LMFDB - Embedded newform 390.2.l.b.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 = [4,0,4] 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			53.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	390.53
Dual form			390.2.l.b.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} +(1.00000 - 1.41421i) q^{3} +1.00000i q^{4} +(-0.707107 - 2.12132i) q^{5} +(1.70711 - 0.292893i) q^{6} +(0.585786 - 0.585786i) 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} +0.828427 q^{14} +(-3.70711 - 1.12132i) q^{15} -1.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(1.29289 - 2.70711i) q^{18} +6.82843i q^{19} +(2.12132 - 0.707107i) q^{20} +(-0.242641 - 1.41421i) q^{21} +(2.82843 - 2.82843i) q^{22} +(2.82843 - 2.82843i) q^{23} +(0.292893 + 1.70711i) q^{24} +(-4.00000 + 3.00000i) q^{25} -1.00000i q^{26} +(-5.00000 - 1.41421i) q^{27} +(0.585786 + 0.585786i) q^{28} +6.00000 q^{29} +(-1.82843 - 3.41421i) q^{30} +3.41421 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.65685 - 4.00000i) q^{33} +4.24264i q^{34} +(-1.65685 - 0.828427i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-2.58579 + 2.58579i) q^{37} +(-4.82843 + 4.82843i) q^{38} +(-1.70711 + 0.292893i) q^{39} +(2.00000 + 1.00000i) q^{40} -2.00000i q^{41} +(0.828427 - 1.17157i) q^{42} +(1.24264 + 1.24264i) q^{43} +4.00000 q^{44} +(-5.29289 + 4.12132i) q^{45} +4.00000 q^{46} +(2.24264 + 2.24264i) q^{47} +(-1.00000 + 1.41421i) q^{48} +6.31371i q^{49} +(-4.94975 - 0.707107i) q^{50} +(7.24264 - 1.24264i) q^{51} +(0.707107 - 0.707107i) q^{52} +(-0.585786 + 0.585786i) q^{53} +(-2.53553 - 4.53553i) q^{54} +(-8.48528 + 2.82843i) q^{55} +0.828427i q^{56} +(9.65685 + 6.82843i) q^{57} +(4.24264 + 4.24264i) q^{58} -4.48528 q^{59} +(1.12132 - 3.70711i) q^{60} +4.82843 q^{61} +(2.41421 + 2.41421i) q^{62} +(-2.24264 - 1.07107i) q^{63} -1.00000i q^{64} +(-1.00000 + 2.00000i) q^{65} +(-1.17157 - 6.82843i) q^{66} +(-0.828427 + 0.828427i) q^{67} +(-3.00000 + 3.00000i) q^{68} +(-1.17157 - 6.82843i) q^{69} +(-0.585786 - 1.75736i) q^{70} +14.2426i q^{71} +(2.70711 + 1.29289i) q^{72} +(-11.0711 - 11.0711i) q^{73} -3.65685 q^{74} +(0.242641 + 8.65685i) q^{75} -6.82843 q^{76} +(-2.34315 - 2.34315i) q^{77} +(-1.41421 - 1.00000i) q^{78} +12.4853i q^{79} +(0.707107 + 2.12132i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(1.41421 - 1.41421i) q^{82} +(6.82843 - 6.82843i) q^{83} +(1.41421 - 0.242641i) q^{84} +(4.24264 - 8.48528i) q^{85} +1.75736i q^{86} +(6.00000 - 8.48528i) q^{87} +(2.82843 + 2.82843i) q^{88} -11.1716 q^{89} +(-6.65685 - 0.828427i) q^{90} -0.828427 q^{91} +(2.82843 + 2.82843i) q^{92} +(3.41421 - 4.82843i) q^{93} +3.17157i q^{94} +(14.4853 - 4.82843i) q^{95} +(-1.70711 + 0.292893i) q^{96} +(9.07107 - 9.07107i) q^{97} +(-4.46447 + 4.46447i) 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
$6$	1.70711	−	0.292893i	0.696923	−	0.119573i
$7$	0.585786	−	0.585786i	0.221406	−	0.221406i	−0.587684	−	0.809091i	$-0.699960\pi$
$7$	0.585786	−	0.585786i	0.221406	−	0.221406i	0.809091	+	0.587684i	$0.199960\pi$
$8$	−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
$14$	0.828427			0.221406
$15$	−3.70711	−	1.12132i	−0.957171	−	0.289524i
$16$	−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	$0.577979\pi$
$18$	1.29289	−	2.70711i	0.304738	−	0.638071i
$19$			6.82843i			1.56655i	0.621676	+	0.783274i	$0.286452\pi$
$19$			6.82843i			1.56655i	−0.621676	+	0.783274i	$0.713548\pi$
$20$	2.12132	−	0.707107i	0.474342	−	0.158114i
$21$	−0.242641	−	1.41421i	−0.0529485	−	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	$0.113071\pi$
$24$	0.292893	+	1.70711i	0.0597866	+	0.348462i
$25$	−4.00000	+	3.00000i	−0.800000	+	0.600000i
$26$		−	1.00000i		−	0.196116i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$	0.585786	+	0.585786i	0.110703	+	0.110703i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.82843	−	3.41421i	−0.333824	−	0.623347i
$31$	3.41421			0.613211			0.306605	−	0.951837i	$-0.400807\pi$
$31$	3.41421			0.613211			0.306605	+	0.951837i	$0.400807\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−5.65685	−	4.00000i	−0.984732	−	0.696311i
$34$			4.24264i			0.727607i
$35$	−1.65685	−	0.828427i	−0.280059	−	0.140030i
$36$	2.82843	−	1.00000i	0.471405	−	0.166667i
$37$	−2.58579	+	2.58579i	−0.425101	+	0.425101i	−0.886956	−	0.461855i	$-0.847184\pi$
$37$	−2.58579	+	2.58579i	−0.425101	+	0.425101i	0.461855	+	0.886956i	$0.347184\pi$
$38$	−4.82843	+	4.82843i	−0.783274	+	0.783274i
$39$	−1.70711	+	0.292893i	−0.273356	+	0.0469005i
$40$	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	$-0.0499160\pi$
$42$	0.828427	−	1.17157i	0.127829	−	0.180778i
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	0.795480	−	0.605979i	$-0.207219\pi$
$43$	1.24264	+	1.24264i	0.189501	+	0.189501i	−0.605979	+	0.795480i	$0.707219\pi$
$44$	4.00000			0.603023
$45$	−5.29289	+	4.12132i	−0.789018	+	0.614370i
$46$	4.00000			0.589768
$47$	2.24264	+	2.24264i	0.327123	+	0.327123i	0.851491	−	0.524369i	$-0.175699\pi$
$47$	2.24264	+	2.24264i	0.327123	+	0.327123i	−0.524369	+	0.851491i	$0.675699\pi$
$48$	−1.00000	+	1.41421i	−0.144338	+	0.204124i
$49$			6.31371i			0.901958i
$50$	−4.94975	−	0.707107i	−0.700000	−	0.100000i
$51$	7.24264	−	1.24264i	1.01417	−	0.174005i
$52$	0.707107	−	0.707107i	0.0980581	−	0.0980581i
$53$	−0.585786	+	0.585786i	−0.0804640	+	0.0804640i	−0.746193	−	0.665729i	$-0.768121\pi$
$53$	−0.585786	+	0.585786i	−0.0804640	+	0.0804640i	0.665729	+	0.746193i	$0.268121\pi$
$54$	−2.53553	−	4.53553i	−0.345042	−	0.617208i
$55$	−8.48528	+	2.82843i	−1.14416	+	0.381385i
$56$			0.828427i			0.110703i
$57$	9.65685	+	6.82843i	1.27908	+	0.904447i
$58$	4.24264	+	4.24264i	0.557086	+	0.557086i
$59$	−4.48528			−0.583934			−0.291967	−	0.956428i	$-0.594310\pi$
$59$	−4.48528			−0.583934			−0.291967	+	0.956428i	$0.594310\pi$
$60$	1.12132	−	3.70711i	0.144762	−	0.478585i
$61$	4.82843			0.618217			0.309108	−	0.951027i	$-0.399969\pi$
$61$	4.82843			0.618217			0.309108	+	0.951027i	$0.399969\pi$
$62$	2.41421	+	2.41421i	0.306605	+	0.306605i
$63$	−2.24264	−	1.07107i	−0.282546	−	0.134942i
$64$		−	1.00000i		−	0.125000i
$65$	−1.00000	+	2.00000i	−0.124035	+	0.248069i
$66$	−1.17157	−	6.82843i	−0.144211	−	0.840521i
$67$	−0.828427	+	0.828427i	−0.101208	+	0.101208i	−0.755898	−	0.654689i	$-0.772799\pi$
$67$	−0.828427	+	0.828427i	−0.101208	+	0.101208i	0.654689	+	0.755898i	$0.272799\pi$
$68$	−3.00000	+	3.00000i	−0.363803	+	0.363803i
$69$	−1.17157	−	6.82843i	−0.141041	−	0.822046i
$70$	−0.585786	−	1.75736i	−0.0700149	−	0.210045i
$71$			14.2426i			1.69029i	0.534537	+	0.845145i	$0.320486\pi$
$71$			14.2426i			1.69029i	−0.534537	+	0.845145i	$0.679514\pi$
$72$	2.70711	+	1.29289i	0.319036	+	0.152369i
$73$	−11.0711	−	11.0711i	−1.29577	−	1.29577i	−0.931160	−	0.364610i	$-0.881202\pi$
$73$	−11.0711	−	11.0711i	−1.29577	−	1.29577i	−0.364610	−	0.931160i	$-0.618798\pi$
$74$	−3.65685			−0.425101
$75$	0.242641	+	8.65685i	0.0280177	+	0.999607i
$76$	−6.82843			−0.783274
$77$	−2.34315	−	2.34315i	−0.267026	−	0.267026i
$78$	−1.41421	−	1.00000i	−0.160128	−	0.113228i
$79$			12.4853i			1.40470i	0.711830	+	0.702352i	$0.247867\pi$
$79$			12.4853i			1.40470i	−0.711830	+	0.702352i	$0.752133\pi$
$80$	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
$83$	6.82843	−	6.82843i	0.749517	−	0.749517i	−0.224871	−	0.974388i	$-0.572196\pi$
$83$	6.82843	−	6.82843i	0.749517	−	0.749517i	0.974388	+	0.224871i	$0.0721961\pi$
$84$	1.41421	−	0.242641i	0.154303	−	0.0264743i
$85$	4.24264	−	8.48528i	0.460179	−	0.920358i
$86$			1.75736i			0.189501i
$87$	6.00000	−	8.48528i	0.643268	−	0.909718i
$88$	2.82843	+	2.82843i	0.301511	+	0.301511i
$89$	−11.1716			−1.18418			−0.592092	−	0.805870i	$-0.701698\pi$
$89$	−11.1716			−1.18418			−0.592092	+	0.805870i	$0.701698\pi$
$90$	−6.65685	−	0.828427i	−0.701694	−	0.0873239i
$91$	−0.828427			−0.0868428
$92$	2.82843	+	2.82843i	0.294884	+	0.294884i
$93$	3.41421	−	4.82843i	0.354037	−	0.500685i
$94$			3.17157i			0.327123i
$95$	14.4853	−	4.82843i	1.48616	−	0.495386i
$96$	−1.70711	+	0.292893i	−0.174231	+	0.0298933i
$97$	9.07107	−	9.07107i	0.921027	−	0.921027i	−0.0760747	−	0.997102i	$-0.524239\pi$
$97$	9.07107	−	9.07107i	0.921027	−	0.921027i	0.997102	+	0.0760747i	$0.0242388\pi$
$98$	−4.46447	+	4.46447i	−0.450979	+	0.450979i
$99$	−11.3137	+	4.00000i	−1.13707	+	0.402015i
$100$	−3.00000	−	4.00000i	−0.300000	−	0.400000i
$101$		−	3.17157i		−	0.315583i	−0.987472	−	0.157792i	$-0.949563\pi$
$101$		−	3.17157i		−	0.315583i	0.987472	−	0.157792i	$-0.0504374\pi$
$102$	6.00000	+	4.24264i	0.594089	+	0.420084i
$103$	12.4853	+	12.4853i	1.23021	+	1.23021i	0.963882	+	0.266329i	$0.0858108\pi$
$103$	12.4853	+	12.4853i	1.23021	+	1.23021i	0.266329	+	0.963882i	$0.414189\pi$
$104$	1.00000			0.0980581
$105$	−2.82843	+	1.51472i	−0.276026	+	0.147821i
$106$	−0.828427			−0.0804640
$107$	−12.0711	−	12.0711i	−1.16695	−	1.16695i	−0.982920	−	0.184034i	$-0.941084\pi$
$107$	−12.0711	−	12.0711i	−1.16695	−	1.16695i	−0.184034	−	0.982920i	$-0.558916\pi$
$108$	1.41421	−	5.00000i	0.136083	−	0.481125i
$109$		−	4.92893i		−	0.472106i	−0.971740	−	0.236053i	$-0.924146\pi$
$109$		−	4.92893i		−	0.472106i	0.971740	−	0.236053i	$-0.0758539\pi$
$110$	−8.00000	−	4.00000i	−0.762770	−	0.381385i
$111$	1.07107	+	6.24264i	0.101661	+	0.592525i
$112$	−0.585786	+	0.585786i	−0.0553516	+	0.0553516i
$113$	−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	+	11.6569i	0.187317	+	1.09176i
$115$	−8.00000	−	4.00000i	−0.746004	−	0.373002i
$116$			6.00000i			0.557086i
$117$	−1.29289	+	2.70711i	−0.119528	+	0.250272i
$118$	−3.17157	−	3.17157i	−0.291967	−	0.291967i
$119$	3.51472			0.322194
$120$	3.41421	−	1.82843i	0.311674	−	0.166912i
$121$	−5.00000			−0.454545
$122$	3.41421	+	3.41421i	0.309108	+	0.309108i
$123$	−2.82843	−	2.00000i	−0.255031	−	0.180334i
$124$			3.41421i			0.306605i
$125$	9.19239	+	6.36396i	0.822192	+	0.569210i
$126$	−0.828427	−	2.34315i	−0.0738022	−	0.208744i
$127$	−3.17157	+	3.17157i	−0.281432	+	0.281432i	−0.833680	−	0.552248i	$-0.813770\pi$
$127$	−3.17157	+	3.17157i	−0.281432	+	0.281432i	0.552248	+	0.833680i	$0.313770\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	3.00000	−	0.514719i	0.264135	−	0.0453184i
$130$	−2.12132	+	0.707107i	−0.186052	+	0.0620174i
$131$			12.9706i			1.13324i	0.823978	+	0.566622i	$0.191750\pi$
$131$			12.9706i			1.13324i	−0.823978	+	0.566622i	$0.808250\pi$
$132$	4.00000	−	5.65685i	0.348155	−	0.492366i
$133$	4.00000	+	4.00000i	0.346844	+	0.346844i
$134$	−1.17157			−0.101208
$135$	0.535534	+	11.6066i	0.0460914	+	0.998937i
$136$	−4.24264			−0.363803
$137$	−15.0711	−	15.0711i	−1.28761	−	1.28761i	−0.936236	−	0.351372i	$-0.885715\pi$
$137$	−15.0711	−	15.0711i	−1.28761	−	1.28761i	−0.351372	−	0.936236i	$-0.614285\pi$
$138$	4.00000	−	5.65685i	0.340503	−	0.481543i
$139$		−	1.65685i		−	0.140533i	−0.997528	−	0.0702663i	$-0.977615\pi$
$139$		−	1.65685i		−	0.140533i	0.997528	−	0.0702663i	$-0.0223849\pi$
$140$	0.828427	−	1.65685i	0.0700149	−	0.140030i
$141$	5.41421	−	0.928932i	0.455959	−	0.0782302i
$142$	−10.0711	+	10.0711i	−0.845145	+	0.845145i
$143$	−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
$146$		−	15.6569i		−	1.29577i
$147$	8.92893	+	6.31371i	0.736446	+	0.520746i
$148$	−2.58579	−	2.58579i	−0.212550	−	0.212550i
$149$	−22.3848			−1.83383			−0.916916	−	0.399080i	$-0.869330\pi$
$149$	−22.3848			−1.83383			−0.916916	+	0.399080i	$0.869330\pi$
$150$	−5.94975	+	6.29289i	−0.485795	+	0.513813i
$151$	1.07107			0.0871623			0.0435811	−	0.999050i	$-0.486123\pi$
$151$	1.07107			0.0871623			0.0435811	+	0.999050i	$0.486123\pi$
$152$	−4.82843	−	4.82843i	−0.391637	−	0.391637i
$153$	5.48528	−	11.4853i	0.443459	−	0.928530i
$154$		−	3.31371i		−	0.267026i
$155$	−2.41421	−	7.24264i	−0.193914	−	0.581743i
$156$	−0.292893	−	1.70711i	−0.0234502	−	0.136678i
$157$	16.2426	−	16.2426i	1.29630	−	1.29630i	0.365488	−	0.930816i	$-0.380902\pi$
$157$	16.2426	−	16.2426i	1.29630	−	1.29630i	0.930816	−	0.365488i	$-0.119098\pi$
$158$	−8.82843	+	8.82843i	−0.702352	+	0.702352i
$159$	0.242641	+	1.41421i	0.0192427	+	0.112154i
$160$	−1.00000	+	2.00000i	−0.0790569	+	0.158114i
$161$		−	3.31371i		−	0.261157i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	2.34315	+	2.34315i	0.183529	+	0.183529i	0.792892	−	0.609362i	$-0.208575\pi$
$163$	2.34315	+	2.34315i	0.183529	+	0.183529i	−0.609362	+	0.792892i	$0.708575\pi$
$164$	2.00000			0.156174
$165$	−4.48528	+	14.8284i	−0.349179	+	1.15439i
$166$	9.65685			0.749517
$167$	−3.41421	−	3.41421i	−0.264200	−	0.264200i	0.562558	−	0.826758i	$-0.309817\pi$
$167$	−3.41421	−	3.41421i	−0.264200	−	0.264200i	−0.826758	+	0.562558i	$0.809817\pi$
$168$	1.17157	+	0.828427i	0.0903888	+	0.0639145i
$169$			1.00000i			0.0769231i
$170$	9.00000	−	3.00000i	0.690268	−	0.230089i
$171$	19.3137	−	6.82843i	1.47696	−	0.522183i
$172$	−1.24264	+	1.24264i	−0.0947505	+	0.0947505i
$173$	17.0711	−	17.0711i	1.29789	−	1.29789i	0.368105	−	0.929784i	$-0.380007\pi$
$173$	17.0711	−	17.0711i	1.29789	−	1.29789i	0.929784	−	0.368105i	$-0.119993\pi$
$174$	10.2426	−	1.75736i	0.776493	−	0.133225i
$175$	−0.585786	+	4.10051i	−0.0442813	+	0.309969i
$176$			4.00000i			0.301511i
$177$	−4.48528	+	6.34315i	−0.337134	+	0.476780i
$178$	−7.89949	−	7.89949i	−0.592092	−	0.592092i
$179$	17.6569			1.31974			0.659868	−	0.751382i	$-0.270612\pi$
$179$	17.6569			1.31974			0.659868	+	0.751382i	$0.270612\pi$
$180$	−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	$0.428419\pi$
$182$	−0.585786	−	0.585786i	−0.0434214	−	0.0434214i
$183$	4.82843	−	6.82843i	0.356928	−	0.504772i
$184$			4.00000i			0.294884i
$185$	7.31371	+	3.65685i	0.537715	+	0.268857i
$186$	5.82843	−	1.00000i	0.427361	−	0.0733236i
$187$	12.0000	−	12.0000i	0.877527	−	0.877527i
$188$	−2.24264	+	2.24264i	−0.163561	+	0.163561i
$189$	−3.75736	+	2.10051i	−0.273308	+	0.152789i
$190$	13.6569	+	6.82843i	0.990772	+	0.495386i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	−1.41421	−	1.00000i	−0.102062	−	0.0721688i
$193$	11.4142	+	11.4142i	0.821613	+	0.821613i	0.986339	−	0.164726i	$-0.0526741\pi$
$193$	11.4142	+	11.4142i	0.821613	+	0.821613i	−0.164726	+	0.986339i	$0.552674\pi$
$194$	12.8284			0.921027
$195$	1.82843	+	3.41421i	0.130936	+	0.244497i
$196$	−6.31371			−0.450979
$197$	−3.75736	−	3.75736i	−0.267701	−	0.267701i	0.560472	−	0.828173i	$-0.310620\pi$
$197$	−3.75736	−	3.75736i	−0.267701	−	0.267701i	−0.828173	+	0.560472i	$0.810620\pi$
$198$	−10.8284	−	5.17157i	−0.769543	−	0.367528i
$199$			22.1421i			1.56961i	0.619740	+	0.784807i	$0.287238\pi$
$199$			22.1421i			1.56961i	−0.619740	+	0.784807i	$0.712762\pi$
$200$	0.707107	−	4.94975i	0.0500000	−	0.350000i
$201$	0.343146	+	2.00000i	0.0242036	+	0.141069i
$202$	2.24264	−	2.24264i	0.157792	−	0.157792i
$203$	3.51472	−	3.51472i	0.246685	−	0.246685i
$204$	1.24264	+	7.24264i	0.0870023	+	0.507086i
$205$	−4.24264	+	1.41421i	−0.296319	+	0.0987730i
$206$			17.6569i			1.23021i
$207$	−10.8284	−	5.17157i	−0.752628	−	0.359449i
$208$	0.707107	+	0.707107i	0.0490290	+	0.0490290i
$209$	27.3137			1.88933
$210$	−3.07107	−	0.928932i	−0.211924	−	0.0641024i
$211$	1.65685			0.114063			0.0570313	−	0.998372i	$-0.481837\pi$
$211$	1.65685			0.114063			0.0570313	+	0.998372i	$0.481837\pi$
$212$	−0.585786	−	0.585786i	−0.0402320	−	0.0402320i
$213$	20.1421	+	14.2426i	1.38012	+	0.975890i
$214$		−	17.0711i		−	1.16695i
$215$	1.75736	−	3.51472i	0.119851	−	0.239702i
$216$	4.53553	−	2.53553i	0.308604	−	0.172521i
$217$	2.00000	−	2.00000i	0.135769	−	0.135769i
$218$	3.48528	−	3.48528i	0.236053	−	0.236053i
$219$	−26.7279	+	4.58579i	−1.80611	+	0.309879i
$220$	−2.82843	−	8.48528i	−0.190693	−	0.572078i
$221$		−	4.24264i		−	0.285391i
$222$	−3.65685	+	5.17157i	−0.245432	+	0.347093i
$223$	−9.65685	−	9.65685i	−0.646671	−	0.646671i	0.305516	−	0.952187i	$-0.401171\pi$
$223$	−9.65685	−	9.65685i	−0.646671	−	0.646671i	−0.952187	+	0.305516i	$0.901171\pi$
$224$	−0.828427			−0.0553516
$225$	12.4853	+	8.31371i	0.832352	+	0.554247i
$226$	−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	$0.779922\pi$
$228$	−6.82843	+	9.65685i	−0.452224	+	0.639541i
$229$		−	17.8995i		−	1.18283i	−0.806367	−	0.591416i	$-0.798569\pi$
$229$		−	17.8995i		−	1.18283i	0.806367	−	0.591416i	$-0.201431\pi$
$230$	−2.82843	−	8.48528i	−0.186501	−	0.559503i
$231$	−5.65685	+	0.970563i	−0.372194	+	0.0638583i
$232$	−4.24264	+	4.24264i	−0.278543	+	0.278543i
$233$	8.65685	−	8.65685i	0.567129	−	0.567129i	−0.364194	−	0.931323i	$-0.618655\pi$
$233$	8.65685	−	8.65685i	0.567129	−	0.567129i	0.931323	+	0.364194i	$0.118655\pi$
$234$	−2.82843	+	1.00000i	−0.184900	+	0.0653720i
$235$	3.17157	−	6.34315i	0.206891	−	0.413781i
$236$		−	4.48528i		−	0.291967i
$237$	17.6569	+	12.4853i	1.14694	+	0.811006i
$238$	2.48528	+	2.48528i	0.161097	+	0.161097i
$239$	19.8995			1.28719			0.643596	−	0.765366i	$-0.277442\pi$
$239$	19.8995			1.28719			0.643596	+	0.765366i	$0.277442\pi$
$240$	3.70711	+	1.12132i	0.239293	+	0.0723809i
$241$	−3.65685			−0.235559			−0.117779	−	0.993040i	$-0.537578\pi$
$241$	−3.65685			−0.235559			−0.117779	+	0.993040i	$0.537578\pi$
$242$	−3.53553	−	3.53553i	−0.227273	−	0.227273i
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$			4.82843i			0.309108i
$245$	13.3934	−	4.46447i	0.855673	−	0.285224i
$246$	−0.585786	−	3.41421i	−0.0373484	−	0.217682i
$247$	4.82843	−	4.82843i	0.307225	−	0.307225i
$248$	−2.41421	+	2.41421i	−0.153303	+	0.153303i
$249$	−2.82843	−	16.4853i	−0.179244	−	1.04471i
$250$	2.00000	+	11.0000i	0.126491	+	0.695701i
$251$			14.3431i			0.905331i	0.891680	+	0.452666i	$0.149527\pi$
$251$			14.3431i			0.905331i	−0.891680	+	0.452666i	$0.850473\pi$
$252$	1.07107	−	2.24264i	0.0674709	−	0.141273i
$253$	−11.3137	−	11.3137i	−0.711287	−	0.711287i
$254$	−4.48528			−0.281432
$255$	−7.75736	−	14.4853i	−0.485785	−	0.907104i
$256$	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	$0.849913\pi$
$258$	2.48528	+	1.75736i	0.154727	+	0.109408i
$259$			3.02944i			0.188240i
$260$	−2.00000	−	1.00000i	−0.124035	−	0.0620174i
$261$	−6.00000	−	16.9706i	−0.371391	−	1.05045i
$262$	−9.17157	+	9.17157i	−0.566622	+	0.566622i
$263$	−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	$0.495763\pi$
$264$	6.82843	−	1.17157i	0.420261	−	0.0721053i
$265$	1.65685	+	0.828427i	0.101780	+	0.0508899i
$266$			5.65685i			0.346844i
$267$	−11.1716	+	15.7990i	−0.683689	+	0.966882i
$268$	−0.828427	−	0.828427i	−0.0506042	−	0.0506042i
$269$	−15.1716			−0.925027			−0.462514	−	0.886612i	$-0.653052\pi$
$269$	−15.1716			−0.925027			−0.462514	+	0.886612i	$0.653052\pi$
$270$	−7.82843	+	8.58579i	−0.476423	+	0.522514i
$271$	−2.24264			−0.136231			−0.0681154	−	0.997677i	$-0.521699\pi$
$271$	−2.24264			−0.136231			−0.0681154	+	0.997677i	$0.521699\pi$
$272$	−3.00000	−	3.00000i	−0.181902	−	0.181902i
$273$	−0.828427	+	1.17157i	−0.0501387	+	0.0709068i
$274$		−	21.3137i		−	1.28761i
$275$	12.0000	+	16.0000i	0.723627	+	0.964836i
$276$	6.82843	−	1.17157i	0.411023	−	0.0705204i
$277$	−15.8995	+	15.8995i	−0.955308	+	0.955308i	−0.999043	−	0.0437351i	$-0.986074\pi$
$277$	−15.8995	+	15.8995i	−0.955308	+	0.955308i	0.0437351	+	0.999043i	$0.486074\pi$
$278$	1.17157	−	1.17157i	0.0702663	−	0.0702663i
$279$	−3.41421	−	9.65685i	−0.204404	−	0.578141i
$280$	1.75736	−	0.585786i	0.105022	−	0.0350074i
$281$		−	0.828427i		−	0.0494198i	−0.999695	−	0.0247099i	$-0.992134\pi$
$281$		−	0.828427i		−	0.0494198i	0.999695	−	0.0247099i	$-0.00786621\pi$
$282$	4.48528	+	3.17157i	0.267095	+	0.188864i
$283$	−17.2426	−	17.2426i	−1.02497	−	1.02497i	−0.999680	−	0.0252884i	$-0.991950\pi$
$283$	−17.2426	−	17.2426i	−1.02497	−	1.02497i	−0.0252884	−	0.999680i	$-0.508050\pi$
$284$	−14.2426			−0.845145
$285$	7.65685	−	25.3137i	0.453553	−	1.49945i
$286$	−4.00000			−0.236525
$287$	−1.17157	−	1.17157i	−0.0691558	−	0.0691558i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$			1.00000i			0.0588235i
$290$	6.00000	−	12.0000i	0.352332	−	0.704664i
$291$	−3.75736	−	21.8995i	−0.220260	−	1.28377i
$292$	11.0711	−	11.0711i	0.647885	−	0.647885i
$293$	4.48528	−	4.48528i	0.262033	−	0.262033i	−0.563847	−	0.825880i	$-0.690679\pi$
$293$	4.48528	−	4.48528i	0.262033	−	0.262033i	0.825880	+	0.563847i	$0.190679\pi$
$294$	1.84924	+	10.7782i	0.107850	+	0.628596i
$295$	3.17157	+	9.51472i	0.184656	+	0.553968i
$296$		−	3.65685i		−	0.212550i
$297$	−5.65685	+	20.0000i	−0.328244	+	1.16052i
$298$	−15.8284	−	15.8284i	−0.916916	−	0.916916i
$299$	−4.00000			−0.231326
$300$	−8.65685	+	0.242641i	−0.499804	+	0.0140089i
$301$	1.45584			0.0839135
$302$	0.757359	+	0.757359i	0.0435811	+	0.0435811i
$303$	−4.48528	−	3.17157i	−0.257673	−	0.182202i
$304$		−	6.82843i		−	0.391637i
$305$	−3.41421	−	10.2426i	−0.195497	−	0.586492i
$306$	12.0000	−	4.24264i	0.685994	−	0.242536i
$307$	7.17157	−	7.17157i	0.409303	−	0.409303i	−0.472192	−	0.881496i	$-0.656537\pi$
$307$	7.17157	−	7.17157i	0.409303	−	0.409303i	0.881496	+	0.472192i	$0.156537\pi$
$308$	2.34315	−	2.34315i	0.133513	−	0.133513i
$309$	30.1421	−	5.17157i	1.71473	−	0.294201i
$310$	3.41421	−	6.82843i	0.193914	−	0.387829i
$311$			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
$313$	1.34315	+	1.34315i	0.0759191	+	0.0759191i	0.744047	−	0.668128i	$-0.232904\pi$
$313$	1.34315	+	1.34315i	0.0759191	+	0.0759191i	−0.668128	+	0.744047i	$0.732904\pi$
$314$	22.9706			1.29630
$315$	−0.686292	+	5.51472i	−0.0386681	+	0.310719i
$316$	−12.4853			−0.702352
$317$	1.65685	+	1.65685i	0.0930582	+	0.0930582i	0.752103	−	0.659045i	$-0.229039\pi$
$317$	1.65685	+	1.65685i	0.0930582	+	0.0930582i	−0.659045	+	0.752103i	$0.729039\pi$
$318$	−0.828427	+	1.17157i	−0.0464559	+	0.0656985i
$319$		−	24.0000i		−	1.34374i
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$	−29.1421	+	5.00000i	−1.62656	+	0.279073i
$322$	2.34315	−	2.34315i	0.130578	−	0.130578i
$323$	−20.4853	+	20.4853i	−1.13983	+	1.13983i
$324$	−5.65685	−	7.00000i	−0.314270	−	0.388889i
$325$	4.94975	+	0.707107i	0.274563	+	0.0392232i
$326$			3.31371i			0.183529i
$327$	−6.97056	−	4.92893i	−0.385473	−	0.272571i
$328$	1.41421	+	1.41421i	0.0780869	+	0.0780869i
$329$	2.62742			0.144854
$330$	−13.6569	+	7.31371i	−0.751785	+	0.402606i
$331$	−32.2843			−1.77450			−0.887252	−	0.461285i	$-0.847389\pi$
$331$	−32.2843			−1.77450			−0.887252	+	0.461285i	$0.847389\pi$
$332$	6.82843	+	6.82843i	0.374759	+	0.374759i
$333$	9.89949	+	4.72792i	0.542489	+	0.259089i
$334$		−	4.82843i		−	0.264200i
$335$	2.34315	+	1.17157i	0.128020	+	0.0640099i
$336$	0.242641	+	1.41421i	0.0132371	+	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
$339$	2.89949	+	16.8995i	0.157479	+	0.917855i
$340$	8.48528	+	4.24264i	0.460179	+	0.230089i
$341$		−	13.6569i		−	0.739560i
$342$	18.4853	+	8.82843i	0.999570	+	0.477387i
$343$	7.79899	+	7.79899i	0.421106	+	0.421106i
$344$	−1.75736			−0.0947505
$345$	−13.6569	+	7.31371i	−0.735260	+	0.393757i
$346$	24.1421			1.29789
$347$	−10.5563	−	10.5563i	−0.566695	−	0.566695i	0.364506	−	0.931201i	$-0.381238\pi$
$347$	−10.5563	−	10.5563i	−0.566695	−	0.566695i	−0.931201	+	0.364506i	$0.881238\pi$
$348$	8.48528	+	6.00000i	0.454859	+	0.321634i
$349$		−	32.7279i		−	1.75189i	−0.482415	−	0.875943i	$-0.660240\pi$
$349$		−	32.7279i		−	1.75189i	0.482415	−	0.875943i	$-0.339760\pi$
$350$	−3.31371	+	2.48528i	−0.177125	+	0.132844i
$351$	2.53553	+	4.53553i	0.135337	+	0.242089i
$352$	−2.82843	+	2.82843i	−0.150756	+	0.150756i
$353$	−25.5563	+	25.5563i	−1.36023	+	1.36023i	−0.486605	+	0.873622i	$0.661765\pi$
$353$	−25.5563	+	25.5563i	−1.36023	+	1.36023i	−0.873622	+	0.486605i	$0.838235\pi$
$354$	−7.65685	+	1.31371i	−0.406957	+	0.0698228i
$355$	30.2132	−	10.0711i	1.60355	−	0.534517i
$356$		−	11.1716i		−	0.592092i
$357$	3.51472	−	4.97056i	0.186019	−	0.263070i
$358$	12.4853	+	12.4853i	0.659868	+	0.659868i
$359$	−23.4142			−1.23575			−0.617877	−	0.786274i	$-0.712007\pi$
$359$	−23.4142			−1.23575			−0.617877	+	0.786274i	$0.712007\pi$
$360$	0.828427	−	6.65685i	0.0436619	−	0.350847i
$361$	−27.6274			−1.45407
$362$	4.24264	+	4.24264i	0.222988	+	0.222988i
$363$	−5.00000	+	7.07107i	−0.262432	+	0.371135i
$364$		−	0.828427i		−	0.0434214i
$365$	−15.6569	+	31.3137i	−0.819517	+	1.63903i
$366$	8.24264	−	1.41421i	0.430850	−	0.0739221i
$367$	14.1421	−	14.1421i	0.738213	−	0.738213i	−0.234019	−	0.972232i	$-0.575188\pi$
$367$	14.1421	−	14.1421i	0.738213	−	0.738213i	0.972232	+	0.234019i	$0.0751877\pi$
$368$	−2.82843	+	2.82843i	−0.147442	+	0.147442i
$369$	−5.65685	+	2.00000i	−0.294484	+	0.104116i
$370$	2.58579	+	7.75736i	0.134429	+	0.403286i
$371$			0.686292i			0.0356305i
$372$	4.82843	+	3.41421i	0.250342	+	0.177019i
$373$	4.92893	+	4.92893i	0.255210	+	0.255210i	0.823103	−	0.567892i	$-0.192241\pi$
$373$	4.92893	+	4.92893i	0.255210	+	0.255210i	−0.567892	+	0.823103i	$0.692241\pi$
$374$	16.9706			0.877527
$375$	18.1924	−	6.63604i	0.939451	−	0.342684i
$376$	−3.17157			−0.163561
$377$	−4.24264	−	4.24264i	−0.218507	−	0.218507i
$378$	−4.14214	−	1.17157i	−0.213048	−	0.0602592i
$379$			38.1421i			1.95923i	0.200884	+	0.979615i	$0.435618\pi$
$379$			38.1421i			1.95923i	−0.200884	+	0.979615i	$0.564382\pi$
$380$	4.82843	+	14.4853i	0.247693	+	0.743079i
$381$	1.31371	+	7.65685i	0.0673033	+	0.392273i
$382$	−2.00000	+	2.00000i	−0.102329	+	0.102329i
$383$	−1.65685	+	1.65685i	−0.0846613	+	0.0846613i	−0.748169	−	0.663508i	$-0.769067\pi$
$383$	−1.65685	+	1.65685i	−0.0846613	+	0.0846613i	0.663508	+	0.748169i	$0.269067\pi$
$384$	−0.292893	−	1.70711i	−0.0149466	−	0.0871154i
$385$	−3.31371	+	6.62742i	−0.168882	+	0.337764i
$386$			16.1421i			0.821613i
$387$	2.27208	−	4.75736i	0.115496	−	0.241830i
$388$	9.07107	+	9.07107i	0.460514	+	0.460514i
$389$	2.00000			0.101404			0.0507020	−	0.998714i	$-0.483854\pi$
$389$	2.00000			0.101404			0.0507020	+	0.998714i	$0.483854\pi$
$390$	−1.12132	+	3.70711i	−0.0567803	+	0.187717i
$391$	16.9706			0.858238
$392$	−4.46447	−	4.46447i	−0.225490	−	0.225490i
$393$	18.3431	+	12.9706i	0.925289	+	0.654278i
$394$		−	5.31371i		−	0.267701i
$395$	26.4853	−	8.82843i	1.33262	−	0.444206i
$396$	−4.00000	−	11.3137i	−0.201008	−	0.568535i
$397$	−9.17157	+	9.17157i	−0.460308	+	0.460308i	−0.898756	−	0.438448i	$-0.855528\pi$
$397$	−9.17157	+	9.17157i	−0.460308	+	0.460308i	0.438448	+	0.898756i	$0.355528\pi$
$398$	−15.6569	+	15.6569i	−0.784807	+	0.784807i
$399$	9.65685	−	1.65685i	0.483447	−	0.0829465i
$400$	4.00000	−	3.00000i	0.200000	−	0.150000i
$401$		−	1.79899i		−	0.0898373i	−0.998991	−	0.0449186i	$-0.985697\pi$
$401$		−	1.79899i		−	0.0898373i	0.998991	−	0.0449186i	$-0.0143029\pi$
$402$	−1.17157	+	1.65685i	−0.0584327	+	0.0826364i
$403$	−2.41421	−	2.41421i	−0.120261	−	0.120261i
$404$	3.17157			0.157792
$405$	16.9497	+	10.8492i	0.842240	+	0.539103i
$406$	4.97056			0.246685
$407$	10.3431	+	10.3431i	0.512691	+	0.512691i
$408$	−4.24264	+	6.00000i	−0.210042	+	0.297044i
$409$			3.17157i			0.156824i	0.996921	+	0.0784121i	$0.0249850\pi$
$409$			3.17157i			0.156824i	−0.996921	+	0.0784121i	$0.975015\pi$
$410$	−4.00000	−	2.00000i	−0.197546	−	0.0987730i
$411$	−36.3848	+	6.24264i	−1.79473	+	0.307927i
$412$	−12.4853	+	12.4853i	−0.615106	+	0.615106i
$413$	−2.62742	+	2.62742i	−0.129287	+	0.129287i
$414$	−4.00000	−	11.3137i	−0.196589	−	0.556038i
$415$	−19.3137	−	9.65685i	−0.948073	−	0.474036i
$416$			1.00000i			0.0490290i
$417$	−2.34315	−	1.65685i	−0.114744	−	0.0811365i
$418$	19.3137	+	19.3137i	0.944664	+	0.944664i
$419$	5.51472			0.269412			0.134706	−	0.990886i	$-0.456991\pi$
$419$	5.51472			0.269412			0.134706	+	0.990886i	$0.456991\pi$
$420$	−1.51472	−	2.82843i	−0.0739107	−	0.138013i
$421$	27.0711			1.31936			0.659682	−	0.751545i	$-0.270691\pi$
$421$	27.0711			1.31936			0.659682	+	0.751545i	$0.270691\pi$
$422$	1.17157	+	1.17157i	0.0570313	+	0.0570313i
$423$	4.10051	−	8.58579i	0.199373	−	0.417455i
$424$		−	0.828427i		−	0.0402320i
$425$	−21.0000	−	3.00000i	−1.01865	−	0.145521i
$426$	4.17157	+	24.3137i	0.202113	+	1.17800i
$427$	2.82843	−	2.82843i	0.136877	−	0.136877i
$428$	12.0711	−	12.0711i	0.583477	−	0.583477i
$429$	1.17157	+	6.82843i	0.0565641	+	0.329680i
$430$	3.72792	−	1.24264i	0.179776	−	0.0599255i
$431$		−	10.9289i		−	0.526428i	−0.964737	−	0.263214i	$-0.915217\pi$
$431$		−	10.9289i		−	0.526428i	0.964737	−	0.263214i	$-0.0847826\pi$
$432$	5.00000	+	1.41421i	0.240563	+	0.0680414i
$433$	−16.3137	−	16.3137i	−0.783987	−	0.783987i	0.196514	−	0.980501i	$-0.437038\pi$
$433$	−16.3137	−	16.3137i	−0.783987	−	0.783987i	−0.980501	+	0.196514i	$0.937038\pi$
$434$	2.82843			0.135769
$435$	−22.2426	−	6.72792i	−1.06645	−	0.322579i
$436$	4.92893			0.236053
$437$	19.3137	+	19.3137i	0.923900	+	0.923900i
$438$	−22.1421	−	15.6569i	−1.05799	−	0.748113i
$439$		−	18.3431i		−	0.875471i	−0.899104	−	0.437735i	$-0.855781\pi$
$439$		−	18.3431i		−	0.875471i	0.899104	−	0.437735i	$-0.144219\pi$
$440$	4.00000	−	8.00000i	0.190693	−	0.381385i
$441$	17.8579	−	6.31371i	0.850374	−	0.300653i
$442$	3.00000	−	3.00000i	0.142695	−	0.142695i
$443$	0.899495	−	0.899495i	0.0427363	−	0.0427363i	−0.685416	−	0.728152i	$-0.740379\pi$
$443$	0.899495	−	0.899495i	0.0427363	−	0.0427363i	0.728152	+	0.685416i	$0.240379\pi$
$444$	−6.24264	+	1.07107i	−0.296263	+	0.0508306i
$445$	7.89949	+	23.6985i	0.374472	+	1.12342i
$446$		−	13.6569i		−	0.646671i
$447$	−22.3848	+	31.6569i	−1.05876	+	1.49732i
$448$	−0.585786	−	0.585786i	−0.0276758	−	0.0276758i
$449$	−17.7990			−0.839986			−0.419993	−	0.907527i	$-0.637968\pi$
$449$	−17.7990			−0.839986			−0.419993	+	0.907527i	$0.637968\pi$
$450$	2.94975	+	14.7071i	0.139052	+	0.693300i
$451$	−8.00000			−0.376705
$452$	−7.00000	−	7.00000i	−0.329252	−	0.329252i
$453$	1.07107	−	1.51472i	0.0503232	−	0.0711677i
$454$		−	2.82843i		−	0.132745i
$455$	0.585786	+	1.75736i	0.0274621	+	0.0823863i
$456$	−11.6569	+	2.00000i	−0.545882	+	0.0936586i
$457$	−21.0711	+	21.0711i	−0.985663	+	0.985663i	−0.999899	−	0.0142357i	$-0.995468\pi$
$457$	−21.0711	+	21.0711i	−0.985663	+	0.985663i	0.0142357	+	0.999899i	$0.495468\pi$
$458$	12.6569	−	12.6569i	0.591416	−	0.591416i
$459$	−10.7574	−	19.2426i	−0.502111	−	0.898170i
$460$	4.00000	−	8.00000i	0.186501	−	0.373002i
$461$			21.6985i			1.01060i	0.862944	+	0.505300i	$0.168618\pi$
$461$			21.6985i			1.01060i	−0.862944	+	0.505300i	$0.831382\pi$
$462$	−4.68629	−	3.31371i	−0.218026	−	0.154168i
$463$	5.65685	+	5.65685i	0.262896	+	0.262896i	0.826230	−	0.563333i	$-0.190481\pi$
$463$	5.65685	+	5.65685i	0.262896	+	0.262896i	−0.563333	+	0.826230i	$0.690481\pi$
$464$	−6.00000			−0.278543
$465$	−12.6569	−	3.82843i	−0.586948	−	0.177539i
$466$	12.2426			0.567129
$467$	−16.8995	−	16.8995i	−0.782015	−	0.782015i	0.198155	−	0.980171i	$-0.436505\pi$
$467$	−16.8995	−	16.8995i	−0.782015	−	0.782015i	−0.980171	+	0.198155i	$0.936505\pi$
$468$	−2.70711	−	1.29289i	−0.125136	−	0.0597640i
$469$			0.970563i			0.0448164i
$470$	6.72792	−	2.24264i	0.310336	−	0.103445i
$471$	−6.72792	−	39.2132i	−0.310006	−	1.80685i
$472$	3.17157	−	3.17157i	0.145983	−	0.145983i
$473$	4.97056	−	4.97056i	0.228547	−	0.228547i
$474$	3.65685	+	21.3137i	0.167965	+	0.978971i
$475$	−20.4853	−	27.3137i	−0.939929	−	1.25324i
$476$			3.51472i			0.161097i
$477$	2.24264	+	1.07107i	0.102683	+	0.0490408i
$478$	14.0711	+	14.0711i	0.643596	+	0.643596i
$479$	24.3848			1.11417			0.557084	−	0.830456i	$-0.311920\pi$
$479$	24.3848			1.11417			0.557084	+	0.830456i	$0.311920\pi$
$480$	1.82843	+	3.41421i	0.0834559	+	0.155837i
$481$	3.65685			0.166738
$482$	−2.58579	−	2.58579i	−0.117779	−	0.117779i
$483$	−4.68629	−	3.31371i	−0.213234	−	0.150779i
$484$		−	5.00000i		−	0.227273i
$485$	−25.6569	−	12.8284i	−1.16502	−	0.582509i
$486$	−10.2929	+	11.7071i	−0.466895	+	0.531045i
$487$	2.92893	−	2.92893i	0.132723	−	0.132723i	−0.637625	−	0.770347i	$-0.720083\pi$
$487$	2.92893	−	2.92893i	0.132723	−	0.132723i	0.770347	+	0.637625i	$0.220083\pi$
$488$	−3.41421	+	3.41421i	−0.154554	+	0.154554i
$489$	5.65685	−	0.970563i	0.255812	−	0.0438904i
$490$	12.6274	+	6.31371i	0.570449	+	0.285224i
$491$		−	13.7990i		−	0.622740i	−0.950289	−	0.311370i	$-0.899212\pi$
$491$		−	13.7990i		−	0.622740i	0.950289	−	0.311370i	$-0.100788\pi$
$492$	2.00000	−	2.82843i	0.0901670	−	0.127515i
$493$	18.0000	+	18.0000i	0.810679	+	0.810679i
$494$	6.82843			0.307225
$495$	16.4853	+	21.1716i	0.740958	+	0.951591i
$496$	−3.41421			−0.153303
$497$	8.34315	+	8.34315i	0.374241	+	0.374241i
$498$	9.65685	−	13.6569i	0.432734	−	0.611978i
$499$			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
$501$	−8.24264	+	1.41421i	−0.368254	+	0.0631824i
$502$	−10.1421	+	10.1421i	−0.452666	+	0.452666i
$503$	16.1421	−	16.1421i	0.719742	−	0.719742i	−0.248810	−	0.968552i	$-0.580039\pi$
$503$	16.1421	−	16.1421i	0.719742	−	0.719742i	0.968552	+	0.248810i	$0.0800395\pi$
$504$	2.34315	−	0.828427i	0.104372	−	0.0369011i
$505$	−6.72792	+	2.24264i	−0.299389	+	0.0997962i
$506$		−	16.0000i		−	0.711287i
$507$	1.41421	+	1.00000i	0.0628074	+	0.0444116i
$508$	−3.17157	−	3.17157i	−0.140716	−	0.140716i
$509$	−41.2132			−1.82674			−0.913372	−	0.407127i	$-0.866531\pi$
$509$	−41.2132			−1.82674			−0.913372	+	0.407127i	$0.866531\pi$
$510$	4.75736	−	15.7279i	0.210659	−	0.696444i
$511$	−12.9706			−0.573784
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	9.65685	−	34.1421i	0.426361	−	1.50741i
$514$		−	9.89949i		−	0.436648i
$515$	17.6569	−	35.3137i	0.778054	−	1.55611i
$516$	0.514719	+	3.00000i	0.0226592	+	0.132068i
$517$	8.97056	−	8.97056i	0.394525	−	0.394525i
$518$	−2.14214	+	2.14214i	−0.0941200	+	0.0941200i
$519$	−7.07107	−	41.2132i	−0.310385	−	1.80906i
$520$	−0.707107	−	2.12132i	−0.0310087	−	0.0930261i
$521$		−	24.9706i		−	1.09398i	−0.837139	−	0.546990i	$-0.815774\pi$
$521$		−	24.9706i		−	1.09398i	0.837139	−	0.546990i	$-0.184226\pi$
$522$	7.75736	−	16.2426i	0.339530	−	0.710921i
$523$	−6.07107	−	6.07107i	−0.265469	−	0.265469i	0.561802	−	0.827272i	$-0.310108\pi$
$523$	−6.07107	−	6.07107i	−0.265469	−	0.265469i	−0.827272	+	0.561802i	$0.810108\pi$
$524$	−12.9706			−0.566622
$525$	5.21320	+	4.92893i	0.227523	+	0.215116i
$526$	−22.6274			−0.986602
$527$	10.2426	+	10.2426i	0.446176	+	0.446176i
$528$	5.65685	+	4.00000i	0.246183	+	0.174078i
$529$			7.00000i			0.304348i
$530$	0.585786	+	1.75736i	0.0254449	+	0.0763348i
$531$	4.48528	+	12.6863i	0.194645	+	0.550538i
$532$	−4.00000	+	4.00000i	−0.173422	+	0.173422i
$533$	−1.41421	+	1.41421i	−0.0612564	+	0.0612564i
$534$	−19.0711	+	3.27208i	−0.825286	+	0.141597i
$535$	−17.0711	+	34.1421i	−0.738047	+	1.47609i
$536$		−	1.17157i		−	0.0506042i
$537$	17.6569	−	24.9706i	0.761950	−	1.07756i
$538$	−10.7279	−	10.7279i	−0.462514	−	0.462514i
$539$	25.2548			1.08780
$540$	−11.6066	+	0.535534i	−0.499469	+	0.0230457i
$541$	−4.24264			−0.182405			−0.0912027	−	0.995832i	$-0.529071\pi$
$541$	−4.24264			−0.182405			−0.0912027	+	0.995832i	$0.529071\pi$
$542$	−1.58579	−	1.58579i	−0.0681154	−	0.0681154i
$543$	6.00000	−	8.48528i	0.257485	−	0.364138i
$544$		−	4.24264i		−	0.181902i
$545$	−10.4558	+	3.48528i	−0.447879	+	0.149293i
$546$	−1.41421	+	0.242641i	−0.0605228	+	0.0103841i
$547$	−20.4142	+	20.4142i	−0.872849	+	0.872849i	−0.992782	−	0.119933i	$-0.961732\pi$
$547$	−20.4142	+	20.4142i	−0.872849	+	0.872849i	0.119933	+	0.992782i	$0.461732\pi$
$548$	15.0711	−	15.0711i	0.643804	−	0.643804i
$549$	−4.82843	−	13.6569i	−0.206072	−	0.582860i
$550$	−2.82843	+	19.7990i	−0.120605	+	0.844232i
$551$			40.9706i			1.74540i
$552$	5.65685	+	4.00000i	0.240772	+	0.170251i
$553$	7.31371	+	7.31371i	0.311011	+	0.311011i
$554$	−22.4853			−0.955308
$555$	12.4853	−	6.68629i	0.529971	−	0.283817i
$556$	1.65685			0.0702663
$557$	−0.928932	−	0.928932i	−0.0393601	−	0.0393601i	0.687153	−	0.726513i	$-0.258860\pi$
$557$	−0.928932	−	0.928932i	−0.0393601	−	0.0393601i	−0.726513	+	0.687153i	$0.758860\pi$
$558$	4.41421	−	9.24264i	0.186869	−	0.391272i
$559$		−	1.75736i		−	0.0743284i
$560$	1.65685	+	0.828427i	0.0700149	+	0.0350074i
$561$	−4.97056	−	28.9706i	−0.209857	−	1.22314i
$562$	0.585786	−	0.585786i	0.0247099	−	0.0247099i
$563$	19.2426	−	19.2426i	0.810981	−	0.810981i	−0.173800	−	0.984781i	$-0.555605\pi$
$563$	19.2426	−	19.2426i	0.810981	−	0.810981i	0.984781	+	0.173800i	$0.0556047\pi$
$564$	0.928932	+	5.41421i	0.0391151	+	0.227980i
$565$	19.7990	+	9.89949i	0.832950	+	0.416475i
$566$		−	24.3848i		−	1.02497i
$567$	−0.786797	+	7.41421i	−0.0330423	+	0.311368i
$568$	−10.0711	−	10.0711i	−0.422573	−	0.422573i
$569$	18.3431			0.768985			0.384492	−	0.923128i	$-0.374377\pi$
$569$	18.3431			0.768985			0.384492	+	0.923128i	$0.374377\pi$
$570$	23.3137	−	12.4853i	0.976504	−	0.522951i
$571$	34.4853			1.44316			0.721582	−	0.692329i	$-0.243415\pi$
$571$	34.4853			1.44316			0.721582	+	0.692329i	$0.243415\pi$
$572$	−2.82843	−	2.82843i	−0.118262	−	0.118262i
$573$	4.00000	+	2.82843i	0.167102	+	0.118159i
$574$		−	1.65685i		−	0.0691558i
$575$	−2.82843	+	19.7990i	−0.117954	+	0.825675i
$576$	−2.82843	+	1.00000i	−0.117851	+	0.0416667i
$577$	−16.0416	+	16.0416i	−0.667822	+	0.667822i	−0.957211	−	0.289390i	$-0.906548\pi$
$577$	−16.0416	+	16.0416i	−0.667822	+	0.667822i	0.289390	+	0.957211i	$0.406548\pi$
$578$	−0.707107	+	0.707107i	−0.0294118	+	0.0294118i
$579$	27.5563	−	4.72792i	1.14520	−	0.196486i
$580$	12.7279	−	4.24264i	0.528498	−	0.176166i
$581$		−	8.00000i		−	0.331896i
$582$	12.8284	−	18.1421i	0.531755	−	0.752016i
$583$	2.34315	+	2.34315i	0.0970432	+	0.0970432i
$584$	15.6569			0.647885
$585$	6.65685	+	0.828427i	0.275227	+	0.0342512i
$586$	6.34315			0.262033
$587$	7.79899	+	7.79899i	0.321899	+	0.321899i	0.849495	−	0.527596i	$-0.176907\pi$
$587$	7.79899	+	7.79899i	0.321899	+	0.321899i	−0.527596	+	0.849495i	$0.676907\pi$
$588$	−6.31371	+	8.92893i	−0.260373	+	0.368223i
$589$			23.3137i			0.960625i
$590$	−4.48528	+	8.97056i	−0.184656	+	0.369312i
$591$	−9.07107	+	1.55635i	−0.373134	+	0.0640197i
$592$	2.58579	−	2.58579i	0.106275	−	0.106275i
$593$	−7.41421	+	7.41421i	−0.304465	+	0.304465i	−0.842758	−	0.538293i	$-0.819069\pi$
$593$	−7.41421	+	7.41421i	−0.304465	+	0.304465i	0.538293	+	0.842758i	$0.319069\pi$
$594$	−18.1421	+	10.1421i	−0.744381	+	0.416137i
$595$	−2.48528	−	7.45584i	−0.101887	−	0.305660i
$596$		−	22.3848i		−	0.916916i
$597$	31.3137	+	22.1421i	1.28158	+	0.906217i
$598$	−2.82843	−	2.82843i	−0.115663	−	0.115663i
$599$	−16.4853			−0.673570			−0.336785	−	0.941582i	$-0.609340\pi$
$599$	−16.4853			−0.673570			−0.336785	+	0.941582i	$0.609340\pi$
$600$	−6.29289	−	5.94975i	−0.256906	−	0.242897i
$601$	−17.6569			−0.720238			−0.360119	−	0.932906i	$-0.617264\pi$
$601$	−17.6569			−0.720238			−0.360119	+	0.932906i	$0.617264\pi$
$602$	1.02944	+	1.02944i	0.0419567	+	0.0419567i
$603$	3.17157	+	1.51472i	0.129156	+	0.0616841i
$604$			1.07107i			0.0435811i
$605$	3.53553	+	10.6066i	0.143740	+	0.431220i
$606$	−0.928932	−	5.41421i	−0.0377353	−	0.219937i
$607$	14.4853	−	14.4853i	0.587939	−	0.587939i	−0.349134	−	0.937073i	$-0.613524\pi$
$607$	14.4853	−	14.4853i	0.587939	−	0.587939i	0.937073	+	0.349134i	$0.113524\pi$
$608$	4.82843	−	4.82843i	0.195819	−	0.195819i
$609$	−1.45584	−	8.48528i	−0.0589938	−	0.343841i
$610$	4.82843	−	9.65685i	0.195497	−	0.390995i
$611$		−	3.17157i		−	0.128308i
$612$	11.4853	+	5.48528i	0.464265	+	0.221729i
$613$	10.3431	+	10.3431i	0.417756	+	0.417756i	0.884430	−	0.466674i	$-0.154548\pi$
$613$	10.3431	+	10.3431i	0.417756	+	0.417756i	−0.466674	+	0.884430i	$0.654548\pi$
$614$	10.1421			0.409303
$615$	−2.24264	+	7.41421i	−0.0904320	+	0.298970i
$616$	3.31371			0.133513
$617$	10.9289	+	10.9289i	0.439982	+	0.439982i	0.892006	−	0.452024i	$-0.149298\pi$
$617$	10.9289	+	10.9289i	0.439982	+	0.439982i	−0.452024	+	0.892006i	$0.649298\pi$
$618$	24.9706	+	17.6569i	1.00446	+	0.710263i
$619$		−	26.6274i		−	1.07025i	−0.844774	−	0.535123i	$-0.820265\pi$
$619$		−	26.6274i		−	1.07025i	0.844774	−	0.535123i	$-0.179735\pi$
$620$	7.24264	−	2.41421i	0.290871	−	0.0969571i
$621$	−18.1421	+	10.1421i	−0.728019	+	0.406990i
$622$	−19.7990	+	19.7990i	−0.793867	+	0.793867i
$623$	−6.54416	+	6.54416i	−0.262186	+	0.262186i
$624$	1.70711	−	0.292893i	0.0683390	−	0.0117251i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$			1.89949i			0.0759191i
$627$	27.3137	−	38.6274i	1.09080	−	1.54263i
$628$	16.2426	+	16.2426i	0.648152	+	0.648152i
$629$	−15.5147			−0.618612
$630$	−4.38478	+	3.41421i	−0.174694	+	0.136026i
$631$	23.8995			0.951424			0.475712	−	0.879601i	$-0.342190\pi$
$631$	23.8995			0.951424			0.475712	+	0.879601i	$0.342190\pi$
$632$	−8.82843	−	8.82843i	−0.351176	−	0.351176i
$633$	1.65685	−	2.34315i	0.0658540	−	0.0931317i
$634$			2.34315i			0.0930582i
$635$	8.97056	+	4.48528i	0.355986	+	0.177993i
$636$	−1.41421	+	0.242641i	−0.0560772	+	0.00962133i
$637$	4.46447	−	4.46447i	0.176889	−	0.176889i
$638$	16.9706	−	16.9706i	0.671871	−	0.671871i
$639$	40.2843	−	14.2426i	1.59362	−	0.563430i
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$		−	10.6863i		−	0.422083i	−0.977477	−	0.211042i	$-0.932314\pi$
$641$		−	10.6863i		−	0.422083i	0.977477	−	0.211042i	$-0.0676855\pi$
$642$	−24.1421	−	17.0711i	−0.952814	−	0.673741i
$643$	22.1421	+	22.1421i	0.873201	+	0.873201i	0.992820	−	0.119619i	$-0.0381674\pi$
$643$	22.1421	+	22.1421i	0.873201	+	0.873201i	−0.119619	+	0.992820i	$0.538167\pi$
$644$	3.31371			0.130578
$645$	−3.21320	−	6.00000i	−0.126520	−	0.236250i
$646$	−28.9706			−1.13983
$647$	−29.3137	−	29.3137i	−1.15244	−	1.15244i	−0.986062	−	0.166379i	$-0.946793\pi$
$647$	−29.3137	−	29.3137i	−1.15244	−	1.15244i	−0.166379	−	0.986062i	$-0.553207\pi$
$648$	0.949747	−	8.94975i	0.0373096	−	0.351579i
$649$			17.9411i			0.704251i
$650$	3.00000	+	4.00000i	0.117670	+	0.156893i
$651$	−0.828427	−	4.82843i	−0.0324686	−	0.189241i
$652$	−2.34315	+	2.34315i	−0.0917647	+	0.0917647i
$653$	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	$0.212544\pi$
$654$	−1.44365	−	8.41421i	−0.0564512	−	0.329022i
$655$	27.5147	−	9.17157i	1.07509	−	0.358363i
$656$			2.00000i			0.0780869i
$657$	−20.2426	+	42.3848i	−0.789741	+	1.65359i
$658$	1.85786	+	1.85786i	0.0724271	+	0.0724271i
$659$	25.5147			0.993912			0.496956	−	0.867776i	$-0.334451\pi$
$659$	25.5147			0.993912			0.496956	+	0.867776i	$0.334451\pi$
$660$	−14.8284	−	4.48528i	−0.577196	−	0.174589i
$661$	48.5269			1.88748			0.943739	−	0.330691i	$-0.107282\pi$
$661$	48.5269			1.88748			0.943739	+	0.330691i	$0.107282\pi$
$662$	−22.8284	−	22.8284i	−0.887252	−	0.887252i
$663$	−6.00000	−	4.24264i	−0.233021	−	0.164771i
$664$			9.65685i			0.374759i
$665$	5.65685	−	11.3137i	0.219363	−	0.438727i
$666$	3.65685	+	10.3431i	0.141700	+	0.400789i
$667$	16.9706	−	16.9706i	0.657103	−	0.657103i
$668$	3.41421	−	3.41421i	0.132100	−	0.132100i
$669$	−23.3137	+	4.00000i	−0.901360	+	0.154649i
$670$	0.828427	+	2.48528i	0.0320049	+	0.0960148i
$671$		−	19.3137i		−	0.745597i
$672$	−0.828427	+	1.17157i	−0.0319573	+	0.0451944i
$673$	−2.85786	−	2.85786i	−0.110163	−	0.110163i	0.649877	−	0.760039i	$-0.274820\pi$
$673$	−2.85786	−	2.85786i	−0.110163	−	0.110163i	−0.760039	+	0.649877i	$0.774820\pi$
$674$	−32.5269			−1.25289
$675$	24.2426	−	9.34315i	0.933100	−	0.359618i
$676$	−1.00000			−0.0384615
$677$	−10.3848	−	10.3848i	−0.399119	−	0.399119i	0.478803	−	0.877922i	$-0.341071\pi$
$677$	−10.3848	−	10.3848i	−0.399119	−	0.399119i	−0.877922	+	0.478803i	$0.841071\pi$
$678$	−9.89949	+	14.0000i	−0.380188	+	0.537667i
$679$		−	10.6274i		−	0.407843i
$680$	3.00000	+	9.00000i	0.115045	+	0.345134i
$681$	−4.82843	+	0.828427i	−0.185026	+	0.0317454i
$682$	9.65685	−	9.65685i	0.369780	−	0.369780i
$683$	−8.82843	+	8.82843i	−0.337810	+	0.337810i	−0.855543	−	0.517732i	$-0.826776\pi$
$683$	−8.82843	+	8.82843i	−0.337810	+	0.337810i	0.517732	+	0.855543i	$0.326776\pi$
$684$	6.82843	+	19.3137i	0.261091	+	0.738478i
$685$	−21.3137	+	42.6274i	−0.814355	+	1.62871i
$686$			11.0294i			0.421106i
$687$	−25.3137	−	17.8995i	−0.965778	−	0.682908i
$688$	−1.24264	−	1.24264i	−0.0473752	−	0.0473752i
$689$	0.828427			0.0315606
$690$	−14.8284	−	4.48528i	−0.564509	−	0.170752i
$691$	−37.6569			−1.43253			−0.716267	−	0.697826i	$-0.754151\pi$
$691$	−37.6569			−1.43253			−0.716267	+	0.697826i	$0.754151\pi$
$692$	17.0711	+	17.0711i	0.648945	+	0.648945i
$693$	−4.28427	+	8.97056i	−0.162746	+	0.340764i
$694$		−	14.9289i		−	0.566695i
$695$	−3.51472	+	1.17157i	−0.133321	+	0.0444403i
$696$	1.75736	+	10.2426i	0.0666125	+	0.388246i
$697$	6.00000	−	6.00000i	0.227266	−	0.227266i
$698$	23.1421	−	23.1421i	0.875943	−	0.875943i
$699$	−3.58579	−	20.8995i	−0.135627	−	0.790491i
$700$	−4.10051	−	0.585786i	−0.154985	−	0.0221406i
$701$			35.4558i			1.33915i	0.742745	+	0.669574i	$0.233523\pi$
$701$			35.4558i			1.33915i	−0.742745	+	0.669574i	$0.766477\pi$
$702$	−1.41421	+	5.00000i	−0.0533761	+	0.188713i
$703$	−17.6569	−	17.6569i	−0.665941	−	0.665941i
$704$	−4.00000			−0.150756
$705$	−5.79899	−	10.8284i	−0.218403	−	0.407822i
$706$	−36.1421			−1.36023
$707$	−1.85786	−	1.85786i	−0.0698722	−	0.0698722i
$708$	−6.34315	−	4.48528i	−0.238390	−	0.168567i
$709$		−	3.27208i		−	0.122885i	−0.998111	−	0.0614427i	$-0.980430\pi$
$709$		−	3.27208i		−	0.122885i	0.998111	−	0.0614427i	$-0.0195702\pi$
$710$	28.4853	+	14.2426i	1.06903	+	0.534517i
$711$	35.3137	−	12.4853i	1.32437	−	0.468235i
$712$	7.89949	−	7.89949i	0.296046	−	0.296046i
$713$	9.65685	−	9.65685i	0.361652	−	0.361652i
$714$	6.00000	−	1.02944i	0.224544	−	0.0385257i
$715$	8.00000	+	4.00000i	0.299183	+	0.149592i
$716$			17.6569i			0.659868i
$717$	19.8995	−	28.1421i	0.743160	−	1.05099i
$718$	−16.5563	−	16.5563i	−0.617877	−	0.617877i
$719$	−12.4853			−0.465622			−0.232811	−	0.972522i	$-0.574792\pi$
$719$	−12.4853			−0.465622			−0.232811	+	0.972522i	$0.574792\pi$
$720$	5.29289	−	4.12132i	0.197254	−	0.153593i
$721$	14.6274			0.544753
$722$	−19.5355	−	19.5355i	−0.727037	−	0.727037i
$723$	−3.65685	+	5.17157i	−0.136000	+	0.192333i
$724$			6.00000i			0.222988i
$725$	−24.0000	+	18.0000i	−0.891338	+	0.668503i
$726$	−8.53553	+	1.46447i	−0.316783	+	0.0543514i
$727$	−25.3137	+	25.3137i	−0.938833	+	0.938833i	−0.998234	−	0.0594007i	$-0.981081\pi$
$727$	−25.3137	+	25.3137i	−0.938833	+	0.938833i	0.0594007	+	0.998234i	$0.481081\pi$
$728$	0.585786	−	0.585786i	0.0217107	−	0.0217107i
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−33.2132	+	11.0711i	−1.22928	+	0.409759i
$731$			7.45584i			0.275764i
$732$	6.82843	+	4.82843i	0.252386	+	0.178464i
$733$	−15.5563	−	15.5563i	−0.574587	−	0.574587i	0.358820	−	0.933407i	$-0.383179\pi$
$733$	−15.5563	−	15.5563i	−0.574587	−	0.574587i	−0.933407	+	0.358820i	$0.883179\pi$
$734$	20.0000			0.738213
$735$	7.07969	−	23.4056i	0.261138	−	0.863328i
$736$	−4.00000			−0.147442
$737$	3.31371	+	3.31371i	0.122062	+	0.122062i
$738$	−5.41421	−	2.58579i	−0.199300	−	0.0951841i
$739$			10.1421i			0.373084i	0.982447	+	0.186542i	$0.0597281\pi$
$739$			10.1421i			0.373084i	−0.982447	+	0.186542i	$0.940272\pi$
$740$	−3.65685	+	7.31371i	−0.134429	+	0.268857i
$741$	−2.00000	−	11.6569i	−0.0734718	−	0.428225i
$742$	−0.485281	+	0.485281i	−0.0178152	+	0.0178152i
$743$	−10.6274	+	10.6274i	−0.389882	+	0.389882i	−0.874645	−	0.484763i	$-0.838906\pi$
$743$	−10.6274	+	10.6274i	−0.389882	+	0.389882i	0.484763	+	0.874645i	$0.338906\pi$
$744$	1.00000	+	5.82843i	0.0366618	+	0.213681i
$745$	15.8284	+	47.4853i	0.579909	+	1.73973i
$746$			6.97056i			0.255210i
$747$	−26.1421	−	12.4853i	−0.956491	−	0.456813i
$748$	12.0000	+	12.0000i	0.438763	+	0.438763i
$749$	−14.1421			−0.516742
$750$	17.5563	+	8.17157i	0.641067	+	0.298384i
$751$	36.2843			1.32403			0.662016	−	0.749490i	$-0.269701\pi$
$751$	36.2843			1.32403			0.662016	+	0.749490i	$0.269701\pi$
$752$	−2.24264	−	2.24264i	−0.0817807	−	0.0817807i
$753$	20.2843	+	14.3431i	0.739200	+	0.522693i
$754$		−	6.00000i		−	0.218507i
$755$	−0.757359	−	2.27208i	−0.0275631	−	0.0826894i
$756$	−2.10051	−	3.75736i	−0.0763946	−	0.136654i
$757$	3.41421	−	3.41421i	0.124092	−	0.124092i	−0.642334	−	0.766425i	$-0.722034\pi$
$757$	3.41421	−	3.41421i	0.124092	−	0.124092i	0.766425	+	0.642334i	$0.222034\pi$
$758$	−26.9706	+	26.9706i	−0.979615	+	0.979615i
$759$	−27.3137	+	4.68629i	−0.991425	+	0.170102i
$760$	−6.82843	+	13.6569i	−0.247693	+	0.495386i
$761$		−	26.4853i		−	0.960091i	−0.877244	−	0.480045i	$-0.840620\pi$
$761$		−	26.4853i		−	0.960091i	0.877244	−	0.480045i	$-0.159380\pi$
$762$	−4.48528	+	6.34315i	−0.162485	+	0.229788i
$763$	−2.88730	−	2.88730i	−0.104527	−	0.104527i
$764$	−2.82843			−0.102329
$765$	−28.2426	−	3.51472i	−1.02111	−	0.127075i
$766$	−2.34315			−0.0846613
$767$	3.17157	+	3.17157i	0.114519	+	0.114519i
$768$	1.00000	−	1.41421i	0.0360844	−	0.0510310i
$769$		−	8.62742i		−	0.311113i	−0.987827	−	0.155556i	$-0.950283\pi$
$769$		−	8.62742i		−	0.311113i	0.987827	−	0.155556i	$-0.0497170\pi$
$770$	−7.02944	+	2.34315i	−0.253323	+	0.0844411i
$771$	−16.8995	+	2.89949i	−0.608620	+	0.104423i
$772$	−11.4142	+	11.4142i	−0.410807	+	0.410807i
$773$	16.2426	−	16.2426i	0.584207	−	0.584207i	−0.351849	−	0.936057i	$-0.614447\pi$
$773$	16.2426	−	16.2426i	0.584207	−	0.584207i	0.936057	+	0.351849i	$0.114447\pi$
$774$	4.97056	−	1.75736i	0.178663	−	0.0631670i
$775$	−13.6569	+	10.2426i	−0.490569	+	0.367927i
$776$			12.8284i			0.460514i
$777$	4.28427	+	3.02944i	0.153697	+	0.108680i
$778$	1.41421	+	1.41421i	0.0507020	+	0.0507020i
$779$	13.6569			0.489308
$780$	−3.41421	+	1.82843i	−0.122248	+	0.0654682i
$781$	56.9706			2.03857
$782$	12.0000	+	12.0000i	0.429119	+	0.429119i
$783$	−30.0000	−	8.48528i	−1.07211	−	0.303239i
$784$		−	6.31371i		−	0.225490i
$785$	−45.9411	−	22.9706i	−1.63971	−	0.819855i
$786$	3.79899	+	22.1421i	0.135505	+	0.789784i
$787$	−5.79899	+	5.79899i	−0.206712	+	0.206712i	−0.802868	−	0.596157i	$-0.796694\pi$
$787$	−5.79899	+	5.79899i	−0.206712	+	0.206712i	0.596157	+	0.802868i	$0.296694\pi$
$788$	3.75736	−	3.75736i	0.133850	−	0.133850i
$789$	6.62742	+	38.6274i	0.235942	+	1.37517i
$790$	24.9706	+	12.4853i	0.888413	+	0.444206i
$791$			8.20101i			0.291594i
$792$	5.17157	−	10.8284i	0.183764	−	0.384771i
$793$	−3.41421	−	3.41421i	−0.121242	−	0.121242i
$794$	−12.9706			−0.460308
$795$	2.82843	−	1.51472i	0.100314	−	0.0537215i
$796$	−22.1421			−0.784807
$797$	6.92893	+	6.92893i	0.245435	+	0.245435i	0.819094	−	0.573659i	$-0.194476\pi$
$797$	6.92893	+	6.92893i	0.245435	+	0.245435i	−0.573659	+	0.819094i	$0.694476\pi$
$798$	8.00000	+	5.65685i	0.283197	+	0.200250i
$799$			13.4558i			0.476034i
$800$	4.94975	+	0.707107i	0.175000	+	0.0250000i
$801$	11.1716	+	31.5980i	0.394728	+	1.11646i
$802$	1.27208	−	1.27208i	0.0449186	−	0.0449186i
$803$	−44.2843	+	44.2843i	−1.56276	+	1.56276i
$804$	−2.00000	+	0.343146i	−0.0705346	+	0.0121018i
$805$	−7.02944	+	2.34315i	−0.247755	+	0.0825850i
$806$		−	3.41421i		−	0.120261i
$807$	−15.1716	+	21.4558i	−0.534065	+	0.755281i
$808$	2.24264	+	2.24264i	0.0788958	+	0.0788958i
$809$	−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
$811$	22.1421			0.777516			0.388758	−	0.921340i	$-0.372904\pi$
$811$	22.1421			0.777516			0.388758	+	0.921340i	$0.372904\pi$
$812$	3.51472	+	3.51472i	0.123342	+	0.123342i
$813$	−2.24264	+	3.17157i	−0.0786528	+	0.111232i
$814$			14.6274i			0.512691i
$815$	3.31371	−	6.62742i	0.116074	−	0.232148i
$816$	−7.24264	+	1.24264i	−0.253543	+	0.0435011i
$817$	−8.48528	+	8.48528i	−0.296862	+	0.296862i
$818$	−2.24264	+	2.24264i	−0.0784121	+	0.0784121i
$819$	0.828427	+	2.34315i	0.0289476	+	0.0818761i
$820$	−1.41421	−	4.24264i	−0.0493865	−	0.148159i
$821$		−	13.6985i		−	0.478080i	−0.971010	−	0.239040i	$-0.923167\pi$
$821$		−	13.6985i		−	0.478080i	0.971010	−	0.239040i	$-0.0768328\pi$
$822$	−30.1421	−	21.3137i	−1.05133	−	0.743401i
$823$	−33.3137	−	33.3137i	−1.16124	−	1.16124i	−0.984204	−	0.177039i	$-0.943348\pi$
$823$	−33.3137	−	33.3137i	−1.16124	−	1.16124i	−0.177039	−	0.984204i	$-0.556652\pi$
$824$	−17.6569			−0.615106
$825$	34.6274	−	0.970563i	1.20557	−	0.0337907i
$826$	−3.71573			−0.129287
$827$	32.8284	+	32.8284i	1.14156	+	1.14156i	0.988166	+	0.153391i	$0.0490193\pi$
$827$	32.8284	+	32.8284i	1.14156	+	1.14156i	0.153391	+	0.988166i	$0.450981\pi$
$828$	5.17157	−	10.8284i	0.179725	−	0.376314i
$829$			37.5147i			1.30294i	0.758674	+	0.651470i	$0.225847\pi$
$829$			37.5147i			1.30294i	−0.758674	+	0.651470i	$0.774153\pi$
$830$	−6.82843	−	20.4853i	−0.237018	−	0.711054i
$831$	6.58579	+	38.3848i	0.228458	+	1.33155i
$832$	−0.707107	+	0.707107i	−0.0245145	+	0.0245145i
$833$	−18.9411	+	18.9411i	−0.656271	+	0.656271i
$834$	−0.485281	−	2.82843i	−0.0168039	−	0.0979404i
$835$	−4.82843	+	9.65685i	−0.167095	+	0.334189i
$836$			27.3137i			0.944664i
$837$	−17.0711	−	4.82843i	−0.590062	−	0.166895i
$838$	3.89949	+	3.89949i	0.134706	+	0.134706i
$839$	20.1005			0.693946			0.346973	−	0.937875i	$-0.387209\pi$
$839$	20.1005			0.693946			0.346973	+	0.937875i	$0.387209\pi$
$840$	0.928932	−	3.07107i	0.0320512	−	0.105962i
$841$	7.00000			0.241379
$842$	19.1421	+	19.1421i	0.659682	+	0.659682i
$843$	−1.17157	−	0.828427i	−0.0403511	−	0.0285325i
$844$			1.65685i			0.0570313i
$845$	2.12132	−	0.707107i	0.0729756	−	0.0243252i
$846$	8.97056	−	3.17157i	0.308414	−	0.109041i
$847$	−2.92893	+	2.92893i	−0.100639	+	0.100639i
$848$	0.585786	−	0.585786i	0.0201160	−	0.0201160i
$849$	−41.6274	+	7.14214i	−1.42865	+	0.245117i
$850$	−12.7279	−	16.9706i	−0.436564	−	0.582086i
$851$			14.6274i			0.501421i
$852$	−14.2426	+	20.1421i	−0.487945	+	0.690058i
$853$	−7.02944	−	7.02944i	−0.240683	−	0.240683i	0.576449	−	0.817133i	$-0.304438\pi$
$853$	−7.02944	−	7.02944i	−0.240683	−	0.240683i	−0.817133	+	0.576449i	$0.804438\pi$
$854$	4.00000			0.136877
$855$	−28.1421	−	36.1421i	−0.962441	−	1.23603i
$856$	17.0711			0.583477
$857$	20.1716	+	20.1716i	0.689048	+	0.689048i	0.962021	−	0.272974i	$-0.0880072\pi$
$857$	20.1716	+	20.1716i	0.689048	+	0.689048i	−0.272974	+	0.962021i	$0.588007\pi$
$858$	−4.00000	+	5.65685i	−0.136558	+	0.193122i
$859$		−	37.7990i		−	1.28968i	−0.764316	−	0.644842i	$-0.776923\pi$
$859$		−	37.7990i		−	1.28968i	0.764316	−	0.644842i	$-0.223077\pi$
$860$	3.51472	+	1.75736i	0.119851	+	0.0599255i
$861$	−2.82843	+	0.485281i	−0.0963925	+	0.0165383i
$862$	7.72792	−	7.72792i	0.263214	−	0.263214i
$863$	−22.2426	+	22.2426i	−0.757148	+	0.757148i	−0.975802	−	0.218654i	$-0.929833\pi$
$863$	−22.2426	+	22.2426i	−0.757148	+	0.757148i	0.218654	+	0.975802i	$0.429833\pi$
$864$	2.53553	+	4.53553i	0.0862606	+	0.154302i
$865$	−48.2843	−	24.1421i	−1.64171	−	0.820857i
$866$		−	23.0711i		−	0.783987i
$867$	1.41421	+	1.00000i	0.0480292	+	0.0339618i
$868$	2.00000	+	2.00000i	0.0678844	+	0.0678844i
$869$	49.9411			1.69414
$870$	−10.9706	−	20.4853i	−0.371937	−	0.694516i
$871$	1.17157			0.0396972
$872$	3.48528	+	3.48528i	0.118027	+	0.118027i
$873$	−34.7279	−	16.5858i	−1.17536	−	0.561344i
$874$			27.3137i			0.923900i
$875$	9.11270	−	1.65685i	0.308065	−	0.0560119i
$876$	−4.58579	−	26.7279i	−0.154939	−	0.903053i
$877$	35.3137	−	35.3137i	1.19246	−	1.19246i	0.216085	−	0.976375i	$-0.430671\pi$
$877$	35.3137	−	35.3137i	1.19246	−	1.19246i	0.976375	−	0.216085i	$-0.0693287\pi$
$878$	12.9706	−	12.9706i	0.437735	−	0.437735i
$879$	−1.85786	−	10.8284i	−0.0626642	−	0.365234i
$880$	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	$-0.0757828\pi$
$882$	17.0919	+	8.16295i	0.575514	+	0.274861i
$883$	22.2132	+	22.2132i	0.747534	+	0.747534i	0.974015	−	0.226482i	$-0.0727223\pi$
$883$	22.2132	+	22.2132i	0.747534	+	0.747534i	−0.226482	+	0.974015i	$0.572722\pi$
$884$	4.24264			0.142695
$885$	16.6274	+	5.02944i	0.558925	+	0.169063i
$886$	1.27208			0.0427363
$887$	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	$0.719725\pi$
$888$	−5.17157	−	3.65685i	−0.173547	−	0.122716i
$889$			3.71573i			0.124622i
$890$	−11.1716	+	22.3431i	−0.374472	+	0.748944i
$891$	22.6274	+	28.0000i	0.758047	+	0.938035i
$892$	9.65685	−	9.65685i	0.323335	−	0.323335i
$893$	−15.3137	+	15.3137i	−0.512454	+	0.512454i
$894$	−38.2132	+	6.55635i	−1.27804	+	0.219277i
$895$	−12.4853	−	37.4558i	−0.417337	−	1.25201i
$896$		−	0.828427i		−	0.0276758i
$897$	−4.00000	+	5.65685i	−0.133556	+	0.188877i
$898$	−12.5858	−	12.5858i	−0.419993	−	0.419993i
$899$	20.4853			0.683222
$900$	−8.31371	+	12.4853i	−0.277124	+	0.416176i
$901$	−3.51472			−0.117092
$902$	−5.65685	−	5.65685i	−0.188353	−	0.188353i
$903$	1.45584	−	2.05887i	0.0484475	−	0.0685151i
$904$		−	9.89949i		−	0.329252i
$905$	−4.24264	−	12.7279i	−0.141030	−	0.423090i
$906$	1.82843	−	0.313708i	0.0607454	−	0.0104223i
$907$	5.10051	−	5.10051i	0.169359	−	0.169359i	−0.617338	−	0.786698i	$-0.711789\pi$
$907$	5.10051	−	5.10051i	0.169359	−	0.169359i	0.786698	+	0.617338i	$0.211789\pi$
$908$	2.00000	−	2.00000i	0.0663723	−	0.0663723i
$909$	−8.97056	+	3.17157i	−0.297535	+	0.105194i
$910$	−0.828427	+	1.65685i	−0.0274621	+	0.0549242i
$911$			1.85786i			0.0615538i	0.999526	+	0.0307769i	$0.00979814\pi$
$911$			1.85786i			0.0615538i	−0.999526	+	0.0307769i	$0.990202\pi$
$912$	−9.65685	−	6.82843i	−0.319770	−	0.226112i
$913$	−27.3137	−	27.3137i	−0.903952	−	0.903952i
$914$	−29.7990			−0.985663
$915$	−17.8995	−	5.41421i	−0.591739	−	0.178988i
$916$	17.8995			0.591416
$917$	7.59798	+	7.59798i	0.250907	+	0.250907i
$918$	6.00000	−	21.2132i	0.198030	−	0.700140i
$919$			9.94113i			0.327927i	0.986466	+	0.163964i	$0.0524280\pi$
$919$			9.94113i			0.327927i	−0.986466	+	0.163964i	$0.947572\pi$
$920$	8.48528	−	2.82843i	0.279751	−	0.0932505i
$921$	−2.97056	−	17.3137i	−0.0978834	−	0.570506i
$922$	−15.3431	+	15.3431i	−0.505300	+	0.505300i
$923$	10.0711	−	10.0711i	0.331493	−	0.331493i
$924$	−0.970563	−	5.65685i	−0.0319292	−	0.186097i
$925$	2.58579	−	18.1005i	0.0850201	−	0.595141i
$926$			8.00000i			0.262896i
$927$	22.8284	−	47.7990i	0.749784	−	1.56992i
$928$	−4.24264	−	4.24264i	−0.139272	−	0.139272i
$929$	57.1127			1.87381			0.936903	−	0.349588i	$-0.113679\pi$
$929$	57.1127			1.87381			0.936903	+	0.349588i	$0.113679\pi$
$930$	−6.24264	−	11.6569i	−0.204704	−	0.382243i
$931$	−43.1127			−1.41296
$932$	8.65685	+	8.65685i	0.283565	+	0.283565i
$933$	39.5980	+	28.0000i	1.29638	+	0.916679i
$934$		−	23.8995i		−	0.782015i
$935$	−33.9411	−	16.9706i	−1.10999	−	0.554997i
$936$	−1.00000	−	2.82843i	−0.0326860	−	0.0924500i
$937$	31.9706	−	31.9706i	1.04443	−	1.04443i	0.0454669	−	0.998966i	$-0.485522\pi$
$937$	31.9706	−	31.9706i	1.04443	−	1.04443i	0.998966	−	0.0454669i	$-0.0144776\pi$
$938$	−0.686292	+	0.686292i	−0.0224082	+	0.0224082i
$939$	3.24264	−	0.556349i	0.105820	−	0.0181558i
$940$	6.34315	+	3.17157i	0.206891	+	0.103445i
$941$			38.8701i			1.26713i	0.773690	+	0.633564i	$0.218409\pi$
$941$			38.8701i			1.26713i	−0.773690	+	0.633564i	$0.781591\pi$
$942$	22.9706	−	32.4853i	0.748421	−	1.05843i
$943$	−5.65685	−	5.65685i	−0.184213	−	0.184213i
$944$	4.48528			0.145983
$945$	7.11270	+	6.48528i	0.231376	+	0.210966i
$946$	7.02944			0.228547
$947$	12.6274	+	12.6274i	0.410336	+	0.410336i	0.881856	−	0.471520i	$-0.156294\pi$
$947$	12.6274	+	12.6274i	0.410336	+	0.410336i	−0.471520	+	0.881856i	$0.656294\pi$
$948$	−12.4853	+	17.6569i	−0.405503	+	0.573468i
$949$			15.6569i			0.508243i
$950$	4.82843	−	33.7990i	0.156655	−	1.09658i
$951$	4.00000	−	0.686292i	0.129709	−	0.0222545i
$952$	−2.48528	+	2.48528i	−0.0805484	+	0.0805484i
$953$	−4.51472	+	4.51472i	−0.146246	+	0.146246i	−0.776439	−	0.630193i	$-0.782976\pi$
$953$	−4.51472	+	4.51472i	−0.146246	+	0.146246i	0.630193	+	0.776439i	$0.282976\pi$
$954$	0.828427	+	2.34315i	0.0268213	+	0.0758621i
$955$	6.00000	−	2.00000i	0.194155	−	0.0647185i
$956$			19.8995i			0.643596i
$957$	−33.9411	−	24.0000i	−1.09716	−	0.775810i
$958$	17.2426	+	17.2426i	0.557084	+	0.557084i
$959$	−17.6569			−0.570170
$960$	−1.12132	+	3.70711i	−0.0361905	+	0.119646i
$961$	−19.3431			−0.623972
$962$	2.58579	+	2.58579i	0.0833691	+	0.0833691i
$963$	−22.0711	+	46.2132i	−0.711230	+	1.48920i
$964$		−	3.65685i		−	0.117779i
$965$	16.1421	−	32.2843i	0.519634	−	1.03927i
$966$	−0.970563	−	5.65685i	−0.0312273	−	0.182006i
$967$	14.6274	−	14.6274i	0.470386	−	0.470386i	−0.431653	−	0.902040i	$-0.642070\pi$
$967$	14.6274	−	14.6274i	0.470386	−	0.470386i	0.902040	+	0.431653i	$0.142070\pi$
$968$	3.53553	−	3.53553i	0.113636	−	0.113636i
$969$	8.48528	+	49.4558i	0.272587	+	1.58875i
$970$	−9.07107	−	27.2132i	−0.291254	−	0.873763i
$971$			8.14214i			0.261294i	0.991429	+	0.130647i	$0.0417054\pi$
$971$			8.14214i			0.261294i	−0.991429	+	0.130647i	$0.958295\pi$
$972$	−15.5563	+	1.00000i	−0.498970	+	0.0320750i
$973$	−0.970563	−	0.970563i	−0.0311148	−	0.0311148i
$974$	4.14214			0.132723
$975$	5.94975	−	6.29289i	0.190544	−	0.201534i
$976$	−4.82843			−0.154554
$977$	21.4142	+	21.4142i	0.685101	+	0.685101i	0.961145	−	0.276044i	$-0.0890235\pi$
$977$	21.4142	+	21.4142i	0.685101	+	0.685101i	−0.276044	+	0.961145i	$0.589023\pi$
$978$	4.68629	+	3.31371i	0.149851	+	0.105961i
$979$			44.6863i			1.42818i
$980$	4.46447	+	13.3934i	0.142612	+	0.427836i
$981$	−13.9411	+	4.92893i	−0.445106	+	0.157369i
$982$	9.75736	−	9.75736i	0.311370	−	0.311370i
$983$	−3.41421	+	3.41421i	−0.108897	+	0.108897i	−0.759456	−	0.650559i	$-0.774535\pi$
$983$	−3.41421	+	3.41421i	−0.108897	+	0.108897i	0.650559	+	0.759456i	$0.274535\pi$
$984$	3.41421	−	0.585786i	0.108841	−	0.0186742i
$985$	−5.31371	+	10.6274i	−0.169309	+	0.338618i
$986$			25.4558i			0.810679i
$987$	2.62742	−	3.71573i	0.0836316	−	0.118273i
$988$	4.82843	+	4.82843i	0.153613	+	0.153613i
$989$	7.02944			0.223523
$990$	−3.31371	+	26.6274i	−0.105317	+	0.846275i
$991$	−5.17157			−0.164280			−0.0821402	−	0.996621i	$-0.526176\pi$
$991$	−5.17157			−0.164280			−0.0821402	+	0.996621i	$0.526176\pi$
$992$	−2.41421	−	2.41421i	−0.0766514	−	0.0766514i
$993$	−32.2843	+	45.6569i	−1.02451	+	1.44888i
$994$			11.7990i			0.374241i
$995$	46.9706	−	15.6569i	1.48907	−	0.496356i
$996$	16.4853	−	2.82843i	0.522356	−	0.0896221i
$997$	21.6985	−	21.6985i	0.687198	−	0.687198i	−0.274414	−	0.961612i	$-0.588484\pi$
$997$	21.6985	−	21.6985i	0.687198	−	0.687198i	0.961612	+	0.274414i	$0.0884838\pi$
$998$	−5.65685	+	5.65685i	−0.179065	+	0.179065i
$999$	16.5858	−	9.27208i	0.524751	−	0.293356i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.l.a.53.1	✓	4	3.2	odd	2
390.2.l.a.287.1	yes	4	5.2	odd	4
390.2.l.b.53.2	yes	4	1.1	even	1	trivial
390.2.l.b.287.2	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} +(1.70711 - 0.292893i) q^{6} +(0.585786 - 0.585786i) 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} +0.828427 q^{14} +(-3.70711 - 1.12132i) q^{15} -1.00000 q^{16} +(3.00000 + 3.00000i) q^{17} +(1.29289 - 2.70711i) q^{18} +6.82843i q^{19} +(2.12132 - 0.707107i) q^{20} +(-0.242641 - 1.41421i) q^{21} +(2.82843 - 2.82843i) q^{22} +(2.82843 - 2.82843i) q^{23} +(0.292893 + 1.70711i) q^{24} +(-4.00000 + 3.00000i) q^{25} -1.00000i q^{26} +(-5.00000 - 1.41421i) q^{27} +(0.585786 + 0.585786i) q^{28} +6.00000 q^{29} +(-1.82843 - 3.41421i) q^{30} +3.41421 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-5.65685 - 4.00000i) q^{33} +4.24264i q^{34} +(-1.65685 - 0.828427i) q^{35} +(2.82843 - 1.00000i) q^{36} +(-2.58579 + 2.58579i) q^{37} +(-4.82843 + 4.82843i) q^{38} +(-1.70711 + 0.292893i) q^{39} +(2.00000 + 1.00000i) q^{40} -2.00000i q^{41} +(0.828427 - 1.17157i) q^{42} +(1.24264 + 1.24264i) q^{43} +4.00000 q^{44} +(-5.29289 + 4.12132i) q^{45} +4.00000 q^{46} +(2.24264 + 2.24264i) q^{47} +(-1.00000 + 1.41421i) q^{48} +6.31371i q^{49} +(-4.94975 - 0.707107i) q^{50} +(7.24264 - 1.24264i) q^{51} +(0.707107 - 0.707107i) q^{52} +(-0.585786 + 0.585786i) q^{53} +(-2.53553 - 4.53553i) q^{54} +(-8.48528 + 2.82843i) q^{55} +0.828427i q^{56} +(9.65685 + 6.82843i) q^{57} +(4.24264 + 4.24264i) q^{58} -4.48528 q^{59} +(1.12132 - 3.70711i) q^{60} +4.82843 q^{61} +(2.41421 + 2.41421i) q^{62} +(-2.24264 - 1.07107i) q^{63} -1.00000i q^{64} +(-1.00000 + 2.00000i) q^{65} +(-1.17157 - 6.82843i) q^{66} +(-0.828427 + 0.828427i) q^{67} +(-3.00000 + 3.00000i) q^{68} +(-1.17157 - 6.82843i) q^{69} +(-0.585786 - 1.75736i) q^{70} +14.2426i q^{71} +(2.70711 + 1.29289i) q^{72} +(-11.0711 - 11.0711i) q^{73} -3.65685 q^{74} +(0.242641 + 8.65685i) q^{75} -6.82843 q^{76} +(-2.34315 - 2.34315i) q^{77} +(-1.41421 - 1.00000i) q^{78} +12.4853i q^{79} +(0.707107 + 2.12132i) q^{80} +(-7.00000 + 5.65685i) q^{81} +(1.41421 - 1.41421i) q^{82} +(6.82843 - 6.82843i) q^{83} +(1.41421 - 0.242641i) q^{84} +(4.24264 - 8.48528i) q^{85} +1.75736i q^{86} +(6.00000 - 8.48528i) q^{87} +(2.82843 + 2.82843i) q^{88} -11.1716 q^{89} +(-6.65685 - 0.828427i) q^{90} -0.828427 q^{91} +(2.82843 + 2.82843i) q^{92} +(3.41421 - 4.82843i) q^{93} +3.17157i q^{94} +(14.4853 - 4.82843i) q^{95} +(-1.70711 + 0.292893i) q^{96} +(9.07107 - 9.07107i) q^{97} +(-4.46447 + 4.46447i) 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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