LMFDB - Embedded newform 390.2.l.a.53.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [390,2,Mod(53,390)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("390.53"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(390, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.53
Dual form			390.2.l.a.287.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(0.292893 + 1.70711i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +(1.00000 - 2.00000i) q^{10} +4.00000i q^{11} +(-1.00000 + 1.41421i) q^{12} +(0.707107 + 0.707107i) q^{13} +4.82843 q^{14} +(1.12132 - 3.70711i) q^{15} -1.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(-1.29289 + 2.70711i) q^{18} +1.17157i q^{19} +(2.12132 - 0.707107i) q^{20} +(8.24264 - 1.41421i) q^{21} +(-2.82843 + 2.82843i) q^{22} +(2.82843 - 2.82843i) q^{23} +(-1.70711 + 0.292893i) q^{24} +(-4.00000 + 3.00000i) q^{25} +1.00000i q^{26} +(-1.41421 + 5.00000i) q^{27} +(3.41421 + 3.41421i) q^{28} -6.00000 q^{29} +(3.41421 - 1.82843i) q^{30} +0.585786 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.00000 + 5.65685i) q^{33} -4.24264i q^{34} +(-9.65685 - 4.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-5.41421 + 5.41421i) q^{37} +(-0.828427 + 0.828427i) q^{38} +(0.292893 + 1.70711i) q^{39} +(2.00000 + 1.00000i) q^{40} +2.00000i q^{41} +(6.82843 + 4.82843i) q^{42} +(-7.24264 - 7.24264i) q^{43} -4.00000 q^{44} +(5.29289 - 4.12132i) q^{45} +4.00000 q^{46} +(6.24264 + 6.24264i) q^{47} +(-1.41421 - 1.00000i) q^{48} -16.3137i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-1.24264 - 7.24264i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(3.41421 - 3.41421i) q^{53} +(-4.53553 + 2.53553i) q^{54} +(8.48528 - 2.82843i) q^{55} +4.82843i q^{56} +(-1.17157 + 1.65685i) q^{57} +(-4.24264 - 4.24264i) q^{58} -12.4853 q^{59} +(3.70711 + 1.12132i) q^{60} -0.828427 q^{61} +(0.414214 + 0.414214i) q^{62} +(13.0711 + 6.24264i) q^{63} -1.00000i q^{64} +(1.00000 - 2.00000i) q^{65} +(-6.82843 + 1.17157i) q^{66} +(4.82843 - 4.82843i) q^{67} +(3.00000 - 3.00000i) q^{68} +(6.82843 - 1.17157i) q^{69} +(-3.41421 - 10.2426i) q^{70} -5.75736i q^{71} +(-2.70711 - 1.29289i) q^{72} +(3.07107 + 3.07107i) q^{73} -7.65685 q^{74} +(-8.65685 + 0.242641i) q^{75} -1.17157 q^{76} +(13.6569 + 13.6569i) q^{77} +(-1.00000 + 1.41421i) q^{78} -4.48528i q^{79} +(0.707107 + 2.12132i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(-1.41421 + 1.41421i) q^{82} +(-1.17157 + 1.17157i) q^{83} +(1.41421 + 8.24264i) q^{84} +(-4.24264 + 8.48528i) q^{85} -10.2426i q^{86} +(-8.48528 - 6.00000i) q^{87} +(-2.82843 - 2.82843i) q^{88} +16.8284 q^{89} +(6.65685 + 0.828427i) q^{90} +4.82843 q^{91} +(2.82843 + 2.82843i) q^{92} +(0.828427 + 0.585786i) q^{93} +8.82843i q^{94} +(2.48528 - 0.828427i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(-5.07107 + 5.07107i) q^{97} +(11.5355 - 11.5355i) q^{98} +(-11.3137 + 4.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{6} + 8 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{12} + 8 q^{14} - 4 q^{15} - 4 q^{16} - 12 q^{17} - 8 q^{18} + 16 q^{21} - 4 q^{24} - 16 q^{25} + 8 q^{28} - 24 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33}+ \cdots + 32 q^{98}+O(q^{100}) $ 4 * q + 4 * q^6 + 8 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^12 + 8 * q^14 - 4 * q^15 - 4 * q^16 - 12 * q^17 - 8 * q^18 + 16 * q^21 - 4 * q^24 - 16 * q^25 + 8 * q^28 - 24 * q^29 + 8 * q^30 + 8 * q^31 - 16 * q^33 - 16 * q^35 - 16 * q^37 + 8 * q^38 + 4 * q^39 + 8 * q^40 + 16 * q^42 - 12 * q^43 - 16 * q^44 + 24 * q^45 + 16 * q^46 + 8 * q^47 + 12 * q^51 + 8 * q^53 - 4 * q^54 - 16 * q^57 - 16 * q^59 + 12 * q^60 + 8 * q^61 - 4 * q^62 + 24 * q^63 + 4 * q^65 - 16 * q^66 + 8 * q^67 + 12 * q^68 + 16 * q^69 - 8 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^74 - 12 * q^75 - 16 * q^76 + 32 * q^77 - 4 * q^78 - 28 * q^81 - 16 * q^83 + 56 * q^89 + 4 * q^90 + 8 * q^91 - 8 * q^93 - 24 * q^95 - 4 * q^96 + 8 * q^97 + 32 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$3$	1.41421	+	1.00000i	0.816497	+	0.577350i
$4$			1.00000i			0.500000i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$5$	−0.707107	−	2.12132i	−0.316228	−	0.948683i
$6$	0.292893	+	1.70711i	0.119573	+	0.696923i
$7$	3.41421	−	3.41421i	1.29045	−	1.29045i	0.355944	−	0.934507i	$-0.384159\pi$
$7$	3.41421	−	3.41421i	1.29045	−	1.29045i	0.934507	−	0.355944i	$-0.115841\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$	1.00000	−	2.00000i	0.316228	−	0.632456i
$11$			4.00000i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$11$			4.00000i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	4.82843			1.29045
$15$	1.12132	−	3.70711i	0.289524	−	0.957171i
$16$	−1.00000			−0.250000
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	0.242536	−	0.970143i	$-0.422021\pi$
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−1.29289	+	2.70711i	−0.304738	+	0.638071i
$19$			1.17157i			0.268777i	0.990929	+	0.134389i	$0.0429070\pi$
$19$			1.17157i			0.268777i	−0.990929	+	0.134389i	$0.957093\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$	8.24264	−	1.41421i	1.79869	−	0.308607i
$22$	−2.82843	+	2.82843i	−0.603023	+	0.603023i
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	−0.347801	−	0.937568i	$-0.613071\pi$
$23$	2.82843	−	2.82843i	0.589768	−	0.589768i	0.937568	+	0.347801i	$0.113071\pi$
$24$	−1.70711	+	0.292893i	−0.348462	+	0.0597866i
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$			1.00000i			0.196116i
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$	3.41421	+	3.41421i	0.645226	+	0.645226i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$	3.41421	−	1.82843i	0.623347	−	0.333824i
$31$	0.585786			0.105210			0.0526052	−	0.998615i	$-0.483248\pi$
$31$	0.585786			0.105210			0.0526052	+	0.998615i	$0.483248\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.00000	+	5.65685i	−0.696311	+	0.984732i
$34$		−	4.24264i		−	0.727607i
$35$	−9.65685	−	4.82843i	−1.63231	−	0.816153i
$36$	−2.82843	+	1.00000i	−0.471405	+	0.166667i
$37$	−5.41421	+	5.41421i	−0.890091	+	0.890091i	−0.994531	−	0.104440i	$-0.966695\pi$
$37$	−5.41421	+	5.41421i	−0.890091	+	0.890091i	0.104440	+	0.994531i	$0.466695\pi$
$38$	−0.828427	+	0.828427i	−0.134389	+	0.134389i
$39$	0.292893	+	1.70711i	0.0469005	+	0.273356i
$40$	2.00000	+	1.00000i	0.316228	+	0.158114i
$41$			2.00000i			0.312348i	0.987730	+	0.156174i	$0.0499160\pi$
$41$			2.00000i			0.312348i	−0.987730	+	0.156174i	$0.950084\pi$
$42$	6.82843	+	4.82843i	1.05365	+	0.745042i
$43$	−7.24264	−	7.24264i	−1.10449	−	1.10449i	−0.993862	−	0.110631i	$-0.964713\pi$
$43$	−7.24264	−	7.24264i	−1.10449	−	1.10449i	−0.110631	−	0.993862i	$-0.535287\pi$
$44$	−4.00000			−0.603023
$45$	5.29289	−	4.12132i	0.789018	−	0.614370i
$46$	4.00000			0.589768
$47$	6.24264	+	6.24264i	0.910583	+	0.910583i	0.996318	−	0.0857352i	$-0.0273239\pi$
$47$	6.24264	+	6.24264i	0.910583	+	0.910583i	−0.0857352	+	0.996318i	$0.527324\pi$
$48$	−1.41421	−	1.00000i	−0.204124	−	0.144338i
$49$		−	16.3137i		−	2.33053i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$	−1.24264	−	7.24264i	−0.174005	−	1.01417i
$52$	−0.707107	+	0.707107i	−0.0980581	+	0.0980581i
$53$	3.41421	−	3.41421i	0.468978	−	0.468978i	−0.432605	−	0.901583i	$-0.642406\pi$
$53$	3.41421	−	3.41421i	0.468978	−	0.468978i	0.901583	+	0.432605i	$0.142406\pi$
$54$	−4.53553	+	2.53553i	−0.617208	+	0.345042i
$55$	8.48528	−	2.82843i	1.14416	−	0.381385i
$56$			4.82843i			0.645226i
$57$	−1.17157	+	1.65685i	−0.155179	+	0.219456i
$58$	−4.24264	−	4.24264i	−0.557086	−	0.557086i
$59$	−12.4853			−1.62545			−0.812723	−	0.582651i	$-0.802016\pi$
$59$	−12.4853			−1.62545			−0.812723	+	0.582651i	$0.802016\pi$
$60$	3.70711	+	1.12132i	0.478585	+	0.144762i
$61$	−0.828427			−0.106069			−0.0530346	−	0.998593i	$-0.516889\pi$
$61$	−0.828427			−0.106069			−0.0530346	+	0.998593i	$0.516889\pi$
$62$	0.414214	+	0.414214i	0.0526052	+	0.0526052i
$63$	13.0711	+	6.24264i	1.64680	+	0.786499i
$64$		−	1.00000i		−	0.125000i
$65$	1.00000	−	2.00000i	0.124035	−	0.248069i
$66$	−6.82843	+	1.17157i	−0.840521	+	0.144211i
$67$	4.82843	−	4.82843i	0.589886	−	0.589886i	−0.347714	−	0.937601i	$-0.613042\pi$
$67$	4.82843	−	4.82843i	0.589886	−	0.589886i	0.937601	+	0.347714i	$0.113042\pi$
$68$	3.00000	−	3.00000i	0.363803	−	0.363803i
$69$	6.82843	−	1.17157i	0.822046	−	0.141041i
$70$	−3.41421	−	10.2426i	−0.408077	−	1.22423i
$71$		−	5.75736i		−	0.683273i	−0.939832	−	0.341636i	$-0.889019\pi$
$71$		−	5.75736i		−	0.683273i	0.939832	−	0.341636i	$-0.110981\pi$
$72$	−2.70711	−	1.29289i	−0.319036	−	0.152369i
$73$	3.07107	+	3.07107i	0.359441	+	0.359441i	0.863607	−	0.504166i	$-0.168200\pi$
$73$	3.07107	+	3.07107i	0.359441	+	0.359441i	−0.504166	+	0.863607i	$0.668200\pi$
$74$	−7.65685			−0.890091
$75$	−8.65685	+	0.242641i	−0.999607	+	0.0280177i
$76$	−1.17157			−0.134389
$77$	13.6569	+	13.6569i	1.55634	+	1.55634i
$78$	−1.00000	+	1.41421i	−0.113228	+	0.160128i
$79$		−	4.48528i		−	0.504634i	−0.967645	−	0.252317i	$-0.918807\pi$
$79$		−	4.48528i		−	0.504634i	0.967645	−	0.252317i	$-0.0811925\pi$
$80$	0.707107	+	2.12132i	0.0790569	+	0.237171i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−1.41421	+	1.41421i	−0.156174	+	0.156174i
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	−0.768476	−	0.639879i	$-0.778984\pi$
$83$	−1.17157	+	1.17157i	−0.128597	+	0.128597i	0.639879	+	0.768476i	$0.278984\pi$
$84$	1.41421	+	8.24264i	0.154303	+	0.899346i
$85$	−4.24264	+	8.48528i	−0.460179	+	0.920358i
$86$		−	10.2426i		−	1.10449i
$87$	−8.48528	−	6.00000i	−0.909718	−	0.643268i
$88$	−2.82843	−	2.82843i	−0.301511	−	0.301511i
$89$	16.8284			1.78381			0.891905	−	0.452223i	$-0.149369\pi$
$89$	16.8284			1.78381			0.891905	+	0.452223i	$0.149369\pi$
$90$	6.65685	+	0.828427i	0.701694	+	0.0873239i
$91$	4.82843			0.506157
$92$	2.82843	+	2.82843i	0.294884	+	0.294884i
$93$	0.828427	+	0.585786i	0.0859039	+	0.0607432i
$94$			8.82843i			0.910583i
$95$	2.48528	−	0.828427i	0.254984	−	0.0849948i
$96$	−0.292893	−	1.70711i	−0.0298933	−	0.174231i
$97$	−5.07107	+	5.07107i	−0.514889	+	0.514889i	−0.916020	−	0.401132i	$-0.868617\pi$
$97$	−5.07107	+	5.07107i	−0.514889	+	0.514889i	0.401132	+	0.916020i	$0.368617\pi$
$98$	11.5355	−	11.5355i	1.16526	−	1.16526i
$99$	−11.3137	+	4.00000i	−1.13707	+	0.402015i
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$			8.82843i			0.878461i	0.898374	+	0.439231i	$0.144749\pi$
$101$			8.82843i			0.878461i	−0.898374	+	0.439231i	$0.855251\pi$
$102$	4.24264	−	6.00000i	0.420084	−	0.594089i
$103$	−4.48528	−	4.48528i	−0.441948	−	0.441948i	0.450718	−	0.892666i	$-0.351168\pi$
$103$	−4.48528	−	4.48528i	−0.441948	−	0.441948i	−0.892666	+	0.450718i	$0.851168\pi$
$104$	−1.00000			−0.0980581
$105$	−8.82843	−	16.4853i	−0.861566	−	1.60880i
$106$	4.82843			0.468978
$107$	−2.07107	−	2.07107i	−0.200218	−	0.200218i	0.599876	−	0.800093i	$-0.295217\pi$
$107$	−2.07107	−	2.07107i	−0.200218	−	0.200218i	−0.800093	+	0.599876i	$0.795217\pi$
$108$	−5.00000	−	1.41421i	−0.481125	−	0.136083i
$109$		−	19.0711i		−	1.82668i	−0.407201	−	0.913339i	$-0.633495\pi$
$109$		−	19.0711i		−	1.82668i	0.407201	−	0.913339i	$-0.366505\pi$
$110$	8.00000	+	4.00000i	0.762770	+	0.381385i
$111$	−13.0711	+	2.24264i	−1.24065	+	0.212862i
$112$	−3.41421	+	3.41421i	−0.322613	+	0.322613i
$113$	7.00000	−	7.00000i	0.658505	−	0.658505i	−0.296522	−	0.955026i	$-0.595827\pi$
$113$	7.00000	−	7.00000i	0.658505	−	0.658505i	0.955026	+	0.296522i	$0.0958267\pi$
$114$	−2.00000	+	0.343146i	−0.187317	+	0.0321385i
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$		−	6.00000i		−	0.557086i
$117$	−1.29289	+	2.70711i	−0.119528	+	0.250272i
$118$	−8.82843	−	8.82843i	−0.812723	−	0.812723i
$119$	−20.4853			−1.87788
$120$	1.82843	+	3.41421i	0.166912	+	0.311674i
$121$	−5.00000			−0.454545
$122$	−0.585786	−	0.585786i	−0.0530346	−	0.0530346i
$123$	−2.00000	+	2.82843i	−0.180334	+	0.255031i
$124$			0.585786i			0.0526052i
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$	4.82843	+	13.6569i	0.430150	+	1.21665i
$127$	−8.82843	+	8.82843i	−0.783396	+	0.783396i	−0.980402	−	0.197006i	$-0.936878\pi$
$127$	−8.82843	+	8.82843i	−0.783396	+	0.783396i	0.197006	+	0.980402i	$0.436878\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−3.00000	−	17.4853i	−0.264135	−	1.53949i
$130$	2.12132	−	0.707107i	0.186052	−	0.0620174i
$131$			20.9706i			1.83221i	0.400942	+	0.916103i	$0.368683\pi$
$131$			20.9706i			1.83221i	−0.400942	+	0.916103i	$0.631317\pi$
$132$	−5.65685	−	4.00000i	−0.492366	−	0.348155i
$133$	4.00000	+	4.00000i	0.346844	+	0.346844i
$134$	6.82843			0.589886
$135$	11.6066	−	0.535534i	0.998937	−	0.0460914i
$136$	4.24264			0.363803
$137$	0.928932	+	0.928932i	0.0793640	+	0.0793640i	0.745674	−	0.666310i	$-0.232127\pi$
$137$	0.928932	+	0.928932i	0.0793640	+	0.0793640i	−0.666310	+	0.745674i	$0.732127\pi$
$138$	5.65685	+	4.00000i	0.481543	+	0.340503i
$139$			9.65685i			0.819084i	0.912291	+	0.409542i	$0.134311\pi$
$139$			9.65685i			0.819084i	−0.912291	+	0.409542i	$0.865689\pi$
$140$	4.82843	−	9.65685i	0.408077	−	0.816153i
$141$	2.58579	+	15.0711i	0.217763	+	1.26921i
$142$	4.07107	−	4.07107i	0.341636	−	0.341636i
$143$	−2.82843	+	2.82843i	−0.236525	+	0.236525i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	4.24264	+	12.7279i	0.352332	+	1.05700i
$146$			4.34315i			0.359441i
$147$	16.3137	−	23.0711i	1.34553	−	1.90287i
$148$	−5.41421	−	5.41421i	−0.445046	−	0.445046i
$149$	−14.3848			−1.17845			−0.589223	−	0.807970i	$-0.700566\pi$
$149$	−14.3848			−1.17845			−0.589223	+	0.807970i	$0.700566\pi$
$150$	−6.29289	−	5.94975i	−0.513813	−	0.485795i
$151$	−13.0711			−1.06371			−0.531854	−	0.846836i	$-0.678505\pi$
$151$	−13.0711			−1.06371			−0.531854	+	0.846836i	$0.678505\pi$
$152$	−0.828427	−	0.828427i	−0.0671943	−	0.0671943i
$153$	5.48528	−	11.4853i	0.443459	−	0.928530i
$154$			19.3137i			1.55634i
$155$	−0.414214	−	1.24264i	−0.0332704	−	0.0998113i
$156$	−1.70711	+	0.292893i	−0.136678	+	0.0234502i
$157$	7.75736	−	7.75736i	0.619105	−	0.619105i	−0.326197	−	0.945302i	$-0.605767\pi$
$157$	7.75736	−	7.75736i	0.619105	−	0.619105i	0.945302	+	0.326197i	$0.105767\pi$
$158$	3.17157	−	3.17157i	0.252317	−	0.252317i
$159$	8.24264	−	1.41421i	0.653684	−	0.112154i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		−	19.3137i		−	1.52213i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	13.6569	+	13.6569i	1.06969	+	1.06969i	0.997383	+	0.0723048i	$0.0230354\pi$
$163$	13.6569	+	13.6569i	1.06969	+	1.06969i	0.0723048	+	0.997383i	$0.476965\pi$
$164$	−2.00000			−0.156174
$165$	14.8284	+	4.48528i	1.15439	+	0.349179i
$166$	−1.65685			−0.128597
$167$	0.585786	+	0.585786i	0.0453295	+	0.0453295i	0.729408	−	0.684079i	$-0.239796\pi$
$167$	0.585786	+	0.585786i	0.0453295	+	0.0453295i	−0.684079	+	0.729408i	$0.739796\pi$
$168$	−4.82843	+	6.82843i	−0.372521	+	0.526825i
$169$			1.00000i			0.0769231i
$170$	−9.00000	+	3.00000i	−0.690268	+	0.230089i
$171$	−3.31371	+	1.17157i	−0.253406	+	0.0895924i
$172$	7.24264	−	7.24264i	0.552246	−	0.552246i
$173$	−2.92893	+	2.92893i	−0.222683	+	0.222683i	−0.809627	−	0.586945i	$-0.800331\pi$
$173$	−2.92893	+	2.92893i	−0.222683	+	0.222683i	0.586945	+	0.809627i	$0.300331\pi$
$174$	−1.75736	−	10.2426i	−0.133225	−	0.776493i
$175$	−3.41421	+	23.8995i	−0.258090	+	1.80663i
$176$		−	4.00000i		−	0.301511i
$177$	−17.6569	−	12.4853i	−1.32717	−	0.938451i
$178$	11.8995	+	11.8995i	0.891905	+	0.891905i
$179$	−6.34315			−0.474109			−0.237054	−	0.971496i	$-0.576182\pi$
$179$	−6.34315			−0.474109			−0.237054	+	0.971496i	$0.576182\pi$
$180$	4.12132	+	5.29289i	0.307185	+	0.394509i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	3.41421	+	3.41421i	0.253078	+	0.253078i
$183$	−1.17157	−	0.828427i	−0.0866052	−	0.0612391i
$184$			4.00000i			0.294884i
$185$	15.3137	+	7.65685i	1.12589	+	0.562943i
$186$	0.171573	+	1.00000i	0.0125803	+	0.0733236i
$187$	12.0000	−	12.0000i	0.877527	−	0.877527i
$188$	−6.24264	+	6.24264i	−0.455291	+	0.455291i
$189$	12.2426	+	21.8995i	0.890521	+	1.59295i
$190$	2.34315	+	1.17157i	0.169990	+	0.0849948i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	1.00000	−	1.41421i	0.0721688	−	0.102062i
$193$	8.58579	+	8.58579i	0.618018	+	0.618018i	0.945023	−	0.327004i	$-0.106039\pi$
$193$	8.58579	+	8.58579i	0.618018	+	0.618018i	−0.327004	+	0.945023i	$0.606039\pi$
$194$	−7.17157			−0.514889
$195$	3.41421	−	1.82843i	0.244497	−	0.130936i
$196$	16.3137			1.16526
$197$	12.2426	+	12.2426i	0.872252	+	0.872252i	0.992718	−	0.120465i	$-0.0384387\pi$
$197$	12.2426	+	12.2426i	0.872252	+	0.872252i	−0.120465	+	0.992718i	$0.538439\pi$
$198$	−10.8284	−	5.17157i	−0.769543	−	0.367528i
$199$		−	6.14214i		−	0.435404i	−0.976015	−	0.217702i	$-0.930144\pi$
$199$		−	6.14214i		−	0.435404i	0.976015	−	0.217702i	$-0.0698562\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$	11.6569	−	2.00000i	0.822211	−	0.141069i
$202$	−6.24264	+	6.24264i	−0.439231	+	0.439231i
$203$	−20.4853	+	20.4853i	−1.43778	+	1.43778i
$204$	7.24264	−	1.24264i	0.507086	−	0.0870023i
$205$	4.24264	−	1.41421i	0.296319	−	0.0987730i
$206$		−	6.34315i		−	0.441948i
$207$	10.8284	+	5.17157i	0.752628	+	0.359449i
$208$	−0.707107	−	0.707107i	−0.0490290	−	0.0490290i
$209$	−4.68629			−0.324158
$210$	5.41421	−	17.8995i	0.373616	−	1.23518i
$211$	−9.65685			−0.664805			−0.332403	−	0.943138i	$-0.607859\pi$
$211$	−9.65685			−0.664805			−0.332403	+	0.943138i	$0.607859\pi$
$212$	3.41421	+	3.41421i	0.234489	+	0.234489i
$213$	5.75736	−	8.14214i	0.394488	−	0.557890i
$214$		−	2.92893i		−	0.200218i
$215$	−10.2426	+	20.4853i	−0.698542	+	1.39708i
$216$	−2.53553	−	4.53553i	−0.172521	−	0.308604i
$217$	2.00000	−	2.00000i	0.135769	−	0.135769i
$218$	13.4853	−	13.4853i	0.913339	−	0.913339i
$219$	1.27208	+	7.41421i	0.0859591	+	0.501006i
$220$	2.82843	+	8.48528i	0.190693	+	0.572078i
$221$		−	4.24264i		−	0.285391i
$222$	−10.8284	−	7.65685i	−0.726756	−	0.513894i
$223$	1.65685	+	1.65685i	0.110951	+	0.110951i	0.760403	−	0.649452i	$-0.225002\pi$
$223$	1.65685	+	1.65685i	0.110951	+	0.110951i	−0.649452	+	0.760403i	$0.725002\pi$
$224$	−4.82843			−0.322613
$225$	−12.4853	−	8.31371i	−0.832352	−	0.554247i
$226$	9.89949			0.658505
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	0.770357	−	0.637613i	$-0.220078\pi$
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	−0.637613	+	0.770357i	$0.720078\pi$
$228$	−1.65685	−	1.17157i	−0.109728	−	0.0775893i
$229$			1.89949i			0.125522i	0.998029	+	0.0627611i	$0.0199906\pi$
$229$			1.89949i			0.125522i	−0.998029	+	0.0627611i	$0.980009\pi$
$230$	−2.82843	−	8.48528i	−0.186501	−	0.559503i
$231$	5.65685	+	32.9706i	0.372194	+	2.16930i
$232$	4.24264	−	4.24264i	0.278543	−	0.278543i
$233$	2.65685	−	2.65685i	0.174056	−	0.174056i	−0.614703	−	0.788759i	$-0.710724\pi$
$233$	2.65685	−	2.65685i	0.174056	−	0.174056i	0.788759	+	0.614703i	$0.210724\pi$
$234$	−2.82843	+	1.00000i	−0.184900	+	0.0653720i
$235$	8.82843	−	17.6569i	0.575903	−	1.15181i
$236$		−	12.4853i		−	0.812723i
$237$	4.48528	−	6.34315i	0.291350	−	0.412032i
$238$	−14.4853	−	14.4853i	−0.938941	−	0.938941i
$239$	−0.100505			−0.00650113			−0.00325057	−	0.999995i	$-0.501035\pi$
$239$	−0.100505			−0.00650113			−0.00325057	+	0.999995i	$0.501035\pi$
$240$	−1.12132	+	3.70711i	−0.0723809	+	0.239293i
$241$	7.65685			0.493221			0.246611	−	0.969115i	$-0.420683\pi$
$241$	7.65685			0.493221			0.246611	+	0.969115i	$0.420683\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$		−	0.828427i		−	0.0530346i
$245$	−34.6066	+	11.5355i	−2.21093	+	0.736978i
$246$	−3.41421	+	0.585786i	−0.217682	+	0.0373484i
$247$	−0.828427	+	0.828427i	−0.0527116	+	0.0527116i
$248$	−0.414214	+	0.414214i	−0.0263026	+	0.0263026i
$249$	−2.82843	+	0.485281i	−0.179244	+	0.0307535i
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$		−	25.6569i		−	1.61945i	−0.586812	−	0.809723i	$-0.699617\pi$
$251$		−	25.6569i		−	1.61945i	0.586812	−	0.809723i	$-0.300383\pi$
$252$	−6.24264	+	13.0711i	−0.393249	+	0.823400i
$253$	11.3137	+	11.3137i	0.711287	+	0.711287i
$254$	−12.4853			−0.783396
$255$	−14.4853	+	7.75736i	−0.907104	+	0.485785i
$256$	1.00000			0.0625000
$257$	7.00000	+	7.00000i	0.436648	+	0.436648i	0.890882	−	0.454234i	$-0.150087\pi$
$257$	7.00000	+	7.00000i	0.436648	+	0.436648i	−0.454234	+	0.890882i	$0.650087\pi$
$258$	10.2426	−	14.4853i	0.637679	−	0.901814i
$259$			36.9706i			2.29724i
$260$	2.00000	+	1.00000i	0.124035	+	0.0620174i
$261$	−6.00000	−	16.9706i	−0.371391	−	1.05045i
$262$	−14.8284	+	14.8284i	−0.916103	+	0.916103i
$263$	16.0000	−	16.0000i	0.986602	−	0.986602i	−0.0133092	−	0.999911i	$-0.504237\pi$
$263$	16.0000	−	16.0000i	0.986602	−	0.986602i	0.999911	+	0.0133092i	$0.00423656\pi$
$264$	−1.17157	−	6.82843i	−0.0721053	−	0.420261i
$265$	−9.65685	−	4.82843i	−0.593216	−	0.296608i
$266$			5.65685i			0.346844i
$267$	23.7990	+	16.8284i	1.45647	+	1.02988i
$268$	4.82843	+	4.82843i	0.294943	+	0.294943i
$269$	20.8284			1.26993			0.634966	−	0.772540i	$-0.281014\pi$
$269$	20.8284			1.26993			0.634966	+	0.772540i	$0.281014\pi$
$270$	8.58579	+	7.82843i	0.522514	+	0.476423i
$271$	6.24264			0.379213			0.189607	−	0.981860i	$-0.439279\pi$
$271$	6.24264			0.379213			0.189607	+	0.981860i	$0.439279\pi$
$272$	3.00000	+	3.00000i	0.181902	+	0.181902i
$273$	6.82843	+	4.82843i	0.413275	+	0.292230i
$274$			1.31371i			0.0793640i
$275$	−12.0000	−	16.0000i	−0.723627	−	0.964836i
$276$	1.17157	+	6.82843i	0.0705204	+	0.411023i
$277$	3.89949	−	3.89949i	0.234298	−	0.234298i	−0.580186	−	0.814484i	$-0.697020\pi$
$277$	3.89949	−	3.89949i	0.234298	−	0.234298i	0.814484	+	0.580186i	$0.197020\pi$
$278$	−6.82843	+	6.82843i	−0.409542	+	0.409542i
$279$	0.585786	+	1.65685i	0.0350701	+	0.0991933i
$280$	10.2426	−	3.41421i	0.612115	−	0.204038i
$281$		−	4.82843i		−	0.288040i	−0.989575	−	0.144020i	$-0.953997\pi$
$281$		−	4.82843i		−	0.288040i	0.989575	−	0.144020i	$-0.0460029\pi$
$282$	−8.82843	+	12.4853i	−0.525725	+	0.743488i
$283$	−8.75736	−	8.75736i	−0.520571	−	0.520571i	0.397173	−	0.917744i	$-0.369991\pi$
$283$	−8.75736	−	8.75736i	−0.520571	−	0.520571i	−0.917744	+	0.397173i	$0.869991\pi$
$284$	5.75736			0.341636
$285$	4.34315	+	1.31371i	0.257266	+	0.0778174i
$286$	−4.00000			−0.236525
$287$	6.82843	+	6.82843i	0.403069	+	0.403069i
$288$	1.29289	−	2.70711i	0.0761845	−	0.159518i
$289$			1.00000i			0.0588235i
$290$	−6.00000	+	12.0000i	−0.352332	+	0.704664i
$291$	−12.2426	+	2.10051i	−0.717676	+	0.123134i
$292$	−3.07107	+	3.07107i	−0.179721	+	0.179721i
$293$	12.4853	−	12.4853i	0.729398	−	0.729398i	−0.241102	−	0.970500i	$-0.577509\pi$
$293$	12.4853	−	12.4853i	0.729398	−	0.729398i	0.970500	+	0.241102i	$0.0775088\pi$
$294$	27.8492	−	4.77817i	1.62420	−	0.278669i
$295$	8.82843	+	26.4853i	0.514011	+	1.54203i
$296$		−	7.65685i		−	0.445046i
$297$	−20.0000	−	5.65685i	−1.16052	−	0.328244i
$298$	−10.1716	−	10.1716i	−0.589223	−	0.589223i
$299$	4.00000			0.231326
$300$	−0.242641	−	8.65685i	−0.0140089	−	0.499804i
$301$	−49.4558			−2.85059
$302$	−9.24264	−	9.24264i	−0.531854	−	0.531854i
$303$	−8.82843	+	12.4853i	−0.507180	+	0.717261i
$304$		−	1.17157i		−	0.0671943i
$305$	0.585786	+	1.75736i	0.0335420	+	0.100626i
$306$	12.0000	−	4.24264i	0.685994	−	0.242536i
$307$	12.8284	−	12.8284i	0.732157	−	0.732157i	−0.238890	−	0.971047i	$-0.576783\pi$
$307$	12.8284	−	12.8284i	0.732157	−	0.732157i	0.971047	+	0.238890i	$0.0767834\pi$
$308$	−13.6569	+	13.6569i	−0.778171	+	0.778171i
$309$	−1.85786	−	10.8284i	−0.105690	−	0.616008i
$310$	0.585786	−	1.17157i	0.0332704	−	0.0665409i
$311$		−	28.0000i		−	1.58773i	−0.608091	−	0.793867i	$-0.708065\pi$
$311$		−	28.0000i		−	1.58773i	0.608091	−	0.793867i	$-0.291935\pi$
$312$	−1.41421	−	1.00000i	−0.0800641	−	0.0566139i
$313$	12.6569	+	12.6569i	0.715408	+	0.715408i	0.967661	−	0.252253i	$-0.0811717\pi$
$313$	12.6569	+	12.6569i	0.715408	+	0.715408i	−0.252253	+	0.967661i	$0.581172\pi$
$314$	10.9706			0.619105
$315$	4.00000	−	32.1421i	0.225374	−	1.81100i
$316$	4.48528			0.252317
$317$	9.65685	+	9.65685i	0.542383	+	0.542383i	0.924227	−	0.381844i	$-0.124711\pi$
$317$	9.65685	+	9.65685i	0.542383	+	0.542383i	−0.381844	+	0.924227i	$0.624711\pi$
$318$	6.82843	+	4.82843i	0.382919	+	0.270765i
$319$		−	24.0000i		−	1.34374i
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$	−0.857864	−	5.00000i	−0.0478813	−	0.279073i
$322$	13.6569	−	13.6569i	0.761067	−	0.761067i
$323$	3.51472	−	3.51472i	0.195564	−	0.195564i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	−4.94975	−	0.707107i	−0.274563	−	0.0392232i
$326$			19.3137i			1.06969i
$327$	19.0711	−	26.9706i	1.05463	−	1.49148i
$328$	−1.41421	−	1.41421i	−0.0780869	−	0.0780869i
$329$	42.6274			2.35013
$330$	7.31371	+	13.6569i	0.402606	+	0.751785i
$331$	24.2843			1.33478			0.667392	−	0.744706i	$-0.267411\pi$
$331$	24.2843			1.33478			0.667392	+	0.744706i	$0.267411\pi$
$332$	−1.17157	−	1.17157i	−0.0642984	−	0.0642984i
$333$	−20.7279	−	9.89949i	−1.13588	−	0.542489i
$334$			0.828427i			0.0453295i
$335$	−13.6569	−	6.82843i	−0.746154	−	0.373077i
$336$	−8.24264	+	1.41421i	−0.449673	+	0.0771517i
$337$	−23.0000	+	23.0000i	−1.25289	+	1.25289i	−0.298471	+	0.954419i	$0.596477\pi$
$337$	−23.0000	+	23.0000i	−1.25289	+	1.25289i	−0.954419	+	0.298471i	$0.903523\pi$
$338$	−0.707107	+	0.707107i	−0.0384615	+	0.0384615i
$339$	16.8995	−	2.89949i	0.917855	−	0.157479i
$340$	−8.48528	−	4.24264i	−0.460179	−	0.230089i
$341$			2.34315i			0.126888i
$342$	−3.17157	−	1.51472i	−0.171499	−	0.0819066i
$343$	−31.7990	−	31.7990i	−1.71698	−	1.71698i
$344$	10.2426			0.552246
$345$	−7.31371	−	13.6569i	−0.393757	−	0.735260i
$346$	−4.14214			−0.222683
$347$	−20.5563	−	20.5563i	−1.10352	−	1.10352i	−0.993982	−	0.109540i	$-0.965062\pi$
$347$	−20.5563	−	20.5563i	−1.10352	−	1.10352i	−0.109540	−	0.993982i	$-0.534938\pi$
$348$	6.00000	−	8.48528i	0.321634	−	0.454859i
$349$		−	7.27208i		−	0.389265i	−0.980876	−	0.194633i	$-0.937649\pi$
$349$		−	7.27208i		−	0.389265i	0.980876	−	0.194633i	$-0.0623515\pi$
$350$	−19.3137	+	14.4853i	−1.03236	+	0.774271i
$351$	−4.53553	+	2.53553i	−0.242089	+	0.135337i
$352$	2.82843	−	2.82843i	0.150756	−	0.150756i
$353$	−5.55635	+	5.55635i	−0.295735	+	0.295735i	−0.839341	−	0.543606i	$-0.817059\pi$
$353$	−5.55635	+	5.55635i	−0.295735	+	0.295735i	0.543606	+	0.839341i	$0.317059\pi$
$354$	−3.65685	−	21.3137i	−0.194360	−	1.13281i
$355$	−12.2132	+	4.07107i	−0.648210	+	0.216070i
$356$			16.8284i			0.891905i
$357$	−28.9706	−	20.4853i	−1.53328	−	1.08420i
$358$	−4.48528	−	4.48528i	−0.237054	−	0.237054i
$359$	20.5858			1.08648			0.543238	−	0.839579i	$-0.317198\pi$
$359$	20.5858			1.08648			0.543238	+	0.839579i	$0.317198\pi$
$360$	−0.828427	+	6.65685i	−0.0436619	+	0.350847i
$361$	17.6274			0.927759
$362$	4.24264	+	4.24264i	0.222988	+	0.222988i
$363$	−7.07107	−	5.00000i	−0.371135	−	0.262432i
$364$			4.82843i			0.253078i
$365$	4.34315	−	8.68629i	0.227331	−	0.454661i
$366$	−0.242641	−	1.41421i	−0.0126830	−	0.0739221i
$367$	−14.1421	+	14.1421i	−0.738213	+	0.738213i	−0.972232	−	0.234019i	$-0.924812\pi$
$367$	−14.1421	+	14.1421i	−0.738213	+	0.738213i	0.234019	+	0.972232i	$0.424812\pi$
$368$	−2.82843	+	2.82843i	−0.147442	+	0.147442i
$369$	−5.65685	+	2.00000i	−0.294484	+	0.104116i
$370$	5.41421	+	16.2426i	0.281472	+	0.844415i
$371$		−	23.3137i		−	1.21039i
$372$	−0.585786	+	0.828427i	−0.0303716	+	0.0429519i
$373$	19.0711	+	19.0711i	0.987462	+	0.987462i	0.999922	−	0.0124599i	$-0.00396622\pi$
$373$	19.0711	+	19.0711i	0.987462	+	0.987462i	−0.0124599	+	0.999922i	$0.503966\pi$
$374$	16.9706			0.877527
$375$	6.63604	+	18.1924i	0.342684	+	0.939451i
$376$	−8.82843			−0.455291
$377$	−4.24264	−	4.24264i	−0.218507	−	0.218507i
$378$	−6.82843	+	24.1421i	−0.351216	+	1.24174i
$379$			9.85786i			0.506364i	0.967419	+	0.253182i	$0.0814772\pi$
$379$			9.85786i			0.506364i	−0.967419	+	0.253182i	$0.918523\pi$
$380$	0.828427	+	2.48528i	0.0424974	+	0.127492i
$381$	−21.3137	+	3.65685i	−1.09193	+	0.187346i
$382$	−2.00000	+	2.00000i	−0.102329	+	0.102329i
$383$	−9.65685	+	9.65685i	−0.493442	+	0.493442i	−0.909389	−	0.415947i	$-0.863450\pi$
$383$	−9.65685	+	9.65685i	−0.493442	+	0.493442i	0.415947	+	0.909389i	$0.363450\pi$
$384$	1.70711	−	0.292893i	0.0871154	−	0.0149466i
$385$	19.3137	−	38.6274i	0.984318	−	1.96864i
$386$			12.1421i			0.618018i
$387$	13.2426	−	27.7279i	0.673161	−	1.40949i
$388$	−5.07107	−	5.07107i	−0.257444	−	0.257444i
$389$	−2.00000			−0.101404			−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000			−0.101404			−0.0507020	+	0.998714i	$0.516146\pi$
$390$	3.70711	+	1.12132i	0.187717	+	0.0567803i
$391$	−16.9706			−0.858238
$392$	11.5355	+	11.5355i	0.582632	+	0.582632i
$393$	−20.9706	+	29.6569i	−1.05782	+	1.49599i
$394$			17.3137i			0.872252i
$395$	−9.51472	+	3.17157i	−0.478737	+	0.159579i
$396$	−4.00000	−	11.3137i	−0.201008	−	0.568535i
$397$	−14.8284	+	14.8284i	−0.744217	+	0.744217i	−0.973387	−	0.229169i	$-0.926399\pi$
$397$	−14.8284	+	14.8284i	−0.744217	+	0.744217i	0.229169	+	0.973387i	$0.426399\pi$
$398$	4.34315	−	4.34315i	0.217702	−	0.217702i
$399$	1.65685	+	9.65685i	0.0829465	+	0.483447i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$		−	37.7990i		−	1.88759i	−0.330529	−	0.943796i	$-0.607227\pi$
$401$		−	37.7990i		−	1.88759i	0.330529	−	0.943796i	$-0.392773\pi$
$402$	9.65685	+	6.82843i	0.481640	+	0.340571i
$403$	0.414214	+	0.414214i	0.0206334	+	0.0206334i
$404$	−8.82843			−0.439231
$405$	16.9497	+	10.8492i	0.842240	+	0.539103i
$406$	−28.9706			−1.43778
$407$	−21.6569	−	21.6569i	−1.07349	−	1.07349i
$408$	6.00000	+	4.24264i	0.297044	+	0.210042i
$409$			8.82843i			0.436538i	0.975889	+	0.218269i	$0.0700410\pi$
$409$			8.82843i			0.436538i	−0.975889	+	0.218269i	$0.929959\pi$
$410$	4.00000	+	2.00000i	0.197546	+	0.0987730i
$411$	0.384776	+	2.24264i	0.0189796	+	0.110621i
$412$	4.48528	−	4.48528i	0.220974	−	0.220974i
$413$	−42.6274	+	42.6274i	−2.09756	+	2.09756i
$414$	4.00000	+	11.3137i	0.196589	+	0.556038i
$415$	3.31371	+	1.65685i	0.162664	+	0.0813318i
$416$		−	1.00000i		−	0.0490290i
$417$	−9.65685	+	13.6569i	−0.472898	+	0.668779i
$418$	−3.31371	−	3.31371i	−0.162079	−	0.162079i
$419$	−22.4853			−1.09848			−0.549239	−	0.835665i	$-0.685082\pi$
$419$	−22.4853			−1.09848			−0.549239	+	0.835665i	$0.685082\pi$
$420$	16.4853	−	8.82843i	0.804399	−	0.430783i
$421$	12.9289			0.630118			0.315059	−	0.949072i	$-0.397976\pi$
$421$	12.9289			0.630118			0.315059	+	0.949072i	$0.397976\pi$
$422$	−6.82843	−	6.82843i	−0.332403	−	0.332403i
$423$	−11.4142	+	23.8995i	−0.554978	+	1.16203i
$424$			4.82843i			0.234489i
$425$	21.0000	+	3.00000i	1.01865	+	0.145521i
$426$	9.82843	−	1.68629i	0.476189	−	0.0817011i
$427$	−2.82843	+	2.82843i	−0.136877	+	0.136877i
$428$	2.07107	−	2.07107i	0.100109	−	0.100109i
$429$	−6.82843	+	1.17157i	−0.329680	+	0.0565641i
$430$	−21.7279	+	7.24264i	−1.04781	+	0.349271i
$431$			25.0711i			1.20763i	0.797124	+	0.603815i	$0.206354\pi$
$431$			25.0711i			1.20763i	−0.797124	+	0.603815i	$0.793646\pi$
$432$	1.41421	−	5.00000i	0.0680414	−	0.240563i
$433$	6.31371	+	6.31371i	0.303417	+	0.303417i	0.842349	−	0.538932i	$-0.181172\pi$
$433$	6.31371	+	6.31371i	0.303417	+	0.303417i	−0.538932	+	0.842349i	$0.681172\pi$
$434$	2.82843			0.135769
$435$	−6.72792	+	22.2426i	−0.322579	+	1.06645i
$436$	19.0711			0.913339
$437$	3.31371	+	3.31371i	0.158516	+	0.158516i
$438$	−4.34315	+	6.14214i	−0.207524	+	0.293483i
$439$		−	29.6569i		−	1.41544i	−0.706491	−	0.707722i	$-0.749723\pi$
$439$		−	29.6569i		−	1.41544i	0.706491	−	0.707722i	$-0.250277\pi$
$440$	−4.00000	+	8.00000i	−0.190693	+	0.381385i
$441$	46.1421	−	16.3137i	2.19724	−	0.776843i
$442$	3.00000	−	3.00000i	0.142695	−	0.142695i
$443$	18.8995	−	18.8995i	0.897942	−	0.897942i	−0.0973118	−	0.995254i	$-0.531024\pi$
$443$	18.8995	−	18.8995i	0.897942	−	0.897942i	0.995254	+	0.0973118i	$0.0310244\pi$
$444$	−2.24264	−	13.0711i	−0.106431	−	0.620325i
$445$	−11.8995	−	35.6985i	−0.564090	−	1.69227i
$446$			2.34315i			0.110951i
$447$	−20.3431	−	14.3848i	−0.962198	−	0.680377i
$448$	−3.41421	−	3.41421i	−0.161306	−	0.161306i
$449$	−21.7990			−1.02876			−0.514379	−	0.857563i	$-0.671978\pi$
$449$	−21.7990			−1.02876			−0.514379	+	0.857563i	$0.671978\pi$
$450$	−2.94975	−	14.7071i	−0.139052	−	0.693300i
$451$	−8.00000			−0.376705
$452$	7.00000	+	7.00000i	0.329252	+	0.329252i
$453$	−18.4853	−	13.0711i	−0.868514	−	0.614132i
$454$			2.82843i			0.132745i
$455$	−3.41421	−	10.2426i	−0.160061	−	0.480182i
$456$	−0.343146	−	2.00000i	−0.0160693	−	0.0936586i
$457$	−6.92893	+	6.92893i	−0.324122	+	0.324122i	−0.850346	−	0.526224i	$-0.823607\pi$
$457$	−6.92893	+	6.92893i	−0.324122	+	0.324122i	0.526224	+	0.850346i	$0.323607\pi$
$458$	−1.34315	+	1.34315i	−0.0627611	+	0.0627611i
$459$	19.2426	−	10.7574i	0.898170	−	0.502111i
$460$	4.00000	−	8.00000i	0.186501	−	0.373002i
$461$			37.6985i			1.75579i	0.478850	+	0.877897i	$0.341054\pi$
$461$			37.6985i			1.75579i	−0.478850	+	0.877897i	$0.658946\pi$
$462$	−19.3137	+	27.3137i	−0.898555	+	1.27075i
$463$	−5.65685	−	5.65685i	−0.262896	−	0.262896i	0.563333	−	0.826230i	$-0.309519\pi$
$463$	−5.65685	−	5.65685i	−0.262896	−	0.262896i	−0.826230	+	0.563333i	$0.809519\pi$
$464$	6.00000			0.278543
$465$	0.656854	−	2.17157i	0.0304609	−	0.100704i
$466$	3.75736			0.174056
$467$	−2.89949	−	2.89949i	−0.134173	−	0.134173i	0.636831	−	0.771004i	$-0.280245\pi$
$467$	−2.89949	−	2.89949i	−0.134173	−	0.134173i	−0.771004	+	0.636831i	$0.780245\pi$
$468$	−2.70711	−	1.29289i	−0.125136	−	0.0597640i
$469$		−	32.9706i		−	1.52244i
$470$	18.7279	−	6.24264i	0.863855	−	0.287952i
$471$	18.7279	−	3.21320i	0.862937	−	0.148057i
$472$	8.82843	−	8.82843i	0.406361	−	0.406361i
$473$	28.9706	−	28.9706i	1.33207	−	1.33207i
$474$	7.65685	−	1.31371i	0.351691	−	0.0603406i
$475$	−3.51472	−	4.68629i	−0.161266	−	0.215022i
$476$		−	20.4853i		−	0.938941i
$477$	13.0711	+	6.24264i	0.598483	+	0.285831i
$478$	−0.0710678	−	0.0710678i	−0.00325057	−	0.00325057i
$479$	12.3848			0.565875			0.282937	−	0.959138i	$-0.408691\pi$
$479$	12.3848			0.565875			0.282937	+	0.959138i	$0.408691\pi$
$480$	−3.41421	+	1.82843i	−0.155837	+	0.0834559i
$481$	−7.65685			−0.349123
$482$	5.41421	+	5.41421i	0.246611	+	0.246611i
$483$	19.3137	−	27.3137i	0.878804	−	1.24282i
$484$		−	5.00000i		−	0.227273i
$485$	14.3431	+	7.17157i	0.651289	+	0.325644i
$486$	−11.7071	−	10.2929i	−0.531045	−	0.466895i
$487$	17.0711	−	17.0711i	0.773564	−	0.773564i	−0.205164	−	0.978728i	$-0.565773\pi$
$487$	17.0711	−	17.0711i	0.773564	−	0.773564i	0.978728	+	0.205164i	$0.0657727\pi$
$488$	0.585786	−	0.585786i	0.0265173	−	0.0265173i
$489$	5.65685	+	32.9706i	0.255812	+	1.49098i
$490$	−32.6274	−	16.3137i	−1.47396	−	0.736978i
$491$		−	25.7990i		−	1.16429i	−0.813084	−	0.582146i	$-0.802213\pi$
$491$		−	25.7990i		−	1.16429i	0.813084	−	0.582146i	$-0.197787\pi$
$492$	−2.82843	−	2.00000i	−0.127515	−	0.0901670i
$493$	18.0000	+	18.0000i	0.810679	+	0.810679i
$494$	−1.17157			−0.0527116
$495$	16.4853	+	21.1716i	0.740958	+	0.951591i
$496$	−0.585786			−0.0263026
$497$	−19.6569	−	19.6569i	−0.881730	−	0.881730i
$498$	−2.34315	−	1.65685i	−0.104999	−	0.0742454i
$499$			8.00000i			0.358129i	0.983837	+	0.179065i	$0.0573071\pi$
$499$			8.00000i			0.358129i	−0.983837	+	0.179065i	$0.942693\pi$
$500$	−6.36396	+	9.19239i	−0.284605	+	0.411096i
$501$	0.242641	+	1.41421i	0.0108404	+	0.0631824i
$502$	18.1421	−	18.1421i	0.809723	−	0.809723i
$503$	12.1421	−	12.1421i	0.541391	−	0.541391i	−0.382546	−	0.923937i	$-0.624952\pi$
$503$	12.1421	−	12.1421i	0.541391	−	0.541391i	0.923937	+	0.382546i	$0.124952\pi$
$504$	−13.6569	+	4.82843i	−0.608325	+	0.215075i
$505$	18.7279	−	6.24264i	0.833382	−	0.277794i
$506$			16.0000i			0.711287i
$507$	−1.00000	+	1.41421i	−0.0444116	+	0.0628074i
$508$	−8.82843	−	8.82843i	−0.391698	−	0.391698i
$509$	−1.21320			−0.0537743			−0.0268871	−	0.999638i	$-0.508559\pi$
$509$	−1.21320			−0.0537743			−0.0268871	+	0.999638i	$0.508559\pi$
$510$	−15.7279	−	4.75736i	−0.696444	−	0.210659i
$511$	20.9706			0.927683
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.85786	−	1.65685i	−0.258631	−	0.0731519i
$514$			9.89949i			0.436648i
$515$	−6.34315	+	12.6863i	−0.279512	+	0.559025i
$516$	17.4853	−	3.00000i	0.769747	−	0.132068i
$517$	−24.9706	+	24.9706i	−1.09820	+	1.09820i
$518$	−26.1421	+	26.1421i	−1.14862	+	1.14862i
$519$	−7.07107	+	1.21320i	−0.310385	+	0.0532537i
$520$	0.707107	+	2.12132i	0.0310087	+	0.0930261i
$521$		−	8.97056i		−	0.393007i	−0.980503	−	0.196504i	$-0.937041\pi$
$521$		−	8.97056i		−	0.393007i	0.980503	−	0.196504i	$-0.0629588\pi$
$522$	7.75736	−	16.2426i	0.339530	−	0.710921i
$523$	8.07107	+	8.07107i	0.352923	+	0.352923i	0.861196	−	0.508273i	$-0.169716\pi$
$523$	8.07107	+	8.07107i	0.352923	+	0.352923i	−0.508273	+	0.861196i	$0.669716\pi$
$524$	−20.9706			−0.916103
$525$	−28.7279	+	30.3848i	−1.25379	+	1.32610i
$526$	22.6274			0.986602
$527$	−1.75736	−	1.75736i	−0.0765518	−	0.0765518i
$528$	4.00000	−	5.65685i	0.174078	−	0.246183i
$529$			7.00000i			0.304348i
$530$	−3.41421	−	10.2426i	−0.148304	−	0.444912i
$531$	−12.4853	−	35.3137i	−0.541815	−	1.53248i
$532$	−4.00000	+	4.00000i	−0.173422	+	0.173422i
$533$	−1.41421	+	1.41421i	−0.0612564	+	0.0612564i
$534$	4.92893	+	28.7279i	0.213296	+	1.24318i
$535$	−2.92893	+	5.85786i	−0.126629	+	0.253258i
$536$			6.82843i			0.294943i
$537$	−8.97056	−	6.34315i	−0.387108	−	0.273727i
$538$	14.7279	+	14.7279i	0.634966	+	0.634966i
$539$	65.2548			2.81072
$540$	0.535534	+	11.6066i	0.0230457	+	0.499469i
$541$	4.24264			0.182405			0.0912027	−	0.995832i	$-0.470929\pi$
$541$	4.24264			0.182405			0.0912027	+	0.995832i	$0.470929\pi$
$542$	4.41421	+	4.41421i	0.189607	+	0.189607i
$543$	8.48528	+	6.00000i	0.364138	+	0.257485i
$544$			4.24264i			0.181902i
$545$	−40.4558	+	13.4853i	−1.73294	+	0.577646i
$546$	1.41421	+	8.24264i	0.0605228	+	0.352752i
$547$	−17.5858	+	17.5858i	−0.751914	+	0.751914i	−0.974836	−	0.222922i	$-0.928440\pi$
$547$	−17.5858	+	17.5858i	−0.751914	+	0.751914i	0.222922	+	0.974836i	$0.428440\pi$
$548$	−0.928932	+	0.928932i	−0.0396820	+	0.0396820i
$549$	−0.828427	−	2.34315i	−0.0353564	−	0.100003i
$550$	2.82843	−	19.7990i	0.120605	−	0.844232i
$551$		−	7.02944i		−	0.299464i
$552$	−4.00000	+	5.65685i	−0.170251	+	0.240772i
$553$	−15.3137	−	15.3137i	−0.651205	−	0.651205i
$554$	5.51472			0.234298
$555$	14.0000	+	26.1421i	0.594267	+	1.10967i
$556$	−9.65685			−0.409542
$557$	15.0711	+	15.0711i	0.638582	+	0.638582i	0.950206	−	0.311624i	$-0.100873\pi$
$557$	15.0711	+	15.0711i	0.638582	+	0.638582i	−0.311624	+	0.950206i	$0.600873\pi$
$558$	−0.757359	+	1.58579i	−0.0320616	+	0.0671317i
$559$		−	10.2426i		−	0.433218i
$560$	9.65685	+	4.82843i	0.408077	+	0.204038i
$561$	28.9706	−	4.97056i	1.22314	−	0.209857i
$562$	3.41421	−	3.41421i	0.144020	−	0.144020i
$563$	−10.7574	+	10.7574i	−0.453369	+	0.453369i	−0.896471	−	0.443102i	$-0.853878\pi$
$563$	−10.7574	+	10.7574i	−0.453369	+	0.453369i	0.443102	+	0.896471i	$0.353878\pi$
$564$	−15.0711	+	2.58579i	−0.634606	+	0.108881i
$565$	−19.7990	−	9.89949i	−0.832950	−	0.416475i
$566$		−	12.3848i		−	0.520571i
$567$	−4.58579	+	43.2132i	−0.192585	+	1.81478i
$568$	4.07107	+	4.07107i	0.170818	+	0.170818i
$569$	−29.6569			−1.24328			−0.621640	−	0.783303i	$-0.713533\pi$
$569$	−29.6569			−1.24328			−0.621640	+	0.783303i	$0.713533\pi$
$570$	2.14214	+	4.00000i	0.0897242	+	0.167542i
$571$	17.5147			0.732968			0.366484	−	0.930424i	$-0.380561\pi$
$571$	17.5147			0.732968			0.366484	+	0.930424i	$0.380561\pi$
$572$	−2.82843	−	2.82843i	−0.118262	−	0.118262i
$573$	−2.82843	+	4.00000i	−0.118159	+	0.167102i
$574$			9.65685i			0.403069i
$575$	−2.82843	+	19.7990i	−0.117954	+	0.825675i
$576$	2.82843	−	1.00000i	0.117851	−	0.0416667i
$577$	32.0416	−	32.0416i	1.33391	−	1.33391i	0.432071	−	0.901840i	$-0.357783\pi$
$577$	32.0416	−	32.0416i	1.33391	−	1.33391i	0.901840	−	0.432071i	$-0.142217\pi$
$578$	−0.707107	+	0.707107i	−0.0294118	+	0.0294118i
$579$	3.55635	+	20.7279i	0.147797	+	0.861423i
$580$	−12.7279	+	4.24264i	−0.528498	+	0.176166i
$581$			8.00000i			0.331896i
$582$	−10.1421	−	7.17157i	−0.420405	−	0.297271i
$583$	13.6569	+	13.6569i	0.565609	+	0.565609i
$584$	−4.34315			−0.179721
$585$	6.65685	+	0.828427i	0.275227	+	0.0342512i
$586$	17.6569			0.729398
$587$	31.7990	+	31.7990i	1.31248	+	1.31248i	0.919579	+	0.392906i	$0.128530\pi$
$587$	31.7990	+	31.7990i	1.31248	+	1.31248i	0.392906	+	0.919579i	$0.371470\pi$
$588$	23.0711	+	16.3137i	0.951435	+	0.672766i
$589$			0.686292i			0.0282781i
$590$	−12.4853	+	24.9706i	−0.514011	+	1.02802i
$591$	5.07107	+	29.5563i	0.208596	+	1.21579i
$592$	5.41421	−	5.41421i	0.222523	−	0.222523i
$593$	4.58579	−	4.58579i	0.188316	−	0.188316i	−0.606652	−	0.794968i	$-0.707488\pi$
$593$	4.58579	−	4.58579i	0.188316	−	0.188316i	0.794968	+	0.606652i	$0.207488\pi$
$594$	−10.1421	−	18.1421i	−0.416137	−	0.744381i
$595$	14.4853	+	43.4558i	0.593839	+	1.78152i
$596$		−	14.3848i		−	0.589223i
$597$	6.14214	−	8.68629i	0.251381	−	0.355506i
$598$	2.82843	+	2.82843i	0.115663	+	0.115663i
$599$	−0.485281			−0.0198281			−0.00991403	−	0.999951i	$-0.503156\pi$
$599$	−0.485281			−0.0198281			−0.00991403	+	0.999951i	$0.503156\pi$
$600$	5.94975	−	6.29289i	0.242897	−	0.256906i
$601$	−6.34315			−0.258742			−0.129371	−	0.991596i	$-0.541296\pi$
$601$	−6.34315			−0.258742			−0.129371	+	0.991596i	$0.541296\pi$
$602$	−34.9706	−	34.9706i	−1.42529	−	1.42529i
$603$	18.4853	+	8.82843i	0.752779	+	0.359521i
$604$		−	13.0711i		−	0.531854i
$605$	3.53553	+	10.6066i	0.143740	+	0.431220i
$606$	−15.0711	+	2.58579i	−0.612220	+	0.105040i
$607$	−2.48528	+	2.48528i	−0.100874	+	0.100874i	−0.755743	−	0.654868i	$-0.772724\pi$
$607$	−2.48528	+	2.48528i	−0.100874	+	0.100874i	0.654868	+	0.755743i	$0.272724\pi$
$608$	0.828427	−	0.828427i	0.0335972	−	0.0335972i
$609$	−49.4558	+	8.48528i	−2.00405	+	0.343841i
$610$	−0.828427	+	1.65685i	−0.0335420	+	0.0670841i
$611$			8.82843i			0.357160i
$612$	11.4853	+	5.48528i	0.464265	+	0.221729i
$613$	21.6569	+	21.6569i	0.874712	+	0.874712i	0.992982	−	0.118269i	$-0.0377347\pi$
$613$	21.6569	+	21.6569i	0.874712	+	0.874712i	−0.118269	+	0.992982i	$0.537735\pi$
$614$	18.1421			0.732157
$615$	7.41421	+	2.24264i	0.298970	+	0.0904320i
$616$	−19.3137			−0.778171
$617$	−25.0711	−	25.0711i	−1.00932	−	1.00932i	−0.999956	−	0.00936706i	$-0.997018\pi$
$617$	−25.0711	−	25.0711i	−1.00932	−	1.00932i	−0.00936706	−	0.999956i	$-0.502982\pi$
$618$	6.34315	−	8.97056i	0.255159	−	0.360849i
$619$			18.6274i			0.748699i	0.927288	+	0.374350i	$0.122134\pi$
$619$			18.6274i			0.748699i	−0.927288	+	0.374350i	$0.877866\pi$
$620$	1.24264	−	0.414214i	0.0499057	−	0.0166352i
$621$	10.1421	+	18.1421i	0.406990	+	0.728019i
$622$	19.7990	−	19.7990i	0.793867	−	0.793867i
$623$	57.4558	−	57.4558i	2.30192	−	2.30192i
$624$	−0.292893	−	1.70711i	−0.0117251	−	0.0683390i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			17.8995i			0.715408i
$627$	−6.62742	−	4.68629i	−0.264674	−	0.187152i
$628$	7.75736	+	7.75736i	0.309552	+	0.309552i
$629$	32.4853			1.29527
$630$	25.5563	−	19.8995i	1.01819	−	0.792815i
$631$	4.10051			0.163239			0.0816193	−	0.996664i	$-0.473991\pi$
$631$	4.10051			0.163239			0.0816193	+	0.996664i	$0.473991\pi$
$632$	3.17157	+	3.17157i	0.126158	+	0.126158i
$633$	−13.6569	−	9.65685i	−0.542811	−	0.383825i
$634$			13.6569i			0.542383i
$635$	24.9706	+	12.4853i	0.990927	+	0.495463i
$636$	1.41421	+	8.24264i	0.0560772	+	0.326842i
$637$	11.5355	−	11.5355i	0.457054	−	0.457054i
$638$	16.9706	−	16.9706i	0.671871	−	0.671871i
$639$	16.2843	−	5.75736i	0.644196	−	0.227758i
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$			33.3137i			1.31581i	0.753100	+	0.657906i	$0.228558\pi$
$641$			33.3137i			1.31581i	−0.753100	+	0.657906i	$0.771442\pi$
$642$	2.92893	−	4.14214i	0.115596	−	0.163477i
$643$	−6.14214	−	6.14214i	−0.242222	−	0.242222i	0.575547	−	0.817769i	$-0.304789\pi$
$643$	−6.14214	−	6.14214i	−0.242222	−	0.242222i	−0.817769	+	0.575547i	$0.804789\pi$
$644$	19.3137			0.761067
$645$	−34.9706	+	18.7279i	−1.37696	+	0.737411i
$646$	4.97056			0.195564
$647$	6.68629	+	6.68629i	0.262865	+	0.262865i	0.826217	−	0.563352i	$-0.190488\pi$
$647$	6.68629	+	6.68629i	0.262865	+	0.262865i	−0.563352	+	0.826217i	$0.690488\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$		−	49.9411i		−	1.96036i
$650$	−3.00000	−	4.00000i	−0.117670	−	0.156893i
$651$	4.82843	−	0.828427i	0.189241	−	0.0324686i
$652$	−13.6569	+	13.6569i	−0.534844	+	0.534844i
$653$	4.24264	−	4.24264i	0.166027	−	0.166027i	−0.619203	−	0.785231i	$-0.712544\pi$
$653$	4.24264	−	4.24264i	0.166027	−	0.166027i	0.785231	+	0.619203i	$0.212544\pi$
$654$	32.5563	−	5.58579i	1.27305	−	0.218422i
$655$	44.4853	−	14.8284i	1.73818	−	0.579395i
$656$		−	2.00000i		−	0.0780869i
$657$	−5.61522	+	11.7574i	−0.219071	+	0.458698i
$658$	30.1421	+	30.1421i	1.17506	+	1.17506i
$659$	−42.4853			−1.65499			−0.827496	−	0.561472i	$-0.810235\pi$
$659$	−42.4853			−1.65499			−0.827496	+	0.561472i	$0.810235\pi$
$660$	−4.48528	+	14.8284i	−0.174589	+	0.577196i
$661$	−16.5269			−0.642822			−0.321411	−	0.946940i	$-0.604157\pi$
$661$	−16.5269			−0.642822			−0.321411	+	0.946940i	$0.604157\pi$
$662$	17.1716	+	17.1716i	0.667392	+	0.667392i
$663$	4.24264	−	6.00000i	0.164771	−	0.233021i
$664$		−	1.65685i		−	0.0642984i
$665$	5.65685	−	11.3137i	0.219363	−	0.438727i
$666$	−7.65685	−	21.6569i	−0.296697	−	0.839186i
$667$	−16.9706	+	16.9706i	−0.657103	+	0.657103i
$668$	−0.585786	+	0.585786i	−0.0226648	+	0.0226648i
$669$	0.686292	+	4.00000i	0.0265336	+	0.154649i
$670$	−4.82843	−	14.4853i	−0.186538	−	0.559615i
$671$		−	3.31371i		−	0.127924i
$672$	−6.82843	−	4.82843i	−0.263412	−	0.186261i
$673$	−31.1421	−	31.1421i	−1.20044	−	1.20044i	−0.974032	−	0.226409i	$-0.927302\pi$
$673$	−31.1421	−	31.1421i	−1.20044	−	1.20044i	−0.226409	−	0.974032i	$-0.572698\pi$
$674$	−32.5269			−1.25289
$675$	−9.34315	−	24.2426i	−0.359618	−	0.933100i
$676$	−1.00000			−0.0384615
$677$	−26.3848	−	26.3848i	−1.01405	−	1.01405i	−0.999900	−	0.0141494i	$-0.995496\pi$
$677$	−26.3848	−	26.3848i	−1.01405	−	1.01405i	−0.0141494	−	0.999900i	$-0.504504\pi$
$678$	14.0000	+	9.89949i	0.537667	+	0.380188i
$679$			34.6274i			1.32888i
$680$	−3.00000	−	9.00000i	−0.115045	−	0.345134i
$681$	0.828427	+	4.82843i	0.0317454	+	0.185026i
$682$	−1.65685	+	1.65685i	−0.0634442	+	0.0634442i
$683$	3.17157	−	3.17157i	0.121357	−	0.121357i	−0.643820	−	0.765177i	$-0.722651\pi$
$683$	3.17157	−	3.17157i	0.121357	−	0.121357i	0.765177	+	0.643820i	$0.222651\pi$
$684$	−1.17157	−	3.31371i	−0.0447962	−	0.126703i
$685$	1.31371	−	2.62742i	0.0501942	−	0.100388i
$686$		−	44.9706i		−	1.71698i
$687$	−1.89949	+	2.68629i	−0.0724703	+	0.102488i
$688$	7.24264	+	7.24264i	0.276123	+	0.276123i
$689$	4.82843			0.183948
$690$	4.48528	−	14.8284i	0.170752	−	0.564509i
$691$	−26.3431			−1.00214			−0.501070	−	0.865407i	$-0.667060\pi$
$691$	−26.3431			−1.00214			−0.501070	+	0.865407i	$0.667060\pi$
$692$	−2.92893	−	2.92893i	−0.111341	−	0.111341i
$693$	−24.9706	+	52.2843i	−0.948553	+	1.98612i
$694$		−	29.0711i		−	1.10352i
$695$	20.4853	−	6.82843i	0.777051	−	0.259017i
$696$	10.2426	−	1.75736i	0.388246	−	0.0666125i
$697$	6.00000	−	6.00000i	0.227266	−	0.227266i
$698$	5.14214	−	5.14214i	0.194633	−	0.194633i
$699$	6.41421	−	1.10051i	0.242608	−	0.0416249i
$700$	−23.8995	−	3.41421i	−0.903316	−	0.129045i
$701$			15.4558i			0.583759i	0.956455	+	0.291880i	$0.0942807\pi$
$701$			15.4558i			0.583759i	−0.956455	+	0.291880i	$0.905719\pi$
$702$	−5.00000	−	1.41421i	−0.188713	−	0.0533761i
$703$	−6.34315	−	6.34315i	−0.239236	−	0.239236i
$704$	4.00000			0.150756
$705$	30.1421	−	16.1421i	1.13522	−	0.607948i
$706$	−7.85786			−0.295735
$707$	30.1421	+	30.1421i	1.13361	+	1.13361i
$708$	12.4853	−	17.6569i	0.469226	−	0.663585i
$709$		−	28.7279i		−	1.07890i	−0.842018	−	0.539450i	$-0.818632\pi$
$709$		−	28.7279i		−	1.07890i	0.842018	−	0.539450i	$-0.181368\pi$
$710$	−11.5147	−	5.75736i	−0.432140	−	0.216070i
$711$	12.6863	−	4.48528i	0.475773	−	0.168211i
$712$	−11.8995	+	11.8995i	−0.445952	+	0.445952i
$713$	1.65685	−	1.65685i	0.0620497	−	0.0620497i
$714$	−6.00000	−	34.9706i	−0.224544	−	1.30874i
$715$	8.00000	+	4.00000i	0.299183	+	0.149592i
$716$		−	6.34315i		−	0.237054i
$717$	−0.142136	−	0.100505i	−0.00530815	−	0.00375343i
$718$	14.5563	+	14.5563i	0.543238	+	0.543238i
$719$	−4.48528			−0.167273			−0.0836364	−	0.996496i	$-0.526653\pi$
$719$	−4.48528			−0.167273			−0.0836364	+	0.996496i	$0.526653\pi$
$720$	−5.29289	+	4.12132i	−0.197254	+	0.153593i
$721$	−30.6274			−1.14062
$722$	12.4645	+	12.4645i	0.463879	+	0.463879i
$723$	10.8284	+	7.65685i	0.402714	+	0.284761i
$724$			6.00000i			0.222988i
$725$	24.0000	−	18.0000i	0.891338	−	0.668503i
$726$	−1.46447	−	8.53553i	−0.0543514	−	0.316783i
$727$	−2.68629	+	2.68629i	−0.0996290	+	0.0996290i	−0.755164	−	0.655535i	$-0.772443\pi$
$727$	−2.68629	+	2.68629i	−0.0996290	+	0.0996290i	0.655535	+	0.755164i	$0.272443\pi$
$728$	−3.41421	+	3.41421i	−0.126539	+	0.126539i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$	9.21320	−	3.07107i	0.340996	−	0.113665i
$731$			43.4558i			1.60727i
$732$	0.828427	−	1.17157i	0.0306195	−	0.0433026i
$733$	15.5563	+	15.5563i	0.574587	+	0.574587i	0.933407	−	0.358820i	$-0.116821\pi$
$733$	15.5563	+	15.5563i	0.574587	+	0.574587i	−0.358820	+	0.933407i	$0.616821\pi$
$734$	−20.0000			−0.738213
$735$	−60.4767	−	18.2929i	−2.23072	−	0.674744i
$736$	−4.00000			−0.147442
$737$	19.3137	+	19.3137i	0.711430	+	0.711430i
$738$	−5.41421	−	2.58579i	−0.199300	−	0.0951841i
$739$		−	18.1421i		−	0.667369i	−0.942685	−	0.333685i	$-0.891708\pi$
$739$		−	18.1421i		−	0.667369i	0.942685	−	0.333685i	$-0.108292\pi$
$740$	−7.65685	+	15.3137i	−0.281472	+	0.562943i
$741$	−2.00000	+	0.343146i	−0.0734718	+	0.0126058i
$742$	16.4853	−	16.4853i	0.605194	−	0.605194i
$743$	−34.6274	+	34.6274i	−1.27036	+	1.27036i	−0.324456	+	0.945901i	$0.605181\pi$
$743$	−34.6274	+	34.6274i	−1.27036	+	1.27036i	−0.945901	+	0.324456i	$0.894819\pi$
$744$	−1.00000	+	0.171573i	−0.0366618	+	0.00629017i
$745$	10.1716	+	30.5147i	0.372658	+	1.11797i
$746$			26.9706i			0.987462i
$747$	−4.48528	−	2.14214i	−0.164108	−	0.0783766i
$748$	12.0000	+	12.0000i	0.438763	+	0.438763i
$749$	−14.1421			−0.516742
$750$	−8.17157	+	17.5563i	−0.298384	+	0.641067i
$751$	−20.2843			−0.740184			−0.370092	−	0.928995i	$-0.620674\pi$
$751$	−20.2843			−0.740184			−0.370092	+	0.928995i	$0.620674\pi$
$752$	−6.24264	−	6.24264i	−0.227646	−	0.227646i
$753$	25.6569	−	36.2843i	0.934988	−	1.32227i
$754$		−	6.00000i		−	0.218507i
$755$	9.24264	+	27.7279i	0.336374	+	1.00912i
$756$	−21.8995	+	12.2426i	−0.796477	+	0.445261i
$757$	0.585786	−	0.585786i	0.0212908	−	0.0212908i	−0.696381	−	0.717672i	$-0.745208\pi$
$757$	0.585786	−	0.585786i	0.0212908	−	0.0212908i	0.717672	+	0.696381i	$0.245208\pi$
$758$	−6.97056	+	6.97056i	−0.253182	+	0.253182i
$759$	4.68629	+	27.3137i	0.170102	+	0.991425i
$760$	−1.17157	+	2.34315i	−0.0424974	+	0.0849948i
$761$			9.51472i			0.344908i	0.985018	+	0.172454i	$0.0551697\pi$
$761$			9.51472i			0.344908i	−0.985018	+	0.172454i	$0.944830\pi$
$762$	−17.6569	−	12.4853i	−0.639640	−	0.452294i
$763$	−65.1127	−	65.1127i	−2.35724	−	2.35724i
$764$	−2.82843			−0.102329
$765$	−28.2426	−	3.51472i	−1.02111	−	0.127075i
$766$	−13.6569			−0.493442
$767$	−8.82843	−	8.82843i	−0.318776	−	0.318776i
$768$	1.41421	+	1.00000i	0.0510310	+	0.0360844i
$769$			36.6274i			1.32082i	0.750906	+	0.660409i	$0.229617\pi$
$769$			36.6274i			1.32082i	−0.750906	+	0.660409i	$0.770383\pi$
$770$	40.9706	−	13.6569i	1.47648	−	0.492159i
$771$	2.89949	+	16.8995i	0.104423	+	0.608620i
$772$	−8.58579	+	8.58579i	−0.309009	+	0.309009i
$773$	−7.75736	+	7.75736i	−0.279013	+	0.279013i	−0.832715	−	0.553702i	$-0.813215\pi$
$773$	−7.75736	+	7.75736i	−0.279013	+	0.279013i	0.553702	+	0.832715i	$0.313215\pi$
$774$	28.9706	−	10.2426i	1.04133	−	0.368164i
$775$	−2.34315	+	1.75736i	−0.0841683	+	0.0631262i
$776$		−	7.17157i		−	0.257444i
$777$	−36.9706	+	52.2843i	−1.32631	+	1.87569i
$778$	−1.41421	−	1.41421i	−0.0507020	−	0.0507020i
$779$	−2.34315			−0.0839519
$780$	1.82843	+	3.41421i	0.0654682	+	0.122248i
$781$	23.0294			0.824058
$782$	−12.0000	−	12.0000i	−0.429119	−	0.429119i
$783$	8.48528	−	30.0000i	0.303239	−	1.07211i
$784$			16.3137i			0.582632i
$785$	−21.9411	−	10.9706i	−0.783112	−	0.391556i
$786$	−35.7990	+	6.14214i	−1.27691	+	0.219083i
$787$	33.7990	−	33.7990i	1.20480	−	1.20480i	0.232116	−	0.972688i	$-0.425435\pi$
$787$	33.7990	−	33.7990i	1.20480	−	1.20480i	0.972688	−	0.232116i	$-0.0745648\pi$
$788$	−12.2426	+	12.2426i	−0.436126	+	0.436126i
$789$	38.6274	−	6.62742i	1.37517	−	0.235942i
$790$	−8.97056	−	4.48528i	−0.319158	−	0.159579i
$791$		−	47.7990i		−	1.69954i
$792$	5.17157	−	10.8284i	0.183764	−	0.384771i
$793$	−0.585786	−	0.585786i	−0.0208019	−	0.0208019i
$794$	−20.9706			−0.744217
$795$	−8.82843	−	16.4853i	−0.313112	−	0.584673i
$796$	6.14214			0.217702
$797$	−21.0711	−	21.0711i	−0.746376	−	0.746376i	0.227421	−	0.973797i	$-0.426971\pi$
$797$	−21.0711	−	21.0711i	−0.746376	−	0.746376i	−0.973797	+	0.227421i	$0.926971\pi$
$798$	−5.65685	+	8.00000i	−0.200250	+	0.283197i
$799$		−	37.4558i		−	1.32509i
$800$	4.94975	+	0.707107i	0.175000	+	0.0250000i
$801$	16.8284	+	47.5980i	0.594603	+	1.68179i
$802$	26.7279	−	26.7279i	0.943796	−	0.943796i
$803$	−12.2843	+	12.2843i	−0.433503	+	0.433503i
$804$	2.00000	+	11.6569i	0.0705346	+	0.411106i
$805$	−40.9706	+	13.6569i	−1.44402	+	0.481341i
$806$			0.585786i			0.0206334i
$807$	29.4558	+	20.8284i	1.03689	+	0.733195i
$808$	−6.24264	−	6.24264i	−0.219615	−	0.219615i
$809$	−22.6274			−0.795538			−0.397769	−	0.917486i	$-0.630215\pi$
$809$	−22.6274			−0.795538			−0.397769	+	0.917486i	$0.630215\pi$
$810$	4.31371	+	19.6569i	0.151568	+	0.690671i
$811$	−6.14214			−0.215680			−0.107840	−	0.994168i	$-0.534393\pi$
$811$	−6.14214			−0.215680			−0.107840	+	0.994168i	$0.534393\pi$
$812$	−20.4853	−	20.4853i	−0.718892	−	0.718892i
$813$	8.82843	+	6.24264i	0.309626	+	0.218939i
$814$		−	30.6274i		−	1.07349i
$815$	19.3137	−	38.6274i	0.676530	−	1.35306i
$816$	1.24264	+	7.24264i	0.0435011	+	0.253543i
$817$	8.48528	−	8.48528i	0.296862	−	0.296862i
$818$	−6.24264	+	6.24264i	−0.218269	+	0.218269i
$819$	4.82843	+	13.6569i	0.168719	+	0.477209i
$820$	1.41421	+	4.24264i	0.0493865	+	0.148159i
$821$		−	45.6985i		−	1.59489i	−0.603393	−	0.797444i	$-0.706185\pi$
$821$		−	45.6985i		−	1.59489i	0.603393	−	0.797444i	$-0.293815\pi$
$822$	−1.31371	+	1.85786i	−0.0458208	+	0.0648005i
$823$	−10.6863	−	10.6863i	−0.372501	−	0.372501i	0.495887	−	0.868387i	$-0.334843\pi$
$823$	−10.6863	−	10.6863i	−0.372501	−	0.372501i	−0.868387	+	0.495887i	$0.834843\pi$
$824$	6.34315			0.220974
$825$	−0.970563	−	34.6274i	−0.0337907	−	1.20557i
$826$	−60.2843			−2.09756
$827$	−27.1716	−	27.1716i	−0.944848	−	0.944848i	0.0537085	−	0.998557i	$-0.482896\pi$
$827$	−27.1716	−	27.1716i	−0.944848	−	0.944848i	−0.998557	+	0.0537085i	$0.982896\pi$
$828$	−5.17157	+	10.8284i	−0.179725	+	0.376314i
$829$			54.4853i			1.89235i	0.323652	+	0.946176i	$0.395089\pi$
$829$			54.4853i			1.89235i	−0.323652	+	0.946176i	$0.604911\pi$
$830$	1.17157	+	3.51472i	0.0406659	+	0.121998i
$831$	9.41421	−	1.61522i	0.326575	−	0.0560315i
$832$	0.707107	−	0.707107i	0.0245145	−	0.0245145i
$833$	−48.9411	+	48.9411i	−1.69571	+	1.69571i
$834$	−16.4853	+	2.82843i	−0.570839	+	0.0979404i
$835$	0.828427	−	1.65685i	0.0286689	−	0.0573378i
$836$		−	4.68629i		−	0.162079i
$837$	−0.828427	+	2.92893i	−0.0286346	+	0.101239i
$838$	−15.8995	−	15.8995i	−0.549239	−	0.549239i
$839$	−39.8995			−1.37748			−0.688742	−	0.725007i	$-0.741837\pi$
$839$	−39.8995			−1.37748			−0.688742	+	0.725007i	$0.741837\pi$
$840$	17.8995	+	5.41421i	0.617591	+	0.186808i
$841$	7.00000			0.241379
$842$	9.14214	+	9.14214i	0.315059	+	0.315059i
$843$	4.82843	−	6.82843i	0.166300	−	0.235184i
$844$		−	9.65685i		−	0.332403i
$845$	2.12132	−	0.707107i	0.0729756	−	0.0243252i
$846$	−24.9706	+	8.82843i	−0.858506	+	0.303528i
$847$	−17.0711	+	17.0711i	−0.586569	+	0.586569i
$848$	−3.41421	+	3.41421i	−0.117245	+	0.117245i
$849$	−3.62742	−	21.1421i	−0.124493	−	0.725596i
$850$	12.7279	+	16.9706i	0.436564	+	0.582086i
$851$			30.6274i			1.04989i
$852$	8.14214	+	5.75736i	0.278945	+	0.197244i
$853$	−40.9706	−	40.9706i	−1.40281	−	1.40281i	−0.791037	−	0.611768i	$-0.790458\pi$
$853$	−40.9706	−	40.9706i	−1.40281	−	1.40281i	−0.611768	−	0.791037i	$-0.709542\pi$
$854$	−4.00000			−0.136877
$855$	4.82843	+	6.20101i	0.165129	+	0.212070i
$856$	2.92893			0.100109
$857$	−25.8284	−	25.8284i	−0.882282	−	0.882282i	0.111484	−	0.993766i	$-0.464440\pi$
$857$	−25.8284	−	25.8284i	−0.882282	−	0.882282i	−0.993766	+	0.111484i	$0.964440\pi$
$858$	−5.65685	−	4.00000i	−0.193122	−	0.136558i
$859$			1.79899i			0.0613807i	0.999529	+	0.0306904i	$0.00977058\pi$
$859$			1.79899i			0.0613807i	−0.999529	+	0.0306904i	$0.990229\pi$
$860$	−20.4853	−	10.2426i	−0.698542	−	0.349271i
$861$	2.82843	+	16.4853i	0.0963925	+	0.561817i
$862$	−17.7279	+	17.7279i	−0.603815	+	0.603815i
$863$	13.7574	−	13.7574i	0.468306	−	0.468306i	−0.433059	−	0.901365i	$-0.642566\pi$
$863$	13.7574	−	13.7574i	0.468306	−	0.468306i	0.901365	+	0.433059i	$0.142566\pi$
$864$	4.53553	−	2.53553i	0.154302	−	0.0862606i
$865$	8.28427	+	4.14214i	0.281674	+	0.140837i
$866$			8.92893i			0.303417i
$867$	−1.00000	+	1.41421i	−0.0339618	+	0.0480292i
$868$	2.00000	+	2.00000i	0.0678844	+	0.0678844i
$869$	17.9411			0.608611
$870$	−20.4853	+	10.9706i	−0.694516	+	0.371937i
$871$	6.82843			0.231372
$872$	13.4853	+	13.4853i	0.456669	+	0.456669i
$873$	−19.4142	−	9.27208i	−0.657072	−	0.313812i
$874$			4.68629i			0.158516i
$875$	53.1127	−	9.65685i	1.79554	−	0.326461i
$876$	−7.41421	+	1.27208i	−0.250503	+	0.0429795i
$877$	12.6863	−	12.6863i	0.428386	−	0.428386i	−0.459693	−	0.888078i	$-0.652040\pi$
$877$	12.6863	−	12.6863i	0.428386	−	0.428386i	0.888078	+	0.459693i	$0.152040\pi$
$878$	20.9706	−	20.9706i	0.707722	−	0.707722i
$879$	30.1421	−	5.17157i	1.01667	−	0.174433i
$880$	−8.48528	+	2.82843i	−0.286039	+	0.0953463i
$881$			14.0000i			0.471672i	0.971793	+	0.235836i	$0.0757828\pi$
$881$			14.0000i			0.471672i	−0.971793	+	0.235836i	$0.924217\pi$
$882$	44.1630	+	21.0919i	1.48704	+	0.710201i
$883$	−20.2132	−	20.2132i	−0.680228	−	0.680228i	0.279823	−	0.960052i	$-0.409724\pi$
$883$	−20.2132	−	20.2132i	−0.680228	−	0.680228i	−0.960052	+	0.279823i	$0.909724\pi$
$884$	4.24264			0.142695
$885$	−14.0000	+	46.2843i	−0.470605	+	1.55583i
$886$	26.7279			0.897942
$887$	−4.00000	−	4.00000i	−0.134307	−	0.134307i	0.636757	−	0.771064i	$-0.280275\pi$
$887$	−4.00000	−	4.00000i	−0.134307	−	0.134307i	−0.771064	+	0.636757i	$0.780275\pi$
$888$	7.65685	−	10.8284i	0.256947	−	0.363378i
$889$			60.2843i			2.02187i
$890$	16.8284	−	33.6569i	0.564090	−	1.12818i
$891$	−22.6274	−	28.0000i	−0.758047	−	0.938035i
$892$	−1.65685	+	1.65685i	−0.0554756	+	0.0554756i
$893$	−7.31371	+	7.31371i	−0.244744	+	0.244744i
$894$	−4.21320	−	24.5563i	−0.140911	−	0.821287i
$895$	4.48528	+	13.4558i	0.149926	+	0.449779i
$896$		−	4.82843i		−	0.161306i
$897$	5.65685	+	4.00000i	0.188877	+	0.133556i
$898$	−15.4142	−	15.4142i	−0.514379	−	0.514379i
$899$	−3.51472			−0.117222
$900$	8.31371	−	12.4853i	0.277124	−	0.416176i
$901$	−20.4853			−0.682464
$902$	−5.65685	−	5.65685i	−0.188353	−	0.188353i
$903$	−69.9411	−	49.4558i	−2.32749	−	1.64579i
$904$			9.89949i			0.329252i
$905$	−4.24264	−	12.7279i	−0.141030	−	0.423090i
$906$	−3.82843	−	22.3137i	−0.127191	−	0.741323i
$907$	24.8995	−	24.8995i	0.826774	−	0.826774i	−0.160295	−	0.987069i	$-0.551245\pi$
$907$	24.8995	−	24.8995i	0.826774	−	0.826774i	0.987069	+	0.160295i	$0.0512446\pi$
$908$	−2.00000	+	2.00000i	−0.0663723	+	0.0663723i
$909$	−24.9706	+	8.82843i	−0.828221	+	0.292820i
$910$	4.82843	−	9.65685i	0.160061	−	0.320122i
$911$		−	30.1421i		−	0.998654i	−0.866414	−	0.499327i	$-0.833581\pi$
$911$		−	30.1421i		−	0.998654i	0.866414	−	0.499327i	$-0.166419\pi$
$912$	1.17157	−	1.65685i	0.0387947	−	0.0548639i
$913$	−4.68629	−	4.68629i	−0.155094	−	0.155094i
$914$	−9.79899			−0.324122
$915$	−0.928932	+	3.07107i	−0.0307096	+	0.101526i
$916$	−1.89949			−0.0627611
$917$	71.5980	+	71.5980i	2.36437	+	2.36437i
$918$	21.2132	+	6.00000i	0.700140	+	0.198030i
$919$		−	57.9411i		−	1.91130i	−0.294503	−	0.955651i	$-0.595154\pi$
$919$		−	57.9411i		−	1.91130i	0.294503	−	0.955651i	$-0.404846\pi$
$920$	8.48528	−	2.82843i	0.279751	−	0.0932505i
$921$	30.9706	−	5.31371i	1.02051	−	0.175093i
$922$	−26.6569	+	26.6569i	−0.877897	+	0.877897i
$923$	4.07107	−	4.07107i	0.134001	−	0.134001i
$924$	−32.9706	+	5.65685i	−1.08465	+	0.186097i
$925$	5.41421	−	37.8995i	0.178018	−	1.24613i
$926$		−	8.00000i		−	0.262896i
$927$	8.20101	−	17.1716i	0.269357	−	0.563988i
$928$	4.24264	+	4.24264i	0.139272	+	0.139272i
$929$	5.11270			0.167742			0.0838711	−	0.996477i	$-0.473272\pi$
$929$	5.11270			0.167742			0.0838711	+	0.996477i	$0.473272\pi$
$930$	2.00000	−	1.07107i	0.0655826	−	0.0351217i
$931$	19.1127			0.626393
$932$	2.65685	+	2.65685i	0.0870282	+	0.0870282i
$933$	28.0000	−	39.5980i	0.916679	−	1.29638i
$934$		−	4.10051i		−	0.134173i
$935$	−33.9411	−	16.9706i	−1.10999	−	0.554997i
$936$	−1.00000	−	2.82843i	−0.0326860	−	0.0924500i
$937$	−1.97056	+	1.97056i	−0.0643755	+	0.0643755i	−0.738562	−	0.674186i	$-0.764495\pi$
$937$	−1.97056	+	1.97056i	−0.0643755	+	0.0643755i	0.674186	+	0.738562i	$0.264495\pi$
$938$	23.3137	−	23.3137i	0.761220	−	0.761220i
$939$	5.24264	+	30.5563i	0.171087	+	0.997169i
$940$	17.6569	+	8.82843i	0.575903	+	0.287952i
$941$			14.8701i			0.484750i	0.970183	+	0.242375i	$0.0779264\pi$
$941$			14.8701i			0.484750i	−0.970183	+	0.242375i	$0.922074\pi$
$942$	15.5147	+	10.9706i	0.505497	+	0.357440i
$943$	5.65685	+	5.65685i	0.184213	+	0.184213i
$944$	12.4853			0.406361
$945$	37.7990	−	41.4558i	1.22960	−	1.34856i
$946$	40.9706			1.33207
$947$	32.6274	+	32.6274i	1.06025	+	1.06025i	0.998065	+	0.0621839i	$0.0198065\pi$
$947$	32.6274	+	32.6274i	1.06025	+	1.06025i	0.0621839	+	0.998065i	$0.480193\pi$
$948$	6.34315	+	4.48528i	0.206016	+	0.145675i
$949$			4.34315i			0.140984i
$950$	0.828427	−	5.79899i	0.0268777	−	0.188144i
$951$	4.00000	+	23.3137i	0.129709	+	0.755999i
$952$	14.4853	−	14.4853i	0.469471	−	0.469471i
$953$	21.4853	−	21.4853i	0.695977	−	0.695977i	−0.267564	−	0.963540i	$-0.586219\pi$
$953$	21.4853	−	21.4853i	0.695977	−	0.695977i	0.963540	+	0.267564i	$0.0862186\pi$
$954$	4.82843	+	13.6569i	0.156326	+	0.442157i
$955$	6.00000	−	2.00000i	0.194155	−	0.0647185i
$956$		−	0.100505i		−	0.00325057i
$957$	24.0000	−	33.9411i	0.775810	−	1.09716i
$958$	8.75736	+	8.75736i	0.282937	+	0.282937i
$959$	6.34315			0.204831
$960$	−3.70711	−	1.12132i	−0.119646	−	0.0361905i
$961$	−30.6569			−0.988931
$962$	−5.41421	−	5.41421i	−0.174561	−	0.174561i
$963$	3.78680	−	7.92893i	0.122028	−	0.255506i
$964$			7.65685i			0.246611i
$965$	12.1421	−	24.2843i	0.390869	−	0.781738i
$966$	32.9706	−	5.65685i	1.06081	−	0.182006i
$967$	−30.6274	+	30.6274i	−0.984911	+	0.984911i	−0.999888	−	0.0149765i	$-0.995233\pi$
$967$	−30.6274	+	30.6274i	−0.984911	+	0.984911i	0.0149765	+	0.999888i	$0.495233\pi$
$968$	3.53553	−	3.53553i	0.113636	−	0.113636i
$969$	8.48528	−	1.45584i	0.272587	−	0.0467685i
$970$	5.07107	+	15.2132i	0.162822	+	0.488467i
$971$			20.1421i			0.646392i	0.946332	+	0.323196i	$0.104757\pi$
$971$			20.1421i			0.646392i	−0.946332	+	0.323196i	$0.895243\pi$
$972$	−1.00000	−	15.5563i	−0.0320750	−	0.498970i
$973$	32.9706	+	32.9706i	1.05699	+	1.05699i
$974$	24.1421			0.773564
$975$	−6.29289	−	5.94975i	−0.201534	−	0.190544i
$976$	0.828427			0.0265173
$977$	−18.5858	−	18.5858i	−0.594612	−	0.594612i	0.344262	−	0.938874i	$-0.388129\pi$
$977$	−18.5858	−	18.5858i	−0.594612	−	0.594612i	−0.938874	+	0.344262i	$0.888129\pi$
$978$	−19.3137	+	27.3137i	−0.617584	+	0.873396i
$979$			67.3137i			2.15136i
$980$	−11.5355	−	34.6066i	−0.368489	−	1.10547i
$981$	53.9411	−	19.0711i	1.72221	−	0.608892i
$982$	18.2426	−	18.2426i	0.582146	−	0.582146i
$983$	0.585786	−	0.585786i	0.0186837	−	0.0186837i	−0.697703	−	0.716387i	$-0.745795\pi$
$983$	0.585786	−	0.585786i	0.0186837	−	0.0186837i	0.716387	+	0.697703i	$0.245795\pi$
$984$	−0.585786	−	3.41421i	−0.0186742	−	0.108841i
$985$	17.3137	−	34.6274i	0.551661	−	1.10332i
$986$			25.4558i			0.810679i
$987$	60.2843	+	42.6274i	1.91887	+	1.35685i
$988$	−0.828427	−	0.828427i	−0.0263558	−	0.0263558i
$989$	−40.9706			−1.30279
$990$	−3.31371	+	26.6274i	−0.105317	+	0.846275i
$991$	−10.8284			−0.343976			−0.171988	−	0.985099i	$-0.555019\pi$
$991$	−10.8284			−0.343976			−0.171988	+	0.985099i	$0.555019\pi$
$992$	−0.414214	−	0.414214i	−0.0131513	−	0.0131513i
$993$	34.3431	+	24.2843i	1.08985	+	0.770638i
$994$		−	27.7990i		−	0.881730i
$995$	−13.0294	+	4.34315i	−0.413061	+	0.137687i
$996$	−0.485281	−	2.82843i	−0.0153767	−	0.0896221i
$997$	−37.6985	+	37.6985i	−1.19392	+	1.19392i	−0.217967	+	0.975956i	$0.569942\pi$
$997$	−37.6985	+	37.6985i	−1.19392	+	1.19392i	−0.975956	+	0.217967i	$0.930058\pi$
$998$	−5.65685	+	5.65685i	−0.179065	+	0.179065i
$999$	−19.4142	−	34.7279i	−0.614239	−	1.09874i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.l.a.53.2	✓	4
3.2	odd	2		390.2.l.b.53.1	yes	4
5.2	odd	4		390.2.l.b.287.1	yes	4
15.2	even	4	inner	390.2.l.a.287.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.l.a.53.2	✓	4	1.1	even	1	trivial
390.2.l.a.287.2	yes	4	15.2	even	4	inner
390.2.l.b.53.1	yes	4	3.2	odd	2
390.2.l.b.287.1	yes	4	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.41421 + 1.00000i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(0.292893 + 1.70711i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.00000 + 2.82843i) q^{9} +(1.00000 - 2.00000i) q^{10} +4.00000i q^{11} +(-1.00000 + 1.41421i) q^{12} +(0.707107 + 0.707107i) q^{13} +4.82843 q^{14} +(1.12132 - 3.70711i) q^{15} -1.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(-1.29289 + 2.70711i) q^{18} +1.17157i q^{19} +(2.12132 - 0.707107i) q^{20} +(8.24264 - 1.41421i) q^{21} +(-2.82843 + 2.82843i) q^{22} +(2.82843 - 2.82843i) q^{23} +(-1.70711 + 0.292893i) q^{24} +(-4.00000 + 3.00000i) q^{25} +1.00000i q^{26} +(-1.41421 + 5.00000i) q^{27} +(3.41421 + 3.41421i) q^{28} -6.00000 q^{29} +(3.41421 - 1.82843i) q^{30} +0.585786 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.00000 + 5.65685i) q^{33} -4.24264i q^{34} +(-9.65685 - 4.82843i) q^{35} +(-2.82843 + 1.00000i) q^{36} +(-5.41421 + 5.41421i) q^{37} +(-0.828427 + 0.828427i) q^{38} +(0.292893 + 1.70711i) q^{39} +(2.00000 + 1.00000i) q^{40} +2.00000i q^{41} +(6.82843 + 4.82843i) q^{42} +(-7.24264 - 7.24264i) q^{43} -4.00000 q^{44} +(5.29289 - 4.12132i) q^{45} +4.00000 q^{46} +(6.24264 + 6.24264i) q^{47} +(-1.41421 - 1.00000i) q^{48} -16.3137i q^{49} +(-4.94975 - 0.707107i) q^{50} +(-1.24264 - 7.24264i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(3.41421 - 3.41421i) q^{53} +(-4.53553 + 2.53553i) q^{54} +(8.48528 - 2.82843i) q^{55} +4.82843i q^{56} +(-1.17157 + 1.65685i) q^{57} +(-4.24264 - 4.24264i) q^{58} -12.4853 q^{59} +(3.70711 + 1.12132i) q^{60} -0.828427 q^{61} +(0.414214 + 0.414214i) q^{62} +(13.0711 + 6.24264i) q^{63} -1.00000i q^{64} +(1.00000 - 2.00000i) q^{65} +(-6.82843 + 1.17157i) q^{66} +(4.82843 - 4.82843i) q^{67} +(3.00000 - 3.00000i) q^{68} +(6.82843 - 1.17157i) q^{69} +(-3.41421 - 10.2426i) q^{70} -5.75736i q^{71} +(-2.70711 - 1.29289i) q^{72} +(3.07107 + 3.07107i) q^{73} -7.65685 q^{74} +(-8.65685 + 0.242641i) q^{75} -1.17157 q^{76} +(13.6569 + 13.6569i) q^{77} +(-1.00000 + 1.41421i) q^{78} -4.48528i q^{79} +(0.707107 + 2.12132i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(-1.41421 + 1.41421i) q^{82} +(-1.17157 + 1.17157i) q^{83} +(1.41421 + 8.24264i) q^{84} +(-4.24264 + 8.48528i) q^{85} -10.2426i q^{86} +(-8.48528 - 6.00000i) q^{87} +(-2.82843 - 2.82843i) q^{88} +16.8284 q^{89} +(6.65685 + 0.828427i) q^{90} +4.82843 q^{91} +(2.82843 + 2.82843i) q^{92} +(0.828427 + 0.585786i) q^{93} +8.82843i q^{94} +(2.48528 - 0.828427i) q^{95} +(-0.292893 - 1.70711i) q^{96} +(-5.07107 + 5.07107i) q^{97} +(11.5355 - 11.5355i) q^{98} +(-11.3137 + 4.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{6} + 8 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{12} + 8 q^{14} - 4 q^{15} - 4 q^{16} - 12 q^{17} - 8 q^{18} + 16 q^{21} - 4 q^{24} - 16 q^{25} + 8 q^{28} - 24 q^{29} + 8 q^{30} + 8 q^{31} - 16 q^{33}+ \cdots + 32 q^{98}+O(q^{100}) \) 4 * q + 4 * q^6 + 8 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^12 + 8 * q^14 - 4 * q^15 - 4 * q^16 - 12 * q^17 - 8 * q^18 + 16 * q^21 - 4 * q^24 - 16 * q^25 + 8 * q^28 - 24 * q^29 + 8 * q^30 + 8 * q^31 - 16 * q^33 - 16 * q^35 - 16 * q^37 + 8 * q^38 + 4 * q^39 + 8 * q^40 + 16 * q^42 - 12 * q^43 - 16 * q^44 + 24 * q^45 + 16 * q^46 + 8 * q^47 + 12 * q^51 + 8 * q^53 - 4 * q^54 - 16 * q^57 - 16 * q^59 + 12 * q^60 + 8 * q^61 - 4 * q^62 + 24 * q^63 + 4 * q^65 - 16 * q^66 + 8 * q^67 + 12 * q^68 + 16 * q^69 - 8 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^74 - 12 * q^75 - 16 * q^76 + 32 * q^77 - 4 * q^78 - 28 * q^81 - 16 * q^83 + 56 * q^89 + 4 * q^90 + 8 * q^91 - 8 * q^93 - 24 * q^95 - 4 * q^96 + 8 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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