656i
$199$	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	$0.0522517\pi$
$200$	3.97342	−	3.03512i	0.280963	−	0.214615i
$201$	−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
$205$	−14.7701	+	4.99574i	−1.03159	+	0.348918i
$206$	−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
$210$	0.448003	+	9.23732i	0.0309152	+	0.637436i
$211$			22.3531i			1.53885i	0.638738	+	0.769425i	$0.279457\pi$
$211$			22.3531i			1.53885i	−0.638738	+	0.769425i	$0.720543\pi$
$212$	−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
$215$	13.1069	−	4.43321i	0.893885	−	0.302343i
$216$	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
$220$	2.51062	−	6.97831i	0.169266	−	0.470478i
$221$	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	$-0.254096\pi$
$223$	20.8452			1.39590			0.697949	+	0.716147i	$0.254096\pi$
$224$	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
$231$	7.98798	+	11.1515i	0.525570	+	0.733714i
$232$		−	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
$235$	−4.64704	+	23.2294i	−0.303140	+	1.51532i
$236$	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	$0.0386990\pi$
$239$			3.74980i			0.242554i	−0.992619	+	0.121277i	$0.961301\pi$
$240$	3.31121	−	1.11996i	0.213737	−	0.0722933i
$241$	−9.64709	−	16.7093i	−0.621424	−	1.07634i	−0.989221	−	0.146432i	$-0.953221\pi$
$241$	−9.64709	−	16.7093i	−0.621424	−	1.07634i	0.367797	−	0.929906i	$-0.380112\pi$
$242$	−2.48391	−	10.7159i	−0.159672	−	0.688843i
$243$	2.85086	−	4.93784i	0.182883	−	0.316763i
$244$	3.42385			0.219189
$245$	15.2430	+	3.55671i	0.973841	+	0.227230i
$246$	−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
$250$	−4.91199	−	10.0435i	−0.310662	−	0.635208i
$251$			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
$255$	25.1508	+	5.03143i	1.57501	+	0.315080i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.56618	+	4.44475i	−0.160074	+	0.277256i	−0.934895	−	0.354925i	$-0.884506\pi$
$257$	−2.56618	+	4.44475i	−0.160074	+	0.277256i	0.774821	+	0.632180i	$0.217840\pi$
$258$	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	$0.953421\pi$
$264$	3.22572	−	4.05896i	0.198530	−	0.249812i
$265$	−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	$0.441824\pi$
$270$	2.43852	−	12.1895i	0.148404	−	0.741831i
$271$	−11.6342	+	20.1511i	−0.706730	+	1.22409i	0.259333	+	0.965788i	$0.416497\pi$
$271$	−11.6342	+	20.1511i	−0.706730	+	1.22409i	−0.966063	+	0.258305i	$0.916836\pi$
$272$		−	7.33780i		−	0.444920i
$273$	2.43224	+	9.69078i	0.147206	+	0.586513i
$274$		−	8.90724i		−	0.538106i
$275$	−14.1996	−	8.56577i	−0.856266	−	0.516535i
$276$	−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
$280$	−0.286589	−	5.90913i	−0.0171270	−	0.353138i
$281$		−	6.50399i		−	0.387995i	−0.981002	−	0.193998i	$-0.937855\pi$
$281$		−	6.50399i		−	0.387995i	0.981002	−	0.193998i	$-0.0621454\pi$
$282$	−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
$285$	19.2034	−	6.49524i	1.13751	−	0.384745i
$286$	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
$290$	−9.80444	−	1.96138i	−0.575737	−	0.115176i
$291$	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
$297$	−6.76520	−	17.1523i	−0.392557	−	0.995276i
$298$	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
$305$	1.50182	−	7.50721i	0.0859939	−	0.429862i
$306$	−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	$0.932311\pi$
$308$	−5.10993	−	7.13363i	−0.291165	−	0.406476i
$309$	−30.0932			−1.71194
$310$	0.713155	+	2.10846i	0.0405045	+	0.119753i
$311$	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	$-0.634621\pi$
$313$	10.3410	−	17.9111i	0.584507	−	1.01240i	0.994937	−	0.100504i	$-0.0320454\pi$
$314$	−18.1668			−1.02521
$315$	−2.92666	−	1.50561i	−0.164899	−	0.0848314i
$316$			3.09874i			0.174318i
$317$	−6.76443	−	3.90544i	−0.379928	−	0.219352i	0.297859	−	0.954610i	$-0.403728\pi$
$317$	−6.76443	−	3.90544i	−0.379928	−	0.219352i	−0.677787	+	0.735258i	$0.737061\pi$
$318$	−2.40806	+	1.39029i	−0.135037	+	0.0779637i
$319$	−13.7961	+	5.44147i	−0.772435	+	0.304664i
$320$	−2.11819	+	0.716443i	−0.118410	+	0.0400504i
$321$	−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
$325$	−7.33210	−	9.59881i	−0.406712	−	0.532446i
$326$	−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
$340$	−16.0890	−	3.21862i	−0.872551	−	0.174554i
$341$	2.58461	+	2.05403i	0.139965	+	0.111232i
$342$	−3.22638			−0.174463
$343$	13.7051	−	12.4567i	0.740007	−	0.672599i
$344$	−6.18781			−0.333624
$345$	9.68066	+	28.6212i	0.521189	+	1.54091i
$346$	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	$-0.405658\pi$
$349$	10.9124			0.584125			0.292063	+	0.956399i	$0.405658\pi$
$350$	−13.0822	−	1.96357i	−0.699274	−	0.104957i
$351$		−	13.4300i		−	0.716840i
$352$	−2.06350	+	2.59653i	−0.109985	+	0.138395i
$353$	1.95844	+	3.39212i	0.104237	+	0.180544i	0.913426	−	0.407004i	$-0.133427\pi$
$353$	1.95844	+	3.39212i	0.104237	+	0.180544i	−0.809189	+	0.587548i	$0.800093\pi$
$354$	11.5415	−	6.66350i	0.613425	−	0.354161i
$355$	−1.67039	+	0.564982i	−0.0886549	+	0.0299861i
$356$			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	0.778886	−	0.627165i	$-0.215785\pi$
$359$	11.8456	+	6.83908i	0.625188	+	0.360953i	−0.153698	+	0.988118i	$0.549118\pi$
$360$	−0.244021	+	1.21980i	−0.0128610	+	0.0642891i
$361$	−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	0.870943	−	0.491383i	$-0.163509\pi$
$367$	0.190067	+	0.329206i	0.00992143	+	0.0171844i	−0.861022	+	0.508568i	$0.830175\pi$
$368$	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	$0.228223\pi$
$374$	−22.6394	+	8.92943i	−1.17066	+	0.461730i
$375$	−17.4361	−	1.20032i	−0.900399	−	0.0619844i
$376$	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	$0.600506\pi$
$380$	−12.2844	+	4.15502i	−0.630178	+	0.213148i
$381$	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	−0.990345	−	0.138624i	$-0.955732\pi$
$383$	−7.34126	+	12.7154i	−0.375121	+	0.649729i	0.615224	+	0.788352i	$0.289066\pi$
$384$	−1.56323			−0.0797731
$385$	−17.8828	+	8.07509i	−0.911390	+	0.411545i
$386$	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	$-0.382171\pi$
$390$	−2.70556	−	7.99906i	−0.137001	−	0.405048i
$391$	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
$395$	6.79438	+	1.35922i	0.341862	+	0.0683896i
$396$	0.676989	+	1.71642i	0.0340200	+	0.0862532i
$397$	9.10381	−	15.7683i	0.456907	−	0.791386i	−0.541889	−	0.840450i	$-0.682291\pi$
$397$	9.10381	−	15.7683i	0.456907	−	0.791386i	0.998796	+	0.0490641i	$0.0156238\pi$
$398$			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	$0.0221461\pi$
$409$	11.3050	+	19.5808i	0.558995	+	0.968207i	−0.438586	+	0.898689i	$0.644521\pi$
$410$	3.05859	−	15.2891i	0.151053	−	0.755075i
$411$	−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
$415$	7.95493	+	23.5190i	0.390492	+	1.15450i
$416$	−2.09211	+	1.20788i	−0.102574	+	0.0592211i
$417$	−14.3847	−	24.9150i	−0.704421	−	1.22009i
$418$	−11.9673	+	15.0586i	−0.585340	+	0.736539i
$419$			22.1700i			1.08307i	0.840677	+	0.541537i	$0.182157\pi$
$419$			22.1700i			1.08307i	−0.840677	+	0.541537i	$0.817843\pi$
$420$	−8.22376	−	4.23068i	−0.401278	−	0.206436i
$421$	−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
$425$	−14.1144	+	33.8654i	−0.684650	+	1.64271i
$426$	−1.23275			−0.0597270
$427$	−6.30282	−	6.50643i	−0.305015	−	0.314868i
$428$	16.8488			0.814420
$429$	−9.80546	−	7.79256i	−0.473412	−	0.376228i
$430$	−2.71419	+	13.5675i	−0.130890	+	0.654285i
$431$	1.49673	−	0.864138i	0.0720950	−	0.0416241i	−0.463519	−	0.886087i	$-0.653413\pi$
$431$	1.49673	−	0.864138i	0.0720950	−	0.0416241i	0.535614	+	0.844463i	$0.320080\pi$
$432$	−2.77967	+	4.81453i	−0.133737	+	0.231639i
$433$	−1.16651			−0.0560588			−0.0280294	−	0.999607i	$-0.508923\pi$
$433$	−1.16651			−0.0560588			−0.0280294	+	0.999607i	$0.508923\pi$
$434$	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	−0.632649	−	0.774439i	$-0.718032\pi$
$439$	7.42466	−	12.8599i	0.354360	−	0.613769i	0.987008	+	0.160670i	$0.0513655\pi$
$440$	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	0.985191	−	0.171463i	$-0.0548495\pi$
$443$	27.9784	+	16.1533i	1.32929	+	0.767468i	0.344104	+	0.938932i	$0.388183\pi$
$444$	5.01725	−	2.89671i	0.238108	−	0.137472i
$445$	8.31986	+	1.66439i	0.394399	+	0.0788996i
$446$	−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	$0.764049\pi$
$450$	2.56752	+	1.07009i	0.121034	+	0.0504447i
$451$	−8.48547	−	21.5138i	−0.399565	−	1.01304i
$452$	6.67214	−	3.85216i	0.313831	−	0.181190i
$453$	−0.466661	−	0.269427i	−0.0219257	−	0.0126588i
$454$			12.0063i			0.563482i
$455$	−14.2750	+	0.692328i	−0.669223	+	0.0324568i
$456$	−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
$460$	−6.19274	−	18.3090i	−0.288738	−	0.853663i
$461$	21.3818			0.995848			0.497924	−	0.867221i	$-0.334096\pi$
$461$	21.3818			0.995848			0.497924	+	0.867221i	$0.334096\pi$
$462$	−13.6515	+	1.34205i	−0.635123	+	0.0624377i
$463$		−	20.7517i		−	0.964415i	−0.876057	−	0.482207i	$-0.839835\pi$
$463$		−	20.7517i		−	0.964415i	0.876057	−	0.482207i	$-0.160165\pi$
$464$	3.87248	+	2.23578i	0.179775	+	0.103793i
$465$	3.41184	+	0.682539i	0.158220	+	0.0316520i
$466$	−0.0103605	−	0.0179449i	−0.000479942	−	0.000831283i
$467$	−0.436949	+	0.756818i	−0.0202196	+	0.0350213i	−0.875958	−	0.482387i	$-0.839770\pi$
$467$	−0.436949	+	0.756818i	−0.0202196	+	0.0350213i	0.855739	+	0.517408i	$0.173103\pi$
$468$			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
$473$	7.53000	+	19.0913i	0.346230	+	0.877820i
$474$	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	0.908428	−	0.418041i	$-0.137283\pi$
$479$	2.01746	+	3.49434i	0.0921801	+	0.159661i	−0.816248	+	0.577702i	$0.803950\pi$
$480$	−0.685686	+	3.42757i	−0.0312971	+	0.156446i
$481$	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
$485$	−2.91419	+	0.985680i	−0.132327	+	0.0447574i
$486$	2.85086	+	4.93784i	0.129318	+	0.223985i
$487$	10.6366	−	6.14105i	0.481991	−	0.278277i	−0.239255	−	0.970957i	$-0.576903\pi$
$487$	10.6366	−	6.14105i	0.481991	−	0.278277i	0.721246	+	0.692679i	$0.243570\pi$
$488$	−1.71192	+	2.96514i	−0.0774952	+	0.134226i
$489$			9.61427i			0.434772i
$490$	−10.7017	+	11.4225i	−0.483454	+	0.516015i
$491$		−	6.98569i		−	0.315260i	−0.987498	−	0.157630i	$-0.949615\pi$
$491$		−	6.98569i		−	0.315260i	0.987498	−	0.157630i	$-0.0503853\pi$
$492$	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
$495$	4.06041	−	0.731503i	0.182502	−	0.0328786i
$496$		−	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	$-0.0742137\pi$
$500$	11.1539	+	0.767849i	0.498819	+	0.0343393i
$501$	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
$506$	−22.4437	−	17.8364i	−0.997744	−	0.792923i
$507$	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
$515$	8.44403	−	42.2095i	0.372088	−	1.85998i
$516$	−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
$520$	1.73075	+	5.11702i	0.0758985	+	0.224396i
$521$	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
$525$	−12.8835	+	16.1759i	−0.562283	+	0.705973i
$526$	11.9483			0.520971
$527$	3.65206	−	6.32556i	0.159086	−	0.275546i
$528$	1.90230	+	4.82304i	0.0827871	+	0.209896i
$529$	25.8570	+	44.7857i	1.12422	+	1.94720i
$530$	−1.27437	−	3.76771i	−0.0553551	−	0.163659i
$531$			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
$535$	7.39049	−	36.9432i	0.319519	−	1.59719i
$536$	−9.76197	+	5.63608i	−0.421653	+	0.243441i
$537$	8.41920	−	14.5825i	0.363315	−	0.629281i
$538$		−	10.9650i		−	0.472733i
$539$	−4.14958	+	22.8425i	−0.178735	+	0.983897i
$540$	9.33719	+	8.20659i	0.401809	+	0.353155i
$541$	−31.8171	−	18.3696i	−1.36792	−	0.789770i	−0.377260	−	0.926107i	$-0.623134\pi$
$541$	−31.8171	−	18.3696i	−1.36792	−	0.789770i	−0.990662	+	0.136337i	$0.956467\pi$
$542$	−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
$550$	14.5180	−	8.01430i	0.619048	−	0.341731i
$551$	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
$555$	−4.15066	−	12.2715i	−0.176186	−	0.520898i
$556$	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
$560$	5.26075	+	2.70637i	0.222307	+	0.114365i
$561$	−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
$565$	−5.51971	−	16.3192i	−0.232216	−	0.686553i
$566$		−	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	0.887929	−	0.459981i	$-0.152144\pi$
$569$	22.2683	+	12.8566i	0.933537	+	0.538978i	0.0456086	+	0.998959i	$0.485477\pi$
$570$	−3.97664	+	19.8782i	−0.166563	+	0.832607i
$571$	−1.28028	+	0.739171i	−0.0535781	+	0.0309333i	−0.526550	−	0.850144i	$-0.676515\pi$
$571$	−1.28028	+	0.739171i	−0.0535781	+	0.0309333i	0.472972	+	0.881078i	$0.343181\pi$
$572$	6.27258	+	4.98492i	0.262270	+	0.208430i
$573$	−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	$0.149963\pi$
$577$	20.1440	+	34.8905i	0.838608	+	1.45251i	−0.0524512	+	0.998623i	$0.516703\pi$
$578$	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
$583$	−4.61856	−	3.67044i	−0.191281	−	0.152014i
$584$	−8.04910	+	4.64715i	−0.333074	+	0.192301i
$585$	2.94674	+	0.589495i	0.121833	+	0.0243726i
$586$	16.8593	+	9.73371i	0.696451	+	0.402096i
$587$	15.4414			0.637335			0.318667	−	0.947867i	$-0.396765\pi$
$587$	15.4414			0.637335			0.318667	+	0.947867i	$0.396765\pi$
$588$	−9.64567	+	5.16734i	−0.397781	+	0.213097i
$589$		−	5.77289i		−	0.237868i
$590$	6.10790	+	18.0582i	0.251458	+	0.743444i
$591$	−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
$595$	23.5012	+	36.4994i	0.963456	+	1.49633i
$596$			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	$0.576784\pi$
$600$	7.21461	+	3.00690i	0.294535	+	0.122756i
$601$	17.7029			0.722115			0.361057	−	0.932544i	$-0.382416\pi$
$601$	17.7029			0.722115			0.361057	+	0.932544i	$0.382416\pi$
$602$	11.3909	+	11.7589i	0.464258	+	0.479255i
$603$			6.27092i			0.255371i
$604$	0.298524	+	0.172353i	0.0121468	+	0.00701294i
$605$	11.6467	−	21.6646i	0.473507	−	0.880790i
$606$	−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
$616$	8.73287	−	0.858510i	0.351857	−	0.0345904i
$617$			2.52801i			0.101774i	0.998704	+	0.0508870i	$0.0162048\pi$
$617$			2.52801i			0.101774i	−0.998704	+	0.0508870i	$0.983795\pi$
$618$	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	$0.253430\pi$
$620$	−2.18256	−	0.436622i	−0.0876538	−	0.0175351i
$621$	−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
$625$	6.57611	−	24.1196i	0.263044	−	0.964784i
$626$	10.3410	+	17.9111i	0.413309	+	0.715872i
$627$	11.0324	+	27.9713i	0.440593	+	1.11706i
$628$	9.08338	−	15.7329i	0.362466	−	0.627810i
$629$	−27.1944			−1.08431
$630$	2.76722	−	1.78176i	0.110249	−	0.0709869i
$631$	−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
$635$	−16.5098	+	5.58420i	−0.655173	+	0.221602i
$636$		−	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
$640$	0.438635	−	2.19262i	0.0173386	−	0.0866711i
$641$	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	$-0.687858\pi$
$643$	−28.2230			−1.11301			−0.556504	+	0.830845i	$0.687858\pi$
$644$	−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	0.664303	−	0.747463i	$-0.268728\pi$
$647$	−8.01674	−	13.8854i	−0.315171	−	0.545892i	−0.979474	+	0.201572i	$0.935395\pi$
$648$	3.51078	+	6.08084i	0.137916	+	0.238878i
$649$	22.1362	+	17.5920i	0.868922	+	0.690547i
$650$	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	$-0.984643\pi$
$653$	−39.3535	−	22.7208i	−1.54002	−	0.889132i	−0.541185	−	0.840904i	$-0.682024\pi$
$654$	−21.0707	+	12.1652i	−0.823930	+	0.475696i
$655$	4.86298	−	24.3088i	0.190012	−	0.949823i
$656$	−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	$-0.606446\pi$
$659$		−	48.4979i		−	1.88921i	0.328212	−	0.944604i	$-0.393554\pi$
$660$	11.4095	−	2.05548i	0.444115	−	0.0800096i
$661$	−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
$665$	30.5098	+	15.6956i	1.18312	+	0.608651i
$666$			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
$670$	8.07586	+	23.8765i	0.311998	+	0.922430i
$671$	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
$675$	22.0896	−	16.8732i	0.850228	−	0.649452i
$676$	−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
$682$	−3.07115	+	1.21132i	−0.117600	+	0.0463840i
$683$	−38.8580	+	22.4347i	−1.48686	+	0.858440i	−0.999888	−	0.0149766i	$-0.995233\pi$
$683$	−38.8580	+	22.4347i	−1.48686	+	0.858440i	−0.486974	+	0.873417i	$0.661899\pi$
$684$	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
$690$	−29.6270	−	5.92689i	−1.12788	−	0.225633i
$691$	−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
$693$	2.01551	−	4.44618i	0.0765630	−	0.168896i
$694$	−14.0289			−0.532528
$695$	38.9827	−	13.1853i	1.47870	−	0.500147i
$696$	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
$700$	8.24161	−	10.3477i	0.311504	−	0.391108i
$701$			20.4291i			0.771598i	0.922583	+	0.385799i	$0.126074\pi$
$701$			20.4291i			0.771598i	−0.922583	+	0.385799i	$0.873926\pi$
$702$	11.6307	+	6.71500i	0.438973	+	0.253441i
$703$	−18.6138	+	10.7467i	−0.702033	+	0.405319i
$704$	−1.21691	−	3.08531i	−0.0458639	−	0.116282i
$705$	−35.0800	+	11.8653i	−1.32119	+	0.446872i
$706$	−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	$0.331341\pi$
$710$	0.345904	−	1.72909i	0.0129816	−	0.0648915i
$711$	−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
$725$	−13.5717	−	17.7674i	−0.504040	−	0.659863i
$726$	12.5656	−	11.7384i	0.466355	−	0.435653i
$727$	−18.1010			−0.671329			−0.335665	−	0.941982i	$-0.608961\pi$
$727$	−18.1010			−0.671329			−0.335665	+	0.941982i	$0.608961\pi$
$728$	6.14663	+	1.75215i	0.227809	+	0.0649391i
$729$	29.9778			1.11029
$730$	6.65884	+	19.6871i	0.246455	+	0.728651i
$731$	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
$735$	7.09910	+	23.4159i	0.261854	+	0.863709i
$736$			8.64373i			0.318612i
$737$	29.2685	+	23.2601i	1.07812	+	0.856797i
$738$	1.93960	+	3.35949i	0.0713977	+	0.123664i
$739$	39.9416	−	23.0603i	1.46928	−	0.848287i	0.469870	−	0.882735i	$-0.344301\pi$
$739$	39.9416	−	23.0603i	1.46928	−	0.848287i	0.999406	+	0.0344480i	$0.0109673\pi$
$740$	2.65519	+	7.85014i	0.0976066	+	0.288577i
$741$			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
$745$	7.32160	+	1.46469i	0.268243	+	0.0536620i
$746$	−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	$0.190392\pi$
$757$			30.9859i			1.12620i	−0.826388	+	0.563101i	$0.809608\pi$
$758$	6.04536	−	10.4709i	0.219577	−	0.380319i
$759$	−41.6891	+	16.4430i	−1.51322	+	0.596843i
$760$	2.54387	−	12.7161i	0.0922757	−	0.461263i
$761$	12.4190	−	21.5103i	0.450187	−	0.779747i	−0.548210	−	0.836341i	$-0.684691\pi$
$761$	12.4190	−	21.5103i	0.450187	−	0.779747i	0.998397	+	0.0565938i	$0.0180240\pi$
$762$	−12.1843			−0.441391
$763$	10.0244	+	39.9402i	0.362907	+	1.44593i
$764$	15.6178			0.565031
$765$	−2.92464	−	8.64677i	−0.105740	−	0.312625i
$766$	−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	$-0.597337\pi$
$769$	−16.6967			−0.602099			−0.301049	+	0.953609i	$0.597337\pi$
$770$	1.94815	−	19.5245i	0.0702064	−	0.703613i
$771$	−8.02303			−0.288942
$772$	−0.956755	+	1.65715i	−0.0344344	+	0.0596421i
$773$	1.87123	+	3.24107i	0.0673036	+	0.116573i	0.897714	−	0.440580i	$-0.145227\pi$
$773$	1.87123	+	3.24107i	0.0673036	+	0.116573i	−0.830410	+	0.557153i	$0.811894\pi$
$774$	−1.72120	−	2.98121i	−0.0618672	−	0.107157i
$775$	−1.91469	+	4.59402i	−0.0687779	+	0.165022i
$776$	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
$780$	8.28017	+	1.65645i	0.296478	+	0.0593104i
$781$	−0.959645	−	2.43305i	−0.0343388	−	0.0870615i
$782$	−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
$795$	−6.09677	−	1.21966i	−0.216230	−	0.0432569i
$796$	−18.8792	−	10.8999i	−0.669156	−	0.386337i
$797$	−48.7853			−1.72806			−0.864032	−	0.503438i	$-0.832068\pi$
$797$	−48.7853			−1.72806			−0.864032	+	0.503438i	$0.832068\pi$
$798$	16.6891	+	17.2283i	0.590789	+	0.609874i
$799$			77.7391i			2.75021i
$800$	−4.61520	−	1.92352i	−0.163172	−	0.0680068i
$801$	−1.82813	+	1.05547i	−0.0645937	+	0.0372932i
$802$	11.0903	+	19.2090i	0.391613	+	0.678294i
$803$	24.1329	+	19.1788i	0.851632	+	0.676806i
$804$			17.6209i			0.621443i
$805$	−23.3932	+	45.4725i	−0.824501	+	1.60270i
$806$	−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	−0.541285	−	0.840839i	$-0.682062\pi$
$809$	−2.38177	+	1.37512i	−0.0837386	+	0.0483465i	0.457546	+	0.889186i	$0.348729\pi$
$810$	14.8729	−	5.03054i	0.522582	−	0.176755i
$811$	−30.7840			−1.08097			−0.540486	−	0.841353i	$-0.681760\pi$
$811$	−30.7840			−1.08097			−0.540486	+	0.841353i	$0.681760\pi$
$812$	−2.87998	−	11.4747i	−0.101068	−	0.402684i
$813$	−36.3740			−1.27569
$814$	9.62290	+	7.64748i	0.337283	+	0.268044i
$815$	−13.4852	−	2.69772i	−0.472367	−	0.0944970i
$816$	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	0.831671	−	0.555269i	$-0.187385\pi$
$821$	21.9663	+	12.6823i	0.766630	+	0.442614i	−0.0650411	+	0.997883i	$0.520718\pi$
$822$	12.0586	−	6.96202i	0.420591	−	0.242828i
$823$	8.96688	−	5.17703i	0.312566	−	0.180460i	−0.335508	−	0.942037i	$-0.608908\pi$
$823$	8.96688	−	5.17703i	0.312566	−	0.180460i	0.648074	+	0.761577i	$0.275575\pi$
$824$	−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	$0.302085\pi$
$830$	−24.3455	−	4.87032i	−0.845044	−	0.169051i
$831$	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
$835$	1.39461	+	4.12320i	0.0482624	+	0.142689i
$836$	−7.05747	−	17.8933i	−0.244088	−	0.618852i
$837$	−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	$-0.106135\pi$
$840$	7.77575	−	5.00664i	0.268289	−	0.172746i
$841$	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
$845$	−15.1749	+	5.13269i	−0.522034	+	0.176570i
$846$	5.89383			0.202634
$847$	−13.2759	−	25.8989i	−0.456164	−	0.889896i
$848$			1.77874i			0.0610823i
$849$	−19.6037	−	11.3182i	−0.672796	−	0.388439i
$850$	−22.2711	−	29.1562i	−0.763892	−	1.00005i
$851$	−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	$0.222559\pi$
$858$	11.6513	−	4.59550i	0.397768	−	0.156888i
$859$	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	−0.495389	−	0.868671i	$-0.664975\pi$
$863$	−43.9294	−	25.3627i	−1.49538	−	0.863355i	−0.999986	+	0.00531596i	$0.998308\pi$
$864$	−2.77967	−	4.81453i	−0.0945662	−	0.163794i
$865$	28.9210	+	5.78565i	0.983343	+	0.196718i
$866$	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
$870$	−5.00798	−	14.8062i	−0.169786	−	0.501979i
$871$	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
$875$	−19.0737	−	22.6096i	−0.644807	−	0.764345i
$876$			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
$880$	−7.29870	+	1.31490i	−0.246039	+	0.0443252i
$881$			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	$0.00787556\pi$
$883$			1.47027i			0.0494785i	−0.999694	+	0.0247393i	$0.992124\pi$
$884$	8.86317	−	15.3515i	0.298101	−	0.516325i
$885$	29.2211	+	5.84569i	0.982257	+	0.196501i
$886$	−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
$891$	14.4890	−	18.2317i	0.485399	−	0.610783i
$892$	−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
$900$	−2.21049	+	1.68850i	−0.0736830	+	0.0562832i
$901$	−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
$905$	3.38280	+	10.0013i	0.112448	+	0.332456i
$906$	0.466661	−	0.269427i	0.0155038	−	0.00895111i
$907$	1.99949	−	1.15440i	0.0663918	−	0.0383313i	−0.466437	−	0.884555i	$-0.654462\pi$
$907$	1.99949	−	1.15440i	0.0663918	−	0.0383313i	0.532828	+	0.846223i	$0.321129\pi$
$908$	−10.3977	−	6.00313i	−0.345061	−	0.199221i
$909$	1.51331			0.0501935
$910$	6.53794	−	12.7087i	0.216730	−	0.421289i
$911$	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
$913$	−34.2573	+	13.5118i	−1.13375	+	0.447174i
$914$	20.0531	+	34.7330i	0.663297	+	1.14886i
$915$	11.3371	−	3.83459i	0.374792	−	0.126767i
$916$		−	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	0.521848	−	0.853038i	$-0.325243\pi$
$919$	1.33444	+	0.770439i	0.0440191	+	0.0254144i	−0.477829	+	0.878453i	$0.658576\pi$
$920$	18.9525	+	3.79144i	0.624844	+	0.125000i
$921$	−10.0125	+	5.78069i	−0.329922	+	0.190480i
$922$	−10.6909	+	18.5171i	−0.352085	+	0.609830i
$923$		−	1.90505i		−	0.0627054i
$924$	5.66348	−	12.4935i	0.186315	−	0.411007i
$925$	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
$935$	−51.2055	−	18.4224i	−1.67460	−	0.602477i
$936$	−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
$940$	22.4408	−	7.59024i	0.731937	−	0.247566i
$941$	9.19669	+	15.9291i	0.299804	+	0.519275i	0.976091	−	0.217363i	$-0.0697455\pi$
$941$	9.19669	+	15.9291i	0.299804	+	0.519275i	−0.676287	+	0.736638i	$0.736412\pi$
$942$	−14.1994	−	24.5941i	−0.462641	−	0.801318i
$943$	−52.1975	−	30.1363i	−1.69979	−	0.981372i
$944$		−	8.52531i		−	0.277475i
$945$	−1.59324	−	32.8509i	−0.0518282	−	1.06864i
$946$	−20.2986	−	3.02449i	−0.659963	−	0.0983346i
$947$	19.5459	+	11.2848i	0.635156	+	0.366707i	0.782746	−	0.622341i	$-0.213818\pi$
$947$	19.5459	+	11.2848i	0.635156	+	0.366707i	−0.147590	+	0.989049i	$0.547152\pi$
$948$	−4.19506	+	2.42202i	−0.136249	+	0.0786635i
$949$	11.2264	+	19.4447i	0.364424	+	0.631200i
$950$	−26.7659	−	11.1555i	−0.868400	−	0.361932i
$951$		−	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
$955$	6.85049	−	34.2439i	0.221677	−	1.10811i
$956$	3.24742	−	1.87490i	0.105029	−	0.0606386i
$957$	−18.1499	−	14.4240i	−0.586703	−	0.466262i
$958$	−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	$0.317852\pi$
$968$	−8.03827	+	7.50907i	−0.258360	+	0.241351i
$969$	57.6116	−	33.2621i	1.85075	−	1.06853i
$970$	0.603472	−	3.01660i	0.0193763	−	0.0968573i
$971$	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
$975$	7.26394	−	17.4287i	0.232632	−	0.558166i
$976$	−1.71192	−	2.96514i	−0.0547974	−	0.0949118i
$977$	23.7125	−	13.6904i	0.758629	−	0.437995i	−0.0701744	−	0.997535i	$-0.522356\pi$
$977$	23.7125	−	13.6904i	0.758629	−	0.437995i	0.828803	+	0.559540i	$0.189022\pi$
$978$	−8.32620	−	4.80713i	−0.266242	−	0.153715i
$979$	−1.85467	+	12.4474i	−0.0592755	+	0.397822i
$980$	−4.54131	−	14.9792i	−0.145067	−	0.478493i
$981$		−	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	$0.0513647\pi$
$983$	19.8353	+	34.3557i	0.632646	+	1.09578i	−0.354362	+	0.935108i	$0.615302\pi$
$984$	5.45017	+	9.43998i	0.173745	+	0.300935i
$985$	31.4266	−	10.6296i	1.00134	−	0.338686i
$986$	−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
$990$	−1.39670	+	3.88217i	−0.0443902	+	0.123383i
$991$	−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.439.19	yes	48
5.4	even	2		770.2.o.b.439.6	yes	48
7.3	odd	6	inner	770.2.o.a.549.6	yes	48
11.10	odd	2		770.2.o.b.439.19	yes	48
35.24	odd	6		770.2.o.b.549.19	yes	48
55.54	odd	2	inner	770.2.o.a.439.6	✓	48
77.10	even	6		770.2.o.b.549.6	yes	48
385.164	even	6	inner	770.2.o.a.549.19	yes	48

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.781614 + 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.11819 + 0.716443i) q^{5} -1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.781614 + 1.35379i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-2.11819 + 0.716443i) q^{5} -1.56323 q^{6} +(-0.725302 + 2.54439i) q^{7} +1.00000 q^{8} +(0.278160 - 0.481787i) q^{9} +(0.438635 - 2.19262i) q^{10} +(-1.21691 - 3.08531i) 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} +(3.97342 - 3.03512i) q^{25} +(2.09211 + 1.20788i) q^{26} +5.55934 q^{27} +(2.56616 - 0.644067i) q^{28} -4.47156i q^{29} +(3.31121 - 1.11996i) q^{30} +(-0.862051 + 0.497705i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.22572 - 4.05896i) q^{33} -7.33780i q^{34} +(-0.286589 - 5.90913i) q^{35} -0.556319 q^{36} +(3.20955 + 1.85303i) q^{37} +(-2.89975 - 5.02252i) q^{38} +(3.27044 - 1.88819i) q^{39} +(-2.11819 + 0.716443i) q^{40} +6.97297 q^{41} +(1.13381 - 3.97747i) q^{42} -6.18781 q^{43} +(-2.06350 + 2.59653i) q^{44} +(-0.244021 + 1.21980i) 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} +(-0.685686 + 3.42757i) q^{60} +(-1.71192 + 2.96514i) q^{61} -0.995411i q^{62} +(1.02411 + 1.05719i) q^{63} +1.00000 q^{64} +(1.73075 + 5.11702i) q^{65} +(1.90230 + 4.82304i) q^{66} +(-9.76197 + 5.63608i) q^{67} +(6.35472 + 3.66890i) q^{68} -13.5121i q^{69} +(5.26075 + 2.70637i) q^{70} +0.788593 q^{71} +(0.278160 - 0.481787i) q^{72} +(-8.04910 + 4.64715i) q^{73} +(-3.20955 + 1.85303i) q^{74} +(7.21461 + 3.00690i) q^{75} +5.79951 q^{76} +(8.73287 - 0.858510i) q^{77} +3.77638i q^{78} +(-2.68359 - 1.54937i) q^{79} +(0.438635 - 2.19262i) 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} +(-1.21691 - 3.08531i) 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} +(2.54387 - 12.7161i) 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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