LMFDB - Embedded newform 462.2.j.d.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(169,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("462.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	462.421
Dual form			462.2.j.d.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} -1.00000 q^{12} +(-1.61803 + 1.17557i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.11803 - 1.53884i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.572949 + 1.76336i) q^{19} +(-1.30902 + 0.951057i) q^{20} -1.00000 q^{21} +(-2.54508 - 2.12663i) q^{22} +1.85410 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(-0.618034 + 1.90211i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(2.00000 - 6.15537i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-1.92705 + 1.40008i) q^{31} -1.00000 q^{32} +(-2.80902 + 1.76336i) q^{33} -2.61803 q^{34} +(-1.30902 + 0.951057i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.881966 + 2.71441i) q^{37} +(1.50000 + 1.08981i) q^{38} +(1.61803 + 1.17557i) q^{39} +(-0.500000 + 1.53884i) q^{40} +(0.118034 + 0.363271i) q^{41} +(-0.809017 + 0.587785i) q^{42} +10.0000 q^{43} +(-3.30902 - 0.224514i) q^{44} +1.61803 q^{45} +(1.50000 - 1.08981i) q^{46} +(-0.763932 - 2.35114i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.92705 - 1.40008i) q^{50} +(-0.809017 + 2.48990i) q^{51} +(0.618034 + 1.90211i) q^{52} +(6.85410 - 4.97980i) q^{53} +1.00000 q^{54} +(-2.00000 + 4.97980i) q^{55} -1.00000 q^{56} +(1.50000 - 1.08981i) q^{57} +(-2.00000 - 6.15537i) q^{58} +(-0.236068 + 0.726543i) q^{59} +(1.30902 + 0.951057i) q^{60} +(8.23607 + 5.98385i) q^{61} +(-0.736068 + 2.26538i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.23607 q^{65} +(-1.23607 + 3.07768i) q^{66} +10.1803 q^{67} +(-2.11803 + 1.53884i) q^{68} +(-0.572949 - 1.76336i) q^{69} +(-0.500000 + 1.53884i) q^{70} +(2.00000 + 1.45309i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.76393 - 11.5842i) q^{73} +(0.881966 + 2.71441i) q^{74} +(-1.92705 + 1.40008i) q^{75} +1.85410 q^{76} +(-3.30902 - 0.224514i) q^{77} +2.00000 q^{78} +(-4.47214 + 3.24920i) q^{79} +(0.500000 + 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.309017 + 0.224514i) q^{82} +(-5.85410 - 4.25325i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(1.30902 + 4.02874i) q^{85} +(8.09017 - 5.87785i) q^{86} -6.47214 q^{87} +(-2.80902 + 1.76336i) q^{88} +8.79837 q^{89} +(1.30902 - 0.951057i) q^{90} +(0.618034 + 1.90211i) q^{91} +(0.572949 - 1.76336i) q^{92} +(1.92705 + 1.40008i) q^{93} +(-2.00000 - 1.45309i) q^{94} +(0.927051 - 2.85317i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-9.85410 + 7.15942i) q^{97} -1.00000 q^{98} +(2.54508 + 2.12663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 + q^3 - q^4 - 3 * q^5 - q^6 - q^7 + q^8 - q^9	$ 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9} - 2 q^{10} - q^{11} - 4 q^{12} - 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} + q^{18} + 9 q^{19} - 3 q^{20} - 4 q^{21} + q^{22} - 6 q^{23} - q^{24} + 6 q^{25} + 2 q^{26} + q^{27} - q^{28} + 8 q^{29} + 2 q^{30} - q^{31} - 4 q^{32} - 9 q^{33} - 6 q^{34} - 3 q^{35} - q^{36} - 8 q^{37} + 6 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} - q^{42} + 40 q^{43} - 11 q^{44} + 2 q^{45} + 6 q^{46} - 12 q^{47} + q^{48} - q^{49} - q^{50} - q^{51} - 2 q^{52} + 14 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} + 6 q^{57} - 8 q^{58} + 8 q^{59} + 3 q^{60} + 24 q^{61} + 6 q^{62} - q^{63} - q^{64} + 4 q^{65} + 4 q^{66} - 4 q^{67} - 4 q^{68} - 9 q^{69} - 2 q^{70} + 8 q^{71} + q^{72} + 24 q^{73} + 8 q^{74} - q^{75} - 6 q^{76} - 11 q^{77} + 8 q^{78} + 2 q^{80} - q^{81} - q^{82} - 10 q^{83} + q^{84} + 3 q^{85} + 10 q^{86} - 8 q^{87} - 9 q^{88} - 14 q^{89} + 3 q^{90} - 2 q^{91} + 9 q^{92} + q^{93} - 8 q^{94} - 3 q^{95} - q^{96} - 26 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 - 3 * q^5 - q^6 - q^7 + q^8 - q^9 - 2 * q^10 - q^11 - 4 * q^12 - 2 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 + q^18 + 9 * q^19 - 3 * q^20 - 4 * q^21 + q^22 - 6 * q^23 - q^24 + 6 * q^25 + 2 * q^26 + q^27 - q^28 + 8 * q^29 + 2 * q^30 - q^31 - 4 * q^32 - 9 * q^33 - 6 * q^34 - 3 * q^35 - q^36 - 8 * q^37 + 6 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 - q^42 + 40 * q^43 - 11 * q^44 + 2 * q^45 + 6 * q^46 - 12 * q^47 + q^48 - q^49 - q^50 - q^51 - 2 * q^52 + 14 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 + 6 * q^57 - 8 * q^58 + 8 * q^59 + 3 * q^60 + 24 * q^61 + 6 * q^62 - q^63 - q^64 + 4 * q^65 + 4 * q^66 - 4 * q^67 - 4 * q^68 - 9 * q^69 - 2 * q^70 + 8 * q^71 + q^72 + 24 * q^73 + 8 * q^74 - q^75 - 6 * q^76 - 11 * q^77 + 8 * q^78 + 2 * q^80 - q^81 - q^82 - 10 * q^83 + q^84 + 3 * q^85 + 10 * q^86 - 8 * q^87 - 9 * q^88 - 14 * q^89 + 3 * q^90 - 2 * q^91 + 9 * q^92 + q^93 - 8 * q^94 - 3 * q^95 - q^96 - 26 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	0.255260	−	0.966872i	$-0.417839\pi$
$5$	−1.30902	−	0.951057i	−0.585410	−	0.425325i	−0.840670	+	0.541547i	$0.817839\pi$
$6$	−0.809017	−	0.587785i	−0.330280	−	0.239962i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−1.61803			−0.511667
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$	−1.00000			−0.288675
$13$	−1.61803	+	1.17557i	−0.448762	+	0.326045i	−0.789107	−	0.614256i	$-0.789456\pi$
$13$	−1.61803	+	1.17557i	−0.448762	+	0.326045i	0.340345	+	0.940301i	$0.389456\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	−0.500000	+	1.53884i	−0.129099	+	0.397327i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.11803	−	1.53884i	−0.513699	−	0.373224i	0.300526	−	0.953774i	$-0.402838\pi$
$17$	−2.11803	−	1.53884i	−0.513699	−	0.373224i	−0.814225	+	0.580550i	$0.802838\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	0.572949	+	1.76336i	0.131444	+	0.404542i	0.995020	−	0.0996765i	$-0.0317808\pi$
$19$	0.572949	+	1.76336i	0.131444	+	0.404542i	−0.863576	+	0.504218i	$0.831781\pi$
$20$	−1.30902	+	0.951057i	−0.292705	+	0.212663i
$21$	−1.00000			−0.218218
$22$	−2.54508	−	2.12663i	−0.542614	−	0.453398i
$23$	1.85410			0.386607			0.193303	−	0.981139i	$-0.438080\pi$
$23$	1.85410			0.386607			0.193303	+	0.981139i	$0.438080\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−0.736068	−	2.26538i	−0.147214	−	0.453077i
$26$	−0.618034	+	1.90211i	−0.121206	+	0.373035i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−0.809017	−	0.587785i	−0.152890	−	0.111081i
$29$	2.00000	−	6.15537i	0.371391	−	1.14302i	−0.574491	−	0.818511i	$-0.694800\pi$
$29$	2.00000	−	6.15537i	0.371391	−	1.14302i	0.945882	−	0.324512i	$-0.105200\pi$
$30$	0.500000	+	1.53884i	0.0912871	+	0.280953i
$31$	−1.92705	+	1.40008i	−0.346109	+	0.251463i	−0.747235	−	0.664560i	$-0.768619\pi$
$31$	−1.92705	+	1.40008i	−0.346109	+	0.251463i	0.401126	+	0.916023i	$0.368619\pi$
$32$	−1.00000			−0.176777
$33$	−2.80902	+	1.76336i	−0.488987	+	0.306961i
$34$	−2.61803			−0.448989
$35$	−1.30902	+	0.951057i	−0.221264	+	0.160758i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−0.881966	+	2.71441i	−0.144994	+	0.446247i	−0.997010	−	0.0772692i	$-0.975380\pi$
$37$	−0.881966	+	2.71441i	−0.144994	+	0.446247i	0.852016	+	0.523516i	$0.175380\pi$
$38$	1.50000	+	1.08981i	0.243332	+	0.176791i
$39$	1.61803	+	1.17557i	0.259093	+	0.188242i
$40$	−0.500000	+	1.53884i	−0.0790569	+	0.243312i
$41$	0.118034	+	0.363271i	0.0184338	+	0.0567334i	0.959850	−	0.280513i	$-0.0905045\pi$
$41$	0.118034	+	0.363271i	0.0184338	+	0.0567334i	−0.941416	+	0.337246i	$0.890505\pi$
$42$	−0.809017	+	0.587785i	−0.124834	+	0.0906972i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−3.30902	−	0.224514i	−0.498853	−	0.0338468i
$45$	1.61803			0.241202
$46$	1.50000	−	1.08981i	0.221163	−	0.160684i
$47$	−0.763932	−	2.35114i	−0.111431	−	0.342949i	0.879755	−	0.475427i	$-0.157707\pi$
$47$	−0.763932	−	2.35114i	−0.111431	−	0.342949i	−0.991186	+	0.132478i	$0.957707\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−1.92705	−	1.40008i	−0.272526	−	0.198002i
$51$	−0.809017	+	2.48990i	−0.113285	+	0.348655i
$52$	0.618034	+	1.90211i	0.0857059	+	0.263776i
$53$	6.85410	−	4.97980i	0.941483	−	0.684028i	−0.00729395	−	0.999973i	$-0.502322\pi$
$53$	6.85410	−	4.97980i	0.941483	−	0.684028i	0.948777	+	0.315946i	$0.102322\pi$
$54$	1.00000			0.136083
$55$	−2.00000	+	4.97980i	−0.269680	+	0.671476i
$56$	−1.00000			−0.133631
$57$	1.50000	−	1.08981i	0.198680	−	0.144349i
$58$	−2.00000	−	6.15537i	−0.262613	−	0.808239i
$59$	−0.236068	+	0.726543i	−0.0307334	+	0.0945878i	−0.965247	−	0.261341i	$-0.915835\pi$
$59$	−0.236068	+	0.726543i	−0.0307334	+	0.0945878i	0.934513	+	0.355929i	$0.115835\pi$
$60$	1.30902	+	0.951057i	0.168993	+	0.122781i
$61$	8.23607	+	5.98385i	1.05452	+	0.766154i	0.973067	−	0.230523i	$-0.0740438\pi$
$61$	8.23607	+	5.98385i	1.05452	+	0.766154i	0.0814536	+	0.996677i	$0.474044\pi$
$62$	−0.736068	+	2.26538i	−0.0934807	+	0.287704i
$63$	0.309017	+	0.951057i	0.0389325	+	0.119822i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	3.23607			0.401385
$66$	−1.23607	+	3.07768i	−0.152149	+	0.378837i
$67$	10.1803			1.24373			0.621863	−	0.783126i	$-0.286376\pi$
$67$	10.1803			1.24373			0.621863	+	0.783126i	$0.286376\pi$
$68$	−2.11803	+	1.53884i	−0.256849	+	0.186612i
$69$	−0.572949	−	1.76336i	−0.0689750	−	0.212283i
$70$	−0.500000	+	1.53884i	−0.0597614	+	0.183927i
$71$	2.00000	+	1.45309i	0.237356	+	0.172449i	0.700105	−	0.714040i	$-0.253137\pi$
$71$	2.00000	+	1.45309i	0.237356	+	0.172449i	−0.462748	+	0.886490i	$0.653137\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	3.76393	−	11.5842i	0.440535	−	1.35583i	−0.446772	−	0.894648i	$-0.647427\pi$
$73$	3.76393	−	11.5842i	0.440535	−	1.35583i	0.887307	−	0.461179i	$-0.152573\pi$
$74$	0.881966	+	2.71441i	0.102526	+	0.315544i
$75$	−1.92705	+	1.40008i	−0.222517	+	0.161668i
$76$	1.85410			0.212680
$77$	−3.30902	−	0.224514i	−0.377097	−	0.0255857i
$78$	2.00000			0.226455
$79$	−4.47214	+	3.24920i	−0.503155	+	0.365563i	−0.810221	−	0.586125i	$-0.800653\pi$
$79$	−4.47214	+	3.24920i	−0.503155	+	0.365563i	0.307066	+	0.951688i	$0.400653\pi$
$80$	0.500000	+	1.53884i	0.0559017	+	0.172048i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	0.309017	+	0.224514i	0.0341252	+	0.0247934i
$83$	−5.85410	−	4.25325i	−0.642571	−	0.466855i	0.218161	−	0.975913i	$-0.429994\pi$
$83$	−5.85410	−	4.25325i	−0.642571	−	0.466855i	−0.860733	+	0.509057i	$0.829994\pi$
$84$	−0.309017	+	0.951057i	−0.0337165	+	0.103769i
$85$	1.30902	+	4.02874i	0.141983	+	0.436978i
$86$	8.09017	−	5.87785i	0.872385	−	0.633825i
$87$	−6.47214			−0.693886
$88$	−2.80902	+	1.76336i	−0.299442	+	0.187974i
$89$	8.79837			0.932626			0.466313	−	0.884620i	$-0.345582\pi$
$89$	8.79837			0.932626			0.466313	+	0.884620i	$0.345582\pi$
$90$	1.30902	−	0.951057i	0.137983	−	0.100250i
$91$	0.618034	+	1.90211i	0.0647876	+	0.199396i
$92$	0.572949	−	1.76336i	0.0597341	−	0.183843i
$93$	1.92705	+	1.40008i	0.199826	+	0.145182i
$94$	−2.00000	−	1.45309i	−0.206284	−	0.149874i
$95$	0.927051	−	2.85317i	0.0951134	−	0.292729i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−9.85410	+	7.15942i	−1.00053	+	0.726929i	−0.962202	−	0.272336i	$-0.912204\pi$
$97$	−9.85410	+	7.15942i	−1.00053	+	0.726929i	−0.0383302	+	0.999265i	$0.512204\pi$
$98$	−1.00000			−0.101015
$99$	2.54508	+	2.12663i	0.255791	+	0.213734i
$100$	−2.38197			−0.238197
$101$	11.0172	−	8.00448i	1.09625	−	0.796475i	0.115810	−	0.993271i	$-0.463054\pi$
$101$	11.0172	−	8.00448i	1.09625	−	0.796475i	0.980444	+	0.196796i	$0.0630536\pi$
$102$	0.809017	+	2.48990i	0.0801046	+	0.246537i
$103$	−3.57295	+	10.9964i	−0.352053	+	1.08351i	0.605645	+	0.795735i	$0.292915\pi$
$103$	−3.57295	+	10.9964i	−0.352053	+	1.08351i	−0.957699	+	0.287773i	$0.907085\pi$
$104$	1.61803	+	1.17557i	0.158661	+	0.115274i
$105$	1.30902	+	0.951057i	0.127747	+	0.0928136i
$106$	2.61803	−	8.05748i	0.254286	−	0.782612i
$107$	2.42705	+	7.46969i	0.234632	+	0.722123i	0.997170	+	0.0751794i	$0.0239529\pi$
$107$	2.42705	+	7.46969i	0.234632	+	0.722123i	−0.762538	+	0.646943i	$0.776047\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	10.8541			1.03963			0.519817	−	0.854278i	$-0.326000\pi$
$109$	10.8541			1.03963			0.519817	+	0.854278i	$0.326000\pi$
$110$	1.30902	+	5.20431i	0.124810	+	0.496212i
$111$	2.85410			0.270899
$112$	−0.809017	+	0.587785i	−0.0764449	+	0.0555405i
$113$	−6.32624	−	19.4702i	−0.595122	−	1.83160i	−0.554116	−	0.832440i	$-0.686944\pi$
$113$	−6.32624	−	19.4702i	−0.595122	−	1.83160i	−0.0410065	−	0.999159i	$-0.513056\pi$
$114$	0.572949	−	1.76336i	0.0536616	−	0.165153i
$115$	−2.42705	−	1.76336i	−0.226324	−	0.164434i
$116$	−5.23607	−	3.80423i	−0.486157	−	0.353214i
$117$	0.618034	−	1.90211i	0.0571373	−	0.175850i
$118$	0.236068	+	0.726543i	0.0217318	+	0.0668837i
$119$	−2.11803	+	1.53884i	−0.194160	+	0.141065i
$120$	1.61803			0.147706
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	10.1803			0.921685
$123$	0.309017	−	0.224514i	0.0278631	−	0.0202437i
$124$	0.736068	+	2.26538i	0.0661009	+	0.203438i
$125$	−3.69098	+	11.3597i	−0.330132	+	1.01604i
$126$	0.809017	+	0.587785i	0.0720730	+	0.0523641i
$127$	10.4721	+	7.60845i	0.929252	+	0.675141i	0.945810	−	0.324722i	$-0.105271\pi$
$127$	10.4721	+	7.60845i	0.929252	+	0.675141i	−0.0165577	+	0.999863i	$0.505271\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−3.09017	−	9.51057i	−0.272074	−	0.837359i
$130$	2.61803	−	1.90211i	0.229617	−	0.166826i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	0.809017	+	3.21644i	0.0704159	+	0.279955i
$133$	1.85410			0.160771
$134$	8.23607	−	5.98385i	0.711488	−	0.516926i
$135$	−0.500000	−	1.53884i	−0.0430331	−	0.132442i
$136$	−0.809017	+	2.48990i	−0.0693726	+	0.213507i
$137$	−0.618034	−	0.449028i	−0.0528022	−	0.0383630i	0.561071	−	0.827768i	$-0.310389\pi$
$137$	−0.618034	−	0.449028i	−0.0528022	−	0.0383630i	−0.613873	+	0.789405i	$0.710389\pi$
$138$	−1.50000	−	1.08981i	−0.127688	−	0.0927711i
$139$	0.190983	−	0.587785i	0.0161990	−	0.0498553i	−0.942630	−	0.333838i	$-0.891656\pi$
$139$	0.190983	−	0.587785i	0.0161990	−	0.0498553i	0.958829	+	0.283983i	$0.0916560\pi$
$140$	0.500000	+	1.53884i	0.0422577	+	0.130056i
$141$	−2.00000	+	1.45309i	−0.168430	+	0.122372i
$142$	2.47214			0.207457
$143$	5.09017	+	4.25325i	0.425661	+	0.355675i
$144$	1.00000			0.0833333
$145$	−8.47214	+	6.15537i	−0.703573	+	0.511175i
$146$	−3.76393	−	11.5842i	−0.311505	−	0.958715i
$147$	−0.309017	+	0.951057i	−0.0254873	+	0.0784418i
$148$	2.30902	+	1.67760i	0.189800	+	0.137898i
$149$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$149$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$150$	−0.736068	+	2.26538i	−0.0600997	+	0.184968i
$151$	0.854102	+	2.62866i	0.0695058	+	0.213917i	0.979776	−	0.200098i	$-0.0641261\pi$
$151$	0.854102	+	2.62866i	0.0695058	+	0.213917i	−0.910270	+	0.414015i	$0.864126\pi$
$152$	1.50000	−	1.08981i	0.121666	−	0.0883956i
$153$	2.61803			0.211656
$154$	−2.80902	+	1.76336i	−0.226357	+	0.142095i
$155$	3.85410			0.309569
$156$	1.61803	−	1.17557i	0.129546	−	0.0941210i
$157$	−3.00000	−	9.23305i	−0.239426	−	0.736878i	−0.996503	−	0.0835524i	$-0.973373\pi$
$157$	−3.00000	−	9.23305i	−0.239426	−	0.736878i	0.757077	−	0.653325i	$-0.226627\pi$
$158$	−1.70820	+	5.25731i	−0.135897	+	0.418249i
$159$	−6.85410	−	4.97980i	−0.543566	−	0.394924i
$160$	1.30902	+	0.951057i	0.103487	+	0.0751876i
$161$	0.572949	−	1.76336i	0.0451547	−	0.138972i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−8.09017	+	5.87785i	−0.633671	+	0.460389i	−0.857670	−	0.514200i	$-0.828089\pi$
$163$	−8.09017	+	5.87785i	−0.633671	+	0.460389i	0.223999	+	0.974589i	$0.428089\pi$
$164$	0.381966			0.0298265
$165$	5.35410	+	0.363271i	0.416816	+	0.0282806i
$166$	−7.23607			−0.561628
$167$	−13.9443	+	10.1311i	−1.07904	+	0.783969i	−0.977515	−	0.210864i	$-0.932372\pi$
$167$	−13.9443	+	10.1311i	−1.07904	+	0.783969i	−0.101525	+	0.994833i	$0.532372\pi$
$168$	0.309017	+	0.951057i	0.0238412	+	0.0733756i
$169$	−2.78115	+	8.55951i	−0.213935	+	0.658424i
$170$	3.42705	+	2.48990i	0.262843	+	0.190966i
$171$	−1.50000	−	1.08981i	−0.114708	−	0.0833401i
$172$	3.09017	−	9.51057i	0.235623	−	0.725174i
$173$	−7.33688	−	22.5806i	−0.557813	−	1.71677i	−0.688397	−	0.725334i	$-0.741685\pi$
$173$	−7.33688	−	22.5806i	−0.557813	−	1.71677i	0.130584	−	0.991437i	$-0.458315\pi$
$174$	−5.23607	+	3.80423i	−0.396945	+	0.288398i
$175$	−2.38197			−0.180060
$176$	−1.23607	+	3.07768i	−0.0931721	+	0.231989i
$177$	0.763932			0.0574206
$178$	7.11803	−	5.17155i	0.533519	−	0.387624i
$179$	4.02786	+	12.3965i	0.301057	+	0.926557i	0.981119	+	0.193403i	$0.0619526\pi$
$179$	4.02786	+	12.3965i	0.301057	+	0.926557i	−0.680063	+	0.733154i	$0.738047\pi$
$180$	0.500000	−	1.53884i	0.0372678	−	0.114698i
$181$	−3.47214	−	2.52265i	−0.258082	−	0.187507i	0.451219	−	0.892413i	$-0.350989\pi$
$181$	−3.47214	−	2.52265i	−0.258082	−	0.187507i	−0.709301	+	0.704906i	$0.750989\pi$
$182$	1.61803	+	1.17557i	0.119937	+	0.0871391i
$183$	3.14590	−	9.68208i	0.232551	−	0.715720i
$184$	−0.572949	−	1.76336i	−0.0422384	−	0.129996i
$185$	3.73607	−	2.71441i	0.274681	−	0.199568i
$186$	2.38197			0.174654
$187$	−3.23607	+	8.05748i	−0.236645	+	0.589221i
$188$	−2.47214			−0.180299
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	−0.927051	−	2.85317i	−0.0672553	−	0.206991i
$191$	−3.82624	+	11.7759i	−0.276857	+	0.852078i	0.711865	+	0.702316i	$0.247851\pi$
$191$	−3.82624	+	11.7759i	−0.276857	+	0.852078i	−0.988722	+	0.149762i	$0.952149\pi$
$192$	0.809017	+	0.587785i	0.0583858	+	0.0424197i
$193$	−20.1074	−	14.6089i	−1.44736	−	1.05157i	−0.986439	−	0.164130i	$-0.947518\pi$
$193$	−20.1074	−	14.6089i	−1.44736	−	1.05157i	−0.460923	−	0.887440i	$-0.652482\pi$
$194$	−3.76393	+	11.5842i	−0.270235	+	0.831696i
$195$	−1.00000	−	3.07768i	−0.0716115	−	0.220397i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−2.18034			−0.155343			−0.0776714	−	0.996979i	$-0.524748\pi$
$197$	−2.18034			−0.155343			−0.0776714	+	0.996979i	$0.524748\pi$
$198$	3.30902	+	0.224514i	0.235162	+	0.0159555i
$199$	6.61803			0.469140			0.234570	−	0.972099i	$-0.424632\pi$
$199$	6.61803			0.469140			0.234570	+	0.972099i	$0.424632\pi$
$200$	−1.92705	+	1.40008i	−0.136263	+	0.0990009i
$201$	−3.14590	−	9.68208i	−0.221895	−	0.682921i
$202$	4.20820	−	12.9515i	0.296088	−	0.911266i
$203$	−5.23607	−	3.80423i	−0.367500	−	0.267004i
$204$	2.11803	+	1.53884i	0.148292	+	0.107740i
$205$	0.190983	−	0.587785i	0.0133388	−	0.0410527i
$206$	3.57295	+	10.9964i	0.248939	+	0.766156i
$207$	−1.50000	+	1.08981i	−0.104257	+	0.0757473i
$208$	2.00000			0.138675
$209$	5.20820	−	3.26944i	0.360259	−	0.226152i
$210$	1.61803			0.111655
$211$	8.61803	−	6.26137i	0.593290	−	0.431050i	−0.250201	−	0.968194i	$-0.580497\pi$
$211$	8.61803	−	6.26137i	0.593290	−	0.431050i	0.843491	+	0.537144i	$0.180497\pi$
$212$	−2.61803	−	8.05748i	−0.179807	−	0.553390i
$213$	0.763932	−	2.35114i	0.0523438	−	0.161098i
$214$	6.35410	+	4.61653i	0.434357	+	0.315579i
$215$	−13.0902	−	9.51057i	−0.892742	−	0.648615i
$216$	0.309017	−	0.951057i	0.0210259	−	0.0647112i
$217$	0.736068	+	2.26538i	0.0499676	+	0.153784i
$218$	8.78115	−	6.37988i	0.594735	−	0.432100i
$219$	−12.1803			−0.823071
$220$	4.11803	+	3.44095i	0.277638	+	0.231989i
$221$	5.23607			0.352216
$222$	2.30902	−	1.67760i	0.154971	−	0.112593i
$223$	4.80902	+	14.8006i	0.322036	+	0.991124i	0.972761	+	0.231810i	$0.0744649\pi$
$223$	4.80902	+	14.8006i	0.322036	+	0.991124i	−0.650725	+	0.759313i	$0.725535\pi$
$224$	−0.309017	+	0.951057i	−0.0206471	+	0.0635451i
$225$	1.92705	+	1.40008i	0.128470	+	0.0933390i
$226$	−16.5623	−	12.0332i	−1.10171	−	0.800438i
$227$	−0.854102	+	2.62866i	−0.0566887	+	0.174470i	−0.975392	−	0.220479i	$-0.929238\pi$
$227$	−0.854102	+	2.62866i	−0.0566887	+	0.174470i	0.918703	+	0.394949i	$0.129238\pi$
$228$	−0.572949	−	1.76336i	−0.0379445	−	0.116781i
$229$	3.23607	−	2.35114i	0.213845	−	0.155368i	−0.475706	−	0.879604i	$-0.657808\pi$
$229$	3.23607	−	2.35114i	0.213845	−	0.155368i	0.689552	+	0.724236i	$0.257808\pi$
$230$	−3.00000			−0.197814
$231$	0.809017	+	3.21644i	0.0532294	+	0.211626i
$232$	−6.47214			−0.424917
$233$	−4.23607	+	3.07768i	−0.277514	+	0.201626i	−0.717832	−	0.696216i	$-0.754866\pi$
$233$	−4.23607	+	3.07768i	−0.277514	+	0.201626i	0.440318	+	0.897842i	$0.354866\pi$
$234$	−0.618034	−	1.90211i	−0.0404021	−	0.124345i
$235$	−1.23607	+	3.80423i	−0.0806322	+	0.248160i
$236$	0.618034	+	0.449028i	0.0402306	+	0.0292292i
$237$	4.47214	+	3.24920i	0.290496	+	0.211058i
$238$	−0.809017	+	2.48990i	−0.0524408	+	0.161396i
$239$	−0.371323	−	1.14281i	−0.0240189	−	0.0739225i	0.938329	−	0.345745i	$-0.112374\pi$
$239$	−0.371323	−	1.14281i	−0.0240189	−	0.0739225i	−0.962347	+	0.271822i	$0.912374\pi$
$240$	1.30902	−	0.951057i	0.0844967	−	0.0613904i
$241$	−11.1246			−0.716599			−0.358300	−	0.933607i	$-0.616643\pi$
$241$	−11.1246			−0.716599			−0.358300	+	0.933607i	$0.616643\pi$
$242$	−4.78115	+	9.90659i	−0.307344	+	0.636820i
$243$	−1.00000			−0.0641500
$244$	8.23607	−	5.98385i	0.527260	−	0.383077i
$245$	0.500000	+	1.53884i	0.0319438	+	0.0983130i
$246$	0.118034	−	0.363271i	0.00752557	−	0.0231613i
$247$	−3.00000	−	2.17963i	−0.190885	−	0.138686i
$248$	1.92705	+	1.40008i	0.122368	+	0.0889055i
$249$	−2.23607	+	6.88191i	−0.141705	+	0.436123i
$250$	3.69098	+	11.3597i	0.233438	+	0.718449i
$251$	−12.5623	+	9.12705i	−0.792926	+	0.576094i	−0.908830	−	0.417166i	$-0.863023\pi$
$251$	−12.5623	+	9.12705i	−0.792926	+	0.576094i	0.115905	+	0.993260i	$0.463023\pi$
$252$	1.00000			0.0629941
$253$	−1.50000	−	5.96361i	−0.0943042	−	0.374929i
$254$	12.9443			0.812196
$255$	3.42705	−	2.48990i	0.214610	−	0.155923i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.75329	+	23.8622i	−0.483637	+	1.48848i	0.350309	+	0.936634i	$0.386077\pi$
$257$	−7.75329	+	23.8622i	−0.483637	+	1.48848i	−0.833945	+	0.551847i	$0.813923\pi$
$258$	−8.09017	−	5.87785i	−0.503672	−	0.365939i
$259$	2.30902	+	1.67760i	0.143475	+	0.104241i
$260$	1.00000	−	3.07768i	0.0620174	−	0.190870i
$261$	2.00000	+	6.15537i	0.123797	+	0.381008i
$262$		0			0
$263$	−12.0344			−0.742075			−0.371038	−	0.928618i	$-0.620998\pi$
$263$	−12.0344			−0.742075			−0.371038	+	0.928618i	$0.620998\pi$
$264$	2.54508	+	2.12663i	0.156639	+	0.130885i
$265$	−13.7082			−0.842088
$266$	1.50000	−	1.08981i	0.0919709	−	0.0668208i
$267$	−2.71885	−	8.36775i	−0.166391	−	0.512098i
$268$	3.14590	−	9.68208i	0.192166	−	0.591427i
$269$	22.5623	+	16.3925i	1.37565	+	0.999467i	0.997272	+	0.0738149i	$0.0235174\pi$
$269$	22.5623	+	16.3925i	1.37565	+	0.999467i	0.378376	+	0.925652i	$0.376483\pi$
$270$	−1.30902	−	0.951057i	−0.0796642	−	0.0578795i
$271$	7.50000	−	23.0826i	0.455593	−	1.40217i	−0.414846	−	0.909892i	$-0.636164\pi$
$271$	7.50000	−	23.0826i	0.455593	−	1.40217i	0.870438	−	0.492278i	$-0.163836\pi$
$272$	0.809017	+	2.48990i	0.0490539	+	0.150972i
$273$	1.61803	−	1.17557i	0.0979279	−	0.0711488i
$274$	−0.763932			−0.0461508
$275$	−6.69098	+	4.20025i	−0.403481	+	0.253285i
$276$	−1.85410			−0.111604
$277$	−2.88197	+	2.09387i	−0.173161	+	0.125809i	−0.670990	−	0.741467i	$-0.734131\pi$
$277$	−2.88197	+	2.09387i	−0.173161	+	0.125809i	0.497829	+	0.867275i	$0.334131\pi$
$278$	−0.190983	−	0.587785i	−0.0114544	−	0.0352530i
$279$	0.736068	−	2.26538i	0.0440672	−	0.135625i
$280$	1.30902	+	0.951057i	0.0782287	+	0.0568365i
$281$	−13.8541	−	10.0656i	−0.826466	−	0.600463i	0.0920910	−	0.995751i	$-0.470645\pi$
$281$	−13.8541	−	10.0656i	−0.826466	−	0.600463i	−0.918557	+	0.395288i	$0.870645\pi$
$282$	−0.763932	+	2.35114i	−0.0454915	+	0.140008i
$283$	−7.88197	−	24.2582i	−0.468534	−	1.44200i	−0.854483	−	0.519480i	$-0.826126\pi$
$283$	−7.88197	−	24.2582i	−0.468534	−	1.44200i	0.385948	−	0.922520i	$-0.373874\pi$
$284$	2.00000	−	1.45309i	0.118678	−	0.0862247i
$285$	−3.00000			−0.177705
$286$	6.61803	+	0.449028i	0.391333	+	0.0265516i
$287$	0.381966			0.0225467
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−3.13525	−	9.64932i	−0.184427	−	0.567607i
$290$	−3.23607	+	9.95959i	−0.190028	+	0.584847i
$291$	9.85410	+	7.15942i	0.577658	+	0.419693i
$292$	−9.85410	−	7.15942i	−0.576668	−	0.418974i
$293$	2.44427	−	7.52270i	0.142796	−	0.439481i	−0.853925	−	0.520396i	$-0.825784\pi$
$293$	2.44427	−	7.52270i	0.142796	−	0.439481i	0.996721	+	0.0809154i	$0.0257844\pi$
$294$	0.309017	+	0.951057i	0.0180222	+	0.0554667i
$295$	1.00000	−	0.726543i	0.0582223	−	0.0423009i
$296$	2.85410			0.165891
$297$	1.23607	−	3.07768i	0.0717239	−	0.178585i
$298$		0			0
$299$	−3.00000	+	2.17963i	−0.173494	+	0.126051i
$300$	0.736068	+	2.26538i	0.0424969	+	0.130792i
$301$	3.09017	−	9.51057i	0.178114	−	0.548180i
$302$	2.23607	+	1.62460i	0.128671	+	0.0934851i
$303$	−11.0172	−	8.00448i	−0.632923	−	0.459845i
$304$	0.572949	−	1.76336i	0.0328609	−	0.101135i
$305$	−5.09017	−	15.6659i	−0.291462	−	0.897029i
$306$	2.11803	−	1.53884i	0.121080	−	0.0879697i
$307$	20.5623			1.17355			0.586776	−	0.809749i	$-0.300397\pi$
$307$	20.5623			1.17355			0.586776	+	0.809749i	$0.300397\pi$
$308$	−1.23607	+	3.07768i	−0.0704315	+	0.175367i
$309$	11.5623			0.657757
$310$	3.11803	−	2.26538i	0.177092	−	0.128665i
$311$	7.27051	+	22.3763i	0.412273	+	1.26885i	0.914668	+	0.404207i	$0.132452\pi$
$311$	7.27051	+	22.3763i	0.412273	+	1.26885i	−0.502395	+	0.864638i	$0.667548\pi$
$312$	0.618034	−	1.90211i	0.0349893	−	0.107686i
$313$	−3.47214	−	2.52265i	−0.196257	−	0.142589i	0.485317	−	0.874338i	$-0.338704\pi$
$313$	−3.47214	−	2.52265i	−0.196257	−	0.142589i	−0.681574	+	0.731749i	$0.738704\pi$
$314$	−7.85410	−	5.70634i	−0.443233	−	0.322027i
$315$	0.500000	−	1.53884i	0.0281718	−	0.0867039i
$316$	1.70820	+	5.25731i	0.0960940	+	0.295747i
$317$	−10.8541	+	7.88597i	−0.609627	+	0.442920i	−0.849283	−	0.527938i	$-0.822965\pi$
$317$	−10.8541	+	7.88597i	−0.609627	+	0.442920i	0.239656	+	0.970858i	$0.422965\pi$
$318$	−8.47214			−0.475094
$319$	−21.4164	−	1.45309i	−1.19909	−	0.0813571i
$320$	1.61803			0.0904508
$321$	6.35410	−	4.61653i	0.354651	−	0.257669i
$322$	−0.572949	−	1.76336i	−0.0319292	−	0.0982680i
$323$	1.50000	−	4.61653i	0.0834622	−	0.256870i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	3.85410	+	2.80017i	0.213787	+	0.155325i
$326$	−3.09017	+	9.51057i	−0.171149	+	0.526741i
$327$	−3.35410	−	10.3229i	−0.185482	−	0.570856i
$328$	0.309017	−	0.224514i	0.0170626	−	0.0123967i
$329$	−2.47214			−0.136293
$330$	4.54508	−	2.85317i	0.250199	−	0.157062i
$331$	7.23607			0.397730			0.198865	−	0.980027i	$-0.436274\pi$
$331$	7.23607			0.397730			0.198865	+	0.980027i	$0.436274\pi$
$332$	−5.85410	+	4.25325i	−0.321286	+	0.233428i
$333$	−0.881966	−	2.71441i	−0.0483314	−	0.148749i
$334$	−5.32624	+	16.3925i	−0.291439	+	0.896956i
$335$	−13.3262	−	9.68208i	−0.728090	−	0.528988i
$336$	0.809017	+	0.587785i	0.0441355	+	0.0320663i
$337$	9.68034	−	29.7930i	0.527322	−	1.62293i	−0.232357	−	0.972631i	$-0.574644\pi$
$337$	9.68034	−	29.7930i	0.527322	−	1.62293i	0.759679	−	0.650299i	$-0.225356\pi$
$338$	2.78115	+	8.55951i	0.151275	+	0.465576i
$339$	−16.5623	+	12.0332i	−0.899541	+	0.653555i
$340$	4.23607			0.229733
$341$	6.06231	+	5.06555i	0.328292	+	0.274315i
$342$	−1.85410			−0.100258
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−3.09017	−	9.51057i	−0.166611	−	0.512775i
$345$	−0.927051	+	2.85317i	−0.0499107	+	0.153609i
$346$	−19.2082	−	13.9556i	−1.03264	−	0.750256i
$347$	−29.3435	−	21.3193i	−1.57524	−	1.14448i	−0.921910	−	0.387405i	$-0.873372\pi$
$347$	−29.3435	−	21.3193i	−1.57524	−	1.14448i	−0.653330	−	0.757073i	$-0.726628\pi$
$348$	−2.00000	+	6.15537i	−0.107211	+	0.329962i
$349$	5.18034	+	15.9434i	0.277297	+	0.853433i	0.988602	+	0.150550i	$0.0481044\pi$
$349$	5.18034	+	15.9434i	0.277297	+	0.853433i	−0.711305	+	0.702883i	$0.751896\pi$
$350$	−1.92705	+	1.40008i	−0.103005	+	0.0748377i
$351$	−2.00000			−0.106752
$352$	0.809017	+	3.21644i	0.0431208	+	0.171437i
$353$	23.8885			1.27146			0.635729	−	0.771912i	$-0.280699\pi$
$353$	23.8885			1.27146			0.635729	+	0.771912i	$0.280699\pi$
$354$	0.618034	−	0.449028i	0.0328481	−	0.0238656i
$355$	−1.23607	−	3.80423i	−0.0656037	−	0.201907i
$356$	2.71885	−	8.36775i	0.144099	−	0.443490i
$357$	2.11803	+	1.53884i	0.112098	+	0.0814441i
$358$	10.5451	+	7.66145i	0.557325	+	0.404920i
$359$	−7.93769	+	24.4297i	−0.418935	+	1.28935i	0.489748	+	0.871864i	$0.337089\pi$
$359$	−7.93769	+	24.4297i	−0.418935	+	1.28935i	−0.908683	+	0.417487i	$0.862911\pi$
$360$	−0.500000	−	1.53884i	−0.0263523	−	0.0811041i
$361$	12.5902	−	9.14729i	0.662641	−	0.481437i
$362$	−4.29180			−0.225572
$363$	7.94427	+	7.60845i	0.416966	+	0.399340i
$364$	2.00000			0.104828
$365$	−15.9443	+	11.5842i	−0.834561	+	0.606344i
$366$	−3.14590	−	9.68208i	−0.164439	−	0.506090i
$367$	3.44427	−	10.6004i	0.179790	−	0.553335i	−0.820030	−	0.572320i	$-0.806043\pi$
$367$	3.44427	−	10.6004i	0.179790	−	0.553335i	0.999820	+	0.0189849i	$0.00604345\pi$
$368$	−1.50000	−	1.08981i	−0.0781929	−	0.0568105i
$369$	−0.309017	−	0.224514i	−0.0160868	−	0.0116877i
$370$	1.42705	−	4.39201i	0.0741888	−	0.228330i
$371$	−2.61803	−	8.05748i	−0.135922	−	0.418324i
$372$	1.92705	−	1.40008i	0.0999129	−	0.0725910i
$373$	30.2705			1.56735			0.783674	−	0.621173i	$-0.213343\pi$
$373$	30.2705			1.56735			0.783674	+	0.621173i	$0.213343\pi$
$374$	2.11803	+	8.42075i	0.109521	+	0.435427i
$375$	11.9443			0.616800
$376$	−2.00000	+	1.45309i	−0.103142	+	0.0749371i
$377$	4.00000	+	12.3107i	0.206010	+	0.634035i
$378$	0.309017	−	0.951057i	0.0158941	−	0.0489171i
$379$	14.0902	+	10.2371i	0.723763	+	0.525845i	0.887584	−	0.460645i	$-0.152382\pi$
$379$	14.0902	+	10.2371i	0.723763	+	0.525845i	−0.163821	+	0.986490i	$0.552382\pi$
$380$	−2.42705	−	1.76336i	−0.124505	−	0.0904582i
$381$	4.00000	−	12.3107i	0.204926	−	0.630698i
$382$	3.82624	+	11.7759i	0.195767	+	0.602510i
$383$	9.61803	−	6.98791i	0.491459	−	0.357066i	−0.314286	−	0.949328i	$-0.601765\pi$
$383$	9.61803	−	6.98791i	0.491459	−	0.357066i	0.805745	+	0.592263i	$0.201765\pi$
$384$	1.00000			0.0510310
$385$	4.11803	+	3.44095i	0.209874	+	0.175367i
$386$	−24.8541			−1.26504
$387$	−8.09017	+	5.87785i	−0.411246	+	0.298788i
$388$	3.76393	+	11.5842i	0.191085	+	0.588098i
$389$	−7.85410	+	24.1724i	−0.398219	+	1.22559i	0.528208	+	0.849115i	$0.322864\pi$
$389$	−7.85410	+	24.1724i	−0.398219	+	1.22559i	−0.926426	+	0.376476i	$0.877136\pi$
$390$	−2.61803	−	1.90211i	−0.132569	−	0.0963172i
$391$	−3.92705	−	2.85317i	−0.198600	−	0.144291i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	−1.76393	+	1.28157i	−0.0888656	+	0.0645646i
$395$	8.94427			0.450035
$396$	2.80902	−	1.76336i	0.141158	−	0.0886120i
$397$	1.41641			0.0710875			0.0355437	−	0.999368i	$-0.488684\pi$
$397$	1.41641			0.0710875			0.0355437	+	0.999368i	$0.488684\pi$
$398$	5.35410	−	3.88998i	0.268377	−	0.194987i
$399$	−0.572949	−	1.76336i	−0.0286833	−	0.0882782i
$400$	−0.736068	+	2.26538i	−0.0368034	+	0.113269i
$401$	27.1803	+	19.7477i	1.35732	+	0.986152i	0.998610	+	0.0527031i	$0.0167837\pi$
$401$	27.1803	+	19.7477i	1.35732	+	0.986152i	0.358711	+	0.933449i	$0.383216\pi$
$402$	−8.23607	−	5.98385i	−0.410778	−	0.298447i
$403$	1.47214	−	4.53077i	0.0733323	−	0.225694i
$404$	−4.20820	−	12.9515i	−0.209366	−	0.644362i
$405$	−1.30902	+	0.951057i	−0.0650456	+	0.0472584i
$406$	−6.47214			−0.321207
$407$	9.44427	+	0.640786i	0.468135	+	0.0317626i
$408$	2.61803			0.129612
$409$	−12.3262	+	8.95554i	−0.609493	+	0.442823i	−0.849236	−	0.528014i	$-0.822937\pi$
$409$	−12.3262	+	8.95554i	−0.609493	+	0.442823i	0.239743	+	0.970836i	$0.422937\pi$
$410$	−0.190983	−	0.587785i	−0.00943198	−	0.0290286i
$411$	−0.236068	+	0.726543i	−0.0116444	+	0.0358377i
$412$	9.35410	+	6.79615i	0.460844	+	0.334822i
$413$	0.618034	+	0.449028i	0.0304115	+	0.0220952i
$414$	−0.572949	+	1.76336i	−0.0281589	+	0.0866642i
$415$	3.61803	+	11.1352i	0.177602	+	0.546604i
$416$	1.61803	−	1.17557i	0.0793306	−	0.0576371i
$417$	−0.618034			−0.0302653
$418$	2.29180	−	5.70634i	0.112095	−	0.279106i
$419$	19.0557			0.930933			0.465467	−	0.885065i	$-0.345887\pi$
$419$	19.0557			0.930933			0.465467	+	0.885065i	$0.345887\pi$
$420$	1.30902	−	0.951057i	0.0638735	−	0.0464068i
$421$	3.57295	+	10.9964i	0.174135	+	0.535932i	0.999593	−	0.0285315i	$-0.00908308\pi$
$421$	3.57295	+	10.9964i	0.174135	+	0.535932i	−0.825458	+	0.564464i	$0.809083\pi$
$422$	3.29180	−	10.1311i	0.160242	−	0.493175i
$423$	2.00000	+	1.45309i	0.0972433	+	0.0706514i
$424$	−6.85410	−	4.97980i	−0.332865	−	0.241840i
$425$	−1.92705	+	5.93085i	−0.0934757	+	0.287689i
$426$	−0.763932	−	2.35114i	−0.0370126	−	0.113913i
$427$	8.23607	−	5.98385i	0.398571	−	0.289579i
$428$	7.85410			0.379642
$429$	2.47214	−	6.15537i	0.119356	−	0.297184i
$430$	−16.1803			−0.780285
$431$	18.3435	−	13.3273i	0.883573	−	0.641954i	−0.0506211	−	0.998718i	$-0.516120\pi$
$431$	18.3435	−	13.3273i	0.883573	−	0.641954i	0.934194	+	0.356764i	$0.116120\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	1.56231	−	4.80828i	0.0750796	−	0.231071i	−0.906473	−	0.422264i	$-0.861236\pi$
$433$	1.56231	−	4.80828i	0.0750796	−	0.231071i	0.981553	+	0.191193i	$0.0612355\pi$
$434$	1.92705	+	1.40008i	0.0925014	+	0.0672062i
$435$	8.47214	+	6.15537i	0.406208	+	0.295127i
$436$	3.35410	−	10.3229i	0.160632	−	0.494376i
$437$	1.06231	+	3.26944i	0.0508170	+	0.156399i
$438$	−9.85410	+	7.15942i	−0.470847	+	0.342091i
$439$	22.3820			1.06823			0.534116	−	0.845411i	$-0.320644\pi$
$439$	22.3820			1.06823			0.534116	+	0.845411i	$0.320644\pi$
$440$	5.35410	+	0.363271i	0.255247	+	0.0173183i
$441$	1.00000			0.0476190
$442$	4.23607	−	3.07768i	0.201489	−	0.146390i
$443$	2.42705	+	7.46969i	0.115313	+	0.354896i	0.992012	−	0.126143i	$-0.0402597\pi$
$443$	2.42705	+	7.46969i	0.115313	+	0.354896i	−0.876699	+	0.481039i	$0.840260\pi$
$444$	0.881966	−	2.71441i	0.0418563	−	0.128820i
$445$	−11.5172	−	8.36775i	−0.545969	−	0.396669i
$446$	12.5902	+	9.14729i	0.596162	+	0.433137i
$447$		0			0
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−26.2705	+	19.0866i	−1.23978	+	0.900754i	−0.997584	−	0.0694725i	$-0.977868\pi$
$449$	−26.2705	+	19.0866i	−1.23978	+	0.900754i	−0.242198	+	0.970227i	$0.577868\pi$
$450$	2.38197			0.112287
$451$	1.07295	−	0.673542i	0.0505232	−	0.0317159i
$452$	−20.4721			−0.962928
$453$	2.23607	−	1.62460i	0.105060	−	0.0763303i
$454$	0.854102	+	2.62866i	0.0400850	+	0.123369i
$455$	1.00000	−	3.07768i	0.0468807	−	0.144284i
$456$	−1.50000	−	1.08981i	−0.0702439	−	0.0510352i
$457$	21.3262	+	15.4944i	0.997599	+	0.724798i	0.961572	−	0.274552i	$-0.0885297\pi$
$457$	21.3262	+	15.4944i	0.997599	+	0.724798i	0.0360272	+	0.999351i	$0.488530\pi$
$458$	1.23607	−	3.80423i	0.0577577	−	0.177760i
$459$	−0.809017	−	2.48990i	−0.0377617	−	0.116218i
$460$	−2.42705	+	1.76336i	−0.113162	+	0.0822169i
$461$	38.9443			1.81382			0.906908	−	0.421329i	$-0.138436\pi$
$461$	38.9443			1.81382			0.906908	+	0.421329i	$0.138436\pi$
$462$	2.54508	+	2.12663i	0.118408	+	0.0989396i
$463$	28.5410			1.32641			0.663207	−	0.748436i	$-0.269195\pi$
$463$	28.5410			1.32641			0.663207	+	0.748436i	$0.269195\pi$
$464$	−5.23607	+	3.80423i	−0.243078	+	0.176607i
$465$	−1.19098	−	3.66547i	−0.0552305	−	0.169982i
$466$	−1.61803	+	4.97980i	−0.0749540	+	0.230685i
$467$	6.38197	+	4.63677i	0.295322	+	0.214564i	0.725573	−	0.688145i	$-0.241575\pi$
$467$	6.38197	+	4.63677i	0.295322	+	0.214564i	−0.430251	+	0.902709i	$0.641575\pi$
$468$	−1.61803	−	1.17557i	−0.0747936	−	0.0543408i
$469$	3.14590	−	9.68208i	0.145264	−	0.447077i
$470$	1.23607	+	3.80423i	0.0570156	+	0.175476i
$471$	−7.85410	+	5.70634i	−0.361898	+	0.262934i
$472$	0.763932			0.0351628
$473$	−8.09017	−	32.1644i	−0.371986	−	1.47892i
$474$	5.52786			0.253903
$475$	3.57295	−	2.59590i	0.163938	−	0.119108i
$476$	0.809017	+	2.48990i	0.0370812	+	0.114124i
$477$	−2.61803	+	8.05748i	−0.119872	+	0.368927i
$478$	−0.972136	−	0.706298i	−0.0444645	−	0.0323053i
$479$	7.70820	+	5.60034i	0.352197	+	0.255886i	0.749790	−	0.661676i	$-0.230154\pi$
$479$	7.70820	+	5.60034i	0.352197	+	0.255886i	−0.397593	+	0.917562i	$0.630154\pi$
$480$	0.500000	−	1.53884i	0.0228218	−	0.0702382i
$481$	−1.76393	−	5.42882i	−0.0804284	−	0.247533i
$482$	−9.00000	+	6.53888i	−0.409939	+	0.297838i
$483$	−1.85410			−0.0843646
$484$	1.95492	+	10.8249i	0.0888598	+	0.492041i
$485$	19.7082			0.894903
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	13.0902	+	40.2874i	0.593172	+	1.82560i	0.563622	+	0.826033i	$0.309408\pi$
$487$	13.0902	+	40.2874i	0.593172	+	1.82560i	0.0295506	+	0.999563i	$0.490592\pi$
$488$	3.14590	−	9.68208i	0.142408	−	0.438287i
$489$	8.09017	+	5.87785i	0.365850	+	0.265806i
$490$	1.30902	+	0.951057i	0.0591354	+	0.0429644i
$491$	−8.42705	+	25.9358i	−0.380307	+	1.17047i	0.559520	+	0.828817i	$0.310985\pi$
$491$	−8.42705	+	25.9358i	−0.380307	+	1.17047i	−0.939828	+	0.341649i	$0.889015\pi$
$492$	−0.118034	−	0.363271i	−0.00532138	−	0.0163775i
$493$	−13.7082	+	9.95959i	−0.617386	+	0.448558i
$494$	−3.70820			−0.166840
$495$	−1.30902	−	5.20431i	−0.0588359	−	0.233916i
$496$	2.38197			0.106953
$497$	2.00000	−	1.45309i	0.0897123	−	0.0651798i
$498$	2.23607	+	6.88191i	0.100201	+	0.308386i
$499$	11.2705	−	34.6871i	0.504537	−	1.55281i	−0.297010	−	0.954874i	$-0.595989\pi$
$499$	11.2705	−	34.6871i	0.504537	−	1.55281i	0.801547	−	0.597932i	$-0.204011\pi$
$500$	9.66312	+	7.02067i	0.432148	+	0.313974i
$501$	13.9443	+	10.1311i	0.622984	+	0.452624i
$502$	−4.79837	+	14.7679i	−0.214162	+	0.659123i
$503$	−0.673762	−	2.07363i	−0.0300416	−	0.0924584i	0.934912	−	0.354881i	$-0.115479\pi$
$503$	−0.673762	−	2.07363i	−0.0300416	−	0.0924584i	−0.964953	+	0.262422i	$0.915479\pi$
$504$	0.809017	−	0.587785i	0.0360365	−	0.0261820i
$505$	−22.0344			−0.980520
$506$	−4.71885	−	3.94298i	−0.209778	−	0.175287i
$507$	9.00000			0.399704
$508$	10.4721	−	7.60845i	0.464626	−	0.337570i
$509$	7.26393	+	22.3561i	0.321968	+	0.990916i	0.972791	+	0.231686i	$0.0744242\pi$
$509$	7.26393	+	22.3561i	0.321968	+	0.990916i	−0.650822	+	0.759230i	$0.725576\pi$
$510$	1.30902	−	4.02874i	0.0579642	−	0.178396i
$511$	−9.85410	−	7.15942i	−0.435920	−	0.316714i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.572949	+	1.76336i	−0.0252963	+	0.0778541i
$514$	7.75329	+	23.8622i	0.341983	+	1.05252i
$515$	15.1353	−	10.9964i	0.666939	−	0.484560i
$516$	−10.0000			−0.440225
$517$	−6.94427	+	4.35926i	−0.305409	+	0.191720i
$518$	2.85410			0.125402
$519$	−19.2082	+	13.9556i	−0.843147	+	0.612582i
$520$	−1.00000	−	3.07768i	−0.0438529	−	0.134965i
$521$	4.06231	−	12.5025i	0.177973	−	0.547744i	−0.821784	−	0.569799i	$-0.807021\pi$
$521$	4.06231	−	12.5025i	0.177973	−	0.547744i	0.999757	+	0.0220552i	$0.00702094\pi$
$522$	5.23607	+	3.80423i	0.229176	+	0.166506i
$523$	−21.9164	−	15.9232i	−0.958338	−	0.696273i	−0.00557354	−	0.999984i	$-0.501774\pi$
$523$	−21.9164	−	15.9232i	−0.958338	−	0.696273i	−0.952764	+	0.303711i	$0.901774\pi$
$524$		0			0
$525$	0.736068	+	2.26538i	0.0321246	+	0.0988695i
$526$	−9.73607	+	7.07367i	−0.424513	+	0.308427i
$527$	6.23607			0.271647
$528$	3.30902	+	0.224514i	0.144006	+	0.00977072i
$529$	−19.5623			−0.850535
$530$	−11.0902	+	8.05748i	−0.481726	+	0.349995i
$531$	−0.236068	−	0.726543i	−0.0102445	−	0.0315293i
$532$	0.572949	−	1.76336i	0.0248405	−	0.0764512i
$533$	−0.618034	−	0.449028i	−0.0267700	−	0.0194496i
$534$	−7.11803	−	5.17155i	−0.308027	−	0.223795i
$535$	3.92705	−	12.0862i	0.169781	−	0.522533i
$536$	−3.14590	−	9.68208i	−0.135882	−	0.418202i
$537$	10.5451	−	7.66145i	0.455054	−	0.330616i
$538$	27.8885			1.20236
$539$	−1.23607	+	3.07768i	−0.0532412	+	0.132565i
$540$	−1.61803			−0.0696291
$541$	−14.6353	+	10.6331i	−0.629219	+	0.457154i	−0.856129	−	0.516761i	$-0.827137\pi$
$541$	−14.6353	+	10.6331i	−0.629219	+	0.457154i	0.226911	+	0.973916i	$0.427137\pi$
$542$	−7.50000	−	23.0826i	−0.322153	−	0.991484i
$543$	−1.32624	+	4.08174i	−0.0569143	+	0.175164i
$544$	2.11803	+	1.53884i	0.0908100	+	0.0659773i
$545$	−14.2082	−	10.3229i	−0.608613	−	0.442183i
$546$	0.618034	−	1.90211i	0.0264494	−	0.0814029i
$547$	8.56231	+	26.3521i	0.366098	+	1.12673i	0.949291	+	0.314399i	$0.101803\pi$
$547$	8.56231	+	26.3521i	0.366098	+	1.12673i	−0.583193	+	0.812334i	$0.698197\pi$
$548$	−0.618034	+	0.449028i	−0.0264011	+	0.0191815i
$549$	−10.1803			−0.434486
$550$	−2.94427	+	7.33094i	−0.125544	+	0.312592i
$551$	12.0000			0.511217
$552$	−1.50000	+	1.08981i	−0.0638442	+	0.0463856i
$553$	1.70820	+	5.25731i	0.0726402	+	0.223564i
$554$	−1.10081	+	3.38795i	−0.0467691	+	0.143940i
$555$	−3.73607	−	2.71441i	−0.158587	−	0.115220i
$556$	−0.500000	−	0.363271i	−0.0212047	−	0.0154061i
$557$	−7.38197	+	22.7194i	−0.312784	+	0.962650i	0.663873	+	0.747845i	$0.268912\pi$
$557$	−7.38197	+	22.7194i	−0.312784	+	0.962650i	−0.976657	+	0.214805i	$0.931088\pi$
$558$	−0.736068	−	2.26538i	−0.0311602	−	0.0959014i
$559$	−16.1803	+	11.7557i	−0.684355	+	0.497213i
$560$	1.61803			0.0683744
$561$	8.66312	+	0.587785i	0.365757	+	0.0248163i
$562$	−17.1246			−0.722358
$563$	34.9787	−	25.4135i	1.47418	−	1.07105i	0.494801	−	0.869006i	$-0.335241\pi$
$563$	34.9787	−	25.4135i	1.47418	−	1.07105i	0.979376	−	0.202046i	$-0.0647590\pi$
$564$	0.763932	+	2.35114i	0.0321673	+	0.0990009i
$565$	−10.2361	+	31.5034i	−0.430635	+	1.32536i
$566$	−20.6353	−	14.9924i	−0.867364	−	0.630177i
$567$	−0.809017	−	0.587785i	−0.0339755	−	0.0246847i
$568$	0.763932	−	2.35114i	0.0320539	−	0.0986517i
$569$	−7.27051	−	22.3763i	−0.304796	−	0.938064i	−0.979753	−	0.200208i	$-0.935838\pi$
$569$	−7.27051	−	22.3763i	−0.304796	−	0.938064i	0.674958	−	0.737856i	$-0.264162\pi$
$570$	−2.42705	+	1.76336i	−0.101658	+	0.0738588i
$571$	−2.87539			−0.120331			−0.0601656	−	0.998188i	$-0.519163\pi$
$571$	−2.87539			−0.120331			−0.0601656	+	0.998188i	$0.519163\pi$
$572$	5.61803	−	3.52671i	0.234902	−	0.147459i
$573$	12.3820			0.517264
$574$	0.309017	−	0.224514i	0.0128981	−	0.00937103i
$575$	−1.36475	−	4.20025i	−0.0569138	−	0.175163i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−28.5623	−	20.7517i	−1.18906	−	0.863906i	−0.195899	−	0.980624i	$-0.562763\pi$
$577$	−28.5623	−	20.7517i	−1.18906	−	0.863906i	−0.993165	+	0.116718i	$0.962763\pi$
$578$	−8.20820	−	5.96361i	−0.341416	−	0.248053i
$579$	−7.68034	+	23.6377i	−0.319184	+	0.982347i
$580$	3.23607	+	9.95959i	0.134370	+	0.413550i
$581$	−5.85410	+	4.25325i	−0.242869	+	0.176455i
$582$	12.1803			0.504891
$583$	−21.5623	−	18.0171i	−0.893019	−	0.746191i
$584$	−12.1803			−0.504026
$585$	−2.61803	+	1.90211i	−0.108242	+	0.0786427i
$586$	−2.44427	−	7.52270i	−0.100972	−	0.310760i
$587$	8.79837	−	27.0786i	0.363148	−	1.11765i	−0.587985	−	0.808872i	$-0.700079\pi$
$587$	8.79837	−	27.0786i	0.363148	−	1.11765i	0.951133	−	0.308782i	$-0.0999214\pi$
$588$	0.809017	+	0.587785i	0.0333633	+	0.0242399i
$589$	−3.57295	−	2.59590i	−0.147221	−	0.106962i
$590$	0.381966	−	1.17557i	0.0157253	−	0.0483975i
$591$	0.673762	+	2.07363i	0.0277149	+	0.0852976i
$592$	2.30902	−	1.67760i	0.0949000	−	0.0689489i
$593$	29.5066			1.21169			0.605845	−	0.795583i	$-0.292835\pi$
$593$	29.5066			1.21169			0.605845	+	0.795583i	$0.292835\pi$
$594$	−0.809017	−	3.21644i	−0.0331944	−	0.131972i
$595$	4.23607			0.173662
$596$		0			0
$597$	−2.04508	−	6.29412i	−0.0836998	−	0.257601i
$598$	−1.14590	+	3.52671i	−0.0468593	+	0.144218i
$599$	5.73607	+	4.16750i	0.234369	+	0.170279i	0.698771	−	0.715345i	$-0.253731\pi$
$599$	5.73607	+	4.16750i	0.234369	+	0.170279i	−0.464402	+	0.885625i	$0.653731\pi$
$600$	1.92705	+	1.40008i	0.0786715	+	0.0571582i
$601$	6.43769	−	19.8132i	0.262599	−	0.808197i	−0.729638	−	0.683834i	$-0.760311\pi$
$601$	6.43769	−	19.8132i	0.262599	−	0.808197i	0.992237	−	0.124363i	$-0.0396887\pi$
$602$	−3.09017	−	9.51057i	−0.125946	−	0.387622i
$603$	−8.23607	+	5.98385i	−0.335399	+	0.243681i
$604$	2.76393			0.112463
$605$	17.6353	+	2.40414i	0.716975	+	0.0977423i
$606$	−13.6180			−0.553195
$607$	18.5902	−	13.5065i	0.754552	−	0.548214i	−0.142683	−	0.989768i	$-0.545573\pi$
$607$	18.5902	−	13.5065i	0.754552	−	0.548214i	0.897234	+	0.441555i	$0.145573\pi$
$608$	−0.572949	−	1.76336i	−0.0232362	−	0.0715135i
$609$	−2.00000	+	6.15537i	−0.0810441	+	0.249428i
$610$	−13.3262	−	9.68208i	−0.539564	−	0.392016i
$611$	4.00000	+	2.90617i	0.161823	+	0.117571i
$612$	0.809017	−	2.48990i	0.0327026	−	0.100648i
$613$	−4.71885	−	14.5231i	−0.190592	−	0.586583i	0.809407	−	0.587248i	$-0.199789\pi$
$613$	−4.71885	−	14.5231i	−0.190592	−	0.586583i	−1.00000		0.000664403i	$0.999789\pi$
$614$	16.6353	−	12.0862i	0.671344	−	0.487760i
$615$	−0.618034			−0.0249215
$616$	0.809017	+	3.21644i	0.0325962	+	0.129594i
$617$	−44.7214			−1.80041			−0.900207	−	0.435462i	$-0.856585\pi$
$617$	−44.7214			−1.80041			−0.900207	+	0.435462i	$0.856585\pi$
$618$	9.35410	−	6.79615i	0.376277	−	0.273381i
$619$	4.59017	+	14.1271i	0.184495	+	0.567816i	0.999939	−	0.0110192i	$-0.00350758\pi$
$619$	4.59017	+	14.1271i	0.184495	+	0.567816i	−0.815445	+	0.578835i	$0.803508\pi$
$620$	1.19098	−	3.66547i	0.0478310	−	0.147209i
$621$	1.50000	+	1.08981i	0.0601929	+	0.0437327i
$622$	19.0344	+	13.8293i	0.763212	+	0.554506i
$623$	2.71885	−	8.36775i	0.108928	−	0.335247i
$624$	−0.618034	−	1.90211i	−0.0247412	−	0.0761455i
$625$	6.00000	−	4.35926i	0.240000	−	0.174370i
$626$	−4.29180			−0.171535
$627$	−4.71885	−	3.94298i	−0.188453	−	0.157468i
$628$	−9.70820			−0.387400
$629$	6.04508	−	4.39201i	0.241033	−	0.175121i
$630$	−0.500000	−	1.53884i	−0.0199205	−	0.0613089i
$631$	−5.72949	+	17.6336i	−0.228087	+	0.701981i	0.769876	+	0.638193i	$0.220318\pi$
$631$	−5.72949	+	17.6336i	−0.228087	+	0.701981i	−0.997964	+	0.0637875i	$0.979682\pi$
$632$	4.47214	+	3.24920i	0.177892	+	0.129246i
$633$	−8.61803	−	6.26137i	−0.342536	−	0.248867i
$634$	−4.14590	+	12.7598i	−0.164655	+	0.506755i
$635$	−6.47214	−	19.9192i	−0.256839	−	0.790469i
$636$	−6.85410	+	4.97980i	−0.271783	+	0.197462i
$637$	2.00000			0.0792429
$638$	−18.1803	+	11.4127i	−0.719767	+	0.451832i
$639$	−2.47214			−0.0977962
$640$	1.30902	−	0.951057i	0.0517434	−	0.0375938i
$641$	1.58359	+	4.87380i	0.0625481	+	0.192503i	0.977447	−	0.211179i	$-0.0677302\pi$
$641$	1.58359	+	4.87380i	0.0625481	+	0.192503i	−0.914899	+	0.403682i	$0.867730\pi$
$642$	2.42705	−	7.46969i	0.0957881	−	0.294805i
$643$	−33.8607	−	24.6012i	−1.33533	−	0.970178i	−0.999602	−	0.0282204i	$-0.991016\pi$
$643$	−33.8607	−	24.6012i	−1.33533	−	0.970178i	−0.335733	−	0.941957i	$-0.608984\pi$
$644$	−1.50000	−	1.08981i	−0.0591083	−	0.0429447i
$645$	−5.00000	+	15.3884i	−0.196875	+	0.605918i
$646$	−1.50000	−	4.61653i	−0.0590167	−	0.181635i
$647$	−28.9443	+	21.0292i	−1.13792	+	0.826745i	−0.986828	−	0.161775i	$-0.948278\pi$
$647$	−28.9443	+	21.0292i	−1.13792	+	0.826745i	−0.151089	+	0.988520i	$0.548278\pi$
$648$	−1.00000			−0.0392837
$649$	2.52786	+	0.171513i	0.0992273	+	0.00673249i
$650$	4.76393			0.186857
$651$	1.92705	−	1.40008i	0.0755271	−	0.0548736i
$652$	3.09017	+	9.51057i	0.121020	+	0.372462i
$653$	5.18034	−	15.9434i	0.202722	−	0.623915i	−0.797077	−	0.603878i	$-0.793621\pi$
$653$	5.18034	−	15.9434i	0.202722	−	0.623915i	0.999799	−	0.0200374i	$-0.00637854\pi$
$654$	−8.78115	−	6.37988i	−0.343370	−	0.249473i
$655$		0			0
$656$	0.118034	−	0.363271i	0.00460845	−	0.0141834i
$657$	3.76393	+	11.5842i	0.146845	+	0.451942i
$658$	−2.00000	+	1.45309i	−0.0779681	+	0.0566472i
$659$	−11.9098			−0.463941			−0.231971	−	0.972723i	$-0.574517\pi$
$659$	−11.9098			−0.463941			−0.231971	+	0.972723i	$0.574517\pi$
$660$	2.00000	−	4.97980i	0.0778499	−	0.193838i
$661$	−44.3607			−1.72543			−0.862715	−	0.505690i	$-0.831238\pi$
$661$	−44.3607			−1.72543			−0.862715	+	0.505690i	$0.831238\pi$
$662$	5.85410	−	4.25325i	0.227526	−	0.165307i
$663$	−1.61803	−	4.97980i	−0.0628392	−	0.193399i
$664$	−2.23607	+	6.88191i	−0.0867763	+	0.267070i
$665$	−2.42705	−	1.76336i	−0.0941170	−	0.0683800i
$666$	−2.30902	−	1.67760i	−0.0894726	−	0.0650056i
$667$	3.70820	−	11.4127i	0.143582	−	0.441901i
$668$	5.32624	+	16.3925i	0.206078	+	0.634244i
$669$	12.5902	−	9.14729i	0.486764	−	0.353655i
$670$	−16.4721			−0.636374
$671$	12.5836	−	31.3319i	0.485784	−	1.20955i
$672$	1.00000			0.0385758
$673$	−23.7984	+	17.2905i	−0.917360	+	0.666501i	−0.942865	−	0.333174i	$-0.891880\pi$
$673$	−23.7984	+	17.2905i	−0.917360	+	0.666501i	0.0255056	+	0.999675i	$0.491880\pi$
$674$	−9.68034	−	29.7930i	−0.372873	−	1.14758i
$675$	0.736068	−	2.26538i	0.0283313	−	0.0871947i
$676$	7.28115	+	5.29007i	0.280044	+	0.203464i
$677$	16.0902	+	11.6902i	0.618395	+	0.449291i	0.852361	−	0.522954i	$-0.175170\pi$
$677$	16.0902	+	11.6902i	0.618395	+	0.449291i	−0.233965	+	0.972245i	$0.575170\pi$
$678$	−6.32624	+	19.4702i	−0.242958	+	0.747747i
$679$	3.76393	+	11.5842i	0.144446	+	0.444560i
$680$	3.42705	−	2.48990i	0.131421	−	0.0954832i
$681$	2.76393			0.105914
$682$	7.88197	+	0.534785i	0.301816	+	0.0204780i
$683$	−21.6180			−0.827191			−0.413596	−	0.910461i	$-0.635727\pi$
$683$	−21.6180			−0.827191			−0.413596	+	0.910461i	$0.635727\pi$
$684$	−1.50000	+	1.08981i	−0.0573539	+	0.0416701i
$685$	0.381966	+	1.17557i	0.0145942	+	0.0449162i
$686$	−0.309017	+	0.951057i	−0.0117983	+	0.0363115i
$687$	−3.23607	−	2.35114i	−0.123464	−	0.0897016i
$688$	−8.09017	−	5.87785i	−0.308435	−	0.224091i
$689$	−5.23607	+	16.1150i	−0.199478	+	0.613931i
$690$	0.927051	+	2.85317i	0.0352922	+	0.108618i
$691$	31.9164	−	23.1886i	1.21416	−	0.882137i	0.218556	−	0.975824i	$-0.429865\pi$
$691$	31.9164	−	23.1886i	1.21416	−	0.882137i	0.995602	+	0.0936875i	$0.0298655\pi$
$692$	−23.7426			−0.902560
$693$	2.80902	−	1.76336i	0.106706	−	0.0669843i
$694$	−36.2705			−1.37681
$695$	−0.809017	+	0.587785i	−0.0306878	+	0.0222960i
$696$	2.00000	+	6.15537i	0.0758098	+	0.233319i
$697$	0.309017	−	0.951057i	0.0117049	−	0.0360238i
$698$	13.5623	+	9.85359i	0.513341	+	0.372964i
$699$	4.23607	+	3.07768i	0.160223	+	0.116409i
$700$	−0.736068	+	2.26538i	−0.0278208	+	0.0856235i
$701$	−8.00000	−	24.6215i	−0.302156	−	0.929940i	−0.980723	−	0.195402i	$-0.937399\pi$
$701$	−8.00000	−	24.6215i	−0.302156	−	0.929940i	0.678567	−	0.734538i	$-0.262601\pi$
$702$	−1.61803	+	1.17557i	−0.0610688	+	0.0443690i
$703$	−5.29180			−0.199584
$704$	2.54508	+	2.12663i	0.0959215	+	0.0801503i
$705$	4.00000			0.150649
$706$	19.3262	−	14.0413i	0.727353	−	0.528453i
$707$	−4.20820	−	12.9515i	−0.158266	−	0.487092i
$708$	0.236068	−	0.726543i	0.00887198	−	0.0273051i
$709$	4.63525	+	3.36771i	0.174081	+	0.126477i	0.671414	−	0.741083i	$-0.265687\pi$
$709$	4.63525	+	3.36771i	0.174081	+	0.126477i	−0.497333	+	0.867560i	$0.665687\pi$
$710$	−3.23607	−	2.35114i	−0.121447	−	0.0882367i
$711$	1.70820	−	5.25731i	0.0640627	−	0.197165i
$712$	−2.71885	−	8.36775i	−0.101893	−	0.313595i
$713$	−3.57295	+	2.59590i	−0.133808	+	0.0972172i
$714$	2.61803			0.0979775
$715$	−2.61803	−	10.4086i	−0.0979089	−	0.389260i
$716$	13.0344			0.487120
$717$	−0.972136	+	0.706298i	−0.0363051	+	0.0263772i
$718$	7.93769	+	24.4297i	0.296232	+	0.911709i
$719$	10.5836	−	32.5729i	0.394701	−	1.21477i	−0.534492	−	0.845173i	$-0.679497\pi$
$719$	10.5836	−	32.5729i	0.394701	−	1.21477i	0.929194	−	0.369593i	$-0.120503\pi$
$720$	−1.30902	−	0.951057i	−0.0487842	−	0.0354438i
$721$	9.35410	+	6.79615i	0.348365	+	0.253102i
$722$	4.80902	−	14.8006i	0.178973	−	0.550823i
$723$	3.43769	+	10.5801i	0.127849	+	0.393479i
$724$	−3.47214	+	2.52265i	−0.129041	+	0.0937537i
$725$	−15.4164			−0.572551
$726$	10.8992	+	1.48584i	0.404507	+	0.0551447i
$727$	−34.6869			−1.28647			−0.643233	−	0.765670i	$-0.722407\pi$
$727$	−34.6869			−1.28647			−0.643233	+	0.765670i	$0.722407\pi$
$728$	1.61803	−	1.17557i	0.0599683	−	0.0435695i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−6.09017	+	18.7436i	−0.225407	+	0.693732i
$731$	−21.1803	−	15.3884i	−0.783383	−	0.569161i
$732$	−8.23607	−	5.98385i	−0.304414	−	0.221170i
$733$	14.1246	−	43.4711i	0.521704	−	1.60564i	−0.249038	−	0.968494i	$-0.580114\pi$
$733$	14.1246	−	43.4711i	0.521704	−	1.60564i	0.770742	−	0.637147i	$-0.219886\pi$
$734$	−3.44427	−	10.6004i	−0.127130	−	0.391267i
$735$	1.30902	−	0.951057i	0.0482838	−	0.0350802i
$736$	−1.85410			−0.0683431
$737$	−8.23607	−	32.7445i	−0.303379	−	1.20616i
$738$	−0.381966			−0.0140604
$739$	−5.76393	+	4.18774i	−0.212030	+	0.154049i	−0.688732	−	0.725016i	$-0.741832\pi$
$739$	−5.76393	+	4.18774i	−0.212030	+	0.154049i	0.476702	+	0.879065i	$0.341832\pi$
$740$	−1.42705	−	4.39201i	−0.0524594	−	0.161454i
$741$	−1.14590	+	3.52671i	−0.0420956	+	0.129557i
$742$	−6.85410	−	4.97980i	−0.251622	−	0.182814i
$743$	−8.78115	−	6.37988i	−0.322149	−	0.234055i	0.414943	−	0.909848i	$-0.363802\pi$
$743$	−8.78115	−	6.37988i	−0.322149	−	0.234055i	−0.737092	+	0.675792i	$0.763802\pi$
$744$	0.736068	−	2.26538i	0.0269856	−	0.0830530i
$745$		0			0
$746$	24.4894	−	17.7926i	0.896619	−	0.651432i
$747$	7.23607			0.264754
$748$	6.66312	+	5.56758i	0.243628	+	0.203571i
$749$	7.85410			0.286983
$750$	9.66312	−	7.02067i	0.352847	−	0.256359i
$751$	0.347524	+	1.06957i	0.0126813	+	0.0390291i	0.957197	−	0.289437i	$-0.0934682\pi$
$751$	0.347524	+	1.06957i	0.0126813	+	0.0390291i	−0.944516	+	0.328467i	$0.893468\pi$
$752$	−0.763932	+	2.35114i	−0.0278577	+	0.0857373i
$753$	12.5623	+	9.12705i	0.457796	+	0.332608i
$754$	10.4721	+	7.60845i	0.381373	+	0.277083i
$755$	1.38197	−	4.25325i	0.0502949	−	0.154792i
$756$	−0.309017	−	0.951057i	−0.0112388	−	0.0345896i
$757$	−17.5902	+	12.7800i	−0.639326	+	0.464497i	−0.859618	−	0.510937i	$-0.829299\pi$
$757$	−17.5902	+	12.7800i	−0.639326	+	0.464497i	0.220293	+	0.975434i	$0.429299\pi$
$758$	17.4164			0.632592
$759$	−5.20820	+	3.26944i	−0.189046	+	0.118673i
$760$	−3.00000			−0.108821
$761$	1.32624	−	0.963568i	0.0480761	−	0.0349293i	−0.563488	−	0.826124i	$-0.690541\pi$
$761$	1.32624	−	0.963568i	0.0480761	−	0.0349293i	0.611564	+	0.791195i	$0.290541\pi$
$762$	−4.00000	−	12.3107i	−0.144905	−	0.445971i
$763$	3.35410	−	10.3229i	0.121427	−	0.373713i
$764$	10.0172	+	7.27794i	0.362410	+	0.263307i
$765$	−3.42705	−	2.48990i	−0.123905	−	0.0900225i
$766$	3.67376	−	11.3067i	0.132738	−	0.408527i
$767$	−0.472136	−	1.45309i	−0.0170478	−	0.0524679i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−32.6525			−1.17748			−0.588739	−	0.808323i	$-0.700375\pi$
$769$	−32.6525			−1.17748			−0.588739	+	0.808323i	$0.700375\pi$
$770$	5.35410	+	0.363271i	0.192948	+	0.0130914i
$771$	25.0902			0.903600
$772$	−20.1074	+	14.6089i	−0.723681	+	0.525785i
$773$	1.56231	+	4.80828i	0.0561922	+	0.172942i	0.975213	−	0.221266i	$-0.0710189\pi$
$773$	1.56231	+	4.80828i	0.0561922	+	0.172942i	−0.919021	+	0.394208i	$0.871019\pi$
$774$	−3.09017	+	9.51057i	−0.111074	+	0.341850i
$775$	4.59017	+	3.33495i	0.164884	+	0.119795i
$776$	9.85410	+	7.15942i	0.353742	+	0.257008i
$777$	0.881966	−	2.71441i	0.0316404	−	0.0973790i
$778$	7.85410	+	24.1724i	0.281583	+	0.866624i
$779$	−0.572949	+	0.416272i	−0.0205280	+	0.0149145i
$780$	−3.23607			−0.115870
$781$	3.05573	−	7.60845i	0.109343	−	0.272252i
$782$	−4.85410			−0.173582
$783$	5.23607	−	3.80423i	0.187122	−	0.135952i
$784$	0.309017	+	0.951057i	0.0110363	+	0.0339663i
$785$	−4.85410	+	14.9394i	−0.173250	+	0.533210i
$786$		0			0
$787$	19.3992	+	14.0943i	0.691506	+	0.502409i	0.877155	−	0.480207i	$-0.159439\pi$
$787$	19.3992	+	14.0943i	0.691506	+	0.502409i	−0.185649	+	0.982616i	$0.559439\pi$
$788$	−0.673762	+	2.07363i	−0.0240018	+	0.0738699i
$789$	3.71885	+	11.4454i	0.132394	+	0.407468i
$790$	7.23607	−	5.25731i	0.257448	−	0.187047i
$791$	−20.4721			−0.727905
$792$	1.23607	−	3.07768i	0.0439218	−	0.109361i
$793$	−20.3607			−0.723029
$794$	1.14590	−	0.832544i	0.0406664	−	0.0295459i
$795$	4.23607	+	13.0373i	0.150238	+	0.462385i
$796$	2.04508	−	6.29412i	0.0724861	−	0.223089i
$797$	−36.5795	−	26.5766i	−1.29571	−	0.941391i	−0.295809	−	0.955247i	$-0.595589\pi$
$797$	−36.5795	−	26.5766i	−1.29571	−	0.941391i	−0.999904	+	0.0138562i	$0.995589\pi$
$798$	−1.50000	−	1.08981i	−0.0530994	−	0.0385790i
$799$	−2.00000	+	6.15537i	−0.0707549	+	0.217761i
$800$	0.736068	+	2.26538i	0.0260239	+	0.0800934i
$801$	−7.11803	+	5.17155i	−0.251503	+	0.182728i
$802$	33.5967			1.18634
$803$	−40.3050	−	2.73466i	−1.42233	−	0.0965039i
$804$	−10.1803			−0.359033
$805$	−2.42705	+	1.76336i	−0.0855423	+	0.0621501i
$806$	−1.47214	−	4.53077i	−0.0518538	−	0.159590i
$807$	8.61803	−	26.5236i	0.303369	−	0.933674i
$808$	−11.0172	−	8.00448i	−0.387584	−	0.281597i
$809$	−1.90983	−	1.38757i	−0.0671460	−	0.0487845i	0.553706	−	0.832712i	$-0.313213\pi$
$809$	−1.90983	−	1.38757i	−0.0671460	−	0.0487845i	−0.620852	+	0.783928i	$0.713213\pi$
$810$	−0.500000	+	1.53884i	−0.0175682	+	0.0540694i
$811$	1.52786	+	4.70228i	0.0536506	+	0.165119i	0.974292	−	0.225291i	$-0.0723332\pi$
$811$	1.52786	+	4.70228i	0.0536506	+	0.165119i	−0.920641	+	0.390410i	$0.872333\pi$
$812$	−5.23607	+	3.80423i	−0.183750	+	0.133502i
$813$	−24.2705			−0.851204
$814$	8.01722	−	5.03280i	0.281003	−	0.176399i
$815$	16.1803			0.566773
$816$	2.11803	−	1.53884i	0.0741460	−	0.0538702i
$817$	5.72949	+	17.6336i	0.200449	+	0.616920i
$818$	−4.70820	+	14.4904i	−0.164618	+	0.506644i
$819$	−1.61803	−	1.17557i	−0.0565387	−	0.0410778i
$820$	−0.500000	−	0.363271i	−0.0174608	−	0.0126860i
$821$	0.763932	−	2.35114i	0.0266614	−	0.0820554i	−0.936840	−	0.349757i	$-0.886264\pi$
$821$	0.763932	−	2.35114i	0.0266614	−	0.0820554i	0.963502	+	0.267702i	$0.0862641\pi$
$822$	0.236068	+	0.726543i	0.00823382	+	0.0253411i
$823$	28.7082	−	20.8577i	1.00071	−	0.727055i	0.0384658	−	0.999260i	$-0.487753\pi$
$823$	28.7082	−	20.8577i	1.00071	−	0.727055i	0.962239	+	0.272205i	$0.0877529\pi$
$824$	11.5623			0.402792
$825$	6.06231	+	5.06555i	0.211062	+	0.176360i
$826$	0.763932			0.0265806
$827$	14.0623	−	10.2169i	0.488994	−	0.355275i	−0.315803	−	0.948825i	$-0.602274\pi$
$827$	14.0623	−	10.2169i	0.488994	−	0.355275i	0.804797	+	0.593550i	$0.202274\pi$
$828$	0.572949	+	1.76336i	0.0199114	+	0.0612808i
$829$	−9.85410	+	30.3278i	−0.342247	+	1.05333i	0.620794	+	0.783974i	$0.286810\pi$
$829$	−9.85410	+	30.3278i	−0.342247	+	1.05333i	−0.963041	+	0.269355i	$0.913190\pi$
$830$	9.47214	+	6.88191i	0.328783	+	0.238875i
$831$	2.88197	+	2.09387i	0.0999743	+	0.0726356i
$832$	0.618034	−	1.90211i	0.0214265	−	0.0659439i
$833$	0.809017	+	2.48990i	0.0280308	+	0.0862699i
$834$	−0.500000	+	0.363271i	−0.0173136	+	0.0125791i
$835$	27.8885			0.965123
$836$	−1.50000	−	5.96361i	−0.0518786	−	0.206256i
$837$	−2.38197			−0.0823328
$838$	15.4164	−	11.2007i	0.532551	−	0.386921i
$839$	−1.72949	−	5.32282i	−0.0597086	−	0.183764i	0.916753	−	0.399454i	$-0.130800\pi$
$839$	−1.72949	−	5.32282i	−0.0597086	−	0.183764i	−0.976462	+	0.215689i	$0.930800\pi$
$840$	0.500000	−	1.53884i	0.0172516	−	0.0530951i
$841$	−10.4271	−	7.57570i	−0.359553	−	0.261231i
$842$	9.35410	+	6.79615i	0.322364	+	0.234211i
$843$	−5.29180	+	16.2865i	−0.182259	+	0.560936i
$844$	−3.29180	−	10.1311i	−0.113308	−	0.348727i
$845$	11.7812	−	8.55951i	0.405284	−	0.294456i
$846$	2.47214			0.0849938
$847$	1.95492	+	10.8249i	0.0671717	+	0.371948i
$848$	−8.47214			−0.290934
$849$	−20.6353	+	14.9924i	−0.708200	+	0.514538i
$850$	1.92705	+	5.93085i	0.0660973	+	0.203427i
$851$	−1.63525	+	5.03280i	−0.0560558	+	0.172522i
$852$	−2.00000	−	1.45309i	−0.0685189	−	0.0497819i
$853$	40.4164	+	29.3642i	1.38383	+	1.00541i	0.996511	+	0.0834675i	$0.0265995\pi$
$853$	40.4164	+	29.3642i	1.38383	+	1.00541i	0.387321	+	0.921945i	$0.373401\pi$
$854$	3.14590	−	9.68208i	0.107650	−	0.331314i
$855$	0.927051	+	2.85317i	0.0317045	+	0.0975763i
$856$	6.35410	−	4.61653i	0.217179	−	0.157790i
$857$	−52.2492			−1.78480			−0.892400	−	0.451246i	$-0.850980\pi$
$857$	−52.2492			−1.78480			−0.892400	+	0.451246i	$0.850980\pi$
$858$	−1.61803	−	6.43288i	−0.0552388	−	0.219615i
$859$	−16.5836			−0.565825			−0.282912	−	0.959146i	$-0.591301\pi$
$859$	−16.5836			−0.565825			−0.282912	+	0.959146i	$0.591301\pi$
$860$	−13.0902	+	9.51057i	−0.446371	+	0.324308i
$861$	−0.118034	−	0.363271i	−0.00402259	−	0.0123803i
$862$	7.00658	−	21.5640i	0.238645	−	0.734474i
$863$	16.9271	+	12.2982i	0.576204	+	0.418636i	0.837353	−	0.546662i	$-0.184102\pi$
$863$	16.9271	+	12.2982i	0.576204	+	0.418636i	−0.261150	+	0.965298i	$0.584102\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−11.8713	+	36.5362i	−0.403637	+	1.24227i
$866$	−1.56231	−	4.80828i	−0.0530893	−	0.163392i
$867$	−8.20820	+	5.96361i	−0.278765	+	0.202535i
$868$	2.38197			0.0808492
$869$	14.0689	+	11.7557i	0.477254	+	0.398785i
$870$	10.4721			0.355039
$871$	−16.4721	+	11.9677i	−0.558137	+	0.405510i
$872$	−3.35410	−	10.3229i	−0.113584	−	0.349576i
$873$	3.76393	−	11.5842i	0.127390	−	0.392065i
$874$	2.78115	+	2.02063i	0.0940739	+	0.0683487i
$875$	9.66312	+	7.02067i	0.326673	+	0.237342i
$876$	−3.76393	+	11.5842i	−0.127171	+	0.391394i
$877$	6.32624	+	19.4702i	0.213622	+	0.657461i	0.999249	+	0.0387597i	$0.0123407\pi$
$877$	6.32624	+	19.4702i	0.213622	+	0.657461i	−0.785627	+	0.618701i	$0.787659\pi$
$878$	18.1074	−	13.1558i	0.611095	−	0.443986i
$879$	−7.90983			−0.266792
$880$	4.54508	−	2.85317i	0.153215	−	0.0961803i
$881$	28.1459			0.948259			0.474130	−	0.880455i	$-0.342763\pi$
$881$	28.1459			0.948259			0.474130	+	0.880455i	$0.342763\pi$
$882$	0.809017	−	0.587785i	0.0272410	−	0.0197918i
$883$	0.360680	+	1.11006i	0.0121378	+	0.0373564i	0.956942	−	0.290279i	$-0.0937482\pi$
$883$	0.360680	+	1.11006i	0.0121378	+	0.0373564i	−0.944804	+	0.327636i	$0.893748\pi$
$884$	1.61803	−	4.97980i	0.0544204	−	0.167489i
$885$	−1.00000	−	0.726543i	−0.0336146	−	0.0244225i
$886$	6.35410	+	4.61653i	0.213470	+	0.155095i
$887$	1.00000	−	3.07768i	0.0335767	−	0.103338i	−0.932864	−	0.360230i	$-0.882698\pi$
$887$	1.00000	−	3.07768i	0.0335767	−	0.103338i	0.966440	+	0.256891i	$0.0826983\pi$
$888$	−0.881966	−	2.71441i	−0.0295968	−	0.0910897i
$889$	10.4721	−	7.60845i	0.351224	−	0.255179i
$890$	−14.2361			−0.477194
$891$	−3.30902	−	0.224514i	−0.110856	−	0.00752150i
$892$	15.5623			0.521065
$893$	3.70820	−	2.69417i	0.124090	−	0.0901569i
$894$		0			0
$895$	6.51722	−	20.0579i	0.217847	−	0.670463i
$896$	0.809017	+	0.587785i	0.0270274	+	0.0196365i
$897$	3.00000	+	2.17963i	0.100167	+	0.0727756i
$898$	−10.0344	+	30.8828i	−0.334854	+	1.03057i
$899$	4.76393	+	14.6619i	0.158886	+	0.489001i
$900$	1.92705	−	1.40008i	0.0642350	−	0.0466695i
$901$	−22.1803			−0.738934
$902$	0.472136	−	1.17557i	0.0157204	−	0.0391422i
$903$	−10.0000			−0.332779
$904$	−16.5623	+	12.0332i	−0.550854	+	0.400219i
$905$	2.14590	+	6.60440i	0.0713321	+	0.219538i
$906$	0.854102	−	2.62866i	0.0283756	−	0.0873312i
$907$	7.38197	+	5.36331i	0.245114	+	0.178086i	0.703559	−	0.710637i	$-0.251593\pi$
$907$	7.38197	+	5.36331i	0.245114	+	0.178086i	−0.458445	+	0.888723i	$0.651593\pi$
$908$	2.23607	+	1.62460i	0.0742065	+	0.0539142i
$909$	−4.20820	+	12.9515i	−0.139577	+	0.429575i
$910$	−1.00000	−	3.07768i	−0.0331497	−	0.102024i
$911$	−10.7639	+	7.82045i	−0.356625	+	0.259103i	−0.751643	−	0.659570i	$-0.770738\pi$
$911$	−10.7639	+	7.82045i	−0.356625	+	0.259103i	0.395018	+	0.918673i	$0.370738\pi$
$912$	−1.85410			−0.0613955
$913$	−8.94427	+	22.2703i	−0.296012	+	0.737040i
$914$	26.3607			0.871934
$915$	−13.3262	+	9.68208i	−0.440552	+	0.320080i
$916$	−1.23607	−	3.80423i	−0.0408408	−	0.125695i
$917$		0			0
$918$	−2.11803	−	1.53884i	−0.0699055	−	0.0507893i
$919$	0.0557281	+	0.0404888i	0.00183830	+	0.00133560i	0.588704	−	0.808349i	$-0.299638\pi$
$919$	0.0557281	+	0.0404888i	0.00183830	+	0.00133560i	−0.586866	+	0.809684i	$0.699638\pi$
$920$	−0.927051	+	2.85317i	−0.0305640	+	0.0940662i
$921$	−6.35410	−	19.5559i	−0.209375	−	0.644389i
$922$	31.5066	−	22.8909i	1.03761	−	0.753871i
$923$	−4.94427			−0.162743
$924$	3.30902	+	0.224514i	0.108859	+	0.00738597i
$925$	6.79837			0.223529
$926$	23.0902	−	16.7760i	0.758790	−	0.551293i
$927$	−3.57295	−	10.9964i	−0.117351	−	0.361169i
$928$	−2.00000	+	6.15537i	−0.0656532	+	0.202060i
$929$	3.35410	+	2.43690i	0.110045	+	0.0799520i	0.641447	−	0.767168i	$-0.278335\pi$
$929$	3.35410	+	2.43690i	0.110045	+	0.0799520i	−0.531402	+	0.847120i	$0.678335\pi$
$930$	−3.11803	−	2.26538i	−0.102244	−	0.0742849i
$931$	0.572949	−	1.76336i	0.0187776	−	0.0577917i
$932$	1.61803	+	4.97980i	0.0530005	+	0.163119i
$933$	19.0344	−	13.8293i	0.623160	−	0.452752i
$934$	7.88854			0.258121
$935$	11.8992	−	7.46969i	0.389145	−	0.244285i
$936$	−2.00000			−0.0653720
$937$	21.5623	−	15.6659i	0.704410	−	0.511784i	−0.176956	−	0.984219i	$-0.556625\pi$
$937$	21.5623	−	15.6659i	0.704410	−	0.511784i	0.881365	+	0.472435i	$0.156625\pi$
$938$	−3.14590	−	9.68208i	−0.102717	−	0.316131i
$939$	−1.32624	+	4.08174i	−0.0432801	+	0.133203i
$940$	3.23607	+	2.35114i	0.105549	+	0.0766858i
$941$	25.1525	+	18.2743i	0.819947	+	0.595727i	0.916697	−	0.399582i	$-0.130845\pi$
$941$	25.1525	+	18.2743i	0.819947	+	0.595727i	−0.0967501	+	0.995309i	$0.530845\pi$
$942$	−3.00000	+	9.23305i	−0.0977453	+	0.300829i
$943$	0.218847	+	0.673542i	0.00712664	+	0.0219335i
$944$	0.618034	−	0.449028i	0.0201153	−	0.0146146i
$945$	−1.61803			−0.0526346
$946$	−25.4508	−	21.2663i	−0.827478	−	0.691426i
$947$	−30.9230			−1.00486			−0.502431	−	0.864617i	$-0.667561\pi$
$947$	−30.9230			−1.00486			−0.502431	+	0.864617i	$0.667561\pi$
$948$	4.47214	−	3.24920i	0.145248	−	0.105529i
$949$	7.52786	+	23.1684i	0.244365	+	0.752078i
$950$	1.36475	−	4.20025i	0.0442782	−	0.136274i
$951$	10.8541	+	7.88597i	0.351968	+	0.255720i
$952$	2.11803	+	1.53884i	0.0686459	+	0.0498741i
$953$	−3.70820	+	11.4127i	−0.120121	+	0.369693i	−0.992981	−	0.118278i	$-0.962263\pi$
$953$	−3.70820	+	11.4127i	−0.120121	+	0.369693i	0.872860	+	0.487971i	$0.162263\pi$
$954$	2.61803	+	8.05748i	0.0847620	+	0.260871i
$955$	16.2082	−	11.7759i	0.524485	−	0.381061i
$956$	−1.20163			−0.0388634
$957$	5.23607	+	20.8172i	0.169258	+	0.672926i
$958$	9.52786			0.307831
$959$	−0.618034	+	0.449028i	−0.0199574	+	0.0144999i
$960$	−0.500000	−	1.53884i	−0.0161374	−	0.0496659i
$961$	−7.82624	+	24.0867i	−0.252459	+	0.776990i
$962$	−4.61803	−	3.35520i	−0.148891	−	0.108176i
$963$	−6.35410	−	4.61653i	−0.204758	−	0.148765i
$964$	−3.43769	+	10.5801i	−0.110721	+	0.340763i
$965$	12.4271	+	38.2465i	0.400041	+	1.23120i
$966$	−1.50000	+	1.08981i	−0.0482617	+	0.0350642i
$967$	−30.0000			−0.964735			−0.482367	−	0.875969i	$-0.660223\pi$
$967$	−30.0000			−0.964735			−0.482367	+	0.875969i	$0.660223\pi$
$968$	7.94427	+	7.60845i	0.255339	+	0.244545i
$969$	−4.85410			−0.155936
$970$	15.9443	−	11.5842i	0.511940	−	0.371946i
$971$	15.0344	+	46.2713i	0.482478	+	1.48492i	0.835600	+	0.549338i	$0.185120\pi$
$971$	15.0344	+	46.2713i	0.482478	+	1.48492i	−0.353122	+	0.935577i	$0.614880\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	−0.500000	−	0.363271i	−0.0160293	−	0.0116459i
$974$	34.2705	+	24.8990i	1.09810	+	0.797815i
$975$	1.47214	−	4.53077i	0.0471461	−	0.145101i
$976$	−3.14590	−	9.68208i	−0.100698	−	0.309916i
$977$	9.70820	−	7.05342i	0.310593	−	0.225659i	−0.421558	−	0.906801i	$-0.638517\pi$
$977$	9.70820	−	7.05342i	0.310593	−	0.225659i	0.732151	+	0.681142i	$0.238517\pi$
$978$	10.0000			0.319765
$979$	−7.11803	−	28.2994i	−0.227493	−	0.904454i
$980$	1.61803			0.0516862
$981$	−8.78115	+	6.37988i	−0.280361	+	0.203694i
$982$	8.42705	+	25.9358i	0.268918	+	0.827645i
$983$	1.74265	−	5.36331i	0.0555818	−	0.171063i	−0.919412	−	0.393296i	$-0.871335\pi$
$983$	1.74265	−	5.36331i	0.0555818	−	0.171063i	0.974994	+	0.222233i	$0.0713346\pi$
$984$	−0.309017	−	0.224514i	−0.00985110	−	0.00715724i
$985$	2.85410	+	2.07363i	0.0909393	+	0.0660712i
$986$	−5.23607	+	16.1150i	−0.166750	+	0.513205i
$987$	0.763932	+	2.35114i	0.0243162	+	0.0748376i
$988$	−3.00000	+	2.17963i	−0.0954427	+	0.0693432i
$989$	18.5410			0.589570
$990$	−4.11803	−	3.44095i	−0.130880	−	0.109361i
$991$	47.5967			1.51196			0.755980	−	0.654594i	$-0.227161\pi$
$991$	47.5967			1.51196			0.755980	+	0.654594i	$0.227161\pi$
$992$	1.92705	−	1.40008i	0.0611839	−	0.0444527i
$993$	−2.23607	−	6.88191i	−0.0709595	−	0.218391i
$994$	0.763932	−	2.35114i	0.0242305	−	0.0745737i
$995$	−8.66312	−	6.29412i	−0.274639	−	0.199537i
$996$	5.85410	+	4.25325i	0.185494	+	0.134770i
$997$	0.0212862	−	0.0655123i	0.000674142	−	0.00207480i	−0.950719	−	0.310054i	$-0.899653\pi$
$997$	0.0212862	−	0.0655123i	0.000674142	−	0.00207480i	0.951393	+	0.307979i	$0.0996528\pi$
$998$	−11.2705	−	34.6871i	−0.356762	−	1.09800i
$999$	−2.30902	+	1.67760i	−0.0730541	+	0.0530769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.j.d.421.1	yes	4
11.2	odd	10		5082.2.a.bp.1.2		2
11.4	even	5	inner	462.2.j.d.169.1	✓	4
11.9	even	5		5082.2.a.bf.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.j.d.169.1	✓	4	11.4	even	5	inner
462.2.j.d.421.1	yes	4	1.1	even	1	trivial
5082.2.a.bf.1.2		2	11.9	even	5
5082.2.a.bp.1.2		2	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.30902 - 0.951057i) q^{5} +(-0.809017 - 0.587785i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} -1.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} -1.00000 q^{12} +(-1.61803 + 1.17557i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(-0.500000 + 1.53884i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.11803 - 1.53884i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(0.572949 + 1.76336i) q^{19} +(-1.30902 + 0.951057i) q^{20} -1.00000 q^{21} +(-2.54508 - 2.12663i) q^{22} +1.85410 q^{23} +(-0.809017 + 0.587785i) q^{24} +(-0.736068 - 2.26538i) q^{25} +(-0.618034 + 1.90211i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-0.809017 - 0.587785i) q^{28} +(2.00000 - 6.15537i) q^{29} +(0.500000 + 1.53884i) q^{30} +(-1.92705 + 1.40008i) q^{31} -1.00000 q^{32} +(-2.80902 + 1.76336i) q^{33} -2.61803 q^{34} +(-1.30902 + 0.951057i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-0.881966 + 2.71441i) q^{37} +(1.50000 + 1.08981i) q^{38} +(1.61803 + 1.17557i) q^{39} +(-0.500000 + 1.53884i) q^{40} +(0.118034 + 0.363271i) q^{41} +(-0.809017 + 0.587785i) q^{42} +10.0000 q^{43} +(-3.30902 - 0.224514i) q^{44} +1.61803 q^{45} +(1.50000 - 1.08981i) q^{46} +(-0.763932 - 2.35114i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-1.92705 - 1.40008i) q^{50} +(-0.809017 + 2.48990i) q^{51} +(0.618034 + 1.90211i) q^{52} +(6.85410 - 4.97980i) q^{53} +1.00000 q^{54} +(-2.00000 + 4.97980i) q^{55} -1.00000 q^{56} +(1.50000 - 1.08981i) q^{57} +(-2.00000 - 6.15537i) q^{58} +(-0.236068 + 0.726543i) q^{59} +(1.30902 + 0.951057i) q^{60} +(8.23607 + 5.98385i) q^{61} +(-0.736068 + 2.26538i) q^{62} +(0.309017 + 0.951057i) q^{63} +(-0.809017 + 0.587785i) q^{64} +3.23607 q^{65} +(-1.23607 + 3.07768i) q^{66} +10.1803 q^{67} +(-2.11803 + 1.53884i) q^{68} +(-0.572949 - 1.76336i) q^{69} +(-0.500000 + 1.53884i) q^{70} +(2.00000 + 1.45309i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.76393 - 11.5842i) q^{73} +(0.881966 + 2.71441i) q^{74} +(-1.92705 + 1.40008i) q^{75} +1.85410 q^{76} +(-3.30902 - 0.224514i) q^{77} +2.00000 q^{78} +(-4.47214 + 3.24920i) q^{79} +(0.500000 + 1.53884i) q^{80} +(0.309017 - 0.951057i) q^{81} +(0.309017 + 0.224514i) q^{82} +(-5.85410 - 4.25325i) q^{83} +(-0.309017 + 0.951057i) q^{84} +(1.30902 + 4.02874i) q^{85} +(8.09017 - 5.87785i) q^{86} -6.47214 q^{87} +(-2.80902 + 1.76336i) q^{88} +8.79837 q^{89} +(1.30902 - 0.951057i) q^{90} +(0.618034 + 1.90211i) q^{91} +(0.572949 - 1.76336i) q^{92} +(1.92705 + 1.40008i) q^{93} +(-2.00000 - 1.45309i) q^{94} +(0.927051 - 2.85317i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-9.85410 + 7.15942i) q^{97} -1.00000 q^{98} +(2.54508 + 2.12663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 + q^3 - q^4 - 3 * q^5 - q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} + q^{3} - q^{4} - 3 q^{5} - q^{6} - q^{7} + q^{8} - q^{9} - 2 q^{10} - q^{11} - 4 q^{12} - 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} + q^{18} + 9 q^{19} - 3 q^{20} - 4 q^{21} + q^{22} - 6 q^{23} - q^{24} + 6 q^{25} + 2 q^{26} + q^{27} - q^{28} + 8 q^{29} + 2 q^{30} - q^{31} - 4 q^{32} - 9 q^{33} - 6 q^{34} - 3 q^{35} - q^{36} - 8 q^{37} + 6 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} - q^{42} + 40 q^{43} - 11 q^{44} + 2 q^{45} + 6 q^{46} - 12 q^{47} + q^{48} - q^{49} - q^{50} - q^{51} - 2 q^{52} + 14 q^{53} + 4 q^{54} - 8 q^{55} - 4 q^{56} + 6 q^{57} - 8 q^{58} + 8 q^{59} + 3 q^{60} + 24 q^{61} + 6 q^{62} - q^{63} - q^{64} + 4 q^{65} + 4 q^{66} - 4 q^{67} - 4 q^{68} - 9 q^{69} - 2 q^{70} + 8 q^{71} + q^{72} + 24 q^{73} + 8 q^{74} - q^{75} - 6 q^{76} - 11 q^{77} + 8 q^{78} + 2 q^{80} - q^{81} - q^{82} - 10 q^{83} + q^{84} + 3 q^{85} + 10 q^{86} - 8 q^{87} - 9 q^{88} - 14 q^{89} + 3 q^{90} - 2 q^{91} + 9 q^{92} + q^{93} - 8 q^{94} - 3 q^{95} - q^{96} - 26 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 - 3 * q^5 - q^6 - q^7 + q^8 - q^9 - 2 * q^10 - q^11 - 4 * q^12 - 2 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 + q^18 + 9 * q^19 - 3 * q^20 - 4 * q^21 + q^22 - 6 * q^23 - q^24 + 6 * q^25 + 2 * q^26 + q^27 - q^28 + 8 * q^29 + 2 * q^30 - q^31 - 4 * q^32 - 9 * q^33 - 6 * q^34 - 3 * q^35 - q^36 - 8 * q^37 + 6 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 - q^42 + 40 * q^43 - 11 * q^44 + 2 * q^45 + 6 * q^46 - 12 * q^47 + q^48 - q^49 - q^50 - q^51 - 2 * q^52 + 14 * q^53 + 4 * q^54 - 8 * q^55 - 4 * q^56 + 6 * q^57 - 8 * q^58 + 8 * q^59 + 3 * q^60 + 24 * q^61 + 6 * q^62 - q^63 - q^64 + 4 * q^65 + 4 * q^66 - 4 * q^67 - 4 * q^68 - 9 * q^69 - 2 * q^70 + 8 * q^71 + q^72 + 24 * q^73 + 8 * q^74 - q^75 - 6 * q^76 - 11 * q^77 + 8 * q^78 + 2 * q^80 - q^81 - q^82 - 10 * q^83 + q^84 + 3 * q^85 + 10 * q^86 - 8 * q^87 - 9 * q^88 - 14 * q^89 + 3 * q^90 - 2 * q^91 + 9 * q^92 + q^93 - 8 * q^94 - 3 * q^95 - q^96 - 26 * q^97 - 4 * q^98 - q^99

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