LMFDB - Embedded newform 390.2.l.b.53.1

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 = [4,0,4] 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			53.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.53
Dual form			390.2.l.b.287.1

$q$-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} +(1.00000 + 1.41421i) 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} +(-1.41421 + 1.00000i) q^{12} +(0.707107 + 0.707107i) q^{13} -4.82843 q^{14} +(-2.29289 + 3.12132i) q^{15} -1.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(2.70711 - 1.29289i) 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} +(-5.00000 + 1.41421i) q^{27} +(3.41421 + 3.41421i) q^{28} +6.00000 q^{29} +(3.82843 - 0.585786i) q^{30} +0.585786 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.65685 - 4.00000i) 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} +(-4.82843 - 6.82843i) q^{42} +(-7.24264 - 7.24264i) q^{43} +4.00000 q^{44} +(-6.70711 - 0.121320i) q^{45} +4.00000 q^{46} +(-6.24264 - 6.24264i) q^{47} +(-1.00000 - 1.41421i) 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} +(-1.65685 + 1.17157i) q^{57} +(-4.24264 - 4.24264i) q^{58} +12.4853 q^{59} +(-3.12132 - 2.29289i) q^{60} -0.828427 q^{61} +(-0.414214 - 0.414214i) q^{62} +(6.24264 + 13.0711i) 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} +(1.29289 + 2.70711i) q^{72} +(3.07107 + 3.07107i) q^{73} +7.65685 q^{74} +(-8.24264 - 2.65685i) q^{75} -1.17157 q^{76} +(-13.6569 - 13.6569i) q^{77} +(1.41421 - 1.00000i) 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} +(6.00000 + 8.48528i) q^{87} +(-2.82843 - 2.82843i) q^{88} -16.8284 q^{89} +(4.65685 + 4.82843i) q^{90} +4.82843 q^{91} +(-2.82843 - 2.82843i) q^{92} +(0.585786 + 0.828427i) 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^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{14} - 12 q^{15} - 4 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} + 4 q^{24} - 16 q^{25} - 20 q^{27} + 8 q^{28} + 24 q^{29} + 4 q^{30} + 8 q^{31}+ \cdots - 32 q^{98}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 + 4 * q^10 - 8 * q^14 - 12 * q^15 - 4 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 + 4 * q^24 - 16 * q^25 - 20 * q^27 + 8 * q^28 + 24 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^35 - 16 * q^37 - 8 * q^38 - 4 * q^39 + 8 * q^40 - 8 * q^42 - 12 * q^43 + 16 * q^44 - 24 * q^45 + 16 * q^46 - 8 * q^47 - 4 * q^48 + 12 * q^51 - 8 * q^53 + 4 * q^54 + 16 * q^57 + 16 * q^59 - 4 * q^60 + 8 * q^61 + 4 * q^62 + 8 * 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 - 16 * q^75 - 16 * q^76 - 32 * q^77 - 28 * q^81 + 16 * q^83 + 24 * q^87 - 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
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$			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	$-0.793963\pi$
$11$		−	4.00000i		−	1.20605i	0.797724	−	0.603023i	$-0.206037\pi$
$12$	−1.41421	+	1.00000i	−0.408248	+	0.288675i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	−4.82843			−1.29045
$15$	−2.29289	+	3.12132i	−0.592022	+	0.805921i
$16$	−1.00000			−0.250000
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	3.00000	+	3.00000i	0.727607	+	0.727607i	−0.242536	+	0.970143i	$0.577979\pi$
$18$	2.70711	−	1.29289i	0.638071	−	0.304738i
$19$			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	−0.937568	−	0.347801i	$-0.886929\pi$
$23$	−2.82843	+	2.82843i	−0.589768	+	0.589768i	0.347801	+	0.937568i	$0.386929\pi$
$24$	1.70711	+	0.292893i	0.348462	+	0.0597866i
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$		−	1.00000i		−	0.196116i
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$	3.41421	+	3.41421i	0.645226	+	0.645226i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	3.82843	−	0.585786i	0.698972	−	0.106949i
$31$	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
$33$	5.65685	−	4.00000i	0.984732	−	0.696311i
$34$		−	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	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$	−4.82843	−	6.82843i	−0.745042	−	1.05365i
$43$	−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
$45$	−6.70711	−	0.121320i	−0.999836	−	0.0180854i
$46$	4.00000			0.589768
$47$	−6.24264	−	6.24264i	−0.910583	−	0.910583i	0.0857352	−	0.996318i	$-0.472676\pi$
$47$	−6.24264	−	6.24264i	−0.910583	−	0.910583i	−0.996318	+	0.0857352i	$0.972676\pi$
$48$	−1.00000	−	1.41421i	−0.144338	−	0.204124i
$49$		−	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	−0.901583	−	0.432605i	$-0.857594\pi$
$53$	−3.41421	+	3.41421i	−0.468978	+	0.468978i	0.432605	+	0.901583i	$0.357594\pi$
$54$	4.53553	+	2.53553i	0.617208	+	0.345042i
$55$	8.48528	−	2.82843i	1.14416	−	0.381385i
$56$		−	4.82843i		−	0.645226i
$57$	−1.65685	+	1.17157i	−0.219456	+	0.155179i
$58$	−4.24264	−	4.24264i	−0.557086	−	0.557086i
$59$	12.4853			1.62545			0.812723	−	0.582651i	$-0.197984\pi$
$59$	12.4853			1.62545			0.812723	+	0.582651i	$0.197984\pi$
$60$	−3.12132	−	2.29289i	−0.402961	−	0.296011i
$61$	−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
$63$	6.24264	+	13.0711i	0.786499	+	1.64680i
$64$		−	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	$0.110981\pi$
$71$			5.75736i			0.683273i	−0.939832	+	0.341636i	$0.889019\pi$
$72$	1.29289	+	2.70711i	0.152369	+	0.319036i
$73$	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
$75$	−8.24264	−	2.65685i	−0.951778	−	0.306787i
$76$	−1.17157			−0.134389
$77$	−13.6569	−	13.6569i	−1.55634	−	1.55634i
$78$	1.41421	−	1.00000i	0.160128	−	0.113228i
$79$		−	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	−0.639879	−	0.768476i	$-0.721016\pi$
$83$	1.17157	−	1.17157i	0.128597	−	0.128597i	0.768476	+	0.639879i	$0.221016\pi$
$84$	−1.41421	+	8.24264i	−0.154303	+	0.899346i
$85$	−4.24264	+	8.48528i	−0.460179	+	0.920358i
$86$			10.2426i			1.10449i
$87$	6.00000	+	8.48528i	0.643268	+	0.909718i
$88$	−2.82843	−	2.82843i	−0.301511	−	0.301511i
$89$	−16.8284			−1.78381			−0.891905	−	0.452223i	$-0.850631\pi$
$89$	−16.8284			−1.78381			−0.891905	+	0.452223i	$0.850631\pi$
$90$	4.65685	+	4.82843i	0.490876	+	0.508961i
$91$	4.82843			0.506157
$92$	−2.82843	−	2.82843i	−0.294884	−	0.294884i
$93$	0.585786	+	0.828427i	0.0607432	+	0.0859039i
$94$			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	$-0.855251\pi$
$101$		−	8.82843i		−	0.878461i	0.898374	−	0.439231i	$-0.144749\pi$
$102$	6.00000	−	4.24264i	0.594089	−	0.420084i
$103$	−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
$105$	2.82843	+	18.4853i	0.276026	+	1.80398i
$106$	4.82843			0.468978
$107$	2.07107	+	2.07107i	0.200218	+	0.200218i	0.800093	−	0.599876i	$-0.204783\pi$
$107$	2.07107	+	2.07107i	0.200218	+	0.200218i	−0.599876	+	0.800093i	$0.704783\pi$
$108$	−1.41421	−	5.00000i	−0.136083	−	0.481125i
$109$		−	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	−0.955026	−	0.296522i	$-0.904173\pi$
$113$	−7.00000	+	7.00000i	−0.658505	+	0.658505i	0.296522	+	0.955026i	$0.404173\pi$
$114$	2.00000	+	0.343146i	0.187317	+	0.0321385i
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$			6.00000i			0.557086i
$117$	−2.70711	+	1.29289i	−0.250272	+	0.119528i
$118$	−8.82843	−	8.82843i	−0.812723	−	0.812723i
$119$	20.4853			1.87788
$120$	0.585786	+	3.82843i	0.0534747	+	0.349486i
$121$	−5.00000			−0.454545
$122$	0.585786	+	0.585786i	0.0530346	+	0.0530346i
$123$	2.82843	−	2.00000i	0.255031	−	0.180334i
$124$			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	$-0.631317\pi$
$131$		−	20.9706i		−	1.83221i	0.400942	−	0.916103i	$-0.368683\pi$
$132$	4.00000	+	5.65685i	0.348155	+	0.492366i
$133$	4.00000	+	4.00000i	0.346844	+	0.346844i
$134$	−6.82843			−0.589886
$135$	−6.53553	−	9.60660i	−0.562489	−	0.826805i
$136$	4.24264			0.363803
$137$	−0.928932	−	0.928932i	−0.0793640	−	0.0793640i	0.666310	−	0.745674i	$-0.267873\pi$
$137$	−0.928932	−	0.928932i	−0.0793640	−	0.0793640i	−0.745674	+	0.666310i	$0.767873\pi$
$138$	4.00000	+	5.65685i	0.340503	+	0.481543i
$139$			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
$147$	23.0711	−	16.3137i	1.90287	−	1.34553i
$148$	−5.41421	−	5.41421i	−0.445046	−	0.445046i
$149$	14.3848			1.17845			0.589223	−	0.807970i	$-0.299434\pi$
$149$	14.3848			1.17845			0.589223	+	0.807970i	$0.299434\pi$
$150$	3.94975	+	7.70711i	0.322496	+	0.629283i
$151$	−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
$153$	−11.4853	+	5.48528i	−0.928530	+	0.443459i
$154$			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
$162$	0.949747	+	8.94975i	0.0746192	+	0.703159i
$163$	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
$165$	12.4853	+	9.17157i	0.971978	+	0.714006i
$166$	−1.65685			−0.128597
$167$	−0.585786	−	0.585786i	−0.0453295	−	0.0453295i	0.684079	−	0.729408i	$-0.260204\pi$
$167$	−0.585786	−	0.585786i	−0.0453295	−	0.0453295i	−0.729408	+	0.684079i	$0.760204\pi$
$168$	6.82843	−	4.82843i	0.526825	−	0.372521i
$169$			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	−0.586945	−	0.809627i	$-0.699669\pi$
$173$	2.92893	−	2.92893i	0.222683	−	0.222683i	0.809627	+	0.586945i	$0.199669\pi$
$174$	1.75736	−	10.2426i	0.133225	−	0.776493i
$175$	−3.41421	+	23.8995i	−0.258090	+	1.80663i
$176$			4.00000i			0.301511i
$177$	12.4853	+	17.6569i	0.938451	+	1.32717i
$178$	11.8995	+	11.8995i	0.891905	+	0.891905i
$179$	6.34315			0.474109			0.237054	−	0.971496i	$-0.423818\pi$
$179$	6.34315			0.474109			0.237054	+	0.971496i	$0.423818\pi$
$180$	0.121320	−	6.70711i	0.00904268	−	0.499918i
$181$	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
$183$	−0.828427	−	1.17157i	−0.0612391	−	0.0866052i
$184$			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	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$	1.41421	−	1.00000i	0.102062	−	0.0721688i
$193$	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
$195$	−3.82843	+	0.585786i	−0.274159	+	0.0419490i
$196$	16.3137			1.16526
$197$	−12.2426	−	12.2426i	−0.872252	−	0.872252i	0.120465	−	0.992718i	$-0.461561\pi$
$197$	−12.2426	−	12.2426i	−0.872252	−	0.872252i	−0.992718	+	0.120465i	$0.961561\pi$
$198$	−5.17157	−	10.8284i	−0.367528	−	0.769543i
$199$		−	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
$207$	−5.17157	−	10.8284i	−0.359449	−	0.752628i
$208$	−0.707107	−	0.707107i	−0.0490290	−	0.0490290i
$209$	4.68629			0.324158
$210$	11.0711	−	15.0711i	0.763976	−	1.04000i
$211$	−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
$213$	−8.14214	+	5.75736i	−0.557890	+	0.394488i
$214$		−	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
$222$	7.65685	+	10.8284i	0.513894	+	0.726756i
$223$	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
$225$	−4.48528	−	14.3137i	−0.299019	−	0.954247i
$226$	9.89949			0.658505
$227$	−2.00000	−	2.00000i	−0.132745	−	0.132745i	0.637613	−	0.770357i	$-0.279922\pi$
$227$	−2.00000	−	2.00000i	−0.132745	−	0.132745i	−0.770357	+	0.637613i	$0.779922\pi$
$228$	−1.17157	−	1.65685i	−0.0775893	−	0.109728i
$229$			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	−0.788759	−	0.614703i	$-0.789276\pi$
$233$	−2.65685	+	2.65685i	−0.174056	+	0.174056i	0.614703	+	0.788759i	$0.289276\pi$
$234$	2.82843	+	1.00000i	0.184900	+	0.0653720i
$235$	8.82843	−	17.6569i	0.575903	−	1.15181i
$236$			12.4853i			0.812723i
$237$	6.34315	−	4.48528i	0.412032	−	0.291350i
$238$	−14.4853	−	14.4853i	−0.938941	−	0.938941i
$239$	0.100505			0.00650113			0.00325057	−	0.999995i	$-0.498965\pi$
$239$	0.100505			0.00650113			0.00325057	+	0.999995i	$0.498965\pi$
$240$	2.29289	−	3.12132i	0.148006	−	0.201480i
$241$	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
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$		−	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	$0.300383\pi$
$251$			25.6569i			1.61945i	−0.586812	+	0.809723i	$0.699617\pi$
$252$	−13.0711	+	6.24264i	−0.823400	+	0.393249i
$253$	11.3137	+	11.3137i	0.711287	+	0.711287i
$254$	12.4853			0.783396
$255$	−16.2426	+	2.48528i	−1.01715	+	0.155634i
$256$	1.00000			0.0625000
$257$	−7.00000	−	7.00000i	−0.436648	−	0.436648i	0.454234	−	0.890882i	$-0.349913\pi$
$257$	−7.00000	−	7.00000i	−0.436648	−	0.436648i	−0.890882	+	0.454234i	$0.849913\pi$
$258$	−14.4853	+	10.2426i	−0.901814	+	0.637679i
$259$			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	−0.999911	−	0.0133092i	$-0.995763\pi$
$263$	−16.0000	+	16.0000i	−0.986602	+	0.986602i	0.0133092	+	0.999911i	$0.495763\pi$
$264$	1.17157	−	6.82843i	0.0721053	−	0.420261i
$265$	−9.65685	−	4.82843i	−0.593216	−	0.296608i
$266$		−	5.65685i		−	0.346844i
$267$	−16.8284	−	23.7990i	−1.02988	−	1.45647i
$268$	4.82843	+	4.82843i	0.294943	+	0.294943i
$269$	−20.8284			−1.26993			−0.634966	−	0.772540i	$-0.718986\pi$
$269$	−20.8284			−1.26993			−0.634966	+	0.772540i	$0.718986\pi$
$270$	−2.17157	+	11.4142i	−0.132158	+	0.694647i
$271$	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
$273$	4.82843	+	6.82843i	0.292230	+	0.413275i
$274$			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	$0.0460029\pi$
$281$			4.82843i			0.288040i	−0.989575	+	0.144020i	$0.953997\pi$
$282$	−12.4853	+	8.82843i	−0.743488	+	0.525725i
$283$	−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
$285$	−3.65685	−	2.68629i	−0.216613	−	0.159122i
$286$	−4.00000			−0.236525
$287$	−6.82843	−	6.82843i	−0.403069	−	0.403069i
$288$	−2.70711	+	1.29289i	−0.159518	+	0.0761845i
$289$			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	−0.970500	−	0.241102i	$-0.922491\pi$
$293$	−12.4853	+	12.4853i	−0.729398	+	0.729398i	0.241102	+	0.970500i	$0.422491\pi$
$294$	−27.8492	−	4.77817i	−1.62420	−	0.278669i
$295$	8.82843	+	26.4853i	0.514011	+	1.54203i
$296$			7.65685i			0.445046i
$297$	5.65685	+	20.0000i	0.328244	+	1.16052i
$298$	−10.1716	−	10.1716i	−0.589223	−	0.589223i
$299$	−4.00000			−0.231326
$300$	2.65685	−	8.24264i	0.153394	−	0.475889i
$301$	−49.4558			−2.85059
$302$	9.24264	+	9.24264i	0.531854	+	0.531854i
$303$	12.4853	−	8.82843i	0.717261	−	0.507180i
$304$		−	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	$0.291935\pi$
$311$			28.0000i			1.58773i	−0.608091	+	0.793867i	$0.708065\pi$
$312$	1.00000	+	1.41421i	0.0566139	+	0.0800641i
$313$	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
$315$	−23.3137	+	22.4853i	−1.31358	+	1.26690i
$316$	4.48528			0.252317
$317$	−9.65685	−	9.65685i	−0.542383	−	0.542383i	0.381844	−	0.924227i	$-0.375289\pi$
$317$	−9.65685	−	9.65685i	−0.542383	−	0.542383i	−0.924227	+	0.381844i	$0.875289\pi$
$318$	4.82843	+	6.82843i	0.270765	+	0.382919i
$319$		−	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
$327$	26.9706	−	19.0711i	1.49148	−	1.05463i
$328$	−1.41421	−	1.41421i	−0.0780869	−	0.0780869i
$329$	−42.6274			−2.35013
$330$	−2.34315	−	15.3137i	−0.128986	−	0.842992i
$331$	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
$333$	−9.89949	−	20.7279i	−0.542489	−	1.13588i
$334$			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
$342$	1.51472	+	3.17157i	0.0819066	+	0.171499i
$343$	−31.7990	−	31.7990i	−1.71698	−	1.71698i
$344$	−10.2426			−0.552246
$345$	−2.34315	−	15.3137i	−0.126151	−	0.824462i
$346$	−4.14214			−0.222683
$347$	20.5563	+	20.5563i	1.10352	+	1.10352i	0.993982	+	0.109540i	$0.0349379\pi$
$347$	20.5563	+	20.5563i	1.10352	+	1.10352i	0.109540	+	0.993982i	$0.465062\pi$
$348$	−8.48528	+	6.00000i	−0.454859	+	0.321634i
$349$		−	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	−0.543606	−	0.839341i	$-0.682941\pi$
$353$	5.55635	−	5.55635i	0.295735	−	0.295735i	0.839341	+	0.543606i	$0.182941\pi$
$354$	3.65685	−	21.3137i	0.194360	−	1.13281i
$355$	−12.2132	+	4.07107i	−0.648210	+	0.216070i
$356$		−	16.8284i		−	0.891905i
$357$	20.4853	+	28.9706i	1.08420	+	1.53328i
$358$	−4.48528	−	4.48528i	−0.237054	−	0.237054i
$359$	−20.5858			−1.08648			−0.543238	−	0.839579i	$-0.682802\pi$
$359$	−20.5858			−1.08648			−0.543238	+	0.839579i	$0.682802\pi$
$360$	−4.82843	+	4.65685i	−0.254480	+	0.245438i
$361$	17.6274			0.927759
$362$	−4.24264	−	4.24264i	−0.222988	−	0.222988i
$363$	−5.00000	−	7.07107i	−0.262432	−	0.371135i
$364$			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
$372$	−0.828427	+	0.585786i	−0.0429519	+	0.0303716i
$373$	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
$375$	−0.192388	−	19.3640i	−0.00993488	−	0.999951i
$376$	−8.82843			−0.455291
$377$	4.24264	+	4.24264i	0.218507	+	0.218507i
$378$	24.1421	−	6.82843i	1.24174	−	0.351216i
$379$			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	−0.415947	−	0.909389i	$-0.636550\pi$
$383$	9.65685	−	9.65685i	0.493442	−	0.493442i	0.909389	+	0.415947i	$0.136550\pi$
$384$	−1.70711	−	0.292893i	−0.0871154	−	0.0149466i
$385$	19.3137	−	38.6274i	0.984318	−	1.96864i
$386$		−	12.1421i		−	0.618018i
$387$	27.7279	−	13.2426i	1.40949	−	0.673161i
$388$	−5.07107	−	5.07107i	−0.257444	−	0.257444i
$389$	2.00000			0.101404			0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000			0.101404			0.0507020	+	0.998714i	$0.483854\pi$
$390$	3.12132	+	2.29289i	0.158054	+	0.116105i
$391$	−16.9706			−0.858238
$392$	−11.5355	−	11.5355i	−0.582632	−	0.582632i
$393$	29.6569	−	20.9706i	1.49599	−	1.05782i
$394$			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	$0.392773\pi$
$401$			37.7990i			1.88759i	−0.330529	+	0.943796i	$0.607227\pi$
$402$	−6.82843	−	9.65685i	−0.340571	−	0.481640i
$403$	0.414214	+	0.414214i	0.0206334	+	0.0206334i
$404$	8.82843			0.439231
$405$	7.05025	−	18.8492i	0.350330	−	0.936626i
$406$	−28.9706			−1.43778
$407$	21.6569	+	21.6569i	1.07349	+	1.07349i
$408$	4.24264	+	6.00000i	0.210042	+	0.297044i
$409$			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
$417$	−13.6569	+	9.65685i	−0.668779	+	0.472898i
$418$	−3.31371	−	3.31371i	−0.162079	−	0.162079i
$419$	22.4853			1.09848			0.549239	−	0.835665i	$-0.314918\pi$
$419$	22.4853			1.09848			0.549239	+	0.835665i	$0.314918\pi$
$420$	−18.4853	+	2.82843i	−0.901989	+	0.138013i
$421$	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
$423$	23.8995	−	11.4142i	1.16203	−	0.554978i
$424$			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	$-0.793646\pi$
$431$		−	25.0711i		−	1.20763i	0.797124	−	0.603815i	$-0.206354\pi$
$432$	5.00000	−	1.41421i	0.240563	−	0.0680414i
$433$	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
$435$	−13.7574	+	18.7279i	−0.659615	+	0.897935i
$436$	19.0711			0.913339
$437$	−3.31371	−	3.31371i	−0.158516	−	0.158516i
$438$	6.14214	−	4.34315i	0.293483	−	0.207524i
$439$		−	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	−0.995254	−	0.0973118i	$-0.968976\pi$
$443$	−18.8995	+	18.8995i	−0.897942	+	0.897942i	0.0973118	+	0.995254i	$0.468976\pi$
$444$	2.24264	−	13.0711i	0.106431	−	0.620325i
$445$	−11.8995	−	35.6985i	−0.564090	−	1.69227i
$446$		−	2.34315i		−	0.110951i
$447$	14.3848	+	20.3431i	0.680377	+	0.962198i
$448$	−3.41421	−	3.41421i	−0.161306	−	0.161306i
$449$	21.7990			1.02876			0.514379	−	0.857563i	$-0.328022\pi$
$449$	21.7990			1.02876			0.514379	+	0.857563i	$0.328022\pi$
$450$	−6.94975	+	13.2929i	−0.327614	+	0.626633i
$451$	−8.00000			−0.376705
$452$	−7.00000	−	7.00000i	−0.329252	−	0.329252i
$453$	−13.0711	−	18.4853i	−0.614132	−	0.868514i
$454$			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	$-0.658946\pi$
$461$		−	37.6985i		−	1.75579i	0.478850	−	0.877897i	$-0.341054\pi$
$462$	−27.3137	+	19.3137i	−1.27075	+	0.898555i
$463$	−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
$465$	−1.34315	+	1.82843i	−0.0622869	+	0.0847913i
$466$	3.75736			0.174056
$467$	2.89949	+	2.89949i	0.134173	+	0.134173i	0.771004	−	0.636831i	$-0.219755\pi$
$467$	2.89949	+	2.89949i	0.134173	+	0.134173i	−0.636831	+	0.771004i	$0.719755\pi$
$468$	−1.29289	−	2.70711i	−0.0597640	−	0.125136i
$469$		−	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
$477$	−6.24264	−	13.0711i	−0.285831	−	0.598483i
$478$	−0.0710678	−	0.0710678i	−0.00325057	−	0.00325057i
$479$	−12.3848			−0.565875			−0.282937	−	0.959138i	$-0.591309\pi$
$479$	−12.3848			−0.565875			−0.282937	+	0.959138i	$0.591309\pi$
$480$	−3.82843	+	0.585786i	−0.174743	+	0.0267374i
$481$	−7.65685			−0.349123
$482$	−5.41421	−	5.41421i	−0.246611	−	0.246611i
$483$	−27.3137	+	19.3137i	−1.24282	+	0.878804i
$484$		−	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	$0.197787\pi$
$491$			25.7990i			1.16429i	−0.813084	+	0.582146i	$0.802213\pi$
$492$	2.00000	+	2.82843i	0.0901670	+	0.127515i
$493$	18.0000	+	18.0000i	0.810679	+	0.810679i
$494$	1.17157			0.0527116
$495$	−0.485281	+	26.8284i	−0.0218118	+	1.20585i
$496$	−0.585786			−0.0263026
$497$	19.6569	+	19.6569i	0.881730	+	0.881730i
$498$	−1.65685	−	2.34315i	−0.0742454	−	0.104999i
$499$			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	−0.923937	−	0.382546i	$-0.875048\pi$
$503$	−12.1421	+	12.1421i	−0.541391	+	0.541391i	0.382546	+	0.923937i	$0.375048\pi$
$504$	13.6569	+	4.82843i	0.608325	+	0.215075i
$505$	18.7279	−	6.24264i	0.833382	−	0.277794i
$506$		−	16.0000i		−	0.711287i
$507$	−1.41421	+	1.00000i	−0.0628074	+	0.0444116i
$508$	−8.82843	−	8.82843i	−0.391698	−	0.391698i
$509$	1.21320			0.0537743			0.0268871	−	0.999638i	$-0.491441\pi$
$509$	1.21320			0.0537743			0.0268871	+	0.999638i	$0.491441\pi$
$510$	13.2426	+	9.72792i	0.586394	+	0.430760i
$511$	20.9706			0.927683
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.65685	−	5.85786i	−0.0731519	−	0.258631i
$514$			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	$0.0629588\pi$
$521$			8.97056i			0.393007i	−0.980503	+	0.196504i	$0.937041\pi$
$522$	16.2426	−	7.75736i	0.710921	−	0.339530i
$523$	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
$525$	−37.2132	+	19.0711i	−1.62412	+	0.832330i
$526$	22.6274			0.986602
$527$	1.75736	+	1.75736i	0.0765518	+	0.0765518i
$528$	−5.65685	+	4.00000i	−0.246183	+	0.174078i
$529$			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
$537$	6.34315	+	8.97056i	0.273727	+	0.387108i
$538$	14.7279	+	14.7279i	0.634966	+	0.634966i
$539$	−65.2548			−2.81072
$540$	9.60660	−	6.53553i	0.413402	−	0.281245i
$541$	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
$543$	6.00000	+	8.48528i	0.257485	+	0.364138i
$544$			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
$552$	−5.65685	+	4.00000i	−0.240772	+	0.170251i
$553$	−15.3137	−	15.3137i	−0.651205	−	0.651205i
$554$	−5.51472			−0.234298
$555$	−4.48528	−	29.3137i	−0.190390	−	1.24430i
$556$	−9.65685			−0.409542
$557$	−15.0711	−	15.0711i	−0.638582	−	0.638582i	0.311624	−	0.950206i	$-0.399127\pi$
$557$	−15.0711	−	15.0711i	−0.638582	−	0.638582i	−0.950206	+	0.311624i	$0.899127\pi$
$558$	1.58579	−	0.757359i	0.0671317	−	0.0320616i
$559$		−	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	−0.443102	−	0.896471i	$-0.646122\pi$
$563$	10.7574	−	10.7574i	0.453369	−	0.453369i	0.896471	+	0.443102i	$0.146122\pi$
$564$	15.0711	+	2.58579i	0.634606	+	0.108881i
$565$	−19.7990	−	9.89949i	−0.832950	−	0.416475i
$566$			12.3848i			0.520571i
$567$	−43.2132	+	4.58579i	−1.81478	+	0.192585i
$568$	4.07107	+	4.07107i	0.170818	+	0.170818i
$569$	29.6569			1.24328			0.621640	−	0.783303i	$-0.286467\pi$
$569$	29.6569			1.24328			0.621640	+	0.783303i	$0.286467\pi$
$570$	0.686292	+	4.48528i	0.0287456	+	0.187868i
$571$	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
$573$	4.00000	−	2.82843i	0.167102	−	0.118159i
$574$			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
$582$	7.17157	+	10.1421i	0.297271	+	0.420405i
$583$	13.6569	+	13.6569i	0.565609	+	0.565609i
$584$	4.34315			0.179721
$585$	−4.65685	−	4.82843i	−0.192537	−	0.199631i
$586$	17.6569			0.729398
$587$	−31.7990	−	31.7990i	−1.31248	−	1.31248i	−0.919579	−	0.392906i	$-0.871470\pi$
$587$	−31.7990	−	31.7990i	−1.31248	−	1.31248i	−0.392906	−	0.919579i	$-0.628530\pi$
$588$	16.3137	+	23.0711i	0.672766	+	0.951435i
$589$			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	−0.794968	−	0.606652i	$-0.792512\pi$
$593$	−4.58579	+	4.58579i	−0.188316	+	0.188316i	0.606652	+	0.794968i	$0.292512\pi$
$594$	10.1421	−	18.1421i	0.416137	−	0.744381i
$595$	14.4853	+	43.4558i	0.593839	+	1.78152i
$596$			14.3848i			0.589223i
$597$	8.68629	−	6.14214i	0.355506	−	0.251381i
$598$	2.82843	+	2.82843i	0.115663	+	0.115663i
$599$	0.485281			0.0198281			0.00991403	−	0.999951i	$-0.496844\pi$
$599$	0.485281			0.0198281			0.00991403	+	0.999951i	$0.496844\pi$
$600$	−7.70711	+	3.94975i	−0.314641	+	0.161248i
$601$	−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
$603$	8.82843	+	18.4853i	0.359521	+	0.752779i
$604$		−	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
$612$	−5.48528	−	11.4853i	−0.221729	−	0.464265i
$613$	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
$615$	6.24264	+	4.58579i	0.251728	+	0.184917i
$616$	−19.3137			−0.778171
$617$	25.0711	+	25.0711i	1.00932	+	1.00932i	0.999956	+	0.00936706i	$0.00298167\pi$
$617$	25.0711	+	25.0711i	1.00932	+	1.00932i	0.00936706	+	0.999956i	$0.497018\pi$
$618$	−8.97056	+	6.34315i	−0.360849	+	0.255159i
$619$			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
$627$	4.68629	+	6.62742i	0.187152	+	0.264674i
$628$	7.75736	+	7.75736i	0.309552	+	0.309552i
$629$	−32.4853			−1.29527
$630$	32.3848	+	0.585786i	1.29024	+	0.0233383i
$631$	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
$633$	−9.65685	−	13.6569i	−0.383825	−	0.542811i
$634$			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	$-0.771442\pi$
$641$		−	33.3137i		−	1.31581i	0.753100	−	0.657906i	$-0.228558\pi$
$642$	4.14214	−	2.92893i	0.163477	−	0.115596i
$643$	−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
$645$	39.2132	−	6.00000i	1.54402	−	0.236250i
$646$	4.97056			0.195564
$647$	−6.68629	−	6.68629i	−0.262865	−	0.262865i	0.563352	−	0.826217i	$-0.309512\pi$
$647$	−6.68629	−	6.68629i	−0.262865	−	0.262865i	−0.826217	+	0.563352i	$0.809512\pi$
$648$	−8.94975	+	0.949747i	−0.351579	+	0.0373096i
$649$		−	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	−0.785231	−	0.619203i	$-0.787456\pi$
$653$	−4.24264	+	4.24264i	−0.166027	+	0.166027i	0.619203	+	0.785231i	$0.287456\pi$
$654$	−32.5563	−	5.58579i	−1.27305	−	0.218422i
$655$	44.4853	−	14.8284i	1.73818	−	0.579395i
$656$			2.00000i			0.0780869i
$657$	−11.7574	+	5.61522i	−0.458698	+	0.219071i
$658$	30.1421	+	30.1421i	1.17506	+	1.17506i
$659$	42.4853			1.65499			0.827496	−	0.561472i	$-0.189765\pi$
$659$	42.4853			1.65499			0.827496	+	0.561472i	$0.189765\pi$
$660$	−9.17157	+	12.4853i	−0.357003	+	0.485989i
$661$	−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
$663$	−6.00000	+	4.24264i	−0.233021	+	0.164771i
$664$		−	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
$672$	4.82843	+	6.82843i	0.186261	+	0.263412i
$673$	−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
$675$	15.7574	−	20.6569i	0.606501	−	0.795083i
$676$	−1.00000			−0.0384615
$677$	26.3848	+	26.3848i	1.01405	+	1.01405i	0.999900	+	0.0141494i	$0.00450406\pi$
$677$	26.3848	+	26.3848i	1.01405	+	1.01405i	0.0141494	+	0.999900i	$0.495496\pi$
$678$	9.89949	+	14.0000i	0.380188	+	0.537667i
$679$			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	−0.765177	−	0.643820i	$-0.777349\pi$
$683$	−3.17157	+	3.17157i	−0.121357	+	0.121357i	0.643820	+	0.765177i	$0.277349\pi$
$684$	1.17157	−	3.31371i	0.0447962	−	0.126703i
$685$	1.31371	−	2.62742i	0.0501942	−	0.100388i
$686$			44.9706i			1.71698i
$687$	−2.68629	+	1.89949i	−0.102488	+	0.0724703i
$688$	7.24264	+	7.24264i	0.276123	+	0.276123i
$689$	−4.82843			−0.183948
$690$	−9.17157	+	12.4853i	−0.349156	+	0.475307i
$691$	−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
$693$	52.2843	−	24.9706i	1.98612	−	0.948553i
$694$		−	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	$-0.905719\pi$
$701$		−	15.4558i		−	0.583759i	0.956455	−	0.291880i	$-0.0942807\pi$
$702$	1.41421	+	5.00000i	0.0533761	+	0.188713i
$703$	−6.34315	−	6.34315i	−0.239236	−	0.239236i
$704$	−4.00000			−0.150756
$705$	33.7990	−	5.17157i	1.27294	−	0.194773i
$706$	−7.85786			−0.295735
$707$	−30.1421	−	30.1421i	−1.13361	−	1.13361i
$708$	−17.6569	+	12.4853i	−0.663585	+	0.469226i
$709$		−	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
$717$	0.100505	+	0.142136i	0.00375343	+	0.00530815i
$718$	14.5563	+	14.5563i	0.543238	+	0.543238i
$719$	4.48528			0.167273			0.0836364	−	0.996496i	$-0.473347\pi$
$719$	4.48528			0.167273			0.0836364	+	0.996496i	$0.473347\pi$
$720$	6.70711	+	0.121320i	0.249959	+	0.00452134i
$721$	−30.6274			−1.14062
$722$	−12.4645	−	12.4645i	−0.463879	−	0.463879i
$723$	7.65685	+	10.8284i	0.284761	+	0.402714i
$724$			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
$732$	1.17157	−	0.828427i	0.0433026	−	0.0306195i
$733$	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
$735$	50.9203	+	37.4056i	1.87822	+	1.37973i
$736$	−4.00000			−0.147442
$737$	−19.3137	−	19.3137i	−0.711430	−	0.711430i
$738$	−2.58579	−	5.41421i	−0.0951841	−	0.199300i
$739$		−	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	$-0.394819\pi$
$743$	34.6274	−	34.6274i	1.27036	−	1.27036i	0.945901	−	0.324456i	$-0.105181\pi$
$744$	1.00000	+	0.171573i	0.0366618	+	0.00629017i
$745$	10.1716	+	30.5147i	0.372658	+	1.11797i
$746$		−	26.9706i		−	0.987462i
$747$	2.14214	+	4.48528i	0.0783766	+	0.164108i
$748$	12.0000	+	12.0000i	0.438763	+	0.438763i
$749$	14.1421			0.516742
$750$	−13.5563	+	13.8284i	−0.495008	+	0.504943i
$751$	−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
$753$	−36.2843	+	25.6569i	−1.32227	+	0.934988i
$754$		−	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	$-0.944830\pi$
$761$		−	9.51472i		−	0.344908i	0.985018	−	0.172454i	$-0.0551697\pi$
$762$	12.4853	+	17.6569i	0.452294	+	0.639640i
$763$	−65.1127	−	65.1127i	−2.35724	−	2.35724i
$764$	2.82843			0.102329
$765$	−19.7574	−	20.4853i	−0.714329	−	0.740647i
$766$	−13.6569			−0.493442
$767$	8.82843	+	8.82843i	0.318776	+	0.318776i
$768$	1.00000	+	1.41421i	0.0360844	+	0.0510310i
$769$			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	−0.553702	−	0.832715i	$-0.686785\pi$
$773$	7.75736	−	7.75736i	0.279013	−	0.279013i	0.832715	+	0.553702i	$0.186785\pi$
$774$	−28.9706	−	10.2426i	−1.04133	−	0.368164i
$775$	−2.34315	+	1.75736i	−0.0841683	+	0.0631262i
$776$			7.17157i			0.257444i
$777$	−52.2843	+	36.9706i	−1.87569	+	1.32631i
$778$	−1.41421	−	1.41421i	−0.0507020	−	0.0507020i
$779$	2.34315			0.0839519
$780$	−0.585786	−	3.82843i	−0.0209745	−	0.137080i
$781$	23.0294			0.824058
$782$	12.0000	+	12.0000i	0.429119	+	0.429119i
$783$	−30.0000	+	8.48528i	−1.07211	+	0.303239i
$784$			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
$792$	10.8284	−	5.17157i	0.384771	−	0.183764i
$793$	−0.585786	−	0.585786i	−0.0208019	−	0.0208019i
$794$	20.9706			0.744217
$795$	−2.82843	−	18.4853i	−0.100314	−	0.655605i
$796$	6.14214			0.217702
$797$	21.0711	+	21.0711i	0.746376	+	0.746376i	0.973797	−	0.227421i	$-0.0730294\pi$
$797$	21.0711	+	21.0711i	0.746376	+	0.746376i	−0.227421	+	0.973797i	$0.573029\pi$
$798$	8.00000	−	5.65685i	0.283197	−	0.200250i
$799$		−	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
$807$	−20.8284	−	29.4558i	−0.733195	−	1.03689i
$808$	−6.24264	−	6.24264i	−0.219615	−	0.219615i
$809$	22.6274			0.795538			0.397769	−	0.917486i	$-0.369785\pi$
$809$	22.6274			0.795538			0.397769	+	0.917486i	$0.369785\pi$
$810$	−18.3137	+	8.34315i	−0.643478	+	0.293148i
$811$	−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
$813$	6.24264	+	8.82843i	0.218939	+	0.309626i
$814$		−	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	$0.293815\pi$
$821$			45.6985i			1.59489i	−0.603393	+	0.797444i	$0.706185\pi$
$822$	−1.85786	+	1.31371i	−0.0648005	+	0.0458208i
$823$	−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
$825$	−10.6274	+	32.9706i	−0.369999	+	1.14789i
$826$	−60.2843			−2.09756
$827$	27.1716	+	27.1716i	0.944848	+	0.944848i	0.998557	−	0.0537085i	$-0.0171042\pi$
$827$	27.1716	+	27.1716i	0.944848	+	0.944848i	−0.0537085	+	0.998557i	$0.517104\pi$
$828$	10.8284	−	5.17157i	0.376314	−	0.179725i
$829$			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
$837$	−2.92893	+	0.828427i	−0.101239	+	0.0286346i
$838$	−15.8995	−	15.8995i	−0.549239	−	0.549239i
$839$	39.8995			1.37748			0.688742	−	0.725007i	$-0.258163\pi$
$839$	39.8995			1.37748			0.688742	+	0.725007i	$0.258163\pi$
$840$	15.0711	+	11.0711i	0.520001	+	0.381988i
$841$	7.00000			0.241379
$842$	−9.14214	−	9.14214i	−0.315059	−	0.315059i
$843$	−6.82843	+	4.82843i	−0.235184	+	0.166300i
$844$		−	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
$852$	−5.75736	−	8.14214i	−0.197244	−	0.278945i
$853$	−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
$855$	0.142136	−	7.85786i	0.00486094	−	0.268733i
$856$	2.92893			0.100109
$857$	25.8284	+	25.8284i	0.882282	+	0.882282i	0.993766	−	0.111484i	$-0.0355604\pi$
$857$	25.8284	+	25.8284i	0.882282	+	0.882282i	−0.111484	+	0.993766i	$0.535560\pi$
$858$	−4.00000	−	5.65685i	−0.136558	−	0.193122i
$859$			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	−0.901365	−	0.433059i	$-0.857434\pi$
$863$	−13.7574	+	13.7574i	−0.468306	+	0.468306i	0.433059	+	0.901365i	$0.357434\pi$
$864$	−4.53553	−	2.53553i	−0.154302	−	0.0862606i
$865$	8.28427	+	4.14214i	0.281674	+	0.140837i
$866$		−	8.92893i		−	0.303417i
$867$	−1.41421	+	1.00000i	−0.0480292	+	0.0339618i
$868$	2.00000	+	2.00000i	0.0678844	+	0.0678844i
$869$	−17.9411			−0.608611
$870$	22.9706	−	3.51472i	0.778775	−	0.119160i
$871$	6.82843			0.231372
$872$	−13.4853	−	13.4853i	−0.456669	−	0.456669i
$873$	−9.27208	−	19.4142i	−0.313812	−	0.657072i
$874$			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	$-0.924217\pi$
$881$		−	14.0000i		−	0.471672i	0.971793	−	0.235836i	$-0.0757828\pi$
$882$	−21.0919	−	44.1630i	−0.710201	−	1.48704i
$883$	−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
$885$	−28.6274	+	38.9706i	−0.962300	+	1.30998i
$886$	26.7279			0.897942
$887$	4.00000	+	4.00000i	0.134307	+	0.134307i	0.771064	−	0.636757i	$-0.219725\pi$
$887$	4.00000	+	4.00000i	0.134307	+	0.134307i	−0.636757	+	0.771064i	$0.719725\pi$
$888$	−10.8284	+	7.65685i	−0.363378	+	0.256947i
$889$			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
$897$	−4.00000	−	5.65685i	−0.133556	−	0.188877i
$898$	−15.4142	−	15.4142i	−0.514379	−	0.514379i
$899$	3.51472			0.117222
$900$	14.3137	−	4.48528i	0.477124	−	0.149509i
$901$	−20.4853			−0.682464
$902$	5.65685	+	5.65685i	0.188353	+	0.188353i
$903$	−49.4558	−	69.9411i	−1.64579	−	2.32749i
$904$			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	$0.166419\pi$
$911$			30.1421i			0.998654i	−0.866414	+	0.499327i	$0.833581\pi$
$912$	1.65685	−	1.17157i	0.0548639	−	0.0387947i
$913$	−4.68629	−	4.68629i	−0.155094	−	0.155094i
$914$	9.79899			0.324122
$915$	1.89949	−	2.58579i	0.0627954	−	0.0854835i
$916$	−1.89949			−0.0627611
$917$	−71.5980	−	71.5980i	−2.36437	−	2.36437i
$918$	6.00000	+	21.2132i	0.198030	+	0.700140i
$919$		−	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
$927$	17.1716	−	8.20101i	0.563988	−	0.269357i
$928$	4.24264	+	4.24264i	0.139272	+	0.139272i
$929$	−5.11270			−0.167742			−0.0838711	−	0.996477i	$-0.526728\pi$
$929$	−5.11270			−0.167742			−0.0838711	+	0.996477i	$0.526728\pi$
$930$	2.24264	−	0.343146i	0.0735391	−	0.0112522i
$931$	19.1127			0.626393
$932$	−2.65685	−	2.65685i	−0.0870282	−	0.0870282i
$933$	−39.5980	+	28.0000i	−1.29638	+	0.916679i
$934$		−	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	$-0.922074\pi$
$941$		−	14.8701i		−	0.484750i	0.970183	−	0.242375i	$-0.0779264\pi$
$942$	−10.9706	−	15.5147i	−0.357440	−	0.505497i
$943$	5.65685	+	5.65685i	0.184213	+	0.184213i
$944$	−12.4853			−0.406361
$945$	−55.1127	−	10.4853i	−1.79282	−	0.341086i
$946$	40.9706			1.33207
$947$	−32.6274	−	32.6274i	−1.06025	−	1.06025i	−0.998065	−	0.0621839i	$-0.980193\pi$
$947$	−32.6274	−	32.6274i	−1.06025	−	1.06025i	−0.0621839	−	0.998065i	$-0.519807\pi$
$948$	4.48528	+	6.34315i	0.145675	+	0.206016i
$949$			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	−0.963540	−	0.267564i	$-0.913781\pi$
$953$	−21.4853	+	21.4853i	−0.695977	+	0.695977i	0.267564	+	0.963540i	$0.413781\pi$
$954$	−4.82843	+	13.6569i	−0.156326	+	0.442157i
$955$	6.00000	−	2.00000i	0.194155	−	0.0647185i
$956$			0.100505i			0.00325057i
$957$	33.9411	−	24.0000i	1.09716	−	0.775810i
$958$	8.75736	+	8.75736i	0.282937	+	0.282937i
$959$	−6.34315			−0.204831
$960$	3.12132	+	2.29289i	0.100740	+	0.0740028i
$961$	−30.6569			−0.988931
$962$	5.41421	+	5.41421i	0.174561	+	0.174561i
$963$	−7.92893	+	3.78680i	−0.255506	+	0.122028i
$964$			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	$-0.895243\pi$
$971$		−	20.1421i		−	0.646392i	0.946332	−	0.323196i	$-0.104757\pi$
$972$	15.5563	+	1.00000i	0.498970	+	0.0320750i
$973$	32.9706	+	32.9706i	1.05699	+	1.05699i
$974$	−24.1421			−0.773564
$975$	−3.94975	−	7.70711i	−0.126493	−	0.246825i
$976$	0.828427			0.0265173
$977$	18.5858	+	18.5858i	0.594612	+	0.594612i	0.938874	−	0.344262i	$-0.111871\pi$
$977$	18.5858	+	18.5858i	0.594612	+	0.594612i	−0.344262	+	0.938874i	$0.611871\pi$
$978$	27.3137	−	19.3137i	0.873396	−	0.617584i
$979$			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	−0.716387	−	0.697703i	$-0.754205\pi$
$983$	−0.585786	+	0.585786i	−0.0186837	+	0.0186837i	0.697703	+	0.716387i	$0.254205\pi$
$984$	0.585786	−	3.41421i	0.0186742	−	0.108841i
$985$	17.3137	−	34.6274i	0.551661	−	1.10332i
$986$		−	25.4558i		−	0.810679i
$987$	−42.6274	−	60.2843i	−1.35685	−	1.91887i
$988$	−0.828427	−	0.828427i	−0.0263558	−	0.0263558i
$989$	40.9706			1.30279
$990$	19.3137	−	18.6274i	0.613830	−	0.592018i
$991$	−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
$993$	24.2843	+	34.3431i	0.770638	+	1.08985i
$994$		−	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.b.53.1	yes	4
3.2	odd	2		390.2.l.a.53.2	✓	4
5.2	odd	4		390.2.l.a.287.2	yes	4
15.2	even	4	inner	390.2.l.b.287.1	yes	4

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

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} +(1.00000 + 1.41421i) 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} +(-1.41421 + 1.00000i) q^{12} +(0.707107 + 0.707107i) q^{13} -4.82843 q^{14} +(-2.29289 + 3.12132i) q^{15} -1.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(2.70711 - 1.29289i) 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} +(-5.00000 + 1.41421i) q^{27} +(3.41421 + 3.41421i) q^{28} +6.00000 q^{29} +(3.82843 - 0.585786i) q^{30} +0.585786 q^{31} +(0.707107 + 0.707107i) q^{32} +(5.65685 - 4.00000i) 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} +(-4.82843 - 6.82843i) q^{42} +(-7.24264 - 7.24264i) q^{43} +4.00000 q^{44} +(-6.70711 - 0.121320i) q^{45} +4.00000 q^{46} +(-6.24264 - 6.24264i) q^{47} +(-1.00000 - 1.41421i) 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} +(-1.65685 + 1.17157i) q^{57} +(-4.24264 - 4.24264i) q^{58} +12.4853 q^{59} +(-3.12132 - 2.29289i) q^{60} -0.828427 q^{61} +(-0.414214 - 0.414214i) q^{62} +(6.24264 + 13.0711i) 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} +(1.29289 + 2.70711i) q^{72} +(3.07107 + 3.07107i) q^{73} +7.65685 q^{74} +(-8.24264 - 2.65685i) q^{75} -1.17157 q^{76} +(-13.6569 - 13.6569i) q^{77} +(1.41421 - 1.00000i) 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} +(6.00000 + 8.48528i) q^{87} +(-2.82843 - 2.82843i) q^{88} -16.8284 q^{89} +(4.65685 + 4.82843i) q^{90} +4.82843 q^{91} +(-2.82843 - 2.82843i) q^{92} +(0.585786 + 0.828427i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{6} + 8 q^{7} - 4 q^{9} + 4 q^{10} - 8 q^{14} - 12 q^{15} - 4 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} + 4 q^{24} - 16 q^{25} - 20 q^{27} + 8 q^{28} + 24 q^{29} + 4 q^{30} + 8 q^{31}+ \cdots - 32 q^{98}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^6 + 8 * q^7 - 4 * q^9 + 4 * q^10 - 8 * q^14 - 12 * q^15 - 4 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 + 4 * q^24 - 16 * q^25 - 20 * q^27 + 8 * q^28 + 24 * q^29 + 4 * q^30 + 8 * q^31 + 16 * q^35 - 16 * q^37 - 8 * q^38 - 4 * q^39 + 8 * q^40 - 8 * q^42 - 12 * q^43 + 16 * q^44 - 24 * q^45 + 16 * q^46 - 8 * q^47 - 4 * q^48 + 12 * q^51 - 8 * q^53 + 4 * q^54 + 16 * q^57 + 16 * q^59 - 4 * q^60 + 8 * q^61 + 4 * q^62 + 8 * 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 - 16 * q^75 - 16 * q^76 - 32 * q^77 - 28 * q^81 + 16 * q^83 + 24 * q^87 - 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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